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filter=lfs diff=lfs merge=lfs -text diff --git a/2023/Robust Unsupervised StyleGAN Image Restoration/22cf3860-c0a9-4cc3-ae76-e2aceeacd7e1_content_list.json b/2023/Robust Unsupervised StyleGAN Image Restoration/22cf3860-c0a9-4cc3-ae76-e2aceeacd7e1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b834ff8f845844ce7f567f4d4b1d0c4213bd0483 --- /dev/null +++ b/2023/Robust Unsupervised StyleGAN Image Restoration/22cf3860-c0a9-4cc3-ae76-e2aceeacd7e1_content_list.json @@ -0,0 +1,1710 @@ +[ + { + "type": "text", + "text": "Robust Unsupervised StyleGAN Image Restoration", + "text_level": 1, + "bbox": [ + 240, + 130, + 756, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yohan Poirier-Ginter\\*, Jean-François Lalonde\\* Inria, Université Côte d'Azur, Université Laval https://lvsn.github.io/RobustUnsupervised/", + "bbox": [ + 303, + 180, + 692, + 233 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/90898fdfe2be1005b020e1012c683e3e8e202c8c33fc2716ec151b598318270b.jpg", + "image_caption": [ + "Figure 1. Our unsupervised StyleGAN image restoration method is robust and effective across a variety of tasks (left, top to bottom: upsampling, denoising, deartifacting, and inpainting) and a wide range of degradation levels. Since it avoids the need for task-specific hyperparameter tuning, it can directly handle combinations of such degradations, e.g., pairs (center) or even all four (right)." + ], + "image_footnote": [], + "bbox": [ + 114, + 244, + 370, + 445 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8df8152cd13b675b505e8ce0a75faf491efddd25832127ae23f3b6fc55c58681.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 370, + 246, + 622, + 445 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/828ad6f3fb4690e6efcdd78d359a743abc3bb1d0e379118fd8a574d7681cf80c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 246, + 880, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 258, + 508, + 336, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "GAN-based image restoration inverts the generative process to repair images corrupted by known degradations. Existing unsupervised methods must be carefully tuned for each task and degradation level. In this work, we make StyleGAN image restoration robust: a single set of hyperparameters works across a wide range of degradation levels. This makes it possible to handle combinations of several degradations, without the need to retune. Our proposed approach relies on a 3-phase progressive latent space extension and a conservative optimizer, which avoids the need for any additional regularization terms. Extensive experiments demonstrate robustness on inpainting, upsampling, denoising, and deartifacting at varying degradations levels, outperforming other StyleGAN-based inversion techniques. Our approach also favorably compares to diffusion-based restoration by yielding much more realistic inversion results. Code is available at the above URL.", + "bbox": [ + 111, + 539, + 485, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 112, + 825, + 243, + 842 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image restoration, the task of recovering a high quality image from a degraded input, is a long-standing problem in image processing and computer vision. Since different restoration tasks—such as denoising, upsampling,", + "bbox": [ + 111, + 851, + 483, + 912 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "deartifacting, etc.—can be quite distinct, many recent approaches [9, 10, 37, 54, 61, 62] propose to solve them in a supervised learning paradigm by leveraging curated datasets specifically designed for the task at hand. Unfortunately, designing task-specific approaches requires retraining large networks on each task separately.", + "bbox": [ + 511, + 508, + 883, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In parallel, the advent of powerful generative models has enabled the emergence of unsupervised restoration methods [42], which do not require task-specific training. The idea is to invert the generative process to recover a clean image. Assuming a known (or approximate) degradation model, the optimization procedure therefore attempts to recover an image that both: 1) closely matches the target degraded image after undergoing a similar degradation model (fidelity); and 2) lies in the space of realistic images learned by the GAN (realism).", + "bbox": [ + 511, + 604, + 883, + 756 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the recent literature, StyleGAN [29-31] has been found to be particularly effective for unsupervised image restoration [13-15, 39, 40] because of the elegant design of its latent space. Indeed, these approaches leverage style inversion techniques [3, 4] to solve for a latent vector that, when given to the generator, creates an image close to the degraded target. Unfortunately, this only works when such a match actually exists in the model distribution, which is rarely the case in practice. Hence, effective methods extend the learned latent space to cre", + "bbox": [ + 511, + 761, + 885, + 912 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22292", + "bbox": [ + 478, + 935, + 519, + 946 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ate additional degrees of freedom to admit more images; this creates the need for additional regularization losses. Hyperparameters must therefore carefully be tuned for each specific task and degradation level.", + "bbox": [ + 111, + 90, + 480, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we make unsupervised StyleGAN image restoration-by-inversion robust to the type and intensity of degradations. Our proposed method employs the same hyperparameters across all tasks and levels and does not rely on any regularization loss. Our approach leans on two key ideas. First, we rely on a 3-phase progressive latent space extension: we begin by optimizing over the learned (global) latent space, then expand it across individual layers of the generator, and finally expand it further across individual filters—where optimization at each phase is initialized with the result of the previous one. Second, we rely on a conservative, normalized gradient descent (NGD) [58] optimizer which is naturally constrained to stay close to its initial point compared to more sophisticated approaches such as Adam [33]. This combination of prudent optimization over a progressively richer latent space avoids additional regularization terms altogether and keeps the overall procedure simple and constant across all tasks. We evaluate our method on upsampling, inpainting, denoising and deartifacting on a wide range of degradation levels, achieving state-of-the-art results on most scenarios even when baselines are optimized on each independently. We also show that our approach outperforms existing techniques on compositions of these tasks without changing hyperparameters.", + "bbox": [ + 114, + 154, + 486, + 530 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a robust 3-phase StyleGAN image restoration framework. Our optimization technique maintains: 1) strong realism when degradations level are high; and 2) high fidelity when they are low. Our method is fully unsupervised, requires no per-task training, and can handle different tasks at different levels without having to adjust hyperparameters.", + "- We demonstrate the effectiveness of the proposed method under diverse and composed degradations. We develop a benchmark of synthetic image restoration tasks—making their degradation levels easy to control—with care taken to avoid unrealistic assumptions. Our method outperforms existing unsupervised [13,40] and diffusion-based [32] approaches." + ], + "bbox": [ + 112, + 532, + 483, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 112, + 762, + 250, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This section covers previous work on StyleGAN inversion by optimization and its use for image restoration, and discusses related works on generative priors. Because the literature on general purpose image restoration is so extensive, we do not attempt to review it here and instead refer the reader to recent surveys [18, 19, 35, 57].", + "bbox": [ + 111, + 789, + 480, + 880 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GANs and StyleGAN inversion Generative adversarial networks [20] (GANs) are a popular technique", + "bbox": [ + 111, + 881, + 483, + 912 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for generative modeling. In particular, the StyleGAN family [28-31] learns a highly compressed latent representation of its domain and stands out for its popularity and generation quality. Great progress has been made in StyleGAN inversion: reversing the generation process to infer latent parameters that generate a given image [59].", + "bbox": [ + 511, + 90, + 883, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Thanks to inversion, StyleGAN has found use in many image editing [23, 43, 51] and restoration [13-15, 39, 40] tasks. Purely optimization-based techniques were studied extensively [3, 4, 26, 44, 46, 66] in the context of image editing. These methods extend the learned latent space of a pretrained StyleGAN model (commonly named $\\mathcal{W}$ ) by adding additional parameters to optimize over it. The most common approach consists of using a different latent code for each layer [3] (dubbed $\\mathcal{W}^+$ ). Going beyond $\\mathcal{W}^+$ has also been explored in [46] who propose to fine-tune generator parameters, and [44] which uses different latent codes for each convolution filter. We build on these techniques by developing an inversion method designed specifically for robust image restoration.", + "bbox": [ + 511, + 183, + 883, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generative priors for unsupervised image restoration Since the initial work of Bora et al. [6], multiple papers have used generative priors for unsupervised image restoration [21, 25]. Pan et al. [42] obtained high-resolution results with BigGAN [7]. They relax their latent inversion method by introducing a coarse-to-fine, layer-by-layer generator fine-tuning. Our method differs in that it addresses robustness and compositionality.", + "bbox": [ + 511, + 397, + 883, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "StyleGAN image restoration Inversion methods designed for editing cannot be applied directly for restoration because loss functions are applied to degraded targets rather than clean images. Previous works address this with additional regularization terms and/or optimizer constraints. Of note, PULSE [40] proposed StyleGAN inversion for image upsampling, using a regularizer minimizing the latent extension to $\\mathcal{W}^+$ and a spherical optimization technique on a Gaussian approximation of $\\mathcal{W}$ . While PULSE succeeds in preserving high realism, it obtains low fidelity when the downsampling factor is small. ILO [15] uses similar regularization techniques, and further extends the latent space by optimizing intermediate feature maps in a progressive fashion (layer-by-layer) while constraining the solutions to sparse deviations from the range. More recently, SGILO [14] proposes to replace this sparsity constraint and instead trains a score-based model to learn the distribution of the outputs of an intermediate layer in the StyleGAN generator. BRGM [39] frames GAN inversion as Bayesian inference and estimates the maximum a-posteriori over the input latent vector that generated the reconstructed image given different regularization constraints. Its followup, L-BRGM [13], jointly optimizes the $\\mathcal{Z}$ (before the mapping network) and $\\mathcal{W}$ spaces, further improving quality. In contrast, our work achieves robustness by", + "bbox": [ + 511, + 518, + 883, + 912 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22293", + "bbox": [ + 478, + 935, + 517, + 946 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/01269686a92a2f9db1a5fa56938d162ae30829b740759797a4d99eed45c43b57.jpg", + "image_caption": [ + "Figure 2. Unsupervised image restoration with StyleGAN attempts to restore a degraded target image $\\pmb{y} = f(\\pmb{y}_{\\mathrm{clean}})$ by finding a generated image $\\pmb{x}_{\\mathrm{clean}}$ that matches this target once also degraded $\\pmb{x} = \\hat{f}(\\pmb{x}_{\\mathrm{clean}})$ (sec. 3); here, $\\hat{f}$ is a differentiable approximation to the degradation function $f$ and $\\pmb{y}_{\\mathrm{clean}}$ is the (unknown) ground truth image." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 482, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "avoiding any such regularization losses.", + "bbox": [ + 112, + 366, + 375, + 381 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Other similar works StyleGAN inversion was used to restore old photographs in [38]. Their method also restores a mixture of degradations, but is designed for real degradations (not robustness) and uses a task-specific encoder, while ours method is fully unsupervised. Multiple supervised methods [22, 34, 36, 56, 64, 65] focus on faces only, whereas our method does not use face-specific loss functions [16], is fully unsupervised, and works across a variety of image domains.", + "bbox": [ + 111, + 383, + 483, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models Denoising diffusion probabilistic models (DDPMs) [53], trained on extremely large datasets (e.g., billions of images for [45, 47, 49]), have recently been shown to outclass GANs when it comes to image generation quality [17]. New approaches have been proposed to tackle image restoration using DDPMs, e.g., Palette [48] obtains excellent results by training the same model for several different tasks. Denoising diffusion restoration models (DDRM) [32] show that pretrained DDPMs can be used for unsupervised restoration tasks, but are limited to linear inverse problems with additive Gaussian noise. In contrast, our method is more flexible since it only requires a differentiable approximation of the degradation function, which can be non-linear.", + "bbox": [ + 111, + 521, + 483, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Image restoration with StyleGAN", + "text_level": 1, + "bbox": [ + 112, + 753, + 418, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in fig. 2, StyleGAN inversion attempts to recover an image $\\pmb{x}_{\\mathrm{clean}}$ that best matches an (unknown) ground truth image $\\pmb{y}_{\\mathrm{clean}}$ . To this end, we aim to search for a latent code $\\pmb{w} \\in \\mathcal{W}$ such that $\\pmb{x}_{\\mathrm{clean}} = G(\\pmb{w})$ best matches $\\pmb{y}_{\\mathrm{clean}}$ under some image distance function $\\ell$ . The resulting minimization problem,", + "bbox": [ + 111, + 782, + 483, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(G (\\tilde {\\boldsymbol {w}}), \\boldsymbol {y} _ {\\text {c l e a n}}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 888, + 482, + 915 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e861fc957b4dc5c6debbbb7fa15903e15ebd59480c06371acceaff9b65850d54.jpg", + "image_caption": [ + "Figure 3. Our 3-phase latent extension (sec. 4.1) approach. (a) Phase I uses a global latent code $\\pmb{w}$ , resulting in a prediction $\\pmb{x}$ . (b) Phase II performs layer-wise latent expansion, resulting in matrix $\\pmb{w}^{+}$ and in a prediction $\\pmb{x}^{+}$ . (c) Phase III performs filter-wise latent expansion, resulting in tensor $\\pmb{w}^{++}$ and the final prediction $\\pmb{x}^{++}$ ." + ], + "image_footnote": [], + "bbox": [ + 517, + 74, + 880, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "can be solved by gradient descent. In image restoration, the ground truth image $\\pmb{y}_{\\mathrm{clean}}$ is unknown: we are instead given a target image $\\pmb{y} = f(\\pmb{y}_{\\mathrm{clean}})$ , the result of a (non-injective, potentially non-differentiable) degradation function $f$ . Assuming that a differentiable approximation $\\hat{f}\\approx f$ can be constructed, restoration is performed by solving for", + "bbox": [ + 511, + 402, + 883, + 508 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(\\hat {f} (G (\\tilde {\\boldsymbol {w}})), \\boldsymbol {y}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 513, + 883, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This can be generalized to compositions of $k$ different. \ndegradations,i.e., $\\{f_i\\}_{i = 1}^k$ ,by solving for", + "bbox": [ + 511, + 547, + 883, + 578 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(\\left[ \\hat {f} _ {k} \\circ \\dots \\circ \\hat {f} _ {2} \\circ \\hat {f} _ {1} \\right] (G (\\tilde {\\boldsymbol {w}})), \\boldsymbol {y}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 584, + 883, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\circ$ is the composition operator. Here, it is assumed that each subfunction $f_{i}$ has a differentiable approximation $\\hat{f}_i$ , and that the order of composition is known.", + "bbox": [ + 511, + 618, + 883, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As described in sec. 2, this naive approach finds solutions that have high realism (look like real faces), but low fidelity (do not match the degraded target). Fidelity is most commonly improved by 1) performing latent extension [3], that is, solving for $\\boldsymbol{w}^{+} \\in \\mathcal{W}^{+}$ which has many more degrees of freedom; and 2) using a better performing optimizer like Adam [33]. These techniques both improve fidelity but also damage realism, motivating the use of regularization losses which must carefully be adjusted for different tasks [13, 39, 40]. In the next section, we show how the choice of latent extension and optimizer avoids the need for these regularizers.", + "bbox": [ + 511, + 662, + 883, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Robust StyleGAN inversion", + "text_level": 1, + "bbox": [ + 511, + 856, + 769, + 872 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose an inversion method designed specifically for robust image restoration, which revisits each aspect", + "bbox": [ + 511, + 881, + 883, + 912 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22294", + "bbox": [ + 478, + 936, + 517, + 948 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "of the unsupervised StyleGAN optimization pipeline, namely latent extension, optimization, and loss functions.", + "bbox": [ + 111, + 90, + 485, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Robust latent extension", + "text_level": 1, + "bbox": [ + 112, + 130, + 330, + 145 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by the intuition that initialization is the best regularization [46], we propose a three-phase latent extension, where each phase is initialized by the outcome of the previous one, see fig. 3. Given a pretrained StyleGAN2 [31] model with $N_{L}$ layers in the generator, we denote style vectors $s_i^l \\in \\mathbb{R}^{512}$ at layer $l \\in [1,N_L]$ used to modulate convolution weights $\\pmb{\\theta}^{l} \\in \\mathbb{R}^{512 \\times 512}$ . Assuming $1 \\times 1$ filters to simplify notation1, each feature map pixel $p^l \\in \\mathbb{R}^{512}$ is processed by", + "bbox": [ + 111, + 152, + 483, + 290 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {i} ^ {l + 1} = \\left(\\boldsymbol {\\theta} _ {i} ^ {l} \\odot \\boldsymbol {s} _ {i} ^ {l}\\right) \\boldsymbol {p} ^ {l}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 225, + 299, + 483, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "producing output feature $p_i^{l + 1}\\in \\mathbb{R}$ where $i\\in [0,512]$ .", + "bbox": [ + 111, + 328, + 470, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Phase I performs global style modulation (fig. 3-(a)), and solves for a single latent vector $\\boldsymbol{w} \\in \\mathcal{W} = \\mathbb{R}^{512}$ shared across all layers as in eq. (3). Prior to optimization, $\\boldsymbol{w}$ is initialized to the mean of $\\mathcal{W}$ over the training set, i.e., $\\mathbb{E}_{\\tilde{\\boldsymbol{w}} \\in \\mathcal{W}}[\\tilde{\\boldsymbol{w}}]$ . Here, the style modulation vector $s_i^l$ in eq. (4) can be written as", + "bbox": [ + 111, + 345, + 483, + 435 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} (\\boldsymbol {w}), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 250, + 446, + 480, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{A}^l$ is the corresponding affine projection layer (which multiplies by a weight matrix and adds a bias).", + "bbox": [ + 111, + 474, + 482, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Phase II performs layer-wise latent extension [3] (fig. 3-(b)), and solves for a latent matrix $\\boldsymbol{w}^{+} \\in \\mathcal{W}^{+} = \\mathbb{R}^{N_{L} \\times 512}$ . Each row of $\\boldsymbol{w}^{+}$ is initialized to $\\boldsymbol{w}$ . Style modulation for this phase becomes", + "bbox": [ + 112, + 506, + 483, + 566 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} \\left(\\boldsymbol {w} _ {l} ^ {+}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 245, + 577, + 480, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Phase III performs filter-wise latent extension (fig. 3-c), and solves for a latent tensor $\\boldsymbol{w}^{++} \\in \\mathcal{W}^{++} = \\mathbb{R}^{N_F \\times N_L \\times 512}$ , where a different latent code is used for each convolution filter and where $N_F$ is the number of such filters. Each submatrix of $\\boldsymbol{w}^{++}$ is initialized to $\\boldsymbol{w}^+$ . Style modulation for this phase becomes", + "bbox": [ + 111, + 606, + 483, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} \\left(\\boldsymbol {w} _ {i, l} ^ {+ +}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 240, + 707, + 480, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Robust optimization", + "text_level": 1, + "bbox": [ + 112, + 747, + 305, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While most inversion approaches use the Adam [33] optimizer to solve eq. (3), we instead propose coupling our 3-phase latent extension with a weaker optimizer, normalized gradient decent (NGD) [58], a simple variant of SGD that normalizes the gradient before each step:", + "bbox": [ + 111, + 768, + 483, + 845 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\nabla} _ {\\boldsymbol {w}} \\ell (\\boldsymbol {w}) = \\frac {\\nabla_ {\\boldsymbol {w}} \\ell (\\boldsymbol {w})}{\\| \\nabla_ {\\boldsymbol {w}} \\ell (\\boldsymbol {w}) \\| _ {2}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 856, + 480, + 888 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Robust StyleGAN inversion." + ], + "code_body": "Output: restored image $x^{++}$ # Phase I \n1 $\\pmb {w} = \\mathbb{E}_{\\tilde{\\pmb{w}}\\in \\mathcal{W}}[\\tilde{\\pmb{w}} ]$ \n2 for 1 to 150 do \n3 $\\begin{array}{r}\\pmb {x}\\gets G(\\pmb {w})\\\\ \\pmb {w}\\gets 0.08\\bar{\\nabla}_{\\pmb{w}}\\ell (\\hat{f} (\\pmb {x}),\\pmb {y}) \\end{array}$ \n4 Phase II \n5 $w^{+} =$ repeat $(\\pmb {w},N_L)$ \n6 for 1 to 150 do \n7 $\\begin{array}{r}\\pmb{x}^{+}\\gets G^{+}(\\pmb{w}^{+}) \\end{array}$ \n8 $\\begin{array}{r}\\pmb {w}^{+}\\gets 0.02\\bar{\\nabla}_{\\pmb{w}}\\ell (\\hat{f} (\\pmb{x}^{+}),\\pmb {y}) \\end{array}$ # Phase III \n9 $w^{+ + } =$ repeat $(\\pmb {w}^{+},N_{F})$ \n10 for 1 to 150 do \n11 $\\begin{array}{r}\\pmb{x}^{+ + }\\gets G^{+ + }(\\pmb{w}^{+ + })\\\\ \\pmb{w}^{+ + }\\gets 0.005\\bar{\\nabla}_{\\pmb{w}^{+ + }}\\ell (\\hat{f} (\\pmb{x}^{+ + }),\\pmb {y}) \\end{array}$ \n12 \n13 return $x^{+ + }$", + "bbox": [ + 516, + 111, + 781, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, the gradient $\\bar{\\nabla}_{\\boldsymbol{w}}\\ell (\\boldsymbol {w})$ is explicitly set to 0 when $||\\nabla_{\\boldsymbol{w}}\\ell (\\boldsymbol {w})||_2 = 0$ . Following latent extension, we normalize each latent code separately (i.e. each row of $\\boldsymbol{w}^{+}$ and $\\boldsymbol{w}^{+ + }$ ). NGD conserves loss scale invariance, a key property of Adam that avoids learning rate adjustments following loss function changes.", + "bbox": [ + 511, + 402, + 883, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Robust loss function", + "text_level": 1, + "bbox": [ + 511, + 503, + 705, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The staple loss function in StyleGAN inversion is the LPIPS [63] perceptual loss combined with a L2 or L1 [4] pixel-wise loss. We found a multiresolution loss function to be much more robust, and use:", + "bbox": [ + 511, + 526, + 883, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\mathrm {M R}} (\\boldsymbol {x}, \\boldsymbol {y}) = \\sum_ {i = 1} ^ {k} \\ell_ {\\mathrm {L P I P S}} \\left(\\phi \\left(\\boldsymbol {x}, 2 ^ {i}\\right), \\phi \\left(\\boldsymbol {y}, 2 ^ {i}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 594, + 882, + 635 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\phi (\\cdot ,2^i)$ downsamples by a factor of $2^{i}$ using average pooling, and we set $k = 6$ for image resolution of $1024^{2}$ . All resolutions are weighted equally, giving our final loss function $\\ell = \\lambda_{\\mathrm{L1}}\\ell_{\\mathrm{L1}} + \\ell_{\\mathrm{MR}}$ with $\\lambda_{\\mathrm{L1}} = 0.1$ .", + "bbox": [ + 511, + 645, + 883, + 707 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Overall algorithm", + "text_level": 1, + "bbox": [ + 511, + 714, + 689, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Alg. 1 provides a detailed pseudo-code of our method. $G^{+}$ and $G^{++}$ denote the synthesis network $G$ after modification to accept $w^{+} \\in \\mathcal{W}^{+}$ and $w^{++} \\in \\mathcal{W}^{++}$ , respectively. Hyperparameters like learning rates and number of steps are explicitly provided since they are held constant across all tasks. Their values were found by cross-validation on a subset of the FFHQ training set.", + "bbox": [ + 511, + 738, + 883, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Benchmarking restoration robustness", + "text_level": 1, + "bbox": [ + 511, + 856, + 852, + 872 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This section first describes the proposed degradation models used in all experiments as well as their respec", + "bbox": [ + 511, + 881, + 883, + 912 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "In the $3 \\times 3$ case, operations are repeated spatially and summed.", + "bbox": [ + 132, + 898, + 478, + 911 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22295", + "bbox": [ + 478, + 935, + 517, + 946 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tive differentiable approximations. It then explains how compositions of tasks were formed.", + "bbox": [ + 112, + 90, + 482, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Individual degradations", + "text_level": 1, + "bbox": [ + 112, + 128, + 333, + 145 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Experiments are performed on four common sources of image degradation: upsampling, inpainting, denoising, and deartifacting. Synthetic models are used to facilitate comparison at different degradation levels. Each degradation is tested at five levels, which are referred to as extra-small (XS), small (S), medium (M), large (L), and extra-large (XL). Parameters for each degradation level will be provided below for each task in that same order. Fig. 4 shows examples of all four degradations at the XS and XL levels, see supp.", + "bbox": [ + 111, + 152, + 483, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Upsampling targets $\\pmb{y}$ are produced by downsampling ground truth images $\\pmb{y}_{\\mathrm{clean}}$ by integer factors $k_{\\mathrm{down}} \\in \\{2,4,8,16,32\\}$ . Downsampling filters are uniformly sampled from the commonly used bilinear, bicubic, and Lanczos filters, which provides a coarse but broad range of aliasing profiles. During inversion, average pooling is used as the approximation $\\hat{f}$ in all cases.", + "bbox": [ + 111, + 303, + 483, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inpainting aims to predict missing regions in an image. To test a variety of masking conditions, random masks are generated by drawing $k_{\\mathrm{strokes}} \\in \\{1,5,9,13,17\\}$ random strokes of width $0.08r$ where $r$ is the image resolution, each stroke connecting two random points situated in the outer thirds of the image. In this task, $\\hat{f} = f$ i.e. we assume that the mask is known. To avoid the bias introduced by black pixels when evaluating the LPIPS loss, identical noise of distribution $\\mathcal{N}(0.5,1)$ is added to the masked region of both the prediction and the target before computing LPIPS.", + "bbox": [ + 111, + 410, + 483, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Denoising targets are generated by using a mixture of Poisson and Bernoulli noise, simulating common sources of noise in cameras, namely shot noise and dead (or hot) pixels respectively. This is a challenging scenario because unlike Gaussian noise, Poisson noise is non-additive and signal-dependent, while Bernoulli noise is biased. Additionally, both are non-differentiable. We used the parameters $k_{\\mathrm{p}} \\in \\{96, 48, 24, 12, 6\\}$ and $k_{\\mathrm{b}} \\in \\{0.04, 0.08, 0.16, 0.32, 0.64\\}$ where $k_{\\mathrm{p}}$ gives the most likely value added to a pixel (independently for each channel) according to a Poisson distribution, and $k_{\\mathrm{b}}$ the probability that all channels of a pixel are replaced with black. We also account for clamping during image serialization, resulting in the overall noise model:", + "bbox": [ + 111, + 575, + 483, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\operatorname {c l a m p} \\left(p ^ {\\prime} \\cdot m\\right)}{2 5 5}, \\text {w h e r e} p ^ {\\prime} \\sim \\mathcal {P} \\left(k _ {\\mathrm {p}} p\\right), m \\sim \\mathcal {B} \\left(k _ {\\mathrm {b}}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 794, + 482, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for a ground truth image pixel value $p \\in [0.0, 1.0]$ and where $\\mathrm{clamp}(\\cdot)$ saturates all values outside of [0, 255]. Note that $p'$ can only take discrete values. For the differentiable approximation $\\hat{f}$ , we replace the (non-differentiable, discrete) Poisson noise with a Gaussian ap", + "bbox": [ + 111, + 835, + 483, + 912 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "proximation $\\mathcal{N}(k_{\\mathrm{p}}p - 0.5,\\sqrt{k_{\\mathrm{p}}p})$ and treat the Bernoulli noise as an unknown mask. We also use a surrogate gradient for clamp:", + "bbox": [ + 511, + 90, + 883, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d}{d p} \\operatorname {c l a m p} (p) \\approx \\frac {d}{d p} \\operatorname {s i g m o i d} (2 \\cdot (p - 0. 5)). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 146, + 882, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Deartifacting is performed on JPEG images compressed with libjpeg [2, 12] at quality levels $k_{\\mathrm{jpeg}} \\in \\{18, 15, 12, 9, 6\\}$ . The lossy part of JPEG compression can be expressed as", + "bbox": [ + 511, + 186, + 883, + 247 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {q u a n t i z e} \\circ \\mathrm {D C T} \\circ \\text {t o} _ {\\text {b l o c k s}} \\circ \\text {c h r o m a} _ {\\text {s u b s a m p l e}}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 258, + 882, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, 4:2:2 chroma subsampling is used. This final quantization step rounds each DCT component $c_{i,j}^{(k)}$ positioned in the $k^{\\text{th}}$ block at indices $i,j$ with", + "bbox": [ + 511, + 290, + 883, + 339 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {q u a n t i z e} \\left(c _ {i, j} ^ {(k)}\\right) = \\left\\lfloor c _ {i, j} ^ {(k)} / Q _ {i, j} \\right], \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 349, + 882, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Q_{i,j} \\in [1,255] \\subset \\mathbb{N}$ is the corresponding value from the quantization table. Rounding is the only non-differentiable part of this chain (the lossless part of JPEG compression does not need to be differentiated). We read the quantization tables from file headers and use Lomnitz's implementation [1] of [52], which proposes differentiable rounding:", + "bbox": [ + 511, + 378, + 883, + 486 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\lfloor p \\rceil \\approx \\lfloor p \\rceil + (p - \\lfloor p \\rceil) ^ {3}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 496, + 882, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use this approximation to define a surrogate gradient (keeping the forward pass exact), and interpolate with a straight-through gradient estimator at $\\alpha = 0.8$ :", + "bbox": [ + 511, + 525, + 883, + 570 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {d}{d p} \\lfloor p \\rceil \\approx \\frac {d}{d p} \\left[ (1 - \\alpha) p + \\alpha (p - \\lfloor p \\rceil) ^ {3} \\right]. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 580, + 880, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Composed degradations", + "text_level": 1, + "bbox": [ + 513, + 622, + 735, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Eq. (3) assumes knowledge of the order in which degradations are applied. In this work, the following restoration order is used:", + "bbox": [ + 511, + 645, + 883, + 689 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {i n p a i n t} \\circ \\text {d e a r i f a c t} \\circ \\text {d e n o i s e} \\circ \\text {u p s a m p l e}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 702, + 880, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Task compositions are created with (subsequences of) this ordering. For example, upsampling and deartifacting form a composition of length 2. All compositions were formed with tasks at degradation level medium (M).", + "bbox": [ + 511, + 729, + 883, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Comparison to StyleGAN-based methods", + "text_level": 1, + "bbox": [ + 511, + 803, + 880, + 820 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1. Models, datasets, and metrics", + "text_level": 1, + "bbox": [ + 511, + 828, + 774, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The PyTorch implementation [41] of StyleGAN2-ADA [28] is used in all experiments. In particular, we use the model pretrained on the FFHQ dataset [30] at $1024 \\times 1024$ resolution. Since the model is trained on", + "bbox": [ + 511, + 849, + 883, + 910 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22296", + "bbox": [ + 478, + 936, + 517, + 948 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8fc68f163d70564b3fc207f5a33bdf4e40fef58e95f288944860b7ff476552e3.jpg", + "image_caption": [ + "Figure 4. Randomly selected qualitative restoration results on each independent task, for both extra-small and extra-large levels of degradation. Top to bottom: (degraded) target, ours, L-BRGM [13], and PULSE [40]. Left to right: upsampling, inpainting, denoising, and deartifacting. Our method shows better robustness to variations in levels of degradation. See supp. for more results." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 320, + 391 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3a025d545e7280eb5becaf2be500242b31cd4fcfcd71cbf8e6b3cfe88ca87fbb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 88, + 506, + 390 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7eaa2780704093d6a469d855c3522662d736056400b15c0844f512de6e9ec19a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 88, + 694, + 390 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/da7ae62f29d1cacfb9dd359a4aba43e4c8a300f78331604c4a13b2c13ccea84b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 89, + 882, + 390 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the entire FFHQ dataset, we gathered an additional 100 test images, dubbed “FFHQ extras” (FFHQ-X), using the same alignment script. Overlap with FFHQ was avoided by filtering by date (see supp.).", + "bbox": [ + 109, + 469, + 482, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance was measured via accuracy, realism, and fidelity metrics. Accuracy was measured with the LPIPS [63] between the predictions and the ground truth images. Realism was measured using the PatchFID [8] (pFID): FID [24] measured on image patches. More specifically, we extracted 1000 random crops of size $128 \\times 128$ per image, computing the FID of all crops from predictions to all crops from our FFHQ-X dataset. Finally, fidelity between degraded predictions and targets was measured using the LPIPS; this was done by degrading predictions with the true degradation to ignore the effect of differentiable approximations.", + "bbox": [ + 109, + 531, + 482, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2. Baselines", + "text_level": 1, + "bbox": [ + 112, + 722, + 220, + 736 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method is compared on FFHQ-X against two unsupervised StyleGAN image restoration techniques, PULSE [40] and the current state of the art L-BRGM [13]. The same pretrained network is used for all approaches.", + "bbox": [ + 109, + 744, + 482, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PULSE [40] We adapted PULSE to use StyleGAN2-ADA and to tasks other than upsampling by increasing the number of steps from 100 to 250 and adjusting the learning rate to 0.8 (manual inspection on validation data) to increase its robustness to novel tasks.", + "bbox": [ + 109, + 805, + 482, + 880 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "L-BRGM [13] We adjust its learning rate $\\lambda_{\\mathrm{lr}} = 0.05$ by manual inspection. L-BRGM uses best-of- $k$ random", + "bbox": [ + 111, + 881, + 482, + 912 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "initialization; because initialization is difficult under high degradations, we doubled the number of samples from 100 to 200 and added a 0.8 truncation [30] to avoid outliers. L-BRGM also performs early stopping by inspecting the ground truth; for a fair comparison, we instead fixed the number of steps to 500 as in BRGM [39].", + "bbox": [ + 511, + 469, + 883, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyperparameter optimization for baselines We optimize the accuracy metric for the baselines hyperparameters for each (task, level) pair individually directly on the $FFHQ-X$ test set (see supp. for more details). In addition, baselines employ the ground truth Bernoulli mask (see sec. 5.1) in their differentiable approximation of eq. (10). Doing so was necessary for good performance.", + "bbox": [ + 511, + 561, + 883, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method We adjust hyperameters (learning rate and number of iterations, see alg. 1) once on validation data, then run our benchmark on the test set with no pertask or per-level hyperparameter adjustment: our method uses the same hyperparameters across all tasks and levels. Our method is not provided the Bernoulli mask. The total number of steps (450) is less than the 500 used for L-BRGM.", + "bbox": [ + 511, + 667, + 883, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.3. Experimental results", + "text_level": 1, + "bbox": [ + 511, + 797, + 709, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Robustness to degradation levels Our benchmark is run on our FFQH-X test set (sec. 6.1) on all five levels of degradation for each individual task, and quantitative results are presented in tab. 1. Recall from sec. 6.2 that our method, which employs a single set of hyperparameters across all experiments, is pitted against baselines", + "bbox": [ + 511, + 821, + 883, + 912 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22297", + "bbox": [ + 478, + 936, + 517, + 948 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2e22e53a6aeae4afc81548707d13e543292d81e3336ad937d363e127a4afff59.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OursPULS L-BRG OursPULS L-BRG Ours
Upsampling (bilinear, bicubic or Lanczos)
XS.493.407.414.432.295.31344.523.617.0
S.492.412.449.353.140.23934.325.522.0
M.495.458.472.261.124.17229.335.422.3
L.501.487.490.185.129.12721.926.020.9
XL.512.506.514.083.095.09024.921.321.3
Denoising (clamped Poisson and Bernoulli mixture)
XS.501.440.425.275.152.15656.127.218.5
S.499.450.434.252.138.14053.728.619.1
M.500.465.446.224.155.13054.522.119.8
L.501.481.457.185.138.11056.424.619.2
XL.504.511.474.134.110.08449.425.117.9
Deartifacting (JPEG compression)
XS.498.442.432.404.341.34952.326.314.8
S.497.448.437.398.352.35049.622.415.4
M.498.461.445.413.357.35733.224.115.4
L.500.475.460.395.367.37446.925.216.0
XL.508.503.490.427.418.41230.822.118.7
Inpainting (random strokes)
XS.498.409.378.464.374.34846.924.412.9
S.501.425.387.356.287.26442.327.214.2
M.509.438.396.283.227.20638.530.114.5
L.513.452.409.231.184.16332.633.115.3
XL.524.460.422.187.157.13236.225.215.9
", + "bbox": [ + 122, + 89, + 475, + 435 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with hyperparameters optimized for each task and level individually. Despite this obvious impediment, our proposed method outperforms baselines in the vast majority of scenarios. In particular, it reaches better accuracy in the majority of tasks against baselines optimized for accuracy, and realism is strictly better. Fig. 4 illustrates the improved visual quality obtained with our method.", + "bbox": [ + 111, + 556, + 483, + 661 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness to compositions Robustness to compositions of degradations was evaluated by forming all possible subsequences of degradations (order in eq. (16)) at medium level. Quantitative results are aggregated in tab. 2, while fig. 5 presents qualitative examples. Our results show that both high fidelity and high realism are maintained with our method, while the baselines struggle under varied degradations.", + "bbox": [ + 111, + 662, + 483, + 782 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "7. Comparison to diffusion models", + "text_level": 1, + "bbox": [ + 112, + 795, + 405, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our approach to the recent \"Denoising diffusion restoration model\" (DDRM) [32], which also does not require problem-specific supervised training and leverages a pre-trained (DDPM [53]) model. Importantly, DCRM is designed only for linear inverse problems with additive Gaussian noise, where the degradation model is", + "bbox": [ + 111, + 821, + 483, + 911 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/af9504541b21cbcce36836c54f2a37f5e47fdc279b6813465a78485deb92a162.jpg", + "table_caption": [ + "Table 1. Quantitative comparison on individual tasks against baselines (\"PULS\" [40] and \"L-BRG\" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Results color-coded as best and second best." + ], + "table_footnote": [], + "table_body": "
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OUR5PULS L-BRG OUR5PULS L-BRG OUR5
2 degradations
NA.517.485.459.328.301.29043.424.217.3
AP.511.478.457.270.231.20429.717.617.0
UA.510.518.508.307.348.28723.720.519.7
NP.511.480.458.125.079.06247.020.919.2
UN.501.519.511.178.149.15333.426.221.1
UP.510.478.485.140.061.08923.935.320.7
3 degradations
UNP.510.526.507.086.062.05128.522.120.1
UAP.525.523.513.205.154.11923.018.420.5
UNA.521.535.533.265.310.29026.220.722.8
NAP.526.502.470.210.197.16038.718.418.5
4 degradations
UNAP.533.546.525.192.177.13125.521.121.8
", + "bbox": [ + 516, + 89, + 885, + 309 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0c236041033f81890c2e66ef6adb80379f25716b63f49370e26ddb861dd42b63.jpg", + "table_caption": [ + "Table 2. Quantitative comparison on composed tasks (at medium levels) against baselines (\"PULS\" [40] and \"L-BRG\" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Acronyms indicate restorations: Upsampling, deNoising, deArtifacting, and/or inPainting. Results color-coded as best and second best." + ], + "table_footnote": [], + "table_body": "
Accur. (LPIPS) ↓Realism (pFID) ↓
DDRMOURSDDRMOURS
Exact Upsampling (known average pooling)
0.4120.44344.7518.92
Inexact Upsampling (unknown nearest-neighbor)
0.5590.53967.0632.81
Linear Denoising (additive Gaussian noise)
0.3360.45243.2819.25
Nonlinear Denoising (clamped additive Gaussian noise)
0.5300.450156.119.06
Inpainting (masking random strokes)
0.2890.30126.1225.71
Uncropping (top left corner unmasked)
0.4680.41834.3317.645
", + "bbox": [ + 557, + 449, + 841, + 646 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative comparison to DDRM [32] on accuracy and realism (see sec. 7). Results are color-coded as best .", + "bbox": [ + 511, + 656, + 883, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "perfectly known. Therefore, for each of the upsampling, denoising and inpainting tasks, we experiment with both: 1) a linear inverse problem with known parameters; and 2) an adjusted version which is either non-linear, where the extract degradation model is unknown, or a more extreme version of the problem. Specifically, we test: average pooling (known, linear) vs nearest-neighbor (unknown) $32 \\times$ (XL) upsampling; additive Gaussian noise (linear) vs clamped (to [0, 255]) additive Gaussian noise (non-linear) with $\\sigma^2 = 0.8$ (XL) for both; and masking strokes (at XL level) vs uncropping the top-left corner (XXL). DDRM is available on CelebA (not FFHQ) at $256 \\times 256$ , so we use the corresponding StyleGAN2-ADA pretrained", + "bbox": [ + 511, + 715, + 883, + 912 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22298", + "bbox": [ + 478, + 936, + 517, + 948 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0dc25b0c6d19b5a73690935d182ba793285ca28427df5f89d63b4ab736204646.jpg", + "image_caption": [ + "Figure 5. Qualitative comparisons on all possible compositions of the four tasks given medium levels of degradation. Samples are chosen randomly, and acronyms indicate the degradations: Upsampling, inPainting, deNoising and/or deArtifacting (sec. 6.3)." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 537, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e0f0b184a35cae0ad3bec11f10fc46215c8222bb5c2e5711e61f848e2ef27c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 88, + 883, + 311 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9788772c3424bc9e816961daf2dbe2abb2a33c464b3ac9a2acead706f2fb127d.jpg", + "image_caption": [ + "Figure 6. Results on LSUN horses and churches [60], AFHQ-v2 Dogs [11] and BreCaHAD [5] at resolution $256 \\times 256$ for small upsampling (U), small denoising (N), medium deartifacting (A), and medium inpainting (P); the left/right halves are the target/restored images. See supp. for details and more results." + ], + "image_footnote": [], + "bbox": [ + 114, + 375, + 482, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model. Due to the reduced resolution, pFID is measured on 250 patches of size $64 \\times 64$ .", + "bbox": [ + 111, + 772, + 482, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interestingly, we find that DDRM reproduces the targets almost perfectly (fidelity is near zero, see supp. for details and qualitative results), to the point where it overfits to any deviation between its degradation model and the true degradation. Tab. 3 presents the accuracy and realism metrics for all the aforementioned tasks. While the accuracy favors DDRM for the tasks which perfectly", + "bbox": [ + 111, + 806, + 483, + 912 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "match its assumptions, our approach outperforms it when this is not the case. In addition, our method provides significantly better realism across all scenarios. Overall, our approach yields high resolution results with more detail, can adapt to non-linear tasks, and it can also cope with larger degradations.", + "bbox": [ + 511, + 378, + 883, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Discussion", + "text_level": 1, + "bbox": [ + 513, + 494, + 625, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Limitations** Our method is not restricted to faces and works with any pretrained StyleGAN, as demonstrated in fig. 6. However, it is inherently limited to the domain learned by the GAN. Training StyleGAN on a large unstructured dataset like ImageNet is difficult but recent papers [27,50,55] have attained some success—applying our method on some of these large-scale models is a promising research avenue. Our method also faces the same ethical considerations as the GAN it relies on. Finally, as with other methods [13,32,40], we also require knowledge of an (approximate) degradation function.", + "bbox": [ + 511, + 525, + 883, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion This paper presents a method which makes StyleGAN-based image restoration robust to both variability in degradation levels and to compositions of different degradations. Our proposed method relies on a conservative optimization procedure over a progressively richer latent space and avoids regularization terms altogether. Using a single set of hyperparameters, we obtain competitive and even state-of-the-art results on several challenging scenarios when compared to baselines that are optimized for each task/level individually.", + "bbox": [ + 511, + 696, + 883, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This research was supported by NSERC grant RGPIN-2020-04799, a MITACS Globalink internship to Y. Poirier-Ginter, and by the Digital Research Alliance Canada.", + "bbox": [ + 511, + 851, + 883, + 910 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22299", + "bbox": [ + 478, + 936, + 517, + 948 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 114, + 89, + 209, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Diffjpeg. https://github.com/mlomnitz/DiffJPEG.", + "[2] Libjpeg. https://libjpeg-turbo.org.", + "[3] Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2StyleGAN: How to embed images into the StyleGAN latent space? In Int. Conf. Comput. Vis., 2019.", + "[4] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan++: How to edit the embedded images? In IEEE Conf. Comput. Vis. Pattern Recog., 2020.", + "[5] Alper Aksac, Douglas J Demetrick, Tansel Ozyer, and Reda Alhajj. Brecahad: a dataset for breast cancer histopathological annotation and diagnosis. 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Improved stylegan embedding: Where are the good latents? arXiv preprint arXiv:2012.09036, 2020." + ], + "bbox": [ + 516, + 92, + 883, + 904 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22301", + "bbox": [ + 478, + 936, + 517, + 948 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Robust Unsupervised StyleGAN Image Restoration/22cf3860-c0a9-4cc3-ae76-e2aceeacd7e1_model.json b/2023/Robust Unsupervised StyleGAN Image Restoration/22cf3860-c0a9-4cc3-ae76-e2aceeacd7e1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..101de74586e298000c7772ef7d9c17547bb6f52a --- /dev/null +++ b/2023/Robust Unsupervised StyleGAN Image Restoration/22cf3860-c0a9-4cc3-ae76-e2aceeacd7e1_model.json @@ -0,0 +1,2420 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.238, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.241, + 0.131, + 0.758, + 0.154 + ], + "angle": 0, + "content": "Robust Unsupervised StyleGAN Image Restoration" + }, + { + "type": "text", + "bbox": [ + 0.305, + 0.181, + 0.694, + 0.234 + ], + "angle": 0, + "content": "Yohan Poirier-Ginter\\*, Jean-François Lalonde\\* Inria, Université Côte d'Azur, Université Laval https://lvsn.github.io/RobustUnsupervised/" + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.246, + 0.372, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.247, + 0.624, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.247, + 0.882, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.454, + 0.885, + 0.497 + ], + "angle": 0, + "content": "Figure 1. Our unsupervised StyleGAN image restoration method is robust and effective across a variety of tasks (left, top to bottom: upsampling, denoising, deartifacting, and inpainting) and a wide range of degradation levels. Since it avoids the need for task-specific hyperparameter tuning, it can directly handle combinations of such degradations, e.g., pairs (center) or even all four (right)." + }, + { + "type": "title", + "bbox": [ + 0.259, + 0.509, + 0.338, + 0.525 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.54, + 0.486, + 0.812 + ], + "angle": 0, + "content": "GAN-based image restoration inverts the generative process to repair images corrupted by known degradations. Existing unsupervised methods must be carefully tuned for each task and degradation level. In this work, we make StyleGAN image restoration robust: a single set of hyperparameters works across a wide range of degradation levels. This makes it possible to handle combinations of several degradations, without the need to retune. Our proposed approach relies on a 3-phase progressive latent space extension and a conservative optimizer, which avoids the need for any additional regularization terms. Extensive experiments demonstrate robustness on inpainting, upsampling, denoising, and deartifacting at varying degradations levels, outperforming other StyleGAN-based inversion techniques. Our approach also favorably compares to diffusion-based restoration by yielding much more realistic inversion results. Code is available at the above URL." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.827, + 0.245, + 0.843 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.852, + 0.485, + 0.914 + ], + "angle": 0, + "content": "Image restoration, the task of recovering a high quality image from a degraded input, is a long-standing problem in image processing and computer vision. Since different restoration tasks—such as denoising, upsampling," + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.51, + 0.885, + 0.601 + ], + "angle": 0, + "content": "deartifacting, etc.—can be quite distinct, many recent approaches [9, 10, 37, 54, 61, 62] propose to solve them in a supervised learning paradigm by leveraging curated datasets specifically designed for the task at hand. Unfortunately, designing task-specific approaches requires retraining large networks on each task separately." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.606, + 0.885, + 0.757 + ], + "angle": 0, + "content": "In parallel, the advent of powerful generative models has enabled the emergence of unsupervised restoration methods [42], which do not require task-specific training. The idea is to invert the generative process to recover a clean image. Assuming a known (or approximate) degradation model, the optimization procedure therefore attempts to recover an image that both: 1) closely matches the target degraded image after undergoing a similar degradation model (fidelity); and 2) lies in the space of realistic images learned by the GAN (realism)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.762, + 0.887, + 0.913 + ], + "angle": 0, + "content": "In the recent literature, StyleGAN [29-31] has been found to be particularly effective for unsupervised image restoration [13-15, 39, 40] because of the elegant design of its latent space. Indeed, these approaches leverage style inversion techniques [3, 4] to solve for a latent vector that, when given to the generator, creates an image close to the degraded target. Unfortunately, this only works when such a match actually exists in the model distribution, which is rarely the case in practice. Hence, effective methods extend the learned latent space to cre" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.936, + 0.521, + 0.948 + ], + "angle": 0, + "content": "22292" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.092, + 0.482, + 0.152 + ], + "angle": 0, + "content": "ate additional degrees of freedom to admit more images; this creates the need for additional regularization losses. Hyperparameters must therefore carefully be tuned for each specific task and degradation level." + }, + { + "type": "text", + "bbox": [ + 0.116, + 0.155, + 0.487, + 0.531 + ], + "angle": 0, + "content": "In this work, we make unsupervised StyleGAN image restoration-by-inversion robust to the type and intensity of degradations. Our proposed method employs the same hyperparameters across all tasks and levels and does not rely on any regularization loss. Our approach leans on two key ideas. First, we rely on a 3-phase progressive latent space extension: we begin by optimizing over the learned (global) latent space, then expand it across individual layers of the generator, and finally expand it further across individual filters—where optimization at each phase is initialized with the result of the previous one. Second, we rely on a conservative, normalized gradient descent (NGD) [58] optimizer which is naturally constrained to stay close to its initial point compared to more sophisticated approaches such as Adam [33]. This combination of prudent optimization over a progressively richer latent space avoids additional regularization terms altogether and keeps the overall procedure simple and constant across all tasks. We evaluate our method on upsampling, inpainting, denoising and deartifacting on a wide range of degradation levels, achieving state-of-the-art results on most scenarios even when baselines are optimized on each independently. We also show that our approach outperforms existing techniques on compositions of these tasks without changing hyperparameters." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.533, + 0.484, + 0.638 + ], + "angle": 0, + "content": "- We propose a robust 3-phase StyleGAN image restoration framework. Our optimization technique maintains: 1) strong realism when degradations level are high; and 2) high fidelity when they are low. Our method is fully unsupervised, requires no per-task training, and can handle different tasks at different levels without having to adjust hyperparameters." + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.64, + 0.484, + 0.744 + ], + "angle": 0, + "content": "- We demonstrate the effectiveness of the proposed method under diverse and composed degradations. We develop a benchmark of synthetic image restoration tasks—making their degradation levels easy to control—with care taken to avoid unrealistic assumptions. Our method outperforms existing unsupervised [13,40] and diffusion-based [32] approaches." + }, + { + "type": "list", + "bbox": [ + 0.114, + 0.533, + 0.484, + 0.744 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.763, + 0.251, + 0.779 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.79, + 0.482, + 0.881 + ], + "angle": 0, + "content": "This section covers previous work on StyleGAN inversion by optimization and its use for image restoration, and discusses related works on generative priors. Because the literature on general purpose image restoration is so extensive, we do not attempt to review it here and instead refer the reader to recent surveys [18, 19, 35, 57]." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.882, + 0.484, + 0.913 + ], + "angle": 0, + "content": "GANs and StyleGAN inversion Generative adversarial networks [20] (GANs) are a popular technique" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.884, + 0.183 + ], + "angle": 0, + "content": "for generative modeling. In particular, the StyleGAN family [28-31] learns a highly compressed latent representation of its domain and stands out for its popularity and generation quality. Great progress has been made in StyleGAN inversion: reversing the generation process to infer latent parameters that generate a given image [59]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.184, + 0.885, + 0.395 + ], + "angle": 0, + "content": "Thanks to inversion, StyleGAN has found use in many image editing [23, 43, 51] and restoration [13-15, 39, 40] tasks. Purely optimization-based techniques were studied extensively [3, 4, 26, 44, 46, 66] in the context of image editing. These methods extend the learned latent space of a pretrained StyleGAN model (commonly named \\(\\mathcal{W}\\)) by adding additional parameters to optimize over it. The most common approach consists of using a different latent code for each layer [3] (dubbed \\(\\mathcal{W}^+\\)). Going beyond \\(\\mathcal{W}^+\\) has also been explored in [46] who propose to fine-tune generator parameters, and [44] which uses different latent codes for each convolution filter. We build on these techniques by developing an inversion method designed specifically for robust image restoration." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.398, + 0.885, + 0.518 + ], + "angle": 0, + "content": "Generative priors for unsupervised image restoration Since the initial work of Bora et al. [6], multiple papers have used generative priors for unsupervised image restoration [21, 25]. Pan et al. [42] obtained high-resolution results with BigGAN [7]. They relax their latent inversion method by introducing a coarse-to-fine, layer-by-layer generator fine-tuning. Our method differs in that it addresses robustness and compositionality." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.52, + 0.885, + 0.913 + ], + "angle": 0, + "content": "StyleGAN image restoration Inversion methods designed for editing cannot be applied directly for restoration because loss functions are applied to degraded targets rather than clean images. Previous works address this with additional regularization terms and/or optimizer constraints. Of note, PULSE [40] proposed StyleGAN inversion for image upsampling, using a regularizer minimizing the latent extension to \\(\\mathcal{W}^+\\) and a spherical optimization technique on a Gaussian approximation of \\(\\mathcal{W}\\). While PULSE succeeds in preserving high realism, it obtains low fidelity when the downsampling factor is small. ILO [15] uses similar regularization techniques, and further extends the latent space by optimizing intermediate feature maps in a progressive fashion (layer-by-layer) while constraining the solutions to sparse deviations from the range. More recently, SGILO [14] proposes to replace this sparsity constraint and instead trains a score-based model to learn the distribution of the outputs of an intermediate layer in the StyleGAN generator. BRGM [39] frames GAN inversion as Bayesian inference and estimates the maximum a-posteriori over the input latent vector that generated the reconstructed image given different regularization constraints. Its followup, L-BRGM [13], jointly optimizes the \\(\\mathcal{Z}\\) (before the mapping network) and \\(\\mathcal{W}\\) spaces, further improving quality. In contrast, our work achieves robustness by" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.936, + 0.519, + 0.948 + ], + "angle": 0, + "content": "22293" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.089, + 0.483, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.251, + 0.485, + 0.336 + ], + "angle": 0, + "content": "Figure 2. Unsupervised image restoration with StyleGAN attempts to restore a degraded target image \\(\\pmb{y} = f(\\pmb{y}_{\\mathrm{clean}})\\) by finding a generated image \\(\\pmb{x}_{\\mathrm{clean}}\\) that matches this target once also degraded \\(\\pmb{x} = \\hat{f}(\\pmb{x}_{\\mathrm{clean}})\\) (sec. 3); here, \\(\\hat{f}\\) is a differentiable approximation to the degradation function \\(f\\) and \\(\\pmb{y}_{\\mathrm{clean}}\\) is the (unknown) ground truth image." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.367, + 0.377, + 0.382 + ], + "angle": 0, + "content": "avoiding any such regularization losses." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.384, + 0.484, + 0.519 + ], + "angle": 0, + "content": "Other similar works StyleGAN inversion was used to restore old photographs in [38]. Their method also restores a mixture of degradations, but is designed for real degradations (not robustness) and uses a task-specific encoder, while ours method is fully unsupervised. Multiple supervised methods [22, 34, 36, 56, 64, 65] focus on faces only, whereas our method does not use face-specific loss functions [16], is fully unsupervised, and works across a variety of image domains." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.522, + 0.484, + 0.734 + ], + "angle": 0, + "content": "Diffusion models Denoising diffusion probabilistic models (DDPMs) [53], trained on extremely large datasets (e.g., billions of images for [45, 47, 49]), have recently been shown to outclass GANs when it comes to image generation quality [17]. New approaches have been proposed to tackle image restoration using DDPMs, e.g., Palette [48] obtains excellent results by training the same model for several different tasks. Denoising diffusion restoration models (DDRM) [32] show that pretrained DDPMs can be used for unsupervised restoration tasks, but are limited to linear inverse problems with additive Gaussian noise. In contrast, our method is more flexible since it only requires a differentiable approximation of the degradation function, which can be non-linear." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.755, + 0.419, + 0.772 + ], + "angle": 0, + "content": "3. Image restoration with StyleGAN" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.783, + 0.484, + 0.873 + ], + "angle": 0, + "content": "As illustrated in fig. 2, StyleGAN inversion attempts to recover an image \\( \\pmb{x}_{\\mathrm{clean}} \\) that best matches an (unknown) ground truth image \\( \\pmb{y}_{\\mathrm{clean}} \\). To this end, we aim to search for a latent code \\( \\pmb{w} \\in \\mathcal{W} \\) such that \\( \\pmb{x}_{\\mathrm{clean}} = G(\\pmb{w}) \\) best matches \\( \\pmb{y}_{\\mathrm{clean}} \\) under some image distance function \\( \\ell \\). The resulting minimization problem," + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.89, + 0.483, + 0.916 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(G (\\tilde {\\boldsymbol {w}}), \\boldsymbol {y} _ {\\text {c l e a n}}\\right), \\tag {1}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.075, + 0.882, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.297, + 0.885, + 0.38 + ], + "angle": 0, + "content": "Figure 3. Our 3-phase latent extension (sec. 4.1) approach. (a) Phase I uses a global latent code \\(\\pmb{w}\\), resulting in a prediction \\(\\pmb{x}\\). (b) Phase II performs layer-wise latent expansion, resulting in matrix \\(\\pmb{w}^{+}\\) and in a prediction \\(\\pmb{x}^{+}\\). (c) Phase III performs filter-wise latent expansion, resulting in tensor \\(\\pmb{w}^{++}\\) and the final prediction \\(\\pmb{x}^{++}\\)." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.404, + 0.885, + 0.51 + ], + "angle": 0, + "content": "can be solved by gradient descent. In image restoration, the ground truth image \\(\\pmb{y}_{\\mathrm{clean}}\\) is unknown: we are instead given a target image \\(\\pmb{y} = f(\\pmb{y}_{\\mathrm{clean}})\\), the result of a (non-injective, potentially non-differentiable) degradation function \\(f\\). Assuming that a differentiable approximation \\(\\hat{f}\\approx f\\) can be constructed, restoration is performed by solving for" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.515, + 0.884, + 0.542 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(\\hat {f} (G (\\tilde {\\boldsymbol {w}})), \\boldsymbol {y}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.548, + 0.884, + 0.579 + ], + "angle": 0, + "content": "This can be generalized to compositions of \\(k\\) different. \ndegradations,i.e., \\(\\{f_i\\}_{i = 1}^k\\) ,by solving for" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.585, + 0.884, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(\\left[ \\hat {f} _ {k} \\circ \\dots \\circ \\hat {f} _ {2} \\circ \\hat {f} _ {1} \\right] (G (\\tilde {\\boldsymbol {w}})), \\boldsymbol {y}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.619, + 0.885, + 0.663 + ], + "angle": 0, + "content": "where \\( \\circ \\) is the composition operator. Here, it is assumed that each subfunction \\( f_{i} \\) has a differentiable approximation \\( \\hat{f}_i \\), and that the order of composition is known." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.664, + 0.885, + 0.845 + ], + "angle": 0, + "content": "As described in sec. 2, this naive approach finds solutions that have high realism (look like real faces), but low fidelity (do not match the degraded target). Fidelity is most commonly improved by 1) performing latent extension [3], that is, solving for \\( \\boldsymbol{w}^{+} \\in \\mathcal{W}^{+} \\) which has many more degrees of freedom; and 2) using a better performing optimizer like Adam [33]. These techniques both improve fidelity but also damage realism, motivating the use of regularization losses which must carefully be adjusted for different tasks [13, 39, 40]. In the next section, we show how the choice of latent extension and optimizer avoids the need for these regularizers." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.857, + 0.77, + 0.873 + ], + "angle": 0, + "content": "4. Robust StyleGAN inversion" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.882, + 0.884, + 0.913 + ], + "angle": 0, + "content": "We propose an inversion method designed specifically for robust image restoration, which revisits each aspect" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.938, + 0.519, + 0.949 + ], + "angle": 0, + "content": "22294" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.112, + 0.092, + 0.486, + 0.122 + ], + "angle": 0, + "content": "of the unsupervised StyleGAN optimization pipeline, namely latent extension, optimization, and loss functions." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.131, + 0.331, + 0.146 + ], + "angle": 0, + "content": "4.1. Robust latent extension" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.154, + 0.485, + 0.291 + ], + "angle": 0, + "content": "Inspired by the intuition that initialization is the best regularization [46], we propose a three-phase latent extension, where each phase is initialized by the outcome of the previous one, see fig. 3. Given a pretrained StyleGAN2 [31] model with \\( N_{L} \\) layers in the generator, we denote style vectors \\( s_i^l \\in \\mathbb{R}^{512} \\) at layer \\( l \\in [1,N_L] \\) used to modulate convolution weights \\( \\pmb{\\theta}^{l} \\in \\mathbb{R}^{512 \\times 512} \\). Assuming \\( 1 \\times 1 \\) filters to simplify notation1, each feature map pixel \\( p^l \\in \\mathbb{R}^{512} \\) is processed by" + }, + { + "type": "equation", + "bbox": [ + 0.226, + 0.3, + 0.484, + 0.32 + ], + "angle": 0, + "content": "\\[\np _ {i} ^ {l + 1} = \\left(\\boldsymbol {\\theta} _ {i} ^ {l} \\odot \\boldsymbol {s} _ {i} ^ {l}\\right) \\boldsymbol {p} ^ {l}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.329, + 0.472, + 0.346 + ], + "angle": 0, + "content": "producing output feature \\(p_i^{l + 1}\\in \\mathbb{R}\\) where \\(i\\in [0,512]\\)." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.346, + 0.484, + 0.436 + ], + "angle": 0, + "content": "Phase I performs global style modulation (fig. 3-(a)), and solves for a single latent vector \\(\\boldsymbol{w} \\in \\mathcal{W} = \\mathbb{R}^{512}\\) shared across all layers as in eq. (3). Prior to optimization, \\(\\boldsymbol{w}\\) is initialized to the mean of \\(\\mathcal{W}\\) over the training set, i.e., \\(\\mathbb{E}_{\\tilde{\\boldsymbol{w}} \\in \\mathcal{W}}[\\tilde{\\boldsymbol{w}}]\\). Here, the style modulation vector \\(s_i^l\\) in eq. (4) can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.251, + 0.447, + 0.482, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} (\\boldsymbol {w}), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.476, + 0.483, + 0.506 + ], + "angle": 0, + "content": "where \\(\\mathcal{A}^l\\) is the corresponding affine projection layer (which multiplies by a weight matrix and adds a bias)." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.507, + 0.484, + 0.567 + ], + "angle": 0, + "content": "Phase II performs layer-wise latent extension [3] (fig. 3-(b)), and solves for a latent matrix \\( \\boldsymbol{w}^{+} \\in \\mathcal{W}^{+} = \\mathbb{R}^{N_{L} \\times 512} \\). Each row of \\( \\boldsymbol{w}^{+} \\) is initialized to \\( \\boldsymbol{w} \\). Style modulation for this phase becomes" + }, + { + "type": "equation", + "bbox": [ + 0.246, + 0.578, + 0.482, + 0.596 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} \\left(\\boldsymbol {w} _ {l} ^ {+}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.607, + 0.485, + 0.698 + ], + "angle": 0, + "content": "Phase III performs filter-wise latent extension (fig. 3-c), and solves for a latent tensor \\(\\boldsymbol{w}^{++} \\in \\mathcal{W}^{++} = \\mathbb{R}^{N_F \\times N_L \\times 512}\\), where a different latent code is used for each convolution filter and where \\(N_F\\) is the number of such filters. Each submatrix of \\(\\boldsymbol{w}^{++}\\) is initialized to \\(\\boldsymbol{w}^+\\). Style modulation for this phase becomes" + }, + { + "type": "equation", + "bbox": [ + 0.241, + 0.708, + 0.482, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} \\left(\\boldsymbol {w} _ {i, l} ^ {+ +}\\right). \\tag {7}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.748, + 0.307, + 0.764 + ], + "angle": 0, + "content": "4.2. Robust optimization" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.77, + 0.484, + 0.847 + ], + "angle": 0, + "content": "While most inversion approaches use the Adam [33] optimizer to solve eq. (3), we instead propose coupling our 3-phase latent extension with a weaker optimizer, normalized gradient decent (NGD) [58], a simple variant of SGD that normalizes the gradient before each step:" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.857, + 0.482, + 0.89 + ], + "angle": 0, + "content": "\\[\n\\bar {\\nabla} _ {\\boldsymbol {w}} \\ell (\\boldsymbol {w}) = \\frac {\\nabla_ {\\boldsymbol {w}} \\ell (\\boldsymbol {w})}{\\| \\nabla_ {\\boldsymbol {w}} \\ell (\\boldsymbol {w}) \\| _ {2}}, \\tag {8}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.133, + 0.899, + 0.479, + 0.912 + ], + "angle": 0, + "content": "In the \\(3 \\times 3\\) case, operations are repeated spatially and summed." + }, + { + "type": "code_caption", + "bbox": [ + 0.523, + 0.095, + 0.809, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Robust StyleGAN inversion." + }, + { + "type": "algorithm", + "bbox": [ + 0.517, + 0.112, + 0.782, + 0.373 + ], + "angle": 0, + "content": "Output: restored image \\(x^{++}\\) # Phase I \n1 \\(\\pmb {w} = \\mathbb{E}_{\\tilde{\\pmb{w}}\\in \\mathcal{W}}[\\tilde{\\pmb{w}} ]\\) \n2 for 1 to 150 do \n3 \\(\\begin{array}{r}\\pmb {x}\\gets G(\\pmb {w})\\\\ \\pmb {w}\\gets 0.08\\bar{\\nabla}_{\\pmb{w}}\\ell (\\hat{f} (\\pmb {x}),\\pmb {y}) \\end{array}\\) \n4 Phase II \n5 \\(w^{+} =\\) repeat \\((\\pmb {w},N_L)\\) \n6 for 1 to 150 do \n7 \\(\\begin{array}{r}\\pmb{x}^{+}\\gets G^{+}(\\pmb{w}^{+}) \\end{array}\\) \n8 \\(\\begin{array}{r}\\pmb {w}^{+}\\gets 0.02\\bar{\\nabla}_{\\pmb{w}}\\ell (\\hat{f} (\\pmb{x}^{+}),\\pmb {y}) \\end{array}\\) # Phase III \n9 \\(w^{+ + } =\\) repeat \\((\\pmb {w}^{+},N_{F})\\) \n10 for 1 to 150 do \n11 \\(\\begin{array}{r}\\pmb{x}^{+ + }\\gets G^{+ + }(\\pmb{w}^{+ + })\\\\ \\pmb{w}^{+ + }\\gets 0.005\\bar{\\nabla}_{\\pmb{w}^{+ + }}\\ell (\\hat{f} (\\pmb{x}^{+ + }),\\pmb {y}) \\end{array}\\) \n12 \n13 return \\(x^{+ + }\\)" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.404, + 0.885, + 0.496 + ], + "angle": 0, + "content": "Here, the gradient \\(\\bar{\\nabla}_{\\boldsymbol{w}}\\ell (\\boldsymbol {w})\\) is explicitly set to 0 when \\(||\\nabla_{\\boldsymbol{w}}\\ell (\\boldsymbol {w})||_2 = 0\\). Following latent extension, we normalize each latent code separately (i.e. each row of \\(\\boldsymbol{w}^{+}\\) and \\(\\boldsymbol{w}^{+ + }\\)). NGD conserves loss scale invariance, a key property of Adam that avoids learning rate adjustments following loss function changes." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.504, + 0.706, + 0.518 + ], + "angle": 0, + "content": "4.3. Robust loss function" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.527, + 0.884, + 0.587 + ], + "angle": 0, + "content": "The staple loss function in StyleGAN inversion is the LPIPS [63] perceptual loss combined with a L2 or L1 [4] pixel-wise loss. We found a multiresolution loss function to be much more robust, and use:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.595, + 0.883, + 0.636 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\mathrm {M R}} (\\boldsymbol {x}, \\boldsymbol {y}) = \\sum_ {i = 1} ^ {k} \\ell_ {\\mathrm {L P I P S}} \\left(\\phi \\left(\\boldsymbol {x}, 2 ^ {i}\\right), \\phi \\left(\\boldsymbol {y}, 2 ^ {i}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.885, + 0.708 + ], + "angle": 0, + "content": "where \\(\\phi (\\cdot ,2^i)\\) downsamples by a factor of \\(2^{i}\\) using average pooling, and we set \\(k = 6\\) for image resolution of \\(1024^{2}\\). All resolutions are weighted equally, giving our final loss function \\(\\ell = \\lambda_{\\mathrm{L1}}\\ell_{\\mathrm{L1}} + \\ell_{\\mathrm{MR}}\\) with \\(\\lambda_{\\mathrm{L1}} = 0.1\\)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.715, + 0.69, + 0.731 + ], + "angle": 0, + "content": "4.4. Overall algorithm" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.739, + 0.885, + 0.845 + ], + "angle": 0, + "content": "Alg. 1 provides a detailed pseudo-code of our method. \\( G^{+} \\) and \\( G^{++} \\) denote the synthesis network \\( G \\) after modification to accept \\( w^{+} \\in \\mathcal{W}^{+} \\) and \\( w^{++} \\in \\mathcal{W}^{++} \\), respectively. Hyperparameters like learning rates and number of steps are explicitly provided since they are held constant across all tasks. Their values were found by cross-validation on a subset of the FFHQ training set." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.857, + 0.854, + 0.873 + ], + "angle": 0, + "content": "5. Benchmarking restoration robustness" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.882, + 0.885, + 0.913 + ], + "angle": 0, + "content": "This section first describes the proposed degradation models used in all experiments as well as their respec" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.936, + 0.518, + 0.948 + ], + "angle": 0, + "content": "22295" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.113, + 0.092, + 0.483, + 0.122 + ], + "angle": 0, + "content": "tive differentiable approximations. It then explains how compositions of tasks were formed." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.13, + 0.334, + 0.146 + ], + "angle": 0, + "content": "5.1. Individual degradations" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.153, + 0.484, + 0.304 + ], + "angle": 0, + "content": "Experiments are performed on four common sources of image degradation: upsampling, inpainting, denoising, and deartifacting. Synthetic models are used to facilitate comparison at different degradation levels. Each degradation is tested at five levels, which are referred to as extra-small (XS), small (S), medium (M), large (L), and extra-large (XL). Parameters for each degradation level will be provided below for each task in that same order. Fig. 4 shows examples of all four degradations at the XS and XL levels, see supp." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.304, + 0.484, + 0.41 + ], + "angle": 0, + "content": "Upsampling targets \\(\\pmb{y}\\) are produced by downsampling ground truth images \\(\\pmb{y}_{\\mathrm{clean}}\\) by integer factors \\(k_{\\mathrm{down}} \\in \\{2,4,8,16,32\\}\\). Downsampling filters are uniformly sampled from the commonly used bilinear, bicubic, and Lanczos filters, which provides a coarse but broad range of aliasing profiles. During inversion, average pooling is used as the approximation \\(\\hat{f}\\) in all cases." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.411, + 0.484, + 0.576 + ], + "angle": 0, + "content": "Inpainting aims to predict missing regions in an image. To test a variety of masking conditions, random masks are generated by drawing \\( k_{\\mathrm{strokes}} \\in \\{1,5,9,13,17\\} \\) random strokes of width \\( 0.08r \\) where \\( r \\) is the image resolution, each stroke connecting two random points situated in the outer thirds of the image. In this task, \\( \\hat{f} = f \\) i.e. we assume that the mask is known. To avoid the bias introduced by black pixels when evaluating the LPIPS loss, identical noise of distribution \\( \\mathcal{N}(0.5,1) \\) is added to the masked region of both the prediction and the target before computing LPIPS." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.577, + 0.484, + 0.788 + ], + "angle": 0, + "content": "Denoising targets are generated by using a mixture of Poisson and Bernoulli noise, simulating common sources of noise in cameras, namely shot noise and dead (or hot) pixels respectively. This is a challenging scenario because unlike Gaussian noise, Poisson noise is non-additive and signal-dependent, while Bernoulli noise is biased. Additionally, both are non-differentiable. We used the parameters \\( k_{\\mathrm{p}} \\in \\{96, 48, 24, 12, 6\\} \\) and \\( k_{\\mathrm{b}} \\in \\{0.04, 0.08, 0.16, 0.32, 0.64\\} \\) where \\( k_{\\mathrm{p}} \\) gives the most likely value added to a pixel (independently for each channel) according to a Poisson distribution, and \\( k_{\\mathrm{b}} \\) the probability that all channels of a pixel are replaced with black. We also account for clamping during image serialization, resulting in the overall noise model:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.795, + 0.483, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\frac {\\operatorname {c l a m p} \\left(p ^ {\\prime} \\cdot m\\right)}{2 5 5}, \\text {w h e r e} p ^ {\\prime} \\sim \\mathcal {P} \\left(k _ {\\mathrm {p}} p\\right), m \\sim \\mathcal {B} \\left(k _ {\\mathrm {b}}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.837, + 0.484, + 0.913 + ], + "angle": 0, + "content": "for a ground truth image pixel value \\( p \\in [0.0, 1.0] \\) and where \\( \\mathrm{clamp}(\\cdot) \\) saturates all values outside of [0, 255]. Note that \\( p' \\) can only take discrete values. For the differentiable approximation \\( \\hat{f} \\), we replace the (non-differentiable, discrete) Poisson noise with a Gaussian ap" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.091, + 0.885, + 0.137 + ], + "angle": 0, + "content": "proximation \\(\\mathcal{N}(k_{\\mathrm{p}}p - 0.5,\\sqrt{k_{\\mathrm{p}}p})\\) and treat the Bernoulli noise as an unknown mask. We also use a surrogate gradient for clamp:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.147, + 0.883, + 0.18 + ], + "angle": 0, + "content": "\\[\n\\frac {d}{d p} \\operatorname {c l a m p} (p) \\approx \\frac {d}{d p} \\operatorname {s i g m o i d} (2 \\cdot (p - 0. 5)). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.187, + 0.885, + 0.248 + ], + "angle": 0, + "content": "Deartifacting is performed on JPEG images compressed with libjpeg [2, 12] at quality levels \\( k_{\\mathrm{jpeg}} \\in \\{18, 15, 12, 9, 6\\} \\). The lossy part of JPEG compression can be expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.26, + 0.883, + 0.29 + ], + "angle": 0, + "content": "\\[\n\\text {q u a n t i z e} \\circ \\mathrm {D C T} \\circ \\text {t o} _ {\\text {b l o c k s}} \\circ \\text {c h r o m a} _ {\\text {s u b s a m p l e}}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.291, + 0.885, + 0.34 + ], + "angle": 0, + "content": "Here, 4:2:2 chroma subsampling is used. This final quantization step rounds each DCT component \\( c_{i,j}^{(k)} \\) positioned in the \\( k^{\\text{th}} \\) block at indices \\( i,j \\) with" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.35, + 0.883, + 0.372 + ], + "angle": 0, + "content": "\\[\n\\operatorname {q u a n t i z e} \\left(c _ {i, j} ^ {(k)}\\right) = \\left\\lfloor c _ {i, j} ^ {(k)} / Q _ {i, j} \\right], \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.38, + 0.884, + 0.487 + ], + "angle": 0, + "content": "where \\( Q_{i,j} \\in [1,255] \\subset \\mathbb{N} \\) is the corresponding value from the quantization table. Rounding is the only non-differentiable part of this chain (the lossless part of JPEG compression does not need to be differentiated). We read the quantization tables from file headers and use Lomnitz's implementation [1] of [52], which proposes differentiable rounding:" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.497, + 0.883, + 0.515 + ], + "angle": 0, + "content": "\\[\n\\lfloor p \\rceil \\approx \\lfloor p \\rceil + (p - \\lfloor p \\rceil) ^ {3}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.526, + 0.884, + 0.571 + ], + "angle": 0, + "content": "We use this approximation to define a surrogate gradient (keeping the forward pass exact), and interpolate with a straight-through gradient estimator at \\(\\alpha = 0.8\\):" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.581, + 0.882, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\frac {d}{d p} \\lfloor p \\rceil \\approx \\frac {d}{d p} \\left[ (1 - \\alpha) p + \\alpha (p - \\lfloor p \\rceil) ^ {3} \\right]. \\tag {15}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.623, + 0.736, + 0.639 + ], + "angle": 0, + "content": "5.2. Composed degradations" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.646, + 0.884, + 0.69 + ], + "angle": 0, + "content": "Eq. (3) assumes knowledge of the order in which degradations are applied. In this work, the following restoration order is used:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.703, + 0.882, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\text {i n p a i n t} \\circ \\text {d e a r i f a c t} \\circ \\text {d e n o i s e} \\circ \\text {u p s a m p l e}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.73, + 0.884, + 0.791 + ], + "angle": 0, + "content": "Task compositions are created with (subsequences of) this ordering. For example, upsampling and deartifacting form a composition of length 2. All compositions were formed with tasks at degradation level medium (M)." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.804, + 0.882, + 0.821 + ], + "angle": 0, + "content": "6. Comparison to StyleGAN-based methods" + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.829, + 0.776, + 0.844 + ], + "angle": 0, + "content": "6.1. Models, datasets, and metrics" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.851, + 0.885, + 0.911 + ], + "angle": 0, + "content": "The PyTorch implementation [41] of StyleGAN2-ADA [28] is used in all experiments. In particular, we use the model pretrained on the FFHQ dataset [30] at \\(1024 \\times 1024\\) resolution. Since the model is trained on" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.938, + 0.519, + 0.949 + ], + "angle": 0, + "content": "22296" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.089, + 0.321, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.089, + 0.508, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.089, + 0.696, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.09, + 0.883, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.402, + 0.884, + 0.445 + ], + "angle": 0, + "content": "Figure 4. Randomly selected qualitative restoration results on each independent task, for both extra-small and extra-large levels of degradation. Top to bottom: (degraded) target, ours, L-BRGM [13], and PULSE [40]. Left to right: upsampling, inpainting, denoising, and deartifacting. Our method shows better robustness to variations in levels of degradation. See supp. for more results." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.47, + 0.483, + 0.531 + ], + "angle": 0, + "content": "the entire FFHQ dataset, we gathered an additional 100 test images, dubbed “FFHQ extras” (FFHQ-X), using the same alignment script. Overlap with FFHQ was avoided by filtering by date (see supp.)." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.532, + 0.483, + 0.713 + ], + "angle": 0, + "content": "Performance was measured via accuracy, realism, and fidelity metrics. Accuracy was measured with the LPIPS [63] between the predictions and the ground truth images. Realism was measured using the PatchFID [8] (pFID): FID [24] measured on image patches. More specifically, we extracted 1000 random crops of size \\(128 \\times 128\\) per image, computing the FID of all crops from predictions to all crops from our FFHQ-X dataset. Finally, fidelity between degraded predictions and targets was measured using the LPIPS; this was done by degrading predictions with the true degradation to ignore the effect of differentiable approximations." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.723, + 0.221, + 0.737 + ], + "angle": 0, + "content": "6.2. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.746, + 0.483, + 0.806 + ], + "angle": 0, + "content": "Our method is compared on FFHQ-X against two unsupervised StyleGAN image restoration techniques, PULSE [40] and the current state of the art L-BRGM [13]. The same pretrained network is used for all approaches." + }, + { + "type": "text", + "bbox": [ + 0.111, + 0.806, + 0.483, + 0.881 + ], + "angle": 0, + "content": "PULSE [40] We adapted PULSE to use StyleGAN2-ADA and to tasks other than upsampling by increasing the number of steps from 100 to 250 and adjusting the learning rate to 0.8 (manual inspection on validation data) to increase its robustness to novel tasks." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.882, + 0.483, + 0.913 + ], + "angle": 0, + "content": "L-BRGM [13] We adjust its learning rate \\(\\lambda_{\\mathrm{lr}} = 0.05\\) by manual inspection. L-BRGM uses best-of- \\(k\\) random" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.47, + 0.885, + 0.561 + ], + "angle": 0, + "content": "initialization; because initialization is difficult under high degradations, we doubled the number of samples from 100 to 200 and added a 0.8 truncation [30] to avoid outliers. L-BRGM also performs early stopping by inspecting the ground truth; for a fair comparison, we instead fixed the number of steps to 500 as in BRGM [39]." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.562, + 0.885, + 0.667 + ], + "angle": 0, + "content": "Hyperparameter optimization for baselines We optimize the accuracy metric for the baselines hyperparameters for each (task, level) pair individually directly on the \\( FFHQ-X \\) test set (see supp. for more details). In addition, baselines employ the ground truth Bernoulli mask (see sec. 5.1) in their differentiable approximation of eq. (10). Doing so was necessary for good performance." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.668, + 0.884, + 0.788 + ], + "angle": 0, + "content": "Our method We adjust hyperameters (learning rate and number of iterations, see alg. 1) once on validation data, then run our benchmark on the test set with no pertask or per-level hyperparameter adjustment: our method uses the same hyperparameters across all tasks and levels. Our method is not provided the Bernoulli mask. The total number of steps (450) is less than the 500 used for L-BRGM." + }, + { + "type": "title", + "bbox": [ + 0.513, + 0.799, + 0.71, + 0.814 + ], + "angle": 0, + "content": "6.3. Experimental results" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.822, + 0.884, + 0.913 + ], + "angle": 0, + "content": "Robustness to degradation levels Our benchmark is run on our FFQH-X test set (sec. 6.1) on all five levels of degradation for each individual task, and quantitative results are presented in tab. 1. Recall from sec. 6.2 that our method, which employs a single set of hyperparameters across all experiments, is pitted against baselines" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.938, + 0.518, + 0.949 + ], + "angle": 0, + "content": "22297" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.123, + 0.09, + 0.477, + 0.436 + ], + "angle": 0, + "content": "
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OursPULS L-BRG OursPULS L-BRG Ours
Upsampling (bilinear, bicubic or Lanczos)
XS.493.407.414.432.295.31344.523.617.0
S.492.412.449.353.140.23934.325.522.0
M.495.458.472.261.124.17229.335.422.3
L.501.487.490.185.129.12721.926.020.9
XL.512.506.514.083.095.09024.921.321.3
Denoising (clamped Poisson and Bernoulli mixture)
XS.501.440.425.275.152.15656.127.218.5
S.499.450.434.252.138.14053.728.619.1
M.500.465.446.224.155.13054.522.119.8
L.501.481.457.185.138.11056.424.619.2
XL.504.511.474.134.110.08449.425.117.9
Deartifacting (JPEG compression)
XS.498.442.432.404.341.34952.326.314.8
S.497.448.437.398.352.35049.622.415.4
M.498.461.445.413.357.35733.224.115.4
L.500.475.460.395.367.37446.925.216.0
XL.508.503.490.427.418.41230.822.118.7
Inpainting (random strokes)
XS.498.409.378.464.374.34846.924.412.9
S.501.425.387.356.287.26442.327.214.2
M.509.438.396.283.227.20638.530.114.5
L.513.452.409.231.184.16332.633.115.3
XL.524.460.422.187.157.13236.225.215.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.112, + 0.446, + 0.484, + 0.531 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on individual tasks against baselines (\"PULS\" [40] and \"L-BRG\" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Results color-coded as best and second best." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.557, + 0.484, + 0.662 + ], + "angle": 0, + "content": "with hyperparameters optimized for each task and level individually. Despite this obvious impediment, our proposed method outperforms baselines in the vast majority of scenarios. In particular, it reaches better accuracy in the majority of tasks against baselines optimized for accuracy, and realism is strictly better. Fig. 4 illustrates the improved visual quality obtained with our method." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.663, + 0.484, + 0.784 + ], + "angle": 0, + "content": "Robustness to compositions Robustness to compositions of degradations was evaluated by forming all possible subsequences of degradations (order in eq. (16)) at medium level. Quantitative results are aggregated in tab. 2, while fig. 5 presents qualitative examples. Our results show that both high fidelity and high realism are maintained with our method, while the baselines struggle under varied degradations." + }, + { + "type": "title", + "bbox": [ + 0.114, + 0.796, + 0.406, + 0.813 + ], + "angle": 0, + "content": "7. Comparison to diffusion models" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.822, + 0.484, + 0.912 + ], + "angle": 0, + "content": "We compare our approach to the recent \"Denoising diffusion restoration model\" (DDRM) [32], which also does not require problem-specific supervised training and leverages a pre-trained (DDPM [53]) model. Importantly, DCRM is designed only for linear inverse problems with additive Gaussian noise, where the degradation model is" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.09, + 0.886, + 0.31 + ], + "angle": 0, + "content": "
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OUR5PULS L-BRG OUR5PULS L-BRG OUR5
2 degradations
NA.517.485.459.328.301.29043.424.217.3
AP.511.478.457.270.231.20429.717.617.0
UA.510.518.508.307.348.28723.720.519.7
NP.511.480.458.125.079.06247.020.919.2
UN.501.519.511.178.149.15333.426.221.1
UP.510.478.485.140.061.08923.935.320.7
3 degradations
UNP.510.526.507.086.062.05128.522.120.1
UAP.525.523.513.205.154.11923.018.420.5
UNA.521.535.533.265.310.29026.220.722.8
NAP.526.502.470.210.197.16038.718.418.5
4 degradations
UNAP.533.546.525.192.177.13125.521.121.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.512, + 0.32, + 0.886, + 0.432 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on composed tasks (at medium levels) against baselines (\"PULS\" [40] and \"L-BRG\" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Acronyms indicate restorations: Upsampling, deNoising, deArtifacting, and/or inPainting. Results color-coded as best and second best." + }, + { + "type": "table", + "bbox": [ + 0.558, + 0.45, + 0.843, + 0.647 + ], + "angle": 0, + "content": "
Accur. (LPIPS) ↓Realism (pFID) ↓
DDRMOURSDDRMOURS
Exact Upsampling (known average pooling)
0.4120.44344.7518.92
Inexact Upsampling (unknown nearest-neighbor)
0.5590.53967.0632.81
Linear Denoising (additive Gaussian noise)
0.3360.45243.2819.25
Nonlinear Denoising (clamped additive Gaussian noise)
0.5300.450156.119.06
Inpainting (masking random strokes)
0.2890.30126.1225.71
Uncropping (top left corner unmasked)
0.4680.41834.3317.645
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.657, + 0.884, + 0.687 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison to DDRM [32] on accuracy and realism (see sec. 7). Results are color-coded as best ." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.716, + 0.885, + 0.913 + ], + "angle": 0, + "content": "perfectly known. Therefore, for each of the upsampling, denoising and inpainting tasks, we experiment with both: 1) a linear inverse problem with known parameters; and 2) an adjusted version which is either non-linear, where the extract degradation model is unknown, or a more extreme version of the problem. Specifically, we test: average pooling (known, linear) vs nearest-neighbor (unknown) \\(32 \\times\\) (XL) upsampling; additive Gaussian noise (linear) vs clamped (to [0, 255]) additive Gaussian noise (non-linear) with \\(\\sigma^2 = 0.8\\) (XL) for both; and masking strokes (at XL level) vs uncropping the top-left corner (XXL). DDRM is available on CelebA (not FFHQ) at \\(256 \\times 256\\), so we use the corresponding StyleGAN2-ADA pretrained" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.938, + 0.519, + 0.949 + ], + "angle": 0, + "content": "22298" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.089, + 0.538, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.538, + 0.089, + 0.884, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.323, + 0.884, + 0.352 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons on all possible compositions of the four tasks given medium levels of degradation. Samples are chosen randomly, and acronyms indicate the degradations: Upsampling, inPainting, deNoising and/or deArtifacting (sec. 6.3)." + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.376, + 0.483, + 0.659 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.112, + 0.67, + 0.483, + 0.741 + ], + "angle": 0, + "content": "Figure 6. Results on LSUN horses and churches [60], AFHQ-v2 Dogs [11] and BreCaHAD [5] at resolution \\(256 \\times 256\\) for small upsampling (U), small denoising (N), medium deartifacting (A), and medium inpainting (P); the left/right halves are the target/restored images. See supp. for details and more results." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.773, + 0.483, + 0.803 + ], + "angle": 0, + "content": "model. Due to the reduced resolution, pFID is measured on 250 patches of size \\(64 \\times 64\\)." + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.807, + 0.484, + 0.913 + ], + "angle": 0, + "content": "Interestingly, we find that DDRM reproduces the targets almost perfectly (fidelity is near zero, see supp. for details and qualitative results), to the point where it overfits to any deviation between its degradation model and the true degradation. Tab. 3 presents the accuracy and realism metrics for all the aforementioned tasks. While the accuracy favors DDRM for the tasks which perfectly" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.379, + 0.885, + 0.469 + ], + "angle": 0, + "content": "match its assumptions, our approach outperforms it when this is not the case. In addition, our method provides significantly better realism across all scenarios. Overall, our approach yields high resolution results with more detail, can adapt to non-linear tasks, and it can also cope with larger degradations." + }, + { + "type": "title", + "bbox": [ + 0.514, + 0.496, + 0.627, + 0.511 + ], + "angle": 0, + "content": "8. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.526, + 0.885, + 0.692 + ], + "angle": 0, + "content": "**Limitations** Our method is not restricted to faces and works with any pretrained StyleGAN, as demonstrated in fig. 6. However, it is inherently limited to the domain learned by the GAN. Training StyleGAN on a large unstructured dataset like ImageNet is difficult but recent papers [27,50,55] have attained some success—applying our method on some of these large-scale models is a promising research avenue. Our method also faces the same ethical considerations as the GAN it relies on. Finally, as with other methods [13,32,40], we also require knowledge of an (approximate) degradation function." + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.697, + 0.885, + 0.848 + ], + "angle": 0, + "content": "Conclusion This paper presents a method which makes StyleGAN-based image restoration robust to both variability in degradation levels and to compositions of different degradations. Our proposed method relies on a conservative optimization procedure over a progressively richer latent space and avoids regularization terms altogether. Using a single set of hyperparameters, we obtain competitive and even state-of-the-art results on several challenging scenarios when compared to baselines that are optimized for each task/level individually." + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.852, + 0.885, + 0.911 + ], + "angle": 0, + "content": "Acknowledgements This research was supported by NSERC grant RGPIN-2020-04799, a MITACS Globalink internship to Y. 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Our unsupervised StyleGAN image restoration method is robust and effective across a variety of tasks (left, top to bottom: upsampling, denoising, deartifacting, and inpainting) and a wide range of degradation levels. Since it avoids the need for task-specific hyperparameter tuning, it can directly handle combinations of such degradations, e.g., pairs (center) or even all four (right). + +![](images/8df8152cd13b675b505e8ce0a75faf491efddd25832127ae23f3b6fc55c58681.jpg) + +![](images/828ad6f3fb4690e6efcdd78d359a743abc3bb1d0e379118fd8a574d7681cf80c.jpg) + +# Abstract + +GAN-based image restoration inverts the generative process to repair images corrupted by known degradations. Existing unsupervised methods must be carefully tuned for each task and degradation level. In this work, we make StyleGAN image restoration robust: a single set of hyperparameters works across a wide range of degradation levels. This makes it possible to handle combinations of several degradations, without the need to retune. Our proposed approach relies on a 3-phase progressive latent space extension and a conservative optimizer, which avoids the need for any additional regularization terms. Extensive experiments demonstrate robustness on inpainting, upsampling, denoising, and deartifacting at varying degradations levels, outperforming other StyleGAN-based inversion techniques. Our approach also favorably compares to diffusion-based restoration by yielding much more realistic inversion results. Code is available at the above URL. + +# 1. Introduction + +Image restoration, the task of recovering a high quality image from a degraded input, is a long-standing problem in image processing and computer vision. Since different restoration tasks—such as denoising, upsampling, + +deartifacting, etc.—can be quite distinct, many recent approaches [9, 10, 37, 54, 61, 62] propose to solve them in a supervised learning paradigm by leveraging curated datasets specifically designed for the task at hand. Unfortunately, designing task-specific approaches requires retraining large networks on each task separately. + +In parallel, the advent of powerful generative models has enabled the emergence of unsupervised restoration methods [42], which do not require task-specific training. The idea is to invert the generative process to recover a clean image. Assuming a known (or approximate) degradation model, the optimization procedure therefore attempts to recover an image that both: 1) closely matches the target degraded image after undergoing a similar degradation model (fidelity); and 2) lies in the space of realistic images learned by the GAN (realism). + +In the recent literature, StyleGAN [29-31] has been found to be particularly effective for unsupervised image restoration [13-15, 39, 40] because of the elegant design of its latent space. Indeed, these approaches leverage style inversion techniques [3, 4] to solve for a latent vector that, when given to the generator, creates an image close to the degraded target. Unfortunately, this only works when such a match actually exists in the model distribution, which is rarely the case in practice. Hence, effective methods extend the learned latent space to cre + +ate additional degrees of freedom to admit more images; this creates the need for additional regularization losses. Hyperparameters must therefore carefully be tuned for each specific task and degradation level. + +In this work, we make unsupervised StyleGAN image restoration-by-inversion robust to the type and intensity of degradations. Our proposed method employs the same hyperparameters across all tasks and levels and does not rely on any regularization loss. Our approach leans on two key ideas. First, we rely on a 3-phase progressive latent space extension: we begin by optimizing over the learned (global) latent space, then expand it across individual layers of the generator, and finally expand it further across individual filters—where optimization at each phase is initialized with the result of the previous one. Second, we rely on a conservative, normalized gradient descent (NGD) [58] optimizer which is naturally constrained to stay close to its initial point compared to more sophisticated approaches such as Adam [33]. This combination of prudent optimization over a progressively richer latent space avoids additional regularization terms altogether and keeps the overall procedure simple and constant across all tasks. We evaluate our method on upsampling, inpainting, denoising and deartifacting on a wide range of degradation levels, achieving state-of-the-art results on most scenarios even when baselines are optimized on each independently. We also show that our approach outperforms existing techniques on compositions of these tasks without changing hyperparameters. + +- We propose a robust 3-phase StyleGAN image restoration framework. Our optimization technique maintains: 1) strong realism when degradations level are high; and 2) high fidelity when they are low. Our method is fully unsupervised, requires no per-task training, and can handle different tasks at different levels without having to adjust hyperparameters. +- We demonstrate the effectiveness of the proposed method under diverse and composed degradations. We develop a benchmark of synthetic image restoration tasks—making their degradation levels easy to control—with care taken to avoid unrealistic assumptions. Our method outperforms existing unsupervised [13,40] and diffusion-based [32] approaches. + +# 2. Related work + +This section covers previous work on StyleGAN inversion by optimization and its use for image restoration, and discusses related works on generative priors. Because the literature on general purpose image restoration is so extensive, we do not attempt to review it here and instead refer the reader to recent surveys [18, 19, 35, 57]. + +GANs and StyleGAN inversion Generative adversarial networks [20] (GANs) are a popular technique + +for generative modeling. In particular, the StyleGAN family [28-31] learns a highly compressed latent representation of its domain and stands out for its popularity and generation quality. Great progress has been made in StyleGAN inversion: reversing the generation process to infer latent parameters that generate a given image [59]. + +Thanks to inversion, StyleGAN has found use in many image editing [23, 43, 51] and restoration [13-15, 39, 40] tasks. Purely optimization-based techniques were studied extensively [3, 4, 26, 44, 46, 66] in the context of image editing. These methods extend the learned latent space of a pretrained StyleGAN model (commonly named $\mathcal{W}$ ) by adding additional parameters to optimize over it. The most common approach consists of using a different latent code for each layer [3] (dubbed $\mathcal{W}^+$ ). Going beyond $\mathcal{W}^+$ has also been explored in [46] who propose to fine-tune generator parameters, and [44] which uses different latent codes for each convolution filter. We build on these techniques by developing an inversion method designed specifically for robust image restoration. + +Generative priors for unsupervised image restoration Since the initial work of Bora et al. [6], multiple papers have used generative priors for unsupervised image restoration [21, 25]. Pan et al. [42] obtained high-resolution results with BigGAN [7]. They relax their latent inversion method by introducing a coarse-to-fine, layer-by-layer generator fine-tuning. Our method differs in that it addresses robustness and compositionality. + +StyleGAN image restoration Inversion methods designed for editing cannot be applied directly for restoration because loss functions are applied to degraded targets rather than clean images. Previous works address this with additional regularization terms and/or optimizer constraints. Of note, PULSE [40] proposed StyleGAN inversion for image upsampling, using a regularizer minimizing the latent extension to $\mathcal{W}^+$ and a spherical optimization technique on a Gaussian approximation of $\mathcal{W}$ . While PULSE succeeds in preserving high realism, it obtains low fidelity when the downsampling factor is small. ILO [15] uses similar regularization techniques, and further extends the latent space by optimizing intermediate feature maps in a progressive fashion (layer-by-layer) while constraining the solutions to sparse deviations from the range. More recently, SGILO [14] proposes to replace this sparsity constraint and instead trains a score-based model to learn the distribution of the outputs of an intermediate layer in the StyleGAN generator. BRGM [39] frames GAN inversion as Bayesian inference and estimates the maximum a-posteriori over the input latent vector that generated the reconstructed image given different regularization constraints. Its followup, L-BRGM [13], jointly optimizes the $\mathcal{Z}$ (before the mapping network) and $\mathcal{W}$ spaces, further improving quality. In contrast, our work achieves robustness by + +![](images/01269686a92a2f9db1a5fa56938d162ae30829b740759797a4d99eed45c43b57.jpg) +Figure 2. Unsupervised image restoration with StyleGAN attempts to restore a degraded target image $\pmb{y} = f(\pmb{y}_{\mathrm{clean}})$ by finding a generated image $\pmb{x}_{\mathrm{clean}}$ that matches this target once also degraded $\pmb{x} = \hat{f}(\pmb{x}_{\mathrm{clean}})$ (sec. 3); here, $\hat{f}$ is a differentiable approximation to the degradation function $f$ and $\pmb{y}_{\mathrm{clean}}$ is the (unknown) ground truth image. + +avoiding any such regularization losses. + +Other similar works StyleGAN inversion was used to restore old photographs in [38]. Their method also restores a mixture of degradations, but is designed for real degradations (not robustness) and uses a task-specific encoder, while ours method is fully unsupervised. Multiple supervised methods [22, 34, 36, 56, 64, 65] focus on faces only, whereas our method does not use face-specific loss functions [16], is fully unsupervised, and works across a variety of image domains. + +Diffusion models Denoising diffusion probabilistic models (DDPMs) [53], trained on extremely large datasets (e.g., billions of images for [45, 47, 49]), have recently been shown to outclass GANs when it comes to image generation quality [17]. New approaches have been proposed to tackle image restoration using DDPMs, e.g., Palette [48] obtains excellent results by training the same model for several different tasks. Denoising diffusion restoration models (DDRM) [32] show that pretrained DDPMs can be used for unsupervised restoration tasks, but are limited to linear inverse problems with additive Gaussian noise. In contrast, our method is more flexible since it only requires a differentiable approximation of the degradation function, which can be non-linear. + +# 3. Image restoration with StyleGAN + +As illustrated in fig. 2, StyleGAN inversion attempts to recover an image $\pmb{x}_{\mathrm{clean}}$ that best matches an (unknown) ground truth image $\pmb{y}_{\mathrm{clean}}$ . To this end, we aim to search for a latent code $\pmb{w} \in \mathcal{W}$ such that $\pmb{x}_{\mathrm{clean}} = G(\pmb{w})$ best matches $\pmb{y}_{\mathrm{clean}}$ under some image distance function $\ell$ . The resulting minimization problem, + +$$ +\boldsymbol {w} = \underset {\tilde {\boldsymbol {w}} \in \mathcal {W}} {\arg \min } \ell \left(G (\tilde {\boldsymbol {w}}), \boldsymbol {y} _ {\text {c l e a n}}\right), \tag {1} +$$ + +![](images/e861fc957b4dc5c6debbbb7fa15903e15ebd59480c06371acceaff9b65850d54.jpg) +Figure 3. Our 3-phase latent extension (sec. 4.1) approach. (a) Phase I uses a global latent code $\pmb{w}$ , resulting in a prediction $\pmb{x}$ . (b) Phase II performs layer-wise latent expansion, resulting in matrix $\pmb{w}^{+}$ and in a prediction $\pmb{x}^{+}$ . (c) Phase III performs filter-wise latent expansion, resulting in tensor $\pmb{w}^{++}$ and the final prediction $\pmb{x}^{++}$ . + +can be solved by gradient descent. In image restoration, the ground truth image $\pmb{y}_{\mathrm{clean}}$ is unknown: we are instead given a target image $\pmb{y} = f(\pmb{y}_{\mathrm{clean}})$ , the result of a (non-injective, potentially non-differentiable) degradation function $f$ . Assuming that a differentiable approximation $\hat{f}\approx f$ can be constructed, restoration is performed by solving for + +$$ +\boldsymbol {w} = \underset {\tilde {\boldsymbol {w}} \in \mathcal {W}} {\arg \min } \ell \left(\hat {f} (G (\tilde {\boldsymbol {w}})), \boldsymbol {y}\right). \tag {2} +$$ + +This can be generalized to compositions of $k$ different. +degradations,i.e., $\{f_i\}_{i = 1}^k$ ,by solving for + +$$ +\boldsymbol {w} = \underset {\tilde {\boldsymbol {w}} \in \mathcal {W}} {\arg \min } \ell \left(\left[ \hat {f} _ {k} \circ \dots \circ \hat {f} _ {2} \circ \hat {f} _ {1} \right] (G (\tilde {\boldsymbol {w}})), \boldsymbol {y}\right), \tag {3} +$$ + +where $\circ$ is the composition operator. Here, it is assumed that each subfunction $f_{i}$ has a differentiable approximation $\hat{f}_i$ , and that the order of composition is known. + +As described in sec. 2, this naive approach finds solutions that have high realism (look like real faces), but low fidelity (do not match the degraded target). Fidelity is most commonly improved by 1) performing latent extension [3], that is, solving for $\boldsymbol{w}^{+} \in \mathcal{W}^{+}$ which has many more degrees of freedom; and 2) using a better performing optimizer like Adam [33]. These techniques both improve fidelity but also damage realism, motivating the use of regularization losses which must carefully be adjusted for different tasks [13, 39, 40]. In the next section, we show how the choice of latent extension and optimizer avoids the need for these regularizers. + +# 4. Robust StyleGAN inversion + +We propose an inversion method designed specifically for robust image restoration, which revisits each aspect + +of the unsupervised StyleGAN optimization pipeline, namely latent extension, optimization, and loss functions. + +# 4.1. Robust latent extension + +Inspired by the intuition that initialization is the best regularization [46], we propose a three-phase latent extension, where each phase is initialized by the outcome of the previous one, see fig. 3. Given a pretrained StyleGAN2 [31] model with $N_{L}$ layers in the generator, we denote style vectors $s_i^l \in \mathbb{R}^{512}$ at layer $l \in [1,N_L]$ used to modulate convolution weights $\pmb{\theta}^{l} \in \mathbb{R}^{512 \times 512}$ . Assuming $1 \times 1$ filters to simplify notation1, each feature map pixel $p^l \in \mathbb{R}^{512}$ is processed by + +$$ +p _ {i} ^ {l + 1} = \left(\boldsymbol {\theta} _ {i} ^ {l} \odot \boldsymbol {s} _ {i} ^ {l}\right) \boldsymbol {p} ^ {l}, \tag {4} +$$ + +producing output feature $p_i^{l + 1}\in \mathbb{R}$ where $i\in [0,512]$ . + +Phase I performs global style modulation (fig. 3-(a)), and solves for a single latent vector $\boldsymbol{w} \in \mathcal{W} = \mathbb{R}^{512}$ shared across all layers as in eq. (3). Prior to optimization, $\boldsymbol{w}$ is initialized to the mean of $\mathcal{W}$ over the training set, i.e., $\mathbb{E}_{\tilde{\boldsymbol{w}} \in \mathcal{W}}[\tilde{\boldsymbol{w}}]$ . Here, the style modulation vector $s_i^l$ in eq. (4) can be written as + +$$ +\boldsymbol {s} _ {i} ^ {l} = \mathcal {A} ^ {l} (\boldsymbol {w}), \tag {5} +$$ + +where $\mathcal{A}^l$ is the corresponding affine projection layer (which multiplies by a weight matrix and adds a bias). + +Phase II performs layer-wise latent extension [3] (fig. 3-(b)), and solves for a latent matrix $\boldsymbol{w}^{+} \in \mathcal{W}^{+} = \mathbb{R}^{N_{L} \times 512}$ . Each row of $\boldsymbol{w}^{+}$ is initialized to $\boldsymbol{w}$ . Style modulation for this phase becomes + +$$ +\boldsymbol {s} _ {i} ^ {l} = \mathcal {A} ^ {l} \left(\boldsymbol {w} _ {l} ^ {+}\right). \tag {6} +$$ + +Phase III performs filter-wise latent extension (fig. 3-c), and solves for a latent tensor $\boldsymbol{w}^{++} \in \mathcal{W}^{++} = \mathbb{R}^{N_F \times N_L \times 512}$ , where a different latent code is used for each convolution filter and where $N_F$ is the number of such filters. Each submatrix of $\boldsymbol{w}^{++}$ is initialized to $\boldsymbol{w}^+$ . Style modulation for this phase becomes + +$$ +\boldsymbol {s} _ {i} ^ {l} = \mathcal {A} ^ {l} \left(\boldsymbol {w} _ {i, l} ^ {+ +}\right). \tag {7} +$$ + +# 4.2. Robust optimization + +While most inversion approaches use the Adam [33] optimizer to solve eq. (3), we instead propose coupling our 3-phase latent extension with a weaker optimizer, normalized gradient decent (NGD) [58], a simple variant of SGD that normalizes the gradient before each step: + +$$ +\bar {\nabla} _ {\boldsymbol {w}} \ell (\boldsymbol {w}) = \frac {\nabla_ {\boldsymbol {w}} \ell (\boldsymbol {w})}{\| \nabla_ {\boldsymbol {w}} \ell (\boldsymbol {w}) \| _ {2}}, \tag {8} +$$ + +Algorithm 1: Robust StyleGAN inversion. +Output: restored image $x^{++}$ # Phase I +1 $\pmb {w} = \mathbb{E}_{\tilde{\pmb{w}}\in \mathcal{W}}[\tilde{\pmb{w}} ]$ +2 for 1 to 150 do +3 $\begin{array}{r}\pmb {x}\gets G(\pmb {w})\\ \pmb {w}\gets 0.08\bar{\nabla}_{\pmb{w}}\ell (\hat{f} (\pmb {x}),\pmb {y}) \end{array}$ +4 Phase II +5 $w^{+} =$ repeat $(\pmb {w},N_L)$ +6 for 1 to 150 do +7 $\begin{array}{r}\pmb{x}^{+}\gets G^{+}(\pmb{w}^{+}) \end{array}$ +8 $\begin{array}{r}\pmb {w}^{+}\gets 0.02\bar{\nabla}_{\pmb{w}}\ell (\hat{f} (\pmb{x}^{+}),\pmb {y}) \end{array}$ # Phase III +9 $w^{+ + } =$ repeat $(\pmb {w}^{+},N_{F})$ +10 for 1 to 150 do +11 $\begin{array}{r}\pmb{x}^{+ + }\gets G^{+ + }(\pmb{w}^{+ + })\\ \pmb{w}^{+ + }\gets 0.005\bar{\nabla}_{\pmb{w}^{+ + }}\ell (\hat{f} (\pmb{x}^{+ + }),\pmb {y}) \end{array}$ +12 +13 return $x^{+ + }$ + +Here, the gradient $\bar{\nabla}_{\boldsymbol{w}}\ell (\boldsymbol {w})$ is explicitly set to 0 when $||\nabla_{\boldsymbol{w}}\ell (\boldsymbol {w})||_2 = 0$ . Following latent extension, we normalize each latent code separately (i.e. each row of $\boldsymbol{w}^{+}$ and $\boldsymbol{w}^{+ + }$ ). NGD conserves loss scale invariance, a key property of Adam that avoids learning rate adjustments following loss function changes. + +# 4.3. Robust loss function + +The staple loss function in StyleGAN inversion is the LPIPS [63] perceptual loss combined with a L2 or L1 [4] pixel-wise loss. We found a multiresolution loss function to be much more robust, and use: + +$$ +\ell_ {\mathrm {M R}} (\boldsymbol {x}, \boldsymbol {y}) = \sum_ {i = 1} ^ {k} \ell_ {\mathrm {L P I P S}} \left(\phi \left(\boldsymbol {x}, 2 ^ {i}\right), \phi \left(\boldsymbol {y}, 2 ^ {i}\right)\right), \tag {9} +$$ + +where $\phi (\cdot ,2^i)$ downsamples by a factor of $2^{i}$ using average pooling, and we set $k = 6$ for image resolution of $1024^{2}$ . All resolutions are weighted equally, giving our final loss function $\ell = \lambda_{\mathrm{L1}}\ell_{\mathrm{L1}} + \ell_{\mathrm{MR}}$ with $\lambda_{\mathrm{L1}} = 0.1$ . + +# 4.4. Overall algorithm + +Alg. 1 provides a detailed pseudo-code of our method. $G^{+}$ and $G^{++}$ denote the synthesis network $G$ after modification to accept $w^{+} \in \mathcal{W}^{+}$ and $w^{++} \in \mathcal{W}^{++}$ , respectively. Hyperparameters like learning rates and number of steps are explicitly provided since they are held constant across all tasks. Their values were found by cross-validation on a subset of the FFHQ training set. + +# 5. Benchmarking restoration robustness + +This section first describes the proposed degradation models used in all experiments as well as their respec + +tive differentiable approximations. It then explains how compositions of tasks were formed. + +# 5.1. Individual degradations + +Experiments are performed on four common sources of image degradation: upsampling, inpainting, denoising, and deartifacting. Synthetic models are used to facilitate comparison at different degradation levels. Each degradation is tested at five levels, which are referred to as extra-small (XS), small (S), medium (M), large (L), and extra-large (XL). Parameters for each degradation level will be provided below for each task in that same order. Fig. 4 shows examples of all four degradations at the XS and XL levels, see supp. + +Upsampling targets $\pmb{y}$ are produced by downsampling ground truth images $\pmb{y}_{\mathrm{clean}}$ by integer factors $k_{\mathrm{down}} \in \{2,4,8,16,32\}$ . Downsampling filters are uniformly sampled from the commonly used bilinear, bicubic, and Lanczos filters, which provides a coarse but broad range of aliasing profiles. During inversion, average pooling is used as the approximation $\hat{f}$ in all cases. + +Inpainting aims to predict missing regions in an image. To test a variety of masking conditions, random masks are generated by drawing $k_{\mathrm{strokes}} \in \{1,5,9,13,17\}$ random strokes of width $0.08r$ where $r$ is the image resolution, each stroke connecting two random points situated in the outer thirds of the image. In this task, $\hat{f} = f$ i.e. we assume that the mask is known. To avoid the bias introduced by black pixels when evaluating the LPIPS loss, identical noise of distribution $\mathcal{N}(0.5,1)$ is added to the masked region of both the prediction and the target before computing LPIPS. + +Denoising targets are generated by using a mixture of Poisson and Bernoulli noise, simulating common sources of noise in cameras, namely shot noise and dead (or hot) pixels respectively. This is a challenging scenario because unlike Gaussian noise, Poisson noise is non-additive and signal-dependent, while Bernoulli noise is biased. Additionally, both are non-differentiable. We used the parameters $k_{\mathrm{p}} \in \{96, 48, 24, 12, 6\}$ and $k_{\mathrm{b}} \in \{0.04, 0.08, 0.16, 0.32, 0.64\}$ where $k_{\mathrm{p}}$ gives the most likely value added to a pixel (independently for each channel) according to a Poisson distribution, and $k_{\mathrm{b}}$ the probability that all channels of a pixel are replaced with black. We also account for clamping during image serialization, resulting in the overall noise model: + +$$ +\frac {\operatorname {c l a m p} \left(p ^ {\prime} \cdot m\right)}{2 5 5}, \text {w h e r e} p ^ {\prime} \sim \mathcal {P} \left(k _ {\mathrm {p}} p\right), m \sim \mathcal {B} \left(k _ {\mathrm {b}}\right), \tag {10} +$$ + +for a ground truth image pixel value $p \in [0.0, 1.0]$ and where $\mathrm{clamp}(\cdot)$ saturates all values outside of [0, 255]. Note that $p'$ can only take discrete values. For the differentiable approximation $\hat{f}$ , we replace the (non-differentiable, discrete) Poisson noise with a Gaussian ap + +proximation $\mathcal{N}(k_{\mathrm{p}}p - 0.5,\sqrt{k_{\mathrm{p}}p})$ and treat the Bernoulli noise as an unknown mask. We also use a surrogate gradient for clamp: + +$$ +\frac {d}{d p} \operatorname {c l a m p} (p) \approx \frac {d}{d p} \operatorname {s i g m o i d} (2 \cdot (p - 0. 5)). \tag {11} +$$ + +Deartifacting is performed on JPEG images compressed with libjpeg [2, 12] at quality levels $k_{\mathrm{jpeg}} \in \{18, 15, 12, 9, 6\}$ . The lossy part of JPEG compression can be expressed as + +$$ +\text {q u a n t i z e} \circ \mathrm {D C T} \circ \text {t o} _ {\text {b l o c k s}} \circ \text {c h r o m a} _ {\text {s u b s a m p l e}}. \tag {12} +$$ + +Here, 4:2:2 chroma subsampling is used. This final quantization step rounds each DCT component $c_{i,j}^{(k)}$ positioned in the $k^{\text{th}}$ block at indices $i,j$ with + +$$ +\operatorname {q u a n t i z e} \left(c _ {i, j} ^ {(k)}\right) = \left\lfloor c _ {i, j} ^ {(k)} / Q _ {i, j} \right], \tag {13} +$$ + +where $Q_{i,j} \in [1,255] \subset \mathbb{N}$ is the corresponding value from the quantization table. Rounding is the only non-differentiable part of this chain (the lossless part of JPEG compression does not need to be differentiated). We read the quantization tables from file headers and use Lomnitz's implementation [1] of [52], which proposes differentiable rounding: + +$$ +\lfloor p \rceil \approx \lfloor p \rceil + (p - \lfloor p \rceil) ^ {3}. \tag {14} +$$ + +We use this approximation to define a surrogate gradient (keeping the forward pass exact), and interpolate with a straight-through gradient estimator at $\alpha = 0.8$ : + +$$ +\frac {d}{d p} \lfloor p \rceil \approx \frac {d}{d p} \left[ (1 - \alpha) p + \alpha (p - \lfloor p \rceil) ^ {3} \right]. \tag {15} +$$ + +# 5.2. Composed degradations + +Eq. (3) assumes knowledge of the order in which degradations are applied. In this work, the following restoration order is used: + +$$ +\text {i n p a i n t} \circ \text {d e a r i f a c t} \circ \text {d e n o i s e} \circ \text {u p s a m p l e}. \tag {16} +$$ + +Task compositions are created with (subsequences of) this ordering. For example, upsampling and deartifacting form a composition of length 2. All compositions were formed with tasks at degradation level medium (M). + +# 6. Comparison to StyleGAN-based methods + +# 6.1. Models, datasets, and metrics + +The PyTorch implementation [41] of StyleGAN2-ADA [28] is used in all experiments. In particular, we use the model pretrained on the FFHQ dataset [30] at $1024 \times 1024$ resolution. Since the model is trained on + +![](images/8fc68f163d70564b3fc207f5a33bdf4e40fef58e95f288944860b7ff476552e3.jpg) +Figure 4. Randomly selected qualitative restoration results on each independent task, for both extra-small and extra-large levels of degradation. Top to bottom: (degraded) target, ours, L-BRGM [13], and PULSE [40]. Left to right: upsampling, inpainting, denoising, and deartifacting. Our method shows better robustness to variations in levels of degradation. See supp. for more results. + +![](images/3a025d545e7280eb5becaf2be500242b31cd4fcfcd71cbf8e6b3cfe88ca87fbb.jpg) + +![](images/7eaa2780704093d6a469d855c3522662d736056400b15c0844f512de6e9ec19a.jpg) + +![](images/da7ae62f29d1cacfb9dd359a4aba43e4c8a300f78331604c4a13b2c13ccea84b.jpg) + +the entire FFHQ dataset, we gathered an additional 100 test images, dubbed “FFHQ extras” (FFHQ-X), using the same alignment script. Overlap with FFHQ was avoided by filtering by date (see supp.). + +Performance was measured via accuracy, realism, and fidelity metrics. Accuracy was measured with the LPIPS [63] between the predictions and the ground truth images. Realism was measured using the PatchFID [8] (pFID): FID [24] measured on image patches. More specifically, we extracted 1000 random crops of size $128 \times 128$ per image, computing the FID of all crops from predictions to all crops from our FFHQ-X dataset. Finally, fidelity between degraded predictions and targets was measured using the LPIPS; this was done by degrading predictions with the true degradation to ignore the effect of differentiable approximations. + +# 6.2. Baselines + +Our method is compared on FFHQ-X against two unsupervised StyleGAN image restoration techniques, PULSE [40] and the current state of the art L-BRGM [13]. The same pretrained network is used for all approaches. + +PULSE [40] We adapted PULSE to use StyleGAN2-ADA and to tasks other than upsampling by increasing the number of steps from 100 to 250 and adjusting the learning rate to 0.8 (manual inspection on validation data) to increase its robustness to novel tasks. + +L-BRGM [13] We adjust its learning rate $\lambda_{\mathrm{lr}} = 0.05$ by manual inspection. L-BRGM uses best-of- $k$ random + +initialization; because initialization is difficult under high degradations, we doubled the number of samples from 100 to 200 and added a 0.8 truncation [30] to avoid outliers. L-BRGM also performs early stopping by inspecting the ground truth; for a fair comparison, we instead fixed the number of steps to 500 as in BRGM [39]. + +Hyperparameter optimization for baselines We optimize the accuracy metric for the baselines hyperparameters for each (task, level) pair individually directly on the $FFHQ-X$ test set (see supp. for more details). In addition, baselines employ the ground truth Bernoulli mask (see sec. 5.1) in their differentiable approximation of eq. (10). Doing so was necessary for good performance. + +Our method We adjust hyperameters (learning rate and number of iterations, see alg. 1) once on validation data, then run our benchmark on the test set with no pertask or per-level hyperparameter adjustment: our method uses the same hyperparameters across all tasks and levels. Our method is not provided the Bernoulli mask. The total number of steps (450) is less than the 500 used for L-BRGM. + +# 6.3. Experimental results + +Robustness to degradation levels Our benchmark is run on our FFQH-X test set (sec. 6.1) on all five levels of degradation for each individual task, and quantitative results are presented in tab. 1. Recall from sec. 6.2 that our method, which employs a single set of hyperparameters across all experiments, is pitted against baselines + +
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OursPULS L-BRG OursPULS L-BRG Ours
Upsampling (bilinear, bicubic or Lanczos)
XS.493.407.414.432.295.31344.523.617.0
S.492.412.449.353.140.23934.325.522.0
M.495.458.472.261.124.17229.335.422.3
L.501.487.490.185.129.12721.926.020.9
XL.512.506.514.083.095.09024.921.321.3
Denoising (clamped Poisson and Bernoulli mixture)
XS.501.440.425.275.152.15656.127.218.5
S.499.450.434.252.138.14053.728.619.1
M.500.465.446.224.155.13054.522.119.8
L.501.481.457.185.138.11056.424.619.2
XL.504.511.474.134.110.08449.425.117.9
Deartifacting (JPEG compression)
XS.498.442.432.404.341.34952.326.314.8
S.497.448.437.398.352.35049.622.415.4
M.498.461.445.413.357.35733.224.115.4
L.500.475.460.395.367.37446.925.216.0
XL.508.503.490.427.418.41230.822.118.7
Inpainting (random strokes)
XS.498.409.378.464.374.34846.924.412.9
S.501.425.387.356.287.26442.327.214.2
M.509.438.396.283.227.20638.530.114.5
L.513.452.409.231.184.16332.633.115.3
XL.524.460.422.187.157.13236.225.215.9
+ +with hyperparameters optimized for each task and level individually. Despite this obvious impediment, our proposed method outperforms baselines in the vast majority of scenarios. In particular, it reaches better accuracy in the majority of tasks against baselines optimized for accuracy, and realism is strictly better. Fig. 4 illustrates the improved visual quality obtained with our method. + +Robustness to compositions Robustness to compositions of degradations was evaluated by forming all possible subsequences of degradations (order in eq. (16)) at medium level. Quantitative results are aggregated in tab. 2, while fig. 5 presents qualitative examples. Our results show that both high fidelity and high realism are maintained with our method, while the baselines struggle under varied degradations. + +# 7. Comparison to diffusion models + +We compare our approach to the recent "Denoising diffusion restoration model" (DDRM) [32], which also does not require problem-specific supervised training and leverages a pre-trained (DDPM [53]) model. Importantly, DCRM is designed only for linear inverse problems with additive Gaussian noise, where the degradation model is + +Table 1. Quantitative comparison on individual tasks against baselines ("PULS" [40] and "L-BRG" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Results color-coded as best and second best. + +
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OUR5PULS L-BRG OUR5PULS L-BRG OUR5
2 degradations
NA.517.485.459.328.301.29043.424.217.3
AP.511.478.457.270.231.20429.717.617.0
UA.510.518.508.307.348.28723.720.519.7
NP.511.480.458.125.079.06247.020.919.2
UN.501.519.511.178.149.15333.426.221.1
UP.510.478.485.140.061.08923.935.320.7
3 degradations
UNP.510.526.507.086.062.05128.522.120.1
UAP.525.523.513.205.154.11923.018.420.5
UNA.521.535.533.265.310.29026.220.722.8
NAP.526.502.470.210.197.16038.718.418.5
4 degradations
UNAP.533.546.525.192.177.13125.521.121.8
+ +Table 2. Quantitative comparison on composed tasks (at medium levels) against baselines ("PULS" [40] and "L-BRG" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Acronyms indicate restorations: Upsampling, deNoising, deArtifacting, and/or inPainting. Results color-coded as best and second best. + +
Accur. (LPIPS) ↓Realism (pFID) ↓
DDRMOURSDDRMOURS
Exact Upsampling (known average pooling)
0.4120.44344.7518.92
Inexact Upsampling (unknown nearest-neighbor)
0.5590.53967.0632.81
Linear Denoising (additive Gaussian noise)
0.3360.45243.2819.25
Nonlinear Denoising (clamped additive Gaussian noise)
0.5300.450156.119.06
Inpainting (masking random strokes)
0.2890.30126.1225.71
Uncropping (top left corner unmasked)
0.4680.41834.3317.645
+ +Table 3. Quantitative comparison to DDRM [32] on accuracy and realism (see sec. 7). Results are color-coded as best . + +perfectly known. Therefore, for each of the upsampling, denoising and inpainting tasks, we experiment with both: 1) a linear inverse problem with known parameters; and 2) an adjusted version which is either non-linear, where the extract degradation model is unknown, or a more extreme version of the problem. Specifically, we test: average pooling (known, linear) vs nearest-neighbor (unknown) $32 \times$ (XL) upsampling; additive Gaussian noise (linear) vs clamped (to [0, 255]) additive Gaussian noise (non-linear) with $\sigma^2 = 0.8$ (XL) for both; and masking strokes (at XL level) vs uncropping the top-left corner (XXL). DDRM is available on CelebA (not FFHQ) at $256 \times 256$ , so we use the corresponding StyleGAN2-ADA pretrained + +![](images/0dc25b0c6d19b5a73690935d182ba793285ca28427df5f89d63b4ab736204646.jpg) +Figure 5. Qualitative comparisons on all possible compositions of the four tasks given medium levels of degradation. Samples are chosen randomly, and acronyms indicate the degradations: Upsampling, inPainting, deNoising and/or deArtifacting (sec. 6.3). + +![](images/6e0f0b184a35cae0ad3bec11f10fc46215c8222bb5c2e5711e61f848e2ef27c7.jpg) + +![](images/9788772c3424bc9e816961daf2dbe2abb2a33c464b3ac9a2acead706f2fb127d.jpg) +Figure 6. Results on LSUN horses and churches [60], AFHQ-v2 Dogs [11] and BreCaHAD [5] at resolution $256 \times 256$ for small upsampling (U), small denoising (N), medium deartifacting (A), and medium inpainting (P); the left/right halves are the target/restored images. See supp. for details and more results. + +model. Due to the reduced resolution, pFID is measured on 250 patches of size $64 \times 64$ . + +Interestingly, we find that DDRM reproduces the targets almost perfectly (fidelity is near zero, see supp. for details and qualitative results), to the point where it overfits to any deviation between its degradation model and the true degradation. Tab. 3 presents the accuracy and realism metrics for all the aforementioned tasks. While the accuracy favors DDRM for the tasks which perfectly + +match its assumptions, our approach outperforms it when this is not the case. In addition, our method provides significantly better realism across all scenarios. Overall, our approach yields high resolution results with more detail, can adapt to non-linear tasks, and it can also cope with larger degradations. + +# 8. Discussion + +**Limitations** Our method is not restricted to faces and works with any pretrained StyleGAN, as demonstrated in fig. 6. However, it is inherently limited to the domain learned by the GAN. Training StyleGAN on a large unstructured dataset like ImageNet is difficult but recent papers [27,50,55] have attained some success—applying our method on some of these large-scale models is a promising research avenue. Our method also faces the same ethical considerations as the GAN it relies on. Finally, as with other methods [13,32,40], we also require knowledge of an (approximate) degradation function. + +Conclusion This paper presents a method which makes StyleGAN-based image restoration robust to both variability in degradation levels and to compositions of different degradations. Our proposed method relies on a conservative optimization procedure over a progressively richer latent space and avoids regularization terms altogether. Using a single set of hyperparameters, we obtain competitive and even state-of-the-art results on several challenging scenarios when compared to baselines that are optimized for each task/level individually. + +Acknowledgements This research was supported by NSERC grant RGPIN-2020-04799, a MITACS Globalink internship to Y. Poirier-Ginter, and by the Digital Research Alliance Canada. + +# References + +[1] Diffjpeg. https://github.com/mlomnitz/DiffJPEG. +[2] Libjpeg. https://libjpeg-turbo.org. +[3] Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2StyleGAN: How to embed images into the StyleGAN latent space? In Int. Conf. Comput. Vis., 2019. +[4] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan++: How to edit the embedded images? In IEEE Conf. Comput. Vis. Pattern Recog., 2020. +[5] Alper Aksac, Douglas J Demetrick, Tansel Ozyer, and Reda Alhajj. Brecahad: a dataset for breast cancer histopathological annotation and diagnosis. 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Our unsupervised StyleGAN image restoration method is robust and effective across a variety of tasks (left, top to bottom: upsampling, denoising, deartifacting, and inpainting) and a wide range of degradation levels. Since it avoids the need for task-specific hyperparameter tuning, it can directly handle combinations of such degradations, e.g., pairs (center) or even all four (right)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 227, + 195, + 381, + 353 + ], + "blocks": [ + { + "bbox": [ + 227, + 195, + 381, + 353 + ], + "lines": [ + { + "bbox": [ + 227, + 195, + 381, + 353 + ], + "spans": [ + { + "bbox": [ + 227, + 195, + 381, + 353 + ], + "type": "image", + "image_path": "8df8152cd13b675b505e8ce0a75faf491efddd25832127ae23f3b6fc55c58681.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 381, + 195, + 539, + 353 + ], + "blocks": [ + { + "bbox": [ + 381, + 195, + 539, + 353 + ], + "lines": [ + { + "bbox": [ + 381, + 195, + 539, + 353 + ], + "spans": [ + { + "bbox": [ + 381, + 195, + 539, + 353 + ], + "type": "image", + "image_path": "828ad6f3fb4690e6efcdd78d359a743abc3bb1d0e379118fd8a574d7681cf80c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 158, + 403, + 206, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 158, + 403, + 206, + 415 + ], + "spans": [ + { + "bbox": [ + 158, + 403, + 206, + 415 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 68, + 427, + 297, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 427, + 297, + 643 + ], + "spans": [ + { + "bbox": [ + 68, + 427, + 297, + 643 + ], + "type": "text", + "content": "GAN-based image restoration inverts the generative process to repair images corrupted by known degradations. Existing unsupervised methods must be carefully tuned for each task and degradation level. In this work, we make StyleGAN image restoration robust: a single set of hyperparameters works across a wide range of degradation levels. This makes it possible to handle combinations of several degradations, without the need to retune. Our proposed approach relies on a 3-phase progressive latent space extension and a conservative optimizer, which avoids the need for any additional regularization terms. Extensive experiments demonstrate robustness on inpainting, upsampling, denoising, and deartifacting at varying degradations levels, outperforming other StyleGAN-based inversion techniques. Our approach also favorably compares to diffusion-based restoration by yielding much more realistic inversion results. Code is available at the above URL." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 654, + 149, + 667 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 654, + 149, + 667 + ], + "spans": [ + { + "bbox": [ + 69, + 654, + 149, + 667 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 674, + 296, + 723 + ], + "type": "text", + "content": "Image restoration, the task of recovering a high quality image from a degraded input, is a long-standing problem in image processing and computer vision. Since different restoration tasks—such as denoising, upsampling," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 403, + 541, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 403, + 541, + 475 + ], + "spans": [ + { + "bbox": [ + 313, + 403, + 541, + 475 + ], + "type": "text", + "content": "deartifacting, etc.—can be quite distinct, many recent approaches [9, 10, 37, 54, 61, 62] propose to solve them in a supervised learning paradigm by leveraging curated datasets specifically designed for the task at hand. Unfortunately, designing task-specific approaches requires retraining large networks on each task separately." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 479, + 541, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 479, + 541, + 599 + ], + "spans": [ + { + "bbox": [ + 313, + 479, + 541, + 599 + ], + "type": "text", + "content": "In parallel, the advent of powerful generative models has enabled the emergence of unsupervised restoration methods [42], which do not require task-specific training. The idea is to invert the generative process to recover a clean image. Assuming a known (or approximate) degradation model, the optimization procedure therefore attempts to recover an image that both: 1) closely matches the target degraded image after undergoing a similar degradation model (fidelity); and 2) lies in the space of realistic images learned by the GAN (realism)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 603, + 542, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 603, + 542, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 603, + 542, + 723 + ], + "type": "text", + "content": "In the recent literature, StyleGAN [29-31] has been found to be particularly effective for unsupervised image restoration [13-15, 39, 40] because of the elegant design of its latent space. Indeed, these approaches leverage style inversion techniques [3, 4] to solve for a latent vector that, when given to the generator, creates an image close to the degraded target. Unfortunately, this only works when such a match actually exists in the model distribution, which is rarely the case in practice. Hence, effective methods extend the learned latent space to cre" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 741, + 318, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 741, + 318, + 750 + ], + "spans": [ + { + "bbox": [ + 293, + 741, + 318, + 750 + ], + "type": "text", + "content": "22292" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 72, + 294, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 72, + 294, + 120 + ], + "spans": [ + { + "bbox": [ + 68, + 72, + 294, + 120 + ], + "type": "text", + "content": "ate additional degrees of freedom to admit more images; this creates the need for additional regularization losses. Hyperparameters must therefore carefully be tuned for each specific task and degradation level." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 122, + 298, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 122, + 298, + 420 + ], + "spans": [ + { + "bbox": [ + 70, + 122, + 298, + 420 + ], + "type": "text", + "content": "In this work, we make unsupervised StyleGAN image restoration-by-inversion robust to the type and intensity of degradations. Our proposed method employs the same hyperparameters across all tasks and levels and does not rely on any regularization loss. Our approach leans on two key ideas. First, we rely on a 3-phase progressive latent space extension: we begin by optimizing over the learned (global) latent space, then expand it across individual layers of the generator, and finally expand it further across individual filters—where optimization at each phase is initialized with the result of the previous one. Second, we rely on a conservative, normalized gradient descent (NGD) [58] optimizer which is naturally constrained to stay close to its initial point compared to more sophisticated approaches such as Adam [33]. This combination of prudent optimization over a progressively richer latent space avoids additional regularization terms altogether and keeps the overall procedure simple and constant across all tasks. We evaluate our method on upsampling, inpainting, denoising and deartifacting on a wide range of degradation levels, achieving state-of-the-art results on most scenarios even when baselines are optimized on each independently. We also show that our approach outperforms existing techniques on compositions of these tasks without changing hyperparameters." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 69, + 422, + 296, + 589 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 69, + 422, + 296, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 422, + 296, + 505 + ], + "spans": [ + { + "bbox": [ + 69, + 422, + 296, + 505 + ], + "type": "text", + "content": "- We propose a robust 3-phase StyleGAN image restoration framework. Our optimization technique maintains: 1) strong realism when degradations level are high; and 2) high fidelity when they are low. Our method is fully unsupervised, requires no per-task training, and can handle different tasks at different levels without having to adjust hyperparameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 506, + 296, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 506, + 296, + 589 + ], + "spans": [ + { + "bbox": [ + 69, + 506, + 296, + 589 + ], + "type": "text", + "content": "- We demonstrate the effectiveness of the proposed method under diverse and composed degradations. We develop a benchmark of synthetic image restoration tasks—making their degradation levels easy to control—with care taken to avoid unrealistic assumptions. Our method outperforms existing unsupervised [13,40] and diffusion-based [32] approaches." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 69, + 604, + 153, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 604, + 153, + 616 + ], + "spans": [ + { + "bbox": [ + 69, + 604, + 153, + 616 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 625, + 294, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 625, + 294, + 697 + ], + "spans": [ + { + "bbox": [ + 68, + 625, + 294, + 697 + ], + "type": "text", + "content": "This section covers previous work on StyleGAN inversion by optimization and its use for image restoration, and discusses related works on generative priors. Because the literature on general purpose image restoration is so extensive, we do not attempt to review it here and instead refer the reader to recent surveys [18, 19, 35, 57]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 698, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 698, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 698, + 296, + 723 + ], + "type": "text", + "content": "GANs and StyleGAN inversion Generative adversarial networks [20] (GANs) are a popular technique" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 541, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 541, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 541, + 144 + ], + "type": "text", + "content": "for generative modeling. In particular, the StyleGAN family [28-31] learns a highly compressed latent representation of its domain and stands out for its popularity and generation quality. Great progress has been made in StyleGAN inversion: reversing the generation process to infer latent parameters that generate a given image [59]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "spans": [ + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "text", + "content": "Thanks to inversion, StyleGAN has found use in many image editing [23, 43, 51] and restoration [13-15, 39, 40] tasks. Purely optimization-based techniques were studied extensively [3, 4, 26, 44, 46, 66] in the context of image editing. These methods extend the learned latent space of a pretrained StyleGAN model (commonly named " + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "text", + "content": ") by adding additional parameters to optimize over it. The most common approach consists of using a different latent code for each layer [3] (dubbed " + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^+" + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "text", + "content": "). Going beyond " + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^+" + }, + { + "bbox": [ + 313, + 145, + 541, + 312 + ], + "type": "text", + "content": " has also been explored in [46] who propose to fine-tune generator parameters, and [44] which uses different latent codes for each convolution filter. We build on these techniques by developing an inversion method designed specifically for robust image restoration." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 315, + 541, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 315, + 541, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 315, + 541, + 410 + ], + "type": "text", + "content": "Generative priors for unsupervised image restoration Since the initial work of Bora et al. [6], multiple papers have used generative priors for unsupervised image restoration [21, 25]. Pan et al. [42] obtained high-resolution results with BigGAN [7]. They relax their latent inversion method by introducing a coarse-to-fine, layer-by-layer generator fine-tuning. Our method differs in that it addresses robustness and compositionality." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "text", + "content": "StyleGAN image restoration Inversion methods designed for editing cannot be applied directly for restoration because loss functions are applied to degraded targets rather than clean images. Previous works address this with additional regularization terms and/or optimizer constraints. Of note, PULSE [40] proposed StyleGAN inversion for image upsampling, using a regularizer minimizing the latent extension to " + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{W}^+" + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "text", + "content": " and a spherical optimization technique on a Gaussian approximation of " + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "text", + "content": ". While PULSE succeeds in preserving high realism, it obtains low fidelity when the downsampling factor is small. ILO [15] uses similar regularization techniques, and further extends the latent space by optimizing intermediate feature maps in a progressive fashion (layer-by-layer) while constraining the solutions to sparse deviations from the range. More recently, SGILO [14] proposes to replace this sparsity constraint and instead trains a score-based model to learn the distribution of the outputs of an intermediate layer in the StyleGAN generator. BRGM [39] frames GAN inversion as Bayesian inference and estimates the maximum a-posteriori over the input latent vector that generated the reconstructed image given different regularization constraints. Its followup, L-BRGM [13], jointly optimizes the " + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "text", + "content": " (before the mapping network) and " + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 313, + 411, + 541, + 723 + ], + "type": "text", + "content": " spaces, further improving quality. In contrast, our work achieves robustness by" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 741, + 317, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 741, + 317, + 750 + ], + "spans": [ + { + "bbox": [ + 293, + 741, + 317, + 750 + ], + "type": "text", + "content": "22293" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 295, + 190 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 295, + 190 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 295, + 190 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 295, + 190 + ], + "type": "image", + "image_path": "01269686a92a2f9db1a5fa56938d162ae30829b740759797a4d99eed45c43b57.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "lines": [ + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "spans": [ + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": "Figure 2. Unsupervised image restoration with StyleGAN attempts to restore a degraded target image " + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{y} = f(\\pmb{y}_{\\mathrm{clean}})" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": " by finding a generated image " + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": " that matches this target once also degraded " + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{x} = \\hat{f}(\\pmb{x}_{\\mathrm{clean}})" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": " (sec. 3); here, " + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\hat{f}" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": " is a differentiable approximation to the degradation function " + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "inline_equation", + "content": "\\pmb{y}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 68, + 198, + 296, + 266 + ], + "type": "text", + "content": " is the (unknown) ground truth image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 290, + 230, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 290, + 230, + 302 + ], + "spans": [ + { + "bbox": [ + 69, + 290, + 230, + 302 + ], + "type": "text", + "content": "avoiding any such regularization losses." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 304, + 296, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 304, + 296, + 411 + ], + "spans": [ + { + "bbox": [ + 68, + 304, + 296, + 411 + ], + "type": "text", + "content": "Other similar works StyleGAN inversion was used to restore old photographs in [38]. Their method also restores a mixture of degradations, but is designed for real degradations (not robustness) and uses a task-specific encoder, while ours method is fully unsupervised. Multiple supervised methods [22, 34, 36, 56, 64, 65] focus on faces only, whereas our method does not use face-specific loss functions [16], is fully unsupervised, and works across a variety of image domains." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 413, + 296, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 413, + 296, + 581 + ], + "spans": [ + { + "bbox": [ + 68, + 413, + 296, + 581 + ], + "type": "text", + "content": "Diffusion models Denoising diffusion probabilistic models (DDPMs) [53], trained on extremely large datasets (e.g., billions of images for [45, 47, 49]), have recently been shown to outclass GANs when it comes to image generation quality [17]. New approaches have been proposed to tackle image restoration using DDPMs, e.g., Palette [48] obtains excellent results by training the same model for several different tasks. Denoising diffusion restoration models (DDRM) [32] show that pretrained DDPMs can be used for unsupervised restoration tasks, but are limited to linear inverse problems with additive Gaussian noise. In contrast, our method is more flexible since it only requires a differentiable approximation of the degradation function, which can be non-linear." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 69, + 597, + 256, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 597, + 256, + 611 + ], + "spans": [ + { + "bbox": [ + 69, + 597, + 256, + 611 + ], + "type": "text", + "content": "3. Image restoration with StyleGAN" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "spans": [ + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": "As illustrated in fig. 2, StyleGAN inversion attempts to recover an image " + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": " that best matches an (unknown) ground truth image " + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{y}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": ". To this end, we aim to search for a latent code " + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{w} \\in \\mathcal{W}" + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{clean}} = G(\\pmb{w})" + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": " best matches " + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\pmb{y}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": " under some image distance function " + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 68, + 620, + 296, + 691 + ], + "type": "text", + "content": ". The resulting minimization problem," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 704, + 295, + 725 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 704, + 295, + 725 + ], + "spans": [ + { + "bbox": [ + 116, + 704, + 295, + 725 + ], + "type": "interline_equation", + "content": "\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(G (\\tilde {\\boldsymbol {w}}), \\boldsymbol {y} _ {\\text {c l e a n}}\\right), \\tag {1}", + "image_path": "5bd87fc6fe11371de5fd6fdb8379ab2b4c3a566e55e14bea5820ddd81d698a1e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 59, + 539, + 227 + ], + "blocks": [ + { + "bbox": [ + 317, + 59, + 539, + 227 + ], + "lines": [ + { + "bbox": [ + 317, + 59, + 539, + 227 + ], + "spans": [ + { + "bbox": [ + 317, + 59, + 539, + 227 + ], + "type": "image", + "image_path": "e861fc957b4dc5c6debbbb7fa15903e15ebd59480c06371acceaff9b65850d54.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "lines": [ + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "spans": [ + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": "Figure 3. Our 3-phase latent extension (sec. 4.1) approach. (a) Phase I uses a global latent code " + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{w}" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": ", resulting in a prediction " + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": ". (b) Phase II performs layer-wise latent expansion, resulting in matrix " + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{+}" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": " and in a prediction " + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{+}" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": ". (c) Phase III performs filter-wise latent expansion, resulting in tensor " + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{w}^{++}" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": " and the final prediction " + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{x}^{++}" + }, + { + "bbox": [ + 313, + 235, + 541, + 300 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "text", + "content": "can be solved by gradient descent. In image restoration, the ground truth image " + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "inline_equation", + "content": "\\pmb{y}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "text", + "content": " is unknown: we are instead given a target image " + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "inline_equation", + "content": "\\pmb{y} = f(\\pmb{y}_{\\mathrm{clean}})" + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "text", + "content": ", the result of a (non-injective, potentially non-differentiable) degradation function " + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "text", + "content": ". Assuming that a differentiable approximation " + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "inline_equation", + "content": "\\hat{f}\\approx f" + }, + { + "bbox": [ + 313, + 319, + 541, + 403 + ], + "type": "text", + "content": " can be constructed, restoration is performed by solving for" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 407, + 541, + 429 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 407, + 541, + 429 + ], + "spans": [ + { + "bbox": [ + 364, + 407, + 541, + 429 + ], + "type": "interline_equation", + "content": "\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(\\hat {f} (G (\\tilde {\\boldsymbol {w}})), \\boldsymbol {y}\\right). \\tag {2}", + "image_path": "de6fdd0ff52f898baf8b0df70b95f6682fb9fa6c67ad3bc693a08f5cccbebf22.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "spans": [ + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "type": "text", + "content": "This can be generalized to compositions of " + }, + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "type": "text", + "content": " different. \ndegradations,i.e., " + }, + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "type": "inline_equation", + "content": "\\{f_i\\}_{i = 1}^k" + }, + { + "bbox": [ + 313, + 434, + 541, + 458 + ], + "type": "text", + "content": " ,by solving for" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 326, + 463, + 541, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 463, + 541, + 485 + ], + "spans": [ + { + "bbox": [ + 326, + 463, + 541, + 485 + ], + "type": "interline_equation", + "content": "\\boldsymbol {w} = \\underset {\\tilde {\\boldsymbol {w}} \\in \\mathcal {W}} {\\arg \\min } \\ell \\left(\\left[ \\hat {f} _ {k} \\circ \\dots \\circ \\hat {f} _ {2} \\circ \\hat {f} _ {1} \\right] (G (\\tilde {\\boldsymbol {w}})), \\boldsymbol {y}\\right), \\tag {3}", + "image_path": "3dab19e54493f2a47f2529dd9a851eb933d920175e078a719a923285400395a6.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "spans": [ + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "text", + "content": " is the composition operator. Here, it is assumed that each subfunction " + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "text", + "content": " has a differentiable approximation " + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "inline_equation", + "content": "\\hat{f}_i" + }, + { + "bbox": [ + 313, + 490, + 541, + 525 + ], + "type": "text", + "content": ", and that the order of composition is known." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 525, + 541, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 525, + 541, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 525, + 541, + 669 + ], + "type": "text", + "content": "As described in sec. 2, this naive approach finds solutions that have high realism (look like real faces), but low fidelity (do not match the degraded target). Fidelity is most commonly improved by 1) performing latent extension [3], that is, solving for " + }, + { + "bbox": [ + 313, + 525, + 541, + 669 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{+} \\in \\mathcal{W}^{+}" + }, + { + "bbox": [ + 313, + 525, + 541, + 669 + ], + "type": "text", + "content": " which has many more degrees of freedom; and 2) using a better performing optimizer like Adam [33]. These techniques both improve fidelity but also damage realism, motivating the use of regularization losses which must carefully be adjusted for different tasks [13, 39, 40]. In the next section, we show how the choice of latent extension and optimizer avoids the need for these regularizers." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 678, + 471, + 691 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 678, + 471, + 691 + ], + "spans": [ + { + "bbox": [ + 313, + 678, + 471, + 691 + ], + "type": "text", + "content": "4. Robust StyleGAN inversion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "type": "text", + "content": "We propose an inversion method designed specifically for robust image restoration, which revisits each aspect" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "spans": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "text", + "content": "22294" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 68, + 72, + 297, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 72, + 297, + 96 + ], + "spans": [ + { + "bbox": [ + 68, + 72, + 297, + 96 + ], + "type": "text", + "content": "of the unsupervised StyleGAN optimization pipeline, namely latent extension, optimization, and loss functions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 103, + 202, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 103, + 202, + 115 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 202, + 115 + ], + "type": "text", + "content": "4.1. Robust latent extension" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "spans": [ + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": "Inspired by the intuition that initialization is the best regularization [46], we propose a three-phase latent extension, where each phase is initialized by the outcome of the previous one, see fig. 3. Given a pretrained StyleGAN2 [31] model with " + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "inline_equation", + "content": "N_{L}" + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": " layers in the generator, we denote style vectors " + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "inline_equation", + "content": "s_i^l \\in \\mathbb{R}^{512}" + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "inline_equation", + "content": "l \\in [1,N_L]" + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": " used to modulate convolution weights " + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}^{l} \\in \\mathbb{R}^{512 \\times 512}" + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": ". Assuming " + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": " filters to simplify notation1, each feature map pixel " + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "inline_equation", + "content": "p^l \\in \\mathbb{R}^{512}" + }, + { + "bbox": [ + 68, + 121, + 296, + 230 + ], + "type": "text", + "content": " is processed by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 138, + 237, + 296, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 237, + 296, + 253 + ], + "spans": [ + { + "bbox": [ + 138, + 237, + 296, + 253 + ], + "type": "interline_equation", + "content": "p _ {i} ^ {l + 1} = \\left(\\boldsymbol {\\theta} _ {i} ^ {l} \\odot \\boldsymbol {s} _ {i} ^ {l}\\right) \\boldsymbol {p} ^ {l}, \\tag {4}", + "image_path": "192173171df012c30c9f0918b9dca7064953a4641bfd1384df8ecd69056dcb3d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "spans": [ + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "type": "text", + "content": "producing output feature " + }, + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "type": "inline_equation", + "content": "p_i^{l + 1}\\in \\mathbb{R}" + }, + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "type": "inline_equation", + "content": "i\\in [0,512]" + }, + { + "bbox": [ + 68, + 260, + 288, + 274 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "spans": [ + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "content": "Phase I performs global style modulation (fig. 3-(a)), and solves for a single latent vector " + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w} \\in \\mathcal{W} = \\mathbb{R}^{512}" + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "content": " shared across all layers as in eq. (3). Prior to optimization, " + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}" + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "content": " is initialized to the mean of " + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "content": " over the training set, i.e., " + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{\\tilde{\\boldsymbol{w}} \\in \\mathcal{W}}[\\tilde{\\boldsymbol{w}}]" + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "content": ". Here, the style modulation vector " + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "inline_equation", + "content": "s_i^l" + }, + { + "bbox": [ + 68, + 274, + 296, + 345 + ], + "type": "text", + "content": " in eq. (4) can be written as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 153, + 354, + 294, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 354, + 294, + 368 + ], + "spans": [ + { + "bbox": [ + 153, + 354, + 294, + 368 + ], + "type": "interline_equation", + "content": "\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} (\\boldsymbol {w}), \\tag {5}", + "image_path": "08bf7c4e14f774a83ed4c5dd70afced8698b35eab7ba5694de80b3abd647c293.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 376, + 295, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 376, + 295, + 400 + ], + "spans": [ + { + "bbox": [ + 68, + 376, + 295, + 400 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 68, + 376, + 295, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{A}^l" + }, + { + "bbox": [ + 68, + 376, + 295, + 400 + ], + "type": "text", + "content": " is the corresponding affine projection layer (which multiplies by a weight matrix and adds a bias)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "text", + "content": "Phase II performs layer-wise latent extension [3] (fig. 3-(b)), and solves for a latent matrix " + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{+} \\in \\mathcal{W}^{+} = \\mathbb{R}^{N_{L} \\times 512}" + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "text", + "content": ". Each row of " + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{+}" + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "text", + "content": " is initialized to " + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}" + }, + { + "bbox": [ + 69, + 401, + 296, + 449 + ], + "type": "text", + "content": ". Style modulation for this phase becomes" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 150, + 457, + 294, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 457, + 294, + 472 + ], + "spans": [ + { + "bbox": [ + 150, + 457, + 294, + 472 + ], + "type": "interline_equation", + "content": "\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} \\left(\\boldsymbol {w} _ {l} ^ {+}\\right). \\tag {6}", + "image_path": "f97ef80e12be6bd389b855a4aff9ebe9cc06784593590de4ce1762b7c91ebeb9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "spans": [ + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "text", + "content": "Phase III performs filter-wise latent extension (fig. 3-c), and solves for a latent tensor " + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{++} \\in \\mathcal{W}^{++} = \\mathbb{R}^{N_F \\times N_L \\times 512}" + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "text", + "content": ", where a different latent code is used for each convolution filter and where " + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "inline_equation", + "content": "N_F" + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "text", + "content": " is the number of such filters. Each submatrix of " + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{++}" + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "text", + "content": " is initialized to " + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^+" + }, + { + "bbox": [ + 68, + 480, + 296, + 552 + ], + "type": "text", + "content": ". Style modulation for this phase becomes" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 147, + 560, + 294, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 560, + 294, + 575 + ], + "spans": [ + { + "bbox": [ + 147, + 560, + 294, + 575 + ], + "type": "interline_equation", + "content": "\\boldsymbol {s} _ {i} ^ {l} = \\mathcal {A} ^ {l} \\left(\\boldsymbol {w} _ {i, l} ^ {+ +}\\right). \\tag {7}", + "image_path": "4f2290fde8cee1aa9625b8215462a8d444306e9feaa16eda9ccfe777187afe5f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 69, + 592, + 187, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 592, + 187, + 605 + ], + "spans": [ + { + "bbox": [ + 69, + 592, + 187, + 605 + ], + "type": "text", + "content": "4.2. Robust optimization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 68, + 609, + 296, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 609, + 296, + 670 + ], + "spans": [ + { + "bbox": [ + 68, + 609, + 296, + 670 + ], + "type": "text", + "content": "While most inversion approaches use the Adam [33] optimizer to solve eq. (3), we instead propose coupling our 3-phase latent extension with a weaker optimizer, normalized gradient decent (NGD) [58], a simple variant of SGD that normalizes the gradient before each step:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 126, + 678, + 294, + 704 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 678, + 294, + 704 + ], + "spans": [ + { + "bbox": [ + 126, + 678, + 294, + 704 + ], + "type": "interline_equation", + "content": "\\bar {\\nabla} _ {\\boldsymbol {w}} \\ell (\\boldsymbol {w}) = \\frac {\\nabla_ {\\boldsymbol {w}} \\ell (\\boldsymbol {w})}{\\| \\nabla_ {\\boldsymbol {w}} \\ell (\\boldsymbol {w}) \\| _ {2}}, \\tag {8}", + "image_path": "faa935e9626e7d4dee801a79eb7f43b71c7288a375d30d1acb4dcfd4791f5778.jpg" + } + ] + } + ], + "index": 14 + }, + { + "type": "code", + "bbox": [ + 316, + 88, + 478, + 295 + ], + "blocks": [ + { + "bbox": [ + 320, + 75, + 495, + 87 + ], + "lines": [ + { + "bbox": [ + 320, + 75, + 495, + 87 + ], + "spans": [ + { + "bbox": [ + 320, + 75, + 495, + 87 + ], + "type": "text", + "content": "Algorithm 1: Robust StyleGAN inversion." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "lines": [ + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "spans": [ + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": "Output: restored image " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "x^{++}" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " # Phase I \n1 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "\\pmb {w} = \\mathbb{E}_{\\tilde{\\pmb{w}}\\in \\mathcal{W}}[\\tilde{\\pmb{w}} ]" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " \n2 for 1 to 150 do \n3 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}\\pmb {x}\\gets G(\\pmb {w})\\\\ \\pmb {w}\\gets 0.08\\bar{\\nabla}_{\\pmb{w}}\\ell (\\hat{f} (\\pmb {x}),\\pmb {y}) \\end{array}" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " \n4 Phase II \n5 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "w^{+} =" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " repeat " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "(\\pmb {w},N_L)" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " \n6 for 1 to 150 do \n7 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}\\pmb{x}^{+}\\gets G^{+}(\\pmb{w}^{+}) \\end{array}" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " \n8 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}\\pmb {w}^{+}\\gets 0.02\\bar{\\nabla}_{\\pmb{w}}\\ell (\\hat{f} (\\pmb{x}^{+}),\\pmb {y}) \\end{array}" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " # Phase III \n9 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "w^{+ + } =" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " repeat " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "(\\pmb {w}^{+},N_{F})" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " \n10 for 1 to 150 do \n11 " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "\\begin{array}{r}\\pmb{x}^{+ + }\\gets G^{+ + }(\\pmb{w}^{+ + })\\\\ \\pmb{w}^{+ + }\\gets 0.005\\bar{\\nabla}_{\\pmb{w}^{+ + }}\\ell (\\hat{f} (\\pmb{x}^{+ + }),\\pmb {y}) \\end{array}" + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "text", + "content": " \n12 \n13 return " + }, + { + "bbox": [ + 316, + 88, + 478, + 295 + ], + "type": "inline_equation", + "content": "x^{+ + }" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "code_body" + } + ], + "index": 17, + "sub_type": "algorithm" + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "spans": [ + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "text", + "content": "Here, the gradient " + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "inline_equation", + "content": "\\bar{\\nabla}_{\\boldsymbol{w}}\\ell (\\boldsymbol {w})" + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "text", + "content": " is explicitly set to 0 when " + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "inline_equation", + "content": "||\\nabla_{\\boldsymbol{w}}\\ell (\\boldsymbol {w})||_2 = 0" + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "text", + "content": ". Following latent extension, we normalize each latent code separately (i.e. each row of " + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{+}" + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w}^{+ + }" + }, + { + "bbox": [ + 313, + 319, + 541, + 392 + ], + "type": "text", + "content": "). NGD conserves loss scale invariance, a key property of Adam that avoids learning rate adjustments following loss function changes." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 399, + 432, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 432, + 410 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 432, + 410 + ], + "type": "text", + "content": "4.3. Robust loss function" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 313, + 417, + 541, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 417, + 541, + 464 + ], + "spans": [ + { + "bbox": [ + 313, + 417, + 541, + 464 + ], + "type": "text", + "content": "The staple loss function in StyleGAN inversion is the LPIPS [63] perceptual loss combined with a L2 or L1 [4] pixel-wise loss. We found a multiresolution loss function to be much more robust, and use:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 329, + 471, + 540, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 471, + 540, + 503 + ], + "spans": [ + { + "bbox": [ + 329, + 471, + 540, + 503 + ], + "type": "interline_equation", + "content": "\\ell_ {\\mathrm {M R}} (\\boldsymbol {x}, \\boldsymbol {y}) = \\sum_ {i = 1} ^ {k} \\ell_ {\\mathrm {L P I P S}} \\left(\\phi \\left(\\boldsymbol {x}, 2 ^ {i}\\right), \\phi \\left(\\boldsymbol {y}, 2 ^ {i}\\right)\\right), \\tag {9}", + "image_path": "c6be10a8d06ca7a2f601741a259463b4ffcddec5da1f6625a9412ca2daca311a.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot ,2^i)" + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": " downsamples by a factor of " + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "inline_equation", + "content": "2^{i}" + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": " using average pooling, and we set " + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "inline_equation", + "content": "k = 6" + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": " for image resolution of " + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "inline_equation", + "content": "1024^{2}" + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": ". All resolutions are weighted equally, giving our final loss function " + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "inline_equation", + "content": "\\ell = \\lambda_{\\mathrm{L1}}\\ell_{\\mathrm{L1}} + \\ell_{\\mathrm{MR}}" + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{L1}} = 0.1" + }, + { + "bbox": [ + 313, + 511, + 541, + 560 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 566, + 422, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 566, + 422, + 578 + ], + "spans": [ + { + "bbox": [ + 313, + 566, + 422, + 578 + ], + "type": "text", + "content": "4.4. Overall algorithm" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "spans": [ + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "content": "Alg. 1 provides a detailed pseudo-code of our method. " + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "inline_equation", + "content": "G^{+}" + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "inline_equation", + "content": "G^{++}" + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "content": " denote the synthesis network " + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "content": " after modification to accept " + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "inline_equation", + "content": "w^{+} \\in \\mathcal{W}^{+}" + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "inline_equation", + "content": "w^{++} \\in \\mathcal{W}^{++}" + }, + { + "bbox": [ + 313, + 585, + 541, + 669 + ], + "type": "text", + "content": ", respectively. Hyperparameters like learning rates and number of steps are explicitly provided since they are held constant across all tasks. Their values were found by cross-validation on a subset of the FFHQ training set." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 678, + 522, + 691 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 678, + 522, + 691 + ], + "spans": [ + { + "bbox": [ + 313, + 678, + 522, + 691 + ], + "type": "text", + "content": "5. Benchmarking restoration robustness" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 698, + 541, + 723 + ], + "type": "text", + "content": "This section first describes the proposed degradation models used in all experiments as well as their respec" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 81, + 712, + 293, + 722 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 712, + 293, + 722 + ], + "spans": [ + { + "bbox": [ + 81, + 712, + 293, + 722 + ], + "type": "text", + "content": "In the " + }, + { + "bbox": [ + 81, + 712, + 293, + 722 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 81, + 712, + 293, + 722 + ], + "type": "text", + "content": " case, operations are repeated spatially and summed." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 741, + 317, + 750 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 741, + 317, + 750 + ], + "spans": [ + { + "bbox": [ + 293, + 741, + 317, + 750 + ], + "type": "text", + "content": "22295" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 69, + 72, + 295, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 72, + 295, + 96 + ], + "spans": [ + { + "bbox": [ + 69, + 72, + 295, + 96 + ], + "type": "text", + "content": "tive differentiable approximations. It then explains how compositions of tasks were formed." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 69, + 102, + 204, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 102, + 204, + 115 + ], + "spans": [ + { + "bbox": [ + 69, + 102, + 204, + 115 + ], + "type": "text", + "content": "5.1. Individual degradations" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 68, + 121, + 296, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 121, + 296, + 240 + ], + "spans": [ + { + "bbox": [ + 68, + 121, + 296, + 240 + ], + "type": "text", + "content": "Experiments are performed on four common sources of image degradation: upsampling, inpainting, denoising, and deartifacting. Synthetic models are used to facilitate comparison at different degradation levels. Each degradation is tested at five levels, which are referred to as extra-small (XS), small (S), medium (M), large (L), and extra-large (XL). Parameters for each degradation level will be provided below for each task in that same order. Fig. 4 shows examples of all four degradations at the XS and XL levels, see supp." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "spans": [ + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "text", + "content": "Upsampling targets " + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "text", + "content": " are produced by downsampling ground truth images " + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "inline_equation", + "content": "\\pmb{y}_{\\mathrm{clean}}" + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "text", + "content": " by integer factors " + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{down}} \\in \\{2,4,8,16,32\\}" + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "text", + "content": ". Downsampling filters are uniformly sampled from the commonly used bilinear, bicubic, and Lanczos filters, which provides a coarse but broad range of aliasing profiles. During inversion, average pooling is used as the approximation " + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "inline_equation", + "content": "\\hat{f}" + }, + { + "bbox": [ + 68, + 240, + 296, + 324 + ], + "type": "text", + "content": " in all cases." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "spans": [ + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "content": "Inpainting aims to predict missing regions in an image. To test a variety of masking conditions, random masks are generated by drawing " + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{strokes}} \\in \\{1,5,9,13,17\\}" + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "content": " random strokes of width " + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "inline_equation", + "content": "0.08r" + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "content": " is the image resolution, each stroke connecting two random points situated in the outer thirds of the image. In this task, " + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "inline_equation", + "content": "\\hat{f} = f" + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "content": " i.e. we assume that the mask is known. To avoid the bias introduced by black pixels when evaluating the LPIPS loss, identical noise of distribution " + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0.5,1)" + }, + { + "bbox": [ + 68, + 325, + 296, + 456 + ], + "type": "text", + "content": " is added to the masked region of both the prediction and the target before computing LPIPS." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "spans": [ + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "text", + "content": "Denoising targets are generated by using a mixture of Poisson and Bernoulli noise, simulating common sources of noise in cameras, namely shot noise and dead (or hot) pixels respectively. This is a challenging scenario because unlike Gaussian noise, Poisson noise is non-additive and signal-dependent, while Bernoulli noise is biased. Additionally, both are non-differentiable. We used the parameters " + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{p}} \\in \\{96, 48, 24, 12, 6\\}" + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{b}} \\in \\{0.04, 0.08, 0.16, 0.32, 0.64\\}" + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{p}}" + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "text", + "content": " gives the most likely value added to a pixel (independently for each channel) according to a Poisson distribution, and " + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{b}}" + }, + { + "bbox": [ + 68, + 456, + 296, + 624 + ], + "type": "text", + "content": " the probability that all channels of a pixel are replaced with black. We also account for clamping during image serialization, resulting in the overall noise model:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 629, + 295, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 629, + 295, + 662 + ], + "spans": [ + { + "bbox": [ + 82, + 629, + 295, + 662 + ], + "type": "interline_equation", + "content": "\\frac {\\operatorname {c l a m p} \\left(p ^ {\\prime} \\cdot m\\right)}{2 5 5}, \\text {w h e r e} p ^ {\\prime} \\sim \\mathcal {P} \\left(k _ {\\mathrm {p}} p\\right), m \\sim \\mathcal {B} \\left(k _ {\\mathrm {b}}\\right), \\tag {10}", + "image_path": "a3629e6dfef5d55bc5930711e7984280fd282c044dbf749afecdfbeb116b4eda.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "text", + "content": "for a ground truth image pixel value " + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "inline_equation", + "content": "p \\in [0.0, 1.0]" + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "text", + "content": " and where " + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "inline_equation", + "content": "\\mathrm{clamp}(\\cdot)" + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "text", + "content": " saturates all values outside of [0, 255]. Note that " + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "inline_equation", + "content": "p'" + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "text", + "content": " can only take discrete values. For the differentiable approximation " + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "inline_equation", + "content": "\\hat{f}" + }, + { + "bbox": [ + 68, + 662, + 296, + 723 + ], + "type": "text", + "content": ", we replace the (non-differentiable, discrete) Poisson noise with a Gaussian ap" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 72, + 541, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 541, + 108 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 541, + 108 + ], + "type": "text", + "content": "proximation " + }, + { + "bbox": [ + 313, + 72, + 541, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(k_{\\mathrm{p}}p - 0.5,\\sqrt{k_{\\mathrm{p}}p})" + }, + { + "bbox": [ + 313, + 72, + 541, + 108 + ], + "type": "text", + "content": " and treat the Bernoulli noise as an unknown mask. We also use a surrogate gradient for clamp:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 332, + 116, + 540, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 116, + 540, + 142 + ], + "spans": [ + { + "bbox": [ + 332, + 116, + 540, + 142 + ], + "type": "interline_equation", + "content": "\\frac {d}{d p} \\operatorname {c l a m p} (p) \\approx \\frac {d}{d p} \\operatorname {s i g m o i d} (2 \\cdot (p - 0. 5)). \\tag {11}", + "image_path": "0816375348383441d78a6138b0970594ff3178324b0b6fb94a06d5ce1a39a6ab.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 148, + 541, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 148, + 541, + 196 + ], + "spans": [ + { + "bbox": [ + 313, + 148, + 541, + 196 + ], + "type": "text", + "content": "Deartifacting is performed on JPEG images compressed with libjpeg [2, 12] at quality levels " + }, + { + "bbox": [ + 313, + 148, + 541, + 196 + ], + "type": "inline_equation", + "content": "k_{\\mathrm{jpeg}} \\in \\{18, 15, 12, 9, 6\\}" + }, + { + "bbox": [ + 313, + 148, + 541, + 196 + ], + "type": "text", + "content": ". The lossy part of JPEG compression can be expressed as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 319, + 205, + 540, + 229 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 205, + 540, + 229 + ], + "spans": [ + { + "bbox": [ + 319, + 205, + 540, + 229 + ], + "type": "interline_equation", + "content": "\\text {q u a n t i z e} \\circ \\mathrm {D C T} \\circ \\text {t o} _ {\\text {b l o c k s}} \\circ \\text {c h r o m a} _ {\\text {s u b s a m p l e}}. \\tag {12}", + "image_path": "4ec7d12d2318f781569f37b1ce8487d317ea10abf66d38b15fde9326f005b1f3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "spans": [ + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "text", + "content": "Here, 4:2:2 chroma subsampling is used. This final quantization step rounds each DCT component " + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "inline_equation", + "content": "c_{i,j}^{(k)}" + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "text", + "content": " positioned in the " + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "inline_equation", + "content": "k^{\\text{th}}" + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "text", + "content": " block at indices " + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "inline_equation", + "content": "i,j" + }, + { + "bbox": [ + 313, + 230, + 541, + 269 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 363, + 277, + 540, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 277, + 540, + 294 + ], + "spans": [ + { + "bbox": [ + 363, + 277, + 540, + 294 + ], + "type": "interline_equation", + "content": "\\operatorname {q u a n t i z e} \\left(c _ {i, j} ^ {(k)}\\right) = \\left\\lfloor c _ {i, j} ^ {(k)} / Q _ {i, j} \\right], \\tag {13}", + "image_path": "d0ed4b8281275f7aa3330019e1944ef7877e3e247313a85a215c4184d891f044.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 300, + 541, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 541, + 385 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 541, + 385 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 313, + 300, + 541, + 385 + ], + "type": "inline_equation", + "content": "Q_{i,j} \\in [1,255] \\subset \\mathbb{N}" + }, + { + "bbox": [ + 313, + 300, + 541, + 385 + ], + "type": "text", + "content": " is the corresponding value from the quantization table. Rounding is the only non-differentiable part of this chain (the lossless part of JPEG compression does not need to be differentiated). We read the quantization tables from file headers and use Lomnitz's implementation [1] of [52], which proposes differentiable rounding:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 375, + 393, + 540, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 393, + 540, + 407 + ], + "spans": [ + { + "bbox": [ + 375, + 393, + 540, + 407 + ], + "type": "interline_equation", + "content": "\\lfloor p \\rceil \\approx \\lfloor p \\rceil + (p - \\lfloor p \\rceil) ^ {3}. \\tag {14}", + "image_path": "8d18a6c68d70d810ee29eabe61a5bed5405e7ebada9f79a9c4a0576decc4f74b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 416, + 541, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 416, + 541, + 452 + ], + "spans": [ + { + "bbox": [ + 313, + 416, + 541, + 452 + ], + "type": "text", + "content": "We use this approximation to define a surrogate gradient (keeping the forward pass exact), and interpolate with a straight-through gradient estimator at " + }, + { + "bbox": [ + 313, + 416, + 541, + 452 + ], + "type": "inline_equation", + "content": "\\alpha = 0.8" + }, + { + "bbox": [ + 313, + 416, + 541, + 452 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 335, + 460, + 539, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 460, + 539, + 485 + ], + "spans": [ + { + "bbox": [ + 335, + 460, + 539, + 485 + ], + "type": "interline_equation", + "content": "\\frac {d}{d p} \\lfloor p \\rceil \\approx \\frac {d}{d p} \\left[ (1 - \\alpha) p + \\alpha (p - \\lfloor p \\rceil) ^ {3} \\right]. \\tag {15}", + "image_path": "4c36d582619555e3891abad7b5cc20108508c41116ed798ad8f1365a756a1e0d.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 314, + 493, + 450, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 493, + 450, + 506 + ], + "spans": [ + { + "bbox": [ + 314, + 493, + 450, + 506 + ], + "type": "text", + "content": "5.2. Composed degradations" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 511, + 541, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 511, + 541, + 546 + ], + "spans": [ + { + "bbox": [ + 313, + 511, + 541, + 546 + ], + "type": "text", + "content": "Eq. (3) assumes knowledge of the order in which degradations are applied. In this work, the following restoration order is used:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 328, + 556, + 539, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 556, + 539, + 569 + ], + "spans": [ + { + "bbox": [ + 328, + 556, + 539, + 569 + ], + "type": "interline_equation", + "content": "\\text {i n p a i n t} \\circ \\text {d e a r i f a c t} \\circ \\text {d e n o i s e} \\circ \\text {u p s a m p l e}. \\tag {16}", + "image_path": "fe6f62899b74e3ba5ebd804cef8f30534614c0973fe80bf2ba45f5048827587b.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 578, + 541, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 578, + 541, + 626 + ], + "spans": [ + { + "bbox": [ + 313, + 578, + 541, + 626 + ], + "type": "text", + "content": "Task compositions are created with (subsequences of) this ordering. For example, upsampling and deartifacting form a composition of length 2. All compositions were formed with tasks at degradation level medium (M)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 313, + 636, + 539, + 650 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 636, + 539, + 650 + ], + "spans": [ + { + "bbox": [ + 313, + 636, + 539, + 650 + ], + "type": "text", + "content": "6. Comparison to StyleGAN-based methods" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 656, + 474, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 656, + 474, + 668 + ], + "spans": [ + { + "bbox": [ + 313, + 656, + 474, + 668 + ], + "type": "text", + "content": "6.1. Models, datasets, and metrics" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 313, + 673, + 541, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 673, + 541, + 721 + ], + "spans": [ + { + "bbox": [ + 313, + 673, + 541, + 721 + ], + "type": "text", + "content": "The PyTorch implementation [41] of StyleGAN2-ADA [28] is used in all experiments. In particular, we use the model pretrained on the FFHQ dataset [30] at " + }, + { + "bbox": [ + 313, + 673, + 541, + 721 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 313, + 673, + 541, + 721 + ], + "type": "text", + "content": " resolution. Since the model is trained on" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "spans": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "text", + "content": "22296" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 196, + 310 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 196, + 310 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 196, + 310 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 196, + 310 + ], + "type": "image", + "image_path": "8fc68f163d70564b3fc207f5a33bdf4e40fef58e95f288944860b7ff476552e3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 318, + 541, + 352 + ], + "lines": [ + { + "bbox": [ + 67, + 318, + 541, + 352 + ], + "spans": [ + { + "bbox": [ + 67, + 318, + 541, + 352 + ], + "type": "text", + "content": "Figure 4. Randomly selected qualitative restoration results on each independent task, for both extra-small and extra-large levels of degradation. Top to bottom: (degraded) target, ours, L-BRGM [13], and PULSE [40]. Left to right: upsampling, inpainting, denoising, and deartifacting. Our method shows better robustness to variations in levels of degradation. See supp. for more results." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 197, + 70, + 310, + 309 + ], + "blocks": [ + { + "bbox": [ + 197, + 70, + 310, + 309 + ], + "lines": [ + { + "bbox": [ + 197, + 70, + 310, + 309 + ], + "spans": [ + { + "bbox": [ + 197, + 70, + 310, + 309 + ], + "type": "image", + "image_path": "3a025d545e7280eb5becaf2be500242b31cd4fcfcd71cbf8e6b3cfe88ca87fbb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 311, + 70, + 425, + 309 + ], + "blocks": [ + { + "bbox": [ + 311, + 70, + 425, + 309 + ], + "lines": [ + { + "bbox": [ + 311, + 70, + 425, + 309 + ], + "spans": [ + { + "bbox": [ + 311, + 70, + 425, + 309 + ], + "type": "image", + "image_path": "7eaa2780704093d6a469d855c3522662d736056400b15c0844f512de6e9ec19a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 426, + 71, + 540, + 309 + ], + "blocks": [ + { + "bbox": [ + 426, + 71, + 540, + 309 + ], + "lines": [ + { + "bbox": [ + 426, + 71, + 540, + 309 + ], + "spans": [ + { + "bbox": [ + 426, + 71, + 540, + 309 + ], + "type": "image", + "image_path": "da7ae62f29d1cacfb9dd359a4aba43e4c8a300f78331604c4a13b2c13ccea84b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 67, + 372, + 295, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 372, + 295, + 420 + ], + "spans": [ + { + "bbox": [ + 67, + 372, + 295, + 420 + ], + "type": "text", + "content": "the entire FFHQ dataset, we gathered an additional 100 test images, dubbed “FFHQ extras” (FFHQ-X), using the same alignment script. Overlap with FFHQ was avoided by filtering by date (see supp.)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 67, + 421, + 295, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 421, + 295, + 564 + ], + "spans": [ + { + "bbox": [ + 67, + 421, + 295, + 564 + ], + "type": "text", + "content": "Performance was measured via accuracy, realism, and fidelity metrics. Accuracy was measured with the LPIPS [63] between the predictions and the ground truth images. Realism was measured using the PatchFID [8] (pFID): FID [24] measured on image patches. More specifically, we extracted 1000 random crops of size " + }, + { + "bbox": [ + 67, + 421, + 295, + 564 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 67, + 421, + 295, + 564 + ], + "type": "text", + "content": " per image, computing the FID of all crops from predictions to all crops from our FFHQ-X dataset. Finally, fidelity between degraded predictions and targets was measured using the LPIPS; this was done by degrading predictions with the true degradation to ignore the effect of differentiable approximations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 69, + 572, + 135, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 572, + 135, + 583 + ], + "spans": [ + { + "bbox": [ + 69, + 572, + 135, + 583 + ], + "type": "text", + "content": "6.2. Baselines" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 67, + 590, + 295, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 590, + 295, + 638 + ], + "spans": [ + { + "bbox": [ + 67, + 590, + 295, + 638 + ], + "type": "text", + "content": "Our method is compared on FFHQ-X against two unsupervised StyleGAN image restoration techniques, PULSE [40] and the current state of the art L-BRGM [13]. The same pretrained network is used for all approaches." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 67, + 638, + 295, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 638, + 295, + 697 + ], + "spans": [ + { + "bbox": [ + 67, + 638, + 295, + 697 + ], + "type": "text", + "content": "PULSE [40] We adapted PULSE to use StyleGAN2-ADA and to tasks other than upsampling by increasing the number of steps from 100 to 250 and adjusting the learning rate to 0.8 (manual inspection on validation data) to increase its robustness to novel tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "type": "text", + "content": "L-BRGM [13] We adjust its learning rate " + }, + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{lr}} = 0.05" + }, + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "type": "text", + "content": " by manual inspection. L-BRGM uses best-of- " + }, + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 68, + 698, + 295, + 723 + ], + "type": "text", + "content": " random" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 372, + 541, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 372, + 541, + 444 + ], + "spans": [ + { + "bbox": [ + 313, + 372, + 541, + 444 + ], + "type": "text", + "content": "initialization; because initialization is difficult under high degradations, we doubled the number of samples from 100 to 200 and added a 0.8 truncation [30] to avoid outliers. L-BRGM also performs early stopping by inspecting the ground truth; for a fair comparison, we instead fixed the number of steps to 500 as in BRGM [39]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 313, + 445, + 541, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 445, + 541, + 528 + ], + "spans": [ + { + "bbox": [ + 313, + 445, + 541, + 528 + ], + "type": "text", + "content": "Hyperparameter optimization for baselines We optimize the accuracy metric for the baselines hyperparameters for each (task, level) pair individually directly on the " + }, + { + "bbox": [ + 313, + 445, + 541, + 528 + ], + "type": "inline_equation", + "content": "FFHQ-X" + }, + { + "bbox": [ + 313, + 445, + 541, + 528 + ], + "type": "text", + "content": " test set (see supp. for more details). In addition, baselines employ the ground truth Bernoulli mask (see sec. 5.1) in their differentiable approximation of eq. (10). Doing so was necessary for good performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 529, + 541, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 541, + 624 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 541, + 624 + ], + "type": "text", + "content": "Our method We adjust hyperameters (learning rate and number of iterations, see alg. 1) once on validation data, then run our benchmark on the test set with no pertask or per-level hyperparameter adjustment: our method uses the same hyperparameters across all tasks and levels. Our method is not provided the Bernoulli mask. The total number of steps (450) is less than the 500 used for L-BRGM." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 632, + 434, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 632, + 434, + 644 + ], + "spans": [ + { + "bbox": [ + 313, + 632, + 434, + 644 + ], + "type": "text", + "content": "6.3. Experimental results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 651, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 541, + 723 + ], + "type": "text", + "content": "Robustness to degradation levels Our benchmark is run on our FFQH-X test set (sec. 6.1) on all five levels of degradation for each individual task, and quantitative results are presented in tab. 1. Recall from sec. 6.2 that our method, which employs a single set of hyperparameters across all experiments, is pitted against baselines" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "spans": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "text", + "content": "22297" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 75, + 71, + 291, + 345 + ], + "blocks": [ + { + "bbox": [ + 75, + 71, + 291, + 345 + ], + "lines": [ + { + "bbox": [ + 75, + 71, + 291, + 345 + ], + "spans": [ + { + "bbox": [ + 75, + 71, + 291, + 345 + ], + "type": "table", + "html": "
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OursPULS L-BRG OursPULS L-BRG Ours
Upsampling (bilinear, bicubic or Lanczos)
XS.493.407.414.432.295.31344.523.617.0
S.492.412.449.353.140.23934.325.522.0
M.495.458.472.261.124.17229.335.422.3
L.501.487.490.185.129.12721.926.020.9
XL.512.506.514.083.095.09024.921.321.3
Denoising (clamped Poisson and Bernoulli mixture)
XS.501.440.425.275.152.15656.127.218.5
S.499.450.434.252.138.14053.728.619.1
M.500.465.446.224.155.13054.522.119.8
L.501.481.457.185.138.11056.424.619.2
XL.504.511.474.134.110.08449.425.117.9
Deartifacting (JPEG compression)
XS.498.442.432.404.341.34952.326.314.8
S.497.448.437.398.352.35049.622.415.4
M.498.461.445.413.357.35733.224.115.4
L.500.475.460.395.367.37446.925.216.0
XL.508.503.490.427.418.41230.822.118.7
Inpainting (random strokes)
XS.498.409.378.464.374.34846.924.412.9
S.501.425.387.356.287.26442.327.214.2
M.509.438.396.283.227.20638.530.114.5
L.513.452.409.231.184.16332.633.115.3
XL.524.460.422.187.157.13236.225.215.9
", + "image_path": "2e22e53a6aeae4afc81548707d13e543292d81e3336ad937d363e127a4afff59.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 68, + 441, + 296, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 441, + 296, + 524 + ], + "spans": [ + { + "bbox": [ + 68, + 441, + 296, + 524 + ], + "type": "text", + "content": "with hyperparameters optimized for each task and level individually. Despite this obvious impediment, our proposed method outperforms baselines in the vast majority of scenarios. In particular, it reaches better accuracy in the majority of tasks against baselines optimized for accuracy, and realism is strictly better. Fig. 4 illustrates the improved visual quality obtained with our method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 68, + 525, + 296, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 525, + 296, + 620 + ], + "spans": [ + { + "bbox": [ + 68, + 525, + 296, + 620 + ], + "type": "text", + "content": "Robustness to compositions Robustness to compositions of degradations was evaluated by forming all possible subsequences of degradations (order in eq. (16)) at medium level. Quantitative results are aggregated in tab. 2, while fig. 5 presents qualitative examples. Our results show that both high fidelity and high realism are maintained with our method, while the baselines struggle under varied degradations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 69, + 630, + 248, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 630, + 248, + 643 + ], + "spans": [ + { + "bbox": [ + 69, + 630, + 248, + 643 + ], + "type": "text", + "content": "7. Comparison to diffusion models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 651, + 296, + 722 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 651, + 296, + 722 + ], + "spans": [ + { + "bbox": [ + 68, + 651, + 296, + 722 + ], + "type": "text", + "content": "We compare our approach to the recent \"Denoising diffusion restoration model\" (DDRM) [32], which also does not require problem-specific supervised training and leverages a pre-trained (DDPM [53]) model. Importantly, DCRM is designed only for linear inverse problems with additive Gaussian noise, where the degradation model is" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 316, + 71, + 542, + 245 + ], + "blocks": [ + { + "bbox": [ + 68, + 353, + 296, + 420 + ], + "lines": [ + { + "bbox": [ + 68, + 353, + 296, + 420 + ], + "spans": [ + { + "bbox": [ + 68, + 353, + 296, + 420 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on individual tasks against baselines (\"PULS\" [40] and \"L-BRG\" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Results color-coded as best and second best." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 71, + 542, + 245 + ], + "lines": [ + { + "bbox": [ + 316, + 71, + 542, + 245 + ], + "spans": [ + { + "bbox": [ + 316, + 71, + 542, + 245 + ], + "type": "table", + "html": "
Accur. (LPIPS) ↓Fidelity (LPIPS) ↓Realism (pFID) ↓
PULS L-BRG OUR5PULS L-BRG OUR5PULS L-BRG OUR5
2 degradations
NA.517.485.459.328.301.29043.424.217.3
AP.511.478.457.270.231.20429.717.617.0
UA.510.518.508.307.348.28723.720.519.7
NP.511.480.458.125.079.06247.020.919.2
UN.501.519.511.178.149.15333.426.221.1
UP.510.478.485.140.061.08923.935.320.7
3 degradations
UNP.510.526.507.086.062.05128.522.120.1
UAP.525.523.513.205.154.11923.018.420.5
UNA.521.535.533.265.310.29026.220.722.8
NAP.526.502.470.210.197.16038.718.418.5
4 degradations
UNAP.533.546.525.192.177.13125.521.121.8
", + "image_path": "af9504541b21cbcce36836c54f2a37f5e47fdc279b6813465a78485deb92a162.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 341, + 356, + 515, + 512 + ], + "blocks": [ + { + "bbox": [ + 313, + 253, + 542, + 342 + ], + "lines": [ + { + "bbox": [ + 313, + 253, + 542, + 342 + ], + "spans": [ + { + "bbox": [ + 313, + 253, + 542, + 342 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on composed tasks (at medium levels) against baselines (\"PULS\" [40] and \"L-BRG\" [13]). Baselines are optimized for accuracy on each row separately, while ours uses the same set of hyperparameters across all. Despite this clear handicap, our method is either on par or outperforms baselines. Acronyms indicate restorations: Upsampling, deNoising, deArtifacting, and/or inPainting. Results color-coded as best and second best." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 341, + 356, + 515, + 512 + ], + "lines": [ + { + "bbox": [ + 341, + 356, + 515, + 512 + ], + "spans": [ + { + "bbox": [ + 341, + 356, + 515, + 512 + ], + "type": "table", + "html": "
Accur. (LPIPS) ↓Realism (pFID) ↓
DDRMOURSDDRMOURS
Exact Upsampling (known average pooling)
0.4120.44344.7518.92
Inexact Upsampling (unknown nearest-neighbor)
0.5590.53967.0632.81
Linear Denoising (additive Gaussian noise)
0.3360.45243.2819.25
Nonlinear Denoising (clamped additive Gaussian noise)
0.5300.450156.119.06
Inpainting (masking random strokes)
0.2890.30126.1225.71
Uncropping (top left corner unmasked)
0.4680.41834.3317.645
", + "image_path": "0c236041033f81890c2e66ef6adb80379f25716b63f49370e26ddb861dd42b63.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 520, + 541, + 544 + ], + "lines": [ + { + "bbox": [ + 313, + 520, + 541, + 544 + ], + "spans": [ + { + "bbox": [ + 313, + 520, + 541, + 544 + ], + "type": "text", + "content": "Table 3. Quantitative comparison to DDRM [32] on accuracy and realism (see sec. 7). Results are color-coded as best ." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "spans": [ + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "text", + "content": "perfectly known. Therefore, for each of the upsampling, denoising and inpainting tasks, we experiment with both: 1) a linear inverse problem with known parameters; and 2) an adjusted version which is either non-linear, where the extract degradation model is unknown, or a more extreme version of the problem. Specifically, we test: average pooling (known, linear) vs nearest-neighbor (unknown) " + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "inline_equation", + "content": "32 \\times" + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "text", + "content": " (XL) upsampling; additive Gaussian noise (linear) vs clamped (to [0, 255]) additive Gaussian noise (non-linear) with " + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "inline_equation", + "content": "\\sigma^2 = 0.8" + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "text", + "content": " (XL) for both; and masking strokes (at XL level) vs uncropping the top-left corner (XXL). DDRM is available on CelebA (not FFHQ) at " + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 313, + 567, + 541, + 723 + ], + "type": "text", + "content": ", so we use the corresponding StyleGAN2-ADA pretrained" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "spans": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "text", + "content": "22298" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 329, + 247 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 329, + 247 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 329, + 247 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 329, + 247 + ], + "type": "image", + "image_path": "0dc25b0c6d19b5a73690935d182ba793285ca28427df5f89d63b4ab736204646.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 255, + 541, + 278 + ], + "lines": [ + { + "bbox": [ + 68, + 255, + 541, + 278 + ], + "spans": [ + { + "bbox": [ + 68, + 255, + 541, + 278 + ], + "type": "text", + "content": "Figure 5. Qualitative comparisons on all possible compositions of the four tasks given medium levels of degradation. Samples are chosen randomly, and acronyms indicate the degradations: Upsampling, inPainting, deNoising and/or deArtifacting (sec. 6.3)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 329, + 70, + 541, + 247 + ], + "blocks": [ + { + "bbox": [ + 329, + 70, + 541, + 247 + ], + "lines": [ + { + "bbox": [ + 329, + 70, + 541, + 247 + ], + "spans": [ + { + "bbox": [ + 329, + 70, + 541, + 247 + ], + "type": "image", + "image_path": "6e0f0b184a35cae0ad3bec11f10fc46215c8222bb5c2e5711e61f848e2ef27c7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 70, + 297, + 295, + 521 + ], + "blocks": [ + { + "bbox": [ + 70, + 297, + 295, + 521 + ], + "lines": [ + { + "bbox": [ + 70, + 297, + 295, + 521 + ], + "spans": [ + { + "bbox": [ + 70, + 297, + 295, + 521 + ], + "type": "image", + "image_path": "9788772c3424bc9e816961daf2dbe2abb2a33c464b3ac9a2acead706f2fb127d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 68, + 530, + 295, + 586 + ], + "lines": [ + { + "bbox": [ + 68, + 530, + 295, + 586 + ], + "spans": [ + { + "bbox": [ + 68, + 530, + 295, + 586 + ], + "type": "text", + "content": "Figure 6. Results on LSUN horses and churches [60], AFHQ-v2 Dogs [11] and BreCaHAD [5] at resolution " + }, + { + "bbox": [ + 68, + 530, + 295, + 586 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 68, + 530, + 295, + 586 + ], + "type": "text", + "content": " for small upsampling (U), small denoising (N), medium deartifacting (A), and medium inpainting (P); the left/right halves are the target/restored images. See supp. for details and more results." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 68, + 612, + 295, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 612, + 295, + 635 + ], + "spans": [ + { + "bbox": [ + 68, + 612, + 295, + 635 + ], + "type": "text", + "content": "model. Due to the reduced resolution, pFID is measured on 250 patches of size " + }, + { + "bbox": [ + 68, + 612, + 295, + 635 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 68, + 612, + 295, + 635 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 68, + 639, + 296, + 723 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 639, + 296, + 723 + ], + "spans": [ + { + "bbox": [ + 68, + 639, + 296, + 723 + ], + "type": "text", + "content": "Interestingly, we find that DDRM reproduces the targets almost perfectly (fidelity is near zero, see supp. for details and qualitative results), to the point where it overfits to any deviation between its degradation model and the true degradation. Tab. 3 presents the accuracy and realism metrics for all the aforementioned tasks. While the accuracy favors DDRM for the tasks which perfectly" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 300, + 541, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 300, + 541, + 371 + ], + "spans": [ + { + "bbox": [ + 313, + 300, + 541, + 371 + ], + "type": "text", + "content": "match its assumptions, our approach outperforms it when this is not the case. In addition, our method provides significantly better realism across all scenarios. Overall, our approach yields high resolution results with more detail, can adapt to non-linear tasks, and it can also cope with larger degradations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 314, + 392, + 383, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 392, + 383, + 404 + ], + "spans": [ + { + "bbox": [ + 314, + 392, + 383, + 404 + ], + "type": "text", + "content": "8. Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 313, + 416, + 541, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 416, + 541, + 548 + ], + "spans": [ + { + "bbox": [ + 313, + 416, + 541, + 548 + ], + "type": "text", + "content": "**Limitations** Our method is not restricted to faces and works with any pretrained StyleGAN, as demonstrated in fig. 6. However, it is inherently limited to the domain learned by the GAN. Training StyleGAN on a large unstructured dataset like ImageNet is difficult but recent papers [27,50,55] have attained some success—applying our method on some of these large-scale models is a promising research avenue. Our method also faces the same ethical considerations as the GAN it relies on. Finally, as with other methods [13,32,40], we also require knowledge of an (approximate) degradation function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 313, + 552, + 541, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 552, + 541, + 671 + ], + "spans": [ + { + "bbox": [ + 313, + 552, + 541, + 671 + ], + "type": "text", + "content": "Conclusion This paper presents a method which makes StyleGAN-based image restoration robust to both variability in degradation levels and to compositions of different degradations. Our proposed method relies on a conservative optimization procedure over a progressively richer latent space and avoids regularization terms altogether. Using a single set of hyperparameters, we obtain competitive and even state-of-the-art results on several challenging scenarios when compared to baselines that are optimized for each task/level individually." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 674, + 541, + 721 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 674, + 541, + 721 + ], + "spans": [ + { + "bbox": [ + 313, + 674, + 541, + 721 + ], + "type": "text", + "content": "Acknowledgements This research was supported by NSERC grant RGPIN-2020-04799, a MITACS Globalink internship to Y. Poirier-Ginter, and by the Digital Research Alliance Canada." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "spans": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "text", + "content": "22299" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 70, + 71, + 128, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 71, + 128, + 83 + ], + "spans": [ + { + "bbox": [ + 70, + 71, + 128, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 71, + 91, + 295, + 721 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 75, + 91, + 280, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 91, + 280, + 102 + ], + "spans": [ + { + "bbox": [ + 75, + 91, + 280, + 102 + ], + "type": "text", + "content": "[1] Diffjpeg. https://github.com/mlomnitz/DiffJPEG." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 75, + 103, + 232, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 103, + 232, + 113 + ], + "spans": [ + { + "bbox": [ + 75, + 103, + 232, + 113 + ], + "type": "text", + "content": "[2] Libjpeg. https://libjpeg-turbo.org." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 114, + 295, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 114, + 295, + 146 + ], + "spans": [ + { + "bbox": [ + 75, + 114, + 295, + 146 + ], + "type": "text", + "content": "[3] Rameen Abdal, Yipeng Qin, and Peter Wonka. 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Improved stylegan embedding: Where are the good latents? arXiv preprint arXiv:2012.09036, 2020." + } + ] + } + ], + "index": 32 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "spans": [ + { + "bbox": [ + 293, + 742, + 317, + 751 + ], + "type": "text", + "content": "22301" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Robust and Scalable Gaussian Process Regression and Its Applications/def98ceb-97d5-4394-a2b2-443884eb66dd_content_list.json b/2023/Robust and Scalable Gaussian Process Regression and Its Applications/def98ceb-97d5-4394-a2b2-443884eb66dd_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2ba6a2bd2d79871f76409eef558c3ea1db551f8e --- /dev/null +++ b/2023/Robust and Scalable Gaussian Process Regression and Its Applications/def98ceb-97d5-4394-a2b2-443884eb66dd_content_list.json @@ -0,0 +1,2097 @@ +[ + { + "type": "text", + "text": "Robust and Scalable Gaussian Process Regression and Its Applications", + "text_level": 1, + "bbox": [ + 129, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yifan Lu $^{1}$ , Jiayi Ma $^{1*}$ , Leyuan Fang $^{2}$ , Xin Tian $^{1}$ , and Junjun Jiang $^{3}$", + "bbox": [ + 199, + 179, + 767, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Wuhan University, China $^{2}$ Hunan University, China $^{3}$ Harbin Institute of Technology, China", + "bbox": [ + 93, + 199, + 875, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lyf048, xin.tian}@whu.edu.cn, {jyma2010, fangleyuan}@gmail.com, jiangjunjun@hit.edu.cn", + "bbox": [ + 98, + 218, + 866, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper introduces a robust and scalable Gaussian process regression (GPR) model via variational learning. This enables the application of Gaussian processes to a wide range of real data, which are often large-scale and contaminated by outliers. Towards this end, we employ a mixture likelihood model where outliers are assumed to be sampled from a uniform distribution. We next derive a variational formulation that jointly infers the mode of data, i.e., inlier or outlier, as well as hyperparameters by maximizing a lower bound of the true log marginal likelihood. Compared to previous robust GPR, our formulation approximates the exact posterior distribution. The inducing variable approximation and stochastic variational inference are further introduced to our variational framework, extending our model to large-scale data. We apply our model to two challenging real-world applications, namely feature matching and dense gene expression imputation. Extensive experiments demonstrate the superiority of our model in terms of robustness and speed. Notably, when matching 4k feature points, its inference is completed in milliseconds with almost no false matches. The code is at github.com/YifanLu2000/Robust-Scalable-GPR.", + "bbox": [ + 75, + 299, + 473, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 636, + 209, + 652 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gaussian processes (GPs) [31] are probably the primary non-parametric method for inference on latent functions. They have a wide range of applications from biology [3] to computer vision [41]. A commonly used observation model for Gaussian process regression (GPR) is the Normal distribution, which brings great convenience to the inference. Unfortunately, a well-known limitation of the Gaussian observation model is its sensitivity to outliers in data. As illustrated in Fig. 1 (b), a few outliers can drastically destroy the entire posterior regression result. This hinders the real-world applications of GPR for many domains, where outliers are often inevitable. This paper intends to conquer the GPR with outlier contaminated data.", + "bbox": [ + 75, + 662, + 468, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The idea of robust regression is not new. Outlier detec", + "bbox": [ + 96, + 859, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/422eeaa15b9fa07532c6070ace79536295c679cfce8350a007917cc3996bfd1c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 268, + 633, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba4e85d82fd04d290f99c63a1570bd1cf7083263db456c972362c9aedd7729cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 268, + 756, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/13370d06014ebd7bdf4c720c3cb41b4eaa3dfb96ed42358fecb539782426169d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 758, + 268, + 883, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bab8f13f8194b03b38e708713d7d3fc42c3a0268df8001011ea10a883e557ea2.jpg", + "image_caption": [ + "Figure 1. Regression with our model. (a) Perform exact GPR from 100 inliers. (b) When there are only 6 outliers in the data, the exact GPR leads to completely wrong results. (c) By comparison, our model is able to recover the exact posterior even facing 100 outliers. (d) The feature matching result using our model. (e) The dense spatial gene expression imputation result using our model." + ], + "image_footnote": [], + "bbox": [ + 508, + 357, + 689, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67dc0e22054a7d3fbba3e5c8064ce53ee21035d388c5175cb432719fd82e7b0e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 358, + 883, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion has been extensively and systematically described in [6,9,10,29]. In the context of GPR, many efforts tried to replace the Gaussian likelihood with other distributions showing heavy-tail behaviors, including Student- $t$ [16,21,28,30], Laplace [22, 30], Gaussian mixture [8, 22, 27], and data-dependent noise model [17]. The challenge with these non-Gaussian likelihoods lies in the inference, which is analytically intractable. To this end, many approximation schemes have been applied, despite having high computational complexity, e.g., Markov Chain Monte Carlo (MCMC) sampling and Expectation Propagation (EP) [22].", + "bbox": [ + 496, + 551, + 892, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose a more effective mixture likelihood model, where uniform distribution accounts for the outliers and Gaussian for inliers. In our formulation, the outliers are independent of the GP and do not affect the computation of the posterior GP, thereby allowing to tolerate more outliers. We next introduce a variational method that jointly determines the modes of data (i.e., inlier or outlier) as well as hyperparameters by maximizing a lower bound to the marginal likelihood. We highlight that the difference between our variational formulation and pervious methods is that the modes of data now become variational parameters and are obtained by minimizing the Kullback-", + "bbox": [ + 496, + 719, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 94, + 886, + 223, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21950", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Leibler (KL) divergence between the variational and the true posterior distribution. Thus, the proposed formulation is less likely to overfit and is able to approximate the exact posterior GP only from inliers, as in Fig. 1 (c).", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by [37], the sparse inducing variable approximation is integrated into our variational framework, which retains the exact GP prior but performs posterior approximation, and reduces the time complexity from $\\mathcal{O}(n^3)$ to $\\mathcal{O}(nm^2)$ . By treating the inducing variables as global variables [18], our variational model enjoys the acceleration by Stochastic Variational Inference (SVI) [20]. It performs stochastic optimization from natural gradient and further decreases the time complexity to $\\mathcal{O}(km^2)$ . This provides a guarantee for our model to scale to large-scale data.", + "bbox": [ + 75, + 152, + 467, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply our robust GPR model to two real-world applications, say feature matching and dense spatial gene expression imputation, as illustrated in the Figs. 1 (d) and (e). Extensive experiments demonstrate the superiority of our method on both numerical data and real applications.", + "bbox": [ + 75, + 301, + 467, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contributions include the following. (i) We present a robust Gaussian process regression model, which uses variational learning to approximate the true exact posterior. (ii) We leverage inducing variables and SVI to adapt our model to large-scale data. (iii) Two applications of our model are described. Extensive experimental validation demonstrates the superiority of our model.", + "bbox": [ + 75, + 378, + 467, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 497, + 225, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robust GPR typically employs non-Gaussian likelihood with heavy tails. Representatively, [22] investigated the Student's- $t$ noise model. They further developed variational inference and MCMC for GPR with Student's- $t$ . In [39], Laplace approximation was used to approximate the log marginal likelihood of Student's- $t$ . The Laplace noise model is also exploited in [22]. [30] introduced Expectation Maximization (EM) algorithm for Student's- $t$ and Laplace. Recently, [8] used mixtures of two Gaussians assuming a lower variance for regular noise and a higher one for outliers, with EM to learn the hyperparameters. In this work, we also use a non-Gaussian likelihood, i.e., mixture model. The difference is that here the outliers are considered to follow a uniform distribution, which is a more reasonable assumption since the sampling distribution of outliers should be independent of the true latent function. Besides, we derive a variational formulation in the GPR setting, which approximates the posterior distribution.", + "bbox": [ + 75, + 522, + 467, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scalable GPR improves the scalability of GPR while maintaining prediction quality for big data. The seminal work [40] adopted Nyström approximation to approximate the kernel matrix using $m$ sparse points. Later, the idea was further promoted by [7, 15, 23, 33], which approximated the prior and performed exact inference. Unlike the prior approximations, the other line is the posterior approximations,", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which retain the exact prior but perform approximate inference. The most well-known work is the elegant variational free energy [37]. It directly approximates the posterior by using variational inference. With the advances in variational inference [20], SVI is introduced to GP [18], which uses natural gradients and results in remarkable computational efficiency. However, as the exact GPR, these scalable GPRs are sensitive to outliers. In contrast, our model can tolerate massive outliers while retaining highly scalability.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Gaussian Process Regression Revisited", + "text_level": 1, + "bbox": [ + 498, + 239, + 846, + 255 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gaussian process is a collection of random variables, for which any finite subset has a joint Gaussian distribution [31]. It is completely specified by a mean function $m(\\mathbf{x})$ and a covariance function $k(\\mathbf{x},\\mathbf{x}^{\\prime})$ where the covariance function typically depends on a set of hyperparameters $\\varphi$ . The GP is usually used as a prior over latent function $f(\\mathbf{x})\\sim \\mathcal{GP}(m,k)$ . We can combine the GP prior with observed data to give a posterior over desired latent function.", + "bbox": [ + 496, + 263, + 890, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Consider a regression problem, where the training data is $\\mathcal{D} = \\{(\\mathbf{x}_i,y_i)\\}_{i = 1}^n$ . Each $y_{i}$ is a noisy realization of the latent function at location $\\mathbf{x}_i$ such that $y_{i} = f_{i} + \\epsilon_{i}$ , where $\\epsilon_{i}\\sim \\mathcal{N}(\\epsilon_{i}|0,\\sigma^{2})$ is typically assumed to be an i.i.d. Gaussian noise and $f_{i} = f(\\mathbf{x}_{i})$ . Denoting all training inputs as $\\mathbf{X}$ , all training outputs $\\mathbf{y}$ , and all latent function values at $\\mathbf{X}$ as $\\mathbf{f}$ . Placing a GP prior on the latent function $f$ , we obtain", + "bbox": [ + 496, + 383, + 890, + 491 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathbf {f} | \\mathbf {X}, \\varphi) \\sim \\mathcal {N} (\\mathbf {f} | m (\\mathbf {X}), \\mathbf {K} _ {n n}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 500, + 890, + 515 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbf{K}_{nn}$ is the covariance function evaluated between all the training points. For simplicity of exposition, the mean function is set to zero $m(\\mathbf{x}) = 0$ . It does not reduce the generalizability of the GP as long as the problem is correctly transformed, e.g., by subtracting the mean of $\\mathbf{y}$ . One can induce a posterior distribution on $\\mathbf{f}$ according to Bayes' rule", + "bbox": [ + 496, + 522, + 890, + 613 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathbf {f} | \\mathcal {D}, \\sigma^ {2}, \\varphi) \\sim \\mathcal {N} (\\mathbf {f} | \\mathbf {K} _ {n n} (\\mathbf {K} _ {n n} ^ {\\epsilon}) ^ {- 1} \\mathbf {y}, \\boldsymbol {\\Sigma}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 627, + 890, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which is also a multivariate normal distribution, where $\\mathbf{K}_{nn}^{\\epsilon} = \\mathbf{K}_{nn} + \\sigma^{2}\\mathbf{I}$ and $\\boldsymbol {\\Sigma} = (\\mathbf{K}_{nn}^{-1} + \\sigma^{-2}\\mathbf{I})^{-1}$ . The posterior distribution of $\\mathbf{f}$ can help to compute the posterior predictive distribution of $\\mathbf{f}_*$ at any test location $\\mathbf{X}_{*}$ :", + "bbox": [ + 496, + 648, + 890, + 709 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p \\left(\\mathbf {f} _ {*} \\mid \\mathcal {D}, \\mathbf {X} _ {*}\\right) = \\int p \\left(\\mathbf {f} _ {*} \\mid \\mathbf {f}, \\mathbf {X} _ {*}\\right) p (\\mathbf {f} \\mid \\mathcal {D}) d \\mathbf {f} \\tag {3} \\\\ = \\mathcal {N} \\left(\\mathbf {f} _ {*} | \\mathbf {K} _ {* n} \\left(\\mathbf {K} _ {n n} ^ {\\epsilon}\\right) ^ {- 1} \\mathbf {y}, \\mathbf {K} _ {* *} - \\mathbf {K} _ {* n} \\left(\\mathbf {K} _ {n n} ^ {\\epsilon}\\right) ^ {- 1} \\mathbf {K} _ {n *}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 715, + 890, + 766 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where, $\\sigma^2$ and $\\varphi$ are omitted for brevity. The above posterior depends on the values of $\\sigma^2$ and $\\varphi$ , which can be inferred by maximizing the log marginal likelihood:", + "bbox": [ + 496, + 773, + 890, + 820 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\log p (\\mathbf {y} \\mid \\sigma^ {2}, \\varphi) = \\log \\mathcal {N} (\\mathbf {y} \\mid \\mathbf {0}, \\mathbf {K} _ {n n} ^ {\\epsilon}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 827, + 890, + 844 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which automatically achieves the bias-variance trade-off.", + "bbox": [ + 500, + 852, + 874, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1Note that the derivation in this paper extends to multiple independent output dimensions is straightforward.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21951", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "4. Robust Gaussian Process Regression Model", + "text_level": 1, + "bbox": [ + 76, + 89, + 465, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In real-world scenarios, a huge discrepancy between the model and data-generating process often occurs, leading to outliers. However, a critical flaw of Gaussian observation model is its non-robustness. This poses a great challenge to GPR in practice. To this end, this section introduces a robust GPR, which identifies the mode of data and simultaneously approximates the posterior of the desired model.", + "bbox": [ + 75, + 114, + 468, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 76, + 229, + 279, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We explicitly consider the generation process of outliers. Since outliers are independent of the latent function, a reasonable assumption is that they obey a uniform distribution $\\frac{1}{a}$ , where the output space is a bounded region that covers the output $\\mathbf{y}$ and $a$ is a constant denoting the volume of the region. The inliers follow a regular Gaussian noise $\\mathcal{N}(y_i|f_i,\\sigma^2)$ . We then associate each data with a latent variable $z_{i} \\in \\{0,1\\}$ , where $z_{i} = 0$ indicates that the observation is generated by outlier distribution and $z_{i} = 1$ inlier. The joint distribution of $(y_{i},z_{i})$ is then a mixture of two models:", + "bbox": [ + 75, + 253, + 470, + 417 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np \\left(y _ {i}, z _ {i} \\mid f _ {i}, \\boldsymbol {\\theta}\\right) = \\left\\{\\left(1 - \\gamma\\right) \\frac {1}{a} \\right\\} ^ {1 - z _ {i}} \\left\\{\\gamma \\mathcal {N} \\left(y _ {i} \\mid f _ {i}, \\sigma^ {2}\\right) \\right\\} ^ {z _ {i}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 426, + 468, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\theta = (\\sigma^2, \\gamma, \\varphi)$ denotes the latent variables set and $\\gamma = p(z_i = 1)$ is the mixing coefficient.", + "bbox": [ + 76, + 465, + 468, + 497 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Prior distributions describe beliefs about the model variables before the inference. As a robust GPR problem, we place a GP prior over the latent function, i.e., Eq. (1). The variable $\\gamma$ controls the probability of occurrence of two models. We suppose it follows a Beta distribution", + "bbox": [ + 75, + 497, + 468, + 571 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np (\\gamma) \\sim \\operatorname {B e t a} (\\gamma | B _ {a}, B _ {b}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 585, + 468, + 601 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $B_{a}$ and $B_{b}$ are hyperparameters. As we will see, $p(\\gamma)$ is conjugate to the posterior and hence easier to handle. For other variables $(\\sigma^2,\\varphi)$ , we introduce noninformative prior.", + "bbox": [ + 75, + 612, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Full joint distribution is obtained by incorporating the above prior distributions as follows:", + "bbox": [ + 75, + 657, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np (\\mathcal {D}, \\mathbf {f}, \\boldsymbol {\\theta}) \\propto p (\\mathbf {f} | \\mathbf {X}) p (\\gamma) \\prod_ {i = 1} ^ {n} p \\left(y _ {i}, z _ {i} \\mid f _ {i}, \\sigma^ {2}, \\gamma\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 698, + 468, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{\\theta} = (\\sigma^2, \\gamma, \\mathbf{Z}, \\varphi)$ and $\\mathbf{Z} \\in \\{0,1\\}^n$ is the indicator variable vector. Our goal is to obtain the posterior $p(\\mathbf{f}, \\pmb{\\theta}|\\mathcal{D})$ , which can be induced from $p(\\mathcal{D}, \\mathbf{f}, \\pmb{\\theta})$ . Nevertheless, as there are two possibilities for each observation, i.e., inlier and outlier, it will generate $2^n$ combinations to be evaluated. Thus, the exact estimation is analytically intractable and approximation is needed. Next, we use the variational inference to approximate the exact posterior. Once the variational distribution is obtained, the posterior predictive distribution can be determined.", + "bbox": [ + 75, + 748, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Variational Inference", + "text_level": 1, + "bbox": [ + 500, + 90, + 700, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We wish to directly approximate the posterior $p(\\mathbf{f},\\boldsymbol {\\theta}|\\mathcal{D})$ using a variational posterior $q(\\mathbf{f},\\boldsymbol {\\theta})$ such that the KL divergence between $p(\\mathbf{f},\\boldsymbol {\\theta}|\\mathcal{D})$ and $q(\\mathbf{f},\\boldsymbol {\\theta})$ is minimized. The minimization is equivalently expressed as maximization of lower bound for the true log marginal likelihood:", + "bbox": [ + 498, + 113, + 893, + 189 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\mathbf {f}, \\boldsymbol {\\theta}) = \\int q (\\mathbf {f}, \\boldsymbol {\\theta}) \\log \\left(\\frac {p (\\mathbf {f} , \\boldsymbol {\\theta} , \\mathcal {D})}{q (\\mathbf {f} , \\boldsymbol {\\theta})}\\right) d \\mathbf {f} d \\boldsymbol {\\theta}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 196, + 890, + 231 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The maximization is, however, intractable since the optimal solution is $\\hat{q} (\\mathbf{f},\\pmb {\\theta}) = p(\\mathbf{f},\\pmb {\\theta}|\\mathcal{D})$ . To this end, we consider instead a restricted distribution of $q(\\mathbf{f},\\pmb {\\theta})$", + "bbox": [ + 498, + 237, + 890, + 282 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mean-field factorization supposes $q(\\mathbf{f},\\pmb {\\theta})$ can be partitioned into disjoint groups. Considering the ease of calculation, we factorize $q(\\mathbf{f},\\pmb {\\theta}) = q_{1}(\\mathbf{f})q_{2}(\\gamma)q_{3}(\\mathbf{Z})q_{4}(\\sigma^{2},\\pmb {\\varphi})$ . Besides, we assume $q_{4}$ is Dirac delta function, i.e., it has a point mass at $(\\sigma^2,\\varphi)$ . With this factorization, the maximization of Eq. (8) is obtained by optimizing each of the factors. For $q_{i}$ , the minimization becomes", + "bbox": [ + 498, + 282, + 890, + 388 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {i} = \\underset {q _ {i}} {\\arg \\min } \\int q _ {i} \\log \\left(\\frac {\\exp \\mathbb {E} _ {j \\neq i} [ \\log p (\\mathbf {f} , \\boldsymbol {\\theta} , \\mathcal {D}) ]}{q _ {i}}\\right) d \\boldsymbol {\\theta} _ {i}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 395, + 890, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbb{E}_{j\\neq i}[\\cdot ]$ denotes the expectation over $q_{j}$ for $j\\neq i$ Note that Eq. (9) is the negative KL divergence between $q_{i}$ and $\\mathbb{E}_{j\\neq i}\\left[\\log p(\\mathbf{f},\\boldsymbol {\\theta},\\mathcal{D})\\right]$ . Thus, the optimal $q_{i}$ is given by", + "bbox": [ + 498, + 441, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\log \\hat {q} _ {i} = \\mathbb {E} _ {j \\neq i} [ \\log p (\\mathbf {f}, \\boldsymbol {\\theta}, \\mathcal {D}) ] + \\text {c o n s t .} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 496, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.3. Sparse Inducing Variable Approximation", + "text_level": 1, + "bbox": [ + 500, + 521, + 852, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The variational posterior approximation presented above can easily integrate sparse inducing variables [37], which allows the reduction of time complexity of GPR from $\\mathcal{O}(n^3)$ to $\\mathcal{O}(nm^2)$ . Introducing $m$ pseudo-inputs $\\mathbf{X}_m$ with inducing variables $\\mathbf{f}_m$ , our goal is to use $\\mathbf{f}_m$ to approximate $q(\\mathbf{f})$ , where $\\mathbf{f}_m$ akin to $\\mathbf{f}$ follows the same GP prior that $p(\\mathbf{f}_m) \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{K}_{mm})$ . We suppose $\\mathbf{f}_m$ is a sufficient statistic for $\\mathbf{f}$ , i.e., for any value $u$ , $p(u|\\mathbf{f}, \\mathbf{f}_m) = p(u|\\mathbf{f}_m)$ holds [37]. In this setting, the augmented variational posterior $q(\\mathbf{f}, \\mathbf{f}_m) = p(\\mathbf{f}|\\mathbf{f}_m)\\phi(\\mathbf{f}_m)$ and augmented latent variables set $\\boldsymbol{\\theta} = (\\gamma, \\sigma^2, \\mathbf{Z}, \\varphi, \\mathbf{X}_m)$ with factorization $q(\\mathbf{f}, \\mathbf{f}_m, \\boldsymbol{\\theta}) = q_1(\\mathbf{f}, \\mathbf{f}_m)q_2(\\gamma)q_3(\\mathbf{Z})q_4(\\sigma^2, \\varphi, \\mathbf{X}_m)$ . The bound (8) becomes", + "bbox": [ + 498, + 544, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\int q (\\mathbf {f}, \\mathbf {f} _ {m}, \\boldsymbol {\\theta}) \\log \\left(\\frac {p \\left(\\mathbf {f} _ {m}\\right) p (\\gamma) p (\\mathbf {y} , \\mathbf {Z} \\mid \\mathbf {f})}{\\phi \\left(\\mathbf {f} _ {m}\\right) q _ {2 - 4}}\\right) d \\mathbf {f} d \\mathbf {f} _ {m} d \\boldsymbol {\\theta}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 747, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the term $p(\\mathbf{f}|\\mathbf{f}_m)$ inside the log is eliminated. In what follows, we maximize the bound analytically by solving the optimal choice of the variational distribution $q(\\mathbf{f},\\mathbf{f}_m,\\boldsymbol {\\theta})$", + "bbox": [ + 498, + 792, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.4. Maximize Lower Bound", + "text_level": 1, + "bbox": [ + 500, + 847, + 720, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To optimize the bound (11) in mean-field factorization, a common approach is to use the coordinate ascent technique,", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21952", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "i.e., optimizing one factor $q_{i}$ while keeping the others $q_{j\\neq i}$ fixed, and cycling through these factors in turn. Convergence is guaranteed because the bound is convex and monotonically increasing with respect to each factor [5]. Next, we give closed-form expressions for factor updates without detailed derivations, which can be found in suppl. material.", + "bbox": [ + 75, + 90, + 467, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Updating $q_{1}(\\mathbf{f},\\mathbf{f}_{m})$ means finding the optimal posterior GP given $q_{2}$ $q_{3}$ , and $q_{4}$ . We denote $p_i = \\mathbb{E}[z_i]$ and $\\mathbf{P} =$ diag $(p_1,p_2,\\dots ,p_n)$ . Integrating over f, (11) becomes", + "bbox": [ + 75, + 181, + 467, + 228 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\int \\phi (\\mathbf {f} _ {m}) \\log \\left(\\frac {p \\left(\\mathbf {f} _ {m}\\right) Q \\left(\\mathbf {f} _ {m} , \\mathbf {y}\\right)}{\\phi \\left(\\mathbf {f} _ {m}\\right)}\\right) d \\mathbf {f} _ {m} + \\text {c o n s t .}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 238, + 467, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 282, + 122, + 294 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\log Q \\left(\\mathbf {f} _ {m}, \\mathbf {y}\\right) = \\log \\mathcal {N} \\left(\\mathbf {y} \\mid \\boldsymbol {\\mu} _ {\\mathbf {f} \\mid \\mathbf {f} _ {m}}, \\sigma^ {2} \\mathbf {P} ^ {- 1}\\right) - \\frac {1}{2 \\sigma^ {2}} \\operatorname {t r} \\left(\\mathbf {P K} _ {\\mathbf {f} \\mid \\mathbf {f} _ {m}}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 294, + 467, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mu_{\\mathbf{f}|\\mathbf{f}_m} = \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{f}_m,$ $\\mathbf{K}_{\\mathbf{f}|\\mathbf{f}_m} = \\mathbf{K}_{nn} - \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{mn}$ are the expectation and covariance of $p(\\mathbf{f}|\\mathbf{f}_m)$ , respectively. With some linear algebraic manipulation, the optimal $\\hat{\\phi} (\\mathbf{f}_m)$ is given by a multivariate Gaussian distribution", + "bbox": [ + 76, + 334, + 467, + 396 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\phi} (\\mathbf {f} _ {m}) \\propto p (\\mathbf {f} _ {m}) Q (\\mathbf {f} _ {m}, \\mathbf {y}) \\tag {14} \\\\ = \\mathcal {N} (\\mathbf {f} _ {m} | \\boldsymbol {\\mu} _ {m}, \\mathbf {A} _ {m}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 397, + 467, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{\\mu}_{m} = \\sigma^{-2}\\mathbf{K}_{mm}\\pmb{\\Sigma}\\mathbf{K}_{mn}\\mathbf{P}\\mathbf{y},\\mathbf{A}_{m} = \\mathbf{K}_{mm}\\pmb{\\Sigma}\\mathbf{K}_{mm},$ and $\\pmb {\\Sigma} = (\\mathbf{K}_{mm} + \\sigma^{-2}\\mathbf{K}_{mn}\\mathbf{P}\\mathbf{K}_{nm})^{-1}$ Note that we can always recover $q(\\mathbf{f})$ from $q(\\mathbf{f},\\mathbf{f}_m) = p(\\mathbf{f}|\\mathbf{f}_m)\\phi (\\mathbf{f}_m)$ by marginalizing out $\\mathbf{f}_m$ , which gives optimal $\\hat{q} (\\mathbf{f}) =$ $\\mathcal{N}(\\mathbf{f}|\\boldsymbol {\\mu}_{\\mathbf{f}},\\mathbf{A})$ , where $\\pmb {\\mu_{\\mathrm{f}}} = \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\pmb {\\mu}_m$ and $\\mathbf{A} =$ $\\mathbf{K}_{\\mathbf{f}|\\mathbf{f}_m} + \\mathbf{K}_{nm}\\pmb{\\Sigma}\\mathbf{K}_{mn}$", + "bbox": [ + 75, + 435, + 467, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 1 With the optimal $\\hat{\\phi}(\\mathbf{f}_m)$ , we obtain $\\langle \\mathcal{N}_i \\rangle = \\exp(\\mathbb{E}[\\log \\mathcal{N}_i])$ as follows", + "bbox": [ + 75, + 540, + 467, + 571 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\langle \\mathcal {N} _ {i} \\rangle = \\mathcal {N} \\left(y _ {i} \\mid \\boldsymbol {\\mu} _ {\\mathbf {f} i}, \\sigma^ {2}\\right) \\exp \\left(- \\frac {1}{2 \\sigma^ {2}} \\mathbf {A} _ {i i}\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 571, + 467, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_i$ denotes $\\mathcal{N}(y_i|f_i,\\sigma^2)$ , $\\pmb{\\mu}_{\\mathbf{fi}}$ is the $i$ -th element of $\\pmb{\\mu}_{\\mathbf{f}}$ , and $\\mathbf{A}_{ii}$ is the $i$ -th diagonal element of $\\mathbf{A}$ .", + "bbox": [ + 75, + 599, + 468, + 631 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Updating $q_{2}(\\gamma)$ indicates updating the inlier ratio or mixture. Suppose $q_{1}, q_{3}$ , and $q_{4}$ are given and note $\\hat{n} = \\operatorname{tr}(\\mathbf{P})$ . According to Eq. (10), we conclude that $\\hat{q}_{2}(\\gamma)$ again follows a Beta distribution", + "bbox": [ + 75, + 643, + 467, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {2} (\\gamma) = \\operatorname {B e t a} (\\gamma | B _ {a} + \\hat {n}, B _ {b} + n - \\hat {n}). \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 717, + 467, + 732 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 2 With the optimal $\\hat{q}_2(\\gamma)$ , according to the properties of Beta distribution, we obtain $\\langle \\gamma \\rangle = \\exp (\\mathbb{E}[\\log \\gamma ])$ and $\\langle 1 - \\gamma \\rangle = \\exp (\\mathbb{E}[\\log (1 - \\gamma)])$ as follows", + "bbox": [ + 75, + 744, + 467, + 789 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\langle \\gamma \\rangle = \\exp (\\psi (B _ {a} + \\hat {n}) - \\psi (B _ {a} + B _ {b} + n)), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 791, + 467, + 813 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\langle 1 - \\gamma \\rangle = \\exp (\\psi (B _ {b} + n - \\hat {n}) - \\psi (B _ {a} + B _ {b} + n)), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 806, + 467, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\psi (\\cdot)$ is the digamma function.", + "bbox": [ + 76, + 827, + 316, + 842 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Updating $q_{3}(\\mathbf{Z})$ represents determining the probability of each data being an inlier given $q_{1}, q_{2}$ , and $q_{4}$ . It encodes the mode of each data point. From Eq. (10), it leads to a", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "further factorization $\\hat{q}_3(\\mathbf{Z}) = \\prod_{i=1}^n \\hat{q}_3^{[i]}(z_i)$ and $\\hat{q}_3^{[i]}(z_i)$ is shown to follow a Bernoulli distribution:", + "bbox": [ + 498, + 88, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {3} ^ {[ i ]} \\left(z _ {i}\\right) = \\left(1 - p _ {i}\\right) ^ {1 - z _ {i}} p _ {i} ^ {z _ {i}}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 119, + 890, + 138 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad p _ {i} = \\frac {\\langle \\gamma \\rangle \\left\\langle \\mathcal {N} _ {i} \\right\\rangle}{\\left. \\langle 1 - \\gamma \\rangle / a + \\langle \\gamma \\rangle \\left\\langle \\mathcal {N} _ {i} \\right\\rangle \\right.}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 151, + 890, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 3 $p_i$ shows the posterior probability of the $i$ -th data being an inlier. It depends on both the deviation between $y_i$ and the posterior mean $\\mu_{\\mathrm{fi}}$ , and the term containing the posterior variance $\\mathbf{A}_{ii}$ . The importance of this variance term is that it encodes the uncertainty of the latent function at $\\mathbf{x}_i$ , which means if we are uncertain about that data, then we cannot identify it as an inlier, even though $y_i$ and $\\mu_{\\mathrm{fi}}$ are close. This is helpful to avoid overfitting.", + "bbox": [ + 496, + 193, + 890, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Updating $q_{4}(\\sigma^{2},\\varphi ,\\mathbf{X}_{m})$ involves the optimization of hyperparameters. Specifically, $\\sigma^2$ controls the noise level, $\\varphi$ represents the shape of the kernel function, and $\\mathbf{X}_m$ is the location of the pseudo-inputs. As assumed previously, $q_{4}(\\sigma^{2},\\varphi ,\\mathbf{X}_{m})$ obeys the Dirac delta distribution, which means we directly maximize the lower bound (11) with respect to $(\\sigma^2,\\varphi ,\\mathbf{X}_m)$ , rather than using Eq. (10).", + "bbox": [ + 496, + 324, + 890, + 430 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given $q_{1}$ , $q_{2}$ , and $q_{3}$ , taking derivative of (11) over $\\sigma^2$ and setting to zero, we obtain a closed-form expression", + "bbox": [ + 498, + 430, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} ^ {2} = \\frac {1}{\\hat {n}} \\left(\\mathbf {y} - \\boldsymbol {\\mu} _ {\\mathbf {f}}\\right) ^ {\\top} \\mathbf {P} \\left(\\mathbf {y} - \\boldsymbol {\\mu} _ {\\mathbf {f}}\\right) + \\frac {1}{\\hat {n}} \\operatorname {t r} (\\mathbf {P A}), \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 460, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{tr}(\\cdot)$ is the trace. The lower bound (11) is, however, difficult to optimize for the remaining hyperparameters $(\\varphi, \\mathbf{X}_m)$ since the integral is intractable. To this end, we use the reverse Jensen's inequality and obtain", + "bbox": [ + 496, + 489, + 890, + 547 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {2} := \\log \\mathcal {N} (\\mathbf {y} | 0, \\mathbf {K} _ {\\mathbf {y}}) - \\frac {1}{2 \\sigma^ {2}} \\operatorname {t r} \\left(\\mathbf {P K} _ {\\mathbf {f} | \\mathbf {f} _ {m}}\\right) + \\text {c o n s t .} \\leq \\mathcal {L}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 558, + 890, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{K_y} = \\sigma^2\\mathbf{P}^{-1} + \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{mn}$ . To set the optimized hyperparameters $(\\varphi, \\mathbf{X}_m)$ , we seek partial derivatives of $\\mathcal{L}_2$ with respect to them. Thereafter, the standard gradient descent algorithm provides the value that maximizes $\\mathcal{L}_2$ .", + "bbox": [ + 496, + 595, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.5. Stochastic Variational Inference", + "text_level": 1, + "bbox": [ + 500, + 665, + 781, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modern applications often involve handling massive data. However, the GPR equipped with variational inference does not easily scale to big data, even with inducing variables. This is because we need to go through the entire training data at each coordinate update. As the training data size grows, the computational overhead becomes larger.", + "bbox": [ + 496, + 688, + 890, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An alternative to coordinate ascent is to use SVI [20], which is similar to stochastic gradient descent (SGD), that performs stochastic optimization from the noisy but cheap-to-compute estimates of the gradient. It iterates between subsampling a subset of data and adjusting the hidden structure solely based on the subset. Thus, SVI is much more efficient than conventional variational inference. To apply SVI to the probabilistic model, a set of global variables is", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21953", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "needed [18]. In our robust GPR setting, the inducing variables $\\mathbf{f}_m$ and mixing coefficient variable $\\gamma$ fill this role.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Natural Gradient. In gradient-based optimization, the natural gradient accounts for the geometric structure of probability parameters and is used in SVI to replace the Euclidean gradient. In exponential families, it is given by premultiplying the usual gradient by the inverse Fisher information matrix $G(\\eta)^{-1}$ , where $\\eta$ is the canonical parameter of the exponential families. Since both $\\phi(\\mathbf{f}_m)$ and $q(\\gamma)$ are exponential family distributions, they enjoy simple natural gradients [19] of the bound (11) such that $g(\\eta) = \\mathbb{E}[\\eta] - \\eta$ , where $g(\\cdot)$ denotes the natural gradient. For Gaussian distribution $\\phi(\\mathbf{f}_m)$ , its canonical parameter is $[\\mathbf{A}_m^{-1}\\boldsymbol{\\mu}_m, -\\frac{1}{2}\\mathbf{A}_m^{-1}]$ . For Beta distribution $q(\\gamma)$ , its canonical parameter is $[B_a + \\hat{n}, B_b + n - \\hat{n}]$ . Thereafter, we obtain the update rule using natural gradient with a step size $\\epsilon_t$", + "bbox": [ + 75, + 121, + 472, + 333 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\eta} ^ {t} = \\boldsymbol {\\eta} ^ {t - 1} + \\varepsilon_ {t} g (\\boldsymbol {\\eta} ^ {t - 1}) = (1 - \\varepsilon_ {t}) \\boldsymbol {\\eta} ^ {t - 1} + \\varepsilon_ {t} \\mathbb {E} [ \\boldsymbol {\\eta} ]. \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 342, + 468, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that when the step size $\\varepsilon_{t} = 1$ , we recover the original variational update in Eq. (14) and Eq. (16). Now, the noisy natural gradient can be easily computed by sampling either individual or mini-batch of the data.", + "bbox": [ + 75, + 372, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.6. Making Predictions", + "text_level": 1, + "bbox": [ + 76, + 441, + 264, + 458 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "So far we have described how to infer the approximate posterior of the latent variables. To make predictions, we use the predictive distribution similar to Eq. (3):", + "bbox": [ + 75, + 465, + 468, + 511 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p \\left(\\mathbf {f} _ {*} \\mid \\mathcal {D}, \\mathbf {X} _ {*}\\right) = \\int p \\left(\\mathbf {f} _ {*} \\mid \\mathbf {f} _ {m}\\right) p \\left(\\mathbf {f} \\mid \\mathbf {f} _ {m}\\right) \\phi \\left(\\mathbf {f} _ {m}\\right) d \\mathbf {f} _ {m} d \\mathbf {f} \\tag {23} \\\\ = \\mathcal {N} \\left(\\mathbf {f} _ {*} | \\mathbf {K} _ {* m} \\mathbf {K} _ {m m} ^ {- 1} \\boldsymbol {\\mu} _ {m}, \\mathbf {K} _ {\\mathbf {f} _ {*} | \\mathbf {f} _ {m}} + \\mathbf {K} _ {* m} \\boldsymbol {\\Sigma} \\mathbf {K} _ {m *}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 511, + 468, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{K}_{\\mathbf{f}_{*}|\\mathbf{f}_{m}} = \\mathbf{K}_{**} - \\mathbf{K}_{*m}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{m*}$ .", + "bbox": [ + 76, + 571, + 352, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Applications", + "text_level": 1, + "bbox": [ + 76, + 601, + 207, + 618 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we describe how to use the proposed GPR model to deal with real-world tasks, including feature matching and dense gene expression imputation.", + "bbox": [ + 75, + 626, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Feature Matching", + "text_level": 1, + "bbox": [ + 76, + 681, + 251, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature matching aims at establishing reliable feature point correspondences. To solve the matching problem in a regression manner, we first construct a putative correspondence set $\\mathcal{P} = \\{(\\mathbf{x}_i,\\mathbf{x}_i')\\}_{i = 1}^n$ by nearest neighbor (NN) matching, where $\\mathbf{x}_i$ and $\\mathbf{x}_i'$ represent the coordinates of feature points. The putative set is then converted to motion vector set, i.e., $\\mathcal{D} = \\{(\\mathbf{x}_i,\\mathbf{y}_i)\\}_{i = 1}^n$ , where $\\mathbf{y}_i = \\mathbf{x}_i' - \\mathbf{x}_i$ . The motion of an object projected on the image plane is known to be slow-and-smooth [38], which is well described by GP. Thus, the motion vectors of inliers can be seen as sampling on the underlying model $\\mathbf{f}$ , while the outliers are spuriously distributed. Our goal is to determine the correctness of each data. The task, however, is non-trivial as there are often", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "massive outliers (even up to $90\\%$ ). Moreover, the feature points in each image can reach several thousands, which requires high computational efficiency. As we will see, our model is robust and fast enough to handle such cases.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference Setting. To apply our model to feature matching, some special considerations need to be set. The feature coordinates are first normalized. For the covariance kernel, we choose the squared exponential (SE) kernel $k(\\mathbf{x},\\mathbf{x}^{\\prime}) = \\lambda^{-1}\\exp (-\\beta \\| \\mathbf{x} - \\mathbf{x}^{\\prime}\\|^{2})$ . We find that fixed hyperparameters work well for most situations, which are empirically set to $\\lambda = 4$ and $\\beta = 0.1$ . The positions of the inducing variables are randomly selected from the training data and kept fixed during inference. The ratio information is also considered as a prior. The mini-batch size is set to $\\max \\left\\{\\frac{n}{8},200\\right\\}$ . After inference convergences, the $i$ -th data is decided to be inlier if $p_i > \\tau$ , where $\\tau$ is a threshold and is set to $\\tau = 0.75$ .", + "bbox": [ + 496, + 152, + 892, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Predictions. One of the attractive properties of our model for this task is that when the training is completed, the resulting posterior GP is able to predict the motion vector of each feature point. Combined with the descriptors' information, we can yield much more correct correspondences rather than being limited to putative set. More correct correspondences are crucial for downstream tasks, as they can significantly improve the accuracy.", + "bbox": [ + 496, + 333, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Dense Gene Expression Imputation", + "text_level": 1, + "bbox": [ + 498, + 460, + 807, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recently, technological advances have made it possible to measure spatially resolved transcriptome-wide mRNA expressions with spatial information in tissue samples. GPR is thus utilized to infer gene expression in discrete samples, generating dense gene expression in 2D, 3D, and even spatiotemporal [3]. Unfortunately, due to equipment malfunctions and process disturbances, the readout data may contain bad spots. In this case, a vanilla GPR may lead to completely wrong results and thus mislead the subsequent analysis. By comparison, the robust GPR developed in this paper copes well with outliers and is able to give meaningful imputation results. For this application, the implementation is simple and requires little extra consideration.", + "bbox": [ + 496, + 484, + 890, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 500, + 693, + 633, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first conduct numerical experiments to evaluate the performance in a fully controlled environment. After that, we apply our model to tackle feature matching problem and compare it with many state-of-the-art methods tailored for feature matching. In the end, the evaluation of gene expression imputation is performed. All experiments are conducted on a desktop with Intel i7-10700 CPU, 16 GB memory with MATLAB except deep learning methods.", + "bbox": [ + 496, + 718, + 890, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1. Numerical Experiments", + "text_level": 1, + "bbox": [ + 500, + 847, + 718, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We study two datasets, i.e., Neal dataset [28] and Friedman dataset [14]. The Neal dataset is one-dimensional data,", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21954", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bf6975106d089e2f181b198558389f9a26f504bb91fd7013d7378b6516549c3a.jpg", + "image_caption": [ + "Figure 2. Visual examples on Neal data. Our model approximates the exact posterior GP using only inliers, even with massive outliers. The legend is shown in the bottom." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 444, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the input $x$ is drawn from a uniform distribution within $[-2.5, 2.5]$ . The target value is calculated as:", + "bbox": [ + 75, + 349, + 468, + 378 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf (x) = 0. 3 + 0. 4 x + 0. 5 \\sin (2. 7 x) + 1. 1 / \\left(1 + x ^ {2}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 381, + 444, + 397 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Gaussian noise is added to the target value with zero mean and variance of 0.1. Next, outliers are injected into the training data, where the value is drawn from uniform distribution within $[-5, 5]$ . The Friedman is 10-dimensional data and the function value depends on the first five dimensions", + "bbox": [ + 75, + 398, + 468, + 472 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {x}) = 1 0 \\sin \\left(\\pi x _ {1} x _ {2}\\right) + 2 0 \\left(x _ {3} - 0. 5\\right) ^ {2} + 1 0 x _ {4} + 5 x _ {5},\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 473, + 455, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "while the remaining dimensions complicate the task by adding a feature selection process. The input $\\mathbf{x}$ is sampled uniformly within $[0,1]^{10}$ . Gaussian noise $\\mathcal{N}(0,0.01)$ is added and random outliers are distributed among [5, 25].", + "bbox": [ + 75, + 491, + 468, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We fix the inlier number to 100 and change the outlier ratio. GPR with Student's- $t$ (St) [32], Laplace (Lap) [32], and Gaussian mixture distribution (MEM) [8], as well as variational free energy (VEF) [37], are chosen as competitors. Some intuitive examples on Neal data are shown in Fig. 2, where outlier ratio increases from 0 to $80\\%$ . We see that the prediction by our model almost exactly reproduces the full GP prediction using only inliers. In contrast, GPR-St and -Lap give poor approximations. GPR-MEM is able to give a better answer, yet still not as good as ours, especially at extremely high outlier ratios.", + "bbox": [ + 75, + 551, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To statistically verify performance, we select mean absolute error (MAE, m), root mean square error (RMSE, r), and negative log of predictive probability (NLP, n) as metrics. 1000 testing points are generated in equal intervals. The statistical results on Neal and Friedman in Table 1 suggest that our method outperforms other alternatives in terms of robustness and accuracy. More results including KL and statistical variance are provided in suppl. material.", + "bbox": [ + 75, + 717, + 468, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2. Feature Matching", + "text_level": 1, + "bbox": [ + 76, + 847, + 250, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We collect three large and diverse feature matching datasets with three different vision tasks, say YFCC100M", + "bbox": [ + 76, + 869, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7ac37f3d520986f63f35272987d6142a96b39cf6cf680f8bd40e8f213296d7bf.jpg", + "table_caption": [ + "Table 1. Quantitative results on Neal and Friedman data with different outlier ratios. Bold indicates the best." + ], + "table_footnote": [], + "table_body": "
Neal [28]
Method10%50%80%
mrnmrnmrn
GPR-VFE [37]0.180.210.730.580.771.750.761.081.96
GPR-St [32]0.030.03-0.410.090.190.390.771.151.66
GPR-Lap [32]0.030.07-1.170.420.561.620.350.722.03
GPR-MEM [8]0.040.08-1.360.060.12-0.660.771.522.04
Ours0.010.02-1.380.030.04-1.250.030.03-0.89
Friedman [14]
Method20%30%50%
mrnmrnmrn
GPR-VFE [37]1.121.242.281.471.623.082.883.166.93
GPR-St [32]0.040.04-0.080.911.103.591.472.187.16
GPR-Lap [32]0.230.290.370.460.610.942.032.233.29
GPR-MEM [8]0.110.21-0.990.130.24-0.662.132.322.98
Ours0.040.06-1.460.060.08-0.350.100.140.55
", + "bbox": [ + 503, + 119, + 890, + 282 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d63bae63fad5a96af15bc558e42713b63d1df2c55e121e76a9bfee1978ae7202.jpg", + "image_caption": [ + "Figure 3. Qualitative illustration of relative pose estimation. We show the true positive in blue and false positive in red. Best viewed in color with $200\\%$ zoom in." + ], + "image_footnote": [], + "bbox": [ + 503, + 295, + 883, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dataset [36] (4000 pairs) for relative pose estimation, CPC dataset [42] (1000 pairs) for fundamental matrix estimation, and HPatches dataset [1] (580 pairs) for homography estimation. Six state-of-the-arts from handcrafted to deep learning are chosen for comparison, namely, MAGSAC++ [2], LPM [26], MCDM [25], CRC [12], PointCN [43], and OANet [44], with baseline ratio test. Briefly, MAGSAC++ is resampling-based method, LPM is a heuristic method that preserves local structure of feature points, CRC interpolates a smooth vector field using Fourier bases, PointCN uses deep neural networks with context normalization to encode global contextual information, OANet further captures local contextual information by clustering unordered correspondences. Note that we assess currently other robust GPR methods are not capable to handle the feature matching problem, thus none of them are chosen for comparison.", + "bbox": [ + 496, + 540, + 890, + 782 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2.1 Relative Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 801, + 725, + 814 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following [44], Yahoo's YFCC100M dataset [36] generates 4000 testing image pairs. SIFT [24] with NN matching is adopted to establish putative correspondences. The maximum number of keypoints for each image is limited to 4000. RANSAC [13] is used to estimate the relative camera pose.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21955", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a2a4c42330d858a74bd3de50c323d75f71b527294e5f94b926e4572308fe6f64.jpg", + "table_caption": [ + "Table 2. Quantitative comparison for relative pose estimation. Bold indicates the best and underline ranks the second." + ], + "table_footnote": [], + "table_body": "
YFCC100M [36]
MethodAUCPRF
@5°@10°@20°
Ratio test28.839.252.124.355.332.8
MSC++ [2]24.933.745.724.355.332.8
PointCN [43]45.154.665.047.273.454.9
OANet [44]53.664.175.851.287.061.7
LPM [26]38.648.859.751.443.645.9
MCDM [25]47.859.470.763.046.552.7
CRC [12]38.148.258.641.257.844.5
Ours53.863.773.885.354.063.7
", + "bbox": [ + 114, + 119, + 428, + 258 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dc04c4bb8db41b27359a91b479060ac3afea0f3337e0a7442160a15dd2c9426b.jpg", + "image_caption": [ + "Figure 4. Visual examples of homography and fundamental matrix estimation. We show the true positive in blue and false positive in red. Best viewed in color with $200\\%$ zoom in." + ], + "image_footnote": [], + "bbox": [ + 84, + 268, + 455, + 433 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We measure the maximum of rotation and translation errors in degree and report the approximate Area Under the Curve (AUC) with thresholds 5, 10, and 20 degrees. Precision, recall, and F1-score before RANSAC with respect to the ground-truth inliers are also presented. See suppl. material for a detailed description of the dataset and the metrics.", + "bbox": [ + 75, + 494, + 467, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Some visualized examples are demonstrated in Fig. 3. Statistics results are comprehensively reported in Table 2. Since deep learning methods such as PointCN and OANet are trained in such dataset with geometric loss, they can capture geometric information and therefore have higher AUC compared to other handcrafted methods. By comparison, our method achieves comparable results to these deep learning methods with much higher precision and F1-score.", + "bbox": [ + 75, + 585, + 467, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2.2 Homography & Fundamental Matrix Estimation", + "text_level": 1, + "bbox": [ + 76, + 724, + 467, + 739 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Homography and fundamental matrix estimation are critical parts in computer vision. The maximum keypoints for HPatches and CPC are limited to 4000. For evaluation metrics, we choose the precision, recall, and F1-score as well as the accuracy of the estimation. For homography estimation, we adopt homography error defined in [11], and for fundamental matrix, we follow [4] and use normalized symmetric geometry distance (NSGD) as the metrics. An estimate is classified as accurate or not by a threshold, which is set to 4 pixels for homography error and 0.05 for the NSGD [4].", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1dbe48d164c483c47c9234ccffd747ca50d995d9c198642eda7b7eb48381e2af.jpg", + "table_caption": [ + "Table 3. Statistical results for homography and fundamental matrix estimation. Bold ranks the first, underline the second." + ], + "table_footnote": [], + "table_body": "
MethodHPatches [1]CPC [42]
Acc.PRFAcc.PRF
Ratio test71.771.651.663.017.012.763.920.5
MSC++ [2]74.487.392.486.06.919.729.619.4
PointCN [43]73.176.985.778.629.319.870.228.8
OANet [44]70.073.577.272.147.034.681.045.4
LPM [26]60.672.550.552.323.821.948.926.1
MCDM [25]77.762.991.073.034.823.061.032.5
CRC [12]71.775.592.580.428.724.847.230.4
Ours78.189.994.391.549.661.559.357.2
Ours*82.473.9109.6-51.939.297.3-
", + "bbox": [ + 501, + 116, + 890, + 255 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b869c03b445fc7fbf651123e7c30fef54ed2c422347dc29b8b6bcf8eff87aa53.jpg", + "table_caption": [ + "Table 4. Ablation studies on feature matching. Bold is the best." + ], + "table_footnote": [], + "table_body": "
MethodPrec.RecallF1Time
CRC [12]50.767.854.968.1
OANet (on GPU) [44]47.975.256.041.2
RS-GPRNo SVI76.366.170.047.1
No inducing variables72.669.069.51.6e5
Opt. Hyperparameters85.061.267.71556
EM optimization67.669.865.543.7
Default88.068.275.69.8
", + "bbox": [ + 519, + 280, + 870, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Several visual examples are provided in Fig. 4. Note that our predictive model is also presented and indicated by the superscript ${}^{*}\\ast$ . It establishes significantly more correct correspondences compared to other methods. Table 3 reports the statistical results. As it indicates, our method outperforms all other methods in the two tasks. When using the predictive model, it can even produce more correct correspondences than the putative set (e.g., the recall in HPatches is higher than 100), thus further improving accuracy.", + "bbox": [ + 496, + 396, + 890, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2.3 Ablation Studies of Feature Matching", + "text_level": 1, + "bbox": [ + 500, + 554, + 815, + 569 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To measure performance, especially runtime, in different settings, we conduct ablation studies on 100 image pairs from YFCC100M. It mainly includes four choices, i.e., not using SVI, not using inducing variables, optimizing the kernel hyperparameters, and using EM optimization instead of variational inference. We also include the CRC and OANet to compare the runtime. The results are reported in Table 4, where we see that our method performs the best with the default setting described in Sect. 5.1. In particular, the running time is much faster compared to other settings and methods.", + "bbox": [ + 496, + 578, + 890, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3. Dense Gene Expression Imputation", + "text_level": 1, + "bbox": [ + 500, + 739, + 805, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We collect two spatial transcriptomics datasets from mouse olfactory bulb and human breast cancer biopsies [34], respectively. Briefly, the spatial transcriptomics gene expression data is measured from thin tissue sections placed on an array with ploy probes and spatially resolved DNA barcodes. These create a grid of circular spots where the mRNA abundance of each spot is measured using probes with the barcodes encoding the spatial locations. The mouse olfactory bulb and human breast cancer biopsies datasets", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21956", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f18ddbf02269356ae12c989aebb22acf2f900a111dfd7aa45aba705fdda444c2.jpg", + "image_caption": [ + "Figure 5. Visualization of dense spatial gene expression imputation. The spatial transcriptomics data is plotted on the top row. The bottom row shows the imputation results of different methods. We stack the spatial transcriptomics (shown as dots) on the imputed results to show the quality of the imputation." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 271, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/55745084f69e7e663fc4106324058dc6db9f1fa989348d7b22a8e582325efa9a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 90, + 462, + 199 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7e2a87e4e76fbbe587afdb4002f46d7baea7049f056a8a401616c3b08ea3db79.jpg", + "table_caption": [ + "Table 5. Statistical results of dense gene expression imputation. Bold indicates the best." + ], + "table_footnote": [], + "table_body": "
Mouse olfactory bulb
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.460.591.250.330.401.10
GPR-St [32]0.070.14-0.570.020.04-1.33
GPR-Lap [32]0.200.270.330.480.540.94
Ours0.030.05-1.990.020.04-2.21
Breast cancer tissue
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.240.351.440.230.331.15
GPR-St [32]0.190.320.370.180.300.22
GPR-Lap [32]0.250.360.560.250.370.53
Ours0.120.16-0.540.110.17-0.39
", + "bbox": [ + 117, + 311, + 429, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "contain 14859 and 12856 measured genes, respectively. To identify spatially variable genes, we adopt SpatialDE [35] and select two patterns for each dataset. We next add 5 random outliers to each identified pattern to simulate the outlier scenario. In the end, different GPR methods are applied to impute dense spatial gene expression.", + "bbox": [ + 75, + 500, + 468, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Two visual examples are presented in Fig. 5, where in each example, the second row shows the imputed results. As can be seen, our method accurately infers the correct gene expression regardless of the outliers. To give quantitative results, we randomly split each dataset into $80\\%$ training data and $20\\%$ test data. As mentioned above, we use the MAE, RMSE, and NLP to measure the performance, and report the statistical results in Table 5. We see that our method always has the lowest error.", + "bbox": [ + 75, + 590, + 468, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Analysis", + "text_level": 1, + "bbox": [ + 76, + 739, + 171, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Optimization Process. We visualize the intermediate results of the optimization process on Neal data with $50\\%$ outliers and present it in the top row of Fig. 6. We see that the field of $p$ in Eq. (19) gradually converges to the inliers. After convergence, the posterior mean and variance functions are very close to the ground truth, and the inducing variables are restricted to the interval of the inliers.", + "bbox": [ + 75, + 763, + 468, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Role of Term $\\mathbf{A}_{ii}$ . We remove the term containing $\\mathbf{A}_{ii}$ in Eq. (15) and show the results in the bottom of Fig. 6.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63607d253c4cdef0168a9b0993d4d1c20ff65bda2af6dc79d4cd66053cea2219.jpg", + "image_caption": [ + "Figure 6. Intermediate results of the optimization process. The top row shows the full model while the bottom removes term $\\mathbf{A}_{ii}$ . We visualize the field of $p$ , which indicates the inlier probability at any location. The deeper the blue color, the higher the probability." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 887, + 204 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7675747a1a2dd41bde5fa61c995b2e69b4a3152c8469d6feffc58aea63ae31f3.jpg", + "image_caption": [ + "Figure 7. Our model deal with different non-uniform outliers." + ], + "image_footnote": [], + "bbox": [ + 519, + 271, + 867, + 332 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62e6027f2054a4ce502523dbd7253a07b2680fd0a94db254e8cfea899846273d.jpg", + "image_caption": [ + "Figure 8. The inference time of each GPR method. Our model with SVI can easily handle big data." + ], + "image_footnote": [], + "bbox": [ + 545, + 359, + 841, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Without variance term, the regression tends to overfit.", + "bbox": [ + 500, + 484, + 852, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Non-uniform Outliers. Different types of non-uniform outliers are tested in Fig. 7. More detailed results are given in suppl. material. Our model exhibits strong generalization and robustness. The reason is that uniform distribution is a very weak assumption with high flexibility. It accommodates many outlier distributions.", + "bbox": [ + 496, + 500, + 890, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Scalability.** We test the runtime towards different problem sizes on Neal data with $50\\%$ outliers. Other methods as well as ours w. and w/o. SVI are included. The number of inducing variables is set to 15 for our method in both two settings. As plotted in Fig. 8, our method can easily scale to large-scale data, especially when equipped with SVI.", + "bbox": [ + 496, + 590, + 890, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 694, + 617, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents a robust and scalable GPR using variational learning. It uses an outlier robust mixture likelihood model, where the uniform distribution accounts for the outliers. A variational formulation is introduced to learn the mode of data and hyperparameters by minimizing the KL divergence between the true posterior distribution and the approximate one. Its most attractive property is that it can rigorously approximate the exact posterior. Inducing variable approximation and SVI further extend our model to big data. We apply our model to feature matching and dense gene expression imputation. Extensive results show the significant improvement over existing robust GPRs.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21957", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. 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In Proceedings of the IEEE International Conference on Computer Vision, pages 5845-5854, 2019. 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 770 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21959", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Robust and Scalable Gaussian Process Regression and Its Applications/def98ceb-97d5-4394-a2b2-443884eb66dd_model.json b/2023/Robust and Scalable Gaussian Process Regression and Its Applications/def98ceb-97d5-4394-a2b2-443884eb66dd_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cf25ac03472a97ccd7a6896fa7c9f95aa5932574 --- /dev/null +++ b/2023/Robust and Scalable Gaussian Process Regression and Its Applications/def98ceb-97d5-4394-a2b2-443884eb66dd_model.json @@ -0,0 +1,2596 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.13, + 0.131, + 0.842, + 0.154 + ], + "angle": 0, + "content": "Robust and Scalable Gaussian Process Regression and Its Applications" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.18, + 0.768, + 0.2 + ], + "angle": 0, + "content": "Yifan Lu\\(^{1}\\), Jiayi Ma\\(^{1*}\\), Leyuan Fang\\(^{2}\\), Xin Tian\\(^{1}\\), and Junjun Jiang\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.2, + 0.877, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\) Wuhan University, China \\(^{2}\\) Hunan University, China \\(^{3}\\) Harbin Institute of Technology, China" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.219, + 0.867, + 0.235 + ], + "angle": 0, + "content": "{lyf048, xin.tian}@whu.edu.cn, {jyma2010, fangleyuan}@gmail.com, jiangjunjun@hit.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.474, + 0.607 + ], + "angle": 0, + "content": "This paper introduces a robust and scalable Gaussian process regression (GPR) model via variational learning. This enables the application of Gaussian processes to a wide range of real data, which are often large-scale and contaminated by outliers. Towards this end, we employ a mixture likelihood model where outliers are assumed to be sampled from a uniform distribution. We next derive a variational formulation that jointly infers the mode of data, i.e., inlier or outlier, as well as hyperparameters by maximizing a lower bound of the true log marginal likelihood. Compared to previous robust GPR, our formulation approximates the exact posterior distribution. The inducing variable approximation and stochastic variational inference are further introduced to our variational framework, extending our model to large-scale data. We apply our model to two challenging real-world applications, namely feature matching and dense gene expression imputation. Extensive experiments demonstrate the superiority of our model in terms of robustness and speed. Notably, when matching 4k feature points, its inference is completed in milliseconds with almost no false matches. The code is at github.com/YifanLu2000/Robust-Scalable-GPR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.637, + 0.21, + 0.654 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.47, + 0.859 + ], + "angle": 0, + "content": "Gaussian processes (GPs) [31] are probably the primary non-parametric method for inference on latent functions. They have a wide range of applications from biology [3] to computer vision [41]. A commonly used observation model for Gaussian process regression (GPR) is the Normal distribution, which brings great convenience to the inference. Unfortunately, a well-known limitation of the Gaussian observation model is its sensitivity to outliers in data. As illustrated in Fig. 1 (b), a few outliers can drastically destroy the entire posterior regression result. This hinders the real-world applications of GPR for many domains, where outliers are often inevitable. This paper intends to conquer the GPR with outlier contaminated data." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.861, + 0.47, + 0.875 + ], + "angle": 0, + "content": "The idea of robust regression is not new. Outlier detec" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.269, + 0.634, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.27, + 0.757, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.759, + 0.27, + 0.885, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.358, + 0.691, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.359, + 0.884, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.441, + 0.895, + 0.526 + ], + "angle": 0, + "content": "Figure 1. Regression with our model. (a) Perform exact GPR from 100 inliers. (b) When there are only 6 outliers in the data, the exact GPR leads to completely wrong results. (c) By comparison, our model is able to recover the exact posterior even facing 100 outliers. (d) The feature matching result using our model. (e) The dense spatial gene expression imputation result using our model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.893, + 0.719 + ], + "angle": 0, + "content": "tion has been extensively and systematically described in [6,9,10,29]. In the context of GPR, many efforts tried to replace the Gaussian likelihood with other distributions showing heavy-tail behaviors, including Student-\\(t\\) [16,21,28,30], Laplace [22, 30], Gaussian mixture [8, 22, 27], and data-dependent noise model [17]. The challenge with these non-Gaussian likelihoods lies in the inference, which is analytically intractable. To this end, many approximation schemes have been applied, despite having high computational complexity, e.g., Markov Chain Monte Carlo (MCMC) sampling and Expectation Propagation (EP) [22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In this paper, we propose a more effective mixture likelihood model, where uniform distribution accounts for the outliers and Gaussian for inliers. In our formulation, the outliers are independent of the GP and do not affect the computation of the posterior GP, thereby allowing to tolerate more outliers. We next introduce a variational method that jointly determines the modes of data (i.e., inlier or outlier) as well as hyperparameters by maximizing a lower bound to the marginal likelihood. We highlight that the difference between our variational formulation and pervious methods is that the modes of data now become variational parameters and are obtained by minimizing the Kullback-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.225, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21950" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "Leibler (KL) divergence between the variational and the true posterior distribution. Thus, the proposed formulation is less likely to overfit and is able to approximate the exact posterior GP only from inliers, as in Fig. 1 (c)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.468, + 0.303 + ], + "angle": 0, + "content": "Inspired by [37], the sparse inducing variable approximation is integrated into our variational framework, which retains the exact GP prior but performs posterior approximation, and reduces the time complexity from \\(\\mathcal{O}(n^3)\\) to \\(\\mathcal{O}(nm^2)\\). By treating the inducing variables as global variables [18], our variational model enjoys the acceleration by Stochastic Variational Inference (SVI) [20]. It performs stochastic optimization from natural gradient and further decreases the time complexity to \\(\\mathcal{O}(km^2)\\). This provides a guarantee for our model to scale to large-scale data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.379 + ], + "angle": 0, + "content": "We apply our robust GPR model to two real-world applications, say feature matching and dense spatial gene expression imputation, as illustrated in the Figs. 1 (d) and (e). Extensive experiments demonstrate the superiority of our method on both numerical data and real applications." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.468, + 0.484 + ], + "angle": 0, + "content": "To summarize, our contributions include the following. (i) We present a robust Gaussian process regression model, which uses variational learning to approximate the true exact posterior. (ii) We leverage inducing variables and SVI to adapt our model to large-scale data. (iii) Two applications of our model are described. Extensive experimental validation demonstrates the superiority of our model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.227, + 0.513 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.468, + 0.794 + ], + "angle": 0, + "content": "Robust GPR typically employs non-Gaussian likelihood with heavy tails. Representatively, [22] investigated the Student's-\\(t\\) noise model. They further developed variational inference and MCMC for GPR with Student's-\\(t\\). In [39], Laplace approximation was used to approximate the log marginal likelihood of Student's-\\(t\\). The Laplace noise model is also exploited in [22]. [30] introduced Expectation Maximization (EM) algorithm for Student's-\\(t\\) and Laplace. Recently, [8] used mixtures of two Gaussians assuming a lower variance for regular noise and a higher one for outliers, with EM to learn the hyperparameters. In this work, we also use a non-Gaussian likelihood, i.e., mixture model. The difference is that here the outliers are considered to follow a uniform distribution, which is a more reasonable assumption since the sampling distribution of outliers should be independent of the true latent function. Besides, we derive a variational formulation in the GPR setting, which approximates the posterior distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Scalable GPR improves the scalability of GPR while maintaining prediction quality for big data. The seminal work [40] adopted Nyström approximation to approximate the kernel matrix using \\( m \\) sparse points. Later, the idea was further promoted by [7, 15, 23, 33], which approximated the prior and performed exact inference. Unlike the prior approximations, the other line is the posterior approximations," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "which retain the exact prior but perform approximate inference. The most well-known work is the elegant variational free energy [37]. It directly approximates the posterior by using variational inference. With the advances in variational inference [20], SVI is introduced to GP [18], which uses natural gradients and results in remarkable computational efficiency. However, as the exact GPR, these scalable GPRs are sensitive to outliers. In contrast, our model can tolerate massive outliers while retaining highly scalability." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.24, + 0.847, + 0.256 + ], + "angle": 0, + "content": "3. Gaussian Process Regression Revisited" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Gaussian process is a collection of random variables, for which any finite subset has a joint Gaussian distribution [31]. It is completely specified by a mean function \\(m(\\mathbf{x})\\) and a covariance function \\(k(\\mathbf{x},\\mathbf{x}^{\\prime})\\) where the covariance function typically depends on a set of hyperparameters \\(\\varphi\\). The GP is usually used as a prior over latent function \\(f(\\mathbf{x})\\sim \\mathcal{GP}(m,k)\\). We can combine the GP prior with observed data to give a posterior over desired latent function." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.492 + ], + "angle": 0, + "content": "Consider a regression problem, where the training data is \\(\\mathcal{D} = \\{(\\mathbf{x}_i,y_i)\\}_{i = 1}^n\\). Each \\(y_{i}\\) is a noisy realization of the latent function at location \\(\\mathbf{x}_i\\) such that \\(y_{i} = f_{i} + \\epsilon_{i}\\), where \\(\\epsilon_{i}\\sim \\mathcal{N}(\\epsilon_{i}|0,\\sigma^{2})\\) is typically assumed to be an i.i.d. Gaussian noise and \\(f_{i} = f(\\mathbf{x}_{i})\\). Denoting all training inputs as \\(\\mathbf{X}\\), all training outputs \\(\\mathbf{y}\\), and all latent function values at \\(\\mathbf{X}\\) as \\(\\mathbf{f}\\). Placing a GP prior on the latent function \\(f\\), we obtain" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.5, + 0.891, + 0.516 + ], + "angle": 0, + "content": "\\[\np (\\mathbf {f} | \\mathbf {X}, \\varphi) \\sim \\mathcal {N} (\\mathbf {f} | m (\\mathbf {X}), \\mathbf {K} _ {n n}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.614 + ], + "angle": 0, + "content": "where \\(\\mathbf{K}_{nn}\\) is the covariance function evaluated between all the training points. For simplicity of exposition, the mean function is set to zero \\(m(\\mathbf{x}) = 0\\). It does not reduce the generalizability of the GP as long as the problem is correctly transformed, e.g., by subtracting the mean of \\(\\mathbf{y}\\). One can induce a posterior distribution on \\(\\mathbf{f}\\) according to Bayes' rule" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.628, + 0.891, + 0.645 + ], + "angle": 0, + "content": "\\[\np (\\mathbf {f} | \\mathcal {D}, \\sigma^ {2}, \\varphi) \\sim \\mathcal {N} (\\mathbf {f} | \\mathbf {K} _ {n n} (\\mathbf {K} _ {n n} ^ {\\epsilon}) ^ {- 1} \\mathbf {y}, \\boldsymbol {\\Sigma}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.891, + 0.71 + ], + "angle": 0, + "content": "which is also a multivariate normal distribution, where \\(\\mathbf{K}_{nn}^{\\epsilon} = \\mathbf{K}_{nn} + \\sigma^{2}\\mathbf{I}\\) and \\(\\boldsymbol {\\Sigma} = (\\mathbf{K}_{nn}^{-1} + \\sigma^{-2}\\mathbf{I})^{-1}\\). The posterior distribution of \\(\\mathbf{f}\\) can help to compute the posterior predictive distribution of \\(\\mathbf{f}_*\\) at any test location \\(\\mathbf{X}_{*}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.717, + 0.891, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p \\left(\\mathbf {f} _ {*} \\mid \\mathcal {D}, \\mathbf {X} _ {*}\\right) = \\int p \\left(\\mathbf {f} _ {*} \\mid \\mathbf {f}, \\mathbf {X} _ {*}\\right) p (\\mathbf {f} \\mid \\mathcal {D}) d \\mathbf {f} \\tag {3} \\\\ = \\mathcal {N} \\left(\\mathbf {f} _ {*} | \\mathbf {K} _ {* n} \\left(\\mathbf {K} _ {n n} ^ {\\epsilon}\\right) ^ {- 1} \\mathbf {y}, \\mathbf {K} _ {* *} - \\mathbf {K} _ {* n} \\left(\\mathbf {K} _ {n n} ^ {\\epsilon}\\right) ^ {- 1} \\mathbf {K} _ {n *}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.891, + 0.821 + ], + "angle": 0, + "content": "where, \\(\\sigma^2\\) and \\(\\varphi\\) are omitted for brevity. The above posterior depends on the values of \\(\\sigma^2\\) and \\(\\varphi\\), which can be inferred by maximizing the log marginal likelihood:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.828, + 0.891, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\log p (\\mathbf {y} \\mid \\sigma^ {2}, \\varphi) = \\log \\mathcal {N} (\\mathbf {y} \\mid \\mathbf {0}, \\mathbf {K} _ {n n} ^ {\\epsilon}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.853, + 0.875, + 0.867 + ], + "angle": 0, + "content": "which automatically achieves the bias-variance trade-off." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.891, + 0.9 + ], + "angle": 0, + "content": "1Note that the derivation in this paper extends to multiple independent output dimensions is straightforward." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21951" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.467, + 0.108 + ], + "angle": 0, + "content": "4. Robust Gaussian Process Regression Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.222 + ], + "angle": 0, + "content": "In real-world scenarios, a huge discrepancy between the model and data-generating process often occurs, leading to outliers. However, a critical flaw of Gaussian observation model is its non-robustness. This poses a great challenge to GPR in practice. To this end, this section introduces a robust GPR, which identifies the mode of data and simultaneously approximates the posterior of the desired model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.231, + 0.281, + 0.246 + ], + "angle": 0, + "content": "4.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.471, + 0.419 + ], + "angle": 0, + "content": "We explicitly consider the generation process of outliers. Since outliers are independent of the latent function, a reasonable assumption is that they obey a uniform distribution \\(\\frac{1}{a}\\), where the output space is a bounded region that covers the output \\(\\mathbf{y}\\) and \\(a\\) is a constant denoting the volume of the region. The inliers follow a regular Gaussian noise \\(\\mathcal{N}(y_i|f_i,\\sigma^2)\\). We then associate each data with a latent variable \\(z_{i} \\in \\{0,1\\}\\), where \\(z_{i} = 0\\) indicates that the observation is generated by outlier distribution and \\(z_{i} = 1\\) inlier. The joint distribution of \\((y_{i},z_{i})\\) is then a mixture of two models:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.428, + 0.47, + 0.457 + ], + "angle": 0, + "content": "\\[\np \\left(y _ {i}, z _ {i} \\mid f _ {i}, \\boldsymbol {\\theta}\\right) = \\left\\{\\left(1 - \\gamma\\right) \\frac {1}{a} \\right\\} ^ {1 - z _ {i}} \\left\\{\\gamma \\mathcal {N} \\left(y _ {i} \\mid f _ {i}, \\sigma^ {2}\\right) \\right\\} ^ {z _ {i}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.467, + 0.469, + 0.498 + ], + "angle": 0, + "content": "where \\(\\theta = (\\sigma^2, \\gamma, \\varphi)\\) denotes the latent variables set and \\(\\gamma = p(z_i = 1)\\) is the mixing coefficient." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.469, + 0.573 + ], + "angle": 0, + "content": "Prior distributions describe beliefs about the model variables before the inference. As a robust GPR problem, we place a GP prior over the latent function, i.e., Eq. (1). The variable \\(\\gamma\\) controls the probability of occurrence of two models. We suppose it follows a Beta distribution" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.586, + 0.469, + 0.602 + ], + "angle": 0, + "content": "\\[\np (\\gamma) \\sim \\operatorname {B e t a} (\\gamma | B _ {a}, B _ {b}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.469, + 0.659 + ], + "angle": 0, + "content": "where \\(B_{a}\\) and \\(B_{b}\\) are hyperparameters. As we will see, \\(p(\\gamma)\\) is conjugate to the posterior and hence easier to handle. For other variables \\((\\sigma^2,\\varphi)\\), we introduce noninformative prior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.688 + ], + "angle": 0, + "content": "Full joint distribution is obtained by incorporating the above prior distributions as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.699, + 0.469, + 0.739 + ], + "angle": 0, + "content": "\\[\np (\\mathcal {D}, \\mathbf {f}, \\boldsymbol {\\theta}) \\propto p (\\mathbf {f} | \\mathbf {X}) p (\\gamma) \\prod_ {i = 1} ^ {n} p \\left(y _ {i}, z _ {i} \\mid f _ {i}, \\sigma^ {2}, \\gamma\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\pmb{\\theta} = (\\sigma^2, \\gamma, \\mathbf{Z}, \\varphi)\\) and \\(\\mathbf{Z} \\in \\{0,1\\}^n\\) is the indicator variable vector. Our goal is to obtain the posterior \\(p(\\mathbf{f}, \\pmb{\\theta}|\\mathcal{D})\\), which can be induced from \\(p(\\mathcal{D}, \\mathbf{f}, \\pmb{\\theta})\\). Nevertheless, as there are two possibilities for each observation, i.e., inlier and outlier, it will generate \\(2^n\\) combinations to be evaluated. Thus, the exact estimation is analytically intractable and approximation is needed. Next, we use the variational inference to approximate the exact posterior. Once the variational distribution is obtained, the posterior predictive distribution can be determined." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.701, + 0.106 + ], + "angle": 0, + "content": "4.2. Variational Inference" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.114, + 0.894, + 0.19 + ], + "angle": 0, + "content": "We wish to directly approximate the posterior \\(p(\\mathbf{f},\\boldsymbol {\\theta}|\\mathcal{D})\\) using a variational posterior \\(q(\\mathbf{f},\\boldsymbol {\\theta})\\) such that the KL divergence between \\(p(\\mathbf{f},\\boldsymbol {\\theta}|\\mathcal{D})\\) and \\(q(\\mathbf{f},\\boldsymbol {\\theta})\\) is minimized. The minimization is equivalently expressed as maximization of lower bound for the true log marginal likelihood:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.197, + 0.892, + 0.232 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\mathbf {f}, \\boldsymbol {\\theta}) = \\int q (\\mathbf {f}, \\boldsymbol {\\theta}) \\log \\left(\\frac {p (\\mathbf {f} , \\boldsymbol {\\theta} , \\mathcal {D})}{q (\\mathbf {f} , \\boldsymbol {\\theta})}\\right) d \\mathbf {f} d \\boldsymbol {\\theta}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.238, + 0.892, + 0.283 + ], + "angle": 0, + "content": "The maximization is, however, intractable since the optimal solution is \\(\\hat{q} (\\mathbf{f},\\pmb {\\theta}) = p(\\mathbf{f},\\pmb {\\theta}|\\mathcal{D})\\) . To this end, we consider instead a restricted distribution of \\(q(\\mathbf{f},\\pmb {\\theta})\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Mean-field factorization supposes \\( q(\\mathbf{f},\\pmb {\\theta}) \\) can be partitioned into disjoint groups. Considering the ease of calculation, we factorize \\( q(\\mathbf{f},\\pmb {\\theta}) = q_{1}(\\mathbf{f})q_{2}(\\gamma)q_{3}(\\mathbf{Z})q_{4}(\\sigma^{2},\\pmb {\\varphi}) \\). Besides, we assume \\( q_{4} \\) is Dirac delta function, i.e., it has a point mass at \\( (\\sigma^2,\\varphi) \\). With this factorization, the maximization of Eq. (8) is obtained by optimizing each of the factors. For \\( q_{i} \\), the minimization becomes" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.396, + 0.892, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {i} = \\underset {q _ {i}} {\\arg \\min } \\int q _ {i} \\log \\left(\\frac {\\exp \\mathbb {E} _ {j \\neq i} [ \\log p (\\mathbf {f} , \\boldsymbol {\\theta} , \\mathcal {D}) ]}{q _ {i}}\\right) d \\boldsymbol {\\theta} _ {i}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.49 + ], + "angle": 0, + "content": "where \\(\\mathbb{E}_{j\\neq i}[\\cdot ]\\) denotes the expectation over \\(q_{j}\\) for \\(j\\neq i\\) Note that Eq. (9) is the negative KL divergence between \\(q_{i}\\) and \\(\\mathbb{E}_{j\\neq i}\\left[\\log p(\\mathbf{f},\\boldsymbol {\\theta},\\mathcal{D})\\right]\\) . Thus, the optimal \\(q_{i}\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.497, + 0.892, + 0.514 + ], + "angle": 0, + "content": "\\[\n\\log \\hat {q} _ {i} = \\mathbb {E} _ {j \\neq i} [ \\log p (\\mathbf {f}, \\boldsymbol {\\theta}, \\mathcal {D}) ] + \\text {c o n s t .} \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.522, + 0.853, + 0.538 + ], + "angle": 0, + "content": "4.3. Sparse Inducing Variable Approximation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.545, + 0.892, + 0.741 + ], + "angle": 0, + "content": "The variational posterior approximation presented above can easily integrate sparse inducing variables [37], which allows the reduction of time complexity of GPR from \\(\\mathcal{O}(n^3)\\) to \\(\\mathcal{O}(nm^2)\\). Introducing \\(m\\) pseudo-inputs \\(\\mathbf{X}_m\\) with inducing variables \\(\\mathbf{f}_m\\), our goal is to use \\(\\mathbf{f}_m\\) to approximate \\(q(\\mathbf{f})\\), where \\(\\mathbf{f}_m\\) akin to \\(\\mathbf{f}\\) follows the same GP prior that \\(p(\\mathbf{f}_m) \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{K}_{mm})\\). We suppose \\(\\mathbf{f}_m\\) is a sufficient statistic for \\(\\mathbf{f}\\), i.e., for any value \\(u\\), \\(p(u|\\mathbf{f}, \\mathbf{f}_m) = p(u|\\mathbf{f}_m)\\) holds [37]. In this setting, the augmented variational posterior \\(q(\\mathbf{f}, \\mathbf{f}_m) = p(\\mathbf{f}|\\mathbf{f}_m)\\phi(\\mathbf{f}_m)\\) and augmented latent variables set \\(\\boldsymbol{\\theta} = (\\gamma, \\sigma^2, \\mathbf{Z}, \\varphi, \\mathbf{X}_m)\\) with factorization \\(q(\\mathbf{f}, \\mathbf{f}_m, \\boldsymbol{\\theta}) = q_1(\\mathbf{f}, \\mathbf{f}_m)q_2(\\gamma)q_3(\\mathbf{Z})q_4(\\sigma^2, \\varphi, \\mathbf{X}_m)\\). The bound (8) becomes" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.748, + 0.892, + 0.794 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\int q (\\mathbf {f}, \\mathbf {f} _ {m}, \\boldsymbol {\\theta}) \\log \\left(\\frac {p \\left(\\mathbf {f} _ {m}\\right) p (\\gamma) p (\\mathbf {y} , \\mathbf {Z} \\mid \\mathbf {f})}{\\phi \\left(\\mathbf {f} _ {m}\\right) q _ {2 - 4}}\\right) d \\mathbf {f} d \\mathbf {f} _ {m} d \\boldsymbol {\\theta}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.794, + 0.892, + 0.84 + ], + "angle": 0, + "content": "where the term \\(p(\\mathbf{f}|\\mathbf{f}_m)\\) inside the log is eliminated. In what follows, we maximize the bound analytically by solving the optimal choice of the variational distribution \\(q(\\mathbf{f},\\mathbf{f}_m,\\boldsymbol {\\theta})\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.722, + 0.862 + ], + "angle": 0, + "content": "4.4. Maximize Lower Bound" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To optimize the bound (11) in mean-field factorization, a common approach is to use the coordinate ascent technique," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21952" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.182 + ], + "angle": 0, + "content": "i.e., optimizing one factor \\( q_{i} \\) while keeping the others \\( q_{j\\neq i} \\) fixed, and cycling through these factors in turn. Convergence is guaranteed because the bound is convex and monotonically increasing with respect to each factor [5]. Next, we give closed-form expressions for factor updates without detailed derivations, which can be found in suppl. material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.182, + 0.468, + 0.229 + ], + "angle": 0, + "content": "Updating \\(q_{1}(\\mathbf{f},\\mathbf{f}_{m})\\) means finding the optimal posterior GP given \\(q_{2}\\) \\(q_{3}\\) , and \\(q_{4}\\) . We denote \\(p_i = \\mathbb{E}[z_i]\\) and \\(\\mathbf{P} =\\) diag \\((p_1,p_2,\\dots ,p_n)\\) . Integrating over f, (11) becomes" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.239, + 0.468, + 0.273 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\int \\phi (\\mathbf {f} _ {m}) \\log \\left(\\frac {p \\left(\\mathbf {f} _ {m}\\right) Q \\left(\\mathbf {f} _ {m} , \\mathbf {y}\\right)}{\\phi \\left(\\mathbf {f} _ {m}\\right)}\\right) d \\mathbf {f} _ {m} + \\text {c o n s t .}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.283, + 0.124, + 0.295 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.295, + 0.468, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\log Q \\left(\\mathbf {f} _ {m}, \\mathbf {y}\\right) = \\log \\mathcal {N} \\left(\\mathbf {y} \\mid \\boldsymbol {\\mu} _ {\\mathbf {f} \\mid \\mathbf {f} _ {m}}, \\sigma^ {2} \\mathbf {P} ^ {- 1}\\right) - \\frac {1}{2 \\sigma^ {2}} \\operatorname {t r} \\left(\\mathbf {P K} _ {\\mathbf {f} \\mid \\mathbf {f} _ {m}}\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.335, + 0.468, + 0.397 + ], + "angle": 0, + "content": "\\(\\mu_{\\mathbf{f}|\\mathbf{f}_m} = \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{f}_m,\\) \\(\\mathbf{K}_{\\mathbf{f}|\\mathbf{f}_m} = \\mathbf{K}_{nn} - \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{mn}\\) are the expectation and covariance of \\(p(\\mathbf{f}|\\mathbf{f}_m)\\), respectively. With some linear algebraic manipulation, the optimal \\(\\hat{\\phi} (\\mathbf{f}_m)\\) is given by a multivariate Gaussian distribution" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.398, + 0.468, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\phi} (\\mathbf {f} _ {m}) \\propto p (\\mathbf {f} _ {m}) Q (\\mathbf {f} _ {m}, \\mathbf {y}) \\tag {14} \\\\ = \\mathcal {N} (\\mathbf {f} _ {m} | \\boldsymbol {\\mu} _ {m}, \\mathbf {A} _ {m}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.468, + 0.528 + ], + "angle": 0, + "content": "where \\(\\pmb{\\mu}_{m} = \\sigma^{-2}\\mathbf{K}_{mm}\\pmb{\\Sigma}\\mathbf{K}_{mn}\\mathbf{P}\\mathbf{y},\\mathbf{A}_{m} = \\mathbf{K}_{mm}\\pmb{\\Sigma}\\mathbf{K}_{mm},\\) and \\(\\pmb {\\Sigma} = (\\mathbf{K}_{mm} + \\sigma^{-2}\\mathbf{K}_{mn}\\mathbf{P}\\mathbf{K}_{nm})^{-1}\\) Note that we can always recover \\(q(\\mathbf{f})\\) from \\(q(\\mathbf{f},\\mathbf{f}_m) = p(\\mathbf{f}|\\mathbf{f}_m)\\phi (\\mathbf{f}_m)\\) by marginalizing out \\(\\mathbf{f}_m\\) , which gives optimal \\(\\hat{q} (\\mathbf{f}) =\\) \\(\\mathcal{N}(\\mathbf{f}|\\boldsymbol {\\mu}_{\\mathbf{f}},\\mathbf{A})\\) , where \\(\\pmb {\\mu_{\\mathrm{f}}} = \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\pmb {\\mu}_m\\) and \\(\\mathbf{A} =\\) \\(\\mathbf{K}_{\\mathbf{f}|\\mathbf{f}_m} + \\mathbf{K}_{nm}\\pmb{\\Sigma}\\mathbf{K}_{mn}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.468, + 0.573 + ], + "angle": 0, + "content": "Remark 1 With the optimal \\(\\hat{\\phi}(\\mathbf{f}_m)\\), we obtain \\(\\langle \\mathcal{N}_i \\rangle = \\exp(\\mathbb{E}[\\log \\mathcal{N}_i])\\) as follows" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.573, + 0.468, + 0.6 + ], + "angle": 0, + "content": "\\[\n\\langle \\mathcal {N} _ {i} \\rangle = \\mathcal {N} \\left(y _ {i} \\mid \\boldsymbol {\\mu} _ {\\mathbf {f} i}, \\sigma^ {2}\\right) \\exp \\left(- \\frac {1}{2 \\sigma^ {2}} \\mathbf {A} _ {i i}\\right), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.632 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_i\\) denotes \\(\\mathcal{N}(y_i|f_i,\\sigma^2)\\), \\(\\pmb{\\mu}_{\\mathbf{fi}}\\) is the \\(i\\)-th element of \\(\\pmb{\\mu}_{\\mathbf{f}}\\), and \\(\\mathbf{A}_{ii}\\) is the \\(i\\)-th diagonal element of \\(\\mathbf{A}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.468, + 0.704 + ], + "angle": 0, + "content": "Updating \\( q_{2}(\\gamma) \\) indicates updating the inlier ratio or mixture. Suppose \\( q_{1}, q_{3} \\), and \\( q_{4} \\) are given and note \\( \\hat{n} = \\operatorname{tr}(\\mathbf{P}) \\). According to Eq. (10), we conclude that \\( \\hat{q}_{2}(\\gamma) \\) again follows a Beta distribution" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.718, + 0.468, + 0.733 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {2} (\\gamma) = \\operatorname {B e t a} (\\gamma | B _ {a} + \\hat {n}, B _ {b} + n - \\hat {n}). \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.468, + 0.79 + ], + "angle": 0, + "content": "Remark 2 With the optimal \\(\\hat{q}_2(\\gamma)\\), according to the properties of Beta distribution, we obtain \\(\\langle \\gamma \\rangle = \\exp (\\mathbb{E}[\\log \\gamma ])\\) and \\(\\langle 1 - \\gamma \\rangle = \\exp (\\mathbb{E}[\\log (1 - \\gamma)])\\) as follows" + }, + { + "type": "equation", + "bbox": [ + 0.119, + 0.792, + 0.468, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\langle \\gamma \\rangle = \\exp (\\psi (B _ {a} + \\hat {n}) - \\psi (B _ {a} + B _ {b} + n)), \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.808, + 0.468, + 0.826 + ], + "angle": 0, + "content": "\\[\n\\langle 1 - \\gamma \\rangle = \\exp (\\psi (B _ {b} + n - \\hat {n}) - \\psi (B _ {a} + B _ {b} + n)), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.828, + 0.318, + 0.843 + ], + "angle": 0, + "content": "where \\(\\psi (\\cdot)\\) is the digamma function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Updating \\( q_{3}(\\mathbf{Z}) \\) represents determining the probability of each data being an inlier given \\( q_{1}, q_{2} \\), and \\( q_{4} \\). It encodes the mode of each data point. From Eq. (10), it leads to a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.121 + ], + "angle": 0, + "content": "further factorization \\(\\hat{q}_3(\\mathbf{Z}) = \\prod_{i=1}^n \\hat{q}_3^{[i]}(z_i)\\) and \\(\\hat{q}_3^{[i]}(z_i)\\) is shown to follow a Bernoulli distribution:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.121, + 0.891, + 0.14 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {3} ^ {[ i ]} \\left(z _ {i}\\right) = \\left(1 - p _ {i}\\right) ^ {1 - z _ {i}} p _ {i} ^ {z _ {i}}, \\tag {18}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.152, + 0.891, + 0.186 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad p _ {i} = \\frac {\\langle \\gamma \\rangle \\left\\langle \\mathcal {N} _ {i} \\right\\rangle}{\\left. \\langle 1 - \\gamma \\rangle / a + \\langle \\gamma \\rangle \\left\\langle \\mathcal {N} _ {i} \\right\\rangle \\right.}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.194, + 0.892, + 0.315 + ], + "angle": 0, + "content": "Remark 3 \\( p_i \\) shows the posterior probability of the \\( i \\)-th data being an inlier. It depends on both the deviation between \\( y_i \\) and the posterior mean \\( \\mu_{\\mathrm{fi}} \\), and the term containing the posterior variance \\( \\mathbf{A}_{ii} \\). The importance of this variance term is that it encodes the uncertainty of the latent function at \\( \\mathbf{x}_i \\), which means if we are uncertain about that data, then we cannot identify it as an inlier, even though \\( y_i \\) and \\( \\mu_{\\mathrm{fi}} \\) are close. This is helpful to avoid overfitting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.431 + ], + "angle": 0, + "content": "Updating \\( q_{4}(\\sigma^{2},\\varphi ,\\mathbf{X}_{m}) \\) involves the optimization of hyperparameters. Specifically, \\( \\sigma^2 \\) controls the noise level, \\( \\varphi \\) represents the shape of the kernel function, and \\( \\mathbf{X}_m \\) is the location of the pseudo-inputs. As assumed previously, \\( q_{4}(\\sigma^{2},\\varphi ,\\mathbf{X}_{m}) \\) obeys the Dirac delta distribution, which means we directly maximize the lower bound (11) with respect to \\( (\\sigma^2,\\varphi ,\\mathbf{X}_m) \\), rather than using Eq. (10)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.891, + 0.461 + ], + "angle": 0, + "content": "Given \\( q_{1} \\), \\( q_{2} \\), and \\( q_{3} \\), taking derivative of (11) over \\( \\sigma^2 \\) and setting to zero, we obtain a closed-form expression" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.462, + 0.891, + 0.49 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} ^ {2} = \\frac {1}{\\hat {n}} \\left(\\mathbf {y} - \\boldsymbol {\\mu} _ {\\mathbf {f}}\\right) ^ {\\top} \\mathbf {P} \\left(\\mathbf {y} - \\boldsymbol {\\mu} _ {\\mathbf {f}}\\right) + \\frac {1}{\\hat {n}} \\operatorname {t r} (\\mathbf {P A}), \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.891, + 0.549 + ], + "angle": 0, + "content": "where \\(\\operatorname{tr}(\\cdot)\\) is the trace. The lower bound (11) is, however, difficult to optimize for the remaining hyperparameters \\((\\varphi, \\mathbf{X}_m)\\) since the integral is intractable. To this end, we use the reverse Jensen's inequality and obtain" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.559, + 0.891, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {2} := \\log \\mathcal {N} (\\mathbf {y} | 0, \\mathbf {K} _ {\\mathbf {y}}) - \\frac {1}{2 \\sigma^ {2}} \\operatorname {t r} \\left(\\mathbf {P K} _ {\\mathbf {f} | \\mathbf {f} _ {m}}\\right) + \\text {c o n s t .} \\leq \\mathcal {L}, \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.891, + 0.658 + ], + "angle": 0, + "content": "where \\(\\mathbf{K_y} = \\sigma^2\\mathbf{P}^{-1} + \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{mn}\\). To set the optimized hyperparameters \\((\\varphi, \\mathbf{X}_m)\\), we seek partial derivatives of \\(\\mathcal{L}_2\\) with respect to them. Thereafter, the standard gradient descent algorithm provides the value that maximizes \\(\\mathcal{L}_2\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.782, + 0.681 + ], + "angle": 0, + "content": "4.5. Stochastic Variational Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.891, + 0.78 + ], + "angle": 0, + "content": "Modern applications often involve handling massive data. However, the GPR equipped with variational inference does not easily scale to big data, even with inducing variables. This is because we need to go through the entire training data at each coordinate update. As the training data size grows, the computational overhead becomes larger." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "An alternative to coordinate ascent is to use SVI [20], which is similar to stochastic gradient descent (SGD), that performs stochastic optimization from the noisy but cheap-to-compute estimates of the gradient. It iterates between subsampling a subset of data and adjusting the hidden structure solely based on the subset. Thus, SVI is much more efficient than conventional variational inference. To apply SVI to the probabilistic model, a set of global variables is" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21953" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "needed [18]. In our robust GPR setting, the inducing variables \\(\\mathbf{f}_m\\) and mixing coefficient variable \\(\\gamma\\) fill this role." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.473, + 0.334 + ], + "angle": 0, + "content": "Natural Gradient. In gradient-based optimization, the natural gradient accounts for the geometric structure of probability parameters and is used in SVI to replace the Euclidean gradient. In exponential families, it is given by premultiplying the usual gradient by the inverse Fisher information matrix \\( G(\\eta)^{-1} \\), where \\( \\eta \\) is the canonical parameter of the exponential families. Since both \\( \\phi(\\mathbf{f}_m) \\) and \\( q(\\gamma) \\) are exponential family distributions, they enjoy simple natural gradients [19] of the bound (11) such that \\( g(\\eta) = \\mathbb{E}[\\eta] - \\eta \\), where \\( g(\\cdot) \\) denotes the natural gradient. For Gaussian distribution \\( \\phi(\\mathbf{f}_m) \\), its canonical parameter is \\( [\\mathbf{A}_m^{-1}\\boldsymbol{\\mu}_m, -\\frac{1}{2}\\mathbf{A}_m^{-1}] \\). For Beta distribution \\( q(\\gamma) \\), its canonical parameter is \\( [B_a + \\hat{n}, B_b + n - \\hat{n}] \\). Thereafter, we obtain the update rule using natural gradient with a step size \\( \\epsilon_t \\)" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.343, + 0.47, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\eta} ^ {t} = \\boldsymbol {\\eta} ^ {t - 1} + \\varepsilon_ {t} g (\\boldsymbol {\\eta} ^ {t - 1}) = (1 - \\varepsilon_ {t}) \\boldsymbol {\\eta} ^ {t - 1} + \\varepsilon_ {t} \\mathbb {E} [ \\boldsymbol {\\eta} ]. \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.373, + 0.47, + 0.433 + ], + "angle": 0, + "content": "Note that when the step size \\(\\varepsilon_{t} = 1\\), we recover the original variational update in Eq. (14) and Eq. (16). Now, the noisy natural gradient can be easily computed by sampling either individual or mini-batch of the data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.442, + 0.266, + 0.459 + ], + "angle": 0, + "content": "4.6. Making Predictions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.512 + ], + "angle": 0, + "content": "So far we have described how to infer the approximate posterior of the latent variables. To make predictions, we use the predictive distribution similar to Eq. (3):" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.512, + 0.469, + 0.562 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p \\left(\\mathbf {f} _ {*} \\mid \\mathcal {D}, \\mathbf {X} _ {*}\\right) = \\int p \\left(\\mathbf {f} _ {*} \\mid \\mathbf {f} _ {m}\\right) p \\left(\\mathbf {f} \\mid \\mathbf {f} _ {m}\\right) \\phi \\left(\\mathbf {f} _ {m}\\right) d \\mathbf {f} _ {m} d \\mathbf {f} \\tag {23} \\\\ = \\mathcal {N} \\left(\\mathbf {f} _ {*} | \\mathbf {K} _ {* m} \\mathbf {K} _ {m m} ^ {- 1} \\boldsymbol {\\mu} _ {m}, \\mathbf {K} _ {\\mathbf {f} _ {*} | \\mathbf {f} _ {m}} + \\mathbf {K} _ {* m} \\boldsymbol {\\Sigma} \\mathbf {K} _ {m *}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.573, + 0.354, + 0.59 + ], + "angle": 0, + "content": "where \\(\\mathbf{K}_{\\mathbf{f}_{*}|\\mathbf{f}_{m}} = \\mathbf{K}_{**} - \\mathbf{K}_{*m}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{m*}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.208, + 0.619 + ], + "angle": 0, + "content": "5. Applications" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.673 + ], + "angle": 0, + "content": "In this section, we describe how to use the proposed GPR model to deal with real-world tasks, including feature matching and dense gene expression imputation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.252, + 0.699 + ], + "angle": 0, + "content": "5.1. Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Feature matching aims at establishing reliable feature point correspondences. To solve the matching problem in a regression manner, we first construct a putative correspondence set \\(\\mathcal{P} = \\{(\\mathbf{x}_i,\\mathbf{x}_i')\\}_{i = 1}^n\\) by nearest neighbor (NN) matching, where \\(\\mathbf{x}_i\\) and \\(\\mathbf{x}_i'\\) represent the coordinates of feature points. The putative set is then converted to motion vector set, i.e., \\(\\mathcal{D} = \\{(\\mathbf{x}_i,\\mathbf{y}_i)\\}_{i = 1}^n\\), where \\(\\mathbf{y}_i = \\mathbf{x}_i' - \\mathbf{x}_i\\). The motion of an object projected on the image plane is known to be slow-and-smooth [38], which is well described by GP. Thus, the motion vectors of inliers can be seen as sampling on the underlying model \\(\\mathbf{f}\\), while the outliers are spuriously distributed. Our goal is to determine the correctness of each data. The task, however, is non-trivial as there are often" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "massive outliers (even up to \\(90\\%\\)). Moreover, the feature points in each image can reach several thousands, which requires high computational efficiency. As we will see, our model is robust and fast enough to handle such cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.893, + 0.333 + ], + "angle": 0, + "content": "Inference Setting. To apply our model to feature matching, some special considerations need to be set. The feature coordinates are first normalized. For the covariance kernel, we choose the squared exponential (SE) kernel \\( k(\\mathbf{x},\\mathbf{x}^{\\prime}) = \\lambda^{-1}\\exp (-\\beta \\| \\mathbf{x} - \\mathbf{x}^{\\prime}\\|^{2}) \\). We find that fixed hyperparameters work well for most situations, which are empirically set to \\( \\lambda = 4 \\) and \\( \\beta = 0.1 \\). The positions of the inducing variables are randomly selected from the training data and kept fixed during inference. The ratio information is also considered as a prior. The mini-batch size is set to \\( \\max \\left\\{\\frac{n}{8},200\\right\\} \\). After inference convergences, the \\( i \\)-th data is decided to be inlier if \\( p_i > \\tau \\), where \\( \\tau \\) is a threshold and is set to \\( \\tau = 0.75 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.892, + 0.456 + ], + "angle": 0, + "content": "Predictions. One of the attractive properties of our model for this task is that when the training is completed, the resulting posterior GP is able to predict the motion vector of each feature point. Combined with the descriptors' information, we can yield much more correct correspondences rather than being limited to putative set. More correct correspondences are crucial for downstream tasks, as they can significantly improve the accuracy." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.462, + 0.808, + 0.479 + ], + "angle": 0, + "content": "5.2. Dense Gene Expression Imputation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Recently, technological advances have made it possible to measure spatially resolved transcriptome-wide mRNA expressions with spatial information in tissue samples. GPR is thus utilized to infer gene expression in discrete samples, generating dense gene expression in 2D, 3D, and even spatiotemporal [3]. Unfortunately, due to equipment malfunctions and process disturbances, the readout data may contain bad spots. In this case, a vanilla GPR may lead to completely wrong results and thus mislead the subsequent analysis. By comparison, the robust GPR developed in this paper copes well with outliers and is able to give meaningful imputation results. For this application, the implementation is simple and requires little extra consideration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.634, + 0.71 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.84 + ], + "angle": 0, + "content": "In this section, we first conduct numerical experiments to evaluate the performance in a fully controlled environment. After that, we apply our model to tackle feature matching problem and compare it with many state-of-the-art methods tailored for feature matching. In the end, the evaluation of gene expression imputation is performed. All experiments are conducted on a desktop with Intel i7-10700 CPU, 16 GB memory with MATLAB except deep learning methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.72, + 0.864 + ], + "angle": 0, + "content": "6.1. Numerical Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We study two datasets, i.e., Neal dataset [28] and Friedman dataset [14]. The Neal dataset is one-dimensional data," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21954" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.445, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.47, + 0.338 + ], + "angle": 0, + "content": "Figure 2. Visual examples on Neal data. Our model approximates the exact posterior GP using only inliers, even with massive outliers. The legend is shown in the bottom." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.469, + 0.38 + ], + "angle": 0, + "content": "where the input \\( x \\) is drawn from a uniform distribution within \\([-2.5, 2.5]\\). The target value is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.382, + 0.445, + 0.398 + ], + "angle": 0, + "content": "\\[\nf (x) = 0. 3 + 0. 4 x + 0. 5 \\sin (2. 7 x) + 1. 1 / \\left(1 + x ^ {2}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.469, + 0.473 + ], + "angle": 0, + "content": "The Gaussian noise is added to the target value with zero mean and variance of 0.1. Next, outliers are injected into the training data, where the value is drawn from uniform distribution within \\([-5, 5]\\). The Friedman is 10-dimensional data and the function value depends on the first five dimensions" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.474, + 0.457, + 0.491 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {x}) = 1 0 \\sin \\left(\\pi x _ {1} x _ {2}\\right) + 2 0 \\left(x _ {3} - 0. 5\\right) ^ {2} + 1 0 x _ {4} + 5 x _ {5},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.551 + ], + "angle": 0, + "content": "while the remaining dimensions complicate the task by adding a feature selection process. The input \\(\\mathbf{x}\\) is sampled uniformly within \\([0,1]^{10}\\). Gaussian noise \\(\\mathcal{N}(0,0.01)\\) is added and random outliers are distributed among [5, 25]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.469, + 0.717 + ], + "angle": 0, + "content": "We fix the inlier number to 100 and change the outlier ratio. GPR with Student's-\\(t\\) (St) [32], Laplace (Lap) [32], and Gaussian mixture distribution (MEM) [8], as well as variational free energy (VEF) [37], are chosen as competitors. Some intuitive examples on Neal data are shown in Fig. 2, where outlier ratio increases from 0 to \\(80\\%\\). We see that the prediction by our model almost exactly reproduces the full GP prediction using only inliers. In contrast, GPR-St and -Lap give poor approximations. GPR-MEM is able to give a better answer, yet still not as good as ours, especially at extremely high outlier ratios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.839 + ], + "angle": 0, + "content": "To statistically verify performance, we select mean absolute error (MAE, m), root mean square error (RMSE, r), and negative log of predictive probability (NLP, n) as metrics. 1000 testing points are generated in equal intervals. The statistical results on Neal and Friedman in Table 1 suggest that our method outperforms other alternatives in terms of robustness and accuracy. More results including KL and statistical variance are provided in suppl. material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.251, + 0.864 + ], + "angle": 0, + "content": "6.2. Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.9 + ], + "angle": 0, + "content": "We collect three large and diverse feature matching datasets with three different vision tasks, say YFCC100M" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 1. Quantitative results on Neal and Friedman data with different outlier ratios. Bold indicates the best." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.12, + 0.892, + 0.284 + ], + "angle": 0, + "content": "
Neal [28]
Method10%50%80%
mrnmrnmrn
GPR-VFE [37]0.180.210.730.580.771.750.761.081.96
GPR-St [32]0.030.03-0.410.090.190.390.771.151.66
GPR-Lap [32]0.030.07-1.170.420.561.620.350.722.03
GPR-MEM [8]0.040.08-1.360.060.12-0.660.771.522.04
Ours0.010.02-1.380.030.04-1.250.030.03-0.89
Friedman [14]
Method20%30%50%
mrnmrnmrn
GPR-VFE [37]1.121.242.281.471.623.082.883.166.93
GPR-St [32]0.040.04-0.080.911.103.591.472.187.16
GPR-Lap [32]0.230.290.370.460.610.942.032.233.29
GPR-MEM [8]0.110.21-0.990.130.24-0.662.132.322.98
Ours0.040.06-1.460.060.08-0.350.100.140.55
" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.296, + 0.885, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.482, + 0.892, + 0.523 + ], + "angle": 0, + "content": "Figure 3. Qualitative illustration of relative pose estimation. We show the true positive in blue and false positive in red. Best viewed in color with \\(200\\%\\) zoom in." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.541, + 0.892, + 0.784 + ], + "angle": 0, + "content": "dataset [36] (4000 pairs) for relative pose estimation, CPC dataset [42] (1000 pairs) for fundamental matrix estimation, and HPatches dataset [1] (580 pairs) for homography estimation. Six state-of-the-arts from handcrafted to deep learning are chosen for comparison, namely, MAGSAC++ [2], LPM [26], MCDM [25], CRC [12], PointCN [43], and OANet [44], with baseline ratio test. Briefly, MAGSAC++ is resampling-based method, LPM is a heuristic method that preserves local structure of feature points, CRC interpolates a smooth vector field using Fourier bases, PointCN uses deep neural networks with context normalization to encode global contextual information, OANet further captures local contextual information by clustering unordered correspondences. Note that we assess currently other robust GPR methods are not capable to handle the feature matching problem, thus none of them are chosen for comparison." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.727, + 0.815 + ], + "angle": 0, + "content": "6.2.1 Relative Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Following [44], Yahoo's YFCC100M dataset [36] generates 4000 testing image pairs. SIFT [24] with NN matching is adopted to establish putative correspondences. The maximum number of keypoints for each image is limited to 4000. RANSAC [13] is used to estimate the relative camera pose." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21955" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.468, + 0.117 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison for relative pose estimation. Bold indicates the best and underline ranks the second." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.12, + 0.429, + 0.26 + ], + "angle": 0, + "content": "
YFCC100M [36]
MethodAUCPRF
@5°@10°@20°
Ratio test28.839.252.124.355.332.8
MSC++ [2]24.933.745.724.355.332.8
PointCN [43]45.154.665.047.273.454.9
OANet [44]53.664.175.851.287.061.7
LPM [26]38.648.859.751.443.645.9
MCDM [25]47.859.470.763.046.552.7
CRC [12]38.148.258.641.257.844.5
Ours53.863.773.885.354.063.7
" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.269, + 0.457, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Figure 4. Visual examples of homography and fundamental matrix estimation. We show the true positive in blue and false positive in red. Best viewed in color with \\(200\\%\\) zoom in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.468, + 0.586 + ], + "angle": 0, + "content": "We measure the maximum of rotation and translation errors in degree and report the approximate Area Under the Curve (AUC) with thresholds 5, 10, and 20 degrees. Precision, recall, and F1-score before RANSAC with respect to the ground-truth inliers are also presented. See suppl. material for a detailed description of the dataset and the metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.468, + 0.707 + ], + "angle": 0, + "content": "Some visualized examples are demonstrated in Fig. 3. Statistics results are comprehensively reported in Table 2. Since deep learning methods such as PointCN and OANet are trained in such dataset with geometric loss, they can capture geometric information and therefore have higher AUC compared to other handcrafted methods. By comparison, our method achieves comparable results to these deep learning methods with much higher precision and F1-score." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.468, + 0.741 + ], + "angle": 0, + "content": "6.2.2 Homography & Fundamental Matrix Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Homography and fundamental matrix estimation are critical parts in computer vision. The maximum keypoints for HPatches and CPC are limited to 4000. For evaluation metrics, we choose the precision, recall, and F1-score as well as the accuracy of the estimation. For homography estimation, we adopt homography error defined in [11], and for fundamental matrix, we follow [4] and use normalized symmetric geometry distance (NSGD) as the metrics. An estimate is classified as accurate or not by a threshold, which is set to 4 pixels for homography error and 0.05 for the NSGD [4]." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 3. Statistical results for homography and fundamental matrix estimation. Bold ranks the first, underline the second." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.117, + 0.892, + 0.256 + ], + "angle": 0, + "content": "
MethodHPatches [1]CPC [42]
Acc.PRFAcc.PRF
Ratio test71.771.651.663.017.012.763.920.5
MSC++ [2]74.487.392.486.06.919.729.619.4
PointCN [43]73.176.985.778.629.319.870.228.8
OANet [44]70.073.577.272.147.034.681.045.4
LPM [26]60.672.550.552.323.821.948.926.1
MCDM [25]77.762.991.073.034.823.061.032.5
CRC [12]71.775.592.580.428.724.847.230.4
Ours78.189.994.391.549.661.559.357.2
Ours*82.473.9109.6-51.939.297.3-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.502, + 0.267, + 0.89, + 0.28 + ], + "angle": 0, + "content": "Table 4. Ablation studies on feature matching. Bold is the best." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.281, + 0.871, + 0.38 + ], + "angle": 0, + "content": "
MethodPrec.RecallF1Time
CRC [12]50.767.854.968.1
OANet (on GPU) [44]47.975.256.041.2
RS-GPRNo SVI76.366.170.047.1
No inducing variables72.669.069.51.6e5
Opt. Hyperparameters85.061.267.71556
EM optimization67.669.865.543.7
Default88.068.275.69.8
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Several visual examples are provided in Fig. 4. Note that our predictive model is also presented and indicated by the superscript \\({}^{*}\\ast\\). It establishes significantly more correct correspondences compared to other methods. Table 3 reports the statistical results. As it indicates, our method outperforms all other methods in the two tasks. When using the predictive model, it can even produce more correct correspondences than the putative set (e.g., the recall in HPatches is higher than 100), thus further improving accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.555, + 0.816, + 0.57 + ], + "angle": 0, + "content": "6.2.3 Ablation Studies of Feature Matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.892, + 0.73 + ], + "angle": 0, + "content": "To measure performance, especially runtime, in different settings, we conduct ablation studies on 100 image pairs from YFCC100M. It mainly includes four choices, i.e., not using SVI, not using inducing variables, optimizing the kernel hyperparameters, and using EM optimization instead of variational inference. We also include the CRC and OANet to compare the runtime. The results are reported in Table 4, where we see that our method performs the best with the default setting described in Sect. 5.1. In particular, the running time is much faster compared to other settings and methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.806, + 0.757 + ], + "angle": 0, + "content": "6.3. Dense Gene Expression Imputation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We collect two spatial transcriptomics datasets from mouse olfactory bulb and human breast cancer biopsies [34], respectively. Briefly, the spatial transcriptomics gene expression data is measured from thin tissue sections placed on an array with ploy probes and spatially resolved DNA barcodes. These create a grid of circular spots where the mRNA abundance of each spot is measured using probes with the barcodes encoding the spatial locations. The mouse olfactory bulb and human breast cancer biopsies datasets" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21956" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.091, + 0.272, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.091, + 0.464, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.203, + 0.47, + 0.273 + ], + "angle": 0, + "content": "Figure 5. Visualization of dense spatial gene expression imputation. The spatial transcriptomics data is plotted on the top row. The bottom row shows the imputation results of different methods. We stack the spatial transcriptomics (shown as dots) on the imputed results to show the quality of the imputation." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.282, + 0.468, + 0.309 + ], + "angle": 0, + "content": "Table 5. Statistical results of dense gene expression imputation. Bold indicates the best." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.313, + 0.43, + 0.486 + ], + "angle": 0, + "content": "
Mouse olfactory bulb
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.460.591.250.330.401.10
GPR-St [32]0.070.14-0.570.020.04-1.33
GPR-Lap [32]0.200.270.330.480.540.94
Ours0.030.05-1.990.020.04-2.21
Breast cancer tissue
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.240.351.440.230.331.15
GPR-St [32]0.190.320.370.180.300.22
GPR-Lap [32]0.250.360.560.250.370.53
Ours0.120.16-0.540.110.17-0.39
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.469, + 0.59 + ], + "angle": 0, + "content": "contain 14859 and 12856 measured genes, respectively. To identify spatially variable genes, we adopt SpatialDE [35] and select two patterns for each dataset. We next add 5 random outliers to each identified pattern to simulate the outlier scenario. In the end, different GPR methods are applied to impute dense spatial gene expression." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.469, + 0.727 + ], + "angle": 0, + "content": "Two visual examples are presented in Fig. 5, where in each example, the second row shows the imputed results. As can be seen, our method accurately infers the correct gene expression regardless of the outliers. To give quantitative results, we randomly split each dataset into \\(80\\%\\) training data and \\(20\\%\\) test data. As mentioned above, we use the MAE, RMSE, and NLP to measure the performance, and report the statistical results in Table 5. We see that our method always has the lowest error." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.173, + 0.758 + ], + "angle": 0, + "content": "7. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.869 + ], + "angle": 0, + "content": "Optimization Process. We visualize the intermediate results of the optimization process on Neal data with \\(50\\%\\) outliers and present it in the top row of Fig. 6. We see that the field of \\(p\\) in Eq. (19) gradually converges to the inliers. After convergence, the posterior mean and variance functions are very close to the ground truth, and the inducing variables are restricted to the interval of the inliers." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The Role of Term \\(\\mathbf{A}_{ii}\\). We remove the term containing \\(\\mathbf{A}_{ii}\\) in Eq. (15) and show the results in the bottom of Fig. 6." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.091, + 0.888, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.206, + 0.892, + 0.262 + ], + "angle": 0, + "content": "Figure 6. Intermediate results of the optimization process. The top row shows the full model while the bottom removes term \\(\\mathbf{A}_{ii}\\). We visualize the field of \\(p\\), which indicates the inlier probability at any location. The deeper the blue color, the higher the probability." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.272, + 0.868, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.502, + 0.338, + 0.89, + 0.352 + ], + "angle": 0, + "content": "Figure 7. Our model deal with different non-uniform outliers." + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.36, + 0.843, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.44, + 0.892, + 0.467 + ], + "angle": 0, + "content": "Figure 8. The inference time of each GPR method. Our model with SVI can easily handle big data." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.485, + 0.854, + 0.499 + ], + "angle": 0, + "content": "Without variance term, the regression tends to overfit." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.891, + 0.59 + ], + "angle": 0, + "content": "Non-uniform Outliers. Different types of non-uniform outliers are tested in Fig. 7. More detailed results are given in suppl. material. Our model exhibits strong generalization and robustness. The reason is that uniform distribution is a very weak assumption with high flexibility. It accommodates many outlier distributions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.681 + ], + "angle": 0, + "content": "**Scalability.** We test the runtime towards different problem sizes on Neal data with \\(50\\%\\) outliers. Other methods as well as ours w. and w/o. SVI are included. The number of inducing variables is set to 15 for our method in both two settings. As plotted in Fig. 8, our method can easily scale to large-scale data, especially when equipped with SVI." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.695, + 0.619, + 0.71 + ], + "angle": 0, + "content": "8. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This paper presents a robust and scalable GPR using variational learning. It uses an outlier robust mixture likelihood model, where the uniform distribution accounts for the outliers. A variational formulation is introduced to learn the mode of data and hyperparameters by minimizing the KL divergence between the true posterior distribution and the approximate one. Its most attractive property is that it can rigorously approximate the exact posterior. Inducing variable approximation and SVI further extend our model to big data. We apply our model to feature matching and dense gene expression imputation. Extensive results show the significant improvement over existing robust GPRs." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21957" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. 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This enables the application of Gaussian processes to a wide range of real data, which are often large-scale and contaminated by outliers. Towards this end, we employ a mixture likelihood model where outliers are assumed to be sampled from a uniform distribution. We next derive a variational formulation that jointly infers the mode of data, i.e., inlier or outlier, as well as hyperparameters by maximizing a lower bound of the true log marginal likelihood. Compared to previous robust GPR, our formulation approximates the exact posterior distribution. The inducing variable approximation and stochastic variational inference are further introduced to our variational framework, extending our model to large-scale data. We apply our model to two challenging real-world applications, namely feature matching and dense gene expression imputation. Extensive experiments demonstrate the superiority of our model in terms of robustness and speed. Notably, when matching 4k feature points, its inference is completed in milliseconds with almost no false matches. The code is at github.com/YifanLu2000/Robust-Scalable-GPR. + +# 1. Introduction + +Gaussian processes (GPs) [31] are probably the primary non-parametric method for inference on latent functions. They have a wide range of applications from biology [3] to computer vision [41]. A commonly used observation model for Gaussian process regression (GPR) is the Normal distribution, which brings great convenience to the inference. Unfortunately, a well-known limitation of the Gaussian observation model is its sensitivity to outliers in data. As illustrated in Fig. 1 (b), a few outliers can drastically destroy the entire posterior regression result. This hinders the real-world applications of GPR for many domains, where outliers are often inevitable. This paper intends to conquer the GPR with outlier contaminated data. + +The idea of robust regression is not new. Outlier detec + +![](images/422eeaa15b9fa07532c6070ace79536295c679cfce8350a007917cc3996bfd1c.jpg) + +![](images/ba4e85d82fd04d290f99c63a1570bd1cf7083263db456c972362c9aedd7729cc.jpg) + +![](images/13370d06014ebd7bdf4c720c3cb41b4eaa3dfb96ed42358fecb539782426169d.jpg) + +![](images/bab8f13f8194b03b38e708713d7d3fc42c3a0268df8001011ea10a883e557ea2.jpg) +Figure 1. Regression with our model. (a) Perform exact GPR from 100 inliers. (b) When there are only 6 outliers in the data, the exact GPR leads to completely wrong results. (c) By comparison, our model is able to recover the exact posterior even facing 100 outliers. (d) The feature matching result using our model. (e) The dense spatial gene expression imputation result using our model. + +![](images/67dc0e22054a7d3fbba3e5c8064ce53ee21035d388c5175cb432719fd82e7b0e.jpg) + +tion has been extensively and systematically described in [6,9,10,29]. In the context of GPR, many efforts tried to replace the Gaussian likelihood with other distributions showing heavy-tail behaviors, including Student- $t$ [16,21,28,30], Laplace [22, 30], Gaussian mixture [8, 22, 27], and data-dependent noise model [17]. The challenge with these non-Gaussian likelihoods lies in the inference, which is analytically intractable. To this end, many approximation schemes have been applied, despite having high computational complexity, e.g., Markov Chain Monte Carlo (MCMC) sampling and Expectation Propagation (EP) [22]. + +In this paper, we propose a more effective mixture likelihood model, where uniform distribution accounts for the outliers and Gaussian for inliers. In our formulation, the outliers are independent of the GP and do not affect the computation of the posterior GP, thereby allowing to tolerate more outliers. We next introduce a variational method that jointly determines the modes of data (i.e., inlier or outlier) as well as hyperparameters by maximizing a lower bound to the marginal likelihood. We highlight that the difference between our variational formulation and pervious methods is that the modes of data now become variational parameters and are obtained by minimizing the Kullback- + +Leibler (KL) divergence between the variational and the true posterior distribution. Thus, the proposed formulation is less likely to overfit and is able to approximate the exact posterior GP only from inliers, as in Fig. 1 (c). + +Inspired by [37], the sparse inducing variable approximation is integrated into our variational framework, which retains the exact GP prior but performs posterior approximation, and reduces the time complexity from $\mathcal{O}(n^3)$ to $\mathcal{O}(nm^2)$ . By treating the inducing variables as global variables [18], our variational model enjoys the acceleration by Stochastic Variational Inference (SVI) [20]. It performs stochastic optimization from natural gradient and further decreases the time complexity to $\mathcal{O}(km^2)$ . This provides a guarantee for our model to scale to large-scale data. + +We apply our robust GPR model to two real-world applications, say feature matching and dense spatial gene expression imputation, as illustrated in the Figs. 1 (d) and (e). Extensive experiments demonstrate the superiority of our method on both numerical data and real applications. + +To summarize, our contributions include the following. (i) We present a robust Gaussian process regression model, which uses variational learning to approximate the true exact posterior. (ii) We leverage inducing variables and SVI to adapt our model to large-scale data. (iii) Two applications of our model are described. Extensive experimental validation demonstrates the superiority of our model. + +# 2. Related Works + +Robust GPR typically employs non-Gaussian likelihood with heavy tails. Representatively, [22] investigated the Student's- $t$ noise model. They further developed variational inference and MCMC for GPR with Student's- $t$ . In [39], Laplace approximation was used to approximate the log marginal likelihood of Student's- $t$ . The Laplace noise model is also exploited in [22]. [30] introduced Expectation Maximization (EM) algorithm for Student's- $t$ and Laplace. Recently, [8] used mixtures of two Gaussians assuming a lower variance for regular noise and a higher one for outliers, with EM to learn the hyperparameters. In this work, we also use a non-Gaussian likelihood, i.e., mixture model. The difference is that here the outliers are considered to follow a uniform distribution, which is a more reasonable assumption since the sampling distribution of outliers should be independent of the true latent function. Besides, we derive a variational formulation in the GPR setting, which approximates the posterior distribution. + +Scalable GPR improves the scalability of GPR while maintaining prediction quality for big data. The seminal work [40] adopted Nyström approximation to approximate the kernel matrix using $m$ sparse points. Later, the idea was further promoted by [7, 15, 23, 33], which approximated the prior and performed exact inference. Unlike the prior approximations, the other line is the posterior approximations, + +which retain the exact prior but perform approximate inference. The most well-known work is the elegant variational free energy [37]. It directly approximates the posterior by using variational inference. With the advances in variational inference [20], SVI is introduced to GP [18], which uses natural gradients and results in remarkable computational efficiency. However, as the exact GPR, these scalable GPRs are sensitive to outliers. In contrast, our model can tolerate massive outliers while retaining highly scalability. + +# 3. Gaussian Process Regression Revisited + +Gaussian process is a collection of random variables, for which any finite subset has a joint Gaussian distribution [31]. It is completely specified by a mean function $m(\mathbf{x})$ and a covariance function $k(\mathbf{x},\mathbf{x}^{\prime})$ where the covariance function typically depends on a set of hyperparameters $\varphi$ . The GP is usually used as a prior over latent function $f(\mathbf{x})\sim \mathcal{GP}(m,k)$ . We can combine the GP prior with observed data to give a posterior over desired latent function. + +Consider a regression problem, where the training data is $\mathcal{D} = \{(\mathbf{x}_i,y_i)\}_{i = 1}^n$ . Each $y_{i}$ is a noisy realization of the latent function at location $\mathbf{x}_i$ such that $y_{i} = f_{i} + \epsilon_{i}$ , where $\epsilon_{i}\sim \mathcal{N}(\epsilon_{i}|0,\sigma^{2})$ is typically assumed to be an i.i.d. Gaussian noise and $f_{i} = f(\mathbf{x}_{i})$ . Denoting all training inputs as $\mathbf{X}$ , all training outputs $\mathbf{y}$ , and all latent function values at $\mathbf{X}$ as $\mathbf{f}$ . Placing a GP prior on the latent function $f$ , we obtain + +$$ +p (\mathbf {f} | \mathbf {X}, \varphi) \sim \mathcal {N} (\mathbf {f} | m (\mathbf {X}), \mathbf {K} _ {n n}), \tag {1} +$$ + +where $\mathbf{K}_{nn}$ is the covariance function evaluated between all the training points. For simplicity of exposition, the mean function is set to zero $m(\mathbf{x}) = 0$ . It does not reduce the generalizability of the GP as long as the problem is correctly transformed, e.g., by subtracting the mean of $\mathbf{y}$ . One can induce a posterior distribution on $\mathbf{f}$ according to Bayes' rule + +$$ +p (\mathbf {f} | \mathcal {D}, \sigma^ {2}, \varphi) \sim \mathcal {N} (\mathbf {f} | \mathbf {K} _ {n n} (\mathbf {K} _ {n n} ^ {\epsilon}) ^ {- 1} \mathbf {y}, \boldsymbol {\Sigma}), \tag {2} +$$ + +which is also a multivariate normal distribution, where $\mathbf{K}_{nn}^{\epsilon} = \mathbf{K}_{nn} + \sigma^{2}\mathbf{I}$ and $\boldsymbol {\Sigma} = (\mathbf{K}_{nn}^{-1} + \sigma^{-2}\mathbf{I})^{-1}$ . The posterior distribution of $\mathbf{f}$ can help to compute the posterior predictive distribution of $\mathbf{f}_*$ at any test location $\mathbf{X}_{*}$ : + +$$ +\begin{array}{l} p \left(\mathbf {f} _ {*} \mid \mathcal {D}, \mathbf {X} _ {*}\right) = \int p \left(\mathbf {f} _ {*} \mid \mathbf {f}, \mathbf {X} _ {*}\right) p (\mathbf {f} \mid \mathcal {D}) d \mathbf {f} \tag {3} \\ = \mathcal {N} \left(\mathbf {f} _ {*} | \mathbf {K} _ {* n} \left(\mathbf {K} _ {n n} ^ {\epsilon}\right) ^ {- 1} \mathbf {y}, \mathbf {K} _ {* *} - \mathbf {K} _ {* n} \left(\mathbf {K} _ {n n} ^ {\epsilon}\right) ^ {- 1} \mathbf {K} _ {n *}\right), \\ \end{array} +$$ + +where, $\sigma^2$ and $\varphi$ are omitted for brevity. The above posterior depends on the values of $\sigma^2$ and $\varphi$ , which can be inferred by maximizing the log marginal likelihood: + +$$ +\log p (\mathbf {y} \mid \sigma^ {2}, \varphi) = \log \mathcal {N} (\mathbf {y} \mid \mathbf {0}, \mathbf {K} _ {n n} ^ {\epsilon}), \tag {4} +$$ + +which automatically achieves the bias-variance trade-off. + +# 4. Robust Gaussian Process Regression Model + +In real-world scenarios, a huge discrepancy between the model and data-generating process often occurs, leading to outliers. However, a critical flaw of Gaussian observation model is its non-robustness. This poses a great challenge to GPR in practice. To this end, this section introduces a robust GPR, which identifies the mode of data and simultaneously approximates the posterior of the desired model. + +# 4.1. Problem Formulation + +We explicitly consider the generation process of outliers. Since outliers are independent of the latent function, a reasonable assumption is that they obey a uniform distribution $\frac{1}{a}$ , where the output space is a bounded region that covers the output $\mathbf{y}$ and $a$ is a constant denoting the volume of the region. The inliers follow a regular Gaussian noise $\mathcal{N}(y_i|f_i,\sigma^2)$ . We then associate each data with a latent variable $z_{i} \in \{0,1\}$ , where $z_{i} = 0$ indicates that the observation is generated by outlier distribution and $z_{i} = 1$ inlier. The joint distribution of $(y_{i},z_{i})$ is then a mixture of two models: + +$$ +p \left(y _ {i}, z _ {i} \mid f _ {i}, \boldsymbol {\theta}\right) = \left\{\left(1 - \gamma\right) \frac {1}{a} \right\} ^ {1 - z _ {i}} \left\{\gamma \mathcal {N} \left(y _ {i} \mid f _ {i}, \sigma^ {2}\right) \right\} ^ {z _ {i}}, \tag {5} +$$ + +where $\theta = (\sigma^2, \gamma, \varphi)$ denotes the latent variables set and $\gamma = p(z_i = 1)$ is the mixing coefficient. + +Prior distributions describe beliefs about the model variables before the inference. As a robust GPR problem, we place a GP prior over the latent function, i.e., Eq. (1). The variable $\gamma$ controls the probability of occurrence of two models. We suppose it follows a Beta distribution + +$$ +p (\gamma) \sim \operatorname {B e t a} (\gamma | B _ {a}, B _ {b}), \tag {6} +$$ + +where $B_{a}$ and $B_{b}$ are hyperparameters. As we will see, $p(\gamma)$ is conjugate to the posterior and hence easier to handle. For other variables $(\sigma^2,\varphi)$ , we introduce noninformative prior. + +Full joint distribution is obtained by incorporating the above prior distributions as follows: + +$$ +p (\mathcal {D}, \mathbf {f}, \boldsymbol {\theta}) \propto p (\mathbf {f} | \mathbf {X}) p (\gamma) \prod_ {i = 1} ^ {n} p \left(y _ {i}, z _ {i} \mid f _ {i}, \sigma^ {2}, \gamma\right), \tag {7} +$$ + +where $\pmb{\theta} = (\sigma^2, \gamma, \mathbf{Z}, \varphi)$ and $\mathbf{Z} \in \{0,1\}^n$ is the indicator variable vector. Our goal is to obtain the posterior $p(\mathbf{f}, \pmb{\theta}|\mathcal{D})$ , which can be induced from $p(\mathcal{D}, \mathbf{f}, \pmb{\theta})$ . Nevertheless, as there are two possibilities for each observation, i.e., inlier and outlier, it will generate $2^n$ combinations to be evaluated. Thus, the exact estimation is analytically intractable and approximation is needed. Next, we use the variational inference to approximate the exact posterior. Once the variational distribution is obtained, the posterior predictive distribution can be determined. + +# 4.2. Variational Inference + +We wish to directly approximate the posterior $p(\mathbf{f},\boldsymbol {\theta}|\mathcal{D})$ using a variational posterior $q(\mathbf{f},\boldsymbol {\theta})$ such that the KL divergence between $p(\mathbf{f},\boldsymbol {\theta}|\mathcal{D})$ and $q(\mathbf{f},\boldsymbol {\theta})$ is minimized. The minimization is equivalently expressed as maximization of lower bound for the true log marginal likelihood: + +$$ +\mathcal {L} (\mathbf {f}, \boldsymbol {\theta}) = \int q (\mathbf {f}, \boldsymbol {\theta}) \log \left(\frac {p (\mathbf {f} , \boldsymbol {\theta} , \mathcal {D})}{q (\mathbf {f} , \boldsymbol {\theta})}\right) d \mathbf {f} d \boldsymbol {\theta}. \tag {8} +$$ + +The maximization is, however, intractable since the optimal solution is $\hat{q} (\mathbf{f},\pmb {\theta}) = p(\mathbf{f},\pmb {\theta}|\mathcal{D})$ . To this end, we consider instead a restricted distribution of $q(\mathbf{f},\pmb {\theta})$ + +Mean-field factorization supposes $q(\mathbf{f},\pmb {\theta})$ can be partitioned into disjoint groups. Considering the ease of calculation, we factorize $q(\mathbf{f},\pmb {\theta}) = q_{1}(\mathbf{f})q_{2}(\gamma)q_{3}(\mathbf{Z})q_{4}(\sigma^{2},\pmb {\varphi})$ . Besides, we assume $q_{4}$ is Dirac delta function, i.e., it has a point mass at $(\sigma^2,\varphi)$ . With this factorization, the maximization of Eq. (8) is obtained by optimizing each of the factors. For $q_{i}$ , the minimization becomes + +$$ +\hat {q} _ {i} = \underset {q _ {i}} {\arg \min } \int q _ {i} \log \left(\frac {\exp \mathbb {E} _ {j \neq i} [ \log p (\mathbf {f} , \boldsymbol {\theta} , \mathcal {D}) ]}{q _ {i}}\right) d \boldsymbol {\theta} _ {i}, \tag {9} +$$ + +where $\mathbb{E}_{j\neq i}[\cdot ]$ denotes the expectation over $q_{j}$ for $j\neq i$ Note that Eq. (9) is the negative KL divergence between $q_{i}$ and $\mathbb{E}_{j\neq i}\left[\log p(\mathbf{f},\boldsymbol {\theta},\mathcal{D})\right]$ . Thus, the optimal $q_{i}$ is given by + +$$ +\log \hat {q} _ {i} = \mathbb {E} _ {j \neq i} [ \log p (\mathbf {f}, \boldsymbol {\theta}, \mathcal {D}) ] + \text {c o n s t .} \tag {10} +$$ + +# 4.3. Sparse Inducing Variable Approximation + +The variational posterior approximation presented above can easily integrate sparse inducing variables [37], which allows the reduction of time complexity of GPR from $\mathcal{O}(n^3)$ to $\mathcal{O}(nm^2)$ . Introducing $m$ pseudo-inputs $\mathbf{X}_m$ with inducing variables $\mathbf{f}_m$ , our goal is to use $\mathbf{f}_m$ to approximate $q(\mathbf{f})$ , where $\mathbf{f}_m$ akin to $\mathbf{f}$ follows the same GP prior that $p(\mathbf{f}_m) \sim \mathcal{N}(\mathbf{0}, \mathbf{K}_{mm})$ . We suppose $\mathbf{f}_m$ is a sufficient statistic for $\mathbf{f}$ , i.e., for any value $u$ , $p(u|\mathbf{f}, \mathbf{f}_m) = p(u|\mathbf{f}_m)$ holds [37]. In this setting, the augmented variational posterior $q(\mathbf{f}, \mathbf{f}_m) = p(\mathbf{f}|\mathbf{f}_m)\phi(\mathbf{f}_m)$ and augmented latent variables set $\boldsymbol{\theta} = (\gamma, \sigma^2, \mathbf{Z}, \varphi, \mathbf{X}_m)$ with factorization $q(\mathbf{f}, \mathbf{f}_m, \boldsymbol{\theta}) = q_1(\mathbf{f}, \mathbf{f}_m)q_2(\gamma)q_3(\mathbf{Z})q_4(\sigma^2, \varphi, \mathbf{X}_m)$ . The bound (8) becomes + +$$ +\mathcal {L} = \int q (\mathbf {f}, \mathbf {f} _ {m}, \boldsymbol {\theta}) \log \left(\frac {p \left(\mathbf {f} _ {m}\right) p (\gamma) p (\mathbf {y} , \mathbf {Z} \mid \mathbf {f})}{\phi \left(\mathbf {f} _ {m}\right) q _ {2 - 4}}\right) d \mathbf {f} d \mathbf {f} _ {m} d \boldsymbol {\theta}, \tag {11} +$$ + +where the term $p(\mathbf{f}|\mathbf{f}_m)$ inside the log is eliminated. In what follows, we maximize the bound analytically by solving the optimal choice of the variational distribution $q(\mathbf{f},\mathbf{f}_m,\boldsymbol {\theta})$ + +# 4.4. Maximize Lower Bound + +To optimize the bound (11) in mean-field factorization, a common approach is to use the coordinate ascent technique, + +i.e., optimizing one factor $q_{i}$ while keeping the others $q_{j\neq i}$ fixed, and cycling through these factors in turn. Convergence is guaranteed because the bound is convex and monotonically increasing with respect to each factor [5]. Next, we give closed-form expressions for factor updates without detailed derivations, which can be found in suppl. material. + +Updating $q_{1}(\mathbf{f},\mathbf{f}_{m})$ means finding the optimal posterior GP given $q_{2}$ $q_{3}$ , and $q_{4}$ . We denote $p_i = \mathbb{E}[z_i]$ and $\mathbf{P} =$ diag $(p_1,p_2,\dots ,p_n)$ . Integrating over f, (11) becomes + +$$ +\mathcal {L} = \int \phi (\mathbf {f} _ {m}) \log \left(\frac {p \left(\mathbf {f} _ {m}\right) Q \left(\mathbf {f} _ {m} , \mathbf {y}\right)}{\phi \left(\mathbf {f} _ {m}\right)}\right) d \mathbf {f} _ {m} + \text {c o n s t .}, \tag {12} +$$ + +where + +$$ +\log Q \left(\mathbf {f} _ {m}, \mathbf {y}\right) = \log \mathcal {N} \left(\mathbf {y} \mid \boldsymbol {\mu} _ {\mathbf {f} \mid \mathbf {f} _ {m}}, \sigma^ {2} \mathbf {P} ^ {- 1}\right) - \frac {1}{2 \sigma^ {2}} \operatorname {t r} \left(\mathbf {P K} _ {\mathbf {f} \mid \mathbf {f} _ {m}}\right), \tag {13} +$$ + +$\mu_{\mathbf{f}|\mathbf{f}_m} = \mathbf{K}_{nm}\mathbf{K}_{mm}^{-1}\mathbf{f}_m,$ $\mathbf{K}_{\mathbf{f}|\mathbf{f}_m} = \mathbf{K}_{nn} - \mathbf{K}_{nm}\mathbf{K}_{mm}^{-1}\mathbf{K}_{mn}$ are the expectation and covariance of $p(\mathbf{f}|\mathbf{f}_m)$ , respectively. With some linear algebraic manipulation, the optimal $\hat{\phi} (\mathbf{f}_m)$ is given by a multivariate Gaussian distribution + +$$ +\begin{array}{l} \hat {\phi} (\mathbf {f} _ {m}) \propto p (\mathbf {f} _ {m}) Q (\mathbf {f} _ {m}, \mathbf {y}) \tag {14} \\ = \mathcal {N} (\mathbf {f} _ {m} | \boldsymbol {\mu} _ {m}, \mathbf {A} _ {m}), \\ \end{array} +$$ + +where $\pmb{\mu}_{m} = \sigma^{-2}\mathbf{K}_{mm}\pmb{\Sigma}\mathbf{K}_{mn}\mathbf{P}\mathbf{y},\mathbf{A}_{m} = \mathbf{K}_{mm}\pmb{\Sigma}\mathbf{K}_{mm},$ and $\pmb {\Sigma} = (\mathbf{K}_{mm} + \sigma^{-2}\mathbf{K}_{mn}\mathbf{P}\mathbf{K}_{nm})^{-1}$ Note that we can always recover $q(\mathbf{f})$ from $q(\mathbf{f},\mathbf{f}_m) = p(\mathbf{f}|\mathbf{f}_m)\phi (\mathbf{f}_m)$ by marginalizing out $\mathbf{f}_m$ , which gives optimal $\hat{q} (\mathbf{f}) =$ $\mathcal{N}(\mathbf{f}|\boldsymbol {\mu}_{\mathbf{f}},\mathbf{A})$ , where $\pmb {\mu_{\mathrm{f}}} = \mathbf{K}_{nm}\mathbf{K}_{mm}^{-1}\pmb {\mu}_m$ and $\mathbf{A} =$ $\mathbf{K}_{\mathbf{f}|\mathbf{f}_m} + \mathbf{K}_{nm}\pmb{\Sigma}\mathbf{K}_{mn}$ + +Remark 1 With the optimal $\hat{\phi}(\mathbf{f}_m)$ , we obtain $\langle \mathcal{N}_i \rangle = \exp(\mathbb{E}[\log \mathcal{N}_i])$ as follows + +$$ +\langle \mathcal {N} _ {i} \rangle = \mathcal {N} \left(y _ {i} \mid \boldsymbol {\mu} _ {\mathbf {f} i}, \sigma^ {2}\right) \exp \left(- \frac {1}{2 \sigma^ {2}} \mathbf {A} _ {i i}\right), \tag {15} +$$ + +where $\mathcal{N}_i$ denotes $\mathcal{N}(y_i|f_i,\sigma^2)$ , $\pmb{\mu}_{\mathbf{fi}}$ is the $i$ -th element of $\pmb{\mu}_{\mathbf{f}}$ , and $\mathbf{A}_{ii}$ is the $i$ -th diagonal element of $\mathbf{A}$ . + +Updating $q_{2}(\gamma)$ indicates updating the inlier ratio or mixture. Suppose $q_{1}, q_{3}$ , and $q_{4}$ are given and note $\hat{n} = \operatorname{tr}(\mathbf{P})$ . According to Eq. (10), we conclude that $\hat{q}_{2}(\gamma)$ again follows a Beta distribution + +$$ +\hat {q} _ {2} (\gamma) = \operatorname {B e t a} (\gamma | B _ {a} + \hat {n}, B _ {b} + n - \hat {n}). \tag {16} +$$ + +Remark 2 With the optimal $\hat{q}_2(\gamma)$ , according to the properties of Beta distribution, we obtain $\langle \gamma \rangle = \exp (\mathbb{E}[\log \gamma ])$ and $\langle 1 - \gamma \rangle = \exp (\mathbb{E}[\log (1 - \gamma)])$ as follows + +$$ +\langle \gamma \rangle = \exp (\psi (B _ {a} + \hat {n}) - \psi (B _ {a} + B _ {b} + n)), \tag {17} +$$ + +$$ +\langle 1 - \gamma \rangle = \exp (\psi (B _ {b} + n - \hat {n}) - \psi (B _ {a} + B _ {b} + n)), \tag {17} +$$ + +where $\psi (\cdot)$ is the digamma function. + +Updating $q_{3}(\mathbf{Z})$ represents determining the probability of each data being an inlier given $q_{1}, q_{2}$ , and $q_{4}$ . It encodes the mode of each data point. From Eq. (10), it leads to a + +further factorization $\hat{q}_3(\mathbf{Z}) = \prod_{i=1}^n \hat{q}_3^{[i]}(z_i)$ and $\hat{q}_3^{[i]}(z_i)$ is shown to follow a Bernoulli distribution: + +$$ +\hat {q} _ {3} ^ {[ i ]} \left(z _ {i}\right) = \left(1 - p _ {i}\right) ^ {1 - z _ {i}} p _ {i} ^ {z _ {i}}, \tag {18} +$$ + +$$ +\text {w h e r e} \quad p _ {i} = \frac {\langle \gamma \rangle \left\langle \mathcal {N} _ {i} \right\rangle}{\left. \langle 1 - \gamma \rangle / a + \langle \gamma \rangle \left\langle \mathcal {N} _ {i} \right\rangle \right.}. \tag {19} +$$ + +Remark 3 $p_i$ shows the posterior probability of the $i$ -th data being an inlier. It depends on both the deviation between $y_i$ and the posterior mean $\mu_{\mathrm{fi}}$ , and the term containing the posterior variance $\mathbf{A}_{ii}$ . The importance of this variance term is that it encodes the uncertainty of the latent function at $\mathbf{x}_i$ , which means if we are uncertain about that data, then we cannot identify it as an inlier, even though $y_i$ and $\mu_{\mathrm{fi}}$ are close. This is helpful to avoid overfitting. + +Updating $q_{4}(\sigma^{2},\varphi ,\mathbf{X}_{m})$ involves the optimization of hyperparameters. Specifically, $\sigma^2$ controls the noise level, $\varphi$ represents the shape of the kernel function, and $\mathbf{X}_m$ is the location of the pseudo-inputs. As assumed previously, $q_{4}(\sigma^{2},\varphi ,\mathbf{X}_{m})$ obeys the Dirac delta distribution, which means we directly maximize the lower bound (11) with respect to $(\sigma^2,\varphi ,\mathbf{X}_m)$ , rather than using Eq. (10). + +Given $q_{1}$ , $q_{2}$ , and $q_{3}$ , taking derivative of (11) over $\sigma^2$ and setting to zero, we obtain a closed-form expression + +$$ +\hat {\sigma} ^ {2} = \frac {1}{\hat {n}} \left(\mathbf {y} - \boldsymbol {\mu} _ {\mathbf {f}}\right) ^ {\top} \mathbf {P} \left(\mathbf {y} - \boldsymbol {\mu} _ {\mathbf {f}}\right) + \frac {1}{\hat {n}} \operatorname {t r} (\mathbf {P A}), \tag {20} +$$ + +where $\operatorname{tr}(\cdot)$ is the trace. The lower bound (11) is, however, difficult to optimize for the remaining hyperparameters $(\varphi, \mathbf{X}_m)$ since the integral is intractable. To this end, we use the reverse Jensen's inequality and obtain + +$$ +\mathcal {L} _ {2} := \log \mathcal {N} (\mathbf {y} | 0, \mathbf {K} _ {\mathbf {y}}) - \frac {1}{2 \sigma^ {2}} \operatorname {t r} \left(\mathbf {P K} _ {\mathbf {f} | \mathbf {f} _ {m}}\right) + \text {c o n s t .} \leq \mathcal {L}, \tag {21} +$$ + +where $\mathbf{K_y} = \sigma^2\mathbf{P}^{-1} + \mathbf{K}_{nm}\mathbf{K}_{mm}^{-1}\mathbf{K}_{mn}$ . To set the optimized hyperparameters $(\varphi, \mathbf{X}_m)$ , we seek partial derivatives of $\mathcal{L}_2$ with respect to them. Thereafter, the standard gradient descent algorithm provides the value that maximizes $\mathcal{L}_2$ . + +# 4.5. Stochastic Variational Inference + +Modern applications often involve handling massive data. However, the GPR equipped with variational inference does not easily scale to big data, even with inducing variables. This is because we need to go through the entire training data at each coordinate update. As the training data size grows, the computational overhead becomes larger. + +An alternative to coordinate ascent is to use SVI [20], which is similar to stochastic gradient descent (SGD), that performs stochastic optimization from the noisy but cheap-to-compute estimates of the gradient. It iterates between subsampling a subset of data and adjusting the hidden structure solely based on the subset. Thus, SVI is much more efficient than conventional variational inference. To apply SVI to the probabilistic model, a set of global variables is + +needed [18]. In our robust GPR setting, the inducing variables $\mathbf{f}_m$ and mixing coefficient variable $\gamma$ fill this role. + +Natural Gradient. In gradient-based optimization, the natural gradient accounts for the geometric structure of probability parameters and is used in SVI to replace the Euclidean gradient. In exponential families, it is given by premultiplying the usual gradient by the inverse Fisher information matrix $G(\eta)^{-1}$ , where $\eta$ is the canonical parameter of the exponential families. Since both $\phi(\mathbf{f}_m)$ and $q(\gamma)$ are exponential family distributions, they enjoy simple natural gradients [19] of the bound (11) such that $g(\eta) = \mathbb{E}[\eta] - \eta$ , where $g(\cdot)$ denotes the natural gradient. For Gaussian distribution $\phi(\mathbf{f}_m)$ , its canonical parameter is $[\mathbf{A}_m^{-1}\boldsymbol{\mu}_m, -\frac{1}{2}\mathbf{A}_m^{-1}]$ . For Beta distribution $q(\gamma)$ , its canonical parameter is $[B_a + \hat{n}, B_b + n - \hat{n}]$ . Thereafter, we obtain the update rule using natural gradient with a step size $\epsilon_t$ + +$$ +\boldsymbol {\eta} ^ {t} = \boldsymbol {\eta} ^ {t - 1} + \varepsilon_ {t} g (\boldsymbol {\eta} ^ {t - 1}) = (1 - \varepsilon_ {t}) \boldsymbol {\eta} ^ {t - 1} + \varepsilon_ {t} \mathbb {E} [ \boldsymbol {\eta} ]. \tag {22} +$$ + +Note that when the step size $\varepsilon_{t} = 1$ , we recover the original variational update in Eq. (14) and Eq. (16). Now, the noisy natural gradient can be easily computed by sampling either individual or mini-batch of the data. + +# 4.6. Making Predictions + +So far we have described how to infer the approximate posterior of the latent variables. To make predictions, we use the predictive distribution similar to Eq. (3): + +$$ +\begin{array}{l} p \left(\mathbf {f} _ {*} \mid \mathcal {D}, \mathbf {X} _ {*}\right) = \int p \left(\mathbf {f} _ {*} \mid \mathbf {f} _ {m}\right) p \left(\mathbf {f} \mid \mathbf {f} _ {m}\right) \phi \left(\mathbf {f} _ {m}\right) d \mathbf {f} _ {m} d \mathbf {f} \tag {23} \\ = \mathcal {N} \left(\mathbf {f} _ {*} | \mathbf {K} _ {* m} \mathbf {K} _ {m m} ^ {- 1} \boldsymbol {\mu} _ {m}, \mathbf {K} _ {\mathbf {f} _ {*} | \mathbf {f} _ {m}} + \mathbf {K} _ {* m} \boldsymbol {\Sigma} \mathbf {K} _ {m *}\right), \\ \end{array} +$$ + +where $\mathbf{K}_{\mathbf{f}_{*}|\mathbf{f}_{m}} = \mathbf{K}_{**} - \mathbf{K}_{*m}\mathbf{K}_{mm}^{-1}\mathbf{K}_{m*}$ . + +# 5. Applications + +In this section, we describe how to use the proposed GPR model to deal with real-world tasks, including feature matching and dense gene expression imputation. + +# 5.1. Feature Matching + +Feature matching aims at establishing reliable feature point correspondences. To solve the matching problem in a regression manner, we first construct a putative correspondence set $\mathcal{P} = \{(\mathbf{x}_i,\mathbf{x}_i')\}_{i = 1}^n$ by nearest neighbor (NN) matching, where $\mathbf{x}_i$ and $\mathbf{x}_i'$ represent the coordinates of feature points. The putative set is then converted to motion vector set, i.e., $\mathcal{D} = \{(\mathbf{x}_i,\mathbf{y}_i)\}_{i = 1}^n$ , where $\mathbf{y}_i = \mathbf{x}_i' - \mathbf{x}_i$ . The motion of an object projected on the image plane is known to be slow-and-smooth [38], which is well described by GP. Thus, the motion vectors of inliers can be seen as sampling on the underlying model $\mathbf{f}$ , while the outliers are spuriously distributed. Our goal is to determine the correctness of each data. The task, however, is non-trivial as there are often + +massive outliers (even up to $90\%$ ). Moreover, the feature points in each image can reach several thousands, which requires high computational efficiency. As we will see, our model is robust and fast enough to handle such cases. + +Inference Setting. To apply our model to feature matching, some special considerations need to be set. The feature coordinates are first normalized. For the covariance kernel, we choose the squared exponential (SE) kernel $k(\mathbf{x},\mathbf{x}^{\prime}) = \lambda^{-1}\exp (-\beta \| \mathbf{x} - \mathbf{x}^{\prime}\|^{2})$ . We find that fixed hyperparameters work well for most situations, which are empirically set to $\lambda = 4$ and $\beta = 0.1$ . The positions of the inducing variables are randomly selected from the training data and kept fixed during inference. The ratio information is also considered as a prior. The mini-batch size is set to $\max \left\{\frac{n}{8},200\right\}$ . After inference convergences, the $i$ -th data is decided to be inlier if $p_i > \tau$ , where $\tau$ is a threshold and is set to $\tau = 0.75$ . + +Predictions. One of the attractive properties of our model for this task is that when the training is completed, the resulting posterior GP is able to predict the motion vector of each feature point. Combined with the descriptors' information, we can yield much more correct correspondences rather than being limited to putative set. More correct correspondences are crucial for downstream tasks, as they can significantly improve the accuracy. + +# 5.2. Dense Gene Expression Imputation + +Recently, technological advances have made it possible to measure spatially resolved transcriptome-wide mRNA expressions with spatial information in tissue samples. GPR is thus utilized to infer gene expression in discrete samples, generating dense gene expression in 2D, 3D, and even spatiotemporal [3]. Unfortunately, due to equipment malfunctions and process disturbances, the readout data may contain bad spots. In this case, a vanilla GPR may lead to completely wrong results and thus mislead the subsequent analysis. By comparison, the robust GPR developed in this paper copes well with outliers and is able to give meaningful imputation results. For this application, the implementation is simple and requires little extra consideration. + +# 6. Experiments + +In this section, we first conduct numerical experiments to evaluate the performance in a fully controlled environment. After that, we apply our model to tackle feature matching problem and compare it with many state-of-the-art methods tailored for feature matching. In the end, the evaluation of gene expression imputation is performed. All experiments are conducted on a desktop with Intel i7-10700 CPU, 16 GB memory with MATLAB except deep learning methods. + +# 6.1. Numerical Experiments + +We study two datasets, i.e., Neal dataset [28] and Friedman dataset [14]. The Neal dataset is one-dimensional data, + +![](images/bf6975106d089e2f181b198558389f9a26f504bb91fd7013d7378b6516549c3a.jpg) +Figure 2. Visual examples on Neal data. Our model approximates the exact posterior GP using only inliers, even with massive outliers. The legend is shown in the bottom. + +where the input $x$ is drawn from a uniform distribution within $[-2.5, 2.5]$ . The target value is calculated as: + +$$ +f (x) = 0. 3 + 0. 4 x + 0. 5 \sin (2. 7 x) + 1. 1 / \left(1 + x ^ {2}\right). +$$ + +The Gaussian noise is added to the target value with zero mean and variance of 0.1. Next, outliers are injected into the training data, where the value is drawn from uniform distribution within $[-5, 5]$ . The Friedman is 10-dimensional data and the function value depends on the first five dimensions + +$$ +f (\mathbf {x}) = 1 0 \sin \left(\pi x _ {1} x _ {2}\right) + 2 0 \left(x _ {3} - 0. 5\right) ^ {2} + 1 0 x _ {4} + 5 x _ {5}, +$$ + +while the remaining dimensions complicate the task by adding a feature selection process. The input $\mathbf{x}$ is sampled uniformly within $[0,1]^{10}$ . Gaussian noise $\mathcal{N}(0,0.01)$ is added and random outliers are distributed among [5, 25]. + +We fix the inlier number to 100 and change the outlier ratio. GPR with Student's- $t$ (St) [32], Laplace (Lap) [32], and Gaussian mixture distribution (MEM) [8], as well as variational free energy (VEF) [37], are chosen as competitors. Some intuitive examples on Neal data are shown in Fig. 2, where outlier ratio increases from 0 to $80\%$ . We see that the prediction by our model almost exactly reproduces the full GP prediction using only inliers. In contrast, GPR-St and -Lap give poor approximations. GPR-MEM is able to give a better answer, yet still not as good as ours, especially at extremely high outlier ratios. + +To statistically verify performance, we select mean absolute error (MAE, m), root mean square error (RMSE, r), and negative log of predictive probability (NLP, n) as metrics. 1000 testing points are generated in equal intervals. The statistical results on Neal and Friedman in Table 1 suggest that our method outperforms other alternatives in terms of robustness and accuracy. More results including KL and statistical variance are provided in suppl. material. + +# 6.2. Feature Matching + +We collect three large and diverse feature matching datasets with three different vision tasks, say YFCC100M + +Table 1. Quantitative results on Neal and Friedman data with different outlier ratios. Bold indicates the best. + +
Neal [28]
Method10%50%80%
mrnmrnmrn
GPR-VFE [37]0.180.210.730.580.771.750.761.081.96
GPR-St [32]0.030.03-0.410.090.190.390.771.151.66
GPR-Lap [32]0.030.07-1.170.420.561.620.350.722.03
GPR-MEM [8]0.040.08-1.360.060.12-0.660.771.522.04
Ours0.010.02-1.380.030.04-1.250.030.03-0.89
Friedman [14]
Method20%30%50%
mrnmrnmrn
GPR-VFE [37]1.121.242.281.471.623.082.883.166.93
GPR-St [32]0.040.04-0.080.911.103.591.472.187.16
GPR-Lap [32]0.230.290.370.460.610.942.032.233.29
GPR-MEM [8]0.110.21-0.990.130.24-0.662.132.322.98
Ours0.040.06-1.460.060.08-0.350.100.140.55
+ +![](images/d63bae63fad5a96af15bc558e42713b63d1df2c55e121e76a9bfee1978ae7202.jpg) +Figure 3. Qualitative illustration of relative pose estimation. We show the true positive in blue and false positive in red. Best viewed in color with $200\%$ zoom in. + +dataset [36] (4000 pairs) for relative pose estimation, CPC dataset [42] (1000 pairs) for fundamental matrix estimation, and HPatches dataset [1] (580 pairs) for homography estimation. Six state-of-the-arts from handcrafted to deep learning are chosen for comparison, namely, MAGSAC++ [2], LPM [26], MCDM [25], CRC [12], PointCN [43], and OANet [44], with baseline ratio test. Briefly, MAGSAC++ is resampling-based method, LPM is a heuristic method that preserves local structure of feature points, CRC interpolates a smooth vector field using Fourier bases, PointCN uses deep neural networks with context normalization to encode global contextual information, OANet further captures local contextual information by clustering unordered correspondences. Note that we assess currently other robust GPR methods are not capable to handle the feature matching problem, thus none of them are chosen for comparison. + +# 6.2.1 Relative Pose Estimation + +Following [44], Yahoo's YFCC100M dataset [36] generates 4000 testing image pairs. SIFT [24] with NN matching is adopted to establish putative correspondences. The maximum number of keypoints for each image is limited to 4000. RANSAC [13] is used to estimate the relative camera pose. + +Table 2. Quantitative comparison for relative pose estimation. Bold indicates the best and underline ranks the second. + +
YFCC100M [36]
MethodAUCPRF
@5°@10°@20°
Ratio test28.839.252.124.355.332.8
MSC++ [2]24.933.745.724.355.332.8
PointCN [43]45.154.665.047.273.454.9
OANet [44]53.664.175.851.287.061.7
LPM [26]38.648.859.751.443.645.9
MCDM [25]47.859.470.763.046.552.7
CRC [12]38.148.258.641.257.844.5
Ours53.863.773.885.354.063.7
+ +![](images/dc04c4bb8db41b27359a91b479060ac3afea0f3337e0a7442160a15dd2c9426b.jpg) +Figure 4. Visual examples of homography and fundamental matrix estimation. We show the true positive in blue and false positive in red. Best viewed in color with $200\%$ zoom in. + +We measure the maximum of rotation and translation errors in degree and report the approximate Area Under the Curve (AUC) with thresholds 5, 10, and 20 degrees. Precision, recall, and F1-score before RANSAC with respect to the ground-truth inliers are also presented. See suppl. material for a detailed description of the dataset and the metrics. + +Some visualized examples are demonstrated in Fig. 3. Statistics results are comprehensively reported in Table 2. Since deep learning methods such as PointCN and OANet are trained in such dataset with geometric loss, they can capture geometric information and therefore have higher AUC compared to other handcrafted methods. By comparison, our method achieves comparable results to these deep learning methods with much higher precision and F1-score. + +# 6.2.2 Homography & Fundamental Matrix Estimation + +Homography and fundamental matrix estimation are critical parts in computer vision. The maximum keypoints for HPatches and CPC are limited to 4000. For evaluation metrics, we choose the precision, recall, and F1-score as well as the accuracy of the estimation. For homography estimation, we adopt homography error defined in [11], and for fundamental matrix, we follow [4] and use normalized symmetric geometry distance (NSGD) as the metrics. An estimate is classified as accurate or not by a threshold, which is set to 4 pixels for homography error and 0.05 for the NSGD [4]. + +Table 3. Statistical results for homography and fundamental matrix estimation. Bold ranks the first, underline the second. + +
MethodHPatches [1]CPC [42]
Acc.PRFAcc.PRF
Ratio test71.771.651.663.017.012.763.920.5
MSC++ [2]74.487.392.486.06.919.729.619.4
PointCN [43]73.176.985.778.629.319.870.228.8
OANet [44]70.073.577.272.147.034.681.045.4
LPM [26]60.672.550.552.323.821.948.926.1
MCDM [25]77.762.991.073.034.823.061.032.5
CRC [12]71.775.592.580.428.724.847.230.4
Ours78.189.994.391.549.661.559.357.2
Ours*82.473.9109.6-51.939.297.3-
+ +Table 4. Ablation studies on feature matching. Bold is the best. + +
MethodPrec.RecallF1Time
CRC [12]50.767.854.968.1
OANet (on GPU) [44]47.975.256.041.2
RS-GPRNo SVI76.366.170.047.1
No inducing variables72.669.069.51.6e5
Opt. Hyperparameters85.061.267.71556
EM optimization67.669.865.543.7
Default88.068.275.69.8
+ +Several visual examples are provided in Fig. 4. Note that our predictive model is also presented and indicated by the superscript ${}^{*}\ast$ . It establishes significantly more correct correspondences compared to other methods. Table 3 reports the statistical results. As it indicates, our method outperforms all other methods in the two tasks. When using the predictive model, it can even produce more correct correspondences than the putative set (e.g., the recall in HPatches is higher than 100), thus further improving accuracy. + +# 6.2.3 Ablation Studies of Feature Matching + +To measure performance, especially runtime, in different settings, we conduct ablation studies on 100 image pairs from YFCC100M. It mainly includes four choices, i.e., not using SVI, not using inducing variables, optimizing the kernel hyperparameters, and using EM optimization instead of variational inference. We also include the CRC and OANet to compare the runtime. The results are reported in Table 4, where we see that our method performs the best with the default setting described in Sect. 5.1. In particular, the running time is much faster compared to other settings and methods. + +# 6.3. Dense Gene Expression Imputation + +We collect two spatial transcriptomics datasets from mouse olfactory bulb and human breast cancer biopsies [34], respectively. Briefly, the spatial transcriptomics gene expression data is measured from thin tissue sections placed on an array with ploy probes and spatially resolved DNA barcodes. These create a grid of circular spots where the mRNA abundance of each spot is measured using probes with the barcodes encoding the spatial locations. The mouse olfactory bulb and human breast cancer biopsies datasets + +![](images/f18ddbf02269356ae12c989aebb22acf2f900a111dfd7aa45aba705fdda444c2.jpg) +Figure 5. Visualization of dense spatial gene expression imputation. The spatial transcriptomics data is plotted on the top row. The bottom row shows the imputation results of different methods. We stack the spatial transcriptomics (shown as dots) on the imputed results to show the quality of the imputation. + +![](images/55745084f69e7e663fc4106324058dc6db9f1fa989348d7b22a8e582325efa9a.jpg) + +Table 5. Statistical results of dense gene expression imputation. Bold indicates the best. + +
Mouse olfactory bulb
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.460.591.250.330.401.10
GPR-St [32]0.070.14-0.570.020.04-1.33
GPR-Lap [32]0.200.270.330.480.540.94
Ours0.030.05-1.990.020.04-2.21
Breast cancer tissue
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.240.351.440.230.331.15
GPR-St [32]0.190.320.370.180.300.22
GPR-Lap [32]0.250.360.560.250.370.53
Ours0.120.16-0.540.110.17-0.39
+ +contain 14859 and 12856 measured genes, respectively. To identify spatially variable genes, we adopt SpatialDE [35] and select two patterns for each dataset. We next add 5 random outliers to each identified pattern to simulate the outlier scenario. In the end, different GPR methods are applied to impute dense spatial gene expression. + +Two visual examples are presented in Fig. 5, where in each example, the second row shows the imputed results. As can be seen, our method accurately infers the correct gene expression regardless of the outliers. To give quantitative results, we randomly split each dataset into $80\%$ training data and $20\%$ test data. As mentioned above, we use the MAE, RMSE, and NLP to measure the performance, and report the statistical results in Table 5. We see that our method always has the lowest error. + +# 7. Analysis + +Optimization Process. We visualize the intermediate results of the optimization process on Neal data with $50\%$ outliers and present it in the top row of Fig. 6. We see that the field of $p$ in Eq. (19) gradually converges to the inliers. After convergence, the posterior mean and variance functions are very close to the ground truth, and the inducing variables are restricted to the interval of the inliers. + +The Role of Term $\mathbf{A}_{ii}$ . We remove the term containing $\mathbf{A}_{ii}$ in Eq. (15) and show the results in the bottom of Fig. 6. + +![](images/63607d253c4cdef0168a9b0993d4d1c20ff65bda2af6dc79d4cd66053cea2219.jpg) +Figure 6. Intermediate results of the optimization process. The top row shows the full model while the bottom removes term $\mathbf{A}_{ii}$ . We visualize the field of $p$ , which indicates the inlier probability at any location. The deeper the blue color, the higher the probability. + +![](images/7675747a1a2dd41bde5fa61c995b2e69b4a3152c8469d6feffc58aea63ae31f3.jpg) +Figure 7. Our model deal with different non-uniform outliers. + +![](images/62e6027f2054a4ce502523dbd7253a07b2680fd0a94db254e8cfea899846273d.jpg) +Figure 8. The inference time of each GPR method. Our model with SVI can easily handle big data. + +Without variance term, the regression tends to overfit. + +Non-uniform Outliers. Different types of non-uniform outliers are tested in Fig. 7. More detailed results are given in suppl. material. Our model exhibits strong generalization and robustness. The reason is that uniform distribution is a very weak assumption with high flexibility. It accommodates many outlier distributions. + +**Scalability.** We test the runtime towards different problem sizes on Neal data with $50\%$ outliers. Other methods as well as ours w. and w/o. SVI are included. The number of inducing variables is set to 15 for our method in both two settings. As plotted in Fig. 8, our method can easily scale to large-scale data, especially when equipped with SVI. + +# 8. Conclusion + +This paper presents a robust and scalable GPR using variational learning. It uses an outlier robust mixture likelihood model, where the uniform distribution accounts for the outliers. A variational formulation is introduced to learn the mode of data and hyperparameters by minimizing the KL divergence between the true posterior distribution and the approximate one. Its most attractive property is that it can rigorously approximate the exact posterior. Inducing variable approximation and SVI further extend our model to big data. We apply our model to feature matching and dense gene expression imputation. Extensive results show the significant improvement over existing robust GPRs. + +# References + +[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. 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This enables the application of Gaussian processes to a wide range of real data, which are often large-scale and contaminated by outliers. Towards this end, we employ a mixture likelihood model where outliers are assumed to be sampled from a uniform distribution. We next derive a variational formulation that jointly infers the mode of data, i.e., inlier or outlier, as well as hyperparameters by maximizing a lower bound of the true log marginal likelihood. Compared to previous robust GPR, our formulation approximates the exact posterior distribution. The inducing variable approximation and stochastic variational inference are further introduced to our variational framework, extending our model to large-scale data. We apply our model to two challenging real-world applications, namely feature matching and dense gene expression imputation. Extensive experiments demonstrate the superiority of our model in terms of robustness and speed. Notably, when matching 4k feature points, its inference is completed in milliseconds with almost no false matches. The code is at github.com/YifanLu2000/Robust-Scalable-GPR." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 504, + 128, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 504, + 128, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 504, + 128, + 517 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 525, + 287, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 680 + ], + "type": "text", + "content": "Gaussian processes (GPs) [31] are probably the primary non-parametric method for inference on latent functions. They have a wide range of applications from biology [3] to computer vision [41]. A commonly used observation model for Gaussian process regression (GPR) is the Normal distribution, which brings great convenience to the inference. Unfortunately, a well-known limitation of the Gaussian observation model is its sensitivity to outliers in data. As illustrated in Fig. 1 (b), a few outliers can drastically destroy the entire posterior regression result. This hinders the real-world applications of GPR for many domains, where outliers are often inevitable. This paper intends to conquer the GPR with outlier contaminated data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 681, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 681, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 59, + 681, + 287, + 693 + ], + "type": "text", + "content": "The idea of robust regression is not new. 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Regression with our model. (a) Perform exact GPR from 100 inliers. (b) When there are only 6 outliers in the data, the exact GPR leads to completely wrong results. (c) By comparison, our model is able to recover the exact posterior even facing 100 outliers. (d) The feature matching result using our model. (e) The dense spatial gene expression imputation result using our model." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 426, + 284, + 541, + 342 + ], + "blocks": [ + { + "bbox": [ + 426, + 284, + 541, + 342 + ], + "lines": [ + { + "bbox": [ + 426, + 284, + 541, + 342 + ], + "spans": [ + { + "bbox": [ + 426, + 284, + 541, + 342 + ], + "type": "image", + "image_path": "67dc0e22054a7d3fbba3e5c8064ce53ee21035d388c5175cb432719fd82e7b0e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 437, + 546, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 546, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 546, + 569 + ], + "type": "text", + "content": "tion has been extensively and systematically described in [6,9,10,29]. In the context of GPR, many efforts tried to replace the Gaussian likelihood with other distributions showing heavy-tail behaviors, including Student-" + }, + { + "bbox": [ + 304, + 437, + 546, + 569 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 437, + 546, + 569 + ], + "type": "text", + "content": " [16,21,28,30], Laplace [22, 30], Gaussian mixture [8, 22, 27], and data-dependent noise model [17]. The challenge with these non-Gaussian likelihoods lies in the inference, which is analytically intractable. To this end, many approximation schemes have been applied, despite having high computational complexity, e.g., Markov Chain Monte Carlo (MCMC) sampling and Expectation Propagation (EP) [22]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 714 + ], + "type": "text", + "content": "In this paper, we propose a more effective mixture likelihood model, where uniform distribution accounts for the outliers and Gaussian for inliers. In our formulation, the outliers are independent of the GP and do not affect the computation of the posterior GP, thereby allowing to tolerate more outliers. We next introduce a variational method that jointly determines the modes of data (i.e., inlier or outlier) as well as hyperparameters by maximizing a lower bound to the marginal likelihood. We highlight that the difference between our variational formulation and pervious methods is that the modes of data now become variational parameters and are obtained by minimizing the Kullback-" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 137, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21950" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "Leibler (KL) divergence between the variational and the true posterior distribution. Thus, the proposed formulation is less likely to overfit and is able to approximate the exact posterior GP only from inliers, as in Fig. 1 (c)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "content": "Inspired by [37], the sparse inducing variable approximation is integrated into our variational framework, which retains the exact GP prior but performs posterior approximation, and reduces the time complexity from " + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(n^3)" + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(nm^2)" + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "content": ". By treating the inducing variables as global variables [18], our variational model enjoys the acceleration by Stochastic Variational Inference (SVI) [20]. It performs stochastic optimization from natural gradient and further decreases the time complexity to " + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(km^2)" + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "content": ". This provides a guarantee for our model to scale to large-scale data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 286, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 286, + 300 + ], + "type": "text", + "content": "We apply our robust GPR model to two real-world applications, say feature matching and dense spatial gene expression imputation, as illustrated in the Figs. 1 (d) and (e). Extensive experiments demonstrate the superiority of our method on both numerical data and real applications." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 286, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 286, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 286, + 383 + ], + "type": "text", + "content": "To summarize, our contributions include the following. (i) We present a robust Gaussian process regression model, which uses variational learning to approximate the true exact posterior. (ii) We leverage inducing variables and SVI to adapt our model to large-scale data. (iii) Two applications of our model are described. Extensive experimental validation demonstrates the superiority of our model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 394, + 138, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 138, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 138, + 406 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "text", + "content": "Robust GPR typically employs non-Gaussian likelihood with heavy tails. Representatively, [22] investigated the Student's-" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "text", + "content": " noise model. They further developed variational inference and MCMC for GPR with Student's-" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "text", + "content": ". In [39], Laplace approximation was used to approximate the log marginal likelihood of Student's-" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "text", + "content": ". The Laplace noise model is also exploited in [22]. [30] introduced Expectation Maximization (EM) algorithm for Student's-" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 414, + 286, + 628 + ], + "type": "text", + "content": " and Laplace. Recently, [8] used mixtures of two Gaussians assuming a lower variance for regular noise and a higher one for outliers, with EM to learn the hyperparameters. In this work, we also use a non-Gaussian likelihood, i.e., mixture model. The difference is that here the outliers are considered to follow a uniform distribution, which is a more reasonable assumption since the sampling distribution of outliers should be independent of the true latent function. Besides, we derive a variational formulation in the GPR setting, which approximates the posterior distribution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Scalable GPR improves the scalability of GPR while maintaining prediction quality for big data. The seminal work [40] adopted Nyström approximation to approximate the kernel matrix using " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " sparse points. Later, the idea was further promoted by [7, 15, 23, 33], which approximated the prior and performed exact inference. Unlike the prior approximations, the other line is the posterior approximations," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "which retain the exact prior but perform approximate inference. The most well-known work is the elegant variational free energy [37]. It directly approximates the posterior by using variational inference. With the advances in variational inference [20], SVI is introduced to GP [18], which uses natural gradients and results in remarkable computational efficiency. However, as the exact GPR, these scalable GPRs are sensitive to outliers. In contrast, our model can tolerate massive outliers while retaining highly scalability." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 190, + 518, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 190, + 518, + 202 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 518, + 202 + ], + "type": "text", + "content": "3. Gaussian Process Regression Revisited" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "text", + "content": "Gaussian process is a collection of random variables, for which any finite subset has a joint Gaussian distribution [31]. It is completely specified by a mean function " + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "inline_equation", + "content": "m(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "text", + "content": " and a covariance function " + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "inline_equation", + "content": "k(\\mathbf{x},\\mathbf{x}^{\\prime})" + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "text", + "content": " where the covariance function typically depends on a set of hyperparameters " + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "text", + "content": ". The GP is usually used as a prior over latent function " + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x})\\sim \\mathcal{GP}(m,k)" + }, + { + "bbox": [ + 304, + 209, + 545, + 304 + ], + "type": "text", + "content": ". We can combine the GP prior with observed data to give a posterior over desired latent function." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": "Consider a regression problem, where the training data is " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(\\mathbf{x}_i,y_i)\\}_{i = 1}^n" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ". Each " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": " is a noisy realization of the latent function at location " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "y_{i} = f_{i} + \\epsilon_{i}" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\epsilon_{i}\\sim \\mathcal{N}(\\epsilon_{i}|0,\\sigma^{2})" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": " is typically assumed to be an i.i.d. Gaussian noise and " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "f_{i} = f(\\mathbf{x}_{i})" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ". Denoting all training inputs as " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ", all training outputs " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ", and all latent function values at " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ". Placing a GP prior on the latent function " + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 304, + 545, + 389 + ], + "type": "text", + "content": ", we obtain" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 358, + 396, + 545, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 396, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 358, + 396, + 545, + 408 + ], + "type": "interline_equation", + "content": "p (\\mathbf {f} | \\mathbf {X}, \\varphi) \\sim \\mathcal {N} (\\mathbf {f} | m (\\mathbf {X}), \\mathbf {K} _ {n n}), \\tag {1}", + "image_path": "5f15b4bc6e424bc1ed8e3a40703a6d1bd6120403b5efc8b98d10b7564a7e2256.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{nn}" + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "content": " is the covariance function evaluated between all the training points. For simplicity of exposition, the mean function is set to zero " + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "inline_equation", + "content": "m(\\mathbf{x}) = 0" + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "content": ". It does not reduce the generalizability of the GP as long as the problem is correctly transformed, e.g., by subtracting the mean of " + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "content": ". One can induce a posterior distribution on " + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 414, + 545, + 486 + ], + "type": "text", + "content": " according to Bayes' rule" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 337, + 497, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 497, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 337, + 497, + 545, + 510 + ], + "type": "interline_equation", + "content": "p (\\mathbf {f} | \\mathcal {D}, \\sigma^ {2}, \\varphi) \\sim \\mathcal {N} (\\mathbf {f} | \\mathbf {K} _ {n n} (\\mathbf {K} _ {n n} ^ {\\epsilon}) ^ {- 1} \\mathbf {y}, \\boldsymbol {\\Sigma}), \\tag {2}", + "image_path": "3b275821103751d8c8652757776992534eeec18d13418bb5fd9e8b8aba1bb2dd.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": "which is also a multivariate normal distribution, where " + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{nn}^{\\epsilon} = \\mathbf{K}_{nn} + \\sigma^{2}\\mathbf{I}" + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\boldsymbol {\\Sigma} = (\\mathbf{K}_{nn}^{-1} + \\sigma^{-2}\\mathbf{I})^{-1}" + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": ". The posterior distribution of " + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": " can help to compute the posterior predictive distribution of " + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_*" + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": " at any test location " + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{*}" + }, + { + "bbox": [ + 304, + 514, + 545, + 562 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 567, + 545, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 567, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 310, + 567, + 545, + 607 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p \\left(\\mathbf {f} _ {*} \\mid \\mathcal {D}, \\mathbf {X} _ {*}\\right) = \\int p \\left(\\mathbf {f} _ {*} \\mid \\mathbf {f}, \\mathbf {X} _ {*}\\right) p (\\mathbf {f} \\mid \\mathcal {D}) d \\mathbf {f} \\tag {3} \\\\ = \\mathcal {N} \\left(\\mathbf {f} _ {*} | \\mathbf {K} _ {* n} \\left(\\mathbf {K} _ {n n} ^ {\\epsilon}\\right) ^ {- 1} \\mathbf {y}, \\mathbf {K} _ {* *} - \\mathbf {K} _ {* n} \\left(\\mathbf {K} _ {n n} ^ {\\epsilon}\\right) ^ {- 1} \\mathbf {K} _ {n *}\\right), \\\\ \\end{array}", + "image_path": "396c7327d1d066d1a895d9d16b4bbc001a8c99f676862ed45af97b04d173fbe9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "text", + "content": " are omitted for brevity. The above posterior depends on the values of " + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 613, + 545, + 650 + ], + "type": "text", + "content": ", which can be inferred by maximizing the log marginal likelihood:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 351, + 655, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 655, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 351, + 655, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\log p (\\mathbf {y} \\mid \\sigma^ {2}, \\varphi) = \\log \\mathcal {N} (\\mathbf {y} \\mid \\mathbf {0}, \\mathbf {K} _ {n n} ^ {\\epsilon}), \\tag {4}", + "image_path": "2a039812b6cf729d9da00475bad62b54295f5e3aa80428a0333475386084660c.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 675, + 535, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 675, + 535, + 686 + ], + "spans": [ + { + "bbox": [ + 306, + 675, + 535, + 686 + ], + "type": "text", + "content": "which automatically achieves the bias-variance trade-off." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "1Note that the derivation in this paper extends to multiple independent output dimensions is straightforward." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21951" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 285, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 285, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 285, + 85 + ], + "type": "text", + "content": "4. Robust Gaussian Process Regression Model" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 175 + ], + "type": "text", + "content": "In real-world scenarios, a huge discrepancy between the model and data-generating process often occurs, leading to outliers. However, a critical flaw of Gaussian observation model is its non-robustness. This poses a great challenge to GPR in practice. To this end, this section introduces a robust GPR, which identifies the mode of data and simultaneously approximates the posterior of the desired model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 182, + 171, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 171, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 171, + 194 + ], + "type": "text", + "content": "4.1. Problem Formulation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": "We explicitly consider the generation process of outliers. Since outliers are independent of the latent function, a reasonable assumption is that they obey a uniform distribution " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\frac{1}{a}" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": ", where the output space is a bounded region that covers the output " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": " is a constant denoting the volume of the region. The inliers follow a regular Gaussian noise " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(y_i|f_i,\\sigma^2)" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": ". We then associate each data with a latent variable " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "z_{i} \\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "z_{i} = 0" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": " indicates that the observation is generated by outlier distribution and " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "z_{i} = 1" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": " inlier. The joint distribution of " + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "inline_equation", + "content": "(y_{i},z_{i})" + }, + { + "bbox": [ + 46, + 201, + 288, + 331 + ], + "type": "text", + "content": " is then a mixture of two models:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 338, + 287, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 338, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 53, + 338, + 287, + 361 + ], + "type": "interline_equation", + "content": "p \\left(y _ {i}, z _ {i} \\mid f _ {i}, \\boldsymbol {\\theta}\\right) = \\left\\{\\left(1 - \\gamma\\right) \\frac {1}{a} \\right\\} ^ {1 - z _ {i}} \\left\\{\\gamma \\mathcal {N} \\left(y _ {i} \\mid f _ {i}, \\sigma^ {2}\\right) \\right\\} ^ {z _ {i}}, \\tag {5}", + "image_path": "d2eb36a4672c05b3a1b913e2dac00c1b3c8ca59156c1dad503d175aa57313739.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "type": "inline_equation", + "content": "\\theta = (\\sigma^2, \\gamma, \\varphi)" + }, + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "type": "text", + "content": " denotes the latent variables set and " + }, + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "type": "inline_equation", + "content": "\\gamma = p(z_i = 1)" + }, + { + "bbox": [ + 47, + 369, + 287, + 394 + ], + "type": "text", + "content": " is the mixing coefficient." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 394, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 453 + ], + "type": "text", + "content": "Prior distributions describe beliefs about the model variables before the inference. As a robust GPR problem, we place a GP prior over the latent function, i.e., Eq. (1). The variable " + }, + { + "bbox": [ + 46, + 394, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 394, + 287, + 453 + ], + "type": "text", + "content": " controls the probability of occurrence of two models. We suppose it follows a Beta distribution" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 464, + 287, + 476 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 464, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 116, + 464, + 287, + 476 + ], + "type": "interline_equation", + "content": "p (\\gamma) \\sim \\operatorname {B e t a} (\\gamma | B _ {a}, B _ {b}), \\tag {6}", + "image_path": "1dc2ea872e300412435bc6478ee3e3a3cc4fdd5b932c7f3ae25804a366758e19.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "inline_equation", + "content": "B_{a}" + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "inline_equation", + "content": "B_{b}" + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "text", + "content": " are hyperparameters. As we will see, " + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "inline_equation", + "content": "p(\\gamma)" + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "text", + "content": " is conjugate to the posterior and hence easier to handle. For other variables " + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "inline_equation", + "content": "(\\sigma^2,\\varphi)" + }, + { + "bbox": [ + 46, + 485, + 287, + 521 + ], + "type": "text", + "content": ", we introduce noninformative prior." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 544 + ], + "type": "text", + "content": "Full joint distribution is obtained by incorporating the above prior distributions as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 70, + 553, + 287, + 585 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 553, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 70, + 553, + 287, + 585 + ], + "type": "interline_equation", + "content": "p (\\mathcal {D}, \\mathbf {f}, \\boldsymbol {\\theta}) \\propto p (\\mathbf {f} | \\mathbf {X}) p (\\gamma) \\prod_ {i = 1} ^ {n} p \\left(y _ {i}, z _ {i} \\mid f _ {i}, \\sigma^ {2}, \\gamma\\right), \\tag {7}", + "image_path": "8a873ab2c65d3711c863e22c893d66358f65fde4e480aa04c076b15c1a3c6784.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta} = (\\sigma^2, \\gamma, \\mathbf{Z}, \\varphi)" + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Z} \\in \\{0,1\\}^n" + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "content": " is the indicator variable vector. Our goal is to obtain the posterior " + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f}, \\pmb{\\theta}|\\mathcal{D})" + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "content": ", which can be induced from " + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "inline_equation", + "content": "p(\\mathcal{D}, \\mathbf{f}, \\pmb{\\theta})" + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "content": ". Nevertheless, as there are two possibilities for each observation, i.e., inlier and outlier, it will generate " + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "inline_equation", + "content": "2^n" + }, + { + "bbox": [ + 46, + 593, + 287, + 713 + ], + "type": "text", + "content": " combinations to be evaluated. Thus, the exact estimation is analytically intractable and approximation is needed. Next, we use the variational inference to approximate the exact posterior. Once the variational distribution is obtained, the posterior predictive distribution can be determined." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 429, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 429, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 429, + 83 + ], + "type": "text", + "content": "4.2. Variational Inference" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "spans": [ + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "text", + "content": "We wish to directly approximate the posterior " + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f},\\boldsymbol {\\theta}|\\mathcal{D})" + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "text", + "content": " using a variational posterior " + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\boldsymbol {\\theta})" + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "text", + "content": " such that the KL divergence between " + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f},\\boldsymbol {\\theta}|\\mathcal{D})" + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\boldsymbol {\\theta})" + }, + { + "bbox": [ + 305, + 90, + 547, + 150 + ], + "type": "text", + "content": " is minimized. The minimization is equivalently expressed as maximization of lower bound for the true log marginal likelihood:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 333, + 156, + 545, + 183 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 156, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 333, + 156, + 545, + 183 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\mathbf {f}, \\boldsymbol {\\theta}) = \\int q (\\mathbf {f}, \\boldsymbol {\\theta}) \\log \\left(\\frac {p (\\mathbf {f} , \\boldsymbol {\\theta} , \\mathcal {D})}{q (\\mathbf {f} , \\boldsymbol {\\theta})}\\right) d \\mathbf {f} d \\boldsymbol {\\theta}. \\tag {8}", + "image_path": "db24891f4a7e8c258c5c655a60403155a83691f0d16dd65a1de33324070fdbbd.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 188, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 188, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 545, + 224 + ], + "type": "text", + "content": "The maximization is, however, intractable since the optimal solution is " + }, + { + "bbox": [ + 305, + 188, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\hat{q} (\\mathbf{f},\\pmb {\\theta}) = p(\\mathbf{f},\\pmb {\\theta}|\\mathcal{D})" + }, + { + "bbox": [ + 305, + 188, + 545, + 224 + ], + "type": "text", + "content": " . To this end, we consider instead a restricted distribution of " + }, + { + "bbox": [ + 305, + 188, + 545, + 224 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\pmb {\\theta})" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "content": "Mean-field factorization supposes " + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\pmb {\\theta})" + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "content": " can be partitioned into disjoint groups. Considering the ease of calculation, we factorize " + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\pmb {\\theta}) = q_{1}(\\mathbf{f})q_{2}(\\gamma)q_{3}(\\mathbf{Z})q_{4}(\\sigma^{2},\\pmb {\\varphi})" + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "content": ". Besides, we assume " + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "inline_equation", + "content": "q_{4}" + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "content": " is Dirac delta function, i.e., it has a point mass at " + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "inline_equation", + "content": "(\\sigma^2,\\varphi)" + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "content": ". With this factorization, the maximization of Eq. (8) is obtained by optimizing each of the factors. For " + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 305, + 224, + 545, + 308 + ], + "type": "text", + "content": ", the minimization becomes" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 311, + 313, + 545, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 313, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 311, + 313, + 545, + 350 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {i} = \\underset {q _ {i}} {\\arg \\min } \\int q _ {i} \\log \\left(\\frac {\\exp \\mathbb {E} _ {j \\neq i} [ \\log p (\\mathbf {f} , \\boldsymbol {\\theta} , \\mathcal {D}) ]}{q _ {i}}\\right) d \\boldsymbol {\\theta} _ {i}, \\tag {9}", + "image_path": "bea0e0d2e42cbbc9ccec7ba09ce502c6cffbd78a3c568f457c2bc044cb8b5a24.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{j\\neq i}[\\cdot ]" + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": " denotes the expectation over " + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "inline_equation", + "content": "q_{j}" + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "inline_equation", + "content": "j\\neq i" + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": " Note that Eq. (9) is the negative KL divergence between " + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\mathbb{E}_{j\\neq i}\\left[\\log p(\\mathbf{f},\\boldsymbol {\\theta},\\mathcal{D})\\right]" + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": " . Thus, the optimal " + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 305, + 350, + 545, + 388 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 347, + 393, + 545, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 393, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 347, + 393, + 545, + 407 + ], + "type": "interline_equation", + "content": "\\log \\hat {q} _ {i} = \\mathbb {E} _ {j \\neq i} [ \\log p (\\mathbf {f}, \\boldsymbol {\\theta}, \\mathcal {D}) ] + \\text {c o n s t .} \\tag {10}", + "image_path": "8b0bdcb60b7a24a5c04598d353cfa21b55f41f1698a2b4b17315b3f90f84cc5c.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 413, + 522, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 522, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 522, + 426 + ], + "type": "text", + "content": "4.3. Sparse Inducing Variable Approximation" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": "The variational posterior approximation presented above can easily integrate sparse inducing variables [37], which allows the reduction of time complexity of GPR from " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(n^3)" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(nm^2)" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ". Introducing " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " pseudo-inputs " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_m" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " with inducing variables " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_m" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ", our goal is to use " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_m" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " to approximate " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f})" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_m" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " akin to " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " follows the same GP prior that " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f}_m) \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{K}_{mm})" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ". We suppose " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_m" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " is a sufficient statistic for " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ", i.e., for any value " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "p(u|\\mathbf{f}, \\mathbf{f}_m) = p(u|\\mathbf{f}_m)" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " holds [37]. In this setting, the augmented variational posterior " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f}, \\mathbf{f}_m) = p(\\mathbf{f}|\\mathbf{f}_m)\\phi(\\mathbf{f}_m)" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " and augmented latent variables set " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\theta} = (\\gamma, \\sigma^2, \\mathbf{Z}, \\varphi, \\mathbf{X}_m)" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": " with factorization " + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f}, \\mathbf{f}_m, \\boldsymbol{\\theta}) = q_1(\\mathbf{f}, \\mathbf{f}_m)q_2(\\gamma)q_3(\\mathbf{Z})q_4(\\sigma^2, \\varphi, \\mathbf{X}_m)" + }, + { + "bbox": [ + 305, + 431, + 545, + 586 + ], + "type": "text", + "content": ". The bound (8) becomes" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 309, + 592, + 545, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 592, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 309, + 592, + 545, + 628 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\int q (\\mathbf {f}, \\mathbf {f} _ {m}, \\boldsymbol {\\theta}) \\log \\left(\\frac {p \\left(\\mathbf {f} _ {m}\\right) p (\\gamma) p (\\mathbf {y} , \\mathbf {Z} \\mid \\mathbf {f})}{\\phi \\left(\\mathbf {f} _ {m}\\right) q _ {2 - 4}}\\right) d \\mathbf {f} d \\mathbf {f} _ {m} d \\boldsymbol {\\theta}, \\tag {11}", + "image_path": "6d01a5a1508fc865578bb30229e02113b50bfce98c5e32da03feb8f18d7e2f72.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 628, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 628, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 628, + 545, + 665 + ], + "type": "text", + "content": "where the term " + }, + { + "bbox": [ + 305, + 628, + 545, + 665 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f}|\\mathbf{f}_m)" + }, + { + "bbox": [ + 305, + 628, + 545, + 665 + ], + "type": "text", + "content": " inside the log is eliminated. In what follows, we maximize the bound analytically by solving the optimal choice of the variational distribution " + }, + { + "bbox": [ + 305, + 628, + 545, + 665 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\mathbf{f}_m,\\boldsymbol {\\theta})" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 671, + 441, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 441, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 441, + 682 + ], + "type": "text", + "content": "4.4. Maximize Lower Bound" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "To optimize the bound (11) in mean-field factorization, a common approach is to use the coordinate ascent technique," + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21952" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": "i.e., optimizing one factor " + }, + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "inline_equation", + "content": "q_{i}" + }, + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": " while keeping the others " + }, + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "inline_equation", + "content": "q_{j\\neq i}" + }, + { + "bbox": [ + 46, + 72, + 286, + 144 + ], + "type": "text", + "content": " fixed, and cycling through these factors in turn. Convergence is guaranteed because the bound is convex and monotonically increasing with respect to each factor [5]. Next, we give closed-form expressions for factor updates without detailed derivations, which can be found in suppl. material." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": "Updating " + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "q_{1}(\\mathbf{f},\\mathbf{f}_{m})" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": " means finding the optimal posterior GP given " + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "q_{2}" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "q_{3}" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "q_{4}" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": " . We denote " + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "p_i = \\mathbb{E}[z_i]" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "\\mathbf{P} =" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": " diag " + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "inline_equation", + "content": "(p_1,p_2,\\dots ,p_n)" + }, + { + "bbox": [ + 46, + 144, + 286, + 181 + ], + "type": "text", + "content": " . Integrating over f, (11) becomes" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 189, + 286, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 189, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 53, + 189, + 286, + 216 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\int \\phi (\\mathbf {f} _ {m}) \\log \\left(\\frac {p \\left(\\mathbf {f} _ {m}\\right) Q \\left(\\mathbf {f} _ {m} , \\mathbf {y}\\right)}{\\phi \\left(\\mathbf {f} _ {m}\\right)}\\right) d \\mathbf {f} _ {m} + \\text {c o n s t .}, \\tag {12}", + "image_path": "13de93e14839be9cb1630dc0ccc57b57ef1837c325f04e8c8b9c85bd54d67dc3.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 224, + 75, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 75, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 75, + 233 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 233, + 286, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 233, + 286, + 265 + ], + "spans": [ + { + "bbox": [ + 48, + 233, + 286, + 265 + ], + "type": "interline_equation", + "content": "\\log Q \\left(\\mathbf {f} _ {m}, \\mathbf {y}\\right) = \\log \\mathcal {N} \\left(\\mathbf {y} \\mid \\boldsymbol {\\mu} _ {\\mathbf {f} \\mid \\mathbf {f} _ {m}}, \\sigma^ {2} \\mathbf {P} ^ {- 1}\\right) - \\frac {1}{2 \\sigma^ {2}} \\operatorname {t r} \\left(\\mathbf {P K} _ {\\mathbf {f} \\mid \\mathbf {f} _ {m}}\\right), \\tag {13}", + "image_path": "a259a915dfee6dd6d11d9ef21433300e2366ed01d964eba0e735d23aa3279f3f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "inline_equation", + "content": "\\mu_{\\mathbf{f}|\\mathbf{f}_m} = \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{f}_m," + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathbf{f}|\\mathbf{f}_m} = \\mathbf{K}_{nn} - \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{mn}" + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "text", + "content": " are the expectation and covariance of " + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "inline_equation", + "content": "p(\\mathbf{f}|\\mathbf{f}_m)" + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "text", + "content": ", respectively. With some linear algebraic manipulation, the optimal " + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "inline_equation", + "content": "\\hat{\\phi} (\\mathbf{f}_m)" + }, + { + "bbox": [ + 47, + 265, + 286, + 314 + ], + "type": "text", + "content": " is given by a multivariate Gaussian distribution" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 315, + 286, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 315, + 286, + 344 + ], + "spans": [ + { + "bbox": [ + 113, + 315, + 286, + 344 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\phi} (\\mathbf {f} _ {m}) \\propto p (\\mathbf {f} _ {m}) Q (\\mathbf {f} _ {m}, \\mathbf {y}) \\tag {14} \\\\ = \\mathcal {N} (\\mathbf {f} _ {m} | \\boldsymbol {\\mu} _ {m}, \\mathbf {A} _ {m}), \\\\ \\end{array}", + "image_path": "bb93ce3f49d5fb021e4498d5962be9c42fe8f41ab707e4c3e516e50eea38f354.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{m} = \\sigma^{-2}\\mathbf{K}_{mm}\\pmb{\\Sigma}\\mathbf{K}_{mn}\\mathbf{P}\\mathbf{y},\\mathbf{A}_{m} = \\mathbf{K}_{mm}\\pmb{\\Sigma}\\mathbf{K}_{mm}," + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\pmb {\\Sigma} = (\\mathbf{K}_{mm} + \\sigma^{-2}\\mathbf{K}_{mn}\\mathbf{P}\\mathbf{K}_{nm})^{-1}" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " Note that we can always recover " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f})" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "q(\\mathbf{f},\\mathbf{f}_m) = p(\\mathbf{f}|\\mathbf{f}_m)\\phi (\\mathbf{f}_m)" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " by marginalizing out " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_m" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " , which gives optimal " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\hat{q} (\\mathbf{f}) =" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\mathbf{f}|\\boldsymbol {\\mu}_{\\mathbf{f}},\\mathbf{A})" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\pmb {\\mu_{\\mathrm{f}}} = \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\pmb {\\mu}_m" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{A} =" + }, + { + "bbox": [ + 46, + 345, + 286, + 418 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathbf{f}|\\mathbf{f}_m} + \\mathbf{K}_{nm}\\pmb{\\Sigma}\\mathbf{K}_{mn}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "type": "text", + "content": "Remark 1 With the optimal " + }, + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "type": "inline_equation", + "content": "\\hat{\\phi}(\\mathbf{f}_m)" + }, + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "type": "text", + "content": ", we obtain " + }, + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "type": "inline_equation", + "content": "\\langle \\mathcal{N}_i \\rangle = \\exp(\\mathbb{E}[\\log \\mathcal{N}_i])" + }, + { + "bbox": [ + 46, + 428, + 286, + 453 + ], + "type": "text", + "content": " as follows" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 87, + 453, + 286, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 453, + 286, + 475 + ], + "spans": [ + { + "bbox": [ + 87, + 453, + 286, + 475 + ], + "type": "interline_equation", + "content": "\\langle \\mathcal {N} _ {i} \\rangle = \\mathcal {N} \\left(y _ {i} \\mid \\boldsymbol {\\mu} _ {\\mathbf {f} i}, \\sigma^ {2}\\right) \\exp \\left(- \\frac {1}{2 \\sigma^ {2}} \\mathbf {A} _ {i i}\\right), \\tag {15}", + "image_path": "cb6e4c8780ee7821f85b9ee12732738a74f6b5abf5546e5938fbe02eb7f404e5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(y_i|f_i,\\sigma^2)" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\mathbf{fi}}" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": "-th element of " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_{\\mathbf{f}}" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ii}" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": "-th diagonal element of " + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 475, + 287, + 500 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "content": "Updating " + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "inline_equation", + "content": "q_{2}(\\gamma)" + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "content": " indicates updating the inlier ratio or mixture. Suppose " + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "inline_equation", + "content": "q_{1}, q_{3}" + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "inline_equation", + "content": "q_{4}" + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "content": " are given and note " + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "inline_equation", + "content": "\\hat{n} = \\operatorname{tr}(\\mathbf{P})" + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "content": ". According to Eq. (10), we conclude that " + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "inline_equation", + "content": "\\hat{q}_{2}(\\gamma)" + }, + { + "bbox": [ + 46, + 510, + 286, + 557 + ], + "type": "text", + "content": " again follows a Beta distribution" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 87, + 568, + 286, + 580 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 568, + 286, + 580 + ], + "spans": [ + { + "bbox": [ + 87, + 568, + 286, + 580 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {2} (\\gamma) = \\operatorname {B e t a} (\\gamma | B _ {a} + \\hat {n}, B _ {b} + n - \\hat {n}). \\tag {16}", + "image_path": "62a41ab9de2a36d09b3e201c466c2c8e0873eafd01af882b5595e5ea86b00847.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "text", + "content": "Remark 2 With the optimal " + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "inline_equation", + "content": "\\hat{q}_2(\\gamma)" + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "text", + "content": ", according to the properties of Beta distribution, we obtain " + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "inline_equation", + "content": "\\langle \\gamma \\rangle = \\exp (\\mathbb{E}[\\log \\gamma ])" + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "inline_equation", + "content": "\\langle 1 - \\gamma \\rangle = \\exp (\\mathbb{E}[\\log (1 - \\gamma)])" + }, + { + "bbox": [ + 46, + 590, + 286, + 625 + ], + "type": "text", + "content": " as follows" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 72, + 627, + 286, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 627, + 286, + 644 + ], + "spans": [ + { + "bbox": [ + 72, + 627, + 286, + 644 + ], + "type": "interline_equation", + "content": "\\langle \\gamma \\rangle = \\exp (\\psi (B _ {a} + \\hat {n}) - \\psi (B _ {a} + B _ {b} + n)), \\tag {17}", + "image_path": "0ee0799b4358a469a92c744d8f58252ccb1466d366747ae752bd54087db41545.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 55, + 639, + 286, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 639, + 286, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 639, + 286, + 654 + ], + "type": "interline_equation", + "content": "\\langle 1 - \\gamma \\rangle = \\exp (\\psi (B _ {b} + n - \\hat {n}) - \\psi (B _ {a} + B _ {b} + n)), \\tag {17}", + "image_path": "26cad3a0b4c4a24b38c7c9188a17e2860ff1316407dd202f793bebcec51bdb14.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 655, + 194, + 667 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 194, + 667 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 194, + 667 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 655, + 194, + 667 + ], + "type": "inline_equation", + "content": "\\psi (\\cdot)" + }, + { + "bbox": [ + 47, + 655, + 194, + 667 + ], + "type": "text", + "content": " is the digamma function." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Updating " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "q_{3}(\\mathbf{Z})" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": " represents determining the probability of each data being an inlier given " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "q_{1}, q_{2}" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "q_{4}" + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": ". It encodes the mode of each data point. From Eq. (10), it leads to a" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "type": "text", + "content": "further factorization " + }, + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\hat{q}_3(\\mathbf{Z}) = \\prod_{i=1}^n \\hat{q}_3^{[i]}(z_i)" + }, + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\hat{q}_3^{[i]}(z_i)" + }, + { + "bbox": [ + 305, + 70, + 545, + 95 + ], + "type": "text", + "content": " is shown to follow a Bernoulli distribution:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 370, + 95, + 545, + 110 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 95, + 545, + 110 + ], + "spans": [ + { + "bbox": [ + 370, + 95, + 545, + 110 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {3} ^ {[ i ]} \\left(z _ {i}\\right) = \\left(1 - p _ {i}\\right) ^ {1 - z _ {i}} p _ {i} ^ {z _ {i}}, \\tag {18}", + "image_path": "a7eabe2560ab74ec08bc5427355df94f307d34e97c7daa4e3c53d7ef877c973a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 120, + 545, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 120, + 545, + 147 + ], + "spans": [ + { + "bbox": [ + 306, + 120, + 545, + 147 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad p _ {i} = \\frac {\\langle \\gamma \\rangle \\left\\langle \\mathcal {N} _ {i} \\right\\rangle}{\\left. \\langle 1 - \\gamma \\rangle / a + \\langle \\gamma \\rangle \\left\\langle \\mathcal {N} _ {i} \\right\\rangle \\right.}. \\tag {19}", + "image_path": "47ea3ca3d276fbf4328c6889e23a13cf3d589226f6b5d1d741754c092a5c8af0.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": "Remark 3 " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": " shows the posterior probability of the " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": "-th data being an inlier. It depends on both the deviation between " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": " and the posterior mean " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mu_{\\mathrm{fi}}" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": ", and the term containing the posterior variance " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ii}" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": ". The importance of this variance term is that it encodes the uncertainty of the latent function at " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": ", which means if we are uncertain about that data, then we cannot identify it as an inlier, even though " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\mu_{\\mathrm{fi}}" + }, + { + "bbox": [ + 304, + 153, + 545, + 249 + ], + "type": "text", + "content": " are close. This is helpful to avoid overfitting." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": "Updating " + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "inline_equation", + "content": "q_{4}(\\sigma^{2},\\varphi ,\\mathbf{X}_{m})" + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": " involves the optimization of hyperparameters. Specifically, " + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": " controls the noise level, " + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": " represents the shape of the kernel function, and " + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_m" + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": " is the location of the pseudo-inputs. As assumed previously, " + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "inline_equation", + "content": "q_{4}(\\sigma^{2},\\varphi ,\\mathbf{X}_{m})" + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": " obeys the Dirac delta distribution, which means we directly maximize the lower bound (11) with respect to " + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "inline_equation", + "content": "(\\sigma^2,\\varphi ,\\mathbf{X}_m)" + }, + { + "bbox": [ + 304, + 257, + 545, + 341 + ], + "type": "text", + "content": ", rather than using Eq. (10)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "q_{1}" + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "q_{2}" + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "q_{3}" + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "text", + "content": ", taking derivative of (11) over " + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\sigma^2" + }, + { + "bbox": [ + 305, + 341, + 545, + 365 + ], + "type": "text", + "content": " and setting to zero, we obtain a closed-form expression" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 328, + 365, + 545, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 365, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 328, + 365, + 545, + 388 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} ^ {2} = \\frac {1}{\\hat {n}} \\left(\\mathbf {y} - \\boldsymbol {\\mu} _ {\\mathbf {f}}\\right) ^ {\\top} \\mathbf {P} \\left(\\mathbf {y} - \\boldsymbol {\\mu} _ {\\mathbf {f}}\\right) + \\frac {1}{\\hat {n}} \\operatorname {t r} (\\mathbf {P A}), \\tag {20}", + "image_path": "67df92d0c20a94fcbfe5dbf130c4a00c533f6c69aab21f62c9540ece619c2907.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\operatorname{tr}(\\cdot)" + }, + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "text", + "content": " is the trace. The lower bound (11) is, however, difficult to optimize for the remaining hyperparameters " + }, + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "inline_equation", + "content": "(\\varphi, \\mathbf{X}_m)" + }, + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "text", + "content": " since the integral is intractable. To this end, we use the reverse Jensen's inequality and obtain" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 309, + 442, + 545, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 442, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 309, + 442, + 545, + 464 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {2} := \\log \\mathcal {N} (\\mathbf {y} | 0, \\mathbf {K} _ {\\mathbf {y}}) - \\frac {1}{2 \\sigma^ {2}} \\operatorname {t r} \\left(\\mathbf {P K} _ {\\mathbf {f} | \\mathbf {f} _ {m}}\\right) + \\text {c o n s t .} \\leq \\mathcal {L}, \\tag {21}", + "image_path": "8c7415c20e81c4ba5367660683ce263eebbcf91f6bba5ab178b495e6573895fe.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{K_y} = \\sigma^2\\mathbf{P}^{-1} + \\mathbf{K}_{nm}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{mn}" + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "text", + "content": ". To set the optimized hyperparameters " + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "inline_equation", + "content": "(\\varphi, \\mathbf{X}_m)" + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "text", + "content": ", we seek partial derivatives of " + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "text", + "content": " with respect to them. Thereafter, the standard gradient descent algorithm provides the value that maximizes " + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 304, + 472, + 545, + 521 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 527, + 478, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 478, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 478, + 539 + ], + "type": "text", + "content": "4.5. Stochastic Variational Inference" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": "Modern applications often involve handling massive data. However, the GPR equipped with variational inference does not easily scale to big data, even with inducing variables. This is because we need to go through the entire training data at each coordinate update. As the training data size grows, the computational overhead becomes larger." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "An alternative to coordinate ascent is to use SVI [20], which is similar to stochastic gradient descent (SGD), that performs stochastic optimization from the noisy but cheap-to-compute estimates of the gradient. It iterates between subsampling a subset of data and adjusting the hidden structure solely based on the subset. Thus, SVI is much more efficient than conventional variational inference. To apply SVI to the probabilistic model, a set of global variables is" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21953" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "needed [18]. In our robust GPR setting, the inducing variables " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_m" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " and mixing coefficient variable " + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": " fill this role." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": "Natural Gradient. In gradient-based optimization, the natural gradient accounts for the geometric structure of probability parameters and is used in SVI to replace the Euclidean gradient. In exponential families, it is given by premultiplying the usual gradient by the inverse Fisher information matrix " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "G(\\eta)^{-1}" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": " is the canonical parameter of the exponential families. Since both " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "\\phi(\\mathbf{f}_m)" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "q(\\gamma)" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": " are exponential family distributions, they enjoy simple natural gradients [19] of the bound (11) such that " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "g(\\eta) = \\mathbb{E}[\\eta] - \\eta" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": " denotes the natural gradient. For Gaussian distribution " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "\\phi(\\mathbf{f}_m)" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": ", its canonical parameter is " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "[\\mathbf{A}_m^{-1}\\boldsymbol{\\mu}_m, -\\frac{1}{2}\\mathbf{A}_m^{-1}]" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": ". For Beta distribution " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "q(\\gamma)" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": ", its canonical parameter is " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "[B_a + \\hat{n}, B_b + n - \\hat{n}]" + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "text", + "content": ". Thereafter, we obtain the update rule using natural gradient with a step size " + }, + { + "bbox": [ + 46, + 96, + 289, + 264 + ], + "type": "inline_equation", + "content": "\\epsilon_t" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 54, + 271, + 287, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 271, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 54, + 271, + 287, + 287 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\eta} ^ {t} = \\boldsymbol {\\eta} ^ {t - 1} + \\varepsilon_ {t} g (\\boldsymbol {\\eta} ^ {t - 1}) = (1 - \\varepsilon_ {t}) \\boldsymbol {\\eta} ^ {t - 1} + \\varepsilon_ {t} \\mathbb {E} [ \\boldsymbol {\\eta} ]. \\tag {22}", + "image_path": "c52786cf6c1c45f392906c46519930f95d0a761d228dd652f44d7d6cf2f78ee1.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 295, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 295, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 295, + 287, + 342 + ], + "type": "text", + "content": "Note that when the step size " + }, + { + "bbox": [ + 46, + 295, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\varepsilon_{t} = 1" + }, + { + "bbox": [ + 46, + 295, + 287, + 342 + ], + "type": "text", + "content": ", we recover the original variational update in Eq. (14) and Eq. (16). Now, the noisy natural gradient can be easily computed by sampling either individual or mini-batch of the data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 350, + 162, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 162, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 162, + 363 + ], + "type": "text", + "content": "4.6. Making Predictions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 369, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 405 + ], + "type": "text", + "content": "So far we have described how to infer the approximate posterior of the latent variables. To make predictions, we use the predictive distribution similar to Eq. (3):" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 60, + 405, + 287, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 405, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 60, + 405, + 287, + 445 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p \\left(\\mathbf {f} _ {*} \\mid \\mathcal {D}, \\mathbf {X} _ {*}\\right) = \\int p \\left(\\mathbf {f} _ {*} \\mid \\mathbf {f} _ {m}\\right) p \\left(\\mathbf {f} \\mid \\mathbf {f} _ {m}\\right) \\phi \\left(\\mathbf {f} _ {m}\\right) d \\mathbf {f} _ {m} d \\mathbf {f} \\tag {23} \\\\ = \\mathcal {N} \\left(\\mathbf {f} _ {*} | \\mathbf {K} _ {* m} \\mathbf {K} _ {m m} ^ {- 1} \\boldsymbol {\\mu} _ {m}, \\mathbf {K} _ {\\mathbf {f} _ {*} | \\mathbf {f} _ {m}} + \\mathbf {K} _ {* m} \\boldsymbol {\\Sigma} \\mathbf {K} _ {m *}\\right), \\\\ \\end{array}", + "image_path": "5c036bba2c4018f3d701a96e9645149cb01fec705475f5b4594739c08cec33af.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 453, + 216, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 216, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 216, + 467 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 453, + 216, + 467 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_{\\mathbf{f}_{*}|\\mathbf{f}_{m}} = \\mathbf{K}_{**} - \\mathbf{K}_{*m}\\mathbf{K}_{mm}^{-1}\\mathbf{K}_{m*}" + }, + { + "bbox": [ + 47, + 453, + 216, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 476, + 127, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 127, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 127, + 490 + ], + "type": "text", + "content": "5. Applications" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 496, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 533 + ], + "type": "text", + "content": "In this section, we describe how to use the proposed GPR model to deal with real-world tasks, including feature matching and dense gene expression imputation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 540, + 154, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 154, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 154, + 553 + ], + "type": "text", + "content": "5.1. Feature Matching" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Feature matching aims at establishing reliable feature point correspondences. To solve the matching problem in a regression manner, we first construct a putative correspondence set " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{(\\mathbf{x}_i,\\mathbf{x}_i')\\}_{i = 1}^n" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " by nearest neighbor (NN) matching, where " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i'" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " represent the coordinates of feature points. The putative set is then converted to motion vector set, i.e., " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(\\mathbf{x}_i,\\mathbf{y}_i)\\}_{i = 1}^n" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_i = \\mathbf{x}_i' - \\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": ". The motion of an object projected on the image plane is known to be slow-and-smooth [38], which is well described by GP. Thus, the motion vectors of inliers can be seen as sampling on the underlying model " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": ", while the outliers are spuriously distributed. Our goal is to determine the correctness of each data. The task, however, is non-trivial as there are often" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "massive outliers (even up to " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "). Moreover, the feature points in each image can reach several thousands, which requires high computational efficiency. As we will see, our model is robust and fast enough to handle such cases." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": "Inference Setting. To apply our model to feature matching, some special considerations need to be set. The feature coordinates are first normalized. For the covariance kernel, we choose the squared exponential (SE) kernel " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "k(\\mathbf{x},\\mathbf{x}^{\\prime}) = \\lambda^{-1}\\exp (-\\beta \\| \\mathbf{x} - \\mathbf{x}^{\\prime}\\|^{2})" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": ". We find that fixed hyperparameters work well for most situations, which are empirically set to " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "\\lambda = 4" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": ". The positions of the inducing variables are randomly selected from the training data and kept fixed during inference. The ratio information is also considered as a prior. The mini-batch size is set to " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "\\max \\left\\{\\frac{n}{8},200\\right\\}" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": ". After inference convergences, the " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": "-th data is decided to be inlier if " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "p_i > \\tau" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": " is a threshold and is set to " + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "inline_equation", + "content": "\\tau = 0.75" + }, + { + "bbox": [ + 304, + 121, + 546, + 263 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 264, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 545, + 361 + ], + "type": "text", + "content": "Predictions. One of the attractive properties of our model for this task is that when the training is completed, the resulting posterior GP is able to predict the motion vector of each feature point. Combined with the descriptors' information, we can yield much more correct correspondences rather than being limited to putative set. More correct correspondences are crucial for downstream tasks, as they can significantly improve the accuracy." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 365, + 494, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 494, + 379 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 494, + 379 + ], + "type": "text", + "content": "5.2. Dense Gene Expression Imputation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 384, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 539 + ], + "type": "text", + "content": "Recently, technological advances have made it possible to measure spatially resolved transcriptome-wide mRNA expressions with spatial information in tissue samples. GPR is thus utilized to infer gene expression in discrete samples, generating dense gene expression in 2D, 3D, and even spatiotemporal [3]. Unfortunately, due to equipment malfunctions and process disturbances, the readout data may contain bad spots. In this case, a vanilla GPR may lead to completely wrong results and thus mislead the subsequent analysis. By comparison, the robust GPR developed in this paper copes well with outliers and is able to give meaningful imputation results. For this application, the implementation is simple and requires little extra consideration." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 549, + 388, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 388, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 388, + 562 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": "In this section, we first conduct numerical experiments to evaluate the performance in a fully controlled environment. After that, we apply our model to tackle feature matching problem and compare it with many state-of-the-art methods tailored for feature matching. In the end, the evaluation of gene expression imputation is performed. All experiments are conducted on a desktop with Intel i7-10700 CPU, 16 GB memory with MATLAB except deep learning methods." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "type": "text", + "content": "6.1. Numerical Experiments" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We study two datasets, i.e., Neal dataset [28] and Friedman dataset [14]. The Neal dataset is one-dimensional data," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21954" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 272, + 232 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 272, + 232 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 272, + 232 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 272, + 232 + ], + "type": "image", + "image_path": "bf6975106d089e2f181b198558389f9a26f504bb91fd7013d7378b6516549c3a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 287, + 267 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 287, + 267 + ], + "type": "text", + "content": "Figure 2. Visual examples on Neal data. Our model approximates the exact posterior GP using only inliers, even with massive outliers. The legend is shown in the bottom." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "type": "text", + "content": "where the input " + }, + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "type": "text", + "content": " is drawn from a uniform distribution within " + }, + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "type": "inline_equation", + "content": "[-2.5, 2.5]" + }, + { + "bbox": [ + 46, + 277, + 287, + 300 + ], + "type": "text", + "content": ". The target value is calculated as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 302, + 272, + 315 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 302, + 272, + 315 + ], + "spans": [ + { + "bbox": [ + 61, + 302, + 272, + 315 + ], + "type": "interline_equation", + "content": "f (x) = 0. 3 + 0. 4 x + 0. 5 \\sin (2. 7 x) + 1. 1 / \\left(1 + x ^ {2}\\right).", + "image_path": "43edd2cc1692abf920ff6d87ac2ecd6c90ae5a93cc4e5c02d70e6e5bd2588486.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 374 + ], + "type": "text", + "content": "The Gaussian noise is added to the target value with zero mean and variance of 0.1. Next, outliers are injected into the training data, where the value is drawn from uniform distribution within " + }, + { + "bbox": [ + 46, + 316, + 287, + 374 + ], + "type": "inline_equation", + "content": "[-5, 5]" + }, + { + "bbox": [ + 46, + 316, + 287, + 374 + ], + "type": "text", + "content": ". The Friedman is 10-dimensional data and the function value depends on the first five dimensions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 375, + 279, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 375, + 279, + 388 + ], + "spans": [ + { + "bbox": [ + 55, + 375, + 279, + 388 + ], + "type": "interline_equation", + "content": "f (\\mathbf {x}) = 1 0 \\sin \\left(\\pi x _ {1} x _ {2}\\right) + 2 0 \\left(x _ {3} - 0. 5\\right) ^ {2} + 1 0 x _ {4} + 5 x _ {5},", + "image_path": "4a4cf761d8e1108fa9c71bef455318e8c14fbb86e7ab211b6d684aae08e88a0b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "text", + "content": "while the remaining dimensions complicate the task by adding a feature selection process. The input " + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "text", + "content": " is sampled uniformly within " + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "inline_equation", + "content": "[0,1]^{10}" + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "text", + "content": ". Gaussian noise " + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,0.01)" + }, + { + "bbox": [ + 46, + 389, + 287, + 436 + ], + "type": "text", + "content": " is added and random outliers are distributed among [5, 25]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "type": "text", + "content": "We fix the inlier number to 100 and change the outlier ratio. GPR with Student's-" + }, + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "type": "text", + "content": " (St) [32], Laplace (Lap) [32], and Gaussian mixture distribution (MEM) [8], as well as variational free energy (VEF) [37], are chosen as competitors. Some intuitive examples on Neal data are shown in Fig. 2, where outlier ratio increases from 0 to " + }, + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 437, + 287, + 567 + ], + "type": "text", + "content": ". We see that the prediction by our model almost exactly reproduces the full GP prediction using only inliers. In contrast, GPR-St and -Lap give poor approximations. GPR-MEM is able to give a better answer, yet still not as good as ours, especially at extremely high outlier ratios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 664 + ], + "type": "text", + "content": "To statistically verify performance, we select mean absolute error (MAE, m), root mean square error (RMSE, r), and negative log of predictive probability (NLP, n) as metrics. 1000 testing points are generated in equal intervals. The statistical results on Neal and Friedman in Table 1 suggest that our method outperforms other alternatives in terms of robustness and accuracy. More results including KL and statistical variance are provided in suppl. material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 153, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 153, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 153, + 684 + ], + "type": "text", + "content": "6.2. Feature Matching" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "content": "We collect three large and diverse feature matching datasets with three different vision tasks, say YFCC100M" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 308, + 95, + 545, + 224 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 91 + ], + "type": "text", + "content": "Table 1. Quantitative results on Neal and Friedman data with different outlier ratios. Bold indicates the best." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 95, + 545, + 224 + ], + "lines": [ + { + "bbox": [ + 308, + 95, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 308, + 95, + 545, + 224 + ], + "type": "table", + "html": "
Neal [28]
Method10%50%80%
mrnmrnmrn
GPR-VFE [37]0.180.210.730.580.771.750.761.081.96
GPR-St [32]0.030.03-0.410.090.190.390.771.151.66
GPR-Lap [32]0.030.07-1.170.420.561.620.350.722.03
GPR-MEM [8]0.040.08-1.360.060.12-0.660.771.522.04
Ours0.010.02-1.380.030.04-1.250.030.03-0.89
Friedman [14]
Method20%30%50%
mrnmrnmrn
GPR-VFE [37]1.121.242.281.471.623.082.883.166.93
GPR-St [32]0.040.04-0.080.911.103.591.472.187.16
GPR-Lap [32]0.230.290.370.460.610.942.032.233.29
GPR-MEM [8]0.110.21-0.990.130.24-0.662.132.322.98
Ours0.040.06-1.460.060.08-0.350.100.140.55
", + "image_path": "7ac37f3d520986f63f35272987d6142a96b39cf6cf680f8bd40e8f213296d7bf.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 308, + 234, + 541, + 380 + ], + "blocks": [ + { + "bbox": [ + 308, + 234, + 541, + 380 + ], + "lines": [ + { + "bbox": [ + 308, + 234, + 541, + 380 + ], + "spans": [ + { + "bbox": [ + 308, + 234, + 541, + 380 + ], + "type": "image", + "image_path": "d63bae63fad5a96af15bc558e42713b63d1df2c55e121e76a9bfee1978ae7202.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 381, + 545, + 414 + ], + "lines": [ + { + "bbox": [ + 306, + 381, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 545, + 414 + ], + "type": "text", + "content": "Figure 3. Qualitative illustration of relative pose estimation. We show the true positive in blue and false positive in red. Best viewed in color with " + }, + { + "bbox": [ + 306, + 381, + 545, + 414 + ], + "type": "inline_equation", + "content": "200\\%" + }, + { + "bbox": [ + 306, + 381, + 545, + 414 + ], + "type": "text", + "content": " zoom in." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 428, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 428, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 428, + 545, + 620 + ], + "type": "text", + "content": "dataset [36] (4000 pairs) for relative pose estimation, CPC dataset [42] (1000 pairs) for fundamental matrix estimation, and HPatches dataset [1] (580 pairs) for homography estimation. Six state-of-the-arts from handcrafted to deep learning are chosen for comparison, namely, MAGSAC++ [2], LPM [26], MCDM [25], CRC [12], PointCN [43], and OANet [44], with baseline ratio test. Briefly, MAGSAC++ is resampling-based method, LPM is a heuristic method that preserves local structure of feature points, CRC interpolates a smooth vector field using Fourier bases, PointCN uses deep neural networks with context normalization to encode global contextual information, OANet further captures local contextual information by clustering unordered correspondences. Note that we assess currently other robust GPR methods are not capable to handle the feature matching problem, thus none of them are chosen for comparison." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 635, + 444, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 444, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 444, + 645 + ], + "type": "text", + "content": "6.2.1 Relative Pose Estimation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Following [44], Yahoo's YFCC100M dataset [36] generates 4000 testing image pairs. SIFT [24] with NN matching is adopted to establish putative correspondences. The maximum number of keypoints for each image is limited to 4000. RANSAC [13] is used to estimate the relative camera pose." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21955" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 95, + 262, + 205 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 286, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 286, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 286, + 92 + ], + "type": "text", + "content": "Table 2. Quantitative comparison for relative pose estimation. Bold indicates the best and underline ranks the second." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 95, + 262, + 205 + ], + "lines": [ + { + "bbox": [ + 70, + 95, + 262, + 205 + ], + "spans": [ + { + "bbox": [ + 70, + 95, + 262, + 205 + ], + "type": "table", + "html": "
YFCC100M [36]
MethodAUCPRF
@5°@10°@20°
Ratio test28.839.252.124.355.332.8
MSC++ [2]24.933.745.724.355.332.8
PointCN [43]45.154.665.047.273.454.9
OANet [44]53.664.175.851.287.061.7
LPM [26]38.648.859.751.443.645.9
MCDM [25]47.859.470.763.046.552.7
CRC [12]38.148.258.641.257.844.5
Ours53.863.773.885.354.063.7
", + "image_path": "a2a4c42330d858a74bd3de50c323d75f71b527294e5f94b926e4572308fe6f64.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 52, + 213, + 279, + 343 + ], + "blocks": [ + { + "bbox": [ + 52, + 213, + 279, + 343 + ], + "lines": [ + { + "bbox": [ + 52, + 213, + 279, + 343 + ], + "spans": [ + { + "bbox": [ + 52, + 213, + 279, + 343 + ], + "type": "image", + "image_path": "dc04c4bb8db41b27359a91b479060ac3afea0f3337e0a7442160a15dd2c9426b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "type": "text", + "content": "Figure 4. Visual examples of homography and fundamental matrix estimation. We show the true positive in blue and false positive in red. Best viewed in color with " + }, + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "type": "inline_equation", + "content": "200\\%" + }, + { + "bbox": [ + 46, + 345, + 287, + 378 + ], + "type": "text", + "content": " zoom in." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 392, + 286, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 286, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 286, + 464 + ], + "type": "text", + "content": "We measure the maximum of rotation and translation errors in degree and report the approximate Area Under the Curve (AUC) with thresholds 5, 10, and 20 degrees. Precision, recall, and F1-score before RANSAC with respect to the ground-truth inliers are also presented. See suppl. material for a detailed description of the dataset and the metrics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 286, + 559 + ], + "type": "text", + "content": "Some visualized examples are demonstrated in Fig. 3. Statistics results are comprehensively reported in Table 2. Since deep learning methods such as PointCN and OANet are trained in such dataset with geometric loss, they can capture geometric information and therefore have higher AUC compared to other handcrafted methods. By comparison, our method achieves comparable results to these deep learning methods with much higher precision and F1-score." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 574, + 286, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 286, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 286, + 586 + ], + "type": "text", + "content": "6.2.2 Homography & Fundamental Matrix Estimation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Homography and fundamental matrix estimation are critical parts in computer vision. The maximum keypoints for HPatches and CPC are limited to 4000. For evaluation metrics, we choose the precision, recall, and F1-score as well as the accuracy of the estimation. For homography estimation, we adopt homography error defined in [11], and for fundamental matrix, we follow [4] and use normalized symmetric geometry distance (NSGD) as the metrics. An estimate is classified as accurate or not by a threshold, which is set to 4 pixels for homography error and 0.05 for the NSGD [4]." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 92, + 545, + 202 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 91 + ], + "type": "text", + "content": "Table 3. Statistical results for homography and fundamental matrix estimation. Bold ranks the first, underline the second." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 92, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 307, + 92, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 307, + 92, + 545, + 202 + ], + "type": "table", + "html": "
MethodHPatches [1]CPC [42]
Acc.PRFAcc.PRF
Ratio test71.771.651.663.017.012.763.920.5
MSC++ [2]74.487.392.486.06.919.729.619.4
PointCN [43]73.176.985.778.629.319.870.228.8
OANet [44]70.073.577.272.147.034.681.045.4
LPM [26]60.672.550.552.323.821.948.926.1
MCDM [25]77.762.991.073.034.823.061.032.5
CRC [12]71.775.592.580.428.724.847.230.4
Ours78.189.994.391.549.661.559.357.2
Ours*82.473.9109.6-51.939.297.3-
", + "image_path": "1dbe48d164c483c47c9234ccffd747ca50d995d9c198642eda7b7eb48381e2af.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 318, + 222, + 533, + 300 + ], + "blocks": [ + { + "bbox": [ + 307, + 211, + 544, + 221 + ], + "lines": [ + { + "bbox": [ + 307, + 211, + 544, + 221 + ], + "spans": [ + { + "bbox": [ + 307, + 211, + 544, + 221 + ], + "type": "text", + "content": "Table 4. Ablation studies on feature matching. Bold is the best." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 222, + 533, + 300 + ], + "lines": [ + { + "bbox": [ + 318, + 222, + 533, + 300 + ], + "spans": [ + { + "bbox": [ + 318, + 222, + 533, + 300 + ], + "type": "table", + "html": "
MethodPrec.RecallF1Time
CRC [12]50.767.854.968.1
OANet (on GPU) [44]47.975.256.041.2
RS-GPRNo SVI76.366.170.047.1
No inducing variables72.669.069.51.6e5
Opt. Hyperparameters85.061.267.71556
EM optimization67.669.865.543.7
Default88.068.275.69.8
", + "image_path": "b869c03b445fc7fbf651123e7c30fef54ed2c422347dc29b8b6bcf8eff87aa53.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "type": "text", + "content": "Several visual examples are provided in Fig. 4. Note that our predictive model is also presented and indicated by the superscript " + }, + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "type": "inline_equation", + "content": "{}^{*}\\ast" + }, + { + "bbox": [ + 304, + 314, + 545, + 422 + ], + "type": "text", + "content": ". It establishes significantly more correct correspondences compared to other methods. Table 3 reports the statistical results. As it indicates, our method outperforms all other methods in the two tasks. When using the predictive model, it can even produce more correct correspondences than the putative set (e.g., the recall in HPatches is higher than 100), thus further improving accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 439, + 499, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 439, + 499, + 451 + ], + "spans": [ + { + "bbox": [ + 306, + 439, + 499, + 451 + ], + "type": "text", + "content": "6.2.3 Ablation Studies of Feature Matching" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 458, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 545, + 578 + ], + "type": "text", + "content": "To measure performance, especially runtime, in different settings, we conduct ablation studies on 100 image pairs from YFCC100M. It mainly includes four choices, i.e., not using SVI, not using inducing variables, optimizing the kernel hyperparameters, and using EM optimization instead of variational inference. We also include the CRC and OANet to compare the runtime. The results are reported in Table 4, where we see that our method performs the best with the default setting described in Sect. 5.1. In particular, the running time is much faster compared to other settings and methods." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 586, + 493, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 493, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 493, + 599 + ], + "type": "text", + "content": "6.3. Dense Gene Expression Imputation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "We collect two spatial transcriptomics datasets from mouse olfactory bulb and human breast cancer biopsies [34], respectively. Briefly, the spatial transcriptomics gene expression data is measured from thin tissue sections placed on an array with ploy probes and spatially resolved DNA barcodes. These create a grid of circular spots where the mRNA abundance of each spot is measured using probes with the barcodes encoding the spatial locations. The mouse olfactory bulb and human breast cancer biopsies datasets" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "21956" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 166, + 158 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 166, + 158 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 166, + 158 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 166, + 158 + ], + "type": "image", + "image_path": "f18ddbf02269356ae12c989aebb22acf2f900a111dfd7aa45aba705fdda444c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 160, + 287, + 216 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 287, + 216 + ], + "type": "text", + "content": "Figure 5. Visualization of dense spatial gene expression imputation. The spatial transcriptomics data is plotted on the top row. The bottom row shows the imputation results of different methods. We stack the spatial transcriptomics (shown as dots) on the imputed results to show the quality of the imputation." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 72, + 283, + 158 + ], + "blocks": [ + { + "bbox": [ + 168, + 72, + 283, + 158 + ], + "lines": [ + { + "bbox": [ + 168, + 72, + 283, + 158 + ], + "spans": [ + { + "bbox": [ + 168, + 72, + 283, + 158 + ], + "type": "image", + "image_path": "55745084f69e7e663fc4106324058dc6db9f1fa989348d7b22a8e582325efa9a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 72, + 247, + 263, + 384 + ], + "blocks": [ + { + "bbox": [ + 47, + 223, + 286, + 244 + ], + "lines": [ + { + "bbox": [ + 47, + 223, + 286, + 244 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 286, + 244 + ], + "type": "text", + "content": "Table 5. Statistical results of dense gene expression imputation. Bold indicates the best." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 247, + 263, + 384 + ], + "lines": [ + { + "bbox": [ + 72, + 247, + 263, + 384 + ], + "spans": [ + { + "bbox": [ + 72, + 247, + 263, + 384 + ], + "type": "table", + "html": "
Mouse olfactory bulb
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.460.591.250.330.401.10
GPR-St [32]0.070.14-0.570.020.04-1.33
GPR-Lap [32]0.200.270.330.480.540.94
Ours0.030.05-1.990.020.04-2.21
Breast cancer tissue
MethodPattern 1Pattern 2
mrnmrn
GPR-Exact0.240.351.440.230.331.15
GPR-St [32]0.190.320.370.180.300.22
GPR-Lap [32]0.250.360.560.250.370.53
Ours0.120.16-0.540.110.17-0.39
", + "image_path": "7e2a87e4e76fbbe587afdb4002f46d7baea7049f056a8a401616c3b08ea3db79.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 396, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 467 + ], + "type": "text", + "content": "contain 14859 and 12856 measured genes, respectively. To identify spatially variable genes, we adopt SpatialDE [35] and select two patterns for each dataset. We next add 5 random outliers to each identified pattern to simulate the outlier scenario. In the end, different GPR methods are applied to impute dense spatial gene expression." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "text", + "content": "Two visual examples are presented in Fig. 5, where in each example, the second row shows the imputed results. As can be seen, our method accurately infers the correct gene expression regardless of the outliers. To give quantitative results, we randomly split each dataset into " + }, + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "text", + "content": " training data and " + }, + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "text", + "content": " test data. As mentioned above, we use the MAE, RMSE, and NLP to measure the performance, and report the statistical results in Table 5. We see that our method always has the lowest error." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 586, + 105, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 105, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 105, + 600 + ], + "type": "text", + "content": "7. Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": "Optimization Process. We visualize the intermediate results of the optimization process on Neal data with " + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": " outliers and present it in the top row of Fig. 6. We see that the field of " + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": " in Eq. (19) gradually converges to the inliers. After convergence, the posterior mean and variance functions are very close to the ground truth, and the inducing variables are restricted to the interval of the inliers." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The Role of Term " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ii}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": ". We remove the term containing " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ii}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " in Eq. (15) and show the results in the bottom of Fig. 6." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 543, + 162 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 543, + 162 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 543, + 162 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 543, + 162 + ], + "type": "image", + "image_path": "63607d253c4cdef0168a9b0993d4d1c20ff65bda2af6dc79d4cd66053cea2219.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "type": "text", + "content": "Figure 6. Intermediate results of the optimization process. The top row shows the full model while the bottom removes term " + }, + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{ii}" + }, + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "type": "text", + "content": ". We visualize the field of " + }, + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 163, + 545, + 207 + ], + "type": "text", + "content": ", which indicates the inlier probability at any location. The deeper the blue color, the higher the probability." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 318, + 215, + 531, + 263 + ], + "blocks": [ + { + "bbox": [ + 318, + 215, + 531, + 263 + ], + "lines": [ + { + "bbox": [ + 318, + 215, + 531, + 263 + ], + "spans": [ + { + "bbox": [ + 318, + 215, + 531, + 263 + ], + "type": "image", + "image_path": "7675747a1a2dd41bde5fa61c995b2e69b4a3152c8469d6feffc58aea63ae31f3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 267, + 544, + 278 + ], + "lines": [ + { + "bbox": [ + 307, + 267, + 544, + 278 + ], + "spans": [ + { + "bbox": [ + 307, + 267, + 544, + 278 + ], + "type": "text", + "content": "Figure 7. Our model deal with different non-uniform outliers." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 334, + 285, + 515, + 347 + ], + "blocks": [ + { + "bbox": [ + 334, + 285, + 515, + 347 + ], + "lines": [ + { + "bbox": [ + 334, + 285, + 515, + 347 + ], + "spans": [ + { + "bbox": [ + 334, + 285, + 515, + 347 + ], + "type": "image", + "image_path": "62e6027f2054a4ce502523dbd7253a07b2680fd0a94db254e8cfea899846273d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 348, + 545, + 369 + ], + "lines": [ + { + "bbox": [ + 306, + 348, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 545, + 369 + ], + "type": "text", + "content": "Figure 8. The inference time of each GPR method. Our model with SVI can easily handle big data." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 384, + 522, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 522, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 522, + 395 + ], + "type": "text", + "content": "Without variance term, the regression tends to overfit." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 396, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 467 + ], + "type": "text", + "content": "Non-uniform Outliers. Different types of non-uniform outliers are tested in Fig. 7. More detailed results are given in suppl. material. Our model exhibits strong generalization and robustness. The reason is that uniform distribution is a very weak assumption with high flexibility. It accommodates many outlier distributions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 468, + 545, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 539 + ], + "type": "text", + "content": "**Scalability.** We test the runtime towards different problem sizes on Neal data with " + }, + { + "bbox": [ + 304, + 468, + 545, + 539 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 468, + 545, + 539 + ], + "type": "text", + "content": " outliers. Other methods as well as ours w. and w/o. SVI are included. The number of inducing variables is set to 15 for our method in both two settings. As plotted in Fig. 8, our method can easily scale to large-scale data, especially when equipped with SVI." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 550, + 378, + 562 + ], + "type": "text", + "content": "8. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "This paper presents a robust and scalable GPR using variational learning. It uses an outlier robust mixture likelihood model, where the uniform distribution accounts for the outliers. A variational formulation is introduced to learn the mode of data and hyperparameters by minimizing the KL divergence between the true posterior distribution and the approximate one. Its most attractive property is that it can rigorously approximate the exact posterior. Inducing variable approximation and SVI further extend our model to big data. We apply our model to feature matching and dense gene expression imputation. Extensive results show the significant improvement over existing robust GPRs." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21957" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Vassileios Balntas, Karel Lenc, Andrea Vedaldi, and Krystian Mikolajczyk. 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Fleet $^{1,2}$ Andrea Tagliafasacchi $^{1,2,3}$", + "bbox": [ + 210, + 179, + 756, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Google Research, Brain Team 2University of Toronto 3Simon Fraser University", + "bbox": [ + 228, + 217, + 736, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural radiance fields (NeRF) excel at synthesizing new views given multi-view, calibrated images of a static scene. When scenes include distractors, which are not persistent during image capture (moving objects, lighting variations, shadows), artifacts appear as view-dependent effects or 'floaters'. To cope with distractors, we advocate a form of robust estimation for NeRF training, modeling distractors in training data as outliers of an optimization problem. Our method successfully removes outliers from a scene and improves upon our baselines, on synthetic and real-world scenes. Our technique is simple to incorporate in modern NeRF frameworks, with few hyper-parameters. It does not assume a priori knowledge of the types of distractors, and is instead focused on the optimization problem rather than pre-processing or modeling transient objects. More results at https://robustnerf.github.io/public.", + "bbox": [ + 75, + 291, + 473, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 554, + 209, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ability to understand the structure of a static 3D scene from 2D images alone is a fundamental problem in computer vision [44]. It finds applications in AR/VR for mapping virtual environments [6, 36, 61], in autonomous robotics for action planning [1], and in photogrammetry to create digital copies of real-world objects [34].", + "bbox": [ + 75, + 575, + 468, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural fields [55] have recently revolutionized this classical task, by storing 3D representations within the weights of a neural network [39]. These representations are optimized by back-propagating image differences. When the fields store view-dependent radiance and volumetric rendering is employed [21], we can capture 3D scenes with photo-realistic accuracy, and we refer to the generated representation as Neural Radiance Fields, or NeRF [25]).", + "bbox": [ + 75, + 667, + 468, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Training of NeRF models generally requires a large collection of images equipped with accurate camera calibration, which can often be recovered via structure-from-motion [37]. Behind its simplicity, NeRF hides several assumptions. As models are typically trained to minimize error in RGB color space, it is of paramount importance", + "bbox": [ + 75, + 787, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1f94b3ae1ab59c57b87c5e4884be69f5c0048ed2a2ee83bf4879413ecd792bef.jpg", + "image_caption": [ + "Figure 1. NeRF assumes photometric consistency in the observed images of a scene. Violations of this assumption, as with the images in the top row, yield reconstructed scenes with inconsistent content in the form of \"floaters\" (highlighted with ellipses). We introduce a simple technique that produces clean reconstruction by automatically ignoring distractors without explicit supervision." + ], + "image_footnote": [], + "bbox": [ + 503, + 267, + 890, + 433 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "that images are photometrically consistent - two photos taken from the same vantage point should be identical up to noise. Unless one employs a method explicitly accounting for it [35], one should manually hold a camera's focus, exposure, white-balance, and ISO fixed.", + "bbox": [ + 496, + 537, + 892, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, properly configuring one's camera is not all that is required to capture high-quality NeRFs – it is also important to avoid distractors: anything that isn't persistent throughout the entire capture session. Distractors come in many shapes and forms, from the hard-shadows cast by the operators as they explore the scene to a pet or child casually walking within the camera's field of view. Distractors are tedious to remove manually, as this would require pixel-by-pixel labeling. They are also tedious to detect, as typical NeRF scenes are trained from hundreds of input images, and the types of distractors are not known a priori. If distractors are ignored, the quality of the reconstruction scene suffers significantly; see Figure 1.", + "bbox": [ + 496, + 613, + 893, + 808 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In a typical capture session, it is difficult to capture multiple images of the same scene from the same viewpoint, rendering distractors challenging to model mathematically. As such, while view-dependent effects are what give NeRF their realistic look, how can the model tell the difference between a distractor and a view-dependent effect?", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "4Work done at Google Research.", + "bbox": [ + 94, + 886, + 271, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20626", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the challenges, the research community has devised several approaches to overcome this issue:", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- If distractors are known to belong to a specific class (e.g., people), one can remove them with a pre-trained semantic segmentation model [35, 43] – this process does not generalize to “unexpected” distractors such as shadows.", + "- One can model distractors as per-image transient phenomena, and control the balance of transient/persistent modeling [23] - however, it is difficult to tune the losses that control this Pareto-optimal objective.", + "- One can model data in time (i.e., high-framerate video) and decompose the scene into static and dynamic (i.e., distractor) components [53] – but this clearly only applies to video rather than photo collection captures." + ], + "bbox": [ + 76, + 121, + 467, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conversely, we approach the problem of distractors by modeling them as outliers in NeRF optimization.", + "bbox": [ + 76, + 301, + 467, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We analyze the aforementioned techniques through the lens of robust estimation, allowing us to understand their behavior, and to design a method that is not only simpler to implement but also more effective (see Figure 1). As a result, we obtain a method that is straightforward to implement, requires minimal-to-no hyper-parameter tuning, and achieves state-of-the-art performance. We evaluate our method:", + "bbox": [ + 75, + 333, + 467, + 436 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- quantitatively, in terms of reconstruction with synthetically, yet photo-realistically, rendered data;", + "- qualitatively on publicly available datasets (often finetuned to work effectively with previous methods);", + "- on a new collection of natural and synthetic scenes, including those autonomously acquired by a robot, allowing us to demonstrate the sensitivity of previous methods to hyper-parameter tuning." + ], + "bbox": [ + 76, + 438, + 467, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 571, + 217, + 585 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We briefly review the basics and notation of Neural Radiance Fields. We then describe recent progress in NeRF research, paying particular attention to techniques for modeling of static/dynamic scenes.", + "bbox": [ + 76, + 593, + 467, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Radiance Fields. A neural radiance field (NeRF) is a continuous volumetric representation of a 3D scene, stored within the parameters of a neural network $\\theta$ . The representation maps a position $\\mathbf{x}$ and view direction $\\mathbf{d}$ to a view-dependent RGB color and view-independent density:", + "bbox": [ + 76, + 659, + 467, + 734 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\begin{array}{l} \\mathbf {c} (\\mathbf {x}, \\mathbf {d}) \\\\ \\sigma (\\mathbf {x}) \\end{array} \\right\\} f (\\mathbf {x}, \\mathbf {d}; \\boldsymbol {\\theta}) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 744, + 467, + 785 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This representation is trained from a collection, $\\{(\\mathbf{C}_i,\\mathbf{T}_i)\\}$ of images $\\mathbf{C}_i$ with corresponding calibration parameters $\\mathbf{T}_i$ (camera extrinsic and intrinsic).", + "bbox": [ + 76, + 794, + 467, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "During training the calibration information is employed to convert each pixel of the image into a ray $\\mathbf{r} = (\\mathbf{o},\\mathbf{d})$ , and rays are drawn randomly from input images to form a training mini-batch $(\\mathbf{r}\\sim \\mathbf{C}_i)$ . The parameters $\\theta$ are optimized to", + "bbox": [ + 76, + 839, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "correctly predict the colors of the pixels in the batch via the L2 photometric-reconstruction loss:", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r g b}} (\\boldsymbol {\\theta}) = \\sum_ {i} \\mathbb {E} _ {\\mathbf {r} \\sim \\mathbf {C} _ {i}} \\left[ \\mathcal {L} _ {\\mathrm {r g b}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 133, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r g b}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2} ^ {2} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 170, + 890, + 191 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Parameterizing the ray as $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}$ , the NeRF model image $\\mathbf{C}(\\mathbf{r};\\boldsymbol{\\theta})$ is generated pixel-by-pixel volumetric rendering based on $\\sigma(\\cdot)$ and $\\mathbf{c}(\\cdot)$ (e.g., see [25, 42]).", + "bbox": [ + 498, + 203, + 890, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent progress on NeRF models. NeRF models have recently been extended in several ways. A major thread has been the speedup of training [15, 27] and inference [6, 13], enabling today's models to be trained in minutes [27], and rendered on mobile in real-time [6]. While initially restricted to forward-facing scenes, researchers quickly found ways to model real-world $360^{\\circ}$ scenes [4, 59], and to reduce the required number of images, via sensor fusion [35] or hand-designed priors [28]. We can now deal with image artifacts such as motion blur [22], exposure [24], and lens distortion [14]. And the requirement of (precise) camera calibrations is quickly being relaxed with the introduction of techniques for local camera refinement [8, 19], or direct inference [58]. While a NeRF typically represents geometry via volumetric density, there exist models custom-tailored to predict surfaces [29, 51], which can be extended to use predicted normals to significantly improve reconstruction quality [50, 57]. Given high-quality normals [47], inferring the (rendering) structure of a scene becomes a possibility [5]. We also note recent papers about additional applications to generalization [56], semantic understanding [48], generative modeling [33], robotics [1], and text-to-3D [31].", + "bbox": [ + 496, + 256, + 890, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modeling non-static scenes. For unstructured scenes like those considered here, the community has focused on reconstructing both static and non-static elements from video. The most direct approach, treating time as an auxiliary input, leads to cloudy geometry and a lack of fine detail [11, 54]. Directly optimizing per-frame latent codes as an auxiliary input has proved more effective [17, 30, 53]. The most widely-adopted approach is to fit a time-conditioned deformation field mapping 3D points between pairs of frames [18, 49] or to a canonical coordinate frame [9, 10, 20, 32, 45]. Given how sparsely spacetime is sampled, all methods require careful regularization, optimization, or additional training signals to achieve acceptable results.", + "bbox": [ + 496, + 597, + 890, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Relatively little attention has been given to removing non-static elements. One common approach is to segment and ignore pixels which are likely to be distractors [35, 43]. While this eliminates larger objects, it fails to account for secondary effects like shadows. Prior attempts to model distractors as outliers still leave residual cloudy geometry [23].", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20627", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fd427e53b06992ad7e2399ed5219e2db17f6d6b5aac0badd013f1d3667e33e83.jpg", + "image_caption": [ + "Figure 2. Ambiguity - A simple 2D scene where a static object (blue) is captured by three cameras. During the first and third capture the scene is not photo-consistent as a distractor was within the field of view. Not photo-consistent portions of the scene can end up being encoded as view-dependent effects - even when we assume ground truth geometry." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 566, + 223 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ff166e4f12987f76838b6513f6e0bb8ec9a53ef5607f55d7408084a762a7996d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 573, + 85, + 875, + 223 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 282, + 168, + 299 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The classical NeRF training losses (3) are effective for capturing scenes that are photometrically consistent, leading to the photo-realistic novel-view synthesis that we are now accustomed to seeing in recent research. However, \"what happens when there are elements of the scene that are not persistent throughout the entire capture session?\" Simple examples of such scenes include those in which an object is only present in some fraction of the observed images, or may not remain in the same position in all observed images. For example, Figure 2 depicts a 2D scene comprising a persistent object (the truck), along with several transient objects (e.g., people and a dog). While rays in blue from the three cameras intersect the truck, the green and orange rays from cameras 1 and 3 intersect transient objects. For video capture and spatio-temporal NeRF models, the persistent objects comprise the \"static\" portion of the scene, while the rest would be called the \"dynamic\".", + "bbox": [ + 75, + 306, + 473, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Sensitivity to outliers", + "text_level": 1, + "bbox": [ + 76, + 575, + 274, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For Lambertian scenes, photo-consistent structure is view independent, as scene radiance only depends on the incident light [16]. For such scenes, view-dependent NeRF models like (1), trained by minimizing (3), admit local optima in which transient objects are explained by view-dependent terms. Figure 2 depicts this, with the outgoing color corresponding to the memorized color of the outlier - i.e. view-dependent radiance. Such models exploit the view-dependent capacity of the model to over-fit observations, effectively memorizing the transient objects. One can alter the model to remove dependence on $\\mathbf{d}$ but the L2 loss remains problematic as least-squares (LS) estimators are sensitive to outliers, or heavy-tailed noise distributions.", + "bbox": [ + 75, + 597, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Under more natural conditions, dropping the Lambertian assumption, the problem becomes more complex as both non-Lambertian reflectance phenomena and outliers can be explained as view-dependent radiance. While we want the models to capture photo-consistent view-dependent radiance, outliers and other transient phenomena should ideally be ignored. And in such cases, optimization with an L2", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "loss (3) yields significant errors in reconstruction; see Figure 1. Problems like these are pervasive in NeRF model fitting, especially in uncontrolled environments with complex reflectance, non-rigidity, or independently moving objects.", + "bbox": [ + 496, + 285, + 890, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Robustness to outliers", + "text_level": 1, + "bbox": [ + 498, + 353, + 705, + 368 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Robustness via semantic segmentation. One way to reduce outlier contamination during NeRF model optimization is to rely on an oracle $\\mathbf{S}$ that specifies whether a given pixel $\\mathbf{r}$ from image $i$ is an outlier, and should therefore be excluded from the empirical loss, replacing (3) with:", + "bbox": [ + 496, + 376, + 892, + 450 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o r a c l e}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\mathbf {S} _ {i} (\\mathbf {r}) \\cdot | | \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) | | _ {2} ^ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 458, + 890, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In practice, a pre-trained (semantic) segmentation network $S$ might serve as an oracle, $\\mathbf{S}_i = S(\\mathbf{C}_i)$ . E.g., Nerf-in-the-wild [23] employed a semantic segmenter to remove pixels occupied by people, as they are outliers in the context of photo-tourism. Urban Radiance Fields [35] segmented out sky pixels, while LOL-NeRF [33] ignored pixels not belonging to faces. The obvious problem with this approach is the need for an oracle to detect arbitrary distractors.", + "bbox": [ + 496, + 484, + 892, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Robust estimators. Another way to reduce sensitivity to outliers is to replace the conventional L2 loss (3) with a robust loss (e.g., [2, 41]), so that photometrically-inconsistent observations can be down-weighted during optimization. Given a robust kernel $\\kappa(\\cdot)$ , we rewrite our training loss as:", + "bbox": [ + 496, + 611, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r o b u s t}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\kappa \\left(\\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 693, + 890, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\kappa(\\cdot)$ is positive and monotonically increasing. MipNeRF [3], for example, employs an L1 loss $\\kappa(\\epsilon) = |\\epsilon|$ , which provides some degree of robustness to outliers during NeRF training. Given our analysis, a valid question is whether we can straightforwardly employ a robust kernel to approach our problem, and if so, given the large variety of robust kernels [2], which is the kernel of choice.", + "bbox": [ + 496, + 719, + 890, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unfortunately, as discussed above, outliers and non-Lambertian effects can both be modelled as view-dependent effects (see Figure 3). As a consequence, with simple application of robust estimators it can be difficult to separate signal from noise. Figure 4 shows examples in which outliers", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20628", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/11ad7dc1cc45fb13dab8eb420d7cc8ad66432e0546b9533578c9214db3f57180.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 87, + 271, + 167 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b2eb3620a00498884b091da8a7002ce0ca793164b22359e7226635d9c8a96708.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 88, + 460, + 167 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d79c260859e20c9b34c744b290b5c9725455d80ee2d5fcfb5fbf68d85187829b.jpg", + "image_caption": [ + "Figure 3. Histograms - Robust estimators perform well when the distribution of residuals agrees with the one implied by the estimator (e.g., Gaussian for L2, Laplacian for L1). Here we visualize the ground-truth distribution of residuals (bottom-left), which is hardly a good match with any simple parametric distribution." + ], + "image_footnote": [], + "bbox": [ + 81, + 167, + 271, + 253 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bc0cfa8000d411cb3d2e6833322a1287d9b33fa4e89c2466baecdf67d05404a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 172, + 460, + 252 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are removed, but fine-grained texture and view-dependent details are also lost, or conversely, fine-grained details are preserved, but outliers cause artifacts in the reconstructed scene. One can also observe mixtures of these cases in which details are not captured well, nor are outliers fully removed. We find that this behaviour occurs consistently for many different robust estimators and parameter settings.", + "bbox": [ + 75, + 345, + 467, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training time can also be problematic. The robust estimator gradient w.r.t. model parameters can be expressed using the chain rule as", + "bbox": [ + 75, + 452, + 468, + 498 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\frac {\\partial \\kappa (\\epsilon (\\boldsymbol {\\theta}))}{\\partial \\boldsymbol {\\theta}} \\right| _ {\\boldsymbol {\\theta} ^ {(t)}} = \\left. \\frac {\\partial \\kappa (\\epsilon)}{\\partial \\epsilon} \\right| _ {\\epsilon (\\boldsymbol {\\theta} ^ {(t)})} \\cdot \\left. \\frac {\\partial \\epsilon (\\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} \\right| _ {\\boldsymbol {\\theta} ^ {(t)}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 510, + 468, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The second factor is the classical NeRF gradient. The first factor is the kernel gradient evaluated at the current error residual $\\epsilon (\\pmb{\\theta}^{(t)})$ . During training, large residuals can equivalently come from high-frequency details that have not yet been learnt, or they may arise from outliers (see Figure 4 (bottom)). This explain why robust optimization, implemented as (5), should not be expected to decouple high-frequency details from outliers. Further, when strongly robust kernels are employed, like redescending estimators, this also explains the loss of visual fidelity. That is, because the gradient of (large) residuals get down-weighted by the (small) gradients of the kernel, slowing down the learning of these fine-grained details (see Figure 4 (top)).", + "bbox": [ + 75, + 559, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Robustness via Trimmed Least Squares", + "text_level": 1, + "bbox": [ + 76, + 768, + 415, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In what follows we advocate a form of iteratively reweighted least-squares (IRLS) with a Trimmed least squares (LS) loss for NeRF model fitting.", + "bbox": [ + 75, + 789, + 468, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Iteratively Reweighted least Squares. IRLS is a widely used method for robust estimation that involves solving a sequence of weighted LS problems, the weights of which are adapted to reduce the influence of outliers. To that end,", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7938b39f31acfdc501893b4a8f3350a2f3af6e6029632895dc97faf118a27321.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 88, + 689, + 169 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8bee22d7570c63c3c8dcb2a2fb19c6b6aacc77cd83387cf79c109fb8235f552f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 90, + 888, + 162 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1632681e93a49b53846aba35cb9a9a030cc78ccb806d3756c22ec532e55ff874.jpg", + "image_caption": [ + "Figure 4. Kernels - (top-left) Family of robust kernels [2], including L2 ( $\\alpha = 2$ ), Charbonnier ( $\\alpha = 1$ ) and Geman-McClure ( $\\alpha = -2$ ). (top-right) Mid-training, residual magnitudes are similar for distractors and fine-grained details, and pixels with large residuals are learned more slowly, as the gradient of re-descending kernels flattens out. (bottom-right) A too aggressive Geman-McClure in down-weighting large residuals removes both outliers and high-frequency detail. (bottom-left) A less aggressive Geman-McClure does not effectively remove outliers." + ], + "image_footnote": [], + "bbox": [ + 501, + 171, + 689, + 244 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eef272506fab0a7293f190e56385e2b5f26c2fe42d91278bc7e3ba201f641252.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 171, + 888, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "at iteration $t$ , one can write the loss as", + "bbox": [ + 500, + 397, + 751, + 411 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r o b u s t}} ^ {\\mathbf {r}, i} \\left(\\boldsymbol {\\theta} ^ {(t)}\\right) = \\omega \\left(\\boldsymbol {\\epsilon} ^ {(t - 1)} (\\mathbf {r})\\right) \\cdot | | \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta} ^ {(t)}) - \\mathbf {C} _ {i} (\\mathbf {r}) | | _ {2} ^ {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 419, + 870, + 440 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\epsilon} ^ {(t - 1)} (\\mathbf {r}) = \\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta} ^ {(t - 1)}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 441, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For weight functions given by $\\omega (\\epsilon) = \\epsilon^{-1}\\cdot \\partial \\kappa (\\epsilon) / \\partial \\epsilon$ one can show that, under suitable conditions, the iteration converges to a local minima of (5) (see [41, Sec. 3]).", + "bbox": [ + 500, + 470, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This framework admits a broad family of losses, including maximum likelihood estimators for heavy-tailed noise processes. Examples in Figure 4 include the Charbonnier loss (smoothed L1), and more aggressive redescending estimators such as the Lorentzian or Geman-McClure [2]. The objective in (4) can also be viewed as a weighted LS objective, the binary weights of which are provided by an oracle. And, as discussed at length below, one can also view several recent methods like NeRFW [23] and $\\mathrm{D}^2\\mathrm{NeRF}$ [53] through the lens of IRLS and weighted LS.", + "bbox": [ + 496, + 517, + 890, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Nevertheless, choosing a suitable weight function $\\omega(\\epsilon)$ for NeRF optimization is non-trivial, due in large part to the intrinsic ambiguity between view-dependent radiance phenomena and outliers. One might try to solve this problem by learning a neural weight function [40], although generating enough annotated training data might be prohibitive. Instead, the approach taken below is to exploit inductive biases in the structure of outliers, combined with the simplicity of a robust, trimmed LS estimator.", + "bbox": [ + 496, + 667, + 890, + 803 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Trimmed Robust Kernels. Our goal is to develop a weight function for use in iteratively weighted LS optimization that is simple and captures useful inductive biases for NeRF optimization. For simplicity we opt for a binary weight function with intuitive parameters that adapts naturally through model fitting so that fine-grained image details that are not", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20629", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c4d7aa68fc1cf767be6cc6e9d208ab8c015e53701c307328f83104d47b5e8f5c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 112, + 89, + 297, + 170 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f91fb7f5b893bb47da572b0df940fc0b094b10279f430799e1478a8e794435e8.jpg", + "image_caption": [ + "residuals - $\\epsilon (\\mathbf{r})$" + ], + "image_footnote": [], + "bbox": [ + 112, + 171, + 297, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d9a7c3c9248e6b0d2e49b80e508445785b7faf30297405fd92a356c86778a670.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 89, + 482, + 170 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/873f6abe2d818eeb1542748a04be93455f2e67da076891565998d6dc7678c5f5.jpg", + "image_caption": [ + "inliers - $\\tilde{\\omega} (\\mathbf{r})$", + "Figure 5. Algorithm - We visualize our weight function computed by residuals on two examples: (top) the residuals of a (mid-training) NeRF rendered from a training viewpoint, (bottom) a toy residual image containing residual of small spatial extent (dot, line) and residuals of large spatial extent (squares). Notice residuals with large magnitude but small spatial extent (texture of the box, dot, line) are included in the optimization, while weaker residuals with larger spatial extent are excluded. Note that while we operate on patches, we visualize the weight function on the whole image to facilitate visualization." + ], + "image_footnote": [], + "bbox": [ + 297, + 171, + 483, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d39ccfe40e70ee86c4959d6925556f5b4f52cee785752e345afb7026b573e088.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 89, + 668, + 170 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3a9ee80c514580cfc6f5f57876a041719846aed5e201e272d35434e954f86f15.jpg", + "image_caption": [ + "diffusion - $\\tilde{\\omega}(\\mathbf{r}) \\oplus \\mathcal{B}_{3 \\times 3}$" + ], + "image_footnote": [], + "bbox": [ + 482, + 171, + 668, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/09be3306f8248a3d9f4bd6c55d6918e93896a53fa487fe67237b06357342877a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 668, + 89, + 857, + 170 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a3df0d1d6602f3b8faab9d6badefac0d455997cc96da692275f316984e52437b.jpg", + "image_caption": [ + "(IRLS) weights - $\\mathcal{W}(\\mathbf{r})$" + ], + "image_footnote": [], + "bbox": [ + 669, + 171, + 857, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "outliers can be learned quickly. It is also important to capture the structured nature of typical outliers, contrary to the typical i.i.d. assumption in most robust estimator formulations. To this end, the weight function should capture spatial smoothness of the outlier process, recognizing that objects typically have continuous local support, and hence outliers are expected to occupy large, connected regions of an image (e.g., the silhouette of a person to be segmented out from a photo-tourism dataset).", + "bbox": [ + 75, + 300, + 468, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Surprisingly, a relatively simple weight function embodies these properties and performs extremely well in practice. The weight function is based on so-called trimmed estimators that are used in trimmed least-squares, like that used in trimmed ICP [7]. We first sort residuals, and assume that residuals below a certain percentile are inliers. Picking the $50\\%$ percentile for convenience (i.e., median), we define", + "bbox": [ + 75, + 436, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\omega} (\\mathbf {r}) = \\epsilon (\\mathbf {r}) \\leq \\mathcal {T} _ {\\epsilon}, \\quad \\mathcal {T} _ {\\epsilon} = \\operatorname {M e d i a n} _ {\\mathbf {r}} \\left\\{\\epsilon (\\mathbf {r}) \\right\\}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 549, + 468, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To capture spatial smoothness of outliers we spatially diffuse inlier/outlier labels $\\omega$ with a $3\\times 3$ box kernel $\\mathcal{B}_{3\\times 3}$ . Formally, we define", + "bbox": [ + 76, + 571, + 468, + 616 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {W} (\\mathbf {r}) = \\left(\\tilde {\\omega} (\\mathbf {r}) * \\mathcal {B} _ {3 \\times 3}\\right) \\geq \\mathcal {T} _ {*}, \\quad \\mathcal {T} _ {*} = 0. 5. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 625, + 468, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This helps to avoid classifying high-frequency details as outliers, allowing them to be captured by the NeRF model during optimization (see Figure 5).", + "bbox": [ + 75, + 647, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While the trimmed weight function (9) improves the robustness of model fitting, it sometimes misclassifies fine-grained image details early in training where the NeRF model first captures coarse-grained structure. These localized texture elements may emerge but only after very long training times. We find that stronger inductive bias to spatially coherence allows fine-grained details to be learned more quickly. To that end, we aggregate the detection of outliers on $16 \\times 16$ neighborhoods; i.e., we label entire $8 \\times 8$ patches as outliers or inliers based on the behavior of $\\mathcal{W}$ in the $16 \\times 16$ neighborhood of the patch. Denoting the $N \\times N$ neighborhood of pixels around $\\mathbf{r}$ as $\\mathcal{R}_N(\\mathbf{r})$ , we define", + "bbox": [ + 75, + 691, + 468, + 873 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\omega \\left(\\mathcal {R} _ {8} (\\mathbf {r})\\right) = \\mathbb {E} _ {\\mathbf {s} \\sim \\mathcal {R} _ {1 6} (\\mathbf {r})} \\left[ \\mathcal {W} (\\mathbf {s}) \\right] \\geq \\mathcal {T} _ {\\mathcal {R}}, \\quad \\mathcal {T} _ {\\mathcal {R}} = 0. 6. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 880, + 468, + 897 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bf26a6902d7a41ed48389fa1f5b89d4469c7a3ae868ee3ba2d6b6dd6db473a18.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 504, + 300, + 586, + 363 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4416c7398ccd94ebc9d367fa80dd34745d1f0b22821109b958a335b77eb5ef87.jpg", + "image_caption": [ + "RobustNeRF" + ], + "image_footnote": [], + "bbox": [ + 604, + 300, + 686, + 362 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0b6c7d1202a0081f52befd0f8113b7eaa05410296dc88312c5fd84db8c93517f.jpg", + "image_caption": [ + "Train View" + ], + "image_footnote": [], + "bbox": [ + 705, + 300, + 787, + 362 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3a02c34a52cb7d88bc69b2089f4a9245d1437487a0c9d1e3882be254e4ca87fc.jpg", + "image_caption": [ + "Distractors" + ], + "image_footnote": [], + "bbox": [ + 808, + 300, + 888, + 362 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/61d593844bc4764698a50b4773d9444124bb85159f02cb5638f6aa39ecafd740.jpg", + "image_caption": [ + "Figure 6. Residuals - For the dataset shown in the top row, we visualize the dynamics of the RobustNeRF training residuals, which show how over time the estimated distractor weights go from being random $(t / T) = 0.5\\%)$ to identify distractor pixels $(t / T) = 100\\%$ without any explicit supervision." + ], + "image_footnote": [], + "bbox": [ + 506, + 380, + 887, + 518 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final weight function is the union of the three masks in Eqns. 8 -10. This robust weight function evolves during optimization, as one expects with IRLS where the weights are a function of the residuals at the previous iteration. That is, the labeling of pixels as inliers/outliers changes during training, and settles around masks similar to the one an oracle would provide as training converges (see Figure 6).", + "bbox": [ + 496, + 609, + 890, + 715 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 727, + 632, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We implement our robust loss function in the MultiNeRF codebase [26] and apply it to mip-NeRF 360 [4]. We dub this method \"RobustNeRF\". To evaluate RobustNeRF, we compare against baselines on several scenes containing different types of distractors. Where possible, we quantitatively compare reconstructions to held-out, distraction-free images; we report three metrics, averaged across held-out frames, namely, PSNR, SSIM [52], and LPIPS [60].", + "bbox": [ + 496, + 750, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare different methods on two collections of scenes, i.e., those provided by the authors of $\\mathrm{D}^2\\mathrm{NeRF}$ , and", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20630", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fd0b180c1026e2be7ccdee830cae294216bd8c940336f0220309076f21627f21.jpg", + "image_caption": [ + "··" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 176, + 202 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/22cb10d1fc054634cd88f8e4e16a0ab3bf0cb02ffedc48c416b29e5cde255850.jpg", + "image_caption": [ + "··" + ], + "image_footnote": [], + "bbox": [ + 179, + 90, + 272, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7a8807948cc6eeba13b5d92f78a16697ee949ec41f3a5424f1ade3c127bec8b5.jpg", + "image_caption": [ + "···" + ], + "image_footnote": [], + "bbox": [ + 274, + 90, + 367, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c1697cdb8d34afb169bc52ec894798f33b8f724db8ce82cf41b82abed8e3d25a.jpg", + "image_caption": [ + "···" + ], + "image_footnote": [], + "bbox": [ + 369, + 90, + 462, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/762874ad94fc2fd98f1240146b07723da08dad632c699a0932c7aa82b5de6a09.jpg", + "image_caption": [ + "Statue" + ], + "image_footnote": [], + "bbox": [ + 83, + 215, + 176, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dbcea64e120747e1ed4cea2e373652528276341671ecec1e4f4912acb22390c0.jpg", + "image_caption": [ + "Android" + ], + "image_footnote": [], + "bbox": [ + 179, + 215, + 272, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/66cc33a619f3416b49a8d2b6c643ed33b59e00a0f8f22684e90cfb6ed0e62fa7.jpg", + "image_caption": [ + "Crab", + "Figure 7. Dataset - Sample training images showing the distractors in each scene. Statue and Android were acquired manually, and the others with a robotic arm. In the robotic setting we have pixel-perfect alignment of distractor vs. distractor-free images." + ], + "image_footnote": [], + "bbox": [ + 274, + 215, + 367, + 268 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d4665e589c43ddd6ae0a880b9b65793acf9e80ac3bc7d18a3a2c1524afd65028.jpg", + "image_caption": [ + "BabyYoda" + ], + "image_footnote": [], + "bbox": [ + 369, + 215, + 462, + 268 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "novel datasets described below. We also present a series of illustrative experiments on synthetic scenes, shedding light on RobustNeRF's efficacy and inner workings.", + "bbox": [ + 75, + 359, + 468, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Baselines", + "text_level": 1, + "bbox": [ + 76, + 417, + 184, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare RobustNeRF to variants of mip-NeRF 360 optimized with different loss functions $(L_{2}, L_{1}$ , and Carbonnier). These variants serve as natural baselines for models with limited or no robustness to outliers. We also compare to $\\mathrm{D}^2\\mathrm{NeRF}$ , a recent method for reconstructing dynamic scenes from monocular video. Unlike our method, $\\mathrm{D}^2\\mathrm{NeRF}$ is designed to reconstruct distractors rather than discard them. While $\\mathrm{D}^2\\mathrm{NeRF}$ is presented as a method for monocular video, it does not presuppose temporal continuity, and can be directly applied to unordered images. We omit additional comparisons to NeRF-W as its performance falls short of $\\mathrm{D}^2\\mathrm{NeRF}$ [53]. For more details on model training, see the supplementary material.", + "bbox": [ + 75, + 438, + 468, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets - Figure 7", + "text_level": 1, + "bbox": [ + 76, + 648, + 261, + 664 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition to scenes from $\\mathrm{D}^2\\mathrm{NeRF}$ , we introduce a set of natural and synthetic scenes. They facilitate the evaluation of RobustNeRF's effectiveness on illustrative use cases, and they enable empirical analysis under controlled conditions.", + "bbox": [ + 75, + 667, + 468, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Natural scenes. We capture seven natural scenes exemplifying different types of distractors. Scenes are captured in three settings, on the street, in an apartment and in a robotics lab. Distractor objects are moved, or are allowed to move, between frames to simulate capture over extended periods of time. We vary the number of unique distractors from 1 (Statue) to 150 (BabyYoda), and their movements. Unlike prior work on monocular video, frames are captured without a clear temporal ordering (see Figure 7). The other three (i.e., Street1, Street2, and Gloss) include view-dependence effects, the results of which are shown in the supplementary", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "material. We also capture additional frames without distractors to enable quantitative evaluations. Camera poses are estimated using COLMAP [38]. A full description of each scene in the supplementary material.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Synthetic scenes. To further evaluate RobustNeRF, we generate synthetic scenes using the Kubric dataset generator [12]. Each scene is constructed by placing a set of simple geometries in an empty, texture-less room. In each scene, a subset of objects remain fixed while the other objects (i.e., distractors) change position from frame to frame. By varying the number of objects, their size, and the way they move, we control the level of distraction in each scene. We use these scenes to examine RobustNeRF's sensitivity to its hyperparameters, see supplementary material.", + "bbox": [ + 496, + 154, + 890, + 305 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Evaluation", + "text_level": 1, + "bbox": [ + 500, + 314, + 619, + 329 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate RobustNeRF on its ability to ignore distractors while accurately reconstructing the static elements of a scene. We train RobustNeRF, $\\mathrm{D}^2\\mathrm{NeRF}$ , and variants of mip-NeRF 360 on scenes where distraction-free frames are available. Models are trained on frames with distractors and evaluated on distractor-free frames.", + "bbox": [ + 496, + 334, + 890, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison to mip-NeRF 360 - Figure 8. On natural scenes, RobustNeRF generally outperforms variants of mip-NeRF 360 by 1.3 to $4.7\\mathrm{dB}$ in PSNR. As $L_{2}, L_{1}$ , and Charbonnier losses weigh all pixels equally, the model is forced to represent, rather than ignore, distractors as \"clouds\" with view-dependent appearance. We find clouds to be most apparent when distractors remain stationary for multiple frames. In contrast, RobustNeRF's loss isolates distractor pixels and assigns them a weight of zero (see Figure 6). To establish an upper bound on reconstruction accuracy, we train mip-NeRF 360 with Charbonnier loss on distraction-free versions of each scene, the images for which are taken from (approximately) the same viewpoints. Reassuringly, RobustNeRF when trained on distraction-free frames, achieves nearly identical accuracy; see Figure 11.", + "bbox": [ + 496, + 428, + 890, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While RobustNeRF consistently outperforms mip-NeRF 360, the gap is smaller in the Apartment scenes (Statue, Android) than the Robotics Lab scenes (Crab, BabyYoda). This can be explained by challenging background geometry, errors in camera parameter estimation, and imperceptible changes to scene appearance. For further discussion, see the supplementary material.", + "bbox": [ + 496, + 654, + 890, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison to $\\mathbf{D}^2\\mathrm{NeRF}$ - Figure 9. Quantitatively, RobustNeRF matches or outperforms $\\mathrm{D}^2\\mathrm{NeRF}$ by as much as $12\\mathrm{dB}$ PSNR depending on the number of unique outlier objects in the capture. Results on $\\mathrm{D}^2\\mathrm{NeRF}$ real scenes are provided in the supplementary material for qualitative comparison. In Statue and Android, 1 and 3 non-rigid objects are moved around the scene, respectively. $\\mathrm{D}^2\\mathrm{NeRF}$ is able to model these objects and thus separate them from the scenes' static content. In the remaining scenes, a much", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20631", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9c0d942be36ab8e476ae45e835cd0345cdf7b4d7694878a0c1c937a0c4711672.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
StatueAndroidCrabBabyYoda
LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑
mip-NeRF 360 (L2)0.360.6619.090.400.6519.350.270.7725.730.310.7522.97
mip-NeRF 360 (L1)0.300.7219.550.400.6619.380.220.7926.690.220.8026.15
mip-NeRF 360 (Ch.)0.300.7319.640.400.6619.530.210.8027.720.230.8025.22
D2NeRF0.480.4919.090.430.5720.610.420.6821.180.440.6517.32
RobustNeRF0.280.7520.890.310.6521.720.210.8130.750.200.8330.87
mip-NeRF 360 (clean)0.190.8023.570.310.7123.100.160.8432.550.160.8432.63
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Evaluation on Natural Scenes - RobustNeRF outperforms baselines and $\\mathrm{D}^2\\mathrm{NeRF}$ [53] on novel view synthesis with real-world captures. The table provides a quantitative comparison of RobustNeRF, $\\mathrm{D}^2\\mathrm{NeRF}$ and mip-NeRF 360 using different reconstruction losses. The last row reports mip-NeRF 360 trained on a distractor-free version of each dataset, giving an upperbound for RobustNeRF performance. We also visualize samples from each scene rendered with each of the methods. See Supplementary Material for more samples." + ], + "image_footnote": [], + "bbox": [ + 83, + 527, + 238, + 619 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fbff17edcd0c79df32fd429ad15ec1ef06b80d4dca1fab87e2456bd3826010ad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 527, + 401, + 619 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e9215e4e4f884ac6d10f101a9563ca8e96bf72151a128a1751def30b93e22c45.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 527, + 563, + 619 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2ab403dd8bd35e27f24f173505838e737fc32feaeaff8ed4698dd5bbd5f6794.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 568, + 527, + 725, + 619 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/06c7d9010e371fb2c3acf11e25eeec78573aa9900a82f80795f0ec317f4a5b25.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 527, + 888, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "larger pool of 100 to 150 unique, non-static objects are used – too many for $\\mathrm{D}^2\\mathrm{NeRF}$ to model effectively. As a result, “cloud” artifacts appear in its static representation, similar to those produced by mip-NeRF 360. In contrast, Robust-NeRF identifies non-static content as outliers and omits it during reconstruction. Although both methods use a similar number of parameters, $\\mathrm{D}^2\\mathrm{NeRF}$ 's peak memory usage is $2.3\\mathrm{x}$ higher than RobustNeRF and $37\\mathrm{x}$ higher when normalizing for batch size. This is a direct consequence of model architecture: $\\mathrm{D}^2\\mathrm{NeRF}$ is tailored to simultaneously modeling static and dynamic content and thus merits higher complexity. To remain comparable, we limit image resolution to 0.2 megapixels for all experiments.", + "bbox": [ + 75, + 699, + 472, + 896 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablations - Figure 10. We ablate elements of the Robust-NeRF loss on the crab scene, comparing to an upper bound on the reconstruction accuracy of mip-NeRF 360 trained on distractor-free (clean) images from identical viewpoints. Our trimmed estimator (8) successfully eliminates distractors at the expense of high frequency texture and a lower PSNR. With smoothing (9), fine details are recovered, at the cost of longer training times. With the spatial window (10), RobustNeRF training time is on-par with mip-NeRF 360. We also ablate patch size and the trimming threshold (see Supplementary Material); we find that RobustNeRF is insensitive to trimming threshold, and that reducing the patch size offsets the gains from smoothing and patching.", + "bbox": [ + 496, + 699, + 890, + 896 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20632", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/81c326f99a2d9f37889109b6a36918676e3c948c687fa65f8e8763fe160cc0f8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CarCarsBagChairsPillow
LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑
NeRF-W [23].218.81424.23.243.87324.51.139.79120.65.150.68123.77.088.93528.24
NSFF [18].200.80624.90.620.37610.29.108.89225.62.682.28412.82.782.3434.55
NeuralDiff [46].065.95231.89.098.92125.93.117.91029.02.112.72224.42.565.65220.09
D2NeRF [53].062.97534.27.090.95326.27.076.97934.14.095.70724.63.076.97936.58
RobustNeRF.013.98837.73.063.95726.31.006.99541.82.007.99241.23.018.99038.95
Train ViewTest ViewNeRF-WNSFFNeuralDiffD2NeRFRobustNeRF
", + "bbox": [ + 81, + 87, + 890, + 277 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/31ab415c63a78f3acd67bea5122ed8b8332933561ca566bba81396917a5ac763.jpg", + "table_caption": [ + "Figure 9. Evaluations on $\\mathbf{D}^2\\mathrm{NeRF}$ Synthetic Scenes - Quantitative and qualitative evaluations on the Kubric synthetic dataset introduced by $\\mathbf{D}^2\\mathrm{NeRF}$ , consisting of 200 training frames (with distractor) and 100 novel views for evaluation (without distractor)." + ], + "table_footnote": [], + "table_body": "
LPIPS↓SSIM↑PSNR↑Updates to PSNR=30
mip-NeRF 360 (L2)0.310.7522.97-
+ robust (8)0.390.6018.21-
+ smoothing (9)0.220.8130.01250K
+ patching (10)0.210.8130.7570K
oracle (clean)0.160.8432.5525K
+ robust+ smoothing+ patching
", + "bbox": [ + 80, + 321, + 467, + 496 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 10. Ablations - Blindly trimming the loss causes details to be lost. Smoothing recovers fine-grained detail, while patch-based evaluation speeds up training and adds more detail. Patching enables the model to reach PSNR of 30, almost $4 \\times$ faster.", + "bbox": [ + 75, + 497, + 468, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Sensitivity - Figure 11. We find that RobustNeRF is remarkably robust to the amount of clutter in a dataset. We define an image as \"cluttered\" if it contains some number of distractor pixels. The figure shows how the reconstruction accuracy of RobustNeRF and mip-NeRF 360 depends on the fraction of training images with distractors, keeping the training set size constant. As the fraction increases, mip-NeRF 360's accuracy steadily drops from 33 to $25\\mathrm{dB}$ , while RobustNeRF's remains steadily above 31 dB throughout. In the distraction-free regime, we find that RobustNeRF mildly under-performs mip-NeRF 360, both in reconstruction quality and the time needed for training. This follows from the statistical inefficiency induced by the trimmed estimator (8), for which a percentage of pixels will be discarded even if they do not correspond to distractors.", + "bbox": [ + 75, + 574, + 468, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 76, + 816, + 204, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We address a central problem in training NeRF models, namely, optimization in the presence of distractors, such as transient or moving objects and photometric phenomena that are not persistent throughout the capture session.", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d20921cfffe3ec11df060f2cc54bfdaeaa6671ce873faf1eb8f2439c641d3b5.jpg", + "image_caption": [ + "Figure 11. Sensitivity and Limitations - (left) Reconstruction accuracy for BabyYoda as we increase the fraction of train images with distractors. (right) Accuracy vs training time on clean BabyYoda images (distractor-free)." + ], + "image_footnote": [], + "bbox": [ + 504, + 318, + 697, + 426 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6aefd32abf79c23dfc1f2bc20cbe57a82060ff522497877b96c668389f8568a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 318, + 888, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Viewed through the lens of robust estimation, we formulate training as a form of iteratively re-weighted least squares, with a variant of trimmed LS, and an inductive bias on the smoothness of the outlier process. RobustNeRF is surprisingly simple, yet effective on a wide range of datasets. RobustNeRF is shown to outperform recent state-of-the-art methods [4, 53], qualitatively and quantitatively, on a suite of synthetic datasets, common benchmark datasets, and new datasets captured by a robot, allowing fine-grained control over distractors for comparison with previous methods. While our experiments explore robust estimation in the context of mip-NeRF 360, the RobustNeRF loss can be incorporated within other NeRF models.", + "bbox": [ + 496, + 502, + 892, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. While RobustNeRF performs well on scenes with distractors, the loss entails some statistical inefficiency. On clean data, this yields somewhat poorer reconstructions, often taking longer to train (see Figure 11). Future work will consider very small distractors, which may require adaptation of the spatial support used for outlier/inlier decisions. It would also be interesting to learn a neural weight function, further improving RobustNeRF; active learning may be useful in this context. Finally, it would be interesting to include our robust loss in other NeRF frameworks.", + "bbox": [ + 496, + 700, + 890, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements We thank Pete Florence and Konstantinos Rematas for helpful feedback, and Tianhao Wu for help with $\\mathrm{D}^2\\mathrm{NeRF}$ experiments.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20633", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michal Adamkiewicz, Timothy Chen, Adam Caccavale, Rachel Gardner, Preston Culbertson, Jeannette Bohg, and Mac Schwager. 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NeuralDiff: Segmenting 3D objects that move in egocentric videos. In Proc. 3DV, 2021. 8", + "[47] Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T. Barron, and Pratul P. Srinivasan. Ref-NeRF: Structured view-dependent appearance for neural radiance fields. Proc. CVPR, 2022. 2", + "[48] Suhani Vora, Noha Radwan, Klaus Greff, Henning Meyer, Kyle Genova, Mehdi SM Sajjadi, Etienne Pot, Andrea Tagliasacchi, and Daniel Duckworth. Nesf: Neural semantic fields for generalizable semantic segmentation of 3d scenes. TMLR, 2021. 2", + "[49] Chaoyang Wang, Ben Eckart, Simon Lucey, and Orazio Gallo. Neural trajectory fields for dynamic novel view synthesis. arXiv preprint arXiv:2105.05994, 2021. 2", + "[50] Jiepeng Wang, Peng Wang, Xiaoxiao Long, Christian Theobalt, Taku Komura, Lingjie Liu, and Wenping Wang. Neuris: Neural reconstruction of indoor scenes using normal priors. arXiv preprint, 2022. 2", + "[51] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Proc. NeurIPS, 2021. 2", + "[52] Z. Wang, A.C. Bovik, H.R. Sheikh, and E.P. Simoncelli. Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 2004. 5", + "[53] Tianhao Wu, Fangcheng Zhong, Forrester Cole, Andrea Tagliasacchi, and Cengiz Oztireli. D2nerf: Self-supervised decoupling of dynamic and static objects from a monocular video. In Proc. NeurIPS, 2022. 2, 4, 6, 7, 8", + "[54] Wenqi Xian, Jia-Bin Huang, Johannes Kopf, and Changil Kim. Space-time neural irradiance fields for free-viewpoint video. In Proc. 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Nerf++: Analyzing and improving neural radiance fields. arXiv preprint arXiv:2010.07492, 2020. 2" + ], + "bbox": [ + 501, + 92, + 890, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20635", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[60] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proc. CVPR, 2018. 5", + "[61] Zihan Zhu, Songyou Peng, Viktor Larsson, Weiwei Xu, Hujun Bao, Zhaopeng Cui, Martin R Oswald, and Marc Pollefeys. Nice-slam: Neural implicit scalable encoding for slam. In Proc. CVPR, 2022. 1" + ], + "bbox": [ + 78, + 90, + 468, + 189 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20636", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/2f329418-58fe-4ad7-b462-6d0d0ce341f1_model.json b/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/2f329418-58fe-4ad7-b462-6d0d0ce341f1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6ad5efd670bcf7a9a4f93873aa98b0ef4b8367b0 --- /dev/null +++ b/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/2f329418-58fe-4ad7-b462-6d0d0ce341f1_model.json @@ -0,0 +1,2972 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.13, + 0.766, + 0.154 + ], + "angle": 0, + "content": "RobustNeRF: Ignoring Distractors with Robust Losses4" + }, + { + "type": "text", + "bbox": [ + 0.211, + 0.18, + 0.757, + 0.217 + ], + "angle": 0, + "content": "Sara Sabour\\(^{1,2}\\) Suhani Vora\\(^{1}\\) Daniel Duckworth\\(^{1}\\) Ivan Krasin\\(^{1}\\) David J. Fleet\\(^{1,2}\\) Andrea Tagliafasacchi\\(^{1,2,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.218, + 0.737, + 0.234 + ], + "angle": 0, + "content": "1Google Research, Brain Team 2University of Toronto 3Simon Fraser University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.284 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.474, + 0.534 + ], + "angle": 0, + "content": "Neural radiance fields (NeRF) excel at synthesizing new views given multi-view, calibrated images of a static scene. When scenes include distractors, which are not persistent during image capture (moving objects, lighting variations, shadows), artifacts appear as view-dependent effects or 'floaters'. To cope with distractors, we advocate a form of robust estimation for NeRF training, modeling distractors in training data as outliers of an optimization problem. Our method successfully removes outliers from a scene and improves upon our baselines, on synthetic and real-world scenes. Our technique is simple to incorporate in modern NeRF frameworks, with few hyper-parameters. It does not assume a priori knowledge of the types of distractors, and is instead focused on the optimization problem rather than pre-processing or modeling transient objects. More results at https://robustnerf.github.io/public." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.555, + 0.21, + 0.57 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.667 + ], + "angle": 0, + "content": "The ability to understand the structure of a static 3D scene from 2D images alone is a fundamental problem in computer vision [44]. It finds applications in AR/VR for mapping virtual environments [6, 36, 61], in autonomous robotics for action planning [1], and in photogrammetry to create digital copies of real-world objects [34]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.788 + ], + "angle": 0, + "content": "Neural fields [55] have recently revolutionized this classical task, by storing 3D representations within the weights of a neural network [39]. These representations are optimized by back-propagating image differences. When the fields store view-dependent radiance and volumetric rendering is employed [21], we can capture 3D scenes with photo-realistic accuracy, and we refer to the generated representation as Neural Radiance Fields, or NeRF [25])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Training of NeRF models generally requires a large collection of images equipped with accurate camera calibration, which can often be recovered via structure-from-motion [37]. Behind its simplicity, NeRF hides several assumptions. As models are typically trained to minimize error in RGB color space, it is of paramount importance" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.268, + 0.891, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.437, + 0.893, + 0.521 + ], + "angle": 0, + "content": "Figure 1. NeRF assumes photometric consistency in the observed images of a scene. Violations of this assumption, as with the images in the top row, yield reconstructed scenes with inconsistent content in the form of \"floaters\" (highlighted with ellipses). We introduce a simple technique that produces clean reconstruction by automatically ignoring distractors without explicit supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.893, + 0.612 + ], + "angle": 0, + "content": "that images are photometrically consistent - two photos taken from the same vantage point should be identical up to noise. Unless one employs a method explicitly accounting for it [35], one should manually hold a camera's focus, exposure, white-balance, and ISO fixed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.809 + ], + "angle": 0, + "content": "However, properly configuring one's camera is not all that is required to capture high-quality NeRFs – it is also important to avoid distractors: anything that isn't persistent throughout the entire capture session. Distractors come in many shapes and forms, from the hard-shadows cast by the operators as they explore the scene to a pet or child casually walking within the camera's field of view. Distractors are tedious to remove manually, as this would require pixel-by-pixel labeling. They are also tedious to detect, as typical NeRF scenes are trained from hundreds of input images, and the types of distractors are not known a priori. If distractors are ignored, the quality of the reconstruction scene suffers significantly; see Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In a typical capture session, it is difficult to capture multiple images of the same scene from the same viewpoint, rendering distractors challenging to model mathematically. As such, while view-dependent effects are what give NeRF their realistic look, how can the model tell the difference between a distractor and a view-dependent effect?" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.272, + 0.9 + ], + "angle": 0, + "content": "4Work done at Google Research." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20626" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "Despite the challenges, the research community has devised several approaches to overcome this issue:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.122, + 0.468, + 0.182 + ], + "angle": 0, + "content": "- If distractors are known to belong to a specific class (e.g., people), one can remove them with a pre-trained semantic segmentation model [35, 43] – this process does not generalize to “unexpected” distractors such as shadows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.183, + 0.468, + 0.242 + ], + "angle": 0, + "content": "- One can model distractors as per-image transient phenomena, and control the balance of transient/persistent modeling [23] - however, it is difficult to tune the losses that control this Pareto-optimal objective." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.243, + 0.468, + 0.302 + ], + "angle": 0, + "content": "- One can model data in time (i.e., high-framerate video) and decompose the scene into static and dynamic (i.e., distractor) components [53] – but this clearly only applies to video rather than photo collection captures." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.122, + 0.468, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.303, + 0.468, + 0.333 + ], + "angle": 0, + "content": "Conversely, we approach the problem of distractors by modeling them as outliers in NeRF optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.468, + 0.438 + ], + "angle": 0, + "content": "We analyze the aforementioned techniques through the lens of robust estimation, allowing us to understand their behavior, and to design a method that is not only simpler to implement but also more effective (see Figure 1). As a result, we obtain a method that is straightforward to implement, requires minimal-to-no hyper-parameter tuning, and achieves state-of-the-art performance. We evaluate our method:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.439, + 0.468, + 0.468 + ], + "angle": 0, + "content": "- quantitatively, in terms of reconstruction with synthetically, yet photo-realistically, rendered data;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.469, + 0.468, + 0.498 + ], + "angle": 0, + "content": "- qualitatively on publicly available datasets (often finetuned to work effectively with previous methods);" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.5, + 0.468, + 0.559 + ], + "angle": 0, + "content": "- on a new collection of natural and synthetic scenes, including those autonomously acquired by a robot, allowing us to demonstrate the sensitivity of previous methods to hyper-parameter tuning." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.439, + 0.468, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.573, + 0.218, + 0.587 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.594, + 0.468, + 0.655 + ], + "angle": 0, + "content": "We briefly review the basics and notation of Neural Radiance Fields. We then describe recent progress in NeRF research, paying particular attention to techniques for modeling of static/dynamic scenes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.66, + 0.468, + 0.736 + ], + "angle": 0, + "content": "Neural Radiance Fields. A neural radiance field (NeRF) is a continuous volumetric representation of a 3D scene, stored within the parameters of a neural network \\(\\theta\\). The representation maps a position \\(\\mathbf{x}\\) and view direction \\(\\mathbf{d}\\) to a view-dependent RGB color and view-independent density:" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.745, + 0.468, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\left. \\begin{array}{l} \\mathbf {c} (\\mathbf {x}, \\mathbf {d}) \\\\ \\sigma (\\mathbf {x}) \\end{array} \\right\\} f (\\mathbf {x}, \\mathbf {d}; \\boldsymbol {\\theta}) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.468, + 0.84 + ], + "angle": 0, + "content": "This representation is trained from a collection, \\(\\{(\\mathbf{C}_i,\\mathbf{T}_i)\\}\\) of images \\(\\mathbf{C}_i\\) with corresponding calibration parameters \\(\\mathbf{T}_i\\) (camera extrinsic and intrinsic)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "During training the calibration information is employed to convert each pixel of the image into a ray \\(\\mathbf{r} = (\\mathbf{o},\\mathbf{d})\\), and rays are drawn randomly from input images to form a training mini-batch \\((\\mathbf{r}\\sim \\mathbf{C}_i)\\). The parameters \\(\\theta\\) are optimized to" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "correctly predict the colors of the pixels in the batch via the L2 photometric-reconstruction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.135, + 0.891, + 0.168 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r g b}} (\\boldsymbol {\\theta}) = \\sum_ {i} \\mathbb {E} _ {\\mathbf {r} \\sim \\mathbf {C} _ {i}} \\left[ \\mathcal {L} _ {\\mathrm {r g b}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) \\right] \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.171, + 0.891, + 0.193 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r g b}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2} ^ {2} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.204, + 0.892, + 0.25 + ], + "angle": 0, + "content": "Parameterizing the ray as \\(\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}\\), the NeRF model image \\(\\mathbf{C}(\\mathbf{r};\\boldsymbol{\\theta})\\) is generated pixel-by-pixel volumetric rendering based on \\(\\sigma(\\cdot)\\) and \\(\\mathbf{c}(\\cdot)\\) (e.g., see [25, 42])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Recent progress on NeRF models. NeRF models have recently been extended in several ways. A major thread has been the speedup of training [15, 27] and inference [6, 13], enabling today's models to be trained in minutes [27], and rendered on mobile in real-time [6]. While initially restricted to forward-facing scenes, researchers quickly found ways to model real-world \\(360^{\\circ}\\) scenes [4, 59], and to reduce the required number of images, via sensor fusion [35] or hand-designed priors [28]. We can now deal with image artifacts such as motion blur [22], exposure [24], and lens distortion [14]. And the requirement of (precise) camera calibrations is quickly being relaxed with the introduction of techniques for local camera refinement [8, 19], or direct inference [58]. While a NeRF typically represents geometry via volumetric density, there exist models custom-tailored to predict surfaces [29, 51], which can be extended to use predicted normals to significantly improve reconstruction quality [50, 57]. Given high-quality normals [47], inferring the (rendering) structure of a scene becomes a possibility [5]. We also note recent papers about additional applications to generalization [56], semantic understanding [48], generative modeling [33], robotics [1], and text-to-3D [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.808 + ], + "angle": 0, + "content": "Modeling non-static scenes. For unstructured scenes like those considered here, the community has focused on reconstructing both static and non-static elements from video. The most direct approach, treating time as an auxiliary input, leads to cloudy geometry and a lack of fine detail [11, 54]. Directly optimizing per-frame latent codes as an auxiliary input has proved more effective [17, 30, 53]. The most widely-adopted approach is to fit a time-conditioned deformation field mapping 3D points between pairs of frames [18, 49] or to a canonical coordinate frame [9, 10, 20, 32, 45]. Given how sparsely spacetime is sampled, all methods require careful regularization, optimization, or additional training signals to achieve acceptable results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Relatively little attention has been given to removing non-static elements. One common approach is to segment and ignore pixels which are likely to be distractors [35, 43]. While this eliminates larger objects, it fails to account for secondary effects like shadows. Prior attempts to model distractors as outliers still leave residual cloudy geometry [23]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20627" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.086, + 0.568, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.575, + 0.087, + 0.877, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.226, + 0.894, + 0.269 + ], + "angle": 0, + "content": "Figure 2. Ambiguity - A simple 2D scene where a static object (blue) is captured by three cameras. During the first and third capture the scene is not photo-consistent as a distractor was within the field of view. Not photo-consistent portions of the scene can end up being encoded as view-dependent effects - even when we assume ground truth geometry." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.284, + 0.169, + 0.3 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.307, + 0.474, + 0.565 + ], + "angle": 0, + "content": "The classical NeRF training losses (3) are effective for capturing scenes that are photometrically consistent, leading to the photo-realistic novel-view synthesis that we are now accustomed to seeing in recent research. However, \"what happens when there are elements of the scene that are not persistent throughout the entire capture session?\" Simple examples of such scenes include those in which an object is only present in some fraction of the observed images, or may not remain in the same position in all observed images. For example, Figure 2 depicts a 2D scene comprising a persistent object (the truck), along with several transient objects (e.g., people and a dog). While rays in blue from the three cameras intersect the truck, the green and orange rays from cameras 1 and 3 intersect transient objects. For video capture and spatio-temporal NeRF models, the persistent objects comprise the \"static\" portion of the scene, while the rest would be called the \"dynamic\"." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.577, + 0.276, + 0.592 + ], + "angle": 0, + "content": "3.1. Sensitivity to outliers" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.794 + ], + "angle": 0, + "content": "For Lambertian scenes, photo-consistent structure is view independent, as scene radiance only depends on the incident light [16]. For such scenes, view-dependent NeRF models like (1), trained by minimizing (3), admit local optima in which transient objects are explained by view-dependent terms. Figure 2 depicts this, with the outgoing color corresponding to the memorized color of the outlier - i.e. view-dependent radiance. Such models exploit the view-dependent capacity of the model to over-fit observations, effectively memorizing the transient objects. One can alter the model to remove dependence on \\(\\mathbf{d}\\) but the L2 loss remains problematic as least-squares (LS) estimators are sensitive to outliers, or heavy-tailed noise distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Under more natural conditions, dropping the Lambertian assumption, the problem becomes more complex as both non-Lambertian reflectance phenomena and outliers can be explained as view-dependent radiance. While we want the models to capture photo-consistent view-dependent radiance, outliers and other transient phenomena should ideally be ignored. And in such cases, optimization with an L2" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.286, + 0.892, + 0.348 + ], + "angle": 0, + "content": "loss (3) yields significant errors in reconstruction; see Figure 1. Problems like these are pervasive in NeRF model fitting, especially in uncontrolled environments with complex reflectance, non-rigidity, or independently moving objects." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.354, + 0.706, + 0.369 + ], + "angle": 0, + "content": "3.2. Robustness to outliers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.893, + 0.452 + ], + "angle": 0, + "content": "Robustness via semantic segmentation. One way to reduce outlier contamination during NeRF model optimization is to rely on an oracle \\(\\mathbf{S}\\) that specifies whether a given pixel \\(\\mathbf{r}\\) from image \\(i\\) is an outlier, and should therefore be excluded from the empirical loss, replacing (3) with:" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.459, + 0.892, + 0.478 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o r a c l e}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\mathbf {S} _ {i} (\\mathbf {r}) \\cdot | | \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) | | _ {2} ^ {2} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.893, + 0.606 + ], + "angle": 0, + "content": "In practice, a pre-trained (semantic) segmentation network \\( S \\) might serve as an oracle, \\( \\mathbf{S}_i = S(\\mathbf{C}_i) \\). E.g., Nerf-in-the-wild [23] employed a semantic segmenter to remove pixels occupied by people, as they are outliers in the context of photo-tourism. Urban Radiance Fields [35] segmented out sky pixels, while LOL-NeRF [33] ignored pixels not belonging to faces. The obvious problem with this approach is the need for an oracle to detect arbitrary distractors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Robust estimators. Another way to reduce sensitivity to outliers is to replace the conventional L2 loss (3) with a robust loss (e.g., [2, 41]), so that photometrically-inconsistent observations can be down-weighted during optimization. Given a robust kernel \\(\\kappa(\\cdot)\\), we rewrite our training loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.694, + 0.892, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r o b u s t}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\kappa \\left(\\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.825 + ], + "angle": 0, + "content": "where \\(\\kappa(\\cdot)\\) is positive and monotonically increasing. MipNeRF [3], for example, employs an L1 loss \\(\\kappa(\\epsilon) = |\\epsilon|\\), which provides some degree of robustness to outliers during NeRF training. Given our analysis, a valid question is whether we can straightforwardly employ a robust kernel to approach our problem, and if so, given the large variety of robust kernels [2], which is the kernel of choice." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Unfortunately, as discussed above, outliers and non-Lambertian effects can both be modelled as view-dependent effects (see Figure 3). As a consequence, with simple application of robust estimators it can be difficult to separate signal from noise. Figure 4 shows examples in which outliers" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20628" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.272, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.089, + 0.462, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.169, + 0.272, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.173, + 0.462, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.258, + 0.47, + 0.328 + ], + "angle": 0, + "content": "Figure 3. Histograms - Robust estimators perform well when the distribution of residuals agrees with the one implied by the estimator (e.g., Gaussian for L2, Laplacian for L1). Here we visualize the ground-truth distribution of residuals (bottom-left), which is hardly a good match with any simple parametric distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.468, + 0.452 + ], + "angle": 0, + "content": "are removed, but fine-grained texture and view-dependent details are also lost, or conversely, fine-grained details are preserved, but outliers cause artifacts in the reconstructed scene. One can also observe mixtures of these cases in which details are not captured well, nor are outliers fully removed. We find that this behaviour occurs consistently for many different robust estimators and parameter settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.469, + 0.499 + ], + "angle": 0, + "content": "Training time can also be problematic. The robust estimator gradient w.r.t. model parameters can be expressed using the chain rule as" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.511, + 0.469, + 0.548 + ], + "angle": 0, + "content": "\\[\n\\left. \\frac {\\partial \\kappa (\\epsilon (\\boldsymbol {\\theta}))}{\\partial \\boldsymbol {\\theta}} \\right| _ {\\boldsymbol {\\theta} ^ {(t)}} = \\left. \\frac {\\partial \\kappa (\\epsilon)}{\\partial \\epsilon} \\right| _ {\\epsilon (\\boldsymbol {\\theta} ^ {(t)})} \\cdot \\left. \\frac {\\partial \\epsilon (\\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} \\right| _ {\\boldsymbol {\\theta} ^ {(t)}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.47, + 0.756 + ], + "angle": 0, + "content": "The second factor is the classical NeRF gradient. The first factor is the kernel gradient evaluated at the current error residual \\(\\epsilon (\\pmb{\\theta}^{(t)})\\). During training, large residuals can equivalently come from high-frequency details that have not yet been learnt, or they may arise from outliers (see Figure 4 (bottom)). This explain why robust optimization, implemented as (5), should not be expected to decouple high-frequency details from outliers. Further, when strongly robust kernels are employed, like redescending estimators, this also explains the loss of visual fidelity. That is, because the gradient of (large) residuals get down-weighted by the (small) gradients of the kernel, slowing down the learning of these fine-grained details (see Figure 4 (top))." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.416, + 0.785 + ], + "angle": 0, + "content": "3.3. Robustness via Trimmed Least Squares" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.79, + 0.469, + 0.835 + ], + "angle": 0, + "content": "In what follows we advocate a form of iteratively reweighted least-squares (IRLS) with a Trimmed least squares (LS) loss for NeRF model fitting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Iteratively Reweighted least Squares. IRLS is a widely used method for robust estimation that involves solving a sequence of weighted LS problems, the weights of which are adapted to reduce the influence of outliers. To that end," + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.691, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.091, + 0.889, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.172, + 0.691, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.172, + 0.889, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.254, + 0.892, + 0.378 + ], + "angle": 0, + "content": "Figure 4. Kernels - (top-left) Family of robust kernels [2], including L2 (\\(\\alpha = 2\\)), Charbonnier (\\(\\alpha = 1\\)) and Geman-McClure (\\(\\alpha = -2\\)). (top-right) Mid-training, residual magnitudes are similar for distractors and fine-grained details, and pixels with large residuals are learned more slowly, as the gradient of re-descending kernels flattens out. (bottom-right) A too aggressive Geman-McClure in down-weighting large residuals removes both outliers and high-frequency detail. (bottom-left) A less aggressive Geman-McClure does not effectively remove outliers." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.398, + 0.753, + 0.412 + ], + "angle": 0, + "content": "at iteration \\(t\\), one can write the loss as" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.42, + 0.872, + 0.441 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r o b u s t}} ^ {\\mathbf {r}, i} \\left(\\boldsymbol {\\theta} ^ {(t)}\\right) = \\omega \\left(\\boldsymbol {\\epsilon} ^ {(t - 1)} (\\mathbf {r})\\right) \\cdot | | \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta} ^ {(t)}) - \\mathbf {C} _ {i} (\\mathbf {r}) | | _ {2} ^ {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.443, + 0.891, + 0.461 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\epsilon} ^ {(t - 1)} (\\mathbf {r}) = \\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta} ^ {(t - 1)}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.472, + 0.891, + 0.517 + ], + "angle": 0, + "content": "For weight functions given by \\(\\omega (\\epsilon) = \\epsilon^{-1}\\cdot \\partial \\kappa (\\epsilon) / \\partial \\epsilon\\) one can show that, under suitable conditions, the iteration converges to a local minima of (5) (see [41, Sec. 3])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.668 + ], + "angle": 0, + "content": "This framework admits a broad family of losses, including maximum likelihood estimators for heavy-tailed noise processes. Examples in Figure 4 include the Charbonnier loss (smoothed L1), and more aggressive redescending estimators such as the Lorentzian or Geman-McClure [2]. The objective in (4) can also be viewed as a weighted LS objective, the binary weights of which are provided by an oracle. And, as discussed at length below, one can also view several recent methods like NeRFW [23] and \\(\\mathrm{D}^2\\mathrm{NeRF}\\) [53] through the lens of IRLS and weighted LS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Nevertheless, choosing a suitable weight function \\(\\omega(\\epsilon)\\) for NeRF optimization is non-trivial, due in large part to the intrinsic ambiguity between view-dependent radiance phenomena and outliers. One might try to solve this problem by learning a neural weight function [40], although generating enough annotated training data might be prohibitive. Instead, the approach taken below is to exploit inductive biases in the structure of outliers, combined with the simplicity of a robust, trimmed LS estimator." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Trimmed Robust Kernels. Our goal is to develop a weight function for use in iteratively weighted LS optimization that is simple and captures useful inductive biases for NeRF optimization. For simplicity we opt for a binary weight function with intuitive parameters that adapts naturally through model fitting so that fine-grained image details that are not" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20629" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.09, + 0.298, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.172, + 0.298, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.199, + 0.259, + 0.212 + ], + "angle": 0, + "content": "residuals - \\(\\epsilon (\\mathbf{r})\\)" + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.09, + 0.483, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.298, + 0.172, + 0.485, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.199, + 0.434, + 0.212 + ], + "angle": 0, + "content": "inliers - \\(\\tilde{\\omega} (\\mathbf{r})\\)" + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.09, + 0.669, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.172, + 0.669, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.199, + 0.648, + 0.212 + ], + "angle": 0, + "content": "diffusion - \\(\\tilde{\\omega}(\\mathbf{r}) \\oplus \\mathcal{B}_{3 \\times 3}\\)" + }, + { + "type": "image", + "bbox": [ + 0.669, + 0.09, + 0.858, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.67, + 0.172, + 0.858, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.199, + 0.836, + 0.212 + ], + "angle": 0, + "content": "(IRLS) weights - \\(\\mathcal{W}(\\mathbf{r})\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.215, + 0.894, + 0.284 + ], + "angle": 0, + "content": "Figure 5. Algorithm - We visualize our weight function computed by residuals on two examples: (top) the residuals of a (mid-training) NeRF rendered from a training viewpoint, (bottom) a toy residual image containing residual of small spatial extent (dot, line) and residuals of large spatial extent (squares). Notice residuals with large magnitude but small spatial extent (texture of the box, dot, line) are included in the optimization, while weaker residuals with larger spatial extent are excluded. Note that while we operate on patches, we visualize the weight function on the whole image to facilitate visualization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.469, + 0.436 + ], + "angle": 0, + "content": "outliers can be learned quickly. It is also important to capture the structured nature of typical outliers, contrary to the typical i.i.d. assumption in most robust estimator formulations. To this end, the weight function should capture spatial smoothness of the outlier process, recognizing that objects typically have continuous local support, and hence outliers are expected to occupy large, connected regions of an image (e.g., the silhouette of a person to be segmented out from a photo-tourism dataset)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.469, + 0.543 + ], + "angle": 0, + "content": "Surprisingly, a relatively simple weight function embodies these properties and performs extremely well in practice. The weight function is based on so-called trimmed estimators that are used in trimmed least-squares, like that used in trimmed ICP [7]. We first sort residuals, and assume that residuals below a certain percentile are inliers. Picking the \\(50\\%\\) percentile for convenience (i.e., median), we define" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.55, + 0.469, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\omega} (\\mathbf {r}) = \\epsilon (\\mathbf {r}) \\leq \\mathcal {T} _ {\\epsilon}, \\quad \\mathcal {T} _ {\\epsilon} = \\operatorname {M e d i a n} _ {\\mathbf {r}} \\left\\{\\epsilon (\\mathbf {r}) \\right\\}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.573, + 0.469, + 0.617 + ], + "angle": 0, + "content": "To capture spatial smoothness of outliers we spatially diffuse inlier/outlier labels \\(\\omega\\) with a \\(3\\times 3\\) box kernel \\(\\mathcal{B}_{3\\times 3}\\). Formally, we define" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.625, + 0.469, + 0.642 + ], + "angle": 0, + "content": "\\[\n\\mathcal {W} (\\mathbf {r}) = \\left(\\tilde {\\omega} (\\mathbf {r}) * \\mathcal {B} _ {3 \\times 3}\\right) \\geq \\mathcal {T} _ {*}, \\quad \\mathcal {T} _ {*} = 0. 5. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.469, + 0.692 + ], + "angle": 0, + "content": "This helps to avoid classifying high-frequency details as outliers, allowing them to be captured by the NeRF model during optimization (see Figure 5)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.469, + 0.874 + ], + "angle": 0, + "content": "While the trimmed weight function (9) improves the robustness of model fitting, it sometimes misclassifies fine-grained image details early in training where the NeRF model first captures coarse-grained structure. These localized texture elements may emerge but only after very long training times. We find that stronger inductive bias to spatially coherence allows fine-grained details to be learned more quickly. To that end, we aggregate the detection of outliers on \\(16 \\times 16\\) neighborhoods; i.e., we label entire \\(8 \\times 8\\) patches as outliers or inliers based on the behavior of \\(\\mathcal{W}\\) in the \\(16 \\times 16\\) neighborhood of the patch. Denoting the \\(N \\times N\\) neighborhood of pixels around \\(\\mathbf{r}\\) as \\(\\mathcal{R}_N(\\mathbf{r})\\), we define" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.881, + 0.469, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\omega \\left(\\mathcal {R} _ {8} (\\mathbf {r})\\right) = \\mathbb {E} _ {\\mathbf {s} \\sim \\mathcal {R} _ {1 6} (\\mathbf {r})} \\left[ \\mathcal {W} (\\mathbf {s}) \\right] \\geq \\mathcal {T} _ {\\mathcal {R}}, \\quad \\mathcal {T} _ {\\mathcal {R}} = 0. 6. \\tag {10}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.301, + 0.587, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.509, + 0.364, + 0.581, + 0.374 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.606, + 0.301, + 0.687, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.613, + 0.364, + 0.679, + 0.373 + ], + "angle": 0, + "content": "RobustNeRF" + }, + { + "type": "image", + "bbox": [ + 0.707, + 0.301, + 0.788, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.364, + 0.777, + 0.373 + ], + "angle": 0, + "content": "Train View" + }, + { + "type": "image", + "bbox": [ + 0.809, + 0.301, + 0.889, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.364, + 0.879, + 0.373 + ], + "angle": 0, + "content": "Distractors" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.381, + 0.888, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Figure 6. Residuals - For the dataset shown in the top row, we visualize the dynamics of the RobustNeRF training residuals, which show how over time the estimated distractor weights go from being random \\((t / T) = 0.5\\%)\\) to identify distractor pixels \\((t / T) = 100\\%\\) without any explicit supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.716 + ], + "angle": 0, + "content": "The final weight function is the union of the three masks in Eqns. 8 -10. This robust weight function evolves during optimization, as one expects with IRLS where the weights are a function of the residuals at the previous iteration. That is, the labeling of pixels as inliers/outliers changes during training, and settles around masks similar to the one an oracle would provide as training converges (see Figure 6)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.728, + 0.633, + 0.745 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.871 + ], + "angle": 0, + "content": "We implement our robust loss function in the MultiNeRF codebase [26] and apply it to mip-NeRF 360 [4]. We dub this method \"RobustNeRF\". To evaluate RobustNeRF, we compare against baselines on several scenes containing different types of distractors. Where possible, we quantitatively compare reconstructions to held-out, distraction-free images; we report three metrics, averaged across held-out frames, namely, PSNR, SSIM [52], and LPIPS [60]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We compare different methods on two collections of scenes, i.e., those provided by the authors of \\(\\mathrm{D}^2\\mathrm{NeRF}\\), and" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20630" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.177, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.206, + 0.14, + 0.212 + ], + "angle": 0, + "content": "··" + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.092, + 0.273, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.206, + 0.234, + 0.212 + ], + "angle": 0, + "content": "··" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.092, + 0.368, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.311, + 0.206, + 0.331, + 0.212 + ], + "angle": 0, + "content": "···" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.092, + 0.464, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.406, + 0.206, + 0.424, + 0.212 + ], + "angle": 0, + "content": "···" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.217, + 0.177, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.271, + 0.152, + 0.281 + ], + "angle": 0, + "content": "Statue" + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.217, + 0.273, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.271, + 0.251, + 0.282 + ], + "angle": 0, + "content": "Android" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.217, + 0.368, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.271, + 0.337, + 0.281 + ], + "angle": 0, + "content": "Crab" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.217, + 0.464, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.271, + 0.448, + 0.282 + ], + "angle": 0, + "content": "BabyYoda" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.286, + 0.47, + 0.342 + ], + "angle": 0, + "content": "Figure 7. Dataset - Sample training images showing the distractors in each scene. Statue and Android were acquired manually, and the others with a robotic arm. In the robotic setting we have pixel-perfect alignment of distractor vs. distractor-free images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.407 + ], + "angle": 0, + "content": "novel datasets described below. We also present a series of illustrative experiments on synthetic scenes, shedding light on RobustNeRF's efficacy and inner workings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.419, + 0.185, + 0.433 + ], + "angle": 0, + "content": "4.1. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.636 + ], + "angle": 0, + "content": "We compare RobustNeRF to variants of mip-NeRF 360 optimized with different loss functions \\((L_{2}, L_{1}\\), and Carbonnier). These variants serve as natural baselines for models with limited or no robustness to outliers. We also compare to \\(\\mathrm{D}^2\\mathrm{NeRF}\\), a recent method for reconstructing dynamic scenes from monocular video. Unlike our method, \\(\\mathrm{D}^2\\mathrm{NeRF}\\) is designed to reconstruct distractors rather than discard them. While \\(\\mathrm{D}^2\\mathrm{NeRF}\\) is presented as a method for monocular video, it does not presuppose temporal continuity, and can be directly applied to unordered images. We omit additional comparisons to NeRF-W as its performance falls short of \\(\\mathrm{D}^2\\mathrm{NeRF}\\) [53]. For more details on model training, see the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.262, + 0.665 + ], + "angle": 0, + "content": "4.2. Datasets - Figure 7" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.47, + 0.73 + ], + "angle": 0, + "content": "In addition to scenes from \\(\\mathrm{D}^2\\mathrm{NeRF}\\), we introduce a set of natural and synthetic scenes. They facilitate the evaluation of RobustNeRF's effectiveness on illustrative use cases, and they enable empirical analysis under controlled conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Natural scenes. We capture seven natural scenes exemplifying different types of distractors. Scenes are captured in three settings, on the street, in an apartment and in a robotics lab. Distractor objects are moved, or are allowed to move, between frames to simulate capture over extended periods of time. We vary the number of unique distractors from 1 (Statue) to 150 (BabyYoda), and their movements. Unlike prior work on monocular video, frames are captured without a clear temporal ordering (see Figure 7). The other three (i.e., Street1, Street2, and Gloss) include view-dependence effects, the results of which are shown in the supplementary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "material. We also capture additional frames without distractors to enable quantitative evaluations. Camera poses are estimated using COLMAP [38]. A full description of each scene in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.155, + 0.892, + 0.306 + ], + "angle": 0, + "content": "Synthetic scenes. To further evaluate RobustNeRF, we generate synthetic scenes using the Kubric dataset generator [12]. Each scene is constructed by placing a set of simple geometries in an empty, texture-less room. In each scene, a subset of objects remain fixed while the other objects (i.e., distractors) change position from frame to frame. By varying the number of objects, their size, and the way they move, we control the level of distraction in each scene. We use these scenes to examine RobustNeRF's sensitivity to its hyperparameters, see supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.315, + 0.62, + 0.33 + ], + "angle": 0, + "content": "4.3. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.892, + 0.424 + ], + "angle": 0, + "content": "We evaluate RobustNeRF on its ability to ignore distractors while accurately reconstructing the static elements of a scene. We train RobustNeRF, \\( \\mathrm{D}^2\\mathrm{NeRF} \\), and variants of mip-NeRF 360 on scenes where distraction-free frames are available. Models are trained on frames with distractors and evaluated on distractor-free frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Comparison to mip-NeRF 360 - Figure 8. On natural scenes, RobustNeRF generally outperforms variants of mip-NeRF 360 by 1.3 to \\(4.7\\mathrm{dB}\\) in PSNR. As \\(L_{2}, L_{1}\\), and Charbonnier losses weigh all pixels equally, the model is forced to represent, rather than ignore, distractors as \"clouds\" with view-dependent appearance. We find clouds to be most apparent when distractors remain stationary for multiple frames. In contrast, RobustNeRF's loss isolates distractor pixels and assigns them a weight of zero (see Figure 6). To establish an upper bound on reconstruction accuracy, we train mip-NeRF 360 with Charbonnier loss on distraction-free versions of each scene, the images for which are taken from (approximately) the same viewpoints. Reassuringly, RobustNeRF when trained on distraction-free frames, achieves nearly identical accuracy; see Figure 11." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.761 + ], + "angle": 0, + "content": "While RobustNeRF consistently outperforms mip-NeRF 360, the gap is smaller in the Apartment scenes (Statue, Android) than the Robotics Lab scenes (Crab, BabyYoda). This can be explained by challenging background geometry, errors in camera parameter estimation, and imperceptible changes to scene appearance. For further discussion, see the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison to \\(\\mathbf{D}^2\\mathrm{NeRF}\\) - Figure 9. Quantitatively, RobustNeRF matches or outperforms \\(\\mathrm{D}^2\\mathrm{NeRF}\\) by as much as \\(12\\mathrm{dB}\\) PSNR depending on the number of unique outlier objects in the capture. Results on \\(\\mathrm{D}^2\\mathrm{NeRF}\\) real scenes are provided in the supplementary material for qualitative comparison. In Statue and Android, 1 and 3 non-rigid objects are moved around the scene, respectively. \\(\\mathrm{D}^2\\mathrm{NeRF}\\) is able to model these objects and thus separate them from the scenes' static content. In the remaining scenes, a much" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20631" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.087, + 0.891, + 0.221 + ], + "angle": 0, + "content": "
StatueAndroidCrabBabyYoda
LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑
mip-NeRF 360 (L2)0.360.6619.090.400.6519.350.270.7725.730.310.7522.97
mip-NeRF 360 (L1)0.300.7219.550.400.6619.380.220.7926.690.220.8026.15
mip-NeRF 360 (Ch.)0.300.7319.640.400.6619.530.210.8027.720.230.8025.22
D2NeRF0.480.4919.090.430.5720.610.420.6821.180.440.6517.32
RobustNeRF0.280.7520.890.310.6521.720.210.8130.750.200.8330.87
mip-NeRF 360 (clean)0.190.8023.570.310.7123.100.160.8432.550.160.8432.63
" + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.226, + 0.216, + 0.239 + ], + "angle": 0, + "content": "MipNeRF360 (L2)" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.241, + 0.24, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.273, + 0.226, + 0.378, + 0.239 + ], + "angle": 0, + "content": "MipNeRF360 (L1)" + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.241, + 0.403, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.434, + 0.226, + 0.54, + 0.239 + ], + "angle": 0, + "content": "MipNeRF360 (Ch)" + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.241, + 0.565, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.226, + 0.675, + 0.238 + ], + "angle": 0, + "content": "\\(\\mathrm{D}^2\\mathrm{NeRF}\\)" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.241, + 0.726, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.226, + 0.849, + 0.237 + ], + "angle": 0, + "content": "RobustNeRF" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.241, + 0.889, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.337, + 0.24, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.337, + 0.402, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.337, + 0.565, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.337, + 0.726, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.337, + 0.889, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.433, + 0.24, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.433, + 0.402, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.433, + 0.565, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.57, + 0.433, + 0.726, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.433, + 0.889, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.529, + 0.24, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.245, + 0.529, + 0.402, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.529, + 0.565, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.529, + 0.726, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.529, + 0.889, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.626, + 0.893, + 0.682 + ], + "angle": 0, + "content": "Figure 8. Evaluation on Natural Scenes - RobustNeRF outperforms baselines and \\(\\mathrm{D}^2\\mathrm{NeRF}\\) [53] on novel view synthesis with real-world captures. The table provides a quantitative comparison of RobustNeRF, \\(\\mathrm{D}^2\\mathrm{NeRF}\\) and mip-NeRF 360 using different reconstruction losses. The last row reports mip-NeRF 360 trained on a distractor-free version of each dataset, giving an upperbound for RobustNeRF performance. We also visualize samples from each scene rendered with each of the methods. See Supplementary Material for more samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.473, + 0.897 + ], + "angle": 0, + "content": "larger pool of 100 to 150 unique, non-static objects are used – too many for \\(\\mathrm{D}^2\\mathrm{NeRF}\\) to model effectively. As a result, “cloud” artifacts appear in its static representation, similar to those produced by mip-NeRF 360. In contrast, Robust-NeRF identifies non-static content as outliers and omits it during reconstruction. Although both methods use a similar number of parameters, \\(\\mathrm{D}^2\\mathrm{NeRF}\\)'s peak memory usage is \\(2.3\\mathrm{x}\\) higher than RobustNeRF and \\(37\\mathrm{x}\\) higher when normalizing for batch size. This is a direct consequence of model architecture: \\(\\mathrm{D}^2\\mathrm{NeRF}\\) is tailored to simultaneously modeling static and dynamic content and thus merits higher complexity. To remain comparable, we limit image resolution to 0.2 megapixels for all experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.897 + ], + "angle": 0, + "content": "Ablations - Figure 10. We ablate elements of the Robust-NeRF loss on the crab scene, comparing to an upper bound on the reconstruction accuracy of mip-NeRF 360 trained on distractor-free (clean) images from identical viewpoints. Our trimmed estimator (8) successfully eliminates distractors at the expense of high frequency texture and a lower PSNR. With smoothing (9), fine details are recovered, at the cost of longer training times. With the spatial window (10), RobustNeRF training time is on-par with mip-NeRF 360. We also ablate patch size and the trimming threshold (see Supplementary Material); we find that RobustNeRF is insensitive to trimming threshold, and that reducing the patch size offsets the gains from smoothing and patching." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20632" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.088, + 0.891, + 0.278 + ], + "angle": 0, + "content": "
CarCarsBagChairsPillow
LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑
NeRF-W [23].218.81424.23.243.87324.51.139.79120.65.150.68123.77.088.93528.24
NSFF [18].200.80624.90.620.37610.29.108.89225.62.682.28412.82.782.3434.55
NeuralDiff [46].065.95231.89.098.92125.93.117.91029.02.112.72224.42.565.65220.09
D2NeRF [53].062.97534.27.090.95326.27.076.97934.14.095.70724.63.076.97936.58
RobustNeRF.013.98837.73.063.95726.31.006.99541.82.007.99241.23.018.99038.95
Train ViewTest ViewNeRF-WNSFFNeuralDiffD2NeRFRobustNeRF
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.28, + 0.893, + 0.309 + ], + "angle": 0, + "content": "Figure 9. Evaluations on \\(\\mathbf{D}^2\\mathrm{NeRF}\\) Synthetic Scenes - Quantitative and qualitative evaluations on the Kubric synthetic dataset introduced by \\(\\mathbf{D}^2\\mathrm{NeRF}\\), consisting of 200 training frames (with distractor) and 100 novel views for evaluation (without distractor)." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.322, + 0.468, + 0.497 + ], + "angle": 0, + "content": "
LPIPS↓SSIM↑PSNR↑Updates to PSNR=30
mip-NeRF 360 (L2)0.310.7522.97-
+ robust (8)0.390.6018.21-
+ smoothing (9)0.220.8130.01250K
+ patching (10)0.210.8130.7570K
oracle (clean)0.160.8432.5525K
+ robust+ smoothing+ patching
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.498, + 0.47, + 0.553 + ], + "angle": 0, + "content": "Figure 10. Ablations - Blindly trimming the loss causes details to be lost. Smoothing recovers fine-grained detail, while patch-based evaluation speeds up training and adds more detail. Patching enables the model to reach PSNR of 30, almost \\(4 \\times\\) faster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.47, + 0.803 + ], + "angle": 0, + "content": "Sensitivity - Figure 11. We find that RobustNeRF is remarkably robust to the amount of clutter in a dataset. We define an image as \"cluttered\" if it contains some number of distractor pixels. The figure shows how the reconstruction accuracy of RobustNeRF and mip-NeRF 360 depends on the fraction of training images with distractors, keeping the training set size constant. As the fraction increases, mip-NeRF 360's accuracy steadily drops from 33 to \\(25\\mathrm{dB}\\), while RobustNeRF's remains steadily above 31 dB throughout. In the distraction-free regime, we find that RobustNeRF mildly under-performs mip-NeRF 360, both in reconstruction quality and the time needed for training. This follows from the statistical inefficiency induced by the trimmed estimator (8), for which a percentage of pixels will be discarded even if they do not correspond to distractors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.205, + 0.833 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We address a central problem in training NeRF models, namely, optimization in the presence of distractors, such as transient or moving objects and photometric phenomena that are not persistent throughout the capture session." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.319, + 0.698, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.319, + 0.89, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.43, + 0.893, + 0.486 + ], + "angle": 0, + "content": "Figure 11. Sensitivity and Limitations - (left) Reconstruction accuracy for BabyYoda as we increase the fraction of train images with distractors. (right) Accuracy vs training time on clean BabyYoda images (distractor-free)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.893, + 0.699 + ], + "angle": 0, + "content": "Viewed through the lens of robust estimation, we formulate training as a form of iteratively re-weighted least squares, with a variant of trimmed LS, and an inductive bias on the smoothness of the outlier process. RobustNeRF is surprisingly simple, yet effective on a wide range of datasets. RobustNeRF is shown to outperform recent state-of-the-art methods [4, 53], qualitatively and quantitatively, on a suite of synthetic datasets, common benchmark datasets, and new datasets captured by a robot, allowing fine-grained control over distractors for comparison with previous methods. While our experiments explore robust estimation in the context of mip-NeRF 360, the RobustNeRF loss can be incorporated within other NeRF models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Limitations. While RobustNeRF performs well on scenes with distractors, the loss entails some statistical inefficiency. On clean data, this yields somewhat poorer reconstructions, often taking longer to train (see Figure 11). Future work will consider very small distractors, which may require adaptation of the spatial support used for outlier/inlier decisions. It would also be interesting to learn a neural weight function, further improving RobustNeRF; active learning may be useful in this context. Finally, it would be interesting to include our robust loss in other NeRF frameworks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.855, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements We thank Pete Florence and Konstantinos Rematas for helpful feedback, and Tianhao Wu for help with \\(\\mathrm{D}^2\\mathrm{NeRF}\\) experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20633" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Michal Adamkiewicz, Timothy Chen, Adam Caccavale, Rachel Gardner, Preston Culbertson, Jeannette Bohg, and Mac Schwager. Vision-only robot navigation in a neural radiance world. 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Fleet $^{1,2}$ Andrea Tagliafasacchi $^{1,2,3}$ + +1Google Research, Brain Team 2University of Toronto 3Simon Fraser University + +# Abstract + +Neural radiance fields (NeRF) excel at synthesizing new views given multi-view, calibrated images of a static scene. When scenes include distractors, which are not persistent during image capture (moving objects, lighting variations, shadows), artifacts appear as view-dependent effects or 'floaters'. To cope with distractors, we advocate a form of robust estimation for NeRF training, modeling distractors in training data as outliers of an optimization problem. Our method successfully removes outliers from a scene and improves upon our baselines, on synthetic and real-world scenes. Our technique is simple to incorporate in modern NeRF frameworks, with few hyper-parameters. It does not assume a priori knowledge of the types of distractors, and is instead focused on the optimization problem rather than pre-processing or modeling transient objects. More results at https://robustnerf.github.io/public. + +# 1. Introduction + +The ability to understand the structure of a static 3D scene from 2D images alone is a fundamental problem in computer vision [44]. It finds applications in AR/VR for mapping virtual environments [6, 36, 61], in autonomous robotics for action planning [1], and in photogrammetry to create digital copies of real-world objects [34]. + +Neural fields [55] have recently revolutionized this classical task, by storing 3D representations within the weights of a neural network [39]. These representations are optimized by back-propagating image differences. When the fields store view-dependent radiance and volumetric rendering is employed [21], we can capture 3D scenes with photo-realistic accuracy, and we refer to the generated representation as Neural Radiance Fields, or NeRF [25]). + +Training of NeRF models generally requires a large collection of images equipped with accurate camera calibration, which can often be recovered via structure-from-motion [37]. Behind its simplicity, NeRF hides several assumptions. As models are typically trained to minimize error in RGB color space, it is of paramount importance + +![](images/1f94b3ae1ab59c57b87c5e4884be69f5c0048ed2a2ee83bf4879413ecd792bef.jpg) +Figure 1. NeRF assumes photometric consistency in the observed images of a scene. Violations of this assumption, as with the images in the top row, yield reconstructed scenes with inconsistent content in the form of "floaters" (highlighted with ellipses). We introduce a simple technique that produces clean reconstruction by automatically ignoring distractors without explicit supervision. + +that images are photometrically consistent - two photos taken from the same vantage point should be identical up to noise. Unless one employs a method explicitly accounting for it [35], one should manually hold a camera's focus, exposure, white-balance, and ISO fixed. + +However, properly configuring one's camera is not all that is required to capture high-quality NeRFs – it is also important to avoid distractors: anything that isn't persistent throughout the entire capture session. Distractors come in many shapes and forms, from the hard-shadows cast by the operators as they explore the scene to a pet or child casually walking within the camera's field of view. Distractors are tedious to remove manually, as this would require pixel-by-pixel labeling. They are also tedious to detect, as typical NeRF scenes are trained from hundreds of input images, and the types of distractors are not known a priori. If distractors are ignored, the quality of the reconstruction scene suffers significantly; see Figure 1. + +In a typical capture session, it is difficult to capture multiple images of the same scene from the same viewpoint, rendering distractors challenging to model mathematically. As such, while view-dependent effects are what give NeRF their realistic look, how can the model tell the difference between a distractor and a view-dependent effect? + +Despite the challenges, the research community has devised several approaches to overcome this issue: + +- If distractors are known to belong to a specific class (e.g., people), one can remove them with a pre-trained semantic segmentation model [35, 43] – this process does not generalize to “unexpected” distractors such as shadows. +- One can model distractors as per-image transient phenomena, and control the balance of transient/persistent modeling [23] - however, it is difficult to tune the losses that control this Pareto-optimal objective. +- One can model data in time (i.e., high-framerate video) and decompose the scene into static and dynamic (i.e., distractor) components [53] – but this clearly only applies to video rather than photo collection captures. + +Conversely, we approach the problem of distractors by modeling them as outliers in NeRF optimization. + +We analyze the aforementioned techniques through the lens of robust estimation, allowing us to understand their behavior, and to design a method that is not only simpler to implement but also more effective (see Figure 1). As a result, we obtain a method that is straightforward to implement, requires minimal-to-no hyper-parameter tuning, and achieves state-of-the-art performance. We evaluate our method: + +- quantitatively, in terms of reconstruction with synthetically, yet photo-realistically, rendered data; +- qualitatively on publicly available datasets (often finetuned to work effectively with previous methods); +- on a new collection of natural and synthetic scenes, including those autonomously acquired by a robot, allowing us to demonstrate the sensitivity of previous methods to hyper-parameter tuning. + +# 2. Related Work + +We briefly review the basics and notation of Neural Radiance Fields. We then describe recent progress in NeRF research, paying particular attention to techniques for modeling of static/dynamic scenes. + +Neural Radiance Fields. A neural radiance field (NeRF) is a continuous volumetric representation of a 3D scene, stored within the parameters of a neural network $\theta$ . The representation maps a position $\mathbf{x}$ and view direction $\mathbf{d}$ to a view-dependent RGB color and view-independent density: + +$$ +\left. \begin{array}{l} \mathbf {c} (\mathbf {x}, \mathbf {d}) \\ \sigma (\mathbf {x}) \end{array} \right\} f (\mathbf {x}, \mathbf {d}; \boldsymbol {\theta}) \tag {1} +$$ + +This representation is trained from a collection, $\{(\mathbf{C}_i,\mathbf{T}_i)\}$ of images $\mathbf{C}_i$ with corresponding calibration parameters $\mathbf{T}_i$ (camera extrinsic and intrinsic). + +During training the calibration information is employed to convert each pixel of the image into a ray $\mathbf{r} = (\mathbf{o},\mathbf{d})$ , and rays are drawn randomly from input images to form a training mini-batch $(\mathbf{r}\sim \mathbf{C}_i)$ . The parameters $\theta$ are optimized to + +correctly predict the colors of the pixels in the batch via the L2 photometric-reconstruction loss: + +$$ +\mathcal {L} _ {\mathrm {r g b}} (\boldsymbol {\theta}) = \sum_ {i} \mathbb {E} _ {\mathbf {r} \sim \mathbf {C} _ {i}} \left[ \mathcal {L} _ {\mathrm {r g b}} ^ {\mathbf {r}, i} (\boldsymbol {\theta}) \right] \tag {2} +$$ + +$$ +\mathcal {L} _ {\mathrm {r g b}} ^ {\mathbf {r}, i} (\boldsymbol {\theta}) = \left| \left| \mathbf {C} (\mathbf {r}; \boldsymbol {\theta}) - \mathbf {C} _ {i} (\mathbf {r}) \right| \right| _ {2} ^ {2} \tag {3} +$$ + +Parameterizing the ray as $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d}$ , the NeRF model image $\mathbf{C}(\mathbf{r};\boldsymbol{\theta})$ is generated pixel-by-pixel volumetric rendering based on $\sigma(\cdot)$ and $\mathbf{c}(\cdot)$ (e.g., see [25, 42]). + +Recent progress on NeRF models. NeRF models have recently been extended in several ways. A major thread has been the speedup of training [15, 27] and inference [6, 13], enabling today's models to be trained in minutes [27], and rendered on mobile in real-time [6]. While initially restricted to forward-facing scenes, researchers quickly found ways to model real-world $360^{\circ}$ scenes [4, 59], and to reduce the required number of images, via sensor fusion [35] or hand-designed priors [28]. We can now deal with image artifacts such as motion blur [22], exposure [24], and lens distortion [14]. And the requirement of (precise) camera calibrations is quickly being relaxed with the introduction of techniques for local camera refinement [8, 19], or direct inference [58]. While a NeRF typically represents geometry via volumetric density, there exist models custom-tailored to predict surfaces [29, 51], which can be extended to use predicted normals to significantly improve reconstruction quality [50, 57]. Given high-quality normals [47], inferring the (rendering) structure of a scene becomes a possibility [5]. We also note recent papers about additional applications to generalization [56], semantic understanding [48], generative modeling [33], robotics [1], and text-to-3D [31]. + +Modeling non-static scenes. For unstructured scenes like those considered here, the community has focused on reconstructing both static and non-static elements from video. The most direct approach, treating time as an auxiliary input, leads to cloudy geometry and a lack of fine detail [11, 54]. Directly optimizing per-frame latent codes as an auxiliary input has proved more effective [17, 30, 53]. The most widely-adopted approach is to fit a time-conditioned deformation field mapping 3D points between pairs of frames [18, 49] or to a canonical coordinate frame [9, 10, 20, 32, 45]. Given how sparsely spacetime is sampled, all methods require careful regularization, optimization, or additional training signals to achieve acceptable results. + +Relatively little attention has been given to removing non-static elements. One common approach is to segment and ignore pixels which are likely to be distractors [35, 43]. While this eliminates larger objects, it fails to account for secondary effects like shadows. Prior attempts to model distractors as outliers still leave residual cloudy geometry [23]. + +![](images/fd427e53b06992ad7e2399ed5219e2db17f6d6b5aac0badd013f1d3667e33e83.jpg) +Figure 2. Ambiguity - A simple 2D scene where a static object (blue) is captured by three cameras. During the first and third capture the scene is not photo-consistent as a distractor was within the field of view. Not photo-consistent portions of the scene can end up being encoded as view-dependent effects - even when we assume ground truth geometry. + +![](images/ff166e4f12987f76838b6513f6e0bb8ec9a53ef5607f55d7408084a762a7996d.jpg) + +# 3. Method + +The classical NeRF training losses (3) are effective for capturing scenes that are photometrically consistent, leading to the photo-realistic novel-view synthesis that we are now accustomed to seeing in recent research. However, "what happens when there are elements of the scene that are not persistent throughout the entire capture session?" Simple examples of such scenes include those in which an object is only present in some fraction of the observed images, or may not remain in the same position in all observed images. For example, Figure 2 depicts a 2D scene comprising a persistent object (the truck), along with several transient objects (e.g., people and a dog). While rays in blue from the three cameras intersect the truck, the green and orange rays from cameras 1 and 3 intersect transient objects. For video capture and spatio-temporal NeRF models, the persistent objects comprise the "static" portion of the scene, while the rest would be called the "dynamic". + +# 3.1. Sensitivity to outliers + +For Lambertian scenes, photo-consistent structure is view independent, as scene radiance only depends on the incident light [16]. For such scenes, view-dependent NeRF models like (1), trained by minimizing (3), admit local optima in which transient objects are explained by view-dependent terms. Figure 2 depicts this, with the outgoing color corresponding to the memorized color of the outlier - i.e. view-dependent radiance. Such models exploit the view-dependent capacity of the model to over-fit observations, effectively memorizing the transient objects. One can alter the model to remove dependence on $\mathbf{d}$ but the L2 loss remains problematic as least-squares (LS) estimators are sensitive to outliers, or heavy-tailed noise distributions. + +Under more natural conditions, dropping the Lambertian assumption, the problem becomes more complex as both non-Lambertian reflectance phenomena and outliers can be explained as view-dependent radiance. While we want the models to capture photo-consistent view-dependent radiance, outliers and other transient phenomena should ideally be ignored. And in such cases, optimization with an L2 + +loss (3) yields significant errors in reconstruction; see Figure 1. Problems like these are pervasive in NeRF model fitting, especially in uncontrolled environments with complex reflectance, non-rigidity, or independently moving objects. + +# 3.2. Robustness to outliers + +Robustness via semantic segmentation. One way to reduce outlier contamination during NeRF model optimization is to rely on an oracle $\mathbf{S}$ that specifies whether a given pixel $\mathbf{r}$ from image $i$ is an outlier, and should therefore be excluded from the empirical loss, replacing (3) with: + +$$ +\mathcal {L} _ {\text {o r a c l e}} ^ {\mathbf {r}, i} (\boldsymbol {\theta}) = \mathbf {S} _ {i} (\mathbf {r}) \cdot | | \mathbf {C} (\mathbf {r}; \boldsymbol {\theta}) - \mathbf {C} _ {i} (\mathbf {r}) | | _ {2} ^ {2} \tag {4} +$$ + +In practice, a pre-trained (semantic) segmentation network $S$ might serve as an oracle, $\mathbf{S}_i = S(\mathbf{C}_i)$ . E.g., Nerf-in-the-wild [23] employed a semantic segmenter to remove pixels occupied by people, as they are outliers in the context of photo-tourism. Urban Radiance Fields [35] segmented out sky pixels, while LOL-NeRF [33] ignored pixels not belonging to faces. The obvious problem with this approach is the need for an oracle to detect arbitrary distractors. + +Robust estimators. Another way to reduce sensitivity to outliers is to replace the conventional L2 loss (3) with a robust loss (e.g., [2, 41]), so that photometrically-inconsistent observations can be down-weighted during optimization. Given a robust kernel $\kappa(\cdot)$ , we rewrite our training loss as: + +$$ +\mathcal {L} _ {\text {r o b u s t}} ^ {\mathbf {r}, i} (\boldsymbol {\theta}) = \kappa \left(\left| \left| \mathbf {C} (\mathbf {r}; \boldsymbol {\theta}) - \mathbf {C} _ {i} (\mathbf {r}) \right| \right| _ {2}\right) \tag {5} +$$ + +where $\kappa(\cdot)$ is positive and monotonically increasing. MipNeRF [3], for example, employs an L1 loss $\kappa(\epsilon) = |\epsilon|$ , which provides some degree of robustness to outliers during NeRF training. Given our analysis, a valid question is whether we can straightforwardly employ a robust kernel to approach our problem, and if so, given the large variety of robust kernels [2], which is the kernel of choice. + +Unfortunately, as discussed above, outliers and non-Lambertian effects can both be modelled as view-dependent effects (see Figure 3). As a consequence, with simple application of robust estimators it can be difficult to separate signal from noise. Figure 4 shows examples in which outliers + +![](images/11ad7dc1cc45fb13dab8eb420d7cc8ad66432e0546b9533578c9214db3f57180.jpg) + +![](images/b2eb3620a00498884b091da8a7002ce0ca793164b22359e7226635d9c8a96708.jpg) + +![](images/d79c260859e20c9b34c744b290b5c9725455d80ee2d5fcfb5fbf68d85187829b.jpg) +Figure 3. Histograms - Robust estimators perform well when the distribution of residuals agrees with the one implied by the estimator (e.g., Gaussian for L2, Laplacian for L1). Here we visualize the ground-truth distribution of residuals (bottom-left), which is hardly a good match with any simple parametric distribution. + +![](images/bc0cfa8000d411cb3d2e6833322a1287d9b33fa4e89c2466baecdf67d05404a1.jpg) + +are removed, but fine-grained texture and view-dependent details are also lost, or conversely, fine-grained details are preserved, but outliers cause artifacts in the reconstructed scene. One can also observe mixtures of these cases in which details are not captured well, nor are outliers fully removed. We find that this behaviour occurs consistently for many different robust estimators and parameter settings. + +Training time can also be problematic. The robust estimator gradient w.r.t. model parameters can be expressed using the chain rule as + +$$ +\left. \frac {\partial \kappa (\epsilon (\boldsymbol {\theta}))}{\partial \boldsymbol {\theta}} \right| _ {\boldsymbol {\theta} ^ {(t)}} = \left. \frac {\partial \kappa (\epsilon)}{\partial \epsilon} \right| _ {\epsilon (\boldsymbol {\theta} ^ {(t)})} \cdot \left. \frac {\partial \epsilon (\boldsymbol {\theta})}{\partial \boldsymbol {\theta}} \right| _ {\boldsymbol {\theta} ^ {(t)}} \tag {6} +$$ + +The second factor is the classical NeRF gradient. The first factor is the kernel gradient evaluated at the current error residual $\epsilon (\pmb{\theta}^{(t)})$ . During training, large residuals can equivalently come from high-frequency details that have not yet been learnt, or they may arise from outliers (see Figure 4 (bottom)). This explain why robust optimization, implemented as (5), should not be expected to decouple high-frequency details from outliers. Further, when strongly robust kernels are employed, like redescending estimators, this also explains the loss of visual fidelity. That is, because the gradient of (large) residuals get down-weighted by the (small) gradients of the kernel, slowing down the learning of these fine-grained details (see Figure 4 (top)). + +# 3.3. Robustness via Trimmed Least Squares + +In what follows we advocate a form of iteratively reweighted least-squares (IRLS) with a Trimmed least squares (LS) loss for NeRF model fitting. + +Iteratively Reweighted least Squares. IRLS is a widely used method for robust estimation that involves solving a sequence of weighted LS problems, the weights of which are adapted to reduce the influence of outliers. To that end, + +![](images/7938b39f31acfdc501893b4a8f3350a2f3af6e6029632895dc97faf118a27321.jpg) + +![](images/8bee22d7570c63c3c8dcb2a2fb19c6b6aacc77cd83387cf79c109fb8235f552f.jpg) + +![](images/1632681e93a49b53846aba35cb9a9a030cc78ccb806d3756c22ec532e55ff874.jpg) +Figure 4. Kernels - (top-left) Family of robust kernels [2], including L2 ( $\alpha = 2$ ), Charbonnier ( $\alpha = 1$ ) and Geman-McClure ( $\alpha = -2$ ). (top-right) Mid-training, residual magnitudes are similar for distractors and fine-grained details, and pixels with large residuals are learned more slowly, as the gradient of re-descending kernels flattens out. (bottom-right) A too aggressive Geman-McClure in down-weighting large residuals removes both outliers and high-frequency detail. (bottom-left) A less aggressive Geman-McClure does not effectively remove outliers. + +![](images/eef272506fab0a7293f190e56385e2b5f26c2fe42d91278bc7e3ba201f641252.jpg) + +at iteration $t$ , one can write the loss as + +$$ +\mathcal {L} _ {\text {r o b u s t}} ^ {\mathbf {r}, i} \left(\boldsymbol {\theta} ^ {(t)}\right) = \omega \left(\boldsymbol {\epsilon} ^ {(t - 1)} (\mathbf {r})\right) \cdot | | \mathbf {C} (\mathbf {r}; \boldsymbol {\theta} ^ {(t)}) - \mathbf {C} _ {i} (\mathbf {r}) | | _ {2} ^ {2} +$$ + +$$ +\boldsymbol {\epsilon} ^ {(t - 1)} (\mathbf {r}) = \left| \left| \mathbf {C} (\mathbf {r}; \boldsymbol {\theta} ^ {(t - 1)}) - \mathbf {C} _ {i} (\mathbf {r}) \right| \right| _ {2} \tag {7} +$$ + +For weight functions given by $\omega (\epsilon) = \epsilon^{-1}\cdot \partial \kappa (\epsilon) / \partial \epsilon$ one can show that, under suitable conditions, the iteration converges to a local minima of (5) (see [41, Sec. 3]). + +This framework admits a broad family of losses, including maximum likelihood estimators for heavy-tailed noise processes. Examples in Figure 4 include the Charbonnier loss (smoothed L1), and more aggressive redescending estimators such as the Lorentzian or Geman-McClure [2]. The objective in (4) can also be viewed as a weighted LS objective, the binary weights of which are provided by an oracle. And, as discussed at length below, one can also view several recent methods like NeRFW [23] and $\mathrm{D}^2\mathrm{NeRF}$ [53] through the lens of IRLS and weighted LS. + +Nevertheless, choosing a suitable weight function $\omega(\epsilon)$ for NeRF optimization is non-trivial, due in large part to the intrinsic ambiguity between view-dependent radiance phenomena and outliers. One might try to solve this problem by learning a neural weight function [40], although generating enough annotated training data might be prohibitive. Instead, the approach taken below is to exploit inductive biases in the structure of outliers, combined with the simplicity of a robust, trimmed LS estimator. + +Trimmed Robust Kernels. Our goal is to develop a weight function for use in iteratively weighted LS optimization that is simple and captures useful inductive biases for NeRF optimization. For simplicity we opt for a binary weight function with intuitive parameters that adapts naturally through model fitting so that fine-grained image details that are not + +![](images/c4d7aa68fc1cf767be6cc6e9d208ab8c015e53701c307328f83104d47b5e8f5c.jpg) + +![](images/f91fb7f5b893bb47da572b0df940fc0b094b10279f430799e1478a8e794435e8.jpg) +residuals - $\epsilon (\mathbf{r})$ + +![](images/d9a7c3c9248e6b0d2e49b80e508445785b7faf30297405fd92a356c86778a670.jpg) + +![](images/873f6abe2d818eeb1542748a04be93455f2e67da076891565998d6dc7678c5f5.jpg) +inliers - $\tilde{\omega} (\mathbf{r})$ +Figure 5. Algorithm - We visualize our weight function computed by residuals on two examples: (top) the residuals of a (mid-training) NeRF rendered from a training viewpoint, (bottom) a toy residual image containing residual of small spatial extent (dot, line) and residuals of large spatial extent (squares). Notice residuals with large magnitude but small spatial extent (texture of the box, dot, line) are included in the optimization, while weaker residuals with larger spatial extent are excluded. Note that while we operate on patches, we visualize the weight function on the whole image to facilitate visualization. + +![](images/d39ccfe40e70ee86c4959d6925556f5b4f52cee785752e345afb7026b573e088.jpg) + +![](images/3a9ee80c514580cfc6f5f57876a041719846aed5e201e272d35434e954f86f15.jpg) +diffusion - $\tilde{\omega}(\mathbf{r}) \oplus \mathcal{B}_{3 \times 3}$ + +![](images/09be3306f8248a3d9f4bd6c55d6918e93896a53fa487fe67237b06357342877a.jpg) + +![](images/a3df0d1d6602f3b8faab9d6badefac0d455997cc96da692275f316984e52437b.jpg) +(IRLS) weights - $\mathcal{W}(\mathbf{r})$ + +outliers can be learned quickly. It is also important to capture the structured nature of typical outliers, contrary to the typical i.i.d. assumption in most robust estimator formulations. To this end, the weight function should capture spatial smoothness of the outlier process, recognizing that objects typically have continuous local support, and hence outliers are expected to occupy large, connected regions of an image (e.g., the silhouette of a person to be segmented out from a photo-tourism dataset). + +Surprisingly, a relatively simple weight function embodies these properties and performs extremely well in practice. The weight function is based on so-called trimmed estimators that are used in trimmed least-squares, like that used in trimmed ICP [7]. We first sort residuals, and assume that residuals below a certain percentile are inliers. Picking the $50\%$ percentile for convenience (i.e., median), we define + +$$ +\tilde {\omega} (\mathbf {r}) = \epsilon (\mathbf {r}) \leq \mathcal {T} _ {\epsilon}, \quad \mathcal {T} _ {\epsilon} = \operatorname {M e d i a n} _ {\mathbf {r}} \left\{\epsilon (\mathbf {r}) \right\}. \tag {8} +$$ + +To capture spatial smoothness of outliers we spatially diffuse inlier/outlier labels $\omega$ with a $3\times 3$ box kernel $\mathcal{B}_{3\times 3}$ . Formally, we define + +$$ +\mathcal {W} (\mathbf {r}) = \left(\tilde {\omega} (\mathbf {r}) * \mathcal {B} _ {3 \times 3}\right) \geq \mathcal {T} _ {*}, \quad \mathcal {T} _ {*} = 0. 5. \tag {9} +$$ + +This helps to avoid classifying high-frequency details as outliers, allowing them to be captured by the NeRF model during optimization (see Figure 5). + +While the trimmed weight function (9) improves the robustness of model fitting, it sometimes misclassifies fine-grained image details early in training where the NeRF model first captures coarse-grained structure. These localized texture elements may emerge but only after very long training times. We find that stronger inductive bias to spatially coherence allows fine-grained details to be learned more quickly. To that end, we aggregate the detection of outliers on $16 \times 16$ neighborhoods; i.e., we label entire $8 \times 8$ patches as outliers or inliers based on the behavior of $\mathcal{W}$ in the $16 \times 16$ neighborhood of the patch. Denoting the $N \times N$ neighborhood of pixels around $\mathbf{r}$ as $\mathcal{R}_N(\mathbf{r})$ , we define + +$$ +\omega \left(\mathcal {R} _ {8} (\mathbf {r})\right) = \mathbb {E} _ {\mathbf {s} \sim \mathcal {R} _ {1 6} (\mathbf {r})} \left[ \mathcal {W} (\mathbf {s}) \right] \geq \mathcal {T} _ {\mathcal {R}}, \quad \mathcal {T} _ {\mathcal {R}} = 0. 6. \tag {10} +$$ + +![](images/bf26a6902d7a41ed48389fa1f5b89d4469c7a3ae868ee3ba2d6b6dd6db473a18.jpg) +Ground Truth + +![](images/4416c7398ccd94ebc9d367fa80dd34745d1f0b22821109b958a335b77eb5ef87.jpg) +RobustNeRF + +![](images/0b6c7d1202a0081f52befd0f8113b7eaa05410296dc88312c5fd84db8c93517f.jpg) +Train View + +![](images/3a02c34a52cb7d88bc69b2089f4a9245d1437487a0c9d1e3882be254e4ca87fc.jpg) +Distractors + +![](images/61d593844bc4764698a50b4773d9444124bb85159f02cb5638f6aa39ecafd740.jpg) +Figure 6. Residuals - For the dataset shown in the top row, we visualize the dynamics of the RobustNeRF training residuals, which show how over time the estimated distractor weights go from being random $(t / T) = 0.5\%)$ to identify distractor pixels $(t / T) = 100\%$ without any explicit supervision. + +The final weight function is the union of the three masks in Eqns. 8 -10. This robust weight function evolves during optimization, as one expects with IRLS where the weights are a function of the residuals at the previous iteration. That is, the labeling of pixels as inliers/outliers changes during training, and settles around masks similar to the one an oracle would provide as training converges (see Figure 6). + +# 4. Experiments + +We implement our robust loss function in the MultiNeRF codebase [26] and apply it to mip-NeRF 360 [4]. We dub this method "RobustNeRF". To evaluate RobustNeRF, we compare against baselines on several scenes containing different types of distractors. Where possible, we quantitatively compare reconstructions to held-out, distraction-free images; we report three metrics, averaged across held-out frames, namely, PSNR, SSIM [52], and LPIPS [60]. + +We compare different methods on two collections of scenes, i.e., those provided by the authors of $\mathrm{D}^2\mathrm{NeRF}$ , and + +![](images/fd0b180c1026e2be7ccdee830cae294216bd8c940336f0220309076f21627f21.jpg) +·· + +![](images/22cb10d1fc054634cd88f8e4e16a0ab3bf0cb02ffedc48c416b29e5cde255850.jpg) +·· + +![](images/7a8807948cc6eeba13b5d92f78a16697ee949ec41f3a5424f1ade3c127bec8b5.jpg) +··· + +![](images/c1697cdb8d34afb169bc52ec894798f33b8f724db8ce82cf41b82abed8e3d25a.jpg) +··· + +![](images/762874ad94fc2fd98f1240146b07723da08dad632c699a0932c7aa82b5de6a09.jpg) +Statue + +![](images/dbcea64e120747e1ed4cea2e373652528276341671ecec1e4f4912acb22390c0.jpg) +Android + +![](images/66cc33a619f3416b49a8d2b6c643ed33b59e00a0f8f22684e90cfb6ed0e62fa7.jpg) +Crab +Figure 7. Dataset - Sample training images showing the distractors in each scene. Statue and Android were acquired manually, and the others with a robotic arm. In the robotic setting we have pixel-perfect alignment of distractor vs. distractor-free images. + +![](images/d4665e589c43ddd6ae0a880b9b65793acf9e80ac3bc7d18a3a2c1524afd65028.jpg) +BabyYoda + +novel datasets described below. We also present a series of illustrative experiments on synthetic scenes, shedding light on RobustNeRF's efficacy and inner workings. + +# 4.1. Baselines + +We compare RobustNeRF to variants of mip-NeRF 360 optimized with different loss functions $(L_{2}, L_{1}$ , and Carbonnier). These variants serve as natural baselines for models with limited or no robustness to outliers. We also compare to $\mathrm{D}^2\mathrm{NeRF}$ , a recent method for reconstructing dynamic scenes from monocular video. Unlike our method, $\mathrm{D}^2\mathrm{NeRF}$ is designed to reconstruct distractors rather than discard them. While $\mathrm{D}^2\mathrm{NeRF}$ is presented as a method for monocular video, it does not presuppose temporal continuity, and can be directly applied to unordered images. We omit additional comparisons to NeRF-W as its performance falls short of $\mathrm{D}^2\mathrm{NeRF}$ [53]. For more details on model training, see the supplementary material. + +# 4.2. Datasets - Figure 7 + +In addition to scenes from $\mathrm{D}^2\mathrm{NeRF}$ , we introduce a set of natural and synthetic scenes. They facilitate the evaluation of RobustNeRF's effectiveness on illustrative use cases, and they enable empirical analysis under controlled conditions. + +Natural scenes. We capture seven natural scenes exemplifying different types of distractors. Scenes are captured in three settings, on the street, in an apartment and in a robotics lab. Distractor objects are moved, or are allowed to move, between frames to simulate capture over extended periods of time. We vary the number of unique distractors from 1 (Statue) to 150 (BabyYoda), and their movements. Unlike prior work on monocular video, frames are captured without a clear temporal ordering (see Figure 7). The other three (i.e., Street1, Street2, and Gloss) include view-dependence effects, the results of which are shown in the supplementary + +material. We also capture additional frames without distractors to enable quantitative evaluations. Camera poses are estimated using COLMAP [38]. A full description of each scene in the supplementary material. + +Synthetic scenes. To further evaluate RobustNeRF, we generate synthetic scenes using the Kubric dataset generator [12]. Each scene is constructed by placing a set of simple geometries in an empty, texture-less room. In each scene, a subset of objects remain fixed while the other objects (i.e., distractors) change position from frame to frame. By varying the number of objects, their size, and the way they move, we control the level of distraction in each scene. We use these scenes to examine RobustNeRF's sensitivity to its hyperparameters, see supplementary material. + +# 4.3. Evaluation + +We evaluate RobustNeRF on its ability to ignore distractors while accurately reconstructing the static elements of a scene. We train RobustNeRF, $\mathrm{D}^2\mathrm{NeRF}$ , and variants of mip-NeRF 360 on scenes where distraction-free frames are available. Models are trained on frames with distractors and evaluated on distractor-free frames. + +Comparison to mip-NeRF 360 - Figure 8. On natural scenes, RobustNeRF generally outperforms variants of mip-NeRF 360 by 1.3 to $4.7\mathrm{dB}$ in PSNR. As $L_{2}, L_{1}$ , and Charbonnier losses weigh all pixels equally, the model is forced to represent, rather than ignore, distractors as "clouds" with view-dependent appearance. We find clouds to be most apparent when distractors remain stationary for multiple frames. In contrast, RobustNeRF's loss isolates distractor pixels and assigns them a weight of zero (see Figure 6). To establish an upper bound on reconstruction accuracy, we train mip-NeRF 360 with Charbonnier loss on distraction-free versions of each scene, the images for which are taken from (approximately) the same viewpoints. Reassuringly, RobustNeRF when trained on distraction-free frames, achieves nearly identical accuracy; see Figure 11. + +While RobustNeRF consistently outperforms mip-NeRF 360, the gap is smaller in the Apartment scenes (Statue, Android) than the Robotics Lab scenes (Crab, BabyYoda). This can be explained by challenging background geometry, errors in camera parameter estimation, and imperceptible changes to scene appearance. For further discussion, see the supplementary material. + +Comparison to $\mathbf{D}^2\mathrm{NeRF}$ - Figure 9. Quantitatively, RobustNeRF matches or outperforms $\mathrm{D}^2\mathrm{NeRF}$ by as much as $12\mathrm{dB}$ PSNR depending on the number of unique outlier objects in the capture. Results on $\mathrm{D}^2\mathrm{NeRF}$ real scenes are provided in the supplementary material for qualitative comparison. In Statue and Android, 1 and 3 non-rigid objects are moved around the scene, respectively. $\mathrm{D}^2\mathrm{NeRF}$ is able to model these objects and thus separate them from the scenes' static content. In the remaining scenes, a much + +
StatueAndroidCrabBabyYoda
LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑
mip-NeRF 360 (L2)0.360.6619.090.400.6519.350.270.7725.730.310.7522.97
mip-NeRF 360 (L1)0.300.7219.550.400.6619.380.220.7926.690.220.8026.15
mip-NeRF 360 (Ch.)0.300.7319.640.400.6619.530.210.8027.720.230.8025.22
D2NeRF0.480.4919.090.430.5720.610.420.6821.180.440.6517.32
RobustNeRF0.280.7520.890.310.6521.720.210.8130.750.200.8330.87
mip-NeRF 360 (clean)0.190.8023.570.310.7123.100.160.8432.550.160.8432.63
+ +![](images/2472bef537acf5ecbf70fd1ccd4e8fdd4925aac7be2d02f5078b3cadb5f67ca5.jpg) +MipNeRF360 (L2) + +![](images/af7d9acea775d2155ed10237b7999d99195bb134366ad25a6c1e360d937f9f42.jpg) +MipNeRF360 (L1) + +![](images/13a1dc7479797324164b7080843547f38b6e2fb62ce563031af7a75ba9138338.jpg) +MipNeRF360 (Ch) + +![](images/714501e76ffdf113f080c6f7b7789dd195653e9a529af0ee71a92d27ba2a2214.jpg) +$\mathrm{D}^2\mathrm{NeRF}$ + +![](images/3ddc66a93c631c646317fe0aa2640bfdf35c5cc4d28f9c65636ca20f691b07c4.jpg) +RobustNeRF + +![](images/7fd91bf56dc9e30d6dcc2265a52d415b47fdfc66e4518b1befa598acb895655d.jpg) + +![](images/0647871967bd735d4b498a761950e451bffe8a160ccfff0372e0513819fbc28f.jpg) + +![](images/b658f6f97a6edd10f1d7a6cdd644fdd1ce388b732f1914e6aaeda8051c38167f.jpg) + +![](images/a779e3c1ee430366f17af15c093cba5a31cacd675bc5a43f4a67457a2f945046.jpg) + +![](images/5d6a9d369db5377343f4d05f840cff309f2bcdbfec3a29c11b9f81bb5d6e35dc.jpg) + +![](images/908fbde1d517ea610c37fcfc2d9fa26961946c3ac07c40f3516176ce479013fe.jpg) + +![](images/941d667498108edd1f131e7b2e9577b587c75b45666ebec28ffe5295b8276fac.jpg) + +![](images/7cdaf75c778f195b955d2151692a4b2e4dcfd3b2cccad382ba65da930cc8d33b.jpg) + +![](images/0c66e136417c9ec76a7ce9cd70ea66232e91904c114038bd3185ee2df4289495.jpg) + +![](images/e32af9c9ac8a43c2649ac21e09d064db9b60e09650a3536d662beeace1b62791.jpg) + +![](images/84ef9a524a3021812a8c9f681d2f616deddd59904b35a59c6139c3e949778e33.jpg) +Figure 8. Evaluation on Natural Scenes - RobustNeRF outperforms baselines and $\mathrm{D}^2\mathrm{NeRF}$ [53] on novel view synthesis with real-world captures. The table provides a quantitative comparison of RobustNeRF, $\mathrm{D}^2\mathrm{NeRF}$ and mip-NeRF 360 using different reconstruction losses. The last row reports mip-NeRF 360 trained on a distractor-free version of each dataset, giving an upperbound for RobustNeRF performance. We also visualize samples from each scene rendered with each of the methods. See Supplementary Material for more samples. + +![](images/fbff17edcd0c79df32fd429ad15ec1ef06b80d4dca1fab87e2456bd3826010ad.jpg) + +![](images/e9215e4e4f884ac6d10f101a9563ca8e96bf72151a128a1751def30b93e22c45.jpg) + +![](images/b2ab403dd8bd35e27f24f173505838e737fc32feaeaff8ed4698dd5bbd5f6794.jpg) + +![](images/06c7d9010e371fb2c3acf11e25eeec78573aa9900a82f80795f0ec317f4a5b25.jpg) + +larger pool of 100 to 150 unique, non-static objects are used – too many for $\mathrm{D}^2\mathrm{NeRF}$ to model effectively. As a result, “cloud” artifacts appear in its static representation, similar to those produced by mip-NeRF 360. In contrast, Robust-NeRF identifies non-static content as outliers and omits it during reconstruction. Although both methods use a similar number of parameters, $\mathrm{D}^2\mathrm{NeRF}$ 's peak memory usage is $2.3\mathrm{x}$ higher than RobustNeRF and $37\mathrm{x}$ higher when normalizing for batch size. This is a direct consequence of model architecture: $\mathrm{D}^2\mathrm{NeRF}$ is tailored to simultaneously modeling static and dynamic content and thus merits higher complexity. To remain comparable, we limit image resolution to 0.2 megapixels for all experiments. + +Ablations - Figure 10. We ablate elements of the Robust-NeRF loss on the crab scene, comparing to an upper bound on the reconstruction accuracy of mip-NeRF 360 trained on distractor-free (clean) images from identical viewpoints. Our trimmed estimator (8) successfully eliminates distractors at the expense of high frequency texture and a lower PSNR. With smoothing (9), fine details are recovered, at the cost of longer training times. With the spatial window (10), RobustNeRF training time is on-par with mip-NeRF 360. We also ablate patch size and the trimming threshold (see Supplementary Material); we find that RobustNeRF is insensitive to trimming threshold, and that reducing the patch size offsets the gains from smoothing and patching. + +
CarCarsBagChairsPillow
LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑
NeRF-W [23].218.81424.23.243.87324.51.139.79120.65.150.68123.77.088.93528.24
NSFF [18].200.80624.90.620.37610.29.108.89225.62.682.28412.82.782.3434.55
NeuralDiff [46].065.95231.89.098.92125.93.117.91029.02.112.72224.42.565.65220.09
D2NeRF [53].062.97534.27.090.95326.27.076.97934.14.095.70724.63.076.97936.58
RobustNeRF.013.98837.73.063.95726.31.006.99541.82.007.99241.23.018.99038.95
Train ViewTest ViewNeRF-WNSFFNeuralDiffD2NeRFRobustNeRF
+ +Figure 9. Evaluations on $\mathbf{D}^2\mathrm{NeRF}$ Synthetic Scenes - Quantitative and qualitative evaluations on the Kubric synthetic dataset introduced by $\mathbf{D}^2\mathrm{NeRF}$ , consisting of 200 training frames (with distractor) and 100 novel views for evaluation (without distractor). + +
LPIPS↓SSIM↑PSNR↑Updates to PSNR=30
mip-NeRF 360 (L2)0.310.7522.97-
+ robust (8)0.390.6018.21-
+ smoothing (9)0.220.8130.01250K
+ patching (10)0.210.8130.7570K
oracle (clean)0.160.8432.5525K
+ robust+ smoothing+ patching
+ +Figure 10. Ablations - Blindly trimming the loss causes details to be lost. Smoothing recovers fine-grained detail, while patch-based evaluation speeds up training and adds more detail. Patching enables the model to reach PSNR of 30, almost $4 \times$ faster. + +Sensitivity - Figure 11. We find that RobustNeRF is remarkably robust to the amount of clutter in a dataset. We define an image as "cluttered" if it contains some number of distractor pixels. The figure shows how the reconstruction accuracy of RobustNeRF and mip-NeRF 360 depends on the fraction of training images with distractors, keeping the training set size constant. As the fraction increases, mip-NeRF 360's accuracy steadily drops from 33 to $25\mathrm{dB}$ , while RobustNeRF's remains steadily above 31 dB throughout. In the distraction-free regime, we find that RobustNeRF mildly under-performs mip-NeRF 360, both in reconstruction quality and the time needed for training. This follows from the statistical inefficiency induced by the trimmed estimator (8), for which a percentage of pixels will be discarded even if they do not correspond to distractors. + +# 5. Conclusions + +We address a central problem in training NeRF models, namely, optimization in the presence of distractors, such as transient or moving objects and photometric phenomena that are not persistent throughout the capture session. + +![](images/8d20921cfffe3ec11df060f2cc54bfdaeaa6671ce873faf1eb8f2439c641d3b5.jpg) +Figure 11. Sensitivity and Limitations - (left) Reconstruction accuracy for BabyYoda as we increase the fraction of train images with distractors. (right) Accuracy vs training time on clean BabyYoda images (distractor-free). + +![](images/6aefd32abf79c23dfc1f2bc20cbe57a82060ff522497877b96c668389f8568a1.jpg) + +Viewed through the lens of robust estimation, we formulate training as a form of iteratively re-weighted least squares, with a variant of trimmed LS, and an inductive bias on the smoothness of the outlier process. RobustNeRF is surprisingly simple, yet effective on a wide range of datasets. RobustNeRF is shown to outperform recent state-of-the-art methods [4, 53], qualitatively and quantitatively, on a suite of synthetic datasets, common benchmark datasets, and new datasets captured by a robot, allowing fine-grained control over distractors for comparison with previous methods. While our experiments explore robust estimation in the context of mip-NeRF 360, the RobustNeRF loss can be incorporated within other NeRF models. + +Limitations. While RobustNeRF performs well on scenes with distractors, the loss entails some statistical inefficiency. On clean data, this yields somewhat poorer reconstructions, often taking longer to train (see Figure 11). Future work will consider very small distractors, which may require adaptation of the spatial support used for outlier/inlier decisions. It would also be interesting to learn a neural weight function, further improving RobustNeRF; active learning may be useful in this context. Finally, it would be interesting to include our robust loss in other NeRF frameworks. + +Acknowledgements We thank Pete Florence and Konstantinos Rematas for helpful feedback, and Tianhao Wu for help with $\mathrm{D}^2\mathrm{NeRF}$ experiments. + +# References + +[1] Michal Adamkiewicz, Timothy Chen, Adam Caccavale, Rachel Gardner, Preston Culbertson, Jeannette Bohg, and Mac Schwager. Vision-only robot navigation in a neural radiance world. 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CVPR, 2022. 1 \ No newline at end of file diff --git a/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/images.zip b/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..55e12451a8b13638e6746d976687ebde1c8a2463 --- /dev/null +++ b/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:31a5a89794b65d4efe3631c87d64a96724ef42cbe51d9e1b266bf9834edb78c5 +size 741443 diff --git a/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/layout.json b/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..92bd08f4a58514035b24638314ac4b68c2580674 --- /dev/null +++ b/2023/RobustNeRF_ Ignoring Distractors With Robust Losses/layout.json @@ -0,0 +1,11106 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 125, + 102, + 468, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 102, + 468, + 121 + ], + "spans": [ + { + "bbox": [ + 125, + 102, + 468, + 121 + ], + "type": "text", + "content": "RobustNeRF: Ignoring Distractors with Robust Losses4" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "spans": [ + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "content": "Sara Sabour" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "content": " Suhani Vora" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "content": " Daniel Duckworth" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "content": " Ivan Krasin" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "content": " David J. Fleet" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "text", + "content": " Andrea Tagliafasacchi" + }, + { + "bbox": [ + 129, + 142, + 463, + 171 + ], + "type": "inline_equation", + "content": "^{1,2,3}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 140, + 172, + 451, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 172, + 451, + 185 + ], + "spans": [ + { + "bbox": [ + 140, + 172, + 451, + 185 + ], + "type": "text", + "content": "1Google Research, Brain Team 2University of Toronto 3Simon Fraser University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 224 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 224 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 231, + 290, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 290, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 290, + 422 + ], + "type": "text", + "content": "Neural radiance fields (NeRF) excel at synthesizing new views given multi-view, calibrated images of a static scene. When scenes include distractors, which are not persistent during image capture (moving objects, lighting variations, shadows), artifacts appear as view-dependent effects or 'floaters'. To cope with distractors, we advocate a form of robust estimation for NeRF training, modeling distractors in training data as outliers of an optimization problem. Our method successfully removes outliers from a scene and improves upon our baselines, on synthetic and real-world scenes. Our technique is simple to incorporate in modern NeRF frameworks, with few hyper-parameters. It does not assume a priori knowledge of the types of distractors, and is instead focused on the optimization problem rather than pre-processing or modeling transient objects. More results at https://robustnerf.github.io/public." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 439, + 128, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 128, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 128, + 451 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 528 + ], + "type": "text", + "content": "The ability to understand the structure of a static 3D scene from 2D images alone is a fundamental problem in computer vision [44]. It finds applications in AR/VR for mapping virtual environments [6, 36, 61], in autonomous robotics for action planning [1], and in photogrammetry to create digital copies of real-world objects [34]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 529, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 624 + ], + "type": "text", + "content": "Neural fields [55] have recently revolutionized this classical task, by storing 3D representations within the weights of a neural network [39]. These representations are optimized by back-propagating image differences. When the fields store view-dependent radiance and volumetric rendering is employed [21], we can capture 3D scenes with photo-realistic accuracy, and we refer to the generated representation as Neural Radiance Fields, or NeRF [25])." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 287, + 696 + ], + "type": "text", + "content": "Training of NeRF models generally requires a large collection of images equipped with accurate camera calibration, which can often be recovered via structure-from-motion [37]. Behind its simplicity, NeRF hides several assumptions. As models are typically trained to minimize error in RGB color space, it is of paramount importance" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 212, + 545, + 343 + ], + "blocks": [ + { + "bbox": [ + 308, + 212, + 545, + 343 + ], + "lines": [ + { + "bbox": [ + 308, + 212, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 308, + 212, + 545, + 343 + ], + "type": "image", + "image_path": "1f94b3ae1ab59c57b87c5e4884be69f5c0048ed2a2ee83bf4879413ecd792bef.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 346, + 546, + 412 + ], + "lines": [ + { + "bbox": [ + 305, + 346, + 546, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 546, + 412 + ], + "type": "text", + "content": "Figure 1. NeRF assumes photometric consistency in the observed images of a scene. Violations of this assumption, as with the images in the top row, yield reconstructed scenes with inconsistent content in the form of \"floaters\" (highlighted with ellipses). We introduce a simple technique that produces clean reconstruction by automatically ignoring distractors without explicit supervision." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 426, + 546, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 484 + ], + "type": "text", + "content": "that images are photometrically consistent - two photos taken from the same vantage point should be identical up to noise. Unless one employs a method explicitly accounting for it [35], one should manually hold a camera's focus, exposure, white-balance, and ISO fixed." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 640 + ], + "type": "text", + "content": "However, properly configuring one's camera is not all that is required to capture high-quality NeRFs – it is also important to avoid distractors: anything that isn't persistent throughout the entire capture session. Distractors come in many shapes and forms, from the hard-shadows cast by the operators as they explore the scene to a pet or child casually walking within the camera's field of view. Distractors are tedious to remove manually, as this would require pixel-by-pixel labeling. They are also tedious to detect, as typical NeRF scenes are trained from hundreds of input images, and the types of distractors are not known a priori. If distractors are ignored, the quality of the reconstruction scene suffers significantly; see Figure 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "In a typical capture session, it is difficult to capture multiple images of the same scene from the same viewpoint, rendering distractors challenging to model mathematically. As such, while view-dependent effects are what give NeRF their realistic look, how can the model tell the difference between a distractor and a view-dependent effect?" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 166, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 166, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 166, + 712 + ], + "type": "text", + "content": "4Work done at Google Research." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20626" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "Despite the challenges, the research community has devised several approaches to overcome this issue:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 286, + 239 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 47, + 96, + 286, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 286, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 286, + 144 + ], + "type": "text", + "content": "- If distractors are known to belong to a specific class (e.g., people), one can remove them with a pre-trained semantic segmentation model [35, 43] – this process does not generalize to “unexpected” distractors such as shadows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 144, + 286, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 286, + 191 + ], + "type": "text", + "content": "- One can model distractors as per-image transient phenomena, and control the balance of transient/persistent modeling [23] - however, it is difficult to tune the losses that control this Pareto-optimal objective." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 192, + 286, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 286, + 239 + ], + "type": "text", + "content": "- One can model data in time (i.e., high-framerate video) and decompose the scene into static and dynamic (i.e., distractor) components [53] – but this clearly only applies to video rather than photo collection captures." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 239, + 286, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 286, + 263 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 286, + 263 + ], + "type": "text", + "content": "Conversely, we approach the problem of distractors by modeling them as outliers in NeRF optimization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 264, + 286, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 286, + 346 + ], + "type": "text", + "content": "We analyze the aforementioned techniques through the lens of robust estimation, allowing us to understand their behavior, and to design a method that is not only simpler to implement but also more effective (see Figure 1). As a result, we obtain a method that is straightforward to implement, requires minimal-to-no hyper-parameter tuning, and achieves state-of-the-art performance. We evaluate our method:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 347, + 286, + 442 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 347, + 286, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 286, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 286, + 370 + ], + "type": "text", + "content": "- quantitatively, in terms of reconstruction with synthetically, yet photo-realistically, rendered data;" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 371, + 286, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 286, + 394 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 286, + 394 + ], + "type": "text", + "content": "- qualitatively on publicly available datasets (often finetuned to work effectively with previous methods);" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 396, + 286, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 286, + 442 + ], + "type": "text", + "content": "- on a new collection of natural and synthetic scenes, including those autonomously acquired by a robot, allowing us to demonstrate the sensitivity of previous methods to hyper-parameter tuning." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 453, + 133, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 133, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 133, + 464 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 470, + 286, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 470, + 286, + 518 + ], + "spans": [ + { + "bbox": [ + 47, + 470, + 286, + 518 + ], + "type": "text", + "content": "We briefly review the basics and notation of Neural Radiance Fields. We then describe recent progress in NeRF research, paying particular attention to techniques for modeling of static/dynamic scenes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "text", + "content": "Neural Radiance Fields. A neural radiance field (NeRF) is a continuous volumetric representation of a 3D scene, stored within the parameters of a neural network " + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "text", + "content": ". The representation maps a position " + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "text", + "content": " and view direction " + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 47, + 522, + 286, + 582 + ], + "type": "text", + "content": " to a view-dependent RGB color and view-independent density:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 125, + 590, + 286, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 590, + 286, + 622 + ], + "spans": [ + { + "bbox": [ + 125, + 590, + 286, + 622 + ], + "type": "interline_equation", + "content": "\\left. \\begin{array}{l} \\mathbf {c} (\\mathbf {x}, \\mathbf {d}) \\\\ \\sigma (\\mathbf {x}) \\end{array} \\right\\} f (\\mathbf {x}, \\mathbf {d}; \\boldsymbol {\\theta}) \\tag {1}", + "image_path": "12d697b5a64da25dbd169bc0d66e2754bec3aadc964777abf6d2ca869a4d996b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "content": "This representation is trained from a collection, " + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{C}_i,\\mathbf{T}_i)\\}" + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "content": " of images " + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_i" + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "content": " with corresponding calibration parameters " + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{T}_i" + }, + { + "bbox": [ + 47, + 629, + 286, + 665 + ], + "type": "text", + "content": " (camera extrinsic and intrinsic)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": "During training the calibration information is employed to convert each pixel of the image into a ray " + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{r} = (\\mathbf{o},\\mathbf{d})" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": ", and rays are drawn randomly from input images to form a training mini-batch " + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "(\\mathbf{r}\\sim \\mathbf{C}_i)" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": ". The parameters " + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": " are optimized to" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "correctly predict the colors of the pixels in the batch via the L2 photometric-reconstruction loss:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 359, + 106, + 545, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 106, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 359, + 106, + 545, + 133 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r g b}} (\\boldsymbol {\\theta}) = \\sum_ {i} \\mathbb {E} _ {\\mathbf {r} \\sim \\mathbf {C} _ {i}} \\left[ \\mathcal {L} _ {\\mathrm {r g b}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) \\right] \\tag {2}", + "image_path": "acc7a4c6669113e680b5bd6eca9175257cb1b0cac35934b10c3665d35fac0289.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 360, + 135, + 545, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 135, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 360, + 135, + 545, + 152 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r g b}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2} ^ {2} \\tag {3}", + "image_path": "2c37e34c711b411ccae2202cd5a1358778f5aed9550952b0b34096cd9edc37da.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "text", + "content": "Parameterizing the ray as " + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "text", + "content": ", the NeRF model image " + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\mathbf{C}(\\mathbf{r};\\boldsymbol{\\theta})" + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "text", + "content": " is generated pixel-by-pixel volumetric rendering based on " + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\mathbf{c}(\\cdot)" + }, + { + "bbox": [ + 305, + 161, + 545, + 198 + ], + "type": "text", + "content": " (e.g., see [25, 42])." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 203, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 545, + 467 + ], + "type": "text", + "content": "Recent progress on NeRF models. NeRF models have recently been extended in several ways. A major thread has been the speedup of training [15, 27] and inference [6, 13], enabling today's models to be trained in minutes [27], and rendered on mobile in real-time [6]. While initially restricted to forward-facing scenes, researchers quickly found ways to model real-world " + }, + { + "bbox": [ + 304, + 203, + 545, + 467 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 203, + 545, + 467 + ], + "type": "text", + "content": " scenes [4, 59], and to reduce the required number of images, via sensor fusion [35] or hand-designed priors [28]. We can now deal with image artifacts such as motion blur [22], exposure [24], and lens distortion [14]. And the requirement of (precise) camera calibrations is quickly being relaxed with the introduction of techniques for local camera refinement [8, 19], or direct inference [58]. While a NeRF typically represents geometry via volumetric density, there exist models custom-tailored to predict surfaces [29, 51], which can be extended to use predicted normals to significantly improve reconstruction quality [50, 57]. Given high-quality normals [47], inferring the (rendering) structure of a scene becomes a possibility [5]. We also note recent papers about additional applications to generalization [56], semantic understanding [48], generative modeling [33], robotics [1], and text-to-3D [31]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 473, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 639 + ], + "type": "text", + "content": "Modeling non-static scenes. For unstructured scenes like those considered here, the community has focused on reconstructing both static and non-static elements from video. The most direct approach, treating time as an auxiliary input, leads to cloudy geometry and a lack of fine detail [11, 54]. Directly optimizing per-frame latent codes as an auxiliary input has proved more effective [17, 30, 53]. The most widely-adopted approach is to fit a time-conditioned deformation field mapping 3D points between pairs of frames [18, 49] or to a canonical coordinate frame [9, 10, 20, 32, 45]. Given how sparsely spacetime is sampled, all methods require careful regularization, optimization, or additional training signals to achieve acceptable results." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Relatively little attention has been given to removing non-static elements. One common approach is to segment and ignore pixels which are likely to be distractors [35, 43]. While this eliminates larger objects, it fails to account for secondary effects like shadows. Prior attempts to model distractors as outliers still leave residual cloudy geometry [23]." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20627" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 68, + 347, + 177 + ], + "blocks": [ + { + "bbox": [ + 53, + 68, + 347, + 177 + ], + "lines": [ + { + "bbox": [ + 53, + 68, + 347, + 177 + ], + "spans": [ + { + "bbox": [ + 53, + 68, + 347, + 177 + ], + "type": "image", + "image_path": "fd427e53b06992ad7e2399ed5219e2db17f6d6b5aac0badd013f1d3667e33e83.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 178, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 547, + 213 + ], + "type": "text", + "content": "Figure 2. Ambiguity - A simple 2D scene where a static object (blue) is captured by three cameras. During the first and third capture the scene is not photo-consistent as a distractor was within the field of view. Not photo-consistent portions of the scene can end up being encoded as view-dependent effects - even when we assume ground truth geometry." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 351, + 68, + 536, + 177 + ], + "blocks": [ + { + "bbox": [ + 351, + 68, + 536, + 177 + ], + "lines": [ + { + "bbox": [ + 351, + 68, + 536, + 177 + ], + "spans": [ + { + "bbox": [ + 351, + 68, + 536, + 177 + ], + "type": "image", + "image_path": "ff166e4f12987f76838b6513f6e0bb8ec9a53ef5607f55d7408084a762a7996d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 224, + 103, + 237 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 103, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 103, + 237 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 243, + 290, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 290, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 290, + 447 + ], + "type": "text", + "content": "The classical NeRF training losses (3) are effective for capturing scenes that are photometrically consistent, leading to the photo-realistic novel-view synthesis that we are now accustomed to seeing in recent research. However, \"what happens when there are elements of the scene that are not persistent throughout the entire capture session?\" Simple examples of such scenes include those in which an object is only present in some fraction of the observed images, or may not remain in the same position in all observed images. For example, Figure 2 depicts a 2D scene comprising a persistent object (the truck), along with several transient objects (e.g., people and a dog). While rays in blue from the three cameras intersect the truck, the green and orange rays from cameras 1 and 3 intersect transient objects. For video capture and spatio-temporal NeRF models, the persistent objects comprise the \"static\" portion of the scene, while the rest would be called the \"dynamic\"." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 456, + 168, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 168, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 168, + 468 + ], + "type": "text", + "content": "3.1. Sensitivity to outliers" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 473, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 628 + ], + "type": "text", + "content": "For Lambertian scenes, photo-consistent structure is view independent, as scene radiance only depends on the incident light [16]. For such scenes, view-dependent NeRF models like (1), trained by minimizing (3), admit local optima in which transient objects are explained by view-dependent terms. Figure 2 depicts this, with the outgoing color corresponding to the memorized color of the outlier - i.e. view-dependent radiance. Such models exploit the view-dependent capacity of the model to over-fit observations, effectively memorizing the transient objects. One can alter the model to remove dependence on " + }, + { + "bbox": [ + 46, + 473, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 473, + 287, + 628 + ], + "type": "text", + "content": " but the L2 loss remains problematic as least-squares (LS) estimators are sensitive to outliers, or heavy-tailed noise distributions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Under more natural conditions, dropping the Lambertian assumption, the problem becomes more complex as both non-Lambertian reflectance phenomena and outliers can be explained as view-dependent radiance. While we want the models to capture photo-consistent view-dependent radiance, outliers and other transient phenomena should ideally be ignored. And in such cases, optimization with an L2" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 226, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 226, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 226, + 545, + 275 + ], + "type": "text", + "content": "loss (3) yields significant errors in reconstruction; see Figure 1. Problems like these are pervasive in NeRF model fitting, especially in uncontrolled environments with complex reflectance, non-rigidity, or independently moving objects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 280, + 432, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 280, + 432, + 292 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 432, + 292 + ], + "type": "text", + "content": "3.2. Robustness to outliers" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "text", + "content": "Robustness via semantic segmentation. One way to reduce outlier contamination during NeRF model optimization is to rely on an oracle " + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "text", + "content": " that specifies whether a given pixel " + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "text", + "content": " from image " + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 298, + 546, + 357 + ], + "type": "text", + "content": " is an outlier, and should therefore be excluded from the empirical loss, replacing (3) with:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 342, + 363, + 545, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 363, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 342, + 363, + 545, + 378 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o r a c l e}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\mathbf {S} _ {i} (\\mathbf {r}) \\cdot | | \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) | | _ {2} ^ {2} \\tag {4}", + "image_path": "bcd15dbaa604f84b3c53d7421e9842e8d4266d5fc0e44282aeb9009617f5e875.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "type": "text", + "content": "In practice, a pre-trained (semantic) segmentation network " + }, + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "type": "text", + "content": " might serve as an oracle, " + }, + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_i = S(\\mathbf{C}_i)" + }, + { + "bbox": [ + 304, + 384, + 546, + 479 + ], + "type": "text", + "content": ". E.g., Nerf-in-the-wild [23] employed a semantic segmenter to remove pixels occupied by people, as they are outliers in the context of photo-tourism. Urban Radiance Fields [35] segmented out sky pixels, while LOL-NeRF [33] ignored pixels not belonging to faces. The obvious problem with this approach is the need for an oracle to detect arbitrary distractors." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 484, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 544 + ], + "type": "text", + "content": "Robust estimators. Another way to reduce sensitivity to outliers is to replace the conventional L2 loss (3) with a robust loss (e.g., [2, 41]), so that photometrically-inconsistent observations can be down-weighted during optimization. Given a robust kernel " + }, + { + "bbox": [ + 304, + 484, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\kappa(\\cdot)" + }, + { + "bbox": [ + 304, + 484, + 545, + 544 + ], + "type": "text", + "content": ", we rewrite our training loss as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 350, + 549, + 545, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 549, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 350, + 549, + 545, + 564 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r o b u s t}} ^ {\\mathbf {r}, i} (\\boldsymbol {\\theta}) = \\kappa \\left(\\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2}\\right) \\tag {5}", + "image_path": "ff2bb85d80f301d6098153f1bf357b79e272f6303215bee078d66bee814306af.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\kappa(\\cdot)" + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "content": " is positive and monotonically increasing. MipNeRF [3], for example, employs an L1 loss " + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\kappa(\\epsilon) = |\\epsilon|" + }, + { + "bbox": [ + 304, + 570, + 545, + 653 + ], + "type": "text", + "content": ", which provides some degree of robustness to outliers during NeRF training. Given our analysis, a valid question is whether we can straightforwardly employ a robust kernel to approach our problem, and if so, given the large variety of robust kernels [2], which is the kernel of choice." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Unfortunately, as discussed above, outliers and non-Lambertian effects can both be modelled as view-dependent effects (see Figure 3). As a consequence, with simple application of robust estimators it can be difficult to separate signal from noise. Figure 4 shows examples in which outliers" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20628" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 166, + 133 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 166, + 133 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 166, + 133 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 166, + 133 + ], + "type": "image", + "image_path": "11ad7dc1cc45fb13dab8eb420d7cc8ad66432e0546b9533578c9214db3f57180.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 282, + 133 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 282, + 133 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 282, + 133 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 282, + 133 + ], + "type": "image", + "image_path": "b2eb3620a00498884b091da8a7002ce0ca793164b22359e7226635d9c8a96708.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 133, + 166, + 201 + ], + "blocks": [ + { + "bbox": [ + 50, + 133, + 166, + 201 + ], + "lines": [ + { + "bbox": [ + 50, + 133, + 166, + 201 + ], + "spans": [ + { + "bbox": [ + 50, + 133, + 166, + 201 + ], + "type": "image", + "image_path": "d79c260859e20c9b34c744b290b5c9725455d80ee2d5fcfb5fbf68d85187829b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 204, + 287, + 259 + ], + "lines": [ + { + "bbox": [ + 46, + 204, + 287, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 287, + 259 + ], + "type": "text", + "content": "Figure 3. Histograms - Robust estimators perform well when the distribution of residuals agrees with the one implied by the estimator (e.g., Gaussian for L2, Laplacian for L1). Here we visualize the ground-truth distribution of residuals (bottom-left), which is hardly a good match with any simple parametric distribution." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 168, + 137, + 282, + 200 + ], + "blocks": [ + { + "bbox": [ + 168, + 137, + 282, + 200 + ], + "lines": [ + { + "bbox": [ + 168, + 137, + 282, + 200 + ], + "spans": [ + { + "bbox": [ + 168, + 137, + 282, + 200 + ], + "type": "image", + "image_path": "bc0cfa8000d411cb3d2e6833322a1287d9b33fa4e89c2466baecdf67d05404a1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 274, + 286, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 286, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 286, + 357 + ], + "type": "text", + "content": "are removed, but fine-grained texture and view-dependent details are also lost, or conversely, fine-grained details are preserved, but outliers cause artifacts in the reconstructed scene. One can also observe mixtures of these cases in which details are not captured well, nor are outliers fully removed. We find that this behaviour occurs consistently for many different robust estimators and parameter settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 358, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 395 + ], + "type": "text", + "content": "Training time can also be problematic. The robust estimator gradient w.r.t. model parameters can be expressed using the chain rule as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 79, + 404, + 287, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 404, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 79, + 404, + 287, + 434 + ], + "type": "interline_equation", + "content": "\\left. \\frac {\\partial \\kappa (\\epsilon (\\boldsymbol {\\theta}))}{\\partial \\boldsymbol {\\theta}} \\right| _ {\\boldsymbol {\\theta} ^ {(t)}} = \\left. \\frac {\\partial \\kappa (\\epsilon)}{\\partial \\epsilon} \\right| _ {\\epsilon (\\boldsymbol {\\theta} ^ {(t)})} \\cdot \\left. \\frac {\\partial \\epsilon (\\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} \\right| _ {\\boldsymbol {\\theta} ^ {(t)}} \\tag {6}", + "image_path": "3bffe4653cd2ab6dc03d35c23f65db51472309419ad6f8439961956843b64220.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 443, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 598 + ], + "type": "text", + "content": "The second factor is the classical NeRF gradient. The first factor is the kernel gradient evaluated at the current error residual " + }, + { + "bbox": [ + 46, + 443, + 287, + 598 + ], + "type": "inline_equation", + "content": "\\epsilon (\\pmb{\\theta}^{(t)})" + }, + { + "bbox": [ + 46, + 443, + 287, + 598 + ], + "type": "text", + "content": ". During training, large residuals can equivalently come from high-frequency details that have not yet been learnt, or they may arise from outliers (see Figure 4 (bottom)). This explain why robust optimization, implemented as (5), should not be expected to decouple high-frequency details from outliers. Further, when strongly robust kernels are employed, like redescending estimators, this also explains the loss of visual fidelity. That is, because the gradient of (large) residuals get down-weighted by the (small) gradients of the kernel, slowing down the learning of these fine-grained details (see Figure 4 (top))." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 609, + 254, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 254, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 254, + 621 + ], + "type": "text", + "content": "3.3. Robustness via Trimmed Least Squares" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 625, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 625, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 287, + 661 + ], + "type": "text", + "content": "In what follows we advocate a form of iteratively reweighted least-squares (IRLS) with a Trimmed least squares (LS) loss for NeRF model fitting." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Iteratively Reweighted least Squares. IRLS is a widely used method for robust estimation that involves solving a sequence of weighted LS problems, the weights of which are adapted to reduce the influence of outliers. To that end," + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 422, + 134 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 422, + 134 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 422, + 134 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 422, + 134 + ], + "type": "image", + "image_path": "7938b39f31acfdc501893b4a8f3350a2f3af6e6029632895dc97faf118a27321.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 430, + 72, + 544, + 129 + ], + "blocks": [ + { + "bbox": [ + 430, + 72, + 544, + 129 + ], + "lines": [ + { + "bbox": [ + 430, + 72, + 544, + 129 + ], + "spans": [ + { + "bbox": [ + 430, + 72, + 544, + 129 + ], + "type": "image", + "image_path": "8bee22d7570c63c3c8dcb2a2fb19c6b6aacc77cd83387cf79c109fb8235f552f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 136, + 422, + 194 + ], + "blocks": [ + { + "bbox": [ + 307, + 136, + 422, + 194 + ], + "lines": [ + { + "bbox": [ + 307, + 136, + 422, + 194 + ], + "spans": [ + { + "bbox": [ + 307, + 136, + 422, + 194 + ], + "type": "image", + "image_path": "1632681e93a49b53846aba35cb9a9a030cc78ccb806d3756c22ec532e55ff874.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "text", + "content": "Figure 4. Kernels - (top-left) Family of robust kernels [2], including L2 (" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "text", + "content": "), Charbonnier (" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "text", + "content": ") and Geman-McClure (" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "inline_equation", + "content": "\\alpha = -2" + }, + { + "bbox": [ + 305, + 201, + 545, + 299 + ], + "type": "text", + "content": "). (top-right) Mid-training, residual magnitudes are similar for distractors and fine-grained details, and pixels with large residuals are learned more slowly, as the gradient of re-descending kernels flattens out. (bottom-right) A too aggressive Geman-McClure in down-weighting large residuals removes both outliers and high-frequency detail. (bottom-left) A less aggressive Geman-McClure does not effectively remove outliers." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 430, + 136, + 544, + 194 + ], + "blocks": [ + { + "bbox": [ + 430, + 136, + 544, + 194 + ], + "lines": [ + { + "bbox": [ + 430, + 136, + 544, + 194 + ], + "spans": [ + { + "bbox": [ + 430, + 136, + 544, + 194 + ], + "type": "image", + "image_path": "eef272506fab0a7293f190e56385e2b5f26c2fe42d91278bc7e3ba201f641252.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 315, + 460, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 315, + 460, + 326 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 460, + 326 + ], + "type": "text", + "content": "at iteration " + }, + { + "bbox": [ + 306, + 315, + 460, + 326 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 306, + 315, + 460, + 326 + ], + "type": "text", + "content": ", one can write the loss as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 332, + 533, + 349 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 332, + 533, + 349 + ], + "spans": [ + { + "bbox": [ + 318, + 332, + 533, + 349 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r o b u s t}} ^ {\\mathbf {r}, i} \\left(\\boldsymbol {\\theta} ^ {(t)}\\right) = \\omega \\left(\\boldsymbol {\\epsilon} ^ {(t - 1)} (\\mathbf {r})\\right) \\cdot | | \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta} ^ {(t)}) - \\mathbf {C} _ {i} (\\mathbf {r}) | | _ {2} ^ {2}", + "image_path": "0248a2d81ec7852b194aa65511ffbcca0416c064a7f54249b92a376ce4afcebc.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 329, + 350, + 545, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 350, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 329, + 350, + 545, + 365 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\epsilon} ^ {(t - 1)} (\\mathbf {r}) = \\left| \\left| \\mathbf {C} (\\mathbf {r}; \\boldsymbol {\\theta} ^ {(t - 1)}) - \\mathbf {C} _ {i} (\\mathbf {r}) \\right| \\right| _ {2} \\tag {7}", + "image_path": "7995dc2c2a5d491913d4cb2dc54e1dbeddb6c89bda06df91074c8c8e3ecac5ad.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 373, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 545, + 409 + ], + "type": "text", + "content": "For weight functions given by " + }, + { + "bbox": [ + 306, + 373, + 545, + 409 + ], + "type": "inline_equation", + "content": "\\omega (\\epsilon) = \\epsilon^{-1}\\cdot \\partial \\kappa (\\epsilon) / \\partial \\epsilon" + }, + { + "bbox": [ + 306, + 373, + 545, + 409 + ], + "type": "text", + "content": " one can show that, under suitable conditions, the iteration converges to a local minima of (5) (see [41, Sec. 3])." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "type": "text", + "content": "This framework admits a broad family of losses, including maximum likelihood estimators for heavy-tailed noise processes. Examples in Figure 4 include the Charbonnier loss (smoothed L1), and more aggressive redescending estimators such as the Lorentzian or Geman-McClure [2]. The objective in (4) can also be viewed as a weighted LS objective, the binary weights of which are provided by an oracle. And, as discussed at length below, one can also view several recent methods like NeRFW [23] and " + }, + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 410, + 545, + 529 + ], + "type": "text", + "content": " [53] through the lens of IRLS and weighted LS." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 529, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 636 + ], + "type": "text", + "content": "Nevertheless, choosing a suitable weight function " + }, + { + "bbox": [ + 304, + 529, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\omega(\\epsilon)" + }, + { + "bbox": [ + 304, + 529, + 545, + 636 + ], + "type": "text", + "content": " for NeRF optimization is non-trivial, due in large part to the intrinsic ambiguity between view-dependent radiance phenomena and outliers. One might try to solve this problem by learning a neural weight function [40], although generating enough annotated training data might be prohibitive. Instead, the approach taken below is to exploit inductive biases in the structure of outliers, combined with the simplicity of a robust, trimmed LS estimator." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "Trimmed Robust Kernels. Our goal is to develop a weight function for use in iteratively weighted LS optimization that is simple and captures useful inductive biases for NeRF optimization. For simplicity we opt for a binary weight function with intuitive parameters that adapts naturally through model fitting so that fine-grained image details that are not" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20629" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 71, + 182, + 135 + ], + "blocks": [ + { + "bbox": [ + 69, + 71, + 182, + 135 + ], + "lines": [ + { + "bbox": [ + 69, + 71, + 182, + 135 + ], + "spans": [ + { + "bbox": [ + 69, + 71, + 182, + 135 + ], + "type": "image", + "image_path": "c4d7aa68fc1cf767be6cc6e9d208ab8c015e53701c307328f83104d47b5e8f5c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 69, + 136, + 182, + 156 + ], + "blocks": [ + { + "bbox": [ + 69, + 136, + 182, + 156 + ], + "lines": [ + { + "bbox": [ + 69, + 136, + 182, + 156 + ], + "spans": [ + { + "bbox": [ + 69, + 136, + 182, + 156 + ], + "type": "image", + "image_path": "f91fb7f5b893bb47da572b0df940fc0b094b10279f430799e1478a8e794435e8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 99, + 157, + 158, + 167 + ], + "lines": [ + { + "bbox": [ + 99, + 157, + 158, + 167 + ], + "spans": [ + { + "bbox": [ + 99, + 157, + 158, + 167 + ], + "type": "text", + "content": "residuals - " + }, + { + "bbox": [ + 99, + 157, + 158, + 167 + ], + "type": "inline_equation", + "content": "\\epsilon (\\mathbf{r})" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 182, + 71, + 295, + 135 + ], + "blocks": [ + { + "bbox": [ + 182, + 71, + 295, + 135 + ], + "lines": [ + { + "bbox": [ + 182, + 71, + 295, + 135 + ], + "spans": [ + { + "bbox": [ + 182, + 71, + 295, + 135 + ], + "type": "image", + "image_path": "d9a7c3c9248e6b0d2e49b80e508445785b7faf30297405fd92a356c86778a670.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 182, + 136, + 296, + 156 + ], + "blocks": [ + { + "bbox": [ + 182, + 136, + 296, + 156 + ], + "lines": [ + { + "bbox": [ + 182, + 136, + 296, + 156 + ], + "spans": [ + { + "bbox": [ + 182, + 136, + 296, + 156 + ], + "type": "image", + "image_path": "873f6abe2d818eeb1542748a04be93455f2e67da076891565998d6dc7678c5f5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 157, + 265, + 167 + ], + "lines": [ + { + "bbox": [ + 214, + 157, + 265, + 167 + ], + "spans": [ + { + "bbox": [ + 214, + 157, + 265, + 167 + ], + "type": "text", + "content": "inliers - " + }, + { + "bbox": [ + 214, + 157, + 265, + 167 + ], + "type": "inline_equation", + "content": "\\tilde{\\omega} (\\mathbf{r})" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 170, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 170, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 547, + 224 + ], + "type": "text", + "content": "Figure 5. Algorithm - We visualize our weight function computed by residuals on two examples: (top) the residuals of a (mid-training) NeRF rendered from a training viewpoint, (bottom) a toy residual image containing residual of small spatial extent (dot, line) and residuals of large spatial extent (squares). Notice residuals with large magnitude but small spatial extent (texture of the box, dot, line) are included in the optimization, while weaker residuals with larger spatial extent are excluded. Note that while we operate on patches, we visualize the weight function on the whole image to facilitate visualization." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 295, + 71, + 409, + 135 + ], + "blocks": [ + { + "bbox": [ + 295, + 71, + 409, + 135 + ], + "lines": [ + { + "bbox": [ + 295, + 71, + 409, + 135 + ], + "spans": [ + { + "bbox": [ + 295, + 71, + 409, + 135 + ], + "type": "image", + "image_path": "d39ccfe40e70ee86c4959d6925556f5b4f52cee785752e345afb7026b573e088.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 295, + 136, + 409, + 156 + ], + "blocks": [ + { + "bbox": [ + 295, + 136, + 409, + 156 + ], + "lines": [ + { + "bbox": [ + 295, + 136, + 409, + 156 + ], + "spans": [ + { + "bbox": [ + 295, + 136, + 409, + 156 + ], + "type": "image", + "image_path": "3a9ee80c514580cfc6f5f57876a041719846aed5e201e272d35434e954f86f15.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 157, + 396, + 167 + ], + "lines": [ + { + "bbox": [ + 307, + 157, + 396, + 167 + ], + "spans": [ + { + "bbox": [ + 307, + 157, + 396, + 167 + ], + "type": "text", + "content": "diffusion - " + }, + { + "bbox": [ + 307, + 157, + 396, + 167 + ], + "type": "inline_equation", + "content": "\\tilde{\\omega}(\\mathbf{r}) \\oplus \\mathcal{B}_{3 \\times 3}" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 409, + 71, + 525, + 135 + ], + "blocks": [ + { + "bbox": [ + 409, + 71, + 525, + 135 + ], + "lines": [ + { + "bbox": [ + 409, + 71, + 525, + 135 + ], + "spans": [ + { + "bbox": [ + 409, + 71, + 525, + 135 + ], + "type": "image", + "image_path": "09be3306f8248a3d9f4bd6c55d6918e93896a53fa487fe67237b06357342877a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 410, + 136, + 525, + 156 + ], + "blocks": [ + { + "bbox": [ + 410, + 136, + 525, + 156 + ], + "lines": [ + { + "bbox": [ + 410, + 136, + 525, + 156 + ], + "spans": [ + { + "bbox": [ + 410, + 136, + 525, + 156 + ], + "type": "image", + "image_path": "a3df0d1d6602f3b8faab9d6badefac0d455997cc96da692275f316984e52437b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 424, + 157, + 511, + 167 + ], + "lines": [ + { + "bbox": [ + 424, + 157, + 511, + 167 + ], + "spans": [ + { + "bbox": [ + 424, + 157, + 511, + 167 + ], + "type": "text", + "content": "(IRLS) weights - " + }, + { + "bbox": [ + 424, + 157, + 511, + 167 + ], + "type": "inline_equation", + "content": "\\mathcal{W}(\\mathbf{r})" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 238, + 287, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 287, + 345 + ], + "type": "text", + "content": "outliers can be learned quickly. It is also important to capture the structured nature of typical outliers, contrary to the typical i.i.d. assumption in most robust estimator formulations. To this end, the weight function should capture spatial smoothness of the outlier process, recognizing that objects typically have continuous local support, and hence outliers are expected to occupy large, connected regions of an image (e.g., the silhouette of a person to be segmented out from a photo-tourism dataset)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 346, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 430 + ], + "type": "text", + "content": "Surprisingly, a relatively simple weight function embodies these properties and performs extremely well in practice. The weight function is based on so-called trimmed estimators that are used in trimmed least-squares, like that used in trimmed ICP [7]. We first sort residuals, and assume that residuals below a certain percentile are inliers. Picking the " + }, + { + "bbox": [ + 46, + 346, + 287, + 430 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 346, + 287, + 430 + ], + "type": "text", + "content": " percentile for convenience (i.e., median), we define" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 77, + 435, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 435, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 77, + 435, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\tilde {\\omega} (\\mathbf {r}) = \\epsilon (\\mathbf {r}) \\leq \\mathcal {T} _ {\\epsilon}, \\quad \\mathcal {T} _ {\\epsilon} = \\operatorname {M e d i a n} _ {\\mathbf {r}} \\left\\{\\epsilon (\\mathbf {r}) \\right\\}. \\tag {8}", + "image_path": "4c84c644c007a6d92d9ec1081ddb0ddc501fcc720818b7b1558280ec87ae6aa3.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "text", + "content": "To capture spatial smoothness of outliers we spatially diffuse inlier/outlier labels " + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "text", + "content": " with a " + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "inline_equation", + "content": "3\\times 3" + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "text", + "content": " box kernel " + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{3\\times 3}" + }, + { + "bbox": [ + 47, + 453, + 287, + 488 + ], + "type": "text", + "content": ". Formally, we define" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 75, + 495, + 287, + 508 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 495, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 75, + 495, + 287, + 508 + ], + "type": "interline_equation", + "content": "\\mathcal {W} (\\mathbf {r}) = \\left(\\tilde {\\omega} (\\mathbf {r}) * \\mathcal {B} _ {3 \\times 3}\\right) \\geq \\mathcal {T} _ {*}, \\quad \\mathcal {T} _ {*} = 0. 5. \\tag {9}", + "image_path": "0a027dcff29e6f719cd85d5b40805a77133edd29753717e8674a2a19b06e68d2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 513, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 513, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 513, + 287, + 548 + ], + "type": "text", + "content": "This helps to avoid classifying high-frequency details as outliers, allowing them to be captured by the NeRF model during optimization (see Figure 5)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": "While the trimmed weight function (9) improves the robustness of model fitting, it sometimes misclassifies fine-grained image details early in training where the NeRF model first captures coarse-grained structure. These localized texture elements may emerge but only after very long training times. We find that stronger inductive bias to spatially coherence allows fine-grained details to be learned more quickly. To that end, we aggregate the detection of outliers on " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": " neighborhoods; i.e., we label entire " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": " patches as outliers or inliers based on the behavior of " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "16 \\times 16" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": " neighborhood of the patch. Denoting the " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": " neighborhood of pixels around " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_N(\\mathbf{r})" + }, + { + "bbox": [ + 46, + 548, + 287, + 692 + ], + "type": "text", + "content": ", we define" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 53, + 697, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 697, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 53, + 697, + 287, + 711 + ], + "type": "interline_equation", + "content": "\\omega \\left(\\mathcal {R} _ {8} (\\mathbf {r})\\right) = \\mathbb {E} _ {\\mathbf {s} \\sim \\mathcal {R} _ {1 6} (\\mathbf {r})} \\left[ \\mathcal {W} (\\mathbf {s}) \\right] \\geq \\mathcal {T} _ {\\mathcal {R}}, \\quad \\mathcal {T} _ {\\mathcal {R}} = 0. 6. \\tag {10}", + "image_path": "1a6341afd17f57ace89958953efbed0d13c034f4c3dd1eb2d56c26372ec931b7.jpg" + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 309, + 238, + 359, + 288 + ], + "blocks": [ + { + "bbox": [ + 309, + 238, + 359, + 288 + ], + "lines": [ + { + "bbox": [ + 309, + 238, + 359, + 288 + ], + "spans": [ + { + "bbox": [ + 309, + 238, + 359, + 288 + ], + "type": "image", + "image_path": "bf26a6902d7a41ed48389fa1f5b89d4469c7a3ae868ee3ba2d6b6dd6db473a18.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 311, + 288, + 355, + 296 + ], + "lines": [ + { + "bbox": [ + 311, + 288, + 355, + 296 + ], + "spans": [ + { + "bbox": [ + 311, + 288, + 355, + 296 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 370, + 238, + 420, + 287 + ], + "blocks": [ + { + "bbox": [ + 370, + 238, + 420, + 287 + ], + "lines": [ + { + "bbox": [ + 370, + 238, + 420, + 287 + ], + "spans": [ + { + "bbox": [ + 370, + 238, + 420, + 287 + ], + "type": "image", + "image_path": "4416c7398ccd94ebc9d367fa80dd34745d1f0b22821109b958a335b77eb5ef87.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 375, + 288, + 415, + 295 + ], + "lines": [ + { + "bbox": [ + 375, + 288, + 415, + 295 + ], + "spans": [ + { + "bbox": [ + 375, + 288, + 415, + 295 + ], + "type": "text", + "content": "RobustNeRF" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 432, + 238, + 482, + 287 + ], + "blocks": [ + { + "bbox": [ + 432, + 238, + 482, + 287 + ], + "lines": [ + { + "bbox": [ + 432, + 238, + 482, + 287 + ], + "spans": [ + { + "bbox": [ + 432, + 238, + 482, + 287 + ], + "type": "image", + "image_path": "0b6c7d1202a0081f52befd0f8113b7eaa05410296dc88312c5fd84db8c93517f.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 439, + 288, + 475, + 295 + ], + "lines": [ + { + "bbox": [ + 439, + 288, + 475, + 295 + ], + "spans": [ + { + "bbox": [ + 439, + 288, + 475, + 295 + ], + "type": "text", + "content": "Train View" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 495, + 238, + 544, + 287 + ], + "blocks": [ + { + "bbox": [ + 495, + 238, + 544, + 287 + ], + "lines": [ + { + "bbox": [ + 495, + 238, + 544, + 287 + ], + "spans": [ + { + "bbox": [ + 495, + 238, + 544, + 287 + ], + "type": "image", + "image_path": "3a02c34a52cb7d88bc69b2089f4a9245d1437487a0c9d1e3882be254e4ca87fc.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 288, + 537, + 295 + ], + "lines": [ + { + "bbox": [ + 501, + 288, + 537, + 295 + ], + "spans": [ + { + "bbox": [ + 501, + 288, + 537, + 295 + ], + "type": "text", + "content": "Distractors" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 310, + 301, + 543, + 411 + ], + "blocks": [ + { + "bbox": [ + 310, + 301, + 543, + 411 + ], + "lines": [ + { + "bbox": [ + 310, + 301, + 543, + 411 + ], + "spans": [ + { + "bbox": [ + 310, + 301, + 543, + 411 + ], + "type": "image", + "image_path": "61d593844bc4764698a50b4773d9444124bb85159f02cb5638f6aa39ecafd740.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "type": "text", + "content": "Figure 6. Residuals - For the dataset shown in the top row, we visualize the dynamics of the RobustNeRF training residuals, which show how over time the estimated distractor weights go from being random " + }, + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "type": "inline_equation", + "content": "(t / T) = 0.5\\%)" + }, + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "type": "text", + "content": " to identify distractor pixels " + }, + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "type": "inline_equation", + "content": "(t / T) = 100\\%" + }, + { + "bbox": [ + 304, + 415, + 545, + 470 + ], + "type": "text", + "content": " without any explicit supervision." + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 567 + ], + "type": "text", + "content": "The final weight function is the union of the three masks in Eqns. 8 -10. This robust weight function evolves during optimization, as one expects with IRLS where the weights are a function of the residuals at the previous iteration. That is, the labeling of pixels as inliers/outliers changes during training, and settles around masks similar to the one an oracle would provide as training converges (see Figure 6)." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 576, + 387, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 576, + 387, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 576, + 387, + 590 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 689 + ], + "type": "text", + "content": "We implement our robust loss function in the MultiNeRF codebase [26] and apply it to mip-NeRF 360 [4]. We dub this method \"RobustNeRF\". To evaluate RobustNeRF, we compare against baselines on several scenes containing different types of distractors. Where possible, we quantitatively compare reconstructions to held-out, distraction-free images; we report three metrics, averaged across held-out frames, namely, PSNR, SSIM [52], and LPIPS [60]." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We compare different methods on two collections of scenes, i.e., those provided by the authors of " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + 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Dataset - Sample training images showing the distractors in each scene. Statue and Android were acquired manually, and the others with a robotic arm. In the robotic setting we have pixel-perfect alignment of distractor vs. distractor-free images." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 226, + 171, + 283, + 213 + ], + "blocks": [ + { + "bbox": [ + 226, + 171, + 283, + 213 + ], + "lines": [ + { + "bbox": [ + 226, + 171, + 283, + 213 + ], + "spans": [ + { + "bbox": [ + 226, + 171, + 283, + 213 + ], + "type": "image", + "image_path": "d4665e589c43ddd6ae0a880b9b65793acf9e80ac3bc7d18a3a2c1524afd65028.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 235, + 214, + 274, + 223 + ], + "lines": [ + { + "bbox": [ + 235, + 214, + 274, + 223 + ], + "spans": [ + { + "bbox": [ + 235, + 214, + 274, + 223 + ], + "type": "text", + "content": "BabyYoda" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 285, + 287, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 322 + ], + "type": "text", + "content": "novel datasets described below. We also present a series of illustrative experiments on synthetic scenes, shedding light on RobustNeRF's efficacy and inner workings." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 331, + 113, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 113, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 113, + 342 + ], + "type": "text", + "content": "4.1. Baselines" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "content": "We compare RobustNeRF to variants of mip-NeRF 360 optimized with different loss functions " + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "inline_equation", + "content": "(L_{2}, L_{1}" + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "content": ", and Carbonnier). These variants serve as natural baselines for models with limited or no robustness to outliers. We also compare to " + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "content": ", a recent method for reconstructing dynamic scenes from monocular video. Unlike our method, " + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "content": " is designed to reconstruct distractors rather than discard them. While " + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "content": " is presented as a method for monocular video, it does not presuppose temporal continuity, and can be directly applied to unordered images. We omit additional comparisons to NeRF-W as its performance falls short of " + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 347, + 287, + 503 + ], + "type": "text", + "content": " [53]. For more details on model training, see the supplementary material." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 514, + 160, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 160, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 160, + 526 + ], + "type": "text", + "content": "4.2. Datasets - Figure 7" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 529, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 578 + ], + "type": "text", + "content": "In addition to scenes from " + }, + { + "bbox": [ + 46, + 529, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 529, + 287, + 578 + ], + "type": "text", + "content": ", we introduce a set of natural and synthetic scenes. They facilitate the evaluation of RobustNeRF's effectiveness on illustrative use cases, and they enable empirical analysis under controlled conditions." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Natural scenes. We capture seven natural scenes exemplifying different types of distractors. Scenes are captured in three settings, on the street, in an apartment and in a robotics lab. Distractor objects are moved, or are allowed to move, between frames to simulate capture over extended periods of time. We vary the number of unique distractors from 1 (Statue) to 150 (BabyYoda), and their movements. Unlike prior work on monocular video, frames are captured without a clear temporal ordering (see Figure 7). The other three (i.e., Street1, Street2, and Gloss) include view-dependence effects, the results of which are shown in the supplementary" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "material. We also capture additional frames without distractors to enable quantitative evaluations. Camera poses are estimated using COLMAP [38]. A full description of each scene in the supplementary material." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 122, + 545, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 122, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 304, + 122, + 545, + 242 + ], + "type": "text", + "content": "Synthetic scenes. To further evaluate RobustNeRF, we generate synthetic scenes using the Kubric dataset generator [12]. Each scene is constructed by placing a set of simple geometries in an empty, texture-less room. In each scene, a subset of objects remain fixed while the other objects (i.e., distractors) change position from frame to frame. By varying the number of objects, their size, and the way they move, we control the level of distraction in each scene. We use these scenes to examine RobustNeRF's sensitivity to its hyperparameters, see supplementary material." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 249, + 379, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 249, + 379, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 249, + 379, + 261 + ], + "type": "text", + "content": "4.3. Evaluation" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 265, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 545, + 335 + ], + "type": "text", + "content": "We evaluate RobustNeRF on its ability to ignore distractors while accurately reconstructing the static elements of a scene. We train RobustNeRF, " + }, + { + "bbox": [ + 304, + 265, + 545, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 265, + 545, + 335 + ], + "type": "text", + "content": ", and variants of mip-NeRF 360 on scenes where distraction-free frames are available. Models are trained on frames with distractors and evaluated on distractor-free frames." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "type": "text", + "content": "Comparison to mip-NeRF 360 - Figure 8. On natural scenes, RobustNeRF generally outperforms variants of mip-NeRF 360 by 1.3 to " + }, + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "type": "inline_equation", + "content": "4.7\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "type": "text", + "content": " in PSNR. As " + }, + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "type": "inline_equation", + "content": "L_{2}, L_{1}" + }, + { + "bbox": [ + 304, + 339, + 545, + 518 + ], + "type": "text", + "content": ", and Charbonnier losses weigh all pixels equally, the model is forced to represent, rather than ignore, distractors as \"clouds\" with view-dependent appearance. We find clouds to be most apparent when distractors remain stationary for multiple frames. In contrast, RobustNeRF's loss isolates distractor pixels and assigns them a weight of zero (see Figure 6). To establish an upper bound on reconstruction accuracy, we train mip-NeRF 360 with Charbonnier loss on distraction-free versions of each scene, the images for which are taken from (approximately) the same viewpoints. Reassuringly, RobustNeRF when trained on distraction-free frames, achieves nearly identical accuracy; see Figure 11." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 518, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 602 + ], + "type": "text", + "content": "While RobustNeRF consistently outperforms mip-NeRF 360, the gap is smaller in the Apartment scenes (Statue, Android) than the Robotics Lab scenes (Crab, BabyYoda). This can be explained by challenging background geometry, errors in camera parameter estimation, and imperceptible changes to scene appearance. For further discussion, see the supplementary material." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Comparison to " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " - Figure 9. Quantitatively, RobustNeRF matches or outperforms " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " by as much as " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "12\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " PSNR depending on the number of unique outlier objects in the capture. Results on " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " real scenes are provided in the supplementary material for qualitative comparison. In Statue and Android, 1 and 3 non-rigid objects are moved around the scene, respectively. " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " is able to model these objects and thus separate them from the scenes' static content. 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StatueAndroidCrabBabyYoda
LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑LPIPS↓SSIM↑PSNR↑
mip-NeRF 360 (L2)0.360.6619.090.400.6519.350.270.7725.730.310.7522.97
mip-NeRF 360 (L1)0.300.7219.550.400.6619.380.220.7926.690.220.8026.15
mip-NeRF 360 (Ch.)0.300.7319.640.400.6619.530.210.8027.720.230.8025.22
D2NeRF0.480.4919.090.430.5720.610.420.6821.180.440.6517.32
RobustNeRF0.280.7520.890.310.6521.720.210.8130.750.200.8330.87
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Evaluation on Natural Scenes - RobustNeRF outperforms baselines and " + }, + { + "bbox": [ + 46, + 495, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 495, + 546, + 540 + ], + "type": "text", + "content": " [53] on novel view synthesis with real-world captures. The table provides a quantitative comparison of RobustNeRF, " + }, + { + "bbox": [ + 46, + 495, + 546, + 540 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 495, + 546, + 540 + ], + "type": "text", + "content": " and mip-NeRF 360 using different reconstruction losses. The last row reports mip-NeRF 360 trained on a distractor-free version of each dataset, giving an upperbound for RobustNeRF performance. We also visualize samples from each scene rendered with each of the methods. See Supplementary Material for more samples." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 149, + 418, + 246, + 491 + ], + "blocks": [ + { + "bbox": [ + 149, + 418, + 246, + 491 + ], + "lines": [ + { + "bbox": [ + 149, + 418, + 246, + 491 + ], + "spans": [ + { + "bbox": [ + 149, + 418, + 246, + 491 + ], + "type": "image", + "image_path": "fbff17edcd0c79df32fd429ad15ec1ef06b80d4dca1fab87e2456bd3826010ad.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 249, + 418, + 345, + 491 + ], + "blocks": [ + { + "bbox": [ + 249, + 418, + 345, + 491 + ], + "lines": [ + { + "bbox": [ + 249, + 418, + 345, + 491 + ], + "spans": [ + { + "bbox": [ + 249, + 418, + 345, + 491 + ], + "type": "image", + "image_path": "e9215e4e4f884ac6d10f101a9563ca8e96bf72151a128a1751def30b93e22c45.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 348, + 418, + 444, + 491 + ], + "blocks": [ + { + "bbox": [ + 348, + 418, + 444, + 491 + ], + "lines": [ + { + "bbox": [ + 348, + 418, + 444, + 491 + ], + "spans": [ + { + "bbox": [ + 348, + 418, + 444, + 491 + ], + "type": "image", + "image_path": "b2ab403dd8bd35e27f24f173505838e737fc32feaeaff8ed4698dd5bbd5f6794.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 447, + 418, + 544, + 491 + ], + "blocks": [ + { + "bbox": [ + 447, + 418, + 544, + 491 + ], + "lines": [ + { + "bbox": [ + 447, + 418, + 544, + 491 + ], + "spans": [ + { + "bbox": [ + 447, + 418, + 544, + 491 + ], + "type": "image", + "image_path": "06c7d9010e371fb2c3acf11e25eeec78573aa9900a82f80795f0ec317f4a5b25.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "content": "larger pool of 100 to 150 unique, non-static objects are used – too many for " + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "content": " to model effectively. As a result, “cloud” artifacts appear in its static representation, similar to those produced by mip-NeRF 360. In contrast, Robust-NeRF identifies non-static content as outliers and omits it during reconstruction. Although both methods use a similar number of parameters, " + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "content": "'s peak memory usage is " + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "inline_equation", + "content": "2.3\\mathrm{x}" + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "content": " higher than RobustNeRF and " + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "inline_equation", + "content": "37\\mathrm{x}" + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "content": " higher when normalizing for batch size. This is a direct consequence of model architecture: " + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 46, + 554, + 289, + 710 + ], + "type": "text", + "content": " is tailored to simultaneously modeling static and dynamic content and thus merits higher complexity. To remain comparable, we limit image resolution to 0.2 megapixels for all experiments." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 554, + 545, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 710 + ], + "type": "text", + "content": "Ablations - Figure 10. We ablate elements of the Robust-NeRF loss on the crab scene, comparing to an upper bound on the reconstruction accuracy of mip-NeRF 360 trained on distractor-free (clean) images from identical viewpoints. Our trimmed estimator (8) successfully eliminates distractors at the expense of high frequency texture and a lower PSNR. With smoothing (9), fine details are recovered, at the cost of longer training times. With the spatial window (10), RobustNeRF training time is on-par with mip-NeRF 360. We also ablate patch size and the trimming threshold (see Supplementary Material); we find that RobustNeRF is insensitive to trimming threshold, and that reducing the patch size offsets the gains from smoothing and patching." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20632" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 69, + 545, + 220 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 545, + 220 + ], + "type": "table", + "html": "
CarCarsBagChairsPillow
LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑LPIPS↓MS-SSIM↑PSNR↑
NeRF-W [23].218.81424.23.243.87324.51.139.79120.65.150.68123.77.088.93528.24
NSFF [18].200.80624.90.620.37610.29.108.89225.62.682.28412.82.782.3434.55
NeuralDiff [46].065.95231.89.098.92125.93.117.91029.02.112.72224.42.565.65220.09
D2NeRF [53].062.97534.27.090.95326.27.076.97934.14.095.70724.63.076.97936.58
RobustNeRF.013.98837.73.063.95726.31.006.99541.82.007.99241.23.018.99038.95
Train ViewTest ViewNeRF-WNSFFNeuralDiffD2NeRFRobustNeRF
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LPIPS↓SSIM↑PSNR↑Updates to PSNR=30
mip-NeRF 360 (L2)0.310.7522.97-
+ robust (8)0.390.6018.21-
+ smoothing (9)0.220.8130.01250K
+ patching (10)0.210.8130.7570K
oracle (clean)0.160.8432.5525K
+ robust+ smoothing+ patching
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Patching enables the model to reach PSNR of 30, almost " + }, + { + "bbox": [ + 46, + 394, + 287, + 437 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 394, + 287, + 437 + ], + "type": "text", + "content": " faster." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 455, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 635 + ], + "type": "text", + "content": "Sensitivity - Figure 11. We find that RobustNeRF is remarkably robust to the amount of clutter in a dataset. We define an image as \"cluttered\" if it contains some number of distractor pixels. The figure shows how the reconstruction accuracy of RobustNeRF and mip-NeRF 360 depends on the fraction of training images with distractors, keeping the training set size constant. As the fraction increases, mip-NeRF 360's accuracy steadily drops from 33 to " + }, + { + "bbox": [ + 46, + 455, + 287, + 635 + ], + "type": "inline_equation", + "content": "25\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 455, + 287, + 635 + ], + "type": "text", + "content": ", while RobustNeRF's remains steadily above 31 dB throughout. In the distraction-free regime, we find that RobustNeRF mildly under-performs mip-NeRF 360, both in reconstruction quality and the time needed for training. This follows from the statistical inefficiency induced by the trimmed estimator (8), for which a percentage of pixels will be discarded even if they do not correspond to distractors." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 125, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 125, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 125, + 659 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "We address a central problem in training NeRF models, namely, optimization in the presence of distractors, such as transient or moving objects and photometric phenomena that are not persistent throughout the capture session." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 252, + 427, + 338 + ], + "blocks": [ + { + "bbox": [ + 309, + 252, + 427, + 338 + ], + "lines": [ + { + "bbox": [ + 309, + 252, + 427, + 338 + ], + "spans": [ + { + "bbox": [ + 309, + 252, + 427, + 338 + ], + "type": "image", + "image_path": "8d20921cfffe3ec11df060f2cc54bfdaeaa6671ce873faf1eb8f2439c641d3b5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 340, + 546, + 384 + ], + "lines": [ + { + "bbox": [ + 305, + 340, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 546, + 384 + ], + "type": "text", + "content": "Figure 11. Sensitivity and Limitations - (left) Reconstruction accuracy for BabyYoda as we increase the fraction of train images with distractors. (right) Accuracy vs training time on clean BabyYoda images (distractor-free)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 434, + 252, + 544, + 338 + ], + "blocks": [ + { + "bbox": [ + 434, + 252, + 544, + 338 + ], + "lines": [ + { + "bbox": [ + 434, + 252, + 544, + 338 + ], + "spans": [ + { + "bbox": [ + 434, + 252, + 544, + 338 + ], + "type": "image", + "image_path": "6aefd32abf79c23dfc1f2bc20cbe57a82060ff522497877b96c668389f8568a1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 398, + 546, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 546, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 546, + 553 + ], + "type": "text", + "content": "Viewed through the lens of robust estimation, we formulate training as a form of iteratively re-weighted least squares, with a variant of trimmed LS, and an inductive bias on the smoothness of the outlier process. RobustNeRF is surprisingly simple, yet effective on a wide range of datasets. RobustNeRF is shown to outperform recent state-of-the-art methods [4, 53], qualitatively and quantitatively, on a suite of synthetic datasets, common benchmark datasets, and new datasets captured by a robot, allowing fine-grained control over distractors for comparison with previous methods. While our experiments explore robust estimation in the context of mip-NeRF 360, the RobustNeRF loss can be incorporated within other NeRF models." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 674 + ], + "type": "text", + "content": "Limitations. While RobustNeRF performs well on scenes with distractors, the loss entails some statistical inefficiency. On clean data, this yields somewhat poorer reconstructions, often taking longer to train (see Figure 11). Future work will consider very small distractors, which may require adaptation of the spatial support used for outlier/inlier decisions. It would also be interesting to learn a neural weight function, further improving RobustNeRF; active learning may be useful in this context. Finally, it would be interesting to include our robust loss in other NeRF frameworks." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements We thank Pete Florence and Konstantinos Rematas for helpful feedback, and Tianhao Wu for help with " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " experiments." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20633" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 715 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Michal Adamkiewicz, Timothy Chen, Adam Caccavale, Rachel Gardner, Preston Culbertson, Jeannette Bohg, and Mac Schwager. 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CVPR, 2022. 1" + } + ] + } + ], + "index": 1 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "20636" + } + ] + } + ], + "index": 3 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Role of Transients in Two-Bounce Non-Line-of-Sight Imaging/dd8b3d32-1f20-46bb-9a36-d731b9d46ed2_content_list.json b/2023/Role of Transients in Two-Bounce Non-Line-of-Sight Imaging/dd8b3d32-1f20-46bb-9a36-d731b9d46ed2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5e17d1f51f1d53780d08bf7b39e4e6c94f1372a0 --- /dev/null +++ b/2023/Role of Transients in Two-Bounce Non-Line-of-Sight Imaging/dd8b3d32-1f20-46bb-9a36-d731b9d46ed2_content_list.json @@ -0,0 +1,1589 @@ +[ + { + "type": "text", + "text": "Role of Transients in Two-Bounce Non-Line-of-Sight Imaging", + "text_level": 1, + "bbox": [ + 174, + 130, + 795, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Siddharth Somasundaram1 Akshit Dave2 Connor Henley1 Ashok Veeraraghavan2 Ramesh Raskar1", + "bbox": [ + 240, + 179, + 720, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Massachusetts Institute of Technology 2Rice University", + "bbox": [ + 248, + 215, + 722, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{sidsoma,co24401,raskar}@mit.edu，{akshat,vashok}@rice.edu", + "bbox": [ + 228, + 236, + 736, + 252 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7aeab3f60d5fffa2bd2ad3467548e8845c54e83e6be1cc168a60191a04250c76.jpg", + "image_caption": [ + "(a) Two-Bounce NLOS" + ], + "image_footnote": [], + "bbox": [ + 86, + 286, + 276, + 472 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/118345b65ad62ac1f6b1a164a33c258b22fb20ad950318959ea43658f57ef8d0.jpg", + "image_caption": [ + "(b) Application Settings" + ], + "image_footnote": [], + "bbox": [ + 279, + 286, + 447, + 472 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/52c0223be557335de100b98aeb25d634c86691168774718254326334a72d2710.jpg", + "image_caption": [ + "(c) Experimental Setup", + "Figure 1. Two-bounce Transient NLOS Imaging. (a) We propose using two-bounce transients for NLOS imaging. Two-bounce signals capture information about the shadows in a scene, and use of transient information can reduce the number of measurements needed for reconstruction by using multiplexed illumination. (b) Our work can be applicable in many scenarios, such as tunnels, corridors, streets, and forests. (c)-(d) We experimentally validate the use of two-bounce transients on real objects. We show that time-of-flight information enables more robust reconstructions of occluded objects while using fewer measurements." + ], + "image_footnote": [], + "bbox": [ + 452, + 286, + 602, + 472 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c2882cdcc836f088655b91a89b156cfbbe64c7a1a2d68e2e585d6f6782bc3ac9.jpg", + "image_caption": [ + "(d) Reconstruction with 10 Measurements" + ], + "image_footnote": [], + "bbox": [ + 604, + 286, + 880, + 472 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 583, + 313, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The goal of non-line-of-sight (NLOS) imaging is to image objects occluded from the camera's field of view using multiply scattered light. Recent works have demonstrated the feasibility of two-bounce (2B) NLOS imaging by scanning a laser and measuring cast shadows of occluded objects in scenes with two relay surfaces. In this work, we study the role of time-of-flight (ToF) measurements, i.e. transients, in 2B-NLOS under multiplexed illumination. Specifically, we study how ToF information can reduce the number of measurements and spatial resolution needed for shape reconstruction. We present our findings with respect to trade-offs in (1) temporal resolution, (2) spatial resolution, and (3) number of image captures by studying SNR and recoverability as functions of system parameters. This leads to a formal definition of the mathematical constraints for 2B lidar. We believe that our work lays an analytical groundwork for design of future NLOS imaging systems, especially as ToF sensors become increasingly ubiquitous.", + "bbox": [ + 75, + 611, + 472, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 583, + 630, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Non-line-of-sight (NLOS) imaging aims to reconstruct objects occluded from direct line of sight and has the potential to be transformative in numerous applications across autonomous driving, search and rescue, and non-invasive medical imaging [24]. The key approach is to measure light that has undergone multiple surface scattering events and computationally invert these measurements to estimate hidden geometries. Recent work used two-bounce light, as shown in Fig. 2a, to reconstruct high quality shapes behind occluders [15]. The key idea is that two-bounce light captures information about the shadows of the occluded object. By scanning the laser source at different points 1 on a relay surface and measuring multiple shadow images, it is possible to reconstruct the hidden object by computing the visual hull [20] of the measured shadows.", + "bbox": [ + 496, + 608, + 890, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Benefits of Two-Bounce Two-bounce (2B) light can be captured using two relay surfaces on opposite sides of the hidden scene (Fig. 1a). This can occur in a variety of real-world settings such as tunnels, hallways, streets, and clit", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9192", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dac7c60efc57b3d2780b5a921c14a32785da739cb4a0e855d406b94c62a09000.jpg", + "image_caption": [ + "(a) Two-Bounce NLOS Imaging" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 267, + 200 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/afdd89e2ce005569ede0fd9f3f24ea328c4a24daef53b9947c7063d6f5e8f52d.jpg", + "image_caption": [ + "(b) Two-Bounce Transient NLOS", + "Figure 2. Two-Bounce NLOS Imaging. (a) Two-bounce NLOS imaging performs 3D reconstruction by using information contained in the shadows of the hidden object when illuminated by one virtual source 1 at a time. (b) In this work, we study the benefits of using transient information for two-bounce NLOS imaging under the presence of multiplexed illumination." + ], + "image_footnote": [], + "bbox": [ + 269, + 88, + 467, + 200 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tered environments like forests (Fig. 1b). For example, imagine an autonomous vehicle in a tunnel being able to see ahead of the car in front of it by using two-bounce signals from the sides of the tunnel. Two-bounce light also helps alleviate the signal-to-noise ratio (SNR) issue in 3B-NLOS imaging, since 3B signals experience significant signal attenuation at each surface scatter event. Furthermore, 2B light captures information about the cast shadows of the hidden object instead of reflectance, as in the 3B case. As a result, the SNR of 2B signals is independent of the object's albedo and can therefore robustly image darker objects.", + "bbox": [ + 75, + 339, + 467, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions In this work, we propose using two-bounce transients for NLOS imaging to enable the use of multiplexed illumination. 3B-NLOS transient imaging systems have been analyzed previously, but we believe we are the first to analyze the use of multiplexed illumination and transient measurements for 2B-NLOS (Fig. 2b). Our key insight is that multiplexed illumination enables measurement of occluded objects with fewer image captures, and 2B transients enable demultiplexing shadows, as shown in Fig. 3. The robust SNR and promise of few-shot capture afforded by 2B transients makes the idea an important direction for few-shot NLOS imaging in general environments. We summarize our contributions below.", + "bbox": [ + 75, + 511, + 467, + 705 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Model: We present new insights into the algebraic formulations of two-bounce lidar for NLOS imaging.", + "- Analysis: We analyze tradeoffs with spatial resolution, temporal resolution, and number of image captures by using quantitative metrics such as SNR and recoverability, as well as qualitative validation from real and simulated results." + ], + "bbox": [ + 96, + 720, + 467, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although we envision the ideas introduced here to inspire future works in single-shot NLOS imaging, we do not claim this as a contribution in this paper.", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scope of This Work All data used for this work is from simulation and a single-pixel SPAD sensor. We do not physically realize few-shot results in this paper due to limited availability of high-resolution SPAD arrays presently. Instead, we emulate SPAD array measurements by scanning a single-pixel SPAD across the field of view and and emulate multiplexed illumination by scanning a laser spot, acquiring individual transient images, and summing the images in post-processing. These measurements, however, are more conducive to our goal of performing analysis that explores the landscape of possibilities in NLOS imaging with advances in ToF sensors. We believe that the ideas and analysis introduced in this work will be increasingly relevant as SPAD array technology matures [19,26,44].", + "bbox": [ + 496, + 90, + 890, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 316, + 640, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Non-Line-of-Sight Imaging", + "text_level": 1, + "bbox": [ + 500, + 340, + 714, + 357 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ToF Methods: The non-line-of-sight imaging (NLOS) problem aims to see around a corner by measuring light reflected off intermediary surfaces. A large body of work models the response of a hidden scene to a temporal pulse of light and generally perform a variant of ellipsoidal tomography or solve a linear inverse problem [3, 5, 11, 12, 18, 39]. The temporal profiles can probe features of the hidden space, such as Fermat paths [42], scene impulse response [23], and individual voxels [28]. Other works derive efficient algorithms using a confocal setup [2, 22, 27] and data-driven techniques [8]. NLOS has also been demonstrated with amplitude modulated continuous wave (AMCW) ToF by exploiting sparsity and fitting measurements to a Lambertian reflectance model [13, 16].", + "bbox": [ + 496, + 363, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Other Active Methods: Chen et al. use steady-state (i.e. time-integrated) intensity information by leveraging partial directionality of diffuse reflectors [7]. Radio wavelengths can also be used to image through walls and/or around them [1, 32, 43]. There has also been significant progress in exploiting speckle correlations [9, 17, 25, 34] and synthetic wave holography [40, 41] for NLOS imaging. Henley et al. demonstrate the use of two-bounce light (i.e. shadows) for NLOS using intensity sensors [15]. An extension of this work uses ToF constraints on two-bounce pathlengths to isolate shadows from ambient background and higher-order inter-reflections [14]. However multiplexing was not used.", + "bbox": [ + 496, + 579, + 890, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Passive Methods: Passive methods make use of optical information already present in the scene without an active source. Many passive approaches exploit polarization cues [10,36], ambient thermal light [21,36], shadows [35], multiview reflections [38], and neural networks [33,37] to reconstruct or make inferences about the scene outside the camera's field of view. Occlusion-assisted imaging makes use of information present at sharp discontinuities in LOS and NLOS scenes by turning them into virtual pinholes [4,30] or", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9193", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/ff5b994feed9ce68024242b3f89d30db7eb411fd529b7290592fedf6504f3d38.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NLOS Imaging DomainKey ComponentsKey Features
Assisting SurfacesSensor TypeLight SourceNumber of CapturesRecovered DimensionsSignal Quality
Passive Occlusion-Aided [4,31,33]Relay Wall/FloorIntensityPassiveLow2DLow (strong background)
Edge Occluders
Three-Bounce Transient [18,27,30,42]Relay Wall/FloorToFActive (Scan)High3DMedium (3-bounce)
Edge Occluders
Two-Bounce Transient (Ours)Two LOS WallsToFActive (Flash)Low3DHigh (2-bounce)
", + "bbox": [ + 104, + 88, + 867, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Comparison of NLOS Methods. Passive approaches require fewer measurements but can either recover up to two dimensions or are strongly affected by ambient noise. Works exploiting three-bounce light paths demonstrate 3D imaging around the corner but require a bounce on the hidden surface, reducing the signal quality. We analyze exploiting two-bounce transients for NLOS imaging.", + "bbox": [ + 75, + 280, + 893, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "virtual pinspecks [31]. Intensity-only methods are difficult to scale to scenarios with arbitrary lighting conditions.", + "bbox": [ + 76, + 349, + 470, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Forward and Adjoint Operators", + "text_level": 1, + "bbox": [ + 76, + 404, + 372, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Setup", + "text_level": 1, + "bbox": [ + 76, + 436, + 228, + 454 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce terminology and notation for our problem formulation. The object of interest lies behind an occluder and is flanked on two sides by planar Lambertian relay surfaces. Without loss of generality, the right wall is the illumination wall $\\mathcal{L}$ and the left wall is the observation wall $\\mathcal{O}$ . Light incident on the illumination wall at a point $l$ is a virtual source. Each virtual source diffusely radiates light towards the observation wall. Light will arrive at a virtual detector $s$ from $l$ if the object doesn't lie along the ray connecting $s$ and $l$ , as shown in Fig. 2a. If the object obstructs this ray, $s$ is said to lie in the shadow of the object. We assume that every virtual source and virtual detector is visible to the laser and camera field of view, respectively. The hidden scene is discretized into a voxel grid described by a binary occupancy (or transparency) function. This implicitly assumes that we are reconstructing opaque surfaces. We neglect the effect of higher order bounces (e.g. interreflections, 3B light) because SPADs can temporally gate out the longer ToF of 3B light. Furthermore, the intensity of higher order bounces will be much lower than that of two-bounce light because all surfaces are assumed to be diffuse.", + "bbox": [ + 75, + 469, + 472, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote light transients as ToF measurements for light that arrives at the virtual detector and shadow transients as ToF measurements for light that didn't arrive at the virtual detector because of the object's shadow. Both of these are two-bounce transients. We show that modeling the problem in terms of shadow transients enables reconstruction of the hidden objects shape by solving a linear inverse problem.", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6f41010c71b9b4e84377d5a0bb51f56fd62c5842531823a5568b6a7bf5682fd8.jpg", + "image_caption": [ + "Figure 3. Time-of-Flight Information for Demultiplexing Shadows. Assume the point $s$ lies in shadow. When using multiplexed illumination, there exists an ambiguity as to whether $s$ lies in the shadow of $l_1$ , $l_2$ , or both. However, the paths $L - l_1 - s - C$ and $L - l_2 - s - C$ have different pathlengths, suggesting the usefulness of ToF information for demultiplexing shadows." + ], + "image_footnote": [], + "bbox": [ + 545, + 347, + 844, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Linear Forward Model", + "text_level": 1, + "bbox": [ + 500, + 650, + 714, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Light Transients Consider the case where the occluded scene is empty. The measured transient is then given by", + "bbox": [ + 500, + 672, + 890, + 705 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ni _ {0} (t; \\mathbf {s}) = \\alpha \\iint_ {\\mathcal {L}} \\frac {\\delta (\\| \\mathbf {l} - \\mathbf {g} \\| + \\| \\mathbf {l} - \\mathbf {s} \\| - c t)}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 709, + 890, + 743 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{g}$ is the location of the laser, $c$ is the speed of light, and $\\alpha$ is the intensity of the laser. We refer to $i_0$ as the empty transient. For simplicity, we ignore $\\alpha$ for the rest of the derivations in this section and assume that the length between the virtual detector and camera is calibrated or known. The numerator of the integrand", + "bbox": [ + 496, + 748, + 893, + 839 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ni (t; \\mathbf {s}, \\mathbf {l}) = \\delta (\\| \\mathbf {l} - \\mathbf {g} \\| + \\| \\mathbf {l} - \\mathbf {s} \\| - c t) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 845, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "describes the equation of an ellipsoid, with foci at $\\mathbf{g}$ and s and major axis length $ct$ . When an object is present in the", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9194", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dc5705168e811c254e22b1d68ae3ba330bd0192dfe1a920cfa8f9180350463ca.jpg", + "image_caption": [ + "Figure 4. Light and Shadow Transients. Three spacetime curves are depicted. (left) Empty transient $i_0$ with no hidden object, (middle) light transient $i_l$ with an object, and (right) shadow transient $i_s = i_0 - i_l$ . Switching from light transients $i_l$ to shadow transients $i_s$ enables derivation of a linear forward model." + ], + "image_footnote": [], + "bbox": [ + 89, + 89, + 459, + 154 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "occluded scene, the measured light transient is given by", + "bbox": [ + 76, + 261, + 444, + 276 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {l} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} V _ {\\mathbf {s}, \\mathbf {l}} \\cdot \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 287, + 468, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V_{\\mathbf{s},1}$ is the visibility between s and l.", + "bbox": [ + 76, + 332, + 359, + 348 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV _ {\\mathbf {s}, \\mathbf {l}} = \\exp \\left(\\oint_ {\\mathbf {l}} ^ {\\mathbf {s}} \\ln \\left(f _ {t} (\\mathbf {x})\\right) d \\mathbf {x}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 353, + 468, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where Eq. (4) computes the product integral along the line connecting $\\mathbf{l}$ and $\\mathbf{s}$ and $f_{t}(\\mathbf{x})\\in \\{0,1\\}$ is the transparency function of voxel $\\mathbf{x}$ in the occluded region.", + "bbox": [ + 76, + 398, + 468, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shadow Transients The non-linearity of Eq. (4) makes model inversion challenging with light transients. Casting the formulation from light space-time to shadow space-time enables a linear formulation of the problem. A shadow transient at $s$ is given by", + "bbox": [ + 76, + 450, + 468, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {s} (t; \\mathbf {s}) = i _ {0} (t; \\mathbf {s}) - i _ {l} (t; \\mathbf {s}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 540, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 4 illustrates the difference between light transients and shadow transients. Shadow transients directly probe voxel occupancy, whereas light transients probe for voxel transparency. For example, if the occluded scene is empty except for voxel $\\mathbf{x}$ , the shadow transient is given by", + "bbox": [ + 76, + 569, + 468, + 645 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {s} (t; \\mathbf {s}, \\mathbf {x}) = \\frac {\\delta (\\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {g} \\| + \\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {s} \\| - c t)}{\\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {s} \\| ^ {2}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 657, + 468, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{l}(\\mathbf{x},\\mathbf{s})$ is a point on the illumination wall that lies along the ray connecting $\\mathbf{x}$ and $\\mathbf{s}$ . If the wall doesn't intersect this ray, $i_s(t;\\mathbf{x},\\mathbf{s}) = 0$ .", + "bbox": [ + 76, + 702, + 467, + 748 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Linear Relaxation Now, consider the general case where a single opaque object lies in the hidden scene. We can describe the shadow transient as", + "bbox": [ + 76, + 755, + 468, + 799 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {s} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} O _ {\\mathbf {s}, \\mathbf {l}} \\cdot \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 809, + 468, + 843 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $O_{\\mathbf{s},1} \\in \\{0,1\\}$ is the occlusion function (denotes if the ray between 1 and s is occluded). It can be expressed as the indicator function", + "bbox": [ + 76, + 854, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} O _ {\\mathbf {s}, \\mathrm {l}} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\oint_ {\\mathrm {l}} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x} > 0 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8} \\\\ \\approx \\oint_ {1} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 84, + 890, + 159 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{o}(\\mathbf{x})$ is the voxel occupancy function of the hidden scene. The linear relaxation in Eq. (8) is possible because NLOS reconstructions typically only consider ToF information, but not radiometric information. The above formulation will preserve the structure of the streak images in spacetime, even if the intensities are overestimated. Combining Eq. (5), (7), and (8), we obtain", + "bbox": [ + 498, + 170, + 890, + 275 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {0} (t; \\mathbf {s}) - i _ {l} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} \\cdot \\left(\\oint_ {\\mathbf {l}} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x}\\right) d \\mathbf {l}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 286, + 890, + 320 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we solve for $f_{o}(\\mathbf{x})$ . We can estimate $i_0$ from the scene geometry and $i_l$ is the measured transient.", + "bbox": [ + 498, + 330, + 890, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discrete Beam Illumination Discretizing $\\mathcal{L}$ as $K$ discrete laser spots and the hidden space into a voxel grid, we can write Eq. (9) as", + "bbox": [ + 498, + 364, + 890, + 411 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ni _ {s} [ t; \\mathbf {s} ] = \\sum_ {k = 1} ^ {K} \\frac {\\delta [ \\| \\mathbf {l} _ {k} - \\mathbf {g} \\| + \\| \\mathbf {l} _ {k} - \\mathbf {s} \\| - c t ]}{\\| \\mathbf {l} _ {k} - \\mathbf {s} \\| ^ {2}} \\cdot \\left(\\sum_ {\\mathbf {x} \\in \\mathcal {P} _ {\\mathbf {l} _ {k}, \\mathbf {s}}} f _ {o} [ \\mathbf {x} ]\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 422, + 900, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{P}_{1,\\mathrm{s}}$ denotes the set of voxels lying along the path between 1 and s. Eq. (10) can be expressed in matrix form", + "bbox": [ + 500, + 479, + 888, + 510 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {s} = \\mathbf {P B f} = \\mathbf {A f}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 523, + 890, + 539 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{I}_s\\in \\mathbb{R}^{n_u n_v n_t}$ is the vectorized space-time measurements, $\\mathbf{f}\\in \\mathbb{R}^{n_x n_y n_z}$ is the voxel occupancies, and $\\mathbf{A}\\in \\mathbb{R}^{n_u n_v n_t\\times n_x n_y n_z}$ is the measurement operator mapping voxel occupancies to space-time measurements. $n_u$ and $n_v$ are the number of pixels along the $u$ and $v$ direction, and $n_t$ is the number of timing bins. $n_x,n_y,$ and $n_z$ are the number of voxels in the $x,y,$ and $z$ directions.", + "bbox": [ + 498, + 551, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{P}$ and $\\mathbf{B}$ model the temporal and spatial relationships, respectively, between virtual sources, virtual detectors, and voxels. $\\mathbf{P} \\in \\mathbb{R}^{n_u n_v n_t \\times n_u n_v K}$ is a block diagonal matrix, with the column space of the $i$ th block $\\mathbf{P}^i \\in \\mathbb{R}^{n_t \\times K}$ containing the corresponding $\\delta(\\cdot)$ functions from Eq. (2) for virtual detector $\\mathbf{s}_i$ and all $K$ virtual sources. $\\mathbf{B} \\in \\mathbb{R}^{n_u n_v K \\times n_x n_y n_z}$ is composed of $n_u n_v$ vertical sub-blocks. Each entry $\\mathbf{B}_{kj}^i \\in \\{0,1\\}$ of the $i$ th sub-block $\\mathbf{B}^i \\in \\mathbb{R}^{K \\times n_x n_y n_z}$ of sub-block $i$ indicates whether voxel $j$ lies along the line connecting virtual detector $\\mathbf{s}_i$ and virtual source $\\mathbf{l}_k$ . The multiplication $\\mathbf{Bf}$ performs the line integral in Eq. (8). The $k$ th column vector of $\\mathbf{P}$ is the space-time impulse response (STIR) to the $k$ th illumination source when the hidden scene is completely occupied (note that we are dealing with shadow transients, not light transients). The $i$ th column of $\\mathbf{A}$ forms the expected space-time measurements", + "bbox": [ + 498, + 656, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9195", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "if only the $i$ th voxel is occupied (i.e. the STIR to a single voxel). We neglect the $r^2$ falloff term in our reconstructions. Additional explanation of the A matrix is provided in the supplementary. The linear model in Eq. (11) resembles that of 3B-bounce NLOS, where $\\mathbf{A}$ is a measurement operator that maps voxels $\\mathbf{f}$ to measurements $\\mathbf{I}$ . However, in 3B-NLOS, the information is encoded into the reflectance of the object, whereas in 2B-NLOS, the information is encoded into the shadows. Therefore, the former is linear with respects to light transients, and the latter is linear with respect to shadow transients.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Reconstruction Algorithm", + "text_level": 1, + "bbox": [ + 76, + 268, + 316, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reconstruction of $\\mathbf{f}$ can be performed by backprojection", + "bbox": [ + 96, + 294, + 468, + 309 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {b p} = \\mathbf {A} ^ {\\top} \\mathbf {I} _ {s}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 316, + 468, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Backprojection produces a low-frequency reconstruction of $\\mathbf{f}$ . In practice, filtering $\\mathbf{f}_{bp}$ with a Laplacian filter", + "bbox": [ + 76, + 345, + 470, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {f b p} = \\left(\\frac {\\partial^ {2}}{\\partial x ^ {2}} + \\frac {\\partial^ {2}}{\\partial y ^ {2}} + \\frac {\\partial^ {2}}{\\partial z ^ {2}}\\right) \\mathbf {f} _ {b p} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 390, + 468, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "has been shown to yield reasonably good results in ellipsoidal tomography in 3-bounce NLOS and line-based tomography in medical imaging. Our linear formulation also enables reconstruction with priors. We recognize that these optimization-based methods would improve reconstruction over unfiltered backprojection, which is equivalent to a low-frequency version of voxel carving in our setup. However, we restrict our focus to unfiltered backprojection because of its convenient relationship with the Gram matrix, which enables further analysis of our method in Sec. 4.2.", + "bbox": [ + 75, + 443, + 468, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Design and Analysis", + "text_level": 1, + "bbox": [ + 76, + 611, + 272, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we analyze how the performance of the proposed two-bounce transient system varies with system parameters and the geometry of LOS relay surfaces. We also analyze the impact of temporal resolution, spatial resolution, and number of measurements on recoverability. The amount of multiplexing in the scene is inversely related to the number of measurements. For example, if 60 laser spots are used and 15 measurements are captured, then each image contains 4 multiplexed shadows. We use SNR, coherence, and FWHM of the PSF to quantify performance.", + "bbox": [ + 75, + 637, + 468, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Voxel SNR Analysis", + "text_level": 1, + "bbox": [ + 76, + 800, + 266, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We quantify the noise characteristics of the measured shadow two-bounce transients using per-voxel SNR. Consider the case where only voxel $\\mathbf{x}$ is occupied in the hidden region. We derive the SNR of the number of \"shadow\" photons received in the measured shadow transient $\\mathbf{I}_s^{\\mathbf{x}}$ . In vector", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4f3db07091b483a62612cdaf18a59324896d0484893c3c68aaf647b579b2ea8a.jpg", + "image_caption": [ + "Figure 5. SNR Analysis. The goal of this analysis is to determine how scene geometry affects the SNR of the two-bounce measurement at each voxel in the hidden scene. The first two cases consider the orientations of the relay surfaces, and the third considers the field of view of the camera. SNR is highest in the middle of the hidden scene for parallel surfaces, orienting the walls closer together increases SNR due to reduced $r^2$ falloff, and SNR is highest closer to the virtual detectors for small FOV cameras." + ], + "image_footnote": [], + "bbox": [ + 511, + 89, + 877, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "form, the occupancy function can be described as $\\delta^{\\mathbf{x}}$ . From Eq. (11), the shadow transient is given by", + "bbox": [ + 498, + 364, + 892, + 396 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {s} ^ {\\mathbf {x}} = \\mathbf {A} \\delta^ {\\mathbf {x}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 404, + 890, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and the light transients measured by the SPAD sensor are given by $\\mathbf{I}_l^{\\mathbf{x}}$ . For this analysis, we account for $r^2$ falloff because it is a physically accurate phenomenon that impacts SNR. From Eq. (5),", + "bbox": [ + 498, + 429, + 892, + 491 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} _ {l} ^ {\\mathbf {x}} = \\mathbf {I} _ {0} - \\mathbf {A} \\delta^ {\\mathbf {x}} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 498, + 890, + 515 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{I}_0$ is the empty transient and assumed to be calibrated. Assuming no SPAD pile-up distortion, the number of photons arriving at the sensor for each time bin of $\\mathbf{I}_l^{\\mathbf{x}}$ follows an independent Poisson distribution [29]. Thus, the total number of photons $P^{\\mathbf{x}}$ measured follows a Poisson distribution with the rate parameter being the sum of all the photon counts for all time bins for all pixels.", + "bbox": [ + 496, + 523, + 892, + 630 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP ^ {\\mathbf {x}} \\sim \\operatorname {P o i s s o n} \\left(\\mathbf {1} ^ {T} \\left(\\mathbf {I} _ {0} - \\mathbf {A} \\delta^ {\\mathbf {x}}\\right)\\right) \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 637, + 890, + 655 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{1} \\in \\mathbb{R}^{n_u n_v n_t}$ is the one vector. Using the fact that SNR of a Poisson distribution is $\\mu / \\sigma = \\sqrt{\\lambda}$ with rate parameter $\\lambda$ , the per-voxel SNR $S^{\\mathbf{x}}$ is given by", + "bbox": [ + 496, + 662, + 892, + 709 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS ^ {\\mathbf {x}} = \\sqrt {\\mathbf {1} ^ {T} \\left(\\mathbf {I} _ {0} - \\mathbf {A} \\boldsymbol {\\delta} ^ {\\mathbf {x}}\\right)} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 718, + 890, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The per-voxel SNR is plotted in Fig. 5 for three different scenarios. The first two scenarios deal with the orientation of the walls, and the third considers the field of view of the camera. In Fig. 5a, we can see that the SNR is higher for center voxels, as more rays connecting the illumination wall and observation wall pass through the center voxels. When the relay walls are oriented towards each other (Fig. 5b), the SNR increases due to reduced $r^2$ falloff. When the camera's field of view is small compared to the laser (Fig. 5c), regions closer to the observation wall have the highest SNR.", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9196", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5e8c362db0744c8c9755964b4fda3be0b9a90703ab8cbc9ccf84fdd8847089e7.jpg", + "image_caption": [ + "Figure 6. Spatially Varying PSF. In two-bounce lidar, the PSF has a double cone shape. The orientation of the double cone varies strongly as a function of the orientation and length of the relay surfaces (i.e. the virtual apertures) and the voxel position." + ], + "image_footnote": [], + "bbox": [ + 102, + 99, + 436, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Recoverability Analysis", + "text_level": 1, + "bbox": [ + 76, + 351, + 294, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Resolution We now study the resolution limits of our method. In particular, we consider two key metrics in our measurement operator: mutual coherence and full width at half maximum (FWHM) of the PSF. We are interested in how (1) temporal resolution, (2) spatial resolution $N$ , and (3) number of measurements $M$ impact each of our metrics. From Eq. (12), we know that the backprojected occupancy can be obtained from the occupancy function by", + "bbox": [ + 75, + 375, + 468, + 496 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {b p} = \\left(\\mathbf {A} ^ {\\top} \\mathbf {A}\\right) \\mathbf {f}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 507, + 468, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{G} = \\mathbf{A}^{\\top}\\mathbf{A}$ is the Gram matrix. We can interpret the columns (or rows) of the Gram matrix to be the spatially varying point spread function (PSF) of the imaging system, as shown in Fig. 6. Each column $\\mathbf{G}_i$ describes how a voxel $\\mathbf{x}_i$ is blurred during backprojection reconstruction.", + "bbox": [ + 75, + 537, + 468, + 613 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We can see the effect of different imaging parameters on the PSF in Fig. 7, where we sweep different values of (1) $M$ and (2) $N$ . In particular, we note that the lobes of the PSF are suppressed when using temporal information, even with low spatial resolution and few number of image measurements. When using no temporal information, the PSF is still roughly centered at the correct location, but has large FWHM. The sharpness of the PSF when using temporal information indicates that it is better suited to applications that require finer voxel resolution with few-shot capture. In case (1) without transients, we see that the FWHM of the PSF is large along both the $x$ and $y$ direction for small values of $M$ . As $M$ approaches the number of illumination spots, the FWHM approaches the theoretical lower bound. In case (2), increased spatial resolution helps better localize the center of the PSF, but the FWHM does not improve. The transient cases are quite robust to both low number of measurements and low spatial resolution. Intuitively, higher values of $N$ in the transient case slightly help accentuate the center voxel", + "bbox": [ + 75, + 614, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by projecting more diverse rays through the center voxel.", + "bbox": [ + 498, + 90, + 877, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Mutual Coherence We wish to further quantify the impact of spatio-temporal resolution and number of measurements on the recoverability of the hidden scene. We know from compressive sensing theory that sparse recovery of the hidden scene is possible when the mutual coherence of $\\mathbf{A}$ is sufficiently small. The mutual coherence is defined as", + "bbox": [ + 498, + 109, + 890, + 200 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mu = \\max _ {1 \\leq i \\neq j \\leq n} \\frac {\\left| \\mathbf {A} _ {i} ^ {\\top} \\mathbf {A} _ {j} \\right|}{\\left| \\mathbf {A} _ {i} \\right| \\left| \\mathbf {A} _ {j} \\right|}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 212, + 890, + 247 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intuitively, the coherence measures the largest \"similarity\" or correlation between any two column vectors in measurement matrix $\\mathbf{A}$ [6]. Physically, this quantifies how similar the STIRs of two different voxels are. If $\\mu = 1$ , then two voxels have the exact same STIR, which means that there exists an ambiguity as to which voxel resulted in a certain spatio-temporal response. Alternatively, $\\mu$ can be defined as the maximum off-diagonal entry of the Gram matrix. Fig. 8 illustrates how the Gram matrix (and subsequently the mutual coherence) is affected by coarser timing resolutions. From compressive sensing theory, we know that a $K$ -sparse scene can be recovered if $K \\leq 0.5(1 + 1 / \\mu)$ , which motivates our empirical analysis of the effect of spatial resolution and temporal resolution on $\\mu$ .", + "bbox": [ + 496, + 256, + 892, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From Fig. 9, we can see the impact that spatial and temporal resolution have on mutual coherence in a single-shot setup with multiplexed illumination. Consider a scene similar to that of Fig. 6, where the walls are $2\\mathrm{m}$ apart, the walls are $3\\mathrm{m}$ long, the axial distance to the walls is $2\\mathrm{m}$ , and the voxel resolution is discretized to $2\\mathrm{cm}$ . Increasing the spatial resolution at a fixed temporal resolution appears to have little to no effect on the mutual coherence. As Kadambi et al. also point out, improvements of coherence through higher spatial resolution are limited by the size of the virtual aperture (i.e. the wall) [16]. On the other hand, the difference between $100~\\mathrm{ps}$ resolution and $10~\\mathrm{ps}$ resolution reduces the coherence from 0.9 to 0.3 for a fixed spatial resolution. Any timing resolution coarser than $\\sim 120$ ps results in a coherence of 1 for multiplexed measurements because pathlength differences for different shadows are no longer resolvable. This analysis motivates the importance of temporal resolution when using multiplexed illumination.", + "bbox": [ + 496, + 468, + 892, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments and Results", + "text_level": 1, + "bbox": [ + 500, + 753, + 733, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We scan a single-pixel SPAD across the field of view on the left wall to mimic the output of a SPAD array. We scan a single laser spot across the right wall, and sum up the corresponding transient images in post-processing to mimic the effect of multiplexing. Further details are provided in the supplementary. We first validate our model using simulated data in Fig. 10, where we demonstrate that we can localize four letters and reconstruct their 2D shape with just a single", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9197", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8917c0c3376b274e4c1aec23ce917105bd1496bf57c63b2ca47e202dafefab2f.jpg", + "image_caption": [ + "Figure 7. PSF as a Function of Number of Measurements and Spatial Resolution. The PSF of the center voxel is shown in the transient and intensity-only case when multiplexed with 60 laser spots. (1) the number of pixels $N = 40$ are kept fixed with the number of measurements $M$ being swept (left) and (2) $M = 10$ is kept fixed and $N$ is swept (right). Transient measurements result in PSFs with narrower FWHMs, even with low spatial resolution and low number of measurements." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 496, + 340 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1edc73563e372c28f865e5f33e9f5ed0763c3157ca12399ed9b489b4d511ba4e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 90, + 890, + 340 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16f0d107255a743cc7c7b3edbfebd1230b98d899f7b505bddff4798abb3c252b.jpg", + "image_caption": [ + "Figure 8. Gram Matrix as a Function of Temporal Resolution. For a defined voxel resolution and fixed spatial resolution. The columns (or rows) of the Gram matrix form the spatially varying PSFs shown in Fig. 6. The off-diagonal streaks describe the coherence between different voxels. As expected, higher temporal resolution decreases the coherence of the Gram matrix, which increases the likelihood of guaranteed sparse recovery." + ], + "image_footnote": [], + "bbox": [ + 89, + 433, + 455, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "capture. We render $i_{o}$ and $i_{l}$ to obtain a noiseless version of the shadow transient for this experiment. Then, we reconstruct the shapes of real mannequins and must estimate $i_{0}$ . Fig. 11 shows that ToF measurements provide a noticeable improvement in image reconstruction. When there's no multiplexing (i.e., the number of laser spots is the same as number of measurements), the intensity-based method is similar to the ToF-based method. However, in the intensity-only case, the object becomes increasingly blurry until it is no longer visible as the amount of multiplexing increases. In the ToF case for single-shot, we can see a blurry image roughly localized where the center of the mannequin is as well as some high-frequency detail. Furthermore, the top view of the ToF reconstructions show that the high-frequency shape of the arms can be reconstructed even with multiplexed illumination, indicating the promise of single", + "bbox": [ + 75, + 659, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a939948ccd7e2441a4107bbde6b02c4135b2b8f32bbefa8083f6280b2129e310.jpg", + "image_caption": [ + "Figure 9. Tradeoffs Between Spatial Resolution and Temporal Resolution. We quantify the tradeoff using mutual coherence. We use the same setup as Fig. 6, but the walls have length $3\\mathrm{m}$ , the walls are space $2\\mathrm{m}$ apart, and the distance to the walls is $2\\mathrm{m}$ . We discretize the voxel resolution to $2\\mathrm{cm}(\\sim 67\\mathrm{ps})$ . The bottom right of the figure, where spatial and temporal resolution are highest is where mutual coherence is the lowest. For a fixed temporal resolution, improvements in coherence quickly plateau. Improvements in temporal resolution dominate improvements in spatial resolution when reducing coherence, suggesting the importance of ToF for demultiplexing illumination in two-bounce NLOS imaging." + ], + "image_footnote": [], + "bbox": [ + 568, + 434, + 823, + 601 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "shot capture with two-bounce ToF information. Fig. 12 shows that poorer temporal resolution results in aliasing artifacts (repeated arms and legs), whereas the rough shape of the object can still be seen with lower spatial resolution. Finally, we compare our method to the probabilistic voxel carving method used in [15] in Fig. 13. Voxel carving results in sharper reconstructions than backprojection.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9198", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73d56e3e1d2c94eac3c110d2cccf8f917bb7ef872fe2dbc3535b42a6c8e81187.jpg", + "image_caption": [ + "Figure 10. Single-Shot Localization. We obtain single-shot reconstructions of the \"N\", \"L\", \"O\", and \"S\" letters in the hidden scene with and without transient information. We see that using transient information, we are able to effectively localize the hidden object and even get a sharp outline of the letters, demonstrating the promise of single-shot capture with two-bounce transients." + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 457, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/052e98ac960dfbd0dda5d08d4c729a58a63172b1586062dfa28ba96a9705a46b.jpg", + "image_caption": [ + "Figure 11. Transients Enable Scene Recovery from Multiplexed Illumination. We perform backprojection of measurements with varying levels of multiplexing. Plotted in the top two rows are $x$ slices of the reconstructed volume. Under no multiplexing (right), intensity is sufficient to carve the shadow along detected pixel. But reconstruction quality sharply deteriorates as we move towards the multiplexing regime (left). When measuring with transients, time-of-flight information allows us to disambiguate between different shadows and recover a rough silhouette of the object even with just a single measurement." + ], + "image_footnote": [], + "bbox": [ + 91, + 391, + 459, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, our method can be improved by filtering or incorporating priors, and is also generalizable to multiplexed illumination by utilizing ToF information.", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ad76127c3b9f4afd934c1107a982ed0d2ca3477e6dc88bdfb5454de7fd317d7e.jpg", + "image_caption": [ + "Figure 12. Spatial Resolution vs. Timing Resolution. We plot reconstructions with different spatio-temporal resolutions. Lower timing resolution results in aliasing artifacts (i.e. repeated arms and legs). Lower spatial resolution introduces hole artifacts." + ], + "image_footnote": [], + "bbox": [ + 517, + 92, + 851, + 280 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd216f0dc7a5bd6663190c42867f44743f539f7e6a813ffe1cf67a6a302b7c89.jpg", + "image_caption": [ + "Figure 13. Scanning Baseline Comparison. We compare to the voxel carving method used in [15] (a) before and (b) after thresholding when scanning 1 laser spot. Our method is more general, but voxel carving yields sharper results with laser scanning." + ], + "image_footnote": [], + "bbox": [ + 511, + 358, + 879, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 500, + 590, + 612, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced the use of two-bounce transients for NLOS imaging. Compared to 3B-NLOS, 2B-NLOS enables more robust imaging of occluded objects in the presence of scenes with arbitrary lighting conditions and low albedo objects. Transient 2B-NLOS is promising for few-shot capture of occluded objects by using multiplexed illumination, especially as SPAD array technology matures. When comparing tradeoffs in temporal resolution, spatial resolution, and number of measurements, we qualitatively and quantitatively verify with real and simulated results that temporal resolution is most important for demultiplexing shadows. We anticipate future work to extend the analysis in this paper to SPAD arrays for real-time NLOS imaging.", + "bbox": [ + 496, + 617, + 893, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 829, + 668, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "AD and AV are supported by NSF Expeditions Award #IIS-1730574 and NSF CAREER Award #IIS-1652633. CH was supported by a Draper Scholarship.", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9199", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Fadel Adib and Dina Katabi. See through walls with wifi! In Proceedings of the ACM SIGCOMM 2013 conference on SIGCOMM, pages 75-86, 2013. 2", + "[2] Byeongjoo Ahn, Akshat Dave, Ashok Veeraraghavan, Ioannis Gkioulekas, and Aswin C Sankaranarayanan. Convolutional approximations to the general non-line-of-sight imaging operator. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 7889-7899, 2019. 2", + "[3] Victor Arellano, Diego Gutierrez, and Adrian Jarabo. Fast back-projection for non-line of sight reconstruction. 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IEEE Open Journal of the Solid-State Circuits Society, 2:3-11, 2021. 2" + ], + "bbox": [ + 501, + 92, + 890, + 428 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9201", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Role of Transients in Two-Bounce Non-Line-of-Sight Imaging/dd8b3d32-1f20-46bb-9a36-d731b9d46ed2_model.json b/2023/Role of Transients in Two-Bounce Non-Line-of-Sight Imaging/dd8b3d32-1f20-46bb-9a36-d731b9d46ed2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..95e175206f909fe3e3dd9028c4c5342a587b788d --- /dev/null +++ b/2023/Role of Transients in Two-Bounce Non-Line-of-Sight Imaging/dd8b3d32-1f20-46bb-9a36-d731b9d46ed2_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.176, + 0.131, + 0.797, + 0.155 + ], + "angle": 0, + "content": "Role of Transients in Two-Bounce Non-Line-of-Sight Imaging" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.18, + 0.721, + 0.216 + ], + "angle": 0, + "content": "Siddharth Somasundaram1 Akshit Dave2 Connor Henley1 Ashok Veeraraghavan2 Ramesh Raskar1" + }, + { + "type": "text", + "bbox": [ + 0.249, + 0.217, + 0.723, + 0.236 + ], + "angle": 0, + "content": "1Massachusetts Institute of Technology 2Rice University" + }, + { + "type": "text", + "bbox": [ + 0.229, + 0.237, + 0.737, + 0.253 + ], + "angle": 0, + "content": "{sidsoma,co24401,raskar}@mit.edu，{akshat,vashok}@rice.edu" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.287, + 0.277, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.477, + 0.25, + 0.489 + ], + "angle": 0, + "content": "(a) Two-Bounce NLOS" + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.287, + 0.449, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.294, + 0.477, + 0.433, + 0.491 + ], + "angle": 0, + "content": "(b) Application Settings" + }, + { + "type": "image", + "bbox": [ + 0.453, + 0.287, + 0.603, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.458, + 0.477, + 0.595, + 0.491 + ], + "angle": 0, + "content": "(c) Experimental Setup" + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.287, + 0.882, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.477, + 0.866, + 0.49 + ], + "angle": 0, + "content": "(d) Reconstruction with 10 Measurements" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.501, + 0.894, + 0.572 + ], + "angle": 0, + "content": "Figure 1. Two-bounce Transient NLOS Imaging. (a) We propose using two-bounce transients for NLOS imaging. Two-bounce signals capture information about the shadows in a scene, and use of transient information can reduce the number of measurements needed for reconstruction by using multiplexed illumination. (b) Our work can be applicable in many scenarios, such as tunnels, corridors, streets, and forests. (c)-(d) We experimentally validate the use of two-bounce transients on real objects. We show that time-of-flight information enables more robust reconstructions of occluded objects while using fewer measurements." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.584, + 0.314, + 0.6 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.473, + 0.884 + ], + "angle": 0, + "content": "The goal of non-line-of-sight (NLOS) imaging is to image objects occluded from the camera's field of view using multiply scattered light. Recent works have demonstrated the feasibility of two-bounce (2B) NLOS imaging by scanning a laser and measuring cast shadows of occluded objects in scenes with two relay surfaces. In this work, we study the role of time-of-flight (ToF) measurements, i.e. transients, in 2B-NLOS under multiplexed illumination. Specifically, we study how ToF information can reduce the number of measurements and spatial resolution needed for shape reconstruction. We present our findings with respect to trade-offs in (1) temporal resolution, (2) spatial resolution, and (3) number of image captures by studying SNR and recoverability as functions of system parameters. This leads to a formal definition of the mathematical constraints for 2B lidar. We believe that our work lays an analytical groundwork for design of future NLOS imaging systems, especially as ToF sensors become increasingly ubiquitous." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.584, + 0.631, + 0.6 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.836 + ], + "angle": 0, + "content": "Non-line-of-sight (NLOS) imaging aims to reconstruct objects occluded from direct line of sight and has the potential to be transformative in numerous applications across autonomous driving, search and rescue, and non-invasive medical imaging [24]. The key approach is to measure light that has undergone multiple surface scattering events and computationally invert these measurements to estimate hidden geometries. Recent work used two-bounce light, as shown in Fig. 2a, to reconstruct high quality shapes behind occluders [15]. The key idea is that two-bounce light captures information about the shadows of the occluded object. By scanning the laser source at different points 1 on a relay surface and measuring multiple shadow images, it is possible to reconstruct the hidden object by computing the visual hull [20] of the measured shadows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Benefits of Two-Bounce Two-bounce (2B) light can be captured using two relay surfaces on opposite sides of the hidden scene (Fig. 1a). This can occur in a variety of real-world settings such as tunnels, hallways, streets, and clit" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9192" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.268, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.204, + 0.253, + 0.216 + ], + "angle": 0, + "content": "(a) Two-Bounce NLOS Imaging" + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.089, + 0.468, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.297, + 0.204, + 0.459, + 0.215 + ], + "angle": 0, + "content": "(b) Two-Bounce Transient NLOS" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.47, + 0.31 + ], + "angle": 0, + "content": "Figure 2. Two-Bounce NLOS Imaging. (a) Two-bounce NLOS imaging performs 3D reconstruction by using information contained in the shadows of the hidden object when illuminated by one virtual source 1 at a time. (b) In this work, we study the benefits of using transient information for two-bounce NLOS imaging under the presence of multiplexed illumination." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.468, + 0.505 + ], + "angle": 0, + "content": "tered environments like forests (Fig. 1b). For example, imagine an autonomous vehicle in a tunnel being able to see ahead of the car in front of it by using two-bounce signals from the sides of the tunnel. Two-bounce light also helps alleviate the signal-to-noise ratio (SNR) issue in 3B-NLOS imaging, since 3B signals experience significant signal attenuation at each surface scatter event. Furthermore, 2B light captures information about the cast shadows of the hidden object instead of reflectance, as in the 3B case. As a result, the SNR of 2B signals is independent of the object's albedo and can therefore robustly image darker objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.468, + 0.707 + ], + "angle": 0, + "content": "Contributions In this work, we propose using two-bounce transients for NLOS imaging to enable the use of multiplexed illumination. 3B-NLOS transient imaging systems have been analyzed previously, but we believe we are the first to analyze the use of multiplexed illumination and transient measurements for 2B-NLOS (Fig. 2b). Our key insight is that multiplexed illumination enables measurement of occluded objects with fewer image captures, and 2B transients enable demultiplexing shadows, as shown in Fig. 3. The robust SNR and promise of few-shot capture afforded by 2B transients makes the idea an important direction for few-shot NLOS imaging in general environments. We summarize our contributions below." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.722, + 0.468, + 0.752 + ], + "angle": 0, + "content": "- Model: We present new insights into the algebraic formulations of two-bounce lidar for NLOS imaging." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.767, + 0.468, + 0.84 + ], + "angle": 0, + "content": "- Analysis: We analyze tradeoffs with spatial resolution, temporal resolution, and number of image captures by using quantitative metrics such as SNR and recoverability, as well as qualitative validation from real and simulated results." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.722, + 0.468, + 0.84 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Although we envision the ideas introduced here to inspire future works in single-shot NLOS imaging, we do not claim this as a contribution in this paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Scope of This Work All data used for this work is from simulation and a single-pixel SPAD sensor. We do not physically realize few-shot results in this paper due to limited availability of high-resolution SPAD arrays presently. Instead, we emulate SPAD array measurements by scanning a single-pixel SPAD across the field of view and and emulate multiplexed illumination by scanning a laser spot, acquiring individual transient images, and summing the images in post-processing. These measurements, however, are more conducive to our goal of performing analysis that explores the landscape of possibilities in NLOS imaging with advances in ToF sensors. We believe that the ideas and analysis introduced in this work will be increasingly relevant as SPAD array technology matures [19,26,44]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.317, + 0.642, + 0.332 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.341, + 0.715, + 0.358 + ], + "angle": 0, + "content": "Non-Line-of-Sight Imaging" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.576 + ], + "angle": 0, + "content": "ToF Methods: The non-line-of-sight imaging (NLOS) problem aims to see around a corner by measuring light reflected off intermediary surfaces. A large body of work models the response of a hidden scene to a temporal pulse of light and generally perform a variant of ellipsoidal tomography or solve a linear inverse problem [3, 5, 11, 12, 18, 39]. The temporal profiles can probe features of the hidden space, such as Fermat paths [42], scene impulse response [23], and individual voxels [28]. Other works derive efficient algorithms using a confocal setup [2, 22, 27] and data-driven techniques [8]. NLOS has also been demonstrated with amplitude modulated continuous wave (AMCW) ToF by exploiting sparsity and fitting measurements to a Lambertian reflectance model [13, 16]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Other Active Methods: Chen et al. use steady-state (i.e. time-integrated) intensity information by leveraging partial directionality of diffuse reflectors [7]. Radio wavelengths can also be used to image through walls and/or around them [1, 32, 43]. There has also been significant progress in exploiting speckle correlations [9, 17, 25, 34] and synthetic wave holography [40, 41] for NLOS imaging. Henley et al. demonstrate the use of two-bounce light (i.e. shadows) for NLOS using intensity sensors [15]. An extension of this work uses ToF constraints on two-bounce pathlengths to isolate shadows from ambient background and higher-order inter-reflections [14]. However multiplexing was not used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Passive Methods: Passive methods make use of optical information already present in the scene without an active source. Many passive approaches exploit polarization cues [10,36], ambient thermal light [21,36], shadows [35], multiview reflections [38], and neural networks [33,37] to reconstruct or make inferences about the scene outside the camera's field of view. Occlusion-assisted imaging makes use of information present at sharp discontinuities in LOS and NLOS scenes by turning them into virtual pinholes [4,30] or" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9193" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.105, + 0.089, + 0.868, + 0.273 + ], + "angle": 0, + "content": "
NLOS Imaging DomainKey ComponentsKey Features
Assisting SurfacesSensor TypeLight SourceNumber of CapturesRecovered DimensionsSignal Quality
Passive Occlusion-Aided [4,31,33]Relay Wall/FloorIntensityPassiveLow2DLow (strong background)
Edge Occluders
Three-Bounce Transient [18,27,30,42]Relay Wall/FloorToFActive (Scan)High3DMedium (3-bounce)
Edge Occluders
Two-Bounce Transient (Ours)Two LOS WallsToFActive (Flash)Low3DHigh (2-bounce)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.281, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Table 1. Comparison of NLOS Methods. Passive approaches require fewer measurements but can either recover up to two dimensions or are strongly affected by ambient noise. Works exploiting three-bounce light paths demonstrate 3D imaging around the corner but require a bounce on the hidden surface, reducing the signal quality. We analyze exploiting two-bounce transients for NLOS imaging." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.35, + 0.471, + 0.381 + ], + "angle": 0, + "content": "virtual pinspecks [31]. Intensity-only methods are difficult to scale to scenarios with arbitrary lighting conditions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.405, + 0.373, + 0.423 + ], + "angle": 0, + "content": "3. Forward and Adjoint Operators" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.438, + 0.229, + 0.455 + ], + "angle": 0, + "content": "3.1. Problem Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.473, + 0.787 + ], + "angle": 0, + "content": "We first introduce terminology and notation for our problem formulation. The object of interest lies behind an occluder and is flanked on two sides by planar Lambertian relay surfaces. Without loss of generality, the right wall is the illumination wall \\(\\mathcal{L}\\) and the left wall is the observation wall \\(\\mathcal{O}\\). Light incident on the illumination wall at a point \\(l\\) is a virtual source. Each virtual source diffusely radiates light towards the observation wall. Light will arrive at a virtual detector \\(s\\) from \\(l\\) if the object doesn't lie along the ray connecting \\(s\\) and \\(l\\), as shown in Fig. 2a. If the object obstructs this ray, \\(s\\) is said to lie in the shadow of the object. We assume that every virtual source and virtual detector is visible to the laser and camera field of view, respectively. The hidden scene is discretized into a voxel grid described by a binary occupancy (or transparency) function. This implicitly assumes that we are reconstructing opaque surfaces. We neglect the effect of higher order bounces (e.g. interreflections, 3B light) because SPADs can temporally gate out the longer ToF of 3B light. Furthermore, the intensity of higher order bounces will be much lower than that of two-bounce light because all surfaces are assumed to be diffuse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We denote light transients as ToF measurements for light that arrives at the virtual detector and shadow transients as ToF measurements for light that didn't arrive at the virtual detector because of the object's shadow. Both of these are two-bounce transients. We show that modeling the problem in terms of shadow transients enables reconstruction of the hidden objects shape by solving a linear inverse problem." + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.348, + 0.845, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.545, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Figure 3. Time-of-Flight Information for Demultiplexing Shadows. Assume the point \\( s \\) lies in shadow. When using multiplexed illumination, there exists an ambiguity as to whether \\( s \\) lies in the shadow of \\( l_1 \\), \\( l_2 \\), or both. However, the paths \\( L - l_1 - s - C \\) and \\( L - l_2 - s - C \\) have different pathlengths, suggesting the usefulness of ToF information for demultiplexing shadows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.715, + 0.667 + ], + "angle": 0, + "content": "3.2. Linear Forward Model" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.674, + 0.892, + 0.706 + ], + "angle": 0, + "content": "Light Transients Consider the case where the occluded scene is empty. The measured transient is then given by" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.71, + 0.892, + 0.744 + ], + "angle": 0, + "content": "\\[\ni _ {0} (t; \\mathbf {s}) = \\alpha \\iint_ {\\mathcal {L}} \\frac {\\delta (\\| \\mathbf {l} - \\mathbf {g} \\| + \\| \\mathbf {l} - \\mathbf {s} \\| - c t)}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.894, + 0.84 + ], + "angle": 0, + "content": "where \\(\\mathbf{g}\\) is the location of the laser, \\(c\\) is the speed of light, and \\(\\alpha\\) is the intensity of the laser. We refer to \\(i_0\\) as the empty transient. For simplicity, we ignore \\(\\alpha\\) for the rest of the derivations in this section and assume that the length between the virtual detector and camera is calibrated or known. The numerator of the integrand" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.847, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\ni (t; \\mathbf {s}, \\mathbf {l}) = \\delta (\\| \\mathbf {l} - \\mathbf {g} \\| + \\| \\mathbf {l} - \\mathbf {s} \\| - c t) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "describes the equation of an ellipsoid, with foci at \\(\\mathbf{g}\\) and s and major axis length \\(ct\\). When an object is present in the" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9194" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.09, + 0.46, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.164, + 0.47, + 0.233 + ], + "angle": 0, + "content": "Figure 4. Light and Shadow Transients. Three spacetime curves are depicted. (left) Empty transient \\( i_0 \\) with no hidden object, (middle) light transient \\( i_l \\) with an object, and (right) shadow transient \\( i_s = i_0 - i_l \\). Switching from light transients \\( i_l \\) to shadow transients \\( i_s \\) enables derivation of a linear forward model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.262, + 0.445, + 0.277 + ], + "angle": 0, + "content": "occluded scene, the measured light transient is given by" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.289, + 0.469, + 0.322 + ], + "angle": 0, + "content": "\\[\ni _ {l} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} V _ {\\mathbf {s}, \\mathbf {l}} \\cdot \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.333, + 0.361, + 0.349 + ], + "angle": 0, + "content": "where \\(V_{\\mathbf{s},1}\\) is the visibility between s and l." + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.354, + 0.469, + 0.388 + ], + "angle": 0, + "content": "\\[\nV _ {\\mathbf {s}, \\mathbf {l}} = \\exp \\left(\\oint_ {\\mathbf {l}} ^ {\\mathbf {s}} \\ln \\left(f _ {t} (\\mathbf {x})\\right) d \\mathbf {x}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.399, + 0.469, + 0.445 + ], + "angle": 0, + "content": "where Eq. (4) computes the product integral along the line connecting \\(\\mathbf{l}\\) and \\(\\mathbf{s}\\) and \\(f_{t}(\\mathbf{x})\\in \\{0,1\\}\\) is the transparency function of voxel \\(\\mathbf{x}\\) in the occluded region." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.452, + 0.469, + 0.528 + ], + "angle": 0, + "content": "Shadow Transients The non-linearity of Eq. (4) makes model inversion challenging with light transients. Casting the formulation from light space-time to shadow space-time enables a linear formulation of the problem. A shadow transient at \\(s\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.541, + 0.469, + 0.557 + ], + "angle": 0, + "content": "\\[\ni _ {s} (t; \\mathbf {s}) = i _ {0} (t; \\mathbf {s}) - i _ {l} (t; \\mathbf {s}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.57, + 0.469, + 0.646 + ], + "angle": 0, + "content": "Fig. 4 illustrates the difference between light transients and shadow transients. Shadow transients directly probe voxel occupancy, whereas light transients probe for voxel transparency. For example, if the occluded scene is empty except for voxel \\(\\mathbf{x}\\), the shadow transient is given by" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.658, + 0.469, + 0.691 + ], + "angle": 0, + "content": "\\[\ni _ {s} (t; \\mathbf {s}, \\mathbf {x}) = \\frac {\\delta (\\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {g} \\| + \\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {s} \\| - c t)}{\\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {s} \\| ^ {2}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.703, + 0.468, + 0.749 + ], + "angle": 0, + "content": "where \\(\\mathbf{l}(\\mathbf{x},\\mathbf{s})\\) is a point on the illumination wall that lies along the ray connecting \\(\\mathbf{x}\\) and \\(\\mathbf{s}\\). If the wall doesn't intersect this ray, \\(i_s(t;\\mathbf{x},\\mathbf{s}) = 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.756, + 0.469, + 0.8 + ], + "angle": 0, + "content": "Linear Relaxation Now, consider the general case where a single opaque object lies in the hidden scene. We can describe the shadow transient as" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.81, + 0.469, + 0.844 + ], + "angle": 0, + "content": "\\[\ni _ {s} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} O _ {\\mathbf {s}, \\mathbf {l}} \\cdot \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.9 + ], + "angle": 0, + "content": "where \\( O_{\\mathbf{s},1} \\in \\{0,1\\} \\) is the occlusion function (denotes if the ray between 1 and s is occluded). It can be expressed as the indicator function" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.085, + 0.891, + 0.16 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} O _ {\\mathbf {s}, \\mathrm {l}} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\oint_ {\\mathrm {l}} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x} > 0 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8} \\\\ \\approx \\oint_ {1} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.171, + 0.892, + 0.276 + ], + "angle": 0, + "content": "where \\( f_{o}(\\mathbf{x}) \\) is the voxel occupancy function of the hidden scene. The linear relaxation in Eq. (8) is possible because NLOS reconstructions typically only consider ToF information, but not radiometric information. The above formulation will preserve the structure of the streak images in spacetime, even if the intensities are overestimated. Combining Eq. (5), (7), and (8), we obtain" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.287, + 0.891, + 0.321 + ], + "angle": 0, + "content": "\\[\ni _ {0} (t; \\mathbf {s}) - i _ {l} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} \\cdot \\left(\\oint_ {\\mathbf {l}} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x}\\right) d \\mathbf {l}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.891, + 0.362 + ], + "angle": 0, + "content": "where we solve for \\( f_{o}(\\mathbf{x}) \\). We can estimate \\( i_0 \\) from the scene geometry and \\( i_l \\) is the measured transient." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.366, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Discrete Beam Illumination Discretizing \\(\\mathcal{L}\\) as \\(K\\) discrete laser spots and the hidden space into a voxel grid, we can write Eq. (9) as" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.423, + 0.901, + 0.48 + ], + "angle": 0, + "content": "\\[\ni _ {s} [ t; \\mathbf {s} ] = \\sum_ {k = 1} ^ {K} \\frac {\\delta [ \\| \\mathbf {l} _ {k} - \\mathbf {g} \\| + \\| \\mathbf {l} _ {k} - \\mathbf {s} \\| - c t ]}{\\| \\mathbf {l} _ {k} - \\mathbf {s} \\| ^ {2}} \\cdot \\left(\\sum_ {\\mathbf {x} \\in \\mathcal {P} _ {\\mathbf {l} _ {k}, \\mathbf {s}}} f _ {o} [ \\mathbf {x} ]\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.481, + 0.89, + 0.511 + ], + "angle": 0, + "content": "where \\(\\mathcal{P}_{1,\\mathrm{s}}\\) denotes the set of voxels lying along the path between 1 and s. Eq. (10) can be expressed in matrix form" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.524, + 0.891, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {s} = \\mathbf {P B f} = \\mathbf {A f}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.552, + 0.892, + 0.656 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}_s\\in \\mathbb{R}^{n_u n_v n_t}\\) is the vectorized space-time measurements, \\(\\mathbf{f}\\in \\mathbb{R}^{n_x n_y n_z}\\) is the voxel occupancies, and \\(\\mathbf{A}\\in \\mathbb{R}^{n_u n_v n_t\\times n_x n_y n_z}\\) is the measurement operator mapping voxel occupancies to space-time measurements. \\(n_u\\) and \\(n_v\\) are the number of pixels along the \\(u\\) and \\(v\\) direction, and \\(n_t\\) is the number of timing bins. \\(n_x,n_y,\\) and \\(n_z\\) are the number of voxels in the \\(x,y,\\) and \\(z\\) directions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.657, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(\\mathbf{P}\\) and \\(\\mathbf{B}\\) model the temporal and spatial relationships, respectively, between virtual sources, virtual detectors, and voxels. \\(\\mathbf{P} \\in \\mathbb{R}^{n_u n_v n_t \\times n_u n_v K}\\) is a block diagonal matrix, with the column space of the \\(i\\)th block \\(\\mathbf{P}^i \\in \\mathbb{R}^{n_t \\times K}\\) containing the corresponding \\(\\delta(\\cdot)\\) functions from Eq. (2) for virtual detector \\(\\mathbf{s}_i\\) and all \\(K\\) virtual sources. \\(\\mathbf{B} \\in \\mathbb{R}^{n_u n_v K \\times n_x n_y n_z}\\) is composed of \\(n_u n_v\\) vertical sub-blocks. Each entry \\(\\mathbf{B}_{kj}^i \\in \\{0,1\\}\\) of the \\(i\\)th sub-block \\(\\mathbf{B}^i \\in \\mathbb{R}^{K \\times n_x n_y n_z}\\) of sub-block \\(i\\) indicates whether voxel \\(j\\) lies along the line connecting virtual detector \\(\\mathbf{s}_i\\) and virtual source \\(\\mathbf{l}_k\\). The multiplication \\(\\mathbf{Bf}\\) performs the line integral in Eq. (8). The \\(k\\)th column vector of \\(\\mathbf{P}\\) is the space-time impulse response (STIR) to the \\(k\\)th illumination source when the hidden scene is completely occupied (note that we are dealing with shadow transients, not light transients). The \\(i\\)th column of \\(\\mathbf{A}\\) forms the expected space-time measurements" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9195" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "if only the \\(i\\)th voxel is occupied (i.e. the STIR to a single voxel). We neglect the \\(r^2\\) falloff term in our reconstructions. Additional explanation of the A matrix is provided in the supplementary. The linear model in Eq. (11) resembles that of 3B-bounce NLOS, where \\(\\mathbf{A}\\) is a measurement operator that maps voxels \\(\\mathbf{f}\\) to measurements \\(\\mathbf{I}\\). However, in 3B-NLOS, the information is encoded into the reflectance of the object, whereas in 2B-NLOS, the information is encoded into the shadows. Therefore, the former is linear with respects to light transients, and the latter is linear with respect to shadow transients." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.27, + 0.317, + 0.287 + ], + "angle": 0, + "content": "3.3. Reconstruction Algorithm" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.295, + 0.47, + 0.31 + ], + "angle": 0, + "content": "Reconstruction of \\(\\mathbf{f}\\) can be performed by backprojection" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.318, + 0.47, + 0.337 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {b p} = \\mathbf {A} ^ {\\top} \\mathbf {I} _ {s}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.347, + 0.471, + 0.379 + ], + "angle": 0, + "content": "Backprojection produces a low-frequency reconstruction of \\(\\mathbf{f}\\). In practice, filtering \\(\\mathbf{f}_{bp}\\) with a Laplacian filter" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.391, + 0.47, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {f b p} = \\left(\\frac {\\partial^ {2}}{\\partial x ^ {2}} + \\frac {\\partial^ {2}}{\\partial y ^ {2}} + \\frac {\\partial^ {2}}{\\partial z ^ {2}}\\right) \\mathbf {f} _ {b p} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.47, + 0.595 + ], + "angle": 0, + "content": "has been shown to yield reasonably good results in ellipsoidal tomography in 3-bounce NLOS and line-based tomography in medical imaging. Our linear formulation also enables reconstruction with priors. We recognize that these optimization-based methods would improve reconstruction over unfiltered backprojection, which is equivalent to a low-frequency version of voxel carving in our setup. However, we restrict our focus to unfiltered backprojection because of its convenient relationship with the Gram matrix, which enables further analysis of our method in Sec. 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.612, + 0.273, + 0.629 + ], + "angle": 0, + "content": "4. Design and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.79 + ], + "angle": 0, + "content": "In this section, we analyze how the performance of the proposed two-bounce transient system varies with system parameters and the geometry of LOS relay surfaces. We also analyze the impact of temporal resolution, spatial resolution, and number of measurements on recoverability. The amount of multiplexing in the scene is inversely related to the number of measurements. For example, if 60 laser spots are used and 15 measurements are captured, then each image contains 4 multiplexed shadows. We use SNR, coherence, and FWHM of the PSF to quantify performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.267, + 0.817 + ], + "angle": 0, + "content": "4.1. Voxel SNR Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We quantify the noise characteristics of the measured shadow two-bounce transients using per-voxel SNR. Consider the case where only voxel \\(\\mathbf{x}\\) is occupied in the hidden region. We derive the SNR of the number of \"shadow\" photons received in the measured shadow transient \\(\\mathbf{I}_s^{\\mathbf{x}}\\). In vector" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.09, + 0.878, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.231, + 0.894, + 0.342 + ], + "angle": 0, + "content": "Figure 5. SNR Analysis. The goal of this analysis is to determine how scene geometry affects the SNR of the two-bounce measurement at each voxel in the hidden scene. The first two cases consider the orientations of the relay surfaces, and the third considers the field of view of the camera. SNR is highest in the middle of the hidden scene for parallel surfaces, orienting the walls closer together increases SNR due to reduced \\( r^2 \\) falloff, and SNR is highest closer to the virtual detectors for small FOV cameras." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.366, + 0.893, + 0.397 + ], + "angle": 0, + "content": "form, the occupancy function can be described as \\(\\delta^{\\mathbf{x}}\\). From Eq. (11), the shadow transient is given by" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.405, + 0.891, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {s} ^ {\\mathbf {x}} = \\mathbf {A} \\delta^ {\\mathbf {x}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.893, + 0.492 + ], + "angle": 0, + "content": "and the light transients measured by the SPAD sensor are given by \\(\\mathbf{I}_l^{\\mathbf{x}}\\). For this analysis, we account for \\(r^2\\) falloff because it is a physically accurate phenomenon that impacts SNR. From Eq. (5)," + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.499, + 0.891, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} _ {l} ^ {\\mathbf {x}} = \\mathbf {I} _ {0} - \\mathbf {A} \\delta^ {\\mathbf {x}} \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.631 + ], + "angle": 0, + "content": "where \\(\\mathbf{I}_0\\) is the empty transient and assumed to be calibrated. Assuming no SPAD pile-up distortion, the number of photons arriving at the sensor for each time bin of \\(\\mathbf{I}_l^{\\mathbf{x}}\\) follows an independent Poisson distribution [29]. Thus, the total number of photons \\(P^{\\mathbf{x}}\\) measured follows a Poisson distribution with the rate parameter being the sum of all the photon counts for all time bins for all pixels." + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.638, + 0.891, + 0.656 + ], + "angle": 0, + "content": "\\[\nP ^ {\\mathbf {x}} \\sim \\operatorname {P o i s s o n} \\left(\\mathbf {1} ^ {T} \\left(\\mathbf {I} _ {0} - \\mathbf {A} \\delta^ {\\mathbf {x}}\\right)\\right) \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.893, + 0.71 + ], + "angle": 0, + "content": "where \\(\\mathbf{1} \\in \\mathbb{R}^{n_u n_v n_t}\\) is the one vector. Using the fact that SNR of a Poisson distribution is \\(\\mu / \\sigma = \\sqrt{\\lambda}\\) with rate parameter \\(\\lambda\\), the per-voxel SNR \\(S^{\\mathbf{x}}\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.719, + 0.891, + 0.743 + ], + "angle": 0, + "content": "\\[\nS ^ {\\mathbf {x}} = \\sqrt {\\mathbf {1} ^ {T} \\left(\\mathbf {I} _ {0} - \\mathbf {A} \\boldsymbol {\\delta} ^ {\\mathbf {x}}\\right)} \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "The per-voxel SNR is plotted in Fig. 5 for three different scenarios. The first two scenarios deal with the orientation of the walls, and the third considers the field of view of the camera. In Fig. 5a, we can see that the SNR is higher for center voxels, as more rays connecting the illumination wall and observation wall pass through the center voxels. When the relay walls are oriented towards each other (Fig. 5b), the SNR increases due to reduced \\( r^2 \\) falloff. When the camera's field of view is small compared to the laser (Fig. 5c), regions closer to the observation wall have the highest SNR." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9196" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.1, + 0.437, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.27, + 0.473, + 0.327 + ], + "angle": 0, + "content": "Figure 6. Spatially Varying PSF. In two-bounce lidar, the PSF has a double cone shape. The orientation of the double cone varies strongly as a function of the orientation and length of the relay surfaces (i.e. the virtual apertures) and the voxel position." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.352, + 0.295, + 0.369 + ], + "angle": 0, + "content": "4.2. Recoverability Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.497 + ], + "angle": 0, + "content": "Resolution We now study the resolution limits of our method. In particular, we consider two key metrics in our measurement operator: mutual coherence and full width at half maximum (FWHM) of the PSF. We are interested in how (1) temporal resolution, (2) spatial resolution \\( N \\), and (3) number of measurements \\( M \\) impact each of our metrics. From Eq. (12), we know that the backprojected occupancy can be obtained from the occupancy function by" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.508, + 0.47, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {b p} = \\left(\\mathbf {A} ^ {\\top} \\mathbf {A}\\right) \\mathbf {f}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.614 + ], + "angle": 0, + "content": "where \\(\\mathbf{G} = \\mathbf{A}^{\\top}\\mathbf{A}\\) is the Gram matrix. We can interpret the columns (or rows) of the Gram matrix to be the spatially varying point spread function (PSF) of the imaging system, as shown in Fig. 6. Each column \\(\\mathbf{G}_i\\) describes how a voxel \\(\\mathbf{x}_i\\) is blurred during backprojection reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.473, + 0.902 + ], + "angle": 0, + "content": "We can see the effect of different imaging parameters on the PSF in Fig. 7, where we sweep different values of (1) \\(M\\) and (2) \\(N\\). In particular, we note that the lobes of the PSF are suppressed when using temporal information, even with low spatial resolution and few number of image measurements. When using no temporal information, the PSF is still roughly centered at the correct location, but has large FWHM. The sharpness of the PSF when using temporal information indicates that it is better suited to applications that require finer voxel resolution with few-shot capture. In case (1) without transients, we see that the FWHM of the PSF is large along both the \\(x\\) and \\(y\\) direction for small values of \\(M\\). As \\(M\\) approaches the number of illumination spots, the FWHM approaches the theoretical lower bound. In case (2), increased spatial resolution helps better localize the center of the PSF, but the FWHM does not improve. The transient cases are quite robust to both low number of measurements and low spatial resolution. Intuitively, higher values of \\(N\\) in the transient case slightly help accentuate the center voxel" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.878, + 0.108 + ], + "angle": 0, + "content": "by projecting more diverse rays through the center voxel." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.111, + 0.892, + 0.202 + ], + "angle": 0, + "content": "Mutual Coherence We wish to further quantify the impact of spatio-temporal resolution and number of measurements on the recoverability of the hidden scene. We know from compressive sensing theory that sparse recovery of the hidden scene is possible when the mutual coherence of \\(\\mathbf{A}\\) is sufficiently small. The mutual coherence is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.213, + 0.892, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\mu = \\max _ {1 \\leq i \\neq j \\leq n} \\frac {\\left| \\mathbf {A} _ {i} ^ {\\top} \\mathbf {A} _ {j} \\right|}{\\left| \\mathbf {A} _ {i} \\right| \\left| \\mathbf {A} _ {j} \\right|}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.893, + 0.469 + ], + "angle": 0, + "content": "Intuitively, the coherence measures the largest \"similarity\" or correlation between any two column vectors in measurement matrix \\(\\mathbf{A}\\) [6]. Physically, this quantifies how similar the STIRs of two different voxels are. If \\(\\mu = 1\\), then two voxels have the exact same STIR, which means that there exists an ambiguity as to which voxel resulted in a certain spatio-temporal response. Alternatively, \\(\\mu\\) can be defined as the maximum off-diagonal entry of the Gram matrix. Fig. 8 illustrates how the Gram matrix (and subsequently the mutual coherence) is affected by coarser timing resolutions. From compressive sensing theory, we know that a \\(K\\)-sparse scene can be recovered if \\(K \\leq 0.5(1 + 1 / \\mu)\\), which motivates our empirical analysis of the effect of spatial resolution and temporal resolution on \\(\\mu\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.893, + 0.742 + ], + "angle": 0, + "content": "From Fig. 9, we can see the impact that spatial and temporal resolution have on mutual coherence in a single-shot setup with multiplexed illumination. Consider a scene similar to that of Fig. 6, where the walls are \\(2\\mathrm{m}\\) apart, the walls are \\(3\\mathrm{m}\\) long, the axial distance to the walls is \\(2\\mathrm{m}\\), and the voxel resolution is discretized to \\(2\\mathrm{cm}\\). Increasing the spatial resolution at a fixed temporal resolution appears to have little to no effect on the mutual coherence. As Kadambi et al. also point out, improvements of coherence through higher spatial resolution are limited by the size of the virtual aperture (i.e. the wall) [16]. On the other hand, the difference between \\(100~\\mathrm{ps}\\) resolution and \\(10~\\mathrm{ps}\\) resolution reduces the coherence from 0.9 to 0.3 for a fixed spatial resolution. Any timing resolution coarser than \\(\\sim 120\\) ps results in a coherence of 1 for multiplexed measurements because pathlength differences for different shadows are no longer resolvable. This analysis motivates the importance of temporal resolution when using multiplexed illumination." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.734, + 0.772 + ], + "angle": 0, + "content": "5. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We scan a single-pixel SPAD across the field of view on the left wall to mimic the output of a SPAD array. We scan a single laser spot across the right wall, and sum up the corresponding transient images in post-processing to mimic the effect of multiplexing. Further details are provided in the supplementary. We first validate our model using simulated data in Fig. 10, where we demonstrate that we can localize four letters and reconstruct their 2D shape with just a single" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9197" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.498, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.091, + 0.892, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.353, + 0.894, + 0.409 + ], + "angle": 0, + "content": "Figure 7. PSF as a Function of Number of Measurements and Spatial Resolution. The PSF of the center voxel is shown in the transient and intensity-only case when multiplexed with 60 laser spots. (1) the number of pixels \\( N = 40 \\) are kept fixed with the number of measurements \\( M \\) being swept (left) and (2) \\( M = 10 \\) is kept fixed and \\( N \\) is swept (right). Transient measurements result in PSFs with narrower FWHMs, even with low spatial resolution and low number of measurements." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.434, + 0.456, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.628 + ], + "angle": 0, + "content": "Figure 8. Gram Matrix as a Function of Temporal Resolution. For a defined voxel resolution and fixed spatial resolution. The columns (or rows) of the Gram matrix form the spatially varying PSFs shown in Fig. 6. The off-diagonal streaks describe the coherence between different voxels. As expected, higher temporal resolution decreases the coherence of the Gram matrix, which increases the likelihood of guaranteed sparse recovery." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.902 + ], + "angle": 0, + "content": "capture. We render \\( i_{o} \\) and \\( i_{l} \\) to obtain a noiseless version of the shadow transient for this experiment. Then, we reconstruct the shapes of real mannequins and must estimate \\( i_{0} \\). Fig. 11 shows that ToF measurements provide a noticeable improvement in image reconstruction. When there's no multiplexing (i.e., the number of laser spots is the same as number of measurements), the intensity-based method is similar to the ToF-based method. However, in the intensity-only case, the object becomes increasingly blurry until it is no longer visible as the amount of multiplexing increases. In the ToF case for single-shot, we can see a blurry image roughly localized where the center of the mannequin is as well as some high-frequency detail. Furthermore, the top view of the ToF reconstructions show that the high-frequency shape of the arms can be reconstructed even with multiplexed illumination, indicating the promise of single" + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.435, + 0.825, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.768 + ], + "angle": 0, + "content": "Figure 9. Tradeoffs Between Spatial Resolution and Temporal Resolution. We quantify the tradeoff using mutual coherence. We use the same setup as Fig. 6, but the walls have length \\(3\\mathrm{m}\\), the walls are space \\(2\\mathrm{m}\\) apart, and the distance to the walls is \\(2\\mathrm{m}\\). We discretize the voxel resolution to \\(2\\mathrm{cm}(\\sim 67\\mathrm{ps})\\). The bottom right of the figure, where spatial and temporal resolution are highest is where mutual coherence is the lowest. For a fixed temporal resolution, improvements in coherence quickly plateau. Improvements in temporal resolution dominate improvements in spatial resolution when reducing coherence, suggesting the importance of ToF for demultiplexing illumination in two-bounce NLOS imaging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "shot capture with two-bounce ToF information. Fig. 12 shows that poorer temporal resolution results in aliasing artifacts (repeated arms and legs), whereas the rough shape of the object can still be seen with lower spatial resolution. Finally, we compare our method to the probabilistic voxel carving method used in [15] in Fig. 13. Voxel carving results in sharper reconstructions than backprojection." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "9198" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.089, + 0.459, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.271, + 0.473, + 0.355 + ], + "angle": 0, + "content": "Figure 10. Single-Shot Localization. We obtain single-shot reconstructions of the \"N\", \"L\", \"O\", and \"S\" letters in the hidden scene with and without transient information. We see that using transient information, we are able to effectively localize the hidden object and even get a sharp outline of the letters, demonstrating the promise of single-shot capture with two-bounce transients." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.392, + 0.46, + 0.652 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.667, + 0.473, + 0.807 + ], + "angle": 0, + "content": "Figure 11. Transients Enable Scene Recovery from Multiplexed Illumination. We perform backprojection of measurements with varying levels of multiplexing. Plotted in the top two rows are \\( x \\) slices of the reconstructed volume. Under no multiplexing (right), intensity is sufficient to carve the shadow along detected pixel. But reconstruction quality sharply deteriorates as we move towards the multiplexing regime (left). When measuring with transients, time-of-flight information allows us to disambiguate between different shadows and recover a rough silhouette of the object even with just a single measurement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "However, our method can be improved by filtering or incorporating priors, and is also generalizable to multiplexed illumination by utilizing ToF information." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.093, + 0.852, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.289, + 0.895, + 0.348 + ], + "angle": 0, + "content": "Figure 12. Spatial Resolution vs. Timing Resolution. We plot reconstructions with different spatio-temporal resolutions. Lower timing resolution results in aliasing artifacts (i.e. repeated arms and legs). Lower spatial resolution introduces hole artifacts." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.359, + 0.88, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.51, + 0.895, + 0.568 + ], + "angle": 0, + "content": "Figure 13. Scanning Baseline Comparison. We compare to the voxel carving method used in [15] (a) before and (b) after thresholding when scanning 1 laser spot. Our method is more general, but voxel carving yields sharper results with laser scanning." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.592, + 0.614, + 0.608 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.895, + 0.816 + ], + "angle": 0, + "content": "In this paper, we introduced the use of two-bounce transients for NLOS imaging. Compared to 3B-NLOS, 2B-NLOS enables more robust imaging of occluded objects in the presence of scenes with arbitrary lighting conditions and low albedo objects. Transient 2B-NLOS is promising for few-shot capture of occluded objects by using multiplexed illumination, especially as SPAD array technology matures. When comparing tradeoffs in temporal resolution, spatial resolution, and number of measurements, we qualitatively and quantitatively verify with real and simulated results that temporal resolution is most important for demultiplexing shadows. We anticipate future work to extend the analysis in this paper to SPAD arrays for real-time NLOS imaging." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.669, + 0.848 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "AD and AV are supported by NSF Expeditions Award #IIS-1730574 and NSF CAREER Award #IIS-1652633. CH was supported by a Draper Scholarship." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9199" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.469, + 0.158 + ], + "angle": 0, + "content": "[1] Fadel Adib and Dina Katabi. See through walls with wifi! In Proceedings of the ACM SIGCOMM 2013 conference on SIGCOMM, pages 75-86, 2013. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.469, + 0.229 + ], + "angle": 0, + "content": "[2] Byeongjoo Ahn, Akshat Dave, Ashok Veeraraghavan, Ioannis Gkioulekas, and Aswin C Sankaranarayanan. Convolutional approximations to the general non-line-of-sight imaging operator. 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Two-bounce Transient NLOS Imaging. (a) We propose using two-bounce transients for NLOS imaging. Two-bounce signals capture information about the shadows in a scene, and use of transient information can reduce the number of measurements needed for reconstruction by using multiplexed illumination. (b) Our work can be applicable in many scenarios, such as tunnels, corridors, streets, and forests. (c)-(d) We experimentally validate the use of two-bounce transients on real objects. We show that time-of-flight information enables more robust reconstructions of occluded objects while using fewer measurements. + +![](images/c2882cdcc836f088655b91a89b156cfbbe64c7a1a2d68e2e585d6f6782bc3ac9.jpg) +(d) Reconstruction with 10 Measurements + +# Abstract + +The goal of non-line-of-sight (NLOS) imaging is to image objects occluded from the camera's field of view using multiply scattered light. Recent works have demonstrated the feasibility of two-bounce (2B) NLOS imaging by scanning a laser and measuring cast shadows of occluded objects in scenes with two relay surfaces. In this work, we study the role of time-of-flight (ToF) measurements, i.e. transients, in 2B-NLOS under multiplexed illumination. Specifically, we study how ToF information can reduce the number of measurements and spatial resolution needed for shape reconstruction. We present our findings with respect to trade-offs in (1) temporal resolution, (2) spatial resolution, and (3) number of image captures by studying SNR and recoverability as functions of system parameters. This leads to a formal definition of the mathematical constraints for 2B lidar. We believe that our work lays an analytical groundwork for design of future NLOS imaging systems, especially as ToF sensors become increasingly ubiquitous. + +# 1. Introduction + +Non-line-of-sight (NLOS) imaging aims to reconstruct objects occluded from direct line of sight and has the potential to be transformative in numerous applications across autonomous driving, search and rescue, and non-invasive medical imaging [24]. The key approach is to measure light that has undergone multiple surface scattering events and computationally invert these measurements to estimate hidden geometries. Recent work used two-bounce light, as shown in Fig. 2a, to reconstruct high quality shapes behind occluders [15]. The key idea is that two-bounce light captures information about the shadows of the occluded object. By scanning the laser source at different points 1 on a relay surface and measuring multiple shadow images, it is possible to reconstruct the hidden object by computing the visual hull [20] of the measured shadows. + +Benefits of Two-Bounce Two-bounce (2B) light can be captured using two relay surfaces on opposite sides of the hidden scene (Fig. 1a). This can occur in a variety of real-world settings such as tunnels, hallways, streets, and clit + +![](images/dac7c60efc57b3d2780b5a921c14a32785da739cb4a0e855d406b94c62a09000.jpg) +(a) Two-Bounce NLOS Imaging + +![](images/afdd89e2ce005569ede0fd9f3f24ea328c4a24daef53b9947c7063d6f5e8f52d.jpg) +(b) Two-Bounce Transient NLOS +Figure 2. Two-Bounce NLOS Imaging. (a) Two-bounce NLOS imaging performs 3D reconstruction by using information contained in the shadows of the hidden object when illuminated by one virtual source 1 at a time. (b) In this work, we study the benefits of using transient information for two-bounce NLOS imaging under the presence of multiplexed illumination. + +tered environments like forests (Fig. 1b). For example, imagine an autonomous vehicle in a tunnel being able to see ahead of the car in front of it by using two-bounce signals from the sides of the tunnel. Two-bounce light also helps alleviate the signal-to-noise ratio (SNR) issue in 3B-NLOS imaging, since 3B signals experience significant signal attenuation at each surface scatter event. Furthermore, 2B light captures information about the cast shadows of the hidden object instead of reflectance, as in the 3B case. As a result, the SNR of 2B signals is independent of the object's albedo and can therefore robustly image darker objects. + +Contributions In this work, we propose using two-bounce transients for NLOS imaging to enable the use of multiplexed illumination. 3B-NLOS transient imaging systems have been analyzed previously, but we believe we are the first to analyze the use of multiplexed illumination and transient measurements for 2B-NLOS (Fig. 2b). Our key insight is that multiplexed illumination enables measurement of occluded objects with fewer image captures, and 2B transients enable demultiplexing shadows, as shown in Fig. 3. The robust SNR and promise of few-shot capture afforded by 2B transients makes the idea an important direction for few-shot NLOS imaging in general environments. We summarize our contributions below. + +- Model: We present new insights into the algebraic formulations of two-bounce lidar for NLOS imaging. +- Analysis: We analyze tradeoffs with spatial resolution, temporal resolution, and number of image captures by using quantitative metrics such as SNR and recoverability, as well as qualitative validation from real and simulated results. + +Although we envision the ideas introduced here to inspire future works in single-shot NLOS imaging, we do not claim this as a contribution in this paper. + +Scope of This Work All data used for this work is from simulation and a single-pixel SPAD sensor. We do not physically realize few-shot results in this paper due to limited availability of high-resolution SPAD arrays presently. Instead, we emulate SPAD array measurements by scanning a single-pixel SPAD across the field of view and and emulate multiplexed illumination by scanning a laser spot, acquiring individual transient images, and summing the images in post-processing. These measurements, however, are more conducive to our goal of performing analysis that explores the landscape of possibilities in NLOS imaging with advances in ToF sensors. We believe that the ideas and analysis introduced in this work will be increasingly relevant as SPAD array technology matures [19,26,44]. + +# 2. Related Work + +# Non-Line-of-Sight Imaging + +ToF Methods: The non-line-of-sight imaging (NLOS) problem aims to see around a corner by measuring light reflected off intermediary surfaces. A large body of work models the response of a hidden scene to a temporal pulse of light and generally perform a variant of ellipsoidal tomography or solve a linear inverse problem [3, 5, 11, 12, 18, 39]. The temporal profiles can probe features of the hidden space, such as Fermat paths [42], scene impulse response [23], and individual voxels [28]. Other works derive efficient algorithms using a confocal setup [2, 22, 27] and data-driven techniques [8]. NLOS has also been demonstrated with amplitude modulated continuous wave (AMCW) ToF by exploiting sparsity and fitting measurements to a Lambertian reflectance model [13, 16]. + +Other Active Methods: Chen et al. use steady-state (i.e. time-integrated) intensity information by leveraging partial directionality of diffuse reflectors [7]. Radio wavelengths can also be used to image through walls and/or around them [1, 32, 43]. There has also been significant progress in exploiting speckle correlations [9, 17, 25, 34] and synthetic wave holography [40, 41] for NLOS imaging. Henley et al. demonstrate the use of two-bounce light (i.e. shadows) for NLOS using intensity sensors [15]. An extension of this work uses ToF constraints on two-bounce pathlengths to isolate shadows from ambient background and higher-order inter-reflections [14]. However multiplexing was not used. + +Passive Methods: Passive methods make use of optical information already present in the scene without an active source. Many passive approaches exploit polarization cues [10,36], ambient thermal light [21,36], shadows [35], multiview reflections [38], and neural networks [33,37] to reconstruct or make inferences about the scene outside the camera's field of view. Occlusion-assisted imaging makes use of information present at sharp discontinuities in LOS and NLOS scenes by turning them into virtual pinholes [4,30] or + +
NLOS Imaging DomainKey ComponentsKey Features
Assisting SurfacesSensor TypeLight SourceNumber of CapturesRecovered DimensionsSignal Quality
Passive Occlusion-Aided [4,31,33]Relay Wall/FloorIntensityPassiveLow2DLow (strong background)
Edge Occluders
Three-Bounce Transient [18,27,30,42]Relay Wall/FloorToFActive (Scan)High3DMedium (3-bounce)
Edge Occluders
Two-Bounce Transient (Ours)Two LOS WallsToFActive (Flash)Low3DHigh (2-bounce)
+ +Table 1. Comparison of NLOS Methods. Passive approaches require fewer measurements but can either recover up to two dimensions or are strongly affected by ambient noise. Works exploiting three-bounce light paths demonstrate 3D imaging around the corner but require a bounce on the hidden surface, reducing the signal quality. We analyze exploiting two-bounce transients for NLOS imaging. + +virtual pinspecks [31]. Intensity-only methods are difficult to scale to scenarios with arbitrary lighting conditions. + +# 3. Forward and Adjoint Operators + +# 3.1. Problem Setup + +We first introduce terminology and notation for our problem formulation. The object of interest lies behind an occluder and is flanked on two sides by planar Lambertian relay surfaces. Without loss of generality, the right wall is the illumination wall $\mathcal{L}$ and the left wall is the observation wall $\mathcal{O}$ . Light incident on the illumination wall at a point $l$ is a virtual source. Each virtual source diffusely radiates light towards the observation wall. Light will arrive at a virtual detector $s$ from $l$ if the object doesn't lie along the ray connecting $s$ and $l$ , as shown in Fig. 2a. If the object obstructs this ray, $s$ is said to lie in the shadow of the object. We assume that every virtual source and virtual detector is visible to the laser and camera field of view, respectively. The hidden scene is discretized into a voxel grid described by a binary occupancy (or transparency) function. This implicitly assumes that we are reconstructing opaque surfaces. We neglect the effect of higher order bounces (e.g. interreflections, 3B light) because SPADs can temporally gate out the longer ToF of 3B light. Furthermore, the intensity of higher order bounces will be much lower than that of two-bounce light because all surfaces are assumed to be diffuse. + +We denote light transients as ToF measurements for light that arrives at the virtual detector and shadow transients as ToF measurements for light that didn't arrive at the virtual detector because of the object's shadow. Both of these are two-bounce transients. We show that modeling the problem in terms of shadow transients enables reconstruction of the hidden objects shape by solving a linear inverse problem. + +![](images/6f41010c71b9b4e84377d5a0bb51f56fd62c5842531823a5568b6a7bf5682fd8.jpg) +Figure 3. Time-of-Flight Information for Demultiplexing Shadows. Assume the point $s$ lies in shadow. When using multiplexed illumination, there exists an ambiguity as to whether $s$ lies in the shadow of $l_1$ , $l_2$ , or both. However, the paths $L - l_1 - s - C$ and $L - l_2 - s - C$ have different pathlengths, suggesting the usefulness of ToF information for demultiplexing shadows. + +# 3.2. Linear Forward Model + +Light Transients Consider the case where the occluded scene is empty. The measured transient is then given by + +$$ +i _ {0} (t; \mathbf {s}) = \alpha \iint_ {\mathcal {L}} \frac {\delta (\| \mathbf {l} - \mathbf {g} \| + \| \mathbf {l} - \mathbf {s} \| - c t)}{\| \mathbf {l} - \mathbf {s} \| ^ {2}} d \mathbf {l}, \tag {1} +$$ + +where $\mathbf{g}$ is the location of the laser, $c$ is the speed of light, and $\alpha$ is the intensity of the laser. We refer to $i_0$ as the empty transient. For simplicity, we ignore $\alpha$ for the rest of the derivations in this section and assume that the length between the virtual detector and camera is calibrated or known. The numerator of the integrand + +$$ +i (t; \mathbf {s}, \mathbf {l}) = \delta (\| \mathbf {l} - \mathbf {g} \| + \| \mathbf {l} - \mathbf {s} \| - c t) \tag {2} +$$ + +describes the equation of an ellipsoid, with foci at $\mathbf{g}$ and s and major axis length $ct$ . When an object is present in the + +![](images/dc5705168e811c254e22b1d68ae3ba330bd0192dfe1a920cfa8f9180350463ca.jpg) +Figure 4. Light and Shadow Transients. Three spacetime curves are depicted. (left) Empty transient $i_0$ with no hidden object, (middle) light transient $i_l$ with an object, and (right) shadow transient $i_s = i_0 - i_l$ . Switching from light transients $i_l$ to shadow transients $i_s$ enables derivation of a linear forward model. + +occluded scene, the measured light transient is given by + +$$ +i _ {l} (t; \mathbf {s}) = \iint_ {\mathcal {L}} V _ {\mathbf {s}, \mathbf {l}} \cdot \frac {i (t ; \mathbf {s} , \mathbf {l})}{\| \mathbf {l} - \mathbf {s} \| ^ {2}} d \mathbf {l}, \tag {3} +$$ + +where $V_{\mathbf{s},1}$ is the visibility between s and l. + +$$ +V _ {\mathbf {s}, \mathbf {l}} = \exp \left(\oint_ {\mathbf {l}} ^ {\mathbf {s}} \ln \left(f _ {t} (\mathbf {x})\right) d \mathbf {x}\right) \tag {4} +$$ + +where Eq. (4) computes the product integral along the line connecting $\mathbf{l}$ and $\mathbf{s}$ and $f_{t}(\mathbf{x})\in \{0,1\}$ is the transparency function of voxel $\mathbf{x}$ in the occluded region. + +Shadow Transients The non-linearity of Eq. (4) makes model inversion challenging with light transients. Casting the formulation from light space-time to shadow space-time enables a linear formulation of the problem. A shadow transient at $s$ is given by + +$$ +i _ {s} (t; \mathbf {s}) = i _ {0} (t; \mathbf {s}) - i _ {l} (t; \mathbf {s}). \tag {5} +$$ + +Fig. 4 illustrates the difference between light transients and shadow transients. Shadow transients directly probe voxel occupancy, whereas light transients probe for voxel transparency. For example, if the occluded scene is empty except for voxel $\mathbf{x}$ , the shadow transient is given by + +$$ +i _ {s} (t; \mathbf {s}, \mathbf {x}) = \frac {\delta (\| \mathbf {l} (\mathbf {x} , \mathbf {s}) - \mathbf {g} \| + \| \mathbf {l} (\mathbf {x} , \mathbf {s}) - \mathbf {s} \| - c t)}{\| \mathbf {l} (\mathbf {x} , \mathbf {s}) - \mathbf {s} \| ^ {2}}, \tag {6} +$$ + +where $\mathbf{l}(\mathbf{x},\mathbf{s})$ is a point on the illumination wall that lies along the ray connecting $\mathbf{x}$ and $\mathbf{s}$ . If the wall doesn't intersect this ray, $i_s(t;\mathbf{x},\mathbf{s}) = 0$ . + +Linear Relaxation Now, consider the general case where a single opaque object lies in the hidden scene. We can describe the shadow transient as + +$$ +i _ {s} (t; \mathbf {s}) = \iint_ {\mathcal {L}} O _ {\mathbf {s}, \mathbf {l}} \cdot \frac {i (t ; \mathbf {s} , \mathbf {l})}{\| \mathbf {l} - \mathbf {s} \| ^ {2}} d \mathbf {l}, \tag {7} +$$ + +where $O_{\mathbf{s},1} \in \{0,1\}$ is the occlusion function (denotes if the ray between 1 and s is occluded). It can be expressed as the indicator function + +$$ +\begin{array}{l} O _ {\mathbf {s}, \mathrm {l}} = \left\{ \begin{array}{l l} 1, & \text {i f} \oint_ {\mathrm {l}} ^ {\mathbf {s}} f _ {o} (\mathbf {x}) d \mathbf {x} > 0 \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {8} \\ \approx \oint_ {1} ^ {\mathbf {s}} f _ {o} (\mathbf {x}) d \mathbf {x}, \\ \end{array} +$$ + +where $f_{o}(\mathbf{x})$ is the voxel occupancy function of the hidden scene. The linear relaxation in Eq. (8) is possible because NLOS reconstructions typically only consider ToF information, but not radiometric information. The above formulation will preserve the structure of the streak images in spacetime, even if the intensities are overestimated. Combining Eq. (5), (7), and (8), we obtain + +$$ +i _ {0} (t; \mathbf {s}) - i _ {l} (t; \mathbf {s}) = \iint_ {\mathcal {L}} \frac {i (t ; \mathbf {s} , \mathbf {l})}{\| \mathbf {l} - \mathbf {s} \| ^ {2}} \cdot \left(\oint_ {\mathbf {l}} ^ {\mathbf {s}} f _ {o} (\mathbf {x}) d \mathbf {x}\right) d \mathbf {l}, \tag {9} +$$ + +where we solve for $f_{o}(\mathbf{x})$ . We can estimate $i_0$ from the scene geometry and $i_l$ is the measured transient. + +Discrete Beam Illumination Discretizing $\mathcal{L}$ as $K$ discrete laser spots and the hidden space into a voxel grid, we can write Eq. (9) as + +$$ +i _ {s} [ t; \mathbf {s} ] = \sum_ {k = 1} ^ {K} \frac {\delta [ \| \mathbf {l} _ {k} - \mathbf {g} \| + \| \mathbf {l} _ {k} - \mathbf {s} \| - c t ]}{\| \mathbf {l} _ {k} - \mathbf {s} \| ^ {2}} \cdot \left(\sum_ {\mathbf {x} \in \mathcal {P} _ {\mathbf {l} _ {k}, \mathbf {s}}} f _ {o} [ \mathbf {x} ]\right), \tag {10} +$$ + +where $\mathcal{P}_{1,\mathrm{s}}$ denotes the set of voxels lying along the path between 1 and s. Eq. (10) can be expressed in matrix form + +$$ +\mathbf {I} _ {s} = \mathbf {P B f} = \mathbf {A f}, \tag {11} +$$ + +where $\mathbf{I}_s\in \mathbb{R}^{n_u n_v n_t}$ is the vectorized space-time measurements, $\mathbf{f}\in \mathbb{R}^{n_x n_y n_z}$ is the voxel occupancies, and $\mathbf{A}\in \mathbb{R}^{n_u n_v n_t\times n_x n_y n_z}$ is the measurement operator mapping voxel occupancies to space-time measurements. $n_u$ and $n_v$ are the number of pixels along the $u$ and $v$ direction, and $n_t$ is the number of timing bins. $n_x,n_y,$ and $n_z$ are the number of voxels in the $x,y,$ and $z$ directions. + +$\mathbf{P}$ and $\mathbf{B}$ model the temporal and spatial relationships, respectively, between virtual sources, virtual detectors, and voxels. $\mathbf{P} \in \mathbb{R}^{n_u n_v n_t \times n_u n_v K}$ is a block diagonal matrix, with the column space of the $i$ th block $\mathbf{P}^i \in \mathbb{R}^{n_t \times K}$ containing the corresponding $\delta(\cdot)$ functions from Eq. (2) for virtual detector $\mathbf{s}_i$ and all $K$ virtual sources. $\mathbf{B} \in \mathbb{R}^{n_u n_v K \times n_x n_y n_z}$ is composed of $n_u n_v$ vertical sub-blocks. Each entry $\mathbf{B}_{kj}^i \in \{0,1\}$ of the $i$ th sub-block $\mathbf{B}^i \in \mathbb{R}^{K \times n_x n_y n_z}$ of sub-block $i$ indicates whether voxel $j$ lies along the line connecting virtual detector $\mathbf{s}_i$ and virtual source $\mathbf{l}_k$ . The multiplication $\mathbf{Bf}$ performs the line integral in Eq. (8). The $k$ th column vector of $\mathbf{P}$ is the space-time impulse response (STIR) to the $k$ th illumination source when the hidden scene is completely occupied (note that we are dealing with shadow transients, not light transients). The $i$ th column of $\mathbf{A}$ forms the expected space-time measurements + +if only the $i$ th voxel is occupied (i.e. the STIR to a single voxel). We neglect the $r^2$ falloff term in our reconstructions. Additional explanation of the A matrix is provided in the supplementary. The linear model in Eq. (11) resembles that of 3B-bounce NLOS, where $\mathbf{A}$ is a measurement operator that maps voxels $\mathbf{f}$ to measurements $\mathbf{I}$ . However, in 3B-NLOS, the information is encoded into the reflectance of the object, whereas in 2B-NLOS, the information is encoded into the shadows. Therefore, the former is linear with respects to light transients, and the latter is linear with respect to shadow transients. + +# 3.3. Reconstruction Algorithm + +Reconstruction of $\mathbf{f}$ can be performed by backprojection + +$$ +\mathbf {f} _ {b p} = \mathbf {A} ^ {\top} \mathbf {I} _ {s}. \tag {12} +$$ + +Backprojection produces a low-frequency reconstruction of $\mathbf{f}$ . In practice, filtering $\mathbf{f}_{bp}$ with a Laplacian filter + +$$ +\mathbf {f} _ {f b p} = \left(\frac {\partial^ {2}}{\partial x ^ {2}} + \frac {\partial^ {2}}{\partial y ^ {2}} + \frac {\partial^ {2}}{\partial z ^ {2}}\right) \mathbf {f} _ {b p} \tag {13} +$$ + +has been shown to yield reasonably good results in ellipsoidal tomography in 3-bounce NLOS and line-based tomography in medical imaging. Our linear formulation also enables reconstruction with priors. We recognize that these optimization-based methods would improve reconstruction over unfiltered backprojection, which is equivalent to a low-frequency version of voxel carving in our setup. However, we restrict our focus to unfiltered backprojection because of its convenient relationship with the Gram matrix, which enables further analysis of our method in Sec. 4.2. + +# 4. Design and Analysis + +In this section, we analyze how the performance of the proposed two-bounce transient system varies with system parameters and the geometry of LOS relay surfaces. We also analyze the impact of temporal resolution, spatial resolution, and number of measurements on recoverability. The amount of multiplexing in the scene is inversely related to the number of measurements. For example, if 60 laser spots are used and 15 measurements are captured, then each image contains 4 multiplexed shadows. We use SNR, coherence, and FWHM of the PSF to quantify performance. + +# 4.1. Voxel SNR Analysis + +We quantify the noise characteristics of the measured shadow two-bounce transients using per-voxel SNR. Consider the case where only voxel $\mathbf{x}$ is occupied in the hidden region. We derive the SNR of the number of "shadow" photons received in the measured shadow transient $\mathbf{I}_s^{\mathbf{x}}$ . In vector + +![](images/4f3db07091b483a62612cdaf18a59324896d0484893c3c68aaf647b579b2ea8a.jpg) +Figure 5. SNR Analysis. The goal of this analysis is to determine how scene geometry affects the SNR of the two-bounce measurement at each voxel in the hidden scene. The first two cases consider the orientations of the relay surfaces, and the third considers the field of view of the camera. SNR is highest in the middle of the hidden scene for parallel surfaces, orienting the walls closer together increases SNR due to reduced $r^2$ falloff, and SNR is highest closer to the virtual detectors for small FOV cameras. + +form, the occupancy function can be described as $\delta^{\mathbf{x}}$ . From Eq. (11), the shadow transient is given by + +$$ +\mathbf {I} _ {s} ^ {\mathbf {x}} = \mathbf {A} \delta^ {\mathbf {x}} \tag {14} +$$ + +and the light transients measured by the SPAD sensor are given by $\mathbf{I}_l^{\mathbf{x}}$ . For this analysis, we account for $r^2$ falloff because it is a physically accurate phenomenon that impacts SNR. From Eq. (5), + +$$ +\mathbf {I} _ {l} ^ {\mathbf {x}} = \mathbf {I} _ {0} - \mathbf {A} \delta^ {\mathbf {x}} \tag {15} +$$ + +where $\mathbf{I}_0$ is the empty transient and assumed to be calibrated. Assuming no SPAD pile-up distortion, the number of photons arriving at the sensor for each time bin of $\mathbf{I}_l^{\mathbf{x}}$ follows an independent Poisson distribution [29]. Thus, the total number of photons $P^{\mathbf{x}}$ measured follows a Poisson distribution with the rate parameter being the sum of all the photon counts for all time bins for all pixels. + +$$ +P ^ {\mathbf {x}} \sim \operatorname {P o i s s o n} \left(\mathbf {1} ^ {T} \left(\mathbf {I} _ {0} - \mathbf {A} \delta^ {\mathbf {x}}\right)\right) \tag {16} +$$ + +where $\mathbf{1} \in \mathbb{R}^{n_u n_v n_t}$ is the one vector. Using the fact that SNR of a Poisson distribution is $\mu / \sigma = \sqrt{\lambda}$ with rate parameter $\lambda$ , the per-voxel SNR $S^{\mathbf{x}}$ is given by + +$$ +S ^ {\mathbf {x}} = \sqrt {\mathbf {1} ^ {T} \left(\mathbf {I} _ {0} - \mathbf {A} \boldsymbol {\delta} ^ {\mathbf {x}}\right)} \tag {17} +$$ + +The per-voxel SNR is plotted in Fig. 5 for three different scenarios. The first two scenarios deal with the orientation of the walls, and the third considers the field of view of the camera. In Fig. 5a, we can see that the SNR is higher for center voxels, as more rays connecting the illumination wall and observation wall pass through the center voxels. When the relay walls are oriented towards each other (Fig. 5b), the SNR increases due to reduced $r^2$ falloff. When the camera's field of view is small compared to the laser (Fig. 5c), regions closer to the observation wall have the highest SNR. + +![](images/5e8c362db0744c8c9755964b4fda3be0b9a90703ab8cbc9ccf84fdd8847089e7.jpg) +Figure 6. Spatially Varying PSF. In two-bounce lidar, the PSF has a double cone shape. The orientation of the double cone varies strongly as a function of the orientation and length of the relay surfaces (i.e. the virtual apertures) and the voxel position. + +# 4.2. Recoverability Analysis + +Resolution We now study the resolution limits of our method. In particular, we consider two key metrics in our measurement operator: mutual coherence and full width at half maximum (FWHM) of the PSF. We are interested in how (1) temporal resolution, (2) spatial resolution $N$ , and (3) number of measurements $M$ impact each of our metrics. From Eq. (12), we know that the backprojected occupancy can be obtained from the occupancy function by + +$$ +\mathbf {f} _ {b p} = \left(\mathbf {A} ^ {\top} \mathbf {A}\right) \mathbf {f}, \tag {18} +$$ + +where $\mathbf{G} = \mathbf{A}^{\top}\mathbf{A}$ is the Gram matrix. We can interpret the columns (or rows) of the Gram matrix to be the spatially varying point spread function (PSF) of the imaging system, as shown in Fig. 6. Each column $\mathbf{G}_i$ describes how a voxel $\mathbf{x}_i$ is blurred during backprojection reconstruction. + +We can see the effect of different imaging parameters on the PSF in Fig. 7, where we sweep different values of (1) $M$ and (2) $N$ . In particular, we note that the lobes of the PSF are suppressed when using temporal information, even with low spatial resolution and few number of image measurements. When using no temporal information, the PSF is still roughly centered at the correct location, but has large FWHM. The sharpness of the PSF when using temporal information indicates that it is better suited to applications that require finer voxel resolution with few-shot capture. In case (1) without transients, we see that the FWHM of the PSF is large along both the $x$ and $y$ direction for small values of $M$ . As $M$ approaches the number of illumination spots, the FWHM approaches the theoretical lower bound. In case (2), increased spatial resolution helps better localize the center of the PSF, but the FWHM does not improve. The transient cases are quite robust to both low number of measurements and low spatial resolution. Intuitively, higher values of $N$ in the transient case slightly help accentuate the center voxel + +by projecting more diverse rays through the center voxel. + +Mutual Coherence We wish to further quantify the impact of spatio-temporal resolution and number of measurements on the recoverability of the hidden scene. We know from compressive sensing theory that sparse recovery of the hidden scene is possible when the mutual coherence of $\mathbf{A}$ is sufficiently small. The mutual coherence is defined as + +$$ +\mu = \max _ {1 \leq i \neq j \leq n} \frac {\left| \mathbf {A} _ {i} ^ {\top} \mathbf {A} _ {j} \right|}{\left| \mathbf {A} _ {i} \right| \left| \mathbf {A} _ {j} \right|}. \tag {19} +$$ + +Intuitively, the coherence measures the largest "similarity" or correlation between any two column vectors in measurement matrix $\mathbf{A}$ [6]. Physically, this quantifies how similar the STIRs of two different voxels are. If $\mu = 1$ , then two voxels have the exact same STIR, which means that there exists an ambiguity as to which voxel resulted in a certain spatio-temporal response. Alternatively, $\mu$ can be defined as the maximum off-diagonal entry of the Gram matrix. Fig. 8 illustrates how the Gram matrix (and subsequently the mutual coherence) is affected by coarser timing resolutions. From compressive sensing theory, we know that a $K$ -sparse scene can be recovered if $K \leq 0.5(1 + 1 / \mu)$ , which motivates our empirical analysis of the effect of spatial resolution and temporal resolution on $\mu$ . + +From Fig. 9, we can see the impact that spatial and temporal resolution have on mutual coherence in a single-shot setup with multiplexed illumination. Consider a scene similar to that of Fig. 6, where the walls are $2\mathrm{m}$ apart, the walls are $3\mathrm{m}$ long, the axial distance to the walls is $2\mathrm{m}$ , and the voxel resolution is discretized to $2\mathrm{cm}$ . Increasing the spatial resolution at a fixed temporal resolution appears to have little to no effect on the mutual coherence. As Kadambi et al. also point out, improvements of coherence through higher spatial resolution are limited by the size of the virtual aperture (i.e. the wall) [16]. On the other hand, the difference between $100~\mathrm{ps}$ resolution and $10~\mathrm{ps}$ resolution reduces the coherence from 0.9 to 0.3 for a fixed spatial resolution. Any timing resolution coarser than $\sim 120$ ps results in a coherence of 1 for multiplexed measurements because pathlength differences for different shadows are no longer resolvable. This analysis motivates the importance of temporal resolution when using multiplexed illumination. + +# 5. Experiments and Results + +We scan a single-pixel SPAD across the field of view on the left wall to mimic the output of a SPAD array. We scan a single laser spot across the right wall, and sum up the corresponding transient images in post-processing to mimic the effect of multiplexing. Further details are provided in the supplementary. We first validate our model using simulated data in Fig. 10, where we demonstrate that we can localize four letters and reconstruct their 2D shape with just a single + +![](images/8917c0c3376b274e4c1aec23ce917105bd1496bf57c63b2ca47e202dafefab2f.jpg) +Figure 7. PSF as a Function of Number of Measurements and Spatial Resolution. The PSF of the center voxel is shown in the transient and intensity-only case when multiplexed with 60 laser spots. (1) the number of pixels $N = 40$ are kept fixed with the number of measurements $M$ being swept (left) and (2) $M = 10$ is kept fixed and $N$ is swept (right). Transient measurements result in PSFs with narrower FWHMs, even with low spatial resolution and low number of measurements. + +![](images/1edc73563e372c28f865e5f33e9f5ed0763c3157ca12399ed9b489b4d511ba4e.jpg) + +![](images/16f0d107255a743cc7c7b3edbfebd1230b98d899f7b505bddff4798abb3c252b.jpg) +Figure 8. Gram Matrix as a Function of Temporal Resolution. For a defined voxel resolution and fixed spatial resolution. The columns (or rows) of the Gram matrix form the spatially varying PSFs shown in Fig. 6. The off-diagonal streaks describe the coherence between different voxels. As expected, higher temporal resolution decreases the coherence of the Gram matrix, which increases the likelihood of guaranteed sparse recovery. + +capture. We render $i_{o}$ and $i_{l}$ to obtain a noiseless version of the shadow transient for this experiment. Then, we reconstruct the shapes of real mannequins and must estimate $i_{0}$ . Fig. 11 shows that ToF measurements provide a noticeable improvement in image reconstruction. When there's no multiplexing (i.e., the number of laser spots is the same as number of measurements), the intensity-based method is similar to the ToF-based method. However, in the intensity-only case, the object becomes increasingly blurry until it is no longer visible as the amount of multiplexing increases. In the ToF case for single-shot, we can see a blurry image roughly localized where the center of the mannequin is as well as some high-frequency detail. Furthermore, the top view of the ToF reconstructions show that the high-frequency shape of the arms can be reconstructed even with multiplexed illumination, indicating the promise of single + +![](images/a939948ccd7e2441a4107bbde6b02c4135b2b8f32bbefa8083f6280b2129e310.jpg) +Figure 9. Tradeoffs Between Spatial Resolution and Temporal Resolution. We quantify the tradeoff using mutual coherence. We use the same setup as Fig. 6, but the walls have length $3\mathrm{m}$ , the walls are space $2\mathrm{m}$ apart, and the distance to the walls is $2\mathrm{m}$ . We discretize the voxel resolution to $2\mathrm{cm}(\sim 67\mathrm{ps})$ . The bottom right of the figure, where spatial and temporal resolution are highest is where mutual coherence is the lowest. For a fixed temporal resolution, improvements in coherence quickly plateau. Improvements in temporal resolution dominate improvements in spatial resolution when reducing coherence, suggesting the importance of ToF for demultiplexing illumination in two-bounce NLOS imaging. + +shot capture with two-bounce ToF information. Fig. 12 shows that poorer temporal resolution results in aliasing artifacts (repeated arms and legs), whereas the rough shape of the object can still be seen with lower spatial resolution. Finally, we compare our method to the probabilistic voxel carving method used in [15] in Fig. 13. Voxel carving results in sharper reconstructions than backprojection. + +![](images/73d56e3e1d2c94eac3c110d2cccf8f917bb7ef872fe2dbc3535b42a6c8e81187.jpg) +Figure 10. Single-Shot Localization. We obtain single-shot reconstructions of the "N", "L", "O", and "S" letters in the hidden scene with and without transient information. We see that using transient information, we are able to effectively localize the hidden object and even get a sharp outline of the letters, demonstrating the promise of single-shot capture with two-bounce transients. + +![](images/052e98ac960dfbd0dda5d08d4c729a58a63172b1586062dfa28ba96a9705a46b.jpg) +Figure 11. Transients Enable Scene Recovery from Multiplexed Illumination. We perform backprojection of measurements with varying levels of multiplexing. Plotted in the top two rows are $x$ slices of the reconstructed volume. Under no multiplexing (right), intensity is sufficient to carve the shadow along detected pixel. But reconstruction quality sharply deteriorates as we move towards the multiplexing regime (left). When measuring with transients, time-of-flight information allows us to disambiguate between different shadows and recover a rough silhouette of the object even with just a single measurement. + +However, our method can be improved by filtering or incorporating priors, and is also generalizable to multiplexed illumination by utilizing ToF information. + +![](images/ad76127c3b9f4afd934c1107a982ed0d2ca3477e6dc88bdfb5454de7fd317d7e.jpg) +Figure 12. Spatial Resolution vs. Timing Resolution. We plot reconstructions with different spatio-temporal resolutions. Lower timing resolution results in aliasing artifacts (i.e. repeated arms and legs). Lower spatial resolution introduces hole artifacts. + +![](images/fd216f0dc7a5bd6663190c42867f44743f539f7e6a813ffe1cf67a6a302b7c89.jpg) +Figure 13. Scanning Baseline Comparison. We compare to the voxel carving method used in [15] (a) before and (b) after thresholding when scanning 1 laser spot. Our method is more general, but voxel carving yields sharper results with laser scanning. + +# 6. Discussion + +In this paper, we introduced the use of two-bounce transients for NLOS imaging. Compared to 3B-NLOS, 2B-NLOS enables more robust imaging of occluded objects in the presence of scenes with arbitrary lighting conditions and low albedo objects. Transient 2B-NLOS is promising for few-shot capture of occluded objects by using multiplexed illumination, especially as SPAD array technology matures. When comparing tradeoffs in temporal resolution, spatial resolution, and number of measurements, we qualitatively and quantitatively verify with real and simulated results that temporal resolution is most important for demultiplexing shadows. We anticipate future work to extend the analysis in this paper to SPAD arrays for real-time NLOS imaging. + +# Acknowledgements + +AD and AV are supported by NSF Expeditions Award #IIS-1730574 and NSF CAREER Award #IIS-1652633. 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Two-bounce Transient NLOS Imaging. (a) We propose using two-bounce transients for NLOS imaging. Two-bounce signals capture information about the shadows in a scene, and use of transient information can reduce the number of measurements needed for reconstruction by using multiplexed illumination. (b) Our work can be applicable in many scenarios, such as tunnels, corridors, streets, and forests. (c)-(d) We experimentally validate the use of two-bounce transients on real objects. We show that time-of-flight information enables more robust reconstructions of occluded objects while using fewer measurements." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 370, + 227, + 539, + 374 + ], + "blocks": [ + { + "bbox": [ + 370, + 227, + 539, + 374 + ], + "lines": [ + { + "bbox": [ + 370, + 227, + 539, + 374 + ], + "spans": [ + { + "bbox": [ + 370, + 227, + 539, + 374 + ], + "type": "image", + "image_path": "c2882cdcc836f088655b91a89b156cfbbe64c7a1a2d68e2e585d6f6782bc3ac9.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 381, + 377, + 529, + 388 + ], + "lines": [ + { + "bbox": [ + 381, + 377, + 529, + 388 + ], + "spans": [ + { + "bbox": [ + 381, + 377, + 529, + 388 + ], + "type": "text", + "content": "(d) Reconstruction with 10 Measurements" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 143, + 462, + 192, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 462, + 192, + 475 + ], + "spans": [ + { + "bbox": [ + 143, + 462, + 192, + 475 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 484, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 289, + 700 + ], + "type": "text", + "content": "The goal of non-line-of-sight (NLOS) imaging is to image objects occluded from the camera's field of view using multiply scattered light. Recent works have demonstrated the feasibility of two-bounce (2B) NLOS imaging by scanning a laser and measuring cast shadows of occluded objects in scenes with two relay surfaces. In this work, we study the role of time-of-flight (ToF) measurements, i.e. transients, in 2B-NLOS under multiplexed illumination. Specifically, we study how ToF information can reduce the number of measurements and spatial resolution needed for shape reconstruction. We present our findings with respect to trade-offs in (1) temporal resolution, (2) spatial resolution, and (3) number of image captures by studying SNR and recoverability as functions of system parameters. This leads to a formal definition of the mathematical constraints for 2B lidar. We believe that our work lays an analytical groundwork for design of future NLOS imaging systems, especially as ToF sensors become increasingly ubiquitous." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 307, + 462, + 386, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 462, + 386, + 475 + ], + "spans": [ + { + "bbox": [ + 307, + 462, + 386, + 475 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 482, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 662 + ], + "type": "text", + "content": "Non-line-of-sight (NLOS) imaging aims to reconstruct objects occluded from direct line of sight and has the potential to be transformative in numerous applications across autonomous driving, search and rescue, and non-invasive medical imaging [24]. The key approach is to measure light that has undergone multiple surface scattering events and computationally invert these measurements to estimate hidden geometries. Recent work used two-bounce light, as shown in Fig. 2a, to reconstruct high quality shapes behind occluders [15]. The key idea is that two-bounce light captures information about the shadows of the occluded object. By scanning the laser source at different points 1 on a relay surface and measuring multiple shadow images, it is possible to reconstruct the hidden object by computing the visual hull [20] of the measured shadows." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Benefits of Two-Bounce Two-bounce (2B) light can be captured using two relay surfaces on opposite sides of the hidden scene (Fig. 1a). This can occur in a variety of real-world settings such as tunnels, hallways, streets, and clit" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9192" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 164, + 159 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 164, + 159 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 164, + 159 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 164, + 159 + ], + "type": "image", + "image_path": "dac7c60efc57b3d2780b5a921c14a32785da739cb4a0e855d406b94c62a09000.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 161, + 154, + 171 + ], + "lines": [ + { + "bbox": [ + 59, + 161, + 154, + 171 + ], + "spans": [ + { + "bbox": [ + 59, + 161, + 154, + 171 + ], + "type": "text", + "content": "(a) Two-Bounce NLOS Imaging" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 165, + 70, + 286, + 159 + ], + "blocks": [ + { + "bbox": [ + 165, + 70, + 286, + 159 + ], + "lines": [ + { + "bbox": [ + 165, + 70, + 286, + 159 + ], + "spans": [ + { + "bbox": [ + 165, + 70, + 286, + 159 + ], + "type": "image", + "image_path": "afdd89e2ce005569ede0fd9f3f24ea328c4a24daef53b9947c7063d6f5e8f52d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 181, + 161, + 280, + 170 + ], + "lines": [ + { + "bbox": [ + 181, + 161, + 280, + 170 + ], + "spans": [ + { + "bbox": [ + 181, + 161, + 280, + 170 + ], + "type": "text", + "content": "(b) Two-Bounce Transient NLOS" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 179, + 287, + 245 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 287, + 245 + ], + "type": "text", + "content": "Figure 2. Two-Bounce NLOS Imaging. (a) Two-bounce NLOS imaging performs 3D reconstruction by using information contained in the shadows of the hidden object when illuminated by one virtual source 1 at a time. (b) In this work, we study the benefits of using transient information for two-bounce NLOS imaging under the presence of multiplexed illumination." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 269, + 286, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 286, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 286, + 399 + ], + "type": "text", + "content": "tered environments like forests (Fig. 1b). For example, imagine an autonomous vehicle in a tunnel being able to see ahead of the car in front of it by using two-bounce signals from the sides of the tunnel. Two-bounce light also helps alleviate the signal-to-noise ratio (SNR) issue in 3B-NLOS imaging, since 3B signals experience significant signal attenuation at each surface scatter event. Furthermore, 2B light captures information about the cast shadows of the hidden object instead of reflectance, as in the 3B case. As a result, the SNR of 2B signals is independent of the object's albedo and can therefore robustly image darker objects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 405, + 286, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 286, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 286, + 559 + ], + "type": "text", + "content": "Contributions In this work, we propose using two-bounce transients for NLOS imaging to enable the use of multiplexed illumination. 3B-NLOS transient imaging systems have been analyzed previously, but we believe we are the first to analyze the use of multiplexed illumination and transient measurements for 2B-NLOS (Fig. 2b). Our key insight is that multiplexed illumination enables measurement of occluded objects with fewer image captures, and 2B transients enable demultiplexing shadows, as shown in Fig. 3. The robust SNR and promise of few-shot capture afforded by 2B transients makes the idea an important direction for few-shot NLOS imaging in general environments. We summarize our contributions below." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 571, + 286, + 665 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 59, + 571, + 286, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 571, + 286, + 595 + ], + "spans": [ + { + "bbox": [ + 59, + 571, + 286, + 595 + ], + "type": "text", + "content": "- Model: We present new insights into the algebraic formulations of two-bounce lidar for NLOS imaging." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 607, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 607, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 59, + 607, + 286, + 665 + ], + "type": "text", + "content": "- Analysis: We analyze tradeoffs with spatial resolution, temporal resolution, and number of image captures by using quantitative metrics such as SNR and recoverability, as well as qualitative validation from real and simulated results." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Although we envision the ideas introduced here to inspire future works in single-shot NLOS imaging, we do not claim this as a contribution in this paper." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": "Scope of This Work All data used for this work is from simulation and a single-pixel SPAD sensor. We do not physically realize few-shot results in this paper due to limited availability of high-resolution SPAD arrays presently. Instead, we emulate SPAD array measurements by scanning a single-pixel SPAD across the field of view and and emulate multiplexed illumination by scanning a laser spot, acquiring individual transient images, and summing the images in post-processing. These measurements, however, are more conducive to our goal of performing analysis that explores the landscape of possibilities in NLOS imaging with advances in ToF sensors. We believe that the ideas and analysis introduced in this work will be increasingly relevant as SPAD array technology matures [19,26,44]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 392, + 262 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 270, + 437, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 437, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 437, + 283 + ], + "type": "text", + "content": "Non-Line-of-Sight Imaging" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 288, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 456 + ], + "type": "text", + "content": "ToF Methods: The non-line-of-sight imaging (NLOS) problem aims to see around a corner by measuring light reflected off intermediary surfaces. A large body of work models the response of a hidden scene to a temporal pulse of light and generally perform a variant of ellipsoidal tomography or solve a linear inverse problem [3, 5, 11, 12, 18, 39]. The temporal profiles can probe features of the hidden space, such as Fermat paths [42], scene impulse response [23], and individual voxels [28]. Other works derive efficient algorithms using a confocal setup [2, 22, 27] and data-driven techniques [8]. NLOS has also been demonstrated with amplitude modulated continuous wave (AMCW) ToF by exploiting sparsity and fitting measurements to a Lambertian reflectance model [13, 16]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "content": "Other Active Methods: Chen et al. use steady-state (i.e. time-integrated) intensity information by leveraging partial directionality of diffuse reflectors [7]. Radio wavelengths can also be used to image through walls and/or around them [1, 32, 43]. There has also been significant progress in exploiting speckle correlations [9, 17, 25, 34] and synthetic wave holography [40, 41] for NLOS imaging. Henley et al. demonstrate the use of two-bounce light (i.e. shadows) for NLOS using intensity sensors [15]. An extension of this work uses ToF constraints on two-bounce pathlengths to isolate shadows from ambient background and higher-order inter-reflections [14]. However multiplexing was not used." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Passive Methods: Passive methods make use of optical information already present in the scene without an active source. Many passive approaches exploit polarization cues [10,36], ambient thermal light [21,36], shadows [35], multiview reflections [38], and neural networks [33,37] to reconstruct or make inferences about the scene outside the camera's field of view. Occlusion-assisted imaging makes use of information present at sharp discontinuities in LOS and NLOS scenes by turning them into virtual pinholes [4,30] or" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9193" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 64, + 70, + 531, + 216 + ], + "blocks": [ + { + "bbox": [ + 64, + 70, + 531, + 216 + ], + "lines": [ + { + "bbox": [ + 64, + 70, + 531, + 216 + ], + "spans": [ + { + "bbox": [ + 64, + 70, + 531, + 216 + ], + "type": "table", + "html": "
NLOS Imaging DomainKey ComponentsKey Features
Assisting SurfacesSensor TypeLight SourceNumber of CapturesRecovered DimensionsSignal Quality
Passive Occlusion-Aided [4,31,33]Relay Wall/FloorIntensityPassiveLow2DLow (strong background)
Edge Occluders
Three-Bounce Transient [18,27,30,42]Relay Wall/FloorToFActive (Scan)High3DMedium (3-bounce)
Edge Occluders
Two-Bounce Transient (Ours)Two LOS WallsToFActive (Flash)Low3DHigh (2-bounce)
", + "image_path": "ff5b994feed9ce68024242b3f89d30db7eb411fd529b7290592fedf6504f3d38.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 222, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 222, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 547, + 257 + ], + "type": "text", + "content": "Table 1. Comparison of NLOS Methods. Passive approaches require fewer measurements but can either recover up to two dimensions or are strongly affected by ambient noise. Works exploiting three-bounce light paths demonstrate 3D imaging around the corner but require a bounce on the hidden surface, reducing the signal quality. We analyze exploiting two-bounce transients for NLOS imaging." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 277, + 288, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 288, + 301 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 288, + 301 + ], + "type": "text", + "content": "virtual pinspecks [31]. Intensity-only methods are difficult to scale to scenarios with arbitrary lighting conditions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 320, + 228, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 228, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 228, + 335 + ], + "type": "text", + "content": "3. Forward and Adjoint Operators" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 346, + 140, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 140, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 140, + 360 + ], + "type": "text", + "content": "3.1. Problem Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": "We first introduce terminology and notation for our problem formulation. The object of interest lies behind an occluder and is flanked on two sides by planar Lambertian relay surfaces. Without loss of generality, the right wall is the illumination wall " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": " and the left wall is the observation wall " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": ". Light incident on the illumination wall at a point " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": " is a virtual source. Each virtual source diffusely radiates light towards the observation wall. Light will arrive at a virtual detector " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": " if the object doesn't lie along the ray connecting " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": ", as shown in Fig. 2a. If the object obstructs this ray, " + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 372, + 289, + 623 + ], + "type": "text", + "content": " is said to lie in the shadow of the object. We assume that every virtual source and virtual detector is visible to the laser and camera field of view, respectively. The hidden scene is discretized into a voxel grid described by a binary occupancy (or transparency) function. This implicitly assumes that we are reconstructing opaque surfaces. We neglect the effect of higher order bounces (e.g. interreflections, 3B light) because SPADs can temporally gate out the longer ToF of 3B light. Furthermore, the intensity of higher order bounces will be much lower than that of two-bounce light because all surfaces are assumed to be diffuse." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "We denote light transients as ToF measurements for light that arrives at the virtual detector and shadow transients as ToF measurements for light that didn't arrive at the virtual detector because of the object's shadow. Both of these are two-bounce transients. We show that modeling the problem in terms of shadow transients enables reconstruction of the hidden objects shape by solving a linear inverse problem." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 334, + 275, + 517, + 425 + ], + "blocks": [ + { + "bbox": [ + 334, + 275, + 517, + 425 + ], + "lines": [ + { + "bbox": [ + 334, + 275, + 517, + 425 + ], + "spans": [ + { + "bbox": [ + 334, + 275, + 517, + 425 + ], + "type": "image", + "image_path": "6f41010c71b9b4e84377d5a0bb51f56fd62c5842531823a5568b6a7bf5682fd8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "lines": [ + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": "Figure 3. Time-of-Flight Information for Demultiplexing Shadows. Assume the point " + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": " lies in shadow. When using multiplexed illumination, there exists an ambiguity as to whether " + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": " lies in the shadow of " + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "inline_equation", + "content": "l_1" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "inline_equation", + "content": "l_2" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": ", or both. However, the paths " + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "inline_equation", + "content": "L - l_1 - s - C" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "inline_equation", + "content": "L - l_2 - s - C" + }, + { + "bbox": [ + 305, + 431, + 545, + 498 + ], + "type": "text", + "content": " have different pathlengths, suggesting the usefulness of ToF information for demultiplexing shadows." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 515, + 437, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 437, + 528 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 437, + 528 + ], + "type": "text", + "content": "3.2. Linear Forward Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 533, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 545, + 559 + ], + "type": "text", + "content": "Light Transients Consider the case where the occluded scene is empty. The measured transient is then given by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 329, + 562, + 545, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 562, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 329, + 562, + 545, + 589 + ], + "type": "interline_equation", + "content": "i _ {0} (t; \\mathbf {s}) = \\alpha \\iint_ {\\mathcal {L}} \\frac {\\delta (\\| \\mathbf {l} - \\mathbf {g} \\| + \\| \\mathbf {l} - \\mathbf {s} \\| - c t)}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {1}", + "image_path": "f996774bc898c4c34e19e12a7a4a0d3cfbcd2f00cc25301cad20fe83655d27df.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "content": " is the location of the laser, " + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "content": " is the speed of light, and " + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "content": " is the intensity of the laser. We refer to " + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "inline_equation", + "content": "i_0" + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "content": " as the empty transient. For simplicity, we ignore " + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 593, + 547, + 665 + ], + "type": "text", + "content": " for the rest of the derivations in this section and assume that the length between the virtual detector and camera is calibrated or known. The numerator of the integrand" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 670, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 670, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 348, + 670, + 545, + 685 + ], + "type": "interline_equation", + "content": "i (t; \\mathbf {s}, \\mathbf {l}) = \\delta (\\| \\mathbf {l} - \\mathbf {g} \\| + \\| \\mathbf {l} - \\mathbf {s} \\| - c t) \\tag {2}", + "image_path": "02f4060b4a9d2ff5c873baa4fbf47592f7b3262d6cf1e100c91818e953a92e35.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "describes the equation of an ellipsoid, with foci at " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " and s and major axis length " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "ct" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": ". When an object is present in the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9194" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 71, + 281, + 122 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 281, + 122 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 281, + 122 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 281, + 122 + ], + "type": "image", + "image_path": "dc5705168e811c254e22b1d68ae3ba330bd0192dfe1a920cfa8f9180350463ca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "lines": [ + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "text", + "content": "Figure 4. Light and Shadow Transients. Three spacetime curves are depicted. (left) Empty transient " + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "inline_equation", + "content": "i_0" + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "text", + "content": " with no hidden object, (middle) light transient " + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "inline_equation", + "content": "i_l" + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "text", + "content": " with an object, and (right) shadow transient " + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "inline_equation", + "content": "i_s = i_0 - i_l" + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "text", + "content": ". Switching from light transients " + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "inline_equation", + "content": "i_l" + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "text", + "content": " to shadow transients " + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "inline_equation", + "content": "i_s" + }, + { + "bbox": [ + 47, + 129, + 287, + 184 + ], + "type": "text", + "content": " enables derivation of a linear forward model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 207, + 272, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 207, + 272, + 219 + ], + "spans": [ + { + "bbox": [ + 47, + 207, + 272, + 219 + ], + "type": "text", + "content": "occluded scene, the measured light transient is given by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 228, + 287, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 228, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 100, + 228, + 287, + 255 + ], + "type": "interline_equation", + "content": "i _ {l} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} V _ {\\mathbf {s}, \\mathbf {l}} \\cdot \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {3}", + "image_path": "053993db1414f201b066a1aea3c780141a7a492f149e0d00c558102d1151960e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 263, + 220, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 263, + 220, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 263, + 220, + 276 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 263, + 220, + 276 + ], + "type": "inline_equation", + "content": "V_{\\mathbf{s},1}" + }, + { + "bbox": [ + 47, + 263, + 220, + 276 + ], + "type": "text", + "content": " is the visibility between s and l." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 280, + 287, + 307 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 280, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 102, + 280, + 287, + 307 + ], + "type": "interline_equation", + "content": "V _ {\\mathbf {s}, \\mathbf {l}} = \\exp \\left(\\oint_ {\\mathbf {l}} ^ {\\mathbf {s}} \\ln \\left(f _ {t} (\\mathbf {x})\\right) d \\mathbf {x}\\right) \\tag {4}", + "image_path": "ec1de17a013d2956d41d18bd742985e3020bc747a4336c36658fbab1ad025fd8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": "where Eq. (4) computes the product integral along the line connecting " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "f_{t}(\\mathbf{x})\\in \\{0,1\\}" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " is the transparency function of voxel " + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 316, + 287, + 352 + ], + "type": "text", + "content": " in the occluded region." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 357, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 287, + 418 + ], + "type": "text", + "content": "Shadow Transients The non-linearity of Eq. (4) makes model inversion challenging with light transients. Casting the formulation from light space-time to shadow space-time enables a linear formulation of the problem. A shadow transient at " + }, + { + "bbox": [ + 47, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 47, + 357, + 287, + 418 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 110, + 428, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 428, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 110, + 428, + 287, + 441 + ], + "type": "interline_equation", + "content": "i _ {s} (t; \\mathbf {s}) = i _ {0} (t; \\mathbf {s}) - i _ {l} (t; \\mathbf {s}). \\tag {5}", + "image_path": "8368fb67177a09f75ed0e2a63d23ec0d2412e1d28b68ffe35058968e306c289b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 451, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 451, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 451, + 287, + 511 + ], + "type": "text", + "content": "Fig. 4 illustrates the difference between light transients and shadow transients. Shadow transients directly probe voxel occupancy, whereas light transients probe for voxel transparency. For example, if the occluded scene is empty except for voxel " + }, + { + "bbox": [ + 47, + 451, + 287, + 511 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 451, + 287, + 511 + ], + "type": "text", + "content": ", the shadow transient is given by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 55, + 521, + 287, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 521, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 55, + 521, + 287, + 547 + ], + "type": "interline_equation", + "content": "i _ {s} (t; \\mathbf {s}, \\mathbf {x}) = \\frac {\\delta (\\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {g} \\| + \\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {s} \\| - c t)}{\\| \\mathbf {l} (\\mathbf {x} , \\mathbf {s}) - \\mathbf {s} \\| ^ {2}}, \\tag {6}", + "image_path": "c9acc5f1ac2a40b54449d6a55931f717e7ad46843b10f44826f104a1967ffb75.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{l}(\\mathbf{x},\\mathbf{s})" + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "text", + "content": " is a point on the illumination wall that lies along the ray connecting " + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "text", + "content": ". If the wall doesn't intersect this ray, " + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "inline_equation", + "content": "i_s(t;\\mathbf{x},\\mathbf{s}) = 0" + }, + { + "bbox": [ + 47, + 556, + 286, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 598, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 287, + 633 + ], + "type": "text", + "content": "Linear Relaxation Now, consider the general case where a single opaque object lies in the hidden scene. We can describe the shadow transient as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 98, + 641, + 287, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 641, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 98, + 641, + 287, + 668 + ], + "type": "interline_equation", + "content": "i _ {s} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} O _ {\\mathbf {s}, \\mathbf {l}} \\cdot \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} d \\mathbf {l}, \\tag {7}", + "image_path": "0ba2aa076907b1f1c5d38e836e6a752eb4dcdc01f1bbd0fe9896ec1450722a66.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "inline_equation", + "content": "O_{\\mathbf{s},1} \\in \\{0,1\\}" + }, + { + "bbox": [ + 47, + 677, + 287, + 712 + ], + "type": "text", + "content": " is the occlusion function (denotes if the ray between 1 and s is occluded). It can be expressed as the indicator function" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 67, + 545, + 126 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 67, + 545, + 126 + ], + "spans": [ + { + "bbox": [ + 358, + 67, + 545, + 126 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} O _ {\\mathbf {s}, \\mathrm {l}} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\oint_ {\\mathrm {l}} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x} > 0 \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {8} \\\\ \\approx \\oint_ {1} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x}, \\\\ \\end{array}", + "image_path": "6250c1645d4a43237673b9b6a9e2d227729149aac7e168f3f3b6161229b13b67.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 135, + 545, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 135, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 305, + 135, + 545, + 218 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 135, + 545, + 218 + ], + "type": "inline_equation", + "content": "f_{o}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 135, + 545, + 218 + ], + "type": "text", + "content": " is the voxel occupancy function of the hidden scene. The linear relaxation in Eq. (8) is possible because NLOS reconstructions typically only consider ToF information, but not radiometric information. The above formulation will preserve the structure of the streak images in spacetime, even if the intensities are overestimated. Combining Eq. (5), (7), and (8), we obtain" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 310, + 227, + 545, + 254 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 227, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 310, + 227, + 545, + 254 + ], + "type": "interline_equation", + "content": "i _ {0} (t; \\mathbf {s}) - i _ {l} (t; \\mathbf {s}) = \\iint_ {\\mathcal {L}} \\frac {i (t ; \\mathbf {s} , \\mathbf {l})}{\\| \\mathbf {l} - \\mathbf {s} \\| ^ {2}} \\cdot \\left(\\oint_ {\\mathbf {l}} ^ {\\mathbf {s}} f _ {o} (\\mathbf {x}) d \\mathbf {x}\\right) d \\mathbf {l}, \\tag {9}", + "image_path": "c32770e52055c8a02110875e7ad0bce2aff4a87b0e414499e620f72b6d703698.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "text", + "content": "where we solve for " + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "inline_equation", + "content": "f_{o}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "text", + "content": ". We can estimate " + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "inline_equation", + "content": "i_0" + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "text", + "content": " from the scene geometry and " + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "inline_equation", + "content": "i_l" + }, + { + "bbox": [ + 305, + 262, + 545, + 286 + ], + "type": "text", + "content": " is the measured transient." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "type": "text", + "content": "Discrete Beam Illumination Discretizing " + }, + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 289, + 545, + 326 + ], + "type": "text", + "content": " discrete laser spots and the hidden space into a voxel grid, we can write Eq. (9) as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 335, + 551, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 551, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 551, + 380 + ], + "type": "interline_equation", + "content": "i _ {s} [ t; \\mathbf {s} ] = \\sum_ {k = 1} ^ {K} \\frac {\\delta [ \\| \\mathbf {l} _ {k} - \\mathbf {g} \\| + \\| \\mathbf {l} _ {k} - \\mathbf {s} \\| - c t ]}{\\| \\mathbf {l} _ {k} - \\mathbf {s} \\| ^ {2}} \\cdot \\left(\\sum_ {\\mathbf {x} \\in \\mathcal {P} _ {\\mathbf {l} _ {k}, \\mathbf {s}}} f _ {o} [ \\mathbf {x} ]\\right), \\tag {10}", + "image_path": "31c58786764a3d913b0f376cbfc6ceb1b382e102f3491dc41111f41772468253.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 380, + 544, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 544, + 404 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 544, + 404 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 380, + 544, + 404 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{1,\\mathrm{s}}" + }, + { + "bbox": [ + 306, + 380, + 544, + 404 + ], + "type": "text", + "content": " denotes the set of voxels lying along the path between 1 and s. Eq. (10) can be expressed in matrix form" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 388, + 415, + 545, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 415, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 388, + 415, + 545, + 427 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {s} = \\mathbf {P B f} = \\mathbf {A f}, \\tag {11}", + "image_path": "d208b30a3585454f17d612022a903aa6a53c0a5936844eff395fb2c88f9dac8b.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_s\\in \\mathbb{R}^{n_u n_v n_t}" + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "text", + "content": " is the vectorized space-time measurements, " + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{f}\\in \\mathbb{R}^{n_x n_y n_z}" + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "text", + "content": " is the voxel occupancies, and " + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\in \\mathbb{R}^{n_u n_v n_t\\times n_x n_y n_z}" + }, + { + "bbox": [ + 305, + 437, + 545, + 519 + ], + "type": "text", + "content": " is the measurement operator mapping voxel occupancies to space-time measurements. 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The " + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "text", + "content": "th column vector of " + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "text", + "content": " is the space-time impulse response (STIR) to the " + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "text", + "content": "th illumination source when the hidden scene is completely occupied (note that we are dealing with shadow transients, not light transients). The " + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "text", + "content": "th column of " + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 305, + 520, + 545, + 713 + ], + "type": "text", + "content": " forms the expected space-time measurements" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9195" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "if only the " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "th voxel is occupied (i.e. the STIR to a single voxel). 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Therefore, the former is linear with respects to light transients, and the latter is linear with respect to shadow transients." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 213, + 194, + 227 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 194, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 194, + 227 + ], + "type": "text", + "content": "3.3. 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In practice, filtering " + }, + { + "bbox": [ + 47, + 274, + 288, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{bp}" + }, + { + "bbox": [ + 47, + 274, + 288, + 300 + ], + "type": "text", + "content": " with a Laplacian filter" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 97, + 309, + 287, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 309, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 97, + 309, + 287, + 342 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {f b p} = \\left(\\frac {\\partial^ {2}}{\\partial x ^ {2}} + \\frac {\\partial^ {2}}{\\partial y ^ {2}} + \\frac {\\partial^ {2}}{\\partial z ^ {2}}\\right) \\mathbf {f} _ {b p} \\tag {13}", + "image_path": "c158477a3da27f0598607961ec9c1076387336b231728281bf65be73ffec052a.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 351, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 471 + ], + "type": "text", + "content": "has been shown to yield reasonably good results in ellipsoidal tomography in 3-bounce NLOS and line-based tomography in medical imaging. Our linear formulation also enables reconstruction with priors. We recognize that these optimization-based methods would improve reconstruction over unfiltered backprojection, which is equivalent to a low-frequency version of voxel carving in our setup. However, we restrict our focus to unfiltered backprojection because of its convenient relationship with the Gram matrix, which enables further analysis of our method in Sec. 4.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 484, + 167, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 484, + 167, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 484, + 167, + 498 + ], + "type": "text", + "content": "4. Design and Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 505, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 625 + ], + "type": "text", + "content": "In this section, we analyze how the performance of the proposed two-bounce transient system varies with system parameters and the geometry of LOS relay surfaces. We also analyze the impact of temporal resolution, spatial resolution, and number of measurements on recoverability. The amount of multiplexing in the scene is inversely related to the number of measurements. For example, if 60 laser spots are used and 15 measurements are captured, then each image contains 4 multiplexed shadows. We use SNR, coherence, and FWHM of the PSF to quantify performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 634, + 163, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 163, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 163, + 647 + ], + "type": "text", + "content": "4.1. Voxel SNR Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "We quantify the noise characteristics of the measured shadow two-bounce transients using per-voxel SNR. Consider the case where only voxel " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " is occupied in the hidden region. We derive the SNR of the number of \"shadow\" photons received in the measured shadow transient " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_s^{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": ". In vector" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 71, + 537, + 175 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 537, + 175 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 537, + 175 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 537, + 175 + ], + "type": "image", + "image_path": "4f3db07091b483a62612cdaf18a59324896d0484893c3c68aaf647b579b2ea8a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 182, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 270 + ], + "type": "text", + "content": "Figure 5. SNR Analysis. The goal of this analysis is to determine how scene geometry affects the SNR of the two-bounce measurement at each voxel in the hidden scene. The first two cases consider the orientations of the relay surfaces, and the third considers the field of view of the camera. SNR is highest in the middle of the hidden scene for parallel surfaces, orienting the walls closer together increases SNR due to reduced " + }, + { + "bbox": [ + 304, + 182, + 547, + 270 + ], + "type": "inline_equation", + "content": "r^2" + }, + { + "bbox": [ + 304, + 182, + 547, + 270 + ], + "type": "text", + "content": " falloff, and SNR is highest closer to the virtual detectors for small FOV cameras." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 289, + 546, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 289, + 546, + 314 + ], + "spans": [ + { + "bbox": [ + 305, + 289, + 546, + 314 + ], + "type": "text", + "content": "form, the occupancy function can be described as " + }, + { + "bbox": [ + 305, + 289, + 546, + 314 + ], + "type": "inline_equation", + "content": "\\delta^{\\mathbf{x}}" + }, + { + "bbox": [ + 305, + 289, + 546, + 314 + ], + "type": "text", + "content": ". From Eq. (11), the shadow transient is given by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 402, + 320, + 545, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 320, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 402, + 320, + 545, + 334 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {s} ^ {\\mathbf {x}} = \\mathbf {A} \\delta^ {\\mathbf {x}} \\tag {14}", + "image_path": "70710fe66b00641e918573a0a9988dc09e716b110eaab385b4a8e7f357320e79.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "type": "text", + "content": "and the light transients measured by the SPAD sensor are given by " + }, + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_l^{\\mathbf{x}}" + }, + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "type": "text", + "content": ". For this analysis, we account for " + }, + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "type": "inline_equation", + "content": "r^2" + }, + { + "bbox": [ + 305, + 340, + 546, + 389 + ], + "type": "text", + "content": " falloff because it is a physically accurate phenomenon that impacts SNR. From Eq. (5)," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 392, + 395, + 545, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 395, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 392, + 395, + 545, + 408 + ], + "type": "interline_equation", + "content": "\\mathbf {I} _ {l} ^ {\\mathbf {x}} = \\mathbf {I} _ {0} - \\mathbf {A} \\delta^ {\\mathbf {x}} \\tag {15}", + "image_path": "e0acbc81dbe3dc93342b3893c690cff530ad73a715776e5030760ba076f68397.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_0" + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "text", + "content": " is the empty transient and assumed to be calibrated. Assuming no SPAD pile-up distortion, the number of photons arriving at the sensor for each time bin of " + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_l^{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "text", + "content": " follows an independent Poisson distribution [29]. Thus, the total number of photons " + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "inline_equation", + "content": "P^{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 415, + 546, + 499 + ], + "type": "text", + "content": " measured follows a Poisson distribution with the rate parameter being the sum of all the photon counts for all time bins for all pixels." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 361, + 505, + 545, + 519 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 505, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 361, + 505, + 545, + 519 + ], + "type": "interline_equation", + "content": "P ^ {\\mathbf {x}} \\sim \\operatorname {P o i s s o n} \\left(\\mathbf {1} ^ {T} \\left(\\mathbf {I} _ {0} - \\mathbf {A} \\delta^ {\\mathbf {x}}\\right)\\right) \\tag {16}", + "image_path": "f4924d29ababf9fd660430a29743f5a1159e63b5555bd6044f194762988c5d29.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "inline_equation", + "content": "\\mathbf{1} \\in \\mathbb{R}^{n_u n_v n_t}" + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "text", + "content": " is the one vector. Using the fact that SNR of a Poisson distribution is " + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "inline_equation", + "content": "\\mu / \\sigma = \\sqrt{\\lambda}" + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "text", + "content": " with rate parameter " + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "text", + "content": ", the per-voxel SNR " + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "inline_equation", + "content": "S^{\\mathbf{x}}" + }, + { + "bbox": [ + 304, + 525, + 546, + 562 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 376, + 569, + 545, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 569, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 376, + 569, + 545, + 588 + ], + "type": "interline_equation", + "content": "S ^ {\\mathbf {x}} = \\sqrt {\\mathbf {1} ^ {T} \\left(\\mathbf {I} _ {0} - \\mathbf {A} \\boldsymbol {\\delta} ^ {\\mathbf {x}}\\right)} \\tag {17}", + "image_path": "5d212e78f0465b6063405060ec67935fd0bcaca60d7a487d1f831a0494d1fa8e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "The per-voxel SNR is plotted in Fig. 5 for three different scenarios. The first two scenarios deal with the orientation of the walls, and the third considers the field of view of the camera. In Fig. 5a, we can see that the SNR is higher for center voxels, as more rays connecting the illumination wall and observation wall pass through the center voxels. When the relay walls are oriented towards each other (Fig. 5b), the SNR increases due to reduced " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "r^2" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " falloff. When the camera's field of view is small compared to the laser (Fig. 5c), regions closer to the observation wall have the highest SNR." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9196" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 79, + 267, + 199 + ], + "blocks": [ + { + "bbox": [ + 63, + 79, + 267, + 199 + ], + "lines": [ + { + "bbox": [ + 63, + 79, + 267, + 199 + ], + "spans": [ + { + "bbox": [ + 63, + 79, + 267, + 199 + ], + "type": "image", + "image_path": "5e8c362db0744c8c9755964b4fda3be0b9a90703ab8cbc9ccf84fdd8847089e7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 213, + 289, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 213, + 289, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 289, + 258 + ], + "type": "text", + "content": "Figure 6. Spatially Varying PSF. In two-bounce lidar, the PSF has a double cone shape. The orientation of the double cone varies strongly as a function of the orientation and length of the relay surfaces (i.e. the virtual apertures) and the voxel position." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 278, + 180, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 180, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 180, + 292 + ], + "type": "text", + "content": "4.2. Recoverability Analysis" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "type": "text", + "content": "Resolution We now study the resolution limits of our method. In particular, we consider two key metrics in our measurement operator: mutual coherence and full width at half maximum (FWHM) of the PSF. We are interested in how (1) temporal resolution, (2) spatial resolution " + }, + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "type": "text", + "content": ", and (3) number of measurements " + }, + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 297, + 287, + 393 + ], + "type": "text", + "content": " impact each of our metrics. From Eq. (12), we know that the backprojected occupancy can be obtained from the occupancy function by" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 402, + 287, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 402, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 133, + 402, + 287, + 417 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {b p} = \\left(\\mathbf {A} ^ {\\top} \\mathbf {A}\\right) \\mathbf {f}, \\tag {18}", + "image_path": "b81690130f368cfc0deb95c138366c35a5b89b0beca2ed11b9aabfceb2a28756.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{G} = \\mathbf{A}^{\\top}\\mathbf{A}" + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "text", + "content": " is the Gram matrix. We can interpret the columns (or rows) of the Gram matrix to be the spatially varying point spread function (PSF) of the imaging system, as shown in Fig. 6. Each column " + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_i" + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "text", + "content": " describes how a voxel " + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 426, + 287, + 486 + ], + "type": "text", + "content": " is blurred during backprojection reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": "We can see the effect of different imaging parameters on the PSF in Fig. 7, where we sweep different values of (1) " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": " and (2) " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": ". In particular, we note that the lobes of the PSF are suppressed when using temporal information, even with low spatial resolution and few number of image measurements. When using no temporal information, the PSF is still roughly centered at the correct location, but has large FWHM. The sharpness of the PSF when using temporal information indicates that it is better suited to applications that require finer voxel resolution with few-shot capture. In case (1) without transients, we see that the FWHM of the PSF is large along both the " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": " direction for small values of " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": " approaches the number of illumination spots, the FWHM approaches the theoretical lower bound. In case (2), increased spatial resolution helps better localize the center of the PSF, but the FWHM does not improve. The transient cases are quite robust to both low number of measurements and low spatial resolution. Intuitively, higher values of " + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 487, + 289, + 714 + ], + "type": "text", + "content": " in the transient case slightly help accentuate the center voxel" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 537, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 537, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 537, + 85 + ], + "type": "text", + "content": "by projecting more diverse rays through the center voxel." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 87, + 545, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 87, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 305, + 87, + 545, + 159 + ], + "type": "text", + "content": "Mutual Coherence We wish to further quantify the impact of spatio-temporal resolution and number of measurements on the recoverability of the hidden scene. We know from compressive sensing theory that sparse recovery of the hidden scene is possible when the mutual coherence of " + }, + { + "bbox": [ + 305, + 87, + 545, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 305, + 87, + 545, + 159 + ], + "type": "text", + "content": " is sufficiently small. The mutual coherence is defined as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 375, + 168, + 545, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 168, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 375, + 168, + 545, + 196 + ], + "type": "interline_equation", + "content": "\\mu = \\max _ {1 \\leq i \\neq j \\leq n} \\frac {\\left| \\mathbf {A} _ {i} ^ {\\top} \\mathbf {A} _ {j} \\right|}{\\left| \\mathbf {A} _ {i} \\right| \\left| \\mathbf {A} _ {j} \\right|}. \\tag {19}", + "image_path": "7c1e64fe84a9b1a3865908e7ca25c33ae13ec1546cdd7faa785e84867f7f5b0f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": "Intuitively, the coherence measures the largest \"similarity\" or correlation between any two column vectors in measurement matrix " + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": " [6]. Physically, this quantifies how similar the STIRs of two different voxels are. If " + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "inline_equation", + "content": "\\mu = 1" + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": ", then two voxels have the exact same STIR, which means that there exists an ambiguity as to which voxel resulted in a certain spatio-temporal response. Alternatively, " + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": " can be defined as the maximum off-diagonal entry of the Gram matrix. Fig. 8 illustrates how the Gram matrix (and subsequently the mutual coherence) is affected by coarser timing resolutions. From compressive sensing theory, we know that a " + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": "-sparse scene can be recovered if " + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "inline_equation", + "content": "K \\leq 0.5(1 + 1 / \\mu)" + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": ", which motivates our empirical analysis of the effect of spatial resolution and temporal resolution on " + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 203, + 546, + 371 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": "From Fig. 9, we can see the impact that spatial and temporal resolution have on mutual coherence in a single-shot setup with multiplexed illumination. Consider a scene similar to that of Fig. 6, where the walls are " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "2\\mathrm{m}" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": " apart, the walls are " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "3\\mathrm{m}" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": " long, the axial distance to the walls is " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "2\\mathrm{m}" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": ", and the voxel resolution is discretized to " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": ". Increasing the spatial resolution at a fixed temporal resolution appears to have little to no effect on the mutual coherence. As Kadambi et al. also point out, improvements of coherence through higher spatial resolution are limited by the size of the virtual aperture (i.e. the wall) [16]. On the other hand, the difference between " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "100~\\mathrm{ps}" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": " resolution and " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "10~\\mathrm{ps}" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": " resolution reduces the coherence from 0.9 to 0.3 for a fixed spatial resolution. Any timing resolution coarser than " + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "inline_equation", + "content": "\\sim 120" + }, + { + "bbox": [ + 304, + 371, + 546, + 587 + ], + "type": "text", + "content": " ps results in a coherence of 1 for multiplexed measurements because pathlength differences for different shadows are no longer resolvable. This analysis motivates the importance of temporal resolution when using multiplexed illumination." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 597, + 449, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 449, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 449, + 611 + ], + "type": "text", + "content": "5. Experiments and Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "We scan a single-pixel SPAD across the field of view on the left wall to mimic the output of a SPAD array. We scan a single laser spot across the right wall, and sum up the corresponding transient images in post-processing to mimic the effect of multiplexing. Further details are provided in the supplementary. We first validate our model using simulated data in Fig. 10, where we demonstrate that we can localize four letters and reconstruct their 2D shape with just a single" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9197" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 304, + 270 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 304, + 270 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 304, + 270 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 304, + 270 + ], + "type": "image", + "image_path": "8917c0c3376b274e4c1aec23ce917105bd1496bf57c63b2ca47e202dafefab2f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "text", + "content": "Figure 7. PSF as a Function of Number of Measurements and Spatial Resolution. The PSF of the center voxel is shown in the transient and intensity-only case when multiplexed with 60 laser spots. (1) the number of pixels " + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "inline_equation", + "content": "N = 40" + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "text", + "content": " are kept fixed with the number of measurements " + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "text", + "content": " being swept (left) and (2) " + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "inline_equation", + "content": "M = 10" + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "text", + "content": " is kept fixed and " + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 279, + 547, + 323 + ], + "type": "text", + "content": " is swept (right). Transient measurements result in PSFs with narrower FWHMs, even with low spatial resolution and low number of measurements." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 306, + 72, + 545, + 270 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 270 + ], + "type": "image", + "image_path": "1edc73563e372c28f865e5f33e9f5ed0763c3157ca12399ed9b489b4d511ba4e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 343, + 279, + 407 + ], + "blocks": [ + { + "bbox": [ + 55, + 343, + 279, + 407 + ], + "lines": [ + { + "bbox": [ + 55, + 343, + 279, + 407 + ], + "spans": [ + { + "bbox": [ + 55, + 343, + 279, + 407 + ], + "type": "image", + "image_path": "16f0d107255a743cc7c7b3edbfebd1230b98d899f7b505bddff4798abb3c252b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 419, + 287, + 497 + ], + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 497 + ], + "type": "text", + "content": "Figure 8. Gram Matrix as a Function of Temporal Resolution. For a defined voxel resolution and fixed spatial resolution. The columns (or rows) of the Gram matrix form the spatially varying PSFs shown in Fig. 6. The off-diagonal streaks describe the coherence between different voxels. As expected, higher temporal resolution decreases the coherence of the Gram matrix, which increases the likelihood of guaranteed sparse recovery." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": "capture. We render " + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "inline_equation", + "content": "i_{o}" + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "inline_equation", + "content": "i_{l}" + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": " to obtain a noiseless version of the shadow transient for this experiment. Then, we reconstruct the shapes of real mannequins and must estimate " + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "inline_equation", + "content": "i_{0}" + }, + { + "bbox": [ + 46, + 522, + 289, + 714 + ], + "type": "text", + "content": ". Fig. 11 shows that ToF measurements provide a noticeable improvement in image reconstruction. When there's no multiplexing (i.e., the number of laser spots is the same as number of measurements), the intensity-based method is similar to the ToF-based method. However, in the intensity-only case, the object becomes increasingly blurry until it is no longer visible as the amount of multiplexing increases. In the ToF case for single-shot, we can see a blurry image roughly localized where the center of the mannequin is as well as some high-frequency detail. Furthermore, the top view of the ToF reconstructions show that the high-frequency shape of the arms can be reconstructed even with multiplexed illumination, indicating the promise of single" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 348, + 344, + 504, + 476 + ], + "blocks": [ + { + "bbox": [ + 348, + 344, + 504, + 476 + ], + "lines": [ + { + "bbox": [ + 348, + 344, + 504, + 476 + ], + "spans": [ + { + "bbox": [ + 348, + 344, + 504, + 476 + ], + "type": "image", + "image_path": "a939948ccd7e2441a4107bbde6b02c4135b2b8f32bbefa8083f6280b2129e310.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "text", + "content": "Figure 9. Tradeoffs Between Spatial Resolution and Temporal Resolution. We quantify the tradeoff using mutual coherence. We use the same setup as Fig. 6, but the walls have length " + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "inline_equation", + "content": "3\\mathrm{m}" + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "text", + "content": ", the walls are space " + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "inline_equation", + "content": "2\\mathrm{m}" + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "text", + "content": " apart, and the distance to the walls is " + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "inline_equation", + "content": "2\\mathrm{m}" + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "text", + "content": ". We discretize the voxel resolution to " + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}(\\sim 67\\mathrm{ps})" + }, + { + "bbox": [ + 304, + 487, + 545, + 608 + ], + "type": "text", + "content": ". The bottom right of the figure, where spatial and temporal resolution are highest is where mutual coherence is the lowest. For a fixed temporal resolution, improvements in coherence quickly plateau. Improvements in temporal resolution dominate improvements in spatial resolution when reducing coherence, suggesting the importance of ToF for demultiplexing illumination in two-bounce NLOS imaging." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "shot capture with two-bounce ToF information. Fig. 12 shows that poorer temporal resolution results in aliasing artifacts (repeated arms and legs), whereas the rough shape of the object can still be seen with lower spatial resolution. Finally, we compare our method to the probabilistic voxel carving method used in [15] in Fig. 13. Voxel carving results in sharper reconstructions than backprojection." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9198" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 70, + 280, + 205 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 280, + 205 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 280, + 205 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 280, + 205 + ], + "type": "image", + "image_path": "73d56e3e1d2c94eac3c110d2cccf8f917bb7ef872fe2dbc3535b42a6c8e81187.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 214, + 289, + 281 + ], + "lines": [ + { + "bbox": [ + 46, + 214, + 289, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 289, + 281 + ], + "type": "text", + "content": "Figure 10. Single-Shot Localization. We obtain single-shot reconstructions of the \"N\", \"L\", \"O\", and \"S\" letters in the hidden scene with and without transient information. We see that using transient information, we are able to effectively localize the hidden object and even get a sharp outline of the letters, demonstrating the promise of single-shot capture with two-bounce transients." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 310, + 281, + 516 + ], + "blocks": [ + { + "bbox": [ + 56, + 310, + 281, + 516 + ], + "lines": [ + { + "bbox": [ + 56, + 310, + 281, + 516 + ], + "spans": [ + { + "bbox": [ + 56, + 310, + 281, + 516 + ], + "type": "image", + "image_path": "052e98ac960dfbd0dda5d08d4c729a58a63172b1586062dfa28ba96a9705a46b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 528, + 289, + 639 + ], + "lines": [ + { + "bbox": [ + 46, + 528, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 289, + 639 + ], + "type": "text", + "content": "Figure 11. Transients Enable Scene Recovery from Multiplexed Illumination. We perform backprojection of measurements with varying levels of multiplexing. Plotted in the top two rows are " + }, + { + "bbox": [ + 46, + 528, + 289, + 639 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 528, + 289, + 639 + ], + "type": "text", + "content": " slices of the reconstructed volume. Under no multiplexing (right), intensity is sufficient to carve the shadow along detected pixel. But reconstruction quality sharply deteriorates as we move towards the multiplexing regime (left). When measuring with transients, time-of-flight information allows us to disambiguate between different shadows and recover a rough silhouette of the object even with just a single measurement." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "However, our method can be improved by filtering or incorporating priors, and is also generalizable to multiplexed illumination by utilizing ToF information." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 317, + 73, + 521, + 222 + ], + "blocks": [ + { + "bbox": [ + 317, + 73, + 521, + 222 + ], + "lines": [ + { + "bbox": [ + 317, + 73, + 521, + 222 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 521, + 222 + ], + "type": "image", + "image_path": "ad76127c3b9f4afd934c1107a982ed0d2ca3477e6dc88bdfb5454de7fd317d7e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 228, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 305, + 228, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 547, + 275 + ], + "type": "text", + "content": "Figure 12. Spatial Resolution vs. Timing Resolution. We plot reconstructions with different spatio-temporal resolutions. Lower timing resolution results in aliasing artifacts (i.e. repeated arms and legs). Lower spatial resolution introduces hole artifacts." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 313, + 284, + 538, + 397 + ], + "blocks": [ + { + "bbox": [ + 313, + 284, + 538, + 397 + ], + "lines": [ + { + "bbox": [ + 313, + 284, + 538, + 397 + ], + "spans": [ + { + "bbox": [ + 313, + 284, + 538, + 397 + ], + "type": "image", + "image_path": "fd216f0dc7a5bd6663190c42867f44743f539f7e6a813ffe1cf67a6a302b7c89.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 403, + 547, + 449 + ], + "lines": [ + { + "bbox": [ + 305, + 403, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 403, + 547, + 449 + ], + "type": "text", + "content": "Figure 13. Scanning Baseline Comparison. We compare to the voxel carving method used in [15] (a) before and (b) after thresholding when scanning 1 laser spot. Our method is more general, but voxel carving yields sharper results with laser scanning." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 468, + 375, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 375, + 481 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 375, + 481 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 489, + 547, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 547, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 547, + 646 + ], + "type": "text", + "content": "In this paper, we introduced the use of two-bounce transients for NLOS imaging. Compared to 3B-NLOS, 2B-NLOS enables more robust imaging of occluded objects in the presence of scenes with arbitrary lighting conditions and low albedo objects. Transient 2B-NLOS is promising for few-shot capture of occluded objects by using multiplexed illumination, especially as SPAD array technology matures. When comparing tradeoffs in temporal resolution, spatial resolution, and number of measurements, we qualitatively and quantitatively verify with real and simulated results that temporal resolution is most important for demultiplexing shadows. We anticipate future work to extend the analysis in this paper to SPAD arrays for real-time NLOS imaging." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 657, + 409, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 409, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 409, + 671 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "AD and AV are supported by NSF Expeditions Award #IIS-1730574 and NSF CAREER Award #IIS-1652633. CH was supported by a Draper Scholarship." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "9199" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "type": "text", + "content": "[1] Fadel Adib and Dina Katabi. 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IEEE Open Journal of the Solid-State Circuits Society, 2:3-11, 2021. 2" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "9201" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_content_list.json b/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..bba8a2967ffc7fe50ec6715c85e10aaacca34cec --- /dev/null +++ b/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_content_list.json @@ -0,0 +1,1538 @@ +[ + { + "type": "text", + "text": "Rotation-Invariant Transformer for Point Cloud Matching", + "text_level": 1, + "bbox": [ + 189, + 130, + 782, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hao Yu $^{1}$ Zheng Qin $^{2}$ Ji Hou $^{3}$ Mahdi Saleh $^{1,4}$ Dongsheng Li $^{2}$ Benjamin Busam $^{1,4}$ Slobodan Ilic $^{1,5}$ TU Munich $^{2}$ NUDT $^{3}$ Meta Reality Labs $^{4}$ 3Dwe.ai $^{5}$ Siemens AG, Munich", + "bbox": [ + 86, + 179, + 915, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 313, + 267 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The intrinsic rotation invariance lies at the core of matching point clouds with handcrafted descriptors. However, it is widely despised by recent deep matchers that obtain the rotation invariance extrinsically via data augmentation. As the finite number of augmented rotations can never span the continuous $SO(3)$ space, these methods usually show instability when facing rotations that are rarely seen. To this end, we introduce RoITr, a Rotation-Invariant Transformer to cope with the pose variations in the point cloud matching task. We contribute both on the local and global levels. Starting from the local level, we introduce an attention mechanism embedded with Point Pair Feature (PPF)-based coordinates to describe the pose-invariant geometry, upon which a novel attention-based encoder-decoder architecture is constructed. We further propose a global transformer with rotation-invariant cross-frame spatial awareness learned by the self-attention mechanism, which significantly improves the feature distinctiveness and makes the model robust with respect to the low overlap. Experiments are conducted on both the rigid and non-rigid public benchmarks, where RoITr outperforms all the state-of-the-art models by a considerable margin in the low-overlapping scenarios. Especially when the rotations are enlarged on the challenging 3DLoMatch benchmark, RoITr surpasses the existing methods by at least 13 and 5 percentage points in terms of Inlier Ratio and Registration Recall, respectively. Code is publicly available1.", + "bbox": [ + 76, + 282, + 473, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The correspondence estimation between a pair of partially-overlapping point clouds is a long-standing task that lies at the core of many computer vision applications, such as tracking [17, 18], reconstruction [22, 23, 39], pose estimation [19, 27, 50] and 3D representation learning [15, 16, 46], etc. In a typical solution, geometry is first encoded into descriptors, and correspondences are then established between two frames by matching the most similar descriptors. As the two frames are observed from different views, depicting the same geometry under different trans", + "bbox": [ + 76, + 726, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81825f8e94531760f124a36a4048f3485bea7faa274c6d8e55532d5c6f8d23a7.jpg", + "image_caption": [ + "Figure 1. Feature Matching Recall (FMR) on 3DLoMatch [19] and Rotated 3DLoMatch. Distance to the diagonal represents the robustness against rotations. Among all the state-of-the-art approaches, RoITr not only ranks first on both benchmarks but also shows the best robustness against the enlarged rotations." + ], + "image_footnote": [], + "bbox": [ + 501, + 250, + 893, + 422 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "formations identically, i.e., the pose-invariance, becomes the key to success in the point cloud matching task.", + "bbox": [ + 498, + 503, + 890, + 534 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since the side effects caused by a global translation can always be easily eliminated, e.g., by aligning the barycenter with the origin, the attention naturally shifts to coping with the rotations. In the past, handcrafted local descriptors [11, 30, 31, 41] were designed to be rotation-invariant so that the same geometry observed from different views can be correctly matched. With the emergence of deep neural models for 3D point analysis, e.g., multilayer perceptrons (MLPs)-based like PointNet [25, 26], convolutions-based like KPConv [6, 40], and the attention-based like PointTransformer [33, 53], recent approaches [1, 7, 9, 10, 13, 19, 20, 27, 32, 48-51] propose to learn descriptors from raw points as an alternative to handcrafted features that are less robust to occlusion and noise. The majority of deep point matchers [7, 10, 19, 20, 27, 34, 48, 50-52] is sensitive to rotations. Consequently, their invariance to rotations must be obtained extrinsically via augmented training to ensure that the same geometry under different poses can be depicted similarly. However, as the training cases can never span the continuous $SO(3)$ space, they always suffer from instability when facing rotations that are rarely seen during training. This can be observed by a significant performance drop under enlarged rotations at inference time. (See Fig. 1.)", + "bbox": [ + 496, + 536, + 892, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There are other works [1, 9, 13, 32, 44] that only lever", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 1, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://github.com/haoyu94/RoITr", + "bbox": [ + 94, + 886, + 284, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5384", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "age deep neural networks to encode the pure geometry with the intrinsically-designed rotation invariance. However, the intrinsic rotation invariance comes at the cost of losing global context. For example, a human's left and right halves are almost identically described, which naturally degrades the distinctiveness of features. Most recently, RIGA [49] is proposed to enhance the distinctiveness of the rotation-invariant descriptors by incorporating a global context, e.g., the left and right halves of a human become distinguishable by knowing there is a chair on the left while a table on the right. However, it lacks a highly-representative geometry encoder since it relies on PointNet [25], which accounts for an ineffective local geometry description. Moreover, as depicting the cross-frame spatial relationships is non-trivial, previous works [19, 27, 34, 50] merely leverage the contextual features in the cross-frame context aggregation, which neglects the positional information. Although RIGA proposes to learn a rotation-invariant position representation by leveraging an additional PointNet, this simple design is hard to model the complex cross-frame positional relationships and leads to less distinctive descriptors.", + "bbox": [ + 76, + 90, + 472, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present Rotation-Invariant Transformer (RoITr) to tackle the problem of point cloud matching under arbitrary pose variations. By using Point Pair Features (PPFs) as the local coordinates, we propose an attention mechanism to learn the pure geometry regardless of the varying poses. Upon it, attention-based layers are further proposed to compose the encoder-decoder architecture for highly-discriminative and rotation-invariant geometry encoding. We demonstrate its superiority over PointTransformer [53], a state-of-the-art attention-based backbone network, in terms of both efficiency and efficacy in Fig. 8 and Tab. 4 (a), respectively. On the global level, the cross-frame position awareness is introduced in a rotation-invariant fashion to facilitate feature distinctiveness. We illustrate its significance over the state-of-the-art design [27] in Tab. 4 (d). Our main contributions are summarized as:", + "bbox": [ + 76, + 407, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An attention mechanism designed to disentangle the geometry and poses, which enables the pose-agnostic geometry description.", + "- An attention-based encoder-decoder architecture that learns highly-representative local geometry in a rotation-invariant fashion.", + "- A global transformer with rotation-invariant cross-frame position awareness that significantly enhances the feature distinctiveness." + ], + "bbox": [ + 94, + 659, + 468, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 814, + 218, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Models with Extrinsic Rotation Invariance. The mainstream of deep learning-based point cloud matching approaches is intrinsically rotation-sensitive. Pioneers [10,51] learn to describe local patches from a rotation-variant input.", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "FCGF [7] leverages fully-convolutional networks to accelerate the geometry description. D3Feat [3] jointly detects and describes sparse keypoints for matching. Predator [19] incorporates the global context to enhance the local descriptors and predicts the overlap regions for keypoint sampling. CoFiNet [50] extracts coarse-to-fine correspondences to alleviate the repeatability issue of keypoints. GeoTrans [27] considers the geometric information in fusing the intra-frame context globally. However, the awareness of spatial positions is missing in the cross-frame aggregation. Lepard [20] extends the non-rigid shape matching [34, 38, 42] to point clouds [28] and proposes a re-positioning module to alleviate the pose variations. REGTR [48] directly regresses the corresponding coordinates and registers point clouds in an end-to-end fashion. Nonetheless, all of these methods suffer from instability with additional rotations.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Methods with Intrinsic Rotation Invariance. A branch of handcrafted descriptors [8, 14, 41] aligns the input to a canonical representation according to an estimated local reference frame (LRF), while the others [11, 30, 31] mine the rotation-invariant components and encode them as the representation of the local geometry. Inspired by that, some deep learning-based methods [1, 4, 9, 13, 32, 34, 49] are designed to be intrinsically rotation-invariant to make the neural models focus on the pose-agnostic pure geometry. As a pioneer, PPF-FoldNet [9] consumes PPF-based patches and learns the descriptors using a FoldingNet [47]-based architecture without supervision. LRF-based works [1, 13, 32, 34] achieve rotation invariance by aligning their input to the defined canonical representation. YOHO [44] adopts a group of rotations to learn a rotation-equivariant feature group and further obtain the invariance via group pooling. A common problem of the rotation-invariant methods is the less distinctive features. Although RIGA [49] incorporates the global context into local descriptors to enhance the feature distinctiveness, its ineffective local geometry encoding and global position description learned by PointNet [25] still constraint the representation ability of its descriptors.", + "bbox": [ + 496, + 333, + 892, + 665 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 672, + 589, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Problem Statement. We tackle the problem of matching a pair of partially-overlapping point clouds $\\mathbf{P} \\in \\mathbb{R}^{n \\times 3}$ and $\\mathbf{Q} \\in \\mathbb{R}^{m \\times 3}$ , and extract a correspondence set $\\hat{\\mathcal{C}} = \\{(\\hat{\\mathbf{p}}_i, \\hat{\\mathbf{q}}_j) | \\hat{\\mathbf{p}}_i \\in \\hat{\\mathbf{P}} \\subseteq \\mathbf{P}, \\hat{\\mathbf{q}}_j \\in \\hat{\\mathbf{Q}} \\subseteq \\mathbf{Q}\\}$ that minimizes:", + "bbox": [ + 498, + 699, + 890, + 761 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{| \\hat {\\mathcal {C}} |} \\sum_ {(\\hat {\\mathbf {p}} _ {i}, \\hat {\\mathbf {q}} _ {j}) \\in \\hat {\\mathcal {C}}} \\| \\mathcal {M} ^ {*} (\\hat {\\mathbf {p}} _ {i}) - \\hat {\\mathbf {q}} _ {j} \\| _ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 767, + 890, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\| \\cdot \\| _2$ denotes the Euclidean norm and $|\\cdot |$ is the set cardinality. $\\mathcal{M}^{*}(\\cdot)$ stands for the ground-truth mapping function that maps $\\hat{\\mathbf{p}}_i$ to its corresponding position in $\\hat{\\mathbf{Q}}$ . In rigid scenarios, it is defined by a transformation $\\mathbf{T}^{*}\\in SE(3)$ . For the non-rigid cases it can be denoted as a per-point flow $\\mathbf{f}_i^*\\in \\mathbb{R}^3$ known as the deformation field.", + "bbox": [ + 496, + 808, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5385", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/352f993e80b8039c3fff593ff3b3710cc2efb699d5437ea5534831fd617b8f8e.jpg", + "image_caption": [ + "(0). Input" + ], + "image_footnote": [], + "bbox": [ + 86, + 89, + 305, + 164 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/db87a1d376332b7b03618dd5794cdaa08a7516290f18cc9528e01d25c924b84b.jpg", + "image_caption": [ + "(2).Aggregation" + ], + "image_footnote": [], + "bbox": [ + 308, + 89, + 656, + 178 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/974288bc32060553067e5aa14d8a1b36e4504339339ba487679a2a0f3eddfa37.jpg", + "image_caption": [ + "(5). Output" + ], + "image_footnote": [], + "bbox": [ + 648, + 97, + 883, + 169 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4e5ef51993cd3abfeb8ba841a2aba0b59cbc3d108e6b058fc3f2d67369ad52e6.jpg", + "image_caption": [ + "(1).Encoder" + ], + "image_footnote": [], + "bbox": [ + 91, + 205, + 303, + 354 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/09130879a56551a0ae9902d954d95aa14320b2226c7bf4ba302d260c1e117218.jpg", + "image_caption": [ + "(3). Decoder" + ], + "image_footnote": [], + "bbox": [ + 310, + 205, + 658, + 354 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ebbdcf4c197d78aed4fe93f07f359b890d055be2d6966b8ff2e9b4e25a40194c.jpg", + "image_caption": [ + "(4). Matching" + ], + "image_footnote": [], + "bbox": [ + 669, + 207, + 883, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Method Overview. An overview of RoITr is shown in Fig. 2. RoITr consists of an encoder-decoder architecture named Point Pair Feature Transformer (PPFTrans) for local geometry encoding and a stack of $g \\times$ global transformers for global context aggregation. Correspondence set $\\hat{C}$ is extracted by the coarse-to-fine matching [50].", + "bbox": [ + 75, + 542, + 468, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. PPF Attention Mechanism", + "text_level": 1, + "bbox": [ + 76, + 648, + 316, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Fig. 3 compares three different self-attention mechanisms. The standard attention [43] only leverages the input context to obtain the Query $\\mathbf{Q}$ and Key $\\mathbf{K}$ to compute the contextual attention $\\mathbf{A}_C$ , as well as the Value $\\mathbf{V}$ that encodes information for the contextual message $\\mathbf{M}_C$ . GeoTrans [27] proposes to learn the positional encoding $\\mathbf{E}$ from the geometry and calculates a second attention $\\mathbf{A}_G$ to reweigh $\\mathbf{A}_C$ . However, the cues contained in the raw geometry are totally neglected. To this end, we propose to learn the pose-agnostic geometric cues $\\mathbf{G}$ and further generate the geometric message $\\mathbf{M}_G$ in the PPF Attention Mechanism (PAM). On the local level, $\\mathbf{M}_G$ is combined with $\\mathbf{M}_C$ for feature enhancement, while on the global level, it is used to learn the rotation-invariant position representation for the cross-frame context aggregation. More specifically, we de", + "bbox": [ + 75, + 674, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c0b712b6186087050f178483da8e9448683cbb6f8c24b4fae9914085547debf4.jpg", + "image_caption": [ + "(a). Standard Attention" + ], + "image_footnote": [], + "bbox": [ + 514, + 544, + 614, + 628 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/050ce13ccd9012d289ebabdf10f1e5aa082cc00677dad1952586dbd8194f9d92.jpg", + "image_caption": [ + "Figure 2. An Overview of RoITr. From left to right: $(\\pmb{0})$ . RoITr takes as input a pair of triplets $\\mathcal{P} = (\\mathbf{P}, \\mathbf{N}, \\mathbf{X})$ and $\\mathcal{Q} = (\\mathbf{Q}, \\mathbf{M}, \\mathbf{Y})$ , each with three dimensions referring to the point cloud, the estimated normals, and the initial features. (1).[§ 3.2] A stack of encoder blocks hierarchically downsamples the points to coarser superpoints and encodes the local geometry, yielding superpoint triplets $\\mathcal{P}'$ and $\\mathcal{Q}'$ . Each encoder block consists of an Attentional Abstraction Layer (AAL) for downsampling and abstraction, followed by $e \\times$ PPF Attention Layers (PALs) for local geometry encoding and context aggregation. Both of them are based on our proposed PPF Attention Mechanism (PAM), which enables the pose-agnostic encoding of pure geometry. (See Fig. 3 and Fig. 4). (2).[§ 3.3] Global information is fused to enhance the superpoint features of $\\mathcal{P}'$ and $\\mathcal{Q}'$ . The geometric cues are globally aggregated as a rotation-invariant position representation, which introduces spatial awareness in the consecutive cross-frame context aggregation. After a stack of $g \\times$ global transformers, the globally-enhanced triplets $\\widetilde{\\mathcal{P}}'$ and $\\widetilde{\\mathcal{Q}}'$ are produced. (3).[§ 3.2] Superpoint triplets $\\mathcal{P}'$ and $\\mathcal{Q}'$ are decoded to point triplets $\\hat{\\mathcal{P}}$ and $\\hat{\\mathcal{Q}}$ by a stack of decoder blocks. Each block consists of a Transition Up Layer (TUL) for upsampling and context aggregation, followed by $d \\times$ PALs. (4).[§ 3.4] By adopting the coarse-to-fine matching [50], $\\widetilde{\\mathcal{P}}'$ and $\\widetilde{\\mathcal{Q}}'$ are matched to generate superpoint correspondences, which are consecutively refined to point correspondences between $\\hat{\\mathcal{P}}$ and $\\hat{\\mathcal{Q}}$ . (5). $\\hat{\\mathcal{C}}$ is established between $\\hat{\\mathcal{P}}$ and $\\hat{\\mathcal{Q}}$ .", + "(b). GeoTrans" + ], + "image_footnote": [], + "bbox": [ + 620, + 542, + 741, + 628 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1ae7e04b44a0ede10cb1f694b3023f8ff8b9887eed7c1e32a5a65db1f3724d8b.jpg", + "image_caption": [ + "(c).PAM (Ours)", + "Figure 3. Illustration of different self-attention computation in the standard attention [43], GeoTrans [27], and PAM." + ], + "image_footnote": [], + "bbox": [ + 746, + 542, + 885, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fine PAM on an Anchor triplet $\\mathcal{P}^A = (\\mathbf{P}^A, \\mathbf{N}^A, \\mathbf{X}^A)$ and a Support triplet $\\mathcal{P}^S = (\\mathbf{P}^S, \\mathbf{N}^S, \\mathbf{X}^S)$ , both with three dimensions referring to the point cloud, the estimated normals, and the associated features, respectively. PAM aggregates the learned context and geometric cues from $\\mathcal{P}^S$ and flows the messages to $\\mathcal{P}^A$ .", + "bbox": [ + 496, + 702, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pose-Agnostic Coordinate Representation. The basis of PAM is the pose-agnostic local coordinate representation that we construct based on PPFs [11]. Let $\\mathcal{P}_i^A \\coloneqq (\\mathbf{p}_i^A \\in \\mathbf{P}^A, \\mathbf{n}_i^A \\in \\mathbf{N}^A, \\mathbf{x}_i^A \\in \\mathbf{X}^A) \\in \\mathcal{P}^A$ denote the triplet constructed by picking the $i^{th}$ item on each dimension. For each $\\mathbf{p}_i^A$ , a subset of $\\mathcal{P}^S$ is first retrieved according to the Euclidean distance w.r.t. $\\mathbf{P}^S$ , denoted as", + "bbox": [ + 496, + 795, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5386", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5081a262fa30968f29b7c9345f2e9eb18f9480785ff18366f83ba9c4b08632b3.jpg", + "image_caption": [ + "Figure 4. Left: The workflow of the PPF Attention Mechanism (PAM). Right: Detailed calculation of the attention." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 472, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{P}_{\\mathcal{N}(i)}^{S} \\coloneqq (\\mathbf{P}_{\\mathcal{N}(i)}^{S}, \\mathbf{N}_{\\mathcal{N}(i)}^{S}, \\mathbf{X}_{\\mathcal{N}(i)}^{S}) \\subseteq \\mathcal{P}^{S}$ , with $\\mathcal{N}(i)$ the indices of $k$ -nearest neighbors. We then adopt PPFs [11] to construct a local coordinate system around each $\\mathbf{p}_i^A$ to represent the pose-agnostic position of $\\mathbf{P}_{\\mathcal{N}(i)}^{S}$ w.r.t. it. The coordinate of point $\\mathbf{p}_j^S \\in \\mathbf{P}_{\\mathcal{N}(i)}^{S}$ is transferred to:", + "bbox": [ + 75, + 280, + 470, + 364 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {e} _ {j} ^ {S} = \\left(\\| \\mathbf {d} \\| _ {2}, \\angle \\left(\\mathbf {n} _ {i} ^ {A}, \\mathbf {d}\\right), \\angle \\left(\\mathbf {n} _ {j} ^ {S}, \\mathbf {d}\\right), \\angle \\left(\\mathbf {n} _ {j} ^ {S}, \\mathbf {n} _ {i} ^ {A}\\right)\\right), \\quad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 375, + 468, + 395 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\mathbf{d} = \\mathbf{p}_j^S -\\mathbf{p}_i^A$ , and $\\mathbf{n}_i^A$ and $\\mathbf{n}_j^S$ the estimated normals of $\\mathbf{p}_i^A$ and $\\mathbf{p}_j^S$ , respectively. $\\angle (\\mathbf{v}_1,\\mathbf{v}_2)$ computes the angles between the two vectors [5, 9]. The transferred coordinates of $\\mathbf{P}_{\\mathcal{N}(i)}^{S}$ are denoted as $\\mathbf{E}_{\\mathcal{N}(i)}^{S}$", + "bbox": [ + 75, + 402, + 468, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "PPF Attention Mechanism. PPF Attention Mechanism (PAM) takes as input the Support triplet $\\mathcal{P}^S$ and the Anchor point cloud $\\mathbf{P}^A$ with estimated normals $\\mathbf{N}^A$ . PAM generates the Anchor features $\\mathbf{X}^A$ by aggregating the pose-agnostic local geometry and highly-representative learned context from $\\mathcal{P}^S$ , which is defined as:", + "bbox": [ + 75, + 468, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} ^ {A} = \\delta \\left(\\mathbf {P} ^ {A}, \\mathbf {N} ^ {A} \\mid \\mathcal {P} ^ {S}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 570, + 468, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\delta(\\cdot)$ representing PAM. As shown in Fig. 4 (a), for each $\\mathbf{p}_i^A \\in \\mathbf{P}^A$ with normal $\\mathbf{n}_i^A$ , we find its nearest point $\\mathbf{p}_j^S \\in \\mathbf{P}^S$ whose associated feature $\\mathbf{x}_j^S$ is assigned to $\\mathbf{p}_i^A$ as the initial description. Then, $k$ -nearest neighbors from $\\mathbf{P}^S$ are retrieved according to the Euclidean distance in 3D space, yielding $\\mathbf{P}_{\\mathcal{N}(i)}^S \\subseteq \\mathbf{P}^S$ and $\\mathbf{X}_{\\mathcal{N}(i)}^S \\subseteq \\mathbf{X}^S$ . Following Eq. 2, $\\mathbf{P}_{\\mathcal{N}(i)}^S$ is transferred to the pose-agnostic position representation $\\mathbf{E}_{\\mathcal{N}(i)}^S$ , which is consecutively projected to the coordinate embedding $\\mathbf{E}_S$ via a linear layer. $\\mathbf{x}_j^S$ and $\\mathbf{X}_{\\mathcal{N}(i)}^S$ are projected to the contextual features $\\mathbf{x}_S$ and $\\mathbf{X}_S$ by a second shared linear layer, respectively. In Fig. 4 (b), the attention mechanism uses five learnable matrices $\\mathbf{W}_G$ , $\\mathbf{W}_E$ , $\\mathbf{W}_Q$ , $\\mathbf{W}_K$ , and $\\mathbf{W}_V$ to project the input. Specifically, $\\mathbf{W}_G$ and $\\mathbf{W}_E$ project the input coordinate representation to the geometric cues and positional encoding by:", + "bbox": [ + 75, + 595, + 470, + 834 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} = \\mathbf {E} _ {S} \\mathbf {W} _ {G} \\quad \\text {a n d} \\quad \\mathbf {E} = \\mathbf {E} _ {S} \\mathbf {W} _ {E}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 847, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "respectively. Similarly, $\\mathbf{W}_Q$ , $\\mathbf{W}_K$ , and $\\mathbf{W}_V$ project the learned context to Query, Key, and Value as:", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {q} = \\mathbf {x} _ {S} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} _ {S} \\mathbf {W} _ {K}, \\text {a n d} \\mathbf {V} = \\mathbf {X} _ {S} \\mathbf {W} _ {V}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 119, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "respectively. The attention a that measures the feature similarity, and the message m that encodes both the pose-agnostic geometry and the representative context read as:", + "bbox": [ + 498, + 142, + 890, + 186 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {q} \\mathbf {E} ^ {T} + \\mathbf {q} \\mathbf {K} ^ {T}}{\\sqrt {c _ {0}}}\\right) \\quad \\text {a n d} \\quad \\mathbf {m} = \\mathbf {a} \\mathbf {G} + \\mathbf {a} \\mathbf {V}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 198, + 890, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "respectively. The message $\\mathbf{m}$ is projected and aggregated to $\\mathbf{x}_j^S$ via an element-wise addition followed by a normalization through LayerNorm [2]. The final linear layer projects the obtained feature to $\\mathbf{x}_i^A$ , from which $\\mathbf{X}^A$ is obtained to formulate the output $\\mathcal{P}^A$ with the known $\\mathbf{P}^A$ and $\\mathbf{N}^A$ .", + "bbox": [ + 498, + 244, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. PPFTrans for Local Geometry Description", + "text_level": 1, + "bbox": [ + 498, + 332, + 862, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overview. As illustrated in Fig. 2, PPFTrans consumes triplets $\\mathcal{P}$ and $\\mathcal{Q}$ . Taking $\\mathcal{P} = (\\mathbf{P},\\mathbf{N},\\mathbf{X})$ as an example, it consists of $\\mathbf{P} \\in \\mathbb{R}^{n \\times 3}$ the points cloud, $\\mathbf{N} \\in \\mathbb{R}^{n \\times 3}$ the normals estimated from $\\mathbf{P}$ , and $\\mathbf{X} = \\vec{\\mathbf{1}} \\in \\mathbb{R}^{n \\times 1}$ the initial point features. The encoder produces the superpoint triplet $\\mathcal{P}' = (\\mathbf{P}',\\mathbf{N}',\\mathbf{X}')$ with $\\mathbf{P}' \\in \\mathbb{R}^{n' \\times 3}$ and $\\mathbf{X}' \\in \\mathbb{R}^{n' \\times c'}$ . With the consecutive decoder, $\\mathcal{P}'$ is decoded to a triplet $\\hat{\\mathcal{P}} = (\\hat{\\mathbf{P}},\\hat{\\mathbf{N}},\\hat{\\mathbf{X}})$ including $\\hat{n}$ points with features $\\hat{\\mathbf{X}} \\in \\mathbb{R}^{\\hat{n} \\times \\hat{c}}$ . Notably, as we adopt a Farthest Point Sampling (FPS) strategy [26], it always satisfies that $\\mathbf{P}' \\subseteq \\hat{\\mathbf{P}} \\subseteq \\mathbf{P}$ . The same goes for a second point cloud $\\mathbf{Q}$ with an input triplet $\\mathcal{Q} = (\\mathbf{Q} \\in \\mathbb{R}^{m \\times 3},\\mathbf{M} \\in \\mathbb{R}^{m \\times 3},\\mathbf{Y} = \\vec{\\mathbf{1}} \\in \\mathbb{R}^{m \\times 1})$ by the shared architecture. In the rest of this paper, we only demonstrate for $\\mathcal{P}$ unless the model processes $\\mathcal{Q}$ differently. Encoder. The encoder is constructed by stacking several encoder blocks, each including an Attentional Abstraction Layer (AAL) followed by $e \\times$ PPF Attention Layers (PALs). Each block consumes the output of the previous block as the Support triplet $\\mathcal{P}^S$ ( $\\mathcal{P}^S = \\mathcal{P}$ for the first block). $\\mathcal{P}^S$ first flows to AAL, where Anchor points $\\mathbf{P}^A$ with associated normals $\\mathbf{N}^A$ are obtained via FPS [26]. The Anchor triplet $\\mathcal{P}^A$ is then generated in AAL via a PAM following Eq. 3. A sequence of PALs is applied for enhancing the Anchor features $\\mathbf{X}^A$ , each updating the features as:", + "bbox": [ + 498, + 357, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} ^ {A} \\leftarrow \\theta (\\mathcal {P} ^ {A}) = \\operatorname {R e L U} \\left(\\mathbf {X} ^ {A} + \\phi \\left(\\delta \\left(\\mathbf {P} ^ {A}, \\mathbf {N} ^ {A} \\mid \\mathcal {P} ^ {A}\\right)\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 731, + 890, + 751 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\phi$ the LayerNorm [2], $\\delta$ the PAM, and $\\theta$ the PAL. $\\leftarrow$ depicts feature updating. The encoder block outputs the updated $\\mathcal{P}^A$ , and the output of the whole encoder is defined as $\\mathcal{P}'$ , which is the output of the final encoder block.", + "bbox": [ + 498, + 763, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoder. We build the decoder by stacking a series of decoder blocks, each consisting of a Transition Up Layer (TUL) followed by $d \\times \\mathrm{PAL}$ . Each block takes the output of the previous block as the Anchor triplet $\\mathcal{P}^A$ ( $\\mathcal{P}^A = \\mathcal{P}'$ for the first block), and takes the Support", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5387", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f4b3f87f9e83497fcc7b10f0844a7cef1f6e7b788a4cf5fc18e8d0079f4a86bd.jpg", + "image_caption": [ + "(a). Geometry-Aware Self-Attention" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 316, + 239 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d764f44f9d306301505fa374dfc9c5743da0b1b9c69a915b710abec5d66a715b.jpg", + "image_caption": [ + "(b). Position-Aware Cross-Attention", + "Figure 5. The computation graph of our global transformer consisting of the Geometry-Aware Self-Attention Module (GSM) and Position-Aware Cross-Attention Module (PCM)." + ], + "image_footnote": [], + "bbox": [ + 320, + 90, + 468, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "triplet $\\mathcal{P}^S$ from the encoder via skip connections. The input flows to TUL, where each feature $\\widetilde{\\mathbf{x}}_j^S\\in \\widetilde{\\mathbf{X}}^S$ assigned to $\\mathbf{p}_j^S\\in \\mathbf{P}^S$ is interpolated by:", + "bbox": [ + 75, + 306, + 468, + 357 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {x}} _ {j} ^ {S} = \\frac {\\sum_ {i \\in \\mathcal {N} (j)} w _ {i} ^ {j} \\mathbf {x} _ {i} ^ {A}}{\\sum_ {i \\in \\mathcal {N} (j)} w _ {i} ^ {j}}, \\text {w i t h} w _ {i} ^ {j} = \\frac {1}{\\left\\| \\mathbf {p} _ {j} ^ {S} - \\mathbf {p} _ {i} ^ {A} \\right\\| _ {2}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 359, + 468, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\mathcal{N}(j)$ the $k$ -nearest neighbors of $\\mathbf{p}_j^S$ in $\\mathbf{P}^A$ . Features are updated by two linear layers as $\\mathcal{P}^S \\gets \\zeta_1(\\mathbf{X}^S) + \\zeta_2(\\widetilde{\\mathbf{X}}^S)$ . A sequence of PALs is adopted after TUL, each enhancing the features as $\\mathcal{P}^S \\gets \\theta(\\mathcal{P}^S)$ according to Eq. 7. The decoder block outputs the updated $\\mathcal{P}^S$ , and the output of the whole decoder is denoted as $\\hat{\\mathcal{P}}$ , which is the output of the final decoder block.", + "bbox": [ + 75, + 410, + 468, + 521 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Global Transformer for Context Aggregation", + "text_level": 1, + "bbox": [ + 76, + 530, + 459, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overview. Our designed global transformer takes as input a pair of triplets $\\mathcal{P}'$ and $\\mathcal{Q}'$ , and enhances the features with the global context, yielding $\\widetilde{\\mathbf{X}}' \\in \\mathbb{R}^{n' \\times c'}$ and $\\widetilde{\\mathbf{Y}}' \\in \\mathbb{R}^{m' \\times c'}$ , respectively. We stack $g \\times$ global transformers, with each including a Geometry-Aware Self-Attention Module (GSM) and a Position-Aware Cross-Attention Module (PCM) (See Fig. 2 and Fig. 5). Different from previous works [19, 27, 48-50] that totally neglect the cross-frame spatial relationships, we propose to learn a rotation-invariant position representation for each superpoint to enable the position-aware cross-frame context aggregation.", + "bbox": [ + 75, + 551, + 468, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Geometry-Aware Self-Attention Module. On the global level, we modify PAM to learn the rotation-invariant position representation and to aggregate the learned context across the whole frame simultaneously. The design of GSM is detailed in Fig. 5 (a). GSM has two branches, where the geometry branch mines the geometric cues from the pairwise rotation-invariant geometry representation proposed in [27], and the context branch aggregates the global context across the frame. We refer the readers to the Appendix for the detailed construction of $\\mathbf{R}' \\in \\mathbb{R}^{n' \\times n' \\times c'}$ and the ablation study on it. Similar to Eq. 4, the geometric cues $\\mathbf{G}'$ and the positional encoding $\\mathbf{E}'$ are linearly projected from", + "bbox": [ + 75, + 719, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathbf{R}^{\\prime}$ . $\\mathbf{E}^{\\prime}$ is further processed in the geometry branch and finally leveraged as the rotation-invariant position representation. In the context branch, $\\mathbf{Q}^{\\prime}$ , $\\mathbf{K}^{\\prime}$ , and $\\mathbf{V}^{\\prime}$ are obtained by linearly mapping the input features $\\mathbf{X}^{\\prime}$ similar to Eq. 5. The hybrid score matrix $\\mathbf{S}^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times n^{\\prime}}$ is computed as:", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} ^ {\\prime} (i, j) = \\frac {\\left(\\mathbf {q} _ {i} ^ {\\prime}\\right) \\left(\\mathbf {e} _ {i , j} ^ {\\prime} + \\mathbf {k} _ {j} ^ {\\prime}\\right) ^ {T}}{\\sqrt {c ^ {\\prime}}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 176, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $\\mathbf{e}_{i,j}^{\\prime} := \\mathbf{E}^{\\prime}(i,j,:)$ , $\\mathbf{q}_i^{\\prime} := \\mathbf{Q}^{\\prime}(i,:)$ , and $\\mathbf{k}_j^{\\prime} := \\mathbf{K}^{\\prime}(j,:)$ the $c^{\\prime}$ -dimension vectors. The hybrid attention $\\mathbf{A}^{\\prime}$ is obtained via a Softmax function over each row of $\\mathbf{S}^{\\prime}$ , and the geometric messages $\\mathbf{M}_G^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times c^{\\prime}}$ are computed as:", + "bbox": [ + 496, + 217, + 890, + 279 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {G} ^ {\\prime} (i,:) = \\sum_ {1 \\leq j \\leq n ^ {\\prime}} a _ {i, j} ^ {\\prime} \\mathbf {g} _ {i, j} ^ {\\prime}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 290, + 890, + 324 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with $a_{i,j}^{\\prime} \\coloneqq \\mathbf{A}^{\\prime}(i,j)$ and $\\mathbf{g}_{i,j}^{\\prime} \\coloneqq \\mathbf{G}^{\\prime}(i,j,:)$ . The contextual messages $\\mathbf{M}_V^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times c^{\\prime}}$ are computed by $\\mathbf{A}^{\\prime}\\mathbf{V}^{\\prime}$ . After a feed-forward network [43], the position representation $\\mathbf{E}_P^{\\prime}$ and globally-enhanced context $\\mathbf{C}_P^{\\prime}$ are generated.", + "bbox": [ + 496, + 329, + 890, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Position-Aware Cross-Attention Module. PCM consumes a pair of doublets $(\\mathbf{E}_P',\\mathbf{C}_P')$ and $(\\mathbf{E}_Q',\\mathbf{C}_Q')$ that are generated from $\\mathcal{P}'$ and $\\mathcal{Q}'$ by a shared GSM, respectively. As the cross-attention is directional, we apply the same PCM twice, with the first aggregation from $\\mathcal{Q}'$ to $\\mathcal{P}'$ (See Fig. 5 (b)), and the second reversed. As the first step, the rotation-invariant position representation is incorporated to make the consecutive cross-attention position-aware, yielding position-aware features $\\mathbf{F}_P' = \\mathbf{E}_P' + \\mathbf{C}_P'$ and $\\mathbf{F}_Q' = \\mathbf{E}_Q' + \\mathbf{C}_Q'$ . Similar to Eq. 5, $\\widetilde{\\mathbf{Q}}',\\widetilde{\\mathbf{K}}'$ , and $\\widetilde{\\mathbf{V}}'$ are computed as the linear projection of $\\mathbf{F}_P',\\mathbf{F}_Q'$ , and $\\mathbf{F}_Q'$ , respectively. The attention matrix $\\widetilde{\\mathbf{A}}\\in \\mathbb{R}^{n'\\times m'}$ is computed via a row-wise softmax function applied on $\\widetilde{\\mathbf{Q}}'\\widetilde{\\mathbf{K}}'^T$ . The fused messages are presented as $\\widetilde{\\mathbf{A}}\\widetilde{\\mathbf{V}}'$ , which are finally mapped to the output features $\\widetilde{\\mathbf{X}}'$ through a feedforward network. As we introduce spatial awareness at the beginning of PCM, both the attention computation and message fusion are aware of the cross-frame positions. After the twice application of PCM, the input features are enhanced as $\\mathcal{P}'\\gets \\widetilde{\\mathbf{X}}'$ and $\\mathcal{Q}'\\gets \\widetilde{\\mathbf{Y}}'$ , respectively. The global aggregation stage finally generates a pair of triplets $\\widetilde{\\mathcal{P}}':=(\\mathbf{P}',\\mathbf{N}',\\widetilde{\\mathbf{X}}')$ and $\\widetilde{\\mathcal{Q}}':=(\\mathbf{Q}',\\mathbf{M}',\\widetilde{\\mathbf{Y}}')$ , with the enhanced features from the last global transformer.", + "bbox": [ + 496, + 393, + 892, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Point Matching and Loss Function", + "text_level": 1, + "bbox": [ + 500, + 756, + 795, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Superpoint Matching. As shown in Fig. 2, the point matching stage consumes a pair of superpoint triplets $\\hat{\\mathcal{P}}'$ and $\\hat{\\mathcal{Q}}'$ obtained from the global transformer, as well as a pair of point triplets $\\hat{\\mathcal{P}}$ and $\\hat{\\mathcal{Q}}$ produced by the decoder. We adopt the coarse-to-fine matching proposed in [50]. Following [27], we first normalize the superpoint features $\\widetilde{\\mathbf{X}}'$ and $\\widetilde{\\mathbf{Y}}'$ onto a unit hypersphere, and measure the pairwise similarity using a Gaussian correlation matrix $\\widetilde{\\mathbf{S}}$ with $\\widetilde{\\mathbf{S}}(i,j) =$", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5388", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$-\\exp \\left(-\\|\\widetilde{\\mathbf{x}}_i'\\widetilde{\\mathbf{y}}_j'\\|_2^2\\right)$ . After a dual-normalization [27,29,37] on $\\widetilde{\\mathbf{S}}$ for global feature correlation, superpoints associated to the top- $k$ entries are selected as the coarse correspondence set $\\mathcal{C}' = \\{(\\mathbf{p}_i',\\mathbf{q}_i')|\\mathbf{p}_i' \\in \\mathbf{P}',\\mathbf{q}_i' \\in \\mathbf{Q}'\\}$ .", + "bbox": [ + 76, + 90, + 467, + 155 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Point Matching. For extracting point correspondences, denser points $\\hat{\\mathbf{P}}$ and $\\hat{\\mathbf{Q}}$ are first assigned to superpoints. To this end, the point-to-node strategy [50] is leveraged, where each point is assigned to its closest superpoint in 3D space. Given a superpoint $\\mathbf{p}_i' \\in \\mathbf{P}'$ , the group of points assigned to it is denoted as $\\hat{\\mathbf{G}}_i^P \\subseteq \\hat{\\mathbf{P}}$ . The group of features associated to $\\hat{\\mathbf{G}}_i^P$ is further defined as $\\hat{\\mathbf{G}}_i^X$ with $\\hat{\\mathbf{G}}_i^X \\subseteq \\hat{X}$ . For each superpoint correspondence $\\mathcal{C}_l' = (\\mathbf{p}_i', \\mathbf{q}_j')$ , the similarity between the corresponding feature groups $\\hat{\\mathbf{G}}_i^X$ and $\\hat{\\mathbf{G}}_j^Y$ is calculated as $\\hat{\\mathbf{S}}_l = \\hat{\\mathbf{G}}_i^X (\\hat{\\mathbf{G}}_j^Y)^T / \\sqrt{\\hat{c}}$ , with $\\hat{c}$ the feature dimension. We then follow [35] to append a stack row and column to $\\hat{\\mathbf{S}}_l$ filled with a learnable parameter $\\alpha$ , and iteratively run the Sinkhorn Algorithm [36]. After removing the slack row and column of $\\hat{\\mathbf{S}}_l$ , the mutual top-k entries, i.e., entries with top- $k$ confidence on both the row and the column, are selected to formulate a point correspondence set $\\hat{\\mathcal{C}}_l$ . The final correspondence set $\\hat{\\mathcal{C}}$ is collected by $\\hat{\\mathcal{C}} = \\bigcup_{l=1}^{|\\mathcal{C}'|} \\hat{\\mathcal{C}}_l$ .", + "bbox": [ + 75, + 156, + 467, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Loss Function. Our loss function reads as $\\mathcal{L} = \\mathcal{L}_s + \\lambda \\mathcal{L}_p$ , with a superpoint matching loss $\\mathcal{L}_s$ and a point matching loss $\\mathcal{L}_p$ balanced by a hyper-parameter $\\lambda$ ( $\\lambda = 1$ by default). The detailed definition is introduced in the Appendix.", + "bbox": [ + 76, + 425, + 467, + 486 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 503, + 200, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate RoITr on both rigid (3DMatch [51] & 3DLoMatch [19]) and non-rigid (4DMatch [20] & 4DLoMatch [20]) benchmarks. For the rigid matching, we further evaluate our correspondences on the registration task, where RANSAC [12] is used. Details of implementation, metrics, and runtime analysis are introduced in the Appendix.", + "bbox": [ + 75, + 529, + 467, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Rigid Indoor Scenes: 3DMatch & 3DLoMatch", + "text_level": 1, + "bbox": [ + 76, + 633, + 467, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. 3DMatch [51] collects 62 indoor scenes, among which 46 are used for training, 8 for validation, and 8 for testing. We use the data processed by [19] where the 3DMatch data is spilt as 3DMatch ( $>30\\%$ overlap) and 3DLoMatch ( $10\\% \\sim 30\\%$ overlap). To evaluate robustness to arbitrary rotations, we follow [49] for creating the rotated benchmarks, where full-range rotations are individually added to the two frames of each point cloud pair.", + "bbox": [ + 75, + 657, + 467, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We follow [19] to use three metrics for evaluation: (1). Inlier Ratio (IR) that computes the ratio of putative correspondences whose residual distance is smaller than a threshold (i.e., $0.1\\mathrm{m}$ ) under the ground-truth transformation; (2). Feature Matching Recall (FMR) that calculates the fraction of point cloud pairs whose IR is larger than a threshold (i.e., $5\\%$ ); (3). Registration Recall (RR) that counts the fraction of point cloud pairs that are cor", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0cb444ff44e69bfba329c78511ad9a59e2054d53c905eacf0c3487fa87501608.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
# Samples=5,0003DMatch3DLoMatch
OriginRotatedOriginRotated
Feature Matching Recall (%) ↑
SpinNet [1]97.497.475.575.2
Predator [19]96.696.278.673.7
CoFiNet [50]98.197.483.178.6
YOHO [44]98.297.879.477.8
RIGA [49]97.998.285.184.5
Lepard [20]98.097.483.179.5
GeoTrans [27]97.997.888.385.8
RoITr (Ours)98.098.289.689.4
Inlier Ratio (%) ↑
SpinNet [1]48.548.725.725.7
Predator [19]58.052.826.722.4
CoFiNet [50]49.846.824.421.5
YOHO [44]64.464.125.923.2
RIGA [49]68.468.532.132.1
Lepard [20]58.653.728.424.4
GeoTrans [27]71.968.243.540.0
RoITr (Ours)82.682.354.353.2
Registration Recall (%) ↑
SpinNet [1]88.893.258.261.8
Predator [19]89.092.059.858.6
CoFiNet [50]89.392.067.562.5
YOHO [44]90.892.565.266.8
RIGA [49]89.393.065.166.9
Lepard [20]92.784.965.449.0
GeoTrans [27]92.092.075.071.8
RoITr (Ours)91.994.774.877.2
", + "bbox": [ + 504, + 89, + 893, + 470 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative results on (Rotated) 3DMatch & 3DLoMatch. 5,000 points/correspondences are used for the evaluation.", + "bbox": [ + 500, + 474, + 890, + 502 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "rectly registered (i.e., with $\\mathrm{RMSE} < 0.2\\mathrm{m}$ ).", + "bbox": [ + 500, + 508, + 799, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with the State-of-the-Art. We compare RoITr with 7 state-of-the-art methods, among which Predator [19], CoFiNet [50], Lepard [20], and GeoTrans [27] are rotation-sensitive models, while SpinNet [1], YOHO [44], and RIGA [49] guarantee the rotation invariance by design. In Tab. 1 we demonstrate the matching and registration results on 3DMatch and 3DLoMatch, as well as on their rotated versions, with 5,000 sampled points/correspondences. Regarding IR, RoITr outperforms all the others by a large margin on both datasets, which indicates our method matches points more correctly. For FMR, we significantly surpass all the others on 3DLoMatch, while staying on par with CoFiNet and YOHO on 3DMatch, which indicates that our model is good at coping with hard cases, i.e., we find at least $5\\%$ inliers on more test data. For the registration evaluation in terms of RR, RoITr achieves comparable performance with GeoTrans and Lepard on 3DMatch, but leads the board together with GeoTrans on 3DLoMatch with an overwhelming advantage over the others. Our stability against additional rotations is further demonstrated on the rotated data, where we outperform all the others with a substantial margin. Qualitative results can be found in Fig. 6.", + "bbox": [ + 496, + 526, + 890, + 859 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2We follow [49] to calculate the RR strictly with RMSE $< 0.2\\mathrm{m}$ on the rotated data, which is slightly different from the RR on the original data.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5389", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ac23312a02beb4a475dda47e424d95133ebb2541ce2ad59f1a91cd2ede8584a7.jpg", + "image_caption": [ + "Figure 6. Qualitative results on 3DLoMatch. GeoTrans [27] is used as the baseline. Columns (b) and (c) show the correspondences, while columns (d) and (e) demonstrate the registration results. Green/red lines indicate inliers/outliers. More cases are shown in the Appendix." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 877, + 296 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1e8eb32eb063570480f6d3285b0a77b8f012cf5924f07754a7dfde9c894e5a77.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
# Samples3DMatch3DLoMatch
500025001000500250500025001000500250
Feature Matching Recall (%)↑
SpinNet [1]97.497.096.496.794.875.575.174.269.062.7
Predator [19]96.696.696.596.396.578.677.476.375.775.3
CoFiNet [50]98.198.398.198.298.383.183.583.383.182.6
YOHO [44]98.297.697.597.796.079.478.176.373.869.1
RIGA [49]97.997.897.797.797.685.185.085.184.385.1
GeoTrans [27]97.997.997.997.997.688.388.688.888.688.3
RoITr (Ours)98.098.097.998.097.989.689.689.589.489.3
Inlier Ratio (%)↑
SpinNet [1]48.546.240.835.129.025.723.720.618.213.1
Predator [19]58.058.457.154.149.326.728.128.327.525.8
CoFiNet [50]49.851.251.952.252.224.425.926.726.826.9
YOHO [44]64.460.755.746.441.225.923.322.618.215.0
RIGA [49]68.469.770.670.971.032.133.434.334.534.6
GeoTrans [27]71.975.276.082.285.143.545.346.252.957.7
RoITr (Ours)82.682.883.083.083.054.354.655.155.255.3
Registration Recall (%)↑
SpinNet [1]88.888.084.579.069.258.256.749.841.026.7
Predator [19]89.089.990.688.586.659.861.262.460.858.1
CoFiNet [50]89.388.988.487.487.067.566.264.263.161.0
YOHO [44]90.890.389.188.684.565.265.563.256.548.0
RIGA [49]89.388.489.189.087.765.164.764.564.161.8
GeoTrans [27]92.091.891.891.491.275.074.874.274.173.5
RoITr (Ours)91.991.791.891.491.074.774.874.874.273.6
", + "bbox": [ + 81, + 333, + 472, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on the Number of Correspondences. We further analyze the influence of a varying number of correspondences. As illustrated in Tab. 2, RoITr shows outstanding performance on both datasets with various correspondences, proving its stability when only a few correspondences are accessible. The same test on the rotated benchmarks is given in the Appendix.", + "bbox": [ + 75, + 654, + 468, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Deformable Objects: 4DMatch & 4DLoMatch", + "text_level": 1, + "bbox": [ + 76, + 770, + 467, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset. 4DMatch [20] contains 1,761 animations randomly selected from DeformingThings4D [21]. The 1,761 sequences are divided into 1,232/176/353 as train/val/test, where the test set is further split into 4DMatch and 4DLoMatch based on an overlap ratio threshold of $45\\%$ . Metrics. We follow [20] to use two different metrics: (1). Inlier Ratio (IR) which is defined as same as the IR on 3DMatch,", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9236b432a4eb3b18d0f396703602995a38897a205f43521d78cd042deb473363.jpg", + "table_caption": [ + "Table 2. Quantitative results on 3DMatch & 3DLoMatch with a varying number of points/correspondences. See the results on rotated data in the Appendix." + ], + "table_footnote": [], + "table_body": "
CategoryMethod4DMatch4DLoMatch
NFMR(%)↑IR(%)↑NFMR(%)↑IR(%)↑
Scene FlowPWC [45]21.620.010.07.2
FLOT [24]27.124.915.210.7
Feature MatchingPredator [19]56.460.432.127.5
GeoTrans [27]83.282.265.463.6
Lepard [20]83.782.766.955.7
RoITr (Ours)83.084.469.467.6
", + "bbox": [ + 503, + 333, + 893, + 421 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative results on 4DMatch & 4DLoMatch.", + "bbox": [ + 524, + 426, + 864, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "but with a different threshold (i.e., $0.04\\mathrm{m}$ ); (2). Non-rigid Feature Matching Recall (NFRM) that measures the fraction of ground-truth matches that can be successfully recovered by the putative correspondences.", + "bbox": [ + 496, + 460, + 892, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with the State-of-the-Art. We compare RoITr with 5 baselines, among which PwC [45] and FLOT [24] are scene flow-based methods, while Predator [19], Lepard [20], GeoTrans [27] are based on feature matching. The results shown in Tab. 3 indicate that although our rotation-invariance is mainly designed for rigid scenarios, RoITr could also achieve outstanding performance in the non-rigid matching task, which further confirms the superiority of our model design. Qualitative results are demonstrated in Fig. 7.", + "bbox": [ + 496, + 521, + 890, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 681, + 653, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Local Attention. We first replace our PPFTrans with PointTransformer (PT) [53] in Tab. 4 (a.1), which leads to a sharp performance drop. We then ablate by embedding our PPF-based local coordinates into PT (Tab. 4 (a.2)) and by adopting the relative coordinates, i.e., $\\mathbf{p}_j - \\mathbf{p}_j$ , used by PT in our PAM (Tab. 4 (a.3)). Our local coordinate representation significantly boosts the performance of PT in the task of point cloud matching and meanwhile makes it rotation-invariant, although its performance is still far behind ours. However, the relative coordinates fail to work in our PAM, as we adopt a more efficient attention mechanism [43] that learns a scalar attention value for each feature $\\mathbf{x} \\in \\mathbb{R}^c$ and is consequently hard to work under varying poses with a", + "bbox": [ + 496, + 703, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5390", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05f21fec257031ee45502721928229e415a594471edac0c8ac5a61e3a223fa87.jpg", + "image_caption": [ + "Figure 7. Qualitative results of non-rigid matching on 4DLoMatch with Lepard [20] as the baseline. Green/red lines indicate inliers/outliers. See the Appendix for more examples." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 468, + 281 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "rotation-sensitive design. As a comparison, PT learns a per-channel vector attention $\\mathbf{a} \\in \\mathbb{R}^c$ for the same feature $\\mathbf{x}$ and could deal with the pose variations, but at the cost of the efficiency as shown in Fig. 8. When the number of channels is increased, our advantage in terms of efficiency is enlarged. As we achieve that with more parameters, the gap becomes more significant when runtime is normalized with the number of parameters in the right figure. With our PPF-based local coordinate, the scalar attention could focus on the pose-agnostic pure geometry and therefore achieves the best performance shown in Tab. 4 (a.4).", + "bbox": [ + 75, + 335, + 468, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Abstraction Layer. We ablate our Attentional Abstraction Layer (AAL) by replacing it with the pooling-based abstraction design used in [25, 26, 53]. We test the max pooling in Tab. 4 (b.1) and the average pooling in Tab. 4 (b.2), both showing a degrading performance compared with our AAL, which demonstrates our superiority.", + "bbox": [ + 75, + 503, + 468, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Backbone. In Tab. 4 (a.1) we have shown our superiority compared with PT [53]. We further replace our PPFTrans with the KPCnv-based backbone network which is widely used in previous deep matchers [19, 27, 50]. The fact that KPCnv falls behind our design demonstrates the advantage of PPFTrans in geometry encoding.", + "bbox": [ + 75, + 595, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Global Transformer. We replace our design with the global transformer of GeoTrans [27] which performs state-of-the-art but without the cross-frame spatial awareness. The dropping results in Tab. 4 (d.1) proves the excellence of our design with the cross-frame position awareness.", + "bbox": [ + 75, + 686, + 468, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The Number of Global Transformers. To demonstrate the importance of being globally aware, we first remove the global transformer. The substantial performance drop confirms the significance of global awareness. Then we add one global transformer and observe an increased performance. In our default setting with 3 global transformers, the model performs the best. However, when the number is increased to 5, the model shows a slight performance drop, which we owe to overfitting. As the data augmentation of rotations", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c79f5972814873dd0680a193dcb9720a19fc8606439b7e3d540e215126e359a0.jpg", + "image_caption": [ + "Figure 8. Left: Runtime comparison between our PPF attention Mechanism (PAM) and the local attention in PointTransformer [53]. Right: Runtime normalized by aligning the number of parameters." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 877, + 247 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/24fe69e841b131b2c4d375ae270ff0ab9af5012c9189f0f4fcbbbc40a0140dca.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryModelOriginRotated
FMRIRRRFMRIRRR
a. Local1. PT [53]79.036.561.676.534.760.0
*2. PPF+PT [53]87.049.969.986.849.471.2
3. Δxyz+Ours------
*4. Ours89.654.374.789.453.277.2
b. Aggregation*1. max pooling85.250.170.585.450.271.9
*2. avg pooling87.852.673.887.252.574.7
*3. Ours89.654.374.789.453.277.2
c. Backbone1. KPCov [40]85.244.470.683.042.371.5
*2. Ours89.654.374.789.453.277.2
d. Global*1. GeoTrans [27]87.753.673.087.553.275.1
*2. Ours89.654.374.789.453.277.2
e. #Global*1. g = 087.237.670.787.537.672.7
*2. g = 187.142.170.886.842.173.0
*3. g = 3 (Ours)89.654.374.789.453.277.2
*4. g = 587.152.572.187.052.473.3
", + "bbox": [ + 503, + 309, + 893, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study on (rotated) 3DLoMatch. 5,000 points/correspondences are leveraged. * indicates the methods with intrinsic rotation invariance. See the Appendix for the results on (rotated) 3DMatch.", + "bbox": [ + 496, + 489, + 893, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "has less effect on an intrinsically rotation-invariant method, more data is required for training a larger model.", + "bbox": [ + 496, + 551, + 890, + 583 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 588, + 619, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduced RoITr - an intrinsically rotation-invariant model for point cloud matching. We proposed PAM (PPF Attention Mechanism) that embeds PPF-based local coordinates to encode rotation-invariant geometry. This design lies at the core of AAL (Attention Abstraction Layer), PAL (PPF Attention Layer), and TUL (Transition Up Layer) which are consecutively stacked to compose PPFTrans (PPF Transformer) for representative and pose-agnostic geometry description. We further enhanced features by introducing a novel global transformer architecture, which ensures the rotation-invariant cross-frame spatial awareness. Extensive experiments are conducted on both rigid and non-rigid benchmarks to demonstrate the superiority of our approach, especially the remarkable robustness against arbitrary rotations. Limitations are discussed in the Appendix.", + "bbox": [ + 496, + 613, + 890, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This paper is supported by the National Natural Science Foundation of China under Grant No. 62025208. We appreciate the help from Lennart Bastian, Mert Karaoglu, Ning Liu, and Zhiying Leng.", + "bbox": [ + 496, + 840, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5391", + "bbox": [ + 482, + 944, + 513, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sheng Ao, Qingyong Hu, Bo Yang, Andrew Markham, and Yulan Guo. Spinnet: Learning a general surface descriptor for 3d point cloud registration. In CVPR, 2021. 1, 2, 6, 7", + "[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 4", + "[3] Xuyang Bai, Zixin Luo, Lei Zhou, Hongbo Fu, Long Quan, and Chiew-Lan Tai. D3feat: Joint learning of dense detection and description of 3d local features. 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In ICCV, 2021. 1, 2, 7, 8" + ], + "bbox": [ + 501, + 92, + 890, + 219 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5393", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_model.json b/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1870eefdaa5480dedc882a1b58ffc845840f40d0 --- /dev/null +++ b/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_model.json @@ -0,0 +1,2222 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.19, + 0.131, + 0.783, + 0.154 + ], + "angle": 0, + "content": "Rotation-Invariant Transformer for Point Cloud Matching" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.18, + 0.916, + 0.218 + ], + "angle": 0, + "content": "Hao Yu\\(^{1}\\) Zheng Qin\\(^{2}\\) Ji Hou\\(^{3}\\) Mahdi Saleh\\(^{1,4}\\) Dongsheng Li\\(^{2}\\) Benjamin Busam\\(^{1,4}\\) Slobodan Ilic\\(^{1,5}\\) TU Munich \\(^{2}\\)NUDT \\(^{3}\\)Meta Reality Labs \\(^{4}\\)3Dwe.ai \\(^{5}\\)Siemens AG, Munich" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.268 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.284, + 0.474, + 0.692 + ], + "angle": 0, + "content": "The intrinsic rotation invariance lies at the core of matching point clouds with handcrafted descriptors. However, it is widely despised by recent deep matchers that obtain the rotation invariance extrinsically via data augmentation. As the finite number of augmented rotations can never span the continuous \\(SO(3)\\) space, these methods usually show instability when facing rotations that are rarely seen. To this end, we introduce RoITr, a Rotation-Invariant Transformer to cope with the pose variations in the point cloud matching task. We contribute both on the local and global levels. Starting from the local level, we introduce an attention mechanism embedded with Point Pair Feature (PPF)-based coordinates to describe the pose-invariant geometry, upon which a novel attention-based encoder-decoder architecture is constructed. We further propose a global transformer with rotation-invariant cross-frame spatial awareness learned by the self-attention mechanism, which significantly improves the feature distinctiveness and makes the model robust with respect to the low overlap. Experiments are conducted on both the rigid and non-rigid public benchmarks, where RoITr outperforms all the state-of-the-art models by a considerable margin in the low-overlapping scenarios. Especially when the rotations are enlarged on the challenging 3DLoMatch benchmark, RoITr surpasses the existing methods by at least 13 and 5 percentage points in terms of Inlier Ratio and Registration Recall, respectively. Code is publicly available1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.21, + 0.717 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.727, + 0.47, + 0.879 + ], + "angle": 0, + "content": "The correspondence estimation between a pair of partially-overlapping point clouds is a long-standing task that lies at the core of many computer vision applications, such as tracking [17, 18], reconstruction [22, 23, 39], pose estimation [19, 27, 50] and 3D representation learning [15, 16, 46], etc. In a typical solution, geometry is first encoded into descriptors, and correspondences are then established between two frames by matching the most similar descriptors. As the two frames are observed from different views, depicting the same geometry under different trans" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.251, + 0.895, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.426, + 0.895, + 0.496 + ], + "angle": 0, + "content": "Figure 1. Feature Matching Recall (FMR) on 3DLoMatch [19] and Rotated 3DLoMatch. Distance to the diagonal represents the robustness against rotations. Among all the state-of-the-art approaches, RoITr not only ranks first on both benchmarks but also shows the best robustness against the enlarged rotations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.505, + 0.892, + 0.535 + ], + "angle": 0, + "content": "formations identically, i.e., the pose-invariance, becomes the key to success in the point cloud matching task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.893, + 0.884 + ], + "angle": 0, + "content": "Since the side effects caused by a global translation can always be easily eliminated, e.g., by aligning the barycenter with the origin, the attention naturally shifts to coping with the rotations. In the past, handcrafted local descriptors [11, 30, 31, 41] were designed to be rotation-invariant so that the same geometry observed from different views can be correctly matched. With the emergence of deep neural models for 3D point analysis, e.g., multilayer perceptrons (MLPs)-based like PointNet [25, 26], convolutions-based like KPConv [6, 40], and the attention-based like PointTransformer [33, 53], recent approaches [1, 7, 9, 10, 13, 19, 20, 27, 32, 48-51] propose to learn descriptors from raw points as an alternative to handcrafted features that are less robust to occlusion and noise. The majority of deep point matchers [7, 10, 19, 20, 27, 34, 48, 50-52] is sensitive to rotations. Consequently, their invariance to rotations must be obtained extrinsically via augmented training to ensure that the same geometry under different poses can be depicted similarly. However, as the training cases can never span the continuous \\(SO(3)\\) space, they always suffer from instability when facing rotations that are rarely seen during training. This can be observed by a significant performance drop under enlarged rotations at inference time. (See Fig. 1.)" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "There are other works [1, 9, 13, 32, 44] that only lever" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.285, + 0.9 + ], + "angle": 0, + "content": "1https://github.com/haoyu94/RoITr" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5384" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.408 + ], + "angle": 0, + "content": "age deep neural networks to encode the pure geometry with the intrinsically-designed rotation invariance. However, the intrinsic rotation invariance comes at the cost of losing global context. For example, a human's left and right halves are almost identically described, which naturally degrades the distinctiveness of features. Most recently, RIGA [49] is proposed to enhance the distinctiveness of the rotation-invariant descriptors by incorporating a global context, e.g., the left and right halves of a human become distinguishable by knowing there is a chair on the left while a table on the right. However, it lacks a highly-representative geometry encoder since it relies on PointNet [25], which accounts for an ineffective local geometry description. Moreover, as depicting the cross-frame spatial relationships is non-trivial, previous works [19, 27, 34, 50] merely leverage the contextual features in the cross-frame context aggregation, which neglects the positional information. Although RIGA proposes to learn a rotation-invariant position representation by leveraging an additional PointNet, this simple design is hard to model the complex cross-frame positional relationships and leads to less distinctive descriptors." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.473, + 0.651 + ], + "angle": 0, + "content": "In this paper, we present Rotation-Invariant Transformer (RoITr) to tackle the problem of point cloud matching under arbitrary pose variations. By using Point Pair Features (PPFs) as the local coordinates, we propose an attention mechanism to learn the pure geometry regardless of the varying poses. Upon it, attention-based layers are further proposed to compose the encoder-decoder architecture for highly-discriminative and rotation-invariant geometry encoding. We demonstrate its superiority over PointTransformer [53], a state-of-the-art attention-based backbone network, in terms of both efficiency and efficacy in Fig. 8 and Tab. 4 (a), respectively. On the global level, the cross-frame position awareness is introduced in a rotation-invariant fashion to facilitate feature distinctiveness. We illustrate its significance over the state-of-the-art design [27] in Tab. 4 (d). Our main contributions are summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.66, + 0.47, + 0.706 + ], + "angle": 0, + "content": "- An attention mechanism designed to disentangle the geometry and poses, which enables the pose-agnostic geometry description." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.709, + 0.47, + 0.754 + ], + "angle": 0, + "content": "- An attention-based encoder-decoder architecture that learns highly-representative local geometry in a rotation-invariant fashion." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.757, + 0.469, + 0.802 + ], + "angle": 0, + "content": "- A global transformer with rotation-invariant cross-frame position awareness that significantly enhances the feature distinctiveness." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.66, + 0.47, + 0.802 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.22, + 0.831 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Models with Extrinsic Rotation Invariance. The mainstream of deep learning-based point cloud matching approaches is intrinsically rotation-sensitive. Pioneers [10,51] learn to describe local patches from a rotation-variant input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "FCGF [7] leverages fully-convolutional networks to accelerate the geometry description. D3Feat [3] jointly detects and describes sparse keypoints for matching. Predator [19] incorporates the global context to enhance the local descriptors and predicts the overlap regions for keypoint sampling. CoFiNet [50] extracts coarse-to-fine correspondences to alleviate the repeatability issue of keypoints. GeoTrans [27] considers the geometric information in fusing the intra-frame context globally. However, the awareness of spatial positions is missing in the cross-frame aggregation. Lepard [20] extends the non-rigid shape matching [34, 38, 42] to point clouds [28] and proposes a re-positioning module to alleviate the pose variations. REGTR [48] directly regresses the corresponding coordinates and registers point clouds in an end-to-end fashion. Nonetheless, all of these methods suffer from instability with additional rotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.893, + 0.666 + ], + "angle": 0, + "content": "Methods with Intrinsic Rotation Invariance. A branch of handcrafted descriptors [8, 14, 41] aligns the input to a canonical representation according to an estimated local reference frame (LRF), while the others [11, 30, 31] mine the rotation-invariant components and encode them as the representation of the local geometry. Inspired by that, some deep learning-based methods [1, 4, 9, 13, 32, 34, 49] are designed to be intrinsically rotation-invariant to make the neural models focus on the pose-agnostic pure geometry. As a pioneer, PPF-FoldNet [9] consumes PPF-based patches and learns the descriptors using a FoldingNet [47]-based architecture without supervision. LRF-based works [1, 13, 32, 34] achieve rotation invariance by aligning their input to the defined canonical representation. YOHO [44] adopts a group of rotations to learn a rotation-equivariant feature group and further obtain the invariance via group pooling. A common problem of the rotation-invariant methods is the less distinctive features. Although RIGA [49] incorporates the global context into local descriptors to enhance the feature distinctiveness, its ineffective local geometry encoding and global position description learned by PointNet [25] still constraint the representation ability of its descriptors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.673, + 0.591, + 0.689 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.7, + 0.892, + 0.762 + ], + "angle": 0, + "content": "Problem Statement. We tackle the problem of matching a pair of partially-overlapping point clouds \\(\\mathbf{P} \\in \\mathbb{R}^{n \\times 3}\\) and \\(\\mathbf{Q} \\in \\mathbb{R}^{m \\times 3}\\), and extract a correspondence set \\(\\hat{\\mathcal{C}} = \\{(\\hat{\\mathbf{p}}_i, \\hat{\\mathbf{q}}_j) | \\hat{\\mathbf{p}}_i \\in \\hat{\\mathbf{P}} \\subseteq \\mathbf{P}, \\hat{\\mathbf{q}}_j \\in \\hat{\\mathbf{Q}} \\subseteq \\mathbf{Q}\\}\\) that minimizes:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.768, + 0.892, + 0.809 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{| \\hat {\\mathcal {C}} |} \\sum_ {(\\hat {\\mathbf {p}} _ {i}, \\hat {\\mathbf {q}} _ {j}) \\in \\hat {\\mathcal {C}}} \\| \\mathcal {M} ^ {*} (\\hat {\\mathbf {p}} _ {i}) - \\hat {\\mathbf {q}} _ {j} \\| _ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\| \\cdot \\| _2\\) denotes the Euclidean norm and \\(|\\cdot |\\) is the set cardinality. \\(\\mathcal{M}^{*}(\\cdot)\\) stands for the ground-truth mapping function that maps \\(\\hat{\\mathbf{p}}_i\\) to its corresponding position in \\(\\hat{\\mathbf{Q}}\\). In rigid scenarios, it is defined by a transformation \\(\\mathbf{T}^{*}\\in SE(3)\\). For the non-rigid cases it can be denoted as a per-point flow \\(\\mathbf{f}_i^*\\in \\mathbb{R}^3\\) known as the deformation field." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5385" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.09, + 0.307, + 0.165 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.09, + 0.657, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.098, + 0.885, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.185, + 0.222, + 0.197 + ], + "angle": 0, + "content": "(0). Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.185, + 0.358, + 0.197 + ], + "angle": 0, + "content": "(1).Encoder" + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.186, + 0.485, + 0.197 + ], + "angle": 0, + "content": "(2).Aggregation" + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.186, + 0.576, + 0.197 + ], + "angle": 0, + "content": "(3). Decoder" + }, + { + "type": "image_caption", + "bbox": [ + 0.585, + 0.186, + 0.661, + 0.198 + ], + "angle": 0, + "content": "(4). Matching" + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.186, + 0.801, + 0.198 + ], + "angle": 0, + "content": "(5). Output" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.207, + 0.304, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.207, + 0.66, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.208, + 0.884, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.367, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Figure 2. An Overview of RoITr. From left to right: \\((\\pmb{0})\\). RoITr takes as input a pair of triplets \\(\\mathcal{P} = (\\mathbf{P}, \\mathbf{N}, \\mathbf{X})\\) and \\(\\mathcal{Q} = (\\mathbf{Q}, \\mathbf{M}, \\mathbf{Y})\\), each with three dimensions referring to the point cloud, the estimated normals, and the initial features. (1).[§ 3.2] A stack of encoder blocks hierarchically downsamples the points to coarser superpoints and encodes the local geometry, yielding superpoint triplets \\(\\mathcal{P}'\\) and \\(\\mathcal{Q}'\\). Each encoder block consists of an Attentional Abstraction Layer (AAL) for downsampling and abstraction, followed by \\(e \\times\\) PPF Attention Layers (PALs) for local geometry encoding and context aggregation. Both of them are based on our proposed PPF Attention Mechanism (PAM), which enables the pose-agnostic encoding of pure geometry. (See Fig. 3 and Fig. 4). (2).[§ 3.3] Global information is fused to enhance the superpoint features of \\(\\mathcal{P}'\\) and \\(\\mathcal{Q}'\\). The geometric cues are globally aggregated as a rotation-invariant position representation, which introduces spatial awareness in the consecutive cross-frame context aggregation. After a stack of \\(g \\times\\) global transformers, the globally-enhanced triplets \\(\\widetilde{\\mathcal{P}}'\\) and \\(\\widetilde{\\mathcal{Q}}'\\) are produced. (3).[§ 3.2] Superpoint triplets \\(\\mathcal{P}'\\) and \\(\\mathcal{Q}'\\) are decoded to point triplets \\(\\hat{\\mathcal{P}}\\) and \\(\\hat{\\mathcal{Q}}\\) by a stack of decoder blocks. Each block consists of a Transition Up Layer (TUL) for upsampling and context aggregation, followed by \\(d \\times\\) PALs. (4).[§ 3.4] By adopting the coarse-to-fine matching [50], \\(\\widetilde{\\mathcal{P}}'\\) and \\(\\widetilde{\\mathcal{Q}}'\\) are matched to generate superpoint correspondences, which are consecutively refined to point correspondences between \\(\\hat{\\mathcal{P}}\\) and \\(\\hat{\\mathcal{Q}}\\). (5). \\(\\hat{\\mathcal{C}}\\) is established between \\(\\hat{\\mathcal{P}}\\) and \\(\\hat{\\mathcal{Q}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.469, + 0.633 + ], + "angle": 0, + "content": "Method Overview. An overview of RoITr is shown in Fig. 2. RoITr consists of an encoder-decoder architecture named Point Pair Feature Transformer (PPFTrans) for local geometry encoding and a stack of \\( g \\times \\) global transformers for global context aggregation. Correspondence set \\( \\hat{C} \\) is extracted by the coarse-to-fine matching [50]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.317, + 0.663 + ], + "angle": 0, + "content": "3.1. PPF Attention Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Overview. Fig. 3 compares three different self-attention mechanisms. The standard attention [43] only leverages the input context to obtain the Query \\(\\mathbf{Q}\\) and Key \\(\\mathbf{K}\\) to compute the contextual attention \\(\\mathbf{A}_C\\), as well as the Value \\(\\mathbf{V}\\) that encodes information for the contextual message \\(\\mathbf{M}_C\\). GeoTrans [27] proposes to learn the positional encoding \\(\\mathbf{E}\\) from the geometry and calculates a second attention \\(\\mathbf{A}_G\\) to reweigh \\(\\mathbf{A}_C\\). However, the cues contained in the raw geometry are totally neglected. To this end, we propose to learn the pose-agnostic geometric cues \\(\\mathbf{G}\\) and further generate the geometric message \\(\\mathbf{M}_G\\) in the PPF Attention Mechanism (PAM). On the local level, \\(\\mathbf{M}_G\\) is combined with \\(\\mathbf{M}_C\\) for feature enhancement, while on the global level, it is used to learn the rotation-invariant position representation for the cross-frame context aggregation. More specifically, we de" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.545, + 0.616, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.516, + 0.639, + 0.62, + 0.649 + ], + "angle": 0, + "content": "(a). Standard Attention" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.543, + 0.742, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.655, + 0.639, + 0.719, + 0.649 + ], + "angle": 0, + "content": "(b). GeoTrans" + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.543, + 0.886, + 0.629 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.782, + 0.639, + 0.856, + 0.649 + ], + "angle": 0, + "content": "(c).PAM (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.666, + 0.89, + 0.693 + ], + "angle": 0, + "content": "Figure 3. Illustration of different self-attention computation in the standard attention [43], GeoTrans [27], and PAM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.891, + 0.794 + ], + "angle": 0, + "content": "fine PAM on an Anchor triplet \\(\\mathcal{P}^A = (\\mathbf{P}^A, \\mathbf{N}^A, \\mathbf{X}^A)\\) and a Support triplet \\(\\mathcal{P}^S = (\\mathbf{P}^S, \\mathbf{N}^S, \\mathbf{X}^S)\\), both with three dimensions referring to the point cloud, the estimated normals, and the associated features, respectively. PAM aggregates the learned context and geometric cues from \\(\\mathcal{P}^S\\) and flows the messages to \\(\\mathcal{P}^A\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.891, + 0.9 + ], + "angle": 0, + "content": "Pose-Agnostic Coordinate Representation. The basis of PAM is the pose-agnostic local coordinate representation that we construct based on PPFs [11]. Let \\(\\mathcal{P}_i^A \\coloneqq (\\mathbf{p}_i^A \\in \\mathbf{P}^A, \\mathbf{n}_i^A \\in \\mathbf{N}^A, \\mathbf{x}_i^A \\in \\mathbf{X}^A) \\in \\mathcal{P}^A\\) denote the triplet constructed by picking the \\(i^{th}\\) item on each dimension. For each \\(\\mathbf{p}_i^A\\), a subset of \\(\\mathcal{P}^S\\) is first retrieved according to the Euclidean distance w.r.t. \\(\\mathbf{P}^S\\), denoted as" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5386" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.246, + 0.47, + 0.274 + ], + "angle": 0, + "content": "Figure 4. Left: The workflow of the PPF Attention Mechanism (PAM). Right: Detailed calculation of the attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.471, + 0.366 + ], + "angle": 0, + "content": "\\(\\mathcal{P}_{\\mathcal{N}(i)}^{S} \\coloneqq (\\mathbf{P}_{\\mathcal{N}(i)}^{S}, \\mathbf{N}_{\\mathcal{N}(i)}^{S}, \\mathbf{X}_{\\mathcal{N}(i)}^{S}) \\subseteq \\mathcal{P}^{S}\\), with \\(\\mathcal{N}(i)\\) the indices of \\(k\\)-nearest neighbors. We then adopt PPFs [11] to construct a local coordinate system around each \\(\\mathbf{p}_i^A\\) to represent the pose-agnostic position of \\(\\mathbf{P}_{\\mathcal{N}(i)}^{S}\\) w.r.t. it. The coordinate of point \\(\\mathbf{p}_j^S \\in \\mathbf{P}_{\\mathcal{N}(i)}^{S}\\) is transferred to:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.375, + 0.47, + 0.396 + ], + "angle": 0, + "content": "\\[\n\\mathbf {e} _ {j} ^ {S} = \\left(\\| \\mathbf {d} \\| _ {2}, \\angle \\left(\\mathbf {n} _ {i} ^ {A}, \\mathbf {d}\\right), \\angle \\left(\\mathbf {n} _ {j} ^ {S}, \\mathbf {d}\\right), \\angle \\left(\\mathbf {n} _ {j} ^ {S}, \\mathbf {n} _ {i} ^ {A}\\right)\\right), \\quad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.47, + 0.47 + ], + "angle": 0, + "content": "with \\(\\mathbf{d} = \\mathbf{p}_j^S -\\mathbf{p}_i^A\\) , and \\(\\mathbf{n}_i^A\\) and \\(\\mathbf{n}_j^S\\) the estimated normals of \\(\\mathbf{p}_i^A\\) and \\(\\mathbf{p}_j^S\\) , respectively. \\(\\angle (\\mathbf{v}_1,\\mathbf{v}_2)\\) computes the angles between the two vectors [5, 9]. The transferred coordinates of \\(\\mathbf{P}_{\\mathcal{N}(i)}^{S}\\) are denoted as \\(\\mathbf{E}_{\\mathcal{N}(i)}^{S}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.558 + ], + "angle": 0, + "content": "PPF Attention Mechanism. PPF Attention Mechanism (PAM) takes as input the Support triplet \\(\\mathcal{P}^S\\) and the Anchor point cloud \\(\\mathbf{P}^A\\) with estimated normals \\(\\mathbf{N}^A\\). PAM generates the Anchor features \\(\\mathbf{X}^A\\) by aggregating the pose-agnostic local geometry and highly-representative learned context from \\(\\mathcal{P}^S\\), which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.193, + 0.571, + 0.47, + 0.591 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} ^ {A} = \\delta \\left(\\mathbf {P} ^ {A}, \\mathbf {N} ^ {A} \\mid \\mathcal {P} ^ {S}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.471, + 0.835 + ], + "angle": 0, + "content": "with \\(\\delta(\\cdot)\\) representing PAM. As shown in Fig. 4 (a), for each \\(\\mathbf{p}_i^A \\in \\mathbf{P}^A\\) with normal \\(\\mathbf{n}_i^A\\), we find its nearest point \\(\\mathbf{p}_j^S \\in \\mathbf{P}^S\\) whose associated feature \\(\\mathbf{x}_j^S\\) is assigned to \\(\\mathbf{p}_i^A\\) as the initial description. Then, \\(k\\)-nearest neighbors from \\(\\mathbf{P}^S\\) are retrieved according to the Euclidean distance in 3D space, yielding \\(\\mathbf{P}_{\\mathcal{N}(i)}^S \\subseteq \\mathbf{P}^S\\) and \\(\\mathbf{X}_{\\mathcal{N}(i)}^S \\subseteq \\mathbf{X}^S\\). Following Eq. 2, \\(\\mathbf{P}_{\\mathcal{N}(i)}^S\\) is transferred to the pose-agnostic position representation \\(\\mathbf{E}_{\\mathcal{N}(i)}^S\\), which is consecutively projected to the coordinate embedding \\(\\mathbf{E}_S\\) via a linear layer. \\(\\mathbf{x}_j^S\\) and \\(\\mathbf{X}_{\\mathcal{N}(i)}^S\\) are projected to the contextual features \\(\\mathbf{x}_S\\) and \\(\\mathbf{X}_S\\) by a second shared linear layer, respectively. In Fig. 4 (b), the attention mechanism uses five learnable matrices \\(\\mathbf{W}_G\\), \\(\\mathbf{W}_E\\), \\(\\mathbf{W}_Q\\), \\(\\mathbf{W}_K\\), and \\(\\mathbf{W}_V\\) to project the input. Specifically, \\(\\mathbf{W}_G\\) and \\(\\mathbf{W}_E\\) project the input coordinate representation to the geometric cues and positional encoding by:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.848, + 0.469, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} = \\mathbf {E} _ {S} \\mathbf {W} _ {G} \\quad \\text {a n d} \\quad \\mathbf {E} = \\mathbf {E} _ {S} \\mathbf {W} _ {E}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "respectively. Similarly, \\(\\mathbf{W}_Q\\), \\(\\mathbf{W}_K\\), and \\(\\mathbf{W}_V\\) project the learned context to Query, Key, and Value as:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.121, + 0.892, + 0.137 + ], + "angle": 0, + "content": "\\[\n\\mathbf {q} = \\mathbf {x} _ {S} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} _ {S} \\mathbf {W} _ {K}, \\text {a n d} \\mathbf {V} = \\mathbf {X} _ {S} \\mathbf {W} _ {V}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.143, + 0.892, + 0.188 + ], + "angle": 0, + "content": "respectively. The attention a that measures the feature similarity, and the message m that encodes both the pose-agnostic geometry and the representative context read as:" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.199, + 0.892, + 0.236 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {q} \\mathbf {E} ^ {T} + \\mathbf {q} \\mathbf {K} ^ {T}}{\\sqrt {c _ {0}}}\\right) \\quad \\text {a n d} \\quad \\mathbf {m} = \\mathbf {a} \\mathbf {G} + \\mathbf {a} \\mathbf {V}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.246, + 0.892, + 0.322 + ], + "angle": 0, + "content": "respectively. The message \\(\\mathbf{m}\\) is projected and aggregated to \\(\\mathbf{x}_j^S\\) via an element-wise addition followed by a normalization through LayerNorm [2]. The final linear layer projects the obtained feature to \\(\\mathbf{x}_i^A\\), from which \\(\\mathbf{X}^A\\) is obtained to formulate the output \\(\\mathcal{P}^A\\) with the known \\(\\mathbf{P}^A\\) and \\(\\mathbf{N}^A\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.333, + 0.863, + 0.35 + ], + "angle": 0, + "content": "3.2. PPFTrans for Local Geometry Description" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.358, + 0.892, + 0.721 + ], + "angle": 0, + "content": "Overview. As illustrated in Fig. 2, PPFTrans consumes triplets \\(\\mathcal{P}\\) and \\(\\mathcal{Q}\\). Taking \\(\\mathcal{P} = (\\mathbf{P},\\mathbf{N},\\mathbf{X})\\) as an example, it consists of \\(\\mathbf{P} \\in \\mathbb{R}^{n \\times 3}\\) the points cloud, \\(\\mathbf{N} \\in \\mathbb{R}^{n \\times 3}\\) the normals estimated from \\(\\mathbf{P}\\), and \\(\\mathbf{X} = \\vec{\\mathbf{1}} \\in \\mathbb{R}^{n \\times 1}\\) the initial point features. The encoder produces the superpoint triplet \\(\\mathcal{P}' = (\\mathbf{P}',\\mathbf{N}',\\mathbf{X}')\\) with \\(\\mathbf{P}' \\in \\mathbb{R}^{n' \\times 3}\\) and \\(\\mathbf{X}' \\in \\mathbb{R}^{n' \\times c'}\\). With the consecutive decoder, \\(\\mathcal{P}'\\) is decoded to a triplet \\(\\hat{\\mathcal{P}} = (\\hat{\\mathbf{P}},\\hat{\\mathbf{N}},\\hat{\\mathbf{X}})\\) including \\(\\hat{n}\\) points with features \\(\\hat{\\mathbf{X}} \\in \\mathbb{R}^{\\hat{n} \\times \\hat{c}}\\). Notably, as we adopt a Farthest Point Sampling (FPS) strategy [26], it always satisfies that \\(\\mathbf{P}' \\subseteq \\hat{\\mathbf{P}} \\subseteq \\mathbf{P}\\). The same goes for a second point cloud \\(\\mathbf{Q}\\) with an input triplet \\(\\mathcal{Q} = (\\mathbf{Q} \\in \\mathbb{R}^{m \\times 3},\\mathbf{M} \\in \\mathbb{R}^{m \\times 3},\\mathbf{Y} = \\vec{\\mathbf{1}} \\in \\mathbb{R}^{m \\times 1})\\) by the shared architecture. In the rest of this paper, we only demonstrate for \\(\\mathcal{P}\\) unless the model processes \\(\\mathcal{Q}\\) differently. Encoder. The encoder is constructed by stacking several encoder blocks, each including an Attentional Abstraction Layer (AAL) followed by \\(e \\times\\) PPF Attention Layers (PALs). Each block consumes the output of the previous block as the Support triplet \\(\\mathcal{P}^S\\) (\\(\\mathcal{P}^S = \\mathcal{P}\\) for the first block). \\(\\mathcal{P}^S\\) first flows to AAL, where Anchor points \\(\\mathbf{P}^A\\) with associated normals \\(\\mathbf{N}^A\\) are obtained via FPS [26]. The Anchor triplet \\(\\mathcal{P}^A\\) is then generated in AAL via a PAM following Eq. 3. A sequence of PALs is applied for enhancing the Anchor features \\(\\mathbf{X}^A\\), each updating the features as:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.732, + 0.892, + 0.752 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} ^ {A} \\leftarrow \\theta (\\mathcal {P} ^ {A}) = \\operatorname {R e L U} \\left(\\mathbf {X} ^ {A} + \\phi \\left(\\delta \\left(\\mathbf {P} ^ {A}, \\mathbf {N} ^ {A} \\mid \\mathcal {P} ^ {A}\\right)\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.764, + 0.892, + 0.824 + ], + "angle": 0, + "content": "with \\(\\phi\\) the LayerNorm [2], \\(\\delta\\) the PAM, and \\(\\theta\\) the PAL. \\(\\leftarrow\\) depicts feature updating. The encoder block outputs the updated \\(\\mathcal{P}^A\\), and the output of the whole encoder is defined as \\(\\mathcal{P}'\\), which is the output of the final encoder block." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Decoder. We build the decoder by stacking a series of decoder blocks, each consisting of a Transition Up Layer (TUL) followed by \\(d \\times \\mathrm{PAL}\\). Each block takes the output of the previous block as the Anchor triplet \\(\\mathcal{P}^A\\) (\\(\\mathcal{P}^A = \\mathcal{P}'\\) for the first block), and takes the Support" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5387" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.091, + 0.318, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.244, + 0.28, + 0.255 + ], + "angle": 0, + "content": "(a). Geometry-Aware Self-Attention" + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.091, + 0.469, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.244, + 0.468, + 0.255 + ], + "angle": 0, + "content": "(b). Position-Aware Cross-Attention" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.259, + 0.47, + 0.3 + ], + "angle": 0, + "content": "Figure 5. The computation graph of our global transformer consisting of the Geometry-Aware Self-Attention Module (GSM) and Position-Aware Cross-Attention Module (PCM)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.469, + 0.358 + ], + "angle": 0, + "content": "triplet \\(\\mathcal{P}^S\\) from the encoder via skip connections. The input flows to TUL, where each feature \\(\\widetilde{\\mathbf{x}}_j^S\\in \\widetilde{\\mathbf{X}}^S\\) assigned to \\(\\mathbf{p}_j^S\\in \\mathbf{P}^S\\) is interpolated by:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.36, + 0.47, + 0.401 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {x}} _ {j} ^ {S} = \\frac {\\sum_ {i \\in \\mathcal {N} (j)} w _ {i} ^ {j} \\mathbf {x} _ {i} ^ {A}}{\\sum_ {i \\in \\mathcal {N} (j)} w _ {i} ^ {j}}, \\text {w i t h} w _ {i} ^ {j} = \\frac {1}{\\left\\| \\mathbf {p} _ {j} ^ {S} - \\mathbf {p} _ {i} ^ {A} \\right\\| _ {2}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.469, + 0.522 + ], + "angle": 0, + "content": "with \\(\\mathcal{N}(j)\\) the \\(k\\)-nearest neighbors of \\(\\mathbf{p}_j^S\\) in \\(\\mathbf{P}^A\\). Features are updated by two linear layers as \\(\\mathcal{P}^S \\gets \\zeta_1(\\mathbf{X}^S) + \\zeta_2(\\widetilde{\\mathbf{X}}^S)\\). A sequence of PALs is adopted after TUL, each enhancing the features as \\(\\mathcal{P}^S \\gets \\theta(\\mathcal{P}^S)\\) according to Eq. 7. The decoder block outputs the updated \\(\\mathcal{P}^S\\), and the output of the whole decoder is denoted as \\(\\hat{\\mathcal{P}}\\), which is the output of the final decoder block." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.46, + 0.548 + ], + "angle": 0, + "content": "3.3. Global Transformer for Context Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.469, + 0.719 + ], + "angle": 0, + "content": "Overview. Our designed global transformer takes as input a pair of triplets \\(\\mathcal{P}'\\) and \\(\\mathcal{Q}'\\), and enhances the features with the global context, yielding \\(\\widetilde{\\mathbf{X}}' \\in \\mathbb{R}^{n' \\times c'}\\) and \\(\\widetilde{\\mathbf{Y}}' \\in \\mathbb{R}^{m' \\times c'}\\), respectively. We stack \\(g \\times\\) global transformers, with each including a Geometry-Aware Self-Attention Module (GSM) and a Position-Aware Cross-Attention Module (PCM) (See Fig. 2 and Fig. 5). Different from previous works [19, 27, 48-50] that totally neglect the cross-frame spatial relationships, we propose to learn a rotation-invariant position representation for each superpoint to enable the position-aware cross-frame context aggregation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Geometry-Aware Self-Attention Module. On the global level, we modify PAM to learn the rotation-invariant position representation and to aggregate the learned context across the whole frame simultaneously. The design of GSM is detailed in Fig. 5 (a). GSM has two branches, where the geometry branch mines the geometric cues from the pairwise rotation-invariant geometry representation proposed in [27], and the context branch aggregates the global context across the frame. We refer the readers to the Appendix for the detailed construction of \\(\\mathbf{R}' \\in \\mathbb{R}^{n' \\times n' \\times c'}\\) and the ablation study on it. Similar to Eq. 4, the geometric cues \\(\\mathbf{G}'\\) and the positional encoding \\(\\mathbf{E}'\\) are linearly projected from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.168 + ], + "angle": 0, + "content": "\\(\\mathbf{R}^{\\prime}\\). \\(\\mathbf{E}^{\\prime}\\) is further processed in the geometry branch and finally leveraged as the rotation-invariant position representation. In the context branch, \\(\\mathbf{Q}^{\\prime}\\), \\(\\mathbf{K}^{\\prime}\\), and \\(\\mathbf{V}^{\\prime}\\) are obtained by linearly mapping the input features \\(\\mathbf{X}^{\\prime}\\) similar to Eq. 5. The hybrid score matrix \\(\\mathbf{S}^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times n^{\\prime}}\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.177, + 0.892, + 0.213 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} ^ {\\prime} (i, j) = \\frac {\\left(\\mathbf {q} _ {i} ^ {\\prime}\\right) \\left(\\mathbf {e} _ {i , j} ^ {\\prime} + \\mathbf {k} _ {j} ^ {\\prime}\\right) ^ {T}}{\\sqrt {c ^ {\\prime}}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.218, + 0.892, + 0.28 + ], + "angle": 0, + "content": "with \\(\\mathbf{e}_{i,j}^{\\prime} := \\mathbf{E}^{\\prime}(i,j,:)\\), \\(\\mathbf{q}_i^{\\prime} := \\mathbf{Q}^{\\prime}(i,:)\\), and \\(\\mathbf{k}_j^{\\prime} := \\mathbf{K}^{\\prime}(j,:)\\) the \\(c^{\\prime}\\)-dimension vectors. The hybrid attention \\(\\mathbf{A}^{\\prime}\\) is obtained via a Softmax function over each row of \\(\\mathbf{S}^{\\prime}\\), and the geometric messages \\(\\mathbf{M}_G^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times c^{\\prime}}\\) are computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.291, + 0.892, + 0.325 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {G} ^ {\\prime} (i,:) = \\sum_ {1 \\leq j \\leq n ^ {\\prime}} a _ {i, j} ^ {\\prime} \\mathbf {g} _ {i, j} ^ {\\prime}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.395 + ], + "angle": 0, + "content": "with \\(a_{i,j}^{\\prime} \\coloneqq \\mathbf{A}^{\\prime}(i,j)\\) and \\(\\mathbf{g}_{i,j}^{\\prime} \\coloneqq \\mathbf{G}^{\\prime}(i,j,:)\\). The contextual messages \\(\\mathbf{M}_V^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times c^{\\prime}}\\) are computed by \\(\\mathbf{A}^{\\prime}\\mathbf{V}^{\\prime}\\). After a feed-forward network [43], the position representation \\(\\mathbf{E}_P^{\\prime}\\) and globally-enhanced context \\(\\mathbf{C}_P^{\\prime}\\) are generated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.893, + 0.747 + ], + "angle": 0, + "content": "Position-Aware Cross-Attention Module. PCM consumes a pair of doublets \\((\\mathbf{E}_P',\\mathbf{C}_P')\\) and \\((\\mathbf{E}_Q',\\mathbf{C}_Q')\\) that are generated from \\(\\mathcal{P}'\\) and \\(\\mathcal{Q}'\\) by a shared GSM, respectively. As the cross-attention is directional, we apply the same PCM twice, with the first aggregation from \\(\\mathcal{Q}'\\) to \\(\\mathcal{P}'\\) (See Fig. 5 (b)), and the second reversed. As the first step, the rotation-invariant position representation is incorporated to make the consecutive cross-attention position-aware, yielding position-aware features \\(\\mathbf{F}_P' = \\mathbf{E}_P' + \\mathbf{C}_P'\\) and \\(\\mathbf{F}_Q' = \\mathbf{E}_Q' + \\mathbf{C}_Q'\\). Similar to Eq. 5, \\(\\widetilde{\\mathbf{Q}}',\\widetilde{\\mathbf{K}}'\\), and \\(\\widetilde{\\mathbf{V}}'\\) are computed as the linear projection of \\(\\mathbf{F}_P',\\mathbf{F}_Q'\\), and \\(\\mathbf{F}_Q'\\), respectively. The attention matrix \\(\\widetilde{\\mathbf{A}}\\in \\mathbb{R}^{n'\\times m'}\\) is computed via a row-wise softmax function applied on \\(\\widetilde{\\mathbf{Q}}'\\widetilde{\\mathbf{K}}'^T\\). The fused messages are presented as \\(\\widetilde{\\mathbf{A}}\\widetilde{\\mathbf{V}}'\\), which are finally mapped to the output features \\(\\widetilde{\\mathbf{X}}'\\) through a feedforward network. As we introduce spatial awareness at the beginning of PCM, both the attention computation and message fusion are aware of the cross-frame positions. After the twice application of PCM, the input features are enhanced as \\(\\mathcal{P}'\\gets \\widetilde{\\mathbf{X}}'\\) and \\(\\mathcal{Q}'\\gets \\widetilde{\\mathbf{Y}}'\\), respectively. The global aggregation stage finally generates a pair of triplets \\(\\widetilde{\\mathcal{P}}':=(\\mathbf{P}',\\mathbf{N}',\\widetilde{\\mathbf{X}}')\\) and \\(\\widetilde{\\mathcal{Q}}':=(\\mathbf{Q}',\\mathbf{M}',\\widetilde{\\mathbf{Y}}')\\), with the enhanced features from the last global transformer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.796, + 0.773 + ], + "angle": 0, + "content": "3.4. Point Matching and Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Superpoint Matching. As shown in Fig. 2, the point matching stage consumes a pair of superpoint triplets \\(\\hat{\\mathcal{P}}'\\) and \\(\\hat{\\mathcal{Q}}'\\) obtained from the global transformer, as well as a pair of point triplets \\(\\hat{\\mathcal{P}}\\) and \\(\\hat{\\mathcal{Q}}\\) produced by the decoder. We adopt the coarse-to-fine matching proposed in [50]. Following [27], we first normalize the superpoint features \\(\\widetilde{\\mathbf{X}}'\\) and \\(\\widetilde{\\mathbf{Y}}'\\) onto a unit hypersphere, and measure the pairwise similarity using a Gaussian correlation matrix \\(\\widetilde{\\mathbf{S}}\\) with \\(\\widetilde{\\mathbf{S}}(i,j) =\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5388" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.468, + 0.156 + ], + "angle": 0, + "content": "\\(-\\exp \\left(-\\|\\widetilde{\\mathbf{x}}_i'\\widetilde{\\mathbf{y}}_j'\\|_2^2\\right)\\). After a dual-normalization [27,29,37] on \\(\\widetilde{\\mathbf{S}}\\) for global feature correlation, superpoints associated to the top-\\(k\\) entries are selected as the coarse correspondence set \\(\\mathcal{C}' = \\{(\\mathbf{p}_i',\\mathbf{q}_i')|\\mathbf{p}_i' \\in \\mathbf{P}',\\mathbf{q}_i' \\in \\mathbf{Q}'\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.157, + 0.468, + 0.426 + ], + "angle": 0, + "content": "Point Matching. For extracting point correspondences, denser points \\(\\hat{\\mathbf{P}}\\) and \\(\\hat{\\mathbf{Q}}\\) are first assigned to superpoints. To this end, the point-to-node strategy [50] is leveraged, where each point is assigned to its closest superpoint in 3D space. Given a superpoint \\(\\mathbf{p}_i' \\in \\mathbf{P}'\\), the group of points assigned to it is denoted as \\(\\hat{\\mathbf{G}}_i^P \\subseteq \\hat{\\mathbf{P}}\\). The group of features associated to \\(\\hat{\\mathbf{G}}_i^P\\) is further defined as \\(\\hat{\\mathbf{G}}_i^X\\) with \\(\\hat{\\mathbf{G}}_i^X \\subseteq \\hat{X}\\). For each superpoint correspondence \\(\\mathcal{C}_l' = (\\mathbf{p}_i', \\mathbf{q}_j')\\), the similarity between the corresponding feature groups \\(\\hat{\\mathbf{G}}_i^X\\) and \\(\\hat{\\mathbf{G}}_j^Y\\) is calculated as \\(\\hat{\\mathbf{S}}_l = \\hat{\\mathbf{G}}_i^X (\\hat{\\mathbf{G}}_j^Y)^T / \\sqrt{\\hat{c}}\\), with \\(\\hat{c}\\) the feature dimension. We then follow [35] to append a stack row and column to \\(\\hat{\\mathbf{S}}_l\\) filled with a learnable parameter \\(\\alpha\\), and iteratively run the Sinkhorn Algorithm [36]. After removing the slack row and column of \\(\\hat{\\mathbf{S}}_l\\), the mutual top-k entries, i.e., entries with top-\\(k\\) confidence on both the row and the column, are selected to formulate a point correspondence set \\(\\hat{\\mathcal{C}}_l\\). The final correspondence set \\(\\hat{\\mathcal{C}}\\) is collected by \\(\\hat{\\mathcal{C}} = \\bigcup_{l=1}^{|\\mathcal{C}'|} \\hat{\\mathcal{C}}_l\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.426, + 0.468, + 0.487 + ], + "angle": 0, + "content": "Loss Function. Our loss function reads as \\(\\mathcal{L} = \\mathcal{L}_s + \\lambda \\mathcal{L}_p\\), with a superpoint matching loss \\(\\mathcal{L}_s\\) and a point matching loss \\(\\mathcal{L}_p\\) balanced by a hyper-parameter \\(\\lambda\\) (\\(\\lambda = 1\\) by default). The detailed definition is introduced in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.504, + 0.201, + 0.52 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.468, + 0.621 + ], + "angle": 0, + "content": "We evaluate RoITr on both rigid (3DMatch [51] & 3DLoMatch [19]) and non-rigid (4DMatch [20] & 4DLoMatch [20]) benchmarks. For the rigid matching, we further evaluate our correspondences on the registration task, where RANSAC [12] is used. Details of implementation, metrics, and runtime analysis are introduced in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.468, + 0.649 + ], + "angle": 0, + "content": "4.1. Rigid Indoor Scenes: 3DMatch & 3DLoMatch" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.468, + 0.779 + ], + "angle": 0, + "content": "Dataset. 3DMatch [51] collects 62 indoor scenes, among which 46 are used for training, 8 for validation, and 8 for testing. We use the data processed by [19] where the 3DMatch data is spilt as 3DMatch (\\(>30\\%\\) overlap) and 3DLoMatch (\\(10\\% \\sim 30\\%\\) overlap). To evaluate robustness to arbitrary rotations, we follow [49] for creating the rotated benchmarks, where full-range rotations are individually added to the two frames of each point cloud pair." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Metrics. We follow [19] to use three metrics for evaluation: (1). Inlier Ratio (IR) that computes the ratio of putative correspondences whose residual distance is smaller than a threshold (i.e., \\(0.1\\mathrm{m}\\)) under the ground-truth transformation; (2). Feature Matching Recall (FMR) that calculates the fraction of point cloud pairs whose IR is larger than a threshold (i.e., \\(5\\%\\)); (3). Registration Recall (RR) that counts the fraction of point cloud pairs that are cor" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.09, + 0.894, + 0.472 + ], + "angle": 0, + "content": "
# Samples=5,0003DMatch3DLoMatch
OriginRotatedOriginRotated
Feature Matching Recall (%) ↑
SpinNet [1]97.497.475.575.2
Predator [19]96.696.278.673.7
CoFiNet [50]98.197.483.178.6
YOHO [44]98.297.879.477.8
RIGA [49]97.998.285.184.5
Lepard [20]98.097.483.179.5
GeoTrans [27]97.997.888.385.8
RoITr (Ours)98.098.289.689.4
Inlier Ratio (%) ↑
SpinNet [1]48.548.725.725.7
Predator [19]58.052.826.722.4
CoFiNet [50]49.846.824.421.5
YOHO [44]64.464.125.923.2
RIGA [49]68.468.532.132.1
Lepard [20]58.653.728.424.4
GeoTrans [27]71.968.243.540.0
RoITr (Ours)82.682.354.353.2
Registration Recall (%) ↑
SpinNet [1]88.893.258.261.8
Predator [19]89.092.059.858.6
CoFiNet [50]89.392.067.562.5
YOHO [44]90.892.565.266.8
RIGA [49]89.393.065.166.9
Lepard [20]92.784.965.449.0
GeoTrans [27]92.092.075.071.8
RoITr (Ours)91.994.774.877.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.475, + 0.892, + 0.503 + ], + "angle": 0, + "content": "Table 1. Quantitative results on (Rotated) 3DMatch & 3DLoMatch. 5,000 points/correspondences are used for the evaluation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.509, + 0.8, + 0.525 + ], + "angle": 0, + "content": "rectly registered (i.e., with \\(\\mathrm{RMSE} < 0.2\\mathrm{m}\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.892, + 0.86 + ], + "angle": 0, + "content": "Comparison with the State-of-the-Art. We compare RoITr with 7 state-of-the-art methods, among which Predator [19], CoFiNet [50], Lepard [20], and GeoTrans [27] are rotation-sensitive models, while SpinNet [1], YOHO [44], and RIGA [49] guarantee the rotation invariance by design. In Tab. 1 we demonstrate the matching and registration results on 3DMatch and 3DLoMatch, as well as on their rotated versions, with 5,000 sampled points/correspondences. Regarding IR, RoITr outperforms all the others by a large margin on both datasets, which indicates our method matches points more correctly. For FMR, we significantly surpass all the others on 3DLoMatch, while staying on par with CoFiNet and YOHO on 3DMatch, which indicates that our model is good at coping with hard cases, i.e., we find at least \\(5\\%\\) inliers on more test data. For the registration evaluation in terms of RR, RoITr achieves comparable performance with GeoTrans and Lepard on 3DMatch, but leads the board together with GeoTrans on 3DLoMatch with an overwhelming advantage over the others. Our stability against additional rotations is further demonstrated on the rotated data, where we outperform all the others with a substantial margin. Qualitative results can be found in Fig. 6." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2We follow [49] to calculate the RR strictly with RMSE \\(< 0.2\\mathrm{m}\\) on the rotated data, which is slightly different from the RR on the original data." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5389" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.878, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.893, + 0.331 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on 3DLoMatch. GeoTrans [27] is used as the baseline. Columns (b) and (c) show the correspondences, while columns (d) and (e) demonstrate the registration results. Green/red lines indicate inliers/outliers. More cases are shown in the Appendix." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.334, + 0.473, + 0.6 + ], + "angle": 0, + "content": "
# Samples3DMatch3DLoMatch
500025001000500250500025001000500250
Feature Matching Recall (%)↑
SpinNet [1]97.497.096.496.794.875.575.174.269.062.7
Predator [19]96.696.696.596.396.578.677.476.375.775.3
CoFiNet [50]98.198.398.198.298.383.183.583.383.182.6
YOHO [44]98.297.697.597.796.079.478.176.373.869.1
RIGA [49]97.997.897.797.797.685.185.085.184.385.1
GeoTrans [27]97.997.997.997.997.688.388.688.888.688.3
RoITr (Ours)98.098.097.998.097.989.689.689.589.489.3
Inlier Ratio (%)↑
SpinNet [1]48.546.240.835.129.025.723.720.618.213.1
Predator [19]58.058.457.154.149.326.728.128.327.525.8
CoFiNet [50]49.851.251.952.252.224.425.926.726.826.9
YOHO [44]64.460.755.746.441.225.923.322.618.215.0
RIGA [49]68.469.770.670.971.032.133.434.334.534.6
GeoTrans [27]71.975.276.082.285.143.545.346.252.957.7
RoITr (Ours)82.682.883.083.083.054.354.655.155.255.3
Registration Recall (%)↑
SpinNet [1]88.888.084.579.069.258.256.749.841.026.7
Predator [19]89.089.990.688.586.659.861.262.460.858.1
CoFiNet [50]89.388.988.487.487.067.566.264.263.161.0
YOHO [44]90.890.389.188.684.565.265.563.256.548.0
RIGA [49]89.388.489.189.087.765.164.764.564.161.8
GeoTrans [27]92.091.891.891.491.275.074.874.274.173.5
RoITr (Ours)91.991.791.891.491.074.774.874.874.273.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.604, + 0.47, + 0.648 + ], + "angle": 0, + "content": "Table 2. Quantitative results on 3DMatch & 3DLoMatch with a varying number of points/correspondences. See the results on rotated data in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.761 + ], + "angle": 0, + "content": "Analysis on the Number of Correspondences. We further analyze the influence of a varying number of correspondences. As illustrated in Tab. 2, RoITr shows outstanding performance on both datasets with various correspondences, proving its stability when only a few correspondences are accessible. The same test on the rotated benchmarks is given in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.468, + 0.788 + ], + "angle": 0, + "content": "4.2. Deformable Objects: 4DMatch & 4DLoMatch" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Dataset. 4DMatch [20] contains 1,761 animations randomly selected from DeformingThings4D [21]. The 1,761 sequences are divided into 1,232/176/353 as train/val/test, where the test set is further split into 4DMatch and 4DLoMatch based on an overlap ratio threshold of \\(45\\%\\). Metrics. We follow [20] to use two different metrics: (1). Inlier Ratio (IR) which is defined as same as the IR on 3DMatch," + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.334, + 0.895, + 0.422 + ], + "angle": 0, + "content": "
CategoryMethod4DMatch4DLoMatch
NFMR(%)↑IR(%)↑NFMR(%)↑IR(%)↑
Scene FlowPWC [45]21.620.010.07.2
FLOT [24]27.124.915.210.7
Feature MatchingPredator [19]56.460.432.127.5
GeoTrans [27]83.282.265.463.6
Lepard [20]83.782.766.955.7
RoITr (Ours)83.084.469.467.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.525, + 0.427, + 0.866, + 0.44 + ], + "angle": 0, + "content": "Table 3. Quantitative results on 4DMatch & 4DLoMatch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.893, + 0.521 + ], + "angle": 0, + "content": "but with a different threshold (i.e., \\(0.04\\mathrm{m}\\)); (2). Non-rigid Feature Matching Recall (NFRM) that measures the fraction of ground-truth matches that can be successfully recovered by the putative correspondences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.673 + ], + "angle": 0, + "content": "Comparison with the State-of-the-Art. We compare RoITr with 5 baselines, among which PwC [45] and FLOT [24] are scene flow-based methods, while Predator [19], Lepard [20], GeoTrans [27] are based on feature matching. The results shown in Tab. 3 indicate that although our rotation-invariance is mainly designed for rigid scenarios, RoITr could also achieve outstanding performance in the non-rigid matching task, which further confirms the superiority of our model design. Qualitative results are demonstrated in Fig. 7." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.654, + 0.698 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Local Attention. We first replace our PPFTrans with PointTransformer (PT) [53] in Tab. 4 (a.1), which leads to a sharp performance drop. We then ablate by embedding our PPF-based local coordinates into PT (Tab. 4 (a.2)) and by adopting the relative coordinates, i.e., \\(\\mathbf{p}_j - \\mathbf{p}_j\\), used by PT in our PAM (Tab. 4 (a.3)). Our local coordinate representation significantly boosts the performance of PT in the task of point cloud matching and meanwhile makes it rotation-invariant, although its performance is still far behind ours. However, the relative coordinates fail to work in our PAM, as we adopt a more efficient attention mechanism [43] that learns a scalar attention value for each feature \\(\\mathbf{x} \\in \\mathbb{R}^c\\) and is consequently hard to work under varying poses with a" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5390" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.47, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.471, + 0.332 + ], + "angle": 0, + "content": "Figure 7. Qualitative results of non-rigid matching on 4DLoMatch with Lepard [20] as the baseline. Green/red lines indicate inliers/outliers. See the Appendix for more examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.47, + 0.501 + ], + "angle": 0, + "content": "rotation-sensitive design. As a comparison, PT learns a per-channel vector attention \\(\\mathbf{a} \\in \\mathbb{R}^c\\) for the same feature \\(\\mathbf{x}\\) and could deal with the pose variations, but at the cost of the efficiency as shown in Fig. 8. When the number of channels is increased, our advantage in terms of efficiency is enlarged. As we achieve that with more parameters, the gap becomes more significant when runtime is normalized with the number of parameters in the right figure. With our PPF-based local coordinate, the scalar attention could focus on the pose-agnostic pure geometry and therefore achieves the best performance shown in Tab. 4 (a.4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Abstraction Layer. We ablate our Attentional Abstraction Layer (AAL) by replacing it with the pooling-based abstraction design used in [25, 26, 53]. We test the max pooling in Tab. 4 (b.1) and the average pooling in Tab. 4 (b.2), both showing a degrading performance compared with our AAL, which demonstrates our superiority." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.687 + ], + "angle": 0, + "content": "Backbone. In Tab. 4 (a.1) we have shown our superiority compared with PT [53]. We further replace our PPFTrans with the KPCnv-based backbone network which is widely used in previous deep matchers [19, 27, 50]. The fact that KPCnv falls behind our design demonstrates the advantage of PPFTrans in geometry encoding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Global Transformer. We replace our design with the global transformer of GeoTrans [27] which performs state-of-the-art but without the cross-frame spatial awareness. The dropping results in Tab. 4 (d.1) proves the excellence of our design with the cross-frame position awareness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The Number of Global Transformers. To demonstrate the importance of being globally aware, we first remove the global transformer. The substantial performance drop confirms the significance of global awareness. Then we add one global transformer and observe an increased performance. In our default setting with 3 global transformers, the model performs the best. However, when the number is increased to 5, the model shows a slight performance drop, which we owe to overfitting. As the data augmentation of rotations" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.878, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.25, + 0.895, + 0.306 + ], + "angle": 0, + "content": "Figure 8. Left: Runtime comparison between our PPF attention Mechanism (PAM) and the local attention in PointTransformer [53]. Right: Runtime normalized by aligning the number of parameters." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.31, + 0.895, + 0.486 + ], + "angle": 0, + "content": "
CategoryModelOriginRotated
FMRIRRRFMRIRRR
a. Local1. PT [53]79.036.561.676.534.760.0
*2. PPF+PT [53]87.049.969.986.849.471.2
3. Δxyz+Ours------
*4. Ours89.654.374.789.453.277.2
b. Aggregation*1. max pooling85.250.170.585.450.271.9
*2. avg pooling87.852.673.887.252.574.7
*3. Ours89.654.374.789.453.277.2
c. Backbone1. KPCov [40]85.244.470.683.042.371.5
*2. Ours89.654.374.789.453.277.2
d. Global*1. GeoTrans [27]87.753.673.087.553.275.1
*2. Ours89.654.374.789.453.277.2
e. #Global*1. g = 087.237.670.787.537.672.7
*2. g = 187.142.170.886.842.173.0
*3. g = 3 (Ours)89.654.374.789.453.277.2
*4. g = 587.152.572.187.052.473.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.491, + 0.895, + 0.547 + ], + "angle": 0, + "content": "Table 4. Ablation study on (rotated) 3DLoMatch. 5,000 points/correspondences are leveraged. * indicates the methods with intrinsic rotation invariance. See the Appendix for the results on (rotated) 3DMatch." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.584 + ], + "angle": 0, + "content": "has less effect on an intrinsically rotation-invariant method, more data is required for training a larger model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.62, + 0.605 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We introduced RoITr - an intrinsically rotation-invariant model for point cloud matching. We proposed PAM (PPF Attention Mechanism) that embeds PPF-based local coordinates to encode rotation-invariant geometry. This design lies at the core of AAL (Attention Abstraction Layer), PAL (PPF Attention Layer), and TUL (Transition Up Layer) which are consecutively stacked to compose PPFTrans (PPF Transformer) for representative and pose-agnostic geometry description. We further enhanced features by introducing a novel global transformer architecture, which ensures the rotation-invariant cross-frame spatial awareness. Extensive experiments are conducted on both rigid and non-rigid benchmarks to demonstrate the superiority of our approach, especially the remarkable robustness against arbitrary rotations. Limitations are discussed in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Acknowledgment. This paper is supported by the National Natural Science Foundation of China under Grant No. 62025208. 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In ICCV, 2021. 1, 2, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.957 + ], + "angle": 0, + "content": "5393" + } + ] +] \ No newline at end of file diff --git a/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_origin.pdf b/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..273d9b9ff02786e2f25d6ba0f31f76482114a3d4 --- /dev/null +++ b/2023/Rotation-Invariant Transformer for Point Cloud Matching/424bbd8d-fe04-4142-91bc-ea8eb4c92ccb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:54b2fc1c3b8e7234e8108c3ea833f77ab38af5ef54492f4b2756246747ba1d30 +size 1245502 diff --git a/2023/Rotation-Invariant Transformer for Point Cloud Matching/full.md b/2023/Rotation-Invariant Transformer for Point Cloud Matching/full.md new file mode 100644 index 0000000000000000000000000000000000000000..99ff27b665a75df2f905276c3f9bfe92987c5247 --- /dev/null +++ b/2023/Rotation-Invariant Transformer for Point Cloud Matching/full.md @@ -0,0 +1,311 @@ +# Rotation-Invariant Transformer for Point Cloud Matching + +Hao Yu $^{1}$ Zheng Qin $^{2}$ Ji Hou $^{3}$ Mahdi Saleh $^{1,4}$ Dongsheng Li $^{2}$ Benjamin Busam $^{1,4}$ Slobodan Ilic $^{1,5}$ TU Munich $^{2}$ NUDT $^{3}$ Meta Reality Labs $^{4}$ 3Dwe.ai $^{5}$ Siemens AG, Munich + +# Abstract + +The intrinsic rotation invariance lies at the core of matching point clouds with handcrafted descriptors. However, it is widely despised by recent deep matchers that obtain the rotation invariance extrinsically via data augmentation. As the finite number of augmented rotations can never span the continuous $SO(3)$ space, these methods usually show instability when facing rotations that are rarely seen. To this end, we introduce RoITr, a Rotation-Invariant Transformer to cope with the pose variations in the point cloud matching task. We contribute both on the local and global levels. Starting from the local level, we introduce an attention mechanism embedded with Point Pair Feature (PPF)-based coordinates to describe the pose-invariant geometry, upon which a novel attention-based encoder-decoder architecture is constructed. We further propose a global transformer with rotation-invariant cross-frame spatial awareness learned by the self-attention mechanism, which significantly improves the feature distinctiveness and makes the model robust with respect to the low overlap. Experiments are conducted on both the rigid and non-rigid public benchmarks, where RoITr outperforms all the state-of-the-art models by a considerable margin in the low-overlapping scenarios. Especially when the rotations are enlarged on the challenging 3DLoMatch benchmark, RoITr surpasses the existing methods by at least 13 and 5 percentage points in terms of Inlier Ratio and Registration Recall, respectively. Code is publicly available1. + +# 1. Introduction + +The correspondence estimation between a pair of partially-overlapping point clouds is a long-standing task that lies at the core of many computer vision applications, such as tracking [17, 18], reconstruction [22, 23, 39], pose estimation [19, 27, 50] and 3D representation learning [15, 16, 46], etc. In a typical solution, geometry is first encoded into descriptors, and correspondences are then established between two frames by matching the most similar descriptors. As the two frames are observed from different views, depicting the same geometry under different trans + +![](images/81825f8e94531760f124a36a4048f3485bea7faa274c6d8e55532d5c6f8d23a7.jpg) +Figure 1. Feature Matching Recall (FMR) on 3DLoMatch [19] and Rotated 3DLoMatch. Distance to the diagonal represents the robustness against rotations. Among all the state-of-the-art approaches, RoITr not only ranks first on both benchmarks but also shows the best robustness against the enlarged rotations. + +formations identically, i.e., the pose-invariance, becomes the key to success in the point cloud matching task. + +Since the side effects caused by a global translation can always be easily eliminated, e.g., by aligning the barycenter with the origin, the attention naturally shifts to coping with the rotations. In the past, handcrafted local descriptors [11, 30, 31, 41] were designed to be rotation-invariant so that the same geometry observed from different views can be correctly matched. With the emergence of deep neural models for 3D point analysis, e.g., multilayer perceptrons (MLPs)-based like PointNet [25, 26], convolutions-based like KPConv [6, 40], and the attention-based like PointTransformer [33, 53], recent approaches [1, 7, 9, 10, 13, 19, 20, 27, 32, 48-51] propose to learn descriptors from raw points as an alternative to handcrafted features that are less robust to occlusion and noise. The majority of deep point matchers [7, 10, 19, 20, 27, 34, 48, 50-52] is sensitive to rotations. Consequently, their invariance to rotations must be obtained extrinsically via augmented training to ensure that the same geometry under different poses can be depicted similarly. However, as the training cases can never span the continuous $SO(3)$ space, they always suffer from instability when facing rotations that are rarely seen during training. This can be observed by a significant performance drop under enlarged rotations at inference time. (See Fig. 1.) + +There are other works [1, 9, 13, 32, 44] that only lever + +age deep neural networks to encode the pure geometry with the intrinsically-designed rotation invariance. However, the intrinsic rotation invariance comes at the cost of losing global context. For example, a human's left and right halves are almost identically described, which naturally degrades the distinctiveness of features. Most recently, RIGA [49] is proposed to enhance the distinctiveness of the rotation-invariant descriptors by incorporating a global context, e.g., the left and right halves of a human become distinguishable by knowing there is a chair on the left while a table on the right. However, it lacks a highly-representative geometry encoder since it relies on PointNet [25], which accounts for an ineffective local geometry description. Moreover, as depicting the cross-frame spatial relationships is non-trivial, previous works [19, 27, 34, 50] merely leverage the contextual features in the cross-frame context aggregation, which neglects the positional information. Although RIGA proposes to learn a rotation-invariant position representation by leveraging an additional PointNet, this simple design is hard to model the complex cross-frame positional relationships and leads to less distinctive descriptors. + +In this paper, we present Rotation-Invariant Transformer (RoITr) to tackle the problem of point cloud matching under arbitrary pose variations. By using Point Pair Features (PPFs) as the local coordinates, we propose an attention mechanism to learn the pure geometry regardless of the varying poses. Upon it, attention-based layers are further proposed to compose the encoder-decoder architecture for highly-discriminative and rotation-invariant geometry encoding. We demonstrate its superiority over PointTransformer [53], a state-of-the-art attention-based backbone network, in terms of both efficiency and efficacy in Fig. 8 and Tab. 4 (a), respectively. On the global level, the cross-frame position awareness is introduced in a rotation-invariant fashion to facilitate feature distinctiveness. We illustrate its significance over the state-of-the-art design [27] in Tab. 4 (d). Our main contributions are summarized as: + +- An attention mechanism designed to disentangle the geometry and poses, which enables the pose-agnostic geometry description. +- An attention-based encoder-decoder architecture that learns highly-representative local geometry in a rotation-invariant fashion. +- A global transformer with rotation-invariant cross-frame position awareness that significantly enhances the feature distinctiveness. + +# 2. Related Work + +Models with Extrinsic Rotation Invariance. The mainstream of deep learning-based point cloud matching approaches is intrinsically rotation-sensitive. Pioneers [10,51] learn to describe local patches from a rotation-variant input. + +FCGF [7] leverages fully-convolutional networks to accelerate the geometry description. D3Feat [3] jointly detects and describes sparse keypoints for matching. Predator [19] incorporates the global context to enhance the local descriptors and predicts the overlap regions for keypoint sampling. CoFiNet [50] extracts coarse-to-fine correspondences to alleviate the repeatability issue of keypoints. GeoTrans [27] considers the geometric information in fusing the intra-frame context globally. However, the awareness of spatial positions is missing in the cross-frame aggregation. Lepard [20] extends the non-rigid shape matching [34, 38, 42] to point clouds [28] and proposes a re-positioning module to alleviate the pose variations. REGTR [48] directly regresses the corresponding coordinates and registers point clouds in an end-to-end fashion. Nonetheless, all of these methods suffer from instability with additional rotations. + +Methods with Intrinsic Rotation Invariance. A branch of handcrafted descriptors [8, 14, 41] aligns the input to a canonical representation according to an estimated local reference frame (LRF), while the others [11, 30, 31] mine the rotation-invariant components and encode them as the representation of the local geometry. Inspired by that, some deep learning-based methods [1, 4, 9, 13, 32, 34, 49] are designed to be intrinsically rotation-invariant to make the neural models focus on the pose-agnostic pure geometry. As a pioneer, PPF-FoldNet [9] consumes PPF-based patches and learns the descriptors using a FoldingNet [47]-based architecture without supervision. LRF-based works [1, 13, 32, 34] achieve rotation invariance by aligning their input to the defined canonical representation. YOHO [44] adopts a group of rotations to learn a rotation-equivariant feature group and further obtain the invariance via group pooling. A common problem of the rotation-invariant methods is the less distinctive features. Although RIGA [49] incorporates the global context into local descriptors to enhance the feature distinctiveness, its ineffective local geometry encoding and global position description learned by PointNet [25] still constraint the representation ability of its descriptors. + +# 3. Method + +Problem Statement. We tackle the problem of matching a pair of partially-overlapping point clouds $\mathbf{P} \in \mathbb{R}^{n \times 3}$ and $\mathbf{Q} \in \mathbb{R}^{m \times 3}$ , and extract a correspondence set $\hat{\mathcal{C}} = \{(\hat{\mathbf{p}}_i, \hat{\mathbf{q}}_j) | \hat{\mathbf{p}}_i \in \hat{\mathbf{P}} \subseteq \mathbf{P}, \hat{\mathbf{q}}_j \in \hat{\mathbf{Q}} \subseteq \mathbf{Q}\}$ that minimizes: + +$$ +\frac {1}{| \hat {\mathcal {C}} |} \sum_ {(\hat {\mathbf {p}} _ {i}, \hat {\mathbf {q}} _ {j}) \in \hat {\mathcal {C}}} \| \mathcal {M} ^ {*} (\hat {\mathbf {p}} _ {i}) - \hat {\mathbf {q}} _ {j} \| _ {2}, \tag {1} +$$ + +where $\| \cdot \| _2$ denotes the Euclidean norm and $|\cdot |$ is the set cardinality. $\mathcal{M}^{*}(\cdot)$ stands for the ground-truth mapping function that maps $\hat{\mathbf{p}}_i$ to its corresponding position in $\hat{\mathbf{Q}}$ . In rigid scenarios, it is defined by a transformation $\mathbf{T}^{*}\in SE(3)$ . For the non-rigid cases it can be denoted as a per-point flow $\mathbf{f}_i^*\in \mathbb{R}^3$ known as the deformation field. + +![](images/352f993e80b8039c3fff593ff3b3710cc2efb699d5437ea5534831fd617b8f8e.jpg) +(0). Input + +![](images/db87a1d376332b7b03618dd5794cdaa08a7516290f18cc9528e01d25c924b84b.jpg) +(2).Aggregation + +![](images/974288bc32060553067e5aa14d8a1b36e4504339339ba487679a2a0f3eddfa37.jpg) +(5). Output + +![](images/4e5ef51993cd3abfeb8ba841a2aba0b59cbc3d108e6b058fc3f2d67369ad52e6.jpg) +(1).Encoder + +![](images/09130879a56551a0ae9902d954d95aa14320b2226c7bf4ba302d260c1e117218.jpg) +(3). Decoder + +![](images/ebbdcf4c197d78aed4fe93f07f359b890d055be2d6966b8ff2e9b4e25a40194c.jpg) +(4). Matching + +Method Overview. An overview of RoITr is shown in Fig. 2. RoITr consists of an encoder-decoder architecture named Point Pair Feature Transformer (PPFTrans) for local geometry encoding and a stack of $g \times$ global transformers for global context aggregation. Correspondence set $\hat{C}$ is extracted by the coarse-to-fine matching [50]. + +# 3.1. PPF Attention Mechanism + +Overview. Fig. 3 compares three different self-attention mechanisms. The standard attention [43] only leverages the input context to obtain the Query $\mathbf{Q}$ and Key $\mathbf{K}$ to compute the contextual attention $\mathbf{A}_C$ , as well as the Value $\mathbf{V}$ that encodes information for the contextual message $\mathbf{M}_C$ . GeoTrans [27] proposes to learn the positional encoding $\mathbf{E}$ from the geometry and calculates a second attention $\mathbf{A}_G$ to reweigh $\mathbf{A}_C$ . However, the cues contained in the raw geometry are totally neglected. To this end, we propose to learn the pose-agnostic geometric cues $\mathbf{G}$ and further generate the geometric message $\mathbf{M}_G$ in the PPF Attention Mechanism (PAM). On the local level, $\mathbf{M}_G$ is combined with $\mathbf{M}_C$ for feature enhancement, while on the global level, it is used to learn the rotation-invariant position representation for the cross-frame context aggregation. More specifically, we de + +![](images/c0b712b6186087050f178483da8e9448683cbb6f8c24b4fae9914085547debf4.jpg) +(a). Standard Attention + +![](images/050ce13ccd9012d289ebabdf10f1e5aa082cc00677dad1952586dbd8194f9d92.jpg) +Figure 2. An Overview of RoITr. From left to right: $(\pmb{0})$ . RoITr takes as input a pair of triplets $\mathcal{P} = (\mathbf{P}, \mathbf{N}, \mathbf{X})$ and $\mathcal{Q} = (\mathbf{Q}, \mathbf{M}, \mathbf{Y})$ , each with three dimensions referring to the point cloud, the estimated normals, and the initial features. (1).[§ 3.2] A stack of encoder blocks hierarchically downsamples the points to coarser superpoints and encodes the local geometry, yielding superpoint triplets $\mathcal{P}'$ and $\mathcal{Q}'$ . Each encoder block consists of an Attentional Abstraction Layer (AAL) for downsampling and abstraction, followed by $e \times$ PPF Attention Layers (PALs) for local geometry encoding and context aggregation. Both of them are based on our proposed PPF Attention Mechanism (PAM), which enables the pose-agnostic encoding of pure geometry. (See Fig. 3 and Fig. 4). (2).[§ 3.3] Global information is fused to enhance the superpoint features of $\mathcal{P}'$ and $\mathcal{Q}'$ . The geometric cues are globally aggregated as a rotation-invariant position representation, which introduces spatial awareness in the consecutive cross-frame context aggregation. After a stack of $g \times$ global transformers, the globally-enhanced triplets $\widetilde{\mathcal{P}}'$ and $\widetilde{\mathcal{Q}}'$ are produced. (3).[§ 3.2] Superpoint triplets $\mathcal{P}'$ and $\mathcal{Q}'$ are decoded to point triplets $\hat{\mathcal{P}}$ and $\hat{\mathcal{Q}}$ by a stack of decoder blocks. Each block consists of a Transition Up Layer (TUL) for upsampling and context aggregation, followed by $d \times$ PALs. (4).[§ 3.4] By adopting the coarse-to-fine matching [50], $\widetilde{\mathcal{P}}'$ and $\widetilde{\mathcal{Q}}'$ are matched to generate superpoint correspondences, which are consecutively refined to point correspondences between $\hat{\mathcal{P}}$ and $\hat{\mathcal{Q}}$ . (5). $\hat{\mathcal{C}}$ is established between $\hat{\mathcal{P}}$ and $\hat{\mathcal{Q}}$ . +(b). GeoTrans + +![](images/1ae7e04b44a0ede10cb1f694b3023f8ff8b9887eed7c1e32a5a65db1f3724d8b.jpg) +(c).PAM (Ours) +Figure 3. Illustration of different self-attention computation in the standard attention [43], GeoTrans [27], and PAM. + +fine PAM on an Anchor triplet $\mathcal{P}^A = (\mathbf{P}^A, \mathbf{N}^A, \mathbf{X}^A)$ and a Support triplet $\mathcal{P}^S = (\mathbf{P}^S, \mathbf{N}^S, \mathbf{X}^S)$ , both with three dimensions referring to the point cloud, the estimated normals, and the associated features, respectively. PAM aggregates the learned context and geometric cues from $\mathcal{P}^S$ and flows the messages to $\mathcal{P}^A$ . + +Pose-Agnostic Coordinate Representation. The basis of PAM is the pose-agnostic local coordinate representation that we construct based on PPFs [11]. Let $\mathcal{P}_i^A \coloneqq (\mathbf{p}_i^A \in \mathbf{P}^A, \mathbf{n}_i^A \in \mathbf{N}^A, \mathbf{x}_i^A \in \mathbf{X}^A) \in \mathcal{P}^A$ denote the triplet constructed by picking the $i^{th}$ item on each dimension. For each $\mathbf{p}_i^A$ , a subset of $\mathcal{P}^S$ is first retrieved according to the Euclidean distance w.r.t. $\mathbf{P}^S$ , denoted as + +![](images/5081a262fa30968f29b7c9345f2e9eb18f9480785ff18366f83ba9c4b08632b3.jpg) +Figure 4. Left: The workflow of the PPF Attention Mechanism (PAM). Right: Detailed calculation of the attention. + +$\mathcal{P}_{\mathcal{N}(i)}^{S} \coloneqq (\mathbf{P}_{\mathcal{N}(i)}^{S}, \mathbf{N}_{\mathcal{N}(i)}^{S}, \mathbf{X}_{\mathcal{N}(i)}^{S}) \subseteq \mathcal{P}^{S}$ , with $\mathcal{N}(i)$ the indices of $k$ -nearest neighbors. We then adopt PPFs [11] to construct a local coordinate system around each $\mathbf{p}_i^A$ to represent the pose-agnostic position of $\mathbf{P}_{\mathcal{N}(i)}^{S}$ w.r.t. it. The coordinate of point $\mathbf{p}_j^S \in \mathbf{P}_{\mathcal{N}(i)}^{S}$ is transferred to: + +$$ +\mathbf {e} _ {j} ^ {S} = \left(\| \mathbf {d} \| _ {2}, \angle \left(\mathbf {n} _ {i} ^ {A}, \mathbf {d}\right), \angle \left(\mathbf {n} _ {j} ^ {S}, \mathbf {d}\right), \angle \left(\mathbf {n} _ {j} ^ {S}, \mathbf {n} _ {i} ^ {A}\right)\right), \quad (2) +$$ + +with $\mathbf{d} = \mathbf{p}_j^S -\mathbf{p}_i^A$ , and $\mathbf{n}_i^A$ and $\mathbf{n}_j^S$ the estimated normals of $\mathbf{p}_i^A$ and $\mathbf{p}_j^S$ , respectively. $\angle (\mathbf{v}_1,\mathbf{v}_2)$ computes the angles between the two vectors [5, 9]. The transferred coordinates of $\mathbf{P}_{\mathcal{N}(i)}^{S}$ are denoted as $\mathbf{E}_{\mathcal{N}(i)}^{S}$ + +PPF Attention Mechanism. PPF Attention Mechanism (PAM) takes as input the Support triplet $\mathcal{P}^S$ and the Anchor point cloud $\mathbf{P}^A$ with estimated normals $\mathbf{N}^A$ . PAM generates the Anchor features $\mathbf{X}^A$ by aggregating the pose-agnostic local geometry and highly-representative learned context from $\mathcal{P}^S$ , which is defined as: + +$$ +\mathcal {P} ^ {A} = \delta \left(\mathbf {P} ^ {A}, \mathbf {N} ^ {A} \mid \mathcal {P} ^ {S}\right), \tag {3} +$$ + +with $\delta(\cdot)$ representing PAM. As shown in Fig. 4 (a), for each $\mathbf{p}_i^A \in \mathbf{P}^A$ with normal $\mathbf{n}_i^A$ , we find its nearest point $\mathbf{p}_j^S \in \mathbf{P}^S$ whose associated feature $\mathbf{x}_j^S$ is assigned to $\mathbf{p}_i^A$ as the initial description. Then, $k$ -nearest neighbors from $\mathbf{P}^S$ are retrieved according to the Euclidean distance in 3D space, yielding $\mathbf{P}_{\mathcal{N}(i)}^S \subseteq \mathbf{P}^S$ and $\mathbf{X}_{\mathcal{N}(i)}^S \subseteq \mathbf{X}^S$ . Following Eq. 2, $\mathbf{P}_{\mathcal{N}(i)}^S$ is transferred to the pose-agnostic position representation $\mathbf{E}_{\mathcal{N}(i)}^S$ , which is consecutively projected to the coordinate embedding $\mathbf{E}_S$ via a linear layer. $\mathbf{x}_j^S$ and $\mathbf{X}_{\mathcal{N}(i)}^S$ are projected to the contextual features $\mathbf{x}_S$ and $\mathbf{X}_S$ by a second shared linear layer, respectively. In Fig. 4 (b), the attention mechanism uses five learnable matrices $\mathbf{W}_G$ , $\mathbf{W}_E$ , $\mathbf{W}_Q$ , $\mathbf{W}_K$ , and $\mathbf{W}_V$ to project the input. Specifically, $\mathbf{W}_G$ and $\mathbf{W}_E$ project the input coordinate representation to the geometric cues and positional encoding by: + +$$ +\mathbf {G} = \mathbf {E} _ {S} \mathbf {W} _ {G} \quad \text {a n d} \quad \mathbf {E} = \mathbf {E} _ {S} \mathbf {W} _ {E}, \tag {4} +$$ + +respectively. Similarly, $\mathbf{W}_Q$ , $\mathbf{W}_K$ , and $\mathbf{W}_V$ project the learned context to Query, Key, and Value as: + +$$ +\mathbf {q} = \mathbf {x} _ {S} \mathbf {W} _ {Q}, \mathbf {K} = \mathbf {X} _ {S} \mathbf {W} _ {K}, \text {a n d} \mathbf {V} = \mathbf {X} _ {S} \mathbf {W} _ {V}, \tag {5} +$$ + +respectively. The attention a that measures the feature similarity, and the message m that encodes both the pose-agnostic geometry and the representative context read as: + +$$ +\mathbf {a} = \operatorname {S o f t m a x} \left(\frac {\mathbf {q} \mathbf {E} ^ {T} + \mathbf {q} \mathbf {K} ^ {T}}{\sqrt {c _ {0}}}\right) \quad \text {a n d} \quad \mathbf {m} = \mathbf {a} \mathbf {G} + \mathbf {a} \mathbf {V}, \tag {6} +$$ + +respectively. The message $\mathbf{m}$ is projected and aggregated to $\mathbf{x}_j^S$ via an element-wise addition followed by a normalization through LayerNorm [2]. The final linear layer projects the obtained feature to $\mathbf{x}_i^A$ , from which $\mathbf{X}^A$ is obtained to formulate the output $\mathcal{P}^A$ with the known $\mathbf{P}^A$ and $\mathbf{N}^A$ . + +# 3.2. PPFTrans for Local Geometry Description + +Overview. As illustrated in Fig. 2, PPFTrans consumes triplets $\mathcal{P}$ and $\mathcal{Q}$ . Taking $\mathcal{P} = (\mathbf{P},\mathbf{N},\mathbf{X})$ as an example, it consists of $\mathbf{P} \in \mathbb{R}^{n \times 3}$ the points cloud, $\mathbf{N} \in \mathbb{R}^{n \times 3}$ the normals estimated from $\mathbf{P}$ , and $\mathbf{X} = \vec{\mathbf{1}} \in \mathbb{R}^{n \times 1}$ the initial point features. The encoder produces the superpoint triplet $\mathcal{P}' = (\mathbf{P}',\mathbf{N}',\mathbf{X}')$ with $\mathbf{P}' \in \mathbb{R}^{n' \times 3}$ and $\mathbf{X}' \in \mathbb{R}^{n' \times c'}$ . With the consecutive decoder, $\mathcal{P}'$ is decoded to a triplet $\hat{\mathcal{P}} = (\hat{\mathbf{P}},\hat{\mathbf{N}},\hat{\mathbf{X}})$ including $\hat{n}$ points with features $\hat{\mathbf{X}} \in \mathbb{R}^{\hat{n} \times \hat{c}}$ . Notably, as we adopt a Farthest Point Sampling (FPS) strategy [26], it always satisfies that $\mathbf{P}' \subseteq \hat{\mathbf{P}} \subseteq \mathbf{P}$ . The same goes for a second point cloud $\mathbf{Q}$ with an input triplet $\mathcal{Q} = (\mathbf{Q} \in \mathbb{R}^{m \times 3},\mathbf{M} \in \mathbb{R}^{m \times 3},\mathbf{Y} = \vec{\mathbf{1}} \in \mathbb{R}^{m \times 1})$ by the shared architecture. In the rest of this paper, we only demonstrate for $\mathcal{P}$ unless the model processes $\mathcal{Q}$ differently. Encoder. The encoder is constructed by stacking several encoder blocks, each including an Attentional Abstraction Layer (AAL) followed by $e \times$ PPF Attention Layers (PALs). Each block consumes the output of the previous block as the Support triplet $\mathcal{P}^S$ ( $\mathcal{P}^S = \mathcal{P}$ for the first block). $\mathcal{P}^S$ first flows to AAL, where Anchor points $\mathbf{P}^A$ with associated normals $\mathbf{N}^A$ are obtained via FPS [26]. The Anchor triplet $\mathcal{P}^A$ is then generated in AAL via a PAM following Eq. 3. A sequence of PALs is applied for enhancing the Anchor features $\mathbf{X}^A$ , each updating the features as: + +$$ +\mathcal {P} ^ {A} \leftarrow \theta (\mathcal {P} ^ {A}) = \operatorname {R e L U} \left(\mathbf {X} ^ {A} + \phi \left(\delta \left(\mathbf {P} ^ {A}, \mathbf {N} ^ {A} \mid \mathcal {P} ^ {A}\right)\right)\right), \tag {7} +$$ + +with $\phi$ the LayerNorm [2], $\delta$ the PAM, and $\theta$ the PAL. $\leftarrow$ depicts feature updating. The encoder block outputs the updated $\mathcal{P}^A$ , and the output of the whole encoder is defined as $\mathcal{P}'$ , which is the output of the final encoder block. + +Decoder. We build the decoder by stacking a series of decoder blocks, each consisting of a Transition Up Layer (TUL) followed by $d \times \mathrm{PAL}$ . Each block takes the output of the previous block as the Anchor triplet $\mathcal{P}^A$ ( $\mathcal{P}^A = \mathcal{P}'$ for the first block), and takes the Support + +![](images/f4b3f87f9e83497fcc7b10f0844a7cef1f6e7b788a4cf5fc18e8d0079f4a86bd.jpg) +(a). Geometry-Aware Self-Attention + +![](images/d764f44f9d306301505fa374dfc9c5743da0b1b9c69a915b710abec5d66a715b.jpg) +(b). Position-Aware Cross-Attention +Figure 5. The computation graph of our global transformer consisting of the Geometry-Aware Self-Attention Module (GSM) and Position-Aware Cross-Attention Module (PCM). + +triplet $\mathcal{P}^S$ from the encoder via skip connections. The input flows to TUL, where each feature $\widetilde{\mathbf{x}}_j^S\in \widetilde{\mathbf{X}}^S$ assigned to $\mathbf{p}_j^S\in \mathbf{P}^S$ is interpolated by: + +$$ +\widetilde {\mathbf {x}} _ {j} ^ {S} = \frac {\sum_ {i \in \mathcal {N} (j)} w _ {i} ^ {j} \mathbf {x} _ {i} ^ {A}}{\sum_ {i \in \mathcal {N} (j)} w _ {i} ^ {j}}, \text {w i t h} w _ {i} ^ {j} = \frac {1}{\left\| \mathbf {p} _ {j} ^ {S} - \mathbf {p} _ {i} ^ {A} \right\| _ {2}}, \tag {8} +$$ + +with $\mathcal{N}(j)$ the $k$ -nearest neighbors of $\mathbf{p}_j^S$ in $\mathbf{P}^A$ . Features are updated by two linear layers as $\mathcal{P}^S \gets \zeta_1(\mathbf{X}^S) + \zeta_2(\widetilde{\mathbf{X}}^S)$ . A sequence of PALs is adopted after TUL, each enhancing the features as $\mathcal{P}^S \gets \theta(\mathcal{P}^S)$ according to Eq. 7. The decoder block outputs the updated $\mathcal{P}^S$ , and the output of the whole decoder is denoted as $\hat{\mathcal{P}}$ , which is the output of the final decoder block. + +# 3.3. Global Transformer for Context Aggregation + +Overview. Our designed global transformer takes as input a pair of triplets $\mathcal{P}'$ and $\mathcal{Q}'$ , and enhances the features with the global context, yielding $\widetilde{\mathbf{X}}' \in \mathbb{R}^{n' \times c'}$ and $\widetilde{\mathbf{Y}}' \in \mathbb{R}^{m' \times c'}$ , respectively. We stack $g \times$ global transformers, with each including a Geometry-Aware Self-Attention Module (GSM) and a Position-Aware Cross-Attention Module (PCM) (See Fig. 2 and Fig. 5). Different from previous works [19, 27, 48-50] that totally neglect the cross-frame spatial relationships, we propose to learn a rotation-invariant position representation for each superpoint to enable the position-aware cross-frame context aggregation. + +Geometry-Aware Self-Attention Module. On the global level, we modify PAM to learn the rotation-invariant position representation and to aggregate the learned context across the whole frame simultaneously. The design of GSM is detailed in Fig. 5 (a). GSM has two branches, where the geometry branch mines the geometric cues from the pairwise rotation-invariant geometry representation proposed in [27], and the context branch aggregates the global context across the frame. We refer the readers to the Appendix for the detailed construction of $\mathbf{R}' \in \mathbb{R}^{n' \times n' \times c'}$ and the ablation study on it. Similar to Eq. 4, the geometric cues $\mathbf{G}'$ and the positional encoding $\mathbf{E}'$ are linearly projected from + +$\mathbf{R}^{\prime}$ . $\mathbf{E}^{\prime}$ is further processed in the geometry branch and finally leveraged as the rotation-invariant position representation. In the context branch, $\mathbf{Q}^{\prime}$ , $\mathbf{K}^{\prime}$ , and $\mathbf{V}^{\prime}$ are obtained by linearly mapping the input features $\mathbf{X}^{\prime}$ similar to Eq. 5. The hybrid score matrix $\mathbf{S}^{\prime} \in \mathbb{R}^{n^{\prime} \times n^{\prime}}$ is computed as: + +$$ +\mathbf {S} ^ {\prime} (i, j) = \frac {\left(\mathbf {q} _ {i} ^ {\prime}\right) \left(\mathbf {e} _ {i , j} ^ {\prime} + \mathbf {k} _ {j} ^ {\prime}\right) ^ {T}}{\sqrt {c ^ {\prime}}}, \tag {9} +$$ + +with $\mathbf{e}_{i,j}^{\prime} := \mathbf{E}^{\prime}(i,j,:)$ , $\mathbf{q}_i^{\prime} := \mathbf{Q}^{\prime}(i,:)$ , and $\mathbf{k}_j^{\prime} := \mathbf{K}^{\prime}(j,:)$ the $c^{\prime}$ -dimension vectors. The hybrid attention $\mathbf{A}^{\prime}$ is obtained via a Softmax function over each row of $\mathbf{S}^{\prime}$ , and the geometric messages $\mathbf{M}_G^{\prime} \in \mathbb{R}^{n^{\prime} \times c^{\prime}}$ are computed as: + +$$ +\mathbf {M} _ {G} ^ {\prime} (i,:) = \sum_ {1 \leq j \leq n ^ {\prime}} a _ {i, j} ^ {\prime} \mathbf {g} _ {i, j} ^ {\prime}, \tag {10} +$$ + +with $a_{i,j}^{\prime} \coloneqq \mathbf{A}^{\prime}(i,j)$ and $\mathbf{g}_{i,j}^{\prime} \coloneqq \mathbf{G}^{\prime}(i,j,:)$ . The contextual messages $\mathbf{M}_V^{\prime} \in \mathbb{R}^{n^{\prime} \times c^{\prime}}$ are computed by $\mathbf{A}^{\prime}\mathbf{V}^{\prime}$ . After a feed-forward network [43], the position representation $\mathbf{E}_P^{\prime}$ and globally-enhanced context $\mathbf{C}_P^{\prime}$ are generated. + +Position-Aware Cross-Attention Module. PCM consumes a pair of doublets $(\mathbf{E}_P',\mathbf{C}_P')$ and $(\mathbf{E}_Q',\mathbf{C}_Q')$ that are generated from $\mathcal{P}'$ and $\mathcal{Q}'$ by a shared GSM, respectively. As the cross-attention is directional, we apply the same PCM twice, with the first aggregation from $\mathcal{Q}'$ to $\mathcal{P}'$ (See Fig. 5 (b)), and the second reversed. As the first step, the rotation-invariant position representation is incorporated to make the consecutive cross-attention position-aware, yielding position-aware features $\mathbf{F}_P' = \mathbf{E}_P' + \mathbf{C}_P'$ and $\mathbf{F}_Q' = \mathbf{E}_Q' + \mathbf{C}_Q'$ . Similar to Eq. 5, $\widetilde{\mathbf{Q}}',\widetilde{\mathbf{K}}'$ , and $\widetilde{\mathbf{V}}'$ are computed as the linear projection of $\mathbf{F}_P',\mathbf{F}_Q'$ , and $\mathbf{F}_Q'$ , respectively. The attention matrix $\widetilde{\mathbf{A}}\in \mathbb{R}^{n'\times m'}$ is computed via a row-wise softmax function applied on $\widetilde{\mathbf{Q}}'\widetilde{\mathbf{K}}'^T$ . The fused messages are presented as $\widetilde{\mathbf{A}}\widetilde{\mathbf{V}}'$ , which are finally mapped to the output features $\widetilde{\mathbf{X}}'$ through a feedforward network. As we introduce spatial awareness at the beginning of PCM, both the attention computation and message fusion are aware of the cross-frame positions. After the twice application of PCM, the input features are enhanced as $\mathcal{P}'\gets \widetilde{\mathbf{X}}'$ and $\mathcal{Q}'\gets \widetilde{\mathbf{Y}}'$ , respectively. The global aggregation stage finally generates a pair of triplets $\widetilde{\mathcal{P}}':=(\mathbf{P}',\mathbf{N}',\widetilde{\mathbf{X}}')$ and $\widetilde{\mathcal{Q}}':=(\mathbf{Q}',\mathbf{M}',\widetilde{\mathbf{Y}}')$ , with the enhanced features from the last global transformer. + +# 3.4. Point Matching and Loss Function + +Superpoint Matching. As shown in Fig. 2, the point matching stage consumes a pair of superpoint triplets $\hat{\mathcal{P}}'$ and $\hat{\mathcal{Q}}'$ obtained from the global transformer, as well as a pair of point triplets $\hat{\mathcal{P}}$ and $\hat{\mathcal{Q}}$ produced by the decoder. We adopt the coarse-to-fine matching proposed in [50]. Following [27], we first normalize the superpoint features $\widetilde{\mathbf{X}}'$ and $\widetilde{\mathbf{Y}}'$ onto a unit hypersphere, and measure the pairwise similarity using a Gaussian correlation matrix $\widetilde{\mathbf{S}}$ with $\widetilde{\mathbf{S}}(i,j) =$ + +$-\exp \left(-\|\widetilde{\mathbf{x}}_i'\widetilde{\mathbf{y}}_j'\|_2^2\right)$ . After a dual-normalization [27,29,37] on $\widetilde{\mathbf{S}}$ for global feature correlation, superpoints associated to the top- $k$ entries are selected as the coarse correspondence set $\mathcal{C}' = \{(\mathbf{p}_i',\mathbf{q}_i')|\mathbf{p}_i' \in \mathbf{P}',\mathbf{q}_i' \in \mathbf{Q}'\}$ . + +Point Matching. For extracting point correspondences, denser points $\hat{\mathbf{P}}$ and $\hat{\mathbf{Q}}$ are first assigned to superpoints. To this end, the point-to-node strategy [50] is leveraged, where each point is assigned to its closest superpoint in 3D space. Given a superpoint $\mathbf{p}_i' \in \mathbf{P}'$ , the group of points assigned to it is denoted as $\hat{\mathbf{G}}_i^P \subseteq \hat{\mathbf{P}}$ . The group of features associated to $\hat{\mathbf{G}}_i^P$ is further defined as $\hat{\mathbf{G}}_i^X$ with $\hat{\mathbf{G}}_i^X \subseteq \hat{X}$ . For each superpoint correspondence $\mathcal{C}_l' = (\mathbf{p}_i', \mathbf{q}_j')$ , the similarity between the corresponding feature groups $\hat{\mathbf{G}}_i^X$ and $\hat{\mathbf{G}}_j^Y$ is calculated as $\hat{\mathbf{S}}_l = \hat{\mathbf{G}}_i^X (\hat{\mathbf{G}}_j^Y)^T / \sqrt{\hat{c}}$ , with $\hat{c}$ the feature dimension. We then follow [35] to append a stack row and column to $\hat{\mathbf{S}}_l$ filled with a learnable parameter $\alpha$ , and iteratively run the Sinkhorn Algorithm [36]. After removing the slack row and column of $\hat{\mathbf{S}}_l$ , the mutual top-k entries, i.e., entries with top- $k$ confidence on both the row and the column, are selected to formulate a point correspondence set $\hat{\mathcal{C}}_l$ . The final correspondence set $\hat{\mathcal{C}}$ is collected by $\hat{\mathcal{C}} = \bigcup_{l=1}^{|\mathcal{C}'|} \hat{\mathcal{C}}_l$ . + +Loss Function. Our loss function reads as $\mathcal{L} = \mathcal{L}_s + \lambda \mathcal{L}_p$ , with a superpoint matching loss $\mathcal{L}_s$ and a point matching loss $\mathcal{L}_p$ balanced by a hyper-parameter $\lambda$ ( $\lambda = 1$ by default). The detailed definition is introduced in the Appendix. + +# 4. Experiment + +We evaluate RoITr on both rigid (3DMatch [51] & 3DLoMatch [19]) and non-rigid (4DMatch [20] & 4DLoMatch [20]) benchmarks. For the rigid matching, we further evaluate our correspondences on the registration task, where RANSAC [12] is used. Details of implementation, metrics, and runtime analysis are introduced in the Appendix. + +# 4.1. Rigid Indoor Scenes: 3DMatch & 3DLoMatch + +Dataset. 3DMatch [51] collects 62 indoor scenes, among which 46 are used for training, 8 for validation, and 8 for testing. We use the data processed by [19] where the 3DMatch data is spilt as 3DMatch ( $>30\%$ overlap) and 3DLoMatch ( $10\% \sim 30\%$ overlap). To evaluate robustness to arbitrary rotations, we follow [49] for creating the rotated benchmarks, where full-range rotations are individually added to the two frames of each point cloud pair. + +Metrics. We follow [19] to use three metrics for evaluation: (1). Inlier Ratio (IR) that computes the ratio of putative correspondences whose residual distance is smaller than a threshold (i.e., $0.1\mathrm{m}$ ) under the ground-truth transformation; (2). Feature Matching Recall (FMR) that calculates the fraction of point cloud pairs whose IR is larger than a threshold (i.e., $5\%$ ); (3). Registration Recall (RR) that counts the fraction of point cloud pairs that are cor + +
# Samples=5,0003DMatch3DLoMatch
OriginRotatedOriginRotated
Feature Matching Recall (%) ↑
SpinNet [1]97.497.475.575.2
Predator [19]96.696.278.673.7
CoFiNet [50]98.197.483.178.6
YOHO [44]98.297.879.477.8
RIGA [49]97.998.285.184.5
Lepard [20]98.097.483.179.5
GeoTrans [27]97.997.888.385.8
RoITr (Ours)98.098.289.689.4
Inlier Ratio (%) ↑
SpinNet [1]48.548.725.725.7
Predator [19]58.052.826.722.4
CoFiNet [50]49.846.824.421.5
YOHO [44]64.464.125.923.2
RIGA [49]68.468.532.132.1
Lepard [20]58.653.728.424.4
GeoTrans [27]71.968.243.540.0
RoITr (Ours)82.682.354.353.2
Registration Recall (%) ↑
SpinNet [1]88.893.258.261.8
Predator [19]89.092.059.858.6
CoFiNet [50]89.392.067.562.5
YOHO [44]90.892.565.266.8
RIGA [49]89.393.065.166.9
Lepard [20]92.784.965.449.0
GeoTrans [27]92.092.075.071.8
RoITr (Ours)91.994.774.877.2
+ +Table 1. Quantitative results on (Rotated) 3DMatch & 3DLoMatch. 5,000 points/correspondences are used for the evaluation. + +rectly registered (i.e., with $\mathrm{RMSE} < 0.2\mathrm{m}$ ). + +Comparison with the State-of-the-Art. We compare RoITr with 7 state-of-the-art methods, among which Predator [19], CoFiNet [50], Lepard [20], and GeoTrans [27] are rotation-sensitive models, while SpinNet [1], YOHO [44], and RIGA [49] guarantee the rotation invariance by design. In Tab. 1 we demonstrate the matching and registration results on 3DMatch and 3DLoMatch, as well as on their rotated versions, with 5,000 sampled points/correspondences. Regarding IR, RoITr outperforms all the others by a large margin on both datasets, which indicates our method matches points more correctly. For FMR, we significantly surpass all the others on 3DLoMatch, while staying on par with CoFiNet and YOHO on 3DMatch, which indicates that our model is good at coping with hard cases, i.e., we find at least $5\%$ inliers on more test data. For the registration evaluation in terms of RR, RoITr achieves comparable performance with GeoTrans and Lepard on 3DMatch, but leads the board together with GeoTrans on 3DLoMatch with an overwhelming advantage over the others. Our stability against additional rotations is further demonstrated on the rotated data, where we outperform all the others with a substantial margin. Qualitative results can be found in Fig. 6. + +![](images/ac23312a02beb4a475dda47e424d95133ebb2541ce2ad59f1a91cd2ede8584a7.jpg) +Figure 6. Qualitative results on 3DLoMatch. GeoTrans [27] is used as the baseline. Columns (b) and (c) show the correspondences, while columns (d) and (e) demonstrate the registration results. Green/red lines indicate inliers/outliers. More cases are shown in the Appendix. + +
# Samples3DMatch3DLoMatch
500025001000500250500025001000500250
Feature Matching Recall (%)↑
SpinNet [1]97.497.096.496.794.875.575.174.269.062.7
Predator [19]96.696.696.596.396.578.677.476.375.775.3
CoFiNet [50]98.198.398.198.298.383.183.583.383.182.6
YOHO [44]98.297.697.597.796.079.478.176.373.869.1
RIGA [49]97.997.897.797.797.685.185.085.184.385.1
GeoTrans [27]97.997.997.997.997.688.388.688.888.688.3
RoITr (Ours)98.098.097.998.097.989.689.689.589.489.3
Inlier Ratio (%)↑
SpinNet [1]48.546.240.835.129.025.723.720.618.213.1
Predator [19]58.058.457.154.149.326.728.128.327.525.8
CoFiNet [50]49.851.251.952.252.224.425.926.726.826.9
YOHO [44]64.460.755.746.441.225.923.322.618.215.0
RIGA [49]68.469.770.670.971.032.133.434.334.534.6
GeoTrans [27]71.975.276.082.285.143.545.346.252.957.7
RoITr (Ours)82.682.883.083.083.054.354.655.155.255.3
Registration Recall (%)↑
SpinNet [1]88.888.084.579.069.258.256.749.841.026.7
Predator [19]89.089.990.688.586.659.861.262.460.858.1
CoFiNet [50]89.388.988.487.487.067.566.264.263.161.0
YOHO [44]90.890.389.188.684.565.265.563.256.548.0
RIGA [49]89.388.489.189.087.765.164.764.564.161.8
GeoTrans [27]92.091.891.891.491.275.074.874.274.173.5
RoITr (Ours)91.991.791.891.491.074.774.874.874.273.6
+ +Analysis on the Number of Correspondences. We further analyze the influence of a varying number of correspondences. As illustrated in Tab. 2, RoITr shows outstanding performance on both datasets with various correspondences, proving its stability when only a few correspondences are accessible. The same test on the rotated benchmarks is given in the Appendix. + +# 4.2. Deformable Objects: 4DMatch & 4DLoMatch + +Dataset. 4DMatch [20] contains 1,761 animations randomly selected from DeformingThings4D [21]. The 1,761 sequences are divided into 1,232/176/353 as train/val/test, where the test set is further split into 4DMatch and 4DLoMatch based on an overlap ratio threshold of $45\%$ . Metrics. We follow [20] to use two different metrics: (1). Inlier Ratio (IR) which is defined as same as the IR on 3DMatch, + +Table 2. Quantitative results on 3DMatch & 3DLoMatch with a varying number of points/correspondences. See the results on rotated data in the Appendix. + +
CategoryMethod4DMatch4DLoMatch
NFMR(%)↑IR(%)↑NFMR(%)↑IR(%)↑
Scene FlowPWC [45]21.620.010.07.2
FLOT [24]27.124.915.210.7
Feature MatchingPredator [19]56.460.432.127.5
GeoTrans [27]83.282.265.463.6
Lepard [20]83.782.766.955.7
RoITr (Ours)83.084.469.467.6
+ +Table 3. Quantitative results on 4DMatch & 4DLoMatch. + +but with a different threshold (i.e., $0.04\mathrm{m}$ ); (2). Non-rigid Feature Matching Recall (NFRM) that measures the fraction of ground-truth matches that can be successfully recovered by the putative correspondences. + +Comparison with the State-of-the-Art. We compare RoITr with 5 baselines, among which PwC [45] and FLOT [24] are scene flow-based methods, while Predator [19], Lepard [20], GeoTrans [27] are based on feature matching. The results shown in Tab. 3 indicate that although our rotation-invariance is mainly designed for rigid scenarios, RoITr could also achieve outstanding performance in the non-rigid matching task, which further confirms the superiority of our model design. Qualitative results are demonstrated in Fig. 7. + +# 4.3. Ablation Study + +Local Attention. We first replace our PPFTrans with PointTransformer (PT) [53] in Tab. 4 (a.1), which leads to a sharp performance drop. We then ablate by embedding our PPF-based local coordinates into PT (Tab. 4 (a.2)) and by adopting the relative coordinates, i.e., $\mathbf{p}_j - \mathbf{p}_j$ , used by PT in our PAM (Tab. 4 (a.3)). Our local coordinate representation significantly boosts the performance of PT in the task of point cloud matching and meanwhile makes it rotation-invariant, although its performance is still far behind ours. However, the relative coordinates fail to work in our PAM, as we adopt a more efficient attention mechanism [43] that learns a scalar attention value for each feature $\mathbf{x} \in \mathbb{R}^c$ and is consequently hard to work under varying poses with a + +![](images/05f21fec257031ee45502721928229e415a594471edac0c8ac5a61e3a223fa87.jpg) +Figure 7. Qualitative results of non-rigid matching on 4DLoMatch with Lepard [20] as the baseline. Green/red lines indicate inliers/outliers. See the Appendix for more examples. + +rotation-sensitive design. As a comparison, PT learns a per-channel vector attention $\mathbf{a} \in \mathbb{R}^c$ for the same feature $\mathbf{x}$ and could deal with the pose variations, but at the cost of the efficiency as shown in Fig. 8. When the number of channels is increased, our advantage in terms of efficiency is enlarged. As we achieve that with more parameters, the gap becomes more significant when runtime is normalized with the number of parameters in the right figure. With our PPF-based local coordinate, the scalar attention could focus on the pose-agnostic pure geometry and therefore achieves the best performance shown in Tab. 4 (a.4). + +Abstraction Layer. We ablate our Attentional Abstraction Layer (AAL) by replacing it with the pooling-based abstraction design used in [25, 26, 53]. We test the max pooling in Tab. 4 (b.1) and the average pooling in Tab. 4 (b.2), both showing a degrading performance compared with our AAL, which demonstrates our superiority. + +Backbone. In Tab. 4 (a.1) we have shown our superiority compared with PT [53]. We further replace our PPFTrans with the KPCnv-based backbone network which is widely used in previous deep matchers [19, 27, 50]. The fact that KPCnv falls behind our design demonstrates the advantage of PPFTrans in geometry encoding. + +Global Transformer. We replace our design with the global transformer of GeoTrans [27] which performs state-of-the-art but without the cross-frame spatial awareness. The dropping results in Tab. 4 (d.1) proves the excellence of our design with the cross-frame position awareness. + +The Number of Global Transformers. To demonstrate the importance of being globally aware, we first remove the global transformer. The substantial performance drop confirms the significance of global awareness. Then we add one global transformer and observe an increased performance. In our default setting with 3 global transformers, the model performs the best. However, when the number is increased to 5, the model shows a slight performance drop, which we owe to overfitting. As the data augmentation of rotations + +![](images/c79f5972814873dd0680a193dcb9720a19fc8606439b7e3d540e215126e359a0.jpg) +Figure 8. Left: Runtime comparison between our PPF attention Mechanism (PAM) and the local attention in PointTransformer [53]. Right: Runtime normalized by aligning the number of parameters. + +
CategoryModelOriginRotated
FMRIRRRFMRIRRR
a. Local1. PT [53]79.036.561.676.534.760.0
*2. PPF+PT [53]87.049.969.986.849.471.2
3. Δxyz+Ours------
*4. Ours89.654.374.789.453.277.2
b. Aggregation*1. max pooling85.250.170.585.450.271.9
*2. avg pooling87.852.673.887.252.574.7
*3. Ours89.654.374.789.453.277.2
c. Backbone1. KPCov [40]85.244.470.683.042.371.5
*2. Ours89.654.374.789.453.277.2
d. Global*1. GeoTrans [27]87.753.673.087.553.275.1
*2. Ours89.654.374.789.453.277.2
e. #Global*1. g = 087.237.670.787.537.672.7
*2. g = 187.142.170.886.842.173.0
*3. g = 3 (Ours)89.654.374.789.453.277.2
*4. g = 587.152.572.187.052.473.3
+ +Table 4. Ablation study on (rotated) 3DLoMatch. 5,000 points/correspondences are leveraged. * indicates the methods with intrinsic rotation invariance. See the Appendix for the results on (rotated) 3DMatch. + +has less effect on an intrinsically rotation-invariant method, more data is required for training a larger model. + +# 5. Conclusion + +We introduced RoITr - an intrinsically rotation-invariant model for point cloud matching. We proposed PAM (PPF Attention Mechanism) that embeds PPF-based local coordinates to encode rotation-invariant geometry. This design lies at the core of AAL (Attention Abstraction Layer), PAL (PPF Attention Layer), and TUL (Transition Up Layer) which are consecutively stacked to compose PPFTrans (PPF Transformer) for representative and pose-agnostic geometry description. We further enhanced features by introducing a novel global transformer architecture, which ensures the rotation-invariant cross-frame spatial awareness. Extensive experiments are conducted on both rigid and non-rigid benchmarks to demonstrate the superiority of our approach, especially the remarkable robustness against arbitrary rotations. Limitations are discussed in the Appendix. + +Acknowledgment. This paper is supported by the National Natural Science Foundation of China under Grant No. 62025208. We appreciate the help from Lennart Bastian, Mert Karaoglu, Ning Liu, and Zhiying Leng. + +# References + +[1] Sheng Ao, Qingyong Hu, Bo Yang, Andrew Markham, and Yulan Guo. Spinnet: Learning a general surface descriptor for 3d point cloud registration. In CVPR, 2021. 1, 2, 6, 7 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 4 +[3] Xuyang Bai, Zixin Luo, Lei Zhou, Hongbo Fu, Long Quan, and Chiew-Lan Tai. D3feat: Joint learning of dense detection and description of 3d local features. 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However, it is widely despised by recent deep matchers that obtain the rotation invariance extrinsically via data augmentation. As the finite number of augmented rotations can never span the continuous " + }, + { + "bbox": [ + 47, + 224, + 290, + 548 + ], + "type": "inline_equation", + "content": "SO(3)" + }, + { + "bbox": [ + 47, + 224, + 290, + 548 + ], + "type": "text", + "content": " space, these methods usually show instability when facing rotations that are rarely seen. To this end, we introduce RoITr, a Rotation-Invariant Transformer to cope with the pose variations in the point cloud matching task. We contribute both on the local and global levels. Starting from the local level, we introduce an attention mechanism embedded with Point Pair Feature (PPF)-based coordinates to describe the pose-invariant geometry, upon which a novel attention-based encoder-decoder architecture is constructed. We further propose a global transformer with rotation-invariant cross-frame spatial awareness learned by the self-attention mechanism, which significantly improves the feature distinctiveness and makes the model robust with respect to the low overlap. Experiments are conducted on both the rigid and non-rigid public benchmarks, where RoITr outperforms all the state-of-the-art models by a considerable margin in the low-overlapping scenarios. Especially when the rotations are enlarged on the challenging 3DLoMatch benchmark, RoITr surpasses the existing methods by at least 13 and 5 percentage points in terms of Inlier Ratio and Registration Recall, respectively. Code is publicly available1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 575, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 287, + 696 + ], + "type": "text", + "content": "The correspondence estimation between a pair of partially-overlapping point clouds is a long-standing task that lies at the core of many computer vision applications, such as tracking [17, 18], reconstruction [22, 23, 39], pose estimation [19, 27, 50] and 3D representation learning [15, 16, 46], etc. In a typical solution, geometry is first encoded into descriptors, and correspondences are then established between two frames by matching the most similar descriptors. As the two frames are observed from different views, depicting the same geometry under different trans" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 198, + 547, + 335 + ], + "blocks": [ + { + "bbox": [ + 307, + 198, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 307, + 198, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 307, + 198, + 547, + 335 + ], + "type": "image", + "image_path": "81825f8e94531760f124a36a4048f3485bea7faa274c6d8e55532d5c6f8d23a7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 337, + 547, + 392 + ], + "lines": [ + { + "bbox": [ + 305, + 337, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 547, + 392 + ], + "type": "text", + "content": "Figure 1. Feature Matching Recall (FMR) on 3DLoMatch [19] and Rotated 3DLoMatch. Distance to the diagonal represents the robustness against rotations. Among all the state-of-the-art approaches, RoITr not only ranks first on both benchmarks but also shows the best robustness against the enlarged rotations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 399, + 545, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 423 + ], + "type": "text", + "content": "formations identically, i.e., the pose-invariance, becomes the key to success in the point cloud matching task." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 425, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 546, + 700 + ], + "type": "text", + "content": "Since the side effects caused by a global translation can always be easily eliminated, e.g., by aligning the barycenter with the origin, the attention naturally shifts to coping with the rotations. In the past, handcrafted local descriptors [11, 30, 31, 41] were designed to be rotation-invariant so that the same geometry observed from different views can be correctly matched. With the emergence of deep neural models for 3D point analysis, e.g., multilayer perceptrons (MLPs)-based like PointNet [25, 26], convolutions-based like KPConv [6, 40], and the attention-based like PointTransformer [33, 53], recent approaches [1, 7, 9, 10, 13, 19, 20, 27, 32, 48-51] propose to learn descriptors from raw points as an alternative to handcrafted features that are less robust to occlusion and noise. The majority of deep point matchers [7, 10, 19, 20, 27, 34, 48, 50-52] is sensitive to rotations. Consequently, their invariance to rotations must be obtained extrinsically via augmented training to ensure that the same geometry under different poses can be depicted similarly. However, as the training cases can never span the continuous " + }, + { + "bbox": [ + 304, + 425, + 546, + 700 + ], + "type": "inline_equation", + "content": "SO(3)" + }, + { + "bbox": [ + 304, + 425, + 546, + 700 + ], + "type": "text", + "content": " space, they always suffer from instability when facing rotations that are rarely seen during training. This can be observed by a significant performance drop under enlarged rotations at inference time. (See Fig. 1.)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "There are other works [1, 9, 13, 32, 44] that only lever" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 174, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 174, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 174, + 712 + ], + "type": "text", + "content": "1https://github.com/haoyu94/RoITr" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5384" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "content": "age deep neural networks to encode the pure geometry with the intrinsically-designed rotation invariance. However, the intrinsic rotation invariance comes at the cost of losing global context. For example, a human's left and right halves are almost identically described, which naturally degrades the distinctiveness of features. Most recently, RIGA [49] is proposed to enhance the distinctiveness of the rotation-invariant descriptors by incorporating a global context, e.g., the left and right halves of a human become distinguishable by knowing there is a chair on the left while a table on the right. However, it lacks a highly-representative geometry encoder since it relies on PointNet [25], which accounts for an ineffective local geometry description. Moreover, as depicting the cross-frame spatial relationships is non-trivial, previous works [19, 27, 34, 50] merely leverage the contextual features in the cross-frame context aggregation, which neglects the positional information. Although RIGA proposes to learn a rotation-invariant position representation by leveraging an additional PointNet, this simple design is hard to model the complex cross-frame positional relationships and leads to less distinctive descriptors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 323, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 289, + 515 + ], + "type": "text", + "content": "In this paper, we present Rotation-Invariant Transformer (RoITr) to tackle the problem of point cloud matching under arbitrary pose variations. By using Point Pair Features (PPFs) as the local coordinates, we propose an attention mechanism to learn the pure geometry regardless of the varying poses. Upon it, attention-based layers are further proposed to compose the encoder-decoder architecture for highly-discriminative and rotation-invariant geometry encoding. We demonstrate its superiority over PointTransformer [53], a state-of-the-art attention-based backbone network, in terms of both efficiency and efficacy in Fig. 8 and Tab. 4 (a), respectively. On the global level, the cross-frame position awareness is introduced in a rotation-invariant fashion to facilitate feature distinctiveness. We illustrate its significance over the state-of-the-art design [27] in Tab. 4 (d). Our main contributions are summarized as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 522, + 287, + 635 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 522, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 522, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 58, + 522, + 287, + 559 + ], + "type": "text", + "content": "- An attention mechanism designed to disentangle the geometry and poses, which enables the pose-agnostic geometry description." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 561, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 561, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 58, + 561, + 287, + 597 + ], + "type": "text", + "content": "- An attention-based encoder-decoder architecture that learns highly-representative local geometry in a rotation-invariant fashion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 599, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 599, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 58, + 599, + 287, + 635 + ], + "type": "text", + "content": "- A global transformer with rotation-invariant cross-frame position awareness that significantly enhances the feature distinctiveness." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "Models with Extrinsic Rotation Invariance. The mainstream of deep learning-based point cloud matching approaches is intrinsically rotation-sensitive. Pioneers [10,51] learn to describe local patches from a rotation-variant input." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "FCGF [7] leverages fully-convolutional networks to accelerate the geometry description. D3Feat [3] jointly detects and describes sparse keypoints for matching. Predator [19] incorporates the global context to enhance the local descriptors and predicts the overlap regions for keypoint sampling. CoFiNet [50] extracts coarse-to-fine correspondences to alleviate the repeatability issue of keypoints. GeoTrans [27] considers the geometric information in fusing the intra-frame context globally. However, the awareness of spatial positions is missing in the cross-frame aggregation. Lepard [20] extends the non-rigid shape matching [34, 38, 42] to point clouds [28] and proposes a re-positioning module to alleviate the pose variations. REGTR [48] directly regresses the corresponding coordinates and registers point clouds in an end-to-end fashion. Nonetheless, all of these methods suffer from instability with additional rotations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 264, + 546, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 546, + 527 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 546, + 527 + ], + "type": "text", + "content": "Methods with Intrinsic Rotation Invariance. A branch of handcrafted descriptors [8, 14, 41] aligns the input to a canonical representation according to an estimated local reference frame (LRF), while the others [11, 30, 31] mine the rotation-invariant components and encode them as the representation of the local geometry. Inspired by that, some deep learning-based methods [1, 4, 9, 13, 32, 34, 49] are designed to be intrinsically rotation-invariant to make the neural models focus on the pose-agnostic pure geometry. As a pioneer, PPF-FoldNet [9] consumes PPF-based patches and learns the descriptors using a FoldingNet [47]-based architecture without supervision. LRF-based works [1, 13, 32, 34] achieve rotation invariance by aligning their input to the defined canonical representation. YOHO [44] adopts a group of rotations to learn a rotation-equivariant feature group and further obtain the invariance via group pooling. A common problem of the rotation-invariant methods is the less distinctive features. Although RIGA [49] incorporates the global context into local descriptors to enhance the feature distinctiveness, its ineffective local geometry encoding and global position description learned by PointNet [25] still constraint the representation ability of its descriptors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 533, + 361, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 361, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 361, + 545 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "text", + "content": "Problem Statement. We tackle the problem of matching a pair of partially-overlapping point clouds " + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} \\in \\mathbb{R}^{m \\times 3}" + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "text", + "content": ", and extract a correspondence set " + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}} = \\{(\\hat{\\mathbf{p}}_i, \\hat{\\mathbf{q}}_j) | \\hat{\\mathbf{p}}_i \\in \\hat{\\mathbf{P}} \\subseteq \\mathbf{P}, \\hat{\\mathbf{q}}_j \\in \\hat{\\mathbf{Q}} \\subseteq \\mathbf{Q}\\}" + }, + { + "bbox": [ + 305, + 554, + 545, + 603 + ], + "type": "text", + "content": " that minimizes:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 362, + 608, + 545, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 608, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 362, + 608, + 545, + 640 + ], + "type": "interline_equation", + "content": "\\frac {1}{| \\hat {\\mathcal {C}} |} \\sum_ {(\\hat {\\mathbf {p}} _ {i}, \\hat {\\mathbf {q}} _ {j}) \\in \\hat {\\mathcal {C}}} \\| \\mathcal {M} ^ {*} (\\hat {\\mathbf {p}} _ {i}) - \\hat {\\mathbf {q}} _ {j} \\| _ {2}, \\tag {1}", + "image_path": "cbc06f58e0d5940175d1ba33f7a38a93e81114cb467c1c5e83d0134819246b15.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _2" + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": " denotes the Euclidean norm and " + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "inline_equation", + "content": "|\\cdot |" + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": " is the set cardinality. " + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}^{*}(\\cdot)" + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": " stands for the ground-truth mapping function that maps " + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{p}}_i" + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": " to its corresponding position in " + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Q}}" + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": ". In rigid scenarios, it is defined by a transformation " + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{T}^{*}\\in SE(3)" + }, + { + "bbox": [ + 304, + 640, + 545, + 714 + ], + "type": "text", + "content": ". 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Decoder" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 190, + 163, + 403, + 281 + ], + "lines": [ + { + "bbox": [ + 190, + 163, + 403, + 281 + ], + "spans": [ + { + "bbox": [ + 190, + 163, + 403, + 281 + ], + "type": "image", + "image_path": "09130879a56551a0ae9902d954d95aa14320b2226c7bf4ba302d260c1e117218.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 410, + 164, + 541, + 281 + ], + "blocks": [ + { + "bbox": [ + 358, + 147, + 404, + 156 + ], + "lines": [ + { + "bbox": [ + 358, + 147, + 404, + 156 + ], + "spans": [ + { + "bbox": [ + 358, + 147, + 404, + 156 + ], + "type": "text", + "content": "(4). Matching" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 410, + 164, + 541, + 281 + ], + "lines": [ + { + "bbox": [ + 410, + 164, + 541, + 281 + ], + "spans": [ + { + "bbox": [ + 410, + 164, + 541, + 281 + ], + "type": "image", + "image_path": "ebbdcf4c197d78aed4fe93f07f359b890d055be2d6966b8ff2e9b4e25a40194c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "type": "text", + "content": "Method Overview. An overview of RoITr is shown in Fig. 2. RoITr consists of an encoder-decoder architecture named Point Pair Feature Transformer (PPFTrans) for local geometry encoding and a stack of " + }, + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "type": "inline_equation", + "content": "g \\times" + }, + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "type": "text", + "content": " global transformers for global context aggregation. Correspondence set " + }, + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 46, + 430, + 287, + 501 + ], + "type": "text", + "content": " is extracted by the coarse-to-fine matching [50]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 514, + 194, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 194, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 194, + 525 + ], + "type": "text", + "content": "3.1. PPF Attention Mechanism" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": "Overview. Fig. 3 compares three different self-attention mechanisms. The standard attention [43] only leverages the input context to obtain the Query " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " and Key " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " to compute the contextual attention " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_C" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": ", as well as the Value " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " that encodes information for the contextual message " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_C" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": ". GeoTrans [27] proposes to learn the positional encoding " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " from the geometry and calculates a second attention " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_G" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " to reweigh " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_C" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": ". However, the cues contained in the raw geometry are totally neglected. To this end, we propose to learn the pose-agnostic geometric cues " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " and further generate the geometric message " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_G" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " in the PPF Attention Mechanism (PAM). On the local level, " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_G" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " is combined with " + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_C" + }, + { + "bbox": [ + 46, + 534, + 287, + 713 + ], + "type": "text", + "content": " for feature enhancement, while on the global level, it is used to learn the rotation-invariant position representation for the cross-frame context aggregation. More specifically, we de" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 315, + 431, + 376, + 498 + ], + "blocks": [ + { + "bbox": [ + 315, + 431, + 376, + 498 + ], + "lines": [ + { + "bbox": [ + 315, + 431, + 376, + 498 + ], + "spans": [ + { + "bbox": [ + 315, + 431, + 376, + 498 + ], + "type": "image", + "image_path": "c0b712b6186087050f178483da8e9448683cbb6f8c24b4fae9914085547debf4.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 506, + 379, + 514 + ], + "lines": [ + { + "bbox": [ + 315, + 506, + 379, + 514 + ], + "spans": [ + { + "bbox": [ + 315, + 506, + 379, + 514 + ], + "type": "text", + "content": "(a). Standard Attention" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 380, + 430, + 454, + 498 + ], + "blocks": [ + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": "Figure 2. An Overview of RoITr. From left to right: " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "(\\pmb{0})" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": ". RoITr takes as input a pair of triplets " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = (\\mathbf{P}, \\mathbf{N}, \\mathbf{X})" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = (\\mathbf{Q}, \\mathbf{M}, \\mathbf{Y})" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": ", each with three dimensions referring to the point cloud, the estimated normals, and the initial features. (1).[§ 3.2] A stack of encoder blocks hierarchically downsamples the points to coarser superpoints and encodes the local geometry, yielding superpoint triplets " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": ". Each encoder block consists of an Attentional Abstraction Layer (AAL) for downsampling and abstraction, followed by " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "e \\times" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " PPF Attention Layers (PALs) for local geometry encoding and context aggregation. Both of them are based on our proposed PPF Attention Mechanism (PAM), which enables the pose-agnostic encoding of pure geometry. (See Fig. 3 and Fig. 4). (2).[§ 3.3] Global information is fused to enhance the superpoint features of " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": ". The geometric cues are globally aggregated as a rotation-invariant position representation, which introduces spatial awareness in the consecutive cross-frame context aggregation. After a stack of " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "g \\times" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " global transformers, the globally-enhanced triplets " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{P}}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{Q}}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " are produced. (3).[§ 3.2] Superpoint triplets " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " are decoded to point triplets " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{Q}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " by a stack of decoder blocks. Each block consists of a Transition Up Layer (TUL) for upsampling and context aggregation, followed by " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "d \\times" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " PALs. (4).[§ 3.4] By adopting the coarse-to-fine matching [50], " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{P}}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{Q}}'" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " are matched to generate superpoint correspondences, which are consecutively refined to point correspondences between " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{Q}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": ". (5). " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " is established between " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{Q}}" + }, + { + "bbox": [ + 46, + 290, + 545, + 422 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 380, + 430, + 454, + 498 + ], + "lines": [ + { + "bbox": [ + 380, + 430, + 454, + 498 + ], + "spans": [ + { + "bbox": [ + 380, + 430, + 454, + 498 + ], + "type": "image", + "image_path": "050ce13ccd9012d289ebabdf10f1e5aa082cc00677dad1952586dbd8194f9d92.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 400, + 506, + 440, + 514 + ], + "lines": [ + { + "bbox": [ + 400, + 506, + 440, + 514 + ], + "spans": [ + { + "bbox": [ + 400, + 506, + 440, + 514 + ], + "type": "text", + "content": "(b). GeoTrans" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 457, + 430, + 542, + 498 + ], + "blocks": [ + { + "bbox": [ + 457, + 430, + 542, + 498 + ], + "lines": [ + { + "bbox": [ + 457, + 430, + 542, + 498 + ], + "spans": [ + { + "bbox": [ + 457, + 430, + 542, + 498 + ], + "type": "image", + "image_path": "1ae7e04b44a0ede10cb1f694b3023f8ff8b9887eed7c1e32a5a65db1f3724d8b.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 478, + 506, + 523, + 514 + ], + "lines": [ + { + "bbox": [ + 478, + 506, + 523, + 514 + ], + "spans": [ + { + "bbox": [ + 478, + 506, + 523, + 514 + ], + "type": "text", + "content": "(c).PAM (Ours)" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 527, + 544, + 548 + ], + "lines": [ + { + "bbox": [ + 306, + 527, + 544, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 544, + 548 + ], + "type": "text", + "content": "Figure 3. Illustration of different self-attention computation in the standard attention [43], GeoTrans [27], and PAM." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": "fine PAM on an Anchor triplet " + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A = (\\mathbf{P}^A, \\mathbf{N}^A, \\mathbf{X}^A)" + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": " and a Support triplet " + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S = (\\mathbf{P}^S, \\mathbf{N}^S, \\mathbf{X}^S)" + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": ", both with three dimensions referring to the point cloud, the estimated normals, and the associated features, respectively. PAM aggregates the learned context and geometric cues from " + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": " and flows the messages to " + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A" + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": "Pose-Agnostic Coordinate Representation. The basis of PAM is the pose-agnostic local coordinate representation that we construct based on PPFs [11]. Let " + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i^A \\coloneqq (\\mathbf{p}_i^A \\in \\mathbf{P}^A, \\mathbf{n}_i^A \\in \\mathbf{N}^A, \\mathbf{x}_i^A \\in \\mathbf{X}^A) \\in \\mathcal{P}^A" + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": " denote the triplet constructed by picking the " + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": " item on each dimension. For each " + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^A" + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": ", a subset of " + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": " is first retrieved according to the Euclidean distance w.r.t. " + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^S" + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": ", denoted as" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5386" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 289, + 185 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 185 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 185 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 185 + ], + "type": "image", + "image_path": "5081a262fa30968f29b7c9345f2e9eb18f9480785ff18366f83ba9c4b08632b3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 287, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 217 + ], + "type": "text", + "content": "Figure 4. Left: The workflow of the PPF Attention Mechanism (PAM). Right: Detailed calculation of the attention." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\mathcal{N}(i)}^{S} \\coloneqq (\\mathbf{P}_{\\mathcal{N}(i)}^{S}, \\mathbf{N}_{\\mathcal{N}(i)}^{S}, \\mathbf{X}_{\\mathcal{N}(i)}^{S}) \\subseteq \\mathcal{P}^{S}" + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(i)" + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "content": " the indices of " + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "content": "-nearest neighbors. We then adopt PPFs [11] to construct a local coordinate system around each " + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^A" + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "content": " to represent the pose-agnostic position of " + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathcal{N}(i)}^{S}" + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "content": " w.r.t. it. The coordinate of point " + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j^S \\in \\mathbf{P}_{\\mathcal{N}(i)}^{S}" + }, + { + "bbox": [ + 46, + 222, + 288, + 289 + ], + "type": "text", + "content": " is transferred to:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 297, + 287, + 313 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 297, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 70, + 297, + 287, + 313 + ], + "type": "interline_equation", + "content": "\\mathbf {e} _ {j} ^ {S} = \\left(\\| \\mathbf {d} \\| _ {2}, \\angle \\left(\\mathbf {n} _ {i} ^ {A}, \\mathbf {d}\\right), \\angle \\left(\\mathbf {n} _ {j} ^ {S}, \\mathbf {d}\\right), \\angle \\left(\\mathbf {n} _ {j} ^ {S}, \\mathbf {n} _ {i} ^ {A}\\right)\\right), \\quad (2)", + "image_path": "d17b0b37b58247bc0dd2c2279a7212eae97c2b5434d3b446431e4bd7bbf198d3.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{d} = \\mathbf{p}_j^S -\\mathbf{p}_i^A" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i^A" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_j^S" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " the estimated normals of " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^A" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j^S" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " , respectively. " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\angle (\\mathbf{v}_1,\\mathbf{v}_2)" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " computes the angles between the two vectors [5, 9]. The transferred coordinates of " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathcal{N}(i)}^{S}" + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "text", + "content": " are denoted as " + }, + { + "bbox": [ + 46, + 319, + 287, + 372 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathcal{N}(i)}^{S}" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "content": "PPF Attention Mechanism. PPF Attention Mechanism (PAM) takes as input the Support triplet " + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "content": " and the Anchor point cloud " + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^A" + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "content": " with estimated normals " + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{N}^A" + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "content": ". PAM generates the Anchor features " + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^A" + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "content": " by aggregating the pose-agnostic local geometry and highly-representative learned context from " + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 46, + 371, + 287, + 441 + ], + "type": "text", + "content": ", which is defined as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 118, + 452, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 452, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 118, + 452, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\mathcal {P} ^ {A} = \\delta \\left(\\mathbf {P} ^ {A}, \\mathbf {N} ^ {A} \\mid \\mathcal {P} ^ {S}\\right), \\tag {3}", + "image_path": "e04432e0e35d67615d51a0865f8f27086da7ab05694737d922922544a6c8d7de.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\delta(\\cdot)" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " representing PAM. As shown in Fig. 4 (a), for each " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^A \\in \\mathbf{P}^A" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " with normal " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_i^A" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ", we find its nearest point " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j^S \\in \\mathbf{P}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " whose associated feature " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " is assigned to " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i^A" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " as the initial description. Then, " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": "-nearest neighbors from " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " are retrieved according to the Euclidean distance in 3D space, yielding " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathcal{N}(i)}^S \\subseteq \\mathbf{P}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathcal{N}(i)}^S \\subseteq \\mathbf{X}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ". Following Eq. 2, " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_{\\mathcal{N}(i)}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " is transferred to the pose-agnostic position representation " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_{\\mathcal{N}(i)}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ", which is consecutively projected to the coordinate embedding " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " via a linear layer. " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathcal{N}(i)}^S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " are projected to the contextual features " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_S" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " by a second shared linear layer, respectively. In Fig. 4 (b), the attention mechanism uses five learnable matrices " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_G" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_E" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_Q" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_K" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_V" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " to project the input. Specifically, " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_G" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_E" + }, + { + "bbox": [ + 46, + 472, + 288, + 661 + ], + "type": "text", + "content": " project the input coordinate representation to the geometric cues and positional encoding by:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 671, + 287, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 671, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 93, + 671, + 287, + 685 + ], + "type": "interline_equation", + "content": "\\mathbf {G} = \\mathbf {E} _ {S} \\mathbf {W} _ {G} \\quad \\text {a n d} \\quad \\mathbf {E} = \\mathbf {E} _ {S} \\mathbf {W} _ {E}, \\tag {4}", + "image_path": "7457668921431f078b0022d0a4a89a06e04e8e9b5ba19f251e4847d2d8451048.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "respectively. Similarly, " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_Q" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_K" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_V" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " project the learned context to Query, Key, and Value as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 320, + 95, + 545, + 108 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 95, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 320, + 95, + 545, + 108 + ], + "type": "interline_equation", + "content": "\\mathbf {q} = \\mathbf {x} _ {S} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} _ {S} \\mathbf {W} _ {K}, \\text {a n d} \\mathbf {V} = \\mathbf {X} _ {S} \\mathbf {W} _ {V}, \\tag {5}", + "image_path": "aac0a54fe287bb76523d16e420c8d3711ddbffab7c2fd74939b5ec41bdb7bb7e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 113, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 113, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 113, + 545, + 148 + ], + "type": "text", + "content": "respectively. The attention a that measures the feature similarity, and the message m that encodes both the pose-agnostic geometry and the representative context read as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 310, + 157, + 545, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 157, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 310, + 157, + 545, + 186 + ], + "type": "interline_equation", + "content": "\\mathbf {a} = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {q} \\mathbf {E} ^ {T} + \\mathbf {q} \\mathbf {K} ^ {T}}{\\sqrt {c _ {0}}}\\right) \\quad \\text {a n d} \\quad \\mathbf {m} = \\mathbf {a} \\mathbf {G} + \\mathbf {a} \\mathbf {V}, \\tag {6}", + "image_path": "72e31af17038b101aac6bf739befb55032ad38a58aac41d757e94119e61e3446.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": "respectively. The message " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": " is projected and aggregated to " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j^S" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": " via an element-wise addition followed by a normalization through LayerNorm [2]. The final linear layer projects the obtained feature to " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^A" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": ", from which " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^A" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": " is obtained to formulate the output " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": " with the known " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^A" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{N}^A" + }, + { + "bbox": [ + 305, + 194, + 545, + 255 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 263, + 528, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 263, + 528, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 263, + 528, + 277 + ], + "type": "text", + "content": "3.2. PPFTrans for Local Geometry Description" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": "Overview. As illustrated in Fig. 2, PPFTrans consumes triplets " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": ". Taking " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = (\\mathbf{P},\\mathbf{N},\\mathbf{X})" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " as an example, it consists of " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{P} \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " the points cloud, " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{N} \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " the normals estimated from " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\vec{\\mathbf{1}} \\in \\mathbb{R}^{n \\times 1}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " the initial point features. The encoder produces the superpoint triplet " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}' = (\\mathbf{P}',\\mathbf{N}',\\mathbf{X}')" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{P}' \\in \\mathbb{R}^{n' \\times 3}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{X}' \\in \\mathbb{R}^{n' \\times c'}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": ". With the consecutive decoder, " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " is decoded to a triplet " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}} = (\\hat{\\mathbf{P}},\\hat{\\mathbf{N}},\\hat{\\mathbf{X}})" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " including " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\hat{n}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " points with features " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{X}} \\in \\mathbb{R}^{\\hat{n} \\times \\hat{c}}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": ". Notably, as we adopt a Farthest Point Sampling (FPS) strategy [26], it always satisfies that " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{P}' \\subseteq \\hat{\\mathbf{P}} \\subseteq \\mathbf{P}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": ". The same goes for a second point cloud " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " with an input triplet " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = (\\mathbf{Q} \\in \\mathbb{R}^{m \\times 3},\\mathbf{M} \\in \\mathbb{R}^{m \\times 3},\\mathbf{Y} = \\vec{\\mathbf{1}} \\in \\mathbb{R}^{m \\times 1})" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " by the shared architecture. In the rest of this paper, we only demonstrate for " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " unless the model processes " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " differently. Encoder. The encoder is constructed by stacking several encoder blocks, each including an Attentional Abstraction Layer (AAL) followed by " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "e \\times" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " PPF Attention Layers (PALs). Each block consumes the output of the previous block as the Support triplet " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S = \\mathcal{P}" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " for the first block). " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " first flows to AAL, where Anchor points " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^A" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " with associated normals " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{N}^A" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " are obtained via FPS [26]. The Anchor triplet " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": " is then generated in AAL via a PAM following Eq. 3. A sequence of PALs is applied for enhancing the Anchor features " + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^A" + }, + { + "bbox": [ + 305, + 283, + 545, + 571 + ], + "type": "text", + "content": ", each updating the features as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 312, + 579, + 545, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 579, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 312, + 579, + 545, + 595 + ], + "type": "interline_equation", + "content": "\\mathcal {P} ^ {A} \\leftarrow \\theta (\\mathcal {P} ^ {A}) = \\operatorname {R e L U} \\left(\\mathbf {X} ^ {A} + \\phi \\left(\\delta \\left(\\mathbf {P} ^ {A}, \\mathbf {N} ^ {A} \\mid \\mathcal {P} ^ {A}\\right)\\right)\\right), \\tag {7}", + "image_path": "203346c0713ff89c946ed56926785c27cbc513f52b5210f502d2f608a3c27ec6.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": " the LayerNorm [2], " + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": " the PAM, and " + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": " the PAL. " + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\leftarrow" + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": " depicts feature updating. The encoder block outputs the updated " + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A" + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": ", and the output of the whole encoder is defined as " + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 305, + 605, + 545, + 652 + ], + "type": "text", + "content": ", which is the output of the final encoder block." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "Decoder. We build the decoder by stacking a series of decoder blocks, each consisting of a Transition Up Layer (TUL) followed by " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "d \\times \\mathrm{PAL}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": ". Each block takes the output of the previous block as the Anchor triplet " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^A = \\mathcal{P}'" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " for the first block), and takes the Support" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5387" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 194, + 190 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 194, + 190 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 194, + 190 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 194, + 190 + ], + "type": "image", + "image_path": "f4b3f87f9e83497fcc7b10f0844a7cef1f6e7b788a4cf5fc18e8d0079f4a86bd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 193, + 171, + 201 + ], + "lines": [ + { + "bbox": [ + 71, + 193, + 171, + 201 + ], + "spans": [ + { + "bbox": [ + 71, + 193, + 171, + 201 + ], + "type": "text", + "content": "(a). Geometry-Aware Self-Attention" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 196, + 72, + 287, + 191 + ], + "blocks": [ + { + "bbox": [ + 196, + 72, + 287, + 191 + ], + "lines": [ + { + "bbox": [ + 196, + 72, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 196, + 72, + 287, + 191 + ], + "type": "image", + "image_path": "d764f44f9d306301505fa374dfc9c5743da0b1b9c69a915b710abec5d66a715b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 193, + 286, + 201 + ], + "lines": [ + { + "bbox": [ + 187, + 193, + 286, + 201 + ], + "spans": [ + { + "bbox": [ + 187, + 193, + 286, + 201 + ], + "type": "text", + "content": "(b). Position-Aware Cross-Attention" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 205, + 287, + 237 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 237 + ], + "type": "text", + "content": "Figure 5. The computation graph of our global transformer consisting of the Geometry-Aware Self-Attention Module (GSM) and Position-Aware Cross-Attention Module (PCM)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "text", + "content": "triplet " + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "text", + "content": " from the encoder via skip connections. The input flows to TUL, where each feature " + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}_j^S\\in \\widetilde{\\mathbf{X}}^S" + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "text", + "content": " assigned to " + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j^S\\in \\mathbf{P}^S" + }, + { + "bbox": [ + 46, + 243, + 287, + 283 + ], + "type": "text", + "content": " is interpolated by:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 285, + 287, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 285, + 287, + 317 + ], + "spans": [ + { + "bbox": [ + 59, + 285, + 287, + 317 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {x}} _ {j} ^ {S} = \\frac {\\sum_ {i \\in \\mathcal {N} (j)} w _ {i} ^ {j} \\mathbf {x} _ {i} ^ {A}}{\\sum_ {i \\in \\mathcal {N} (j)} w _ {i} ^ {j}}, \\text {w i t h} w _ {i} ^ {j} = \\frac {1}{\\left\\| \\mathbf {p} _ {j} ^ {S} - \\mathbf {p} _ {i} ^ {A} \\right\\| _ {2}}, \\tag {8}", + "image_path": "841f3c2935e9de571d0115b70ee8d7e475d9a5796c9978550c1447a9fb6bb937.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(j)" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": " the " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": "-nearest neighbors of " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j^S" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathbf{P}^A" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": ". Features are updated by two linear layers as " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S \\gets \\zeta_1(\\mathbf{X}^S) + \\zeta_2(\\widetilde{\\mathbf{X}}^S)" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": ". A sequence of PALs is adopted after TUL, each enhancing the features as " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S \\gets \\theta(\\mathcal{P}^S)" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": " according to Eq. 7. The decoder block outputs the updated " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{P}^S" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": ", and the output of the whole decoder is denoted as " + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 325, + 287, + 413 + ], + "type": "text", + "content": ", which is the output of the final decoder block." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 420, + 281, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 281, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 281, + 434 + ], + "type": "text", + "content": "3.3. Global Transformer for Context Aggregation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "content": "Overview. Our designed global transformer takes as input a pair of triplets " + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'" + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "content": ", and enhances the features with the global context, yielding " + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{X}}' \\in \\mathbb{R}^{n' \\times c'}" + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Y}}' \\in \\mathbb{R}^{m' \\times c'}" + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "content": ", respectively. We stack " + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "inline_equation", + "content": "g \\times" + }, + { + "bbox": [ + 46, + 437, + 287, + 569 + ], + "type": "text", + "content": " global transformers, with each including a Geometry-Aware Self-Attention Module (GSM) and a Position-Aware Cross-Attention Module (PCM) (See Fig. 2 and Fig. 5). Different from previous works [19, 27, 48-50] that totally neglect the cross-frame spatial relationships, we propose to learn a rotation-invariant position representation for each superpoint to enable the position-aware cross-frame context aggregation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": "Geometry-Aware Self-Attention Module. On the global level, we modify PAM to learn the rotation-invariant position representation and to aggregate the learned context across the whole frame simultaneously. The design of GSM is detailed in Fig. 5 (a). GSM has two branches, where the geometry branch mines the geometric cues from the pairwise rotation-invariant geometry representation proposed in [27], and the context branch aggregates the global context across the frame. We refer the readers to the Appendix for the detailed construction of " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{R}' \\in \\mathbb{R}^{n' \\times n' \\times c'}" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " and the ablation study on it. Similar to Eq. 4, the geometric cues " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{G}'" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " and the positional encoding " + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{E}'" + }, + { + "bbox": [ + 46, + 570, + 287, + 714 + ], + "type": "text", + "content": " are linearly projected from" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{R}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{E}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " is further processed in the geometry branch and finally leveraged as the rotation-invariant position representation. In the context branch, " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{K}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " are obtained by linearly mapping the input features " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^{\\prime}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " similar to Eq. 5. The hybrid score matrix " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times n^{\\prime}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 365, + 140, + 545, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 140, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 365, + 140, + 545, + 168 + ], + "type": "interline_equation", + "content": "\\mathbf {S} ^ {\\prime} (i, j) = \\frac {\\left(\\mathbf {q} _ {i} ^ {\\prime}\\right) \\left(\\mathbf {e} _ {i , j} ^ {\\prime} + \\mathbf {k} _ {j} ^ {\\prime}\\right) ^ {T}}{\\sqrt {c ^ {\\prime}}}, \\tag {9}", + "image_path": "54d757650a352fd3a6e15f971d3d4844eff7ff6d191cc8376840132c73c3026a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_{i,j}^{\\prime} := \\mathbf{E}^{\\prime}(i,j,:)" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i^{\\prime} := \\mathbf{Q}^{\\prime}(i,:)" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_j^{\\prime} := \\mathbf{K}^{\\prime}(j,:)" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": " the " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "c^{\\prime}" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": "-dimension vectors. The hybrid attention " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{\\prime}" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": " is obtained via a Softmax function over each row of " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^{\\prime}" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": ", and the geometric messages " + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_G^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times c^{\\prime}}" + }, + { + "bbox": [ + 304, + 172, + 545, + 221 + ], + "type": "text", + "content": " are computed as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 367, + 230, + 545, + 257 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 230, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 367, + 230, + 545, + 257 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {G} ^ {\\prime} (i,:) = \\sum_ {1 \\leq j \\leq n ^ {\\prime}} a _ {i, j} ^ {\\prime} \\mathbf {g} _ {i, j} ^ {\\prime}, \\tag {10}", + "image_path": "4cf0fee6423e7437b12875a063fe4989fc4b39300795f609d866538f5f2d7390.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "a_{i,j}^{\\prime} \\coloneqq \\mathbf{A}^{\\prime}(i,j)" + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{i,j}^{\\prime} \\coloneqq \\mathbf{G}^{\\prime}(i,j,:)" + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": ". The contextual messages " + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_V^{\\prime} \\in \\mathbb{R}^{n^{\\prime} \\times c^{\\prime}}" + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": " are computed by " + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{\\prime}\\mathbf{V}^{\\prime}" + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": ". After a feed-forward network [43], the position representation " + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_P^{\\prime}" + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": " and globally-enhanced context " + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_P^{\\prime}" + }, + { + "bbox": [ + 304, + 261, + 545, + 312 + ], + "type": "text", + "content": " are generated." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": "Position-Aware Cross-Attention Module. PCM consumes a pair of doublets " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "(\\mathbf{E}_P',\\mathbf{C}_P')" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "(\\mathbf{E}_Q',\\mathbf{C}_Q')" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " that are generated from " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " by a shared GSM, respectively. As the cross-attention is directional, we apply the same PCM twice, with the first aggregation from " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " (See Fig. 5 (b)), and the second reversed. As the first step, the rotation-invariant position representation is incorporated to make the consecutive cross-attention position-aware, yielding position-aware features " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_P' = \\mathbf{E}_P' + \\mathbf{C}_P'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_Q' = \\mathbf{E}_Q' + \\mathbf{C}_Q'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ". Similar to Eq. 5, " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Q}}',\\widetilde{\\mathbf{K}}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{V}}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " are computed as the linear projection of " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_P',\\mathbf{F}_Q'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_Q'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ", respectively. The attention matrix " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{A}}\\in \\mathbb{R}^{n'\\times m'}" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " is computed via a row-wise softmax function applied on " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Q}}'\\widetilde{\\mathbf{K}}'^T" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ". The fused messages are presented as " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{A}}\\widetilde{\\mathbf{V}}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ", which are finally mapped to the output features " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{X}}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " through a feedforward network. As we introduce spatial awareness at the beginning of PCM, both the attention computation and message fusion are aware of the cross-frame positions. After the twice application of PCM, the input features are enhanced as " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{P}'\\gets \\widetilde{\\mathbf{X}}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}'\\gets \\widetilde{\\mathbf{Y}}'" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ", respectively. The global aggregation stage finally generates a pair of triplets " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{P}}':=(\\mathbf{P}',\\mathbf{N}',\\widetilde{\\mathbf{X}}')" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathcal{Q}}':=(\\mathbf{Q}',\\mathbf{M}',\\widetilde{\\mathbf{Y}}')" + }, + { + "bbox": [ + 304, + 312, + 546, + 591 + ], + "type": "text", + "content": ", with the enhanced features from the last global transformer." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 599, + 487, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 487, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 487, + 612 + ], + "type": "text", + "content": "3.4. Point Matching and Loss Function" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Superpoint Matching. As shown in Fig. 2, the point matching stage consumes a pair of superpoint triplets " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}'" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{Q}}'" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " obtained from the global transformer, as well as a pair of point triplets " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{Q}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " produced by the decoder. We adopt the coarse-to-fine matching proposed in [50]. Following [27], we first normalize the superpoint features " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{X}}'" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Y}}'" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " onto a unit hypersphere, and measure the pairwise similarity using a Gaussian correlation matrix " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{S}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{S}}(i,j) =" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5388" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "inline_equation", + "content": "-\\exp \\left(-\\|\\widetilde{\\mathbf{x}}_i'\\widetilde{\\mathbf{y}}_j'\\|_2^2\\right)" + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "text", + "content": ". After a dual-normalization [27,29,37] on " + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{S}}" + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "text", + "content": " for global feature correlation, superpoints associated to the top-" + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "text", + "content": " entries are selected as the coarse correspondence set " + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "inline_equation", + "content": "\\mathcal{C}' = \\{(\\mathbf{p}_i',\\mathbf{q}_i')|\\mathbf{p}_i' \\in \\mathbf{P}',\\mathbf{q}_i' \\in \\mathbf{Q}'\\}" + }, + { + "bbox": [ + 47, + 72, + 286, + 123 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": "Point Matching. For extracting point correspondences, denser points " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{P}}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Q}}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " are first assigned to superpoints. To this end, the point-to-node strategy [50] is leveraged, where each point is assigned to its closest superpoint in 3D space. Given a superpoint " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i' \\in \\mathbf{P}'" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ", the group of points assigned to it is denoted as " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_i^P \\subseteq \\hat{\\mathbf{P}}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ". The group of features associated to " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_i^P" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " is further defined as " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_i^X" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_i^X \\subseteq \\hat{X}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ". For each superpoint correspondence " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_l' = (\\mathbf{p}_i', \\mathbf{q}_j')" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ", the similarity between the corresponding feature groups " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_i^X" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{G}}_j^Y" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " is calculated as " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{S}}_l = \\hat{\\mathbf{G}}_i^X (\\hat{\\mathbf{G}}_j^Y)^T / \\sqrt{\\hat{c}}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{c}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " the feature dimension. We then follow [35] to append a stack row and column to " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{S}}_l" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " filled with a learnable parameter " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ", and iteratively run the Sinkhorn Algorithm [36]. After removing the slack row and column of " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{S}}_l" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ", the mutual top-k entries, i.e., entries with top-" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " confidence on both the row and the column, are selected to formulate a point correspondence set " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}_l" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": ". The final correspondence set " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}}" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": " is collected by " + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{C}} = \\bigcup_{l=1}^{|\\mathcal{C}'|} \\hat{\\mathcal{C}}_l" + }, + { + "bbox": [ + 46, + 124, + 286, + 337 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "content": "Loss Function. Our loss function reads as " + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\mathcal{L}_s + \\lambda \\mathcal{L}_p" + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "content": ", with a superpoint matching loss " + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "content": " and a point matching loss " + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "content": " balanced by a hyper-parameter " + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 47, + 337, + 286, + 385 + ], + "type": "text", + "content": " by default). The detailed definition is introduced in the Appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 399, + 123, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 123, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 123, + 411 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 419, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 286, + 491 + ], + "type": "text", + "content": "We evaluate RoITr on both rigid (3DMatch [51] & 3DLoMatch [19]) and non-rigid (4DMatch [20] & 4DLoMatch [20]) benchmarks. For the rigid matching, we further evaluate our correspondences on the registration task, where RANSAC [12] is used. Details of implementation, metrics, and runtime analysis are introduced in the Appendix." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 502, + 286, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 286, + 514 + ], + "type": "text", + "content": "4.1. Rigid Indoor Scenes: 3DMatch & 3DLoMatch" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "type": "text", + "content": "Dataset. 3DMatch [51] collects 62 indoor scenes, among which 46 are used for training, 8 for validation, and 8 for testing. We use the data processed by [19] where the 3DMatch data is spilt as 3DMatch (" + }, + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "type": "inline_equation", + "content": ">30\\%" + }, + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "type": "text", + "content": " overlap) and 3DLoMatch (" + }, + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "type": "inline_equation", + "content": "10\\% \\sim 30\\%" + }, + { + "bbox": [ + 46, + 521, + 286, + 616 + ], + "type": "text", + "content": " overlap). To evaluate robustness to arbitrary rotations, we follow [49] for creating the rotated benchmarks, where full-range rotations are individually added to the two frames of each point cloud pair." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "Metrics. We follow [19] to use three metrics for evaluation: (1). Inlier Ratio (IR) that computes the ratio of putative correspondences whose residual distance is smaller than a threshold (i.e., " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{m}" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": ") under the ground-truth transformation; (2). Feature Matching Recall (FMR) that calculates the fraction of point cloud pairs whose IR is larger than a threshold (i.e., " + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "); (3). Registration Recall (RR) that counts the fraction of point cloud pairs that are cor" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 309, + 71, + 547, + 373 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 547, + 373 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 547, + 373 + ], + "type": "table", + "html": "
# Samples=5,0003DMatch3DLoMatch
OriginRotatedOriginRotated
Feature Matching Recall (%) ↑
SpinNet [1]97.497.475.575.2
Predator [19]96.696.278.673.7
CoFiNet [50]98.197.483.178.6
YOHO [44]98.297.879.477.8
RIGA [49]97.998.285.184.5
Lepard [20]98.097.483.179.5
GeoTrans [27]97.997.888.385.8
RoITr (Ours)98.098.289.689.4
Inlier Ratio (%) ↑
SpinNet [1]48.548.725.725.7
Predator [19]58.052.826.722.4
CoFiNet [50]49.846.824.421.5
YOHO [44]64.464.125.923.2
RIGA [49]68.468.532.132.1
Lepard [20]58.653.728.424.4
GeoTrans [27]71.968.243.540.0
RoITr (Ours)82.682.354.353.2
Registration Recall (%) ↑
SpinNet [1]88.893.258.261.8
Predator [19]89.092.059.858.6
CoFiNet [50]89.392.067.562.5
YOHO [44]90.892.565.266.8
RIGA [49]89.393.065.166.9
Lepard [20]92.784.965.449.0
GeoTrans [27]92.092.075.071.8
RoITr (Ours)91.994.774.877.2
", + "image_path": "0cb444ff44e69bfba329c78511ad9a59e2054d53c905eacf0c3487fa87501608.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 376, + 545, + 398 + ], + "lines": [ + { + "bbox": [ + 306, + 376, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 545, + 398 + ], + "type": "text", + "content": "Table 1. Quantitative results on (Rotated) 3DMatch & 3DLoMatch. 5,000 points/correspondences are used for the evaluation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 403, + 489, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 489, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 489, + 415 + ], + "type": "text", + "content": "rectly registered (i.e., with " + }, + { + "bbox": [ + 306, + 403, + 489, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{RMSE} < 0.2\\mathrm{m}" + }, + { + "bbox": [ + 306, + 403, + 489, + 415 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 417, + 545, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 545, + 681 + ], + "type": "text", + "content": "Comparison with the State-of-the-Art. We compare RoITr with 7 state-of-the-art methods, among which Predator [19], CoFiNet [50], Lepard [20], and GeoTrans [27] are rotation-sensitive models, while SpinNet [1], YOHO [44], and RIGA [49] guarantee the rotation invariance by design. In Tab. 1 we demonstrate the matching and registration results on 3DMatch and 3DLoMatch, as well as on their rotated versions, with 5,000 sampled points/correspondences. Regarding IR, RoITr outperforms all the others by a large margin on both datasets, which indicates our method matches points more correctly. For FMR, we significantly surpass all the others on 3DLoMatch, while staying on par with CoFiNet and YOHO on 3DMatch, which indicates that our model is good at coping with hard cases, i.e., we find at least " + }, + { + "bbox": [ + 304, + 417, + 545, + 681 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 417, + 545, + 681 + ], + "type": "text", + "content": " inliers on more test data. For the registration evaluation in terms of RR, RoITr achieves comparable performance with GeoTrans and Lepard on 3DMatch, but leads the board together with GeoTrans on 3DLoMatch with an overwhelming advantage over the others. Our stability against additional rotations is further demonstrated on the rotated data, where we outperform all the others with a substantial margin. Qualitative results can be found in Fig. 6." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "2We follow [49] to calculate the RR strictly with RMSE " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "< 0.2\\mathrm{m}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " on the rotated data, which is slightly different from the RR on the original data." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5389" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 537, + 235 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 537, + 235 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 537, + 235 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 537, + 235 + ], + "type": "image", + "image_path": "ac23312a02beb4a475dda47e424d95133ebb2541ce2ad59f1a91cd2ede8584a7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 546, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 546, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 546, + 262 + ], + "type": "text", + "content": "Figure 6. Qualitative results on 3DLoMatch. GeoTrans [27] is used as the baseline. Columns (b) and (c) show the correspondences, while columns (d) and (e) demonstrate the registration results. Green/red lines indicate inliers/outliers. More cases are shown in the Appendix." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 264, + 289, + 475 + ], + "blocks": [ + { + "bbox": [ + 50, + 264, + 289, + 475 + ], + "lines": [ + { + "bbox": [ + 50, + 264, + 289, + 475 + ], + "spans": [ + { + "bbox": [ + 50, + 264, + 289, + 475 + ], + "type": "table", + "html": "
# Samples3DMatch3DLoMatch
500025001000500250500025001000500250
Feature Matching Recall (%)↑
SpinNet [1]97.497.096.496.794.875.575.174.269.062.7
Predator [19]96.696.696.596.396.578.677.476.375.775.3
CoFiNet [50]98.198.398.198.298.383.183.583.383.182.6
YOHO [44]98.297.697.597.796.079.478.176.373.869.1
RIGA [49]97.997.897.797.797.685.185.085.184.385.1
GeoTrans [27]97.997.997.997.997.688.388.688.888.688.3
RoITr (Ours)98.098.097.998.097.989.689.689.589.489.3
Inlier Ratio (%)↑
SpinNet [1]48.546.240.835.129.025.723.720.618.213.1
Predator [19]58.058.457.154.149.326.728.128.327.525.8
CoFiNet [50]49.851.251.952.252.224.425.926.726.826.9
YOHO [44]64.460.755.746.441.225.923.322.618.215.0
RIGA [49]68.469.770.670.971.032.133.434.334.534.6
GeoTrans [27]71.975.276.082.285.143.545.346.252.957.7
RoITr (Ours)82.682.883.083.083.054.354.655.155.255.3
Registration Recall (%)↑
SpinNet [1]88.888.084.579.069.258.256.749.841.026.7
Predator [19]89.089.990.688.586.659.861.262.460.858.1
CoFiNet [50]89.388.988.487.487.067.566.264.263.161.0
YOHO [44]90.890.389.188.684.565.265.563.256.548.0
RIGA [49]89.388.489.189.087.765.164.764.564.161.8
GeoTrans [27]92.091.891.891.491.275.074.874.274.173.5
RoITr (Ours)91.991.791.891.491.074.774.874.874.273.6
", + "image_path": "1e8eb32eb063570480f6d3285b0a77b8f012cf5924f07754a7dfde9c894e5a77.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 602 + ], + "type": "text", + "content": "Analysis on the Number of Correspondences. We further analyze the influence of a varying number of correspondences. As illustrated in Tab. 2, RoITr shows outstanding performance on both datasets with various correspondences, proving its stability when only a few correspondences are accessible. The same test on the rotated benchmarks is given in the Appendix." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 610, + 286, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 286, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 286, + 624 + ], + "type": "text", + "content": "4.2. Deformable Objects: 4DMatch & 4DLoMatch" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "Dataset. 4DMatch [20] contains 1,761 animations randomly selected from DeformingThings4D [21]. The 1,761 sequences are divided into 1,232/176/353 as train/val/test, where the test set is further split into 4DMatch and 4DLoMatch based on an overlap ratio threshold of " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "45\\%" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": ". Metrics. We follow [20] to use two different metrics: (1). Inlier Ratio (IR) which is defined as same as the IR on 3DMatch," + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 308, + 264, + 547, + 334 + ], + "blocks": [ + { + "bbox": [ + 46, + 478, + 287, + 513 + ], + "lines": [ + { + "bbox": [ + 46, + 478, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 287, + 513 + ], + "type": "text", + "content": "Table 2. Quantitative results on 3DMatch & 3DLoMatch with a varying number of points/correspondences. See the results on rotated data in the Appendix." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 264, + 547, + 334 + ], + "lines": [ + { + "bbox": [ + 308, + 264, + 547, + 334 + ], + "spans": [ + { + "bbox": [ + 308, + 264, + 547, + 334 + ], + "type": "table", + "html": "
CategoryMethod4DMatch4DLoMatch
NFMR(%)↑IR(%)↑NFMR(%)↑IR(%)↑
Scene FlowPWC [45]21.620.010.07.2
FLOT [24]27.124.915.210.7
Feature MatchingPredator [19]56.460.432.127.5
GeoTrans [27]83.282.265.463.6
Lepard [20]83.782.766.955.7
RoITr (Ours)83.084.469.467.6
", + "image_path": "9236b432a4eb3b18d0f396703602995a38897a205f43521d78cd042deb473363.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 321, + 338, + 529, + 348 + ], + "lines": [ + { + "bbox": [ + 321, + 338, + 529, + 348 + ], + "spans": [ + { + "bbox": [ + 321, + 338, + 529, + 348 + ], + "type": "text", + "content": "Table 3. Quantitative results on 4DMatch & 4DLoMatch." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 365, + 546, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 412 + ], + "type": "text", + "content": "but with a different threshold (i.e., " + }, + { + "bbox": [ + 304, + 365, + 546, + 412 + ], + "type": "inline_equation", + "content": "0.04\\mathrm{m}" + }, + { + "bbox": [ + 304, + 365, + 546, + 412 + ], + "type": "text", + "content": "); (2). Non-rigid Feature Matching Recall (NFRM) that measures the fraction of ground-truth matches that can be successfully recovered by the putative correspondences." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 413, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 533 + ], + "type": "text", + "content": "Comparison with the State-of-the-Art. We compare RoITr with 5 baselines, among which PwC [45] and FLOT [24] are scene flow-based methods, while Predator [19], Lepard [20], GeoTrans [27] are based on feature matching. The results shown in Tab. 3 indicate that although our rotation-invariance is mainly designed for rigid scenarios, RoITr could also achieve outstanding performance in the non-rigid matching task, which further confirms the superiority of our model design. Qualitative results are demonstrated in Fig. 7." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 540, + 400, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 400, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 400, + 552 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "content": "Local Attention. We first replace our PPFTrans with PointTransformer (PT) [53] in Tab. 4 (a.1), which leads to a sharp performance drop. We then ablate by embedding our PPF-based local coordinates into PT (Tab. 4 (a.2)) and by adopting the relative coordinates, i.e., " + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_j - \\mathbf{p}_j" + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "content": ", used by PT in our PAM (Tab. 4 (a.3)). Our local coordinate representation significantly boosts the performance of PT in the task of point cloud matching and meanwhile makes it rotation-invariant, although its performance is still far behind ours. However, the relative coordinates fail to work in our PAM, as we adopt a more efficient attention mechanism [43] that learns a scalar attention value for each feature " + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 304, + 557, + 546, + 713 + ], + "type": "text", + "content": " and is consequently hard to work under varying poses with a" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5390" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 287, + 223 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 287, + 223 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 287, + 223 + ], + "type": "image", + "image_path": "05f21fec257031ee45502721928229e415a594471edac0c8ac5a61e3a223fa87.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 288, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 288, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 288, + 262 + ], + "type": "text", + "content": "Figure 7. Qualitative results of non-rigid matching on 4DLoMatch with Lepard [20] as the baseline. Green/red lines indicate inliers/outliers. See the Appendix for more examples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "type": "text", + "content": "rotation-sensitive design. As a comparison, PT learns a per-channel vector attention " + }, + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{a} \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "type": "text", + "content": " for the same feature " + }, + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 266, + 287, + 396 + ], + "type": "text", + "content": " and could deal with the pose variations, but at the cost of the efficiency as shown in Fig. 8. When the number of channels is increased, our advantage in terms of efficiency is enlarged. As we achieve that with more parameters, the gap becomes more significant when runtime is normalized with the number of parameters in the right figure. With our PPF-based local coordinate, the scalar attention could focus on the pose-agnostic pure geometry and therefore achieves the best performance shown in Tab. 4 (a.4)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 399, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 471 + ], + "type": "text", + "content": "Abstraction Layer. We ablate our Attentional Abstraction Layer (AAL) by replacing it with the pooling-based abstraction design used in [25, 26, 53]. We test the max pooling in Tab. 4 (b.1) and the average pooling in Tab. 4 (b.2), both showing a degrading performance compared with our AAL, which demonstrates our superiority." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": "Backbone. In Tab. 4 (a.1) we have shown our superiority compared with PT [53]. We further replace our PPFTrans with the KPCnv-based backbone network which is widely used in previous deep matchers [19, 27, 50]. The fact that KPCnv falls behind our design demonstrates the advantage of PPFTrans in geometry encoding." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 604 + ], + "type": "text", + "content": "Global Transformer. We replace our design with the global transformer of GeoTrans [27] which performs state-of-the-art but without the cross-frame spatial awareness. The dropping results in Tab. 4 (d.1) proves the excellence of our design with the cross-frame position awareness." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "The Number of Global Transformers. To demonstrate the importance of being globally aware, we first remove the global transformer. The substantial performance drop confirms the significance of global awareness. Then we add one global transformer and observe an increased performance. In our default setting with 3 global transformers, the model performs the best. However, when the number is increased to 5, the model shows a slight performance drop, which we owe to overfitting. As the data augmentation of rotations" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 537, + 196 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 537, + 196 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 537, + 196 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 537, + 196 + ], + "type": "image", + "image_path": "c79f5972814873dd0680a193dcb9720a19fc8606439b7e3d540e215126e359a0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 198, + 547, + 242 + ], + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 242 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 242 + ], + "type": "text", + "content": "Figure 8. Left: Runtime comparison between our PPF attention Mechanism (PAM) and the local attention in PointTransformer [53]. Right: Runtime normalized by aligning the number of parameters." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 245, + 547, + 384 + ], + "blocks": [ + { + "bbox": [ + 308, + 245, + 547, + 384 + ], + "lines": [ + { + "bbox": [ + 308, + 245, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 308, + 245, + 547, + 384 + ], + "type": "table", + "html": "
CategoryModelOriginRotated
FMRIRRRFMRIRRR
a. Local1. PT [53]79.036.561.676.534.760.0
*2. PPF+PT [53]87.049.969.986.849.471.2
3. Δxyz+Ours------
*4. Ours89.654.374.789.453.277.2
b. Aggregation*1. max pooling85.250.170.585.450.271.9
*2. avg pooling87.852.673.887.252.574.7
*3. Ours89.654.374.789.453.277.2
c. Backbone1. KPCov [40]85.244.470.683.042.371.5
*2. Ours89.654.374.789.453.277.2
d. Global*1. GeoTrans [27]87.753.673.087.553.275.1
*2. Ours89.654.374.789.453.277.2
e. #Global*1. g = 087.237.670.787.537.672.7
*2. g = 187.142.170.886.842.173.0
*3. g = 3 (Ours)89.654.374.789.453.277.2
*4. g = 587.152.572.187.052.473.3
", + "image_path": "24fe69e841b131b2c4d375ae270ff0ab9af5012c9189f0f4fcbbbc40a0140dca.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 388, + 547, + 433 + ], + "lines": [ + { + "bbox": [ + 304, + 388, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 547, + 433 + ], + "type": "text", + "content": "Table 4. Ablation study on (rotated) 3DLoMatch. 5,000 points/correspondences are leveraged. * indicates the methods with intrinsic rotation invariance. See the Appendix for the results on (rotated) 3DMatch." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 437, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 462 + ], + "type": "text", + "content": "has less effect on an intrinsically rotation-invariant method, more data is required for training a larger model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 466, + 379, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 379, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 379, + 479 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 486, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 665 + ], + "type": "text", + "content": "We introduced RoITr - an intrinsically rotation-invariant model for point cloud matching. We proposed PAM (PPF Attention Mechanism) that embeds PPF-based local coordinates to encode rotation-invariant geometry. This design lies at the core of AAL (Attention Abstraction Layer), PAL (PPF Attention Layer), and TUL (Transition Up Layer) which are consecutively stacked to compose PPFTrans (PPF Transformer) for representative and pose-agnostic geometry description. We further enhanced features by introducing a novel global transformer architecture, which ensures the rotation-invariant cross-frame spatial awareness. Extensive experiments are conducted on both rigid and non-rigid benchmarks to demonstrate the superiority of our approach, especially the remarkable robustness against arbitrary rotations. Limitations are discussed in the Appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 714 + ], + "type": "text", + "content": "Acknowledgment. This paper is supported by the National Natural Science Foundation of China under Grant No. 62025208. We appreciate the help from Lennart Bastian, Mert Karaoglu, Ning Liu, and Zhiying Leng." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 758 + ], + "type": "text", + "content": "5391" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Sheng Ao, Qingyong Hu, Bo Yang, Andrew Markham, and Yulan Guo. 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Gary Chan $^{1}$ $^{1}$ HKUST, $^{2}$ Rutgers University, $^{3}$ Texas State University", + "bbox": [ + 236, + 179, + 728, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To design fast neural networks, many works have been focusing on reducing the number of floating-point operations (FLOPs). We observe that such reduction in FLOPs, however, does not necessarily lead to a similar level of reduction in latency. This mainly stems from inefficiently low floating-point operations per second (FLOPS). To achieve faster networks, we revisit popular operators and demonstrate that such low FLOPS is mainly due to frequent memory access of the operators, especially the depthwise convolution. We hence propose a novel partial convolution (PCnv) that extracts spatial features more efficiently, by cutting down redundant computation and memory access simultaneously. Building upon our PCnv, we further propose FasterNet, a new family of neural networks, which attains substantially higher running speed than others on a wide range of devices, without compromising on accuracy for various vision tasks. For example, on ImageNet-1k, our tiny FasterNet-T0 is $2.8 \\times 3.3 \\times$ and $2.4 \\times$ faster than MobileViT-XXS on GPU, CPU, and ARM processors, respectively, while being $2.9\\%$ more accurate. Our large FasterNet-L achieves impressive $83.5\\%$ top-1 accuracy, on par with the emerging Swin-B, while having $36\\%$ higher inference throughput on GPU, as well as saving $37\\%$ compute time on CPU. Code is available at https://github.com/JierunChen/FasterNet.", + "bbox": [ + 75, + 300, + 473, + 679 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 708, + 209, + 723 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural networks have undergone rapid development in various computer vision tasks such as image classification, detection and segmentation. While their impressive performance has powered many applications, a roaring trend is to pursue fast neural networks with low latency and high throughput for great user experiences, instant responses, safety reasons, etc.", + "bbox": [ + 75, + 733, + 468, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "How to be fast? Instead of asking for more costly computing devices, researchers and practitioners prefer to design cost-effective fast neural networks with reduced computational complexity, mainly measured in the number of", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8cfeebc3fde8d06bfd86b330dae02078ebc45c79a1a14f32c35eaaaa1393820.jpg", + "image_caption": [ + "(a) Convolution" + ], + "image_footnote": [], + "bbox": [ + 501, + 267, + 692, + 321 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1d015ffc47d7943c325b92090435436c20108bf9c1713ea630e73d7b6ad1b0b6.jpg", + "image_caption": [ + "(b) Depthwise/Group Convolution" + ], + "image_footnote": [], + "bbox": [ + 700, + 267, + 890, + 321 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef34393040525a2e7dacb9ed8654cc27ceb71d56a7f92940dd88d05170faf8d2.jpg", + "image_caption": [ + "(c) Partial Convolution (ours)", + "Figure 1. Our partial convolution (PConv) is fast and efficient by applying filters on only a few input channels while leaving the remaining ones untouched. PConv obtains lower FLOPs than the regular convolution and higher FLOPS than the depthwise/group convolution." + ], + "image_footnote": [], + "bbox": [ + 547, + 344, + 736, + 392 + ], + "page_idx": 0 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Input/output", + "Filter", + "\\*Convolution", + "$\\rightarrow$ Identity" + ], + "bbox": [ + 769, + 359, + 852, + 402 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "floating-point operations (FLOPs) $^1$ . MobileNets [20, 21, 47], ShuffleNets [40, 76] and GhostNet [13], among others, leverage the depthwise convolution (DWConv) [48] and/or group convolution (GConv) [27] to extract spatial features. However, in the effort to reduce FLOPs, the operators often suffer from the side effect of increased memory access. MicroNet [29] further decomposes and sparsifies the network to push its FLOPs to an extremely low level. Despite its improvement in FLOPs, this approach experiences inefficient fragmented computation. Besides, the above networks are often accompanied by additional data manipulations, such as concatenation, shuffling, and pooling, whose running time tends to be significant for tiny models.", + "bbox": [ + 496, + 508, + 890, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Apart from the above pure convolutional neural networks (CNNs), there is an emerging interest in making vision transformers (ViTs) [11] and multilayer perceptrons (MLPs) architectures [57] smaller and faster. For example, MobileViTs [42, 43, 63] and MobileFormer [6] reduce the computational complexity by combining DWConv with a modified attention mechanism. However, they still suffer from the aforementioned issue with DWConv and also need dedicated hardware support for the modified attention mechanism. The use of advanced yet time-consuming nor", + "bbox": [ + 496, + 707, + 890, + 859 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1We follow a widely adopted definition of FLOPs, as the number of multiply-adds [36, 76].", + "bbox": [ + 500, + 875, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12021", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bc689bdb3a1a6f8205702f0379a1f5c1f8be0e664dd4c0e302b8927ca1ec1b3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 202, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bcfdc95e5623ea475b3f4225deff2acec6dc75fdab39cada93fdc6eb8e26e653.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 205, + 88, + 436, + 260 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/52013b4b7475c1d42f589de8b8dc903a733f7e78b03a0098e6384b5eb0496566.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 446, + 90, + 648, + 241 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/173d56cec53757d48dc7e1af33b12d573a1492f15e75fd81fcccb8649b4d37eb.jpg", + "image_caption": [ + "(b)", + "Figure 2. (a) FLOPS under varied FLOPs on CPU. Many existing neural networks suffer from low computational speed issues. Their effective FLOPS are lower than the popular ResNet50. By contrast, our FasterNet attains higher FLOPS. (b) Latency under varied FLOPs on CPU. Our FasterNet obtains lower latency than others with the same amount of FLOPs." + ], + "image_footnote": [], + "bbox": [ + 648, + 90, + 890, + 262 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "malization and activation layers may also limit their speed on devices.", + "bbox": [ + 75, + 337, + 468, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "All these issues together lead to the following question: Are these \"fast\" neural networks really fast? To answer this, we examine the relationship between latency and FLOPs, which is captured by", + "bbox": [ + 75, + 367, + 468, + 428 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nL a t e n c y = \\frac {F L O P s}{F L O P S}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 438, + 468, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where FLOPS is short for floating-point operations per second, as a measure of the effective computational speed. While there are many attempts to reduce FLOPs, they seldom consider optimizing FLOPS at the same time to achieve truly low latency. To better understand the situation, we compare the FLOPS of typical neural networks on an Intel CPU. The results in Fig. 2 show that many existing neural networks suffer from low FLOPS, and their FLOPS is generally lower than the popular ResNet50. With such low FLOPS, these \"fast\" neural networks are actually not fast enough. Their reduction in FLOPs cannot be translated into the exact amount of reduction in latency. In some cases, there is no improvement, and it even leads to worse latency. For example, CycleMLP-B1 [5] has half of FLOPs of ResNet50 [16] but runs more slowly (i.e., CycleMLP-B1 vs. ResNet50: 116.1ms vs. 73.0ms). Note that this discrepancy between FLOPs and latency has also been noticed in previous works [40, 42] but remains unresolved partially because they employ the DWConv/GConv and various data manipulations with low FLOPS. It is deemed there are no better alternatives available.", + "bbox": [ + 75, + 477, + 468, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper aims to eliminate the discrepancy by developing a simple yet fast and effective operator that maintains high FLOPS with reduced FLOPs. Specifically, we reexamine existing operators, particularly DWConv, in terms of the computational speed - FLOPS. We uncover that the main reason causing the low FLOPS issue is frequent memory access. We then propose a novel partial convolution (PCov)", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "as a competitive alternative that reduces the computational redundancy as well as the number of memory access. Fig. 1 illustrates the design of our PConv. It takes advantage of redundancy within the feature maps and systematically applies a regular convolution (Conv) on only a part of the input channels while leaving the remaining ones untouched. By nature, PConv has lower FLOPs than the regular Conv while having higher FLOPS than the DWConv/GConv. In other words, PConv better exploits the on-device computational capacity. PConv is also effective in extracting spatial features as empirically validated later in the paper.", + "bbox": [ + 496, + 337, + 890, + 502 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We further introduce FasterNet, which is primarily built upon our PConv, as a new family of networks that run highly fast on various devices. In particular, our FasterNet achieves state-of-the-art performance for classification, detection, and segmentation tasks while having much lower latency and higher throughput. For example, our tiny FasterNet-T0 is $2.8 \\times 3.3 \\times$ and $2.4 \\times$ faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being $2.9\\%$ more accurate on ImageNet-1k. Our large FasterNet-L achieves $83.5\\%$ top-1 accuracy, on par with the emerging Swin-B [35], while offering $36\\%$ higher throughput on GPU and saving $37\\%$ compute time on CPU. To summarize, our contributions are as follows:", + "bbox": [ + 496, + 503, + 892, + 699 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We point out the importance of achieving higher FLOPS beyond simply reducing FLOPs for faster neural networks.", + "- We introduce a simple yet fast and effective operator called PConv, which has a high potential to replace the existing go-to choice, DWConv.", + "- We introduce FasterNet which runs favorably and universally fast on a variety of devices such as GPU, CPU, and ARM processors.", + "- We conduct extensive experiments on various tasks and validate the high speed and effectiveness of our PConv and FasterNet." + ], + "bbox": [ + 517, + 705, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12022", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We briefly review prior works on fast and efficient neural networks and differentiate this work from them.", + "bbox": [ + 76, + 114, + 468, + 145 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CNN. CNNs are the mainstream architecture in the computer vision field, especially when it comes to deployment in practice, where being fast is as important as being accurate. Though there have been numerous studies [7, 8, 17, 29, 48, 49, 75, 78] to achieve higher efficiency, the rationale behind them is more or less to perform a low-rank approximation. Specifically, the group convolution [27] and the depthwise separable convolution [48] (consisting of depthwise and pointwise convolutions) are probably the most popular ones. They have been widely adopted in mobile/edge-oriented networks, such as MobileNets [20, 21, 47], ShuffleNets [40, 76], GhostNet [13], EfficientNets [54, 55], TinyNet [14], Xception [8], CondenseNet [23, 70], TVConv [4], MnasNet [53], and FBNet [67]. While they exploit the redundancy in filters to reduce the number of parameters and FLOPs, they suffer from increased memory access when increasing the network width to compensate for the accuracy drop. By contrast, we consider the redundancy in feature maps and propose a partial convolution to reduce FLOPs and memory access simultaneously.", + "bbox": [ + 76, + 155, + 472, + 473 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ViT, MLP, and variants. There is a growing interest in studying ViT ever since Dosovitskiy et al. [11] expanded the application scope of transformers [62] from machine translation [62] or forecasting [66] to the computer vision field. Many follow-up works have attempted to improve ViT in terms of training setting [51, 58, 59] and model design [12, 34, 35, 65, 77]. One notable trend is to pursue a better accuracy-latency trade-off by reducing the complexity of the attention operator [1, 25, 39, 56, 61], incorporating convolution into ViTs [6, 10, 50], or doing both [3, 30, 43, 45]. Besides, other studies [5, 31, 57] propose to replace the attention with simple MLP-based operators. However, they often evolve to be CNN-like [33]. In this paper, we focus on analyzing the convolution operations, particularly DWConv, due to the following reasons: First, the advantage of attention over convolution is unclear or debatable [36, 64]. Second, the attention-based mechanism generally runs slower than its convolutional counterparts and thus becomes less favorable for the current industry [22, 42]. Finally, DW-Conv is still a popular choice in many hybrid models, so it is worth a careful examination.", + "bbox": [ + 76, + 481, + 472, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Design of PConv and FasterNet", + "text_level": 1, + "bbox": [ + 76, + 814, + 364, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first revisit DWConv and analyze the issue with its frequent memory access. We then introduce PConv as a competitive alternative operator to resolve the issue. After that, we introduce FasterNet and explain its", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/43b8b037deb68c10cea574d7d56f635729de216ab6d0f26d1b74b15ba6828430.jpg", + "image_caption": [ + "Figure 3. Visualization of feature maps in an intermediate layer of a pre-trained ResNet50, with the top-left image as the input. Qualitatively, we can see the high redundancies across different channels." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 887, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "details, including design considerations.", + "bbox": [ + 500, + 320, + 764, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 344, + 629, + 361 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DWConv is a popular variant of Conv and has been widely adopted as a key building block for many neural networks. For an input $\\mathbf{I} \\in \\mathbb{R}^{c \\times h \\times w}$ , DWConv applies $c$ filters $\\mathbf{W} \\in \\mathbb{R}^{k \\times k}$ to compute the output $\\mathbf{O} \\in \\mathbb{R}^{c \\times h \\times w}$ . As shown in Fig. 1(b), each filter slides spatially on one input channel and contributes to one output channel. This depthwise computation makes DWConv have as low FLOPs as $h \\times w \\times k^2 \\times c$ compared to a regular Conv with $h \\times w \\times k^2 \\times c^2$ . While effective in reducing FLOPs, a DWConv, which is typically followed by a pointwise convolution, or PWConv, cannot be simply used to replace a regular Conv as it would incur a severe accuracy drop. Thus, in practice the channel number $c$ (or the network width) of DWConv is increased to $c'(c' > c)$ to compensate the accuracy drop, e.g., the width is expanded by six times for the DWConv in the inverted residual blocks [47]. This, however, results in much higher memory access that can cause non-negligible delay and slow down the overall computation, especially for I/O-bound devices. In particular, the number of memory access now escalates to", + "bbox": [ + 496, + 367, + 893, + 671 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh \\times w \\times 2 c ^ {\\prime} + k ^ {2} \\times c ^ {\\prime} \\approx h \\times w \\times 2 c ^ {\\prime}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 680, + 890, + 698 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which is higher than that of a regular Conv, i.e.,", + "bbox": [ + 500, + 708, + 815, + 723 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh \\times w \\times 2 c + k ^ {2} \\times c ^ {2} \\approx h \\times w \\times 2 c. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 734, + 890, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that the $h \\times w \\times 2c'$ memory access is spent on the I/O operation, which is deemed to be already the minimum cost and hard to optimize further.", + "bbox": [ + 498, + 762, + 893, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Partial convolution as a basic operator", + "text_level": 1, + "bbox": [ + 500, + 816, + 831, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We below demonstrate that the cost can be further optimized by leveraging the feature maps' redundancy. As visualized in Fig. 3, the feature maps share high similarities among different channels. This redundancy has also", + "bbox": [ + 498, + 840, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12023", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "been covered in many other works [13, 74], but few of them make full use of it in a simple yet effective way.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we propose a simple PConv to reduce computational redundancy and memory access simultaneously. The bottom-left corner in Fig. 4 illustrates how our PConv works. It simply applies a regular Conv on only a part of the input channels for spatial feature extraction and leaves the remaining channels untouched. For contiguous or regular memory access, we consider the first or last consecutive $c_p$ channels as the representatives of the whole feature maps for computation. Without loss of generality, we consider the input and output feature maps to have the same number of channels. Therefore, the FLOPs of a PConv are only", + "bbox": [ + 75, + 121, + 470, + 287 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh \\times w \\times k ^ {2} \\times c _ {p} ^ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 297, + 468, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With a typical partial ratio $r = \\frac{c_p}{c} = \\frac{1}{4}$ , the FLOPs of a PConv is only $\\frac{1}{16}$ of a regular Conv. Besides, PConv has a smaller amount of memory access, i.e.,", + "bbox": [ + 76, + 330, + 468, + 377 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh \\times w \\times 2 c _ {p} + k ^ {2} \\times c _ {p} ^ {2} \\approx h \\times w \\times 2 c _ {p}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 387, + 468, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which is only $\\frac{1}{4}$ of a regular Conv for $r = \\frac{1}{4}$ .", + "bbox": [ + 76, + 417, + 372, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since there are only $c_p$ channels utilized for spatial feature extraction, one may ask if we can simply remove the remaining $(c - c_p)$ channels? If so, PConv would degrade to a regular Conv with fewer channels, which deviates from our objective to reduce redundancy. Note that we keep the remaining channels untouched instead of removing them from the feature maps. It is because they are useful for a subsequent PWConv layer, which allows the feature information to flow through all channels.", + "bbox": [ + 75, + 435, + 468, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. PConv followed by PWConv", + "text_level": 1, + "bbox": [ + 76, + 580, + 331, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To fully and efficiently leverage the information from all channels, we further append a pointwise convolution (PW-Conv) to our PConv. Their effective receptive field together on the input feature maps looks like a T-shaped Conv, which focuses more on the center position compared to a regular Conv uniformly processing a patch, as shown in Fig. 5. To justify this T-shaped receptive field, we first evaluate the importance of each position by calculating the position-wise Frobenius norm. We assume that a position tends to be more important if it has a larger Frobenius norm than other positions. For a regular Conv filter $\\mathbf{F} \\in \\mathbb{R}^{k^2 \\times c}$ , the Frobenius norm at position $i$ is calculated by $\\| \\mathbf{F}_i \\| = \\sqrt{\\sum_{j=1}^{c} |f_{ij}|^2}$ , for $i = 1, 2, 3\\ldots, k^2$ . We consider a salient position to be the one with the maximum Frobenius norm. We then collectively examine each filter in a pre-trained ResNet18, find out their salient positions, and plot a histogram of the salient positions. Results in Fig. 6 show that the center position turns out to be the salient position most frequently among the filters. In other words, the center position weighs more", + "bbox": [ + 75, + 603, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "than its surrounding neighbors. This is consistent with the T-shaped computation which concentrates on the center position.", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the T-shaped Conv can be directly used for efficient computation, we show that it is better to decompose the T-shaped Conv into a PConv and a PWConv because the decomposition exploits the inter-filter redundancy and further saves FLOPs. For the same input $\\mathbf{I} \\in \\mathbb{R}^{c \\times h \\times w}$ and output $\\mathbf{O} \\in \\mathbb{R}^{c \\times h \\times w}$ , a T-shaped Conv's FLOPs can be calculated as", + "bbox": [ + 496, + 136, + 890, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh \\times w \\times \\left(k ^ {2} \\times c _ {p} \\times c + c \\times \\left(c - c _ {p}\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 253, + 890, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which is higher than the FLOPs of a PConv and a PWConv, i.e.,", + "bbox": [ + 496, + 282, + 890, + 311 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nh \\times w \\times \\left(k ^ {2} \\times c _ {p} ^ {2} + c \\times c _ {p}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 313, + 890, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c > c_p$ and $c - c_p > c_p$ (e.g. when $c_p = \\frac{c}{4}$ ). Besides, we can readily leverage the regular Conv for the two-step implementation.", + "bbox": [ + 496, + 338, + 890, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. FasterNet as a general backbone", + "text_level": 1, + "bbox": [ + 498, + 393, + 785, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given our novel PConv and off-the-shelf PWConv as the primary building operators, we further propose FasterNet, a new family of neural networks that runs favorably fast and is highly effective for many vision tasks. We aim to keep the architecture as simple as possible, without bells and whistles, to make it hardware-friendly in general.", + "bbox": [ + 496, + 416, + 890, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We present the overall architecture in Fig. 4. It has four hierarchical stages, each of which is preceded by an embedding layer (a regular Conv $4 \\times 4$ with stride 4) or a merging layer (a regular Conv $2 \\times 2$ with stride 2) for spatial downsampling and channel number expanding. Each stage has a stack of FasterNet blocks. We observe that the blocks in the last two stages consume less memory access and tend to have higher FLOPS, as empirically validated in Tab. 1. Thus, we put more FasterNet blocks and correspondingly assign more computations to the last two stages. Each FasterNet block has a PConv layer followed by two PWConv (or Conv $1 \\times 1$ ) layers. Together, they appear as inverted residual blocks where the middle layer has an expanded number of channels, and a shortcut connection is placed to reuse the input features.", + "bbox": [ + 496, + 508, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In addition to the above operators, the normalization and activation layers are also indispensable for high-performing neural networks. Many prior works [13, 16, 47], however, overuse such layers throughout the network, which may limit the feature diversity and thus hurt the performance. It can also slow down the overall computation. By contrast, we put them only after each middle PWConv to preserve the feature diversity and achieve lower latency. Besides, we use the batch normalization (BN) [26] instead of other alternative ones [2, 60, 68]. The benefit of BN is that it can be merged into its adjacent Conv layers for faster inference", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12024", + "bbox": [ + 480, + 924, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4cbebcfcba214df5a0773b9aac408ea26fe033a4af1473a805836ce83676b38c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 145, + 83, + 823, + 305 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/70be33816e6e05deda16ab9e60a97129c8caba1c4290915d28b7400b1ac8fd84.jpg", + "image_caption": [ + "(a) PConv + PWConv" + ], + "image_footnote": [], + "bbox": [ + 96, + 373, + 215, + 443 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1cc9a62bb3d40acb040421f220c81886e43d4bbeade06a31e06c9d39b0107c51.jpg", + "image_caption": [ + "(b) T-shaped Conv" + ], + "image_footnote": [], + "bbox": [ + 238, + 375, + 328, + 441 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fb412d9f49483344d931ecb60a4c7b368f1ddac0868fdaca07ac7ead2459edc1.jpg", + "image_caption": [ + "(c) regular Conv", + "Figure 5. Comparison of convolutional variants. A PConv followed by a PWConv (a) resembles a T-shaped Conv (b), which spends more computation on the center position compared to a regular Conv (c)." + ], + "image_footnote": [], + "bbox": [ + 357, + 373, + 450, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "while being as effective as the others. As for the activation layers, we empirically choose GELU [18] for smaller FasterNet variants and ReLU [44] for bigger FasterNet variants, considering both running time and effectiveness. The last three layers, i.e. a global average pooling, a Conv $1 \\times 1$ , and a fully-connected layer, are used together for feature transformation and classification.", + "bbox": [ + 75, + 536, + 468, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To serve a wide range of applications under different computational budgets, we provide tiny, small, medium, and large variants of FasterNet, referred to as FasterNet-T0/1/2, FasterNet-S, FasterNet-M, and FasterNet-L, respectively. They share a similar architecture but vary in depth and width. Detailed architecture specifications are provided in the appendix.", + "bbox": [ + 75, + 643, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 766, + 282, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first examine the computational speed of our PConv and its effectiveness when combined with a PWConv. We then comprehensively evaluate the performance of our FasterNet for classification, detection, and segmentation tasks. Finally, we conduct a brief ablation study.", + "bbox": [ + 75, + 792, + 468, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To benchmark the latency and throughput, we choose the following three typical processors, which cover a wide", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c3e91ad083f5845c8ed7743c6664f13f9076194653b00f9c257d1e8f0f658866.jpg", + "image_caption": [ + "Figure 4. Overall architecture of our FasterNet. It has four hierarchical stages, each with a stack of FasterNet blocks and preceded by an embedding or merging layer. The last three layers are used for feature classification. Within each FasterNet block, a PConv layer is followed by two PWConv layers. We put normalization and activation layers only after the middle layer to preserve the feature diversity and achieve lower latency.", + "Figure 6. Histogram of salient position distribution for the regular Conv $3 \\times 3$ filters in a pre-trained ResNet18. The histogram contains four kinds of bars, corresponding to different stages in the network. In all stages, the center position (position 5) appears as a salient position most frequently." + ], + "image_footnote": [], + "bbox": [ + 500, + 359, + 887, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "range of computational capacity: GPU (2080Ti), CPU (Intel i9-9900X, using a single thread), and ARM (Cortex-A72, using a single thread). We report their latency for inputs with a batch size of 1 and throughput for inputs with a batch size of 32. During inference, the BN layers are merged to their adjacent layers wherever applicable.", + "bbox": [ + 498, + 551, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. PConv is fast with high FLOPS", + "text_level": 1, + "bbox": [ + 500, + 650, + 774, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We below show that our PConv is fast and better exploits the on-device computational capacity. Specifically, we stack 10 layers of pure PConv and take feature maps of typical dimensions as inputs. We then measure FLOPs and latency/throughput on GPU, CPU, and ARM processors, which also allow us to further compute FLOPS. We repeat the same procedure for other convolutional variants and make comparisons.", + "bbox": [ + 496, + 674, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Results in Tab. 1 show that PConv is overall an appealing choice for high FLOPS with reduced FLOPs. It has only $\\frac{1}{16}$ FLOPs of a regular Conv and achieves $10.5\\times$ , $6.2\\times$ , and $22.8\\times$ higher FLOPS than the DWConv on GPU, CPU, and ARM, respectively. We are unsurprised to see that the regular Conv has the highest FLOPS as it has been constantly optimized for years. However, its total FLOPs and", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12025", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/57398df037efacea461ed9e36ffe849a481051795f3dd9e649ed57795f9f4b0b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
OperatorFeature map sizeFLOPs (M), ×10 layersGPU Throughput (fps)FLOPS (G/s)CPU Latency (ms)FLOPS (G/s)ARM Latency (ms)FLOPS (G/s)
Conv 3×396×56×5626013010782435.6772.90779.573.33
192×28×28260148931271728.4191.53619.644.19
384×14×14260145581185431.8581.66595.094.37
768×7×726013159821262.7141.47662.173.92
Average-10151-71.89-3.95
GConv 3×3 (16 groups)96×56×56162288846921.907.42166.300.97
192×28×281621081117547.5821.4496.221.68
384×14×141621553425144.4036.8863.572.55
768×7×71621600025984.2837.9765.202.49
Average-1833-25.93-1.92
DWConv 3×396×56×5627.09119403233.597.52108.700.24
192×28×2813.54233583151.976.8682.010.16
384×14×146.77463773131.066.3594.890.07
768×7×73.38888893020.684.93150.890.02
Average-313-6.42-0.12
PConv 3×3 (ours, with r = 1/4)96×56×56162921514935.4629.6785.301.90
192×28×281621436023263.0952.4366.462.44
384×14×141622440839543.5845.2549.983.24
768×7×71623286653245.0232.2748.303.35
Average-3274-39.91-2.73
", + "bbox": [ + 151, + 88, + 818, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "latency/throughput are unaffordable. GConv and DWConv, despite their significant reduction in FLOPs, suffer from a drastic decrease in FLOPS. In addition, they tend to increase the number of channels to compensate for the performance drop, which, however, increase their latency.", + "bbox": [ + 75, + 411, + 470, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. PConv is effective together with PWConv", + "text_level": 1, + "bbox": [ + 76, + 496, + 429, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We next show that a PConv followed by a PWConv is effective in approximating a regular Conv to transform the feature maps. To this end, we first build four datasets by feeding the ImageNet-1k val split images into a pre-trained ResNet50, and extract the feature maps before and after the first Conv $3 \\times 3$ in each of the four stages. Each feature map dataset is further spilt into the train $(70\\%)$ , val $(10\\%)$ , and test $(20\\%)$ subsets. We then build a simple network consisting of a PConv followed by a PWConv and train it on the feature map datasets with a mean squared error loss. For comparison, we also build and train networks for DWConv + PWConv and GConv + PWConv under the same setting.", + "bbox": [ + 75, + 518, + 468, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 2 shows that PConv + PWConv achieve the lowest test loss, meaning that they better approximate a regular Conv in feature transformation. The results also suggest that it is sufficient and efficient to capture spatial features from only a part of the feature maps. PConv shows a great potential to be the new go-to choice in designing fast and effective neural networks.", + "bbox": [ + 75, + 700, + 470, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. FasterNet on ImageNet-1k classification", + "text_level": 1, + "bbox": [ + 76, + 816, + 419, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To verify the effectiveness and efficiency of our FasterNet, we first conduct experiments on the large-scale ImageNet-1k classification dataset [46]. It covers 1k categories of common objects and contains about 1.3M la", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6e4606f3000e463c4f2ccd6c994236e18415b170c6a41f56fadf70af6dfdbf6c.jpg", + "table_caption": [ + "Table 1. On-device FLOPS for different operations. PConv appears as an appealing choice for high FLOPS with reduced FLOPs." + ], + "table_footnote": [], + "table_body": "
StageDWConv+PWConvGConv+PWConv(16 groups)PConv+PWConvr = 1/4
10.00890.00650.0069
20.01580.01370.0136
30.02140.02020.0172
40.01300.01280.0115
Average0.01480.01330.0123
", + "bbox": [ + 522, + 412, + 870, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. A PConv followed by a PWConv well approximates the regular Conv $3 \\times 3$ at different stages of a pre-trained ResNet50. PConv + PWConv together have the lowest test loss on average.", + "bbox": [ + 498, + 526, + 890, + 570 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "beled images for training and 50k labeled images for validation. We train our models for 300 epochs using AdamW optimizer [38]. We set the batch size to 2048 for the FasterNet-M/L and 4096 for other variants. We use cosine learning rate scheduler [37] with a peak value of $0.001 \\cdot$ batch size/1024 and a 20-epoch linear warmup. We apply commonly-used regularization and augmentation techniques, including Weight Decay [28], Stochastic Depth [24], Label Smoothing [52], Mixup [73], Cutmix [72] and Rand Augment [9], with varying magnitudes for different FasterNet variants. To reduce the training time, we use $192 \\times 192$ resolution for the first 280 training epochs and $224 \\times 224$ for the remaining 20 epochs. For fair comparison, we do not use knowledge distillation [19] and neural architecture search [79]. We report our top-1 accuracy on the validation set with a center crop at $224 \\times 224$ resolution and a 0.9 crop ratio. Detailed training and validation settings are provided in the appendix.", + "bbox": [ + 496, + 582, + 890, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 7 and Tab. 3 demonstrate the superiority of our FasterNet over state-of-the-art classification models. The trade-off curves in Fig. 7 clearly show that FasterNet sets", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12026", + "bbox": [ + 480, + 925, + 519, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/815b3c3a86d1a130a402adcae33bb24083901f97882f97150fb926cc712b2e97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 85, + 467, + 301 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ee0963af0ff702c4f7440623b2fef107742aa7aa992df772c6ff8f22d9f3054.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 303, + 467, + 455 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5959c7303514d8b8e2d1673f69f30c473f3e2009cb5c8ddc69a8bd14351a9e35.jpg", + "image_caption": [ + "Figure 7. FasterNet has the highest efficiency in balancing accuracy-throughput and accuracy-latency trade-offs for different devices. To save space and make the plots more proportionate, we showcase network variants within a certain range of latency. Full plots can be found in the appendix, which show consistent results." + ], + "image_footnote": [], + "bbox": [ + 80, + 459, + 465, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the new state-of-the-art in balancing accuracy and latency/throughput among all the networks examined. From another perspective, FasterNet runs faster than various CNN, ViT and MLP models on a wide range of devices, when having similar top-1 accuracy. As quantitatively shown in Tab. 3, FasterNet-T0 is $2.8 \\times 3.3 \\times$ and $2.4 \\times$ faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being $2.9\\%$ more accurate. Our large FasterNet-L achieves $83.5\\%$ top-1 accuracy, comparable to the emerging Swin-B [35] and ConvNeXt-B [36] while having $36\\%$ and $28\\%$ higher inference throughput on GPU, as well as saving $37\\%$ and $15\\%$ compute time on CPU. Given such promising results, we highlight that our FasterNet is", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5d23304daed3ad28732bde0f3b7a1fd6fb4b2f5cad8e2e0f0c42d4ab6692b4f0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NetworkParams (M)FLOPs (G)Throughput on GPU (fps) ↑Latency on CPU (ms) ↓Latency on ARM (ms) ↓Acc. (%)
ShuffleNetV2 ×1.5 [40]3.50.30487812.126672.6
MobileNetV2 [47]3.50.31419812.244272.0
MobileViT-XXS [42]1.30.42239330.834869.0
EdgeNeXt-XXS [41]1.30.26276515.723971.2
FasterNet-T03.90.3468079.214371.9
GhostNet ×1.3 [13]7.40.24298817.948175.7
ShuffleNetV2 ×2 [40]7.40.59333917.840374.9
MobileNetV2 ×1.4 [47]6.10.60271122.665074.7
MobileViT-XS [42]2.31.05139240.864874.8
EdgeNeXt-XS [41]2.30.54173824.443475.0
PVT-Tiny [65]13.21.94126655.670875.1
FasterNet-T17.60.85378217.728576.2
CycleMLP-B1 [5]15.22.10865116.189279.1
PoolFormer-S12 [71]11.91.82143949.066577.2
MobileViT-S [42]5.62.03103956.794178.4
EdgeNeXt-S [41]5.61.26112839.274379.4
ResNet50 [16, 36]25.64.1195973.0113178.8
FasterNet-T215.01.91199133.549778.9
CycleMLP-B2 [5]26.83.90528186.3150281.6
PoolFormer-S24 [71]21.43.4174892.8126180.3
PoolFormer-S36 [71]30.95.00507138.0186081.4
ConvNeXt-T [36]28.64.4765786.3188982.1
Swin-T [35]28.34.51609122.2142481.3
PVT-Small [65]24.53.8368989.6134579.8
PVT-Medium [65]44.26.69438143.6214281.2
FasterNet-S31.14.56102971.2110381.3
PoolFormer-M36 [71]56.28.80320215.0297982.1
ConvNeXt-S [36]50.28.71377153.2348483.1
Swin-S [35]49.68.77348224.2261383.0
PVT-Large [65]61.49.85306203.4310181.7
FasterNet-M53.58.74500129.5209283.0
PoolFormer-M48 [71]73.511.59242281.8OOM82.5
ConvNeXt-B [36]88.615.38253257.1OOM83.8
Swin-B [35]87.815.47237349.2OOM83.5
FasterNet-L93.515.52323219.5OOM83.5
", + "bbox": [ + 501, + 84, + 890, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Comparison on ImageNet-1k benchmark. Models with similar top-1 accuracy are grouped together. For each group, our FasterNet achieves the highest throughput on GPU and the lowest latency on CPU and ARM. All models are evaluated at $224 \\times 224$ resolution except for the MobileViT and EdgeNeXt with $256 \\times 256$ . OOM is short for out of memory.", + "bbox": [ + 496, + 592, + 890, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "much simpler than many other models in terms of architectural design, which showcases the feasibility of designing simple yet powerful neural networks.", + "bbox": [ + 496, + 696, + 890, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. FasterNet on downstream tasks", + "text_level": 1, + "bbox": [ + 498, + 755, + 777, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To further evaluate the generalization ability of FasterNet, we conduct experiments on the challenging COCO dataset [32] for object detection and instance segmentation. As a common practice, we employ the ImageNet pre-trained FasterNet as a backbone and equip it with the popular Mask R-CNN detector [15]. To highlight the effectiveness of the backbone itself, we simply follow PoolFormer [71] and adopt an AdamW optimizer, a $1\\times$ training", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12027", + "bbox": [ + 480, + 925, + 517, + 936 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c5f70244aef2e32f5512124b593580c255e602f3bc0a47d09897dd295233bd84.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BackboneParams (M)FLOPs (G)Latency on GPU (ms)\\(AP^b\\)\\(AP_{50}^b\\)\\(AP_{75}^b\\)\\(AP^m\\)\\(AP_{50}^m\\)\\(AP_{75}^m\\)
ResNet50 [16]44.225354.938.058.641.434.455.136.7
PoolFormer-S24 [71]41.0233111.040.162.243.437.059.139.6
PVT-Small [65]44.123889.540.462.943.837.860.140.3
FasterNet-S49.025854.339.961.243.636.958.139.7
ResNet101 [16]63.232968.940.461.144.236.457.738.8
ResNeXt101-32×4d [69]62.833380.541.962.545.937.559.440.2
PoolFormer-S36 [71]50.5266146.941.063.144.837.760.140.0
PVT-Medium [65]63.9295117.342.064.445.639.061.642.1
FasterNet-M71.234471.443.064.447.439.161.542.3
ResNeXt101-64×4d [69]101.9487112.942.863.847.338.460.641.3
PVT-Large [65]81.0358152.242.965.046.639.561.942.5
FasterNet-L110.948493.844.065.648.239.962.343.0
", + "bbox": [ + 119, + 88, + 849, + 295 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7038d17176173fd3f66cbaf3bc12fe53d4593c585ef6a012831af2873370e950.jpg", + "table_caption": [ + "Table 4. Results on COCO object detection and instance segmentation benchmarks. FLOPs are calculated with image size (1280, 800)." + ], + "table_footnote": [ + "Table 5. Ablation on the partial ratio, normalization, and activation of FasterNet. Rows highlighted in grey are the default settings. $\\mathrm{T0}^*$ denotes T0 variants with modified network width and depth." + ], + "table_body": "
AblationVariantThroughput on GPU (fps)Latency on CPU (ms)Latency on ARM (ms)Acc. (%)
Partial ratioT0* w/ r = 1/266269.614571.7
T0 w/ r = 1/468079.214371.9
T0* w/ r = 1/862048.914071.3
NormalizationT0 w/ BN68079.214371.9
T0 w/ LN551510.715971.9
ActivationT0 w/ ReLU69298.211471.3
T0* w/ ReLU58669.314371.7
T0 w/ GELU68079.214371.9
T2 w/ ReLU199133.549778.9
T2 w/ GELU198535.455778.7
", + "bbox": [ + 81, + 329, + 468, + 534 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "schedule (12 epochs), a batch size of 16, and other training settings without further hyper-parameter tuning.", + "bbox": [ + 75, + 595, + 468, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 4 shows the results for comparison between FasterNet and representative models. FasterNet consistently outperforms ResNet and ResNext by having higher average precision (AP) with similar latency. Specifically, FasterNet-S yields $+1.9$ higher box AP and $+2.4$ higher mask AP compared to the standard baseline ResNet50. FasterNet is also competitive against the ViT variants. Under similar FLOPs, FasterNet-L reduces PVT-Large's latency by $38\\%$ , i.e., from $152.2\\mathrm{ms}$ to $93.8\\mathrm{ms}$ on GPU, and achieves $+1.1$ higher box AP and $+0.4$ higher mask AP.", + "bbox": [ + 75, + 627, + 468, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 786, + 225, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct a brief ablation study on the value of partial ratio $r$ and the choices of activation and normalization layers. We compare different variants in terms of ImageNet top-1 accuracy and on-device latency/throughput. Results are summarized in Tab. 5. For the partial ratio $r$ , we set it to $\\frac{1}{4}$ for all FasterNet variants by default, which achieves", + "bbox": [ + 75, + 809, + 468, + 904 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "higher accuracy, higher throughput, and lower latency at similar complexity. A too large partial ratio $r$ would make PConv degrade to a regular Conv, while a too small value would render PConv less effective in capturing the spatial features. For the normalization layers, we choose BatchNorm over LayerNorm because BatchNorm can be merged into its adjacent convolutional layers for faster inference while it is as effective as LayerNorm in our experiment. For the activation function, interestingly, we empirically found that GELU fits FasterNet-T0/T1 models more efficiently than ReLU. It, however, becomes opposite for FasterNet-T2/S/M/L. Here we only show two examples in Tab. 5 due to space constraint. We conjecture that GELU strengthens FasterNet-T0/T1 by having higher non-linearity, while the benefit fades away for larger FasterNet variants.", + "bbox": [ + 496, + 330, + 890, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 575, + 617, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have investigated the common and unresolved issue that many established neural networks suffer from low floating-point operations per second (FLOPS). We have revisited a bottleneck operator, DWConv, and analyzed its main cause for a slowdown - frequent memory access. To overcome the issue and achieve faster neural networks, we have proposed a simple yet fast and effective operator, PConv, that can be readily plugged into many existing networks. We have further introduced our general-purpose FasterNet, built upon our PConv, that achieves state-of-the-art speed and accuracy trade-off on various devices and vision tasks. We hope that our PConv and FasterNet would inspire more research on simple yet effective neural networks, going beyond academia to impact the industry and community directly.", + "bbox": [ + 496, + 602, + 890, + 829 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported, in part, by Hong Kong General Research Fund under grant number 16200120. The work of C.-H. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.129, + 0.131, + 0.842, + 0.152 + ], + "angle": 0, + "content": "Run, Don’t Walk: Chasing Higher FLOPS for Faster Neural Networks" + }, + { + "type": "text", + "bbox": [ + 0.238, + 0.18, + 0.73, + 0.235 + ], + "angle": 0, + "content": "Jierun Chen\\(^{1}\\), Shiu-hong Kao\\(^{1}\\), Hao He\\(^{1}\\) \nWeipeng Zhuo\\(^{1}\\), Song Wen\\(^{2}\\), Chul-Ho Lee\\(^{3}\\), S.-H. Gary Chan\\(^{1}\\) \n\\(^{1}\\)HKUST, \\(^{2}\\)Rutgers University, \\(^{3}\\)Texas State University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.68 + ], + "angle": 0, + "content": "To design fast neural networks, many works have been focusing on reducing the number of floating-point operations (FLOPs). We observe that such reduction in FLOPs, however, does not necessarily lead to a similar level of reduction in latency. This mainly stems from inefficiently low floating-point operations per second (FLOPS). To achieve faster networks, we revisit popular operators and demonstrate that such low FLOPS is mainly due to frequent memory access of the operators, especially the depthwise convolution. We hence propose a novel partial convolution (PCnv) that extracts spatial features more efficiently, by cutting down redundant computation and memory access simultaneously. Building upon our PCnv, we further propose FasterNet, a new family of neural networks, which attains substantially higher running speed than others on a wide range of devices, without compromising on accuracy for various vision tasks. For example, on ImageNet-1k, our tiny FasterNet-T0 is \\(2.8 \\times 3.3 \\times\\) and \\(2.4 \\times\\) faster than MobileViT-XXS on GPU, CPU, and ARM processors, respectively, while being \\(2.9\\%\\) more accurate. Our large FasterNet-L achieves impressive \\(83.5\\%\\) top-1 accuracy, on par with the emerging Swin-B, while having \\(36\\%\\) higher inference throughput on GPU, as well as saving \\(37\\%\\) compute time on CPU. Code is available at https://github.com/JierunChen/FasterNet." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.709, + 0.21, + 0.724 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.84 + ], + "angle": 0, + "content": "Neural networks have undergone rapid development in various computer vision tasks such as image classification, detection and segmentation. While their impressive performance has powered many applications, a roaring trend is to pursue fast neural networks with low latency and high throughput for great user experiences, instant responses, safety reasons, etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "How to be fast? Instead of asking for more costly computing devices, researchers and practitioners prefer to design cost-effective fast neural networks with reduced computational complexity, mainly measured in the number of" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.268, + 0.693, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.544, + 0.324, + 0.625, + 0.335 + ], + "angle": 0, + "content": "(a) Convolution" + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.268, + 0.892, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.707, + 0.324, + 0.879, + 0.337 + ], + "angle": 0, + "content": "(b) Depthwise/Group Convolution" + }, + { + "type": "image", + "bbox": [ + 0.549, + 0.345, + 0.738, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.395, + 0.724, + 0.407 + ], + "angle": 0, + "content": "(c) Partial Convolution (ours)" + }, + { + "type": "text", + "bbox": [ + 0.77, + 0.36, + 0.853, + 0.371 + ], + "angle": 0, + "content": "Input/output" + }, + { + "type": "text", + "bbox": [ + 0.771, + 0.372, + 0.819, + 0.381 + ], + "angle": 0, + "content": "Filter" + }, + { + "type": "text", + "bbox": [ + 0.771, + 0.382, + 0.853, + 0.392 + ], + "angle": 0, + "content": "\\*Convolution" + }, + { + "type": "text", + "bbox": [ + 0.771, + 0.393, + 0.83, + 0.404 + ], + "angle": 0, + "content": "\\(\\rightarrow\\) Identity" + }, + { + "type": "list", + "bbox": [ + 0.77, + 0.36, + 0.853, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.484 + ], + "angle": 0, + "content": "Figure 1. Our partial convolution (PConv) is fast and efficient by applying filters on only a few input channels while leaving the remaining ones untouched. PConv obtains lower FLOPs than the regular convolution and higher FLOPS than the depthwise/group convolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.706 + ], + "angle": 0, + "content": "floating-point operations (FLOPs)\\(^1\\). MobileNets [20, 21, 47], ShuffleNets [40, 76] and GhostNet [13], among others, leverage the depthwise convolution (DWConv) [48] and/or group convolution (GConv) [27] to extract spatial features. However, in the effort to reduce FLOPs, the operators often suffer from the side effect of increased memory access. MicroNet [29] further decomposes and sparsifies the network to push its FLOPs to an extremely low level. Despite its improvement in FLOPs, this approach experiences inefficient fragmented computation. Besides, the above networks are often accompanied by additional data manipulations, such as concatenation, shuffling, and pooling, whose running time tends to be significant for tiny models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.708, + 0.892, + 0.86 + ], + "angle": 0, + "content": "Apart from the above pure convolutional neural networks (CNNs), there is an emerging interest in making vision transformers (ViTs) [11] and multilayer perceptrons (MLPs) architectures [57] smaller and faster. For example, MobileViTs [42, 43, 63] and MobileFormer [6] reduce the computational complexity by combining DWConv with a modified attention mechanism. However, they still suffer from the aforementioned issue with DWConv and also need dedicated hardware support for the modified attention mechanism. The use of advanced yet time-consuming nor" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.894, + 0.901 + ], + "angle": 0, + "content": "1We follow a widely adopted definition of FLOPs, as the number of multiply-adds [36, 76]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.518, + 0.937 + ], + "angle": 0, + "content": "12021" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.203, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.206, + 0.089, + 0.437, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.263, + 0.339, + 0.274 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.447, + 0.091, + 0.65, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.091, + 0.892, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.263, + 0.69, + 0.274 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.274, + 0.894, + 0.318 + ], + "angle": 0, + "content": "Figure 2. (a) FLOPS under varied FLOPs on CPU. Many existing neural networks suffer from low computational speed issues. Their effective FLOPS are lower than the popular ResNet50. By contrast, our FasterNet attains higher FLOPS. (b) Latency under varied FLOPs on CPU. Our FasterNet obtains lower latency than others with the same amount of FLOPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.338, + 0.47, + 0.367 + ], + "angle": 0, + "content": "malization and activation layers may also limit their speed on devices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.469, + 0.429 + ], + "angle": 0, + "content": "All these issues together lead to the following question: Are these \"fast\" neural networks really fast? To answer this, we examine the relationship between latency and FLOPs, which is captured by" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.439, + 0.47, + 0.47 + ], + "angle": 0, + "content": "\\[\nL a t e n c y = \\frac {F L O P s}{F L O P S}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.794 + ], + "angle": 0, + "content": "where FLOPS is short for floating-point operations per second, as a measure of the effective computational speed. While there are many attempts to reduce FLOPs, they seldom consider optimizing FLOPS at the same time to achieve truly low latency. To better understand the situation, we compare the FLOPS of typical neural networks on an Intel CPU. The results in Fig. 2 show that many existing neural networks suffer from low FLOPS, and their FLOPS is generally lower than the popular ResNet50. With such low FLOPS, these \"fast\" neural networks are actually not fast enough. Their reduction in FLOPs cannot be translated into the exact amount of reduction in latency. In some cases, there is no improvement, and it even leads to worse latency. For example, CycleMLP-B1 [5] has half of FLOPs of ResNet50 [16] but runs more slowly (i.e., CycleMLP-B1 vs. ResNet50: 116.1ms vs. 73.0ms). Note that this discrepancy between FLOPs and latency has also been noticed in previous works [40, 42] but remains unresolved partially because they employ the DWConv/GConv and various data manipulations with low FLOPS. It is deemed there are no better alternatives available." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.902 + ], + "angle": 0, + "content": "This paper aims to eliminate the discrepancy by developing a simple yet fast and effective operator that maintains high FLOPS with reduced FLOPs. Specifically, we reexamine existing operators, particularly DWConv, in terms of the computational speed - FLOPS. We uncover that the main reason causing the low FLOPS issue is frequent memory access. We then propose a novel partial convolution (PCov)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.892, + 0.503 + ], + "angle": 0, + "content": "as a competitive alternative that reduces the computational redundancy as well as the number of memory access. Fig. 1 illustrates the design of our PConv. It takes advantage of redundancy within the feature maps and systematically applies a regular convolution (Conv) on only a part of the input channels while leaving the remaining ones untouched. By nature, PConv has lower FLOPs than the regular Conv while having higher FLOPS than the DWConv/GConv. In other words, PConv better exploits the on-device computational capacity. PConv is also effective in extracting spatial features as empirically validated later in the paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.893, + 0.7 + ], + "angle": 0, + "content": "We further introduce FasterNet, which is primarily built upon our PConv, as a new family of networks that run highly fast on various devices. In particular, our FasterNet achieves state-of-the-art performance for classification, detection, and segmentation tasks while having much lower latency and higher throughput. For example, our tiny FasterNet-T0 is \\(2.8 \\times 3.3 \\times\\) and \\(2.4 \\times\\) faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being \\(2.9\\%\\) more accurate on ImageNet-1k. Our large FasterNet-L achieves \\(83.5\\%\\) top-1 accuracy, on par with the emerging Swin-B [35], while offering \\(36\\%\\) higher throughput on GPU and saving \\(37\\%\\) compute time on CPU. To summarize, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.707, + 0.891, + 0.751 + ], + "angle": 0, + "content": "- We point out the importance of achieving higher FLOPS beyond simply reducing FLOPs for faster neural networks." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.757, + 0.89, + 0.801 + ], + "angle": 0, + "content": "- We introduce a simple yet fast and effective operator called PConv, which has a high potential to replace the existing go-to choice, DWConv." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.806, + 0.891, + 0.851 + ], + "angle": 0, + "content": "- We introduce FasterNet which runs favorably and universally fast on a variety of devices such as GPU, CPU, and ARM processors." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.856, + 0.891, + 0.9 + ], + "angle": 0, + "content": "- We conduct extensive experiments on various tasks and validate the high speed and effectiveness of our PConv and FasterNet." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.707, + 0.891, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "12022" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.116, + 0.47, + 0.146 + ], + "angle": 0, + "content": "We briefly review prior works on fast and efficient neural networks and differentiate this work from them." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.156, + 0.473, + 0.474 + ], + "angle": 0, + "content": "CNN. CNNs are the mainstream architecture in the computer vision field, especially when it comes to deployment in practice, where being fast is as important as being accurate. Though there have been numerous studies [7, 8, 17, 29, 48, 49, 75, 78] to achieve higher efficiency, the rationale behind them is more or less to perform a low-rank approximation. Specifically, the group convolution [27] and the depthwise separable convolution [48] (consisting of depthwise and pointwise convolutions) are probably the most popular ones. They have been widely adopted in mobile/edge-oriented networks, such as MobileNets [20, 21, 47], ShuffleNets [40, 76], GhostNet [13], EfficientNets [54, 55], TinyNet [14], Xception [8], CondenseNet [23, 70], TVConv [4], MnasNet [53], and FBNet [67]. While they exploit the redundancy in filters to reduce the number of parameters and FLOPs, they suffer from increased memory access when increasing the network width to compensate for the accuracy drop. By contrast, we consider the redundancy in feature maps and propose a partial convolution to reduce FLOPs and memory access simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.482, + 0.473, + 0.799 + ], + "angle": 0, + "content": "ViT, MLP, and variants. There is a growing interest in studying ViT ever since Dosovitskiy et al. [11] expanded the application scope of transformers [62] from machine translation [62] or forecasting [66] to the computer vision field. Many follow-up works have attempted to improve ViT in terms of training setting [51, 58, 59] and model design [12, 34, 35, 65, 77]. One notable trend is to pursue a better accuracy-latency trade-off by reducing the complexity of the attention operator [1, 25, 39, 56, 61], incorporating convolution into ViTs [6, 10, 50], or doing both [3, 30, 43, 45]. Besides, other studies [5, 31, 57] propose to replace the attention with simple MLP-based operators. However, they often evolve to be CNN-like [33]. In this paper, we focus on analyzing the convolution operations, particularly DWConv, due to the following reasons: First, the advantage of attention over convolution is unclear or debatable [36, 64]. Second, the attention-based mechanism generally runs slower than its convolutional counterparts and thus becomes less favorable for the current industry [22, 42]. Finally, DW-Conv is still a popular choice in many hybrid models, so it is worth a careful examination." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.365, + 0.831 + ], + "angle": 0, + "content": "3. Design of PConv and FasterNet" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this section, we first revisit DWConv and analyze the issue with its frequent memory access. We then introduce PConv as a competitive alternative operator to resolve the issue. After that, we introduce FasterNet and explain its" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.091, + 0.888, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.244, + 0.895, + 0.3 + ], + "angle": 0, + "content": "Figure 3. Visualization of feature maps in an intermediate layer of a pre-trained ResNet50, with the top-left image as the input. Qualitatively, we can see the high redundancies across different channels." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.321, + 0.766, + 0.336 + ], + "angle": 0, + "content": "details, including design considerations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.345, + 0.63, + 0.362 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.895, + 0.672 + ], + "angle": 0, + "content": "DWConv is a popular variant of Conv and has been widely adopted as a key building block for many neural networks. For an input \\(\\mathbf{I} \\in \\mathbb{R}^{c \\times h \\times w}\\), DWConv applies \\(c\\) filters \\(\\mathbf{W} \\in \\mathbb{R}^{k \\times k}\\) to compute the output \\(\\mathbf{O} \\in \\mathbb{R}^{c \\times h \\times w}\\). As shown in Fig. 1(b), each filter slides spatially on one input channel and contributes to one output channel. This depthwise computation makes DWConv have as low FLOPs as \\(h \\times w \\times k^2 \\times c\\) compared to a regular Conv with \\(h \\times w \\times k^2 \\times c^2\\). While effective in reducing FLOPs, a DWConv, which is typically followed by a pointwise convolution, or PWConv, cannot be simply used to replace a regular Conv as it would incur a severe accuracy drop. Thus, in practice the channel number \\(c\\) (or the network width) of DWConv is increased to \\(c'(c' > c)\\) to compensate the accuracy drop, e.g., the width is expanded by six times for the DWConv in the inverted residual blocks [47]. This, however, results in much higher memory access that can cause non-negligible delay and slow down the overall computation, especially for I/O-bound devices. In particular, the number of memory access now escalates to" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.681, + 0.892, + 0.699 + ], + "angle": 0, + "content": "\\[\nh \\times w \\times 2 c ^ {\\prime} + k ^ {2} \\times c ^ {\\prime} \\approx h \\times w \\times 2 c ^ {\\prime}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.709, + 0.816, + 0.724 + ], + "angle": 0, + "content": "which is higher than that of a regular Conv, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.735, + 0.892, + 0.752 + ], + "angle": 0, + "content": "\\[\nh \\times w \\times 2 c + k ^ {2} \\times c ^ {2} \\approx h \\times w \\times 2 c. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.763, + 0.894, + 0.809 + ], + "angle": 0, + "content": "Note that the \\( h \\times w \\times 2c' \\) memory access is spent on the I/O operation, which is deemed to be already the minimum cost and hard to optimize further." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.833, + 0.835 + ], + "angle": 0, + "content": "3.2. Partial convolution as a basic operator" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We below demonstrate that the cost can be further optimized by leveraging the feature maps' redundancy. As visualized in Fig. 3, the feature maps share high similarities among different channels. This redundancy has also" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "12023" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "been covered in many other works [13, 74], but few of them make full use of it in a simple yet effective way." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.471, + 0.289 + ], + "angle": 0, + "content": "Specifically, we propose a simple PConv to reduce computational redundancy and memory access simultaneously. The bottom-left corner in Fig. 4 illustrates how our PConv works. It simply applies a regular Conv on only a part of the input channels for spatial feature extraction and leaves the remaining channels untouched. For contiguous or regular memory access, we consider the first or last consecutive \\( c_p \\) channels as the representatives of the whole feature maps for computation. Without loss of generality, we consider the input and output feature maps to have the same number of channels. Therefore, the FLOPs of a PConv are only" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.299, + 0.47, + 0.32 + ], + "angle": 0, + "content": "\\[\nh \\times w \\times k ^ {2} \\times c _ {p} ^ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.331, + 0.47, + 0.378 + ], + "angle": 0, + "content": "With a typical partial ratio \\( r = \\frac{c_p}{c} = \\frac{1}{4} \\), the FLOPs of a PConv is only \\( \\frac{1}{16} \\) of a regular Conv. Besides, PConv has a smaller amount of memory access, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.388, + 0.469, + 0.408 + ], + "angle": 0, + "content": "\\[\nh \\times w \\times 2 c _ {p} + k ^ {2} \\times c _ {p} ^ {2} \\approx h \\times w \\times 2 c _ {p}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.418, + 0.374, + 0.435 + ], + "angle": 0, + "content": "which is only \\(\\frac{1}{4}\\) of a regular Conv for \\(r = \\frac{1}{4}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.47, + 0.571 + ], + "angle": 0, + "content": "Since there are only \\( c_p \\) channels utilized for spatial feature extraction, one may ask if we can simply remove the remaining \\( (c - c_p) \\) channels? If so, PConv would degrade to a regular Conv with fewer channels, which deviates from our objective to reduce redundancy. Note that we keep the remaining channels untouched instead of removing them from the feature maps. It is because they are useful for a subsequent PWConv layer, which allows the feature information to flow through all channels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.332, + 0.597 + ], + "angle": 0, + "content": "3.3. PConv followed by PWConv" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To fully and efficiently leverage the information from all channels, we further append a pointwise convolution (PW-Conv) to our PConv. Their effective receptive field together on the input feature maps looks like a T-shaped Conv, which focuses more on the center position compared to a regular Conv uniformly processing a patch, as shown in Fig. 5. To justify this T-shaped receptive field, we first evaluate the importance of each position by calculating the position-wise Frobenius norm. We assume that a position tends to be more important if it has a larger Frobenius norm than other positions. For a regular Conv filter \\(\\mathbf{F} \\in \\mathbb{R}^{k^2 \\times c}\\), the Frobenius norm at position \\(i\\) is calculated by \\(\\| \\mathbf{F}_i \\| = \\sqrt{\\sum_{j=1}^{c} |f_{ij}|^2}\\), for \\(i = 1, 2, 3\\ldots, k^2\\). We consider a salient position to be the one with the maximum Frobenius norm. We then collectively examine each filter in a pre-trained ResNet18, find out their salient positions, and plot a histogram of the salient positions. Results in Fig. 6 show that the center position turns out to be the salient position most frequently among the filters. In other words, the center position weighs more" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "than its surrounding neighbors. This is consistent with the T-shaped computation which concentrates on the center position." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.243 + ], + "angle": 0, + "content": "While the T-shaped Conv can be directly used for efficient computation, we show that it is better to decompose the T-shaped Conv into a PConv and a PWConv because the decomposition exploits the inter-filter redundancy and further saves FLOPs. For the same input \\(\\mathbf{I} \\in \\mathbb{R}^{c \\times h \\times w}\\) and output \\(\\mathbf{O} \\in \\mathbb{R}^{c \\times h \\times w}\\), a T-shaped Conv's FLOPs can be calculated as" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.255, + 0.892, + 0.273 + ], + "angle": 0, + "content": "\\[\nh \\times w \\times \\left(k ^ {2} \\times c _ {p} \\times c + c \\times \\left(c - c _ {p}\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.313 + ], + "angle": 0, + "content": "which is higher than the FLOPs of a PConv and a PWConv, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.314, + 0.892, + 0.333 + ], + "angle": 0, + "content": "\\[\nh \\times w \\times \\left(k ^ {2} \\times c _ {p} ^ {2} + c \\times c _ {p}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.384 + ], + "angle": 0, + "content": "where \\( c > c_p \\) and \\( c - c_p > c_p \\) (e.g. when \\( c_p = \\frac{c}{4} \\)). Besides, we can readily leverage the regular Conv for the two-step implementation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.394, + 0.787, + 0.41 + ], + "angle": 0, + "content": "3.4. FasterNet as a general backbone" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.417, + 0.892, + 0.507 + ], + "angle": 0, + "content": "Given our novel PConv and off-the-shelf PWConv as the primary building operators, we further propose FasterNet, a new family of neural networks that runs favorably fast and is highly effective for many vision tasks. We aim to keep the architecture as simple as possible, without bells and whistles, to make it hardware-friendly in general." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.735 + ], + "angle": 0, + "content": "We present the overall architecture in Fig. 4. It has four hierarchical stages, each of which is preceded by an embedding layer (a regular Conv \\(4 \\times 4\\) with stride 4) or a merging layer (a regular Conv \\(2 \\times 2\\) with stride 2) for spatial downsampling and channel number expanding. Each stage has a stack of FasterNet blocks. We observe that the blocks in the last two stages consume less memory access and tend to have higher FLOPS, as empirically validated in Tab. 1. Thus, we put more FasterNet blocks and correspondingly assign more computations to the last two stages. Each FasterNet block has a PConv layer followed by two PWConv (or Conv \\(1 \\times 1\\)) layers. Together, they appear as inverted residual blocks where the middle layer has an expanded number of channels, and a shortcut connection is placed to reuse the input features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In addition to the above operators, the normalization and activation layers are also indispensable for high-performing neural networks. Many prior works [13, 16, 47], however, overuse such layers throughout the network, which may limit the feature diversity and thus hurt the performance. It can also slow down the overall computation. By contrast, we put them only after each middle PWConv to preserve the feature diversity and achieve lower latency. Besides, we use the batch normalization (BN) [26] instead of other alternative ones [2, 60, 68]. The benefit of BN is that it can be merged into its adjacent Conv layers for faster inference" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "12024" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.146, + 0.084, + 0.825, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.308, + 0.895, + 0.365 + ], + "angle": 0, + "content": "Figure 4. Overall architecture of our FasterNet. It has four hierarchical stages, each with a stack of FasterNet blocks and preceded by an embedding or merging layer. The last three layers are used for feature classification. Within each FasterNet block, a PConv layer is followed by two PWConv layers. We put normalization and activation layers only after the middle layer to preserve the feature diversity and achieve lower latency." + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.374, + 0.216, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.446, + 0.223, + 0.458 + ], + "angle": 0, + "content": "(a) PConv + PWConv" + }, + { + "type": "image", + "bbox": [ + 0.239, + 0.376, + 0.33, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.445, + 0.341, + 0.458 + ], + "angle": 0, + "content": "(b) T-shaped Conv" + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.374, + 0.451, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.352, + 0.447, + 0.448, + 0.459 + ], + "angle": 0, + "content": "(c) regular Conv" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.517 + ], + "angle": 0, + "content": "Figure 5. Comparison of convolutional variants. A PConv followed by a PWConv (a) resembles a T-shaped Conv (b), which spends more computation on the center position compared to a regular Conv (c)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.469, + 0.642 + ], + "angle": 0, + "content": "while being as effective as the others. As for the activation layers, we empirically choose GELU [18] for smaller FasterNet variants and ReLU [44] for bigger FasterNet variants, considering both running time and effectiveness. The last three layers, i.e. a global average pooling, a Conv \\( 1 \\times 1 \\), and a fully-connected layer, are used together for feature transformation and classification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.75 + ], + "angle": 0, + "content": "To serve a wide range of applications under different computational budgets, we provide tiny, small, medium, and large variants of FasterNet, referred to as FasterNet-T0/1/2, FasterNet-S, FasterNet-M, and FasterNet-L, respectively. They share a similar architecture but vary in depth and width. Detailed architecture specifications are provided in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.767, + 0.283, + 0.784 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.469, + 0.869 + ], + "angle": 0, + "content": "We first examine the computational speed of our PConv and its effectiveness when combined with a PWConv. We then comprehensively evaluate the performance of our FasterNet for classification, detection, and segmentation tasks. Finally, we conduct a brief ablation study." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To benchmark the latency and throughput, we choose the following three typical processors, which cover a wide" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.361, + 0.888, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.466, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Figure 6. Histogram of salient position distribution for the regular Conv \\(3 \\times 3\\) filters in a pre-trained ResNet18. The histogram contains four kinds of bars, corresponding to different stages in the network. In all stages, the center position (position 5) appears as a salient position most frequently." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.552, + 0.892, + 0.643 + ], + "angle": 0, + "content": "range of computational capacity: GPU (2080Ti), CPU (Intel i9-9900X, using a single thread), and ARM (Cortex-A72, using a single thread). We report their latency for inputs with a batch size of 1 and throughput for inputs with a batch size of 32. During inference, the BN layers are merged to their adjacent layers wherever applicable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.776, + 0.668 + ], + "angle": 0, + "content": "4.1. PConv is fast with high FLOPS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.795 + ], + "angle": 0, + "content": "We below show that our PConv is fast and better exploits the on-device computational capacity. Specifically, we stack 10 layers of pure PConv and take feature maps of typical dimensions as inputs. We then measure FLOPs and latency/throughput on GPU, CPU, and ARM processors, which also allow us to further compute FLOPS. We repeat the same procedure for other convolutional variants and make comparisons." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Results in Tab. 1 show that PConv is overall an appealing choice for high FLOPS with reduced FLOPs. It has only \\(\\frac{1}{16}\\) FLOPs of a regular Conv and achieves \\(10.5\\times\\), \\(6.2\\times\\), and \\(22.8\\times\\) higher FLOPS than the DWConv on GPU, CPU, and ARM, respectively. We are unsurprised to see that the regular Conv has the highest FLOPS as it has been constantly optimized for years. However, its total FLOPs and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "12025" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.153, + 0.089, + 0.819, + 0.381 + ], + "angle": 0, + "content": "
OperatorFeature map sizeFLOPs (M), ×10 layersGPU Throughput (fps)FLOPS (G/s)CPU Latency (ms)FLOPS (G/s)ARM Latency (ms)FLOPS (G/s)
Conv 3×396×56×5626013010782435.6772.90779.573.33
192×28×28260148931271728.4191.53619.644.19
384×14×14260145581185431.8581.66595.094.37
768×7×726013159821262.7141.47662.173.92
Average-10151-71.89-3.95
GConv 3×3 (16 groups)96×56×56162288846921.907.42166.300.97
192×28×281621081117547.5821.4496.221.68
384×14×141621553425144.4036.8863.572.55
768×7×71621600025984.2837.9765.202.49
Average-1833-25.93-1.92
DWConv 3×396×56×5627.09119403233.597.52108.700.24
192×28×2813.54233583151.976.8682.010.16
384×14×146.77463773131.066.3594.890.07
768×7×73.38888893020.684.93150.890.02
Average-313-6.42-0.12
PConv 3×3 (ours, with r = 1/4)96×56×56162921514935.4629.6785.301.90
192×28×281621436023263.0952.4366.462.44
384×14×141622440839543.5845.2549.983.24
768×7×71623286653245.0232.2748.303.35
Average-3274-39.91-2.73
" + }, + { + "type": "table_caption", + "bbox": [ + 0.103, + 0.385, + 0.866, + 0.4 + ], + "angle": 0, + "content": "Table 1. On-device FLOPS for different operations. PConv appears as an appealing choice for high FLOPS with reduced FLOPs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.471, + 0.489 + ], + "angle": 0, + "content": "latency/throughput are unaffordable. GConv and DWConv, despite their significant reduction in FLOPs, suffer from a drastic decrease in FLOPS. In addition, they tend to increase the number of channels to compensate for the performance drop, which, however, increase their latency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.497, + 0.43, + 0.513 + ], + "angle": 0, + "content": "4.2. PConv is effective together with PWConv" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.701 + ], + "angle": 0, + "content": "We next show that a PConv followed by a PWConv is effective in approximating a regular Conv to transform the feature maps. To this end, we first build four datasets by feeding the ImageNet-1k val split images into a pre-trained ResNet50, and extract the feature maps before and after the first Conv \\(3 \\times 3\\) in each of the four stages. Each feature map dataset is further spilt into the train \\((70\\%)\\), val \\((10\\%)\\), and test \\((20\\%)\\) subsets. We then build a simple network consisting of a PConv followed by a PWConv and train it on the feature map datasets with a mean squared error loss. For comparison, we also build and train networks for DWConv + PWConv and GConv + PWConv under the same setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.471, + 0.807 + ], + "angle": 0, + "content": "Tab. 2 shows that PConv + PWConv achieve the lowest test loss, meaning that they better approximate a regular Conv in feature transformation. The results also suggest that it is sufficient and efficient to capture spatial features from only a part of the feature maps. PConv shows a great potential to be the new go-to choice in designing fast and effective neural networks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.421, + 0.833 + ], + "angle": 0, + "content": "4.3. FasterNet on ImageNet-1k classification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To verify the effectiveness and efficiency of our FasterNet, we first conduct experiments on the large-scale ImageNet-1k classification dataset [46]. It covers 1k categories of common objects and contains about 1.3M la" + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.414, + 0.871, + 0.522 + ], + "angle": 0, + "content": "
StageDWConv+PWConvGConv+PWConv(16 groups)PConv+PWConvr = 1/4
10.00890.00650.0069
20.01580.01370.0136
30.02140.02020.0172
40.01300.01280.0115
Average0.01480.01330.0123
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.527, + 0.892, + 0.571 + ], + "angle": 0, + "content": "Table 2. A PConv followed by a PWConv well approximates the regular Conv \\(3 \\times 3\\) at different stages of a pre-trained ResNet50. PConv + PWConv together have the lowest test loss on average." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.854 + ], + "angle": 0, + "content": "beled images for training and 50k labeled images for validation. We train our models for 300 epochs using AdamW optimizer [38]. We set the batch size to 2048 for the FasterNet-M/L and 4096 for other variants. We use cosine learning rate scheduler [37] with a peak value of \\(0.001 \\cdot\\) batch size/1024 and a 20-epoch linear warmup. We apply commonly-used regularization and augmentation techniques, including Weight Decay [28], Stochastic Depth [24], Label Smoothing [52], Mixup [73], Cutmix [72] and Rand Augment [9], with varying magnitudes for different FasterNet variants. To reduce the training time, we use \\(192 \\times 192\\) resolution for the first 280 training epochs and \\(224 \\times 224\\) for the remaining 20 epochs. For fair comparison, we do not use knowledge distillation [19] and neural architecture search [79]. We report our top-1 accuracy on the validation set with a center crop at \\(224 \\times 224\\) resolution and a 0.9 crop ratio. Detailed training and validation settings are provided in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Fig. 7 and Tab. 3 demonstrate the superiority of our FasterNet over state-of-the-art classification models. The trade-off curves in Fig. 7 clearly show that FasterNet sets" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.52, + 0.938 + ], + "angle": 0, + "content": "12026" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.087, + 0.468, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.304, + 0.468, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.46, + 0.467, + 0.612 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.682 + ], + "angle": 0, + "content": "Figure 7. FasterNet has the highest efficiency in balancing accuracy-throughput and accuracy-latency trade-offs for different devices. To save space and make the plots more proportionate, we showcase network variants within a certain range of latency. Full plots can be found in the appendix, which show consistent results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.901 + ], + "angle": 0, + "content": "the new state-of-the-art in balancing accuracy and latency/throughput among all the networks examined. From another perspective, FasterNet runs faster than various CNN, ViT and MLP models on a wide range of devices, when having similar top-1 accuracy. As quantitatively shown in Tab. 3, FasterNet-T0 is \\(2.8 \\times 3.3 \\times\\) and \\(2.4 \\times\\) faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being \\(2.9\\%\\) more accurate. Our large FasterNet-L achieves \\(83.5\\%\\) top-1 accuracy, comparable to the emerging Swin-B [35] and ConvNeXt-B [36] while having \\(36\\%\\) and \\(28\\%\\) higher inference throughput on GPU, as well as saving \\(37\\%\\) and \\(15\\%\\) compute time on CPU. Given such promising results, we highlight that our FasterNet is" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.085, + 0.892, + 0.589 + ], + "angle": 0, + "content": "
NetworkParams (M)FLOPs (G)Throughput on GPU (fps) ↑Latency on CPU (ms) ↓Latency on ARM (ms) ↓Acc. (%)
ShuffleNetV2 ×1.5 [40]3.50.30487812.126672.6
MobileNetV2 [47]3.50.31419812.244272.0
MobileViT-XXS [42]1.30.42239330.834869.0
EdgeNeXt-XXS [41]1.30.26276515.723971.2
FasterNet-T03.90.3468079.214371.9
GhostNet ×1.3 [13]7.40.24298817.948175.7
ShuffleNetV2 ×2 [40]7.40.59333917.840374.9
MobileNetV2 ×1.4 [47]6.10.60271122.665074.7
MobileViT-XS [42]2.31.05139240.864874.8
EdgeNeXt-XS [41]2.30.54173824.443475.0
PVT-Tiny [65]13.21.94126655.670875.1
FasterNet-T17.60.85378217.728576.2
CycleMLP-B1 [5]15.22.10865116.189279.1
PoolFormer-S12 [71]11.91.82143949.066577.2
MobileViT-S [42]5.62.03103956.794178.4
EdgeNeXt-S [41]5.61.26112839.274379.4
ResNet50 [16, 36]25.64.1195973.0113178.8
FasterNet-T215.01.91199133.549778.9
CycleMLP-B2 [5]26.83.90528186.3150281.6
PoolFormer-S24 [71]21.43.4174892.8126180.3
PoolFormer-S36 [71]30.95.00507138.0186081.4
ConvNeXt-T [36]28.64.4765786.3188982.1
Swin-T [35]28.34.51609122.2142481.3
PVT-Small [65]24.53.8368989.6134579.8
PVT-Medium [65]44.26.69438143.6214281.2
FasterNet-S31.14.56102971.2110381.3
PoolFormer-M36 [71]56.28.80320215.0297982.1
ConvNeXt-S [36]50.28.71377153.2348483.1
Swin-S [35]49.68.77348224.2261383.0
PVT-Large [65]61.49.85306203.4310181.7
FasterNet-M53.58.74500129.5209283.0
PoolFormer-M48 [71]73.511.59242281.8OOM82.5
ConvNeXt-B [36]88.615.38253257.1OOM83.8
Swin-B [35]87.815.47237349.2OOM83.5
FasterNet-L93.515.52323219.5OOM83.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.677 + ], + "angle": 0, + "content": "Table 3. Comparison on ImageNet-1k benchmark. Models with similar top-1 accuracy are grouped together. For each group, our FasterNet achieves the highest throughput on GPU and the lowest latency on CPU and ARM. All models are evaluated at \\(224 \\times 224\\) resolution except for the MobileViT and EdgeNeXt with \\(256 \\times 256\\). OOM is short for out of memory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.892, + 0.743 + ], + "angle": 0, + "content": "much simpler than many other models in terms of architectural design, which showcases the feasibility of designing simple yet powerful neural networks." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.756, + 0.779, + 0.77 + ], + "angle": 0, + "content": "4.4. FasterNet on downstream tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To further evaluate the generalization ability of FasterNet, we conduct experiments on the challenging COCO dataset [32] for object detection and instance segmentation. As a common practice, we employ the ImageNet pre-trained FasterNet as a backbone and equip it with the popular Mask R-CNN detector [15]. To highlight the effectiveness of the backbone itself, we simply follow PoolFormer [71] and adopt an AdamW optimizer, a \\(1\\times\\) training" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "12027" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.851, + 0.296 + ], + "angle": 0, + "content": "
BackboneParams (M)FLOPs (G)Latency on GPU (ms)\\(AP^b\\)\\(AP_{50}^b\\)\\(AP_{75}^b\\)\\(AP^m\\)\\(AP_{50}^m\\)\\(AP_{75}^m\\)
ResNet50 [16]44.225354.938.058.641.434.455.136.7
PoolFormer-S24 [71]41.0233111.040.162.243.437.059.139.6
PVT-Small [65]44.123889.540.462.943.837.860.140.3
FasterNet-S49.025854.339.961.243.636.958.139.7
ResNet101 [16]63.232968.940.461.144.236.457.738.8
ResNeXt101-32×4d [69]62.833380.541.962.545.937.559.440.2
PoolFormer-S36 [71]50.5266146.941.063.144.837.760.140.0
PVT-Medium [65]63.9295117.342.064.445.639.061.642.1
FasterNet-M71.234471.443.064.447.439.161.542.3
ResNeXt101-64×4d [69]101.9487112.942.863.847.338.460.641.3
PVT-Large [65]81.0358152.242.965.046.639.561.942.5
FasterNet-L110.948493.844.065.648.239.962.343.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.085, + 0.3, + 0.882, + 0.314 + ], + "angle": 0, + "content": "Table 4. Results on COCO object detection and instance segmentation benchmarks. FLOPs are calculated with image size (1280, 800)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.33, + 0.47, + 0.535 + ], + "angle": 0, + "content": "
AblationVariantThroughput on GPU (fps)Latency on CPU (ms)Latency on ARM (ms)Acc. (%)
Partial ratioT0* w/ r = 1/266269.614571.7
T0 w/ r = 1/468079.214371.9
T0* w/ r = 1/862048.914071.3
NormalizationT0 w/ BN68079.214371.9
T0 w/ LN551510.715971.9
ActivationT0 w/ ReLU69298.211471.3
T0* w/ ReLU58669.314371.7
T0 w/ GELU68079.214371.9
T2 w/ ReLU199133.549778.9
T2 w/ GELU198535.455778.7
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.537, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Table 5. Ablation on the partial ratio, normalization, and activation of FasterNet. Rows highlighted in grey are the default settings. \\( \\mathrm{T0}^* \\) denotes T0 variants with modified network width and depth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.627 + ], + "angle": 0, + "content": "schedule (12 epochs), a batch size of 16, and other training settings without further hyper-parameter tuning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.469, + 0.779 + ], + "angle": 0, + "content": "Tab. 4 shows the results for comparison between FasterNet and representative models. FasterNet consistently outperforms ResNet and ResNext by having higher average precision (AP) with similar latency. Specifically, FasterNet-S yields \\(+1.9\\) higher box AP and \\(+2.4\\) higher mask AP compared to the standard baseline ResNet50. FasterNet is also competitive against the ViT variants. Under similar FLOPs, FasterNet-L reduces PVT-Large's latency by \\(38\\%\\), i.e., from \\(152.2\\mathrm{ms}\\) to \\(93.8\\mathrm{ms}\\) on GPU, and achieves \\(+1.1\\) higher box AP and \\(+0.4\\) higher mask AP." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.227, + 0.803 + ], + "angle": 0, + "content": "4.5. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.905 + ], + "angle": 0, + "content": "We conduct a brief ablation study on the value of partial ratio \\( r \\) and the choices of activation and normalization layers. We compare different variants in terms of ImageNet top-1 accuracy and on-device latency/throughput. Results are summarized in Tab. 5. For the partial ratio \\( r \\), we set it to \\( \\frac{1}{4} \\) for all FasterNet variants by default, which achieves" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.892, + 0.558 + ], + "angle": 0, + "content": "higher accuracy, higher throughput, and lower latency at similar complexity. A too large partial ratio \\( r \\) would make PConv degrade to a regular Conv, while a too small value would render PConv less effective in capturing the spatial features. For the normalization layers, we choose BatchNorm over LayerNorm because BatchNorm can be merged into its adjacent convolutional layers for faster inference while it is as effective as LayerNorm in our experiment. For the activation function, interestingly, we empirically found that GELU fits FasterNet-T0/T1 models more efficiently than ReLU. It, however, becomes opposite for FasterNet-T2/S/M/L. Here we only show two examples in Tab. 5 due to space constraint. We conjecture that GELU strengthens FasterNet-T0/T1 by having higher non-linearity, while the benefit fades away for larger FasterNet variants." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.619, + 0.592 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.83 + ], + "angle": 0, + "content": "In this paper, we have investigated the common and unresolved issue that many established neural networks suffer from low floating-point operations per second (FLOPS). We have revisited a bottleneck operator, DWConv, and analyzed its main cause for a slowdown - frequent memory access. To overcome the issue and achieve faster neural networks, we have proposed a simple yet fast and effective operator, PConv, that can be readily plugged into many existing networks. We have further introduced our general-purpose FasterNet, built upon our PConv, that achieves state-of-the-art speed and accuracy trade-off on various devices and vision tasks. We hope that our PConv and FasterNet would inspire more research on simple yet effective neural networks, going beyond academia to impact the industry and community directly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This work was supported, in part, by Hong Kong General Research Fund under grant number 16200120. The work of C.-H. 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Neural architecture search with reinforcement learning. arXiv preprint arXiv:1611.01578, 2016. 6" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.854 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.927, + 0.518, + 0.938 + ], + "angle": 0, + "content": "12031" + } + ] +] \ No newline at end of file diff --git a/2023/Run, Don't Walk_ Chasing Higher FLOPS for Faster Neural Networks/6a2198d1-cecd-4fd5-b373-fd2aeb690abb_origin.pdf b/2023/Run, Don't Walk_ Chasing Higher FLOPS for Faster Neural Networks/6a2198d1-cecd-4fd5-b373-fd2aeb690abb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e7a2f94bb46c96d947b6a60f5fe2e9b93135cf92 --- /dev/null +++ b/2023/Run, Don't Walk_ Chasing Higher FLOPS for Faster Neural Networks/6a2198d1-cecd-4fd5-b373-fd2aeb690abb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a7ad310892017e2f6407eb1484103c5e9c047b9cb693af5eddd3da32449bacd7 +size 886667 diff --git a/2023/Run, Don't Walk_ Chasing Higher FLOPS for Faster Neural Networks/full.md b/2023/Run, Don't Walk_ Chasing Higher FLOPS for Faster Neural Networks/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ea41af8ae420df826e7f216c53ab83499ed78c11 --- /dev/null +++ b/2023/Run, Don't Walk_ Chasing Higher FLOPS for Faster Neural Networks/full.md @@ -0,0 +1,338 @@ +# Run, Don’t Walk: Chasing Higher FLOPS for Faster Neural Networks + +Jierun Chen $^{1}$ , Shiu-hong Kao $^{1}$ , Hao He $^{1}$ +Weipeng Zhuo $^{1}$ , Song Wen $^{2}$ , Chul-Ho Lee $^{3}$ , S.-H. Gary Chan $^{1}$ $^{1}$ HKUST, $^{2}$ Rutgers University, $^{3}$ Texas State University + +# Abstract + +To design fast neural networks, many works have been focusing on reducing the number of floating-point operations (FLOPs). We observe that such reduction in FLOPs, however, does not necessarily lead to a similar level of reduction in latency. This mainly stems from inefficiently low floating-point operations per second (FLOPS). To achieve faster networks, we revisit popular operators and demonstrate that such low FLOPS is mainly due to frequent memory access of the operators, especially the depthwise convolution. We hence propose a novel partial convolution (PCnv) that extracts spatial features more efficiently, by cutting down redundant computation and memory access simultaneously. Building upon our PCnv, we further propose FasterNet, a new family of neural networks, which attains substantially higher running speed than others on a wide range of devices, without compromising on accuracy for various vision tasks. For example, on ImageNet-1k, our tiny FasterNet-T0 is $2.8 \times 3.3 \times$ and $2.4 \times$ faster than MobileViT-XXS on GPU, CPU, and ARM processors, respectively, while being $2.9\%$ more accurate. Our large FasterNet-L achieves impressive $83.5\%$ top-1 accuracy, on par with the emerging Swin-B, while having $36\%$ higher inference throughput on GPU, as well as saving $37\%$ compute time on CPU. Code is available at https://github.com/JierunChen/FasterNet. + +# 1. Introduction + +Neural networks have undergone rapid development in various computer vision tasks such as image classification, detection and segmentation. While their impressive performance has powered many applications, a roaring trend is to pursue fast neural networks with low latency and high throughput for great user experiences, instant responses, safety reasons, etc. + +How to be fast? Instead of asking for more costly computing devices, researchers and practitioners prefer to design cost-effective fast neural networks with reduced computational complexity, mainly measured in the number of + +![](images/c8cfeebc3fde8d06bfd86b330dae02078ebc45c79a1a14f32c35eaaaa1393820.jpg) +(a) Convolution + +![](images/1d015ffc47d7943c325b92090435436c20108bf9c1713ea630e73d7b6ad1b0b6.jpg) +(b) Depthwise/Group Convolution + +![](images/ef34393040525a2e7dacb9ed8654cc27ceb71d56a7f92940dd88d05170faf8d2.jpg) +(c) Partial Convolution (ours) +Figure 1. Our partial convolution (PConv) is fast and efficient by applying filters on only a few input channels while leaving the remaining ones untouched. PConv obtains lower FLOPs than the regular convolution and higher FLOPS than the depthwise/group convolution. + +Input/output +Filter +\*Convolution +$\rightarrow$ Identity + +floating-point operations (FLOPs) $^1$ . MobileNets [20, 21, 47], ShuffleNets [40, 76] and GhostNet [13], among others, leverage the depthwise convolution (DWConv) [48] and/or group convolution (GConv) [27] to extract spatial features. However, in the effort to reduce FLOPs, the operators often suffer from the side effect of increased memory access. MicroNet [29] further decomposes and sparsifies the network to push its FLOPs to an extremely low level. Despite its improvement in FLOPs, this approach experiences inefficient fragmented computation. Besides, the above networks are often accompanied by additional data manipulations, such as concatenation, shuffling, and pooling, whose running time tends to be significant for tiny models. + +Apart from the above pure convolutional neural networks (CNNs), there is an emerging interest in making vision transformers (ViTs) [11] and multilayer perceptrons (MLPs) architectures [57] smaller and faster. For example, MobileViTs [42, 43, 63] and MobileFormer [6] reduce the computational complexity by combining DWConv with a modified attention mechanism. However, they still suffer from the aforementioned issue with DWConv and also need dedicated hardware support for the modified attention mechanism. The use of advanced yet time-consuming nor + +![](images/bc689bdb3a1a6f8205702f0379a1f5c1f8be0e664dd4c0e302b8927ca1ec1b3b.jpg) + +![](images/bcfdc95e5623ea475b3f4225deff2acec6dc75fdab39cada93fdc6eb8e26e653.jpg) +(a) + +![](images/52013b4b7475c1d42f589de8b8dc903a733f7e78b03a0098e6384b5eb0496566.jpg) + +![](images/173d56cec53757d48dc7e1af33b12d573a1492f15e75fd81fcccb8649b4d37eb.jpg) +(b) +Figure 2. (a) FLOPS under varied FLOPs on CPU. Many existing neural networks suffer from low computational speed issues. Their effective FLOPS are lower than the popular ResNet50. By contrast, our FasterNet attains higher FLOPS. (b) Latency under varied FLOPs on CPU. Our FasterNet obtains lower latency than others with the same amount of FLOPs. + +malization and activation layers may also limit their speed on devices. + +All these issues together lead to the following question: Are these "fast" neural networks really fast? To answer this, we examine the relationship between latency and FLOPs, which is captured by + +$$ +L a t e n c y = \frac {F L O P s}{F L O P S}, \tag {1} +$$ + +where FLOPS is short for floating-point operations per second, as a measure of the effective computational speed. While there are many attempts to reduce FLOPs, they seldom consider optimizing FLOPS at the same time to achieve truly low latency. To better understand the situation, we compare the FLOPS of typical neural networks on an Intel CPU. The results in Fig. 2 show that many existing neural networks suffer from low FLOPS, and their FLOPS is generally lower than the popular ResNet50. With such low FLOPS, these "fast" neural networks are actually not fast enough. Their reduction in FLOPs cannot be translated into the exact amount of reduction in latency. In some cases, there is no improvement, and it even leads to worse latency. For example, CycleMLP-B1 [5] has half of FLOPs of ResNet50 [16] but runs more slowly (i.e., CycleMLP-B1 vs. ResNet50: 116.1ms vs. 73.0ms). Note that this discrepancy between FLOPs and latency has also been noticed in previous works [40, 42] but remains unresolved partially because they employ the DWConv/GConv and various data manipulations with low FLOPS. It is deemed there are no better alternatives available. + +This paper aims to eliminate the discrepancy by developing a simple yet fast and effective operator that maintains high FLOPS with reduced FLOPs. Specifically, we reexamine existing operators, particularly DWConv, in terms of the computational speed - FLOPS. We uncover that the main reason causing the low FLOPS issue is frequent memory access. We then propose a novel partial convolution (PCov) + +as a competitive alternative that reduces the computational redundancy as well as the number of memory access. Fig. 1 illustrates the design of our PConv. It takes advantage of redundancy within the feature maps and systematically applies a regular convolution (Conv) on only a part of the input channels while leaving the remaining ones untouched. By nature, PConv has lower FLOPs than the regular Conv while having higher FLOPS than the DWConv/GConv. In other words, PConv better exploits the on-device computational capacity. PConv is also effective in extracting spatial features as empirically validated later in the paper. + +We further introduce FasterNet, which is primarily built upon our PConv, as a new family of networks that run highly fast on various devices. In particular, our FasterNet achieves state-of-the-art performance for classification, detection, and segmentation tasks while having much lower latency and higher throughput. For example, our tiny FasterNet-T0 is $2.8 \times 3.3 \times$ and $2.4 \times$ faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being $2.9\%$ more accurate on ImageNet-1k. Our large FasterNet-L achieves $83.5\%$ top-1 accuracy, on par with the emerging Swin-B [35], while offering $36\%$ higher throughput on GPU and saving $37\%$ compute time on CPU. To summarize, our contributions are as follows: + +- We point out the importance of achieving higher FLOPS beyond simply reducing FLOPs for faster neural networks. +- We introduce a simple yet fast and effective operator called PConv, which has a high potential to replace the existing go-to choice, DWConv. +- We introduce FasterNet which runs favorably and universally fast on a variety of devices such as GPU, CPU, and ARM processors. +- We conduct extensive experiments on various tasks and validate the high speed and effectiveness of our PConv and FasterNet. + +# 2. Related Work + +We briefly review prior works on fast and efficient neural networks and differentiate this work from them. + +CNN. CNNs are the mainstream architecture in the computer vision field, especially when it comes to deployment in practice, where being fast is as important as being accurate. Though there have been numerous studies [7, 8, 17, 29, 48, 49, 75, 78] to achieve higher efficiency, the rationale behind them is more or less to perform a low-rank approximation. Specifically, the group convolution [27] and the depthwise separable convolution [48] (consisting of depthwise and pointwise convolutions) are probably the most popular ones. They have been widely adopted in mobile/edge-oriented networks, such as MobileNets [20, 21, 47], ShuffleNets [40, 76], GhostNet [13], EfficientNets [54, 55], TinyNet [14], Xception [8], CondenseNet [23, 70], TVConv [4], MnasNet [53], and FBNet [67]. While they exploit the redundancy in filters to reduce the number of parameters and FLOPs, they suffer from increased memory access when increasing the network width to compensate for the accuracy drop. By contrast, we consider the redundancy in feature maps and propose a partial convolution to reduce FLOPs and memory access simultaneously. + +ViT, MLP, and variants. There is a growing interest in studying ViT ever since Dosovitskiy et al. [11] expanded the application scope of transformers [62] from machine translation [62] or forecasting [66] to the computer vision field. Many follow-up works have attempted to improve ViT in terms of training setting [51, 58, 59] and model design [12, 34, 35, 65, 77]. One notable trend is to pursue a better accuracy-latency trade-off by reducing the complexity of the attention operator [1, 25, 39, 56, 61], incorporating convolution into ViTs [6, 10, 50], or doing both [3, 30, 43, 45]. Besides, other studies [5, 31, 57] propose to replace the attention with simple MLP-based operators. However, they often evolve to be CNN-like [33]. In this paper, we focus on analyzing the convolution operations, particularly DWConv, due to the following reasons: First, the advantage of attention over convolution is unclear or debatable [36, 64]. Second, the attention-based mechanism generally runs slower than its convolutional counterparts and thus becomes less favorable for the current industry [22, 42]. Finally, DW-Conv is still a popular choice in many hybrid models, so it is worth a careful examination. + +# 3. Design of PConv and FasterNet + +In this section, we first revisit DWConv and analyze the issue with its frequent memory access. We then introduce PConv as a competitive alternative operator to resolve the issue. After that, we introduce FasterNet and explain its + +![](images/43b8b037deb68c10cea574d7d56f635729de216ab6d0f26d1b74b15ba6828430.jpg) +Figure 3. Visualization of feature maps in an intermediate layer of a pre-trained ResNet50, with the top-left image as the input. Qualitatively, we can see the high redundancies across different channels. + +details, including design considerations. + +# 3.1. Preliminary + +DWConv is a popular variant of Conv and has been widely adopted as a key building block for many neural networks. For an input $\mathbf{I} \in \mathbb{R}^{c \times h \times w}$ , DWConv applies $c$ filters $\mathbf{W} \in \mathbb{R}^{k \times k}$ to compute the output $\mathbf{O} \in \mathbb{R}^{c \times h \times w}$ . As shown in Fig. 1(b), each filter slides spatially on one input channel and contributes to one output channel. This depthwise computation makes DWConv have as low FLOPs as $h \times w \times k^2 \times c$ compared to a regular Conv with $h \times w \times k^2 \times c^2$ . While effective in reducing FLOPs, a DWConv, which is typically followed by a pointwise convolution, or PWConv, cannot be simply used to replace a regular Conv as it would incur a severe accuracy drop. Thus, in practice the channel number $c$ (or the network width) of DWConv is increased to $c'(c' > c)$ to compensate the accuracy drop, e.g., the width is expanded by six times for the DWConv in the inverted residual blocks [47]. This, however, results in much higher memory access that can cause non-negligible delay and slow down the overall computation, especially for I/O-bound devices. In particular, the number of memory access now escalates to + +$$ +h \times w \times 2 c ^ {\prime} + k ^ {2} \times c ^ {\prime} \approx h \times w \times 2 c ^ {\prime}, \tag {2} +$$ + +which is higher than that of a regular Conv, i.e., + +$$ +h \times w \times 2 c + k ^ {2} \times c ^ {2} \approx h \times w \times 2 c. \tag {3} +$$ + +Note that the $h \times w \times 2c'$ memory access is spent on the I/O operation, which is deemed to be already the minimum cost and hard to optimize further. + +# 3.2. Partial convolution as a basic operator + +We below demonstrate that the cost can be further optimized by leveraging the feature maps' redundancy. As visualized in Fig. 3, the feature maps share high similarities among different channels. This redundancy has also + +been covered in many other works [13, 74], but few of them make full use of it in a simple yet effective way. + +Specifically, we propose a simple PConv to reduce computational redundancy and memory access simultaneously. The bottom-left corner in Fig. 4 illustrates how our PConv works. It simply applies a regular Conv on only a part of the input channels for spatial feature extraction and leaves the remaining channels untouched. For contiguous or regular memory access, we consider the first or last consecutive $c_p$ channels as the representatives of the whole feature maps for computation. Without loss of generality, we consider the input and output feature maps to have the same number of channels. Therefore, the FLOPs of a PConv are only + +$$ +h \times w \times k ^ {2} \times c _ {p} ^ {2}. \tag {4} +$$ + +With a typical partial ratio $r = \frac{c_p}{c} = \frac{1}{4}$ , the FLOPs of a PConv is only $\frac{1}{16}$ of a regular Conv. Besides, PConv has a smaller amount of memory access, i.e., + +$$ +h \times w \times 2 c _ {p} + k ^ {2} \times c _ {p} ^ {2} \approx h \times w \times 2 c _ {p}, \tag {5} +$$ + +which is only $\frac{1}{4}$ of a regular Conv for $r = \frac{1}{4}$ . + +Since there are only $c_p$ channels utilized for spatial feature extraction, one may ask if we can simply remove the remaining $(c - c_p)$ channels? If so, PConv would degrade to a regular Conv with fewer channels, which deviates from our objective to reduce redundancy. Note that we keep the remaining channels untouched instead of removing them from the feature maps. It is because they are useful for a subsequent PWConv layer, which allows the feature information to flow through all channels. + +# 3.3. PConv followed by PWConv + +To fully and efficiently leverage the information from all channels, we further append a pointwise convolution (PW-Conv) to our PConv. Their effective receptive field together on the input feature maps looks like a T-shaped Conv, which focuses more on the center position compared to a regular Conv uniformly processing a patch, as shown in Fig. 5. To justify this T-shaped receptive field, we first evaluate the importance of each position by calculating the position-wise Frobenius norm. We assume that a position tends to be more important if it has a larger Frobenius norm than other positions. For a regular Conv filter $\mathbf{F} \in \mathbb{R}^{k^2 \times c}$ , the Frobenius norm at position $i$ is calculated by $\| \mathbf{F}_i \| = \sqrt{\sum_{j=1}^{c} |f_{ij}|^2}$ , for $i = 1, 2, 3\ldots, k^2$ . We consider a salient position to be the one with the maximum Frobenius norm. We then collectively examine each filter in a pre-trained ResNet18, find out their salient positions, and plot a histogram of the salient positions. Results in Fig. 6 show that the center position turns out to be the salient position most frequently among the filters. In other words, the center position weighs more + +than its surrounding neighbors. This is consistent with the T-shaped computation which concentrates on the center position. + +While the T-shaped Conv can be directly used for efficient computation, we show that it is better to decompose the T-shaped Conv into a PConv and a PWConv because the decomposition exploits the inter-filter redundancy and further saves FLOPs. For the same input $\mathbf{I} \in \mathbb{R}^{c \times h \times w}$ and output $\mathbf{O} \in \mathbb{R}^{c \times h \times w}$ , a T-shaped Conv's FLOPs can be calculated as + +$$ +h \times w \times \left(k ^ {2} \times c _ {p} \times c + c \times \left(c - c _ {p}\right)\right), \tag {6} +$$ + +which is higher than the FLOPs of a PConv and a PWConv, i.e., + +$$ +h \times w \times \left(k ^ {2} \times c _ {p} ^ {2} + c \times c _ {p}\right), \tag {7} +$$ + +where $c > c_p$ and $c - c_p > c_p$ (e.g. when $c_p = \frac{c}{4}$ ). Besides, we can readily leverage the regular Conv for the two-step implementation. + +# 3.4. FasterNet as a general backbone + +Given our novel PConv and off-the-shelf PWConv as the primary building operators, we further propose FasterNet, a new family of neural networks that runs favorably fast and is highly effective for many vision tasks. We aim to keep the architecture as simple as possible, without bells and whistles, to make it hardware-friendly in general. + +We present the overall architecture in Fig. 4. It has four hierarchical stages, each of which is preceded by an embedding layer (a regular Conv $4 \times 4$ with stride 4) or a merging layer (a regular Conv $2 \times 2$ with stride 2) for spatial downsampling and channel number expanding. Each stage has a stack of FasterNet blocks. We observe that the blocks in the last two stages consume less memory access and tend to have higher FLOPS, as empirically validated in Tab. 1. Thus, we put more FasterNet blocks and correspondingly assign more computations to the last two stages. Each FasterNet block has a PConv layer followed by two PWConv (or Conv $1 \times 1$ ) layers. Together, they appear as inverted residual blocks where the middle layer has an expanded number of channels, and a shortcut connection is placed to reuse the input features. + +In addition to the above operators, the normalization and activation layers are also indispensable for high-performing neural networks. Many prior works [13, 16, 47], however, overuse such layers throughout the network, which may limit the feature diversity and thus hurt the performance. It can also slow down the overall computation. By contrast, we put them only after each middle PWConv to preserve the feature diversity and achieve lower latency. Besides, we use the batch normalization (BN) [26] instead of other alternative ones [2, 60, 68]. The benefit of BN is that it can be merged into its adjacent Conv layers for faster inference + +![](images/4cbebcfcba214df5a0773b9aac408ea26fe033a4af1473a805836ce83676b38c.jpg) + +![](images/70be33816e6e05deda16ab9e60a97129c8caba1c4290915d28b7400b1ac8fd84.jpg) +(a) PConv + PWConv + +![](images/1cc9a62bb3d40acb040421f220c81886e43d4bbeade06a31e06c9d39b0107c51.jpg) +(b) T-shaped Conv + +![](images/fb412d9f49483344d931ecb60a4c7b368f1ddac0868fdaca07ac7ead2459edc1.jpg) +(c) regular Conv +Figure 5. Comparison of convolutional variants. A PConv followed by a PWConv (a) resembles a T-shaped Conv (b), which spends more computation on the center position compared to a regular Conv (c). + +while being as effective as the others. As for the activation layers, we empirically choose GELU [18] for smaller FasterNet variants and ReLU [44] for bigger FasterNet variants, considering both running time and effectiveness. The last three layers, i.e. a global average pooling, a Conv $1 \times 1$ , and a fully-connected layer, are used together for feature transformation and classification. + +To serve a wide range of applications under different computational budgets, we provide tiny, small, medium, and large variants of FasterNet, referred to as FasterNet-T0/1/2, FasterNet-S, FasterNet-M, and FasterNet-L, respectively. They share a similar architecture but vary in depth and width. Detailed architecture specifications are provided in the appendix. + +# 4. Experimental Results + +We first examine the computational speed of our PConv and its effectiveness when combined with a PWConv. We then comprehensively evaluate the performance of our FasterNet for classification, detection, and segmentation tasks. Finally, we conduct a brief ablation study. + +To benchmark the latency and throughput, we choose the following three typical processors, which cover a wide + +![](images/c3e91ad083f5845c8ed7743c6664f13f9076194653b00f9c257d1e8f0f658866.jpg) +Figure 4. Overall architecture of our FasterNet. It has four hierarchical stages, each with a stack of FasterNet blocks and preceded by an embedding or merging layer. The last three layers are used for feature classification. Within each FasterNet block, a PConv layer is followed by two PWConv layers. We put normalization and activation layers only after the middle layer to preserve the feature diversity and achieve lower latency. +Figure 6. Histogram of salient position distribution for the regular Conv $3 \times 3$ filters in a pre-trained ResNet18. The histogram contains four kinds of bars, corresponding to different stages in the network. In all stages, the center position (position 5) appears as a salient position most frequently. + +range of computational capacity: GPU (2080Ti), CPU (Intel i9-9900X, using a single thread), and ARM (Cortex-A72, using a single thread). We report their latency for inputs with a batch size of 1 and throughput for inputs with a batch size of 32. During inference, the BN layers are merged to their adjacent layers wherever applicable. + +# 4.1. PConv is fast with high FLOPS + +We below show that our PConv is fast and better exploits the on-device computational capacity. Specifically, we stack 10 layers of pure PConv and take feature maps of typical dimensions as inputs. We then measure FLOPs and latency/throughput on GPU, CPU, and ARM processors, which also allow us to further compute FLOPS. We repeat the same procedure for other convolutional variants and make comparisons. + +Results in Tab. 1 show that PConv is overall an appealing choice for high FLOPS with reduced FLOPs. It has only $\frac{1}{16}$ FLOPs of a regular Conv and achieves $10.5\times$ , $6.2\times$ , and $22.8\times$ higher FLOPS than the DWConv on GPU, CPU, and ARM, respectively. We are unsurprised to see that the regular Conv has the highest FLOPS as it has been constantly optimized for years. However, its total FLOPs and + +
OperatorFeature map sizeFLOPs (M), ×10 layersGPU Throughput (fps)FLOPS (G/s)CPU Latency (ms)FLOPS (G/s)ARM Latency (ms)FLOPS (G/s)
Conv 3×396×56×5626013010782435.6772.90779.573.33
192×28×28260148931271728.4191.53619.644.19
384×14×14260145581185431.8581.66595.094.37
768×7×726013159821262.7141.47662.173.92
Average-10151-71.89-3.95
GConv 3×3 (16 groups)96×56×56162288846921.907.42166.300.97
192×28×281621081117547.5821.4496.221.68
384×14×141621553425144.4036.8863.572.55
768×7×71621600025984.2837.9765.202.49
Average-1833-25.93-1.92
DWConv 3×396×56×5627.09119403233.597.52108.700.24
192×28×2813.54233583151.976.8682.010.16
384×14×146.77463773131.066.3594.890.07
768×7×73.38888893020.684.93150.890.02
Average-313-6.42-0.12
PConv 3×3 (ours, with r = 1/4)96×56×56162921514935.4629.6785.301.90
192×28×281621436023263.0952.4366.462.44
384×14×141622440839543.5845.2549.983.24
768×7×71623286653245.0232.2748.303.35
Average-3274-39.91-2.73
+ +latency/throughput are unaffordable. GConv and DWConv, despite their significant reduction in FLOPs, suffer from a drastic decrease in FLOPS. In addition, they tend to increase the number of channels to compensate for the performance drop, which, however, increase their latency. + +# 4.2. PConv is effective together with PWConv + +We next show that a PConv followed by a PWConv is effective in approximating a regular Conv to transform the feature maps. To this end, we first build four datasets by feeding the ImageNet-1k val split images into a pre-trained ResNet50, and extract the feature maps before and after the first Conv $3 \times 3$ in each of the four stages. Each feature map dataset is further spilt into the train $(70\%)$ , val $(10\%)$ , and test $(20\%)$ subsets. We then build a simple network consisting of a PConv followed by a PWConv and train it on the feature map datasets with a mean squared error loss. For comparison, we also build and train networks for DWConv + PWConv and GConv + PWConv under the same setting. + +Tab. 2 shows that PConv + PWConv achieve the lowest test loss, meaning that they better approximate a regular Conv in feature transformation. The results also suggest that it is sufficient and efficient to capture spatial features from only a part of the feature maps. PConv shows a great potential to be the new go-to choice in designing fast and effective neural networks. + +# 4.3. FasterNet on ImageNet-1k classification + +To verify the effectiveness and efficiency of our FasterNet, we first conduct experiments on the large-scale ImageNet-1k classification dataset [46]. It covers 1k categories of common objects and contains about 1.3M la + +Table 1. On-device FLOPS for different operations. PConv appears as an appealing choice for high FLOPS with reduced FLOPs. + +
StageDWConv+PWConvGConv+PWConv(16 groups)PConv+PWConvr = 1/4
10.00890.00650.0069
20.01580.01370.0136
30.02140.02020.0172
40.01300.01280.0115
Average0.01480.01330.0123
+ +Table 2. A PConv followed by a PWConv well approximates the regular Conv $3 \times 3$ at different stages of a pre-trained ResNet50. PConv + PWConv together have the lowest test loss on average. + +beled images for training and 50k labeled images for validation. We train our models for 300 epochs using AdamW optimizer [38]. We set the batch size to 2048 for the FasterNet-M/L and 4096 for other variants. We use cosine learning rate scheduler [37] with a peak value of $0.001 \cdot$ batch size/1024 and a 20-epoch linear warmup. We apply commonly-used regularization and augmentation techniques, including Weight Decay [28], Stochastic Depth [24], Label Smoothing [52], Mixup [73], Cutmix [72] and Rand Augment [9], with varying magnitudes for different FasterNet variants. To reduce the training time, we use $192 \times 192$ resolution for the first 280 training epochs and $224 \times 224$ for the remaining 20 epochs. For fair comparison, we do not use knowledge distillation [19] and neural architecture search [79]. We report our top-1 accuracy on the validation set with a center crop at $224 \times 224$ resolution and a 0.9 crop ratio. Detailed training and validation settings are provided in the appendix. + +Fig. 7 and Tab. 3 demonstrate the superiority of our FasterNet over state-of-the-art classification models. The trade-off curves in Fig. 7 clearly show that FasterNet sets + +![](images/815b3c3a86d1a130a402adcae33bb24083901f97882f97150fb926cc712b2e97.jpg) + +![](images/9ee0963af0ff702c4f7440623b2fef107742aa7aa992df772c6ff8f22d9f3054.jpg) + +![](images/5959c7303514d8b8e2d1673f69f30c473f3e2009cb5c8ddc69a8bd14351a9e35.jpg) +Figure 7. FasterNet has the highest efficiency in balancing accuracy-throughput and accuracy-latency trade-offs for different devices. To save space and make the plots more proportionate, we showcase network variants within a certain range of latency. Full plots can be found in the appendix, which show consistent results. + +the new state-of-the-art in balancing accuracy and latency/throughput among all the networks examined. From another perspective, FasterNet runs faster than various CNN, ViT and MLP models on a wide range of devices, when having similar top-1 accuracy. As quantitatively shown in Tab. 3, FasterNet-T0 is $2.8 \times 3.3 \times$ and $2.4 \times$ faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being $2.9\%$ more accurate. Our large FasterNet-L achieves $83.5\%$ top-1 accuracy, comparable to the emerging Swin-B [35] and ConvNeXt-B [36] while having $36\%$ and $28\%$ higher inference throughput on GPU, as well as saving $37\%$ and $15\%$ compute time on CPU. Given such promising results, we highlight that our FasterNet is + +
NetworkParams (M)FLOPs (G)Throughput on GPU (fps) ↑Latency on CPU (ms) ↓Latency on ARM (ms) ↓Acc. (%)
ShuffleNetV2 ×1.5 [40]3.50.30487812.126672.6
MobileNetV2 [47]3.50.31419812.244272.0
MobileViT-XXS [42]1.30.42239330.834869.0
EdgeNeXt-XXS [41]1.30.26276515.723971.2
FasterNet-T03.90.3468079.214371.9
GhostNet ×1.3 [13]7.40.24298817.948175.7
ShuffleNetV2 ×2 [40]7.40.59333917.840374.9
MobileNetV2 ×1.4 [47]6.10.60271122.665074.7
MobileViT-XS [42]2.31.05139240.864874.8
EdgeNeXt-XS [41]2.30.54173824.443475.0
PVT-Tiny [65]13.21.94126655.670875.1
FasterNet-T17.60.85378217.728576.2
CycleMLP-B1 [5]15.22.10865116.189279.1
PoolFormer-S12 [71]11.91.82143949.066577.2
MobileViT-S [42]5.62.03103956.794178.4
EdgeNeXt-S [41]5.61.26112839.274379.4
ResNet50 [16, 36]25.64.1195973.0113178.8
FasterNet-T215.01.91199133.549778.9
CycleMLP-B2 [5]26.83.90528186.3150281.6
PoolFormer-S24 [71]21.43.4174892.8126180.3
PoolFormer-S36 [71]30.95.00507138.0186081.4
ConvNeXt-T [36]28.64.4765786.3188982.1
Swin-T [35]28.34.51609122.2142481.3
PVT-Small [65]24.53.8368989.6134579.8
PVT-Medium [65]44.26.69438143.6214281.2
FasterNet-S31.14.56102971.2110381.3
PoolFormer-M36 [71]56.28.80320215.0297982.1
ConvNeXt-S [36]50.28.71377153.2348483.1
Swin-S [35]49.68.77348224.2261383.0
PVT-Large [65]61.49.85306203.4310181.7
FasterNet-M53.58.74500129.5209283.0
PoolFormer-M48 [71]73.511.59242281.8OOM82.5
ConvNeXt-B [36]88.615.38253257.1OOM83.8
Swin-B [35]87.815.47237349.2OOM83.5
FasterNet-L93.515.52323219.5OOM83.5
+ +Table 3. Comparison on ImageNet-1k benchmark. Models with similar top-1 accuracy are grouped together. For each group, our FasterNet achieves the highest throughput on GPU and the lowest latency on CPU and ARM. All models are evaluated at $224 \times 224$ resolution except for the MobileViT and EdgeNeXt with $256 \times 256$ . OOM is short for out of memory. + +much simpler than many other models in terms of architectural design, which showcases the feasibility of designing simple yet powerful neural networks. + +# 4.4. FasterNet on downstream tasks + +To further evaluate the generalization ability of FasterNet, we conduct experiments on the challenging COCO dataset [32] for object detection and instance segmentation. As a common practice, we employ the ImageNet pre-trained FasterNet as a backbone and equip it with the popular Mask R-CNN detector [15]. To highlight the effectiveness of the backbone itself, we simply follow PoolFormer [71] and adopt an AdamW optimizer, a $1\times$ training + +
BackboneParams (M)FLOPs (G)Latency on GPU (ms)\(AP^b\)\(AP_{50}^b\)\(AP_{75}^b\)\(AP^m\)\(AP_{50}^m\)\(AP_{75}^m\)
ResNet50 [16]44.225354.938.058.641.434.455.136.7
PoolFormer-S24 [71]41.0233111.040.162.243.437.059.139.6
PVT-Small [65]44.123889.540.462.943.837.860.140.3
FasterNet-S49.025854.339.961.243.636.958.139.7
ResNet101 [16]63.232968.940.461.144.236.457.738.8
ResNeXt101-32×4d [69]62.833380.541.962.545.937.559.440.2
PoolFormer-S36 [71]50.5266146.941.063.144.837.760.140.0
PVT-Medium [65]63.9295117.342.064.445.639.061.642.1
FasterNet-M71.234471.443.064.447.439.161.542.3
ResNeXt101-64×4d [69]101.9487112.942.863.847.338.460.641.3
PVT-Large [65]81.0358152.242.965.046.639.561.942.5
FasterNet-L110.948493.844.065.648.239.962.343.0
+ +Table 4. Results on COCO object detection and instance segmentation benchmarks. FLOPs are calculated with image size (1280, 800). + +
AblationVariantThroughput on GPU (fps)Latency on CPU (ms)Latency on ARM (ms)Acc. (%)
Partial ratioT0* w/ r = 1/266269.614571.7
T0 w/ r = 1/468079.214371.9
T0* w/ r = 1/862048.914071.3
NormalizationT0 w/ BN68079.214371.9
T0 w/ LN551510.715971.9
ActivationT0 w/ ReLU69298.211471.3
T0* w/ ReLU58669.314371.7
T0 w/ GELU68079.214371.9
T2 w/ ReLU199133.549778.9
T2 w/ GELU198535.455778.7
+ +Table 5. Ablation on the partial ratio, normalization, and activation of FasterNet. Rows highlighted in grey are the default settings. $\mathrm{T0}^*$ denotes T0 variants with modified network width and depth. + +schedule (12 epochs), a batch size of 16, and other training settings without further hyper-parameter tuning. + +Tab. 4 shows the results for comparison between FasterNet and representative models. FasterNet consistently outperforms ResNet and ResNext by having higher average precision (AP) with similar latency. Specifically, FasterNet-S yields $+1.9$ higher box AP and $+2.4$ higher mask AP compared to the standard baseline ResNet50. FasterNet is also competitive against the ViT variants. Under similar FLOPs, FasterNet-L reduces PVT-Large's latency by $38\%$ , i.e., from $152.2\mathrm{ms}$ to $93.8\mathrm{ms}$ on GPU, and achieves $+1.1$ higher box AP and $+0.4$ higher mask AP. + +# 4.5. Ablation study + +We conduct a brief ablation study on the value of partial ratio $r$ and the choices of activation and normalization layers. We compare different variants in terms of ImageNet top-1 accuracy and on-device latency/throughput. Results are summarized in Tab. 5. For the partial ratio $r$ , we set it to $\frac{1}{4}$ for all FasterNet variants by default, which achieves + +higher accuracy, higher throughput, and lower latency at similar complexity. A too large partial ratio $r$ would make PConv degrade to a regular Conv, while a too small value would render PConv less effective in capturing the spatial features. For the normalization layers, we choose BatchNorm over LayerNorm because BatchNorm can be merged into its adjacent convolutional layers for faster inference while it is as effective as LayerNorm in our experiment. For the activation function, interestingly, we empirically found that GELU fits FasterNet-T0/T1 models more efficiently than ReLU. It, however, becomes opposite for FasterNet-T2/S/M/L. Here we only show two examples in Tab. 5 due to space constraint. We conjecture that GELU strengthens FasterNet-T0/T1 by having higher non-linearity, while the benefit fades away for larger FasterNet variants. + +# 5. Conclusion + +In this paper, we have investigated the common and unresolved issue that many established neural networks suffer from low floating-point operations per second (FLOPS). We have revisited a bottleneck operator, DWConv, and analyzed its main cause for a slowdown - frequent memory access. To overcome the issue and achieve faster neural networks, we have proposed a simple yet fast and effective operator, PConv, that can be readily plugged into many existing networks. We have further introduced our general-purpose FasterNet, built upon our PConv, that achieves state-of-the-art speed and accuracy trade-off on various devices and vision tasks. 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While their impressive performance has powered many applications, a roaring trend is to pursue fast neural networks with low latency and high throughput for great user experiences, instant responses, safety reasons, etc." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "How to be fast? Instead of asking for more costly computing devices, researchers and practitioners prefer to design cost-effective fast neural networks with reduced computational complexity, mainly measured in the number of" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 212, + 424, + 255 + ], + "blocks": [ + { + "bbox": [ + 307, + 212, + 424, + 255 + ], + "lines": [ + { + "bbox": [ + 307, + 212, + 424, + 255 + ], + "spans": [ + { + "bbox": [ + 307, + 212, + 424, + 255 + ], + "type": "image", + "image_path": "c8cfeebc3fde8d06bfd86b330dae02078ebc45c79a1a14f32c35eaaaa1393820.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 256, + 382, + 265 + ], + "lines": [ + { + "bbox": [ + 332, + 256, + 382, + 265 + ], + "spans": [ + { + "bbox": [ + 332, + 256, + 382, + 265 + ], + "type": "text", + "content": "(a) Convolution" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 429, + 212, + 545, + 255 + ], + "blocks": [ + { + "bbox": [ + 429, + 212, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 429, + 212, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 429, + 212, + 545, + 255 + ], + "type": "image", + "image_path": "1d015ffc47d7943c325b92090435436c20108bf9c1713ea630e73d7b6ad1b0b6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 256, + 537, + 266 + ], + "lines": [ + { + "bbox": [ + 432, + 256, + 537, + 266 + ], + "spans": [ + { + "bbox": [ + 432, + 256, + 537, + 266 + ], + "type": "text", + "content": "(b) Depthwise/Group Convolution" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 335, + 273, + 451, + 311 + ], + "blocks": [ + { + "bbox": [ + 335, + 273, + 451, + 311 + ], + "lines": [ + { + "bbox": [ + 335, + 273, + 451, + 311 + ], + "spans": [ + { + "bbox": [ + 335, + 273, + 451, + 311 + ], + "type": "image", + "image_path": "ef34393040525a2e7dacb9ed8654cc27ceb71d56a7f92940dd88d05170faf8d2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 312, + 443, + 322 + ], + "lines": [ + { + "bbox": [ + 345, + 312, + 443, + 322 + ], + "spans": [ + { + "bbox": [ + 345, + 312, + 443, + 322 + ], + "type": "text", + "content": "(c) Partial Convolution (ours)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 328, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 304, + 328, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 547, + 383 + ], + "type": "text", + "content": "Figure 1. Our partial convolution (PConv) is fast and efficient by applying filters on only a few input channels while leaving the remaining ones untouched. PConv obtains lower FLOPs than the regular convolution and higher FLOPS than the depthwise/group convolution." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 471, + 285, + 522, + 319 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 471, + 285, + 522, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 471, + 285, + 522, + 293 + ], + "spans": [ + { + "bbox": [ + 471, + 285, + 522, + 293 + ], + "type": "text", + "content": "Input/output" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 471, + 294, + 501, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 471, + 294, + 501, + 301 + ], + "spans": [ + { + "bbox": [ + 471, + 294, + 501, + 301 + ], + "type": "text", + "content": "Filter" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 471, + 302, + 522, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 471, + 302, + 522, + 310 + ], + "spans": [ + { + "bbox": [ + 471, + 302, + 522, + 310 + ], + "type": "text", + "content": "\\*Convolution" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 471, + 311, + 507, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 471, + 311, + 507, + 319 + ], + "spans": [ + { + "bbox": [ + 471, + 311, + 507, + 319 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 471, + 311, + 507, + 319 + ], + "type": "text", + "content": " Identity" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "text", + "content": "floating-point operations (FLOPs)" + }, + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "text", + "content": ". MobileNets [20, 21, 47], ShuffleNets [40, 76] and GhostNet [13], among others, leverage the depthwise convolution (DWConv) [48] and/or group convolution (GConv) [27] to extract spatial features. However, in the effort to reduce FLOPs, the operators often suffer from the side effect of increased memory access. MicroNet [29] further decomposes and sparsifies the network to push its FLOPs to an extremely low level. Despite its improvement in FLOPs, this approach experiences inefficient fragmented computation. Besides, the above networks are often accompanied by additional data manipulations, such as concatenation, shuffling, and pooling, whose running time tends to be significant for tiny models." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 560, + 545, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 560, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 560, + 545, + 681 + ], + "type": "text", + "content": "Apart from the above pure convolutional neural networks (CNNs), there is an emerging interest in making vision transformers (ViTs) [11] and multilayer perceptrons (MLPs) architectures [57] smaller and faster. For example, MobileViTs [42, 43, 63] and MobileFormer [6] reduce the computational complexity by combining DWConv with a modified attention mechanism. However, they still suffer from the aforementioned issue with DWConv and also need dedicated hardware support for the modified attention mechanism. The use of advanced yet time-consuming nor" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 547, + 713 + ], + "type": "text", + "content": "1We follow a widely adopted definition of FLOPs, as the number of multiply-adds [36, 76]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "12021" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 124, + 190 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 124, + 190 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 124, + 190 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 124, + 190 + ], + "type": "image", + "image_path": "bc689bdb3a1a6f8205702f0379a1f5c1f8be0e664dd4c0e302b8927ca1ec1b3b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 126, + 70, + 267, + 206 + ], + "blocks": [ + { + "bbox": [ + 126, + 70, + 267, + 206 + ], + "lines": [ + { + "bbox": [ + 126, + 70, + 267, + 206 + ], + "spans": [ + { + "bbox": [ + 126, + 70, + 267, + 206 + ], + "type": "image", + "image_path": "bcfdc95e5623ea475b3f4225deff2acec6dc75fdab39cada93fdc6eb8e26e653.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 196, + 208, + 207, + 217 + ], + "lines": [ + { + "bbox": [ + 196, + 208, + 207, + 217 + ], + "spans": [ + { + "bbox": [ + 196, + 208, + 207, + 217 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 273, + 72, + 397, + 191 + ], + "blocks": [ + { + "bbox": [ + 273, + 72, + 397, + 191 + ], + "lines": [ + { + "bbox": [ + 273, + 72, + 397, + 191 + ], + "spans": [ + { + "bbox": [ + 273, + 72, + 397, + 191 + ], + "type": "image", + "image_path": "52013b4b7475c1d42f589de8b8dc903a733f7e78b03a0098e6384b5eb0496566.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 397, + 72, + 545, + 208 + ], + "blocks": [ + { + "bbox": [ + 397, + 72, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 397, + 72, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 397, + 72, + 545, + 208 + ], + "type": "image", + "image_path": "173d56cec53757d48dc7e1af33b12d573a1492f15e75fd81fcccb8649b4d37eb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 410, + 208, + 422, + 217 + ], + "lines": [ + { + "bbox": [ + 410, + 208, + 422, + 217 + ], + "spans": [ + { + "bbox": [ + 410, + 208, + 422, + 217 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 217, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 45, + 217, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 45, + 217, + 547, + 251 + ], + "type": "text", + "content": "Figure 2. (a) FLOPS under varied FLOPs on CPU. Many existing neural networks suffer from low computational speed issues. Their effective FLOPS are lower than the popular ResNet50. By contrast, our FasterNet attains higher FLOPS. (b) Latency under varied FLOPs on CPU. Our FasterNet obtains lower latency than others with the same amount of FLOPs." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 267, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 267, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 287, + 290 + ], + "type": "text", + "content": "malization and activation layers may also limit their speed on devices." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 291, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 287, + 339 + ], + "type": "text", + "content": "All these issues together lead to the following question: Are these \"fast\" neural networks really fast? To answer this, we examine the relationship between latency and FLOPs, which is captured by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 119, + 347, + 287, + 372 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 347, + 287, + 372 + ], + "spans": [ + { + "bbox": [ + 119, + 347, + 287, + 372 + ], + "type": "interline_equation", + "content": "L a t e n c y = \\frac {F L O P s}{F L O P S}, \\tag {1}", + "image_path": "ad3bcb2cbd2b90843ad82b03f10ff56f350a2bb85fcf88ffad5784296d2f058a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 378, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 628 + ], + "type": "text", + "content": "where FLOPS is short for floating-point operations per second, as a measure of the effective computational speed. While there are many attempts to reduce FLOPs, they seldom consider optimizing FLOPS at the same time to achieve truly low latency. To better understand the situation, we compare the FLOPS of typical neural networks on an Intel CPU. The results in Fig. 2 show that many existing neural networks suffer from low FLOPS, and their FLOPS is generally lower than the popular ResNet50. With such low FLOPS, these \"fast\" neural networks are actually not fast enough. Their reduction in FLOPs cannot be translated into the exact amount of reduction in latency. In some cases, there is no improvement, and it even leads to worse latency. For example, CycleMLP-B1 [5] has half of FLOPs of ResNet50 [16] but runs more slowly (i.e., CycleMLP-B1 vs. ResNet50: 116.1ms vs. 73.0ms). Note that this discrepancy between FLOPs and latency has also been noticed in previous works [40, 42] but remains unresolved partially because they employ the DWConv/GConv and various data manipulations with low FLOPS. It is deemed there are no better alternatives available." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "This paper aims to eliminate the discrepancy by developing a simple yet fast and effective operator that maintains high FLOPS with reduced FLOPs. Specifically, we reexamine existing operators, particularly DWConv, in terms of the computational speed - FLOPS. We uncover that the main reason causing the low FLOPS issue is frequent memory access. We then propose a novel partial convolution (PCov)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 267, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 545, + 398 + ], + "type": "text", + "content": "as a competitive alternative that reduces the computational redundancy as well as the number of memory access. Fig. 1 illustrates the design of our PConv. It takes advantage of redundancy within the feature maps and systematically applies a regular convolution (Conv) on only a part of the input channels while leaving the remaining ones untouched. By nature, PConv has lower FLOPs than the regular Conv while having higher FLOPS than the DWConv/GConv. In other words, PConv better exploits the on-device computational capacity. PConv is also effective in extracting spatial features as empirically validated later in the paper." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": "We further introduce FasterNet, which is primarily built upon our PConv, as a new family of networks that run highly fast on various devices. In particular, our FasterNet achieves state-of-the-art performance for classification, detection, and segmentation tasks while having much lower latency and higher throughput. For example, our tiny FasterNet-T0 is " + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "inline_equation", + "content": "2.8 \\times 3.3 \\times" + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "inline_equation", + "content": "2.4 \\times" + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": " faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being " + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": " more accurate on ImageNet-1k. Our large FasterNet-L achieves " + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "inline_equation", + "content": "83.5\\%" + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": " top-1 accuracy, on par with the emerging Swin-B [35], while offering " + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "inline_equation", + "content": "36\\%" + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": " higher throughput on GPU and saving " + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "inline_equation", + "content": "37\\%" + }, + { + "bbox": [ + 304, + 399, + 546, + 554 + ], + "type": "text", + "content": " compute time on CPU. To summarize, our contributions are as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 559, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 317, + 559, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 559, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 317, + 559, + 545, + 594 + ], + "type": "text", + "content": "- We point out the importance of achieving higher FLOPS beyond simply reducing FLOPs for faster neural networks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 599, + 544, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 599, + 544, + 634 + ], + "spans": [ + { + "bbox": [ + 317, + 599, + 544, + 634 + ], + "type": "text", + "content": "- We introduce a simple yet fast and effective operator called PConv, which has a high potential to replace the existing go-to choice, DWConv." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 638, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 638, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 317, + 638, + 545, + 673 + ], + "type": "text", + "content": "- We introduce FasterNet which runs favorably and universally fast on a variety of devices such as GPU, CPU, and ARM processors." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 677, + 545, + 712 + ], + "type": "text", + "content": "- We conduct extensive experiments on various tasks and validate the high speed and effectiveness of our PConv and FasterNet." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "12022" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 287, + 115 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 287, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 287, + 115 + ], + "type": "text", + "content": "We briefly review prior works on fast and efficient neural networks and differentiate this work from them." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 123, + 289, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 123, + 289, + 375 + ], + "spans": [ + { + "bbox": [ + 47, + 123, + 289, + 375 + ], + "type": "text", + "content": "CNN. CNNs are the mainstream architecture in the computer vision field, especially when it comes to deployment in practice, where being fast is as important as being accurate. Though there have been numerous studies [7, 8, 17, 29, 48, 49, 75, 78] to achieve higher efficiency, the rationale behind them is more or less to perform a low-rank approximation. Specifically, the group convolution [27] and the depthwise separable convolution [48] (consisting of depthwise and pointwise convolutions) are probably the most popular ones. They have been widely adopted in mobile/edge-oriented networks, such as MobileNets [20, 21, 47], ShuffleNets [40, 76], GhostNet [13], EfficientNets [54, 55], TinyNet [14], Xception [8], CondenseNet [23, 70], TVConv [4], MnasNet [53], and FBNet [67]. While they exploit the redundancy in filters to reduce the number of parameters and FLOPs, they suffer from increased memory access when increasing the network width to compensate for the accuracy drop. By contrast, we consider the redundancy in feature maps and propose a partial convolution to reduce FLOPs and memory access simultaneously." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 381, + 289, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 289, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 289, + 632 + ], + "type": "text", + "content": "ViT, MLP, and variants. There is a growing interest in studying ViT ever since Dosovitskiy et al. [11] expanded the application scope of transformers [62] from machine translation [62] or forecasting [66] to the computer vision field. Many follow-up works have attempted to improve ViT in terms of training setting [51, 58, 59] and model design [12, 34, 35, 65, 77]. One notable trend is to pursue a better accuracy-latency trade-off by reducing the complexity of the attention operator [1, 25, 39, 56, 61], incorporating convolution into ViTs [6, 10, 50], or doing both [3, 30, 43, 45]. Besides, other studies [5, 31, 57] propose to replace the attention with simple MLP-based operators. However, they often evolve to be CNN-like [33]. In this paper, we focus on analyzing the convolution operations, particularly DWConv, due to the following reasons: First, the advantage of attention over convolution is unclear or debatable [36, 64]. Second, the attention-based mechanism generally runs slower than its convolutional counterparts and thus becomes less favorable for the current industry [22, 42]. Finally, DW-Conv is still a popular choice in many hybrid models, so it is worth a careful examination." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 645, + 223, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 223, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 223, + 658 + ], + "type": "text", + "content": "3. Design of PConv and FasterNet" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "In this section, we first revisit DWConv and analyze the issue with its frequent memory access. We then introduce PConv as a competitive alternative operator to resolve the issue. After that, we introduce FasterNet and explain its" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 543, + 190 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 543, + 190 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 543, + 190 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 543, + 190 + ], + "type": "image", + "image_path": "43b8b037deb68c10cea574d7d56f635729de216ab6d0f26d1b74b15ba6828430.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 193, + 547, + 237 + ], + "lines": [ + { + "bbox": [ + 305, + 193, + 547, + 237 + ], + "spans": [ + { + "bbox": [ + 305, + 193, + 547, + 237 + ], + "type": "text", + "content": "Figure 3. Visualization of feature maps in an intermediate layer of a pre-trained ResNet50, with the top-left image as the input. Qualitatively, we can see the high redundancies across different channels." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 254, + 468, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 254, + 468, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 254, + 468, + 266 + ], + "type": "text", + "content": "details, including design considerations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 273, + 385, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 273, + 385, + 286 + ], + "spans": [ + { + "bbox": [ + 306, + 273, + 385, + 286 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": "DWConv is a popular variant of Conv and has been widely adopted as a key building block for many neural networks. For an input " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": ", DWConv applies " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": " filters " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{k \\times k}" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": " to compute the output " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{O} \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": ". As shown in Fig. 1(b), each filter slides spatially on one input channel and contributes to one output channel. This depthwise computation makes DWConv have as low FLOPs as " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "h \\times w \\times k^2 \\times c" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": " compared to a regular Conv with " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "h \\times w \\times k^2 \\times c^2" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": ". While effective in reducing FLOPs, a DWConv, which is typically followed by a pointwise convolution, or PWConv, cannot be simply used to replace a regular Conv as it would incur a severe accuracy drop. Thus, in practice the channel number " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": " (or the network width) of DWConv is increased to " + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "inline_equation", + "content": "c'(c' > c)" + }, + { + "bbox": [ + 304, + 291, + 547, + 532 + ], + "type": "text", + "content": " to compensate the accuracy drop, e.g., the width is expanded by six times for the DWConv in the inverted residual blocks [47]. This, however, results in much higher memory access that can cause non-negligible delay and slow down the overall computation, especially for I/O-bound devices. In particular, the number of memory access now escalates to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 345, + 539, + 545, + 553 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 539, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 345, + 539, + 545, + 553 + ], + "type": "interline_equation", + "content": "h \\times w \\times 2 c ^ {\\prime} + k ^ {2} \\times c ^ {\\prime} \\approx h \\times w \\times 2 c ^ {\\prime}, \\tag {2}", + "image_path": "ee90e2a09ad4b23aaa58c6d9e213e84a20e03f1f5c091e70e96b713aaf795402.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 561, + 499, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 499, + 573 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 499, + 573 + ], + "type": "text", + "content": "which is higher than that of a regular Conv, i.e.," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 347, + 582, + 545, + 595 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 582, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 347, + 582, + 545, + 595 + ], + "type": "interline_equation", + "content": "h \\times w \\times 2 c + k ^ {2} \\times c ^ {2} \\approx h \\times w \\times 2 c. \\tag {3}", + "image_path": "0029a4cc6f8905b5fc3f7ecc1acb6ec5ced7765a6515d69d9952af8dbeec6f2b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 604, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 604, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 305, + 604, + 547, + 640 + ], + "type": "text", + "content": "Note that the " + }, + { + "bbox": [ + 305, + 604, + 547, + 640 + ], + "type": "inline_equation", + "content": "h \\times w \\times 2c'" + }, + { + "bbox": [ + 305, + 604, + 547, + 640 + ], + "type": "text", + "content": " memory access is spent on the I/O operation, which is deemed to be already the minimum cost and hard to optimize further." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 647, + 509, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 509, + 661 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 509, + 661 + ], + "type": "text", + "content": "3.2. Partial convolution as a basic operator" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "text", + "content": "We below demonstrate that the cost can be further optimized by leveraging the feature maps' redundancy. As visualized in Fig. 3, the feature maps share high similarities among different channels. This redundancy has also" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "12023" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "been covered in many other works [13, 74], but few of them make full use of it in a simple yet effective way." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 288, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 288, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 288, + 228 + ], + "type": "text", + "content": "Specifically, we propose a simple PConv to reduce computational redundancy and memory access simultaneously. The bottom-left corner in Fig. 4 illustrates how our PConv works. It simply applies a regular Conv on only a part of the input channels for spatial feature extraction and leaves the remaining channels untouched. For contiguous or regular memory access, we consider the first or last consecutive " + }, + { + "bbox": [ + 46, + 96, + 288, + 228 + ], + "type": "inline_equation", + "content": "c_p" + }, + { + "bbox": [ + 46, + 96, + 288, + 228 + ], + "type": "text", + "content": " channels as the representatives of the whole feature maps for computation. Without loss of generality, we consider the input and output feature maps to have the same number of channels. Therefore, the FLOPs of a PConv are only" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 129, + 236, + 287, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 236, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 129, + 236, + 287, + 253 + ], + "type": "interline_equation", + "content": "h \\times w \\times k ^ {2} \\times c _ {p} ^ {2}. \\tag {4}", + "image_path": "efc69f0eafad4bd4f125721c14c6242d8e9861cb4d1da3bf66cd7f3c9dcf1c2c.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "content": "With a typical partial ratio " + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "inline_equation", + "content": "r = \\frac{c_p}{c} = \\frac{1}{4}" + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "content": ", the FLOPs of a PConv is only " + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "inline_equation", + "content": "\\frac{1}{16}" + }, + { + "bbox": [ + 47, + 262, + 287, + 299 + ], + "type": "text", + "content": " of a regular Conv. Besides, PConv has a smaller amount of memory access, i.e.," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 307, + 287, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 307, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 83, + 307, + 287, + 323 + ], + "type": "interline_equation", + "content": "h \\times w \\times 2 c _ {p} + k ^ {2} \\times c _ {p} ^ {2} \\approx h \\times w \\times 2 c _ {p}, \\tag {5}", + "image_path": "2b4981f02b44449549bfb91a55219f1562fc42a822dd4f8c826c937e4aa76324.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "type": "text", + "content": "which is only " + }, + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "type": "inline_equation", + "content": "\\frac{1}{4}" + }, + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "type": "text", + "content": " of a regular Conv for " + }, + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "type": "inline_equation", + "content": "r = \\frac{1}{4}" + }, + { + "bbox": [ + 47, + 331, + 228, + 344 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "type": "text", + "content": "Since there are only " + }, + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "type": "inline_equation", + "content": "c_p" + }, + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "type": "text", + "content": " channels utilized for spatial feature extraction, one may ask if we can simply remove the remaining " + }, + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "type": "inline_equation", + "content": "(c - c_p)" + }, + { + "bbox": [ + 46, + 345, + 287, + 452 + ], + "type": "text", + "content": " channels? If so, PConv would degrade to a regular Conv with fewer channels, which deviates from our objective to reduce redundancy. Note that we keep the remaining channels untouched instead of removing them from the feature maps. It is because they are useful for a subsequent PWConv layer, which allows the feature information to flow through all channels." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 460, + 203, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 203, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 203, + 472 + ], + "type": "text", + "content": "3.3. PConv followed by PWConv" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "text", + "content": "To fully and efficiently leverage the information from all channels, we further append a pointwise convolution (PW-Conv) to our PConv. Their effective receptive field together on the input feature maps looks like a T-shaped Conv, which focuses more on the center position compared to a regular Conv uniformly processing a patch, as shown in Fig. 5. To justify this T-shaped receptive field, we first evaluate the importance of each position by calculating the position-wise Frobenius norm. We assume that a position tends to be more important if it has a larger Frobenius norm than other positions. For a regular Conv filter " + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{k^2 \\times c}" + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "text", + "content": ", the Frobenius norm at position " + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "text", + "content": " is calculated by " + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\| \\mathbf{F}_i \\| = \\sqrt{\\sum_{j=1}^{c} |f_{ij}|^2}" + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "inline_equation", + "content": "i = 1, 2, 3\\ldots, k^2" + }, + { + "bbox": [ + 46, + 478, + 288, + 713 + ], + "type": "text", + "content": ". We consider a salient position to be the one with the maximum Frobenius norm. We then collectively examine each filter in a pre-trained ResNet18, find out their salient positions, and plot a histogram of the salient positions. Results in Fig. 6 show that the center position turns out to be the salient position most frequently among the filters. In other words, the center position weighs more" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "than its surrounding neighbors. This is consistent with the T-shaped computation which concentrates on the center position." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": "While the T-shaped Conv can be directly used for efficient computation, we show that it is better to decompose the T-shaped Conv into a PConv and a PWConv because the decomposition exploits the inter-filter redundancy and further saves FLOPs. For the same input " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": " and output " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathbf{O} \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": ", a T-shaped Conv's FLOPs can be calculated as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 343, + 201, + 545, + 216 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 201, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 343, + 201, + 545, + 216 + ], + "type": "interline_equation", + "content": "h \\times w \\times \\left(k ^ {2} \\times c _ {p} \\times c + c \\times \\left(c - c _ {p}\\right)\\right), \\tag {6}", + "image_path": "de63bdf0146e9d9c14564ae304310409111284bede856887ae8b8368a69366f0.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 224, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 247 + ], + "type": "text", + "content": "which is higher than the FLOPs of a PConv and a PWConv, i.e.," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 248, + 545, + 263 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 248, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 365, + 248, + 545, + 263 + ], + "type": "interline_equation", + "content": "h \\times w \\times \\left(k ^ {2} \\times c _ {p} ^ {2} + c \\times c _ {p}\\right), \\tag {7}", + "image_path": "6f15a3fe897416717afe834376e77dac8cf6553824c753da2e522c21d7b35f6c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "inline_equation", + "content": "c > c_p" + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "inline_equation", + "content": "c - c_p > c_p" + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "text", + "content": " (e.g. when " + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "inline_equation", + "content": "c_p = \\frac{c}{4}" + }, + { + "bbox": [ + 304, + 268, + 545, + 304 + ], + "type": "text", + "content": "). Besides, we can readily leverage the regular Conv for the two-step implementation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 312, + 481, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 481, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 481, + 324 + ], + "type": "text", + "content": "3.4. FasterNet as a general backbone" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 330, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 330, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 330, + 545, + 401 + ], + "type": "text", + "content": "Given our novel PConv and off-the-shelf PWConv as the primary building operators, we further propose FasterNet, a new family of neural networks that runs favorably fast and is highly effective for many vision tasks. We aim to keep the architecture as simple as possible, without bells and whistles, to make it hardware-friendly in general." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": "We present the overall architecture in Fig. 4. It has four hierarchical stages, each of which is preceded by an embedding layer (a regular Conv " + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": " with stride 4) or a merging layer (a regular Conv " + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": " with stride 2) for spatial downsampling and channel number expanding. Each stage has a stack of FasterNet blocks. We observe that the blocks in the last two stages consume less memory access and tend to have higher FLOPS, as empirically validated in Tab. 1. Thus, we put more FasterNet blocks and correspondingly assign more computations to the last two stages. Each FasterNet block has a PConv layer followed by two PWConv (or Conv " + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 403, + 545, + 582 + ], + "type": "text", + "content": ") layers. Together, they appear as inverted residual blocks where the middle layer has an expanded number of channels, and a shortcut connection is placed to reuse the input features." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "In addition to the above operators, the normalization and activation layers are also indispensable for high-performing neural networks. Many prior works [13, 16, 47], however, overuse such layers throughout the network, which may limit the feature diversity and thus hurt the performance. It can also slow down the overall computation. By contrast, we put them only after each middle PWConv to preserve the feature diversity and achieve lower latency. Besides, we use the batch normalization (BN) [26] instead of other alternative ones [2, 60, 68]. The benefit of BN is that it can be merged into its adjacent Conv layers for faster inference" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 732, + 317, + 742 + ], + "type": "text", + "content": "12024" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 89, + 66, + 504, + 242 + ], + "blocks": [ + { + "bbox": [ + 89, + 66, + 504, + 242 + ], + "lines": [ + { + "bbox": [ + 89, + 66, + 504, + 242 + ], + "spans": [ + { + "bbox": [ + 89, + 66, + 504, + 242 + ], + "type": "image", + "image_path": "4cbebcfcba214df5a0773b9aac408ea26fe033a4af1473a805836ce83676b38c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 296, + 132, + 351 + ], + "blocks": [ + { + "bbox": [ + 59, + 296, + 132, + 351 + ], + "lines": [ + { + "bbox": [ + 59, + 296, + 132, + 351 + ], + "spans": [ + { + "bbox": [ + 59, + 296, + 132, + 351 + ], + "type": "image", + "image_path": "70be33816e6e05deda16ab9e60a97129c8caba1c4290915d28b7400b1ac8fd84.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 353, + 136, + 362 + ], + "lines": [ + { + "bbox": [ + 56, + 353, + 136, + 362 + ], + "spans": [ + { + "bbox": [ + 56, + 353, + 136, + 362 + ], + "type": "text", + "content": "(a) PConv + PWConv" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 146, + 297, + 201, + 350 + ], + "blocks": [ + { + "bbox": [ + 146, + 297, + 201, + 350 + ], + "lines": [ + { + "bbox": [ + 146, + 297, + 201, + 350 + ], + "spans": [ + { + "bbox": [ + 146, + 297, + 201, + 350 + ], + "type": "image", + "image_path": "1cc9a62bb3d40acb040421f220c81886e43d4bbeade06a31e06c9d39b0107c51.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 141, + 352, + 208, + 362 + ], + "lines": [ + { + "bbox": [ + 141, + 352, + 208, + 362 + ], + "spans": [ + { + "bbox": [ + 141, + 352, + 208, + 362 + ], + "type": "text", + "content": "(b) T-shaped Conv" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 219, + 296, + 276, + 354 + ], + "blocks": [ + { + "bbox": [ + 219, + 296, + 276, + 354 + ], + "lines": [ + { + "bbox": [ + 219, + 296, + 276, + 354 + ], + "spans": [ + { + "bbox": [ + 219, + 296, + 276, + 354 + ], + "type": "image", + "image_path": "fb412d9f49483344d931ecb60a4c7b368f1ddac0868fdaca07ac7ead2459edc1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 215, + 354, + 274, + 363 + ], + "lines": [ + { + "bbox": [ + 215, + 354, + 274, + 363 + ], + "spans": [ + { + "bbox": [ + 215, + 354, + 274, + 363 + ], + "type": "text", + "content": "(c) regular Conv" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 364, + 287, + 409 + ], + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 409 + ], + "type": "text", + "content": "Figure 5. Comparison of convolutional variants. A PConv followed by a PWConv (a) resembles a T-shaped Conv (b), which spends more computation on the center position compared to a regular Conv (c)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 425, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 508 + ], + "type": "text", + "content": "while being as effective as the others. As for the activation layers, we empirically choose GELU [18] for smaller FasterNet variants and ReLU [44] for bigger FasterNet variants, considering both running time and effectiveness. The last three layers, i.e. a global average pooling, a Conv " + }, + { + "bbox": [ + 46, + 425, + 287, + 508 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 425, + 287, + 508 + ], + "type": "text", + "content": ", and a fully-connected layer, are used together for feature transformation and classification." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 510, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 594 + ], + "type": "text", + "content": "To serve a wide range of applications under different computational budgets, we provide tiny, small, medium, and large variants of FasterNet, referred to as FasterNet-T0/1/2, FasterNet-S, FasterNet-M, and FasterNet-L, respectively. They share a similar architecture but vary in depth and width. Detailed architecture specifications are provided in the appendix." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 607, + 173, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 607, + 173, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 607, + 173, + 620 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "content": "We first examine the computational speed of our PConv and its effectiveness when combined with a PWConv. We then comprehensively evaluate the performance of our FasterNet for classification, detection, and segmentation tasks. Finally, we conduct a brief ablation study." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To benchmark the latency and throughput, we choose the following three typical processors, which cover a wide" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 306, + 285, + 543, + 366 + ], + "blocks": [ + { + "bbox": [ + 46, + 243, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 547, + 289 + ], + "type": "text", + "content": "Figure 4. Overall architecture of our FasterNet. It has four hierarchical stages, each with a stack of FasterNet blocks and preceded by an embedding or merging layer. The last three layers are used for feature classification. Within each FasterNet block, a PConv layer is followed by two PWConv layers. We put normalization and activation layers only after the middle layer to preserve the feature diversity and achieve lower latency." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 285, + 543, + 366 + ], + "lines": [ + { + "bbox": [ + 306, + 285, + 543, + 366 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 543, + 366 + ], + "type": "image", + "image_path": "c3e91ad083f5845c8ed7743c6664f13f9076194653b00f9c257d1e8f0f658866.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 369, + 545, + 425 + ], + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 425 + ], + "type": "text", + "content": "Figure 6. Histogram of salient position distribution for the regular Conv " + }, + { + "bbox": [ + 305, + 369, + 545, + 425 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 305, + 369, + 545, + 425 + ], + "type": "text", + "content": " filters in a pre-trained ResNet18. The histogram contains four kinds of bars, corresponding to different stages in the network. In all stages, the center position (position 5) appears as a salient position most frequently." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 509 + ], + "type": "text", + "content": "range of computational capacity: GPU (2080Ti), CPU (Intel i9-9900X, using a single thread), and ARM (Cortex-A72, using a single thread). We report their latency for inputs with a batch size of 1 and throughput for inputs with a batch size of 32. During inference, the BN layers are merged to their adjacent layers wherever applicable." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 515, + 474, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 474, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 474, + 529 + ], + "type": "text", + "content": "4.1. PConv is fast with high FLOPS" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 534, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 629 + ], + "type": "text", + "content": "We below show that our PConv is fast and better exploits the on-device computational capacity. Specifically, we stack 10 layers of pure PConv and take feature maps of typical dimensions as inputs. We then measure FLOPs and latency/throughput on GPU, CPU, and ARM processors, which also allow us to further compute FLOPS. We repeat the same procedure for other convolutional variants and make comparisons." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Results in Tab. 1 show that PConv is overall an appealing choice for high FLOPS with reduced FLOPs. It has only " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\frac{1}{16}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " FLOPs of a regular Conv and achieves " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "10.5\\times" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "6.2\\times" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "22.8\\times" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " higher FLOPS than the DWConv on GPU, CPU, and ARM, respectively. We are unsurprised to see that the regular Conv has the highest FLOPS as it has been constantly optimized for years. However, its total FLOPs and" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "12025" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 93, + 70, + 501, + 301 + ], + "blocks": [ + { + "bbox": [ + 93, + 70, + 501, + 301 + ], + "lines": [ + { + "bbox": [ + 93, + 70, + 501, + 301 + ], + "spans": [ + { + "bbox": [ + 93, + 70, + 501, + 301 + ], + "type": "table", + "html": "
OperatorFeature map sizeFLOPs (M), ×10 layersGPU Throughput (fps)FLOPS (G/s)CPU Latency (ms)FLOPS (G/s)ARM Latency (ms)FLOPS (G/s)
Conv 3×396×56×5626013010782435.6772.90779.573.33
192×28×28260148931271728.4191.53619.644.19
384×14×14260145581185431.8581.66595.094.37
768×7×726013159821262.7141.47662.173.92
Average-10151-71.89-3.95
GConv 3×3 (16 groups)96×56×56162288846921.907.42166.300.97
192×28×281621081117547.5821.4496.221.68
384×14×141621553425144.4036.8863.572.55
768×7×71621600025984.2837.9765.202.49
Average-1833-25.93-1.92
DWConv 3×396×56×5627.09119403233.597.52108.700.24
192×28×2813.54233583151.976.8682.010.16
384×14×146.77463773131.066.3594.890.07
768×7×73.38888893020.684.93150.890.02
Average-313-6.42-0.12
PConv 3×3 (ours, with r = 1/4)96×56×56162921514935.4629.6785.301.90
192×28×281621436023263.0952.4366.462.44
384×14×141622440839543.5845.2549.983.24
768×7×71623286653245.0232.2748.303.35
Average-3274-39.91-2.73
", + "image_path": "57398df037efacea461ed9e36ffe849a481051795f3dd9e649ed57795f9f4b0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 326, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 288, + 387 + ], + "type": "text", + "content": "latency/throughput are unaffordable. GConv and DWConv, despite their significant reduction in FLOPs, suffer from a drastic decrease in FLOPS. In addition, they tend to increase the number of channels to compensate for the performance drop, which, however, increase their latency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 393, + 263, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 393, + 263, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 393, + 263, + 406 + ], + "type": "text", + "content": "4.2. PConv is effective together with PWConv" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "content": "We next show that a PConv followed by a PWConv is effective in approximating a regular Conv to transform the feature maps. To this end, we first build four datasets by feeding the ImageNet-1k val split images into a pre-trained ResNet50, and extract the feature maps before and after the first Conv " + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "content": " in each of the four stages. Each feature map dataset is further spilt into the train " + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "inline_equation", + "content": "(70\\%)" + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "content": ", val " + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "inline_equation", + "content": "(10\\%)" + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "content": ", and test " + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "inline_equation", + "content": "(20\\%)" + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "content": " subsets. We then build a simple network consisting of a PConv followed by a PWConv and train it on the feature map datasets with a mean squared error loss. For comparison, we also build and train networks for DWConv + PWConv and GConv + PWConv under the same setting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 555, + 288, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 288, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 288, + 639 + ], + "type": "text", + "content": "Tab. 2 shows that PConv + PWConv achieve the lowest test loss, meaning that they better approximate a regular Conv in feature transformation. The results also suggest that it is sufficient and efficient to capture spatial features from only a part of the feature maps. PConv shows a great potential to be the new go-to choice in designing fast and effective neural networks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 647, + 257, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 257, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 257, + 659 + ], + "type": "text", + "content": "4.3. FasterNet on ImageNet-1k classification" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "To verify the effectiveness and efficiency of our FasterNet, we first conduct experiments on the large-scale ImageNet-1k classification dataset [46]. It covers 1k categories of common objects and contains about 1.3M la" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 320, + 327, + 533, + 413 + ], + "blocks": [ + { + "bbox": [ + 63, + 304, + 529, + 316 + ], + "lines": [ + { + "bbox": [ + 63, + 304, + 529, + 316 + ], + "spans": [ + { + "bbox": [ + 63, + 304, + 529, + 316 + ], + "type": "text", + "content": "Table 1. On-device FLOPS for different operations. PConv appears as an appealing choice for high FLOPS with reduced FLOPs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 320, + 327, + 533, + 413 + ], + "lines": [ + { + "bbox": [ + 320, + 327, + 533, + 413 + ], + "spans": [ + { + "bbox": [ + 320, + 327, + 533, + 413 + ], + "type": "table", + "html": "
StageDWConv+PWConvGConv+PWConv(16 groups)PConv+PWConvr = 1/4
10.00890.00650.0069
20.01580.01370.0136
30.02140.02020.0172
40.01300.01280.0115
Average0.01480.01330.0123
", + "image_path": "6e4606f3000e463c4f2ccd6c994236e18415b170c6a41f56fadf70af6dfdbf6c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 417, + 545, + 452 + ], + "lines": [ + { + "bbox": [ + 305, + 417, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 417, + 545, + 452 + ], + "type": "text", + "content": "Table 2. A PConv followed by a PWConv well approximates the regular Conv " + }, + { + "bbox": [ + 305, + 417, + 545, + 452 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 305, + 417, + 545, + 452 + ], + "type": "text", + "content": " at different stages of a pre-trained ResNet50. PConv + PWConv together have the lowest test loss on average." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "text", + "content": "beled images for training and 50k labeled images for validation. We train our models for 300 epochs using AdamW optimizer [38]. We set the batch size to 2048 for the FasterNet-M/L and 4096 for other variants. We use cosine learning rate scheduler [37] with a peak value of " + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "inline_equation", + "content": "0.001 \\cdot" + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "text", + "content": " batch size/1024 and a 20-epoch linear warmup. We apply commonly-used regularization and augmentation techniques, including Weight Decay [28], Stochastic Depth [24], Label Smoothing [52], Mixup [73], Cutmix [72] and Rand Augment [9], with varying magnitudes for different FasterNet variants. To reduce the training time, we use " + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "inline_equation", + "content": "192 \\times 192" + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "text", + "content": " resolution for the first 280 training epochs and " + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "text", + "content": " for the remaining 20 epochs. For fair comparison, we do not use knowledge distillation [19] and neural architecture search [79]. We report our top-1 accuracy on the validation set with a center crop at " + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 461, + 545, + 676 + ], + "type": "text", + "content": " resolution and a 0.9 crop ratio. Detailed training and validation settings are provided in the appendix." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Fig. 7 and Tab. 3 demonstrate the superiority of our FasterNet over state-of-the-art classification models. The trade-off curves in Fig. 7 clearly show that FasterNet sets" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 318, + 742 + ], + "type": "text", + "content": "12026" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 68, + 286, + 239 + ], + "blocks": [ + { + "bbox": [ + 49, + 68, + 286, + 239 + ], + "lines": [ + { + "bbox": [ + 49, + 68, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 49, + 68, + 286, + 239 + ], + "type": "image", + "image_path": "815b3c3a86d1a130a402adcae33bb24083901f97882f97150fb926cc712b2e97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 240, + 286, + 361 + ], + "blocks": [ + { + "bbox": [ + 49, + 240, + 286, + 361 + ], + "lines": [ + { + "bbox": [ + 49, + 240, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 49, + 240, + 286, + 361 + ], + "type": "image", + "image_path": "9ee0963af0ff702c4f7440623b2fef107742aa7aa992df772c6ff8f22d9f3054.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 364, + 285, + 484 + ], + "blocks": [ + { + "bbox": [ + 49, + 364, + 285, + 484 + ], + "lines": [ + { + "bbox": [ + 49, + 364, + 285, + 484 + ], + "spans": [ + { + "bbox": [ + 49, + 364, + 285, + 484 + ], + "type": "image", + "image_path": "5959c7303514d8b8e2d1673f69f30c473f3e2009cb5c8ddc69a8bd14351a9e35.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 484, + 287, + 540 + ], + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 540 + ], + "type": "text", + "content": "Figure 7. FasterNet has the highest efficiency in balancing accuracy-throughput and accuracy-latency trade-offs for different devices. To save space and make the plots more proportionate, we showcase network variants within a certain range of latency. Full plots can be found in the appendix, which show consistent results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": "the new state-of-the-art in balancing accuracy and latency/throughput among all the networks examined. From another perspective, FasterNet runs faster than various CNN, ViT and MLP models on a wide range of devices, when having similar top-1 accuracy. As quantitatively shown in Tab. 3, FasterNet-T0 is " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "2.8 \\times 3.3 \\times" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "2.4 \\times" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " faster than MobileViT-XXS [42] on GPU, CPU, and ARM processors, respectively, while being " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "2.9\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " more accurate. Our large FasterNet-L achieves " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "83.5\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " top-1 accuracy, comparable to the emerging Swin-B [35] and ConvNeXt-B [36] while having " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "36\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "28\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " higher inference throughput on GPU, as well as saving " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "37\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " compute time on CPU. Given such promising results, we highlight that our FasterNet is" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 307, + 67, + 545, + 466 + ], + "blocks": [ + { + "bbox": [ + 307, + 67, + 545, + 466 + ], + "lines": [ + { + "bbox": [ + 307, + 67, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 307, + 67, + 545, + 466 + ], + "type": "table", + "html": "
NetworkParams (M)FLOPs (G)Throughput on GPU (fps) ↑Latency on CPU (ms) ↓Latency on ARM (ms) ↓Acc. (%)
ShuffleNetV2 ×1.5 [40]3.50.30487812.126672.6
MobileNetV2 [47]3.50.31419812.244272.0
MobileViT-XXS [42]1.30.42239330.834869.0
EdgeNeXt-XXS [41]1.30.26276515.723971.2
FasterNet-T03.90.3468079.214371.9
GhostNet ×1.3 [13]7.40.24298817.948175.7
ShuffleNetV2 ×2 [40]7.40.59333917.840374.9
MobileNetV2 ×1.4 [47]6.10.60271122.665074.7
MobileViT-XS [42]2.31.05139240.864874.8
EdgeNeXt-XS [41]2.30.54173824.443475.0
PVT-Tiny [65]13.21.94126655.670875.1
FasterNet-T17.60.85378217.728576.2
CycleMLP-B1 [5]15.22.10865116.189279.1
PoolFormer-S12 [71]11.91.82143949.066577.2
MobileViT-S [42]5.62.03103956.794178.4
EdgeNeXt-S [41]5.61.26112839.274379.4
ResNet50 [16, 36]25.64.1195973.0113178.8
FasterNet-T215.01.91199133.549778.9
CycleMLP-B2 [5]26.83.90528186.3150281.6
PoolFormer-S24 [71]21.43.4174892.8126180.3
PoolFormer-S36 [71]30.95.00507138.0186081.4
ConvNeXt-T [36]28.64.4765786.3188982.1
Swin-T [35]28.34.51609122.2142481.3
PVT-Small [65]24.53.8368989.6134579.8
PVT-Medium [65]44.26.69438143.6214281.2
FasterNet-S31.14.56102971.2110381.3
PoolFormer-M36 [71]56.28.80320215.0297982.1
ConvNeXt-S [36]50.28.71377153.2348483.1
Swin-S [35]49.68.77348224.2261383.0
PVT-Large [65]61.49.85306203.4310181.7
FasterNet-M53.58.74500129.5209283.0
PoolFormer-M48 [71]73.511.59242281.8OOM82.5
ConvNeXt-B [36]88.615.38253257.1OOM83.8
Swin-B [35]87.815.47237349.2OOM83.5
FasterNet-L93.515.52323219.5OOM83.5
", + "image_path": "5d23304daed3ad28732bde0f3b7a1fd6fb4b2f5cad8e2e0f0c42d4ab6692b4f0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "type": "text", + "content": "Table 3. Comparison on ImageNet-1k benchmark. Models with similar top-1 accuracy are grouped together. For each group, our FasterNet achieves the highest throughput on GPU and the lowest latency on CPU and ARM. All models are evaluated at " + }, + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "type": "text", + "content": " resolution except for the MobileViT and EdgeNeXt with " + }, + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 469, + 545, + 536 + ], + "type": "text", + "content": ". OOM is short for out of memory." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 552, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 545, + 588 + ], + "type": "text", + "content": "much simpler than many other models in terms of architectural design, which showcases the feasibility of designing simple yet powerful neural networks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 598, + 476, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 598, + 476, + 609 + ], + "spans": [ + { + "bbox": [ + 305, + 598, + 476, + 609 + ], + "type": "text", + "content": "4.4. FasterNet on downstream tasks" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "To further evaluate the generalization ability of FasterNet, we conduct experiments on the challenging COCO dataset [32] for object detection and instance segmentation. As a common practice, we employ the ImageNet pre-trained FasterNet as a backbone and equip it with the popular Mask R-CNN detector [15]. To highlight the effectiveness of the backbone itself, we simply follow PoolFormer [71] and adopt an AdamW optimizer, a " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "1\\times" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " training" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 733, + 317, + 742 + ], + "type": "text", + "content": "12027" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 520, + 234 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 520, + 234 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 520, + 234 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 520, + 234 + ], + "type": "table", + "html": "
BackboneParams (M)FLOPs (G)Latency on GPU (ms)\\(AP^b\\)\\(AP_{50}^b\\)\\(AP_{75}^b\\)\\(AP^m\\)\\(AP_{50}^m\\)\\(AP_{75}^m\\)
ResNet50 [16]44.225354.938.058.641.434.455.136.7
PoolFormer-S24 [71]41.0233111.040.162.243.437.059.139.6
PVT-Small [65]44.123889.540.462.943.837.860.140.3
FasterNet-S49.025854.339.961.243.636.958.139.7
ResNet101 [16]63.232968.940.461.144.236.457.738.8
ResNeXt101-32×4d [69]62.833380.541.962.545.937.559.440.2
PoolFormer-S36 [71]50.5266146.941.063.144.837.760.140.0
PVT-Medium [65]63.9295117.342.064.445.639.061.642.1
FasterNet-M71.234471.443.064.447.439.161.542.3
ResNeXt101-64×4d [69]101.9487112.942.863.847.338.460.641.3
PVT-Large [65]81.0358152.242.965.046.639.561.942.5
FasterNet-L110.948493.844.065.648.239.962.343.0
", + "image_path": "c5f70244aef2e32f5512124b593580c255e602f3bc0a47d09897dd295233bd84.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 261, + 287, + 423 + ], + "blocks": [ + { + "bbox": [ + 52, + 237, + 539, + 248 + ], + "lines": [ + { + "bbox": [ + 52, + 237, + 539, + 248 + ], + "spans": [ + { + "bbox": [ + 52, + 237, + 539, + 248 + ], + "type": "text", + "content": "Table 4. Results on COCO object detection and instance segmentation benchmarks. FLOPs are calculated with image size (1280, 800)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 261, + 287, + 423 + ], + "lines": [ + { + "bbox": [ + 50, + 261, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 50, + 261, + 287, + 423 + ], + "type": "table", + "html": "
AblationVariantThroughput on GPU (fps)Latency on CPU (ms)Latency on ARM (ms)Acc. (%)
Partial ratioT0* w/ r = 1/266269.614571.7
T0 w/ r = 1/468079.214371.9
T0* w/ r = 1/862048.914071.3
NormalizationT0 w/ BN68079.214371.9
T0 w/ LN551510.715971.9
ActivationT0 w/ ReLU69298.211471.3
T0* w/ ReLU58669.314371.7
T0 w/ GELU68079.214371.9
T2 w/ ReLU199133.549778.9
T2 w/ GELU198535.455778.7
", + "image_path": "7038d17176173fd3f66cbaf3bc12fe53d4593c585ef6a012831af2873370e950.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "lines": [ + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "type": "text", + "content": "Table 5. Ablation on the partial ratio, normalization, and activation of FasterNet. Rows highlighted in grey are the default settings. " + }, + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "type": "inline_equation", + "content": "\\mathrm{T0}^*" + }, + { + "bbox": [ + 47, + 425, + 287, + 460 + ], + "type": "text", + "content": " denotes T0 variants with modified network width and depth." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 496 + ], + "type": "text", + "content": "schedule (12 epochs), a batch size of 16, and other training settings without further hyper-parameter tuning." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": "Tab. 4 shows the results for comparison between FasterNet and representative models. FasterNet consistently outperforms ResNet and ResNext by having higher average precision (AP) with similar latency. Specifically, FasterNet-S yields " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "+1.9" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " higher box AP and " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "+2.4" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " higher mask AP compared to the standard baseline ResNet50. FasterNet is also competitive against the ViT variants. Under similar FLOPs, FasterNet-L reduces PVT-Large's latency by " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": ", i.e., from " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "152.2\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "93.8\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " on GPU, and achieves " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "+1.1" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " higher box AP and " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "+0.4" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " higher mask AP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 623, + 138, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 138, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 138, + 635 + ], + "type": "text", + "content": "4.5. Ablation study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "text", + "content": "We conduct a brief ablation study on the value of partial ratio " + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "text", + "content": " and the choices of activation and normalization layers. We compare different variants in terms of ImageNet top-1 accuracy and on-device latency/throughput. Results are summarized in Tab. 5. For the partial ratio " + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "text", + "content": ", we set it to " + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "inline_equation", + "content": "\\frac{1}{4}" + }, + { + "bbox": [ + 46, + 641, + 287, + 716 + ], + "type": "text", + "content": " for all FasterNet variants by default, which achieves" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": "higher accuracy, higher throughput, and lower latency at similar complexity. A too large partial ratio " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": " would make PConv degrade to a regular Conv, while a too small value would render PConv less effective in capturing the spatial features. For the normalization layers, we choose BatchNorm over LayerNorm because BatchNorm can be merged into its adjacent convolutional layers for faster inference while it is as effective as LayerNorm in our experiment. For the activation function, interestingly, we empirically found that GELU fits FasterNet-T0/T1 models more efficiently than ReLU. It, however, becomes opposite for FasterNet-T2/S/M/L. Here we only show two examples in Tab. 5 due to space constraint. We conjecture that GELU strengthens FasterNet-T0/T1 by having higher non-linearity, while the benefit fades away for larger FasterNet variants." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 456, + 378, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 378, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 378, + 468 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 477, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 657 + ], + "type": "text", + "content": "In this paper, we have investigated the common and unresolved issue that many established neural networks suffer from low floating-point operations per second (FLOPS). We have revisited a bottleneck operator, DWConv, and analyzed its main cause for a slowdown - frequent memory access. To overcome the issue and achieve faster neural networks, we have proposed a simple yet fast and effective operator, PConv, that can be readily plugged into many existing networks. We have further introduced our general-purpose FasterNet, built upon our PConv, that achieves state-of-the-art speed and accuracy trade-off on various devices and vision tasks. We hope that our PConv and FasterNet would inspire more research on simple yet effective neural networks, going beyond academia to impact the industry and community directly." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This work was supported, in part, by Hong Kong General Research Fund under grant number 16200120. The work of C.-H. 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Neural architecture search with reinforcement learning. arXiv preprint arXiv:1611.01578, 2016. 6" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 294, + 734, + 317, + 742 + ], + "type": "text", + "content": "12031" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_content_list.json b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..53a7e7e87608c892d2c365ba6f3eadc78a2c831c --- /dev/null +++ b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_content_list.json @@ -0,0 +1,1506 @@ +[ + { + "type": "text", + "text": "$\\mathrm{S}^{3}\\mathrm{C}$ : Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning", + "text_level": 1, + "bbox": [ + 163, + 128, + 805, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wei Suo $^{1*}$ , Mengyang Sun $^{2*}$ , Weisong Liu $^{1}$ , Yiqi Gao $^{1}$ , Peng Wang $^{1\\dagger}$ , Yanning Zhang $^{1\\dagger}$ , Qi Wu $^{3}$ $^{1}$ School of Computer Science and Ningbo Institute, Northwestern Polytechnical University, China. \n $^{2}$ School of Cybersecurity, Northwestern Polytechnical University, China. \n $^{3}$ University of Adelaide, Australia.", + "bbox": [ + 96, + 202, + 872, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{suowei1994,sunmenmian,liuweisong,gyqjz}@mail.nwpu.edu.cn", + "bbox": [ + 228, + 276, + 736, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{peng.wang, ynzhang}@nwpu.edu.cn, qi.wu01@adelaide.edu.au", + "bbox": [ + 228, + 295, + 723, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "VQA Natural Language Explanation (VQA-NLE) task aims to explain the decision-making process of VQA models in natural language. Unlike traditional attention or gradient analysis, free-text rationales can be easier to understand and gain users' trust. Existing methods mostly use post-hoc or self-rationalization models to obtain a plausible explanation. However, these frameworks are bottlenecked by the following challenges: 1) the reasoning process cannot be faithfully responded to and suffer from the problem of logical inconsistency. 2) Human-annotated explanations are expensive and time-consuming to collect. In this paper, we propose a new Semi-Supervised VQA-NLE via Self-Critical Learning $(S^3 C)$ , which evaluates the candidate explanations by answering rewards to improve the logical consistency between answers and rationales. With a semi-supervised learning framework, the $S^3 C$ can benefit from a tremendous amount of samples without human-annotated explanations. A large number of automatic measures and human evaluations all show the effectiveness of our method. Meanwhile, the framework achieves a new state-of-the-art performance on the two VQA-NLE datasets.", + "bbox": [ + 75, + 375, + 473, + 693 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 734, + 207, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks have enabled significant breakthroughs in a variety of vision-language (VL) tasks such as image captioning [10, 47] and visual question answering (VQA) [2, 39]. Unfortunately, most of them are black box systems, which makes it challenging to gain users' trust [20]. Explaining the decision-making process of deep VL models is a long-standing and essential problem.", + "bbox": [ + 75, + 761, + 468, + 867 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/af310065e8d5f1bdc8df7d8c31b4609c45d4ba16f61dad695af4654d8d7b5216.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 345, + 897, + 421 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c5759907e61c6aea5ef5031fae6ab82cc0a7fb498d64b875941375cdd035402c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 422, + 897, + 494 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c16a8892e5fba59ebcfaa7daacb1445d0ba698e7ddee1afd6e25253591b95f64.jpg", + "image_caption": [ + "Figure 1. Paradigm comparison of different VQA-NLE methods. (a) Post-hoc explanation method adopts two independent models to predict answers and explanations respectively. (b) Self-rationalization method uses a united VL model to simultaneously generate answers and explanations. (c) Our self-critical strategy utilizes answer scores as rewards and obtains more reliable rationales with semi-supervised learning." + ], + "image_footnote": [], + "bbox": [ + 504, + 498, + 897, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some approaches depend on attention mechanisms [2, 30] or gradient-based localization [50] to acquire visual explanations, which can highlight some contributing image regions for the predicted answers. However, simple visualization cannot explain how these areas support the answers and they are also hard to comprehend [20, 48]. Conversely, Natural Language Explanation (NLE) task [6, 38] can explain the decision-making process of a model by generating a natural language sentence. The language-based explanations are more accessible for users to understand, and they can also help researchers optimize the structure of models [34].", + "bbox": [ + 496, + 718, + 890, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, some models of NLE in the VL commu", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally to this work.", + "bbox": [ + 94, + 875, + 351, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 96, + 887, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2646", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "nity have achieved pretty-well results, especially for VQANLE [20,34,41,48,58]. They can guide models to generate natural language sentences and interpret how the models get answers. Specifically, the first research line usually treats VQA-NLE as a predict-then-explain task [20, 34, 41, 58], namely post-hoc explanations method. As shown in Fig. 1 (a), these methods first depend on pre-trained VL models (such as UNITER [8] or Oscar [25]) to gain answers. Then the fused multi-modal features and the predicted answers are fed into a separated language model (e.g., LSTM [16] or Transformer [54]) to generate corresponding explanations. As shown in Fig. 1 (b), the other line [48] relies on a united VL model while generating both answers and explanations, which is known as the self-rationalization method. This framework can simultaneously predict an answer and generate a rationale by formulating the answer as a text-generation task along with the explanation.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Though significant progress has been made, the two paradigms are still restricted by the following challenges: 1) For the first paradigm, since the decision-making model and interpretation part are two separate modules, it would inevitably lead to unfaithful responses to the reasoning process of the decision models. 2) Due to the lack of explicitly logical relationship modeling, previous work [19] has proved that the straightforward self-rationalization frameworks suffer from the problem of logical inconsistency. 3) The above strategies all require an amount of human-annotated explanations, which are expensive and time-consuming to collect [62].", + "bbox": [ + 75, + 348, + 472, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To solve the above challenges, inspired by [5, 51], we argue that a reasonable rationale can assist the model in obtaining a correct answer, and vice versa, the answer can be converted as an evaluation criterion for possible explanations. In this paper, we propose a new Semi-Supervised VQA-NLE method with Self-Critical learning, which is called $S^3 C$ for short. As shown in Fig.1 (c), given images and related questions, we first leverage a prompting mechanism to construct answer and explanation templates, which can guide the pre-trained VL model to generate answers and multiple candidate explanations based on sequence sampling [2]. Then we design a new self-critical method that converts the answer scores as rewards and encourages the model to generate the explanations which contribute to improving the answer scores. In particular, to reduce the dependency on expensive human annotations, we further extend our method to the semi-supervised version, which utilizes the unlabelled samples1 (i.e., conventional VQA data [4, 36]) to significantly enhance the self-interpretability of the model. With the self-critical strategy and the semi-supervised learning, our method effectively models the logical relationships and promotes the logical", + "bbox": [ + 75, + 530, + 472, + 864 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "consistency between answer-explanation pairs. According to automatic measures and human evaluations, the $S^3 C$ outperforms the state-of-the-art models for the VQA-NLE task on the widely used two datasets and provides a new paradigm for our community. In summary, we make the following contributions:", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) We propose a new self-critical VQA-NLE method that can model the logical relationships between answer-explanation pairs and evaluate the generated rationales by answering rewards. This strategy effectively improves the logical consistency and the reliability of the interpretations.", + "2) We develop an advanced semi-supervised learning framework for VQA-NLE, which utilizes amounts of samples without human-annotated explanations to boost the self-interpretability of the model further. To the best of our knowledge, we are the first to explore semi-supervised learning on the VQA Natural Language Explanation.", + "3) The proposed $S^3 C$ achieves new state-of-the-art performance on VQA-X [13] and A-OKVQA [49] benchmark datasets. Meanwhile, automatic measures and human evaluations all show the effectiveness of our method." + ], + "bbox": [ + 496, + 184, + 893, + 415 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 438, + 638, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Explainability in Visual Question Answering", + "text_level": 1, + "bbox": [ + 500, + 465, + 879, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The visual question answering (VQA) is firstly proposed by [33] that requires an intelligent agent to generate an answer by giving an image and a question. Many approaches have been introduced such as joint embedding [13, 61], attention mechanisms [3, 31], memory networks [32, 59] and graph neural networks [23, 56]. Although the VQA task has been well studied, the reasoning process of the models is always agnostic. Some methods apply visualization technologies to achieve visual explanation, such as Grad-CAM [50] and U-CAM [42]. However, because image visualization cannot support the answer based on the attended areas [57], in this paper, we focus on improving free-text explanations that are more convenient and easier for users to understand. In this topic, the early work is proposed by [41]. The paper conducts the VQA-X dataset and utilizes human annotations to inspire the decision-making process of VQA models. [20] designs a new model that combines a pre-trained language model and a VL model to generate free-text explanations. [60] combines stronger pre-trained VL model (i.e. Oscar [25]) and generation model (i.e. GPT-2 [46]) to obtain better results. Recently, [48] proposes a unified model which can simultaneously predict answers and explanations based on a pre-trained caption model. Unlike previous methods, we introduce a new self-critical strategy to model the logical relationships between answers and rationales. It can encourage the model to enhance logical consistency and generate more reasonable explanations.", + "bbox": [ + 496, + 493, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1In this paper, we use \"unlabelled samples\" and \"labelled samples\" to indicate the question-answer (QA) pairs without/with human explanations.", + "bbox": [ + 76, + 875, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2647", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Pre-trained models and Prompt learning", + "text_level": 1, + "bbox": [ + 76, + 90, + 426, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pre-trained models have been applied in many fields, such as various NLP tasks [12,46] and VL tasks [29,52,65]. Most of these pre-trained models utilize a stack of Transformer structures as the backbone. To generalize the pretrained models to other downstream tasks, previous works mostly fine-tune whole models on each downstream VL task. However, the ability of pre-trained models would be limited due to the mismatch between pre-trained tasks and downstream tasks. Hence, prompt learning [9, 18, 45, 64] is proposed, and it can keep the optimization consistency. [45] designs the templates to transfer the knowledge to downstream tasks. [9] uses a textual generation framework for uniform optimization. In this paper, we use the pre-trained model based on the image caption task as our backbone. It has been proved that these additional pre-train tasks (e.g., image feature regression or mask language tokens) cannot significantly improve the performance for explanations [48]. Meanwhile, we apply different language prompt templates to motivate the model to generate corresponding answers and rationales.", + "bbox": [ + 75, + 113, + 472, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Semi-supervised learning", + "text_level": 1, + "bbox": [ + 76, + 426, + 308, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The development of deep learning depends on a large number of labelled data, while there are many cases in that only a small amount of data can be obtained [44]. To solve this challenge, Semi-supervised learning is proposed [44], which aims to train models using a small number of labelled data and amounts of unlabelled data. For example, [22] proposes a generatively semi-supervised framework based on variational autoencoders, and it can jointly optimize the model and variational parameters. Recently, [63] simultaneously leverages self-supervised and semi-supervised learning to address image classification tasks. To our knowledge, our work is the first semi-supervised learning framework for the VQA-NLE task, which effectively alleviates the reliance on expensive human annotations and further boost the self-interpretability of the model.", + "bbox": [ + 75, + 450, + 472, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 693, + 169, + 709 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce our Semi-Supervised VQANLE method with the Self-Critical learning $(S^3 C)$ framework. Our aim is to strengthen the logical consistency between answer-explanation pairs and improve the reliability of the rationales. As shown in Fig. 2, the $S^3 C$ comprises an \"Answer-Explanation Prompt\" module and a \"Self-Critical Reinforcement\" module. Unlike previous approaches, our method first uses a prompting mechanism to generate answers and candidate explanations. Then, we design a new self-critical module that converts the answer scores as rewards to evaluate these reasons. Furthermore, this strategy can conveniently apply the unlabelled QA pairs to enrich", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "training data and enhance the self-interpretability. Next, we describe the components of our model in detail.", + "bbox": [ + 496, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Pre-trained Vision-Language Backbone", + "text_level": 1, + "bbox": [ + 498, + 132, + 841, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an image $I \\in \\mathbb{R}^{W \\times H \\times 3}$ and a natural language question $Q = \\{q_t\\}_{t=1}^T$ , where $q_t$ represents the $t$ -th word, $T$ is the length of the question and $W \\times H \\times 3$ denotes the size of the image. Our goal is to predict the answer and generate a corresponding free-text rationale. Following previous works [48, 49], we adopt the CLIP vision encoder [45] and a pre-trained image caption model (i.e., ClipCap [37]) as our basic backbone. During pre-training, the VL model uses image embeddings from the CLIP as prefixes and fine-tunes a language model (i.e., GPT-2 [46]) to generate image captions. We refer readers to [37] for more information about the pre-trained model. In this paper, we consider the image $I$ and question $Q$ as the prefixes of the answer-explanation sequences. Specifically, we first apply ViT-B [14] and \"classification token\" from the CLIP to obtain the image features. Then, a group of light and simple Multi-Layer Perceptron (MLP) is utilized for transforming the image features to the $V = \\{v_s\\}_{s=1}^S$ , $v_s \\in \\mathbb{R}^c$ , where the dimension size $c = 768$ and the image sequence length $S = 10$ . The above computations can be formulated as follows:", + "bbox": [ + 496, + 154, + 890, + 470 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nv _ {1}, v _ {2}, \\dots , v _ {S} = \\operatorname {M L P} (\\operatorname {C L I P} (I)). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 473, + 890, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that we only update the mapping network (i.e., MLP) during training, while the original visual encoder parameters from the CLIP would remain frozen. For question $Q$ , each word $q_{t}$ would be mapped to the corresponding word embedding $e_{t} \\in \\mathbb{R}^{c}$ by the pre-trained caption model. Finally, we obtain the image and question sequences $Z$ :", + "bbox": [ + 496, + 497, + 890, + 589 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nZ = \\overbrace {\\left[ v _ {1} , v _ {2} , \\cdots , v _ {S} \\right.} ^ {\\text {i m a g e}} \\underbrace {e _ {1} , e _ {2} , \\cdots , e _ {T}} _ {\\substack {\\text {q u e s t i o n} \\\\ \\text {e m b d e d i n g}}} \\bigg ], \\tag{2}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 601, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $Z$ is the concatenated multi-modal prefixes.", + "bbox": [ + 500, + 669, + 833, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Answer-Explanation Prompt Module", + "text_level": 1, + "bbox": [ + 500, + 695, + 821, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It has been proved that the prompting mechanism can maintain the same optimization objectives between pretrained and downstream tasks [18, 28]. Considering the convenience and explainability, we leverage hand-crafted prompts as templates to enable the model to generate answers or explanations. As shown in Fig. 2, the $S^3 C$ includes two different kinds of templates, which are introduced respectively as follows.", + "bbox": [ + 496, + 719, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Base Answer Template. The core idea of our $S^3 C$ is to use the answer scores as evaluation criteria. Hence, we first establish a basic answer template to acquire base answer scores. Different from previous works [20, 41], our", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2648", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6c9a1ae1014099259c66fe6acd5d5ccb3871a086fe23b1181827247d177149a2.jpg", + "image_caption": [ + "Figure 2. Overview of our Semi-Supervised VQA-NLE method via Self-Critical learning $(S^3 C)$ framework. Given images and corresponding questions for labelled and unlabelled samples, we first use Answer-Explanation Prompt module to obtain the base answer scores and candidate explanations with a pre-trained VL model. Then these reasons are reorganized and fed back into the model to capture the explanatory answer score. Further, our Self-Critical Reinforcement module evaluates the generated explanations and returns the rewards to improve the self-interpretability of the model." + ], + "image_footnote": [], + "bbox": [ + 86, + 94, + 885, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "method treats the visual question answering task as a generation task so that the model can produce answers without a predefined answer space. Specifically, for a given image and question sequence $Z$ , we use natural language tokens \"the answer is\" to inspire the model to generate proper answers. By concatenating the language prompt, the base answer template $Z_{a} = [Z; \\langle \\text{answer} \\rangle]$ can be obtained, where $[; ]$ and $\\langle \\text{answer} \\rangle$ indicate concatenation operation and the specific language prompts, respectively. During training, the base answer template and ground-true answer label $A = \\{a_{n}\\}_{n=1}^{N}$ are fed into the VL model, where $a_{n}$ is the $n$ -th answer token and $N$ denotes the length of the answer label. Next, we compute the answer loss conditioned on the $Z_{a}$ in an autoregressive fashion:", + "bbox": [ + 75, + 450, + 472, + 664 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a} = - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\log P \\left(a _ {n} \\mid Z _ {a}, a _ {1}, a _ {2}, \\dots , a _ {n - 1}; \\theta\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 671, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ denotes the parameters of the VL model. Moreover, based on the indexes of ground-true answers, we can acquire average probability $p_{\\theta}^{b}(A)$ as our base answer score.", + "bbox": [ + 76, + 719, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Explanation Generation Template. To produce a reasonable rationale, we leverage the language prompt \"the reason is\" to motivate the model to generate free-text explanations. Like the base answer template, an explanation generation template $Z_{e} = [Z; \\langle \\text{reason} \\rangle]$ is constructed, where $\\langle \\text{reason} \\rangle$ is the natural language tokens. For labelled samples, we follow Eq. 3 in the autoregressive fashion and the cross-entropy loss to compute explanation loss $L_{e}$ . Because there are no human-annotated explanations available, we", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "would not compute any loss for unlabelled QA samples.", + "bbox": [ + 500, + 450, + 870, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Self-Critical Reinforcement Module", + "text_level": 1, + "bbox": [ + 500, + 481, + 812, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To gain logically consistent rationales, in this module, we expand the searching space by introducing sequence sampling algorithm [2] and generate a set of candidate explanations. Besides, the answer scores are treated as rewards to encourage the model to output more detailed interpretations. It's worth noting that the above operations would be implemented on both labelled and unlabelled samples.", + "bbox": [ + 496, + 506, + 890, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Candidate Explanation Generation. Benefiting from the language-based prompting strategy and the pre-trained VL model, our explanation generation template can easily guide the model to produce human-readable sentences. Hence, for unlabelled QA samples, we directly apply the explanation generation template $Z_{e}$ to generate the candidate rationales. To be more specific, we utilize beam search [2] to sample the top- $K$ words from the VL model probability distribution at each time step and maintain these sequences with the highest probability. Then, these generated sentences are integrated into candidate explanations $R_{s} = \\{r_{k}^{s}\\}_{k = 1}^{K}$ for each QA pair without human-annotated explanations, where $r_k^s$ and $K$ indicate $k$ -th rationale and the size of beam search, respectively. Moreover, for labelled samples, a similar mechanism is used to build the corresponding explanation set $R_{f} = \\{r_{k}^{f}\\}_{k = 1}^{K}$ . The above operations are implemented in all samples for the following reasons: 1) Larger search space. As shown in Fig. 2, \"frying food is unhealthy\" and \"it includes many calories\"", + "bbox": [ + 496, + 613, + 892, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2649", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "can both be rational explanations for the answer \"no\". The expanded search space provides more possibilities for generating reliable rationales. 2) Avoid overfitting. For labelled samples, although we can depend on human explanations to train the model, these labels are still one-sided and subjective. Using the sequence sampling strategy can prevent the model from overfitting these specific annotations [2,47]. In the end, because the labelled and unlabelled samples would be integrated into a mini-batch during training, we simplify $R_{f}$ and $R_{s}$ into $R = \\{r_k\\}_{k=1}^K$ to indicate the candidate explanations for each sample.", + "bbox": [ + 75, + 90, + 472, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Self-Critical Reward. Inspired by [5, 51], an ideal rationale can help the model to infer the answer better. Based on this insight, we argue that the answer scores can be converted as self-critical rewards to evaluate these candidate explanations. Considering that this is a non-differentiable operation, we adopt reinforcement learning method [47] to achieve end-to-end training. In particular, given a sample and corresponding candidate explanations $R$ , we design a new input template:", + "bbox": [ + 75, + 257, + 472, + 393 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {r} ^ {k} = [ Z; \\langle r e a s o n \\rangle ; r _ {k}; \\langle a n s w e r \\rangle ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 402, + 468, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Z_{r}^{k}$ denotes the template of adding possible rationale $r_{k}$ . Then, this template is fed back into the model and obtains average probability $p_{\\theta}^{r}(A)$ about the answer, namely explanatory answer scores, where $A$ is the ground-truth answer for the sample. Meanwhile, we use the average probability $p_{\\theta}^{b}(A)$ from the output of the base answer template as the base scores. By applying reinforcement learning, the gradient is calculated by:", + "bbox": [ + 75, + 431, + 472, + 555 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\theta} L _ {r} (\\theta) = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(p _ {\\theta} ^ {r} (A) - p _ {\\theta} ^ {b} (A)\\right) \\nabla_ {\\theta} \\operatorname {l o g} p _ {\\theta} \\left(r _ {k}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 565, + 468, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p_{\\theta}(r_k)$ is the probability of $k$ -th explanations. Based on the above computation, this gradient would tend to increase the probability of $k$ -th rationales when the answer score $p_{\\theta}^{r}(A)$ higher than the scores $p_{\\theta}^{b}(A)$ from the base answer template. Finally, for labelled samples, we append the human-annotated rationales to the candidate explanation $R$ and predict the answers by cross-entropy loss, namely $L_{ea}$ .", + "bbox": [ + 75, + 617, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Loss", + "text_level": 1, + "bbox": [ + 76, + 732, + 148, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the process of training, the overall loss function can be represented as follows:", + "bbox": [ + 75, + 755, + 468, + 786 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {a} + L _ {e} + L _ {e a} + \\lambda L _ {r}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 797, + 468, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is used for balancing these two different types of losses (i.e., cross-entropy loss and reinforcement loss). At inference time, our model would first generate the rationales about QA pairs, then we use the explanatory template (i.e., Eq. 4) to obtain the corresponding answers.", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 90, + 624, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental setting", + "text_level": 1, + "bbox": [ + 500, + 114, + 696, + 131 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. Following previous methods [48, 49], we mainly carry out the experiments on the two different VQANLE datasets: VQA-X [41] and A-OKVQA [49]. Meanwhile, since explain annotations are expensive and time-consuming, we also utilize large-scale VQA v2.0 [15] and OK-VQA [36] datasets to build the semi-supervised learning paradigm. Next, we will introduce the four datasets.", + "bbox": [ + 496, + 138, + 890, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VQA-X. It is a vision-language dataset that provides explanations for justifying the answers. VQA-X is collected from the Visual Question Answering (VQA) dataset [4] where the images are obtained from the MSCOCO [27]. It consists of 28K images and 33K QA pairs, split into 29K/1.4K/1.9K for training, validation and testing. Meanwhile, VQA-X constructs complementary pairs which provide a question and two semantically similar images with different answers.", + "bbox": [ + 496, + 244, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A-OKVQA. Compared to the VQA-X, the questions of A-OKVQA generally are required commonsense reasoning about the scene described in the images. It includes 24,903 Question/Answer/Rationale triplets, split into $17.1\\mathrm{K} / 1.1\\mathrm{K} / 6.7\\mathrm{K}$ for training, validation and testing. It collects images from the COCO 2017 [7] dataset, and is further filtered to obtain $23.7\\mathrm{K}$ unique images. Compared with previous datasets, the A-OKVQA has richer questions and requires broader areas of knowledge for reasoning.", + "bbox": [ + 496, + 381, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VQA & OK-VQA. We use VQA v2.0 and OK-VQA to provide large-scale unlabelled datasets for semi-supervised learning. The VQA v2.0 dataset is widely used for many previous works [2, 52]. It consists of 443k questions and 195k images. To select explainable questions instead of some obvious cases (e.g., How many...?, What color...?), we filter out these questions from VQA v2.0 and obtain the $\\sim 90\\mathrm{k}$ additional questions based on the rules [41]. On the other hand, we also use knowledge-based OK-VQA [36] dataset to provide unlabelled knowledge-based QA pairs. It contains a total of 14k questions on 14k images.", + "bbox": [ + 496, + 517, + 890, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Following [37], each image is first pre-processed (such as including image resize, center crop, and normalize) by CLIP [45]. Meanwhile, we fix the ViT-B weights from the CLIP visual encoder to accelerate the training speed. For the mapping network, the image sequence length $S = 10$ and the embedding size is 768. The AdamW [21] is used as our optimizer with the weight decay 1e-5, and the batch size and beam size $K$ are set to 4 and 2. The weight coefficient $\\lambda$ is set to 10. We train all models on the four 1080Ti GPUs for 30 epochs with a learning rate of 1e-5.", + "bbox": [ + 496, + 684, + 890, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Evaluation Measures", + "text_level": 1, + "bbox": [ + 500, + 861, + 697, + 876 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Automatic Metering. Following [48, 60], we use the auto", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2650", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e6eda03b43de5d0d1ce034a25bc5d1f3741e2e12f4632b9b28221ee9ae4f7ef4.jpg", + "table_caption": [ + "Table 1. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are unfiltered scores. $S^3 C^*$ denotes the model without unlabelled samples." + ], + "table_footnote": [], + "table_body": "
VQA-X
ApproachB4MRSCAccHuman
CAPS [41]5.912.626.311.935.268.6-
PJ-X [41]19.518.243.415.171.376.465.4
FME [58]24.419.547.717.988.875.5-
NLX-GPT [48]25.621.548.720.297.283.170.2
S3C*(ours)26.522.049.020.9100.583.773.9
S3C(ours)27.822.850.721.5104.485.677.4
", + "bbox": [ + 81, + 142, + 444, + 237 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9d9db038b4ead71b9d70515ea371f9b815f8f90b17037e6a262483fd9d5503c4.jpg", + "table_caption": [ + "Table 2. Comparison with the state-of-the-art methods on the A-OKVQA. Note that these results are unfiltered scores. $S^3 C^*$ denotes the model without unlabelled samples." + ], + "table_footnote": [], + "table_body": "
AOKVQA
ApproachB4MRSCAcc valAcc testHuman
ViLBERT [29]-----30.625.9-
LXMERT [52]-----30.725.9-
KRISP [35]-----33.727.1-
Clipcap [49]-----30.825.9-
e-UG [20]15.118.142.414.951.530.525.644.1
NLX-GPT [48]20.117.046.315.865.432.728.746.9
\\( S^2C^{*'} \\) (ours)21.817.947.317.370.633.029.649.4
\\( S^3C \\) (ours)22.518.548.418.174.434.233.554.7
", + "bbox": [ + 496, + 142, + 883, + 248 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5938ddc4399a3bab2f4a2431c7b8a6f600490b95bdaced85fe09bba08461188a.jpg", + "table_caption": [ + "Table 3. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are filtered scores. $S^3 C^*$ denotes the model without unlabelled samples." + ], + "table_footnote": [], + "table_body": "
B1B2B3B4MRSCAccHuman
RVT [34]51.937.025.617.419.242.115.852.568.660.5
PJ-X [41]57.442.230.922.719.746.017.182.776.469.3
FME [58]59.143.431.723.120.447.118.487.075.5-
QA-only [20]51.036.425.317.318.641.914.949.9--
e-UG [20]57.342.731.423.222.145.720.174.180.571.4
NLX-GPT [48]64.249.537.628.523.151.522.1110.683.273.7
S3C*(ours)64.449.938.029.123.451.922.7112.183.775.9
S3C(ours)64.750.538.830.723.952.123.0116.785.679.2
", + "bbox": [ + 200, + 301, + 767, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "matic metrics BLEU [40],METEOR[11],ROUGE-L[26], SPICE[1] and CIDEr[55] to evaluate generated explanations.For the evaluation of predicted answers, we follow [48,60] to compute the VQA accuracy.", + "bbox": [ + 75, + 454, + 467, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Human Evaluation. Automatic VQA-NLE measures do not always reflect the correctness and logicality of the explanations [20, 53], thus we also build human evaluations. The process is similar to [20, 34]. Specifically, for each explanation, three human evaluators are required to decide whether an explanation can justify the answer and select an option (including \"yes, weak yes, weak no and no\"). The selection will be mapped to scores $(1, \\frac{2}{3}, \\frac{1}{3}$ and 0). The final scores are computed by averaging among all test samples. Meanwhile, these evaluators are asked to choose the reasons for unqualified explanations. We follow [20] to define three kinds of aspects to evaluate the explanations: irrelevant explanations, insufficient explanations and meaningless explanations. First, the irrelevant explanations may not match the image, for example, \"have a long neck\" is a good explanation for the answer \"giraffes\" when asked \"what animals are these?\", but the image may display cows. Second, the insufficient explanations only describe the image but cannot corroborate the answers. For example, the sentence \"there are some people\" does not sufficiently justify the question \"do people have a party?\". Lastly, some nonsensical sentences could be judged as contradictory explanations, such as \"a man is a woman\". For each sample, the human evaluators can select multiple shortcomings. More details of the human evaluation can be found in the [20].", + "bbox": [ + 75, + 523, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Quantitative evaluation.", + "text_level": 1, + "bbox": [ + 500, + 454, + 718, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Automatic Evaluation. We compare our method with the state-of-the-art models on the VQA-X and A-OKVQA datasets in Table 1-3. The B4, M, R, S, C, Acc and Human are short for BLEU-4, METEOR, ROUGE-L, SPICE, CIDEr, Answer precision and Human evaluation. We use \"unfiltered\" to indicate that the explanations are evaluated regardless of whether the answer is true or false. While \"filtered\" is to only consider the explanations which have correct answers. From Table 1, the $S^3 C^*$ denotes that we only apply the self-critical framework without using unlabelled samples, while the row $S^3 C$ indicates our method in the semi-supervised setting. We observe that the proposed framework outperforms both the post-hoc explanation methods [41, 58] and the self-rationalization method [48]. Meanwhile, it's worth noting that although the NLX-GPT uses a more powerful pre-trained VL model with larger pre-trained datasets (i.e., COCO captions [27], Flicker30k [43] and Visual Genome [24]), our method still obtains 3.3 absolute gains on the CIDEr indicator with fewer pre-trained data (only using COCO captions). Furthermore, when we utilize our proposed semi-supervised paradigm, the results are further improved by 7.2 points. These results show that our model can generate more reliable explanations and it can benefit from the amount of data without human-explanation labels. We also report the accuracy of answers in the column of \"Acc\". It can be observed that our self-critical method with semi-supervised learning can simultaneously boost the precision of answers and cor", + "bbox": [ + 496, + 477, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2651", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/da21cabd57c16c24a7e2169ce89c73de4852738715211d6249d7ca49aab58162.jpg", + "table_caption": [ + "Table 4. Main shortcomings. The main shortcomings of unqualified explanations on the VQA-X dataset. For each sample, human evaluators can select multiple shortcomings." + ], + "table_footnote": [], + "table_body": "
ModelIrrelevant explanationsInsufficient explanationsMeaningless explanations
RVT [34]25.7%33.5%11.4%
PJ-X [41]21.1%28.4%9.2%
e-UG [20]22.8%25.4%8.7%
NLX-GPT [48]20.3%22.2%9.1%
S3C (ours)17.3%18.9%8.2%
", + "bbox": [ + 81, + 141, + 468, + 243 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9384a847859a37b77b0e223920bb38a1ba6644d8f4857f0151c7dcc6ca18dda1.jpg", + "table_caption": [ + "Table 5. Cross-dataset testing. We alternately use the VQA-X and A-OKVQA as source dataset and target dataset to test the generalization of our framework." + ], + "table_footnote": [], + "table_body": "
VQA-X→A-OKVQA
ApproachB4MRSCAcc
NLX-GPT [48]10.712.734.210.735.410.4
S3C(ours)12.013.334.312.545.318.8
A-OKVQA→VQA-X
ApproachB4MRSCAcc
NLX-GPT [48]9.113.632.89.133.242.4
S3C(ours)10.915.034.110.438.643.8
", + "bbox": [ + 519, + 142, + 880, + 253 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e1eac8ada72bf5d72678ba027f7e008e2317a7cf3997c08c3e1cd6c72cd59876.jpg", + "table_caption": [ + "Table 6. Ablation study. We ablate key components to demonstrate the effectiveness of our method. SCR and Semi are Self-Critical Reinforcement module and Semi-supervised learning paradigm respectively." + ], + "table_footnote": [], + "table_body": "
questionimageanswerexplanationSCRSemiB4MRSCAcc
1✓✓✓--------80.1
2✓✓-✓--24.420.747.319.590.4-
3✓✓✓✓--27.522.950.421.9109.182.2
4✓✓✓✓✓-29.123.451.922.7112.183.7
5✓✓✓✓✓✓30.723.952.123.0116.785.6
", + "bbox": [ + 140, + 306, + 823, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "responding explanations.", + "bbox": [ + 76, + 424, + 243, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 2, we evaluate our method on the A-OKVQA dataset. The results show that the $S^3 C$ can outperform all the previous works [17, 29, 35, 48, 49, 52]. Especially, compared to the SOTA model [48], there are 9.0 points and $4.8\\%$ improvements in the CIDEr and answer accuracy based on our model. It demonstrates that our model can benefit from semi-supervised learning and generate explanations about commonsense reasoning.", + "bbox": [ + 75, + 446, + 468, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, to prove the algorithm's validity, we follow [20, 48] to report the filtered scores for the VQAX dataset in Table 3. Through filtering the correct answers, our method can outperform whatever post-hoc [20, 34, 41, 58] and self-rationalization [48] methods. Meanwhile, the proposed $S^3 C$ achieves a new state-of-the-art with the CIDEr score improved by 6.1 points to 116.7 and boost the answer accuracy by $2.4\\%$ to 85.6.", + "bbox": [ + 75, + 575, + 468, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Human Evaluation. To evaluate the faithfulness and correctness of these generated explanations, we conduct the human evaluation that is shown in the column of \"Human\" in Table 1-3. The experimental results further prove our method has better self-interpretability for the VQA-NLE task. Moreover, we also ask the human evaluators to select the shortcomings for each unqualified explanation on the VQA-X dataset. As shown in Table 4, we build three shortcoming options (i.e., irrelevant explanations, insufficient explanations and meaningless explanations) with a multi-choice process. These results indicate that the $S^3 C$ can obtain relatively better rationales and empirically confirm the effectiveness of our method.", + "bbox": [ + 75, + 703, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Cross-dataset Performance.", + "text_level": 1, + "bbox": [ + 500, + 422, + 748, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We propose cross-dataset experiments to measure the generalization and reliability of our framework. For all we know, there is very little research on cross-dataset explanation generation. As shown in the first two rows of Table 5, we use the VQA-X and the A-OKVQA as the source dataset and target dataset to test the generalization ability of our framework. Specifically, we use the weights from the state-of-the-art method [48], which are trained on the VQA-X dataset and tested on the A-OKVQA dataset to obtain the results of the NLX-GPT. From the comparisons of six indicators, we find that our self-critical model has better generalization from the general VQA to the knowledge-based VQA. This suggests that $S^3 C$ can learn commonsense from visual question answering and generate better explanations and answers. Meanwhile, when we exchange the source dataset and target dataset as shown in the last two rows of Table 5, our framework can still surpass the existing SOTA model on all evaluation measures. These quantitative results effectively demonstrate the generalization and stability of our model.", + "bbox": [ + 496, + 446, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Studies.", + "text_level": 1, + "bbox": [ + 500, + 756, + 668, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 6, we conduct several ablation studies on the VQA-X to demonstrate the effectiveness of our method. In particular, we first build the experiments in the 1-3 rows of Table 6, which use our Answer-Explanation Prompt module with cross-entropy loss as the baseline models. It can be found that when we simultaneously generate both answers and interpretations, the answer accuracy and CIDEr can achieve significant improvements. Meanwhile,", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2652", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e01d8549bb6df38c2dafa143287e46634835e7efea7ff386f6c873aac75eb11.jpg", + "image_caption": [ + "(a) Is this man dressed formal?" + ], + "image_footnote": [], + "bbox": [ + 111, + 97, + 308, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca253b406d47da5ce9e8dd0643f14741dc101b45433029313006510d4e8be934.jpg", + "image_caption": [ + "Ours: [yes] ", + "(b) Is he in a swimming pool?", + "NLX: [yes] ", + "Ours: [no] " + ], + "image_footnote": [], + "bbox": [ + 387, + 97, + 584, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/39ae1e8ba51b4a97e658d08b9090d5b5fe7801fe50db87ef8fd67f5798d0bfac.jpg", + "image_caption": [ + "(c) What is the elephant doing?", + "NLX: [drinking] ", + "Ours: [drinking]" + ], + "image_footnote": [], + "bbox": [ + 653, + 97, + 848, + 191 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c4f860296fc1546b20f04255e426a9cdbc3d82adb6d7857051de46cd6ac72882.jpg", + "image_caption": [ + "NLX: [no] ", + "(d) Are the people having a party?", + "NLX: [no] ", + "Ours: [yes] ", + "GT: [yes] ", + "Figure 3. Some generation results on the VQA-X datasets. The [ ] and $<<$ indicate answers and explanations respectively. We show the results of the state-of-the-art NLX-GPT [48], our method and ground-truth (they are short for NLX, Ours and GT)." + ], + "image_footnote": [], + "bbox": [ + 111, + 251, + 305, + 347 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/245f9a6f2d0c2769e88489f6a21f838f96135dde6cd9756a73f082c8f5875f4d.jpg", + "image_caption": [ + "GT: [yes] ", + "GT: [no] ", + "(e) Does this animal appear to be looking", + "at the camera?", + "NLX: [yes] ", + "Ours: [no] ", + "GT: [no] " + ], + "image_footnote": [], + "bbox": [ + 387, + 251, + 584, + 347 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7bec96df02b62f6838cf074149ae4a727fd068f7ab72ee06b34553bac058bac9.jpg", + "image_caption": [ + "GT: [drinking]", + "(f) Is this a bar?", + "NLX: [yes] ", + "Ours: [yes] ", + "GT: [yes] " + ], + "image_footnote": [], + "bbox": [ + 653, + 251, + 849, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "these results also prove that the answer-explanation pairs have inherent consistency and they can promote each other. Further, we establish the Self-Critical Reinforcement module as shown in the fourth row, and the result of accuracy and CIDEr are boosted by $1.5\\%$ and 3.0 points. It suggests that our self-critical method with sequence sampling strategy can encourage the model to generate more reliable explanations and correct answers. Finally, when we extend our model to the semi-supervised setting, the performance improves to 85.6 on the accuracy and 116.7 on the CIDEr over the baseline model (i.e., the row 5 of Table 6) by $3.4\\%$ and 7.6 points. The results demonstrate that our framework is remarkably effective in improving the logical consistency and the self-interpretability of the model.", + "bbox": [ + 75, + 484, + 472, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Qualitative evaluation.", + "text_level": 1, + "bbox": [ + 76, + 709, + 287, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Fig. 3, we show some qualitative results from NLX-GPT [48] and our $S^3 C$ method on the VQA-X dataset. Through overall comparison, our model achieves better logical consistency between answers and explanations. For example, in Fig. 3 (a), although the SOTA method [48] correctly identifies the significant symbol of formal dress (i.e., tie), the predicted answer is \"no\" that is contradictory to the explanation. On the contrary, our method not only obtains a more complete and faithful rationale but also generates a logically consistent answer. Additionally, the $S^3 C$ can also produce more persuasive and", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "trusty sentences. For instance, in Fig. 3 (b)-(f), the generated sentences contain scene description \"having a good time\" and fine-grained rationale \"the trunk is in the water\".", + "bbox": [ + 496, + 484, + 890, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 549, + 617, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a new Semi-Supervised VQANLE method via Self-Critical Learning $(S^3 C)$ . Different from previous works, our method first utilizes the prompting mechanism to motivate the model to generate answers and candidate explanations. Meanwhile, we design a novel Self-Critical Reinforcement module, which converts the answer scores as rewards to evaluate these possible rationales. Furthermore, our framework can benefit from an abundance of question-answer pairs without human-annotated explanations and further boost the self-interpretability of the model. With the automatic measures and human evaluations, our $S^3 C$ achieves a new state-of-the-art on multiple benchmarks and provides a new paradigm for our community.", + "bbox": [ + 496, + 575, + 890, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 790, + 666, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key RD Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03).", + "bbox": [ + 496, + 816, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2653", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 13041-13049, 2020." + ], + "bbox": [ + 78, + 90, + 470, + 799 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2656", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_model.json b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..daee8a36891d9dbd9ba3a05253a9a1f226a5e1c1 --- /dev/null +++ b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_model.json @@ -0,0 +1,2477 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.165, + 0.13, + 0.806, + 0.176 + ], + "angle": 0, + "content": "\\(\\mathrm{S}^{3}\\mathrm{C}\\): Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.203, + 0.873, + 0.275 + ], + "angle": 0, + "content": "Wei Suo\\(^{1*}\\), Mengyang Sun\\(^{2*}\\), Weisong Liu\\(^{1}\\), Yiqi Gao\\(^{1}\\), Peng Wang\\(^{1\\dagger}\\), Yanning Zhang\\(^{1\\dagger}\\), Qi Wu\\(^{3}\\) \n\\(^{1}\\)School of Computer Science and Ningbo Institute, Northwestern Polytechnical University, China. \n\\(^{2}\\)School of Cybersecurity, Northwestern Polytechnical University, China. \n\\(^{3}\\)University of Adelaide, Australia." + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.277, + 0.737, + 0.293 + ], + "angle": 0, + "content": "{suowei1994,sunmenmian,liuweisong,gyqjz}@mail.nwpu.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.296, + 0.724, + 0.31 + ], + "angle": 0, + "content": "{peng.wang, ynzhang}@nwpu.edu.cn, qi.wu01@adelaide.edu.au" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.474, + 0.694 + ], + "angle": 0, + "content": "VQA Natural Language Explanation (VQA-NLE) task aims to explain the decision-making process of VQA models in natural language. Unlike traditional attention or gradient analysis, free-text rationales can be easier to understand and gain users' trust. Existing methods mostly use post-hoc or self-rationalization models to obtain a plausible explanation. However, these frameworks are bottlenecked by the following challenges: 1) the reasoning process cannot be faithfully responded to and suffer from the problem of logical inconsistency. 2) Human-annotated explanations are expensive and time-consuming to collect. In this paper, we propose a new Semi-Supervised VQA-NLE via Self-Critical Learning \\((S^3 C)\\), which evaluates the candidate explanations by answering rewards to improve the logical consistency between answers and rationales. With a semi-supervised learning framework, the \\(S^3 C\\) can benefit from a tremendous amount of samples without human-annotated explanations. A large number of automatic measures and human evaluations all show the effectiveness of our method. Meanwhile, the framework achieves a new state-of-the-art performance on the two VQA-NLE datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.736, + 0.208, + 0.751 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Deep neural networks have enabled significant breakthroughs in a variety of vision-language (VL) tasks such as image captioning [10, 47] and visual question answering (VQA) [2, 39]. Unfortunately, most of them are black box systems, which makes it challenging to gain users' trust [20]. Explaining the decision-making process of deep VL models is a long-standing and essential problem." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.347, + 0.898, + 0.422 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.424, + 0.898, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.499, + 0.898, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.693 + ], + "angle": 0, + "content": "Figure 1. Paradigm comparison of different VQA-NLE methods. (a) Post-hoc explanation method adopts two independent models to predict answers and explanations respectively. (b) Self-rationalization method uses a united VL model to simultaneously generate answers and explanations. (c) Our self-critical strategy utilizes answer scores as rewards and obtains more reliable rationales with semi-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.885 + ], + "angle": 0, + "content": "Some approaches depend on attention mechanisms [2, 30] or gradient-based localization [50] to acquire visual explanations, which can highlight some contributing image regions for the predicted answers. However, simple visualization cannot explain how these areas support the answers and they are also hard to comprehend [20, 48]. Conversely, Natural Language Explanation (NLE) task [6, 38] can explain the decision-making process of a model by generating a natural language sentence. The language-based explanations are more accessible for users to understand, and they can also help researchers optimize the structure of models [34]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recently, some models of NLE in the VL commu" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.875, + 0.352, + 0.888 + ], + "angle": 0, + "content": "*These authors contributed equally to this work." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.227, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.095, + 0.875, + 0.352, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2646" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "nity have achieved pretty-well results, especially for VQANLE [20,34,41,48,58]. They can guide models to generate natural language sentences and interpret how the models get answers. Specifically, the first research line usually treats VQA-NLE as a predict-then-explain task [20, 34, 41, 58], namely post-hoc explanations method. As shown in Fig. 1 (a), these methods first depend on pre-trained VL models (such as UNITER [8] or Oscar [25]) to gain answers. Then the fused multi-modal features and the predicted answers are fed into a separated language model (e.g., LSTM [16] or Transformer [54]) to generate corresponding explanations. As shown in Fig. 1 (b), the other line [48] relies on a united VL model while generating both answers and explanations, which is known as the self-rationalization method. This framework can simultaneously predict an answer and generate a rationale by formulating the answer as a text-generation task along with the explanation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.473, + 0.529 + ], + "angle": 0, + "content": "Though significant progress has been made, the two paradigms are still restricted by the following challenges: 1) For the first paradigm, since the decision-making model and interpretation part are two separate modules, it would inevitably lead to unfaithful responses to the reasoning process of the decision models. 2) Due to the lack of explicitly logical relationship modeling, previous work [19] has proved that the straightforward self-rationalization frameworks suffer from the problem of logical inconsistency. 3) The above strategies all require an amount of human-annotated explanations, which are expensive and time-consuming to collect [62]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.473, + 0.865 + ], + "angle": 0, + "content": "To solve the above challenges, inspired by [5, 51], we argue that a reasonable rationale can assist the model in obtaining a correct answer, and vice versa, the answer can be converted as an evaluation criterion for possible explanations. In this paper, we propose a new Semi-Supervised VQA-NLE method with Self-Critical learning, which is called \\( S^3 C \\) for short. As shown in Fig.1 (c), given images and related questions, we first leverage a prompting mechanism to construct answer and explanation templates, which can guide the pre-trained VL model to generate answers and multiple candidate explanations based on sequence sampling [2]. Then we design a new self-critical method that converts the answer scores as rewards and encourages the model to generate the explanations which contribute to improving the answer scores. In particular, to reduce the dependency on expensive human annotations, we further extend our method to the semi-supervised version, which utilizes the unlabelled samples1 (i.e., conventional VQA data [4, 36]) to significantly enhance the self-interpretability of the model. With the self-critical strategy and the semi-supervised learning, our method effectively models the logical relationships and promotes the logical" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.182 + ], + "angle": 0, + "content": "consistency between answer-explanation pairs. According to automatic measures and human evaluations, the \\( S^3 C \\) outperforms the state-of-the-art models for the VQA-NLE task on the widely used two datasets and provides a new paradigm for our community. In summary, we make the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.185, + 0.895, + 0.261 + ], + "angle": 0, + "content": "1) We propose a new self-critical VQA-NLE method that can model the logical relationships between answer-explanation pairs and evaluate the generated rationales by answering rewards. This strategy effectively improves the logical consistency and the reliability of the interpretations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.895, + 0.354 + ], + "angle": 0, + "content": "2) We develop an advanced semi-supervised learning framework for VQA-NLE, which utilizes amounts of samples without human-annotated explanations to boost the self-interpretability of the model further. To the best of our knowledge, we are the first to explore semi-supervised learning on the VQA Natural Language Explanation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.416 + ], + "angle": 0, + "content": "3) The proposed \\( S^3 C \\) achieves new state-of-the-art performance on VQA-X [13] and A-OKVQA [49] benchmark datasets. Meanwhile, automatic measures and human evaluations all show the effectiveness of our method." + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.185, + 0.895, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.439, + 0.639, + 0.455 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.467, + 0.88, + 0.484 + ], + "angle": 0, + "content": "2.1. Explainability in Visual Question Answering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The visual question answering (VQA) is firstly proposed by [33] that requires an intelligent agent to generate an answer by giving an image and a question. Many approaches have been introduced such as joint embedding [13, 61], attention mechanisms [3, 31], memory networks [32, 59] and graph neural networks [23, 56]. Although the VQA task has been well studied, the reasoning process of the models is always agnostic. Some methods apply visualization technologies to achieve visual explanation, such as Grad-CAM [50] and U-CAM [42]. However, because image visualization cannot support the answer based on the attended areas [57], in this paper, we focus on improving free-text explanations that are more convenient and easier for users to understand. In this topic, the early work is proposed by [41]. The paper conducts the VQA-X dataset and utilizes human annotations to inspire the decision-making process of VQA models. [20] designs a new model that combines a pre-trained language model and a VL model to generate free-text explanations. [60] combines stronger pre-trained VL model (i.e. Oscar [25]) and generation model (i.e. GPT-2 [46]) to obtain better results. Recently, [48] proposes a unified model which can simultaneously predict answers and explanations based on a pre-trained caption model. Unlike previous methods, we introduce a new self-critical strategy to model the logical relationships between answers and rationales. It can encourage the model to enhance logical consistency and generate more reasonable explanations." + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.472, + 0.903 + ], + "angle": 0, + "content": "1In this paper, we use \"unlabelled samples\" and \"labelled samples\" to indicate the question-answer (QA) pairs without/with human explanations." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "2647" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.427, + 0.108 + ], + "angle": 0, + "content": "2.2. Pre-trained models and Prompt learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.419 + ], + "angle": 0, + "content": "Pre-trained models have been applied in many fields, such as various NLP tasks [12,46] and VL tasks [29,52,65]. Most of these pre-trained models utilize a stack of Transformer structures as the backbone. To generalize the pretrained models to other downstream tasks, previous works mostly fine-tune whole models on each downstream VL task. However, the ability of pre-trained models would be limited due to the mismatch between pre-trained tasks and downstream tasks. Hence, prompt learning [9, 18, 45, 64] is proposed, and it can keep the optimization consistency. [45] designs the templates to transfer the knowledge to downstream tasks. [9] uses a textual generation framework for uniform optimization. In this paper, we use the pre-trained model based on the image caption task as our backbone. It has been proved that these additional pre-train tasks (e.g., image feature regression or mask language tokens) cannot significantly improve the performance for explanations [48]. Meanwhile, we apply different language prompt templates to motivate the model to generate corresponding answers and rationales." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.428, + 0.31, + 0.445 + ], + "angle": 0, + "content": "2.3. Semi-supervised learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.473, + 0.681 + ], + "angle": 0, + "content": "The development of deep learning depends on a large number of labelled data, while there are many cases in that only a small amount of data can be obtained [44]. To solve this challenge, Semi-supervised learning is proposed [44], which aims to train models using a small number of labelled data and amounts of unlabelled data. For example, [22] proposes a generatively semi-supervised framework based on variational autoencoders, and it can jointly optimize the model and variational parameters. Recently, [63] simultaneously leverages self-supervised and semi-supervised learning to address image classification tasks. To our knowledge, our work is the first semi-supervised learning framework for the VQA-NLE task, which effectively alleviates the reliance on expensive human annotations and further boost the self-interpretability of the model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.694, + 0.17, + 0.71 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this section, we introduce our Semi-Supervised VQANLE method with the Self-Critical learning \\((S^3 C)\\) framework. Our aim is to strengthen the logical consistency between answer-explanation pairs and improve the reliability of the rationales. As shown in Fig. 2, the \\(S^3 C\\) comprises an \"Answer-Explanation Prompt\" module and a \"Self-Critical Reinforcement\" module. Unlike previous approaches, our method first uses a prompting mechanism to generate answers and candidate explanations. Then, we design a new self-critical module that converts the answer scores as rewards to evaluate these reasons. Furthermore, this strategy can conveniently apply the unlabelled QA pairs to enrich" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "training data and enhance the self-interpretability. Next, we describe the components of our model in detail." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.133, + 0.842, + 0.149 + ], + "angle": 0, + "content": "3.1. Pre-trained Vision-Language Backbone" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.155, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Given an image \\(I \\in \\mathbb{R}^{W \\times H \\times 3}\\) and a natural language question \\(Q = \\{q_t\\}_{t=1}^T\\), where \\(q_t\\) represents the \\(t\\)-th word, \\(T\\) is the length of the question and \\(W \\times H \\times 3\\) denotes the size of the image. Our goal is to predict the answer and generate a corresponding free-text rationale. Following previous works [48, 49], we adopt the CLIP vision encoder [45] and a pre-trained image caption model (i.e., ClipCap [37]) as our basic backbone. During pre-training, the VL model uses image embeddings from the CLIP as prefixes and fine-tunes a language model (i.e., GPT-2 [46]) to generate image captions. We refer readers to [37] for more information about the pre-trained model. In this paper, we consider the image \\(I\\) and question \\(Q\\) as the prefixes of the answer-explanation sequences. Specifically, we first apply ViT-B [14] and \"classification token\" from the CLIP to obtain the image features. Then, a group of light and simple Multi-Layer Perceptron (MLP) is utilized for transforming the image features to the \\(V = \\{v_s\\}_{s=1}^S\\), \\(v_s \\in \\mathbb{R}^c\\), where the dimension size \\(c = 768\\) and the image sequence length \\(S = 10\\). The above computations can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.474, + 0.892, + 0.492 + ], + "angle": 0, + "content": "\\[\nv _ {1}, v _ {2}, \\dots , v _ {S} = \\operatorname {M L P} (\\operatorname {C L I P} (I)). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Note that we only update the mapping network (i.e., MLP) during training, while the original visual encoder parameters from the CLIP would remain frozen. For question \\( Q \\), each word \\( q_{t} \\) would be mapped to the corresponding word embedding \\( e_{t} \\in \\mathbb{R}^{c} \\) by the pre-trained caption model. Finally, we obtain the image and question sequences \\( Z \\):" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.602, + 0.892, + 0.659 + ], + "angle": 0, + "content": "\\[\nZ = \\overbrace {\\left[ v _ {1} , v _ {2} , \\cdots , v _ {S} \\right.} ^ {\\text {i m a g e}} \\underbrace {e _ {1} , e _ {2} , \\cdots , e _ {T}} _ {\\substack {\\text {q u e s t i o n} \\\\ \\text {e m b d e d i n g}}} \\bigg ], \\tag{2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.67, + 0.834, + 0.685 + ], + "angle": 0, + "content": "where \\( Z \\) is the concatenated multi-modal prefixes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.822, + 0.712 + ], + "angle": 0, + "content": "3.2. Answer-Explanation Prompt Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.84 + ], + "angle": 0, + "content": "It has been proved that the prompting mechanism can maintain the same optimization objectives between pretrained and downstream tasks [18, 28]. Considering the convenience and explainability, we leverage hand-crafted prompts as templates to enable the model to generate answers or explanations. As shown in Fig. 2, the \\( S^3 C \\) includes two different kinds of templates, which are introduced respectively as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Base Answer Template. The core idea of our \\( S^3 C \\) is to use the answer scores as evaluation criteria. Hence, we first establish a basic answer template to acquire base answer scores. Different from previous works [20, 41], our" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2648" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.095, + 0.887, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.355, + 0.896, + 0.427 + ], + "angle": 0, + "content": "Figure 2. Overview of our Semi-Supervised VQA-NLE method via Self-Critical learning \\((S^3 C)\\) framework. Given images and corresponding questions for labelled and unlabelled samples, we first use Answer-Explanation Prompt module to obtain the base answer scores and candidate explanations with a pre-trained VL model. Then these reasons are reorganized and fed back into the model to capture the explanatory answer score. Further, our Self-Critical Reinforcement module evaluates the generated explanations and returns the rewards to improve the self-interpretability of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.473, + 0.665 + ], + "angle": 0, + "content": "method treats the visual question answering task as a generation task so that the model can produce answers without a predefined answer space. Specifically, for a given image and question sequence \\( Z \\), we use natural language tokens \"the answer is\" to inspire the model to generate proper answers. By concatenating the language prompt, the base answer template \\( Z_{a} = [Z; \\langle \\text{answer} \\rangle] \\) can be obtained, where \\( [; ] \\) and \\( \\langle \\text{answer} \\rangle \\) indicate concatenation operation and the specific language prompts, respectively. During training, the base answer template and ground-true answer label \\( A = \\{a_{n}\\}_{n=1}^{N} \\) are fed into the VL model, where \\( a_{n} \\) is the \\( n \\)-th answer token and \\( N \\) denotes the length of the answer label. Next, we compute the answer loss conditioned on the \\( Z_{a} \\) in an autoregressive fashion:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.672, + 0.47, + 0.713 + ], + "angle": 0, + "content": "\\[\nL _ {a} = - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\log P \\left(a _ {n} \\mid Z _ {a}, a _ {1}, a _ {2}, \\dots , a _ {n - 1}; \\theta\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.47, + 0.766 + ], + "angle": 0, + "content": "where \\(\\theta\\) denotes the parameters of the VL model. Moreover, based on the indexes of ground-true answers, we can acquire average probability \\(p_{\\theta}^{b}(A)\\) as our base answer score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Explanation Generation Template. To produce a reasonable rationale, we leverage the language prompt \"the reason is\" to motivate the model to generate free-text explanations. Like the base answer template, an explanation generation template \\( Z_{e} = [Z; \\langle \\text{reason} \\rangle] \\) is constructed, where \\( \\langle \\text{reason} \\rangle \\) is the natural language tokens. For labelled samples, we follow Eq. 3 in the autoregressive fashion and the cross-entropy loss to compute explanation loss \\( L_{e} \\). Because there are no human-annotated explanations available, we" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.452, + 0.871, + 0.468 + ], + "angle": 0, + "content": "would not compute any loss for unlabelled QA samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.482, + 0.813, + 0.497 + ], + "angle": 0, + "content": "3.3. Self-Critical Reinforcement Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.612 + ], + "angle": 0, + "content": "To gain logically consistent rationales, in this module, we expand the searching space by introducing sequence sampling algorithm [2] and generate a set of candidate explanations. Besides, the answer scores are treated as rewards to encourage the model to output more detailed interpretations. It's worth noting that the above operations would be implemented on both labelled and unlabelled samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Candidate Explanation Generation. Benefiting from the language-based prompting strategy and the pre-trained VL model, our explanation generation template can easily guide the model to produce human-readable sentences. Hence, for unlabelled QA samples, we directly apply the explanation generation template \\( Z_{e} \\) to generate the candidate rationales. To be more specific, we utilize beam search [2] to sample the top- \\( K \\) words from the VL model probability distribution at each time step and maintain these sequences with the highest probability. Then, these generated sentences are integrated into candidate explanations \\( R_{s} = \\{r_{k}^{s}\\}_{k = 1}^{K} \\) for each QA pair without human-annotated explanations, where \\( r_k^s \\) and \\( K \\) indicate \\( k \\)-th rationale and the size of beam search, respectively. Moreover, for labelled samples, a similar mechanism is used to build the corresponding explanation set \\( R_{f} = \\{r_{k}^{f}\\}_{k = 1}^{K} \\). The above operations are implemented in all samples for the following reasons: 1) Larger search space. As shown in Fig. 2, \"frying food is unhealthy\" and \"it includes many calories\"" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2649" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.257 + ], + "angle": 0, + "content": "can both be rational explanations for the answer \"no\". The expanded search space provides more possibilities for generating reliable rationales. 2) Avoid overfitting. For labelled samples, although we can depend on human explanations to train the model, these labels are still one-sided and subjective. Using the sequence sampling strategy can prevent the model from overfitting these specific annotations [2,47]. In the end, because the labelled and unlabelled samples would be integrated into a mini-batch during training, we simplify \\( R_{f} \\) and \\( R_{s} \\) into \\( R = \\{r_k\\}_{k=1}^K \\) to indicate the candidate explanations for each sample." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.258, + 0.473, + 0.395 + ], + "angle": 0, + "content": "Self-Critical Reward. Inspired by [5, 51], an ideal rationale can help the model to infer the answer better. Based on this insight, we argue that the answer scores can be converted as self-critical rewards to evaluate these candidate explanations. Considering that this is a non-differentiable operation, we adopt reinforcement learning method [47] to achieve end-to-end training. In particular, given a sample and corresponding candidate explanations \\( R \\), we design a new input template:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.404, + 0.47, + 0.422 + ], + "angle": 0, + "content": "\\[\nZ _ {r} ^ {k} = [ Z; \\langle r e a s o n \\rangle ; r _ {k}; \\langle a n s w e r \\rangle ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.473, + 0.556 + ], + "angle": 0, + "content": "where \\( Z_{r}^{k} \\) denotes the template of adding possible rationale \\( r_{k} \\). Then, this template is fed back into the model and obtains average probability \\( p_{\\theta}^{r}(A) \\) about the answer, namely explanatory answer scores, where \\( A \\) is the ground-truth answer for the sample. Meanwhile, we use the average probability \\( p_{\\theta}^{b}(A) \\) from the output of the base answer template as the base scores. By applying reinforcement learning, the gradient is calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.566, + 0.47, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\theta} L _ {r} (\\theta) = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(p _ {\\theta} ^ {r} (A) - p _ {\\theta} ^ {b} (A)\\right) \\nabla_ {\\theta} \\operatorname {l o g} p _ {\\theta} \\left(r _ {k}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.47, + 0.725 + ], + "angle": 0, + "content": "where \\( p_{\\theta}(r_k) \\) is the probability of \\( k \\)-th explanations. Based on the above computation, this gradient would tend to increase the probability of \\( k \\)-th rationales when the answer score \\( p_{\\theta}^{r}(A) \\) higher than the scores \\( p_{\\theta}^{b}(A) \\) from the base answer template. Finally, for labelled samples, we append the human-annotated rationales to the candidate explanation \\( R \\) and predict the answers by cross-entropy loss, namely \\( L_{ea} \\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.733, + 0.15, + 0.747 + ], + "angle": 0, + "content": "3.4. Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.787 + ], + "angle": 0, + "content": "During the process of training, the overall loss function can be represented as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.798, + 0.469, + 0.814 + ], + "angle": 0, + "content": "\\[\nL = L _ {a} + L _ {e} + L _ {e a} + \\lambda L _ {r}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is used for balancing these two different types of losses (i.e., cross-entropy loss and reinforcement loss). At inference time, our model would first generate the rationales about QA pairs, then we use the explanatory template (i.e., Eq. 4) to obtain the corresponding answers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.625, + 0.108 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.697, + 0.132 + ], + "angle": 0, + "content": "4.1. Experimental setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.892, + 0.244 + ], + "angle": 0, + "content": "Datasets. Following previous methods [48, 49], we mainly carry out the experiments on the two different VQANLE datasets: VQA-X [41] and A-OKVQA [49]. Meanwhile, since explain annotations are expensive and time-consuming, we also utilize large-scale VQA v2.0 [15] and OK-VQA [36] datasets to build the semi-supervised learning paradigm. Next, we will introduce the four datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.38 + ], + "angle": 0, + "content": "VQA-X. It is a vision-language dataset that provides explanations for justifying the answers. VQA-X is collected from the Visual Question Answering (VQA) dataset [4] where the images are obtained from the MSCOCO [27]. It consists of 28K images and 33K QA pairs, split into 29K/1.4K/1.9K for training, validation and testing. Meanwhile, VQA-X constructs complementary pairs which provide a question and two semantically similar images with different answers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.518 + ], + "angle": 0, + "content": "A-OKVQA. Compared to the VQA-X, the questions of A-OKVQA generally are required commonsense reasoning about the scene described in the images. It includes 24,903 Question/Answer/Rationale triplets, split into \\(17.1\\mathrm{K} / 1.1\\mathrm{K} / 6.7\\mathrm{K}\\) for training, validation and testing. It collects images from the COCO 2017 [7] dataset, and is further filtered to obtain \\(23.7\\mathrm{K}\\) unique images. Compared with previous datasets, the A-OKVQA has richer questions and requires broader areas of knowledge for reasoning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.684 + ], + "angle": 0, + "content": "VQA & OK-VQA. We use VQA v2.0 and OK-VQA to provide large-scale unlabelled datasets for semi-supervised learning. The VQA v2.0 dataset is widely used for many previous works [2, 52]. It consists of 443k questions and 195k images. To select explainable questions instead of some obvious cases (e.g., How many...?, What color...?), we filter out these questions from VQA v2.0 and obtain the \\(\\sim 90\\mathrm{k}\\) additional questions based on the rules [41]. On the other hand, we also use knowledge-based OK-VQA [36] dataset to provide unlabelled knowledge-based QA pairs. It contains a total of 14k questions on 14k images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.851 + ], + "angle": 0, + "content": "Implementation Details. Following [37], each image is first pre-processed (such as including image resize, center crop, and normalize) by CLIP [45]. Meanwhile, we fix the ViT-B weights from the CLIP visual encoder to accelerate the training speed. For the mapping network, the image sequence length \\( S = 10 \\) and the embedding size is 768. The AdamW [21] is used as our optimizer with the weight decay 1e-5, and the batch size and beam size \\( K \\) are set to 4 and 2. The weight coefficient \\( \\lambda \\) is set to 10. We train all models on the four 1080Ti GPUs for 30 epochs with a learning rate of 1e-5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.862, + 0.698, + 0.877 + ], + "angle": 0, + "content": "4.2. Evaluation Measures" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Automatic Metering. Following [48, 60], we use the auto" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2650" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.447, + 0.131 + ], + "angle": 0, + "content": "Table 1. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are unfiltered scores. \\( S^3 C^* \\) denotes the model without unlabelled samples." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.143, + 0.446, + 0.238 + ], + "angle": 0, + "content": "
VQA-X
ApproachB4MRSCAccHuman
CAPS [41]5.912.626.311.935.268.6-
PJ-X [41]19.518.243.415.171.376.465.4
FME [58]24.419.547.717.988.875.5-
NLX-GPT [48]25.621.548.720.297.283.170.2
S3C*(ours)26.522.049.020.9100.583.773.9
S3C(ours)27.822.850.721.5104.485.677.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.491, + 0.089, + 0.885, + 0.131 + ], + "angle": 0, + "content": "Table 2. Comparison with the state-of-the-art methods on the A-OKVQA. Note that these results are unfiltered scores. \\( S^3 C^* \\) denotes the model without unlabelled samples." + }, + { + "type": "table", + "bbox": [ + 0.497, + 0.143, + 0.885, + 0.249 + ], + "angle": 0, + "content": "
AOKVQA
ApproachB4MRSCAcc valAcc testHuman
ViLBERT [29]-----30.625.9-
LXMERT [52]-----30.725.9-
KRISP [35]-----33.727.1-
Clipcap [49]-----30.825.9-
e-UG [20]15.118.142.414.951.530.525.644.1
NLX-GPT [48]20.117.046.315.865.432.728.746.9
\\( S^2C^{*'} \\) (ours)21.817.947.317.370.633.029.649.4
\\( S^3C \\) (ours)22.518.548.418.174.434.233.554.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.262, + 0.89, + 0.292 + ], + "angle": 0, + "content": "Table 3. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are filtered scores. \\( S^3 C^* \\) denotes the model without unlabelled samples." + }, + { + "type": "table", + "bbox": [ + 0.202, + 0.302, + 0.769, + 0.43 + ], + "angle": 0, + "content": "
B1B2B3B4MRSCAccHuman
RVT [34]51.937.025.617.419.242.115.852.568.660.5
PJ-X [41]57.442.230.922.719.746.017.182.776.469.3
FME [58]59.143.431.723.120.447.118.487.075.5-
QA-only [20]51.036.425.317.318.641.914.949.9--
e-UG [20]57.342.731.423.222.145.720.174.180.571.4
NLX-GPT [48]64.249.537.628.523.151.522.1110.683.273.7
S3C*(ours)64.449.938.029.123.451.922.7112.183.775.9
S3C(ours)64.750.538.830.723.952.123.0116.785.679.2
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.468, + 0.516 + ], + "angle": 0, + "content": "matic metrics BLEU [40],METEOR[11],ROUGE-L[26], SPICE[1] and CIDEr[55] to evaluate generated explanations.For the evaluation of predicted answers, we follow [48,60] to compute the VQA accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Human Evaluation. Automatic VQA-NLE measures do not always reflect the correctness and logicality of the explanations [20, 53], thus we also build human evaluations. The process is similar to [20, 34]. Specifically, for each explanation, three human evaluators are required to decide whether an explanation can justify the answer and select an option (including \"yes, weak yes, weak no and no\"). The selection will be mapped to scores \\((1, \\frac{2}{3}, \\frac{1}{3}\\) and 0). The final scores are computed by averaging among all test samples. Meanwhile, these evaluators are asked to choose the reasons for unqualified explanations. We follow [20] to define three kinds of aspects to evaluate the explanations: irrelevant explanations, insufficient explanations and meaningless explanations. First, the irrelevant explanations may not match the image, for example, \"have a long neck\" is a good explanation for the answer \"giraffes\" when asked \"what animals are these?\", but the image may display cows. Second, the insufficient explanations only describe the image but cannot corroborate the answers. For example, the sentence \"there are some people\" does not sufficiently justify the question \"do people have a party?\". Lastly, some nonsensical sentences could be judged as contradictory explanations, such as \"a man is a woman\". For each sample, the human evaluators can select multiple shortcomings. More details of the human evaluation can be found in the [20]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.455, + 0.72, + 0.47 + ], + "angle": 0, + "content": "4.3. Quantitative evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Automatic Evaluation. We compare our method with the state-of-the-art models on the VQA-X and A-OKVQA datasets in Table 1-3. The B4, M, R, S, C, Acc and Human are short for BLEU-4, METEOR, ROUGE-L, SPICE, CIDEr, Answer precision and Human evaluation. We use \"unfiltered\" to indicate that the explanations are evaluated regardless of whether the answer is true or false. While \"filtered\" is to only consider the explanations which have correct answers. From Table 1, the \\(S^3 C^*\\) denotes that we only apply the self-critical framework without using unlabelled samples, while the row \\(S^3 C\\) indicates our method in the semi-supervised setting. We observe that the proposed framework outperforms both the post-hoc explanation methods [41, 58] and the self-rationalization method [48]. Meanwhile, it's worth noting that although the NLX-GPT uses a more powerful pre-trained VL model with larger pre-trained datasets (i.e., COCO captions [27], Flicker30k [43] and Visual Genome [24]), our method still obtains 3.3 absolute gains on the CIDEr indicator with fewer pre-trained data (only using COCO captions). Furthermore, when we utilize our proposed semi-supervised paradigm, the results are further improved by 7.2 points. These results show that our model can generate more reliable explanations and it can benefit from the amount of data without human-explanation labels. We also report the accuracy of answers in the column of \"Acc\". It can be observed that our self-critical method with semi-supervised learning can simultaneously boost the precision of answers and cor" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2651" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.132 + ], + "angle": 0, + "content": "Table 4. Main shortcomings. The main shortcomings of unqualified explanations on the VQA-X dataset. For each sample, human evaluators can select multiple shortcomings." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.142, + 0.469, + 0.244 + ], + "angle": 0, + "content": "
ModelIrrelevant explanationsInsufficient explanationsMeaningless explanations
RVT [34]25.7%33.5%11.4%
PJ-X [41]21.1%28.4%9.2%
e-UG [20]22.8%25.4%8.7%
NLX-GPT [48]20.3%22.2%9.1%
S3C (ours)17.3%18.9%8.2%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.515, + 0.089, + 0.886, + 0.132 + ], + "angle": 0, + "content": "Table 5. Cross-dataset testing. We alternately use the VQA-X and A-OKVQA as source dataset and target dataset to test the generalization of our framework." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.143, + 0.882, + 0.255 + ], + "angle": 0, + "content": "
VQA-X→A-OKVQA
ApproachB4MRSCAcc
NLX-GPT [48]10.712.734.210.735.410.4
S3C(ours)12.013.334.312.545.318.8
A-OKVQA→VQA-X
ApproachB4MRSCAcc
NLX-GPT [48]9.113.632.89.133.242.4
S3C(ours)10.915.034.110.438.643.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.269, + 0.892, + 0.298 + ], + "angle": 0, + "content": "Table 6. Ablation study. We ablate key components to demonstrate the effectiveness of our method. SCR and Semi are Self-Critical Reinforcement module and Semi-supervised learning paradigm respectively." + }, + { + "type": "table", + "bbox": [ + 0.141, + 0.308, + 0.825, + 0.4 + ], + "angle": 0, + "content": "
questionimageanswerexplanationSCRSemiB4MRSCAcc
1✓✓✓--------80.1
2✓✓-✓--24.420.747.319.590.4-
3✓✓✓✓--27.522.950.421.9109.182.2
4✓✓✓✓✓-29.123.451.922.7112.183.7
5✓✓✓✓✓✓30.723.952.123.0116.785.6
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.425, + 0.245, + 0.44 + ], + "angle": 0, + "content": "responding explanations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.569 + ], + "angle": 0, + "content": "In Table 2, we evaluate our method on the A-OKVQA dataset. The results show that the \\( S^3 C \\) can outperform all the previous works [17, 29, 35, 48, 49, 52]. Especially, compared to the SOTA model [48], there are 9.0 points and \\( 4.8\\% \\) improvements in the CIDEr and answer accuracy based on our model. It demonstrates that our model can benefit from semi-supervised learning and generate explanations about commonsense reasoning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.698 + ], + "angle": 0, + "content": "In addition, to prove the algorithm's validity, we follow [20, 48] to report the filtered scores for the VQAX dataset in Table 3. Through filtering the correct answers, our method can outperform whatever post-hoc [20, 34, 41, 58] and self-rationalization [48] methods. Meanwhile, the proposed \\( S^3 C \\) achieves a new state-of-the-art with the CIDEr score improved by 6.1 points to 116.7 and boost the answer accuracy by \\( 2.4\\% \\) to 85.6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Human Evaluation. To evaluate the faithfulness and correctness of these generated explanations, we conduct the human evaluation that is shown in the column of \"Human\" in Table 1-3. The experimental results further prove our method has better self-interpretability for the VQA-NLE task. Moreover, we also ask the human evaluators to select the shortcomings for each unqualified explanation on the VQA-X dataset. As shown in Table 4, we build three shortcoming options (i.e., irrelevant explanations, insufficient explanations and meaningless explanations) with a multi-choice process. These results indicate that the \\( S^3 C \\) can obtain relatively better rationales and empirically confirm the effectiveness of our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.424, + 0.749, + 0.44 + ], + "angle": 0, + "content": "4.4. Cross-dataset Performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.892, + 0.749 + ], + "angle": 0, + "content": "We propose cross-dataset experiments to measure the generalization and reliability of our framework. For all we know, there is very little research on cross-dataset explanation generation. As shown in the first two rows of Table 5, we use the VQA-X and the A-OKVQA as the source dataset and target dataset to test the generalization ability of our framework. Specifically, we use the weights from the state-of-the-art method [48], which are trained on the VQA-X dataset and tested on the A-OKVQA dataset to obtain the results of the NLX-GPT. From the comparisons of six indicators, we find that our self-critical model has better generalization from the general VQA to the knowledge-based VQA. This suggests that \\( S^3 C \\) can learn commonsense from visual question answering and generate better explanations and answers. Meanwhile, when we exchange the source dataset and target dataset as shown in the last two rows of Table 5, our framework can still surpass the existing SOTA model on all evaluation measures. These quantitative results effectively demonstrate the generalization and stability of our model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.669, + 0.772 + ], + "angle": 0, + "content": "4.5. Ablation Studies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 6, we conduct several ablation studies on the VQA-X to demonstrate the effectiveness of our method. In particular, we first build the experiments in the 1-3 rows of Table 6, which use our Answer-Explanation Prompt module with cross-entropy loss as the baseline models. It can be found that when we simultaneously generate both answers and interpretations, the answer accuracy and CIDEr can achieve significant improvements. Meanwhile," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2652" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.112, + 0.098, + 0.31, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.194, + 0.24, + 0.204 + ], + "angle": 0, + "content": "(a) Is this man dressed formal?" + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.205, + 0.25, + 0.216 + ], + "angle": 0, + "content": "NLX: [no] " + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.216, + 0.325, + 0.227 + ], + "angle": 0, + "content": "Ours: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.227, + 0.353, + 0.238 + ], + "angle": 0, + "content": "GT: [yes] " + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.098, + 0.585, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.194, + 0.522, + 0.205 + ], + "angle": 0, + "content": "(b) Is he in a swimming pool?" + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.205, + 0.544, + 0.216 + ], + "angle": 0, + "content": "NLX: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.216, + 0.57, + 0.228 + ], + "angle": 0, + "content": "Ours: [no] " + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.228, + 0.603, + 0.238 + ], + "angle": 0, + "content": "GT: [no] " + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.098, + 0.849, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.194, + 0.795, + 0.204 + ], + "angle": 0, + "content": "(c) What is the elephant doing?" + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.205, + 0.819, + 0.216 + ], + "angle": 0, + "content": "NLX: [drinking] " + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.216, + 0.855, + 0.227 + ], + "angle": 0, + "content": "Ours: [drinking]" + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.227, + 0.854, + 0.238 + ], + "angle": 0, + "content": "GT: [drinking]" + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.252, + 0.306, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.349, + 0.258, + 0.36 + ], + "angle": 0, + "content": "(d) Are the people having a party?" + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.36, + 0.295, + 0.371 + ], + "angle": 0, + "content": "NLX: [no] " + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.371, + 0.366, + 0.383 + ], + "angle": 0, + "content": "Ours: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.383, + 0.302, + 0.393 + ], + "angle": 0, + "content": "GT: [yes] " + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.252, + 0.585, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.349, + 0.576, + 0.36 + ], + "angle": 0, + "content": "(e) Does this animal appear to be looking" + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.36, + 0.45, + 0.37 + ], + "angle": 0, + "content": "at the camera?" + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.371, + 0.572, + 0.382 + ], + "angle": 0, + "content": "NLX: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.382, + 0.617, + 0.393 + ], + "angle": 0, + "content": "Ours: [no] " + }, + { + "type": "image_caption", + "bbox": [ + 0.375, + 0.393, + 0.619, + 0.405 + ], + "angle": 0, + "content": "GT: [no] " + }, + { + "type": "image", + "bbox": [ + 0.654, + 0.252, + 0.85, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.349, + 0.72, + 0.359 + ], + "angle": 0, + "content": "(f) Is this a bar?" + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.36, + 0.868, + 0.371 + ], + "angle": 0, + "content": "NLX: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.372, + 0.82, + 0.392 + ], + "angle": 0, + "content": "Ours: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.393, + 0.886, + 0.416 + ], + "angle": 0, + "content": "GT: [yes] " + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.431, + 0.892, + 0.459 + ], + "angle": 0, + "content": "Figure 3. Some generation results on the VQA-X datasets. The [ ] and \\(<<\\) indicate answers and explanations respectively. We show the results of the state-of-the-art NLX-GPT [48], our method and ground-truth (they are short for NLX, Ours and GT)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.473, + 0.698 + ], + "angle": 0, + "content": "these results also prove that the answer-explanation pairs have inherent consistency and they can promote each other. Further, we establish the Self-Critical Reinforcement module as shown in the fourth row, and the result of accuracy and CIDEr are boosted by \\(1.5\\%\\) and 3.0 points. It suggests that our self-critical method with sequence sampling strategy can encourage the model to generate more reliable explanations and correct answers. Finally, when we extend our model to the semi-supervised setting, the performance improves to 85.6 on the accuracy and 116.7 on the CIDEr over the baseline model (i.e., the row 5 of Table 6) by \\(3.4\\%\\) and 7.6 points. The results demonstrate that our framework is remarkably effective in improving the logical consistency and the self-interpretability of the model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.288, + 0.726 + ], + "angle": 0, + "content": "4.6. Qualitative evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As shown in Fig. 3, we show some qualitative results from NLX-GPT [48] and our \\( S^3 C \\) method on the VQA-X dataset. Through overall comparison, our model achieves better logical consistency between answers and explanations. For example, in Fig. 3 (a), although the SOTA method [48] correctly identifies the significant symbol of formal dress (i.e., tie), the predicted answer is \"no\" that is contradictory to the explanation. On the contrary, our method not only obtains a more complete and faithful rationale but also generates a logically consistent answer. Additionally, the \\( S^3 C \\) can also produce more persuasive and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.532 + ], + "angle": 0, + "content": "trusty sentences. For instance, in Fig. 3 (b)-(f), the generated sentences contain scene description \"having a good time\" and fine-grained rationale \"the trunk is in the water\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.619, + 0.565 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.774 + ], + "angle": 0, + "content": "In this paper, we propose a new Semi-Supervised VQANLE method via Self-Critical Learning \\((S^3 C)\\). Different from previous works, our method first utilizes the prompting mechanism to motivate the model to generate answers and candidate explanations. Meanwhile, we design a novel Self-Critical Reinforcement module, which converts the answer scores as rewards to evaluate these possible rationales. Furthermore, our framework can benefit from an abundance of question-answer pairs without human-annotated explanations and further boost the self-interpretability of the model. With the automatic measures and human evaluations, our \\( S^3 C \\) achieves a new state-of-the-art on multiple benchmarks and provides a new paradigm for our community." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.791, + 0.667, + 0.808 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key RD Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2653" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 13041-13049, 2020." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "2656" + } + ] +] \ No newline at end of file diff --git a/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_origin.pdf b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..69f927b3b1f6dc2d20d5552dff924eb993d8f38a --- /dev/null +++ b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/6ead34e8-75d6-4d08-a4ab-1da1402619c2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4feb930de5f1f5810c4ed84e42b5370ea67e835f64c0bced3680625240924bbb +size 1390444 diff --git a/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/full.md b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4a4b9bd73fc9c7dc40a37fe7ef8544398c6f2ac1 --- /dev/null +++ b/2023/S3C_ Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning/full.md @@ -0,0 +1,322 @@ +# $\mathrm{S}^{3}\mathrm{C}$ : Semi-Supervised VQA Natural Language Explanation via Self-Critical Learning + +Wei Suo $^{1*}$ , Mengyang Sun $^{2*}$ , Weisong Liu $^{1}$ , Yiqi Gao $^{1}$ , Peng Wang $^{1\dagger}$ , Yanning Zhang $^{1\dagger}$ , Qi Wu $^{3}$ $^{1}$ School of Computer Science and Ningbo Institute, Northwestern Polytechnical University, China. + $^{2}$ School of Cybersecurity, Northwestern Polytechnical University, China. + $^{3}$ University of Adelaide, Australia. + +{suowei1994,sunmenmian,liuweisong,gyqjz}@mail.nwpu.edu.cn + +{peng.wang, ynzhang}@nwpu.edu.cn, qi.wu01@adelaide.edu.au + +# Abstract + +VQA Natural Language Explanation (VQA-NLE) task aims to explain the decision-making process of VQA models in natural language. Unlike traditional attention or gradient analysis, free-text rationales can be easier to understand and gain users' trust. Existing methods mostly use post-hoc or self-rationalization models to obtain a plausible explanation. However, these frameworks are bottlenecked by the following challenges: 1) the reasoning process cannot be faithfully responded to and suffer from the problem of logical inconsistency. 2) Human-annotated explanations are expensive and time-consuming to collect. In this paper, we propose a new Semi-Supervised VQA-NLE via Self-Critical Learning $(S^3 C)$ , which evaluates the candidate explanations by answering rewards to improve the logical consistency between answers and rationales. With a semi-supervised learning framework, the $S^3 C$ can benefit from a tremendous amount of samples without human-annotated explanations. A large number of automatic measures and human evaluations all show the effectiveness of our method. Meanwhile, the framework achieves a new state-of-the-art performance on the two VQA-NLE datasets. + +# 1. Introduction + +Deep neural networks have enabled significant breakthroughs in a variety of vision-language (VL) tasks such as image captioning [10, 47] and visual question answering (VQA) [2, 39]. Unfortunately, most of them are black box systems, which makes it challenging to gain users' trust [20]. Explaining the decision-making process of deep VL models is a long-standing and essential problem. + +![](images/af310065e8d5f1bdc8df7d8c31b4609c45d4ba16f61dad695af4654d8d7b5216.jpg) + +![](images/c5759907e61c6aea5ef5031fae6ab82cc0a7fb498d64b875941375cdd035402c.jpg) + +![](images/c16a8892e5fba59ebcfaa7daacb1445d0ba698e7ddee1afd6e25253591b95f64.jpg) +Figure 1. Paradigm comparison of different VQA-NLE methods. (a) Post-hoc explanation method adopts two independent models to predict answers and explanations respectively. (b) Self-rationalization method uses a united VL model to simultaneously generate answers and explanations. (c) Our self-critical strategy utilizes answer scores as rewards and obtains more reliable rationales with semi-supervised learning. + +Some approaches depend on attention mechanisms [2, 30] or gradient-based localization [50] to acquire visual explanations, which can highlight some contributing image regions for the predicted answers. However, simple visualization cannot explain how these areas support the answers and they are also hard to comprehend [20, 48]. Conversely, Natural Language Explanation (NLE) task [6, 38] can explain the decision-making process of a model by generating a natural language sentence. The language-based explanations are more accessible for users to understand, and they can also help researchers optimize the structure of models [34]. + +Recently, some models of NLE in the VL commu + +nity have achieved pretty-well results, especially for VQANLE [20,34,41,48,58]. They can guide models to generate natural language sentences and interpret how the models get answers. Specifically, the first research line usually treats VQA-NLE as a predict-then-explain task [20, 34, 41, 58], namely post-hoc explanations method. As shown in Fig. 1 (a), these methods first depend on pre-trained VL models (such as UNITER [8] or Oscar [25]) to gain answers. Then the fused multi-modal features and the predicted answers are fed into a separated language model (e.g., LSTM [16] or Transformer [54]) to generate corresponding explanations. As shown in Fig. 1 (b), the other line [48] relies on a united VL model while generating both answers and explanations, which is known as the self-rationalization method. This framework can simultaneously predict an answer and generate a rationale by formulating the answer as a text-generation task along with the explanation. + +Though significant progress has been made, the two paradigms are still restricted by the following challenges: 1) For the first paradigm, since the decision-making model and interpretation part are two separate modules, it would inevitably lead to unfaithful responses to the reasoning process of the decision models. 2) Due to the lack of explicitly logical relationship modeling, previous work [19] has proved that the straightforward self-rationalization frameworks suffer from the problem of logical inconsistency. 3) The above strategies all require an amount of human-annotated explanations, which are expensive and time-consuming to collect [62]. + +To solve the above challenges, inspired by [5, 51], we argue that a reasonable rationale can assist the model in obtaining a correct answer, and vice versa, the answer can be converted as an evaluation criterion for possible explanations. In this paper, we propose a new Semi-Supervised VQA-NLE method with Self-Critical learning, which is called $S^3 C$ for short. As shown in Fig.1 (c), given images and related questions, we first leverage a prompting mechanism to construct answer and explanation templates, which can guide the pre-trained VL model to generate answers and multiple candidate explanations based on sequence sampling [2]. Then we design a new self-critical method that converts the answer scores as rewards and encourages the model to generate the explanations which contribute to improving the answer scores. In particular, to reduce the dependency on expensive human annotations, we further extend our method to the semi-supervised version, which utilizes the unlabelled samples1 (i.e., conventional VQA data [4, 36]) to significantly enhance the self-interpretability of the model. With the self-critical strategy and the semi-supervised learning, our method effectively models the logical relationships and promotes the logical + +consistency between answer-explanation pairs. According to automatic measures and human evaluations, the $S^3 C$ outperforms the state-of-the-art models for the VQA-NLE task on the widely used two datasets and provides a new paradigm for our community. In summary, we make the following contributions: + +1) We propose a new self-critical VQA-NLE method that can model the logical relationships between answer-explanation pairs and evaluate the generated rationales by answering rewards. This strategy effectively improves the logical consistency and the reliability of the interpretations. +2) We develop an advanced semi-supervised learning framework for VQA-NLE, which utilizes amounts of samples without human-annotated explanations to boost the self-interpretability of the model further. To the best of our knowledge, we are the first to explore semi-supervised learning on the VQA Natural Language Explanation. +3) The proposed $S^3 C$ achieves new state-of-the-art performance on VQA-X [13] and A-OKVQA [49] benchmark datasets. Meanwhile, automatic measures and human evaluations all show the effectiveness of our method. + +# 2. Related work + +# 2.1. Explainability in Visual Question Answering + +The visual question answering (VQA) is firstly proposed by [33] that requires an intelligent agent to generate an answer by giving an image and a question. Many approaches have been introduced such as joint embedding [13, 61], attention mechanisms [3, 31], memory networks [32, 59] and graph neural networks [23, 56]. Although the VQA task has been well studied, the reasoning process of the models is always agnostic. Some methods apply visualization technologies to achieve visual explanation, such as Grad-CAM [50] and U-CAM [42]. However, because image visualization cannot support the answer based on the attended areas [57], in this paper, we focus on improving free-text explanations that are more convenient and easier for users to understand. In this topic, the early work is proposed by [41]. The paper conducts the VQA-X dataset and utilizes human annotations to inspire the decision-making process of VQA models. [20] designs a new model that combines a pre-trained language model and a VL model to generate free-text explanations. [60] combines stronger pre-trained VL model (i.e. Oscar [25]) and generation model (i.e. GPT-2 [46]) to obtain better results. Recently, [48] proposes a unified model which can simultaneously predict answers and explanations based on a pre-trained caption model. Unlike previous methods, we introduce a new self-critical strategy to model the logical relationships between answers and rationales. It can encourage the model to enhance logical consistency and generate more reasonable explanations. + +# 2.2. Pre-trained models and Prompt learning + +Pre-trained models have been applied in many fields, such as various NLP tasks [12,46] and VL tasks [29,52,65]. Most of these pre-trained models utilize a stack of Transformer structures as the backbone. To generalize the pretrained models to other downstream tasks, previous works mostly fine-tune whole models on each downstream VL task. However, the ability of pre-trained models would be limited due to the mismatch between pre-trained tasks and downstream tasks. Hence, prompt learning [9, 18, 45, 64] is proposed, and it can keep the optimization consistency. [45] designs the templates to transfer the knowledge to downstream tasks. [9] uses a textual generation framework for uniform optimization. In this paper, we use the pre-trained model based on the image caption task as our backbone. It has been proved that these additional pre-train tasks (e.g., image feature regression or mask language tokens) cannot significantly improve the performance for explanations [48]. Meanwhile, we apply different language prompt templates to motivate the model to generate corresponding answers and rationales. + +# 2.3. Semi-supervised learning + +The development of deep learning depends on a large number of labelled data, while there are many cases in that only a small amount of data can be obtained [44]. To solve this challenge, Semi-supervised learning is proposed [44], which aims to train models using a small number of labelled data and amounts of unlabelled data. For example, [22] proposes a generatively semi-supervised framework based on variational autoencoders, and it can jointly optimize the model and variational parameters. Recently, [63] simultaneously leverages self-supervised and semi-supervised learning to address image classification tasks. To our knowledge, our work is the first semi-supervised learning framework for the VQA-NLE task, which effectively alleviates the reliance on expensive human annotations and further boost the self-interpretability of the model. + +# 3. Method + +In this section, we introduce our Semi-Supervised VQANLE method with the Self-Critical learning $(S^3 C)$ framework. Our aim is to strengthen the logical consistency between answer-explanation pairs and improve the reliability of the rationales. As shown in Fig. 2, the $S^3 C$ comprises an "Answer-Explanation Prompt" module and a "Self-Critical Reinforcement" module. Unlike previous approaches, our method first uses a prompting mechanism to generate answers and candidate explanations. Then, we design a new self-critical module that converts the answer scores as rewards to evaluate these reasons. Furthermore, this strategy can conveniently apply the unlabelled QA pairs to enrich + +training data and enhance the self-interpretability. Next, we describe the components of our model in detail. + +# 3.1. Pre-trained Vision-Language Backbone + +Given an image $I \in \mathbb{R}^{W \times H \times 3}$ and a natural language question $Q = \{q_t\}_{t=1}^T$ , where $q_t$ represents the $t$ -th word, $T$ is the length of the question and $W \times H \times 3$ denotes the size of the image. Our goal is to predict the answer and generate a corresponding free-text rationale. Following previous works [48, 49], we adopt the CLIP vision encoder [45] and a pre-trained image caption model (i.e., ClipCap [37]) as our basic backbone. During pre-training, the VL model uses image embeddings from the CLIP as prefixes and fine-tunes a language model (i.e., GPT-2 [46]) to generate image captions. We refer readers to [37] for more information about the pre-trained model. In this paper, we consider the image $I$ and question $Q$ as the prefixes of the answer-explanation sequences. Specifically, we first apply ViT-B [14] and "classification token" from the CLIP to obtain the image features. Then, a group of light and simple Multi-Layer Perceptron (MLP) is utilized for transforming the image features to the $V = \{v_s\}_{s=1}^S$ , $v_s \in \mathbb{R}^c$ , where the dimension size $c = 768$ and the image sequence length $S = 10$ . The above computations can be formulated as follows: + +$$ +v _ {1}, v _ {2}, \dots , v _ {S} = \operatorname {M L P} (\operatorname {C L I P} (I)). \tag {1} +$$ + +Note that we only update the mapping network (i.e., MLP) during training, while the original visual encoder parameters from the CLIP would remain frozen. For question $Q$ , each word $q_{t}$ would be mapped to the corresponding word embedding $e_{t} \in \mathbb{R}^{c}$ by the pre-trained caption model. Finally, we obtain the image and question sequences $Z$ : + +$$ +Z = \overbrace {\left[ v _ {1} , v _ {2} , \cdots , v _ {S} \right.} ^ {\text {i m a g e}} \underbrace {e _ {1} , e _ {2} , \cdots , e _ {T}} _ {\substack {\text {q u e s t i o n} \\ \text {e m b d e d i n g}}} \bigg ], \tag{2} +$$ + +where $Z$ is the concatenated multi-modal prefixes. + +# 3.2. Answer-Explanation Prompt Module + +It has been proved that the prompting mechanism can maintain the same optimization objectives between pretrained and downstream tasks [18, 28]. Considering the convenience and explainability, we leverage hand-crafted prompts as templates to enable the model to generate answers or explanations. As shown in Fig. 2, the $S^3 C$ includes two different kinds of templates, which are introduced respectively as follows. + +Base Answer Template. The core idea of our $S^3 C$ is to use the answer scores as evaluation criteria. Hence, we first establish a basic answer template to acquire base answer scores. Different from previous works [20, 41], our + +![](images/6c9a1ae1014099259c66fe6acd5d5ccb3871a086fe23b1181827247d177149a2.jpg) +Figure 2. Overview of our Semi-Supervised VQA-NLE method via Self-Critical learning $(S^3 C)$ framework. Given images and corresponding questions for labelled and unlabelled samples, we first use Answer-Explanation Prompt module to obtain the base answer scores and candidate explanations with a pre-trained VL model. Then these reasons are reorganized and fed back into the model to capture the explanatory answer score. Further, our Self-Critical Reinforcement module evaluates the generated explanations and returns the rewards to improve the self-interpretability of the model. + +method treats the visual question answering task as a generation task so that the model can produce answers without a predefined answer space. Specifically, for a given image and question sequence $Z$ , we use natural language tokens "the answer is" to inspire the model to generate proper answers. By concatenating the language prompt, the base answer template $Z_{a} = [Z; \langle \text{answer} \rangle]$ can be obtained, where $[; ]$ and $\langle \text{answer} \rangle$ indicate concatenation operation and the specific language prompts, respectively. During training, the base answer template and ground-true answer label $A = \{a_{n}\}_{n=1}^{N}$ are fed into the VL model, where $a_{n}$ is the $n$ -th answer token and $N$ denotes the length of the answer label. Next, we compute the answer loss conditioned on the $Z_{a}$ in an autoregressive fashion: + +$$ +L _ {a} = - \frac {1}{N} \sum_ {n = 1} ^ {N} \log P \left(a _ {n} \mid Z _ {a}, a _ {1}, a _ {2}, \dots , a _ {n - 1}; \theta\right), \tag {3} +$$ + +where $\theta$ denotes the parameters of the VL model. Moreover, based on the indexes of ground-true answers, we can acquire average probability $p_{\theta}^{b}(A)$ as our base answer score. + +Explanation Generation Template. To produce a reasonable rationale, we leverage the language prompt "the reason is" to motivate the model to generate free-text explanations. Like the base answer template, an explanation generation template $Z_{e} = [Z; \langle \text{reason} \rangle]$ is constructed, where $\langle \text{reason} \rangle$ is the natural language tokens. For labelled samples, we follow Eq. 3 in the autoregressive fashion and the cross-entropy loss to compute explanation loss $L_{e}$ . Because there are no human-annotated explanations available, we + +would not compute any loss for unlabelled QA samples. + +# 3.3. Self-Critical Reinforcement Module + +To gain logically consistent rationales, in this module, we expand the searching space by introducing sequence sampling algorithm [2] and generate a set of candidate explanations. Besides, the answer scores are treated as rewards to encourage the model to output more detailed interpretations. It's worth noting that the above operations would be implemented on both labelled and unlabelled samples. + +Candidate Explanation Generation. Benefiting from the language-based prompting strategy and the pre-trained VL model, our explanation generation template can easily guide the model to produce human-readable sentences. Hence, for unlabelled QA samples, we directly apply the explanation generation template $Z_{e}$ to generate the candidate rationales. To be more specific, we utilize beam search [2] to sample the top- $K$ words from the VL model probability distribution at each time step and maintain these sequences with the highest probability. Then, these generated sentences are integrated into candidate explanations $R_{s} = \{r_{k}^{s}\}_{k = 1}^{K}$ for each QA pair without human-annotated explanations, where $r_k^s$ and $K$ indicate $k$ -th rationale and the size of beam search, respectively. Moreover, for labelled samples, a similar mechanism is used to build the corresponding explanation set $R_{f} = \{r_{k}^{f}\}_{k = 1}^{K}$ . The above operations are implemented in all samples for the following reasons: 1) Larger search space. As shown in Fig. 2, "frying food is unhealthy" and "it includes many calories" + +can both be rational explanations for the answer "no". The expanded search space provides more possibilities for generating reliable rationales. 2) Avoid overfitting. For labelled samples, although we can depend on human explanations to train the model, these labels are still one-sided and subjective. Using the sequence sampling strategy can prevent the model from overfitting these specific annotations [2,47]. In the end, because the labelled and unlabelled samples would be integrated into a mini-batch during training, we simplify $R_{f}$ and $R_{s}$ into $R = \{r_k\}_{k=1}^K$ to indicate the candidate explanations for each sample. + +Self-Critical Reward. Inspired by [5, 51], an ideal rationale can help the model to infer the answer better. Based on this insight, we argue that the answer scores can be converted as self-critical rewards to evaluate these candidate explanations. Considering that this is a non-differentiable operation, we adopt reinforcement learning method [47] to achieve end-to-end training. In particular, given a sample and corresponding candidate explanations $R$ , we design a new input template: + +$$ +Z _ {r} ^ {k} = [ Z; \langle r e a s o n \rangle ; r _ {k}; \langle a n s w e r \rangle ], \tag {4} +$$ + +where $Z_{r}^{k}$ denotes the template of adding possible rationale $r_{k}$ . Then, this template is fed back into the model and obtains average probability $p_{\theta}^{r}(A)$ about the answer, namely explanatory answer scores, where $A$ is the ground-truth answer for the sample. Meanwhile, we use the average probability $p_{\theta}^{b}(A)$ from the output of the base answer template as the base scores. By applying reinforcement learning, the gradient is calculated by: + +$$ +\nabla_ {\theta} L _ {r} (\theta) = - \frac {1}{K} \sum_ {k = 1} ^ {K} \left(p _ {\theta} ^ {r} (A) - p _ {\theta} ^ {b} (A)\right) \nabla_ {\theta} \operatorname {l o g} p _ {\theta} \left(r _ {k}\right), \tag {5} +$$ + +where $p_{\theta}(r_k)$ is the probability of $k$ -th explanations. Based on the above computation, this gradient would tend to increase the probability of $k$ -th rationales when the answer score $p_{\theta}^{r}(A)$ higher than the scores $p_{\theta}^{b}(A)$ from the base answer template. Finally, for labelled samples, we append the human-annotated rationales to the candidate explanation $R$ and predict the answers by cross-entropy loss, namely $L_{ea}$ . + +# 3.4. Loss + +During the process of training, the overall loss function can be represented as follows: + +$$ +L = L _ {a} + L _ {e} + L _ {e a} + \lambda L _ {r}, \tag {6} +$$ + +where $\lambda$ is used for balancing these two different types of losses (i.e., cross-entropy loss and reinforcement loss). At inference time, our model would first generate the rationales about QA pairs, then we use the explanatory template (i.e., Eq. 4) to obtain the corresponding answers. + +# 4. Experiment + +# 4.1. Experimental setting + +Datasets. Following previous methods [48, 49], we mainly carry out the experiments on the two different VQANLE datasets: VQA-X [41] and A-OKVQA [49]. Meanwhile, since explain annotations are expensive and time-consuming, we also utilize large-scale VQA v2.0 [15] and OK-VQA [36] datasets to build the semi-supervised learning paradigm. Next, we will introduce the four datasets. + +VQA-X. It is a vision-language dataset that provides explanations for justifying the answers. VQA-X is collected from the Visual Question Answering (VQA) dataset [4] where the images are obtained from the MSCOCO [27]. It consists of 28K images and 33K QA pairs, split into 29K/1.4K/1.9K for training, validation and testing. Meanwhile, VQA-X constructs complementary pairs which provide a question and two semantically similar images with different answers. + +A-OKVQA. Compared to the VQA-X, the questions of A-OKVQA generally are required commonsense reasoning about the scene described in the images. It includes 24,903 Question/Answer/Rationale triplets, split into $17.1\mathrm{K} / 1.1\mathrm{K} / 6.7\mathrm{K}$ for training, validation and testing. It collects images from the COCO 2017 [7] dataset, and is further filtered to obtain $23.7\mathrm{K}$ unique images. Compared with previous datasets, the A-OKVQA has richer questions and requires broader areas of knowledge for reasoning. + +VQA & OK-VQA. We use VQA v2.0 and OK-VQA to provide large-scale unlabelled datasets for semi-supervised learning. The VQA v2.0 dataset is widely used for many previous works [2, 52]. It consists of 443k questions and 195k images. To select explainable questions instead of some obvious cases (e.g., How many...?, What color...?), we filter out these questions from VQA v2.0 and obtain the $\sim 90\mathrm{k}$ additional questions based on the rules [41]. On the other hand, we also use knowledge-based OK-VQA [36] dataset to provide unlabelled knowledge-based QA pairs. It contains a total of 14k questions on 14k images. + +Implementation Details. Following [37], each image is first pre-processed (such as including image resize, center crop, and normalize) by CLIP [45]. Meanwhile, we fix the ViT-B weights from the CLIP visual encoder to accelerate the training speed. For the mapping network, the image sequence length $S = 10$ and the embedding size is 768. The AdamW [21] is used as our optimizer with the weight decay 1e-5, and the batch size and beam size $K$ are set to 4 and 2. The weight coefficient $\lambda$ is set to 10. We train all models on the four 1080Ti GPUs for 30 epochs with a learning rate of 1e-5. + +# 4.2. Evaluation Measures + +Automatic Metering. Following [48, 60], we use the auto + +Table 1. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are unfiltered scores. $S^3 C^*$ denotes the model without unlabelled samples. + +
VQA-X
ApproachB4MRSCAccHuman
CAPS [41]5.912.626.311.935.268.6-
PJ-X [41]19.518.243.415.171.376.465.4
FME [58]24.419.547.717.988.875.5-
NLX-GPT [48]25.621.548.720.297.283.170.2
S3C*(ours)26.522.049.020.9100.583.773.9
S3C(ours)27.822.850.721.5104.485.677.4
+ +Table 2. Comparison with the state-of-the-art methods on the A-OKVQA. Note that these results are unfiltered scores. $S^3 C^*$ denotes the model without unlabelled samples. + +
AOKVQA
ApproachB4MRSCAcc valAcc testHuman
ViLBERT [29]-----30.625.9-
LXMERT [52]-----30.725.9-
KRISP [35]-----33.727.1-
Clipcap [49]-----30.825.9-
e-UG [20]15.118.142.414.951.530.525.644.1
NLX-GPT [48]20.117.046.315.865.432.728.746.9
\( S^2C^{*'} \) (ours)21.817.947.317.370.633.029.649.4
\( S^3C \) (ours)22.518.548.418.174.434.233.554.7
+ +Table 3. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are filtered scores. $S^3 C^*$ denotes the model without unlabelled samples. + +
B1B2B3B4MRSCAccHuman
RVT [34]51.937.025.617.419.242.115.852.568.660.5
PJ-X [41]57.442.230.922.719.746.017.182.776.469.3
FME [58]59.143.431.723.120.447.118.487.075.5-
QA-only [20]51.036.425.317.318.641.914.949.9--
e-UG [20]57.342.731.423.222.145.720.174.180.571.4
NLX-GPT [48]64.249.537.628.523.151.522.1110.683.273.7
S3C*(ours)64.449.938.029.123.451.922.7112.183.775.9
S3C(ours)64.750.538.830.723.952.123.0116.785.679.2
+ +matic metrics BLEU [40],METEOR[11],ROUGE-L[26], SPICE[1] and CIDEr[55] to evaluate generated explanations.For the evaluation of predicted answers, we follow [48,60] to compute the VQA accuracy. + +Human Evaluation. Automatic VQA-NLE measures do not always reflect the correctness and logicality of the explanations [20, 53], thus we also build human evaluations. The process is similar to [20, 34]. Specifically, for each explanation, three human evaluators are required to decide whether an explanation can justify the answer and select an option (including "yes, weak yes, weak no and no"). The selection will be mapped to scores $(1, \frac{2}{3}, \frac{1}{3}$ and 0). The final scores are computed by averaging among all test samples. Meanwhile, these evaluators are asked to choose the reasons for unqualified explanations. We follow [20] to define three kinds of aspects to evaluate the explanations: irrelevant explanations, insufficient explanations and meaningless explanations. First, the irrelevant explanations may not match the image, for example, "have a long neck" is a good explanation for the answer "giraffes" when asked "what animals are these?", but the image may display cows. Second, the insufficient explanations only describe the image but cannot corroborate the answers. For example, the sentence "there are some people" does not sufficiently justify the question "do people have a party?". Lastly, some nonsensical sentences could be judged as contradictory explanations, such as "a man is a woman". For each sample, the human evaluators can select multiple shortcomings. More details of the human evaluation can be found in the [20]. + +# 4.3. Quantitative evaluation. + +Automatic Evaluation. We compare our method with the state-of-the-art models on the VQA-X and A-OKVQA datasets in Table 1-3. The B4, M, R, S, C, Acc and Human are short for BLEU-4, METEOR, ROUGE-L, SPICE, CIDEr, Answer precision and Human evaluation. We use "unfiltered" to indicate that the explanations are evaluated regardless of whether the answer is true or false. While "filtered" is to only consider the explanations which have correct answers. From Table 1, the $S^3 C^*$ denotes that we only apply the self-critical framework without using unlabelled samples, while the row $S^3 C$ indicates our method in the semi-supervised setting. We observe that the proposed framework outperforms both the post-hoc explanation methods [41, 58] and the self-rationalization method [48]. Meanwhile, it's worth noting that although the NLX-GPT uses a more powerful pre-trained VL model with larger pre-trained datasets (i.e., COCO captions [27], Flicker30k [43] and Visual Genome [24]), our method still obtains 3.3 absolute gains on the CIDEr indicator with fewer pre-trained data (only using COCO captions). Furthermore, when we utilize our proposed semi-supervised paradigm, the results are further improved by 7.2 points. These results show that our model can generate more reliable explanations and it can benefit from the amount of data without human-explanation labels. We also report the accuracy of answers in the column of "Acc". It can be observed that our self-critical method with semi-supervised learning can simultaneously boost the precision of answers and cor + +Table 4. Main shortcomings. The main shortcomings of unqualified explanations on the VQA-X dataset. For each sample, human evaluators can select multiple shortcomings. + +
ModelIrrelevant explanationsInsufficient explanationsMeaningless explanations
RVT [34]25.7%33.5%11.4%
PJ-X [41]21.1%28.4%9.2%
e-UG [20]22.8%25.4%8.7%
NLX-GPT [48]20.3%22.2%9.1%
S3C (ours)17.3%18.9%8.2%
+ +Table 5. Cross-dataset testing. We alternately use the VQA-X and A-OKVQA as source dataset and target dataset to test the generalization of our framework. + +
VQA-X→A-OKVQA
ApproachB4MRSCAcc
NLX-GPT [48]10.712.734.210.735.410.4
S3C(ours)12.013.334.312.545.318.8
A-OKVQA→VQA-X
ApproachB4MRSCAcc
NLX-GPT [48]9.113.632.89.133.242.4
S3C(ours)10.915.034.110.438.643.8
+ +Table 6. Ablation study. We ablate key components to demonstrate the effectiveness of our method. SCR and Semi are Self-Critical Reinforcement module and Semi-supervised learning paradigm respectively. + +
questionimageanswerexplanationSCRSemiB4MRSCAcc
1✓✓✓--------80.1
2✓✓-✓--24.420.747.319.590.4-
3✓✓✓✓--27.522.950.421.9109.182.2
4✓✓✓✓✓-29.123.451.922.7112.183.7
5✓✓✓✓✓✓30.723.952.123.0116.785.6
+ +responding explanations. + +In Table 2, we evaluate our method on the A-OKVQA dataset. The results show that the $S^3 C$ can outperform all the previous works [17, 29, 35, 48, 49, 52]. Especially, compared to the SOTA model [48], there are 9.0 points and $4.8\%$ improvements in the CIDEr and answer accuracy based on our model. It demonstrates that our model can benefit from semi-supervised learning and generate explanations about commonsense reasoning. + +In addition, to prove the algorithm's validity, we follow [20, 48] to report the filtered scores for the VQAX dataset in Table 3. Through filtering the correct answers, our method can outperform whatever post-hoc [20, 34, 41, 58] and self-rationalization [48] methods. Meanwhile, the proposed $S^3 C$ achieves a new state-of-the-art with the CIDEr score improved by 6.1 points to 116.7 and boost the answer accuracy by $2.4\%$ to 85.6. + +Human Evaluation. To evaluate the faithfulness and correctness of these generated explanations, we conduct the human evaluation that is shown in the column of "Human" in Table 1-3. The experimental results further prove our method has better self-interpretability for the VQA-NLE task. Moreover, we also ask the human evaluators to select the shortcomings for each unqualified explanation on the VQA-X dataset. As shown in Table 4, we build three shortcoming options (i.e., irrelevant explanations, insufficient explanations and meaningless explanations) with a multi-choice process. These results indicate that the $S^3 C$ can obtain relatively better rationales and empirically confirm the effectiveness of our method. + +# 4.4. Cross-dataset Performance. + +We propose cross-dataset experiments to measure the generalization and reliability of our framework. For all we know, there is very little research on cross-dataset explanation generation. As shown in the first two rows of Table 5, we use the VQA-X and the A-OKVQA as the source dataset and target dataset to test the generalization ability of our framework. Specifically, we use the weights from the state-of-the-art method [48], which are trained on the VQA-X dataset and tested on the A-OKVQA dataset to obtain the results of the NLX-GPT. From the comparisons of six indicators, we find that our self-critical model has better generalization from the general VQA to the knowledge-based VQA. This suggests that $S^3 C$ can learn commonsense from visual question answering and generate better explanations and answers. Meanwhile, when we exchange the source dataset and target dataset as shown in the last two rows of Table 5, our framework can still surpass the existing SOTA model on all evaluation measures. These quantitative results effectively demonstrate the generalization and stability of our model. + +# 4.5. Ablation Studies. + +As shown in Table 6, we conduct several ablation studies on the VQA-X to demonstrate the effectiveness of our method. In particular, we first build the experiments in the 1-3 rows of Table 6, which use our Answer-Explanation Prompt module with cross-entropy loss as the baseline models. It can be found that when we simultaneously generate both answers and interpretations, the answer accuracy and CIDEr can achieve significant improvements. Meanwhile, + +![](images/7e01d8549bb6df38c2dafa143287e46634835e7efea7ff386f6c873aac75eb11.jpg) +(a) Is this man dressed formal? + +![](images/ca253b406d47da5ce9e8dd0643f14741dc101b45433029313006510d4e8be934.jpg) +Ours: [yes] +(b) Is he in a swimming pool? +NLX: [yes] +Ours: [no] + +![](images/39ae1e8ba51b4a97e658d08b9090d5b5fe7801fe50db87ef8fd67f5798d0bfac.jpg) +(c) What is the elephant doing? +NLX: [drinking] +Ours: [drinking] + +![](images/c4f860296fc1546b20f04255e426a9cdbc3d82adb6d7857051de46cd6ac72882.jpg) +NLX: [no] +(d) Are the people having a party? +NLX: [no] +Ours: [yes] +GT: [yes] +Figure 3. Some generation results on the VQA-X datasets. The [ ] and $<<$ indicate answers and explanations respectively. We show the results of the state-of-the-art NLX-GPT [48], our method and ground-truth (they are short for NLX, Ours and GT). + +![](images/245f9a6f2d0c2769e88489f6a21f838f96135dde6cd9756a73f082c8f5875f4d.jpg) +GT: [yes] +GT: [no] +(e) Does this animal appear to be looking +at the camera? +NLX: [yes] +Ours: [no] +GT: [no] + +![](images/7bec96df02b62f6838cf074149ae4a727fd068f7ab72ee06b34553bac058bac9.jpg) +GT: [drinking] +(f) Is this a bar? +NLX: [yes] +Ours: [yes] +GT: [yes] + +these results also prove that the answer-explanation pairs have inherent consistency and they can promote each other. Further, we establish the Self-Critical Reinforcement module as shown in the fourth row, and the result of accuracy and CIDEr are boosted by $1.5\%$ and 3.0 points. It suggests that our self-critical method with sequence sampling strategy can encourage the model to generate more reliable explanations and correct answers. Finally, when we extend our model to the semi-supervised setting, the performance improves to 85.6 on the accuracy and 116.7 on the CIDEr over the baseline model (i.e., the row 5 of Table 6) by $3.4\%$ and 7.6 points. The results demonstrate that our framework is remarkably effective in improving the logical consistency and the self-interpretability of the model. + +# 4.6. Qualitative evaluation. + +As shown in Fig. 3, we show some qualitative results from NLX-GPT [48] and our $S^3 C$ method on the VQA-X dataset. Through overall comparison, our model achieves better logical consistency between answers and explanations. For example, in Fig. 3 (a), although the SOTA method [48] correctly identifies the significant symbol of formal dress (i.e., tie), the predicted answer is "no" that is contradictory to the explanation. On the contrary, our method not only obtains a more complete and faithful rationale but also generates a logically consistent answer. Additionally, the $S^3 C$ can also produce more persuasive and + +trusty sentences. For instance, in Fig. 3 (b)-(f), the generated sentences contain scene description "having a good time" and fine-grained rationale "the trunk is in the water". + +# 5. Conclusion + +In this paper, we propose a new Semi-Supervised VQANLE method via Self-Critical Learning $(S^3 C)$ . Different from previous works, our method first utilizes the prompting mechanism to motivate the model to generate answers and candidate explanations. Meanwhile, we design a novel Self-Critical Reinforcement module, which converts the answer scores as rewards to evaluate these possible rationales. Furthermore, our framework can benefit from an abundance of question-answer pairs without human-annotated explanations and further boost the self-interpretability of the model. With the automatic measures and human evaluations, our $S^3 C$ achieves a new state-of-the-art on multiple benchmarks and provides a new paradigm for our community. + +# Acknowledgements + +This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key RD Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03). + +# References + +[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Spice: Semantic propositional image caption evaluation. In European conference on computer vision, pages 382-398. Springer, 2016. +[2] Peter Anderson, Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. Bottom-up and top-down attention for image captioning and visual question answering. 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Unified vision-language pretraining for image captioning and vqa. 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Unlike traditional attention or gradient analysis, free-text rationales can be easier to understand and gain users' trust. Existing methods mostly use post-hoc or self-rationalization models to obtain a plausible explanation. However, these frameworks are bottlenecked by the following challenges: 1) the reasoning process cannot be faithfully responded to and suffer from the problem of logical inconsistency. 2) Human-annotated explanations are expensive and time-consuming to collect. In this paper, we propose a new Semi-Supervised VQA-NLE via Self-Critical Learning " + }, + { + "bbox": [ + 46, + 297, + 290, + 549 + ], + "type": "inline_equation", + "content": "(S^3 C)" + }, + { + "bbox": [ + 46, + 297, + 290, + 549 + ], + "type": "text", + "content": ", which evaluates the candidate explanations by answering rewards to improve the logical consistency between answers and rationales. 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Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 603, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 603, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 603, + 287, + 687 + ], + "type": "text", + "content": "Deep neural networks have enabled significant breakthroughs in a variety of vision-language (VL) tasks such as image captioning [10, 47] and visual question answering (VQA) [2, 39]. Unfortunately, most of them are black box systems, which makes it challenging to gain users' trust [20]. 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Paradigm comparison of different VQA-NLE methods. (a) Post-hoc explanation method adopts two independent models to predict answers and explanations respectively. (b) Self-rationalization method uses a united VL model to simultaneously generate answers and explanations. (c) Our self-critical strategy utilizes answer scores as rewards and obtains more reliable rationales with semi-supervised learning." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 569, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 700 + ], + "type": "text", + "content": "Some approaches depend on attention mechanisms [2, 30] or gradient-based localization [50] to acquire visual explanations, which can highlight some contributing image regions for the predicted answers. However, simple visualization cannot explain how these areas support the answers and they are also hard to comprehend [20, 48]. Conversely, Natural Language Explanation (NLE) task [6, 38] can explain the decision-making process of a model by generating a natural language sentence. The language-based explanations are more accessible for users to understand, and they can also help researchers optimize the structure of models [34]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Recently, some models of NLE in the VL commu" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 215, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 215, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 215, + 703 + ], + "type": "text", + "content": "*These authors contributed equally to this work." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2646" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "nity have achieved pretty-well results, especially for VQANLE [20,34,41,48,58]. They can guide models to generate natural language sentences and interpret how the models get answers. Specifically, the first research line usually treats VQA-NLE as a predict-then-explain task [20, 34, 41, 58], namely post-hoc explanations method. As shown in Fig. 1 (a), these methods first depend on pre-trained VL models (such as UNITER [8] or Oscar [25]) to gain answers. Then the fused multi-modal features and the predicted answers are fed into a separated language model (e.g., LSTM [16] or Transformer [54]) to generate corresponding explanations. As shown in Fig. 1 (b), the other line [48] relies on a united VL model while generating both answers and explanations, which is known as the self-rationalization method. This framework can simultaneously predict an answer and generate a rationale by formulating the answer as a text-generation task along with the explanation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 289, + 418 + ], + "type": "text", + "content": "Though significant progress has been made, the two paradigms are still restricted by the following challenges: 1) For the first paradigm, since the decision-making model and interpretation part are two separate modules, it would inevitably lead to unfaithful responses to the reasoning process of the decision models. 2) Due to the lack of explicitly logical relationship modeling, previous work [19] has proved that the straightforward self-rationalization frameworks suffer from the problem of logical inconsistency. 3) The above strategies all require an amount of human-annotated explanations, which are expensive and time-consuming to collect [62]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 420, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 289, + 685 + ], + "type": "text", + "content": "To solve the above challenges, inspired by [5, 51], we argue that a reasonable rationale can assist the model in obtaining a correct answer, and vice versa, the answer can be converted as an evaluation criterion for possible explanations. In this paper, we propose a new Semi-Supervised VQA-NLE method with Self-Critical learning, which is called " + }, + { + "bbox": [ + 46, + 420, + 289, + 685 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 420, + 289, + 685 + ], + "type": "text", + "content": " for short. As shown in Fig.1 (c), given images and related questions, we first leverage a prompting mechanism to construct answer and explanation templates, which can guide the pre-trained VL model to generate answers and multiple candidate explanations based on sequence sampling [2]. Then we design a new self-critical method that converts the answer scores as rewards and encourages the model to generate the explanations which contribute to improving the answer scores. In particular, to reduce the dependency on expensive human annotations, we further extend our method to the semi-supervised version, which utilizes the unlabelled samples1 (i.e., conventional VQA data [4, 36]) to significantly enhance the self-interpretability of the model. With the self-critical strategy and the semi-supervised learning, our method effectively models the logical relationships and promotes the logical" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "consistency between answer-explanation pairs. According to automatic measures and human evaluations, the " + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": " outperforms the state-of-the-art models for the VQA-NLE task on the widely used two datasets and provides a new paradigm for our community. In summary, we make the following contributions:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 146, + 547, + 329 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 304, + 146, + 547, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 547, + 206 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 547, + 206 + ], + "type": "text", + "content": "1) We propose a new self-critical VQA-NLE method that can model the logical relationships between answer-explanation pairs and evaluate the generated rationales by answering rewards. This strategy effectively improves the logical consistency and the reliability of the interpretations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 209, + 547, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 547, + 280 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 547, + 280 + ], + "type": "text", + "content": "2) We develop an advanced semi-supervised learning framework for VQA-NLE, which utilizes amounts of samples without human-annotated explanations to boost the self-interpretability of the model further. To the best of our knowledge, we are the first to explore semi-supervised learning on the VQA Natural Language Explanation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 282, + 547, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 329 + ], + "type": "text", + "content": "3) The proposed " + }, + { + "bbox": [ + 304, + 282, + 547, + 329 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 282, + 547, + 329 + ], + "type": "text", + "content": " achieves new state-of-the-art performance on VQA-X [13] and A-OKVQA [49] benchmark datasets. Meanwhile, automatic measures and human evaluations all show the effectiveness of our method." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 347, + 391, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 347, + 391, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 347, + 391, + 360 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 369, + 538, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 538, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 538, + 383 + ], + "type": "text", + "content": "2.1. Explainability in Visual Question Answering" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 391, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 547, + 715 + ], + "type": "text", + "content": "The visual question answering (VQA) is firstly proposed by [33] that requires an intelligent agent to generate an answer by giving an image and a question. Many approaches have been introduced such as joint embedding [13, 61], attention mechanisms [3, 31], memory networks [32, 59] and graph neural networks [23, 56]. Although the VQA task has been well studied, the reasoning process of the models is always agnostic. Some methods apply visualization technologies to achieve visual explanation, such as Grad-CAM [50] and U-CAM [42]. However, because image visualization cannot support the answer based on the attended areas [57], in this paper, we focus on improving free-text explanations that are more convenient and easier for users to understand. In this topic, the early work is proposed by [41]. The paper conducts the VQA-X dataset and utilizes human annotations to inspire the decision-making process of VQA models. [20] designs a new model that combines a pre-trained language model and a VL model to generate free-text explanations. [60] combines stronger pre-trained VL model (i.e. Oscar [25]) and generation model (i.e. GPT-2 [46]) to obtain better results. Recently, [48] proposes a unified model which can simultaneously predict answers and explanations based on a pre-trained caption model. Unlike previous methods, we introduce a new self-critical strategy to model the logical relationships between answers and rationales. It can encourage the model to enhance logical consistency and generate more reasonable explanations." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 715 + ], + "type": "text", + "content": "1In this paper, we use \"unlabelled samples\" and \"labelled samples\" to indicate the question-answer (QA) pairs without/with human explanations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "2647" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 261, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 261, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 261, + 85 + ], + "type": "text", + "content": "2.2. Pre-trained models and Prompt learning" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 331 + ], + "type": "text", + "content": "Pre-trained models have been applied in many fields, such as various NLP tasks [12,46] and VL tasks [29,52,65]. Most of these pre-trained models utilize a stack of Transformer structures as the backbone. To generalize the pretrained models to other downstream tasks, previous works mostly fine-tune whole models on each downstream VL task. However, the ability of pre-trained models would be limited due to the mismatch between pre-trained tasks and downstream tasks. Hence, prompt learning [9, 18, 45, 64] is proposed, and it can keep the optimization consistency. [45] designs the templates to transfer the knowledge to downstream tasks. [9] uses a textual generation framework for uniform optimization. In this paper, we use the pre-trained model based on the image caption task as our backbone. It has been proved that these additional pre-train tasks (e.g., image feature regression or mask language tokens) cannot significantly improve the performance for explanations [48]. Meanwhile, we apply different language prompt templates to motivate the model to generate corresponding answers and rationales." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 338, + 189, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 189, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 189, + 352 + ], + "type": "text", + "content": "2.3. Semi-supervised learning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 289, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 289, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 289, + 539 + ], + "type": "text", + "content": "The development of deep learning depends on a large number of labelled data, while there are many cases in that only a small amount of data can be obtained [44]. To solve this challenge, Semi-supervised learning is proposed [44], which aims to train models using a small number of labelled data and amounts of unlabelled data. For example, [22] proposes a generatively semi-supervised framework based on variational autoencoders, and it can jointly optimize the model and variational parameters. Recently, [63] simultaneously leverages self-supervised and semi-supervised learning to address image classification tasks. To our knowledge, our work is the first semi-supervised learning framework for the VQA-NLE task, which effectively alleviates the reliance on expensive human annotations and further boost the self-interpretability of the model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 549, + 104, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 104, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 104, + 562 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "In this section, we introduce our Semi-Supervised VQANLE method with the Self-Critical learning " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "(S^3 C)" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " framework. Our aim is to strengthen the logical consistency between answer-explanation pairs and improve the reliability of the rationales. As shown in Fig. 2, the " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " comprises an \"Answer-Explanation Prompt\" module and a \"Self-Critical Reinforcement\" module. Unlike previous approaches, our method first uses a prompting mechanism to generate answers and candidate explanations. Then, we design a new self-critical module that converts the answer scores as rewards to evaluate these reasons. Furthermore, this strategy can conveniently apply the unlabelled QA pairs to enrich" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 96 + ], + "type": "text", + "content": "training data and enhance the self-interpretability. Next, we describe the components of our model in detail." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 105, + 515, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 105, + 515, + 118 + ], + "spans": [ + { + "bbox": [ + 305, + 105, + 515, + 118 + ], + "type": "text", + "content": "3.1. Pre-trained Vision-Language Backbone" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": "Given an image " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{W \\times H \\times 3}" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " and a natural language question " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "Q = \\{q_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "q_t" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": "-th word, " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " is the length of the question and " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "W \\times H \\times 3" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " denotes the size of the image. Our goal is to predict the answer and generate a corresponding free-text rationale. Following previous works [48, 49], we adopt the CLIP vision encoder [45] and a pre-trained image caption model (i.e., ClipCap [37]) as our basic backbone. During pre-training, the VL model uses image embeddings from the CLIP as prefixes and fine-tunes a language model (i.e., GPT-2 [46]) to generate image captions. We refer readers to [37] for more information about the pre-trained model. In this paper, we consider the image " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " and question " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " as the prefixes of the answer-explanation sequences. Specifically, we first apply ViT-B [14] and \"classification token\" from the CLIP to obtain the image features. Then, a group of light and simple Multi-Layer Perceptron (MLP) is utilized for transforming the image features to the " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "V = \\{v_s\\}_{s=1}^S" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "v_s \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": ", where the dimension size " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "c = 768" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": " and the image sequence length " + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "inline_equation", + "content": "S = 10" + }, + { + "bbox": [ + 304, + 122, + 545, + 373 + ], + "type": "text", + "content": ". The above computations can be formulated as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 353, + 375, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 375, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 353, + 375, + 545, + 389 + ], + "type": "interline_equation", + "content": "v _ {1}, v _ {2}, \\dots , v _ {S} = \\operatorname {M L P} (\\operatorname {C L I P} (I)). \\tag {1}", + "image_path": "5c62ccc04927a406285785b07f3b37559a03e2ce4df051bee2346e1747ddb74d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "text", + "content": "Note that we only update the mapping network (i.e., MLP) during training, while the original visual encoder parameters from the CLIP would remain frozen. For question " + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "text", + "content": ", each word " + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "text", + "content": " would be mapped to the corresponding word embedding " + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "inline_equation", + "content": "e_{t} \\in \\mathbb{R}^{c}" + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "text", + "content": " by the pre-trained caption model. Finally, we obtain the image and question sequences " + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 304, + 394, + 545, + 467 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 350, + 476, + 545, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 476, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 350, + 476, + 545, + 521 + ], + "type": "interline_equation", + "content": "Z = \\overbrace {\\left[ v _ {1} , v _ {2} , \\cdots , v _ {S} \\right.} ^ {\\text {i m a g e}} \\underbrace {e _ {1} , e _ {2} , \\cdots , e _ {T}} _ {\\substack {\\text {q u e s t i o n} \\\\ \\text {e m b d e d i n g}}} \\bigg ], \\tag{2}", + "image_path": "f7af52c4ce95b2b5909fde15456418e59af9930f45353c9b46a06496a8d687fc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 530, + 510, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 530, + 510, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 530, + 510, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 530, + 510, + 542 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 306, + 530, + 510, + 542 + ], + "type": "text", + "content": " is the concatenated multi-modal prefixes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 551, + 503, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 551, + 503, + 563 + ], + "spans": [ + { + "bbox": [ + 306, + 551, + 503, + 563 + ], + "type": "text", + "content": "3.2. Answer-Explanation Prompt Module" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": "It has been proved that the prompting mechanism can maintain the same optimization objectives between pretrained and downstream tasks [18, 28]. Considering the convenience and explainability, we leverage hand-crafted prompts as templates to enable the model to generate answers or explanations. As shown in Fig. 2, the " + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 570, + 545, + 665 + ], + "type": "text", + "content": " includes two different kinds of templates, which are introduced respectively as follows." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Base Answer Template. The core idea of our " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " is to use the answer scores as evaluation criteria. Hence, we first establish a basic answer template to acquire base answer scores. Different from previous works [20, 41], our" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2648" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 75, + 542, + 270 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 542, + 270 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 542, + 270 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 542, + 270 + ], + "type": "image", + "image_path": "6c9a1ae1014099259c66fe6acd5d5ccb3871a086fe23b1181827247d177149a2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 281, + 548, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 548, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 548, + 338 + ], + "type": "text", + "content": "Figure 2. Overview of our Semi-Supervised VQA-NLE method via Self-Critical learning " + }, + { + "bbox": [ + 46, + 281, + 548, + 338 + ], + "type": "inline_equation", + "content": "(S^3 C)" + }, + { + "bbox": [ + 46, + 281, + 548, + 338 + ], + "type": "text", + "content": " framework. Given images and corresponding questions for labelled and unlabelled samples, we first use Answer-Explanation Prompt module to obtain the base answer scores and candidate explanations with a pre-trained VL model. Then these reasons are reorganized and fed back into the model to capture the explanatory answer score. Further, our Self-Critical Reinforcement module evaluates the generated explanations and returns the rewards to improve the self-interpretability of the model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": "method treats the visual question answering task as a generation task so that the model can produce answers without a predefined answer space. Specifically, for a given image and question sequence " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": ", we use natural language tokens \"the answer is\" to inspire the model to generate proper answers. By concatenating the language prompt, the base answer template " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "Z_{a} = [Z; \\langle \\text{answer} \\rangle]" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " can be obtained, where " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "[; ]" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "\\langle \\text{answer} \\rangle" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " indicate concatenation operation and the specific language prompts, respectively. During training, the base answer template and ground-true answer label " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "A = \\{a_{n}\\}_{n=1}^{N}" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " are fed into the VL model, where " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "a_{n}" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": "-th answer token and " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " denotes the length of the answer label. Next, we compute the answer loss conditioned on the " + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "inline_equation", + "content": "Z_{a}" + }, + { + "bbox": [ + 46, + 357, + 289, + 526 + ], + "type": "text", + "content": " in an autoregressive fashion:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 532, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 532, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 58, + 532, + 287, + 564 + ], + "type": "interline_equation", + "content": "L _ {a} = - \\frac {1}{N} \\sum_ {n = 1} ^ {N} \\log P \\left(a _ {n} \\mid Z _ {a}, a _ {1}, a _ {2}, \\dots , a _ {n - 1}; \\theta\\right), \\tag {3}", + "image_path": "c09e103511812d969fea3a3a4ed85ace02aee4bb474b3451849866536ee67db0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "type": "text", + "content": " denotes the parameters of the VL model. Moreover, based on the indexes of ground-true answers, we can acquire average probability " + }, + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "type": "inline_equation", + "content": "p_{\\theta}^{b}(A)" + }, + { + "bbox": [ + 47, + 570, + 287, + 606 + ], + "type": "text", + "content": " as our base answer score." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Explanation Generation Template. To produce a reasonable rationale, we leverage the language prompt \"the reason is\" to motivate the model to generate free-text explanations. Like the base answer template, an explanation generation template " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "Z_{e} = [Z; \\langle \\text{reason} \\rangle]" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " is constructed, where " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\langle \\text{reason} \\rangle" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " is the natural language tokens. For labelled samples, we follow Eq. 3 in the autoregressive fashion and the cross-entropy loss to compute explanation loss " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{e}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": ". Because there are no human-annotated explanations available, we" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 357, + 533, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 533, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 533, + 370 + ], + "type": "text", + "content": "would not compute any loss for unlabelled QA samples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 381, + 497, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 497, + 393 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 497, + 393 + ], + "type": "text", + "content": "3.3. Self-Critical Reinforcement Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 401, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 484 + ], + "type": "text", + "content": "To gain logically consistent rationales, in this module, we expand the searching space by introducing sequence sampling algorithm [2] and generate a set of candidate explanations. Besides, the answer scores are treated as rewards to encourage the model to output more detailed interpretations. It's worth noting that the above operations would be implemented on both labelled and unlabelled samples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": "Candidate Explanation Generation. Benefiting from the language-based prompting strategy and the pre-trained VL model, our explanation generation template can easily guide the model to produce human-readable sentences. Hence, for unlabelled QA samples, we directly apply the explanation generation template " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "Z_{e}" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": " to generate the candidate rationales. To be more specific, we utilize beam search [2] to sample the top- " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": " words from the VL model probability distribution at each time step and maintain these sequences with the highest probability. Then, these generated sentences are integrated into candidate explanations " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "R_{s} = \\{r_{k}^{s}\\}_{k = 1}^{K}" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": " for each QA pair without human-annotated explanations, where " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "r_k^s" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": " indicate " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": "-th rationale and the size of beam search, respectively. Moreover, for labelled samples, a similar mechanism is used to build the corresponding explanation set " + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "inline_equation", + "content": "R_{f} = \\{r_{k}^{f}\\}_{k = 1}^{K}" + }, + { + "bbox": [ + 304, + 486, + 546, + 715 + ], + "type": "text", + "content": ". The above operations are implemented in all samples for the following reasons: 1) Larger search space. As shown in Fig. 2, \"frying food is unhealthy\" and \"it includes many calories\"" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2649" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": "can both be rational explanations for the answer \"no\". The expanded search space provides more possibilities for generating reliable rationales. 2) Avoid overfitting. For labelled samples, although we can depend on human explanations to train the model, these labels are still one-sided and subjective. Using the sequence sampling strategy can prevent the model from overfitting these specific annotations [2,47]. In the end, because the labelled and unlabelled samples would be integrated into a mini-batch during training, we simplify " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "R_{f}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "R_{s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "inline_equation", + "content": "R = \\{r_k\\}_{k=1}^K" + }, + { + "bbox": [ + 46, + 72, + 289, + 203 + ], + "type": "text", + "content": " to indicate the candidate explanations for each sample." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 204, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 204, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 204, + 289, + 312 + ], + "type": "text", + "content": "Self-Critical Reward. Inspired by [5, 51], an ideal rationale can help the model to infer the answer better. Based on this insight, we argue that the answer scores can be converted as self-critical rewards to evaluate these candidate explanations. Considering that this is a non-differentiable operation, we adopt reinforcement learning method [47] to achieve end-to-end training. In particular, given a sample and corresponding candidate explanations " + }, + { + "bbox": [ + 46, + 204, + 289, + 312 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 204, + 289, + 312 + ], + "type": "text", + "content": ", we design a new input template:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 94, + 319, + 287, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 319, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 94, + 319, + 287, + 334 + ], + "type": "interline_equation", + "content": "Z _ {r} ^ {k} = [ Z; \\langle r e a s o n \\rangle ; r _ {k}; \\langle a n s w e r \\rangle ], \\tag {4}", + "image_path": "9629d290f77aeb35135d92a8d25754a6d2969792a335662c37073d03debcbc7a.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "inline_equation", + "content": "Z_{r}^{k}" + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "content": " denotes the template of adding possible rationale " + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "inline_equation", + "content": "r_{k}" + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "content": ". Then, this template is fed back into the model and obtains average probability " + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "inline_equation", + "content": "p_{\\theta}^{r}(A)" + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "content": " about the answer, namely explanatory answer scores, where " + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "content": " is the ground-truth answer for the sample. Meanwhile, we use the average probability " + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "inline_equation", + "content": "p_{\\theta}^{b}(A)" + }, + { + "bbox": [ + 46, + 342, + 289, + 440 + ], + "type": "text", + "content": " from the output of the base answer template as the base scores. By applying reinforcement learning, the gradient is calculated by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 448, + 287, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 448, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 53, + 448, + 287, + 480 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\theta} L _ {r} (\\theta) = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\left(p _ {\\theta} ^ {r} (A) - p _ {\\theta} ^ {b} (A)\\right) \\nabla_ {\\theta} \\operatorname {l o g} p _ {\\theta} \\left(r _ {k}\\right), \\tag {5}", + "image_path": "25f560a5f892c7ee17dd34d9105ca83a0f1175181e33e91db58fc4fc44ba451b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "p_{\\theta}(r_k)" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": " is the probability of " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": "-th explanations. Based on the above computation, this gradient would tend to increase the probability of " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": "-th rationales when the answer score " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "p_{\\theta}^{r}(A)" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": " higher than the scores " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "p_{\\theta}^{b}(A)" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": " from the base answer template. Finally, for labelled samples, we append the human-annotated rationales to the candidate explanation " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": " and predict the answers by cross-entropy loss, namely " + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "inline_equation", + "content": "L_{ea}" + }, + { + "bbox": [ + 46, + 489, + 287, + 574 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 580, + 91, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 91, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 91, + 591 + ], + "type": "text", + "content": "3.4. Loss" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 598, + 287, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 623 + ], + "type": "text", + "content": "During the process of training, the overall loss function can be represented as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 108, + 632, + 287, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 632, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 108, + 632, + 287, + 644 + ], + "type": "interline_equation", + "content": "L = L _ {a} + L _ {e} + L _ {e a} + \\lambda L _ {r}, \\tag {6}", + "image_path": "f1768ec3b143e825b951048649afd9068292127b52d24c44a8efa32124e2903c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " is used for balancing these two different types of losses (i.e., cross-entropy loss and reinforcement loss). At inference time, our model would first generate the rationales about QA pairs, then we use the explanatory template (i.e., Eq. 4) to obtain the corresponding answers." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 382, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 382, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 382, + 85 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 91, + 426, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 426, + 104 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 426, + 104 + ], + "type": "text", + "content": "4.1. Experimental setting" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 110, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 193 + ], + "type": "text", + "content": "Datasets. Following previous methods [48, 49], we mainly carry out the experiments on the two different VQANLE datasets: VQA-X [41] and A-OKVQA [49]. Meanwhile, since explain annotations are expensive and time-consuming, we also utilize large-scale VQA v2.0 [15] and OK-VQA [36] datasets to build the semi-supervised learning paradigm. Next, we will introduce the four datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 194, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 300 + ], + "type": "text", + "content": "VQA-X. It is a vision-language dataset that provides explanations for justifying the answers. VQA-X is collected from the Visual Question Answering (VQA) dataset [4] where the images are obtained from the MSCOCO [27]. It consists of 28K images and 33K QA pairs, split into 29K/1.4K/1.9K for training, validation and testing. Meanwhile, VQA-X constructs complementary pairs which provide a question and two semantically similar images with different answers." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "type": "text", + "content": "A-OKVQA. Compared to the VQA-X, the questions of A-OKVQA generally are required commonsense reasoning about the scene described in the images. It includes 24,903 Question/Answer/Rationale triplets, split into " + }, + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "type": "inline_equation", + "content": "17.1\\mathrm{K} / 1.1\\mathrm{K} / 6.7\\mathrm{K}" + }, + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "type": "text", + "content": " for training, validation and testing. It collects images from the COCO 2017 [7] dataset, and is further filtered to obtain " + }, + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "type": "inline_equation", + "content": "23.7\\mathrm{K}" + }, + { + "bbox": [ + 304, + 302, + 545, + 410 + ], + "type": "text", + "content": " unique images. Compared with previous datasets, the A-OKVQA has richer questions and requires broader areas of knowledge for reasoning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 410, + 545, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 541 + ], + "type": "text", + "content": "VQA & OK-VQA. We use VQA v2.0 and OK-VQA to provide large-scale unlabelled datasets for semi-supervised learning. The VQA v2.0 dataset is widely used for many previous works [2, 52]. It consists of 443k questions and 195k images. To select explainable questions instead of some obvious cases (e.g., How many...?, What color...?), we filter out these questions from VQA v2.0 and obtain the " + }, + { + "bbox": [ + 304, + 410, + 545, + 541 + ], + "type": "inline_equation", + "content": "\\sim 90\\mathrm{k}" + }, + { + "bbox": [ + 304, + 410, + 545, + 541 + ], + "type": "text", + "content": " additional questions based on the rules [41]. On the other hand, we also use knowledge-based OK-VQA [36] dataset to provide unlabelled knowledge-based QA pairs. It contains a total of 14k questions on 14k images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "content": "Implementation Details. Following [37], each image is first pre-processed (such as including image resize, center crop, and normalize) by CLIP [45]. Meanwhile, we fix the ViT-B weights from the CLIP visual encoder to accelerate the training speed. For the mapping network, the image sequence length " + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "inline_equation", + "content": "S = 10" + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "content": " and the embedding size is 768. The AdamW [21] is used as our optimizer with the weight decay 1e-5, and the batch size and beam size " + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "content": " are set to 4 and 2. The weight coefficient " + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 542, + 545, + 673 + ], + "type": "text", + "content": " is set to 10. We train all models on the four 1080Ti GPUs for 30 epochs with a learning rate of 1e-5." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 682, + 427, + 694 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 682, + 427, + 694 + ], + "spans": [ + { + "bbox": [ + 306, + 682, + 427, + 694 + ], + "type": "text", + "content": "4.2. Evaluation Measures" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Automatic Metering. Following [48, 60], we use the auto" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2650" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 113, + 272, + 188 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 273, + 103 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 273, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 273, + 103 + ], + "type": "text", + "content": "Table 1. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are unfiltered scores. " + }, + { + "bbox": [ + 47, + 70, + 273, + 103 + ], + "type": "inline_equation", + "content": "S^3 C^*" + }, + { + "bbox": [ + 47, + 70, + 273, + 103 + ], + "type": "text", + "content": " denotes the model without unlabelled samples." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 113, + 272, + 188 + ], + "lines": [ + { + "bbox": [ + 50, + 113, + 272, + 188 + ], + "spans": [ + { + "bbox": [ + 50, + 113, + 272, + 188 + ], + "type": "table", + "html": "
VQA-X
ApproachB4MRSCAccHuman
CAPS [41]5.912.626.311.935.268.6-
PJ-X [41]19.518.243.415.171.376.465.4
FME [58]24.419.547.717.988.875.5-
NLX-GPT [48]25.621.548.720.297.283.170.2
S3C*(ours)26.522.049.020.9100.583.773.9
S3C(ours)27.822.850.721.5104.485.677.4
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AOKVQA
ApproachB4MRSCAcc valAcc testHuman
ViLBERT [29]-----30.625.9-
LXMERT [52]-----30.725.9-
KRISP [35]-----33.727.1-
Clipcap [49]-----30.825.9-
e-UG [20]15.118.142.414.951.530.525.644.1
NLX-GPT [48]20.117.046.315.865.432.728.746.9
\\( S^2C^{*'} \\) (ours)21.817.947.317.370.633.029.649.4
\\( S^3C \\) (ours)22.518.548.418.174.434.233.554.7
", + "image_path": "9d9db038b4ead71b9d70515ea371f9b815f8f90b17037e6a262483fd9d5503c4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 123, + 239, + 470, + 340 + ], + "blocks": [ + { + "bbox": [ + 46, + 207, + 544, + 231 + ], + "lines": [ + { + "bbox": [ + 46, + 207, + 544, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 544, + 231 + ], + "type": "text", + "content": "Table 3. Comparison with the state-of-the-art methods on the VQA-X. Note that these results are filtered scores. " + }, + { + "bbox": [ + 46, + 207, + 544, + 231 + ], + "type": "inline_equation", + "content": "S^3 C^*" + }, + { + "bbox": [ + 46, + 207, + 544, + 231 + ], + "type": "text", + "content": " denotes the model without unlabelled samples." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 123, + 239, + 470, + 340 + ], + "lines": [ + { + "bbox": [ + 123, + 239, + 470, + 340 + ], + "spans": [ + { + "bbox": [ + 123, + 239, + 470, + 340 + ], + "type": "table", + "html": "
B1B2B3B4MRSCAccHuman
RVT [34]51.937.025.617.419.242.115.852.568.660.5
PJ-X [41]57.442.230.922.719.746.017.182.776.469.3
FME [58]59.143.431.723.120.447.118.487.075.5-
QA-only [20]51.036.425.317.318.641.914.949.9--
e-UG [20]57.342.731.423.222.145.720.174.180.571.4
NLX-GPT [48]64.249.537.628.523.151.522.1110.683.273.7
S3C*(ours)64.449.938.029.123.451.922.7112.183.775.9
S3C(ours)64.750.538.830.723.952.123.0116.785.679.2
", + "image_path": "5938ddc4399a3bab2f4a2431c7b8a6f600490b95bdaced85fe09bba08461188a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 360, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 286, + 408 + ], + "type": "text", + "content": "matic metrics BLEU [40],METEOR[11],ROUGE-L[26], SPICE[1] and CIDEr[55] to evaluate generated explanations.For the evaluation of predicted answers, we follow [48,60] to compute the VQA accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 415, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 286, + 713 + ], + "type": "text", + "content": "Human Evaluation. Automatic VQA-NLE measures do not always reflect the correctness and logicality of the explanations [20, 53], thus we also build human evaluations. The process is similar to [20, 34]. Specifically, for each explanation, three human evaluators are required to decide whether an explanation can justify the answer and select an option (including \"yes, weak yes, weak no and no\"). The selection will be mapped to scores " + }, + { + "bbox": [ + 46, + 415, + 286, + 713 + ], + "type": "inline_equation", + "content": "(1, \\frac{2}{3}, \\frac{1}{3}" + }, + { + "bbox": [ + 46, + 415, + 286, + 713 + ], + "type": "text", + "content": " and 0). The final scores are computed by averaging among all test samples. Meanwhile, these evaluators are asked to choose the reasons for unqualified explanations. We follow [20] to define three kinds of aspects to evaluate the explanations: irrelevant explanations, insufficient explanations and meaningless explanations. First, the irrelevant explanations may not match the image, for example, \"have a long neck\" is a good explanation for the answer \"giraffes\" when asked \"what animals are these?\", but the image may display cows. Second, the insufficient explanations only describe the image but cannot corroborate the answers. For example, the sentence \"there are some people\" does not sufficiently justify the question \"do people have a party?\". Lastly, some nonsensical sentences could be judged as contradictory explanations, such as \"a man is a woman\". For each sample, the human evaluators can select multiple shortcomings. More details of the human evaluation can be found in the [20]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 360, + 440, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 440, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 440, + 372 + ], + "type": "text", + "content": "4.3. Quantitative evaluation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "type": "text", + "content": "Automatic Evaluation. We compare our method with the state-of-the-art models on the VQA-X and A-OKVQA datasets in Table 1-3. The B4, M, R, S, C, Acc and Human are short for BLEU-4, METEOR, ROUGE-L, SPICE, CIDEr, Answer precision and Human evaluation. We use \"unfiltered\" to indicate that the explanations are evaluated regardless of whether the answer is true or false. While \"filtered\" is to only consider the explanations which have correct answers. From Table 1, the " + }, + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "type": "inline_equation", + "content": "S^3 C^*" + }, + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "type": "text", + "content": " denotes that we only apply the self-critical framework without using unlabelled samples, while the row " + }, + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 378, + 545, + 713 + ], + "type": "text", + "content": " indicates our method in the semi-supervised setting. We observe that the proposed framework outperforms both the post-hoc explanation methods [41, 58] and the self-rationalization method [48]. Meanwhile, it's worth noting that although the NLX-GPT uses a more powerful pre-trained VL model with larger pre-trained datasets (i.e., COCO captions [27], Flicker30k [43] and Visual Genome [24]), our method still obtains 3.3 absolute gains on the CIDEr indicator with fewer pre-trained data (only using COCO captions). Furthermore, when we utilize our proposed semi-supervised paradigm, the results are further improved by 7.2 points. These results show that our model can generate more reliable explanations and it can benefit from the amount of data without human-explanation labels. We also report the accuracy of answers in the column of \"Acc\". It can be observed that our self-critical method with semi-supervised learning can simultaneously boost the precision of answers and cor" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2651" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 112, + 287, + 193 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": "Table 4. Main shortcomings. The main shortcomings of unqualified explanations on the VQA-X dataset. For each sample, human evaluators can select multiple shortcomings." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 112, + 287, + 193 + ], + "lines": [ + { + "bbox": [ + 50, + 112, + 287, + 193 + ], + "spans": [ + { + "bbox": [ + 50, + 112, + 287, + 193 + ], + "type": "table", + "html": "
ModelIrrelevant explanationsInsufficient explanationsMeaningless explanations
RVT [34]25.7%33.5%11.4%
PJ-X [41]21.1%28.4%9.2%
e-UG [20]22.8%25.4%8.7%
NLX-GPT [48]20.3%22.2%9.1%
S3C (ours)17.3%18.9%8.2%
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VQA-X→A-OKVQA
ApproachB4MRSCAcc
NLX-GPT [48]10.712.734.210.735.410.4
S3C(ours)12.013.334.312.545.318.8
A-OKVQA→VQA-X
ApproachB4MRSCAcc
NLX-GPT [48]9.113.632.89.133.242.4
S3C(ours)10.915.034.110.438.643.8
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questionimageanswerexplanationSCRSemiB4MRSCAcc
1✓✓✓--------80.1
2✓✓-✓--24.420.747.319.590.4-
3✓✓✓✓--27.522.950.421.9109.182.2
4✓✓✓✓✓-29.123.451.922.7112.183.7
5✓✓✓✓✓✓30.723.952.123.0116.785.6
", + "image_path": "e1eac8ada72bf5d72678ba027f7e008e2317a7cf3997c08c3e1cd6c72cd59876.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 336, + 149, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 149, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 149, + 348 + ], + "type": "text", + "content": "responding explanations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "type": "text", + "content": "In Table 2, we evaluate our method on the A-OKVQA dataset. The results show that the " + }, + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "type": "text", + "content": " can outperform all the previous works [17, 29, 35, 48, 49, 52]. Especially, compared to the SOTA model [48], there are 9.0 points and " + }, + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "type": "inline_equation", + "content": "4.8\\%" + }, + { + "bbox": [ + 46, + 354, + 287, + 450 + ], + "type": "text", + "content": " improvements in the CIDEr and answer accuracy based on our model. It demonstrates that our model can benefit from semi-supervised learning and generate explanations about commonsense reasoning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": "In addition, to prove the algorithm's validity, we follow [20, 48] to report the filtered scores for the VQAX dataset in Table 3. Through filtering the correct answers, our method can outperform whatever post-hoc [20, 34, 41, 58] and self-rationalization [48] methods. Meanwhile, the proposed " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " achieves a new state-of-the-art with the CIDEr score improved by 6.1 points to 116.7 and boost the answer accuracy by " + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 46, + 456, + 287, + 552 + ], + "type": "text", + "content": " to 85.6." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": "Human Evaluation. To evaluate the faithfulness and correctness of these generated explanations, we conduct the human evaluation that is shown in the column of \"Human\" in Table 1-3. The experimental results further prove our method has better self-interpretability for the VQA-NLE task. Moreover, we also ask the human evaluators to select the shortcomings for each unqualified explanation on the VQA-X dataset. As shown in Table 4, we build three shortcoming options (i.e., irrelevant explanations, insufficient explanations and meaningless explanations) with a multi-choice process. These results indicate that the " + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": " can obtain relatively better rationales and empirically confirm the effectiveness of our method." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 335, + 458, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 458, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 458, + 348 + ], + "type": "text", + "content": "4.4. Cross-dataset Performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 354, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 593 + ], + "type": "text", + "content": "We propose cross-dataset experiments to measure the generalization and reliability of our framework. For all we know, there is very little research on cross-dataset explanation generation. As shown in the first two rows of Table 5, we use the VQA-X and the A-OKVQA as the source dataset and target dataset to test the generalization ability of our framework. Specifically, we use the weights from the state-of-the-art method [48], which are trained on the VQA-X dataset and tested on the A-OKVQA dataset to obtain the results of the NLX-GPT. From the comparisons of six indicators, we find that our self-critical model has better generalization from the general VQA to the knowledge-based VQA. This suggests that " + }, + { + "bbox": [ + 304, + 354, + 545, + 593 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 354, + 545, + 593 + ], + "type": "text", + "content": " can learn commonsense from visual question answering and generate better explanations and answers. Meanwhile, when we exchange the source dataset and target dataset as shown in the last two rows of Table 5, our framework can still surpass the existing SOTA model on all evaluation measures. These quantitative results effectively demonstrate the generalization and stability of our model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 599, + 409, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 409, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 409, + 611 + ], + "type": "text", + "content": "4.5. Ablation Studies." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "As shown in Table 6, we conduct several ablation studies on the VQA-X to demonstrate the effectiveness of our method. In particular, we first build the experiments in the 1-3 rows of Table 6, which use our Answer-Explanation Prompt module with cross-entropy loss as the baseline models. It can be found that when we simultaneously generate both answers and interpretations, the answer accuracy and CIDEr can achieve significant improvements. 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Some generation results on the VQA-X datasets. The [ ] and " + }, + { + "bbox": [ + 46, + 341, + 545, + 363 + ], + "type": "inline_equation", + "content": "<<" + }, + { + "bbox": [ + 46, + 341, + 545, + 363 + ], + "type": "text", + "content": " indicate answers and explanations respectively. We show the results of the state-of-the-art NLX-GPT [48], our method and ground-truth (they are short for NLX, Ours and GT)." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 237, + 199, + 358, + 275 + ], + "blocks": [ + { + "bbox": [ + 54, + 179, + 216, + 188 + ], + "lines": [ + { + "bbox": [ + 54, + 179, + 216, + 188 + ], + "spans": [ + { + "bbox": [ + 54, + 179, + 216, + 188 + ], + "type": "text", + "content": "GT: [yes] " + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 229, + 180, + 369, + 188 + ], + "lines": [ + { + "bbox": [ + 229, + 180, + 369, + 188 + ], + "spans": [ + { + "bbox": [ + 229, + 180, + 369, + 188 + ], + "type": "text", + "content": "GT: [no] " + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 237, + 199, + 358, + 275 + ], + "lines": [ + { + "bbox": [ + 237, + 199, + 358, + 275 + ], + 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], + "type": "text", + "content": "GT: [drinking]" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 400, + 199, + 520, + 275 + ], + "lines": [ + { + "bbox": [ + 400, + 199, + 520, + 275 + ], + "spans": [ + { + "bbox": [ + 400, + 199, + 520, + 275 + ], + "type": "image", + "image_path": "7bec96df02b62f6838cf074149ae4a727fd068f7ab72ee06b34553bac058bac9.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 276, + 440, + 284 + ], + "lines": [ + { + "bbox": [ + 392, + 276, + 440, + 284 + ], + "spans": [ + { + "bbox": [ + 392, + 276, + 440, + 284 + ], + "type": "text", + "content": "(f) Is this a bar?" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 392, + 285, + 531, + 293 + ], + "lines": [ + { + "bbox": [ + 392, + 285, + 531, + 293 + ], + "spans": [ + { + "bbox": [ + 392, + 285, + 531, + 293 + ], + "type": "text", + "content": "NLX: [yes] " + } + ] 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can promote each other. Further, we establish the Self-Critical Reinforcement module as shown in the fourth row, and the result of accuracy and CIDEr are boosted by " + }, + { + "bbox": [ + 46, + 384, + 289, + 552 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 46, + 384, + 289, + 552 + ], + "type": "text", + "content": " and 3.0 points. It suggests that our self-critical method with sequence sampling strategy can encourage the model to generate more reliable explanations and correct answers. Finally, when we extend our model to the semi-supervised setting, the performance improves to 85.6 on the accuracy and 116.7 on the CIDEr over the baseline model (i.e., the row 5 of Table 6) by " + }, + { + "bbox": [ + 46, + 384, + 289, + 552 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 46, + 384, + 289, + 552 + ], + "type": "text", + "content": " and 7.6 points. The results demonstrate that our framework is remarkably effective in improving the logical consistency and the self-interpretability of the model." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 47, + 562, + 176, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 176, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 176, + 574 + ], + "type": "text", + "content": "4.6. Qualitative evaluation." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "As shown in Fig. 3, we show some qualitative results from NLX-GPT [48] and our " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " method on the VQA-X dataset. Through overall comparison, our model achieves better logical consistency between answers and explanations. For example, in Fig. 3 (a), although the SOTA method [48] correctly identifies the significant symbol of formal dress (i.e., tie), the predicted answer is \"no\" that is contradictory to the explanation. On the contrary, our method not only obtains a more complete and faithful rationale but also generates a logically consistent answer. Additionally, the " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " can also produce more persuasive and" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 384, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 421 + ], + "type": "text", + "content": "trusty sentences. For instance, in Fig. 3 (b)-(f), the generated sentences contain scene description \"having a good time\" and fine-grained rationale \"the trunk is in the water\"." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 435, + 378, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 378, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 378, + 447 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "type": "text", + "content": "In this paper, we propose a new Semi-Supervised VQANLE method via Self-Critical Learning " + }, + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "type": "inline_equation", + "content": "(S^3 C)" + }, + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "type": "text", + "content": ". Different from previous works, our method first utilizes the prompting mechanism to motivate the model to generate answers and candidate explanations. Meanwhile, we design a novel Self-Critical Reinforcement module, which converts the answer scores as rewards to evaluate these possible rationales. Furthermore, our framework can benefit from an abundance of question-answer pairs without human-annotated explanations and further boost the self-interpretability of the model. With the automatic measures and human evaluations, our " + }, + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "type": "inline_equation", + "content": "S^3 C" + }, + { + "bbox": [ + 304, + 456, + 545, + 613 + ], + "type": "text", + "content": " achieves a new state-of-the-art on multiple benchmarks and provides a new paradigm for our community." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 626, + 408, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 626, + 408, + 639 + ], + "spans": [ + { + "bbox": [ + 306, + 626, + 408, + 639 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 647, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by National Key R&D Program of China (No.2020AAA0106900), the National Natural Science Foundation of China (No.U19B2037), Shaanxi Provincial Key RD Program (No.2021KWZ-03), and Natural Science Basic Research Program of Shaanxi (No.2021JCW-03)." + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2653" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. 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These methods gradually refine the reference points to the center of target objects and imbue object queries with the updated central reference information for spatially conditional attention. However, centralizing reference points may severely deteriorate queries' saliency and confuse detectors due to the indiscriminative spatial prior. To bridge the gap between the reference points of salient queries and Transformer detectors, we propose SAlient Point-based DETR (SAP-DETR) by treating object detection as a transformation from salient points to instance objects. Concretely, we explicitly initialize a query-specific reference point for each object query, gradually aggregate them into an instance object, and then predict the distance from each side of the bounding box to these points. By rapidly attending to query-specific reference regions and the conditional box edges, SAP-DETR can effectively bridge the gap between the salient point and the query-based Transformer detector with a significant convergence speed. Experimentally, SAP-DETR achieves $1.4 \\times$ convergence speed with competitive performance and stably promotes the SoTA approaches by $\\sim 1.0$ AP. Based on ResNet-DC-101, SAP-DETR achieves 46.9 AP. The code will be released at https://github.com/liuyang-ict/SAP-DETR.", + "bbox": [ + 73, + 376, + 473, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 782, + 209, + 797 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Object detection is a fundamental task in computer vision, whose target is to recognize and localize each object from input images. In the last decade, various detec", + "bbox": [ + 75, + 808, + 470, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e0e7be2e248a69d58cb6ea61a192c0e5d95c0e8c9cff5ff9a8341202b046f68c.jpg", + "image_caption": [ + "Figure 1. Comparison of SAP-DETR and DAB-DETR under 3-layer decoder model and 36-epoch training scheme. (a) Statistics of the query count in different classification score intervals. (b) and (c) Visualize the distribution of all reference points (pink) and highlight the top-20 classification score queries with their bounding boxes (blue) and reference points (red) in different decoder layers. (d) Visualize the outputs of positive queries and ground truth (red) during the training process, each query has a representative color for its reference point and bounding box. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 506, + 345, + 888, + 529 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tors [6,11,14,18,20,22] based on Convolutional Neural Networks (CNNs), have received widespread attention and made significant progress. Recently, Carion et al. [2] proposed a new end-to-end paradigm for object detection based on the Transformer [24], called DEtction TRansformer (DETR), which treats object detection as a problem of set prediction. In DETR, a set of learnable positional encodings, namely object queries, are employed to aggregate instance features from the context image in Transformer Decoder. The predictions of queries are finally assigned to the ground truth via bipartite matching to achieve end-to-end detection.", + "bbox": [ + 496, + 686, + 893, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the promising results of DETR, its application is largely limited by considerably longer training time compared to conventional CNNs. To address this problem, many", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was done when working as an intern at AI Lab, Lenovo Research, Beijing, China.", + "bbox": [ + 75, + 862, + 468, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15539", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "variants attempted to take a close look at query paradigm and introduced various spatial priors for model convergence and efficacy. According to the type of spatial prior, they can be categorized into implicit and explicit methods. The implicit ones [5, 16, 31] attempt to decouple a reference point from the object query and make use of this spatial prior to attend to the image context features efficiently. The current state-of-the-arts (SoTAs) are dominated by the explicit ones [13, 25], which suggest to instantiate a position with spatial prior for each query, i.e., explicit reference coordinates with a center point or an anchor box. These reference coordinates serve as helpful priors and enable the queries to focus on their expected regions easily. For instance, Anchor DETR [25] introduced an anchor concept (center point with different box size patterns) to formulate the query position and directly regressed the central offsets of the bounding boxes. DABDETR [13] further stretched the center point to a 4D anchor box concept $[cx, cy, w, h]$ to refine proposal bonding boxes in a cascaded manner. However, instantiating the query location as a target center may severely degrade the classification accuracy and convergence speed. As illustrated in Fig. 1, there exist many plausible queries [19] with high-quality classification scores (Fig. 1(a) within red box) and box Intersection over Union (IoU, see the redundant blue boxes in Fig. 1(b) and (c)), which only brings a slight improvement on precision rate but inevitably confuses the detector on the positive query assignments when training with bipartite matching strategy. This is because the plausible predictions are considered in negative classification loss, which severely decelerates the model convergence. As shown in Fig. 1(b) and (c), the predefined reference point of the positive query may not be the nearest one to the center of the ground truth bounding box, and the reference points tend to be centralized or marginalized (cyan arrows in Fig. 1(b)), hence losing the spatial specificity. With further insight into the one-to-one label assignment during the training process, we find that the query, whose reference point is closest to the center point, also has a high-quality IoU, but it still exists a disparity with the positive query in the classification confidence. Therefore, we argue that such a centralized spatial prior may cause degeneration of target consistency in both classification and localization tasks, which leads to inconsistent predictions.", + "bbox": [ + 76, + 90, + 472, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, the mentioned central point-based variants also have difficulties in detecting occluded objects. For example, Fig. 1(d) shows that DAB-DETR detects the left baseman twice, while the query point in SAP-DETR is not necessarily the center point, so the query point of the bounding box for the occluded baseman is from a pixel on the occluded baseman on the top right area instead of from the left baseman. One solution for center-based method [25] is to predefine different receptive fields (similar to the scaling anchor box in YOLO [17]) for the position of each query. However, increasing the diversity of the receptive fields for", + "bbox": [ + 76, + 734, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "each position query is unsuitable for non-overlapped targets, as it still generates massive indistinguishable predictions for one position as same as other center-based models.", + "bbox": [ + 496, + 90, + 893, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To bridge these gaps, in this paper, we present a novel framework for Transformer detector, called SAclient Point-based DETR (SAP-DETR), which treats object detection as a transformation from salient points to instance objects. Instead of regressing the reference point to the target center, we define the reference point belonging to one positive query as a salient point, keep this query-specific spatial prior with a scaling amplitude, and then gradually update them to an instance object by predicting the distance from each side of the bounding box. Specifically, we tile the mesh-grid referenced points and initialize their center/corner as the query-specific reference point. To disentangle the reference sparsity as well as stabilize the training process, a movable strategy with scaling amplitude is applied for reference point adjustment, which prompts queries to consider their reference grid as the salient region to perform image context attention. By localizing each side of the bounding box layer by layer, such query-specific spatial prior enables compensation for the over-smooth/inadequacy problem during center-based detection, thereby vastly promoting model convergence speed. Inspired by [5, 13, 16], we also take advantage of both Gaussian spatial prior and conditional cross-attention mechanism, and then a salient point enhanced cross-attention mechanism is developed to distinguish the salient region and other conditional extreme regions from the context image features.", + "bbox": [ + 496, + 138, + 895, + 516 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We bridge the gap between salient points and query-based Transformer detector by speedily attending to the query-specific region and other conditional regions. The extensive experiments have shown that SAP-DETR achieves superior convergence speed and performance. To the best of our knowledge, this is the first work to introduce the salient point based regression into end-to-end query-based Transformer detectors. Our contributions can be summarized as follows.", + "bbox": [ + 496, + 517, + 893, + 638 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) We introduce the salient point concept into query-based Transformer detectors by assigning query-specific reference points to object queries. Unlike center-based methods, we restrict the reference location and define the point of the positive query as the salient one, hence enlarging the discrepancy of query as well as reducing the redundant predictions (see Fig. 1). Thanks to the efficacy of the query-specific prior, our SAP-DETR accelerates the convergence speed greatly, achieving competitive performance with $30\\%$ fewer training epochs. The proposed movable strategy further boosts SAP-DETR to a new SoTA performance.", + "2) We devise a point-enhanced cross-attention mechanism to imbue query with spatial prior based on both reference point and box sides for final specific region attention.", + "3) Evaluation over COCO dataset has demonstrated that SAP-DETR achieves superior convergence speed and detection accuracy. Under the same training settings, SAP-DETR" + ], + "bbox": [ + 496, + 640, + 895, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15540", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "outperforms the SoTA approaches with a large margin.", + "bbox": [ + 76, + 90, + 439, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 119, + 218, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Anchor-Free Object Detectors. Classical anchor-free object detectors can be grouped into center-based and keypoint-based approaches. The center-based approaches aim to localize the target objects based on the central locations [11] or predefined ROI [22]. For example, FCOS [22] treated all points within the bounding box as positive ones to predict their distances from each side $([\\ell, t, r, b])$ , and a centerness score was then considered to prohibit the low-quality prediction whose point is located near the border. Compared with FCOS, we also restrict the candidate queries within the bounding box but treat only one as positive to perform end-to-end object detection via an inner matching cost.", + "bbox": [ + 75, + 145, + 470, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The target of keypoint-based approaches is to localize the specific object locations and assign them to the predefined keypoints of the object for box localized training. For instance, diagonal corner points were considered in CornerNet [8], center point was further grouped into CenterNet [29], and ExtremeNet [30] added some conjectural extreme points for object localization. These works showed an impressive performance, but the complicated keypoint matching may limit their upper bound. Our SAP-DETR takes the advantage of salient point regression to focus on the distinct regions without complicated point-based supervision.", + "bbox": [ + 75, + 327, + 468, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Query-Based Transformer Detectors. DETR [2] pioneered a new paradigm of Transformer detector for end-to-end object detection without any post-processing [1]. In DETR, a new representation, namely object query, aggregates the instance features and then yields a detection result for each instance object [15]. Following DETR, many voterists put efforts on the optimization of convergence and accuracy.", + "bbox": [ + 75, + 492, + 468, + 598 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sun et al. [21] revealed that the main reason for slow convergence of DETR is attributed to the Transformer decoder, and they considered an encoder-only structure to alleviate such a problem. For in-depth understanding of the object query, one way is to generate a series of implicit spatial priors from queries to guide feature aggregation in cross-attention layers. SMCA [5] applied a Gaussian-like attention map to augment the query-concerned features spatially. The reference point concept was first introduced by Deformable DETR [31], where the sampling offsets are predicted by each reference point to perform deformable cross-attention. Following such a concept, Conditional DETR [16] reformulated the attention operation and rebuilt positional queries based on the reference points to facilitate extreme region discrimination. Another way is towards position-instantiation explicitly, where this position information enables to directly conduct positional query generation. Anchor DETR [25] utilized a predefined 2D anchor point $[cx, cy]$ to explicitly capitalize on the spatial prior during cross-attention and box regression. DAB-DETR [13] extended such a 2D concept to", + "bbox": [ + 75, + 599, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/610de358f6711972cd0b18bdd81eb531a04351f72a5b205d48cb34f2440f488e.jpg", + "image_caption": [ + "Figure 2. Illustration of SAP-DETR. Each object query in SAP-DETR is assigned to a specific grid region and initialized by the corner/center of the grid as its reference point. A learnable 4D coordinate represents the distance from the four sides of the box to the reference point. Both reference points and box sides are served as positional encodings added/concatenated to content embeddings. All embeddings are refined to predict target objects gradually." + ], + "image_footnote": [], + "bbox": [ + 531, + 87, + 864, + 369 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a 4D anchor box $[cx, cy, w, h]$ and refined it layer-by-layer.", + "bbox": [ + 500, + 494, + 888, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The recent accelerating convergence methods are based on auxiliary queries for facilitating detector discrimination. DN-DETR [9] demonstrates the slow model convergence is mainly caused by the instability of bipartite matching, thus providing a denoising training to eliminate this issue. DINO [28] inherits this advance and further introduces negative queries to perform contrastive denoising. Group-DETR [4] proposes a group-wise one-to-many label assignment to match multiple positive object queries with more gradients for fast DETR convergence.", + "bbox": [ + 496, + 511, + 893, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The most relevant approaches to ours are Point-DETR [3] and SAM-DETR [26, 27]. The former applied a point encoder for annotated point label infusion in teacher model, and the latter directly updated content embeddings by extracting salient points from image features for query-image semantic alignment. Unlike these concepts, we redefine the salient point from the perspective of the positive query's position and replace the center-concept prior with the query-specific position, thereby attending extreme regions, differentiating queries' saliency, and alleviating redundant predictions.", + "bbox": [ + 496, + 662, + 893, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 829, + 589, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose SAP-DETR to bridge the gap between salient points and query-based detectors. Following DETR, the extracted image features are fed into Transformer encoder", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15541", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "after adding positional encodings, and then re-aggregated by object queries in Transformer decoder. In pursuit of the query-specific prior, we dispense a movable strategy for each query based on a fixed grid region. The query, whose reference region overlaps with ground truth objects, is allowed to predict the relative offsets from four sides of the bounding box to the points. Given the query-specific reference point and the proposal box sides, we propose salient point enhanced cross-attention mechanism to imbue query with spatial prior, thereby attending to extreme regions effectively. Additionally, we discuss two common issues in DETR-like models and address them for further improvements.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Salient Points-Based Object Detection", + "text_level": 1, + "bbox": [ + 76, + 281, + 405, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overview. Previous methods [13, 16, 25] normally decompose the object query into both content and position embeddings (queries), and form a center-based anchor point/box prior on the position ones. Unlike the central concept, we tile a fixed mesh-grid region, initialize their left-top corner as the reference points with 2D coordinate $\\boldsymbol{r} = \\{x, y\\} \\in [0,1]^2$ , and instantiate a learnable 4D offset distance $s = \\{\\ell, t, r, b\\} \\in [0,1]^4$ from the reference point to the sides of proposal bounding box for each object query. The object query can be referred as $q = \\{\\mathbf{e}; r, s\\}$ , where $\\mathbf{e} \\in \\mathbb{R}^d$ is the content embedding with $d$ dimension. Instead of regressing the center, width, and height of a bounding box, we follow FCOS [22] and directly supervise the 4D offset from the four sides of a bounding box to the reference point. The final box prediction is formulated as $\\hat{\\boldsymbol{b}} = \\{\\hat{x} - \\hat{\\ell}, \\hat{y} - \\hat{\\bar{t}}, \\hat{x} + \\hat{r}, \\hat{y} + \\hat{b}\\}$ . Ideally, we here fix the reference point $\\{\\hat{x}, \\hat{y}\\} = \\{x, y\\}$ (the movable update strategy is introduced in the next subsection) and only update the 4D box side prediction layer by layer. The prediction for each decoder layer can be calculated by", + "bbox": [ + 75, + 303, + 473, + 592 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\boldsymbol {s} _ {l} = \\operatorname {B o x H e a d} _ {l} (\\boldsymbol {s} _ {l - 1}, \\boldsymbol {e} _ {l - 1}, \\boldsymbol {r} _ {l - 1}),\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 602, + 393, + 618 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {s}} _ {l} = \\sigma \\left(\\sigma^ {- 1} \\left(\\boldsymbol {s} _ {l - 1}\\right) + \\Delta \\boldsymbol {s} _ {l}\\right), \\quad \\boldsymbol {s} _ {l} = \\operatorname {D e t a c h} (\\hat {\\boldsymbol {s}} _ {l}),\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 621, + 429, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {r} _ {l} = \\hat {\\boldsymbol {r}} _ {l} = \\boldsymbol {r} _ {l - 1}, \\quad \\hat {\\boldsymbol {b}} _ {l} = \\left\\{\\hat {\\boldsymbol {r}} _ {l} - \\hat {\\boldsymbol {s}} _ {l} [: 2 ], \\hat {\\boldsymbol {r}} _ {l} + \\hat {\\boldsymbol {s}} _ {l} [2: ] \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 643, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma$ and $\\sigma^{-1}$ are the sigmoid and inverse sigmoid operation, respectively. $\\Delta s_{l}$ denotes the side offset prediction. $\\hat{s}_l$ , $\\hat{r}_l$ , and $\\hat{\\pmb{b}}_l$ are the predicted side distance, reference points, and box location from the $l$ decoder layer, respectively. The BoxHead is the prediction head following the layer- $l$ decoder, which is independent between different decoder layers in our settings. Detach operation follows DAB-DETR [13].", + "bbox": [ + 75, + 674, + 470, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the training process, each query is only allowed to predict the bounding boxes that overlap its reference region. We adapt this rule into the one-to-one bipartite matching process via an inner matching cost $\\mathcal{L}_{\\mathrm{inner}}$ . Given $N$ queries $\\mathbf{Q} = \\{\\pmb{q}_1,\\pmb{q}_2,\\dots ,\\pmb{q}_N\\}$ and $M$ ground truth objects $\\mathbf{G} = \\{\\pmb{g}_1,\\pmb{g}_2,\\dots ,\\pmb{g}_M\\}$ , the $\\mathcal{L}_{\\mathrm{inner}}(\\pmb{g}_i,\\pmb{q}_j)$ of each query-box pair is a step function to penalize the reference point $\\pmb{r}_j$ of $\\pmb{q}_j$ with value of $k$ when $\\pmb{r}_j$ is outside the bounding box of", + "bbox": [ + 75, + 780, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$g_{i}$ . We denote $i \\in [1, M]$ and $j \\in [1, N]$ as the index of query and ground truth, respectively. $k$ can be viewed as a penalty cost, and default to $10^{5}$ . The final permutation of the one-to-one label assignment is formulated as", + "bbox": [ + 496, + 90, + 893, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n n e r}} \\left(\\boldsymbol {g} _ {i}, \\boldsymbol {q} _ {j}\\right) := \\mathbf {k} _ {\\boldsymbol {r} _ {j} \\notin \\boldsymbol {g} _ {i}},\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 162, + 779, + 179 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\eta} = \\underset {\\eta \\in \\mathfrak {Y} _ {N}} {\\operatorname {a r g m i n}} \\sum_ {i} ^ {N} \\mathcal {L} _ {\\text {m a t c h}} + \\mathcal {L} _ {\\text {i n n e r}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 181, + 890, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{match}}$ is the original pair-wise matching cost consist of both classification and localization costs [2]. $\\eta \\in \\mathfrak{V}_N$ is a permutation of $N$ elements for bipartite matching.", + "bbox": [ + 496, + 231, + 890, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Movable Reference Point. Due to the sparseness of the fixed reference point, some small and slender objects may be indistinguishable when there is no reference point inside these objects. Despite the bipartite matching forcing each object to be assigned to one object query, the positive query, whose reference point is outside the assigned bounding box, is unable to accurately regress the distance from each side by a value between 0 and 1. One straightforward solution is to adjust the locations of reference points inside the ground truth bounding boxes to ensure that each object can be detected by an inner reference point. Similar to the aforementioned box refinement, we first perform a movable reference point design to dynamically update the reference points of each query layer by layer. However, such a full-image point regression inevitably expands the search space as vast variable determinations, causing the final reference point to be trapped in an unexpected corner of the bounding box. To reduce the training search spaces, we scale the offset amplitude of points within their specific grid regions, as illustrated in Fig. 3. Such an operation limits the range of offset values, and hence prevents a large searching space. It is implemented by applying the sigmoid activation $\\sigma$ and multiplying a scale factor $s_{\\mathrm{grid}}$ whose value equals to the height and width of one grid. The update process of the reference points is formulated as", + "bbox": [ + 496, + 277, + 893, + 654 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\boldsymbol {r} _ {l} ^ {\\prime} = \\operatorname {P o i n t H e a d} _ {l} \\left(\\boldsymbol {s} _ {l - 1}, \\boldsymbol {e} _ {l - 1}, \\boldsymbol {r} _ {l - 1}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 665, + 821, + 681 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\boldsymbol {r} _ {l} = \\sigma \\left(\\sigma^ {- 1} \\left(\\boldsymbol {r} _ {l - 1} - \\boldsymbol {r} _ {0}\\right) + \\Delta \\boldsymbol {r} _ {l} ^ {\\prime}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 685, + 890, + 702 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {r}} _ {l} = \\boldsymbol {r} _ {0} + \\Delta \\boldsymbol {r} _ {l} \\cdot \\boldsymbol {s} _ {\\text {g r i d}}, \\quad \\boldsymbol {r} _ {l} = \\operatorname {D e t a c h} (\\hat {\\boldsymbol {r}} _ {l}),\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 705, + 834, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Delta \\boldsymbol{r}_l'$ and $\\Delta \\boldsymbol{r}_l$ are the predicted offsets from $\\boldsymbol{r}_l$ to both $\\boldsymbol{r}_{l-1}$ and $\\boldsymbol{r}_0$ before the sigmoid activation $\\sigma$ , respectively.", + "bbox": [ + 500, + 732, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Salient Point Enhanced Cross-Attention", + "text_level": 1, + "bbox": [ + 500, + 771, + 841, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In cross-attention layers, existing center-based methods are limited to the attention on both center and sides of the ground truth bounding box, causing detector confusion among the queries with the same center and side attention. To this end, we expect the queries to focus on their specific regions based on the reference points, four box sides, and other conditional regions in different heads. Accordingly,", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15542", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/db807192e02719a82d755a7878de64a4f620ef8a0f63351e89cf8572332e9f7c.jpg", + "image_caption": [ + "Figure 3. Movable reference point. The reference points are initialized by the center/corner points of the mesh-grid. Based on the inner loss, only the green dashed box can be predicted by the inner points when reference points are fixed. By moving the reference points within their grid, the blue dashed boxes can be detected accurately without extended searching space." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 472, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we consider an improved Gaussian [5] $\\mathbf{G}$ and conditional attention [16] $\\mathbf{A}_{\\mathrm{peca}}$ to enhance query specificity and spatially extreme region discrimination. The final attention map $\\mathbf{A}_{\\mathrm{cross}}$ is the sum of the two attentions $\\mathbf{A}_{\\mathrm{cross}} = \\mathbf{G} + \\mathbf{A}_{\\mathrm{peca}}$ .", + "bbox": [ + 75, + 318, + 468, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Side Directed Gaussian (SDG). Similar to the movable strategy, we enforce the predicted Gaussian attention to be inside the proposal bounding box to reduce the searching space. Given a reference point $r$ , the offset scales $\\mathbf{o} \\in [-1,1]^2$ for $H$ heads are produced by a simple MLP with a tanh activation, and then multiply to the two sides of the proposal bounding box for head-specific point offset generation, where the direction is guided by the sign of the offset scales. The head-specific points are generated by Algorithm 1. For each head, the Gaussian-like spatial weight map $G_{i}$ effecting on each pixel $(x,y)$ of context features is then formulated as", + "bbox": [ + 75, + 380, + 473, + 546 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nG _ {i} (x, y) = \\exp \\left(- \\frac {\\left(x - c _ {w , i}\\right) ^ {2}}{v _ {w , i} ^ {2}} - \\frac {\\left(y - c _ {h , i}\\right) ^ {2}}{v _ {h , i} ^ {2}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 556, + 468, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Point Enhanced Cross-Attention (PECA). As aforementioned, the semantic class for the query is closely related to its referenced location in our SAP-DETR. To enhance the correlation between queries and their references, we concatenate the locations to the content queries after the sinusoidal positional encoding (PE). Take a close look at the conditional attention [16], we find that the linear positional embedding mostly focuses on one box side in each attention head. So we introduce a more straightforward attention mechanism, where the four side coordinates are concatenated and assigned to the corresponding head for side attention. The process of PECA is formulated as", + "bbox": [ + 75, + 604, + 472, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} \\mathbf {A} _ {\\text {p e c a}} & = \\mathbf {e} _ {q} \\mathbf {e} _ {k} ^ {\\top} + \\mathbf {T P E} (\\boldsymbol {r} _ {q}) \\mathbf {P E} (\\boldsymbol {r} _ {k}) ^ {\\top} \\\\ & + \\mathbf {T} g (\\mathbf {P E} (\\boldsymbol {r} _ {q} - \\{\\ell , t \\}, \\boldsymbol {r} _ {q} + \\{r, b \\})) \\mathbf {P E} (\\boldsymbol {r} _ {k}) ^ {\\top}, \\end{array} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 792, + 468, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g$ is a linear layer mapping 4D-PE into 2D to keep channel dimension consistency. T [16] is a scaling transformation matrix. More details of T and comparison with conditional cross-attention are available in Appendix C.", + "bbox": [ + 75, + 839, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Side Directed Gaussian", + "text_level": 1, + "bbox": [ + 500, + 90, + 746, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Content embedding e, reference point $r$ and box s.", + "bbox": [ + 500, + 109, + 852, + 123 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Head-specific points $\\mathbf{c} = \\{(c_{w,i}, c_{h,i}) | i \\in H\\}$ and head-specific attention $\\mathbf{v} = \\{(v_{w,i}, v_{h,i}) | i \\in H\\}$ .", + "bbox": [ + 500, + 123, + 893, + 151 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Predict offset scale and attention scale based on content embedding, $\\mathbf{o} = \\tanh (\\mathrm{MLP}(\\mathbf{e}))$ , $\\mathbf{v} = \\mathrm{MLP}(\\mathbf{e})$", + "2: for $h\\gets 1\\in H$ do", + "3: Select the index of direction guided by the sign of offset scale, $\\{a,b\\} = \\mathrm{sgn}(\\mathbf{o}_i) + \\{1,2\\}$ , $a,b\\in \\{0,1,2,3\\}$ ;", + "4: According to the index of direction, predict head-specific point, $\\mathbf{c}_i = \\mathbf{o}_i\\cdot \\mathbf{s}[a,b] + \\mathbf{r}$", + "5: end for", + "6: return $\\mathbf{c}_i, \\mathbf{v}_i, \\forall i = 1, \\dots, H$" + ], + "bbox": [ + 508, + 151, + 893, + 275 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. SAP-DETR with Denoising Strategy", + "text_level": 1, + "bbox": [ + 500, + 308, + 813, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To further explore the capability of our proposed SAP-DETR, we develop SAP-DN-DETR and SAP-DINO-DETR by adding the denoising auxiliary loss [9,28] into the training process. In the denoised SAP-DETR, the main difference from both DN-DETR and DINO lies in the noise design. Instead of the center point, we perform the box jittering and randomly sample a point from the intersection region between the original bounding box and the jittering one as the reference point. As the denoising strategy only serves as an auxiliary training loss increasing the training cost, the variants of denoising models are test-free whose Params and GFLOPs are the same as SAP-DETR models.", + "bbox": [ + 496, + 332, + 893, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 531, + 705, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 556, + 717, + 573 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct the experiments on the COCO 2017 [12] object detection dataset, containing about 118K training images and 5K validation images. All models are evaluated by the standard COCO evaluation metrics. We follow the vanilla DETR [2] structure that consists of a CNN backbone, a stack of Transformer encoder-decoder layers, and two prediction heads for class label and bounding box prediction. We use ImageNet-pretrained ResNet [7] as our backbone, and report results based on the ResNet and its $\\times 1/16$ -resolution extension ResNet-DC. Unlike DAB-DETR [13] sharing box and label head for each layer, we share the class head except the first layer and use an independent box head for the box regression of each layer (for more details please refer to Appendix D). As the mesh-grid initialization for reference points in SAP-DETR, we consider the number of queries $N$ as a perfect square for uniform distribution. Unless otherwise specified, we use $N = 400$ queries in the experiments. Precisely, we also provide a comparison under $N = 300$ in Tab. 2, the standard setting in DETR-like models.", + "bbox": [ + 496, + 580, + 893, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt two different Transformer structures for experiments where a 3-layer encoder-decoder stack is evaluated to", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15543", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e67c17b52b62bc18f59407f49da518ec9d46208e46c8ed65384428ba5d8ecd32.jpg", + "image_caption": [ + "Figure 4. Comparison of performance and training losses curves." + ], + "image_footnote": [], + "bbox": [ + 187, + 87, + 379, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c4e4471d6732af893721aadaca57cebf551f6985172900d817e0947edfa5e3c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 87, + 580, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a2fba28d8751276d87d046916bae807f8b5b51e25a59642266ec0fb9122b2506.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 583, + 85, + 781, + 210 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "demonstrate our lightweight model efficacy compared with the traditional CNN detectors, and a 6-layer encoder-decoder stack is aligned with previous DETR variants to investigate the performance of large model. Both are trained on two training schemes: the 12-epoch and 36-epoch schemes with a learning rate drop after 11 and 30 epochs, respectively. All models are trained on the Nvidia A100 GPUs with batch size of 16 and 8 for ResNet and ResNet-DC, respectively. For more training details, please refer to Appendix F.", + "bbox": [ + 75, + 250, + 472, + 387 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 393, + 217, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Tab. 1 and Tab. 2, we comprehensively compare our proposed SAP-DETR with the traditional CNN detectors [18], the original DETR [2], and other DETR-like detectors [5, 13, 16, 25, 26, 31] on COCO 2017 validation dataset. For in-depth analysis, we conduct the comparison in two aspects: model convergence and efficacy.", + "bbox": [ + 75, + 417, + 470, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Convergence. Compared with traditional CNN detectors, Transformer detectors are always subject to laborious training time. For example, under the same 12-epoch training scheme, Faster RCNN [18] still achieves good performance, but the mainstream DETR-like models may suffer from inadequate training and perform poorly without the help of auxiliary losses [9]. Under the 12-epoch training scheme, our proposed SAP-DETR can accelerate model convergence significantly, boosting DAB-DETR [13] by 3.9 AP and 2.7 AP on 3-layer and 6-layer encoder-decoder structures, respectively. Compared with the current SoTA, our SAP-DETR also outperforms SAM-DETR [26] by $\\sim 1.3$ AP, with reducing $\\sim 17\\%$ parameters and $\\sim 10\\%$ GFLOPs. Take a close look at the training process, as illustrated in Fig. 4, SAP-DETR conducts with rapid descent curves in both classification and box regression losses. Notably, there is a large margin in classification loss between ours and SoTA methods, which is benefited from the query-specific reference point, hence boosting model performance in early epochs.", + "bbox": [ + 75, + 507, + 470, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Efficacy. To analyze model efficacy, we report results on long training epochs and high-resolution features in Tab. 1. Under the 36-epoch training scheme, SAP-DETR achieves superior performance among all single-scale Transformer detectors, especially on middle and large targets. For example, SAP-DETR boosts DAB-DETR by $2.0\\mathrm{AP}_{\\mathrm{M}}$ and $4.1\\mathrm{AP}_{\\mathrm{L}}$ with 3-layer models, $1.0\\mathrm{AP}_{\\mathrm{M}}$ and $1.9\\mathrm{AP}_{\\mathrm{L}}$ with", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6-layer models, which further verifies the effectiveness of our proposed salient point concept for overlapping object detection. Along with layer increase, a deficient upper-bound of SAM-DETR is exposed, with obviously lower 0.5 AP promotion compared to our 1.0 AP improvement. Persuasively, we also report the 50-epoch training results based on the 300-query setting. To align with our mesh-grid initialization strategy, we tile a $17 \\times 18$ mesh-grid (306 queries) for each reference point initialization. Tab. 2 shows our main results and the most representative approaches with their original reported performance. Notably, SAP-DETR outperforms the current SoTAs with comparable costs based on all backbones. With low-resolution features ( $\\times 1/32$ ), it significantly boosts both middle and large object detection accuracy.", + "bbox": [ + 496, + 250, + 893, + 462 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Combine with Other Fast Convergence Methods. As shown in Tab. 3, we compare our SAP-DETR variants with the current fast convergence methods [4, 9, 28]. With such a subtle modification, our SAP-DETR (grey rows) results in a significant performance improvement compared with the original methods (white rows). Under the 12-epoch training scheme, there exist 0.5-1.9 AP improvements on DN-DETR [9] and 0.7-1.6 AP improvements on Group-DETR [4], but the promotions are slightly reduced when implemented on DINO [28]. We hypothesise that there exists the same effect between the negative query of contrastive denoising [28] and our query-salient reference point. Moreover, we observe that the performance improvements largely originate from the large object detection, especially based on ResNet-DC5 family backbones. We speculate that DETR may prefer the high-resolution features ( $\\times 1/16$ ) rather than the low-resolution ones ( $\\times 1/32$ ), and our SAP-DETR can distinguish the salient points accurately on the high-resolution, thereby taking full advantage of the large object detection.", + "bbox": [ + 496, + 462, + 895, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 760, + 653, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of Each Component. To offer an intuitionistic comparison of model convergence for each component, Tab. 4 reports the effectiveness of them based on the 3-layer encoder-decoder structure and 12-epoch training scheme. I). The proposed salient point concept based on content embeddings improves the performance from 32.3 AP to 33.5", + "bbox": [ + 496, + 784, + 893, + 876 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1https://github.com/facebookresearch/detectron2", + "bbox": [ + 517, + 886, + 781, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15544", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f0e495db48712226ee91ed149febaa6e161ba66f364fb9954946855d4923b05a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method#Epochs#Params(M)GFLOPsAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
3-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36338215.828.015.45.316.724.6
Deformable DETR-R50 [31]36307737.157.639.418.340.851.6
SMCA-DETR-R50 [5]12 / 36--28.8 / 37.748.1 / 58.729.9 / 40.113.8 / 19.431.3 / 40.541.3 / 54.8
Conditional DETR-R50 [16]12 / 36408229.6 / 37.148.7 / 57.930.7 / 39.013.0 / 17.632.3 / 40.343.1 / 55.0
Anchor DETR-R50 [25]12 / 36317930.8 / 37.651.1 / 58.731.8 / 39.714.3 / 18.834.1 / 41.544.3 / 53.5
DAB-DETR-R50 [13]12 / 36348332.3 / 39.051.3 / 58.634.0 / 41.815.7 / 20.035.2 / 42.545.7 / 56.0
SAM-DETR-w/SMCA-R50 [26]12 / 36418935.1 / 40.454.7 / 60.736.7 / 42.716.0 / 20.238.4 / 44.452.1 / 58.3
SAP-DETR-R50 (Ours)12 / 36368436.2 / 41.256.2 / 61.637.9 / 43.416.4 / 21.039.5 / 44.553.8 / 60.1
6-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36428914.024.414.04.213.722.5
Deformable DETR-R50 [31]36348138.058.240.418.541.754.2
SMCA-DETR-R50 [5]12 / 36--32.4 / 40.152.3 / 61.434.0 / 42.815.5 / 20.334.9 / 43.347.7 / 57.1
Conditional DETR-R50 [16]12 / 36449033.1 / 40.253.0 / 61.034.8 / 42.414.5 / 19.935.9 / 43.549.2 / 58.8
Anchor DETR-R50 [25]12 / 36378533.7 / 39.754.5 / 60.535.1 / 41.915.6 / 19.937.3 / 43.549.8 / 57.3
DAB-DETR-R50 [13]12 / 36449234.9 / 41.055.5 / 61.736.4 / 43.416.2 / 21.338.4 / 44.751.5 / 58.9
SAM-DETR-w/SMCA-R50 [26]12 / 365910536.2 / 40.957.2 / 62.237.4 / 43.116.1 / 20.139.8 / 44.755.3 / 60.7
SAP-DETR-R50 (Ours)12 / 36479437.5 / 42.258.5 / 62.739.2 / 44.617.3 / 22.640.6 / 45.755.4 / 60.8
", + "bbox": [ + 99, + 88, + 870, + 308 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/af9d626399bf3a1424d9d21efba19a0704c74c33aff6a018ede81bfd149db747.jpg", + "table_caption": [ + "Table 1. Comparison between Transformer necks. Based on ResNet-50 backbone, all models are trained by the official source codes with their original settings and evaluated on COCO val2017. All models uses 400 queries except Anchor DETR, while Anchor DETR uses 200 queries with 2 pattern embeddings. GFLOPs and Params are measured by $\\text{Detectron}^2$ ." + ], + "table_footnote": [], + "table_body": "
Method#Epochs#Params(M)GFLOPsAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)Infer. \\( Time(s / img)^{\\dagger} \\)
ResNet-50 Backbone
Faster RCNN-FPN-R50 [10, 18]1084218042.062.145.526.645.553.40.039
DETR-R50 [2]500418642.062.444.220.545.861.10.040
Deformable DETR-R50 [31]50347839.459.642.320.643.055.50.043
SMCA-DETR-R50 [5]50428641.0--21.944.359.10.045
Conditional DETR-R50 [16]50449040.961.843.320.844.659.20.057
Anchor DETR-R50 [25]50398542.163.144.922.346.260.00.050
DAB-DETR-R50 [13]5044\\( 90^† \\)42.263.144.721.545.760.30.059
SAM-DETR-w/SMCA-R50 [26]505810041.863.243.922.145.960.90.065
SAP-DETR-R50 (Ours)50479243.163.845.422.947.162.10.063
ResNet-101 Backbone
Faster RCNN-FPN-R101 [10, 18]1086024644.063.947.827.248.156.00.050
DETR-R101 [2]5006015243.563.846.421.948.061.80.066
Conditional DETR-R101 [16]506315642.863.746.021.746.660.90.070
Anchor DETR-R101 [25]505815043.564.346.623.247.761.40.068
DAB-DETR-R101 [13]5063\\( 157^† \\)43.563.946.623.647.361.50.072
SAP-DETR-R101 (Ours)506715844.464.947.124.148.763.10.078
DC5-ResNet-50 Backbone
DETR-DC5-R50 [2]5004118743.363.145.922.547.361.10.087
Conditional DETR-DC5-R50 [16]504419543.864.446.724.047.660.70.093
Anchor DETR-DC5-R50 [25]503915144.264.747.524.748.260.60.069
DAB-DETR-DC5-R50 [13]5044\\( 194^† \\)44.565.147.725.348.262.30.094
SAM-DETR-w/SMCA-DC5-R50 [26]505821045.065.447.926.249.063.30.126
SAP-DETR-DC5-R50 (Ours)504719746.065.548.926.450.262.60.116
DC5-ResNet-101 Backbone
DETR-DC5-R101 [2]5006025344.964.747.723.749.562.30.101
Conditional DETR-DC5-R101 [16]506326245.065.648.426.148.962.80.105
Anchor DETR-DC5-R101 [25]505822745.165.748.825.849.461.60.083
DAB-DETR-DC5-R101 [13]5063\\( 263^† \\)45.865.949.327.049.863.80.110
SAP-DETR-DC5-R101 (Ours)506726646.966.750.527.951.364.30.130
", + "bbox": [ + 98, + 362, + 870, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison of Transformer necks with 300 queries on COCO val2017. All results are reported from their original paper. All models uses 300 queries except Anchor DETR, while Anchor DETR uses 100 queries with 3 pattern embeddings. All inference speeds are measured by a single Nvidia A100 GPU. † denotes the results are measured by ourselves.", + "bbox": [ + 75, + 710, + 893, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "AP compared to baseline DAB-DETR (row 8-9). Such a query-specific spatial prior enables queries to attend to their expected region from content features (see Figures in Appendix G) and reduces the false detection rate on occluded and partial objects (see Fig. 1(d)), hence boosting detection performance on middle and large objects. However, there exists a drop in small object detection (15.7 APs vs. 14.3 APs), for which we consider that the failure is mainly caused", + "bbox": [ + 75, + 765, + 472, + 887 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "by the query sparsity. 2). Therefore, the movable strategy is applied to alleviate the constraint, improving the final model by $1.0\\mathrm{AP}$ and $0.6\\mathrm{AP}_{\\mathrm{S}}$ (row 1 and 6). 3). Compared with the final model, the inner loss greatly improves the performance on high-quality $\\mathrm{AP}_{75}$ and large objects $\\mathrm{AP}_{\\mathrm{L}}$ detection (row 1 and 7), with just a slight drop on low-quality object $\\mathrm{AP}_{50}$ . That is reasonable because the outside reference points are unable to localize objects accurately, and this phenomenon", + "bbox": [ + 496, + 765, + 893, + 887 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15545", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/20d6ddd9750f06eeb1fa780dc674d1a5a429f28f28f646e61a1b317c601627f8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BackboneEpochw/ SAPDN-DETR [9]DINO (Single-Scale) [28]Group DETR [4]
AP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APL
R5012✓(Ours)38.3 / 58.6 / 40.518.4 / 41.6 / 57.139.7 / 58.3 / 42.419.1 / 43.7 / 57.139.1 / - / -19.7 / 42.5 / 56.8
39.5 / 59.7 / 41.518.7 / 42.8 / 59.040.0 / 60.1 / 42.120.2 / 43.4 / 58.539.8 / 60.2 / 42.020.2 / 43.5 / 58.6
R10112✓(Ours)40.5 / 60.8 / 43.019.3 / 44.3 / 59.641.9 / 60.8 / 44.422.5 / 46.3 / 59.5- / - / -- / - / -
41.0 / 61.2 / 43.419.8 / 45.3 / 60.041.5 / 61.4 / 43.620.3 / 45.2 / 60.041.1 / 61.5 / 43.420.5 / 45.5 / 59.4
R50-DC12✓(Ours)41.7 / 61.4 / 44.121.2 / 45.0 / 60.243.6 / 61.4 / 47.024.8 / 47.3 / 59.541.9 / - / -23.3 / 45.6 / 58.4
43.6 / 62.5 / 46.223.3 / 47.3 / 61.044.0 / 63.1 / 46.524.8 / 47.3 / 61.143.9 / 63.2 / 46.824.5 / 47.6 / 61.3
R101-DC12✓(Ours)43.4 / 61.9 / 47.224.8 / 46.8 / 59.445.4 / 63.5 / 49.226.4 / 49.5 / 61.1- / - / -- / - / -
44.6 / 63.9 / 48.025.5 / 48.9 / 62.545.6 / 64.5 / 48.725.0 / 49.7 / 62.544.4 / 63.9 / 47.425.9 / 48.5 / 61.4
", + "bbox": [ + 119, + 88, + 854, + 200 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/32be50eeddec82a689fc94ef01756152c3c617029bb5f1e4522e5711f0a553dd.jpg", + "table_caption": [ + "Table 3. Comparison with denoised methods on COCO dataset based on the 12-epoch training schedule and 300 object queries." + ], + "table_footnote": [], + "table_body": "
CommentMovableInner LossPECASDGAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
SAP-DETR (Ours)✓✓✓✓36.256.237.916.439.553.8
-SDG✓✓✓35.656.236.916.338.952.7
-PECA✓✓✓34.855.536.015.737.352.0
-PECA & SDG✓✓34.054.935.315.036.751.5
-Movable✓✓✓35.255.436.815.838.553.8
-Inner Loss✓✓✓35.956.337.416.239.352.5
DAB-DETR (Baseline)----32.351.334.015.735.245.7
+Salient Point Concept----33.554.335.114.336.551.0
", + "bbox": [ + 119, + 234, + 849, + 330 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bfe2dfcf6438eb46ef01ad8830cf28ffb81daf459a4571ee5e1b0268a7e20227.jpg", + "table_caption": [ + "Table 4. Ablation on each components" + ], + "table_footnote": [], + "table_body": "
Inner Cost (Linner)Movable within Grid (sgrid)APAPSAPMAPL
35.917.038.852.7
✓26.311.328.039.5
✓✓36.216.439.553.8
", + "bbox": [ + 78, + 364, + 468, + 417 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3854a99cdefcd33b32e9cc587580d384c38233fb149d2d205dd74e8137192ae2.jpg", + "table_caption": [ + "Table 5. Ablation on scaling factor of grid" + ], + "table_footnote": [], + "table_body": "
PECAScaling Factor of SDGAPAPSAPMAPL
33.614.736.050.7
✓35.717.538.852.6
✓✓36.216.439.553.8
", + "bbox": [ + 78, + 446, + 468, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation on scaling factor of SDG", + "bbox": [ + 143, + 510, + 401, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "always exists in large objects. 4). For salient point enhanced cross-attention, both SDG and PECA serve as the essential components, independently emerging 0.8 AP and 1.6 AP improvements compared to the standard model (rows 2-4). Interestingly, there exists an effectiveness overlap on small objects, with only $0.1\\mathrm{AP}_{\\mathrm{S}}$ improvement when adding SDG to the equipped PECA model (row 1 and 2). We argue that the Gaussian-like map of SDG might be easily overlapped with PECA on small objects.", + "bbox": [ + 75, + 535, + 468, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Scaling Factor of Movable Strategy. We perform an ablation study on the scaling factor of the movable strategy and further investigate the effectiveness of the inner cost in Tab. 5. Notably, it is observed that there exists a conflict between the inner loss and the global search strategy, behaving a sharp drop when only reserving the inner loss. Furthermore, searching within the grid enables the detector to more attend to small objects and avoid a drastic deterioration in normal object detection. See Appendix E for more detailed analyses. Scaling Factor of SDG. We also compare our side-directed manner with the standard offset prediction method in Tab. 6. Based on PECA, the side-directed scaling factor may limit the detector on small object detection but significantly promote the performance on other objects. This phenomenon would be broken without the help of PECA in which a preci", + "bbox": [ + 75, + 672, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "itous decline is emerged on all-scale object detection (row 5 in Tab. 4 vs. row 1 in Tab. 6). We hypothesise that it because the predicted reference points may be outside of the proposal boxes, or even the region of the image.", + "bbox": [ + 496, + 366, + 890, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 441, + 617, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose SAP-DETR for promoting model convergence by treating object detection as a transformation from the salient points to the instance objects. Our SAP-DETR explicitly initializes a query-specific reference point for each object query, gradually aggregates them into an instance object, and predicts the distance from each side of the bounding box. By speedily attending to the query-specific region and other extreme regions from contextual image features, it thus can effectively bridge the gap between the salient points and the query-based Transformer detector. Our extensive experiments have demonstrated that SAP-DETR achieves superior model convergence speed. With the same training settings, our proposed SAP-DETR outperforms SoTA approaches with large margins.", + "bbox": [ + 496, + 469, + 893, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Future Work", + "text_level": 1, + "bbox": [ + 500, + 696, + 635, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This point-based design for DETR-like models also comes with remaining issues, in particular regarding training with deformable attention, multi-scale features, and negative query design. Following current center-based methods working for similar issues, we expect future work to successfully address them for point-based design of SAP-DETR.", + "bbox": [ + 496, + 722, + 893, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 829, + 666, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank the Lenovo Research AI Master platform for computing GPU supports without which this work would not be possible.", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15546", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. 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In ICLR, 2020. 2, 3, 6, 7, 10" + ], + "bbox": [ + 503, + 92, + 890, + 816 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "15547", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/909bbbe4-4e26-472f-ab37-1d60d8bab4b6_model.json b/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/909bbbe4-4e26-472f-ab37-1d60d8bab4b6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a540b8b2f0fcf3e5b59b9018819c73d41c5148a8 --- /dev/null +++ b/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/909bbbe4-4e26-472f-ab37-1d60d8bab4b6_model.json @@ -0,0 +1,1824 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.116, + 0.13, + 0.853, + 0.177 + ], + "angle": 0, + "content": "SAP-DETR: Bridging the Gap between Salient Points and Queries-Based Transformer Detector for Fast Model Convergence" + }, + { + "type": "text", + "bbox": [ + 0.186, + 0.202, + 0.783, + 0.24 + ], + "angle": 0, + "content": "Yang Liu\\(^{1,3}\\) * Yao Zhang\\(^{1,3}\\) * Yixin Wang\\(^{2}\\) * Yang Zhang\\(^{4}\\) Jiang Tian\\(^{4}\\) Zhongchao Shi\\(^{4}\\) Jianping Fan\\(^{4}\\) Zhiqiang He\\(^{1,3,5\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.239, + 0.87, + 0.275 + ], + "angle": 0, + "content": "\\(^{1}\\)Institute of Computing Technology (ICT), Chinese Academy of Sciences \\(^{2}\\)Stanford University \\(^{3}\\)University of Chinese Academy of Sciences \\(^{4}\\)AI Lab, Lenovo Research \\(^{5}\\)Lenovo Ltd." + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.277, + 0.766, + 0.293 + ], + "angle": 0, + "content": "{liuyang20c,zhangyao215}@mails.ucas.ac.cn yxinwang@stanford.edu" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.295, + 0.719, + 0.31 + ], + "angle": 0, + "content": "{zhangyang20,tianjiang1,shizc2,jfan1,hezq}@lenovo.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.377, + 0.474, + 0.754 + ], + "angle": 0, + "content": "Recently, the dominant DETR-based approaches apply central-concept spatial prior to accelerating Transformer detector convergence. These methods gradually refine the reference points to the center of target objects and imbue object queries with the updated central reference information for spatially conditional attention. However, centralizing reference points may severely deteriorate queries' saliency and confuse detectors due to the indiscriminative spatial prior. To bridge the gap between the reference points of salient queries and Transformer detectors, we propose SAlient Point-based DETR (SAP-DETR) by treating object detection as a transformation from salient points to instance objects. Concretely, we explicitly initialize a query-specific reference point for each object query, gradually aggregate them into an instance object, and then predict the distance from each side of the bounding box to these points. By rapidly attending to query-specific reference regions and the conditional box edges, SAP-DETR can effectively bridge the gap between the salient point and the query-based Transformer detector with a significant convergence speed. Experimentally, SAP-DETR achieves \\(1.4 \\times\\) convergence speed with competitive performance and stably promotes the SoTA approaches by \\(\\sim 1.0\\) AP. Based on ResNet-DC-101, SAP-DETR achieves 46.9 AP. The code will be released at https://github.com/liuyang-ict/SAP-DETR." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.783, + 0.21, + 0.799 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.809, + 0.472, + 0.854 + ], + "angle": 0, + "content": "Object detection is a fundamental task in computer vision, whose target is to recognize and localize each object from input images. In the last decade, various detec" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.346, + 0.89, + 0.53 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.544, + 0.895, + 0.67 + ], + "angle": 0, + "content": "Figure 1. Comparison of SAP-DETR and DAB-DETR under 3-layer decoder model and 36-epoch training scheme. (a) Statistics of the query count in different classification score intervals. (b) and (c) Visualize the distribution of all reference points (pink) and highlight the top-20 classification score queries with their bounding boxes (blue) and reference points (red) in different decoder layers. (d) Visualize the outputs of positive queries and ground truth (red) during the training process, each query has a representative color for its reference point and bounding box. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.895, + 0.854 + ], + "angle": 0, + "content": "tors [6,11,14,18,20,22] based on Convolutional Neural Networks (CNNs), have received widespread attention and made significant progress. Recently, Carion et al. [2] proposed a new end-to-end paradigm for object detection based on the Transformer [24], called DEtction TRansformer (DETR), which treats object detection as a problem of set prediction. In DETR, a set of learnable positional encodings, namely object queries, are employed to aggregate instance features from the context image in Transformer Decoder. The predictions of queries are finally assigned to the ground truth via bipartite matching to achieve end-to-end detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Despite the promising results of DETR, its application is largely limited by considerably longer training time compared to conventional CNNs. To address this problem, many" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.888 + ], + "angle": 0, + "content": "*This work was done when working as an intern at AI Lab, Lenovo Research, Beijing, China." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15539" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.727 + ], + "angle": 0, + "content": "variants attempted to take a close look at query paradigm and introduced various spatial priors for model convergence and efficacy. According to the type of spatial prior, they can be categorized into implicit and explicit methods. The implicit ones [5, 16, 31] attempt to decouple a reference point from the object query and make use of this spatial prior to attend to the image context features efficiently. The current state-of-the-arts (SoTAs) are dominated by the explicit ones [13, 25], which suggest to instantiate a position with spatial prior for each query, i.e., explicit reference coordinates with a center point or an anchor box. These reference coordinates serve as helpful priors and enable the queries to focus on their expected regions easily. For instance, Anchor DETR [25] introduced an anchor concept (center point with different box size patterns) to formulate the query position and directly regressed the central offsets of the bounding boxes. DABDETR [13] further stretched the center point to a 4D anchor box concept \\([cx, cy, w, h]\\) to refine proposal bonding boxes in a cascaded manner. However, instantiating the query location as a target center may severely degrade the classification accuracy and convergence speed. As illustrated in Fig. 1, there exist many plausible queries [19] with high-quality classification scores (Fig. 1(a) within red box) and box Intersection over Union (IoU, see the redundant blue boxes in Fig. 1(b) and (c)), which only brings a slight improvement on precision rate but inevitably confuses the detector on the positive query assignments when training with bipartite matching strategy. This is because the plausible predictions are considered in negative classification loss, which severely decelerates the model convergence. As shown in Fig. 1(b) and (c), the predefined reference point of the positive query may not be the nearest one to the center of the ground truth bounding box, and the reference points tend to be centralized or marginalized (cyan arrows in Fig. 1(b)), hence losing the spatial specificity. With further insight into the one-to-one label assignment during the training process, we find that the query, whose reference point is closest to the center point, also has a high-quality IoU, but it still exists a disparity with the positive query in the classification confidence. Therefore, we argue that such a centralized spatial prior may cause degeneration of target consistency in both classification and localization tasks, which leads to inconsistent predictions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.736, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Furthermore, the mentioned central point-based variants also have difficulties in detecting occluded objects. For example, Fig. 1(d) shows that DAB-DETR detects the left baseman twice, while the query point in SAP-DETR is not necessarily the center point, so the query point of the bounding box for the occluded baseman is from a pixel on the occluded baseman on the top right area instead of from the left baseman. One solution for center-based method [25] is to predefine different receptive fields (similar to the scaling anchor box in YOLO [17]) for the position of each query. However, increasing the diversity of the receptive fields for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.137 + ], + "angle": 0, + "content": "each position query is unsuitable for non-overlapped targets, as it still generates massive indistinguishable predictions for one position as same as other center-based models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.897, + 0.517 + ], + "angle": 0, + "content": "To bridge these gaps, in this paper, we present a novel framework for Transformer detector, called SAclient Point-based DETR (SAP-DETR), which treats object detection as a transformation from salient points to instance objects. Instead of regressing the reference point to the target center, we define the reference point belonging to one positive query as a salient point, keep this query-specific spatial prior with a scaling amplitude, and then gradually update them to an instance object by predicting the distance from each side of the bounding box. Specifically, we tile the mesh-grid referenced points and initialize their center/corner as the query-specific reference point. To disentangle the reference sparsity as well as stabilize the training process, a movable strategy with scaling amplitude is applied for reference point adjustment, which prompts queries to consider their reference grid as the salient region to perform image context attention. By localizing each side of the bounding box layer by layer, such query-specific spatial prior enables compensation for the over-smooth/inadequacy problem during center-based detection, thereby vastly promoting model convergence speed. Inspired by [5, 13, 16], we also take advantage of both Gaussian spatial prior and conditional cross-attention mechanism, and then a salient point enhanced cross-attention mechanism is developed to distinguish the salient region and other conditional extreme regions from the context image features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.895, + 0.639 + ], + "angle": 0, + "content": "We bridge the gap between salient points and query-based Transformer detector by speedily attending to the query-specific region and other conditional regions. The extensive experiments have shown that SAP-DETR achieves superior convergence speed and performance. To the best of our knowledge, this is the first work to introduce the salient point based regression into end-to-end query-based Transformer detectors. Our contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.897, + 0.807 + ], + "angle": 0, + "content": "1) We introduce the salient point concept into query-based Transformer detectors by assigning query-specific reference points to object queries. Unlike center-based methods, we restrict the reference location and define the point of the positive query as the salient one, hence enlarging the discrepancy of query as well as reducing the redundant predictions (see Fig. 1). Thanks to the efficacy of the query-specific prior, our SAP-DETR accelerates the convergence speed greatly, achieving competitive performance with \\(30\\%\\) fewer training epochs. The proposed movable strategy further boosts SAP-DETR to a new SoTA performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.895, + 0.854 + ], + "angle": 0, + "content": "2) We devise a point-enhanced cross-attention mechanism to imbue query with spatial prior based on both reference point and box sides for final specific region attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "3) Evaluation over COCO dataset has demonstrated that SAP-DETR achieves superior convergence speed and detection accuracy. Under the same training settings, SAP-DETR" + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.641, + 0.897, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "15540" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.44, + 0.108 + ], + "angle": 0, + "content": "outperforms the SoTA approaches with a large margin." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.121, + 0.219, + 0.136 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.146, + 0.471, + 0.327 + ], + "angle": 0, + "content": "Anchor-Free Object Detectors. Classical anchor-free object detectors can be grouped into center-based and keypoint-based approaches. The center-based approaches aim to localize the target objects based on the central locations [11] or predefined ROI [22]. For example, FCOS [22] treated all points within the bounding box as positive ones to predict their distances from each side \\(([\\ell, t, r, b])\\), and a centerness score was then considered to prohibit the low-quality prediction whose point is located near the border. Compared with FCOS, we also restrict the candidate queries within the bounding box but treat only one as positive to perform end-to-end object detection via an inner matching cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.47, + 0.493 + ], + "angle": 0, + "content": "The target of keypoint-based approaches is to localize the specific object locations and assign them to the predefined keypoints of the object for box localized training. For instance, diagonal corner points were considered in CornerNet [8], center point was further grouped into CenterNet [29], and ExtremeNet [30] added some conjectural extreme points for object localization. These works showed an impressive performance, but the complicated keypoint matching may limit their upper bound. Our SAP-DETR takes the advantage of salient point regression to focus on the distinct regions without complicated point-based supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.599 + ], + "angle": 0, + "content": "Query-Based Transformer Detectors. DETR [2] pioneered a new paradigm of Transformer detector for end-to-end object detection without any post-processing [1]. In DETR, a new representation, namely object query, aggregates the instance features and then yields a detection result for each instance object [15]. Following DETR, many voterists put efforts on the optimization of convergence and accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Sun et al. [21] revealed that the main reason for slow convergence of DETR is attributed to the Transformer decoder, and they considered an encoder-only structure to alleviate such a problem. For in-depth understanding of the object query, one way is to generate a series of implicit spatial priors from queries to guide feature aggregation in cross-attention layers. SMCA [5] applied a Gaussian-like attention map to augment the query-concerned features spatially. The reference point concept was first introduced by Deformable DETR [31], where the sampling offsets are predicted by each reference point to perform deformable cross-attention. Following such a concept, Conditional DETR [16] reformulated the attention operation and rebuilt positional queries based on the reference points to facilitate extreme region discrimination. Another way is towards position-instantiation explicitly, where this position information enables to directly conduct positional query generation. Anchor DETR [25] utilized a predefined 2D anchor point \\([cx, cy]\\) to explicitly capitalize on the spatial prior during cross-attention and box regression. DAB-DETR [13] extended such a 2D concept to" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.088, + 0.865, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.379, + 0.895, + 0.478 + ], + "angle": 0, + "content": "Figure 2. Illustration of SAP-DETR. Each object query in SAP-DETR is assigned to a specific grid region and initialized by the corner/center of the grid as its reference point. A learnable 4D coordinate represents the distance from the four sides of the box to the reference point. Both reference points and box sides are served as positional encodings added/concatenated to content embeddings. All embeddings are refined to predict target objects gradually." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.496, + 0.89, + 0.512 + ], + "angle": 0, + "content": "a 4D anchor box \\([cx, cy, w, h]\\) and refined it layer-by-layer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.895, + 0.663 + ], + "angle": 0, + "content": "The recent accelerating convergence methods are based on auxiliary queries for facilitating detector discrimination. DN-DETR [9] demonstrates the slow model convergence is mainly caused by the instability of bipartite matching, thus providing a denoising training to eliminate this issue. DINO [28] inherits this advance and further introduces negative queries to perform contrastive denoising. Group-DETR [4] proposes a group-wise one-to-many label assignment to match multiple positive object queries with more gradients for fast DETR convergence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.895, + 0.815 + ], + "angle": 0, + "content": "The most relevant approaches to ours are Point-DETR [3] and SAM-DETR [26, 27]. The former applied a point encoder for annotated point label infusion in teacher model, and the latter directly updated content embeddings by extracting salient points from image features for query-image semantic alignment. Unlike these concepts, we redefine the salient point from the perspective of the positive query's position and replace the center-concept prior with the query-specific position, thereby attending extreme regions, differentiating queries' saliency, and alleviating redundant predictions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.591, + 0.845 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We propose SAP-DETR to bridge the gap between salient points and query-based detectors. Following DETR, the extracted image features are fed into Transformer encoder" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15541" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "after adding positional encodings, and then re-aggregated by object queries in Transformer decoder. In pursuit of the query-specific prior, we dispense a movable strategy for each query based on a fixed grid region. The query, whose reference region overlaps with ground truth objects, is allowed to predict the relative offsets from four sides of the bounding box to the points. Given the query-specific reference point and the proposal box sides, we propose salient point enhanced cross-attention mechanism to imbue query with spatial prior, thereby attending to extreme regions effectively. Additionally, we discuss two common issues in DETR-like models and address them for further improvements." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.282, + 0.406, + 0.297 + ], + "angle": 0, + "content": "3.1. Salient Points-Based Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.474, + 0.593 + ], + "angle": 0, + "content": "Overview. Previous methods [13, 16, 25] normally decompose the object query into both content and position embeddings (queries), and form a center-based anchor point/box prior on the position ones. Unlike the central concept, we tile a fixed mesh-grid region, initialize their left-top corner as the reference points with 2D coordinate \\( \\boldsymbol{r} = \\{x, y\\} \\in [0,1]^2 \\), and instantiate a learnable 4D offset distance \\( s = \\{\\ell, t, r, b\\} \\in [0,1]^4 \\) from the reference point to the sides of proposal bounding box for each object query. The object query can be referred as \\( q = \\{\\mathbf{e}; r, s\\} \\), where \\( \\mathbf{e} \\in \\mathbb{R}^d \\) is the content embedding with \\( d \\) dimension. Instead of regressing the center, width, and height of a bounding box, we follow FCOS [22] and directly supervise the 4D offset from the four sides of a bounding box to the reference point. The final box prediction is formulated as \\( \\hat{\\boldsymbol{b}} = \\{\\hat{x} - \\hat{\\ell}, \\hat{y} - \\hat{\\bar{t}}, \\hat{x} + \\hat{r}, \\hat{y} + \\hat{b}\\} \\). Ideally, we here fix the reference point \\( \\{\\hat{x}, \\hat{y}\\} = \\{x, y\\} \\) (the movable update strategy is introduced in the next subsection) and only update the 4D box side prediction layer by layer. The prediction for each decoder layer can be calculated by" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.603, + 0.395, + 0.619 + ], + "angle": 0, + "content": "\\[\n\\Delta \\boldsymbol {s} _ {l} = \\operatorname {B o x H e a d} _ {l} (\\boldsymbol {s} _ {l - 1}, \\boldsymbol {e} _ {l - 1}, \\boldsymbol {r} _ {l - 1}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.622, + 0.431, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {s}} _ {l} = \\sigma \\left(\\sigma^ {- 1} \\left(\\boldsymbol {s} _ {l - 1}\\right) + \\Delta \\boldsymbol {s} _ {l}\\right), \\quad \\boldsymbol {s} _ {l} = \\operatorname {D e t a c h} (\\hat {\\boldsymbol {s}} _ {l}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.644, + 0.47, + 0.674 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {r} _ {l} = \\hat {\\boldsymbol {r}} _ {l} = \\boldsymbol {r} _ {l - 1}, \\quad \\hat {\\boldsymbol {b}} _ {l} = \\left\\{\\hat {\\boldsymbol {r}} _ {l} - \\hat {\\boldsymbol {s}} _ {l} [: 2 ], \\hat {\\boldsymbol {r}} _ {l} + \\hat {\\boldsymbol {s}} _ {l} [2: ] \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.472, + 0.78 + ], + "angle": 0, + "content": "where \\(\\sigma\\) and \\(\\sigma^{-1}\\) are the sigmoid and inverse sigmoid operation, respectively. \\(\\Delta s_{l}\\) denotes the side offset prediction. \\(\\hat{s}_l\\), \\(\\hat{r}_l\\), and \\(\\hat{\\pmb{b}}_l\\) are the predicted side distance, reference points, and box location from the \\(l\\) decoder layer, respectively. The BoxHead is the prediction head following the layer-\\(l\\) decoder, which is independent between different decoder layers in our settings. Detach operation follows DAB-DETR [13]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.902 + ], + "angle": 0, + "content": "During the training process, each query is only allowed to predict the bounding boxes that overlap its reference region. We adapt this rule into the one-to-one bipartite matching process via an inner matching cost \\(\\mathcal{L}_{\\mathrm{inner}}\\). Given \\(N\\) queries \\(\\mathbf{Q} = \\{\\pmb{q}_1,\\pmb{q}_2,\\dots ,\\pmb{q}_N\\}\\) and \\(M\\) ground truth objects \\(\\mathbf{G} = \\{\\pmb{g}_1,\\pmb{g}_2,\\dots ,\\pmb{g}_M\\}\\), the \\(\\mathcal{L}_{\\mathrm{inner}}(\\pmb{g}_i,\\pmb{q}_j)\\) of each query-box pair is a step function to penalize the reference point \\(\\pmb{r}_j\\) of \\(\\pmb{q}_j\\) with value of \\(k\\) when \\(\\pmb{r}_j\\) is outside the bounding box of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.152 + ], + "angle": 0, + "content": "\\(g_{i}\\). We denote \\(i \\in [1, M]\\) and \\(j \\in [1, N]\\) as the index of query and ground truth, respectively. \\(k\\) can be viewed as a penalty cost, and default to \\(10^{5}\\). The final permutation of the one-to-one label assignment is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.163, + 0.781, + 0.18 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n n e r}} \\left(\\boldsymbol {g} _ {i}, \\boldsymbol {q} _ {j}\\right) := \\mathbf {k} _ {\\boldsymbol {r} _ {j} \\notin \\boldsymbol {g} _ {i}},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.183, + 0.892, + 0.223 + ], + "angle": 0, + "content": "\\[\n\\hat {\\eta} = \\underset {\\eta \\in \\mathfrak {Y} _ {N}} {\\operatorname {a r g m i n}} \\sum_ {i} ^ {N} \\mathcal {L} _ {\\text {m a t c h}} + \\mathcal {L} _ {\\text {i n n e r}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.232, + 0.892, + 0.277 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{match}}\\) is the original pair-wise matching cost consist of both classification and localization costs [2]. \\(\\eta \\in \\mathfrak{V}_N\\) is a permutation of \\(N\\) elements for bipartite matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.895, + 0.655 + ], + "angle": 0, + "content": "Movable Reference Point. Due to the sparseness of the fixed reference point, some small and slender objects may be indistinguishable when there is no reference point inside these objects. Despite the bipartite matching forcing each object to be assigned to one object query, the positive query, whose reference point is outside the assigned bounding box, is unable to accurately regress the distance from each side by a value between 0 and 1. One straightforward solution is to adjust the locations of reference points inside the ground truth bounding boxes to ensure that each object can be detected by an inner reference point. Similar to the aforementioned box refinement, we first perform a movable reference point design to dynamically update the reference points of each query layer by layer. However, such a full-image point regression inevitably expands the search space as vast variable determinations, causing the final reference point to be trapped in an unexpected corner of the bounding box. To reduce the training search spaces, we scale the offset amplitude of points within their specific grid regions, as illustrated in Fig. 3. Such an operation limits the range of offset values, and hence prevents a large searching space. It is implemented by applying the sigmoid activation \\(\\sigma\\) and multiplying a scale factor \\(s_{\\mathrm{grid}}\\) whose value equals to the height and width of one grid. The update process of the reference points is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.666, + 0.822, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\Delta \\boldsymbol {r} _ {l} ^ {\\prime} = \\operatorname {P o i n t H e a d} _ {l} \\left(\\boldsymbol {s} _ {l - 1}, \\boldsymbol {e} _ {l - 1}, \\boldsymbol {r} _ {l - 1}\\right),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.686, + 0.892, + 0.703 + ], + "angle": 0, + "content": "\\[\n\\Delta \\boldsymbol {r} _ {l} = \\sigma \\left(\\sigma^ {- 1} \\left(\\boldsymbol {r} _ {l - 1} - \\boldsymbol {r} _ {0}\\right) + \\Delta \\boldsymbol {r} _ {l} ^ {\\prime}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.707, + 0.836, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {r}} _ {l} = \\boldsymbol {r} _ {0} + \\Delta \\boldsymbol {r} _ {l} \\cdot \\boldsymbol {s} _ {\\text {g r i d}}, \\quad \\boldsymbol {r} _ {l} = \\operatorname {D e t a c h} (\\hat {\\boldsymbol {r}} _ {l}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.733, + 0.892, + 0.764 + ], + "angle": 0, + "content": "where \\(\\Delta \\boldsymbol{r}_l'\\) and \\(\\Delta \\boldsymbol{r}_l\\) are the predicted offsets from \\(\\boldsymbol{r}_l\\) to both \\(\\boldsymbol{r}_{l-1}\\) and \\(\\boldsymbol{r}_0\\) before the sigmoid activation \\(\\sigma\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.843, + 0.787 + ], + "angle": 0, + "content": "3.2. Salient Point Enhanced Cross-Attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In cross-attention layers, existing center-based methods are limited to the attention on both center and sides of the ground truth bounding box, causing detector confusion among the queries with the same center and side attention. To this end, we expect the queries to focus on their specific regions based on the reference points, four box sides, and other conditional regions in different heads. Accordingly," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15542" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.473, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.221, + 0.473, + 0.306 + ], + "angle": 0, + "content": "Figure 3. Movable reference point. The reference points are initialized by the center/corner points of the mesh-grid. Based on the inner loss, only the green dashed box can be predicted by the inner points when reference points are fixed. By moving the reference points within their grid, the blue dashed boxes can be detected accurately without extended searching space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.47, + 0.381 + ], + "angle": 0, + "content": "we consider an improved Gaussian [5] \\(\\mathbf{G}\\) and conditional attention [16] \\(\\mathbf{A}_{\\mathrm{peca}}\\) to enhance query specificity and spatially extreme region discrimination. The final attention map \\(\\mathbf{A}_{\\mathrm{cross}}\\) is the sum of the two attentions \\(\\mathbf{A}_{\\mathrm{cross}} = \\mathbf{G} + \\mathbf{A}_{\\mathrm{peca}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.474, + 0.547 + ], + "angle": 0, + "content": "Side Directed Gaussian (SDG). Similar to the movable strategy, we enforce the predicted Gaussian attention to be inside the proposal bounding box to reduce the searching space. Given a reference point \\( r \\), the offset scales \\( \\mathbf{o} \\in [-1,1]^2 \\) for \\( H \\) heads are produced by a simple MLP with a tanh activation, and then multiply to the two sides of the proposal bounding box for head-specific point offset generation, where the direction is guided by the sign of the offset scales. The head-specific points are generated by Algorithm 1. For each head, the Gaussian-like spatial weight map \\( G_{i} \\) effecting on each pixel \\( (x,y) \\) of context features is then formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.557, + 0.47, + 0.598 + ], + "angle": 0, + "content": "\\[\nG _ {i} (x, y) = \\exp \\left(- \\frac {\\left(x - c _ {w , i}\\right) ^ {2}}{v _ {w , i} ^ {2}} - \\frac {\\left(y - c _ {h , i}\\right) ^ {2}}{v _ {h , i} ^ {2}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.473, + 0.788 + ], + "angle": 0, + "content": "Point Enhanced Cross-Attention (PECA). As aforementioned, the semantic class for the query is closely related to its referenced location in our SAP-DETR. To enhance the correlation between queries and their references, we concatenate the locations to the content queries after the sinusoidal positional encoding (PE). Take a close look at the conditional attention [16], we find that the linear positional embedding mostly focuses on one box side in each attention head. So we introduce a more straightforward attention mechanism, where the four side coordinates are concatenated and assigned to the corresponding head for side attention. The process of PECA is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.794, + 0.47, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} \\mathbf {A} _ {\\text {p e c a}} & = \\mathbf {e} _ {q} \\mathbf {e} _ {k} ^ {\\top} + \\mathbf {T P E} (\\boldsymbol {r} _ {q}) \\mathbf {P E} (\\boldsymbol {r} _ {k}) ^ {\\top} \\\\ & + \\mathbf {T} g (\\mathbf {P E} (\\boldsymbol {r} _ {q} - \\{\\ell , t \\}, \\boldsymbol {r} _ {q} + \\{r, b \\})) \\mathbf {P E} (\\boldsymbol {r} _ {k}) ^ {\\top}, \\end{array} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\( g \\) is a linear layer mapping 4D-PE into 2D to keep channel dimension consistency. T [16] is a scaling transformation matrix. More details of T and comparison with conditional cross-attention are available in Appendix C." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.747, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Side Directed Gaussian" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.111, + 0.854, + 0.124 + ], + "angle": 0, + "content": "Input: Content embedding e, reference point \\( r \\) and box s." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.124, + 0.894, + 0.152 + ], + "angle": 0, + "content": "Output: Head-specific points \\(\\mathbf{c} = \\{(c_{w,i}, c_{h,i}) | i \\in H\\}\\) and head-specific attention \\(\\mathbf{v} = \\{(v_{w,i}, v_{h,i}) | i \\in H\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.152, + 0.894, + 0.18 + ], + "angle": 0, + "content": "1: Predict offset scale and attention scale based on content embedding, \\(\\mathbf{o} = \\tanh (\\mathrm{MLP}(\\mathbf{e}))\\), \\(\\mathbf{v} = \\mathrm{MLP}(\\mathbf{e})\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.18, + 0.645, + 0.193 + ], + "angle": 0, + "content": "2: for \\(h\\gets 1\\in H\\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.193, + 0.892, + 0.222 + ], + "angle": 0, + "content": "3: Select the index of direction guided by the sign of offset scale, \\(\\{a,b\\} = \\mathrm{sgn}(\\mathbf{o}_i) + \\{1,2\\}\\), \\(a,b\\in \\{0,1,2,3\\}\\);" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.222, + 0.892, + 0.249 + ], + "angle": 0, + "content": "4: According to the index of direction, predict head-specific point, \\(\\mathbf{c}_i = \\mathbf{o}_i\\cdot \\mathbf{s}[a,b] + \\mathbf{r}\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.25, + 0.576, + 0.261 + ], + "angle": 0, + "content": "5: end for" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.262, + 0.704, + 0.276 + ], + "angle": 0, + "content": "6: return \\(\\mathbf{c}_i, \\mathbf{v}_i, \\forall i = 1, \\dots, H\\)" + }, + { + "type": "list", + "bbox": [ + 0.509, + 0.152, + 0.894, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.309, + 0.814, + 0.326 + ], + "angle": 0, + "content": "3.3. SAP-DETR with Denoising Strategy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.895, + 0.514 + ], + "angle": 0, + "content": "To further explore the capability of our proposed SAP-DETR, we develop SAP-DN-DETR and SAP-DINO-DETR by adding the denoising auxiliary loss [9,28] into the training process. In the denoised SAP-DETR, the main difference from both DN-DETR and DINO lies in the noise design. Instead of the center point, we perform the box jittering and randomly sample a point from the intersection region between the original bounding box and the jittering one as the reference point. As the denoising strategy only serves as an auxiliary training loss increasing the training cost, the variants of denoising models are test-free whose Params and GFLOPs are the same as SAP-DETR models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.532, + 0.706, + 0.549 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.718, + 0.574 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.895, + 0.869 + ], + "angle": 0, + "content": "We conduct the experiments on the COCO 2017 [12] object detection dataset, containing about 118K training images and 5K validation images. All models are evaluated by the standard COCO evaluation metrics. We follow the vanilla DETR [2] structure that consists of a CNN backbone, a stack of Transformer encoder-decoder layers, and two prediction heads for class label and bounding box prediction. We use ImageNet-pretrained ResNet [7] as our backbone, and report results based on the ResNet and its \\(\\times 1/16\\)-resolution extension ResNet-DC. Unlike DAB-DETR [13] sharing box and label head for each layer, we share the class head except the first layer and use an independent box head for the box regression of each layer (for more details please refer to Appendix D). As the mesh-grid initialization for reference points in SAP-DETR, we consider the number of queries \\(N\\) as a perfect square for uniform distribution. Unless otherwise specified, we use \\(N = 400\\) queries in the experiments. Precisely, we also provide a comparison under \\(N = 300\\) in Tab. 2, the standard setting in DETR-like models." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We adopt two different Transformer structures for experiments where a 3-layer encoder-decoder stack is evaluated to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15543" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.188, + 0.088, + 0.38, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.088, + 0.581, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.087, + 0.782, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.291, + 0.22, + 0.678, + 0.234 + ], + "angle": 0, + "content": "Figure 4. Comparison of performance and training losses curves." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.251, + 0.473, + 0.388 + ], + "angle": 0, + "content": "demonstrate our lightweight model efficacy compared with the traditional CNN detectors, and a 6-layer encoder-decoder stack is aligned with previous DETR variants to investigate the performance of large model. Both are trained on two training schemes: the 12-epoch and 36-epoch schemes with a learning rate drop after 11 and 30 epochs, respectively. All models are trained on the Nvidia A100 GPUs with batch size of 16 and 8 for ResNet and ResNet-DC, respectively. For more training details, please refer to Appendix F." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.395, + 0.218, + 0.41 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.471, + 0.509 + ], + "angle": 0, + "content": "As shown in Tab. 1 and Tab. 2, we comprehensively compare our proposed SAP-DETR with the traditional CNN detectors [18], the original DETR [2], and other DETR-like detectors [5, 13, 16, 25, 26, 31] on COCO 2017 validation dataset. For in-depth analysis, we conduct the comparison in two aspects: model convergence and efficacy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.472, + 0.795 + ], + "angle": 0, + "content": "Model Convergence. Compared with traditional CNN detectors, Transformer detectors are always subject to laborious training time. For example, under the same 12-epoch training scheme, Faster RCNN [18] still achieves good performance, but the mainstream DETR-like models may suffer from inadequate training and perform poorly without the help of auxiliary losses [9]. Under the 12-epoch training scheme, our proposed SAP-DETR can accelerate model convergence significantly, boosting DAB-DETR [13] by 3.9 AP and 2.7 AP on 3-layer and 6-layer encoder-decoder structures, respectively. Compared with the current SoTA, our SAP-DETR also outperforms SAM-DETR [26] by \\(\\sim 1.3\\) AP, with reducing \\(\\sim 17\\%\\) parameters and \\(\\sim 10\\%\\) GFLOPs. Take a close look at the training process, as illustrated in Fig. 4, SAP-DETR conducts with rapid descent curves in both classification and box regression losses. Notably, there is a large margin in classification loss between ours and SoTA methods, which is benefited from the query-specific reference point, hence boosting model performance in early epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Model Efficacy. To analyze model efficacy, we report results on long training epochs and high-resolution features in Tab. 1. Under the 36-epoch training scheme, SAP-DETR achieves superior performance among all single-scale Transformer detectors, especially on middle and large targets. For example, SAP-DETR boosts DAB-DETR by \\(2.0\\mathrm{AP}_{\\mathrm{M}}\\) and \\(4.1\\mathrm{AP}_{\\mathrm{L}}\\) with 3-layer models, \\(1.0\\mathrm{AP}_{\\mathrm{M}}\\) and \\(1.9\\mathrm{AP}_{\\mathrm{L}}\\) with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.463 + ], + "angle": 0, + "content": "6-layer models, which further verifies the effectiveness of our proposed salient point concept for overlapping object detection. Along with layer increase, a deficient upper-bound of SAM-DETR is exposed, with obviously lower 0.5 AP promotion compared to our 1.0 AP improvement. Persuasively, we also report the 50-epoch training results based on the 300-query setting. To align with our mesh-grid initialization strategy, we tile a \\(17 \\times 18\\) mesh-grid (306 queries) for each reference point initialization. Tab. 2 shows our main results and the most representative approaches with their original reported performance. Notably, SAP-DETR outperforms the current SoTAs with comparable costs based on all backbones. With low-resolution features (\\(\\times 1/32\\)), it significantly boosts both middle and large object detection accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.897, + 0.751 + ], + "angle": 0, + "content": "Combine with Other Fast Convergence Methods. As shown in Tab. 3, we compare our SAP-DETR variants with the current fast convergence methods [4, 9, 28]. With such a subtle modification, our SAP-DETR (grey rows) results in a significant performance improvement compared with the original methods (white rows). Under the 12-epoch training scheme, there exist 0.5-1.9 AP improvements on DN-DETR [9] and 0.7-1.6 AP improvements on Group-DETR [4], but the promotions are slightly reduced when implemented on DINO [28]. We hypothesise that there exists the same effect between the negative query of contrastive denoising [28] and our query-salient reference point. Moreover, we observe that the performance improvements largely originate from the large object detection, especially based on ResNet-DC5 family backbones. We speculate that DETR may prefer the high-resolution features (\\( \\times 1/16 \\)) rather than the low-resolution ones (\\( \\times 1/32 \\)), and our SAP-DETR can distinguish the salient points accurately on the high-resolution, thereby taking full advantage of the large object detection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.761, + 0.655, + 0.777 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.895, + 0.877 + ], + "angle": 0, + "content": "Effectiveness of Each Component. To offer an intuitionistic comparison of model convergence for each component, Tab. 4 reports the effectiveness of them based on the 3-layer encoder-decoder structure and 12-epoch training scheme. I). The proposed salient point concept based on content embeddings improves the performance from 32.3 AP to 33.5" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.782, + 0.901 + ], + "angle": 0, + "content": "1https://github.com/facebookresearch/detectron2" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15544" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.872, + 0.309 + ], + "angle": 0, + "content": "
Method#Epochs#Params(M)GFLOPsAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
3-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36338215.828.015.45.316.724.6
Deformable DETR-R50 [31]36307737.157.639.418.340.851.6
SMCA-DETR-R50 [5]12 / 36--28.8 / 37.748.1 / 58.729.9 / 40.113.8 / 19.431.3 / 40.541.3 / 54.8
Conditional DETR-R50 [16]12 / 36408229.6 / 37.148.7 / 57.930.7 / 39.013.0 / 17.632.3 / 40.343.1 / 55.0
Anchor DETR-R50 [25]12 / 36317930.8 / 37.651.1 / 58.731.8 / 39.714.3 / 18.834.1 / 41.544.3 / 53.5
DAB-DETR-R50 [13]12 / 36348332.3 / 39.051.3 / 58.634.0 / 41.815.7 / 20.035.2 / 42.545.7 / 56.0
SAM-DETR-w/SMCA-R50 [26]12 / 36418935.1 / 40.454.7 / 60.736.7 / 42.716.0 / 20.238.4 / 44.452.1 / 58.3
SAP-DETR-R50 (Ours)12 / 36368436.2 / 41.256.2 / 61.637.9 / 43.416.4 / 21.039.5 / 44.553.8 / 60.1
6-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36428914.024.414.04.213.722.5
Deformable DETR-R50 [31]36348138.058.240.418.541.754.2
SMCA-DETR-R50 [5]12 / 36--32.4 / 40.152.3 / 61.434.0 / 42.815.5 / 20.334.9 / 43.347.7 / 57.1
Conditional DETR-R50 [16]12 / 36449033.1 / 40.253.0 / 61.034.8 / 42.414.5 / 19.935.9 / 43.549.2 / 58.8
Anchor DETR-R50 [25]12 / 36378533.7 / 39.754.5 / 60.535.1 / 41.915.6 / 19.937.3 / 43.549.8 / 57.3
DAB-DETR-R50 [13]12 / 36449234.9 / 41.055.5 / 61.736.4 / 43.416.2 / 21.338.4 / 44.751.5 / 58.9
SAM-DETR-w/SMCA-R50 [26]12 / 365910536.2 / 40.957.2 / 62.237.4 / 43.116.1 / 20.139.8 / 44.755.3 / 60.7
SAP-DETR-R50 (Ours)12 / 36479437.5 / 42.258.5 / 62.739.2 / 44.617.3 / 22.640.6 / 45.755.4 / 60.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.317, + 0.895, + 0.36 + ], + "angle": 0, + "content": "Table 1. Comparison between Transformer necks. Based on ResNet-50 backbone, all models are trained by the official source codes with their original settings and evaluated on COCO val2017. All models uses 400 queries except Anchor DETR, while Anchor DETR uses 200 queries with 2 pattern embeddings. GFLOPs and Params are measured by \\( \\text{Detectron}^2 \\)." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.363, + 0.872, + 0.707 + ], + "angle": 0, + "content": "
Method#Epochs#Params(M)GFLOPsAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)Infer. \\( Time(s / img)^{\\dagger} \\)
ResNet-50 Backbone
Faster RCNN-FPN-R50 [10, 18]1084218042.062.145.526.645.553.40.039
DETR-R50 [2]500418642.062.444.220.545.861.10.040
Deformable DETR-R50 [31]50347839.459.642.320.643.055.50.043
SMCA-DETR-R50 [5]50428641.0--21.944.359.10.045
Conditional DETR-R50 [16]50449040.961.843.320.844.659.20.057
Anchor DETR-R50 [25]50398542.163.144.922.346.260.00.050
DAB-DETR-R50 [13]5044\\( 90^† \\)42.263.144.721.545.760.30.059
SAM-DETR-w/SMCA-R50 [26]505810041.863.243.922.145.960.90.065
SAP-DETR-R50 (Ours)50479243.163.845.422.947.162.10.063
ResNet-101 Backbone
Faster RCNN-FPN-R101 [10, 18]1086024644.063.947.827.248.156.00.050
DETR-R101 [2]5006015243.563.846.421.948.061.80.066
Conditional DETR-R101 [16]506315642.863.746.021.746.660.90.070
Anchor DETR-R101 [25]505815043.564.346.623.247.761.40.068
DAB-DETR-R101 [13]5063\\( 157^† \\)43.563.946.623.647.361.50.072
SAP-DETR-R101 (Ours)506715844.464.947.124.148.763.10.078
DC5-ResNet-50 Backbone
DETR-DC5-R50 [2]5004118743.363.145.922.547.361.10.087
Conditional DETR-DC5-R50 [16]504419543.864.446.724.047.660.70.093
Anchor DETR-DC5-R50 [25]503915144.264.747.524.748.260.60.069
DAB-DETR-DC5-R50 [13]5044\\( 194^† \\)44.565.147.725.348.262.30.094
SAM-DETR-w/SMCA-DC5-R50 [26]505821045.065.447.926.249.063.30.126
SAP-DETR-DC5-R50 (Ours)504719746.065.548.926.450.262.60.116
DC5-ResNet-101 Backbone
DETR-DC5-R101 [2]5006025344.964.747.723.749.562.30.101
Conditional DETR-DC5-R101 [16]506326245.065.648.426.148.962.80.105
Anchor DETR-DC5-R101 [25]505822745.165.748.825.849.461.60.083
DAB-DETR-DC5-R101 [13]5063\\( 263^† \\)45.865.949.327.049.863.80.110
SAP-DETR-DC5-R101 (Ours)506726646.966.750.527.951.364.30.130
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.712, + 0.895, + 0.756 + ], + "angle": 0, + "content": "Table 2. Comparison of Transformer necks with 300 queries on COCO val2017. All results are reported from their original paper. All models uses 300 queries except Anchor DETR, while Anchor DETR uses 100 queries with 3 pattern embeddings. All inference speeds are measured by a single Nvidia A100 GPU. † denotes the results are measured by ourselves." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.766, + 0.473, + 0.888 + ], + "angle": 0, + "content": "AP compared to baseline DAB-DETR (row 8-9). Such a query-specific spatial prior enables queries to attend to their expected region from content features (see Figures in Appendix G) and reduces the false detection rate on occluded and partial objects (see Fig. 1(d)), hence boosting detection performance on middle and large objects. However, there exists a drop in small object detection (15.7 APs vs. 14.3 APs), for which we consider that the failure is mainly caused" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.766, + 0.895, + 0.888 + ], + "angle": 0, + "content": "by the query sparsity. 2). Therefore, the movable strategy is applied to alleviate the constraint, improving the final model by \\(1.0\\mathrm{AP}\\) and \\(0.6\\mathrm{AP}_{\\mathrm{S}}\\) (row 1 and 6). 3). Compared with the final model, the inner loss greatly improves the performance on high-quality \\(\\mathrm{AP}_{75}\\) and large objects \\(\\mathrm{AP}_{\\mathrm{L}}\\) detection (row 1 and 7), with just a slight drop on low-quality object \\(\\mathrm{AP}_{50}\\). That is reasonable because the outside reference points are unable to localize objects accurately, and this phenomenon" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15545" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.855, + 0.201 + ], + "angle": 0, + "content": "
BackboneEpochw/ SAPDN-DETR [9]DINO (Single-Scale) [28]Group DETR [4]
AP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APL
R5012✓(Ours)38.3 / 58.6 / 40.518.4 / 41.6 / 57.139.7 / 58.3 / 42.419.1 / 43.7 / 57.139.1 / - / -19.7 / 42.5 / 56.8
39.5 / 59.7 / 41.518.7 / 42.8 / 59.040.0 / 60.1 / 42.120.2 / 43.4 / 58.539.8 / 60.2 / 42.020.2 / 43.5 / 58.6
R10112✓(Ours)40.5 / 60.8 / 43.019.3 / 44.3 / 59.641.9 / 60.8 / 44.422.5 / 46.3 / 59.5- / - / -- / - / -
41.0 / 61.2 / 43.419.8 / 45.3 / 60.041.5 / 61.4 / 43.620.3 / 45.2 / 60.041.1 / 61.5 / 43.420.5 / 45.5 / 59.4
R50-DC12✓(Ours)41.7 / 61.4 / 44.121.2 / 45.0 / 60.243.6 / 61.4 / 47.024.8 / 47.3 / 59.541.9 / - / -23.3 / 45.6 / 58.4
43.6 / 62.5 / 46.223.3 / 47.3 / 61.044.0 / 63.1 / 46.524.8 / 47.3 / 61.143.9 / 63.2 / 46.824.5 / 47.6 / 61.3
R101-DC12✓(Ours)43.4 / 61.9 / 47.224.8 / 46.8 / 59.445.4 / 63.5 / 49.226.4 / 49.5 / 61.1- / - / -- / - / -
44.6 / 63.9 / 48.025.5 / 48.9 / 62.545.6 / 64.5 / 48.725.0 / 49.7 / 62.544.4 / 63.9 / 47.425.9 / 48.5 / 61.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.108, + 0.206, + 0.86, + 0.221 + ], + "angle": 0, + "content": "Table 3. Comparison with denoised methods on COCO dataset based on the 12-epoch training schedule and 300 object queries." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.235, + 0.851, + 0.331 + ], + "angle": 0, + "content": "
CommentMovableInner LossPECASDGAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
SAP-DETR (Ours)✓✓✓✓36.256.237.916.439.553.8
-SDG✓✓✓35.656.236.916.338.952.7
-PECA✓✓✓34.855.536.015.737.352.0
-PECA & SDG✓✓34.054.935.315.036.751.5
-Movable✓✓✓35.255.436.815.838.553.8
-Inner Loss✓✓✓35.956.337.416.239.352.5
DAB-DETR (Baseline)----32.351.334.015.735.245.7
+Salient Point Concept----33.554.335.114.336.551.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.369, + 0.335, + 0.6, + 0.35 + ], + "angle": 0, + "content": "Table 4. Ablation on each components" + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.365, + 0.47, + 0.418 + ], + "angle": 0, + "content": "
Inner Cost (Linner)Movable within Grid (sgrid)APAPSAPMAPL
35.917.038.852.7
✓26.311.328.039.5
✓✓36.216.439.553.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.147, + 0.427, + 0.4, + 0.44 + ], + "angle": 0, + "content": "Table 5. Ablation on scaling factor of grid" + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.447, + 0.469, + 0.501 + ], + "angle": 0, + "content": "
PECAScaling Factor of SDGAPAPSAPMAPL
33.614.736.050.7
✓35.717.538.852.6
✓✓36.216.439.553.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.144, + 0.511, + 0.402, + 0.525 + ], + "angle": 0, + "content": "Table 6. Ablation on scaling factor of SDG" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.672 + ], + "angle": 0, + "content": "always exists in large objects. 4). For salient point enhanced cross-attention, both SDG and PECA serve as the essential components, independently emerging 0.8 AP and 1.6 AP improvements compared to the standard model (rows 2-4). Interestingly, there exists an effectiveness overlap on small objects, with only \\(0.1\\mathrm{AP}_{\\mathrm{S}}\\) improvement when adding SDG to the equipped PECA model (row 1 and 2). We argue that the Gaussian-like map of SDG might be easily overlapped with PECA on small objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.472, + 0.904 + ], + "angle": 0, + "content": "Scaling Factor of Movable Strategy. We perform an ablation study on the scaling factor of the movable strategy and further investigate the effectiveness of the inner cost in Tab. 5. Notably, it is observed that there exists a conflict between the inner loss and the global search strategy, behaving a sharp drop when only reserving the inner loss. Furthermore, searching within the grid enables the detector to more attend to small objects and avoid a drastic deterioration in normal object detection. See Appendix E for more detailed analyses. Scaling Factor of SDG. We also compare our side-directed manner with the standard offset prediction method in Tab. 6. Based on PECA, the side-directed scaling factor may limit the detector on small object detection but significantly promote the performance on other objects. This phenomenon would be broken without the help of PECA in which a preci" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.429 + ], + "angle": 0, + "content": "itous decline is emerged on all-scale object detection (row 5 in Tab. 4 vs. row 1 in Tab. 6). We hypothesise that it because the predicted reference points may be outside of the proposal boxes, or even the region of the image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.443, + 0.619, + 0.459 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.895, + 0.681 + ], + "angle": 0, + "content": "In this paper, we propose SAP-DETR for promoting model convergence by treating object detection as a transformation from the salient points to the instance objects. Our SAP-DETR explicitly initializes a query-specific reference point for each object query, gradually aggregates them into an instance object, and predicts the distance from each side of the bounding box. By speedily attending to the query-specific region and other extreme regions from contextual image features, it thus can effectively bridge the gap between the salient points and the query-based Transformer detector. Our extensive experiments have demonstrated that SAP-DETR achieves superior model convergence speed. With the same training settings, our proposed SAP-DETR outperforms SoTA approaches with large margins." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.697, + 0.636, + 0.713 + ], + "angle": 0, + "content": "6. Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.894, + 0.814 + ], + "angle": 0, + "content": "This point-based design for DETR-like models also comes with remaining issues, in particular regarding training with deformable attention, multi-scale features, and negative query design. Following current center-based methods working for similar issues, we expect future work to successfully address them for point-based design of SAP-DETR." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.667, + 0.846 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We thank the Lenovo Research AI Master platform for computing GPU supports without which this work would not be possible." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15546" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. Soft-nms-improving object detection with one line of code. 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In ICLR, 2020. 2, 3, 6, 7, 10" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.817 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15547" + } + ] +] \ No newline at end of file diff --git a/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/909bbbe4-4e26-472f-ab37-1d60d8bab4b6_origin.pdf b/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/909bbbe4-4e26-472f-ab37-1d60d8bab4b6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e035c12f5fc150782950940c5948a6ce9c370f78 --- /dev/null +++ b/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/909bbbe4-4e26-472f-ab37-1d60d8bab4b6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4041f74fc5012d002d394546532efcbb5d9ebaf2fbf62bae196979cbfcf9dba5 +size 3355680 diff --git a/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/full.md b/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/full.md new file mode 100644 index 0000000000000000000000000000000000000000..980397f5f94cf7c994f79a469d2f044b8aa9dd6f --- /dev/null +++ b/2023/SAP-DETR_ Bridging the Gap Between Salient Points and Queries-Based Transformer Detector for Fast Model Convergency/full.md @@ -0,0 +1,268 @@ +# SAP-DETR: Bridging the Gap between Salient Points and Queries-Based Transformer Detector for Fast Model Convergence + +Yang Liu $^{1,3}$ * Yao Zhang $^{1,3}$ * Yixin Wang $^{2}$ * Yang Zhang $^{4}$ Jiang Tian $^{4}$ Zhongchao Shi $^{4}$ Jianping Fan $^{4}$ Zhiqiang He $^{1,3,5\dagger}$ + +$^{1}$ Institute of Computing Technology (ICT), Chinese Academy of Sciences $^{2}$ Stanford University $^{3}$ University of Chinese Academy of Sciences $^{4}$ AI Lab, Lenovo Research $^{5}$ Lenovo Ltd. + +{liuyang20c,zhangyao215}@mails.ucas.ac.cn yxinwang@stanford.edu + +{zhangyang20,tianjiang1,shizc2,jfan1,hezq}@lenovo.com + +# Abstract + +Recently, the dominant DETR-based approaches apply central-concept spatial prior to accelerating Transformer detector convergence. These methods gradually refine the reference points to the center of target objects and imbue object queries with the updated central reference information for spatially conditional attention. However, centralizing reference points may severely deteriorate queries' saliency and confuse detectors due to the indiscriminative spatial prior. To bridge the gap between the reference points of salient queries and Transformer detectors, we propose SAlient Point-based DETR (SAP-DETR) by treating object detection as a transformation from salient points to instance objects. Concretely, we explicitly initialize a query-specific reference point for each object query, gradually aggregate them into an instance object, and then predict the distance from each side of the bounding box to these points. By rapidly attending to query-specific reference regions and the conditional box edges, SAP-DETR can effectively bridge the gap between the salient point and the query-based Transformer detector with a significant convergence speed. Experimentally, SAP-DETR achieves $1.4 \times$ convergence speed with competitive performance and stably promotes the SoTA approaches by $\sim 1.0$ AP. Based on ResNet-DC-101, SAP-DETR achieves 46.9 AP. The code will be released at https://github.com/liuyang-ict/SAP-DETR. + +# 1. Introduction + +Object detection is a fundamental task in computer vision, whose target is to recognize and localize each object from input images. In the last decade, various detec + +![](images/e0e7be2e248a69d58cb6ea61a192c0e5d95c0e8c9cff5ff9a8341202b046f68c.jpg) +Figure 1. Comparison of SAP-DETR and DAB-DETR under 3-layer decoder model and 36-epoch training scheme. (a) Statistics of the query count in different classification score intervals. (b) and (c) Visualize the distribution of all reference points (pink) and highlight the top-20 classification score queries with their bounding boxes (blue) and reference points (red) in different decoder layers. (d) Visualize the outputs of positive queries and ground truth (red) during the training process, each query has a representative color for its reference point and bounding box. Best viewed in color. + +tors [6,11,14,18,20,22] based on Convolutional Neural Networks (CNNs), have received widespread attention and made significant progress. Recently, Carion et al. [2] proposed a new end-to-end paradigm for object detection based on the Transformer [24], called DEtction TRansformer (DETR), which treats object detection as a problem of set prediction. In DETR, a set of learnable positional encodings, namely object queries, are employed to aggregate instance features from the context image in Transformer Decoder. The predictions of queries are finally assigned to the ground truth via bipartite matching to achieve end-to-end detection. + +Despite the promising results of DETR, its application is largely limited by considerably longer training time compared to conventional CNNs. To address this problem, many + +variants attempted to take a close look at query paradigm and introduced various spatial priors for model convergence and efficacy. According to the type of spatial prior, they can be categorized into implicit and explicit methods. The implicit ones [5, 16, 31] attempt to decouple a reference point from the object query and make use of this spatial prior to attend to the image context features efficiently. The current state-of-the-arts (SoTAs) are dominated by the explicit ones [13, 25], which suggest to instantiate a position with spatial prior for each query, i.e., explicit reference coordinates with a center point or an anchor box. These reference coordinates serve as helpful priors and enable the queries to focus on their expected regions easily. For instance, Anchor DETR [25] introduced an anchor concept (center point with different box size patterns) to formulate the query position and directly regressed the central offsets of the bounding boxes. DABDETR [13] further stretched the center point to a 4D anchor box concept $[cx, cy, w, h]$ to refine proposal bonding boxes in a cascaded manner. However, instantiating the query location as a target center may severely degrade the classification accuracy and convergence speed. As illustrated in Fig. 1, there exist many plausible queries [19] with high-quality classification scores (Fig. 1(a) within red box) and box Intersection over Union (IoU, see the redundant blue boxes in Fig. 1(b) and (c)), which only brings a slight improvement on precision rate but inevitably confuses the detector on the positive query assignments when training with bipartite matching strategy. This is because the plausible predictions are considered in negative classification loss, which severely decelerates the model convergence. As shown in Fig. 1(b) and (c), the predefined reference point of the positive query may not be the nearest one to the center of the ground truth bounding box, and the reference points tend to be centralized or marginalized (cyan arrows in Fig. 1(b)), hence losing the spatial specificity. With further insight into the one-to-one label assignment during the training process, we find that the query, whose reference point is closest to the center point, also has a high-quality IoU, but it still exists a disparity with the positive query in the classification confidence. Therefore, we argue that such a centralized spatial prior may cause degeneration of target consistency in both classification and localization tasks, which leads to inconsistent predictions. + +Furthermore, the mentioned central point-based variants also have difficulties in detecting occluded objects. For example, Fig. 1(d) shows that DAB-DETR detects the left baseman twice, while the query point in SAP-DETR is not necessarily the center point, so the query point of the bounding box for the occluded baseman is from a pixel on the occluded baseman on the top right area instead of from the left baseman. One solution for center-based method [25] is to predefine different receptive fields (similar to the scaling anchor box in YOLO [17]) for the position of each query. However, increasing the diversity of the receptive fields for + +each position query is unsuitable for non-overlapped targets, as it still generates massive indistinguishable predictions for one position as same as other center-based models. + +To bridge these gaps, in this paper, we present a novel framework for Transformer detector, called SAclient Point-based DETR (SAP-DETR), which treats object detection as a transformation from salient points to instance objects. Instead of regressing the reference point to the target center, we define the reference point belonging to one positive query as a salient point, keep this query-specific spatial prior with a scaling amplitude, and then gradually update them to an instance object by predicting the distance from each side of the bounding box. Specifically, we tile the mesh-grid referenced points and initialize their center/corner as the query-specific reference point. To disentangle the reference sparsity as well as stabilize the training process, a movable strategy with scaling amplitude is applied for reference point adjustment, which prompts queries to consider their reference grid as the salient region to perform image context attention. By localizing each side of the bounding box layer by layer, such query-specific spatial prior enables compensation for the over-smooth/inadequacy problem during center-based detection, thereby vastly promoting model convergence speed. Inspired by [5, 13, 16], we also take advantage of both Gaussian spatial prior and conditional cross-attention mechanism, and then a salient point enhanced cross-attention mechanism is developed to distinguish the salient region and other conditional extreme regions from the context image features. + +We bridge the gap between salient points and query-based Transformer detector by speedily attending to the query-specific region and other conditional regions. The extensive experiments have shown that SAP-DETR achieves superior convergence speed and performance. To the best of our knowledge, this is the first work to introduce the salient point based regression into end-to-end query-based Transformer detectors. Our contributions can be summarized as follows. + +1) We introduce the salient point concept into query-based Transformer detectors by assigning query-specific reference points to object queries. Unlike center-based methods, we restrict the reference location and define the point of the positive query as the salient one, hence enlarging the discrepancy of query as well as reducing the redundant predictions (see Fig. 1). Thanks to the efficacy of the query-specific prior, our SAP-DETR accelerates the convergence speed greatly, achieving competitive performance with $30\%$ fewer training epochs. The proposed movable strategy further boosts SAP-DETR to a new SoTA performance. +2) We devise a point-enhanced cross-attention mechanism to imbue query with spatial prior based on both reference point and box sides for final specific region attention. +3) Evaluation over COCO dataset has demonstrated that SAP-DETR achieves superior convergence speed and detection accuracy. Under the same training settings, SAP-DETR + +outperforms the SoTA approaches with a large margin. + +# 2. Related Work + +Anchor-Free Object Detectors. Classical anchor-free object detectors can be grouped into center-based and keypoint-based approaches. The center-based approaches aim to localize the target objects based on the central locations [11] or predefined ROI [22]. For example, FCOS [22] treated all points within the bounding box as positive ones to predict their distances from each side $([\ell, t, r, b])$ , and a centerness score was then considered to prohibit the low-quality prediction whose point is located near the border. Compared with FCOS, we also restrict the candidate queries within the bounding box but treat only one as positive to perform end-to-end object detection via an inner matching cost. + +The target of keypoint-based approaches is to localize the specific object locations and assign them to the predefined keypoints of the object for box localized training. For instance, diagonal corner points were considered in CornerNet [8], center point was further grouped into CenterNet [29], and ExtremeNet [30] added some conjectural extreme points for object localization. These works showed an impressive performance, but the complicated keypoint matching may limit their upper bound. Our SAP-DETR takes the advantage of salient point regression to focus on the distinct regions without complicated point-based supervision. + +Query-Based Transformer Detectors. DETR [2] pioneered a new paradigm of Transformer detector for end-to-end object detection without any post-processing [1]. In DETR, a new representation, namely object query, aggregates the instance features and then yields a detection result for each instance object [15]. Following DETR, many voterists put efforts on the optimization of convergence and accuracy. + +Sun et al. [21] revealed that the main reason for slow convergence of DETR is attributed to the Transformer decoder, and they considered an encoder-only structure to alleviate such a problem. For in-depth understanding of the object query, one way is to generate a series of implicit spatial priors from queries to guide feature aggregation in cross-attention layers. SMCA [5] applied a Gaussian-like attention map to augment the query-concerned features spatially. The reference point concept was first introduced by Deformable DETR [31], where the sampling offsets are predicted by each reference point to perform deformable cross-attention. Following such a concept, Conditional DETR [16] reformulated the attention operation and rebuilt positional queries based on the reference points to facilitate extreme region discrimination. Another way is towards position-instantiation explicitly, where this position information enables to directly conduct positional query generation. Anchor DETR [25] utilized a predefined 2D anchor point $[cx, cy]$ to explicitly capitalize on the spatial prior during cross-attention and box regression. DAB-DETR [13] extended such a 2D concept to + +![](images/610de358f6711972cd0b18bdd81eb531a04351f72a5b205d48cb34f2440f488e.jpg) +Figure 2. Illustration of SAP-DETR. Each object query in SAP-DETR is assigned to a specific grid region and initialized by the corner/center of the grid as its reference point. A learnable 4D coordinate represents the distance from the four sides of the box to the reference point. Both reference points and box sides are served as positional encodings added/concatenated to content embeddings. All embeddings are refined to predict target objects gradually. + +a 4D anchor box $[cx, cy, w, h]$ and refined it layer-by-layer. + +The recent accelerating convergence methods are based on auxiliary queries for facilitating detector discrimination. DN-DETR [9] demonstrates the slow model convergence is mainly caused by the instability of bipartite matching, thus providing a denoising training to eliminate this issue. DINO [28] inherits this advance and further introduces negative queries to perform contrastive denoising. Group-DETR [4] proposes a group-wise one-to-many label assignment to match multiple positive object queries with more gradients for fast DETR convergence. + +The most relevant approaches to ours are Point-DETR [3] and SAM-DETR [26, 27]. The former applied a point encoder for annotated point label infusion in teacher model, and the latter directly updated content embeddings by extracting salient points from image features for query-image semantic alignment. Unlike these concepts, we redefine the salient point from the perspective of the positive query's position and replace the center-concept prior with the query-specific position, thereby attending extreme regions, differentiating queries' saliency, and alleviating redundant predictions. + +# 3. Method + +We propose SAP-DETR to bridge the gap between salient points and query-based detectors. Following DETR, the extracted image features are fed into Transformer encoder + +after adding positional encodings, and then re-aggregated by object queries in Transformer decoder. In pursuit of the query-specific prior, we dispense a movable strategy for each query based on a fixed grid region. The query, whose reference region overlaps with ground truth objects, is allowed to predict the relative offsets from four sides of the bounding box to the points. Given the query-specific reference point and the proposal box sides, we propose salient point enhanced cross-attention mechanism to imbue query with spatial prior, thereby attending to extreme regions effectively. Additionally, we discuss two common issues in DETR-like models and address them for further improvements. + +# 3.1. Salient Points-Based Object Detection + +Overview. Previous methods [13, 16, 25] normally decompose the object query into both content and position embeddings (queries), and form a center-based anchor point/box prior on the position ones. Unlike the central concept, we tile a fixed mesh-grid region, initialize their left-top corner as the reference points with 2D coordinate $\boldsymbol{r} = \{x, y\} \in [0,1]^2$ , and instantiate a learnable 4D offset distance $s = \{\ell, t, r, b\} \in [0,1]^4$ from the reference point to the sides of proposal bounding box for each object query. The object query can be referred as $q = \{\mathbf{e}; r, s\}$ , where $\mathbf{e} \in \mathbb{R}^d$ is the content embedding with $d$ dimension. Instead of regressing the center, width, and height of a bounding box, we follow FCOS [22] and directly supervise the 4D offset from the four sides of a bounding box to the reference point. The final box prediction is formulated as $\hat{\boldsymbol{b}} = \{\hat{x} - \hat{\ell}, \hat{y} - \hat{\bar{t}}, \hat{x} + \hat{r}, \hat{y} + \hat{b}\}$ . Ideally, we here fix the reference point $\{\hat{x}, \hat{y}\} = \{x, y\}$ (the movable update strategy is introduced in the next subsection) and only update the 4D box side prediction layer by layer. The prediction for each decoder layer can be calculated by + +$$ +\Delta \boldsymbol {s} _ {l} = \operatorname {B o x H e a d} _ {l} (\boldsymbol {s} _ {l - 1}, \boldsymbol {e} _ {l - 1}, \boldsymbol {r} _ {l - 1}), +$$ + +$$ +\hat {\boldsymbol {s}} _ {l} = \sigma \left(\sigma^ {- 1} \left(\boldsymbol {s} _ {l - 1}\right) + \Delta \boldsymbol {s} _ {l}\right), \quad \boldsymbol {s} _ {l} = \operatorname {D e t a c h} (\hat {\boldsymbol {s}} _ {l}), +$$ + +$$ +\boldsymbol {r} _ {l} = \hat {\boldsymbol {r}} _ {l} = \boldsymbol {r} _ {l - 1}, \quad \hat {\boldsymbol {b}} _ {l} = \left\{\hat {\boldsymbol {r}} _ {l} - \hat {\boldsymbol {s}} _ {l} [: 2 ], \hat {\boldsymbol {r}} _ {l} + \hat {\boldsymbol {s}} _ {l} [2: ] \right\}, \tag {1} +$$ + +where $\sigma$ and $\sigma^{-1}$ are the sigmoid and inverse sigmoid operation, respectively. $\Delta s_{l}$ denotes the side offset prediction. $\hat{s}_l$ , $\hat{r}_l$ , and $\hat{\pmb{b}}_l$ are the predicted side distance, reference points, and box location from the $l$ decoder layer, respectively. The BoxHead is the prediction head following the layer- $l$ decoder, which is independent between different decoder layers in our settings. Detach operation follows DAB-DETR [13]. + +During the training process, each query is only allowed to predict the bounding boxes that overlap its reference region. We adapt this rule into the one-to-one bipartite matching process via an inner matching cost $\mathcal{L}_{\mathrm{inner}}$ . Given $N$ queries $\mathbf{Q} = \{\pmb{q}_1,\pmb{q}_2,\dots ,\pmb{q}_N\}$ and $M$ ground truth objects $\mathbf{G} = \{\pmb{g}_1,\pmb{g}_2,\dots ,\pmb{g}_M\}$ , the $\mathcal{L}_{\mathrm{inner}}(\pmb{g}_i,\pmb{q}_j)$ of each query-box pair is a step function to penalize the reference point $\pmb{r}_j$ of $\pmb{q}_j$ with value of $k$ when $\pmb{r}_j$ is outside the bounding box of + +$g_{i}$ . We denote $i \in [1, M]$ and $j \in [1, N]$ as the index of query and ground truth, respectively. $k$ can be viewed as a penalty cost, and default to $10^{5}$ . The final permutation of the one-to-one label assignment is formulated as + +$$ +\mathcal {L} _ {\text {i n n e r}} \left(\boldsymbol {g} _ {i}, \boldsymbol {q} _ {j}\right) := \mathbf {k} _ {\boldsymbol {r} _ {j} \notin \boldsymbol {g} _ {i}}, +$$ + +$$ +\hat {\eta} = \underset {\eta \in \mathfrak {Y} _ {N}} {\operatorname {a r g m i n}} \sum_ {i} ^ {N} \mathcal {L} _ {\text {m a t c h}} + \mathcal {L} _ {\text {i n n e r}}, \tag {2} +$$ + +where $\mathcal{L}_{\mathrm{match}}$ is the original pair-wise matching cost consist of both classification and localization costs [2]. $\eta \in \mathfrak{V}_N$ is a permutation of $N$ elements for bipartite matching. + +Movable Reference Point. Due to the sparseness of the fixed reference point, some small and slender objects may be indistinguishable when there is no reference point inside these objects. Despite the bipartite matching forcing each object to be assigned to one object query, the positive query, whose reference point is outside the assigned bounding box, is unable to accurately regress the distance from each side by a value between 0 and 1. One straightforward solution is to adjust the locations of reference points inside the ground truth bounding boxes to ensure that each object can be detected by an inner reference point. Similar to the aforementioned box refinement, we first perform a movable reference point design to dynamically update the reference points of each query layer by layer. However, such a full-image point regression inevitably expands the search space as vast variable determinations, causing the final reference point to be trapped in an unexpected corner of the bounding box. To reduce the training search spaces, we scale the offset amplitude of points within their specific grid regions, as illustrated in Fig. 3. Such an operation limits the range of offset values, and hence prevents a large searching space. It is implemented by applying the sigmoid activation $\sigma$ and multiplying a scale factor $s_{\mathrm{grid}}$ whose value equals to the height and width of one grid. The update process of the reference points is formulated as + +$$ +\Delta \boldsymbol {r} _ {l} ^ {\prime} = \operatorname {P o i n t H e a d} _ {l} \left(\boldsymbol {s} _ {l - 1}, \boldsymbol {e} _ {l - 1}, \boldsymbol {r} _ {l - 1}\right), +$$ + +$$ +\Delta \boldsymbol {r} _ {l} = \sigma \left(\sigma^ {- 1} \left(\boldsymbol {r} _ {l - 1} - \boldsymbol {r} _ {0}\right) + \Delta \boldsymbol {r} _ {l} ^ {\prime}\right), \tag {3} +$$ + +$$ +\hat {\boldsymbol {r}} _ {l} = \boldsymbol {r} _ {0} + \Delta \boldsymbol {r} _ {l} \cdot \boldsymbol {s} _ {\text {g r i d}}, \quad \boldsymbol {r} _ {l} = \operatorname {D e t a c h} (\hat {\boldsymbol {r}} _ {l}), +$$ + +where $\Delta \boldsymbol{r}_l'$ and $\Delta \boldsymbol{r}_l$ are the predicted offsets from $\boldsymbol{r}_l$ to both $\boldsymbol{r}_{l-1}$ and $\boldsymbol{r}_0$ before the sigmoid activation $\sigma$ , respectively. + +# 3.2. Salient Point Enhanced Cross-Attention + +In cross-attention layers, existing center-based methods are limited to the attention on both center and sides of the ground truth bounding box, causing detector confusion among the queries with the same center and side attention. To this end, we expect the queries to focus on their specific regions based on the reference points, four box sides, and other conditional regions in different heads. Accordingly, + +![](images/db807192e02719a82d755a7878de64a4f620ef8a0f63351e89cf8572332e9f7c.jpg) +Figure 3. Movable reference point. The reference points are initialized by the center/corner points of the mesh-grid. Based on the inner loss, only the green dashed box can be predicted by the inner points when reference points are fixed. By moving the reference points within their grid, the blue dashed boxes can be detected accurately without extended searching space. + +we consider an improved Gaussian [5] $\mathbf{G}$ and conditional attention [16] $\mathbf{A}_{\mathrm{peca}}$ to enhance query specificity and spatially extreme region discrimination. The final attention map $\mathbf{A}_{\mathrm{cross}}$ is the sum of the two attentions $\mathbf{A}_{\mathrm{cross}} = \mathbf{G} + \mathbf{A}_{\mathrm{peca}}$ . + +Side Directed Gaussian (SDG). Similar to the movable strategy, we enforce the predicted Gaussian attention to be inside the proposal bounding box to reduce the searching space. Given a reference point $r$ , the offset scales $\mathbf{o} \in [-1,1]^2$ for $H$ heads are produced by a simple MLP with a tanh activation, and then multiply to the two sides of the proposal bounding box for head-specific point offset generation, where the direction is guided by the sign of the offset scales. The head-specific points are generated by Algorithm 1. For each head, the Gaussian-like spatial weight map $G_{i}$ effecting on each pixel $(x,y)$ of context features is then formulated as + +$$ +G _ {i} (x, y) = \exp \left(- \frac {\left(x - c _ {w , i}\right) ^ {2}}{v _ {w , i} ^ {2}} - \frac {\left(y - c _ {h , i}\right) ^ {2}}{v _ {h , i} ^ {2}}\right). \tag {4} +$$ + +Point Enhanced Cross-Attention (PECA). As aforementioned, the semantic class for the query is closely related to its referenced location in our SAP-DETR. To enhance the correlation between queries and their references, we concatenate the locations to the content queries after the sinusoidal positional encoding (PE). Take a close look at the conditional attention [16], we find that the linear positional embedding mostly focuses on one box side in each attention head. So we introduce a more straightforward attention mechanism, where the four side coordinates are concatenated and assigned to the corresponding head for side attention. The process of PECA is formulated as + +$$ +\begin{array}{r l} \mathbf {A} _ {\text {p e c a}} & = \mathbf {e} _ {q} \mathbf {e} _ {k} ^ {\top} + \mathbf {T P E} (\boldsymbol {r} _ {q}) \mathbf {P E} (\boldsymbol {r} _ {k}) ^ {\top} \\ & + \mathbf {T} g (\mathbf {P E} (\boldsymbol {r} _ {q} - \{\ell , t \}, \boldsymbol {r} _ {q} + \{r, b \})) \mathbf {P E} (\boldsymbol {r} _ {k}) ^ {\top}, \end{array} \tag {5} +$$ + +where $g$ is a linear layer mapping 4D-PE into 2D to keep channel dimension consistency. T [16] is a scaling transformation matrix. More details of T and comparison with conditional cross-attention are available in Appendix C. + +# Algorithm 1 Side Directed Gaussian + +Input: Content embedding e, reference point $r$ and box s. + +Output: Head-specific points $\mathbf{c} = \{(c_{w,i}, c_{h,i}) | i \in H\}$ and head-specific attention $\mathbf{v} = \{(v_{w,i}, v_{h,i}) | i \in H\}$ . + +1: Predict offset scale and attention scale based on content embedding, $\mathbf{o} = \tanh (\mathrm{MLP}(\mathbf{e}))$ , $\mathbf{v} = \mathrm{MLP}(\mathbf{e})$ +2: for $h\gets 1\in H$ do +3: Select the index of direction guided by the sign of offset scale, $\{a,b\} = \mathrm{sgn}(\mathbf{o}_i) + \{1,2\}$ , $a,b\in \{0,1,2,3\}$ ; +4: According to the index of direction, predict head-specific point, $\mathbf{c}_i = \mathbf{o}_i\cdot \mathbf{s}[a,b] + \mathbf{r}$ +5: end for +6: return $\mathbf{c}_i, \mathbf{v}_i, \forall i = 1, \dots, H$ + +# 3.3. SAP-DETR with Denoising Strategy + +To further explore the capability of our proposed SAP-DETR, we develop SAP-DN-DETR and SAP-DINO-DETR by adding the denoising auxiliary loss [9,28] into the training process. In the denoised SAP-DETR, the main difference from both DN-DETR and DINO lies in the noise design. Instead of the center point, we perform the box jittering and randomly sample a point from the intersection region between the original bounding box and the jittering one as the reference point. As the denoising strategy only serves as an auxiliary training loss increasing the training cost, the variants of denoising models are test-free whose Params and GFLOPs are the same as SAP-DETR models. + +# 4. Experimental Results + +# 4.1. Implementation Details + +We conduct the experiments on the COCO 2017 [12] object detection dataset, containing about 118K training images and 5K validation images. All models are evaluated by the standard COCO evaluation metrics. We follow the vanilla DETR [2] structure that consists of a CNN backbone, a stack of Transformer encoder-decoder layers, and two prediction heads for class label and bounding box prediction. We use ImageNet-pretrained ResNet [7] as our backbone, and report results based on the ResNet and its $\times 1/16$ -resolution extension ResNet-DC. Unlike DAB-DETR [13] sharing box and label head for each layer, we share the class head except the first layer and use an independent box head for the box regression of each layer (for more details please refer to Appendix D). As the mesh-grid initialization for reference points in SAP-DETR, we consider the number of queries $N$ as a perfect square for uniform distribution. Unless otherwise specified, we use $N = 400$ queries in the experiments. Precisely, we also provide a comparison under $N = 300$ in Tab. 2, the standard setting in DETR-like models. + +We adopt two different Transformer structures for experiments where a 3-layer encoder-decoder stack is evaluated to + +![](images/e67c17b52b62bc18f59407f49da518ec9d46208e46c8ed65384428ba5d8ecd32.jpg) +Figure 4. Comparison of performance and training losses curves. + +![](images/c4e4471d6732af893721aadaca57cebf551f6985172900d817e0947edfa5e3c0.jpg) + +![](images/a2fba28d8751276d87d046916bae807f8b5b51e25a59642266ec0fb9122b2506.jpg) + +demonstrate our lightweight model efficacy compared with the traditional CNN detectors, and a 6-layer encoder-decoder stack is aligned with previous DETR variants to investigate the performance of large model. Both are trained on two training schemes: the 12-epoch and 36-epoch schemes with a learning rate drop after 11 and 30 epochs, respectively. All models are trained on the Nvidia A100 GPUs with batch size of 16 and 8 for ResNet and ResNet-DC, respectively. For more training details, please refer to Appendix F. + +# 4.2. Main Results + +As shown in Tab. 1 and Tab. 2, we comprehensively compare our proposed SAP-DETR with the traditional CNN detectors [18], the original DETR [2], and other DETR-like detectors [5, 13, 16, 25, 26, 31] on COCO 2017 validation dataset. For in-depth analysis, we conduct the comparison in two aspects: model convergence and efficacy. + +Model Convergence. Compared with traditional CNN detectors, Transformer detectors are always subject to laborious training time. For example, under the same 12-epoch training scheme, Faster RCNN [18] still achieves good performance, but the mainstream DETR-like models may suffer from inadequate training and perform poorly without the help of auxiliary losses [9]. Under the 12-epoch training scheme, our proposed SAP-DETR can accelerate model convergence significantly, boosting DAB-DETR [13] by 3.9 AP and 2.7 AP on 3-layer and 6-layer encoder-decoder structures, respectively. Compared with the current SoTA, our SAP-DETR also outperforms SAM-DETR [26] by $\sim 1.3$ AP, with reducing $\sim 17\%$ parameters and $\sim 10\%$ GFLOPs. Take a close look at the training process, as illustrated in Fig. 4, SAP-DETR conducts with rapid descent curves in both classification and box regression losses. Notably, there is a large margin in classification loss between ours and SoTA methods, which is benefited from the query-specific reference point, hence boosting model performance in early epochs. + +Model Efficacy. To analyze model efficacy, we report results on long training epochs and high-resolution features in Tab. 1. Under the 36-epoch training scheme, SAP-DETR achieves superior performance among all single-scale Transformer detectors, especially on middle and large targets. For example, SAP-DETR boosts DAB-DETR by $2.0\mathrm{AP}_{\mathrm{M}}$ and $4.1\mathrm{AP}_{\mathrm{L}}$ with 3-layer models, $1.0\mathrm{AP}_{\mathrm{M}}$ and $1.9\mathrm{AP}_{\mathrm{L}}$ with + +6-layer models, which further verifies the effectiveness of our proposed salient point concept for overlapping object detection. Along with layer increase, a deficient upper-bound of SAM-DETR is exposed, with obviously lower 0.5 AP promotion compared to our 1.0 AP improvement. Persuasively, we also report the 50-epoch training results based on the 300-query setting. To align with our mesh-grid initialization strategy, we tile a $17 \times 18$ mesh-grid (306 queries) for each reference point initialization. Tab. 2 shows our main results and the most representative approaches with their original reported performance. Notably, SAP-DETR outperforms the current SoTAs with comparable costs based on all backbones. With low-resolution features ( $\times 1/32$ ), it significantly boosts both middle and large object detection accuracy. + +Combine with Other Fast Convergence Methods. As shown in Tab. 3, we compare our SAP-DETR variants with the current fast convergence methods [4, 9, 28]. With such a subtle modification, our SAP-DETR (grey rows) results in a significant performance improvement compared with the original methods (white rows). Under the 12-epoch training scheme, there exist 0.5-1.9 AP improvements on DN-DETR [9] and 0.7-1.6 AP improvements on Group-DETR [4], but the promotions are slightly reduced when implemented on DINO [28]. We hypothesise that there exists the same effect between the negative query of contrastive denoising [28] and our query-salient reference point. Moreover, we observe that the performance improvements largely originate from the large object detection, especially based on ResNet-DC5 family backbones. We speculate that DETR may prefer the high-resolution features ( $\times 1/16$ ) rather than the low-resolution ones ( $\times 1/32$ ), and our SAP-DETR can distinguish the salient points accurately on the high-resolution, thereby taking full advantage of the large object detection. + +# 4.3. Ablation Study + +Effectiveness of Each Component. To offer an intuitionistic comparison of model convergence for each component, Tab. 4 reports the effectiveness of them based on the 3-layer encoder-decoder structure and 12-epoch training scheme. I). The proposed salient point concept based on content embeddings improves the performance from 32.3 AP to 33.5 + +
Method#Epochs#Params(M)GFLOPsAP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
3-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36338215.828.015.45.316.724.6
Deformable DETR-R50 [31]36307737.157.639.418.340.851.6
SMCA-DETR-R50 [5]12 / 36--28.8 / 37.748.1 / 58.729.9 / 40.113.8 / 19.431.3 / 40.541.3 / 54.8
Conditional DETR-R50 [16]12 / 36408229.6 / 37.148.7 / 57.930.7 / 39.013.0 / 17.632.3 / 40.343.1 / 55.0
Anchor DETR-R50 [25]12 / 36317930.8 / 37.651.1 / 58.731.8 / 39.714.3 / 18.834.1 / 41.544.3 / 53.5
DAB-DETR-R50 [13]12 / 36348332.3 / 39.051.3 / 58.634.0 / 41.815.7 / 20.035.2 / 42.545.7 / 56.0
SAM-DETR-w/SMCA-R50 [26]12 / 36418935.1 / 40.454.7 / 60.736.7 / 42.716.0 / 20.238.4 / 44.452.1 / 58.3
SAP-DETR-R50 (Ours)12 / 36368436.2 / 41.256.2 / 61.637.9 / 43.416.4 / 21.039.5 / 44.553.8 / 60.1
6-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36428914.024.414.04.213.722.5
Deformable DETR-R50 [31]36348138.058.240.418.541.754.2
SMCA-DETR-R50 [5]12 / 36--32.4 / 40.152.3 / 61.434.0 / 42.815.5 / 20.334.9 / 43.347.7 / 57.1
Conditional DETR-R50 [16]12 / 36449033.1 / 40.253.0 / 61.034.8 / 42.414.5 / 19.935.9 / 43.549.2 / 58.8
Anchor DETR-R50 [25]12 / 36378533.7 / 39.754.5 / 60.535.1 / 41.915.6 / 19.937.3 / 43.549.8 / 57.3
DAB-DETR-R50 [13]12 / 36449234.9 / 41.055.5 / 61.736.4 / 43.416.2 / 21.338.4 / 44.751.5 / 58.9
SAM-DETR-w/SMCA-R50 [26]12 / 365910536.2 / 40.957.2 / 62.237.4 / 43.116.1 / 20.139.8 / 44.755.3 / 60.7
SAP-DETR-R50 (Ours)12 / 36479437.5 / 42.258.5 / 62.739.2 / 44.617.3 / 22.640.6 / 45.755.4 / 60.8
+ +Table 1. Comparison between Transformer necks. Based on ResNet-50 backbone, all models are trained by the official source codes with their original settings and evaluated on COCO val2017. All models uses 400 queries except Anchor DETR, while Anchor DETR uses 200 queries with 2 pattern embeddings. GFLOPs and Params are measured by $\text{Detectron}^2$ . + +
Method#Epochs#Params(M)GFLOPsAP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)Infer. \( Time(s / img)^{\dagger} \)
ResNet-50 Backbone
Faster RCNN-FPN-R50 [10, 18]1084218042.062.145.526.645.553.40.039
DETR-R50 [2]500418642.062.444.220.545.861.10.040
Deformable DETR-R50 [31]50347839.459.642.320.643.055.50.043
SMCA-DETR-R50 [5]50428641.0--21.944.359.10.045
Conditional DETR-R50 [16]50449040.961.843.320.844.659.20.057
Anchor DETR-R50 [25]50398542.163.144.922.346.260.00.050
DAB-DETR-R50 [13]5044\( 90^† \)42.263.144.721.545.760.30.059
SAM-DETR-w/SMCA-R50 [26]505810041.863.243.922.145.960.90.065
SAP-DETR-R50 (Ours)50479243.163.845.422.947.162.10.063
ResNet-101 Backbone
Faster RCNN-FPN-R101 [10, 18]1086024644.063.947.827.248.156.00.050
DETR-R101 [2]5006015243.563.846.421.948.061.80.066
Conditional DETR-R101 [16]506315642.863.746.021.746.660.90.070
Anchor DETR-R101 [25]505815043.564.346.623.247.761.40.068
DAB-DETR-R101 [13]5063\( 157^† \)43.563.946.623.647.361.50.072
SAP-DETR-R101 (Ours)506715844.464.947.124.148.763.10.078
DC5-ResNet-50 Backbone
DETR-DC5-R50 [2]5004118743.363.145.922.547.361.10.087
Conditional DETR-DC5-R50 [16]504419543.864.446.724.047.660.70.093
Anchor DETR-DC5-R50 [25]503915144.264.747.524.748.260.60.069
DAB-DETR-DC5-R50 [13]5044\( 194^† \)44.565.147.725.348.262.30.094
SAM-DETR-w/SMCA-DC5-R50 [26]505821045.065.447.926.249.063.30.126
SAP-DETR-DC5-R50 (Ours)504719746.065.548.926.450.262.60.116
DC5-ResNet-101 Backbone
DETR-DC5-R101 [2]5006025344.964.747.723.749.562.30.101
Conditional DETR-DC5-R101 [16]506326245.065.648.426.148.962.80.105
Anchor DETR-DC5-R101 [25]505822745.165.748.825.849.461.60.083
DAB-DETR-DC5-R101 [13]5063\( 263^† \)45.865.949.327.049.863.80.110
SAP-DETR-DC5-R101 (Ours)506726646.966.750.527.951.364.30.130
+ +Table 2. Comparison of Transformer necks with 300 queries on COCO val2017. All results are reported from their original paper. All models uses 300 queries except Anchor DETR, while Anchor DETR uses 100 queries with 3 pattern embeddings. All inference speeds are measured by a single Nvidia A100 GPU. † denotes the results are measured by ourselves. + +AP compared to baseline DAB-DETR (row 8-9). Such a query-specific spatial prior enables queries to attend to their expected region from content features (see Figures in Appendix G) and reduces the false detection rate on occluded and partial objects (see Fig. 1(d)), hence boosting detection performance on middle and large objects. However, there exists a drop in small object detection (15.7 APs vs. 14.3 APs), for which we consider that the failure is mainly caused + +by the query sparsity. 2). Therefore, the movable strategy is applied to alleviate the constraint, improving the final model by $1.0\mathrm{AP}$ and $0.6\mathrm{AP}_{\mathrm{S}}$ (row 1 and 6). 3). Compared with the final model, the inner loss greatly improves the performance on high-quality $\mathrm{AP}_{75}$ and large objects $\mathrm{AP}_{\mathrm{L}}$ detection (row 1 and 7), with just a slight drop on low-quality object $\mathrm{AP}_{50}$ . That is reasonable because the outside reference points are unable to localize objects accurately, and this phenomenon + +
BackboneEpochw/ SAPDN-DETR [9]DINO (Single-Scale) [28]Group DETR [4]
AP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APL
R5012✓(Ours)38.3 / 58.6 / 40.518.4 / 41.6 / 57.139.7 / 58.3 / 42.419.1 / 43.7 / 57.139.1 / - / -19.7 / 42.5 / 56.8
39.5 / 59.7 / 41.518.7 / 42.8 / 59.040.0 / 60.1 / 42.120.2 / 43.4 / 58.539.8 / 60.2 / 42.020.2 / 43.5 / 58.6
R10112✓(Ours)40.5 / 60.8 / 43.019.3 / 44.3 / 59.641.9 / 60.8 / 44.422.5 / 46.3 / 59.5- / - / -- / - / -
41.0 / 61.2 / 43.419.8 / 45.3 / 60.041.5 / 61.4 / 43.620.3 / 45.2 / 60.041.1 / 61.5 / 43.420.5 / 45.5 / 59.4
R50-DC12✓(Ours)41.7 / 61.4 / 44.121.2 / 45.0 / 60.243.6 / 61.4 / 47.024.8 / 47.3 / 59.541.9 / - / -23.3 / 45.6 / 58.4
43.6 / 62.5 / 46.223.3 / 47.3 / 61.044.0 / 63.1 / 46.524.8 / 47.3 / 61.143.9 / 63.2 / 46.824.5 / 47.6 / 61.3
R101-DC12✓(Ours)43.4 / 61.9 / 47.224.8 / 46.8 / 59.445.4 / 63.5 / 49.226.4 / 49.5 / 61.1- / - / -- / - / -
44.6 / 63.9 / 48.025.5 / 48.9 / 62.545.6 / 64.5 / 48.725.0 / 49.7 / 62.544.4 / 63.9 / 47.425.9 / 48.5 / 61.4
+ +Table 3. Comparison with denoised methods on COCO dataset based on the 12-epoch training schedule and 300 object queries. + +
CommentMovableInner LossPECASDGAP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
SAP-DETR (Ours)✓✓✓✓36.256.237.916.439.553.8
-SDG✓✓✓35.656.236.916.338.952.7
-PECA✓✓✓34.855.536.015.737.352.0
-PECA & SDG✓✓34.054.935.315.036.751.5
-Movable✓✓✓35.255.436.815.838.553.8
-Inner Loss✓✓✓35.956.337.416.239.352.5
DAB-DETR (Baseline)----32.351.334.015.735.245.7
+Salient Point Concept----33.554.335.114.336.551.0
+ +Table 4. Ablation on each components + +
Inner Cost (Linner)Movable within Grid (sgrid)APAPSAPMAPL
35.917.038.852.7
✓26.311.328.039.5
✓✓36.216.439.553.8
+ +Table 5. Ablation on scaling factor of grid + +
PECAScaling Factor of SDGAPAPSAPMAPL
33.614.736.050.7
✓35.717.538.852.6
✓✓36.216.439.553.8
+ +Table 6. Ablation on scaling factor of SDG + +always exists in large objects. 4). For salient point enhanced cross-attention, both SDG and PECA serve as the essential components, independently emerging 0.8 AP and 1.6 AP improvements compared to the standard model (rows 2-4). Interestingly, there exists an effectiveness overlap on small objects, with only $0.1\mathrm{AP}_{\mathrm{S}}$ improvement when adding SDG to the equipped PECA model (row 1 and 2). We argue that the Gaussian-like map of SDG might be easily overlapped with PECA on small objects. + +Scaling Factor of Movable Strategy. We perform an ablation study on the scaling factor of the movable strategy and further investigate the effectiveness of the inner cost in Tab. 5. Notably, it is observed that there exists a conflict between the inner loss and the global search strategy, behaving a sharp drop when only reserving the inner loss. Furthermore, searching within the grid enables the detector to more attend to small objects and avoid a drastic deterioration in normal object detection. See Appendix E for more detailed analyses. Scaling Factor of SDG. We also compare our side-directed manner with the standard offset prediction method in Tab. 6. Based on PECA, the side-directed scaling factor may limit the detector on small object detection but significantly promote the performance on other objects. This phenomenon would be broken without the help of PECA in which a preci + +itous decline is emerged on all-scale object detection (row 5 in Tab. 4 vs. row 1 in Tab. 6). We hypothesise that it because the predicted reference points may be outside of the proposal boxes, or even the region of the image. + +# 5. Conclusion + +In this paper, we propose SAP-DETR for promoting model convergence by treating object detection as a transformation from the salient points to the instance objects. Our SAP-DETR explicitly initializes a query-specific reference point for each object query, gradually aggregates them into an instance object, and predicts the distance from each side of the bounding box. By speedily attending to the query-specific region and other extreme regions from contextual image features, it thus can effectively bridge the gap between the salient points and the query-based Transformer detector. Our extensive experiments have demonstrated that SAP-DETR achieves superior model convergence speed. With the same training settings, our proposed SAP-DETR outperforms SoTA approaches with large margins. + +# 6. Future Work + +This point-based design for DETR-like models also comes with remaining issues, in particular regarding training with deformable attention, multi-scale features, and negative query design. Following current center-based methods working for similar issues, we expect future work to successfully address them for point-based design of SAP-DETR. + +# Acknowledgements + +We thank the Lenovo Research AI Master platform for computing GPU supports without which this work would not be possible. + +# References + +[1] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. Soft-nms-improving object detection with one line of code. In ICCV, pages 5561-5569, 2017. 3 +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In ECCV, pages 213-229. Springer, 2020. 1, 3, 4, 5, 6, 7, 10 +[3] Liangyu Chen, Tong Yang, Xiangyu Zhang, Wei Zhang, and Jian Sun. Points as queries: Weakly semi-supervised object detection by points. In CVPR, pages 8823-8832, 2021. 3 +[4] Qiang Chen, Xiaokang Chen, Gang Zeng, and Jingdong Wang. 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"Recently, the dominant DETR-based approaches apply central-concept spatial prior to accelerating Transformer detector convergence. These methods gradually refine the reference points to the center of target objects and imbue object queries with the updated central reference information for spatially conditional attention. However, centralizing reference points may severely deteriorate queries' saliency and confuse detectors due to the indiscriminative spatial prior. To bridge the gap between the reference points of salient queries and Transformer detectors, we propose SAlient Point-based DETR (SAP-DETR) by treating object detection as a transformation from salient points to instance objects. Concretely, we explicitly initialize a query-specific reference point for each object query, gradually aggregate them into an instance object, and then predict the distance from each side of the bounding box to these points. By rapidly attending to query-specific reference regions and the conditional box edges, SAP-DETR can effectively bridge the gap between the salient point and the query-based Transformer detector with a significant convergence speed. Experimentally, SAP-DETR achieves " + }, + { + "bbox": [ + 45, + 298, + 290, + 597 + ], + "type": "inline_equation", + "content": "1.4 \\times" + }, + { + "bbox": [ + 45, + 298, + 290, + 597 + ], + "type": "text", + "content": " convergence speed with competitive performance and stably promotes the SoTA approaches by " + }, + { + "bbox": [ + 45, + 298, + 290, + 597 + ], + "type": "inline_equation", + "content": "\\sim 1.0" + }, + { + "bbox": [ + 45, + 298, + 290, + 597 + ], + "type": "text", + "content": " AP. Based on ResNet-DC-101, SAP-DETR achieves 46.9 AP. The code will be released at https://github.com/liuyang-ict/SAP-DETR." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 620, + 128, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 128, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 128, + 632 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 640, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 640, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 640, + 288, + 676 + ], + "type": "text", + "content": "Object detection is a fundamental task in computer vision, whose target is to recognize and localize each object from input images. In the last decade, various detec" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 274, + 544, + 419 + ], + "blocks": [ + { + "bbox": [ + 310, + 274, + 544, + 419 + ], + "lines": [ + { + "bbox": [ + 310, + 274, + 544, + 419 + ], + "spans": [ + { + "bbox": [ + 310, + 274, + 544, + 419 + ], + "type": "image", + "image_path": "e0e7be2e248a69d58cb6ea61a192c0e5d95c0e8c9cff5ff9a8341202b046f68c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 430, + 547, + 530 + ], + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 530 + ], + "type": "text", + "content": "Figure 1. Comparison of SAP-DETR and DAB-DETR under 3-layer decoder model and 36-epoch training scheme. (a) Statistics of the query count in different classification score intervals. (b) and (c) Visualize the distribution of all reference points (pink) and highlight the top-20 classification score queries with their bounding boxes (blue) and reference points (red) in different decoder layers. (d) Visualize the outputs of positive queries and ground truth (red) during the training process, each query has a representative color for its reference point and bounding box. Best viewed in color." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 544, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 676 + ], + "type": "text", + "content": "tors [6,11,14,18,20,22] based on Convolutional Neural Networks (CNNs), have received widespread attention and made significant progress. Recently, Carion et al. [2] proposed a new end-to-end paradigm for object detection based on the Transformer [24], called DEtction TRansformer (DETR), which treats object detection as a problem of set prediction. In DETR, a set of learnable positional encodings, namely object queries, are employed to aggregate instance features from the context image in Transformer Decoder. The predictions of queries are finally assigned to the ground truth via bipartite matching to achieve end-to-end detection." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Despite the promising results of DETR, its application is largely limited by considerably longer training time compared to conventional CNNs. To address this problem, many" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 683, + 287, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 703 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 703 + ], + "type": "text", + "content": "*This work was done when working as an intern at AI Lab, Lenovo Research, Beijing, China." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15539" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 575 + ], + "type": "text", + "content": "variants attempted to take a close look at query paradigm and introduced various spatial priors for model convergence and efficacy. According to the type of spatial prior, they can be categorized into implicit and explicit methods. The implicit ones [5, 16, 31] attempt to decouple a reference point from the object query and make use of this spatial prior to attend to the image context features efficiently. The current state-of-the-arts (SoTAs) are dominated by the explicit ones [13, 25], which suggest to instantiate a position with spatial prior for each query, i.e., explicit reference coordinates with a center point or an anchor box. These reference coordinates serve as helpful priors and enable the queries to focus on their expected regions easily. For instance, Anchor DETR [25] introduced an anchor concept (center point with different box size patterns) to formulate the query position and directly regressed the central offsets of the bounding boxes. DABDETR [13] further stretched the center point to a 4D anchor box concept " + }, + { + "bbox": [ + 47, + 72, + 289, + 575 + ], + "type": "inline_equation", + "content": "[cx, cy, w, h]" + }, + { + "bbox": [ + 47, + 72, + 289, + 575 + ], + "type": "text", + "content": " to refine proposal bonding boxes in a cascaded manner. However, instantiating the query location as a target center may severely degrade the classification accuracy and convergence speed. As illustrated in Fig. 1, there exist many plausible queries [19] with high-quality classification scores (Fig. 1(a) within red box) and box Intersection over Union (IoU, see the redundant blue boxes in Fig. 1(b) and (c)), which only brings a slight improvement on precision rate but inevitably confuses the detector on the positive query assignments when training with bipartite matching strategy. This is because the plausible predictions are considered in negative classification loss, which severely decelerates the model convergence. As shown in Fig. 1(b) and (c), the predefined reference point of the positive query may not be the nearest one to the center of the ground truth bounding box, and the reference points tend to be centralized or marginalized (cyan arrows in Fig. 1(b)), hence losing the spatial specificity. With further insight into the one-to-one label assignment during the training process, we find that the query, whose reference point is closest to the center point, also has a high-quality IoU, but it still exists a disparity with the positive query in the classification confidence. Therefore, we argue that such a centralized spatial prior may cause degeneration of target consistency in both classification and localization tasks, which leads to inconsistent predictions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 582, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 289, + 714 + ], + "type": "text", + "content": "Furthermore, the mentioned central point-based variants also have difficulties in detecting occluded objects. For example, Fig. 1(d) shows that DAB-DETR detects the left baseman twice, while the query point in SAP-DETR is not necessarily the center point, so the query point of the bounding box for the occluded baseman is from a pixel on the occluded baseman on the top right area instead of from the left baseman. One solution for center-based method [25] is to predefine different receptive fields (similar to the scaling anchor box in YOLO [17]) for the position of each query. However, increasing the diversity of the receptive fields for" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 108 + ], + "type": "text", + "content": "each position query is unsuitable for non-overlapped targets, as it still generates massive indistinguishable predictions for one position as same as other center-based models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 110, + 548, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 548, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 548, + 409 + ], + "type": "text", + "content": "To bridge these gaps, in this paper, we present a novel framework for Transformer detector, called SAclient Point-based DETR (SAP-DETR), which treats object detection as a transformation from salient points to instance objects. Instead of regressing the reference point to the target center, we define the reference point belonging to one positive query as a salient point, keep this query-specific spatial prior with a scaling amplitude, and then gradually update them to an instance object by predicting the distance from each side of the bounding box. Specifically, we tile the mesh-grid referenced points and initialize their center/corner as the query-specific reference point. To disentangle the reference sparsity as well as stabilize the training process, a movable strategy with scaling amplitude is applied for reference point adjustment, which prompts queries to consider their reference grid as the salient region to perform image context attention. By localizing each side of the bounding box layer by layer, such query-specific spatial prior enables compensation for the over-smooth/inadequacy problem during center-based detection, thereby vastly promoting model convergence speed. Inspired by [5, 13, 16], we also take advantage of both Gaussian spatial prior and conditional cross-attention mechanism, and then a salient point enhanced cross-attention mechanism is developed to distinguish the salient region and other conditional extreme regions from the context image features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 410, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 547, + 506 + ], + "type": "text", + "content": "We bridge the gap between salient points and query-based Transformer detector by speedily attending to the query-specific region and other conditional regions. The extensive experiments have shown that SAP-DETR achieves superior convergence speed and performance. To the best of our knowledge, this is the first work to introduce the salient point based regression into end-to-end query-based Transformer detectors. Our contributions can be summarized as follows." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 507, + 548, + 713 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 304, + 507, + 548, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 548, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 548, + 639 + ], + "type": "text", + "content": "1) We introduce the salient point concept into query-based Transformer detectors by assigning query-specific reference points to object queries. Unlike center-based methods, we restrict the reference location and define the point of the positive query as the salient one, hence enlarging the discrepancy of query as well as reducing the redundant predictions (see Fig. 1). Thanks to the efficacy of the query-specific prior, our SAP-DETR accelerates the convergence speed greatly, achieving competitive performance with " + }, + { + "bbox": [ + 304, + 507, + 548, + 639 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 507, + 548, + 639 + ], + "type": "text", + "content": " fewer training epochs. The proposed movable strategy further boosts SAP-DETR to a new SoTA performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 640, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 547, + 676 + ], + "type": "text", + "content": "2) We devise a point-enhanced cross-attention mechanism to imbue query with spatial prior based on both reference point and box sides for final specific region attention." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "3) Evaluation over COCO dataset has demonstrated that SAP-DETR achieves superior convergence speed and detection accuracy. Under the same training settings, SAP-DETR" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15540" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 269, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 269, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 269, + 85 + ], + "type": "text", + "content": "outperforms the SoTA approaches with a large margin." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 95, + 134, + 107 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 95, + 134, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 134, + 107 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 115, + 288, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 115, + 288, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 115, + 288, + 258 + ], + "type": "text", + "content": "Anchor-Free Object Detectors. Classical anchor-free object detectors can be grouped into center-based and keypoint-based approaches. The center-based approaches aim to localize the target objects based on the central locations [11] or predefined ROI [22]. For example, FCOS [22] treated all points within the bounding box as positive ones to predict their distances from each side " + }, + { + "bbox": [ + 46, + 115, + 288, + 258 + ], + "type": "inline_equation", + "content": "([\\ell, t, r, b])" + }, + { + "bbox": [ + 46, + 115, + 288, + 258 + ], + "type": "text", + "content": ", and a centerness score was then considered to prohibit the low-quality prediction whose point is located near the border. Compared with FCOS, we also restrict the candidate queries within the bounding box but treat only one as positive to perform end-to-end object detection via an inner matching cost." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 259, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 287, + 390 + ], + "type": "text", + "content": "The target of keypoint-based approaches is to localize the specific object locations and assign them to the predefined keypoints of the object for box localized training. For instance, diagonal corner points were considered in CornerNet [8], center point was further grouped into CenterNet [29], and ExtremeNet [30] added some conjectural extreme points for object localization. These works showed an impressive performance, but the complicated keypoint matching may limit their upper bound. Our SAP-DETR takes the advantage of salient point regression to focus on the distinct regions without complicated point-based supervision." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 474 + ], + "type": "text", + "content": "Query-Based Transformer Detectors. DETR [2] pioneered a new paradigm of Transformer detector for end-to-end object detection without any post-processing [1]. In DETR, a new representation, namely object query, aggregates the instance features and then yields a detection result for each instance object [15]. Following DETR, many voterists put efforts on the optimization of convergence and accuracy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 475, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 288, + 714 + ], + "type": "text", + "content": "Sun et al. [21] revealed that the main reason for slow convergence of DETR is attributed to the Transformer decoder, and they considered an encoder-only structure to alleviate such a problem. For in-depth understanding of the object query, one way is to generate a series of implicit spatial priors from queries to guide feature aggregation in cross-attention layers. SMCA [5] applied a Gaussian-like attention map to augment the query-concerned features spatially. The reference point concept was first introduced by Deformable DETR [31], where the sampling offsets are predicted by each reference point to perform deformable cross-attention. Following such a concept, Conditional DETR [16] reformulated the attention operation and rebuilt positional queries based on the reference points to facilitate extreme region discrimination. Another way is towards position-instantiation explicitly, where this position information enables to directly conduct positional query generation. Anchor DETR [25] utilized a predefined 2D anchor point " + }, + { + "bbox": [ + 46, + 475, + 288, + 714 + ], + "type": "inline_equation", + "content": "[cx, cy]" + }, + { + "bbox": [ + 46, + 475, + 288, + 714 + ], + "type": "text", + "content": " to explicitly capitalize on the spatial prior during cross-attention and box regression. DAB-DETR [13] extended such a 2D concept to" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 325, + 69, + 529, + 293 + ], + "blocks": [ + { + "bbox": [ + 325, + 69, + 529, + 293 + ], + "lines": [ + { + "bbox": [ + 325, + 69, + 529, + 293 + ], + "spans": [ + { + "bbox": [ + 325, + 69, + 529, + 293 + ], + "type": "image", + "image_path": "610de358f6711972cd0b18bdd81eb531a04351f72a5b205d48cb34f2440f488e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 300, + 547, + 378 + ], + "lines": [ + { + "bbox": [ + 305, + 300, + 547, + 378 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 547, + 378 + ], + "type": "text", + "content": "Figure 2. Illustration of SAP-DETR. Each object query in SAP-DETR is assigned to a specific grid region and initialized by the corner/center of the grid as its reference point. A learnable 4D coordinate represents the distance from the four sides of the box to the reference point. Both reference points and box sides are served as positional encodings added/concatenated to content embeddings. All embeddings are refined to predict target objects gradually." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 392, + 544, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 544, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 544, + 405 + ], + "type": "text", + "content": "a 4D anchor box " + }, + { + "bbox": [ + 306, + 392, + 544, + 405 + ], + "type": "inline_equation", + "content": "[cx, cy, w, h]" + }, + { + "bbox": [ + 306, + 392, + 544, + 405 + ], + "type": "text", + "content": " and refined it layer-by-layer." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 405, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 547, + 525 + ], + "type": "text", + "content": "The recent accelerating convergence methods are based on auxiliary queries for facilitating detector discrimination. DN-DETR [9] demonstrates the slow model convergence is mainly caused by the instability of bipartite matching, thus providing a denoising training to eliminate this issue. DINO [28] inherits this advance and further introduces negative queries to perform contrastive denoising. Group-DETR [4] proposes a group-wise one-to-many label assignment to match multiple positive object queries with more gradients for fast DETR convergence." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 525, + 547, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 645 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 645 + ], + "type": "text", + "content": "The most relevant approaches to ours are Point-DETR [3] and SAM-DETR [26, 27]. The former applied a point encoder for annotated point label infusion in teacher model, and the latter directly updated content embeddings by extracting salient points from image features for query-image semantic alignment. Unlike these concepts, we redefine the salient point from the perspective of the positive query's position and replace the center-concept prior with the query-specific position, thereby attending extreme regions, differentiating queries' saliency, and alleviating redundant predictions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 657, + 361, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 361, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 361, + 669 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "We propose SAP-DETR to bridge the gap between salient points and query-based detectors. Following DETR, the extracted image features are fed into Transformer encoder" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15541" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "after adding positional encodings, and then re-aggregated by object queries in Transformer decoder. In pursuit of the query-specific prior, we dispense a movable strategy for each query based on a fixed grid region. The query, whose reference region overlaps with ground truth objects, is allowed to predict the relative offsets from four sides of the bounding box to the points. Given the query-specific reference point and the proposal box sides, we propose salient point enhanced cross-attention mechanism to imbue query with spatial prior, thereby attending to extreme regions effectively. Additionally, we discuss two common issues in DETR-like models and address them for further improvements." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 223, + 248, + 235 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 223, + 248, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 248, + 235 + ], + "type": "text", + "content": "3.1. Salient Points-Based Object Detection" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": "Overview. Previous methods [13, 16, 25] normally decompose the object query into both content and position embeddings (queries), and form a center-based anchor point/box prior on the position ones. Unlike the central concept, we tile a fixed mesh-grid region, initialize their left-top corner as the reference points with 2D coordinate " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r} = \\{x, y\\} \\in [0,1]^2" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": ", and instantiate a learnable 4D offset distance " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "s = \\{\\ell, t, r, b\\} \\in [0,1]^4" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": " from the reference point to the sides of proposal bounding box for each object query. The object query can be referred as " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "q = \\{\\mathbf{e}; r, s\\}" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{e} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": " is the content embedding with " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": " dimension. Instead of regressing the center, width, and height of a bounding box, we follow FCOS [22] and directly supervise the 4D offset from the four sides of a bounding box to the reference point. The final box prediction is formulated as " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\hat{\\boldsymbol{b}} = \\{\\hat{x} - \\hat{\\ell}, \\hat{y} - \\hat{\\bar{t}}, \\hat{x} + \\hat{r}, \\hat{y} + \\hat{b}\\}" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": ". Ideally, we here fix the reference point " + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\{\\hat{x}, \\hat{y}\\} = \\{x, y\\}" + }, + { + "bbox": [ + 46, + 240, + 290, + 469 + ], + "type": "text", + "content": " (the movable update strategy is introduced in the next subsection) and only update the 4D box side prediction layer by layer. The prediction for each decoder layer can be calculated by" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 477, + 241, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 477, + 241, + 490 + ], + "spans": [ + { + "bbox": [ + 94, + 477, + 241, + 490 + ], + "type": "interline_equation", + "content": "\\Delta \\boldsymbol {s} _ {l} = \\operatorname {B o x H e a d} _ {l} (\\boldsymbol {s} _ {l - 1}, \\boldsymbol {e} _ {l - 1}, \\boldsymbol {r} _ {l - 1}),", + "image_path": "f65d4202672cd24eec94b68deba0be93cda4731cc3868b6050e19afcc7cc49d5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 72, + 492, + 263, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 492, + 263, + 506 + ], + "spans": [ + { + "bbox": [ + 72, + 492, + 263, + 506 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {s}} _ {l} = \\sigma \\left(\\sigma^ {- 1} \\left(\\boldsymbol {s} _ {l - 1}\\right) + \\Delta \\boldsymbol {s} _ {l}\\right), \\quad \\boldsymbol {s} _ {l} = \\operatorname {D e t a c h} (\\hat {\\boldsymbol {s}} _ {l}),", + "image_path": "d0a6fad1d61624bd76fa84010cc508e8831f08d85975ef049c97f68e0b29f2bb.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 63, + 510, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 510, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 63, + 510, + 287, + 533 + ], + "type": "interline_equation", + "content": "\\boldsymbol {r} _ {l} = \\hat {\\boldsymbol {r}} _ {l} = \\boldsymbol {r} _ {l - 1}, \\quad \\hat {\\boldsymbol {b}} _ {l} = \\left\\{\\hat {\\boldsymbol {r}} _ {l} - \\hat {\\boldsymbol {s}} _ {l} [: 2 ], \\hat {\\boldsymbol {r}} _ {l} + \\hat {\\boldsymbol {s}} _ {l} [2: ] \\right\\}, \\tag {1}", + "image_path": "2beccd91c1d274608d8e433e06bfb018c02abacdf2ed400944944d43e7539673.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "\\sigma^{-1}" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": " are the sigmoid and inverse sigmoid operation, respectively. " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "\\Delta s_{l}" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": " denotes the side offset prediction. " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "\\hat{s}_l" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "\\hat{r}_l" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{b}}_l" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": " are the predicted side distance, reference points, and box location from the " + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": " decoder layer, respectively. The BoxHead is the prediction head following the layer-" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 534, + 288, + 617 + ], + "type": "text", + "content": " decoder, which is independent between different decoder layers in our settings. Detach operation follows DAB-DETR [13]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": "During the training process, each query is only allowed to predict the bounding boxes that overlap its reference region. We adapt this rule into the one-to-one bipartite matching process via an inner matching cost " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{inner}}" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": ". Given " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " queries " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Q} = \\{\\pmb{q}_1,\\pmb{q}_2,\\dots ,\\pmb{q}_N\\}" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " ground truth objects " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{G} = \\{\\pmb{g}_1,\\pmb{g}_2,\\dots ,\\pmb{g}_M\\}" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{inner}}(\\pmb{g}_i,\\pmb{q}_j)" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " of each query-box pair is a step function to penalize the reference point " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{r}_j" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{q}_j" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " with value of " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{r}_j" + }, + { + "bbox": [ + 46, + 618, + 289, + 714 + ], + "type": "text", + "content": " is outside the bounding box of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "inline_equation", + "content": "g_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": ". We denote " + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "inline_equation", + "content": "i \\in [1, M]" + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "inline_equation", + "content": "j \\in [1, N]" + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": " as the index of query and ground truth, respectively. " + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": " can be viewed as a penalty cost, and default to " + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "inline_equation", + "content": "10^{5}" + }, + { + "bbox": [ + 304, + 72, + 547, + 120 + ], + "type": "text", + "content": ". The final permutation of the one-to-one label assignment is formulated as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 377, + 129, + 477, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 129, + 477, + 142 + ], + "spans": [ + { + "bbox": [ + 377, + 129, + 477, + 142 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n n e r}} \\left(\\boldsymbol {g} _ {i}, \\boldsymbol {q} _ {j}\\right) := \\mathbf {k} _ {\\boldsymbol {r} _ {j} \\notin \\boldsymbol {g} _ {i}},", + "image_path": "bf1420a5caedffb592145083be12cdda914b97fc3792c32b18fb7bc70bfae443.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 364, + 144, + 545, + 176 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 144, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 364, + 144, + 545, + 176 + ], + "type": "interline_equation", + "content": "\\hat {\\eta} = \\underset {\\eta \\in \\mathfrak {Y} _ {N}} {\\operatorname {a r g m i n}} \\sum_ {i} ^ {N} \\mathcal {L} _ {\\text {m a t c h}} + \\mathcal {L} _ {\\text {i n n e r}}, \\tag {2}", + "image_path": "de9339253465e099b61024f01ba208a170554a2ba58eddcb77decc80aecaab87.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{match}}" + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "text", + "content": " is the original pair-wise matching cost consist of both classification and localization costs [2]. " + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "inline_equation", + "content": "\\eta \\in \\mathfrak{V}_N" + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "text", + "content": " is a permutation of " + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 183, + 545, + 219 + ], + "type": "text", + "content": " elements for bipartite matching." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "type": "text", + "content": "Movable Reference Point. Due to the sparseness of the fixed reference point, some small and slender objects may be indistinguishable when there is no reference point inside these objects. Despite the bipartite matching forcing each object to be assigned to one object query, the positive query, whose reference point is outside the assigned bounding box, is unable to accurately regress the distance from each side by a value between 0 and 1. One straightforward solution is to adjust the locations of reference points inside the ground truth bounding boxes to ensure that each object can be detected by an inner reference point. Similar to the aforementioned box refinement, we first perform a movable reference point design to dynamically update the reference points of each query layer by layer. However, such a full-image point regression inevitably expands the search space as vast variable determinations, causing the final reference point to be trapped in an unexpected corner of the bounding box. To reduce the training search spaces, we scale the offset amplitude of points within their specific grid regions, as illustrated in Fig. 3. Such an operation limits the range of offset values, and hence prevents a large searching space. It is implemented by applying the sigmoid activation " + }, + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "type": "text", + "content": " and multiplying a scale factor " + }, + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "type": "inline_equation", + "content": "s_{\\mathrm{grid}}" + }, + { + "bbox": [ + 304, + 220, + 547, + 518 + ], + "type": "text", + "content": " whose value equals to the height and width of one grid. The update process of the reference points is formulated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 350, + 527, + 503, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 527, + 503, + 540 + ], + "spans": [ + { + "bbox": [ + 350, + 527, + 503, + 540 + ], + "type": "interline_equation", + "content": "\\Delta \\boldsymbol {r} _ {l} ^ {\\prime} = \\operatorname {P o i n t H e a d} _ {l} \\left(\\boldsymbol {s} _ {l - 1}, \\boldsymbol {e} _ {l - 1}, \\boldsymbol {r} _ {l - 1}\\right),", + "image_path": "63f145c9e515385473225126456ca240bcb39ade10dd70611aadc3496a551d35.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 355, + 543, + 545, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 543, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 355, + 543, + 545, + 556 + ], + "type": "interline_equation", + "content": "\\Delta \\boldsymbol {r} _ {l} = \\sigma \\left(\\sigma^ {- 1} \\left(\\boldsymbol {r} _ {l - 1} - \\boldsymbol {r} _ {0}\\right) + \\Delta \\boldsymbol {r} _ {l} ^ {\\prime}\\right), \\tag {3}", + "image_path": "dcf075b079658323a813989f4cb2f8f2121027d8820111915c53081625883c4f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 341, + 559, + 511, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 559, + 511, + 572 + ], + "spans": [ + { + "bbox": [ + 341, + 559, + 511, + 572 + ], + "type": "interline_equation", + "content": "\\hat {\\boldsymbol {r}} _ {l} = \\boldsymbol {r} _ {0} + \\Delta \\boldsymbol {r} _ {l} \\cdot \\boldsymbol {s} _ {\\text {g r i d}}, \\quad \\boldsymbol {r} _ {l} = \\operatorname {D e t a c h} (\\hat {\\boldsymbol {r}} _ {l}),", + "image_path": "875c3a0dd5e28cfb35bffcc3d06bfed2db8ef23431c47e4617348fe884a7735e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\Delta \\boldsymbol{r}_l'" + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\Delta \\boldsymbol{r}_l" + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": " are the predicted offsets from " + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}_l" + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": " to both " + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}_{l-1}" + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{r}_0" + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": " before the sigmoid activation " + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 306, + 580, + 545, + 605 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 611, + 515, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 515, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 515, + 623 + ], + "type": "text", + "content": "3.2. Salient Point Enhanced Cross-Attention" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "In cross-attention layers, existing center-based methods are limited to the attention on both center and sides of the ground truth bounding box, causing detector confusion among the queries with the same center and side attention. To this end, we expect the queries to focus on their specific regions based on the reference points, four box sides, and other conditional regions in different heads. Accordingly," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15542" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 289, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 289, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 289, + 167 + ], + "type": "image", + "image_path": "db807192e02719a82d755a7878de64a4f620ef8a0f63351e89cf8572332e9f7c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 175, + 289, + 242 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 289, + 242 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 289, + 242 + ], + "type": "text", + "content": "Figure 3. Movable reference point. The reference points are initialized by the center/corner points of the mesh-grid. Based on the inner loss, only the green dashed box can be predicted by the inner points when reference points are fixed. By moving the reference points within their grid, the blue dashed boxes can be detected accurately without extended searching space." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "text", + "content": "we consider an improved Gaussian [5] " + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{G}" + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "text", + "content": " and conditional attention [16] " + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\mathrm{peca}}" + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "text", + "content": " to enhance query specificity and spatially extreme region discrimination. The final attention map " + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\mathrm{cross}}" + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "text", + "content": " is the sum of the two attentions " + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_{\\mathrm{cross}} = \\mathbf{G} + \\mathbf{A}_{\\mathrm{peca}}" + }, + { + "bbox": [ + 46, + 252, + 287, + 301 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "content": "Side Directed Gaussian (SDG). Similar to the movable strategy, we enforce the predicted Gaussian attention to be inside the proposal bounding box to reduce the searching space. Given a reference point " + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "content": ", the offset scales " + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "inline_equation", + "content": "\\mathbf{o} \\in [-1,1]^2" + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "content": " heads are produced by a simple MLP with a tanh activation, and then multiply to the two sides of the proposal bounding box for head-specific point offset generation, where the direction is guided by the sign of the offset scales. The head-specific points are generated by Algorithm 1. For each head, the Gaussian-like spatial weight map " + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "content": " effecting on each pixel " + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 301, + 290, + 433 + ], + "type": "text", + "content": " of context features is then formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 72, + 441, + 287, + 473 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 441, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 72, + 441, + 287, + 473 + ], + "type": "interline_equation", + "content": "G _ {i} (x, y) = \\exp \\left(- \\frac {\\left(x - c _ {w , i}\\right) ^ {2}}{v _ {w , i} ^ {2}} - \\frac {\\left(y - c _ {h , i}\\right) ^ {2}}{v _ {h , i} ^ {2}}\\right). \\tag {4}", + "image_path": "90f4969432c95f931bf27c5a116eb13cf6fdb89008f7c697ff574739f85d3590.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 479, + 289, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 289, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 289, + 624 + ], + "type": "text", + "content": "Point Enhanced Cross-Attention (PECA). As aforementioned, the semantic class for the query is closely related to its referenced location in our SAP-DETR. To enhance the correlation between queries and their references, we concatenate the locations to the content queries after the sinusoidal positional encoding (PE). Take a close look at the conditional attention [16], we find that the linear positional embedding mostly focuses on one box side in each attention head. So we introduce a more straightforward attention mechanism, where the four side coordinates are concatenated and assigned to the corresponding head for side attention. The process of PECA is formulated as" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 628, + 287, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 628, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 52, + 628, + 287, + 662 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} \\mathbf {A} _ {\\text {p e c a}} & = \\mathbf {e} _ {q} \\mathbf {e} _ {k} ^ {\\top} + \\mathbf {T P E} (\\boldsymbol {r} _ {q}) \\mathbf {P E} (\\boldsymbol {r} _ {k}) ^ {\\top} \\\\ & + \\mathbf {T} g (\\mathbf {P E} (\\boldsymbol {r} _ {q} - \\{\\ell , t \\}, \\boldsymbol {r} _ {q} + \\{r, b \\})) \\mathbf {P E} (\\boldsymbol {r} _ {k}) ^ {\\top}, \\end{array} \\tag {5}", + "image_path": "d854a74ded1ed3e45ca9d429f13a23e9ebd6701778ecc082faab4b4d780a6ad7.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": " is a linear layer mapping 4D-PE into 2D to keep channel dimension consistency. T [16] is a scaling transformation matrix. More details of T and comparison with conditional cross-attention are available in Appendix C." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 457, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 457, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 457, + 83 + ], + "type": "text", + "content": "Algorithm 1 Side Directed Gaussian" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 87, + 522, + 98 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 87, + 522, + 98 + ], + "spans": [ + { + "bbox": [ + 306, + 87, + 522, + 98 + ], + "type": "text", + "content": "Input: Content embedding e, reference point " + }, + { + "bbox": [ + 306, + 87, + 522, + 98 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 306, + 87, + 522, + 98 + ], + "type": "text", + "content": " and box s." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 98, + 547, + 120 + ], + "type": "text", + 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do" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "type": "text", + "content": "3: Select the index of direction guided by the sign of offset scale, " + }, + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "type": "inline_equation", + "content": "\\{a,b\\} = \\mathrm{sgn}(\\mathbf{o}_i) + \\{1,2\\}" + }, + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "type": "inline_equation", + "content": "a,b\\in \\{0,1,2,3\\}" + }, + { + "bbox": [ + 311, + 152, + 545, + 175 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 311, + 175, + 545, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 175, + 545, + 197 + ], + "spans": [ + { + "bbox": [ + 311, + 175, + 545, + 197 + ], + "type": "text", + "content": "4: According to the index of direction, predict head-specific point, " + }, + { + "bbox": [ + 311, + 175, + 545, + 197 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i = \\mathbf{o}_i\\cdot \\mathbf{s}[a,b] + \\mathbf{r}" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 311, + 198, + 352, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 198, + 352, + 206 + ], + "spans": [ + { + "bbox": [ + 311, + 198, + 352, + 206 + ], + "type": "text", + "content": "5: end for" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 311, + 207, + 430, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 207, + 430, + 218 + ], + "spans": [ + { + "bbox": [ + 311, + 207, + 430, + 218 + ], + "type": "text", + "content": "6: return " + }, + { + "bbox": [ + 311, + 207, + 430, + 218 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i, \\mathbf{v}_i, \\forall i = 1, \\dots, H" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 244, + 498, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 244, + 498, + 258 + ], + "spans": [ + { + "bbox": [ + 306, + 244, + 498, + 258 + ], + "type": "text", + "content": "3.3. SAP-DETR with Denoising Strategy" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 263, + 547, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 547, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 547, + 407 + ], + "type": "text", + "content": "To further explore the capability of our proposed SAP-DETR, we develop SAP-DN-DETR and SAP-DINO-DETR by adding the denoising auxiliary loss [9,28] into the training process. In the denoised SAP-DETR, the main difference from both DN-DETR and DINO lies in the noise design. Instead of the center point, we perform the box jittering and randomly sample a point from the intersection region between the original bounding box and the jittering one as the reference point. As the denoising strategy only serves as an auxiliary training loss increasing the training cost, the variants of denoising models are test-free whose Params and GFLOPs are the same as SAP-DETR models." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 421, + 432, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 421, + 432, + 434 + ], + "spans": [ + { + "bbox": [ + 306, + 421, + 432, + 434 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 441, + 439, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 439, + 454 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 439, + 454 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "text", + "content": "We conduct the experiments on the COCO 2017 [12] object detection dataset, containing about 118K training images and 5K validation images. All models are evaluated by the standard COCO evaluation metrics. We follow the vanilla DETR [2] structure that consists of a CNN backbone, a stack of Transformer encoder-decoder layers, and two prediction heads for class label and bounding box prediction. We use ImageNet-pretrained ResNet [7] as our backbone, and report results based on the ResNet and its " + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "inline_equation", + "content": "\\times 1/16" + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "text", + "content": "-resolution extension ResNet-DC. Unlike DAB-DETR [13] sharing box and label head for each layer, we share the class head except the first layer and use an independent box head for the box regression of each layer (for more details please refer to Appendix D). As the mesh-grid initialization for reference points in SAP-DETR, we consider the number of queries " + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "text", + "content": " as a perfect square for uniform distribution. Unless otherwise specified, we use " + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "inline_equation", + "content": "N = 400" + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "text", + "content": " queries in the experiments. Precisely, we also provide a comparison under " + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "inline_equation", + "content": "N = 300" + }, + { + "bbox": [ + 304, + 460, + 547, + 688 + ], + "type": "text", + "content": " in Tab. 2, the standard setting in DETR-like models." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "We adopt two different Transformer structures for experiments where a 3-layer encoder-decoder stack is evaluated to" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15543" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 69, + 232, + 167 + ], + "blocks": [ + { + "bbox": [ + 115, + 69, + 232, + 167 + ], + "lines": [ + { + "bbox": [ + 115, + 69, + 232, + 167 + ], + "spans": [ + { + "bbox": [ + 115, + 69, + 232, + 167 + ], + "type": "image", + "image_path": "e67c17b52b62bc18f59407f49da518ec9d46208e46c8ed65384428ba5d8ecd32.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 178, + 174, + 414, + 185 + ], + "lines": [ + { + "bbox": [ + 178, + 174, + 414, + 185 + ], + "spans": [ + { + "bbox": [ + 178, + 174, + 414, + 185 + ], + "type": "text", + "content": "Figure 4. Comparison of performance and training losses curves." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 236, + 69, + 355, + 167 + ], + "blocks": [ + { + "bbox": [ + 236, + 69, + 355, + 167 + ], + "lines": [ + { + "bbox": [ + 236, + 69, + 355, + 167 + ], + "spans": [ + { + "bbox": [ + 236, + 69, + 355, + 167 + ], + "type": "image", + "image_path": "c4e4471d6732af893721aadaca57cebf551f6985172900d817e0947edfa5e3c0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 357, + 68, + 478, + 167 + ], + "blocks": [ + { + "bbox": [ + 357, + 68, + 478, + 167 + ], + "lines": [ + { + "bbox": [ + 357, + 68, + 478, + 167 + ], + "spans": [ + { + "bbox": [ + 357, + 68, + 478, + 167 + ], + "type": "image", + "image_path": "a2fba28d8751276d87d046916bae807f8b5b51e25a59642266ec0fb9122b2506.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 198, + 289, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 289, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 289, + 307 + ], + "type": "text", + "content": "demonstrate our lightweight model efficacy compared with the traditional CNN detectors, and a 6-layer encoder-decoder stack is aligned with previous DETR variants to investigate the performance of large model. Both are trained on two training schemes: the 12-epoch and 36-epoch schemes with a learning rate drop after 11 and 30 epochs, respectively. All models are trained on the Nvidia A100 GPUs with batch size of 16 and 8 for ResNet and ResNet-DC, respectively. For more training details, please refer to Appendix F." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 312, + 133, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 133, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 133, + 324 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 331, + 288, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 403 + ], + "type": "text", + "content": "As shown in Tab. 1 and Tab. 2, we comprehensively compare our proposed SAP-DETR with the traditional CNN detectors [18], the original DETR [2], and other DETR-like detectors [5, 13, 16, 25, 26, 31] on COCO 2017 validation dataset. For in-depth analysis, we conduct the comparison in two aspects: model convergence and efficacy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "text", + "content": "Model Convergence. Compared with traditional CNN detectors, Transformer detectors are always subject to laborious training time. For example, under the same 12-epoch training scheme, Faster RCNN [18] still achieves good performance, but the mainstream DETR-like models may suffer from inadequate training and perform poorly without the help of auxiliary losses [9]. Under the 12-epoch training scheme, our proposed SAP-DETR can accelerate model convergence significantly, boosting DAB-DETR [13] by 3.9 AP and 2.7 AP on 3-layer and 6-layer encoder-decoder structures, respectively. Compared with the current SoTA, our SAP-DETR also outperforms SAM-DETR [26] by " + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "inline_equation", + "content": "\\sim 1.3" + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "text", + "content": " AP, with reducing " + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "inline_equation", + "content": "\\sim 17\\%" + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "text", + "content": " parameters and " + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "inline_equation", + "content": "\\sim 10\\%" + }, + { + "bbox": [ + 46, + 402, + 288, + 629 + ], + "type": "text", + "content": " GFLOPs. Take a close look at the training process, as illustrated in Fig. 4, SAP-DETR conducts with rapid descent curves in both classification and box regression losses. Notably, there is a large margin in classification loss between ours and SoTA methods, which is benefited from the query-specific reference point, hence boosting model performance in early epochs." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Model Efficacy. To analyze model efficacy, we report results on long training epochs and high-resolution features in Tab. 1. Under the 36-epoch training scheme, SAP-DETR achieves superior performance among all single-scale Transformer detectors, especially on middle and large targets. For example, SAP-DETR boosts DAB-DETR by " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "2.0\\mathrm{AP}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "4.1\\mathrm{AP}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " with 3-layer models, " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "1.0\\mathrm{AP}_{\\mathrm{M}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "1.9\\mathrm{AP}_{\\mathrm{L}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "text", + "content": "6-layer models, which further verifies the effectiveness of our proposed salient point concept for overlapping object detection. Along with layer increase, a deficient upper-bound of SAM-DETR is exposed, with obviously lower 0.5 AP promotion compared to our 1.0 AP improvement. Persuasively, we also report the 50-epoch training results based on the 300-query setting. To align with our mesh-grid initialization strategy, we tile a " + }, + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "inline_equation", + "content": "17 \\times 18" + }, + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "text", + "content": " mesh-grid (306 queries) for each reference point initialization. Tab. 2 shows our main results and the most representative approaches with their original reported performance. Notably, SAP-DETR outperforms the current SoTAs with comparable costs based on all backbones. With low-resolution features (" + }, + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "inline_equation", + "content": "\\times 1/32" + }, + { + "bbox": [ + 304, + 198, + 547, + 366 + ], + "type": "text", + "content": "), it significantly boosts both middle and large object detection accuracy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "type": "text", + "content": "Combine with Other Fast Convergence Methods. As shown in Tab. 3, we compare our SAP-DETR variants with the current fast convergence methods [4, 9, 28]. With such a subtle modification, our SAP-DETR (grey rows) results in a significant performance improvement compared with the original methods (white rows). Under the 12-epoch training scheme, there exist 0.5-1.9 AP improvements on DN-DETR [9] and 0.7-1.6 AP improvements on Group-DETR [4], but the promotions are slightly reduced when implemented on DINO [28]. We hypothesise that there exists the same effect between the negative query of contrastive denoising [28] and our query-salient reference point. Moreover, we observe that the performance improvements largely originate from the large object detection, especially based on ResNet-DC5 family backbones. We speculate that DETR may prefer the high-resolution features (" + }, + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "type": "inline_equation", + "content": "\\times 1/16" + }, + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "type": "text", + "content": ") rather than the low-resolution ones (" + }, + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "type": "inline_equation", + "content": "\\times 1/32" + }, + { + "bbox": [ + 304, + 366, + 548, + 594 + ], + "type": "text", + "content": "), and our SAP-DETR can distinguish the salient points accurately on the high-resolution, thereby taking full advantage of the large object detection." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 602, + 400, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 602, + 400, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 602, + 400, + 615 + ], + "type": "text", + "content": "4.3. 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The proposed salient point concept based on content embeddings improves the performance from 32.3 AP to 33.5" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 478, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 478, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 478, + 713 + ], + "type": "text", + "content": "1https://github.com/facebookresearch/detectron2" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15544" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 533, + 244 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 533, + 244 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 533, + 244 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 533, + 244 + ], + "type": "table", + "html": "
Method#Epochs#Params(M)GFLOPsAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
3-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36338215.828.015.45.316.724.6
Deformable DETR-R50 [31]36307737.157.639.418.340.851.6
SMCA-DETR-R50 [5]12 / 36--28.8 / 37.748.1 / 58.729.9 / 40.113.8 / 19.431.3 / 40.541.3 / 54.8
Conditional DETR-R50 [16]12 / 36408229.6 / 37.148.7 / 57.930.7 / 39.013.0 / 17.632.3 / 40.343.1 / 55.0
Anchor DETR-R50 [25]12 / 36317930.8 / 37.651.1 / 58.731.8 / 39.714.3 / 18.834.1 / 41.544.3 / 53.5
DAB-DETR-R50 [13]12 / 36348332.3 / 39.051.3 / 58.634.0 / 41.815.7 / 20.035.2 / 42.545.7 / 56.0
SAM-DETR-w/SMCA-R50 [26]12 / 36418935.1 / 40.454.7 / 60.736.7 / 42.716.0 / 20.238.4 / 44.452.1 / 58.3
SAP-DETR-R50 (Ours)12 / 36368436.2 / 41.256.2 / 61.637.9 / 43.416.4 / 21.039.5 / 44.553.8 / 60.1
6-Layer Encoder-Decoder Transformer Neck with ResNet-50 Backbone
DETR-R50 [2]36428914.024.414.04.213.722.5
Deformable DETR-R50 [31]36348138.058.240.418.541.754.2
SMCA-DETR-R50 [5]12 / 36--32.4 / 40.152.3 / 61.434.0 / 42.815.5 / 20.334.9 / 43.347.7 / 57.1
Conditional DETR-R50 [16]12 / 36449033.1 / 40.253.0 / 61.034.8 / 42.414.5 / 19.935.9 / 43.549.2 / 58.8
Anchor DETR-R50 [25]12 / 36378533.7 / 39.754.5 / 60.535.1 / 41.915.6 / 19.937.3 / 43.549.8 / 57.3
DAB-DETR-R50 [13]12 / 36449234.9 / 41.055.5 / 61.736.4 / 43.416.2 / 21.338.4 / 44.751.5 / 58.9
SAM-DETR-w/SMCA-R50 [26]12 / 365910536.2 / 40.957.2 / 62.237.4 / 43.116.1 / 20.139.8 / 44.755.3 / 60.7
SAP-DETR-R50 (Ours)12 / 36479437.5 / 42.258.5 / 62.739.2 / 44.617.3 / 22.640.6 / 45.755.4 / 60.8
", + "image_path": "f0e495db48712226ee91ed149febaa6e161ba66f364fb9954946855d4923b05a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 60, + 287, + 533, + 559 + ], + "blocks": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": "Table 1. Comparison between Transformer necks. Based on ResNet-50 backbone, all models are trained by the official source codes with their original settings and evaluated on COCO val2017. All models uses 400 queries except Anchor DETR, while Anchor DETR uses 200 queries with 2 pattern embeddings. GFLOPs and Params are measured by " + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\text{Detectron}^2" + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 287, + 533, + 559 + ], + "lines": [ + { + "bbox": [ + 60, + 287, + 533, + 559 + ], + "spans": [ + { + "bbox": [ + 60, + 287, + 533, + 559 + ], + "type": "table", + "html": "
Method#Epochs#Params(M)GFLOPsAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)Infer. \\( Time(s / img)^{\\dagger} \\)
ResNet-50 Backbone
Faster RCNN-FPN-R50 [10, 18]1084218042.062.145.526.645.553.40.039
DETR-R50 [2]500418642.062.444.220.545.861.10.040
Deformable DETR-R50 [31]50347839.459.642.320.643.055.50.043
SMCA-DETR-R50 [5]50428641.0--21.944.359.10.045
Conditional DETR-R50 [16]50449040.961.843.320.844.659.20.057
Anchor DETR-R50 [25]50398542.163.144.922.346.260.00.050
DAB-DETR-R50 [13]5044\\( 90^† \\)42.263.144.721.545.760.30.059
SAM-DETR-w/SMCA-R50 [26]505810041.863.243.922.145.960.90.065
SAP-DETR-R50 (Ours)50479243.163.845.422.947.162.10.063
ResNet-101 Backbone
Faster RCNN-FPN-R101 [10, 18]1086024644.063.947.827.248.156.00.050
DETR-R101 [2]5006015243.563.846.421.948.061.80.066
Conditional DETR-R101 [16]506315642.863.746.021.746.660.90.070
Anchor DETR-R101 [25]505815043.564.346.623.247.761.40.068
DAB-DETR-R101 [13]5063\\( 157^† \\)43.563.946.623.647.361.50.072
SAP-DETR-R101 (Ours)506715844.464.947.124.148.763.10.078
DC5-ResNet-50 Backbone
DETR-DC5-R50 [2]5004118743.363.145.922.547.361.10.087
Conditional DETR-DC5-R50 [16]504419543.864.446.724.047.660.70.093
Anchor DETR-DC5-R50 [25]503915144.264.747.524.748.260.60.069
DAB-DETR-DC5-R50 [13]5044\\( 194^† \\)44.565.147.725.348.262.30.094
SAM-DETR-w/SMCA-DC5-R50 [26]505821045.065.447.926.249.063.30.126
SAP-DETR-DC5-R50 (Ours)504719746.065.548.926.450.262.60.116
DC5-ResNet-101 Backbone
DETR-DC5-R101 [2]5006025344.964.747.723.749.562.30.101
Conditional DETR-DC5-R101 [16]506326245.065.648.426.148.962.80.105
Anchor DETR-DC5-R101 [25]505822745.165.748.825.849.461.60.083
DAB-DETR-DC5-R101 [13]5063\\( 263^† \\)45.865.949.327.049.863.80.110
SAP-DETR-DC5-R101 (Ours)506726646.966.750.527.951.364.30.130
", + "image_path": "af9d626399bf3a1424d9d21efba19a0704c74c33aff6a018ede81bfd149db747.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 563, + 547, + 598 + ], + "lines": [ + { + "bbox": [ + 46, + 563, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 547, + 598 + ], + "type": "text", + "content": "Table 2. Comparison of Transformer necks with 300 queries on COCO val2017. All results are reported from their original paper. All models uses 300 queries except Anchor DETR, while Anchor DETR uses 100 queries with 3 pattern embeddings. All inference speeds are measured by a single Nvidia A100 GPU. † denotes the results are measured by ourselves." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 606, + 289, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 606, + 289, + 703 + ], + "spans": [ + { + "bbox": [ + 46, + 606, + 289, + 703 + ], + "type": "text", + "content": "AP compared to baseline DAB-DETR (row 8-9). Such a query-specific spatial prior enables queries to attend to their expected region from content features (see Figures in Appendix G) and reduces the false detection rate on occluded and partial objects (see Fig. 1(d)), hence boosting detection performance on middle and large objects. However, there exists a drop in small object detection (15.7 APs vs. 14.3 APs), for which we consider that the failure is mainly caused" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "content": "by the query sparsity. 2). Therefore, the movable strategy is applied to alleviate the constraint, improving the final model by " + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "inline_equation", + "content": "1.0\\mathrm{AP}" + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "inline_equation", + "content": "0.6\\mathrm{AP}_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "content": " (row 1 and 6). 3). Compared with the final model, the inner loss greatly improves the performance on high-quality " + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{75}" + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "content": " and large objects " + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{L}}" + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "content": " detection (row 1 and 7), with just a slight drop on low-quality object " + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 304, + 606, + 547, + 703 + ], + "type": "text", + "content": ". That is reasonable because the outside reference points are unable to localize objects accurately, and this phenomenon" + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15545" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 523, + 159 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 523, + 159 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 523, + 159 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 523, + 159 + ], + "type": "table", + "html": "
BackboneEpochw/ SAPDN-DETR [9]DINO (Single-Scale) [28]Group DETR [4]
AP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APLAP / AP50 / AP75APS / APM / APL
R5012✓(Ours)38.3 / 58.6 / 40.518.4 / 41.6 / 57.139.7 / 58.3 / 42.419.1 / 43.7 / 57.139.1 / - / -19.7 / 42.5 / 56.8
39.5 / 59.7 / 41.518.7 / 42.8 / 59.040.0 / 60.1 / 42.120.2 / 43.4 / 58.539.8 / 60.2 / 42.020.2 / 43.5 / 58.6
R10112✓(Ours)40.5 / 60.8 / 43.019.3 / 44.3 / 59.641.9 / 60.8 / 44.422.5 / 46.3 / 59.5- / - / -- / - / -
41.0 / 61.2 / 43.419.8 / 45.3 / 60.041.5 / 61.4 / 43.620.3 / 45.2 / 60.041.1 / 61.5 / 43.420.5 / 45.5 / 59.4
R50-DC12✓(Ours)41.7 / 61.4 / 44.121.2 / 45.0 / 60.243.6 / 61.4 / 47.024.8 / 47.3 / 59.541.9 / - / -23.3 / 45.6 / 58.4
43.6 / 62.5 / 46.223.3 / 47.3 / 61.044.0 / 63.1 / 46.524.8 / 47.3 / 61.143.9 / 63.2 / 46.824.5 / 47.6 / 61.3
R101-DC12✓(Ours)43.4 / 61.9 / 47.224.8 / 46.8 / 59.445.4 / 63.5 / 49.226.4 / 49.5 / 61.1- / - / -- / - / -
44.6 / 63.9 / 48.025.5 / 48.9 / 62.545.6 / 64.5 / 48.725.0 / 49.7 / 62.544.4 / 63.9 / 47.425.9 / 48.5 / 61.4
", + "image_path": "20d6ddd9750f06eeb1fa780dc674d1a5a429f28f28f646e61a1b317c601627f8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 73, + 186, + 520, + 262 + ], + "blocks": [ + { + "bbox": [ + 66, + 163, + 526, + 175 + ], + "lines": [ + { + "bbox": [ + 66, + 163, + 526, + 175 + ], + "spans": [ + { + "bbox": [ + 66, + 163, + 526, + 175 + ], + "type": "text", + "content": "Table 3. Comparison with denoised methods on COCO dataset based on the 12-epoch training schedule and 300 object queries." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 186, + 520, + 262 + ], + "lines": [ + { + "bbox": [ + 73, + 186, + 520, + 262 + ], + "spans": [ + { + "bbox": [ + 73, + 186, + 520, + 262 + ], + "type": "table", + "html": "
CommentMovableInner LossPECASDGAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
SAP-DETR (Ours)✓✓✓✓36.256.237.916.439.553.8
-SDG✓✓✓35.656.236.916.338.952.7
-PECA✓✓✓34.855.536.015.737.352.0
-PECA & SDG✓✓34.054.935.315.036.751.5
-Movable✓✓✓35.255.436.815.838.553.8
-Inner Loss✓✓✓35.956.337.416.239.352.5
DAB-DETR (Baseline)----32.351.334.015.735.245.7
+Salient Point Concept----33.554.335.114.336.551.0
", + "image_path": "32be50eeddec82a689fc94ef01756152c3c617029bb5f1e4522e5711f0a553dd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 289, + 287, + 331 + ], + "blocks": [ + { + "bbox": [ + 225, + 265, + 367, + 277 + ], + "lines": [ + { + "bbox": [ + 225, + 265, + 367, + 277 + ], + "spans": [ + { + "bbox": [ + 225, + 265, + 367, + 277 + ], + "type": "text", + "content": "Table 4. Ablation on each components" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 289, + 287, + 331 + ], + "lines": [ + { + "bbox": [ + 48, + 289, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 48, + 289, + 287, + 331 + ], + "type": "table", + "html": "
Inner Cost (Linner)Movable within Grid (sgrid)APAPSAPMAPL
35.917.038.852.7
✓26.311.328.039.5
✓✓36.216.439.553.8
", + "image_path": "bfe2dfcf6438eb46ef01ad8830cf28ffb81daf459a4571ee5e1b0268a7e20227.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 48, + 354, + 287, + 396 + ], + "blocks": [ + { + "bbox": [ + 89, + 338, + 244, + 348 + ], + "lines": [ + { + "bbox": [ + 89, + 338, + 244, + 348 + ], + "spans": [ + { + "bbox": [ + 89, + 338, + 244, + 348 + ], + "type": "text", + "content": "Table 5. Ablation on scaling factor of grid" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 354, + 287, + 396 + ], + "lines": [ + { + "bbox": [ + 48, + 354, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 48, + 354, + 287, + 396 + ], + "type": "table", + "html": "
PECAScaling Factor of SDGAPAPSAPMAPL
33.614.736.050.7
✓35.717.538.852.6
✓✓36.216.439.553.8
", + "image_path": "3854a99cdefcd33b32e9cc587580d384c38233fb149d2d205dd74e8137192ae2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 404, + 246, + 415 + ], + "lines": [ + { + "bbox": [ + 88, + 404, + 246, + 415 + ], + "spans": [ + { + "bbox": [ + 88, + 404, + 246, + 415 + ], + "type": "text", + "content": "Table 6. Ablation on scaling factor of SDG" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "type": "text", + "content": "always exists in large objects. 4). For salient point enhanced cross-attention, both SDG and PECA serve as the essential components, independently emerging 0.8 AP and 1.6 AP improvements compared to the standard model (rows 2-4). Interestingly, there exists an effectiveness overlap on small objects, with only " + }, + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{AP}_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 424, + 287, + 532 + ], + "type": "text", + "content": " improvement when adding SDG to the equipped PECA model (row 1 and 2). We argue that the Gaussian-like map of SDG might be easily overlapped with PECA on small objects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 715 + ], + "type": "text", + "content": "Scaling Factor of Movable Strategy. We perform an ablation study on the scaling factor of the movable strategy and further investigate the effectiveness of the inner cost in Tab. 5. Notably, it is observed that there exists a conflict between the inner loss and the global search strategy, behaving a sharp drop when only reserving the inner loss. Furthermore, searching within the grid enables the detector to more attend to small objects and avoid a drastic deterioration in normal object detection. See Appendix E for more detailed analyses. Scaling Factor of SDG. We also compare our side-directed manner with the standard offset prediction method in Tab. 6. Based on PECA, the side-directed scaling factor may limit the detector on small object detection but significantly promote the performance on other objects. This phenomenon would be broken without the help of PECA in which a preci" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 290, + 545, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 339 + ], + "type": "text", + "content": "itous decline is emerged on all-scale object detection (row 5 in Tab. 4 vs. row 1 in Tab. 6). We hypothesise that it because the predicted reference points may be outside of the proposal boxes, or even the region of the image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 350, + 378, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 378, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 378, + 363 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 372, + 547, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 547, + 539 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 547, + 539 + ], + "type": "text", + "content": "In this paper, we propose SAP-DETR for promoting model convergence by treating object detection as a transformation from the salient points to the instance objects. Our SAP-DETR explicitly initializes a query-specific reference point for each object query, gradually aggregates them into an instance object, and predicts the distance from each side of the bounding box. By speedily attending to the query-specific region and other extreme regions from contextual image features, it thus can effectively bridge the gap between the salient points and the query-based Transformer detector. Our extensive experiments have demonstrated that SAP-DETR achieves superior model convergence speed. With the same training settings, our proposed SAP-DETR outperforms SoTA approaches with large margins." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 552, + 389, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 389, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 389, + 564 + ], + "type": "text", + "content": "6. Future Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 644 + ], + "type": "text", + "content": "This point-based design for DETR-like models also comes with remaining issues, in particular regarding training with deformable attention, multi-scale features, and negative query design. Following current center-based methods working for similar issues, we expect future work to successfully address them for point-based design of SAP-DETR." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 657, + 408, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 408, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 408, + 670 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "We thank the Lenovo Research AI Master platform for computing GPU supports without which this work would not be possible." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15546" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. 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In ICLR, 2020. 2, 3, 6, 7, 10" + } + ] + } + ], + "index": 33 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15547" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SCADE_ NeRFs from Space Carving With Ambiguity-Aware Depth Estimates/cb201944-e311-4584-9847-096959c3a596_content_list.json b/2023/SCADE_ NeRFs from Space Carving With Ambiguity-Aware Depth Estimates/cb201944-e311-4584-9847-096959c3a596_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..51d710f34297cd85e72c821eca90676b6f5f0a0f --- /dev/null +++ b/2023/SCADE_ NeRFs from Space Carving With Ambiguity-Aware Depth Estimates/cb201944-e311-4584-9847-096959c3a596_content_list.json @@ -0,0 +1,1770 @@ +[ + { + "type": "text", + "text": "SCADE: NeRFs from Space Carving with Ambiguity-Aware Depth Estimates", + "text_level": 1, + "bbox": [ + 94, + 114, + 875, + 138 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mikaela Angelina Uy $^{1,2}$ Ricardo Martin-Brualla $^{2}$ Leonidas Guibas $^{1,2}$ Ke Li $^{2,3}$", + "bbox": [ + 158, + 148, + 803, + 170 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Stanford University $^{2}$ Google $^{3}$ Simon Fraser University", + "bbox": [ + 241, + 174, + 723, + 194 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f95b9fa5adb6316ff5da22e4504071a144ea972361b019bf087b8333209ab4ed.jpg", + "image_caption": [ + "Figure 1. SCADE Overview. We present SCADE, a novel technique for NeRF reconstruction under sparse, unconstrained views for in-the-wild indoor scenes. We leverage on generalizable monocular depth priors and address to represent the inherent ambiguities of monocular depth by exploiting our ambiguity-aware depth estimates (left). Our approach accounts for multimodality of both distributions using our novel space carving loss that seeks to disambiguate and find the common mode to fuse the information between different views (middle). SCADE enables better photometric reconstruction especially in highly ambiguous scenes, e.g. non-opaque surfaces (right)." + ], + "image_footnote": [], + "bbox": [ + 109, + 202, + 864, + 411 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 491, + 313, + 507 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural radiance fields (NeRFs) have enabled high fidelity 3D reconstruction from multiple 2D input views. However, a well-known drawback of NeRFs is the less-than-ideal performance under a small number of views, due to insufficient constraints enforced by volumetric rendering. To address this issue, we introduce SCADE, a novel technique that improves NeRF reconstruction quality on sparse, unconstrained input views for in-the-wild indoor scenes. To constrain NeRF reconstruction, we leverage geometric priors in the form of per-view depth estimates produced with state-of-the-art monocular depth estimation models, which can generalize across scenes. A key challenge is that monocular depth estimation is an ill-posed problem, with inherent ambiguities. To handle this issue, we propose a new method that learns to predict, for each view, a continuous, multimodal distribution of depth estimates using conditional Implicit Maximum Likelihood Estimation (cIMLE). In order to disambiguate exploiting multiple views, we introduce an original space carving loss that guides the NeRF representation to fuse multiple hypothesized depth maps from each view and distill from them a common geometry that is consistent with all views. Experiments show that our approach enables higher fidelity novel view synthesis from sparse views. Our project page can be found at scade-spacecarving-nerfs.github.io.", + "bbox": [ + 73, + 530, + 473, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 491, + 632, + 507 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural radiance fields (NeRF) [24] have enabled high fidelity novel view synthesis from dozens of input views. Such number of views are difficult to obtain in practice, however. When given only a small number of sparse views, vanilla NeRF tends to struggle with reconstructing shape accurately, due to inadequate constraints enforced by the volume rendering loss alone.", + "bbox": [ + 496, + 511, + 893, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shape priors can help remedy this problem. Various forms of shape priors have been proposed for NeRFs, such as object category-level priors [13], and handcrafted data-independent priors [25]. The former requires knowledge of category labels and is not applicable to scenes, and the latter is agnostic to the specifics of the scene and only encodes low-level regularity (e.g., local smoothness). A form of prior that is both scene-dependent and category-agnostic is per-view monocular depth estimates, which have been explored in prior work [6, 32]. Unfortunately, monocular depth estimates are often inaccurate, due to estimation errors and inherent ambiguities, such as albedo vs. shading (cf. check shadow illusion), concavity vs. convexity (cf. hollow face illusion), distance vs. scale (cf. miniature cinematography), etc. As a result, the incorrect or inconsistent priors imposed by such depth estimates may mislead the NeRF into reconstructing incorrect shape and produce artifacts in the generated views.", + "bbox": [ + 496, + 618, + 895, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we propose a method that embraces the uncertainty and ambiguities present in monocular depth esti", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16518", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mates, by modelling a probability distribution over depth estimates. The ambiguities are retained at the stage of monocular depth estimation, and are only resolved once information from multiple views are fused together. We do so with a principled loss defined on probability distributions over depth estimates for different views. This loss selects the subset of modes of probability distributions that are consistent across all views and matches them with the modes of the depth distribution along different rays as modelled by the NeRF. It turns out that this operation can be interpreted as a probabilistic analogue of classical depth-based space carving [17]. For this reason, we dub our method Space Carving with Ambiguity-aware Depth Estimates, or SCADE for short.", + "bbox": [ + 75, + 90, + 472, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to prior approaches of depth supervision [6,32] that only supervise the moments of NeRF's depth distribution (rather than the modes), our key innovation is that we supervise the modes of NeRF's depth distribution. The supervisory signal provided by the former is weaker than the latter, because the former only constrains the value of an integral aggregated along the ray, whereas the latter constrains the values at different individual points along the ray. Hence, the supervisory signal provided by the former is 2D (because it integrates over a ray), whereas the supervisory signal provided by the our method is 3D (because it is point-wise) and thus can be more fine-grained.", + "bbox": [ + 75, + 282, + 472, + 458 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An important technical challenge is modelling probability distributions over depth estimates. Classical approaches use simple distributions with closed-form probability densities such as Gaussian or Laplace distributions. Unfortunately these distributions are not very expressive, since they only have a single mode (known as \"unimodal\") and have a fixed shape for the tails. Since each interpretation of an ambiguous image should be a distinct mode, these simple unimodal distributions cannot capture the complex ambiguities in depth estimates. Naive extensions like a mixture of Gaussians are also not ideal because some images are more ambiguous than others, and so the number of modes needed may differ for the depth estimates of different images. Moreover, learning such a mixture requires backpropagating through E-M, which is nontrivial. Any attempt at modifying the probability density to make it capable of handling a variable number of modes can easily run into an intractable partition function [4, 10, 31], which makes learning difficult because maximum likelihood requires the ability to evaluate the probability density, which is a function of the partition function.", + "bbox": [ + 75, + 459, + 472, + 752 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To get around this conundrum, we propose representing the probability distribution with a set of samples generated from a neural network. Such a distribution can be learned with a conditional GAN; however, because GANs suffer from mode collapse, they cannot model multiple modes [11] and are therefore unsuited to modelling ambiguity. Instead, we propose leveraging conditional Implicit Maximum Likelihood Estimation (cIMLE) [19, 28] to learn the distribution, which is designed to avoid mode collapse.", + "bbox": [ + 75, + 753, + 472, + 885 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We consider the challenging setting of leveraging out-of", + "bbox": [ + 96, + 885, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/89ae8a01be14ce67f619ad8b234580bd782b76021c3c70019a5b9d7fbb59aa90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 526, + 93, + 607, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a06fd61cd86dab5c1198a5da0f1e188d15aa7047d12b01b972958a739eeec331.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 93, + 694, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/68d33f6a715203b18ec8f4c3b82c6cb7b9e4b4f0b15c1a3d22ce704b35e778c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 93, + 777, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/13559aab43aa532959f7217e43d80f5dd5c5d23b0037c75dad3323d3954e0466.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 93, + 857, + 152 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/22fce397da257929668b856372fb7391c94c99ce422710eedf4bda265c1f0754.jpg", + "image_caption": [ + "Input Image" + ], + "image_footnote": [], + "bbox": [ + 532, + 155, + 602, + 223 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6b3d450c6b39276ec11d0710dfd745893d459c0730b59fac991eb1a3c2ac5c7f.jpg", + "image_caption": [ + "Ambiguity-Aware Depth Estimates" + ], + "image_footnote": [], + "bbox": [ + 620, + 155, + 691, + 223 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e81b800d71ea46699ae5cf16dcac3e985927f8f81fd5d4df9b54df2184be02b6.jpg", + "image_caption": [ + "Figure 2. Ambiguities from a single image. We show samples from our ambiguity-aware depth estimates that is able to handle different types of ambiguities. (Top) An image of a chair taken from the top-view. Without context of the scene, it is unclear that it is an image of a chair. We show different samples from our ambiguity-aware depth estimates that are able to capture different degrees of convexity. (Bottom) An image of a cardboard under bad lighting conditions that capture the albedo vs shading ambiguity that is also represented by our different samples." + ], + "image_footnote": [], + "bbox": [ + 702, + 155, + 772, + 223 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d8d127bc3b443638620fdab80b812ae0ca16954b16deff9a3bd0cf586025dffd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 155, + 852, + 223 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "domain depth priors to train NeRFs on real-world indoor scenes with sparse views. Under this setting, the depth priors we use are trained on a different dataset (e.g., Taskonomy) from the scenes our NeRFs are trained on (e.g., ScanNet). This setting is more challenging than usual due to domain gap between the dataset the prior is trained on and the scenes NeRF is asked to reconstruct. We demonstrate that our method outperforms vanilla NeRF and NeRFs with supervision from depth-based priors in novel view synthesis.", + "bbox": [ + 496, + 366, + 893, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our key contributions include:", + "bbox": [ + 519, + 500, + 803, + 512 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An method that allows the creation of NeRFs in unconstrained indoor settings from only a modest number of 2D views by introducing a sophisticated way to exploit ambiguity-aware monocular depth estimation.", + "- A novel way to sample distributions over image depth estimates based on conditional Implicit Maximum Likelihood Estimation that can represent depth ambiguities and capture a variable number of discrete depth modes.", + "- A new space-carving loss that can be used in the NeRF formulation to optimize for a mode-seeking 3D density that helps select consistent depth modes across the views and thus compensate for the under-constrained photometric information in the few view regime." + ], + "bbox": [ + 517, + 521, + 893, + 732 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 746, + 640, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel View Synthesis and 3D Reconstruction. Reconstructing the structure of a scene from a few views is a long standing problem in computer vision with a long literature. Neural Radiance Fields or NeRF [24] revolutionized the field by showing how to use weights of an MLP to represent a scene that is rendered using volume rendering [23]. A key innovation was the use of positional encoding [37, 38] to increase the effective capacity of the MLPs that model a emitted radiance and density as a function of position and", + "bbox": [ + 496, + 767, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16519", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "viewing direction. Extensions of NeRF include works on unconstrained photo collections [22], dynamic scenes [20], deformable scenes [27], and reflective materials [1,39].", + "bbox": [ + 75, + 90, + 470, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A critical shortcoming of NeRF is its reliance on having many input views of a scene. Several approaches have been proposed, including adding patch likelihood losses [25], data-driven priors [36, 48], semantic consistency prior [12], image features [41], or surface [25, 39], occupancy [26], and depth [15, 32, 43] priors. DS-NeRF [6] uses the sparse point reconstructions recovered during Structure-from-Motion, to supervise the depth of sparse points in the recovered NeRF. In the same spirit, DDP [32] uses a depth completion network, that takes as input sparse point cloud projected to one an input view, and produces a depth estimate. Both works [15, 32] model depth with uncertainty but only supervise with moments of NeRF's depth distribution. In contrast, our work is able to represent multimodal depth estimates, which can handle the inherit ambiguities of depth estimation, and is able to seek the modes for each depth estimate to make a consistent prediction of the scene structure.", + "bbox": [ + 75, + 136, + 472, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by traditional multi-view stereo, MVS-NeRF [3] and RC-MVSNet [2] incorporate the use cost volumes [9] to NeRF. To construct the cost volumes, these works look for agreement between features to look for correspondences, which is difficult under the setting of large variations in appearance or viewpoint. In contrast, our approach introduces a novel space carving loss that does not rely on feature correspondences and instead directly defines the loss in 3D.", + "bbox": [ + 75, + 385, + 470, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another line of works focuses on geometry reconstruction [40, 45, 49] by using the volumetric rendering scheme to learn a neural SDF representation. These works tackle a different problem on modeling geometry reconstruction, unlike NeRFs whose focus is modeling appearance for novel view synthesis, where our work falls under.", + "bbox": [ + 75, + 503, + 470, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Depth Estimation from Single View. Depth estimation from a single image is a complex task due multiple ambiguities, including scene scale and shading / albedo ambiguities. Early efforts used MRFs to compute predictions on superpixels [33]. The advent of consumer depth cameras like Kinect [53] enabled the acquisition of larger scale indoor 3D datasets [35], leading to methods that used deep neural networks to predict depth from a single color image [7]. Nonetheless, scaling datasets for depth estimation remained a challenge. Deep3D [44] enabled the creation of stereo views by training on a large dataset of stereo movies, while [8] used the self-supervision of left-right consistency to learn depth from stereo views from driving cars. This approach was extended to videos where the egomotion is also estimated and self-supervision happens across time [54]. MegaDepth [21] uses the depth from SfM reconstructions of internet photos, together with semantic segmentation that conveys ordinal depth supervision cues, i.e. transient objects must be in front of the static scenes. Most recent, multi-task learning has shown promise in training depth estimators that work well in out-of-domain data [30].", + "bbox": [ + 75, + 590, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In some cases, surface normal estimation has fewer pitfalls than direct depth estimation, as it suffers somewhat less from scale ambiguities. GeoNet [29] jointly estimates depth and surface normals, then uses the geometric relation between them to refine the estimates. LeRes [46] uses a second geometry reasoning module that refines a focal length estimate and the depth itself. Our depth estimation approach is derived from LeReS without the second stage, as the focal length is already estimated during SfM for NeRF scenes.", + "bbox": [ + 496, + 90, + 893, + 223 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most relevant is the work of Kendall and Gal [15], that learns depth estimation in a Bayesian setting, where their objective maximizes the likelihood under a predicted distribution. In our work, we use instead a multimodal depth estimation technique built on cIMLE [19], which makes our prior robust to ambiguities in depth prediction.", + "bbox": [ + 496, + 223, + 893, + 311 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background", + "text_level": 1, + "bbox": [ + 498, + 324, + 627, + 340 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Neural Radiance Fields (NeRF)", + "text_level": 1, + "bbox": [ + 498, + 348, + 777, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A neural radiance field [24], or NeRF for short, represents a field in 3D space, where each point represents an infinitesimal particle with a certain opacity that emits varying amounts of light along different viewing directions. The opacity at a point is represented as a volume density, and the amount of emitted light is represented as a colour. Mathematically, a NeRF is represented as two parameterized functions, a volume density $\\sigma_{\\theta}:\\mathbb{R}^{3}\\to \\mathbb{R}_{\\geq 0}$ and a colour $\\mathbf{c}_{\\psi}:\\mathbb{R}^3\\times S^2\\rightarrow [0,255]^3$ . The former maps a 3D coordinate $\\mathbf{x}\\in \\mathbb{R}^3$ to a volume density $\\sigma \\in \\mathbb{R}_{\\geq 0}$ , and the latter maps a 3D coordinate $\\mathbf{x}\\in \\mathbb{R}^3$ and a viewing direction $\\mathbf{d}\\in S^2$ to a colour $\\mathbf{c}\\in [0,255]^3$ .", + "bbox": [ + 496, + 364, + 893, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To render a NeRF from a view, we shoot rays from each pixel on the camera sensor and integrate over the product of colour, volume density and visibility along the ray to arrive at each pixel value. Visibility at a point is represented with transmittance, which accumulates the exponentiated negative volume density multiplicatively up to the point. The higher transmittance at a point, the more visible the point is from the camera. Mathematically, if the camera ray is $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}$ , where $\\mathbf{o}$ is the camera centre and $\\mathbf{d}$ is the ray direction, the pixel value $\\hat{I}_{\\theta,\\psi}(\\mathbf{o},\\mathbf{d})$ we would have is:", + "bbox": [ + 496, + 541, + 893, + 688 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {I} _ {\\theta , \\psi} (\\mathbf {o}, \\mathbf {d}) := \\int_ {t _ {n}} ^ {t _ {f}} T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) \\sigma_ {\\theta} (\\mathbf {o} + t \\mathbf {d}) \\mathbf {c} _ {\\psi} (\\mathbf {o} + t \\mathbf {d}, \\mathbf {d}) d t \\\\ \\text {w h e r e} T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\sigma_ {\\theta} (\\mathbf {o} + s \\mathbf {d}) \\mathrm {d} s\\right). \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 698, + 893, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the expressions above, $t_n$ and $t_f$ denote the points the ray intersects with the near plane and far plane respectively.", + "bbox": [ + 496, + 795, + 890, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Inverse Rendering with NeRF", + "text_level": 1, + "bbox": [ + 500, + 833, + 766, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of real-world images from known views, inverse rendering aims to find the scene whose rendered images match the real-world images. If we use $I(\\mathbf{o}, \\mathbf{d})$ to de", + "bbox": [ + 496, + 856, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16520", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "note the pixel value for the ray $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}$ , this problem can be cast as an optimization problem, namely:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta , \\psi} \\sum_ {\\mathbf {o}} \\sum_ {\\mathbf {d}} \\| \\hat {I} _ {\\theta , \\psi} (\\mathbf {o}, \\mathbf {d}) - I (\\mathbf {o}, \\mathbf {d}) \\| _ {2} ^ {2} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 131, + 468, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If $\\hat{I}_{\\theta, \\psi}(\\mathbf{o}, \\mathbf{d})$ is differentiable w.r.t. the parameters $\\theta, \\psi$ , this problem can be tackled straightforwardly with gradient-based optimization. To enable this, the volume density function $\\sigma_{\\theta}$ and the colour function $\\mathbf{c}_{\\psi}$ are chosen to be neural networks. As a result, inverse rendering amounts to training the NeRF to reconstruct the scene in a way that is consistent with the images that are given. Once the NeRF is trained, novel view synthesis can be achieved by rendering the NeRF from new, unseen views.", + "bbox": [ + 75, + 167, + 470, + 299 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since this optimization problem is underconstrained, in general many views are needed to reconstruct the scene accurately. Yet, in practical applications, typically only a few views are available, hence priors are needed to provide sufficient constraints. In this paper, we consider priors in the form of monocular depth estimates from each view. The monocular depth estimates are trained on different datasets from the dataset NeRF is trained on to simulate real-world conditions where there is a domain gap between what the prior was trained on and what the NeRF is trained on.", + "bbox": [ + 75, + 300, + 468, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Ray Termination Distance", + "text_level": 1, + "bbox": [ + 76, + 449, + 313, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to leverage depth priors, a natural way is to use them to constrain the ray termination distance. Because NeRF can represent non-opaque surfaces, there is no single ray termination distance. Instead, there is a distribution of ray termination distances. The cumulative distribution function (CDF) of this distribution represents the probability that the ray terminates before reaching a given point. It turns out that the probability density of this distribution $f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t)$ is given by [6]:", + "bbox": [ + 75, + 465, + 468, + 597 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) = T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) \\sigma_ {\\theta} (\\mathbf {o} + t \\mathbf {d}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 609, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 636, + 166, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Supervising Ray Termination Distance", + "text_level": 1, + "bbox": [ + 76, + 660, + 408, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If all surfaces were opaque and the ground truth depth were given, supervising NeRF with the ground truth depth would be straightforward. All that is needed is to make the NeRFs distribution of ray termination distances as close as possible to a delta distribution centred at the ground truth depth. However, when the ground truth depth is not known, we have to use monocular depth estimates as supervision. The challenge is that unlike ground truth depth, monocular depth estimates may not be stereo-consistent, due to estimation error and inherent ambiguity. As a result, it may not be possible to find a scene that is consistent with the depth estimates from every view. Therefore, in order to reconstruct the scene, we must model the uncertainty and ambiguity in the depth estimates, which can be mathematically characterized by distributions. Such ambiguities cannot be resolved from", + "bbox": [ + 75, + 680, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d79b1f9b1912712bf049c99bd1ce552f3d28968c73f444a03701056de739514e.jpg", + "image_caption": [ + "Figure 3. Network Architecture for our Ambiguity-aware Depth Estimates." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 890, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a single view and can often be resolved from multiple views. So we need an method that can fuse together uncertain depth estimates from different views.", + "bbox": [ + 498, + 296, + 893, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A natural way of representing uncertainty is through a probability distribution. When there are ambiguities, the distribution of depth estimates are typically multimodal, i.e., their probability densities have disjoint peaks, where each mode represents one interpretation of the scene structure. For example, albedo vs shading ambiguity as shown in Figure 2 can result in multiple plausible interpretations and make the distribution multimodal.", + "bbox": [ + 496, + 340, + 892, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An added challenge arises when non-opaque surfaces are present. In this case, there is no single ground truth depth, and so the distribution of ground truth depths is multimodal. So even after training the NeRF, the distribution of ray termination distances induced by NeRF should be multimodal, as illustrated in the glass walls in Figure 1.", + "bbox": [ + 496, + 458, + 893, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prior methods compute moments (i.e., mean and/or variance) of the distribution of depth estimates or ray termination distance induced by NeRF. For example, DS-NeRF [6] predicts the mean depth estimate and uses reprojection error as a proxy for the variance. It then minimizes the KL divergence from the distribution of ray termination distances induced by NeRF to a Gaussian whose moments match those of the depth estimates. DDP [32] fits a Gaussian to distribution of ray termination distances and maximizes the likelihood of the depth estimate under the Gaussian.", + "bbox": [ + 496, + 547, + 893, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Distilling complex distributions to moments has the drawback of ignoring their possible multimodality. Because both the distribution of depth estimates and ray termination distances are potentially multimodal, it is important to handle the multimodality.", + "bbox": [ + 496, + 694, + 893, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. SCADE", + "text_level": 1, + "bbox": [ + 500, + 773, + 596, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now present our novel method Space Carving with Ambiguity-aware Depth Estimates (SCADE). Our contributions address the existing problems and drawbacks mentioned in the previous section. First, SCADE accounts for the multimodality of both the distributions of monocular depth estimates and ray termination distances that arise due to inherent ambiguities (Sec 4.2.1) and non-opaque surfaces.", + "bbox": [ + 496, + 797, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16521", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Second, SCADE is also able to resolve these ambiguities by fusing together information from multiple views through our space carving loss (Sec 4.2.3) that uses the reverse cross entropy loss. Because this a loss on the distribution rather than moments of the distribution (which was the paradigm in prior work [6, 32]), it achieves supervision in 3D rather than 2D. Third, our loss formulation is sample-based (Sec 4.2.2) and so is computationally efficient to optimize.", + "bbox": [ + 75, + 90, + 472, + 209 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.1 Our Ambiguity-aware Depth Estimates", + "text_level": 1, + "bbox": [ + 76, + 215, + 405, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We handle multimodality of monocular depth distributions by introducing our ambiguity-aware depth estimation module to account for ambiguities in depth estimation from a single view (Figure 1, 2). In contrast to existing monocular depth estimation networks [47] that predict single point estimates for depth, we model the inherent uncertainty in monocular depth estimation by representing the distribution as a set of samples generated by a neural network. We propose leveraging conditional Implicit Maximum Likelihood estimation (cIMLE) [19] to learn a multimodal distribution of depth estimates. We chose cIMLE rather than conditional GANs [14] in order to avoid mode collapse, which can lead to a unimodal distribution.", + "bbox": [ + 75, + 231, + 472, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 3 shows our network architecture. Concretely, we combine cIMLE with a state-of-the-art monocular depth estimation network, LeReS [47]. Our ambiguity-aware depth estimation module $(G)$ takes an input image $(I)$ and a latent code $z\\sim \\mathcal{N}(0,\\mathbf{I})$ and outputs a conditional depth sample $G(I,z)$ for the input image $I$ . To inject randomness into the network, we follow the technique used in [14] and incorporate AdaIn layers into the network backbone that predicts a scale and shift to the intermediate network features. Specifically, we added four AdaIn layers to the encoder of the depth estimation backbone.", + "bbox": [ + 75, + 422, + 472, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.2 Sample-based Losses on Distributions", + "text_level": 1, + "bbox": [ + 76, + 590, + 393, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We desire to achieve an agreement between the distributions from our ambiguity-aware prior and the ray termination distance from NeRF to constrain the NeRF optimization under the sparse view set-up using our learned prior. As distributions are continuous, taking their analytical integral is computationally intractable. Thus, in order to define a differentiable loss function for our optimization problem, we result in a sample-based loss on these two distributions.", + "bbox": [ + 75, + 606, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Samples from depth prior. As previously described, we leverage cIMLE to sample from our ambiguity-aware depth prior. Sampling $z_{1},\\ldots ,z_{M}\\sim \\mathcal{N}(0,\\mathbf{I})$ , we get depth map samples $G(I,z_1),\\dots,G(I,z_M)$ for input image $I$ . Hence we denote corresponding samples to estimate and represent the distribution for ray $\\mathbf{r}$ as $y_{1},y_{2},\\dots,y_{M}\\sim G_{\\mathbf{o,d}}$ .", + "bbox": [ + 75, + 731, + 468, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Samples from NeRF. For the distribution given by the ray termination distances modelled by NeRF, we sample from its probability density function $f_{\\theta ,\\mathbf{o},\\mathbf{d}}$ (Eq. 3) with inverse transform sampling. Concretely, we define the probability mass function for ray $\\mathbf{r}$ as $f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i)$ as given in Eq. 3 with", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5ce69a59f9693151cf0118715c9aa7a4632ba34e4fa87d3d6c04f8224a7bbbb2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 542, + 92, + 694, + 160 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f0f60911c43cb08167196bca975a3842d6efec53ccdedbaafe3d95dc4a38fd5a.jpg", + "image_caption": [ + "2D Expected Depth" + ], + "image_footnote": [], + "bbox": [ + 542, + 162, + 694, + 228 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9e3fb50f9689e1cee02dd5c1e8baba0ac80730b0def19b79a7f53c0861ad64f9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 92, + 846, + 160 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/095433d6285bfd4172af0cf62ac7b64bbf1bcdd6b6a6d1de52d37ce1fe9081d0.jpg", + "image_caption": [ + "3D Space Carving (Ours)", + "Figure 4. Our space carving loss supervises the ray termination in 3D as opposed to existing approaches that supervise on 2D expected depth. As shown, this clears out clouds of dust in space. Moreover supervising in 3D allows for wide baseline input views and still finds the common mode that correctly snaps the surfaces." + ], + "image_footnote": [], + "bbox": [ + 696, + 162, + 844, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "samples $t_1,\\ldots ,t_K$ , where $t_i\\in [t_n,t_f]\\forall i$ . By inverse transform sampling, we first compute the cumulative distribution function (CDF) of the ray termination distribution at samples $t_i$ , which we denote as $F_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i) = \\sum_{j < i}f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i)$ . Thus our samples $x_{1},x_{2},\\dots,x_{N}$ of ray termination distances from NeRF are then given by:", + "bbox": [ + 498, + 313, + 893, + 402 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {i} = F _ {\\theta , \\mathbf {o}, \\mathbf {d}} ^ {- 1} (u _ {i}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 410, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $u_{i}\\sim \\mathcal{U}(0,1)$", + "bbox": [ + 630, + 433, + 761, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.3 Our Space Carving Loss", + "text_level": 1, + "bbox": [ + 498, + 460, + 725, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now introduce our novel space carving loss utilizes the samples from both multimodal distributions to constrain the NeRF optimization. The goal is to find a subset of modes captured in the monocular depth distributions from each view that are globally consistent. In doing so, we can fuse together the information from the different views, since the inherent ambiguities are only resolved given information from multiple views. This would allow us to find a common shape that is consistent across all views and \"snap\" objects surfaces together.", + "bbox": [ + 496, + 477, + 890, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We thus desire a loss that has mode seeking behavior, that is the modes of the distribution being trained should be a subset of the modes of the distribution that provides supervision. One such loss is the reverse cross entropy, which is the cross entropy from the NeRF ray termination distance distribution to the distribution of our ambiguity-aware depth estimates:", + "bbox": [ + 496, + 623, + 893, + 726 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH \\left(f _ {\\theta , \\mathbf {o}, \\mathbf {d}}, G _ {\\mathbf {o}, \\mathbf {d}}\\right) = - \\mathbb {E} _ {f _ {\\theta , \\mathbf {o}, \\mathbf {d}}} [ \\log G _ {\\mathbf {o}, \\mathbf {d}} ]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 734, + 890, + 753 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in the IMLE papers [19, 28], this is equivalent to penalizing the minimum of the L2 norm between the samples from the two distributions, please see [18] for the full proof. Hence, our space carving loss is given by", + "bbox": [ + 496, + 760, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s p a c e ＿ c a r v i n g}} (\\mathbf {r}) = \\sum_ {i \\in [ N ]} \\min _ {j \\in [ M ]} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 828, + 890, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Because our novel space carving loss operates on distributions rather than moments of distributions, we can have", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16522", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "different supervision targets for different points along the ray. In contrast, if the loss were to only to operate on moments, which are integrals along the ray, this only yields the same supervision target for all points along the ray. Therefore, our loss allows us to supervise in 3D, unlike prior methods [6, 32] (which use losses on moments) that supervise in 2D. 3D supervision allows us to clear out dust in space, since in order to move a sample from the ray termination distance distribution farther in depth, the loss would have to decrease the probability density of all the points in front of it. These advantages are highlighted in Figure 4.", + "bbox": [ + 75, + 90, + 472, + 252 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our total loss to optimize and train our NeRF model is given by", + "bbox": [ + 75, + 252, + 470, + 282 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {p h o t o m e t r i c}} + \\lambda \\mathcal {L} _ {\\text {s p a c e ＿ c a r v i n g}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 292, + 468, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{photometric}}$ is the standard MSE loss on the predicted and ground truth image. See Fig. 1 for our overall pipeline.", + "bbox": [ + 75, + 320, + 468, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 363, + 163, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we present our experimental evaluation to demonstrate the advantages of SCADE.", + "bbox": [ + 75, + 381, + 468, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 416, + 362, + 430 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on ScanNet [5] and an in-the-wild dataset we collected1. We use the sparse-view ScanNet data used by DDP [32] in their evaluations, which comprises of three sample scenes each with 18 to 20 train images and 8 test images. To further test the robustness of our method, we further evaluated our method on three in-the-wild scenes collected using an iPhoneX. We captured sparse views in three different scenes - basement, kitchen and lounge, where each scene has 18 to 23 train images and 8 test images. Following similar data preprocessing steps as DDP [32], we ran SfM [34] on all images to obtain camera poses for NeRF training. For quantitative comparison, we follow the original NeRF [24] paper and report the PSNR, SSIM [42] and LPIPS [52] on the novel test views.", + "bbox": [ + 75, + 431, + 472, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 646, + 294, + 661 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train our ambiguity-aware prior on the Taskonomy [50] dataset and initialize the weights with the pretrained LeReS [47] model. We use $M = 20$ depth estimates in our experiments. See supplement for additional details.", + "bbox": [ + 75, + 662, + 470, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Experiments on ScanNet", + "text_level": 1, + "bbox": [ + 76, + 726, + 303, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate on ScanNet following the evaluation from DDP [32]. We compare to the original NeRF [24] (Vanilla NeRF) and the recent state-of-the-art NeRF with depth prior-based supervision, Dense Depth Prior [32] (DDP). Table 1 shows SCADE quantitatively outperforming the baselines. Because we are interested in simulating real-world conditions with a domain gap between the prior and the NeRF, our setting requires the use of out-of-domain priors. Since DDP uses a in-domain prior, we retrain DDP's depth completion", + "bbox": [ + 75, + 744, + 472, + 878 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/949b1024709f36574ef8fca2f848b5a09b39f2c61a19449dd8a1bfcb1d311674.jpg", + "image_caption": [ + "Figure 5. Depth and Fusion Comparison. Depth map and fusion comparison between SCADE and DDP." + ], + "image_footnote": [], + "bbox": [ + 503, + 82, + 888, + 190 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9e79add36f31f9f730a8d851dc39149f2ae384c31bbc009d5a948066029dffb3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]19.030.6700.398
NerfingMVS [47]16.290.6260.502
IBRNet [41]13.250.5290.673
MVSNeRF [3]15.670.5330.635
DS-NeRF [6]20.850.7130.344
DDP [32]19.290.6950.368
SCADE (Ours)21.540.7320.292
", + "bbox": [ + 501, + 226, + 890, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. ScanNet Results. Results for DS-NeRF and NerfingMVS follow what was reported in prior literature [32]. Because our setting requires out-of-domain priors, the results for DDP are with out-of-domain priors. The results of DDP with in-domain priors are (20.96, 0.737, 0.236) for PSNR, SSIM and LPIPS, respectively.", + "bbox": [ + 498, + 369, + 890, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "network using their official code and hyperparameters on Taskonomy [50], i.e. the same out-of-domain dataset that our prior is trained on.", + "bbox": [ + 498, + 446, + 890, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 6 shows our qualitative results. As shown, compared to the baselines, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (first, third and last column). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (second column), the back of the chair (fourth column) and the legs of the piano stool (fifth column). Moreover, Fig. 5 shows rendered depthmaps and fusion results using [51] on a Scannet scene. Notice that SCADE is able to recover better geometry compared to DDP - see corner of the calendar, cabinets and office chair in the right image.", + "bbox": [ + 496, + 491, + 893, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.4. Experiments on In-the-Wild Data", + "text_level": 1, + "bbox": [ + 500, + 660, + 794, + 675 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further test the robustness of SCADE, we further evaluate on data collected in-the-wild with a standard phone camera (iPhoneX). The intrinsics for different views are different and are not known to the algorithm. As shown in Table 2, SCADE with the same out-of-domain prior (trained on Taskonomy) outperforms the baselines on in-the-wild captured data, which demonstrates its robustness. Figure 7 shows qualitative examples. Interestingly, we are able to recover the room behind the glass better the baselines, whose results are more blurry (first, third and fourth column). We are also able to recover objects behind the glass such as the monitor and chair (first column). As discussed in Sect. 4.1, non-opaque surfaces are the most challenging because both the ground truth distribution of ray termination distances induced by NeRF and the distribution of estimated depths", + "bbox": [ + 496, + 679, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1Also see supplement for results on the Tanks and Temples dataset [16].", + "bbox": [ + 94, + 886, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16523", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e9189b41264e143ca49e61725e478d56b531c4f517a25de627d60d97f175c7fe.jpg", + "image_caption": [ + "Figure 6. Qualitative results on ScanNet. As shown, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (1st, 3rd, last columns). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (2nd column), the back of the chair (4th column) and the legs of the piano stool (5th column)." + ], + "image_footnote": [], + "bbox": [ + 99, + 90, + 869, + 343 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fe37034eb23db24e5a1050fedb62f31d15d23bdfad568a658cd709102a20d220.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]20.460.7130.398
DDP [32]21.280.7270.366
SCADE (Ours)22.820.7430.347
", + "bbox": [ + 78, + 397, + 468, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "from the prior must be multimodal. This validates the ability of our model to capture the multimodal distributions.", + "bbox": [ + 75, + 494, + 468, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Similar to the ScanNet results, we are able to recover crisp shapes of objects such as the thin table leg and the white chair (second and last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (fifth and last column).", + "bbox": [ + 75, + 525, + 468, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 606, + 230, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Supervision on full distribution vs moments We first validate the importance of using our novel space carving loss that supervises the full distribution of ray termination distance rather than just its moments. The latter integrates along the ray, and so provides one target value for the entire ray, which effectively makes it 2D supervision. The former provides different target values for different samples along the same ray, which makes it 3D supervision. We adapt our method to use 2D supervision proposed in the recent MonoSDF [49], which computes the expected ray termination distance and aligns the output depth map with a monocular depth estimation prior using the MiDaS [30] loss. We use our learned prior as the monocular depth estimate. Table 3 validates the effectiveness of our space carving loss.", + "bbox": [ + 75, + 625, + 470, + 832 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multimodal prior vs unimodal prior. Our prior models does not constrain the depth distribution to a particular form and allows it to be multimodal. In contrast, DDP's depth completion prior assumes a Gaussian, which is unimodal.", + "bbox": [ + 75, + 840, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ffe62631a9c24eccb06a7e079ddd2ff92556d3af67acf0602456f18dfce15e89.jpg", + "table_caption": [ + "Table 2. In-the-wild Results." + ], + "table_footnote": [], + "table_body": "
PSNR ↑SSIM ↑LPIPS ↓
MonoSDF supervision20.130.7100.332
DDP prior - single sample20.850.7120.320
DDP prior - multiple samples21.000.7180.316
Our prior - single sample21.220.7140.318
SCADE (Ours)21.540.7320.292
", + "bbox": [ + 501, + 397, + 890, + 507 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation Study. Results on the Scannet dataset. MonoSDF supervision refers to supervising with MonoSDF loss on expected ray termination distance using our prior.", + "bbox": [ + 498, + 511, + 893, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We ablate our prior against DDP's by sampling from their Gaussian distribution. We train with our space carving loss using both a single sample, as well as $M$ samples drawn from DDP's prior. As shown in Table 3, while both perform better than the 2D supervision provided by MonoSDF, but they are subpar compared to using our multimodal prior.", + "bbox": [ + 496, + 561, + 893, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multiple vs single sample. Finally, we also ablate on using a single sample vs multiple samples for our space carving loss. For the single sample set-up, we supervise using the sample mean of the depth estimates, which is equivalent to the maximum likelihood estimate of the depth under Gaussian likelihood. Results in Table 3 show the importance of using multiple samples for our space carving loss.", + "bbox": [ + 496, + 657, + 893, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sparsity. We further show addt'l results under varying number of views in Tab 4. Note that in general sparsity is not fully reflected by the absolute number of views, because all else being equal, a larger scene requires more views to attain complete coverage. Following prior work [32], we also report the average number of views that see the same point as another measure of sparsity. As shown, our setting is at the edge of the theoretical lower limit of 2 for general-purpose reconstruction, which shows view sparsity.", + "bbox": [ + 496, + 768, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16524", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e2362ab6a15190dbdcc9d678e22a5b9e89861b7021b641f07fec5373cdc845d.jpg", + "image_caption": [ + "Figure 7. Qualitative results on In-the-Wild data. As shown, we are able to recover the room behind the glass better the baselines, whose results are more blurry (1st, 3rd, 4th column). Also, SCADE is able to recover crisp shapes of objects such as the thin table leg and the white chair (2nd, last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (5th, last column)." + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 869, + 345 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8a0faede98243af031aa79b018a997b7fb9b6baf0046a053c27e95fac9f5a15c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ave. #views visible1.871.982.012.2
absolute #views18202224
DDP / SCADE19.35/ 21.6622.4/ 23.6723.10/ 24.0023.56/ 24.84
", + "bbox": [ + 78, + 398, + 470, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. PSNR for DDP [32]/SCADE on scene781 of Scannet.", + "bbox": [ + 86, + 450, + 459, + 464 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/29b97ea9fa589445999cb9da35c0638f35b86213f46f987167af3609e7216b4d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 468, + 303, + 573 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d6aa5d3f52bf5f17bac43561c98b1ea27cd406ae972d63e2f89a5253283b950.jpg", + "image_caption": [ + "Figure 8. Depth Mode Discussion. a) Train images from Taskonomy [50] and their labels. Notice that non-opaque surfaces are labelled differently. b) Output of our prior on reflective surfaces." + ], + "image_footnote": [], + "bbox": [ + 308, + 468, + 467, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Discussion on our Ambiguity-Aware Prior", + "text_level": 1, + "bbox": [ + 76, + 628, + 434, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We provide addt'l details on our ambiguity-aware prior on i) how and why it works, ii) its performance on reflective surfaces, which is a common failure case for depth estimate, and iii) provide an intuition on how what our depth modes look like. i) We achieve variable depth modes by exploiting inconsistently labeled training data. As shown in Fig 8-a, in Taskonomy [50], different training images with non-opaque surfaces label depth differently: shooting through the glass (left), on the glass (middle), or a mixture of both (right). Despite multiple possible depth labels, each image only has one ground truth label. Training with cIMLE allows our prior to model these multiple possible (ambiguous) outputs through sampling $^2$ , even when given only one label per image. Interestingly when testing our prior on a test image with a mirror, we find that it is able to capture variable modes", + "bbox": [ + 75, + 646, + 472, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "on reflective surfaces, including the \"correct\" flat surface as shown in Fig 8-b. An intuition of what the depth modes look like is for example if a ray intersects $n - 1$ non-opaque surfaces, the $n$ modes are intersections with the non-opaque surfaces and the terminating point on the opaque surface.", + "bbox": [ + 496, + 401, + 890, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 479, + 617, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a new approach towards NeRF reconstruction that can work with a modest number of in-the-wild views of an indoor scene. We address the underconstrained nature of this problem by regularizing the NeRF optimization with additional depth estimates for each view. Our key technical contribution is to model multimodality in the depth estimates, which can capture inherent ambiguities in monocular depth estimation as well as the possible presence of non-opaque surfaces. We resolve ambiguities using a novel space carving loss that fuses the multimodal depth estimates from different views and seeks the modes that are consistent across views so as to arrive at a globally consistent 3D reconstruction. The improved recovery of shape and appearance enables higher fidelity novel view synthesis from sparse views.", + "bbox": [ + 496, + 497, + 893, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Future Work. The performance of our method is constrained by the quality of the monocular depth priors. While we found that our prior generalizes well across domains, if the domain gap is too great, the performance of our method will degrade. A future direction would be to detect when this happens and dynamically adjust the strength of depth supervision in response.", + "bbox": [ + 496, + 720, + 893, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. We sincerely thank the Teleportation and CCI team in Google for all the insightful discussions during the summer. We also thank Mirko Visontai for internship logistics, Guandao Yang for experiment set-up assist, and Weicheng Kuo for looking over the paper.", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "2See supplement for more qualitative examples on our ambiguity-aware depth estimates.", + "bbox": [ + 76, + 875, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16525", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sai Bi, Zexiang Xu, Pratul Srinivasan, Ben Mildenhall, Kalyan Sunkavalli, Miloš Hasan, Yannick Hold-Geoffroy, David Kriegman, and Ravi Ramamoorthi. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1851-1858, 2017. 3" + ], + "bbox": [ + 501, + 92, + 893, + 683 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16527", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SCADE_ NeRFs from Space Carving With Ambiguity-Aware Depth Estimates/cb201944-e311-4584-9847-096959c3a596_model.json b/2023/SCADE_ NeRFs from Space Carving With Ambiguity-Aware Depth Estimates/cb201944-e311-4584-9847-096959c3a596_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b2c36addf7fa7b49d94b750c69a3a13c6413fca2 --- /dev/null +++ b/2023/SCADE_ NeRFs from Space Carving With Ambiguity-Aware Depth Estimates/cb201944-e311-4584-9847-096959c3a596_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.116, + 0.877, + 0.139 + ], + "angle": 0, + "content": "SCADE: NeRFs from Space Carving with Ambiguity-Aware Depth Estimates" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.15, + 0.804, + 0.171 + ], + "angle": 0, + "content": "Mikaela Angelina Uy\\(^{1,2}\\) Ricardo Martin-Brualla\\(^{2}\\) Leonidas Guibas\\(^{1,2}\\) Ke Li\\(^{2,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.175, + 0.724, + 0.195 + ], + "angle": 0, + "content": "\\(^{1}\\)Stanford University \\(^{2}\\)Google \\(^{3}\\)Simon Fraser University" + }, + { + "type": "image", + "bbox": [ + 0.11, + 0.203, + 0.865, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.414, + 0.896, + 0.485 + ], + "angle": 0, + "content": "Figure 1. SCADE Overview. We present SCADE, a novel technique for NeRF reconstruction under sparse, unconstrained views for in-the-wild indoor scenes. We leverage on generalizable monocular depth priors and address to represent the inherent ambiguities of monocular depth by exploiting our ambiguity-aware depth estimates (left). Our approach accounts for multimodality of both distributions using our novel space carving loss that seeks to disambiguate and find the common mode to fuse the information between different views (middle). SCADE enables better photometric reconstruction especially in highly ambiguous scenes, e.g. non-opaque surfaces (right)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.492, + 0.314, + 0.508 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.531, + 0.474, + 0.885 + ], + "angle": 0, + "content": "Neural radiance fields (NeRFs) have enabled high fidelity 3D reconstruction from multiple 2D input views. However, a well-known drawback of NeRFs is the less-than-ideal performance under a small number of views, due to insufficient constraints enforced by volumetric rendering. To address this issue, we introduce SCADE, a novel technique that improves NeRF reconstruction quality on sparse, unconstrained input views for in-the-wild indoor scenes. To constrain NeRF reconstruction, we leverage geometric priors in the form of per-view depth estimates produced with state-of-the-art monocular depth estimation models, which can generalize across scenes. A key challenge is that monocular depth estimation is an ill-posed problem, with inherent ambiguities. To handle this issue, we propose a new method that learns to predict, for each view, a continuous, multimodal distribution of depth estimates using conditional Implicit Maximum Likelihood Estimation (cIMLE). In order to disambiguate exploiting multiple views, we introduce an original space carving loss that guides the NeRF representation to fuse multiple hypothesized depth maps from each view and distill from them a common geometry that is consistent with all views. Experiments show that our approach enables higher fidelity novel view synthesis from sparse views. Our project page can be found at scade-spacecarving-nerfs.github.io." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.492, + 0.633, + 0.508 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.895, + 0.617 + ], + "angle": 0, + "content": "Neural radiance fields (NeRF) [24] have enabled high fidelity novel view synthesis from dozens of input views. Such number of views are difficult to obtain in practice, however. When given only a small number of sparse views, vanilla NeRF tends to struggle with reconstructing shape accurately, due to inadequate constraints enforced by the volume rendering loss alone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.896, + 0.869 + ], + "angle": 0, + "content": "Shape priors can help remedy this problem. Various forms of shape priors have been proposed for NeRFs, such as object category-level priors [13], and handcrafted data-independent priors [25]. The former requires knowledge of category labels and is not applicable to scenes, and the latter is agnostic to the specifics of the scene and only encodes low-level regularity (e.g., local smoothness). A form of prior that is both scene-dependent and category-agnostic is per-view monocular depth estimates, which have been explored in prior work [6, 32]. Unfortunately, monocular depth estimates are often inaccurate, due to estimation errors and inherent ambiguities, such as albedo vs. shading (cf. check shadow illusion), concavity vs. convexity (cf. hollow face illusion), distance vs. scale (cf. miniature cinematography), etc. As a result, the incorrect or inconsistent priors imposed by such depth estimates may mislead the NeRF into reconstructing incorrect shape and produce artifacts in the generated views." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "In this paper, we propose a method that embraces the uncertainty and ambiguities present in monocular depth esti" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16518" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.282 + ], + "angle": 0, + "content": "mates, by modelling a probability distribution over depth estimates. The ambiguities are retained at the stage of monocular depth estimation, and are only resolved once information from multiple views are fused together. We do so with a principled loss defined on probability distributions over depth estimates for different views. This loss selects the subset of modes of probability distributions that are consistent across all views and matches them with the modes of the depth distribution along different rays as modelled by the NeRF. It turns out that this operation can be interpreted as a probabilistic analogue of classical depth-based space carving [17]. For this reason, we dub our method Space Carving with Ambiguity-aware Depth Estimates, or SCADE for short." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.283, + 0.473, + 0.459 + ], + "angle": 0, + "content": "Compared to prior approaches of depth supervision [6,32] that only supervise the moments of NeRF's depth distribution (rather than the modes), our key innovation is that we supervise the modes of NeRF's depth distribution. The supervisory signal provided by the former is weaker than the latter, because the former only constrains the value of an integral aggregated along the ray, whereas the latter constrains the values at different individual points along the ray. Hence, the supervisory signal provided by the former is 2D (because it integrates over a ray), whereas the supervisory signal provided by the our method is 3D (because it is point-wise) and thus can be more fine-grained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.753 + ], + "angle": 0, + "content": "An important technical challenge is modelling probability distributions over depth estimates. Classical approaches use simple distributions with closed-form probability densities such as Gaussian or Laplace distributions. Unfortunately these distributions are not very expressive, since they only have a single mode (known as \"unimodal\") and have a fixed shape for the tails. Since each interpretation of an ambiguous image should be a distinct mode, these simple unimodal distributions cannot capture the complex ambiguities in depth estimates. Naive extensions like a mixture of Gaussians are also not ideal because some images are more ambiguous than others, and so the number of modes needed may differ for the depth estimates of different images. Moreover, learning such a mixture requires backpropagating through E-M, which is nontrivial. Any attempt at modifying the probability density to make it capable of handling a variable number of modes can easily run into an intractable partition function [4, 10, 31], which makes learning difficult because maximum likelihood requires the ability to evaluate the probability density, which is a function of the partition function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.473, + 0.886 + ], + "angle": 0, + "content": "To get around this conundrum, we propose representing the probability distribution with a set of samples generated from a neural network. Such a distribution can be learned with a conditional GAN; however, because GANs suffer from mode collapse, they cannot model multiple modes [11] and are therefore unsuited to modelling ambiguity. Instead, we propose leveraging conditional Implicit Maximum Likelihood Estimation (cIMLE) [19, 28] to learn the distribution, which is designed to avoid mode collapse." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.473, + 0.902 + ], + "angle": 0, + "content": "We consider the challenging setting of leveraging out-of" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.094, + 0.609, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.094, + 0.695, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.094, + 0.778, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.781, + 0.094, + 0.858, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.156, + 0.603, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.156, + 0.692, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.156, + 0.773, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.156, + 0.854, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.227, + 0.594, + 0.236 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.227, + 0.807, + 0.236 + ], + "angle": 0, + "content": "Ambiguity-Aware Depth Estimates" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.237, + 0.895, + 0.357 + ], + "angle": 0, + "content": "Figure 2. Ambiguities from a single image. We show samples from our ambiguity-aware depth estimates that is able to handle different types of ambiguities. (Top) An image of a chair taken from the top-view. Without context of the scene, it is unclear that it is an image of a chair. We show different samples from our ambiguity-aware depth estimates that are able to capture different degrees of convexity. (Bottom) An image of a cardboard under bad lighting conditions that capture the albedo vs shading ambiguity that is also represented by our different samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.895, + 0.499 + ], + "angle": 0, + "content": "domain depth priors to train NeRFs on real-world indoor scenes with sparse views. Under this setting, the depth priors we use are trained on a different dataset (e.g., Taskonomy) from the scenes our NeRFs are trained on (e.g., ScanNet). This setting is more challenging than usual due to domain gap between the dataset the prior is trained on and the scenes NeRF is asked to reconstruct. We demonstrate that our method outperforms vanilla NeRF and NeRFs with supervision from depth-based priors in novel view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.5, + 0.805, + 0.513 + ], + "angle": 0, + "content": "In summary, our key contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.522, + 0.894, + 0.582 + ], + "angle": 0, + "content": "- An method that allows the creation of NeRFs in unconstrained indoor settings from only a modest number of 2D views by introducing a sophisticated way to exploit ambiguity-aware monocular depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.591, + 0.894, + 0.65 + ], + "angle": 0, + "content": "- A novel way to sample distributions over image depth estimates based on conditional Implicit Maximum Likelihood Estimation that can represent depth ambiguities and capture a variable number of discrete depth modes." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.659, + 0.894, + 0.733 + ], + "angle": 0, + "content": "- A new space-carving loss that can be used in the NeRF formulation to optimize for a mode-seeking 3D density that helps select consistent depth modes across the views and thus compensate for the under-constrained photometric information in the few view regime." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.522, + 0.894, + 0.733 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.747, + 0.642, + 0.763 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.768, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Novel View Synthesis and 3D Reconstruction. Reconstructing the structure of a scene from a few views is a long standing problem in computer vision with a long literature. Neural Radiance Fields or NeRF [24] revolutionized the field by showing how to use weights of an MLP to represent a scene that is rendered using volume rendering [23]. A key innovation was the use of positional encoding [37, 38] to increase the effective capacity of the MLPs that model a emitted radiance and density as a function of position and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16519" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.136 + ], + "angle": 0, + "content": "viewing direction. Extensions of NeRF include works on unconstrained photo collections [22], dynamic scenes [20], deformable scenes [27], and reflective materials [1,39]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.473, + 0.385 + ], + "angle": 0, + "content": "A critical shortcoming of NeRF is its reliance on having many input views of a scene. Several approaches have been proposed, including adding patch likelihood losses [25], data-driven priors [36, 48], semantic consistency prior [12], image features [41], or surface [25, 39], occupancy [26], and depth [15, 32, 43] priors. DS-NeRF [6] uses the sparse point reconstructions recovered during Structure-from-Motion, to supervise the depth of sparse points in the recovered NeRF. In the same spirit, DDP [32] uses a depth completion network, that takes as input sparse point cloud projected to one an input view, and produces a depth estimate. Both works [15, 32] model depth with uncertainty but only supervise with moments of NeRF's depth distribution. In contrast, our work is able to represent multimodal depth estimates, which can handle the inherit ambiguities of depth estimation, and is able to seek the modes for each depth estimate to make a consistent prediction of the scene structure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.472, + 0.502 + ], + "angle": 0, + "content": "Inspired by traditional multi-view stereo, MVS-NeRF [3] and RC-MVSNet [2] incorporate the use cost volumes [9] to NeRF. To construct the cost volumes, these works look for agreement between features to look for correspondences, which is difficult under the setting of large variations in appearance or viewpoint. In contrast, our approach introduces a novel space carving loss that does not rely on feature correspondences and instead directly defines the loss in 3D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.472, + 0.59 + ], + "angle": 0, + "content": "Another line of works focuses on geometry reconstruction [40, 45, 49] by using the volumetric rendering scheme to learn a neural SDF representation. These works tackle a different problem on modeling geometry reconstruction, unlike NeRFs whose focus is modeling appearance for novel view synthesis, where our work falls under." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Depth Estimation from Single View. Depth estimation from a single image is a complex task due multiple ambiguities, including scene scale and shading / albedo ambiguities. Early efforts used MRFs to compute predictions on superpixels [33]. The advent of consumer depth cameras like Kinect [53] enabled the acquisition of larger scale indoor 3D datasets [35], leading to methods that used deep neural networks to predict depth from a single color image [7]. Nonetheless, scaling datasets for depth estimation remained a challenge. Deep3D [44] enabled the creation of stereo views by training on a large dataset of stereo movies, while [8] used the self-supervision of left-right consistency to learn depth from stereo views from driving cars. This approach was extended to videos where the egomotion is also estimated and self-supervision happens across time [54]. MegaDepth [21] uses the depth from SfM reconstructions of internet photos, together with semantic segmentation that conveys ordinal depth supervision cues, i.e. transient objects must be in front of the static scenes. Most recent, multi-task learning has shown promise in training depth estimators that work well in out-of-domain data [30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.224 + ], + "angle": 0, + "content": "In some cases, surface normal estimation has fewer pitfalls than direct depth estimation, as it suffers somewhat less from scale ambiguities. GeoNet [29] jointly estimates depth and surface normals, then uses the geometric relation between them to refine the estimates. LeRes [46] uses a second geometry reasoning module that refines a focal length estimate and the depth itself. Our depth estimation approach is derived from LeReS without the second stage, as the focal length is already estimated during SfM for NeRF scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.895, + 0.313 + ], + "angle": 0, + "content": "Most relevant is the work of Kendall and Gal [15], that learns depth estimation in a Bayesian setting, where their objective maximizes the likelihood under a predicted distribution. In our work, we use instead a multimodal depth estimation technique built on cIMLE [19], which makes our prior robust to ambiguities in depth prediction." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.325, + 0.629, + 0.342 + ], + "angle": 0, + "content": "3. Background" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.349, + 0.779, + 0.364 + ], + "angle": 0, + "content": "3.1. Neural Radiance Fields (NeRF)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.895, + 0.541 + ], + "angle": 0, + "content": "A neural radiance field [24], or NeRF for short, represents a field in 3D space, where each point represents an infinitesimal particle with a certain opacity that emits varying amounts of light along different viewing directions. The opacity at a point is represented as a volume density, and the amount of emitted light is represented as a colour. Mathematically, a NeRF is represented as two parameterized functions, a volume density \\(\\sigma_{\\theta}:\\mathbb{R}^{3}\\to \\mathbb{R}_{\\geq 0}\\) and a colour \\(\\mathbf{c}_{\\psi}:\\mathbb{R}^3\\times S^2\\rightarrow [0,255]^3\\). The former maps a 3D coordinate \\(\\mathbf{x}\\in \\mathbb{R}^3\\) to a volume density \\(\\sigma \\in \\mathbb{R}_{\\geq 0}\\), and the latter maps a 3D coordinate \\(\\mathbf{x}\\in \\mathbb{R}^3\\) and a viewing direction \\(\\mathbf{d}\\in S^2\\) to a colour \\(\\mathbf{c}\\in [0,255]^3\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.895, + 0.689 + ], + "angle": 0, + "content": "To render a NeRF from a view, we shoot rays from each pixel on the camera sensor and integrate over the product of colour, volume density and visibility along the ray to arrive at each pixel value. Visibility at a point is represented with transmittance, which accumulates the exponentiated negative volume density multiplicatively up to the point. The higher transmittance at a point, the more visible the point is from the camera. Mathematically, if the camera ray is \\(\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}\\), where \\(\\mathbf{o}\\) is the camera centre and \\(\\mathbf{d}\\) is the ray direction, the pixel value \\(\\hat{I}_{\\theta,\\psi}(\\mathbf{o},\\mathbf{d})\\) we would have is:" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.699, + 0.894, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {I} _ {\\theta , \\psi} (\\mathbf {o}, \\mathbf {d}) := \\int_ {t _ {n}} ^ {t _ {f}} T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) \\sigma_ {\\theta} (\\mathbf {o} + t \\mathbf {d}) \\mathbf {c} _ {\\psi} (\\mathbf {o} + t \\mathbf {d}, \\mathbf {d}) d t \\\\ \\text {w h e r e} T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\sigma_ {\\theta} (\\mathbf {o} + s \\mathbf {d}) \\mathrm {d} s\\right). \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.826 + ], + "angle": 0, + "content": "In the expressions above, \\( t_n \\) and \\( t_f \\) denote the points the ray intersects with the near plane and far plane respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.834, + 0.767, + 0.85 + ], + "angle": 0, + "content": "3.2. Inverse Rendering with NeRF" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Given a set of real-world images from known views, inverse rendering aims to find the scene whose rendered images match the real-world images. If we use \\( I(\\mathbf{o}, \\mathbf{d}) \\) to de" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "16520" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "note the pixel value for the ray \\(\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}\\), this problem can be cast as an optimization problem, namely:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.132, + 0.47, + 0.164 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta , \\psi} \\sum_ {\\mathbf {o}} \\sum_ {\\mathbf {d}} \\| \\hat {I} _ {\\theta , \\psi} (\\mathbf {o}, \\mathbf {d}) - I (\\mathbf {o}, \\mathbf {d}) \\| _ {2} ^ {2} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.168, + 0.471, + 0.3 + ], + "angle": 0, + "content": "If \\(\\hat{I}_{\\theta, \\psi}(\\mathbf{o}, \\mathbf{d})\\) is differentiable w.r.t. the parameters \\(\\theta, \\psi\\), this problem can be tackled straightforwardly with gradient-based optimization. To enable this, the volume density function \\(\\sigma_{\\theta}\\) and the colour function \\(\\mathbf{c}_{\\psi}\\) are chosen to be neural networks. As a result, inverse rendering amounts to training the NeRF to reconstruct the scene in a way that is consistent with the images that are given. Once the NeRF is trained, novel view synthesis can be achieved by rendering the NeRF from new, unseen views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.469, + 0.448 + ], + "angle": 0, + "content": "Since this optimization problem is underconstrained, in general many views are needed to reconstruct the scene accurately. Yet, in practical applications, typically only a few views are available, hence priors are needed to provide sufficient constraints. In this paper, we consider priors in the form of monocular depth estimates from each view. The monocular depth estimates are trained on different datasets from the dataset NeRF is trained on to simulate real-world conditions where there is a domain gap between what the prior was trained on and what the NeRF is trained on." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.45, + 0.315, + 0.464 + ], + "angle": 0, + "content": "3.3. Ray Termination Distance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.47, + 0.598 + ], + "angle": 0, + "content": "In order to leverage depth priors, a natural way is to use them to constrain the ray termination distance. Because NeRF can represent non-opaque surfaces, there is no single ray termination distance. Instead, there is a distribution of ray termination distances. The cumulative distribution function (CDF) of this distribution represents the probability that the ray terminates before reaching a given point. It turns out that the probability density of this distribution \\( f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t) \\) is given by [6]:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.61, + 0.47, + 0.627 + ], + "angle": 0, + "content": "\\[\nf _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) = T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) \\sigma_ {\\theta} (\\mathbf {o} + t \\mathbf {d}) \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.637, + 0.168, + 0.652 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.661, + 0.41, + 0.677 + ], + "angle": 0, + "content": "4.1. Supervising Ray Termination Distance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.471, + 0.901 + ], + "angle": 0, + "content": "If all surfaces were opaque and the ground truth depth were given, supervising NeRF with the ground truth depth would be straightforward. All that is needed is to make the NeRFs distribution of ray termination distances as close as possible to a delta distribution centred at the ground truth depth. However, when the ground truth depth is not known, we have to use monocular depth estimates as supervision. The challenge is that unlike ground truth depth, monocular depth estimates may not be stereo-consistent, due to estimation error and inherent ambiguity. As a result, it may not be possible to find a scene that is consistent with the depth estimates from every view. Therefore, in order to reconstruct the scene, we must model the uncertainty and ambiguity in the depth estimates, which can be mathematically characterized by distributions. Such ambiguities cannot be resolved from" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.088, + 0.892, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.263, + 0.892, + 0.29 + ], + "angle": 0, + "content": "Figure 3. Network Architecture for our Ambiguity-aware Depth Estimates." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.297, + 0.894, + 0.34 + ], + "angle": 0, + "content": "a single view and can often be resolved from multiple views. So we need an method that can fuse together uncertain depth estimates from different views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.893, + 0.457 + ], + "angle": 0, + "content": "A natural way of representing uncertainty is through a probability distribution. When there are ambiguities, the distribution of depth estimates are typically multimodal, i.e., their probability densities have disjoint peaks, where each mode represents one interpretation of the scene structure. For example, albedo vs shading ambiguity as shown in Figure 2 can result in multiple plausible interpretations and make the distribution multimodal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.894, + 0.547 + ], + "angle": 0, + "content": "An added challenge arises when non-opaque surfaces are present. In this case, there is no single ground truth depth, and so the distribution of ground truth depths is multimodal. So even after training the NeRF, the distribution of ray termination distances induced by NeRF should be multimodal, as illustrated in the glass walls in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.894, + 0.693 + ], + "angle": 0, + "content": "Prior methods compute moments (i.e., mean and/or variance) of the distribution of depth estimates or ray termination distance induced by NeRF. For example, DS-NeRF [6] predicts the mean depth estimate and uses reprojection error as a proxy for the variance. It then minimizes the KL divergence from the distribution of ray termination distances induced by NeRF to a Gaussian whose moments match those of the depth estimates. DDP [32] fits a Gaussian to distribution of ray termination distances and maximizes the likelihood of the depth estimate under the Gaussian." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.695, + 0.894, + 0.768 + ], + "angle": 0, + "content": "Distilling complex distributions to moments has the drawback of ignoring their possible multimodality. Because both the distribution of depth estimates and ray termination distances are potentially multimodal, it is important to handle the multimodality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.775, + 0.598, + 0.789 + ], + "angle": 0, + "content": "4.2. SCADE" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We now present our novel method Space Carving with Ambiguity-aware Depth Estimates (SCADE). Our contributions address the existing problems and drawbacks mentioned in the previous section. First, SCADE accounts for the multimodality of both the distributions of monocular depth estimates and ray termination distances that arise due to inherent ambiguities (Sec 4.2.1) and non-opaque surfaces." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16521" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.21 + ], + "angle": 0, + "content": "Second, SCADE is also able to resolve these ambiguities by fusing together information from multiple views through our space carving loss (Sec 4.2.3) that uses the reverse cross entropy loss. Because this a loss on the distribution rather than moments of the distribution (which was the paradigm in prior work [6, 32]), it achieves supervision in 3D rather than 2D. Third, our loss formulation is sample-based (Sec 4.2.2) and so is computationally efficient to optimize." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.217, + 0.406, + 0.231 + ], + "angle": 0, + "content": "4.2.1 Our Ambiguity-aware Depth Estimates" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.232, + 0.473, + 0.422 + ], + "angle": 0, + "content": "We handle multimodality of monocular depth distributions by introducing our ambiguity-aware depth estimation module to account for ambiguities in depth estimation from a single view (Figure 1, 2). In contrast to existing monocular depth estimation networks [47] that predict single point estimates for depth, we model the inherent uncertainty in monocular depth estimation by representing the distribution as a set of samples generated by a neural network. We propose leveraging conditional Implicit Maximum Likelihood estimation (cIMLE) [19] to learn a multimodal distribution of depth estimates. We chose cIMLE rather than conditional GANs [14] in order to avoid mode collapse, which can lead to a unimodal distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.473, + 0.584 + ], + "angle": 0, + "content": "Figure 3 shows our network architecture. Concretely, we combine cIMLE with a state-of-the-art monocular depth estimation network, LeReS [47]. Our ambiguity-aware depth estimation module \\((G)\\) takes an input image \\((I)\\) and a latent code \\(z\\sim \\mathcal{N}(0,\\mathbf{I})\\) and outputs a conditional depth sample \\(G(I,z)\\) for the input image \\(I\\). To inject randomness into the network, we follow the technique used in [14] and incorporate AdaIn layers into the network backbone that predicts a scale and shift to the intermediate network features. Specifically, we added four AdaIn layers to the encoder of the depth estimation backbone." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.592, + 0.395, + 0.606 + ], + "angle": 0, + "content": "4.2.2 Sample-based Losses on Distributions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.47, + 0.725 + ], + "angle": 0, + "content": "We desire to achieve an agreement between the distributions from our ambiguity-aware prior and the ray termination distance from NeRF to constrain the NeRF optimization under the sparse view set-up using our learned prior. As distributions are continuous, taking their analytical integral is computationally intractable. Thus, in order to define a differentiable loss function for our optimization problem, we result in a sample-based loss on these two distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Samples from depth prior. As previously described, we leverage cIMLE to sample from our ambiguity-aware depth prior. Sampling \\( z_{1},\\ldots ,z_{M}\\sim \\mathcal{N}(0,\\mathbf{I}) \\), we get depth map samples \\( G(I,z_1),\\dots,G(I,z_M) \\) for input image \\( I \\). Hence we denote corresponding samples to estimate and represent the distribution for ray \\( \\mathbf{r} \\) as \\( y_{1},y_{2},\\dots,y_{M}\\sim G_{\\mathbf{o,d}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.827, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Samples from NeRF. For the distribution given by the ray termination distances modelled by NeRF, we sample from its probability density function \\( f_{\\theta ,\\mathbf{o},\\mathbf{d}} \\) (Eq. 3) with inverse transform sampling. Concretely, we define the probability mass function for ray \\( \\mathbf{r} \\) as \\( f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i) \\) as given in Eq. 3 with" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.093, + 0.695, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.163, + 0.695, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.578, + 0.23, + 0.66, + 0.239 + ], + "angle": 0, + "content": "2D Expected Depth" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.093, + 0.847, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.163, + 0.846, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.23, + 0.824, + 0.239 + ], + "angle": 0, + "content": "3D Space Carving (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.24, + 0.894, + 0.308 + ], + "angle": 0, + "content": "Figure 4. Our space carving loss supervises the ray termination in 3D as opposed to existing approaches that supervise on 2D expected depth. As shown, this clears out clouds of dust in space. Moreover supervising in 3D allows for wide baseline input views and still finds the common mode that correctly snaps the surfaces." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.314, + 0.894, + 0.404 + ], + "angle": 0, + "content": "samples \\(t_1,\\ldots ,t_K\\) , where \\(t_i\\in [t_n,t_f]\\forall i\\) . By inverse transform sampling, we first compute the cumulative distribution function (CDF) of the ray termination distribution at samples \\(t_i\\) , which we denote as \\(F_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i) = \\sum_{j < i}f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i)\\) . Thus our samples \\(x_{1},x_{2},\\dots,x_{N}\\) of ray termination distances from NeRF are then given by:" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.411, + 0.892, + 0.437 + ], + "angle": 0, + "content": "\\[\nx _ {i} = F _ {\\theta , \\mathbf {o}, \\mathbf {d}} ^ {- 1} (u _ {i}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.631, + 0.434, + 0.762, + 0.449 + ], + "angle": 0, + "content": "where \\(u_{i}\\sim \\mathcal{U}(0,1)\\)" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.462, + 0.726, + 0.477 + ], + "angle": 0, + "content": "4.2.3 Our Space Carving Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.624 + ], + "angle": 0, + "content": "We now introduce our novel space carving loss utilizes the samples from both multimodal distributions to constrain the NeRF optimization. The goal is to find a subset of modes captured in the monocular depth distributions from each view that are globally consistent. In doing so, we can fuse together the information from the different views, since the inherent ambiguities are only resolved given information from multiple views. This would allow us to find a common shape that is consistent across all views and \"snap\" objects surfaces together." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.894, + 0.727 + ], + "angle": 0, + "content": "We thus desire a loss that has mode seeking behavior, that is the modes of the distribution being trained should be a subset of the modes of the distribution that provides supervision. One such loss is the reverse cross entropy, which is the cross entropy from the NeRF ray termination distance distribution to the distribution of our ambiguity-aware depth estimates:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.736, + 0.892, + 0.754 + ], + "angle": 0, + "content": "\\[\nH \\left(f _ {\\theta , \\mathbf {o}, \\mathbf {d}}, G _ {\\mathbf {o}, \\mathbf {d}}\\right) = - \\mathbb {E} _ {f _ {\\theta , \\mathbf {o}, \\mathbf {d}}} [ \\log G _ {\\mathbf {o}, \\mathbf {d}} ]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.892, + 0.822 + ], + "angle": 0, + "content": "As shown in the IMLE papers [19, 28], this is equivalent to penalizing the minimum of the L2 norm between the samples from the two distributions, please see [18] for the full proof. Hence, our space carving loss is given by" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.829, + 0.892, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s p a c e ＿ c a r v i n g}} (\\mathbf {r}) = \\sum_ {i \\in [ N ]} \\min _ {j \\in [ M ]} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Because our novel space carving loss operates on distributions rather than moments of distributions, we can have" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16522" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.253 + ], + "angle": 0, + "content": "different supervision targets for different points along the ray. In contrast, if the loss were to only to operate on moments, which are integrals along the ray, this only yields the same supervision target for all points along the ray. Therefore, our loss allows us to supervise in 3D, unlike prior methods [6, 32] (which use losses on moments) that supervise in 2D. 3D supervision allows us to clear out dust in space, since in order to move a sample from the ray termination distance distribution farther in depth, the loss would have to decrease the probability density of all the points in front of it. These advantages are highlighted in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.472, + 0.283 + ], + "angle": 0, + "content": "Our total loss to optimize and train our NeRF model is given by" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.294, + 0.47, + 0.311 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {p h o t o m e t r i c}} + \\lambda \\mathcal {L} _ {\\text {s p a c e ＿ c a r v i n g}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.47, + 0.352 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{photometric}}\\) is the standard MSE loss on the predicted and ground truth image. See Fig. 1 for our overall pipeline." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.364, + 0.165, + 0.379 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.47, + 0.412 + ], + "angle": 0, + "content": "In this section, we present our experimental evaluation to demonstrate the advantages of SCADE." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.417, + 0.364, + 0.431 + ], + "angle": 0, + "content": "5.1. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.473, + 0.637 + ], + "angle": 0, + "content": "We evaluate our method on ScanNet [5] and an in-the-wild dataset we collected1. We use the sparse-view ScanNet data used by DDP [32] in their evaluations, which comprises of three sample scenes each with 18 to 20 train images and 8 test images. To further test the robustness of our method, we further evaluated our method on three in-the-wild scenes collected using an iPhoneX. We captured sparse views in three different scenes - basement, kitchen and lounge, where each scene has 18 to 23 train images and 8 test images. Following similar data preprocessing steps as DDP [32], we ran SfM [34] on all images to obtain camera poses for NeRF training. For quantitative comparison, we follow the original NeRF [24] paper and report the PSNR, SSIM [42] and LPIPS [52] on the novel test views." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.647, + 0.295, + 0.662 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.472, + 0.722 + ], + "angle": 0, + "content": "We train our ambiguity-aware prior on the Taskonomy [50] dataset and initialize the weights with the pretrained LeReS [47] model. We use \\( M = 20 \\) depth estimates in our experiments. See supplement for additional details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.305, + 0.743 + ], + "angle": 0, + "content": "5.3. Experiments on ScanNet" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.473, + 0.879 + ], + "angle": 0, + "content": "We evaluate on ScanNet following the evaluation from DDP [32]. We compare to the original NeRF [24] (Vanilla NeRF) and the recent state-of-the-art NeRF with depth prior-based supervision, Dense Depth Prior [32] (DDP). Table 1 shows SCADE quantitatively outperforming the baselines. Because we are interested in simulating real-world conditions with a domain gap between the prior and the NeRF, our setting requires the use of out-of-domain priors. Since DDP uses a in-domain prior, we retrain DDP's depth completion" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.468, + 0.901 + ], + "angle": 0, + "content": "1Also see supplement for results on the Tanks and Temples dataset [16]." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.083, + 0.89, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.195, + 0.892, + 0.223 + ], + "angle": 0, + "content": "Figure 5. Depth and Fusion Comparison. Depth map and fusion comparison between SCADE and DDP." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.227, + 0.892, + 0.367 + ], + "angle": 0, + "content": "
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]19.030.6700.398
NerfingMVS [47]16.290.6260.502
IBRNet [41]13.250.5290.673
MVSNeRF [3]15.670.5330.635
DS-NeRF [6]20.850.7130.344
DDP [32]19.290.6950.368
SCADE (Ours)21.540.7320.292
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.371, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Table 1. ScanNet Results. Results for DS-NeRF and NerfingMVS follow what was reported in prior literature [32]. Because our setting requires out-of-domain priors, the results for DDP are with out-of-domain priors. The results of DDP with in-domain priors are (20.96, 0.737, 0.236) for PSNR, SSIM and LPIPS, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.447, + 0.892, + 0.492 + ], + "angle": 0, + "content": "network using their official code and hyperparameters on Taskonomy [50], i.e. the same out-of-domain dataset that our prior is trained on." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.895, + 0.655 + ], + "angle": 0, + "content": "Figure 6 shows our qualitative results. As shown, compared to the baselines, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (first, third and last column). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (second column), the back of the chair (fourth column) and the legs of the piano stool (fifth column). Moreover, Fig. 5 shows rendered depthmaps and fusion results using [51] on a Scannet scene. Notice that SCADE is able to recover better geometry compared to DDP - see corner of the calendar, cabinets and office chair in the right image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.661, + 0.795, + 0.676 + ], + "angle": 0, + "content": "5.4. Experiments on In-the-Wild Data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To further test the robustness of SCADE, we further evaluate on data collected in-the-wild with a standard phone camera (iPhoneX). The intrinsics for different views are different and are not known to the algorithm. As shown in Table 2, SCADE with the same out-of-domain prior (trained on Taskonomy) outperforms the baselines on in-the-wild captured data, which demonstrates its robustness. Figure 7 shows qualitative examples. Interestingly, we are able to recover the room behind the glass better the baselines, whose results are more blurry (first, third and fourth column). We are also able to recover objects behind the glass such as the monitor and chair (first column). As discussed in Sect. 4.1, non-opaque surfaces are the most challenging because both the ground truth distribution of ray termination distances induced by NeRF and the distribution of estimated depths" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16523" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.091, + 0.87, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.346, + 0.895, + 0.388 + ], + "angle": 0, + "content": "Figure 6. Qualitative results on ScanNet. As shown, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (1st, 3rd, last columns). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (2nd column), the back of the chair (4th column) and the legs of the piano stool (5th column)." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.398, + 0.47, + 0.478 + ], + "angle": 0, + "content": "
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]20.460.7130.398
DDP [32]21.280.7270.366
SCADE (Ours)22.820.7430.347
" + }, + { + "type": "table_caption", + "bbox": [ + 0.184, + 0.48, + 0.362, + 0.492 + ], + "angle": 0, + "content": "Table 2. In-the-wild Results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.47, + 0.526 + ], + "angle": 0, + "content": "from the prior must be multimodal. This validates the ability of our model to capture the multimodal distributions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.47, + 0.6 + ], + "angle": 0, + "content": "Similar to the ScanNet results, we are able to recover crisp shapes of objects such as the thin table leg and the white chair (second and last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (fifth and last column)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.607, + 0.231, + 0.623 + ], + "angle": 0, + "content": "5.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.471, + 0.833 + ], + "angle": 0, + "content": "Supervision on full distribution vs moments We first validate the importance of using our novel space carving loss that supervises the full distribution of ray termination distance rather than just its moments. The latter integrates along the ray, and so provides one target value for the entire ray, which effectively makes it 2D supervision. The former provides different target values for different samples along the same ray, which makes it 3D supervision. We adapt our method to use 2D supervision proposed in the recent MonoSDF [49], which computes the expected ray termination distance and aligns the output depth map with a monocular depth estimation prior using the MiDaS [30] loss. We use our learned prior as the monocular depth estimate. Table 3 validates the effectiveness of our space carving loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.842, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Multimodal prior vs unimodal prior. Our prior models does not constrain the depth distribution to a particular form and allows it to be multimodal. In contrast, DDP's depth completion prior assumes a Gaussian, which is unimodal." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.398, + 0.892, + 0.508 + ], + "angle": 0, + "content": "
PSNR ↑SSIM ↑LPIPS ↓
MonoSDF supervision20.130.7100.332
DDP prior - single sample20.850.7120.320
DDP prior - multiple samples21.000.7180.316
Our prior - single sample21.220.7140.318
SCADE (Ours)21.540.7320.292
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.512, + 0.895, + 0.554 + ], + "angle": 0, + "content": "Table 3. Ablation Study. Results on the Scannet dataset. MonoSDF supervision refers to supervising with MonoSDF loss on expected ray termination distance using our prior." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.894, + 0.652 + ], + "angle": 0, + "content": "We ablate our prior against DDP's by sampling from their Gaussian distribution. We train with our space carving loss using both a single sample, as well as \\( M \\) samples drawn from DDP's prior. As shown in Table 3, while both perform better than the 2D supervision provided by MonoSDF, but they are subpar compared to using our multimodal prior." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.895, + 0.763 + ], + "angle": 0, + "content": "Multiple vs single sample. Finally, we also ablate on using a single sample vs multiple samples for our space carving loss. For the single sample set-up, we supervise using the sample mean of the depth estimates, which is equivalent to the maximum likelihood estimate of the depth under Gaussian likelihood. Results in Table 3 show the importance of using multiple samples for our space carving loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.769, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Sparsity. We further show addt'l results under varying number of views in Tab 4. Note that in general sparsity is not fully reflected by the absolute number of views, because all else being equal, a larger scene requires more views to attain complete coverage. Following prior work [32], we also report the average number of views that see the same point as another measure of sparsity. As shown, our setting is at the edge of the theoretical lower limit of 2 for general-purpose reconstruction, which shows view sparsity." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16524" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.87, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.348, + 0.895, + 0.391 + ], + "angle": 0, + "content": "Figure 7. Qualitative results on In-the-Wild data. As shown, we are able to recover the room behind the glass better the baselines, whose results are more blurry (1st, 3rd, 4th column). Also, SCADE is able to recover crisp shapes of objects such as the thin table leg and the white chair (2nd, last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (5th, last column)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.399, + 0.472, + 0.449 + ], + "angle": 0, + "content": "
ave. #views visible1.871.982.012.2
absolute #views18202224
DDP / SCADE19.35/ 21.6622.4/ 23.6723.10/ 24.0023.56/ 24.84
" + }, + { + "type": "table_caption", + "bbox": [ + 0.088, + 0.451, + 0.46, + 0.465 + ], + "angle": 0, + "content": "Table 4. PSNR for DDP [32]/SCADE on scene781 of Scannet." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.469, + 0.305, + 0.574 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.469, + 0.468, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.578, + 0.471, + 0.618 + ], + "angle": 0, + "content": "Figure 8. Depth Mode Discussion. a) Train images from Taskonomy [50] and their labels. Notice that non-opaque surfaces are labelled differently. b) Output of our prior on reflective surfaces." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.63, + 0.436, + 0.646 + ], + "angle": 0, + "content": "5.6. Discussion on our Ambiguity-Aware Prior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.647, + 0.473, + 0.866 + ], + "angle": 0, + "content": "We provide addt'l details on our ambiguity-aware prior on i) how and why it works, ii) its performance on reflective surfaces, which is a common failure case for depth estimate, and iii) provide an intuition on how what our depth modes look like. i) We achieve variable depth modes by exploiting inconsistently labeled training data. As shown in Fig 8-a, in Taskonomy [50], different training images with non-opaque surfaces label depth differently: shooting through the glass (left), on the glass (middle), or a mixture of both (right). Despite multiple possible depth labels, each image only has one ground truth label. Training with cIMLE allows our prior to model these multiple possible (ambiguous) outputs through sampling\\(^2\\), even when given only one label per image. Interestingly when testing our prior on a test image with a mirror, we find that it is able to capture variable modes" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.47, + 0.903 + ], + "angle": 0, + "content": "2See supplement for more qualitative examples on our ambiguity-aware depth estimates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.892, + 0.476 + ], + "angle": 0, + "content": "on reflective surfaces, including the \"correct\" flat surface as shown in Fig 8-b. An intuition of what the depth modes look like is for example if a ray intersects \\( n - 1 \\) non-opaque surfaces, the \\( n \\) modes are intersections with the non-opaque surfaces and the terminating point on the opaque surface." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.48, + 0.619, + 0.495 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.895, + 0.718 + ], + "angle": 0, + "content": "In this paper, we present a new approach towards NeRF reconstruction that can work with a modest number of in-the-wild views of an indoor scene. We address the underconstrained nature of this problem by regularizing the NeRF optimization with additional depth estimates for each view. Our key technical contribution is to model multimodality in the depth estimates, which can capture inherent ambiguities in monocular depth estimation as well as the possible presence of non-opaque surfaces. We resolve ambiguities using a novel space carving loss that fuses the multimodal depth estimates from different views and seeks the modes that are consistent across views so as to arrive at a globally consistent 3D reconstruction. The improved recovery of shape and appearance enables higher fidelity novel view synthesis from sparse views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.721, + 0.894, + 0.825 + ], + "angle": 0, + "content": "Limitations and Future Work. The performance of our method is constrained by the quality of the monocular depth priors. While we found that our prior generalizes well across domains, if the domain gap is too great, the performance of our method will degrade. A future direction would be to detect when this happens and dynamically adjust the strength of depth supervision in response." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.827, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. We sincerely thank the Teleportation and CCI team in Google for all the insightful discussions during the summer. We also thank Mirko Visontai for internship logistics, Guandao Yang for experiment set-up assist, and Weicheng Kuo for looking over the paper." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16525" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.472, + 0.183 + ], + "angle": 0, + "content": "[1] Sai Bi, Zexiang Xu, Pratul Srinivasan, Ben Mildenhall, Kalyan Sunkavalli, Miloš Hasan, Yannick Hold-Geoffroy, David Kriegman, and Ravi Ramamoorthi. Neural reflectance fields for appearance acquisition. arXiv preprint arXiv:2008.03824, 2020. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Di Chang, Aljaž Božić, Tong Zhang, Qingsong Yan, Yingcong Chen, Sabine Susstrunk, and Matthias Nießner. 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SCADE Overview. We present SCADE, a novel technique for NeRF reconstruction under sparse, unconstrained views for in-the-wild indoor scenes. We leverage on generalizable monocular depth priors and address to represent the inherent ambiguities of monocular depth by exploiting our ambiguity-aware depth estimates (left). Our approach accounts for multimodality of both distributions using our novel space carving loss that seeks to disambiguate and find the common mode to fuse the information between different views (middle). SCADE enables better photometric reconstruction especially in highly ambiguous scenes, e.g. non-opaque surfaces (right). + +# Abstract + +Neural radiance fields (NeRFs) have enabled high fidelity 3D reconstruction from multiple 2D input views. However, a well-known drawback of NeRFs is the less-than-ideal performance under a small number of views, due to insufficient constraints enforced by volumetric rendering. To address this issue, we introduce SCADE, a novel technique that improves NeRF reconstruction quality on sparse, unconstrained input views for in-the-wild indoor scenes. To constrain NeRF reconstruction, we leverage geometric priors in the form of per-view depth estimates produced with state-of-the-art monocular depth estimation models, which can generalize across scenes. A key challenge is that monocular depth estimation is an ill-posed problem, with inherent ambiguities. To handle this issue, we propose a new method that learns to predict, for each view, a continuous, multimodal distribution of depth estimates using conditional Implicit Maximum Likelihood Estimation (cIMLE). In order to disambiguate exploiting multiple views, we introduce an original space carving loss that guides the NeRF representation to fuse multiple hypothesized depth maps from each view and distill from them a common geometry that is consistent with all views. Experiments show that our approach enables higher fidelity novel view synthesis from sparse views. Our project page can be found at scade-spacecarving-nerfs.github.io. + +# 1. Introduction + +Neural radiance fields (NeRF) [24] have enabled high fidelity novel view synthesis from dozens of input views. Such number of views are difficult to obtain in practice, however. When given only a small number of sparse views, vanilla NeRF tends to struggle with reconstructing shape accurately, due to inadequate constraints enforced by the volume rendering loss alone. + +Shape priors can help remedy this problem. Various forms of shape priors have been proposed for NeRFs, such as object category-level priors [13], and handcrafted data-independent priors [25]. The former requires knowledge of category labels and is not applicable to scenes, and the latter is agnostic to the specifics of the scene and only encodes low-level regularity (e.g., local smoothness). A form of prior that is both scene-dependent and category-agnostic is per-view monocular depth estimates, which have been explored in prior work [6, 32]. Unfortunately, monocular depth estimates are often inaccurate, due to estimation errors and inherent ambiguities, such as albedo vs. shading (cf. check shadow illusion), concavity vs. convexity (cf. hollow face illusion), distance vs. scale (cf. miniature cinematography), etc. As a result, the incorrect or inconsistent priors imposed by such depth estimates may mislead the NeRF into reconstructing incorrect shape and produce artifacts in the generated views. + +In this paper, we propose a method that embraces the uncertainty and ambiguities present in monocular depth esti + +mates, by modelling a probability distribution over depth estimates. The ambiguities are retained at the stage of monocular depth estimation, and are only resolved once information from multiple views are fused together. We do so with a principled loss defined on probability distributions over depth estimates for different views. This loss selects the subset of modes of probability distributions that are consistent across all views and matches them with the modes of the depth distribution along different rays as modelled by the NeRF. It turns out that this operation can be interpreted as a probabilistic analogue of classical depth-based space carving [17]. For this reason, we dub our method Space Carving with Ambiguity-aware Depth Estimates, or SCADE for short. + +Compared to prior approaches of depth supervision [6,32] that only supervise the moments of NeRF's depth distribution (rather than the modes), our key innovation is that we supervise the modes of NeRF's depth distribution. The supervisory signal provided by the former is weaker than the latter, because the former only constrains the value of an integral aggregated along the ray, whereas the latter constrains the values at different individual points along the ray. Hence, the supervisory signal provided by the former is 2D (because it integrates over a ray), whereas the supervisory signal provided by the our method is 3D (because it is point-wise) and thus can be more fine-grained. + +An important technical challenge is modelling probability distributions over depth estimates. Classical approaches use simple distributions with closed-form probability densities such as Gaussian or Laplace distributions. Unfortunately these distributions are not very expressive, since they only have a single mode (known as "unimodal") and have a fixed shape for the tails. Since each interpretation of an ambiguous image should be a distinct mode, these simple unimodal distributions cannot capture the complex ambiguities in depth estimates. Naive extensions like a mixture of Gaussians are also not ideal because some images are more ambiguous than others, and so the number of modes needed may differ for the depth estimates of different images. Moreover, learning such a mixture requires backpropagating through E-M, which is nontrivial. Any attempt at modifying the probability density to make it capable of handling a variable number of modes can easily run into an intractable partition function [4, 10, 31], which makes learning difficult because maximum likelihood requires the ability to evaluate the probability density, which is a function of the partition function. + +To get around this conundrum, we propose representing the probability distribution with a set of samples generated from a neural network. Such a distribution can be learned with a conditional GAN; however, because GANs suffer from mode collapse, they cannot model multiple modes [11] and are therefore unsuited to modelling ambiguity. Instead, we propose leveraging conditional Implicit Maximum Likelihood Estimation (cIMLE) [19, 28] to learn the distribution, which is designed to avoid mode collapse. + +We consider the challenging setting of leveraging out-of + +![](images/89ae8a01be14ce67f619ad8b234580bd782b76021c3c70019a5b9d7fbb59aa90.jpg) + +![](images/a06fd61cd86dab5c1198a5da0f1e188d15aa7047d12b01b972958a739eeec331.jpg) + +![](images/68d33f6a715203b18ec8f4c3b82c6cb7b9e4b4f0b15c1a3d22ce704b35e778c8.jpg) + +![](images/13559aab43aa532959f7217e43d80f5dd5c5d23b0037c75dad3323d3954e0466.jpg) + +![](images/22fce397da257929668b856372fb7391c94c99ce422710eedf4bda265c1f0754.jpg) +Input Image + +![](images/6b3d450c6b39276ec11d0710dfd745893d459c0730b59fac991eb1a3c2ac5c7f.jpg) +Ambiguity-Aware Depth Estimates + +![](images/e81b800d71ea46699ae5cf16dcac3e985927f8f81fd5d4df9b54df2184be02b6.jpg) +Figure 2. Ambiguities from a single image. We show samples from our ambiguity-aware depth estimates that is able to handle different types of ambiguities. (Top) An image of a chair taken from the top-view. Without context of the scene, it is unclear that it is an image of a chair. We show different samples from our ambiguity-aware depth estimates that are able to capture different degrees of convexity. (Bottom) An image of a cardboard under bad lighting conditions that capture the albedo vs shading ambiguity that is also represented by our different samples. + +![](images/d8d127bc3b443638620fdab80b812ae0ca16954b16deff9a3bd0cf586025dffd.jpg) + +domain depth priors to train NeRFs on real-world indoor scenes with sparse views. Under this setting, the depth priors we use are trained on a different dataset (e.g., Taskonomy) from the scenes our NeRFs are trained on (e.g., ScanNet). This setting is more challenging than usual due to domain gap between the dataset the prior is trained on and the scenes NeRF is asked to reconstruct. We demonstrate that our method outperforms vanilla NeRF and NeRFs with supervision from depth-based priors in novel view synthesis. + +In summary, our key contributions include: + +- An method that allows the creation of NeRFs in unconstrained indoor settings from only a modest number of 2D views by introducing a sophisticated way to exploit ambiguity-aware monocular depth estimation. +- A novel way to sample distributions over image depth estimates based on conditional Implicit Maximum Likelihood Estimation that can represent depth ambiguities and capture a variable number of discrete depth modes. +- A new space-carving loss that can be used in the NeRF formulation to optimize for a mode-seeking 3D density that helps select consistent depth modes across the views and thus compensate for the under-constrained photometric information in the few view regime. + +# 2. Related Work + +Novel View Synthesis and 3D Reconstruction. Reconstructing the structure of a scene from a few views is a long standing problem in computer vision with a long literature. Neural Radiance Fields or NeRF [24] revolutionized the field by showing how to use weights of an MLP to represent a scene that is rendered using volume rendering [23]. A key innovation was the use of positional encoding [37, 38] to increase the effective capacity of the MLPs that model a emitted radiance and density as a function of position and + +viewing direction. Extensions of NeRF include works on unconstrained photo collections [22], dynamic scenes [20], deformable scenes [27], and reflective materials [1,39]. + +A critical shortcoming of NeRF is its reliance on having many input views of a scene. Several approaches have been proposed, including adding patch likelihood losses [25], data-driven priors [36, 48], semantic consistency prior [12], image features [41], or surface [25, 39], occupancy [26], and depth [15, 32, 43] priors. DS-NeRF [6] uses the sparse point reconstructions recovered during Structure-from-Motion, to supervise the depth of sparse points in the recovered NeRF. In the same spirit, DDP [32] uses a depth completion network, that takes as input sparse point cloud projected to one an input view, and produces a depth estimate. Both works [15, 32] model depth with uncertainty but only supervise with moments of NeRF's depth distribution. In contrast, our work is able to represent multimodal depth estimates, which can handle the inherit ambiguities of depth estimation, and is able to seek the modes for each depth estimate to make a consistent prediction of the scene structure. + +Inspired by traditional multi-view stereo, MVS-NeRF [3] and RC-MVSNet [2] incorporate the use cost volumes [9] to NeRF. To construct the cost volumes, these works look for agreement between features to look for correspondences, which is difficult under the setting of large variations in appearance or viewpoint. In contrast, our approach introduces a novel space carving loss that does not rely on feature correspondences and instead directly defines the loss in 3D. + +Another line of works focuses on geometry reconstruction [40, 45, 49] by using the volumetric rendering scheme to learn a neural SDF representation. These works tackle a different problem on modeling geometry reconstruction, unlike NeRFs whose focus is modeling appearance for novel view synthesis, where our work falls under. + +Depth Estimation from Single View. Depth estimation from a single image is a complex task due multiple ambiguities, including scene scale and shading / albedo ambiguities. Early efforts used MRFs to compute predictions on superpixels [33]. The advent of consumer depth cameras like Kinect [53] enabled the acquisition of larger scale indoor 3D datasets [35], leading to methods that used deep neural networks to predict depth from a single color image [7]. Nonetheless, scaling datasets for depth estimation remained a challenge. Deep3D [44] enabled the creation of stereo views by training on a large dataset of stereo movies, while [8] used the self-supervision of left-right consistency to learn depth from stereo views from driving cars. This approach was extended to videos where the egomotion is also estimated and self-supervision happens across time [54]. MegaDepth [21] uses the depth from SfM reconstructions of internet photos, together with semantic segmentation that conveys ordinal depth supervision cues, i.e. transient objects must be in front of the static scenes. Most recent, multi-task learning has shown promise in training depth estimators that work well in out-of-domain data [30]. + +In some cases, surface normal estimation has fewer pitfalls than direct depth estimation, as it suffers somewhat less from scale ambiguities. GeoNet [29] jointly estimates depth and surface normals, then uses the geometric relation between them to refine the estimates. LeRes [46] uses a second geometry reasoning module that refines a focal length estimate and the depth itself. Our depth estimation approach is derived from LeReS without the second stage, as the focal length is already estimated during SfM for NeRF scenes. + +Most relevant is the work of Kendall and Gal [15], that learns depth estimation in a Bayesian setting, where their objective maximizes the likelihood under a predicted distribution. In our work, we use instead a multimodal depth estimation technique built on cIMLE [19], which makes our prior robust to ambiguities in depth prediction. + +# 3. Background + +# 3.1. Neural Radiance Fields (NeRF) + +A neural radiance field [24], or NeRF for short, represents a field in 3D space, where each point represents an infinitesimal particle with a certain opacity that emits varying amounts of light along different viewing directions. The opacity at a point is represented as a volume density, and the amount of emitted light is represented as a colour. Mathematically, a NeRF is represented as two parameterized functions, a volume density $\sigma_{\theta}:\mathbb{R}^{3}\to \mathbb{R}_{\geq 0}$ and a colour $\mathbf{c}_{\psi}:\mathbb{R}^3\times S^2\rightarrow [0,255]^3$ . The former maps a 3D coordinate $\mathbf{x}\in \mathbb{R}^3$ to a volume density $\sigma \in \mathbb{R}_{\geq 0}$ , and the latter maps a 3D coordinate $\mathbf{x}\in \mathbb{R}^3$ and a viewing direction $\mathbf{d}\in S^2$ to a colour $\mathbf{c}\in [0,255]^3$ . + +To render a NeRF from a view, we shoot rays from each pixel on the camera sensor and integrate over the product of colour, volume density and visibility along the ray to arrive at each pixel value. Visibility at a point is represented with transmittance, which accumulates the exponentiated negative volume density multiplicatively up to the point. The higher transmittance at a point, the more visible the point is from the camera. Mathematically, if the camera ray is $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d}$ , where $\mathbf{o}$ is the camera centre and $\mathbf{d}$ is the ray direction, the pixel value $\hat{I}_{\theta,\psi}(\mathbf{o},\mathbf{d})$ we would have is: + +$$ +\begin{array}{l} \hat {I} _ {\theta , \psi} (\mathbf {o}, \mathbf {d}) := \int_ {t _ {n}} ^ {t _ {f}} T _ {\theta , \mathbf {o}, \mathbf {d}} (t) \sigma_ {\theta} (\mathbf {o} + t \mathbf {d}) \mathbf {c} _ {\psi} (\mathbf {o} + t \mathbf {d}, \mathbf {d}) d t \\ \text {w h e r e} T _ {\theta , \mathbf {o}, \mathbf {d}} (t) = \exp \left(- \int_ {t _ {n}} ^ {t} \sigma_ {\theta} (\mathbf {o} + s \mathbf {d}) \mathrm {d} s\right). \tag {1} \\ \end{array} +$$ + +In the expressions above, $t_n$ and $t_f$ denote the points the ray intersects with the near plane and far plane respectively. + +# 3.2. Inverse Rendering with NeRF + +Given a set of real-world images from known views, inverse rendering aims to find the scene whose rendered images match the real-world images. If we use $I(\mathbf{o}, \mathbf{d})$ to de + +note the pixel value for the ray $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d}$ , this problem can be cast as an optimization problem, namely: + +$$ +\min _ {\theta , \psi} \sum_ {\mathbf {o}} \sum_ {\mathbf {d}} \| \hat {I} _ {\theta , \psi} (\mathbf {o}, \mathbf {d}) - I (\mathbf {o}, \mathbf {d}) \| _ {2} ^ {2} \tag {2} +$$ + +If $\hat{I}_{\theta, \psi}(\mathbf{o}, \mathbf{d})$ is differentiable w.r.t. the parameters $\theta, \psi$ , this problem can be tackled straightforwardly with gradient-based optimization. To enable this, the volume density function $\sigma_{\theta}$ and the colour function $\mathbf{c}_{\psi}$ are chosen to be neural networks. As a result, inverse rendering amounts to training the NeRF to reconstruct the scene in a way that is consistent with the images that are given. Once the NeRF is trained, novel view synthesis can be achieved by rendering the NeRF from new, unseen views. + +Since this optimization problem is underconstrained, in general many views are needed to reconstruct the scene accurately. Yet, in practical applications, typically only a few views are available, hence priors are needed to provide sufficient constraints. In this paper, we consider priors in the form of monocular depth estimates from each view. The monocular depth estimates are trained on different datasets from the dataset NeRF is trained on to simulate real-world conditions where there is a domain gap between what the prior was trained on and what the NeRF is trained on. + +# 3.3. Ray Termination Distance + +In order to leverage depth priors, a natural way is to use them to constrain the ray termination distance. Because NeRF can represent non-opaque surfaces, there is no single ray termination distance. Instead, there is a distribution of ray termination distances. The cumulative distribution function (CDF) of this distribution represents the probability that the ray terminates before reaching a given point. It turns out that the probability density of this distribution $f_{\theta ,\mathbf{o},\mathbf{d}}(t)$ is given by [6]: + +$$ +f _ {\theta , \mathbf {o}, \mathbf {d}} (t) = T _ {\theta , \mathbf {o}, \mathbf {d}} (t) \sigma_ {\theta} (\mathbf {o} + t \mathbf {d}) \tag {3} +$$ + +# 4. Method + +# 4.1. Supervising Ray Termination Distance + +If all surfaces were opaque and the ground truth depth were given, supervising NeRF with the ground truth depth would be straightforward. All that is needed is to make the NeRFs distribution of ray termination distances as close as possible to a delta distribution centred at the ground truth depth. However, when the ground truth depth is not known, we have to use monocular depth estimates as supervision. The challenge is that unlike ground truth depth, monocular depth estimates may not be stereo-consistent, due to estimation error and inherent ambiguity. As a result, it may not be possible to find a scene that is consistent with the depth estimates from every view. Therefore, in order to reconstruct the scene, we must model the uncertainty and ambiguity in the depth estimates, which can be mathematically characterized by distributions. Such ambiguities cannot be resolved from + +![](images/d79b1f9b1912712bf049c99bd1ce552f3d28968c73f444a03701056de739514e.jpg) +Figure 3. Network Architecture for our Ambiguity-aware Depth Estimates. + +a single view and can often be resolved from multiple views. So we need an method that can fuse together uncertain depth estimates from different views. + +A natural way of representing uncertainty is through a probability distribution. When there are ambiguities, the distribution of depth estimates are typically multimodal, i.e., their probability densities have disjoint peaks, where each mode represents one interpretation of the scene structure. For example, albedo vs shading ambiguity as shown in Figure 2 can result in multiple plausible interpretations and make the distribution multimodal. + +An added challenge arises when non-opaque surfaces are present. In this case, there is no single ground truth depth, and so the distribution of ground truth depths is multimodal. So even after training the NeRF, the distribution of ray termination distances induced by NeRF should be multimodal, as illustrated in the glass walls in Figure 1. + +Prior methods compute moments (i.e., mean and/or variance) of the distribution of depth estimates or ray termination distance induced by NeRF. For example, DS-NeRF [6] predicts the mean depth estimate and uses reprojection error as a proxy for the variance. It then minimizes the KL divergence from the distribution of ray termination distances induced by NeRF to a Gaussian whose moments match those of the depth estimates. DDP [32] fits a Gaussian to distribution of ray termination distances and maximizes the likelihood of the depth estimate under the Gaussian. + +Distilling complex distributions to moments has the drawback of ignoring their possible multimodality. Because both the distribution of depth estimates and ray termination distances are potentially multimodal, it is important to handle the multimodality. + +# 4.2. SCADE + +We now present our novel method Space Carving with Ambiguity-aware Depth Estimates (SCADE). Our contributions address the existing problems and drawbacks mentioned in the previous section. First, SCADE accounts for the multimodality of both the distributions of monocular depth estimates and ray termination distances that arise due to inherent ambiguities (Sec 4.2.1) and non-opaque surfaces. + +Second, SCADE is also able to resolve these ambiguities by fusing together information from multiple views through our space carving loss (Sec 4.2.3) that uses the reverse cross entropy loss. Because this a loss on the distribution rather than moments of the distribution (which was the paradigm in prior work [6, 32]), it achieves supervision in 3D rather than 2D. Third, our loss formulation is sample-based (Sec 4.2.2) and so is computationally efficient to optimize. + +# 4.2.1 Our Ambiguity-aware Depth Estimates + +We handle multimodality of monocular depth distributions by introducing our ambiguity-aware depth estimation module to account for ambiguities in depth estimation from a single view (Figure 1, 2). In contrast to existing monocular depth estimation networks [47] that predict single point estimates for depth, we model the inherent uncertainty in monocular depth estimation by representing the distribution as a set of samples generated by a neural network. We propose leveraging conditional Implicit Maximum Likelihood estimation (cIMLE) [19] to learn a multimodal distribution of depth estimates. We chose cIMLE rather than conditional GANs [14] in order to avoid mode collapse, which can lead to a unimodal distribution. + +Figure 3 shows our network architecture. Concretely, we combine cIMLE with a state-of-the-art monocular depth estimation network, LeReS [47]. Our ambiguity-aware depth estimation module $(G)$ takes an input image $(I)$ and a latent code $z\sim \mathcal{N}(0,\mathbf{I})$ and outputs a conditional depth sample $G(I,z)$ for the input image $I$ . To inject randomness into the network, we follow the technique used in [14] and incorporate AdaIn layers into the network backbone that predicts a scale and shift to the intermediate network features. Specifically, we added four AdaIn layers to the encoder of the depth estimation backbone. + +# 4.2.2 Sample-based Losses on Distributions + +We desire to achieve an agreement between the distributions from our ambiguity-aware prior and the ray termination distance from NeRF to constrain the NeRF optimization under the sparse view set-up using our learned prior. As distributions are continuous, taking their analytical integral is computationally intractable. Thus, in order to define a differentiable loss function for our optimization problem, we result in a sample-based loss on these two distributions. + +Samples from depth prior. As previously described, we leverage cIMLE to sample from our ambiguity-aware depth prior. Sampling $z_{1},\ldots ,z_{M}\sim \mathcal{N}(0,\mathbf{I})$ , we get depth map samples $G(I,z_1),\dots,G(I,z_M)$ for input image $I$ . Hence we denote corresponding samples to estimate and represent the distribution for ray $\mathbf{r}$ as $y_{1},y_{2},\dots,y_{M}\sim G_{\mathbf{o,d}}$ . + +Samples from NeRF. For the distribution given by the ray termination distances modelled by NeRF, we sample from its probability density function $f_{\theta ,\mathbf{o},\mathbf{d}}$ (Eq. 3) with inverse transform sampling. Concretely, we define the probability mass function for ray $\mathbf{r}$ as $f_{\theta ,\mathbf{o},\mathbf{d}}(t_i)$ as given in Eq. 3 with + +![](images/5ce69a59f9693151cf0118715c9aa7a4632ba34e4fa87d3d6c04f8224a7bbbb2.jpg) + +![](images/f0f60911c43cb08167196bca975a3842d6efec53ccdedbaafe3d95dc4a38fd5a.jpg) +2D Expected Depth + +![](images/9e3fb50f9689e1cee02dd5c1e8baba0ac80730b0def19b79a7f53c0861ad64f9.jpg) + +![](images/095433d6285bfd4172af0cf62ac7b64bbf1bcdd6b6a6d1de52d37ce1fe9081d0.jpg) +3D Space Carving (Ours) +Figure 4. Our space carving loss supervises the ray termination in 3D as opposed to existing approaches that supervise on 2D expected depth. As shown, this clears out clouds of dust in space. Moreover supervising in 3D allows for wide baseline input views and still finds the common mode that correctly snaps the surfaces. + +samples $t_1,\ldots ,t_K$ , where $t_i\in [t_n,t_f]\forall i$ . By inverse transform sampling, we first compute the cumulative distribution function (CDF) of the ray termination distribution at samples $t_i$ , which we denote as $F_{\theta ,\mathbf{o},\mathbf{d}}(t_i) = \sum_{j < i}f_{\theta ,\mathbf{o},\mathbf{d}}(t_i)$ . Thus our samples $x_{1},x_{2},\dots,x_{N}$ of ray termination distances from NeRF are then given by: + +$$ +x _ {i} = F _ {\theta , \mathbf {o}, \mathbf {d}} ^ {- 1} (u _ {i}), \tag {4} +$$ + +where $u_{i}\sim \mathcal{U}(0,1)$ + +# 4.2.3 Our Space Carving Loss + +We now introduce our novel space carving loss utilizes the samples from both multimodal distributions to constrain the NeRF optimization. The goal is to find a subset of modes captured in the monocular depth distributions from each view that are globally consistent. In doing so, we can fuse together the information from the different views, since the inherent ambiguities are only resolved given information from multiple views. This would allow us to find a common shape that is consistent across all views and "snap" objects surfaces together. + +We thus desire a loss that has mode seeking behavior, that is the modes of the distribution being trained should be a subset of the modes of the distribution that provides supervision. One such loss is the reverse cross entropy, which is the cross entropy from the NeRF ray termination distance distribution to the distribution of our ambiguity-aware depth estimates: + +$$ +H \left(f _ {\theta , \mathbf {o}, \mathbf {d}}, G _ {\mathbf {o}, \mathbf {d}}\right) = - \mathbb {E} _ {f _ {\theta , \mathbf {o}, \mathbf {d}}} [ \log G _ {\mathbf {o}, \mathbf {d}} ]. \tag {5} +$$ + +As shown in the IMLE papers [19, 28], this is equivalent to penalizing the minimum of the L2 norm between the samples from the two distributions, please see [18] for the full proof. Hence, our space carving loss is given by + +$$ +\mathcal {L} _ {\text {s p a c e ＿ c a r v i n g}} (\mathbf {r}) = \sum_ {i \in [ N ]} \min _ {j \in [ M ]} \| x _ {i} - y _ {j} \| _ {2} ^ {2}. \tag {6} +$$ + +Because our novel space carving loss operates on distributions rather than moments of distributions, we can have + +different supervision targets for different points along the ray. In contrast, if the loss were to only to operate on moments, which are integrals along the ray, this only yields the same supervision target for all points along the ray. Therefore, our loss allows us to supervise in 3D, unlike prior methods [6, 32] (which use losses on moments) that supervise in 2D. 3D supervision allows us to clear out dust in space, since in order to move a sample from the ray termination distance distribution farther in depth, the loss would have to decrease the probability density of all the points in front of it. These advantages are highlighted in Figure 4. + +Our total loss to optimize and train our NeRF model is given by + +$$ +\mathcal {L} = \mathcal {L} _ {\text {p h o t o m e t r i c}} + \lambda \mathcal {L} _ {\text {s p a c e ＿ c a r v i n g}}, \tag {7} +$$ + +where $\mathcal{L}_{\mathrm{photometric}}$ is the standard MSE loss on the predicted and ground truth image. See Fig. 1 for our overall pipeline. + +# 5. Results + +In this section, we present our experimental evaluation to demonstrate the advantages of SCADE. + +# 5.1. Datasets and Evaluation Metrics + +We evaluate our method on ScanNet [5] and an in-the-wild dataset we collected1. We use the sparse-view ScanNet data used by DDP [32] in their evaluations, which comprises of three sample scenes each with 18 to 20 train images and 8 test images. To further test the robustness of our method, we further evaluated our method on three in-the-wild scenes collected using an iPhoneX. We captured sparse views in three different scenes - basement, kitchen and lounge, where each scene has 18 to 23 train images and 8 test images. Following similar data preprocessing steps as DDP [32], we ran SfM [34] on all images to obtain camera poses for NeRF training. For quantitative comparison, we follow the original NeRF [24] paper and report the PSNR, SSIM [42] and LPIPS [52] on the novel test views. + +# 5.2. Implementation Details + +We train our ambiguity-aware prior on the Taskonomy [50] dataset and initialize the weights with the pretrained LeReS [47] model. We use $M = 20$ depth estimates in our experiments. See supplement for additional details. + +# 5.3. Experiments on ScanNet + +We evaluate on ScanNet following the evaluation from DDP [32]. We compare to the original NeRF [24] (Vanilla NeRF) and the recent state-of-the-art NeRF with depth prior-based supervision, Dense Depth Prior [32] (DDP). Table 1 shows SCADE quantitatively outperforming the baselines. Because we are interested in simulating real-world conditions with a domain gap between the prior and the NeRF, our setting requires the use of out-of-domain priors. Since DDP uses a in-domain prior, we retrain DDP's depth completion + +![](images/949b1024709f36574ef8fca2f848b5a09b39f2c61a19449dd8a1bfcb1d311674.jpg) +Figure 5. Depth and Fusion Comparison. Depth map and fusion comparison between SCADE and DDP. + +
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]19.030.6700.398
NerfingMVS [47]16.290.6260.502
IBRNet [41]13.250.5290.673
MVSNeRF [3]15.670.5330.635
DS-NeRF [6]20.850.7130.344
DDP [32]19.290.6950.368
SCADE (Ours)21.540.7320.292
+ +Table 1. ScanNet Results. Results for DS-NeRF and NerfingMVS follow what was reported in prior literature [32]. Because our setting requires out-of-domain priors, the results for DDP are with out-of-domain priors. The results of DDP with in-domain priors are (20.96, 0.737, 0.236) for PSNR, SSIM and LPIPS, respectively. + +network using their official code and hyperparameters on Taskonomy [50], i.e. the same out-of-domain dataset that our prior is trained on. + +Figure 6 shows our qualitative results. As shown, compared to the baselines, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (first, third and last column). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (second column), the back of the chair (fourth column) and the legs of the piano stool (fifth column). Moreover, Fig. 5 shows rendered depthmaps and fusion results using [51] on a Scannet scene. Notice that SCADE is able to recover better geometry compared to DDP - see corner of the calendar, cabinets and office chair in the right image. + +# 5.4. Experiments on In-the-Wild Data + +To further test the robustness of SCADE, we further evaluate on data collected in-the-wild with a standard phone camera (iPhoneX). The intrinsics for different views are different and are not known to the algorithm. As shown in Table 2, SCADE with the same out-of-domain prior (trained on Taskonomy) outperforms the baselines on in-the-wild captured data, which demonstrates its robustness. Figure 7 shows qualitative examples. Interestingly, we are able to recover the room behind the glass better the baselines, whose results are more blurry (first, third and fourth column). We are also able to recover objects behind the glass such as the monitor and chair (first column). As discussed in Sect. 4.1, non-opaque surfaces are the most challenging because both the ground truth distribution of ray termination distances induced by NeRF and the distribution of estimated depths + +![](images/e9189b41264e143ca49e61725e478d56b531c4f517a25de627d60d97f175c7fe.jpg) +Figure 6. Qualitative results on ScanNet. As shown, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (1st, 3rd, last columns). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (2nd column), the back of the chair (4th column) and the legs of the piano stool (5th column). + +
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]20.460.7130.398
DDP [32]21.280.7270.366
SCADE (Ours)22.820.7430.347
+ +from the prior must be multimodal. This validates the ability of our model to capture the multimodal distributions. + +Similar to the ScanNet results, we are able to recover crisp shapes of objects such as the thin table leg and the white chair (second and last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (fifth and last column). + +# 5.5. Ablation Study + +Supervision on full distribution vs moments We first validate the importance of using our novel space carving loss that supervises the full distribution of ray termination distance rather than just its moments. The latter integrates along the ray, and so provides one target value for the entire ray, which effectively makes it 2D supervision. The former provides different target values for different samples along the same ray, which makes it 3D supervision. We adapt our method to use 2D supervision proposed in the recent MonoSDF [49], which computes the expected ray termination distance and aligns the output depth map with a monocular depth estimation prior using the MiDaS [30] loss. We use our learned prior as the monocular depth estimate. Table 3 validates the effectiveness of our space carving loss. + +Multimodal prior vs unimodal prior. Our prior models does not constrain the depth distribution to a particular form and allows it to be multimodal. In contrast, DDP's depth completion prior assumes a Gaussian, which is unimodal. + +Table 2. In-the-wild Results. + +
PSNR ↑SSIM ↑LPIPS ↓
MonoSDF supervision20.130.7100.332
DDP prior - single sample20.850.7120.320
DDP prior - multiple samples21.000.7180.316
Our prior - single sample21.220.7140.318
SCADE (Ours)21.540.7320.292
+ +Table 3. Ablation Study. Results on the Scannet dataset. MonoSDF supervision refers to supervising with MonoSDF loss on expected ray termination distance using our prior. + +We ablate our prior against DDP's by sampling from their Gaussian distribution. We train with our space carving loss using both a single sample, as well as $M$ samples drawn from DDP's prior. As shown in Table 3, while both perform better than the 2D supervision provided by MonoSDF, but they are subpar compared to using our multimodal prior. + +Multiple vs single sample. Finally, we also ablate on using a single sample vs multiple samples for our space carving loss. For the single sample set-up, we supervise using the sample mean of the depth estimates, which is equivalent to the maximum likelihood estimate of the depth under Gaussian likelihood. Results in Table 3 show the importance of using multiple samples for our space carving loss. + +Sparsity. We further show addt'l results under varying number of views in Tab 4. Note that in general sparsity is not fully reflected by the absolute number of views, because all else being equal, a larger scene requires more views to attain complete coverage. Following prior work [32], we also report the average number of views that see the same point as another measure of sparsity. As shown, our setting is at the edge of the theoretical lower limit of 2 for general-purpose reconstruction, which shows view sparsity. + +![](images/7e2362ab6a15190dbdcc9d678e22a5b9e89861b7021b641f07fec5373cdc845d.jpg) +Figure 7. Qualitative results on In-the-Wild data. As shown, we are able to recover the room behind the glass better the baselines, whose results are more blurry (1st, 3rd, 4th column). Also, SCADE is able to recover crisp shapes of objects such as the thin table leg and the white chair (2nd, last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (5th, last column). + +
ave. #views visible1.871.982.012.2
absolute #views18202224
DDP / SCADE19.35/ 21.6622.4/ 23.6723.10/ 24.0023.56/ 24.84
+ +Table 4. PSNR for DDP [32]/SCADE on scene781 of Scannet. + +![](images/29b97ea9fa589445999cb9da35c0638f35b86213f46f987167af3609e7216b4d.jpg) + +![](images/4d6aa5d3f52bf5f17bac43561c98b1ea27cd406ae972d63e2f89a5253283b950.jpg) +Figure 8. Depth Mode Discussion. a) Train images from Taskonomy [50] and their labels. Notice that non-opaque surfaces are labelled differently. b) Output of our prior on reflective surfaces. + +# 5.6. Discussion on our Ambiguity-Aware Prior + +We provide addt'l details on our ambiguity-aware prior on i) how and why it works, ii) its performance on reflective surfaces, which is a common failure case for depth estimate, and iii) provide an intuition on how what our depth modes look like. i) We achieve variable depth modes by exploiting inconsistently labeled training data. As shown in Fig 8-a, in Taskonomy [50], different training images with non-opaque surfaces label depth differently: shooting through the glass (left), on the glass (middle), or a mixture of both (right). Despite multiple possible depth labels, each image only has one ground truth label. Training with cIMLE allows our prior to model these multiple possible (ambiguous) outputs through sampling $^2$ , even when given only one label per image. Interestingly when testing our prior on a test image with a mirror, we find that it is able to capture variable modes + +on reflective surfaces, including the "correct" flat surface as shown in Fig 8-b. An intuition of what the depth modes look like is for example if a ray intersects $n - 1$ non-opaque surfaces, the $n$ modes are intersections with the non-opaque surfaces and the terminating point on the opaque surface. + +# 6. Conclusion + +In this paper, we present a new approach towards NeRF reconstruction that can work with a modest number of in-the-wild views of an indoor scene. We address the underconstrained nature of this problem by regularizing the NeRF optimization with additional depth estimates for each view. Our key technical contribution is to model multimodality in the depth estimates, which can capture inherent ambiguities in monocular depth estimation as well as the possible presence of non-opaque surfaces. We resolve ambiguities using a novel space carving loss that fuses the multimodal depth estimates from different views and seeks the modes that are consistent across views so as to arrive at a globally consistent 3D reconstruction. The improved recovery of shape and appearance enables higher fidelity novel view synthesis from sparse views. + +Limitations and Future Work. The performance of our method is constrained by the quality of the monocular depth priors. While we found that our prior generalizes well across domains, if the domain gap is too great, the performance of our method will degrade. A future direction would be to detect when this happens and dynamically adjust the strength of depth supervision in response. + +Acknowledgements. We sincerely thank the Teleportation and CCI team in Google for all the insightful discussions during the summer. We also thank Mirko Visontai for internship logistics, Guandao Yang for experiment set-up assist, and Weicheng Kuo for looking over the paper. + +# References + +[1] Sai Bi, Zexiang Xu, Pratul Srinivasan, Ben Mildenhall, Kalyan Sunkavalli, Miloš Hasan, Yannick Hold-Geoffroy, David Kriegman, and Ravi Ramamoorthi. Neural reflectance fields for appearance acquisition. arXiv preprint arXiv:2008.03824, 2020. 3 +[2] Di Chang, Aljaž Božić, Tong Zhang, Qingsong Yan, Yingcong Chen, Sabine Susstrunk, and Matthias Nießner. Rc-mvsnet: Unsupervised multi-view stereo with neural rendering. 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SCADE Overview. We present SCADE, a novel technique for NeRF reconstruction under sparse, unconstrained views for in-the-wild indoor scenes. We leverage on generalizable monocular depth priors and address to represent the inherent ambiguities of monocular depth by exploiting our ambiguity-aware depth estimates (left). Our approach accounts for multimodality of both distributions using our novel space carving loss that seeks to disambiguate and find the common mode to fuse the information between different views (middle). SCADE enables better photometric reconstruction especially in highly ambiguous scenes, e.g. non-opaque surfaces (right)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 389, + 192, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 389, + 192, + 402 + ], + "spans": [ + { + "bbox": [ + 143, + 389, + 192, + 402 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 420, + 290, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 420, + 290, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 420, + 290, + 700 + ], + "type": "text", + "content": "Neural radiance fields (NeRFs) have enabled high fidelity 3D reconstruction from multiple 2D input views. However, a well-known drawback of NeRFs is the less-than-ideal performance under a small number of views, due to insufficient constraints enforced by volumetric rendering. To address this issue, we introduce SCADE, a novel technique that improves NeRF reconstruction quality on sparse, unconstrained input views for in-the-wild indoor scenes. To constrain NeRF reconstruction, we leverage geometric priors in the form of per-view depth estimates produced with state-of-the-art monocular depth estimation models, which can generalize across scenes. A key challenge is that monocular depth estimation is an ill-posed problem, with inherent ambiguities. To handle this issue, we propose a new method that learns to predict, for each view, a continuous, multimodal distribution of depth estimates using conditional Implicit Maximum Likelihood Estimation (cIMLE). In order to disambiguate exploiting multiple views, we introduce an original space carving loss that guides the NeRF representation to fuse multiple hypothesized depth maps from each view and distill from them a common geometry that is consistent with all views. Experiments show that our approach enables higher fidelity novel view synthesis from sparse views. Our project page can be found at scade-spacecarving-nerfs.github.io." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 389, + 387, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 389, + 387, + 402 + ], + "spans": [ + { + "bbox": [ + 307, + 389, + 387, + 402 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 405, + 547, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 547, + 488 + ], + "type": "text", + "content": "Neural radiance fields (NeRF) [24] have enabled high fidelity novel view synthesis from dozens of input views. Such number of views are difficult to obtain in practice, however. When given only a small number of sparse views, vanilla NeRF tends to struggle with reconstructing shape accurately, due to inadequate constraints enforced by the volume rendering loss alone." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 490, + 548, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 548, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 548, + 688 + ], + "type": "text", + "content": "Shape priors can help remedy this problem. Various forms of shape priors have been proposed for NeRFs, such as object category-level priors [13], and handcrafted data-independent priors [25]. The former requires knowledge of category labels and is not applicable to scenes, and the latter is agnostic to the specifics of the scene and only encodes low-level regularity (e.g., local smoothness). A form of prior that is both scene-dependent and category-agnostic is per-view monocular depth estimates, which have been explored in prior work [6, 32]. Unfortunately, monocular depth estimates are often inaccurate, due to estimation errors and inherent ambiguities, such as albedo vs. shading (cf. check shadow illusion), concavity vs. convexity (cf. hollow face illusion), distance vs. scale (cf. miniature cinematography), etc. As a result, the incorrect or inconsistent priors imposed by such depth estimates may mislead the NeRF into reconstructing incorrect shape and produce artifacts in the generated views." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "In this paper, we propose a method that embraces the uncertainty and ambiguities present in monocular depth esti" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16518" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 223 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 223 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 223 + ], + "type": "text", + "content": "mates, by modelling a probability distribution over depth estimates. The ambiguities are retained at the stage of monocular depth estimation, and are only resolved once information from multiple views are fused together. We do so with a principled loss defined on probability distributions over depth estimates for different views. This loss selects the subset of modes of probability distributions that are consistent across all views and matches them with the modes of the depth distribution along different rays as modelled by the NeRF. It turns out that this operation can be interpreted as a probabilistic analogue of classical depth-based space carving [17]. For this reason, we dub our method Space Carving with Ambiguity-aware Depth Estimates, or SCADE for short." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 224, + 289, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 363 + ], + "type": "text", + "content": "Compared to prior approaches of depth supervision [6,32] that only supervise the moments of NeRF's depth distribution (rather than the modes), our key innovation is that we supervise the modes of NeRF's depth distribution. The supervisory signal provided by the former is weaker than the latter, because the former only constrains the value of an integral aggregated along the ray, whereas the latter constrains the values at different individual points along the ray. Hence, the supervisory signal provided by the former is 2D (because it integrates over a ray), whereas the supervisory signal provided by the our method is 3D (because it is point-wise) and thus can be more fine-grained." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 364, + 289, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 596 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 596 + ], + "type": "text", + "content": "An important technical challenge is modelling probability distributions over depth estimates. Classical approaches use simple distributions with closed-form probability densities such as Gaussian or Laplace distributions. Unfortunately these distributions are not very expressive, since they only have a single mode (known as \"unimodal\") and have a fixed shape for the tails. Since each interpretation of an ambiguous image should be a distinct mode, these simple unimodal distributions cannot capture the complex ambiguities in depth estimates. Naive extensions like a mixture of Gaussians are also not ideal because some images are more ambiguous than others, and so the number of modes needed may differ for the depth estimates of different images. Moreover, learning such a mixture requires backpropagating through E-M, which is nontrivial. Any attempt at modifying the probability density to make it capable of handling a variable number of modes can easily run into an intractable partition function [4, 10, 31], which makes learning difficult because maximum likelihood requires the ability to evaluate the probability density, which is a function of the partition function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 597, + 289, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 289, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 289, + 701 + ], + "type": "text", + "content": "To get around this conundrum, we propose representing the probability distribution with a set of samples generated from a neural network. Such a distribution can be learned with a conditional GAN; however, because GANs suffer from mode collapse, they cannot model multiple modes [11] and are therefore unsuited to modelling ambiguity. Instead, we propose leveraging conditional Implicit Maximum Likelihood Estimation (cIMLE) [19, 28] to learn the distribution, which is designed to avoid mode collapse." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 289, + 714 + ], + "type": "text", + "content": "We consider the challenging setting of leveraging out-of" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 322, + 74, + 372, + 121 + ], + "blocks": [ + { + "bbox": [ + 322, + 74, + 372, + 121 + ], + "lines": [ + { + "bbox": [ + 322, + 74, + 372, + 121 + ], + "spans": [ + { + "bbox": [ + 322, + 74, + 372, + 121 + ], + "type": "image", + "image_path": "89ae8a01be14ce67f619ad8b234580bd782b76021c3c70019a5b9d7fbb59aa90.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 375, + 74, + 425, + 121 + ], + "blocks": [ + { + "bbox": [ + 375, + 74, + 425, + 121 + ], + "lines": [ + { + "bbox": [ + 375, + 74, + 425, + 121 + ], + "spans": [ + { + "bbox": [ + 375, + 74, + 425, + 121 + ], + "type": "image", + "image_path": "a06fd61cd86dab5c1198a5da0f1e188d15aa7047d12b01b972958a739eeec331.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 427, + 74, + 476, + 121 + ], + "blocks": [ + { + "bbox": [ + 427, + 74, + 476, + 121 + ], + "lines": [ + { + "bbox": [ + 427, + 74, + 476, + 121 + ], + "spans": [ + { + "bbox": [ + 427, + 74, + 476, + 121 + ], + "type": "image", + "image_path": "68d33f6a715203b18ec8f4c3b82c6cb7b9e4b4f0b15c1a3d22ce704b35e778c8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 477, + 74, + 525, + 121 + ], + "blocks": [ + { + "bbox": [ + 477, + 74, + 525, + 121 + ], + "lines": [ + { + "bbox": [ + 477, + 74, + 525, + 121 + ], + "spans": [ + { + "bbox": [ + 477, + 74, + 525, + 121 + ], + "type": "image", + "image_path": "13559aab43aa532959f7217e43d80f5dd5c5d23b0037c75dad3323d3954e0466.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 326, + 123, + 369, + 177 + ], + "blocks": [ + { + "bbox": [ + 326, + 123, + 369, + 177 + ], + "lines": [ + { + "bbox": [ + 326, + 123, + 369, + 177 + ], + "spans": [ + { + "bbox": [ + 326, + 123, + 369, + 177 + ], + "type": "image", + "image_path": "22fce397da257929668b856372fb7391c94c99ce422710eedf4bda265c1f0754.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 179, + 363, + 186 + ], + "lines": [ + { + "bbox": [ + 331, + 179, + 363, + 186 + ], + "spans": [ + { + "bbox": [ + 331, + 179, + 363, + 186 + ], + "type": "text", + "content": "Input Image" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 380, + 123, + 423, + 177 + ], + "blocks": [ + { + "bbox": [ + 380, + 123, + 423, + 177 + ], + "lines": [ + { + "bbox": [ + 380, + 123, + 423, + 177 + ], + "spans": [ + { + "bbox": [ + 380, + 123, + 423, + 177 + ], + "type": "image", + "image_path": "6b3d450c6b39276ec11d0710dfd745893d459c0730b59fac991eb1a3c2ac5c7f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 406, + 179, + 493, + 186 + ], + "lines": [ + { + "bbox": [ + 406, + 179, + 493, + 186 + ], + "spans": [ + { + "bbox": [ + 406, + 179, + 493, + 186 + ], + "type": "text", + "content": "Ambiguity-Aware Depth Estimates" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 430, + 123, + 473, + 177 + ], + "blocks": [ + { + "bbox": [ + 430, + 123, + 473, + 177 + ], + "lines": [ + { + "bbox": [ + 430, + 123, + 473, + 177 + ], + "spans": [ + { + "bbox": [ + 430, + 123, + 473, + 177 + ], + "type": "image", + "image_path": "e81b800d71ea46699ae5cf16dcac3e985927f8f81fd5d4df9b54df2184be02b6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 187, + 547, + 282 + ], + "lines": [ + { + "bbox": [ + 304, + 187, + 547, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 187, + 547, + 282 + ], + "type": "text", + "content": "Figure 2. Ambiguities from a single image. We show samples from our ambiguity-aware depth estimates that is able to handle different types of ambiguities. (Top) An image of a chair taken from the top-view. Without context of the scene, it is unclear that it is an image of a chair. We show different samples from our ambiguity-aware depth estimates that are able to capture different degrees of convexity. (Bottom) An image of a cardboard under bad lighting conditions that capture the albedo vs shading ambiguity that is also represented by our different samples." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 481, + 123, + 522, + 177 + ], + "blocks": [ + { + "bbox": [ + 481, + 123, + 522, + 177 + ], + "lines": [ + { + "bbox": [ + 481, + 123, + 522, + 177 + ], + "spans": [ + { + "bbox": [ + 481, + 123, + 522, + 177 + ], + "type": "image", + "image_path": "d8d127bc3b443638620fdab80b812ae0ca16954b16deff9a3bd0cf586025dffd.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 290, + 547, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 547, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 547, + 395 + ], + "type": "text", + "content": "domain depth priors to train NeRFs on real-world indoor scenes with sparse views. Under this setting, the depth priors we use are trained on a different dataset (e.g., Taskonomy) from the scenes our NeRFs are trained on (e.g., ScanNet). This setting is more challenging than usual due to domain gap between the dataset the prior is trained on and the scenes NeRF is asked to reconstruct. We demonstrate that our method outperforms vanilla NeRF and NeRFs with supervision from depth-based priors in novel view synthesis." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 396, + 492, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 396, + 492, + 406 + ], + "spans": [ + { + "bbox": [ + 318, + 396, + 492, + 406 + ], + "type": "text", + "content": "In summary, our key contributions include:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 413, + 547, + 580 + ], + "type": "list", + "angle": 0, + "index": 21, + "blocks": [ + { + "bbox": [ + 317, + 413, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 413, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 317, + 413, + 547, + 460 + ], + "type": "text", + "content": "- An method that allows the creation of NeRFs in unconstrained indoor settings from only a modest number of 2D views by introducing a sophisticated way to exploit ambiguity-aware monocular depth estimation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 468, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 468, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 317, + 468, + 547, + 514 + ], + "type": "text", + "content": "- A novel way to sample distributions over image depth estimates based on conditional Implicit Maximum Likelihood Estimation that can represent depth ambiguities and capture a variable number of discrete depth modes." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 317, + 521, + 547, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 521, + 547, + 580 + ], + "spans": [ + { + "bbox": [ + 317, + 521, + 547, + 580 + ], + "type": "text", + "content": "- A new space-carving loss that can be used in the NeRF formulation to optimize for a mode-seeking 3D density that helps select consistent depth modes across the views and thus compensate for the under-constrained photometric information in the few view regime." + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 591, + 392, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 591, + 392, + 604 + ], + "spans": [ + { + "bbox": [ + 306, + 591, + 392, + 604 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 608, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 608, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 608, + 547, + 714 + ], + "type": "text", + "content": "Novel View Synthesis and 3D Reconstruction. Reconstructing the structure of a scene from a few views is a long standing problem in computer vision with a long literature. Neural Radiance Fields or NeRF [24] revolutionized the field by showing how to use weights of an MLP to represent a scene that is rendered using volume rendering [23]. A key innovation was the use of positional encoding [37, 38] to increase the effective capacity of the MLPs that model a emitted radiance and density as a function of position and" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16519" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 107 + ], + "type": "text", + "content": "viewing direction. Extensions of NeRF include works on unconstrained photo collections [22], dynamic scenes [20], deformable scenes [27], and reflective materials [1,39]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 289, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 289, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 289, + 304 + ], + "type": "text", + "content": "A critical shortcoming of NeRF is its reliance on having many input views of a scene. Several approaches have been proposed, including adding patch likelihood losses [25], data-driven priors [36, 48], semantic consistency prior [12], image features [41], or surface [25, 39], occupancy [26], and depth [15, 32, 43] priors. DS-NeRF [6] uses the sparse point reconstructions recovered during Structure-from-Motion, to supervise the depth of sparse points in the recovered NeRF. In the same spirit, DDP [32] uses a depth completion network, that takes as input sparse point cloud projected to one an input view, and produces a depth estimate. Both works [15, 32] model depth with uncertainty but only supervise with moments of NeRF's depth distribution. In contrast, our work is able to represent multimodal depth estimates, which can handle the inherit ambiguities of depth estimation, and is able to seek the modes for each depth estimate to make a consistent prediction of the scene structure." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 305, + 288, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 288, + 397 + ], + "type": "text", + "content": "Inspired by traditional multi-view stereo, MVS-NeRF [3] and RC-MVSNet [2] incorporate the use cost volumes [9] to NeRF. To construct the cost volumes, these works look for agreement between features to look for correspondences, which is difficult under the setting of large variations in appearance or viewpoint. In contrast, our approach introduces a novel space carving loss that does not rely on feature correspondences and instead directly defines the loss in 3D." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 399, + 288, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 288, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 288, + 467 + ], + "type": "text", + "content": "Another line of works focuses on geometry reconstruction [40, 45, 49] by using the volumetric rendering scheme to learn a neural SDF representation. These works tackle a different problem on modeling geometry reconstruction, unlike NeRFs whose focus is modeling appearance for novel view synthesis, where our work falls under." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 468, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 289, + 714 + ], + "type": "text", + "content": "Depth Estimation from Single View. Depth estimation from a single image is a complex task due multiple ambiguities, including scene scale and shading / albedo ambiguities. Early efforts used MRFs to compute predictions on superpixels [33]. The advent of consumer depth cameras like Kinect [53] enabled the acquisition of larger scale indoor 3D datasets [35], leading to methods that used deep neural networks to predict depth from a single color image [7]. Nonetheless, scaling datasets for depth estimation remained a challenge. Deep3D [44] enabled the creation of stereo views by training on a large dataset of stereo movies, while [8] used the self-supervision of left-right consistency to learn depth from stereo views from driving cars. This approach was extended to videos where the egomotion is also estimated and self-supervision happens across time [54]. MegaDepth [21] uses the depth from SfM reconstructions of internet photos, together with semantic segmentation that conveys ordinal depth supervision cues, i.e. transient objects must be in front of the static scenes. Most recent, multi-task learning has shown promise in training depth estimators that work well in out-of-domain data [30]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 177 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 177 + ], + "type": "text", + "content": "In some cases, surface normal estimation has fewer pitfalls than direct depth estimation, as it suffers somewhat less from scale ambiguities. GeoNet [29] jointly estimates depth and surface normals, then uses the geometric relation between them to refine the estimates. LeRes [46] uses a second geometry reasoning module that refines a focal length estimate and the depth itself. Our depth estimation approach is derived from LeReS without the second stage, as the focal length is already estimated during SfM for NeRF scenes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 177, + 547, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 247 + ], + "type": "text", + "content": "Most relevant is the work of Kendall and Gal [15], that learns depth estimation in a Bayesian setting, where their objective maximizes the likelihood under a predicted distribution. In our work, we use instead a multimodal depth estimation technique built on cIMLE [19], which makes our prior robust to ambiguities in depth prediction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 257, + 384, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 384, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 384, + 270 + ], + "type": "text", + "content": "3. Background" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 276, + 476, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 276, + 476, + 288 + ], + "spans": [ + { + "bbox": [ + 305, + 276, + 476, + 288 + ], + "type": "text", + "content": "3.1. Neural Radiance Fields (NeRF)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": "A neural radiance field [24], or NeRF for short, represents a field in 3D space, where each point represents an infinitesimal particle with a certain opacity that emits varying amounts of light along different viewing directions. The opacity at a point is represented as a volume density, and the amount of emitted light is represented as a colour. Mathematically, a NeRF is represented as two parameterized functions, a volume density " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}:\\mathbb{R}^{3}\\to \\mathbb{R}_{\\geq 0}" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": " and a colour " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\psi}:\\mathbb{R}^3\\times S^2\\rightarrow [0,255]^3" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": ". The former maps a 3D coordinate " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{x}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": " to a volume density " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}_{\\geq 0}" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": ", and the latter maps a 3D coordinate " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{x}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": " and a viewing direction " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{d}\\in S^2" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": " to a colour " + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{c}\\in [0,255]^3" + }, + { + "bbox": [ + 304, + 289, + 547, + 428 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "text", + "content": "To render a NeRF from a view, we shoot rays from each pixel on the camera sensor and integrate over the product of colour, volume density and visibility along the ray to arrive at each pixel value. Visibility at a point is represented with transmittance, which accumulates the exponentiated negative volume density multiplicatively up to the point. The higher transmittance at a point, the more visible the point is from the camera. Mathematically, if the camera ray is " + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "text", + "content": " is the camera centre and " + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "text", + "content": " is the ray direction, the pixel value " + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "inline_equation", + "content": "\\hat{I}_{\\theta,\\psi}(\\mathbf{o},\\mathbf{d})" + }, + { + "bbox": [ + 304, + 429, + 547, + 545 + ], + "type": "text", + "content": " we would have is:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 310, + 553, + 547, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 553, + 547, + 622 + ], + "spans": [ + { + "bbox": [ + 310, + 553, + 547, + 622 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {I} _ {\\theta , \\psi} (\\mathbf {o}, \\mathbf {d}) := \\int_ {t _ {n}} ^ {t _ {f}} T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) \\sigma_ {\\theta} (\\mathbf {o} + t \\mathbf {d}) \\mathbf {c} _ {\\psi} (\\mathbf {o} + t \\mathbf {d}, \\mathbf {d}) d t \\\\ \\text {w h e r e} T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\sigma_ {\\theta} (\\mathbf {o} + s \\mathbf {d}) \\mathrm {d} s\\right). \\tag {1} \\\\ \\end{array}", + "image_path": "cdeab19b816ffce361fe3c76d03ff366a36758448e027a9a0531839506e7954c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "type": "text", + "content": "In the expressions above, " + }, + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 304, + 630, + 545, + 654 + ], + "type": "text", + "content": " denote the points the ray intersects with the near plane and far plane respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 660, + 469, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 660, + 469, + 673 + ], + "spans": [ + { + "bbox": [ + 306, + 660, + 469, + 673 + ], + "type": "text", + "content": "3.2. Inverse Rendering with NeRF" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 678, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 547, + 714 + ], + "type": "text", + "content": "Given a set of real-world images from known views, inverse rendering aims to find the scene whose rendered images match the real-world images. If we use " + }, + { + "bbox": [ + 304, + 678, + 547, + 714 + ], + "type": "inline_equation", + "content": "I(\\mathbf{o}, \\mathbf{d})" + }, + { + "bbox": [ + 304, + 678, + 547, + 714 + ], + "type": "text", + "content": " to de" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "16520" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "note the pixel value for the ray " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ", this problem can be cast as an optimization problem, namely:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 91, + 104, + 287, + 129 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 104, + 287, + 129 + ], + "spans": [ + { + "bbox": [ + 91, + 104, + 287, + 129 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta , \\psi} \\sum_ {\\mathbf {o}} \\sum_ {\\mathbf {d}} \\| \\hat {I} _ {\\theta , \\psi} (\\mathbf {o}, \\mathbf {d}) - I (\\mathbf {o}, \\mathbf {d}) \\| _ {2} ^ {2} \\tag {2}", + "image_path": "dfd9e4ed2313059d2a4c0aa8b4a634e130b6cc772e35a7b30c045cbe35981e0b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "text", + "content": "If " + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "inline_equation", + "content": "\\hat{I}_{\\theta, \\psi}(\\mathbf{o}, \\mathbf{d})" + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "text", + "content": " is differentiable w.r.t. the parameters " + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "inline_equation", + "content": "\\theta, \\psi" + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "text", + "content": ", this problem can be tackled straightforwardly with gradient-based optimization. To enable this, the volume density function " + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}" + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "text", + "content": " and the colour function " + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\psi}" + }, + { + "bbox": [ + 46, + 133, + 288, + 237 + ], + "type": "text", + "content": " are chosen to be neural networks. As a result, inverse rendering amounts to training the NeRF to reconstruct the scene in a way that is consistent with the images that are given. Once the NeRF is trained, novel view synthesis can be achieved by rendering the NeRF from new, unseen views." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 238, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 287, + 354 + ], + "type": "text", + "content": "Since this optimization problem is underconstrained, in general many views are needed to reconstruct the scene accurately. Yet, in practical applications, typically only a few views are available, hence priors are needed to provide sufficient constraints. In this paper, we consider priors in the form of monocular depth estimates from each view. The monocular depth estimates are trained on different datasets from the dataset NeRF is trained on to simulate real-world conditions where there is a domain gap between what the prior was trained on and what the NeRF is trained on." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 356, + 192, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 356, + 192, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 192, + 367 + ], + "type": "text", + "content": "3.3. Ray Termination Distance" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 369, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 473 + ], + "type": "text", + "content": "In order to leverage depth priors, a natural way is to use them to constrain the ray termination distance. Because NeRF can represent non-opaque surfaces, there is no single ray termination distance. Instead, there is a distribution of ray termination distances. The cumulative distribution function (CDF) of this distribution represents the probability that the ray terminates before reaching a given point. It turns out that the probability density of this distribution " + }, + { + "bbox": [ + 46, + 369, + 287, + 473 + ], + "type": "inline_equation", + "content": "f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t)" + }, + { + "bbox": [ + 46, + 369, + 287, + 473 + ], + "type": "text", + "content": " is given by [6]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 100, + 483, + 287, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 483, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 100, + 483, + 287, + 496 + ], + "type": "interline_equation", + "content": "f _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) = T _ {\\theta , \\mathbf {o}, \\mathbf {d}} (t) \\sigma_ {\\theta} (\\mathbf {o} + t \\mathbf {d}) \\tag {3}", + "image_path": "b57f9058a08d605265cfa962fd174753c03af1cf0067ef2662e3bf12fc95117d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 504, + 102, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 504, + 102, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 504, + 102, + 516 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 523, + 250, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 250, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 250, + 536 + ], + "type": "text", + "content": "4.1. Supervising Ray Termination Distance" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 539, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 288, + 713 + ], + "type": "text", + "content": "If all surfaces were opaque and the ground truth depth were given, supervising NeRF with the ground truth depth would be straightforward. All that is needed is to make the NeRFs distribution of ray termination distances as close as possible to a delta distribution centred at the ground truth depth. However, when the ground truth depth is not known, we have to use monocular depth estimates as supervision. The challenge is that unlike ground truth depth, monocular depth estimates may not be stereo-consistent, due to estimation error and inherent ambiguity. As a result, it may not be possible to find a scene that is consistent with the depth estimates from every view. Therefore, in order to reconstruct the scene, we must model the uncertainty and ambiguity in the depth estimates, which can be mathematically characterized by distributions. Such ambiguities cannot be resolved from" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 545, + 198 + ], + "type": "image", + "image_path": "d79b1f9b1912712bf049c99bd1ce552f3d28968c73f444a03701056de739514e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 208, + 545, + 229 + ], + "lines": [ + { + "bbox": [ + 305, + 208, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 305, + 208, + 545, + 229 + ], + "type": "text", + "content": "Figure 3. Network Architecture for our Ambiguity-aware Depth Estimates." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 235, + 547, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 235, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 305, + 235, + 547, + 269 + ], + "type": "text", + "content": "a single view and can often be resolved from multiple views. So we need an method that can fuse together uncertain depth estimates from different views." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 270, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 546, + 361 + ], + "type": "text", + "content": "A natural way of representing uncertainty is through a probability distribution. When there are ambiguities, the distribution of depth estimates are typically multimodal, i.e., their probability densities have disjoint peaks, where each mode represents one interpretation of the scene structure. For example, albedo vs shading ambiguity as shown in Figure 2 can result in multiple plausible interpretations and make the distribution multimodal." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 363, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 433 + ], + "type": "text", + "content": "An added challenge arises when non-opaque surfaces are present. In this case, there is no single ground truth depth, and so the distribution of ground truth depths is multimodal. So even after training the NeRF, the distribution of ray termination distances induced by NeRF should be multimodal, as illustrated in the glass walls in Figure 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 434, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 547, + 548 + ], + "type": "text", + "content": "Prior methods compute moments (i.e., mean and/or variance) of the distribution of depth estimates or ray termination distance induced by NeRF. For example, DS-NeRF [6] predicts the mean depth estimate and uses reprojection error as a proxy for the variance. It then minimizes the KL divergence from the distribution of ray termination distances induced by NeRF to a Gaussian whose moments match those of the depth estimates. DDP [32] fits a Gaussian to distribution of ray termination distances and maximizes the likelihood of the depth estimate under the Gaussian." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 550, + 547, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 550, + 547, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 550, + 547, + 608 + ], + "type": "text", + "content": "Distilling complex distributions to moments has the drawback of ignoring their possible multimodality. Because both the distribution of depth estimates and ray termination distances are potentially multimodal, it is important to handle the multimodality." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 613, + 365, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 613, + 365, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 613, + 365, + 624 + ], + "type": "text", + "content": "4.2. SCADE" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 632, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 547, + 713 + ], + "type": "text", + "content": "We now present our novel method Space Carving with Ambiguity-aware Depth Estimates (SCADE). Our contributions address the existing problems and drawbacks mentioned in the previous section. First, SCADE accounts for the multimodality of both the distributions of monocular depth estimates and ray termination distances that arise due to inherent ambiguities (Sec 4.2.1) and non-opaque surfaces." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16521" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 166 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 166 + ], + "type": "text", + "content": "Second, SCADE is also able to resolve these ambiguities by fusing together information from multiple views through our space carving loss (Sec 4.2.3) that uses the reverse cross entropy loss. Because this a loss on the distribution rather than moments of the distribution (which was the paradigm in prior work [6, 32]), it achieves supervision in 3D rather than 2D. Third, our loss formulation is sample-based (Sec 4.2.2) and so is computationally efficient to optimize." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 171, + 248, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 248, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 248, + 182 + ], + "type": "text", + "content": "4.2.1 Our Ambiguity-aware Depth Estimates" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 183, + 289, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 183, + 289, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 289, + 334 + ], + "type": "text", + "content": "We handle multimodality of monocular depth distributions by introducing our ambiguity-aware depth estimation module to account for ambiguities in depth estimation from a single view (Figure 1, 2). In contrast to existing monocular depth estimation networks [47] that predict single point estimates for depth, we model the inherent uncertainty in monocular depth estimation by representing the distribution as a set of samples generated by a neural network. We propose leveraging conditional Implicit Maximum Likelihood estimation (cIMLE) [19] to learn a multimodal distribution of depth estimates. We chose cIMLE rather than conditional GANs [14] in order to avoid mode collapse, which can lead to a unimodal distribution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "content": "Figure 3 shows our network architecture. Concretely, we combine cIMLE with a state-of-the-art monocular depth estimation network, LeReS [47]. Our ambiguity-aware depth estimation module " + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "inline_equation", + "content": "(G)" + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "content": " takes an input image " + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "inline_equation", + "content": "(I)" + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "content": " and a latent code " + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "inline_equation", + "content": "z\\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "content": " and outputs a conditional depth sample " + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "inline_equation", + "content": "G(I,z)" + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "content": " for the input image " + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 335, + 289, + 462 + ], + "type": "text", + "content": ". To inject randomness into the network, we follow the technique used in [14] and incorporate AdaIn layers into the network backbone that predicts a scale and shift to the intermediate network features. Specifically, we added four AdaIn layers to the encoder of the depth estimation backbone." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 468, + 241, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 241, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 241, + 479 + ], + "type": "text", + "content": "4.2.2 Sample-based Losses on Distributions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 480, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 287, + 574 + ], + "type": "text", + "content": "We desire to achieve an agreement between the distributions from our ambiguity-aware prior and the ray termination distance from NeRF to constrain the NeRF optimization under the sparse view set-up using our learned prior. As distributions are continuous, taking their analytical integral is computationally intractable. Thus, in order to define a differentiable loss function for our optimization problem, we result in a sample-based loss on these two distributions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "content": "Samples from depth prior. As previously described, we leverage cIMLE to sample from our ambiguity-aware depth prior. Sampling " + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "inline_equation", + "content": "z_{1},\\ldots ,z_{M}\\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "content": ", we get depth map samples " + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "inline_equation", + "content": "G(I,z_1),\\dots,G(I,z_M)" + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "content": " for input image " + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "content": ". Hence we denote corresponding samples to estimate and represent the distribution for ray " + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "inline_equation", + "content": "y_{1},y_{2},\\dots,y_{M}\\sim G_{\\mathbf{o,d}}" + }, + { + "bbox": [ + 46, + 579, + 287, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "Samples from NeRF. For the distribution given by the ray termination distances modelled by NeRF, we sample from its probability density function " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta ,\\mathbf{o},\\mathbf{d}}" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": " (Eq. 3) with inverse transform sampling. Concretely, we define the probability mass function for ray " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "inline_equation", + "content": "f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i)" + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": " as given in Eq. 3 with" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 332, + 73, + 425, + 127 + ], + "blocks": [ + { + "bbox": [ + 332, + 73, + 425, + 127 + ], + "lines": [ + { + "bbox": [ + 332, + 73, + 425, + 127 + ], + "spans": [ + { + "bbox": [ + 332, + 73, + 425, + 127 + ], + "type": "image", + "image_path": "5ce69a59f9693151cf0118715c9aa7a4632ba34e4fa87d3d6c04f8224a7bbbb2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 332, + 129, + 425, + 181 + ], + "blocks": [ + { + "bbox": [ + 332, + 129, + 425, + 181 + ], + "lines": [ + { + "bbox": [ + 332, + 129, + 425, + 181 + ], + "spans": [ + { + "bbox": [ + 332, + 129, + 425, + 181 + ], + "type": "image", + "image_path": "f0f60911c43cb08167196bca975a3842d6efec53ccdedbaafe3d95dc4a38fd5a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 182, + 403, + 189 + ], + "lines": [ + { + "bbox": [ + 353, + 182, + 403, + 189 + ], + "spans": [ + { + "bbox": [ + 353, + 182, + 403, + 189 + ], + "type": "text", + "content": "2D Expected Depth" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 426, + 73, + 518, + 127 + ], + "blocks": [ + { + "bbox": [ + 426, + 73, + 518, + 127 + ], + "lines": [ + { + "bbox": [ + 426, + 73, + 518, + 127 + ], + "spans": [ + { + "bbox": [ + 426, + 73, + 518, + 127 + ], + "type": "image", + "image_path": "9e3fb50f9689e1cee02dd5c1e8baba0ac80730b0def19b79a7f53c0861ad64f9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 426, + 129, + 517, + 181 + ], + "blocks": [ + { + "bbox": [ + 426, + 129, + 517, + 181 + ], + "lines": [ + { + "bbox": [ + 426, + 129, + 517, + 181 + ], + "spans": [ + { + "bbox": [ + 426, + 129, + 517, + 181 + ], + "type": "image", + "image_path": "095433d6285bfd4172af0cf62ac7b64bbf1bcdd6b6a6d1de52d37ce1fe9081d0.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 182, + 504, + 189 + ], + "lines": [ + { + "bbox": [ + 440, + 182, + 504, + 189 + ], + "spans": [ + { + "bbox": [ + 440, + 182, + 504, + 189 + ], + "type": "text", + "content": "3D Space Carving (Ours)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 190, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 305, + 190, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 547, + 243 + ], + "type": "text", + "content": "Figure 4. Our space carving loss supervises the ray termination in 3D as opposed to existing approaches that supervise on 2D expected depth. As shown, this clears out clouds of dust in space. Moreover supervising in 3D allows for wide baseline input views and still finds the common mode that correctly snaps the surfaces." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "content": "samples " + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "inline_equation", + "content": "t_1,\\ldots ,t_K" + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "inline_equation", + "content": "t_i\\in [t_n,t_f]\\forall i" + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "content": " . By inverse transform sampling, we first compute the cumulative distribution function (CDF) of the ray termination distribution at samples " + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "content": " , which we denote as " + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "inline_equation", + "content": "F_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i) = \\sum_{j < i}f_{\\theta ,\\mathbf{o},\\mathbf{d}}(t_i)" + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "content": " . Thus our samples " + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "inline_equation", + "content": "x_{1},x_{2},\\dots,x_{N}" + }, + { + "bbox": [ + 305, + 248, + 547, + 319 + ], + "type": "text", + "content": " of ray termination distances from NeRF are then given by:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 395, + 325, + 545, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 325, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 395, + 325, + 545, + 346 + ], + "type": "interline_equation", + "content": "x _ {i} = F _ {\\theta , \\mathbf {o}, \\mathbf {d}} ^ {- 1} (u _ {i}), \\tag {4}", + "image_path": "2a1a3b6ac464ea8cea47ee3a350d440f3fc4d5ea0cfd0a4dcd6013da9ef5fed4.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 386, + 343, + 466, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 386, + 343, + 466, + 355 + ], + "spans": [ + { + "bbox": [ + 386, + 343, + 466, + 355 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 386, + 343, + 466, + 355 + ], + "type": "inline_equation", + "content": "u_{i}\\sim \\mathcal{U}(0,1)" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 365, + 444, + 377 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 444, + 377 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 444, + 377 + ], + "type": "text", + "content": "4.2.3 Our Space Carving Loss" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 378, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 545, + 494 + ], + "type": "text", + "content": "We now introduce our novel space carving loss utilizes the samples from both multimodal distributions to constrain the NeRF optimization. The goal is to find a subset of modes captured in the monocular depth distributions from each view that are globally consistent. In doing so, we can fuse together the information from the different views, since the inherent ambiguities are only resolved given information from multiple views. This would allow us to find a common shape that is consistent across all views and \"snap\" objects surfaces together." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 494, + 547, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 547, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 547, + 575 + ], + "type": "text", + "content": "We thus desire a loss that has mode seeking behavior, that is the modes of the distribution being trained should be a subset of the modes of the distribution that provides supervision. One such loss is the reverse cross entropy, which is the cross entropy from the NeRF ray termination distance distribution to the distribution of our ambiguity-aware depth estimates:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 345, + 582, + 545, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 582, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 345, + 582, + 545, + 597 + ], + "type": "interline_equation", + "content": "H \\left(f _ {\\theta , \\mathbf {o}, \\mathbf {d}}, G _ {\\mathbf {o}, \\mathbf {d}}\\right) = - \\mathbb {E} _ {f _ {\\theta , \\mathbf {o}, \\mathbf {d}}} [ \\log G _ {\\mathbf {o}, \\mathbf {d}} ]. \\tag {5}", + "image_path": "242762a66fc0caf21581aebf7413f290d460d7e6e6b9826e895ccb2c9651c8fc.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 602, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 545, + 651 + ], + "type": "text", + "content": "As shown in the IMLE papers [19, 28], this is equivalent to penalizing the minimum of the L2 norm between the samples from the two distributions, please see [18] for the full proof. Hence, our space carving loss is given by" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 340, + 656, + 545, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 656, + 545, + 684 + ], + "spans": [ + { + "bbox": [ + 340, + 656, + 545, + 684 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s p a c e ＿ c a r v i n g}} (\\mathbf {r}) = \\sum_ {i \\in [ N ]} \\min _ {j \\in [ M ]} \\| x _ {i} - y _ {j} \\| _ {2} ^ {2}. \\tag {6}", + "image_path": "1337a65ea6b7f4fe46e245aa898308c8a63caa50b3bf5727920a2ee2e8867b1e.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "Because our novel space carving loss operates on distributions rather than moments of distributions, we can have" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16522" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 200 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 200 + ], + "type": "text", + "content": "different supervision targets for different points along the ray. In contrast, if the loss were to only to operate on moments, which are integrals along the ray, this only yields the same supervision target for all points along the ray. Therefore, our loss allows us to supervise in 3D, unlike prior methods [6, 32] (which use losses on moments) that supervise in 2D. 3D supervision allows us to clear out dust in space, since in order to move a sample from the ray termination distance distribution farther in depth, the loss would have to decrease the probability density of all the points in front of it. These advantages are highlighted in Figure 4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 200, + 288, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 288, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 288, + 224 + ], + "type": "text", + "content": "Our total loss to optimize and train our NeRF model is given by" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 100, + 232, + 287, + 246 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 232, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 100, + 232, + 287, + 246 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {p h o t o m e t r i c}} + \\lambda \\mathcal {L} _ {\\text {s p a c e ＿ c a r v i n g}}, \\tag {7}", + "image_path": "5fcd64bd50c889d23038a4cec155e707f3ecc68ae92dff2fb3b170aaf0658dcb.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 254, + 287, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 278 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 254, + 287, + 278 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{photometric}}" + }, + { + "bbox": [ + 46, + 254, + 287, + 278 + ], + "type": "text", + "content": " is the standard MSE loss on the predicted and ground truth image. See Fig. 1 for our overall pipeline." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 288, + 100, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 100, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 100, + 300 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 302, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 287, + 326 + ], + "type": "text", + "content": "In this section, we present our experimental evaluation to demonstrate the advantages of SCADE." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 330, + 222, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 330, + 222, + 341 + ], + "spans": [ + { + "bbox": [ + 47, + 330, + 222, + 341 + ], + "type": "text", + "content": "5.1. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 342, + 289, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 289, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 289, + 504 + ], + "type": "text", + "content": "We evaluate our method on ScanNet [5] and an in-the-wild dataset we collected1. We use the sparse-view ScanNet data used by DDP [32] in their evaluations, which comprises of three sample scenes each with 18 to 20 train images and 8 test images. To further test the robustness of our method, we further evaluated our method on three in-the-wild scenes collected using an iPhoneX. We captured sparse views in three different scenes - basement, kitchen and lounge, where each scene has 18 to 23 train images and 8 test images. Following similar data preprocessing steps as DDP [32], we ran SfM [34] on all images to obtain camera poses for NeRF training. For quantitative comparison, we follow the original NeRF [24] paper and report the PSNR, SSIM [42] and LPIPS [52] on the novel test views." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 512, + 180, + 524 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 180, + 524 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 180, + 524 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 525, + 288, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 288, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 288, + 571 + ], + "type": "text", + "content": "We train our ambiguity-aware prior on the Taskonomy [50] dataset and initialize the weights with the pretrained LeReS [47] model. We use " + }, + { + "bbox": [ + 46, + 525, + 288, + 571 + ], + "type": "inline_equation", + "content": "M = 20" + }, + { + "bbox": [ + 46, + 525, + 288, + 571 + ], + "type": "text", + "content": " depth estimates in our experiments. See supplement for additional details." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 575, + 186, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 186, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 186, + 588 + ], + "type": "text", + "content": "5.3. Experiments on ScanNet" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 590, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 289, + 696 + ], + "type": "text", + "content": "We evaluate on ScanNet following the evaluation from DDP [32]. We compare to the original NeRF [24] (Vanilla NeRF) and the recent state-of-the-art NeRF with depth prior-based supervision, Dense Depth Prior [32] (DDP). Table 1 shows SCADE quantitatively outperforming the baselines. Because we are interested in simulating real-world conditions with a domain gap between the prior and the NeRF, our setting requires the use of out-of-domain priors. Since DDP uses a in-domain prior, we retrain DDP's depth completion" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 308, + 65, + 544, + 151 + ], + "blocks": [ + { + "bbox": [ + 308, + 65, + 544, + 151 + ], + "lines": [ + { + "bbox": [ + 308, + 65, + 544, + 151 + ], + "spans": [ + { + "bbox": [ + 308, + 65, + 544, + 151 + ], + "type": "image", + "image_path": "949b1024709f36574ef8fca2f848b5a09b39f2c61a19449dd8a1bfcb1d311674.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 154, + 545, + 176 + ], + "lines": [ + { + "bbox": [ + 306, + 154, + 545, + 176 + ], + "spans": [ + { + "bbox": [ + 306, + 154, + 545, + 176 + ], + "type": "text", + "content": "Figure 5. Depth and Fusion Comparison. Depth map and fusion comparison between SCADE and DDP." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 307, + 179, + 545, + 290 + ], + "blocks": [ + { + "bbox": [ + 307, + 179, + 545, + 290 + ], + "lines": [ + { + "bbox": [ + 307, + 179, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 307, + 179, + 545, + 290 + ], + "type": "table", + "html": "
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]19.030.6700.398
NerfingMVS [47]16.290.6260.502
IBRNet [41]13.250.5290.673
MVSNeRF [3]15.670.5330.635
DS-NeRF [6]20.850.7130.344
DDP [32]19.290.6950.368
SCADE (Ours)21.540.7320.292
", + "image_path": "9e79add36f31f9f730a8d851dc39149f2ae384c31bbc009d5a948066029dffb3.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 293, + 545, + 348 + ], + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 348 + ], + "type": "text", + "content": "Table 1. ScanNet Results. Results for DS-NeRF and NerfingMVS follow what was reported in prior literature [32]. Because our setting requires out-of-domain priors, the results for DDP are with out-of-domain priors. The results of DDP with in-domain priors are (20.96, 0.737, 0.236) for PSNR, SSIM and LPIPS, respectively." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 354, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 354, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 545, + 389 + ], + "type": "text", + "content": "network using their official code and hyperparameters on Taskonomy [50], i.e. the same out-of-domain dataset that our prior is trained on." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 389, + 547, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 547, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 547, + 518 + ], + "type": "text", + "content": "Figure 6 shows our qualitative results. As shown, compared to the baselines, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (first, third and last column). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (second column), the back of the chair (fourth column) and the legs of the piano stool (fifth column). Moreover, Fig. 5 shows rendered depthmaps and fusion results using [51] on a Scannet scene. Notice that SCADE is able to recover better geometry compared to DDP - see corner of the calendar, cabinets and office chair in the right image." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 523, + 486, + 535 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 523, + 486, + 535 + ], + "spans": [ + { + "bbox": [ + 306, + 523, + 486, + 535 + ], + "type": "text", + "content": "5.4. Experiments on In-the-Wild Data" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 538, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 547, + 713 + ], + "type": "text", + "content": "To further test the robustness of SCADE, we further evaluate on data collected in-the-wild with a standard phone camera (iPhoneX). The intrinsics for different views are different and are not known to the algorithm. As shown in Table 2, SCADE with the same out-of-domain prior (trained on Taskonomy) outperforms the baselines on in-the-wild captured data, which demonstrates its robustness. Figure 7 shows qualitative examples. Interestingly, we are able to recover the room behind the glass better the baselines, whose results are more blurry (first, third and fourth column). We are also able to recover objects behind the glass such as the monitor and chair (first column). As discussed in Sect. 4.1, non-opaque surfaces are the most challenging because both the ground truth distribution of ray termination distances induced by NeRF and the distribution of estimated depths" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "text", + "content": "1Also see supplement for results on the Tanks and Temples dataset [16]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16523" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 72, + 532, + 272 + ], + "blocks": [ + { + "bbox": [ + 61, + 72, + 532, + 272 + ], + "lines": [ + { + "bbox": [ + 61, + 72, + 532, + 272 + ], + "spans": [ + { + "bbox": [ + 61, + 72, + 532, + 272 + ], + "type": "image", + "image_path": "e9189b41264e143ca49e61725e478d56b531c4f517a25de627d60d97f175c7fe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 547, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 547, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 547, + 307 + ], + "type": "text", + "content": "Figure 6. Qualitative results on ScanNet. As shown, SCADE is able to avoid producing the clouds of dust that are present in the results of baselines (1st, 3rd, last columns). Moreover, SCADE is also able to snap and recover objects in the scene such as the details on the blinds (2nd column), the back of the chair (4th column) and the legs of the piano stool (5th column)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 315, + 287, + 378 + ], + "blocks": [ + { + "bbox": [ + 48, + 315, + 287, + 378 + ], + "lines": [ + { + "bbox": [ + 48, + 315, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 48, + 315, + 287, + 378 + ], + "type": "table", + "html": "
PSNR ↑SSIM ↑LPIPS ↓
Vanilla NeRF [24]20.460.7130.398
DDP [32]21.280.7270.366
SCADE (Ours)22.820.7430.347
", + "image_path": "fe37034eb23db24e5a1050fedb62f31d15d23bdfad568a658cd709102a20d220.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 392, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 416 + ], + "type": "text", + "content": "from the prior must be multimodal. This validates the ability of our model to capture the multimodal distributions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 416, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 287, + 475 + ], + "type": "text", + "content": "Similar to the ScanNet results, we are able to recover crisp shapes of objects such as the thin table leg and the white chair (second and last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (fifth and last column)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 480, + 141, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 141, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 141, + 493 + ], + "type": "text", + "content": "5.5. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 495, + 288, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 288, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 288, + 659 + ], + "type": "text", + "content": "Supervision on full distribution vs moments We first validate the importance of using our novel space carving loss that supervises the full distribution of ray termination distance rather than just its moments. The latter integrates along the ray, and so provides one target value for the entire ray, which effectively makes it 2D supervision. The former provides different target values for different samples along the same ray, which makes it 3D supervision. We adapt our method to use 2D supervision proposed in the recent MonoSDF [49], which computes the expected ray termination distance and aligns the output depth map with a monocular depth estimation prior using the MiDaS [30] loss. We use our learned prior as the monocular depth estimate. Table 3 validates the effectiveness of our space carving loss." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 666, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 289, + 715 + ], + "type": "text", + "content": "Multimodal prior vs unimodal prior. Our prior models does not constrain the depth distribution to a particular form and allows it to be multimodal. In contrast, DDP's depth completion prior assumes a Gaussian, which is unimodal." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 315, + 545, + 402 + ], + "blocks": [ + { + "bbox": [ + 112, + 380, + 221, + 389 + ], + "lines": [ + { + "bbox": [ + 112, + 380, + 221, + 389 + ], + "spans": [ + { + "bbox": [ + 112, + 380, + 221, + 389 + ], + "type": "text", + "content": "Table 2. In-the-wild Results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 315, + 545, + 402 + ], + "lines": [ + { + "bbox": [ + 307, + 315, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 307, + 315, + 545, + 402 + ], + "type": "table", + "html": "
PSNR ↑SSIM ↑LPIPS ↓
MonoSDF supervision20.130.7100.332
DDP prior - single sample20.850.7120.320
DDP prior - multiple samples21.000.7180.316
Our prior - single sample21.220.7140.318
SCADE (Ours)21.540.7320.292
", + "image_path": "ffe62631a9c24eccb06a7e079ddd2ff92556d3af67acf0602456f18dfce15e89.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 405, + 547, + 438 + ], + "lines": [ + { + "bbox": [ + 305, + 405, + 547, + 438 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 547, + 438 + ], + "type": "text", + "content": "Table 3. Ablation Study. Results on the Scannet dataset. MonoSDF supervision refers to supervising with MonoSDF loss on expected ray termination distance using our prior." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 445, + 547, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 516 + ], + "type": "text", + "content": "We ablate our prior against DDP's by sampling from their Gaussian distribution. We train with our space carving loss using both a single sample, as well as " + }, + { + "bbox": [ + 304, + 445, + 547, + 516 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 445, + 547, + 516 + ], + "type": "text", + "content": " samples drawn from DDP's prior. As shown in Table 3, while both perform better than the 2D supervision provided by MonoSDF, but they are subpar compared to using our multimodal prior." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 604 + ], + "type": "text", + "content": "Multiple vs single sample. Finally, we also ablate on using a single sample vs multiple samples for our space carving loss. For the single sample set-up, we supervise using the sample mean of the depth estimates, which is equivalent to the maximum likelihood estimate of the depth under Gaussian likelihood. Results in Table 3 show the importance of using multiple samples for our space carving loss." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 609, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 547, + 713 + ], + "type": "text", + "content": "Sparsity. We further show addt'l results under varying number of views in Tab 4. Note that in general sparsity is not fully reflected by the absolute number of views, because all else being equal, a larger scene requires more views to attain complete coverage. Following prior work [32], we also report the average number of views that see the same point as another measure of sparsity. As shown, our setting is at the edge of the theoretical lower limit of 2 for general-purpose reconstruction, which shows view sparsity." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16524" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 532, + 274 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 532, + 274 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 532, + 274 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 532, + 274 + ], + "type": "image", + "image_path": "7e2362ab6a15190dbdcc9d678e22a5b9e89861b7021b641f07fec5373cdc845d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 275, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 547, + 309 + ], + "type": "text", + "content": "Figure 7. Qualitative results on In-the-Wild data. As shown, we are able to recover the room behind the glass better the baselines, whose results are more blurry (1st, 3rd, 4th column). Also, SCADE is able to recover crisp shapes of objects such as the thin table leg and the white chair (2nd, last column), and we are also able to clear up dust near the microwave and printer compared to the baselines (5th, last column)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 316, + 288, + 355 + ], + "blocks": [ + { + "bbox": [ + 48, + 316, + 288, + 355 + ], + "lines": [ + { + "bbox": [ + 48, + 316, + 288, + 355 + ], + "spans": [ + { + "bbox": [ + 48, + 316, + 288, + 355 + ], + "type": "table", + "html": "
ave. #views visible1.871.982.012.2
absolute #views18202224
DDP / SCADE19.35/ 21.6622.4/ 23.6723.10/ 24.0023.56/ 24.84
", + "image_path": "8a0faede98243af031aa79b018a997b7fb9b6baf0046a053c27e95fac9f5a15c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 357, + 281, + 368 + ], + "lines": [ + { + "bbox": [ + 53, + 357, + 281, + 368 + ], + "spans": [ + { + "bbox": [ + 53, + 357, + 281, + 368 + ], + "type": "text", + "content": "Table 4. PSNR for DDP [32]/SCADE on scene781 of Scannet." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 371, + 186, + 454 + ], + "blocks": [ + { + "bbox": [ + 48, + 371, + 186, + 454 + ], + "lines": [ + { + "bbox": [ + 48, + 371, + 186, + 454 + ], + "spans": [ + { + "bbox": [ + 48, + 371, + 186, + 454 + ], + "type": "image", + "image_path": "29b97ea9fa589445999cb9da35c0638f35b86213f46f987167af3609e7216b4d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 189, + 371, + 286, + 456 + ], + "blocks": [ + { + "bbox": [ + 189, + 371, + 286, + 456 + ], + "lines": [ + { + "bbox": [ + 189, + 371, + 286, + 456 + ], + "spans": [ + { + "bbox": [ + 189, + 371, + 286, + 456 + ], + "type": "image", + "image_path": "4d6aa5d3f52bf5f17bac43561c98b1ea27cd406ae972d63e2f89a5253283b950.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 457, + 288, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 457, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 288, + 489 + ], + "type": "text", + "content": "Figure 8. Depth Mode Discussion. a) Train images from Taskonomy [50] and their labels. Notice that non-opaque surfaces are labelled differently. b) Output of our prior on reflective surfaces." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 498, + 266, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 266, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 266, + 511 + ], + "type": "text", + "content": "5.6. Discussion on our Ambiguity-Aware Prior" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 512, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 512, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 512, + 289, + 685 + ], + "type": "text", + "content": "We provide addt'l details on our ambiguity-aware prior on i) how and why it works, ii) its performance on reflective surfaces, which is a common failure case for depth estimate, and iii) provide an intuition on how what our depth modes look like. i) We achieve variable depth modes by exploiting inconsistently labeled training data. As shown in Fig 8-a, in Taskonomy [50], different training images with non-opaque surfaces label depth differently: shooting through the glass (left), on the glass (middle), or a mixture of both (right). Despite multiple possible depth labels, each image only has one ground truth label. Training with cIMLE allows our prior to model these multiple possible (ambiguous) outputs through sampling" + }, + { + "bbox": [ + 46, + 512, + 289, + 685 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 512, + 289, + 685 + ], + "type": "text", + "content": ", even when given only one label per image. Interestingly when testing our prior on a test image with a mirror, we find that it is able to capture variable modes" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "type": "text", + "content": "on reflective surfaces, including the \"correct\" flat surface as shown in Fig 8-b. An intuition of what the depth modes look like is for example if a ray intersects " + }, + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "type": "text", + "content": " non-opaque surfaces, the " + }, + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 318, + 545, + 376 + ], + "type": "text", + "content": " modes are intersections with the non-opaque surfaces and the terminating point on the opaque surface." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 380, + 378, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 378, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 378, + 392 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 394, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 547, + 568 + ], + "type": "text", + "content": "In this paper, we present a new approach towards NeRF reconstruction that can work with a modest number of in-the-wild views of an indoor scene. We address the underconstrained nature of this problem by regularizing the NeRF optimization with additional depth estimates for each view. Our key technical contribution is to model multimodality in the depth estimates, which can capture inherent ambiguities in monocular depth estimation as well as the possible presence of non-opaque surfaces. We resolve ambiguities using a novel space carving loss that fuses the multimodal depth estimates from different views and seeks the modes that are consistent across views so as to arrive at a globally consistent 3D reconstruction. The improved recovery of shape and appearance enables higher fidelity novel view synthesis from sparse views." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 571, + 547, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 547, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 547, + 653 + ], + "type": "text", + "content": "Limitations and Future Work. The performance of our method is constrained by the quality of the monocular depth priors. While we found that our prior generalizes well across domains, if the domain gap is too great, the performance of our method will degrade. A future direction would be to detect when this happens and dynamically adjust the strength of depth supervision in response." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgements. We sincerely thank the Teleportation and CCI team in Google for all the insightful discussions during the summer. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 1851-1858, 2017. 3" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16527" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_content_list.json b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4ffb0591f4ba8212196c481906da6d70a10ec0f7 --- /dev/null +++ b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_content_list.json @@ -0,0 +1,1377 @@ +[ + { + "type": "text", + "text": "SCConv: Spatial and Channel Reconstruction Convolution for Feature Redundancy", + "text_level": 1, + "bbox": [ + 127, + 128, + 841, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiafeng Li $^{1}$ , Ying Wen $^{1*}$ , Lianghua He $^{2}$", + "bbox": [ + 346, + 202, + 653, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Communication and Electronic Engineering, East China Normal University, Shanghai, China. $^{2}$ Department of Computer Science and Technology, Tongji University, Shanghai, China.", + "bbox": [ + 88, + 220, + 913, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "51205904113@stu.ecnu.edu.cn;ywen@cs.ecnu.edu.cn;helianghua@tongji.edu.cn", + "bbox": [ + 178, + 258, + 816, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Convolutional Neural Networks (CNNs) have achieved remarkable performance in various computer vision tasks but this comes at the cost of tremendous computational resources, partly due to convolutional layers extracting redundant features. Recent works either compress well-trained large-scale models or explore well-designed lightweight models. In this paper, we make an attempt to exploit spatial and channel redundancy among features for CNN compression and propose an efficient convolution module, called SCConv (Spatial and Channel reconstruction Convolution), to decrease redundant computing and facilitate representative feature learning. The proposed SCConv consists of two units: spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). SRU utilizes a separate-and-reconstruct method to suppress the spatial redundancy while CRU uses a split-transform-and-fuse strategy to diminish the channel redundancy. In addition, SCConv is a plug-and-play architectural unit that can be used to replace standard convolution in various convolutional neural networks directly. Experimental results show that SCConv-embedded models are able to achieve better performance by reducing redundant features with significantly lower complexity and computational costs.", + "bbox": [ + 75, + 340, + 472, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 715, + 209, + 732 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, convolutional neural networks (CNNs) have obtained widespread applications in computer vision tasks [24] due to its ability in obtaining representative features. However, such success relies heavily on intensive resources of computation and storage, which poses severe challenges to their efficient deployment on resource-constrained environments. Therefore, to address these challenges, various types of model compression strategies and network designs have been explored to improve network ef", + "bbox": [ + 75, + 742, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ficiency [1, 2, 26]. The former includes network pruning, weight quantization, low-rank factorization, and knowledge distillation. To be specific, network pruning [17, 22, 30] is a straightforward way to prune the uncritical neuron connections from an existing learned big model to make it thinner. Weight quantization [9] mainly focuses on converting network weights from floating-point types to integer ones to save computation resources. Low-rank factorization [5] applies the matrix decomposition techniques to estimate the informative parameters. Knowledge distillation [11, 34] generates small student networks with the guidance of a well-trained big teacher network. The common part of these compression techniques is that they have been regarded as post-processing steps, thus their performance is usually upper bounded by the given initial model. Meanwhile, the accuracy of these methods drastically drops while achieving a high compression rate.", + "bbox": [ + 500, + 309, + 893, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Network design is another alternative way, which aims at reducing the inherent redundancy in dense model parameters and further developing a lightweight network model. For example, ResNet [10] and DenseNet [14] utilize an efficient shortcut connection to improve the network topology, which connects all preceding feature maps to diminish the redundant parameters. ResNeXt [31] replaces traditional convolutions with sparsely connected group convolutions to reduce inter-channel connectivity. Networks like Xception [4], MobileNet [12] and MobileNeXt [35] disentangle standard convolution into depth-wise convolution and point-wise convolution to further decrease the connection density between channels. MicroNet [19] adopts microfactorized convolution to handle extremely low FLOPs by integrating sparse connectivity into convolution. In addition, EfficientNet [27] learns to automatically search optimal network architectures to lower the redundancy in dense model parameters.", + "bbox": [ + 496, + 566, + 893, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Moreover, in CNN architecture design, bottleneck structure has been well adopted, in which $3 \\times 3$ convolutional layers account for a majority of the model parameters and FLOPs. Therefore various efficient convolutional opera", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author (e-mail: ywen@cs.ecnu.edu.cn)", + "bbox": [ + 94, + 886, + 388, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6153", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/876397cb6e401a1a1963e6f3ed60b2d85aa203d0a0867f9177f4a0930e41b0d6.jpg", + "image_caption": [ + "Figure 1. The architecture of SCConv integrated with Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU). This figure shows the exact position of our SCConv module within a ResBlock." + ], + "image_footnote": [], + "bbox": [ + 137, + 85, + 834, + 213 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tions, such as group-wise convolution (GWC), depth-wise convolution (DWC) and point-wise convolution (PWC), a variant of the standard convolution, are proposed to replace the existing expensive convolutional operation. GWC, which was first introduced in AlexNet [16], can be regarded as a sparse convolution connection method that each output channel is connected to only a certain group of input channels. DWC [13] proposes to bring more efficiency by keeping each channel separately convolved with filters and without interaction between channels. PWC is used to keep the information flowing across channels and enable dimensionality reduction by reducing the number of filters. These operations are similar in sparse connectivity and have benefits in the number of parameters and FLOPs, which illustrates that redundancy in channel dimension can be reduced reasonably. Hence, a variety of convolution operations are proposed to explore redundancy reduction. For example, MobileNet [12] introduces inverted residual blocks using DWC and PWC to filter the features, which decreases the number of parameters while accelerating the training. ShuffleNet [33] resorts to point-wise group convolution and channel shuffle operation to improve the information flow between different channel groups. HetConv [25] designs heterogeneous convolutional filters where a $3 \\times 3$ convolution kernels and a $1 \\times 1$ convolution kernels are included in one single filter to extract features. TiedBlockConv [28] shares the same convolutional filter over equal blocks of channels to produce multiple responses within a single filter. SPConv [32] divides the input channels into two groups for different processing but needs a relatively large amount of calculation while extracting internal information. GhostNet [8] considers the redundancy between feature maps and uses cheap operations like DWC to learn redundant features. SilmConv [23] adopts the operation of reducing the channels of features and flipping the weights to reduce feature redundancy. In addition, orthogonal to channel redundancy, OctConv [3] proposes octave convolution to separate convolutional filters into high-frequency and low-frequency components, processing the latter in low resolution to alleviate the spatial redundancy, which reduces calculations while keeping the same number of parameters.", + "bbox": [ + 76, + 277, + 472, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "All these prior studies have proven that there indeed exists considerable redundancy in the deep neural networks, not only in dense model parameters but also in the spatial and channel dimension of feature maps. However, all the above methods either focus on reducing the redundancy in channel dimension or in spatial dimension, making the network still suffer from the problems of feature redundancy.", + "bbox": [ + 496, + 277, + 890, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, different from prior work, we design a two-step procedure to exploit the redundancy of intermediate feature maps, with the goal of reducing the number of parameters and computation without performance loss. To this end, we propose a novel CNN compression approach to jointly reduce spatial and channel redundancy in the convolutional layers, termed as SCConv (Spatial and Channel reconstruction Convolution), which consists of two units, spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). The proposed SCConv module, which can be embedded into various architectures without additional modifications, is designed to efficiently restrict feature redundancy. This module not only cuts down on the number of model parameters and FLOPs but enhances the capability of feature representation. We summarize our contributions as follows:", + "bbox": [ + 496, + 383, + 892, + 625 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a spatial reconstruction unit, termed as SRU, which separates redundant features based on weights and reconstructs them to suppress the redundancy in spatial dimension and strengthen the representation of features.", + "- We propose a channel reconstruction unit, termed as CRU, which utilizes a split-transform-and-fuse strategy to diminish the redundancy in channel dimension as well as the computational costs and storage.", + "- We design a plug-and-play operation named SCConv combining SRU and CRU in a sequential manner to replace standard convolution for operating on a variety of backbone CNNs. It turns out that SCConv can substantially save the computing load yet enhance the model performance on challenging tasks." + ], + "bbox": [ + 517, + 638, + 890, + 885 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6154", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/25c6d98ef6edc95d65e0ca96b6b67f4a04991eda78f228ceb8091009848fd76e.jpg", + "image_caption": [ + "Figure 2. The architecture of Spatial Reconstruction Unit." + ], + "image_footnote": [], + "bbox": [ + 135, + 88, + 834, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Methodology", + "text_level": 1, + "bbox": [ + 76, + 342, + 210, + 359 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the proposed SCConv as illustrated in Figure 1, which consists of two units, Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU), placed in a sequential manner. Concretely, for the intermediate input features $X$ in the bottleneck residual block, we first obtain the spatial-refined features $X^w$ through SRU operation and subsequently we utilize CRU operation to gain the channel-refined features $Y$ . We exploit both spatial and channel redundancy among features in our SCConv module, which can be seamlessly integrated into any CNN architecture to decrease redundancy among intermediate feature maps and boost the feature representation of CNNs.", + "bbox": [ + 75, + 369, + 470, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. SRU for Spatial Redundancy", + "text_level": 1, + "bbox": [ + 76, + 579, + 334, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To exploit the spatial redundancy of features, we introduce Spatial Reconstruction Unit (SRU) as shown in Figure 2, which utilizes a Separate-and-Reconstruct operation. Separate operation aims to separate those informative feature maps from less informative ones corresponding to the spatial content. We leverage the scaling factors in Group Normalization (GN) [29] layers to assess the informative content of different feature maps. To be concrete, given an intermediate feature map $X \\in \\mathbb{R}^{N \\times C \\times H \\times W}$ , where $N$ is the batch axis, $C$ is the channel axis, $H$ and $W$ are the spatial height and width axes. We first standardize the input feature $X$ by subtracting mean $\\mu$ and dividing by standard deviation $\\sigma$ as follows:", + "bbox": [ + 75, + 603, + 468, + 799 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nX _ {o u t} = G N (X) = \\gamma \\frac {X - \\mu}{\\sqrt {\\sigma^ {2} + \\varepsilon}} + \\beta \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 810, + 468, + 842 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mu$ and $\\sigma$ are the mean and standard deviation in $X$ , $\\varepsilon$ is a small positive constant added for the sake of division stability, $\\gamma$ and $\\beta$ are trainable affine transformation.", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Noted that we leverage the trainable parameters $\\gamma \\in R^{C}$ in $GN$ layers as a way to measure the variance of spatial pixels for each batch and channel. The richer spatial information reflects more variation in spatial pixels contributing to a larger $\\gamma$ . The normalized correlation weights $W_{\\gamma} \\in R^{C}$ are obtained by equation 2, which indicates the importance of different feature maps.", + "bbox": [ + 496, + 343, + 890, + 450 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nW _ {\\gamma} = \\left\\{w _ {i} \\right\\} = \\frac {\\gamma_ {i}}{\\sum_ {j = 1} ^ {C} \\gamma_ {j}}, i, j = 1, 2, \\dots , C \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 460, + 890, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then the weight values of feature maps reweighted by $W_{\\gamma}$ are mapped to the range (0, 1) by the sigmoid function and gated by a threshold. We set those weights above the threshold to 1 to obtain the informative weights $W_{1}$ while setting them to 0 to gain the non-informative weights $W_{2}$ (the threshold is set to 0.5 in the experiments). The whole process of acquiring $W$ can be expressed as equation 3:", + "bbox": [ + 496, + 508, + 890, + 614 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nW = \\operatorname {G a t e} \\left(\\operatorname {S i g m o i d} \\left(W _ {\\gamma} \\left(G N (X)\\right)\\right)\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 627, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finally, we multiply input features $X$ by $W_{1}$ and $W_{2}$ respectively, yielding two weighted features: the informative ones $X_{1}^{w}$ and less informative ones $X_{2}^{w}$ . Thus we successfully separate the input features into two parts: $X_{1}^{w}$ has informative and expressive spatial contents while $X_{2}^{w}$ has little or no information, which is regarded as redundant.", + "bbox": [ + 496, + 657, + 890, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to reduce the spatial redundancy, we further propose a Reconstruct operation that features with rich information sum up with less informative ones to generate features with richer information and save spatial space. Instead of adding these two parts directly, we adopt a cross reconstruct operation to sufficiently combine the weighted two different informative features and strengthen the information flow between them. Afterwards we concatenate the cross-reconstructed features $X^{w1}$ and $X^{w2}$ to obtain the spatial-refined feature maps $X^w$ . The whole process of $Re$ -", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6155", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/118d6c0d9c525f5c625cc78517dd9d2ee958421d3871790678b1795d8b6665d4.jpg", + "image_caption": [ + "Figure 3. The architecture of Channel Reconstruction Unit." + ], + "image_footnote": [], + "bbox": [ + 135, + 88, + 834, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "construct operation can be expressed as :", + "bbox": [ + 76, + 330, + 349, + 345 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{c} X _ {1} ^ {w} = W _ {1} \\otimes X, \\\\ X _ {2} ^ {w} = W _ {2} \\otimes X, \\\\ X _ {1 1} ^ {w} \\oplus X _ {2 2} ^ {w} = X ^ {w 1}, \\\\ X _ {2 1} ^ {w} \\oplus X _ {1 2} ^ {w} = X ^ {w 2}, \\\\ X ^ {w 1} \\cup X ^ {w 2} = X ^ {w}. \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 351, + 468, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\otimes$ is element-wise multiplication, $\\oplus$ is element-wise summation, $\\cup$ is concatenation. After the SRU is applied to the intermediate input features $X$ , not only do we separate the informative features from less informative ones, but also we reconstruct them to enhance the representative features and suppress the redundant features in spatial dimension. Nevertheless, the spatial-refined feature maps $X^w$ still remain redundant in channel dimension.", + "bbox": [ + 75, + 452, + 472, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2. CRU for Channel Redundancy", + "text_level": 1, + "bbox": [ + 76, + 580, + 349, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To exploit the channel redundancy of features, we introduce Channel Reconstruction Unit (CRU) as shown in Figure 3, which utilizes a Split-Transform-and-Fuse strategy. Normally, we use repetitive standard $k \\times k$ convolutions to extract features, resulting in some relatively redundant feature maps along the channel dimension. Let $M^k \\in \\mathbb{R}^{c \\times k \\times k}$ denotes a $k \\times k$ convolution kernel and $X, Y \\in \\mathbb{R}^{c \\times h \\times w}$ denotes the input and convolved output features respectively. A standard convolution can be defined as $Y = M^k X$ . To be specific, we replace the standard convolution with CRU, which is implemented via three operators - Split, Transform and Fuse.", + "bbox": [ + 75, + 604, + 468, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Split: For given spatial-refined features $X^w \\in \\mathbb{R}^{c \\times h \\times w}$ , we first split the channels of $X^w$ into two parts with $\\alpha C$ channels and $(1 - \\alpha)C$ channels respectively, as shown in the split part of Figure 3, where $0 \\leq \\alpha \\leq 1$ is a split ratio. Subsequently, we further utilize $1 \\times 1$ convolutions to", + "bbox": [ + 75, + 803, + 470, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "squeeze the channels of feature maps for its computing efficiency. Here we introduce a squeeze ratio $r$ to control the feature channels to balance the computational cost of the CRU ( $r = 2$ is a typical setting in the experiments). After the split and squeeze operations, we divide the spatial-refined features $X^w$ into the upper part $X_{up}$ and the lower part $X_{low}$ .", + "bbox": [ + 500, + 330, + 890, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transform: $X_{up}$ is fed into the upper transformation stage, serving as a \"Rich Feature Extractor\". We adopt efficient convolutional operations (i.e. GWC and PWC) to replace the expensive standard $k \\times k$ convolutions to extract high-level representative information as well as reduce the computational cost. Owing to sparse convolution connections, GWC reduces the amount of parameters and calculations but cuts off the information flow between channel groups. While PWC compensates for the information loss and helps the information flow across feature channels. Thus we perform $k \\times k$ GWC (we set group size $g = 2$ in the experiments) and $1 \\times 1$ PWC operations on the same $X_{up}$ . Afterward, we sum up the output to form a merged representative feature maps $Y_{1}$ as shown in the Transform part of Figure 3. The upper transformation stage can be formulated as:", + "bbox": [ + 496, + 452, + 892, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY _ {1} = M ^ {G} X _ {u p} + M ^ {P _ {1}} X _ {u p} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 693, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M^G \\in \\mathbb{R}^{\\frac{\\alpha c}{gr} \\times k \\times k \\times c}$ , $M^{P_1} \\in \\mathbb{R}^{\\frac{\\alpha c}{r} \\times 1 \\times 1 \\times c}$ is a learnable weight matrix of GWC and PWC, $X_{up} \\in \\mathbb{R}^{\\frac{\\alpha c}{r} \\times h \\times w}$ and $Y_1 \\in \\mathbb{R}^{c \\times h \\times w}$ are the upper input and output feature maps respectively. In short, the upper transformation stage leverages a combination of GWC and PWC on the same feature maps $X_{up}$ to extract rich representative features $Y_1$ with less computational cost.", + "bbox": [ + 496, + 717, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$X_{low}$ is fed into the lower transformation stage, where we apply cheap $1 \\times 1$ PWC operations to generate feature maps with shallow hidden details as a supplementary to the Rich Feature Extractor. In addition, we reuse features $X_{low}$ to obtain more feature maps without extra cost. Lastly, we", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "For simplicity, we omit the bias term.", + "bbox": [ + 94, + 886, + 303, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6156", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "concatenate the generated and reused features to form the output of the lower stage $Y_{2}$ as follows:", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nY _ {2} = M ^ {P _ {2}} X _ {l o w} \\cup X _ {l o w} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 128, + 468, + 146 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M^{P_2} \\in \\mathbb{R}^{\\frac{(1 - \\alpha)c}{r} \\times 1 \\times (1 - \\frac{1 - \\alpha}{r})c}$ is a learnable weight matrix of PWC, $\\cup$ is concatenation operation, $X_{low} \\in \\mathbb{R}^{\\frac{(1 - \\alpha)c}{r} \\times h \\times w}$ and $Y_2 \\in \\mathbb{R}^{c \\times h \\times w}$ are the lower input and output feature maps respectively. In a word, the lower transformation stage reuses preceding features $X_{low}$ and utilizes cheap $1 \\times 1$ PWC to obtain features $Y_2$ with supplementary detailed information.", + "bbox": [ + 76, + 152, + 468, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fuse: After the transformation is performed, instead of direct concatenating or adding two types of features, we utilize the simplified SKNet method [18] to adaptively merge the output features $Y_{1}$ and $Y_{2}$ from upper and lower transformation stage as shown in the Fuse part of Figure 3. We first apply a global average pooling (Pooling) to collect global spatial information with channel-wise statistics $S_{m}\\in \\mathbb{R}^{c\\times 1\\times 1}$ , which is calculated as:", + "bbox": [ + 76, + 282, + 470, + 402 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {m} = \\operatorname {P o o l i n g} \\left(Y _ {m}\\right) = \\frac {1}{H \\times W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} Y _ {c} (i, j), m = 1, 2 \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 409, + 470, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, we stack the upper and lower global channelwise descriptor $S_{1}$ , $S_{2}$ together and use channel-wise soft attention operation to generate feature importance vector $\\beta_{1},\\beta_{2}\\in \\mathbb{R}^{c}$ as follows:", + "bbox": [ + 76, + 465, + 468, + 526 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\beta_ {1} = \\frac {e ^ {s _ {1}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \\beta_ {2} = \\frac {e ^ {s _ {2}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \\beta_ {1} + \\beta_ {2} = 1 \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 531, + 468, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, under the guidance of feature importance vector $\\beta_{1},\\beta_{2}$ , the channel-refined features $Y$ can be obtained by merging the upper features $Y_{1}$ and the lower features $Y_{2}$ in a channel-wise manner as follows:", + "bbox": [ + 76, + 566, + 468, + 626 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nY = \\beta_ {1} Y _ {1} + \\beta_ {2} Y _ {2} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 633, + 468, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In brief, we adopt CRU, using Split-Transform-and-Fuse strategy, to further diminish the redundancy of spatial-refined feature maps $X^w$ along the channel dimension. Furthermore, CRU extracts rich representative features through lightweight convolutional operations while proceeds redundant features with cheap operation and feature reuse schemes. Overall, CRU can be used individually or in conjunction with SRU operation. By arranging the SRU and CRU in a sequential manner, the proposed SCConv is established, which is highly efficient and capable of replacing standard convolution operations.", + "bbox": [ + 75, + 657, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2.3. Analysis on Complexities", + "text_level": 1, + "bbox": [ + 76, + 832, + 307, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our SCConv is designed as a plug-and-play module that can be easily embedded into various existing well-designed neural architectures to reduce computation and", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "storage costs. In the SCConv module, all of the parameters are concentrated on the transformation stage. Hence we analyze the reduction of theoretical memory usage. The parameters of standard convolution $Y = M^{k}X$ can be calculated as:", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP _ {s} = k \\times k \\times C _ {1} \\times C _ {2} = k ^ {2} C _ {1} C _ {2} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 178, + 890, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $k$ is kernel size of the convolution, $C_1$ and $C_2$ are the number of input and output feature channels.", + "bbox": [ + 496, + 207, + 890, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The parameters of the proposed SCConv module consist of:", + "bbox": [ + 496, + 238, + 890, + 267 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} P _ {s c} = 1 \\times 1 \\times \\alpha C _ {1} \\times \\frac {\\alpha C _ {1}}{r} + k \\times k \\times \\frac {\\alpha C _ {1}}{g r} \\times \\frac {C _ {2}}{g} \\times g \\\\ + 1 \\times 1 \\times \\frac {\\alpha C _ {1}}{r} \\times C _ {2} + (1 - \\alpha) C _ {1} \\times \\frac {(1 - \\alpha) C _ {1}}{r} \\\\ + 1 \\times 1 \\times \\frac {(1 - \\alpha) C _ {1}}{r} \\times \\left(C _ {2} - \\frac {1 - \\alpha}{r} C _ {1}\\right) \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 277, + 890, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ denotes the split ratio, $r$ refers to the squeeze ratio, $g$ is the group size of GWC operation, $C_1$ and $C_2$ are input and output feature channels respectively. Here, we give a comparison to show the performance of the proposed SCConv. In the experiment, the general parameter set is $\\alpha = \\frac{1}{2}$ , $r = 2$ , $g = 2$ , $k = 3$ , $C_1 = C_2 = C$ , the amount of parameters can be reduced by 5 times where $P_s / P_{sc} \\approx 5$ while the model achieves better performance than standard convolution.", + "bbox": [ + 496, + 388, + 890, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3. Experiments", + "text_level": 1, + "bbox": [ + 500, + 539, + 632, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To evaluate the effectiveness of the proposed SCConv, in this section, we perform a series of experiments on image classification and object detection with only the widely used $3 \\times 3$ kernels being replaced by SCConv module. Image classification benchmarks include CIFAR-10 [15], CIFAR-100 [15] and ImageNet-1K [16]. Object detection benchmarks include PASCAL VOC [6] and MS COCO [21]. Top-1 accuracy is reported as the evaluation metric for image classification and the mean average precision (mAP) is used to measure accuracy of object detection. For fair comparisons, all models in each experiment, including re-implemented baselines and SCConv-equipped models, are trained from scratch on 2 NVIDIA Tesla V100 GPUs with the default data augmentation and training strategy and no other tricks are used. In each experiment, we train several times with the same configuration to prevent the impact of fluctuations and report the median of results.", + "bbox": [ + 496, + 564, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 830, + 705, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. CIFAR dataset, including CIFAR-10 and CIFAR-100, consists of 50k training images and 10k validation images, which are divided into 10 and 100 classes", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6157", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "respectively. ImageNet-1K dataset is a large-scale image classification dataset, containing 1.28 million training images and 50k validation images from 1k classes. PASCAL VOC dataset, which has 20 classes, contains more than 22k images for training and 5k images for validation. MS COCO dataset, which is divided into 80 classes, has more than 118k images for training and 5k images for validation.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training and Inference. 1) For CIFAR-10 and CIFAR-100, we follow a similar training scheme in [10]. Networks are trained for 200 epochs with SGD optimizer with a weight decay of $5 \\times e^{-4}$ and a momentum of 0.9. The learning rate is initialized to 0.05 and is decayed by 0.1 at 100 and 150 of the epochs. It trains with a mini-batch size of 128 on one GPU. Besides, according to different architectures of networks, we set $(h, w)$ to (8, 8) for ResNet, WideResNet, ResNeXt and set it to (4, 4) for DenseNet. 2) For ImageNet-1K dataset, we follow standard practices and perform data augmentation with random cropping to size $224 \\times 224$ pixels. We apply SGD with a momentum of 0.9 and a weight decay of $1 \\times e^{-4}$ . The initial learning rate is set to 0.1 and divided by every 30 epochs for a total of 100 epochs. 3) For PASCAL VOC dataset, we use SGD optimizer and set the batch size to 32. The initial learning rate is set to 0.1 with a 500 iterations warmup. We train 20k iterations totally and reduce the learning rate by a factor of 10 at 10k and 18k iterations. 4) For MS COCO dataset, we use SGD optimizer and set the initial learning rate to 0.1 and batch size to 16. The total iterations are set to 180k and the learning rate is divided by 10 at 120k and 160k iterations.", + "bbox": [ + 75, + 220, + 473, + 554 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 565, + 243, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies to inspect the relative effectiveness of different components in the proposed SCCov module. We choose ResNet50 as the baseline network by replacing standard $3 \\times 3$ convolution to conduct the following ablation experiments on CIFAR100.", + "bbox": [ + 75, + 589, + 470, + 666 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SRU and CRU Our SCConv module includes a spatial reconstruction unit (SRU) and a channel reconstruction unit (CRU). Firstly we only apply SRU or CRU on ResNet50 to examine the efficiency of a single unit. As shown in Table 1, only embedding with SRU $(\\mathrm{ResNet50 + S})$ achieves nearly $1\\%$ improvement without extra increment in FLOPs, while solely embedding with CRU $(\\mathrm{ResNet50 + C})$ can save $38\\%$ parameters and FLOPs with $0.8\\%$ increase of Top-1 accuracy. The results imply that the single-unit-embedded model boosts the accuracy significantly. In addition, we compare three different ways of arranging the SRU and CRU: sequential spatial-channel $(\\mathrm{S + C})$ , sequential channel-spatial $(\\mathrm{C + S})$ , and parallel use of both units $(\\mathrm{C\\& S})$ . We find that the spatial-first order $(\\mathrm{S + C})$ achieves the best accuracy", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b92471f137d83a4b31b5c64623dc3da926162a7bd78ba6fa9d8ea1c80cc2db34.jpg", + "table_caption": [ + "Table 1. Experimental results with different combination methods of SRU and CRU on CIFAR-100 dataset. (S and C is short for SRU and CRU respectively)" + ], + "table_footnote": [], + "table_body": "
DescriptionParamsFLOPsTop-1ACC(%)
ResNet5023.71M1.30G78.60
ResNet50 + S23.53M1.30G79.59
ResNet50 + C14.74M843.81M79.21
ResNet50 + C & S14.74M843.81M79.26
ResNet50 + C + S14.74M843.81M79.54
ResNet50 + S + C14.74M843.81M79.89
", + "bbox": [ + 532, + 141, + 864, + 247 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "than other combination methods. Thus we adopt a sequential spatial-first combination $(\\mathrm{S} + \\mathrm{C})$ strategy to formulate our SCConv and further improve the model performance.", + "bbox": [ + 496, + 272, + 893, + 319 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/57cbc0a28e440e4ff4b64ed487cea302788d96c9d404570cb34c270698daf85a.jpg", + "image_caption": [ + "Figure 4. The trade-off between FLOPs and Accuracy on CIFAR100 with different split ratios $\\alpha$ in SCConv-embedded ResNet50." + ], + "image_footnote": [], + "bbox": [ + 532, + 338, + 861, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis on split ratio $\\alpha$ To explore the effect of different split ratios $\\alpha$ in CRU module, we vary the split ratio from 1/8 to 7/8 gradually to compare the accuracy versus FLOPs on CIFAR-100. As shown in Figure 4, the accuracy of SCConv-embedded ResNet50 rises with the increase of the split ratio $\\alpha$ . The higher $\\alpha$ represents the model can obtain richer feature information in the transformation stage of CRU, thereby improving the model's overall performance. When $\\alpha = 1/2$ , the whole network achieves the best flops-accuracy trade-off. Thus we adopt the optimal split ratio $\\alpha = 1/2$ for SCConv in the following experiments for a better trade-off between performance and efficiency.", + "bbox": [ + 496, + 578, + 893, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualization To explore the feature representation of the proposed SRU method, we visualize the feature maps of the first stage of the original ResNet50 and SRU-embedded ResNet50 in Figure 5. It can be observed that the pattern in features of SRU-embedded ResNet50 is enriched in comparison with original ResNet50. Not only the redundant features is diminished but the representative features are strengthened and diversified. The visualization demon", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6158", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6eabb80b3ede336bbca958789e258d59cd8c9daef161b0e30844cc20a960fbdf.jpg", + "image_caption": [ + "Figure 5. Left: Features from the first-stage of original ResNet50, Right: Features from the first-stage of SRU-embedded ResNet50." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 467, + 227 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "strates the SRU is capable of generating representative and expressive features.", + "bbox": [ + 76, + 292, + 467, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.3. Image Classification on CIFAR", + "text_level": 1, + "bbox": [ + 76, + 330, + 352, + 347 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "After studying the structure of the proposed SCConv module for efficient feature learning, we continue to evaluate the SCConv-embedded architecture on various baseline models and further make a comparison with the SOTA methods over classification accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset. The related SOTA approaches include OctConv [3], GhostNet [8], SPConv [32], SlimConv [23], TiedConv [28]. All experiments are conducted by replacing the original convolutional layers with the corresponding convolution methods.", + "bbox": [ + 75, + 354, + 467, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As can be seen in Table 2, in all cases, our SCConv-embedded models outperform all prior networks for accuracy. For ResNet-56 model, the SCConv-R56 requires only $62.7\\%$ parameters and FLOPs of the counterpart ResNet56 while bringing over a $1\\%$ accuracy increase on both datasets. For ResNet-50 model, the SCConv-R50 achieves better accuracy (nearly $1\\%$ and $1.3\\%$ ) but around $37\\%$ parameters and $34\\%$ FLOPs reduction than the counterpart ResNet50 on CIFAR-10 and CIFAR-100. Besides, the SCConv-R50 requires the same computational costs as SlimConv-R50 while bringing higher (over $1\\%$ ) promotion of accuracy. To show the generality of the proposed method, we apply SCConv and other SOTA methods to ResNeXt-29, WideResNet-28, and DenseNet-121. It can be observed that the SCConv-embedded models still achieve superior performance than other works with comparable model computations. For instance, the SCConv-RX29 achieves over $2.3\\%$ improvement of accuracy while the computation is on par with the GhostNet-RX29. The SCConv-WRN28 achieves better accuracy (nearly $1.3\\%$ ) than the SlimConv-WRN28 while saving parameters and FLOPs by $11.7\\%$ and $15.5\\%$ .", + "bbox": [ + 75, + 521, + 467, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.4. Image Classification on ImageNet", + "text_level": 1, + "bbox": [ + 76, + 847, + 370, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct experiments for ResNet50 on the ImageNet-1K dataset, comparing the performance of our approach", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c2964bfc849c5a418739a27db3be6c3434c88daaede617fc8eb10390ad89c13c.jpg", + "table_caption": [ + "Table 2. Comparison of SOTA methods for common CNN architectures over Top-1 accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset." + ], + "table_footnote": [], + "table_body": "
Network ArchitectureFLOPsParamsCIFAR-10ACC(%)CIFAR-100ACC(%)
ResNet56 (R56)126.84M0.86M93.2771.50
OctConv-R56 (α=1/2)126.84M0.62M93.1170.93
SPConv-R56 (α=1/2)87.95M0.58M93.4971.51
GhostNet-R56 (s=2)68.35M0.45M92.3570.42
SlimConv-R56 (k=1)88.82M0.60M93.5171.71
TiedConv-R56 (b=2)94.99M0.54M92.8771.10
SCConv-R56 (Ours)79.55M0.52M94.1272.56
ResNet50 (R50)1.30G23.52M95.0978.60
OctConv-R50 (α=1/2)727.26M23.52M95.2578.91
GhostNet-R50 (s=2)632.45M14.56M94.3077.54
SlimConv-R50 (k=4/3)853.50M14.83M95.0578.85
SPConv-R50 (α=1/2)972.31M16.14M95.3279.23
SlimConv-R50 (k=1)942.38M16.78M95.3579.26
TiedConv-R50 (b=2)998.78M15.03M95.4479.52
SCConv-R50 (Ours)831.18M14.69M95.9279.89
ResNeXt-29 (RX29)4.55G28.27M95.6881.54
GhostNet-RX29 (s=2)3.60G22.22M95.1480.23
SPConv-RX29 (α=1/2)4.79G31.17M96.0381.76
SlimConv-RX29 (k=4/3)4.38G28.24M95.8581.93
TiedConv-RX29 (b=2)5.96G24.67M95.6681.32
SCConv-RX29 (Ours)3.57G22.31M96.2082.56
WideResNet-28 (WRN28)5.96G36.55M95.2179.40
GhostNet-WRN28 (s=2)3.98G22.12M95.2579.27
SPConv-WRN28 (α=1/2)4.16G24.20M95.3780.25
SlimConv-WRN28 (k=1)4.25G25.00M95.4379.52
TiedConv-WRN28 (b=2)4.54G22.03M95.4878.61
SCConv-WRN28 (Ours)3.75G21.12M95.6480.83
DenseNet-121 (D121)898.23M7.05M95.0979.43
GhostNet-D121 (s=2)517.36M5.04M93.9678.51
SPConv-D121 (α=1/2)641.54M5.69M95.1579.64
SlimConv-D121 (k=1)670.21M5.97M94.6378.90
TiedConv-D121 (b=2)695.68M5.45M95.2379.73
SCConv-D121 (Ours)594.34M5.45M95.3780.24
", + "bbox": [ + 508, + 142, + 887, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with the recent SOTA methods including OctConv [3], SPConv [32], GhostNet [8], SlimConv [23], PfLayer [7], TiedConv [28]etc. Noted that we only replace the bottleneck $3 \\times 3$ convolutions with the corresponding convolution methods. As shown in Table 3, our SCConv-R50- $\\alpha = 1/2$ can achieve $34.4\\%$ computation reductions with $0.26\\%$ accuracy increase over the ResNet50 model. When we further increase the split ratio $\\alpha$ to $3/4$ , our approach gains superior performance to all other state-of-the-art methods in the growth of accuracy.", + "bbox": [ + 496, + 577, + 890, + 729 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For instance, the SCConv-R50_α=3/4 achieves over 0.6% improvement of accuracy while the computation is on a par with the PflLayer-R50_max. In addition, the SCConv-R50_α=1/2 gains better performance than SlimConv-R50_k=4/3 with comparable calculations. To further prove the effectiveness of SCConv, we embed it with the deep model ResNet101. With nearly 62% of computation costs, our SCConv-R101 brings a 0.68% accuracy increase over the baseline model.", + "bbox": [ + 496, + 731, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides, for better comparison, we select several state-of-the-art methods to draw the FLOPs v.s. Top-1 accu", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6159", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/59e46f0eae8336508aeec61811a4915825fc5f06d0c76b2fef1ff5826abef762.jpg", + "table_caption": [ + "Table 3. Image classification results on ImageNet-1K dataset." + ], + "table_footnote": [], + "table_body": "
Network ArchitectureFLOPs(G)Params(M)Top-1 (%)
ResNet50 (R50) (Baseline)4.0925.5676.15
Versatile-R50 (NIPS2018)1.8018.775.50
GhostNet-R50_s=2 (CVPR2020)2.1513.9575.18
SlimConv-R50_k=8/3 (TIP2021)1.8812.1075.32
SPConv-R50_α=1/2 (IJCAI2020)2.9718.3476.26
OctConv-R50_α=1/2 (CVPR2020)2.4025.5676.34
SlimConv-R50_k=4/3 (TIP2021)2.6516.7676.12
PfLayer-R50_max (ICLR2022)2.9018.0076.15
SlimConv-R50_k=1 (TIP2021)3.0018.8176.32
TiedConv-R50_b=2 (AAAI2021)3.1917.0776.04
SCConv-R50_α=1/22.7016.7876.41
SCConv-R50_α=3/42.8717.6976.79
ResNet_101(R101)(Baseline)7.8344.5577.25
SCConv-R1014.9028.0077.93
", + "bbox": [ + 98, + 114, + 452, + 289 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a11e0080101f5347dc97c2ad1b7121f866c8cdf6bafe776d672d4aa2203c58a.jpg", + "image_caption": [ + "Figure 6. Top1-Accuracy v.s. FLOPs for ResNet50 on ImageNet." + ], + "image_footnote": [], + "bbox": [ + 117, + 306, + 428, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "racy curve. From an overall view of Figure 6, the curve of our proposed model is above all other methods including ResNet, GhostNet, SP-ResNet, and SlimConv. It shows that our proposed model gains higher accuracy with lower computation costs. As for the same performance, the model with our SCConv performs more compactly than others.", + "bbox": [ + 75, + 530, + 468, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.5. Object Detection", + "text_level": 1, + "bbox": [ + 76, + 631, + 243, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to further evaluate the generalization ability of SCConv, we conduct experiments on two datasets for object detection tasks. The one-stage RetinaNet [20] is used as a detection framework. We adopt the backbone network of ResNet-50, ResNet-101, and SCConv-embedded model acts as a drop-in replacement for the backbone feature extractor.", + "bbox": [ + 75, + 654, + 468, + 758 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/89991246240b9efa9b5eb73967b0c5b78c23cdb6f9f69c32e268765f2aaa0c20.jpg", + "table_caption": [ + "Table 4. Object detection experiments on the PASCAL VOC 2007 and 2012 dataset." + ], + "table_footnote": [], + "table_body": "
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0977.8955.3152.26
SPConv-R5019.76/49.2378.0555.4752.48
SlimConv-R5018.81/47.1277.9655.3852.42
SCConv-R5016.78/41.3678.6856.2653.16
ResNet101(R101)44.55/121.379.2356.3153.32
SCConv-R10127.90/75.2680.3657.0554.12
", + "bbox": [ + 84, + 811, + 464, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8c21c5667f882da2ef660fa3f5610bc4c1e755c6df9b1eff3d5c3f03a38d1fd4.jpg", + "table_caption": [ + "Table 5. Object detection results on MS COCO val2017." + ], + "table_footnote": [], + "table_body": "
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0954.237.435.2
SPConv-R5019.76/49.2354.537.635.3
SlimConv-R5018.81/47.1254.037.135.0
SCConv-R5016.78/41.3655.138.235.6
", + "bbox": [ + 509, + 114, + 885, + 178 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the PASCAL VOC dataset, as shown in Table 4, the AP@ [.5] of RetinaNet with the SCConv-R50 and SCConv-R101 are $78.68\\%$ and $80.36\\%$ , exceeding original ResNet50 and ResNet101 by $0.8\\%$ and $1.1\\%$ while reducing parameters and FLOPs by $34.1\\%$ and $37\\%$ . For the MS COCO dataset, as shown in Table 5, the AP@ [.5] of RetinaNet with SCConv-R50 is $55.1\\%$ , outperforming original ResNet-50 by $0.9\\%$ with over 22G FLOPs decreased.", + "bbox": [ + 496, + 194, + 890, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition, our approach consistently surpasses current state-of-the-art methods on both datasets. For instance, the mAP@[.5,.95] of SCConv-R50 exceeds the SlimConv-R50 by nearly $0.8\\%$ and $0.6\\%$ on PASCAL VOC and MS COCO datasets. In short, these results prove that the SCConv module not only brings performance improvement but helps the network learn better representative features with a smaller amount of parameters, making it possible for object detection to be deployed on resource-limited devices.", + "bbox": [ + 496, + 315, + 892, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 464, + 617, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented a novel spatial and channel reconstruction module (SCConv), an efficient architectural unit to decrease computational cost and model storage while improving the performance of CNN models by reducing spatial and channel redundancies that widely exist in standard convolution. We diminish the redundancy in feature maps with two distinctive modules, SRU and CRU, which achieve considerable performance improvement while cutting a substantial amount of computation loads. Besides, SCConv is a plug-and-play module and generic to replace the standard convolution without any model architecture adjustment. In addition, the extensive experiments with various SOTA methods on image classification and object detection have indicated the superiority of SCConv-embedded models for striking a much better tradeoff between performance and model efficiency. Finally, we hope the proposed method can inspire research for more efficient architectural design.", + "bbox": [ + 496, + 489, + 892, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was supported in part by the 2030 National Key Research and Development Program of China (2018AAA0100500), National Nature Science Foundation of China (62273150, 62171323), Shanghai Natural Science Foundation (22ZR1421000), Shanghai Outstanding Academic Leaders Plan (21XD1430600), Science and Technology Commission of Shanghai Municipality (22DZ2229004).", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6160", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jierun Chen, Tianlang He, Weipeng Zhuo, Li Ma, Sangtae Ha, and S-H Gary Chan. 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Springer, 2020. 1" + ], + "bbox": [ + 78, + 90, + 468, + 599 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6162", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_model.json b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f6c44002b371eef8e7d2ea93ab18be90fa9c2989 --- /dev/null +++ b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_model.json @@ -0,0 +1,1815 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.129, + 0.13, + 0.842, + 0.176 + ], + "angle": 0, + "content": "SCConv: Spatial and Channel Reconstruction Convolution for Feature Redundancy" + }, + { + "type": "text", + "bbox": [ + 0.347, + 0.203, + 0.654, + 0.221 + ], + "angle": 0, + "content": "Jiafeng Li\\(^{1}\\), Ying Wen\\(^{1*}\\), Lianghua He\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.221, + 0.914, + 0.257 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Communication and Electronic Engineering, East China Normal University, Shanghai, China. \\(^{2}\\)Department of Computer Science and Technology, Tongji University, Shanghai, China." + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.26, + 0.818, + 0.275 + ], + "angle": 0, + "content": "51205904113@stu.ecnu.edu.cn;ywen@cs.ecnu.edu.cn;helianghua@tongji.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.473, + 0.691 + ], + "angle": 0, + "content": "Convolutional Neural Networks (CNNs) have achieved remarkable performance in various computer vision tasks but this comes at the cost of tremendous computational resources, partly due to convolutional layers extracting redundant features. Recent works either compress well-trained large-scale models or explore well-designed lightweight models. In this paper, we make an attempt to exploit spatial and channel redundancy among features for CNN compression and propose an efficient convolution module, called SCConv (Spatial and Channel reconstruction Convolution), to decrease redundant computing and facilitate representative feature learning. The proposed SCConv consists of two units: spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). SRU utilizes a separate-and-reconstruct method to suppress the spatial redundancy while CRU uses a split-transform-and-fuse strategy to diminish the channel redundancy. In addition, SCConv is a plug-and-play architectural unit that can be used to replace standard convolution in various convolutional neural networks directly. Experimental results show that SCConv-embedded models are able to achieve better performance by reducing redundant features with significantly lower complexity and computational costs." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.717, + 0.21, + 0.733 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.47, + 0.879 + ], + "angle": 0, + "content": "In recent years, convolutional neural networks (CNNs) have obtained widespread applications in computer vision tasks [24] due to its ability in obtaining representative features. However, such success relies heavily on intensive resources of computation and storage, which poses severe challenges to their efficient deployment on resource-constrained environments. Therefore, to address these challenges, various types of model compression strategies and network designs have been explored to improve network ef" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.31, + 0.895, + 0.567 + ], + "angle": 0, + "content": "ficiency [1, 2, 26]. The former includes network pruning, weight quantization, low-rank factorization, and knowledge distillation. To be specific, network pruning [17, 22, 30] is a straightforward way to prune the uncritical neuron connections from an existing learned big model to make it thinner. Weight quantization [9] mainly focuses on converting network weights from floating-point types to integer ones to save computation resources. Low-rank factorization [5] applies the matrix decomposition techniques to estimate the informative parameters. Knowledge distillation [11, 34] generates small student networks with the guidance of a well-trained big teacher network. The common part of these compression techniques is that they have been regarded as post-processing steps, thus their performance is usually upper bounded by the given initial model. Meanwhile, the accuracy of these methods drastically drops while achieving a high compression rate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.895, + 0.84 + ], + "angle": 0, + "content": "Network design is another alternative way, which aims at reducing the inherent redundancy in dense model parameters and further developing a lightweight network model. For example, ResNet [10] and DenseNet [14] utilize an efficient shortcut connection to improve the network topology, which connects all preceding feature maps to diminish the redundant parameters. ResNeXt [31] replaces traditional convolutions with sparsely connected group convolutions to reduce inter-channel connectivity. Networks like Xception [4], MobileNet [12] and MobileNeXt [35] disentangle standard convolution into depth-wise convolution and point-wise convolution to further decrease the connection density between channels. MicroNet [19] adopts microfactorized convolution to handle extremely low FLOPs by integrating sparse connectivity into convolution. In addition, EfficientNet [27] learns to automatically search optimal network architectures to lower the redundancy in dense model parameters." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Moreover, in CNN architecture design, bottleneck structure has been well adopted, in which \\(3 \\times 3\\) convolutional layers account for a majority of the model parameters and FLOPs. Therefore various efficient convolutional opera" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.39, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author (e-mail: ywen@cs.ecnu.edu.cn)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6153" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.138, + 0.087, + 0.835, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.223, + 0.895, + 0.253 + ], + "angle": 0, + "content": "Figure 1. The architecture of SCConv integrated with Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU). This figure shows the exact position of our SCConv module within a ResBlock." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.279, + 0.473, + 0.899 + ], + "angle": 0, + "content": "tions, such as group-wise convolution (GWC), depth-wise convolution (DWC) and point-wise convolution (PWC), a variant of the standard convolution, are proposed to replace the existing expensive convolutional operation. GWC, which was first introduced in AlexNet [16], can be regarded as a sparse convolution connection method that each output channel is connected to only a certain group of input channels. DWC [13] proposes to bring more efficiency by keeping each channel separately convolved with filters and without interaction between channels. PWC is used to keep the information flowing across channels and enable dimensionality reduction by reducing the number of filters. These operations are similar in sparse connectivity and have benefits in the number of parameters and FLOPs, which illustrates that redundancy in channel dimension can be reduced reasonably. Hence, a variety of convolution operations are proposed to explore redundancy reduction. For example, MobileNet [12] introduces inverted residual blocks using DWC and PWC to filter the features, which decreases the number of parameters while accelerating the training. ShuffleNet [33] resorts to point-wise group convolution and channel shuffle operation to improve the information flow between different channel groups. HetConv [25] designs heterogeneous convolutional filters where a \\( 3 \\times 3 \\) convolution kernels and a \\( 1 \\times 1 \\) convolution kernels are included in one single filter to extract features. TiedBlockConv [28] shares the same convolutional filter over equal blocks of channels to produce multiple responses within a single filter. SPConv [32] divides the input channels into two groups for different processing but needs a relatively large amount of calculation while extracting internal information. GhostNet [8] considers the redundancy between feature maps and uses cheap operations like DWC to learn redundant features. SilmConv [23] adopts the operation of reducing the channels of features and flipping the weights to reduce feature redundancy. In addition, orthogonal to channel redundancy, OctConv [3] proposes octave convolution to separate convolutional filters into high-frequency and low-frequency components, processing the latter in low resolution to alleviate the spatial redundancy, which reduces calculations while keeping the same number of parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.279, + 0.892, + 0.384 + ], + "angle": 0, + "content": "All these prior studies have proven that there indeed exists considerable redundancy in the deep neural networks, not only in dense model parameters but also in the spatial and channel dimension of feature maps. However, all the above methods either focus on reducing the redundancy in channel dimension or in spatial dimension, making the network still suffer from the problems of feature redundancy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.893, + 0.626 + ], + "angle": 0, + "content": "In this paper, different from prior work, we design a two-step procedure to exploit the redundancy of intermediate feature maps, with the goal of reducing the number of parameters and computation without performance loss. To this end, we propose a novel CNN compression approach to jointly reduce spatial and channel redundancy in the convolutional layers, termed as SCConv (Spatial and Channel reconstruction Convolution), which consists of two units, spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). The proposed SCConv module, which can be embedded into various architectures without additional modifications, is designed to efficiently restrict feature redundancy. This module not only cuts down on the number of model parameters and FLOPs but enhances the capability of feature representation. We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.639, + 0.892, + 0.715 + ], + "angle": 0, + "content": "- We propose a spatial reconstruction unit, termed as SRU, which separates redundant features based on weights and reconstructs them to suppress the redundancy in spatial dimension and strengthen the representation of features." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.725, + 0.892, + 0.786 + ], + "angle": 0, + "content": "- We propose a channel reconstruction unit, termed as CRU, which utilizes a split-transform-and-fuse strategy to diminish the redundancy in channel dimension as well as the computational costs and storage." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.795, + 0.892, + 0.886 + ], + "angle": 0, + "content": "- We design a plug-and-play operation named SCConv combining SRU and CRU in a sequential manner to replace standard convolution for operating on a variety of backbone CNNs. It turns out that SCConv can substantially save the computing load yet enhance the model performance on challenging tasks." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.639, + 0.892, + 0.886 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6154" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.089, + 0.835, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.304, + 0.658, + 0.318 + ], + "angle": 0, + "content": "Figure 2. The architecture of Spatial Reconstruction Unit." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.343, + 0.212, + 0.361 + ], + "angle": 0, + "content": "2. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.471, + 0.566 + ], + "angle": 0, + "content": "In this section, we introduce the proposed SCConv as illustrated in Figure 1, which consists of two units, Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU), placed in a sequential manner. Concretely, for the intermediate input features \\( X \\) in the bottleneck residual block, we first obtain the spatial-refined features \\( X^w \\) through SRU operation and subsequently we utilize CRU operation to gain the channel-refined features \\( Y \\). We exploit both spatial and channel redundancy among features in our SCConv module, which can be seamlessly integrated into any CNN architecture to decrease redundancy among intermediate feature maps and boost the feature representation of CNNs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.58, + 0.336, + 0.596 + ], + "angle": 0, + "content": "2.1. SRU for Spatial Redundancy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.604, + 0.47, + 0.8 + ], + "angle": 0, + "content": "To exploit the spatial redundancy of features, we introduce Spatial Reconstruction Unit (SRU) as shown in Figure 2, which utilizes a Separate-and-Reconstruct operation. Separate operation aims to separate those informative feature maps from less informative ones corresponding to the spatial content. We leverage the scaling factors in Group Normalization (GN) [29] layers to assess the informative content of different feature maps. To be concrete, given an intermediate feature map \\(X \\in \\mathbb{R}^{N \\times C \\times H \\times W}\\), where \\(N\\) is the batch axis, \\(C\\) is the channel axis, \\(H\\) and \\(W\\) are the spatial height and width axes. We first standardize the input feature \\(X\\) by subtracting mean \\(\\mu\\) and dividing by standard deviation \\(\\sigma\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.811, + 0.469, + 0.843 + ], + "angle": 0, + "content": "\\[\nX _ {o u t} = G N (X) = \\gamma \\frac {X - \\mu}{\\sqrt {\\sigma^ {2} + \\varepsilon}} + \\beta \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mu\\) and \\(\\sigma\\) are the mean and standard deviation in \\(X\\), \\(\\varepsilon\\) is a small positive constant added for the sake of division stability, \\(\\gamma\\) and \\(\\beta\\) are trainable affine transformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.451 + ], + "angle": 0, + "content": "Noted that we leverage the trainable parameters \\(\\gamma \\in R^{C}\\) in \\(GN\\) layers as a way to measure the variance of spatial pixels for each batch and channel. The richer spatial information reflects more variation in spatial pixels contributing to a larger \\(\\gamma\\). The normalized correlation weights \\(W_{\\gamma} \\in R^{C}\\) are obtained by equation 2, which indicates the importance of different feature maps." + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.462, + 0.892, + 0.497 + ], + "angle": 0, + "content": "\\[\nW _ {\\gamma} = \\left\\{w _ {i} \\right\\} = \\frac {\\gamma_ {i}}{\\sum_ {j = 1} ^ {C} \\gamma_ {j}}, i, j = 1, 2, \\dots , C \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.616 + ], + "angle": 0, + "content": "Then the weight values of feature maps reweighted by \\( W_{\\gamma} \\) are mapped to the range (0, 1) by the sigmoid function and gated by a threshold. We set those weights above the threshold to 1 to obtain the informative weights \\( W_{1} \\) while setting them to 0 to gain the non-informative weights \\( W_{2} \\) (the threshold is set to 0.5 in the experiments). The whole process of acquiring \\( W \\) can be expressed as equation 3:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.628, + 0.892, + 0.645 + ], + "angle": 0, + "content": "\\[\nW = \\operatorname {G a t e} \\left(\\operatorname {S i g m o i d} \\left(W _ {\\gamma} \\left(G N (X)\\right)\\right)\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Finally, we multiply input features \\( X \\) by \\( W_{1} \\) and \\( W_{2} \\) respectively, yielding two weighted features: the informative ones \\( X_{1}^{w} \\) and less informative ones \\( X_{2}^{w} \\). Thus we successfully separate the input features into two parts: \\( X_{1}^{w} \\) has informative and expressive spatial contents while \\( X_{2}^{w} \\) has little or no information, which is regarded as redundant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In order to reduce the spatial redundancy, we further propose a Reconstruct operation that features with rich information sum up with less informative ones to generate features with richer information and save spatial space. Instead of adding these two parts directly, we adopt a cross reconstruct operation to sufficiently combine the weighted two different informative features and strengthen the information flow between them. Afterwards we concatenate the cross-reconstructed features \\( X^{w1} \\) and \\( X^{w2} \\) to obtain the spatial-refined feature maps \\( X^w \\). The whole process of \\( Re \\)-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6155" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.089, + 0.835, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.307, + 0.289, + 0.663, + 0.304 + ], + "angle": 0, + "content": "Figure 3. The architecture of Channel Reconstruction Unit." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.331, + 0.351, + 0.346 + ], + "angle": 0, + "content": "construct operation can be expressed as :" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.352, + 0.47, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{c} X _ {1} ^ {w} = W _ {1} \\otimes X, \\\\ X _ {2} ^ {w} = W _ {2} \\otimes X, \\\\ X _ {1 1} ^ {w} \\oplus X _ {2 2} ^ {w} = X ^ {w 1}, \\\\ X _ {2 1} ^ {w} \\oplus X _ {1 2} ^ {w} = X ^ {w 2}, \\\\ X ^ {w 1} \\cup X ^ {w 2} = X ^ {w}. \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.575 + ], + "angle": 0, + "content": "where \\(\\otimes\\) is element-wise multiplication, \\(\\oplus\\) is element-wise summation, \\(\\cup\\) is concatenation. After the SRU is applied to the intermediate input features \\(X\\), not only do we separate the informative features from less informative ones, but also we reconstruct them to enhance the representative features and suppress the redundant features in spatial dimension. Nevertheless, the spatial-refined feature maps \\(X^w\\) still remain redundant in channel dimension." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.582, + 0.351, + 0.599 + ], + "angle": 0, + "content": "2.2. CRU for Channel Redundancy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.47, + 0.788 + ], + "angle": 0, + "content": "To exploit the channel redundancy of features, we introduce Channel Reconstruction Unit (CRU) as shown in Figure 3, which utilizes a Split-Transform-and-Fuse strategy. Normally, we use repetitive standard \\(k \\times k\\) convolutions to extract features, resulting in some relatively redundant feature maps along the channel dimension. Let \\(M^k \\in \\mathbb{R}^{c \\times k \\times k}\\) denotes a \\(k \\times k\\) convolution kernel and \\(X, Y \\in \\mathbb{R}^{c \\times h \\times w}\\) denotes the input and convolved output features respectively. A standard convolution can be defined as \\(Y = M^k X\\). To be specific, we replace the standard convolution with CRU, which is implemented via three operators - Split, Transform and Fuse." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.804, + 0.471, + 0.88 + ], + "angle": 0, + "content": "Split: For given spatial-refined features \\( X^w \\in \\mathbb{R}^{c \\times h \\times w} \\), we first split the channels of \\( X^w \\) into two parts with \\( \\alpha C \\) channels and \\( (1 - \\alpha)C \\) channels respectively, as shown in the split part of Figure 3, where \\( 0 \\leq \\alpha \\leq 1 \\) is a split ratio. Subsequently, we further utilize \\( 1 \\times 1 \\) convolutions to" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.331, + 0.892, + 0.437 + ], + "angle": 0, + "content": "squeeze the channels of feature maps for its computing efficiency. Here we introduce a squeeze ratio \\( r \\) to control the feature channels to balance the computational cost of the CRU (\\( r = 2 \\) is a typical setting in the experiments). After the split and squeeze operations, we divide the spatial-refined features \\( X^w \\) into the upper part \\( X_{up} \\) and the lower part \\( X_{low} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.893, + 0.693 + ], + "angle": 0, + "content": "Transform: \\( X_{up} \\) is fed into the upper transformation stage, serving as a \"Rich Feature Extractor\". We adopt efficient convolutional operations (i.e. GWC and PWC) to replace the expensive standard \\( k \\times k \\) convolutions to extract high-level representative information as well as reduce the computational cost. Owing to sparse convolution connections, GWC reduces the amount of parameters and calculations but cuts off the information flow between channel groups. While PWC compensates for the information loss and helps the information flow across feature channels. Thus we perform \\( k \\times k \\) GWC (we set group size \\( g = 2 \\) in the experiments) and \\( 1 \\times 1 \\) PWC operations on the same \\( X_{up} \\). Afterward, we sum up the output to form a merged representative feature maps \\( Y_{1} \\) as shown in the Transform part of Figure 3. The upper transformation stage can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.694, + 0.892, + 0.713 + ], + "angle": 0, + "content": "\\[\nY _ {1} = M ^ {G} X _ {u p} + M ^ {P _ {1}} X _ {u p} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.825 + ], + "angle": 0, + "content": "where \\( M^G \\in \\mathbb{R}^{\\frac{\\alpha c}{gr} \\times k \\times k \\times c} \\), \\( M^{P_1} \\in \\mathbb{R}^{\\frac{\\alpha c}{r} \\times 1 \\times 1 \\times c} \\) is a learnable weight matrix of GWC and PWC, \\( X_{up} \\in \\mathbb{R}^{\\frac{\\alpha c}{r} \\times h \\times w} \\) and \\( Y_1 \\in \\mathbb{R}^{c \\times h \\times w} \\) are the upper input and output feature maps respectively. In short, the upper transformation stage leverages a combination of GWC and PWC on the same feature maps \\( X_{up} \\) to extract rich representative features \\( Y_1 \\) with less computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(X_{low}\\) is fed into the lower transformation stage, where we apply cheap \\(1 \\times 1\\) PWC operations to generate feature maps with shallow hidden details as a supplementary to the Rich Feature Extractor. In addition, we reuse features \\(X_{low}\\) to obtain more feature maps without extra cost. Lastly, we" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.305, + 0.9 + ], + "angle": 0, + "content": "For simplicity, we omit the bias term." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6156" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "concatenate the generated and reused features to form the output of the lower stage \\( Y_{2} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.129, + 0.469, + 0.147 + ], + "angle": 0, + "content": "\\[\nY _ {2} = M ^ {P _ {2}} X _ {l o w} \\cup X _ {l o w} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.154, + 0.47, + 0.266 + ], + "angle": 0, + "content": "where \\( M^{P_2} \\in \\mathbb{R}^{\\frac{(1 - \\alpha)c}{r} \\times 1 \\times (1 - \\frac{1 - \\alpha}{r})c} \\) is a learnable weight matrix of PWC, \\( \\cup \\) is concatenation operation, \\( X_{low} \\in \\mathbb{R}^{\\frac{(1 - \\alpha)c}{r} \\times h \\times w} \\) and \\( Y_2 \\in \\mathbb{R}^{c \\times h \\times w} \\) are the lower input and output feature maps respectively. In a word, the lower transformation stage reuses preceding features \\( X_{low} \\) and utilizes cheap \\( 1 \\times 1 \\) PWC to obtain features \\( Y_2 \\) with supplementary detailed information." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.283, + 0.471, + 0.404 + ], + "angle": 0, + "content": "Fuse: After the transformation is performed, instead of direct concatenating or adding two types of features, we utilize the simplified SKNet method [18] to adaptively merge the output features \\( Y_{1} \\) and \\( Y_{2} \\) from upper and lower transformation stage as shown in the Fuse part of Figure 3. We first apply a global average pooling (Pooling) to collect global spatial information with channel-wise statistics \\( S_{m}\\in \\mathbb{R}^{c\\times 1\\times 1} \\), which is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.41, + 0.472, + 0.466 + ], + "angle": 0, + "content": "\\[\nS _ {m} = \\operatorname {P o o l i n g} \\left(Y _ {m}\\right) = \\frac {1}{H \\times W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} Y _ {c} (i, j), m = 1, 2 \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.466, + 0.469, + 0.527 + ], + "angle": 0, + "content": "Next, we stack the upper and lower global channelwise descriptor \\(S_{1}\\), \\(S_{2}\\) together and use channel-wise soft attention operation to generate feature importance vector \\(\\beta_{1},\\beta_{2}\\in \\mathbb{R}^{c}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.532, + 0.469, + 0.563 + ], + "angle": 0, + "content": "\\[\n\\beta_ {1} = \\frac {e ^ {s _ {1}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \\beta_ {2} = \\frac {e ^ {s _ {2}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \\beta_ {1} + \\beta_ {2} = 1 \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.567, + 0.469, + 0.627 + ], + "angle": 0, + "content": "Finally, under the guidance of feature importance vector \\(\\beta_{1},\\beta_{2}\\), the channel-refined features \\(Y\\) can be obtained by merging the upper features \\(Y_{1}\\) and the lower features \\(Y_{2}\\) in a channel-wise manner as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.635, + 0.469, + 0.652 + ], + "angle": 0, + "content": "\\[\nY = \\beta_ {1} Y _ {1} + \\beta_ {2} Y _ {2} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.825 + ], + "angle": 0, + "content": "In brief, we adopt CRU, using Split-Transform-and-Fuse strategy, to further diminish the redundancy of spatial-refined feature maps \\( X^w \\) along the channel dimension. Furthermore, CRU extracts rich representative features through lightweight convolutional operations while proceeds redundant features with cheap operation and feature reuse schemes. Overall, CRU can be used individually or in conjunction with SRU operation. By arranging the SRU and CRU in a sequential manner, the proposed SCConv is established, which is highly efficient and capable of replacing standard convolution operations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.308, + 0.849 + ], + "angle": 0, + "content": "2.3. Analysis on Complexities" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Our SCConv is designed as a plug-and-play module that can be easily embedded into various existing well-designed neural architectures to reduce computation and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "storage costs. In the SCConv module, all of the parameters are concentrated on the transformation stage. Hence we analyze the reduction of theoretical memory usage. The parameters of standard convolution \\( Y = M^{k}X \\) can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.179, + 0.892, + 0.196 + ], + "angle": 0, + "content": "\\[\nP _ {s} = k \\times k \\times C _ {1} \\times C _ {2} = k ^ {2} C _ {1} C _ {2} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.208, + 0.891, + 0.238 + ], + "angle": 0, + "content": "where \\(k\\) is kernel size of the convolution, \\(C_1\\) and \\(C_2\\) are the number of input and output feature channels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.239, + 0.892, + 0.268 + ], + "angle": 0, + "content": "The parameters of the proposed SCConv module consist of:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.278, + 0.891, + 0.388 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} P _ {s c} = 1 \\times 1 \\times \\alpha C _ {1} \\times \\frac {\\alpha C _ {1}}{r} + k \\times k \\times \\frac {\\alpha C _ {1}}{g r} \\times \\frac {C _ {2}}{g} \\times g \\\\ + 1 \\times 1 \\times \\frac {\\alpha C _ {1}}{r} \\times C _ {2} + (1 - \\alpha) C _ {1} \\times \\frac {(1 - \\alpha) C _ {1}}{r} \\\\ + 1 \\times 1 \\times \\frac {(1 - \\alpha) C _ {1}}{r} \\times \\left(C _ {2} - \\frac {1 - \\alpha}{r} C _ {1}\\right) \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.892, + 0.524 + ], + "angle": 0, + "content": "where \\(\\alpha\\) denotes the split ratio, \\(r\\) refers to the squeeze ratio, \\(g\\) is the group size of GWC operation, \\(C_1\\) and \\(C_2\\) are input and output feature channels respectively. Here, we give a comparison to show the performance of the proposed SCConv. In the experiment, the general parameter set is \\(\\alpha = \\frac{1}{2}\\), \\(r = 2\\), \\(g = 2\\), \\(k = 3\\), \\(C_1 = C_2 = C\\), the amount of parameters can be reduced by 5 times where \\(P_s / P_{sc} \\approx 5\\) while the model achieves better performance than standard convolution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.633, + 0.557 + ], + "angle": 0, + "content": "3. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.822 + ], + "angle": 0, + "content": "To evaluate the effectiveness of the proposed SCConv, in this section, we perform a series of experiments on image classification and object detection with only the widely used \\(3 \\times 3\\) kernels being replaced by SCConv module. Image classification benchmarks include CIFAR-10 [15], CIFAR-100 [15] and ImageNet-1K [16]. Object detection benchmarks include PASCAL VOC [6] and MS COCO [21]. Top-1 accuracy is reported as the evaluation metric for image classification and the mean average precision (mAP) is used to measure accuracy of object detection. For fair comparisons, all models in each experiment, including re-implemented baselines and SCConv-equipped models, are trained from scratch on 2 NVIDIA Tesla V100 GPUs with the default data augmentation and training strategy and no other tricks are used. In each experiment, we train several times with the same configuration to prevent the impact of fluctuations and report the median of results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.707, + 0.848 + ], + "angle": 0, + "content": "3.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset. CIFAR dataset, including CIFAR-10 and CIFAR-100, consists of 50k training images and 10k validation images, which are divided into 10 and 100 classes" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6157" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "respectively. ImageNet-1K dataset is a large-scale image classification dataset, containing 1.28 million training images and 50k validation images from 1k classes. PASCAL VOC dataset, which has 20 classes, contains more than 22k images for training and 5k images for validation. MS COCO dataset, which is divided into 80 classes, has more than 118k images for training and 5k images for validation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.221, + 0.474, + 0.555 + ], + "angle": 0, + "content": "Training and Inference. 1) For CIFAR-10 and CIFAR-100, we follow a similar training scheme in [10]. Networks are trained for 200 epochs with SGD optimizer with a weight decay of \\(5 \\times e^{-4}\\) and a momentum of 0.9. The learning rate is initialized to 0.05 and is decayed by 0.1 at 100 and 150 of the epochs. It trains with a mini-batch size of 128 on one GPU. Besides, according to different architectures of networks, we set \\((h, w)\\) to (8, 8) for ResNet, WideResNet, ResNeXt and set it to (4, 4) for DenseNet. 2) For ImageNet-1K dataset, we follow standard practices and perform data augmentation with random cropping to size \\(224 \\times 224\\) pixels. We apply SGD with a momentum of 0.9 and a weight decay of \\(1 \\times e^{-4}\\). The initial learning rate is set to 0.1 and divided by every 30 epochs for a total of 100 epochs. 3) For PASCAL VOC dataset, we use SGD optimizer and set the batch size to 32. The initial learning rate is set to 0.1 with a 500 iterations warmup. We train 20k iterations totally and reduce the learning rate by a factor of 10 at 10k and 18k iterations. 4) For MS COCO dataset, we use SGD optimizer and set the initial learning rate to 0.1 and batch size to 16. The total iterations are set to 180k and the learning rate is divided by 10 at 120k and 160k iterations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.566, + 0.245, + 0.581 + ], + "angle": 0, + "content": "3.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.471, + 0.667 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies to inspect the relative effectiveness of different components in the proposed SCCov module. We choose ResNet50 as the baseline network by replacing standard \\(3 \\times 3\\) convolution to conduct the following ablation experiments on CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "SRU and CRU Our SCConv module includes a spatial reconstruction unit (SRU) and a channel reconstruction unit (CRU). Firstly we only apply SRU or CRU on ResNet50 to examine the efficiency of a single unit. As shown in Table 1, only embedding with SRU \\((\\mathrm{ResNet50 + S})\\) achieves nearly \\(1\\%\\) improvement without extra increment in FLOPs, while solely embedding with CRU \\((\\mathrm{ResNet50 + C})\\) can save \\(38\\%\\) parameters and FLOPs with \\(0.8\\%\\) increase of Top-1 accuracy. The results imply that the single-unit-embedded model boosts the accuracy significantly. In addition, we compare three different ways of arranging the SRU and CRU: sequential spatial-channel \\((\\mathrm{S + C})\\), sequential channel-spatial \\((\\mathrm{C + S})\\), and parallel use of both units \\((\\mathrm{C\\& S})\\). We find that the spatial-first order \\((\\mathrm{S + C})\\) achieves the best accuracy" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Experimental results with different combination methods of SRU and CRU on CIFAR-100 dataset. (S and C is short for SRU and CRU respectively)" + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.142, + 0.866, + 0.248 + ], + "angle": 0, + "content": "
DescriptionParamsFLOPsTop-1ACC(%)
ResNet5023.71M1.30G78.60
ResNet50 + S23.53M1.30G79.59
ResNet50 + C14.74M843.81M79.21
ResNet50 + C & S14.74M843.81M79.26
ResNet50 + C + S14.74M843.81M79.54
ResNet50 + S + C14.74M843.81M79.89
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.895, + 0.32 + ], + "angle": 0, + "content": "than other combination methods. Thus we adopt a sequential spatial-first combination \\((\\mathrm{S} + \\mathrm{C})\\) strategy to formulate our SCConv and further improve the model performance." + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.339, + 0.862, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.513, + 0.892, + 0.542 + ], + "angle": 0, + "content": "Figure 4. The trade-off between FLOPs and Accuracy on CIFAR100 with different split ratios \\(\\alpha\\) in SCConv-embedded ResNet50." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.895, + 0.761 + ], + "angle": 0, + "content": "Analysis on split ratio \\(\\alpha\\) To explore the effect of different split ratios \\(\\alpha\\) in CRU module, we vary the split ratio from 1/8 to 7/8 gradually to compare the accuracy versus FLOPs on CIFAR-100. As shown in Figure 4, the accuracy of SCConv-embedded ResNet50 rises with the increase of the split ratio \\(\\alpha\\). The higher \\(\\alpha\\) represents the model can obtain richer feature information in the transformation stage of CRU, thereby improving the model's overall performance. When \\(\\alpha = 1/2\\), the whole network achieves the best flops-accuracy trade-off. Thus we adopt the optimal split ratio \\(\\alpha = 1/2\\) for SCConv in the following experiments for a better trade-off between performance and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Visualization To explore the feature representation of the proposed SRU method, we visualize the feature maps of the first stage of the original ResNet50 and SRU-embedded ResNet50 in Figure 5. It can be observed that the pattern in features of SRU-embedded ResNet50 is enriched in comparison with original ResNet50. Not only the redundant features is diminished but the representative features are strengthened and diversified. The visualization demon" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6158" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.088, + 0.468, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.239, + 0.468, + 0.267 + ], + "angle": 0, + "content": "Figure 5. Left: Features from the first-stage of original ResNet50, Right: Features from the first-stage of SRU-embedded ResNet50." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.293, + 0.468, + 0.323 + ], + "angle": 0, + "content": "strates the SRU is capable of generating representative and expressive features." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.332, + 0.353, + 0.348 + ], + "angle": 0, + "content": "3.3. Image Classification on CIFAR" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.468, + 0.506 + ], + "angle": 0, + "content": "After studying the structure of the proposed SCConv module for efficient feature learning, we continue to evaluate the SCConv-embedded architecture on various baseline models and further make a comparison with the SOTA methods over classification accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset. The related SOTA approaches include OctConv [3], GhostNet [8], SPConv [32], SlimConv [23], TiedConv [28]. All experiments are conducted by replacing the original convolutional layers with the corresponding convolution methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.839 + ], + "angle": 0, + "content": "As can be seen in Table 2, in all cases, our SCConv-embedded models outperform all prior networks for accuracy. For ResNet-56 model, the SCConv-R56 requires only \\(62.7\\%\\) parameters and FLOPs of the counterpart ResNet56 while bringing over a \\(1\\%\\) accuracy increase on both datasets. For ResNet-50 model, the SCConv-R50 achieves better accuracy (nearly \\(1\\%\\) and \\(1.3\\%\\)) but around \\(37\\%\\) parameters and \\(34\\%\\) FLOPs reduction than the counterpart ResNet50 on CIFAR-10 and CIFAR-100. Besides, the SCConv-R50 requires the same computational costs as SlimConv-R50 while bringing higher (over \\(1\\%\\)) promotion of accuracy. To show the generality of the proposed method, we apply SCConv and other SOTA methods to ResNeXt-29, WideResNet-28, and DenseNet-121. It can be observed that the SCConv-embedded models still achieve superior performance than other works with comparable model computations. For instance, the SCConv-RX29 achieves over \\(2.3\\%\\) improvement of accuracy while the computation is on par with the GhostNet-RX29. The SCConv-WRN28 achieves better accuracy (nearly \\(1.3\\%\\)) than the SlimConv-WRN28 while saving parameters and FLOPs by \\(11.7\\%\\) and \\(15.5\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.371, + 0.864 + ], + "angle": 0, + "content": "3.4. Image Classification on ImageNet" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We conduct experiments for ResNet50 on the ImageNet-1K dataset, comparing the performance of our approach" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.13 + ], + "angle": 0, + "content": "Table 2. Comparison of SOTA methods for common CNN architectures over Top-1 accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset." + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.143, + 0.888, + 0.548 + ], + "angle": 0, + "content": "
Network ArchitectureFLOPsParamsCIFAR-10ACC(%)CIFAR-100ACC(%)
ResNet56 (R56)126.84M0.86M93.2771.50
OctConv-R56 (α=1/2)126.84M0.62M93.1170.93
SPConv-R56 (α=1/2)87.95M0.58M93.4971.51
GhostNet-R56 (s=2)68.35M0.45M92.3570.42
SlimConv-R56 (k=1)88.82M0.60M93.5171.71
TiedConv-R56 (b=2)94.99M0.54M92.8771.10
SCConv-R56 (Ours)79.55M0.52M94.1272.56
ResNet50 (R50)1.30G23.52M95.0978.60
OctConv-R50 (α=1/2)727.26M23.52M95.2578.91
GhostNet-R50 (s=2)632.45M14.56M94.3077.54
SlimConv-R50 (k=4/3)853.50M14.83M95.0578.85
SPConv-R50 (α=1/2)972.31M16.14M95.3279.23
SlimConv-R50 (k=1)942.38M16.78M95.3579.26
TiedConv-R50 (b=2)998.78M15.03M95.4479.52
SCConv-R50 (Ours)831.18M14.69M95.9279.89
ResNeXt-29 (RX29)4.55G28.27M95.6881.54
GhostNet-RX29 (s=2)3.60G22.22M95.1480.23
SPConv-RX29 (α=1/2)4.79G31.17M96.0381.76
SlimConv-RX29 (k=4/3)4.38G28.24M95.8581.93
TiedConv-RX29 (b=2)5.96G24.67M95.6681.32
SCConv-RX29 (Ours)3.57G22.31M96.2082.56
WideResNet-28 (WRN28)5.96G36.55M95.2179.40
GhostNet-WRN28 (s=2)3.98G22.12M95.2579.27
SPConv-WRN28 (α=1/2)4.16G24.20M95.3780.25
SlimConv-WRN28 (k=1)4.25G25.00M95.4379.52
TiedConv-WRN28 (b=2)4.54G22.03M95.4878.61
SCConv-WRN28 (Ours)3.75G21.12M95.6480.83
DenseNet-121 (D121)898.23M7.05M95.0979.43
GhostNet-D121 (s=2)517.36M5.04M93.9678.51
SPConv-D121 (α=1/2)641.54M5.69M95.1579.64
SlimConv-D121 (k=1)670.21M5.97M94.6378.90
TiedConv-D121 (b=2)695.68M5.45M95.2379.73
SCConv-D121 (Ours)594.34M5.45M95.3780.24
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.73 + ], + "angle": 0, + "content": "with the recent SOTA methods including OctConv [3], SPConv [32], GhostNet [8], SlimConv [23], PfLayer [7], TiedConv [28]etc. Noted that we only replace the bottleneck \\(3 \\times 3\\) convolutions with the corresponding convolution methods. As shown in Table 3, our SCConv-R50-\\(\\alpha = 1/2\\) can achieve \\(34.4\\%\\) computation reductions with \\(0.26\\%\\) accuracy increase over the ResNet50 model. When we further increase the split ratio \\(\\alpha\\) to \\(3/4\\), our approach gains superior performance to all other state-of-the-art methods in the growth of accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.867 + ], + "angle": 0, + "content": "For instance, the SCConv-R50_α=3/4 achieves over 0.6% improvement of accuracy while the computation is on a par with the PflLayer-R50_max. In addition, the SCConv-R50_α=1/2 gains better performance than SlimConv-R50_k=4/3 with comparable calculations. To further prove the effectiveness of SCConv, we embed it with the deep model ResNet101. With nearly 62% of computation costs, our SCConv-R101 brings a 0.68% accuracy increase over the baseline model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Besides, for better comparison, we select several state-of-the-art methods to draw the FLOPs v.s. Top-1 accu" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6159" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.09, + 0.455, + 0.104 + ], + "angle": 0, + "content": "Table 3. Image classification results on ImageNet-1K dataset." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.115, + 0.454, + 0.29 + ], + "angle": 0, + "content": "
Network ArchitectureFLOPs(G)Params(M)Top-1 (%)
ResNet50 (R50) (Baseline)4.0925.5676.15
Versatile-R50 (NIPS2018)1.8018.775.50
GhostNet-R50_s=2 (CVPR2020)2.1513.9575.18
SlimConv-R50_k=8/3 (TIP2021)1.8812.1075.32
SPConv-R50_α=1/2 (IJCAI2020)2.9718.3476.26
OctConv-R50_α=1/2 (CVPR2020)2.4025.5676.34
SlimConv-R50_k=4/3 (TIP2021)2.6516.7676.12
PfLayer-R50_max (ICLR2022)2.9018.0076.15
SlimConv-R50_k=1 (TIP2021)3.0018.8176.32
TiedConv-R50_b=2 (AAAI2021)3.1917.0776.04
SCConv-R50_α=1/22.7016.7876.41
SCConv-R50_α=3/42.8717.6976.79
ResNet_101(R101)(Baseline)7.8344.5577.25
SCConv-R1014.9028.0077.93
" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.307, + 0.429, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.49, + 0.468, + 0.504 + ], + "angle": 0, + "content": "Figure 6. Top1-Accuracy v.s. FLOPs for ResNet50 on ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.47, + 0.622 + ], + "angle": 0, + "content": "racy curve. From an overall view of Figure 6, the curve of our proposed model is above all other methods including ResNet, GhostNet, SP-ResNet, and SlimConv. It shows that our proposed model gains higher accuracy with lower computation costs. As for the same performance, the model with our SCConv performs more compactly than others." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.632, + 0.245, + 0.648 + ], + "angle": 0, + "content": "3.5. Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.76 + ], + "angle": 0, + "content": "In order to further evaluate the generalization ability of SCConv, we conduct experiments on two datasets for object detection tasks. The one-stage RetinaNet [20] is used as a detection framework. We adopt the backbone network of ResNet-50, ResNet-101, and SCConv-embedded model acts as a drop-in replacement for the backbone feature extractor." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.772, + 0.468, + 0.8 + ], + "angle": 0, + "content": "Table 4. Object detection experiments on the PASCAL VOC 2007 and 2012 dataset." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.812, + 0.465, + 0.899 + ], + "angle": 0, + "content": "
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0977.8955.3152.26
SPConv-R5019.76/49.2378.0555.4752.48
SlimConv-R5018.81/47.1277.9655.3852.42
SCConv-R5016.78/41.3678.6856.2653.16
ResNet101(R101)44.55/121.379.2356.3153.32
SCConv-R10127.90/75.2680.3657.0554.12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.528, + 0.09, + 0.864, + 0.103 + ], + "angle": 0, + "content": "Table 5. Object detection results on MS COCO val2017." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.115, + 0.887, + 0.179 + ], + "angle": 0, + "content": "
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0954.237.435.2
SPConv-R5019.76/49.2354.537.635.3
SlimConv-R5018.81/47.1254.037.135.0
SCConv-R5016.78/41.3655.138.235.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.195, + 0.892, + 0.315 + ], + "angle": 0, + "content": "For the PASCAL VOC dataset, as shown in Table 4, the AP@ [.5] of RetinaNet with the SCConv-R50 and SCConv-R101 are \\(78.68\\%\\) and \\(80.36\\%\\), exceeding original ResNet50 and ResNet101 by \\(0.8\\%\\) and \\(1.1\\%\\) while reducing parameters and FLOPs by \\(34.1\\%\\) and \\(37\\%\\). For the MS COCO dataset, as shown in Table 5, the AP@ [.5] of RetinaNet with SCConv-R50 is \\(55.1\\%\\), outperforming original ResNet-50 by \\(0.9\\%\\) with over 22G FLOPs decreased." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.893, + 0.452 + ], + "angle": 0, + "content": "In addition, our approach consistently surpasses current state-of-the-art methods on both datasets. For instance, the mAP@[.5,.95] of SCConv-R50 exceeds the SlimConv-R50 by nearly \\(0.8\\%\\) and \\(0.6\\%\\) on PASCAL VOC and MS COCO datasets. In short, these results prove that the SCConv module not only brings performance improvement but helps the network learn better representative features with a smaller amount of parameters, making it possible for object detection to be deployed on resource-limited devices." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.465, + 0.619, + 0.48 + ], + "angle": 0, + "content": "4. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.763 + ], + "angle": 0, + "content": "In this paper, we have presented a novel spatial and channel reconstruction module (SCConv), an efficient architectural unit to decrease computational cost and model storage while improving the performance of CNN models by reducing spatial and channel redundancies that widely exist in standard convolution. We diminish the redundancy in feature maps with two distinctive modules, SRU and CRU, which achieve considerable performance improvement while cutting a substantial amount of computation loads. Besides, SCConv is a plug-and-play module and generic to replace the standard convolution without any model architecture adjustment. In addition, the extensive experiments with various SOTA methods on image classification and object detection have indicated the superiority of SCConv-embedded models for striking a much better tradeoff between performance and model efficiency. Finally, we hope the proposed method can inspire research for more efficient architectural design." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments This work was supported in part by the 2030 National Key Research and Development Program of China (2018AAA0100500), National Nature Science Foundation of China (62273150, 62171323), Shanghai Natural Science Foundation (22ZR1421000), Shanghai Outstanding Academic Leaders Plan (21XD1430600), Science and Technology Commission of Shanghai Municipality (22DZ2229004)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6160" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Jierun Chen, Tianlang He, Weipeng Zhuo, Li Ma, Sangtae Ha, and S-H Gary Chan. 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Springer, 2020. 1" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.601 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6162" + } + ] +] \ No newline at end of file diff --git a/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_origin.pdf b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..fcdb349447f1bdbe280388d8ad8ac316514f8618 --- /dev/null +++ b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/cde54b77-44c6-4dda-8761-9969150d4bec_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:467891d73b716417f798bed0ecea835c1b33508abe850613459207c482d795a2 +size 1522015 diff --git a/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/full.md b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3251fa91eaf8df097f88b9a226497ca7e45e75d2 --- /dev/null +++ b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/full.md @@ -0,0 +1,271 @@ +# SCConv: Spatial and Channel Reconstruction Convolution for Feature Redundancy + +Jiafeng Li $^{1}$ , Ying Wen $^{1*}$ , Lianghua He $^{2}$ + +$^{1}$ School of Communication and Electronic Engineering, East China Normal University, Shanghai, China. $^{2}$ Department of Computer Science and Technology, Tongji University, Shanghai, China. + +51205904113@stu.ecnu.edu.cn;ywen@cs.ecnu.edu.cn;helianghua@tongji.edu.cn + +# Abstract + +Convolutional Neural Networks (CNNs) have achieved remarkable performance in various computer vision tasks but this comes at the cost of tremendous computational resources, partly due to convolutional layers extracting redundant features. Recent works either compress well-trained large-scale models or explore well-designed lightweight models. In this paper, we make an attempt to exploit spatial and channel redundancy among features for CNN compression and propose an efficient convolution module, called SCConv (Spatial and Channel reconstruction Convolution), to decrease redundant computing and facilitate representative feature learning. The proposed SCConv consists of two units: spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). SRU utilizes a separate-and-reconstruct method to suppress the spatial redundancy while CRU uses a split-transform-and-fuse strategy to diminish the channel redundancy. In addition, SCConv is a plug-and-play architectural unit that can be used to replace standard convolution in various convolutional neural networks directly. Experimental results show that SCConv-embedded models are able to achieve better performance by reducing redundant features with significantly lower complexity and computational costs. + +# 1. Introduction + +In recent years, convolutional neural networks (CNNs) have obtained widespread applications in computer vision tasks [24] due to its ability in obtaining representative features. However, such success relies heavily on intensive resources of computation and storage, which poses severe challenges to their efficient deployment on resource-constrained environments. Therefore, to address these challenges, various types of model compression strategies and network designs have been explored to improve network ef + +ficiency [1, 2, 26]. The former includes network pruning, weight quantization, low-rank factorization, and knowledge distillation. To be specific, network pruning [17, 22, 30] is a straightforward way to prune the uncritical neuron connections from an existing learned big model to make it thinner. Weight quantization [9] mainly focuses on converting network weights from floating-point types to integer ones to save computation resources. Low-rank factorization [5] applies the matrix decomposition techniques to estimate the informative parameters. Knowledge distillation [11, 34] generates small student networks with the guidance of a well-trained big teacher network. The common part of these compression techniques is that they have been regarded as post-processing steps, thus their performance is usually upper bounded by the given initial model. Meanwhile, the accuracy of these methods drastically drops while achieving a high compression rate. + +Network design is another alternative way, which aims at reducing the inherent redundancy in dense model parameters and further developing a lightweight network model. For example, ResNet [10] and DenseNet [14] utilize an efficient shortcut connection to improve the network topology, which connects all preceding feature maps to diminish the redundant parameters. ResNeXt [31] replaces traditional convolutions with sparsely connected group convolutions to reduce inter-channel connectivity. Networks like Xception [4], MobileNet [12] and MobileNeXt [35] disentangle standard convolution into depth-wise convolution and point-wise convolution to further decrease the connection density between channels. MicroNet [19] adopts microfactorized convolution to handle extremely low FLOPs by integrating sparse connectivity into convolution. In addition, EfficientNet [27] learns to automatically search optimal network architectures to lower the redundancy in dense model parameters. + +Moreover, in CNN architecture design, bottleneck structure has been well adopted, in which $3 \times 3$ convolutional layers account for a majority of the model parameters and FLOPs. Therefore various efficient convolutional opera + +![](images/876397cb6e401a1a1963e6f3ed60b2d85aa203d0a0867f9177f4a0930e41b0d6.jpg) +Figure 1. The architecture of SCConv integrated with Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU). This figure shows the exact position of our SCConv module within a ResBlock. + +tions, such as group-wise convolution (GWC), depth-wise convolution (DWC) and point-wise convolution (PWC), a variant of the standard convolution, are proposed to replace the existing expensive convolutional operation. GWC, which was first introduced in AlexNet [16], can be regarded as a sparse convolution connection method that each output channel is connected to only a certain group of input channels. DWC [13] proposes to bring more efficiency by keeping each channel separately convolved with filters and without interaction between channels. PWC is used to keep the information flowing across channels and enable dimensionality reduction by reducing the number of filters. These operations are similar in sparse connectivity and have benefits in the number of parameters and FLOPs, which illustrates that redundancy in channel dimension can be reduced reasonably. Hence, a variety of convolution operations are proposed to explore redundancy reduction. For example, MobileNet [12] introduces inverted residual blocks using DWC and PWC to filter the features, which decreases the number of parameters while accelerating the training. ShuffleNet [33] resorts to point-wise group convolution and channel shuffle operation to improve the information flow between different channel groups. HetConv [25] designs heterogeneous convolutional filters where a $3 \times 3$ convolution kernels and a $1 \times 1$ convolution kernels are included in one single filter to extract features. TiedBlockConv [28] shares the same convolutional filter over equal blocks of channels to produce multiple responses within a single filter. SPConv [32] divides the input channels into two groups for different processing but needs a relatively large amount of calculation while extracting internal information. GhostNet [8] considers the redundancy between feature maps and uses cheap operations like DWC to learn redundant features. SilmConv [23] adopts the operation of reducing the channels of features and flipping the weights to reduce feature redundancy. In addition, orthogonal to channel redundancy, OctConv [3] proposes octave convolution to separate convolutional filters into high-frequency and low-frequency components, processing the latter in low resolution to alleviate the spatial redundancy, which reduces calculations while keeping the same number of parameters. + +All these prior studies have proven that there indeed exists considerable redundancy in the deep neural networks, not only in dense model parameters but also in the spatial and channel dimension of feature maps. However, all the above methods either focus on reducing the redundancy in channel dimension or in spatial dimension, making the network still suffer from the problems of feature redundancy. + +In this paper, different from prior work, we design a two-step procedure to exploit the redundancy of intermediate feature maps, with the goal of reducing the number of parameters and computation without performance loss. To this end, we propose a novel CNN compression approach to jointly reduce spatial and channel redundancy in the convolutional layers, termed as SCConv (Spatial and Channel reconstruction Convolution), which consists of two units, spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). The proposed SCConv module, which can be embedded into various architectures without additional modifications, is designed to efficiently restrict feature redundancy. This module not only cuts down on the number of model parameters and FLOPs but enhances the capability of feature representation. We summarize our contributions as follows: + +- We propose a spatial reconstruction unit, termed as SRU, which separates redundant features based on weights and reconstructs them to suppress the redundancy in spatial dimension and strengthen the representation of features. +- We propose a channel reconstruction unit, termed as CRU, which utilizes a split-transform-and-fuse strategy to diminish the redundancy in channel dimension as well as the computational costs and storage. +- We design a plug-and-play operation named SCConv combining SRU and CRU in a sequential manner to replace standard convolution for operating on a variety of backbone CNNs. It turns out that SCConv can substantially save the computing load yet enhance the model performance on challenging tasks. + +![](images/25c6d98ef6edc95d65e0ca96b6b67f4a04991eda78f228ceb8091009848fd76e.jpg) +Figure 2. The architecture of Spatial Reconstruction Unit. + +# 2. Methodology + +In this section, we introduce the proposed SCConv as illustrated in Figure 1, which consists of two units, Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU), placed in a sequential manner. Concretely, for the intermediate input features $X$ in the bottleneck residual block, we first obtain the spatial-refined features $X^w$ through SRU operation and subsequently we utilize CRU operation to gain the channel-refined features $Y$ . We exploit both spatial and channel redundancy among features in our SCConv module, which can be seamlessly integrated into any CNN architecture to decrease redundancy among intermediate feature maps and boost the feature representation of CNNs. + +# 2.1. SRU for Spatial Redundancy + +To exploit the spatial redundancy of features, we introduce Spatial Reconstruction Unit (SRU) as shown in Figure 2, which utilizes a Separate-and-Reconstruct operation. Separate operation aims to separate those informative feature maps from less informative ones corresponding to the spatial content. We leverage the scaling factors in Group Normalization (GN) [29] layers to assess the informative content of different feature maps. To be concrete, given an intermediate feature map $X \in \mathbb{R}^{N \times C \times H \times W}$ , where $N$ is the batch axis, $C$ is the channel axis, $H$ and $W$ are the spatial height and width axes. We first standardize the input feature $X$ by subtracting mean $\mu$ and dividing by standard deviation $\sigma$ as follows: + +$$ +X _ {o u t} = G N (X) = \gamma \frac {X - \mu}{\sqrt {\sigma^ {2} + \varepsilon}} + \beta \tag {1} +$$ + +where $\mu$ and $\sigma$ are the mean and standard deviation in $X$ , $\varepsilon$ is a small positive constant added for the sake of division stability, $\gamma$ and $\beta$ are trainable affine transformation. + +Noted that we leverage the trainable parameters $\gamma \in R^{C}$ in $GN$ layers as a way to measure the variance of spatial pixels for each batch and channel. The richer spatial information reflects more variation in spatial pixels contributing to a larger $\gamma$ . The normalized correlation weights $W_{\gamma} \in R^{C}$ are obtained by equation 2, which indicates the importance of different feature maps. + +$$ +W _ {\gamma} = \left\{w _ {i} \right\} = \frac {\gamma_ {i}}{\sum_ {j = 1} ^ {C} \gamma_ {j}}, i, j = 1, 2, \dots , C \tag {2} +$$ + +Then the weight values of feature maps reweighted by $W_{\gamma}$ are mapped to the range (0, 1) by the sigmoid function and gated by a threshold. We set those weights above the threshold to 1 to obtain the informative weights $W_{1}$ while setting them to 0 to gain the non-informative weights $W_{2}$ (the threshold is set to 0.5 in the experiments). The whole process of acquiring $W$ can be expressed as equation 3: + +$$ +W = \operatorname {G a t e} \left(\operatorname {S i g m o i d} \left(W _ {\gamma} \left(G N (X)\right)\right)\right) \tag {3} +$$ + +Finally, we multiply input features $X$ by $W_{1}$ and $W_{2}$ respectively, yielding two weighted features: the informative ones $X_{1}^{w}$ and less informative ones $X_{2}^{w}$ . Thus we successfully separate the input features into two parts: $X_{1}^{w}$ has informative and expressive spatial contents while $X_{2}^{w}$ has little or no information, which is regarded as redundant. + +In order to reduce the spatial redundancy, we further propose a Reconstruct operation that features with rich information sum up with less informative ones to generate features with richer information and save spatial space. Instead of adding these two parts directly, we adopt a cross reconstruct operation to sufficiently combine the weighted two different informative features and strengthen the information flow between them. Afterwards we concatenate the cross-reconstructed features $X^{w1}$ and $X^{w2}$ to obtain the spatial-refined feature maps $X^w$ . The whole process of $Re$ - + +![](images/118d6c0d9c525f5c625cc78517dd9d2ee958421d3871790678b1795d8b6665d4.jpg) +Figure 3. The architecture of Channel Reconstruction Unit. + +construct operation can be expressed as : + +$$ +\left\{ \begin{array}{c} X _ {1} ^ {w} = W _ {1} \otimes X, \\ X _ {2} ^ {w} = W _ {2} \otimes X, \\ X _ {1 1} ^ {w} \oplus X _ {2 2} ^ {w} = X ^ {w 1}, \\ X _ {2 1} ^ {w} \oplus X _ {1 2} ^ {w} = X ^ {w 2}, \\ X ^ {w 1} \cup X ^ {w 2} = X ^ {w}. \end{array} \right. \tag {4} +$$ + +where $\otimes$ is element-wise multiplication, $\oplus$ is element-wise summation, $\cup$ is concatenation. After the SRU is applied to the intermediate input features $X$ , not only do we separate the informative features from less informative ones, but also we reconstruct them to enhance the representative features and suppress the redundant features in spatial dimension. Nevertheless, the spatial-refined feature maps $X^w$ still remain redundant in channel dimension. + +# 2.2. CRU for Channel Redundancy + +To exploit the channel redundancy of features, we introduce Channel Reconstruction Unit (CRU) as shown in Figure 3, which utilizes a Split-Transform-and-Fuse strategy. Normally, we use repetitive standard $k \times k$ convolutions to extract features, resulting in some relatively redundant feature maps along the channel dimension. Let $M^k \in \mathbb{R}^{c \times k \times k}$ denotes a $k \times k$ convolution kernel and $X, Y \in \mathbb{R}^{c \times h \times w}$ denotes the input and convolved output features respectively. A standard convolution can be defined as $Y = M^k X$ . To be specific, we replace the standard convolution with CRU, which is implemented via three operators - Split, Transform and Fuse. + +Split: For given spatial-refined features $X^w \in \mathbb{R}^{c \times h \times w}$ , we first split the channels of $X^w$ into two parts with $\alpha C$ channels and $(1 - \alpha)C$ channels respectively, as shown in the split part of Figure 3, where $0 \leq \alpha \leq 1$ is a split ratio. Subsequently, we further utilize $1 \times 1$ convolutions to + +squeeze the channels of feature maps for its computing efficiency. Here we introduce a squeeze ratio $r$ to control the feature channels to balance the computational cost of the CRU ( $r = 2$ is a typical setting in the experiments). After the split and squeeze operations, we divide the spatial-refined features $X^w$ into the upper part $X_{up}$ and the lower part $X_{low}$ . + +Transform: $X_{up}$ is fed into the upper transformation stage, serving as a "Rich Feature Extractor". We adopt efficient convolutional operations (i.e. GWC and PWC) to replace the expensive standard $k \times k$ convolutions to extract high-level representative information as well as reduce the computational cost. Owing to sparse convolution connections, GWC reduces the amount of parameters and calculations but cuts off the information flow between channel groups. While PWC compensates for the information loss and helps the information flow across feature channels. Thus we perform $k \times k$ GWC (we set group size $g = 2$ in the experiments) and $1 \times 1$ PWC operations on the same $X_{up}$ . Afterward, we sum up the output to form a merged representative feature maps $Y_{1}$ as shown in the Transform part of Figure 3. The upper transformation stage can be formulated as: + +$$ +Y _ {1} = M ^ {G} X _ {u p} + M ^ {P _ {1}} X _ {u p} \tag {5} +$$ + +where $M^G \in \mathbb{R}^{\frac{\alpha c}{gr} \times k \times k \times c}$ , $M^{P_1} \in \mathbb{R}^{\frac{\alpha c}{r} \times 1 \times 1 \times c}$ is a learnable weight matrix of GWC and PWC, $X_{up} \in \mathbb{R}^{\frac{\alpha c}{r} \times h \times w}$ and $Y_1 \in \mathbb{R}^{c \times h \times w}$ are the upper input and output feature maps respectively. In short, the upper transformation stage leverages a combination of GWC and PWC on the same feature maps $X_{up}$ to extract rich representative features $Y_1$ with less computational cost. + +$X_{low}$ is fed into the lower transformation stage, where we apply cheap $1 \times 1$ PWC operations to generate feature maps with shallow hidden details as a supplementary to the Rich Feature Extractor. In addition, we reuse features $X_{low}$ to obtain more feature maps without extra cost. Lastly, we + +concatenate the generated and reused features to form the output of the lower stage $Y_{2}$ as follows: + +$$ +Y _ {2} = M ^ {P _ {2}} X _ {l o w} \cup X _ {l o w} \tag {6} +$$ + +where $M^{P_2} \in \mathbb{R}^{\frac{(1 - \alpha)c}{r} \times 1 \times (1 - \frac{1 - \alpha}{r})c}$ is a learnable weight matrix of PWC, $\cup$ is concatenation operation, $X_{low} \in \mathbb{R}^{\frac{(1 - \alpha)c}{r} \times h \times w}$ and $Y_2 \in \mathbb{R}^{c \times h \times w}$ are the lower input and output feature maps respectively. In a word, the lower transformation stage reuses preceding features $X_{low}$ and utilizes cheap $1 \times 1$ PWC to obtain features $Y_2$ with supplementary detailed information. + +Fuse: After the transformation is performed, instead of direct concatenating or adding two types of features, we utilize the simplified SKNet method [18] to adaptively merge the output features $Y_{1}$ and $Y_{2}$ from upper and lower transformation stage as shown in the Fuse part of Figure 3. We first apply a global average pooling (Pooling) to collect global spatial information with channel-wise statistics $S_{m}\in \mathbb{R}^{c\times 1\times 1}$ , which is calculated as: + +$$ +S _ {m} = \operatorname {P o o l i n g} \left(Y _ {m}\right) = \frac {1}{H \times W} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} Y _ {c} (i, j), m = 1, 2 \tag {7} +$$ + +Next, we stack the upper and lower global channelwise descriptor $S_{1}$ , $S_{2}$ together and use channel-wise soft attention operation to generate feature importance vector $\beta_{1},\beta_{2}\in \mathbb{R}^{c}$ as follows: + +$$ +\beta_ {1} = \frac {e ^ {s _ {1}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \beta_ {2} = \frac {e ^ {s _ {2}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \beta_ {1} + \beta_ {2} = 1 \tag {8} +$$ + +Finally, under the guidance of feature importance vector $\beta_{1},\beta_{2}$ , the channel-refined features $Y$ can be obtained by merging the upper features $Y_{1}$ and the lower features $Y_{2}$ in a channel-wise manner as follows: + +$$ +Y = \beta_ {1} Y _ {1} + \beta_ {2} Y _ {2} \tag {9} +$$ + +In brief, we adopt CRU, using Split-Transform-and-Fuse strategy, to further diminish the redundancy of spatial-refined feature maps $X^w$ along the channel dimension. Furthermore, CRU extracts rich representative features through lightweight convolutional operations while proceeds redundant features with cheap operation and feature reuse schemes. Overall, CRU can be used individually or in conjunction with SRU operation. By arranging the SRU and CRU in a sequential manner, the proposed SCConv is established, which is highly efficient and capable of replacing standard convolution operations. + +# 2.3. Analysis on Complexities + +Our SCConv is designed as a plug-and-play module that can be easily embedded into various existing well-designed neural architectures to reduce computation and + +storage costs. In the SCConv module, all of the parameters are concentrated on the transformation stage. Hence we analyze the reduction of theoretical memory usage. The parameters of standard convolution $Y = M^{k}X$ can be calculated as: + +$$ +P _ {s} = k \times k \times C _ {1} \times C _ {2} = k ^ {2} C _ {1} C _ {2} \tag {10} +$$ + +where $k$ is kernel size of the convolution, $C_1$ and $C_2$ are the number of input and output feature channels. + +The parameters of the proposed SCConv module consist of: + +$$ +\begin{array}{l} P _ {s c} = 1 \times 1 \times \alpha C _ {1} \times \frac {\alpha C _ {1}}{r} + k \times k \times \frac {\alpha C _ {1}}{g r} \times \frac {C _ {2}}{g} \times g \\ + 1 \times 1 \times \frac {\alpha C _ {1}}{r} \times C _ {2} + (1 - \alpha) C _ {1} \times \frac {(1 - \alpha) C _ {1}}{r} \\ + 1 \times 1 \times \frac {(1 - \alpha) C _ {1}}{r} \times \left(C _ {2} - \frac {1 - \alpha}{r} C _ {1}\right) \tag {11} \\ \end{array} +$$ + +where $\alpha$ denotes the split ratio, $r$ refers to the squeeze ratio, $g$ is the group size of GWC operation, $C_1$ and $C_2$ are input and output feature channels respectively. Here, we give a comparison to show the performance of the proposed SCConv. In the experiment, the general parameter set is $\alpha = \frac{1}{2}$ , $r = 2$ , $g = 2$ , $k = 3$ , $C_1 = C_2 = C$ , the amount of parameters can be reduced by 5 times where $P_s / P_{sc} \approx 5$ while the model achieves better performance than standard convolution. + +# 3. Experiments + +To evaluate the effectiveness of the proposed SCConv, in this section, we perform a series of experiments on image classification and object detection with only the widely used $3 \times 3$ kernels being replaced by SCConv module. Image classification benchmarks include CIFAR-10 [15], CIFAR-100 [15] and ImageNet-1K [16]. Object detection benchmarks include PASCAL VOC [6] and MS COCO [21]. Top-1 accuracy is reported as the evaluation metric for image classification and the mean average precision (mAP) is used to measure accuracy of object detection. For fair comparisons, all models in each experiment, including re-implemented baselines and SCConv-equipped models, are trained from scratch on 2 NVIDIA Tesla V100 GPUs with the default data augmentation and training strategy and no other tricks are used. In each experiment, we train several times with the same configuration to prevent the impact of fluctuations and report the median of results. + +# 3.1. Experimental Settings + +Dataset. CIFAR dataset, including CIFAR-10 and CIFAR-100, consists of 50k training images and 10k validation images, which are divided into 10 and 100 classes + +respectively. ImageNet-1K dataset is a large-scale image classification dataset, containing 1.28 million training images and 50k validation images from 1k classes. PASCAL VOC dataset, which has 20 classes, contains more than 22k images for training and 5k images for validation. MS COCO dataset, which is divided into 80 classes, has more than 118k images for training and 5k images for validation. + +Training and Inference. 1) For CIFAR-10 and CIFAR-100, we follow a similar training scheme in [10]. Networks are trained for 200 epochs with SGD optimizer with a weight decay of $5 \times e^{-4}$ and a momentum of 0.9. The learning rate is initialized to 0.05 and is decayed by 0.1 at 100 and 150 of the epochs. It trains with a mini-batch size of 128 on one GPU. Besides, according to different architectures of networks, we set $(h, w)$ to (8, 8) for ResNet, WideResNet, ResNeXt and set it to (4, 4) for DenseNet. 2) For ImageNet-1K dataset, we follow standard practices and perform data augmentation with random cropping to size $224 \times 224$ pixels. We apply SGD with a momentum of 0.9 and a weight decay of $1 \times e^{-4}$ . The initial learning rate is set to 0.1 and divided by every 30 epochs for a total of 100 epochs. 3) For PASCAL VOC dataset, we use SGD optimizer and set the batch size to 32. The initial learning rate is set to 0.1 with a 500 iterations warmup. We train 20k iterations totally and reduce the learning rate by a factor of 10 at 10k and 18k iterations. 4) For MS COCO dataset, we use SGD optimizer and set the initial learning rate to 0.1 and batch size to 16. The total iterations are set to 180k and the learning rate is divided by 10 at 120k and 160k iterations. + +# 3.2. Ablation Studies + +In this section, we conduct ablation studies to inspect the relative effectiveness of different components in the proposed SCCov module. We choose ResNet50 as the baseline network by replacing standard $3 \times 3$ convolution to conduct the following ablation experiments on CIFAR100. + +SRU and CRU Our SCConv module includes a spatial reconstruction unit (SRU) and a channel reconstruction unit (CRU). Firstly we only apply SRU or CRU on ResNet50 to examine the efficiency of a single unit. As shown in Table 1, only embedding with SRU $(\mathrm{ResNet50 + S})$ achieves nearly $1\%$ improvement without extra increment in FLOPs, while solely embedding with CRU $(\mathrm{ResNet50 + C})$ can save $38\%$ parameters and FLOPs with $0.8\%$ increase of Top-1 accuracy. The results imply that the single-unit-embedded model boosts the accuracy significantly. In addition, we compare three different ways of arranging the SRU and CRU: sequential spatial-channel $(\mathrm{S + C})$ , sequential channel-spatial $(\mathrm{C + S})$ , and parallel use of both units $(\mathrm{C\& S})$ . We find that the spatial-first order $(\mathrm{S + C})$ achieves the best accuracy + +Table 1. Experimental results with different combination methods of SRU and CRU on CIFAR-100 dataset. (S and C is short for SRU and CRU respectively) + +
DescriptionParamsFLOPsTop-1ACC(%)
ResNet5023.71M1.30G78.60
ResNet50 + S23.53M1.30G79.59
ResNet50 + C14.74M843.81M79.21
ResNet50 + C & S14.74M843.81M79.26
ResNet50 + C + S14.74M843.81M79.54
ResNet50 + S + C14.74M843.81M79.89
+ +than other combination methods. Thus we adopt a sequential spatial-first combination $(\mathrm{S} + \mathrm{C})$ strategy to formulate our SCConv and further improve the model performance. + +![](images/57cbc0a28e440e4ff4b64ed487cea302788d96c9d404570cb34c270698daf85a.jpg) +Figure 4. The trade-off between FLOPs and Accuracy on CIFAR100 with different split ratios $\alpha$ in SCConv-embedded ResNet50. + +Analysis on split ratio $\alpha$ To explore the effect of different split ratios $\alpha$ in CRU module, we vary the split ratio from 1/8 to 7/8 gradually to compare the accuracy versus FLOPs on CIFAR-100. As shown in Figure 4, the accuracy of SCConv-embedded ResNet50 rises with the increase of the split ratio $\alpha$ . The higher $\alpha$ represents the model can obtain richer feature information in the transformation stage of CRU, thereby improving the model's overall performance. When $\alpha = 1/2$ , the whole network achieves the best flops-accuracy trade-off. Thus we adopt the optimal split ratio $\alpha = 1/2$ for SCConv in the following experiments for a better trade-off between performance and efficiency. + +Visualization To explore the feature representation of the proposed SRU method, we visualize the feature maps of the first stage of the original ResNet50 and SRU-embedded ResNet50 in Figure 5. It can be observed that the pattern in features of SRU-embedded ResNet50 is enriched in comparison with original ResNet50. Not only the redundant features is diminished but the representative features are strengthened and diversified. The visualization demon + +![](images/6eabb80b3ede336bbca958789e258d59cd8c9daef161b0e30844cc20a960fbdf.jpg) +Figure 5. Left: Features from the first-stage of original ResNet50, Right: Features from the first-stage of SRU-embedded ResNet50. + +strates the SRU is capable of generating representative and expressive features. + +# 3.3. Image Classification on CIFAR + +After studying the structure of the proposed SCConv module for efficient feature learning, we continue to evaluate the SCConv-embedded architecture on various baseline models and further make a comparison with the SOTA methods over classification accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset. The related SOTA approaches include OctConv [3], GhostNet [8], SPConv [32], SlimConv [23], TiedConv [28]. All experiments are conducted by replacing the original convolutional layers with the corresponding convolution methods. + +As can be seen in Table 2, in all cases, our SCConv-embedded models outperform all prior networks for accuracy. For ResNet-56 model, the SCConv-R56 requires only $62.7\%$ parameters and FLOPs of the counterpart ResNet56 while bringing over a $1\%$ accuracy increase on both datasets. For ResNet-50 model, the SCConv-R50 achieves better accuracy (nearly $1\%$ and $1.3\%$ ) but around $37\%$ parameters and $34\%$ FLOPs reduction than the counterpart ResNet50 on CIFAR-10 and CIFAR-100. Besides, the SCConv-R50 requires the same computational costs as SlimConv-R50 while bringing higher (over $1\%$ ) promotion of accuracy. To show the generality of the proposed method, we apply SCConv and other SOTA methods to ResNeXt-29, WideResNet-28, and DenseNet-121. It can be observed that the SCConv-embedded models still achieve superior performance than other works with comparable model computations. For instance, the SCConv-RX29 achieves over $2.3\%$ improvement of accuracy while the computation is on par with the GhostNet-RX29. The SCConv-WRN28 achieves better accuracy (nearly $1.3\%$ ) than the SlimConv-WRN28 while saving parameters and FLOPs by $11.7\%$ and $15.5\%$ . + +# 3.4. Image Classification on ImageNet + +We conduct experiments for ResNet50 on the ImageNet-1K dataset, comparing the performance of our approach + +Table 2. Comparison of SOTA methods for common CNN architectures over Top-1 accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset. + +
Network ArchitectureFLOPsParamsCIFAR-10ACC(%)CIFAR-100ACC(%)
ResNet56 (R56)126.84M0.86M93.2771.50
OctConv-R56 (α=1/2)126.84M0.62M93.1170.93
SPConv-R56 (α=1/2)87.95M0.58M93.4971.51
GhostNet-R56 (s=2)68.35M0.45M92.3570.42
SlimConv-R56 (k=1)88.82M0.60M93.5171.71
TiedConv-R56 (b=2)94.99M0.54M92.8771.10
SCConv-R56 (Ours)79.55M0.52M94.1272.56
ResNet50 (R50)1.30G23.52M95.0978.60
OctConv-R50 (α=1/2)727.26M23.52M95.2578.91
GhostNet-R50 (s=2)632.45M14.56M94.3077.54
SlimConv-R50 (k=4/3)853.50M14.83M95.0578.85
SPConv-R50 (α=1/2)972.31M16.14M95.3279.23
SlimConv-R50 (k=1)942.38M16.78M95.3579.26
TiedConv-R50 (b=2)998.78M15.03M95.4479.52
SCConv-R50 (Ours)831.18M14.69M95.9279.89
ResNeXt-29 (RX29)4.55G28.27M95.6881.54
GhostNet-RX29 (s=2)3.60G22.22M95.1480.23
SPConv-RX29 (α=1/2)4.79G31.17M96.0381.76
SlimConv-RX29 (k=4/3)4.38G28.24M95.8581.93
TiedConv-RX29 (b=2)5.96G24.67M95.6681.32
SCConv-RX29 (Ours)3.57G22.31M96.2082.56
WideResNet-28 (WRN28)5.96G36.55M95.2179.40
GhostNet-WRN28 (s=2)3.98G22.12M95.2579.27
SPConv-WRN28 (α=1/2)4.16G24.20M95.3780.25
SlimConv-WRN28 (k=1)4.25G25.00M95.4379.52
TiedConv-WRN28 (b=2)4.54G22.03M95.4878.61
SCConv-WRN28 (Ours)3.75G21.12M95.6480.83
DenseNet-121 (D121)898.23M7.05M95.0979.43
GhostNet-D121 (s=2)517.36M5.04M93.9678.51
SPConv-D121 (α=1/2)641.54M5.69M95.1579.64
SlimConv-D121 (k=1)670.21M5.97M94.6378.90
TiedConv-D121 (b=2)695.68M5.45M95.2379.73
SCConv-D121 (Ours)594.34M5.45M95.3780.24
+ +with the recent SOTA methods including OctConv [3], SPConv [32], GhostNet [8], SlimConv [23], PfLayer [7], TiedConv [28]etc. Noted that we only replace the bottleneck $3 \times 3$ convolutions with the corresponding convolution methods. As shown in Table 3, our SCConv-R50- $\alpha = 1/2$ can achieve $34.4\%$ computation reductions with $0.26\%$ accuracy increase over the ResNet50 model. When we further increase the split ratio $\alpha$ to $3/4$ , our approach gains superior performance to all other state-of-the-art methods in the growth of accuracy. + +For instance, the SCConv-R50_α=3/4 achieves over 0.6% improvement of accuracy while the computation is on a par with the PflLayer-R50_max. In addition, the SCConv-R50_α=1/2 gains better performance than SlimConv-R50_k=4/3 with comparable calculations. To further prove the effectiveness of SCConv, we embed it with the deep model ResNet101. With nearly 62% of computation costs, our SCConv-R101 brings a 0.68% accuracy increase over the baseline model. + +Besides, for better comparison, we select several state-of-the-art methods to draw the FLOPs v.s. Top-1 accu + +Table 3. Image classification results on ImageNet-1K dataset. + +
Network ArchitectureFLOPs(G)Params(M)Top-1 (%)
ResNet50 (R50) (Baseline)4.0925.5676.15
Versatile-R50 (NIPS2018)1.8018.775.50
GhostNet-R50_s=2 (CVPR2020)2.1513.9575.18
SlimConv-R50_k=8/3 (TIP2021)1.8812.1075.32
SPConv-R50_α=1/2 (IJCAI2020)2.9718.3476.26
OctConv-R50_α=1/2 (CVPR2020)2.4025.5676.34
SlimConv-R50_k=4/3 (TIP2021)2.6516.7676.12
PfLayer-R50_max (ICLR2022)2.9018.0076.15
SlimConv-R50_k=1 (TIP2021)3.0018.8176.32
TiedConv-R50_b=2 (AAAI2021)3.1917.0776.04
SCConv-R50_α=1/22.7016.7876.41
SCConv-R50_α=3/42.8717.6976.79
ResNet_101(R101)(Baseline)7.8344.5577.25
SCConv-R1014.9028.0077.93
+ +![](images/7a11e0080101f5347dc97c2ad1b7121f866c8cdf6bafe776d672d4aa2203c58a.jpg) +Figure 6. Top1-Accuracy v.s. FLOPs for ResNet50 on ImageNet. + +racy curve. From an overall view of Figure 6, the curve of our proposed model is above all other methods including ResNet, GhostNet, SP-ResNet, and SlimConv. It shows that our proposed model gains higher accuracy with lower computation costs. As for the same performance, the model with our SCConv performs more compactly than others. + +# 3.5. Object Detection + +In order to further evaluate the generalization ability of SCConv, we conduct experiments on two datasets for object detection tasks. The one-stage RetinaNet [20] is used as a detection framework. We adopt the backbone network of ResNet-50, ResNet-101, and SCConv-embedded model acts as a drop-in replacement for the backbone feature extractor. + +Table 4. Object detection experiments on the PASCAL VOC 2007 and 2012 dataset. + +
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0977.8955.3152.26
SPConv-R5019.76/49.2378.0555.4752.48
SlimConv-R5018.81/47.1277.9655.3852.42
SCConv-R5016.78/41.3678.6856.2653.16
ResNet101(R101)44.55/121.379.2356.3153.32
SCConv-R10127.90/75.2680.3657.0554.12
+ +Table 5. Object detection results on MS COCO val2017. + +
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0954.237.435.2
SPConv-R5019.76/49.2354.537.635.3
SlimConv-R5018.81/47.1254.037.135.0
SCConv-R5016.78/41.3655.138.235.6
+ +For the PASCAL VOC dataset, as shown in Table 4, the AP@ [.5] of RetinaNet with the SCConv-R50 and SCConv-R101 are $78.68\%$ and $80.36\%$ , exceeding original ResNet50 and ResNet101 by $0.8\%$ and $1.1\%$ while reducing parameters and FLOPs by $34.1\%$ and $37\%$ . For the MS COCO dataset, as shown in Table 5, the AP@ [.5] of RetinaNet with SCConv-R50 is $55.1\%$ , outperforming original ResNet-50 by $0.9\%$ with over 22G FLOPs decreased. + +In addition, our approach consistently surpasses current state-of-the-art methods on both datasets. For instance, the mAP@[.5,.95] of SCConv-R50 exceeds the SlimConv-R50 by nearly $0.8\%$ and $0.6\%$ on PASCAL VOC and MS COCO datasets. In short, these results prove that the SCConv module not only brings performance improvement but helps the network learn better representative features with a smaller amount of parameters, making it possible for object detection to be deployed on resource-limited devices. + +# 4. Conclusion + +In this paper, we have presented a novel spatial and channel reconstruction module (SCConv), an efficient architectural unit to decrease computational cost and model storage while improving the performance of CNN models by reducing spatial and channel redundancies that widely exist in standard convolution. We diminish the redundancy in feature maps with two distinctive modules, SRU and CRU, which achieve considerable performance improvement while cutting a substantial amount of computation loads. Besides, SCConv is a plug-and-play module and generic to replace the standard convolution without any model architecture adjustment. In addition, the extensive experiments with various SOTA methods on image classification and object detection have indicated the superiority of SCConv-embedded models for striking a much better tradeoff between performance and model efficiency. Finally, we hope the proposed method can inspire research for more efficient architectural design. + +Acknowledgments This work was supported in part by the 2030 National Key Research and Development Program of China (2018AAA0100500), National Nature Science Foundation of China (62273150, 62171323), Shanghai Natural Science Foundation (22ZR1421000), Shanghai Outstanding Academic Leaders Plan (21XD1430600), Science and Technology Commission of Shanghai Municipality (22DZ2229004). + +# References + +[1] Jierun Chen, Tianlang He, Weipeng Zhuo, Li Ma, Sangtae Ha, and S-H Gary Chan. Tvconv: Efficient translation variant convolution for layout-aware visual processing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12548-12558, 2022. 1 +[2] Yinpeng Chen, Xiyang Dai, Dongdong Chen, Mengchen Liu, Xiaoyi Dong, Lu Yuan, and Zicheng Liu. Mobileformer: Bridging mobilenet and transformer. 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Springer, 2020. 1 \ No newline at end of file diff --git a/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/images.zip b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..48be26a9f29c7f93f06f9c253839cb695648fef8 --- /dev/null +++ b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:35b0e069265aa4892bf9d0d5568c0f1532b6c3900705d3a7f533b6efa9f2514a +size 582934 diff --git a/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/layout.json b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..32df784eb6aa1ba5a35ffb24abd9254390a8bc29 --- /dev/null +++ b/2023/SCConv_ Spatial and Channel Reconstruction Convolution for Feature Redundancy/layout.json @@ -0,0 +1,8837 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 102, + 515, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 102, + 515, + 139 + ], + "spans": [ + { + "bbox": [ + 78, + 102, + 515, + 139 + ], + "type": "text", + "content": "SCConv: Spatial and Channel Reconstruction Convolution for Feature Redundancy" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "spans": [ + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "text", + "content": "Jiafeng Li" + }, + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "text", + "content": ", Ying Wen" + }, + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "text", + "content": ", Lianghua He" + }, + { + "bbox": [ + 212, + 160, + 400, + 175 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 175, + 559, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 175, + 559, + 203 + ], + "spans": [ + { + "bbox": [ + 54, + 175, + 559, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 54, + 175, + 559, + 203 + ], + "type": "text", + "content": "School of Communication and Electronic Engineering, East China Normal University, Shanghai, China. " + }, + { + "bbox": [ + 54, + 175, + 559, + 203 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 175, + 559, + 203 + ], + "type": "text", + "content": "Department of Computer Science and Technology, Tongji University, Shanghai, China." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 109, + 205, + 500, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 205, + 500, + 217 + ], + "spans": [ + { + "bbox": [ + 109, + 205, + 500, + 217 + ], + "type": "text", + "content": "51205904113@stu.ecnu.edu.cn;ywen@cs.ecnu.edu.cn;helianghua@tongji.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 270, + 289, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 547 + ], + "type": "text", + "content": "Convolutional Neural Networks (CNNs) have achieved remarkable performance in various computer vision tasks but this comes at the cost of tremendous computational resources, partly due to convolutional layers extracting redundant features. Recent works either compress well-trained large-scale models or explore well-designed lightweight models. In this paper, we make an attempt to exploit spatial and channel redundancy among features for CNN compression and propose an efficient convolution module, called SCConv (Spatial and Channel reconstruction Convolution), to decrease redundant computing and facilitate representative feature learning. The proposed SCConv consists of two units: spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). SRU utilizes a separate-and-reconstruct method to suppress the spatial redundancy while CRU uses a split-transform-and-fuse strategy to diminish the channel redundancy. In addition, SCConv is a plug-and-play architectural unit that can be used to replace standard convolution in various convolutional neural networks directly. 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However, such success relies heavily on intensive resources of computation and storage, which poses severe challenges to their efficient deployment on resource-constrained environments. Therefore, to address these challenges, various types of model compression strategies and network designs have been explored to improve network ef" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 245, + 547, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 245, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 245, + 547, + 449 + ], + "type": "text", + "content": "ficiency [1, 2, 26]. The former includes network pruning, weight quantization, low-rank factorization, and knowledge distillation. To be specific, network pruning [17, 22, 30] is a straightforward way to prune the uncritical neuron connections from an existing learned big model to make it thinner. Weight quantization [9] mainly focuses on converting network weights from floating-point types to integer ones to save computation resources. Low-rank factorization [5] applies the matrix decomposition techniques to estimate the informative parameters. Knowledge distillation [11, 34] generates small student networks with the guidance of a well-trained big teacher network. The common part of these compression techniques is that they have been regarded as post-processing steps, thus their performance is usually upper bounded by the given initial model. Meanwhile, the accuracy of these methods drastically drops while achieving a high compression rate." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 665 + ], + "type": "text", + "content": "Network design is another alternative way, which aims at reducing the inherent redundancy in dense model parameters and further developing a lightweight network model. For example, ResNet [10] and DenseNet [14] utilize an efficient shortcut connection to improve the network topology, which connects all preceding feature maps to diminish the redundant parameters. ResNeXt [31] replaces traditional convolutions with sparsely connected group convolutions to reduce inter-channel connectivity. Networks like Xception [4], MobileNet [12] and MobileNeXt [35] disentangle standard convolution into depth-wise convolution and point-wise convolution to further decrease the connection density between channels. MicroNet [19] adopts microfactorized convolution to handle extremely low FLOPs by integrating sparse connectivity into convolution. In addition, EfficientNet [27] learns to automatically search optimal network architectures to lower the redundancy in dense model parameters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "Moreover, in CNN architecture design, bottleneck structure has been well adopted, in which " + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": " convolutional layers account for a majority of the model parameters and FLOPs. Therefore various efficient convolutional opera" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 238, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 238, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 238, + 713 + ], + "type": "text", + "content": "*Corresponding author (e-mail: ywen@cs.ecnu.edu.cn)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6153" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 84, + 68, + 511, + 169 + ], + "blocks": [ + { + "bbox": [ + 84, + 68, + 511, + 169 + ], + "lines": [ + { + "bbox": [ + 84, + 68, + 511, + 169 + ], + "spans": [ + { + "bbox": [ + 84, + 68, + 511, + 169 + ], + "type": "image", + "image_path": "876397cb6e401a1a1963e6f3ed60b2d85aa203d0a0867f9177f4a0930e41b0d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 176, + 547, + 200 + ], + "lines": [ + { + "bbox": [ + 46, + 176, + 547, + 200 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 547, + 200 + ], + "type": "text", + "content": "Figure 1. The architecture of SCConv integrated with Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU). This figure shows the exact position of our SCConv module within a ResBlock." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "type": "text", + "content": "tions, such as group-wise convolution (GWC), depth-wise convolution (DWC) and point-wise convolution (PWC), a variant of the standard convolution, are proposed to replace the existing expensive convolutional operation. GWC, which was first introduced in AlexNet [16], can be regarded as a sparse convolution connection method that each output channel is connected to only a certain group of input channels. DWC [13] proposes to bring more efficiency by keeping each channel separately convolved with filters and without interaction between channels. PWC is used to keep the information flowing across channels and enable dimensionality reduction by reducing the number of filters. These operations are similar in sparse connectivity and have benefits in the number of parameters and FLOPs, which illustrates that redundancy in channel dimension can be reduced reasonably. Hence, a variety of convolution operations are proposed to explore redundancy reduction. For example, MobileNet [12] introduces inverted residual blocks using DWC and PWC to filter the features, which decreases the number of parameters while accelerating the training. ShuffleNet [33] resorts to point-wise group convolution and channel shuffle operation to improve the information flow between different channel groups. HetConv [25] designs heterogeneous convolutional filters where a " + }, + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "type": "text", + "content": " convolution kernels and a " + }, + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 47, + 220, + 289, + 712 + ], + "type": "text", + "content": " convolution kernels are included in one single filter to extract features. TiedBlockConv [28] shares the same convolutional filter over equal blocks of channels to produce multiple responses within a single filter. SPConv [32] divides the input channels into two groups for different processing but needs a relatively large amount of calculation while extracting internal information. GhostNet [8] considers the redundancy between feature maps and uses cheap operations like DWC to learn redundant features. SilmConv [23] adopts the operation of reducing the channels of features and flipping the weights to reduce feature redundancy. In addition, orthogonal to channel redundancy, OctConv [3] proposes octave convolution to separate convolutional filters into high-frequency and low-frequency components, processing the latter in low resolution to alleviate the spatial redundancy, which reduces calculations while keeping the same number of parameters." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 220, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 304 + ], + "type": "text", + "content": "All these prior studies have proven that there indeed exists considerable redundancy in the deep neural networks, not only in dense model parameters but also in the spatial and channel dimension of feature maps. However, all the above methods either focus on reducing the redundancy in channel dimension or in spatial dimension, making the network still suffer from the problems of feature redundancy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 304, + 546, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 546, + 495 + ], + "type": "text", + "content": "In this paper, different from prior work, we design a two-step procedure to exploit the redundancy of intermediate feature maps, with the goal of reducing the number of parameters and computation without performance loss. To this end, we propose a novel CNN compression approach to jointly reduce spatial and channel redundancy in the convolutional layers, termed as SCConv (Spatial and Channel reconstruction Convolution), which consists of two units, spatial reconstruction unit (SRU) and channel reconstruction unit (CRU). The proposed SCConv module, which can be embedded into various architectures without additional modifications, is designed to efficiently restrict feature redundancy. This module not only cuts down on the number of model parameters and FLOPs but enhances the capability of feature representation. We summarize our contributions as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 506, + 545, + 701 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 506, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 506, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 317, + 506, + 545, + 566 + ], + "type": "text", + "content": "- We propose a spatial reconstruction unit, termed as SRU, which separates redundant features based on weights and reconstructs them to suppress the redundancy in spatial dimension and strengthen the representation of features." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 574, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 574, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 317, + 574, + 545, + 622 + ], + "type": "text", + "content": "- We propose a channel reconstruction unit, termed as CRU, which utilizes a split-transform-and-fuse strategy to diminish the redundancy in channel dimension as well as the computational costs and storage." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 629, + 545, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 629, + 545, + 701 + ], + "spans": [ + { + "bbox": [ + 317, + 629, + 545, + 701 + ], + "type": "text", + "content": "- We design a plug-and-play operation named SCConv combining SRU and CRU in a sequential manner to replace standard convolution for operating on a variety of backbone CNNs. It turns out that SCConv can substantially save the computing load yet enhance the model performance on challenging tasks." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6154" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 70, + 511, + 232 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 511, + 232 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 511, + 232 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 511, + 232 + ], + "type": "image", + "image_path": "25c6d98ef6edc95d65e0ca96b6b67f4a04991eda78f228ceb8091009848fd76e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 190, + 240, + 402, + 251 + ], + "lines": [ + { + "bbox": [ + 190, + 240, + 402, + 251 + ], + "spans": [ + { + "bbox": [ + 190, + 240, + 402, + 251 + ], + "type": "text", + "content": "Figure 2. The architecture of Spatial Reconstruction Unit." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 271, + 129, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 129, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 129, + 285 + ], + "type": "text", + "content": "2. Methodology" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "text", + "content": "In this section, we introduce the proposed SCConv as illustrated in Figure 1, which consists of two units, Spatial Reconstruction Unit (SRU) and Channel Reconstruction Unit (CRU), placed in a sequential manner. Concretely, for the intermediate input features " + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "text", + "content": " in the bottleneck residual block, we first obtain the spatial-refined features " + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "inline_equation", + "content": "X^w" + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "text", + "content": " through SRU operation and subsequently we utilize CRU operation to gain the channel-refined features " + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 293, + 288, + 448 + ], + "type": "text", + "content": ". We exploit both spatial and channel redundancy among features in our SCConv module, which can be seamlessly integrated into any CNN architecture to decrease redundancy among intermediate feature maps and boost the feature representation of CNNs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 459, + 205, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 459, + 205, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 205, + 472 + ], + "type": "text", + "content": "2.1. SRU for Spatial Redundancy" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": "To exploit the spatial redundancy of features, we introduce Spatial Reconstruction Unit (SRU) as shown in Figure 2, which utilizes a Separate-and-Reconstruct operation. Separate operation aims to separate those informative feature maps from less informative ones corresponding to the spatial content. We leverage the scaling factors in Group Normalization (GN) [29] layers to assess the informative content of different feature maps. To be concrete, given an intermediate feature map " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{N \\times C \\times H \\times W}" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " is the batch axis, " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " is the channel axis, " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " are the spatial height and width axes. We first standardize the input feature " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " by subtracting mean " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " and dividing by standard deviation " + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 478, + 287, + 633 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 642, + 287, + 667 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 642, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 94, + 642, + 287, + 667 + ], + "type": "interline_equation", + "content": "X _ {o u t} = G N (X) = \\gamma \\frac {X - \\mu}{\\sqrt {\\sigma^ {2} + \\varepsilon}} + \\beta \\tag {1}", + "image_path": "a4ee31e0e6e11d7260c939b5289e58bffcf55e53e698f9e88f7ea94ad1b4a543.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " are the mean and standard deviation in " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " is a small positive constant added for the sake of division stability, " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": " are trainable affine transformation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "text", + "content": "Noted that we leverage the trainable parameters " + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "inline_equation", + "content": "\\gamma \\in R^{C}" + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "inline_equation", + "content": "GN" + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "text", + "content": " layers as a way to measure the variance of spatial pixels for each batch and channel. The richer spatial information reflects more variation in spatial pixels contributing to a larger " + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "text", + "content": ". The normalized correlation weights " + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "inline_equation", + "content": "W_{\\gamma} \\in R^{C}" + }, + { + "bbox": [ + 304, + 272, + 545, + 357 + ], + "type": "text", + "content": " are obtained by equation 2, which indicates the importance of different feature maps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 332, + 365, + 545, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 365, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 332, + 365, + 545, + 393 + ], + "type": "interline_equation", + "content": "W _ {\\gamma} = \\left\\{w _ {i} \\right\\} = \\frac {\\gamma_ {i}}{\\sum_ {j = 1} ^ {C} \\gamma_ {j}}, i, j = 1, 2, \\dots , C \\tag {2}", + "image_path": "1c4648189c6f1dc1a776b859694bf40a7adebce2f419b8de1e39ec0d1958ac7c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": "Then the weight values of feature maps reweighted by " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "W_{\\gamma}" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": " are mapped to the range (0, 1) by the sigmoid function and gated by a threshold. We set those weights above the threshold to 1 to obtain the informative weights " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "W_{1}" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": " while setting them to 0 to gain the non-informative weights " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "W_{2}" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": " (the threshold is set to 0.5 in the experiments). The whole process of acquiring " + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 403, + 545, + 487 + ], + "type": "text", + "content": " can be expressed as equation 3:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 497, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 497, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 347, + 497, + 545, + 510 + ], + "type": "interline_equation", + "content": "W = \\operatorname {G a t e} \\left(\\operatorname {S i g m o i d} \\left(W _ {\\gamma} \\left(G N (X)\\right)\\right)\\right) \\tag {3}", + "image_path": "7bd54a84e0eb2628a4eed0de7943a01a345aa6064ca1593eb8a417aeeb9235f7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": "Finally, we multiply input features " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "W_{1}" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "W_{2}" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " respectively, yielding two weighted features: the informative ones " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "X_{1}^{w}" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " and less informative ones " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "X_{2}^{w}" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": ". Thus we successfully separate the input features into two parts: " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "X_{1}^{w}" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " has informative and expressive spatial contents while " + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "inline_equation", + "content": "X_{2}^{w}" + }, + { + "bbox": [ + 304, + 521, + 545, + 593 + ], + "type": "text", + "content": " has little or no information, which is regarded as redundant." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "In order to reduce the spatial redundancy, we further propose a Reconstruct operation that features with rich information sum up with less informative ones to generate features with richer information and save spatial space. Instead of adding these two parts directly, we adopt a cross reconstruct operation to sufficiently combine the weighted two different informative features and strengthen the information flow between them. Afterwards we concatenate the cross-reconstructed features " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "X^{w1}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "X^{w2}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " to obtain the spatial-refined feature maps " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "X^w" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". The whole process of " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "Re" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6155" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 70, + 511, + 222 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 511, + 222 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 511, + 222 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 511, + 222 + ], + "type": "image", + "image_path": "118d6c0d9c525f5c625cc78517dd9d2ee958421d3871790678b1795d8b6665d4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 228, + 405, + 240 + ], + "lines": [ + { + "bbox": [ + 187, + 228, + 405, + 240 + ], + "spans": [ + { + "bbox": [ + 187, + 228, + 405, + 240 + ], + "type": "text", + "content": "Figure 3. The architecture of Channel Reconstruction Unit." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 262, + 214, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 214, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 214, + 274 + ], + "type": "text", + "content": "construct operation can be expressed as :" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 278, + 287, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 278, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 116, + 278, + 287, + 354 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{c} X _ {1} ^ {w} = W _ {1} \\otimes X, \\\\ X _ {2} ^ {w} = W _ {2} \\otimes X, \\\\ X _ {1 1} ^ {w} \\oplus X _ {2 2} ^ {w} = X ^ {w 1}, \\\\ X _ {2 1} ^ {w} \\oplus X _ {1 2} ^ {w} = X ^ {w 2}, \\\\ X ^ {w 1} \\cup X ^ {w 2} = X ^ {w}. \\end{array} \\right. \\tag {4}", + "image_path": "263bbcc35dd77ab24f7b51023b7fe492b6791fc26c1beb6e6ec77fb39045bbb5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "content": " is element-wise multiplication, " + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "content": " is element-wise summation, " + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "inline_equation", + "content": "\\cup" + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "content": " is concatenation. After the SRU is applied to the intermediate input features " + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "content": ", not only do we separate the informative features from less informative ones, but also we reconstruct them to enhance the representative features and suppress the redundant features in spatial dimension. Nevertheless, the spatial-refined feature maps " + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "inline_equation", + "content": "X^w" + }, + { + "bbox": [ + 46, + 358, + 289, + 455 + ], + "type": "text", + "content": " still remain redundant in channel dimension." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 460, + 214, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 214, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 214, + 474 + ], + "type": "text", + "content": "2.2. CRU for Channel Redundancy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "content": "To exploit the channel redundancy of features, we introduce Channel Reconstruction Unit (CRU) as shown in Figure 3, which utilizes a Split-Transform-and-Fuse strategy. Normally, we use repetitive standard " + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "content": " convolutions to extract features, resulting in some relatively redundant feature maps along the channel dimension. Let " + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "inline_equation", + "content": "M^k \\in \\mathbb{R}^{c \\times k \\times k}" + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "content": " denotes a " + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "content": " convolution kernel and " + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "inline_equation", + "content": "X, Y \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "content": " denotes the input and convolved output features respectively. A standard convolution can be defined as " + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "inline_equation", + "content": "Y = M^k X" + }, + { + "bbox": [ + 46, + 479, + 287, + 624 + ], + "type": "text", + "content": ". To be specific, we replace the standard convolution with CRU, which is implemented via three operators - Split, Transform and Fuse." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": "Split: For given spatial-refined features " + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "inline_equation", + "content": "X^w \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": ", we first split the channels of " + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "inline_equation", + "content": "X^w" + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": " into two parts with " + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "inline_equation", + "content": "\\alpha C" + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": " channels and " + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "inline_equation", + "content": "(1 - \\alpha)C" + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": " channels respectively, as shown in the split part of Figure 3, where " + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "inline_equation", + "content": "0 \\leq \\alpha \\leq 1" + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": " is a split ratio. Subsequently, we further utilize " + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 636, + 288, + 696 + ], + "type": "text", + "content": " convolutions to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "content": "squeeze the channels of feature maps for its computing efficiency. Here we introduce a squeeze ratio " + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "content": " to control the feature channels to balance the computational cost of the CRU (" + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "inline_equation", + "content": "r = 2" + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "content": " is a typical setting in the experiments). After the split and squeeze operations, we divide the spatial-refined features " + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "inline_equation", + "content": "X^w" + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "content": " into the upper part " + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "inline_equation", + "content": "X_{up}" + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "content": " and the lower part " + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "inline_equation", + "content": "X_{low}" + }, + { + "bbox": [ + 306, + 262, + 545, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": "Transform: " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "X_{up}" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": " is fed into the upper transformation stage, serving as a \"Rich Feature Extractor\". We adopt efficient convolutional operations (i.e. GWC and PWC) to replace the expensive standard " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": " convolutions to extract high-level representative information as well as reduce the computational cost. Owing to sparse convolution connections, GWC reduces the amount of parameters and calculations but cuts off the information flow between channel groups. While PWC compensates for the information loss and helps the information flow across feature channels. Thus we perform " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": " GWC (we set group size " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "g = 2" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": " in the experiments) and " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": " PWC operations on the same " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "X_{up}" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": ". Afterward, we sum up the output to form a merged representative feature maps " + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "inline_equation", + "content": "Y_{1}" + }, + { + "bbox": [ + 304, + 358, + 546, + 548 + ], + "type": "text", + "content": " as shown in the Transform part of Figure 3. The upper transformation stage can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 363, + 549, + 545, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 549, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 363, + 549, + 545, + 564 + ], + "type": "interline_equation", + "content": "Y _ {1} = M ^ {G} X _ {u p} + M ^ {P _ {1}} X _ {u p} \\tag {5}", + "image_path": "3356c01bff99f77acaa7aefe9b879a6786c1f7fe06a2641741d75e5f6b8618c3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "inline_equation", + "content": "M^G \\in \\mathbb{R}^{\\frac{\\alpha c}{gr} \\times k \\times k \\times c}" + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "inline_equation", + "content": "M^{P_1} \\in \\mathbb{R}^{\\frac{\\alpha c}{r} \\times 1 \\times 1 \\times c}" + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": " is a learnable weight matrix of GWC and PWC, " + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "inline_equation", + "content": "X_{up} \\in \\mathbb{R}^{\\frac{\\alpha c}{r} \\times h \\times w}" + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "inline_equation", + "content": "Y_1 \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": " are the upper input and output feature maps respectively. In short, the upper transformation stage leverages a combination of GWC and PWC on the same feature maps " + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "inline_equation", + "content": "X_{up}" + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": " to extract rich representative features " + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "inline_equation", + "content": "Y_1" + }, + { + "bbox": [ + 304, + 568, + 545, + 653 + ], + "type": "text", + "content": " with less computational cost." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{low}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " is fed into the lower transformation stage, where we apply cheap " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " PWC operations to generate feature maps with shallow hidden details as a supplementary to the Rich Feature Extractor. In addition, we reuse features " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{low}" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " to obtain more feature maps without extra cost. Lastly, we" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 186, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 186, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 186, + 712 + ], + "type": "text", + "content": "For simplicity, we omit the bias term." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6156" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "concatenate the generated and reused features to form the output of the lower stage " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "Y_{2}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 102, + 287, + 116 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 102, + 287, + 116 + ], + "spans": [ + { + "bbox": [ + 116, + 102, + 287, + 116 + ], + "type": "interline_equation", + "content": "Y _ {2} = M ^ {P _ {2}} X _ {l o w} \\cup X _ {l o w} \\tag {6}", + "image_path": "aeed15dc393ffe353773501cf0cba6b8657f7e6f365ec01d719c873c58b96d54.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "M^{P_2} \\in \\mathbb{R}^{\\frac{(1 - \\alpha)c}{r} \\times 1 \\times (1 - \\frac{1 - \\alpha}{r})c}" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " is a learnable weight matrix of PWC, " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "\\cup" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " is concatenation operation, " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "X_{low} \\in \\mathbb{R}^{\\frac{(1 - \\alpha)c}{r} \\times h \\times w}" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "Y_2 \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " are the lower input and output feature maps respectively. In a word, the lower transformation stage reuses preceding features " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "X_{low}" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " and utilizes cheap " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " PWC to obtain features " + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "inline_equation", + "content": "Y_2" + }, + { + "bbox": [ + 47, + 121, + 287, + 210 + ], + "type": "text", + "content": " with supplementary detailed information." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "text", + "content": "Fuse: After the transformation is performed, instead of direct concatenating or adding two types of features, we utilize the simplified SKNet method [18] to adaptively merge the output features " + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "inline_equation", + "content": "Y_{1}" + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "inline_equation", + "content": "Y_{2}" + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "text", + "content": " from upper and lower transformation stage as shown in the Fuse part of Figure 3. We first apply a global average pooling (Pooling) to collect global spatial information with channel-wise statistics " + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "inline_equation", + "content": "S_{m}\\in \\mathbb{R}^{c\\times 1\\times 1}" + }, + { + "bbox": [ + 47, + 224, + 288, + 319 + ], + "type": "text", + "content": ", which is calculated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 324, + 288, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 288, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 288, + 369 + ], + "type": "interline_equation", + "content": "S _ {m} = \\operatorname {P o o l i n g} \\left(Y _ {m}\\right) = \\frac {1}{H \\times W} \\sum_ {i = 1} ^ {H} \\sum_ {j = 1} ^ {W} Y _ {c} (i, j), m = 1, 2 \\tag {7}", + "image_path": "012f05d6b46ab222542436e9d52526c506c6ac6b6855ced8d1010f8801212999.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "text", + "content": "Next, we stack the upper and lower global channelwise descriptor " + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "text", + "content": " together and use channel-wise soft attention operation to generate feature importance vector " + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\beta_{1},\\beta_{2}\\in \\mathbb{R}^{c}" + }, + { + "bbox": [ + 47, + 369, + 287, + 417 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 421, + 287, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 421, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 62, + 421, + 287, + 445 + ], + "type": "interline_equation", + "content": "\\beta_ {1} = \\frac {e ^ {s _ {1}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \\beta_ {2} = \\frac {e ^ {s _ {2}}}{e ^ {s _ {1}} + e ^ {s _ {2}}}, \\beta_ {1} + \\beta_ {2} = 1 \\tag {8}", + "image_path": "8ebede5f772487abd74d437f3bd8912ea094bf2e1473a7c3f285c1dffb955136.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "text", + "content": "Finally, under the guidance of feature importance vector " + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\beta_{1},\\beta_{2}" + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "text", + "content": ", the channel-refined features " + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "text", + "content": " can be obtained by merging the upper features " + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "inline_equation", + "content": "Y_{1}" + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "text", + "content": " and the lower features " + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "inline_equation", + "content": "Y_{2}" + }, + { + "bbox": [ + 47, + 449, + 287, + 496 + ], + "type": "text", + "content": " in a channel-wise manner as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 124, + 502, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 502, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 124, + 502, + 287, + 516 + ], + "type": "interline_equation", + "content": "Y = \\beta_ {1} Y _ {1} + \\beta_ {2} Y _ {2} \\tag {9}", + "image_path": "0b94b913d7113aa552011129dfd5d2d94fd75acb3453e360ee29eec3a32ee2fd.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": "In brief, we adopt CRU, using Split-Transform-and-Fuse strategy, to further diminish the redundancy of spatial-refined feature maps " + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "inline_equation", + "content": "X^w" + }, + { + "bbox": [ + 46, + 521, + 287, + 653 + ], + "type": "text", + "content": " along the channel dimension. Furthermore, CRU extracts rich representative features through lightweight convolutional operations while proceeds redundant features with cheap operation and feature reuse schemes. Overall, CRU can be used individually or in conjunction with SRU operation. By arranging the SRU and CRU in a sequential manner, the proposed SCConv is established, which is highly efficient and capable of replacing standard convolution operations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 659, + 188, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 188, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 188, + 672 + ], + "type": "text", + "content": "2.3. Analysis on Complexities" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Our SCConv is designed as a plug-and-play module that can be easily embedded into various existing well-designed neural architectures to reduce computation and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "storage costs. In the SCConv module, all of the parameters are concentrated on the transformation stage. Hence we analyze the reduction of theoretical memory usage. The parameters of standard convolution " + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "Y = M^{k}X" + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": " can be calculated as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 348, + 141, + 545, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 141, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 348, + 141, + 545, + 155 + ], + "type": "interline_equation", + "content": "P _ {s} = k \\times k \\times C _ {1} \\times C _ {2} = k ^ {2} C _ {1} C _ {2} \\tag {10}", + "image_path": "f8eb5d00a09182ace142f319223f6090935eb8fc60752b07d33178df979b71b1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "text", + "content": " is kernel size of the convolution, " + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "inline_equation", + "content": "C_1" + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "inline_equation", + "content": "C_2" + }, + { + "bbox": [ + 304, + 164, + 545, + 188 + ], + "type": "text", + "content": " are the number of input and output feature channels." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 189, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 189, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 189, + 545, + 212 + ], + "type": "text", + "content": "The parameters of the proposed SCConv module consist of:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 308, + 220, + 545, + 307 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 220, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 308, + 220, + 545, + 307 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} P _ {s c} = 1 \\times 1 \\times \\alpha C _ {1} \\times \\frac {\\alpha C _ {1}}{r} + k \\times k \\times \\frac {\\alpha C _ {1}}{g r} \\times \\frac {C _ {2}}{g} \\times g \\\\ + 1 \\times 1 \\times \\frac {\\alpha C _ {1}}{r} \\times C _ {2} + (1 - \\alpha) C _ {1} \\times \\frac {(1 - \\alpha) C _ {1}}{r} \\\\ + 1 \\times 1 \\times \\frac {(1 - \\alpha) C _ {1}}{r} \\times \\left(C _ {2} - \\frac {1 - \\alpha}{r} C _ {1}\\right) \\tag {11} \\\\ \\end{array}", + "image_path": "d392404c805cdb0a53cc823a765658776e37c42f28ef02246877a12e54cd8513.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": " denotes the split ratio, " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": " refers to the squeeze ratio, " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": " is the group size of GWC operation, " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "C_1" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "C_2" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": " are input and output feature channels respectively. Here, we give a comparison to show the performance of the proposed SCConv. In the experiment, the general parameter set is " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "\\alpha = \\frac{1}{2}" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "r = 2" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "g = 2" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "C_1 = C_2 = C" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": ", the amount of parameters can be reduced by 5 times where " + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "inline_equation", + "content": "P_s / P_{sc} \\approx 5" + }, + { + "bbox": [ + 304, + 308, + 545, + 415 + ], + "type": "text", + "content": " while the model achieves better performance than standard convolution." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 427, + 387, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 387, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 387, + 441 + ], + "type": "text", + "content": "3. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 447, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 651 + ], + "type": "text", + "content": "To evaluate the effectiveness of the proposed SCConv, in this section, we perform a series of experiments on image classification and object detection with only the widely used " + }, + { + "bbox": [ + 304, + 447, + 545, + 651 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 447, + 545, + 651 + ], + "type": "text", + "content": " kernels being replaced by SCConv module. Image classification benchmarks include CIFAR-10 [15], CIFAR-100 [15] and ImageNet-1K [16]. Object detection benchmarks include PASCAL VOC [6] and MS COCO [21]. Top-1 accuracy is reported as the evaluation metric for image classification and the mean average precision (mAP) is used to measure accuracy of object detection. For fair comparisons, all models in each experiment, including re-implemented baselines and SCConv-equipped models, are trained from scratch on 2 NVIDIA Tesla V100 GPUs with the default data augmentation and training strategy and no other tricks are used. In each experiment, we train several times with the same configuration to prevent the impact of fluctuations and report the median of results." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 658, + 432, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 432, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 432, + 671 + ], + "type": "text", + "content": "3.1. Experimental Settings" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Dataset. CIFAR dataset, including CIFAR-10 and CIFAR-100, consists of 50k training images and 10k validation images, which are divided into 10 and 100 classes" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6157" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "respectively. ImageNet-1K dataset is a large-scale image classification dataset, containing 1.28 million training images and 50k validation images from 1k classes. PASCAL VOC dataset, which has 20 classes, contains more than 22k images for training and 5k images for validation. MS COCO dataset, which is divided into 80 classes, has more than 118k images for training and 5k images for validation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "text", + "content": "Training and Inference. 1) For CIFAR-10 and CIFAR-100, we follow a similar training scheme in [10]. Networks are trained for 200 epochs with SGD optimizer with a weight decay of " + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "inline_equation", + "content": "5 \\times e^{-4}" + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "text", + "content": " and a momentum of 0.9. The learning rate is initialized to 0.05 and is decayed by 0.1 at 100 and 150 of the epochs. It trains with a mini-batch size of 128 on one GPU. Besides, according to different architectures of networks, we set " + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "inline_equation", + "content": "(h, w)" + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "text", + "content": " to (8, 8) for ResNet, WideResNet, ResNeXt and set it to (4, 4) for DenseNet. 2) For ImageNet-1K dataset, we follow standard practices and perform data augmentation with random cropping to size " + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "text", + "content": " pixels. We apply SGD with a momentum of 0.9 and a weight decay of " + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "inline_equation", + "content": "1 \\times e^{-4}" + }, + { + "bbox": [ + 46, + 175, + 290, + 439 + ], + "type": "text", + "content": ". The initial learning rate is set to 0.1 and divided by every 30 epochs for a total of 100 epochs. 3) For PASCAL VOC dataset, we use SGD optimizer and set the batch size to 32. The initial learning rate is set to 0.1 with a 500 iterations warmup. We train 20k iterations totally and reduce the learning rate by a factor of 10 at 10k and 18k iterations. 4) For MS COCO dataset, we use SGD optimizer and set the initial learning rate to 0.1 and batch size to 16. The total iterations are set to 180k and the learning rate is divided by 10 at 120k and 160k iterations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 448, + 149, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 448, + 149, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 448, + 149, + 460 + ], + "type": "text", + "content": "3.2. Ablation Studies" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 467, + 288, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 288, + 528 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 288, + 528 + ], + "type": "text", + "content": "In this section, we conduct ablation studies to inspect the relative effectiveness of different components in the proposed SCCov module. We choose ResNet50 as the baseline network by replacing standard " + }, + { + "bbox": [ + 46, + 467, + 288, + 528 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 467, + 288, + 528 + ], + "type": "text", + "content": " convolution to conduct the following ablation experiments on CIFAR100." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "SRU and CRU Our SCConv module includes a spatial reconstruction unit (SRU) and a channel reconstruction unit (CRU). Firstly we only apply SRU or CRU on ResNet50 to examine the efficiency of a single unit. As shown in Table 1, only embedding with SRU " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{ResNet50 + S})" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " achieves nearly " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " improvement without extra increment in FLOPs, while solely embedding with CRU " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{ResNet50 + C})" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " can save " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " parameters and FLOPs with " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " increase of Top-1 accuracy. The results imply that the single-unit-embedded model boosts the accuracy significantly. In addition, we compare three different ways of arranging the SRU and CRU: sequential spatial-channel " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{S + C})" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", sequential channel-spatial " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{C + S})" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", and parallel use of both units " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{C\\& S})" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ". We find that the spatial-first order " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathrm{S + C})" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " achieves the best accuracy" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 326, + 112, + 529, + 196 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Experimental results with different combination methods of SRU and CRU on CIFAR-100 dataset. (S and C is short for SRU and CRU respectively)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 112, + 529, + 196 + ], + "lines": [ + { + "bbox": [ + 326, + 112, + 529, + 196 + ], + "spans": [ + { + "bbox": [ + 326, + 112, + 529, + 196 + ], + "type": "table", + "html": "
DescriptionParamsFLOPsTop-1ACC(%)
ResNet5023.71M1.30G78.60
ResNet50 + S23.53M1.30G79.59
ResNet50 + C14.74M843.81M79.21
ResNet50 + C & S14.74M843.81M79.26
ResNet50 + C + S14.74M843.81M79.54
ResNet50 + S + C14.74M843.81M79.89
", + "image_path": "b92471f137d83a4b31b5c64623dc3da926162a7bd78ba6fa9d8ea1c80cc2db34.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 216, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 547, + 253 + ], + "type": "text", + "content": "than other combination methods. Thus we adopt a sequential spatial-first combination " + }, + { + "bbox": [ + 304, + 216, + 547, + 253 + ], + "type": "inline_equation", + "content": "(\\mathrm{S} + \\mathrm{C})" + }, + { + "bbox": [ + 304, + 216, + 547, + 253 + ], + "type": "text", + "content": " strategy to formulate our SCConv and further improve the model performance." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 326, + 268, + 527, + 396 + ], + "blocks": [ + { + "bbox": [ + 326, + 268, + 527, + 396 + ], + "lines": [ + { + "bbox": [ + 326, + 268, + 527, + 396 + ], + "spans": [ + { + "bbox": [ + 326, + 268, + 527, + 396 + ], + "type": "image", + "image_path": "57cbc0a28e440e4ff4b64ed487cea302788d96c9d404570cb34c270698daf85a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 406, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 306, + 406, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 545, + 429 + ], + "type": "text", + "content": "Figure 4. The trade-off between FLOPs and Accuracy on CIFAR100 with different split ratios " + }, + { + "bbox": [ + 306, + 406, + 545, + 429 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 306, + 406, + 545, + 429 + ], + "type": "text", + "content": " in SCConv-embedded ResNet50." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": "Analysis on split ratio " + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": " To explore the effect of different split ratios " + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": " in CRU module, we vary the split ratio from 1/8 to 7/8 gradually to compare the accuracy versus FLOPs on CIFAR-100. As shown in Figure 4, the accuracy of SCConv-embedded ResNet50 rises with the increase of the split ratio " + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": ". The higher " + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": " represents the model can obtain richer feature information in the transformation stage of CRU, thereby improving the model's overall performance. When " + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\alpha = 1/2" + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": ", the whole network achieves the best flops-accuracy trade-off. Thus we adopt the optimal split ratio " + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\alpha = 1/2" + }, + { + "bbox": [ + 304, + 458, + 547, + 602 + ], + "type": "text", + "content": " for SCConv in the following experiments for a better trade-off between performance and efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Visualization To explore the feature representation of the proposed SRU method, we visualize the feature maps of the first stage of the original ResNet50 and SRU-embedded ResNet50 in Figure 5. It can be observed that the pattern in features of SRU-embedded ResNet50 is enriched in comparison with original ResNet50. Not only the redundant features is diminished but the representative features are strengthened and diversified. The visualization demon" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6158" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 286, + 180 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 286, + 180 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 286, + 180 + ], + "type": "image", + "image_path": "6eabb80b3ede336bbca958789e258d59cd8c9daef161b0e30844cc20a960fbdf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 189, + 286, + 211 + ], + "lines": [ + { + "bbox": [ + 47, + 189, + 286, + 211 + ], + "spans": [ + { + "bbox": [ + 47, + 189, + 286, + 211 + ], + "type": "text", + "content": "Figure 5. Left: Features from the first-stage of original ResNet50, Right: Features from the first-stage of SRU-embedded ResNet50." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 232, + 286, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 286, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 286, + 255 + ], + "type": "text", + "content": "strates the SRU is capable of generating representative and expressive features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 262, + 216, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 262, + 216, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 262, + 216, + 275 + ], + "type": "text", + "content": "3.3. Image Classification on CIFAR" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 286, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 286, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 286, + 400 + ], + "type": "text", + "content": "After studying the structure of the proposed SCConv module for efficient feature learning, we continue to evaluate the SCConv-embedded architecture on various baseline models and further make a comparison with the SOTA methods over classification accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset. The related SOTA approaches include OctConv [3], GhostNet [8], SPConv [32], SlimConv [23], TiedConv [28]. All experiments are conducted by replacing the original convolutional layers with the corresponding convolution methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": "As can be seen in Table 2, in all cases, our SCConv-embedded models outperform all prior networks for accuracy. For ResNet-56 model, the SCConv-R56 requires only " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "62.7\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " parameters and FLOPs of the counterpart ResNet56 while bringing over a " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " accuracy increase on both datasets. For ResNet-50 model, the SCConv-R50 achieves better accuracy (nearly " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": ") but around " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "37\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " parameters and " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " FLOPs reduction than the counterpart ResNet50 on CIFAR-10 and CIFAR-100. Besides, the SCConv-R50 requires the same computational costs as SlimConv-R50 while bringing higher (over " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": ") promotion of accuracy. To show the generality of the proposed method, we apply SCConv and other SOTA methods to ResNeXt-29, WideResNet-28, and DenseNet-121. It can be observed that the SCConv-embedded models still achieve superior performance than other works with comparable model computations. For instance, the SCConv-RX29 achieves over " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " improvement of accuracy while the computation is on par with the GhostNet-RX29. The SCConv-WRN28 achieves better accuracy (nearly " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": ") than the SlimConv-WRN28 while saving parameters and FLOPs by " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "11.7\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "inline_equation", + "content": "15.5\\%" + }, + { + "bbox": [ + 46, + 413, + 286, + 664 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 671, + 227, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 227, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 227, + 684 + ], + "type": "text", + "content": "3.4. Image Classification on ImageNet" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "We conduct experiments for ResNet50 on the ImageNet-1K dataset, comparing the performance of our approach" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 311, + 113, + 543, + 434 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 102 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 102 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 102 + ], + "type": "text", + "content": "Table 2. Comparison of SOTA methods for common CNN architectures over Top-1 accuracy, the number of parameters and FLOPs on CIFAR-10 and CIFAR-100 dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 311, + 113, + 543, + 434 + ], + "lines": [ + { + "bbox": [ + 311, + 113, + 543, + 434 + ], + "spans": [ + { + "bbox": [ + 311, + 113, + 543, + 434 + ], + "type": "table", + "html": "
Network ArchitectureFLOPsParamsCIFAR-10ACC(%)CIFAR-100ACC(%)
ResNet56 (R56)126.84M0.86M93.2771.50
OctConv-R56 (α=1/2)126.84M0.62M93.1170.93
SPConv-R56 (α=1/2)87.95M0.58M93.4971.51
GhostNet-R56 (s=2)68.35M0.45M92.3570.42
SlimConv-R56 (k=1)88.82M0.60M93.5171.71
TiedConv-R56 (b=2)94.99M0.54M92.8771.10
SCConv-R56 (Ours)79.55M0.52M94.1272.56
ResNet50 (R50)1.30G23.52M95.0978.60
OctConv-R50 (α=1/2)727.26M23.52M95.2578.91
GhostNet-R50 (s=2)632.45M14.56M94.3077.54
SlimConv-R50 (k=4/3)853.50M14.83M95.0578.85
SPConv-R50 (α=1/2)972.31M16.14M95.3279.23
SlimConv-R50 (k=1)942.38M16.78M95.3579.26
TiedConv-R50 (b=2)998.78M15.03M95.4479.52
SCConv-R50 (Ours)831.18M14.69M95.9279.89
ResNeXt-29 (RX29)4.55G28.27M95.6881.54
GhostNet-RX29 (s=2)3.60G22.22M95.1480.23
SPConv-RX29 (α=1/2)4.79G31.17M96.0381.76
SlimConv-RX29 (k=4/3)4.38G28.24M95.8581.93
TiedConv-RX29 (b=2)5.96G24.67M95.6681.32
SCConv-RX29 (Ours)3.57G22.31M96.2082.56
WideResNet-28 (WRN28)5.96G36.55M95.2179.40
GhostNet-WRN28 (s=2)3.98G22.12M95.2579.27
SPConv-WRN28 (α=1/2)4.16G24.20M95.3780.25
SlimConv-WRN28 (k=1)4.25G25.00M95.4379.52
TiedConv-WRN28 (b=2)4.54G22.03M95.4878.61
SCConv-WRN28 (Ours)3.75G21.12M95.6480.83
DenseNet-121 (D121)898.23M7.05M95.0979.43
GhostNet-D121 (s=2)517.36M5.04M93.9678.51
SPConv-D121 (α=1/2)641.54M5.69M95.1579.64
SlimConv-D121 (k=1)670.21M5.97M94.6378.90
TiedConv-D121 (b=2)695.68M5.45M95.2379.73
SCConv-D121 (Ours)594.34M5.45M95.3780.24
", + "image_path": "c2964bfc849c5a418739a27db3be6c3434c88daaede617fc8eb10390ad89c13c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": "with the recent SOTA methods including OctConv [3], SPConv [32], GhostNet [8], SlimConv [23], PfLayer [7], TiedConv [28]etc. Noted that we only replace the bottleneck " + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": " convolutions with the corresponding convolution methods. As shown in Table 3, our SCConv-R50-" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\alpha = 1/2" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": " can achieve " + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "inline_equation", + "content": "34.4\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": " computation reductions with " + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "inline_equation", + "content": "0.26\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": " accuracy increase over the ResNet50 model. When we further increase the split ratio " + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "inline_equation", + "content": "3/4" + }, + { + "bbox": [ + 304, + 457, + 545, + 578 + ], + "type": "text", + "content": ", our approach gains superior performance to all other state-of-the-art methods in the growth of accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "type": "text", + "content": "For instance, the SCConv-R50_α=3/4 achieves over 0.6% improvement of accuracy while the computation is on a par with the PflLayer-R50_max. In addition, the SCConv-R50_α=1/2 gains better performance than SlimConv-R50_k=4/3 with comparable calculations. To further prove the effectiveness of SCConv, we embed it with the deep model ResNet101. With nearly 62% of computation costs, our SCConv-R101 brings a 0.68% accuracy increase over the baseline model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Besides, for better comparison, we select several state-of-the-art methods to draw the FLOPs v.s. Top-1 accu" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6159" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 91, + 277, + 229 + ], + "blocks": [ + { + "bbox": [ + 55, + 71, + 278, + 82 + ], + "lines": [ + { + "bbox": [ + 55, + 71, + 278, + 82 + ], + "spans": [ + { + "bbox": [ + 55, + 71, + 278, + 82 + ], + "type": "text", + "content": "Table 3. Image classification results on ImageNet-1K dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 91, + 277, + 229 + ], + "lines": [ + { + "bbox": [ + 60, + 91, + 277, + 229 + ], + "spans": [ + { + "bbox": [ + 60, + 91, + 277, + 229 + ], + "type": "table", + "html": "
Network ArchitectureFLOPs(G)Params(M)Top-1 (%)
ResNet50 (R50) (Baseline)4.0925.5676.15
Versatile-R50 (NIPS2018)1.8018.775.50
GhostNet-R50_s=2 (CVPR2020)2.1513.9575.18
SlimConv-R50_k=8/3 (TIP2021)1.8812.1075.32
SPConv-R50_α=1/2 (IJCAI2020)2.9718.3476.26
OctConv-R50_α=1/2 (CVPR2020)2.4025.5676.34
SlimConv-R50_k=4/3 (TIP2021)2.6516.7676.12
PfLayer-R50_max (ICLR2022)2.9018.0076.15
SlimConv-R50_k=1 (TIP2021)3.0018.8176.32
TiedConv-R50_b=2 (AAAI2021)3.1917.0776.04
SCConv-R50_α=1/22.7016.7876.41
SCConv-R50_α=3/42.8717.6976.79
ResNet_101(R101)(Baseline)7.8344.5577.25
SCConv-R1014.9028.0077.93
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BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0977.8955.3152.26
SPConv-R5019.76/49.2378.0555.4752.48
SlimConv-R5018.81/47.1277.9655.3852.42
SCConv-R5016.78/41.3678.6856.2653.16
ResNet101(R101)44.55/121.379.2356.3153.32
SCConv-R10127.90/75.2680.3657.0554.12
", + "image_path": "89991246240b9efa9b5eb73967b0c5b78c23cdb6f9f69c32e268765f2aaa0c20.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 312, + 91, + 542, + 141 + ], + "blocks": [ + { + "bbox": [ + 323, + 71, + 528, + 81 + ], + "lines": [ + { + "bbox": [ + 323, + 71, + 528, + 81 + ], + "spans": [ + { + "bbox": [ + 323, + 71, + 528, + 81 + ], + "type": "text", + "content": "Table 5. Object detection results on MS COCO val2017." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 91, + 542, + 141 + ], + "lines": [ + { + "bbox": [ + 312, + 91, + 542, + 141 + ], + "spans": [ + { + "bbox": [ + 312, + 91, + 542, + 141 + ], + "type": "table", + "html": "
BackboneParams(M)/FLOPs(G)AP@.5AP@.75mAP@ [.5, .95]
ResNet50(R50)25.56/63.0954.237.435.2
SPConv-R5019.76/49.2354.537.635.3
SlimConv-R5018.81/47.1254.037.135.0
SCConv-R5016.78/41.3655.138.235.6
", + "image_path": "8c21c5667f882da2ef660fa3f5610bc4c1e755c6df9b1eff3d5c3f03a38d1fd4.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": "For the PASCAL VOC dataset, as shown in Table 4, the AP@ [.5] of RetinaNet with the SCConv-R50 and SCConv-R101 are " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "78.68\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "80.36\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": ", exceeding original ResNet50 and ResNet101 by " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": " while reducing parameters and FLOPs by " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "34.1\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "37\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": ". For the MS COCO dataset, as shown in Table 5, the AP@ [.5] of RetinaNet with SCConv-R50 is " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "55.1\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": ", outperforming original ResNet-50 by " + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 304, + 154, + 545, + 249 + ], + "type": "text", + "content": " with over 22G FLOPs decreased." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "type": "text", + "content": "In addition, our approach consistently surpasses current state-of-the-art methods on both datasets. For instance, the mAP@[.5,.95] of SCConv-R50 exceeds the SlimConv-R50 by nearly " + }, + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 304, + 250, + 546, + 357 + ], + "type": "text", + "content": " on PASCAL VOC and MS COCO datasets. In short, these results prove that the SCConv module not only brings performance improvement but helps the network learn better representative features with a smaller amount of parameters, making it possible for object detection to be deployed on resource-limited devices." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 368, + 378, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 368, + 378, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 368, + 378, + 380 + ], + "type": "text", + "content": "4. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 388, + 546, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 604 + ], + "type": "text", + "content": "In this paper, we have presented a novel spatial and channel reconstruction module (SCConv), an efficient architectural unit to decrease computational cost and model storage while improving the performance of CNN models by reducing spatial and channel redundancies that widely exist in standard convolution. We diminish the redundancy in feature maps with two distinctive modules, SRU and CRU, which achieve considerable performance improvement while cutting a substantial amount of computation loads. Besides, SCConv is a plug-and-play module and generic to replace the standard convolution without any model architecture adjustment. In addition, the extensive experiments with various SOTA methods on image classification and object detection have indicated the superiority of SCConv-embedded models for striking a much better tradeoff between performance and model efficiency. Finally, we hope the proposed method can inspire research for more efficient architectural design." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments This work was supported in part by the 2030 National Key Research and Development Program of China (2018AAA0100500), National Nature Science Foundation of China (62273150, 62171323), Shanghai Natural Science Foundation (22ZR1421000), Shanghai Outstanding Academic Leaders Plan (21XD1430600), Science and Technology Commission of Shanghai Municipality (22DZ2229004)." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6160" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Jierun Chen, Tianlang He, Weipeng Zhuo, Li Ma, Sangtae Ha, and S-H Gary Chan. 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Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset.", + "bbox": [ + 73, + 300, + 470, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available1.", + "bbox": [ + 75, + 481, + 468, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 720, + 207, + 736 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scene flow estimation [27] is a fundamental problem in computer vision with various use-cases, such as autonomous driving, scene parsing, pose estimation, and object tracking, to name a few. Given two consecutive observations of a 3D scene, the aim is to compute the dynamics of the scene between the observations. Scene flow prediction based on 2D images has been thoroughly investigated in the literature [17, 19, 28, 32, 33]. However, in light of the", + "bbox": [ + 75, + 744, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bce42a77079dac70b97a54467c894ef5e76783731facbe2b96c430c73521e2c7.jpg", + "image_caption": [ + "Figure 1. Flow accuracy on the KITTI benchmark vs. the train set size. Our method is trained on one or two orders of magnitude less data while surpassing the performance of the competing techniques [4, 13, 14, 16, 21, 24, 30, 31] by a large margin. Please see Table 1 for the complete details of the evaluation settings." + ], + "image_footnote": [], + "bbox": [ + 501, + 268, + 883, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "recent proliferation of 3D sensors, such as LiDAR, there is a surge of interest in scene flow methods that operate directly on the 3D data [10, 13, 16, 21, 34].", + "bbox": [ + 496, + 536, + 890, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Liu et al. [16] were among the first to pursue this research avenue. They proposed FlowNet3D, a fully-supervised neural network that learned to regress the flow between 3D point clouds and showed remarkable performance improvement over image-based techniques [1, 19, 29]. Since their method required ground-truth flow annotations, which are scarce for real-world data, they turned to training on a large synthetic dataset that compromised the generalization capability to real-world LiDAR data.", + "bbox": [ + 496, + 582, + 890, + 717 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Follow-up works devised self-supervised learning schemes [13, 21] and narrowed the domain gap by training on unannotated LiDAR point cloud pairs. However, similar to Liu et al. [16], they used a regression approach in which the model should learn to compute the flow in the free 3D space. This task is extremely challenging, given the irregular nature of point clouds, and requires a large amount of training data for the network to converge.", + "bbox": [ + 496, + 718, + 890, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In another line of work [8, 11, 24], researchers leveraged point cloud correspondence for scene flow prediction. In this approach, the flow is computed as the translation of a point in the first point cloud (source) to its softly corre", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://github.com/itailang/SCOOP", + "bbox": [ + 76, + 875, + 344, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The work was done during an internship at Google Research.", + "bbox": [ + 76, + 887, + 405, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5281", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c0a621e9eb17471535411910c52fbe536c008cf81f217eb156788d51a87b250.jpg", + "image_caption": [ + "Figure 2. Comparison of scene flow approaches. Given a pair of point clouds, FlowNet3D [16] learns to regress the flow in the free 3D space, and the trained model is frozen for testing. FLOT [24] concurrently trains two network components: one that computes point correspondence and another that regresses a correction to the resulting correspondence flow. Neural Prior [15] optimizes the flow between the point clouds from scratch without learning. In contrast to previous work, we take a hybrid approach. We train a pure correspondence model without flow regression, which serves for flow initialization. Then, we directly optimize only the flow refinement at the test-time." + ], + "image_footnote": [], + "bbox": [ + 91, + 87, + 880, + 202 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sponding point in the second one (target). The softly corresponding point is a weighted sum of target points based on point similarity in a learned latent space. Thus, rather than the challenging regression problem in the 3D ambient space, the flow estimation task boils down to point feature learning and is reduced to the convex combination space [26] of existing target points. However, to relax this constraint, another network component is trained to regress flow corrections. The joint training of point representation and flow refinement burdens the learning process and retains the reliance on large datasets with flow supervision.", + "bbox": [ + 75, + 304, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another emerging approach is an optimization-only flow computation [15, 23]. In this case, no training data is involved, and the flow is optimized at run-time for each scene separately. Despite the high accuracy such a dedicated optimization achieves, it requires a long processing time.", + "bbox": [ + 75, + 473, + 468, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We present SCOOP, a hybrid flow estimation method that can be learned from a small amount of training data. SCOOP consists of two parts: a self-supervised neural network for point cloud correspondence and a direct flow refinement optimization module. During the training phase, the network learns to extract point features for soft point matches, which initialize the flow between the point clouds. In contrast to previous work, our network is focused on learning just the point embeddings, allowing its training on a very small dataset, as shown in Figure 1. Additionally, we consider the confidence of the network in the computed correspondences to guide the learning process better.", + "bbox": [ + 75, + 550, + 470, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Then, instead of training another network for regressing flow updates, we define an optimization problem and directly optimize residual flow refinement vectors at runtime. The optimization objective encourages a coherent flow field while retaining the translated source points close to the target point cloud. Our design choices improve the accuracy compared to learning-based methods and reduce the processing time with respect to the optimization-only approach [15, 23]. For both correspondence learning and refinement optimization, we use a self-supervised distance objective and a smoothness prior instead of ground-truth", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "flow labels. Figure 2 presents the difference between our approach and leading previous ones.", + "bbox": [ + 498, + 304, + 890, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we propose a hybrid flow prediction approach for point clouds based on self-supervised correspondence learning and direct run-time residual flow optimization. Using well-established datasets in the scene flow literature, we show that our approach yields clear performance improvement over existing state-of-the-art methods while using a fraction of the training data and without employing any ground-truth flow supervision.", + "bbox": [ + 496, + 335, + 892, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 470, + 640, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Flow regression. A common approach for scene flow estimation on point clouds is to train a flow regression model [4,10,16,31,34]. It is a neural network that computes the flow vectors between the point clouds in the ambient 3D space. Liu et al. [16] proposed FlowNet3D, which encoded the point clouds into a latent space, mixed point features with a flow embedding layer, and regressed the scene flow by decoding the mixed point features. FlowNet3D was trained in a fully-supervised manner, using an $l_{2}$ loss with respect to ground-truth flow annotations.", + "bbox": [ + 496, + 497, + 890, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Liu et al. [16] inspired a line of follow-up works [4, 13, 21, 30, 31]. Wang et al. [31] added spatial and temporal attention layers to FlowNet3D's architecture. In Bi-PointFlowNet [4], the authors propagated features from each point cloud bidirectionally, augmenting the point feature representation. Mittal et al. [21] discarded flow supervision by utilizing a self-supervised nearest neighbor loss and cycle consistency between the forward and revers scene flows, and Li et al. [13, 14] extracted flow labels for training from the data itself. Similar to the latter methods, we also refrain from ground-truth flow supervision in our training scheme. However, rather than flow regression, we base our technique on soft point matches in the scene, which simplifies the flow estimation problem.", + "bbox": [ + 496, + 648, + 892, + 861 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point cloud correspondence. Finding correspondences is widely applied to various vision tasks [12, 24, 35, 37].", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5282", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several methods have been proposed for dense mapping between non-rigid point cloud shapes [7, 9, 12, 36]. Recently, Lang et al. [12] suggested constructing one point cloud by the other using latent space similarity and the point coordinates themselves rather than regressing the corresponding point cloud [9, 36]. Inspired by Lang's work, we do not use flow regression in our model and concentrate the learning process on point feature representation. However, while Lang et al. operated on complete shapes with one-to-one correspondence, our method accommodates scenes with partial objects where a perfect match may not exist.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Researchers have taken the correspondence approach to the scene flow problem as well [8, 11, 24]. FLOT [24] computed an optimal transport plan that served for an initial flow between the point clouds and further regressed flow refinement with a series of learned convolutions. Our work builds on FLOT but differs from it in three main aspects. First, we exclude flow regression from our training scheme and instead apply direct run-time optimization to refine the initial correspondence-based flow. Second, we use the model's confidence in the computed point matches to improve the point feature learning. Third, we do not use any groundtruth flow annotations, neither for the correspondence training nor for the refinement optimization, whereas FLOT relies on fully-supervised scene flow data.", + "bbox": [ + 75, + 258, + 472, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Optimization-based scene flow. Pontes et al. [23] suggested a scene flow estimation technique that does not involve learning. Instead, the flow was optimized completely at run-time, such that the warped source is close to the target point cloud while demanding the flow to be \"as-rigid-as-possible\". Pontes et al. encoded this prior by minimizing the graph Laplacian defined over the source points. In follow-up work [15], the explicit graph was replaced by a neural prior, which implicitly regularized the optimized flow field. In contrast to these papers, we initialize the flow with a learned correspondence model and optimize only the residual flow refinement at run-time.", + "bbox": [ + 75, + 479, + 472, + 661 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 676, + 169, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A point cloud is a set of unordered 3D points $X \\in \\mathbb{R}^{n \\times 3}$ , where $n$ is the number of points. Given a pair of point clouds of a scene, denoted as $X, Y \\in \\mathbb{R}^{n \\times 3}$ and referred to as source and target, respectively, our goal is to estimate a flow field $F^* \\in \\mathbb{R}^{n \\times 3}$ describing the per-point motion from $X$ to $Y$ .", + "bbox": [ + 75, + 702, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We tackle this problem via self-supervised soft correspondence learning between the two point clouds and a direct flow refinement optimization. An overview of the method is shown in Figure 3. First, a deep neural network is used to extract point features. Then, we calculate a matching cost between points in the learned feature space. Based on this cost, we solve an optimal transport", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "problem to compute a softly matched target point for each source point, where the difference between the two is regarded as the correspondence-based flow. Finally, we refine the flow field by demanding its consistency across neighboring source points and obtain our estimated scene flow. In both correspondence learning and flow refinement, no ground-truth flow labels are employed.", + "bbox": [ + 496, + 90, + 893, + 198 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Matching Cost", + "text_level": 1, + "bbox": [ + 498, + 204, + 650, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The cost of matching a point $x_{i} \\in X$ to a point $y_{j} \\in Y$ is determined based on the point representation learned by a deep neural network. The network consumes the raw point clouds $X, Y$ and computes point features $\\Phi_{X}, \\Phi_{Y} \\in \\mathbb{R}^{n \\times d}$ , where $d$ is the per-point feature dimension. The network's architecture is based on PointNet++ [25]. Its details are given in the supplemental material.", + "bbox": [ + 496, + 227, + 893, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by previous work [12, 13, 24], we first compute the cosine similarity in the learned feature space:", + "bbox": [ + 498, + 333, + 893, + 364 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i j} = \\frac {\\Phi_ {X} ^ {i} \\cdot \\left(\\Phi_ {Y} ^ {j}\\right) ^ {\\top}}{\\left| \\left| \\Phi_ {X} ^ {i} \\right| \\right| _ {2} \\left| \\left| \\Phi_ {Y} ^ {j} \\right| \\right| _ {2}}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 369, + 890, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Phi_X^i, \\Phi_Y^j \\in \\mathbb{R}^d$ are the $i$ 'th and $j$ 'th rows of $\\Phi_X$ and $\\Phi_Y$ , respectively. Then, the cost is set to", + "bbox": [ + 498, + 414, + 893, + 446 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i j} = 1 - S _ {i j} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 453, + 890, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for points with a Euclidean distance less than 10 meters and to $\\infty$ otherwise to avoid flow between points too far apart.", + "bbox": [ + 498, + 476, + 890, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Soft Correspondence", + "text_level": 1, + "bbox": [ + 498, + 513, + 697, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Finding correspondence between the source and target point clouds can be modeled as an optimal transport problem, where each source point is assigned with a mass $\\frac{1}{n}$ that is transported to the target points [13, 24]. Similar to FLOT [24], we use the relaxed transport problem:", + "bbox": [ + 496, + 537, + 893, + 614 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} T ^ {*} = \\underset {T \\in \\mathbb {R} _ {+} ^ {n \\times n}} {\\operatorname {a r g m i n}} \\sum_ {i j} \\left(C _ {i j} T _ {i j} + \\epsilon T _ {i j} (\\log T _ {i j} - 1)\\right) \\\\ + \\lambda (\\mathsf {K L} (T 1 _ {n}, \\frac {1}{n} 1 _ {n}) + \\mathsf {K L} (T ^ {\\top} 1 _ {n}, \\frac {1}{n} 1 _ {n})), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 619, + 844, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $C_{ij} \\geq 0$ is the matching cost from Equation 2 and $T_{ij} \\geq 0$ is the amount of mass transported between points. The parameters $\\epsilon, \\lambda \\geq 0$ control the relaxation of the problem. $1_n \\in \\mathbb{R}^n$ is a vector with all entries equal 1. KL is the Kullback-Leibler divergence used for soft preservation of the transported mass between the point clouds.", + "bbox": [ + 496, + 688, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The second term in the summation operation in Equation 3 is an entropic regularization, which enables solving the problem efficiently by the Sinkhorn algorithm [5,6]. We use this algorithm to estimate the optimal transport matrix $T^{*}$ from $C$ to represent the soft correspondence between the point clouds. The complete derivation of the transport problem and the Sinkhorn algorithm's details are given in the supplementary material.", + "bbox": [ + 496, + 780, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5283", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Correspondence-Based Flow", + "text_level": 1, + "bbox": [ + 76, + 90, + 331, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We leverage the optimal transport plan $T^{*}$ to compute correspondence weights for the source and target points for an initial estimate of the scene flow. Different from FLOT [24], which includes all the target points as candidates for each source point, we consider only target points with maximal transport amount from the source point. This design choice focuses our flow estimation pipeline on the most relevant target candidates and improves the method's results.", + "bbox": [ + 75, + 113, + 468, + 248 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For a point $x_{i} \\in X$ , the matching weights are calculated as follows:", + "bbox": [ + 76, + 250, + 468, + 277 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i j} = \\frac {e ^ {T _ {i j} ^ {*}}}{\\sum_ {l \\in \\mathcal {N} _ {Y} \\left(x _ {i}\\right)} e ^ {T _ {i l} ^ {*}}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 276, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_Y(x_i)$ is a neighborhood containing the $k_{s}$ indices of the $\\{y_j\\}$ points with the top mass transport $\\{T_{ij}^*\\}$ . The softly corresponding point $\\hat{y}_{x_i}$ to $x_{i}$ is:", + "bbox": [ + 76, + 321, + 468, + 368 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {Y} \\left(x _ {i}\\right)} w _ {i j} y _ {j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 378, + 468, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and the initial estimated flow for the point $x_{i}$ is:", + "bbox": [ + 76, + 424, + 393, + 439 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i} = \\hat {y} _ {x _ {i}} - x _ {i}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 452, + 468, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that if we define $\\widehat{T}_{ij}^{*} = w_{ij}$ for $j\\in \\mathcal{N}_Y(x_i)$ and 0 otherwise, we get the initial flow field as:", + "bbox": [ + 76, + 479, + 468, + 513 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF = \\widehat {T} ^ {*} Y - X = \\widehat {Y} - X, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 521, + 468, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\widehat{Y} \\in \\mathbb{R}^{n \\times 3}$ contains the points $\\{\\hat{y}_{x_i}\\}$ .", + "bbox": [ + 76, + 551, + 367, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Training Objective", + "text_level": 1, + "bbox": [ + 76, + 578, + 258, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To learn point representation suitable for scene flow without ground-truth supervision, we apply the flowing loss terms. First, for a tractable flow estimation, we would like each softly corresponding point $\\hat{y}_{x_i}$ to have a nearby target point $y_{j}$ . It may be achieved by the nearest-neighbor distance term, as done by Mittal et al. [21]:", + "bbox": [ + 75, + 602, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} \\min _ {y _ {j} \\in Y} \\| \\hat {y} _ {x _ {i}} - y _ {j} \\| _ {2} ^ {2}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 703, + 468, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the correspondence quality for the source points can vary. For example, points on a flat region will have less distinctive correspondences than points with geometrically unique features. Thus, we augment the distance term in Equation 8 with the matching confidence of each point.", + "bbox": [ + 75, + 751, + 468, + 827 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The confidence measure is based on the correspondence similarity that we define as:", + "bbox": [ + 76, + 827, + 468, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {Y} (x _ {i})} w _ {i j} S _ {i j}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 869, + 468, + 904 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7f533893eb5fb9cb282914d1e57b5880596150f2d36fc902bfbf07d388c05c4a.jpg", + "image_caption": [ + "Figure 3. The proposed method. SCOOP includes two components: a learned point cloud correspondence model and a flow refinement module. The model learns deep point embeddings $\\Phi_X, \\Phi_Y$ to establish soft point matches based on a matching cost $C$ in the latent space. The initial flow $F$ from the training phase is the difference between the softly corresponding point cloud $\\widehat{Y}$ and the source point cloud $X$ . At the test-time, we freeze the trained model and optimize a residual flow refinement $R^*$ to produce a smooth and consistent scene flow $F^*$ between the point clouds." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The value of $s_{x_i}$ is in the range $[-1, 1]$ . To get a confidence value between 0 and 1, we trim the negative values, set the matching confidence of $x_i$ to be $p_{x_i} = \\max(s_{x_i}, 0)$ , and use $p_{x_i}$ to define our confidence-aware distance loss:", + "bbox": [ + 498, + 454, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t}} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} p _ {x _ {i}} \\min _ {y _ {j} \\in Y} \\| \\hat {y} _ {x _ {i}} - y _ {j} \\| _ {2} ^ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 521, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The loss term $\\mathcal{L}_{dist}$ can be minimized by either minimizing $p_{x_i}$ or the distance between $\\hat{y}_{x_i}$ and its nearest neighbor $y_j\\in Y$ . To avoid the degenerate solution of $p_{x_i} = 0$ for all $x_{i}\\in X$ , we add a confidence loss term:", + "bbox": [ + 498, + 563, + 890, + 623 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n f}} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} 1 - p _ {x _ {i}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 601, + 628, + 890, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which penalizes the degenerate solution.", + "bbox": [ + 500, + 670, + 767, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Additionally, to preserve the geometric structure of the source point cloud, we would like the flow field to be smooth. That is, neighboring source points should have a similar flow prediction. Thus, we regularize the learning process with a flow smoothness loss [11]:", + "bbox": [ + 498, + 685, + 890, + 761 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f l o w}} = \\frac {1}{| X | k _ {f}} \\sum_ {x _ {i} \\in X} \\sum_ {l \\in N _ {X} \\left(x _ {i}\\right)} \\| f _ {i} - f _ {l} \\| _ {1}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 766, + 890, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N_{X}(x_{i})$ is the Euclidean neighborhood of $x_{i}$ in $X \\backslash x_{i}$ of size $k_{f}$ . The overall training objective is:", + "bbox": [ + 498, + 810, + 888, + 840 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d i s t}} + \\alpha_ {\\text {c o n f}} \\mathcal {L} _ {\\text {c o n f}} + \\alpha_ {\\text {f l o w}} \\mathcal {L} _ {\\text {f l o w}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 848, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{conf}$ and $\\alpha_{flow}$ are hyperparameters, balancing the contribution of the different loss terms.", + "bbox": [ + 498, + 869, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5284", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Flow Refinement Optimization", + "text_level": 1, + "bbox": [ + 76, + 90, + 349, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The advantage of the correspondence-based flow, presented in Equation 7, is that the softly matching points are in the vicinity of the surface of objects in the target scene. However, it limits the flow to the convex hull [26] of points in the target point cloud. We enable the flow to deviate from this constraint by a flow refinement optimization step at runtime.", + "bbox": [ + 75, + 113, + 468, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instead of training an additional neural network part to regress flow corrections, as done by Puy et al. [24], we directly optimize a flow refinement component $R^{*} \\in \\mathbb{R}^{n \\times 3}$ using the self-supervised distance and smoothness losses defined in Equations 10 and 12, respectively. An illustration of these losses is depicted in Figure 4.", + "bbox": [ + 75, + 219, + 468, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The optimization problem for the flow refinement takes the form:", + "bbox": [ + 75, + 310, + 468, + 339 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} R ^ {*} = \\operatorname * {a r g m i n} _ {R \\in \\mathbb {R} ^ {n \\times 3}} \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} \\min _ {y _ {j} \\in Y} p _ {x _ {i}} | | x _ {i} + (f _ {i} + r _ {i}) - y _ {j} | | _ {2} ^ {2} \\\\ + \\lambda_ {f l o w} \\frac {1}{| X | k _ {f}} \\sum_ {x _ {i} \\in X} \\sum_ {l \\in N _ {X} \\left(x _ {i}\\right)} \\left\\| \\left(f _ {i} + r _ {i}\\right) - \\left(f _ {l} + r _ {l}\\right) \\right\\| _ {1}, \\tag {14} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 347, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $r_i \\in R$ is the flow refinement for point $x_i$ , and the refined scene flow is $F^* = F + R^*$ . Our flow refinement module further preserves the structure of the source point cloud, where the target points $\\{y_j\\}$ are used as anchors to guide the refined flow and keep the proximity to the underlying target surface.", + "bbox": [ + 75, + 450, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 556, + 209, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate SCOOP's performance using widely spread datasets and compare it with recent state-of-the-art (SOTA) works on scene flow estimation. Additionally, we demonstrate the influence of the flow refinement module, analyze the performance and run-time duration, and verify our design choices with an ablation study.", + "bbox": [ + 75, + 580, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 681, + 266, + 698 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We adopt two common datasets in the scene flow literature, FlyingThings3D [18] and KITTI [19, 20]. Originally, these benchmarks did not include point cloud data. They were processed to a point cloud format by Liu et al. [16] and denoted as $\\mathrm{FT3D_o}$ and $\\mathrm{KITTI_o}$ , respectively.", + "bbox": [ + 75, + 704, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathrm{FT3D_o}$ is a large-scale synthetic dataset with 18,000/2,000 train/validation scene examples of randomly moving objects from the ShapeNet collection [3]. Each example contains a pair of point clouds and ground-truth flow vectors. Since the objects' motion is randomized, they may appear or disappear from the view of the scene and create occlusions. The dataset also includes a mask for points whose flow is invalid due to occlusions.", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/36a035cbc4cc88c32ed7335340ae30a589c9b40ce1885c6be217774e5e016b59.jpg", + "image_caption": [ + "Figure 4. Illustration of the flow refinement objective. The initial flow $\\{f_i\\}$ stems from the translation of the source points $\\{x_i\\}$ (red) to their softly corresponding ones $\\{\\hat{y}_{x_i}\\}$ (magenta). The flow is refined with a distance loss that keeps the proximity of the translated points to the target points $\\{y_j\\}$ (green) and a smoothness loss that encourages similar flow vectors (dashed purple) for neighboring points. The optimization process results in a flow field $\\{f_i^*\\}$ (blue) that preserves the structure of the source point cloud and warps it close to the implicit surface of the target point cloud." + ], + "image_footnote": [], + "bbox": [ + 504, + 94, + 890, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The $\\mathrm{KITTI_o}$ dataset contains 150 real-world LiDAR scenes. Every scene includes source and target point clouds with flow annotations for the source points. Ground points are removed, and the source points are considered to have a valid flow [16]. $\\mathrm{KITTI_o}$ was further split by Mittal et al. [21] into sets of 100 and 50 examples, marked as $\\mathrm{KITTI_v}$ and $\\mathrm{KITTI_t}$ , respectively, for fine-tuning experiments. Li et al. [13] also built a large unlabeled LiDAR dataset for self-supervised learning on real-world data. They took raw Li-DAR scans from the KITTI scenes [19,20], disjoint from the $\\mathrm{KITTI_o}$ data, and created a training set of 6,068 instances denoted as $\\mathrm{KITTI_r}$ .", + "bbox": [ + 496, + 349, + 890, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. We use well-established evaluation metrics from previous works [16, 21, 24]: End-Point-Error $EPE[m]$ , Strict Accuracy $AS[\\%]$ , Relaxed Accuracy $AR[\\%]$ , and Outliers $Out.[\\%]$ . These metrics are based on the point error $e_i$ and the relative error $e_i^{rel}$ :", + "bbox": [ + 498, + 537, + 890, + 613 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ne _ {i} = \\left\\| f _ {i} ^ {*} - f _ {i} ^ {g t} \\right\\| _ {2}, \\quad e _ {i} ^ {r e l} = \\frac {\\left\\| f _ {i} ^ {*} - f _ {i} ^ {g t} \\right\\| _ {2}}{\\left\\| f _ {i} ^ {g t} \\right\\| _ {2}}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 621, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $f_{i}^{*}$ and $f_{i}^{gt}$ are the predicted and ground-truth flow for point $x_{i}$ , respectively. The EPE is the average point error, measured in meters; $AS$ is the percentage of points whose $e_{i} < 0.05[m]$ or $e_{i}^{rel} < 5\\%$ ; $AR$ is the percentage of points for which $e_{i} < 0.1[m]$ or $e_{i}^{rel} < 10\\%$ ; and Out. is the percentage of points with $e_{i} > 0.3[m]$ or $e_{i}^{rel} > 10\\%$ .", + "bbox": [ + 496, + 666, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. SCOOP is implemented in PyTorch [22], where the publicly available PointNet++ [25] implementation is adapted for our point feature embedding. The model is trained on $n = 2,048$ points, sampled at random from the source and target point clouds of the scene examples. Only the 3D coordinates of the points are used as input to the model. The parameters $\\epsilon$ and $\\lambda$ from Equation 3 are defined as learnable variables and optimized as part of the learning process. The point feature", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5285", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/afd81a584301ecdf6ed3ff4900b014c3b7655e9f657c268c5cd6ba62cfe1f178.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSupervisionTrain dataTest dataEPE↓AS↑AR↑Out.↓
FlowNet3D [16]FullFT3Do(18,000)KITTIo0.17327.660.964.9
FLOT [24]FullFT3Do(18,000)KITTIo0.10745.174.046.3
FESTA [31]FullFT3Do(18,000)KITTIo0.09444.983.4-
3DFlow [30]FullFT3Do(18,000)KITTIo0.07381.989.026.1
BiPFN [4]FullFT3Do(18,000)KITTIo0.06576.990.626.4
SCOOP (ours)SelfFT3Do(1,800)KITTIo0.06379.791.024.4
SCOOP+(ours)SelfFT3Do(1,800)KITTIo0.04791.395.018.6
JGF [21]Full + Self + SelfFT3Do(18,000) + nuScenes (700) + KITTIv(100)KITTIt0.10546.579.4-
SPF [13]Self + SelfKITTIr(6,068) + KITTIv(100)KITTIt0.08941.775.0-
RigidFlow [14]SelfKITTIr(6,068)KITTIt0.11738.869.7-
SCOOP (ours)SelfKITTIv(100)KITTIt0.05280.692.919.7
Graph Prior [23]SelfN/A (optimization-only)KITTIt0.08284.088.5-
Neural Prior [15]SelfN/A (optimization-only)KITTIt0.03692.396.2-
SCOOP+(ours)SelfKITTIv(100)KITTIt0.03993.696.515.2
", + "bbox": [ + 81, + 88, + 890, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison. We compare scene flow evaluation metrics for different supervision settings, train data, and test data. The number of training examples is indicated in parentheses. $EPE$ , $AS$ , $AR$ , and $Out$ . stand for End-Point-Error, Strict Accuracy, Relaxed Accuracy, and Outliers, respectively. The symbol $^+$ indicates an evaluation using all the points in the test point clouds, as done for the optimization-only methods [15, 23]. While other baselines apply fully-supervised training, our method yields better performance without employing ground-truth flow labels. Besides, SCOOP can be trained only on $\\mathrm{KITTI_v}$ , with as few as 100 training instances. In contrast, alternative learning-based methods use additional training data, such as nuScenes, or a large dataset, such as $\\mathrm{KITTI_r}$ . Please see further details in subsections 4.1 and 4.2.", + "bbox": [ + 75, + 335, + 892, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dimension is $d = 128$ . For the neighborhood sizes we use $k_{s} = 64$ , $k_{f} = 32$ , and the losses' hyperparameters are set to $\\alpha_{conf} = 0.1$ , $\\alpha_{flow} = 10$ .", + "bbox": [ + 75, + 460, + 468, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As in previous work [14, 16, 21, 24], we evaluate SCOOP on point clouds of 2,048 points randomly sampled from the source and target. However, the full point clouds of $\\mathrm{KITTI_o}$ and $\\mathrm{KITTI_t}$ are an order of magnitude larger and have different cardinality. Thus, for a complete evaluation of the entire scene flow, we also utilize our method (denoted as $\\mathrm{SCOOP^{+}}$ for this case) to exploit the whole point cloud information and test the performance for the original resolution. Additional implementation details appear in the supplementary.", + "bbox": [ + 75, + 506, + 468, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Baseline methods.** Our method is contrasted with the recent methods FlowNet3D [16], FLOT [24], FESTA [31], 3DFlow [30], and BiPFN [4]. These methods require ground-truth flow supervision. Additionally, we compare our results with the recent self-supervised flow models of Mittal et al. [21] and Li et al. [13,14], and the optimization-based techniques Graph Prior [23] and Neural Prior [15].", + "bbox": [ + 75, + 652, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Scene Flow Results", + "text_level": 1, + "bbox": [ + 76, + 770, + 261, + 786 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cross-dataset evaluation. We demonstrate the generalization power of SCOOP by training it on the $\\mathrm{FT3D_o}$ and testing its performance on $\\mathrm{KITTI_o}$ . Table 1 summarises the results. The alternative methods [4, 16, 24, 30, 31] are trained on $\\mathrm{FT3D_o}$ in a fully-supervised fashion: their models are learned with the ground-truth flow information, and the points with an occluded flow are excluded from the", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "training objective using the mask provided in the dataset.", + "bbox": [ + 498, + 460, + 875, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In contrast, our model is trained in a completely self-supervised manner. We assume no knowledge of the flow annotations nor the occlusion mask and do not use them in our losses. Additionally, we use only 1,800 randomly selected examples from $\\mathrm{FT3D_o}$ , while the competitors employ all 18,000 scene instances. Still, SCOOP improves over the SOTA method BiPFN [4] in all the evaluation metrics. Moreover, utilizing the entire point cloud data further increases our performance.", + "bbox": [ + 496, + 476, + 890, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FlowNet3D [16], FESTA [31], 3DFlow [30], and BiPFN [4] are regression-based networks that predict the flow in the 3D ambient space. The models adapt to the characteristics of the synthetic training set, and the generalization to the real-world test data is limited. FLOT [24] leverages point cloud correspondence based on learned point features, which eases the flow prediction problem. However, it also jointly learns to regress a flow correction component that burdens the point representation training process.", + "bbox": [ + 496, + 611, + 892, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SCOOP, on the other hand, is focused only on learning point embeddings suitable for scene flow estimation, guided by our self-supervised losses. It extracts discriminative features, which transfer well across the $\\mathrm{FT3D_o}$ and $\\mathrm{KITTI_o}$ datasets, and enables to compute the correspondence-based flow between the point clouds. In contrast to FLOT, we delegate the flow refinement process to the test phase, directly optimize it in a self-supervised fashion, and surpass their flow estimation performance.", + "bbox": [ + 496, + 750, + 893, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 5 shows a visual comparison between the results", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5286", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/38465836362c175ccc4816d298dc607ec7bfa981fd3ad0a12ca9b34abe8eaecc.jpg", + "image_caption": [ + "Figure 5. Visual comparison of scene flow results for a KITTI $_0$ example scene. The training was done on the FT3D $_0$ dataset. The source and target point clouds are shown in red and green, respectively. The warped source point cloud by FLOT [24] (left) and by our method (right) is presented in blue. While the result of FLOT deviates from the surface of the target, SCOOP preserves the source point cloud's structure and computes its accurate flow." + ], + "image_footnote": [], + "bbox": [ + 98, + 85, + 491, + 354 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d8467e44bf3f5e591eba4911726529bbd0f6bd230d45b2625311015dfdcefd4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 85, + 870, + 354 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of FLOT and our method. The warped source point cloud by FLOT is noisy, and the structure of objects in the scene is compromised. On the contrary, SCOOP produces a coherent flow field across neighboring points, preserves their local geometry, and accurately predicts the scene flow. Additional visualizations are presented in the supplementary.", + "bbox": [ + 75, + 444, + 468, + 535 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training on a small dataset. Since our model does not include a flow regression component and has to learn only point features, it can be trained on a very limited amount of data. To demonstrate this ability, we train it from scratch on the 100 point cloud pairs of $\\mathrm{KITTI_v}$ and use $\\mathrm{KITTI_t}$ for testing. The results of this experiment are presented in Table 1.", + "bbox": [ + 75, + 547, + 468, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different from our work, the competing methods of Mittal et al. [21] and Li et al. [13, 14] are based on flow regression and require a large amount of training data. Mittal et al. utilize a fully-supervised pre-training on $\\mathrm{FT3D_o}$ , and the additional outdoor flow dataset nuScenes [2], before fin-tuning on $\\mathrm{KITTI_v}$ . Li et al. [13, 14] train their model on the large $\\mathrm{KITTI_r}$ dataset. Our SCOOP outperforms these other methods while being trained only on $\\mathrm{KITTI_v}$ , which is almost two orders of magnitudes smaller than $\\mathrm{KITTI_r}$ .", + "bbox": [ + 75, + 641, + 468, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The pure optimization methods [15, 23] find the solution per scene separately, which might lead to sub-optimal local minima. In contrast, we leverage the correspondence statistics learned from the data and adapt the initial flow to the scene at hand by our residual run-time optimization. The initial correspondence flow serves as a good starting point for the optimization phase, yielding a similar or better final result compared to the optimization-only alternatives.", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The influence of flow refinement. Our flow results before and after refinement are presented in Figure 6. Posing the learning part of SCOOP as a correspondence problem enables its effective training on a small dataset. However, the flow predictions from the training phase are confined to a linear combination of existing target points, which may not represent the exact flow of the scene. Moreover, wrong matches for the source points can occur and cause flow errors. In such cases, our refinement module comes into play.", + "bbox": [ + 496, + 444, + 890, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the output flow from the trained correspondence model, the refinement module optimizes correction vectors subject to two objectives: a warped source point should be close to a target point; neighboring source points should have a similar flow. These objectives help fixing inconsistencies in the flow field and increase the flow accuracy. As seen in Figure 6, our refinement step improves the initial flow estimation and results in an accurate flow field, which is similar to the ground-truth scene flow.", + "bbox": [ + 496, + 580, + 890, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Performance and Time Analysis", + "text_level": 1, + "bbox": [ + 500, + 726, + 782, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We analyze the performance-time trade-off in Figure 7 by recording the $EPE$ and inference time for different methods. The measurements were done on an Nvidia Titan Xp GPU for computing the flow for complete point clouds of the $\\mathrm{KITTI_t}$ dataset.", + "bbox": [ + 496, + 750, + 890, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network-only methods [13, 14, 21] tend to be fast but with limited accuracy. Optimizing the flow prediction separately for each scene [15] results in a low $EPE$ . However, it takes a long time. Our hybrid method bridges the trade-off gap between these two approaches. $\\mathrm{SCOOP}^{+}$ offers a work-", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5287", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e49e6035a237e4a4d3af4748748f9527e50d1fac325d1118ade3002e0a440da8.jpg", + "image_caption": [ + "Figure 6. The flow refinement effect. We demonstrate the effect on data from $\\mathrm{KITTI}_{\\mathrm{t}}$ . The source point cloud is in red, and the target is in green. Our correspondence model was trained on the $\\mathrm{KITTI}_{\\mathrm{v}}$ dataset, and its flow estimation before refinement is shown in magenta (left). The optimized refined flow is presented in blue (center). We also show the ground-truth scene flow in purple for reference (right). The refined flow better covers the target point cloud (top center ellipse). It also breaches the convex hull of the given target points and enables computing the correct flow for source points whose target is missing (bottom center ellipse)." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 205, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7e11abd9b177023434aa35d0bad63efb5e60331603e61c981ce4032b1b18a083.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 88, + 330, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/91d248c33792d98da1d61724ec5893643a8cbf76779934fcdf73f5f18ffb7a69.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 88, + 459, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing point with more than $50\\%$ error reduction over the feedforward models and about $8\\times$ faster inference time than the optimization-only Neural Prior work. $\\mathrm{SCOOP^{+}}$ also enables a different balance between time and performance, as seen in Figure 7. By reducing the number of run-time optimization steps, the user can shorten the inference time, achieving a working point closer to that of the network-only models.", + "bbox": [ + 75, + 460, + 468, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 575, + 230, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The design choices in our method are verified by ablation experiments presented in Table 2. We change one element each time and keep all the others the same. The following ablative settings were examined: (a) use all target points for soft correspondence instead of the ones with the highest transport amount (Equation 5); (b) ignore the point matching confidence by setting $p_{x_i} = 1$ in Equation 10 and $\\alpha_{conf} = 0$ in Equation 13; (c) exclude the smoothness flow loss $\\mathcal{L}_{flow}$ from Equation 13; and (d) turn off the flow refinement module.", + "bbox": [ + 75, + 598, + 468, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The ablation study validates the contribution of the proposed components to the method's performance. Considering a subset of target points for correspondence enables the model to concentrate on the most relevant candidates for flow estimation. The matching confidence emphasizes the influence of the more confident points in our confidence-aware distance loss $\\mathcal{L}_{dist}$ . The smoothness loss term is important for regularizing the point representation learning to obtain similar features across neighboring points. Lastly, our flow refinement optimization improves the consistency", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0964de2f15a5a6a40ee68454998e10d126bb51941660d994e52b51f33c11a47f.jpg", + "image_caption": [ + "Figure 7. Flow estimation error vs. inference time for the KITTI dataset. $\\mathrm{SCOOP^{+}}$ has a lower error than the network-only models and a shorter inference time than the optimization-only methods. It also allows different balances along the error and time trade-off, as presented by the blue curve." + ], + "image_footnote": [], + "bbox": [ + 508, + 93, + 883, + 251 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/129c171aa9422125be1ae066a2216a6fc2e37549e56b7bd16126537b06a9e2ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SettingEPE↓AS↑
(a) All target points as candidates (ks = n)0.04791.1
(b) W/O confidence (pxi = 1, αconf = 0)0.04490.3
(c) W/O smoothness loss term (αflow = 0)0.05686.6
(d) W/O flow refinement (R* = 0)0.11543.8
Our complete method0.03993.6
", + "bbox": [ + 504, + 349, + 888, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Component ablative settings. SCOOP was trained on $\\mathrm{KITTI_v}$ and evaluated on $\\mathrm{KITTI_t}$ . The results show that the best performance is obtained with our complete method. Additional details about the ablation experiments are given in subsection 4.4.", + "bbox": [ + 498, + 460, + 892, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of the flow field and reduces the $EPE$ substantially. In the supplementary material, we provide an ablation study on the $\\mathrm{FT3D_o}$ train set size and find that a $10\\%$ fraction of the data suffices for our method to realize its potential.", + "bbox": [ + 498, + 542, + 890, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 618, + 627, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presented SCOOP, a novel self-supervised scene flow estimation method for 3D point clouds based on correspondence learning and flow refinement optimization. Previous works suggested learning a flow regression model, training a neural network that jointly learned point cloud correspondence and flow refinement, or optimizing the flow completely at run-time without learning.", + "bbox": [ + 496, + 643, + 893, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In contrast, we split the flow prediction process into two simpler problems. Our correspondence model is focused only on learning point features to initialize the flow from soft matches between the point clouds. Then, we directly optimize a residual flow refinement at run-time. This approach enables SCOOP to be trained on a small set of point cloud scenes without utilizing ground-truth supervision while outperforming state-of-the-art fully-supervised and self-supervised learning methods, as well as optimization-based alternative techniques.", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5288", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Thomas Brox and Jitendra Malik. Large Displacement Optical Flow: Descriptor Matching in Variational Motion Estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(3):500-513, 2011. 1", + "[2] Holger Caesar, Varun Bankiti, Alex H. 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FESTA: Flow Estimation via Spatial-Temporal Attention for Scene Point Clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 14173-14182, 2021. 1, 2, 6", + "[32] Andreas Wedel, Thomas Brox, Tobi Vaudrey, Clemens Rabe, Uwe Franke, and Daniel Cremers. Stereoscopic Scene Flow Computation for 3D Motion Understanding. International Journal of Computer Vision, 95:29-51, 2011. 1", + "[33] Andreas Wedel, Clemens Rabe, Tobi Vaudrey, Thomas Brox, Uwe Franke, and Daniel Cremers. Efficient Dense Scene Flow from Sparse or Dense Stereo Data. In David Forsyth, Philip Torr, and Andrew Zisserman, editors, Proceedings of the Seventh IEEE International Conference on Computer Vision (ECCV), pages 739-751, Berlin, Heidelberg, 2008. Springer Berlin Heidelberg. 1", + "[34] Wenxuan Wu, Zhi Yuan Wang, Zhuwen Li, Wei Liu, and Li Fuxin. PointPWC-Net: Cost Volume on Point Clouds for (Self-) Supervised Scene Flow Estimation. 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In Advances in Neural Information Processing Systems (NeurIPS), 2022. 2" + ], + "bbox": [ + 78, + 92, + 467, + 892 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5290", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/2d0fc651-4e0b-4b27-8a33-61605dae5a3b_model.json b/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/2d0fc651-4e0b-4b27-8a33-61605dae5a3b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5c2725413f8217fbdb9e2c402bdb3b7779abccb8 --- /dev/null +++ b/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/2d0fc651-4e0b-4b27-8a33-61605dae5a3b_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.088, + 0.131, + 0.882, + 0.153 + ], + "angle": 0, + "content": "SCOOP: Self-Supervised Correspondence and Optimization-Based Scene Flow" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.179, + 0.208, + 0.2 + ], + "angle": 0, + "content": "Itai Lang\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.248, + 0.181, + 0.346, + 0.199 + ], + "angle": 0, + "content": "Dror Aiger2" + }, + { + "type": "text", + "bbox": [ + 0.387, + 0.182, + 0.51, + 0.198 + ], + "angle": 0, + "content": "Forrester Cole" + }, + { + "type": "text", + "bbox": [ + 0.551, + 0.181, + 0.657, + 0.197 + ], + "angle": 0, + "content": "Shai Avidan" + }, + { + "type": "text", + "bbox": [ + 0.698, + 0.182, + 0.862, + 0.197 + ], + "angle": 0, + "content": "Michael Rubinstein2" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.199, + 0.475, + 0.217 + ], + "angle": 0, + "content": "1Tel Aviv University" + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.199, + 0.66, + 0.217 + ], + "angle": 0, + "content": "2Google Research" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.22, + 0.471, + 0.234 + ], + "angle": 0, + "content": "{itailang@mail, avidan@eng}.tau.ac.il" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.22, + 0.806, + 0.234 + ], + "angle": 0, + "content": "{aigerd, fcole, mrub}@google.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.313, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.301, + 0.471, + 0.481 + ], + "angle": 0, + "content": "Scene flow estimation is a long-standing problem in computer vision, where the goal is to find the 3D motion of a scene from its consecutive observations. Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.47, + 0.693 + ], + "angle": 0, + "content": "We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.721, + 0.208, + 0.737 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Scene flow estimation [27] is a fundamental problem in computer vision with various use-cases, such as autonomous driving, scene parsing, pose estimation, and object tracking, to name a few. Given two consecutive observations of a 3D scene, the aim is to compute the dynamics of the scene between the observations. Scene flow prediction based on 2D images has been thoroughly investigated in the literature [17, 19, 28, 32, 33]. However, in light of the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.27, + 0.885, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.439, + 0.892, + 0.509 + ], + "angle": 0, + "content": "Figure 1. Flow accuracy on the KITTI benchmark vs. the train set size. Our method is trained on one or two orders of magnitude less data while surpassing the performance of the competing techniques [4, 13, 14, 16, 21, 24, 30, 31] by a large margin. Please see Table 1 for the complete details of the evaluation settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.581 + ], + "angle": 0, + "content": "recent proliferation of 3D sensors, such as LiDAR, there is a surge of interest in scene flow methods that operate directly on the 3D data [10, 13, 16, 21, 34]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Liu et al. [16] were among the first to pursue this research avenue. They proposed FlowNet3D, a fully-supervised neural network that learned to regress the flow between 3D point clouds and showed remarkable performance improvement over image-based techniques [1, 19, 29]. Since their method required ground-truth flow annotations, which are scarce for real-world data, they turned to training on a large synthetic dataset that compromised the generalization capability to real-world LiDAR data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Follow-up works devised self-supervised learning schemes [13, 21] and narrowed the domain gap by training on unannotated LiDAR point cloud pairs. However, similar to Liu et al. [16], they used a regression approach in which the model should learn to compute the flow in the free 3D space. This task is extremely challenging, given the irregular nature of point clouds, and requires a large amount of training data for the network to converge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In another line of work [8, 11, 24], researchers leveraged point cloud correspondence for scene flow prediction. In this approach, the flow is computed as the translation of a point in the first point cloud (source) to its softly corre" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.346, + 0.888 + ], + "angle": 0, + "content": "1https://github.com/itailang/SCOOP" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.888, + 0.406, + 0.9 + ], + "angle": 0, + "content": "*The work was done during an internship at Google Research." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.875, + 0.406, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5281" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.088, + 0.881, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.208, + 0.896, + 0.28 + ], + "angle": 0, + "content": "Figure 2. Comparison of scene flow approaches. Given a pair of point clouds, FlowNet3D [16] learns to regress the flow in the free 3D space, and the trained model is frozen for testing. FLOT [24] concurrently trains two network components: one that computes point correspondence and another that regresses a correction to the resulting correspondence flow. Neural Prior [15] optimizes the flow between the point clouds from scratch without learning. In contrast to previous work, we take a hybrid approach. We train a pure correspondence model without flow regression, which serves for flow initialization. Then, we directly optimize only the flow refinement at the test-time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.472 + ], + "angle": 0, + "content": "sponding point in the second one (target). The softly corresponding point is a weighted sum of target points based on point similarity in a learned latent space. Thus, rather than the challenging regression problem in the 3D ambient space, the flow estimation task boils down to point feature learning and is reduced to the convex combination space [26] of existing target points. However, to relax this constraint, another network component is trained to regress flow corrections. The joint training of point representation and flow refinement burdens the learning process and retains the reliance on large datasets with flow supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.55 + ], + "angle": 0, + "content": "Another emerging approach is an optimization-only flow computation [15, 23]. In this case, no training data is involved, and the flow is optimized at run-time for each scene separately. Despite the high accuracy such a dedicated optimization achieves, it requires a long processing time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.471, + 0.734 + ], + "angle": 0, + "content": "We present SCOOP, a hybrid flow estimation method that can be learned from a small amount of training data. SCOOP consists of two parts: a self-supervised neural network for point cloud correspondence and a direct flow refinement optimization module. During the training phase, the network learns to extract point features for soft point matches, which initialize the flow between the point clouds. In contrast to previous work, our network is focused on learning just the point embeddings, allowing its training on a very small dataset, as shown in Figure 1. Additionally, we consider the confidence of the network in the computed correspondences to guide the learning process better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Then, instead of training another network for regressing flow updates, we define an optimization problem and directly optimize residual flow refinement vectors at runtime. The optimization objective encourages a coherent flow field while retaining the translated source points close to the target point cloud. Our design choices improve the accuracy compared to learning-based methods and reduce the processing time with respect to the optimization-only approach [15, 23]. For both correspondence learning and refinement optimization, we use a self-supervised distance objective and a smoothness prior instead of ground-truth" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.305, + 0.892, + 0.335 + ], + "angle": 0, + "content": "flow labels. Figure 2 presents the difference between our approach and leading previous ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.893, + 0.457 + ], + "angle": 0, + "content": "In summary, we propose a hybrid flow prediction approach for point clouds based on self-supervised correspondence learning and direct run-time residual flow optimization. Using well-established datasets in the scene flow literature, we show that our approach yields clear performance improvement over existing state-of-the-art methods while using a fraction of the training data and without employing any ground-truth flow supervision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.472, + 0.642, + 0.487 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.649 + ], + "angle": 0, + "content": "Flow regression. A common approach for scene flow estimation on point clouds is to train a flow regression model [4,10,16,31,34]. It is a neural network that computes the flow vectors between the point clouds in the ambient 3D space. Liu et al. [16] proposed FlowNet3D, which encoded the point clouds into a latent space, mixed point features with a flow embedding layer, and regressed the scene flow by decoding the mixed point features. FlowNet3D was trained in a fully-supervised manner, using an \\(l_{2}\\) loss with respect to ground-truth flow annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.893, + 0.862 + ], + "angle": 0, + "content": "Liu et al. [16] inspired a line of follow-up works [4, 13, 21, 30, 31]. Wang et al. [31] added spatial and temporal attention layers to FlowNet3D's architecture. In Bi-PointFlowNet [4], the authors propagated features from each point cloud bidirectionally, augmenting the point feature representation. Mittal et al. [21] discarded flow supervision by utilizing a self-supervised nearest neighbor loss and cycle consistency between the forward and revers scene flows, and Li et al. [13, 14] extracted flow labels for training from the data itself. Similar to the latter methods, we also refrain from ground-truth flow supervision in our training scheme. However, rather than flow regression, we base our technique on soft point matches in the scene, which simplifies the flow estimation problem." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Point cloud correspondence. Finding correspondences is widely applied to various vision tasks [12, 24, 35, 37]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5282" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "Several methods have been proposed for dense mapping between non-rigid point cloud shapes [7, 9, 12, 36]. Recently, Lang et al. [12] suggested constructing one point cloud by the other using latent space similarity and the point coordinates themselves rather than regressing the corresponding point cloud [9, 36]. Inspired by Lang's work, we do not use flow regression in our model and concentrate the learning process on point feature representation. However, while Lang et al. operated on complete shapes with one-to-one correspondence, our method accommodates scenes with partial objects where a perfect match may not exist." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.259, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Researchers have taken the correspondence approach to the scene flow problem as well [8, 11, 24]. FLOT [24] computed an optimal transport plan that served for an initial flow between the point clouds and further regressed flow refinement with a series of learned convolutions. Our work builds on FLOT but differs from it in three main aspects. First, we exclude flow regression from our training scheme and instead apply direct run-time optimization to refine the initial correspondence-based flow. Second, we use the model's confidence in the computed point matches to improve the point feature learning. Third, we do not use any groundtruth flow annotations, neither for the correspondence training nor for the refinement optimization, whereas FLOT relies on fully-supervised scene flow data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.473, + 0.662 + ], + "angle": 0, + "content": "Optimization-based scene flow. Pontes et al. [23] suggested a scene flow estimation technique that does not involve learning. Instead, the flow was optimized completely at run-time, such that the warped source is close to the target point cloud while demanding the flow to be \"as-rigid-as-possible\". Pontes et al. encoded this prior by minimizing the graph Laplacian defined over the source points. In follow-up work [15], the explicit graph was replaced by a neural prior, which implicitly regularized the optimized flow field. In contrast to these papers, we initialize the flow with a learned correspondence model and optimize only the residual flow refinement at run-time." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.678, + 0.17, + 0.693 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.794 + ], + "angle": 0, + "content": "A point cloud is a set of unordered 3D points \\(X \\in \\mathbb{R}^{n \\times 3}\\), where \\(n\\) is the number of points. Given a pair of point clouds of a scene, denoted as \\(X, Y \\in \\mathbb{R}^{n \\times 3}\\) and referred to as source and target, respectively, our goal is to estimate a flow field \\(F^* \\in \\mathbb{R}^{n \\times 3}\\) describing the per-point motion from \\(X\\) to \\(Y\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We tackle this problem via self-supervised soft correspondence learning between the two point clouds and a direct flow refinement optimization. An overview of the method is shown in Figure 3. First, a deep neural network is used to extract point features. Then, we calculate a matching cost between points in the learned feature space. Based on this cost, we solve an optimal transport" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.199 + ], + "angle": 0, + "content": "problem to compute a softly matched target point for each source point, where the difference between the two is regarded as the correspondence-based flow. Finally, we refine the flow field by demanding its consistency across neighboring source points and obtain our estimated scene flow. In both correspondence learning and flow refinement, no ground-truth flow labels are employed." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.205, + 0.651, + 0.221 + ], + "angle": 0, + "content": "3.1. Matching Cost" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.894, + 0.333 + ], + "angle": 0, + "content": "The cost of matching a point \\( x_{i} \\in X \\) to a point \\( y_{j} \\in Y \\) is determined based on the point representation learned by a deep neural network. The network consumes the raw point clouds \\( X, Y \\) and computes point features \\( \\Phi_{X}, \\Phi_{Y} \\in \\mathbb{R}^{n \\times d} \\), where \\( d \\) is the per-point feature dimension. The network's architecture is based on PointNet++ [25]. Its details are given in the supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.334, + 0.894, + 0.365 + ], + "angle": 0, + "content": "Inspired by previous work [12, 13, 24], we first compute the cosine similarity in the learned feature space:" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.37, + 0.892, + 0.409 + ], + "angle": 0, + "content": "\\[\nS _ {i j} = \\frac {\\Phi_ {X} ^ {i} \\cdot \\left(\\Phi_ {Y} ^ {j}\\right) ^ {\\top}}{\\left| \\left| \\Phi_ {X} ^ {i} \\right| \\right| _ {2} \\left| \\left| \\Phi_ {Y} ^ {j} \\right| \\right| _ {2}}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.415, + 0.894, + 0.447 + ], + "angle": 0, + "content": "where \\(\\Phi_X^i, \\Phi_Y^j \\in \\mathbb{R}^d\\) are the \\(i\\)'th and \\(j\\)'th rows of \\(\\Phi_X\\) and \\(\\Phi_Y\\), respectively. Then, the cost is set to" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.454, + 0.892, + 0.471 + ], + "angle": 0, + "content": "\\[\nC _ {i j} = 1 - S _ {i j} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.477, + 0.892, + 0.508 + ], + "angle": 0, + "content": "for points with a Euclidean distance less than 10 meters and to \\(\\infty\\) otherwise to avoid flow between points too far apart." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.515, + 0.698, + 0.531 + ], + "angle": 0, + "content": "3.2. Soft Correspondence" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.894, + 0.615 + ], + "angle": 0, + "content": "Finding correspondence between the source and target point clouds can be modeled as an optimal transport problem, where each source point is assigned with a mass \\(\\frac{1}{n}\\) that is transported to the target points [13, 24]. Similar to FLOT [24], we use the relaxed transport problem:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.621, + 0.845, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} T ^ {*} = \\underset {T \\in \\mathbb {R} _ {+} ^ {n \\times n}} {\\operatorname {a r g m i n}} \\sum_ {i j} \\left(C _ {i j} T _ {i j} + \\epsilon T _ {i j} (\\log T _ {i j} - 1)\\right) \\\\ + \\lambda (\\mathsf {K L} (T 1 _ {n}, \\frac {1}{n} 1 _ {n}) + \\mathsf {K L} (T ^ {\\top} 1 _ {n}, \\frac {1}{n} 1 _ {n})), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.78 + ], + "angle": 0, + "content": "where \\( C_{ij} \\geq 0 \\) is the matching cost from Equation 2 and \\( T_{ij} \\geq 0 \\) is the amount of mass transported between points. The parameters \\( \\epsilon, \\lambda \\geq 0 \\) control the relaxation of the problem. \\( 1_n \\in \\mathbb{R}^n \\) is a vector with all entries equal 1. KL is the Kullback-Leibler divergence used for soft preservation of the transported mass between the point clouds." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.902 + ], + "angle": 0, + "content": "The second term in the summation operation in Equation 3 is an entropic regularization, which enables solving the problem efficiently by the Sinkhorn algorithm [5,6]. We use this algorithm to estimate the optimal transport matrix \\( T^{*} \\) from \\( C \\) to represent the soft correspondence between the point clouds. The complete derivation of the transport problem and the Sinkhorn algorithm's details are given in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5283" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.333, + 0.108 + ], + "angle": 0, + "content": "3.3. Correspondence-Based Flow" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.249 + ], + "angle": 0, + "content": "We leverage the optimal transport plan \\( T^{*} \\) to compute correspondence weights for the source and target points for an initial estimate of the scene flow. Different from FLOT [24], which includes all the target points as candidates for each source point, we consider only target points with maximal transport amount from the source point. This design choice focuses our flow estimation pipeline on the most relevant target candidates and improves the method's results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.251, + 0.47, + 0.278 + ], + "angle": 0, + "content": "For a point \\( x_{i} \\in X \\), the matching weights are calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.277, + 0.47, + 0.317 + ], + "angle": 0, + "content": "\\[\nw _ {i j} = \\frac {e ^ {T _ {i j} ^ {*}}}{\\sum_ {l \\in \\mathcal {N} _ {Y} \\left(x _ {i}\\right)} e ^ {T _ {i l} ^ {*}}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.322, + 0.47, + 0.369 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_Y(x_i)\\) is a neighborhood containing the \\(k_{s}\\) indices of the \\(\\{y_j\\}\\) points with the top mass transport \\(\\{T_{ij}^*\\}\\). The softly corresponding point \\(\\hat{y}_{x_i}\\) to \\(x_{i}\\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.379, + 0.47, + 0.415 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {Y} \\left(x _ {i}\\right)} w _ {i j} y _ {j}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.425, + 0.395, + 0.44 + ], + "angle": 0, + "content": "and the initial estimated flow for the point \\( x_{i} \\) is:" + }, + { + "type": "equation", + "bbox": [ + 0.222, + 0.453, + 0.469, + 0.469 + ], + "angle": 0, + "content": "\\[\nf _ {i} = \\hat {y} _ {x _ {i}} - x _ {i}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.481, + 0.469, + 0.514 + ], + "angle": 0, + "content": "Note that if we define \\(\\widehat{T}_{ij}^{*} = w_{ij}\\) for \\(j\\in \\mathcal{N}_Y(x_i)\\) and 0 otherwise, we get the initial flow field as:" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.522, + 0.469, + 0.543 + ], + "angle": 0, + "content": "\\[\nF = \\widehat {T} ^ {*} Y - X = \\widehat {Y} - X, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.552, + 0.369, + 0.571 + ], + "angle": 0, + "content": "where \\(\\widehat{Y} \\in \\mathbb{R}^{n \\times 3}\\) contains the points \\(\\{\\hat{y}_{x_i}\\}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.579, + 0.259, + 0.596 + ], + "angle": 0, + "content": "3.4. Training Objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.469, + 0.693 + ], + "angle": 0, + "content": "To learn point representation suitable for scene flow without ground-truth supervision, we apply the flowing loss terms. First, for a tractable flow estimation, we would like each softly corresponding point \\(\\hat{y}_{x_i}\\) to have a nearby target point \\(y_{j}\\). It may be achieved by the nearest-neighbor distance term, as done by Mittal et al. [21]:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.704, + 0.469, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} \\min _ {y _ {j} \\in Y} \\| \\hat {y} _ {x _ {i}} - y _ {j} \\| _ {2} ^ {2}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.752, + 0.469, + 0.828 + ], + "angle": 0, + "content": "However, the correspondence quality for the source points can vary. For example, points on a flat region will have less distinctive correspondences than points with geometrically unique features. Thus, we augment the distance term in Equation 8 with the matching confidence of each point." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.828, + 0.469, + 0.858 + ], + "angle": 0, + "content": "The confidence measure is based on the correspondence similarity that we define as:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.87, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\ns _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {Y} (x _ {i})} w _ {i j} S _ {i j}. \\tag {9}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.891, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.308, + 0.893, + 0.433 + ], + "angle": 0, + "content": "Figure 3. The proposed method. SCOOP includes two components: a learned point cloud correspondence model and a flow refinement module. The model learns deep point embeddings \\(\\Phi_X, \\Phi_Y\\) to establish soft point matches based on a matching cost \\(C\\) in the latent space. The initial flow \\(F\\) from the training phase is the difference between the softly corresponding point cloud \\(\\widehat{Y}\\) and the source point cloud \\(X\\). At the test-time, we freeze the trained model and optimize a residual flow refinement \\(R^*\\) to produce a smooth and consistent scene flow \\(F^*\\) between the point clouds." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.455, + 0.892, + 0.517 + ], + "angle": 0, + "content": "The value of \\( s_{x_i} \\) is in the range \\([-1, 1]\\). To get a confidence value between 0 and 1, we trim the negative values, set the matching confidence of \\( x_i \\) to be \\( p_{x_i} = \\max(s_{x_i}, 0) \\), and use \\( p_{x_i} \\) to define our confidence-aware distance loss:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.522, + 0.891, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d i s t}} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} p _ {x _ {i}} \\min _ {y _ {j} \\in Y} \\| \\hat {y} _ {x _ {i}} - y _ {j} \\| _ {2} ^ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.564, + 0.892, + 0.624 + ], + "angle": 0, + "content": "The loss term \\(\\mathcal{L}_{dist}\\) can be minimized by either minimizing \\(p_{x_i}\\) or the distance between \\(\\hat{y}_{x_i}\\) and its nearest neighbor \\(y_j\\in Y\\). To avoid the degenerate solution of \\(p_{x_i} = 0\\) for all \\(x_{i}\\in X\\), we add a confidence loss term:" + }, + { + "type": "equation", + "bbox": [ + 0.602, + 0.629, + 0.891, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n f}} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} 1 - p _ {x _ {i}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.671, + 0.768, + 0.685 + ], + "angle": 0, + "content": "which penalizes the degenerate solution." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.686, + 0.892, + 0.762 + ], + "angle": 0, + "content": "Additionally, to preserve the geometric structure of the source point cloud, we would like the flow field to be smooth. That is, neighboring source points should have a similar flow prediction. Thus, we regularize the learning process with a flow smoothness loss [11]:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.767, + 0.891, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f l o w}} = \\frac {1}{| X | k _ {f}} \\sum_ {x _ {i} \\in X} \\sum_ {l \\in N _ {X} \\left(x _ {i}\\right)} \\| f _ {i} - f _ {l} \\| _ {1}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.89, + 0.842 + ], + "angle": 0, + "content": "where \\( N_{X}(x_{i}) \\) is the Euclidean neighborhood of \\( x_{i} \\) in \\( X \\backslash x_{i} \\) of size \\( k_{f} \\). The overall training objective is:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.849, + 0.891, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d i s t}} + \\alpha_ {\\text {c o n f}} \\mathcal {L} _ {\\text {c o n f}} + \\alpha_ {\\text {f l o w}} \\mathcal {L} _ {\\text {f l o w}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.9 + ], + "angle": 0, + "content": "where \\(\\alpha_{conf}\\) and \\(\\alpha_{flow}\\) are hyperparameters, balancing the contribution of the different loss terms." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5284" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.351, + 0.108 + ], + "angle": 0, + "content": "3.5. Flow Refinement Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.219 + ], + "angle": 0, + "content": "The advantage of the correspondence-based flow, presented in Equation 7, is that the softly matching points are in the vicinity of the surface of objects in the target scene. However, it limits the flow to the convex hull [26] of points in the target point cloud. We enable the flow to deviate from this constraint by a flow refinement optimization step at runtime." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.22, + 0.469, + 0.31 + ], + "angle": 0, + "content": "Instead of training an additional neural network part to regress flow corrections, as done by Puy et al. [24], we directly optimize a flow refinement component \\( R^{*} \\in \\mathbb{R}^{n \\times 3} \\) using the self-supervised distance and smoothness losses defined in Equations 10 and 12, respectively. An illustration of these losses is depicted in Figure 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.469, + 0.34 + ], + "angle": 0, + "content": "The optimization problem for the flow refinement takes the form:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.348, + 0.469, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} R ^ {*} = \\operatorname * {a r g m i n} _ {R \\in \\mathbb {R} ^ {n \\times 3}} \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} \\min _ {y _ {j} \\in Y} p _ {x _ {i}} | | x _ {i} + (f _ {i} + r _ {i}) - y _ {j} | | _ {2} ^ {2} \\\\ + \\lambda_ {f l o w} \\frac {1}{| X | k _ {f}} \\sum_ {x _ {i} \\in X} \\sum_ {l \\in N _ {X} \\left(x _ {i}\\right)} \\left\\| \\left(f _ {i} + r _ {i}\\right) - \\left(f _ {l} + r _ {l}\\right) \\right\\| _ {1}, \\tag {14} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.543 + ], + "angle": 0, + "content": "where \\( r_i \\in R \\) is the flow refinement for point \\( x_i \\), and the refined scene flow is \\( F^* = F + R^* \\). Our flow refinement module further preserves the structure of the source point cloud, where the target points \\( \\{y_j\\} \\) are used as anchors to guide the refined flow and keep the proximity to the underlying target surface." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.21, + 0.573 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.582, + 0.469, + 0.673 + ], + "angle": 0, + "content": "In this section, we evaluate SCOOP's performance using widely spread datasets and compare it with recent state-of-the-art (SOTA) works on scene flow estimation. Additionally, we demonstrate the influence of the flow refinement module, analyze the performance and run-time duration, and verify our design choices with an ablation study." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.267, + 0.699 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Datasets. We adopt two common datasets in the scene flow literature, FlyingThings3D [18] and KITTI [19, 20]. Originally, these benchmarks did not include point cloud data. They were processed to a point cloud format by Liu et al. [16] and denoted as \\(\\mathrm{FT3D_o}\\) and \\(\\mathrm{KITTI_o}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "\\(\\mathrm{FT3D_o}\\) is a large-scale synthetic dataset with 18,000/2,000 train/validation scene examples of randomly moving objects from the ShapeNet collection [3]. Each example contains a pair of point clouds and ground-truth flow vectors. Since the objects' motion is randomized, they may appear or disappear from the view of the scene and create occlusions. The dataset also includes a mask for points whose flow is invalid due to occlusions." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.095, + 0.891, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.2, + 0.892, + 0.326 + ], + "angle": 0, + "content": "Figure 4. Illustration of the flow refinement objective. The initial flow \\(\\{f_i\\}\\) stems from the translation of the source points \\(\\{x_i\\}\\) (red) to their softly corresponding ones \\(\\{\\hat{y}_{x_i}\\}\\) (magenta). The flow is refined with a distance loss that keeps the proximity of the translated points to the target points \\(\\{y_j\\}\\) (green) and a smoothness loss that encourages similar flow vectors (dashed purple) for neighboring points. The optimization process results in a flow field \\(\\{f_i^*\\}\\) (blue) that preserves the structure of the source point cloud and warps it close to the implicit surface of the target point cloud." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.531 + ], + "angle": 0, + "content": "The \\(\\mathrm{KITTI_o}\\) dataset contains 150 real-world LiDAR scenes. Every scene includes source and target point clouds with flow annotations for the source points. Ground points are removed, and the source points are considered to have a valid flow [16]. \\(\\mathrm{KITTI_o}\\) was further split by Mittal et al. [21] into sets of 100 and 50 examples, marked as \\(\\mathrm{KITTI_v}\\) and \\(\\mathrm{KITTI_t}\\), respectively, for fine-tuning experiments. Li et al. [13] also built a large unlabeled LiDAR dataset for self-supervised learning on real-world data. They took raw Li-DAR scans from the KITTI scenes [19,20], disjoint from the \\(\\mathrm{KITTI_o}\\) data, and created a training set of 6,068 instances denoted as \\(\\mathrm{KITTI_r}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.614 + ], + "angle": 0, + "content": "Evaluation metrics. We use well-established evaluation metrics from previous works [16, 21, 24]: End-Point-Error \\( EPE[m] \\), Strict Accuracy \\( AS[\\%] \\), Relaxed Accuracy \\( AR[\\%] \\), and Outliers \\( Out.[\\%] \\). These metrics are based on the point error \\( e_i \\) and the relative error \\( e_i^{rel} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.622, + 0.892, + 0.658 + ], + "angle": 0, + "content": "\\[\ne _ {i} = \\left\\| f _ {i} ^ {*} - f _ {i} ^ {g t} \\right\\| _ {2}, \\quad e _ {i} ^ {r e l} = \\frac {\\left\\| f _ {i} ^ {*} - f _ {i} ^ {g t} \\right\\| _ {2}}{\\left\\| f _ {i} ^ {g t} \\right\\| _ {2}}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.892, + 0.76 + ], + "angle": 0, + "content": "where \\( f_{i}^{*} \\) and \\( f_{i}^{gt} \\) are the predicted and ground-truth flow for point \\( x_{i} \\), respectively. The EPE is the average point error, measured in meters; \\( AS \\) is the percentage of points whose \\( e_{i} < 0.05[m] \\) or \\( e_{i}^{rel} < 5\\% \\); \\( AR \\) is the percentage of points for which \\( e_{i} < 0.1[m] \\) or \\( e_{i}^{rel} < 10\\% \\); and Out. is the percentage of points with \\( e_{i} > 0.3[m] \\) or \\( e_{i}^{rel} > 10\\% \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details. SCOOP is implemented in PyTorch [22], where the publicly available PointNet++ [25] implementation is adapted for our point feature embedding. The model is trained on \\( n = 2,048 \\) points, sampled at random from the source and target point clouds of the scene examples. Only the 3D coordinates of the points are used as input to the model. The parameters \\( \\epsilon \\) and \\( \\lambda \\) from Equation 3 are defined as learnable variables and optimized as part of the learning process. The point feature" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "5285" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.326 + ], + "angle": 0, + "content": "
MethodSupervisionTrain dataTest dataEPE↓AS↑AR↑Out.↓
FlowNet3D [16]FullFT3Do(18,000)KITTIo0.17327.660.964.9
FLOT [24]FullFT3Do(18,000)KITTIo0.10745.174.046.3
FESTA [31]FullFT3Do(18,000)KITTIo0.09444.983.4-
3DFlow [30]FullFT3Do(18,000)KITTIo0.07381.989.026.1
BiPFN [4]FullFT3Do(18,000)KITTIo0.06576.990.626.4
SCOOP (ours)SelfFT3Do(1,800)KITTIo0.06379.791.024.4
SCOOP+(ours)SelfFT3Do(1,800)KITTIo0.04791.395.018.6
JGF [21]Full + Self + SelfFT3Do(18,000) + nuScenes (700) + KITTIv(100)KITTIt0.10546.579.4-
SPF [13]Self + SelfKITTIr(6,068) + KITTIv(100)KITTIt0.08941.775.0-
RigidFlow [14]SelfKITTIr(6,068)KITTIt0.11738.869.7-
SCOOP (ours)SelfKITTIv(100)KITTIt0.05280.692.919.7
Graph Prior [23]SelfN/A (optimization-only)KITTIt0.08284.088.5-
Neural Prior [15]SelfN/A (optimization-only)KITTIt0.03692.396.2-
SCOOP+(ours)SelfKITTIv(100)KITTIt0.03993.696.515.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.336, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison. We compare scene flow evaluation metrics for different supervision settings, train data, and test data. The number of training examples is indicated in parentheses. \\(EPE\\), \\(AS\\), \\(AR\\), and \\(Out\\). stand for End-Point-Error, Strict Accuracy, Relaxed Accuracy, and Outliers, respectively. The symbol \\(^+\\) indicates an evaluation using all the points in the test point clouds, as done for the optimization-only methods [15, 23]. While other baselines apply fully-supervised training, our method yields better performance without employing ground-truth flow labels. Besides, SCOOP can be trained only on \\(\\mathrm{KITTI_v}\\), with as few as 100 training instances. In contrast, alternative learning-based methods use additional training data, such as nuScenes, or a large dataset, such as \\(\\mathrm{KITTI_r}\\). Please see further details in subsections 4.1 and 4.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.506 + ], + "angle": 0, + "content": "dimension is \\( d = 128 \\). For the neighborhood sizes we use \\( k_{s} = 64 \\), \\( k_{f} = 32 \\), and the losses' hyperparameters are set to \\( \\alpha_{conf} = 0.1 \\), \\( \\alpha_{flow} = 10 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.645 + ], + "angle": 0, + "content": "As in previous work [14, 16, 21, 24], we evaluate SCOOP on point clouds of 2,048 points randomly sampled from the source and target. However, the full point clouds of \\(\\mathrm{KITTI_o}\\) and \\(\\mathrm{KITTI_t}\\) are an order of magnitude larger and have different cardinality. Thus, for a complete evaluation of the entire scene flow, we also utilize our method (denoted as \\(\\mathrm{SCOOP^{+}}\\) for this case) to exploit the whole point cloud information and test the performance for the original resolution. Additional implementation details appear in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.47, + 0.76 + ], + "angle": 0, + "content": "**Baseline methods.** Our method is contrasted with the recent methods FlowNet3D [16], FLOT [24], FESTA [31], 3DFlow [30], and BiPFN [4]. These methods require ground-truth flow supervision. Additionally, we compare our results with the recent self-supervised flow models of Mittal et al. [21] and Li et al. [13,14], and the optimization-based techniques Graph Prior [23] and Neural Prior [15]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.262, + 0.787 + ], + "angle": 0, + "content": "4.2. Scene Flow Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Cross-dataset evaluation. We demonstrate the generalization power of SCOOP by training it on the \\(\\mathrm{FT3D_o}\\) and testing its performance on \\(\\mathrm{KITTI_o}\\). Table 1 summarises the results. The alternative methods [4, 16, 24, 30, 31] are trained on \\(\\mathrm{FT3D_o}\\) in a fully-supervised fashion: their models are learned with the ground-truth flow information, and the points with an occluded flow are excluded from the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.877, + 0.476 + ], + "angle": 0, + "content": "training objective using the mask provided in the dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.612 + ], + "angle": 0, + "content": "In contrast, our model is trained in a completely self-supervised manner. We assume no knowledge of the flow annotations nor the occlusion mask and do not use them in our losses. Additionally, we use only 1,800 randomly selected examples from \\(\\mathrm{FT3D_o}\\), while the competitors employ all 18,000 scene instances. Still, SCOOP improves over the SOTA method BiPFN [4] in all the evaluation metrics. Moreover, utilizing the entire point cloud data further increases our performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.893, + 0.749 + ], + "angle": 0, + "content": "FlowNet3D [16], FESTA [31], 3DFlow [30], and BiPFN [4] are regression-based networks that predict the flow in the 3D ambient space. The models adapt to the characteristics of the synthetic training set, and the generalization to the real-world test data is limited. FLOT [24] leverages point cloud correspondence based on learned point features, which eases the flow prediction problem. However, it also jointly learns to regress a flow correction component that burdens the point representation training process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.885 + ], + "angle": 0, + "content": "SCOOP, on the other hand, is focused only on learning point embeddings suitable for scene flow estimation, guided by our self-supervised losses. It extracts discriminative features, which transfer well across the \\(\\mathrm{FT3D_o}\\) and \\(\\mathrm{KITTI_o}\\) datasets, and enables to compute the correspondence-based flow between the point clouds. In contrast to FLOT, we delegate the flow refinement process to the test phase, directly optimize it in a self-supervised fashion, and surpass their flow estimation performance." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Figure 5 shows a visual comparison between the results" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5286" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.087, + 0.492, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.087, + 0.872, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.894, + 0.418 + ], + "angle": 0, + "content": "Figure 5. Visual comparison of scene flow results for a KITTI\\(_0\\) example scene. The training was done on the FT3D\\(_0\\) dataset. The source and target point clouds are shown in red and green, respectively. The warped source point cloud by FLOT [24] (left) and by our method (right) is presented in blue. While the result of FLOT deviates from the surface of the target, SCOOP preserves the source point cloud's structure and computes its accurate flow." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.536 + ], + "angle": 0, + "content": "of FLOT and our method. The warped source point cloud by FLOT is noisy, and the structure of objects in the scene is compromised. On the contrary, SCOOP produces a coherent flow field across neighboring points, preserves their local geometry, and accurately predicts the scene flow. Additional visualizations are presented in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.641 + ], + "angle": 0, + "content": "Training on a small dataset. Since our model does not include a flow regression component and has to learn only point features, it can be trained on a very limited amount of data. To demonstrate this ability, we train it from scratch on the 100 point cloud pairs of \\(\\mathrm{KITTI_v}\\) and use \\(\\mathrm{KITTI_t}\\) for testing. The results of this experiment are presented in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Different from our work, the competing methods of Mittal et al. [21] and Li et al. [13, 14] are based on flow regression and require a large amount of training data. Mittal et al. utilize a fully-supervised pre-training on \\(\\mathrm{FT3D_o}\\), and the additional outdoor flow dataset nuScenes [2], before fin-tuning on \\(\\mathrm{KITTI_v}\\). Li et al. [13, 14] train their model on the large \\(\\mathrm{KITTI_r}\\) dataset. Our SCOOP outperforms these other methods while being trained only on \\(\\mathrm{KITTI_v}\\), which is almost two orders of magnitudes smaller than \\(\\mathrm{KITTI_r}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The pure optimization methods [15, 23] find the solution per scene separately, which might lead to sub-optimal local minima. In contrast, we leverage the correspondence statistics learned from the data and adapt the initial flow to the scene at hand by our residual run-time optimization. The initial correspondence flow serves as a good starting point for the optimization phase, yielding a similar or better final result compared to the optimization-only alternatives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.581 + ], + "angle": 0, + "content": "The influence of flow refinement. Our flow results before and after refinement are presented in Figure 6. Posing the learning part of SCOOP as a correspondence problem enables its effective training on a small dataset. However, the flow predictions from the training phase are confined to a linear combination of existing target points, which may not represent the exact flow of the scene. Moreover, wrong matches for the source points can occur and cause flow errors. In such cases, our refinement module comes into play." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.717 + ], + "angle": 0, + "content": "Given the output flow from the trained correspondence model, the refinement module optimizes correction vectors subject to two objectives: a warped source point should be close to a target point; neighboring source points should have a similar flow. These objectives help fixing inconsistencies in the flow field and increase the flow accuracy. As seen in Figure 6, our refinement step improves the initial flow estimation and results in an accurate flow field, which is similar to the ground-truth scene flow." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.783, + 0.743 + ], + "angle": 0, + "content": "4.3. Performance and Time Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.825 + ], + "angle": 0, + "content": "We analyze the performance-time trade-off in Figure 7 by recording the \\(EPE\\) and inference time for different methods. The measurements were done on an Nvidia Titan Xp GPU for computing the flow for complete point clouds of the \\(\\mathrm{KITTI_t}\\) dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Network-only methods [13, 14, 21] tend to be fast but with limited accuracy. Optimizing the flow prediction separately for each scene [15] results in a low \\( EPE \\). However, it takes a long time. Our hybrid method bridges the trade-off gap between these two approaches. \\( \\mathrm{SCOOP}^{+} \\) offers a work-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5287" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.207, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.089, + 0.331, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.342, + 0.089, + 0.46, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.473, + 0.435 + ], + "angle": 0, + "content": "Figure 6. The flow refinement effect. We demonstrate the effect on data from \\(\\mathrm{KITTI}_{\\mathrm{t}}\\). The source point cloud is in red, and the target is in green. Our correspondence model was trained on the \\(\\mathrm{KITTI}_{\\mathrm{v}}\\) dataset, and its flow estimation before refinement is shown in magenta (left). The optimized refined flow is presented in blue (center). We also show the ground-truth scene flow in purple for reference (right). The refined flow better covers the target point cloud (top center ellipse). It also breaches the convex hull of the given target points and enables computing the correct flow for source points whose target is missing (bottom center ellipse)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.568 + ], + "angle": 0, + "content": "ing point with more than \\(50\\%\\) error reduction over the feedforward models and about \\(8\\times\\) faster inference time than the optimization-only Neural Prior work. \\(\\mathrm{SCOOP^{+}}\\) also enables a different balance between time and performance, as seen in Figure 7. By reducing the number of run-time optimization steps, the user can shorten the inference time, achieving a working point closer to that of the network-only models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.232, + 0.592 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.749 + ], + "angle": 0, + "content": "The design choices in our method are verified by ablation experiments presented in Table 2. We change one element each time and keep all the others the same. The following ablative settings were examined: (a) use all target points for soft correspondence instead of the ones with the highest transport amount (Equation 5); (b) ignore the point matching confidence by setting \\( p_{x_i} = 1 \\) in Equation 10 and \\( \\alpha_{conf} = 0 \\) in Equation 13; (c) exclude the smoothness flow loss \\( \\mathcal{L}_{flow} \\) from Equation 13; and (d) turn off the flow refinement module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The ablation study validates the contribution of the proposed components to the method's performance. Considering a subset of target points for correspondence enables the model to concentrate on the most relevant candidates for flow estimation. The matching confidence emphasizes the influence of the more confident points in our confidence-aware distance loss \\(\\mathcal{L}_{dist}\\). The smoothness loss term is important for regularizing the point representation learning to obtain similar features across neighboring points. Lastly, our flow refinement optimization improves the consistency" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.094, + 0.885, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.26, + 0.895, + 0.331 + ], + "angle": 0, + "content": "Figure 7. Flow estimation error vs. inference time for the KITTI dataset. \\(\\mathrm{SCOOP^{+}}\\) has a lower error than the network-only models and a shorter inference time than the optimization-only methods. It also allows different balances along the error and time trade-off, as presented by the blue curve." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.35, + 0.89, + 0.451 + ], + "angle": 0, + "content": "
SettingEPE↓AS↑
(a) All target points as candidates (ks = n)0.04791.1
(b) W/O confidence (pxi = 1, αconf = 0)0.04490.3
(c) W/O smoothness loss term (αflow = 0)0.05686.6
(d) W/O flow refinement (R* = 0)0.11543.8
Our complete method0.03993.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.461, + 0.893, + 0.517 + ], + "angle": 0, + "content": "Table 2. Component ablative settings. SCOOP was trained on \\(\\mathrm{KITTI_v}\\) and evaluated on \\(\\mathrm{KITTI_t}\\). The results show that the best performance is obtained with our complete method. Additional details about the ablation experiments are given in subsection 4.4." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.543, + 0.892, + 0.605 + ], + "angle": 0, + "content": "of the flow field and reduces the \\(EPE\\) substantially. In the supplementary material, we provide an ablation study on the \\(\\mathrm{FT3D_o}\\) train set size and find that a \\(10\\%\\) fraction of the data suffices for our method to realize its potential." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.628, + 0.634 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.894, + 0.75 + ], + "angle": 0, + "content": "This paper presented SCOOP, a novel self-supervised scene flow estimation method for 3D point clouds based on correspondence learning and flow refinement optimization. Previous works suggested learning a flow regression model, training a neural network that jointly learned point cloud correspondence and flow refinement, or optimizing the flow completely at run-time without learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In contrast, we split the flow prediction process into two simpler problems. Our correspondence model is focused only on learning point features to initialize the flow from soft matches between the point clouds. Then, we directly optimize a residual flow refinement at run-time. This approach enables SCOOP to be trained on a small set of point cloud scenes without utilizing ground-truth supervision while outperforming state-of-the-art fully-supervised and self-supervised learning methods, as well as optimization-based alternative techniques." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5288" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Thomas Brox and Jitendra Malik. Large Displacement Optical Flow: Descriptor Matching in Variational Motion Estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 33(3):500-513, 2011. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.255 + ], + "angle": 0, + "content": "[2] Holger Caesar, Varun Bankiti, Alex H. 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Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset. + +We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available1. + +# 1. Introduction + +Scene flow estimation [27] is a fundamental problem in computer vision with various use-cases, such as autonomous driving, scene parsing, pose estimation, and object tracking, to name a few. Given two consecutive observations of a 3D scene, the aim is to compute the dynamics of the scene between the observations. Scene flow prediction based on 2D images has been thoroughly investigated in the literature [17, 19, 28, 32, 33]. However, in light of the + +![](images/bce42a77079dac70b97a54467c894ef5e76783731facbe2b96c430c73521e2c7.jpg) +Figure 1. Flow accuracy on the KITTI benchmark vs. the train set size. Our method is trained on one or two orders of magnitude less data while surpassing the performance of the competing techniques [4, 13, 14, 16, 21, 24, 30, 31] by a large margin. Please see Table 1 for the complete details of the evaluation settings. + +recent proliferation of 3D sensors, such as LiDAR, there is a surge of interest in scene flow methods that operate directly on the 3D data [10, 13, 16, 21, 34]. + +Liu et al. [16] were among the first to pursue this research avenue. They proposed FlowNet3D, a fully-supervised neural network that learned to regress the flow between 3D point clouds and showed remarkable performance improvement over image-based techniques [1, 19, 29]. Since their method required ground-truth flow annotations, which are scarce for real-world data, they turned to training on a large synthetic dataset that compromised the generalization capability to real-world LiDAR data. + +Follow-up works devised self-supervised learning schemes [13, 21] and narrowed the domain gap by training on unannotated LiDAR point cloud pairs. However, similar to Liu et al. [16], they used a regression approach in which the model should learn to compute the flow in the free 3D space. This task is extremely challenging, given the irregular nature of point clouds, and requires a large amount of training data for the network to converge. + +In another line of work [8, 11, 24], researchers leveraged point cloud correspondence for scene flow prediction. In this approach, the flow is computed as the translation of a point in the first point cloud (source) to its softly corre + +![](images/4c0a621e9eb17471535411910c52fbe536c008cf81f217eb156788d51a87b250.jpg) +Figure 2. Comparison of scene flow approaches. Given a pair of point clouds, FlowNet3D [16] learns to regress the flow in the free 3D space, and the trained model is frozen for testing. FLOT [24] concurrently trains two network components: one that computes point correspondence and another that regresses a correction to the resulting correspondence flow. Neural Prior [15] optimizes the flow between the point clouds from scratch without learning. In contrast to previous work, we take a hybrid approach. We train a pure correspondence model without flow regression, which serves for flow initialization. Then, we directly optimize only the flow refinement at the test-time. + +sponding point in the second one (target). The softly corresponding point is a weighted sum of target points based on point similarity in a learned latent space. Thus, rather than the challenging regression problem in the 3D ambient space, the flow estimation task boils down to point feature learning and is reduced to the convex combination space [26] of existing target points. However, to relax this constraint, another network component is trained to regress flow corrections. The joint training of point representation and flow refinement burdens the learning process and retains the reliance on large datasets with flow supervision. + +Another emerging approach is an optimization-only flow computation [15, 23]. In this case, no training data is involved, and the flow is optimized at run-time for each scene separately. Despite the high accuracy such a dedicated optimization achieves, it requires a long processing time. + +We present SCOOP, a hybrid flow estimation method that can be learned from a small amount of training data. SCOOP consists of two parts: a self-supervised neural network for point cloud correspondence and a direct flow refinement optimization module. During the training phase, the network learns to extract point features for soft point matches, which initialize the flow between the point clouds. In contrast to previous work, our network is focused on learning just the point embeddings, allowing its training on a very small dataset, as shown in Figure 1. Additionally, we consider the confidence of the network in the computed correspondences to guide the learning process better. + +Then, instead of training another network for regressing flow updates, we define an optimization problem and directly optimize residual flow refinement vectors at runtime. The optimization objective encourages a coherent flow field while retaining the translated source points close to the target point cloud. Our design choices improve the accuracy compared to learning-based methods and reduce the processing time with respect to the optimization-only approach [15, 23]. For both correspondence learning and refinement optimization, we use a self-supervised distance objective and a smoothness prior instead of ground-truth + +flow labels. Figure 2 presents the difference between our approach and leading previous ones. + +In summary, we propose a hybrid flow prediction approach for point clouds based on self-supervised correspondence learning and direct run-time residual flow optimization. Using well-established datasets in the scene flow literature, we show that our approach yields clear performance improvement over existing state-of-the-art methods while using a fraction of the training data and without employing any ground-truth flow supervision. + +# 2. Related Work + +Flow regression. A common approach for scene flow estimation on point clouds is to train a flow regression model [4,10,16,31,34]. It is a neural network that computes the flow vectors between the point clouds in the ambient 3D space. Liu et al. [16] proposed FlowNet3D, which encoded the point clouds into a latent space, mixed point features with a flow embedding layer, and regressed the scene flow by decoding the mixed point features. FlowNet3D was trained in a fully-supervised manner, using an $l_{2}$ loss with respect to ground-truth flow annotations. + +Liu et al. [16] inspired a line of follow-up works [4, 13, 21, 30, 31]. Wang et al. [31] added spatial and temporal attention layers to FlowNet3D's architecture. In Bi-PointFlowNet [4], the authors propagated features from each point cloud bidirectionally, augmenting the point feature representation. Mittal et al. [21] discarded flow supervision by utilizing a self-supervised nearest neighbor loss and cycle consistency between the forward and revers scene flows, and Li et al. [13, 14] extracted flow labels for training from the data itself. Similar to the latter methods, we also refrain from ground-truth flow supervision in our training scheme. However, rather than flow regression, we base our technique on soft point matches in the scene, which simplifies the flow estimation problem. + +Point cloud correspondence. Finding correspondences is widely applied to various vision tasks [12, 24, 35, 37]. + +Several methods have been proposed for dense mapping between non-rigid point cloud shapes [7, 9, 12, 36]. Recently, Lang et al. [12] suggested constructing one point cloud by the other using latent space similarity and the point coordinates themselves rather than regressing the corresponding point cloud [9, 36]. Inspired by Lang's work, we do not use flow regression in our model and concentrate the learning process on point feature representation. However, while Lang et al. operated on complete shapes with one-to-one correspondence, our method accommodates scenes with partial objects where a perfect match may not exist. + +Researchers have taken the correspondence approach to the scene flow problem as well [8, 11, 24]. FLOT [24] computed an optimal transport plan that served for an initial flow between the point clouds and further regressed flow refinement with a series of learned convolutions. Our work builds on FLOT but differs from it in three main aspects. First, we exclude flow regression from our training scheme and instead apply direct run-time optimization to refine the initial correspondence-based flow. Second, we use the model's confidence in the computed point matches to improve the point feature learning. Third, we do not use any groundtruth flow annotations, neither for the correspondence training nor for the refinement optimization, whereas FLOT relies on fully-supervised scene flow data. + +Optimization-based scene flow. Pontes et al. [23] suggested a scene flow estimation technique that does not involve learning. Instead, the flow was optimized completely at run-time, such that the warped source is close to the target point cloud while demanding the flow to be "as-rigid-as-possible". Pontes et al. encoded this prior by minimizing the graph Laplacian defined over the source points. In follow-up work [15], the explicit graph was replaced by a neural prior, which implicitly regularized the optimized flow field. In contrast to these papers, we initialize the flow with a learned correspondence model and optimize only the residual flow refinement at run-time. + +# 3. Method + +A point cloud is a set of unordered 3D points $X \in \mathbb{R}^{n \times 3}$ , where $n$ is the number of points. Given a pair of point clouds of a scene, denoted as $X, Y \in \mathbb{R}^{n \times 3}$ and referred to as source and target, respectively, our goal is to estimate a flow field $F^* \in \mathbb{R}^{n \times 3}$ describing the per-point motion from $X$ to $Y$ . + +We tackle this problem via self-supervised soft correspondence learning between the two point clouds and a direct flow refinement optimization. An overview of the method is shown in Figure 3. First, a deep neural network is used to extract point features. Then, we calculate a matching cost between points in the learned feature space. Based on this cost, we solve an optimal transport + +problem to compute a softly matched target point for each source point, where the difference between the two is regarded as the correspondence-based flow. Finally, we refine the flow field by demanding its consistency across neighboring source points and obtain our estimated scene flow. In both correspondence learning and flow refinement, no ground-truth flow labels are employed. + +# 3.1. Matching Cost + +The cost of matching a point $x_{i} \in X$ to a point $y_{j} \in Y$ is determined based on the point representation learned by a deep neural network. The network consumes the raw point clouds $X, Y$ and computes point features $\Phi_{X}, \Phi_{Y} \in \mathbb{R}^{n \times d}$ , where $d$ is the per-point feature dimension. The network's architecture is based on PointNet++ [25]. Its details are given in the supplemental material. + +Inspired by previous work [12, 13, 24], we first compute the cosine similarity in the learned feature space: + +$$ +S _ {i j} = \frac {\Phi_ {X} ^ {i} \cdot \left(\Phi_ {Y} ^ {j}\right) ^ {\top}}{\left| \left| \Phi_ {X} ^ {i} \right| \right| _ {2} \left| \left| \Phi_ {Y} ^ {j} \right| \right| _ {2}}, \tag {1} +$$ + +where $\Phi_X^i, \Phi_Y^j \in \mathbb{R}^d$ are the $i$ 'th and $j$ 'th rows of $\Phi_X$ and $\Phi_Y$ , respectively. Then, the cost is set to + +$$ +C _ {i j} = 1 - S _ {i j} \tag {2} +$$ + +for points with a Euclidean distance less than 10 meters and to $\infty$ otherwise to avoid flow between points too far apart. + +# 3.2. Soft Correspondence + +Finding correspondence between the source and target point clouds can be modeled as an optimal transport problem, where each source point is assigned with a mass $\frac{1}{n}$ that is transported to the target points [13, 24]. Similar to FLOT [24], we use the relaxed transport problem: + +$$ +\begin{array}{l} T ^ {*} = \underset {T \in \mathbb {R} _ {+} ^ {n \times n}} {\operatorname {a r g m i n}} \sum_ {i j} \left(C _ {i j} T _ {i j} + \epsilon T _ {i j} (\log T _ {i j} - 1)\right) \\ + \lambda (\mathsf {K L} (T 1 _ {n}, \frac {1}{n} 1 _ {n}) + \mathsf {K L} (T ^ {\top} 1 _ {n}, \frac {1}{n} 1 _ {n})), \\ \end{array} +$$ + +where $C_{ij} \geq 0$ is the matching cost from Equation 2 and $T_{ij} \geq 0$ is the amount of mass transported between points. The parameters $\epsilon, \lambda \geq 0$ control the relaxation of the problem. $1_n \in \mathbb{R}^n$ is a vector with all entries equal 1. KL is the Kullback-Leibler divergence used for soft preservation of the transported mass between the point clouds. + +The second term in the summation operation in Equation 3 is an entropic regularization, which enables solving the problem efficiently by the Sinkhorn algorithm [5,6]. We use this algorithm to estimate the optimal transport matrix $T^{*}$ from $C$ to represent the soft correspondence between the point clouds. The complete derivation of the transport problem and the Sinkhorn algorithm's details are given in the supplementary material. + +# 3.3. Correspondence-Based Flow + +We leverage the optimal transport plan $T^{*}$ to compute correspondence weights for the source and target points for an initial estimate of the scene flow. Different from FLOT [24], which includes all the target points as candidates for each source point, we consider only target points with maximal transport amount from the source point. This design choice focuses our flow estimation pipeline on the most relevant target candidates and improves the method's results. + +For a point $x_{i} \in X$ , the matching weights are calculated as follows: + +$$ +w _ {i j} = \frac {e ^ {T _ {i j} ^ {*}}}{\sum_ {l \in \mathcal {N} _ {Y} \left(x _ {i}\right)} e ^ {T _ {i l} ^ {*}}}, \tag {4} +$$ + +where $\mathcal{N}_Y(x_i)$ is a neighborhood containing the $k_{s}$ indices of the $\{y_j\}$ points with the top mass transport $\{T_{ij}^*\}$ . The softly corresponding point $\hat{y}_{x_i}$ to $x_{i}$ is: + +$$ +\hat {y} _ {x _ {i}} = \sum_ {j \in \mathcal {N} _ {Y} \left(x _ {i}\right)} w _ {i j} y _ {j}, \tag {5} +$$ + +and the initial estimated flow for the point $x_{i}$ is: + +$$ +f _ {i} = \hat {y} _ {x _ {i}} - x _ {i}. \tag {6} +$$ + +Note that if we define $\widehat{T}_{ij}^{*} = w_{ij}$ for $j\in \mathcal{N}_Y(x_i)$ and 0 otherwise, we get the initial flow field as: + +$$ +F = \widehat {T} ^ {*} Y - X = \widehat {Y} - X, \tag {7} +$$ + +where $\widehat{Y} \in \mathbb{R}^{n \times 3}$ contains the points $\{\hat{y}_{x_i}\}$ . + +# 3.4. Training Objective + +To learn point representation suitable for scene flow without ground-truth supervision, we apply the flowing loss terms. First, for a tractable flow estimation, we would like each softly corresponding point $\hat{y}_{x_i}$ to have a nearby target point $y_{j}$ . It may be achieved by the nearest-neighbor distance term, as done by Mittal et al. [21]: + +$$ +\mathcal {D} = \frac {1}{| X |} \sum_ {x _ {i} \in X} \min _ {y _ {j} \in Y} \| \hat {y} _ {x _ {i}} - y _ {j} \| _ {2} ^ {2}. \tag {8} +$$ + +However, the correspondence quality for the source points can vary. For example, points on a flat region will have less distinctive correspondences than points with geometrically unique features. Thus, we augment the distance term in Equation 8 with the matching confidence of each point. + +The confidence measure is based on the correspondence similarity that we define as: + +$$ +s _ {x _ {i}} = \sum_ {j \in \mathcal {N} _ {Y} (x _ {i})} w _ {i j} S _ {i j}. \tag {9} +$$ + +![](images/7f533893eb5fb9cb282914d1e57b5880596150f2d36fc902bfbf07d388c05c4a.jpg) +Figure 3. The proposed method. SCOOP includes two components: a learned point cloud correspondence model and a flow refinement module. The model learns deep point embeddings $\Phi_X, \Phi_Y$ to establish soft point matches based on a matching cost $C$ in the latent space. The initial flow $F$ from the training phase is the difference between the softly corresponding point cloud $\widehat{Y}$ and the source point cloud $X$ . At the test-time, we freeze the trained model and optimize a residual flow refinement $R^*$ to produce a smooth and consistent scene flow $F^*$ between the point clouds. + +The value of $s_{x_i}$ is in the range $[-1, 1]$ . To get a confidence value between 0 and 1, we trim the negative values, set the matching confidence of $x_i$ to be $p_{x_i} = \max(s_{x_i}, 0)$ , and use $p_{x_i}$ to define our confidence-aware distance loss: + +$$ +\mathcal {L} _ {\text {d i s t}} = \frac {1}{| X |} \sum_ {x _ {i} \in X} p _ {x _ {i}} \min _ {y _ {j} \in Y} \| \hat {y} _ {x _ {i}} - y _ {j} \| _ {2} ^ {2}. \tag {10} +$$ + +The loss term $\mathcal{L}_{dist}$ can be minimized by either minimizing $p_{x_i}$ or the distance between $\hat{y}_{x_i}$ and its nearest neighbor $y_j\in Y$ . To avoid the degenerate solution of $p_{x_i} = 0$ for all $x_{i}\in X$ , we add a confidence loss term: + +$$ +\mathcal {L} _ {\text {c o n f}} = \frac {1}{| X |} \sum_ {x _ {i} \in X} 1 - p _ {x _ {i}}, \tag {11} +$$ + +which penalizes the degenerate solution. + +Additionally, to preserve the geometric structure of the source point cloud, we would like the flow field to be smooth. That is, neighboring source points should have a similar flow prediction. Thus, we regularize the learning process with a flow smoothness loss [11]: + +$$ +\mathcal {L} _ {\text {f l o w}} = \frac {1}{| X | k _ {f}} \sum_ {x _ {i} \in X} \sum_ {l \in N _ {X} \left(x _ {i}\right)} \| f _ {i} - f _ {l} \| _ {1}, \tag {12} +$$ + +where $N_{X}(x_{i})$ is the Euclidean neighborhood of $x_{i}$ in $X \backslash x_{i}$ of size $k_{f}$ . The overall training objective is: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {d i s t}} + \alpha_ {\text {c o n f}} \mathcal {L} _ {\text {c o n f}} + \alpha_ {\text {f l o w}} \mathcal {L} _ {\text {f l o w}}, \tag {13} +$$ + +where $\alpha_{conf}$ and $\alpha_{flow}$ are hyperparameters, balancing the contribution of the different loss terms. + +# 3.5. Flow Refinement Optimization + +The advantage of the correspondence-based flow, presented in Equation 7, is that the softly matching points are in the vicinity of the surface of objects in the target scene. However, it limits the flow to the convex hull [26] of points in the target point cloud. We enable the flow to deviate from this constraint by a flow refinement optimization step at runtime. + +Instead of training an additional neural network part to regress flow corrections, as done by Puy et al. [24], we directly optimize a flow refinement component $R^{*} \in \mathbb{R}^{n \times 3}$ using the self-supervised distance and smoothness losses defined in Equations 10 and 12, respectively. An illustration of these losses is depicted in Figure 4. + +The optimization problem for the flow refinement takes the form: + +$$ +\begin{array}{l} R ^ {*} = \operatorname * {a r g m i n} _ {R \in \mathbb {R} ^ {n \times 3}} \frac {1}{| X |} \sum_ {x _ {i} \in X} \min _ {y _ {j} \in Y} p _ {x _ {i}} | | x _ {i} + (f _ {i} + r _ {i}) - y _ {j} | | _ {2} ^ {2} \\ + \lambda_ {f l o w} \frac {1}{| X | k _ {f}} \sum_ {x _ {i} \in X} \sum_ {l \in N _ {X} \left(x _ {i}\right)} \left\| \left(f _ {i} + r _ {i}\right) - \left(f _ {l} + r _ {l}\right) \right\| _ {1}, \tag {14} \\ \end{array} +$$ + +where $r_i \in R$ is the flow refinement for point $x_i$ , and the refined scene flow is $F^* = F + R^*$ . Our flow refinement module further preserves the structure of the source point cloud, where the target points $\{y_j\}$ are used as anchors to guide the refined flow and keep the proximity to the underlying target surface. + +# 4. Experiments + +In this section, we evaluate SCOOP's performance using widely spread datasets and compare it with recent state-of-the-art (SOTA) works on scene flow estimation. Additionally, we demonstrate the influence of the flow refinement module, analyze the performance and run-time duration, and verify our design choices with an ablation study. + +# 4.1. Experimental Setup + +Datasets. We adopt two common datasets in the scene flow literature, FlyingThings3D [18] and KITTI [19, 20]. Originally, these benchmarks did not include point cloud data. They were processed to a point cloud format by Liu et al. [16] and denoted as $\mathrm{FT3D_o}$ and $\mathrm{KITTI_o}$ , respectively. + +$\mathrm{FT3D_o}$ is a large-scale synthetic dataset with 18,000/2,000 train/validation scene examples of randomly moving objects from the ShapeNet collection [3]. Each example contains a pair of point clouds and ground-truth flow vectors. Since the objects' motion is randomized, they may appear or disappear from the view of the scene and create occlusions. The dataset also includes a mask for points whose flow is invalid due to occlusions. + +![](images/36a035cbc4cc88c32ed7335340ae30a589c9b40ce1885c6be217774e5e016b59.jpg) +Figure 4. Illustration of the flow refinement objective. The initial flow $\{f_i\}$ stems from the translation of the source points $\{x_i\}$ (red) to their softly corresponding ones $\{\hat{y}_{x_i}\}$ (magenta). The flow is refined with a distance loss that keeps the proximity of the translated points to the target points $\{y_j\}$ (green) and a smoothness loss that encourages similar flow vectors (dashed purple) for neighboring points. The optimization process results in a flow field $\{f_i^*\}$ (blue) that preserves the structure of the source point cloud and warps it close to the implicit surface of the target point cloud. + +The $\mathrm{KITTI_o}$ dataset contains 150 real-world LiDAR scenes. Every scene includes source and target point clouds with flow annotations for the source points. Ground points are removed, and the source points are considered to have a valid flow [16]. $\mathrm{KITTI_o}$ was further split by Mittal et al. [21] into sets of 100 and 50 examples, marked as $\mathrm{KITTI_v}$ and $\mathrm{KITTI_t}$ , respectively, for fine-tuning experiments. Li et al. [13] also built a large unlabeled LiDAR dataset for self-supervised learning on real-world data. They took raw Li-DAR scans from the KITTI scenes [19,20], disjoint from the $\mathrm{KITTI_o}$ data, and created a training set of 6,068 instances denoted as $\mathrm{KITTI_r}$ . + +Evaluation metrics. We use well-established evaluation metrics from previous works [16, 21, 24]: End-Point-Error $EPE[m]$ , Strict Accuracy $AS[\%]$ , Relaxed Accuracy $AR[\%]$ , and Outliers $Out.[\%]$ . These metrics are based on the point error $e_i$ and the relative error $e_i^{rel}$ : + +$$ +e _ {i} = \left\| f _ {i} ^ {*} - f _ {i} ^ {g t} \right\| _ {2}, \quad e _ {i} ^ {r e l} = \frac {\left\| f _ {i} ^ {*} - f _ {i} ^ {g t} \right\| _ {2}}{\left\| f _ {i} ^ {g t} \right\| _ {2}}, \tag {15} +$$ + +where $f_{i}^{*}$ and $f_{i}^{gt}$ are the predicted and ground-truth flow for point $x_{i}$ , respectively. The EPE is the average point error, measured in meters; $AS$ is the percentage of points whose $e_{i} < 0.05[m]$ or $e_{i}^{rel} < 5\%$ ; $AR$ is the percentage of points for which $e_{i} < 0.1[m]$ or $e_{i}^{rel} < 10\%$ ; and Out. is the percentage of points with $e_{i} > 0.3[m]$ or $e_{i}^{rel} > 10\%$ . + +Implementation details. SCOOP is implemented in PyTorch [22], where the publicly available PointNet++ [25] implementation is adapted for our point feature embedding. The model is trained on $n = 2,048$ points, sampled at random from the source and target point clouds of the scene examples. Only the 3D coordinates of the points are used as input to the model. The parameters $\epsilon$ and $\lambda$ from Equation 3 are defined as learnable variables and optimized as part of the learning process. The point feature + +
MethodSupervisionTrain dataTest dataEPE↓AS↑AR↑Out.↓
FlowNet3D [16]FullFT3Do(18,000)KITTIo0.17327.660.964.9
FLOT [24]FullFT3Do(18,000)KITTIo0.10745.174.046.3
FESTA [31]FullFT3Do(18,000)KITTIo0.09444.983.4-
3DFlow [30]FullFT3Do(18,000)KITTIo0.07381.989.026.1
BiPFN [4]FullFT3Do(18,000)KITTIo0.06576.990.626.4
SCOOP (ours)SelfFT3Do(1,800)KITTIo0.06379.791.024.4
SCOOP+(ours)SelfFT3Do(1,800)KITTIo0.04791.395.018.6
JGF [21]Full + Self + SelfFT3Do(18,000) + nuScenes (700) + KITTIv(100)KITTIt0.10546.579.4-
SPF [13]Self + SelfKITTIr(6,068) + KITTIv(100)KITTIt0.08941.775.0-
RigidFlow [14]SelfKITTIr(6,068)KITTIt0.11738.869.7-
SCOOP (ours)SelfKITTIv(100)KITTIt0.05280.692.919.7
Graph Prior [23]SelfN/A (optimization-only)KITTIt0.08284.088.5-
Neural Prior [15]SelfN/A (optimization-only)KITTIt0.03692.396.2-
SCOOP+(ours)SelfKITTIv(100)KITTIt0.03993.696.515.2
+ +Table 1. Quantitative comparison. We compare scene flow evaluation metrics for different supervision settings, train data, and test data. The number of training examples is indicated in parentheses. $EPE$ , $AS$ , $AR$ , and $Out$ . stand for End-Point-Error, Strict Accuracy, Relaxed Accuracy, and Outliers, respectively. The symbol $^+$ indicates an evaluation using all the points in the test point clouds, as done for the optimization-only methods [15, 23]. While other baselines apply fully-supervised training, our method yields better performance without employing ground-truth flow labels. Besides, SCOOP can be trained only on $\mathrm{KITTI_v}$ , with as few as 100 training instances. In contrast, alternative learning-based methods use additional training data, such as nuScenes, or a large dataset, such as $\mathrm{KITTI_r}$ . Please see further details in subsections 4.1 and 4.2. + +dimension is $d = 128$ . For the neighborhood sizes we use $k_{s} = 64$ , $k_{f} = 32$ , and the losses' hyperparameters are set to $\alpha_{conf} = 0.1$ , $\alpha_{flow} = 10$ . + +As in previous work [14, 16, 21, 24], we evaluate SCOOP on point clouds of 2,048 points randomly sampled from the source and target. However, the full point clouds of $\mathrm{KITTI_o}$ and $\mathrm{KITTI_t}$ are an order of magnitude larger and have different cardinality. Thus, for a complete evaluation of the entire scene flow, we also utilize our method (denoted as $\mathrm{SCOOP^{+}}$ for this case) to exploit the whole point cloud information and test the performance for the original resolution. Additional implementation details appear in the supplementary. + +**Baseline methods.** Our method is contrasted with the recent methods FlowNet3D [16], FLOT [24], FESTA [31], 3DFlow [30], and BiPFN [4]. These methods require ground-truth flow supervision. Additionally, we compare our results with the recent self-supervised flow models of Mittal et al. [21] and Li et al. [13,14], and the optimization-based techniques Graph Prior [23] and Neural Prior [15]. + +# 4.2. Scene Flow Results + +Cross-dataset evaluation. We demonstrate the generalization power of SCOOP by training it on the $\mathrm{FT3D_o}$ and testing its performance on $\mathrm{KITTI_o}$ . Table 1 summarises the results. The alternative methods [4, 16, 24, 30, 31] are trained on $\mathrm{FT3D_o}$ in a fully-supervised fashion: their models are learned with the ground-truth flow information, and the points with an occluded flow are excluded from the + +training objective using the mask provided in the dataset. + +In contrast, our model is trained in a completely self-supervised manner. We assume no knowledge of the flow annotations nor the occlusion mask and do not use them in our losses. Additionally, we use only 1,800 randomly selected examples from $\mathrm{FT3D_o}$ , while the competitors employ all 18,000 scene instances. Still, SCOOP improves over the SOTA method BiPFN [4] in all the evaluation metrics. Moreover, utilizing the entire point cloud data further increases our performance. + +FlowNet3D [16], FESTA [31], 3DFlow [30], and BiPFN [4] are regression-based networks that predict the flow in the 3D ambient space. The models adapt to the characteristics of the synthetic training set, and the generalization to the real-world test data is limited. FLOT [24] leverages point cloud correspondence based on learned point features, which eases the flow prediction problem. However, it also jointly learns to regress a flow correction component that burdens the point representation training process. + +SCOOP, on the other hand, is focused only on learning point embeddings suitable for scene flow estimation, guided by our self-supervised losses. It extracts discriminative features, which transfer well across the $\mathrm{FT3D_o}$ and $\mathrm{KITTI_o}$ datasets, and enables to compute the correspondence-based flow between the point clouds. In contrast to FLOT, we delegate the flow refinement process to the test phase, directly optimize it in a self-supervised fashion, and surpass their flow estimation performance. + +Figure 5 shows a visual comparison between the results + +![](images/38465836362c175ccc4816d298dc607ec7bfa981fd3ad0a12ca9b34abe8eaecc.jpg) +Figure 5. Visual comparison of scene flow results for a KITTI $_0$ example scene. The training was done on the FT3D $_0$ dataset. The source and target point clouds are shown in red and green, respectively. The warped source point cloud by FLOT [24] (left) and by our method (right) is presented in blue. While the result of FLOT deviates from the surface of the target, SCOOP preserves the source point cloud's structure and computes its accurate flow. + +![](images/7d8467e44bf3f5e591eba4911726529bbd0f6bd230d45b2625311015dfdcefd4.jpg) + +of FLOT and our method. The warped source point cloud by FLOT is noisy, and the structure of objects in the scene is compromised. On the contrary, SCOOP produces a coherent flow field across neighboring points, preserves their local geometry, and accurately predicts the scene flow. Additional visualizations are presented in the supplementary. + +Training on a small dataset. Since our model does not include a flow regression component and has to learn only point features, it can be trained on a very limited amount of data. To demonstrate this ability, we train it from scratch on the 100 point cloud pairs of $\mathrm{KITTI_v}$ and use $\mathrm{KITTI_t}$ for testing. The results of this experiment are presented in Table 1. + +Different from our work, the competing methods of Mittal et al. [21] and Li et al. [13, 14] are based on flow regression and require a large amount of training data. Mittal et al. utilize a fully-supervised pre-training on $\mathrm{FT3D_o}$ , and the additional outdoor flow dataset nuScenes [2], before fin-tuning on $\mathrm{KITTI_v}$ . Li et al. [13, 14] train their model on the large $\mathrm{KITTI_r}$ dataset. Our SCOOP outperforms these other methods while being trained only on $\mathrm{KITTI_v}$ , which is almost two orders of magnitudes smaller than $\mathrm{KITTI_r}$ . + +The pure optimization methods [15, 23] find the solution per scene separately, which might lead to sub-optimal local minima. In contrast, we leverage the correspondence statistics learned from the data and adapt the initial flow to the scene at hand by our residual run-time optimization. The initial correspondence flow serves as a good starting point for the optimization phase, yielding a similar or better final result compared to the optimization-only alternatives. + +The influence of flow refinement. Our flow results before and after refinement are presented in Figure 6. Posing the learning part of SCOOP as a correspondence problem enables its effective training on a small dataset. However, the flow predictions from the training phase are confined to a linear combination of existing target points, which may not represent the exact flow of the scene. Moreover, wrong matches for the source points can occur and cause flow errors. In such cases, our refinement module comes into play. + +Given the output flow from the trained correspondence model, the refinement module optimizes correction vectors subject to two objectives: a warped source point should be close to a target point; neighboring source points should have a similar flow. These objectives help fixing inconsistencies in the flow field and increase the flow accuracy. As seen in Figure 6, our refinement step improves the initial flow estimation and results in an accurate flow field, which is similar to the ground-truth scene flow. + +# 4.3. Performance and Time Analysis + +We analyze the performance-time trade-off in Figure 7 by recording the $EPE$ and inference time for different methods. The measurements were done on an Nvidia Titan Xp GPU for computing the flow for complete point clouds of the $\mathrm{KITTI_t}$ dataset. + +Network-only methods [13, 14, 21] tend to be fast but with limited accuracy. Optimizing the flow prediction separately for each scene [15] results in a low $EPE$ . However, it takes a long time. Our hybrid method bridges the trade-off gap between these two approaches. $\mathrm{SCOOP}^{+}$ offers a work- + +![](images/e49e6035a237e4a4d3af4748748f9527e50d1fac325d1118ade3002e0a440da8.jpg) +Figure 6. The flow refinement effect. We demonstrate the effect on data from $\mathrm{KITTI}_{\mathrm{t}}$ . The source point cloud is in red, and the target is in green. Our correspondence model was trained on the $\mathrm{KITTI}_{\mathrm{v}}$ dataset, and its flow estimation before refinement is shown in magenta (left). The optimized refined flow is presented in blue (center). We also show the ground-truth scene flow in purple for reference (right). The refined flow better covers the target point cloud (top center ellipse). It also breaches the convex hull of the given target points and enables computing the correct flow for source points whose target is missing (bottom center ellipse). + +![](images/7e11abd9b177023434aa35d0bad63efb5e60331603e61c981ce4032b1b18a083.jpg) + +![](images/91d248c33792d98da1d61724ec5893643a8cbf76779934fcdf73f5f18ffb7a69.jpg) + +ing point with more than $50\%$ error reduction over the feedforward models and about $8\times$ faster inference time than the optimization-only Neural Prior work. $\mathrm{SCOOP^{+}}$ also enables a different balance between time and performance, as seen in Figure 7. By reducing the number of run-time optimization steps, the user can shorten the inference time, achieving a working point closer to that of the network-only models. + +# 4.4. Ablation Study + +The design choices in our method are verified by ablation experiments presented in Table 2. We change one element each time and keep all the others the same. The following ablative settings were examined: (a) use all target points for soft correspondence instead of the ones with the highest transport amount (Equation 5); (b) ignore the point matching confidence by setting $p_{x_i} = 1$ in Equation 10 and $\alpha_{conf} = 0$ in Equation 13; (c) exclude the smoothness flow loss $\mathcal{L}_{flow}$ from Equation 13; and (d) turn off the flow refinement module. + +The ablation study validates the contribution of the proposed components to the method's performance. Considering a subset of target points for correspondence enables the model to concentrate on the most relevant candidates for flow estimation. The matching confidence emphasizes the influence of the more confident points in our confidence-aware distance loss $\mathcal{L}_{dist}$ . The smoothness loss term is important for regularizing the point representation learning to obtain similar features across neighboring points. Lastly, our flow refinement optimization improves the consistency + +![](images/0964de2f15a5a6a40ee68454998e10d126bb51941660d994e52b51f33c11a47f.jpg) +Figure 7. Flow estimation error vs. inference time for the KITTI dataset. $\mathrm{SCOOP^{+}}$ has a lower error than the network-only models and a shorter inference time than the optimization-only methods. It also allows different balances along the error and time trade-off, as presented by the blue curve. + +
SettingEPE↓AS↑
(a) All target points as candidates (ks = n)0.04791.1
(b) W/O confidence (pxi = 1, αconf = 0)0.04490.3
(c) W/O smoothness loss term (αflow = 0)0.05686.6
(d) W/O flow refinement (R* = 0)0.11543.8
Our complete method0.03993.6
+ +Table 2. Component ablative settings. SCOOP was trained on $\mathrm{KITTI_v}$ and evaluated on $\mathrm{KITTI_t}$ . The results show that the best performance is obtained with our complete method. Additional details about the ablation experiments are given in subsection 4.4. + +of the flow field and reduces the $EPE$ substantially. In the supplementary material, we provide an ablation study on the $\mathrm{FT3D_o}$ train set size and find that a $10\%$ fraction of the data suffices for our method to realize its potential. + +# 5. Conclusions + +This paper presented SCOOP, a novel self-supervised scene flow estimation method for 3D point clouds based on correspondence learning and flow refinement optimization. Previous works suggested learning a flow regression model, training a neural network that jointly learned point cloud correspondence and flow refinement, or optimizing the flow completely at run-time without learning. + +In contrast, we split the flow prediction process into two simpler problems. Our correspondence model is focused only on learning point features to initialize the flow from soft matches between the point clouds. Then, we directly optimize a residual flow refinement at run-time. This approach enables SCOOP to be trained on a small set of point cloud scenes without utilizing ground-truth supervision while outperforming state-of-the-art fully-supervised and self-supervised learning methods, as well as optimization-based alternative techniques. + +# References + +[1] Thomas Brox and Jitendra Malik. Large Displacement Optical Flow: Descriptor Matching in Variational Motion Estimation. 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In David Forsyth, Philip Torr, and Andrew Zisserman, editors, Proceedings of the Seventh IEEE International Conference on Computer Vision (ECCV), pages 739-751, Berlin, Heidelberg, 2008. Springer Berlin Heidelberg. 1 +[34] Wenxuan Wu, Zhi Yuan Wang, Zhuwen Li, Wei Liu, and Li Fuxin. PointPWC-Net: Cost Volume on Point Clouds for (Self-) Supervised Scene Flow Estimation. In Proceedings of the European Conference on Computer Vision (ECCV), pages 88–107, 2020. 1, 2 +[35] Xin Wu, Hao Zhao, Shunkai Li, Yingdian Cao, and Hongbin Zha. SC-wLS: Towards Interpretable Feed-forward Camera Re-localization. In Proceedings of the European Conference on Computer Vision (ECCV), pages 585-601, 2022. 2 +[36] Yiming Zeng, Yue Qian, Zhiyu Zhu, Junhui Hou, Hui Yuan, and Ying He. CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 6052-6061, 2021. 3 +[37] Chengliang Zhong, Peixing You, Xiaoxue Chen, Hao Zhao, Fuchun Sun, Guyue Zhou, Xiaodong Mu, Chuang Gan, and Wenbing Huang. SNAKE: Shape-aware Neural 3D Keypoint Field. In Advances in Neural Information Processing Systems (NeurIPS), 2022. 2 \ No newline at end of file diff --git a/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/images.zip b/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..08f596cc59f6e1d9cf53f27ad71fa03f948384b8 --- /dev/null +++ b/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fd62076907b34dbed6ff914a7672c01be8b9dd582c33051d4dd73f84b73bdb74 +size 614848 diff --git a/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/layout.json b/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5f3be92446be3a19594e1e1a7b049b07e7d63f93 --- /dev/null +++ b/2023/SCOOP_ Self-Supervised Correspondence and Optimization-Based Scene Flow/layout.json @@ -0,0 +1,9695 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 53, + 103, + 539, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 103, + 539, + 121 + ], + "spans": [ + { + "bbox": [ + 53, + 103, + 539, + 121 + ], + "type": "text", + "content": "SCOOP: Self-Supervised Correspondence and Optimization-Based Scene Flow" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 141, + 127, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 141, + 127, + 158 + ], + "spans": [ + { + "bbox": [ + 64, + 141, + 127, + 158 + ], + "type": "text", + "content": "Itai Lang" + }, + { + "bbox": [ + 64, + 141, + 127, + 158 + ], + "type": "inline_equation", + "content": "^{1,2*}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 151, + 143, + 211, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 151, + 143, + 211, + 157 + ], + "spans": [ + { + "bbox": [ + 151, + 143, + 211, + 157 + ], + "type": "text", + "content": "Dror Aiger2" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 236, + 144, + 312, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 236, + 144, + 312, + 156 + ], + "spans": [ + { + "bbox": [ + 236, + 144, + 312, + 156 + ], + "type": "text", + "content": "Forrester Cole" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 337, + 143, + 402, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 143, + 402, + 156 + ], + "spans": [ + { + "bbox": [ + 337, + 143, + 402, + 156 + ], + "type": "text", + "content": "Shai Avidan" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 427, + 144, + 527, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 427, + 144, + 527, + 156 + ], + "spans": [ + { + "bbox": [ + 427, + 144, + 527, + 156 + ], + "type": "text", + "content": "Michael Rubinstein2" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 190, + 157, + 290, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 157, + 290, + 171 + ], + "spans": [ + { + "bbox": [ + 190, + 157, + 290, + 171 + ], + "type": "text", + "content": "1Tel Aviv University" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 157, + 403, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 157, + 403, + 171 + ], + "spans": [ + { + "bbox": [ + 315, + 157, + 403, + 171 + ], + "type": "text", + "content": "2Google Research" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 88, + 174, + 288, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 174, + 288, + 185 + ], + "spans": [ + { + "bbox": [ + 88, + 174, + 288, + 185 + ], + "type": "text", + "content": "{itailang@mail, avidan@eng}.tau.ac.il" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 320, + 174, + 493, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 174, + 493, + 185 + ], + "spans": [ + { + "bbox": [ + 320, + 174, + 493, + 185 + ], + "type": "text", + "content": "{aigerd, fcole, mrub}@google.com" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 143, + 213, + 191, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 191, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 191, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 45, + 238, + 288, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 238, + 288, + 380 + ], + "spans": [ + { + "bbox": [ + 45, + 238, + 288, + 380 + ], + "type": "text", + "content": "Scene flow estimation is a long-standing problem in computer vision, where the goal is to find the 3D motion of a scene from its consecutive observations. Recently, there have been efforts to compute the scene flow from 3D point clouds. A common approach is to train a regression model that consumes source and target point clouds and outputs the per-point translation vector. An alternative is to learn point matches between the point clouds concurrently with regressing a refinement of the initial correspondence flow. In both cases, the learning task is very challenging since the flow regression is done in the free 3D space, and a typical solution is to resort to a large annotated synthetic dataset." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 381, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 287, + 548 + ], + "type": "text", + "content": "We introduce SCOOP, a new method for scene flow estimation that can be learned on a small amount of data without employing ground-truth flow supervision. In contrast to previous work, we train a pure correspondence model focused on learning point feature representation and initialize the flow as the difference between a source point and its softly corresponding target point. Then, in the run-time phase, we directly optimize a flow refinement component with a self-supervised objective, which leads to a coherent and accurate flow field between the point clouds. Experiments on widespread datasets demonstrate the performance gains achieved by our method compared to existing leading techniques while using a fraction of the training data. Our code is publicly available1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 571, + 127, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 127, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 127, + 583 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 686 + ], + "type": "text", + "content": "Scene flow estimation [27] is a fundamental problem in computer vision with various use-cases, such as autonomous driving, scene parsing, pose estimation, and object tracking, to name a few. Given two consecutive observations of a 3D scene, the aim is to compute the dynamics of the scene between the observations. Scene flow prediction based on 2D images has been thoroughly investigated in the literature [17, 19, 28, 32, 33]. However, in light of the" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 307, + 213, + 541, + 340 + ], + "blocks": [ + { + "bbox": [ + 307, + 213, + 541, + 340 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 541, + 340 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 541, + 340 + ], + "type": "image", + "image_path": "bce42a77079dac70b97a54467c894ef5e76783731facbe2b96c430c73521e2c7.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 347, + 545, + 403 + ], + "lines": [ + { + "bbox": [ + 305, + 347, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 347, + 545, + 403 + ], + "type": "text", + "content": "Figure 1. Flow accuracy on the KITTI benchmark vs. the train set size. Our method is trained on one or two orders of magnitude less data while surpassing the performance of the competing techniques [4, 13, 14, 16, 21, 24, 30, 31] by a large margin. Please see Table 1 for the complete details of the evaluation settings." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 425, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 460 + ], + "type": "text", + "content": "recent proliferation of 3D sensors, such as LiDAR, there is a surge of interest in scene flow methods that operate directly on the 3D data [10, 13, 16, 21, 34]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 461, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 568 + ], + "type": "text", + "content": "Liu et al. [16] were among the first to pursue this research avenue. They proposed FlowNet3D, a fully-supervised neural network that learned to regress the flow between 3D point clouds and showed remarkable performance improvement over image-based techniques [1, 19, 29]. Since their method required ground-truth flow annotations, which are scarce for real-world data, they turned to training on a large synthetic dataset that compromised the generalization capability to real-world LiDAR data." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": "Follow-up works devised self-supervised learning schemes [13, 21] and narrowed the domain gap by training on unannotated LiDAR point cloud pairs. However, similar to Liu et al. [16], they used a regression approach in which the model should learn to compute the flow in the free 3D space. This task is extremely challenging, given the irregular nature of point clouds, and requires a large amount of training data for the network to converge." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "In another line of work [8, 11, 24], researchers leveraged point cloud correspondence for scene flow prediction. In this approach, the flow is computed as the translation of a point in the first point cloud (source) to its softly corre" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 211, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 211, + 703 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 211, + 703 + ], + "type": "text", + "content": "1https://github.com/itailang/SCOOP" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 703, + 248, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 703, + 248, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 703, + 248, + 712 + ], + "type": "text", + "content": "*The work was done during an internship at Google Research." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "5281" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 69, + 539, + 160 + ], + "blocks": [ + { + "bbox": [ + 56, + 69, + 539, + 160 + ], + "lines": [ + { + "bbox": [ + 56, + 69, + 539, + 160 + ], + "spans": [ + { + "bbox": [ + 56, + 69, + 539, + 160 + ], + "type": "image", + "image_path": "4c0a621e9eb17471535411910c52fbe536c008cf81f217eb156788d51a87b250.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 164, + 548, + 221 + ], + "lines": [ + { + "bbox": [ + 46, + 164, + 548, + 221 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 548, + 221 + ], + "type": "text", + "content": "Figure 2. Comparison of scene flow approaches. Given a pair of point clouds, FlowNet3D [16] learns to regress the flow in the free 3D space, and the trained model is frozen for testing. FLOT [24] concurrently trains two network components: one that computes point correspondence and another that regresses a correction to the resulting correspondence flow. Neural Prior [15] optimizes the flow between the point clouds from scratch without learning. In contrast to previous work, we take a hybrid approach. We train a pure correspondence model without flow regression, which serves for flow initialization. Then, we directly optimize only the flow refinement at the test-time." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 373 + ], + "type": "text", + "content": "sponding point in the second one (target). The softly corresponding point is a weighted sum of target points based on point similarity in a learned latent space. Thus, rather than the challenging regression problem in the 3D ambient space, the flow estimation task boils down to point feature learning and is reduced to the convex combination space [26] of existing target points. However, to relax this constraint, another network component is trained to regress flow corrections. The joint training of point representation and flow refinement burdens the learning process and retains the reliance on large datasets with flow supervision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 375, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 435 + ], + "type": "text", + "content": "Another emerging approach is an optimization-only flow computation [15, 23]. In this case, no training data is involved, and the flow is optimized at run-time for each scene separately. Despite the high accuracy such a dedicated optimization achieves, it requires a long processing time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 436, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 288, + 581 + ], + "type": "text", + "content": "We present SCOOP, a hybrid flow estimation method that can be learned from a small amount of training data. SCOOP consists of two parts: a self-supervised neural network for point cloud correspondence and a direct flow refinement optimization module. During the training phase, the network learns to extract point features for soft point matches, which initialize the flow between the point clouds. In contrast to previous work, our network is focused on learning just the point embeddings, allowing its training on a very small dataset, as shown in Figure 1. Additionally, we consider the confidence of the network in the computed correspondences to guide the learning process better." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "Then, instead of training another network for regressing flow updates, we define an optimization problem and directly optimize residual flow refinement vectors at runtime. The optimization objective encourages a coherent flow field while retaining the translated source points close to the target point cloud. Our design choices improve the accuracy compared to learning-based methods and reduce the processing time with respect to the optimization-only approach [15, 23]. For both correspondence learning and refinement optimization, we use a self-supervised distance objective and a smoothness prior instead of ground-truth" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 241, + 545, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 241, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 305, + 241, + 545, + 265 + ], + "type": "text", + "content": "flow labels. Figure 2 presents the difference between our approach and leading previous ones." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 266, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 546, + 361 + ], + "type": "text", + "content": "In summary, we propose a hybrid flow prediction approach for point clouds based on self-supervised correspondence learning and direct run-time residual flow optimization. Using well-established datasets in the scene flow literature, we show that our approach yields clear performance improvement over existing state-of-the-art methods while using a fraction of the training data and without employing any ground-truth flow supervision." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 373, + 392, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 392, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 392, + 385 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 394, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 514 + ], + "type": "text", + "content": "Flow regression. A common approach for scene flow estimation on point clouds is to train a flow regression model [4,10,16,31,34]. It is a neural network that computes the flow vectors between the point clouds in the ambient 3D space. Liu et al. [16] proposed FlowNet3D, which encoded the point clouds into a latent space, mixed point features with a flow embedding layer, and regressed the scene flow by decoding the mixed point features. FlowNet3D was trained in a fully-supervised manner, using an " + }, + { + "bbox": [ + 304, + 394, + 545, + 514 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 394, + 545, + 514 + ], + "type": "text", + "content": " loss with respect to ground-truth flow annotations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 514, + 546, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 546, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 546, + 682 + ], + "type": "text", + "content": "Liu et al. [16] inspired a line of follow-up works [4, 13, 21, 30, 31]. Wang et al. [31] added spatial and temporal attention layers to FlowNet3D's architecture. In Bi-PointFlowNet [4], the authors propagated features from each point cloud bidirectionally, augmenting the point feature representation. Mittal et al. [21] discarded flow supervision by utilizing a self-supervised nearest neighbor loss and cycle consistency between the forward and revers scene flows, and Li et al. [13, 14] extracted flow labels for training from the data itself. Similar to the latter methods, we also refrain from ground-truth flow supervision in our training scheme. However, rather than flow regression, we base our technique on soft point matches in the scene, which simplifies the flow estimation problem." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Point cloud correspondence. Finding correspondences is widely applied to various vision tasks [12, 24, 35, 37]." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5282" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "Several methods have been proposed for dense mapping between non-rigid point cloud shapes [7, 9, 12, 36]. Recently, Lang et al. [12] suggested constructing one point cloud by the other using latent space similarity and the point coordinates themselves rather than regressing the corresponding point cloud [9, 36]. Inspired by Lang's work, we do not use flow regression in our model and concentrate the learning process on point feature representation. However, while Lang et al. operated on complete shapes with one-to-one correspondence, our method accommodates scenes with partial objects where a perfect match may not exist." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 205, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 289, + 373 + ], + "type": "text", + "content": "Researchers have taken the correspondence approach to the scene flow problem as well [8, 11, 24]. FLOT [24] computed an optimal transport plan that served for an initial flow between the point clouds and further regressed flow refinement with a series of learned convolutions. Our work builds on FLOT but differs from it in three main aspects. First, we exclude flow regression from our training scheme and instead apply direct run-time optimization to refine the initial correspondence-based flow. Second, we use the model's confidence in the computed point matches to improve the point feature learning. Third, we do not use any groundtruth flow annotations, neither for the correspondence training nor for the refinement optimization, whereas FLOT relies on fully-supervised scene flow data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 380, + 289, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 289, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 289, + 524 + ], + "type": "text", + "content": "Optimization-based scene flow. Pontes et al. [23] suggested a scene flow estimation technique that does not involve learning. Instead, the flow was optimized completely at run-time, such that the warped source is close to the target point cloud while demanding the flow to be \"as-rigid-as-possible\". Pontes et al. encoded this prior by minimizing the graph Laplacian defined over the source points. In follow-up work [15], the explicit graph was replaced by a neural prior, which implicitly regularized the optimized flow field. In contrast to these papers, we initialize the flow with a learned correspondence model and optimize only the residual flow refinement at run-time." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 104, + 548 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": "A point cloud is a set of unordered 3D points " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "X \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " is the number of points. Given a pair of point clouds of a scene, denoted as " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "X, Y \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " and referred to as source and target, respectively, our goal is to estimate a flow field " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "F^* \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " describing the per-point motion from " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 556, + 287, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "We tackle this problem via self-supervised soft correspondence learning between the two point clouds and a direct flow refinement optimization. An overview of the method is shown in Figure 3. First, a deep neural network is used to extract point features. Then, we calculate a matching cost between points in the learned feature space. Based on this cost, we solve an optimal transport" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": "problem to compute a softly matched target point for each source point, where the difference between the two is regarded as the correspondence-based flow. Finally, we refine the flow field by demanding its consistency across neighboring source points and obtain our estimated scene flow. In both correspondence learning and flow refinement, no ground-truth flow labels are employed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 162, + 398, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 162, + 398, + 175 + ], + "spans": [ + { + "bbox": [ + 305, + 162, + 398, + 175 + ], + "type": "text", + "content": "3.1. Matching Cost" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "content": "The cost of matching a point " + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "inline_equation", + "content": "x_{i} \\in X" + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "content": " to a point " + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "inline_equation", + "content": "y_{j} \\in Y" + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "content": " is determined based on the point representation learned by a deep neural network. The network consumes the raw point clouds " + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "inline_equation", + "content": "X, Y" + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "content": " and computes point features " + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "inline_equation", + "content": "\\Phi_{X}, \\Phi_{Y} \\in \\mathbb{R}^{n \\times d}" + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 180, + 547, + 263 + ], + "type": "text", + "content": " is the per-point feature dimension. The network's architecture is based on PointNet++ [25]. Its details are given in the supplemental material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 264, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 264, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 264, + 547, + 289 + ], + "type": "text", + "content": "Inspired by previous work [12, 13, 24], we first compute the cosine similarity in the learned feature space:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 378, + 293, + 545, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 293, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 378, + 293, + 545, + 323 + ], + "type": "interline_equation", + "content": "S _ {i j} = \\frac {\\Phi_ {X} ^ {i} \\cdot \\left(\\Phi_ {Y} ^ {j}\\right) ^ {\\top}}{\\left| \\left| \\Phi_ {X} ^ {i} \\right| \\right| _ {2} \\left| \\left| \\Phi_ {Y} ^ {j} \\right| \\right| _ {2}}, \\tag {1}", + "image_path": "bc932dece88ada41a50740de28056d9d574cabbcada0e772b26d0aef8f0cf6ad.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\Phi_X^i, \\Phi_Y^j \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "content": "'th and " + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "content": "'th rows of " + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\Phi_X" + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\Phi_Y" + }, + { + "bbox": [ + 305, + 328, + 547, + 354 + ], + "type": "text", + "content": ", respectively. Then, the cost is set to" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 394, + 359, + 545, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 359, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 394, + 359, + 545, + 373 + ], + "type": "interline_equation", + "content": "C _ {i j} = 1 - S _ {i j} \\tag {2}", + "image_path": "1019e8cd92011ab458804039daa2e5bf32efd38109844bd93f014f5db2a7ea22.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 377, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 377, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 305, + 377, + 545, + 402 + ], + "type": "text", + "content": "for points with a Euclidean distance less than 10 meters and to " + }, + { + "bbox": [ + 305, + 377, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\infty" + }, + { + "bbox": [ + 305, + 377, + 545, + 402 + ], + "type": "text", + "content": " otherwise to avoid flow between points too far apart." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 407, + 427, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 427, + 420 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 427, + 420 + ], + "type": "text", + "content": "3.2. Soft Correspondence" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 426, + 547, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 487 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 487 + ], + "type": "text", + "content": "Finding correspondence between the source and target point clouds can be modeled as an optimal transport problem, where each source point is assigned with a mass " + }, + { + "bbox": [ + 304, + 426, + 547, + 487 + ], + "type": "inline_equation", + "content": "\\frac{1}{n}" + }, + { + "bbox": [ + 304, + 426, + 547, + 487 + ], + "type": "text", + "content": " that is transported to the target points [13, 24]. Similar to FLOT [24], we use the relaxed transport problem:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 321, + 491, + 517, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 491, + 517, + 542 + ], + "spans": [ + { + "bbox": [ + 321, + 491, + 517, + 542 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} T ^ {*} = \\underset {T \\in \\mathbb {R} _ {+} ^ {n \\times n}} {\\operatorname {a r g m i n}} \\sum_ {i j} \\left(C _ {i j} T _ {i j} + \\epsilon T _ {i j} (\\log T _ {i j} - 1)\\right) \\\\ + \\lambda (\\mathsf {K L} (T 1 _ {n}, \\frac {1}{n} 1 _ {n}) + \\mathsf {K L} (T ^ {\\top} 1 _ {n}, \\frac {1}{n} 1 _ {n})), \\\\ \\end{array}", + "image_path": "6927e8491a2df319b602aa8895efeb44535805d6dfcc90f1f422a24cd08a7f98.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "inline_equation", + "content": "C_{ij} \\geq 0" + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": " is the matching cost from Equation 2 and " + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "inline_equation", + "content": "T_{ij} \\geq 0" + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": " is the amount of mass transported between points. The parameters " + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\epsilon, \\lambda \\geq 0" + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": " control the relaxation of the problem. " + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "inline_equation", + "content": "1_n \\in \\mathbb{R}^n" + }, + { + "bbox": [ + 304, + 545, + 545, + 617 + ], + "type": "text", + "content": " is a vector with all entries equal 1. KL is the Kullback-Leibler divergence used for soft preservation of the transported mass between the point clouds." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": "The second term in the summation operation in Equation 3 is an entropic regularization, which enables solving the problem efficiently by the Sinkhorn algorithm [5,6]. We use this algorithm to estimate the optimal transport matrix " + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "inline_equation", + "content": "T^{*}" + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": " to represent the soft correspondence between the point clouds. The complete derivation of the transport problem and the Sinkhorn algorithm's details are given in the supplementary material." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5283" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 203, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 203, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 203, + 85 + ], + "type": "text", + "content": "3.3. Correspondence-Based Flow" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 197 + ], + "type": "text", + "content": "We leverage the optimal transport plan " + }, + { + "bbox": [ + 46, + 90, + 287, + 197 + ], + "type": "inline_equation", + "content": "T^{*}" + }, + { + "bbox": [ + 46, + 90, + 287, + 197 + ], + "type": "text", + "content": " to compute correspondence weights for the source and target points for an initial estimate of the scene flow. Different from FLOT [24], which includes all the target points as candidates for each source point, we consider only target points with maximal transport amount from the source point. This design choice focuses our flow estimation pipeline on the most relevant target candidates and improves the method's results." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "text", + "content": "For a point " + }, + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "inline_equation", + "content": "x_{i} \\in X" + }, + { + "bbox": [ + 47, + 198, + 287, + 220 + ], + "type": "text", + "content": ", the matching weights are calculated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 117, + 219, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 219, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 117, + 219, + 287, + 251 + ], + "type": "interline_equation", + "content": "w _ {i j} = \\frac {e ^ {T _ {i j} ^ {*}}}{\\sum_ {l \\in \\mathcal {N} _ {Y} \\left(x _ {i}\\right)} e ^ {T _ {i l} ^ {*}}}, \\tag {4}", + "image_path": "7da668541d5fc8fdda54bd33e037283958676b50feea3726124b7be1bb804001.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_Y(x_i)" + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": " is a neighborhood containing the " + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "inline_equation", + "content": "k_{s}" + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": " indices of the " + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "inline_equation", + "content": "\\{y_j\\}" + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": " points with the top mass transport " + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "inline_equation", + "content": "\\{T_{ij}^*\\}" + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": ". The softly corresponding point " + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "inline_equation", + "content": "\\hat{y}_{x_i}" + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 255, + 287, + 292 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 119, + 300, + 287, + 328 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 300, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 119, + 300, + 287, + 328 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {Y} \\left(x _ {i}\\right)} w _ {i j} y _ {j}, \\tag {5}", + "image_path": "05e3e401418dbd476af4a22c0a862f628217758b2a1cecfce7864832ce82738b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 336, + 241, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 241, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 241, + 348 + ], + "type": "text", + "content": "and the initial estimated flow for the point " + }, + { + "bbox": [ + 47, + 336, + 241, + 348 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 336, + 241, + 348 + ], + "type": "text", + "content": " is:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 135, + 358, + 287, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 358, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 135, + 358, + 287, + 371 + ], + "type": "interline_equation", + "content": "f _ {i} = \\hat {y} _ {x _ {i}} - x _ {i}. \\tag {6}", + "image_path": "5c3f91eadcc8f47ce06bbcdbcac9fb45e1cd7262d2c2d584f8d27eaee5ec0650.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "type": "text", + "content": "Note that if we define " + }, + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "type": "inline_equation", + "content": "\\widehat{T}_{ij}^{*} = w_{ij}" + }, + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "type": "inline_equation", + "content": "j\\in \\mathcal{N}_Y(x_i)" + }, + { + "bbox": [ + 47, + 380, + 287, + 407 + ], + "type": "text", + "content": " and 0 otherwise, we get the initial flow field as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 111, + 413, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 413, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 111, + 413, + 287, + 430 + ], + "type": "interline_equation", + "content": "F = \\widehat {T} ^ {*} Y - X = \\widehat {Y} - X, \\tag {7}", + "image_path": "e8b793b0fd227b65323aabf3944d0724b6d0cefada5f296425a1ac07772c59de.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "spans": [ + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "type": "inline_equation", + "content": "\\widehat{Y} \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "type": "text", + "content": " contains the points " + }, + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "type": "inline_equation", + "content": "\\{\\hat{y}_{x_i}\\}" + }, + { + "bbox": [ + 47, + 437, + 225, + 452 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 458, + 158, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 158, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 158, + 472 + ], + "type": "text", + "content": "3.4. Training Objective" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "content": "To learn point representation suitable for scene flow without ground-truth supervision, we apply the flowing loss terms. First, for a tractable flow estimation, we would like each softly corresponding point " + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\hat{y}_{x_i}" + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "content": " to have a nearby target point " + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "inline_equation", + "content": "y_{j}" + }, + { + "bbox": [ + 46, + 477, + 287, + 548 + ], + "type": "text", + "content": ". It may be achieved by the nearest-neighbor distance term, as done by Mittal et al. [21]:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 97, + 557, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 557, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 97, + 557, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\mathcal {D} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} \\min _ {y _ {j} \\in Y} \\| \\hat {y} _ {x _ {i}} - y _ {j} \\| _ {2} ^ {2}. \\tag {8}", + "image_path": "d01e7fcf95d3e4ab31e10c9cbe41681d09b08dae347438a30fbcec3b47b7a741.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 595, + 287, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 595, + 287, + 655 + ], + "spans": [ + { + "bbox": [ + 46, + 595, + 287, + 655 + ], + "type": "text", + "content": "However, the correspondence quality for the source points can vary. For example, points on a flat region will have less distinctive correspondences than points with geometrically unique features. Thus, we augment the distance term in Equation 8 with the matching confidence of each point." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 655, + 287, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 287, + 679 + ], + "type": "text", + "content": "The confidence measure is based on the correspondence similarity that we define as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 118, + 689, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 689, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 118, + 689, + 287, + 716 + ], + "type": "interline_equation", + "content": "s _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {Y} (x _ {i})} w _ {i j} S _ {i j}. \\tag {9}", + "image_path": "f0e39690a1d10f1cab6031872dbc4936f02a9aa02854fc2cf23be2ca1edf2c04.jpg" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 232 + ], + "type": "image", + "image_path": "7f533893eb5fb9cb282914d1e57b5880596150f2d36fc902bfbf07d388c05c4a.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "lines": [ + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": "Figure 3. The proposed method. SCOOP includes two components: a learned point cloud correspondence model and a flow refinement module. The model learns deep point embeddings " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "\\Phi_X, \\Phi_Y" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": " to establish soft point matches based on a matching cost " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": " in the latent space. The initial flow " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": " from the training phase is the difference between the softly corresponding point cloud " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "\\widehat{Y}" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": " and the source point cloud " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": ". At the test-time, we freeze the trained model and optimize a residual flow refinement " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "R^*" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": " to produce a smooth and consistent scene flow " + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "inline_equation", + "content": "F^*" + }, + { + "bbox": [ + 305, + 243, + 546, + 342 + ], + "type": "text", + "content": " between the point clouds." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "content": "The value of " + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "inline_equation", + "content": "s_{x_i}" + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "content": " is in the range " + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "content": ". To get a confidence value between 0 and 1, we trim the negative values, set the matching confidence of " + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "content": " to be " + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "inline_equation", + "content": "p_{x_i} = \\max(s_{x_i}, 0)" + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "content": ", and use " + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "inline_equation", + "content": "p_{x_i}" + }, + { + "bbox": [ + 305, + 360, + 545, + 409 + ], + "type": "text", + "content": " to define our confidence-aware distance loss:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 343, + 413, + 545, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 413, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 343, + 413, + 545, + 442 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d i s t}} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} p _ {x _ {i}} \\min _ {y _ {j} \\in Y} \\| \\hat {y} _ {x _ {i}} - y _ {j} \\| _ {2} ^ {2}. \\tag {10}", + "image_path": "f91ca00ddf91ab3800c252f6e1c0f5fa06dba46db9299cea6418cc911dd4f37b.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": "The loss term " + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dist}" + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": " can be minimized by either minimizing " + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "inline_equation", + "content": "p_{x_i}" + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": " or the distance between " + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\hat{y}_{x_i}" + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": " and its nearest neighbor " + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "inline_equation", + "content": "y_j\\in Y" + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": ". To avoid the degenerate solution of " + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "inline_equation", + "content": "p_{x_i} = 0" + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "inline_equation", + "content": "x_{i}\\in X" + }, + { + "bbox": [ + 305, + 446, + 545, + 494 + ], + "type": "text", + "content": ", we add a confidence loss term:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 368, + 498, + 545, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 368, + 498, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 368, + 498, + 545, + 526 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n f}} = \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} 1 - p _ {x _ {i}}, \\tag {11}", + "image_path": "560d9396d4cccf8234676104515d731063a3b58b29f46c0e9296ac5ece53cfcf.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 531, + 470, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 531, + 470, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 531, + 470, + 542 + ], + "type": "text", + "content": "which penalizes the degenerate solution." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 543, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 543, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 305, + 543, + 545, + 603 + ], + "type": "text", + "content": "Additionally, to preserve the geometric structure of the source point cloud, we would like the flow field to be smooth. That is, neighboring source points should have a similar flow prediction. Thus, we regularize the learning process with a flow smoothness loss [11]:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 330, + 607, + 545, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 607, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 330, + 607, + 545, + 637 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f l o w}} = \\frac {1}{| X | k _ {f}} \\sum_ {x _ {i} \\in X} \\sum_ {l \\in N _ {X} \\left(x _ {i}\\right)} \\| f _ {i} - f _ {l} \\| _ {1}, \\tag {12}", + "image_path": "c8129936765098b8b3f8c51c213e51919db56c058acba4868ed268c369cbf342.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "inline_equation", + "content": "N_{X}(x_{i})" + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "text", + "content": " is the Euclidean neighborhood of " + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "inline_equation", + "content": "X \\backslash x_{i}" + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "inline_equation", + "content": "k_{f}" + }, + { + "bbox": [ + 305, + 642, + 544, + 666 + ], + "type": "text", + "content": ". The overall training objective is:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 324, + 672, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 672, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 324, + 672, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {d i s t}} + \\alpha_ {\\text {c o n f}} \\mathcal {L} _ {\\text {c o n f}} + \\alpha_ {\\text {f l o w}} \\mathcal {L} _ {\\text {f l o w}}, \\tag {13}", + "image_path": "512e2d90f7bc88ef45a96d01a0b08dc5ca8e68f2c112f3ae66d368ab57084d4a.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\alpha_{conf}" + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\alpha_{flow}" + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": " are hyperparameters, balancing the contribution of the different loss terms." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5284" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 214, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 214, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 214, + 85 + ], + "type": "text", + "content": "3.5. Flow Refinement Optimization" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 173 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 173 + ], + "type": "text", + "content": "The advantage of the correspondence-based flow, presented in Equation 7, is that the softly matching points are in the vicinity of the surface of objects in the target scene. However, it limits the flow to the convex hull [26] of points in the target point cloud. We enable the flow to deviate from this constraint by a flow refinement optimization step at runtime." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 174, + 287, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 174, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 287, + 245 + ], + "type": "text", + "content": "Instead of training an additional neural network part to regress flow corrections, as done by Puy et al. [24], we directly optimize a flow refinement component " + }, + { + "bbox": [ + 46, + 174, + 287, + 245 + ], + "type": "inline_equation", + "content": "R^{*} \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 46, + 174, + 287, + 245 + ], + "type": "text", + "content": " using the self-supervised distance and smoothness losses defined in Equations 10 and 12, respectively. An illustration of these losses is depicted in Figure 4." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 246, + 287, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 269 + ], + "type": "text", + "content": "The optimization problem for the flow refinement takes the form:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 275, + 287, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 287, + 350 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} R ^ {*} = \\operatorname * {a r g m i n} _ {R \\in \\mathbb {R} ^ {n \\times 3}} \\frac {1}{| X |} \\sum_ {x _ {i} \\in X} \\min _ {y _ {j} \\in Y} p _ {x _ {i}} | | x _ {i} + (f _ {i} + r _ {i}) - y _ {j} | | _ {2} ^ {2} \\\\ + \\lambda_ {f l o w} \\frac {1}{| X | k _ {f}} \\sum_ {x _ {i} \\in X} \\sum_ {l \\in N _ {X} \\left(x _ {i}\\right)} \\left\\| \\left(f _ {i} + r _ {i}\\right) - \\left(f _ {l} + r _ {l}\\right) \\right\\| _ {1}, \\tag {14} \\\\ \\end{array}", + "image_path": "74c87726c0702c53220f22b4986a0b03ca03b889b1c7e4f4e752bdd7ed34876b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "inline_equation", + "content": "r_i \\in R" + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "text", + "content": " is the flow refinement for point " + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "text", + "content": ", and the refined scene flow is " + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "inline_equation", + "content": "F^* = F + R^*" + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "text", + "content": ". Our flow refinement module further preserves the structure of the source point cloud, where the target points " + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "inline_equation", + "content": "\\{y_j\\}" + }, + { + "bbox": [ + 46, + 357, + 287, + 430 + ], + "type": "text", + "content": " are used as anchors to guide the refined flow and keep the proximity to the underlying target surface." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 441, + 128, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 128, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 128, + 453 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 460, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 533 + ], + "type": "text", + "content": "In this section, we evaluate SCOOP's performance using widely spread datasets and compare it with recent state-of-the-art (SOTA) works on scene flow estimation. Additionally, we demonstrate the influence of the flow refinement module, analyze the performance and run-time duration, and verify our design choices with an ablation study." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 540, + 163, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 163, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 163, + 553 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "type": "text", + "content": "Datasets. We adopt two common datasets in the scene flow literature, FlyingThings3D [18] and KITTI [19, 20]. Originally, these benchmarks did not include point cloud data. They were processed to a point cloud format by Liu et al. [16] and denoted as " + }, + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 46, + 558, + 287, + 617 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": " is a large-scale synthetic dataset with 18,000/2,000 train/validation scene examples of randomly moving objects from the ShapeNet collection [3]. Each example contains a pair of point clouds and ground-truth flow vectors. Since the objects' motion is randomized, they may appear or disappear from the view of the scene and create occlusions. The dataset also includes a mask for points whose flow is invalid due to occlusions." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 75, + 545, + 150 + ], + "blocks": [ + { + "bbox": [ + 309, + 75, + 545, + 150 + ], + "lines": [ + { + "bbox": [ + 309, + 75, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 309, + 75, + 545, + 150 + ], + "type": "image", + "image_path": "36a035cbc4cc88c32ed7335340ae30a589c9b40ce1885c6be217774e5e016b59.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "text", + "content": "Figure 4. Illustration of the flow refinement objective. The initial flow " + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\{f_i\\}" + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "text", + "content": " stems from the translation of the source points " + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\{x_i\\}" + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "text", + "content": " (red) to their softly corresponding ones " + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\{\\hat{y}_{x_i}\\}" + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "text", + "content": " (magenta). The flow is refined with a distance loss that keeps the proximity of the translated points to the target points " + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\{y_j\\}" + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "text", + "content": " (green) and a smoothness loss that encourages similar flow vectors (dashed purple) for neighboring points. The optimization process results in a flow field " + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\{f_i^*\\}" + }, + { + "bbox": [ + 304, + 158, + 545, + 258 + ], + "type": "text", + "content": " (blue) that preserves the structure of the source point cloud and warps it close to the implicit surface of the target point cloud." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": " dataset contains 150 real-world LiDAR scenes. Every scene includes source and target point clouds with flow annotations for the source points. Ground points are removed, and the source points are considered to have a valid flow [16]. " + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": " was further split by Mittal et al. [21] into sets of 100 and 50 examples, marked as " + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_v}" + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_t}" + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": ", respectively, for fine-tuning experiments. Li et al. [13] also built a large unlabeled LiDAR dataset for self-supervised learning on real-world data. They took raw Li-DAR scans from the KITTI scenes [19,20], disjoint from the " + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": " data, and created a training set of 6,068 instances denoted as " + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_r}" + }, + { + "bbox": [ + 304, + 277, + 545, + 420 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": "Evaluation metrics. We use well-established evaluation metrics from previous works [16, 21, 24]: End-Point-Error " + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "inline_equation", + "content": "EPE[m]" + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": ", Strict Accuracy " + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "inline_equation", + "content": "AS[\\%]" + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": ", Relaxed Accuracy " + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "inline_equation", + "content": "AR[\\%]" + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": ", and Outliers " + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "inline_equation", + "content": "Out.[\\%]" + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": ". These metrics are based on the point error " + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": " and the relative error " + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "inline_equation", + "content": "e_i^{rel}" + }, + { + "bbox": [ + 305, + 426, + 545, + 486 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 328, + 492, + 545, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 492, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 328, + 492, + 545, + 521 + ], + "type": "interline_equation", + "content": "e _ {i} = \\left\\| f _ {i} ^ {*} - f _ {i} ^ {g t} \\right\\| _ {2}, \\quad e _ {i} ^ {r e l} = \\frac {\\left\\| f _ {i} ^ {*} - f _ {i} ^ {g t} \\right\\| _ {2}}{\\left\\| f _ {i} ^ {g t} \\right\\| _ {2}}, \\tag {15}", + "image_path": "b07158a3221812b311fe658d8f5c2ebbbaf0dde8ff09b13a1f1ecfda66d87f62.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "f_{i}^{*}" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "f_{i}^{gt}" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " are the predicted and ground-truth flow for point " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": ", respectively. The EPE is the average point error, measured in meters; " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "AS" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " is the percentage of points whose " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "e_{i} < 0.05[m]" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "e_{i}^{rel} < 5\\%" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "AR" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " is the percentage of points for which " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "e_{i} < 0.1[m]" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "e_{i}^{rel} < 10\\%" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": "; and Out. is the percentage of points with " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "e_{i} > 0.3[m]" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "inline_equation", + "content": "e_{i}^{rel} > 10\\%" + }, + { + "bbox": [ + 304, + 528, + 545, + 601 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Implementation details. SCOOP is implemented in PyTorch [22], where the publicly available PointNet++ [25] implementation is adapted for our point feature embedding. The model is trained on " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "n = 2,048" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " points, sampled at random from the source and target point clouds of the scene examples. Only the 3D coordinates of the points are used as input to the model. The parameters " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " from Equation 3 are defined as learnable variables and optimized as part of the learning process. The point feature" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5285" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 258 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 258 + ], + "type": "table", + "html": "
MethodSupervisionTrain dataTest dataEPE↓AS↑AR↑Out.↓
FlowNet3D [16]FullFT3Do(18,000)KITTIo0.17327.660.964.9
FLOT [24]FullFT3Do(18,000)KITTIo0.10745.174.046.3
FESTA [31]FullFT3Do(18,000)KITTIo0.09444.983.4-
3DFlow [30]FullFT3Do(18,000)KITTIo0.07381.989.026.1
BiPFN [4]FullFT3Do(18,000)KITTIo0.06576.990.626.4
SCOOP (ours)SelfFT3Do(1,800)KITTIo0.06379.791.024.4
SCOOP+(ours)SelfFT3Do(1,800)KITTIo0.04791.395.018.6
JGF [21]Full + Self + SelfFT3Do(18,000) + nuScenes (700) + KITTIv(100)KITTIt0.10546.579.4-
SPF [13]Self + SelfKITTIr(6,068) + KITTIv(100)KITTIt0.08941.775.0-
RigidFlow [14]SelfKITTIr(6,068)KITTIt0.11738.869.7-
SCOOP (ours)SelfKITTIv(100)KITTIt0.05280.692.919.7
Graph Prior [23]SelfN/A (optimization-only)KITTIt0.08284.088.5-
Neural Prior [15]SelfN/A (optimization-only)KITTIt0.03692.396.2-
SCOOP+(ours)SelfKITTIv(100)KITTIt0.03993.696.515.2
", + "image_path": "afd81a584301ecdf6ed3ff4900b014c3b7655e9f657c268c5cd6ba62cfe1f178.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": "Table 1. Quantitative comparison. We compare scene flow evaluation metrics for different supervision settings, train data, and test data. The number of training examples is indicated in parentheses. " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "EPE" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "AS" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "AR" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "Out" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": ". stand for End-Point-Error, Strict Accuracy, Relaxed Accuracy, and Outliers, respectively. The symbol " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": " indicates an evaluation using all the points in the test point clouds, as done for the optimization-only methods [15, 23]. While other baselines apply fully-supervised training, our method yields better performance without employing ground-truth flow labels. Besides, SCOOP can be trained only on " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_v}" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": ", with as few as 100 training instances. In contrast, alternative learning-based methods use additional training data, such as nuScenes, or a large dataset, such as " + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_r}" + }, + { + "bbox": [ + 46, + 266, + 546, + 344 + ], + "type": "text", + "content": ". Please see further details in subsections 4.1 and 4.2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": "dimension is " + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "inline_equation", + "content": "d = 128" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": ". For the neighborhood sizes we use " + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "inline_equation", + "content": "k_{s} = 64" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "inline_equation", + "content": "k_{f} = 32" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": ", and the losses' hyperparameters are set to " + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\alpha_{conf} = 0.1" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "inline_equation", + "content": "\\alpha_{flow} = 10" + }, + { + "bbox": [ + 46, + 365, + 287, + 400 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "text", + "content": "As in previous work [14, 16, 21, 24], we evaluate SCOOP on point clouds of 2,048 points randomly sampled from the source and target. However, the full point clouds of " + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_t}" + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "text", + "content": " are an order of magnitude larger and have different cardinality. Thus, for a complete evaluation of the entire scene flow, we also utilize our method (denoted as " + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathrm{SCOOP^{+}}" + }, + { + "bbox": [ + 46, + 401, + 287, + 510 + ], + "type": "text", + "content": " for this case) to exploit the whole point cloud information and test the performance for the original resolution. Additional implementation details appear in the supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 517, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 601 + ], + "type": "text", + "content": "**Baseline methods.** Our method is contrasted with the recent methods FlowNet3D [16], FLOT [24], FESTA [31], 3DFlow [30], and BiPFN [4]. These methods require ground-truth flow supervision. Additionally, we compare our results with the recent self-supervised flow models of Mittal et al. [21] and Li et al. [13,14], and the optimization-based techniques Graph Prior [23] and Neural Prior [15]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 610, + 160, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 160, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 160, + 623 + ], + "type": "text", + "content": "4.2. Scene Flow Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Cross-dataset evaluation. We demonstrate the generalization power of SCOOP by training it on the " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": " and testing its performance on " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": ". Table 1 summarises the results. The alternative methods [4, 16, 24, 30, 31] are trained on " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": " in a fully-supervised fashion: their models are learned with the ground-truth flow information, and the points with an occluded flow are excluded from the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 365, + 536, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 536, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 536, + 376 + ], + "type": "text", + "content": "training objective using the mask provided in the dataset." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 377, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 484 + ], + "type": "text", + "content": "In contrast, our model is trained in a completely self-supervised manner. We assume no knowledge of the flow annotations nor the occlusion mask and do not use them in our losses. Additionally, we use only 1,800 randomly selected examples from " + }, + { + "bbox": [ + 304, + 377, + 545, + 484 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 304, + 377, + 545, + 484 + ], + "type": "text", + "content": ", while the competitors employ all 18,000 scene instances. Still, SCOOP improves over the SOTA method BiPFN [4] in all the evaluation metrics. Moreover, utilizing the entire point cloud data further increases our performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 546, + 593 + ], + "type": "text", + "content": "FlowNet3D [16], FESTA [31], 3DFlow [30], and BiPFN [4] are regression-based networks that predict the flow in the 3D ambient space. The models adapt to the characteristics of the synthetic training set, and the generalization to the real-world test data is limited. FLOT [24] leverages point cloud correspondence based on learned point features, which eases the flow prediction problem. However, it also jointly learns to regress a flow correction component that burdens the point representation training process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "type": "text", + "content": "SCOOP, on the other hand, is focused only on learning point embeddings suitable for scene flow estimation, guided by our self-supervised losses. It extracts discriminative features, which transfer well across the " + }, + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_o}" + }, + { + "bbox": [ + 304, + 594, + 547, + 700 + ], + "type": "text", + "content": " datasets, and enables to compute the correspondence-based flow between the point clouds. In contrast to FLOT, we delegate the flow refinement process to the test phase, directly optimize it in a self-supervised fashion, and surpass their flow estimation performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Figure 5 shows a visual comparison between the results" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5286" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 68, + 301, + 281 + ], + "blocks": [ + { + "bbox": [ + 60, + 68, + 301, + 281 + ], + "lines": [ + { + "bbox": [ + 60, + 68, + 301, + 281 + ], + "spans": [ + { + "bbox": [ + 60, + 68, + 301, + 281 + ], + "type": "image", + "image_path": "38465836362c175ccc4816d298dc607ec7bfa981fd3ad0a12ca9b34abe8eaecc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "text", + "content": "Figure 5. Visual comparison of scene flow results for a KITTI" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "inline_equation", + "content": "_0" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "text", + "content": " example scene. The training was done on the FT3D" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "inline_equation", + "content": "_0" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "text", + "content": " dataset. The source and target point clouds are shown in red and green, respectively. The warped source point cloud by FLOT [24] (left) and by our method (right) is presented in blue. While the result of FLOT deviates from the surface of the target, SCOOP preserves the source point cloud's structure and computes its accurate flow." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 310, + 68, + 533, + 281 + ], + "blocks": [ + { + "bbox": [ + 310, + 68, + 533, + 281 + ], + "lines": [ + { + "bbox": [ + 310, + 68, + 533, + 281 + ], + "spans": [ + { + "bbox": [ + 310, + 68, + 533, + 281 + ], + "type": "image", + "image_path": "7d8467e44bf3f5e591eba4911726529bbd0f6bd230d45b2625311015dfdcefd4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 287, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 424 + ], + "type": "text", + "content": "of FLOT and our method. The warped source point cloud by FLOT is noisy, and the structure of objects in the scene is compromised. On the contrary, SCOOP produces a coherent flow field across neighboring points, preserves their local geometry, and accurately predicts the scene flow. Additional visualizations are presented in the supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "type": "text", + "content": "Training on a small dataset. Since our model does not include a flow regression component and has to learn only point features, it can be trained on a very limited amount of data. To demonstrate this ability, we train it from scratch on the 100 point cloud pairs of " + }, + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_v}" + }, + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "type": "text", + "content": " and use " + }, + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_t}" + }, + { + "bbox": [ + 46, + 434, + 287, + 507 + ], + "type": "text", + "content": " for testing. The results of this experiment are presented in Table 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": "Different from our work, the competing methods of Mittal et al. [21] and Li et al. [13, 14] are based on flow regression and require a large amount of training data. Mittal et al. utilize a fully-supervised pre-training on " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ", and the additional outdoor flow dataset nuScenes [2], before fin-tuning on " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_v}" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ". Li et al. [13, 14] train their model on the large " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_r}" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": " dataset. Our SCOOP outperforms these other methods while being trained only on " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_v}" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": ", which is almost two orders of magnitudes smaller than " + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_r}" + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "The pure optimization methods [15, 23] find the solution per scene separately, which might lead to sub-optimal local minima. In contrast, we leverage the correspondence statistics learned from the data and adapt the initial flow to the scene at hand by our residual run-time optimization. The initial correspondence flow serves as a good starting point for the optimization phase, yielding a similar or better final result compared to the optimization-only alternatives." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 352, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 460 + ], + "type": "text", + "content": "The influence of flow refinement. Our flow results before and after refinement are presented in Figure 6. Posing the learning part of SCOOP as a correspondence problem enables its effective training on a small dataset. However, the flow predictions from the training phase are confined to a linear combination of existing target points, which may not represent the exact flow of the scene. Moreover, wrong matches for the source points can occur and cause flow errors. In such cases, our refinement module comes into play." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 567 + ], + "type": "text", + "content": "Given the output flow from the trained correspondence model, the refinement module optimizes correction vectors subject to two objectives: a warped source point should be close to a target point; neighboring source points should have a similar flow. These objectives help fixing inconsistencies in the flow field and increase the flow accuracy. As seen in Figure 6, our refinement step improves the initial flow estimation and results in an accurate flow field, which is similar to the ground-truth scene flow." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 575, + 479, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 479, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 479, + 588 + ], + "type": "text", + "content": "4.3. Performance and Time Analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "content": "We analyze the performance-time trade-off in Figure 7 by recording the " + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "inline_equation", + "content": "EPE" + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "content": " and inference time for different methods. The measurements were done on an Nvidia Titan Xp GPU for computing the flow for complete point clouds of the " + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_t}" + }, + { + "bbox": [ + 304, + 594, + 545, + 653 + ], + "type": "text", + "content": " dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Network-only methods [13, 14, 21] tend to be fast but with limited accuracy. Optimizing the flow prediction separately for each scene [15] results in a low " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "EPE" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": ". However, it takes a long time. Our hybrid method bridges the trade-off gap between these two approaches. " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{SCOOP}^{+}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " offers a work-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5287" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 126, + 224 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 126, + 224 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 126, + 224 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 126, + 224 + ], + "type": "image", + "image_path": "e49e6035a237e4a4d3af4748748f9527e50d1fac325d1118ade3002e0a440da8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "type": "text", + "content": "Figure 6. The flow refinement effect. We demonstrate the effect on data from " + }, + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI}_{\\mathrm{t}}" + }, + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "type": "text", + "content": ". The source point cloud is in red, and the target is in green. Our correspondence model was trained on the " + }, + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI}_{\\mathrm{v}}" + }, + { + "bbox": [ + 46, + 233, + 289, + 344 + ], + "type": "text", + "content": " dataset, and its flow estimation before refinement is shown in magenta (left). The optimized refined flow is presented in blue (center). We also show the ground-truth scene flow in purple for reference (right). The refined flow better covers the target point cloud (top center ellipse). It also breaches the convex hull of the given target points and enables computing the correct flow for source points whose target is missing (bottom center ellipse)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 132, + 70, + 202, + 224 + ], + "blocks": [ + { + "bbox": [ + 132, + 70, + 202, + 224 + ], + "lines": [ + { + "bbox": [ + 132, + 70, + 202, + 224 + ], + "spans": [ + { + "bbox": [ + 132, + 70, + 202, + 224 + ], + "type": "image", + "image_path": "7e11abd9b177023434aa35d0bad63efb5e60331603e61c981ce4032b1b18a083.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 209, + 70, + 281, + 224 + ], + "blocks": [ + { + "bbox": [ + 209, + 70, + 281, + 224 + ], + "lines": [ + { + "bbox": [ + 209, + 70, + 281, + 224 + ], + "spans": [ + { + "bbox": [ + 209, + 70, + 281, + 224 + ], + "type": "image", + "image_path": "91d248c33792d98da1d61724ec5893643a8cbf76779934fcdf73f5f18ffb7a69.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "content": "ing point with more than " + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "content": " error reduction over the feedforward models and about " + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "inline_equation", + "content": "8\\times" + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "content": " faster inference time than the optimization-only Neural Prior work. " + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathrm{SCOOP^{+}}" + }, + { + "bbox": [ + 46, + 365, + 287, + 449 + ], + "type": "text", + "content": " also enables a different balance between time and performance, as seen in Figure 7. By reducing the number of run-time optimization steps, the user can shorten the inference time, achieving a working point closer to that of the network-only models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 456, + 141, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 141, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 141, + 468 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": "The design choices in our method are verified by ablation experiments presented in Table 2. We change one element each time and keep all the others the same. The following ablative settings were examined: (a) use all target points for soft correspondence instead of the ones with the highest transport amount (Equation 5); (b) ignore the point matching confidence by setting " + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "p_{x_i} = 1" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " in Equation 10 and " + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\alpha_{conf} = 0" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " in Equation 13; (c) exclude the smoothness flow loss " + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{flow}" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " from Equation 13; and (d) turn off the flow refinement module." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "The ablation study validates the contribution of the proposed components to the method's performance. Considering a subset of target points for correspondence enables the model to concentrate on the most relevant candidates for flow estimation. The matching confidence emphasizes the influence of the more confident points in our confidence-aware distance loss " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{dist}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ". The smoothness loss term is important for regularizing the point representation learning to obtain similar features across neighboring points. Lastly, our flow refinement optimization improves the consistency" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 311, + 74, + 541, + 199 + ], + "blocks": [ + { + "bbox": [ + 311, + 74, + 541, + 199 + ], + "lines": [ + { + "bbox": [ + 311, + 74, + 541, + 199 + ], + "spans": [ + { + "bbox": [ + 311, + 74, + 541, + 199 + ], + "type": "image", + "image_path": "0964de2f15a5a6a40ee68454998e10d126bb51941660d994e52b51f33c11a47f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 205, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 305, + 205, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 547, + 262 + ], + "type": "text", + "content": "Figure 7. Flow estimation error vs. inference time for the KITTI dataset. " + }, + { + "bbox": [ + 305, + 205, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\mathrm{SCOOP^{+}}" + }, + { + "bbox": [ + 305, + 205, + 547, + 262 + ], + "type": "text", + "content": " has a lower error than the network-only models and a shorter inference time than the optimization-only methods. It also allows different balances along the error and time trade-off, as presented by the blue curve." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 277, + 544, + 357 + ], + "blocks": [ + { + "bbox": [ + 309, + 277, + 544, + 357 + ], + "lines": [ + { + "bbox": [ + 309, + 277, + 544, + 357 + ], + "spans": [ + { + "bbox": [ + 309, + 277, + 544, + 357 + ], + "type": "table", + "html": "
SettingEPE↓AS↑
(a) All target points as candidates (ks = n)0.04791.1
(b) W/O confidence (pxi = 1, αconf = 0)0.04490.3
(c) W/O smoothness loss term (αflow = 0)0.05686.6
(d) W/O flow refinement (R* = 0)0.11543.8
Our complete method0.03993.6
", + "image_path": "129c171aa9422125be1ae066a2216a6fc2e37549e56b7bd16126537b06a9e2ff.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "lines": [ + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "type": "text", + "content": "Table 2. Component ablative settings. SCOOP was trained on " + }, + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_v}" + }, + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "type": "text", + "content": " and evaluated on " + }, + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "type": "inline_equation", + "content": "\\mathrm{KITTI_t}" + }, + { + "bbox": [ + 305, + 365, + 546, + 409 + ], + "type": "text", + "content": ". The results show that the best performance is obtained with our complete method. Additional details about the ablation experiments are given in subsection 4.4." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "content": "of the flow field and reduces the " + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "inline_equation", + "content": "EPE" + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "content": " substantially. In the supplementary material, we provide an ablation study on the " + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathrm{FT3D_o}" + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "content": " train set size and find that a " + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 430, + 545, + 479 + ], + "type": "text", + "content": " fraction of the data suffices for our method to realize its potential." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 490, + 384, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 384, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 384, + 502 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 594 + ], + "type": "text", + "content": "This paper presented SCOOP, a novel self-supervised scene flow estimation method for 3D point clouds based on correspondence learning and flow refinement optimization. Previous works suggested learning a flow regression model, training a neural network that jointly learned point cloud correspondence and flow refinement, or optimizing the flow completely at run-time without learning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "In contrast, we split the flow prediction process into two simpler problems. Our correspondence model is focused only on learning point features to initialize the flow from soft matches between the point clouds. Then, we directly optimize a residual flow refinement at run-time. This approach enables SCOOP to be trained on a small set of point cloud scenes without utilizing ground-truth supervision while outperforming state-of-the-art fully-supervised and self-supervised learning methods, as well as optimization-based alternative techniques." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5288" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Thomas Brox and Jitendra Malik. 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Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France \n $^{3}$ The Hong Kong University of Science and Technology (Guangzhou), China \n $^{4}$ The Hong Kong University of Science and Technology, HK SAR, China", + "bbox": [ + 147, + 233, + 820, + 287 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 321, + 313, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliucambridge.github.io/scotch_and_soda/", + "bbox": [ + 75, + 354, + 473, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 632, + 209, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shadow is an inherent part of videos, and they have an adverse effect on a wide variety of video vision tasks. Therefore, the development of robust video shadow detection techniques, to alleviate those negative effects, is of great interest for the community. Video shadow detection is usually formulated as a segmentation problem for videos, however and due to the nature of the problem, shadow detection greatly differs from other segmentation tasks such as object segmentation. For inferring the presence of shadows in an image, one has to account for the global content information such as light source orientation, and the presence of objects casting shadows. Importantly, in a given video, shadows considerably change appearance (deformation) from frame to frame due to light variation and object motion. Finally, shadows can span over different backgrounds over different frames, making approaches relying", + "bbox": [ + 75, + 657, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5057fe85cdd37c557357f5ca0bcfc3bfcb284cea781af364473a971d48128457.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 319, + 890, + 496 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1117fbbafd7cb96bcef0abbccbbfc409fcd73da374fd93dafc6570a73d7f0c56.jpg", + "image_caption": [ + "Figure 1. Overview of our SCOTCH and SODA framework. A MiT encoder extracts multi-scale features for each frame of the video (stage 1). Then, our deformation attention trajectory is applied to features individually to incorporate temporal information (stage 2). Finally, an MLP layer combines the multi-scale information to generate the segmentation masks (stage 3). The model is trained to contrast shadow and non-shadow features, by minimising our shadow contrastive loss with massive positive shadow pairs." + ], + "image_footnote": [], + "bbox": [ + 503, + 498, + 890, + 585 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "on texture information unreliable.", + "bbox": [ + 498, + 731, + 723, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Particularly, video shadow detection methods can be broadly divided into two main categories. The first category refers to image shadow detection (ISD) [9,15,35,36,43,46]. This family of techniques computes the shadow detection frame by frame. Although computationally saving, these methods are incapable of handling temporal information. The second category refers to video shadow detection (VSD) [6, 9, 14, 16, 25]. These methods offer higher performance as the analysis involves spatial-temporal information. Hence, our main focus is video shadow detection.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10449", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "State-of-the-art video shadow detection methods rely on deep neural networks, which are trained on large annotated datasets. Specifically, those methods are composed of three parts: (i) a feature extraction network that extracts spatial features for each frame of the video; (ii) a temporal aggregation mechanism [6, 14] enriching spatial features with information from different frames; and (iii) a decoder, that maps video features to segmentation masks. Additionally, some works enforce consistency between frames prediction by using additional training criterion [9,25]. We retain from these studies that the design of the temporal aggregation mechanism and the temporal consistency loss is crucial to the performance of a video shadow detection network, and we will investigate both of those aspects in this work.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The current temporal aggregation mechanisms available in the literature were typically designed for video tasks such as video action recognition, or video object segmentation. Currently, the most widely used temporal aggregation mechanism is based on a variant of the self-attention mechanism [1, 29, 32, 40, 41]. Recently, trajectory attention [29] has been shown to provide state-of-the-art results on video processing. Intuitively, trajectory attention aggregates information along the object's moving trajectory, while ignoring the context information, deemed as irrelevant. However, shadows in videos are subject to strong deformations, making them difficult to track, and thus they might cause the trajectory attention to fail.", + "bbox": [ + 75, + 304, + 472, + 500 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we first introduce the ShadOw Deformation Attention trajectory (SODA), a spatial-temporal aggregation mechanism designed to better handle the large shadow deformations that occur in videos. SODA operates in two steps. First, for each spatial location, an associated token is computed between the given spatial location and the video, which contains information in every time-step for the given spatial location. Second, by aggregating every associated spatial token, a new token is yielded with enriched spatial deformation information. Aggregating spatial-location-to-video information along the spatial dimension helps the network to detect shape changes in videos.", + "bbox": [ + 75, + 502, + 472, + 684 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Besides, we introduce the Shadow COnTrastive meCHanism (SCOTCH), a supervised contrastive loss with massive positive shadow pairs aiming to drive our network to learn more discriminative features for the shadow regions in different videos. Specifically, in training, we add a contrastive loss at the coarsest layer of the encoder, driving the features from shadow regions close together, and far from the features from the non-shadow region. Intuitively, this contrastive mechanism drives the encoder to learn high-level representations of shadow, invariant to all the various factors of shadow variations, such as shape and illumination.", + "bbox": [ + 75, + 685, + 472, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 96, + 853, + 398, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We introduce a new video shadow detection framework, in which we highlight:", + "bbox": [ + 94, + 869, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- SODA, a new type of trajectory attention that harmonise the features of the different video frames at each resolution.", + "bbox": [ + 550, + 90, + 890, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- SCOTCH, a contrastive loss that highlights a massive positive shadow pairs strategy in order to make our encoder learn more robust high-level representations of shadows.", + "bbox": [ + 550, + 141, + 893, + 202 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We evaluate our proposed framework on the video shadow benchmark dataset ViSha [6], and compare with the state-of-the-art methods. Numerical and visual experimental results demonstrate that our approach outperforms, by a large margin, existing ones on video shadow detection. Furthermore, we provide an ablation study to further support the effectiveness of the technical contributions.", + "bbox": [ + 517, + 207, + 893, + 327 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 340, + 640, + 357 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The task of video shadow detection has been extensively investigated in the community, in which solutions largely rely on analysing single frames (image shadow detection) or continuous multiple frames (video shadow detection). In this section, we review the existing techniques in turn, and then summarize the recent achievements in the video processing area to better illustrate the difference between existing work and our work.", + "bbox": [ + 496, + 366, + 893, + 488 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Image Shadow Detection", + "text_level": 1, + "bbox": [ + 500, + 497, + 725, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image shadow detection (ISD) can be cast as a semantic segmentation problem, where image object segmentation (IOS) methods can be used to solve this problem [8, 13, 19, 21, 22, 42]. However, IOS methods are not specifically designed for shadow detection. Hence, when re-training these methods directly for shadow detection, the performance is unsatisfactory due to the data bias.", + "bbox": [ + 496, + 520, + 890, + 626 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Techniques focused on image shadow detection incorporate problem-specific shadow knowledge into the model architecture and the training criterion [7,9,15,16,35,36,43, 46]. For example, BDRAR [46] introduces a bidirectional pyramidal architecture for shadow detection. DSD [43] presents a distraction-aware shadow-module to reduce false positives. Chen et al. [7] make use of non-labelled data, during training, with a task-specific semi-supervised learning mechanism called MTMT. Wang et al. investigate the detection of shadows along with their corresponding objects [35, 36]. Finally, FSDNet [16] proposes a compact image shadow detection network. Whilst ISD techniques have demonstrated potential results, their performance on videos is limited by the lack of temporal information.", + "bbox": [ + 496, + 627, + 893, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Video Shadow Detection", + "text_level": 1, + "bbox": [ + 500, + 847, + 723, + 861 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another body of researchers has explored the task of shadow detection from the lens of video analysis. The work", + "bbox": [ + 500, + 869, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10450", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of [6] proposes the TVSD model. It relies on a dual-gated co-attention module, to aggregate features from different frames, and uses a contrastive learning mechanism to drive the encoder to discriminate frames from different videos. Hu et al. [14] introduce an optical flow warping module to aggregate features from different frames. STICT [25] uses transfer learning, to transfer the knowledge of a supervised image shadow detection network to a video shadow detection network, without labelled videos, by training the network prediction to be consistent with respect to temporal interpolation [33]. Moreover, the technique called SCCor [9] presents a weakly supervised correspondence learning mechanism to enhance the temporal similarity of features corresponding to shadow region across frames.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Progresses in Video Processing", + "text_level": 1, + "bbox": [ + 76, + 313, + 349, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The specific nature of videos, containing spatial and temporal information, has motivated the design of deep neural network architectures for different video processing applications. Models based on 3D CNN [17, 31] process videos by sequentially aggregating the spatio-temporal local information using 3D convolutional filters, but fail to effectively capture long-range temporal dependencies. To alleviate this limitation, architectures using recurrent networks were introduced in [2, 30]. Moreover, another set of works uses spatio-temporal memory bank mechanism [27] or spatiotemporal attention mechanism [32] into the coarse layers of 3D CNN architectures [18, 26, 37] to better integrate the temporal information for video processing.", + "bbox": [ + 75, + 335, + 472, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The success of the transformer network architecture, on a wide variety of vision tasks [4, 10], has motivated the use of transformer for video tasks. While the self-attention mechanism in transformers appears to be well suited to capture the long-range dependencies in videos, applying transformers to videos raises many challenges, such as the quadratic complexity in the input sequence length, and the large data requirement induced by the lack of problem-specific inductive bias. The works of [1, 41] propose to separate spatial and temporal attention to reduce computational complexity, and the authors of [40] propose to apply multiple encoders on multiple views of the video. Recently, trajectory attention [29] was introduced as a way to incorporate an inductive bias in the self-attention operation to capture objects moving trajectories for better video recognition tasks.", + "bbox": [ + 75, + 534, + 472, + 761 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.4. Existing Works & Comparison to Our Work", + "text_level": 1, + "bbox": [ + 76, + 770, + 454, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "All precedent works on VSD [6, 14, 25, 33] rely on convolutional neural network architectures. To the best of our knowledge, our work is the first video shadow detection approach based on transformers.", + "bbox": [ + 75, + 794, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Moreover, whilst the work of [29] also considers a type of attention trajectory, their modelling hypothesis is that the video objects do not change shape over time. This is", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "a strong assumption to fulfill for several vision applications such as shadow detection; as shadows significantly change shape from frame to frame. Our work first mitigates this issue by modelling in the trajectories the inherent deformation of the shadows. Notice that TVSD [6] uses an image-level contrastive loss between frames from different videos, and SC-Cor [9] uses weakly-supervised correspondence learning for driving similar features from shadow-region close together. Unlike these works, we introduce a supervised contrastive strategy to contrast shadow features from non-shadow features. We underline that existing contrastive-based techniques assume that supervised contrastive learning is not performing better than its counterpart. In this work, we show that a well-designed supervised contrastive strategy indeed improves over existing works.", + "bbox": [ + 496, + 90, + 893, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 329, + 635, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce all the components of the video shadow detection method presented in this work. After a global description of our framework (i), we introduce SODA, our new video self-attention module (ii), and we describe the training criterion of our model, which includes SCOTCH, our shadow contrastive mechanism (iii).", + "bbox": [ + 496, + 354, + 893, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework Architecture Overview", + "text_level": 1, + "bbox": [ + 500, + 452, + 805, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed framework is composed of three main stages. The overall workflow is illustrated in Figure 1, and details are provided next.", + "bbox": [ + 496, + 474, + 892, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stage 1: Feature Extraction. In this stage, Mix Transformer (MiT) [39] is adopted as the encoder. MiT takes video clips as input, and it outputs a set of different-resolution spatial feature maps. Unlike ViT [10], which only generates single-resolution feature maps, the hierarchical structure of MiT can generate CNN-like multi-level multi-scale feature maps. These feature maps contain from high-resolution detailed information to low-resolution semantic information. By incorporating different levels of resolutions, the performance of tasks such as semantic segmentation can be boosted [39]. In this stage, MiT only encodes the spatial information of the given video clips (input), that is, the temporal information is not yet incorporated.", + "bbox": [ + 496, + 522, + 893, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stage 2: Harmonising Spatial and Temporal Information. The multi-scale feature maps from Stage 1 are then processed by the newly introduced shadow deformation attention trajectory module (SODA). The goal of this module is to capture the shadow's deformation trajectory along the frames in the video clips. Our deformation attention trajectory module processes independently each feature map with different-resolution. These processed feature maps are used as input to the decoder in the next stage.", + "bbox": [ + 496, + 734, + 893, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stage 3: Mask Shadow Generation. In this stage, a light-weighted decoder, with only MLP layers, is adopted to", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10451", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2af1f1a52de438f22161156e6b582642ddff225c82edeabd23188814e763467c.jpg", + "image_caption": [ + "Figure 2. Deformation attention trajectory module. The input feature maps $z$ is used to generate $q, k, v$ , respectively. The $q$ and $k$ are first used to calculate the pointwise $st$ -to- $st$ similarity, followed by a softmax on $t$ to get the time attention. The time attention aggregated $v$ can generate $s$ -to- $st$ (spatial-location-to-video) attention, named deformation attention. Then, the spatial-location-to-video attention is integrated along the spatial dimension to capture the deformation attention trajectory. Lastly, the deformation attention trajectory is used to generate the final feature map $z'$ with a second self-attention $(\\hat{q}, \\hat{k}, \\hat{v})$ . In this figure, each square represents a spatial feature map. (The channel dimension is not represented for simplicity)." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 893, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "reconstruct the shadow's segmentation masks. The decoder aims to mix the high- & low- resolution information, from processed feature maps, for better semantic segmentation. The output of the decoder is a segmented video that marks out the shadows in each frame of the video.", + "bbox": [ + 75, + 348, + 470, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. SODA: ShadOw Deformation Attention trajectory", + "text_level": 1, + "bbox": [ + 76, + 436, + 468, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transformers have revolutionised several tasks in the computer vision area. The key is the self-attention mechanism that can accommodate with any given type of data and domain. However, for videos, the standard self-attention does not differentiate the spatial dimensions from the temporal dimension. This can lead the attention to focus on the redundant spatial information while neglecting the informative temporal variations in the videos. Nonetheless, video analysis is inherent to such temporality. Most recently, trajectory attention [29] has proposed to accommodate somehow with such issues. However and even though trajectory attention has demonstrated potential results, it has a major limitation – the objects are assumed not to change over time. This is a major constraint in several video tasks including shadow detection; as shadows significantly undergo deformation from one frame to another. In this subsection, we introduce a new scheme called ShadOw Deformation Attention trajectory (SODA) to mitigate current drawbacks of the literature.", + "bbox": [ + 75, + 476, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Like in the classical self-attention setting, it begins with an input feature map generated from the encoder. Specifically, let us denote $f_{d} \\in \\mathbb{R}^{t \\times \\frac{h}{d} \\times \\frac{w}{d} \\times c}$ , the generated feature map from the encoder, where $d$ is the spatial down-sampling ratio, $c$ is the number of feature channels, and $t$ is the number of time frames in the video. $f_{d}$ is reshaped to a sequence of 1D token embedding denoted as $z \\in \\mathbb{R}^{n \\times c}$ , where $n = t \\times \\frac{h}{d} \\times \\frac{w}{d}$ . As shown in the left part of Figure 2, $z$ is then mapped to a set of query-", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "key-value vectors $q, k, v \\in \\mathbb{R}^{n \\times c}$ using linear projections $q = w_{q} \\cdot z$ , $k = w_{k} \\cdot z$ , $v = w_{v} \\cdot z$ , with projection matrices $w_{q}, w_{k}, w_{v} \\in \\mathbb{R}^{n \\times n}$ .", + "bbox": [ + 498, + 348, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our scheme considers two main parts: (i) temporal attention between the spatial location and video (Attention on Time in Figure 2), (ii) intra-space attention to capture deformation statuses within a spatial scene (Deformation Attention Trajectory in Figure 2). For the first part, given a space-time position in the video $st \\in \\{1, \\dots, n\\}$ , and a spatial location $s' \\in \\{1, \\dots, m\\}$ , where $m = \\frac{n}{t}$ , the temporal attention (deformation) between the space-time position $st$ and the spatial locations $s'$ is computed as:", + "bbox": [ + 498, + 393, + 892, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {s t s ^ {\\prime}} = \\sum_ {t ^ {\\prime}} v _ {s ^ {\\prime} t ^ {\\prime}} \\cdot \\frac {\\exp \\left\\langle q _ {s t} , k _ {s ^ {\\prime} t ^ {\\prime}} \\right\\rangle}{\\sum_ {\\bar {t}} \\exp \\left\\langle q _ {s t} , k _ {s ^ {\\prime} \\bar {t}} \\right\\rangle} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 539, + 890, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For brevity, the notation is slightly abused by omitting the \"softmax operation on time dimension\" in the Fig. 2 applied to the fraction, as well as the scaling parameter $\\sqrt{n}$ (we will keep this notation convention throughout the paper). The deformation encodes the connection between one space-time position and one spatial location, which indicates how the content of the space-time position $st$ is presented in spatial location $s'$ .", + "bbox": [ + 496, + 577, + 890, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the temporal attentions are computed, the intraspace attention is then estimated to aggregate the spatial-location-to-video responses to space-level deformation. To do this, the computed deformation tokens are projected to a new set of query-key-value vectors using linear projections:", + "bbox": [ + 496, + 699, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {q} _ {s t} = \\hat {w} _ {q} \\cdot \\hat {y} _ {s t s}, \\hat {k} _ {s t s ^ {\\prime}} = \\hat {w} _ {k} \\cdot \\hat {y} _ {s t s ^ {\\prime}}, \\hat {v} _ {s t s ^ {\\prime}} = \\hat {w} _ {v} \\cdot \\hat {y} _ {s t s ^ {\\prime}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 777, + 890, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{y}_{sts}$ is the temporal connection from $st$ to the same spatial location $s$ , and $\\hat{q}_{st}$ corresponds to the deformation reference point $st$ that is used to aggregate the location-to-video connection:", + "bbox": [ + 496, + 801, + 890, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {s t} = \\sum_ {s ^ {\\prime}} \\hat {v} _ {s t s ^ {\\prime}} \\cdot \\frac {\\exp \\left\\langle \\hat {q} _ {s t} , \\hat {k} _ {s t s ^ {\\prime}} \\right\\rangle}{\\sum_ {\\bar {s}} \\exp \\left\\langle \\hat {q} _ {s t} , \\hat {k} _ {s t \\bar {s}} \\right\\rangle} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 864, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10452", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{y}_{st}$ is the deformation attention output. The meaningful location-to-video tokens are pooled out to form the full space-level deformation status. By computing the intraspace attention, the attended feature map can capture the deformation status in different frames of the video, thus boosting the video shadow detection performance.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. SCOTCH: Shadow COOnTrastive meCHanism", + "text_level": 1, + "bbox": [ + 76, + 190, + 464, + 207 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrastive learning [5, 20, 23] has been proven to be an effective mechanism for learning distinctive features. By contrasting the positive pairs with high similarity and negative pairs with low similarity, the learned feature maps can be more discriminative in downstream tasks including classification and segmentation. In previous video shadow detection task [6], positive and negative pairs are sampled from frames from the same video and from two different videos respectively. Since the frames from one video have high similarity image content, the contrastive mechanism can help to discriminate different video content.", + "bbox": [ + 75, + 214, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, the key element in video shadow detection is the shadow itself instead of the video content. With the goal of boosting the detection performance, we introduce SCOTCH, a Shadow COnTrastive meCHanism. SCOTCH seeks to better guide the segmentation process for shadows and non-shadows regions in the videos. Specifically, to learn a unified shadow feature for different videos, positive pairs are sampled from the shadow regions from different frames in different videos, whilst negative pairs are sampled as shadow and non-shadow regions on the frames in different videos. We underline that unlike the classical contrastive loss used for unsupervised learning [5, 28], where there is only a small number of positive pairs, we proposed a massive positive shadow paired contrastive loss. The key idea behind our loss is that - we seek to not only maximise the difference between shadow and non-shadow features, but also maximise the similarity between features of shadows presented in different videos. All shadow and non-shadow features are cropped from the last layer of the encoder presented in Section 3.1, with the supervision of the segmentation masks. The contrastive loss reads:", + "bbox": [ + 75, + 380, + 470, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\ell_ {\\text {c o n t r a s t}} \\left(\\boldsymbol {v}, \\boldsymbol {v} ^ {+}, \\boldsymbol {v} ^ {-}\\right) = \\\\ - \\log \\left[ \\frac {\\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {+} / \\tau\\right)}{\\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {+} / \\tau\\right) + \\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {-} / \\tau\\right)} \\right] \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 707, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\pmb{v} \\in \\mathbb{R}^c$ is the query shadow feature. Moreover, $\\pmb{v}_n^+$ , $\\pmb{v}_n^-\\in \\mathbb{R}^{n\\times c}$ are the positive and negative groups respectively, and $\\tau$ is a temperature hyperparameter. The final loss is computed across all frames in a mini-batch fashion.", + "bbox": [ + 76, + 794, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimisation Scheme for Shadow Detection. Finally, to compute the shadow segmentation loss, we follow the default setting in [6]. We use the binary cross entropy (BCE)", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "loss with a lovasz-hinge loss [3]. These two terms are added to define the shadow segmentation loss as follows:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {s e g} = \\ell_ {b c e} + \\lambda_ {1} \\ell_ {h i n g e} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 132, + 890, + 148 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our optimisation scheme is then given by (4) and (5) as:", + "bbox": [ + 498, + 159, + 870, + 175 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\text {f i n a l}} = \\ell_ {\\text {b c e}} + \\lambda_ {1} \\ell_ {\\text {h i n g e}} + \\lambda_ {2} \\ell_ {\\text {c o n t r a s t}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 186, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are two hyper-parameters weighting the relative effect of the hinge loss and the contrastive loss in the final loss. In the following experiments, $\\lambda_{1},\\lambda_{2}$ were empirically set to a value of 1 and 0.1, respectively.", + "bbox": [ + 496, + 212, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 498, + 285, + 705, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section details all experiments performed to validate our proposed framework.", + "bbox": [ + 498, + 310, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 498, + 348, + 779, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Description. We utilise the largest and latest Video Shadow dataset (ViSha) [6] to evaluate the effectiveness of our proposed VSD method. The ViSha dataset has 120 videos, and each video contains between 29 and 101 frames. ViSha is composed of a total of 11,685 frames corresponding to a total duration of 390 seconds of video.", + "bbox": [ + 496, + 372, + 890, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Pre-processing. We follow the setting introduced in ViSha [6]. That is, we use the same train-test split, with 50 videos for training and 70 videos for testing. During training, we also use the same data augmentation strategy as [6] to enrich the variety of the dataset. Specifically, during training, images are re-scaled to size $512 \\times 512$ , and are randomly flipped horizontally. In testing, only re-scaling to the unified size $512 \\times 512$ is used.", + "bbox": [ + 496, + 462, + 890, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following the evaluation protocol used in [6, 9, 25], we employ four common evaluation metrics to measure the shadow detection accuracy: MAE, $\\mathbf{F}_{\\beta}$ , IoU, and BER. Lower MAE and BER scores, and higher $\\mathbf{F}_{\\beta}$ and IoU scores indicate a better video shadow detection result. Moreover, we also provide the shadow BER (S-BER) and the non-shadow BER scores (N-BER) to further compare different VSD methods.", + "bbox": [ + 496, + 583, + 890, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. Our proposed segmentation architecture is built using the PyTorch-lightning [11] deep-learning framework. The parameters of the feature extraction encoder are initialised using the weights from the MiT-B3 model pre-trained for image segmentation on ADE20K dataset [44, 45], publicly available on HuggingFace [38]. The remaining parameters (attention modules and the MLP decoder) are randomly initialised using \"Xavier\" methods [12]. During training, AdamW optimizer [24] is used with an initial learning rate of $1 \\times 10^{-6}$ without decay. All experiments and ablation studies are trained for 36 epochs, for a training time of approximately 12 hours on NVIDIA A100 GPU with 80G RAM with batch size of 8.", + "bbox": [ + 496, + 704, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10453", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/bed0d97172781ffb985b3f56b8a07142f6a60bba45becd1e9b4fc8ed9b6aea80.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METHODSEVALUATION METRICS
TasksTechniquesMAE ↓Fβ↑IoU ↑BER ↓S-BER ↓N-BER ↓
IOS★ FPN [19]0.0440.7070.51219.4936.592.40
PSPNet [42]0.0510.6420.47619.7536.443.07
DSS [13]0.0450.6960.50219.7736.962.59
R3Net [8]0.0440.7100.50220.4037.373.55
ISDBDRAR [46]0.0500.6950.48421.2940.282.31
★ DSD [43]0.0430.7020.51819.8837.891.88
MTMT [7]0.0430.7290.51720.2838.711.86
FSDNet [16]0.0570.6710.48620.5738.063.06
VOSPDBM [30]0.0660.6230.46619.7334.325.16
COSNet [26]0.0400.7050.51420.5039.221.79
★ FEELVOS [34]0.0430.7100.51219.7637.272.26
STM [27]0.0680.5970.40825.6947.443.96
VSDTVSD [6]0.0330.7570.56717.7033.971.45
STICT [25]0.0460.7020.54516.6029.583.59
SC-Cor [9]0.0420.7620.61513.6124.312.91
★ SCOTCH and SODA0.0290.7930.6409.06616.261.44
", + "bbox": [ + 202, + 88, + 767, + 343 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Comparisons between our proposed technique and SOTA techniques on the ViSha dataset. \"MAE\" denotes mean absolute error, $\\mathrm{F}_{\\beta}$ denotes F-measure score, \"IoU\" denotes intersection over union, \"BER\" denotes balance error rate, and \"S-BER\" means shadow BER, \"N-BER\" means non-shadow BER. The $\\uparrow$ denotes the higher the value is the better the performance is, whilst the $\\downarrow$ means the opposite. $\\star$ indicates the best performed network in each category.", + "bbox": [ + 75, + 353, + 890, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison to SOTA Techniques", + "text_level": 1, + "bbox": [ + 76, + 425, + 370, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared Methods. Video shadow detection is a relatively recent topic, and there are only three directly-related methods designed for this task. Hence, following existing VSD methods, we make comparisons against 4 different kinds of methods, including image object segmentation (IOS), image shadow detection (ISD), video object segmentation (VOS), and video shadow detection (VSD). For IOS, they are FPN [19], PSPNet [42], DSS [13], and $\\mathbf{R}^3$ -Net [8], while the ISD methods are BDRAR [46], DSD [43], MTMT [7], and FSDNet [16]. The compared VOS methods include PDBM [30], COSNet [26], FEELVOS [34], and STM [27], while compared VSD methods are TVSD [6], STICT [25], and SC-Cor [9]. We obtain the results by re-training their network parameters with unified training parameters or by downloading the results from the TVSD [6] repository.", + "bbox": [ + 75, + 455, + 468, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Comparisons. Table 1 summarises MAE, $\\mathrm{F}_{\\beta}$ , IoU, and BER scores of our network against SOTA techniques. For each category, we use $\\star$ to mark out the method with the best performance. From these quantitative results, we observe that the IOS and ISD report readily competing results. These results are expected as the modelling hypothesis for both families of techniques relies on only the image level analysis. Whilst VOS techniques consider also temporal information, these techniques are customised as a general framework for video object segmentation. However, shadow detection is more complex due to the fast change in appearance between frames. Notably, we observe that VSD techniques indeed provide a substantial performance", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "improvement compared to other methods; as they are designed considering the complexity of shadows.", + "bbox": [ + 498, + 425, + 890, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "More importantly, our method outperforms all other techniques by a significant margin for all evaluation metrics - further supporting the superiority of our approach. In particular, our method yields to a balanced error rate of 9.066 which is more than 4 points below SC-Cor, the latest SOTA technique, in terms of BER. The error rate for the shadow label (denoted as S-BER in Table 1) of our method is 8 points below SC-Cor. We also underline that our significant improvement in performance comes with a negligible computational cost. We report the test time in Table 2, where we observe that our SCOTCH and SODA framework only requires a fraction of time than compared methods.", + "bbox": [ + 496, + 458, + 892, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual Comparison. Figure 3 visually compares the shadow segmentation masks from our method and the compared methods on different input video frames. For video frames with black objects at the first three rows, we find that compared methods tend to wrongly identify those black objects as shadow ones, while our method can still accurately detect shadow pixels under the corruption of black objects. Moreover, compared methods tend to miss some shadow regions when the input video frames contain multiple shadow detection, as shown in the 4-th row to the 8-th row of Figure 3. On the contrary, our method can identify all these shadow regions of input video frames, and our detection results are most consistent with the ground truth in the 2nd column of Figure 3. We also provide the video segmentation masks on the project page to demonstrate the temporal coherence of the results provided by our method.", + "bbox": [ + 496, + 641, + 893, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model size and inference time. Table 2 further", + "bbox": [ + 517, + 885, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10454", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/944c0d77c3da05f49a98b0be323249522ffc409e3b80d969131bae23fbe5276d.jpg", + "image_caption": [ + "Figure 3. Visual comparisons of video shadow detection results produced by our network (SCOTCH and SODA) and compared methods. Apparently, our method can more accurately identify shadow pixels and our results are more consistent with the ground truth in the 2nd column. The video segmentation results can be found on the project page. (d-e) are the methods with the highest performance in IOS, ISD, and VOS in Table 1, whilst (g-i) are all from the VSD area." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 890, + 512 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/59fa63752842ce47ee50f185eaf369862f5692497edc0d373ca9bcbdae7e239c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
NetworksParamsGMACsTimeBER
TVSD [6]243.32158.8932.417.70
STCIT [25]104.6840.9913.516.60
SC-Cor [9]232.63218.421.813.61
SCOTCH and SODA211.79122.469.159.006
", + "bbox": [ + 81, + 593, + 467, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison of model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Specifically, the units for Params and Time are (MB) and (Mins), respectively. We denote the best and second best in bold and underline font.", + "bbox": [ + 75, + 686, + 468, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "compares our network and three state-of-the-art video shadow detection methods in terms of the model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Apparently, among the three compared VSD methods, STICT has the smallest testing time (13.5 minutes). Compared to STICT, our method further reduces the inference time from 13.5 minutes to 9.15 minutes to test all 70 testing videos", + "bbox": [ + 75, + 780, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with 6,897 images. Although our method takes 2nd rank in terms of the model size and computational complexity, they are only larger than STICT. This is because we only use a light-weighted MLP layer as the decoder to integrate the multi-resolution feature maps, which is computational-saving. In terms of performance, our method has a superior BER performance than STICT by reducing the BER score from 16.60 to 9.006, which indicates that with a minor compromise on the model size, our method can more accurately identify video shadows than STICT, TVSD, and SC-Cor.", + "bbox": [ + 496, + 595, + 890, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 756, + 653, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 3, we perform ablation studies on our main contributions to evaluate the effectiveness of each component.", + "bbox": [ + 496, + 780, + 888, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baseline with MiT backbone. In order to evaluate the role of the MiT backbone on the final performance of our method, we define the segmentation network with MiT backbone as the baseline, which is trained by using the classical segmentation loss (5), but without the deformation attention trajectory and shadow level contrastive mechanism.", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10455", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/38e1f0dc0bcd10dc235428ade4485f9a3a9de0324c4c5c148ff4072b8a473578.jpg", + "table_caption": [], + "table_footnote": [ + "Table 3. Ablation study on different components of our proposed methods on the ViSha dataset. The $\\uparrow$ denotes the higher the value is the better the performance is, whilst the $\\downarrow$ means the opposite. “ $\\dagger$ ” denotes our final methods with the highest performance in all evaluation metrics. Notations: best, second best, third best." + ], + "table_body": "
ComponentsEvaluation Metrics
BackboneAttentionContrastMAE ↓Fβ ↑IoU ↑BER ↓
MiTXX0.0480.7550.58413.18
MiTTrajectoryX0.0480.7600.59312.35
MiTSODAX0.0410.7910.61310.55
MiTXImage0.0480.7610.58812.85
MiTXShadow0.0410.7670.59212.02
MiTXSCOTCH0.0340.7710.60611.29
†MiTSODASCOTCH0.0290.7930.6409.066
", + "bbox": [ + 81, + 88, + 467, + 222 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This baseline already provides results on par or better than the previous three works in the VSD area (see Table 1 for comparison), even without considering any kind of temporal information. This illustrates the superior performance of the MiT transformer-based architecture over convolutional architectures on the task of video shadow detection.", + "bbox": [ + 75, + 319, + 468, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Attention mechanisms. We then evaluate the effectiveness of different attention mechanisms, including trajectory attention [29] and our newly introduced shadow deformation attention. Both types of attention modules provide an improvement over the baseline, which was to be expected as those modules give the ability to consider the temporal information within the videos. Our deformation attention trajectory module also appears to provide better results than the trajectory attention, indicating the importance of considering the deformation in the design of the attention module.", + "bbox": [ + 75, + 411, + 468, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Contrastive losses. Next, we compare the effect of two types of contrastive criterion, the image level contrastive loss used in TVSD [6], and our feature-level shadow contrastive loss. The inter-frame contrastive learning slightly improves the baseline, whereas our shadow contrastive loss provides a significant improvement over the baseline. Those results illustrate the superiority of the features-level contrastive loss over the frame-level contrastive loss.", + "bbox": [ + 75, + 563, + 468, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Final model. SCOTCH reduces the variance of the spatial shadow features, while SODA processes the spatial features at different time-step to consider the temporal information in the video. Thus, SCOTCH and SODA have a complementary effect, as feeding SODA with more robust spatial features from SCOTCH, we are able to reach the best performance, outperforming all the previous settings.", + "bbox": [ + 75, + 684, + 468, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Attention Map Visualisation", + "text_level": 1, + "bbox": [ + 76, + 801, + 330, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Figure 4, we visually compare the attention maps from the baseline model (second row) with our proposed SCOTCH and SODA (third row). We can observe that the baseline model highlights the object part, whilst ours focuses more on the shadow region with the help of contrastive", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f38a4f7dec373e3f9c004375cd539591ee02e4dfa722910fa68afd554f0bcda3.jpg", + "image_caption": [ + "Figure 4. Attention maps visualisation. The low-resolution layers of the MiT encoder are selected for the visualization, with the query from the center of the ground truth shadow mask. From top to bottom row are the input video blended with segmentation mask, attention maps for baseline MiT methods, and attention maps from ours SCOTCH and SODA with deformation attention trajectory and shadow contrastive mechanism." + ], + "image_footnote": [], + "bbox": [ + 501, + 89, + 890, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "learning. We can also observe that the baseline model might lose track of shape in different frames (third column), whilst our approach provides consistent shape information at different times with the help of the deformation attention trajectory. Hence, the model using the shadow deformation attention trajectory and the shadow contrastive loss is better at tracking the shadow region during different frames, while ignoring the non-shadow part of the image.", + "bbox": [ + 496, + 397, + 890, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 534, + 617, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced SCOTCH and SODA, a new transformer video shadow detection framework. We developed shadow deformation attention trajectory (SODA), a self-attention module specially designed to handle the shadow deformation in videos, and we introduced a shadow contrastive mechanism (SCOTCH) to guide our network to better discriminate between shadow and non-shadow features. We demonstrate the effectiveness of the contributions with ablation studies. Finally, we show that our proposed method outperforms by a large margin concurrent video shadow segmentation works on the ViSha dataset.", + "bbox": [ + 496, + 560, + 890, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by Girton Postgraduate Research Scholarships, GSK Ph.D. Scholarship, CMIH, CCIMI, Philip Leverhulme Prize, Royal Society Wolfson Fellowship, EPSRC Advanced Career Fellowship EP/V029428/1, EPSRC grants EP/S026045/1, EP/T003553/1, EP/N014588/1, EP/T017961/1, Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, EU Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, and Guangzhou Municipal Science and Technology Project Grant No. 2023A03J0671.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10456", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 121–136, 2018. 1, 2, 6" + ], + "bbox": [ + 501, + 90, + 892, + 681 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10458", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SCOTCH and SODA_ A Transformer Video Shadow Detection Framework/db4a242e-46af-47cc-9782-646b5ef8b2a3_model.json b/2023/SCOTCH and SODA_ A Transformer Video Shadow Detection Framework/db4a242e-46af-47cc-9782-646b5ef8b2a3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fb1410acd60e485f8e49be19ded5d71586b7fbec --- /dev/null +++ b/2023/SCOTCH and SODA_ A Transformer Video Shadow Detection Framework/db4a242e-46af-47cc-9782-646b5ef8b2a3_model.json @@ -0,0 +1,1914 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.131, + 0.865, + 0.152 + ], + "angle": 0, + "content": "SCOTCH and SODA: A Transformer Video Shadow Detection Framework" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.18, + 0.764, + 0.234 + ], + "angle": 0, + "content": "Lihao Liu\\(^{1}\\), Jean Prost\\(^{2}\\), Lei Zhu\\(^{3,4}\\), Nicolas Papadakis\\(^{2}\\), Pietro Li\\(^{1}\\), Carola-Bibiane Schonlieb\\(^{1}\\), Angelica I Aviles-Rivero\\(^{1}\\) \n\\(^{1}\\) University of Cambridge, United Kingdom" + }, + { + "type": "text", + "bbox": [ + 0.148, + 0.234, + 0.821, + 0.288 + ], + "angle": 0, + "content": "\\(^{2}\\) Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France \n\\(^{3}\\) The Hong Kong University of Science and Technology (Guangzhou), China \n\\(^{4}\\) The Hong Kong University of Science and Technology, HK SAR, China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.322, + 0.314, + 0.339 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.474, + 0.613 + ], + "angle": 0, + "content": "Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliucambridge.github.io/scotch_and_soda/" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.633, + 0.21, + 0.649 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Shadow is an inherent part of videos, and they have an adverse effect on a wide variety of video vision tasks. Therefore, the development of robust video shadow detection techniques, to alleviate those negative effects, is of great interest for the community. Video shadow detection is usually formulated as a segmentation problem for videos, however and due to the nature of the problem, shadow detection greatly differs from other segmentation tasks such as object segmentation. For inferring the presence of shadows in an image, one has to account for the global content information such as light source orientation, and the presence of objects casting shadows. Importantly, in a given video, shadows considerably change appearance (deformation) from frame to frame due to light variation and object motion. Finally, shadows can span over different backgrounds over different frames, making approaches relying" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.32, + 0.892, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.499, + 0.892, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.71 + ], + "angle": 0, + "content": "Figure 1. Overview of our SCOTCH and SODA framework. A MiT encoder extracts multi-scale features for each frame of the video (stage 1). Then, our deformation attention trajectory is applied to features individually to incorporate temporal information (stage 2). Finally, an MLP layer combines the multi-scale information to generate the segmentation masks (stage 3). The model is trained to contrast shadow and non-shadow features, by minimising our shadow contrastive loss with massive positive shadow pairs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.732, + 0.725, + 0.746 + ], + "angle": 0, + "content": "on texture information unreliable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Particularly, video shadow detection methods can be broadly divided into two main categories. The first category refers to image shadow detection (ISD) [9,15,35,36,43,46]. This family of techniques computes the shadow detection frame by frame. Although computationally saving, these methods are incapable of handling temporal information. The second category refers to video shadow detection (VSD) [6, 9, 14, 16, 25]. These methods offer higher performance as the analysis involves spatial-temporal information. Hence, our main focus is video shadow detection." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10449" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "State-of-the-art video shadow detection methods rely on deep neural networks, which are trained on large annotated datasets. Specifically, those methods are composed of three parts: (i) a feature extraction network that extracts spatial features for each frame of the video; (ii) a temporal aggregation mechanism [6, 14] enriching spatial features with information from different frames; and (iii) a decoder, that maps video features to segmentation masks. Additionally, some works enforce consistency between frames prediction by using additional training criterion [9,25]. We retain from these studies that the design of the temporal aggregation mechanism and the temporal consistency loss is crucial to the performance of a video shadow detection network, and we will investigate both of those aspects in this work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.501 + ], + "angle": 0, + "content": "The current temporal aggregation mechanisms available in the literature were typically designed for video tasks such as video action recognition, or video object segmentation. Currently, the most widely used temporal aggregation mechanism is based on a variant of the self-attention mechanism [1, 29, 32, 40, 41]. Recently, trajectory attention [29] has been shown to provide state-of-the-art results on video processing. Intuitively, trajectory attention aggregates information along the object's moving trajectory, while ignoring the context information, deemed as irrelevant. However, shadows in videos are subject to strong deformations, making them difficult to track, and thus they might cause the trajectory attention to fail." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.473, + 0.685 + ], + "angle": 0, + "content": "In this work, we first introduce the ShadOw Deformation Attention trajectory (SODA), a spatial-temporal aggregation mechanism designed to better handle the large shadow deformations that occur in videos. SODA operates in two steps. First, for each spatial location, an associated token is computed between the given spatial location and the video, which contains information in every time-step for the given spatial location. Second, by aggregating every associated spatial token, a new token is yielded with enriched spatial deformation information. Aggregating spatial-location-to-video information along the spatial dimension helps the network to detect shape changes in videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.473, + 0.852 + ], + "angle": 0, + "content": "Besides, we introduce the Shadow COnTrastive meCHanism (SCOTCH), a supervised contrastive loss with massive positive shadow pairs aiming to drive our network to learn more discriminative features for the shadow regions in different videos. Specifically, in training, we add a contrastive loss at the coarsest layer of the encoder, driving the features from shadow regions close together, and far from the features from the non-shadow region. Intuitively, this contrastive mechanism drives the encoder to learn high-level representations of shadow, invariant to all the various factors of shadow variations, such as shape and illumination." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.854, + 0.399, + 0.868 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We introduce a new video shadow detection framework, in which we highlight:" + }, + { + "type": "text", + "bbox": [ + 0.551, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "- SODA, a new type of trajectory attention that harmonise the features of the different video frames at each resolution." + }, + { + "type": "text", + "bbox": [ + 0.551, + 0.142, + 0.894, + 0.203 + ], + "angle": 0, + "content": "- SCOTCH, a contrastive loss that highlights a massive positive shadow pairs strategy in order to make our encoder learn more robust high-level representations of shadows." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.208, + 0.895, + 0.328 + ], + "angle": 0, + "content": "- We evaluate our proposed framework on the video shadow benchmark dataset ViSha [6], and compare with the state-of-the-art methods. Numerical and visual experimental results demonstrate that our approach outperforms, by a large margin, existing ones on video shadow detection. Furthermore, we provide an ablation study to further support the effectiveness of the technical contributions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.342, + 0.642, + 0.358 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.895, + 0.489 + ], + "angle": 0, + "content": "The task of video shadow detection has been extensively investigated in the community, in which solutions largely rely on analysing single frames (image shadow detection) or continuous multiple frames (video shadow detection). In this section, we review the existing techniques in turn, and then summarize the recent achievements in the video processing area to better illustrate the difference between existing work and our work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.727, + 0.513 + ], + "angle": 0, + "content": "2.1. Image Shadow Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Image shadow detection (ISD) can be cast as a semantic segmentation problem, where image object segmentation (IOS) methods can be used to solve this problem [8, 13, 19, 21, 22, 42]. However, IOS methods are not specifically designed for shadow detection. Hence, when re-training these methods directly for shadow detection, the performance is unsatisfactory due to the data bias." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.84 + ], + "angle": 0, + "content": "Techniques focused on image shadow detection incorporate problem-specific shadow knowledge into the model architecture and the training criterion [7,9,15,16,35,36,43, 46]. For example, BDRAR [46] introduces a bidirectional pyramidal architecture for shadow detection. DSD [43] presents a distraction-aware shadow-module to reduce false positives. Chen et al. [7] make use of non-labelled data, during training, with a task-specific semi-supervised learning mechanism called MTMT. Wang et al. investigate the detection of shadows along with their corresponding objects [35, 36]. Finally, FSDNet [16] proposes a compact image shadow detection network. Whilst ISD techniques have demonstrated potential results, their performance on videos is limited by the lack of temporal information." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.724, + 0.862 + ], + "angle": 0, + "content": "2.2. Video Shadow Detection" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Another body of researchers has explored the task of shadow detection from the lens of video analysis. The work" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10450" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "of [6] proposes the TVSD model. It relies on a dual-gated co-attention module, to aggregate features from different frames, and uses a contrastive learning mechanism to drive the encoder to discriminate frames from different videos. Hu et al. [14] introduce an optical flow warping module to aggregate features from different frames. STICT [25] uses transfer learning, to transfer the knowledge of a supervised image shadow detection network to a video shadow detection network, without labelled videos, by training the network prediction to be consistent with respect to temporal interpolation [33]. Moreover, the technique called SCCor [9] presents a weakly supervised correspondence learning mechanism to enhance the temporal similarity of features corresponding to shadow region across frames." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.314, + 0.351, + 0.33 + ], + "angle": 0, + "content": "2.3. Progresses in Video Processing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.534 + ], + "angle": 0, + "content": "The specific nature of videos, containing spatial and temporal information, has motivated the design of deep neural network architectures for different video processing applications. Models based on 3D CNN [17, 31] process videos by sequentially aggregating the spatio-temporal local information using 3D convolutional filters, but fail to effectively capture long-range temporal dependencies. To alleviate this limitation, architectures using recurrent networks were introduced in [2, 30]. Moreover, another set of works uses spatio-temporal memory bank mechanism [27] or spatiotemporal attention mechanism [32] into the coarse layers of 3D CNN architectures [18, 26, 37] to better integrate the temporal information for video processing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.473, + 0.762 + ], + "angle": 0, + "content": "The success of the transformer network architecture, on a wide variety of vision tasks [4, 10], has motivated the use of transformer for video tasks. While the self-attention mechanism in transformers appears to be well suited to capture the long-range dependencies in videos, applying transformers to videos raises many challenges, such as the quadratic complexity in the input sequence length, and the large data requirement induced by the lack of problem-specific inductive bias. The works of [1, 41] propose to separate spatial and temporal attention to reduce computational complexity, and the authors of [40] propose to apply multiple encoders on multiple views of the video. Recently, trajectory attention [29] was introduced as a way to incorporate an inductive bias in the self-attention operation to capture objects moving trajectories for better video recognition tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.771, + 0.455, + 0.788 + ], + "angle": 0, + "content": "2.4. Existing Works & Comparison to Our Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.856 + ], + "angle": 0, + "content": "All precedent works on VSD [6, 14, 25, 33] rely on convolutional neural network architectures. To the best of our knowledge, our work is the first video shadow detection approach based on transformers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Moreover, whilst the work of [29] also considers a type of attention trajectory, their modelling hypothesis is that the video objects do not change shape over time. This is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.32 + ], + "angle": 0, + "content": "a strong assumption to fulfill for several vision applications such as shadow detection; as shadows significantly change shape from frame to frame. Our work first mitigates this issue by modelling in the trajectories the inherent deformation of the shadows. Notice that TVSD [6] uses an image-level contrastive loss between frames from different videos, and SC-Cor [9] uses weakly-supervised correspondence learning for driving similar features from shadow-region close together. Unlike these works, we introduce a supervised contrastive strategy to contrast shadow features from non-shadow features. We underline that existing contrastive-based techniques assume that supervised contrastive learning is not performing better than its counterpart. In this work, we show that a well-designed supervised contrastive strategy indeed improves over existing works." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.33, + 0.636, + 0.347 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.894, + 0.446 + ], + "angle": 0, + "content": "In this section, we introduce all the components of the video shadow detection method presented in this work. After a global description of our framework (i), we introduce SODA, our new video self-attention module (ii), and we describe the training criterion of our model, which includes SCOTCH, our shadow contrastive mechanism (iii)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.453, + 0.807, + 0.468 + ], + "angle": 0, + "content": "3.1. Framework Architecture Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.893, + 0.521 + ], + "angle": 0, + "content": "Our proposed framework is composed of three main stages. The overall workflow is illustrated in Figure 1, and details are provided next." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Stage 1: Feature Extraction. In this stage, Mix Transformer (MiT) [39] is adopted as the encoder. MiT takes video clips as input, and it outputs a set of different-resolution spatial feature maps. Unlike ViT [10], which only generates single-resolution feature maps, the hierarchical structure of MiT can generate CNN-like multi-level multi-scale feature maps. These feature maps contain from high-resolution detailed information to low-resolution semantic information. By incorporating different levels of resolutions, the performance of tasks such as semantic segmentation can be boosted [39]. In this stage, MiT only encodes the spatial information of the given video clips (input), that is, the temporal information is not yet incorporated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.87 + ], + "angle": 0, + "content": "Stage 2: Harmonising Spatial and Temporal Information. The multi-scale feature maps from Stage 1 are then processed by the newly introduced shadow deformation attention trajectory module (SODA). The goal of this module is to capture the shadow's deformation trajectory along the frames in the video clips. Our deformation attention trajectory module processes independently each feature map with different-resolution. These processed feature maps are used as input to the decoder in the next stage." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Stage 3: Mask Shadow Generation. In this stage, a light-weighted decoder, with only MLP layers, is adopted to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10451" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.086, + 0.895, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.249, + 0.895, + 0.334 + ], + "angle": 0, + "content": "Figure 2. Deformation attention trajectory module. The input feature maps \\( z \\) is used to generate \\( q, k, v \\), respectively. The \\( q \\) and \\( k \\) are first used to calculate the pointwise \\( st \\)-to- \\( st \\) similarity, followed by a softmax on \\( t \\) to get the time attention. The time attention aggregated \\( v \\) can generate \\( s \\)-to- \\( st \\) (spatial-location-to-video) attention, named deformation attention. Then, the spatial-location-to-video attention is integrated along the spatial dimension to capture the deformation attention trajectory. Lastly, the deformation attention trajectory is used to generate the final feature map \\( z' \\) with a second self-attention \\( (\\hat{q}, \\hat{k}, \\hat{v}) \\). In this figure, each square represents a spatial feature map. (The channel dimension is not represented for simplicity)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.471, + 0.424 + ], + "angle": 0, + "content": "reconstruct the shadow's segmentation masks. The decoder aims to mix the high- & low- resolution information, from processed feature maps, for better semantic segmentation. The output of the decoder is a segmented video that marks out the shadows in each frame of the video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.437, + 0.47, + 0.468 + ], + "angle": 0, + "content": "3.2. SODA: ShadOw Deformation Attention trajectory" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Transformers have revolutionised several tasks in the computer vision area. The key is the self-attention mechanism that can accommodate with any given type of data and domain. However, for videos, the standard self-attention does not differentiate the spatial dimensions from the temporal dimension. This can lead the attention to focus on the redundant spatial information while neglecting the informative temporal variations in the videos. Nonetheless, video analysis is inherent to such temporality. Most recently, trajectory attention [29] has proposed to accommodate somehow with such issues. However and even though trajectory attention has demonstrated potential results, it has a major limitation – the objects are assumed not to change over time. This is a major constraint in several video tasks including shadow detection; as shadows significantly undergo deformation from one frame to another. In this subsection, we introduce a new scheme called ShadOw Deformation Attention trajectory (SODA) to mitigate current drawbacks of the literature." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Like in the classical self-attention setting, it begins with an input feature map generated from the encoder. Specifically, let us denote \\( f_{d} \\in \\mathbb{R}^{t \\times \\frac{h}{d} \\times \\frac{w}{d} \\times c} \\), the generated feature map from the encoder, where \\( d \\) is the spatial down-sampling ratio, \\( c \\) is the number of feature channels, and \\( t \\) is the number of time frames in the video. \\( f_{d} \\) is reshaped to a sequence of 1D token embedding denoted as \\( z \\in \\mathbb{R}^{n \\times c} \\), where \\( n = t \\times \\frac{h}{d} \\times \\frac{w}{d} \\). As shown in the left part of Figure 2, \\( z \\) is then mapped to a set of query-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.349, + 0.892, + 0.394 + ], + "angle": 0, + "content": "key-value vectors \\(q, k, v \\in \\mathbb{R}^{n \\times c}\\) using linear projections \\(q = w_{q} \\cdot z\\), \\(k = w_{k} \\cdot z\\), \\(v = w_{v} \\cdot z\\), with projection matrices \\(w_{q}, w_{k}, w_{v} \\in \\mathbb{R}^{n \\times n}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Our scheme considers two main parts: (i) temporal attention between the spatial location and video (Attention on Time in Figure 2), (ii) intra-space attention to capture deformation statuses within a spatial scene (Deformation Attention Trajectory in Figure 2). For the first part, given a space-time position in the video \\(st \\in \\{1, \\dots, n\\}\\), and a spatial location \\(s' \\in \\{1, \\dots, m\\}\\), where \\(m = \\frac{n}{t}\\), the temporal attention (deformation) between the space-time position \\(st\\) and the spatial locations \\(s'\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.54, + 0.892, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {s t s ^ {\\prime}} = \\sum_ {t ^ {\\prime}} v _ {s ^ {\\prime} t ^ {\\prime}} \\cdot \\frac {\\exp \\left\\langle q _ {s t} , k _ {s ^ {\\prime} t ^ {\\prime}} \\right\\rangle}{\\sum_ {\\bar {t}} \\exp \\left\\langle q _ {s t} , k _ {s ^ {\\prime} \\bar {t}} \\right\\rangle} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.699 + ], + "angle": 0, + "content": "For brevity, the notation is slightly abused by omitting the \"softmax operation on time dimension\" in the Fig. 2 applied to the fraction, as well as the scaling parameter \\(\\sqrt{n}\\) (we will keep this notation convention throughout the paper). The deformation encodes the connection between one space-time position and one spatial location, which indicates how the content of the space-time position \\(st\\) is presented in spatial location \\(s'\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.775 + ], + "angle": 0, + "content": "Once the temporal attentions are computed, the intraspace attention is then estimated to aggregate the spatial-location-to-video responses to space-level deformation. To do this, the computed deformation tokens are projected to a new set of query-key-value vectors using linear projections:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.779, + 0.891, + 0.798 + ], + "angle": 0, + "content": "\\[\n\\hat {q} _ {s t} = \\hat {w} _ {q} \\cdot \\hat {y} _ {s t s}, \\hat {k} _ {s t s ^ {\\prime}} = \\hat {w} _ {k} \\cdot \\hat {y} _ {s t s ^ {\\prime}}, \\hat {v} _ {s t s ^ {\\prime}} = \\hat {w} _ {v} \\cdot \\hat {y} _ {s t s ^ {\\prime}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.803, + 0.892, + 0.862 + ], + "angle": 0, + "content": "where \\(\\hat{y}_{sts}\\) is the temporal connection from \\(st\\) to the same spatial location \\(s\\), and \\(\\hat{q}_{st}\\) corresponds to the deformation reference point \\(st\\) that is used to aggregate the location-to-video connection:" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.866, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {s t} = \\sum_ {s ^ {\\prime}} \\hat {v} _ {s t s ^ {\\prime}} \\cdot \\frac {\\exp \\left\\langle \\hat {q} _ {s t} , \\hat {k} _ {s t s ^ {\\prime}} \\right\\rangle}{\\sum_ {\\bar {s}} \\exp \\left\\langle \\hat {q} _ {s t} , \\hat {k} _ {s t \\bar {s}} \\right\\rangle} \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10452" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "where \\(\\hat{y}_{st}\\) is the deformation attention output. The meaningful location-to-video tokens are pooled out to form the full space-level deformation status. By computing the intraspace attention, the attended feature map can capture the deformation status in different frames of the video, thus boosting the video shadow detection performance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.191, + 0.465, + 0.208 + ], + "angle": 0, + "content": "3.3. SCOTCH: Shadow COOnTrastive meCHanism" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.469, + 0.38 + ], + "angle": 0, + "content": "Contrastive learning [5, 20, 23] has been proven to be an effective mechanism for learning distinctive features. By contrasting the positive pairs with high similarity and negative pairs with low similarity, the learned feature maps can be more discriminative in downstream tasks including classification and segmentation. In previous video shadow detection task [6], positive and negative pairs are sampled from frames from the same video and from two different videos respectively. Since the frames from one video have high similarity image content, the contrastive mechanism can help to discriminate different video content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.471, + 0.698 + ], + "angle": 0, + "content": "However, the key element in video shadow detection is the shadow itself instead of the video content. With the goal of boosting the detection performance, we introduce SCOTCH, a Shadow COnTrastive meCHanism. SCOTCH seeks to better guide the segmentation process for shadows and non-shadows regions in the videos. Specifically, to learn a unified shadow feature for different videos, positive pairs are sampled from the shadow regions from different frames in different videos, whilst negative pairs are sampled as shadow and non-shadow regions on the frames in different videos. We underline that unlike the classical contrastive loss used for unsupervised learning [5, 28], where there is only a small number of positive pairs, we proposed a massive positive shadow paired contrastive loss. The key idea behind our loss is that - we seek to not only maximise the difference between shadow and non-shadow features, but also maximise the similarity between features of shadows presented in different videos. All shadow and non-shadow features are cropped from the last layer of the encoder presented in Section 3.1, with the supervision of the segmentation masks. The contrastive loss reads:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.708, + 0.469, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\ell_ {\\text {c o n t r a s t}} \\left(\\boldsymbol {v}, \\boldsymbol {v} ^ {+}, \\boldsymbol {v} ^ {-}\\right) = \\\\ - \\log \\left[ \\frac {\\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {+} / \\tau\\right)}{\\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {+} / \\tau\\right) + \\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {-} / \\tau\\right)} \\right] \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(\\pmb{v} \\in \\mathbb{R}^c\\) is the query shadow feature. Moreover, \\(\\pmb{v}_n^+\\), \\(\\pmb{v}_n^-\\in \\mathbb{R}^{n\\times c}\\) are the positive and negative groups respectively, and \\(\\tau\\) is a temperature hyperparameter. The final loss is computed across all frames in a mini-batch fashion." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Optimisation Scheme for Shadow Detection. Finally, to compute the shadow segmentation loss, we follow the default setting in [6]. We use the binary cross entropy (BCE)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "loss with a lovasz-hinge loss [3]. These two terms are added to define the shadow segmentation loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.133, + 0.892, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\ell_ {s e g} = \\ell_ {b c e} + \\lambda_ {1} \\ell_ {h i n g e} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.16, + 0.871, + 0.176 + ], + "angle": 0, + "content": "Our optimisation scheme is then given by (4) and (5) as:" + }, + { + "type": "equation", + "bbox": [ + 0.564, + 0.187, + 0.892, + 0.203 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\text {f i n a l}} = \\ell_ {\\text {b c e}} + \\lambda_ {1} \\ell_ {\\text {h i n g e}} + \\lambda_ {2} \\ell_ {\\text {c o n t r a s t}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.274 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are two hyper-parameters weighting the relative effect of the hinge loss and the contrastive loss in the final loss. In the following experiments, \\(\\lambda_{1},\\lambda_{2}\\) were empirically set to a value of 1 and 0.1, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.286, + 0.706, + 0.303 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.311, + 0.892, + 0.341 + ], + "angle": 0, + "content": "This section details all experiments performed to validate our proposed framework." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.349, + 0.78, + 0.365 + ], + "angle": 0, + "content": "4.1. Dataset and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Data Description. We utilise the largest and latest Video Shadow dataset (ViSha) [6] to evaluate the effectiveness of our proposed VSD method. The ViSha dataset has 120 videos, and each video contains between 29 and 101 frames. ViSha is composed of a total of 11,685 frames corresponding to a total duration of 390 seconds of video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Data Pre-processing. We follow the setting introduced in ViSha [6]. That is, we use the same train-test split, with 50 videos for training and 70 videos for testing. During training, we also use the same data augmentation strategy as [6] to enrich the variety of the dataset. Specifically, during training, images are re-scaled to size \\(512 \\times 512\\), and are randomly flipped horizontally. In testing, only re-scaling to the unified size \\(512 \\times 512\\) is used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Evaluation Metrics. Following the evaluation protocol used in [6, 9, 25], we employ four common evaluation metrics to measure the shadow detection accuracy: MAE, \\(\\mathbf{F}_{\\beta}\\), IoU, and BER. Lower MAE and BER scores, and higher \\(\\mathbf{F}_{\\beta}\\) and IoU scores indicate a better video shadow detection result. Moreover, we also provide the shadow BER (S-BER) and the non-shadow BER scores (N-BER) to further compare different VSD methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Implementation Details. Our proposed segmentation architecture is built using the PyTorch-lightning [11] deep-learning framework. The parameters of the feature extraction encoder are initialised using the weights from the MiT-B3 model pre-trained for image segmentation on ADE20K dataset [44, 45], publicly available on HuggingFace [38]. The remaining parameters (attention modules and the MLP decoder) are randomly initialised using \"Xavier\" methods [12]. During training, AdamW optimizer [24] is used with an initial learning rate of \\(1 \\times 10^{-6}\\) without decay. All experiments and ablation studies are trained for 36 epochs, for a training time of approximately 12 hours on NVIDIA A100 GPU with 80G RAM with batch size of 8." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10453" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.204, + 0.089, + 0.768, + 0.344 + ], + "angle": 0, + "content": "
METHODSEVALUATION METRICS
TasksTechniquesMAE ↓Fβ↑IoU ↑BER ↓S-BER ↓N-BER ↓
IOS★ FPN [19]0.0440.7070.51219.4936.592.40
PSPNet [42]0.0510.6420.47619.7536.443.07
DSS [13]0.0450.6960.50219.7736.962.59
R3Net [8]0.0440.7100.50220.4037.373.55
ISDBDRAR [46]0.0500.6950.48421.2940.282.31
★ DSD [43]0.0430.7020.51819.8837.891.88
MTMT [7]0.0430.7290.51720.2838.711.86
FSDNet [16]0.0570.6710.48620.5738.063.06
VOSPDBM [30]0.0660.6230.46619.7334.325.16
COSNet [26]0.0400.7050.51420.5039.221.79
★ FEELVOS [34]0.0430.7100.51219.7637.272.26
STM [27]0.0680.5970.40825.6947.443.96
VSDTVSD [6]0.0330.7570.56717.7033.971.45
STICT [25]0.0460.7020.54516.6029.583.59
SC-Cor [9]0.0420.7620.61513.6124.312.91
★ SCOTCH and SODA0.0290.7930.6409.06616.261.44
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.354, + 0.892, + 0.412 + ], + "angle": 0, + "content": "Table 1. Comparisons between our proposed technique and SOTA techniques on the ViSha dataset. \"MAE\" denotes mean absolute error, \\( \\mathrm{F}_{\\beta} \\) denotes F-measure score, \"IoU\" denotes intersection over union, \"BER\" denotes balance error rate, and \"S-BER\" means shadow BER, \"N-BER\" means non-shadow BER. The \\( \\uparrow \\) denotes the higher the value is the better the performance is, whilst the \\( \\downarrow \\) means the opposite. \\( \\star \\) indicates the best performed network in each category." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.426, + 0.371, + 0.442 + ], + "angle": 0, + "content": "4.2. Comparison to SOTA Techniques" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.47, + 0.698 + ], + "angle": 0, + "content": "Compared Methods. Video shadow detection is a relatively recent topic, and there are only three directly-related methods designed for this task. Hence, following existing VSD methods, we make comparisons against 4 different kinds of methods, including image object segmentation (IOS), image shadow detection (ISD), video object segmentation (VOS), and video shadow detection (VSD). For IOS, they are FPN [19], PSPNet [42], DSS [13], and \\(\\mathbf{R}^3\\)-Net [8], while the ISD methods are BDRAR [46], DSD [43], MTMT [7], and FSDNet [16]. The compared VOS methods include PDBM [30], COSNet [26], FEELVOS [34], and STM [27], while compared VSD methods are TVSD [6], STICT [25], and SC-Cor [9]. We obtain the results by re-training their network parameters with unified training parameters or by downloading the results from the TVSD [6] repository." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Quantitative Comparisons. Table 1 summarises MAE, \\(\\mathrm{F}_{\\beta}\\), IoU, and BER scores of our network against SOTA techniques. For each category, we use \\(\\star\\) to mark out the method with the best performance. From these quantitative results, we observe that the IOS and ISD report readily competing results. These results are expected as the modelling hypothesis for both families of techniques relies on only the image level analysis. Whilst VOS techniques consider also temporal information, these techniques are customised as a general framework for video object segmentation. However, shadow detection is more complex due to the fast change in appearance between frames. Notably, we observe that VSD techniques indeed provide a substantial performance" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.457 + ], + "angle": 0, + "content": "improvement compared to other methods; as they are designed considering the complexity of shadows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.64 + ], + "angle": 0, + "content": "More importantly, our method outperforms all other techniques by a significant margin for all evaluation metrics - further supporting the superiority of our approach. In particular, our method yields to a balanced error rate of 9.066 which is more than 4 points below SC-Cor, the latest SOTA technique, in terms of BER. The error rate for the shadow label (denoted as S-BER in Table 1) of our method is 8 points below SC-Cor. We also underline that our significant improvement in performance comes with a negligible computational cost. We report the test time in Table 2, where we observe that our SCOTCH and SODA framework only requires a fraction of time than compared methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.894, + 0.884 + ], + "angle": 0, + "content": "Visual Comparison. Figure 3 visually compares the shadow segmentation masks from our method and the compared methods on different input video frames. For video frames with black objects at the first three rows, we find that compared methods tend to wrongly identify those black objects as shadow ones, while our method can still accurately detect shadow pixels under the corruption of black objects. Moreover, compared methods tend to miss some shadow regions when the input video frames contain multiple shadow detection, as shown in the 4-th row to the 8-th row of Figure 3. On the contrary, our method can identify all these shadow regions of input video frames, and our detection results are most consistent with the ground truth in the 2nd column of Figure 3. We also provide the video segmentation masks on the project page to demonstrate the temporal coherence of the results provided by our method." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Model size and inference time. Table 2 further" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10454" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.892, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.525, + 0.895, + 0.581 + ], + "angle": 0, + "content": "Figure 3. Visual comparisons of video shadow detection results produced by our network (SCOTCH and SODA) and compared methods. Apparently, our method can more accurately identify shadow pixels and our results are more consistent with the ground truth in the 2nd column. The video segmentation results can be found on the project page. (d-e) are the methods with the highest performance in IOS, ISD, and VOS in Table 1, whilst (g-i) are all from the VSD area." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.594, + 0.468, + 0.677 + ], + "angle": 0, + "content": "
NetworksParamsGMACsTimeBER
TVSD [6]243.32158.8932.417.70
STCIT [25]104.6840.9913.516.60
SC-Cor [9]232.63218.421.813.61
SCOTCH and SODA211.79122.469.159.006
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.756 + ], + "angle": 0, + "content": "Table 2. Comparison of model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Specifically, the units for Params and Time are (MB) and (Mins), respectively. We denote the best and second best in bold and underline font." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.901 + ], + "angle": 0, + "content": "compares our network and three state-of-the-art video shadow detection methods in terms of the model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Apparently, among the three compared VSD methods, STICT has the smallest testing time (13.5 minutes). Compared to STICT, our method further reduces the inference time from 13.5 minutes to 9.15 minutes to test all 70 testing videos" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.749 + ], + "angle": 0, + "content": "with 6,897 images. Although our method takes 2nd rank in terms of the model size and computational complexity, they are only larger than STICT. This is because we only use a light-weighted MLP layer as the decoder to integrate the multi-resolution feature maps, which is computational-saving. In terms of performance, our method has a superior BER performance than STICT by reducing the BER score from 16.60 to 9.006, which indicates that with a minor compromise on the model size, our method can more accurately identify video shadows than STICT, TVSD, and SC-Cor." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.655, + 0.773 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.89, + 0.81 + ], + "angle": 0, + "content": "In Table 3, we perform ablation studies on our main contributions to evaluate the effectiveness of each component." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Baseline with MiT backbone. In order to evaluate the role of the MiT backbone on the final performance of our method, we define the segmentation network with MiT backbone as the baseline, which is trained by using the classical segmentation loss (5), but without the deformation attention trajectory and shadow level contrastive mechanism." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10455" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.223 + ], + "angle": 0, + "content": "
ComponentsEvaluation Metrics
BackboneAttentionContrastMAE ↓Fβ ↑IoU ↑BER ↓
MiTXX0.0480.7550.58413.18
MiTTrajectoryX0.0480.7600.59312.35
MiTSODAX0.0410.7910.61310.55
MiTXImage0.0480.7610.58812.85
MiTXShadow0.0410.7670.59212.02
MiTXSCOTCH0.0340.7710.60611.29
†MiTSODASCOTCH0.0290.7930.6409.066
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.233, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Table 3. Ablation study on different components of our proposed methods on the ViSha dataset. The \\(\\uparrow\\) denotes the higher the value is the better the performance is, whilst the \\(\\downarrow\\) means the opposite. “\\(\\dagger\\)” denotes our final methods with the highest performance in all evaluation metrics. Notations: best, second best, third best." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.469, + 0.41 + ], + "angle": 0, + "content": "This baseline already provides results on par or better than the previous three works in the VSD area (see Table 1 for comparison), even without considering any kind of temporal information. This illustrates the superior performance of the MiT transformer-based architecture over convolutional architectures on the task of video shadow detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.469, + 0.562 + ], + "angle": 0, + "content": "Attention mechanisms. We then evaluate the effectiveness of different attention mechanisms, including trajectory attention [29] and our newly introduced shadow deformation attention. Both types of attention modules provide an improvement over the baseline, which was to be expected as those modules give the ability to consider the temporal information within the videos. Our deformation attention trajectory module also appears to provide better results than the trajectory attention, indicating the importance of considering the deformation in the design of the attention module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.469, + 0.682 + ], + "angle": 0, + "content": "Contrastive losses. Next, we compare the effect of two types of contrastive criterion, the image level contrastive loss used in TVSD [6], and our feature-level shadow contrastive loss. The inter-frame contrastive learning slightly improves the baseline, whereas our shadow contrastive loss provides a significant improvement over the baseline. Those results illustrate the superiority of the features-level contrastive loss over the frame-level contrastive loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.469, + 0.79 + ], + "angle": 0, + "content": "Final model. SCOTCH reduces the variance of the spatial shadow features, while SODA processes the spatial features at different time-step to consider the temporal information in the video. Thus, SCOTCH and SODA have a complementary effect, as feeding SODA with more robust spatial features from SCOTCH, we are able to reach the best performance, outperforming all the previous settings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.331, + 0.817 + ], + "angle": 0, + "content": "4.4. Attention Map Visualisation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In Figure 4, we visually compare the attention maps from the baseline model (second row) with our proposed SCOTCH and SODA (third row). We can observe that the baseline model highlights the object part, whilst ours focuses more on the shadow region with the help of contrastive" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.09, + 0.892, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.283, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Figure 4. Attention maps visualisation. The low-resolution layers of the MiT encoder are selected for the visualization, with the query from the center of the ground truth shadow mask. From top to bottom row are the input video blended with segmentation mask, attention maps for baseline MiT methods, and attention maps from ours SCOTCH and SODA with deformation attention trajectory and shadow contrastive mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.52 + ], + "angle": 0, + "content": "learning. We can also observe that the baseline model might lose track of shape in different frames (third column), whilst our approach provides consistent shape information at different times with the help of the deformation attention trajectory. Hence, the model using the shadow deformation attention trajectory and the shadow contrastive loss is better at tracking the shadow region during different frames, while ignoring the non-shadow part of the image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.535, + 0.618, + 0.55 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.727 + ], + "angle": 0, + "content": "In this paper, we introduced SCOTCH and SODA, a new transformer video shadow detection framework. We developed shadow deformation attention trajectory (SODA), a self-attention module specially designed to handle the shadow deformation in videos, and we introduced a shadow contrastive mechanism (SCOTCH) to guide our network to better discriminate between shadow and non-shadow features. We demonstrate the effectiveness of the contributions with ablation studies. Finally, we show that our proposed method outperforms by a large margin concurrent video shadow segmentation works on the ViSha dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by Girton Postgraduate Research Scholarships, GSK Ph.D. Scholarship, CMIH, CCIMI, Philip Leverhulme Prize, Royal Society Wolfson Fellowship, EPSRC Advanced Career Fellowship EP/V029428/1, EPSRC grants EP/S026045/1, EP/T003553/1, EP/N014588/1, EP/T017961/1, Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, EU Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, and Guangzhou Municipal Science and Technology Project Grant No. 2023A03J0671." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10456" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. 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Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France + $^{3}$ The Hong Kong University of Science and Technology (Guangzhou), China + $^{4}$ The Hong Kong University of Science and Technology, HK SAR, China + +# Abstract + +Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliucambridge.github.io/scotch_and_soda/ + +# 1. Introduction + +Shadow is an inherent part of videos, and they have an adverse effect on a wide variety of video vision tasks. Therefore, the development of robust video shadow detection techniques, to alleviate those negative effects, is of great interest for the community. Video shadow detection is usually formulated as a segmentation problem for videos, however and due to the nature of the problem, shadow detection greatly differs from other segmentation tasks such as object segmentation. For inferring the presence of shadows in an image, one has to account for the global content information such as light source orientation, and the presence of objects casting shadows. Importantly, in a given video, shadows considerably change appearance (deformation) from frame to frame due to light variation and object motion. Finally, shadows can span over different backgrounds over different frames, making approaches relying + +![](images/5057fe85cdd37c557357f5ca0bcfc3bfcb284cea781af364473a971d48128457.jpg) + +![](images/1117fbbafd7cb96bcef0abbccbbfc409fcd73da374fd93dafc6570a73d7f0c56.jpg) +Figure 1. Overview of our SCOTCH and SODA framework. A MiT encoder extracts multi-scale features for each frame of the video (stage 1). Then, our deformation attention trajectory is applied to features individually to incorporate temporal information (stage 2). Finally, an MLP layer combines the multi-scale information to generate the segmentation masks (stage 3). The model is trained to contrast shadow and non-shadow features, by minimising our shadow contrastive loss with massive positive shadow pairs. + +on texture information unreliable. + +Particularly, video shadow detection methods can be broadly divided into two main categories. The first category refers to image shadow detection (ISD) [9,15,35,36,43,46]. This family of techniques computes the shadow detection frame by frame. Although computationally saving, these methods are incapable of handling temporal information. The second category refers to video shadow detection (VSD) [6, 9, 14, 16, 25]. These methods offer higher performance as the analysis involves spatial-temporal information. Hence, our main focus is video shadow detection. + +State-of-the-art video shadow detection methods rely on deep neural networks, which are trained on large annotated datasets. Specifically, those methods are composed of three parts: (i) a feature extraction network that extracts spatial features for each frame of the video; (ii) a temporal aggregation mechanism [6, 14] enriching spatial features with information from different frames; and (iii) a decoder, that maps video features to segmentation masks. Additionally, some works enforce consistency between frames prediction by using additional training criterion [9,25]. We retain from these studies that the design of the temporal aggregation mechanism and the temporal consistency loss is crucial to the performance of a video shadow detection network, and we will investigate both of those aspects in this work. + +The current temporal aggregation mechanisms available in the literature were typically designed for video tasks such as video action recognition, or video object segmentation. Currently, the most widely used temporal aggregation mechanism is based on a variant of the self-attention mechanism [1, 29, 32, 40, 41]. Recently, trajectory attention [29] has been shown to provide state-of-the-art results on video processing. Intuitively, trajectory attention aggregates information along the object's moving trajectory, while ignoring the context information, deemed as irrelevant. However, shadows in videos are subject to strong deformations, making them difficult to track, and thus they might cause the trajectory attention to fail. + +In this work, we first introduce the ShadOw Deformation Attention trajectory (SODA), a spatial-temporal aggregation mechanism designed to better handle the large shadow deformations that occur in videos. SODA operates in two steps. First, for each spatial location, an associated token is computed between the given spatial location and the video, which contains information in every time-step for the given spatial location. Second, by aggregating every associated spatial token, a new token is yielded with enriched spatial deformation information. Aggregating spatial-location-to-video information along the spatial dimension helps the network to detect shape changes in videos. + +Besides, we introduce the Shadow COnTrastive meCHanism (SCOTCH), a supervised contrastive loss with massive positive shadow pairs aiming to drive our network to learn more discriminative features for the shadow regions in different videos. Specifically, in training, we add a contrastive loss at the coarsest layer of the encoder, driving the features from shadow regions close together, and far from the features from the non-shadow region. Intuitively, this contrastive mechanism drives the encoder to learn high-level representations of shadow, invariant to all the various factors of shadow variations, such as shape and illumination. + +In summary, our contributions are as follows: + +- We introduce a new video shadow detection framework, in which we highlight: + +- SODA, a new type of trajectory attention that harmonise the features of the different video frames at each resolution. + +- SCOTCH, a contrastive loss that highlights a massive positive shadow pairs strategy in order to make our encoder learn more robust high-level representations of shadows. + +- We evaluate our proposed framework on the video shadow benchmark dataset ViSha [6], and compare with the state-of-the-art methods. Numerical and visual experimental results demonstrate that our approach outperforms, by a large margin, existing ones on video shadow detection. Furthermore, we provide an ablation study to further support the effectiveness of the technical contributions. + +# 2. Related Work + +The task of video shadow detection has been extensively investigated in the community, in which solutions largely rely on analysing single frames (image shadow detection) or continuous multiple frames (video shadow detection). In this section, we review the existing techniques in turn, and then summarize the recent achievements in the video processing area to better illustrate the difference between existing work and our work. + +# 2.1. Image Shadow Detection + +Image shadow detection (ISD) can be cast as a semantic segmentation problem, where image object segmentation (IOS) methods can be used to solve this problem [8, 13, 19, 21, 22, 42]. However, IOS methods are not specifically designed for shadow detection. Hence, when re-training these methods directly for shadow detection, the performance is unsatisfactory due to the data bias. + +Techniques focused on image shadow detection incorporate problem-specific shadow knowledge into the model architecture and the training criterion [7,9,15,16,35,36,43, 46]. For example, BDRAR [46] introduces a bidirectional pyramidal architecture for shadow detection. DSD [43] presents a distraction-aware shadow-module to reduce false positives. Chen et al. [7] make use of non-labelled data, during training, with a task-specific semi-supervised learning mechanism called MTMT. Wang et al. investigate the detection of shadows along with their corresponding objects [35, 36]. Finally, FSDNet [16] proposes a compact image shadow detection network. Whilst ISD techniques have demonstrated potential results, their performance on videos is limited by the lack of temporal information. + +# 2.2. Video Shadow Detection + +Another body of researchers has explored the task of shadow detection from the lens of video analysis. The work + +of [6] proposes the TVSD model. It relies on a dual-gated co-attention module, to aggregate features from different frames, and uses a contrastive learning mechanism to drive the encoder to discriminate frames from different videos. Hu et al. [14] introduce an optical flow warping module to aggregate features from different frames. STICT [25] uses transfer learning, to transfer the knowledge of a supervised image shadow detection network to a video shadow detection network, without labelled videos, by training the network prediction to be consistent with respect to temporal interpolation [33]. Moreover, the technique called SCCor [9] presents a weakly supervised correspondence learning mechanism to enhance the temporal similarity of features corresponding to shadow region across frames. + +# 2.3. Progresses in Video Processing + +The specific nature of videos, containing spatial and temporal information, has motivated the design of deep neural network architectures for different video processing applications. Models based on 3D CNN [17, 31] process videos by sequentially aggregating the spatio-temporal local information using 3D convolutional filters, but fail to effectively capture long-range temporal dependencies. To alleviate this limitation, architectures using recurrent networks were introduced in [2, 30]. Moreover, another set of works uses spatio-temporal memory bank mechanism [27] or spatiotemporal attention mechanism [32] into the coarse layers of 3D CNN architectures [18, 26, 37] to better integrate the temporal information for video processing. + +The success of the transformer network architecture, on a wide variety of vision tasks [4, 10], has motivated the use of transformer for video tasks. While the self-attention mechanism in transformers appears to be well suited to capture the long-range dependencies in videos, applying transformers to videos raises many challenges, such as the quadratic complexity in the input sequence length, and the large data requirement induced by the lack of problem-specific inductive bias. The works of [1, 41] propose to separate spatial and temporal attention to reduce computational complexity, and the authors of [40] propose to apply multiple encoders on multiple views of the video. Recently, trajectory attention [29] was introduced as a way to incorporate an inductive bias in the self-attention operation to capture objects moving trajectories for better video recognition tasks. + +# 2.4. Existing Works & Comparison to Our Work + +All precedent works on VSD [6, 14, 25, 33] rely on convolutional neural network architectures. To the best of our knowledge, our work is the first video shadow detection approach based on transformers. + +Moreover, whilst the work of [29] also considers a type of attention trajectory, their modelling hypothesis is that the video objects do not change shape over time. This is + +a strong assumption to fulfill for several vision applications such as shadow detection; as shadows significantly change shape from frame to frame. Our work first mitigates this issue by modelling in the trajectories the inherent deformation of the shadows. Notice that TVSD [6] uses an image-level contrastive loss between frames from different videos, and SC-Cor [9] uses weakly-supervised correspondence learning for driving similar features from shadow-region close together. Unlike these works, we introduce a supervised contrastive strategy to contrast shadow features from non-shadow features. We underline that existing contrastive-based techniques assume that supervised contrastive learning is not performing better than its counterpart. In this work, we show that a well-designed supervised contrastive strategy indeed improves over existing works. + +# 3. Methodology + +In this section, we introduce all the components of the video shadow detection method presented in this work. After a global description of our framework (i), we introduce SODA, our new video self-attention module (ii), and we describe the training criterion of our model, which includes SCOTCH, our shadow contrastive mechanism (iii). + +# 3.1. Framework Architecture Overview + +Our proposed framework is composed of three main stages. The overall workflow is illustrated in Figure 1, and details are provided next. + +Stage 1: Feature Extraction. In this stage, Mix Transformer (MiT) [39] is adopted as the encoder. MiT takes video clips as input, and it outputs a set of different-resolution spatial feature maps. Unlike ViT [10], which only generates single-resolution feature maps, the hierarchical structure of MiT can generate CNN-like multi-level multi-scale feature maps. These feature maps contain from high-resolution detailed information to low-resolution semantic information. By incorporating different levels of resolutions, the performance of tasks such as semantic segmentation can be boosted [39]. In this stage, MiT only encodes the spatial information of the given video clips (input), that is, the temporal information is not yet incorporated. + +Stage 2: Harmonising Spatial and Temporal Information. The multi-scale feature maps from Stage 1 are then processed by the newly introduced shadow deformation attention trajectory module (SODA). The goal of this module is to capture the shadow's deformation trajectory along the frames in the video clips. Our deformation attention trajectory module processes independently each feature map with different-resolution. These processed feature maps are used as input to the decoder in the next stage. + +Stage 3: Mask Shadow Generation. In this stage, a light-weighted decoder, with only MLP layers, is adopted to + +![](images/2af1f1a52de438f22161156e6b582642ddff225c82edeabd23188814e763467c.jpg) +Figure 2. Deformation attention trajectory module. The input feature maps $z$ is used to generate $q, k, v$ , respectively. The $q$ and $k$ are first used to calculate the pointwise $st$ -to- $st$ similarity, followed by a softmax on $t$ to get the time attention. The time attention aggregated $v$ can generate $s$ -to- $st$ (spatial-location-to-video) attention, named deformation attention. Then, the spatial-location-to-video attention is integrated along the spatial dimension to capture the deformation attention trajectory. Lastly, the deformation attention trajectory is used to generate the final feature map $z'$ with a second self-attention $(\hat{q}, \hat{k}, \hat{v})$ . In this figure, each square represents a spatial feature map. (The channel dimension is not represented for simplicity). + +reconstruct the shadow's segmentation masks. The decoder aims to mix the high- & low- resolution information, from processed feature maps, for better semantic segmentation. The output of the decoder is a segmented video that marks out the shadows in each frame of the video. + +# 3.2. SODA: ShadOw Deformation Attention trajectory + +Transformers have revolutionised several tasks in the computer vision area. The key is the self-attention mechanism that can accommodate with any given type of data and domain. However, for videos, the standard self-attention does not differentiate the spatial dimensions from the temporal dimension. This can lead the attention to focus on the redundant spatial information while neglecting the informative temporal variations in the videos. Nonetheless, video analysis is inherent to such temporality. Most recently, trajectory attention [29] has proposed to accommodate somehow with such issues. However and even though trajectory attention has demonstrated potential results, it has a major limitation – the objects are assumed not to change over time. This is a major constraint in several video tasks including shadow detection; as shadows significantly undergo deformation from one frame to another. In this subsection, we introduce a new scheme called ShadOw Deformation Attention trajectory (SODA) to mitigate current drawbacks of the literature. + +Like in the classical self-attention setting, it begins with an input feature map generated from the encoder. Specifically, let us denote $f_{d} \in \mathbb{R}^{t \times \frac{h}{d} \times \frac{w}{d} \times c}$ , the generated feature map from the encoder, where $d$ is the spatial down-sampling ratio, $c$ is the number of feature channels, and $t$ is the number of time frames in the video. $f_{d}$ is reshaped to a sequence of 1D token embedding denoted as $z \in \mathbb{R}^{n \times c}$ , where $n = t \times \frac{h}{d} \times \frac{w}{d}$ . As shown in the left part of Figure 2, $z$ is then mapped to a set of query- + +key-value vectors $q, k, v \in \mathbb{R}^{n \times c}$ using linear projections $q = w_{q} \cdot z$ , $k = w_{k} \cdot z$ , $v = w_{v} \cdot z$ , with projection matrices $w_{q}, w_{k}, w_{v} \in \mathbb{R}^{n \times n}$ . + +Our scheme considers two main parts: (i) temporal attention between the spatial location and video (Attention on Time in Figure 2), (ii) intra-space attention to capture deformation statuses within a spatial scene (Deformation Attention Trajectory in Figure 2). For the first part, given a space-time position in the video $st \in \{1, \dots, n\}$ , and a spatial location $s' \in \{1, \dots, m\}$ , where $m = \frac{n}{t}$ , the temporal attention (deformation) between the space-time position $st$ and the spatial locations $s'$ is computed as: + +$$ +\hat {y} _ {s t s ^ {\prime}} = \sum_ {t ^ {\prime}} v _ {s ^ {\prime} t ^ {\prime}} \cdot \frac {\exp \left\langle q _ {s t} , k _ {s ^ {\prime} t ^ {\prime}} \right\rangle}{\sum_ {\bar {t}} \exp \left\langle q _ {s t} , k _ {s ^ {\prime} \bar {t}} \right\rangle} \tag {1} +$$ + +For brevity, the notation is slightly abused by omitting the "softmax operation on time dimension" in the Fig. 2 applied to the fraction, as well as the scaling parameter $\sqrt{n}$ (we will keep this notation convention throughout the paper). The deformation encodes the connection between one space-time position and one spatial location, which indicates how the content of the space-time position $st$ is presented in spatial location $s'$ . + +Once the temporal attentions are computed, the intraspace attention is then estimated to aggregate the spatial-location-to-video responses to space-level deformation. To do this, the computed deformation tokens are projected to a new set of query-key-value vectors using linear projections: + +$$ +\hat {q} _ {s t} = \hat {w} _ {q} \cdot \hat {y} _ {s t s}, \hat {k} _ {s t s ^ {\prime}} = \hat {w} _ {k} \cdot \hat {y} _ {s t s ^ {\prime}}, \hat {v} _ {s t s ^ {\prime}} = \hat {w} _ {v} \cdot \hat {y} _ {s t s ^ {\prime}} \tag {2} +$$ + +where $\hat{y}_{sts}$ is the temporal connection from $st$ to the same spatial location $s$ , and $\hat{q}_{st}$ corresponds to the deformation reference point $st$ that is used to aggregate the location-to-video connection: + +$$ +\hat {y} _ {s t} = \sum_ {s ^ {\prime}} \hat {v} _ {s t s ^ {\prime}} \cdot \frac {\exp \left\langle \hat {q} _ {s t} , \hat {k} _ {s t s ^ {\prime}} \right\rangle}{\sum_ {\bar {s}} \exp \left\langle \hat {q} _ {s t} , \hat {k} _ {s t \bar {s}} \right\rangle} \tag {3} +$$ + +where $\hat{y}_{st}$ is the deformation attention output. The meaningful location-to-video tokens are pooled out to form the full space-level deformation status. By computing the intraspace attention, the attended feature map can capture the deformation status in different frames of the video, thus boosting the video shadow detection performance. + +# 3.3. SCOTCH: Shadow COOnTrastive meCHanism + +Contrastive learning [5, 20, 23] has been proven to be an effective mechanism for learning distinctive features. By contrasting the positive pairs with high similarity and negative pairs with low similarity, the learned feature maps can be more discriminative in downstream tasks including classification and segmentation. In previous video shadow detection task [6], positive and negative pairs are sampled from frames from the same video and from two different videos respectively. Since the frames from one video have high similarity image content, the contrastive mechanism can help to discriminate different video content. + +However, the key element in video shadow detection is the shadow itself instead of the video content. With the goal of boosting the detection performance, we introduce SCOTCH, a Shadow COnTrastive meCHanism. SCOTCH seeks to better guide the segmentation process for shadows and non-shadows regions in the videos. Specifically, to learn a unified shadow feature for different videos, positive pairs are sampled from the shadow regions from different frames in different videos, whilst negative pairs are sampled as shadow and non-shadow regions on the frames in different videos. We underline that unlike the classical contrastive loss used for unsupervised learning [5, 28], where there is only a small number of positive pairs, we proposed a massive positive shadow paired contrastive loss. The key idea behind our loss is that - we seek to not only maximise the difference between shadow and non-shadow features, but also maximise the similarity between features of shadows presented in different videos. All shadow and non-shadow features are cropped from the last layer of the encoder presented in Section 3.1, with the supervision of the segmentation masks. The contrastive loss reads: + +$$ +\begin{array}{l} \ell_ {\text {c o n t r a s t}} \left(\boldsymbol {v}, \boldsymbol {v} ^ {+}, \boldsymbol {v} ^ {-}\right) = \\ - \log \left[ \frac {\sum_ {n = 1} ^ {N} \exp \left(\boldsymbol {v} \cdot \boldsymbol {v} _ {n} ^ {+} / \tau\right)}{\sum_ {n = 1} ^ {N} \exp \left(\boldsymbol {v} \cdot \boldsymbol {v} _ {n} ^ {+} / \tau\right) + \sum_ {n = 1} ^ {N} \exp \left(\boldsymbol {v} \cdot \boldsymbol {v} _ {n} ^ {-} / \tau\right)} \right] \tag {4} \\ \end{array} +$$ + +where $\pmb{v} \in \mathbb{R}^c$ is the query shadow feature. Moreover, $\pmb{v}_n^+$ , $\pmb{v}_n^-\in \mathbb{R}^{n\times c}$ are the positive and negative groups respectively, and $\tau$ is a temperature hyperparameter. The final loss is computed across all frames in a mini-batch fashion. + +Optimisation Scheme for Shadow Detection. Finally, to compute the shadow segmentation loss, we follow the default setting in [6]. We use the binary cross entropy (BCE) + +loss with a lovasz-hinge loss [3]. These two terms are added to define the shadow segmentation loss as follows: + +$$ +\ell_ {s e g} = \ell_ {b c e} + \lambda_ {1} \ell_ {h i n g e} \tag {5} +$$ + +Our optimisation scheme is then given by (4) and (5) as: + +$$ +\ell_ {\text {f i n a l}} = \ell_ {\text {b c e}} + \lambda_ {1} \ell_ {\text {h i n g e}} + \lambda_ {2} \ell_ {\text {c o n t r a s t}} \tag {6} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are two hyper-parameters weighting the relative effect of the hinge loss and the contrastive loss in the final loss. In the following experiments, $\lambda_{1},\lambda_{2}$ were empirically set to a value of 1 and 0.1, respectively. + +# 4. Experimental Results + +This section details all experiments performed to validate our proposed framework. + +# 4.1. Dataset and Evaluation Metrics + +Data Description. We utilise the largest and latest Video Shadow dataset (ViSha) [6] to evaluate the effectiveness of our proposed VSD method. The ViSha dataset has 120 videos, and each video contains between 29 and 101 frames. ViSha is composed of a total of 11,685 frames corresponding to a total duration of 390 seconds of video. + +Data Pre-processing. We follow the setting introduced in ViSha [6]. That is, we use the same train-test split, with 50 videos for training and 70 videos for testing. During training, we also use the same data augmentation strategy as [6] to enrich the variety of the dataset. Specifically, during training, images are re-scaled to size $512 \times 512$ , and are randomly flipped horizontally. In testing, only re-scaling to the unified size $512 \times 512$ is used. + +Evaluation Metrics. Following the evaluation protocol used in [6, 9, 25], we employ four common evaluation metrics to measure the shadow detection accuracy: MAE, $\mathbf{F}_{\beta}$ , IoU, and BER. Lower MAE and BER scores, and higher $\mathbf{F}_{\beta}$ and IoU scores indicate a better video shadow detection result. Moreover, we also provide the shadow BER (S-BER) and the non-shadow BER scores (N-BER) to further compare different VSD methods. + +Implementation Details. Our proposed segmentation architecture is built using the PyTorch-lightning [11] deep-learning framework. The parameters of the feature extraction encoder are initialised using the weights from the MiT-B3 model pre-trained for image segmentation on ADE20K dataset [44, 45], publicly available on HuggingFace [38]. The remaining parameters (attention modules and the MLP decoder) are randomly initialised using "Xavier" methods [12]. During training, AdamW optimizer [24] is used with an initial learning rate of $1 \times 10^{-6}$ without decay. All experiments and ablation studies are trained for 36 epochs, for a training time of approximately 12 hours on NVIDIA A100 GPU with 80G RAM with batch size of 8. + +
METHODSEVALUATION METRICS
TasksTechniquesMAE ↓Fβ↑IoU ↑BER ↓S-BER ↓N-BER ↓
IOS★ FPN [19]0.0440.7070.51219.4936.592.40
PSPNet [42]0.0510.6420.47619.7536.443.07
DSS [13]0.0450.6960.50219.7736.962.59
R3Net [8]0.0440.7100.50220.4037.373.55
ISDBDRAR [46]0.0500.6950.48421.2940.282.31
★ DSD [43]0.0430.7020.51819.8837.891.88
MTMT [7]0.0430.7290.51720.2838.711.86
FSDNet [16]0.0570.6710.48620.5738.063.06
VOSPDBM [30]0.0660.6230.46619.7334.325.16
COSNet [26]0.0400.7050.51420.5039.221.79
★ FEELVOS [34]0.0430.7100.51219.7637.272.26
STM [27]0.0680.5970.40825.6947.443.96
VSDTVSD [6]0.0330.7570.56717.7033.971.45
STICT [25]0.0460.7020.54516.6029.583.59
SC-Cor [9]0.0420.7620.61513.6124.312.91
★ SCOTCH and SODA0.0290.7930.6409.06616.261.44
+ +Table 1. Comparisons between our proposed technique and SOTA techniques on the ViSha dataset. "MAE" denotes mean absolute error, $\mathrm{F}_{\beta}$ denotes F-measure score, "IoU" denotes intersection over union, "BER" denotes balance error rate, and "S-BER" means shadow BER, "N-BER" means non-shadow BER. The $\uparrow$ denotes the higher the value is the better the performance is, whilst the $\downarrow$ means the opposite. $\star$ indicates the best performed network in each category. + +# 4.2. Comparison to SOTA Techniques + +Compared Methods. Video shadow detection is a relatively recent topic, and there are only three directly-related methods designed for this task. Hence, following existing VSD methods, we make comparisons against 4 different kinds of methods, including image object segmentation (IOS), image shadow detection (ISD), video object segmentation (VOS), and video shadow detection (VSD). For IOS, they are FPN [19], PSPNet [42], DSS [13], and $\mathbf{R}^3$ -Net [8], while the ISD methods are BDRAR [46], DSD [43], MTMT [7], and FSDNet [16]. The compared VOS methods include PDBM [30], COSNet [26], FEELVOS [34], and STM [27], while compared VSD methods are TVSD [6], STICT [25], and SC-Cor [9]. We obtain the results by re-training their network parameters with unified training parameters or by downloading the results from the TVSD [6] repository. + +Quantitative Comparisons. Table 1 summarises MAE, $\mathrm{F}_{\beta}$ , IoU, and BER scores of our network against SOTA techniques. For each category, we use $\star$ to mark out the method with the best performance. From these quantitative results, we observe that the IOS and ISD report readily competing results. These results are expected as the modelling hypothesis for both families of techniques relies on only the image level analysis. Whilst VOS techniques consider also temporal information, these techniques are customised as a general framework for video object segmentation. However, shadow detection is more complex due to the fast change in appearance between frames. Notably, we observe that VSD techniques indeed provide a substantial performance + +improvement compared to other methods; as they are designed considering the complexity of shadows. + +More importantly, our method outperforms all other techniques by a significant margin for all evaluation metrics - further supporting the superiority of our approach. In particular, our method yields to a balanced error rate of 9.066 which is more than 4 points below SC-Cor, the latest SOTA technique, in terms of BER. The error rate for the shadow label (denoted as S-BER in Table 1) of our method is 8 points below SC-Cor. We also underline that our significant improvement in performance comes with a negligible computational cost. We report the test time in Table 2, where we observe that our SCOTCH and SODA framework only requires a fraction of time than compared methods. + +Visual Comparison. Figure 3 visually compares the shadow segmentation masks from our method and the compared methods on different input video frames. For video frames with black objects at the first three rows, we find that compared methods tend to wrongly identify those black objects as shadow ones, while our method can still accurately detect shadow pixels under the corruption of black objects. Moreover, compared methods tend to miss some shadow regions when the input video frames contain multiple shadow detection, as shown in the 4-th row to the 8-th row of Figure 3. On the contrary, our method can identify all these shadow regions of input video frames, and our detection results are most consistent with the ground truth in the 2nd column of Figure 3. We also provide the video segmentation masks on the project page to demonstrate the temporal coherence of the results provided by our method. + +Model size and inference time. Table 2 further + +![](images/944c0d77c3da05f49a98b0be323249522ffc409e3b80d969131bae23fbe5276d.jpg) +Figure 3. Visual comparisons of video shadow detection results produced by our network (SCOTCH and SODA) and compared methods. Apparently, our method can more accurately identify shadow pixels and our results are more consistent with the ground truth in the 2nd column. The video segmentation results can be found on the project page. (d-e) are the methods with the highest performance in IOS, ISD, and VOS in Table 1, whilst (g-i) are all from the VSD area. + +
NetworksParamsGMACsTimeBER
TVSD [6]243.32158.8932.417.70
STCIT [25]104.6840.9913.516.60
SC-Cor [9]232.63218.421.813.61
SCOTCH and SODA211.79122.469.159.006
+ +Table 2. Comparison of model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Specifically, the units for Params and Time are (MB) and (Mins), respectively. We denote the best and second best in bold and underline font. + +compares our network and three state-of-the-art video shadow detection methods in terms of the model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Apparently, among the three compared VSD methods, STICT has the smallest testing time (13.5 minutes). Compared to STICT, our method further reduces the inference time from 13.5 minutes to 9.15 minutes to test all 70 testing videos + +with 6,897 images. Although our method takes 2nd rank in terms of the model size and computational complexity, they are only larger than STICT. This is because we only use a light-weighted MLP layer as the decoder to integrate the multi-resolution feature maps, which is computational-saving. In terms of performance, our method has a superior BER performance than STICT by reducing the BER score from 16.60 to 9.006, which indicates that with a minor compromise on the model size, our method can more accurately identify video shadows than STICT, TVSD, and SC-Cor. + +# 4.3. Ablation Study + +In Table 3, we perform ablation studies on our main contributions to evaluate the effectiveness of each component. + +Baseline with MiT backbone. In order to evaluate the role of the MiT backbone on the final performance of our method, we define the segmentation network with MiT backbone as the baseline, which is trained by using the classical segmentation loss (5), but without the deformation attention trajectory and shadow level contrastive mechanism. + +
ComponentsEvaluation Metrics
BackboneAttentionContrastMAE ↓Fβ ↑IoU ↑BER ↓
MiTXX0.0480.7550.58413.18
MiTTrajectoryX0.0480.7600.59312.35
MiTSODAX0.0410.7910.61310.55
MiTXImage0.0480.7610.58812.85
MiTXShadow0.0410.7670.59212.02
MiTXSCOTCH0.0340.7710.60611.29
†MiTSODASCOTCH0.0290.7930.6409.066
+ +Table 3. Ablation study on different components of our proposed methods on the ViSha dataset. The $\uparrow$ denotes the higher the value is the better the performance is, whilst the $\downarrow$ means the opposite. “ $\dagger$ ” denotes our final methods with the highest performance in all evaluation metrics. Notations: best, second best, third best. + +This baseline already provides results on par or better than the previous three works in the VSD area (see Table 1 for comparison), even without considering any kind of temporal information. This illustrates the superior performance of the MiT transformer-based architecture over convolutional architectures on the task of video shadow detection. + +Attention mechanisms. We then evaluate the effectiveness of different attention mechanisms, including trajectory attention [29] and our newly introduced shadow deformation attention. Both types of attention modules provide an improvement over the baseline, which was to be expected as those modules give the ability to consider the temporal information within the videos. Our deformation attention trajectory module also appears to provide better results than the trajectory attention, indicating the importance of considering the deformation in the design of the attention module. + +Contrastive losses. Next, we compare the effect of two types of contrastive criterion, the image level contrastive loss used in TVSD [6], and our feature-level shadow contrastive loss. The inter-frame contrastive learning slightly improves the baseline, whereas our shadow contrastive loss provides a significant improvement over the baseline. Those results illustrate the superiority of the features-level contrastive loss over the frame-level contrastive loss. + +Final model. SCOTCH reduces the variance of the spatial shadow features, while SODA processes the spatial features at different time-step to consider the temporal information in the video. Thus, SCOTCH and SODA have a complementary effect, as feeding SODA with more robust spatial features from SCOTCH, we are able to reach the best performance, outperforming all the previous settings. + +# 4.4. Attention Map Visualisation + +In Figure 4, we visually compare the attention maps from the baseline model (second row) with our proposed SCOTCH and SODA (third row). We can observe that the baseline model highlights the object part, whilst ours focuses more on the shadow region with the help of contrastive + +![](images/f38a4f7dec373e3f9c004375cd539591ee02e4dfa722910fa68afd554f0bcda3.jpg) +Figure 4. Attention maps visualisation. The low-resolution layers of the MiT encoder are selected for the visualization, with the query from the center of the ground truth shadow mask. From top to bottom row are the input video blended with segmentation mask, attention maps for baseline MiT methods, and attention maps from ours SCOTCH and SODA with deformation attention trajectory and shadow contrastive mechanism. + +learning. We can also observe that the baseline model might lose track of shape in different frames (third column), whilst our approach provides consistent shape information at different times with the help of the deformation attention trajectory. Hence, the model using the shadow deformation attention trajectory and the shadow contrastive loss is better at tracking the shadow region during different frames, while ignoring the non-shadow part of the image. + +# 5. Conclusion + +In this paper, we introduced SCOTCH and SODA, a new transformer video shadow detection framework. We developed shadow deformation attention trajectory (SODA), a self-attention module specially designed to handle the shadow deformation in videos, and we introduced a shadow contrastive mechanism (SCOTCH) to guide our network to better discriminate between shadow and non-shadow features. We demonstrate the effectiveness of the contributions with ablation studies. Finally, we show that our proposed method outperforms by a large margin concurrent video shadow segmentation works on the ViSha dataset. + +Acknowledgements. This work is supported by Girton Postgraduate Research Scholarships, GSK Ph.D. Scholarship, CMIH, CCIMI, Philip Leverhulme Prize, Royal Society Wolfson Fellowship, EPSRC Advanced Career Fellowship EP/V029428/1, EPSRC grants EP/S026045/1, EP/T003553/1, EP/N014588/1, EP/T017961/1, Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, EU Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, and Guangzhou Municipal Science and Technology Project Grant No. 2023A03J0671. + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6836-6846, 2021. 2, 3 +[2] Nicolas Ballas, Li Yao, Chris Pal, and Aaron Courville. 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In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliucambridge.github.io/scotch_and_soda/" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 128, + 514 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 289, + 715 + ], + "type": "text", + "content": "Shadow is an inherent part of videos, and they have an adverse effect on a wide variety of video vision tasks. Therefore, the development of robust video shadow detection techniques, to alleviate those negative effects, is of great interest for the community. Video shadow detection is usually formulated as a segmentation problem for videos, however and due to the nature of the problem, shadow detection greatly differs from other segmentation tasks such as object segmentation. For inferring the presence of shadows in an image, one has to account for the global content information such as light source orientation, and the presence of objects casting shadows. Importantly, in a given video, shadows considerably change appearance (deformation) from frame to frame due to light variation and object motion. Finally, shadows can span over different backgrounds over different frames, making approaches relying" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 253, + 545, + 393 + ], + "blocks": [ + { + "bbox": [ + 307, + 253, + 545, + 393 + ], + "lines": [ + { + "bbox": [ + 307, + 253, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 307, + 253, + 545, + 393 + ], + "type": "image", + "image_path": "5057fe85cdd37c557357f5ca0bcfc3bfcb284cea781af364473a971d48128457.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 308, + 395, + 545, + 464 + ], + "blocks": [ + { + "bbox": [ + 308, + 395, + 545, + 464 + ], + "lines": [ + { + "bbox": [ + 308, + 395, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 308, + 395, + 545, + 464 + ], + "type": "image", + "image_path": "1117fbbafd7cb96bcef0abbccbbfc409fcd73da374fd93dafc6570a73d7f0c56.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 473, + 547, + 562 + ], + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 562 + ], + "type": "text", + "content": "Figure 1. Overview of our SCOTCH and SODA framework. A MiT encoder extracts multi-scale features for each frame of the video (stage 1). Then, our deformation attention trajectory is applied to features individually to incorporate temporal information (stage 2). Finally, an MLP layer combines the multi-scale information to generate the segmentation masks (stage 3). The model is trained to contrast shadow and non-shadow features, by minimising our shadow contrastive loss with massive positive shadow pairs." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 579, + 443, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 579, + 443, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 579, + 443, + 590 + ], + "type": "text", + "content": "on texture information unreliable." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Particularly, video shadow detection methods can be broadly divided into two main categories. The first category refers to image shadow detection (ISD) [9,15,35,36,43,46]. This family of techniques computes the shadow detection frame by frame. Although computationally saving, these methods are incapable of handling temporal information. The second category refers to video shadow detection (VSD) [6, 9, 14, 16, 25]. These methods offer higher performance as the analysis involves spatial-temporal information. Hence, our main focus is video shadow detection." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10449" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "State-of-the-art video shadow detection methods rely on deep neural networks, which are trained on large annotated datasets. Specifically, those methods are composed of three parts: (i) a feature extraction network that extracts spatial features for each frame of the video; (ii) a temporal aggregation mechanism [6, 14] enriching spatial features with information from different frames; and (iii) a decoder, that maps video features to segmentation masks. Additionally, some works enforce consistency between frames prediction by using additional training criterion [9,25]. We retain from these studies that the design of the temporal aggregation mechanism and the temporal consistency loss is crucial to the performance of a video shadow detection network, and we will investigate both of those aspects in this work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 396 + ], + "type": "text", + "content": "The current temporal aggregation mechanisms available in the literature were typically designed for video tasks such as video action recognition, or video object segmentation. Currently, the most widely used temporal aggregation mechanism is based on a variant of the self-attention mechanism [1, 29, 32, 40, 41]. Recently, trajectory attention [29] has been shown to provide state-of-the-art results on video processing. Intuitively, trajectory attention aggregates information along the object's moving trajectory, while ignoring the context information, deemed as irrelevant. However, shadows in videos are subject to strong deformations, making them difficult to track, and thus they might cause the trajectory attention to fail." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 398, + 289, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 289, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 289, + 542 + ], + "type": "text", + "content": "In this work, we first introduce the ShadOw Deformation Attention trajectory (SODA), a spatial-temporal aggregation mechanism designed to better handle the large shadow deformations that occur in videos. SODA operates in two steps. First, for each spatial location, an associated token is computed between the given spatial location and the video, which contains information in every time-step for the given spatial location. Second, by aggregating every associated spatial token, a new token is yielded with enriched spatial deformation information. Aggregating spatial-location-to-video information along the spatial dimension helps the network to detect shape changes in videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 543, + 289, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 289, + 674 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 289, + 674 + ], + "type": "text", + "content": "Besides, we introduce the Shadow COnTrastive meCHanism (SCOTCH), a supervised contrastive loss with massive positive shadow pairs aiming to drive our network to learn more discriminative features for the shadow regions in different videos. Specifically, in training, we add a contrastive loss at the coarsest layer of the encoder, driving the features from shadow regions close together, and far from the features from the non-shadow region. Intuitively, this contrastive mechanism drives the encoder to learn high-level representations of shadow, invariant to all the various factors of shadow variations, such as shape and illumination." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 676, + 244, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 676, + 244, + 687 + ], + "spans": [ + { + "bbox": [ + 59, + 676, + 244, + 687 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- We introduce a new video shadow detection framework, in which we highlight:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 337, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 337, + 72, + 545, + 107 + ], + "type": "text", + "content": "- SODA, a new type of trajectory attention that harmonise the features of the different video frames at each resolution." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 337, + 112, + 547, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 112, + 547, + 160 + ], + "spans": [ + { + "bbox": [ + 337, + 112, + 547, + 160 + ], + "type": "text", + "content": "- SCOTCH, a contrastive loss that highlights a massive positive shadow pairs strategy in order to make our encoder learn more robust high-level representations of shadows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 164, + 547, + 259 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 164, + 547, + 259 + ], + "spans": [ + { + "bbox": [ + 317, + 164, + 547, + 259 + ], + "type": "text", + "content": "- We evaluate our proposed framework on the video shadow benchmark dataset ViSha [6], and compare with the state-of-the-art methods. Numerical and visual experimental results demonstrate that our approach outperforms, by a large margin, existing ones on video shadow detection. Furthermore, we provide an ablation study to further support the effectiveness of the technical contributions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 270, + 392, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 392, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 392, + 283 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 290, + 547, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 547, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 547, + 387 + ], + "type": "text", + "content": "The task of video shadow detection has been extensively investigated in the community, in which solutions largely rely on analysing single frames (image shadow detection) or continuous multiple frames (video shadow detection). In this section, we review the existing techniques in turn, and then summarize the recent achievements in the video processing area to better illustrate the difference between existing work and our work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 394, + 444, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 394, + 444, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 394, + 444, + 406 + ], + "type": "text", + "content": "2.1. Image Shadow Detection" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 412, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 496 + ], + "type": "text", + "content": "Image shadow detection (ISD) can be cast as a semantic segmentation problem, where image object segmentation (IOS) methods can be used to solve this problem [8, 13, 19, 21, 22, 42]. However, IOS methods are not specifically designed for shadow detection. Hence, when re-training these methods directly for shadow detection, the performance is unsatisfactory due to the data bias." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 497, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 665 + ], + "type": "text", + "content": "Techniques focused on image shadow detection incorporate problem-specific shadow knowledge into the model architecture and the training criterion [7,9,15,16,35,36,43, 46]. For example, BDRAR [46] introduces a bidirectional pyramidal architecture for shadow detection. DSD [43] presents a distraction-aware shadow-module to reduce false positives. Chen et al. [7] make use of non-labelled data, during training, with a task-specific semi-supervised learning mechanism called MTMT. Wang et al. investigate the detection of shadows along with their corresponding objects [35, 36]. Finally, FSDNet [16] proposes a compact image shadow detection network. Whilst ISD techniques have demonstrated potential results, their performance on videos is limited by the lack of temporal information." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 671, + 443, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 443, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 443, + 682 + ], + "type": "text", + "content": "2.2. Video Shadow Detection" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 713 + ], + "type": "text", + "content": "Another body of researchers has explored the task of shadow detection from the lens of video analysis. The work" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10450" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "of [6] proposes the TVSD model. It relies on a dual-gated co-attention module, to aggregate features from different frames, and uses a contrastive learning mechanism to drive the encoder to discriminate frames from different videos. Hu et al. [14] introduce an optical flow warping module to aggregate features from different frames. STICT [25] uses transfer learning, to transfer the knowledge of a supervised image shadow detection network to a video shadow detection network, without labelled videos, by training the network prediction to be consistent with respect to temporal interpolation [33]. Moreover, the technique called SCCor [9] presents a weakly supervised correspondence learning mechanism to enhance the temporal similarity of features corresponding to shadow region across frames." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 248, + 214, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 248, + 214, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 214, + 261 + ], + "type": "text", + "content": "2.3. Progresses in Video Processing" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 422 + ], + "type": "text", + "content": "The specific nature of videos, containing spatial and temporal information, has motivated the design of deep neural network architectures for different video processing applications. Models based on 3D CNN [17, 31] process videos by sequentially aggregating the spatio-temporal local information using 3D convolutional filters, but fail to effectively capture long-range temporal dependencies. To alleviate this limitation, architectures using recurrent networks were introduced in [2, 30]. Moreover, another set of works uses spatio-temporal memory bank mechanism [27] or spatiotemporal attention mechanism [32] into the coarse layers of 3D CNN architectures [18, 26, 37] to better integrate the temporal information for video processing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 423, + 289, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 289, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 289, + 603 + ], + "type": "text", + "content": "The success of the transformer network architecture, on a wide variety of vision tasks [4, 10], has motivated the use of transformer for video tasks. While the self-attention mechanism in transformers appears to be well suited to capture the long-range dependencies in videos, applying transformers to videos raises many challenges, such as the quadratic complexity in the input sequence length, and the large data requirement induced by the lack of problem-specific inductive bias. The works of [1, 41] propose to separate spatial and temporal attention to reduce computational complexity, and the authors of [40] propose to apply multiple encoders on multiple views of the video. Recently, trajectory attention [29] was introduced as a way to incorporate an inductive bias in the self-attention operation to capture objects moving trajectories for better video recognition tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 610, + 278, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 278, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 278, + 624 + ], + "type": "text", + "content": "2.4. Existing Works & Comparison to Our Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 677 + ], + "type": "text", + "content": "All precedent works on VSD [6, 14, 25, 33] rely on convolutional neural network architectures. To the best of our knowledge, our work is the first video shadow detection approach based on transformers." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Moreover, whilst the work of [29] also considers a type of attention trajectory, their modelling hypothesis is that the video objects do not change shape over time. This is" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "content": "a strong assumption to fulfill for several vision applications such as shadow detection; as shadows significantly change shape from frame to frame. Our work first mitigates this issue by modelling in the trajectories the inherent deformation of the shadows. Notice that TVSD [6] uses an image-level contrastive loss between frames from different videos, and SC-Cor [9] uses weakly-supervised correspondence learning for driving similar features from shadow-region close together. Unlike these works, we introduce a supervised contrastive strategy to contrast shadow features from non-shadow features. We underline that existing contrastive-based techniques assume that supervised contrastive learning is not performing better than its counterpart. In this work, we show that a well-designed supervised contrastive strategy indeed improves over existing works." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 261, + 389, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 261, + 389, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 389, + 274 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 281, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 547, + 353 + ], + "type": "text", + "content": "In this section, we introduce all the components of the video shadow detection method presented in this work. After a global description of our framework (i), we introduce SODA, our new video self-attention module (ii), and we describe the training criterion of our model, which includes SCOTCH, our shadow contrastive mechanism (iii)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 358, + 493, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 493, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 493, + 370 + ], + "type": "text", + "content": "3.1. Framework Architecture Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 376, + 546, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 412 + ], + "type": "text", + "content": "Our proposed framework is composed of three main stages. The overall workflow is illustrated in Figure 1, and details are provided next." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 414, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 547, + 581 + ], + "type": "text", + "content": "Stage 1: Feature Extraction. In this stage, Mix Transformer (MiT) [39] is adopted as the encoder. MiT takes video clips as input, and it outputs a set of different-resolution spatial feature maps. Unlike ViT [10], which only generates single-resolution feature maps, the hierarchical structure of MiT can generate CNN-like multi-level multi-scale feature maps. These feature maps contain from high-resolution detailed information to low-resolution semantic information. By incorporating different levels of resolutions, the performance of tasks such as semantic segmentation can be boosted [39]. In this stage, MiT only encodes the spatial information of the given video clips (input), that is, the temporal information is not yet incorporated." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 689 + ], + "type": "text", + "content": "Stage 2: Harmonising Spatial and Temporal Information. The multi-scale feature maps from Stage 1 are then processed by the newly introduced shadow deformation attention trajectory module (SODA). The goal of this module is to capture the shadow's deformation trajectory along the frames in the video clips. Our deformation attention trajectory module processes independently each feature map with different-resolution. These processed feature maps are used as input to the decoder in the next stage." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Stage 3: Mask Shadow Generation. In this stage, a light-weighted decoder, with only MLP layers, is adopted to" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10451" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 547, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 547, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 547, + 190 + ], + "type": "image", + "image_path": "2af1f1a52de438f22161156e6b582642ddff225c82edeabd23188814e763467c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": "Figure 2. Deformation attention trajectory module. The input feature maps " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " is used to generate " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "q, k, v" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": ", respectively. The " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " are first used to calculate the pointwise " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": "-to- " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " similarity, followed by a softmax on " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " to get the time attention. The time attention aggregated " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " can generate " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": "-to- " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " (spatial-location-to-video) attention, named deformation attention. Then, the spatial-location-to-video attention is integrated along the spatial dimension to capture the deformation attention trajectory. Lastly, the deformation attention trajectory is used to generate the final feature map " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "z'" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": " with a second self-attention " + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "inline_equation", + "content": "(\\hat{q}, \\hat{k}, \\hat{v})" + }, + { + "bbox": [ + 46, + 197, + 547, + 264 + ], + "type": "text", + "content": ". In this figure, each square represents a spatial feature map. (The channel dimension is not represented for simplicity)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 288, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 288, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 288, + 335 + ], + "type": "text", + "content": "reconstruct the shadow's segmentation masks. The decoder aims to mix the high- & low- resolution information, from processed feature maps, for better semantic segmentation. The output of the decoder is a segmented video that marks out the shadows in each frame of the video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 346, + 287, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 370 + ], + "type": "text", + "content": "3.2. SODA: ShadOw Deformation Attention trajectory" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 377, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 604 + ], + "type": "text", + "content": "Transformers have revolutionised several tasks in the computer vision area. The key is the self-attention mechanism that can accommodate with any given type of data and domain. However, for videos, the standard self-attention does not differentiate the spatial dimensions from the temporal dimension. This can lead the attention to focus on the redundant spatial information while neglecting the informative temporal variations in the videos. Nonetheless, video analysis is inherent to such temporality. Most recently, trajectory attention [29] has proposed to accommodate somehow with such issues. However and even though trajectory attention has demonstrated potential results, it has a major limitation – the objects are assumed not to change over time. This is a major constraint in several video tasks including shadow detection; as shadows significantly undergo deformation from one frame to another. In this subsection, we introduce a new scheme called ShadOw Deformation Attention trajectory (SODA) to mitigate current drawbacks of the literature." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Like in the classical self-attention setting, it begins with an input feature map generated from the encoder. Specifically, let us denote " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "f_{d} \\in \\mathbb{R}^{t \\times \\frac{h}{d} \\times \\frac{w}{d} \\times c}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", the generated feature map from the encoder, where " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " is the spatial down-sampling ratio, " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " is the number of feature channels, and " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " is the number of time frames in the video. " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " is reshaped to a sequence of 1D token embedding denoted as " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "z \\in \\mathbb{R}^{n \\times c}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "n = t \\times \\frac{h}{d} \\times \\frac{w}{d}" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": ". As shown in the left part of Figure 2, " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " is then mapped to a set of query-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "content": "key-value vectors " + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "q, k, v \\in \\mathbb{R}^{n \\times c}" + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "content": " using linear projections " + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "q = w_{q} \\cdot z" + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "k = w_{k} \\cdot z" + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "v = w_{v} \\cdot z" + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "content": ", with projection matrices " + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "inline_equation", + "content": "w_{q}, w_{k}, w_{v} \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 305, + 276, + 545, + 312 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "content": "Our scheme considers two main parts: (i) temporal attention between the spatial location and video (Attention on Time in Figure 2), (ii) intra-space attention to capture deformation statuses within a spatial scene (Deformation Attention Trajectory in Figure 2). For the first part, given a space-time position in the video " + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "inline_equation", + "content": "st \\in \\{1, \\dots, n\\}" + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "content": ", and a spatial location " + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "inline_equation", + "content": "s' \\in \\{1, \\dots, m\\}" + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "inline_equation", + "content": "m = \\frac{n}{t}" + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "content": ", the temporal attention (deformation) between the space-time position " + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "content": " and the spatial locations " + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 305, + 312, + 546, + 419 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 351, + 427, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 427, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 351, + 427, + 545, + 455 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {s t s ^ {\\prime}} = \\sum_ {t ^ {\\prime}} v _ {s ^ {\\prime} t ^ {\\prime}} \\cdot \\frac {\\exp \\left\\langle q _ {s t} , k _ {s ^ {\\prime} t ^ {\\prime}} \\right\\rangle}{\\sum_ {\\bar {t}} \\exp \\left\\langle q _ {s t} , k _ {s ^ {\\prime} \\bar {t}} \\right\\rangle} \\tag {1}", + "image_path": "b01950918914ca3d84fd47d2a8d9de20064b5fd102ca04ee8a5d9aff0b1480ef.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "text", + "content": "For brevity, the notation is slightly abused by omitting the \"softmax operation on time dimension\" in the Fig. 2 applied to the fraction, as well as the scaling parameter " + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "inline_equation", + "content": "\\sqrt{n}" + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "text", + "content": " (we will keep this notation convention throughout the paper). The deformation encodes the connection between one space-time position and one spatial location, which indicates how the content of the space-time position " + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "text", + "content": " is presented in spatial location " + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "inline_equation", + "content": "s'" + }, + { + "bbox": [ + 304, + 457, + 545, + 553 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "text", + "content": "Once the temporal attentions are computed, the intraspace attention is then estimated to aggregate the spatial-location-to-video responses to space-level deformation. To do this, the computed deformation tokens are projected to a new set of query-key-value vectors using linear projections:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 310, + 616, + 545, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 616, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 310, + 616, + 545, + 632 + ], + "type": "interline_equation", + "content": "\\hat {q} _ {s t} = \\hat {w} _ {q} \\cdot \\hat {y} _ {s t s}, \\hat {k} _ {s t s ^ {\\prime}} = \\hat {w} _ {k} \\cdot \\hat {y} _ {s t s ^ {\\prime}}, \\hat {v} _ {s t s ^ {\\prime}} = \\hat {w} _ {v} \\cdot \\hat {y} _ {s t s ^ {\\prime}} \\tag {2}", + "image_path": "3ef466eeed9e34f6f3be7e286bbd4aeba226b09b7f62e80e6c40d53fb7fe774c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "inline_equation", + "content": "\\hat{y}_{sts}" + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "content": " is the temporal connection from " + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "content": " to the same spatial location " + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "inline_equation", + "content": "\\hat{q}_{st}" + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "content": " corresponds to the deformation reference point " + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "inline_equation", + "content": "st" + }, + { + "bbox": [ + 304, + 635, + 545, + 682 + ], + "type": "text", + "content": " that is used to aggregate the location-to-video connection:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 353, + 685, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 685, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 353, + 685, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {s t} = \\sum_ {s ^ {\\prime}} \\hat {v} _ {s t s ^ {\\prime}} \\cdot \\frac {\\exp \\left\\langle \\hat {q} _ {s t} , \\hat {k} _ {s t s ^ {\\prime}} \\right\\rangle}{\\sum_ {\\bar {s}} \\exp \\left\\langle \\hat {q} _ {s t} , \\hat {k} _ {s t \\bar {s}} \\right\\rangle} \\tag {3}", + "image_path": "81b31c73927f93268bd313acaba4753060e9b5c45dfd40d60de1ca9d311750ca.jpg" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10452" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\hat{y}_{st}" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " is the deformation attention output. The meaningful location-to-video tokens are pooled out to form the full space-level deformation status. By computing the intraspace attention, the attended feature map can capture the deformation status in different frames of the video, thus boosting the video shadow detection performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 151, + 284, + 164 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 151, + 284, + 164 + ], + "spans": [ + { + "bbox": [ + 47, + 151, + 284, + 164 + ], + "type": "text", + "content": "3.3. SCOTCH: Shadow COOnTrastive meCHanism" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 170, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 287, + 300 + ], + "type": "text", + "content": "Contrastive learning [5, 20, 23] has been proven to be an effective mechanism for learning distinctive features. By contrasting the positive pairs with high similarity and negative pairs with low similarity, the learned feature maps can be more discriminative in downstream tasks including classification and segmentation. In previous video shadow detection task [6], positive and negative pairs are sampled from frames from the same video and from two different videos respectively. Since the frames from one video have high similarity image content, the contrastive mechanism can help to discriminate different video content." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 301, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 288, + 552 + ], + "type": "text", + "content": "However, the key element in video shadow detection is the shadow itself instead of the video content. With the goal of boosting the detection performance, we introduce SCOTCH, a Shadow COnTrastive meCHanism. SCOTCH seeks to better guide the segmentation process for shadows and non-shadows regions in the videos. Specifically, to learn a unified shadow feature for different videos, positive pairs are sampled from the shadow regions from different frames in different videos, whilst negative pairs are sampled as shadow and non-shadow regions on the frames in different videos. We underline that unlike the classical contrastive loss used for unsupervised learning [5, 28], where there is only a small number of positive pairs, we proposed a massive positive shadow paired contrastive loss. The key idea behind our loss is that - we seek to not only maximise the difference between shadow and non-shadow features, but also maximise the similarity between features of shadows presented in different videos. All shadow and non-shadow features are cropped from the last layer of the encoder presented in Section 3.1, with the supervision of the segmentation masks. The contrastive loss reads:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 560, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 560, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 48, + 560, + 287, + 620 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\ell_ {\\text {c o n t r a s t}} \\left(\\boldsymbol {v}, \\boldsymbol {v} ^ {+}, \\boldsymbol {v} ^ {-}\\right) = \\\\ - \\log \\left[ \\frac {\\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {+} / \\tau\\right)}{\\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {+} / \\tau\\right) + \\sum_ {n = 1} ^ {N} \\exp \\left(\\boldsymbol {v} \\cdot \\boldsymbol {v} _ {n} ^ {-} / \\tau\\right)} \\right] \\tag {4} \\\\ \\end{array}", + "image_path": "8026fc637e00d90d4e25c41c6ebb391b9ff7e262fb20e0c1738b44fd14175916.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{v} \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": " is the query shadow feature. Moreover, " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{v}_n^+" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pmb{v}_n^-\\in \\mathbb{R}^{n\\times c}" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": " are the positive and negative groups respectively, and " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": " is a temperature hyperparameter. The final loss is computed across all frames in a mini-batch fashion." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Optimisation Scheme for Shadow Detection. Finally, to compute the shadow segmentation loss, we follow the default setting in [6]. We use the binary cross entropy (BCE)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "loss with a lovasz-hinge loss [3]. These two terms are added to define the shadow segmentation loss as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 377, + 105, + 545, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 105, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 377, + 105, + 545, + 118 + ], + "type": "interline_equation", + "content": "\\ell_ {s e g} = \\ell_ {b c e} + \\lambda_ {1} \\ell_ {h i n g e} \\tag {5}", + "image_path": "6d556cd657c21aa0b39b9baedb9818f50b43df734cfe5b1015d6d3945d278857.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 126, + 533, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 126, + 533, + 139 + ], + "spans": [ + { + "bbox": [ + 305, + 126, + 533, + 139 + ], + "type": "text", + "content": "Our optimisation scheme is then given by (4) and (5) as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 345, + 148, + 545, + 160 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 148, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 345, + 148, + 545, + 160 + ], + "type": "interline_equation", + "content": "\\ell_ {\\text {f i n a l}} = \\ell_ {\\text {b c e}} + \\lambda_ {1} \\ell_ {\\text {h i n g e}} + \\lambda_ {2} \\ell_ {\\text {c o n t r a s t}} \\tag {6}", + "image_path": "2fd6781fbbb35c94cf514cf6727087d14c0456e000d0289ddeab5bfc02c84966.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "text", + "content": " are two hyper-parameters weighting the relative effect of the hinge loss and the contrastive loss in the final loss. In the following experiments, " + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "inline_equation", + "content": "\\lambda_{1},\\lambda_{2}" + }, + { + "bbox": [ + 304, + 168, + 545, + 217 + ], + "type": "text", + "content": " were empirically set to a value of 1 and 0.1, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 226, + 432, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 226, + 432, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 226, + 432, + 239 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 246, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 246, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 246, + 545, + 270 + ], + "type": "text", + "content": "This section details all experiments performed to validate our proposed framework." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 276, + 477, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 276, + 477, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 276, + 477, + 289 + ], + "type": "text", + "content": "4.1. Dataset and Evaluation Metrics" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 295, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 545, + 366 + ], + "type": "text", + "content": "Data Description. We utilise the largest and latest Video Shadow dataset (ViSha) [6] to evaluate the effectiveness of our proposed VSD method. The ViSha dataset has 120 videos, and each video contains between 29 and 101 frames. ViSha is composed of a total of 11,685 frames corresponding to a total duration of 390 seconds of video." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "type": "text", + "content": "Data Pre-processing. We follow the setting introduced in ViSha [6]. That is, we use the same train-test split, with 50 videos for training and 70 videos for testing. During training, we also use the same data augmentation strategy as [6] to enrich the variety of the dataset. Specifically, during training, images are re-scaled to size " + }, + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "type": "text", + "content": ", and are randomly flipped horizontally. In testing, only re-scaling to the unified size " + }, + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 366, + 545, + 461 + ], + "type": "text", + "content": " is used." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": "Evaluation Metrics. Following the evaluation protocol used in [6, 9, 25], we employ four common evaluation metrics to measure the shadow detection accuracy: MAE, " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\beta}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": ", IoU, and BER. Lower MAE and BER scores, and higher " + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\beta}" + }, + { + "bbox": [ + 304, + 462, + 545, + 557 + ], + "type": "text", + "content": " and IoU scores indicate a better video shadow detection result. Moreover, we also provide the shadow BER (S-BER) and the non-shadow BER scores (N-BER) to further compare different VSD methods." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": "Implementation Details. Our proposed segmentation architecture is built using the PyTorch-lightning [11] deep-learning framework. The parameters of the feature extraction encoder are initialised using the weights from the MiT-B3 model pre-trained for image segmentation on ADE20K dataset [44, 45], publicly available on HuggingFace [38]. The remaining parameters (attention modules and the MLP decoder) are randomly initialised using \"Xavier\" methods [12]. During training, AdamW optimizer [24] is used with an initial learning rate of " + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 304, + 558, + 545, + 712 + ], + "type": "text", + "content": " without decay. All experiments and ablation studies are trained for 36 epochs, for a training time of approximately 12 hours on NVIDIA A100 GPU with 80G RAM with batch size of 8." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10453" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 124, + 70, + 470, + 272 + ], + "blocks": [ + { + "bbox": [ + 124, + 70, + 470, + 272 + ], + "lines": [ + { + "bbox": [ + 124, + 70, + 470, + 272 + ], + "spans": [ + { + "bbox": [ + 124, + 70, + 470, + 272 + ], + "type": "table", + "html": "
METHODSEVALUATION METRICS
TasksTechniquesMAE ↓Fβ↑IoU ↑BER ↓S-BER ↓N-BER ↓
IOS★ FPN [19]0.0440.7070.51219.4936.592.40
PSPNet [42]0.0510.6420.47619.7536.443.07
DSS [13]0.0450.6960.50219.7736.962.59
R3Net [8]0.0440.7100.50220.4037.373.55
ISDBDRAR [46]0.0500.6950.48421.2940.282.31
★ DSD [43]0.0430.7020.51819.8837.891.88
MTMT [7]0.0430.7290.51720.2838.711.86
FSDNet [16]0.0570.6710.48620.5738.063.06
VOSPDBM [30]0.0660.6230.46619.7334.325.16
COSNet [26]0.0400.7050.51420.5039.221.79
★ FEELVOS [34]0.0430.7100.51219.7637.272.26
STM [27]0.0680.5970.40825.6947.443.96
VSDTVSD [6]0.0330.7570.56717.7033.971.45
STICT [25]0.0460.7020.54516.6029.583.59
SC-Cor [9]0.0420.7620.61513.6124.312.91
★ SCOTCH and SODA0.0290.7930.6409.06616.261.44
", + "image_path": "bed0d97172781ffb985b3f56b8a07142f6a60bba45becd1e9b4fc8ed9b6aea80.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "text", + "content": "Table 1. Comparisons between our proposed technique and SOTA techniques on the ViSha dataset. \"MAE\" denotes mean absolute error, " + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\mathrm{F}_{\\beta}" + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "text", + "content": " denotes F-measure score, \"IoU\" denotes intersection over union, \"BER\" denotes balance error rate, and \"S-BER\" means shadow BER, \"N-BER\" means non-shadow BER. The " + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "text", + "content": " denotes the higher the value is the better the performance is, whilst the " + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "text", + "content": " means the opposite. " + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 280, + 545, + 326 + ], + "type": "text", + "content": " indicates the best performed network in each category." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 337, + 227, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 227, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 227, + 350 + ], + "type": "text", + "content": "4.2. Comparison to SOTA Techniques" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 552 + ], + "type": "text", + "content": "Compared Methods. Video shadow detection is a relatively recent topic, and there are only three directly-related methods designed for this task. Hence, following existing VSD methods, we make comparisons against 4 different kinds of methods, including image object segmentation (IOS), image shadow detection (ISD), video object segmentation (VOS), and video shadow detection (VSD). For IOS, they are FPN [19], PSPNet [42], DSS [13], and " + }, + { + "bbox": [ + 46, + 361, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{R}^3" + }, + { + "bbox": [ + 46, + 361, + 287, + 552 + ], + "type": "text", + "content": "-Net [8], while the ISD methods are BDRAR [46], DSD [43], MTMT [7], and FSDNet [16]. The compared VOS methods include PDBM [30], COSNet [26], FEELVOS [34], and STM [27], while compared VSD methods are TVSD [6], STICT [25], and SC-Cor [9]. We obtain the results by re-training their network parameters with unified training parameters or by downloading the results from the TVSD [6] repository." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "Quantitative Comparisons. Table 1 summarises MAE, " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{F}_{\\beta}" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": ", IoU, and BER scores of our network against SOTA techniques. For each category, we use " + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": " to mark out the method with the best performance. From these quantitative results, we observe that the IOS and ISD report readily competing results. These results are expected as the modelling hypothesis for both families of techniques relies on only the image level analysis. Whilst VOS techniques consider also temporal information, these techniques are customised as a general framework for video object segmentation. However, shadow detection is more complex due to the fast change in appearance between frames. Notably, we observe that VSD techniques indeed provide a substantial performance" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 337, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 337, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 337, + 545, + 361 + ], + "type": "text", + "content": "improvement compared to other methods; as they are designed considering the complexity of shadows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 363, + 546, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 546, + 506 + ], + "type": "text", + "content": "More importantly, our method outperforms all other techniques by a significant margin for all evaluation metrics - further supporting the superiority of our approach. In particular, our method yields to a balanced error rate of 9.066 which is more than 4 points below SC-Cor, the latest SOTA technique, in terms of BER. The error rate for the shadow label (denoted as S-BER in Table 1) of our method is 8 points below SC-Cor. We also underline that our significant improvement in performance comes with a negligible computational cost. We report the test time in Table 2, where we observe that our SCOTCH and SODA framework only requires a fraction of time than compared methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 508, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 700 + ], + "type": "text", + "content": "Visual Comparison. Figure 3 visually compares the shadow segmentation masks from our method and the compared methods on different input video frames. For video frames with black objects at the first three rows, we find that compared methods tend to wrongly identify those black objects as shadow ones, while our method can still accurately detect shadow pixels under the corruption of black objects. Moreover, compared methods tend to miss some shadow regions when the input video frames contain multiple shadow detection, as shown in the 4-th row to the 8-th row of Figure 3. On the contrary, our method can identify all these shadow regions of input video frames, and our detection results are most consistent with the ground truth in the 2nd column of Figure 3. We also provide the video segmentation masks on the project page to demonstrate the temporal coherence of the results provided by our method." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "content": "Model size and inference time. Table 2 further" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10454" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 545, + 406 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 545, + 406 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 545, + 406 + ], + "type": "image", + "image_path": "944c0d77c3da05f49a98b0be323249522ffc409e3b80d969131bae23fbe5276d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 415, + 547, + 460 + ], + "lines": [ + { + "bbox": [ + 46, + 415, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 547, + 460 + ], + "type": "text", + "content": "Figure 3. Visual comparisons of video shadow detection results produced by our network (SCOTCH and SODA) and compared methods. Apparently, our method can more accurately identify shadow pixels and our results are more consistent with the ground truth in the 2nd column. The video segmentation results can be found on the project page. (d-e) are the methods with the highest performance in IOS, ISD, and VOS in Table 1, whilst (g-i) are all from the VSD area." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 470, + 286, + 536 + ], + "blocks": [ + { + "bbox": [ + 50, + 470, + 286, + 536 + ], + "lines": [ + { + "bbox": [ + 50, + 470, + 286, + 536 + ], + "spans": [ + { + "bbox": [ + 50, + 470, + 286, + 536 + ], + "type": "table", + "html": "
NetworksParamsGMACsTimeBER
TVSD [6]243.32158.8932.417.70
STCIT [25]104.6840.9913.516.60
SC-Cor [9]232.63218.421.813.61
SCOTCH and SODA211.79122.469.159.006
", + "image_path": "59fa63752842ce47ee50f185eaf369862f5692497edc0d373ca9bcbdae7e239c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 544, + 287, + 598 + ], + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 598 + ], + "type": "text", + "content": "Table 2. Comparison of model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Specifically, the units for Params and Time are (MB) and (Mins), respectively. We denote the best and second best in bold and underline font." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 713 + ], + "type": "text", + "content": "compares our network and three state-of-the-art video shadow detection methods in terms of the model size (Params), computational complexity (GMACs), inference time (Time), and segmentation accuracy (BER). Apparently, among the three compared VSD methods, STICT has the smallest testing time (13.5 minutes). Compared to STICT, our method further reduces the inference time from 13.5 minutes to 9.15 minutes to test all 70 testing videos" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 472, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 593 + ], + "type": "text", + "content": "with 6,897 images. Although our method takes 2nd rank in terms of the model size and computational complexity, they are only larger than STICT. This is because we only use a light-weighted MLP layer as the decoder to integrate the multi-resolution feature maps, which is computational-saving. In terms of performance, our method has a superior BER performance than STICT by reducing the BER score from 16.60 to 9.006, which indicates that with a minor compromise on the model size, our method can more accurately identify video shadows than STICT, TVSD, and SC-Cor." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 599, + 400, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 400, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 400, + 612 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 544, + 641 + ], + "type": "text", + "content": "In Table 3, we perform ablation studies on our main contributions to evaluate the effectiveness of each component." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "Baseline with MiT backbone. In order to evaluate the role of the MiT backbone on the final performance of our method, we define the segmentation network with MiT backbone as the baseline, which is trained by using the classical segmentation loss (5), but without the deformation attention trajectory and shadow level contrastive mechanism." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10455" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 176 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 176 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 176 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 176 + ], + "type": "table", + "html": "
ComponentsEvaluation Metrics
BackboneAttentionContrastMAE ↓Fβ ↑IoU ↑BER ↓
MiTXX0.0480.7550.58413.18
MiTTrajectoryX0.0480.7600.59312.35
MiTSODAX0.0410.7910.61310.55
MiTXImage0.0480.7610.58812.85
MiTXShadow0.0410.7670.59212.02
MiTXSCOTCH0.0340.7710.60611.29
†MiTSODASCOTCH0.0290.7930.6409.066
", + "image_path": "38e1f0dc0bcd10dc235428ade4485f9a3a9de0324c4c5c148ff4072b8a473578.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "lines": [ + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "text", + "content": "Table 3. Ablation study on different components of our proposed methods on the ViSha dataset. The " + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\uparrow" + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "text", + "content": " denotes the higher the value is the better the performance is, whilst the " + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "text", + "content": " means the opposite. “" + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 47, + 184, + 287, + 240 + ], + "type": "text", + "content": "” denotes our final methods with the highest performance in all evaluation metrics. Notations: best, second best, third best." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 253, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 324 + ], + "type": "text", + "content": "This baseline already provides results on par or better than the previous three works in the VSD area (see Table 1 for comparison), even without considering any kind of temporal information. This illustrates the superior performance of the MiT transformer-based architecture over convolutional architectures on the task of video shadow detection." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 326, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 287, + 445 + ], + "type": "text", + "content": "Attention mechanisms. We then evaluate the effectiveness of different attention mechanisms, including trajectory attention [29] and our newly introduced shadow deformation attention. Both types of attention modules provide an improvement over the baseline, which was to be expected as those modules give the ability to consider the temporal information within the videos. Our deformation attention trajectory module also appears to provide better results than the trajectory attention, indicating the importance of considering the deformation in the design of the attention module." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 446, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 540 + ], + "type": "text", + "content": "Contrastive losses. Next, we compare the effect of two types of contrastive criterion, the image level contrastive loss used in TVSD [6], and our feature-level shadow contrastive loss. The inter-frame contrastive learning slightly improves the baseline, whereas our shadow contrastive loss provides a significant improvement over the baseline. Those results illustrate the superiority of the features-level contrastive loss over the frame-level contrastive loss." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 542, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 625 + ], + "type": "text", + "content": "Final model. SCOTCH reduces the variance of the spatial shadow features, while SODA processes the spatial features at different time-step to consider the temporal information in the video. Thus, SCOTCH and SODA have a complementary effect, as feeding SODA with more robust spatial features from SCOTCH, we are able to reach the best performance, outperforming all the previous settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 202, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 202, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 202, + 647 + ], + "type": "text", + "content": "4.4. Attention Map Visualisation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "In Figure 4, we visually compare the attention maps from the baseline model (second row) with our proposed SCOTCH and SODA (third row). We can observe that the baseline model highlights the object part, whilst ours focuses more on the shadow region with the help of contrastive" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 71, + 545, + 217 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 217 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 217 + ], + "type": "image", + "image_path": "f38a4f7dec373e3f9c004375cd539591ee02e4dfa722910fa68afd554f0bcda3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 224, + 545, + 301 + ], + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 301 + ], + "type": "text", + "content": "Figure 4. Attention maps visualisation. The low-resolution layers of the MiT encoder are selected for the visualization, with the query from the center of the ground truth shadow mask. From top to bottom row are the input video blended with segmentation mask, attention maps for baseline MiT methods, and attention maps from ours SCOTCH and SODA with deformation attention trajectory and shadow contrastive mechanism." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 315, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 411 + ], + "type": "text", + "content": "learning. We can also observe that the baseline model might lose track of shape in different frames (third column), whilst our approach provides consistent shape information at different times with the help of the deformation attention trajectory. Hence, the model using the shadow deformation attention trajectory and the shadow contrastive loss is better at tracking the shadow region during different frames, while ignoring the non-shadow part of the image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 423, + 378, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 423, + 378, + 435 + ], + "spans": [ + { + "bbox": [ + 306, + 423, + 378, + 435 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 575 + ], + "type": "text", + "content": "In this paper, we introduced SCOTCH and SODA, a new transformer video shadow detection framework. We developed shadow deformation attention trajectory (SODA), a self-attention module specially designed to handle the shadow deformation in videos, and we introduced a shadow contrastive mechanism (SCOTCH) to guide our network to better discriminate between shadow and non-shadow features. We demonstrate the effectiveness of the contributions with ablation studies. Finally, we show that our proposed method outperforms by a large margin concurrent video shadow segmentation works on the ViSha dataset." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by Girton Postgraduate Research Scholarships, GSK Ph.D. Scholarship, CMIH, CCIMI, Philip Leverhulme Prize, Royal Society Wolfson Fellowship, EPSRC Advanced Career Fellowship EP/V029428/1, EPSRC grants EP/S026045/1, EP/T003553/1, EP/N014588/1, EP/T017961/1, Wellcome Innovator Awards 215733/Z/19/Z and 221633/Z/20/Z, EU Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 777826 NoMADS, and Guangzhou Municipal Science and Technology Project Grant No. 2023A03J0671." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10456" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. 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To address the above-mentioned problems, we propose the following three solutions: 1) Redesigning the completion sub-network. We design a novel completion sub-network, which consists of several Multi-Path Blocks (MPBs) to aggregate multi-scale features and is free from the lossy downsampling operations. 2) Distilling rich knowledge from the multi-frame model. We design a novel knowledge distillation objective, dubbed Dense-to-Sparse Knowledge Distillation (DSKD). It transfers the dense, relation-based semantic knowledge from the multi-frame teacher to the single-frame student, significantly improving the representation learning of the single-frame model. 3) Completion label rectification. We propose a simple yet effective label rectification strategy, which uses off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels, greatly improving the performance of deep models especially for those moving objects. Extensive experiments are conducted in two public SSC benchmarks, i.e., SemanticKITTI and SemanticPOSS. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge and surpasses the competitive S3CNet [3] by $7.2\\mathrm{mIoU}$ . SCPNet also outperforms previous completion algorithms on the SemanticPOSS dataset. Besides, our method also achieves competitive results on SemanticKITTI semantic segmentation tasks, showing that knowledge learned in the scene completion is beneficial to the segmentation task.", + "bbox": [ + 75, + 350, + 472, + 764 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 77, + 790, + 208, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic scene completion (SSC) [20] aims at inferring", + "bbox": [ + 95, + 828, + 468, + 844 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "both geometry and semantics of the scene from an incomplete and sparse observation, which is a crucial component in 3D scene understanding. Performing semantic scene completion in the outdoor scenarios is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for those moving objects (See Fig. 1 (a)).", + "bbox": [ + 499, + 321, + 890, + 419 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent years have witnessed an explosion of methods in the outdoor scene completion field [3, 19, 22, 25, 29, 32]. For example, S3CNet [3] performs 2D and 3D completion tasks jointly and achieves impressive performance on SemanticKITTI [1]. JS3C-Net [29] performs semantic segmentation first and then feeds the segmentation features to the completion sub-network. The coarse-to-fine refinement module is further put forward to improve the completion quality. Although significant progress has been achieved in this area, these methods heavily rely on the voxelwise completion labels and show unsatisfactory completion performance on the small, distant objects and crowded scenes. Moreover, the long traces of dynamic objects in original completion labels will hamper the learning of completion models, which is overlooked in the previous literature [20].", + "bbox": [ + 497, + 420, + 892, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the preceding problems, we propose three solutions from the aspects of the completion sub-network redesign, distillation of multi-frame knowledge as well as completion label rectification. Specifically, we first make a comprehensive overhaul of the completion sub-network. We adopt the completion-first principle and make the completion module directly process the raw voxel features. Besides, we avoid the use of downsampling operations since they inevitably introduce information loss and cause severe misclassification for those small objects and crowded scenes. To improve the completion quality on objects of diverse scales, we design Multi-Path Blocks (MPBs) with varied kernel sizes, which aggregate multi-scale features and fully utilize the rich contextual information.", + "bbox": [ + 497, + 629, + 894, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Second, to combat against the sparse and incomplete input signals, we make the single-scan student model distil knowledge from the multi-frame teacher model. However,", + "bbox": [ + 497, + 824, + 894, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 129, + 49, + 200, + 85 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 252, + 48, + 791, + 87 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†: Corresponding author.", + "bbox": [ + 100, + 853, + 236, + 866 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17642", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5548e25d074e71744d67fb72d13ef5f39e1ce4b33c55731bec8a3df69ee7c831.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 125, + 294, + 231 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/326df470ed4a8e9c69bc83ea969b5e4b92385116bc996deb9185123e8469c6aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 125, + 505, + 231 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/443333509d57fa346df5e14ecb11a57190e4e782d1869b60b288f298a9e57669.jpg", + "image_caption": [ + "(a)", + "(b)", + "Figure 1. Left: challenges of semantic scene completion, i.e., (a) sparse and incomplete input, varying completion difficulty for objects of diverse scales and (b) long traces of dynamic objects in completion labels. Traces of cars and persons are highlighted by yellow ellipses. Right: (c) performance comparison of various completion algorithms on SemanticKITTI semantic scene completion challenge." + ], + "image_footnote": [], + "bbox": [ + 82, + 245, + 292, + 349 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/33e42b8253b5d7575d8e644d425e2c5371e6fe57d3a57334a009c83688e285ad.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 245, + 504, + 349 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3d3fb28a18539c33a7b3339eb1c9ae4c99a6f16b80a1946c92b4f61107490234.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 509, + 125, + 887, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mimicking the probabilistic knowledge of each point/voxel brings marginal gains. Instead, we propose to distill the pairwise similarity information. Considering the sparsity and unorderness of features, we align the features using their indices and then force the consistency between the pairwise similarity maps of student features and those of teacher features, make the student benefit from the relational knowledge of the teacher. The resulting Dense-to-Sparse Knowledge Distillation objective is termed DSKD, which is specifically designed for the scene completion task.", + "bbox": [ + 75, + 408, + 468, + 545 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Finally, to address the long traces of those dynamic objects in the completion labels, we propose a simple yet effective label rectification strategy. The core idea is to use off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels. The rectified completion labels are more accurate and reliable, greatly improving the completion qualities of deep models on those moving objects.", + "bbox": [ + 75, + 547, + 468, + 656 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct experiments on two large-scale outdoor scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge ${}^{1}$ and outperforms the S3CNet [3] by ${7.2}\\mathrm{{mIoU}}$ . SCPNet also achieves better performance than other completion algorithms on the SemanticPOSS dataset. The learned knowledge from the completion task also benefits the segmentation task, making our SCPNet achieve superior performance on the SemanticKITTI semantic segmentation task.", + "bbox": [ + 75, + 657, + 468, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows.", + "bbox": [ + 95, + 796, + 396, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- The comprehensive redesign of the completion sub", + "bbox": [ + 95, + 819, + 467, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "network. We unveil several key factors to building strong completion networks.", + "bbox": [ + 529, + 409, + 889, + 435 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To cope with the sparsity and incompleteness of the input, we propose to distill the dense relation-based knowledge from the multi-frame model. Note that we are the first to apply knowledge distillation to the semantic scene completion task.", + "- To address the long traces of moving objects in completion labels, we present the completion label rectification strategy.", + "- Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge, outperforming the previous SOTA S3CNet [3] by $7.2\\mathrm{mIoU}$ . Competitive performance is also shown in SemanticPOSS completion task and SemanticKITTI semantic segmentation task." + ], + "bbox": [ + 517, + 442, + 890, + 637 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 499, + 649, + 638, + 663 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic scene completion. Early works on scene completion mainly concentrates on the indoor scenarios [5, 6, 15, 22]. The point cloud in indoor scenarios is dense, small-scale and has uniform density. By contrast, point cloud in outdoor scenes is sparse, large-scale and has varying density, which poses great challenges to the semantic scene completion algorithms [3,20,25,29,32]. Various algorithms have been proposed, for instance, LMSCNet [19] uses a mixture of 2D and 3D convolutions to build the efficient completion backbone. S3CNet [3] performs 2D and 3D scene completion simultaneously, and fuses the results by the proposed dynamic voxel fusion module. JS3C-Net [29] attaches the completion network to the segmentation backbone and refines the completion outputs via the point-voxel", + "bbox": [ + 497, + 672, + 890, + 866 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1https://codalab.lisn.upsaclay.fr/competitions/7170#results till 2022-11-12 00:00 Pacific Time, and our method is termed SCPNet.", + "bbox": [ + 77, + 842, + 467, + 864 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17643", + "bbox": [ + 465, + 885, + 504, + 897 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/41557f97fbe5b3abd0c6b55b2979121df3e3a08f0aebbb9b9ccfb37d70a024d9.jpg", + "image_caption": [ + "Figure 2. Framework overview of SCPNet. There are two SCPNets, one is teacher and the other is student, and they have the same architecture. The teacher takes multi-frame point cloud as input while the student takes the single-frame point cloud as input. The dense-to-sparse knowledge distillation loss is proposed to transfer the dense semantic knowledge from teacher to student. In each SCPNet, there are two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The point cloud is first processed by a stack of MLPs to extract point features. These point features are voxelized and then fed to the completion sub-network to produce denser voxel features. The produced voxel features are further fed to the segmentation sub-network to generate the ultimate voxelwise output. For the completion sub-network, it is comprised of several multi-path blocks, free from the lossy downsampling operations. For the segmentation sub-network, it is adapted from the Cylinder3D network." + ], + "image_footnote": [], + "bbox": [ + 80, + 125, + 890, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "interaction module. Compared with previous completion networks, our SCPNet is free from the lossy downsampling operations. Besides, our network is built on several MPBs that aggregate multi-scale features and can achieve high completion quality in objects of various sizes.", + "bbox": [ + 75, + 461, + 468, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge distillation. Knowledge distillation (KD) originates from the pioneering work of G. Hinton et al. [8]. Its primary objective is to transfer the dark knowledge from the large over-parameterized teacher model to the small compact student model. A large number of methods have been proposed and various forms of knowledge [21, 24, 27, 33] have been designed, e.g., intermediate features [11, 21], visual attention maps [10, 33], region-level affinity scores [9], similarity scores of different samples [24, 26], etc. It is noteworthy that the majority of the distillation methods concentrate on the 2D tasks. Only a few distillation methods have focused on 3D domains, e.g., PVKD [12] and SparseKD [31]. To our knowledge, this is the first work that applies knowledge distillation to the semantic scene completion task. We propose to transfer the dense, relation-based semantic knowledge from the multi-frame model to the single-frame one.", + "bbox": [ + 75, + 533, + 470, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 75, + 785, + 211, + 802 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The objective of the semantic scene completion task is to infer the complete geometric and semantic layout given the incomplete and sparse input. Formally, given the input point cloud $\\mathbf{X} \\in \\mathbb{R}^{N \\times 3}$ , the network needs to assign a label to", + "bbox": [ + 75, + 809, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "each voxel of the $L\\times W\\times H$ voxel space to indicate whether it is empty or belongs to a specific class $c\\in \\{0,1,2,\\dots,C - 1\\}$ , where $C$ is the number of classes, $L$ , $W$ and $H$ are the length, width and height of the voxel space, respectively. We denote the voxelwise output as $\\mathbf{O}\\in \\mathbb{R}^{L\\times W\\times H\\times C}$ .", + "bbox": [ + 497, + 461, + 890, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Framework overview", + "text_level": 1, + "bbox": [ + 497, + 539, + 699, + 552 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, our SCPNet is comprised of two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The completion sub-network is designed based on several key design principles. The segmentation sub-network is built upon Cylinder3D [35, 36], with some minor modifications. In the following sections, we first detail the completion sub-network and introduce several design principles that are vital to building a strong completion sub-network. The knowledge distillation of multi-frame model and the completion label rectification will be explained thereafter.", + "bbox": [ + 497, + 560, + 890, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Redesigning the Completion Sub-network", + "text_level": 1, + "bbox": [ + 497, + 720, + 855, + 735 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Take JS3C-Net [29] as example. The original JS3C-Net first performs semantic segmentation and then conducts completion upon the segmentation features. Although this pipeline can benefit from the segmentation outputs, there are several drawbacks in this framework. First, the parameters in the completion sub-network are much fewer than the segmentation sub-network, thus yielding unsatisfactory completion performance. Second, there are downsampling and upsampling blocks in the completion sub-network. The", + "bbox": [ + 497, + 741, + 890, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17644", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/762d5a6528c211475cce53132b2c13e3afcecfd392f53beb3ec7163a59c2ae96.jpg", + "image_caption": [ + "Figure 3. A schematic overview of the designed completion network. It is built upon the Multi-Path Blocks (MPBs) that contain $3 \\times 3 \\times 3$ , $5 \\times 5 \\times 5$ and $7 \\times 7 \\times 7$ convolution blocks (ConvBlock). In each convolution block, there is no convolution bias and no batch normalization to maintain sparsity during completion." + ], + "image_footnote": [], + "bbox": [ + 78, + 123, + 467, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "downsampling operations will inevitably lose the information of the original point cloud and the upsampling operation will cause over dilation and shape distortion.", + "bbox": [ + 75, + 353, + 468, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address the aforementioned problems, we make a comprehensive overhaul of the completion sub-network. More concretely, there are three principles in the design of the completion sub-network, i.e., maintaining sparsity, no downsampling and aggregating multi-scale features.", + "bbox": [ + 75, + 396, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Maintain sparsity. The completion sub-network needs the vanilla dense convolution for dilation while the segmentation sub-network uses sparse convolution for efficient processing. However, the bias of the convolution weight, running mean and beta of BN layers will break the sparsity of the original voxel features, thus substantially increasing the computation burden of the segmentation sub-network. Therefore, to reduce the overall computation cost and enjoy the high efficiency of sparse convolution, we remove all the convolution bias and the BN layers in the completion subnetwork. In this condition, the voxel features produced by the completion sub-network can still keep the sparse property and the segmentation sub-network can use sparse convolution to process these sparse voxel features.", + "bbox": [ + 75, + 465, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "No downsampling. In popular completion networks such as S3CNet [3] and JS3C-Net [29], there are several downsampling and upsampling blocks in the completion part. The downsampling operations will inevitably lose the information of the original point cloud, causing severe completion and classification errors for small objects and crowded scenes. Therefore, we discard all downsampling and upsampling operations to relieve the information loss, maximally retaining the information of the raw point cloud. Besides, as opposed to JS3C-Net which takes the segmentation-first baseline, we adopt the completion-first principle. Concretely, we make the completion sub-network directly process the raw voxel features produced by the voxelization process. And the completion sub-network can also benefit from the large number of parameters of the segmen", + "bbox": [ + 75, + 659, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b7958eb1c53ed443c2cf23d491b4c7751bd52f6351dc7edd97db55cca82b3fe3.jpg", + "image_caption": [ + "Figure 4. Comparison between single-frame and multi-frame point cloud. The multi-frame input is obviously denser than the single frame and the objects are easier to be identified, significantly reducing the completion difficulty." + ], + "image_footnote": [], + "bbox": [ + 504, + 123, + 694, + 226 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8bf4b0ae91c1d4bc2aae4a9dcbb94563698b99ac349f7f6766c479d8efaa4169.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 695, + 124, + 887, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tation sub-network.", + "bbox": [ + 499, + 304, + 630, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Aggregate multi-scale features. To aggregate multi-scale features, we design the multi-path block which is comprised of $3 \\times 3 \\times 3$ , $5 \\times 5 \\times 5$ and $7 \\times 7 \\times 7$ convolution blocks. As shown in Fig. 3, there are three branches in the completion sub-network. The upper branch contains one MPB and the bottom branch is a residual connection. The middle branch is constructed by a $3 \\times 3 \\times 3$ convolution block, two MPBs and a $3 \\times 3 \\times 3$ convolution block. After the completion sub-network, we obtain the dense completed voxel features. We extract the non-empty voxel features as well as their voxel indices from the completed voxel features. The generated sparse voxel features are sent to the segmentation sub-network to produce the voxelwise segmentation output.", + "bbox": [ + 497, + 318, + 890, + 497 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Modifications on the segmentation sub-network. Recall that, for the segmentation part, we take the Cylinder3D [36] as the backbone. Since the voxelwise completion labels are defined based on the cubic partition, we replace the cylindrical partition of Cylinder3D with conventional cubic partition. Besides, the original point refinement module consumes much GPU memory and brings limited gains, we discard this module to save memory usage.", + "bbox": [ + 497, + 500, + 890, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Distilling Multi-frame Knowledge", + "text_level": 1, + "bbox": [ + 499, + 621, + 794, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since single frame point cloud is sparse and incomplete in the outdoor scenarios, directly performing semantic scene completion from the single-frame input is extremely difficult. It is natural to wonder if we can construct a multi-frame model and then distil the dense semantic knowledge from this multi-frame network. From Fig. 4, it is evident that the multi-frame input significantly reduces the completion difficulty since multiple frames have much more points in the scene and objects are easier to be identified. The completion difficulty will gradually decrease as the number of input point cloud frames increases. Therefore, we construct the multi-frame teacher which takes denser point cloud as input and achieves better completion performance.", + "bbox": [ + 497, + 643, + 890, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by [12], we make the single-frame model distil the relation-based structural knowledge from the multiframe teacher network. Since the original voxel features", + "bbox": [ + 497, + 825, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17645", + "bbox": [ + 465, + 885, + 504, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8d96145bce7cc6a06ad460ad4e87ed61c1e608c32793af3b90503c3d97068657.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 127, + 272, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/393ab21ecb691377ca7f94ade1563a807dac2588ebd7a4789f87aa89d61d35f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 275, + 127, + 460, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c2d6a95e0fc532b071eae4847e005c738d0a8d78a048f7c330cd13285cbe32bf.jpg", + "image_caption": [ + "Figure 5. Top: original completion labels which have long traces of dynamic objects, e.g., car and person. Bottom: rectified completion labels. The proposed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate." + ], + "image_footnote": [], + "bbox": [ + 82, + 222, + 272, + 315 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fb96fe933c0b6195eaed6a4859a8a2f383352eb40779a62dc61e4d2f17245ef3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 273, + 222, + 460, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are in the sparse form, we leverage the sparse features and their indices to perform knowledge distillation. We denote the voxel features and corresponding indices of the teacher and student as $F_{T} \\in \\mathbb{R}^{N_{m} \\times C_{f}}$ , $F_{S} \\in \\mathbb{R}^{N_{s} \\times C_{f}}$ , $\\mathcal{I}_{T} \\in \\mathbb{R}^{N_{m} \\times 3}$ and $\\mathcal{I}_{S} \\in \\mathbb{R}^{N_{s} \\times 3}$ , respectively. $N_{m}$ is the number of non-empty voxel features in the multi-frame, $N_{s}$ is the number of non-empty voxel features in the single-frame, $C_{f}$ is the number of channels of the voxel features. Note that the indices of teacher features and student features are sorted and $\\mathcal{I}_{S}(i,j) = \\mathcal{I}_{T}(i,j)$ , where $i \\in \\{1, \\dots, N_{s}\\}$ and $j \\in \\{1, 2, 3\\}$ . We first compute the pairwise relational knowledge of the student model:", + "bbox": [ + 75, + 402, + 468, + 568 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} _ {S} (i, j) = \\frac {F _ {S} (i) ^ {\\top} F _ {S} (j)}{\\| F _ {S} (i) \\| _ {2} \\| F _ {S} (j) \\| _ {2}}, i, j \\in \\{1, \\dots , N _ {s} \\} \\quad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 95, + 590, + 468, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The relational knowledge of the teacher model $\\mathbf{P}_T$ is calculated in a similar way. The relational knowledge captures the similarity of each pair of voxel features and serve as important clues of the surrounding environment, which can be taken as high-level knowledge to be learned by the single-frame student model. The proposed Dense-to-Sparse Knowledge Distillation (DSKD) loss is given as below:", + "bbox": [ + 75, + 631, + 468, + 730 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {d s k d}} \\left(\\mathbf {P} _ {S}, \\mathbf {P} _ {T}\\right) = \\frac {1}{N _ {s} ^ {2}} \\sum_ {i = 1} ^ {N _ {s}} \\sum_ {j = 1} ^ {N _ {s}} \\left\\| \\mathbf {P} _ {S} (i, j) - \\mathbf {P} _ {T} (i, j) \\right\\| _ {2} ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 85, + 751, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Completion Label Rectification", + "text_level": 1, + "bbox": [ + 77, + 815, + 352, + 831 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generation of completion labels. As pointed out by [20], for outdoor semantic scene completion, the ground-truth", + "bbox": [ + 75, + 838, + 468, + 866 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Pseudocode of Label Rectification." + ], + "code_body": "L_c: completion label (256x256x32) \n# L_s: semantic segmentation label (Nx1) \n# L_p: panoptic segmentation label (Nx1) \n# S_c: classes of moving objects; u: unlabeled class \nfor C_i in S_c: \n # voxel position of completion label for class C_i \n P_c_i = getInd(L_c, C_i) \n L_p_i = L_p[L_s == C_i] # instance label of class C_i \n P_dif = [] \n if len(L_p_i) == 0: \n P_dif = P_c_i \n elif len(L_p_i) > 0 and len(P_c_i) > 0: \n # mask of voxel position bound for instance d_j \n M_c = zeros([256, 256, 32]) \n # point position of class C_i \n P_i = P[L_s == C_i, :] \n # voxel position of class C_i \n P_s_i = voxelize(P_i) \n D_i = unique(L_p_i) # all instance ids \n for d_j in D_i: \n # voxel position for instance d_j \n M_j = P_s_i[L_p_i == d_j] \n (x_min, x_max, y_min, y_max, z_min, z_max) = bound(M_j) \n M_c[x_min: x_max, y_min: y_max, z_min: z_max] = 1000 \n # voxel position for instance label of class C_i \n P_p_i = getInd(M_c, 1000) \n P_dif = difference(P_c_i, P_p_i) \n if len(P_dif) > 0: \n for p_i in range(P_dif.shape[0]): \n L_c[P_dif[p_i, 0], P_dif[p_i, 1], P_dif[p_i, 2]] = u", + "bbox": [ + 500, + 146, + 890, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "completion labels are obtained by concatenating the segmentation labels of multiple consecutive point cloud frames. Specifically, for the $t$ -th frame, the corresponding completion labels $L_{t}^{c}$ are constructed in the following way:", + "bbox": [ + 497, + 460, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t} ^ {c} = \\operatorname {c o n c a t} \\left[ L _ {t} ^ {s}; T _ {t + 1 \\rightarrow t} L _ {t + 1} ^ {s}; \\dots ; T _ {t + T - 1 \\rightarrow t} L _ {t + T - 1} ^ {s} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 536, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{t}^{s}$ are the segmentation labels for the $t$ -th frame, $T$ is the number of frames used for concatenation, $T_{t+1 \\to t}$ is the transformation matrix that transforms the coordinate from $(t+1)$ -th frame to the $t$ -th frame, and $\\mathrm{concat}[\\ldots; \\ldots]$ is the concatenating operation. The concatenation of multiple frames will lead to long traces for those moving objects, such as car and person. A vivid example is shown in Fig. 5. The long traces of those dynamic objects are obviously irrational and will hamper the learning of deep models.", + "bbox": [ + 497, + 576, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Completion label rectification. To remove the long traces of moving objects in the completion labels, we resort to the panoptic segmentation labels. Specifically, given the panoptic labels of class $i$ , we first voxelize the labels and obtain the voxelwise panoptic labels for class $i$ . For each instance of class $i$ , we calculate the bound of each instance, forming a cube. We union the cubes of all instances and use them to process the original voxelwise completion labels, filtering those voxels that are outside the cubes. The process is repeated for all classes that contain dynamic objects. The detailed information of the label rectification algorithm is shown in Algorithm 1. As shown in Fig. 5, the pro", + "bbox": [ + 497, + 700, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17646", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e39df793487dc2c4f41e6251d8f14160a6025bb3c43c63ed5efc407f8224f91a.jpg", + "table_caption": [ + "Table 1. Quantitative results of semantic scene completion algorithms on SemanticKITTI test set. Note that the online server still uses the original completion labels to evaluate algorithms. Bold - best in column for all single-frame methods." + ], + "table_footnote": [], + "table_body": "
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SSCNet-Full [22]16.150.024.30.50.81.24.30.30.30.051.227.130.86.434.519.935.318.229.013.16.7
ESSCNet [34]17.541.826.40.35.45.09.12.92.70.143.826.928.110.329.823.335.820.128.716.416.7
LMSCNet-SS [19]17.656.730.90.00.01.50.80.00.00.064.829.034.74.638.121.341.319.932.115.00.8
TDS [7]17.750.629.50.00.02.50.10.00.00.062.223.331.66.534.124.140.121.933.116.96.9
UDNet [37]19.559.433.90.80.43.84.40.50.30.362.028.235.19.139.524.440.923.232.318.813.1
Local-DIFs [18]22.757.734.83.62.44.44.82.51.10.067.940.142.911.440.429.042.226.539.121.317.5
SSA-SC [32]23.558.836.513.94.65.77.44.42.60.772.237.443.710.943.630.743.525.641.814.56.9
JS3C-Net [29]23.856.633.314.48.87.212.78.05.10.464.734.939.914.139.430.443.119.640.518.915.9
S3CNet [3]29.545.631.241.545.06.716.145.935.816.042.017.022.57.952.231.339.534.021.231.024.3
SCPNet (#frame=1)36.756.146.433.234.913.829.128.224.71.868.551.349.830.738.844.746.440.148.740.425.1
SCPNet (#frame=4)47.568.559.048.551.121.037.847.635.010.579.757.760.032.850.254.156.947.158.048.348.0
", + "bbox": [ + 77, + 152, + 892, + 300 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "posed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate.", + "bbox": [ + 75, + 314, + 468, + 355 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Overall objective", + "text_level": 1, + "bbox": [ + 75, + 362, + 243, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall loss function is comprised of three terms, i.e., the cross entropy loss, the lovasz-softmax loss [2] and the proposed distillation loss.", + "bbox": [ + 75, + 384, + 468, + 425 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c e}} + \\alpha \\mathcal {L} _ {\\text {l o v a s z}} + \\beta \\mathcal {L} _ {\\mathrm {d s k d}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 448, + 468, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are the loss coefficients to balance the effect of each loss term.", + "bbox": [ + 75, + 473, + 468, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 75, + 511, + 208, + 527 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Following the practice of popular scene completion models [3, 29], we conduct experiments on two popular LiDAR semantic scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. As to SemanticKITTI, it has 22 point cloud sequences. Sequences 00 to 10, 08 and 11 to 21 are used for training, validation and testing, respectively. 19 classes are chosen for training and evaluation after merging classes with distinct moving status and discarding classes with very few points. As for SemanticPOSS, it has 2, 988 frames and 11 classes are selected for evaluation. Although SemanticPOSS is smaller than SemanticKITTI in terms of dataset size, it is much more challenging since it contains a larger quantity of moving objects than SemanticKITTI, such as person and rider.", + "bbox": [ + 75, + 534, + 468, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. Following [12, 36], we adopt the intersection-over-union (IoU) of each class and mIoU of all classes as the evaluation metric. The IoU of class $i$ is calculated via: $IoU_{i} = \\frac{TP_{i}}{TP_{i} + FP_{i} + FN_{i}}$ , where $TP_{i}$ , $FP_{i}$ and $FN_{i}$ denote the true positive, false positive and false negative of class $i$ , respectively. For semantic scene completion, the dimension of the completion label is $256 \\times 256 \\times 32$ . We also report the completion mIoU which is the class-agnostic version of mIoU. Note that mIoU is the major evaluation metric for the semantic scene completion task.", + "bbox": [ + 75, + 728, + 468, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. The output size of Cylinder3D is set as $256 \\times 256 \\times 32$ to adapt to the completion task. The number of training epochs is set as 30 and the initial learning rate is set as 0.0015. We use Adam [14] as the optimizer. Gradient norm clip is set 10 to stabilize the training process. $\\alpha$ and $\\beta$ are set as 1 and 3, 000, respectively. We filter points that are outside the point cloud range of the voxelwise completion labels. For SemanticKITTI, we first train the model on the training set and then finetune it on both training and validation sets before submitting the predictions of test set to the online server.", + "bbox": [ + 497, + 314, + 890, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline KD algorithms. We take the vanilla knowledge distillation [8], FitNets [21], NST [13], PKT [17] and PVKD [12] as baseline distillation algorithms. Vanilla knowledge distillation takes the softened logits as the distilled knowledge. FitNets directly mimics the teacher features. NST adopts the maximum mean discrepancy to minimize the distance between student features and teacher features. PKT models the teacher knowledge as a probability distribution and then forces the consistency of the probability distribution between the teacher and the student. PVKD distils the voxelwise output and inter-voxel affinity knowledge. And we discard the original pointwise output distillation and inter-point affinity distillation of PVKD since they consume much GPU memory and bring marginal gains.", + "bbox": [ + 497, + 467, + 890, + 663 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Results", + "text_level": 1, + "bbox": [ + 499, + 676, + 591, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results. We summarize the performance of SCPNet and state-of-the-art semantic scene completion methods in Table 1 and 2. On SemanticKITTI, our SCPNet significantly outperforms other scene completion algorithms in terms of mIoU. For example, our SCPNet is 7.2 mIoU higher than S3CNet [3]. On classes such as car, other-vehicle, road, parking, sidewalk, dense, terrain and other-ground, the performance gap between SCPNet and S3CNet is more than 10 IoU. Our SCPNet also achieves superior performance on SemanticPOSS val set. On classes such as car, trunk, pole, fence and bike, SCPNet is at least 5 IoU higher than JS3C-Net [29]. The impressive performance on", + "bbox": [ + 497, + 700, + 890, + 866 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17647", + "bbox": [ + 465, + 885, + 504, + 897 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/cf6f8acd8728aad0c778ed6dd15483f31bc09c2d851e06dd3e1d0311f48db063.jpg", + "table_caption": [ + "Table 2. Quantitative results of semantic scene completion algorithms on SemanticPOSS val set. Note that the completion labels are processed by the proposed rectification algorithm. Bold - best in column for all single-frame methods." + ], + "table_footnote": [], + "table_body": "
MethodsmIoUcompletionpersonridercartrunkplantstraffic-signpolebuildingfencebikeground
SSCNet-Full [22]15.253.55.30.31.35.639.61.02.628.73.426.043.1
LMSCNet-SS [19]16.552.37.70.30.64.037.71.98.236.813.825.845.1
MotionSC [25]17.652.77.80.50.53.939.82.28.539.213.130.847.0
JS3C-Net [29]22.758.118.90.27.13.647.82.20.046.326.643.453.2
SCPNet (#frame=1)26.356.39.23.312.411.049.63.111.150.140.848.749.8
SCPNet (#frame=4)33.660.721.45.034.58.955.37.831.050.347.955.152.3
", + "bbox": [ + 77, + 152, + 892, + 294 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6d35ce77e01d3c5e82d40a79e2250a218b880ad5ef0b0cbc25119f91ebc0f4dd.jpg", + "table_caption": [ + "Table 3. Quantitative results of our SCPNet and state-of-the-art LiDAR semantic segmentation methods on SemanticKITTI test set. C3D + SCPNet denotes Cylinder3D initialized from the trained weight of SCPNet. Bold - best in column." + ], + "table_footnote": [], + "table_body": "
MethodsmIoULatency (ms)carbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic
SPVNAS [23]66.425997.351.550.859.858.865.765.243.790.267.675.216.991.365.986.173.471.064.266.9
AF2S3Net [4]69.7-94.565.486.839.241.180.780.474.391.368.872.553.587.963.270.268.553.761.571.0
RPVNet [28]70.3-97.668.468.744.261.175.974.473.493.470.380.733.393.572.186.575.171.764.861.4
PVKD [12]71.27697.067.969.353.560.275.173.550.591.870.977.541.092.469.486.573.871.964.965.8
2DPASS [30]72.9-97.063.663.461.161.577.981.374.189.767.474.740.093.572.986.273.971.065.070.4
Cylinder3D [36]68.917097.167.663.850.858.573.769.248.092.265.077.032.390.766.585.672.569.862.466.2
C3D + SCPNet71.597.560.956.358.665.970.771.858.793.672.180.936.293.372.186.274.171.666.771.8
", + "bbox": [ + 77, + 326, + 892, + 447 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/95b52d0bbf284132fd52d8df933af26223d903e59a8d0a28f0ca3f83d17dd46f.jpg", + "table_caption": [ + "Table 4. Comparison between different knowledge distillation algorithms and the proposed DSKD on the SemanticKITTI val set." + ], + "table_footnote": [], + "table_body": "
MethodsmIoU
SCPNet w/o DSKD34.4
+ KD [8]33.8
+ FitNets [21]33.8
+ PKT [17]34.6
+ PVKD [12]36.2
+ NST [13]36.3
+ DSKD37.2
", + "bbox": [ + 164, + 489, + 376, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "two large-scale benchmarks strongly demonstrate the superiority of our SCPNet.", + "bbox": [ + 75, + 624, + 468, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Besides, we use the trained weight of the segmentation sub-network as initialization to train Cylinder3D on the SemanticKITTI semantic segmentation task. From Table 3, Cylinder3D initialized from trained weight of the completion task outperforms the original Cylinder3D model by 2.6 mIoU, and achieves impressive segmentation performance among various competitive LiDAR segmentation models such as 2DPASS [30], PVKD [12] and RPVNet [28]. The encouraging results show that knowledge learned in the completion task is also beneficial to the segmentation task.", + "bbox": [ + 75, + 655, + 468, + 793 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with baseline KD algorithms. From Table 4, it is evident that the proposed DSKD method can bring more gains than conventional knowledge distillation algorithms. For instance, compared with FitNets [21] which directly mimics the teacher features, our DSKD can bring more than", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "2 mIoU, showing the effectiveness of the proposed relation-based distillation algorithm. The vanilla KD objective and FitNets hamper the performance of the base model, indicating that directly mimicking the logits or features can not boost the completion performance.", + "bbox": [ + 497, + 459, + 890, + 528 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative results. We also provide visual comparison between JS3C-Net [29], SCPNet (single-frame) and SCPNet (multi-frame). As can be seen from Fig. 6, our SCPNet (single-frame) make more accurate completion predictions than JS3C-Net on road and vegetation. On long, thin objects such as poles, our single-frame model also yields high-quality completion results compared with JS3C-Net. The predictions of our single-frame model also resemble those of the multi-frame network, demonstrating the efficacy of the proposed DSKD algorithm.", + "bbox": [ + 497, + 529, + 892, + 668 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Ablation studies", + "text_level": 1, + "bbox": [ + 499, + 676, + 660, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiments are conducted in SemanticKITTI val set.", + "bbox": [ + 517, + 699, + 875, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of completion label rectification. We report the performance of our SCPNet on completion labels with and without rectification. From Table 5, it is evident that the proposed rectification strategy greatly enhances the performance of SCPNet on those dynamic objects, e.g., car and person. For example, the completion label rectification can bring 8.1, 24.5, 26.1 and 17.6 IoU improvement on car, person, bicyclist and motorcyclist, respectively. The impressive performance gains strongly demonstrate the effectiveness of the label rectification algorithm.", + "bbox": [ + 497, + 713, + 890, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the completion sub-network. To examine the", + "bbox": [ + 499, + 852, + 890, + 866 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17648", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/565012982eacdd839c5fecb4765e7abfc657baa4dc7e0cd34a649ecbf21b7d87.jpg", + "image_caption": [ + "Figure 6. Visual comparison of different methods on the SemanticKITTI validation set. From left to right: predictions of JS3C-Net [29], SCPNet (single frame), SCPNet (multi-frame) and ground-truth. Regions that have large prediction errors are highlighted by red ellipses." + ], + "image_footnote": [], + "bbox": [ + 80, + 123, + 890, + 369 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/353206b6dc0738681135a2fd60bd4a9b1883bb17a8a9f641f6789084a142c8a1.jpg", + "table_caption": [ + "Table 5. Impact of completion label rectification on the performance." + ], + "table_footnote": [], + "table_body": "
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SCPNet37.249.950.528.531.758.441.419.419.90.270.560.952.020.234.133.035.333.751.938.327.5
SCPNet + label rectification40.852.158.627.034.754.241.943.946.017.870.660.253.17.733.932.241.932.052.438.728.9
", + "bbox": [ + 78, + 423, + 892, + 490 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/94cc4abdc4febacaad6410de7217cb8e8cd302dec18ee1ad8005ec62455a731f.jpg", + "table_caption": [ + "Table 6. Impact of the completion sub-network, DSKD and down-sampling operation on the performance.", + "(a) Completion sub-network" + ], + "table_footnote": [], + "table_body": "
mIoU
JS3C-Net [29]24.0
JS3C-Net + completion-subnet30.8
", + "bbox": [ + 132, + 546, + 415, + 591 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5fe54dd927b17bbd58a4ccb3295e9164e8cd67be45a6af6ae70a3029ef436e72.jpg", + "table_caption": [ + "(b) DSKD" + ], + "table_footnote": [], + "table_body": "
mIoU
SCPNet w/o DSKD34.4
SCPNet w/ DSKD37.2
", + "bbox": [ + 166, + 604, + 378, + 649 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6116978dc596a03adc70e47d56e9cf14cf008273fe74ef4cf61d175908c2b218.jpg", + "table_caption": [ + "(c) Downsampling operation" + ], + "table_footnote": [], + "table_body": "
mIoU
SCPNet w/o downsampling37.2
SCPNet w/ downsampling33.1
", + "bbox": [ + 142, + 662, + 403, + 707 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "effect of our completion sub-network, we add it to JS3C-Net. The detailed performance is shown in Table 6 (a). Our completion sub-network can bring $6.8\\mathrm{mIoU}$ improvement to JS3C-Net, which strongly demonstrates the effectiveness and generalization of the proposed completion sub-network.", + "bbox": [ + 75, + 725, + 468, + 795 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of DSKD. We compare the performance of our SCPNet with and without the proposed DSKD in Table 6 (b). The proposed distillation method can bring $2.8\\mathrm{mIoU}$ improvement to our SCPNet, showing the benefit of distilling relation-based knowledge from the multi-frame model.", + "bbox": [ + 75, + 796, + 468, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the downsampling operation. We add the downsampling operation to our completion sub-network and examine its effect. As reported in Table 6 (c), the downsampling operation hampers the completion performance of our SCPNet. Specifically, the completion performance of SCPNet decreases from $37.2\\mathrm{mIoU}$ to $33.1\\mathrm{mIoU}$ . The negative results show that the no-downsampling principle is vital to the success of the completion sub-network redesign.", + "bbox": [ + 497, + 507, + 892, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 499, + 650, + 618, + 663 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To address the challenges of the semantic scene completion task, we propose three solutions from the aspects of the completion network redesign, dense-to-sparse knowledge distillation as well as completion label rectification. The resulting completion network, termed SCPNet, achieves superior completion performance in two large-scale semantic scene completion benchmarks, i.e., SemanticKITTI and SemanticPOSS. The learned knowledge on the completion task is also beneficial to the semantic segmentation task.", + "bbox": [ + 497, + 680, + 890, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is partially supported by the National Key R&D Program of China (No. 2022ZD0160100), and in part by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100).", + "bbox": [ + 497, + 809, + 892, + 866 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17649", + "bbox": [ + 465, + 885, + 505, + 897 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 124, + 173, + 138 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. SemanticKITTI: A Dataset for Semantic Scene Understanding of Lidar Sequences. In IEEE International Conference on Computer Vision, pages 9297-9307, 2019. 1, 2, 6", + "[2] Maxim Berman, Amal Rannen Triki, and Matthew B. Blaschko. 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IEEE, 2021. 6" + ], + "bbox": [ + 78, + 125, + 468, + 858 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17651", + "bbox": [ + 465, + 887, + 502, + 897 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SCPNet_ Semantic Scene Completion on Point Cloud/a1134f69-6375-42b9-9a92-868bfcf809a3_model.json b/2023/SCPNet_ Semantic Scene Completion on Point Cloud/a1134f69-6375-42b9-9a92-868bfcf809a3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7a590787f0adaf3a32be7c2e16d52c8558b85680 --- /dev/null +++ b/2023/SCPNet_ Semantic Scene Completion on Point Cloud/a1134f69-6375-42b9-9a92-868bfcf809a3_model.json @@ -0,0 +1,1969 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.13, + 0.051, + 0.201, + 0.086 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.253, + 0.049, + 0.793, + 0.088 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.217, + 0.162, + 0.755, + 0.183 + ], + "angle": 0, + "content": "SCPNet: Semantic Scene Completion on Point Cloud" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.208, + 0.758, + 0.241 + ], + "angle": 0, + "content": "Zhaoyang Xia\\(^{1}\\), Youquan Liu\\(^{1}\\), Xin Li\\(^{2}\\), Xinge Zhu\\(^{3}\\), Yuexin Ma\\(^{4}\\), Yikang Li\\(^{1}\\), Yuenan Hou\\(^{1\\dagger}\\), and Yu Qiao\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.241, + 0.749, + 0.292 + ], + "angle": 0, + "content": "\\(^{1}\\)Shanghai AI Laboratory \\(^{2}\\)East China Normal University \\(^{3}\\)The Chinese University of Hong Kong \\(^{4}\\)ShanghaiTech University \\(^{1}\\) {houyuenan, liyikang, qiaoyu} @pjlab.org.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.321, + 0.314, + 0.336 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.473, + 0.765 + ], + "angle": 0, + "content": "Training deep models for semantic scene completion (SSC) is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for moving objects. To address the above-mentioned problems, we propose the following three solutions: 1) Redesigning the completion sub-network. We design a novel completion sub-network, which consists of several Multi-Path Blocks (MPBs) to aggregate multi-scale features and is free from the lossy downsampling operations. 2) Distilling rich knowledge from the multi-frame model. We design a novel knowledge distillation objective, dubbed Dense-to-Sparse Knowledge Distillation (DSKD). It transfers the dense, relation-based semantic knowledge from the multi-frame teacher to the single-frame student, significantly improving the representation learning of the single-frame model. 3) Completion label rectification. We propose a simple yet effective label rectification strategy, which uses off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels, greatly improving the performance of deep models especially for those moving objects. Extensive experiments are conducted in two public SSC benchmarks, i.e., SemanticKITTI and SemanticPOSS. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge and surpasses the competitive S3CNet [3] by \\(7.2\\mathrm{mIoU}\\). SCPNet also outperforms previous completion algorithms on the SemanticPOSS dataset. Besides, our method also achieves competitive results on SemanticKITTI semantic segmentation tasks, showing that knowledge learned in the scene completion is beneficial to the segmentation task." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.792, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.83, + 0.47, + 0.845 + ], + "angle": 0, + "content": "Semantic scene completion (SSC) [20] aims at inferring" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.322, + 0.892, + 0.42 + ], + "angle": 0, + "content": "both geometry and semantics of the scene from an incomplete and sparse observation, which is a crucial component in 3D scene understanding. Performing semantic scene completion in the outdoor scenarios is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for those moving objects (See Fig. 1 (a))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.893, + 0.629 + ], + "angle": 0, + "content": "Recent years have witnessed an explosion of methods in the outdoor scene completion field [3, 19, 22, 25, 29, 32]. For example, S3CNet [3] performs 2D and 3D completion tasks jointly and achieves impressive performance on SemanticKITTI [1]. JS3C-Net [29] performs semantic segmentation first and then feeds the segmentation features to the completion sub-network. The coarse-to-fine refinement module is further put forward to improve the completion quality. Although significant progress has been achieved in this area, these methods heavily rely on the voxelwise completion labels and show unsatisfactory completion performance on the small, distant objects and crowded scenes. Moreover, the long traces of dynamic objects in original completion labels will hamper the learning of completion models, which is overlooked in the previous literature [20]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.895, + 0.824 + ], + "angle": 0, + "content": "To address the preceding problems, we propose three solutions from the aspects of the completion sub-network redesign, distillation of multi-frame knowledge as well as completion label rectification. Specifically, we first make a comprehensive overhaul of the completion sub-network. We adopt the completion-first principle and make the completion module directly process the raw voxel features. Besides, we avoid the use of downsampling operations since they inevitably introduce information loss and cause severe misclassification for those small objects and crowded scenes. To improve the completion quality on objects of diverse scales, we design Multi-Path Blocks (MPBs) with varied kernel sizes, which aggregate multi-scale features and fully utilize the rich contextual information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Second, to combat against the sparse and incomplete input signals, we make the single-scan student model distil knowledge from the multi-frame teacher model. However," + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.854, + 0.238, + 0.867 + ], + "angle": 0, + "content": "†: Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.899 + ], + "angle": 0, + "content": "17642" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.126, + 0.295, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.127, + 0.507, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.234, + 0.305, + 0.246 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.246, + 0.293, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.246, + 0.505, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.352, + 0.305, + 0.363 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.127, + 0.889, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.351, + 0.729, + 0.362 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.893, + 0.404 + ], + "angle": 0, + "content": "Figure 1. Left: challenges of semantic scene completion, i.e., (a) sparse and incomplete input, varying completion difficulty for objects of diverse scales and (b) long traces of dynamic objects in completion labels. Traces of cars and persons are highlighted by yellow ellipses. Right: (c) performance comparison of various completion algorithms on SemanticKITTI semantic scene completion challenge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.469, + 0.546 + ], + "angle": 0, + "content": "mimicking the probabilistic knowledge of each point/voxel brings marginal gains. Instead, we propose to distill the pairwise similarity information. Considering the sparsity and unorderness of features, we align the features using their indices and then force the consistency between the pairwise similarity maps of student features and those of teacher features, make the student benefit from the relational knowledge of the teacher. The resulting Dense-to-Sparse Knowledge Distillation objective is termed DSKD, which is specifically designed for the scene completion task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.469, + 0.657 + ], + "angle": 0, + "content": "Finally, to address the long traces of those dynamic objects in the completion labels, we propose a simple yet effective label rectification strategy. The core idea is to use off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels. The rectified completion labels are more accurate and reliable, greatly improving the completion qualities of deep models on those moving objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.795 + ], + "angle": 0, + "content": "We conduct experiments on two large-scale outdoor scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge \\( {}^{1} \\) and outperforms the S3CNet [3] by \\( {7.2}\\mathrm{{mIoU}} \\) . SCPNet also achieves better performance than other completion algorithms on the SemanticPOSS dataset. The learned knowledge from the completion task also benefits the segmentation task, making our SCPNet achieve superior performance on the SemanticKITTI semantic segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.797, + 0.398, + 0.809 + ], + "angle": 0, + "content": "Our contributions are summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.82, + 0.468, + 0.833 + ], + "angle": 0, + "content": "- The comprehensive redesign of the completion sub" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.41, + 0.89, + 0.436 + ], + "angle": 0, + "content": "network. We unveil several key factors to building strong completion networks." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.444, + 0.891, + 0.513 + ], + "angle": 0, + "content": "- To cope with the sparsity and incompleteness of the input, we propose to distill the dense relation-based knowledge from the multi-frame model. Note that we are the first to apply knowledge distillation to the semantic scene completion task." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.521, + 0.89, + 0.562 + ], + "angle": 0, + "content": "- To address the long traces of moving objects in completion labels, we present the completion label rectification strategy." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.57, + 0.89, + 0.638 + ], + "angle": 0, + "content": "- Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge, outperforming the previous SOTA S3CNet [3] by \\(7.2\\mathrm{mIoU}\\). Competitive performance is also shown in SemanticPOSS completion task and SemanticKITTI semantic segmentation task." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.444, + 0.891, + 0.638 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.65, + 0.64, + 0.664 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Semantic scene completion. Early works on scene completion mainly concentrates on the indoor scenarios [5, 6, 15, 22]. The point cloud in indoor scenarios is dense, small-scale and has uniform density. By contrast, point cloud in outdoor scenes is sparse, large-scale and has varying density, which poses great challenges to the semantic scene completion algorithms [3,20,25,29,32]. Various algorithms have been proposed, for instance, LMSCNet [19] uses a mixture of 2D and 3D convolutions to build the efficient completion backbone. S3CNet [3] performs 2D and 3D scene completion simultaneously, and fuses the results by the proposed dynamic voxel fusion module. JS3C-Net [29] attaches the completion network to the segmentation backbone and refines the completion outputs via the point-voxel" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.843, + 0.468, + 0.865 + ], + "angle": 0, + "content": "1https://codalab.lisn.upsaclay.fr/competitions/7170#results till 2022-11-12 00:00 Pacific Time, and our method is termed SCPNet." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.505, + 0.898 + ], + "angle": 0, + "content": "17643" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.126, + 0.891, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.35, + 0.893, + 0.452 + ], + "angle": 0, + "content": "Figure 2. Framework overview of SCPNet. There are two SCPNets, one is teacher and the other is student, and they have the same architecture. The teacher takes multi-frame point cloud as input while the student takes the single-frame point cloud as input. The dense-to-sparse knowledge distillation loss is proposed to transfer the dense semantic knowledge from teacher to student. In each SCPNet, there are two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The point cloud is first processed by a stack of MLPs to extract point features. These point features are voxelized and then fed to the completion sub-network to produce denser voxel features. The produced voxel features are further fed to the segmentation sub-network to generate the ultimate voxelwise output. For the completion sub-network, it is comprised of several multi-path blocks, free from the lossy downsampling operations. For the segmentation sub-network, it is adapted from the Cylinder3D network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.47, + 0.532 + ], + "angle": 0, + "content": "interaction module. Compared with previous completion networks, our SCPNet is free from the lossy downsampling operations. Besides, our network is built on several MPBs that aggregate multi-scale features and can achieve high completion quality in objects of various sizes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.534, + 0.471, + 0.769 + ], + "angle": 0, + "content": "Knowledge distillation. Knowledge distillation (KD) originates from the pioneering work of G. Hinton et al. [8]. Its primary objective is to transfer the dark knowledge from the large over-parameterized teacher model to the small compact student model. A large number of methods have been proposed and various forms of knowledge [21, 24, 27, 33] have been designed, e.g., intermediate features [11, 21], visual attention maps [10, 33], region-level affinity scores [9], similarity scores of different samples [24, 26], etc. It is noteworthy that the majority of the distillation methods concentrate on the 2D tasks. Only a few distillation methods have focused on 3D domains, e.g., PVKD [12] and SparseKD [31]. To our knowledge, this is the first work that applies knowledge distillation to the semantic scene completion task. We propose to transfer the dense, relation-based semantic knowledge from the multi-frame model to the single-frame one." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.212, + 0.803 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.868 + ], + "angle": 0, + "content": "The objective of the semantic scene completion task is to infer the complete geometric and semantic layout given the incomplete and sparse input. Formally, given the input point cloud \\(\\mathbf{X} \\in \\mathbb{R}^{N \\times 3}\\), the network needs to assign a label to" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.463, + 0.892, + 0.532 + ], + "angle": 0, + "content": "each voxel of the \\(L\\times W\\times H\\) voxel space to indicate whether it is empty or belongs to a specific class \\(c\\in \\{0,1,2,\\dots,C - 1\\}\\), where \\(C\\) is the number of classes, \\(L\\), \\(W\\) and \\(H\\) are the length, width and height of the voxel space, respectively. We denote the voxelwise output as \\(\\mathbf{O}\\in \\mathbb{R}^{L\\times W\\times H\\times C}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.54, + 0.7, + 0.553 + ], + "angle": 0, + "content": "3.1. Framework overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.713 + ], + "angle": 0, + "content": "As shown in Fig. 2, our SCPNet is comprised of two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The completion sub-network is designed based on several key design principles. The segmentation sub-network is built upon Cylinder3D [35, 36], with some minor modifications. In the following sections, we first detail the completion sub-network and introduce several design principles that are vital to building a strong completion sub-network. The knowledge distillation of multi-frame model and the completion label rectification will be explained thereafter." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.721, + 0.857, + 0.736 + ], + "angle": 0, + "content": "3.2. Redesigning the Completion Sub-network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Take JS3C-Net [29] as example. The original JS3C-Net first performs semantic segmentation and then conducts completion upon the segmentation features. Although this pipeline can benefit from the segmentation outputs, there are several drawbacks in this framework. First, the parameters in the completion sub-network are much fewer than the segmentation sub-network, thus yielding unsatisfactory completion performance. Second, there are downsampling and upsampling blocks in the completion sub-network. The" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "17644" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.124, + 0.468, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.47, + 0.337 + ], + "angle": 0, + "content": "Figure 3. A schematic overview of the designed completion network. It is built upon the Multi-Path Blocks (MPBs) that contain \\(3 \\times 3 \\times 3\\), \\(5 \\times 5 \\times 5\\) and \\(7 \\times 7 \\times 7\\) convolution blocks (ConvBlock). In each convolution block, there is no convolution bias and no batch normalization to maintain sparsity during completion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.469, + 0.397 + ], + "angle": 0, + "content": "downsampling operations will inevitably lose the information of the original point cloud and the upsampling operation will cause over dilation and shape distortion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.469, + 0.466 + ], + "angle": 0, + "content": "To address the aforementioned problems, we make a comprehensive overhaul of the completion sub-network. More concretely, there are three principles in the design of the completion sub-network, i.e., maintaining sparsity, no downsampling and aggregating multi-scale features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.469, + 0.659 + ], + "angle": 0, + "content": "Maintain sparsity. The completion sub-network needs the vanilla dense convolution for dilation while the segmentation sub-network uses sparse convolution for efficient processing. However, the bias of the convolution weight, running mean and beta of BN layers will break the sparsity of the original voxel features, thus substantially increasing the computation burden of the segmentation sub-network. Therefore, to reduce the overall computation cost and enjoy the high efficiency of sparse convolution, we remove all the convolution bias and the BN layers in the completion subnetwork. In this condition, the voxel features produced by the completion sub-network can still keep the sparse property and the segmentation sub-network can use sparse convolution to process these sparse voxel features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.867 + ], + "angle": 0, + "content": "No downsampling. In popular completion networks such as S3CNet [3] and JS3C-Net [29], there are several downsampling and upsampling blocks in the completion part. The downsampling operations will inevitably lose the information of the original point cloud, causing severe completion and classification errors for small objects and crowded scenes. Therefore, we discard all downsampling and upsampling operations to relieve the information loss, maximally retaining the information of the raw point cloud. Besides, as opposed to JS3C-Net which takes the segmentation-first baseline, we adopt the completion-first principle. Concretely, we make the completion sub-network directly process the raw voxel features produced by the voxelization process. And the completion sub-network can also benefit from the large number of parameters of the segmen" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.124, + 0.695, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.125, + 0.889, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.233, + 0.892, + 0.284 + ], + "angle": 0, + "content": "Figure 4. Comparison between single-frame and multi-frame point cloud. The multi-frame input is obviously denser than the single frame and the objects are easier to be identified, significantly reducing the completion difficulty." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.305, + 0.631, + 0.317 + ], + "angle": 0, + "content": "tation sub-network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.892, + 0.498 + ], + "angle": 0, + "content": "Aggregate multi-scale features. To aggregate multi-scale features, we design the multi-path block which is comprised of \\(3 \\times 3 \\times 3\\), \\(5 \\times 5 \\times 5\\) and \\(7 \\times 7 \\times 7\\) convolution blocks. As shown in Fig. 3, there are three branches in the completion sub-network. The upper branch contains one MPB and the bottom branch is a residual connection. The middle branch is constructed by a \\(3 \\times 3 \\times 3\\) convolution block, two MPBs and a \\(3 \\times 3 \\times 3\\) convolution block. After the completion sub-network, we obtain the dense completed voxel features. We extract the non-empty voxel features as well as their voxel indices from the completed voxel features. The generated sparse voxel features are sent to the segmentation sub-network to produce the voxelwise segmentation output." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.891, + 0.61 + ], + "angle": 0, + "content": "Modifications on the segmentation sub-network. Recall that, for the segmentation part, we take the Cylinder3D [36] as the backbone. Since the voxelwise completion labels are defined based on the cubic partition, we replace the cylindrical partition of Cylinder3D with conventional cubic partition. Besides, the original point refinement module consumes much GPU memory and brings limited gains, we discard this module to save memory usage." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.622, + 0.795, + 0.637 + ], + "angle": 0, + "content": "3.3. Distilling Multi-frame Knowledge" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Since single frame point cloud is sparse and incomplete in the outdoor scenarios, directly performing semantic scene completion from the single-frame input is extremely difficult. It is natural to wonder if we can construct a multi-frame model and then distil the dense semantic knowledge from this multi-frame network. From Fig. 4, it is evident that the multi-frame input significantly reduces the completion difficulty since multiple frames have much more points in the scene and objects are easier to be identified. The completion difficulty will gradually decrease as the number of input point cloud frames increases. Therefore, we construct the multi-frame teacher which takes denser point cloud as input and achieves better completion performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Inspired by [12], we make the single-frame model distil the relation-based structural knowledge from the multiframe teacher network. Since the original voxel features" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.505, + 0.898 + ], + "angle": 0, + "content": "17645" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.085, + 0.128, + 0.273, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.128, + 0.462, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.223, + 0.273, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.223, + 0.462, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.321, + 0.47, + 0.386 + ], + "angle": 0, + "content": "Figure 5. Top: original completion labels which have long traces of dynamic objects, e.g., car and person. Bottom: rectified completion labels. The proposed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.47, + 0.569 + ], + "angle": 0, + "content": "are in the sparse form, we leverage the sparse features and their indices to perform knowledge distillation. We denote the voxel features and corresponding indices of the teacher and student as \\(F_{T} \\in \\mathbb{R}^{N_{m} \\times C_{f}}\\), \\(F_{S} \\in \\mathbb{R}^{N_{s} \\times C_{f}}\\), \\(\\mathcal{I}_{T} \\in \\mathbb{R}^{N_{m} \\times 3}\\) and \\(\\mathcal{I}_{S} \\in \\mathbb{R}^{N_{s} \\times 3}\\), respectively. \\(N_{m}\\) is the number of non-empty voxel features in the multi-frame, \\(N_{s}\\) is the number of non-empty voxel features in the single-frame, \\(C_{f}\\) is the number of channels of the voxel features. Note that the indices of teacher features and student features are sorted and \\(\\mathcal{I}_{S}(i,j) = \\mathcal{I}_{T}(i,j)\\), where \\(i \\in \\{1, \\dots, N_{s}\\}\\) and \\(j \\in \\{1, 2, 3\\}\\). We first compute the pairwise relational knowledge of the student model:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.591, + 0.47, + 0.626 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} _ {S} (i, j) = \\frac {F _ {S} (i) ^ {\\top} F _ {S} (j)}{\\| F _ {S} (i) \\| _ {2} \\| F _ {S} (j) \\| _ {2}}, i, j \\in \\{1, \\dots , N _ {s} \\} \\quad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.469, + 0.731 + ], + "angle": 0, + "content": "The relational knowledge of the teacher model \\(\\mathbf{P}_T\\) is calculated in a similar way. The relational knowledge captures the similarity of each pair of voxel features and serve as important clues of the surrounding environment, which can be taken as high-level knowledge to be learned by the single-frame student model. The proposed Dense-to-Sparse Knowledge Distillation (DSKD) loss is given as below:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.752, + 0.469, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {d s k d}} \\left(\\mathbf {P} _ {S}, \\mathbf {P} _ {T}\\right) = \\frac {1}{N _ {s} ^ {2}} \\sum_ {i = 1} ^ {N _ {s}} \\sum_ {j = 1} ^ {N _ {s}} \\left\\| \\mathbf {P} _ {S} (i, j) - \\mathbf {P} _ {T} (i, j) \\right\\| _ {2} ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.817, + 0.353, + 0.832 + ], + "angle": 0, + "content": "3.4. Completion Label Rectification" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.839, + 0.469, + 0.867 + ], + "angle": 0, + "content": "Generation of completion labels. As pointed out by [20], for outdoor semantic scene completion, the ground-truth" + }, + { + "type": "code_caption", + "bbox": [ + 0.502, + 0.126, + 0.822, + 0.139 + ], + "angle": 0, + "content": "Algorithm 1 Pseudocode of Label Rectification." + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.147, + 0.892, + 0.421 + ], + "angle": 0, + "content": "L_c: completion label (256x256x32) \n# L_s: semantic segmentation label (Nx1) \n# L_p: panoptic segmentation label (Nx1) \n# S_c: classes of moving objects; u: unlabeled class \nfor C_i in S_c: \n # voxel position of completion label for class C_i \n P_c_i = getInd(L_c, C_i) \n L_p_i = L_p[L_s == C_i] # instance label of class C_i \n P_dif = [] \n if len(L_p_i) == 0: \n P_dif = P_c_i \n elif len(L_p_i) > 0 and len(P_c_i) > 0: \n # mask of voxel position bound for instance d_j \n M_c = zeros([256, 256, 32]) \n # point position of class C_i \n P_i = P[L_s == C_i, :] \n # voxel position of class C_i \n P_s_i = voxelize(P_i) \n D_i = unique(L_p_i) # all instance ids \n for d_j in D_i: \n # voxel position for instance d_j \n M_j = P_s_i[L_p_i == d_j] \n (x_min, x_max, y_min, y_max, z_min, z_max) = bound(M_j) \n M_c[x_min: x_max, y_min: y_max, z_min: z_max] = 1000 \n # voxel position for instance label of class C_i \n P_p_i = getInd(M_c, 1000) \n P_dif = difference(P_c_i, P_p_i) \n if len(P_dif) > 0: \n for p_i in range(P_dif.shape[0]): \n L_c[P_dif[p_i, 0], P_dif[p_i, 1], P_dif[p_i, 2]] = u" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.518 + ], + "angle": 0, + "content": "completion labels are obtained by concatenating the segmentation labels of multiple consecutive point cloud frames. Specifically, for the \\(t\\)-th frame, the corresponding completion labels \\(L_{t}^{c}\\) are constructed in the following way:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.538, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\nL _ {t} ^ {c} = \\operatorname {c o n c a t} \\left[ L _ {t} ^ {s}; T _ {t + 1 \\rightarrow t} L _ {t + 1} ^ {s}; \\dots ; T _ {t + T - 1 \\rightarrow t} L _ {t + T - 1} ^ {s} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.701 + ], + "angle": 0, + "content": "where \\(L_{t}^{s}\\) are the segmentation labels for the \\(t\\)-th frame, \\(T\\) is the number of frames used for concatenation, \\(T_{t+1 \\to t}\\) is the transformation matrix that transforms the coordinate from \\((t+1)\\)-th frame to the \\(t\\)-th frame, and \\(\\mathrm{concat}[\\ldots; \\ldots]\\) is the concatenating operation. The concatenation of multiple frames will lead to long traces for those moving objects, such as car and person. A vivid example is shown in Fig. 5. The long traces of those dynamic objects are obviously irrational and will hamper the learning of deep models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Completion label rectification. To remove the long traces of moving objects in the completion labels, we resort to the panoptic segmentation labels. Specifically, given the panoptic labels of class \\( i \\), we first voxelize the labels and obtain the voxelwise panoptic labels for class \\( i \\). For each instance of class \\( i \\), we calculate the bound of each instance, forming a cube. We union the cubes of all instances and use them to process the original voxelwise completion labels, filtering those voxels that are outside the cubes. The process is repeated for all classes that contain dynamic objects. The detailed information of the label rectification algorithm is shown in Algorithm 1. As shown in Fig. 5, the pro" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "17646" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.124, + 0.894, + 0.15 + ], + "angle": 0, + "content": "Table 1. Quantitative results of semantic scene completion algorithms on SemanticKITTI test set. Note that the online server still uses the original completion labels to evaluate algorithms. Bold - best in column for all single-frame methods." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.153, + 0.894, + 0.301 + ], + "angle": 0, + "content": "
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SSCNet-Full [22]16.150.024.30.50.81.24.30.30.30.051.227.130.86.434.519.935.318.229.013.16.7
ESSCNet [34]17.541.826.40.35.45.09.12.92.70.143.826.928.110.329.823.335.820.128.716.416.7
LMSCNet-SS [19]17.656.730.90.00.01.50.80.00.00.064.829.034.74.638.121.341.319.932.115.00.8
TDS [7]17.750.629.50.00.02.50.10.00.00.062.223.331.66.534.124.140.121.933.116.96.9
UDNet [37]19.559.433.90.80.43.84.40.50.30.362.028.235.19.139.524.440.923.232.318.813.1
Local-DIFs [18]22.757.734.83.62.44.44.82.51.10.067.940.142.911.440.429.042.226.539.121.317.5
SSA-SC [32]23.558.836.513.94.65.77.44.42.60.772.237.443.710.943.630.743.525.641.814.56.9
JS3C-Net [29]23.856.633.314.48.87.212.78.05.10.464.734.939.914.139.430.443.119.640.518.915.9
S3CNet [3]29.545.631.241.545.06.716.145.935.816.042.017.022.57.952.231.339.534.021.231.024.3
SCPNet (#frame=1)36.756.146.433.234.913.829.128.224.71.868.551.349.830.738.844.746.440.148.740.425.1
SCPNet (#frame=4)47.568.559.048.551.121.037.847.635.010.579.757.760.032.850.254.156.947.158.048.348.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.315, + 0.47, + 0.356 + ], + "angle": 0, + "content": "posed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.363, + 0.245, + 0.379 + ], + "angle": 0, + "content": "3.5. Overall objective" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.426 + ], + "angle": 0, + "content": "The overall loss function is comprised of three terms, i.e., the cross entropy loss, the lovasz-softmax loss [2] and the proposed distillation loss." + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.45, + 0.469, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c e}} + \\alpha \\mathcal {L} _ {\\text {l o v a s z}} + \\beta \\mathcal {L} _ {\\mathrm {d s k d}}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.501 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are the loss coefficients to balance the effect of each loss term." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.512, + 0.21, + 0.528 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.729 + ], + "angle": 0, + "content": "Datasets. Following the practice of popular scene completion models [3, 29], we conduct experiments on two popular LiDAR semantic scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. As to SemanticKITTI, it has 22 point cloud sequences. Sequences 00 to 10, 08 and 11 to 21 are used for training, validation and testing, respectively. 19 classes are chosen for training and evaluation after merging classes with distinct moving status and discarding classes with very few points. As for SemanticPOSS, it has 2, 988 frames and 11 classes are selected for evaluation. Although SemanticPOSS is smaller than SemanticKITTI in terms of dataset size, it is much more challenging since it contains a larger quantity of moving objects than SemanticKITTI, such as person and rider." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Evaluation metrics. Following [12, 36], we adopt the intersection-over-union (IoU) of each class and mIoU of all classes as the evaluation metric. The IoU of class \\(i\\) is calculated via: \\( IoU_{i} = \\frac{TP_{i}}{TP_{i} + FP_{i} + FN_{i}} \\), where \\(TP_{i}\\), \\(FP_{i}\\) and \\(FN_{i}\\) denote the true positive, false positive and false negative of class \\(i\\), respectively. For semantic scene completion, the dimension of the completion label is \\(256 \\times 256 \\times 32\\). We also report the completion mIoU which is the class-agnostic version of mIoU. Note that mIoU is the major evaluation metric for the semantic scene completion task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.315, + 0.892, + 0.466 + ], + "angle": 0, + "content": "Implementation details. The output size of Cylinder3D is set as \\(256 \\times 256 \\times 32\\) to adapt to the completion task. The number of training epochs is set as 30 and the initial learning rate is set as 0.0015. We use Adam [14] as the optimizer. Gradient norm clip is set 10 to stabilize the training process. \\(\\alpha\\) and \\(\\beta\\) are set as 1 and 3, 000, respectively. We filter points that are outside the point cloud range of the voxelwise completion labels. For SemanticKITTI, we first train the model on the training set and then finetune it on both training and validation sets before submitting the predictions of test set to the online server." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.664 + ], + "angle": 0, + "content": "Baseline KD algorithms. We take the vanilla knowledge distillation [8], FitNets [21], NST [13], PKT [17] and PVKD [12] as baseline distillation algorithms. Vanilla knowledge distillation takes the softened logits as the distilled knowledge. FitNets directly mimics the teacher features. NST adopts the maximum mean discrepancy to minimize the distance between student features and teacher features. PKT models the teacher knowledge as a probability distribution and then forces the consistency of the probability distribution between the teacher and the student. PVKD distils the voxelwise output and inter-voxel affinity knowledge. And we discard the original pointwise output distillation and inter-point affinity distillation of PVKD since they consume much GPU memory and bring marginal gains." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.677, + 0.593, + 0.691 + ], + "angle": 0, + "content": "4.1. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Quantitative results. We summarize the performance of SCPNet and state-of-the-art semantic scene completion methods in Table 1 and 2. On SemanticKITTI, our SCPNet significantly outperforms other scene completion algorithms in terms of mIoU. For example, our SCPNet is 7.2 mIoU higher than S3CNet [3]. On classes such as car, other-vehicle, road, parking, sidewalk, dense, terrain and other-ground, the performance gap between SCPNet and S3CNet is more than 10 IoU. Our SCPNet also achieves superior performance on SemanticPOSS val set. On classes such as car, trunk, pole, fence and bike, SCPNet is at least 5 IoU higher than JS3C-Net [29]. The impressive performance on" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.505, + 0.898 + ], + "angle": 0, + "content": "17647" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.124, + 0.894, + 0.151 + ], + "angle": 0, + "content": "Table 2. Quantitative results of semantic scene completion algorithms on SemanticPOSS val set. Note that the completion labels are processed by the proposed rectification algorithm. Bold - best in column for all single-frame methods." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.153, + 0.894, + 0.295 + ], + "angle": 0, + "content": "
MethodsmIoUcompletionpersonridercartrunkplantstraffic-signpolebuildingfencebikeground
SSCNet-Full [22]15.253.55.30.31.35.639.61.02.628.73.426.043.1
LMSCNet-SS [19]16.552.37.70.30.64.037.71.98.236.813.825.845.1
MotionSC [25]17.652.77.80.50.53.939.82.28.539.213.130.847.0
JS3C-Net [29]22.758.118.90.27.13.647.82.20.046.326.643.453.2
SCPNet (#frame=1)26.356.39.23.312.411.049.63.111.150.140.848.749.8
SCPNet (#frame=4)33.660.721.45.034.58.955.37.831.050.347.955.152.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.298, + 0.892, + 0.324 + ], + "angle": 0, + "content": "Table 3. Quantitative results of our SCPNet and state-of-the-art LiDAR semantic segmentation methods on SemanticKITTI test set. C3D + SCPNet denotes Cylinder3D initialized from the trained weight of SCPNet. Bold - best in column." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.327, + 0.893, + 0.448 + ], + "angle": 0, + "content": "
MethodsmIoULatency (ms)carbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic
SPVNAS [23]66.425997.351.550.859.858.865.765.243.790.267.675.216.991.365.986.173.471.064.266.9
AF2S3Net [4]69.7-94.565.486.839.241.180.780.474.391.368.872.553.587.963.270.268.553.761.571.0
RPVNet [28]70.3-97.668.468.744.261.175.974.473.493.470.380.733.393.572.186.575.171.764.861.4
PVKD [12]71.27697.067.969.353.560.275.173.550.591.870.977.541.092.469.486.573.871.964.965.8
2DPASS [30]72.9-97.063.663.461.161.577.981.374.189.767.474.740.093.572.986.273.971.065.070.4
Cylinder3D [36]68.917097.167.663.850.858.573.769.248.092.265.077.032.390.766.585.672.569.862.466.2
C3D + SCPNet71.597.560.956.358.665.970.771.858.793.672.180.936.293.372.186.274.171.666.771.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.458, + 0.47, + 0.484 + ], + "angle": 0, + "content": "Table 4. Comparison between different knowledge distillation algorithms and the proposed DSKD on the SemanticKITTI val set." + }, + { + "type": "table", + "bbox": [ + 0.166, + 0.49, + 0.378, + 0.607 + ], + "angle": 0, + "content": "
MethodsmIoU
SCPNet w/o DSKD34.4
+ KD [8]33.8
+ FitNets [21]33.8
+ PKT [17]34.6
+ PVKD [12]36.2
+ NST [13]36.3
+ DSKD37.2
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.625, + 0.47, + 0.653 + ], + "angle": 0, + "content": "two large-scale benchmarks strongly demonstrate the superiority of our SCPNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Besides, we use the trained weight of the segmentation sub-network as initialization to train Cylinder3D on the SemanticKITTI semantic segmentation task. From Table 3, Cylinder3D initialized from trained weight of the completion task outperforms the original Cylinder3D model by 2.6 mIoU, and achieves impressive segmentation performance among various competitive LiDAR segmentation models such as 2DPASS [30], PVKD [12] and RPVNet [28]. The encouraging results show that knowledge learned in the completion task is also beneficial to the segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.798, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Comparison with baseline KD algorithms. From Table 4, it is evident that the proposed DSKD method can bring more gains than conventional knowledge distillation algorithms. For instance, compared with FitNets [21] which directly mimics the teacher features, our DSKD can bring more than" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.529 + ], + "angle": 0, + "content": "2 mIoU, showing the effectiveness of the proposed relation-based distillation algorithm. The vanilla KD objective and FitNets hamper the performance of the base model, indicating that directly mimicking the logits or features can not boost the completion performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.893, + 0.669 + ], + "angle": 0, + "content": "Qualitative results. We also provide visual comparison between JS3C-Net [29], SCPNet (single-frame) and SCPNet (multi-frame). As can be seen from Fig. 6, our SCPNet (single-frame) make more accurate completion predictions than JS3C-Net on road and vegetation. On long, thin objects such as poles, our single-frame model also yields high-quality completion results compared with JS3C-Net. The predictions of our single-frame model also resemble those of the multi-frame network, demonstrating the efficacy of the proposed DSKD algorithm." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.662, + 0.692 + ], + "angle": 0, + "content": "4.2. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.7, + 0.876, + 0.713 + ], + "angle": 0, + "content": "Experiments are conducted in SemanticKITTI val set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.852 + ], + "angle": 0, + "content": "Effect of completion label rectification. We report the performance of our SCPNet on completion labels with and without rectification. From Table 5, it is evident that the proposed rectification strategy greatly enhances the performance of SCPNet on those dynamic objects, e.g., car and person. For example, the completion label rectification can bring 8.1, 24.5, 26.1 and 17.6 IoU improvement on car, person, bicyclist and motorcyclist, respectively. The impressive performance gains strongly demonstrate the effectiveness of the label rectification algorithm." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.853, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Effect of the completion sub-network. To examine the" + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "17648" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.124, + 0.891, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.376, + 0.893, + 0.403 + ], + "angle": 0, + "content": "Figure 6. Visual comparison of different methods on the SemanticKITTI validation set. From left to right: predictions of JS3C-Net [29], SCPNet (single frame), SCPNet (multi-frame) and ground-truth. Regions that have large prediction errors are highlighted by red ellipses." + }, + { + "type": "table_caption", + "bbox": [ + 0.279, + 0.409, + 0.691, + 0.422 + ], + "angle": 0, + "content": "Table 5. Impact of completion label rectification on the performance." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.425, + 0.893, + 0.491 + ], + "angle": 0, + "content": "
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SCPNet37.249.950.528.531.758.441.419.419.90.270.560.952.020.234.133.035.333.751.938.327.5
SCPNet + label rectification40.852.158.627.034.754.241.943.946.017.870.660.253.17.733.932.241.932.052.438.728.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.533 + ], + "angle": 0, + "content": "Table 6. Impact of the completion sub-network, DSKD and down-sampling operation on the performance." + }, + { + "type": "table_caption", + "bbox": [ + 0.198, + 0.535, + 0.35, + 0.546 + ], + "angle": 0, + "content": "(a) Completion sub-network" + }, + { + "type": "table", + "bbox": [ + 0.133, + 0.547, + 0.416, + 0.592 + ], + "angle": 0, + "content": "
mIoU
JS3C-Net [29]24.0
JS3C-Net + completion-subnet30.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.245, + 0.592, + 0.303, + 0.603 + ], + "angle": 0, + "content": "(b) DSKD" + }, + { + "type": "table", + "bbox": [ + 0.168, + 0.605, + 0.379, + 0.65 + ], + "angle": 0, + "content": "
mIoU
SCPNet w/o DSKD34.4
SCPNet w/ DSKD37.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.199, + 0.651, + 0.35, + 0.661 + ], + "angle": 0, + "content": "(c) Downsampling operation" + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.663, + 0.405, + 0.709 + ], + "angle": 0, + "content": "
mIoU
SCPNet w/o downsampling37.2
SCPNet w/ downsampling33.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.796 + ], + "angle": 0, + "content": "effect of our completion sub-network, we add it to JS3C-Net. The detailed performance is shown in Table 6 (a). Our completion sub-network can bring \\(6.8\\mathrm{mIoU}\\) improvement to JS3C-Net, which strongly demonstrates the effectiveness and generalization of the proposed completion sub-network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Effect of DSKD. We compare the performance of our SCPNet with and without the proposed DSKD in Table 6 (b). The proposed distillation method can bring \\(2.8\\mathrm{mIoU}\\) improvement to our SCPNet, showing the benefit of distilling relation-based knowledge from the multi-frame model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.893, + 0.62 + ], + "angle": 0, + "content": "Effect of the downsampling operation. We add the downsampling operation to our completion sub-network and examine its effect. As reported in Table 6 (c), the downsampling operation hampers the completion performance of our SCPNet. Specifically, the completion performance of SCPNet decreases from \\(37.2\\mathrm{mIoU}\\) to \\(33.1\\mathrm{mIoU}\\). The negative results show that the no-downsampling principle is vital to the success of the completion sub-network redesign." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.619, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.806 + ], + "angle": 0, + "content": "To address the challenges of the semantic scene completion task, we propose three solutions from the aspects of the completion network redesign, dense-to-sparse knowledge distillation as well as completion label rectification. The resulting completion network, termed SCPNet, achieves superior completion performance in two large-scale semantic scene completion benchmarks, i.e., SemanticKITTI and SemanticPOSS. The learned knowledge on the completion task is also beneficial to the semantic segmentation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.867 + ], + "angle": 0, + "content": "Acknowledgements. This work is partially supported by the National Key R&D Program of China (No. 2022ZD0160100), and in part by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100)." + }, + { + "type": "page_number", + "bbox": [ + 0.466, + 0.887, + 0.506, + 0.898 + ], + "angle": 0, + "content": "17649" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.125, + 0.174, + 0.139 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.148, + 0.47, + 0.211 + ], + "angle": 0, + "content": "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. SemanticKITTI: A Dataset for Semantic Scene Understanding of Lidar Sequences. In IEEE International Conference on Computer Vision, pages 9297-9307, 2019. 1, 2, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.213, + 0.472, + 0.288 + ], + "angle": 0, + "content": "[2] Maxim Berman, Amal Rannen Triki, and Matthew B. Blaschko. 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IEEE, 2021. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.127, + 0.47, + 0.859 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.467, + 0.888, + 0.503, + 0.898 + ], + "angle": 0, + "content": "17651" + } + ] +] \ No newline at end of file diff --git a/2023/SCPNet_ Semantic Scene Completion on Point Cloud/a1134f69-6375-42b9-9a92-868bfcf809a3_origin.pdf b/2023/SCPNet_ Semantic Scene Completion on Point Cloud/a1134f69-6375-42b9-9a92-868bfcf809a3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5644ee60b3c5091ee997ca4dd191a5380084b9cc --- /dev/null +++ b/2023/SCPNet_ Semantic Scene Completion on Point Cloud/a1134f69-6375-42b9-9a92-868bfcf809a3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4e11af57e97b53b2297badd55ec56414c8779a92c88c583476055d15626facad +size 368935 diff --git a/2023/SCPNet_ Semantic Scene Completion on Point Cloud/full.md b/2023/SCPNet_ Semantic Scene Completion on Point Cloud/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5acca70964ecc2197265a01165f4264f6cb810c9 --- /dev/null +++ b/2023/SCPNet_ Semantic Scene Completion on Point Cloud/full.md @@ -0,0 +1,306 @@ +# SCPNet: Semantic Scene Completion on Point Cloud + +Zhaoyang Xia $^{1}$ , Youquan Liu $^{1}$ , Xin Li $^{2}$ , Xinge Zhu $^{3}$ , Yuexin Ma $^{4}$ , Yikang Li $^{1}$ , Yuenan Hou $^{1\dagger}$ , and Yu Qiao $^{1}$ + +$^{1}$ Shanghai AI Laboratory $^{2}$ East China Normal University $^{3}$ The Chinese University of Hong Kong $^{4}$ ShanghaiTech University $^{1}$ {houyuenan, liyikang, qiaoyu} @pjlab.org.cn + +# Abstract + +Training deep models for semantic scene completion (SSC) is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for moving objects. To address the above-mentioned problems, we propose the following three solutions: 1) Redesigning the completion sub-network. We design a novel completion sub-network, which consists of several Multi-Path Blocks (MPBs) to aggregate multi-scale features and is free from the lossy downsampling operations. 2) Distilling rich knowledge from the multi-frame model. We design a novel knowledge distillation objective, dubbed Dense-to-Sparse Knowledge Distillation (DSKD). It transfers the dense, relation-based semantic knowledge from the multi-frame teacher to the single-frame student, significantly improving the representation learning of the single-frame model. 3) Completion label rectification. We propose a simple yet effective label rectification strategy, which uses off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels, greatly improving the performance of deep models especially for those moving objects. Extensive experiments are conducted in two public SSC benchmarks, i.e., SemanticKITTI and SemanticPOSS. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge and surpasses the competitive S3CNet [3] by $7.2\mathrm{mIoU}$ . SCPNet also outperforms previous completion algorithms on the SemanticPOSS dataset. Besides, our method also achieves competitive results on SemanticKITTI semantic segmentation tasks, showing that knowledge learned in the scene completion is beneficial to the segmentation task. + +# 1. Introduction + +Semantic scene completion (SSC) [20] aims at inferring + +both geometry and semantics of the scene from an incomplete and sparse observation, which is a crucial component in 3D scene understanding. Performing semantic scene completion in the outdoor scenarios is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for those moving objects (See Fig. 1 (a)). + +Recent years have witnessed an explosion of methods in the outdoor scene completion field [3, 19, 22, 25, 29, 32]. For example, S3CNet [3] performs 2D and 3D completion tasks jointly and achieves impressive performance on SemanticKITTI [1]. JS3C-Net [29] performs semantic segmentation first and then feeds the segmentation features to the completion sub-network. The coarse-to-fine refinement module is further put forward to improve the completion quality. Although significant progress has been achieved in this area, these methods heavily rely on the voxelwise completion labels and show unsatisfactory completion performance on the small, distant objects and crowded scenes. Moreover, the long traces of dynamic objects in original completion labels will hamper the learning of completion models, which is overlooked in the previous literature [20]. + +To address the preceding problems, we propose three solutions from the aspects of the completion sub-network redesign, distillation of multi-frame knowledge as well as completion label rectification. Specifically, we first make a comprehensive overhaul of the completion sub-network. We adopt the completion-first principle and make the completion module directly process the raw voxel features. Besides, we avoid the use of downsampling operations since they inevitably introduce information loss and cause severe misclassification for those small objects and crowded scenes. To improve the completion quality on objects of diverse scales, we design Multi-Path Blocks (MPBs) with varied kernel sizes, which aggregate multi-scale features and fully utilize the rich contextual information. + +Second, to combat against the sparse and incomplete input signals, we make the single-scan student model distil knowledge from the multi-frame teacher model. However, + +![](images/5548e25d074e71744d67fb72d13ef5f39e1ce4b33c55731bec8a3df69ee7c831.jpg) + +![](images/326df470ed4a8e9c69bc83ea969b5e4b92385116bc996deb9185123e8469c6aa.jpg) + +![](images/443333509d57fa346df5e14ecb11a57190e4e782d1869b60b288f298a9e57669.jpg) +(a) +(b) +Figure 1. Left: challenges of semantic scene completion, i.e., (a) sparse and incomplete input, varying completion difficulty for objects of diverse scales and (b) long traces of dynamic objects in completion labels. Traces of cars and persons are highlighted by yellow ellipses. Right: (c) performance comparison of various completion algorithms on SemanticKITTI semantic scene completion challenge. + +![](images/33e42b8253b5d7575d8e644d425e2c5371e6fe57d3a57334a009c83688e285ad.jpg) + +![](images/3d3fb28a18539c33a7b3339eb1c9ae4c99a6f16b80a1946c92b4f61107490234.jpg) +(c) + +mimicking the probabilistic knowledge of each point/voxel brings marginal gains. Instead, we propose to distill the pairwise similarity information. Considering the sparsity and unorderness of features, we align the features using their indices and then force the consistency between the pairwise similarity maps of student features and those of teacher features, make the student benefit from the relational knowledge of the teacher. The resulting Dense-to-Sparse Knowledge Distillation objective is termed DSKD, which is specifically designed for the scene completion task. + +Finally, to address the long traces of those dynamic objects in the completion labels, we propose a simple yet effective label rectification strategy. The core idea is to use off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels. The rectified completion labels are more accurate and reliable, greatly improving the completion qualities of deep models on those moving objects. + +We conduct experiments on two large-scale outdoor scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge ${}^{1}$ and outperforms the S3CNet [3] by ${7.2}\mathrm{{mIoU}}$ . SCPNet also achieves better performance than other completion algorithms on the SemanticPOSS dataset. The learned knowledge from the completion task also benefits the segmentation task, making our SCPNet achieve superior performance on the SemanticKITTI semantic segmentation task. + +Our contributions are summarized as follows. + +- The comprehensive redesign of the completion sub + +network. We unveil several key factors to building strong completion networks. + +- To cope with the sparsity and incompleteness of the input, we propose to distill the dense relation-based knowledge from the multi-frame model. Note that we are the first to apply knowledge distillation to the semantic scene completion task. +- To address the long traces of moving objects in completion labels, we present the completion label rectification strategy. +- Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge, outperforming the previous SOTA S3CNet [3] by $7.2\mathrm{mIoU}$ . Competitive performance is also shown in SemanticPOSS completion task and SemanticKITTI semantic segmentation task. + +# 2. Related Work + +Semantic scene completion. Early works on scene completion mainly concentrates on the indoor scenarios [5, 6, 15, 22]. The point cloud in indoor scenarios is dense, small-scale and has uniform density. By contrast, point cloud in outdoor scenes is sparse, large-scale and has varying density, which poses great challenges to the semantic scene completion algorithms [3,20,25,29,32]. Various algorithms have been proposed, for instance, LMSCNet [19] uses a mixture of 2D and 3D convolutions to build the efficient completion backbone. S3CNet [3] performs 2D and 3D scene completion simultaneously, and fuses the results by the proposed dynamic voxel fusion module. JS3C-Net [29] attaches the completion network to the segmentation backbone and refines the completion outputs via the point-voxel + +![](images/41557f97fbe5b3abd0c6b55b2979121df3e3a08f0aebbb9b9ccfb37d70a024d9.jpg) +Figure 2. Framework overview of SCPNet. There are two SCPNets, one is teacher and the other is student, and they have the same architecture. The teacher takes multi-frame point cloud as input while the student takes the single-frame point cloud as input. The dense-to-sparse knowledge distillation loss is proposed to transfer the dense semantic knowledge from teacher to student. In each SCPNet, there are two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The point cloud is first processed by a stack of MLPs to extract point features. These point features are voxelized and then fed to the completion sub-network to produce denser voxel features. The produced voxel features are further fed to the segmentation sub-network to generate the ultimate voxelwise output. For the completion sub-network, it is comprised of several multi-path blocks, free from the lossy downsampling operations. For the segmentation sub-network, it is adapted from the Cylinder3D network. + +interaction module. Compared with previous completion networks, our SCPNet is free from the lossy downsampling operations. Besides, our network is built on several MPBs that aggregate multi-scale features and can achieve high completion quality in objects of various sizes. + +Knowledge distillation. Knowledge distillation (KD) originates from the pioneering work of G. Hinton et al. [8]. Its primary objective is to transfer the dark knowledge from the large over-parameterized teacher model to the small compact student model. A large number of methods have been proposed and various forms of knowledge [21, 24, 27, 33] have been designed, e.g., intermediate features [11, 21], visual attention maps [10, 33], region-level affinity scores [9], similarity scores of different samples [24, 26], etc. It is noteworthy that the majority of the distillation methods concentrate on the 2D tasks. Only a few distillation methods have focused on 3D domains, e.g., PVKD [12] and SparseKD [31]. To our knowledge, this is the first work that applies knowledge distillation to the semantic scene completion task. We propose to transfer the dense, relation-based semantic knowledge from the multi-frame model to the single-frame one. + +# 3. Methodology + +The objective of the semantic scene completion task is to infer the complete geometric and semantic layout given the incomplete and sparse input. Formally, given the input point cloud $\mathbf{X} \in \mathbb{R}^{N \times 3}$ , the network needs to assign a label to + +each voxel of the $L\times W\times H$ voxel space to indicate whether it is empty or belongs to a specific class $c\in \{0,1,2,\dots,C - 1\}$ , where $C$ is the number of classes, $L$ , $W$ and $H$ are the length, width and height of the voxel space, respectively. We denote the voxelwise output as $\mathbf{O}\in \mathbb{R}^{L\times W\times H\times C}$ . + +# 3.1. Framework overview + +As shown in Fig. 2, our SCPNet is comprised of two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The completion sub-network is designed based on several key design principles. The segmentation sub-network is built upon Cylinder3D [35, 36], with some minor modifications. In the following sections, we first detail the completion sub-network and introduce several design principles that are vital to building a strong completion sub-network. The knowledge distillation of multi-frame model and the completion label rectification will be explained thereafter. + +# 3.2. Redesigning the Completion Sub-network + +Take JS3C-Net [29] as example. The original JS3C-Net first performs semantic segmentation and then conducts completion upon the segmentation features. Although this pipeline can benefit from the segmentation outputs, there are several drawbacks in this framework. First, the parameters in the completion sub-network are much fewer than the segmentation sub-network, thus yielding unsatisfactory completion performance. Second, there are downsampling and upsampling blocks in the completion sub-network. The + +![](images/762d5a6528c211475cce53132b2c13e3afcecfd392f53beb3ec7163a59c2ae96.jpg) +Figure 3. A schematic overview of the designed completion network. It is built upon the Multi-Path Blocks (MPBs) that contain $3 \times 3 \times 3$ , $5 \times 5 \times 5$ and $7 \times 7 \times 7$ convolution blocks (ConvBlock). In each convolution block, there is no convolution bias and no batch normalization to maintain sparsity during completion. + +downsampling operations will inevitably lose the information of the original point cloud and the upsampling operation will cause over dilation and shape distortion. + +To address the aforementioned problems, we make a comprehensive overhaul of the completion sub-network. More concretely, there are three principles in the design of the completion sub-network, i.e., maintaining sparsity, no downsampling and aggregating multi-scale features. + +Maintain sparsity. The completion sub-network needs the vanilla dense convolution for dilation while the segmentation sub-network uses sparse convolution for efficient processing. However, the bias of the convolution weight, running mean and beta of BN layers will break the sparsity of the original voxel features, thus substantially increasing the computation burden of the segmentation sub-network. Therefore, to reduce the overall computation cost and enjoy the high efficiency of sparse convolution, we remove all the convolution bias and the BN layers in the completion subnetwork. In this condition, the voxel features produced by the completion sub-network can still keep the sparse property and the segmentation sub-network can use sparse convolution to process these sparse voxel features. + +No downsampling. In popular completion networks such as S3CNet [3] and JS3C-Net [29], there are several downsampling and upsampling blocks in the completion part. The downsampling operations will inevitably lose the information of the original point cloud, causing severe completion and classification errors for small objects and crowded scenes. Therefore, we discard all downsampling and upsampling operations to relieve the information loss, maximally retaining the information of the raw point cloud. Besides, as opposed to JS3C-Net which takes the segmentation-first baseline, we adopt the completion-first principle. Concretely, we make the completion sub-network directly process the raw voxel features produced by the voxelization process. And the completion sub-network can also benefit from the large number of parameters of the segmen + +![](images/b7958eb1c53ed443c2cf23d491b4c7751bd52f6351dc7edd97db55cca82b3fe3.jpg) +Figure 4. Comparison between single-frame and multi-frame point cloud. The multi-frame input is obviously denser than the single frame and the objects are easier to be identified, significantly reducing the completion difficulty. + +![](images/8bf4b0ae91c1d4bc2aae4a9dcbb94563698b99ac349f7f6766c479d8efaa4169.jpg) + +tation sub-network. + +Aggregate multi-scale features. To aggregate multi-scale features, we design the multi-path block which is comprised of $3 \times 3 \times 3$ , $5 \times 5 \times 5$ and $7 \times 7 \times 7$ convolution blocks. As shown in Fig. 3, there are three branches in the completion sub-network. The upper branch contains one MPB and the bottom branch is a residual connection. The middle branch is constructed by a $3 \times 3 \times 3$ convolution block, two MPBs and a $3 \times 3 \times 3$ convolution block. After the completion sub-network, we obtain the dense completed voxel features. We extract the non-empty voxel features as well as their voxel indices from the completed voxel features. The generated sparse voxel features are sent to the segmentation sub-network to produce the voxelwise segmentation output. + +Modifications on the segmentation sub-network. Recall that, for the segmentation part, we take the Cylinder3D [36] as the backbone. Since the voxelwise completion labels are defined based on the cubic partition, we replace the cylindrical partition of Cylinder3D with conventional cubic partition. Besides, the original point refinement module consumes much GPU memory and brings limited gains, we discard this module to save memory usage. + +# 3.3. Distilling Multi-frame Knowledge + +Since single frame point cloud is sparse and incomplete in the outdoor scenarios, directly performing semantic scene completion from the single-frame input is extremely difficult. It is natural to wonder if we can construct a multi-frame model and then distil the dense semantic knowledge from this multi-frame network. From Fig. 4, it is evident that the multi-frame input significantly reduces the completion difficulty since multiple frames have much more points in the scene and objects are easier to be identified. The completion difficulty will gradually decrease as the number of input point cloud frames increases. Therefore, we construct the multi-frame teacher which takes denser point cloud as input and achieves better completion performance. + +Inspired by [12], we make the single-frame model distil the relation-based structural knowledge from the multiframe teacher network. Since the original voxel features + +![](images/8d96145bce7cc6a06ad460ad4e87ed61c1e608c32793af3b90503c3d97068657.jpg) + +![](images/393ab21ecb691377ca7f94ade1563a807dac2588ebd7a4789f87aa89d61d35f6.jpg) + +![](images/c2d6a95e0fc532b071eae4847e005c738d0a8d78a048f7c330cd13285cbe32bf.jpg) +Figure 5. Top: original completion labels which have long traces of dynamic objects, e.g., car and person. Bottom: rectified completion labels. The proposed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate. + +![](images/fb96fe933c0b6195eaed6a4859a8a2f383352eb40779a62dc61e4d2f17245ef3.jpg) + +are in the sparse form, we leverage the sparse features and their indices to perform knowledge distillation. We denote the voxel features and corresponding indices of the teacher and student as $F_{T} \in \mathbb{R}^{N_{m} \times C_{f}}$ , $F_{S} \in \mathbb{R}^{N_{s} \times C_{f}}$ , $\mathcal{I}_{T} \in \mathbb{R}^{N_{m} \times 3}$ and $\mathcal{I}_{S} \in \mathbb{R}^{N_{s} \times 3}$ , respectively. $N_{m}$ is the number of non-empty voxel features in the multi-frame, $N_{s}$ is the number of non-empty voxel features in the single-frame, $C_{f}$ is the number of channels of the voxel features. Note that the indices of teacher features and student features are sorted and $\mathcal{I}_{S}(i,j) = \mathcal{I}_{T}(i,j)$ , where $i \in \{1, \dots, N_{s}\}$ and $j \in \{1, 2, 3\}$ . We first compute the pairwise relational knowledge of the student model: + +$$ +\mathbf {P} _ {S} (i, j) = \frac {F _ {S} (i) ^ {\top} F _ {S} (j)}{\| F _ {S} (i) \| _ {2} \| F _ {S} (j) \| _ {2}}, i, j \in \{1, \dots , N _ {s} \} \quad (1) +$$ + +The relational knowledge of the teacher model $\mathbf{P}_T$ is calculated in a similar way. The relational knowledge captures the similarity of each pair of voxel features and serve as important clues of the surrounding environment, which can be taken as high-level knowledge to be learned by the single-frame student model. The proposed Dense-to-Sparse Knowledge Distillation (DSKD) loss is given as below: + +$$ +\mathcal {L} _ {\mathrm {d s k d}} \left(\mathbf {P} _ {S}, \mathbf {P} _ {T}\right) = \frac {1}{N _ {s} ^ {2}} \sum_ {i = 1} ^ {N _ {s}} \sum_ {j = 1} ^ {N _ {s}} \left\| \mathbf {P} _ {S} (i, j) - \mathbf {P} _ {T} (i, j) \right\| _ {2} ^ {2}. \tag {2} +$$ + +# 3.4. Completion Label Rectification + +Generation of completion labels. As pointed out by [20], for outdoor semantic scene completion, the ground-truth + +Algorithm 1 Pseudocode of Label Rectification. +L_c: completion label (256x256x32) +# L_s: semantic segmentation label (Nx1) +# L_p: panoptic segmentation label (Nx1) +# S_c: classes of moving objects; u: unlabeled class +for C_i in S_c: + # voxel position of completion label for class C_i + P_c_i = getInd(L_c, C_i) + L_p_i = L_p[L_s == C_i] # instance label of class C_i + P_dif = [] + if len(L_p_i) == 0: + P_dif = P_c_i + elif len(L_p_i) > 0 and len(P_c_i) > 0: + # mask of voxel position bound for instance d_j + M_c = zeros([256, 256, 32]) + # point position of class C_i + P_i = P[L_s == C_i, :] + # voxel position of class C_i + P_s_i = voxelize(P_i) + D_i = unique(L_p_i) # all instance ids + for d_j in D_i: + # voxel position for instance d_j + M_j = P_s_i[L_p_i == d_j] + (x_min, x_max, y_min, y_max, z_min, z_max) = bound(M_j) + M_c[x_min: x_max, y_min: y_max, z_min: z_max] = 1000 + # voxel position for instance label of class C_i + P_p_i = getInd(M_c, 1000) + P_dif = difference(P_c_i, P_p_i) + if len(P_dif) > 0: + for p_i in range(P_dif.shape[0]): + L_c[P_dif[p_i, 0], P_dif[p_i, 1], P_dif[p_i, 2]] = u + +completion labels are obtained by concatenating the segmentation labels of multiple consecutive point cloud frames. Specifically, for the $t$ -th frame, the corresponding completion labels $L_{t}^{c}$ are constructed in the following way: + +$$ +L _ {t} ^ {c} = \operatorname {c o n c a t} \left[ L _ {t} ^ {s}; T _ {t + 1 \rightarrow t} L _ {t + 1} ^ {s}; \dots ; T _ {t + T - 1 \rightarrow t} L _ {t + T - 1} ^ {s} \right], \tag {3} +$$ + +where $L_{t}^{s}$ are the segmentation labels for the $t$ -th frame, $T$ is the number of frames used for concatenation, $T_{t+1 \to t}$ is the transformation matrix that transforms the coordinate from $(t+1)$ -th frame to the $t$ -th frame, and $\mathrm{concat}[\ldots; \ldots]$ is the concatenating operation. The concatenation of multiple frames will lead to long traces for those moving objects, such as car and person. A vivid example is shown in Fig. 5. The long traces of those dynamic objects are obviously irrational and will hamper the learning of deep models. + +Completion label rectification. To remove the long traces of moving objects in the completion labels, we resort to the panoptic segmentation labels. Specifically, given the panoptic labels of class $i$ , we first voxelize the labels and obtain the voxelwise panoptic labels for class $i$ . For each instance of class $i$ , we calculate the bound of each instance, forming a cube. We union the cubes of all instances and use them to process the original voxelwise completion labels, filtering those voxels that are outside the cubes. The process is repeated for all classes that contain dynamic objects. The detailed information of the label rectification algorithm is shown in Algorithm 1. As shown in Fig. 5, the pro + +Table 1. Quantitative results of semantic scene completion algorithms on SemanticKITTI test set. Note that the online server still uses the original completion labels to evaluate algorithms. Bold - best in column for all single-frame methods. + +
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SSCNet-Full [22]16.150.024.30.50.81.24.30.30.30.051.227.130.86.434.519.935.318.229.013.16.7
ESSCNet [34]17.541.826.40.35.45.09.12.92.70.143.826.928.110.329.823.335.820.128.716.416.7
LMSCNet-SS [19]17.656.730.90.00.01.50.80.00.00.064.829.034.74.638.121.341.319.932.115.00.8
TDS [7]17.750.629.50.00.02.50.10.00.00.062.223.331.66.534.124.140.121.933.116.96.9
UDNet [37]19.559.433.90.80.43.84.40.50.30.362.028.235.19.139.524.440.923.232.318.813.1
Local-DIFs [18]22.757.734.83.62.44.44.82.51.10.067.940.142.911.440.429.042.226.539.121.317.5
SSA-SC [32]23.558.836.513.94.65.77.44.42.60.772.237.443.710.943.630.743.525.641.814.56.9
JS3C-Net [29]23.856.633.314.48.87.212.78.05.10.464.734.939.914.139.430.443.119.640.518.915.9
S3CNet [3]29.545.631.241.545.06.716.145.935.816.042.017.022.57.952.231.339.534.021.231.024.3
SCPNet (#frame=1)36.756.146.433.234.913.829.128.224.71.868.551.349.830.738.844.746.440.148.740.425.1
SCPNet (#frame=4)47.568.559.048.551.121.037.847.635.010.579.757.760.032.850.254.156.947.158.048.348.0
+ +posed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate. + +# 3.5. Overall objective + +The overall loss function is comprised of three terms, i.e., the cross entropy loss, the lovasz-softmax loss [2] and the proposed distillation loss. + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {c e}} + \alpha \mathcal {L} _ {\text {l o v a s z}} + \beta \mathcal {L} _ {\mathrm {d s k d}}, \tag {4} +$$ + +where $\alpha$ and $\beta$ are the loss coefficients to balance the effect of each loss term. + +# 4. Experiments + +Datasets. Following the practice of popular scene completion models [3, 29], we conduct experiments on two popular LiDAR semantic scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. As to SemanticKITTI, it has 22 point cloud sequences. Sequences 00 to 10, 08 and 11 to 21 are used for training, validation and testing, respectively. 19 classes are chosen for training and evaluation after merging classes with distinct moving status and discarding classes with very few points. As for SemanticPOSS, it has 2, 988 frames and 11 classes are selected for evaluation. Although SemanticPOSS is smaller than SemanticKITTI in terms of dataset size, it is much more challenging since it contains a larger quantity of moving objects than SemanticKITTI, such as person and rider. + +Evaluation metrics. Following [12, 36], we adopt the intersection-over-union (IoU) of each class and mIoU of all classes as the evaluation metric. The IoU of class $i$ is calculated via: $IoU_{i} = \frac{TP_{i}}{TP_{i} + FP_{i} + FN_{i}}$ , where $TP_{i}$ , $FP_{i}$ and $FN_{i}$ denote the true positive, false positive and false negative of class $i$ , respectively. For semantic scene completion, the dimension of the completion label is $256 \times 256 \times 32$ . We also report the completion mIoU which is the class-agnostic version of mIoU. Note that mIoU is the major evaluation metric for the semantic scene completion task. + +Implementation details. The output size of Cylinder3D is set as $256 \times 256 \times 32$ to adapt to the completion task. The number of training epochs is set as 30 and the initial learning rate is set as 0.0015. We use Adam [14] as the optimizer. Gradient norm clip is set 10 to stabilize the training process. $\alpha$ and $\beta$ are set as 1 and 3, 000, respectively. We filter points that are outside the point cloud range of the voxelwise completion labels. For SemanticKITTI, we first train the model on the training set and then finetune it on both training and validation sets before submitting the predictions of test set to the online server. + +Baseline KD algorithms. We take the vanilla knowledge distillation [8], FitNets [21], NST [13], PKT [17] and PVKD [12] as baseline distillation algorithms. Vanilla knowledge distillation takes the softened logits as the distilled knowledge. FitNets directly mimics the teacher features. NST adopts the maximum mean discrepancy to minimize the distance between student features and teacher features. PKT models the teacher knowledge as a probability distribution and then forces the consistency of the probability distribution between the teacher and the student. PVKD distils the voxelwise output and inter-voxel affinity knowledge. And we discard the original pointwise output distillation and inter-point affinity distillation of PVKD since they consume much GPU memory and bring marginal gains. + +# 4.1. Results + +Quantitative results. We summarize the performance of SCPNet and state-of-the-art semantic scene completion methods in Table 1 and 2. On SemanticKITTI, our SCPNet significantly outperforms other scene completion algorithms in terms of mIoU. For example, our SCPNet is 7.2 mIoU higher than S3CNet [3]. On classes such as car, other-vehicle, road, parking, sidewalk, dense, terrain and other-ground, the performance gap between SCPNet and S3CNet is more than 10 IoU. Our SCPNet also achieves superior performance on SemanticPOSS val set. On classes such as car, trunk, pole, fence and bike, SCPNet is at least 5 IoU higher than JS3C-Net [29]. The impressive performance on + +Table 2. Quantitative results of semantic scene completion algorithms on SemanticPOSS val set. Note that the completion labels are processed by the proposed rectification algorithm. Bold - best in column for all single-frame methods. + +
MethodsmIoUcompletionpersonridercartrunkplantstraffic-signpolebuildingfencebikeground
SSCNet-Full [22]15.253.55.30.31.35.639.61.02.628.73.426.043.1
LMSCNet-SS [19]16.552.37.70.30.64.037.71.98.236.813.825.845.1
MotionSC [25]17.652.77.80.50.53.939.82.28.539.213.130.847.0
JS3C-Net [29]22.758.118.90.27.13.647.82.20.046.326.643.453.2
SCPNet (#frame=1)26.356.39.23.312.411.049.63.111.150.140.848.749.8
SCPNet (#frame=4)33.660.721.45.034.58.955.37.831.050.347.955.152.3
+ +Table 3. Quantitative results of our SCPNet and state-of-the-art LiDAR semantic segmentation methods on SemanticKITTI test set. C3D + SCPNet denotes Cylinder3D initialized from the trained weight of SCPNet. Bold - best in column. + +
MethodsmIoULatency (ms)carbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic
SPVNAS [23]66.425997.351.550.859.858.865.765.243.790.267.675.216.991.365.986.173.471.064.266.9
AF2S3Net [4]69.7-94.565.486.839.241.180.780.474.391.368.872.553.587.963.270.268.553.761.571.0
RPVNet [28]70.3-97.668.468.744.261.175.974.473.493.470.380.733.393.572.186.575.171.764.861.4
PVKD [12]71.27697.067.969.353.560.275.173.550.591.870.977.541.092.469.486.573.871.964.965.8
2DPASS [30]72.9-97.063.663.461.161.577.981.374.189.767.474.740.093.572.986.273.971.065.070.4
Cylinder3D [36]68.917097.167.663.850.858.573.769.248.092.265.077.032.390.766.585.672.569.862.466.2
C3D + SCPNet71.597.560.956.358.665.970.771.858.793.672.180.936.293.372.186.274.171.666.771.8
+ +Table 4. Comparison between different knowledge distillation algorithms and the proposed DSKD on the SemanticKITTI val set. + +
MethodsmIoU
SCPNet w/o DSKD34.4
+ KD [8]33.8
+ FitNets [21]33.8
+ PKT [17]34.6
+ PVKD [12]36.2
+ NST [13]36.3
+ DSKD37.2
+ +two large-scale benchmarks strongly demonstrate the superiority of our SCPNet. + +Besides, we use the trained weight of the segmentation sub-network as initialization to train Cylinder3D on the SemanticKITTI semantic segmentation task. From Table 3, Cylinder3D initialized from trained weight of the completion task outperforms the original Cylinder3D model by 2.6 mIoU, and achieves impressive segmentation performance among various competitive LiDAR segmentation models such as 2DPASS [30], PVKD [12] and RPVNet [28]. The encouraging results show that knowledge learned in the completion task is also beneficial to the segmentation task. + +Comparison with baseline KD algorithms. From Table 4, it is evident that the proposed DSKD method can bring more gains than conventional knowledge distillation algorithms. For instance, compared with FitNets [21] which directly mimics the teacher features, our DSKD can bring more than + +2 mIoU, showing the effectiveness of the proposed relation-based distillation algorithm. The vanilla KD objective and FitNets hamper the performance of the base model, indicating that directly mimicking the logits or features can not boost the completion performance. + +Qualitative results. We also provide visual comparison between JS3C-Net [29], SCPNet (single-frame) and SCPNet (multi-frame). As can be seen from Fig. 6, our SCPNet (single-frame) make more accurate completion predictions than JS3C-Net on road and vegetation. On long, thin objects such as poles, our single-frame model also yields high-quality completion results compared with JS3C-Net. The predictions of our single-frame model also resemble those of the multi-frame network, demonstrating the efficacy of the proposed DSKD algorithm. + +# 4.2. Ablation studies + +Experiments are conducted in SemanticKITTI val set. + +Effect of completion label rectification. We report the performance of our SCPNet on completion labels with and without rectification. From Table 5, it is evident that the proposed rectification strategy greatly enhances the performance of SCPNet on those dynamic objects, e.g., car and person. For example, the completion label rectification can bring 8.1, 24.5, 26.1 and 17.6 IoU improvement on car, person, bicyclist and motorcyclist, respectively. The impressive performance gains strongly demonstrate the effectiveness of the label rectification algorithm. + +Effect of the completion sub-network. To examine the + +![](images/565012982eacdd839c5fecb4765e7abfc657baa4dc7e0cd34a649ecbf21b7d87.jpg) +Figure 6. Visual comparison of different methods on the SemanticKITTI validation set. From left to right: predictions of JS3C-Net [29], SCPNet (single frame), SCPNet (multi-frame) and ground-truth. Regions that have large prediction errors are highlighted by red ellipses. + +Table 5. Impact of completion label rectification on the performance. + +
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SCPNet37.249.950.528.531.758.441.419.419.90.270.560.952.020.234.133.035.333.751.938.327.5
SCPNet + label rectification40.852.158.627.034.754.241.943.946.017.870.660.253.17.733.932.241.932.052.438.728.9
+ +Table 6. Impact of the completion sub-network, DSKD and down-sampling operation on the performance. +(a) Completion sub-network + +
mIoU
JS3C-Net [29]24.0
JS3C-Net + completion-subnet30.8
+ +(b) DSKD + +
mIoU
SCPNet w/o DSKD34.4
SCPNet w/ DSKD37.2
+ +(c) Downsampling operation + +
mIoU
SCPNet w/o downsampling37.2
SCPNet w/ downsampling33.1
+ +effect of our completion sub-network, we add it to JS3C-Net. The detailed performance is shown in Table 6 (a). Our completion sub-network can bring $6.8\mathrm{mIoU}$ improvement to JS3C-Net, which strongly demonstrates the effectiveness and generalization of the proposed completion sub-network. + +Effect of DSKD. We compare the performance of our SCPNet with and without the proposed DSKD in Table 6 (b). The proposed distillation method can bring $2.8\mathrm{mIoU}$ improvement to our SCPNet, showing the benefit of distilling relation-based knowledge from the multi-frame model. + +Effect of the downsampling operation. We add the downsampling operation to our completion sub-network and examine its effect. As reported in Table 6 (c), the downsampling operation hampers the completion performance of our SCPNet. Specifically, the completion performance of SCPNet decreases from $37.2\mathrm{mIoU}$ to $33.1\mathrm{mIoU}$ . The negative results show that the no-downsampling principle is vital to the success of the completion sub-network redesign. + +# 5. Conclusion + +To address the challenges of the semantic scene completion task, we propose three solutions from the aspects of the completion network redesign, dense-to-sparse knowledge distillation as well as completion label rectification. The resulting completion network, termed SCPNet, achieves superior completion performance in two large-scale semantic scene completion benchmarks, i.e., SemanticKITTI and SemanticPOSS. The learned knowledge on the completion task is also beneficial to the semantic segmentation task. + +Acknowledgements. This work is partially supported by the National Key R&D Program of China (No. 2022ZD0160100), and in part by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100). + +# References + +[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. 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objects of diverse scales as well as the inherent label noise for moving objects. To address the above-mentioned problems, we propose the following three solutions: 1) Redesigning the completion sub-network. We design a novel completion sub-network, which consists of several Multi-Path Blocks (MPBs) to aggregate multi-scale features and is free from the lossy downsampling operations. 2) Distilling rich knowledge from the multi-frame model. We design a novel knowledge distillation objective, dubbed Dense-to-Sparse Knowledge Distillation (DSKD). It transfers the dense, relation-based semantic knowledge from the multi-frame teacher to the single-frame student, significantly improving the representation learning of the single-frame model. 3) Completion label rectification. We propose a simple yet effective label rectification strategy, which uses off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels, greatly improving the performance of deep models especially for those moving objects. Extensive experiments are conducted in two public SSC benchmarks, i.e., SemanticKITTI and SemanticPOSS. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge and surpasses the competitive S3CNet [3] by " + }, + { + "bbox": [ + 45, + 295, + 281, + 644 + ], + "type": "inline_equation", + "content": "7.2\\mathrm{mIoU}" + }, + { + "bbox": [ + 45, + 295, + 281, + 644 + ], + "type": "text", + "content": ". SCPNet also outperforms previous completion algorithms on the SemanticPOSS dataset. Besides, our method also achieves competitive results on SemanticKITTI semantic segmentation tasks, showing that knowledge learned in the scene completion is beneficial to the segmentation task." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 666, + 124, + 679 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 124, + 679 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 124, + 679 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 57, + 698, + 279, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 698, + 279, + 711 + ], + "spans": [ + { + "bbox": [ + 57, + 698, + 279, + 711 + ], + "type": "text", + "content": "Semantic scene completion (SSC) [20] aims at inferring" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 297, + 271, + 530, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 271, + 530, + 353 + ], + "spans": [ + { + "bbox": [ + 297, + 271, + 530, + 353 + ], + "type": "text", + "content": "both geometry and semantics of the scene from an incomplete and sparse observation, which is a crucial component in 3D scene understanding. Performing semantic scene completion in the outdoor scenarios is challenging due to the sparse and incomplete input, a large quantity of objects of diverse scales as well as the inherent label noise for those moving objects (See Fig. 1 (a))." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 354, + 531, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 354, + 531, + 529 + ], + "spans": [ + { + "bbox": [ + 296, + 354, + 531, + 529 + ], + "type": "text", + "content": "Recent years have witnessed an explosion of methods in the outdoor scene completion field [3, 19, 22, 25, 29, 32]. For example, S3CNet [3] performs 2D and 3D completion tasks jointly and achieves impressive performance on SemanticKITTI [1]. JS3C-Net [29] performs semantic segmentation first and then feeds the segmentation features to the completion sub-network. The coarse-to-fine refinement module is further put forward to improve the completion quality. Although significant progress has been achieved in this area, these methods heavily rely on the voxelwise completion labels and show unsatisfactory completion performance on the small, distant objects and crowded scenes. Moreover, the long traces of dynamic objects in original completion labels will hamper the learning of completion models, which is overlooked in the previous literature [20]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 530, + 532, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 530, + 532, + 693 + ], + "spans": [ + { + "bbox": [ + 296, + 530, + 532, + 693 + ], + "type": "text", + "content": "To address the preceding problems, we propose three solutions from the aspects of the completion sub-network redesign, distillation of multi-frame knowledge as well as completion label rectification. Specifically, we first make a comprehensive overhaul of the completion sub-network. We adopt the completion-first principle and make the completion module directly process the raw voxel features. Besides, we avoid the use of downsampling operations since they inevitably introduce information loss and cause severe misclassification for those small objects and crowded scenes. To improve the completion quality on objects of diverse scales, we design Multi-Path Blocks (MPBs) with varied kernel sizes, which aggregate multi-scale features and fully utilize the rich contextual information." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 296, + 694, + 532, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 694, + 532, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 694, + 532, + 730 + ], + "type": "text", + "content": "Second, to combat against the sparse and incomplete input signals, we make the single-scan student model distil knowledge from the multi-frame teacher model. However," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "spans": [ + { + "bbox": [ + 77, + 42, + 119, + 72 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "spans": [ + { + "bbox": [ + 150, + 41, + 471, + 74 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 719, + 141, + 730 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 719, + 141, + 730 + ], + "spans": [ + { + "bbox": [ + 60, + 719, + 141, + 730 + ], + "type": "text", + "content": "†: Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "17642" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 106, + 175, + 195 + ], + "blocks": [ + { + "bbox": [ + 48, + 106, + 175, + 195 + ], + "lines": [ + { + "bbox": [ + 48, + 106, + 175, + 195 + ], + "spans": [ + { + "bbox": [ + 48, + 106, + 175, + 195 + ], + "type": "image", + "image_path": "5548e25d074e71744d67fb72d13ef5f39e1ce4b33c55731bec8a3df69ee7c831.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 176, + 106, + 301, + 195 + ], + "blocks": [ + { + "bbox": [ + 176, + 106, + 301, + 195 + ], + "lines": [ + { + "bbox": [ + 176, + 106, + 301, + 195 + ], + "spans": [ + { + "bbox": [ + 176, + 106, + 301, + 195 + ], + "type": "image", + "image_path": "326df470ed4a8e9c69bc83ea969b5e4b92385116bc996deb9185123e8469c6aa.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 207, + 174, + 294 + ], + "blocks": [ + { + "bbox": [ + 170, + 197, + 181, + 207 + ], + "lines": [ + { + "bbox": [ + 170, + 197, + 181, + 207 + ], + "spans": [ + { + "bbox": [ + 170, + 197, + 181, + 207 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 207, + 174, + 294 + ], + "lines": [ + { + "bbox": [ + 49, + 207, + 174, + 294 + ], + "spans": [ + { + "bbox": [ + 49, + 207, + 174, + 294 + ], + "type": "image", + "image_path": "443333509d57fa346df5e14ecb11a57190e4e782d1869b60b288f298a9e57669.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 170, + 296, + 181, + 305 + ], + "lines": [ + { + "bbox": [ + 170, + 296, + 181, + 305 + ], + "spans": [ + { + "bbox": [ + 170, + 296, + 181, + 305 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 308, + 531, + 340 + ], + "lines": [ + { + "bbox": [ + 45, + 308, + 531, + 340 + ], + "spans": [ + { + "bbox": [ + 45, + 308, + 531, + 340 + ], + "type": "text", + "content": "Figure 1. Left: challenges of semantic scene completion, i.e., (a) sparse and incomplete input, varying completion difficulty for objects of diverse scales and (b) long traces of dynamic objects in completion labels. Traces of cars and persons are highlighted by yellow ellipses. Right: (c) performance comparison of various completion algorithms on SemanticKITTI semantic scene completion challenge." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 174, + 207, + 300, + 294 + ], + "blocks": [ + { + "bbox": [ + 174, + 207, + 300, + 294 + ], + "lines": [ + { + "bbox": [ + 174, + 207, + 300, + 294 + ], + "spans": [ + { + "bbox": [ + 174, + 207, + 300, + 294 + ], + "type": "image", + "image_path": "33e42b8253b5d7575d8e644d425e2c5371e6fe57d3a57334a009c83688e285ad.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 303, + 106, + 528, + 294 + ], + "blocks": [ + { + "bbox": [ + 303, + 106, + 528, + 294 + ], + "lines": [ + { + "bbox": [ + 303, + 106, + 528, + 294 + ], + "spans": [ + { + "bbox": [ + 303, + 106, + 528, + 294 + ], + "type": "image", + "image_path": "3d3fb28a18539c33a7b3339eb1c9ae4c99a6f16b80a1946c92b4f61107490234.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 295, + 433, + 304 + ], + "lines": [ + { + "bbox": [ + 422, + 295, + 433, + 304 + ], + "spans": [ + { + "bbox": [ + 422, + 295, + 433, + 304 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 344, + 279, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 344, + 279, + 459 + ], + "spans": [ + { + "bbox": [ + 45, + 344, + 279, + 459 + ], + "type": "text", + "content": "mimicking the probabilistic knowledge of each point/voxel brings marginal gains. Instead, we propose to distill the pairwise similarity information. Considering the sparsity and unorderness of features, we align the features using their indices and then force the consistency between the pairwise similarity maps of student features and those of teacher features, make the student benefit from the relational knowledge of the teacher. The resulting Dense-to-Sparse Knowledge Distillation objective is termed DSKD, which is specifically designed for the scene completion task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 461, + 279, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 461, + 279, + 553 + ], + "spans": [ + { + "bbox": [ + 45, + 461, + 279, + 553 + ], + "type": "text", + "content": "Finally, to address the long traces of those dynamic objects in the completion labels, we propose a simple yet effective label rectification strategy. The core idea is to use off-the-shelf panoptic segmentation labels to remove the traces of dynamic objects in completion labels. The rectified completion labels are more accurate and reliable, greatly improving the completion qualities of deep models on those moving objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "spans": [ + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "type": "text", + "content": "We conduct experiments on two large-scale outdoor scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge " + }, + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "type": "inline_equation", + "content": "{}^{1}" + }, + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "type": "text", + "content": " and outperforms the S3CNet [3] by " + }, + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "type": "inline_equation", + "content": "{7.2}\\mathrm{{mIoU}}" + }, + { + "bbox": [ + 45, + 554, + 279, + 669 + ], + "type": "text", + "content": " . SCPNet also achieves better performance than other completion algorithms on the SemanticPOSS dataset. The learned knowledge from the completion task also benefits the segmentation task, making our SCPNet achieve superior performance on the SemanticKITTI semantic segmentation task." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 57, + 671, + 236, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 671, + 236, + 681 + ], + "spans": [ + { + "bbox": [ + 57, + 671, + 236, + 681 + ], + "type": "text", + "content": "Our contributions are summarized as follows." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 57, + 690, + 278, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 690, + 278, + 701 + ], + "spans": [ + { + "bbox": [ + 57, + 690, + 278, + 701 + ], + "type": "text", + "content": "- The comprehensive redesign of the completion sub" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 315, + 345, + 529, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 345, + 529, + 367 + ], + "spans": [ + { + "bbox": [ + 315, + 345, + 529, + 367 + ], + "type": "text", + "content": "network. We unveil several key factors to building strong completion networks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 308, + 373, + 530, + 537 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 308, + 373, + 530, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 373, + 530, + 431 + ], + "spans": [ + { + "bbox": [ + 308, + 373, + 530, + 431 + ], + "type": "text", + "content": "- To cope with the sparsity and incompleteness of the input, we propose to distill the dense relation-based knowledge from the multi-frame model. Note that we are the first to apply knowledge distillation to the semantic scene completion task." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 308, + 438, + 529, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 438, + 529, + 473 + ], + "spans": [ + { + "bbox": [ + 308, + 438, + 529, + 473 + ], + "type": "text", + "content": "- To address the long traces of moving objects in completion labels, we present the completion label rectification strategy." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 308, + 479, + 529, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 479, + 529, + 537 + ], + "spans": [ + { + "bbox": [ + 308, + 479, + 529, + 537 + ], + "type": "text", + "content": "- Our SCPNet ranks 1st on SemanticKITTI semantic scene completion challenge, outperforming the previous SOTA S3CNet [3] by " + }, + { + "bbox": [ + 308, + 479, + 529, + 537 + ], + "type": "inline_equation", + "content": "7.2\\mathrm{mIoU}" + }, + { + "bbox": [ + 308, + 479, + 529, + 537 + ], + "type": "text", + "content": ". Competitive performance is also shown in SemanticPOSS completion task and SemanticKITTI semantic segmentation task." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 297, + 547, + 380, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 547, + 380, + 559 + ], + "spans": [ + { + "bbox": [ + 297, + 547, + 380, + 559 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 566, + 530, + 730 + ], + "type": "text", + "content": "Semantic scene completion. Early works on scene completion mainly concentrates on the indoor scenarios [5, 6, 15, 22]. The point cloud in indoor scenarios is dense, small-scale and has uniform density. By contrast, point cloud in outdoor scenes is sparse, large-scale and has varying density, which poses great challenges to the semantic scene completion algorithms [3,20,25,29,32]. Various algorithms have been proposed, for instance, LMSCNet [19] uses a mixture of 2D and 3D convolutions to build the efficient completion backbone. S3CNet [3] performs 2D and 3D scene completion simultaneously, and fuses the results by the proposed dynamic voxel fusion module. JS3C-Net [29] attaches the completion network to the segmentation backbone and refines the completion outputs via the point-voxel" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 709, + 278, + 728 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 709, + 278, + 728 + ], + "spans": [ + { + "bbox": [ + 46, + 709, + 278, + 728 + ], + "type": "text", + "content": "1https://codalab.lisn.upsaclay.fr/competitions/7170#results till 2022-11-12 00:00 Pacific Time, and our method is termed SCPNet." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "text", + "content": "17643" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 106, + 530, + 288 + ], + "blocks": [ + { + "bbox": [ + 48, + 106, + 530, + 288 + ], + "lines": [ + { + "bbox": [ + 48, + 106, + 530, + 288 + ], + "spans": [ + { + "bbox": [ + 48, + 106, + 530, + 288 + ], + "type": "image", + "image_path": "41557f97fbe5b3abd0c6b55b2979121df3e3a08f0aebbb9b9ccfb37d70a024d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 294, + 531, + 380 + ], + "lines": [ + { + "bbox": [ + 45, + 294, + 531, + 380 + ], + "spans": [ + { + "bbox": [ + 45, + 294, + 531, + 380 + ], + "type": "text", + "content": "Figure 2. Framework overview of SCPNet. There are two SCPNets, one is teacher and the other is student, and they have the same architecture. The teacher takes multi-frame point cloud as input while the student takes the single-frame point cloud as input. The dense-to-sparse knowledge distillation loss is proposed to transfer the dense semantic knowledge from teacher to student. In each SCPNet, there are two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The point cloud is first processed by a stack of MLPs to extract point features. These point features are voxelized and then fed to the completion sub-network to produce denser voxel features. The produced voxel features are further fed to the segmentation sub-network to generate the ultimate voxelwise output. For the completion sub-network, it is comprised of several multi-path blocks, free from the lossy downsampling operations. For the segmentation sub-network, it is adapted from the Cylinder3D network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 389, + 279, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 389, + 279, + 447 + ], + "spans": [ + { + "bbox": [ + 45, + 389, + 279, + 447 + ], + "type": "text", + "content": "interaction module. Compared with previous completion networks, our SCPNet is free from the lossy downsampling operations. Besides, our network is built on several MPBs that aggregate multi-scale features and can achieve high completion quality in objects of various sizes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 449, + 280, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 449, + 280, + 647 + ], + "spans": [ + { + "bbox": [ + 45, + 449, + 280, + 647 + ], + "type": "text", + "content": "Knowledge distillation. Knowledge distillation (KD) originates from the pioneering work of G. Hinton et al. [8]. Its primary objective is to transfer the dark knowledge from the large over-parameterized teacher model to the small compact student model. A large number of methods have been proposed and various forms of knowledge [21, 24, 27, 33] have been designed, e.g., intermediate features [11, 21], visual attention maps [10, 33], region-level affinity scores [9], similarity scores of different samples [24, 26], etc. It is noteworthy that the majority of the distillation methods concentrate on the 2D tasks. Only a few distillation methods have focused on 3D domains, e.g., PVKD [12] and SparseKD [31]. To our knowledge, this is the first work that applies knowledge distillation to the semantic scene completion task. We propose to transfer the dense, relation-based semantic knowledge from the multi-frame model to the single-frame one." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 661, + 126, + 676 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 661, + 126, + 676 + ], + "spans": [ + { + "bbox": [ + 45, + 661, + 126, + 676 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": "The objective of the semantic scene completion task is to infer the complete geometric and semantic layout given the incomplete and sparse input. Formally, given the input point cloud " + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 45, + 682, + 279, + 730 + ], + "type": "text", + "content": ", the network needs to assign a label to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "spans": [ + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": "each voxel of the " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "L\\times W\\times H" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": " voxel space to indicate whether it is empty or belongs to a specific class " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "c\\in \\{0,1,2,\\dots,C - 1\\}" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": " is the number of classes, " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": " are the length, width and height of the voxel space, respectively. We denote the voxelwise output as " + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{O}\\in \\mathbb{R}^{L\\times W\\times H\\times C}" + }, + { + "bbox": [ + 296, + 389, + 530, + 447 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 296, + 454, + 416, + 465 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 454, + 416, + 465 + ], + "spans": [ + { + "bbox": [ + 296, + 454, + 416, + 465 + ], + "type": "text", + "content": "3.1. Framework overview" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 296, + 472, + 530, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 472, + 530, + 600 + ], + "spans": [ + { + "bbox": [ + 296, + 472, + 530, + 600 + ], + "type": "text", + "content": "As shown in Fig. 2, our SCPNet is comprised of two sub-networks, i.e., the completion sub-network and the segmentation sub-network. The completion sub-network is designed based on several key design principles. The segmentation sub-network is built upon Cylinder3D [35, 36], with some minor modifications. In the following sections, we first detail the completion sub-network and introduce several design principles that are vital to building a strong completion sub-network. The knowledge distillation of multi-frame model and the completion label rectification will be explained thereafter." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 607, + 509, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 607, + 509, + 619 + ], + "spans": [ + { + "bbox": [ + 296, + 607, + 509, + 619 + ], + "type": "text", + "content": "3.2. Redesigning the Completion Sub-network" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 624, + 530, + 730 + ], + "type": "text", + "content": "Take JS3C-Net [29] as example. The original JS3C-Net first performs semantic segmentation and then conducts completion upon the segmentation features. Although this pipeline can benefit from the segmentation outputs, there are several drawbacks in this framework. First, the parameters in the completion sub-network are much fewer than the segmentation sub-network, thus yielding unsatisfactory completion performance. Second, there are downsampling and upsampling blocks in the completion sub-network. The" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "17644" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 104, + 278, + 225 + ], + "blocks": [ + { + "bbox": [ + 47, + 104, + 278, + 225 + ], + "lines": [ + { + "bbox": [ + 47, + 104, + 278, + 225 + ], + "spans": [ + { + "bbox": [ + 47, + 104, + 278, + 225 + ], + "type": "image", + "image_path": "762d5a6528c211475cce53132b2c13e3afcecfd392f53beb3ec7163a59c2ae96.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "lines": [ + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "spans": [ + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "text", + "content": "Figure 3. A schematic overview of the designed completion network. It is built upon the Multi-Path Blocks (MPBs) that contain " + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "inline_equation", + "content": "5 \\times 5 \\times 5" + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 45, + 229, + 279, + 283 + ], + "type": "text", + "content": " convolution blocks (ConvBlock). In each convolution block, there is no convolution bias and no batch normalization to maintain sparsity during completion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 298, + 279, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 298, + 279, + 334 + ], + "spans": [ + { + "bbox": [ + 45, + 298, + 279, + 334 + ], + "type": "text", + "content": "downsampling operations will inevitably lose the information of the original point cloud and the upsampling operation will cause over dilation and shape distortion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 334, + 279, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 334, + 279, + 392 + ], + "spans": [ + { + "bbox": [ + 45, + 334, + 279, + 392 + ], + "type": "text", + "content": "To address the aforementioned problems, we make a comprehensive overhaul of the completion sub-network. More concretely, there are three principles in the design of the completion sub-network, i.e., maintaining sparsity, no downsampling and aggregating multi-scale features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 392, + 279, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 392, + 279, + 554 + ], + "spans": [ + { + "bbox": [ + 45, + 392, + 279, + 554 + ], + "type": "text", + "content": "Maintain sparsity. The completion sub-network needs the vanilla dense convolution for dilation while the segmentation sub-network uses sparse convolution for efficient processing. However, the bias of the convolution weight, running mean and beta of BN layers will break the sparsity of the original voxel features, thus substantially increasing the computation burden of the segmentation sub-network. Therefore, to reduce the overall computation cost and enjoy the high efficiency of sparse convolution, we remove all the convolution bias and the BN layers in the completion subnetwork. In this condition, the voxel features produced by the completion sub-network can still keep the sparse property and the segmentation sub-network can use sparse convolution to process these sparse voxel features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 555, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 555, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 555, + 279, + 730 + ], + "type": "text", + "content": "No downsampling. In popular completion networks such as S3CNet [3] and JS3C-Net [29], there are several downsampling and upsampling blocks in the completion part. The downsampling operations will inevitably lose the information of the original point cloud, causing severe completion and classification errors for small objects and crowded scenes. Therefore, we discard all downsampling and upsampling operations to relieve the information loss, maximally retaining the information of the raw point cloud. Besides, as opposed to JS3C-Net which takes the segmentation-first baseline, we adopt the completion-first principle. Concretely, we make the completion sub-network directly process the raw voxel features produced by the voxelization process. And the completion sub-network can also benefit from the large number of parameters of the segmen" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 300, + 104, + 413, + 191 + ], + "blocks": [ + { + "bbox": [ + 300, + 104, + 413, + 191 + ], + "lines": [ + { + "bbox": [ + 300, + 104, + 413, + 191 + ], + "spans": [ + { + "bbox": [ + 300, + 104, + 413, + 191 + ], + "type": "image", + "image_path": "b7958eb1c53ed443c2cf23d491b4c7751bd52f6351dc7edd97db55cca82b3fe3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 296, + 196, + 530, + 239 + ], + "lines": [ + { + "bbox": [ + 296, + 196, + 530, + 239 + ], + "spans": [ + { + "bbox": [ + 296, + 196, + 530, + 239 + ], + "type": "text", + "content": "Figure 4. Comparison between single-frame and multi-frame point cloud. The multi-frame input is obviously denser than the single frame and the objects are easier to be identified, significantly reducing the completion difficulty." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 414, + 105, + 528, + 191 + ], + "blocks": [ + { + "bbox": [ + 414, + 105, + 528, + 191 + ], + "lines": [ + { + "bbox": [ + 414, + 105, + 528, + 191 + ], + "spans": [ + { + "bbox": [ + 414, + 105, + 528, + 191 + ], + "type": "image", + "image_path": "8bf4b0ae91c1d4bc2aae4a9dcbb94563698b99ac349f7f6766c479d8efaa4169.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 297, + 256, + 375, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 256, + 375, + 266 + ], + "spans": [ + { + "bbox": [ + 297, + 256, + 375, + 266 + ], + "type": "text", + "content": "tation sub-network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "spans": [ + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "content": "Aggregate multi-scale features. To aggregate multi-scale features, we design the multi-path block which is comprised of " + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "inline_equation", + "content": "5 \\times 5 \\times 5" + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "inline_equation", + "content": "7 \\times 7 \\times 7" + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "content": " convolution blocks. As shown in Fig. 3, there are three branches in the completion sub-network. The upper branch contains one MPB and the bottom branch is a residual connection. The middle branch is constructed by a " + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "content": " convolution block, two MPBs and a " + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 296, + 268, + 530, + 419 + ], + "type": "text", + "content": " convolution block. After the completion sub-network, we obtain the dense completed voxel features. We extract the non-empty voxel features as well as their voxel indices from the completed voxel features. The generated sparse voxel features are sent to the segmentation sub-network to produce the voxelwise segmentation output." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 421, + 530, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 421, + 530, + 513 + ], + "spans": [ + { + "bbox": [ + 296, + 421, + 530, + 513 + ], + "type": "text", + "content": "Modifications on the segmentation sub-network. Recall that, for the segmentation part, we take the Cylinder3D [36] as the backbone. Since the voxelwise completion labels are defined based on the cubic partition, we replace the cylindrical partition of Cylinder3D with conventional cubic partition. Besides, the original point refinement module consumes much GPU memory and brings limited gains, we discard this module to save memory usage." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 523, + 473, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 523, + 473, + 536 + ], + "spans": [ + { + "bbox": [ + 297, + 523, + 473, + 536 + ], + "type": "text", + "content": "3.3. Distilling Multi-frame Knowledge" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 542, + 530, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 542, + 530, + 693 + ], + "spans": [ + { + "bbox": [ + 296, + 542, + 530, + 693 + ], + "type": "text", + "content": "Since single frame point cloud is sparse and incomplete in the outdoor scenarios, directly performing semantic scene completion from the single-frame input is extremely difficult. It is natural to wonder if we can construct a multi-frame model and then distil the dense semantic knowledge from this multi-frame network. From Fig. 4, it is evident that the multi-frame input significantly reduces the completion difficulty since multiple frames have much more points in the scene and objects are easier to be identified. The completion difficulty will gradually decrease as the number of input point cloud frames increases. Therefore, we construct the multi-frame teacher which takes denser point cloud as input and achieves better completion performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 695, + 530, + 730 + ], + "type": "text", + "content": "Inspired by [12], we make the single-frame model distil the relation-based structural knowledge from the multiframe teacher network. Since the original voxel features" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "text", + "content": "17645" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 107, + 162, + 186 + ], + "blocks": [ + { + "bbox": [ + 50, + 107, + 162, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 107, + 162, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 107, + 162, + 186 + ], + "type": "image", + "image_path": "8d96145bce7cc6a06ad460ad4e87ed61c1e608c32793af3b90503c3d97068657.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 164, + 107, + 274, + 186 + ], + "blocks": [ + { + "bbox": [ + 164, + 107, + 274, + 186 + ], + "lines": [ + { + "bbox": [ + 164, + 107, + 274, + 186 + ], + "spans": [ + { + "bbox": [ + 164, + 107, + 274, + 186 + ], + "type": "image", + "image_path": "393ab21ecb691377ca7f94ade1563a807dac2588ebd7a4789f87aa89d61d35f6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 187, + 162, + 266 + ], + "blocks": [ + { + "bbox": [ + 49, + 187, + 162, + 266 + ], + "lines": [ + { + "bbox": [ + 49, + 187, + 162, + 266 + ], + "spans": [ + { + "bbox": [ + 49, + 187, + 162, + 266 + ], + "type": "image", + "image_path": "c2d6a95e0fc532b071eae4847e005c738d0a8d78a048f7c330cd13285cbe32bf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 270, + 279, + 325 + ], + "lines": [ + { + "bbox": [ + 45, + 270, + 279, + 325 + ], + "spans": [ + { + "bbox": [ + 45, + 270, + 279, + 325 + ], + "type": "text", + "content": "Figure 5. Top: original completion labels which have long traces of dynamic objects, e.g., car and person. Bottom: rectified completion labels. The proposed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 163, + 187, + 274, + 266 + ], + "blocks": [ + { + "bbox": [ + 163, + 187, + 274, + 266 + ], + "lines": [ + { + "bbox": [ + 163, + 187, + 274, + 266 + ], + "spans": [ + { + "bbox": [ + 163, + 187, + 274, + 266 + ], + "type": "image", + "image_path": "fb96fe933c0b6195eaed6a4859a8a2f383352eb40779a62dc61e4d2f17245ef3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "spans": [ + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": "are in the sparse form, we leverage the sparse features and their indices to perform knowledge distillation. We denote the voxel features and corresponding indices of the teacher and student as " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "F_{T} \\in \\mathbb{R}^{N_{m} \\times C_{f}}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "F_{S} \\in \\mathbb{R}^{N_{s} \\times C_{f}}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{T} \\in \\mathbb{R}^{N_{m} \\times 3}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{S} \\in \\mathbb{R}^{N_{s} \\times 3}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "N_{m}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": " is the number of non-empty voxel features in the multi-frame, " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "N_{s}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": " is the number of non-empty voxel features in the single-frame, " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "C_{f}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": " is the number of channels of the voxel features. Note that the indices of teacher features and student features are sorted and " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{I}_{S}(i,j) = \\mathcal{I}_{T}(i,j)" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "i \\in \\{1, \\dots, N_{s}\\}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "inline_equation", + "content": "j \\in \\{1, 2, 3\\}" + }, + { + "bbox": [ + 45, + 339, + 279, + 479 + ], + "type": "text", + "content": ". We first compute the pairwise relational knowledge of the student model:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 497, + 279, + 527 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 497, + 279, + 527 + ], + "spans": [ + { + "bbox": [ + 57, + 497, + 279, + 527 + ], + "type": "interline_equation", + "content": "\\mathbf {P} _ {S} (i, j) = \\frac {F _ {S} (i) ^ {\\top} F _ {S} (j)}{\\| F _ {S} (i) \\| _ {2} \\| F _ {S} (j) \\| _ {2}}, i, j \\in \\{1, \\dots , N _ {s} \\} \\quad (1)", + "image_path": "8d01bbdaab4bdcec7d56e236069443784cc88d945d4cb030e0578693f915f662.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 532, + 279, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 532, + 279, + 615 + ], + "spans": [ + { + "bbox": [ + 45, + 532, + 279, + 615 + ], + "type": "text", + "content": "The relational knowledge of the teacher model " + }, + { + "bbox": [ + 45, + 532, + 279, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_T" + }, + { + "bbox": [ + 45, + 532, + 279, + 615 + ], + "type": "text", + "content": " is calculated in a similar way. The relational knowledge captures the similarity of each pair of voxel features and serve as important clues of the surrounding environment, which can be taken as high-level knowledge to be learned by the single-frame student model. The proposed Dense-to-Sparse Knowledge Distillation (DSKD) loss is given as below:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 633, + 279, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 633, + 279, + 679 + ], + "spans": [ + { + "bbox": [ + 51, + 633, + 279, + 679 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {d s k d}} \\left(\\mathbf {P} _ {S}, \\mathbf {P} _ {T}\\right) = \\frac {1}{N _ {s} ^ {2}} \\sum_ {i = 1} ^ {N _ {s}} \\sum_ {j = 1} ^ {N _ {s}} \\left\\| \\mathbf {P} _ {S} (i, j) - \\mathbf {P} _ {T} (i, j) \\right\\| _ {2} ^ {2}. \\tag {2}", + "image_path": "95235b7afa4dbe2a82fc8af55b89258bd3c7f2646b71328103c4185f01f42e2c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 687, + 210, + 700 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 687, + 210, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 687, + 210, + 700 + ], + "type": "text", + "content": "3.4. Completion Label Rectification" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 706, + 279, + 730 + ], + "type": "text", + "content": "Generation of completion labels. As pointed out by [20], for outdoor semantic scene completion, the ground-truth" + } + ] + } + ], + "index": 10 + }, + { + "type": "code", + "bbox": [ + 298, + 123, + 530, + 354 + ], + "blocks": [ + { + "bbox": [ + 298, + 106, + 489, + 117 + ], + "lines": [ + { + "bbox": [ + 298, + 106, + 489, + 117 + ], + "spans": [ + { + "bbox": [ + 298, + 106, + 489, + 117 + ], + "type": "text", + "content": "Algorithm 1 Pseudocode of Label Rectification." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 298, + 123, + 530, + 354 + ], + "lines": [ + { + "bbox": [ + 298, + 123, + 530, + 354 + ], + "spans": [ + { + "bbox": [ + 298, + 123, + 530, + 354 + ], + "type": "text", + "content": "L_c: completion label (256x256x32) \n# L_s: semantic segmentation label (Nx1) \n# L_p: panoptic segmentation label (Nx1) \n# S_c: classes of moving objects; u: unlabeled class \nfor C_i in S_c: \n # voxel position of completion label for class C_i \n P_c_i = getInd(L_c, C_i) \n L_p_i = L_p[L_s == C_i] # instance label of class C_i \n P_dif = [] \n if len(L_p_i) == 0: \n P_dif = P_c_i \n elif len(L_p_i) > 0 and len(P_c_i) > 0: \n # mask of voxel position bound for instance d_j \n M_c = zeros([256, 256, 32]) \n # point position of class C_i \n P_i = P[L_s == C_i, :] \n # voxel position of class C_i \n P_s_i = voxelize(P_i) \n D_i = unique(L_p_i) # all instance ids \n for d_j in D_i: \n # voxel position for instance d_j \n M_j = P_s_i[L_p_i == d_j] \n (x_min, x_max, y_min, y_max, z_min, z_max) = bound(M_j) \n M_c[x_min: x_max, y_min: y_max, z_min: z_max] = 1000 \n # voxel position for instance label of class C_i \n P_p_i = getInd(M_c, 1000) \n P_dif = difference(P_c_i, P_p_i) \n if len(P_dif) > 0: \n for p_i in range(P_dif.shape[0]): \n L_c[P_dif[p_i, 0], P_dif[p_i, 1], P_dif[p_i, 2]] = u" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "code_body" + } + ], + "index": 12, + "sub_type": "algorithm" + }, + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "spans": [ + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "type": "text", + "content": "completion labels are obtained by concatenating the segmentation labels of multiple consecutive point cloud frames. Specifically, for the " + }, + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "type": "text", + "content": "-th frame, the corresponding completion labels " + }, + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "type": "inline_equation", + "content": "L_{t}^{c}" + }, + { + "bbox": [ + 296, + 388, + 530, + 436 + ], + "type": "text", + "content": " are constructed in the following way:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 452, + 530, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 530, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 530, + 477 + ], + "type": "interline_equation", + "content": "L _ {t} ^ {c} = \\operatorname {c o n c a t} \\left[ L _ {t} ^ {s}; T _ {t + 1 \\rightarrow t} L _ {t + 1} ^ {s}; \\dots ; T _ {t + T - 1 \\rightarrow t} L _ {t + T - 1} ^ {s} \\right], \\tag {3}", + "image_path": "667a0e5783f733a6653857f0d13c8a97daaa92f7aeebe3583632f6ef8163b7a8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "spans": [ + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "L_{t}^{s}" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": " are the segmentation labels for the " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": "-th frame, " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": " is the number of frames used for concatenation, " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "T_{t+1 \\to t}" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": " is the transformation matrix that transforms the coordinate from " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "(t+1)" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": "-th frame to the " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": "-th frame, and " + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "inline_equation", + "content": "\\mathrm{concat}[\\ldots; \\ldots]" + }, + { + "bbox": [ + 296, + 485, + 530, + 590 + ], + "type": "text", + "content": " is the concatenating operation. The concatenation of multiple frames will lead to long traces for those moving objects, such as car and person. A vivid example is shown in Fig. 5. The long traces of those dynamic objects are obviously irrational and will hamper the learning of deep models." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": "Completion label rectification. To remove the long traces of moving objects in the completion labels, we resort to the panoptic segmentation labels. Specifically, given the panoptic labels of class " + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": ", we first voxelize the labels and obtain the voxelwise panoptic labels for class " + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": ". For each instance of class " + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": ", we calculate the bound of each instance, forming a cube. We union the cubes of all instances and use them to process the original voxelwise completion labels, filtering those voxels that are outside the cubes. The process is repeated for all classes that contain dynamic objects. The detailed information of the label rectification algorithm is shown in Algorithm 1. As shown in Fig. 5, the pro" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "17646" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 46, + 128, + 531, + 253 + ], + "blocks": [ + { + "bbox": [ + 45, + 104, + 531, + 126 + ], + "lines": [ + { + "bbox": [ + 45, + 104, + 531, + 126 + ], + "spans": [ + { + "bbox": [ + 45, + 104, + 531, + 126 + ], + "type": "text", + "content": "Table 1. Quantitative results of semantic scene completion algorithms on SemanticKITTI test set. Note that the online server still uses the original completion labels to evaluate algorithms. Bold - best in column for all single-frame methods." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 46, + 128, + 531, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 128, + 531, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 128, + 531, + 253 + ], + "type": "table", + "html": "
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SSCNet-Full [22]16.150.024.30.50.81.24.30.30.30.051.227.130.86.434.519.935.318.229.013.16.7
ESSCNet [34]17.541.826.40.35.45.09.12.92.70.143.826.928.110.329.823.335.820.128.716.416.7
LMSCNet-SS [19]17.656.730.90.00.01.50.80.00.00.064.829.034.74.638.121.341.319.932.115.00.8
TDS [7]17.750.629.50.00.02.50.10.00.00.062.223.331.66.534.124.140.121.933.116.96.9
UDNet [37]19.559.433.90.80.43.84.40.50.30.362.028.235.19.139.524.440.923.232.318.813.1
Local-DIFs [18]22.757.734.83.62.44.44.82.51.10.067.940.142.911.440.429.042.226.539.121.317.5
SSA-SC [32]23.558.836.513.94.65.77.44.42.60.772.237.443.710.943.630.743.525.641.814.56.9
JS3C-Net [29]23.856.633.314.48.87.212.78.05.10.464.734.939.914.139.430.443.119.640.518.915.9
S3CNet [3]29.545.631.241.545.06.716.145.935.816.042.017.022.57.952.231.339.534.021.231.024.3
SCPNet (#frame=1)36.756.146.433.234.913.829.128.224.71.868.551.349.830.738.844.746.440.148.740.425.1
SCPNet (#frame=4)47.568.559.048.551.121.037.847.635.010.579.757.760.032.850.254.156.947.158.048.348.0
", + "image_path": "e39df793487dc2c4f41e6251d8f14160a6025bb3c43c63ed5efc407f8224f91a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 265, + 279, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 265, + 279, + 299 + ], + "spans": [ + { + "bbox": [ + 45, + 265, + 279, + 299 + ], + "type": "text", + "content": "posed label rectification operation can effectively remove the long traces of moving objects, making the completion labels more accurate." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 305, + 145, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 305, + 145, + 319 + ], + "spans": [ + { + "bbox": [ + 45, + 305, + 145, + 319 + ], + "type": "text", + "content": "3.5. Overall objective" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 324, + 279, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 324, + 279, + 358 + ], + "spans": [ + { + "bbox": [ + 45, + 324, + 279, + 358 + ], + "type": "text", + "content": "The overall loss function is comprised of three terms, i.e., the cross entropy loss, the lovasz-softmax loss [2] and the proposed distillation loss." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 101, + 378, + 279, + 391 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 378, + 279, + 391 + ], + "spans": [ + { + "bbox": [ + 101, + 378, + 279, + 391 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c e}} + \\alpha \\mathcal {L} _ {\\text {l o v a s z}} + \\beta \\mathcal {L} _ {\\mathrm {d s k d}}, \\tag {4}", + "image_path": "3fbf7577b8f7687faad68102586276e61a582b57d7fe4921e48b3db8e4a59663.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "spans": [ + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 45, + 399, + 279, + 421 + ], + "type": "text", + "content": " are the loss coefficients to balance the effect of each loss term." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 431, + 124, + 444 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 431, + 124, + 444 + ], + "spans": [ + { + "bbox": [ + 45, + 431, + 124, + 444 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 450, + 279, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 450, + 279, + 613 + ], + "spans": [ + { + "bbox": [ + 45, + 450, + 279, + 613 + ], + "type": "text", + "content": "Datasets. Following the practice of popular scene completion models [3, 29], we conduct experiments on two popular LiDAR semantic scene completion benchmarks, i.e., SemanticKITTI [1] and SemanticPOSS [16]. As to SemanticKITTI, it has 22 point cloud sequences. Sequences 00 to 10, 08 and 11 to 21 are used for training, validation and testing, respectively. 19 classes are chosen for training and evaluation after merging classes with distinct moving status and discarding classes with very few points. As for SemanticPOSS, it has 2, 988 frames and 11 classes are selected for evaluation. Although SemanticPOSS is smaller than SemanticKITTI in terms of dataset size, it is much more challenging since it contains a larger quantity of moving objects than SemanticKITTI, such as person and rider." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": "Evaluation metrics. Following [12, 36], we adopt the intersection-over-union (IoU) of each class and mIoU of all classes as the evaluation metric. The IoU of class " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " is calculated via: " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "IoU_{i} = \\frac{TP_{i}}{TP_{i} + FP_{i} + FN_{i}}" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "TP_{i}" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "FP_{i}" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "FN_{i}" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": " denote the true positive, false positive and false negative of class " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": ", respectively. For semantic scene completion, the dimension of the completion label is " + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 32" + }, + { + "bbox": [ + 45, + 613, + 279, + 730 + ], + "type": "text", + "content": ". We also report the completion mIoU which is the class-agnostic version of mIoU. Note that mIoU is the major evaluation metric for the semantic scene completion task." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "spans": [ + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "text", + "content": "Implementation details. The output size of Cylinder3D is set as " + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 32" + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "text", + "content": " to adapt to the completion task. The number of training epochs is set as 30 and the initial learning rate is set as 0.0015. We use Adam [14] as the optimizer. Gradient norm clip is set 10 to stabilize the training process. " + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 296, + 265, + 530, + 392 + ], + "type": "text", + "content": " are set as 1 and 3, 000, respectively. We filter points that are outside the point cloud range of the voxelwise completion labels. For SemanticKITTI, we first train the model on the training set and then finetune it on both training and validation sets before submitting the predictions of test set to the online server." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 296, + 394, + 530, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 394, + 530, + 559 + ], + "spans": [ + { + "bbox": [ + 296, + 394, + 530, + 559 + ], + "type": "text", + "content": "Baseline KD algorithms. We take the vanilla knowledge distillation [8], FitNets [21], NST [13], PKT [17] and PVKD [12] as baseline distillation algorithms. Vanilla knowledge distillation takes the softened logits as the distilled knowledge. FitNets directly mimics the teacher features. NST adopts the maximum mean discrepancy to minimize the distance between student features and teacher features. PKT models the teacher knowledge as a probability distribution and then forces the consistency of the probability distribution between the teacher and the student. PVKD distils the voxelwise output and inter-voxel affinity knowledge. And we discard the original pointwise output distillation and inter-point affinity distillation of PVKD since they consume much GPU memory and bring marginal gains." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 297, + 570, + 352, + 581 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 570, + 352, + 581 + ], + "spans": [ + { + "bbox": [ + 297, + 570, + 352, + 581 + ], + "type": "text", + "content": "4.1. Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 590, + 530, + 730 + ], + "type": "text", + "content": "Quantitative results. We summarize the performance of SCPNet and state-of-the-art semantic scene completion methods in Table 1 and 2. On SemanticKITTI, our SCPNet significantly outperforms other scene completion algorithms in terms of mIoU. For example, our SCPNet is 7.2 mIoU higher than S3CNet [3]. On classes such as car, other-vehicle, road, parking, sidewalk, dense, terrain and other-ground, the performance gap between SCPNet and S3CNet is more than 10 IoU. Our SCPNet also achieves superior performance on SemanticPOSS val set. On classes such as car, trunk, pole, fence and bike, SCPNet is at least 5 IoU higher than JS3C-Net [29]. The impressive performance on" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 300, + 756 + ], + "type": "text", + "content": "17647" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 46, + 128, + 531, + 248 + ], + "blocks": [ + { + "bbox": [ + 45, + 104, + 531, + 127 + ], + "lines": [ + { + "bbox": [ + 45, + 104, + 531, + 127 + ], + "spans": [ + { + "bbox": [ + 45, + 104, + 531, + 127 + ], + "type": "text", + "content": "Table 2. Quantitative results of semantic scene completion algorithms on SemanticPOSS val set. Note that the completion labels are processed by the proposed rectification algorithm. Bold - best in column for all single-frame methods." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 46, + 128, + 531, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 128, + 531, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 128, + 531, + 248 + ], + "type": "table", + "html": "
MethodsmIoUcompletionpersonridercartrunkplantstraffic-signpolebuildingfencebikeground
SSCNet-Full [22]15.253.55.30.31.35.639.61.02.628.73.426.043.1
LMSCNet-SS [19]16.552.37.70.30.64.037.71.98.236.813.825.845.1
MotionSC [25]17.652.77.80.50.53.939.82.28.539.213.130.847.0
JS3C-Net [29]22.758.118.90.27.13.647.82.20.046.326.643.453.2
SCPNet (#frame=1)26.356.39.23.312.411.049.63.111.150.140.848.749.8
SCPNet (#frame=4)33.660.721.45.034.58.955.37.831.050.347.955.152.3
", + "image_path": "cf6f8acd8728aad0c778ed6dd15483f31bc09c2d851e06dd3e1d0311f48db063.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 46, + 275, + 531, + 377 + ], + "blocks": [ + { + "bbox": [ + 45, + 250, + 530, + 272 + ], + "lines": [ + { + "bbox": [ + 45, + 250, + 530, + 272 + ], + "spans": [ + { + "bbox": [ + 45, + 250, + 530, + 272 + ], + "type": "text", + "content": "Table 3. Quantitative results of our SCPNet and state-of-the-art LiDAR semantic segmentation methods on SemanticKITTI test set. C3D + SCPNet denotes Cylinder3D initialized from the trained weight of SCPNet. Bold - best in column." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 46, + 275, + 531, + 377 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 531, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 531, + 377 + ], + "type": "table", + "html": "
MethodsmIoULatency (ms)carbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic
SPVNAS [23]66.425997.351.550.859.858.865.765.243.790.267.675.216.991.365.986.173.471.064.266.9
AF2S3Net [4]69.7-94.565.486.839.241.180.780.474.391.368.872.553.587.963.270.268.553.761.571.0
RPVNet [28]70.3-97.668.468.744.261.175.974.473.493.470.380.733.393.572.186.575.171.764.861.4
PVKD [12]71.27697.067.969.353.560.275.173.550.591.870.977.541.092.469.486.573.871.964.965.8
2DPASS [30]72.9-97.063.663.461.161.577.981.374.189.767.474.740.093.572.986.273.971.065.070.4
Cylinder3D [36]68.917097.167.663.850.858.573.769.248.092.265.077.032.390.766.585.672.569.862.466.2
C3D + SCPNet71.597.560.956.358.665.970.771.858.793.672.180.936.293.372.186.274.171.666.771.8
", + "image_path": "6d35ce77e01d3c5e82d40a79e2250a218b880ad5ef0b0cbc25119f91ebc0f4dd.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 98, + 412, + 224, + 511 + ], + "blocks": [ + { + "bbox": [ + 45, + 385, + 279, + 407 + ], + "lines": [ + { + "bbox": [ + 45, + 385, + 279, + 407 + ], + "spans": [ + { + "bbox": [ + 45, + 385, + 279, + 407 + ], + "type": "text", + "content": "Table 4. Comparison between different knowledge distillation algorithms and the proposed DSKD on the SemanticKITTI val set." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 98, + 412, + 224, + 511 + ], + "lines": [ + { + "bbox": [ + 98, + 412, + 224, + 511 + ], + "spans": [ + { + "bbox": [ + 98, + 412, + 224, + 511 + ], + "type": "table", + "html": "
MethodsmIoU
SCPNet w/o DSKD34.4
+ KD [8]33.8
+ FitNets [21]33.8
+ PKT [17]34.6
+ PVKD [12]36.2
+ NST [13]36.3
+ DSKD37.2
", + "image_path": "95b52d0bbf284132fd52d8df933af26223d903e59a8d0a28f0ca3f83d17dd46f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 526, + 279, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 526, + 279, + 549 + ], + "spans": [ + { + "bbox": [ + 45, + 526, + 279, + 549 + ], + "type": "text", + "content": "two large-scale benchmarks strongly demonstrate the superiority of our SCPNet." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 552, + 279, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 552, + 279, + 668 + ], + "spans": [ + { + "bbox": [ + 45, + 552, + 279, + 668 + ], + "type": "text", + "content": "Besides, we use the trained weight of the segmentation sub-network as initialization to train Cylinder3D on the SemanticKITTI semantic segmentation task. From Table 3, Cylinder3D initialized from trained weight of the completion task outperforms the original Cylinder3D model by 2.6 mIoU, and achieves impressive segmentation performance among various competitive LiDAR segmentation models such as 2DPASS [30], PVKD [12] and RPVNet [28]. The encouraging results show that knowledge learned in the completion task is also beneficial to the segmentation task." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "Comparison with baseline KD algorithms. From Table 4, it is evident that the proposed DSKD method can bring more gains than conventional knowledge distillation algorithms. For instance, compared with FitNets [21] which directly mimics the teacher features, our DSKD can bring more than" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 296, + 387, + 530, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 387, + 530, + 445 + ], + "spans": [ + { + "bbox": [ + 296, + 387, + 530, + 445 + ], + "type": "text", + "content": "2 mIoU, showing the effectiveness of the proposed relation-based distillation algorithm. The vanilla KD objective and FitNets hamper the performance of the base model, indicating that directly mimicking the logits or features can not boost the completion performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 296, + 446, + 531, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 446, + 531, + 563 + ], + "spans": [ + { + "bbox": [ + 296, + 446, + 531, + 563 + ], + "type": "text", + "content": "Qualitative results. We also provide visual comparison between JS3C-Net [29], SCPNet (single-frame) and SCPNet (multi-frame). As can be seen from Fig. 6, our SCPNet (single-frame) make more accurate completion predictions than JS3C-Net on road and vegetation. On long, thin objects such as poles, our single-frame model also yields high-quality completion results compared with JS3C-Net. The predictions of our single-frame model also resemble those of the multi-frame network, demonstrating the efficacy of the proposed DSKD algorithm." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 297, + 570, + 393, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 570, + 393, + 582 + ], + "spans": [ + { + "bbox": [ + 297, + 570, + 393, + 582 + ], + "type": "text", + "content": "4.2. Ablation studies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 589, + 521, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 589, + 521, + 600 + ], + "spans": [ + { + "bbox": [ + 308, + 589, + 521, + 600 + ], + "type": "text", + "content": "Experiments are conducted in SemanticKITTI val set." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 601, + 530, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 601, + 530, + 717 + ], + "spans": [ + { + "bbox": [ + 296, + 601, + 530, + 717 + ], + "type": "text", + "content": "Effect of completion label rectification. We report the performance of our SCPNet on completion labels with and without rectification. From Table 5, it is evident that the proposed rectification strategy greatly enhances the performance of SCPNet on those dynamic objects, e.g., car and person. For example, the completion label rectification can bring 8.1, 24.5, 26.1 and 17.6 IoU improvement on car, person, bicyclist and motorcyclist, respectively. The impressive performance gains strongly demonstrate the effectiveness of the label rectification algorithm." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 718, + 530, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 718, + 530, + 730 + ], + "spans": [ + { + "bbox": [ + 297, + 718, + 530, + 730 + ], + "type": "text", + "content": "Effect of the completion sub-network. To examine the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "17648" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 104, + 530, + 311 + ], + "blocks": [ + { + "bbox": [ + 48, + 104, + 530, + 311 + ], + "lines": [ + { + "bbox": [ + 48, + 104, + 530, + 311 + ], + "spans": [ + { + "bbox": [ + 48, + 104, + 530, + 311 + ], + "type": "image", + "image_path": "565012982eacdd839c5fecb4765e7abfc657baa4dc7e0cd34a649ecbf21b7d87.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 316, + 531, + 339 + ], + "lines": [ + { + "bbox": [ + 45, + 316, + 531, + 339 + ], + "spans": [ + { + "bbox": [ + 45, + 316, + 531, + 339 + ], + "type": "text", + "content": "Figure 6. Visual comparison of different methods on the SemanticKITTI validation set. From left to right: predictions of JS3C-Net [29], SCPNet (single frame), SCPNet (multi-frame) and ground-truth. Regions that have large prediction errors are highlighted by red ellipses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 357, + 531, + 413 + ], + "blocks": [ + { + "bbox": [ + 166, + 344, + 411, + 355 + ], + "lines": [ + { + "bbox": [ + 166, + 344, + 411, + 355 + ], + "spans": [ + { + "bbox": [ + 166, + 344, + 411, + 355 + ], + "type": "text", + "content": "Table 5. Impact of completion label rectification on the performance." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 357, + 531, + 413 + ], + "lines": [ + { + "bbox": [ + 47, + 357, + 531, + 413 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 531, + 413 + ], + "type": "table", + "html": "
MethodsmIoUcompletioncarbicyclemotorcycletruckother-vehiclepersonbicyclistmotorcyclistroadparkingsidewalkother-groundbuildingfencevegetationtrunkterrainpoletraffic-sign
SCPNet37.249.950.528.531.758.441.419.419.90.270.560.952.020.234.133.035.333.751.938.327.5
SCPNet + label rectification40.852.158.627.034.754.241.943.946.017.870.660.253.17.733.932.241.932.052.438.728.9
", + "image_path": "353206b6dc0738681135a2fd60bd4a9b1883bb17a8a9f641f6789084a142c8a1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 79, + 460, + 247, + 498 + ], + "blocks": [ + { + "bbox": [ + 45, + 426, + 279, + 448 + ], + "lines": [ + { + "bbox": [ + 45, + 426, + 279, + 448 + ], + "spans": [ + { + "bbox": [ + 45, + 426, + 279, + 448 + ], + "type": "text", + "content": "Table 6. Impact of the completion sub-network, DSKD and down-sampling operation on the performance." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 117, + 450, + 208, + 459 + ], + "lines": [ + { + "bbox": [ + 117, + 450, + 208, + 459 + ], + "spans": [ + { + "bbox": [ + 117, + 450, + 208, + 459 + ], + "type": "text", + "content": "(a) Completion sub-network" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 79, + 460, + 247, + 498 + ], + "lines": [ + { + "bbox": [ + 79, + 460, + 247, + 498 + ], + "spans": [ + { + "bbox": [ + 79, + 460, + 247, + 498 + ], + "type": "table", + "html": "
mIoU
JS3C-Net [29]24.0
JS3C-Net + completion-subnet30.8
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mIoU
SCPNet w/o DSKD34.4
SCPNet w/ DSKD37.2
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mIoU
SCPNet w/o downsampling37.2
SCPNet w/ downsampling33.1
", + "image_path": "6116978dc596a03adc70e47d56e9cf14cf008273fe74ef4cf61d175908c2b218.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 611, + 279, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 611, + 279, + 670 + ], + "spans": [ + { + "bbox": [ + 45, + 611, + 279, + 670 + ], + "type": "text", + "content": "effect of our completion sub-network, we add it to JS3C-Net. The detailed performance is shown in Table 6 (a). Our completion sub-network can bring " + }, + { + "bbox": [ + 45, + 611, + 279, + 670 + ], + "type": "inline_equation", + "content": "6.8\\mathrm{mIoU}" + }, + { + "bbox": [ + 45, + 611, + 279, + 670 + ], + "type": "text", + "content": " improvement to JS3C-Net, which strongly demonstrates the effectiveness and generalization of the proposed completion sub-network." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "spans": [ + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": "Effect of DSKD. We compare the performance of our SCPNet with and without the proposed DSKD in Table 6 (b). The proposed distillation method can bring " + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "inline_equation", + "content": "2.8\\mathrm{mIoU}" + }, + { + "bbox": [ + 45, + 671, + 279, + 730 + ], + "type": "text", + "content": " improvement to our SCPNet, showing the benefit of distilling relation-based knowledge from the multi-frame model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "spans": [ + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "type": "text", + "content": "Effect of the downsampling operation. We add the downsampling operation to our completion sub-network and examine its effect. As reported in Table 6 (c), the downsampling operation hampers the completion performance of our SCPNet. Specifically, the completion performance of SCPNet decreases from " + }, + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "type": "inline_equation", + "content": "37.2\\mathrm{mIoU}" + }, + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "type": "inline_equation", + "content": "33.1\\mathrm{mIoU}" + }, + { + "bbox": [ + 296, + 427, + 531, + 522 + ], + "type": "text", + "content": ". The negative results show that the no-downsampling principle is vital to the success of the completion sub-network redesign." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 548, + 368, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 548, + 368, + 559 + ], + "spans": [ + { + "bbox": [ + 297, + 548, + 368, + 559 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 296, + 573, + 530, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 573, + 530, + 678 + ], + "spans": [ + { + "bbox": [ + 296, + 573, + 530, + 678 + ], + "type": "text", + "content": "To address the challenges of the semantic scene completion task, we propose three solutions from the aspects of the completion network redesign, dense-to-sparse knowledge distillation as well as completion label rectification. The resulting completion network, termed SCPNet, achieves superior completion performance in two large-scale semantic scene completion benchmarks, i.e., SemanticKITTI and SemanticPOSS. The learned knowledge on the completion task is also beneficial to the semantic segmentation task." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "spans": [ + { + "bbox": [ + 296, + 682, + 531, + 730 + ], + "type": "text", + "content": "Acknowledgements. This work is partially supported by the National Key R&D Program of China (No. 2022ZD0160100), and in part by Shanghai Committee of Science and Technology (Grant No. 21DZ1100100)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 746, + 301, + 756 + ], + "type": "text", + "content": "17649" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "spans": [ + { + "bbox": [ + 47, + 105, + 103, + 117 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 124, + 280, + 729 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 51, + 124, + 279, + 177 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 124, + 279, + 177 + ], + "spans": [ + { + "bbox": [ + 51, + 124, + 279, + 177 + ], + "type": "text", + "content": "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. 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IEEE, 2021. 6" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 277, + 747, + 299, + 756 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 277, + 747, + 299, + 756 + ], + "spans": [ + { + "bbox": [ + 277, + 747, + 299, + 756 + ], + "type": "text", + "content": "17651" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 595, + 842 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_content_list.json b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b1160003380c129bb5a9b68148e855d61d4045d9 --- /dev/null +++ b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_content_list.json @@ -0,0 +1,1839 @@ +[ + { + "type": "text", + "text": "SCoDA: Domain Adaptive Shape Completion for Real Scans", + "text_level": 1, + "bbox": [ + 179, + 130, + 789, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yushuang Wu $^{1,2,3}$ Zizheng Yan $^{1,2,3}$ Ce Chen $^{1,2}$ Lai Wei $^{4}$ Xiao Li $^{5}$", + "bbox": [ + 197, + 179, + 769, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Guanbin Li $^{6,7}$ Yihao Li $^{1,2}$ Shuguang Cui $^{2,1}$ Xiaoguang Han $^{2,1\\#}$", + "bbox": [ + 214, + 198, + 753, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ FNii, CUHKSZ $^{2}$ SSE, CUHKSZ $^{3}$ SRIBD $^{4}$ SDS, CUHKSZ $^{5}$ Microsoft Research Asia $^{6}$ Sun Yat-sen University $^{7}$ Research Institute, Sun Yat-sen University, Shenzhen", + "bbox": [ + 114, + 215, + 854, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{yushuangwu, zizhengyan, cechen, laiwei1}@link.cuhk.edu.cn luoheliyihao@mail.ustc.edu.cn {shuguangcui, hanxiaoguang}@cuhk.edu.cn liguanbin@mail.sysu.edu.cn li.xiao@microsoft.com", + "bbox": [ + 91, + 253, + 875, + 286 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/359178af258d434aa2849ed22bbd12ac7961ad3ac768de275af832fa9c6aab89.jpg", + "image_caption": [ + "Figure 1. The proposed task SCoDA aims to transfer the knowledge in the synthetic domain to the reconstruction of noisy and incomplete real scans. A dataset, ScanSalon, with paired real scans and 3D models is contributed. Project page: yushuang-wu.github.io/SCoDA." + ], + "image_footnote": [], + "bbox": [ + 140, + 297, + 831, + 488 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 534, + 313, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D shape completion from point clouds is a challenging task, especially from scans of real-world objects. Considering the paucity of 3D shape ground truths for real scans, existing works mainly focus on benchmarking this task on synthetic data, e.g. 3D computer-aided design models. However, the domain gap between synthetic and real data limits the generalizability of these methods. Thus, we propose a new task, SCoDA, for the domain adaptation of real scan shape completion from synthetic data. A new dataset, ScanSalon, is contributed with a bunch of elaborate 3D models created by skillful artists according to scans. To address this new task, we propose a novel cross-domain feature fusion method for knowledge transfer and a novel volume-consistent self-training framework for robust learning from real data. Extensive experiments prove our method is effective to bring an improvement of $6\\% \\sim 7\\%$ mIoU.", + "bbox": [ + 75, + 566, + 473, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 843, + 207, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shape completion and reconstruction from scans is a practical 3D digitization task that is of great significance", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in applications of virtual and augmented reality. It takes a scanned point cloud as input and aims to recover the 3D shape of the target object. The completion of real scans is challenging for the poor quality of point clouds and the deficiency of 3D shape ground truths. Existing methods exploit synthetic data, e.g. 3D computer-aided design (CAD) models to alleviate the demand for real object shapes. For example, authors of [18, 26, 35] simulate the scanning process to obtain point clouds from CAD models with paired ground truth shapes to train learning-based reconstruction models. However, there still exist distinctions between the simulated and real scan because the latter is scanned from a real object with complex scanning noise and occlusion, which limits the generalization quality.", + "bbox": [ + 496, + 535, + 892, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Considering the underexploration in this field, we propose a new task, SCoDA, Domain Adaptive Shape Completion, that aims to transfer the knowledge from the synthetic domain with rich clean shapes (source domain) into the shape completion of real scans (target domain), as illustrated in Fig. 1. To this end, we, for the first time, build an object-centric dataset, ScanSalon, which consists of real Scans with Shape manual annotations. Our ScanSalon contains a bunch of 3D models that are paired with real scans of objects in six categories: chair, desk/table, sofa, bed, lamp,", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17630", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and car. The 3D models are manually created of high quality by skillful artists for around $10\\%$ of real scans, which can serve as the evaluation ground truths of shape completion or as the few labels for semi-supervised domain adaptation. See Fig. 1 for some examples, and details of ScanSalon are exposed in Sec. 4.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main challenge of the proposed SCoDA task lies in the domain gap between synthetic and real point clouds. Due to the intrinsic complexity of the scanning process, e.g., the scanner parameters and object materials, it is difficult to simulate the scans in terms of sparsity, noisy extent, etc. More importantly, real scans are usually incomplete resulting from the scene layout and object occlusion during scanning, which can hardly be simulated. Thus, we propose a novel domain adaptive shape completion approach to transfer the rich knowledge from the synthetic domain to the real one. At first, the reconstruction module in our approach is based on an implicit function for continuous shape completion [18, 54, 58]. For an effective transfer, we observe that although the local patterns of real scans (e.g., noise, sparsity, and incompleteness) are distinct from the simulated synthetic ones, the global topology or structure in a same category is usually similar between the synthetic and real data, for example, a chair from either the synthetic or real domain usually consists of a seat, a backrest, legs, etc. (see Fig. 1). In other words, the global topology is more likely to be domain invariant, while the local patterns are more likely to be domain specific. Accordingly, we propose a cross-domain feature fusion (CDFF) module to combine the global features and local features learned in the synthetic and real domain, respectively, which helps recover both fine details and global structures in the implicit reconstruction stage. Moreover, a novel volume-consistent selftraining (VCST) framework is developed to encourage self-supervised learning from the target data. Specifically, we create two views of real scans by dropping different clusters of points to produce incompleteness of different extent, and the model is forced to make consistent implicit predictions at each spatial volume, which encourages the model's robustness to the incompleteness of real scans.", + "bbox": [ + 75, + 181, + 472, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To construct a benchmark on the proposed new task, we implement some existing solutions to related tasks as baselines, and develop extensive experiments for the baselines and our method on ScanSalon. These experiments also demonstrate the effectiveness of the proposed method.", + "bbox": [ + 75, + 696, + 468, + 772 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our key contributions are four-fold:", + "bbox": [ + 96, + 776, + 416, + 791 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a new task, SCoDA, namely domain adaptive shape completion for real scans; A dataset ScanSalon that contains 800 elaborate 3D models paired with real scans in 6 categories is contributed.", + "- A novel cross-domain feature fusion module is designed to combine the knowledge of global shapes and local patterns learned in the synthetic and real domain," + ], + "bbox": [ + 94, + 794, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "respectively. Such a feature fusion manner may also inspire the works in the 2D domain adaption field.", + "bbox": [ + 529, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A volume-consistent self-training framework is proposed to improve the robustness of shape completion to the complex incompleteness of real scans.", + "- A benchmark with multiple methods evaluated is constructed for the task of SCoDA based on ScanSalon; Extensive experiments also demonstrate the superiority of the proposed method." + ], + "bbox": [ + 517, + 121, + 890, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 246, + 640, + 263 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Shape Completion Shape completion or reconstruction from point clouds is a branch of 3D reconstruction task [20, 47, 54, 68, 72, 91, 94]. The recovered shape can be represented as dense points [45, 46, 60] (i.e., point cloud completion or consolidation), polygonal meshes [28, 35, 48, 78], manifold atlases [4, 25, 27, 32, 83], voxel grids [20, 34, 85], or implicit representations [18, 26, 40, 61, 70, 82]. Among them, the task of point cloud completion is related to our work, which aims to recover a complete, dense, and clean point cloud for the 3D shape, from a partial, sparse, and noisy input scanned by sensors. The pioneering work, PCN [99], proposes a coarse-to-fine completion framework with an encoder-decoder architecture, which encodes the partial points into global features and recovers the fined results in the decoding stage. The following works explore further to better exploit local or multi-scale features for higher-quality completion [38, 49, 57, 73, 76, 77, 80, 81, 89, 92, 95, 98, 99, 101]. In addition, the implicit representation based approaches now attract increasing attention because of its superior property that enables continuous shape recovery for objects with arbitrary topologies [17, 18, 54, 58]. Although numerous efforts have been contributed, the existing approaches are usually performed on point clouds scanned from synthetic data via simulation, and a straightforward application on real scans results in an unsatisfactory performance due to the domain gap between synthetic and real scans [18, 26, 64]. For the task of point completion, some works also adopt unsupervised or weakly-supervised learning techniques to learn from unlabeled data [8, 14, 33, 79, 86, 87, 100]. Another line of works retrieve suitable models from 3D CAD repositories and deform them as the estimated shape ground truths of object scans [3, 75]. Differently, our work first proposes the task of domain adaptive shape completion for real scans, which aims to sufficiently transfer the knowledge from the label-rich synthetic domain into real scan shape completion.", + "bbox": [ + 496, + 276, + 890, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2D Domain Adaptation Domain adaptation has been a popular research topic in various 2D vision tasks, including image recognition [5, 11, 15, 22, 24, 29, 50, 67], semantic segmentation [16, 36, 52, 53], and object detection [12, 42, 55, 65]. Existing works can broadly be categorized as (i)", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17631", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "adversarial-based methods [12, 13, 15, 16, 22, 67] that train a discriminator to discriminate the source and the target domain, (ii) alignment-based methods [11, 24, 29, 65, 78] that use pre-defined metrics to align the source and the target domain, and (iii) self-training-based methods [5, 36, 52, 53, 55] that exploit the pseudo labels of the target domain to train the model. Recently, consistency-based self-training methods have become the most popular approach due to their impressive performance. One key factor in the success of consistency training is the augmentations applied to the inputs [31, 71, 93], e.g., stronger augmentations have better performance in domain adaptive image recognition [5]. To this end, we design a novel consistency training framework specialized for the shape completion task. Furthermore, we propose to conduct knowledge transfer via a cross-domain feature fusion manner, which has not been explored by existing works, to our best knowledge.", + "bbox": [ + 75, + 90, + 472, + 348 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Domain Adaptation In the 3D vision field, existing works on domain adaptation are mainly committed to the task of point cloud understanding, including classification, part segmentation, and semantic segmentation. For object-centric point clouds, PointDAN [63] constructs a domain adaptive classification benchmark by collecting point clouds from ShapeNet [10], ModelNet [88], and ScanNet [23] datasets to compose 3 different domains. It also proposes an adversarial representation learning approach with feature alignment at both local and global levels. The following works improve the classification precision by adopting techniques of consistency training [44], self-training [9, 103], multimodal learning [2], or learning from self-supervised tasks [1, 37, 51, 69]. Another line of works are committed to scene-centric point cloud analysis, i.e., point cloud semantic segmentation [6, 7, 39, 41, 59, 66, 84, 90, 96, 102]. Considering the exhaustive annotation process for 3D point semantics, they propose to transfer the segmentation knowledge in synthetic scenes into real-world point clouds [41, 84, 90, 102]. Besides, there are a few attempts contributed to domain adaptive single-view reconstruction (SVR) [43, 62, 97], which is highly related to our work. Except for the difference in tasks (SVR v.s. shape completion), these works usually apply existing domain adaptation techniques to the target task, while we propose a novel domain adaptation method based on cross-domain feature fusion, which may also inspire others working on domain adaption.", + "bbox": [ + 75, + 349, + 472, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 768, + 169, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "IF-Nets are a promising reconstruction method for their impressive performance [18], which is also successfully used in many applications [19, 56]. Constructed on IF-Nets, our approach first improves the representation learning by proposing a novel cross-domain feature fusion module, which aims to transfer the knowledge on the global-level object shape learned in the label-rich synthetic domain into", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the real domain. Secondly, to exhaust the domain-specific information in the real data, a novel volume-consistent self-training method is proposed for the specific shape completion task, which also leads to a robust implicit prediction of IF-Nets. An illustration is presented in Fig. 2.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Implicit Feature Networks", + "text_level": 1, + "bbox": [ + 498, + 176, + 741, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce IF-Nets [18] as our reconstruction framework. An IF-Net is composed of a 3D convolution neural network encoder $g(\\cdot)$ for multi-scale feature extraction and a multi-layer perceptron (MLP) $f(\\cdot)$ for implicit shape decoding.", + "bbox": [ + 496, + 199, + 893, + 275 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a point cloud sample $P$ , it is first converted into a discrete voxel representation $\\mathbf{X} \\in \\mathbb{R}^{N \\times N \\times N}$ , where $N \\in \\mathbb{N}$ is the resolution of the input space. $\\mathbf{X}$ is then fed into the $L$ -layer encoder $g(\\cdot)$ to generate a set of multiscale features $\\{\\mathbf{F}_1, \\dots, \\mathbf{F}_L\\}$ , then they are upsampled to the same spatial dimension and been concatenated along the channel dimension to create the final feature $\\mathbf{F} =$ concat( $\\{\\mathrm{upsample}(\\mathbf{F}_1), \\dots, \\mathrm{upsample}(\\mathbf{F}_L)\\}$ ). Formally:", + "bbox": [ + 496, + 276, + 893, + 398 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ng (\\mathbf {X}) = \\mathbf {F}, \\quad \\mathbf {X} \\in \\mathbb {R} ^ {N \\times N \\times N}, \\mathbf {F} \\in \\mathbb {R} ^ {d \\times N \\times N \\times N},\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 407, + 864, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $d$ is the feature channel number that equals the summation of the channel numbers of $\\mathbf{F}_i$ . Note that $\\mathbf{F}$ has a 3D structure aligned with the input $\\mathbf{X}$ . Given a point query $\\mathbf{p} \\in \\mathbb{R}^3$ , continuous features $\\mathbf{F}(\\mathbf{p})$ at this point can be extracted from $\\mathbf{F}$ using trilinear interpolation.", + "bbox": [ + 496, + 436, + 892, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, the encoding at the point $\\mathbf{p}$ is fed into a point-wise decoder $f(\\cdot)$ to give a binary prediction indicating if the point lies inside or outside the shape:", + "bbox": [ + 496, + 513, + 893, + 559 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {F}, \\mathbf {p}) = f (\\mathbf {F} (\\mathbf {p})) \\mapsto \\{0, 1 \\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 571, + 800, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the occupancy value $o(\\mathbf{p}) \\in \\{0,1\\}$ at each position $\\mathbf{p}$ pre-computed according to the ground truth shape mesh, a binary cross-entropy loss is used to train $g$ and $f$ :", + "bbox": [ + 496, + 599, + 892, + 646 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min L _ {I F} = \\operatorname {B C E} \\left(f (\\mathbf {F}, \\mathbf {p}), o (\\mathbf {p})\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 656, + 812, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that the prediction values can also be continuous signed distance values as in [58].", + "bbox": [ + 496, + 686, + 890, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Cross-Domain Feature Fusion", + "text_level": 1, + "bbox": [ + 500, + 726, + 767, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The training of a naive IF-Net demands ground truth shapes for generating numerous occupancy labels to supervise the output of $f(\\cdot)$ , yet most of the real scans are unpaired with shape ground truths. So we develop a cross-domain feature fusion module to well transfer the knowledge in the label-rich source domain. Our idea of exploiting the source knowledge stems from an important observation: although synthetic data have distinct local patterns from real scans, the global-level knowledge (e.g., the common structure and coarse shape) of a certain category can", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17632", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9b6304c49bdf1f51f86bd8b5cb1626104a2f60801d445ca279e6b003a2133e8d.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed method. Two IF-Net encoders are used for the source and the target domain, respectively, and they share an implicit function decoder. The cross-domain feature fusion (CDFF) works by adaptively combining the global-level and local-level knowledge learned from the source and target domain, respectively. The volume-consistency self-training (VCST) works by enforcing the prediction consistency between two different augmented views to learn the local details." + ], + "image_footnote": [], + "bbox": [ + 135, + 88, + 831, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "be shared in both domains. Besides, the target data with few labels may be enough for learning rich local-level information. On the other hand, IF-Nets conduct shape completion via exploiting local representations, so it is important to extract high-quality local-level features without introducing bias from the source domain.", + "bbox": [ + 75, + 382, + 468, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To this end, we develop a cross-domain feature fusion module (CDFF) for knowledge transfer. First, two shape encoders, $g_{s}(\\cdot)$ and $g_{t}(\\cdot)$ , are used for feature extraction of source and target data, generating $\\mathbf{F}_s$ and $\\mathbf{F}_t$ , respectively. As explained above, $\\mathbf{F}_s$ contains rich global information, and $\\mathbf{F}_t$ is more reliable in providing domain-specific local-level representations. A simple linear combination is adopted to fuse them into $\\mathbf{F}$ :", + "bbox": [ + 75, + 473, + 468, + 592 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} = \\mathbf {w} \\cdot \\mathbf {F} _ {s} + (1 - \\mathbf {w}) \\cdot \\mathbf {F} _ {t},\n$$\n", + "text_format": "latex", + "bbox": [ + 178, + 599, + 366, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{w} \\in [0,1]^d$ is a channel-wise weight vector. To better combine the advantages of $\\mathbf{F}_s$ and $\\mathbf{F}_t$ , the computation of $\\mathbf{w}$ takes two aspects into account: (i) exploiting the global-level features in $\\mathbf{F}_s$ while believing $\\mathbf{F}_t$ for local ones (based on our observation), and (ii) learning $\\mathbf{w}$ adaptively to maintain the flexibility. The adaptive weight vector $\\mathbf{w}$ is computed as:", + "bbox": [ + 75, + 622, + 468, + 728 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} = \\alpha \\cdot h \\left(\\mathbf {F} _ {s} \\odot \\mathbf {F} _ {t}\\right) + \\mathbf {w} ^ {0},\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 728, + 364, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha \\in \\mathbb{R}^{+}$ is the ratio of adaptiveness, $h(\\cdot)\\mapsto [0,1]^d$ is a two-layer MLP with a sigmoid activation at the output layer, and $\\odot$ indicates the operation of element-wise multiplication plus a global pooling on the spatial dimension (returns a vector of dimension $d$ ). $\\mathbf{w}^0\\in [0,1]^d$ is a constant weight vector that implies a prior derived from our observation, of which each value $w_{i}^{0}$ is simply defined by a linear mapping as follows:", + "bbox": [ + 75, + 747, + 470, + 868 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} ^ {0} = \\frac {l _ {i}}{L + 1}, i \\in \\{1, 2, \\dots , d \\},\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 875, + 380, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l_{i}\\in \\{1,2,\\dots ,L\\}$ indicates which layer the $i$ -th channel belongs to. In this way, the deeper layer one channel is from, the more the computation of $\\mathbf{F}$ in this channel relies on $\\mathbf{F}_s$ , as the deeper layers of IF-Nets capture more global information. In addition, a clipping operation is applied to $\\mathbf{w}$ to limit all values to [0, 1].", + "bbox": [ + 496, + 382, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Volume-Consistent Self-training", + "text_level": 1, + "bbox": [ + 498, + 483, + 782, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With few shape ground truths in the target domain, it is hard to learn rich information in a supervised manner. A typical way is to adopt self-supervised learning to learn from the data itself. In the task of SCoDA, the incompleteness is a significant characteristic of real scans that hampers the shape completion quality. Thus, we create two views of scans with different levels of incompleteness, and encourage the model to make consistent implicit predictions on their volume occupancy. Such a volume-consistent self-training (VCST) encourages the model to keep robust to various incompleteness and \"imagine\" the missing parts for shape completion.", + "bbox": [ + 496, + 507, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, we first adopt an unsupervised clustering algorithm (e.g., $k$ -means clustering) to partition the point cloud into $K$ different parts (see Fig. 2 for examples). The clustering is based only on the spatial positions of points and thus coarsely splits an object scan into multiple components. With the pre-computed partitions, two views $\\mathbf{X}^A$ and $\\mathbf{X}^B$ can be generated by randomly dropping different clusters of points from the original real scan, with $K_A$ and $K_B$ clusters left, respectively, where $K \\geq K_A > K_B$ . Besides, two random downsamplings are also conducted on the two views to create different sparsity. Note that the clustering-based augmentation is actually a surface-aware augmentation. Compared with volume-based ones that randomly mask some spatial volumes, our augmentation strat", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17633", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "egy implies more object-part knowledge to some extent.", + "bbox": [ + 76, + 90, + 446, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given the two views of input, their features are extracted by $g(\\cdot)$ and then taken by $f(\\cdot)$ to give implicit predictions:", + "bbox": [ + 76, + 106, + 467, + 136 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ng \\left(\\mathbf {X} ^ {v}\\right) = \\mathbf {F} ^ {v}, v = A, B,\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 161, + 352, + 176 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {F} ^ {v}, \\mathbf {p}) \\mapsto \\{0, 1 \\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 181, + 321, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that $\\mathbf{F}^v$ can also be generated via our CDFF module. Here we simplify the formulation to better present our VCST. The consistency constraint is imposed on the implicit predictions of $f(\\mathbf{F}^A, \\mathbf{p})$ and $f(\\mathbf{F}^B, \\mathbf{p})$ with the same point query $\\mathbf{p}$ :", + "bbox": [ + 75, + 207, + 467, + 282 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min L _ {C T} = \\operatorname {B C E} \\left(f \\left(\\mathbf {F} ^ {B}, \\mathbf {p}\\right), f \\left(\\mathbf {F} ^ {A}, \\mathbf {p}\\right)\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 291, + 411, + 309 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{BCE}(\\cdot ,\\cdot)$ indicates the binary cross-entropy loss. The consistency objective can be viewed as using the prediction from view $A$ as the pseudo label of view $B$ , because $\\mathbf{X}^B$ has a poorer completeness than $\\mathbf{X}^A$ with $K_{B} < K_{A}$ . As there will be noises in the implicit predictions due to the limited shape ground truths of target data, using the noisy prediction as the pseudo label will mislead the training. Therefore, a thresholding operation is performed to mask the predictions with low confidence in $f(\\mathbf{F}^{A},\\mathbf{p})$ . The overall loss function is a summation of $L_{IF}$ and $L_{CT}$ .", + "bbox": [ + 75, + 319, + 467, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Dataset", + "text_level": 1, + "bbox": [ + 76, + 483, + 165, + 498 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/75c986c6fb6b5054376985142a087137891c01410a20ab91b2f95bd2442f007d.jpg", + "image_caption": [ + "Figure 3. The procedure of 3D model crafting. From left to right: (i) extracting the object scan from a scene; (ii) constructing a coarse mesh frame to fit the scan; (iii) adding fine details; (iv) adjusting the defects detected by inspectors." + ], + "image_footnote": [], + "bbox": [ + 81, + 520, + 464, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overview The proposed ScanSalon dataset collects 7,644 real scans, of which 800 objects are equipped with 3D shape (artificial) ground truths. All models or scans are from 6 categories of objects, with 5 common indoor objects: chair, desk (or table), sofa, bed, and lamp, and 1 outdoor object: car. Detailed statistics are listed in Tab. 1. In Fig. 4, we exhibit some samples of real scans and corresponding 3D shapes in ScanSalon. More visualizations could be seen in the supplementary materials.", + "bbox": [ + 75, + 686, + 467, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Collection The real scans are collected from two datasets, the ScanNet [23] and KITTI [30] dataset for indoor and outdoor objects, respectively. The object scans are extracted from a scene point cloud according to the point-level instance segmentation annotations provided by the two", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1ed107dee7221100eddc80810e7936ee3ce67abc502697e258e0e8d83ee6b1e7.jpg", + "table_caption": [ + "Table 1. Statistics of the proposed dataset ScanSalon." + ], + "table_footnote": [], + "table_body": "
ChairDeskSofaBedLampCarTotal
Real Scans4,6511,6304283651334377,644
Paired Models49716143362043800
", + "bbox": [ + 504, + 108, + 897, + 159 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "datasets, and then rotated and normalized into the same pose and scale, with the aid of pose annotations provided by the Scan2CAD [3] and KITTI [30] dataset. These data are also aligned with models in the ShapeNet database [10], which provides a bunch of synthetic models as the source domain.", + "bbox": [ + 496, + 172, + 890, + 247 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Shape Annotation for Real Scans Two skillful artists participate in the annotation procedure. In addition to the real scans, we provide several photos for each scan from different viewpoints (selected from the videos contained in the ScanNet and KITTI datasets), which provide 2D references to improve the model quality. A brief creation pipeline is shown in Fig. 3, where the artists are required to create the shapes according to both scans and photo references (see Fig. 4), overcome the distractions of scan noise, and recover the incompleteness by his/her rich experience when the photo references are poor or inadequate. They use professional 3D software, Maya to create models. On average, it takes $0.5 \\sim 1.0$ person-hours to create a 3D model and the creation of all 800 models takes 2.5 months in total. For each created model, another 8 inspectors are invited to verify their (i) recovery extent compared with the real objects in photos and (ii) matching extent with the given scan, and the defects will be fed back to artists for further adjustments until no defects are detected by any inspector. Considering the inaccessibility of the objects in scans from ScanNet and KITTI, we have made our greatest efforts to create artificial ground truth shapes for these scans.", + "bbox": [ + 496, + 250, + 890, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 597, + 630, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Settings", + "text_level": 1, + "bbox": [ + 500, + 622, + 596, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benchmark setting We define two settings for the proposed task, which give only $3\\%$ and $5\\%$ shape ground truths (e.g. 47 and 140 chair models randomly sampled from all 4,651 chair scans, respectively) of real scans in the training set, and the rest of samples with corresponding 3D models compose the test set. Note that the $3\\%$ labeled samples are covered in the $5\\%$ labels for observing a cross-setting comparison when given more labels. For evaluation, we consider two metrics to measure the shape completion quality, mIoU: mean volumetric intersection over union (higher is better), and CD: $l_{2}$ chamfer distance (lower is better). The former measures the matching extent of the defined volumes and the latter measures the surface accuracy.", + "bbox": [ + 496, + 648, + 890, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines We implement four baseline methods to construct the benchmark of the new task. (i) IF-Net: a naive IF", + "bbox": [ + 500, + 847, + 890, + 876 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1https://www.autodesk.com/products/maya", + "bbox": [ + 517, + 886, + 746, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17634", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f8c7d1b9f5c981c315159be09b911d308d86c518599663a5346a60dd598d9842.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 127, + 95, + 207, + 150 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/95af52b5234d22f97c8fe601b139f9695acf9ab957e45ad8023fe9d7b22a0b43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 230, + 98, + 302, + 160 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2d8973aa0a3f94d6495cded470b0073b640ab69b978a2586c707544ca8159b96.jpg", + "image_caption": [ + "Figure 4. ScanSalon data visualization. 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"type": "table", + "img_path": "images/289bc02c36314c7efadb0742d3cfbe88b431afeec4406cf7751da61ab094b9be.jpg", + "table_caption": [ + "Table 2. Experiment results on the $3\\%$ and $5\\%$ labels setting of the SCoDA task. The units of CD and mIoU value are $1 \\times 10^{-3}$ and $\\%$ , respectively. Red text indicates the best and blue text indicates the second best result, respectively (similarly hereinafter).", + "(a) Results on the $3\\%$ labels setting." + ], + "table_footnote": [], + "table_body": "
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.5756.102.4443.040.6579.031.6467.301.6739.890.7474.771.4560.02
SelfSup1.4958.553.4942.970.5581.161.5968.582.4151.420.6278.751.6963.57
PtComp1.6157.332.1644.260.5179.901.5268.231.9546.970.5980.351.3962.84
Adversarial1.7458.542.9946.020.4681.421.3771.322.4356.390.6778.911.6165.43
Ours1.5860.772.3648.620.4282.001.5773.051.6258.570.4180.961.3267.32
", + "bbox": [ + 81, + 462, + 887, + 566 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8b8fa2f3f0ee36171c1c05085ccb09bb49ed62a1466e2a074a0d9e3ffa9c85bd.jpg", + "table_caption": [ + "(b) Results on the $5\\%$ labels setting." + ], + "table_footnote": [], + "table_body": "
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.8856.982.1444.870.5082.040.6676.051.7251.330.5280.131.2465.23
SelfSup2.0859.422.7346.390.5182.250.6177.221.4662.020.4381.891.0968.06
PtComp1.3457.981.8346.200.3282.660.6179.071.4461.610.4381.891.0068.24
Adversarial1.7160.582.1348.460.4183.540.5180.811.3364.220.4181.861.0869.91
Ours1.3761.482.0950.930.3182.710.4182.271.5767.800.4683.121.0471.39
", + "bbox": [ + 81, + 584, + 887, + 690 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Net [18] is adopted without any other designs and is trained on all supervised samples (including synthetic and real labels); (ii) SelfSup: a self-supervised IF-Net that conducts feature-level consistency (by minimizing the distance between two domain feature vectors) on unsupervised samples [50]; (iii) PtComp: a domain adaptive point completion method [14] is re-implemented to align the real scan inputs with the synthetic ones, incorporated with an extra IF-Net for implicit shape reconstruction. Note the encoder and decoder used in [14] are revised into a voxel-based 3D CNN to incorporate with IF-Net; (iv) Adversarial: a domain adaptive IF-Net is exploited with adversarial feature learning [43, 74, 87] to learn domain-invariant features. The de", + "bbox": [ + 75, + 698, + 468, + 893 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tailed implementation details of each baseline are included in the supplementary materials for the space limit.", + "bbox": [ + 498, + 698, + 890, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details We adopt a 6-layer 3DCNN as the encoder with a 4-layer MLP as the decoder to implement the IF-Nets, using the official codes released by [18]. Following [18], the channel dimension of multi-scale features is 2,583, and a resolution $N = 32$ is used for the training of reconstruction. For evaluation, we use a higher resolution with $N = 128$ . In the CDFF module, $\\alpha$ is set to 0.2 to better combine the advantages of $\\mathbf{F}_s$ and $\\mathbf{F}_t$ . For the augmentation strategy in VCST, $K_A$ is randomly selected from $\\{7,8\\}$ , and $K_B$ is randomly selected from $\\{5,6,7\\}$ for each data sample. The downsampling randomly sam", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17635", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/22c1aada6de3b961586eca6a4adac1a08ee6c374e605e34544c01ce03663eba6.jpg", + "table_caption": [ + "Table 3. Ablation on using the single module of CDFF or VCST." + ], + "table_footnote": [], + "table_body": "
ChairBedLamp
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
CDFF+VCST1.5860.771.5773.051.6258.57
CDFF only1.4958.551.9171.191.7353.18
VCST only2.0859.421.6372.621.8550.18
", + "bbox": [ + 81, + 109, + 467, + 185 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/06edb63d634a3f959217e95e7de081e717448da281aa1d017d72d8911e0f02e2.jpg", + "table_caption": [ + "Table 4. Analysis of the design of the CDFF module." + ], + "table_footnote": [], + "table_body": "
FusionObserv.AdaptiveCD↓mIoU↑
Ours✓✓✓1.4958.55
F = Fs1.57 (+0.08)56.10 (-2.45)
F = Ft2.22 (+0.73)54.98 (-3.57)
Non-Adap.✓✓1.92 (+0.43)57.77 (-0.78)
Contrad.✓✓1.96 (+0.47)56.62 (-1.93)
", + "bbox": [ + 81, + 210, + 467, + 289 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "plies 1k points from each scan (no sampling when has $< 1\\mathrm{k}$ points). A thresholding operation is adopted to filter out predictions with a confidence in (0.1, 0.9) (viewed as unconfident predictions) from view $A$ to guarantee the quality of consistency training [71]. All models are trained with an Adam optimizer and a learning rate $1 \\times 10^{-4}$ , with a minibatch size 4. $L_{CT}$ only works on unsupervised data. More implementation details of our method are introduced in the supplementary materials.", + "bbox": [ + 75, + 299, + 468, + 435 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 76, + 446, + 171, + 462 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative comparison The performance of baseline methods and ours are listed in Tab. 2 on the $3\\%$ and $5\\%$ labels settings. It can be seen that our method is superior to all baselines. On the $3\\%$ labels setting, our method achieves $1.32 \\times 10^{-3}$ on CD and $67.32\\%$ on mIoU on average, which is higher than the second best \"Adversarial\" by $\\sim 0.3 \\times 10^{-3}$ CD and $\\sim 2\\%$ mIoU. Besides, our method achieves good performances consistently over all 6 categories, most of which get a top rank over all 5 methods. The adversarial domain adaption method achieves the top mIoU among all baseline methods. Besides, our method also achieves the best performance on the $5\\%$ setting for both average CD and mIoU. In addition, it can be observed that an extra $2\\%$ labels bring an improvement of around $5\\%$ mIoU to all methods, and the improvements are especially significant for the categories \"bed\" and \"lamp\", which shows the promising practical value to provide a few more real-data labels to boost the shape completion quality from real scans.", + "bbox": [ + 75, + 474, + 468, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison We visualize the shape completion results of different methods in Fig. 5 to qualitatively compare baselines and our method. With the implicit prediction at each grid, a threshold of 0.5 is used to justify whether an occupancy is predicted here. The resulting occupancy grids with resolution 128 are then transformed into a mesh using the marching cubes algorithm [21]. The visualizations present the superiority of the proposed method, which achieves better completion for missing parts and generates fewer defects almost in all samples of Fig. 5.", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/94664c61c9e7e277c10fc123346afb99e15639e4d915fca6756880e473d06c67.jpg", + "table_caption": [ + "Table 5. Analysis of the design of the VCST module." + ], + "table_footnote": [], + "table_body": "
Random Volume SurfaceCD↓mIoU↑
w/o consistency training1.5756.10
✓3.65 (+2.08)47.60 (-8.50)
✓2.03 (+0.46)57.55 (+1.45)
✓2.37 (+0.80)59.03 (+2.93)
✓✓2.08 (+0.51)59.42 (+3.32)
✓✓2.37 (+0.80)58.13 (+2.03)
✓✓✓2.30 (+0.73)58.55 (+2.45)
", + "bbox": [ + 532, + 109, + 852, + 210 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation", + "text_level": 1, + "bbox": [ + 500, + 229, + 602, + 244 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Single module We first conduct ablative studies on using the CDFF or VCST module only. The results on 3 categories of the $3\\%$ label setting confirm the effectiveness of either of them, see Tab. 3. Besides, integrating both two methods brings an extra performance gain, which shows the complementary functions of these two modules.", + "bbox": [ + 496, + 256, + 890, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CDFF variants Next, we implement ablations on different variants of the proposed two modules, and all experiments are conducted on the \"chair\" category under the $3\\%$ label setting. For the CDFF module, we experiment such variants: (i) using the whole features generated by $g_{s}$ rather than via feature fusion $(\\mathbf{F} = \\mathbf{F}_s)$ ; (ii) without fusion but using the whole features generated by $g_{t}$ $(\\mathbf{F} = \\mathbf{F}_{t})$ ; (iii) conducting feature fusion but with a non-adaptive manner, specifically, $w_{i}$ is set to 0 for the bottom 3 layers and 1 for the top 3 layers (Non-Adap.); (iv) conducting adaptive feature fusion but in a manner contradictory to our observation (Contradict.), where we compute $\\mathbf{w}_0$ via $w_{i}^{0} = 1 - l_{i} / (L + 1)$ instead. The results in Tab. 4 show that (i) fully using $\\mathbf{F}_s$ as $\\mathbf{F}$ is equivalent to using a naive IF-Net that has a lower performance; (ii) using $\\mathbf{F}_t$ as $\\mathbf{F}$ results in a significant performance drop because $g_{t}$ can hardly learn high-quality global representations with a few labels; (iii) using a non-adaptive feature fusion that complies with our observation also leads to a performance drop but performs better than those without fusion; (iv) a fusion contradictory to our observation brings a $\\sim 2\\%$ mIoU drop, which further supports the reasonableness of our observation.", + "bbox": [ + 496, + 352, + 890, + 684 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VCST variants Related to our VCST design, we try different combinations to achieve the best augmentation strategy. Alternative strategies include random downsampling, surface-aware sampling (clustering-based), volume-aware sampling, and adding noise. Among them, adding noise has no effect on the performance whatever other augmentations are used, which may be caused by the voxelization operation in IF-Nets. Thus we try the following variants with the combination of the other three augmentation strategies. Note that we control the dropping ratio to guarantee the expected number of dropped points (if only using dropping) are the same for all settings. The results in Tab. 5 show that: (1) the consistency training with random downsampling only crashed (the 2nd row), using volume-", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17636", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8f679287d4cee3dda884eb93a77369161ea3772fec2a805af1b4ab236f598d1b.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison between different methods on shape completion with only $3\\%$ labels for training." + ], + "image_footnote": [], + "bbox": [ + 160, + 87, + 803, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "aware or surface-aware augmentation only can still work, but the surface-aware one performs better (the 3rd and 4th row), and the 4th row is the version used in our standard VCST; (3) the volume-aware augmentation can bring minor improvements on mIoU with or without random downsampling (the 3rd and 5th row), which is worse than our surface-aware one, and using both two of them even makes a negative effect (the last row). The reason for the failure of using random downsampling only is that the consistency training fails when two views are very similar in a global fashion. An intuitive explanation for (3) is that compared with our surface-aware augmentation, the incompleteness created by the volume-aware one has a larger gap with real scans. The qualitative comparisons between different variants are included in the supplementary materials.", + "bbox": [ + 75, + 577, + 472, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 815, + 194, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a new task, domain adaptive shape completion of real scans, which aims to transfer the knowledge in the label-rich synthetic domain into the more challenging real domain. We construct a new dataset that", + "bbox": [ + 75, + 840, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "contains elaborate 3D models created by professional artists for $10\\%$ of real scans in 6 categories, which can serve for the learning of deep reconstruction models and evaluation. Besides, we develop a new domain adaptive shape completion framework with two novel modules, cross-domain feature fusion and volume-consistent self-training, to better exploit both the synthetic and real data. Extensive experiments validate the superiority and effectiveness of our method and a benchmark is constructed on the proposed task.", + "bbox": [ + 496, + 577, + 890, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment The work was supported in part by NSFC-62172348, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by NSFC-62172348, Outstanding Yound Fund of Guangdong Province with No. 2023B1515020055, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055).", + "bbox": [ + 496, + 714, + 892, + 893 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17637", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Idan Achituve, Haggai Maron, and Gal Chechik. 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In ICCV, 2021. 3" + ], + "bbox": [ + 80, + 90, + 467, + 332 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "17641", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_model.json b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d5438371a16db86267333c0e0279d3b2450540c4 --- /dev/null +++ b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_model.json @@ -0,0 +1,2930 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.131, + 0.79, + 0.154 + ], + "angle": 0, + "content": "SCoDA: Domain Adaptive Shape Completion for Real Scans" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.18, + 0.771, + 0.199 + ], + "angle": 0, + "content": "Yushuang Wu\\(^{1,2,3}\\) Zizheng Yan\\(^{1,2,3}\\) Ce Chen\\(^{1,2}\\) Lai Wei\\(^{4}\\) Xiao Li\\(^{5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.215, + 0.199, + 0.754, + 0.218 + ], + "angle": 0, + "content": "Guanbin Li\\(^{6,7}\\) Yihao Li\\(^{1,2}\\) Shuguang Cui\\(^{2,1}\\) Xiaoguang Han\\(^{2,1\\#}\\)" + }, + { + "type": "text", + "bbox": [ + 0.115, + 0.217, + 0.856, + 0.253 + ], + "angle": 0, + "content": "\\(^{1}\\)FNii, CUHKSZ \\(^{2}\\)SSE, CUHKSZ \\(^{3}\\)SRIBD \\(^{4}\\)SDS, CUHKSZ \\(^{5}\\)Microsoft Research Asia \\(^{6}\\)Sun Yat-sen University \\(^{7}\\)Research Institute, Sun Yat-sen University, Shenzhen" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.255, + 0.876, + 0.287 + ], + "angle": 0, + "content": "{yushuangwu, zizhengyan, cechen, laiwei1}@link.cuhk.edu.cn luoheliyihao@mail.ustc.edu.cn {shuguangcui, hanxiaoguang}@cuhk.edu.cn liguanbin@mail.sysu.edu.cn li.xiao@microsoft.com" + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.298, + 0.832, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.494, + 0.893, + 0.522 + ], + "angle": 0, + "content": "Figure 1. The proposed task SCoDA aims to transfer the knowledge in the synthetic domain to the reconstruction of noisy and incomplete real scans. A dataset, ScanSalon, with paired real scans and 3D models is contributed. Project page: yushuang-wu.github.io/SCoDA." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.535, + 0.314, + 0.55 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.474, + 0.812 + ], + "angle": 0, + "content": "3D shape completion from point clouds is a challenging task, especially from scans of real-world objects. Considering the paucity of 3D shape ground truths for real scans, existing works mainly focus on benchmarking this task on synthetic data, e.g. 3D computer-aided design models. However, the domain gap between synthetic and real data limits the generalizability of these methods. Thus, we propose a new task, SCoDA, for the domain adaptation of real scan shape completion from synthetic data. A new dataset, ScanSalon, is contributed with a bunch of elaborate 3D models created by skillful artists according to scans. To address this new task, we propose a novel cross-domain feature fusion method for knowledge transfer and a novel volume-consistent self-training framework for robust learning from real data. Extensive experiments prove our method is effective to bring an improvement of \\(6\\% \\sim 7\\%\\) mIoU." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.844, + 0.208, + 0.859 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Shape completion and reconstruction from scans is a practical 3D digitization task that is of great significance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.893, + 0.748 + ], + "angle": 0, + "content": "in applications of virtual and augmented reality. It takes a scanned point cloud as input and aims to recover the 3D shape of the target object. The completion of real scans is challenging for the poor quality of point clouds and the deficiency of 3D shape ground truths. Existing methods exploit synthetic data, e.g. 3D computer-aided design (CAD) models to alleviate the demand for real object shapes. For example, authors of [18, 26, 35] simulate the scanning process to obtain point clouds from CAD models with paired ground truth shapes to train learning-based reconstruction models. However, there still exist distinctions between the simulated and real scan because the latter is scanned from a real object with complex scanning noise and occlusion, which limits the generalization quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Considering the underexploration in this field, we propose a new task, SCoDA, Domain Adaptive Shape Completion, that aims to transfer the knowledge from the synthetic domain with rich clean shapes (source domain) into the shape completion of real scans (target domain), as illustrated in Fig. 1. To this end, we, for the first time, build an object-centric dataset, ScanSalon, which consists of real Scans with Shape manual annotations. Our ScanSalon contains a bunch of 3D models that are paired with real scans of objects in six categories: chair, desk/table, sofa, bed, lamp," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17630" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "and car. The 3D models are manually created of high quality by skillful artists for around \\(10\\%\\) of real scans, which can serve as the evaluation ground truths of shape completion or as the few labels for semi-supervised domain adaptation. See Fig. 1 for some examples, and details of ScanSalon are exposed in Sec. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.473, + 0.695 + ], + "angle": 0, + "content": "The main challenge of the proposed SCoDA task lies in the domain gap between synthetic and real point clouds. Due to the intrinsic complexity of the scanning process, e.g., the scanner parameters and object materials, it is difficult to simulate the scans in terms of sparsity, noisy extent, etc. More importantly, real scans are usually incomplete resulting from the scene layout and object occlusion during scanning, which can hardly be simulated. Thus, we propose a novel domain adaptive shape completion approach to transfer the rich knowledge from the synthetic domain to the real one. At first, the reconstruction module in our approach is based on an implicit function for continuous shape completion [18, 54, 58]. For an effective transfer, we observe that although the local patterns of real scans (e.g., noise, sparsity, and incompleteness) are distinct from the simulated synthetic ones, the global topology or structure in a same category is usually similar between the synthetic and real data, for example, a chair from either the synthetic or real domain usually consists of a seat, a backrest, legs, etc. (see Fig. 1). In other words, the global topology is more likely to be domain invariant, while the local patterns are more likely to be domain specific. Accordingly, we propose a cross-domain feature fusion (CDFF) module to combine the global features and local features learned in the synthetic and real domain, respectively, which helps recover both fine details and global structures in the implicit reconstruction stage. Moreover, a novel volume-consistent selftraining (VCST) framework is developed to encourage self-supervised learning from the target data. Specifically, we create two views of real scans by dropping different clusters of points to produce incompleteness of different extent, and the model is forced to make consistent implicit predictions at each spatial volume, which encourages the model's robustness to the incompleteness of real scans." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.773 + ], + "angle": 0, + "content": "To construct a benchmark on the proposed new task, we implement some existing solutions to related tasks as baselines, and develop extensive experiments for the baselines and our method on ScanSalon. These experiments also demonstrate the effectiveness of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.777, + 0.418, + 0.792 + ], + "angle": 0, + "content": "In summary, our key contributions are four-fold:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.795, + 0.469, + 0.856 + ], + "angle": 0, + "content": "- We propose a new task, SCoDA, namely domain adaptive shape completion for real scans; A dataset ScanSalon that contains 800 elaborate 3D models paired with real scans in 6 categories is contributed." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.857, + 0.469, + 0.902 + ], + "angle": 0, + "content": "- A novel cross-domain feature fusion module is designed to combine the knowledge of global shapes and local patterns learned in the synthetic and real domain," + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.795, + 0.469, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "respectively. Such a feature fusion manner may also inspire the works in the 2D domain adaption field." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.122, + 0.892, + 0.167 + ], + "angle": 0, + "content": "- A volume-consistent self-training framework is proposed to improve the robustness of shape completion to the complex incompleteness of real scans." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.168, + 0.892, + 0.228 + ], + "angle": 0, + "content": "- A benchmark with multiple methods evaluated is constructed for the task of SCoDA based on ScanSalon; Extensive experiments also demonstrate the superiority of the proposed method." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.122, + 0.892, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.247, + 0.642, + 0.264 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Shape Completion Shape completion or reconstruction from point clouds is a branch of 3D reconstruction task [20, 47, 54, 68, 72, 91, 94]. The recovered shape can be represented as dense points [45, 46, 60] (i.e., point cloud completion or consolidation), polygonal meshes [28, 35, 48, 78], manifold atlases [4, 25, 27, 32, 83], voxel grids [20, 34, 85], or implicit representations [18, 26, 40, 61, 70, 82]. Among them, the task of point cloud completion is related to our work, which aims to recover a complete, dense, and clean point cloud for the 3D shape, from a partial, sparse, and noisy input scanned by sensors. The pioneering work, PCN [99], proposes a coarse-to-fine completion framework with an encoder-decoder architecture, which encodes the partial points into global features and recovers the fined results in the decoding stage. The following works explore further to better exploit local or multi-scale features for higher-quality completion [38, 49, 57, 73, 76, 77, 80, 81, 89, 92, 95, 98, 99, 101]. In addition, the implicit representation based approaches now attract increasing attention because of its superior property that enables continuous shape recovery for objects with arbitrary topologies [17, 18, 54, 58]. Although numerous efforts have been contributed, the existing approaches are usually performed on point clouds scanned from synthetic data via simulation, and a straightforward application on real scans results in an unsatisfactory performance due to the domain gap between synthetic and real scans [18, 26, 64]. For the task of point completion, some works also adopt unsupervised or weakly-supervised learning techniques to learn from unlabeled data [8, 14, 33, 79, 86, 87, 100]. Another line of works retrieve suitable models from 3D CAD repositories and deform them as the estimated shape ground truths of object scans [3, 75]. Differently, our work first proposes the task of domain adaptive shape completion for real scans, which aims to sufficiently transfer the knowledge from the label-rich synthetic domain into real scan shape completion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "2D Domain Adaptation Domain adaptation has been a popular research topic in various 2D vision tasks, including image recognition [5, 11, 15, 22, 24, 29, 50, 67], semantic segmentation [16, 36, 52, 53], and object detection [12, 42, 55, 65]. Existing works can broadly be categorized as (i)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17631" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.349 + ], + "angle": 0, + "content": "adversarial-based methods [12, 13, 15, 16, 22, 67] that train a discriminator to discriminate the source and the target domain, (ii) alignment-based methods [11, 24, 29, 65, 78] that use pre-defined metrics to align the source and the target domain, and (iii) self-training-based methods [5, 36, 52, 53, 55] that exploit the pseudo labels of the target domain to train the model. Recently, consistency-based self-training methods have become the most popular approach due to their impressive performance. One key factor in the success of consistency training is the augmentations applied to the inputs [31, 71, 93], e.g., stronger augmentations have better performance in domain adaptive image recognition [5]. To this end, we design a novel consistency training framework specialized for the shape completion task. Furthermore, we propose to conduct knowledge transfer via a cross-domain feature fusion manner, which has not been explored by existing works, to our best knowledge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.761 + ], + "angle": 0, + "content": "3D Domain Adaptation In the 3D vision field, existing works on domain adaptation are mainly committed to the task of point cloud understanding, including classification, part segmentation, and semantic segmentation. For object-centric point clouds, PointDAN [63] constructs a domain adaptive classification benchmark by collecting point clouds from ShapeNet [10], ModelNet [88], and ScanNet [23] datasets to compose 3 different domains. It also proposes an adversarial representation learning approach with feature alignment at both local and global levels. The following works improve the classification precision by adopting techniques of consistency training [44], self-training [9, 103], multimodal learning [2], or learning from self-supervised tasks [1, 37, 51, 69]. Another line of works are committed to scene-centric point cloud analysis, i.e., point cloud semantic segmentation [6, 7, 39, 41, 59, 66, 84, 90, 96, 102]. Considering the exhaustive annotation process for 3D point semantics, they propose to transfer the segmentation knowledge in synthetic scenes into real-world point clouds [41, 84, 90, 102]. Besides, there are a few attempts contributed to domain adaptive single-view reconstruction (SVR) [43, 62, 97], which is highly related to our work. Except for the difference in tasks (SVR v.s. shape completion), these works usually apply existing domain adaptation techniques to the target task, while we propose a novel domain adaptation method based on cross-domain feature fusion, which may also inspire others working on domain adaption." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.77, + 0.17, + 0.785 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.903 + ], + "angle": 0, + "content": "IF-Nets are a promising reconstruction method for their impressive performance [18], which is also successfully used in many applications [19, 56]. Constructed on IF-Nets, our approach first improves the representation learning by proposing a novel cross-domain feature fusion module, which aims to transfer the knowledge on the global-level object shape learned in the label-rich synthetic domain into" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "the real domain. Secondly, to exhaust the domain-specific information in the real data, a novel volume-consistent self-training method is proposed for the specific shape completion task, which also leads to a robust implicit prediction of IF-Nets. An illustration is presented in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.177, + 0.742, + 0.193 + ], + "angle": 0, + "content": "3.1. Implicit Feature Networks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.894, + 0.276 + ], + "angle": 0, + "content": "We first introduce IF-Nets [18] as our reconstruction framework. An IF-Net is composed of a 3D convolution neural network encoder \\( g(\\cdot) \\) for multi-scale feature extraction and a multi-layer perceptron (MLP) \\( f(\\cdot) \\) for implicit shape decoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.894, + 0.399 + ], + "angle": 0, + "content": "Given a point cloud sample \\(P\\), it is first converted into a discrete voxel representation \\(\\mathbf{X} \\in \\mathbb{R}^{N \\times N \\times N}\\), where \\(N \\in \\mathbb{N}\\) is the resolution of the input space. \\(\\mathbf{X}\\) is then fed into the \\(L\\)-layer encoder \\(g(\\cdot)\\) to generate a set of multiscale features \\(\\{\\mathbf{F}_1, \\dots, \\mathbf{F}_L\\}\\), then they are upsampled to the same spatial dimension and been concatenated along the channel dimension to create the final feature \\(\\mathbf{F} =\\) concat(\\(\\{\\mathrm{upsample}(\\mathbf{F}_1), \\dots, \\mathrm{upsample}(\\mathbf{F}_L)\\}\\)). Formally:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.408, + 0.866, + 0.427 + ], + "angle": 0, + "content": "\\[\ng (\\mathbf {X}) = \\mathbf {F}, \\quad \\mathbf {X} \\in \\mathbb {R} ^ {N \\times N \\times N}, \\mathbf {F} \\in \\mathbb {R} ^ {d \\times N \\times N \\times N},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.893, + 0.514 + ], + "angle": 0, + "content": "where \\(d\\) is the feature channel number that equals the summation of the channel numbers of \\(\\mathbf{F}_i\\). Note that \\(\\mathbf{F}\\) has a 3D structure aligned with the input \\(\\mathbf{X}\\). Given a point query \\(\\mathbf{p} \\in \\mathbb{R}^3\\), continuous features \\(\\mathbf{F}(\\mathbf{p})\\) at this point can be extracted from \\(\\mathbf{F}\\) using trilinear interpolation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.894, + 0.56 + ], + "angle": 0, + "content": "Then, the encoding at the point \\(\\mathbf{p}\\) is fed into a point-wise decoder \\(f(\\cdot)\\) to give a binary prediction indicating if the point lies inside or outside the shape:" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.572, + 0.801, + 0.589 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {F}, \\mathbf {p}) = f (\\mathbf {F} (\\mathbf {p})) \\mapsto \\{0, 1 \\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.893, + 0.647 + ], + "angle": 0, + "content": "Given the occupancy value \\( o(\\mathbf{p}) \\in \\{0,1\\} \\) at each position \\( \\mathbf{p} \\) pre-computed according to the ground truth shape mesh, a binary cross-entropy loss is used to train \\( g \\) and \\( f \\):" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.657, + 0.813, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\min L _ {I F} = \\operatorname {B C E} \\left(f (\\mathbf {F}, \\mathbf {p}), o (\\mathbf {p})\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.717 + ], + "angle": 0, + "content": "Note that the prediction values can also be continuous signed distance values as in [58]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.768, + 0.741 + ], + "angle": 0, + "content": "3.2. Cross-Domain Feature Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The training of a naive IF-Net demands ground truth shapes for generating numerous occupancy labels to supervise the output of \\( f(\\cdot) \\), yet most of the real scans are unpaired with shape ground truths. So we develop a cross-domain feature fusion module to well transfer the knowledge in the label-rich source domain. Our idea of exploiting the source knowledge stems from an important observation: although synthetic data have distinct local patterns from real scans, the global-level knowledge (e.g., the common structure and coarse shape) of a certain category can" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17632" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.089, + 0.833, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.318, + 0.895, + 0.377 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed method. Two IF-Net encoders are used for the source and the target domain, respectively, and they share an implicit function decoder. The cross-domain feature fusion (CDFF) works by adaptively combining the global-level and local-level knowledge learned from the source and target domain, respectively. The volume-consistency self-training (VCST) works by enforcing the prediction consistency between two different augmented views to learn the local details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.47, + 0.472 + ], + "angle": 0, + "content": "be shared in both domains. Besides, the target data with few labels may be enough for learning rich local-level information. On the other hand, IF-Nets conduct shape completion via exploiting local representations, so it is important to extract high-quality local-level features without introducing bias from the source domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.593 + ], + "angle": 0, + "content": "To this end, we develop a cross-domain feature fusion module (CDFF) for knowledge transfer. First, two shape encoders, \\( g_{s}(\\cdot) \\) and \\( g_{t}(\\cdot) \\), are used for feature extraction of source and target data, generating \\( \\mathbf{F}_s \\) and \\( \\mathbf{F}_t \\), respectively. As explained above, \\( \\mathbf{F}_s \\) contains rich global information, and \\( \\mathbf{F}_t \\) is more reliable in providing domain-specific local-level representations. A simple linear combination is adopted to fuse them into \\( \\mathbf{F} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.179, + 0.601, + 0.367, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} = \\mathbf {w} \\cdot \\mathbf {F} _ {s} + (1 - \\mathbf {w}) \\cdot \\mathbf {F} _ {t},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.729 + ], + "angle": 0, + "content": "where \\(\\mathbf{w} \\in [0,1]^d\\) is a channel-wise weight vector. To better combine the advantages of \\(\\mathbf{F}_s\\) and \\(\\mathbf{F}_t\\), the computation of \\(\\mathbf{w}\\) takes two aspects into account: (i) exploiting the global-level features in \\(\\mathbf{F}_s\\) while believing \\(\\mathbf{F}_t\\) for local ones (based on our observation), and (ii) learning \\(\\mathbf{w}\\) adaptively to maintain the flexibility. The adaptive weight vector \\(\\mathbf{w}\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.729, + 0.365, + 0.744 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} = \\alpha \\cdot h \\left(\\mathbf {F} _ {s} \\odot \\mathbf {F} _ {t}\\right) + \\mathbf {w} ^ {0},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.471, + 0.869 + ], + "angle": 0, + "content": "where \\(\\alpha \\in \\mathbb{R}^{+}\\) is the ratio of adaptiveness, \\(h(\\cdot)\\mapsto [0,1]^d\\) is a two-layer MLP with a sigmoid activation at the output layer, and \\(\\odot\\) indicates the operation of element-wise multiplication plus a global pooling on the spatial dimension (returns a vector of dimension \\(d\\)). \\(\\mathbf{w}^0\\in [0,1]^d\\) is a constant weight vector that implies a prior derived from our observation, of which each value \\(w_{i}^{0}\\) is simply defined by a linear mapping as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.875, + 0.382, + 0.906 + ], + "angle": 0, + "content": "\\[\nw _ {i} ^ {0} = \\frac {l _ {i}}{L + 1}, i \\in \\{1, 2, \\dots , d \\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.476 + ], + "angle": 0, + "content": "where \\(l_{i}\\in \\{1,2,\\dots ,L\\}\\) indicates which layer the \\(i\\) -th channel belongs to. In this way, the deeper layer one channel is from, the more the computation of \\(\\mathbf{F}\\) in this channel relies on \\(\\mathbf{F}_s\\) , as the deeper layers of IF-Nets capture more global information. In addition, a clipping operation is applied to \\(\\mathbf{w}\\) to limit all values to [0, 1]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.484, + 0.783, + 0.501 + ], + "angle": 0, + "content": "3.3. Volume-Consistent Self-training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.689 + ], + "angle": 0, + "content": "With few shape ground truths in the target domain, it is hard to learn rich information in a supervised manner. A typical way is to adopt self-supervised learning to learn from the data itself. In the task of SCoDA, the incompleteness is a significant characteristic of real scans that hampers the shape completion quality. Thus, we create two views of scans with different levels of incompleteness, and encourage the model to make consistent implicit predictions on their volume occupancy. Such a volume-consistent self-training (VCST) encourages the model to keep robust to various incompleteness and \"imagine\" the missing parts for shape completion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Specifically, we first adopt an unsupervised clustering algorithm (e.g., \\(k\\)-means clustering) to partition the point cloud into \\(K\\) different parts (see Fig. 2 for examples). The clustering is based only on the spatial positions of points and thus coarsely splits an object scan into multiple components. With the pre-computed partitions, two views \\(\\mathbf{X}^A\\) and \\(\\mathbf{X}^B\\) can be generated by randomly dropping different clusters of points from the original real scan, with \\(K_A\\) and \\(K_B\\) clusters left, respectively, where \\(K \\geq K_A > K_B\\). Besides, two random downsamplings are also conducted on the two views to create different sparsity. Note that the clustering-based augmentation is actually a surface-aware augmentation. Compared with volume-based ones that randomly mask some spatial volumes, our augmentation strat" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17633" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.447, + 0.106 + ], + "angle": 0, + "content": "egy implies more object-part knowledge to some extent." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.107, + 0.468, + 0.137 + ], + "angle": 0, + "content": "Given the two views of input, their features are extracted by \\( g(\\cdot) \\) and then taken by \\( f(\\cdot) \\) to give implicit predictions:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.162, + 0.354, + 0.178 + ], + "angle": 0, + "content": "\\[\ng \\left(\\mathbf {X} ^ {v}\\right) = \\mathbf {F} ^ {v}, v = A, B,\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.182, + 0.323, + 0.198 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {F} ^ {v}, \\mathbf {p}) \\mapsto \\{0, 1 \\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.208, + 0.468, + 0.283 + ], + "angle": 0, + "content": "Note that \\(\\mathbf{F}^v\\) can also be generated via our CDFF module. Here we simplify the formulation to better present our VCST. The consistency constraint is imposed on the implicit predictions of \\(f(\\mathbf{F}^A, \\mathbf{p})\\) and \\(f(\\mathbf{F}^B, \\mathbf{p})\\) with the same point query \\(\\mathbf{p}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.292, + 0.412, + 0.31 + ], + "angle": 0, + "content": "\\[\n\\min L _ {C T} = \\operatorname {B C E} \\left(f \\left(\\mathbf {F} ^ {B}, \\mathbf {p}\\right), f \\left(\\mathbf {F} ^ {A}, \\mathbf {p}\\right)\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.468, + 0.471 + ], + "angle": 0, + "content": "where \\(\\mathrm{BCE}(\\cdot ,\\cdot)\\) indicates the binary cross-entropy loss. The consistency objective can be viewed as using the prediction from view \\(A\\) as the pseudo label of view \\(B\\), because \\(\\mathbf{X}^B\\) has a poorer completeness than \\(\\mathbf{X}^A\\) with \\(K_{B} < K_{A}\\). As there will be noises in the implicit predictions due to the limited shape ground truths of target data, using the noisy prediction as the pseudo label will mislead the training. Therefore, a thresholding operation is performed to mask the predictions with low confidence in \\(f(\\mathbf{F}^{A},\\mathbf{p})\\). The overall loss function is a summation of \\(L_{IF}\\) and \\(L_{CT}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.484, + 0.166, + 0.499 + ], + "angle": 0, + "content": "4. Dataset" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.521, + 0.465, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.621, + 0.468, + 0.677 + ], + "angle": 0, + "content": "Figure 3. The procedure of 3D model crafting. From left to right: (i) extracting the object scan from a scene; (ii) constructing a coarse mesh frame to fit the scan; (iii) adding fine details; (iv) adjusting the defects detected by inspectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.468, + 0.822 + ], + "angle": 0, + "content": "Overview The proposed ScanSalon dataset collects 7,644 real scans, of which 800 objects are equipped with 3D shape (artificial) ground truths. All models or scans are from 6 categories of objects, with 5 common indoor objects: chair, desk (or table), sofa, bed, and lamp, and 1 outdoor object: car. Detailed statistics are listed in Tab. 1. In Fig. 4, we exhibit some samples of real scans and corresponding 3D shapes in ScanSalon. More visualizations could be seen in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Data Collection The real scans are collected from two datasets, the ScanNet [23] and KITTI [30] dataset for indoor and outdoor objects, respectively. The object scans are extracted from a scene point cloud according to the point-level instance segmentation annotations provided by the two" + }, + { + "type": "table_caption", + "bbox": [ + 0.537, + 0.092, + 0.854, + 0.106 + ], + "angle": 0, + "content": "Table 1. Statistics of the proposed dataset ScanSalon." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.109, + 0.898, + 0.16 + ], + "angle": 0, + "content": "
ChairDeskSofaBedLampCarTotal
Real Scans4,6511,6304283651334377,644
Paired Models49716143362043800
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.173, + 0.892, + 0.248 + ], + "angle": 0, + "content": "datasets, and then rotated and normalized into the same pose and scale, with the aid of pose annotations provided by the Scan2CAD [3] and KITTI [30] dataset. These data are also aligned with models in the ShapeNet database [10], which provides a bunch of synthetic models as the source domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.25, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Shape Annotation for Real Scans Two skillful artists participate in the annotation procedure. In addition to the real scans, we provide several photos for each scan from different viewpoints (selected from the videos contained in the ScanNet and KITTI datasets), which provide 2D references to improve the model quality. A brief creation pipeline is shown in Fig. 3, where the artists are required to create the shapes according to both scans and photo references (see Fig. 4), overcome the distractions of scan noise, and recover the incompleteness by his/her rich experience when the photo references are poor or inadequate. They use professional 3D software, Maya to create models. On average, it takes \\(0.5 \\sim 1.0\\) person-hours to create a 3D model and the creation of all 800 models takes 2.5 months in total. For each created model, another 8 inspectors are invited to verify their (i) recovery extent compared with the real objects in photos and (ii) matching extent with the given scan, and the defects will be fed back to artists for further adjustments until no defects are detected by any inspector. Considering the inaccessibility of the objects in scans from ScanNet and KITTI, we have made our greatest efforts to create artificial ground truth shapes for these scans." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.598, + 0.631, + 0.615 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.623, + 0.597, + 0.638 + ], + "angle": 0, + "content": "5.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.892, + 0.844 + ], + "angle": 0, + "content": "Benchmark setting We define two settings for the proposed task, which give only \\(3\\%\\) and \\(5\\%\\) shape ground truths (e.g. 47 and 140 chair models randomly sampled from all 4,651 chair scans, respectively) of real scans in the training set, and the rest of samples with corresponding 3D models compose the test set. Note that the \\(3\\%\\) labeled samples are covered in the \\(5\\%\\) labels for observing a cross-setting comparison when given more labels. For evaluation, we consider two metrics to measure the shape completion quality, mIoU: mean volumetric intersection over union (higher is better), and CD: \\(l_{2}\\) chamfer distance (lower is better). The former measures the matching extent of the defined volumes and the latter measures the surface accuracy." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.848, + 0.891, + 0.877 + ], + "angle": 0, + "content": "Baselines We implement four baseline methods to construct the benchmark of the new task. (i) IF-Net: a naive IF" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.748, + 0.901 + ], + "angle": 0, + "content": "1https://www.autodesk.com/products/maya" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17634" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.096, + 0.208, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.099, + 0.303, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.089, + 0.366, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.096, + 0.437, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.096, + 0.534, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.089, + 0.609, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.096, + 0.686, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.096, + 0.784, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.089, + 0.852, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.131, + 0.179, + 0.203, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.179, + 0.296, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.371, + 0.182, + 0.454, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.468, + 0.185, + 0.552, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.176, + 0.691, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.717, + 0.177, + 0.787, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.163, + 0.852, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.131, + 0.26, + 0.211, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.26, + 0.305, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.368, + 0.257, + 0.454, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.466, + 0.261, + 0.551, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.262, + 0.696, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.261, + 0.793, + 0.302 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.242, + 0.852, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.131, + 0.336, + 0.215, + 0.379 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.335, + 0.308, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.393, + 0.323, + 0.438, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.324, + 0.534, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.33, + 0.696, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.331, + 0.791, + 0.387 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.33, + 0.852, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.395, + 0.87, + 0.409 + ], + "angle": 0, + "content": "Figure 4. ScanSalon data visualization. Each tuple includes: point cloud (left), created mesh (middle), and photo references (right)." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.419, + 0.89, + 0.447 + ], + "angle": 0, + "content": "Table 2. Experiment results on the \\(3\\%\\) and \\(5\\%\\) labels setting of the SCoDA task. The units of CD and mIoU value are \\(1 \\times 10^{-3}\\) and \\(\\%\\), respectively. Red text indicates the best and blue text indicates the second best result, respectively (similarly hereinafter)." + }, + { + "type": "table_caption", + "bbox": [ + 0.378, + 0.45, + 0.591, + 0.462 + ], + "angle": 0, + "content": "(a) Results on the \\(3\\%\\) labels setting." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.463, + 0.888, + 0.567 + ], + "angle": 0, + "content": "
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.5756.102.4443.040.6579.031.6467.301.6739.890.7474.771.4560.02
SelfSup1.4958.553.4942.970.5581.161.5968.582.4151.420.6278.751.6963.57
PtComp1.6157.332.1644.260.5179.901.5268.231.9546.970.5980.351.3962.84
Adversarial1.7458.542.9946.020.4681.421.3771.322.4356.390.6778.911.6165.43
Ours1.5860.772.3648.620.4282.001.5773.051.6258.570.4180.961.3267.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.378, + 0.572, + 0.591, + 0.585 + ], + "angle": 0, + "content": "(b) Results on the \\(5\\%\\) labels setting." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.585, + 0.888, + 0.691 + ], + "angle": 0, + "content": "
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.8856.982.1444.870.5082.040.6676.051.7251.330.5280.131.2465.23
SelfSup2.0859.422.7346.390.5182.250.6177.221.4662.020.4381.891.0968.06
PtComp1.3457.981.8346.200.3282.660.6179.071.4461.610.4381.891.0068.24
Adversarial1.7160.582.1348.460.4183.540.5180.811.3364.220.4181.861.0869.91
Ours1.3761.482.0950.930.3182.710.4182.271.5767.800.4683.121.0471.39
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.47, + 0.895 + ], + "angle": 0, + "content": "Net [18] is adopted without any other designs and is trained on all supervised samples (including synthetic and real labels); (ii) SelfSup: a self-supervised IF-Net that conducts feature-level consistency (by minimizing the distance between two domain feature vectors) on unsupervised samples [50]; (iii) PtComp: a domain adaptive point completion method [14] is re-implemented to align the real scan inputs with the synthetic ones, incorporated with an extra IF-Net for implicit shape reconstruction. Note the encoder and decoder used in [14] are revised into a voxel-based 3D CNN to incorporate with IF-Net; (iv) Adversarial: a domain adaptive IF-Net is exploited with adversarial feature learning [43, 74, 87] to learn domain-invariant features. The de" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.699, + 0.891, + 0.73 + ], + "angle": 0, + "content": "tailed implementation details of each baseline are included in the supplementary materials for the space limit." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation details We adopt a 6-layer 3DCNN as the encoder with a 4-layer MLP as the decoder to implement the IF-Nets, using the official codes released by [18]. Following [18], the channel dimension of multi-scale features is 2,583, and a resolution \\(N = 32\\) is used for the training of reconstruction. For evaluation, we use a higher resolution with \\(N = 128\\). In the CDFF module, \\(\\alpha\\) is set to 0.2 to better combine the advantages of \\(\\mathbf{F}_s\\) and \\(\\mathbf{F}_t\\). For the augmentation strategy in VCST, \\(K_A\\) is randomly selected from \\(\\{7,8\\}\\), and \\(K_B\\) is randomly selected from \\(\\{5,6,7\\}\\) for each data sample. The downsampling randomly sam" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17635" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.092, + 0.466, + 0.107 + ], + "angle": 0, + "content": "Table 3. Ablation on using the single module of CDFF or VCST." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.11, + 0.468, + 0.186 + ], + "angle": 0, + "content": "
ChairBedLamp
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
CDFF+VCST1.5860.771.5773.051.6258.57
CDFF only1.4958.551.9171.191.7353.18
VCST only2.0859.421.6372.621.8550.18
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.194, + 0.431, + 0.208 + ], + "angle": 0, + "content": "Table 4. Analysis of the design of the CDFF module." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.211, + 0.468, + 0.29 + ], + "angle": 0, + "content": "
FusionObserv.AdaptiveCD↓mIoU↑
Ours✓✓✓1.4958.55
F = Fs1.57 (+0.08)56.10 (-2.45)
F = Ft2.22 (+0.73)54.98 (-3.57)
Non-Adap.✓✓1.92 (+0.43)57.77 (-0.78)
Contrad.✓✓1.96 (+0.47)56.62 (-1.93)
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.47, + 0.436 + ], + "angle": 0, + "content": "plies 1k points from each scan (no sampling when has \\( < 1\\mathrm{k} \\) points). A thresholding operation is adopted to filter out predictions with a confidence in (0.1, 0.9) (viewed as unconfident predictions) from view \\( A \\) to guarantee the quality of consistency training [71]. All models are trained with an Adam optimizer and a learning rate \\( 1 \\times 10^{-4} \\), with a minibatch size 4. \\( L_{CT} \\) only works on unsupervised data. More implementation details of our method are introduced in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.448, + 0.172, + 0.463 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Quantitative comparison The performance of baseline methods and ours are listed in Tab. 2 on the \\(3\\%\\) and \\(5\\%\\) labels settings. It can be seen that our method is superior to all baselines. On the \\(3\\%\\) labels setting, our method achieves \\(1.32 \\times 10^{-3}\\) on CD and \\(67.32\\%\\) on mIoU on average, which is higher than the second best \"Adversarial\" by \\(\\sim 0.3 \\times 10^{-3}\\) CD and \\(\\sim 2\\%\\) mIoU. Besides, our method achieves good performances consistently over all 6 categories, most of which get a top rank over all 5 methods. The adversarial domain adaption method achieves the top mIoU among all baseline methods. Besides, our method also achieves the best performance on the \\(5\\%\\) setting for both average CD and mIoU. In addition, it can be observed that an extra \\(2\\%\\) labels bring an improvement of around \\(5\\%\\) mIoU to all methods, and the improvements are especially significant for the categories \"bed\" and \"lamp\", which shows the promising practical value to provide a few more real-data labels to boost the shape completion quality from real scans." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Qualitative comparison We visualize the shape completion results of different methods in Fig. 5 to qualitatively compare baselines and our method. With the implicit prediction at each grid, a threshold of 0.5 is used to justify whether an occupancy is predicted here. The resulting occupancy grids with resolution 128 are then transformed into a mesh using the marching cubes algorithm [21]. The visualizations present the superiority of the proposed method, which achieves better completion for missing parts and generates fewer defects almost in all samples of Fig. 5." + }, + { + "type": "table_caption", + "bbox": [ + 0.537, + 0.092, + 0.854, + 0.107 + ], + "angle": 0, + "content": "Table 5. Analysis of the design of the VCST module." + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.11, + 0.854, + 0.212 + ], + "angle": 0, + "content": "
Random Volume SurfaceCD↓mIoU↑
w/o consistency training1.5756.10
✓3.65 (+2.08)47.60 (-8.50)
✓2.03 (+0.46)57.55 (+1.45)
✓2.37 (+0.80)59.03 (+2.93)
✓✓2.08 (+0.51)59.42 (+3.32)
✓✓2.37 (+0.80)58.13 (+2.03)
✓✓✓2.30 (+0.73)58.55 (+2.45)
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.23, + 0.604, + 0.245 + ], + "angle": 0, + "content": "5.3. Ablation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.257, + 0.892, + 0.349 + ], + "angle": 0, + "content": "Single module We first conduct ablative studies on using the CDFF or VCST module only. The results on 3 categories of the \\(3\\%\\) label setting confirm the effectiveness of either of them, see Tab. 3. Besides, integrating both two methods brings an extra performance gain, which shows the complementary functions of these two modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.892, + 0.685 + ], + "angle": 0, + "content": "CDFF variants Next, we implement ablations on different variants of the proposed two modules, and all experiments are conducted on the \"chair\" category under the \\(3\\%\\) label setting. For the CDFF module, we experiment such variants: (i) using the whole features generated by \\(g_{s}\\) rather than via feature fusion \\((\\mathbf{F} = \\mathbf{F}_s)\\); (ii) without fusion but using the whole features generated by \\(g_{t}\\) \\((\\mathbf{F} = \\mathbf{F}_{t})\\); (iii) conducting feature fusion but with a non-adaptive manner, specifically, \\(w_{i}\\) is set to 0 for the bottom 3 layers and 1 for the top 3 layers (Non-Adap.); (iv) conducting adaptive feature fusion but in a manner contradictory to our observation (Contradict.), where we compute \\(\\mathbf{w}_0\\) via \\(w_{i}^{0} = 1 - l_{i} / (L + 1)\\) instead. The results in Tab. 4 show that (i) fully using \\(\\mathbf{F}_s\\) as \\(\\mathbf{F}\\) is equivalent to using a naive IF-Net that has a lower performance; (ii) using \\(\\mathbf{F}_t\\) as \\(\\mathbf{F}\\) results in a significant performance drop because \\(g_{t}\\) can hardly learn high-quality global representations with a few labels; (iii) using a non-adaptive feature fusion that complies with our observation also leads to a performance drop but performs better than those without fusion; (iv) a fusion contradictory to our observation brings a \\(\\sim 2\\%\\) mIoU drop, which further supports the reasonableness of our observation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "VCST variants Related to our VCST design, we try different combinations to achieve the best augmentation strategy. Alternative strategies include random downsampling, surface-aware sampling (clustering-based), volume-aware sampling, and adding noise. Among them, adding noise has no effect on the performance whatever other augmentations are used, which may be caused by the voxelization operation in IF-Nets. Thus we try the following variants with the combination of the other three augmentation strategies. Note that we control the dropping ratio to guarantee the expected number of dropped points (if only using dropping) are the same for all settings. The results in Tab. 5 show that: (1) the consistency training with random downsampling only crashed (the 2nd row), using volume-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17636" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.161, + 0.088, + 0.805, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.558, + 0.825, + 0.573 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison between different methods on shape completion with only \\(3\\%\\) labels for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.473, + 0.804 + ], + "angle": 0, + "content": "aware or surface-aware augmentation only can still work, but the surface-aware one performs better (the 3rd and 4th row), and the 4th row is the version used in our standard VCST; (3) the volume-aware augmentation can bring minor improvements on mIoU with or without random downsampling (the 3rd and 5th row), which is worse than our surface-aware one, and using both two of them even makes a negative effect (the last row). The reason for the failure of using random downsampling only is that the consistency training fails when two views are very similar in a global fashion. An intuitive explanation for (3) is that compared with our surface-aware augmentation, the incompleteness created by the volume-aware one has a larger gap with real scans. The qualitative comparisons between different variants are included in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.196, + 0.831 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.472, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a new task, domain adaptive shape completion of real scans, which aims to transfer the knowledge in the label-rich synthetic domain into the more challenging real domain. We construct a new dataset that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.713 + ], + "angle": 0, + "content": "contains elaborate 3D models created by professional artists for \\(10\\%\\) of real scans in 6 categories, which can serve for the learning of deep reconstruction models and evaluation. Besides, we develop a new domain adaptive shape completion framework with two novel modules, cross-domain feature fusion and volume-consistent self-training, to better exploit both the synthetic and real data. Extensive experiments validate the superiority and effectiveness of our method and a benchmark is constructed on the proposed task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.893, + 0.895 + ], + "angle": 0, + "content": "Acknowledgment The work was supported in part by NSFC-62172348, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by NSFC-62172348, Outstanding Yound Fund of Guangdong Province with No. 2023B1515020055, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17637" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.468, + 0.156 + ], + "angle": 0, + "content": "[1] Idan Achituve, Haggai Maron, and Gal Chechik. Self-supervised learning for domain adaptation on point clouds. 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In ICCV, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.081, + 0.092, + 0.468, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "17641" + } + ] +] \ No newline at end of file diff --git a/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_origin.pdf b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..315105e95791e48902dbf787daae4d3efe151d2c --- /dev/null +++ b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/a2de3a81-2619-4975-9f69-e49ad0b14643_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9ac80c20752bf910a1a4c0227a64411adeb97d6ac75d935b976223bac30a23fd +size 10028340 diff --git a/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/full.md b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/full.md new file mode 100644 index 0000000000000000000000000000000000000000..950557639081f439a9ab3f30443d454f40a8bd71 --- /dev/null +++ b/2023/SCoDA_ Domain Adaptive Shape Completion for Real Scans/full.md @@ -0,0 +1,386 @@ +# SCoDA: Domain Adaptive Shape Completion for Real Scans + +Yushuang Wu $^{1,2,3}$ Zizheng Yan $^{1,2,3}$ Ce Chen $^{1,2}$ Lai Wei $^{4}$ Xiao Li $^{5}$ + +Guanbin Li $^{6,7}$ Yihao Li $^{1,2}$ Shuguang Cui $^{2,1}$ Xiaoguang Han $^{2,1\#}$ + +$^{1}$ FNii, CUHKSZ $^{2}$ SSE, CUHKSZ $^{3}$ SRIBD $^{4}$ SDS, CUHKSZ $^{5}$ Microsoft Research Asia $^{6}$ Sun Yat-sen University $^{7}$ Research Institute, Sun Yat-sen University, Shenzhen + +{yushuangwu, zizhengyan, cechen, laiwei1}@link.cuhk.edu.cn luoheliyihao@mail.ustc.edu.cn {shuguangcui, hanxiaoguang}@cuhk.edu.cn liguanbin@mail.sysu.edu.cn li.xiao@microsoft.com + +![](images/359178af258d434aa2849ed22bbd12ac7961ad3ac768de275af832fa9c6aab89.jpg) +Figure 1. The proposed task SCoDA aims to transfer the knowledge in the synthetic domain to the reconstruction of noisy and incomplete real scans. A dataset, ScanSalon, with paired real scans and 3D models is contributed. Project page: yushuang-wu.github.io/SCoDA. + +# Abstract + +3D shape completion from point clouds is a challenging task, especially from scans of real-world objects. Considering the paucity of 3D shape ground truths for real scans, existing works mainly focus on benchmarking this task on synthetic data, e.g. 3D computer-aided design models. However, the domain gap between synthetic and real data limits the generalizability of these methods. Thus, we propose a new task, SCoDA, for the domain adaptation of real scan shape completion from synthetic data. A new dataset, ScanSalon, is contributed with a bunch of elaborate 3D models created by skillful artists according to scans. To address this new task, we propose a novel cross-domain feature fusion method for knowledge transfer and a novel volume-consistent self-training framework for robust learning from real data. Extensive experiments prove our method is effective to bring an improvement of $6\% \sim 7\%$ mIoU. + +# 1. Introduction + +Shape completion and reconstruction from scans is a practical 3D digitization task that is of great significance + +in applications of virtual and augmented reality. It takes a scanned point cloud as input and aims to recover the 3D shape of the target object. The completion of real scans is challenging for the poor quality of point clouds and the deficiency of 3D shape ground truths. Existing methods exploit synthetic data, e.g. 3D computer-aided design (CAD) models to alleviate the demand for real object shapes. For example, authors of [18, 26, 35] simulate the scanning process to obtain point clouds from CAD models with paired ground truth shapes to train learning-based reconstruction models. However, there still exist distinctions between the simulated and real scan because the latter is scanned from a real object with complex scanning noise and occlusion, which limits the generalization quality. + +Considering the underexploration in this field, we propose a new task, SCoDA, Domain Adaptive Shape Completion, that aims to transfer the knowledge from the synthetic domain with rich clean shapes (source domain) into the shape completion of real scans (target domain), as illustrated in Fig. 1. To this end, we, for the first time, build an object-centric dataset, ScanSalon, which consists of real Scans with Shape manual annotations. Our ScanSalon contains a bunch of 3D models that are paired with real scans of objects in six categories: chair, desk/table, sofa, bed, lamp, + +and car. The 3D models are manually created of high quality by skillful artists for around $10\%$ of real scans, which can serve as the evaluation ground truths of shape completion or as the few labels for semi-supervised domain adaptation. See Fig. 1 for some examples, and details of ScanSalon are exposed in Sec. 4. + +The main challenge of the proposed SCoDA task lies in the domain gap between synthetic and real point clouds. Due to the intrinsic complexity of the scanning process, e.g., the scanner parameters and object materials, it is difficult to simulate the scans in terms of sparsity, noisy extent, etc. More importantly, real scans are usually incomplete resulting from the scene layout and object occlusion during scanning, which can hardly be simulated. Thus, we propose a novel domain adaptive shape completion approach to transfer the rich knowledge from the synthetic domain to the real one. At first, the reconstruction module in our approach is based on an implicit function for continuous shape completion [18, 54, 58]. For an effective transfer, we observe that although the local patterns of real scans (e.g., noise, sparsity, and incompleteness) are distinct from the simulated synthetic ones, the global topology or structure in a same category is usually similar between the synthetic and real data, for example, a chair from either the synthetic or real domain usually consists of a seat, a backrest, legs, etc. (see Fig. 1). In other words, the global topology is more likely to be domain invariant, while the local patterns are more likely to be domain specific. Accordingly, we propose a cross-domain feature fusion (CDFF) module to combine the global features and local features learned in the synthetic and real domain, respectively, which helps recover both fine details and global structures in the implicit reconstruction stage. Moreover, a novel volume-consistent selftraining (VCST) framework is developed to encourage self-supervised learning from the target data. Specifically, we create two views of real scans by dropping different clusters of points to produce incompleteness of different extent, and the model is forced to make consistent implicit predictions at each spatial volume, which encourages the model's robustness to the incompleteness of real scans. + +To construct a benchmark on the proposed new task, we implement some existing solutions to related tasks as baselines, and develop extensive experiments for the baselines and our method on ScanSalon. These experiments also demonstrate the effectiveness of the proposed method. + +In summary, our key contributions are four-fold: + +- We propose a new task, SCoDA, namely domain adaptive shape completion for real scans; A dataset ScanSalon that contains 800 elaborate 3D models paired with real scans in 6 categories is contributed. +- A novel cross-domain feature fusion module is designed to combine the knowledge of global shapes and local patterns learned in the synthetic and real domain, + +respectively. Such a feature fusion manner may also inspire the works in the 2D domain adaption field. + +- A volume-consistent self-training framework is proposed to improve the robustness of shape completion to the complex incompleteness of real scans. +- A benchmark with multiple methods evaluated is constructed for the task of SCoDA based on ScanSalon; Extensive experiments also demonstrate the superiority of the proposed method. + +# 2. Related Work + +Shape Completion Shape completion or reconstruction from point clouds is a branch of 3D reconstruction task [20, 47, 54, 68, 72, 91, 94]. The recovered shape can be represented as dense points [45, 46, 60] (i.e., point cloud completion or consolidation), polygonal meshes [28, 35, 48, 78], manifold atlases [4, 25, 27, 32, 83], voxel grids [20, 34, 85], or implicit representations [18, 26, 40, 61, 70, 82]. Among them, the task of point cloud completion is related to our work, which aims to recover a complete, dense, and clean point cloud for the 3D shape, from a partial, sparse, and noisy input scanned by sensors. The pioneering work, PCN [99], proposes a coarse-to-fine completion framework with an encoder-decoder architecture, which encodes the partial points into global features and recovers the fined results in the decoding stage. The following works explore further to better exploit local or multi-scale features for higher-quality completion [38, 49, 57, 73, 76, 77, 80, 81, 89, 92, 95, 98, 99, 101]. In addition, the implicit representation based approaches now attract increasing attention because of its superior property that enables continuous shape recovery for objects with arbitrary topologies [17, 18, 54, 58]. Although numerous efforts have been contributed, the existing approaches are usually performed on point clouds scanned from synthetic data via simulation, and a straightforward application on real scans results in an unsatisfactory performance due to the domain gap between synthetic and real scans [18, 26, 64]. For the task of point completion, some works also adopt unsupervised or weakly-supervised learning techniques to learn from unlabeled data [8, 14, 33, 79, 86, 87, 100]. Another line of works retrieve suitable models from 3D CAD repositories and deform them as the estimated shape ground truths of object scans [3, 75]. Differently, our work first proposes the task of domain adaptive shape completion for real scans, which aims to sufficiently transfer the knowledge from the label-rich synthetic domain into real scan shape completion. + +2D Domain Adaptation Domain adaptation has been a popular research topic in various 2D vision tasks, including image recognition [5, 11, 15, 22, 24, 29, 50, 67], semantic segmentation [16, 36, 52, 53], and object detection [12, 42, 55, 65]. Existing works can broadly be categorized as (i) + +adversarial-based methods [12, 13, 15, 16, 22, 67] that train a discriminator to discriminate the source and the target domain, (ii) alignment-based methods [11, 24, 29, 65, 78] that use pre-defined metrics to align the source and the target domain, and (iii) self-training-based methods [5, 36, 52, 53, 55] that exploit the pseudo labels of the target domain to train the model. Recently, consistency-based self-training methods have become the most popular approach due to their impressive performance. One key factor in the success of consistency training is the augmentations applied to the inputs [31, 71, 93], e.g., stronger augmentations have better performance in domain adaptive image recognition [5]. To this end, we design a novel consistency training framework specialized for the shape completion task. Furthermore, we propose to conduct knowledge transfer via a cross-domain feature fusion manner, which has not been explored by existing works, to our best knowledge. + +3D Domain Adaptation In the 3D vision field, existing works on domain adaptation are mainly committed to the task of point cloud understanding, including classification, part segmentation, and semantic segmentation. For object-centric point clouds, PointDAN [63] constructs a domain adaptive classification benchmark by collecting point clouds from ShapeNet [10], ModelNet [88], and ScanNet [23] datasets to compose 3 different domains. It also proposes an adversarial representation learning approach with feature alignment at both local and global levels. The following works improve the classification precision by adopting techniques of consistency training [44], self-training [9, 103], multimodal learning [2], or learning from self-supervised tasks [1, 37, 51, 69]. Another line of works are committed to scene-centric point cloud analysis, i.e., point cloud semantic segmentation [6, 7, 39, 41, 59, 66, 84, 90, 96, 102]. Considering the exhaustive annotation process for 3D point semantics, they propose to transfer the segmentation knowledge in synthetic scenes into real-world point clouds [41, 84, 90, 102]. Besides, there are a few attempts contributed to domain adaptive single-view reconstruction (SVR) [43, 62, 97], which is highly related to our work. Except for the difference in tasks (SVR v.s. shape completion), these works usually apply existing domain adaptation techniques to the target task, while we propose a novel domain adaptation method based on cross-domain feature fusion, which may also inspire others working on domain adaption. + +# 3. Method + +IF-Nets are a promising reconstruction method for their impressive performance [18], which is also successfully used in many applications [19, 56]. Constructed on IF-Nets, our approach first improves the representation learning by proposing a novel cross-domain feature fusion module, which aims to transfer the knowledge on the global-level object shape learned in the label-rich synthetic domain into + +the real domain. Secondly, to exhaust the domain-specific information in the real data, a novel volume-consistent self-training method is proposed for the specific shape completion task, which also leads to a robust implicit prediction of IF-Nets. An illustration is presented in Fig. 2. + +# 3.1. Implicit Feature Networks + +We first introduce IF-Nets [18] as our reconstruction framework. An IF-Net is composed of a 3D convolution neural network encoder $g(\cdot)$ for multi-scale feature extraction and a multi-layer perceptron (MLP) $f(\cdot)$ for implicit shape decoding. + +Given a point cloud sample $P$ , it is first converted into a discrete voxel representation $\mathbf{X} \in \mathbb{R}^{N \times N \times N}$ , where $N \in \mathbb{N}$ is the resolution of the input space. $\mathbf{X}$ is then fed into the $L$ -layer encoder $g(\cdot)$ to generate a set of multiscale features $\{\mathbf{F}_1, \dots, \mathbf{F}_L\}$ , then they are upsampled to the same spatial dimension and been concatenated along the channel dimension to create the final feature $\mathbf{F} =$ concat( $\{\mathrm{upsample}(\mathbf{F}_1), \dots, \mathrm{upsample}(\mathbf{F}_L)\}$ ). Formally: + +$$ +g (\mathbf {X}) = \mathbf {F}, \quad \mathbf {X} \in \mathbb {R} ^ {N \times N \times N}, \mathbf {F} \in \mathbb {R} ^ {d \times N \times N \times N}, +$$ + +where $d$ is the feature channel number that equals the summation of the channel numbers of $\mathbf{F}_i$ . Note that $\mathbf{F}$ has a 3D structure aligned with the input $\mathbf{X}$ . Given a point query $\mathbf{p} \in \mathbb{R}^3$ , continuous features $\mathbf{F}(\mathbf{p})$ at this point can be extracted from $\mathbf{F}$ using trilinear interpolation. + +Then, the encoding at the point $\mathbf{p}$ is fed into a point-wise decoder $f(\cdot)$ to give a binary prediction indicating if the point lies inside or outside the shape: + +$$ +f (\mathbf {F}, \mathbf {p}) = f (\mathbf {F} (\mathbf {p})) \mapsto \{0, 1 \}. +$$ + +Given the occupancy value $o(\mathbf{p}) \in \{0,1\}$ at each position $\mathbf{p}$ pre-computed according to the ground truth shape mesh, a binary cross-entropy loss is used to train $g$ and $f$ : + +$$ +\min L _ {I F} = \operatorname {B C E} \left(f (\mathbf {F}, \mathbf {p}), o (\mathbf {p})\right). +$$ + +Note that the prediction values can also be continuous signed distance values as in [58]. + +# 3.2. Cross-Domain Feature Fusion + +The training of a naive IF-Net demands ground truth shapes for generating numerous occupancy labels to supervise the output of $f(\cdot)$ , yet most of the real scans are unpaired with shape ground truths. So we develop a cross-domain feature fusion module to well transfer the knowledge in the label-rich source domain. Our idea of exploiting the source knowledge stems from an important observation: although synthetic data have distinct local patterns from real scans, the global-level knowledge (e.g., the common structure and coarse shape) of a certain category can + +![](images/9b6304c49bdf1f51f86bd8b5cb1626104a2f60801d445ca279e6b003a2133e8d.jpg) +Figure 2. Overview of the proposed method. Two IF-Net encoders are used for the source and the target domain, respectively, and they share an implicit function decoder. The cross-domain feature fusion (CDFF) works by adaptively combining the global-level and local-level knowledge learned from the source and target domain, respectively. The volume-consistency self-training (VCST) works by enforcing the prediction consistency between two different augmented views to learn the local details. + +be shared in both domains. Besides, the target data with few labels may be enough for learning rich local-level information. On the other hand, IF-Nets conduct shape completion via exploiting local representations, so it is important to extract high-quality local-level features without introducing bias from the source domain. + +To this end, we develop a cross-domain feature fusion module (CDFF) for knowledge transfer. First, two shape encoders, $g_{s}(\cdot)$ and $g_{t}(\cdot)$ , are used for feature extraction of source and target data, generating $\mathbf{F}_s$ and $\mathbf{F}_t$ , respectively. As explained above, $\mathbf{F}_s$ contains rich global information, and $\mathbf{F}_t$ is more reliable in providing domain-specific local-level representations. A simple linear combination is adopted to fuse them into $\mathbf{F}$ : + +$$ +\mathbf {F} = \mathbf {w} \cdot \mathbf {F} _ {s} + (1 - \mathbf {w}) \cdot \mathbf {F} _ {t}, +$$ + +where $\mathbf{w} \in [0,1]^d$ is a channel-wise weight vector. To better combine the advantages of $\mathbf{F}_s$ and $\mathbf{F}_t$ , the computation of $\mathbf{w}$ takes two aspects into account: (i) exploiting the global-level features in $\mathbf{F}_s$ while believing $\mathbf{F}_t$ for local ones (based on our observation), and (ii) learning $\mathbf{w}$ adaptively to maintain the flexibility. The adaptive weight vector $\mathbf{w}$ is computed as: + +$$ +\mathbf {w} = \alpha \cdot h \left(\mathbf {F} _ {s} \odot \mathbf {F} _ {t}\right) + \mathbf {w} ^ {0}, +$$ + +where $\alpha \in \mathbb{R}^{+}$ is the ratio of adaptiveness, $h(\cdot)\mapsto [0,1]^d$ is a two-layer MLP with a sigmoid activation at the output layer, and $\odot$ indicates the operation of element-wise multiplication plus a global pooling on the spatial dimension (returns a vector of dimension $d$ ). $\mathbf{w}^0\in [0,1]^d$ is a constant weight vector that implies a prior derived from our observation, of which each value $w_{i}^{0}$ is simply defined by a linear mapping as follows: + +$$ +w _ {i} ^ {0} = \frac {l _ {i}}{L + 1}, i \in \{1, 2, \dots , d \}, +$$ + +where $l_{i}\in \{1,2,\dots ,L\}$ indicates which layer the $i$ -th channel belongs to. In this way, the deeper layer one channel is from, the more the computation of $\mathbf{F}$ in this channel relies on $\mathbf{F}_s$ , as the deeper layers of IF-Nets capture more global information. In addition, a clipping operation is applied to $\mathbf{w}$ to limit all values to [0, 1]. + +# 3.3. Volume-Consistent Self-training + +With few shape ground truths in the target domain, it is hard to learn rich information in a supervised manner. A typical way is to adopt self-supervised learning to learn from the data itself. In the task of SCoDA, the incompleteness is a significant characteristic of real scans that hampers the shape completion quality. Thus, we create two views of scans with different levels of incompleteness, and encourage the model to make consistent implicit predictions on their volume occupancy. Such a volume-consistent self-training (VCST) encourages the model to keep robust to various incompleteness and "imagine" the missing parts for shape completion. + +Specifically, we first adopt an unsupervised clustering algorithm (e.g., $k$ -means clustering) to partition the point cloud into $K$ different parts (see Fig. 2 for examples). The clustering is based only on the spatial positions of points and thus coarsely splits an object scan into multiple components. With the pre-computed partitions, two views $\mathbf{X}^A$ and $\mathbf{X}^B$ can be generated by randomly dropping different clusters of points from the original real scan, with $K_A$ and $K_B$ clusters left, respectively, where $K \geq K_A > K_B$ . Besides, two random downsamplings are also conducted on the two views to create different sparsity. Note that the clustering-based augmentation is actually a surface-aware augmentation. Compared with volume-based ones that randomly mask some spatial volumes, our augmentation strat + +egy implies more object-part knowledge to some extent. + +Given the two views of input, their features are extracted by $g(\cdot)$ and then taken by $f(\cdot)$ to give implicit predictions: + +$$ +g \left(\mathbf {X} ^ {v}\right) = \mathbf {F} ^ {v}, v = A, B, +$$ + +$$ +f (\mathbf {F} ^ {v}, \mathbf {p}) \mapsto \{0, 1 \}. +$$ + +Note that $\mathbf{F}^v$ can also be generated via our CDFF module. Here we simplify the formulation to better present our VCST. The consistency constraint is imposed on the implicit predictions of $f(\mathbf{F}^A, \mathbf{p})$ and $f(\mathbf{F}^B, \mathbf{p})$ with the same point query $\mathbf{p}$ : + +$$ +\min L _ {C T} = \operatorname {B C E} \left(f \left(\mathbf {F} ^ {B}, \mathbf {p}\right), f \left(\mathbf {F} ^ {A}, \mathbf {p}\right)\right), +$$ + +where $\mathrm{BCE}(\cdot ,\cdot)$ indicates the binary cross-entropy loss. The consistency objective can be viewed as using the prediction from view $A$ as the pseudo label of view $B$ , because $\mathbf{X}^B$ has a poorer completeness than $\mathbf{X}^A$ with $K_{B} < K_{A}$ . As there will be noises in the implicit predictions due to the limited shape ground truths of target data, using the noisy prediction as the pseudo label will mislead the training. Therefore, a thresholding operation is performed to mask the predictions with low confidence in $f(\mathbf{F}^{A},\mathbf{p})$ . The overall loss function is a summation of $L_{IF}$ and $L_{CT}$ . + +# 4. Dataset + +![](images/75c986c6fb6b5054376985142a087137891c01410a20ab91b2f95bd2442f007d.jpg) +Figure 3. The procedure of 3D model crafting. From left to right: (i) extracting the object scan from a scene; (ii) constructing a coarse mesh frame to fit the scan; (iii) adding fine details; (iv) adjusting the defects detected by inspectors. + +Overview The proposed ScanSalon dataset collects 7,644 real scans, of which 800 objects are equipped with 3D shape (artificial) ground truths. All models or scans are from 6 categories of objects, with 5 common indoor objects: chair, desk (or table), sofa, bed, and lamp, and 1 outdoor object: car. Detailed statistics are listed in Tab. 1. In Fig. 4, we exhibit some samples of real scans and corresponding 3D shapes in ScanSalon. More visualizations could be seen in the supplementary materials. + +Data Collection The real scans are collected from two datasets, the ScanNet [23] and KITTI [30] dataset for indoor and outdoor objects, respectively. The object scans are extracted from a scene point cloud according to the point-level instance segmentation annotations provided by the two + +Table 1. Statistics of the proposed dataset ScanSalon. + +
ChairDeskSofaBedLampCarTotal
Real Scans4,6511,6304283651334377,644
Paired Models49716143362043800
+ +datasets, and then rotated and normalized into the same pose and scale, with the aid of pose annotations provided by the Scan2CAD [3] and KITTI [30] dataset. These data are also aligned with models in the ShapeNet database [10], which provides a bunch of synthetic models as the source domain. + +Shape Annotation for Real Scans Two skillful artists participate in the annotation procedure. In addition to the real scans, we provide several photos for each scan from different viewpoints (selected from the videos contained in the ScanNet and KITTI datasets), which provide 2D references to improve the model quality. A brief creation pipeline is shown in Fig. 3, where the artists are required to create the shapes according to both scans and photo references (see Fig. 4), overcome the distractions of scan noise, and recover the incompleteness by his/her rich experience when the photo references are poor or inadequate. They use professional 3D software, Maya to create models. On average, it takes $0.5 \sim 1.0$ person-hours to create a 3D model and the creation of all 800 models takes 2.5 months in total. For each created model, another 8 inspectors are invited to verify their (i) recovery extent compared with the real objects in photos and (ii) matching extent with the given scan, and the defects will be fed back to artists for further adjustments until no defects are detected by any inspector. Considering the inaccessibility of the objects in scans from ScanNet and KITTI, we have made our greatest efforts to create artificial ground truth shapes for these scans. + +# 5. Experiments + +# 5.1. Settings + +Benchmark setting We define two settings for the proposed task, which give only $3\%$ and $5\%$ shape ground truths (e.g. 47 and 140 chair models randomly sampled from all 4,651 chair scans, respectively) of real scans in the training set, and the rest of samples with corresponding 3D models compose the test set. Note that the $3\%$ labeled samples are covered in the $5\%$ labels for observing a cross-setting comparison when given more labels. For evaluation, we consider two metrics to measure the shape completion quality, mIoU: mean volumetric intersection over union (higher is better), and CD: $l_{2}$ chamfer distance (lower is better). The former measures the matching extent of the defined volumes and the latter measures the surface accuracy. + +Baselines We implement four baseline methods to construct the benchmark of the new task. (i) IF-Net: a naive IF + +![](images/f8c7d1b9f5c981c315159be09b911d308d86c518599663a5346a60dd598d9842.jpg) + +![](images/95af52b5234d22f97c8fe601b139f9695acf9ab957e45ad8023fe9d7b22a0b43.jpg) + +![](images/2d8973aa0a3f94d6495cded470b0073b640ab69b978a2586c707544ca8159b96.jpg) +Figure 4. ScanSalon data visualization. Each tuple includes: point cloud (left), created mesh (middle), and photo references (right). + +![](images/42f0331aa13c067a3ea5b18c2f1be9927335df351a92816c8dda748053a5ec63.jpg) + +![](images/435167f3d5adf43139d5588d681583af2683fc4018c0c36475fbbc32bff227e8.jpg) + +![](images/5ea2fd97f47bd457f4038e21c27132cc01d938d57833c2d4dffeb443cf5ce2d0.jpg) + +![](images/f7844eb1282d9244b67fd98d0f57e570fb614f6a9de732834dfe9cbcd570e98b.jpg) + +![](images/f0954387f759ee6a7e9c4e2473b8eae85527120b71919ae09aa35eefe7547ed5.jpg) + +![](images/8cd7277a2c6deec1d1194c919fc75088a804567230edd261fd9fe3ddac304808.jpg) + +![](images/eb6fee0b004b29fc4c116e3c38558f2f53052fc711e5fd3a8b421d1486b0336b.jpg) + +![](images/2e60bb7f304dd7524d8768260d48ca687571549d1d6903e5f1e24d65c2cc9949.jpg) + +![](images/239f83ebd70addc97b099eeb4298f42e9777278d41c7fd38ae50f483b14bf24b.jpg) + +![](images/569b45ce239ffd3ac9705dc582999996f9880634ca2357daab8447d2ec739889.jpg) + +![](images/c3c67de784df8e8f68b40a0283c5889d60a72ddbbd893b9ff05b0df2727ac453.jpg) + +![](images/b67d73a32ff98c07cdef264d5d6d4f84e4b48f38ad69d87f2d679101a533a122.jpg) + +![](images/35988af664ac3ab33a1433191ab82936659c61ecf97a50b911da59e3a6822fb6.jpg) + +![](images/ee3bd45d31460134b5c64b10be7972cf9154200c150efb65e6cf78721aad894b.jpg) + +![](images/0f5a246e7f02350939521efcc6bdfd348e4278bf30bcfab8099b4b8f29948c82.jpg) + +![](images/1bd0ebe59604336cc36524541f7ad640a40ed19703f80c29ad1381a7da78a829.jpg) + +![](images/528cfd262fec70a0927c7c291d900adf46739ba6464b887c4d09c29928559850.jpg) + +![](images/d6c1d67cfca280d631efd57d4673fc5078fb24ca9a9cb4f80f3b1c590c9173f9.jpg) + +![](images/805ec908cabda757e25994fe32f9e4d4ed69cd9b297bf70b8136aa084a4e8dd9.jpg) + +![](images/9bbed576a327f52ada08f140945e144f18b088a118dc7ac9543a44778e56551d.jpg) + +![](images/942a6abbd8ce194e7c26632a0af49f9ae4d4a514947cfaaa04dc732135b4805d.jpg) + +![](images/3e8212183d8824c6766d2671d769b6a38124b29f178b54afbf4d8b3d7f293081.jpg) + +![](images/fa8614c8649919afd19ec546522366ce541c80413fe8709fac715590970ae482.jpg) + +![](images/77c52d2f9565dc1160415be1ea920c844e42bfc749135ea356c847a9137597c2.jpg) + +Table 2. Experiment results on the $3\%$ and $5\%$ labels setting of the SCoDA task. The units of CD and mIoU value are $1 \times 10^{-3}$ and $\%$ , respectively. Red text indicates the best and blue text indicates the second best result, respectively (similarly hereinafter). +(a) Results on the $3\%$ labels setting. + +
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.5756.102.4443.040.6579.031.6467.301.6739.890.7474.771.4560.02
SelfSup1.4958.553.4942.970.5581.161.5968.582.4151.420.6278.751.6963.57
PtComp1.6157.332.1644.260.5179.901.5268.231.9546.970.5980.351.3962.84
Adversarial1.7458.542.9946.020.4681.421.3771.322.4356.390.6778.911.6165.43
Ours1.5860.772.3648.620.4282.001.5773.051.6258.570.4180.961.3267.32
+ +(b) Results on the $5\%$ labels setting. + +
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.8856.982.1444.870.5082.040.6676.051.7251.330.5280.131.2465.23
SelfSup2.0859.422.7346.390.5182.250.6177.221.4662.020.4381.891.0968.06
PtComp1.3457.981.8346.200.3282.660.6179.071.4461.610.4381.891.0068.24
Adversarial1.7160.582.1348.460.4183.540.5180.811.3364.220.4181.861.0869.91
Ours1.3761.482.0950.930.3182.710.4182.271.5767.800.4683.121.0471.39
+ +Net [18] is adopted without any other designs and is trained on all supervised samples (including synthetic and real labels); (ii) SelfSup: a self-supervised IF-Net that conducts feature-level consistency (by minimizing the distance between two domain feature vectors) on unsupervised samples [50]; (iii) PtComp: a domain adaptive point completion method [14] is re-implemented to align the real scan inputs with the synthetic ones, incorporated with an extra IF-Net for implicit shape reconstruction. Note the encoder and decoder used in [14] are revised into a voxel-based 3D CNN to incorporate with IF-Net; (iv) Adversarial: a domain adaptive IF-Net is exploited with adversarial feature learning [43, 74, 87] to learn domain-invariant features. The de + +tailed implementation details of each baseline are included in the supplementary materials for the space limit. + +Implementation details We adopt a 6-layer 3DCNN as the encoder with a 4-layer MLP as the decoder to implement the IF-Nets, using the official codes released by [18]. Following [18], the channel dimension of multi-scale features is 2,583, and a resolution $N = 32$ is used for the training of reconstruction. For evaluation, we use a higher resolution with $N = 128$ . In the CDFF module, $\alpha$ is set to 0.2 to better combine the advantages of $\mathbf{F}_s$ and $\mathbf{F}_t$ . For the augmentation strategy in VCST, $K_A$ is randomly selected from $\{7,8\}$ , and $K_B$ is randomly selected from $\{5,6,7\}$ for each data sample. The downsampling randomly sam + +Table 3. Ablation on using the single module of CDFF or VCST. + +
ChairBedLamp
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
CDFF+VCST1.5860.771.5773.051.6258.57
CDFF only1.4958.551.9171.191.7353.18
VCST only2.0859.421.6372.621.8550.18
+ +Table 4. Analysis of the design of the CDFF module. + +
FusionObserv.AdaptiveCD↓mIoU↑
Ours✓✓✓1.4958.55
F = Fs1.57 (+0.08)56.10 (-2.45)
F = Ft2.22 (+0.73)54.98 (-3.57)
Non-Adap.✓✓1.92 (+0.43)57.77 (-0.78)
Contrad.✓✓1.96 (+0.47)56.62 (-1.93)
+ +plies 1k points from each scan (no sampling when has $< 1\mathrm{k}$ points). A thresholding operation is adopted to filter out predictions with a confidence in (0.1, 0.9) (viewed as unconfident predictions) from view $A$ to guarantee the quality of consistency training [71]. All models are trained with an Adam optimizer and a learning rate $1 \times 10^{-4}$ , with a minibatch size 4. $L_{CT}$ only works on unsupervised data. More implementation details of our method are introduced in the supplementary materials. + +# 5.2. Results + +Quantitative comparison The performance of baseline methods and ours are listed in Tab. 2 on the $3\%$ and $5\%$ labels settings. It can be seen that our method is superior to all baselines. On the $3\%$ labels setting, our method achieves $1.32 \times 10^{-3}$ on CD and $67.32\%$ on mIoU on average, which is higher than the second best "Adversarial" by $\sim 0.3 \times 10^{-3}$ CD and $\sim 2\%$ mIoU. Besides, our method achieves good performances consistently over all 6 categories, most of which get a top rank over all 5 methods. The adversarial domain adaption method achieves the top mIoU among all baseline methods. Besides, our method also achieves the best performance on the $5\%$ setting for both average CD and mIoU. In addition, it can be observed that an extra $2\%$ labels bring an improvement of around $5\%$ mIoU to all methods, and the improvements are especially significant for the categories "bed" and "lamp", which shows the promising practical value to provide a few more real-data labels to boost the shape completion quality from real scans. + +Qualitative comparison We visualize the shape completion results of different methods in Fig. 5 to qualitatively compare baselines and our method. With the implicit prediction at each grid, a threshold of 0.5 is used to justify whether an occupancy is predicted here. The resulting occupancy grids with resolution 128 are then transformed into a mesh using the marching cubes algorithm [21]. The visualizations present the superiority of the proposed method, which achieves better completion for missing parts and generates fewer defects almost in all samples of Fig. 5. + +Table 5. Analysis of the design of the VCST module. + +
Random Volume SurfaceCD↓mIoU↑
w/o consistency training1.5756.10
✓3.65 (+2.08)47.60 (-8.50)
✓2.03 (+0.46)57.55 (+1.45)
✓2.37 (+0.80)59.03 (+2.93)
✓✓2.08 (+0.51)59.42 (+3.32)
✓✓2.37 (+0.80)58.13 (+2.03)
✓✓✓2.30 (+0.73)58.55 (+2.45)
+ +# 5.3. Ablation + +Single module We first conduct ablative studies on using the CDFF or VCST module only. The results on 3 categories of the $3\%$ label setting confirm the effectiveness of either of them, see Tab. 3. Besides, integrating both two methods brings an extra performance gain, which shows the complementary functions of these two modules. + +CDFF variants Next, we implement ablations on different variants of the proposed two modules, and all experiments are conducted on the "chair" category under the $3\%$ label setting. For the CDFF module, we experiment such variants: (i) using the whole features generated by $g_{s}$ rather than via feature fusion $(\mathbf{F} = \mathbf{F}_s)$ ; (ii) without fusion but using the whole features generated by $g_{t}$ $(\mathbf{F} = \mathbf{F}_{t})$ ; (iii) conducting feature fusion but with a non-adaptive manner, specifically, $w_{i}$ is set to 0 for the bottom 3 layers and 1 for the top 3 layers (Non-Adap.); (iv) conducting adaptive feature fusion but in a manner contradictory to our observation (Contradict.), where we compute $\mathbf{w}_0$ via $w_{i}^{0} = 1 - l_{i} / (L + 1)$ instead. The results in Tab. 4 show that (i) fully using $\mathbf{F}_s$ as $\mathbf{F}$ is equivalent to using a naive IF-Net that has a lower performance; (ii) using $\mathbf{F}_t$ as $\mathbf{F}$ results in a significant performance drop because $g_{t}$ can hardly learn high-quality global representations with a few labels; (iii) using a non-adaptive feature fusion that complies with our observation also leads to a performance drop but performs better than those without fusion; (iv) a fusion contradictory to our observation brings a $\sim 2\%$ mIoU drop, which further supports the reasonableness of our observation. + +VCST variants Related to our VCST design, we try different combinations to achieve the best augmentation strategy. Alternative strategies include random downsampling, surface-aware sampling (clustering-based), volume-aware sampling, and adding noise. Among them, adding noise has no effect on the performance whatever other augmentations are used, which may be caused by the voxelization operation in IF-Nets. Thus we try the following variants with the combination of the other three augmentation strategies. Note that we control the dropping ratio to guarantee the expected number of dropped points (if only using dropping) are the same for all settings. The results in Tab. 5 show that: (1) the consistency training with random downsampling only crashed (the 2nd row), using volume- + +![](images/8f679287d4cee3dda884eb93a77369161ea3772fec2a805af1b4ab236f598d1b.jpg) +Figure 5. Qualitative comparison between different methods on shape completion with only $3\%$ labels for training. + +aware or surface-aware augmentation only can still work, but the surface-aware one performs better (the 3rd and 4th row), and the 4th row is the version used in our standard VCST; (3) the volume-aware augmentation can bring minor improvements on mIoU with or without random downsampling (the 3rd and 5th row), which is worse than our surface-aware one, and using both two of them even makes a negative effect (the last row). The reason for the failure of using random downsampling only is that the consistency training fails when two views are very similar in a global fashion. An intuitive explanation for (3) is that compared with our surface-aware augmentation, the incompleteness created by the volume-aware one has a larger gap with real scans. The qualitative comparisons between different variants are included in the supplementary materials. + +# 6. Conclusion + +In this paper, we propose a new task, domain adaptive shape completion of real scans, which aims to transfer the knowledge in the label-rich synthetic domain into the more challenging real domain. We construct a new dataset that + +contains elaborate 3D models created by professional artists for $10\%$ of real scans in 6 categories, which can serve for the learning of deep reconstruction models and evaluation. Besides, we develop a new domain adaptive shape completion framework with two novel modules, cross-domain feature fusion and volume-consistent self-training, to better exploit both the synthetic and real data. Extensive experiments validate the superiority and effectiveness of our method and a benchmark is constructed on the proposed task. + +Acknowledgment The work was supported in part by NSFC-62172348, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by NSFC-62172348, Outstanding Yound Fund of Guangdong Province with No. 2023B1515020055, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055). + +# References + +[1] Idan Achituve, Haggai Maron, and Gal Chechik. Self-supervised learning for domain adaptation on point clouds. In WACV, 2021. 3 +[2] Mohamed Afham, Isuru Dissanayake, Dinithi Dissanayake, Amaya Dharmasiri, Kanchana Thilakarathna, and Ranga Rodrigo. Crosspoint: Self-supervised cross-modal contrastive learning for 3d point cloud understanding. 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The proposed task SCoDA aims to transfer the knowledge in the synthetic domain to the reconstruction of noisy and incomplete real scans. A dataset, ScanSalon, with paired real scans and 3D models is contributed. Project page: yushuang-wu.github.io/SCoDA." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 423, + 192, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 423, + 192, + 435 + ], + "spans": [ + { + "bbox": [ + 143, + 423, + 192, + 435 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 449, + 290, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 290, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 290, + 643 + ], + "type": "text", + "content": "3D shape completion from point clouds is a challenging task, especially from scans of real-world objects. Considering the paucity of 3D shape ground truths for real scans, existing works mainly focus on benchmarking this task on synthetic data, e.g. 3D computer-aided design models. However, the domain gap between synthetic and real data limits the generalizability of these methods. Thus, we propose a new task, SCoDA, for the domain adaptation of real scan shape completion from synthetic data. A new dataset, ScanSalon, is contributed with a bunch of elaborate 3D models created by skillful artists according to scans. To address this new task, we propose a novel cross-domain feature fusion method for knowledge transfer and a novel volume-consistent self-training framework for robust learning from real data. Extensive experiments prove our method is effective to bring an improvement of " + }, + { + "bbox": [ + 46, + 449, + 290, + 643 + ], + "type": "inline_equation", + "content": "6\\% \\sim 7\\%" + }, + { + "bbox": [ + 46, + 449, + 290, + 643 + ], + "type": "text", + "content": " mIoU." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 668, + 127, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 668, + 127, + 680 + ], + "spans": [ + { + "bbox": [ + 47, + 668, + 127, + 680 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Shape completion and reconstruction from scans is a practical 3D digitization task that is of great significance" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 424, + 546, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 546, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 546, + 592 + ], + "type": "text", + "content": "in applications of virtual and augmented reality. It takes a scanned point cloud as input and aims to recover the 3D shape of the target object. The completion of real scans is challenging for the poor quality of point clouds and the deficiency of 3D shape ground truths. Existing methods exploit synthetic data, e.g. 3D computer-aided design (CAD) models to alleviate the demand for real object shapes. For example, authors of [18, 26, 35] simulate the scanning process to obtain point clouds from CAD models with paired ground truth shapes to train learning-based reconstruction models. However, there still exist distinctions between the simulated and real scan because the latter is scanned from a real object with complex scanning noise and occlusion, which limits the generalization quality." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "Considering the underexploration in this field, we propose a new task, SCoDA, Domain Adaptive Shape Completion, that aims to transfer the knowledge from the synthetic domain with rich clean shapes (source domain) into the shape completion of real scans (target domain), as illustrated in Fig. 1. To this end, we, for the first time, build an object-centric dataset, ScanSalon, which consists of real Scans with Shape manual annotations. Our ScanSalon contains a bunch of 3D models that are paired with real scans of objects in six categories: chair, desk/table, sofa, bed, lamp," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17630" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "and car. The 3D models are manually created of high quality by skillful artists for around " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " of real scans, which can serve as the evaluation ground truths of shape completion or as the few labels for semi-supervised domain adaptation. See Fig. 1 for some examples, and details of ScanSalon are exposed in Sec. 4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 289, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 289, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 289, + 550 + ], + "type": "text", + "content": "The main challenge of the proposed SCoDA task lies in the domain gap between synthetic and real point clouds. Due to the intrinsic complexity of the scanning process, e.g., the scanner parameters and object materials, it is difficult to simulate the scans in terms of sparsity, noisy extent, etc. More importantly, real scans are usually incomplete resulting from the scene layout and object occlusion during scanning, which can hardly be simulated. Thus, we propose a novel domain adaptive shape completion approach to transfer the rich knowledge from the synthetic domain to the real one. At first, the reconstruction module in our approach is based on an implicit function for continuous shape completion [18, 54, 58]. For an effective transfer, we observe that although the local patterns of real scans (e.g., noise, sparsity, and incompleteness) are distinct from the simulated synthetic ones, the global topology or structure in a same category is usually similar between the synthetic and real data, for example, a chair from either the synthetic or real domain usually consists of a seat, a backrest, legs, etc. (see Fig. 1). In other words, the global topology is more likely to be domain invariant, while the local patterns are more likely to be domain specific. Accordingly, we propose a cross-domain feature fusion (CDFF) module to combine the global features and local features learned in the synthetic and real domain, respectively, which helps recover both fine details and global structures in the implicit reconstruction stage. Moreover, a novel volume-consistent selftraining (VCST) framework is developed to encourage self-supervised learning from the target data. Specifically, we create two views of real scans by dropping different clusters of points to produce incompleteness of different extent, and the model is forced to make consistent implicit predictions at each spatial volume, which encourages the model's robustness to the incompleteness of real scans." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 552, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 612 + ], + "type": "text", + "content": "To construct a benchmark on the proposed new task, we implement some existing solutions to related tasks as baselines, and develop extensive experiments for the baselines and our method on ScanSalon. These experiments also demonstrate the effectiveness of the proposed method." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 615, + 255, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 615, + 255, + 627 + ], + "spans": [ + { + "bbox": [ + 59, + 615, + 255, + 627 + ], + "type": "text", + "content": "In summary, our key contributions are four-fold:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 629, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 629, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 629, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 58, + 629, + 287, + 677 + ], + "type": "text", + "content": "- We propose a new task, SCoDA, namely domain adaptive shape completion for real scans; A dataset ScanSalon that contains 800 elaborate 3D models paired with real scans in 6 categories is contributed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 678, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 678, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 678, + 287, + 714 + ], + "type": "text", + "content": "- A novel cross-domain feature fusion module is designed to combine the knowledge of global shapes and local patterns learned in the synthetic and real domain," + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 96 + ], + "type": "text", + "content": "respectively. Such a feature fusion manner may also inspire the works in the 2D domain adaption field." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 96, + 545, + 180 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 96, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 96, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 317, + 96, + 545, + 132 + ], + "type": "text", + "content": "- A volume-consistent self-training framework is proposed to improve the robustness of shape completion to the complex incompleteness of real scans." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 133, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 133, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 317, + 133, + 545, + 180 + ], + "type": "text", + "content": "- A benchmark with multiple methods evaluated is constructed for the task of SCoDA based on ScanSalon; Extensive experiments also demonstrate the superiority of the proposed method." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 195, + 392, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 195, + 392, + 209 + ], + "spans": [ + { + "bbox": [ + 306, + 195, + 392, + 209 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 219, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 545, + 651 + ], + "type": "text", + "content": "Shape Completion Shape completion or reconstruction from point clouds is a branch of 3D reconstruction task [20, 47, 54, 68, 72, 91, 94]. The recovered shape can be represented as dense points [45, 46, 60] (i.e., point cloud completion or consolidation), polygonal meshes [28, 35, 48, 78], manifold atlases [4, 25, 27, 32, 83], voxel grids [20, 34, 85], or implicit representations [18, 26, 40, 61, 70, 82]. Among them, the task of point cloud completion is related to our work, which aims to recover a complete, dense, and clean point cloud for the 3D shape, from a partial, sparse, and noisy input scanned by sensors. The pioneering work, PCN [99], proposes a coarse-to-fine completion framework with an encoder-decoder architecture, which encodes the partial points into global features and recovers the fined results in the decoding stage. The following works explore further to better exploit local or multi-scale features for higher-quality completion [38, 49, 57, 73, 76, 77, 80, 81, 89, 92, 95, 98, 99, 101]. In addition, the implicit representation based approaches now attract increasing attention because of its superior property that enables continuous shape recovery for objects with arbitrary topologies [17, 18, 54, 58]. Although numerous efforts have been contributed, the existing approaches are usually performed on point clouds scanned from synthetic data via simulation, and a straightforward application on real scans results in an unsatisfactory performance due to the domain gap between synthetic and real scans [18, 26, 64]. For the task of point completion, some works also adopt unsupervised or weakly-supervised learning techniques to learn from unlabeled data [8, 14, 33, 79, 86, 87, 100]. Another line of works retrieve suitable models from 3D CAD repositories and deform them as the estimated shape ground truths of object scans [3, 75]. Differently, our work first proposes the task of domain adaptive shape completion for real scans, which aims to sufficiently transfer the knowledge from the label-rich synthetic domain into real scan shape completion." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "2D Domain Adaptation Domain adaptation has been a popular research topic in various 2D vision tasks, including image recognition [5, 11, 15, 22, 24, 29, 50, 67], semantic segmentation [16, 36, 52, 53], and object detection [12, 42, 55, 65]. Existing works can broadly be categorized as (i)" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17631" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": "adversarial-based methods [12, 13, 15, 16, 22, 67] that train a discriminator to discriminate the source and the target domain, (ii) alignment-based methods [11, 24, 29, 65, 78] that use pre-defined metrics to align the source and the target domain, and (iii) self-training-based methods [5, 36, 52, 53, 55] that exploit the pseudo labels of the target domain to train the model. Recently, consistency-based self-training methods have become the most popular approach due to their impressive performance. One key factor in the success of consistency training is the augmentations applied to the inputs [31, 71, 93], e.g., stronger augmentations have better performance in domain adaptive image recognition [5]. To this end, we design a novel consistency training framework specialized for the shape completion task. Furthermore, we propose to conduct knowledge transfer via a cross-domain feature fusion manner, which has not been explored by existing works, to our best knowledge." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 602 + ], + "type": "text", + "content": "3D Domain Adaptation In the 3D vision field, existing works on domain adaptation are mainly committed to the task of point cloud understanding, including classification, part segmentation, and semantic segmentation. For object-centric point clouds, PointDAN [63] constructs a domain adaptive classification benchmark by collecting point clouds from ShapeNet [10], ModelNet [88], and ScanNet [23] datasets to compose 3 different domains. It also proposes an adversarial representation learning approach with feature alignment at both local and global levels. The following works improve the classification precision by adopting techniques of consistency training [44], self-training [9, 103], multimodal learning [2], or learning from self-supervised tasks [1, 37, 51, 69]. Another line of works are committed to scene-centric point cloud analysis, i.e., point cloud semantic segmentation [6, 7, 39, 41, 59, 66, 84, 90, 96, 102]. Considering the exhaustive annotation process for 3D point semantics, they propose to transfer the segmentation knowledge in synthetic scenes into real-world point clouds [41, 84, 90, 102]. Besides, there are a few attempts contributed to domain adaptive single-view reconstruction (SVR) [43, 62, 97], which is highly related to our work. Except for the difference in tasks (SVR v.s. shape completion), these works usually apply existing domain adaptation techniques to the target task, while we propose a novel domain adaptation method based on cross-domain feature fusion, which may also inspire others working on domain adaption." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 609, + 104, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 104, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 104, + 621 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "IF-Nets are a promising reconstruction method for their impressive performance [18], which is also successfully used in many applications [19, 56]. Constructed on IF-Nets, our approach first improves the representation learning by proposing a novel cross-domain feature fusion module, which aims to transfer the knowledge on the global-level object shape learned in the label-rich synthetic domain into" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "the real domain. Secondly, to exhaust the domain-specific information in the real data, a novel volume-consistent self-training method is proposed for the specific shape completion task, which also leads to a robust implicit prediction of IF-Nets. An illustration is presented in Fig. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 140, + 454, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 140, + 454, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 140, + 454, + 152 + ], + "type": "text", + "content": "3.1. Implicit Feature Networks" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "type": "text", + "content": "We first introduce IF-Nets [18] as our reconstruction framework. An IF-Net is composed of a 3D convolution neural network encoder " + }, + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "type": "text", + "content": " for multi-scale feature extraction and a multi-layer perceptron (MLP) " + }, + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 158, + 547, + 218 + ], + "type": "text", + "content": " for implicit shape decoding." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": "Given a point cloud sample " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": ", it is first converted into a discrete voxel representation " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N \\times N \\times N}" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "N \\in \\mathbb{N}" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": " is the resolution of the input space. " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": " is then fed into the " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": "-layer encoder " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": " to generate a set of multiscale features " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{F}_1, \\dots, \\mathbf{F}_L\\}" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": ", then they are upsampled to the same spatial dimension and been concatenated along the channel dimension to create the final feature " + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{F} =" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": " concat(" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{upsample}(\\mathbf{F}_1), \\dots, \\mathrm{upsample}(\\mathbf{F}_L)\\}" + }, + { + "bbox": [ + 304, + 219, + 547, + 316 + ], + "type": "text", + "content": "). Formally:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 322, + 323, + 529, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 323, + 529, + 338 + ], + "spans": [ + { + "bbox": [ + 322, + 323, + 529, + 338 + ], + "type": "interline_equation", + "content": "g (\\mathbf {X}) = \\mathbf {F}, \\quad \\mathbf {X} \\in \\mathbb {R} ^ {N \\times N \\times N}, \\mathbf {F} \\in \\mathbb {R} ^ {d \\times N \\times N \\times N},", + "image_path": "d03a97521eac204e7f9855c051cf96389b618a04af2c7df472b64b6ca4a809d2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": " is the feature channel number that equals the summation of the channel numbers of " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_i" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": " has a 3D structure aligned with the input " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": ". Given a point query " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": ", continuous features " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{F}(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": " at this point can be extracted from " + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 346, + 546, + 407 + ], + "type": "text", + "content": " using trilinear interpolation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "type": "text", + "content": "Then, the encoding at the point " + }, + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "type": "text", + "content": " is fed into a point-wise decoder " + }, + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 407, + 547, + 443 + ], + "type": "text", + "content": " to give a binary prediction indicating if the point lies inside or outside the shape:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 362, + 453, + 490, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 453, + 490, + 466 + ], + "spans": [ + { + "bbox": [ + 362, + 453, + 490, + 466 + ], + "type": "interline_equation", + "content": "f (\\mathbf {F}, \\mathbf {p}) = f (\\mathbf {F} (\\mathbf {p})) \\mapsto \\{0, 1 \\}.", + "image_path": "ce619b6a2f38bff4ed6ae4e768807fc5a989bd5f2fb8aed3a8857b3d48ebc010.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "text", + "content": "Given the occupancy value " + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "inline_equation", + "content": "o(\\mathbf{p}) \\in \\{0,1\\}" + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "text", + "content": " at each position " + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "text", + "content": " pre-computed according to the ground truth shape mesh, a binary cross-entropy loss is used to train " + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 475, + 546, + 512 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 353, + 520, + 497, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 520, + 497, + 534 + ], + "spans": [ + { + "bbox": [ + 353, + 520, + 497, + 534 + ], + "type": "interline_equation", + "content": "\\min L _ {I F} = \\operatorname {B C E} \\left(f (\\mathbf {F}, \\mathbf {p}), o (\\mathbf {p})\\right).", + "image_path": "b63df10cd5f2b26f7fd68cb4850b0caca5ddeab5894476b7bea56abae306618b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 544, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 567 + ], + "type": "text", + "content": "Note that the prediction values can also be continuous signed distance values as in [58]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 575, + 470, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 470, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 470, + 586 + ], + "type": "text", + "content": "3.2. Cross-Domain Feature Fusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "The training of a naive IF-Net demands ground truth shapes for generating numerous occupancy labels to supervise the output of " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": ", yet most of the real scans are unpaired with shape ground truths. So we develop a cross-domain feature fusion module to well transfer the knowledge in the label-rich source domain. Our idea of exploiting the source knowledge stems from an important observation: although synthetic data have distinct local patterns from real scans, the global-level knowledge (e.g., the common structure and coarse shape) of a certain category can" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17632" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 70, + 509, + 247 + ], + "blocks": [ + { + "bbox": [ + 83, + 70, + 509, + 247 + ], + "lines": [ + { + "bbox": [ + 83, + 70, + 509, + 247 + ], + "spans": [ + { + "bbox": [ + 83, + 70, + 509, + 247 + ], + "type": "image", + "image_path": "9b6304c49bdf1f51f86bd8b5cb1626104a2f60801d445ca279e6b003a2133e8d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 547, + 298 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed method. Two IF-Net encoders are used for the source and the target domain, respectively, and they share an implicit function decoder. The cross-domain feature fusion (CDFF) works by adaptively combining the global-level and local-level knowledge learned from the source and target domain, respectively. The volume-consistency self-training (VCST) works by enforcing the prediction consistency between two different augmented views to learn the local details." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 303, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 373 + ], + "type": "text", + "content": "be shared in both domains. Besides, the target data with few labels may be enough for learning rich local-level information. On the other hand, IF-Nets conduct shape completion via exploiting local representations, so it is important to extract high-quality local-level features without introducing bias from the source domain." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": "To this end, we develop a cross-domain feature fusion module (CDFF) for knowledge transfer. First, two shape encoders, " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "g_{s}(\\cdot)" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "g_{t}(\\cdot)" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": ", are used for feature extraction of source and target data, generating " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": ", respectively. As explained above, " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": " contains rich global information, and " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": " is more reliable in providing domain-specific local-level representations. A simple linear combination is adopted to fuse them into " + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 375, + 287, + 469 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 109, + 475, + 224, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 475, + 224, + 488 + ], + "spans": [ + { + "bbox": [ + 109, + 475, + 224, + 488 + ], + "type": "interline_equation", + "content": "\\mathbf {F} = \\mathbf {w} \\cdot \\mathbf {F} _ {s} + (1 - \\mathbf {w}) \\cdot \\mathbf {F} _ {t},", + "image_path": "00e3b21c3ecc06b7c5a21c3329a333aa0b77364fd1c2a51d92bedaba8ad12fc5.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{w} \\in [0,1]^d" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " is a channel-wise weight vector. To better combine the advantages of " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": ", the computation of " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " takes two aspects into account: (i) exploiting the global-level features in " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " while believing " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " for local ones (based on our observation), and (ii) learning " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " adaptively to maintain the flexibility. The adaptive weight vector " + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 493, + 287, + 577 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 110, + 577, + 223, + 589 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 577, + 223, + 589 + ], + "spans": [ + { + "bbox": [ + 110, + 577, + 223, + 589 + ], + "type": "interline_equation", + "content": "\\mathbf {w} = \\alpha \\cdot h \\left(\\mathbf {F} _ {s} \\odot \\mathbf {F} _ {t}\\right) + \\mathbf {w} ^ {0},", + "image_path": "f2440868c67eb11eebac2ebd15f1ce179400850792d26d3f4f63fce6b7291b3b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\mathbb{R}^{+}" + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": " is the ratio of adaptiveness, " + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "inline_equation", + "content": "h(\\cdot)\\mapsto [0,1]^d" + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": " is a two-layer MLP with a sigmoid activation at the output layer, and " + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": " indicates the operation of element-wise multiplication plus a global pooling on the spatial dimension (returns a vector of dimension " + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^0\\in [0,1]^d" + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": " is a constant weight vector that implies a prior derived from our observation, of which each value " + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "inline_equation", + "content": "w_{i}^{0}" + }, + { + "bbox": [ + 46, + 592, + 288, + 688 + ], + "type": "text", + "content": " is simply defined by a linear mapping as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 101, + 693, + 233, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 693, + 233, + 717 + ], + "spans": [ + { + "bbox": [ + 101, + 693, + 233, + 717 + ], + "type": "interline_equation", + "content": "w _ {i} ^ {0} = \\frac {l _ {i}}{L + 1}, i \\in \\{1, 2, \\dots , d \\},", + "image_path": "30d9606211d2602853c3ade557787de52f276e5aa14e29092751c335c7ee568f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "inline_equation", + "content": "l_{i}\\in \\{1,2,\\dots ,L\\}" + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "content": " indicates which layer the " + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "content": " -th channel belongs to. In this way, the deeper layer one channel is from, the more the computation of " + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "content": " in this channel relies on " + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "content": " , as the deeper layers of IF-Nets capture more global information. In addition, a clipping operation is applied to " + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 303, + 545, + 376 + ], + "type": "text", + "content": " to limit all values to [0, 1]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 383, + 479, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 479, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 479, + 396 + ], + "type": "text", + "content": "3.3. Volume-Consistent Self-training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 402, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 545 + ], + "type": "text", + "content": "With few shape ground truths in the target domain, it is hard to learn rich information in a supervised manner. A typical way is to adopt self-supervised learning to learn from the data itself. In the task of SCoDA, the incompleteness is a significant characteristic of real scans that hampers the shape completion quality. Thus, we create two views of scans with different levels of incompleteness, and encourage the model to make consistent implicit predictions on their volume occupancy. Such a volume-consistent self-training (VCST) encourages the model to keep robust to various incompleteness and \"imagine\" the missing parts for shape completion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Specifically, we first adopt an unsupervised clustering algorithm (e.g., " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "-means clustering) to partition the point cloud into " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " different parts (see Fig. 2 for examples). The clustering is based only on the spatial positions of points and thus coarsely splits an object scan into multiple components. With the pre-computed partitions, two views " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^A" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^B" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " can be generated by randomly dropping different clusters of points from the original real scan, with " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "K_A" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "K_B" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " clusters left, respectively, where " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "K \\geq K_A > K_B" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": ". Besides, two random downsamplings are also conducted on the two views to create different sparsity. Note that the clustering-based augmentation is actually a surface-aware augmentation. Compared with volume-based ones that randomly mask some spatial volumes, our augmentation strat" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17633" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 273, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 273, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 273, + 83 + ], + "type": "text", + "content": "egy implies more object-part knowledge to some extent." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "type": "text", + "content": "Given the two views of input, their features are extracted by " + }, + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "type": "text", + "content": " and then taken by " + }, + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 47, + 84, + 286, + 108 + ], + "type": "text", + "content": " to give implicit predictions:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 116, + 128, + 216, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 128, + 216, + 140 + ], + "spans": [ + { + "bbox": [ + 116, + 128, + 216, + 140 + ], + "type": "interline_equation", + "content": "g \\left(\\mathbf {X} ^ {v}\\right) = \\mathbf {F} ^ {v}, v = A, B,", + "image_path": "cf93e64a5d2f7d6374a957cf46e069054fa4f76b2e3a47fdaebd2974d6a9b955.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 117, + 144, + 197, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 144, + 197, + 156 + ], + "spans": [ + { + "bbox": [ + 117, + 144, + 197, + 156 + ], + "type": "interline_equation", + "content": "f (\\mathbf {F} ^ {v}, \\mathbf {p}) \\mapsto \\{0, 1 \\}.", + "image_path": "8dcf975bc3df182af37f7536457de283e2d374478aba89634b0a07cb944cd57f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^v" + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "text", + "content": " can also be generated via our CDFF module. Here we simplify the formulation to better present our VCST. The consistency constraint is imposed on the implicit predictions of " + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "inline_equation", + "content": "f(\\mathbf{F}^A, \\mathbf{p})" + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "inline_equation", + "content": "f(\\mathbf{F}^B, \\mathbf{p})" + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "text", + "content": " with the same point query " + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 164, + 286, + 224 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 231, + 252, + 245 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 231, + 252, + 245 + ], + "spans": [ + { + "bbox": [ + 80, + 231, + 252, + 245 + ], + "type": "interline_equation", + "content": "\\min L _ {C T} = \\operatorname {B C E} \\left(f \\left(\\mathbf {F} ^ {B}, \\mathbf {p}\\right), f \\left(\\mathbf {F} ^ {A}, \\mathbf {p}\\right)\\right),", + "image_path": "a427bf85a1a17749fd54546853d35ea3468539856e25319b9fe59ecc5937ff3f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "\\mathrm{BCE}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": " indicates the binary cross-entropy loss. The consistency objective can be viewed as using the prediction from view " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": " as the pseudo label of view " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": ", because " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^B" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": " has a poorer completeness than " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^A" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "K_{B} < K_{A}" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": ". As there will be noises in the implicit predictions due to the limited shape ground truths of target data, using the noisy prediction as the pseudo label will mislead the training. Therefore, a thresholding operation is performed to mask the predictions with low confidence in " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "f(\\mathbf{F}^{A},\\mathbf{p})" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": ". The overall loss function is a summation of " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "L_{IF}" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "inline_equation", + "content": "L_{CT}" + }, + { + "bbox": [ + 46, + 253, + 286, + 373 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 383, + 101, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 101, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 101, + 395 + ], + "type": "text", + "content": "4. Dataset" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 50, + 412, + 284, + 485 + ], + "blocks": [ + { + "bbox": [ + 50, + 412, + 284, + 485 + ], + "lines": [ + { + "bbox": [ + 50, + 412, + 284, + 485 + ], + "spans": [ + { + "bbox": [ + 50, + 412, + 284, + 485 + ], + "type": "image", + "image_path": "75c986c6fb6b5054376985142a087137891c01410a20ab91b2f95bd2442f007d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 491, + 286, + 536 + ], + "lines": [ + { + "bbox": [ + 46, + 491, + 286, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 286, + 536 + ], + "type": "text", + "content": "Figure 3. The procedure of 3D model crafting. From left to right: (i) extracting the object scan from a scene; (ii) constructing a coarse mesh frame to fit the scan; (iii) adding fine details; (iv) adjusting the defects detected by inspectors." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "content": "Overview The proposed ScanSalon dataset collects 7,644 real scans, of which 800 objects are equipped with 3D shape (artificial) ground truths. All models or scans are from 6 categories of objects, with 5 common indoor objects: chair, desk (or table), sofa, bed, and lamp, and 1 outdoor object: car. Detailed statistics are listed in Tab. 1. In Fig. 4, we exhibit some samples of real scans and corresponding 3D shapes in ScanSalon. More visualizations could be seen in the supplementary materials." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "Data Collection The real scans are collected from two datasets, the ScanNet [23] and KITTI [30] dataset for indoor and outdoor objects, respectively. The object scans are extracted from a scene point cloud according to the point-level instance segmentation annotations provided by the two" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 86, + 549, + 126 + ], + "blocks": [ + { + "bbox": [ + 328, + 72, + 522, + 83 + ], + "lines": [ + { + "bbox": [ + 328, + 72, + 522, + 83 + ], + "spans": [ + { + "bbox": [ + 328, + 72, + 522, + 83 + ], + "type": "text", + "content": "Table 1. Statistics of the proposed dataset ScanSalon." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 86, + 549, + 126 + ], + "lines": [ + { + "bbox": [ + 309, + 86, + 549, + 126 + ], + "spans": [ + { + "bbox": [ + 309, + 86, + 549, + 126 + ], + "type": "table", + "html": "
ChairDeskSofaBedLampCarTotal
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", + "image_path": "1ed107dee7221100eddc80810e7936ee3ce67abc502697e258e0e8d83ee6b1e7.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 137, + 545, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 545, + 196 + ], + "type": "text", + "content": "datasets, and then rotated and normalized into the same pose and scale, with the aid of pose annotations provided by the Scan2CAD [3] and KITTI [30] dataset. These data are also aligned with models in the ShapeNet database [10], which provides a bunch of synthetic models as the source domain." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 198, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 461 + ], + "type": "text", + "content": "Shape Annotation for Real Scans Two skillful artists participate in the annotation procedure. In addition to the real scans, we provide several photos for each scan from different viewpoints (selected from the videos contained in the ScanNet and KITTI datasets), which provide 2D references to improve the model quality. A brief creation pipeline is shown in Fig. 3, where the artists are required to create the shapes according to both scans and photo references (see Fig. 4), overcome the distractions of scan noise, and recover the incompleteness by his/her rich experience when the photo references are poor or inadequate. They use professional 3D software, Maya to create models. On average, it takes " + }, + { + "bbox": [ + 304, + 198, + 545, + 461 + ], + "type": "inline_equation", + "content": "0.5 \\sim 1.0" + }, + { + "bbox": [ + 304, + 198, + 545, + 461 + ], + "type": "text", + "content": " person-hours to create a 3D model and the creation of all 800 models takes 2.5 months in total. For each created model, another 8 inspectors are invited to verify their (i) recovery extent compared with the real objects in photos and (ii) matching extent with the given scan, and the defects will be fed back to artists for further adjustments until no defects are detected by any inspector. Considering the inaccessibility of the objects in scans from ScanNet and KITTI, we have made our greatest efforts to create artificial ground truth shapes for these scans." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 473, + 386, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 473, + 386, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 473, + 386, + 487 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 493, + 365, + 505 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 493, + 365, + 505 + ], + "spans": [ + { + "bbox": [ + 306, + 493, + 365, + 505 + ], + "type": "text", + "content": "5.1. Settings" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "content": "Benchmark setting We define two settings for the proposed task, which give only " + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "content": " shape ground truths (e.g. 47 and 140 chair models randomly sampled from all 4,651 chair scans, respectively) of real scans in the training set, and the rest of samples with corresponding 3D models compose the test set. Note that the " + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "content": " labeled samples are covered in the " + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "content": " labels for observing a cross-setting comparison when given more labels. For evaluation, we consider two metrics to measure the shape completion quality, mIoU: mean volumetric intersection over union (higher is better), and CD: " + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 304, + 514, + 545, + 668 + ], + "type": "text", + "content": " chamfer distance (lower is better). The former measures the matching extent of the defined volumes and the latter measures the surface accuracy." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 671, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 545, + 694 + ], + "type": "text", + "content": "Baselines We implement four baseline methods to construct the benchmark of the new task. 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Experiment results on the " + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "text", + "content": " labels setting of the SCoDA task. The units of CD and mIoU value are " + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "inline_equation", + "content": "\\%" + }, + { + "bbox": [ + 46, + 331, + 544, + 354 + ], + "type": "text", + "content": ", respectively. Red text indicates the best and blue text indicates the second best result, respectively (similarly hereinafter)." + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 231, + 356, + 361, + 365 + ], + "lines": [ + { + "bbox": [ + 231, + 356, + 361, + 365 + ], + "spans": [ + { + "bbox": [ + 231, + 356, + 361, + 365 + ], + "type": "text", + "content": "(a) Results on the " + }, + { + "bbox": [ + 231, + 356, + 361, + 365 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 231, + 356, + 361, + 365 + ], + "type": "text", + "content": " labels setting." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 366, + 543, + 449 + ], + "lines": [ + { + "bbox": [ + 50, + 366, + 543, + 449 + ], + "spans": [ + { + "bbox": [ + 50, + 366, + 543, + 449 + ], + "type": "table", + "html": "
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.5756.102.4443.040.6579.031.6467.301.6739.890.7474.771.4560.02
SelfSup1.4958.553.4942.970.5581.161.5968.582.4151.420.6278.751.6963.57
PtComp1.6157.332.1644.260.5179.901.5268.231.9546.970.5980.351.3962.84
Adversarial1.7458.542.9946.020.4681.421.3771.322.4356.390.6778.911.6165.43
Ours1.5860.772.3648.620.4282.001.5773.051.6258.570.4180.961.3267.32
", + "image_path": "289bc02c36314c7efadb0742d3cfbe88b431afeec4406cf7751da61ab094b9be.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "table_body" + } + ], + "index": 33 + }, + { + "type": "table", + "bbox": [ + 50, + 463, + 543, + 547 + ], + "blocks": [ + { + "bbox": [ + 231, + 453, + 361, + 463 + ], + "lines": [ + { + "bbox": [ + 231, + 453, + 361, + 463 + ], + "spans": [ + { + "bbox": [ + 231, + 453, + 361, + 463 + ], + "type": "text", + "content": "(b) Results on the " + }, + { + "bbox": [ + 231, + 453, + 361, + 463 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 231, + 453, + 361, + 463 + ], + "type": "text", + "content": " labels setting." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 463, + 543, + 547 + ], + "lines": [ + { + "bbox": [ + 50, + 463, + 543, + 547 + ], + "spans": [ + { + "bbox": [ + 50, + 463, + 543, + 547 + ], + "type": "table", + "html": "
MethodChairDeskSofaBedLampCarAverage
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
IF-Net1.8856.982.1444.870.5082.040.6676.051.7251.330.5280.131.2465.23
SelfSup2.0859.422.7346.390.5182.250.6177.221.4662.020.4381.891.0968.06
PtComp1.3457.981.8346.200.3282.660.6179.071.4461.610.4381.891.0068.24
Adversarial1.7160.582.1348.460.4183.540.5180.811.3364.220.4181.861.0869.91
Ours1.3761.482.0950.930.3182.710.4182.271.5767.800.4683.121.0471.39
", + "image_path": "8b8fa2f3f0ee36171c1c05085ccb09bb49ed62a1466e2a074a0d9e3ffa9c85bd.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "table_body" + } + ], + "index": 35 + }, + { + "bbox": [ + 46, + 553, + 287, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 708 + ], + "type": "text", + "content": "Net [18] is adopted without any other designs and is trained on all supervised samples (including synthetic and real labels); (ii) SelfSup: a self-supervised IF-Net that conducts feature-level consistency (by minimizing the distance between two domain feature vectors) on unsupervised samples [50]; (iii) PtComp: a domain adaptive point completion method [14] is re-implemented to align the real scan inputs with the synthetic ones, incorporated with an extra IF-Net for implicit shape reconstruction. Note the encoder and decoder used in [14] are revised into a voxel-based 3D CNN to incorporate with IF-Net; (iv) Adversarial: a domain adaptive IF-Net is exploited with adversarial feature learning [43, 74, 87] to learn domain-invariant features. The de" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 553, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 553, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 305, + 553, + 545, + 578 + ], + "type": "text", + "content": "tailed implementation details of each baseline are included in the supplementary materials for the space limit." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Implementation details We adopt a 6-layer 3DCNN as the encoder with a 4-layer MLP as the decoder to implement the IF-Nets, using the official codes released by [18]. Following [18], the channel dimension of multi-scale features is 2,583, and a resolution " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "N = 32" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " is used for the training of reconstruction. For evaluation, we use a higher resolution with " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "N = 128" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ". In the CDFF module, " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " is set to 0.2 to better combine the advantages of " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ". For the augmentation strategy in VCST, " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_A" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " is randomly selected from " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{7,8\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "K_B" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " is randomly selected from " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{5,6,7\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " for each data sample. The downsampling randomly sam" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "17635" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 87, + 286, + 147 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 285, + 84 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 285, + 84 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 285, + 84 + ], + "type": "text", + "content": "Table 3. Ablation on using the single module of CDFF or VCST." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 87, + 286, + 147 + ], + "lines": [ + { + "bbox": [ + 50, + 87, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 50, + 87, + 286, + 147 + ], + "type": "table", + "html": "
ChairBedLamp
CD↓mIoU↑CD↓mIoU↑CD↓mIoU↑
CDFF+VCST1.5860.771.5773.051.6258.57
CDFF only1.4958.551.9171.191.7353.18
VCST only2.0859.421.6372.621.8550.18
", + "image_path": "22c1aada6de3b961586eca6a4adac1a08ee6c374e605e34544c01ce03663eba6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 167, + 286, + 229 + ], + "blocks": [ + { + "bbox": [ + 70, + 153, + 263, + 164 + ], + "lines": [ + { + "bbox": [ + 70, + 153, + 263, + 164 + ], + "spans": [ + { + "bbox": [ + 70, + 153, + 263, + 164 + ], + "type": "text", + "content": "Table 4. Analysis of the design of the CDFF module." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 167, + 286, + 229 + ], + "lines": [ + { + "bbox": [ + 50, + 167, + 286, + 229 + ], + "spans": [ + { + "bbox": [ + 50, + 167, + 286, + 229 + ], + "type": "table", + "html": "
FusionObserv.AdaptiveCD↓mIoU↑
Ours✓✓✓1.4958.55
F = Fs1.57 (+0.08)56.10 (-2.45)
F = Ft2.22 (+0.73)54.98 (-3.57)
Non-Adap.✓✓1.92 (+0.43)57.77 (-0.78)
Contrad.✓✓1.96 (+0.47)56.62 (-1.93)
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A thresholding operation is adopted to filter out predictions with a confidence in (0.1, 0.9) (viewed as unconfident predictions) from view " + }, + { + "bbox": [ + 46, + 237, + 287, + 345 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 237, + 287, + 345 + ], + "type": "text", + "content": " to guarantee the quality of consistency training [71]. All models are trained with an Adam optimizer and a learning rate " + }, + { + "bbox": [ + 46, + 237, + 287, + 345 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 237, + 287, + 345 + ], + "type": "text", + "content": ", with a minibatch size 4. " + }, + { + "bbox": [ + 46, + 237, + 287, + 345 + ], + "type": "inline_equation", + "content": "L_{CT}" + }, + { + "bbox": [ + 46, + 237, + 287, + 345 + ], + "type": "text", + "content": " only works on unsupervised data. More implementation details of our method are introduced in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 354, + 105, + 366 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 105, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 105, + 366 + ], + "type": "text", + "content": "5.2. Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": "Quantitative comparison The performance of baseline methods and ours are listed in Tab. 2 on the " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " labels settings. It can be seen that our method is superior to all baselines. On the " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " labels setting, our method achieves " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "1.32 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " on CD and " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "67.32\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " on mIoU on average, which is higher than the second best \"Adversarial\" by " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\sim 0.3 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " CD and " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\sim 2\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " mIoU. Besides, our method achieves good performances consistently over all 6 categories, most of which get a top rank over all 5 methods. The adversarial domain adaption method achieves the top mIoU among all baseline methods. Besides, our method also achieves the best performance on the " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " setting for both average CD and mIoU. In addition, it can be observed that an extra " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " labels bring an improvement of around " + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 590 + ], + "type": "text", + "content": " mIoU to all methods, and the improvements are especially significant for the categories \"bed\" and \"lamp\", which shows the promising practical value to provide a few more real-data labels to boost the shape completion quality from real scans." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Qualitative comparison We visualize the shape completion results of different methods in Fig. 5 to qualitatively compare baselines and our method. With the implicit prediction at each grid, a threshold of 0.5 is used to justify whether an occupancy is predicted here. The resulting occupancy grids with resolution 128 are then transformed into a mesh using the marching cubes algorithm [21]. The visualizations present the superiority of the proposed method, which achieves better completion for missing parts and generates fewer defects almost in all samples of Fig. 5." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 326, + 87, + 522, + 167 + ], + "blocks": [ + { + "bbox": [ + 328, + 72, + 522, + 84 + ], + "lines": [ + { + "bbox": [ + 328, + 72, + 522, + 84 + ], + "spans": [ + { + "bbox": [ + 328, + 72, + 522, + 84 + ], + "type": "text", + "content": "Table 5. Analysis of the design of the VCST module." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 87, + 522, + 167 + ], + "lines": [ + { + "bbox": [ + 326, + 87, + 522, + 167 + ], + "spans": [ + { + "bbox": [ + 326, + 87, + 522, + 167 + ], + "type": "table", + "html": "
Random Volume SurfaceCD↓mIoU↑
w/o consistency training1.5756.10
✓3.65 (+2.08)47.60 (-8.50)
✓2.03 (+0.46)57.55 (+1.45)
✓2.37 (+0.80)59.03 (+2.93)
✓✓2.08 (+0.51)59.42 (+3.32)
✓✓2.37 (+0.80)58.13 (+2.03)
✓✓✓2.30 (+0.73)58.55 (+2.45)
", + "image_path": "94664c61c9e7e277c10fc123346afb99e15639e4d915fca6756880e473d06c67.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 182, + 369, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 182, + 369, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 182, + 369, + 194 + ], + "type": "text", + "content": "5.3. Ablation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 203, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 203, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 203, + 545, + 276 + ], + "type": "text", + "content": "Single module We first conduct ablative studies on using the CDFF or VCST module only. The results on 3 categories of the " + }, + { + "bbox": [ + 304, + 203, + 545, + 276 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 203, + 545, + 276 + ], + "type": "text", + "content": " label setting confirm the effectiveness of either of them, see Tab. 3. Besides, integrating both two methods brings an extra performance gain, which shows the complementary functions of these two modules." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": "CDFF variants Next, we implement ablations on different variants of the proposed two modules, and all experiments are conducted on the \"chair\" category under the " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " label setting. For the CDFF module, we experiment such variants: (i) using the whole features generated by " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "g_{s}" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " rather than via feature fusion " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "(\\mathbf{F} = \\mathbf{F}_s)" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": "; (ii) without fusion but using the whole features generated by " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "(\\mathbf{F} = \\mathbf{F}_{t})" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": "; (iii) conducting feature fusion but with a non-adaptive manner, specifically, " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " is set to 0 for the bottom 3 layers and 1 for the top 3 layers (Non-Adap.); (iv) conducting adaptive feature fusion but in a manner contradictory to our observation (Contradict.), where we compute " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_0" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " via " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "w_{i}^{0} = 1 - l_{i} / (L + 1)" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " instead. The results in Tab. 4 show that (i) fully using " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_s" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " is equivalent to using a naive IF-Net that has a lower performance; (ii) using " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_t" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " results in a significant performance drop because " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "g_{t}" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " can hardly learn high-quality global representations with a few labels; (iii) using a non-adaptive feature fusion that complies with our observation also leads to a performance drop but performs better than those without fusion; (iv) a fusion contradictory to our observation brings a " + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\sim 2\\%" + }, + { + "bbox": [ + 304, + 279, + 545, + 542 + ], + "type": "text", + "content": " mIoU drop, which further supports the reasonableness of our observation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "VCST variants Related to our VCST design, we try different combinations to achieve the best augmentation strategy. Alternative strategies include random downsampling, surface-aware sampling (clustering-based), volume-aware sampling, and adding noise. Among them, adding noise has no effect on the performance whatever other augmentations are used, which may be caused by the voxelization operation in IF-Nets. Thus we try the following variants with the combination of the other three augmentation strategies. Note that we control the dropping ratio to guarantee the expected number of dropped points (if only using dropping) are the same for all settings. The results in Tab. 5 show that: (1) the consistency training with random downsampling only crashed (the 2nd row), using volume-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17636" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 98, + 69, + 492, + 437 + ], + "blocks": [ + { + "bbox": [ + 98, + 69, + 492, + 437 + ], + "lines": [ + { + "bbox": [ + 98, + 69, + 492, + 437 + ], + "spans": [ + { + "bbox": [ + 98, + 69, + 492, + 437 + ], + "type": "image", + "image_path": "8f679287d4cee3dda884eb93a77369161ea3772fec2a805af1b4ab236f598d1b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 441, + 504, + 453 + ], + "lines": [ + { + "bbox": [ + 88, + 441, + 504, + 453 + ], + "spans": [ + { + "bbox": [ + 88, + 441, + 504, + 453 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison between different methods on shape completion with only " + }, + { + "bbox": [ + 88, + 441, + 504, + 453 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 88, + 441, + 504, + 453 + ], + "type": "text", + "content": " labels for training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 457, + 289, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 289, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 289, + 636 + ], + "type": "text", + "content": "aware or surface-aware augmentation only can still work, but the surface-aware one performs better (the 3rd and 4th row), and the 4th row is the version used in our standard VCST; (3) the volume-aware augmentation can bring minor improvements on mIoU with or without random downsampling (the 3rd and 5th row), which is worse than our surface-aware one, and using both two of them even makes a negative effect (the last row). The reason for the failure of using random downsampling only is that the consistency training fails when two views are very similar in a global fashion. An intuitive explanation for (3) is that compared with our surface-aware augmentation, the incompleteness created by the volume-aware one has a larger gap with real scans. The qualitative comparisons between different variants are included in the supplementary materials." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 646, + 119, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 119, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 119, + 658 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 666, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we propose a new task, domain adaptive shape completion of real scans, which aims to transfer the knowledge in the label-rich synthetic domain into the more challenging real domain. We construct a new dataset that" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 457, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 564 + ], + "type": "text", + "content": "contains elaborate 3D models created by professional artists for " + }, + { + "bbox": [ + 304, + 457, + 545, + 564 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 457, + 545, + 564 + ], + "type": "text", + "content": " of real scans in 6 categories, which can serve for the learning of deep reconstruction models and evaluation. Besides, we develop a new domain adaptive shape completion framework with two novel modules, cross-domain feature fusion and volume-consistent self-training, to better exploit both the synthetic and real data. Extensive experiments validate the superiority and effectiveness of our method and a benchmark is constructed on the proposed task." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 566, + 546, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 546, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 546, + 708 + ], + "type": "text", + "content": "Acknowledgment The work was supported in part by NSFC-62172348, the Basic Research Project No. HZQB-KCZYZ-2021067 of Hetao Shenzhen-HK S&T Cooperation Zone. It was also partially supported by NSFC-62172348, Outstanding Yound Fund of Guangdong Province with No. 2023B1515020055, the National Key R&D Program of China with grant No. 2018YFB1800800, by Shenzhen Outstanding Talents Training Fund 202002, by Guangdong Research Projects No. 2017ZT07X152 and No. 2019CX01X104, by the Guangdong Provincial Key Laboratory of Future Networks of Intelligence (Grant No. 2022B1212010001), and by Shenzhen Key Laboratory of Big Data and Artificial Intelligence (Grant No. ZDSYS201707251409055)." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17637" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 58, + 91, + 286, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 286, + 123 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 286, + 123 + ], + "type": "text", + "content": "[1] Idan Achituve, Haggai Maron, and Gal Chechik. 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However, acquiring pixel-level expert annotations is extremely expensive and laborious in medical imaging fields. Unsupervised domain adaptation (UDA) can alleviate this problem, which makes it possible to use annotated data in one imaging modality to train a network that can successfully perform segmentation on target imaging modality with no labels. In this work, we propose SDC-UDA, a simple yet effective volumetric UDA framework for Slice-Direction Continuous cross-modality medical image segmentation which combines intra- and inter-slice self-attentive image translation, uncertainty-constrained pseudo-label refinement, and volumetric self-training. Our method is distinguished from previous methods on UDA for medical image segmentation in that it can obtain continuous segmentation in the slice direction, thereby ensuring higher accuracy and potential in clinical practice. We validate SDC-UDA with multiple publicly available cross-modality medical image segmentation datasets and achieve state-of-the-art segmentation performance, not to mention the superior slice-direction continuity of prediction compared to previous studies.", + "bbox": [ + 75, + 420, + 472, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 799, + 207, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the surprising development of deep learning (DL), many studies are now showing remarkable performance in various applications [8, 16, 20]. However, when a DL model", + "bbox": [ + 76, + 825, + 468, + 871 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/892a2278f666ddf7e04fe99f6555a4e9543bc934cfe83576975b71be25143b45.jpg", + "image_caption": [ + "(A) Previous UDA for medical image segmentation frameworks", + "Figure 1. An illustration that describes the comparison between our proposed method with previous methods. (A) Previous UDA for medical image segmentation studies mostly utilize 2D UDA, which leads to inconsistent predictions in the slice direction when the predictions are stacked. (B) The proposed framework (SDC-UDA) considers volumetric information in the translation and segmentation process, respectively, which leads to improved slice-direction continuity of segmentation that is much practical for clinical use." + ], + "image_footnote": [], + "bbox": [ + 508, + 390, + 888, + 555 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "faces data from an unseen domain, performance degradation occurs [9, 32]. Resolving this issue is important for the DL techniques to be applied in real world since collecting data from all domains and labeling them is very impractical and inefficient. Unsupervised Domain Adaptation (UDA) aims to alleviate this problem by adapting a model trained on source domain data to target domain, without the necessity of supervision in the target domain. Data dependency is more serious in medical image segmentation field since acquiring pixel-level expert annotation is extremely expensive and time-consuming [3, 22, 37].", + "bbox": [ + 496, + 719, + 890, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous studies on UDA in the field of cross-modality med", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution. † Corresponding author.", + "bbox": [ + 76, + 886, + 339, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7412", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/89eb8878777566d137aee2cf6fe3b2ca555d7e8da15d00081cb8d30fdd326f68.jpg", + "image_caption": [ + "Figure 2. Overview of our volumetric UDA framework. First, source-to-target image transformation is performed via unpaired image translation with intra- and inter-slice self-attention (stage 1-2). Second, volumetric self-training is performed (stage 3-5). During self-training, uncertainty-constrained pseudo-label refinement is conducted to improve pseudo-labels, thereby maximizing the effect of self-training (stage 4). The reverse loop of image translation is omitted for ease of illustration. Detailed architecture of image translation network is described in Fig. 3. Best viewed in color and on high-resolution display. II-SA: Intra- and inter-slice self-attention." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 885, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ical image segmentation are normally conducted by simultaneously learning 2D image translation and target-domain segmentation, inferring the trained model on each slice of target data, and then stacking the predictions in the slice direction (Fig. 1). As a result, they can lead to inconsistent or fluctuating predictions in the slice direction that are not revealed in quantitative metrics and may interrupt accurate analysis of target structure, making it difficult to use in real world clinical practice. In contrast, SDC-UDA can achieve improved slice-direction continuity by incorporating volumetric natures of medical imaging, which has not been thoroughly explored in previous works. It efficiently generates synthetic target volumes with neighbor-aware image translation by utilizing intra- and inter-slice self-attention module [27]. Then, volumetric self-training is followed with uncertainty-constrained pseudo-label refinement strategy that adaptively increases the accuracy of pseudo-labels according to the target data (Fig. 2). Preliminary version of this work has won the 1st place in an unsupervised cross-modality domain adaptation for medical image segmentation challenge [7, 26]. We updated the framework and extended it to multiple datasets. The main contribution of our work can be summarized as follows:", + "bbox": [ + 75, + 448, + 472, + 809 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present SDC-UDA, a unified volumetric UDA framework for cross-modality medical image segmentation.", + "- Intra- and inter-slice self-attention for efficient medical image translation: Proposed 2.5D translation frame" + ], + "bbox": [ + 94, + 816, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "work with intra- and inter-slice self-attention module leads to increased anatomy preservation and slicedirection smoothness in the synthesized volume, enabling the synthetic volume to be used effectively in the following self-training steps.", + "bbox": [ + 529, + 448, + 890, + 525 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Volumetric self-training with uncertainty-constrained pseudo-label refinement: We propose a novel uncertainty-constrained pseudo-label refinement module that can adaptively enhance the accuracy (i.e., sensitivity or specificity) of pseudo-labels, thereby maximizing the performance of self-training on medical image segmentation.", + "- SDC-UDA was validated on multiple public datasets with different data characteristics for cross-modality medical image segmentation. It not only surpassed the performance of previous methods, but also showed superior slice-direction segmentation continuity which can provide precise analysis in clinical practice." + ], + "bbox": [ + 517, + 536, + 890, + 758 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 775, + 640, + 791 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. UDA for medical image segmentation.", + "text_level": 1, + "bbox": [ + 500, + 800, + 826, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "UDA for semantic segmentation is one of the most popular themes among UDA-related studies [12,18,21,31]. Especially, UDA on medical image segmentation is very attractive [3, 6, 13, 15, 22, 37] since it can address the difficulty of obtaining expensive expert-level manual annota", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7413", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tions. Recent studies on UDA for medical image segmentation are mostly based on image adaptation in which domain translation and segmentation networks are trained end-to-end, thereby utilizing the source-to-target transformed images for training segmentation on target domain. [13, 22, 37] combined image-to-image translation and segmentation into a single network. [3] added feature adaptation with adversarial training using the segmentation output of the synthetic and real target domain images to better preserve the geometry of the structures-of-interest. Moreover, [15] added both the synthetic and real target domain images and their corresponding segmentation probability maps to adversarial training to preserve not only the geometry of target anatomies but also their appearance (i.e., intensities). [11] utilized deep symmetric networks to further align the features of two domains.", + "bbox": [ + 75, + 90, + 472, + 330 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work differs from previous works in the following aspects: Previous works mostly train 2D-level image translation with target-domain segmentation and stack the segmentation of each target slice in the slice direction [4, 11, 15, 30]. Since the segmentation network does not consider the anatomical structure in the slice direction, this can lead to high variability of segmentation result even in adjacent slices. In contrast, SDC-UDA splits target-domain segmentation from image translation and therefore is not constrained to 2D framework. Consequently, SDC-UDA can effectively incorporate volumetric information in the translation and segmentation process, respectively. Moreover, in addition to the commonly used cross-modality medical image segmentation dataset [17, 19, 40], SDC-UDA has also been validated in the challenging task of cross-modality segmentation of small multi-class structures which are vestibular schwannoma (VS) and cochlea (i.e., CrossMoDA dataset [7, 24, 25]). Previous studies locate target organs to the center of the preprocessed images and the majority of slices contain at least one target organ, whereas VS and cochleas in CrossMoDA dataset occupy extremely small fraction of the total voxels (0.028% and 0.002% for VS and cochlea, respectively, compared to approximately 3% in average in another dataset [40]) which more reflects the real-world clinical imaging environment [4, 15].", + "bbox": [ + 75, + 333, + 472, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Self-training on UDA for medical image segmentation.", + "text_level": 1, + "bbox": [ + 76, + 724, + 468, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-training belongs to semi-supervised learning which has emerged to improve the resources and cost put into data labeling [35, 41]. In self-training, a teacher model is first trained using only the labeled data. Next, pseudolabels with high confidence are inferred by passing the unlabeled data on the trained model. With the labeled data and pseudo-labeled data, a larger dataset can be used to train a student model that performs better than the teacher model trained only on labeled data. Numerous attempts", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "were made to apply self-training into semantic segmentation [23, 39, 42, 43] as pixel-level annotations are expensive. Since pseudo-labels tend to be noisy labels, previous studies attempted to refine pseudo-labels to increase accuracy, thereby providing better supervision to unlabeled data. [33] updated pseudo-labels by enhancing the sensitivity of pseudo-labels via selective voting. [29] proposed region growing on the super-pixels where the pseudo-labels serve as the initial seed points. [10] utilized uncertainty-weighted binary cross entropy loss to penalize high uncertainty region.", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed pseudo-label refinement strategy is effective in two aspects: 1) sensitivity and specificity-enhancing refinement can be adaptively used according to the characteristic of target data, and 2) it is a safer way to handle uncertainty maps since even the correctly segmented regions can have high uncertainty, and using uncertainty map to weight the loss function in the following training can therefore guide the model to wrong direction.", + "bbox": [ + 496, + 257, + 893, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 396, + 599, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Unpaired image translation with intra- and inter-slice self-attention module.", + "text_level": 1, + "bbox": [ + 500, + 421, + 890, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Many recent works on UDA for medical image segmentation have been developed on 2D framework, without considering the volumetric nature of medical imaging (2D multi-slice sequence or 3D sequence) [3, 13, 15, 22]. Previous 2D UDA approaches split the 3D volume into 2D slices, and re-stack their translations into 3D volume afterward. Since the slices are processed individually, re-building the translated volume usually requires additional post-processing such as slice-direction interpolation, which still can not perfectly resolve problems such as slicedirection discontinuity. This remain a problem when conducting following steps such as self-training for volumetric segmentation. Although there exist frameworks such as 3DCycleGAN which aim to conduct translation 3D volumewise, they are rarely used due to typical drawbacks such as optimization complexity, computational burden, or the degradation of translation quality [5, 28].", + "bbox": [ + 496, + 460, + 890, + 718 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To remedy both lack of volumetric consideration of 2D and optimization-efficiency issue of 3D methods, we propose a simple and effective pixel-level domain translation method for medical volume data by translating a stack of source domain images into target domain with both intra- and inter-slice self-attention module. Unlike previous 2D methods that only translated within a single slice, our approach leverages information from adjacent slices in the slice-direction. This is similar to recent advances in video processing, which exploit information both within and between frames [1,2]. In contrast to 3D methods that require expensive computational cost, ours do not necessitate heavy", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7414", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e73e7a199840ea4086870cd25088b83f4482473c839f62c8772858a09ac306ae.jpg", + "image_caption": [ + "Figure 3. Illustration of the proposed 2.5D image translation with intra- and inter-slice self-attention module. Source domain volume data is cropped to a mini-volume, and fed to CNN encoder $G_{E}$ as a stack of batches. The weights of $G_{E}$ are shared during batch update. The encoded feature maps are embedded to non-overlapping patches, which become the input of intra- & inter-slice attention module $A$ . Within $A$ , intra- and inter-slice attention learns the volumetric information." + ], + "image_footnote": [], + "bbox": [ + 83, + 87, + 893, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "computation, enabling translation without intense down-sampling which 3D-based translations suffer from [28].", + "bbox": [ + 75, + 431, + 468, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shown in Fig.3, proposed framework consists of sequential modules of encoder $G_{E}$ , intra- and inter-slice self-attention II-SA and decoder $G_{D}$ . Taking three continuous slices $x_{t - 1},x_{t},x_{t + 1}$ of a volume as input, they are first fed to a 2D CNN encoder $G_{E}$ separately. Encoded features $G_{E}(x_{t - 1}),G_{E}(x_{t}),G_{E}(x_{t + 1})$ are then fed to transformer-based attention module II-SA together, as feature maps from continuous frames. Before II-SA, each slice is embedded into small patches $\\mathbf{z}$ of size $p$ as $\\mathbf{z}_{t - 1:t + 1}^n = P(G_E(x_{t - 1:t + 1}))|_{n = 1:N}$ , where $N = W_{G_E(x)}\\cdot H_{G_E(x)} / p^2$ . $W_{G_E(x)},H_{G_E(y)}$ are each width, height of encoded feature map $G_{E}(x)$ , respectively. In transformer-based attention module II-SA, two types attention $A_{inter}$ and $A_{intra}$ exist. First, for the consideration of adjacent slices, learnable positional encoding is added to capture relative positional information within mini-volume patches. An inter-slice attention module is $A_{inter} = A(\\mathbf{z}_{t - 1}^{k},\\mathbf{z}_{t}^{k},\\mathbf{z}_{t + 1}^{k})|_{k = 1:N}$ . And for the consideration of nearby pixels within a slice, an intra-slice self-attention exists, as $A_{intra} = A(\\mathbf{z}_j^1,\\mathbf{z}_j^2,\\dots,\\mathbf{z}_j^N)|_{j = t - 1:t + 1}$ . The attention module is identical for both intra- and interslice attention, which is", + "bbox": [ + 75, + 460, + 472, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA = \\sigma \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {K}}}\\right) V \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 797, + 468, + 834 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": ", where $Q = W_{Q}\\cdot LN(\\mathbf{z})$ , $K = W_{K}\\cdot LN(\\mathbf{z})$ , and $V = W_{V}\\cdot LN(\\mathbf{z})$ are query, key and value embeddings, respectively. $LN$ denotes layer-normalization, $\\sigma$ denotes soft-max operation and $d_{K}$ denotes embedding dimension.", + "bbox": [ + 76, + 839, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For maximum efficiency of translation, inter-slice attention occurs on the adjacent patches over slice-direction only for computational efficiency. After attention module, a 2D CNN decoder $G_{D}$ reconstructs partial volume sets in the same way as done in $G_{E}$ , constructing a translated 2.5D mini-volume. In inference step, only the center slices of mini-volume is stacked one by one to construct a whole translated volume.", + "bbox": [ + 496, + 431, + 893, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Volumetric self-training with uncertainty-constrained pseudo-label refinement.", + "text_level": 1, + "bbox": [ + 498, + 563, + 890, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Even if the source-to-target transformed images are well generated, there may still exist some distribution gap with the real target domain data, and it is difficult to completely replace it. With self-training, pseudo-labels for the unlabeled target domain data can be obtained and used to provide supervision to the target domain data, thereby mitigating the domain gap from the model's perspective. We propose to utilize volumetric self-training to close the domain gap, with a simple and novel pseudo-label refinement strategy to maximize the effect of self-training. The steps are as follows.", + "bbox": [ + 496, + 602, + 890, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.1. Training segmentation with labeled synthetic scans. With the synthetic data $\\tilde{x}^t$ converted from source domain and the annotations $y^{s}$ on the source scans (i.e., labeled synthetic dataset), we first train a teacher segmentation network $f_{teacher}$ that minimizes the segmentation loss:", + "bbox": [ + 496, + 784, + 890, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum L _ {\\text {s e g}} \\left(y ^ {s}, f _ {\\text {t e a c h e r}} \\left(\\tilde {x} ^ {t}\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 875, + 890, + 897 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7415", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d6f14700959c4d628c4354c8a3c620e66e5fa645e33b30baf577e1c43db19db5.jpg", + "image_caption": [ + "(a) Sensitivity-preserving Pseudo Label Refinement", + "Figure 4. Illustration of the proposed uncertainty-constrained pseudo-label refinement module on vestibular schwannoma of CrossMoDA dataset. Sensitivity/specificity enhancing refinement can be performed in parallel, and either one or a combination of the two can be used according to the characteristics of each class in the dataset. Best viewed in color and on high-resolution display." + ], + "image_footnote": [], + "bbox": [ + 83, + 101, + 467, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.2. Inferring pseudo-labels on unlabeled target domain data. Once the teacher model is trained, pseudolabels $\\tilde{y}^t$ of the non-annotated real data $x^t$ can be obtained by passing real target scans to the trained segmentation model $f_{teacher}$ .", + "bbox": [ + 75, + 503, + 468, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {y} _ {i} ^ {t} = f _ {\\text {t e a c h e r}} \\left(\\left\\{x _ {i} ^ {t} \\right\\} _ {i = 1} ^ {N _ {t}}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 592, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.3. Uncertainty-constrained pseudo-label refinement for sensitivity / specificity enhancement. Since the pseudo-labels are noisy labels, they must be refined to increase accuracy and guide self-training to better direction. We devise a sensitivity and specificity enhancing pseudo-label refinement module that refines pseudo-labels based on image intensities, current pseudo-label, and high-uncertainty regions.", + "bbox": [ + 75, + 619, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sensitivity-enhancing pseudo-label refinement. With the inference of pseudo-labels, uncertainty (i.e., entropy) maps corresponding to each class are computed according to the following equation:", + "bbox": [ + 75, + 753, + 468, + 816 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nU = p \\log p \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 830, + 468, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": ", where $p$ is the output probability map of each class. To enhance the sensitivity of pseudo-labels, highly uncertain regions outside the range of pseudo-labels are detected. Then,", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "if the pixel intensity in this region is within a certain range of image intensity included in the current pseudo-label, this region is included to be part of pseudo-label. The equation can be formulated as:", + "bbox": [ + 496, + 90, + 892, + 150 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {I n i t i z e} \\tilde {y} _ {r} ^ {t} = \\tilde {y} ^ {t}. \\tilde {y} _ {r} ^ {t} (i, j) = 1 \\text {i f}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 157, + 813, + 175 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\operatorname {m e a n} \\left(x ^ {t} \\left(\\tilde {y} ^ {t}\\right)\\right) \\times \\alpha < x _ {U H} ^ {t} (i, j) < \\operatorname {m e a n} \\left(x ^ {t} \\left(\\tilde {y} ^ {t}\\right)\\right) \\times \\beta \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 178, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x^{t}$ , $\\tilde{y}^{t}$ , $\\tilde{y}_{r}^{t}$ , and $x_{UH}^{t}$ represent target domain image, pseudo-label, refined pseudo-label, and image cropped with high-uncertainty region mask, respectively. This approach is grounded on the assumption that 1) pixels that have similar intensity and 2) are close to each other in medical image are likely to belong to the same class. The workflow is described with images in Fig. 4.", + "bbox": [ + 496, + 222, + 892, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specificity-enhancing pseudo-label refinement. To enhance specificity of pseudo-labels, highly uncertain regions inside the range of pseudo-labels are detected. Then, if the pixel intensity in this region is outside a certain range of image intensity included in the current pseudo-label, it is excluded from the current pseudo-label.", + "bbox": [ + 496, + 343, + 892, + 434 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {I n i t i z e} \\tilde {y} _ {r} ^ {t} = \\tilde {y} ^ {t}. \\tilde {y} _ {r} ^ {t} (i, j) = 0 \\text {i f}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 441, + 816, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {U H} ^ {t} (i, j) < \\operatorname {m e a n} \\left(x ^ {t} (\\tilde {y} ^ {t})\\right) \\times \\alpha o r \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 463, + 890, + 481 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {U H} ^ {t} (i, j) > \\operatorname {m e a n} \\left(x ^ {t} (\\tilde {y} ^ {t})\\right) \\times \\beta\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 483, + 820, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.4. Retraining segmentation with combined data. Synthetic target scans have distribution gap with the real target scans, but they are paired with perfect annotations. On the other hand, real target scans are paired with pseudolabels, which are yet incomplete. We incorporate both pairs to self-training, to maximize the generalization ability and minimize the performance degradation caused by difference in distributions. With the combined data of labeled synthetic target scans $(\\tilde{x}^t,y^s)$ and pseudo-labeled real target scans $(x^{t},\\tilde{y}_{r}^{t})$ , we train a student segmentation $f_{student}$ to minimize", + "bbox": [ + 496, + 510, + 890, + 675 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = \\sum L _ {s e g} \\left(y ^ {s}, f _ {s t u d e n t} \\left(\\tilde {x} ^ {t}\\right)\\right) + \\sum L _ {s e g} \\left(\\tilde {y} _ {r} ^ {t}, f _ {s t u d e n t} \\left(x ^ {t}\\right)\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 684, + 898, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Despite not being ground truth labels, it has been reported in the previous literature that the self-training scheme and the pseudo-labels increases the performance and generalization ability of the model on unseen data by utilizing unlabeled data into training [35].", + "bbox": [ + 496, + 719, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 806, + 632, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 500, + 832, + 594, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CrossMoDA dataset. CrossMoDA dataset [7] for vestibular schwannoma and cochlea segmentation consists of 105 labeled contrast-enhanced T1 (ceT1) MRI scans and", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7416", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "105 unlabeled high-resolution T2 (hrT2) MRI scans. The direction of domain adaptation was from ceT1 to hrT2 since the annotations of hrT2 scans are not publicly available. Evaluation was performed online on 32 inaccessible hrT2 scans through an official leaderboard. Please refer to the supplementary material for examples of each domain data.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cardiac structure segmentation dataset. 2017 Multi-Modality Whole Heart Segmentation (MMWHS) challenge dataset [40] which consists of 20 MRI and 20 CT volumes was used for cardiac segmentation. Domain adaptation was performed from MRI to CT, with $80\\%$ of each modality used for training and $20\\%$ (i.e., 4 volumes) of randomly selected CT scans used for evaluation. Target cardiac structures for segmentation were ascending aorta (AA), left atrium blood cavity (LAC), the left ventricle blood cavity (LVC), and myocardium of left ventricle (MYO). With a fixed coronal plane resolution of $256 \\times 256$ , MRI and CT volumes were manually cropped to cover the 4 cardiac substructures. Please refer to the supplementary material for examples of each domain data.", + "bbox": [ + 75, + 196, + 473, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 424, + 290, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unpaired image translation with intra- and inter-slice self-attention module. Intra- and inter-slice attentive translation is based on 2D framework, where image slices are fed to 2D CNN $E$ as a stacked batches of size $(B \\times 3,1,H,W)$ , where $H$ and $W$ each denote height and width. After $G_{E}$ , encoded feature map is reshaped to $(B,3,H,W)$ and fed to the attention module for the consideration of slice-direction attention. Patch size $p$ was set as 2. Transposed convolution is used to convert embedded patches back to 2D feature maps. For a stack of mini-volume generated at $G$ , we implement 2D discriminator $D$ for adversarial training of domain translation. For real input to $D$ , 3 consecutive slices were randomly extracted from the target volumes.", + "bbox": [ + 75, + 446, + 470, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Uncertainty-constrained pseudo-label refinement. For each class, grid searching was conducted on how to set the threshold for masking the high-uncertainty region and also on whether to use either one, or both of the sensitivity and specificity enhancing refinement. For CrossMoDA dataset, combining sensitivity and specificity-enhancing refinement in both classes (i.e., VS and Cochlea) with uncertainty threshold of 0.3 led to the best result. For cardiac dataset, the same threshold value was used and using only specificity-enhancing refinement for all classes except one (i.e., AA) led to the best result. This is attributed to the fact that the contrast difference between adjacent substructures was very weak in cardiac CT which led to noisier pseudo-label when sensitivity-enhancing module was used. Please refer to the tables in supplementary material for ablation results. $\\alpha$ and $\\beta$ were set as 0.6 and", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Ablation study on the components of the proposed method on CrossMoDA dataset. ST and PL denote self-training and pseudo-label, respectively. Best results are bolded.", + "bbox": [ + 498, + 89, + 890, + 131 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c74d83c95f6bf1b8a326e3c21a021b007bdc4e22e040d880109a976b6c40579f.jpg", + "table_caption": [ + "CrossMoDA (T1→T2)" + ], + "table_footnote": [], + "table_body": "
Dice (↑)ASSD (↓)
MethodsVSCVSC
Baseline71.572.75.911.83
+ intra/inter-slice attention80.374.51.660.67
+ ST w/o PL refinement83.276.70.580.79
+ ST w/ PL refinement84.684.90.510.14
", + "bbox": [ + 501, + 157, + 890, + 253 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/982fc0d4c6c0553ad58cb3e16cf72818909852a0239abdbb1946e1178909018e.jpg", + "image_caption": [ + "Source CeT1" + ], + "image_footnote": [], + "bbox": [ + 501, + 266, + 696, + 382 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/05b5fc1ffe04e3354d66fec5bd45076c61e1e0566077c0ff8c97bb8b2d454af7.jpg", + "image_caption": [ + "Synthetic HrT2 (2D)" + ], + "image_footnote": [], + "bbox": [ + 696, + 267, + 888, + 382 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/73d3d8440f9602c64a49600e4e46a632854254b83dc5b37dc2ac8acfe75292f7.jpg", + "image_caption": [ + "Synthetic HrT2 (2.5D)" + ], + "image_footnote": [], + "bbox": [ + 501, + 400, + 696, + 515 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4d1ee04ef9a28f728aba46e160b830d88876e926a2ae6f3af1b9e417cdcb3883.jpg", + "image_caption": [ + "Synthetic HrT2 (Ours)", + "Figure 5. Representative case showing the effect of intra- and inter-slice self-attentive image translation. Translation was performed using axial slices and the resulting volume is being observed from sagittal direction. Best viewed in color and on high-resolution display." + ], + "image_footnote": [], + "bbox": [ + 696, + 398, + 888, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1.4, respectively.", + "text_level": 1, + "bbox": [ + 501, + 641, + 612, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Volumetric self-training. For volumetric segmentation self-training, 3D U-Net based architecture constructed from nnU-Net [14] was used. Segmentation was trained for 100 epochs using a combination of Dice and cross entropy loss with stochastic gradient descent optimizer. The initial learning rate and batch size were 1e-2 and 2, respectively. Detailed information on network architecture and training strategy can be found in the supplementary materials.", + "bbox": [ + 498, + 671, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Results", + "text_level": 1, + "bbox": [ + 500, + 801, + 591, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of intra- and inter-slice self-attention module in image translation. Fig. 5 shows a representative case that presents how the quality of the synthetic image changes depending on the design of the image translation network. Compared with the proposed method (ours), slice-direction", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7417", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/909fc05bcdd829e56590efc7745d5ac9f766f678766d8ab84859df06a073ec5e.jpg", + "table_caption": [ + "Table 2. Comparison of quantitative results between SDC-UDA and previous non-medical and medical UDA methods. CycleGAN, CyCADA, ADVENT, and FDA represent non-medical UDA methods while SIFA and PSIGAN represent recent medical UDA methods. Best results are bolded.", + "VS and Cochlea (T1 $\\rightarrow$ T2)", + "Cardiac structures $(\\mathbf{MR}\\rightarrow \\mathbf{CT})$" + ], + "table_footnote": [ + "1 Since the ground truth for CrossMoDA Dataset is not available, fully-supervised results are referred from the dataset owner's paper [7]. These figures correspond to the upper bound and are the evaluation results from larger test set (N=137) than the one used in our study." + ], + "table_body": "
MethodsDice (↑)ASSD (↓)Dice (↑)ASSD (↓)
VSCMeanVSCMeanAALACLVCMYOMeanAALACLVCMYOMean
Non-MedicalFully-supervised192.587.790.10.20.10.1595.992.093.088.292.31.02.51.81.71.8
w/o adaptation11.50.05.824.0NANA48.452.020.04.731.318.834.532.036.430.4
CycleGAN [38]39.70.019.810.1NANA58.359.861.523.150.711.410.69.214.811.5
CyCADA [12]39.20.119.710.518.114.357.262.165.047.257.98.49.08.27.98.4
ADVENT [34]8.30.04.217.1NANA68.271.878.850.767.49.66.64.75.16.5
FDA [36]12.50.06.313.520.517.046.568.473.855.761.110.27.64.35.06.8
MedicalSIFA [4]47.219.733.519.13.311.276.388.174.262.475.36.13.97.14.85.5
PSIGAN [15]57.337.247.35.52.84.167.287.080.360.873.87.54.25.54.75.5
SDC-UDA (ours)84.684.984.80.510.140.3395.891.088.666.685.51.12.83.26.33.3
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"image_caption": [], + "image_footnote": [], + "bbox": [ + 640, + 508, + 720, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/02e3abfec7d6fbffff2d189c6b50a9a1f466dc729a8fa1e6d30be6e1e8c0bf1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 508, + 800, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/54db3e98163eace222f5f75e65c6c9eea791384c5b78e8ff69c01896e45e1075.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 802, + 508, + 890, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1dec07f507513843aeb710fa97458fa0ea05168c36a7548896a9ba1259b8452d.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 570, + 160, + 635 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aa2b8676e4efbd15ff386c48c912ca70b429f6faf08d34ede63051c3084d17ca.jpg", + "image_caption": [ + "Source" + ], + "image_footnote": [], + "bbox": [ + 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Comparison of qualitative results between SDC-UDA and previous non-medical and medical UDA methods. Since the ground truth of CrossMoDA dataset is not accessible, we requested to the data owner a few of the label slices and used them to make this figure. The numbers indicate Dice values of each substructure in the slice. Sup denotes the fully-supervised result." + ], + "image_footnote": [], + "bbox": [ + 400, + 570, + 558, + 635 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/833859bc75c8f79e3a4ef16fe0e84c7761f5c6ad2d9351823fe6560ffea5c8fe.jpg", + "image_caption": [ + "PSIGAN" + ], + "image_footnote": [], + "bbox": [ + 560, + 570, + 638, + 635 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/48000d8fe52b0191fe98cc47871a18b7f08f92e1dc658bde10c3ae6dbc8182c5.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 640, + 570, + 720, + 635 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89175fefda6350e537a864d693539e4f056751cf39cdbe5f1595b448f969b69a.jpg", + "image_caption": [ + "Sup." + ], + "image_footnote": [], + "bbox": [ + 720, + 570, + 800, + 635 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce81217a24b4bb3267d99c44b37c28a383d65198b2beea71e3034cccd68225ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 802, + 570, + 890, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "inconsistency of pixel intensity was observed in the translated image due to the variation derived from slice-by-slice prediction with a 2D network (blue arrows). This was not completely overcome even with a 2.5D network that puts two adjacent slices together in the network. Also, in both 2D and 2.5D networks, it was found that the anatomy of the source image was distorted in the translated image (red and green arrows). On the other hand, it was observed that the aforementioned problems were alleviated when utilizing the intra- and inter-slice self-attention module", + "bbox": [ + 75, + 736, + 472, + 888 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that effectively considers neighboring anatomy. Table 1 shows the increase of final segmentation performance by incorporating intra- and inter-slice self-attention in image translation network compared to baseline that utilizes pure unpaired image translation followed by 3D segmentation network.", + "bbox": [ + 496, + 737, + 893, + 828 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of uncertainty-constrained pseudo-label refinement and volumetric self-training. Since the target domain ground truth is inaccessible for the CrossMoDA", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7418", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ade02f77d4fc773ef3d52f0fd9300ba4097eb0fb95875a5a57468b15ec766c99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 90, + 269, + 198 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d6fd011ed1c84a2290bd77ccbac87d235df80760e7130f775fb8948325ddca8f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 90, + 460, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/232ff38bb3ae42dfa618e016944bf8cc2eb48a3a7c8bd6a294d5c9f51d168e1a.jpg", + "image_caption": [ + "Figure 7. Representative cases demonstrating the superior slice-direction continuity of segmentation by the proposed method compared to other medical UDA methods on cardiac dataset. The plots show graphs of Dice coefficient for each slice. (a), (b), (c), and (d) denote AA, LAC, LVC, and MYO class, respectively. Best viewed in color." + ], + "image_footnote": [], + "bbox": [ + 84, + 200, + 271, + 309 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1f0e770e44f706ce0d72ec3c1f0564f74fc4582780e2a6c87a8ae526512756d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 200, + 460, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dataset, the effectiveness of pseudo-label refinement was verified by comparing the performance of self-training before and after pseudo-label refinement. For cardiac datasets for which ground truth is available, it was verified by comparing dice coefficients with labels before and after pseudo-label refinement (please refer to supplementary material). Table 1 shows the improvement of target domain segmentation performance by applying the proposed uncertainty-constrained pseudo-label refinement on CrossMoDA dataset. It can be seen that volumetric self-training combined with the proposed uncertainty-constrained pseudo-label refinement increases the quantitative metrics in both VS and C by a large margin, whereas pure self-training only increase the performance in VS.", + "bbox": [ + 75, + 441, + 468, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparative studies. The proposed method is compared with six popular UDA methods that are CycleGAN [38], CyCADA [12], ADVENT [34], FDA [36], SIFA [4], and PSIGAN [15]. The first four methods are from natural image field whereas the last two are UDA for medical image segmentation methods. Fully-supervised and without-adaptation results are presented to provide upper bound and lower bound, respectively. Please note that the full-supervised result of CrossMoDA dataset, for which the ground truth segmentation mask is not available, is referred from the paper of the dataset owner [7].", + "bbox": [ + 75, + 672, + 467, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2 and Fig. 6 shows quantitative and qualitative results of comparative studies between the proposed method and previous methods. SDC-UDA far exceeds the results of UDA for semantic segmentation studies in the non-medical", + "bbox": [ + 75, + 839, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "field, and shows better results in multiple tasks compared to the recent studies in the medical field. In particular, there was a significant performance gap between the proposed method and comparison methods in the CrossMoDA dataset compared to the cardiac dataset. This is probably attributed to the fact that previous studies on medical UDA are dedicated to datasets in which the data are cropped around the target organs and the foreground objects occupy a large portion of the data. In contrast, SDC-UDA shows that both target structures in the CrossMoDA dataset are segmented with high accuracy.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Slice-direction continuity of segmentation compared to previous studies. Fig. 7 shows the excellent slice-direction continuity of segmentation by the proposed method compared to the previous studies on the MMWHS cardiac dataset. Fig. 7-(a), (b), (c), and (d) plot the slice-wise Dice values from representative cases of AA, LAC, LVC, and MYO, respectively. Our SDC-UDA shows gradual and consistent segmentation performance in the slice-direction whereas SIFA and PSIGAN, which are recently proposed medical UDA methods, show very inconsistent and sometimes sudden fluctuations of segmentation performance in the slice direction. This suggests the potential of the proposed method to be useful in the clinical practice where precise volumetric segmentation is required to analyze the patient's status with high confidence.", + "bbox": [ + 496, + 272, + 890, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 512, + 617, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we proposed SDC-UDA, a novel volumetric UDA framework for slice-direction continuous cross-modality medical image segmentation, and validated it on multiple public datasets. SDC-UDA effectively translates medical volumes through intra- and inter-slice self-attention and better adapts to target domain via volumetric self-training enhanced by simple yet effective pseudo-label refinement strategy that utilizes uncertainty maps. Ablation studies demonstrated the effectiveness of each component and comparative studies showed the superior performance of the proposed method.", + "bbox": [ + 496, + 537, + 890, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This research was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-TF2103-01 in constructing hardware systems and multi-modal studies. It was also supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2021R1A4A1031437, 2022R1A2C2008983), Artificial Intelligence Graduate School Program at Yonsei University [No. 2020-0-01361], the KIST Institutional Program (Project No.2E31051-21-204), and partially supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002).", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7419", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 3" + ], + "bbox": [ + 501, + 92, + 890, + 768 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7421", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/20148cfd-bd1f-4726-9d6d-b13924bbcc1e_model.json b/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/20148cfd-bd1f-4726-9d6d-b13924bbcc1e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a446b6f1aac02b0b5d89bc33a71d166e9b18cfcd --- /dev/null +++ b/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/20148cfd-bd1f-4726-9d6d-b13924bbcc1e_model.json @@ -0,0 +1,2519 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.13, + 0.856, + 0.177 + ], + "angle": 0, + "content": "SDC-UDA: Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.203, + 0.25, + 0.222 + ], + "angle": 0, + "content": "Hyungseob Shin\\*" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.203, + 0.426, + 0.222 + ], + "angle": 0, + "content": "Hyeongyu Kim\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.464, + 0.204, + 0.578, + 0.222 + ], + "angle": 0, + "content": "Sewon \\(\\mathrm{Kim}^{4,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.616, + 0.204, + 0.72, + 0.222 + ], + "angle": 0, + "content": "Yohan Jun7,8" + }, + { + "type": "text", + "bbox": [ + 0.757, + 0.204, + 0.868, + 0.222 + ], + "angle": 0, + "content": "Taejoon \\(\\mathrm{Eo^{1,6}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.404, + 0.228, + 0.565, + 0.247 + ], + "angle": 0, + "content": "Dosik Hwang\\(^{1,2,3,9\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.266, + 0.859, + 0.3 + ], + "angle": 0, + "content": "\\(\\{^{1}\\text{School of Electrical and Electronic Engineering}, {}^{2}\\text{Department of Oral and Maxillofacial Radiology, College of Dentistry}, {}^{3}\\text{Department of Radiology and Center for Clinical Imaging Data Science, College of Medicine}\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.301, + 0.876, + 0.318 + ], + "angle": 0, + "content": "@Yonsei University \\(^{4}\\)Naver AI Lab \\(^{5}\\)Naver Cloud \\(^{6}\\)Probe Medical, Inc. \\(^{7}\\)Martinos Center for Biomedical Imaging" + }, + { + "type": "text", + "bbox": [ + 0.146, + 0.319, + 0.825, + 0.335 + ], + "angle": 0, + "content": "\\(^{8}\\)Harvard Medical School \\(^{9}\\)Center for Healthcare Robotics, Korea Institute of Science and Technology" + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.338, + 0.692, + 0.353 + ], + "angle": 0, + "content": "{whatzupsup, lion4309, dosik.hwang}@yonsei.ac.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.388, + 0.313, + 0.403 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.473, + 0.769 + ], + "angle": 0, + "content": "Recent advances in deep learning-based medical image segmentation studies achieve nearly human-level performance in fully supervised manner. However, acquiring pixel-level expert annotations is extremely expensive and laborious in medical imaging fields. Unsupervised domain adaptation (UDA) can alleviate this problem, which makes it possible to use annotated data in one imaging modality to train a network that can successfully perform segmentation on target imaging modality with no labels. In this work, we propose SDC-UDA, a simple yet effective volumetric UDA framework for Slice-Direction Continuous cross-modality medical image segmentation which combines intra- and inter-slice self-attentive image translation, uncertainty-constrained pseudo-label refinement, and volumetric self-training. Our method is distinguished from previous methods on UDA for medical image segmentation in that it can obtain continuous segmentation in the slice direction, thereby ensuring higher accuracy and potential in clinical practice. We validate SDC-UDA with multiple publicly available cross-modality medical image segmentation datasets and achieve state-of-the-art segmentation performance, not to mention the superior slice-direction continuity of prediction compared to previous studies." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.8, + 0.208, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.47, + 0.872 + ], + "angle": 0, + "content": "With the surprising development of deep learning (DL), many studies are now showing remarkable performance in various applications [8, 16, 20]. However, when a DL model" + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.388, + 0.764, + 0.399 + ], + "angle": 0, + "content": "(A) Previous UDA for medical image segmentation frameworks" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.391, + 0.889, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.69 + ], + "angle": 0, + "content": "Figure 1. An illustration that describes the comparison between our proposed method with previous methods. (A) Previous UDA for medical image segmentation studies mostly utilize 2D UDA, which leads to inconsistent predictions in the slice direction when the predictions are stacked. (B) The proposed framework (SDC-UDA) considers volumetric information in the translation and segmentation process, respectively, which leads to improved slice-direction continuity of segmentation that is much practical for clinical use." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.885 + ], + "angle": 0, + "content": "faces data from an unseen domain, performance degradation occurs [9, 32]. Resolving this issue is important for the DL techniques to be applied in real world since collecting data from all domains and labeling them is very impractical and inefficient. Unsupervised Domain Adaptation (UDA) aims to alleviate this problem by adapting a model trained on source domain data to target domain, without the necessity of supervision in the target domain. Data dependency is more serious in medical image segmentation field since acquiring pixel-level expert annotation is extremely expensive and time-consuming [3, 22, 37]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Previous studies on UDA in the field of cross-modality med" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.887, + 0.341, + 0.901 + ], + "angle": 0, + "content": "* Equal contribution. † Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7412" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.887, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.893, + 0.424 + ], + "angle": 0, + "content": "Figure 2. Overview of our volumetric UDA framework. First, source-to-target image transformation is performed via unpaired image translation with intra- and inter-slice self-attention (stage 1-2). Second, volumetric self-training is performed (stage 3-5). During self-training, uncertainty-constrained pseudo-label refinement is conducted to improve pseudo-labels, thereby maximizing the effect of self-training (stage 4). The reverse loop of image translation is omitted for ease of illustration. Detailed architecture of image translation network is described in Fig. 3. Best viewed in color and on high-resolution display. II-SA: Intra- and inter-slice self-attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.473, + 0.81 + ], + "angle": 0, + "content": "ical image segmentation are normally conducted by simultaneously learning 2D image translation and target-domain segmentation, inferring the trained model on each slice of target data, and then stacking the predictions in the slice direction (Fig. 1). As a result, they can lead to inconsistent or fluctuating predictions in the slice direction that are not revealed in quantitative metrics and may interrupt accurate analysis of target structure, making it difficult to use in real world clinical practice. In contrast, SDC-UDA can achieve improved slice-direction continuity by incorporating volumetric natures of medical imaging, which has not been thoroughly explored in previous works. It efficiently generates synthetic target volumes with neighbor-aware image translation by utilizing intra- and inter-slice self-attention module [27]. Then, volumetric self-training is followed with uncertainty-constrained pseudo-label refinement strategy that adaptively increases the accuracy of pseudo-labels according to the target data (Fig. 2). Preliminary version of this work has won the 1st place in an unsupervised cross-modality domain adaptation for medical image segmentation challenge [7, 26]. We updated the framework and extended it to multiple datasets. The main contribution of our work can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.818, + 0.47, + 0.863 + ], + "angle": 0, + "content": "- We present SDC-UDA, a unified volumetric UDA framework for cross-modality medical image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- Intra- and inter-slice self-attention for efficient medical image translation: Proposed 2.5D translation frame" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.818, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.449, + 0.892, + 0.526 + ], + "angle": 0, + "content": "work with intra- and inter-slice self-attention module leads to increased anatomy preservation and slicedirection smoothness in the synthesized volume, enabling the synthetic volume to be used effectively in the following self-training steps." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.537, + 0.892, + 0.643 + ], + "angle": 0, + "content": "- Volumetric self-training with uncertainty-constrained pseudo-label refinement: We propose a novel uncertainty-constrained pseudo-label refinement module that can adaptively enhance the accuracy (i.e., sensitivity or specificity) of pseudo-labels, thereby maximizing the performance of self-training on medical image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.655, + 0.892, + 0.76 + ], + "angle": 0, + "content": "- SDC-UDA was validated on multiple public datasets with different data characteristics for cross-modality medical image segmentation. It not only surpassed the performance of previous methods, but also showed superior slice-direction segmentation continuity which can provide precise analysis in clinical practice." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.537, + 0.892, + 0.76 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.776, + 0.641, + 0.792 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.828, + 0.818 + ], + "angle": 0, + "content": "2.1. UDA for medical image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "UDA for semantic segmentation is one of the most popular themes among UDA-related studies [12,18,21,31]. Especially, UDA on medical image segmentation is very attractive [3, 6, 13, 15, 22, 37] since it can address the difficulty of obtaining expensive expert-level manual annota" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7413" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.332 + ], + "angle": 0, + "content": "tions. Recent studies on UDA for medical image segmentation are mostly based on image adaptation in which domain translation and segmentation networks are trained end-to-end, thereby utilizing the source-to-target transformed images for training segmentation on target domain. [13, 22, 37] combined image-to-image translation and segmentation into a single network. [3] added feature adaptation with adversarial training using the segmentation output of the synthetic and real target domain images to better preserve the geometry of the structures-of-interest. Moreover, [15] added both the synthetic and real target domain images and their corresponding segmentation probability maps to adversarial training to preserve not only the geometry of target anatomies but also their appearance (i.e., intensities). [11] utilized deep symmetric networks to further align the features of two domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.473, + 0.712 + ], + "angle": 0, + "content": "Our work differs from previous works in the following aspects: Previous works mostly train 2D-level image translation with target-domain segmentation and stack the segmentation of each target slice in the slice direction [4, 11, 15, 30]. Since the segmentation network does not consider the anatomical structure in the slice direction, this can lead to high variability of segmentation result even in adjacent slices. In contrast, SDC-UDA splits target-domain segmentation from image translation and therefore is not constrained to 2D framework. Consequently, SDC-UDA can effectively incorporate volumetric information in the translation and segmentation process, respectively. Moreover, in addition to the commonly used cross-modality medical image segmentation dataset [17, 19, 40], SDC-UDA has also been validated in the challenging task of cross-modality segmentation of small multi-class structures which are vestibular schwannoma (VS) and cochlea (i.e., CrossMoDA dataset [7, 24, 25]). Previous studies locate target organs to the center of the preprocessed images and the majority of slices contain at least one target organ, whereas VS and cochleas in CrossMoDA dataset occupy extremely small fraction of the total voxels (0.028% and 0.002% for VS and cochlea, respectively, compared to approximately 3% in average in another dataset [40]) which more reflects the real-world clinical imaging environment [4, 15]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.47, + 0.755 + ], + "angle": 0, + "content": "2.2. Self-training on UDA for medical image segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Self-training belongs to semi-supervised learning which has emerged to improve the resources and cost put into data labeling [35, 41]. In self-training, a teacher model is first trained using only the labeled data. Next, pseudolabels with high confidence are inferred by passing the unlabeled data on the trained model. With the labeled data and pseudo-labeled data, a larger dataset can be used to train a student model that performs better than the teacher model trained only on labeled data. Numerous attempts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "were made to apply self-training into semantic segmentation [23, 39, 42, 43] as pixel-level annotations are expensive. Since pseudo-labels tend to be noisy labels, previous studies attempted to refine pseudo-labels to increase accuracy, thereby providing better supervision to unlabeled data. [33] updated pseudo-labels by enhancing the sensitivity of pseudo-labels via selective voting. [29] proposed region growing on the super-pixels where the pseudo-labels serve as the initial seed points. [10] utilized uncertainty-weighted binary cross entropy loss to penalize high uncertainty region." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.895, + 0.38 + ], + "angle": 0, + "content": "The proposed pseudo-label refinement strategy is effective in two aspects: 1) sensitivity and specificity-enhancing refinement can be adaptively used according to the characteristic of target data, and 2) it is a safer way to handle uncertainty maps since even the correctly segmented regions can have high uncertainty, and using uncertainty map to weight the loss function in the following training can therefore guide the model to wrong direction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.397, + 0.6, + 0.412 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.892, + 0.453 + ], + "angle": 0, + "content": "3.1. Unpaired image translation with intra- and inter-slice self-attention module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Many recent works on UDA for medical image segmentation have been developed on 2D framework, without considering the volumetric nature of medical imaging (2D multi-slice sequence or 3D sequence) [3, 13, 15, 22]. Previous 2D UDA approaches split the 3D volume into 2D slices, and re-stack their translations into 3D volume afterward. Since the slices are processed individually, re-building the translated volume usually requires additional post-processing such as slice-direction interpolation, which still can not perfectly resolve problems such as slicedirection discontinuity. This remain a problem when conducting following steps such as self-training for volumetric segmentation. Although there exist frameworks such as 3DCycleGAN which aim to conduct translation 3D volumewise, they are rarely used due to typical drawbacks such as optimization complexity, computational burden, or the degradation of translation quality [5, 28]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To remedy both lack of volumetric consideration of 2D and optimization-efficiency issue of 3D methods, we propose a simple and effective pixel-level domain translation method for medical volume data by translating a stack of source domain images into target domain with both intra- and inter-slice self-attention module. Unlike previous 2D methods that only translated within a single slice, our approach leverages information from adjacent slices in the slice-direction. This is similar to recent advances in video processing, which exploit information both within and between frames [1,2]. In contrast to 3D methods that require expensive computational cost, ours do not necessitate heavy" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7414" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.895, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.349, + 0.895, + 0.406 + ], + "angle": 0, + "content": "Figure 3. Illustration of the proposed 2.5D image translation with intra- and inter-slice self-attention module. Source domain volume data is cropped to a mini-volume, and fed to CNN encoder \\( G_{E} \\) as a stack of batches. The weights of \\( G_{E} \\) are shared during batch update. The encoded feature maps are embedded to non-overlapping patches, which become the input of intra- & inter-slice attention module \\( A \\). Within \\( A \\), intra- and inter-slice attention learns the volumetric information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.461 + ], + "angle": 0, + "content": "computation, enabling translation without intense down-sampling which 3D-based translations suffer from [28]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.473, + 0.793 + ], + "angle": 0, + "content": "Shown in Fig.3, proposed framework consists of sequential modules of encoder \\( G_{E} \\), intra- and inter-slice self-attention II-SA and decoder \\( G_{D} \\). Taking three continuous slices \\( x_{t - 1},x_{t},x_{t + 1} \\) of a volume as input, they are first fed to a 2D CNN encoder \\( G_{E} \\) separately. Encoded features \\( G_{E}(x_{t - 1}),G_{E}(x_{t}),G_{E}(x_{t + 1}) \\) are then fed to transformer-based attention module II-SA together, as feature maps from continuous frames. Before II-SA, each slice is embedded into small patches \\( \\mathbf{z} \\) of size \\( p \\) as \\( \\mathbf{z}_{t - 1:t + 1}^n = P(G_E(x_{t - 1:t + 1}))|_{n = 1:N} \\), where \\( N = W_{G_E(x)}\\cdot H_{G_E(x)} / p^2 \\). \\( W_{G_E(x)},H_{G_E(y)} \\) are each width, height of encoded feature map \\( G_{E}(x) \\), respectively. In transformer-based attention module II-SA, two types attention \\( A_{inter} \\) and \\( A_{intra} \\) exist. First, for the consideration of adjacent slices, learnable positional encoding is added to capture relative positional information within mini-volume patches. An inter-slice attention module is \\( A_{inter} = A(\\mathbf{z}_{t - 1}^{k},\\mathbf{z}_{t}^{k},\\mathbf{z}_{t + 1}^{k})|_{k = 1:N} \\). And for the consideration of nearby pixels within a slice, an intra-slice self-attention exists, as \\( A_{intra} = A(\\mathbf{z}_j^1,\\mathbf{z}_j^2,\\dots,\\mathbf{z}_j^N)|_{j = t - 1:t + 1} \\). The attention module is identical for both intra- and interslice attention, which is" + }, + { + "type": "equation", + "bbox": [ + 0.216, + 0.799, + 0.47, + 0.835 + ], + "angle": 0, + "content": "\\[\nA = \\sigma \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {K}}}\\right) V \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": ", where \\(Q = W_{Q}\\cdot LN(\\mathbf{z})\\), \\(K = W_{K}\\cdot LN(\\mathbf{z})\\), and \\(V = W_{V}\\cdot LN(\\mathbf{z})\\) are query, key and value embeddings, respectively. \\(LN\\) denotes layer-normalization, \\(\\sigma\\) denotes soft-max operation and \\(d_{K}\\) denotes embedding dimension." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.895, + 0.552 + ], + "angle": 0, + "content": "For maximum efficiency of translation, inter-slice attention occurs on the adjacent patches over slice-direction only for computational efficiency. After attention module, a 2D CNN decoder \\( G_{D} \\) reconstructs partial volume sets in the same way as done in \\( G_{E} \\), constructing a translated 2.5D mini-volume. In inference step, only the center slices of mini-volume is stacked one by one to construct a whole translated volume." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.564, + 0.892, + 0.596 + ], + "angle": 0, + "content": "3.2. Volumetric self-training with uncertainty-constrained pseudo-label refinement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.892, + 0.77 + ], + "angle": 0, + "content": "Even if the source-to-target transformed images are well generated, there may still exist some distribution gap with the real target domain data, and it is difficult to completely replace it. With self-training, pseudo-labels for the unlabeled target domain data can be obtained and used to provide supervision to the target domain data, thereby mitigating the domain gap from the model's perspective. We propose to utilize volumetric self-training to close the domain gap, with a simple and novel pseudo-label refinement strategy to maximize the effect of self-training. The steps are as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.785, + 0.892, + 0.862 + ], + "angle": 0, + "content": "3.2.1. Training segmentation with labeled synthetic scans. With the synthetic data \\(\\tilde{x}^t\\) converted from source domain and the annotations \\(y^{s}\\) on the source scans (i.e., labeled synthetic dataset), we first train a teacher segmentation network \\(f_{teacher}\\) that minimizes the segmentation loss:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.876, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum L _ {\\text {s e g}} \\left(y ^ {s}, f _ {\\text {t e a c h e r}} \\left(\\tilde {x} ^ {t}\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7415" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.09, + 0.331, + 0.101 + ], + "angle": 0, + "content": "(a) Sensitivity-preserving Pseudo Label Refinement" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.102, + 0.468, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.393, + 0.472, + 0.478 + ], + "angle": 0, + "content": "Figure 4. Illustration of the proposed uncertainty-constrained pseudo-label refinement module on vestibular schwannoma of CrossMoDA dataset. Sensitivity/specificity enhancing refinement can be performed in parallel, and either one or a combination of the two can be used according to the characteristics of each class in the dataset. Best viewed in color and on high-resolution display." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.58 + ], + "angle": 0, + "content": "3.2.2. Inferring pseudo-labels on unlabeled target domain data. Once the teacher model is trained, pseudolabels \\(\\tilde{y}^t\\) of the non-annotated real data \\(x^t\\) can be obtained by passing real target scans to the trained segmentation model \\(f_{teacher}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.593, + 0.469, + 0.613 + ], + "angle": 0, + "content": "\\[\n\\tilde {y} _ {i} ^ {t} = f _ {\\text {t e a c h e r}} \\left(\\left\\{x _ {i} ^ {t} \\right\\} _ {i = 1} ^ {N _ {t}}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.47, + 0.741 + ], + "angle": 0, + "content": "3.2.3. Uncertainty-constrained pseudo-label refinement for sensitivity / specificity enhancement. Since the pseudo-labels are noisy labels, they must be refined to increase accuracy and guide self-training to better direction. We devise a sensitivity and specificity enhancing pseudo-label refinement module that refines pseudo-labels based on image intensities, current pseudo-label, and high-uncertainty regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.47, + 0.817 + ], + "angle": 0, + "content": "Sensitivity-enhancing pseudo-label refinement. With the inference of pseudo-labels, uncertainty (i.e., entropy) maps corresponding to each class are computed according to the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.232, + 0.832, + 0.469, + 0.849 + ], + "angle": 0, + "content": "\\[\nU = p \\log p \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": ", where \\( p \\) is the output probability map of each class. To enhance the sensitivity of pseudo-labels, highly uncertain regions outside the range of pseudo-labels are detected. Then," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.151 + ], + "angle": 0, + "content": "if the pixel intensity in this region is within a certain range of image intensity included in the current pseudo-label, this region is included to be part of pseudo-label. The equation can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.158, + 0.815, + 0.176 + ], + "angle": 0, + "content": "\\[\n\\text {I n i t i z e} \\tilde {y} _ {r} ^ {t} = \\tilde {y} ^ {t}. \\tilde {y} _ {r} ^ {t} (i, j) = 1 \\text {i f}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.179, + 0.891, + 0.212 + ], + "angle": 0, + "content": "\\[\n\\left. \\operatorname {m e a n} \\left(x ^ {t} \\left(\\tilde {y} ^ {t}\\right)\\right) \\times \\alpha < x _ {U H} ^ {t} (i, j) < \\operatorname {m e a n} \\left(x ^ {t} \\left(\\tilde {y} ^ {t}\\right)\\right) \\times \\beta \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.223, + 0.893, + 0.33 + ], + "angle": 0, + "content": "where \\( x^{t} \\), \\( \\tilde{y}^{t} \\), \\( \\tilde{y}_{r}^{t} \\), and \\( x_{UH}^{t} \\) represent target domain image, pseudo-label, refined pseudo-label, and image cropped with high-uncertainty region mask, respectively. This approach is grounded on the assumption that 1) pixels that have similar intensity and 2) are close to each other in medical image are likely to belong to the same class. The workflow is described with images in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Specificity-enhancing pseudo-label refinement. To enhance specificity of pseudo-labels, highly uncertain regions inside the range of pseudo-labels are detected. Then, if the pixel intensity in this region is outside a certain range of image intensity included in the current pseudo-label, it is excluded from the current pseudo-label." + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.443, + 0.817, + 0.461 + ], + "angle": 0, + "content": "\\[\n\\text {I n i t i z e} \\tilde {y} _ {r} ^ {t} = \\tilde {y} ^ {t}. \\tilde {y} _ {r} ^ {t} (i, j) = 0 \\text {i f}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.464, + 0.891, + 0.482 + ], + "angle": 0, + "content": "\\[\nx _ {U H} ^ {t} (i, j) < \\operatorname {m e a n} \\left(x ^ {t} (\\tilde {y} ^ {t})\\right) \\times \\alpha o r \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.484, + 0.821, + 0.502 + ], + "angle": 0, + "content": "\\[\nx _ {U H} ^ {t} (i, j) > \\operatorname {m e a n} \\left(x ^ {t} (\\tilde {y} ^ {t})\\right) \\times \\beta\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.511, + 0.892, + 0.676 + ], + "angle": 0, + "content": "3.2.4. Retraining segmentation with combined data. Synthetic target scans have distribution gap with the real target scans, but they are paired with perfect annotations. On the other hand, real target scans are paired with pseudolabels, which are yet incomplete. We incorporate both pairs to self-training, to maximize the generalization ability and minimize the performance degradation caused by difference in distributions. With the combined data of labeled synthetic target scans \\((\\tilde{x}^t,y^s)\\) and pseudo-labeled real target scans \\((x^{t},\\tilde{y}_{r}^{t})\\), we train a student segmentation \\(f_{student}\\) to minimize" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.685, + 0.9, + 0.719 + ], + "angle": 0, + "content": "\\[\nL = \\sum L _ {s e g} \\left(y ^ {s}, f _ {s t u d e n t} \\left(\\tilde {x} ^ {t}\\right)\\right) + \\sum L _ {s e g} \\left(\\tilde {y} _ {r} ^ {t}, f _ {s t u d e n t} \\left(x ^ {t}\\right)\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Despite not being ground truth labels, it has been reported in the previous literature that the self-training scheme and the pseudo-labels increases the performance and generalization ability of the model on unseen data by utilizing unlabeled data into training [35]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.808, + 0.633, + 0.825 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.596, + 0.847 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "CrossMoDA dataset. CrossMoDA dataset [7] for vestibular schwannoma and cochlea segmentation consists of 105 labeled contrast-enhanced T1 (ceT1) MRI scans and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7416" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.471, + 0.182 + ], + "angle": 0, + "content": "105 unlabeled high-resolution T2 (hrT2) MRI scans. The direction of domain adaptation was from ceT1 to hrT2 since the annotations of hrT2 scans are not publicly available. Evaluation was performed online on 32 inaccessible hrT2 scans through an official leaderboard. Please refer to the supplementary material for examples of each domain data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.474, + 0.41 + ], + "angle": 0, + "content": "Cardiac structure segmentation dataset. 2017 Multi-Modality Whole Heart Segmentation (MMWHS) challenge dataset [40] which consists of 20 MRI and 20 CT volumes was used for cardiac segmentation. Domain adaptation was performed from MRI to CT, with \\(80\\%\\) of each modality used for training and \\(20\\%\\) (i.e., 4 volumes) of randomly selected CT scans used for evaluation. Target cardiac structures for segmentation were ascending aorta (AA), left atrium blood cavity (LAC), the left ventricle blood cavity (LVC), and myocardium of left ventricle (MYO). With a fixed coronal plane resolution of \\(256 \\times 256\\), MRI and CT volumes were manually cropped to cover the 4 cardiac substructures. Please refer to the supplementary material for examples of each domain data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.425, + 0.292, + 0.44 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.471, + 0.645 + ], + "angle": 0, + "content": "Unpaired image translation with intra- and inter-slice self-attention module. Intra- and inter-slice attentive translation is based on 2D framework, where image slices are fed to 2D CNN \\( E \\) as a stacked batches of size \\( (B \\times 3,1,H,W) \\), where \\( H \\) and \\( W \\) each denote height and width. After \\( G_{E} \\), encoded feature map is reshaped to \\( (B,3,H,W) \\) and fed to the attention module for the consideration of slice-direction attention. Patch size \\( p \\) was set as 2. Transposed convolution is used to convert embedded patches back to 2D feature maps. For a stack of mini-volume generated at \\( G \\), we implement 2D discriminator \\( D \\) for adversarial training of domain translation. For real input to \\( D \\), 3 consecutive slices were randomly extracted from the target volumes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Uncertainty-constrained pseudo-label refinement. For each class, grid searching was conducted on how to set the threshold for masking the high-uncertainty region and also on whether to use either one, or both of the sensitivity and specificity enhancing refinement. For CrossMoDA dataset, combining sensitivity and specificity-enhancing refinement in both classes (i.e., VS and Cochlea) with uncertainty threshold of 0.3 led to the best result. For cardiac dataset, the same threshold value was used and using only specificity-enhancing refinement for all classes except one (i.e., AA) led to the best result. This is attributed to the fact that the contrast difference between adjacent substructures was very weak in cardiac CT which led to noisier pseudo-label when sensitivity-enhancing module was used. Please refer to the tables in supplementary material for ablation results. \\(\\alpha\\) and \\(\\beta\\) were set as 0.6 and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 1. Ablation study on the components of the proposed method on CrossMoDA dataset. ST and PL denote self-training and pseudo-label, respectively. Best results are bolded." + }, + { + "type": "table_caption", + "bbox": [ + 0.618, + 0.144, + 0.773, + 0.158 + ], + "angle": 0, + "content": "CrossMoDA (T1→T2)" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.159, + 0.892, + 0.254 + ], + "angle": 0, + "content": "
Dice (↑)ASSD (↓)
MethodsVSCVSC
Baseline71.572.75.911.83
+ intra/inter-slice attention80.374.51.660.67
+ ST w/o PL refinement83.276.70.580.79
+ ST w/ PL refinement84.684.90.510.14
" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.267, + 0.697, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.385, + 0.642, + 0.396 + ], + "angle": 0, + "content": "Source CeT1" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.268, + 0.89, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.385, + 0.855, + 0.398 + ], + "angle": 0, + "content": "Synthetic HrT2 (2D)" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.401, + 0.697, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.518, + 0.671, + 0.532 + ], + "angle": 0, + "content": "Synthetic HrT2 (2.5D)" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.4, + 0.89, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.518, + 0.872, + 0.532 + ], + "angle": 0, + "content": "Synthetic HrT2 (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.545, + 0.892, + 0.615 + ], + "angle": 0, + "content": "Figure 5. Representative case showing the effect of intra- and inter-slice self-attentive image translation. Translation was performed using axial slices and the resulting volume is being observed from sagittal direction. Best viewed in color and on high-resolution display." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.642, + 0.614, + 0.657 + ], + "angle": 0, + "content": "1.4, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.672, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Volumetric self-training. For volumetric segmentation self-training, 3D U-Net based architecture constructed from nnU-Net [14] was used. Segmentation was trained for 100 epochs using a combination of Dice and cross entropy loss with stochastic gradient descent optimizer. The initial learning rate and batch size were 1e-2 and 2, respectively. Detailed information on network architecture and training strategy can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.593, + 0.817 + ], + "angle": 0, + "content": "4.3. Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of intra- and inter-slice self-attention module in image translation. Fig. 5 shows a representative case that presents how the quality of the synthetic image changes depending on the design of the image translation network. Compared with the proposed method (ours), slice-direction" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7417" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.131 + ], + "angle": 0, + "content": "Table 2. Comparison of quantitative results between SDC-UDA and previous non-medical and medical UDA methods. CycleGAN, CyCADA, ADVENT, and FDA represent non-medical UDA methods while SIFA and PSIGAN represent recent medical UDA methods. Best results are bolded." + }, + { + "type": "table_caption", + "bbox": [ + 0.26, + 0.144, + 0.411, + 0.155 + ], + "angle": 0, + "content": "VS and Cochlea (T1 \\(\\rightarrow\\) T2)" + }, + { + "type": "table_caption", + "bbox": [ + 0.587, + 0.144, + 0.763, + 0.155 + ], + "angle": 0, + "content": "Cardiac structures \\((\\mathbf{MR}\\rightarrow \\mathbf{CT})\\)" + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.155, + 0.895, + 0.292 + ], + "angle": 0, + "content": "
MethodsDice (↑)ASSD (↓)Dice (↑)ASSD (↓)
VSCMeanVSCMeanAALACLVCMYOMeanAALACLVCMYOMean
Non-MedicalFully-supervised192.587.790.10.20.10.1595.992.093.088.292.31.02.51.81.71.8
w/o adaptation11.50.05.824.0NANA48.452.020.04.731.318.834.532.036.430.4
CycleGAN [38]39.70.019.810.1NANA58.359.861.523.150.711.410.69.214.811.5
CyCADA [12]39.20.119.710.518.114.357.262.165.047.257.98.49.08.27.98.4
ADVENT [34]8.30.04.217.1NANA68.271.878.850.767.49.66.64.75.16.5
FDA [36]12.50.06.313.520.517.046.568.473.855.761.110.27.64.35.06.8
MedicalSIFA [4]47.219.733.519.13.311.276.388.174.262.475.36.13.97.14.85.5
PSIGAN [15]57.337.247.35.52.84.167.287.080.360.873.87.54.25.54.75.5
SDC-UDA (ours)84.684.984.80.510.140.3395.891.088.666.685.51.12.83.26.33.3
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.088, + 0.293, + 0.892, + 0.318 + ], + "angle": 0, + "content": "1 Since the ground truth for CrossMoDA Dataset is not available, fully-supervised results are referred from the dataset owner's paper [7]. These figures correspond to the upper bound and are the evaluation results from larger test set (N=137) than the one used in our study." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.332, + 0.182, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.41, + 0.182, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.493, + 0.154, + 0.506 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.332, + 0.284, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.207, + 0.493, + 0.258, + 0.506 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.332, + 0.384, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.493, + 0.374, + 0.506 + ], + "angle": 0, + "content": "CycleGAN" + }, + { + "type": "image", + "bbox": [ + 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0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.722, + 0.571, + 0.801, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.803, + 0.571, + 0.891, + 0.636 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.64, + 0.146, + 0.655 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.64, + 0.23, + 0.654 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.64, + 0.317, + 0.654 + ], + "angle": 0, + "content": "CycADA" + }, + { + "type": "image_caption", + "bbox": [ + 0.332, + 0.64, + 0.398, + 0.654 + ], + "angle": 0, + "content": "ADVENT" + }, + { + "type": "image_caption", + "bbox": [ + 0.429, + 0.64, + 0.462, + 0.653 + ], + "angle": 0, + "content": "FDA" + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.64, + 0.545, + 0.653 + ], + "angle": 0, + "content": "SIFA" + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.64, + 0.638, + 0.653 + ], + "angle": 0, + "content": "PSIGAN" + }, + { + "type": "image_caption", + "bbox": [ + 0.67, + 0.64, + 0.706, + 0.654 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.752, + 0.64, + 0.785, + 0.654 + ], + "angle": 0, + "content": "Sup." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.669, + 0.895, + 0.713 + ], + "angle": 0, + "content": "Figure 6. Comparison of qualitative results between SDC-UDA and previous non-medical and medical UDA methods. Since the ground truth of CrossMoDA dataset is not accessible, we requested to the data owner a few of the label slices and used them to make this figure. The numbers indicate Dice values of each substructure in the slice. Sup denotes the fully-supervised result." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.473, + 0.89 + ], + "angle": 0, + "content": "inconsistency of pixel intensity was observed in the translated image due to the variation derived from slice-by-slice prediction with a 2D network (blue arrows). This was not completely overcome even with a 2.5D network that puts two adjacent slices together in the network. Also, in both 2D and 2.5D networks, it was found that the anatomy of the source image was distorted in the translated image (red and green arrows). On the other hand, it was observed that the aforementioned problems were alleviated when utilizing the intra- and inter-slice self-attention module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.895, + 0.829 + ], + "angle": 0, + "content": "that effectively considers neighboring anatomy. Table 1 shows the increase of final segmentation performance by incorporating intra- and inter-slice self-attention in image translation network compared to baseline that utilizes pure unpaired image translation followed by 3D segmentation network." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Effect of uncertainty-constrained pseudo-label refinement and volumetric self-training. Since the target domain ground truth is inaccessible for the CrossMoDA" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7418" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.092, + 0.271, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.092, + 0.462, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.201, + 0.272, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.201, + 0.462, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Figure 7. Representative cases demonstrating the superior slice-direction continuity of segmentation by the proposed method compared to other medical UDA methods on cardiac dataset. The plots show graphs of Dice coefficient for each slice. (a), (b), (c), and (d) denote AA, LAC, LVC, and MYO class, respectively. Best viewed in color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.655 + ], + "angle": 0, + "content": "dataset, the effectiveness of pseudo-label refinement was verified by comparing the performance of self-training before and after pseudo-label refinement. For cardiac datasets for which ground truth is available, it was verified by comparing dice coefficients with labels before and after pseudo-label refinement (please refer to supplementary material). Table 1 shows the improvement of target domain segmentation performance by applying the proposed uncertainty-constrained pseudo-label refinement on CrossMoDA dataset. It can be seen that volumetric self-training combined with the proposed uncertainty-constrained pseudo-label refinement increases the quantitative metrics in both VS and C by a large margin, whereas pure self-training only increase the performance in VS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.468, + 0.839 + ], + "angle": 0, + "content": "Comparative studies. The proposed method is compared with six popular UDA methods that are CycleGAN [38], CyCADA [12], ADVENT [34], FDA [36], SIFA [4], and PSIGAN [15]. The first four methods are from natural image field whereas the last two are UDA for medical image segmentation methods. Fully-supervised and without-adaptation results are presented to provide upper bound and lower bound, respectively. Please note that the full-supervised result of CrossMoDA dataset, for which the ground truth segmentation mask is not available, is referred from the paper of the dataset owner [7]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Table 2 and Fig. 6 shows quantitative and qualitative results of comparative studies between the proposed method and previous methods. SDC-UDA far exceeds the results of UDA for semantic segmentation studies in the non-medical" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "field, and shows better results in multiple tasks compared to the recent studies in the medical field. In particular, there was a significant performance gap between the proposed method and comparison methods in the CrossMoDA dataset compared to the cardiac dataset. This is probably attributed to the fact that previous studies on medical UDA are dedicated to datasets in which the data are cropped around the target organs and the foreground objects occupy a large portion of the data. In contrast, SDC-UDA shows that both target structures in the CrossMoDA dataset are segmented with high accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.892, + 0.5 + ], + "angle": 0, + "content": "Slice-direction continuity of segmentation compared to previous studies. Fig. 7 shows the excellent slice-direction continuity of segmentation by the proposed method compared to the previous studies on the MMWHS cardiac dataset. Fig. 7-(a), (b), (c), and (d) plot the slice-wise Dice values from representative cases of AA, LAC, LVC, and MYO, respectively. Our SDC-UDA shows gradual and consistent segmentation performance in the slice-direction whereas SIFA and PSIGAN, which are recently proposed medical UDA methods, show very inconsistent and sometimes sudden fluctuations of segmentation performance in the slice direction. This suggests the potential of the proposed method to be useful in the clinical practice where precise volumetric segmentation is required to analyze the patient's status with high confidence." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.513, + 0.618, + 0.529 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.705 + ], + "angle": 0, + "content": "In this study, we proposed SDC-UDA, a novel volumetric UDA framework for slice-direction continuous cross-modality medical image segmentation, and validated it on multiple public datasets. SDC-UDA effectively translates medical volumes through intra- and inter-slice self-attention and better adapts to target domain via volumetric self-training enhanced by simple yet effective pseudo-label refinement strategy that utilizes uncertainty maps. Ablation studies demonstrated the effectiveness of each component and comparative studies showed the superior performance of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This research was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-TF2103-01 in constructing hardware systems and multi-modal studies. It was also supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2021R1A4A1031437, 2022R1A2C2008983), Artificial Intelligence Graduate School Program at Yonsei University [No. 2020-0-01361], the KIST Institutional Program (Project No.2E31051-21-204), and partially supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7419" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. 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Pseudoseg: Designing pseudo labels for semantic segmentation. arXiv preprint arXiv:2010.09713, 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.769 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.956 + ], + "angle": 0, + "content": "7421" + } + ] +] \ No newline at end of file diff --git a/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/20148cfd-bd1f-4726-9d6d-b13924bbcc1e_origin.pdf b/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/20148cfd-bd1f-4726-9d6d-b13924bbcc1e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eef92ffb9500faf6d814487cad4bd0b57fcecfcd --- /dev/null +++ b/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/20148cfd-bd1f-4726-9d6d-b13924bbcc1e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f13bf042822141058e09363984d7ef543412823cd7f119622fbeb261d151527d +size 7229836 diff --git a/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/full.md b/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..eaf1e7d8f4b69a9afa5689a856ea06923b188f48 --- /dev/null +++ b/2023/SDC-UDA_ Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation/full.md @@ -0,0 +1,361 @@ +# SDC-UDA: Volumetric Unsupervised Domain Adaptation Framework for Slice-Direction Continuous Cross-Modality Medical Image Segmentation + +Hyungseob Shin\* + +Hyeongyu Kim $^{1*}$ + +Sewon $\mathrm{Kim}^{4,5}$ + +Yohan Jun7,8 + +Taejoon $\mathrm{Eo^{1,6}}$ + +Dosik Hwang $^{1,2,3,9\dagger}$ + +$\{^{1}\text{School of Electrical and Electronic Engineering}, {}^{2}\text{Department of Oral and Maxillofacial Radiology, College of Dentistry}, {}^{3}\text{Department of Radiology and Center for Clinical Imaging Data Science, College of Medicine}\}$ + +@Yonsei University $^{4}$ Naver AI Lab $^{5}$ Naver Cloud $^{6}$ Probe Medical, Inc. $^{7}$ Martinos Center for Biomedical Imaging + +$^{8}$ Harvard Medical School $^{9}$ Center for Healthcare Robotics, Korea Institute of Science and Technology + +{whatzupsup, lion4309, dosik.hwang}@yonsei.ac.kr + +# Abstract + +Recent advances in deep learning-based medical image segmentation studies achieve nearly human-level performance in fully supervised manner. However, acquiring pixel-level expert annotations is extremely expensive and laborious in medical imaging fields. Unsupervised domain adaptation (UDA) can alleviate this problem, which makes it possible to use annotated data in one imaging modality to train a network that can successfully perform segmentation on target imaging modality with no labels. In this work, we propose SDC-UDA, a simple yet effective volumetric UDA framework for Slice-Direction Continuous cross-modality medical image segmentation which combines intra- and inter-slice self-attentive image translation, uncertainty-constrained pseudo-label refinement, and volumetric self-training. Our method is distinguished from previous methods on UDA for medical image segmentation in that it can obtain continuous segmentation in the slice direction, thereby ensuring higher accuracy and potential in clinical practice. We validate SDC-UDA with multiple publicly available cross-modality medical image segmentation datasets and achieve state-of-the-art segmentation performance, not to mention the superior slice-direction continuity of prediction compared to previous studies. + +# 1. Introduction + +With the surprising development of deep learning (DL), many studies are now showing remarkable performance in various applications [8, 16, 20]. However, when a DL model + +![](images/892a2278f666ddf7e04fe99f6555a4e9543bc934cfe83576975b71be25143b45.jpg) +(A) Previous UDA for medical image segmentation frameworks +Figure 1. An illustration that describes the comparison between our proposed method with previous methods. (A) Previous UDA for medical image segmentation studies mostly utilize 2D UDA, which leads to inconsistent predictions in the slice direction when the predictions are stacked. (B) The proposed framework (SDC-UDA) considers volumetric information in the translation and segmentation process, respectively, which leads to improved slice-direction continuity of segmentation that is much practical for clinical use. + +faces data from an unseen domain, performance degradation occurs [9, 32]. Resolving this issue is important for the DL techniques to be applied in real world since collecting data from all domains and labeling them is very impractical and inefficient. Unsupervised Domain Adaptation (UDA) aims to alleviate this problem by adapting a model trained on source domain data to target domain, without the necessity of supervision in the target domain. Data dependency is more serious in medical image segmentation field since acquiring pixel-level expert annotation is extremely expensive and time-consuming [3, 22, 37]. + +Previous studies on UDA in the field of cross-modality med + +![](images/89eb8878777566d137aee2cf6fe3b2ca555d7e8da15d00081cb8d30fdd326f68.jpg) +Figure 2. Overview of our volumetric UDA framework. First, source-to-target image transformation is performed via unpaired image translation with intra- and inter-slice self-attention (stage 1-2). Second, volumetric self-training is performed (stage 3-5). During self-training, uncertainty-constrained pseudo-label refinement is conducted to improve pseudo-labels, thereby maximizing the effect of self-training (stage 4). The reverse loop of image translation is omitted for ease of illustration. Detailed architecture of image translation network is described in Fig. 3. Best viewed in color and on high-resolution display. II-SA: Intra- and inter-slice self-attention. + +ical image segmentation are normally conducted by simultaneously learning 2D image translation and target-domain segmentation, inferring the trained model on each slice of target data, and then stacking the predictions in the slice direction (Fig. 1). As a result, they can lead to inconsistent or fluctuating predictions in the slice direction that are not revealed in quantitative metrics and may interrupt accurate analysis of target structure, making it difficult to use in real world clinical practice. In contrast, SDC-UDA can achieve improved slice-direction continuity by incorporating volumetric natures of medical imaging, which has not been thoroughly explored in previous works. It efficiently generates synthetic target volumes with neighbor-aware image translation by utilizing intra- and inter-slice self-attention module [27]. Then, volumetric self-training is followed with uncertainty-constrained pseudo-label refinement strategy that adaptively increases the accuracy of pseudo-labels according to the target data (Fig. 2). Preliminary version of this work has won the 1st place in an unsupervised cross-modality domain adaptation for medical image segmentation challenge [7, 26]. We updated the framework and extended it to multiple datasets. The main contribution of our work can be summarized as follows: + +- We present SDC-UDA, a unified volumetric UDA framework for cross-modality medical image segmentation. +- Intra- and inter-slice self-attention for efficient medical image translation: Proposed 2.5D translation frame + +work with intra- and inter-slice self-attention module leads to increased anatomy preservation and slicedirection smoothness in the synthesized volume, enabling the synthetic volume to be used effectively in the following self-training steps. + +- Volumetric self-training with uncertainty-constrained pseudo-label refinement: We propose a novel uncertainty-constrained pseudo-label refinement module that can adaptively enhance the accuracy (i.e., sensitivity or specificity) of pseudo-labels, thereby maximizing the performance of self-training on medical image segmentation. +- SDC-UDA was validated on multiple public datasets with different data characteristics for cross-modality medical image segmentation. It not only surpassed the performance of previous methods, but also showed superior slice-direction segmentation continuity which can provide precise analysis in clinical practice. + +# 2. Related Work + +# 2.1. UDA for medical image segmentation. + +UDA for semantic segmentation is one of the most popular themes among UDA-related studies [12,18,21,31]. Especially, UDA on medical image segmentation is very attractive [3, 6, 13, 15, 22, 37] since it can address the difficulty of obtaining expensive expert-level manual annota + +tions. Recent studies on UDA for medical image segmentation are mostly based on image adaptation in which domain translation and segmentation networks are trained end-to-end, thereby utilizing the source-to-target transformed images for training segmentation on target domain. [13, 22, 37] combined image-to-image translation and segmentation into a single network. [3] added feature adaptation with adversarial training using the segmentation output of the synthetic and real target domain images to better preserve the geometry of the structures-of-interest. Moreover, [15] added both the synthetic and real target domain images and their corresponding segmentation probability maps to adversarial training to preserve not only the geometry of target anatomies but also their appearance (i.e., intensities). [11] utilized deep symmetric networks to further align the features of two domains. + +Our work differs from previous works in the following aspects: Previous works mostly train 2D-level image translation with target-domain segmentation and stack the segmentation of each target slice in the slice direction [4, 11, 15, 30]. Since the segmentation network does not consider the anatomical structure in the slice direction, this can lead to high variability of segmentation result even in adjacent slices. In contrast, SDC-UDA splits target-domain segmentation from image translation and therefore is not constrained to 2D framework. Consequently, SDC-UDA can effectively incorporate volumetric information in the translation and segmentation process, respectively. Moreover, in addition to the commonly used cross-modality medical image segmentation dataset [17, 19, 40], SDC-UDA has also been validated in the challenging task of cross-modality segmentation of small multi-class structures which are vestibular schwannoma (VS) and cochlea (i.e., CrossMoDA dataset [7, 24, 25]). Previous studies locate target organs to the center of the preprocessed images and the majority of slices contain at least one target organ, whereas VS and cochleas in CrossMoDA dataset occupy extremely small fraction of the total voxels (0.028% and 0.002% for VS and cochlea, respectively, compared to approximately 3% in average in another dataset [40]) which more reflects the real-world clinical imaging environment [4, 15]. + +# 2.2. Self-training on UDA for medical image segmentation. + +Self-training belongs to semi-supervised learning which has emerged to improve the resources and cost put into data labeling [35, 41]. In self-training, a teacher model is first trained using only the labeled data. Next, pseudolabels with high confidence are inferred by passing the unlabeled data on the trained model. With the labeled data and pseudo-labeled data, a larger dataset can be used to train a student model that performs better than the teacher model trained only on labeled data. Numerous attempts + +were made to apply self-training into semantic segmentation [23, 39, 42, 43] as pixel-level annotations are expensive. Since pseudo-labels tend to be noisy labels, previous studies attempted to refine pseudo-labels to increase accuracy, thereby providing better supervision to unlabeled data. [33] updated pseudo-labels by enhancing the sensitivity of pseudo-labels via selective voting. [29] proposed region growing on the super-pixels where the pseudo-labels serve as the initial seed points. [10] utilized uncertainty-weighted binary cross entropy loss to penalize high uncertainty region. + +The proposed pseudo-label refinement strategy is effective in two aspects: 1) sensitivity and specificity-enhancing refinement can be adaptively used according to the characteristic of target data, and 2) it is a safer way to handle uncertainty maps since even the correctly segmented regions can have high uncertainty, and using uncertainty map to weight the loss function in the following training can therefore guide the model to wrong direction. + +# 3. Methods + +# 3.1. Unpaired image translation with intra- and inter-slice self-attention module. + +Many recent works on UDA for medical image segmentation have been developed on 2D framework, without considering the volumetric nature of medical imaging (2D multi-slice sequence or 3D sequence) [3, 13, 15, 22]. Previous 2D UDA approaches split the 3D volume into 2D slices, and re-stack their translations into 3D volume afterward. Since the slices are processed individually, re-building the translated volume usually requires additional post-processing such as slice-direction interpolation, which still can not perfectly resolve problems such as slicedirection discontinuity. This remain a problem when conducting following steps such as self-training for volumetric segmentation. Although there exist frameworks such as 3DCycleGAN which aim to conduct translation 3D volumewise, they are rarely used due to typical drawbacks such as optimization complexity, computational burden, or the degradation of translation quality [5, 28]. + +To remedy both lack of volumetric consideration of 2D and optimization-efficiency issue of 3D methods, we propose a simple and effective pixel-level domain translation method for medical volume data by translating a stack of source domain images into target domain with both intra- and inter-slice self-attention module. Unlike previous 2D methods that only translated within a single slice, our approach leverages information from adjacent slices in the slice-direction. This is similar to recent advances in video processing, which exploit information both within and between frames [1,2]. In contrast to 3D methods that require expensive computational cost, ours do not necessitate heavy + +![](images/e73e7a199840ea4086870cd25088b83f4482473c839f62c8772858a09ac306ae.jpg) +Figure 3. Illustration of the proposed 2.5D image translation with intra- and inter-slice self-attention module. Source domain volume data is cropped to a mini-volume, and fed to CNN encoder $G_{E}$ as a stack of batches. The weights of $G_{E}$ are shared during batch update. The encoded feature maps are embedded to non-overlapping patches, which become the input of intra- & inter-slice attention module $A$ . Within $A$ , intra- and inter-slice attention learns the volumetric information. + +computation, enabling translation without intense down-sampling which 3D-based translations suffer from [28]. + +Shown in Fig.3, proposed framework consists of sequential modules of encoder $G_{E}$ , intra- and inter-slice self-attention II-SA and decoder $G_{D}$ . Taking three continuous slices $x_{t - 1},x_{t},x_{t + 1}$ of a volume as input, they are first fed to a 2D CNN encoder $G_{E}$ separately. Encoded features $G_{E}(x_{t - 1}),G_{E}(x_{t}),G_{E}(x_{t + 1})$ are then fed to transformer-based attention module II-SA together, as feature maps from continuous frames. Before II-SA, each slice is embedded into small patches $\mathbf{z}$ of size $p$ as $\mathbf{z}_{t - 1:t + 1}^n = P(G_E(x_{t - 1:t + 1}))|_{n = 1:N}$ , where $N = W_{G_E(x)}\cdot H_{G_E(x)} / p^2$ . $W_{G_E(x)},H_{G_E(y)}$ are each width, height of encoded feature map $G_{E}(x)$ , respectively. In transformer-based attention module II-SA, two types attention $A_{inter}$ and $A_{intra}$ exist. First, for the consideration of adjacent slices, learnable positional encoding is added to capture relative positional information within mini-volume patches. An inter-slice attention module is $A_{inter} = A(\mathbf{z}_{t - 1}^{k},\mathbf{z}_{t}^{k},\mathbf{z}_{t + 1}^{k})|_{k = 1:N}$ . And for the consideration of nearby pixels within a slice, an intra-slice self-attention exists, as $A_{intra} = A(\mathbf{z}_j^1,\mathbf{z}_j^2,\dots,\mathbf{z}_j^N)|_{j = t - 1:t + 1}$ . The attention module is identical for both intra- and interslice attention, which is + +$$ +A = \sigma \left(\frac {Q K ^ {T}}{\sqrt {d _ {K}}}\right) V \tag {1} +$$ + +, where $Q = W_{Q}\cdot LN(\mathbf{z})$ , $K = W_{K}\cdot LN(\mathbf{z})$ , and $V = W_{V}\cdot LN(\mathbf{z})$ are query, key and value embeddings, respectively. $LN$ denotes layer-normalization, $\sigma$ denotes soft-max operation and $d_{K}$ denotes embedding dimension. + +For maximum efficiency of translation, inter-slice attention occurs on the adjacent patches over slice-direction only for computational efficiency. After attention module, a 2D CNN decoder $G_{D}$ reconstructs partial volume sets in the same way as done in $G_{E}$ , constructing a translated 2.5D mini-volume. In inference step, only the center slices of mini-volume is stacked one by one to construct a whole translated volume. + +# 3.2. Volumetric self-training with uncertainty-constrained pseudo-label refinement. + +Even if the source-to-target transformed images are well generated, there may still exist some distribution gap with the real target domain data, and it is difficult to completely replace it. With self-training, pseudo-labels for the unlabeled target domain data can be obtained and used to provide supervision to the target domain data, thereby mitigating the domain gap from the model's perspective. We propose to utilize volumetric self-training to close the domain gap, with a simple and novel pseudo-label refinement strategy to maximize the effect of self-training. The steps are as follows. + +3.2.1. Training segmentation with labeled synthetic scans. With the synthetic data $\tilde{x}^t$ converted from source domain and the annotations $y^{s}$ on the source scans (i.e., labeled synthetic dataset), we first train a teacher segmentation network $f_{teacher}$ that minimizes the segmentation loss: + +$$ +\mathcal {L} = \sum L _ {\text {s e g}} \left(y ^ {s}, f _ {\text {t e a c h e r}} \left(\tilde {x} ^ {t}\right)\right) \tag {2} +$$ + +![](images/d6f14700959c4d628c4354c8a3c620e66e5fa645e33b30baf577e1c43db19db5.jpg) +(a) Sensitivity-preserving Pseudo Label Refinement +Figure 4. Illustration of the proposed uncertainty-constrained pseudo-label refinement module on vestibular schwannoma of CrossMoDA dataset. Sensitivity/specificity enhancing refinement can be performed in parallel, and either one or a combination of the two can be used according to the characteristics of each class in the dataset. Best viewed in color and on high-resolution display. + +3.2.2. Inferring pseudo-labels on unlabeled target domain data. Once the teacher model is trained, pseudolabels $\tilde{y}^t$ of the non-annotated real data $x^t$ can be obtained by passing real target scans to the trained segmentation model $f_{teacher}$ . + +$$ +\tilde {y} _ {i} ^ {t} = f _ {\text {t e a c h e r}} \left(\left\{x _ {i} ^ {t} \right\} _ {i = 1} ^ {N _ {t}}\right) \tag {3} +$$ + +3.2.3. Uncertainty-constrained pseudo-label refinement for sensitivity / specificity enhancement. Since the pseudo-labels are noisy labels, they must be refined to increase accuracy and guide self-training to better direction. We devise a sensitivity and specificity enhancing pseudo-label refinement module that refines pseudo-labels based on image intensities, current pseudo-label, and high-uncertainty regions. + +Sensitivity-enhancing pseudo-label refinement. With the inference of pseudo-labels, uncertainty (i.e., entropy) maps corresponding to each class are computed according to the following equation: + +$$ +U = p \log p \tag {4} +$$ + +, where $p$ is the output probability map of each class. To enhance the sensitivity of pseudo-labels, highly uncertain regions outside the range of pseudo-labels are detected. Then, + +if the pixel intensity in this region is within a certain range of image intensity included in the current pseudo-label, this region is included to be part of pseudo-label. The equation can be formulated as: + +$$ +\text {I n i t i z e} \tilde {y} _ {r} ^ {t} = \tilde {y} ^ {t}. \tilde {y} _ {r} ^ {t} (i, j) = 1 \text {i f} +$$ + +$$ +\left. \operatorname {m e a n} \left(x ^ {t} \left(\tilde {y} ^ {t}\right)\right) \times \alpha < x _ {U H} ^ {t} (i, j) < \operatorname {m e a n} \left(x ^ {t} \left(\tilde {y} ^ {t}\right)\right) \times \beta \right. \tag {5} +$$ + +where $x^{t}$ , $\tilde{y}^{t}$ , $\tilde{y}_{r}^{t}$ , and $x_{UH}^{t}$ represent target domain image, pseudo-label, refined pseudo-label, and image cropped with high-uncertainty region mask, respectively. This approach is grounded on the assumption that 1) pixels that have similar intensity and 2) are close to each other in medical image are likely to belong to the same class. The workflow is described with images in Fig. 4. + +Specificity-enhancing pseudo-label refinement. To enhance specificity of pseudo-labels, highly uncertain regions inside the range of pseudo-labels are detected. Then, if the pixel intensity in this region is outside a certain range of image intensity included in the current pseudo-label, it is excluded from the current pseudo-label. + +$$ +\text {I n i t i z e} \tilde {y} _ {r} ^ {t} = \tilde {y} ^ {t}. \tilde {y} _ {r} ^ {t} (i, j) = 0 \text {i f} +$$ + +$$ +x _ {U H} ^ {t} (i, j) < \operatorname {m e a n} \left(x ^ {t} (\tilde {y} ^ {t})\right) \times \alpha o r \tag {6} +$$ + +$$ +x _ {U H} ^ {t} (i, j) > \operatorname {m e a n} \left(x ^ {t} (\tilde {y} ^ {t})\right) \times \beta +$$ + +3.2.4. Retraining segmentation with combined data. Synthetic target scans have distribution gap with the real target scans, but they are paired with perfect annotations. On the other hand, real target scans are paired with pseudolabels, which are yet incomplete. We incorporate both pairs to self-training, to maximize the generalization ability and minimize the performance degradation caused by difference in distributions. With the combined data of labeled synthetic target scans $(\tilde{x}^t,y^s)$ and pseudo-labeled real target scans $(x^{t},\tilde{y}_{r}^{t})$ , we train a student segmentation $f_{student}$ to minimize + +$$ +L = \sum L _ {s e g} \left(y ^ {s}, f _ {s t u d e n t} \left(\tilde {x} ^ {t}\right)\right) + \sum L _ {s e g} \left(\tilde {y} _ {r} ^ {t}, f _ {s t u d e n t} \left(x ^ {t}\right)\right) \tag {7} +$$ + +Despite not being ground truth labels, it has been reported in the previous literature that the self-training scheme and the pseudo-labels increases the performance and generalization ability of the model on unseen data by utilizing unlabeled data into training [35]. + +# 4. Experiments + +# 4.1. Dataset + +CrossMoDA dataset. CrossMoDA dataset [7] for vestibular schwannoma and cochlea segmentation consists of 105 labeled contrast-enhanced T1 (ceT1) MRI scans and + +105 unlabeled high-resolution T2 (hrT2) MRI scans. The direction of domain adaptation was from ceT1 to hrT2 since the annotations of hrT2 scans are not publicly available. Evaluation was performed online on 32 inaccessible hrT2 scans through an official leaderboard. Please refer to the supplementary material for examples of each domain data. + +Cardiac structure segmentation dataset. 2017 Multi-Modality Whole Heart Segmentation (MMWHS) challenge dataset [40] which consists of 20 MRI and 20 CT volumes was used for cardiac segmentation. Domain adaptation was performed from MRI to CT, with $80\%$ of each modality used for training and $20\%$ (i.e., 4 volumes) of randomly selected CT scans used for evaluation. Target cardiac structures for segmentation were ascending aorta (AA), left atrium blood cavity (LAC), the left ventricle blood cavity (LVC), and myocardium of left ventricle (MYO). With a fixed coronal plane resolution of $256 \times 256$ , MRI and CT volumes were manually cropped to cover the 4 cardiac substructures. Please refer to the supplementary material for examples of each domain data. + +# 4.2. Implementation details + +Unpaired image translation with intra- and inter-slice self-attention module. Intra- and inter-slice attentive translation is based on 2D framework, where image slices are fed to 2D CNN $E$ as a stacked batches of size $(B \times 3,1,H,W)$ , where $H$ and $W$ each denote height and width. After $G_{E}$ , encoded feature map is reshaped to $(B,3,H,W)$ and fed to the attention module for the consideration of slice-direction attention. Patch size $p$ was set as 2. Transposed convolution is used to convert embedded patches back to 2D feature maps. For a stack of mini-volume generated at $G$ , we implement 2D discriminator $D$ for adversarial training of domain translation. For real input to $D$ , 3 consecutive slices were randomly extracted from the target volumes. + +Uncertainty-constrained pseudo-label refinement. For each class, grid searching was conducted on how to set the threshold for masking the high-uncertainty region and also on whether to use either one, or both of the sensitivity and specificity enhancing refinement. For CrossMoDA dataset, combining sensitivity and specificity-enhancing refinement in both classes (i.e., VS and Cochlea) with uncertainty threshold of 0.3 led to the best result. For cardiac dataset, the same threshold value was used and using only specificity-enhancing refinement for all classes except one (i.e., AA) led to the best result. This is attributed to the fact that the contrast difference between adjacent substructures was very weak in cardiac CT which led to noisier pseudo-label when sensitivity-enhancing module was used. Please refer to the tables in supplementary material for ablation results. $\alpha$ and $\beta$ were set as 0.6 and + +Table 1. Ablation study on the components of the proposed method on CrossMoDA dataset. ST and PL denote self-training and pseudo-label, respectively. Best results are bolded. + +CrossMoDA (T1→T2) + +
Dice (↑)ASSD (↓)
MethodsVSCVSC
Baseline71.572.75.911.83
+ intra/inter-slice attention80.374.51.660.67
+ ST w/o PL refinement83.276.70.580.79
+ ST w/ PL refinement84.684.90.510.14
+ +![](images/982fc0d4c6c0553ad58cb3e16cf72818909852a0239abdbb1946e1178909018e.jpg) +Source CeT1 + +![](images/05b5fc1ffe04e3354d66fec5bd45076c61e1e0566077c0ff8c97bb8b2d454af7.jpg) +Synthetic HrT2 (2D) + +![](images/73d3d8440f9602c64a49600e4e46a632854254b83dc5b37dc2ac8acfe75292f7.jpg) +Synthetic HrT2 (2.5D) + +![](images/4d1ee04ef9a28f728aba46e160b830d88876e926a2ae6f3af1b9e417cdcb3883.jpg) +Synthetic HrT2 (Ours) +Figure 5. Representative case showing the effect of intra- and inter-slice self-attentive image translation. Translation was performed using axial slices and the resulting volume is being observed from sagittal direction. Best viewed in color and on high-resolution display. + +# 1.4, respectively. + +Volumetric self-training. For volumetric segmentation self-training, 3D U-Net based architecture constructed from nnU-Net [14] was used. Segmentation was trained for 100 epochs using a combination of Dice and cross entropy loss with stochastic gradient descent optimizer. The initial learning rate and batch size were 1e-2 and 2, respectively. Detailed information on network architecture and training strategy can be found in the supplementary materials. + +# 4.3. Results + +Effect of intra- and inter-slice self-attention module in image translation. Fig. 5 shows a representative case that presents how the quality of the synthetic image changes depending on the design of the image translation network. Compared with the proposed method (ours), slice-direction + +Table 2. Comparison of quantitative results between SDC-UDA and previous non-medical and medical UDA methods. CycleGAN, CyCADA, ADVENT, and FDA represent non-medical UDA methods while SIFA and PSIGAN represent recent medical UDA methods. Best results are bolded. +VS and Cochlea (T1 $\rightarrow$ T2) +Cardiac structures $(\mathbf{MR}\rightarrow \mathbf{CT})$ + +
MethodsDice (↑)ASSD (↓)Dice (↑)ASSD (↓)
VSCMeanVSCMeanAALACLVCMYOMeanAALACLVCMYOMean
Non-MedicalFully-supervised192.587.790.10.20.10.1595.992.093.088.292.31.02.51.81.71.8
w/o adaptation11.50.05.824.0NANA48.452.020.04.731.318.834.532.036.430.4
CycleGAN [38]39.70.019.810.1NANA58.359.861.523.150.711.410.69.214.811.5
CyCADA [12]39.20.119.710.518.114.357.262.165.047.257.98.49.08.27.98.4
ADVENT [34]8.30.04.217.1NANA68.271.878.850.767.49.66.64.75.16.5
FDA [36]12.50.06.313.520.517.046.568.473.855.761.110.27.64.35.06.8
MedicalSIFA [4]47.219.733.519.13.311.276.388.174.262.475.36.13.97.14.85.5
PSIGAN [15]57.337.247.35.52.84.167.287.080.360.873.87.54.25.54.75.5
SDC-UDA (ours)84.684.984.80.510.140.3395.891.088.666.685.51.12.83.26.33.3
+ +1 Since the ground truth for CrossMoDA Dataset is not available, fully-supervised results are referred from the dataset owner's paper [7]. These figures correspond to the upper bound and are the evaluation results from larger test set (N=137) than the one used in our study. + +![](images/c35b06a4de185b1871cca3c22a1b45457dd4750afdb6b610bd7560792305e2db.jpg) + +![](images/de04ad0b1e6408af26707ec93de5ce09a8f77cd7db1e99d2441d7b70285836b7.jpg) +Image + +![](images/a392911b6614730b1a8ce471d6504f70ce89d5cba54d8388a32c8880007d8c5b.jpg) +Source + +![](images/0c01e393d62c6efe10bc5b25d3c1e239f32cffed4e7024a0b46febb22782a777.jpg) +CycleGAN + +![](images/bbd0aca9f45565939dac0fb873d8dad56b09d82524a2f4f27a3fac392f566814.jpg) +CycADA + +![](images/1275b80ffbdbd207736b914a49e80cd3982335447cf40c4f028f1c18d04cc2bf.jpg) +SIFA + +![](images/6c5dc7241e40223c7545c034c9354d3f5c4ce3ce9f6291bbcaeca2e1348b6a3d.jpg) +PSIGAN + +![](images/c55a1cc5125036ae38f17beec2e0377c096d52fd18237147e0c68e4d5c3c8116.jpg) +Ours + +![](images/7b7069139fe016eb0bf4fb2d222323977cfefa8dddeb4a78d0fd5cdbb23f165d.jpg) +GT + +![](images/bdda3a6ebcc1068d5bf91b00368ca35f2c7b29fad57ba6c564af4ed3fa3c2b30.jpg) + +![](images/395de99457f6cb9cff44bb9b8414fb87e563227374969aa83423e15e3b650510.jpg) + +![](images/9dc3b588079d85a57404f244ed9dff51e5a5faca3993c62d35ac5d5fc6d54958.jpg) + +![](images/e44713124b271d5a2f48217c86b2800b991f1c5b7bc89de45b6057384da91e30.jpg) + +![](images/eee478a1a3675fb59f03f3f67f550e0f916173f3fa7bab80345a17c702cabd90.jpg) + +![](images/91776e9e2af846231e4d435229a315fa5353fd6cd9001ebb446c60d68bd8a54c.jpg) + +![](images/7e131d170eeca917fe72f845c458f90ae41141f83e3fb0767ccc4af2f19524f7.jpg) + +![](images/71ba9a27fa92a9f08ad4d5de1d159117fa11dd553cdcae9c0c7260f32592a756.jpg) + +![](images/02e3abfec7d6fbffff2d189c6b50a9a1f466dc729a8fa1e6d30be6e1e8c0bf1b.jpg) + +![](images/54db3e98163eace222f5f75e65c6c9eea791384c5b78e8ff69c01896e45e1075.jpg) + +![](images/1dec07f507513843aeb710fa97458fa0ea05168c36a7548896a9ba1259b8452d.jpg) +Image + +![](images/aa2b8676e4efbd15ff386c48c912ca70b429f6faf08d34ede63051c3084d17ca.jpg) +Source + +![](images/2bcffbe35830c1072758f719d8d77db540669324d26743fdb87a216fcd2f4aa2.jpg) +CycADA + +![](images/2c3916131a498cff3142c124e5cd7c5ee4812a763627cee53161f791a757acf6.jpg) +ADVENT + +![](images/f978fa0f2e7b3e5da2a3261e22e6729ab2cd8d32ec9241162b92be52ae70b2ff.jpg) +FDA +SIFA +Figure 6. Comparison of qualitative results between SDC-UDA and previous non-medical and medical UDA methods. Since the ground truth of CrossMoDA dataset is not accessible, we requested to the data owner a few of the label slices and used them to make this figure. The numbers indicate Dice values of each substructure in the slice. Sup denotes the fully-supervised result. + +![](images/833859bc75c8f79e3a4ef16fe0e84c7761f5c6ad2d9351823fe6560ffea5c8fe.jpg) +PSIGAN + +![](images/48000d8fe52b0191fe98cc47871a18b7f08f92e1dc658bde10c3ae6dbc8182c5.jpg) +Ours + +![](images/89175fefda6350e537a864d693539e4f056751cf39cdbe5f1595b448f969b69a.jpg) +Sup. + +![](images/ce81217a24b4bb3267d99c44b37c28a383d65198b2beea71e3034cccd68225ab.jpg) + +inconsistency of pixel intensity was observed in the translated image due to the variation derived from slice-by-slice prediction with a 2D network (blue arrows). This was not completely overcome even with a 2.5D network that puts two adjacent slices together in the network. Also, in both 2D and 2.5D networks, it was found that the anatomy of the source image was distorted in the translated image (red and green arrows). On the other hand, it was observed that the aforementioned problems were alleviated when utilizing the intra- and inter-slice self-attention module + +that effectively considers neighboring anatomy. Table 1 shows the increase of final segmentation performance by incorporating intra- and inter-slice self-attention in image translation network compared to baseline that utilizes pure unpaired image translation followed by 3D segmentation network. + +Effect of uncertainty-constrained pseudo-label refinement and volumetric self-training. Since the target domain ground truth is inaccessible for the CrossMoDA + +![](images/ade02f77d4fc773ef3d52f0fd9300ba4097eb0fb95875a5a57468b15ec766c99.jpg) + +![](images/d6fd011ed1c84a2290bd77ccbac87d235df80760e7130f775fb8948325ddca8f.jpg) + +![](images/232ff38bb3ae42dfa618e016944bf8cc2eb48a3a7c8bd6a294d5c9f51d168e1a.jpg) +Figure 7. Representative cases demonstrating the superior slice-direction continuity of segmentation by the proposed method compared to other medical UDA methods on cardiac dataset. The plots show graphs of Dice coefficient for each slice. (a), (b), (c), and (d) denote AA, LAC, LVC, and MYO class, respectively. Best viewed in color. + +![](images/1f0e770e44f706ce0d72ec3c1f0564f74fc4582780e2a6c87a8ae526512756d5.jpg) + +dataset, the effectiveness of pseudo-label refinement was verified by comparing the performance of self-training before and after pseudo-label refinement. For cardiac datasets for which ground truth is available, it was verified by comparing dice coefficients with labels before and after pseudo-label refinement (please refer to supplementary material). Table 1 shows the improvement of target domain segmentation performance by applying the proposed uncertainty-constrained pseudo-label refinement on CrossMoDA dataset. It can be seen that volumetric self-training combined with the proposed uncertainty-constrained pseudo-label refinement increases the quantitative metrics in both VS and C by a large margin, whereas pure self-training only increase the performance in VS. + +Comparative studies. The proposed method is compared with six popular UDA methods that are CycleGAN [38], CyCADA [12], ADVENT [34], FDA [36], SIFA [4], and PSIGAN [15]. The first four methods are from natural image field whereas the last two are UDA for medical image segmentation methods. Fully-supervised and without-adaptation results are presented to provide upper bound and lower bound, respectively. Please note that the full-supervised result of CrossMoDA dataset, for which the ground truth segmentation mask is not available, is referred from the paper of the dataset owner [7]. + +Table 2 and Fig. 6 shows quantitative and qualitative results of comparative studies between the proposed method and previous methods. SDC-UDA far exceeds the results of UDA for semantic segmentation studies in the non-medical + +field, and shows better results in multiple tasks compared to the recent studies in the medical field. In particular, there was a significant performance gap between the proposed method and comparison methods in the CrossMoDA dataset compared to the cardiac dataset. This is probably attributed to the fact that previous studies on medical UDA are dedicated to datasets in which the data are cropped around the target organs and the foreground objects occupy a large portion of the data. In contrast, SDC-UDA shows that both target structures in the CrossMoDA dataset are segmented with high accuracy. + +Slice-direction continuity of segmentation compared to previous studies. Fig. 7 shows the excellent slice-direction continuity of segmentation by the proposed method compared to the previous studies on the MMWHS cardiac dataset. Fig. 7-(a), (b), (c), and (d) plot the slice-wise Dice values from representative cases of AA, LAC, LVC, and MYO, respectively. Our SDC-UDA shows gradual and consistent segmentation performance in the slice-direction whereas SIFA and PSIGAN, which are recently proposed medical UDA methods, show very inconsistent and sometimes sudden fluctuations of segmentation performance in the slice direction. This suggests the potential of the proposed method to be useful in the clinical practice where precise volumetric segmentation is required to analyze the patient's status with high confidence. + +# 5. Conclusion + +In this study, we proposed SDC-UDA, a novel volumetric UDA framework for slice-direction continuous cross-modality medical image segmentation, and validated it on multiple public datasets. SDC-UDA effectively translates medical volumes through intra- and inter-slice self-attention and better adapts to target domain via volumetric self-training enhanced by simple yet effective pseudo-label refinement strategy that utilizes uncertainty maps. Ablation studies demonstrated the effectiveness of each component and comparative studies showed the superior performance of the proposed method. + +Acknowledgements. This research was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-TF2103-01 in constructing hardware systems and multi-modal studies. It was also supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2021R1A4A1031437, 2022R1A2C2008983), Artificial Intelligence Graduate School Program at Yonsei University [No. 2020-0-01361], the KIST Institutional Program (Project No.2E31051-21-204), and partially supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002). + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. Vivit: A video vision transformer. In Proceedings of the IEEE/CVF international conference on computer vision, pages 6836-6846, 2021. 3 +[2] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? 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However, acquiring pixel-level expert annotations is extremely expensive and laborious in medical imaging fields. Unsupervised domain adaptation (UDA) can alleviate this problem, which makes it possible to use annotated data in one imaging modality to train a network that can successfully perform segmentation on target imaging modality with no labels. In this work, we propose SDC-UDA, a simple yet effective volumetric UDA framework for Slice-Direction Continuous cross-modality medical image segmentation which combines intra- and inter-slice self-attentive image translation, uncertainty-constrained pseudo-label refinement, and volumetric self-training. Our method is distinguished from previous methods on UDA for medical image segmentation in that it can obtain continuous segmentation in the slice direction, thereby ensuring higher accuracy and potential in clinical practice. We validate SDC-UDA with multiple publicly available cross-modality medical image segmentation datasets and achieve state-of-the-art segmentation performance, not to mention the superior slice-direction continuity of prediction compared to previous studies." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 633, + 127, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 127, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 127, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 654, + 287, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 690 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 690 + ], + "type": "text", + "content": "With the surprising development of deep learning (DL), many studies are now showing remarkable performance in various applications [8, 16, 20]. However, when a DL model" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 311, + 309, + 544, + 440 + ], + "blocks": [ + { + "bbox": [ + 308, + 307, + 467, + 316 + ], + "lines": [ + { + "bbox": [ + 308, + 307, + 467, + 316 + ], + "spans": [ + { + "bbox": [ + 308, + 307, + 467, + 316 + ], + "type": "text", + "content": "(A) Previous UDA for medical image segmentation frameworks" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 311, + 309, + 544, + 440 + ], + "lines": [ + { + "bbox": [ + 311, + 309, + 544, + 440 + ], + "spans": [ + { + "bbox": [ + 311, + 309, + 544, + 440 + ], + "type": "image", + "image_path": "892a2278f666ddf7e04fe99f6555a4e9543bc934cfe83576975b71be25143b45.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 449, + 545, + 546 + ], + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 546 + ], + "type": "text", + "content": "Figure 1. An illustration that describes the comparison between our proposed method with previous methods. (A) Previous UDA for medical image segmentation studies mostly utilize 2D UDA, which leads to inconsistent predictions in the slice direction when the predictions are stacked. (B) The proposed framework (SDC-UDA) considers volumetric information in the translation and segmentation process, respectively, which leads to improved slice-direction continuity of segmentation that is much practical for clinical use." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 700 + ], + "type": "text", + "content": "faces data from an unseen domain, performance degradation occurs [9, 32]. Resolving this issue is important for the DL techniques to be applied in real world since collecting data from all domains and labeling them is very impractical and inefficient. Unsupervised Domain Adaptation (UDA) aims to alleviate this problem by adapting a model trained on source domain data to target domain, without the necessity of supervision in the target domain. Data dependency is more serious in medical image segmentation field since acquiring pixel-level expert annotation is extremely expensive and time-consuming [3, 22, 37]." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Previous studies on UDA in the field of cross-modality med" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 702, + 208, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 702, + 208, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 702, + 208, + 713 + ], + "type": "text", + "content": "* Equal contribution. † Corresponding author." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7412" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 542, + 270 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 542, + 270 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 542, + 270 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 542, + 270 + ], + "type": "image", + "image_path": "89eb8878777566d137aee2cf6fe3b2ca555d7e8da15d00081cb8d30fdd326f68.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 546, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 546, + 335 + ], + "type": "text", + "content": "Figure 2. Overview of our volumetric UDA framework. First, source-to-target image transformation is performed via unpaired image translation with intra- and inter-slice self-attention (stage 1-2). Second, volumetric self-training is performed (stage 3-5). During self-training, uncertainty-constrained pseudo-label refinement is conducted to improve pseudo-labels, thereby maximizing the effect of self-training (stage 4). The reverse loop of image translation is omitted for ease of illustration. Detailed architecture of image translation network is described in Fig. 3. Best viewed in color and on high-resolution display. II-SA: Intra- and inter-slice self-attention." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 355, + 289, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 289, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 289, + 641 + ], + "type": "text", + "content": "ical image segmentation are normally conducted by simultaneously learning 2D image translation and target-domain segmentation, inferring the trained model on each slice of target data, and then stacking the predictions in the slice direction (Fig. 1). As a result, they can lead to inconsistent or fluctuating predictions in the slice direction that are not revealed in quantitative metrics and may interrupt accurate analysis of target structure, making it difficult to use in real world clinical practice. In contrast, SDC-UDA can achieve improved slice-direction continuity by incorporating volumetric natures of medical imaging, which has not been thoroughly explored in previous works. It efficiently generates synthetic target volumes with neighbor-aware image translation by utilizing intra- and inter-slice self-attention module [27]. Then, volumetric self-training is followed with uncertainty-constrained pseudo-label refinement strategy that adaptively increases the accuracy of pseudo-labels according to the target data (Fig. 2). Preliminary version of this work has won the 1st place in an unsupervised cross-modality domain adaptation for medical image segmentation challenge [7, 26]. We updated the framework and extended it to multiple datasets. The main contribution of our work can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 647, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 647, + 287, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 647, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 58, + 647, + 287, + 683 + ], + "type": "text", + "content": "- We present SDC-UDA, a unified volumetric UDA framework for cross-modality medical image segmentation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- Intra- and inter-slice self-attention for efficient medical image translation: Proposed 2.5D translation frame" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 355, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 355, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 324, + 355, + 545, + 416 + ], + "type": "text", + "content": "work with intra- and inter-slice self-attention module leads to increased anatomy preservation and slicedirection smoothness in the synthesized volume, enabling the synthetic volume to be used effectively in the following self-training steps." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 425, + 545, + 601 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 425, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 425, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 317, + 425, + 545, + 509 + ], + "type": "text", + "content": "- Volumetric self-training with uncertainty-constrained pseudo-label refinement: We propose a novel uncertainty-constrained pseudo-label refinement module that can adaptively enhance the accuracy (i.e., sensitivity or specificity) of pseudo-labels, thereby maximizing the performance of self-training on medical image segmentation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 518, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 518, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 317, + 518, + 545, + 601 + ], + "type": "text", + "content": "- SDC-UDA was validated on multiple public datasets with different data characteristics for cross-modality medical image segmentation. It not only surpassed the performance of previous methods, but also showed superior slice-direction segmentation continuity which can provide precise analysis in clinical practice." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 614, + 392, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 614, + 392, + 627 + ], + "spans": [ + { + "bbox": [ + 306, + 614, + 392, + 627 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 634, + 506, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 506, + 647 + ], + "type": "text", + "content": "2.1. UDA for medical image segmentation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "UDA for semantic segmentation is one of the most popular themes among UDA-related studies [12,18,21,31]. Especially, UDA on medical image segmentation is very attractive [3, 6, 13, 15, 22, 37] since it can address the difficulty of obtaining expensive expert-level manual annota" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7413" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 262 + ], + "type": "text", + "content": "tions. Recent studies on UDA for medical image segmentation are mostly based on image adaptation in which domain translation and segmentation networks are trained end-to-end, thereby utilizing the source-to-target transformed images for training segmentation on target domain. [13, 22, 37] combined image-to-image translation and segmentation into a single network. [3] added feature adaptation with adversarial training using the segmentation output of the synthetic and real target domain images to better preserve the geometry of the structures-of-interest. Moreover, [15] added both the synthetic and real target domain images and their corresponding segmentation probability maps to adversarial training to preserve not only the geometry of target anatomies but also their appearance (i.e., intensities). [11] utilized deep symmetric networks to further align the features of two domains." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 289, + 563 + ], + "type": "text", + "content": "Our work differs from previous works in the following aspects: Previous works mostly train 2D-level image translation with target-domain segmentation and stack the segmentation of each target slice in the slice direction [4, 11, 15, 30]. Since the segmentation network does not consider the anatomical structure in the slice direction, this can lead to high variability of segmentation result even in adjacent slices. In contrast, SDC-UDA splits target-domain segmentation from image translation and therefore is not constrained to 2D framework. Consequently, SDC-UDA can effectively incorporate volumetric information in the translation and segmentation process, respectively. Moreover, in addition to the commonly used cross-modality medical image segmentation dataset [17, 19, 40], SDC-UDA has also been validated in the challenging task of cross-modality segmentation of small multi-class structures which are vestibular schwannoma (VS) and cochlea (i.e., CrossMoDA dataset [7, 24, 25]). Previous studies locate target organs to the center of the preprocessed images and the majority of slices contain at least one target organ, whereas VS and cochleas in CrossMoDA dataset occupy extremely small fraction of the total voxels (0.028% and 0.002% for VS and cochlea, respectively, compared to approximately 3% in average in another dataset [40]) which more reflects the real-world clinical imaging environment [4, 15]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "text", + "content": "2.2. Self-training on UDA for medical image segmentation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Self-training belongs to semi-supervised learning which has emerged to improve the resources and cost put into data labeling [35, 41]. In self-training, a teacher model is first trained using only the labeled data. Next, pseudolabels with high confidence are inferred by passing the unlabeled data on the trained model. With the labeled data and pseudo-labeled data, a larger dataset can be used to train a student model that performs better than the teacher model trained only on labeled data. Numerous attempts" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "were made to apply self-training into semantic segmentation [23, 39, 42, 43] as pixel-level annotations are expensive. Since pseudo-labels tend to be noisy labels, previous studies attempted to refine pseudo-labels to increase accuracy, thereby providing better supervision to unlabeled data. [33] updated pseudo-labels by enhancing the sensitivity of pseudo-labels via selective voting. [29] proposed region growing on the super-pixels where the pseudo-labels serve as the initial seed points. [10] utilized uncertainty-weighted binary cross entropy loss to penalize high uncertainty region." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 204, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 300 + ], + "type": "text", + "content": "The proposed pseudo-label refinement strategy is effective in two aspects: 1) sensitivity and specificity-enhancing refinement can be adaptively used according to the characteristic of target data, and 2) it is a safer way to handle uncertainty maps since even the correctly segmented regions can have high uncertainty, and using uncertainty map to weight the loss function in the following training can therefore guide the model to wrong direction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 314, + 367, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 367, + 326 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 367, + 326 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 334, + 545, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 545, + 358 + ], + "type": "text", + "content": "3.1. Unpaired image translation with intra- and inter-slice self-attention module." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 365, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 569 + ], + "type": "text", + "content": "Many recent works on UDA for medical image segmentation have been developed on 2D framework, without considering the volumetric nature of medical imaging (2D multi-slice sequence or 3D sequence) [3, 13, 15, 22]. Previous 2D UDA approaches split the 3D volume into 2D slices, and re-stack their translations into 3D volume afterward. Since the slices are processed individually, re-building the translated volume usually requires additional post-processing such as slice-direction interpolation, which still can not perfectly resolve problems such as slicedirection discontinuity. This remain a problem when conducting following steps such as self-training for volumetric segmentation. Although there exist frameworks such as 3DCycleGAN which aim to conduct translation 3D volumewise, they are rarely used due to typical drawbacks such as optimization complexity, computational burden, or the degradation of translation quality [5, 28]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "To remedy both lack of volumetric consideration of 2D and optimization-efficiency issue of 3D methods, we propose a simple and effective pixel-level domain translation method for medical volume data by translating a stack of source domain images into target domain with both intra- and inter-slice self-attention module. Unlike previous 2D methods that only translated within a single slice, our approach leverages information from adjacent slices in the slice-direction. This is similar to recent advances in video processing, which exploit information both within and between frames [1,2]. In contrast to 3D methods that require expensive computational cost, ours do not necessitate heavy" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7414" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 547, + 266 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 547, + 266 + ], + "type": "image", + "image_path": "e73e7a199840ea4086870cd25088b83f4482473c839f62c8772858a09ac306ae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "text", + "content": "Figure 3. Illustration of the proposed 2.5D image translation with intra- and inter-slice self-attention module. Source domain volume data is cropped to a mini-volume, and fed to CNN encoder " + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "inline_equation", + "content": "G_{E}" + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "text", + "content": " as a stack of batches. The weights of " + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "inline_equation", + "content": "G_{E}" + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "text", + "content": " are shared during batch update. The encoded feature maps are embedded to non-overlapping patches, which become the input of intra- & inter-slice attention module " + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "text", + "content": ". Within " + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 276, + 547, + 321 + ], + "type": "text", + "content": ", intra- and inter-slice attention learns the volumetric information." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 342, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 365 + ], + "type": "text", + "content": "computation, enabling translation without intense down-sampling which 3D-based translations suffer from [28]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": "Shown in Fig.3, proposed framework consists of sequential modules of encoder " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "G_{E}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ", intra- and inter-slice self-attention II-SA and decoder " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "G_{D}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ". Taking three continuous slices " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "x_{t - 1},x_{t},x_{t + 1}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " of a volume as input, they are first fed to a 2D CNN encoder " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "G_{E}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " separately. Encoded features " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "G_{E}(x_{t - 1}),G_{E}(x_{t}),G_{E}(x_{t + 1})" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " are then fed to transformer-based attention module II-SA together, as feature maps from continuous frames. Before II-SA, each slice is embedded into small patches " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1:t + 1}^n = P(G_E(x_{t - 1:t + 1}))|_{n = 1:N}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "N = W_{G_E(x)}\\cdot H_{G_E(x)} / p^2" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "W_{G_E(x)},H_{G_E(y)}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " are each width, height of encoded feature map " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "G_{E}(x)" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ", respectively. In transformer-based attention module II-SA, two types attention " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "A_{inter}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "A_{intra}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": " exist. First, for the consideration of adjacent slices, learnable positional encoding is added to capture relative positional information within mini-volume patches. An inter-slice attention module is " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "A_{inter} = A(\\mathbf{z}_{t - 1}^{k},\\mathbf{z}_{t}^{k},\\mathbf{z}_{t + 1}^{k})|_{k = 1:N}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ". And for the consideration of nearby pixels within a slice, an intra-slice self-attention exists, as " + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "inline_equation", + "content": "A_{intra} = A(\\mathbf{z}_j^1,\\mathbf{z}_j^2,\\dots,\\mathbf{z}_j^N)|_{j = t - 1:t + 1}" + }, + { + "bbox": [ + 46, + 365, + 289, + 628 + ], + "type": "text", + "content": ". The attention module is identical for both intra- and interslice attention, which is" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 132, + 632, + 287, + 661 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 632, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 132, + 632, + 287, + 661 + ], + "type": "interline_equation", + "content": "A = \\sigma \\left(\\frac {Q K ^ {T}}{\\sqrt {d _ {K}}}\\right) V \\tag {1}", + "image_path": "cea506299d109d7b10c0ad4a2615b1b5dcc359a0957c9d0245776533c87f7212.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "Q = W_{Q}\\cdot LN(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "K = W_{K}\\cdot LN(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "V = W_{V}\\cdot LN(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " are query, key and value embeddings, respectively. " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "LN" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " denotes layer-normalization, " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " denotes soft-max operation and " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "d_{K}" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": " denotes embedding dimension." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "type": "text", + "content": "For maximum efficiency of translation, inter-slice attention occurs on the adjacent patches over slice-direction only for computational efficiency. After attention module, a 2D CNN decoder " + }, + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "type": "inline_equation", + "content": "G_{D}" + }, + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "type": "text", + "content": " reconstructs partial volume sets in the same way as done in " + }, + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "type": "inline_equation", + "content": "G_{E}" + }, + { + "bbox": [ + 304, + 342, + 547, + 437 + ], + "type": "text", + "content": ", constructing a translated 2.5D mini-volume. In inference step, only the center slices of mini-volume is stacked one by one to construct a whole translated volume." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 446, + 545, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 545, + 472 + ], + "type": "text", + "content": "3.2. Volumetric self-training with uncertainty-constrained pseudo-label refinement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 477, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 545, + 609 + ], + "type": "text", + "content": "Even if the source-to-target transformed images are well generated, there may still exist some distribution gap with the real target domain data, and it is difficult to completely replace it. With self-training, pseudo-labels for the unlabeled target domain data can be obtained and used to provide supervision to the target domain data, thereby mitigating the domain gap from the model's perspective. We propose to utilize volumetric self-training to close the domain gap, with a simple and novel pseudo-label refinement strategy to maximize the effect of self-training. The steps are as follows." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "text", + "content": "3.2.1. Training segmentation with labeled synthetic scans. With the synthetic data " + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "inline_equation", + "content": "\\tilde{x}^t" + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "text", + "content": " converted from source domain and the annotations " + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "inline_equation", + "content": "y^{s}" + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "text", + "content": " on the source scans (i.e., labeled synthetic dataset), we first train a teacher segmentation network " + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "inline_equation", + "content": "f_{teacher}" + }, + { + "bbox": [ + 304, + 621, + 545, + 682 + ], + "type": "text", + "content": " that minimizes the segmentation loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 361, + 693, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 693, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 361, + 693, + 545, + 711 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum L _ {\\text {s e g}} \\left(y ^ {s}, f _ {\\text {t e a c h e r}} \\left(\\tilde {x} ^ {t}\\right)\\right) \\tag {2}", + "image_path": "cfb9cf6d045893dbfb6cbc7bd1c30e0cb9cf240b47757651e243e94a6c1ce837.jpg" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7415" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 80, + 286, + 304 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 202, + 79 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 202, + 79 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 202, + 79 + ], + "type": "text", + "content": "(a) Sensitivity-preserving Pseudo Label Refinement" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 80, + 286, + 304 + ], + "lines": [ + { + "bbox": [ + 51, + 80, + 286, + 304 + ], + "spans": [ + { + "bbox": [ + 51, + 80, + 286, + 304 + ], + "type": "image", + "image_path": "d6f14700959c4d628c4354c8a3c620e66e5fa645e33b30baf577e1c43db19db5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 311, + 288, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 311, + 288, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 288, + 378 + ], + "type": "text", + "content": "Figure 4. Illustration of the proposed uncertainty-constrained pseudo-label refinement module on vestibular schwannoma of CrossMoDA dataset. Sensitivity/specificity enhancing refinement can be performed in parallel, and either one or a combination of the two can be used according to the characteristics of each class in the dataset. Best viewed in color and on high-resolution display." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "text", + "content": "3.2.2. Inferring pseudo-labels on unlabeled target domain data. Once the teacher model is trained, pseudolabels " + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\tilde{y}^t" + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "text", + "content": " of the non-annotated real data " + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "x^t" + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "text", + "content": " can be obtained by passing real target scans to the trained segmentation model " + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "f_{teacher}" + }, + { + "bbox": [ + 46, + 399, + 287, + 459 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 117, + 469, + 287, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 469, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 117, + 469, + 287, + 485 + ], + "type": "interline_equation", + "content": "\\tilde {y} _ {i} ^ {t} = f _ {\\text {t e a c h e r}} \\left(\\left\\{x _ {i} ^ {t} \\right\\} _ {i = 1} ^ {N _ {t}}\\right) \\tag {3}", + "image_path": "37ca4b31be9779050b87d1f3ce2e707ab615a3fe37c2706adffbd3664823b7d7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 491, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 586 + ], + "type": "text", + "content": "3.2.3. Uncertainty-constrained pseudo-label refinement for sensitivity / specificity enhancement. Since the pseudo-labels are noisy labels, they must be refined to increase accuracy and guide self-training to better direction. We devise a sensitivity and specificity enhancing pseudo-label refinement module that refines pseudo-labels based on image intensities, current pseudo-label, and high-uncertainty regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 597, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 647 + ], + "type": "text", + "content": "Sensitivity-enhancing pseudo-label refinement. With the inference of pseudo-labels, uncertainty (i.e., entropy) maps corresponding to each class are computed according to the following equation:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 658, + 287, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 658, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 141, + 658, + 287, + 672 + ], + "type": "interline_equation", + "content": "U = p \\log p \\tag {4}", + "image_path": "d36ecbd2ca7a4fa475ab6505bfb06355b741ab135bf555bb3d8aa350c6994554.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " is the output probability map of each class. To enhance the sensitivity of pseudo-labels, highly uncertain regions outside the range of pseudo-labels are detected. Then," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 546, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 119 + ], + "type": "text", + "content": "if the pixel intensity in this region is within a certain range of image intensity included in the current pseudo-label, this region is included to be part of pseudo-label. The equation can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 362, + 125, + 498, + 139 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 125, + 498, + 139 + ], + "spans": [ + { + "bbox": [ + 362, + 125, + 498, + 139 + ], + "type": "interline_equation", + "content": "\\text {I n i t i z e} \\tilde {y} _ {r} ^ {t} = \\tilde {y} ^ {t}. \\tilde {y} _ {r} ^ {t} (i, j) = 1 \\text {i f}", + "image_path": "71f6f4b9f79eb712ef0b3dee5260a41f718003e0594feab0d62e1b31557e508c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 141, + 545, + 167 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 141, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 308, + 141, + 545, + 167 + ], + "type": "interline_equation", + "content": "\\left. \\operatorname {m e a n} \\left(x ^ {t} \\left(\\tilde {y} ^ {t}\\right)\\right) \\times \\alpha < x _ {U H} ^ {t} (i, j) < \\operatorname {m e a n} \\left(x ^ {t} \\left(\\tilde {y} ^ {t}\\right)\\right) \\times \\beta \\right. \\tag {5}", + "image_path": "888a311be4283f860cee7558fc0e44198b61b424aa58394d8adbbdefcded9b5a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "spans": [ + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "inline_equation", + "content": "x^{t}" + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "inline_equation", + "content": "\\tilde{y}^{t}" + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{r}^{t}" + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "inline_equation", + "content": "x_{UH}^{t}" + }, + { + "bbox": [ + 304, + 176, + 546, + 261 + ], + "type": "text", + "content": " represent target domain image, pseudo-label, refined pseudo-label, and image cropped with high-uncertainty region mask, respectively. This approach is grounded on the assumption that 1) pixels that have similar intensity and 2) are close to each other in medical image are likely to belong to the same class. The workflow is described with images in Fig. 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 272, + 546, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 546, + 344 + ], + "type": "text", + "content": "Specificity-enhancing pseudo-label refinement. To enhance specificity of pseudo-labels, highly uncertain regions inside the range of pseudo-labels are detected. Then, if the pixel intensity in this region is outside a certain range of image intensity included in the current pseudo-label, it is excluded from the current pseudo-label." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 365, + 350, + 500, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 350, + 500, + 365 + ], + "spans": [ + { + "bbox": [ + 365, + 350, + 500, + 365 + ], + "type": "interline_equation", + "content": "\\text {I n i t i z e} \\tilde {y} _ {r} ^ {t} = \\tilde {y} ^ {t}. \\tilde {y} _ {r} ^ {t} (i, j) = 0 \\text {i f}", + "image_path": "3605cbda31de57b97c3fcd22b89bf8a4126b002a974d20d48b93eb5d96aefb5a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 350, + 367, + 545, + 381 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 367, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 350, + 367, + 545, + 381 + ], + "type": "interline_equation", + "content": "x _ {U H} ^ {t} (i, j) < \\operatorname {m e a n} \\left(x ^ {t} (\\tilde {y} ^ {t})\\right) \\times \\alpha o r \\tag {6}", + "image_path": "8867e3545c6c6937c6e9e6dcbeb9e097518d63de7abd23fc40f1ec5210b29d7b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 362, + 383, + 502, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 383, + 502, + 397 + ], + "spans": [ + { + "bbox": [ + 362, + 383, + 502, + 397 + ], + "type": "interline_equation", + "content": "x _ {U H} ^ {t} (i, j) > \\operatorname {m e a n} \\left(x ^ {t} (\\tilde {y} ^ {t})\\right) \\times \\beta", + "image_path": "8a72b825b6a771544d82306c66501f9c6af2d048c9325d6b1e5426ca758cc4df.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "text", + "content": "3.2.4. Retraining segmentation with combined data. Synthetic target scans have distribution gap with the real target scans, but they are paired with perfect annotations. On the other hand, real target scans are paired with pseudolabels, which are yet incomplete. We incorporate both pairs to self-training, to maximize the generalization ability and minimize the performance degradation caused by difference in distributions. With the combined data of labeled synthetic target scans " + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "inline_equation", + "content": "(\\tilde{x}^t,y^s)" + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "text", + "content": " and pseudo-labeled real target scans " + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "inline_equation", + "content": "(x^{t},\\tilde{y}_{r}^{t})" + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "text", + "content": ", we train a student segmentation " + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "inline_equation", + "content": "f_{student}" + }, + { + "bbox": [ + 304, + 404, + 545, + 535 + ], + "type": "text", + "content": " to minimize" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 542, + 550, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 542, + 550, + 569 + ], + "spans": [ + { + "bbox": [ + 306, + 542, + 550, + 569 + ], + "type": "interline_equation", + "content": "L = \\sum L _ {s e g} \\left(y ^ {s}, f _ {s t u d e n t} \\left(\\tilde {x} ^ {t}\\right)\\right) + \\sum L _ {s e g} \\left(\\tilde {y} _ {r} ^ {t}, f _ {s t u d e n t} \\left(x ^ {t}\\right)\\right) \\tag {7}", + "image_path": "865ff89f4b0c8dd6245e91746dccb4dfea75be878d32f1ca0d7ddca6f59ced56.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 629 + ], + "type": "text", + "content": "Despite not being ground truth labels, it has been reported in the previous literature that the self-training scheme and the pseudo-labels increases the performance and generalization ability of the model on unseen data by utilizing unlabeled data into training [35]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 639, + 387, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 387, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 387, + 653 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 659, + 364, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 364, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 364, + 670 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "CrossMoDA dataset. CrossMoDA dataset [7] for vestibular schwannoma and cochlea segmentation consists of 105 labeled contrast-enhanced T1 (ceT1) MRI scans and" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7416" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "105 unlabeled high-resolution T2 (hrT2) MRI scans. The direction of domain adaptation was from ceT1 to hrT2 since the annotations of hrT2 scans are not publicly available. Evaluation was performed online on 32 inaccessible hrT2 scans through an official leaderboard. Please refer to the supplementary material for examples of each domain data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "text", + "content": "Cardiac structure segmentation dataset. 2017 Multi-Modality Whole Heart Segmentation (MMWHS) challenge dataset [40] which consists of 20 MRI and 20 CT volumes was used for cardiac segmentation. Domain adaptation was performed from MRI to CT, with " + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "text", + "content": " of each modality used for training and " + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "text", + "content": " (i.e., 4 volumes) of randomly selected CT scans used for evaluation. Target cardiac structures for segmentation were ascending aorta (AA), left atrium blood cavity (LAC), the left ventricle blood cavity (LVC), and myocardium of left ventricle (MYO). With a fixed coronal plane resolution of " + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 156, + 290, + 324 + ], + "type": "text", + "content": ", MRI and CT volumes were manually cropped to cover the 4 cardiac substructures. Please refer to the supplementary material for examples of each domain data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 336, + 178, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 178, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 178, + 348 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": "Unpaired image translation with intra- and inter-slice self-attention module. 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After " + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "inline_equation", + "content": "G_{E}" + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": ", encoded feature map is reshaped to " + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "inline_equation", + "content": "(B,3,H,W)" + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": " and fed to the attention module for the consideration of slice-direction attention. Patch size " + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": " was set as 2. Transposed convolution is used to convert embedded patches back to 2D feature maps. For a stack of mini-volume generated at " + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": ", we implement 2D discriminator " + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": " for adversarial training of domain translation. For real input to " + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 354, + 288, + 510 + ], + "type": "text", + "content": ", 3 consecutive slices were randomly extracted from the target volumes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "Uncertainty-constrained pseudo-label refinement. For each class, grid searching was conducted on how to set the threshold for masking the high-uncertainty region and also on whether to use either one, or both of the sensitivity and specificity enhancing refinement. For CrossMoDA dataset, combining sensitivity and specificity-enhancing refinement in both classes (i.e., VS and Cochlea) with uncertainty threshold of 0.3 led to the best result. For cardiac dataset, the same threshold value was used and using only specificity-enhancing refinement for all classes except one (i.e., AA) led to the best result. This is attributed to the fact that the contrast difference between adjacent substructures was very weak in cardiac CT which led to noisier pseudo-label when sensitivity-enhancing module was used. Please refer to the tables in supplementary material for ablation results. 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Dice (↑)ASSD (↓)
MethodsVSCVSC
Baseline71.572.75.911.83
+ intra/inter-slice attention80.374.51.660.67
+ ST w/o PL refinement83.276.70.580.79
+ ST w/ PL refinement84.684.90.510.14
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Representative case showing the effect of intra- and inter-slice self-attentive image translation. Translation was performed using axial slices and the resulting volume is being observed from sagittal direction. Best viewed in color and on high-resolution display." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 307, + 508, + 375, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 508, + 375, + 520 + ], + "spans": [ + { + "bbox": [ + 307, + 508, + 375, + 520 + ], + "type": "text", + "content": "1.4, respectively." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 532, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 532, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 532, + 545, + 628 + ], + "type": "text", + "content": "Volumetric self-training. 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MethodsDice (↑)ASSD (↓)Dice (↑)ASSD (↓)
VSCMeanVSCMeanAALACLVCMYOMeanAALACLVCMYOMean
Non-MedicalFully-supervised192.587.790.10.20.10.1595.992.093.088.292.31.02.51.81.71.8
w/o adaptation11.50.05.824.0NANA48.452.020.04.731.318.834.532.036.430.4
CycleGAN [38]39.70.019.810.1NANA58.359.861.523.150.711.410.69.214.811.5
CyCADA [12]39.20.119.710.518.114.357.262.165.047.257.98.49.08.27.98.4
ADVENT [34]8.30.04.217.1NANA68.271.878.850.767.49.66.64.75.16.5
FDA [36]12.50.06.313.520.517.046.568.473.855.761.110.27.64.35.06.8
MedicalSIFA [4]47.219.733.519.13.311.276.388.174.262.475.36.13.97.14.85.5
PSIGAN [15]57.337.247.35.52.84.167.287.080.360.873.87.54.25.54.75.5
SDC-UDA (ours)84.684.984.80.510.140.3395.891.088.666.685.51.12.83.26.33.3
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Comparison of qualitative results between SDC-UDA and previous non-medical and medical UDA methods. Since the ground truth of CrossMoDA dataset is not accessible, we requested to the data owner a few of the label slices and used them to make this figure. The numbers indicate Dice values of each substructure in the slice. 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This was not completely overcome even with a 2.5D network that puts two adjacent slices together in the network. Also, in both 2D and 2.5D networks, it was found that the anatomy of the source image was distorted in the translated image (red and green arrows). On the other hand, it was observed that the aforementioned problems were alleviated when utilizing the intra- and inter-slice self-attention module" + } + ] + } + ], + "index": 51 + }, + { + "bbox": [ + 304, + 584, + 547, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 547, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 547, + 656 + ], + "type": "text", + "content": "that effectively considers neighboring anatomy. Table 1 shows the increase of final segmentation performance by incorporating intra- and inter-slice self-attention in image translation network compared to baseline that utilizes pure unpaired image translation followed by 3D segmentation network." + } + ] + } + ], + "index": 52 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Effect of uncertainty-constrained pseudo-label refinement and volumetric self-training. 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Representative cases demonstrating the superior slice-direction continuity of segmentation by the proposed method compared to other medical UDA methods on cardiac dataset. The plots show graphs of Dice coefficient for each slice. (a), (b), (c), and (d) denote AA, LAC, LVC, and MYO class, respectively. Best viewed in color." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 170, + 159, + 282, + 245 + ], + "blocks": [ + { + "bbox": [ + 170, + 159, + 282, + 245 + ], + "lines": [ + { + "bbox": [ + 170, + 159, + 282, + 245 + ], + "spans": [ + { + "bbox": [ + 170, + 159, + 282, + 245 + ], + "type": "image", + "image_path": "1f0e770e44f706ce0d72ec3c1f0564f74fc4582780e2a6c87a8ae526512756d5.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 518 + ], + "type": "text", + "content": "dataset, the effectiveness of pseudo-label refinement was verified by comparing the performance of self-training before and after pseudo-label refinement. For cardiac datasets for which ground truth is available, it was verified by comparing dice coefficients with labels before and after pseudo-label refinement (please refer to supplementary material). Table 1 shows the improvement of target domain segmentation performance by applying the proposed uncertainty-constrained pseudo-label refinement on CrossMoDA dataset. It can be seen that volumetric self-training combined with the proposed uncertainty-constrained pseudo-label refinement increases the quantitative metrics in both VS and C by a large margin, whereas pure self-training only increase the performance in VS." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 286, + 664 + ], + "type": "text", + "content": "Comparative studies. The proposed method is compared with six popular UDA methods that are CycleGAN [38], CyCADA [12], ADVENT [34], FDA [36], SIFA [4], and PSIGAN [15]. The first four methods are from natural image field whereas the last two are UDA for medical image segmentation methods. Fully-supervised and without-adaptation results are presented to provide upper bound and lower bound, respectively. Please note that the full-supervised result of CrossMoDA dataset, for which the ground truth segmentation mask is not available, is referred from the paper of the dataset owner [7]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 712 + ], + "type": "text", + "content": "Table 2 and Fig. 6 shows quantitative and qualitative results of comparative studies between the proposed method and previous methods. SDC-UDA far exceeds the results of UDA for semantic segmentation studies in the non-medical" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "field, and shows better results in multiple tasks compared to the recent studies in the medical field. In particular, there was a significant performance gap between the proposed method and comparison methods in the CrossMoDA dataset compared to the cardiac dataset. This is probably attributed to the fact that previous studies on medical UDA are dedicated to datasets in which the data are cropped around the target organs and the foreground objects occupy a large portion of the data. In contrast, SDC-UDA shows that both target structures in the CrossMoDA dataset are segmented with high accuracy." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 216, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 545, + 396 + ], + "type": "text", + "content": "Slice-direction continuity of segmentation compared to previous studies. Fig. 7 shows the excellent slice-direction continuity of segmentation by the proposed method compared to the previous studies on the MMWHS cardiac dataset. Fig. 7-(a), (b), (c), and (d) plot the slice-wise Dice values from representative cases of AA, LAC, LVC, and MYO, respectively. Our SDC-UDA shows gradual and consistent segmentation performance in the slice-direction whereas SIFA and PSIGAN, which are recently proposed medical UDA methods, show very inconsistent and sometimes sudden fluctuations of segmentation performance in the slice direction. This suggests the potential of the proposed method to be useful in the clinical practice where precise volumetric segmentation is required to analyze the patient's status with high confidence." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 406, + 378, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 406, + 378, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 378, + 418 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 545, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 558 + ], + "type": "text", + "content": "In this study, we proposed SDC-UDA, a novel volumetric UDA framework for slice-direction continuous cross-modality medical image segmentation, and validated it on multiple public datasets. SDC-UDA effectively translates medical volumes through intra- and inter-slice self-attention and better adapts to target domain via volumetric self-training enhanced by simple yet effective pseudo-label refinement strategy that utilizes uncertainty maps. Ablation studies demonstrated the effectiveness of each component and comparative studies showed the superior performance of the proposed method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This research was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-TF2103-01 in constructing hardware systems and multi-modal studies. It was also supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT (2021R1A4A1031437, 2022R1A2C2008983), Artificial Intelligence Graduate School Program at Yonsei University [No. 2020-0-01361], the KIST Institutional Program (Project No.2E31051-21-204), and partially supported by the Yonsei Signature Research Cluster Program of 2022 (2022-22-0002)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7419" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. 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Applications of SDFusion. The proposed diffusion-based model enables various applications. (left) SDFusion can generate shapes conditioned on different input modalities, including partial shapes, images, and text. SDFusion can even jointly handle multiple conditioning modalities while controlling the strength for each of them. (right) We leverage pretrained 2D models to texture 3D shapes generated by SDFusion." + ], + "image_footnote": [], + "bbox": [ + 83, + 266, + 563, + 645 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/64a7ea6e8b31dc05f792fc8e90e0c96188305e83e829d46ee8edbd4df694d0b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 266, + 880, + 645 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 714, + 313, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we present a novel framework built to simplify 3D asset generation for amateur users. To enable interactive generation, our method supports a variety of input modalities that can be easily provided by a human, including images, text, partially observed shapes and combinations of these, further allowing to adjust the strength of each input. At the core of our approach is an encoder-decoder, compressing 3D shapes into a compact latent representation, upon which a diffusion model is learned. To enable a variety of multi-modal inputs, we employ task-specific encoders with dropout followed by a cross-attention", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mechanism. Due to its flexibility, our model naturally supports a variety of tasks, outperforming prior works on shape completion, image-based 3D reconstruction, and text-to-3D. Most interestingly, our model can combine all these tasks into one swiss-army-knife tool, enabling the user to perform shape generation using incomplete shapes, images, and textual descriptions at the same time, providing the relative weights for each input and facilitating interactivity. Despite our approach being shape-only, we further show an efficient method to texture the generated shape using large-scale text-to-image models.", + "bbox": [ + 496, + 715, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4456", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 89, + 207, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generating 3D assets is a cornerstone of immersive augmented/virtual reality experiences. Without realistic and diverse objects, virtual worlds will look void and engagement will remain low. Despite this need, manually creating and editing 3D assets is a notoriously difficult task, requiring creativity, 3D design skills, and access to sophisticated software with a very steep learning curve. This makes 3D asset creation inaccessible for inexperienced users. Yet, in many cases, such as interior design, users more often than not have a reasonably good understanding of what they want to create. In those cases, an image or a rough sketch is sometimes accompanied by text indicating details of the asset, which are hard to express graphically for an amateur.", + "bbox": [ + 76, + 114, + 467, + 311 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Due to this need, it is not surprising that democratizing the 3D content creation process has become an active research area. Conventional 3D generative models require direct 3D supervision in the form of point clouds [2, 21], signed distance functions (SDFs) [9, 25], voxels [42, 47], etc. Recently, first efforts have been made to explore the learning of 3D geometry from multi-view supervision with known camera poses by incorporating inductive biases via neural rendering techniques [5, 6, 14, 37, 52]. While compelling results have been demonstrated, training is often very time-consuming and ignores available 3D data that can be used to obtain good shape priors. We foresee an ideal collaborative paradigm for generative methods where models trained on 3D data provide detailed and accurate geometry, while models trained on 2D data provide diverse appearances. A first proof of concept is shown in Figure 1.", + "bbox": [ + 76, + 311, + 467, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our pursuit of flexible and high-quality 3D shape generation, we introduce SDFusion, a diffusion-based generative model with a signed distance function (SDF) under the hood, acting as our 3D representation. Compared to other 3D representations, SDFs are known to represent well high-resolution shapes with arbitrary topology [9, 18, 23, 30]. However, 3D representations are infamous for demanding high computational resources, limiting most existing 3D generative models to voxel grids of $32^{3}$ resolution and point clouds of $2K$ points. To side-step this issue, we first utilize an auto-encoder to compress 3D shapes into a more compact low-dimensional representation. Because of this, SDFusion can easily scale up to a $128^{3}$ resolution. To learn the probability distribution over the introduced latent space, we leverage diffusion models, which have recently been used with great success in various 2D generation tasks [4, 19, 22, 26, 35, 40]. Furthermore, we adopt task-specific encoders and a cross-attention [34] mechanism to support multiple conditioning inputs, and apply classifier-free guidance [17] to enable flexible conditioning usage. Because of these strategies, SDFusion can not only use a variety of conditions from multiple modalities, but also adjust their importance weight, as shown in Figure 1. Compared", + "bbox": [ + 76, + 553, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to a recently proposed autoregressive model [25] that also adopts an encoded latent space, SDFusion achieves superior sample quality, while offering more flexibility to handle multiple conditions and, at the same time, features reduced memory usage. With SDFusion, we study the interplay between models trained on 2D and 3D data. Given 3D shapes generated by SDFusion, we take advantage of an off-the-shelf 2D diffusion model [34], neural rendering [24], and score distillation sampling [31] to texture the shapes given text descriptions as conditional variables.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct extensive experiments on the ShapeNet [7], BuildingNet [38], and Pix3D [43] datasets. We show that SDFusion quantitatively and qualitatively outperforms prior work in shape completion, 3D reconstruction from images, and text-to-shape tasks. We further demonstrate the capability of jointly controlling the generative model via multiple conditioning modalities, the flexibility of adjusting relative weight among modalities, and the ability to texture 3D shapes given textual descriptions, as shown in Figure 1.", + "bbox": [ + 496, + 242, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize the main contributions as follows:", + "bbox": [ + 519, + 380, + 846, + 393 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose SDFusion, a diffusion-based 3D generative model which uses a signed distance function as its 3D representation and a latent space for diffusion.", + "- SDFusion enables conditional generation with multiple modalities, and provides flexible usage by adjusting the weight among modalities.", + "- We demonstrate a pipeline to synthesize textured 3D objects benefiting from an interplay between 2D and 3D generative models." + ], + "bbox": [ + 519, + 397, + 890, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 549, + 638, + 564 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Generative Models. Different from 2D images, it is less clear how to effectively represent 3D data. Indeed, various representations with different pros and cons have been explored, particularly when considering 3D generative models. For instance, 3D generative models have been explored for point clouds [2, 21], voxel grids [20, 42, 47], meshes [51], signed distance functions (SDFs) [9, 11, 25], etc. In this work, we aim to generate an SDF. Compared to other representations, SDFs exhibit a reasonable tradeoff regarding expressivity, memory efficiency, and direct applicability to downstream tasks. Moreover, conditioning 3D generation of SDFs on different modalities further enables many applications, including shape completion, 3D reconstruction from images, 3D generation from text, etc. The proposed framework can handle these tasks in a single model which makes it different from prior work.", + "bbox": [ + 496, + 566, + 890, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, thanks to the advancement of neural rendering [24], a new stream of research has emerged to learn 3D generation and manipulation from only 2D supervision [1, 5, 6, 28, 37, 39, 41, 49]. We believe the interplay between two streams of work is promising in the foreseeable future.", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4457", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b79ce888074a397a7e1cb86c0b09c8499a11d240ff921668c81f1f5469194fc5.jpg", + "image_caption": [ + "Figure 2. SDFusion Overview. (left) To enable high-resolution generation, we first encode 3D shapes into a latent space, where a diffusion model is trained. Furthermore, to enable flexible conditional generation, we adopt class-specific encoders along with classifier-free guidance to enable multi-modality conditioning. (right) At inference time, we can control the importance of each conditioning modality." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 619, + 271 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7a57bc53c09b20dd04c441ad31c9d10b319506f2b190e4ff1e6783669307d0d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 89, + 883, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models. Diffusion models have recently emerged as a popular family of generative models with competitive sample quality. In particular, diffusion models have shown impressive quality, diversity, and expressiveness in various tasks such as image synthesis [13,15,16,27], super-resolution [36], image editing [10, 22, 40], text-to-image synthesis [4, 19, 26, 33, 35], etc. In contrast to the flourishing research on diffusion models for 2D data, diffusion models have not yet been fully explored for 3D data. Notable exceptions include attempts to apply diffusion models to point clouds [21, 53].", + "bbox": [ + 75, + 329, + 468, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Differently, in this work, we apply diffusion models on SDF representations. As reasonable resolutions of SDFs are demanding to model, we study the use of a latent diffusion technique [34] and the classifier-free conditional generation mechanism [17], both of which have been shown to yield promising results when being used in 2D diffusion models.", + "bbox": [ + 75, + 494, + 470, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 599, + 187, + 617 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim at synthesizing 3D shapes using diffusion models. Towards this goal, we model the distribution over 3D shapes $\\mathbf{X}$ , a volumetric Truncated Signed Distance Field (T-SDF). However, applying diffusion models directly on reasonably high-resolution 3D shapes is computationally very demanding. Therefore, we first compress the 3D shape into a discretized and compact latent space (Section 3.1). This allows us to apply diffusion models in a lower-dimensional space (Section 3.2). The proposed framework can further incorporate various user conditions such as partial shapes, images, and text (Section 3.3). Finally, we showcase an interplay between the proposed framework and diffusion models trained on 2D data to texture 3D shapes (Section 3.4).", + "bbox": [ + 75, + 625, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. 3D Shape Compression of SDF", + "text_level": 1, + "bbox": [ + 76, + 847, + 349, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A 3D shape representation is high-dimensional and thus difficult to model. To make learning of high-resolution 3D", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "shape distributions via diffusion models feasible, we compress the 3D shape $\\mathbf{X}$ into a lower-dimensional yet compact latent space. For this, we leverage a 3D-variant of the Vector Quantised-Variational AutoEncoder (VQ-VAE) [29]. Specifically, the employed 3D VQ-VAE contains an encoder $E_{\\varphi}$ to encode the 3D shape into the latent space, and a decoder $D_{\\tau}$ to decode the latent vectors back to 3D space. Given an input shape represented via the T-SDF $\\mathbf{X} \\in \\mathbb{R}^{D \\times D \\times D}$ , we have", + "bbox": [ + 496, + 329, + 893, + 465 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} = E _ {\\varphi} (\\mathbf {X}), \\quad \\text {a n d} \\quad \\mathbf {X} ^ {\\prime} = D _ {\\tau} (\\mathrm {V Q} (\\mathbf {z})), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 472, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{z} \\in \\mathbb{R}^{d \\times d \\times d}$ is the latent vector, latent dimension $d$ is smaller than 3D shape dimension $D$ , and VQ is the quantization step which maps the latent variable $\\mathbf{z}$ to the nearest element in the codebook $\\mathcal{Z}$ . The encoder $E_{\\varphi}$ , decoder $D_{\\tau}$ , and codebook $\\mathcal{Z}$ are jointly optimized. We pre-train the VQ-VAE with reconstruction loss, commitment loss, and VQ objective, similar to [29] using ShapeNet or BuildingNet data. For more details please see the supplementary material.", + "bbox": [ + 496, + 496, + 892, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Latent Diffusion Model for SDF", + "text_level": 1, + "bbox": [ + 498, + 641, + 782, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Using the trained encoder $E_{\\varphi}$ , we can now encode any given SDF into a compact and low-dimensional latent variable $\\mathbf{z} = E_{\\varphi}(\\mathbf{X})$ . We can then train a diffusion model on this latent representation. Fundamentally, a diffusion model learns to sample from a target distribution by reversing a progressive noise diffusion process. Given a sample $\\mathbf{z}$ , we obtain $\\mathbf{z}_t, t \\in \\{1, \\dots, T\\}$ by gradually adding Gaussian noise with a variance schedule. Then we use a time-conditional 3D UNet $\\epsilon_{\\theta}$ as our denoising model. To train the denoising 3D UNet, we adopt the simplified objective proposed by Ho et al. [15]:", + "bbox": [ + 496, + 664, + 890, + 830 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s i m p l e}} (\\theta) := \\mathbb {E} _ {\\mathbf {z}, \\epsilon \\sim N (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t) \\| ^ {2} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 838, + 890, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At inference time, we sample $\\widehat{\\mathbf{z}}$ by gradually denoising a noise variable sampled from the standard normal distribu", + "bbox": [ + 498, + 869, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4458", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion $N(0,1)$ , and leverage the trained decoder $D_{\\tau}$ to map the denoised code $\\widehat{\\mathbf{z}}$ back to a 3D T-SDF shape representation $\\widehat{\\mathbf{X}} = D_{\\tau}(\\widehat{\\mathbf{z}})$ , as shown in Figure 2.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Learning the Conditional Distribution", + "text_level": 1, + "bbox": [ + 76, + 147, + 405, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Being able to randomly sample shapes provides limited ability for interaction. Therefore, learning of a conditional distribution is essential for user applications. Importantly, multiple forms of conditional inputs are desirable such that the model can account for various kinds of scenarios. Thanks to the flexible conditional mechanism provided by a latent diffusion model [34], we can incorporate multiple conditional input modalities at once with task-specific encoders $E_{\\phi}$ and a cross-attention module. To further allow for more flexibility in controlling the distribution, we adopt classifier-free guidance for conditional generation. The objective function reads as follows:", + "bbox": [ + 75, + 171, + 468, + 352 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL \\left(\\theta , \\left\\{\\phi_ {i} \\right\\}\\right) := \\underset {\\mathbf {z}, \\mathbf {c}, \\epsilon , t} {\\mathbb {E}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{D \\circ E _ {\\phi_ {i}} \\left(\\mathbf {c} _ {i}\\right) \\right\\}\\right) \\| ^ {2} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 364, + 467, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $E_{\\phi_i}(\\mathbf{c}_i)$ is the task-specific encoder for the $i^{\\mathrm{th}}$ modality, $D$ is a dropout operation enabling classifier-free guidance, and $F$ is a feature aggregation function. In this work, $F$ refers to a simple concatenation.", + "bbox": [ + 76, + 406, + 467, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At inference time, given conditions from multiple modalities, we perform classifier-free guidance as follows", + "bbox": [ + 76, + 468, + 468, + 498 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{E _ {\\phi_ {i}} \\forall i \\right\\}\\right) = \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\emptyset\\right) + \\\\ \\sum_ {i} s _ {i} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{E _ {\\phi_ {i}} \\left(\\mathbf {c} _ {i}\\right), E _ {\\phi_ {j}} \\left(\\mathbf {c} _ {j}\\right): \\mathbf {c} _ {j} = \\emptyset \\forall j \\neq i \\right\\}\\right) \\right. \\\\ - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\emptyset)), \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 523, + 468, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s_i$ denotes the weight of conditions from the $i^{\\text{th}}$ modality and $\\varnothing$ denotes a condition filled with zeros. Intuitively, modalities with larger weights play more important roles in guiding the conditional generation.", + "bbox": [ + 75, + 607, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this work, we study SDFusion combined with three conditional modalities applied separately or jointly. For shape completion, given a partial observation of a shape, we perform blended diffusion similar to [4]. For single-view 3D reconstruction, we adopt CLIP [32] as the image encoder. For text-guided 3D generation, we adopt BERT [12] as the text encoder. The encoded features are then used to modulate the diffusion process with cross-attention. Please refer to the supplementary material for more details.", + "bbox": [ + 75, + 669, + 468, + 804 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. 3D Shape Texturing with a 2D Model", + "text_level": 1, + "bbox": [ + 76, + 815, + 397, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While sampled 3D data often exhibits compellingly detailed geometry, textures of 3D data are generally more difficult to collect and even more often of limited quality. Here, we explore how to make the best use of 2D data and", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b64a6d4ffe0be1f22b80c79da498ae9421ea6f0ca993f96702db62774161d6ac.jpg", + "image_caption": [ + "Figure 3. 3D Shape Texturing. We demonstrate an application where models trained on 2D and 3D data are combined. The shapes generated by SDFusion are converted to a density tensor, then the color information is learned via neural rendering. The gradients are provided by an off-the-shelf 2D diffusion model [34]." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 890, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "models, so as to aid 3D asset generation. Thanks to the recent success of neural rendering [24] and 2D text-to-image models trained on extremely large-scale data [34], using a 2D model to perform 3D synthesis is made possible with a score distillation sampling technique [31].", + "bbox": [ + 496, + 328, + 890, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we illustrate the procedure of texturing a 3D shape given a guiding input sentence $S$ . Starting from a generated T-SDF $\\mathbf{X}$ , we first convert it to a density tensor $\\sigma$ by using VolSDF [50]. Our goal is to learn a 5D radiance field to obtain color $F_{\\theta}:(\\mathbf{x},\\mathbf{d})\\rightarrow \\mathbf{c}$ , similar to the conventional NeRF [24] setting. However, different from the conventional NeRF setting, the density tensor is fixed. With a sampled camera pose, we can render an image $I$ by alpha-compositing the densities and colors along the rays for each pixel. Then, we distill the knowledge from a pre-trained stable diffusion model [34], denoted as a 2D UNet $\\tilde{\\epsilon}_{\\phi}(\\mathbf{z}_t,t,S)$ that predicts the noise at timestep $t$ . The most straightforward way to update $F_{\\theta}$ is to obtain and backpropagate gradients all the way from the noise prediction loss term of the stable diffusion loss function to the input. However, the UNet Jacobian term is in practice expensive to compute. Therefore, it was proposed in [31] to bypass the UNet and treat $\\tilde{\\epsilon}_{\\phi}$ as a frozen critic providing scores by computing", + "bbox": [ + 496, + 404, + 892, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {t, \\epsilon} \\left[ \\frac {\\partial I \\left(F _ {\\theta} (\\cdot)\\right)}{\\partial \\theta} w (t) \\left(\\tilde {\\epsilon} _ {\\phi} \\left(\\mathbf {z} _ {t}, t, S\\right) - \\epsilon\\right) \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 684, + 890, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $w$ is a time-dependent weight function defined in the stable diffusion model. The mechanism is called Score Distillation Sampling. Please refer to [31] for details. The score then provides an update direction to $F_{\\theta}$ . We illustrate the process in Figure 3.", + "bbox": [ + 496, + 726, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 815, + 632, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we conduct extensive qualitative and quantitative experiments to demonstrate the efficacy and generalizability of SDFusion. We evaluate methods on three tasks: shape completion, single-view 3D reconstruction,", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4459", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b864b12fe0495a537e2d28c1c06ed0d6d6e4e3df9dbe89e80d134d567fa9ed33.jpg", + "image_caption": [ + "Figure 4. Shape Completion. (Top) We compare SDFusion with AutoSDF [25] and MPC [45] on ShapeNet and BuildingNet data. SDFusion generates shapes of better quality and diversity, while being consistent with the input partial shapes. We convert the generated SDFs from SDFusion and AutoSDF to point clouds to compare with MPC. Please refer to the supplementary materials for SDF comparisons on BuildingNet for better visualization. (Bottom) We present more results on diverse shape completion using various object categories." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 893, + 508 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a76164908b9cd87b6d56752fff9f233fca40d3248ba97192ec2d78fd6ceb3575.jpg", + "table_caption": [ + "Table 1. Quantitative comparison of Shape Completion. We evaluate methods on fidelity (UHD) and diversity (TMD) using the ShapeNet and BuildingNet data. SDFusion outperforms other methods in both metrics, especially diversity." + ], + "table_footnote": [], + "table_body": "
MethodShapeNetBuildingNet
UHD ↓TMD ↑UHD ↓TMD ↑
MPC [45]0.06270.03030.13500.0467
AutoSDF [25]0.05670.03410.12080.0649
Ours0.05570.08850.11160.0745
", + "bbox": [ + 112, + 643, + 431, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and text-guided generation. We then demonstrate two additional use cases: multi-conditional generation and 3D shape texturing.", + "bbox": [ + 75, + 770, + 468, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Shape Completion", + "text_level": 1, + "bbox": [ + 76, + 830, + 256, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the shape completion task on the ShapeNet [7] and the BuildingNet [38] datasets. ShapeNet is a large-scale 3D CAD model dataset with 16 common", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f3b88be92d04ea231c9b7c0de5da3bc83ece6af9f5100c51ad61bb3e204a8413.jpg", + "table_caption": [ + "Table 2. Quantitative evaluation of single-view reconstruction. We evaluate methods on the Pix3D dataset using Chamfer Distance and F-Score. We outperform other methods in both metrics." + ], + "table_footnote": [], + "table_body": "
MethodCD ↓F-Score ↑
Pix2Vox [46]3.0010.385
ResNet2TSDF4.5820.351
ResNet2Voxel4.6700.357
AutoSDF [25]2.2670.415
Ours1.8520.432
", + "bbox": [ + 578, + 630, + 810, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "object classes. We use the train/test splits provided by Xu et al. [48]. BuildingNet is a new large-scale 3D building model dataset. Compared to objects in ShapeNet, building models provide more geometric details and thus require higher resolution for representing the data. Hence, we use an SDF of $64^{3}$ resolution for ShapeNet, and a $128^{3}$ resolution for BuildingNet. For both datasets, we compare the completion quantitatively by providing the bottom half of the ground truth shape as input, and evaluating the com", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4460", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4982631dedb466d6b1c3968e6522c15001f4e05dcda8a624c4f622cd09a78d58.jpg", + "image_caption": [ + "Figure 5. Single-view 3D Reconstruction. (Top) We qualitatively compare all methods on the Pix3D dataset. SDFusion generates shapes with the best visual quality. (Bottom) Here we present more reconstruction results from SDFusion." + ], + "image_footnote": [], + "bbox": [ + 78, + 71, + 890, + 262 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/81462bbcbcf7833c1c0d9d88fc3da001f7e6c8310f69b2bdff14057fd7a4c42d.jpg", + "table_caption": [ + "Table 3. Quantitative evaluation of text-guided generation. We compare the proposed SDFusion method, AutoSDF, and real data using a pretrained neural evaluator on the ShapeGlot dataset. $P$ denotes the neural evaluator preference rate for the target $P(\\mathrm{Tr})$ or the distractor $P(\\mathrm{Dis})$ . If the preference is too close ( $\\leq 0.2$ ), we count the comparison as confused (conf.). Rows sum to $100\\%$ ." + ], + "table_footnote": [], + "table_body": "
Target (Tr)Distractor (Dis)P(Tr)P(Dis)P(conf.)
OursAutoSDF [25]49%36%15%
OursGT33%45%22%
AutoSDF [25]GT30%49%21%
", + "bbox": [ + 91, + 417, + 447, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "pleted shapes generated by different methods.", + "bbox": [ + 75, + 508, + 379, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare SDFusion to the state-of-the-art point cloud completion method MPC [45] and the autoregressive SDF generation method AutoSDF [25]. We adopt metrics from MPC [45]. For each partial shape, we generate $k$ complete shapes. To evaluate completion fidelity, we measure the Unidirectional Hausdorff Distance (UHD) between partial shapes and generated shapes. To evaluate completion diversity, we measure the Total Mutual Difference (TMD) by computing the average Chamfer distance among $k$ generated shapes. We use $k = 10$ in the experiments.", + "bbox": [ + 75, + 523, + 468, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table 1, the proposed SDFusion performs favorably compared to all methods in the completion fidelity metric, and outperforms the baselines substantially in completion diversity. The advantages of fidelity and diversity are also apparent in Figure 4. Especially on the BuildingNet dataset, SDFusion shows its advantages in modeling high-resolution and diverse data. AutoSDF and MPC struggle to model the distribution correctly.", + "bbox": [ + 75, + 676, + 468, + 796 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Single-view 3D Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 805, + 349, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we assess 3D shape reconstruction from a single image on the real-world benchmark Pix3D [43] dataset. We use the provided train/test splits on the chair category. In the absence of official splits for other categories, we randomly split the dataset into disjoint train/test splits.", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare with the ResNet2TSDF and ResNet2Voxel baselines. Both encode images and directly output 3D shapes in the form of a T-SDF and a voxel grid. We also compare to two state-of-the-art methods for 3D reconstruction, i.e., Pix2Vox [46] and AutoSDF [25]. We evaluate all methods after aligning resolutions to $32^{3}$ voxels. We use Chamfer Distance (CD), and F-score@1% [44] as evaluation metrics.", + "bbox": [ + 496, + 323, + 890, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitatively, as shown in Table 2, SDFusion outperforms other methods on both metrics. Qualitatively, SDFusion generates 3D shapes that are of higher visual quality and are more visually consistent with the objects shown in the images, regardless of camera poses, as shown in Figure 5.", + "bbox": [ + 496, + 445, + 890, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Text-guided Generation", + "text_level": 1, + "bbox": [ + 500, + 547, + 718, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we evaluate 3D shape generation conditioned on text input. For a qualitative comparison, we use the Text2shape dataset [8] that provides descriptions for the 'chair' and 'table' categories in ShapeNet. For a quantitative evaluation, we adopt the ShapeGlot [3] dataset which provides text utterances describing the difference between a target shape and two distractors based on the ShapeNet dataset. We compare SDFusion with AutoSDF, which recently demonstrated state-of-the-art results on the text-guided 3D shape generation task.", + "bbox": [ + 496, + 566, + 890, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow the evaluation pipeline proposed by Shape-Glot [3]. We train a neural evaluator to distinguish the target shape from a distractor given the description. Given two shapes from different methods, the neural evaluator provides a confidence score for each of them based on the binary classification logits. For the absolute difference between two confidence scores $\\leq 0.2$ , we count the comparison as confused (conf.).", + "bbox": [ + 496, + 719, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Table 3, SDFusion quantitatively outperforms AutoSDF by a large margin with a low confusion rate. SDFusion also performs better than AutoSDF when compared with ground truth data. Qualitatively, we show", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4461", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f20af8e41c1172832f3b2cbc165790c1f1ba7803502e6863b35bbff3b0f55421.jpg", + "image_caption": [ + "Figure 6. Text-guided 3D shape generation. (Top) We compare SDFusion with AutoSDF on the Text2Shape dataset. SDFusion generates shapes with higher quality while conforming to the description. (Bottom) We present more diverse and interesting text-guided generation results from SDFusion." + ], + "image_footnote": [], + "bbox": [ + 76, + 71, + 890, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8da77c3219723d65e350b2fd2f3429bd7fb869c29f287c619eb24a388c7ef231.jpg", + "image_caption": [ + "Figure 7. Conditional generation from multiple modalities. Here, we present generated samples from joint conditions of (left) partial shape and text and (right) partial shapes and images. The generated results are diverse and consistent with the provided conditions." + ], + "image_footnote": [], + "bbox": [ + 86, + 440, + 480, + 579 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3cb3e9356dd8feef7abfb85f3e891191d9bd91b8db7d237389b894688bc2482.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 440, + 883, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "in Figure 5 that SDFusion not only generates shapes with better quality, but that the generated shapes are also more diverse. Notably, SDFusion reacts to very specific descriptions like \"L-shaped table\" and \"table with two surfaces.\" It generates objects of high diversity while remaining faithful to the provided description.", + "bbox": [ + 75, + 643, + 468, + 736 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Multi-conditional Generation", + "text_level": 1, + "bbox": [ + 76, + 744, + 339, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to the conditional generation tasks which take a single conditioning variable as input, we further demonstrate the efficacy of SDFusion in handling multiple modalities. First, SDFusion can jointly consider multiple conditioning modalities. On the left of Figure 7, we present the diverse generation conditional on both partial shapes and text. On the right of Figure 7, we show that given partial shapes and images, SDFusion can complete the different parts based on images. When there is ambiguity in images", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(e.g., rear-view of chairs), SDFusion can produce diverse predictions. Second, as shown in Figure 8, SDFusion can not only be jointly conditioned on multiple inputs, but a weight can be used to control the importance of the conditioning modalities, enabling more flexible user control. For example, for the left sample in Figure 8, the larger the weight for the input image, the more similar the results are to the shapes in the image. Similarly, the larger the weight for input text, the more \"egg-shaped\" the results. We envision such a fine-grained form of control to be particularly useful for interactive user applications.", + "bbox": [ + 496, + 643, + 890, + 811 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5.3D Shape Texturing", + "text_level": 1, + "bbox": [ + 500, + 820, + 692, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we showcase an application that uses SDFusion to generate 3D shapes of detailed geometry, and uses a pretrained text-to-image 2D diffusion model [34] to provide textures. As shown in Figure 9, the diffusion model", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4462", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0d894de63d586eb529c60605590324c8c9fdf2e1b3262f8e990263f8bc63d3c2.jpg", + "image_caption": [ + "Figure 8. Multiple conditioning variables with weight control. Given a partial shape, an image, and a sentence as conditional input, we show that the model is sensitive to weights that control the importance of different modalities." + ], + "image_footnote": [], + "bbox": [ + 98, + 77, + 869, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/af1cd8c2902b578633c86bf50cf9759826c84a93a38516105b43ef2ec94b47b6.jpg", + "image_caption": [ + "Figure 9. 3D Shape Texturing. We texture the generated 3D shapes with a 2D diffusion model trained on large-scale data. This permits to generate textures from diverse textual inputs, including style and material descriptions. The pipeline can also generate diverse results given the same input description." + ], + "image_footnote": [], + "bbox": [ + 78, + 375, + 890, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pre-trained on large-scale 2D data can provide semantically meaningful and diverse guidance to texture the 3D shapes. The model shows superior expressiveness to interpret abstract concepts (e.g., Chinese- and Halloween-style) and materials (e.g., gingerbread, cream cheese). Given a single description, the texturing pipeline can also generate diverse results, as shown in the rightmost part of Figure 9.", + "bbox": [ + 75, + 588, + 468, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 713, + 194, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present SDFusion, an attempt to adopt diffusion models to signed distance functions for 3D shape generation. To alleviate the computationally demanding nature of 3D representations, we first encode 3D shapes into an expressive low-dimensional latent space, which we use to train the diffusion model. To enable flexible conditional usage, we adopt class-specific encoders along with a cross-attention mechanism for handling conditions from multiple modalities, and leverage classifier-free guidance to facilitate weight control among modalities. Foreseeing the potential of a collaborative symbiosis between models trained", + "bbox": [ + 75, + 734, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "on 2D and 3D data, we further demonstrate an application that takes advantage of a pretrained 2D text-to-image model to texture a generated 3D shape.", + "bbox": [ + 496, + 588, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although the results look promising and exciting, there are quite a few future directions for improvement. First, SDFusion is trained on high-quality signed distance function representations. To make the model more general and to enable the use of more diverse data, a model that operates on various 3D representations simultaneously is desirable. Another future direction is related to the diversity of the data: we currently apply SDFusion on object-centric data. It is interesting to apply the model to more challenging scenarios (e.g., entire 3D scenes). Finally, we believe there is room to further explore how to combine models trained on 2D and 3D data.", + "bbox": [ + 496, + 633, + 892, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: Work supported in part by NSF under Grants 2008387, 2045586, 2106825, MRI 1725729, and NIFA award 2020-67021-32799. Thanks to NVIDIA for providing a GPU for debugging.", + "bbox": [ + 496, + 815, + 893, + 876 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4463", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdal, Hsin-Ying Lee, Peihao Zhu, Menglei Chai, Aliaksandr Siarohin, Peter Wonka, and Sergey Tulyakov. 3davatargan: Bridging domains for personalized editable avatars. 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In ICCV, 2021. 3" + ], + "bbox": [ + 501, + 92, + 890, + 388 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4465", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/f29ee3dd-8b63-4289-b6a4-d6e103a0e949_model.json b/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/f29ee3dd-8b63-4289-b6a4-d6e103a0e949_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ea1522498214567f6c6890223651546a90a37f8f --- /dev/null +++ b/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/f29ee3dd-8b63-4289-b6a4-d6e103a0e949_model.json @@ -0,0 +1,1936 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.087, + 0.131, + 0.882, + 0.152 + ], + "angle": 0, + "content": "SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.18, + 0.892, + 0.252 + ], + "angle": 0, + "content": "Yen-Chi Cheng\\(^{1}\\) Hsin-Ying Lee\\(^{2}\\) Sergey Tulyakov\\(^{2}\\) Alexander Schwing\\(^{1*}\\) Liangyan Gui\\(^{1*}\\) \n\\(^{1}\\)University of Illinois Urbana-Champaign \\(^{2}\\)Snap Research \n{yenchic3,aschwing,lgui}@illinois.edu {hlee5,stulyakov}@snap.com \nhttps://yccyenchicheng.github.io/SDFusion/" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.267, + 0.565, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.267, + 0.882, + 0.646 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.651, + 0.895, + 0.708 + ], + "angle": 0, + "content": "Figure 1. Applications of SDFusion. The proposed diffusion-based model enables various applications. (left) SDFusion can generate shapes conditioned on different input modalities, including partial shapes, images, and text. SDFusion can even jointly handle multiple conditioning modalities while controlling the strength for each of them. (right) We leverage pretrained 2D models to texture 3D shapes generated by SDFusion." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.715, + 0.314, + 0.731 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this work, we present a novel framework built to simplify 3D asset generation for amateur users. To enable interactive generation, our method supports a variety of input modalities that can be easily provided by a human, including images, text, partially observed shapes and combinations of these, further allowing to adjust the strength of each input. At the core of our approach is an encoder-decoder, compressing 3D shapes into a compact latent representation, upon which a diffusion model is learned. To enable a variety of multi-modal inputs, we employ task-specific encoders with dropout followed by a cross-attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.895, + 0.884 + ], + "angle": 0, + "content": "mechanism. Due to its flexibility, our model naturally supports a variety of tasks, outperforming prior works on shape completion, image-based 3D reconstruction, and text-to-3D. Most interestingly, our model can combine all these tasks into one swiss-army-knife tool, enabling the user to perform shape generation using incomplete shapes, images, and textual descriptions at the same time, providing the relative weights for each input and facilitating interactivity. Despite our approach being shape-only, we further show an efficient method to texture the generated shape using large-scale text-to-image models." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4456" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.208, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.468, + 0.312 + ], + "angle": 0, + "content": "Generating 3D assets is a cornerstone of immersive augmented/virtual reality experiences. Without realistic and diverse objects, virtual worlds will look void and engagement will remain low. Despite this need, manually creating and editing 3D assets is a notoriously difficult task, requiring creativity, 3D design skills, and access to sophisticated software with a very steep learning curve. This makes 3D asset creation inaccessible for inexperienced users. Yet, in many cases, such as interior design, users more often than not have a reasonably good understanding of what they want to create. In those cases, an image or a rough sketch is sometimes accompanied by text indicating details of the asset, which are hard to express graphically for an amateur." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.313, + 0.468, + 0.553 + ], + "angle": 0, + "content": "Due to this need, it is not surprising that democratizing the 3D content creation process has become an active research area. Conventional 3D generative models require direct 3D supervision in the form of point clouds [2, 21], signed distance functions (SDFs) [9, 25], voxels [42, 47], etc. Recently, first efforts have been made to explore the learning of 3D geometry from multi-view supervision with known camera poses by incorporating inductive biases via neural rendering techniques [5, 6, 14, 37, 52]. While compelling results have been demonstrated, training is often very time-consuming and ignores available 3D data that can be used to obtain good shape priors. We foresee an ideal collaborative paradigm for generative methods where models trained on 3D data provide detailed and accurate geometry, while models trained on 2D data provide diverse appearances. A first proof of concept is shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In our pursuit of flexible and high-quality 3D shape generation, we introduce SDFusion, a diffusion-based generative model with a signed distance function (SDF) under the hood, acting as our 3D representation. Compared to other 3D representations, SDFs are known to represent well high-resolution shapes with arbitrary topology [9, 18, 23, 30]. However, 3D representations are infamous for demanding high computational resources, limiting most existing 3D generative models to voxel grids of \\(32^{3}\\) resolution and point clouds of \\(2K\\) points. To side-step this issue, we first utilize an auto-encoder to compress 3D shapes into a more compact low-dimensional representation. Because of this, SDFusion can easily scale up to a \\(128^{3}\\) resolution. To learn the probability distribution over the introduced latent space, we leverage diffusion models, which have recently been used with great success in various 2D generation tasks [4, 19, 22, 26, 35, 40]. Furthermore, we adopt task-specific encoders and a cross-attention [34] mechanism to support multiple conditioning inputs, and apply classifier-free guidance [17] to enable flexible conditioning usage. Because of these strategies, SDFusion can not only use a variety of conditions from multiple modalities, but also adjust their importance weight, as shown in Figure 1. Compared" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "to a recently proposed autoregressive model [25] that also adopts an encoded latent space, SDFusion achieves superior sample quality, while offering more flexibility to handle multiple conditions and, at the same time, features reduced memory usage. With SDFusion, we study the interplay between models trained on 2D and 3D data. Given 3D shapes generated by SDFusion, we take advantage of an off-the-shelf 2D diffusion model [34], neural rendering [24], and score distillation sampling [31] to texture the shapes given text descriptions as conditional variables." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.38 + ], + "angle": 0, + "content": "We conduct extensive experiments on the ShapeNet [7], BuildingNet [38], and Pix3D [43] datasets. We show that SDFusion quantitatively and qualitatively outperforms prior work in shape completion, 3D reconstruction from images, and text-to-shape tasks. We further demonstrate the capability of jointly controlling the generative model via multiple conditioning modalities, the flexibility of adjusting relative weight among modalities, and the ability to texture 3D shapes given textual descriptions, as shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.381, + 0.847, + 0.395 + ], + "angle": 0, + "content": "We summarize the main contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.398, + 0.891, + 0.442 + ], + "angle": 0, + "content": "- We propose SDFusion, a diffusion-based 3D generative model which uses a signed distance function as its 3D representation and a latent space for diffusion." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.443, + 0.891, + 0.487 + ], + "angle": 0, + "content": "- SDFusion enables conditional generation with multiple modalities, and provides flexible usage by adjusting the weight among modalities." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.488, + 0.891, + 0.532 + ], + "angle": 0, + "content": "- We demonstrate a pipeline to synthesize textured 3D objects benefiting from an interplay between 2D and 3D generative models." + }, + { + "type": "list", + "bbox": [ + 0.52, + 0.398, + 0.891, + 0.532 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.64, + 0.565 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.809 + ], + "angle": 0, + "content": "3D Generative Models. Different from 2D images, it is less clear how to effectively represent 3D data. Indeed, various representations with different pros and cons have been explored, particularly when considering 3D generative models. For instance, 3D generative models have been explored for point clouds [2, 21], voxel grids [20, 42, 47], meshes [51], signed distance functions (SDFs) [9, 11, 25], etc. In this work, we aim to generate an SDF. Compared to other representations, SDFs exhibit a reasonable tradeoff regarding expressivity, memory efficiency, and direct applicability to downstream tasks. Moreover, conditioning 3D generation of SDFs on different modalities further enables many applications, including shape completion, 3D reconstruction from images, 3D generation from text, etc. The proposed framework can handle these tasks in a single model which makes it different from prior work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Recently, thanks to the advancement of neural rendering [24], a new stream of research has emerged to learn 3D generation and manipulation from only 2D supervision [1, 5, 6, 28, 37, 39, 41, 49]. We believe the interplay between two streams of work is promising in the foreseeable future." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4457" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.62, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.09, + 0.885, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.895, + 0.319 + ], + "angle": 0, + "content": "Figure 2. SDFusion Overview. (left) To enable high-resolution generation, we first encode 3D shapes into a latent space, where a diffusion model is trained. Furthermore, to enable flexible conditional generation, we adopt class-specific encoders along with classifier-free guidance to enable multi-modality conditioning. (right) At inference time, we can control the importance of each conditioning modality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.495 + ], + "angle": 0, + "content": "Diffusion Models. Diffusion models have recently emerged as a popular family of generative models with competitive sample quality. In particular, diffusion models have shown impressive quality, diversity, and expressiveness in various tasks such as image synthesis [13,15,16,27], super-resolution [36], image editing [10, 22, 40], text-to-image synthesis [4, 19, 26, 33, 35], etc. In contrast to the flourishing research on diffusion models for 2D data, diffusion models have not yet been fully explored for 3D data. Notable exceptions include attempts to apply diffusion models to point clouds [21, 53]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.471, + 0.587 + ], + "angle": 0, + "content": "Differently, in this work, we apply diffusion models on SDF representations. As reasonable resolutions of SDFs are demanding to model, we study the use of a latent diffusion technique [34] and the classifier-free conditional generation mechanism [17], both of which have been shown to yield promising results when being used in 2D diffusion models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.601, + 0.188, + 0.618 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.837 + ], + "angle": 0, + "content": "We aim at synthesizing 3D shapes using diffusion models. Towards this goal, we model the distribution over 3D shapes \\(\\mathbf{X}\\), a volumetric Truncated Signed Distance Field (T-SDF). However, applying diffusion models directly on reasonably high-resolution 3D shapes is computationally very demanding. Therefore, we first compress the 3D shape into a discretized and compact latent space (Section 3.1). This allows us to apply diffusion models in a lower-dimensional space (Section 3.2). The proposed framework can further incorporate various user conditions such as partial shapes, images, and text (Section 3.3). Finally, we showcase an interplay between the proposed framework and diffusion models trained on 2D data to texture 3D shapes (Section 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.351, + 0.865 + ], + "angle": 0, + "content": "3.1. 3D Shape Compression of SDF" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "A 3D shape representation is high-dimensional and thus difficult to model. To make learning of high-resolution 3D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.895, + 0.466 + ], + "angle": 0, + "content": "shape distributions via diffusion models feasible, we compress the 3D shape \\(\\mathbf{X}\\) into a lower-dimensional yet compact latent space. For this, we leverage a 3D-variant of the Vector Quantised-Variational AutoEncoder (VQ-VAE) [29]. Specifically, the employed 3D VQ-VAE contains an encoder \\(E_{\\varphi}\\) to encode the 3D shape into the latent space, and a decoder \\(D_{\\tau}\\) to decode the latent vectors back to 3D space. Given an input shape represented via the T-SDF \\(\\mathbf{X} \\in \\mathbb{R}^{D \\times D \\times D}\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.473, + 0.892, + 0.491 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} = E _ {\\varphi} (\\mathbf {X}), \\quad \\text {a n d} \\quad \\mathbf {X} ^ {\\prime} = D _ {\\tau} (\\mathrm {V Q} (\\mathbf {z})), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.893, + 0.633 + ], + "angle": 0, + "content": "where \\(\\mathbf{z} \\in \\mathbb{R}^{d \\times d \\times d}\\) is the latent vector, latent dimension \\(d\\) is smaller than 3D shape dimension \\(D\\), and VQ is the quantization step which maps the latent variable \\(\\mathbf{z}\\) to the nearest element in the codebook \\(\\mathcal{Z}\\). The encoder \\(E_{\\varphi}\\), decoder \\(D_{\\tau}\\), and codebook \\(\\mathcal{Z}\\) are jointly optimized. We pre-train the VQ-VAE with reconstruction loss, commitment loss, and VQ objective, similar to [29] using ShapeNet or BuildingNet data. For more details please see the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.642, + 0.783, + 0.658 + ], + "angle": 0, + "content": "3.2. Latent Diffusion Model for SDF" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.665, + 0.892, + 0.832 + ], + "angle": 0, + "content": "Using the trained encoder \\( E_{\\varphi} \\), we can now encode any given SDF into a compact and low-dimensional latent variable \\( \\mathbf{z} = E_{\\varphi}(\\mathbf{X}) \\). We can then train a diffusion model on this latent representation. Fundamentally, a diffusion model learns to sample from a target distribution by reversing a progressive noise diffusion process. Given a sample \\( \\mathbf{z} \\), we obtain \\( \\mathbf{z}_t, t \\in \\{1, \\dots, T\\} \\) by gradually adding Gaussian noise with a variance schedule. Then we use a time-conditional 3D UNet \\( \\epsilon_{\\theta} \\) as our denoising model. To train the denoising 3D UNet, we adopt the simplified objective proposed by Ho et al. [15]:" + }, + { + "type": "equation", + "bbox": [ + 0.539, + 0.839, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s i m p l e}} (\\theta) := \\mathbb {E} _ {\\mathbf {z}, \\epsilon \\sim N (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t) \\| ^ {2} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "At inference time, we sample \\(\\widehat{\\mathbf{z}}\\) by gradually denoising a noise variable sampled from the standard normal distribu" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4458" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.138 + ], + "angle": 0, + "content": "tion \\(N(0,1)\\), and leverage the trained decoder \\(D_{\\tau}\\) to map the denoised code \\(\\widehat{\\mathbf{z}}\\) back to a 3D T-SDF shape representation \\(\\widehat{\\mathbf{X}} = D_{\\tau}(\\widehat{\\mathbf{z}})\\), as shown in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.148, + 0.406, + 0.166 + ], + "angle": 0, + "content": "3.3. Learning the Conditional Distribution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.172, + 0.47, + 0.353 + ], + "angle": 0, + "content": "Being able to randomly sample shapes provides limited ability for interaction. Therefore, learning of a conditional distribution is essential for user applications. Importantly, multiple forms of conditional inputs are desirable such that the model can account for various kinds of scenarios. Thanks to the flexible conditional mechanism provided by a latent diffusion model [34], we can incorporate multiple conditional input modalities at once with task-specific encoders \\( E_{\\phi} \\) and a cross-attention module. To further allow for more flexibility in controlling the distribution, we adopt classifier-free guidance for conditional generation. The objective function reads as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.365, + 0.468, + 0.407 + ], + "angle": 0, + "content": "\\[\nL \\left(\\theta , \\left\\{\\phi_ {i} \\right\\}\\right) := \\underset {\\mathbf {z}, \\mathbf {c}, \\epsilon , t} {\\mathbb {E}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{D \\circ E _ {\\phi_ {i}} \\left(\\mathbf {c} _ {i}\\right) \\right\\}\\right) \\| ^ {2} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.407, + 0.468, + 0.467 + ], + "angle": 0, + "content": "where \\( E_{\\phi_i}(\\mathbf{c}_i) \\) is the task-specific encoder for the \\( i^{\\mathrm{th}} \\) modality, \\( D \\) is a dropout operation enabling classifier-free guidance, and \\( F \\) is a feature aggregation function. In this work, \\( F \\) refers to a simple concatenation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.469, + 0.469, + 0.499 + ], + "angle": 0, + "content": "At inference time, given conditions from multiple modalities, we perform classifier-free guidance as follows" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.524, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{E _ {\\phi_ {i}} \\forall i \\right\\}\\right) = \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\emptyset\\right) + \\\\ \\sum_ {i} s _ {i} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{E _ {\\phi_ {i}} \\left(\\mathbf {c} _ {i}\\right), E _ {\\phi_ {j}} \\left(\\mathbf {c} _ {j}\\right): \\mathbf {c} _ {j} = \\emptyset \\forall j \\neq i \\right\\}\\right) \\right. \\\\ - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\emptyset)), \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.469, + 0.669 + ], + "angle": 0, + "content": "where \\( s_i \\) denotes the weight of conditions from the \\( i^{\\text{th}} \\) modality and \\( \\varnothing \\) denotes a condition filled with zeros. Intuitively, modalities with larger weights play more important roles in guiding the conditional generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.469, + 0.805 + ], + "angle": 0, + "content": "In this work, we study SDFusion combined with three conditional modalities applied separately or jointly. For shape completion, given a partial observation of a shape, we perform blended diffusion similar to [4]. For single-view 3D reconstruction, we adopt CLIP [32] as the image encoder. For text-guided 3D generation, we adopt BERT [12] as the text encoder. The encoded features are then used to modulate the diffusion process with cross-attention. Please refer to the supplementary material for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.398, + 0.833 + ], + "angle": 0, + "content": "3.4. 3D Shape Texturing with a 2D Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "While sampled 3D data often exhibits compellingly detailed geometry, textures of 3D data are generally more difficult to collect and even more often of limited quality. Here, we explore how to make the best use of 2D data and" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.091, + 0.891, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.314 + ], + "angle": 0, + "content": "Figure 3. 3D Shape Texturing. We demonstrate an application where models trained on 2D and 3D data are combined. The shapes generated by SDFusion are converted to a density tensor, then the color information is learned via neural rendering. The gradients are provided by an off-the-shelf 2D diffusion model [34]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.404 + ], + "angle": 0, + "content": "models, so as to aid 3D asset generation. Thanks to the recent success of neural rendering [24] and 2D text-to-image models trained on extremely large-scale data [34], using a 2D model to perform 3D synthesis is made possible with a score distillation sampling technique [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.893, + 0.677 + ], + "angle": 0, + "content": "Here, we illustrate the procedure of texturing a 3D shape given a guiding input sentence \\(S\\). Starting from a generated T-SDF \\(\\mathbf{X}\\), we first convert it to a density tensor \\(\\sigma\\) by using VolSDF [50]. Our goal is to learn a 5D radiance field to obtain color \\(F_{\\theta}:(\\mathbf{x},\\mathbf{d})\\rightarrow \\mathbf{c}\\), similar to the conventional NeRF [24] setting. However, different from the conventional NeRF setting, the density tensor is fixed. With a sampled camera pose, we can render an image \\(I\\) by alpha-compositing the densities and colors along the rays for each pixel. Then, we distill the knowledge from a pre-trained stable diffusion model [34], denoted as a 2D UNet \\(\\tilde{\\epsilon}_{\\phi}(\\mathbf{z}_t,t,S)\\) that predicts the noise at timestep \\(t\\). The most straightforward way to update \\(F_{\\theta}\\) is to obtain and backpropagate gradients all the way from the noise prediction loss term of the stable diffusion loss function to the input. However, the UNet Jacobian term is in practice expensive to compute. Therefore, it was proposed in [31] to bypass the UNet and treat \\(\\tilde{\\epsilon}_{\\phi}\\) as a frozen critic providing scores by computing" + }, + { + "type": "equation", + "bbox": [ + 0.559, + 0.685, + 0.891, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {t, \\epsilon} \\left[ \\frac {\\partial I \\left(F _ {\\theta} (\\cdot)\\right)}{\\partial \\theta} w (t) \\left(\\tilde {\\epsilon} _ {\\phi} \\left(\\mathbf {z} _ {t}, t, S\\right) - \\epsilon\\right) \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.803 + ], + "angle": 0, + "content": "where \\( w \\) is a time-dependent weight function defined in the stable diffusion model. The mechanism is called Score Distillation Sampling. Please refer to [31] for details. The score then provides an update direction to \\( F_{\\theta} \\). We illustrate the process in Figure 3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.633, + 0.833 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we conduct extensive qualitative and quantitative experiments to demonstrate the efficacy and generalizability of SDFusion. We evaluate methods on three tasks: shape completion, single-view 3D reconstruction," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4459" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.895, + 0.509 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.518, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Figure 4. Shape Completion. (Top) We compare SDFusion with AutoSDF [25] and MPC [45] on ShapeNet and BuildingNet data. SDFusion generates shapes of better quality and diversity, while being consistent with the input partial shapes. We convert the generated SDFs from SDFusion and AutoSDF to point clouds to compare with MPC. Please refer to the supplementary materials for SDF comparisons on BuildingNet for better visualization. (Bottom) We present more results on diverse shape completion using various object categories." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.642 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of Shape Completion. We evaluate methods on fidelity (UHD) and diversity (TMD) using the ShapeNet and BuildingNet data. SDFusion outperforms other methods in both metrics, especially diversity." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.645, + 0.432, + 0.743 + ], + "angle": 0, + "content": "
MethodShapeNetBuildingNet
UHD ↓TMD ↑UHD ↓TMD ↑
MPC [45]0.06270.03030.13500.0467
AutoSDF [25]0.05670.03410.12080.0649
Ours0.05570.08850.11160.0745
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.47, + 0.818 + ], + "angle": 0, + "content": "and text-guided generation. We then demonstrate two additional use cases: multi-conditional generation and 3D shape texturing." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.258, + 0.848 + ], + "angle": 0, + "content": "4.1. Shape Completion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We evaluate the shape completion task on the ShapeNet [7] and the BuildingNet [38] datasets. ShapeNet is a large-scale 3D CAD model dataset with 16 common" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.585, + 0.892, + 0.626 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation of single-view reconstruction. We evaluate methods on the Pix3D dataset using Chamfer Distance and F-Score. We outperform other methods in both metrics." + }, + { + "type": "table", + "bbox": [ + 0.58, + 0.631, + 0.812, + 0.738 + ], + "angle": 0, + "content": "
MethodCD ↓F-Score ↑
Pix2Vox [46]3.0010.385
ResNet2TSDF4.5820.351
ResNet2Voxel4.6700.357
AutoSDF [25]2.2670.415
Ours1.8520.432
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "object classes. We use the train/test splits provided by Xu et al. [48]. BuildingNet is a new large-scale 3D building model dataset. Compared to objects in ShapeNet, building models provide more geometric details and thus require higher resolution for representing the data. Hence, we use an SDF of \\(64^{3}\\) resolution for ShapeNet, and a \\(128^{3}\\) resolution for BuildingNet. For both datasets, we compare the completion quantitatively by providing the bottom half of the ground truth shape as input, and evaluating the com" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4460" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.072, + 0.891, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.893, + 0.304 + ], + "angle": 0, + "content": "Figure 5. Single-view 3D Reconstruction. (Top) We qualitatively compare all methods on the Pix3D dataset. SDFusion generates shapes with the best visual quality. (Bottom) Here we present more reconstruction results from SDFusion." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.323, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation of text-guided generation. We compare the proposed SDFusion method, AutoSDF, and real data using a pretrained neural evaluator on the ShapeGlot dataset. \\(P\\) denotes the neural evaluator preference rate for the target \\(P(\\mathrm{Tr})\\) or the distractor \\(P(\\mathrm{Dis})\\). If the preference is too close (\\(\\leq 0.2\\)), we count the comparison as confused (conf.). Rows sum to \\(100\\%\\)." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.418, + 0.449, + 0.491 + ], + "angle": 0, + "content": "
Target (Tr)Distractor (Dis)P(Tr)P(Dis)P(conf.)
OursAutoSDF [25]49%36%15%
OursGT33%45%22%
AutoSDF [25]GT30%49%21%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.38, + 0.525 + ], + "angle": 0, + "content": "pleted shapes generated by different methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.525, + 0.469, + 0.675 + ], + "angle": 0, + "content": "We compare SDFusion to the state-of-the-art point cloud completion method MPC [45] and the autoregressive SDF generation method AutoSDF [25]. We adopt metrics from MPC [45]. For each partial shape, we generate \\( k \\) complete shapes. To evaluate completion fidelity, we measure the Unidirectional Hausdorff Distance (UHD) between partial shapes and generated shapes. To evaluate completion diversity, we measure the Total Mutual Difference (TMD) by computing the average Chamfer distance among \\( k \\) generated shapes. We use \\( k = 10 \\) in the experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.469, + 0.797 + ], + "angle": 0, + "content": "As shown in Table 1, the proposed SDFusion performs favorably compared to all methods in the completion fidelity metric, and outperforms the baselines substantially in completion diversity. The advantages of fidelity and diversity are also apparent in Figure 4. Especially on the BuildingNet dataset, SDFusion shows its advantages in modeling high-resolution and diverse data. AutoSDF and MPC struggle to model the distribution correctly." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.806, + 0.35, + 0.822 + ], + "angle": 0, + "content": "4.2. Single-view 3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Next, we assess 3D shape reconstruction from a single image on the real-world benchmark Pix3D [43] dataset. We use the provided train/test splits on the chair category. In the absence of official splits for other categories, we randomly split the dataset into disjoint train/test splits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.445 + ], + "angle": 0, + "content": "We compare with the ResNet2TSDF and ResNet2Voxel baselines. Both encode images and directly output 3D shapes in the form of a T-SDF and a voxel grid. We also compare to two state-of-the-art methods for 3D reconstruction, i.e., Pix2Vox [46] and AutoSDF [25]. We evaluate all methods after aligning resolutions to \\(32^{3}\\) voxels. We use Chamfer Distance (CD), and F-score@1% [44] as evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.535 + ], + "angle": 0, + "content": "Quantitatively, as shown in Table 2, SDFusion outperforms other methods on both metrics. Qualitatively, SDFusion generates 3D shapes that are of higher visual quality and are more visually consistent with the objects shown in the images, regardless of camera poses, as shown in Figure 5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.719, + 0.563 + ], + "angle": 0, + "content": "4.3. Text-guided Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Next, we evaluate 3D shape generation conditioned on text input. For a qualitative comparison, we use the Text2shape dataset [8] that provides descriptions for the 'chair' and 'table' categories in ShapeNet. For a quantitative evaluation, we adopt the ShapeGlot [3] dataset which provides text utterances describing the difference between a target shape and two distractors based on the ShapeNet dataset. We compare SDFusion with AutoSDF, which recently demonstrated state-of-the-art results on the text-guided 3D shape generation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.839 + ], + "angle": 0, + "content": "We follow the evaluation pipeline proposed by Shape-Glot [3]. We train a neural evaluator to distinguish the target shape from a distractor given the description. Given two shapes from different methods, the neural evaluator provides a confidence score for each of them based on the binary classification logits. For the absolute difference between two confidence scores \\(\\leq 0.2\\), we count the comparison as confused (conf.)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As shown in Table 3, SDFusion quantitatively outperforms AutoSDF by a large margin with a low confusion rate. SDFusion also performs better than AutoSDF when compared with ground truth data. Qualitatively, we show" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4461" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.072, + 0.892, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.392, + 0.893, + 0.434 + ], + "angle": 0, + "content": "Figure 6. Text-guided 3D shape generation. (Top) We compare SDFusion with AutoSDF on the Text2Shape dataset. SDFusion generates shapes with higher quality while conforming to the description. (Bottom) We present more diverse and interesting text-guided generation results from SDFusion." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.441, + 0.482, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.441, + 0.885, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.603, + 0.893, + 0.634 + ], + "angle": 0, + "content": "Figure 7. Conditional generation from multiple modalities. Here, we present generated samples from joint conditions of (left) partial shape and text and (right) partial shapes and images. The generated results are diverse and consistent with the provided conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.737 + ], + "angle": 0, + "content": "in Figure 5 that SDFusion not only generates shapes with better quality, but that the generated shapes are also more diverse. Notably, SDFusion reacts to very specific descriptions like \"L-shaped table\" and \"table with two surfaces.\" It generates objects of high diversity while remaining faithful to the provided description." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.745, + 0.341, + 0.76 + ], + "angle": 0, + "content": "4.4. Multi-conditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In addition to the conditional generation tasks which take a single conditioning variable as input, we further demonstrate the efficacy of SDFusion in handling multiple modalities. First, SDFusion can jointly consider multiple conditioning modalities. On the left of Figure 7, we present the diverse generation conditional on both partial shapes and text. On the right of Figure 7, we show that given partial shapes and images, SDFusion can complete the different parts based on images. When there is ambiguity in images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.812 + ], + "angle": 0, + "content": "(e.g., rear-view of chairs), SDFusion can produce diverse predictions. Second, as shown in Figure 8, SDFusion can not only be jointly conditioned on multiple inputs, but a weight can be used to control the importance of the conditioning modalities, enabling more flexible user control. For example, for the left sample in Figure 8, the larger the weight for the input image, the more similar the results are to the shapes in the image. Similarly, the larger the weight for input text, the more \"egg-shaped\" the results. We envision such a fine-grained form of control to be particularly useful for interactive user applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.821, + 0.693, + 0.837 + ], + "angle": 0, + "content": "4.5.3D Shape Texturing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Finally, we showcase an application that uses SDFusion to generate 3D shapes of detailed geometry, and uses a pretrained text-to-image 2D diffusion model [34] to provide textures. As shown in Figure 9, the diffusion model" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4462" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.078, + 0.87, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.343, + 0.893, + 0.371 + ], + "angle": 0, + "content": "Figure 8. Multiple conditioning variables with weight control. Given a partial shape, an image, and a sentence as conditional input, we show that the model is sensitive to weights that control the importance of different modalities." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.376, + 0.891, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.531, + 0.893, + 0.573 + ], + "angle": 0, + "content": "Figure 9. 3D Shape Texturing. We texture the generated 3D shapes with a 2D diffusion model trained on large-scale data. This permits to generate textures from diverse textual inputs, including style and material descriptions. The pipeline can also generate diverse results given the same input description." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.695 + ], + "angle": 0, + "content": "pre-trained on large-scale 2D data can provide semantically meaningful and diverse guidance to texture the 3D shapes. The model shows superior expressiveness to interpret abstract concepts (e.g., Chinese- and Halloween-style) and materials (e.g., gingerbread, cream cheese). Given a single description, the texturing pipeline can also generate diverse results, as shown in the rightmost part of Figure 9." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.714, + 0.196, + 0.729 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In this work, we present SDFusion, an attempt to adopt diffusion models to signed distance functions for 3D shape generation. To alleviate the computationally demanding nature of 3D representations, we first encode 3D shapes into an expressive low-dimensional latent space, which we use to train the diffusion model. To enable flexible conditional usage, we adopt class-specific encoders along with a cross-attention mechanism for handling conditions from multiple modalities, and leverage classifier-free guidance to facilitate weight control among modalities. Foreseeing the potential of a collaborative symbiosis between models trained" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.589, + 0.892, + 0.634 + ], + "angle": 0, + "content": "on 2D and 3D data, we further demonstrate an application that takes advantage of a pretrained 2D text-to-image model to texture a generated 3D shape." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.893, + 0.814 + ], + "angle": 0, + "content": "Although the results look promising and exciting, there are quite a few future directions for improvement. First, SDFusion is trained on high-quality signed distance function representations. To make the model more general and to enable the use of more diverse data, a model that operates on various 3D representations simultaneously is desirable. Another future direction is related to the diversity of the data: we currently apply SDFusion on object-centric data. It is interesting to apply the model to more challenging scenarios (e.g., entire 3D scenes). Finally, we believe there is room to further explore how to combine models trained on 2D and 3D data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.816, + 0.894, + 0.877 + ], + "angle": 0, + "content": "Acknowledgements: Work supported in part by NSF under Grants 2008387, 2045586, 2106825, MRI 1725729, and NIFA award 2020-67021-32799. Thanks to NVIDIA for providing a GPU for debugging." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4463" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Rameen Abdal, Hsin-Ying Lee, Peihao Zhu, Menglei Chai, Aliaksandr Siarohin, Peter Wonka, and Sergey Tulyakov. 3davatargan: Bridging domains for personalized editable avatars. In CVPR, 2023. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.47, + 0.214 + ], + "angle": 0, + "content": "[2] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. 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In ICCV, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4465" + } + ] +] \ No newline at end of file diff --git a/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/f29ee3dd-8b63-4289-b6a4-d6e103a0e949_origin.pdf b/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/f29ee3dd-8b63-4289-b6a4-d6e103a0e949_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e15396b94f96200708876bc9c8be39bf5f2da611 --- /dev/null +++ b/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/f29ee3dd-8b63-4289-b6a4-d6e103a0e949_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:81e8b30d6dd47e2fafdaacba3077350c86e04d09617aced710e037df168df29e +size 4789556 diff --git a/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/full.md b/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..eebd4368db03a05325c9d49eb8215a0ea732be72 --- /dev/null +++ b/2023/SDFusion_ Multimodal 3D Shape Completion, Reconstruction, and Generation/full.md @@ -0,0 +1,264 @@ +# SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation + +Yen-Chi Cheng $^{1}$ Hsin-Ying Lee $^{2}$ Sergey Tulyakov $^{2}$ Alexander Schwing $^{1*}$ Liangyan Gui $^{1*}$ $^{1}$ University of Illinois Urbana-Champaign $^{2}$ Snap Research +{yenchic3,aschwing,lgui}@illinois.edu {hlee5,stulyakov}@snap.com +https://yccyenchicheng.github.io/SDFusion/ + +![](images/f0be5fc02417a55fe3d079f9e977c2f0d1388b505a427df5d821064bdae1ff65.jpg) +Figure 1. Applications of SDFusion. The proposed diffusion-based model enables various applications. (left) SDFusion can generate shapes conditioned on different input modalities, including partial shapes, images, and text. SDFusion can even jointly handle multiple conditioning modalities while controlling the strength for each of them. (right) We leverage pretrained 2D models to texture 3D shapes generated by SDFusion. + +![](images/64a7ea6e8b31dc05f792fc8e90e0c96188305e83e829d46ee8edbd4df694d0b2.jpg) + +# Abstract + +In this work, we present a novel framework built to simplify 3D asset generation for amateur users. To enable interactive generation, our method supports a variety of input modalities that can be easily provided by a human, including images, text, partially observed shapes and combinations of these, further allowing to adjust the strength of each input. At the core of our approach is an encoder-decoder, compressing 3D shapes into a compact latent representation, upon which a diffusion model is learned. To enable a variety of multi-modal inputs, we employ task-specific encoders with dropout followed by a cross-attention + +mechanism. Due to its flexibility, our model naturally supports a variety of tasks, outperforming prior works on shape completion, image-based 3D reconstruction, and text-to-3D. Most interestingly, our model can combine all these tasks into one swiss-army-knife tool, enabling the user to perform shape generation using incomplete shapes, images, and textual descriptions at the same time, providing the relative weights for each input and facilitating interactivity. Despite our approach being shape-only, we further show an efficient method to texture the generated shape using large-scale text-to-image models. + +# 1. Introduction + +Generating 3D assets is a cornerstone of immersive augmented/virtual reality experiences. Without realistic and diverse objects, virtual worlds will look void and engagement will remain low. Despite this need, manually creating and editing 3D assets is a notoriously difficult task, requiring creativity, 3D design skills, and access to sophisticated software with a very steep learning curve. This makes 3D asset creation inaccessible for inexperienced users. Yet, in many cases, such as interior design, users more often than not have a reasonably good understanding of what they want to create. In those cases, an image or a rough sketch is sometimes accompanied by text indicating details of the asset, which are hard to express graphically for an amateur. + +Due to this need, it is not surprising that democratizing the 3D content creation process has become an active research area. Conventional 3D generative models require direct 3D supervision in the form of point clouds [2, 21], signed distance functions (SDFs) [9, 25], voxels [42, 47], etc. Recently, first efforts have been made to explore the learning of 3D geometry from multi-view supervision with known camera poses by incorporating inductive biases via neural rendering techniques [5, 6, 14, 37, 52]. While compelling results have been demonstrated, training is often very time-consuming and ignores available 3D data that can be used to obtain good shape priors. We foresee an ideal collaborative paradigm for generative methods where models trained on 3D data provide detailed and accurate geometry, while models trained on 2D data provide diverse appearances. A first proof of concept is shown in Figure 1. + +In our pursuit of flexible and high-quality 3D shape generation, we introduce SDFusion, a diffusion-based generative model with a signed distance function (SDF) under the hood, acting as our 3D representation. Compared to other 3D representations, SDFs are known to represent well high-resolution shapes with arbitrary topology [9, 18, 23, 30]. However, 3D representations are infamous for demanding high computational resources, limiting most existing 3D generative models to voxel grids of $32^{3}$ resolution and point clouds of $2K$ points. To side-step this issue, we first utilize an auto-encoder to compress 3D shapes into a more compact low-dimensional representation. Because of this, SDFusion can easily scale up to a $128^{3}$ resolution. To learn the probability distribution over the introduced latent space, we leverage diffusion models, which have recently been used with great success in various 2D generation tasks [4, 19, 22, 26, 35, 40]. Furthermore, we adopt task-specific encoders and a cross-attention [34] mechanism to support multiple conditioning inputs, and apply classifier-free guidance [17] to enable flexible conditioning usage. Because of these strategies, SDFusion can not only use a variety of conditions from multiple modalities, but also adjust their importance weight, as shown in Figure 1. Compared + +to a recently proposed autoregressive model [25] that also adopts an encoded latent space, SDFusion achieves superior sample quality, while offering more flexibility to handle multiple conditions and, at the same time, features reduced memory usage. With SDFusion, we study the interplay between models trained on 2D and 3D data. Given 3D shapes generated by SDFusion, we take advantage of an off-the-shelf 2D diffusion model [34], neural rendering [24], and score distillation sampling [31] to texture the shapes given text descriptions as conditional variables. + +We conduct extensive experiments on the ShapeNet [7], BuildingNet [38], and Pix3D [43] datasets. We show that SDFusion quantitatively and qualitatively outperforms prior work in shape completion, 3D reconstruction from images, and text-to-shape tasks. We further demonstrate the capability of jointly controlling the generative model via multiple conditioning modalities, the flexibility of adjusting relative weight among modalities, and the ability to texture 3D shapes given textual descriptions, as shown in Figure 1. + +We summarize the main contributions as follows: + +- We propose SDFusion, a diffusion-based 3D generative model which uses a signed distance function as its 3D representation and a latent space for diffusion. +- SDFusion enables conditional generation with multiple modalities, and provides flexible usage by adjusting the weight among modalities. +- We demonstrate a pipeline to synthesize textured 3D objects benefiting from an interplay between 2D and 3D generative models. + +# 2. Related Work + +3D Generative Models. Different from 2D images, it is less clear how to effectively represent 3D data. Indeed, various representations with different pros and cons have been explored, particularly when considering 3D generative models. For instance, 3D generative models have been explored for point clouds [2, 21], voxel grids [20, 42, 47], meshes [51], signed distance functions (SDFs) [9, 11, 25], etc. In this work, we aim to generate an SDF. Compared to other representations, SDFs exhibit a reasonable tradeoff regarding expressivity, memory efficiency, and direct applicability to downstream tasks. Moreover, conditioning 3D generation of SDFs on different modalities further enables many applications, including shape completion, 3D reconstruction from images, 3D generation from text, etc. The proposed framework can handle these tasks in a single model which makes it different from prior work. + +Recently, thanks to the advancement of neural rendering [24], a new stream of research has emerged to learn 3D generation and manipulation from only 2D supervision [1, 5, 6, 28, 37, 39, 41, 49]. We believe the interplay between two streams of work is promising in the foreseeable future. + +![](images/b79ce888074a397a7e1cb86c0b09c8499a11d240ff921668c81f1f5469194fc5.jpg) +Figure 2. SDFusion Overview. (left) To enable high-resolution generation, we first encode 3D shapes into a latent space, where a diffusion model is trained. Furthermore, to enable flexible conditional generation, we adopt class-specific encoders along with classifier-free guidance to enable multi-modality conditioning. (right) At inference time, we can control the importance of each conditioning modality. + +![](images/7a57bc53c09b20dd04c441ad31c9d10b319506f2b190e4ff1e6783669307d0d0.jpg) + +Diffusion Models. Diffusion models have recently emerged as a popular family of generative models with competitive sample quality. In particular, diffusion models have shown impressive quality, diversity, and expressiveness in various tasks such as image synthesis [13,15,16,27], super-resolution [36], image editing [10, 22, 40], text-to-image synthesis [4, 19, 26, 33, 35], etc. In contrast to the flourishing research on diffusion models for 2D data, diffusion models have not yet been fully explored for 3D data. Notable exceptions include attempts to apply diffusion models to point clouds [21, 53]. + +Differently, in this work, we apply diffusion models on SDF representations. As reasonable resolutions of SDFs are demanding to model, we study the use of a latent diffusion technique [34] and the classifier-free conditional generation mechanism [17], both of which have been shown to yield promising results when being used in 2D diffusion models. + +# 3. Approach + +We aim at synthesizing 3D shapes using diffusion models. Towards this goal, we model the distribution over 3D shapes $\mathbf{X}$ , a volumetric Truncated Signed Distance Field (T-SDF). However, applying diffusion models directly on reasonably high-resolution 3D shapes is computationally very demanding. Therefore, we first compress the 3D shape into a discretized and compact latent space (Section 3.1). This allows us to apply diffusion models in a lower-dimensional space (Section 3.2). The proposed framework can further incorporate various user conditions such as partial shapes, images, and text (Section 3.3). Finally, we showcase an interplay between the proposed framework and diffusion models trained on 2D data to texture 3D shapes (Section 3.4). + +# 3.1. 3D Shape Compression of SDF + +A 3D shape representation is high-dimensional and thus difficult to model. To make learning of high-resolution 3D + +shape distributions via diffusion models feasible, we compress the 3D shape $\mathbf{X}$ into a lower-dimensional yet compact latent space. For this, we leverage a 3D-variant of the Vector Quantised-Variational AutoEncoder (VQ-VAE) [29]. Specifically, the employed 3D VQ-VAE contains an encoder $E_{\varphi}$ to encode the 3D shape into the latent space, and a decoder $D_{\tau}$ to decode the latent vectors back to 3D space. Given an input shape represented via the T-SDF $\mathbf{X} \in \mathbb{R}^{D \times D \times D}$ , we have + +$$ +\mathbf {z} = E _ {\varphi} (\mathbf {X}), \quad \text {a n d} \quad \mathbf {X} ^ {\prime} = D _ {\tau} (\mathrm {V Q} (\mathbf {z})), \tag {1} +$$ + +where $\mathbf{z} \in \mathbb{R}^{d \times d \times d}$ is the latent vector, latent dimension $d$ is smaller than 3D shape dimension $D$ , and VQ is the quantization step which maps the latent variable $\mathbf{z}$ to the nearest element in the codebook $\mathcal{Z}$ . The encoder $E_{\varphi}$ , decoder $D_{\tau}$ , and codebook $\mathcal{Z}$ are jointly optimized. We pre-train the VQ-VAE with reconstruction loss, commitment loss, and VQ objective, similar to [29] using ShapeNet or BuildingNet data. For more details please see the supplementary material. + +# 3.2. Latent Diffusion Model for SDF + +Using the trained encoder $E_{\varphi}$ , we can now encode any given SDF into a compact and low-dimensional latent variable $\mathbf{z} = E_{\varphi}(\mathbf{X})$ . We can then train a diffusion model on this latent representation. Fundamentally, a diffusion model learns to sample from a target distribution by reversing a progressive noise diffusion process. Given a sample $\mathbf{z}$ , we obtain $\mathbf{z}_t, t \in \{1, \dots, T\}$ by gradually adding Gaussian noise with a variance schedule. Then we use a time-conditional 3D UNet $\epsilon_{\theta}$ as our denoising model. To train the denoising 3D UNet, we adopt the simplified objective proposed by Ho et al. [15]: + +$$ +L _ {\text {s i m p l e}} (\theta) := \mathbb {E} _ {\mathbf {z}, \epsilon \sim N (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} (\mathbf {z} _ {t}, t) \| ^ {2} \right]. \tag {2} +$$ + +At inference time, we sample $\widehat{\mathbf{z}}$ by gradually denoising a noise variable sampled from the standard normal distribu + +tion $N(0,1)$ , and leverage the trained decoder $D_{\tau}$ to map the denoised code $\widehat{\mathbf{z}}$ back to a 3D T-SDF shape representation $\widehat{\mathbf{X}} = D_{\tau}(\widehat{\mathbf{z}})$ , as shown in Figure 2. + +# 3.3. Learning the Conditional Distribution + +Being able to randomly sample shapes provides limited ability for interaction. Therefore, learning of a conditional distribution is essential for user applications. Importantly, multiple forms of conditional inputs are desirable such that the model can account for various kinds of scenarios. Thanks to the flexible conditional mechanism provided by a latent diffusion model [34], we can incorporate multiple conditional input modalities at once with task-specific encoders $E_{\phi}$ and a cross-attention module. To further allow for more flexibility in controlling the distribution, we adopt classifier-free guidance for conditional generation. The objective function reads as follows: + +$$ +L \left(\theta , \left\{\phi_ {i} \right\}\right) := \underset {\mathbf {z}, \mathbf {c}, \epsilon , t} {\mathbb {E}} \left[ \| \epsilon - \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, F \left\{D \circ E _ {\phi_ {i}} \left(\mathbf {c} _ {i}\right) \right\}\right) \| ^ {2} \right], \tag {3} +$$ + +where $E_{\phi_i}(\mathbf{c}_i)$ is the task-specific encoder for the $i^{\mathrm{th}}$ modality, $D$ is a dropout operation enabling classifier-free guidance, and $F$ is a feature aggregation function. In this work, $F$ refers to a simple concatenation. + +At inference time, given conditions from multiple modalities, we perform classifier-free guidance as follows + +$$ +\begin{array}{l} \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, F \left\{E _ {\phi_ {i}} \forall i \right\}\right) = \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, \emptyset\right) + \\ \sum_ {i} s _ {i} \left(\epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, F \left\{E _ {\phi_ {i}} \left(\mathbf {c} _ {i}\right), E _ {\phi_ {j}} \left(\mathbf {c} _ {j}\right): \mathbf {c} _ {j} = \emptyset \forall j \neq i \right\}\right) \right. \\ - \epsilon_ {\theta} (\mathbf {z} _ {t}, t, \emptyset)), \tag {4} \\ \end{array} +$$ + +where $s_i$ denotes the weight of conditions from the $i^{\text{th}}$ modality and $\varnothing$ denotes a condition filled with zeros. Intuitively, modalities with larger weights play more important roles in guiding the conditional generation. + +In this work, we study SDFusion combined with three conditional modalities applied separately or jointly. For shape completion, given a partial observation of a shape, we perform blended diffusion similar to [4]. For single-view 3D reconstruction, we adopt CLIP [32] as the image encoder. For text-guided 3D generation, we adopt BERT [12] as the text encoder. The encoded features are then used to modulate the diffusion process with cross-attention. Please refer to the supplementary material for more details. + +# 3.4. 3D Shape Texturing with a 2D Model + +While sampled 3D data often exhibits compellingly detailed geometry, textures of 3D data are generally more difficult to collect and even more often of limited quality. Here, we explore how to make the best use of 2D data and + +![](images/b64a6d4ffe0be1f22b80c79da498ae9421ea6f0ca993f96702db62774161d6ac.jpg) +Figure 3. 3D Shape Texturing. We demonstrate an application where models trained on 2D and 3D data are combined. The shapes generated by SDFusion are converted to a density tensor, then the color information is learned via neural rendering. The gradients are provided by an off-the-shelf 2D diffusion model [34]. + +models, so as to aid 3D asset generation. Thanks to the recent success of neural rendering [24] and 2D text-to-image models trained on extremely large-scale data [34], using a 2D model to perform 3D synthesis is made possible with a score distillation sampling technique [31]. + +Here, we illustrate the procedure of texturing a 3D shape given a guiding input sentence $S$ . Starting from a generated T-SDF $\mathbf{X}$ , we first convert it to a density tensor $\sigma$ by using VolSDF [50]. Our goal is to learn a 5D radiance field to obtain color $F_{\theta}:(\mathbf{x},\mathbf{d})\rightarrow \mathbf{c}$ , similar to the conventional NeRF [24] setting. However, different from the conventional NeRF setting, the density tensor is fixed. With a sampled camera pose, we can render an image $I$ by alpha-compositing the densities and colors along the rays for each pixel. Then, we distill the knowledge from a pre-trained stable diffusion model [34], denoted as a 2D UNet $\tilde{\epsilon}_{\phi}(\mathbf{z}_t,t,S)$ that predicts the noise at timestep $t$ . The most straightforward way to update $F_{\theta}$ is to obtain and backpropagate gradients all the way from the noise prediction loss term of the stable diffusion loss function to the input. However, the UNet Jacobian term is in practice expensive to compute. Therefore, it was proposed in [31] to bypass the UNet and treat $\tilde{\epsilon}_{\phi}$ as a frozen critic providing scores by computing + +$$ +\mathbb {E} _ {t, \epsilon} \left[ \frac {\partial I \left(F _ {\theta} (\cdot)\right)}{\partial \theta} w (t) \left(\tilde {\epsilon} _ {\phi} \left(\mathbf {z} _ {t}, t, S\right) - \epsilon\right) \right], \tag {5} +$$ + +where $w$ is a time-dependent weight function defined in the stable diffusion model. The mechanism is called Score Distillation Sampling. Please refer to [31] for details. The score then provides an update direction to $F_{\theta}$ . We illustrate the process in Figure 3. + +# 4. Experiments + +In this section, we conduct extensive qualitative and quantitative experiments to demonstrate the efficacy and generalizability of SDFusion. We evaluate methods on three tasks: shape completion, single-view 3D reconstruction, + +![](images/b864b12fe0495a537e2d28c1c06ed0d6d6e4e3df9dbe89e80d134d567fa9ed33.jpg) +Figure 4. Shape Completion. (Top) We compare SDFusion with AutoSDF [25] and MPC [45] on ShapeNet and BuildingNet data. SDFusion generates shapes of better quality and diversity, while being consistent with the input partial shapes. We convert the generated SDFs from SDFusion and AutoSDF to point clouds to compare with MPC. Please refer to the supplementary materials for SDF comparisons on BuildingNet for better visualization. (Bottom) We present more results on diverse shape completion using various object categories. + +Table 1. Quantitative comparison of Shape Completion. We evaluate methods on fidelity (UHD) and diversity (TMD) using the ShapeNet and BuildingNet data. SDFusion outperforms other methods in both metrics, especially diversity. + +
MethodShapeNetBuildingNet
UHD ↓TMD ↑UHD ↓TMD ↑
MPC [45]0.06270.03030.13500.0467
AutoSDF [25]0.05670.03410.12080.0649
Ours0.05570.08850.11160.0745
+ +and text-guided generation. We then demonstrate two additional use cases: multi-conditional generation and 3D shape texturing. + +# 4.1. Shape Completion + +We evaluate the shape completion task on the ShapeNet [7] and the BuildingNet [38] datasets. ShapeNet is a large-scale 3D CAD model dataset with 16 common + +Table 2. Quantitative evaluation of single-view reconstruction. We evaluate methods on the Pix3D dataset using Chamfer Distance and F-Score. We outperform other methods in both metrics. + +
MethodCD ↓F-Score ↑
Pix2Vox [46]3.0010.385
ResNet2TSDF4.5820.351
ResNet2Voxel4.6700.357
AutoSDF [25]2.2670.415
Ours1.8520.432
+ +object classes. We use the train/test splits provided by Xu et al. [48]. BuildingNet is a new large-scale 3D building model dataset. Compared to objects in ShapeNet, building models provide more geometric details and thus require higher resolution for representing the data. Hence, we use an SDF of $64^{3}$ resolution for ShapeNet, and a $128^{3}$ resolution for BuildingNet. For both datasets, we compare the completion quantitatively by providing the bottom half of the ground truth shape as input, and evaluating the com + +![](images/4982631dedb466d6b1c3968e6522c15001f4e05dcda8a624c4f622cd09a78d58.jpg) +Figure 5. Single-view 3D Reconstruction. (Top) We qualitatively compare all methods on the Pix3D dataset. SDFusion generates shapes with the best visual quality. (Bottom) Here we present more reconstruction results from SDFusion. + +Table 3. Quantitative evaluation of text-guided generation. We compare the proposed SDFusion method, AutoSDF, and real data using a pretrained neural evaluator on the ShapeGlot dataset. $P$ denotes the neural evaluator preference rate for the target $P(\mathrm{Tr})$ or the distractor $P(\mathrm{Dis})$ . If the preference is too close ( $\leq 0.2$ ), we count the comparison as confused (conf.). Rows sum to $100\%$ . + +
Target (Tr)Distractor (Dis)P(Tr)P(Dis)P(conf.)
OursAutoSDF [25]49%36%15%
OursGT33%45%22%
AutoSDF [25]GT30%49%21%
+ +pleted shapes generated by different methods. + +We compare SDFusion to the state-of-the-art point cloud completion method MPC [45] and the autoregressive SDF generation method AutoSDF [25]. We adopt metrics from MPC [45]. For each partial shape, we generate $k$ complete shapes. To evaluate completion fidelity, we measure the Unidirectional Hausdorff Distance (UHD) between partial shapes and generated shapes. To evaluate completion diversity, we measure the Total Mutual Difference (TMD) by computing the average Chamfer distance among $k$ generated shapes. We use $k = 10$ in the experiments. + +As shown in Table 1, the proposed SDFusion performs favorably compared to all methods in the completion fidelity metric, and outperforms the baselines substantially in completion diversity. The advantages of fidelity and diversity are also apparent in Figure 4. Especially on the BuildingNet dataset, SDFusion shows its advantages in modeling high-resolution and diverse data. AutoSDF and MPC struggle to model the distribution correctly. + +# 4.2. Single-view 3D Reconstruction + +Next, we assess 3D shape reconstruction from a single image on the real-world benchmark Pix3D [43] dataset. We use the provided train/test splits on the chair category. In the absence of official splits for other categories, we randomly split the dataset into disjoint train/test splits. + +We compare with the ResNet2TSDF and ResNet2Voxel baselines. Both encode images and directly output 3D shapes in the form of a T-SDF and a voxel grid. We also compare to two state-of-the-art methods for 3D reconstruction, i.e., Pix2Vox [46] and AutoSDF [25]. We evaluate all methods after aligning resolutions to $32^{3}$ voxels. We use Chamfer Distance (CD), and F-score@1% [44] as evaluation metrics. + +Quantitatively, as shown in Table 2, SDFusion outperforms other methods on both metrics. Qualitatively, SDFusion generates 3D shapes that are of higher visual quality and are more visually consistent with the objects shown in the images, regardless of camera poses, as shown in Figure 5. + +# 4.3. Text-guided Generation + +Next, we evaluate 3D shape generation conditioned on text input. For a qualitative comparison, we use the Text2shape dataset [8] that provides descriptions for the 'chair' and 'table' categories in ShapeNet. For a quantitative evaluation, we adopt the ShapeGlot [3] dataset which provides text utterances describing the difference between a target shape and two distractors based on the ShapeNet dataset. We compare SDFusion with AutoSDF, which recently demonstrated state-of-the-art results on the text-guided 3D shape generation task. + +We follow the evaluation pipeline proposed by Shape-Glot [3]. We train a neural evaluator to distinguish the target shape from a distractor given the description. Given two shapes from different methods, the neural evaluator provides a confidence score for each of them based on the binary classification logits. For the absolute difference between two confidence scores $\leq 0.2$ , we count the comparison as confused (conf.). + +As shown in Table 3, SDFusion quantitatively outperforms AutoSDF by a large margin with a low confusion rate. SDFusion also performs better than AutoSDF when compared with ground truth data. Qualitatively, we show + +![](images/f20af8e41c1172832f3b2cbc165790c1f1ba7803502e6863b35bbff3b0f55421.jpg) +Figure 6. Text-guided 3D shape generation. (Top) We compare SDFusion with AutoSDF on the Text2Shape dataset. SDFusion generates shapes with higher quality while conforming to the description. (Bottom) We present more diverse and interesting text-guided generation results from SDFusion. + +![](images/8da77c3219723d65e350b2fd2f3429bd7fb869c29f287c619eb24a388c7ef231.jpg) +Figure 7. Conditional generation from multiple modalities. Here, we present generated samples from joint conditions of (left) partial shape and text and (right) partial shapes and images. The generated results are diverse and consistent with the provided conditions. + +![](images/e3cb3e9356dd8feef7abfb85f3e891191d9bd91b8db7d237389b894688bc2482.jpg) + +in Figure 5 that SDFusion not only generates shapes with better quality, but that the generated shapes are also more diverse. Notably, SDFusion reacts to very specific descriptions like "L-shaped table" and "table with two surfaces." It generates objects of high diversity while remaining faithful to the provided description. + +# 4.4. Multi-conditional Generation + +In addition to the conditional generation tasks which take a single conditioning variable as input, we further demonstrate the efficacy of SDFusion in handling multiple modalities. First, SDFusion can jointly consider multiple conditioning modalities. On the left of Figure 7, we present the diverse generation conditional on both partial shapes and text. On the right of Figure 7, we show that given partial shapes and images, SDFusion can complete the different parts based on images. When there is ambiguity in images + +(e.g., rear-view of chairs), SDFusion can produce diverse predictions. Second, as shown in Figure 8, SDFusion can not only be jointly conditioned on multiple inputs, but a weight can be used to control the importance of the conditioning modalities, enabling more flexible user control. For example, for the left sample in Figure 8, the larger the weight for the input image, the more similar the results are to the shapes in the image. Similarly, the larger the weight for input text, the more "egg-shaped" the results. We envision such a fine-grained form of control to be particularly useful for interactive user applications. + +# 4.5.3D Shape Texturing + +Finally, we showcase an application that uses SDFusion to generate 3D shapes of detailed geometry, and uses a pretrained text-to-image 2D diffusion model [34] to provide textures. As shown in Figure 9, the diffusion model + +![](images/0d894de63d586eb529c60605590324c8c9fdf2e1b3262f8e990263f8bc63d3c2.jpg) +Figure 8. Multiple conditioning variables with weight control. Given a partial shape, an image, and a sentence as conditional input, we show that the model is sensitive to weights that control the importance of different modalities. + +![](images/af1cd8c2902b578633c86bf50cf9759826c84a93a38516105b43ef2ec94b47b6.jpg) +Figure 9. 3D Shape Texturing. We texture the generated 3D shapes with a 2D diffusion model trained on large-scale data. This permits to generate textures from diverse textual inputs, including style and material descriptions. The pipeline can also generate diverse results given the same input description. + +pre-trained on large-scale 2D data can provide semantically meaningful and diverse guidance to texture the 3D shapes. The model shows superior expressiveness to interpret abstract concepts (e.g., Chinese- and Halloween-style) and materials (e.g., gingerbread, cream cheese). Given a single description, the texturing pipeline can also generate diverse results, as shown in the rightmost part of Figure 9. + +# 5. Conclusion + +In this work, we present SDFusion, an attempt to adopt diffusion models to signed distance functions for 3D shape generation. To alleviate the computationally demanding nature of 3D representations, we first encode 3D shapes into an expressive low-dimensional latent space, which we use to train the diffusion model. To enable flexible conditional usage, we adopt class-specific encoders along with a cross-attention mechanism for handling conditions from multiple modalities, and leverage classifier-free guidance to facilitate weight control among modalities. Foreseeing the potential of a collaborative symbiosis between models trained + +on 2D and 3D data, we further demonstrate an application that takes advantage of a pretrained 2D text-to-image model to texture a generated 3D shape. + +Although the results look promising and exciting, there are quite a few future directions for improvement. First, SDFusion is trained on high-quality signed distance function representations. To make the model more general and to enable the use of more diverse data, a model that operates on various 3D representations simultaneously is desirable. Another future direction is related to the diversity of the data: we currently apply SDFusion on object-centric data. 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Most interestingly, our model can combine all these tasks into one swiss-army-knife tool, enabling the user to perform shape generation using incomplete shapes, images, and textual descriptions at the same time, providing the relative weights for each input and facilitating interactivity. Despite our approach being shape-only, we further show an efficient method to texture the generated shape using large-scale text-to-image models." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4456" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 286, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 286, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 286, + 247 + ], + "type": "text", + "content": "Generating 3D assets is a cornerstone of immersive augmented/virtual reality experiences. Without realistic and diverse objects, virtual worlds will look void and engagement will remain low. Despite this need, manually creating and editing 3D assets is a notoriously difficult task, requiring creativity, 3D design skills, and access to sophisticated software with a very steep learning curve. This makes 3D asset creation inaccessible for inexperienced users. Yet, in many cases, such as interior design, users more often than not have a reasonably good understanding of what they want to create. In those cases, an image or a rough sketch is sometimes accompanied by text indicating details of the asset, which are hard to express graphically for an amateur." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 247, + 286, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 286, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 286, + 437 + ], + "type": "text", + "content": "Due to this need, it is not surprising that democratizing the 3D content creation process has become an active research area. Conventional 3D generative models require direct 3D supervision in the form of point clouds [2, 21], signed distance functions (SDFs) [9, 25], voxels [42, 47], etc. Recently, first efforts have been made to explore the learning of 3D geometry from multi-view supervision with known camera poses by incorporating inductive biases via neural rendering techniques [5, 6, 14, 37, 52]. While compelling results have been demonstrated, training is often very time-consuming and ignores available 3D data that can be used to obtain good shape priors. We foresee an ideal collaborative paradigm for generative methods where models trained on 3D data provide detailed and accurate geometry, while models trained on 2D data provide diverse appearances. A first proof of concept is shown in Figure 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "text", + "content": "In our pursuit of flexible and high-quality 3D shape generation, we introduce SDFusion, a diffusion-based generative model with a signed distance function (SDF) under the hood, acting as our 3D representation. Compared to other 3D representations, SDFs are known to represent well high-resolution shapes with arbitrary topology [9, 18, 23, 30]. However, 3D representations are infamous for demanding high computational resources, limiting most existing 3D generative models to voxel grids of " + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "inline_equation", + "content": "32^{3}" + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "text", + "content": " resolution and point clouds of " + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "inline_equation", + "content": "2K" + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "text", + "content": " points. To side-step this issue, we first utilize an auto-encoder to compress 3D shapes into a more compact low-dimensional representation. Because of this, SDFusion can easily scale up to a " + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 47, + 438, + 286, + 713 + ], + "type": "text", + "content": " resolution. To learn the probability distribution over the introduced latent space, we leverage diffusion models, which have recently been used with great success in various 2D generation tasks [4, 19, 22, 26, 35, 40]. Furthermore, we adopt task-specific encoders and a cross-attention [34] mechanism to support multiple conditioning inputs, and apply classifier-free guidance [17] to enable flexible conditioning usage. Because of these strategies, SDFusion can not only use a variety of conditions from multiple modalities, but also adjust their importance weight, as shown in Figure 1. Compared" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "to a recently proposed autoregressive model [25] that also adopts an encoded latent space, SDFusion achieves superior sample quality, while offering more flexibility to handle multiple conditions and, at the same time, features reduced memory usage. With SDFusion, we study the interplay between models trained on 2D and 3D data. Given 3D shapes generated by SDFusion, we take advantage of an off-the-shelf 2D diffusion model [34], neural rendering [24], and score distillation sampling [31] to texture the shapes given text descriptions as conditional variables." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 300 + ], + "type": "text", + "content": "We conduct extensive experiments on the ShapeNet [7], BuildingNet [38], and Pix3D [43] datasets. We show that SDFusion quantitatively and qualitatively outperforms prior work in shape completion, 3D reconstruction from images, and text-to-shape tasks. We further demonstrate the capability of jointly controlling the generative model via multiple conditioning modalities, the flexibility of adjusting relative weight among modalities, and the ability to texture 3D shapes given textual descriptions, as shown in Figure 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 301, + 518, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 301, + 518, + 312 + ], + "spans": [ + { + "bbox": [ + 318, + 301, + 518, + 312 + ], + "type": "text", + "content": "We summarize the main contributions as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 318, + 315, + 545, + 421 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 318, + 315, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 315, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 318, + 315, + 545, + 350 + ], + "type": "text", + "content": "- We propose SDFusion, a diffusion-based 3D generative model which uses a signed distance function as its 3D representation and a latent space for diffusion." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 318, + 350, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 350, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 318, + 350, + 545, + 385 + ], + "type": "text", + "content": "- SDFusion enables conditional generation with multiple modalities, and provides flexible usage by adjusting the weight among modalities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 386, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 386, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 318, + 386, + 545, + 421 + ], + "type": "text", + "content": "- We demonstrate a pipeline to synthesize textured 3D objects benefiting from an interplay between 2D and 3D generative models." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 435, + 391, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 391, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 391, + 447 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 640 + ], + "type": "text", + "content": "3D Generative Models. Different from 2D images, it is less clear how to effectively represent 3D data. Indeed, various representations with different pros and cons have been explored, particularly when considering 3D generative models. For instance, 3D generative models have been explored for point clouds [2, 21], voxel grids [20, 42, 47], meshes [51], signed distance functions (SDFs) [9, 11, 25], etc. In this work, we aim to generate an SDF. Compared to other representations, SDFs exhibit a reasonable tradeoff regarding expressivity, memory efficiency, and direct applicability to downstream tasks. Moreover, conditioning 3D generation of SDFs on different modalities further enables many applications, including shape completion, 3D reconstruction from images, 3D generation from text, etc. The proposed framework can handle these tasks in a single model which makes it different from prior work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "Recently, thanks to the advancement of neural rendering [24], a new stream of research has emerged to learn 3D generation and manipulation from only 2D supervision [1, 5, 6, 28, 37, 39, 41, 49]. We believe the interplay between two streams of work is promising in the foreseeable future." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4457" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 379, + 215 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 379, + 215 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 379, + 215 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 379, + 215 + ], + "type": "image", + "image_path": "b79ce888074a397a7e1cb86c0b09c8499a11d240ff921668c81f1f5469194fc5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 218, + 547, + 252 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 547, + 252 + ], + "type": "text", + "content": "Figure 2. SDFusion Overview. (left) To enable high-resolution generation, we first encode 3D shapes into a latent space, where a diffusion model is trained. Furthermore, to enable flexible conditional generation, we adopt class-specific encoders along with classifier-free guidance to enable multi-modality conditioning. (right) At inference time, we can control the importance of each conditioning modality." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 383, + 71, + 541, + 215 + ], + "blocks": [ + { + "bbox": [ + 383, + 71, + 541, + 215 + ], + "lines": [ + { + "bbox": [ + 383, + 71, + 541, + 215 + ], + "spans": [ + { + "bbox": [ + 383, + 71, + 541, + 215 + ], + "type": "image", + "image_path": "7a57bc53c09b20dd04c441ad31c9d10b319506f2b190e4ff1e6783669307d0d0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 261, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 392 + ], + "type": "text", + "content": "Diffusion Models. Diffusion models have recently emerged as a popular family of generative models with competitive sample quality. In particular, diffusion models have shown impressive quality, diversity, and expressiveness in various tasks such as image synthesis [13,15,16,27], super-resolution [36], image editing [10, 22, 40], text-to-image synthesis [4, 19, 26, 33, 35], etc. In contrast to the flourishing research on diffusion models for 2D data, diffusion models have not yet been fully explored for 3D data. Notable exceptions include attempts to apply diffusion models to point clouds [21, 53]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 288, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 288, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 288, + 464 + ], + "type": "text", + "content": "Differently, in this work, we apply diffusion models on SDF representations. As reasonable resolutions of SDFs are demanding to model, we study the use of a latent diffusion technique [34] and the classifier-free conditional generation mechanism [17], both of which have been shown to yield promising results when being used in 2D diffusion models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 475, + 115, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 115, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 115, + 489 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 495, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 662 + ], + "type": "text", + "content": "We aim at synthesizing 3D shapes using diffusion models. Towards this goal, we model the distribution over 3D shapes " + }, + { + "bbox": [ + 46, + 495, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 495, + 287, + 662 + ], + "type": "text", + "content": ", a volumetric Truncated Signed Distance Field (T-SDF). However, applying diffusion models directly on reasonably high-resolution 3D shapes is computationally very demanding. Therefore, we first compress the 3D shape into a discretized and compact latent space (Section 3.1). This allows us to apply diffusion models in a lower-dimensional space (Section 3.2). The proposed framework can further incorporate various user conditions such as partial shapes, images, and text (Section 3.3). Finally, we showcase an interplay between the proposed framework and diffusion models trained on 2D data to texture 3D shapes (Section 3.4)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 214, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 214, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 214, + 685 + ], + "type": "text", + "content": "3.1. 3D Shape Compression of SDF" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "A 3D shape representation is high-dimensional and thus difficult to model. To make learning of high-resolution 3D" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "text", + "content": "shape distributions via diffusion models feasible, we compress the 3D shape " + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "text", + "content": " into a lower-dimensional yet compact latent space. For this, we leverage a 3D-variant of the Vector Quantised-Variational AutoEncoder (VQ-VAE) [29]. Specifically, the employed 3D VQ-VAE contains an encoder " + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "inline_equation", + "content": "E_{\\varphi}" + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "text", + "content": " to encode the 3D shape into the latent space, and a decoder " + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "inline_equation", + "content": "D_{\\tau}" + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "text", + "content": " to decode the latent vectors back to 3D space. Given an input shape represented via the T-SDF " + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{D \\times D \\times D}" + }, + { + "bbox": [ + 304, + 261, + 547, + 369 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 342, + 374, + 545, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 374, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 342, + 374, + 545, + 388 + ], + "type": "interline_equation", + "content": "\\mathbf {z} = E _ {\\varphi} (\\mathbf {X}), \\quad \\text {a n d} \\quad \\mathbf {X} ^ {\\prime} = D _ {\\tau} (\\mathrm {V Q} (\\mathbf {z})), \\tag {1}", + "image_path": "5419f69ab9fcf774309f39b828a7a57bd4f79fb2d5b421970bd608c25e8f1e4f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\in \\mathbb{R}^{d \\times d \\times d}" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": " is the latent vector, latent dimension " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": " is smaller than 3D shape dimension " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": ", and VQ is the quantization step which maps the latent variable " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": " to the nearest element in the codebook " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": ". The encoder " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "E_{\\varphi}" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": ", decoder " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "D_{\\tau}" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": ", and codebook " + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}" + }, + { + "bbox": [ + 304, + 393, + 546, + 501 + ], + "type": "text", + "content": " are jointly optimized. We pre-train the VQ-VAE with reconstruction loss, commitment loss, and VQ objective, similar to [29] using ShapeNet or BuildingNet data. For more details please see the supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 508, + 479, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 508, + 479, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 508, + 479, + 521 + ], + "type": "text", + "content": "3.2. Latent Diffusion Model for SDF" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "content": "Using the trained encoder " + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "inline_equation", + "content": "E_{\\varphi}" + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "content": ", we can now encode any given SDF into a compact and low-dimensional latent variable " + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = E_{\\varphi}(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "content": ". We can then train a diffusion model on this latent representation. Fundamentally, a diffusion model learns to sample from a target distribution by reversing a progressive noise diffusion process. Given a sample " + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "content": ", we obtain " + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t, t \\in \\{1, \\dots, T\\}" + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "content": " by gradually adding Gaussian noise with a variance schedule. Then we use a time-conditional 3D UNet " + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 526, + 545, + 658 + ], + "type": "text", + "content": " as our denoising model. To train the denoising 3D UNet, we adopt the simplified objective proposed by Ho et al. [15]:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 664, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 664, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 329, + 664, + 545, + 685 + ], + "type": "interline_equation", + "content": "L _ {\\text {s i m p l e}} (\\theta) := \\mathbb {E} _ {\\mathbf {z}, \\epsilon \\sim N (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t) \\| ^ {2} \\right]. \\tag {2}", + "image_path": "f1b46010d1811e043b8d7734423fc1d7b835c258d1d72772eeede31c0c6af544.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "content": "At inference time, we sample " + }, + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{z}}" + }, + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "content": " by gradually denoising a noise variable sampled from the standard normal distribu" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4458" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "tion " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "N(0,1)" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": ", and leverage the trained decoder " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "D_{\\tau}" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " to map the denoised code " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{z}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": " back to a 3D T-SDF shape representation " + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathbf{X}} = D_{\\tau}(\\widehat{\\mathbf{z}})" + }, + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": ", as shown in Figure 2." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 117, + 248, + 131 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 117, + 248, + 131 + ], + "spans": [ + { + "bbox": [ + 47, + 117, + 248, + 131 + ], + "type": "text", + "content": "3.3. Learning the Conditional Distribution" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 136, + 287, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 136, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 136, + 287, + 279 + ], + "type": "text", + "content": "Being able to randomly sample shapes provides limited ability for interaction. Therefore, learning of a conditional distribution is essential for user applications. Importantly, multiple forms of conditional inputs are desirable such that the model can account for various kinds of scenarios. Thanks to the flexible conditional mechanism provided by a latent diffusion model [34], we can incorporate multiple conditional input modalities at once with task-specific encoders " + }, + { + "bbox": [ + 46, + 136, + 287, + 279 + ], + "type": "inline_equation", + "content": "E_{\\phi}" + }, + { + "bbox": [ + 46, + 136, + 287, + 279 + ], + "type": "text", + "content": " and a cross-attention module. To further allow for more flexibility in controlling the distribution, we adopt classifier-free guidance for conditional generation. The objective function reads as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 289, + 286, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 289, + 286, + 322 + ], + "spans": [ + { + "bbox": [ + 48, + 289, + 286, + 322 + ], + "type": "interline_equation", + "content": "L \\left(\\theta , \\left\\{\\phi_ {i} \\right\\}\\right) := \\underset {\\mathbf {z}, \\mathbf {c}, \\epsilon , t} {\\mathbb {E}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{D \\circ E _ {\\phi_ {i}} \\left(\\mathbf {c} _ {i}\\right) \\right\\}\\right) \\| ^ {2} \\right], \\tag {3}", + "image_path": "7405eb590deb31c5193a3b1ea1e9e20fa8321481cbac907b5adf129f88261a51.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "inline_equation", + "content": "E_{\\phi_i}(\\mathbf{c}_i)" + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "content": " is the task-specific encoder for the " + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "content": " modality, " + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "content": " is a dropout operation enabling classifier-free guidance, and " + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "content": " is a feature aggregation function. In this work, " + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 47, + 322, + 286, + 369 + ], + "type": "text", + "content": " refers to a simple concatenation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 371, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 287, + 395 + ], + "type": "text", + "content": "At inference time, given conditions from multiple modalities, we perform classifier-free guidance as follows" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 415, + 287, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 415, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 52, + 415, + 287, + 480 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{E _ {\\phi_ {i}} \\forall i \\right\\}\\right) = \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\emptyset\\right) + \\\\ \\sum_ {i} s _ {i} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, F \\left\\{E _ {\\phi_ {i}} \\left(\\mathbf {c} _ {i}\\right), E _ {\\phi_ {j}} \\left(\\mathbf {c} _ {j}\\right): \\mathbf {c} _ {j} = \\emptyset \\forall j \\neq i \\right\\}\\right) \\right. \\\\ - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}, t, \\emptyset)), \\tag {4} \\\\ \\end{array}", + "image_path": "88ca5eae5db8c2c1b9dcc114d678a46ac738565a51e99b3e69c7a6ad53596cd2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "text", + "content": " denotes the weight of conditions from the " + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "inline_equation", + "content": "i^{\\text{th}}" + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "text", + "content": " modality and " + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\varnothing" + }, + { + "bbox": [ + 46, + 481, + 287, + 529 + ], + "type": "text", + "content": " denotes a condition filled with zeros. Intuitively, modalities with larger weights play more important roles in guiding the conditional generation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 530, + 287, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 637 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 637 + ], + "type": "text", + "content": "In this work, we study SDFusion combined with three conditional modalities applied separately or jointly. For shape completion, given a partial observation of a shape, we perform blended diffusion similar to [4]. For single-view 3D reconstruction, we adopt CLIP [32] as the image encoder. For text-guided 3D generation, we adopt BERT [12] as the text encoder. The encoded features are then used to modulate the diffusion process with cross-attention. Please refer to the supplementary material for more details." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 646, + 243, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 243, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 243, + 659 + ], + "type": "text", + "content": "3.4. 3D Shape Texturing with a 2D Model" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "While sampled 3D data often exhibits compellingly detailed geometry, textures of 3D data are generally more difficult to collect and even more often of limited quality. Here, we explore how to make the best use of 2D data and" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 545, + 183 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 183 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 183 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 183 + ], + "type": "image", + "image_path": "b64a6d4ffe0be1f22b80c79da498ae9421ea6f0ca993f96702db62774161d6ac.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 193, + 545, + 248 + ], + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 248 + ], + "type": "text", + "content": "Figure 3. 3D Shape Texturing. We demonstrate an application where models trained on 2D and 3D data are combined. The shapes generated by SDFusion are converted to a density tensor, then the color information is learned via neural rendering. The gradients are provided by an off-the-shelf 2D diffusion model [34]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 260, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 319 + ], + "type": "text", + "content": "models, so as to aid 3D asset generation. Thanks to the recent success of neural rendering [24] and 2D text-to-image models trained on extremely large-scale data [34], using a 2D model to perform 3D synthesis is made possible with a score distillation sampling technique [31]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": "Here, we illustrate the procedure of texturing a 3D shape given a guiding input sentence " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": ". Starting from a generated T-SDF " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": ", we first convert it to a density tensor " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": " by using VolSDF [50]. Our goal is to learn a 5D radiance field to obtain color " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "F_{\\theta}:(\\mathbf{x},\\mathbf{d})\\rightarrow \\mathbf{c}" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": ", similar to the conventional NeRF [24] setting. However, different from the conventional NeRF setting, the density tensor is fixed. With a sampled camera pose, we can render an image " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": " by alpha-compositing the densities and colors along the rays for each pixel. Then, we distill the knowledge from a pre-trained stable diffusion model [34], denoted as a 2D UNet " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}(\\mathbf{z}_t,t,S)" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": " that predicts the noise at timestep " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": ". The most straightforward way to update " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": " is to obtain and backpropagate gradients all the way from the noise prediction loss term of the stable diffusion loss function to the input. However, the UNet Jacobian term is in practice expensive to compute. Therefore, it was proposed in [31] to bypass the UNet and treat " + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}" + }, + { + "bbox": [ + 304, + 320, + 546, + 536 + ], + "type": "text", + "content": " as a frozen critic providing scores by computing" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 342, + 542, + 545, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 542, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 342, + 542, + 545, + 570 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {t, \\epsilon} \\left[ \\frac {\\partial I \\left(F _ {\\theta} (\\cdot)\\right)}{\\partial \\theta} w (t) \\left(\\tilde {\\epsilon} _ {\\phi} \\left(\\mathbf {z} _ {t}, t, S\\right) - \\epsilon\\right) \\right], \\tag {5}", + "image_path": "318d6f00cdf7454b6f48af89d3fe02f0088e81eee7fc5ae8c46679947ebdec14.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "type": "text", + "content": " is a time-dependent weight function defined in the stable diffusion model. The mechanism is called Score Distillation Sampling. Please refer to [31] for details. The score then provides an update direction to " + }, + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 304, + 575, + 545, + 635 + ], + "type": "text", + "content": ". We illustrate the process in Figure 3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 646, + 387, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 387, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 387, + 659 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "In this section, we conduct extensive qualitative and quantitative experiments to demonstrate the efficacy and generalizability of SDFusion. We evaluate methods on three tasks: shape completion, single-view 3D reconstruction," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4459" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 547, + 403 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 547, + 403 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 547, + 403 + ], + "type": "image", + "image_path": "b864b12fe0495a537e2d28c1c06ed0d6d6e4e3df9dbe89e80d134d567fa9ed33.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 410, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 46, + 410, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 547, + 456 + ], + "type": "text", + "content": "Figure 4. Shape Completion. (Top) We compare SDFusion with AutoSDF [25] and MPC [45] on ShapeNet and BuildingNet data. SDFusion generates shapes of better quality and diversity, while being consistent with the input partial shapes. We convert the generated SDFs from SDFusion and AutoSDF to point clouds to compare with MPC. Please refer to the supplementary materials for SDF comparisons on BuildingNet for better visualization. (Bottom) We present more results on diverse shape completion using various object categories." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 69, + 510, + 264, + 588 + ], + "blocks": [ + { + "bbox": [ + 46, + 462, + 288, + 508 + ], + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 508 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of Shape Completion. We evaluate methods on fidelity (UHD) and diversity (TMD) using the ShapeNet and BuildingNet data. SDFusion outperforms other methods in both metrics, especially diversity." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 510, + 264, + 588 + ], + "lines": [ + { + "bbox": [ + 69, + 510, + 264, + 588 + ], + "spans": [ + { + "bbox": [ + 69, + 510, + 264, + 588 + ], + "type": "table", + "html": "
MethodShapeNetBuildingNet
UHD ↓TMD ↑UHD ↓TMD ↑
MPC [45]0.06270.03030.13500.0467
AutoSDF [25]0.05670.03410.12080.0649
Ours0.05570.08850.11160.0745
", + "image_path": "a76164908b9cd87b6d56752fff9f233fca40d3248ba97192ec2d78fd6ceb3575.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 610, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 287, + 647 + ], + "type": "text", + "content": "and text-guided generation. We then demonstrate two additional use cases: multi-conditional generation and 3D shape texturing." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 157, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 157, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 157, + 671 + ], + "type": "text", + "content": "4.1. Shape Completion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "We evaluate the shape completion task on the ShapeNet [7] and the BuildingNet [38] datasets. ShapeNet is a large-scale 3D CAD model dataset with 16 common" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 354, + 499, + 496, + 584 + ], + "blocks": [ + { + "bbox": [ + 305, + 463, + 545, + 495 + ], + "lines": [ + { + "bbox": [ + 305, + 463, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 545, + 495 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation of single-view reconstruction. We evaluate methods on the Pix3D dataset using Chamfer Distance and F-Score. We outperform other methods in both metrics." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 354, + 499, + 496, + 584 + ], + "lines": [ + { + "bbox": [ + 354, + 499, + 496, + 584 + ], + "spans": [ + { + "bbox": [ + 354, + 499, + 496, + 584 + ], + "type": "table", + "html": "
MethodCD ↓F-Score ↑
Pix2Vox [46]3.0010.385
ResNet2TSDF4.5820.351
ResNet2Voxel4.6700.357
AutoSDF [25]2.2670.415
Ours1.8520.432
", + "image_path": "f3b88be92d04ea231c9b7c0de5da3bc83ece6af9f5100c51ad61bb3e204a8413.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "object classes. We use the train/test splits provided by Xu et al. [48]. BuildingNet is a new large-scale 3D building model dataset. Compared to objects in ShapeNet, building models provide more geometric details and thus require higher resolution for representing the data. Hence, we use an SDF of " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "64^{3}" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " resolution for ShapeNet, and a " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "128^{3}" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " resolution for BuildingNet. For both datasets, we compare the completion quantitatively by providing the bottom half of the ground truth shape as input, and evaluating the com" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4460" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 57, + 545, + 208 + ], + "blocks": [ + { + "bbox": [ + 48, + 57, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 48, + 57, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 48, + 57, + 545, + 208 + ], + "type": "image", + "image_path": "4982631dedb466d6b1c3968e6522c15001f4e05dcda8a624c4f622cd09a78d58.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 216, + 546, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 546, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 546, + 240 + ], + "type": "text", + "content": "Figure 5. Single-view 3D Reconstruction. (Top) We qualitatively compare all methods on the Pix3D dataset. SDFusion generates shapes with the best visual quality. (Bottom) Here we present more reconstruction results from SDFusion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 331, + 274, + 388 + ], + "blocks": [ + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation of text-guided generation. We compare the proposed SDFusion method, AutoSDF, and real data using a pretrained neural evaluator on the ShapeGlot dataset. " + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "text", + "content": " denotes the neural evaluator preference rate for the target " + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "inline_equation", + "content": "P(\\mathrm{Tr})" + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "text", + "content": " or the distractor " + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "inline_equation", + "content": "P(\\mathrm{Dis})" + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "text", + "content": ". If the preference is too close (" + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\leq 0.2" + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "text", + "content": "), we count the comparison as confused (conf.). Rows sum to " + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 255, + 287, + 321 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 331, + 274, + 388 + ], + "lines": [ + { + "bbox": [ + 56, + 331, + 274, + 388 + ], + "spans": [ + { + "bbox": [ + 56, + 331, + 274, + 388 + ], + "type": "table", + "html": "
Target (Tr)Distractor (Dis)P(Tr)P(Dis)P(conf.)
OursAutoSDF [25]49%36%15%
OursGT33%45%22%
AutoSDF [25]GT30%49%21%
", + "image_path": "81462bbcbcf7833c1c0d9d88fc3da001f7e6c8310f69b2bdff14057fd7a4c42d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 403, + 232, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 232, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 232, + 415 + ], + "type": "text", + "content": "pleted shapes generated by different methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "text", + "content": "We compare SDFusion to the state-of-the-art point cloud completion method MPC [45] and the autoregressive SDF generation method AutoSDF [25]. We adopt metrics from MPC [45]. For each partial shape, we generate " + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "text", + "content": " complete shapes. To evaluate completion fidelity, we measure the Unidirectional Hausdorff Distance (UHD) between partial shapes and generated shapes. To evaluate completion diversity, we measure the Total Mutual Difference (TMD) by computing the average Chamfer distance among " + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "text", + "content": " generated shapes. We use " + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 46, + 415, + 287, + 534 + ], + "type": "text", + "content": " in the experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 536, + 287, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 631 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 631 + ], + "type": "text", + "content": "As shown in Table 1, the proposed SDFusion performs favorably compared to all methods in the completion fidelity metric, and outperforms the baselines substantially in completion diversity. The advantages of fidelity and diversity are also apparent in Figure 4. Especially on the BuildingNet dataset, SDFusion shows its advantages in modeling high-resolution and diverse data. AutoSDF and MPC struggle to model the distribution correctly." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 638, + 214, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 638, + 214, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 638, + 214, + 651 + ], + "type": "text", + "content": "4.2. Single-view 3D Reconstruction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Next, we assess 3D shape reconstruction from a single image on the real-world benchmark Pix3D [43] dataset. We use the provided train/test splits on the chair category. In the absence of official splits for other categories, we randomly split the dataset into disjoint train/test splits." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 256, + 545, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 352 + ], + "type": "text", + "content": "We compare with the ResNet2TSDF and ResNet2Voxel baselines. Both encode images and directly output 3D shapes in the form of a T-SDF and a voxel grid. We also compare to two state-of-the-art methods for 3D reconstruction, i.e., Pix2Vox [46] and AutoSDF [25]. We evaluate all methods after aligning resolutions to " + }, + { + "bbox": [ + 304, + 256, + 545, + 352 + ], + "type": "inline_equation", + "content": "32^{3}" + }, + { + "bbox": [ + 304, + 256, + 545, + 352 + ], + "type": "text", + "content": " voxels. We use Chamfer Distance (CD), and F-score@1% [44] as evaluation metrics." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 353, + 545, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 423 + ], + "type": "text", + "content": "Quantitatively, as shown in Table 2, SDFusion outperforms other methods on both metrics. Qualitatively, SDFusion generates 3D shapes that are of higher visual quality and are more visually consistent with the objects shown in the images, regardless of camera poses, as shown in Figure 5." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 434, + 440, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 440, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 440, + 445 + ], + "type": "text", + "content": "4.3. Text-guided Generation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 568 + ], + "type": "text", + "content": "Next, we evaluate 3D shape generation conditioned on text input. For a qualitative comparison, we use the Text2shape dataset [8] that provides descriptions for the 'chair' and 'table' categories in ShapeNet. For a quantitative evaluation, we adopt the ShapeGlot [3] dataset which provides text utterances describing the difference between a target shape and two distractors based on the ShapeNet dataset. We compare SDFusion with AutoSDF, which recently demonstrated state-of-the-art results on the text-guided 3D shape generation task." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 664 + ], + "type": "text", + "content": "We follow the evaluation pipeline proposed by Shape-Glot [3]. We train a neural evaluator to distinguish the target shape from a distractor given the description. Given two shapes from different methods, the neural evaluator provides a confidence score for each of them based on the binary classification logits. For the absolute difference between two confidence scores " + }, + { + "bbox": [ + 304, + 570, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\leq 0.2" + }, + { + "bbox": [ + 304, + 570, + 545, + 664 + ], + "type": "text", + "content": ", we count the comparison as confused (conf.)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "As shown in Table 3, SDFusion quantitatively outperforms AutoSDF by a large margin with a low confusion rate. SDFusion also performs better than AutoSDF when compared with ground truth data. Qualitatively, we show" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4461" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 57, + 545, + 299 + ], + "blocks": [ + { + "bbox": [ + 47, + 57, + 545, + 299 + ], + "lines": [ + { + "bbox": [ + 47, + 57, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 57, + 545, + 299 + ], + "type": "image", + "image_path": "f20af8e41c1172832f3b2cbc165790c1f1ba7803502e6863b35bbff3b0f55421.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 310, + 546, + 343 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 546, + 343 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 546, + 343 + ], + "type": "text", + "content": "Figure 6. Text-guided 3D shape generation. (Top) We compare SDFusion with AutoSDF on the Text2Shape dataset. SDFusion generates shapes with higher quality while conforming to the description. (Bottom) We present more diverse and interesting text-guided generation results from SDFusion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 349, + 294, + 459 + ], + "blocks": [ + { + "bbox": [ + 53, + 349, + 294, + 459 + ], + "lines": [ + { + "bbox": [ + 53, + 349, + 294, + 459 + ], + "spans": [ + { + "bbox": [ + 53, + 349, + 294, + 459 + ], + "type": "image", + "image_path": "8da77c3219723d65e350b2fd2f3429bd7fb869c29f287c619eb24a388c7ef231.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 477, + 546, + 502 + ], + "lines": [ + { + "bbox": [ + 46, + 477, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 546, + 502 + ], + "type": "text", + "content": "Figure 7. Conditional generation from multiple modalities. Here, we present generated samples from joint conditions of (left) partial shape and text and (right) partial shapes and images. The generated results are diverse and consistent with the provided conditions." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 306, + 349, + 541, + 458 + ], + "blocks": [ + { + "bbox": [ + 306, + 349, + 541, + 458 + ], + "lines": [ + { + "bbox": [ + 306, + 349, + 541, + 458 + ], + "spans": [ + { + "bbox": [ + 306, + 349, + 541, + 458 + ], + "type": "image", + "image_path": "e3cb3e9356dd8feef7abfb85f3e891191d9bd91b8db7d237389b894688bc2482.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 510, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 583 + ], + "type": "text", + "content": "in Figure 5 that SDFusion not only generates shapes with better quality, but that the generated shapes are also more diverse. Notably, SDFusion reacts to very specific descriptions like \"L-shaped table\" and \"table with two surfaces.\" It generates objects of high diversity while remaining faithful to the provided description." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 590, + 208, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 208, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 208, + 601 + ], + "type": "text", + "content": "4.4. Multi-conditional Generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "In addition to the conditional generation tasks which take a single conditioning variable as input, we further demonstrate the efficacy of SDFusion in handling multiple modalities. First, SDFusion can jointly consider multiple conditioning modalities. On the left of Figure 7, we present the diverse generation conditional on both partial shapes and text. On the right of Figure 7, we show that given partial shapes and images, SDFusion can complete the different parts based on images. When there is ambiguity in images" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 510, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 643 + ], + "type": "text", + "content": "(e.g., rear-view of chairs), SDFusion can produce diverse predictions. Second, as shown in Figure 8, SDFusion can not only be jointly conditioned on multiple inputs, but a weight can be used to control the importance of the conditioning modalities, enabling more flexible user control. For example, for the left sample in Figure 8, the larger the weight for the input image, the more similar the results are to the shapes in the image. Similarly, the larger the weight for input text, the more \"egg-shaped\" the results. We envision such a fine-grained form of control to be particularly useful for interactive user applications." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 650, + 424, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 650, + 424, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 650, + 424, + 662 + ], + "type": "text", + "content": "4.5.3D Shape Texturing" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Finally, we showcase an application that uses SDFusion to generate 3D shapes of detailed geometry, and uses a pretrained text-to-image 2D diffusion model [34] to provide textures. As shown in Figure 9, the diffusion model" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4462" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 61, + 532, + 261 + ], + "blocks": [ + { + "bbox": [ + 60, + 61, + 532, + 261 + ], + "lines": [ + { + "bbox": [ + 60, + 61, + 532, + 261 + ], + "spans": [ + { + "bbox": [ + 60, + 61, + 532, + 261 + ], + "type": "image", + "image_path": "0d894de63d586eb529c60605590324c8c9fdf2e1b3262f8e990263f8bc63d3c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 271, + 546, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 271, + 546, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 546, + 293 + ], + "type": "text", + "content": "Figure 8. Multiple conditioning variables with weight control. Given a partial shape, an image, and a sentence as conditional input, we show that the model is sensitive to weights that control the importance of different modalities." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 297, + 545, + 411 + ], + "blocks": [ + { + "bbox": [ + 48, + 297, + 545, + 411 + ], + "lines": [ + { + "bbox": [ + 48, + 297, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 48, + 297, + 545, + 411 + ], + "type": "image", + "image_path": "af1cd8c2902b578633c86bf50cf9759826c84a93a38516105b43ef2ec94b47b6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 420, + 546, + 453 + ], + "lines": [ + { + "bbox": [ + 46, + 420, + 546, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 546, + 453 + ], + "type": "text", + "content": "Figure 9. 3D Shape Texturing. We texture the generated 3D shapes with a 2D diffusion model trained on large-scale data. This permits to generate textures from diverse textual inputs, including style and material descriptions. The pipeline can also generate diverse results given the same input description." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 466, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 287, + 550 + ], + "type": "text", + "content": "pre-trained on large-scale 2D data can provide semantically meaningful and diverse guidance to texture the 3D shapes. The model shows superior expressiveness to interpret abstract concepts (e.g., Chinese- and Halloween-style) and materials (e.g., gingerbread, cream cheese). Given a single description, the texturing pipeline can also generate diverse results, as shown in the rightmost part of Figure 9." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 565, + 119, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 565, + 119, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 119, + 577 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 713 + ], + "type": "text", + "content": "In this work, we present SDFusion, an attempt to adopt diffusion models to signed distance functions for 3D shape generation. To alleviate the computationally demanding nature of 3D representations, we first encode 3D shapes into an expressive low-dimensional latent space, which we use to train the diffusion model. To enable flexible conditional usage, we adopt class-specific encoders along with a cross-attention mechanism for handling conditions from multiple modalities, and leverage classifier-free guidance to facilitate weight control among modalities. Foreseeing the potential of a collaborative symbiosis between models trained" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 466, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 466, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 466, + 545, + 502 + ], + "type": "text", + "content": "on 2D and 3D data, we further demonstrate an application that takes advantage of a pretrained 2D text-to-image model to texture a generated 3D shape." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 502, + 546, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 546, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 546, + 644 + ], + "type": "text", + "content": "Although the results look promising and exciting, there are quite a few future directions for improvement. First, SDFusion is trained on high-quality signed distance function representations. To make the model more general and to enable the use of more diverse data, a model that operates on various 3D representations simultaneously is desirable. Another future direction is related to the diversity of the data: we currently apply SDFusion on object-centric data. It is interesting to apply the model to more challenging scenarios (e.g., entire 3D scenes). Finally, we believe there is room to further explore how to combine models trained on 2D and 3D data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 646, + 547, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 646, + 547, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 646, + 547, + 694 + ], + "type": "text", + "content": "Acknowledgements: Work supported in part by NSF under Grants 2008387, 2045586, 2106825, MRI 1725729, and NIFA award 2020-67021-32799. Thanks to NVIDIA for providing a GPU for debugging." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4463" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Rameen Abdal, Hsin-Ying Lee, Peihao Zhu, Menglei Chai, Aliaksandr Siarohin, Peter Wonka, and Sergey Tulyakov. 3davatargan: Bridging domains for personalized editable avatars. 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However, humans and some animals have bilateral symmetry and various orientations, which lead to severe mispredictions of symmetrical parts. Besides, point cloud noise disrupts consistent representations for point cloud and thus degrades the shape correspondence accuracy. To address the above issues, we propose a Self-Ensembling ORientation-aware Network termed SE-ORNet. The key of our approach is to exploit an orientation estimation module with a domain adaptive discriminator to align the orientations of point cloud pairs, which significantly alleviates the mispredictions of symmetrical parts. Additionally, we design a self-ensembling framework for unsupervised point cloud shape correspondence. In this framework, the disturbances of point cloud noise are overcome by perturbing the inputs of the student and teacher networks with different data augmentations and constraining the consistency of predictions. Extensive experiments on both human and animal datasets show that our SE-ORNet can surpass state-of-the-art unsupervised point cloud shape correspondence methods.", + "bbox": [ + 76, + 340, + 473, + 675 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 698, + 209, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the cost of LiDAR and depth cameras falling, it is more accessible to obtain 3D point cloud data. For real-world applications, such as articulated motion transfer [5, 26] and non-rigid human body alignment [3], the correspondence between two point clouds is indispensable. However, we are hard to directly obtain the correspondence between two raw point clouds due to various object orientations and un unified coordinate systems.", + "bbox": [ + 75, + 724, + 468, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To accurately find the point-to-point correspondence be", + "bbox": [ + 96, + 847, + 467, + 862 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/727df288c26d4f6dd287d6590efcad369bbe008afbe8eb4f57d3608c4ab39b1c.jpg", + "image_caption": [ + "Figure 1. The visualization of dense point matching results. Three point cloud pairs have different relative rotation angles. GT denotes ground truth. The correspondence is visualized by transferring colors from source to target according to matching results. The baseline predicts many false matches, especially for symmetrical, similar parts of the object. Our method achieves accurate matches for these parts with our orientation estimation module." + ], + "image_footnote": [], + "bbox": [ + 555, + 316, + 834, + 477 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tween two point clouds, spectral-based methods [1, 9, 15, 19, 28] have been proven as practical shape correspondence methods by computing functional mapping between the projected features and learning a transformation for the correspondence. Nevertheless, the spectral-based methods suffer from complicated pre-processing steps and the necessity for connectivity information between points. With the rapid development of deep learning, many fully supervised point cloud shape correspondence methods [4, 8, 16] have been proposed to lead to remarkable progress. However, these methods rely on a large amount of carefully annotated point cloud pairs, which are expensive and time-consuming to collect. To relieve the annotation cost of fully supervised methods, unsupervised methods [12, 32] that utilize unlabeled data for model training have attracted more and more attention. CorrNet3D [32] proposes the first unsupervised deep learning framework for building dense correspondence between point clouds in an end-to-end manner. DPC [12] models the local point cloud structure by exploring the proximity of points using DGCNN [29] and designs reconstruction losses to extract continuous point cloud rep", + "bbox": [ + 496, + 583, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 1, + 807, + 21 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 323, + 16, + 722, + 30 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 31, + 754, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution", + "bbox": [ + 94, + 875, + 205, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Corresponding Author", + "bbox": [ + 96, + 887, + 222, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5364", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "resentations. However, in the scanning process of 3D scanner, due to light, vibration and other factors, point cloud noise will be inevitably generated. Meanwhile, the preprocessing of point cloud (such as random subsampling) will also introduce noise. Unfortunately, the previous methods fail to adequately consider the point cloud noise, which negatively impacts the point cloud representations. Besides the noise, existing methods lack attention to symmetrical parts of the body. The mismatching issue of symmetrical parts is challenging in this task, which was also spotted by the previous method [32] but has yet to be solved.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By studying the previous point-based shape correspondence methods [4, 8, 12, 16, 32], we summarize two key issues that need consideration to achieve a more accurate shape correspondence: 1) How to overcome the disturbance of point cloud noise to get robust and consistent point cloud representations? Point cloud noise perturbs the spatial coordinates of point cloud and interferes with local structure modeling. Therefore, it is necessary to overcome noise disturbances. 2) How to solve the mismatching issue of symmetrical parts in point clouds with different body orientations? As shown in Figure 1, for the pair of bilaterally symmetrical human point clouds facing the opposite directions, existing methods predict the completely reverse and seriously wrong point cloud correspondence due to the similar structure and position. The specific relative rotation angles lead to severe mispredictions of symmetrical parts.", + "bbox": [ + 75, + 261, + 472, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve the above goals, we propose a Self-Ensembling Orientation-aware Network (SE-ORNet) for unsupervised point cloud shape correspondence. We integrate orientation modeling and consistent point cloud representations under a unified self-ensembling framework, which consists of a pair of teacher and student models, an orientation estimation module, and an adaptive domain discriminator. Firstly, we design a new augmentation scheme to produce augmented samples with rotation and Gaussian noise, and record the rotation angles as rotation angle labels. Then, we formulate soft labels and consistency losses to encourage consensus among ensemble predictions of augmented and raw samples, aiming to perceive the difference in body orientation and overcome the point cloud noise disturbance to obtain consistent point cloud representations. In addition, we design a plug-and-play lightweight Orientation Estimation Module, which aligns the orientations of two point clouds to solve the mismatching issue of symmetrical parts in point clouds. Without the real label of relative rotation angle between the source and target, we supervise the training with the rotation angle labels and calculate angle losses. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. Therefore, we design a discriminator to achieve domain adaptation and calculate the domain losses. Furthermore, the discriminator facilitates the Orientation Estima", + "bbox": [ + 75, + 508, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion Module to mine the valuable knowledge in the rotation-augmented samples to compensate for the information loss of the real relative rotation angles.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the main contributions of this work are as follows: (i) We design a plug-and-play lightweight Orientation Estimation Module that accurately aligns the orientations of point cloud pairs to achieve correct matching results of symmetrical parts. (ii) We integrate point cloud orientation modeling and consistent point cloud representation learning with the disturbance of point cloud noise into a unified self-ensembling framework. (iii) Our method attains state-of-the-art performance on both human and animal benchmarks, and extensive experimental results verify the superiority of our designs.", + "bbox": [ + 496, + 136, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 316, + 640, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this Section, we give a brief overview of related works on point cloud shape correspondence, including learning on point clouds, shape correspondence, and self-ensembling approaches.", + "bbox": [ + 496, + 340, + 890, + 400 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning on Point Clouds. PointNet [21] learns from global information through multi-layer perceptrons and max-pooling operation. PointNet++ [22] devises a hierarchical architecture that recursively partitions the point cloud to extract local features more effectively. Recent works explore local aggregators via relations [23, 31, 33], and graphs [29, 34]. PointCNN [13] transforms neighboring points to the canonical order to apply traditional convolution on point clouds. DGCNN [29] creates a graph in the feature space and designs EdgeConv [29] to learn the edge features of the graph in each layer. However, the methods are commonly based on some assumptions of implicit local geometry, which may result in sensitivity to point cloud disturbances.", + "bbox": [ + 496, + 402, + 892, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Shape Correspondence. As an active research area in computer vision and graphics, point cloud shape correspondence methods roughly include spectral-based methods [1,9,15,19,28] and point-based methods [4,8,12,16,32]. Spectral-based methods require connectivity information to compute the LBO eigenvectors as basis functions and infer a linear transformation for shape correspondence. However, with regard to point cloud data, connectivity information is difficult to obtain directly while point-based methods directly process point clouds without connectivity information to find the dense point-to-point mapping between two point clouds with deformable 3D shapes. Deprelle et al. [4] propose representing shapes as the deformation and combination of learnable elementary 3D structures. Groueix et al. [8] employ an encoder-decoder architecture to obtain and constrain the similarity matrix with manually annotated labels. The deep learning methods train their neural networks in a data-driven manner and improve performance to a large extent. However, manually labeling the point-to-point cor", + "bbox": [ + 496, + 613, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5365", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d9fd6cf8db6c168bb7a930a5232fec6ff9b6b2b5b0aee730b3505306a20e1c3c.jpg", + "image_caption": [ + "Figure 2. The overview of our self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. $X_{s}$ is generated from the raw source point cloud $X$ by random rotation and Gaussian noise, while $Y_{s}$ is only augmented by Gaussian noise. We design the Orientation Estimation Module to estimate the rotation $\\theta$ of the source with respect to the target and align the point cloud in position space. Afterward, the aligned point cloud pairs are input to the teacher and student models, respectively, and the correspondence is predicted through a DGCNN backbone. Finally, we supervise the student model by the consistency losses and the construction losses, and the teacher model updates the parameters using the exponential moving average (EMA) strategy. The gradient reversal layer (GRL) acts as the identity function during forward propagation, but is multiplied by -1 during backward propagation." + ], + "image_footnote": [], + "bbox": [ + 178, + 85, + 789, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "respondence between two point clouds in 3D space takes much time and effort. Therefore, some unsupervised point cloud shape correspondence methods [12, 32] are proposed to reduce the overhead of labeling. CorrNet3D [32] is the first unsupervised deep learning framework. DPC [12] designs several reconstruction losses to smooth point cloud representations. Due to the lack of annotation, the mismatching issue of symmetrical parts in point clouds with different orientations has become an undeniable problem in unsupervised shape correspondence area.", + "bbox": [ + 75, + 402, + 470, + 553 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Self-ensembling Approaches. Self-ensembling approaches improve the model generalization by encouraging consensus among ensemble predictions of unknown samples with small perturbations. $\\Gamma$ model [24] consists of two identical parallel branches that respectively take raw images and corrupted images as inputs. In contrast to $\\Gamma$ model, $\\Pi$ model [11] integrates two parallel branches into a single branch. As an extension of the $\\Pi$ model, the temporal model [11] forces the consistency between the outputs and the aggregated outputs over previous training epochs. Mean Teacher [27] replaces network prediction average with network parameter average via the exponential moving average (EMA) strategy. We design a framework similar to Mean Teacher and adapt it for the unsupervised point cloud shape correspondence task. The proposed framework facilitates the network to yield consistent and accurate predictions under noise perturbations and orientation rotations.", + "bbox": [ + 75, + 554, + 468, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 821, + 166, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 847, + 186, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The unsupervised point cloud shape correspondence is to find the mapping $f: X \\to Y$ between two point clouds", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "source $X$ and target $Y$ ) without ground-truth correspondence annotations. Figure 2 illustrates the pipeline of our approach. Given source $X$ and target $Y$ point clouds, we utilize random rotation and Gaussian noise to generate the augmented source point cloud $X_{s}$ , while we augment $Y$ by Gaussian noise to obtain $Y_{s}$ . Due to the absence of the relative rotation angle labels $\\theta, \\theta_{s}$ , we use the rotation angle labels $\\theta_{x}$ to guide the Orientation Estimation Module learning and transfer the valuable information by the adversarial domain adaptation method. The aligned point cloud pairs are input to the teacher and student models, respectively, and we use the DGCNN [29] backbone to output the similarity matrices. After that, we generate two reconstructed point clouds $\\hat{X}, \\hat{Y}$ based on the predicted similarity matrices by the student model. Finally, the student model is supervised by the consistency losses and the construction losses, while the parameters of teacher model are updated by the exponential moving average (EMA) strategy.", + "bbox": [ + 496, + 402, + 890, + 675 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Orientation Estimation", + "text_level": 1, + "bbox": [ + 500, + 691, + 714, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We provide the overview of the orientation estimation in Figure 3. The encoded features $P_{in}^{s}, P_{in}^{t}$ are fed into the Feature Interaction Module (FIM) for feature fusion. The fused features $P_{out}$ are enhanced by a single-layer edge-conv. To predict the relative orientation, the features $\\hat{P}_{in}$ are fed into the classification head. We also input $\\hat{P}_{in}$ into the discriminator to determine whether the pair comes from the same shape or from different shapes.", + "bbox": [ + 496, + 717, + 890, + 837 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature Interaction Module. As shown in Figure 4, the feature interaction module is a query-based graph convolution. The point features in the source point cloud are updated by querying points with similar features in the tar", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5366", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/44d0a37bd76cc1df63782fcd1b61dc6db626a3c04e7ab9cc6f3aa0a770590a0c.jpg", + "image_caption": [ + "Figure 3. The overview of Orientation Estimation." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 455, + 195 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "get point cloud. Let $P_{in}^{s}, P_{in}^{t}$ be the inputs of the feature interaction module. For each point $p_i \\in P_{in}^{s}$ , we first consider it as a query to search for the k-nearest neighbors $q_i^j, 1 \\leq j \\leq k$ in the target point cloud $P_{in}^{t}$ with respect to the Euclidean distance defined in the $C_1$ -dimensional feature space. To better model the relative rotation relationships in space, we use spatial position differences and feature differences as features of each edge, denoted as $(p_i, q_i^j - p_i)$ , where $p_i, q_i^j \\in \\mathcal{R}^{(C_1 + 3)}$ . Then we use a multilayer perceptron (MLP) to compute a new feature $e_{ji} = \\mathrm{MLP}(p_i, q_i^j - p_i)$ from each edge. For each point, we aggregate its k edge features into a new point feature through Max pooling and ReLU activation. In addition, we add a linear layer that skip-connects the output $P_{out}$ with the input to make the block residual.", + "bbox": [ + 75, + 220, + 468, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Rotation Classification Head. We concatenate the output feature $P_{out}$ and the enhanced feature as the input $\\hat{P}_{in}$ of the Rotation Classification Head. Inspired by the orientation prediction in the point cloud detection methods [18,20], we consider the prediction of relative rotation angle as a classification task. That coarsely aligning the orientations of the source and target point clouds is enough to solve the problem of mismatching issue of symmetrical parts in point clouds. Thus, we pre-define $M$ equally divided angle bins and then use an MLP head to classify the relative rotation angle into those pre-defined categories. Specifically, we compress $\\hat{P}_{in}$ using maximum pooling and average pooling to obtain the global features and then predict the probability distribution of the relative rotation angle. Finally, we choose the angle bin with the highest probability as the relative rotation angle of the source and target point clouds.", + "bbox": [ + 75, + 450, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Adversarial Domain Adaptation. Due to the absence of relative rotation angle $\\theta, \\theta_s$ , we utilize the relative rotation angle $\\theta_x$ to guide the Orientation Estimation Module learning. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. To eliminate the domain gap, we use a discriminator to identify whether the input features $\\hat{P}_{in}$ of the classification head are from the rotation-augmented samples or the real samples. Specifically, we use a PointNet-like module to process the features $\\hat{P}_{in}$ and predict the probability $d_i$ that the $P_{in}$ is from the real samples:", + "bbox": [ + 75, + 695, + 468, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} = \\mathrm {M L P} _ {2} \\left\\{\\max _ {N} \\left\\{\\mathrm {M L P} _ {1} \\left[ \\hat {P} _ {i n} \\right] \\right\\} \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 876, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c792e900c6dcd405a7afb923cfea4111281dffffb55c9242941222192ab1d51b.jpg", + "image_caption": [ + "Figure 4. The Feature Interaction Module (FIM)." + ], + "image_footnote": [], + "bbox": [ + 581, + 88, + 808, + 170 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where max refers to the global Max pooling. By using the discriminator, we train the model to disregard the distinction between the two domains and instead prioritize learning the relative rotation information.", + "bbox": [ + 498, + 191, + 890, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relative Rotation Angle Supervision. The angle loss is computed with a cross entropy loss:", + "bbox": [ + 498, + 252, + 890, + 282 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a n g l e}} = - \\sum_ {i = 1} ^ {M} \\theta_ {x} ^ {i} \\log \\left(\\hat {\\theta} _ {x} ^ {i}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 292, + 890, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M$ is the number of the pre-defined angle bins, $\\hat{\\theta}_x^i$ and $\\theta_x^i$ denote the predicted probability distribution of relative rotation angle and the rotation angle label, respectively. The domain loss is computed with a Focal Loss [14]:", + "bbox": [ + 498, + 345, + 890, + 406 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d o m a i n}} = - \\left(1 - d _ {i}\\right) ^ {\\gamma} \\log \\left(d _ {i}\\right), \\gamma > 1, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 417, + 890, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{domain}$ denotes the domain loss and $\\gamma$ denotes the tunable focusing parameter.", + "bbox": [ + 498, + 445, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Self-Ensembling Framework", + "text_level": 1, + "bbox": [ + 500, + 484, + 756, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Table 7, the point cloud orientation and Gaussian noise are two crucial factors in the unsupervised point cloud shape correspondence task. The existing methods ignore noise interference on the point cloud correspondence, making it difficult to obtain robust point cloud representations. To address the above problems, we utilize the Mean Teacher architecture [27] and design two consistency losses to constrain the student model for robust feature representations under orientation disturbance and Gaussian noise interference.", + "bbox": [ + 496, + 507, + 890, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Stochastic Transform. We apply stochastic transformations that include rotation and Gaussian noise on the point clouds for the student network formulated as $\\tau = (\\mathcal{R},\\mathcal{N})$ . More specifically, given the raw point cloud pair $(X,Y)$ , we first apply Gaussian noise to the target point cloud $Y$ :", + "bbox": [ + 496, + 657, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {i} ^ {s} = y _ {i} + n _ {i}, n _ {i} \\sim \\mathcal {N} (0, \\sigma^ {2}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 744, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(0,\\sigma^2)$ means the Gaussian distribution with the 0 mean and $\\sigma$ standard deviation. Then, we utilize Gaussian noise and random rotation along the vertical $z$ -axis to augment the source point cloud $X$ :", + "bbox": [ + 496, + 771, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {i} ^ {s} = \\mathcal {R} \\left(\\theta_ {x}\\right) \\odot x _ {i} + n _ {i}, n _ {i} \\sim \\mathcal {N} \\left(0, \\sigma^ {2}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 842, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{R}$ denotes the rotation around the $z$ -axis and $\\theta_{x}$ is the rotation angle sampled from $[0, 2\\pi]$ .", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5367", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Architecture of Teacher & Student Models. Given the raw and augmented point cloud pairs $(X,Y)$ , $(X_s,Y_s)$ , we use the Orientation Estimation Module to align source and target orientations. Then, our approach follows the Mean Teacher paradigm [27] and inputs the aligned point cloud pairs $(\\tilde{X}_s,Y_s)$ , $(\\tilde{X},Y)$ into the student and teacher models, respectively. We use a variant of DGCNN [29] backbone to embed the aligned source $\\tilde{X}$ and target $Y$ point clouds to a high-dimensional feature space as $F_x,F_y\\in \\mathcal{R}^{N\\times C}$ . Unlike DGCNN, which uses dynamic graphs to select neighbors, we follow [12] to use static graphs for the neighbors. Specifically, we select the k-nearest neighbors in the coordinate space instead of the feature space. Then, we use the cosine similarity $S_{xy}$ of source and target point features $F_x,F_y$ to measure their correspondence.", + "bbox": [ + 76, + 90, + 472, + 318 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i j} = \\frac {F _ {x} ^ {i} \\cdot \\left(F _ {y} ^ {j}\\right) ^ {T}}{\\| F _ {x} ^ {i} \\| _ {2} \\| F _ {y} ^ {j} \\| _ {2}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 328, + 468, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $F_x^i, F_y^j$ are the $i^{\\text{th}}$ and $j^{\\text{th}}$ rows of $F_x, F_y$ , respectively, and $(\\cdot)^T$ denotes a transpose operation.", + "bbox": [ + 76, + 377, + 468, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Soft Label & Consistency Loss. To enhance the perception of local structures and the robustness of the model, we design two consistency losses to maintain feature consistency under Gaussian noise and orientation disturbances. We utilize the cross-similarity $S_{xy}^{t}$ obtained from the teacher model as a soft label and the Smooth $L_{1}$ loss to constrain the cross-similarities $S_{x_s y_s}^s$ of the student model:", + "bbox": [ + 76, + 409, + 468, + 517 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c c s} = \\operatorname {S m o o t h} L _ {1} \\left(S _ {x y} ^ {t}, S _ {x _ {s} y _ {s}} ^ {s}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 527, + 468, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{ccs}$ denotes the consistency loss of the cross-similarities. To reduce the interference of point cloud orientation on correspondence estimation, we model the feature consistency of the strongly augmented source $X_{s}$ and raw source $X$ . We constrain the consistency of the self-similarities $S_{xx}$ to ensure the consistency of neighboring points with similar features. We use the feature embedding $F_{x}$ of the source point cloud to compute the self-similarity $S_{xx}$ by Equation (6). Then, we use the Smooth $L_{1}$ loss to constrain the self-similarities $S_{x_s x_s}^s$ of the student model with the self-similarities $S_{xx}^{t}$ from the teacher model:", + "bbox": [ + 76, + 556, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c s s} = \\operatorname {S m o o t h} L _ {1} \\left(S _ {x x} ^ {t}, S _ {x _ {s} x _ {s}} ^ {s}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 733, + 468, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{css}}$ denotes the consistency loss of the self-similarities. The above two consistency losses ensure the robustness of feature embedding under Gaussian noise and orientation disturbances for accurate correspondence.", + "bbox": [ + 76, + 762, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Model Training & Inference", + "text_level": 1, + "bbox": [ + 76, + 832, + 330, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to the above mentioned consistency losses, angle loss, and domain loss, we use reconstruction losses to promote a unique point matching between the shape pair.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following the previous work [12], we perform the cross-construction operation to construct the target shape $\\hat{Y}$ by using the feature similarity $S_{xy}$ between source and target point clouds, and the target point coordinates $Y$ as follows:", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {\\mathcal {Y}} (x _ {i})} \\frac {e ^ {s _ {i j}}}{\\sum l \\in \\mathcal {N} _ {\\mathcal {Y}} (x _ {i}) e ^ {s _ {i l}}} y _ {j}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 159, + 890, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_{\\mathcal{Y}}(x_i)$ is latent k-nearest neighbors of $x_{i}$ in the target $Y$ . When the source and target point clouds are identical, we refer to the construction operation as selfconstruction. As shown in Figure 2, we obtain the point clouds $\\hat{Y}_s^x,\\hat{X}_s^x,\\hat{X}_s^y,\\hat{Y}_s^y$ by cross-construction and selfconstruction. Then, we constrain the training with the construction loss as follows:", + "bbox": [ + 496, + 207, + 890, + 311 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o n s}} = \\lambda_ {c c} \\left(\\mathrm {C D} \\left(Y _ {s}, \\hat {Y} _ {s} ^ {x}\\right) + \\mathrm {C D} \\left(X _ {s}, \\hat {X} _ {s} ^ {y}\\right)\\right) \\tag {10} \\\\ + \\lambda_ {s c} \\left(\\mathrm {C D} \\left(Y _ {s}, \\hat {Y} _ {s} ^ {y}\\right) + \\mathrm {C D} \\left(X _ {s}, \\hat {X} _ {s} ^ {x}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 320, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{cc},\\lambda_{sc}$ are hyperparameters and CD means the Chamfer Distance. Finally, we add a regularization term to correspond close points in the source to close points in the target.", + "bbox": [ + 496, + 369, + 890, + 429 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {n o r m}} = \\sum_ {i} \\sum_ {l \\in \\mathcal {N} _ {\\mathcal {Y}} \\left(x _ {i}\\right)} e ^ {\\left\\| x _ {i} - x _ {l} \\right\\| _ {2} ^ {2} / \\alpha} \\| \\hat {y} _ {x _ {i}} - \\hat {y} _ {x _ {l}} \\| _ {2} ^ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 438, + 890, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_{\\mathcal{Y}}(x_i)$ is the same as defined in Equation 9 and $\\alpha$ is a hyperparameter. To sum up, the total loss of our unsupervised point cloud shape correspondence method is:", + "bbox": [ + 496, + 481, + 890, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c c s}} + \\lambda_ {2} \\mathcal {L} _ {\\text {c s s}} + \\lambda_ {3} \\mathcal {L} _ {\\text {a n g l e}} \\tag {12} \\\\ + \\lambda_ {4} \\mathcal {L} _ {\\text {d o m a i n}} + \\mathcal {L} _ {\\text {c o n s}} + \\lambda_ {5} \\mathcal {L} _ {\\text {n o r m}}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 537, + 890, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{i}$ is a hyperparameter, balancing the contribution of different loss terms. During inference, we set the closest point $y_{j}^{*}$ in the feature space for each point $x_{i}$ as its corresponding point. This selection rule can be formulated as:", + "bbox": [ + 496, + 580, + 890, + 642 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf \\left(x _ {i}\\right) = y _ {j ^ {*}}, j ^ {*} = \\underset {j} {\\operatorname {a r g m a x}} \\left(s _ {i j}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 651, + 890, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 686, + 633, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 710, + 689, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. To demonstrate the effectiveness and generalization of our method, we perform experiments on human and animal datasets. We conduct experiments on human datasets according to DPC's [12] scheme. For the large-scale dataset, we randomly downsample the SURREAL [8] dataset, which contains 230000 training shapes, into 2000 shape pairs as the training set. For the test set, we use the SHREC'19 [17] dataset, which contains 44 real human models, and pair them into 430 annotated test examples. To further verify the ability of our method to learn discriminative feature expression with a small data size, we train", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5368", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SE-ORNet on the pairs randomly sampled from 44 SHREC instances, and the testing is still conducted on the official 430 SHREC'19 pairs.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For animal datasets, we also conduct experiments with different dataset scales. We use the large-scale SMAL [35] dataset and TOSCA [2] dataset as the training set and test set, respectively. SMAL dataset consists of parameterized models of various animals, and we randomly sample SMAL to obtain the corresponding shape pairs as the training set. TOSCA is generated by deforming three template meshes (human, dog, and horse) into multiple poses. We pair the 41 animal figures in TOSCA from the same category to form a training set of 260 samples and a test set of 286 samples. Because the number of points in different shapes varies, we make a random downsample of the original point cloud to a fixed number $n = 1024$ , as done in CorrNet3D [32].", + "bbox": [ + 75, + 136, + 468, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. The evaluation metrics include the average correspondence error and the correspondence accuracy. Based on the Euclidean-based measure, the average correspondence error is defined for a pair of source and target shapes $(X,Y)$ as follows:", + "bbox": [ + 75, + 332, + 468, + 407 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\ne r r = \\frac {1}{n} \\sum_ {x _ {i} \\in X} \\| f (x _ {i}) - y _ {g t} \\| _ {2}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 165, + 419, + 468, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $y_{gt} \\in Y$ is the ground-truth matching point to $x_{i}$ . The unit is centimeter(cm). And the correspondence accuracy can be formulated as:", + "bbox": [ + 75, + 465, + 468, + 510 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {a c c} (\\epsilon) = \\frac {1}{n} \\sum_ {x _ {i} \\in X} \\mathbb {I} \\left(\\left\\| f \\left(x _ {i}\\right) - y _ {g t} \\right\\| _ {2} < \\epsilon d\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 111, + 520, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbb{I}(\\cdot)$ is the indicator function, $d$ is the maximal Euclidean distance between points in $Y$ , and $\\epsilon \\in [0,1]$ is an error tolerance.", + "bbox": [ + 75, + 568, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. For a fair comparison with existing methods [12, 32], we use the same DGCNN [29] backbone with four EdgeConv blocks as the feature extractor in the self-ensembling framework. The standard deviation $\\sigma$ in Equation (4) is set as 0.1 for human datasets and 0.15 for animal datasets. In the Orientation Estimation Module, the feature encoding module is a simplified DGCNN with three EdgeConv [29] blocks whose layer output sizes are 64, 128, and 256. The $k$ of k-NN is set as 24, and the slope of all LeakyReLU is 0.2. We feed the output of the last layer into the proposed feature interaction module with the output size 256. Then we refine the feature by an EdgeConv layer with the same output size. The angle classification head consists of three Linear-BN-ReLU and an Output Linear. The channels are 256, 128, and 128 for the three Linear-BN-ReLU. The last Linear outputs the probability for classification. We set the number of bins $M$ as 8 in the angle classification head, where each bin represents a range of $45^{\\circ}$ . The domain discriminator is a PointNet-like", + "bbox": [ + 75, + 613, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/26012345ab2853711dedf6fe133b2d6a28af08ff995ac9c6d302df1f0b9fb3ad.jpg", + "table_caption": [ + "Table 1. Comparison on SHREC and SURREAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result." + ], + "table_footnote": [], + "table_body": "
MethodInputSHRECSURREAL
acc ↑err ↓acc ↑err ↓
Diff-FMaps [16]Point//4.0%7.1
3D-CODED [8]Point//2.1%8.1
Elementary [4]Point//2.3%7.6
CorrNet3D [32]Point0.4%33.86.0%6.9
DPC [12]Point15.3%5.617.7%6.1
OursPoint17.5%5.121.5%4.6
", + "bbox": [ + 514, + 148, + 874, + 260 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/107a83b25ce13f5d2525a9db379c9eefe94efa4280ee007a26dcef9240ccc411.jpg", + "image_caption": [ + "Figure 5. Correspondence accuracy at various error tolerances for human datasets. The methods are trained on the SHREC or SURREAL dataset and evaluated on SHREC'19 test pairs. Compared with other methods, our approach achieves an impressive performance improvement." + ], + "image_footnote": [], + "bbox": [ + 542, + 266, + 841, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "module consisting of two MLPs in Equation (1). The channels of $\\mathrm{MLP}_1$ are 512, 256, and 128, while the channels of $\\mathrm{MLP}_2$ are 256, 128, and 256. We follow [12] and use a neighborhood size $k = 10$ in Equation (9) and (11). $\\lambda_{c}c$ and $\\lambda_{s}c$ in Equation (10) are set as 1 and 10, respectively. $\\lambda_1$ , $\\lambda_2$ , $\\lambda_3$ , $\\lambda_4$ , and $\\lambda_5$ in Equation (12) are set as 0.1, 0.1, 1.0, 0.8, and 1.0, respectively.", + "bbox": [ + 498, + 489, + 890, + 597 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison on Human Datasets", + "text_level": 1, + "bbox": [ + 500, + 604, + 785, + 621 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a fair comparison with existing methods, we do not use any post-processing or additional connectivity information. In addition, we follow DPC [12] and train our model on the SURREAL and SHREC datasets, respectively. Then we test our model on the official 430 SHREC'19 pairs.", + "bbox": [ + 496, + 628, + 890, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on SHREC dataset. As shown in Table 1, our approach shows significant performance improvements on the SHREC benchmark and achieves new SOTA performance by $2.2\\%$ improvements in accuracy and 0.5 reductions in error. To show the improvement under different error tolerances, we present the correspondence accuracy for point-based methods trained on SHREC and evaluated on the SHREC'19 test set. As shown in Figure 5, our method achieves better results with different error tolerances.", + "bbox": [ + 496, + 704, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cross-dataset Generalization. In Table 1 and Figure 5, we also report the comparison with other methods on the SURREAL benchmark. The models are trained on the SURREAL dataset and evaluated on the SHREC'19 test", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5369", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6e503290434487ad61e5fa206cdc9f498bd7ed578727dea3d3d90ee1c614b9c2.jpg", + "table_caption": [ + "Table 2. Comparison on TOSCA and SMAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result." + ], + "table_footnote": [], + "table_body": "
MethodTOSCASMAL
acc ↑err ↓acc ↑err ↓
3D-CODED [8]//0.5%19.2
Elementary [4]//0.5%13.7
CorrNet3D [32]0.3%32.75.3%9.8
DPC [12]34.7%2.833.2%5.8
Ours38.2%2.736.4%3.9
", + "bbox": [ + 117, + 148, + 426, + 246 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6f11d9c1729f333741605711ea606ddd67eb2e681e4d3aab894d93ad39fe994.jpg", + "image_caption": [ + "Figure 6. Correspondence accuracy at various error tolerances for animal datasets. The methods are trained on the TOSCA or SMAL dataset and evaluated on the official TOSCA test pairs. Compared with other methods, our method achieves a desirable performance improvement." + ], + "image_footnote": [], + "bbox": [ + 119, + 248, + 421, + 395 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "set. The large-scale training set of the SURREAL dataset helps the deep learning-based methods perform better, even though there is a domain gap between the SURREAL and SHREC datasets. With our proposed method, the correspondence accuracy reaches $21.5\\%$ at an error tolerance of 0.01, and the average correspondence error is reduced to 4.6 on the SHREC'19 test set.", + "bbox": [ + 75, + 472, + 468, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Comparison on Animal Datasets", + "text_level": 1, + "bbox": [ + 76, + 588, + 362, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the adaptability of our method to point clouds of different shapes, we conduct experiments on two animal benchmarks. Similar to human datasets, we train our method on TOSCA and SMAL datasets respectively, and test on the TOSCA test dataset. Table 2 and Figure 6 show the competitive results on TOSCA and SMAL benchmarks. Our method achieves a $3.5\\%$ accuracy improvement on the TOSCA benchmark and a $3.2\\%$ accuracy improvement on the SMAL benchmark. Compared with the human datasets, the animal datasets have various shapes with aligned orientations. Thus, the above performance gains come mainly from our self-ensembling framework, which can learn reliable features on complex data. To verify the effect of the Orientation Estimation Module, we test our method and baseline using different augmented test sets in Section 4.6.", + "bbox": [ + 75, + 611, + 470, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison on Real-world Dataset", + "text_level": 1, + "bbox": [ + 76, + 847, + 383, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CMU Panoptic [10] is a dataset of scanned point clouds of human subjects in various poses, containing noise, out", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a7ba02fc1cf56ea80256635f14ff12d1a0f292c064d0a754f38ed654cd0c8b70.jpg", + "table_caption": [ + "Table 3. Comparison on CMU-Panoptic benchmark. Here, err means average Euclidean keypoint error (cm)." + ], + "table_footnote": [], + "table_body": "
3D-CODED [8]DIF-Net [25]CorrNet [32]IFMatch [7]Ours
err17.115.314.88.53.2
", + "bbox": [ + 503, + 116, + 885, + 141 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8c28718a10be7afb816e055ec150779210815971d61a02fdf59512e6bad5632a.jpg", + "table_caption": [ + "Table 4. Comparison on SHREC'20 benchmark. The training dataset is indicated in the bracket." + ], + "table_footnote": [], + "table_body": "
MethodSHREC’20 [SURREAL]SHREC’20 [SMAL]
acc ↑err ↓acc ↑err ↓
DPC [12]25.0%3.224.5%7.5
Ours29.9%1.225.4%2.9
", + "bbox": [ + 506, + 167, + 879, + 217 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/035dcf8e24dae9e6eb9c9448bfb76c18bae76d2076c28eb99474a2443e9b98f9.jpg", + "table_caption": [ + "Table 5. Evaluation of the model with different designs on SURREAL. $\\mathcal{L}_{css}$ is the consistency loss of the self-similarities, $\\mathcal{L}_{ccs}$ is the consistency loss of the cross-similarities, $\\tau$ means the stochastic transform, OEM means we use the Orientation Estimation Module, FIM is the Feature Interaction Module, and DAM is the Domain Adaptation Module." + ], + "table_footnote": [], + "table_body": "
τLccsLcssOEMFIMDAMSURREAL
acc ↑err ↓
XXXXXX17.7%6.1
✓✓XXXX18.8%5.7
✓✓✓XXX19.2%5.6
✓✓✓✓XX19.5%5.5
✓✓✓✓✓X20.4%5.1
✓✓✓✓✓✓21.5%4.6
", + "bbox": [ + 519, + 305, + 864, + 417 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "liers, occlusions, and clutter. Meanwhile, SHREC'20 [6] dataset contains real scans of various four-legged animal models. As shown in Table 3 and Table 4, we provide the results under two real scan datasets, demonstrating the remarkable robustness of our model to noise.", + "bbox": [ + 496, + 429, + 890, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 513, + 653, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation of the model with different designs. In this section, we perform extensive ablation studies on the SUR-REAL dataset to evaluate the effectiveness of each design. Table 5 demonstrates the performance of the model with different designs. Specifically, the first line is the results of DPC [12], which is our baseline model. The second row indicates that the self-ensembling framework with a stochastic transform achieves a better performance than the original model. By using $\\mathcal{L}_{\\mathrm{css}}$ to constrain the consistency of source features before and after augmentation, the correspondence accuracy can be improved by $0.4\\%$ , as shown in the third row. As shown in the fourth row, adding the Orientation Evaluation Module without the Feature Interaction Module and the Domain Adaptation Module, the performance has a slight improvement. In the fifth row, by introducing the Feature Interaction Module into the Orientation Evaluation Module, the correspondence accuracy can be improved by $0.9\\%$ . Finally, after utilizing the Domain Adaptation Module, the correspondence accuracy is improved by $1.1\\%$ .", + "bbox": [ + 496, + 537, + 890, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of the Self-Ensembling Framework. As shown in Table 6, we modify the self-ensembling framework to show the effect of each designed component. Removing either of the consistency losses leads to a drop in performance, which indicates that constraining the student net", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5370", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/185b76f2ccef2739dd01d8045563154cc7705f9f1ede96008e1250c8143dfd36.jpg", + "table_caption": [ + "Table 6. Effect of the Self-Ensembling Framework on SUR-REAL. Here, we modify the self-ensembling framework to show the effect of each designed component. $\\mathcal{N}$ means Gaussian noise, and $\\mathcal{R}$ means random rotation along the vertical $z$ -axis." + ], + "table_footnote": [], + "table_body": "
SURREALw/o LCssw/o LCSSw/o Nw/o R
acc ↑19.9%20.3%20.6%18.8%
err ↓5.35.14.95.7
", + "bbox": [ + 104, + 148, + 439, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9af870379442b70c6ec5cb5a4da8714704fd5c240ada4666e4eb254c5e26de3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 145, + 208, + 189, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/43d48cf8e3210133edaf3ff8a62692fc822dcda86c1258efa00448fc15686316.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 207, + 256, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8c75a687ddac695771fcb316940078991edd48363a1dd26002d8326d2f93b868.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 214, + 325, + 261 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9f3a63e70db2efbeab97bcaf8fe9abc6b5e0b7ae257d482921280962f36dc9f6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 210, + 411, + 267 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93a16187dbed881f24cb220f26392f50b841e2668ccc8418f44ce3165dcfdfea.jpg", + "image_caption": [ + "图1-2", + "" + ], + "image_footnote": [], + "bbox": [ + 143, + 268, + 184, + 318 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b16d5cc372bb6aa502aed4c346e5564a64e66ea220c99c32694da03e41470de5.jpg", + "image_caption": [ + "Source", + "" + ], + "image_footnote": [], + "bbox": [ + 225, + 267, + 245, + 320 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9aaa9fba9bc3cce6dd83f86eb3e28655883754fe4701b43774fe9819f2e78359.jpg", + "image_caption": [ + "Source(K)" + ], + "image_footnote": [], + "bbox": [ + 285, + 267, + 326, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bb9fd3dcb1f990be42da66d386179e8d860706cc245c66bcebfb3bcf84080075.jpg", + "image_caption": [ + "1. Probability distribution", + "Figure 7. Effect of the Orientation Estimation Module. We visualize of the point clouds before and after orientation rectification on SHREC'19 test set. We denote the raw source point cloud as Source and the rectified one as Source(R). Besides, we provide the probability distributions of the relative rotation angle prediction." + ], + "image_footnote": [], + "bbox": [ + 339, + 267, + 410, + 324 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/14c9f496f20b71cf50250a038add92a61161f70cf53ff73d922609e93c6aae99.jpg", + "table_caption": [ + "Table 7. Robustness Analysis. To verify the robustness of our method, we test our method and baselines using different augmented test sets. $\\mathcal{N}$ means Gaussian noise with standard deviation $\\sigma$ of 0.1 and $\\mathcal{R}$ means random rotation along the vertical $z$ -axis." + ], + "table_footnote": [], + "table_body": "
NRSURREAL(B)SURREALSMAL(B)SMAL
acc ↑err ↓acc ↑err ↓acc ↑err ↓acc ↑err ↓
XX17.47%6.3021.55%4.6533.79%5.7836.39%3.88
✓X14.38%8.7421.55%4.6630.21%6.0636.15%3.92
X✓8.99%9.3317.59%5.819.98%12.2428.16%5.63
✓✓7.80%11.2817.58%5.799.54%12.8027.60%5.89
", + "bbox": [ + 86, + 460, + 452, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "work with soft labels facilitates the consistency of the point cloud representations. When Gaussian noise and rotation augmentation are removed, the model performances show different degrees of degradation. The above experiments illustrate our self-ensemble method can obtain a more robust feature representation of the point cloud through data augmentation and consistency losses.", + "bbox": [ + 75, + 561, + 468, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the Orientation Estimation Module. To verify the effect of the proposed Orientation Estimation Module, we visualize the point clouds after orientation rectification and the probability distributions of the relative rotation angle predictions. As shown in Figure 7, our method can accurately estimate the relative rotation angle and align the point cloud orientation of the source with that of the target. More results refer to the supplementary materials.", + "bbox": [ + 75, + 669, + 468, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Robustness Analysis", + "text_level": 1, + "bbox": [ + 76, + 801, + 267, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To verify the robustness of our method, we use different augmentations on the test set. As shown in Table 7, we use Gaussian noise and random rotation for data augmentation of the test sets. Compared to our method, the baseline shows a significant performance decrease for test sets", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/050575b18857d86d97de0f7bf204533e93e651e5fed83a4c174b2b2bc313e10a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 560, + 73, + 602, + 135 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2309a5aa0f7f10e54ac65fa66727f89727438a886dada8b8f19f1279e0c7e1be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 83, + 681, + 135 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2baf8af0858b491fe4b6500825569d562cfbcadeecd83e787ebd13f3e85c0cc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 83, + 754, + 135 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db1001576d9ab054d99c0b623f88a6c539c08e4b65cee6f141a08e7fc95af7ea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 83, + 826, + 135 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7164318afdeea78dc97c8758295f13040827a62709bcb35a220e3e302fe4aabd.jpg", + "image_caption": [ + "Target" + ], + "image_footnote": [], + "bbox": [ + 560, + 141, + 599, + 203 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8884cf7ef63990b0459385d0a8cabbb47c2d41ec5bbeb912a6c950126a682d1e.jpg", + "image_caption": [ + "Source (Baseline)", + "Figure 8. Visualization of the correspondence results with rotation augmentation. With rotation augmentation on point cloud pairs, the baseline shows regrettable performances, while our method still retains desirable performances." + ], + "image_footnote": [], + "bbox": [ + 625, + 151, + 679, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cbd6a061659981308461c44d11f46630624985d0e88e407e805d8d72ca6458f4.jpg", + "image_caption": [ + "Source (Ours)" + ], + "image_footnote": [], + "bbox": [ + 700, + 152, + 753, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/413bcd26e99af84e0a06d200187d1be072dcfd7d67efdb7b5b5bc2bd315dc2fb.jpg", + "image_caption": [ + "Source (GT)" + ], + "image_footnote": [], + "bbox": [ + 774, + 152, + 826, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/401b3c9691120e65b4e245645387c967f5e7d23cfb377b3a1b7881a7c5fcbaac.jpg", + "image_caption": [ + "Figure 9. Visualization of point cloud pairs with deformations on real scanned Owlii dataset. In each pair, the left one is the source and the right one is the target." + ], + "image_footnote": [], + "bbox": [ + 542, + 287, + 609, + 345 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ecc06dfcda3ba40ed71fe2e4d7797419c2e43fe4b430cffe839e8bcf379559f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 617, + 287, + 681, + 345 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e1555c591551d5d7278c6edad92ee38a02f6dcdaea66029dd660984f773e566c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 287, + 767, + 345 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/129a0867a825bc653c4ff06bc3b8f2a0ca40635194d4e924196fdaa906604732.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 777, + 287, + 846, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "with Gaussian noise. For test sets with random rotation, the baseline performance is greatly degraded, while our method retains an acceptable performance. Figure 8 shows that our SE-ORNet can handle the orientation inconsistency issue of source and target well. To further verify the robustness and generalization of our method, we conduct experiments on the real scanned Owlii dataset [30] and present the visualization in Figure 9. The results show that our SE-ORNet trained on the synthetic SURREAL dataset still produces impressive performance on the real scanned dataset, demonstrating strong generalization and robustness.", + "bbox": [ + 496, + 405, + 890, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 599, + 617, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. To the best of our knowledge, SE-ORNet is the first self-ensembling network in this area. To solve the mismatching issue of symmetrical parts in point clouds with different body orientations, we design a plug-and-play lightweight orientation estimation module to align the orientations of two point clouds. Extensive experiments conducted on four shape correspondence benchmarks demonstrate the superior performance of SE-ORNet.", + "bbox": [ + 496, + 630, + 890, + 781 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 810, + 686, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 12150007) and National Defense Basic Scientific Research program of China (Grant JCKY2020903B002).", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5371", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 6365-6373, 2017. 6" + ], + "bbox": [ + 78, + 90, + 468, + 556 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5373", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SE-ORNet_ Self-Ensembling Orientation-Aware Network for Unsupervised Point Cloud Shape Correspondence/94ea60f5-77d0-47dc-8f2c-3fe79d2f954a_model.json b/2023/SE-ORNet_ Self-Ensembling Orientation-Aware Network for Unsupervised Point Cloud Shape Correspondence/94ea60f5-77d0-47dc-8f2c-3fe79d2f954a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f9ae0e1f6d5807fe0a11f9a86f769c7d214cb690 --- /dev/null +++ b/2023/SE-ORNet_ Self-Ensembling Orientation-Aware Network for Unsupervised Point Cloud Shape Correspondence/94ea60f5-77d0-47dc-8f2c-3fe79d2f954a_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.022 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.325, + 0.017, + 0.723, + 0.031 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.032, + 0.755, + 0.047 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.131, + 0.892, + 0.177 + ], + "angle": 0, + "content": "SE-ORNet: Self-Ensembling Orientation-aware Network for Unsupervised Point Cloud Shape Correspondence" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.203, + 0.917, + 0.223 + ], + "angle": 0, + "content": "Jiacheng Deng\\(^{1,\\ast}\\), Chuxin Wang\\(^{1,\\ast}\\), Jiahao Lu\\(^{1}\\), Jianfeng He\\(^{1}\\), Tianzhu Zhang\\(^{1,3,\\dagger}\\), Jiyang Yu\\(^{2}\\), Zhe Zhang\\(^{3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.224, + 0.857, + 0.24 + ], + "angle": 0, + "content": "1University of Science and Technology of China, 2China Academy of Space Technology, 3Deep Space Exploration Lab" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.242, + 0.817, + 0.257 + ], + "angle": 0, + "content": "{dengjc,wcx0602,lujiahao,hejf}@mail.ustc.edu.cn，tzzhang@ustc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.317, + 0.26, + 0.684, + 0.275 + ], + "angle": 0, + "content": "yujiyang@spacechina.com, cnclepsz@126.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.342, + 0.474, + 0.676 + ], + "angle": 0, + "content": "Unsupervised point cloud shape correspondence aims to obtain dense point-to-point correspondences between point clouds without manually annotated pairs. However, humans and some animals have bilateral symmetry and various orientations, which lead to severe mispredictions of symmetrical parts. Besides, point cloud noise disrupts consistent representations for point cloud and thus degrades the shape correspondence accuracy. To address the above issues, we propose a Self-Ensembling ORientation-aware Network termed SE-ORNet. The key of our approach is to exploit an orientation estimation module with a domain adaptive discriminator to align the orientations of point cloud pairs, which significantly alleviates the mispredictions of symmetrical parts. Additionally, we design a self-ensembling framework for unsupervised point cloud shape correspondence. In this framework, the disturbances of point cloud noise are overcome by perturbing the inputs of the student and teacher networks with different data augmentations and constraining the consistency of predictions. Extensive experiments on both human and animal datasets show that our SE-ORNet can surpass state-of-the-art unsupervised point cloud shape correspondence methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.699, + 0.21, + 0.715 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.846 + ], + "angle": 0, + "content": "With the cost of LiDAR and depth cameras falling, it is more accessible to obtain 3D point cloud data. For real-world applications, such as articulated motion transfer [5, 26] and non-rigid human body alignment [3], the correspondence between two point clouds is indispensable. However, we are hard to directly obtain the correspondence between two raw point clouds due to various object orientations and un unified coordinate systems." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.848, + 0.468, + 0.863 + ], + "angle": 0, + "content": "To accurately find the point-to-point correspondence be" + }, + { + "type": "image", + "bbox": [ + 0.557, + 0.317, + 0.836, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.48, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Figure 1. The visualization of dense point matching results. Three point cloud pairs have different relative rotation angles. GT denotes ground truth. The correspondence is visualized by transferring colors from source to target according to matching results. The baseline predicts many false matches, especially for symmetrical, similar parts of the object. Our method achieves accurate matches for these parts with our orientation estimation module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.903 + ], + "angle": 0, + "content": "tween two point clouds, spectral-based methods [1, 9, 15, 19, 28] have been proven as practical shape correspondence methods by computing functional mapping between the projected features and learning a transformation for the correspondence. Nevertheless, the spectral-based methods suffer from complicated pre-processing steps and the necessity for connectivity information between points. With the rapid development of deep learning, many fully supervised point cloud shape correspondence methods [4, 8, 16] have been proposed to lead to remarkable progress. However, these methods rely on a large amount of carefully annotated point cloud pairs, which are expensive and time-consuming to collect. To relieve the annotation cost of fully supervised methods, unsupervised methods [12, 32] that utilize unlabeled data for model training have attracted more and more attention. CorrNet3D [32] proposes the first unsupervised deep learning framework for building dense correspondence between point clouds in an end-to-end manner. DPC [12] models the local point cloud structure by exploring the proximity of points using DGCNN [29] and designs reconstruction losses to extract continuous point cloud rep" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.207, + 0.888 + ], + "angle": 0, + "content": "*Equal Contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.223, + 0.9 + ], + "angle": 0, + "content": "†Corresponding Author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.223, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5364" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "resentations. However, in the scanning process of 3D scanner, due to light, vibration and other factors, point cloud noise will be inevitably generated. Meanwhile, the preprocessing of point cloud (such as random subsampling) will also introduce noise. Unfortunately, the previous methods fail to adequately consider the point cloud noise, which negatively impacts the point cloud representations. Besides the noise, existing methods lack attention to symmetrical parts of the body. The mismatching issue of symmetrical parts is challenging in this task, which was also spotted by the previous method [32] but has yet to be solved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.473, + 0.504 + ], + "angle": 0, + "content": "By studying the previous point-based shape correspondence methods [4, 8, 12, 16, 32], we summarize two key issues that need consideration to achieve a more accurate shape correspondence: 1) How to overcome the disturbance of point cloud noise to get robust and consistent point cloud representations? Point cloud noise perturbs the spatial coordinates of point cloud and interferes with local structure modeling. Therefore, it is necessary to overcome noise disturbances. 2) How to solve the mismatching issue of symmetrical parts in point clouds with different body orientations? As shown in Figure 1, for the pair of bilaterally symmetrical human point clouds facing the opposite directions, existing methods predict the completely reverse and seriously wrong point cloud correspondence due to the similar structure and position. The specific relative rotation angles lead to severe mispredictions of symmetrical parts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To achieve the above goals, we propose a Self-Ensembling Orientation-aware Network (SE-ORNet) for unsupervised point cloud shape correspondence. We integrate orientation modeling and consistent point cloud representations under a unified self-ensembling framework, which consists of a pair of teacher and student models, an orientation estimation module, and an adaptive domain discriminator. Firstly, we design a new augmentation scheme to produce augmented samples with rotation and Gaussian noise, and record the rotation angles as rotation angle labels. Then, we formulate soft labels and consistency losses to encourage consensus among ensemble predictions of augmented and raw samples, aiming to perceive the difference in body orientation and overcome the point cloud noise disturbance to obtain consistent point cloud representations. In addition, we design a plug-and-play lightweight Orientation Estimation Module, which aligns the orientations of two point clouds to solve the mismatching issue of symmetrical parts in point clouds. Without the real label of relative rotation angle between the source and target, we supervise the training with the rotation angle labels and calculate angle losses. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. Therefore, we design a discriminator to achieve domain adaptation and calculate the domain losses. Furthermore, the discriminator facilitates the Orientation Estima" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "tion Module to mine the valuable knowledge in the rotation-augmented samples to compensate for the information loss of the real relative rotation angles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.895, + 0.304 + ], + "angle": 0, + "content": "In summary, the main contributions of this work are as follows: (i) We design a plug-and-play lightweight Orientation Estimation Module that accurately aligns the orientations of point cloud pairs to achieve correct matching results of symmetrical parts. (ii) We integrate point cloud orientation modeling and consistent point cloud representation learning with the disturbance of point cloud noise into a unified self-ensembling framework. (iii) Our method attains state-of-the-art performance on both human and animal benchmarks, and extensive experimental results verify the superiority of our designs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.317, + 0.642, + 0.334 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.401 + ], + "angle": 0, + "content": "In this Section, we give a brief overview of related works on point cloud shape correspondence, including learning on point clouds, shape correspondence, and self-ensembling approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.893, + 0.612 + ], + "angle": 0, + "content": "Learning on Point Clouds. PointNet [21] learns from global information through multi-layer perceptrons and max-pooling operation. PointNet++ [22] devises a hierarchical architecture that recursively partitions the point cloud to extract local features more effectively. Recent works explore local aggregators via relations [23, 31, 33], and graphs [29, 34]. PointCNN [13] transforms neighboring points to the canonical order to apply traditional convolution on point clouds. DGCNN [29] creates a graph in the feature space and designs EdgeConv [29] to learn the edge features of the graph in each layer. However, the methods are commonly based on some assumptions of implicit local geometry, which may result in sensitivity to point cloud disturbances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Shape Correspondence. As an active research area in computer vision and graphics, point cloud shape correspondence methods roughly include spectral-based methods [1,9,15,19,28] and point-based methods [4,8,12,16,32]. Spectral-based methods require connectivity information to compute the LBO eigenvectors as basis functions and infer a linear transformation for shape correspondence. However, with regard to point cloud data, connectivity information is difficult to obtain directly while point-based methods directly process point clouds without connectivity information to find the dense point-to-point mapping between two point clouds with deformable 3D shapes. Deprelle et al. [4] propose representing shapes as the deformation and combination of learnable elementary 3D structures. Groueix et al. [8] employ an encoder-decoder architecture to obtain and constrain the similarity matrix with manually annotated labels. The deep learning methods train their neural networks in a data-driven manner and improve performance to a large extent. However, manually labeling the point-to-point cor" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5365" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.179, + 0.086, + 0.79, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.894, + 0.397 + ], + "angle": 0, + "content": "Figure 2. The overview of our self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. \\( X_{s} \\) is generated from the raw source point cloud \\( X \\) by random rotation and Gaussian noise, while \\( Y_{s} \\) is only augmented by Gaussian noise. We design the Orientation Estimation Module to estimate the rotation \\( \\theta \\) of the source with respect to the target and align the point cloud in position space. Afterward, the aligned point cloud pairs are input to the teacher and student models, respectively, and the correspondence is predicted through a DGCNN backbone. Finally, we supervise the student model by the consistency losses and the construction losses, and the teacher model updates the parameters using the exponential moving average (EMA) strategy. The gradient reversal layer (GRL) acts as the identity function during forward propagation, but is multiplied by -1 during backward propagation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.404, + 0.471, + 0.554 + ], + "angle": 0, + "content": "respondence between two point clouds in 3D space takes much time and effort. Therefore, some unsupervised point cloud shape correspondence methods [12, 32] are proposed to reduce the overhead of labeling. CorrNet3D [32] is the first unsupervised deep learning framework. DPC [12] designs several reconstruction losses to smooth point cloud representations. Due to the lack of annotation, the mismatching issue of symmetrical parts in point clouds with different orientations has become an undeniable problem in unsupervised shape correspondence area." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.47, + 0.812 + ], + "angle": 0, + "content": "Self-ensembling Approaches. Self-ensembling approaches improve the model generalization by encouraging consensus among ensemble predictions of unknown samples with small perturbations. \\(\\Gamma\\) model [24] consists of two identical parallel branches that respectively take raw images and corrupted images as inputs. In contrast to \\(\\Gamma\\) model, \\(\\Pi\\) model [11] integrates two parallel branches into a single branch. As an extension of the \\(\\Pi\\) model, the temporal model [11] forces the consistency between the outputs and the aggregated outputs over previous training epochs. Mean Teacher [27] replaces network prediction average with network parameter average via the exponential moving average (EMA) strategy. We design a framework similar to Mean Teacher and adapt it for the unsupervised point cloud shape correspondence task. The proposed framework facilitates the network to yield consistent and accurate predictions under noise perturbations and orientation rotations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.168, + 0.837 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.187, + 0.862 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The unsupervised point cloud shape correspondence is to find the mapping \\( f: X \\to Y \\) between two point clouds" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.892, + 0.676 + ], + "angle": 0, + "content": "source \\(X\\) and target \\(Y\\)) without ground-truth correspondence annotations. Figure 2 illustrates the pipeline of our approach. Given source \\(X\\) and target \\(Y\\) point clouds, we utilize random rotation and Gaussian noise to generate the augmented source point cloud \\(X_{s}\\), while we augment \\(Y\\) by Gaussian noise to obtain \\(Y_{s}\\). Due to the absence of the relative rotation angle labels \\(\\theta, \\theta_{s}\\), we use the rotation angle labels \\(\\theta_{x}\\) to guide the Orientation Estimation Module learning and transfer the valuable information by the adversarial domain adaptation method. The aligned point cloud pairs are input to the teacher and student models, respectively, and we use the DGCNN [29] backbone to output the similarity matrices. After that, we generate two reconstructed point clouds \\(\\hat{X}, \\hat{Y}\\) based on the predicted similarity matrices by the student model. Finally, the student model is supervised by the consistency losses and the construction losses, while the parameters of teacher model are updated by the exponential moving average (EMA) strategy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.692, + 0.715, + 0.707 + ], + "angle": 0, + "content": "3.2. Orientation Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.838 + ], + "angle": 0, + "content": "We provide the overview of the orientation estimation in Figure 3. The encoded features \\( P_{in}^{s}, P_{in}^{t} \\) are fed into the Feature Interaction Module (FIM) for feature fusion. The fused features \\( P_{out} \\) are enhanced by a single-layer edge-conv. To predict the relative orientation, the features \\( \\hat{P}_{in} \\) are fed into the classification head. We also input \\( \\hat{P}_{in} \\) into the discriminator to determine whether the pair comes from the same shape or from different shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Feature Interaction Module. As shown in Figure 4, the feature interaction module is a query-based graph convolution. The point features in the source point cloud are updated by querying points with similar features in the tar" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5366" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.457, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.196, + 0.432, + 0.207 + ], + "angle": 0, + "content": "Figure 3. The overview of Orientation Estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.222, + 0.47, + 0.448 + ], + "angle": 0, + "content": "get point cloud. Let \\( P_{in}^{s}, P_{in}^{t} \\) be the inputs of the feature interaction module. For each point \\( p_i \\in P_{in}^{s} \\), we first consider it as a query to search for the k-nearest neighbors \\( q_i^j, 1 \\leq j \\leq k \\) in the target point cloud \\( P_{in}^{t} \\) with respect to the Euclidean distance defined in the \\( C_1 \\)-dimensional feature space. To better model the relative rotation relationships in space, we use spatial position differences and feature differences as features of each edge, denoted as \\( (p_i, q_i^j - p_i) \\), where \\( p_i, q_i^j \\in \\mathcal{R}^{(C_1 + 3)} \\). Then we use a multilayer perceptron (MLP) to compute a new feature \\( e_{ji} = \\mathrm{MLP}(p_i, q_i^j - p_i) \\) from each edge. For each point, we aggregate its k edge features into a new point feature through Max pooling and ReLU activation. In addition, we add a linear layer that skip-connects the output \\( P_{out} \\) with the input to make the block residual." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.469, + 0.693 + ], + "angle": 0, + "content": "Rotation Classification Head. We concatenate the output feature \\( P_{out} \\) and the enhanced feature as the input \\( \\hat{P}_{in} \\) of the Rotation Classification Head. Inspired by the orientation prediction in the point cloud detection methods [18,20], we consider the prediction of relative rotation angle as a classification task. That coarsely aligning the orientations of the source and target point clouds is enough to solve the problem of mismatching issue of symmetrical parts in point clouds. Thus, we pre-define \\( M \\) equally divided angle bins and then use an MLP head to classify the relative rotation angle into those pre-defined categories. Specifically, we compress \\( \\hat{P}_{in} \\) using maximum pooling and average pooling to obtain the global features and then predict the probability distribution of the relative rotation angle. Finally, we choose the angle bin with the highest probability as the relative rotation angle of the source and target point clouds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.862 + ], + "angle": 0, + "content": "Adversarial Domain Adaptation. Due to the absence of relative rotation angle \\(\\theta, \\theta_s\\), we utilize the relative rotation angle \\(\\theta_x\\) to guide the Orientation Estimation Module learning. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. To eliminate the domain gap, we use a discriminator to identify whether the input features \\(\\hat{P}_{in}\\) of the classification head are from the rotation-augmented samples or the real samples. Specifically, we use a PointNet-like module to process the features \\(\\hat{P}_{in}\\) and predict the probability \\(d_i\\) that the \\(P_{in}\\) is from the real samples:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.877, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\nd _ {i} = \\mathrm {M L P} _ {2} \\left\\{\\max _ {N} \\left\\{\\mathrm {M L P} _ {1} \\left[ \\hat {P} _ {i n} \\right] \\right\\} \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.089, + 0.81, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.172, + 0.85, + 0.185 + ], + "angle": 0, + "content": "Figure 4. The Feature Interaction Module (FIM)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.192, + 0.892, + 0.252 + ], + "angle": 0, + "content": "where max refers to the global Max pooling. By using the discriminator, we train the model to disregard the distinction between the two domains and instead prioritize learning the relative rotation information." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.253, + 0.892, + 0.283 + ], + "angle": 0, + "content": "Relative Rotation Angle Supervision. The angle loss is computed with a cross entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.293, + 0.892, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a n g l e}} = - \\sum_ {i = 1} ^ {M} \\theta_ {x} ^ {i} \\log \\left(\\hat {\\theta} _ {x} ^ {i}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.347, + 0.892, + 0.407 + ], + "angle": 0, + "content": "where \\(M\\) is the number of the pre-defined angle bins, \\(\\hat{\\theta}_x^i\\) and \\(\\theta_x^i\\) denote the predicted probability distribution of relative rotation angle and the rotation angle label, respectively. The domain loss is computed with a Focal Loss [14]:" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.418, + 0.892, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d o m a i n}} = - \\left(1 - d _ {i}\\right) ^ {\\gamma} \\log \\left(d _ {i}\\right), \\gamma > 1, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.446, + 0.892, + 0.476 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{domain}\\) denotes the domain loss and \\(\\gamma\\) denotes the tunable focusing parameter." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.757, + 0.501 + ], + "angle": 0, + "content": "3.3. Self-Ensembling Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.657 + ], + "angle": 0, + "content": "As shown in Table 7, the point cloud orientation and Gaussian noise are two crucial factors in the unsupervised point cloud shape correspondence task. The existing methods ignore noise interference on the point cloud correspondence, making it difficult to obtain robust point cloud representations. To address the above problems, we utilize the Mean Teacher architecture [27] and design two consistency losses to constrain the student model for robust feature representations under orientation disturbance and Gaussian noise interference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.735 + ], + "angle": 0, + "content": "Stochastic Transform. We apply stochastic transformations that include rotation and Gaussian noise on the point clouds for the student network formulated as \\(\\tau = (\\mathcal{R},\\mathcal{N})\\). More specifically, given the raw point cloud pair \\((X,Y)\\), we first apply Gaussian noise to the target point cloud \\(Y\\):" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.745, + 0.891, + 0.763 + ], + "angle": 0, + "content": "\\[\ny _ {i} ^ {s} = y _ {i} + n _ {i}, n _ {i} \\sim \\mathcal {N} (0, \\sigma^ {2}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.772, + 0.892, + 0.833 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(0,\\sigma^2)\\) means the Gaussian distribution with the 0 mean and \\(\\sigma\\) standard deviation. Then, we utilize Gaussian noise and random rotation along the vertical \\(z\\)-axis to augment the source point cloud \\(X\\):" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.843, + 0.891, + 0.861 + ], + "angle": 0, + "content": "\\[\nx _ {i} ^ {s} = \\mathcal {R} \\left(\\theta_ {x}\\right) \\odot x _ {i} + n _ {i}, n _ {i} \\sim \\mathcal {N} \\left(0, \\sigma^ {2}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}\\) denotes the rotation around the \\(z\\)-axis and \\(\\theta_{x}\\) is the rotation angle sampled from \\([0, 2\\pi]\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.319 + ], + "angle": 0, + "content": "Architecture of Teacher & Student Models. Given the raw and augmented point cloud pairs \\((X,Y)\\), \\((X_s,Y_s)\\), we use the Orientation Estimation Module to align source and target orientations. Then, our approach follows the Mean Teacher paradigm [27] and inputs the aligned point cloud pairs \\((\\tilde{X}_s,Y_s)\\), \\((\\tilde{X},Y)\\) into the student and teacher models, respectively. We use a variant of DGCNN [29] backbone to embed the aligned source \\(\\tilde{X}\\) and target \\(Y\\) point clouds to a high-dimensional feature space as \\(F_x,F_y\\in \\mathcal{R}^{N\\times C}\\). Unlike DGCNN, which uses dynamic graphs to select neighbors, we follow [12] to use static graphs for the neighbors. Specifically, we select the k-nearest neighbors in the coordinate space instead of the feature space. Then, we use the cosine similarity \\(S_{xy}\\) of source and target point features \\(F_x,F_y\\) to measure their correspondence." + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.329, + 0.47, + 0.368 + ], + "angle": 0, + "content": "\\[\ns _ {i j} = \\frac {F _ {x} ^ {i} \\cdot \\left(F _ {y} ^ {j}\\right) ^ {T}}{\\| F _ {x} ^ {i} \\| _ {2} \\| F _ {y} ^ {j} \\| _ {2}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.378, + 0.469, + 0.41 + ], + "angle": 0, + "content": "where \\( F_x^i, F_y^j \\) are the \\( i^{\\text{th}} \\) and \\( j^{\\text{th}} \\) rows of \\( F_x, F_y \\), respectively, and \\( (\\cdot)^T \\) denotes a transpose operation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.41, + 0.469, + 0.518 + ], + "angle": 0, + "content": "Soft Label & Consistency Loss. To enhance the perception of local structures and the robustness of the model, we design two consistency losses to maintain feature consistency under Gaussian noise and orientation disturbances. We utilize the cross-similarity \\( S_{xy}^{t} \\) obtained from the teacher model as a soft label and the Smooth \\( L_{1} \\) loss to constrain the cross-similarities \\( S_{x_s y_s}^s \\) of the student model:" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.529, + 0.469, + 0.548 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c c s} = \\operatorname {S m o o t h} L _ {1} \\left(S _ {x y} ^ {t}, S _ {x _ {s} y _ {s}} ^ {s}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.557, + 0.47, + 0.725 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{ccs}\\) denotes the consistency loss of the cross-similarities. To reduce the interference of point cloud orientation on correspondence estimation, we model the feature consistency of the strongly augmented source \\(X_{s}\\) and raw source \\(X\\). We constrain the consistency of the self-similarities \\(S_{xx}\\) to ensure the consistency of neighboring points with similar features. We use the feature embedding \\(F_{x}\\) of the source point cloud to compute the self-similarity \\(S_{xx}\\) by Equation (6). Then, we use the Smooth \\(L_{1}\\) loss to constrain the self-similarities \\(S_{x_s x_s}^s\\) of the student model with the self-similarities \\(S_{xx}^{t}\\) from the teacher model:" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.734, + 0.469, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c s s} = \\operatorname {S m o o t h} L _ {1} \\left(S _ {x x} ^ {t}, S _ {x _ {s} x _ {s}} ^ {s}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.763, + 0.469, + 0.824 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{css}}\\) denotes the consistency loss of the self-similarities. The above two consistency losses ensure the robustness of feature embedding under Gaussian noise and orientation disturbances for accurate correspondence." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.833, + 0.331, + 0.849 + ], + "angle": 0, + "content": "3.4. Model Training & Inference" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "In addition to the above mentioned consistency losses, angle loss, and domain loss, we use reconstruction losses to promote a unique point matching between the shape pair." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Following the previous work [12], we perform the cross-construction operation to construct the target shape \\(\\hat{Y}\\) by using the feature similarity \\(S_{xy}\\) between source and target point clouds, and the target point coordinates \\(Y\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.16, + 0.892, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {\\mathcal {Y}} (x _ {i})} \\frac {e ^ {s _ {i j}}}{\\sum l \\in \\mathcal {N} _ {\\mathcal {Y}} (x _ {i}) e ^ {s _ {i l}}} y _ {j}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.208, + 0.892, + 0.313 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_{\\mathcal{Y}}(x_i)\\) is latent k-nearest neighbors of \\(x_{i}\\) in the target \\(Y\\) . When the source and target point clouds are identical, we refer to the construction operation as selfconstruction. As shown in Figure 2, we obtain the point clouds \\(\\hat{Y}_s^x,\\hat{X}_s^x,\\hat{X}_s^y,\\hat{Y}_s^y\\) by cross-construction and selfconstruction. Then, we constrain the training with the construction loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.321, + 0.892, + 0.361 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {c o n s}} = \\lambda_ {c c} \\left(\\mathrm {C D} \\left(Y _ {s}, \\hat {Y} _ {s} ^ {x}\\right) + \\mathrm {C D} \\left(X _ {s}, \\hat {X} _ {s} ^ {y}\\right)\\right) \\tag {10} \\\\ + \\lambda_ {s c} \\left(\\mathrm {C D} \\left(Y _ {s}, \\hat {Y} _ {s} ^ {y}\\right) + \\mathrm {C D} \\left(X _ {s}, \\hat {X} _ {s} ^ {x}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.892, + 0.43 + ], + "angle": 0, + "content": "where \\(\\lambda_{cc},\\lambda_{sc}\\) are hyperparameters and CD means the Chamfer Distance. Finally, we add a regularization term to correspond close points in the source to close points in the target." + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.439, + 0.892, + 0.473 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {n o r m}} = \\sum_ {i} \\sum_ {l \\in \\mathcal {N} _ {\\mathcal {Y}} \\left(x _ {i}\\right)} e ^ {\\left\\| x _ {i} - x _ {l} \\right\\| _ {2} ^ {2} / \\alpha} \\| \\hat {y} _ {x _ {i}} - \\hat {y} _ {x _ {l}} \\| _ {2} ^ {2}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.892, + 0.528 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_{\\mathcal{Y}}(x_i)\\) is the same as defined in Equation 9 and \\(\\alpha\\) is a hyperparameter. To sum up, the total loss of our unsupervised point cloud shape correspondence method is:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.538, + 0.892, + 0.572 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c c s}} + \\lambda_ {2} \\mathcal {L} _ {\\text {c s s}} + \\lambda_ {3} \\mathcal {L} _ {\\text {a n g l e}} \\tag {12} \\\\ + \\lambda_ {4} \\mathcal {L} _ {\\text {d o m a i n}} + \\mathcal {L} _ {\\text {c o n s}} + \\lambda_ {5} \\mathcal {L} _ {\\text {n o r m}}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.643 + ], + "angle": 0, + "content": "where \\(\\lambda_{i}\\) is a hyperparameter, balancing the contribution of different loss terms. During inference, we set the closest point \\(y_{j}^{*}\\) in the feature space for each point \\(x_{i}\\) as its corresponding point. This selection rule can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.652, + 0.892, + 0.678 + ], + "angle": 0, + "content": "\\[\nf \\left(x _ {i}\\right) = y _ {j ^ {*}}, j ^ {*} = \\underset {j} {\\operatorname {a r g m a x}} \\left(s _ {i j}\\right). \\tag {13}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.687, + 0.634, + 0.704 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.691, + 0.728 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset. To demonstrate the effectiveness and generalization of our method, we perform experiments on human and animal datasets. We conduct experiments on human datasets according to DPC's [12] scheme. For the large-scale dataset, we randomly downsample the SURREAL [8] dataset, which contains 230000 training shapes, into 2000 shape pairs as the training set. For the test set, we use the SHREC'19 [17] dataset, which contains 44 real human models, and pair them into 430 annotated test examples. To further verify the ability of our method to learn discriminative feature expression with a small data size, we train" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5368" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.136 + ], + "angle": 0, + "content": "SE-ORNet on the pairs randomly sampled from 44 SHREC instances, and the testing is still conducted on the official 430 SHREC'19 pairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.47, + 0.333 + ], + "angle": 0, + "content": "For animal datasets, we also conduct experiments with different dataset scales. We use the large-scale SMAL [35] dataset and TOSCA [2] dataset as the training set and test set, respectively. SMAL dataset consists of parameterized models of various animals, and we randomly sample SMAL to obtain the corresponding shape pairs as the training set. TOSCA is generated by deforming three template meshes (human, dog, and horse) into multiple poses. We pair the 41 animal figures in TOSCA from the same category to form a training set of 260 samples and a test set of 286 samples. Because the number of points in different shapes varies, we make a random downsample of the original point cloud to a fixed number \\( n = 1024 \\), as done in CorrNet3D [32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.469, + 0.409 + ], + "angle": 0, + "content": "Evaluation Metrics. The evaluation metrics include the average correspondence error and the correspondence accuracy. Based on the Euclidean-based measure, the average correspondence error is defined for a pair of source and target shapes \\((X,Y)\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.166, + 0.42, + 0.469, + 0.455 + ], + "angle": 0, + "content": "\\[\ne r r = \\frac {1}{n} \\sum_ {x _ {i} \\in X} \\| f (x _ {i}) - y _ {g t} \\| _ {2}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.469, + 0.511 + ], + "angle": 0, + "content": "where \\( y_{gt} \\in Y \\) is the ground-truth matching point to \\( x_{i} \\). The unit is centimeter(cm). And the correspondence accuracy can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.112, + 0.521, + 0.469, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\operatorname {a c c} (\\epsilon) = \\frac {1}{n} \\sum_ {x _ {i} \\in X} \\mathbb {I} \\left(\\left\\| f \\left(x _ {i}\\right) - y _ {g t} \\right\\| _ {2} < \\epsilon d\\right), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.613 + ], + "angle": 0, + "content": "where \\(\\mathbb{I}(\\cdot)\\) is the indicator function, \\(d\\) is the maximal Euclidean distance between points in \\(Y\\), and \\(\\epsilon \\in [0,1]\\) is an error tolerance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. For a fair comparison with existing methods [12, 32], we use the same DGCNN [29] backbone with four EdgeConv blocks as the feature extractor in the self-ensembling framework. The standard deviation \\(\\sigma\\) in Equation (4) is set as 0.1 for human datasets and 0.15 for animal datasets. In the Orientation Estimation Module, the feature encoding module is a simplified DGCNN with three EdgeConv [29] blocks whose layer output sizes are 64, 128, and 256. The \\(k\\) of k-NN is set as 24, and the slope of all LeakyReLU is 0.2. We feed the output of the last layer into the proposed feature interaction module with the output size 256. Then we refine the feature by an EdgeConv layer with the same output size. The angle classification head consists of three Linear-BN-ReLU and an Output Linear. The channels are 256, 128, and 128 for the three Linear-BN-ReLU. The last Linear outputs the probability for classification. We set the number of bins \\(M\\) as 8 in the angle classification head, where each bin represents a range of \\(45^{\\circ}\\). The domain discriminator is a PointNet-like" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.145 + ], + "angle": 0, + "content": "Table 1. Comparison on SHREC and SURREAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.149, + 0.875, + 0.261 + ], + "angle": 0, + "content": "
MethodInputSHRECSURREAL
acc ↑err ↓acc ↑err ↓
Diff-FMaps [16]Point//4.0%7.1
3D-CODED [8]Point//2.1%8.1
Elementary [4]Point//2.3%7.6
CorrNet3D [32]Point0.4%33.86.0%6.9
DPC [12]Point15.3%5.617.7%6.1
OursPoint17.5%5.121.5%4.6
" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.267, + 0.843, + 0.413 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.414, + 0.892, + 0.483 + ], + "angle": 0, + "content": "Figure 5. Correspondence accuracy at various error tolerances for human datasets. The methods are trained on the SHREC or SURREAL dataset and evaluated on SHREC'19 test pairs. Compared with other methods, our approach achieves an impressive performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.491, + 0.892, + 0.598 + ], + "angle": 0, + "content": "module consisting of two MLPs in Equation (1). The channels of \\(\\mathrm{MLP}_1\\) are 512, 256, and 128, while the channels of \\(\\mathrm{MLP}_2\\) are 256, 128, and 256. We follow [12] and use a neighborhood size \\(k = 10\\) in Equation (9) and (11). \\(\\lambda_{c}c\\) and \\(\\lambda_{s}c\\) in Equation (10) are set as 1 and 10, respectively. \\(\\lambda_1\\), \\(\\lambda_2\\), \\(\\lambda_3\\), \\(\\lambda_4\\), and \\(\\lambda_5\\) in Equation (12) are set as 0.1, 0.1, 1.0, 0.8, and 1.0, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.787, + 0.622 + ], + "angle": 0, + "content": "4.2. Comparison on Human Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.704 + ], + "angle": 0, + "content": "For a fair comparison with existing methods, we do not use any post-processing or additional connectivity information. In addition, we follow DPC [12] and train our model on the SURREAL and SHREC datasets, respectively. Then we test our model on the official 430 SHREC'19 pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Evaluation on SHREC dataset. As shown in Table 1, our approach shows significant performance improvements on the SHREC benchmark and achieves new SOTA performance by \\(2.2\\%\\) improvements in accuracy and 0.5 reductions in error. To show the improvement under different error tolerances, we present the correspondence accuracy for point-based methods trained on SHREC and evaluated on the SHREC'19 test set. As shown in Figure 5, our method achieves better results with different error tolerances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Cross-dataset Generalization. In Table 1 and Figure 5, we also report the comparison with other methods on the SURREAL benchmark. The models are trained on the SURREAL dataset and evaluated on the SHREC'19 test" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5369" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.146 + ], + "angle": 0, + "content": "Table 2. Comparison on TOSCA and SMAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.149, + 0.427, + 0.247 + ], + "angle": 0, + "content": "
MethodTOSCASMAL
acc ↑err ↓acc ↑err ↓
3D-CODED [8]//0.5%19.2
Elementary [4]//0.5%13.7
CorrNet3D [32]0.3%32.75.3%9.8
DPC [12]34.7%2.833.2%5.8
Ours38.2%2.736.4%3.9
" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.249, + 0.422, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.397, + 0.47, + 0.466 + ], + "angle": 0, + "content": "Figure 6. Correspondence accuracy at various error tolerances for animal datasets. The methods are trained on the TOSCA or SMAL dataset and evaluated on the official TOSCA test pairs. Compared with other methods, our method achieves a desirable performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.581 + ], + "angle": 0, + "content": "set. The large-scale training set of the SURREAL dataset helps the deep learning-based methods perform better, even though there is a domain gap between the SURREAL and SHREC datasets. With our proposed method, the correspondence accuracy reaches \\(21.5\\%\\) at an error tolerance of 0.01, and the average correspondence error is reduced to 4.6 on the SHREC'19 test set." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.589, + 0.364, + 0.605 + ], + "angle": 0, + "content": "4.3. Comparison on Animal Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.839 + ], + "angle": 0, + "content": "To verify the adaptability of our method to point clouds of different shapes, we conduct experiments on two animal benchmarks. Similar to human datasets, we train our method on TOSCA and SMAL datasets respectively, and test on the TOSCA test dataset. Table 2 and Figure 6 show the competitive results on TOSCA and SMAL benchmarks. Our method achieves a \\(3.5\\%\\) accuracy improvement on the TOSCA benchmark and a \\(3.2\\%\\) accuracy improvement on the SMAL benchmark. Compared with the human datasets, the animal datasets have various shapes with aligned orientations. Thus, the above performance gains come mainly from our self-ensembling framework, which can learn reliable features on complex data. To verify the effect of the Orientation Estimation Module, we test our method and baseline using different augmented test sets in Section 4.6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.385, + 0.864 + ], + "angle": 0, + "content": "4.4. Comparison on Real-world Dataset" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "CMU Panoptic [10] is a dataset of scanned point clouds of human subjects in various poses, containing noise, out" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.116 + ], + "angle": 0, + "content": "Table 3. Comparison on CMU-Panoptic benchmark. Here, err means average Euclidean keypoint error (cm)." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.117, + 0.887, + 0.142 + ], + "angle": 0, + "content": "
3D-CODED [8]DIF-Net [25]CorrNet [32]IFMatch [7]Ours
err17.115.314.88.53.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.144, + 0.891, + 0.169 + ], + "angle": 0, + "content": "Table 4. Comparison on SHREC'20 benchmark. The training dataset is indicated in the bracket." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.169, + 0.88, + 0.218 + ], + "angle": 0, + "content": "
MethodSHREC’20 [SURREAL]SHREC’20 [SMAL]
acc ↑err ↓acc ↑err ↓
DPC [12]25.0%3.224.5%7.5
Ours29.9%1.225.4%2.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.22, + 0.892, + 0.302 + ], + "angle": 0, + "content": "Table 5. Evaluation of the model with different designs on SURREAL. \\( \\mathcal{L}_{css} \\) is the consistency loss of the self-similarities, \\( \\mathcal{L}_{ccs} \\) is the consistency loss of the cross-similarities, \\( \\tau \\) means the stochastic transform, OEM means we use the Orientation Estimation Module, FIM is the Feature Interaction Module, and DAM is the Domain Adaptation Module." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.306, + 0.866, + 0.419 + ], + "angle": 0, + "content": "
τLccsLcssOEMFIMDAMSURREAL
acc ↑err ↓
XXXXXX17.7%6.1
✓✓XXXX18.8%5.7
✓✓✓XXX19.2%5.6
✓✓✓✓XX19.5%5.5
✓✓✓✓✓X20.4%5.1
✓✓✓✓✓✓21.5%4.6
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.505 + ], + "angle": 0, + "content": "liers, occlusions, and clutter. Meanwhile, SHREC'20 [6] dataset contains real scans of various four-legged animal models. As shown in Table 3 and Table 4, we provide the results under two real scan datasets, demonstrating the remarkable robustness of our model to noise." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.515, + 0.654, + 0.532 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.826 + ], + "angle": 0, + "content": "Evaluation of the model with different designs. In this section, we perform extensive ablation studies on the SUR-REAL dataset to evaluate the effectiveness of each design. Table 5 demonstrates the performance of the model with different designs. Specifically, the first line is the results of DPC [12], which is our baseline model. The second row indicates that the self-ensembling framework with a stochastic transform achieves a better performance than the original model. By using \\(\\mathcal{L}_{\\mathrm{css}}\\) to constrain the consistency of source features before and after augmentation, the correspondence accuracy can be improved by \\(0.4\\%\\), as shown in the third row. As shown in the fourth row, adding the Orientation Evaluation Module without the Feature Interaction Module and the Domain Adaptation Module, the performance has a slight improvement. In the fifth row, by introducing the Feature Interaction Module into the Orientation Evaluation Module, the correspondence accuracy can be improved by \\(0.9\\%\\). Finally, after utilizing the Domain Adaptation Module, the correspondence accuracy is improved by \\(1.1\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of the Self-Ensembling Framework. As shown in Table 6, we modify the self-ensembling framework to show the effect of each designed component. Removing either of the consistency losses leads to a drop in performance, which indicates that constraining the student net" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5370" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.146 + ], + "angle": 0, + "content": "Table 6. Effect of the Self-Ensembling Framework on SUR-REAL. Here, we modify the self-ensembling framework to show the effect of each designed component. \\(\\mathcal{N}\\) means Gaussian noise, and \\(\\mathcal{R}\\) means random rotation along the vertical \\(z\\)-axis." + }, + { + "type": "table", + "bbox": [ + 0.106, + 0.149, + 0.44, + 0.202 + ], + "angle": 0, + "content": "
SURREALw/o LCssw/o LCSSw/o Nw/o R
acc ↑19.9%20.3%20.6%18.8%
err ↓5.35.14.95.7
" + }, + { + "type": "image", + "bbox": [ + 0.146, + 0.209, + 0.191, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.208, + 0.258, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.215, + 0.326, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.212, + 0.412, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.145, + 0.27, + 0.186, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.268, + 0.246, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.268, + 0.328, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.268, + 0.411, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.328, + 0.175, + 0.331 + ], + "angle": 0, + "content": "图1-2" + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.328, + 0.199, + 0.331 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.328, + 0.246, + 0.331 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image_caption", + "bbox": [ + 0.25, + 0.328, + 0.272, + 0.331 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.328, + 0.322, + 0.331 + ], + "angle": 0, + "content": "Source(K)" + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.328, + 0.412, + 0.331 + ], + "angle": 0, + "content": "1. Probability distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.331, + 0.469, + 0.399 + ], + "angle": 0, + "content": "Figure 7. Effect of the Orientation Estimation Module. We visualize of the point clouds before and after orientation rectification on SHREC'19 test set. We denote the raw source point cloud as Source and the rectified one as Source(R). Besides, we provide the probability distributions of the relative rotation angle prediction." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.403, + 0.469, + 0.457 + ], + "angle": 0, + "content": "Table 7. Robustness Analysis. To verify the robustness of our method, we test our method and baselines using different augmented test sets. \\(\\mathcal{N}\\) means Gaussian noise with standard deviation \\(\\sigma\\) of 0.1 and \\(\\mathcal{R}\\) means random rotation along the vertical \\(z\\)-axis." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.461, + 0.454, + 0.549 + ], + "angle": 0, + "content": "
NRSURREAL(B)SURREALSMAL(B)SMAL
acc ↑err ↓acc ↑err ↓acc ↑err ↓acc ↑err ↓
XX17.47%6.3021.55%4.6533.79%5.7836.39%3.88
✓X14.38%8.7421.55%4.6630.21%6.0636.15%3.92
X✓8.99%9.3317.59%5.819.98%12.2428.16%5.63
✓✓7.80%11.2817.58%5.799.54%12.8027.60%5.89
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.469, + 0.668 + ], + "angle": 0, + "content": "work with soft labels facilitates the consistency of the point cloud representations. When Gaussian noise and rotation augmentation are removed, the model performances show different degrees of degradation. The above experiments illustrate our self-ensemble method can obtain a more robust feature representation of the point cloud through data augmentation and consistency losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.67, + 0.469, + 0.79 + ], + "angle": 0, + "content": "Effect of the Orientation Estimation Module. To verify the effect of the proposed Orientation Estimation Module, we visualize the point clouds after orientation rectification and the probability distributions of the relative rotation angle predictions. As shown in Figure 7, our method can accurately estimate the relative rotation angle and align the point cloud orientation of the source with that of the target. More results refer to the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.269, + 0.817 + ], + "angle": 0, + "content": "4.6. Robustness Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.9 + ], + "angle": 0, + "content": "To verify the robustness of our method, we use different augmentations on the test set. As shown in Table 7, we use Gaussian noise and random rotation for data augmentation of the test sets. Compared to our method, the baseline shows a significant performance decrease for test sets" + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.074, + 0.603, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.084, + 0.682, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.084, + 0.755, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.084, + 0.828, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.562, + 0.142, + 0.6, + 0.204 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.57, + 0.21, + 0.593, + 0.218 + ], + "angle": 0, + "content": "Target" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.152, + 0.681, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.625, + 0.21, + 0.685, + 0.217 + ], + "angle": 0, + "content": "Source (Baseline)" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.153, + 0.754, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.21, + 0.756, + 0.217 + ], + "angle": 0, + "content": "Source (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.153, + 0.828, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.783, + 0.209, + 0.826, + 0.217 + ], + "angle": 0, + "content": "Source (GT)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.22, + 0.892, + 0.275 + ], + "angle": 0, + "content": "Figure 8. Visualization of the correspondence results with rotation augmentation. With rotation augmentation on point cloud pairs, the baseline shows regrettable performances, while our method still retains desirable performances." + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.289, + 0.611, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.289, + 0.683, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.289, + 0.769, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.289, + 0.847, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.388 + ], + "angle": 0, + "content": "Figure 9. Visualization of point cloud pairs with deformations on real scanned Owlii dataset. In each pair, the left one is the source and the right one is the target." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.406, + 0.892, + 0.572 + ], + "angle": 0, + "content": "with Gaussian noise. For test sets with random rotation, the baseline performance is greatly degraded, while our method retains an acceptable performance. Figure 8 shows that our SE-ORNet can handle the orientation inconsistency issue of source and target well. To further verify the robustness and generalization of our method, we conduct experiments on the real scanned Owlii dataset [30] and present the visualization in Figure 9. The results show that our SE-ORNet trained on the synthetic SURREAL dataset still produces impressive performance on the real scanned dataset, demonstrating strong generalization and robustness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.601, + 0.619, + 0.617 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.782 + ], + "angle": 0, + "content": "In this paper, we propose a self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. To the best of our knowledge, SE-ORNet is the first self-ensembling network in this area. To solve the mismatching issue of symmetrical parts in point clouds with different body orientations, we design a plug-and-play lightweight orientation estimation module to align the orientations of two point clouds. Extensive experiments conducted on four shape correspondence benchmarks demonstrate the superior performance of SE-ORNet." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.811, + 0.687, + 0.827 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 12150007) and National Defense Basic Scientific Research program of China (Grant JCKY2020903B002)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5371" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. 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However, humans and some animals have bilateral symmetry and various orientations, which lead to severe mispredictions of symmetrical parts. Besides, point cloud noise disrupts consistent representations for point cloud and thus degrades the shape correspondence accuracy. To address the above issues, we propose a Self-Ensembling ORientation-aware Network termed SE-ORNet. The key of our approach is to exploit an orientation estimation module with a domain adaptive discriminator to align the orientations of point cloud pairs, which significantly alleviates the mispredictions of symmetrical parts. Additionally, we design a self-ensembling framework for unsupervised point cloud shape correspondence. In this framework, the disturbances of point cloud noise are overcome by perturbing the inputs of the student and teacher networks with different data augmentations and constraining the consistency of predictions. Extensive experiments on both human and animal datasets show that our SE-ORNet can surpass state-of-the-art unsupervised point cloud shape correspondence methods. + +# 1. Introduction + +With the cost of LiDAR and depth cameras falling, it is more accessible to obtain 3D point cloud data. For real-world applications, such as articulated motion transfer [5, 26] and non-rigid human body alignment [3], the correspondence between two point clouds is indispensable. However, we are hard to directly obtain the correspondence between two raw point clouds due to various object orientations and un unified coordinate systems. + +To accurately find the point-to-point correspondence be + +![](images/727df288c26d4f6dd287d6590efcad369bbe008afbe8eb4f57d3608c4ab39b1c.jpg) +Figure 1. The visualization of dense point matching results. Three point cloud pairs have different relative rotation angles. GT denotes ground truth. The correspondence is visualized by transferring colors from source to target according to matching results. The baseline predicts many false matches, especially for symmetrical, similar parts of the object. Our method achieves accurate matches for these parts with our orientation estimation module. + +tween two point clouds, spectral-based methods [1, 9, 15, 19, 28] have been proven as practical shape correspondence methods by computing functional mapping between the projected features and learning a transformation for the correspondence. Nevertheless, the spectral-based methods suffer from complicated pre-processing steps and the necessity for connectivity information between points. With the rapid development of deep learning, many fully supervised point cloud shape correspondence methods [4, 8, 16] have been proposed to lead to remarkable progress. However, these methods rely on a large amount of carefully annotated point cloud pairs, which are expensive and time-consuming to collect. To relieve the annotation cost of fully supervised methods, unsupervised methods [12, 32] that utilize unlabeled data for model training have attracted more and more attention. CorrNet3D [32] proposes the first unsupervised deep learning framework for building dense correspondence between point clouds in an end-to-end manner. DPC [12] models the local point cloud structure by exploring the proximity of points using DGCNN [29] and designs reconstruction losses to extract continuous point cloud rep + +resentations. However, in the scanning process of 3D scanner, due to light, vibration and other factors, point cloud noise will be inevitably generated. Meanwhile, the preprocessing of point cloud (such as random subsampling) will also introduce noise. Unfortunately, the previous methods fail to adequately consider the point cloud noise, which negatively impacts the point cloud representations. Besides the noise, existing methods lack attention to symmetrical parts of the body. The mismatching issue of symmetrical parts is challenging in this task, which was also spotted by the previous method [32] but has yet to be solved. + +By studying the previous point-based shape correspondence methods [4, 8, 12, 16, 32], we summarize two key issues that need consideration to achieve a more accurate shape correspondence: 1) How to overcome the disturbance of point cloud noise to get robust and consistent point cloud representations? Point cloud noise perturbs the spatial coordinates of point cloud and interferes with local structure modeling. Therefore, it is necessary to overcome noise disturbances. 2) How to solve the mismatching issue of symmetrical parts in point clouds with different body orientations? As shown in Figure 1, for the pair of bilaterally symmetrical human point clouds facing the opposite directions, existing methods predict the completely reverse and seriously wrong point cloud correspondence due to the similar structure and position. The specific relative rotation angles lead to severe mispredictions of symmetrical parts. + +To achieve the above goals, we propose a Self-Ensembling Orientation-aware Network (SE-ORNet) for unsupervised point cloud shape correspondence. We integrate orientation modeling and consistent point cloud representations under a unified self-ensembling framework, which consists of a pair of teacher and student models, an orientation estimation module, and an adaptive domain discriminator. Firstly, we design a new augmentation scheme to produce augmented samples with rotation and Gaussian noise, and record the rotation angles as rotation angle labels. Then, we formulate soft labels and consistency losses to encourage consensus among ensemble predictions of augmented and raw samples, aiming to perceive the difference in body orientation and overcome the point cloud noise disturbance to obtain consistent point cloud representations. In addition, we design a plug-and-play lightweight Orientation Estimation Module, which aligns the orientations of two point clouds to solve the mismatching issue of symmetrical parts in point clouds. Without the real label of relative rotation angle between the source and target, we supervise the training with the rotation angle labels and calculate angle losses. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. Therefore, we design a discriminator to achieve domain adaptation and calculate the domain losses. Furthermore, the discriminator facilitates the Orientation Estima + +tion Module to mine the valuable knowledge in the rotation-augmented samples to compensate for the information loss of the real relative rotation angles. + +In summary, the main contributions of this work are as follows: (i) We design a plug-and-play lightweight Orientation Estimation Module that accurately aligns the orientations of point cloud pairs to achieve correct matching results of symmetrical parts. (ii) We integrate point cloud orientation modeling and consistent point cloud representation learning with the disturbance of point cloud noise into a unified self-ensembling framework. (iii) Our method attains state-of-the-art performance on both human and animal benchmarks, and extensive experimental results verify the superiority of our designs. + +# 2. Related Work + +In this Section, we give a brief overview of related works on point cloud shape correspondence, including learning on point clouds, shape correspondence, and self-ensembling approaches. + +Learning on Point Clouds. PointNet [21] learns from global information through multi-layer perceptrons and max-pooling operation. PointNet++ [22] devises a hierarchical architecture that recursively partitions the point cloud to extract local features more effectively. Recent works explore local aggregators via relations [23, 31, 33], and graphs [29, 34]. PointCNN [13] transforms neighboring points to the canonical order to apply traditional convolution on point clouds. DGCNN [29] creates a graph in the feature space and designs EdgeConv [29] to learn the edge features of the graph in each layer. However, the methods are commonly based on some assumptions of implicit local geometry, which may result in sensitivity to point cloud disturbances. + +Shape Correspondence. As an active research area in computer vision and graphics, point cloud shape correspondence methods roughly include spectral-based methods [1,9,15,19,28] and point-based methods [4,8,12,16,32]. Spectral-based methods require connectivity information to compute the LBO eigenvectors as basis functions and infer a linear transformation for shape correspondence. However, with regard to point cloud data, connectivity information is difficult to obtain directly while point-based methods directly process point clouds without connectivity information to find the dense point-to-point mapping between two point clouds with deformable 3D shapes. Deprelle et al. [4] propose representing shapes as the deformation and combination of learnable elementary 3D structures. Groueix et al. [8] employ an encoder-decoder architecture to obtain and constrain the similarity matrix with manually annotated labels. The deep learning methods train their neural networks in a data-driven manner and improve performance to a large extent. However, manually labeling the point-to-point cor + +![](images/d9fd6cf8db6c168bb7a930a5232fec6ff9b6b2b5b0aee730b3505306a20e1c3c.jpg) +Figure 2. The overview of our self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. $X_{s}$ is generated from the raw source point cloud $X$ by random rotation and Gaussian noise, while $Y_{s}$ is only augmented by Gaussian noise. We design the Orientation Estimation Module to estimate the rotation $\theta$ of the source with respect to the target and align the point cloud in position space. Afterward, the aligned point cloud pairs are input to the teacher and student models, respectively, and the correspondence is predicted through a DGCNN backbone. Finally, we supervise the student model by the consistency losses and the construction losses, and the teacher model updates the parameters using the exponential moving average (EMA) strategy. The gradient reversal layer (GRL) acts as the identity function during forward propagation, but is multiplied by -1 during backward propagation. + +respondence between two point clouds in 3D space takes much time and effort. Therefore, some unsupervised point cloud shape correspondence methods [12, 32] are proposed to reduce the overhead of labeling. CorrNet3D [32] is the first unsupervised deep learning framework. DPC [12] designs several reconstruction losses to smooth point cloud representations. Due to the lack of annotation, the mismatching issue of symmetrical parts in point clouds with different orientations has become an undeniable problem in unsupervised shape correspondence area. + +Self-ensembling Approaches. Self-ensembling approaches improve the model generalization by encouraging consensus among ensemble predictions of unknown samples with small perturbations. $\Gamma$ model [24] consists of two identical parallel branches that respectively take raw images and corrupted images as inputs. In contrast to $\Gamma$ model, $\Pi$ model [11] integrates two parallel branches into a single branch. As an extension of the $\Pi$ model, the temporal model [11] forces the consistency between the outputs and the aggregated outputs over previous training epochs. Mean Teacher [27] replaces network prediction average with network parameter average via the exponential moving average (EMA) strategy. We design a framework similar to Mean Teacher and adapt it for the unsupervised point cloud shape correspondence task. The proposed framework facilitates the network to yield consistent and accurate predictions under noise perturbations and orientation rotations. + +# 3. Method + +# 3.1. Overview + +The unsupervised point cloud shape correspondence is to find the mapping $f: X \to Y$ between two point clouds + +source $X$ and target $Y$ ) without ground-truth correspondence annotations. Figure 2 illustrates the pipeline of our approach. Given source $X$ and target $Y$ point clouds, we utilize random rotation and Gaussian noise to generate the augmented source point cloud $X_{s}$ , while we augment $Y$ by Gaussian noise to obtain $Y_{s}$ . Due to the absence of the relative rotation angle labels $\theta, \theta_{s}$ , we use the rotation angle labels $\theta_{x}$ to guide the Orientation Estimation Module learning and transfer the valuable information by the adversarial domain adaptation method. The aligned point cloud pairs are input to the teacher and student models, respectively, and we use the DGCNN [29] backbone to output the similarity matrices. After that, we generate two reconstructed point clouds $\hat{X}, \hat{Y}$ based on the predicted similarity matrices by the student model. Finally, the student model is supervised by the consistency losses and the construction losses, while the parameters of teacher model are updated by the exponential moving average (EMA) strategy. + +# 3.2. Orientation Estimation + +We provide the overview of the orientation estimation in Figure 3. The encoded features $P_{in}^{s}, P_{in}^{t}$ are fed into the Feature Interaction Module (FIM) for feature fusion. The fused features $P_{out}$ are enhanced by a single-layer edge-conv. To predict the relative orientation, the features $\hat{P}_{in}$ are fed into the classification head. We also input $\hat{P}_{in}$ into the discriminator to determine whether the pair comes from the same shape or from different shapes. + +Feature Interaction Module. As shown in Figure 4, the feature interaction module is a query-based graph convolution. The point features in the source point cloud are updated by querying points with similar features in the tar + +![](images/44d0a37bd76cc1df63782fcd1b61dc6db626a3c04e7ab9cc6f3aa0a770590a0c.jpg) +Figure 3. The overview of Orientation Estimation. + +get point cloud. Let $P_{in}^{s}, P_{in}^{t}$ be the inputs of the feature interaction module. For each point $p_i \in P_{in}^{s}$ , we first consider it as a query to search for the k-nearest neighbors $q_i^j, 1 \leq j \leq k$ in the target point cloud $P_{in}^{t}$ with respect to the Euclidean distance defined in the $C_1$ -dimensional feature space. To better model the relative rotation relationships in space, we use spatial position differences and feature differences as features of each edge, denoted as $(p_i, q_i^j - p_i)$ , where $p_i, q_i^j \in \mathcal{R}^{(C_1 + 3)}$ . Then we use a multilayer perceptron (MLP) to compute a new feature $e_{ji} = \mathrm{MLP}(p_i, q_i^j - p_i)$ from each edge. For each point, we aggregate its k edge features into a new point feature through Max pooling and ReLU activation. In addition, we add a linear layer that skip-connects the output $P_{out}$ with the input to make the block residual. + +Rotation Classification Head. We concatenate the output feature $P_{out}$ and the enhanced feature as the input $\hat{P}_{in}$ of the Rotation Classification Head. Inspired by the orientation prediction in the point cloud detection methods [18,20], we consider the prediction of relative rotation angle as a classification task. That coarsely aligning the orientations of the source and target point clouds is enough to solve the problem of mismatching issue of symmetrical parts in point clouds. Thus, we pre-define $M$ equally divided angle bins and then use an MLP head to classify the relative rotation angle into those pre-defined categories. Specifically, we compress $\hat{P}_{in}$ using maximum pooling and average pooling to obtain the global features and then predict the probability distribution of the relative rotation angle. Finally, we choose the angle bin with the highest probability as the relative rotation angle of the source and target point clouds. + +Adversarial Domain Adaptation. Due to the absence of relative rotation angle $\theta, \theta_s$ , we utilize the relative rotation angle $\theta_x$ to guide the Orientation Estimation Module learning. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. To eliminate the domain gap, we use a discriminator to identify whether the input features $\hat{P}_{in}$ of the classification head are from the rotation-augmented samples or the real samples. Specifically, we use a PointNet-like module to process the features $\hat{P}_{in}$ and predict the probability $d_i$ that the $P_{in}$ is from the real samples: + +$$ +d _ {i} = \mathrm {M L P} _ {2} \left\{\max _ {N} \left\{\mathrm {M L P} _ {1} \left[ \hat {P} _ {i n} \right] \right\} \right\}, \tag {1} +$$ + +![](images/c792e900c6dcd405a7afb923cfea4111281dffffb55c9242941222192ab1d51b.jpg) +Figure 4. The Feature Interaction Module (FIM). + +where max refers to the global Max pooling. By using the discriminator, we train the model to disregard the distinction between the two domains and instead prioritize learning the relative rotation information. + +Relative Rotation Angle Supervision. The angle loss is computed with a cross entropy loss: + +$$ +\mathcal {L} _ {\text {a n g l e}} = - \sum_ {i = 1} ^ {M} \theta_ {x} ^ {i} \log \left(\hat {\theta} _ {x} ^ {i}\right), \tag {2} +$$ + +where $M$ is the number of the pre-defined angle bins, $\hat{\theta}_x^i$ and $\theta_x^i$ denote the predicted probability distribution of relative rotation angle and the rotation angle label, respectively. The domain loss is computed with a Focal Loss [14]: + +$$ +\mathcal {L} _ {\text {d o m a i n}} = - \left(1 - d _ {i}\right) ^ {\gamma} \log \left(d _ {i}\right), \gamma > 1, \tag {3} +$$ + +where $\mathcal{L}_{domain}$ denotes the domain loss and $\gamma$ denotes the tunable focusing parameter. + +# 3.3. Self-Ensembling Framework + +As shown in Table 7, the point cloud orientation and Gaussian noise are two crucial factors in the unsupervised point cloud shape correspondence task. The existing methods ignore noise interference on the point cloud correspondence, making it difficult to obtain robust point cloud representations. To address the above problems, we utilize the Mean Teacher architecture [27] and design two consistency losses to constrain the student model for robust feature representations under orientation disturbance and Gaussian noise interference. + +Stochastic Transform. We apply stochastic transformations that include rotation and Gaussian noise on the point clouds for the student network formulated as $\tau = (\mathcal{R},\mathcal{N})$ . More specifically, given the raw point cloud pair $(X,Y)$ , we first apply Gaussian noise to the target point cloud $Y$ : + +$$ +y _ {i} ^ {s} = y _ {i} + n _ {i}, n _ {i} \sim \mathcal {N} (0, \sigma^ {2}), \tag {4} +$$ + +where $\mathcal{N}(0,\sigma^2)$ means the Gaussian distribution with the 0 mean and $\sigma$ standard deviation. Then, we utilize Gaussian noise and random rotation along the vertical $z$ -axis to augment the source point cloud $X$ : + +$$ +x _ {i} ^ {s} = \mathcal {R} \left(\theta_ {x}\right) \odot x _ {i} + n _ {i}, n _ {i} \sim \mathcal {N} \left(0, \sigma^ {2}\right), \tag {5} +$$ + +where $\mathcal{R}$ denotes the rotation around the $z$ -axis and $\theta_{x}$ is the rotation angle sampled from $[0, 2\pi]$ . + +Architecture of Teacher & Student Models. Given the raw and augmented point cloud pairs $(X,Y)$ , $(X_s,Y_s)$ , we use the Orientation Estimation Module to align source and target orientations. Then, our approach follows the Mean Teacher paradigm [27] and inputs the aligned point cloud pairs $(\tilde{X}_s,Y_s)$ , $(\tilde{X},Y)$ into the student and teacher models, respectively. We use a variant of DGCNN [29] backbone to embed the aligned source $\tilde{X}$ and target $Y$ point clouds to a high-dimensional feature space as $F_x,F_y\in \mathcal{R}^{N\times C}$ . Unlike DGCNN, which uses dynamic graphs to select neighbors, we follow [12] to use static graphs for the neighbors. Specifically, we select the k-nearest neighbors in the coordinate space instead of the feature space. Then, we use the cosine similarity $S_{xy}$ of source and target point features $F_x,F_y$ to measure their correspondence. + +$$ +s _ {i j} = \frac {F _ {x} ^ {i} \cdot \left(F _ {y} ^ {j}\right) ^ {T}}{\| F _ {x} ^ {i} \| _ {2} \| F _ {y} ^ {j} \| _ {2}}, \tag {6} +$$ + +where $F_x^i, F_y^j$ are the $i^{\text{th}}$ and $j^{\text{th}}$ rows of $F_x, F_y$ , respectively, and $(\cdot)^T$ denotes a transpose operation. + +Soft Label & Consistency Loss. To enhance the perception of local structures and the robustness of the model, we design two consistency losses to maintain feature consistency under Gaussian noise and orientation disturbances. We utilize the cross-similarity $S_{xy}^{t}$ obtained from the teacher model as a soft label and the Smooth $L_{1}$ loss to constrain the cross-similarities $S_{x_s y_s}^s$ of the student model: + +$$ +\mathcal {L} _ {c c s} = \operatorname {S m o o t h} L _ {1} \left(S _ {x y} ^ {t}, S _ {x _ {s} y _ {s}} ^ {s}\right), \tag {7} +$$ + +where $\mathcal{L}_{ccs}$ denotes the consistency loss of the cross-similarities. To reduce the interference of point cloud orientation on correspondence estimation, we model the feature consistency of the strongly augmented source $X_{s}$ and raw source $X$ . We constrain the consistency of the self-similarities $S_{xx}$ to ensure the consistency of neighboring points with similar features. We use the feature embedding $F_{x}$ of the source point cloud to compute the self-similarity $S_{xx}$ by Equation (6). Then, we use the Smooth $L_{1}$ loss to constrain the self-similarities $S_{x_s x_s}^s$ of the student model with the self-similarities $S_{xx}^{t}$ from the teacher model: + +$$ +\mathcal {L} _ {c s s} = \operatorname {S m o o t h} L _ {1} \left(S _ {x x} ^ {t}, S _ {x _ {s} x _ {s}} ^ {s}\right), \tag {8} +$$ + +where $\mathcal{L}_{\mathrm{css}}$ denotes the consistency loss of the self-similarities. The above two consistency losses ensure the robustness of feature embedding under Gaussian noise and orientation disturbances for accurate correspondence. + +# 3.4. Model Training & Inference + +In addition to the above mentioned consistency losses, angle loss, and domain loss, we use reconstruction losses to promote a unique point matching between the shape pair. + +Following the previous work [12], we perform the cross-construction operation to construct the target shape $\hat{Y}$ by using the feature similarity $S_{xy}$ between source and target point clouds, and the target point coordinates $Y$ as follows: + +$$ +\hat {y} _ {x _ {i}} = \sum_ {j \in \mathcal {N} _ {\mathcal {Y}} (x _ {i})} \frac {e ^ {s _ {i j}}}{\sum l \in \mathcal {N} _ {\mathcal {Y}} (x _ {i}) e ^ {s _ {i l}}} y _ {j}, \tag {9} +$$ + +where $\mathcal{N}_{\mathcal{Y}}(x_i)$ is latent k-nearest neighbors of $x_{i}$ in the target $Y$ . When the source and target point clouds are identical, we refer to the construction operation as selfconstruction. As shown in Figure 2, we obtain the point clouds $\hat{Y}_s^x,\hat{X}_s^x,\hat{X}_s^y,\hat{Y}_s^y$ by cross-construction and selfconstruction. Then, we constrain the training with the construction loss as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {c o n s}} = \lambda_ {c c} \left(\mathrm {C D} \left(Y _ {s}, \hat {Y} _ {s} ^ {x}\right) + \mathrm {C D} \left(X _ {s}, \hat {X} _ {s} ^ {y}\right)\right) \tag {10} \\ + \lambda_ {s c} \left(\mathrm {C D} \left(Y _ {s}, \hat {Y} _ {s} ^ {y}\right) + \mathrm {C D} \left(X _ {s}, \hat {X} _ {s} ^ {x}\right)\right), \\ \end{array} +$$ + +where $\lambda_{cc},\lambda_{sc}$ are hyperparameters and CD means the Chamfer Distance. Finally, we add a regularization term to correspond close points in the source to close points in the target. + +$$ +\mathcal {L} _ {\text {n o r m}} = \sum_ {i} \sum_ {l \in \mathcal {N} _ {\mathcal {Y}} \left(x _ {i}\right)} e ^ {\left\| x _ {i} - x _ {l} \right\| _ {2} ^ {2} / \alpha} \| \hat {y} _ {x _ {i}} - \hat {y} _ {x _ {l}} \| _ {2} ^ {2}, \tag {11} +$$ + +where $\mathcal{N}_{\mathcal{Y}}(x_i)$ is the same as defined in Equation 9 and $\alpha$ is a hyperparameter. To sum up, the total loss of our unsupervised point cloud shape correspondence method is: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {c c s}} + \lambda_ {2} \mathcal {L} _ {\text {c s s}} + \lambda_ {3} \mathcal {L} _ {\text {a n g l e}} \tag {12} \\ + \lambda_ {4} \mathcal {L} _ {\text {d o m a i n}} + \mathcal {L} _ {\text {c o n s}} + \lambda_ {5} \mathcal {L} _ {\text {n o r m}}, \\ \end{array} +$$ + +where $\lambda_{i}$ is a hyperparameter, balancing the contribution of different loss terms. During inference, we set the closest point $y_{j}^{*}$ in the feature space for each point $x_{i}$ as its corresponding point. This selection rule can be formulated as: + +$$ +f \left(x _ {i}\right) = y _ {j ^ {*}}, j ^ {*} = \underset {j} {\operatorname {a r g m a x}} \left(s _ {i j}\right). \tag {13} +$$ + +# 4. Experiments + +# 4.1. Experimental Setup + +Dataset. To demonstrate the effectiveness and generalization of our method, we perform experiments on human and animal datasets. We conduct experiments on human datasets according to DPC's [12] scheme. For the large-scale dataset, we randomly downsample the SURREAL [8] dataset, which contains 230000 training shapes, into 2000 shape pairs as the training set. For the test set, we use the SHREC'19 [17] dataset, which contains 44 real human models, and pair them into 430 annotated test examples. To further verify the ability of our method to learn discriminative feature expression with a small data size, we train + +SE-ORNet on the pairs randomly sampled from 44 SHREC instances, and the testing is still conducted on the official 430 SHREC'19 pairs. + +For animal datasets, we also conduct experiments with different dataset scales. We use the large-scale SMAL [35] dataset and TOSCA [2] dataset as the training set and test set, respectively. SMAL dataset consists of parameterized models of various animals, and we randomly sample SMAL to obtain the corresponding shape pairs as the training set. TOSCA is generated by deforming three template meshes (human, dog, and horse) into multiple poses. We pair the 41 animal figures in TOSCA from the same category to form a training set of 260 samples and a test set of 286 samples. Because the number of points in different shapes varies, we make a random downsample of the original point cloud to a fixed number $n = 1024$ , as done in CorrNet3D [32]. + +Evaluation Metrics. The evaluation metrics include the average correspondence error and the correspondence accuracy. Based on the Euclidean-based measure, the average correspondence error is defined for a pair of source and target shapes $(X,Y)$ as follows: + +$$ +e r r = \frac {1}{n} \sum_ {x _ {i} \in X} \| f (x _ {i}) - y _ {g t} \| _ {2}, \tag {14} +$$ + +where $y_{gt} \in Y$ is the ground-truth matching point to $x_{i}$ . The unit is centimeter(cm). And the correspondence accuracy can be formulated as: + +$$ +\operatorname {a c c} (\epsilon) = \frac {1}{n} \sum_ {x _ {i} \in X} \mathbb {I} \left(\left\| f \left(x _ {i}\right) - y _ {g t} \right\| _ {2} < \epsilon d\right), \tag {15} +$$ + +where $\mathbb{I}(\cdot)$ is the indicator function, $d$ is the maximal Euclidean distance between points in $Y$ , and $\epsilon \in [0,1]$ is an error tolerance. + +Implementation Details. For a fair comparison with existing methods [12, 32], we use the same DGCNN [29] backbone with four EdgeConv blocks as the feature extractor in the self-ensembling framework. The standard deviation $\sigma$ in Equation (4) is set as 0.1 for human datasets and 0.15 for animal datasets. In the Orientation Estimation Module, the feature encoding module is a simplified DGCNN with three EdgeConv [29] blocks whose layer output sizes are 64, 128, and 256. The $k$ of k-NN is set as 24, and the slope of all LeakyReLU is 0.2. We feed the output of the last layer into the proposed feature interaction module with the output size 256. Then we refine the feature by an EdgeConv layer with the same output size. The angle classification head consists of three Linear-BN-ReLU and an Output Linear. The channels are 256, 128, and 128 for the three Linear-BN-ReLU. The last Linear outputs the probability for classification. We set the number of bins $M$ as 8 in the angle classification head, where each bin represents a range of $45^{\circ}$ . The domain discriminator is a PointNet-like + +Table 1. Comparison on SHREC and SURREAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result. + +
MethodInputSHRECSURREAL
acc ↑err ↓acc ↑err ↓
Diff-FMaps [16]Point//4.0%7.1
3D-CODED [8]Point//2.1%8.1
Elementary [4]Point//2.3%7.6
CorrNet3D [32]Point0.4%33.86.0%6.9
DPC [12]Point15.3%5.617.7%6.1
OursPoint17.5%5.121.5%4.6
+ +![](images/107a83b25ce13f5d2525a9db379c9eefe94efa4280ee007a26dcef9240ccc411.jpg) +Figure 5. Correspondence accuracy at various error tolerances for human datasets. The methods are trained on the SHREC or SURREAL dataset and evaluated on SHREC'19 test pairs. Compared with other methods, our approach achieves an impressive performance improvement. + +module consisting of two MLPs in Equation (1). The channels of $\mathrm{MLP}_1$ are 512, 256, and 128, while the channels of $\mathrm{MLP}_2$ are 256, 128, and 256. We follow [12] and use a neighborhood size $k = 10$ in Equation (9) and (11). $\lambda_{c}c$ and $\lambda_{s}c$ in Equation (10) are set as 1 and 10, respectively. $\lambda_1$ , $\lambda_2$ , $\lambda_3$ , $\lambda_4$ , and $\lambda_5$ in Equation (12) are set as 0.1, 0.1, 1.0, 0.8, and 1.0, respectively. + +# 4.2. Comparison on Human Datasets + +For a fair comparison with existing methods, we do not use any post-processing or additional connectivity information. In addition, we follow DPC [12] and train our model on the SURREAL and SHREC datasets, respectively. Then we test our model on the official 430 SHREC'19 pairs. + +Evaluation on SHREC dataset. As shown in Table 1, our approach shows significant performance improvements on the SHREC benchmark and achieves new SOTA performance by $2.2\%$ improvements in accuracy and 0.5 reductions in error. To show the improvement under different error tolerances, we present the correspondence accuracy for point-based methods trained on SHREC and evaluated on the SHREC'19 test set. As shown in Figure 5, our method achieves better results with different error tolerances. + +Cross-dataset Generalization. In Table 1 and Figure 5, we also report the comparison with other methods on the SURREAL benchmark. The models are trained on the SURREAL dataset and evaluated on the SHREC'19 test + +Table 2. Comparison on TOSCA and SMAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result. + +
MethodTOSCASMAL
acc ↑err ↓acc ↑err ↓
3D-CODED [8]//0.5%19.2
Elementary [4]//0.5%13.7
CorrNet3D [32]0.3%32.75.3%9.8
DPC [12]34.7%2.833.2%5.8
Ours38.2%2.736.4%3.9
+ +![](images/b6f11d9c1729f333741605711ea606ddd67eb2e681e4d3aab894d93ad39fe994.jpg) +Figure 6. Correspondence accuracy at various error tolerances for animal datasets. The methods are trained on the TOSCA or SMAL dataset and evaluated on the official TOSCA test pairs. Compared with other methods, our method achieves a desirable performance improvement. + +set. The large-scale training set of the SURREAL dataset helps the deep learning-based methods perform better, even though there is a domain gap between the SURREAL and SHREC datasets. With our proposed method, the correspondence accuracy reaches $21.5\%$ at an error tolerance of 0.01, and the average correspondence error is reduced to 4.6 on the SHREC'19 test set. + +# 4.3. Comparison on Animal Datasets + +To verify the adaptability of our method to point clouds of different shapes, we conduct experiments on two animal benchmarks. Similar to human datasets, we train our method on TOSCA and SMAL datasets respectively, and test on the TOSCA test dataset. Table 2 and Figure 6 show the competitive results on TOSCA and SMAL benchmarks. Our method achieves a $3.5\%$ accuracy improvement on the TOSCA benchmark and a $3.2\%$ accuracy improvement on the SMAL benchmark. Compared with the human datasets, the animal datasets have various shapes with aligned orientations. Thus, the above performance gains come mainly from our self-ensembling framework, which can learn reliable features on complex data. To verify the effect of the Orientation Estimation Module, we test our method and baseline using different augmented test sets in Section 4.6. + +# 4.4. Comparison on Real-world Dataset + +CMU Panoptic [10] is a dataset of scanned point clouds of human subjects in various poses, containing noise, out + +Table 3. Comparison on CMU-Panoptic benchmark. Here, err means average Euclidean keypoint error (cm). + +
3D-CODED [8]DIF-Net [25]CorrNet [32]IFMatch [7]Ours
err17.115.314.88.53.2
+ +Table 4. Comparison on SHREC'20 benchmark. The training dataset is indicated in the bracket. + +
MethodSHREC’20 [SURREAL]SHREC’20 [SMAL]
acc ↑err ↓acc ↑err ↓
DPC [12]25.0%3.224.5%7.5
Ours29.9%1.225.4%2.9
+ +Table 5. Evaluation of the model with different designs on SURREAL. $\mathcal{L}_{css}$ is the consistency loss of the self-similarities, $\mathcal{L}_{ccs}$ is the consistency loss of the cross-similarities, $\tau$ means the stochastic transform, OEM means we use the Orientation Estimation Module, FIM is the Feature Interaction Module, and DAM is the Domain Adaptation Module. + +
τLccsLcssOEMFIMDAMSURREAL
acc ↑err ↓
XXXXXX17.7%6.1
✓✓XXXX18.8%5.7
✓✓✓XXX19.2%5.6
✓✓✓✓XX19.5%5.5
✓✓✓✓✓X20.4%5.1
✓✓✓✓✓✓21.5%4.6
+ +liers, occlusions, and clutter. Meanwhile, SHREC'20 [6] dataset contains real scans of various four-legged animal models. As shown in Table 3 and Table 4, we provide the results under two real scan datasets, demonstrating the remarkable robustness of our model to noise. + +# 4.5. Ablation Study + +Evaluation of the model with different designs. In this section, we perform extensive ablation studies on the SUR-REAL dataset to evaluate the effectiveness of each design. Table 5 demonstrates the performance of the model with different designs. Specifically, the first line is the results of DPC [12], which is our baseline model. The second row indicates that the self-ensembling framework with a stochastic transform achieves a better performance than the original model. By using $\mathcal{L}_{\mathrm{css}}$ to constrain the consistency of source features before and after augmentation, the correspondence accuracy can be improved by $0.4\%$ , as shown in the third row. As shown in the fourth row, adding the Orientation Evaluation Module without the Feature Interaction Module and the Domain Adaptation Module, the performance has a slight improvement. In the fifth row, by introducing the Feature Interaction Module into the Orientation Evaluation Module, the correspondence accuracy can be improved by $0.9\%$ . Finally, after utilizing the Domain Adaptation Module, the correspondence accuracy is improved by $1.1\%$ . + +Effect of the Self-Ensembling Framework. As shown in Table 6, we modify the self-ensembling framework to show the effect of each designed component. Removing either of the consistency losses leads to a drop in performance, which indicates that constraining the student net + +Table 6. Effect of the Self-Ensembling Framework on SUR-REAL. Here, we modify the self-ensembling framework to show the effect of each designed component. $\mathcal{N}$ means Gaussian noise, and $\mathcal{R}$ means random rotation along the vertical $z$ -axis. + +
SURREALw/o LCssw/o LCSSw/o Nw/o R
acc ↑19.9%20.3%20.6%18.8%
err ↓5.35.14.95.7
+ +![](images/b9af870379442b70c6ec5cb5a4da8714704fd5c240ada4666e4eb254c5e26de3.jpg) + +![](images/43d48cf8e3210133edaf3ff8a62692fc822dcda86c1258efa00448fc15686316.jpg) + +![](images/8c75a687ddac695771fcb316940078991edd48363a1dd26002d8326d2f93b868.jpg) + +![](images/9f3a63e70db2efbeab97bcaf8fe9abc6b5e0b7ae257d482921280962f36dc9f6.jpg) + +![](images/93a16187dbed881f24cb220f26392f50b841e2668ccc8418f44ce3165dcfdfea.jpg) +图1-2 + +![](images/b16d5cc372bb6aa502aed4c346e5564a64e66ea220c99c32694da03e41470de5.jpg) +Source + +![](images/9aaa9fba9bc3cce6dd83f86eb3e28655883754fe4701b43774fe9819f2e78359.jpg) +Source(K) + +![](images/bb9fd3dcb1f990be42da66d386179e8d860706cc245c66bcebfb3bcf84080075.jpg) +1. Probability distribution +Figure 7. Effect of the Orientation Estimation Module. We visualize of the point clouds before and after orientation rectification on SHREC'19 test set. We denote the raw source point cloud as Source and the rectified one as Source(R). Besides, we provide the probability distributions of the relative rotation angle prediction. + +Table 7. Robustness Analysis. To verify the robustness of our method, we test our method and baselines using different augmented test sets. $\mathcal{N}$ means Gaussian noise with standard deviation $\sigma$ of 0.1 and $\mathcal{R}$ means random rotation along the vertical $z$ -axis. + +
NRSURREAL(B)SURREALSMAL(B)SMAL
acc ↑err ↓acc ↑err ↓acc ↑err ↓acc ↑err ↓
XX17.47%6.3021.55%4.6533.79%5.7836.39%3.88
✓X14.38%8.7421.55%4.6630.21%6.0636.15%3.92
X✓8.99%9.3317.59%5.819.98%12.2428.16%5.63
✓✓7.80%11.2817.58%5.799.54%12.8027.60%5.89
+ +work with soft labels facilitates the consistency of the point cloud representations. When Gaussian noise and rotation augmentation are removed, the model performances show different degrees of degradation. The above experiments illustrate our self-ensemble method can obtain a more robust feature representation of the point cloud through data augmentation and consistency losses. + +Effect of the Orientation Estimation Module. To verify the effect of the proposed Orientation Estimation Module, we visualize the point clouds after orientation rectification and the probability distributions of the relative rotation angle predictions. As shown in Figure 7, our method can accurately estimate the relative rotation angle and align the point cloud orientation of the source with that of the target. More results refer to the supplementary materials. + +# 4.6. Robustness Analysis + +To verify the robustness of our method, we use different augmentations on the test set. As shown in Table 7, we use Gaussian noise and random rotation for data augmentation of the test sets. Compared to our method, the baseline shows a significant performance decrease for test sets + +![](images/050575b18857d86d97de0f7bf204533e93e651e5fed83a4c174b2b2bc313e10a.jpg) + +![](images/2309a5aa0f7f10e54ac65fa66727f89727438a886dada8b8f19f1279e0c7e1be.jpg) + +![](images/2baf8af0858b491fe4b6500825569d562cfbcadeecd83e787ebd13f3e85c0cc8.jpg) + +![](images/db1001576d9ab054d99c0b623f88a6c539c08e4b65cee6f141a08e7fc95af7ea.jpg) + +![](images/7164318afdeea78dc97c8758295f13040827a62709bcb35a220e3e302fe4aabd.jpg) +Target + +![](images/8884cf7ef63990b0459385d0a8cabbb47c2d41ec5bbeb912a6c950126a682d1e.jpg) +Source (Baseline) +Figure 8. Visualization of the correspondence results with rotation augmentation. With rotation augmentation on point cloud pairs, the baseline shows regrettable performances, while our method still retains desirable performances. + +![](images/cbd6a061659981308461c44d11f46630624985d0e88e407e805d8d72ca6458f4.jpg) +Source (Ours) + +![](images/413bcd26e99af84e0a06d200187d1be072dcfd7d67efdb7b5b5bc2bd315dc2fb.jpg) +Source (GT) + +![](images/401b3c9691120e65b4e245645387c967f5e7d23cfb377b3a1b7881a7c5fcbaac.jpg) +Figure 9. Visualization of point cloud pairs with deformations on real scanned Owlii dataset. In each pair, the left one is the source and the right one is the target. + +![](images/8ecc06dfcda3ba40ed71fe2e4d7797419c2e43fe4b430cffe839e8bcf379559f.jpg) + +![](images/e1555c591551d5d7278c6edad92ee38a02f6dcdaea66029dd660984f773e566c.jpg) + +![](images/129a0867a825bc653c4ff06bc3b8f2a0ca40635194d4e924196fdaa906604732.jpg) + +with Gaussian noise. For test sets with random rotation, the baseline performance is greatly degraded, while our method retains an acceptable performance. Figure 8 shows that our SE-ORNet can handle the orientation inconsistency issue of source and target well. To further verify the robustness and generalization of our method, we conduct experiments on the real scanned Owlii dataset [30] and present the visualization in Figure 9. The results show that our SE-ORNet trained on the synthetic SURREAL dataset still produces impressive performance on the real scanned dataset, demonstrating strong generalization and robustness. + +# 5. Conclusion + +In this paper, we propose a self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. To the best of our knowledge, SE-ORNet is the first self-ensembling network in this area. To solve the mismatching issue of symmetrical parts in point clouds with different body orientations, we design a plug-and-play lightweight orientation estimation module to align the orientations of two point clouds. Extensive experiments conducted on four shape correspondence benchmarks demonstrate the superior performance of SE-ORNet. + +# 6. Acknowledgements + +This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 12150007) and National Defense Basic Scientific Research program of China (Grant JCKY2020903B002). + +# References + +[1] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proceedings of the National Academy of Sciences, 103(5):1168-1172, 2006. 1, 2 +[2] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. Numerical geometry of non-rigid shapes. 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However, humans and some animals have bilateral symmetry and various orientations, which lead to severe mispredictions of symmetrical parts. Besides, point cloud noise disrupts consistent representations for point cloud and thus degrades the shape correspondence accuracy. To address the above issues, we propose a Self-Ensembling ORientation-aware Network termed SE-ORNet. The key of our approach is to exploit an orientation estimation module with a domain adaptive discriminator to align the orientations of point cloud pairs, which significantly alleviates the mispredictions of symmetrical parts. Additionally, we design a self-ensembling framework for unsupervised point cloud shape correspondence. In this framework, the disturbances of point cloud noise are overcome by perturbing the inputs of the student and teacher networks with different data augmentations and constraining the consistency of predictions. 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The visualization of dense point matching results. Three point cloud pairs have different relative rotation angles. GT denotes ground truth. The correspondence is visualized by transferring colors from source to target according to matching results. The baseline predicts many false matches, especially for symmetrical, similar parts of the object. Our method achieves accurate matches for these parts with our orientation estimation module." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 715 + ], + "type": "text", + "content": "tween two point clouds, spectral-based methods [1, 9, 15, 19, 28] have been proven as practical shape correspondence methods by computing functional mapping between the projected features and learning a transformation for the correspondence. Nevertheless, the spectral-based methods suffer from complicated pre-processing steps and the necessity for connectivity information between points. With the rapid development of deep learning, many fully supervised point cloud shape correspondence methods [4, 8, 16] have been proposed to lead to remarkable progress. 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However, in the scanning process of 3D scanner, due to light, vibration and other factors, point cloud noise will be inevitably generated. Meanwhile, the preprocessing of point cloud (such as random subsampling) will also introduce noise. Unfortunately, the previous methods fail to adequately consider the point cloud noise, which negatively impacts the point cloud representations. Besides the noise, existing methods lack attention to symmetrical parts of the body. The mismatching issue of symmetrical parts is challenging in this task, which was also spotted by the previous method [32] but has yet to be solved." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 207, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 289, + 399 + ], + "type": "text", + "content": "By studying the previous point-based shape correspondence methods [4, 8, 12, 16, 32], we summarize two key issues that need consideration to achieve a more accurate shape correspondence: 1) How to overcome the disturbance of point cloud noise to get robust and consistent point cloud representations? Point cloud noise perturbs the spatial coordinates of point cloud and interferes with local structure modeling. Therefore, it is necessary to overcome noise disturbances. 2) How to solve the mismatching issue of symmetrical parts in point clouds with different body orientations? As shown in Figure 1, for the pair of bilaterally symmetrical human point clouds facing the opposite directions, existing methods predict the completely reverse and seriously wrong point cloud correspondence due to the similar structure and position. The specific relative rotation angles lead to severe mispredictions of symmetrical parts." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 403, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 289, + 714 + ], + "type": "text", + "content": "To achieve the above goals, we propose a Self-Ensembling Orientation-aware Network (SE-ORNet) for unsupervised point cloud shape correspondence. We integrate orientation modeling and consistent point cloud representations under a unified self-ensembling framework, which consists of a pair of teacher and student models, an orientation estimation module, and an adaptive domain discriminator. Firstly, we design a new augmentation scheme to produce augmented samples with rotation and Gaussian noise, and record the rotation angles as rotation angle labels. Then, we formulate soft labels and consistency losses to encourage consensus among ensemble predictions of augmented and raw samples, aiming to perceive the difference in body orientation and overcome the point cloud noise disturbance to obtain consistent point cloud representations. In addition, we design a plug-and-play lightweight Orientation Estimation Module, which aligns the orientations of two point clouds to solve the mismatching issue of symmetrical parts in point clouds. Without the real label of relative rotation angle between the source and target, we supervise the training with the rotation angle labels and calculate angle losses. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. Therefore, we design a discriminator to achieve domain adaptation and calculate the domain losses. Furthermore, the discriminator facilitates the Orientation Estima" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "tion Module to mine the valuable knowledge in the rotation-augmented samples to compensate for the information loss of the real relative rotation angles." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 108, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 547, + 240 + ], + "type": "text", + "content": "In summary, the main contributions of this work are as follows: (i) We design a plug-and-play lightweight Orientation Estimation Module that accurately aligns the orientations of point cloud pairs to achieve correct matching results of symmetrical parts. (ii) We integrate point cloud orientation modeling and consistent point cloud representation learning with the disturbance of point cloud noise into a unified self-ensembling framework. (iii) Our method attains state-of-the-art performance on both human and animal benchmarks, and extensive experimental results verify the superiority of our designs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 251, + 392, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 392, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 392, + 264 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 270, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 317 + ], + "type": "text", + "content": "In this Section, we give a brief overview of related works on point cloud shape correspondence, including learning on point clouds, shape correspondence, and self-ensembling approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 319, + 546, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 546, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 546, + 484 + ], + "type": "text", + "content": "Learning on Point Clouds. PointNet [21] learns from global information through multi-layer perceptrons and max-pooling operation. PointNet++ [22] devises a hierarchical architecture that recursively partitions the point cloud to extract local features more effectively. Recent works explore local aggregators via relations [23, 31, 33], and graphs [29, 34]. PointCNN [13] transforms neighboring points to the canonical order to apply traditional convolution on point clouds. DGCNN [29] creates a graph in the feature space and designs EdgeConv [29] to learn the edge features of the graph in each layer. However, the methods are commonly based on some assumptions of implicit local geometry, which may result in sensitivity to point cloud disturbances." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 713 + ], + "type": "text", + "content": "Shape Correspondence. As an active research area in computer vision and graphics, point cloud shape correspondence methods roughly include spectral-based methods [1,9,15,19,28] and point-based methods [4,8,12,16,32]. Spectral-based methods require connectivity information to compute the LBO eigenvectors as basis functions and infer a linear transformation for shape correspondence. However, with regard to point cloud data, connectivity information is difficult to obtain directly while point-based methods directly process point clouds without connectivity information to find the dense point-to-point mapping between two point clouds with deformable 3D shapes. Deprelle et al. [4] propose representing shapes as the deformation and combination of learnable elementary 3D structures. Groueix et al. [8] employ an encoder-decoder architecture to obtain and constrain the similarity matrix with manually annotated labels. The deep learning methods train their neural networks in a data-driven manner and improve performance to a large extent. However, manually labeling the point-to-point cor" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5365" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 68, + 483, + 235 + ], + "blocks": [ + { + "bbox": [ + 109, + 68, + 483, + 235 + ], + "lines": [ + { + "bbox": [ + 109, + 68, + 483, + 235 + ], + "spans": [ + { + "bbox": [ + 109, + 68, + 483, + 235 + ], + "type": "image", + "image_path": "d9fd6cf8db6c168bb7a930a5232fec6ff9b6b2b5b0aee730b3505306a20e1c3c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "text", + "content": "Figure 2. The overview of our self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. " + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "text", + "content": " is generated from the raw source point cloud " + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "text", + "content": " by random rotation and Gaussian noise, while " + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "inline_equation", + "content": "Y_{s}" + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "text", + "content": " is only augmented by Gaussian noise. We design the Orientation Estimation Module to estimate the rotation " + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 236, + 547, + 314 + ], + "type": "text", + "content": " of the source with respect to the target and align the point cloud in position space. Afterward, the aligned point cloud pairs are input to the teacher and student models, respectively, and the correspondence is predicted through a DGCNN backbone. Finally, we supervise the student model by the consistency losses and the construction losses, and the teacher model updates the parameters using the exponential moving average (EMA) strategy. The gradient reversal layer (GRL) acts as the identity function during forward propagation, but is multiplied by -1 during backward propagation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 319, + 288, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 438 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 438 + ], + "type": "text", + "content": "respondence between two point clouds in 3D space takes much time and effort. Therefore, some unsupervised point cloud shape correspondence methods [12, 32] are proposed to reduce the overhead of labeling. CorrNet3D [32] is the first unsupervised deep learning framework. DPC [12] designs several reconstruction losses to smooth point cloud representations. Due to the lack of annotation, the mismatching issue of symmetrical parts in point clouds with different orientations has become an undeniable problem in unsupervised shape correspondence area." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "text", + "content": "Self-ensembling Approaches. Self-ensembling approaches improve the model generalization by encouraging consensus among ensemble predictions of unknown samples with small perturbations. " + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "text", + "content": " model [24] consists of two identical parallel branches that respectively take raw images and corrupted images as inputs. In contrast to " + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\Gamma" + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "text", + "content": " model, " + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "text", + "content": " model [11] integrates two parallel branches into a single branch. As an extension of the " + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 46, + 439, + 287, + 643 + ], + "type": "text", + "content": " model, the temporal model [11] forces the consistency between the outputs and the aggregated outputs over previous training epochs. Mean Teacher [27] replaces network prediction average with network parameter average via the exponential moving average (EMA) strategy. We design a framework similar to Mean Teacher and adapt it for the unsupervised point cloud shape correspondence task. The proposed framework facilitates the network to yield consistent and accurate predictions under noise perturbations and orientation rotations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 651, + 102, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 102, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 102, + 662 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 671, + 114, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 114, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 114, + 682 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The unsupervised point cloud shape correspondence is to find the mapping " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "f: X \\to Y" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " between two point clouds" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": "source " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": ") without ground-truth correspondence annotations. Figure 2 illustrates the pipeline of our approach. Given source " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": " point clouds, we utilize random rotation and Gaussian noise to generate the augmented source point cloud " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": ", while we augment " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": " by Gaussian noise to obtain " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "Y_{s}" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": ". Due to the absence of the relative rotation angle labels " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\theta, \\theta_{s}" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": ", we use the rotation angle labels " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\theta_{x}" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": " to guide the Orientation Estimation Module learning and transfer the valuable information by the adversarial domain adaptation method. The aligned point cloud pairs are input to the teacher and student models, respectively, and we use the DGCNN [29] backbone to output the similarity matrices. After that, we generate two reconstructed point clouds " + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "inline_equation", + "content": "\\hat{X}, \\hat{Y}" + }, + { + "bbox": [ + 304, + 319, + 545, + 535 + ], + "type": "text", + "content": " based on the predicted similarity matrices by the student model. Finally, the student model is supervised by the consistency losses and the construction losses, while the parameters of teacher model are updated by the exponential moving average (EMA) strategy." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 548, + 437, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 437, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 437, + 559 + ], + "type": "text", + "content": "3.2. Orientation Estimation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "text", + "content": "We provide the overview of the orientation estimation in Figure 3. The encoded features " + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "inline_equation", + "content": "P_{in}^{s}, P_{in}^{t}" + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "text", + "content": " are fed into the Feature Interaction Module (FIM) for feature fusion. The fused features " + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "text", + "content": " are enhanced by a single-layer edge-conv. To predict the relative orientation, the features " + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "inline_equation", + "content": "\\hat{P}_{in}" + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "text", + "content": " are fed into the classification head. We also input " + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "inline_equation", + "content": "\\hat{P}_{in}" + }, + { + "bbox": [ + 304, + 568, + 545, + 663 + ], + "type": "text", + "content": " into the discriminator to determine whether the pair comes from the same shape or from different shapes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Feature Interaction Module. As shown in Figure 4, the feature interaction module is a query-based graph convolution. The point features in the source point cloud are updated by querying points with similar features in the tar" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5366" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 279, + 155 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 279, + 155 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 279, + 155 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 279, + 155 + ], + "type": "image", + "image_path": "44d0a37bd76cc1df63782fcd1b61dc6db626a3c04e7ab9cc6f3aa0a770590a0c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 155, + 264, + 163 + ], + "lines": [ + { + "bbox": [ + 70, + 155, + 264, + 163 + ], + "spans": [ + { + "bbox": [ + 70, + 155, + 264, + 163 + ], + "type": "text", + "content": "Figure 3. The overview of Orientation Estimation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": "get point cloud. Let " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "P_{in}^{s}, P_{in}^{t}" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": " be the inputs of the feature interaction module. For each point " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "p_i \\in P_{in}^{s}" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": ", we first consider it as a query to search for the k-nearest neighbors " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "q_i^j, 1 \\leq j \\leq k" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": " in the target point cloud " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "P_{in}^{t}" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": " with respect to the Euclidean distance defined in the " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "C_1" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": "-dimensional feature space. To better model the relative rotation relationships in space, we use spatial position differences and feature differences as features of each edge, denoted as " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "(p_i, q_i^j - p_i)" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "p_i, q_i^j \\in \\mathcal{R}^{(C_1 + 3)}" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": ". Then we use a multilayer perceptron (MLP) to compute a new feature " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "e_{ji} = \\mathrm{MLP}(p_i, q_i^j - p_i)" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": " from each edge. For each point, we aggregate its k edge features into a new point feature through Max pooling and ReLU activation. In addition, we add a linear layer that skip-connects the output " + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 46, + 175, + 287, + 354 + ], + "type": "text", + "content": " with the input to make the block residual." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "text", + "content": "Rotation Classification Head. We concatenate the output feature " + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "text", + "content": " and the enhanced feature as the input " + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\hat{P}_{in}" + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "text", + "content": " of the Rotation Classification Head. Inspired by the orientation prediction in the point cloud detection methods [18,20], we consider the prediction of relative rotation angle as a classification task. That coarsely aligning the orientations of the source and target point clouds is enough to solve the problem of mismatching issue of symmetrical parts in point clouds. Thus, we pre-define " + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "text", + "content": " equally divided angle bins and then use an MLP head to classify the relative rotation angle into those pre-defined categories. Specifically, we compress " + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\hat{P}_{in}" + }, + { + "bbox": [ + 46, + 357, + 287, + 548 + ], + "type": "text", + "content": " using maximum pooling and average pooling to obtain the global features and then predict the probability distribution of the relative rotation angle. Finally, we choose the angle bin with the highest probability as the relative rotation angle of the source and target point clouds." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": "Adversarial Domain Adaptation. Due to the absence of relative rotation angle " + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\theta, \\theta_s" + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": ", we utilize the relative rotation angle " + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\theta_x" + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": " to guide the Orientation Estimation Module learning. However, there is a noticeable domain gap between the rotation-augmented samples and the real samples. To eliminate the domain gap, we use a discriminator to identify whether the input features " + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\hat{P}_{in}" + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": " of the classification head are from the rotation-augmented samples or the real samples. Specifically, we use a PointNet-like module to process the features " + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\hat{P}_{in}" + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": " and predict the probability " + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": " that the " + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "inline_equation", + "content": "P_{in}" + }, + { + "bbox": [ + 46, + 551, + 287, + 682 + ], + "type": "text", + "content": " is from the real samples:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 88, + 694, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 694, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 88, + 694, + 287, + 717 + ], + "type": "interline_equation", + "content": "d _ {i} = \\mathrm {M L P} _ {2} \\left\\{\\max _ {N} \\left\\{\\mathrm {M L P} _ {1} \\left[ \\hat {P} _ {i n} \\right] \\right\\} \\right\\}, \\tag {1}", + "image_path": "b231787b2cf75f09e0e00fa717cdd52dfdf8fae57861f40702038d1dd69edde7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 356, + 70, + 495, + 135 + ], + "blocks": [ + { + "bbox": [ + 356, + 70, + 495, + 135 + ], + "lines": [ + { + "bbox": [ + 356, + 70, + 495, + 135 + ], + "spans": [ + { + "bbox": [ + 356, + 70, + 495, + 135 + ], + "type": "image", + "image_path": "c792e900c6dcd405a7afb923cfea4111281dffffb55c9242941222192ab1d51b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 136, + 520, + 146 + ], + "lines": [ + { + "bbox": [ + 331, + 136, + 520, + 146 + ], + "spans": [ + { + "bbox": [ + 331, + 136, + 520, + 146 + ], + "type": "text", + "content": "Figure 4. The Feature Interaction Module (FIM)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 152, + 545, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 152, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 545, + 199 + ], + "type": "text", + "content": "where max refers to the global Max pooling. By using the discriminator, we train the model to disregard the distinction between the two domains and instead prioritize learning the relative rotation information." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 200, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 200, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 200, + 545, + 224 + ], + "type": "text", + "content": "Relative Rotation Angle Supervision. The angle loss is computed with a cross entropy loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 365, + 232, + 545, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 232, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 365, + 232, + 545, + 265 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a n g l e}} = - \\sum_ {i = 1} ^ {M} \\theta_ {x} ^ {i} \\log \\left(\\hat {\\theta} _ {x} ^ {i}\\right), \\tag {2}", + "image_path": "f843e2686eb13f950fe3c486150ea995b811aea2071ee5360bc6d5533baba1cc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "text", + "content": " is the number of the pre-defined angle bins, " + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\hat{\\theta}_x^i" + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "inline_equation", + "content": "\\theta_x^i" + }, + { + "bbox": [ + 305, + 274, + 545, + 322 + ], + "type": "text", + "content": " denote the predicted probability distribution of relative rotation angle and the rotation angle label, respectively. The domain loss is computed with a Focal Loss [14]:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 343, + 331, + 545, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 331, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 343, + 331, + 545, + 345 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d o m a i n}} = - \\left(1 - d _ {i}\\right) ^ {\\gamma} \\log \\left(d _ {i}\\right), \\gamma > 1, \\tag {3}", + "image_path": "4c0a9a6b180bfbf6d11dd32c227eaafd0c2a5aaa67ea20cab84b93f13124fe5a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{domain}" + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "content": " denotes the domain loss and " + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 353, + 545, + 376 + ], + "type": "text", + "content": " denotes the tunable focusing parameter." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 384, + 463, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 463, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 463, + 396 + ], + "type": "text", + "content": "3.3. Self-Ensembling Framework" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 402, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 520 + ], + "type": "text", + "content": "As shown in Table 7, the point cloud orientation and Gaussian noise are two crucial factors in the unsupervised point cloud shape correspondence task. The existing methods ignore noise interference on the point cloud correspondence, making it difficult to obtain robust point cloud representations. To address the above problems, we utilize the Mean Teacher architecture [27] and design two consistency losses to constrain the student model for robust feature representations under orientation disturbance and Gaussian noise interference." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "text", + "content": "Stochastic Transform. We apply stochastic transformations that include rotation and Gaussian noise on the point clouds for the student network formulated as " + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\tau = (\\mathcal{R},\\mathcal{N})" + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "text", + "content": ". More specifically, given the raw point cloud pair " + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "inline_equation", + "content": "(X,Y)" + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "text", + "content": ", we first apply Gaussian noise to the target point cloud " + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 521, + 545, + 582 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 364, + 590, + 545, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 590, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 364, + 590, + 545, + 604 + ], + "type": "interline_equation", + "content": "y _ {i} ^ {s} = y _ {i} + n _ {i}, n _ {i} \\sim \\mathcal {N} (0, \\sigma^ {2}), \\tag {4}", + "image_path": "6a388200832c0150da9796cc91e9fa46396ed337064ba97a44f209c7c86ad808.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(0,\\sigma^2)" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": " means the Gaussian distribution with the 0 mean and " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": " standard deviation. Then, we utilize Gaussian noise and random rotation along the vertical " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": "-axis to augment the source point cloud " + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 611, + 545, + 659 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 344, + 667, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 667, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 344, + 667, + 545, + 681 + ], + "type": "interline_equation", + "content": "x _ {i} ^ {s} = \\mathcal {R} \\left(\\theta_ {x}\\right) \\odot x _ {i} + n _ {i}, n _ {i} \\sim \\mathcal {N} \\left(0, \\sigma^ {2}\\right), \\tag {5}", + "image_path": "d78b20f45c742aee3b4351385736f6a06fca7049832d62279dd6dccb4527b512.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " denotes the rotation around the " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "-axis and " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{x}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the rotation angle sampled from " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "[0, 2\\pi]" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5367" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": "Architecture of Teacher & Student Models. Given the raw and augmented point cloud pairs " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "(X,Y)" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "(X_s,Y_s)" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": ", we use the Orientation Estimation Module to align source and target orientations. Then, our approach follows the Mean Teacher paradigm [27] and inputs the aligned point cloud pairs " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "(\\tilde{X}_s,Y_s)" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "(\\tilde{X},Y)" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": " into the student and teacher models, respectively. We use a variant of DGCNN [29] backbone to embed the aligned source " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "\\tilde{X}" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": " and target " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": " point clouds to a high-dimensional feature space as " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "F_x,F_y\\in \\mathcal{R}^{N\\times C}" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": ". Unlike DGCNN, which uses dynamic graphs to select neighbors, we follow [12] to use static graphs for the neighbors. Specifically, we select the k-nearest neighbors in the coordinate space instead of the feature space. Then, we use the cosine similarity " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "S_{xy}" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": " of source and target point features " + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "F_x,F_y" + }, + { + "bbox": [ + 47, + 72, + 289, + 252 + ], + "type": "text", + "content": " to measure their correspondence." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 124, + 260, + 287, + 291 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 260, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 124, + 260, + 287, + 291 + ], + "type": "interline_equation", + "content": "s _ {i j} = \\frac {F _ {x} ^ {i} \\cdot \\left(F _ {y} ^ {j}\\right) ^ {T}}{\\| F _ {x} ^ {i} \\| _ {2} \\| F _ {y} ^ {j} \\| _ {2}}, \\tag {6}", + "image_path": "f930a8377339256fee382b9de8c2fe8f2ffcc4f24fb4651e75a00c6510905cc5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "inline_equation", + "content": "F_x^i, F_y^j" + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "inline_equation", + "content": "i^{\\text{th}}" + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "inline_equation", + "content": "j^{\\text{th}}" + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "content": " rows of " + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "inline_equation", + "content": "F_x, F_y" + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "content": ", respectively, and " + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "inline_equation", + "content": "(\\cdot)^T" + }, + { + "bbox": [ + 47, + 299, + 287, + 324 + ], + "type": "text", + "content": " denotes a transpose operation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "text", + "content": "Soft Label & Consistency Loss. To enhance the perception of local structures and the robustness of the model, we design two consistency losses to maintain feature consistency under Gaussian noise and orientation disturbances. We utilize the cross-similarity " + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "inline_equation", + "content": "S_{xy}^{t}" + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "text", + "content": " obtained from the teacher model as a soft label and the Smooth " + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "text", + "content": " loss to constrain the cross-similarities " + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "inline_equation", + "content": "S_{x_s y_s}^s" + }, + { + "bbox": [ + 47, + 324, + 287, + 410 + ], + "type": "text", + "content": " of the student model:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 100, + 418, + 287, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 418, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 100, + 418, + 287, + 434 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c c s} = \\operatorname {S m o o t h} L _ {1} \\left(S _ {x y} ^ {t}, S _ {x _ {s} y _ {s}} ^ {s}\\right), \\tag {7}", + "image_path": "73369dc691e515ef0847e65f7794794ecb1c691e6b1caa91aba8abdee5606cf0.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ccs}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " denotes the consistency loss of the cross-similarities. To reduce the interference of point cloud orientation on correspondence estimation, we model the feature consistency of the strongly augmented source " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "X_{s}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " and raw source " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": ". We constrain the consistency of the self-similarities " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "S_{xx}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " to ensure the consistency of neighboring points with similar features. We use the feature embedding " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "F_{x}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " of the source point cloud to compute the self-similarity " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "S_{xx}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " by Equation (6). Then, we use the Smooth " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " loss to constrain the self-similarities " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "S_{x_s x_s}^s" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " of the student model with the self-similarities " + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "inline_equation", + "content": "S_{xx}^{t}" + }, + { + "bbox": [ + 47, + 441, + 287, + 574 + ], + "type": "text", + "content": " from the teacher model:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 99, + 581, + 287, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 581, + 287, + 596 + ], + "spans": [ + { + "bbox": [ + 99, + 581, + 287, + 596 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c s s} = \\operatorname {S m o o t h} L _ {1} \\left(S _ {x x} ^ {t}, S _ {x _ {s} x _ {s}} ^ {s}\\right), \\tag {8}", + "image_path": "c4bf8ba09e698d09a2f2b46a0373d786675d7bfd63206f7a2f027a657ef510eb.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 604, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 287, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 604, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{css}}" + }, + { + "bbox": [ + 47, + 604, + 287, + 652 + ], + "type": "text", + "content": " denotes the consistency loss of the self-similarities. The above two consistency losses ensure the robustness of feature embedding under Gaussian noise and orientation disturbances for accurate correspondence." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 659, + 202, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 202, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 202, + 672 + ], + "type": "text", + "content": "3.4. Model Training & Inference" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "In addition to the above mentioned consistency losses, angle loss, and domain loss, we use reconstruction losses to promote a unique point matching between the shape pair." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "Following the previous work [12], we perform the cross-construction operation to construct the target shape " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " by using the feature similarity " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "S_{xy}" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " between source and target point clouds, and the target point coordinates " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 354, + 126, + 545, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 126, + 545, + 158 + ], + "spans": [ + { + "bbox": [ + 354, + 126, + 545, + 158 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {x _ {i}} = \\sum_ {j \\in \\mathcal {N} _ {\\mathcal {Y}} (x _ {i})} \\frac {e ^ {s _ {i j}}}{\\sum l \\in \\mathcal {N} _ {\\mathcal {Y}} (x _ {i}) e ^ {s _ {i l}}} y _ {j}, \\tag {9}", + "image_path": "95ad3553edb0d36ba76f43446e7881e5f684bcb49b749da9e02ead3cb78ed6d3.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{Y}}(x_i)" + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "text", + "content": " is latent k-nearest neighbors of " + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "text", + "content": " in the target " + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "text", + "content": " . When the source and target point clouds are identical, we refer to the construction operation as selfconstruction. As shown in Figure 2, we obtain the point clouds " + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "inline_equation", + "content": "\\hat{Y}_s^x,\\hat{X}_s^x,\\hat{X}_s^y,\\hat{Y}_s^y" + }, + { + "bbox": [ + 304, + 164, + 545, + 247 + ], + "type": "text", + "content": " by cross-construction and selfconstruction. Then, we constrain the training with the construction loss as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 322, + 254, + 545, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 254, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 322, + 254, + 545, + 285 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {c o n s}} = \\lambda_ {c c} \\left(\\mathrm {C D} \\left(Y _ {s}, \\hat {Y} _ {s} ^ {x}\\right) + \\mathrm {C D} \\left(X _ {s}, \\hat {X} _ {s} ^ {y}\\right)\\right) \\tag {10} \\\\ + \\lambda_ {s c} \\left(\\mathrm {C D} \\left(Y _ {s}, \\hat {Y} _ {s} ^ {y}\\right) + \\mathrm {C D} \\left(X _ {s}, \\hat {X} _ {s} ^ {x}\\right)\\right), \\\\ \\end{array}", + "image_path": "c2f723907cee14646c836e09e9ab2a56ce78890240fb174879001a86d9fc050f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 293, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 293, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\lambda_{cc},\\lambda_{sc}" + }, + { + "bbox": [ + 304, + 293, + 545, + 340 + ], + "type": "text", + "content": " are hyperparameters and CD means the Chamfer Distance. Finally, we add a regularization term to correspond close points in the source to close points in the target." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 316, + 347, + 545, + 374 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 347, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 316, + 347, + 545, + 374 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {n o r m}} = \\sum_ {i} \\sum_ {l \\in \\mathcal {N} _ {\\mathcal {Y}} \\left(x _ {i}\\right)} e ^ {\\left\\| x _ {i} - x _ {l} \\right\\| _ {2} ^ {2} / \\alpha} \\| \\hat {y} _ {x _ {i}} - \\hat {y} _ {x _ {l}} \\| _ {2} ^ {2}, \\tag {11}", + "image_path": "6b4835c4b67a7e09c8af436634b1b067195ccdca39adfbfc9357fb91c3df1e6f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{Y}}(x_i)" + }, + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "type": "text", + "content": " is the same as defined in Equation 9 and " + }, + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 381, + 545, + 418 + ], + "type": "text", + "content": " is a hyperparameter. To sum up, the total loss of our unsupervised point cloud shape correspondence method is:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 325, + 426, + 545, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 426, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 325, + 426, + 545, + 453 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {c c s}} + \\lambda_ {2} \\mathcal {L} _ {\\text {c s s}} + \\lambda_ {3} \\mathcal {L} _ {\\text {a n g l e}} \\tag {12} \\\\ + \\lambda_ {4} \\mathcal {L} _ {\\text {d o m a i n}} + \\mathcal {L} _ {\\text {c o n s}} + \\lambda_ {5} \\mathcal {L} _ {\\text {n o r m}}, \\\\ \\end{array}", + "image_path": "eab886a7d426ef9792a8da4d60cc3c09877ddb0a6b72696b86ee37f8b35ddaf7.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "content": " is a hyperparameter, balancing the contribution of different loss terms. During inference, we set the closest point " + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "inline_equation", + "content": "y_{j}^{*}" + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "content": " in the feature space for each point " + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 460, + 545, + 509 + ], + "type": "text", + "content": " as its corresponding point. This selection rule can be formulated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 358, + 516, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 516, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 358, + 516, + 545, + 536 + ], + "type": "interline_equation", + "content": "f \\left(x _ {i}\\right) = y _ {j ^ {*}}, j ^ {*} = \\underset {j} {\\operatorname {a r g m a x}} \\left(s _ {i j}\\right). \\tag {13}", + "image_path": "b674f4f585ef87b511a785cebce46767e13f083eba1b1fb4e829e566bfe75ee6.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 544, + 388, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 388, + 557 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 388, + 557 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 563, + 422, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 422, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 422, + 576 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Dataset. To demonstrate the effectiveness and generalization of our method, we perform experiments on human and animal datasets. We conduct experiments on human datasets according to DPC's [12] scheme. For the large-scale dataset, we randomly downsample the SURREAL [8] dataset, which contains 230000 training shapes, into 2000 shape pairs as the training set. For the test set, we use the SHREC'19 [17] dataset, which contains 44 real human models, and pair them into 430 annotated test examples. To further verify the ability of our method to learn discriminative feature expression with a small data size, we train" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5368" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "SE-ORNet on the pairs randomly sampled from 44 SHREC instances, and the testing is still conducted on the official 430 SHREC'19 pairs." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 287, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 287, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 287, + 263 + ], + "type": "text", + "content": "For animal datasets, we also conduct experiments with different dataset scales. We use the large-scale SMAL [35] dataset and TOSCA [2] dataset as the training set and test set, respectively. SMAL dataset consists of parameterized models of various animals, and we randomly sample SMAL to obtain the corresponding shape pairs as the training set. TOSCA is generated by deforming three template meshes (human, dog, and horse) into multiple poses. We pair the 41 animal figures in TOSCA from the same category to form a training set of 260 samples and a test set of 286 samples. Because the number of points in different shapes varies, we make a random downsample of the original point cloud to a fixed number " + }, + { + "bbox": [ + 46, + 108, + 287, + 263 + ], + "type": "inline_equation", + "content": "n = 1024" + }, + { + "bbox": [ + 46, + 108, + 287, + 263 + ], + "type": "text", + "content": ", as done in CorrNet3D [32]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "type": "text", + "content": "Evaluation Metrics. The evaluation metrics include the average correspondence error and the correspondence accuracy. Based on the Euclidean-based measure, the average correspondence error is defined for a pair of source and target shapes " + }, + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "type": "inline_equation", + "content": "(X,Y)" + }, + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 101, + 332, + 287, + 360 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 101, + 332, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 101, + 332, + 287, + 360 + ], + "type": "interline_equation", + "content": "e r r = \\frac {1}{n} \\sum_ {x _ {i} \\in X} \\| f (x _ {i}) - y _ {g t} \\| _ {2}, \\tag {14}", + "image_path": "39c08a06cf12fc4664070b1b99eddb961c406b39e96fdef557d00452f7697c3c.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "type": "inline_equation", + "content": "y_{gt} \\in Y" + }, + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "type": "text", + "content": " is the ground-truth matching point to " + }, + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 369, + 287, + 404 + ], + "type": "text", + "content": ". The unit is centimeter(cm). And the correspondence accuracy can be formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 68, + 412, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 68, + 412, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 68, + 412, + 287, + 441 + ], + "type": "interline_equation", + "content": "\\operatorname {a c c} (\\epsilon) = \\frac {1}{n} \\sum_ {x _ {i} \\in X} \\mathbb {I} \\left(\\left\\| f \\left(x _ {i}\\right) - y _ {g t} \\right\\| _ {2} < \\epsilon d\\right), \\tag {15}", + "image_path": "f611858df0a1b19a58d96686e57ffb32ca5abffac18bf99520734b3a16d87ab9.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbb{I}(\\cdot)" + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "text", + "content": " is the indicator function, " + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "text", + "content": " is the maximal Euclidean distance between points in " + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "inline_equation", + "content": "Y" + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\epsilon \\in [0,1]" + }, + { + "bbox": [ + 46, + 450, + 287, + 485 + ], + "type": "text", + "content": " is an error tolerance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": "Implementation Details. For a fair comparison with existing methods [12, 32], we use the same DGCNN [29] backbone with four EdgeConv blocks as the feature extractor in the self-ensembling framework. The standard deviation " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " in Equation (4) is set as 0.1 for human datasets and 0.15 for animal datasets. In the Orientation Estimation Module, the feature encoding module is a simplified DGCNN with three EdgeConv [29] blocks whose layer output sizes are 64, 128, and 256. The " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " of k-NN is set as 24, and the slope of all LeakyReLU is 0.2. We feed the output of the last layer into the proposed feature interaction module with the output size 256. Then we refine the feature by an EdgeConv layer with the same output size. The angle classification head consists of three Linear-BN-ReLU and an Output Linear. The channels are 256, 128, and 128 for the three Linear-BN-ReLU. The last Linear outputs the probability for classification. We set the number of bins " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": " as 8 in the angle classification head, where each bin represents a range of " + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 46, + 486, + 287, + 713 + ], + "type": "text", + "content": ". The domain discriminator is a PointNet-like" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 118, + 535, + 206 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 114 + ], + "type": "text", + "content": "Table 1. Comparison on SHREC and SURREAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 118, + 535, + 206 + ], + "lines": [ + { + "bbox": [ + 315, + 118, + 535, + 206 + ], + "spans": [ + { + "bbox": [ + 315, + 118, + 535, + 206 + ], + "type": "table", + "html": "
MethodInputSHRECSURREAL
acc ↑err ↓acc ↑err ↓
Diff-FMaps [16]Point//4.0%7.1
3D-CODED [8]Point//2.1%8.1
Elementary [4]Point//2.3%7.6
CorrNet3D [32]Point0.4%33.86.0%6.9
DPC [12]Point15.3%5.617.7%6.1
OursPoint17.5%5.121.5%4.6
", + "image_path": "26012345ab2853711dedf6fe133b2d6a28af08ff995ac9c6d302df1f0b9fb3ad.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 332, + 211, + 515, + 327 + ], + "blocks": [ + { + "bbox": [ + 332, + 211, + 515, + 327 + ], + "lines": [ + { + "bbox": [ + 332, + 211, + 515, + 327 + ], + "spans": [ + { + "bbox": [ + 332, + 211, + 515, + 327 + ], + "type": "image", + "image_path": "107a83b25ce13f5d2525a9db379c9eefe94efa4280ee007a26dcef9240ccc411.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 327, + 545, + 382 + ], + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 382 + ], + "type": "text", + "content": "Figure 5. Correspondence accuracy at various error tolerances for human datasets. The methods are trained on the SHREC or SURREAL dataset and evaluated on SHREC'19 test pairs. Compared with other methods, our approach achieves an impressive performance improvement." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": "module consisting of two MLPs in Equation (1). The channels of " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}_1" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": " are 512, 256, and 128, while the channels of " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\mathrm{MLP}_2" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": " are 256, 128, and 256. We follow [12] and use a neighborhood size " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "k = 10" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": " in Equation (9) and (11). " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_{c}c" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_{s}c" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": " in Equation (10) are set as 1 and 10, respectively. " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_1" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_3" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_4" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\lambda_5" + }, + { + "bbox": [ + 305, + 388, + 545, + 473 + ], + "type": "text", + "content": " in Equation (12) are set as 0.1, 0.1, 1.0, 0.8, and 1.0, respectively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 479, + 481, + 492 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 481, + 492 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 481, + 492 + ], + "type": "text", + "content": "4.2. Comparison on Human Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": "For a fair comparison with existing methods, we do not use any post-processing or additional connectivity information. In addition, we follow DPC [12] and train our model on the SURREAL and SHREC datasets, respectively. Then we test our model on the official 430 SHREC'19 pairs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "content": "Evaluation on SHREC dataset. As shown in Table 1, our approach shows significant performance improvements on the SHREC benchmark and achieves new SOTA performance by " + }, + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "content": " improvements in accuracy and 0.5 reductions in error. To show the improvement under different error tolerances, we present the correspondence accuracy for point-based methods trained on SHREC and evaluated on the SHREC'19 test set. As shown in Figure 5, our method achieves better results with different error tolerances." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Cross-dataset Generalization. In Table 1 and Figure 5, we also report the comparison with other methods on the SURREAL benchmark. The models are trained on the SURREAL dataset and evaluated on the SHREC'19 test" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5369" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 118, + 261, + 195 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 115 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 115 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 115 + ], + "type": "text", + "content": "Table 2. Comparison on TOSCA and SMAL benchmarks. Here, acc means the correspondence accuracy at an error tolerance of 0.01, while err refers to the average correspondence error. Higher accuracy and lower error reflect a better result." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 118, + 261, + 195 + ], + "lines": [ + { + "bbox": [ + 72, + 118, + 261, + 195 + ], + "spans": [ + { + "bbox": [ + 72, + 118, + 261, + 195 + ], + "type": "table", + "html": "
MethodTOSCASMAL
acc ↑err ↓acc ↑err ↓
3D-CODED [8]//0.5%19.2
Elementary [4]//0.5%13.7
CorrNet3D [32]0.3%32.75.3%9.8
DPC [12]34.7%2.833.2%5.8
Ours38.2%2.736.4%3.9
", + "image_path": "6e503290434487ad61e5fa206cdc9f498bd7ed578727dea3d3d90ee1c614b9c2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 73, + 197, + 258, + 313 + ], + "blocks": [ + { + "bbox": [ + 73, + 197, + 258, + 313 + ], + "lines": [ + { + "bbox": [ + 73, + 197, + 258, + 313 + ], + "spans": [ + { + "bbox": [ + 73, + 197, + 258, + 313 + ], + "type": "image", + "image_path": "b6f11d9c1729f333741605711ea606ddd67eb2e681e4d3aab894d93ad39fe994.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 314, + 287, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 314, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 287, + 369 + ], + "type": "text", + "content": "Figure 6. Correspondence accuracy at various error tolerances for animal datasets. The methods are trained on the TOSCA or SMAL dataset and evaluated on the official TOSCA test pairs. Compared with other methods, our method achieves a desirable performance improvement." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 374, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 460 + ], + "type": "text", + "content": "set. The large-scale training set of the SURREAL dataset helps the deep learning-based methods perform better, even though there is a domain gap between the SURREAL and SHREC datasets. With our proposed method, the correspondence accuracy reaches " + }, + { + "bbox": [ + 46, + 374, + 287, + 460 + ], + "type": "inline_equation", + "content": "21.5\\%" + }, + { + "bbox": [ + 46, + 374, + 287, + 460 + ], + "type": "text", + "content": " at an error tolerance of 0.01, and the average correspondence error is reduced to 4.6 on the SHREC'19 test set." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 466, + 222, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 222, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 222, + 479 + ], + "type": "text", + "content": "4.3. Comparison on Animal Datasets" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "type": "text", + "content": "To verify the adaptability of our method to point clouds of different shapes, we conduct experiments on two animal benchmarks. Similar to human datasets, we train our method on TOSCA and SMAL datasets respectively, and test on the TOSCA test dataset. Table 2 and Figure 6 show the competitive results on TOSCA and SMAL benchmarks. Our method achieves a " + }, + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "type": "text", + "content": " accuracy improvement on the TOSCA benchmark and a " + }, + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 46, + 484, + 288, + 664 + ], + "type": "text", + "content": " accuracy improvement on the SMAL benchmark. Compared with the human datasets, the animal datasets have various shapes with aligned orientations. Thus, the above performance gains come mainly from our self-ensembling framework, which can learn reliable features on complex data. To verify the effect of the Orientation Estimation Module, we test our method and baseline using different augmented test sets in Section 4.6." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 235, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 235, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 235, + 684 + ], + "type": "text", + "content": "4.4. Comparison on Real-world Dataset" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "CMU Panoptic [10] is a dataset of scanned point clouds of human subjects in various poses, containing noise, out" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 92, + 542, + 112 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 91 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 91 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 91 + ], + "type": "text", + "content": "Table 3. Comparison on CMU-Panoptic benchmark. Here, err means average Euclidean keypoint error (cm)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 92, + 542, + 112 + ], + "lines": [ + { + "bbox": [ + 308, + 92, + 542, + 112 + ], + "spans": [ + { + "bbox": [ + 308, + 92, + 542, + 112 + ], + "type": "table", + "html": "
3D-CODED [8]DIF-Net [25]CorrNet [32]IFMatch [7]Ours
err17.115.314.88.53.2
", + "image_path": "a7ba02fc1cf56ea80256635f14ff12d1a0f292c064d0a754f38ed654cd0c8b70.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 310, + 133, + 538, + 172 + ], + "blocks": [ + { + "bbox": [ + 306, + 114, + 545, + 133 + ], + "lines": [ + { + "bbox": [ + 306, + 114, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 114, + 545, + 133 + ], + "type": "text", + "content": "Table 4. Comparison on SHREC'20 benchmark. The training dataset is indicated in the bracket." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 133, + 538, + 172 + ], + "lines": [ + { + "bbox": [ + 310, + 133, + 538, + 172 + ], + "spans": [ + { + "bbox": [ + 310, + 133, + 538, + 172 + ], + "type": "table", + "html": "
MethodSHREC’20 [SURREAL]SHREC’20 [SMAL]
acc ↑err ↓acc ↑err ↓
DPC [12]25.0%3.224.5%7.5
Ours29.9%1.225.4%2.9
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τLccsLcssOEMFIMDAMSURREAL
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By using " + }, + { + "bbox": [ + 304, + 426, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{css}}" + }, + { + "bbox": [ + 304, + 426, + 545, + 654 + ], + "type": "text", + "content": " to constrain the consistency of source features before and after augmentation, the correspondence accuracy can be improved by " + }, + { + "bbox": [ + 304, + 426, + 545, + 654 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 654 + ], + "type": "text", + "content": ", as shown in the third row. As shown in the fourth row, adding the Orientation Evaluation Module without the Feature Interaction Module and the Domain Adaptation Module, the performance has a slight improvement. 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SURREALw/o LCssw/o LCSSw/o Nw/o R
acc ↑19.9%20.3%20.6%18.8%
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Probability distribution" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 262, + 287, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 287, + 316 + ], + "type": "text", + "content": "Figure 7. Effect of the Orientation Estimation Module. We visualize of the point clouds before and after orientation rectification on SHREC'19 test set. We denote the raw source point cloud as Source and the rectified one as Source(R). Besides, we provide the probability distributions of the relative rotation angle prediction." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 53, + 365, + 277, + 434 + ], + "blocks": [ + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "lines": [ + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "text", + "content": "Table 7. Robustness Analysis. To verify the robustness of our method, we test our method and baselines using different augmented test sets. " + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "text", + "content": " means Gaussian noise with standard deviation " + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "text", + "content": " of 0.1 and " + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "text", + "content": " means random rotation along the vertical " + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 319, + 287, + 361 + ], + "type": "text", + "content": "-axis." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 365, + 277, + 434 + ], + "lines": [ + { + "bbox": [ + 53, + 365, + 277, + 434 + ], + "spans": [ + { + "bbox": [ + 53, + 365, + 277, + 434 + ], + "type": "table", + "html": "
NRSURREAL(B)SURREALSMAL(B)SMAL
acc ↑err ↓acc ↑err ↓acc ↑err ↓acc ↑err ↓
XX17.47%6.3021.55%4.6533.79%5.7836.39%3.88
✓X14.38%8.7421.55%4.6630.21%6.0636.15%3.92
X✓8.99%9.3317.59%5.819.98%12.2428.16%5.63
✓✓7.80%11.2817.58%5.799.54%12.8027.60%5.89
", + "image_path": "14c9f496f20b71cf50250a038add92a61161f70cf53ff73d922609e93c6aae99.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 445, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 529 + ], + "type": "text", + "content": "work with soft labels facilitates the consistency of the point cloud representations. When Gaussian noise and rotation augmentation are removed, the model performances show different degrees of degradation. The above experiments illustrate our self-ensemble method can obtain a more robust feature representation of the point cloud through data augmentation and consistency losses." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 530, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 530, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 530, + 287, + 625 + ], + "type": "text", + "content": "Effect of the Orientation Estimation Module. To verify the effect of the proposed Orientation Estimation Module, we visualize the point clouds after orientation rectification and the probability distributions of the relative rotation angle predictions. As shown in Figure 7, our method can accurately estimate the relative rotation angle and align the point cloud orientation of the source with that of the target. More results refer to the supplementary materials." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 47, + 635, + 164, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 164, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 164, + 647 + ], + "type": "text", + "content": "4.6. Robustness Analysis" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "To verify the robustness of our method, we use different augmentations on the test set. As shown in Table 7, we use Gaussian noise and random rotation for data augmentation of the test sets. 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Visualization of the correspondence results with rotation augmentation. With rotation augmentation on point cloud pairs, the baseline shows regrettable performances, while our method still retains desirable performances." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 429, + 121, + 461, + 163 + ], + "blocks": [ + { + "bbox": [ + 429, + 121, + 461, + 163 + ], + "lines": [ + { + "bbox": [ + 429, + 121, + 461, + 163 + ], + "spans": [ + { + "bbox": [ + 429, + 121, + 461, + 163 + ], + "type": "image", + "image_path": "cbd6a061659981308461c44d11f46630624985d0e88e407e805d8d72ca6458f4.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 430, + 166, + 462, + 171 + ], + "lines": [ + { + "bbox": [ + 430, + 166, + 462, + 171 + ], + "spans": [ + { + "bbox": [ + 430, + 166, + 462, + 171 + ], + "type": "text", + "content": "Source (Ours)" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 31 + }, + { + "type": "image", + "bbox": [ + 474, + 121, + 506, + 163 + ], + "blocks": [ + { + "bbox": [ + 474, + 121, + 506, + 163 + ], + "lines": [ + { + "bbox": [ + 474, + 121, + 506, + 163 + ], + "spans": [ + { + "bbox": [ + 474, + 121, + 506, + 163 + ], + "type": "image", + "image_path": "413bcd26e99af84e0a06d200187d1be072dcfd7d67efdb7b5b5bc2bd315dc2fb.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 479, + 165, + 505, + 171 + ], + "lines": [ + { + "bbox": [ + 479, + 165, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 479, + 165, + 505, + 171 + ], + "type": "text", + "content": "Source (GT)" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 332, + 228, + 373, + 274 + ], + "blocks": [ + { + "bbox": [ + 332, + 228, + 373, + 274 + ], + "lines": [ + { + "bbox": [ + 332, + 228, + 373, + 274 + ], + "spans": [ + { + "bbox": [ + 332, + 228, + 373, + 274 + ], + "type": "image", + "image_path": "401b3c9691120e65b4e245645387c967f5e7d23cfb377b3a1b7881a7c5fcbaac.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 275, + 545, + 307 + ], + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 307 + ], + "type": "text", + "content": "Figure 9. Visualization of point cloud pairs with deformations on real scanned Owlii dataset. In each pair, the left one is the source and the right one is the target." + } + ] + } + ], + "index": 40, + "angle": 0, + "type": "image_caption" + } + ], + "index": 36 + }, + { + "type": "image", + "bbox": [ + 378, + 228, + 417, + 274 + ], + "blocks": [ + { + "bbox": [ + 378, + 228, + 417, + 274 + ], + "lines": [ + { + "bbox": [ + 378, + 228, + 417, + 274 + ], + "spans": [ + { + "bbox": [ + 378, + 228, + 417, + 274 + ], + "type": "image", + "image_path": "8ecc06dfcda3ba40ed71fe2e4d7797419c2e43fe4b430cffe839e8bcf379559f.jpg" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_body" + } + ], + "index": 37 + }, + { + "type": "image", + "bbox": [ + 428, + 228, + 470, + 274 + ], + "blocks": [ + { + "bbox": [ + 428, + 228, + 470, + 274 + ], + "lines": [ + { + "bbox": [ + 428, + 228, + 470, + 274 + ], + "spans": [ + { + "bbox": [ + 428, + 228, + 470, + 274 + ], + "type": "image", + "image_path": "e1555c591551d5d7278c6edad92ee38a02f6dcdaea66029dd660984f773e566c.jpg" + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_body" + } + ], + "index": 38 + }, + { + "type": "image", + "bbox": [ + 476, + 228, + 518, + 274 + ], + "blocks": [ + { + "bbox": [ + 476, + 228, + 518, + 274 + ], + "lines": [ + { + "bbox": [ + 476, + 228, + 518, + 274 + ], + "spans": [ + { + "bbox": [ + 476, + 228, + 518, + 274 + ], + "type": "image", + "image_path": "129a0867a825bc653c4ff06bc3b8f2a0ca40635194d4e924196fdaa906604732.jpg" + } + ] + } + ], + "index": 39, + "angle": 0, + "type": "image_body" + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 321, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 321, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 321, + 545, + 453 + ], + "type": "text", + "content": "with Gaussian noise. For test sets with random rotation, the baseline performance is greatly degraded, while our method retains an acceptable performance. Figure 8 shows that our SE-ORNet can handle the orientation inconsistency issue of source and target well. To further verify the robustness and generalization of our method, we conduct experiments on the real scanned Owlii dataset [30] and present the visualization in Figure 9. The results show that our SE-ORNet trained on the synthetic SURREAL dataset still produces impressive performance on the real scanned dataset, demonstrating strong generalization and robustness." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 306, + 475, + 378, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 378, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 378, + 488 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 499, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 545, + 619 + ], + "type": "text", + "content": "In this paper, we propose a self-ensembling orientation-aware network for unsupervised point cloud shape correspondence. To the best of our knowledge, SE-ORNet is the first self-ensembling network in this area. To solve the mismatching issue of symmetrical parts in point clouds with different body orientations, we design a plug-and-play lightweight orientation estimation module to align the orientations of two point clouds. Extensive experiments conducted on four shape correspondence benchmarks demonstrate the superior performance of SE-ORNet." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 306, + 642, + 420, + 654 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 642, + 420, + 654 + ], + "spans": [ + { + "bbox": [ + 306, + 642, + 420, + 654 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "This work was partially supported by the National Nature Science Foundation of China (Grant 62022078, Grant 12150007) and National Defense Basic Scientific Research program of China (Grant JCKY2020903B002)." + } + ] + } + ], + "index": 45 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5371" + } + ] + } + ], + "index": 46 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Alexander M Bronstein, Michael M Bronstein, and Ron Kimmel. 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SECAD-Net for CAD reconstruction. Starting from a voxel grid (top), SECAD-Net learns Sketch-Extrude operations to reconstruct CAD models (bottom), without any supervision of part segmentation and sketch labels." + ], + "image_footnote": [], + "bbox": [ + 81, + 301, + 895, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 507, + 313, + 522 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Reverse engineering CAD models from raw geometry is a classic but strenuous research problem. Previous learning-based methods rely heavily on labels due to the supervised design patterns or reconstruct CAD shapes that are not easily editable. In this work, we introduce SECAD-Net, an end-to-end neural network aimed at reconstructing compact and easy-to-edit CAD models in a self-supervised manner. Drawing inspiration from the modeling language that is most commonly used in modern CAD software, we propose to learn 2D sketches and 3D extrusion parameters from raw shapes, from which a set of extrusion cylinders can be generated by extruding each sketch from a 2D plane into a 3D body. By incorporating the Boolean operation (i.e., union), these cylinders can be combined to closely approximate the target geometry. We advocate the use of implicit fields for sketch representation, which allows for creating CAD variations by interpolating latent codes in the sketch latent space. Extensive experiments on both ABC and Fusion 360 datasets demonstrate the effectiveness of our method, and show superiority over state-of-the-art alternatives including the closely related method for supervised CAD reconstruction. We further apply our ap", + "bbox": [ + 75, + 540, + 473, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "proach to CAD editing and single-view CAD reconstruction. Code will be released at https://github.com/BunnySoCrazy/SECAD-Net.", + "bbox": [ + 500, + 508, + 893, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 585, + 632, + 602 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CAD reconstruction is one of the most sought-after geometric modeling technologies, which plays a substantial role in reverse engineering in case of the original design document is missing or the CAD model of a real object is not available. It empowers users to reproduce CAD models from other representations and supports the designer to create new variations to facilitate various engineering and manufacturing applications.", + "bbox": [ + 496, + 612, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The advance in 3D scanning technologies has promoted the paradigm shift from time-consuming and laborious manual dimensions to automatic CAD reconstruction. A typical line of works [3,6,35,47] first reconstructs a polygon mesh from the scanned point cloud, then followed by mesh segmentation and primitive extraction to obtain a boundary representation (B-rep). Finally, a CAD shape parser is applied to convert the B-rep into a sequence of modeling operations. Recently, inspired by the substantial success of point set learning [1, 32, 49] and deep 3D representations [9,28,30], a number of methods have exploited neural", + "bbox": [ + 496, + 734, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: jianwei.guo@nlpr.ia.ac.cn", + "bbox": [ + 94, + 886, + 364, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16816", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "networks to improve the above pipeline, e.g., detecting and fitting primitives to raw point clouds directly [25, 27, 40]. A few works (e.g., CSG-Net [39], UCSG-Net [19], and CSG-Stump [33]) further parse point cloud inputs into a constructive solid geometry (CSG) tree by predicting a set of primitives that are then combined with Boolean operations. Although achieving encouraging compact representation, they only output a set of simple primitives with limited types (e.g., planes, cylinders, spheres), which restricts their representation capability for reconstructing complex and more general 3D shapes. CAPRI-Net [59] introduces quadric surface primitives and the difference operation based on BSP-Net [8] to produce complicated convex and concave shapes via a CSG tree. However, controlling the implicit equation and parameters of quadric primitives is difficult for designers to edit the reconstructed models. Thus, the editability of those methods is quite limited.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we develop a novel and versatile deep neural framework, named SECAD-Net, to reconstruct high-quality and editable CAD models. Our approach is inspired by the observation that a CAD model is usually designed as a command sequence of operations [7, 38, 50, 51, 57], i.e., a set of planar 2D sketches are first drawn then extruded into 3D solid shapes for Boolean operations to create the final model. At the heart of our approach is to learn the sketch and extrude modeling operations, rather than CSG with parametric primitives. To determine the position and axis of each sketch plane, SECAD-Net first learns multiple extrusion boxes to decompose the entire shape into multiple local regions. Afterward, for the local profile in each box, we utilize a fully connected network to learn the implicit representation of the sketch. An extrusion operator is then designed to calculate the implicit expression of the cylinders according to the predicted sketch and extrusion parameters. We finally apply a union operation to assemble all extrusion cylinders into the final CAD model.", + "bbox": [ + 75, + 347, + 472, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Benefiting from our representation, our approach is flexible and efficient to construct a wide range of 3D shapes. As the predictions of our method are fully interpretable, it allows users to express their ideas to create variations or improve the design by operating on 2D sketches or 3D cylinders intuitively. To summarize, our work makes the following contributions:", + "bbox": [ + 75, + 633, + 472, + 741 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel deep neural network for reverse engineering CAD models with self-supervision, leading to faithful reconstructions that closely approximate the target geometry.", + "- SECAD-Net is capable of learning implicit sketches and differentiable extrusions from raw 3D shapes without the guidance of ground truth sketch labels.", + "- Extensive experiments demonstrate the superiority of SECAD-Net through comprehensive comparisons. We" + ], + "bbox": [ + 94, + 747, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "also showcase its immediate applications to CAD interpolation, editing, and single-view reconstruction.", + "bbox": [ + 531, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 135, + 638, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural implicit representation. 3D shapes can be represented either explicitly (e.g., point sets, voxels, meshes) or implicitly (e.g., signed-distance functions, indicator functions), each of them comes with its own advantages and drawbacks. Recently, there is an explosion of neural implicit representations [9, 28, 30] that allow for generating detail-rich 3D shapes by predicting the underlying signed distance fields. Thanks to the ability to learn priors over shapes, many deep implicit works have been proposed to solve various 3D tasks, such as shape representation and completion [2, 10, 42], image-based 3D reconstruction [45, 52, 58], shape abstraction [16, 44] and novel view synthesis [12, 29]. Theoretically, any of the above shape representations can be used to represent sketches. However, primitive-based methods usually suppress the ability cap of shape representation. In this work, we choose to fit an implicit sketch representation using a neural network, and show its superiority over other representations (e.g., BSP [8]) in the ablation study, see Sec. 5.4.", + "bbox": [ + 496, + 160, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Reverse engineering CAD reconstruction. Over the past decades, reverse engineering has been extensively studied; it aims at converting measured data (a surface mesh or a point cloud) into solid 3D models that can be further edited and manufactured by industries. Traditional approaches addressing this problem consist of the following tasks: (1) segmentation of the point clouds/meshes [5,41,60], (2) fitting of parametric primitives to segmented regions [11, 36, 55], (3) finishing operations for CAD modeling [4, 24]. Important drawbacks of these conventional methods are the time-consuming process and the requirement of a skilled operator to guide the reconstruction [6].", + "bbox": [ + 496, + 448, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the release of several large-scale CAD datasets (e.g., ABC [21], Fusion 360 [50]), SketchGraphs [37]), numerous approaches have explored deep learning to address primitive segmentation/detection [25, 56], parametric curve or surface inference from point clouds [17, 27, 31, 40, 48] or B-rep models [18, 23]. However, by only outputting individual curves or surfaces, these methods lack the CAD modeling operations that are needed to build solid models. Focusing on CAD generation rather than reconstruction task as ours, some approaches propose deep generative models that predict sequences of CAD modeling operations to produce CAD designs [26, 50, 51, 53, 54]. Aiming at CAD reconstruction involving inverse CSG modeling [15], CSGNet [39] first develops a neural model that parses a shape into a sequence of CSG operations. More recent works follow the line of CSG parsing by advancing the inference without any supervision [19], or improving representation capability with a three-layer reformulation of the classic", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16817", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/11aba17092ac48e580551f23216bf6e7e5299f8ef332fdd603cb9027cd6fcaed.jpg", + "image_caption": [ + "Figure 2. Network architecture for SECAD-Net: The embedding $\\mathbf{z}$ encoded from the voxel input is first fed to the extrusion box head to predict extrusion boxes. It is also sent to the sketch head network to calculate the sketch SDF $\\hat{S}_{\\mathrm{sk}}^i$ after concatenating with the linear transformed sampling point. $\\hat{S}_{\\mathrm{cyl}}^i$ stands for the SDF of the cylinder, which is acquired by extruding $\\hat{S}_{\\mathrm{sk}}^i$ with height $h_i$ . Then we convert $\\hat{S}_{\\mathrm{cyl}}^i$ to occupancy of cylinder $\\hat{\\mathcal{O}}_i$ and finally obtain the complete shape by union all the occupancies." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 890, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CSG-tree [33], or handling richer geometric and topological variations by introducing quadric surface primitives [59]. While achieving high-quality reconstruction, CSG tends to combine a large number of shape primitives that are not as flexible as the extrusions of 2D sketches and are also not easily user edited to control the final geometry.", + "bbox": [ + 75, + 354, + 468, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivated by modern design tools, supervised methods are proposed [22, 46] utilizing the sketch-extrude procedural models and learning 2D sketches that can be extruded to 3D shapes. In contrast to their reliance on 2D labels, SECAD-Net is trained in a self-supervised manner. Most closely related to our work is ExtrudeNet [34]. SECAD-Net distinguishes itself from ExtrudeNet in several significant aspects: i) Following the traditional reconstruction process, ExtrudeNet first predicts the parameters of Bézier curves and then converts them into SDFs. In contrast, we jumped out of this paradigm and directly used neural networks to predict the 2D implicit fields of the profiles. ii) ExtrudeNet adopts closed Bézier curves to avoid self-intersection in sketches. This makes ExtrudeNet can only predict star-shaped profiles, which limits the expressive power of their CAD shapes. Our method does not impose any restrictions on the shape of the profile, thus having greater flexibility in shape expression. iii) To pursue the reconstruction effect, ExtrudeNet relies on a larger number of primitives, while our method is able to predict more compact CAD shapes.", + "bbox": [ + 75, + 446, + 472, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problem Statement and Overview", + "text_level": 1, + "bbox": [ + 76, + 763, + 383, + 780 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we present an overview of the proposed approach. To precisely explain our techniques, we first provide the definition of several related terminologies (Fig. 3).", + "bbox": [ + 76, + 789, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 845, + 218, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1 (Loop, Profile and Sketch) In CAD terminology, a sketch is represented by a collection of geometric", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7c8a862f7f54ac6d221647cc07f5bca000ea160b1a330cef40046863790a015d.jpg", + "image_caption": [ + "Figure 3. Definitions of CAD terminologies used in this paper. Note that the axis of the sketch plane in the figure is the same as the z-axis in the extrusion box." + ], + "image_footnote": [], + "bbox": [ + 501, + 352, + 890, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "primitives. By referring to a closed curve as a loop and an enclosed region composed of one or multiple inner/outer loops as a profile, we define a sketch as the collection of one profile and its loops.", + "bbox": [ + 496, + 558, + 893, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 2 (Sketch plane and Extrusion box) A sketch plane is a finite plane with width $w$ and length $l$ , containing one or more sketches with the same extrusion height $h$ . Then we define an extrusion box as a cuboid with the sketch plane as the base and $2h$ as the height.", + "bbox": [ + 496, + 635, + 893, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 3 (Cylinder primitive and Cylinder) In this work, a cylinder refers to the shape obtained by extruding a sketch, and a cylinder primitive is obtained by performing an extrude operation on a closed area formed by a loop. A cylinder may contain one cylinder primitive or be obtained from several cylinder primitives through the Difference operation used in CSG modeling.", + "bbox": [ + 496, + 727, + 893, + 833 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Overview", + "text_level": 1, + "bbox": [ + 500, + 845, + 609, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We formulate the problem of CAD reconstruction as sketch and extrude inference: taking an input 3D shape,", + "bbox": [ + 500, + 869, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16818", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SECAD-Net aims to reconstruct the CAD model by predicting a set of geometric proxies that are decomposed to sketch-extrude operations. The overall pipeline of SECAD-Net is visualized in Fig. 2. Given a 3D voxel model, we first map it into a latent feature embedding $\\mathbf{z}$ by using an encoder based on a 3D convolutional network. An extrusion box head network is then applied to predict the parameters of the sketch planes from $\\mathbf{z}$ . We employ $N$ sketch head network to independently learn $N$ 2D signed distance fields (SDFs) as the implicit representation of a sketch. Next, we design a differentiable extrusion operator to calculate the SDF of the 3D cylinder primitives corresponding to the sketches. Finally, an occupancy transformation operation and a union operation transform the multiple SDFs into the full 3D reconstructed shape as the output of the network.", + "bbox": [ + 75, + 90, + 472, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 329, + 168, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Sketch-Extrude Inferring", + "text_level": 1, + "bbox": [ + 76, + 354, + 308, + 371 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We apply a standard 3D CNN encoder to extract a shape code $\\mathbf{z}$ with size 256 from the input voxel. The code is then passed to the proposed SECAD-Net to output the sketch and extrusion cylinder parameters. Below we introduce the main modules of SECAD-Net following the order of data transmission during prediction.", + "bbox": [ + 75, + 378, + 468, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Extrusion box prediction. We first apply a fully connected layer to predict the parameters of the extrusion boxes. Taking the feature encoding $\\mathbf{z}$ as input, a decoder, refereed to sketch box head, outputs a set of sketch boxes $\\mathcal{B} = \\{\\mathbf{s}_i,\\mathbf{c}_i,\\mathbf{r}_i\\mid i\\in N\\}$ , where $\\mathbf{s}_i\\in \\mathbb{R}^3$ describes the 2D size (i.e., length and width) of the box, $\\mathbf{c}_i\\in \\mathbb{R}^3$ represents the predicted position of the box's center, and $\\mathbf{r}_i\\in \\mathbb{R}^4$ is the rotation quaternion. The positive z-axis of the extrusion box determines the axial direction $\\mathbf{e}_i$ of the sketch plane, and the height of the extrusion box is twice the height of the extrude operation (see Fig. 3).", + "bbox": [ + 75, + 468, + 468, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D sketch inference. The sketches in each sketch plane depict the shape contained within the sketch box. Inspired by the recent neural implicit shapes [2, 46], we encode the shape of each sketch into a sketch latent space. To this end, we first project the 3D sampling points w.r.t the corresponding occupancy value onto the sketch plane along the axis $\\mathbf{e}_i$ . A sketch head network (SK-head) then computes the signed distance from each sampling point to the sketch contour. The distance is negative for points in the sketch and positive for points outside. Each SK-head contains $N_{lay}$ layers of fully connected layers, with softplus activation functions used between layers, and we clamp the output distance to [-1,1] in the last layer. Each 2D point is concatenated with the feature encoding $\\mathbf{z}$ as a global condition before being fed into the SK-head. Regarding the $i$ -th SK-head as an implicit function $f_i$ , then formally we get:", + "bbox": [ + 75, + 633, + 470, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {S}} _ {\\mathbf {s k}} ^ {i} = f _ {i} \\left(\\mathbf {x} _ {i} ^ {t}, \\mathbf {z}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_i^t$ is the result of a linear transformation of the sampling points contained in the $i$ -th extrusion box, which can be expressed as $\\mathbf{r}_i^{-1}(\\mathbf{x}_i - \\mathbf{c}_i)$ . $\\hat{S}_{\\mathrm{sk}}^i$ represents the signed distance field of the $i$ -th sketch plane.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Differentiable extrusion. Next, we calculate the SDF of a cylinder based on the 2D distance field and the extrusion height $h$ . We denote $\\Omega$ as the volume between two hyperplanes $p^u$ and $p^l$ , where $p^u$ and $p^l$ are the upper and lower surfaces on which the cylinder is located. Similarly, we define $\\Psi$ as the volume inside the infinite cylinder where the side of the cylinder is located. The implicit field of the $i$ -th cylinder, $\\hat{S}_{\\mathrm{cyl}}^i$ , is equal to one of the following cases: (1) the distance from a point $\\mathbf{x}_i$ to $p^u$ or $p^l$ , when $\\mathbf{x}_i \\in \\Omega \\cap \\Psi^\\complement$ , where superscript $\\complement$ stands for complement; (2) $\\hat{S}_{\\mathrm{sk}}^i$ , when $\\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi$ ; (3) the distance from $\\mathbf{x}_i$ to the intersection curves of the cylinder and hyperplanes, when $\\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi^\\complement$ ; (4) the maximum distance between $\\hat{S}_{\\mathrm{sk}}^i$ and the point to $p^u$ or $p^l$ , when $\\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi$ . The sub-formulas for each case are as follows:", + "bbox": [ + 496, + 151, + 892, + 383 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {S}} _ {\\mathrm {c y l}} ^ {i} = \\left\\{ \\begin{array}{l l} \\max \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right) & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} \\leq 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| \\leq h _ {i}\\right) \\\\ \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} \\leq 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| > h _ {i}\\right) \\\\ \\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} > 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| \\leq h _ {i}\\right) \\\\ \\left\\| \\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right) \\right\\| _ {2} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} > 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| > h _ {i}\\right) \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 388, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Combining the above four sub-formulas with the max and min operations, the following result is obtained:", + "bbox": [ + 496, + 479, + 890, + 510 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {S} _ {\\mathrm {c y l}} ^ {i} = \\min \\left(\\max \\left(\\hat {S} _ {\\mathrm {s k}} ^ {i}, \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right), 0\\right) \\\\ + \\left. \\left\\| m a x \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, 0\\right), m a x \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}, 0\\right) \\right\\| _ {2} \\right. \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 515, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Occupancy conversion and assembly. The occupancy function represents points inside the shape as 1 and points outside the shape as 0, which can be transformed by SDF. Following [13, 33], we use the Sigmoid function to perform differentiable transformation operations:", + "bbox": [ + 496, + 568, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {O}} _ {i} = \\operatorname {S i g m o i d} (- \\eta \\cdot \\hat {\\mathcal {S}} _ {\\mathrm {c y l}} ^ {i}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 648, + 890, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We finally assemble the occupancy $\\hat{O}_i$ of each cylinder to obtain the reconstructed shape. In order to express complex shapes, many works use intersection, union, and difference operations in CSG in the assembly stage [8,19,33,59]. In contrast to them, we only use the union operation, because the extrusion cylinders can naturally represent concave shapes. This helps us avoid designing intricate loss functions or employing multi-stage training strategies without losing the flexibility of reconstructing shape representations. We adopt the Softmax to compute the union operation as it is shown to be effective in avoiding vanishing gradients [33]:", + "bbox": [ + 496, + 674, + 892, + 856 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathcal {O}} _ {t o t a l} = \\sum_ {i} ^ {N} \\operatorname {S o f t m a x} (\\varphi \\cdot \\hat {\\mathcal {O}} _ {i}) \\cdot \\hat {\\mathcal {O}} _ {i}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 862, + 890, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16819", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\varphi$ is the modulating coefficient and $\\hat{\\mathcal{O}}_{total}$ is the occupancy representation of the final reconstructed shape.", + "bbox": [ + 76, + 89, + 468, + 122 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Loss Function", + "text_level": 1, + "bbox": [ + 76, + 130, + 222, + 143 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train SECAD-Net in a self-supervised fashion through the minimization of the sum of two objective terms. The supervision signal is mainly quantified by the reconstruction loss, which measures the mean squared error between the predicted shape occupancy $\\hat{\\mathcal{O}}_{total}$ and the ground truth $\\mathcal{O}_{total}^{*}$ :", + "bbox": [ + 76, + 152, + 468, + 244 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c o n}} = \\mathbb {E} _ {x \\in \\mathbf {X}} \\left[ \\left(\\hat {\\mathcal {O}} _ {\\text {t o t a l}} - \\mathcal {O} _ {\\text {t o t a l}} ^ {*}\\right) ^ {2} \\right], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 253, + 468, + 280 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x$ is a randomly sampled point in the shape volume.", + "bbox": [ + 76, + 287, + 460, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, we find that applying only $\\mathcal{L}_{\\text{recon}}$ makes the network always learn fragmented cylinders. To tackle this problem, we design a 2D sketch loss to facilitate the network to learn the axis of the sketch plane and the complete profile. Specifically, each sketch plane cuts the voxel model to form an occupancy cross-section $\\mathcal{O}_{cs}^{i^*}$ . We project the 3D sampling points inside the $i$ -th extrusion box $\\mathcal{B}^i$ onto the sketch plane along the axial direction, and calculate the difference between the occupancy value of the projected points $\\hat{\\mathcal{O}}_{proj}$ and ground truth $\\mathcal{O}_{cs}^{i^*}$ :", + "bbox": [ + 75, + 303, + 468, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s k e t c h}} = \\sum_ {i = 1} ^ {N} \\mathbb {E} _ {x \\in \\mathcal {B} ^ {i}} \\left[ \\left(\\hat {\\mathcal {O}} _ {\\text {p r o j}} ^ {i} - \\mathcal {O} _ {\\text {c s}} ^ {i ^ {*}}\\right) ^ {2} \\right]. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 464, + 468, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall objective of SECAD-Net is defined as the combination of the above two terms:", + "bbox": [ + 76, + 513, + 467, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e c o n}} + \\lambda \\mathcal {L} _ {\\text {s k e t c h}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 556, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda$ is a balance factor.", + "bbox": [ + 76, + 582, + 261, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. CAD Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 604, + 272, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The output of SECAD-Net during the training phase is an implicit occupancy function of the 3D shape. In the prediction stage, we reconstruct CAD models by using sketch-extrude operations instead of the marching cubes method. Sketch and extrusion. To convert a 2D implicit field (Fig. 4 (a)) in the sketch latent space into an editable sketch, we input uniform 2D sampling points to the SK-head, and attach the implicit value to the position of the sampling point to obtain an explicit image-like 2D profile (Fig. 4 (b)). We then use the Teh-Chin chain approximation [43] to extract the contours of the profiles and the hierarchical relationships between them. We further apply Dierckx's fitting [14] to convert the contours into closed B-splines (Fig. 4 (c)).", + "bbox": [ + 75, + 628, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After extruding each sketch to get the cylinder primitives according to half the height of $\\mathcal{B}^i$ , we assemble cylinder primitives into cylinders by alternately performing union or difference operations according to the hierarchical relationship between contours (primitive at hierarchy 0 difference", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f43568e8d49bcec6a03058a1063c8adb639ba2d141ae98d180614909fc77aca3.jpg", + "image_caption": [ + "(a) Implicit Field" + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 620, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3d162500a42b2569680b9764fe087b8773c77c5001d225e8e9378bcc1eb2642c.jpg", + "image_caption": [ + "(b) Sample Points with Occupancy" + ], + "image_footnote": [], + "bbox": [ + 625, + 88, + 750, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b959cc0e8ec1e50a7b16e45c01195b1235bde5a33a8c7444c6093b7fe1db6ca7.jpg", + "image_caption": [ + "(c) Fitted Sketch Splines", + "Figure 4. Illustration of converting 2D implicit sketches into the closed B-splines." + ], + "image_footnote": [], + "bbox": [ + 756, + 89, + 888, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "primitives at hierarchy 1 in the case of Fig. 4). Finally, we take the union of all cylinders to obtain the CAD model.", + "bbox": [ + 496, + 263, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Post-processing. We take two post-processing operations to clean up overlapping and shredded shapes in the result. First, for any two cylinders, when their overlapping coefficient is greater than 0.95, the smaller of them is discarded. Second, we delete all cylinders whose height is less than 0.01 in the reconstruction result. We demonstrate our final reconstructions in Fig. 5 and Fig. 6.", + "bbox": [ + 496, + 292, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 498, + 409, + 715, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SECAD-Net is implemented in PyTorch and trained on a TITAN RTX GPU from NVIDIA®. We train our model using an Adam optimizer [20] with learning rate $1 \\times 10^{-4}$ and beta parameters (0.5, 0.99). We set both the number of MLP layers in the sketch head network and the number of output cylinders to 4. For hyper-parameters in Eq. 4, Eq. 5 and Eq. 8, we set $\\eta = 150$ , $\\varphi = 25$ and $\\lambda = 0.01$ in default, which generally works well in our experiments. Employing a similar training strategy to [59], we first pretrain SECAD-Net on the training datasets for 1,000 epochs using batch size 24, which takes about 8 hours, and finetuning on each test shape for 300 epochs, which takes about 3 minutes per shape.", + "bbox": [ + 496, + 433, + 890, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 498, + 643, + 702, + 660 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we examine the performance of SECAD-Net on the ABC dataset [21] and Fusion 360 Gallery [50]. Through extensive comparisons and ablation studies, we demonstrate the effectiveness of our approach and show its superiority over state-of-the-art reference approaches for CAD reconstruction.", + "bbox": [ + 496, + 670, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Setup", + "text_level": 1, + "bbox": [ + 500, + 771, + 580, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset preparation. For the ABC dataset, the voxel grids and sampling point data are provided by [59]. We use 5,000 groups of data for training and 1,000 for testing. For Fusion 360, which does not contain available voxels, we first randomly select 6,000 meshes, then discretize them into internally filled voxels. The train-test split is the same as ABC. We obtain sampling points with the corresponding occu", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16820", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0dd610fde718182c52591725fd32ae0469b3b44f8d46ff575a999ee74a963d08.jpg", + "table_caption": [ + "Table 1. Quantitative comparison between reconstruction results on ABC dataset." + ], + "table_footnote": [], + "table_body": "
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]1.8491.2550.82012.84
CSG-Stump [33]4.0310.7540.82817.18
ExtrudeNet [34]0.4710.9140.85214.46
Ours0.3300.7240.8634.30
", + "bbox": [ + 78, + 127, + 468, + 213 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c2d4eb0b5e8637306509967df8436c07382166d90c21d79e639557eb83c84226.jpg", + "table_caption": [ + "Table 2. Quantitative comparison between reconstruction results on Fusion 360 dataset." + ], + "table_footnote": [], + "table_body": "
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]2.9505.2770.77010.84
CSG-Stump [33]2.7814.5900.74412.08
Point2Cyl [46]13.88914.6570.6692.76
ExtrudeNet [34]2.2633.5580.81915.72
Ours2.0523.2820.8035.44
", + "bbox": [ + 78, + 266, + 468, + 367 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "pancy value following [9]. The resolution of voxel shapes is $64^3$ for both datasets, and the number of sampling points is 8,192. Considering that fine-tuning each method and generating high-accuracy meshes is time-consuming, we take 50 shapes from each dataset to form 100 shapes for quantitative evaluation.", + "bbox": [ + 75, + 393, + 468, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. For quantitative evaluations, we follow the metrics that are commonly used in previous methods [33, 59], including symmetric Chamfer Distance (CD), Normal Consistency (NC), Edge Chamfer Distance (ECD). Details of computing these metrics are given in the supplemental materials. Additionally, we also report the number of generated primitives, $\\# p$ , as a measure of how easy the output CAD results are to edit.", + "bbox": [ + 75, + 484, + 468, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison on CAD Reconstruction", + "text_level": 1, + "bbox": [ + 76, + 619, + 395, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We thoroughly compare our method with two types of primitive-based CAD reconstruction methods that output editable CAD models, including two CSG-like methods (i.e., UCSG-Net [19], CSG-Stump [33]) and two cylinder decomposition counterpart (i.e., point2Cyl [46]), ExtrudeNet [34]. For each method, we adopt the implementation provided by the corresponding authors, and use the same training strategy for training and fine-tuning. For CSG-Stump, we set the number of intersection nodes to 64, making it output a comparable number of primitives to other methods. Those methods provide a plethora of comparisons to other techniques and establish themselves as state-of-the-art. Note that for point2Cyl, we only report its results on Fusion 360 dataset, as the ABC dataset does not provide the labels needed to train point2Cyl.", + "bbox": [ + 75, + 643, + 468, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative results on the ABC and Fusion 360 datasets are reported in Table 1 and Table 2, respectively. It can be", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e831fc7b15c6d7986cfe8bdbfda7c461815dc702822dea46ec98ad517cb10fd.jpg", + "image_caption": [ + "Figure 5. Visual comparison between reconstruction results on ABC dataset." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 890, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "seen that the proposed SECAD-Net outperforms both kinds of methods on all evaluation metrics while still generating a relatively small number of primitives. Fig. 5 and Fig. 6 display several qualitative comparison results. For fairness, all the reconstructed CAD models are visualized using marching cubes (MC) with 256 resolution. Visually as shown in the figures, our method achieves much better geometry and topological fidelity with more accurate structures (e.g., holes, junctions) and sharper features.", + "bbox": [ + 496, + 488, + 890, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. CAD Generation via Sketch Interpolation", + "text_level": 1, + "bbox": [ + 500, + 635, + 854, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Although without ground truth labels as guidance, SECAD-Net can learn plausible 2D sketches from raw 3D shapes. Thanks to the implicit sketch representation, we are able to generate different CAD variations when a pair of shapes is interpolated in the complete and continuous sketch latent space, as shown in Fig. 7. The results suggest that the generated sketch is gradually transformed even if the pair of shapes have significantly different structures, and we draw two further conclusions: (1) the predicted position of each extrusion box is relatively deterministic, although the input shape is different (see the left and right column sketches in the leftmost group); (2) when an extrusion box does not contain a shape, our SK-head does not generate a sketch, making the network output an adaptive number of cylinders (see the middle column sketches of the leftmost and the rightmost groups).", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16821", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a4b9b7be7df895b025b8cc6511770be79bfd077128697089dd40c836cbdd3945.jpg", + "image_caption": [ + "Figure 6. Visual comparison between reconstruction results on Fusion 360 dataset." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 472, + 489 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7db4df0a90ab7cd8a0b3791d847d1f287376a6bbaf63e63d3bfa4d625f898790.jpg", + "table_caption": [ + "Table 3. Ablation study on network design and sketch loss. We adopted setting (e) in the final model." + ], + "table_footnote": [], + "table_body": "
Settings(a)(b)(c)(d)(e)
Nsh14444
Nlay22244
Ncyl44844
Lsketch✓✓✓×✓
CD↓2.6270.9931.5040.3360.330
ECD↓1.7540.8821.0980.7720.724
NC↑0.7130.8350.7610.8630.863
", + "bbox": [ + 78, + 584, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablations", + "text_level": 1, + "bbox": [ + 76, + 739, + 187, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform ablation studies to carefully analyze the efficiency of major components of our designed model. All quantitative metrics are measured on the ABC dataset.", + "bbox": [ + 75, + 763, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of network design and sketch loss. We first examine the effect of the number of components/parameters in SECAD-Net, including the number of SK-heads $(N_{sh})$ , the number of fully connected layers $(N_{lay})$ in each SK-head, and the number of output cylinders $(N_{cyl})$ . Then we show the necessity of the sketch loss by deactivating it to train the", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/60a82da82e2ceb5b2f4842af712cc46a844d7cf30e569537f7dec8812c9e875b.jpg", + "image_caption": [ + "Figure 7. For each example, we encode the sketches of top and bottom shapes in latent vector space and then linearly interpolate the corresponding latent codes." + ], + "image_footnote": [], + "bbox": [ + 498, + 88, + 888, + 492 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5b223a8c592fcec07fd668be0b27954bb4e9e7dd2ef99fb66ac5e882532e7536.jpg", + "table_caption": [ + "Table 4. Ablation study on sketch representation." + ], + "table_footnote": [], + "table_body": "
RepresentationCD↓ECD↓NC↑#P↓
Box primitives0.5230.9820.8255.38
BSP0.6120.8380.8525.84
SK-head (Ours)0.3300.7240.8634.30
", + "bbox": [ + 501, + 589, + 890, + 659 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "network. The quantified results are presented in Table 3. Settings (a), (b), and (c) show that reducing the number of SK-heads or increasing the number of cylinder outputs will damage the model prediction accuracy. Settings (b), (d), and (e) show that increasing the number of MLP layers in SK-head or enabling $\\mathcal{L}_{\\text {sketch }}$ will improve the prediction accuracy.", + "bbox": [ + 496, + 686, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of implicit sketch representation. To assess the efficiency of neural implicit sketch representation, we adopt two other classical shape representations, namely binary space partitioning (BSP [8]) and box-like primitives, to compare with our SK-head in SECAD-Net. For BSP, we set the number of output convex shapes to 8, each containing 12 partitions. The assembly method is consistent with [8] to", + "bbox": [ + 496, + 795, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16822", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc6c5ae9c9e12a9d8dab39b75285c4adc6d596c0d3c38b4b388d2551890e005e.jpg", + "image_caption": [ + "Figure 8. Visual comparison results for ablation study on sketch representation." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 468, + 308 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/182685481d978c3ace4fe0da18b3f9e6353e165a7f849dd85b6f22ac34433edc.jpg", + "image_caption": [ + "Figure 9. SECAD-Net can aid in more applications. Left: the results of single-view reconstruction. Right: a subsequent CAD editing by changing the predicted cylinder primitives." + ], + "image_footnote": [], + "bbox": [ + 81, + 373, + 468, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "represent 2D sketches. For box-like primitives, 24 rectangles are predicted. We divide them into two subsets in half, take the union operation separately, and subtract the other from one of the union results. The numerical and visual comparison results are shown in Table 4 and Fig. 8, respectively. It can be seen that our implicit field can represent the smoothest shape while obtaining the best reconstruction results.", + "bbox": [ + 75, + 779, + 470, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Other Applications", + "text_level": 1, + "bbox": [ + 500, + 90, + 684, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "By replacing the voxel encoder, SECAD-Net is flexible to reconstruct CAD models from other input shape representations, e.g., images and point clouds. Fig. 9 shows the results of SECAD-Net in solving single-view reconstruction (SVR) task. Following the training strategy of previous work [8, 9], we first use voxel data to complete the training of the 3D auto-encoding task, and then train an image encoder with the feature encoding of each shape as the target. The voxels and input images used for the SVR task are obtained directly from Fusion 360. Replacing more input representations, while feasible and meaningful, is not the focus of this paper and we leave it to future research.", + "bbox": [ + 496, + 116, + 890, + 297 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, the parameters of both 2D sketches and 3D cylinders are available, thus the CAD results output from SECAD-Net can be directly loaded into existing CAD software for further editing. As shown in the right side of Fig. 9, interpretable CAD variations can be produced via specific editing operations, such as sketch-level curve editing, primitive-level displacement, rotation, scaling, and Boolean operations between primitives.", + "bbox": [ + 496, + 300, + 892, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 500, + 444, + 769, + 459 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented a novel neural network that successively learns shape sketch and extrusion without any expensive annotations of shape segmentation and labels as the supervision. Our approach is able to learn smooth sketches, followed by the differentiable extrusion to reconstruct CAD models that are close to the ground truth. We evaluate SECAD-Net using diverse CAD datasets and demonstrate the advantages of our approach by ablation studies and comparing it to the state-of-the-art methods. We further demonstrate our method's applicability in single-image CAD reconstruction. Additionally, the CAD shapes generated by our approach can be directly fed into off-the-shelf CAD software for sketch-level or cylinder primitive-level editing.", + "bbox": [ + 496, + 472, + 890, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In future work, we plan to extend our approach to learn more CAD-related operations such as revolve, bevel, and sweep. Besides, we find that current deep learning models perform poorly on datasets with large differences in shape geometry and structure. Therefore, another promising direction is to explore how to improve the generalization of neural networks and enhance the realism of the generated shapes by learning structural and topological information.", + "bbox": [ + 496, + 671, + 892, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. We thank the anonymous reviewer for their valuable suggestions. This work is partially funded by the National Natural Science Foundation of China (U22B2034, 62172416, U21A20515, 62172415), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022131).", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16823", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. PMLR, 2018. 1", + "[2] Matan Atzmon and Yaron Lipman. SAL: Sign agnostic learning of shapes from raw data. 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Graph., 28(8):2879-2894, 2022. 2" + ], + "bbox": [ + 78, + 92, + 467, + 500 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "16826", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/94d1495e-0d51-4b2c-8690-ac04468c5645_model.json b/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/94d1495e-0d51-4b2c-8690-ac04468c5645_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d6a3d52cb476f735f91894be14e42927b3bcea86 --- /dev/null +++ b/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/94d1495e-0d51-4b2c-8690-ac04468c5645_model.json @@ -0,0 +1,2279 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.178 + ], + "angle": 0, + "content": "SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.203, + 0.762, + 0.222 + ], + "angle": 0, + "content": "Pu Li\\(^{1,2}\\) Jianwei Guo\\(^{1,2*}\\) Xiaopeng Zhang\\(^{1,2}\\) Dong-Ming Yan\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.223, + 0.737, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\)MAIS, Institute of Automation, Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.24, + 0.79, + 0.258 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Artificial Intelligence, University of Chinese Academy of Sciences" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.303, + 0.896, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.467, + 0.895, + 0.496 + ], + "angle": 0, + "content": "Figure 1. SECAD-Net for CAD reconstruction. Starting from a voxel grid (top), SECAD-Net learns Sketch-Extrude operations to reconstruct CAD models (bottom), without any supervision of part segmentation and sketch labels." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.508, + 0.314, + 0.523 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.474, + 0.875 + ], + "angle": 0, + "content": "Reverse engineering CAD models from raw geometry is a classic but strenuous research problem. Previous learning-based methods rely heavily on labels due to the supervised design patterns or reconstruct CAD shapes that are not easily editable. In this work, we introduce SECAD-Net, an end-to-end neural network aimed at reconstructing compact and easy-to-edit CAD models in a self-supervised manner. Drawing inspiration from the modeling language that is most commonly used in modern CAD software, we propose to learn 2D sketches and 3D extrusion parameters from raw shapes, from which a set of extrusion cylinders can be generated by extruding each sketch from a 2D plane into a 3D body. By incorporating the Boolean operation (i.e., union), these cylinders can be combined to closely approximate the target geometry. We advocate the use of implicit fields for sketch representation, which allows for creating CAD variations by interpolating latent codes in the sketch latent space. Extensive experiments on both ABC and Fusion 360 datasets demonstrate the effectiveness of our method, and show superiority over state-of-the-art alternatives including the closely related method for supervised CAD reconstruction. We further apply our ap" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.509, + 0.895, + 0.555 + ], + "angle": 0, + "content": "proach to CAD editing and single-view CAD reconstruction. Code will be released at https://github.com/BunnySoCrazy/SECAD-Net." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.587, + 0.633, + 0.603 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.734 + ], + "angle": 0, + "content": "CAD reconstruction is one of the most sought-after geometric modeling technologies, which plays a substantial role in reverse engineering in case of the original design document is missing or the CAD model of a real object is not available. It empowers users to reproduce CAD models from other representations and supports the designer to create new variations to facilitate various engineering and manufacturing applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.902 + ], + "angle": 0, + "content": "The advance in 3D scanning technologies has promoted the paradigm shift from time-consuming and laborious manual dimensions to automatic CAD reconstruction. A typical line of works [3,6,35,47] first reconstructs a polygon mesh from the scanned point cloud, then followed by mesh segmentation and primitive extraction to obtain a boundary representation (B-rep). Finally, a CAD shape parser is applied to convert the B-rep into a sequence of modeling operations. Recently, inspired by the substantial success of point set learning [1, 32, 49] and deep 3D representations [9,28,30], a number of methods have exploited neural" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.365, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: jianwei.guo@nlpr.ia.ac.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16816" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "networks to improve the above pipeline, e.g., detecting and fitting primitives to raw point clouds directly [25, 27, 40]. A few works (e.g., CSG-Net [39], UCSG-Net [19], and CSG-Stump [33]) further parse point cloud inputs into a constructive solid geometry (CSG) tree by predicting a set of primitives that are then combined with Boolean operations. Although achieving encouraging compact representation, they only output a set of simple primitives with limited types (e.g., planes, cylinders, spheres), which restricts their representation capability for reconstructing complex and more general 3D shapes. CAPRI-Net [59] introduces quadric surface primitives and the difference operation based on BSP-Net [8] to produce complicated convex and concave shapes via a CSG tree. However, controlling the implicit equation and parameters of quadric primitives is difficult for designers to edit the reconstructed models. Thus, the editability of those methods is quite limited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.635 + ], + "angle": 0, + "content": "In this paper, we develop a novel and versatile deep neural framework, named SECAD-Net, to reconstruct high-quality and editable CAD models. Our approach is inspired by the observation that a CAD model is usually designed as a command sequence of operations [7, 38, 50, 51, 57], i.e., a set of planar 2D sketches are first drawn then extruded into 3D solid shapes for Boolean operations to create the final model. At the heart of our approach is to learn the sketch and extrude modeling operations, rather than CSG with parametric primitives. To determine the position and axis of each sketch plane, SECAD-Net first learns multiple extrusion boxes to decompose the entire shape into multiple local regions. Afterward, for the local profile in each box, we utilize a fully connected network to learn the implicit representation of the sketch. An extrusion operator is then designed to calculate the implicit expression of the cylinders according to the predicted sketch and extrusion parameters. We finally apply a union operation to assemble all extrusion cylinders into the final CAD model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.473, + 0.742 + ], + "angle": 0, + "content": "Benefiting from our representation, our approach is flexible and efficient to construct a wide range of 3D shapes. As the predictions of our method are fully interpretable, it allows users to express their ideas to create variations or improve the design by operating on 2D sketches or 3D cylinders intuitively. To summarize, our work makes the following contributions:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.748, + 0.47, + 0.81 + ], + "angle": 0, + "content": "- We present a novel deep neural network for reverse engineering CAD models with self-supervision, leading to faithful reconstructions that closely approximate the target geometry." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.817, + 0.47, + 0.863 + ], + "angle": 0, + "content": "- SECAD-Net is capable of learning implicit sketches and differentiable extrusions from raw 3D shapes without the guidance of ground truth sketch labels." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the superiority of SECAD-Net through comprehensive comparisons. We" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.748, + 0.472, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "also showcase its immediate applications to CAD interpolation, editing, and single-view reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.136, + 0.64, + 0.151 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.161, + 0.892, + 0.448 + ], + "angle": 0, + "content": "Neural implicit representation. 3D shapes can be represented either explicitly (e.g., point sets, voxels, meshes) or implicitly (e.g., signed-distance functions, indicator functions), each of them comes with its own advantages and drawbacks. Recently, there is an explosion of neural implicit representations [9, 28, 30] that allow for generating detail-rich 3D shapes by predicting the underlying signed distance fields. Thanks to the ability to learn priors over shapes, many deep implicit works have been proposed to solve various 3D tasks, such as shape representation and completion [2, 10, 42], image-based 3D reconstruction [45, 52, 58], shape abstraction [16, 44] and novel view synthesis [12, 29]. Theoretically, any of the above shape representations can be used to represent sketches. However, primitive-based methods usually suppress the ability cap of shape representation. In this work, we choose to fit an implicit sketch representation using a neural network, and show its superiority over other representations (e.g., BSP [8]) in the ablation study, see Sec. 5.4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Reverse engineering CAD reconstruction. Over the past decades, reverse engineering has been extensively studied; it aims at converting measured data (a surface mesh or a point cloud) into solid 3D models that can be further edited and manufactured by industries. Traditional approaches addressing this problem consist of the following tasks: (1) segmentation of the point clouds/meshes [5,41,60], (2) fitting of parametric primitives to segmented regions [11, 36, 55], (3) finishing operations for CAD modeling [4, 24]. Important drawbacks of these conventional methods are the time-consuming process and the requirement of a skilled operator to guide the reconstruction [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With the release of several large-scale CAD datasets (e.g., ABC [21], Fusion 360 [50]), SketchGraphs [37]), numerous approaches have explored deep learning to address primitive segmentation/detection [25, 56], parametric curve or surface inference from point clouds [17, 27, 31, 40, 48] or B-rep models [18, 23]. However, by only outputting individual curves or surfaces, these methods lack the CAD modeling operations that are needed to build solid models. Focusing on CAD generation rather than reconstruction task as ours, some approaches propose deep generative models that predict sequences of CAD modeling operations to produce CAD designs [26, 50, 51, 53, 54]. Aiming at CAD reconstruction involving inverse CSG modeling [15], CSGNet [39] first develops a neural model that parses a shape into a sequence of CSG operations. More recent works follow the line of CSG parsing by advancing the inference without any supervision [19], or improving representation capability with a three-layer reformulation of the classic" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16817" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.271, + 0.897, + 0.332 + ], + "angle": 0, + "content": "Figure 2. Network architecture for SECAD-Net: The embedding \\(\\mathbf{z}\\) encoded from the voxel input is first fed to the extrusion box head to predict extrusion boxes. It is also sent to the sketch head network to calculate the sketch SDF \\(\\hat{S}_{\\mathrm{sk}}^i\\) after concatenating with the linear transformed sampling point. \\(\\hat{S}_{\\mathrm{cyl}}^i\\) stands for the SDF of the cylinder, which is acquired by extruding \\(\\hat{S}_{\\mathrm{sk}}^i\\) with height \\(h_i\\). Then we convert \\(\\hat{S}_{\\mathrm{cyl}}^i\\) to occupancy of cylinder \\(\\hat{\\mathcal{O}}_i\\) and finally obtain the complete shape by union all the occupancies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.47, + 0.446 + ], + "angle": 0, + "content": "CSG-tree [33], or handling richer geometric and topological variations by introducing quadric surface primitives [59]. While achieving high-quality reconstruction, CSG tends to combine a large number of shape primitives that are not as flexible as the extrusions of 2D sketches and are also not easily user edited to control the final geometry." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.447, + 0.473, + 0.751 + ], + "angle": 0, + "content": "Motivated by modern design tools, supervised methods are proposed [22, 46] utilizing the sketch-extrude procedural models and learning 2D sketches that can be extruded to 3D shapes. In contrast to their reliance on 2D labels, SECAD-Net is trained in a self-supervised manner. Most closely related to our work is ExtrudeNet [34]. SECAD-Net distinguishes itself from ExtrudeNet in several significant aspects: i) Following the traditional reconstruction process, ExtrudeNet first predicts the parameters of Bézier curves and then converts them into SDFs. In contrast, we jumped out of this paradigm and directly used neural networks to predict the 2D implicit fields of the profiles. ii) ExtrudeNet adopts closed Bézier curves to avoid self-intersection in sketches. This makes ExtrudeNet can only predict star-shaped profiles, which limits the expressive power of their CAD shapes. Our method does not impose any restrictions on the shape of the profile, thus having greater flexibility in shape expression. iii) To pursue the reconstruction effect, ExtrudeNet relies on a larger number of primitives, while our method is able to predict more compact CAD shapes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.765, + 0.385, + 0.781 + ], + "angle": 0, + "content": "3. Problem Statement and Overview" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.79, + 0.47, + 0.837 + ], + "angle": 0, + "content": "In this section, we present an overview of the proposed approach. To precisely explain our techniques, we first provide the definition of several related terminologies (Fig. 3)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.219, + 0.862 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Definition 1 (Loop, Profile and Sketch) In CAD terminology, a sketch is represented by a collection of geometric" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.353, + 0.891, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.488, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Figure 3. Definitions of CAD terminologies used in this paper. Note that the axis of the sketch plane in the figure is the same as the z-axis in the extrusion box." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.895, + 0.621 + ], + "angle": 0, + "content": "primitives. By referring to a closed curve as a loop and an enclosed region composed of one or multiple inner/outer loops as a profile, we define a sketch as the collection of one profile and its loops." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.894, + 0.713 + ], + "angle": 0, + "content": "Definition 2 (Sketch plane and Extrusion box) A sketch plane is a finite plane with width \\( w \\) and length \\( l \\), containing one or more sketches with the same extrusion height \\( h \\). Then we define an extrusion box as a cuboid with the sketch plane as the base and \\( 2h \\) as the height." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.894, + 0.834 + ], + "angle": 0, + "content": "Definition 3 (Cylinder primitive and Cylinder) In this work, a cylinder refers to the shape obtained by extruding a sketch, and a cylinder primitive is obtained by performing an extrude operation on a closed area formed by a loop. A cylinder may contain one cylinder primitive or be obtained from several cylinder primitives through the Difference operation used in CSG modeling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.611, + 0.861 + ], + "angle": 0, + "content": "3.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "We formulate the problem of CAD reconstruction as sketch and extrude inference: taking an input 3D shape," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16818" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.319 + ], + "angle": 0, + "content": "SECAD-Net aims to reconstruct the CAD model by predicting a set of geometric proxies that are decomposed to sketch-extrude operations. The overall pipeline of SECAD-Net is visualized in Fig. 2. Given a 3D voxel model, we first map it into a latent feature embedding \\(\\mathbf{z}\\) by using an encoder based on a 3D convolutional network. An extrusion box head network is then applied to predict the parameters of the sketch planes from \\(\\mathbf{z}\\). We employ \\(N\\) sketch head network to independently learn \\(N\\) 2D signed distance fields (SDFs) as the implicit representation of a sketch. Next, we design a differentiable extrusion operator to calculate the SDF of the 3D cylinder primitives corresponding to the sketches. Finally, an occupancy transformation operation and a union operation transform the multiple SDFs into the full 3D reconstructed shape as the output of the network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.33, + 0.169, + 0.345 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.355, + 0.31, + 0.372 + ], + "angle": 0, + "content": "4.1. Sketch-Extrude Inferring" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.469 + ], + "angle": 0, + "content": "We apply a standard 3D CNN encoder to extract a shape code \\(\\mathbf{z}\\) with size 256 from the input voxel. The code is then passed to the proposed SECAD-Net to output the sketch and extrusion cylinder parameters. Below we introduce the main modules of SECAD-Net following the order of data transmission during prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.635 + ], + "angle": 0, + "content": "Extrusion box prediction. We first apply a fully connected layer to predict the parameters of the extrusion boxes. Taking the feature encoding \\(\\mathbf{z}\\) as input, a decoder, refereed to sketch box head, outputs a set of sketch boxes \\(\\mathcal{B} = \\{\\mathbf{s}_i,\\mathbf{c}_i,\\mathbf{r}_i\\mid i\\in N\\}\\), where \\(\\mathbf{s}_i\\in \\mathbb{R}^3\\) describes the 2D size (i.e., length and width) of the box, \\(\\mathbf{c}_i\\in \\mathbb{R}^3\\) represents the predicted position of the box's center, and \\(\\mathbf{r}_i\\in \\mathbb{R}^4\\) is the rotation quaternion. The positive z-axis of the extrusion box determines the axial direction \\(\\mathbf{e}_i\\) of the sketch plane, and the height of the extrusion box is twice the height of the extrude operation (see Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.471, + 0.877 + ], + "angle": 0, + "content": "2D sketch inference. The sketches in each sketch plane depict the shape contained within the sketch box. Inspired by the recent neural implicit shapes [2, 46], we encode the shape of each sketch into a sketch latent space. To this end, we first project the 3D sampling points w.r.t the corresponding occupancy value onto the sketch plane along the axis \\(\\mathbf{e}_i\\). A sketch head network (SK-head) then computes the signed distance from each sampling point to the sketch contour. The distance is negative for points in the sketch and positive for points outside. Each SK-head contains \\(N_{lay}\\) layers of fully connected layers, with softplus activation functions used between layers, and we clamp the output distance to [-1,1] in the last layer. Each 2D point is concatenated with the feature encoding \\(\\mathbf{z}\\) as a global condition before being fed into the SK-head. Regarding the \\(i\\)-th SK-head as an implicit function \\(f_i\\), then formally we get:" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.884, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {S}} _ {\\mathbf {s k}} ^ {i} = f _ {i} \\left(\\mathbf {x} _ {i} ^ {t}, \\mathbf {z}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_i^t\\) is the result of a linear transformation of the sampling points contained in the \\(i\\)-th extrusion box, which can be expressed as \\(\\mathbf{r}_i^{-1}(\\mathbf{x}_i - \\mathbf{c}_i)\\). \\(\\hat{S}_{\\mathrm{sk}}^i\\) represents the signed distance field of the \\(i\\)-th sketch plane." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.893, + 0.384 + ], + "angle": 0, + "content": "Differentiable extrusion. Next, we calculate the SDF of a cylinder based on the 2D distance field and the extrusion height \\( h \\). We denote \\( \\Omega \\) as the volume between two hyperplanes \\( p^u \\) and \\( p^l \\), where \\( p^u \\) and \\( p^l \\) are the upper and lower surfaces on which the cylinder is located. Similarly, we define \\( \\Psi \\) as the volume inside the infinite cylinder where the side of the cylinder is located. The implicit field of the \\( i \\)-th cylinder, \\( \\hat{S}_{\\mathrm{cyl}}^i \\), is equal to one of the following cases: (1) the distance from a point \\( \\mathbf{x}_i \\) to \\( p^u \\) or \\( p^l \\), when \\( \\mathbf{x}_i \\in \\Omega \\cap \\Psi^\\complement \\), where superscript \\( \\complement \\) stands for complement; (2) \\( \\hat{S}_{\\mathrm{sk}}^i \\), when \\( \\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi \\); (3) the distance from \\( \\mathbf{x}_i \\) to the intersection curves of the cylinder and hyperplanes, when \\( \\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi^\\complement \\); (4) the maximum distance between \\( \\hat{S}_{\\mathrm{sk}}^i \\) and the point to \\( p^u \\) or \\( p^l \\), when \\( \\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi \\). The sub-formulas for each case are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.389, + 0.892, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {S}} _ {\\mathrm {c y l}} ^ {i} = \\left\\{ \\begin{array}{l l} \\max \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right) & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} \\leq 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| \\leq h _ {i}\\right) \\\\ \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} \\leq 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| > h _ {i}\\right) \\\\ \\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} > 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| \\leq h _ {i}\\right) \\\\ \\left\\| \\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right) \\right\\| _ {2} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} > 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| > h _ {i}\\right) \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.511 + ], + "angle": 0, + "content": "Combining the above four sub-formulas with the max and min operations, the following result is obtained:" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.516, + 0.891, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {S} _ {\\mathrm {c y l}} ^ {i} = \\min \\left(\\max \\left(\\hat {S} _ {\\mathrm {s k}} ^ {i}, \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right), 0\\right) \\\\ + \\left. \\left\\| m a x \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, 0\\right), m a x \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}, 0\\right) \\right\\| _ {2} \\right. \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Occupancy conversion and assembly. The occupancy function represents points inside the shape as 1 and points outside the shape as 0, which can be transformed by SDF. Following [13, 33], we use the Sigmoid function to perform differentiable transformation operations:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.649, + 0.891, + 0.669 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {O}} _ {i} = \\operatorname {S i g m o i d} (- \\eta \\cdot \\hat {\\mathcal {S}} _ {\\mathrm {c y l}} ^ {i}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.857 + ], + "angle": 0, + "content": "We finally assemble the occupancy \\(\\hat{O}_i\\) of each cylinder to obtain the reconstructed shape. In order to express complex shapes, many works use intersection, union, and difference operations in CSG in the assembly stage [8,19,33,59]. In contrast to them, we only use the union operation, because the extrusion cylinders can naturally represent concave shapes. This helps us avoid designing intricate loss functions or employing multi-stage training strategies without losing the flexibility of reconstructing shape representations. We adopt the Softmax to compute the union operation as it is shown to be effective in avoiding vanishing gradients [33]:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.863, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathcal {O}} _ {t o t a l} = \\sum_ {i} ^ {N} \\operatorname {S o f t m a x} (\\varphi \\cdot \\hat {\\mathcal {O}} _ {i}) \\cdot \\hat {\\mathcal {O}} _ {i}, \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16819" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.123 + ], + "angle": 0, + "content": "where \\(\\varphi\\) is the modulating coefficient and \\(\\hat{\\mathcal{O}}_{total}\\) is the occupancy representation of the final reconstructed shape." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.131, + 0.223, + 0.145 + ], + "angle": 0, + "content": "4.2. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.154, + 0.469, + 0.246 + ], + "angle": 0, + "content": "We train SECAD-Net in a self-supervised fashion through the minimization of the sum of two objective terms. The supervision signal is mainly quantified by the reconstruction loss, which measures the mean squared error between the predicted shape occupancy \\(\\hat{\\mathcal{O}}_{total}\\) and the ground truth \\(\\mathcal{O}_{total}^{*}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.255, + 0.469, + 0.281 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c o n}} = \\mathbb {E} _ {x \\in \\mathbf {X}} \\left[ \\left(\\hat {\\mathcal {O}} _ {\\text {t o t a l}} - \\mathcal {O} _ {\\text {t o t a l}} ^ {*}\\right) ^ {2} \\right], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.289, + 0.462, + 0.304 + ], + "angle": 0, + "content": "where \\(x\\) is a randomly sampled point in the shape volume." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.469, + 0.456 + ], + "angle": 0, + "content": "However, we find that applying only \\(\\mathcal{L}_{\\text{recon}}\\) makes the network always learn fragmented cylinders. To tackle this problem, we design a 2D sketch loss to facilitate the network to learn the axis of the sketch plane and the complete profile. Specifically, each sketch plane cuts the voxel model to form an occupancy cross-section \\(\\mathcal{O}_{cs}^{i^*}\\). We project the 3D sampling points inside the \\(i\\)-th extrusion box \\(\\mathcal{B}^i\\) onto the sketch plane along the axial direction, and calculate the difference between the occupancy value of the projected points \\(\\hat{\\mathcal{O}}_{proj}\\) and ground truth \\(\\mathcal{O}_{cs}^{i^*}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.465, + 0.469, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s k e t c h}} = \\sum_ {i = 1} ^ {N} \\mathbb {E} _ {x \\in \\mathcal {B} ^ {i}} \\left[ \\left(\\hat {\\mathcal {O}} _ {\\text {p r o j}} ^ {i} - \\mathcal {O} _ {\\text {c s}} ^ {i ^ {*}}\\right) ^ {2} \\right]. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.515, + 0.468, + 0.544 + ], + "angle": 0, + "content": "The overall objective of SECAD-Net is defined as the combination of the above two terms:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.557, + 0.469, + 0.572 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e c o n}} + \\lambda \\mathcal {L} _ {\\text {s k e t c h}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.583, + 0.262, + 0.597 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a balance factor." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.274, + 0.621 + ], + "angle": 0, + "content": "4.3. CAD Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.825 + ], + "angle": 0, + "content": "The output of SECAD-Net during the training phase is an implicit occupancy function of the 3D shape. In the prediction stage, we reconstruct CAD models by using sketch-extrude operations instead of the marching cubes method. Sketch and extrusion. To convert a 2D implicit field (Fig. 4 (a)) in the sketch latent space into an editable sketch, we input uniform 2D sampling points to the SK-head, and attach the implicit value to the position of the sampling point to obtain an explicit image-like 2D profile (Fig. 4 (b)). We then use the Teh-Chin chain approximation [43] to extract the contours of the profiles and the hierarchical relationships between them. We further apply Dierckx's fitting [14] to convert the contours into closed B-splines (Fig. 4 (c))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "After extruding each sketch to get the cylinder primitives according to half the height of \\(\\mathcal{B}^i\\), we assemble cylinder primitives into cylinders by alternately performing union or difference operations according to the hierarchical relationship between contours (primitive at hierarchy 0 difference" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.621, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.187, + 0.595, + 0.196 + ], + "angle": 0, + "content": "(a) Implicit Field" + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.089, + 0.75, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.187, + 0.759, + 0.197 + ], + "angle": 0, + "content": "(b) Sample Points with Occupancy" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.09, + 0.89, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.187, + 0.88, + 0.196 + ], + "angle": 0, + "content": "(c) Fitted Sketch Splines" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.208, + 0.892, + 0.235 + ], + "angle": 0, + "content": "Figure 4. Illustration of converting 2D implicit sketches into the closed B-splines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.293 + ], + "angle": 0, + "content": "primitives at hierarchy 1 in the case of Fig. 4). Finally, we take the union of all cylinders to obtain the CAD model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Post-processing. We take two post-processing operations to clean up overlapping and shredded shapes in the result. First, for any two cylinders, when their overlapping coefficient is greater than 0.95, the smaller of them is discarded. Second, we delete all cylinders whose height is less than 0.01 in the reconstruction result. We demonstrate our final reconstructions in Fig. 5 and Fig. 6." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.41, + 0.716, + 0.426 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.892, + 0.631 + ], + "angle": 0, + "content": "SECAD-Net is implemented in PyTorch and trained on a TITAN RTX GPU from NVIDIA®. We train our model using an Adam optimizer [20] with learning rate \\(1 \\times 10^{-4}\\) and beta parameters (0.5, 0.99). We set both the number of MLP layers in the sketch head network and the number of output cylinders to 4. For hyper-parameters in Eq. 4, Eq. 5 and Eq. 8, we set \\(\\eta = 150\\), \\(\\varphi = 25\\) and \\(\\lambda = 0.01\\) in default, which generally works well in our experiments. Employing a similar training strategy to [59], we first pretrain SECAD-Net on the training datasets for 1,000 epochs using batch size 24, which takes about 8 hours, and finetuning on each test shape for 300 epochs, which takes about 3 minutes per shape." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.645, + 0.704, + 0.661 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.76 + ], + "angle": 0, + "content": "In this section, we examine the performance of SECAD-Net on the ABC dataset [21] and Fusion 360 Gallery [50]. Through extensive comparisons and ablation studies, we demonstrate the effectiveness of our approach and show its superiority over state-of-the-art reference approaches for CAD reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.581, + 0.788 + ], + "angle": 0, + "content": "5.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset preparation. For the ABC dataset, the voxel grids and sampling point data are provided by [59]. We use 5,000 groups of data for training and 1,000 for testing. For Fusion 360, which does not contain available voxels, we first randomly select 6,000 meshes, then discretize them into internally filled voxels. The train-test split is the same as ABC. We obtain sampling points with the corresponding occu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16820" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison between reconstruction results on ABC dataset." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.128, + 0.47, + 0.214 + ], + "angle": 0, + "content": "
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]1.8491.2550.82012.84
CSG-Stump [33]4.0310.7540.82817.18
ExtrudeNet [34]0.4710.9140.85214.46
Ours0.3300.7240.8634.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.228, + 0.469, + 0.256 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison between reconstruction results on Fusion 360 dataset." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.267, + 0.469, + 0.368 + ], + "angle": 0, + "content": "
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]2.9505.2770.77010.84
CSG-Stump [33]2.7814.5900.74412.08
Point2Cyl [46]13.88914.6570.6692.76
ExtrudeNet [34]2.2633.5580.81915.72
Ours2.0523.2820.8035.44
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.469, + 0.485 + ], + "angle": 0, + "content": "pancy value following [9]. The resolution of voxel shapes is \\(64^3\\) for both datasets, and the number of sampling points is 8,192. Considering that fine-tuning each method and generating high-accuracy meshes is time-consuming, we take 50 shapes from each dataset to form 100 shapes for quantitative evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.469, + 0.607 + ], + "angle": 0, + "content": "Evaluation metrics. For quantitative evaluations, we follow the metrics that are commonly used in previous methods [33, 59], including symmetric Chamfer Distance (CD), Normal Consistency (NC), Edge Chamfer Distance (ECD). Details of computing these metrics are given in the supplemental materials. Additionally, we also report the number of generated primitives, \\(\\# p\\), as a measure of how easy the output CAD results are to edit." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.62, + 0.396, + 0.635 + ], + "angle": 0, + "content": "5.2. Comparison on CAD Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.469, + 0.869 + ], + "angle": 0, + "content": "We thoroughly compare our method with two types of primitive-based CAD reconstruction methods that output editable CAD models, including two CSG-like methods (i.e., UCSG-Net [19], CSG-Stump [33]) and two cylinder decomposition counterpart (i.e., point2Cyl [46]), ExtrudeNet [34]. For each method, we adopt the implementation provided by the corresponding authors, and use the same training strategy for training and fine-tuning. For CSG-Stump, we set the number of intersection nodes to 64, making it output a comparable number of primitives to other methods. Those methods provide a plethora of comparisons to other techniques and establish themselves as state-of-the-art. Note that for point2Cyl, we only report its results on Fusion 360 dataset, as the ABC dataset does not provide the labels needed to train point2Cyl." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Quantitative results on the ABC and Fusion 360 datasets are reported in Table 1 and Table 2, respectively. It can be" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.892, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.434, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Figure 5. Visual comparison between reconstruction results on ABC dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.626 + ], + "angle": 0, + "content": "seen that the proposed SECAD-Net outperforms both kinds of methods on all evaluation metrics while still generating a relatively small number of primitives. Fig. 5 and Fig. 6 display several qualitative comparison results. For fairness, all the reconstructed CAD models are visualized using marching cubes (MC) with 256 resolution. Visually as shown in the figures, our method achieves much better geometry and topological fidelity with more accurate structures (e.g., holes, junctions) and sharper features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.855, + 0.652 + ], + "angle": 0, + "content": "5.3. CAD Generation via Sketch Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Although without ground truth labels as guidance, SECAD-Net can learn plausible 2D sketches from raw 3D shapes. Thanks to the implicit sketch representation, we are able to generate different CAD variations when a pair of shapes is interpolated in the complete and continuous sketch latent space, as shown in Fig. 7. The results suggest that the generated sketch is gradually transformed even if the pair of shapes have significantly different structures, and we draw two further conclusions: (1) the predicted position of each extrusion box is relatively deterministic, although the input shape is different (see the left and right column sketches in the leftmost group); (2) when an extrusion box does not contain a shape, our SK-head does not generate a sketch, making the network output an adaptive number of cylinders (see the middle column sketches of the leftmost and the rightmost groups)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16821" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.473, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.503, + 0.471, + 0.531 + ], + "angle": 0, + "content": "Figure 6. Visual comparison between reconstruction results on Fusion 360 dataset." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.574 + ], + "angle": 0, + "content": "Table 3. Ablation study on network design and sketch loss. We adopted setting (e) in the final model." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.585, + 0.47, + 0.717 + ], + "angle": 0, + "content": "
Settings(a)(b)(c)(d)(e)
Nsh14444
Nlay22244
Ncyl44844
Lsketch✓✓✓×✓
CD↓2.6270.9931.5040.3360.330
ECD↓1.7540.8821.0980.7720.724
NC↑0.7130.8350.7610.8630.863
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.189, + 0.756 + ], + "angle": 0, + "content": "5.4. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.809 + ], + "angle": 0, + "content": "We perform ablation studies to carefully analyze the efficiency of major components of our designed model. All quantitative metrics are measured on the ABC dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Effect of network design and sketch loss. We first examine the effect of the number of components/parameters in SECAD-Net, including the number of SK-heads \\((N_{sh})\\), the number of fully connected layers \\((N_{lay})\\) in each SK-head, and the number of output cylinders \\((N_{cyl})\\). Then we show the necessity of the sketch loss by deactivating it to train the" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.089, + 0.889, + 0.493 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.505, + 0.892, + 0.548 + ], + "angle": 0, + "content": "Figure 7. For each example, we encode the sketches of top and bottom shapes in latent vector space and then linearly interpolate the corresponding latent codes." + }, + { + "type": "table_caption", + "bbox": [ + 0.549, + 0.566, + 0.842, + 0.58 + ], + "angle": 0, + "content": "Table 4. Ablation study on sketch representation." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.59, + 0.892, + 0.66 + ], + "angle": 0, + "content": "
RepresentationCD↓ECD↓NC↑#P↓
Box primitives0.5230.9820.8255.38
BSP0.6120.8380.8525.84
SK-head (Ours)0.3300.7240.8634.30
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.794 + ], + "angle": 0, + "content": "network. The quantified results are presented in Table 3. Settings (a), (b), and (c) show that reducing the number of SK-heads or increasing the number of cylinder outputs will damage the model prediction accuracy. Settings (b), (d), and (e) show that increasing the number of MLP layers in SK-head or enabling \\(\\mathcal{L}_{\\text {sketch }}\\) will improve the prediction accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Effect of implicit sketch representation. To assess the efficiency of neural implicit sketch representation, we adopt two other classical shape representations, namely binary space partitioning (BSP [8]) and box-like primitives, to compare with our SK-head in SECAD-Net. For BSP, we set the number of output convex shapes to 8, each containing 12 partitions. The assembly method is consistent with [8] to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16822" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.079, + 0.088, + 0.47, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.318, + 0.471, + 0.348 + ], + "angle": 0, + "content": "Figure 8. Visual comparison results for ablation study on sketch representation." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.374, + 0.47, + 0.685 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.697, + 0.471, + 0.741 + ], + "angle": 0, + "content": "Figure 9. SECAD-Net can aid in more applications. Left: the results of single-view reconstruction. Right: a subsequent CAD editing by changing the predicted cylinder primitives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.9 + ], + "angle": 0, + "content": "represent 2D sketches. For box-like primitives, 24 rectangles are predicted. We divide them into two subsets in half, take the union operation separately, and subtract the other from one of the union results. The numerical and visual comparison results are shown in Table 4 and Fig. 8, respectively. It can be seen that our implicit field can represent the smoothest shape while obtaining the best reconstruction results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.685, + 0.108 + ], + "angle": 0, + "content": "5.5. Other Applications" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.892, + 0.299 + ], + "angle": 0, + "content": "By replacing the voxel encoder, SECAD-Net is flexible to reconstruct CAD models from other input shape representations, e.g., images and point clouds. Fig. 9 shows the results of SECAD-Net in solving single-view reconstruction (SVR) task. Following the training strategy of previous work [8, 9], we first use voxel data to complete the training of the 3D auto-encoding task, and then train an image encoder with the feature encoding of each shape as the target. The voxels and input images used for the SVR task are obtained directly from Fusion 360. Replacing more input representations, while feasible and meaningful, is not the focus of this paper and we leave it to future research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.893, + 0.422 + ], + "angle": 0, + "content": "Finally, the parameters of both 2D sketches and 3D cylinders are available, thus the CAD results output from SECAD-Net can be directly loaded into existing CAD software for further editing. As shown in the right side of Fig. 9, interpretable CAD variations can be produced via specific editing operations, such as sketch-level curve editing, primitive-level displacement, rotation, scaling, and Boolean operations between primitives." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.445, + 0.771, + 0.46 + ], + "angle": 0, + "content": "6. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.669 + ], + "angle": 0, + "content": "We have presented a novel neural network that successively learns shape sketch and extrusion without any expensive annotations of shape segmentation and labels as the supervision. Our approach is able to learn smooth sketches, followed by the differentiable extrusion to reconstruct CAD models that are close to the ground truth. We evaluate SECAD-Net using diverse CAD datasets and demonstrate the advantages of our approach by ablation studies and comparing it to the state-of-the-art methods. We further demonstrate our method's applicability in single-image CAD reconstruction. Additionally, the CAD shapes generated by our approach can be directly fed into off-the-shelf CAD software for sketch-level or cylinder primitive-level editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.893, + 0.793 + ], + "angle": 0, + "content": "In future work, we plan to extend our approach to learn more CAD-related operations such as revolve, bevel, and sweep. Besides, we find that current deep learning models perform poorly on datasets with large differences in shape geometry and structure. Therefore, another promising direction is to explore how to improve the generalization of neural networks and enhance the realism of the generated shapes by learning structural and topological information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. We thank the anonymous reviewer for their valuable suggestions. This work is partially funded by the National Natural Science Foundation of China (U22B2034, 62172416, U21A20515, 62172415), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022131)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16823" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. 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Graph., 28(8):2879-2894, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.468, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "16826" + } + ] +] \ No newline at end of file diff --git a/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/94d1495e-0d51-4b2c-8690-ac04468c5645_origin.pdf b/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/94d1495e-0d51-4b2c-8690-ac04468c5645_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..deac977b9183f1743c674a93be3dd6455d949c2e --- /dev/null +++ b/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/94d1495e-0d51-4b2c-8690-ac04468c5645_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:990d3b2e04573e664b0deb65d993e2799218d2150d2287efe9c1432b37529822 +size 9489585 diff --git a/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/full.md b/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..353bfbf48d508e6e4e5b53e92d8acca22a2aee5e --- /dev/null +++ b/2023/SECAD-Net_ Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations/full.md @@ -0,0 +1,313 @@ +# SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations + +Pu Li $^{1,2}$ Jianwei Guo $^{1,2*}$ Xiaopeng Zhang $^{1,2}$ Dong-Ming Yan $^{1,2}$ + +$^{1}$ MAIS, Institute of Automation, Chinese Academy of Sciences + +$^{2}$ School of Artificial Intelligence, University of Chinese Academy of Sciences + +![](images/5089da2c1cc2485f74c69b7266de110ede597588b38a139f51f2aafe16d22d39.jpg) +Figure 1. SECAD-Net for CAD reconstruction. Starting from a voxel grid (top), SECAD-Net learns Sketch-Extrude operations to reconstruct CAD models (bottom), without any supervision of part segmentation and sketch labels. + +# Abstract + +Reverse engineering CAD models from raw geometry is a classic but strenuous research problem. Previous learning-based methods rely heavily on labels due to the supervised design patterns or reconstruct CAD shapes that are not easily editable. In this work, we introduce SECAD-Net, an end-to-end neural network aimed at reconstructing compact and easy-to-edit CAD models in a self-supervised manner. Drawing inspiration from the modeling language that is most commonly used in modern CAD software, we propose to learn 2D sketches and 3D extrusion parameters from raw shapes, from which a set of extrusion cylinders can be generated by extruding each sketch from a 2D plane into a 3D body. By incorporating the Boolean operation (i.e., union), these cylinders can be combined to closely approximate the target geometry. We advocate the use of implicit fields for sketch representation, which allows for creating CAD variations by interpolating latent codes in the sketch latent space. Extensive experiments on both ABC and Fusion 360 datasets demonstrate the effectiveness of our method, and show superiority over state-of-the-art alternatives including the closely related method for supervised CAD reconstruction. We further apply our ap + +proach to CAD editing and single-view CAD reconstruction. Code will be released at https://github.com/BunnySoCrazy/SECAD-Net. + +# 1. Introduction + +CAD reconstruction is one of the most sought-after geometric modeling technologies, which plays a substantial role in reverse engineering in case of the original design document is missing or the CAD model of a real object is not available. It empowers users to reproduce CAD models from other representations and supports the designer to create new variations to facilitate various engineering and manufacturing applications. + +The advance in 3D scanning technologies has promoted the paradigm shift from time-consuming and laborious manual dimensions to automatic CAD reconstruction. A typical line of works [3,6,35,47] first reconstructs a polygon mesh from the scanned point cloud, then followed by mesh segmentation and primitive extraction to obtain a boundary representation (B-rep). Finally, a CAD shape parser is applied to convert the B-rep into a sequence of modeling operations. Recently, inspired by the substantial success of point set learning [1, 32, 49] and deep 3D representations [9,28,30], a number of methods have exploited neural + +networks to improve the above pipeline, e.g., detecting and fitting primitives to raw point clouds directly [25, 27, 40]. A few works (e.g., CSG-Net [39], UCSG-Net [19], and CSG-Stump [33]) further parse point cloud inputs into a constructive solid geometry (CSG) tree by predicting a set of primitives that are then combined with Boolean operations. Although achieving encouraging compact representation, they only output a set of simple primitives with limited types (e.g., planes, cylinders, spheres), which restricts their representation capability for reconstructing complex and more general 3D shapes. CAPRI-Net [59] introduces quadric surface primitives and the difference operation based on BSP-Net [8] to produce complicated convex and concave shapes via a CSG tree. However, controlling the implicit equation and parameters of quadric primitives is difficult for designers to edit the reconstructed models. Thus, the editability of those methods is quite limited. + +In this paper, we develop a novel and versatile deep neural framework, named SECAD-Net, to reconstruct high-quality and editable CAD models. Our approach is inspired by the observation that a CAD model is usually designed as a command sequence of operations [7, 38, 50, 51, 57], i.e., a set of planar 2D sketches are first drawn then extruded into 3D solid shapes for Boolean operations to create the final model. At the heart of our approach is to learn the sketch and extrude modeling operations, rather than CSG with parametric primitives. To determine the position and axis of each sketch plane, SECAD-Net first learns multiple extrusion boxes to decompose the entire shape into multiple local regions. Afterward, for the local profile in each box, we utilize a fully connected network to learn the implicit representation of the sketch. An extrusion operator is then designed to calculate the implicit expression of the cylinders according to the predicted sketch and extrusion parameters. We finally apply a union operation to assemble all extrusion cylinders into the final CAD model. + +Benefiting from our representation, our approach is flexible and efficient to construct a wide range of 3D shapes. As the predictions of our method are fully interpretable, it allows users to express their ideas to create variations or improve the design by operating on 2D sketches or 3D cylinders intuitively. To summarize, our work makes the following contributions: + +- We present a novel deep neural network for reverse engineering CAD models with self-supervision, leading to faithful reconstructions that closely approximate the target geometry. +- SECAD-Net is capable of learning implicit sketches and differentiable extrusions from raw 3D shapes without the guidance of ground truth sketch labels. +- Extensive experiments demonstrate the superiority of SECAD-Net through comprehensive comparisons. We + +also showcase its immediate applications to CAD interpolation, editing, and single-view reconstruction. + +# 2. Related work + +Neural implicit representation. 3D shapes can be represented either explicitly (e.g., point sets, voxels, meshes) or implicitly (e.g., signed-distance functions, indicator functions), each of them comes with its own advantages and drawbacks. Recently, there is an explosion of neural implicit representations [9, 28, 30] that allow for generating detail-rich 3D shapes by predicting the underlying signed distance fields. Thanks to the ability to learn priors over shapes, many deep implicit works have been proposed to solve various 3D tasks, such as shape representation and completion [2, 10, 42], image-based 3D reconstruction [45, 52, 58], shape abstraction [16, 44] and novel view synthesis [12, 29]. Theoretically, any of the above shape representations can be used to represent sketches. However, primitive-based methods usually suppress the ability cap of shape representation. In this work, we choose to fit an implicit sketch representation using a neural network, and show its superiority over other representations (e.g., BSP [8]) in the ablation study, see Sec. 5.4. + +Reverse engineering CAD reconstruction. Over the past decades, reverse engineering has been extensively studied; it aims at converting measured data (a surface mesh or a point cloud) into solid 3D models that can be further edited and manufactured by industries. Traditional approaches addressing this problem consist of the following tasks: (1) segmentation of the point clouds/meshes [5,41,60], (2) fitting of parametric primitives to segmented regions [11, 36, 55], (3) finishing operations for CAD modeling [4, 24]. Important drawbacks of these conventional methods are the time-consuming process and the requirement of a skilled operator to guide the reconstruction [6]. + +With the release of several large-scale CAD datasets (e.g., ABC [21], Fusion 360 [50]), SketchGraphs [37]), numerous approaches have explored deep learning to address primitive segmentation/detection [25, 56], parametric curve or surface inference from point clouds [17, 27, 31, 40, 48] or B-rep models [18, 23]. However, by only outputting individual curves or surfaces, these methods lack the CAD modeling operations that are needed to build solid models. Focusing on CAD generation rather than reconstruction task as ours, some approaches propose deep generative models that predict sequences of CAD modeling operations to produce CAD designs [26, 50, 51, 53, 54]. Aiming at CAD reconstruction involving inverse CSG modeling [15], CSGNet [39] first develops a neural model that parses a shape into a sequence of CSG operations. More recent works follow the line of CSG parsing by advancing the inference without any supervision [19], or improving representation capability with a three-layer reformulation of the classic + +![](images/11aba17092ac48e580551f23216bf6e7e5299f8ef332fdd603cb9027cd6fcaed.jpg) +Figure 2. Network architecture for SECAD-Net: The embedding $\mathbf{z}$ encoded from the voxel input is first fed to the extrusion box head to predict extrusion boxes. It is also sent to the sketch head network to calculate the sketch SDF $\hat{S}_{\mathrm{sk}}^i$ after concatenating with the linear transformed sampling point. $\hat{S}_{\mathrm{cyl}}^i$ stands for the SDF of the cylinder, which is acquired by extruding $\hat{S}_{\mathrm{sk}}^i$ with height $h_i$ . Then we convert $\hat{S}_{\mathrm{cyl}}^i$ to occupancy of cylinder $\hat{\mathcal{O}}_i$ and finally obtain the complete shape by union all the occupancies. + +CSG-tree [33], or handling richer geometric and topological variations by introducing quadric surface primitives [59]. While achieving high-quality reconstruction, CSG tends to combine a large number of shape primitives that are not as flexible as the extrusions of 2D sketches and are also not easily user edited to control the final geometry. + +Motivated by modern design tools, supervised methods are proposed [22, 46] utilizing the sketch-extrude procedural models and learning 2D sketches that can be extruded to 3D shapes. In contrast to their reliance on 2D labels, SECAD-Net is trained in a self-supervised manner. Most closely related to our work is ExtrudeNet [34]. SECAD-Net distinguishes itself from ExtrudeNet in several significant aspects: i) Following the traditional reconstruction process, ExtrudeNet first predicts the parameters of Bézier curves and then converts them into SDFs. In contrast, we jumped out of this paradigm and directly used neural networks to predict the 2D implicit fields of the profiles. ii) ExtrudeNet adopts closed Bézier curves to avoid self-intersection in sketches. This makes ExtrudeNet can only predict star-shaped profiles, which limits the expressive power of their CAD shapes. Our method does not impose any restrictions on the shape of the profile, thus having greater flexibility in shape expression. iii) To pursue the reconstruction effect, ExtrudeNet relies on a larger number of primitives, while our method is able to predict more compact CAD shapes. + +# 3. Problem Statement and Overview + +In this section, we present an overview of the proposed approach. To precisely explain our techniques, we first provide the definition of several related terminologies (Fig. 3). + +# 3.1. Preliminaries + +Definition 1 (Loop, Profile and Sketch) In CAD terminology, a sketch is represented by a collection of geometric + +![](images/7c8a862f7f54ac6d221647cc07f5bca000ea160b1a330cef40046863790a015d.jpg) +Figure 3. Definitions of CAD terminologies used in this paper. Note that the axis of the sketch plane in the figure is the same as the z-axis in the extrusion box. + +primitives. By referring to a closed curve as a loop and an enclosed region composed of one or multiple inner/outer loops as a profile, we define a sketch as the collection of one profile and its loops. + +Definition 2 (Sketch plane and Extrusion box) A sketch plane is a finite plane with width $w$ and length $l$ , containing one or more sketches with the same extrusion height $h$ . Then we define an extrusion box as a cuboid with the sketch plane as the base and $2h$ as the height. + +Definition 3 (Cylinder primitive and Cylinder) In this work, a cylinder refers to the shape obtained by extruding a sketch, and a cylinder primitive is obtained by performing an extrude operation on a closed area formed by a loop. A cylinder may contain one cylinder primitive or be obtained from several cylinder primitives through the Difference operation used in CSG modeling. + +# 3.2. Overview + +We formulate the problem of CAD reconstruction as sketch and extrude inference: taking an input 3D shape, + +SECAD-Net aims to reconstruct the CAD model by predicting a set of geometric proxies that are decomposed to sketch-extrude operations. The overall pipeline of SECAD-Net is visualized in Fig. 2. Given a 3D voxel model, we first map it into a latent feature embedding $\mathbf{z}$ by using an encoder based on a 3D convolutional network. An extrusion box head network is then applied to predict the parameters of the sketch planes from $\mathbf{z}$ . We employ $N$ sketch head network to independently learn $N$ 2D signed distance fields (SDFs) as the implicit representation of a sketch. Next, we design a differentiable extrusion operator to calculate the SDF of the 3D cylinder primitives corresponding to the sketches. Finally, an occupancy transformation operation and a union operation transform the multiple SDFs into the full 3D reconstructed shape as the output of the network. + +# 4. Method + +# 4.1. Sketch-Extrude Inferring + +We apply a standard 3D CNN encoder to extract a shape code $\mathbf{z}$ with size 256 from the input voxel. The code is then passed to the proposed SECAD-Net to output the sketch and extrusion cylinder parameters. Below we introduce the main modules of SECAD-Net following the order of data transmission during prediction. + +Extrusion box prediction. We first apply a fully connected layer to predict the parameters of the extrusion boxes. Taking the feature encoding $\mathbf{z}$ as input, a decoder, refereed to sketch box head, outputs a set of sketch boxes $\mathcal{B} = \{\mathbf{s}_i,\mathbf{c}_i,\mathbf{r}_i\mid i\in N\}$ , where $\mathbf{s}_i\in \mathbb{R}^3$ describes the 2D size (i.e., length and width) of the box, $\mathbf{c}_i\in \mathbb{R}^3$ represents the predicted position of the box's center, and $\mathbf{r}_i\in \mathbb{R}^4$ is the rotation quaternion. The positive z-axis of the extrusion box determines the axial direction $\mathbf{e}_i$ of the sketch plane, and the height of the extrusion box is twice the height of the extrude operation (see Fig. 3). + +2D sketch inference. The sketches in each sketch plane depict the shape contained within the sketch box. Inspired by the recent neural implicit shapes [2, 46], we encode the shape of each sketch into a sketch latent space. To this end, we first project the 3D sampling points w.r.t the corresponding occupancy value onto the sketch plane along the axis $\mathbf{e}_i$ . A sketch head network (SK-head) then computes the signed distance from each sampling point to the sketch contour. The distance is negative for points in the sketch and positive for points outside. Each SK-head contains $N_{lay}$ layers of fully connected layers, with softplus activation functions used between layers, and we clamp the output distance to [-1,1] in the last layer. Each 2D point is concatenated with the feature encoding $\mathbf{z}$ as a global condition before being fed into the SK-head. Regarding the $i$ -th SK-head as an implicit function $f_i$ , then formally we get: + +$$ +\hat {\mathcal {S}} _ {\mathbf {s k}} ^ {i} = f _ {i} \left(\mathbf {x} _ {i} ^ {t}, \mathbf {z}\right), \tag {1} +$$ + +where $\mathbf{x}_i^t$ is the result of a linear transformation of the sampling points contained in the $i$ -th extrusion box, which can be expressed as $\mathbf{r}_i^{-1}(\mathbf{x}_i - \mathbf{c}_i)$ . $\hat{S}_{\mathrm{sk}}^i$ represents the signed distance field of the $i$ -th sketch plane. + +Differentiable extrusion. Next, we calculate the SDF of a cylinder based on the 2D distance field and the extrusion height $h$ . We denote $\Omega$ as the volume between two hyperplanes $p^u$ and $p^l$ , where $p^u$ and $p^l$ are the upper and lower surfaces on which the cylinder is located. Similarly, we define $\Psi$ as the volume inside the infinite cylinder where the side of the cylinder is located. The implicit field of the $i$ -th cylinder, $\hat{S}_{\mathrm{cyl}}^i$ , is equal to one of the following cases: (1) the distance from a point $\mathbf{x}_i$ to $p^u$ or $p^l$ , when $\mathbf{x}_i \in \Omega \cap \Psi^\complement$ , where superscript $\complement$ stands for complement; (2) $\hat{S}_{\mathrm{sk}}^i$ , when $\mathbf{x}_i \in \Omega^\complement \cap \Psi$ ; (3) the distance from $\mathbf{x}_i$ to the intersection curves of the cylinder and hyperplanes, when $\mathbf{x}_i \in \Omega^\complement \cap \Psi^\complement$ ; (4) the maximum distance between $\hat{S}_{\mathrm{sk}}^i$ and the point to $p^u$ or $p^l$ , when $\mathbf{x}_i \in \Omega^\complement \cap \Psi$ . The sub-formulas for each case are as follows: + +$$ +\hat {\mathcal {S}} _ {\mathrm {c y l}} ^ {i} = \left\{ \begin{array}{l l} \max \left(\hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i}, \left| \mathbf {x} _ {i _ {z}} \right| - h _ {i}\right) & , \left(\hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i} \leq 0\right) \wedge \left(\left| \mathbf {x} _ {i _ {z}} \right| \leq h _ {i}\right) \\ \left| \mathbf {x} _ {i _ {z}} \right| - h _ {i} & , \left(\hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i} \leq 0\right) \wedge \left(\left| \mathbf {x} _ {i _ {z}} \right| > h _ {i}\right) \\ \hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i} & , \left(\hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i} > 0\right) \wedge \left(\left| \mathbf {x} _ {i _ {z}} \right| \leq h _ {i}\right) \\ \left\| \hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i}, \left(\left| \mathbf {x} _ {i _ {z}} \right| - h _ {i}\right) \right\| _ {2} & , \left(\hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i} > 0\right) \wedge \left(\left| \mathbf {x} _ {i _ {z}} \right| > h _ {i}\right) \end{array} \right. \tag {2} +$$ + +Combining the above four sub-formulas with the max and min operations, the following result is obtained: + +$$ +\begin{array}{l} \hat {S} _ {\mathrm {c y l}} ^ {i} = \min \left(\max \left(\hat {S} _ {\mathrm {s k}} ^ {i}, \left| \mathbf {x} _ {i _ {z}} \right| - h _ {i}\right), 0\right) \\ + \left. \left\| m a x \left(\hat {\mathcal {S}} _ {\mathrm {s k}} ^ {i}, 0\right), m a x \left(\left| \mathbf {x} _ {i _ {z}} \right| - h _ {i}, 0\right) \right\| _ {2} \right. \tag {3} \\ \end{array} +$$ + +Occupancy conversion and assembly. The occupancy function represents points inside the shape as 1 and points outside the shape as 0, which can be transformed by SDF. Following [13, 33], we use the Sigmoid function to perform differentiable transformation operations: + +$$ +\hat {\mathcal {O}} _ {i} = \operatorname {S i g m o i d} (- \eta \cdot \hat {\mathcal {S}} _ {\mathrm {c y l}} ^ {i}). \tag {4} +$$ + +We finally assemble the occupancy $\hat{O}_i$ of each cylinder to obtain the reconstructed shape. In order to express complex shapes, many works use intersection, union, and difference operations in CSG in the assembly stage [8,19,33,59]. In contrast to them, we only use the union operation, because the extrusion cylinders can naturally represent concave shapes. This helps us avoid designing intricate loss functions or employing multi-stage training strategies without losing the flexibility of reconstructing shape representations. We adopt the Softmax to compute the union operation as it is shown to be effective in avoiding vanishing gradients [33]: + +$$ +\hat {\mathcal {O}} _ {t o t a l} = \sum_ {i} ^ {N} \operatorname {S o f t m a x} (\varphi \cdot \hat {\mathcal {O}} _ {i}) \cdot \hat {\mathcal {O}} _ {i}, \tag {5} +$$ + +where $\varphi$ is the modulating coefficient and $\hat{\mathcal{O}}_{total}$ is the occupancy representation of the final reconstructed shape. + +# 4.2. Loss Function + +We train SECAD-Net in a self-supervised fashion through the minimization of the sum of two objective terms. The supervision signal is mainly quantified by the reconstruction loss, which measures the mean squared error between the predicted shape occupancy $\hat{\mathcal{O}}_{total}$ and the ground truth $\mathcal{O}_{total}^{*}$ : + +$$ +\mathcal {L} _ {\text {r e c o n}} = \mathbb {E} _ {x \in \mathbf {X}} \left[ \left(\hat {\mathcal {O}} _ {\text {t o t a l}} - \mathcal {O} _ {\text {t o t a l}} ^ {*}\right) ^ {2} \right], \tag {6} +$$ + +where $x$ is a randomly sampled point in the shape volume. + +However, we find that applying only $\mathcal{L}_{\text{recon}}$ makes the network always learn fragmented cylinders. To tackle this problem, we design a 2D sketch loss to facilitate the network to learn the axis of the sketch plane and the complete profile. Specifically, each sketch plane cuts the voxel model to form an occupancy cross-section $\mathcal{O}_{cs}^{i^*}$ . We project the 3D sampling points inside the $i$ -th extrusion box $\mathcal{B}^i$ onto the sketch plane along the axial direction, and calculate the difference between the occupancy value of the projected points $\hat{\mathcal{O}}_{proj}$ and ground truth $\mathcal{O}_{cs}^{i^*}$ : + +$$ +\mathcal {L} _ {\text {s k e t c h}} = \sum_ {i = 1} ^ {N} \mathbb {E} _ {x \in \mathcal {B} ^ {i}} \left[ \left(\hat {\mathcal {O}} _ {\text {p r o j}} ^ {i} - \mathcal {O} _ {\text {c s}} ^ {i ^ {*}}\right) ^ {2} \right]. \tag {7} +$$ + +The overall objective of SECAD-Net is defined as the combination of the above two terms: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {r e c o n}} + \lambda \mathcal {L} _ {\text {s k e t c h}}, \tag {8} +$$ + +where $\lambda$ is a balance factor. + +# 4.3. CAD Reconstruction + +The output of SECAD-Net during the training phase is an implicit occupancy function of the 3D shape. In the prediction stage, we reconstruct CAD models by using sketch-extrude operations instead of the marching cubes method. Sketch and extrusion. To convert a 2D implicit field (Fig. 4 (a)) in the sketch latent space into an editable sketch, we input uniform 2D sampling points to the SK-head, and attach the implicit value to the position of the sampling point to obtain an explicit image-like 2D profile (Fig. 4 (b)). We then use the Teh-Chin chain approximation [43] to extract the contours of the profiles and the hierarchical relationships between them. We further apply Dierckx's fitting [14] to convert the contours into closed B-splines (Fig. 4 (c)). + +After extruding each sketch to get the cylinder primitives according to half the height of $\mathcal{B}^i$ , we assemble cylinder primitives into cylinders by alternately performing union or difference operations according to the hierarchical relationship between contours (primitive at hierarchy 0 difference + +![](images/f43568e8d49bcec6a03058a1063c8adb639ba2d141ae98d180614909fc77aca3.jpg) +(a) Implicit Field + +![](images/3d162500a42b2569680b9764fe087b8773c77c5001d225e8e9378bcc1eb2642c.jpg) +(b) Sample Points with Occupancy + +![](images/b959cc0e8ec1e50a7b16e45c01195b1235bde5a33a8c7444c6093b7fe1db6ca7.jpg) +(c) Fitted Sketch Splines +Figure 4. Illustration of converting 2D implicit sketches into the closed B-splines. + +primitives at hierarchy 1 in the case of Fig. 4). Finally, we take the union of all cylinders to obtain the CAD model. + +Post-processing. We take two post-processing operations to clean up overlapping and shredded shapes in the result. First, for any two cylinders, when their overlapping coefficient is greater than 0.95, the smaller of them is discarded. Second, we delete all cylinders whose height is less than 0.01 in the reconstruction result. We demonstrate our final reconstructions in Fig. 5 and Fig. 6. + +# 4.4. Implementation Details + +SECAD-Net is implemented in PyTorch and trained on a TITAN RTX GPU from NVIDIA®. We train our model using an Adam optimizer [20] with learning rate $1 \times 10^{-4}$ and beta parameters (0.5, 0.99). We set both the number of MLP layers in the sketch head network and the number of output cylinders to 4. For hyper-parameters in Eq. 4, Eq. 5 and Eq. 8, we set $\eta = 150$ , $\varphi = 25$ and $\lambda = 0.01$ in default, which generally works well in our experiments. Employing a similar training strategy to [59], we first pretrain SECAD-Net on the training datasets for 1,000 epochs using batch size 24, which takes about 8 hours, and finetuning on each test shape for 300 epochs, which takes about 3 minutes per shape. + +# 5. Experimental Results + +In this section, we examine the performance of SECAD-Net on the ABC dataset [21] and Fusion 360 Gallery [50]. Through extensive comparisons and ablation studies, we demonstrate the effectiveness of our approach and show its superiority over state-of-the-art reference approaches for CAD reconstruction. + +# 5.1. Setup + +Dataset preparation. For the ABC dataset, the voxel grids and sampling point data are provided by [59]. We use 5,000 groups of data for training and 1,000 for testing. For Fusion 360, which does not contain available voxels, we first randomly select 6,000 meshes, then discretize them into internally filled voxels. The train-test split is the same as ABC. We obtain sampling points with the corresponding occu + +Table 1. Quantitative comparison between reconstruction results on ABC dataset. + +
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]1.8491.2550.82012.84
CSG-Stump [33]4.0310.7540.82817.18
ExtrudeNet [34]0.4710.9140.85214.46
Ours0.3300.7240.8634.30
+ +Table 2. Quantitative comparison between reconstruction results on Fusion 360 dataset. + +
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]2.9505.2770.77010.84
CSG-Stump [33]2.7814.5900.74412.08
Point2Cyl [46]13.88914.6570.6692.76
ExtrudeNet [34]2.2633.5580.81915.72
Ours2.0523.2820.8035.44
+ +pancy value following [9]. The resolution of voxel shapes is $64^3$ for both datasets, and the number of sampling points is 8,192. Considering that fine-tuning each method and generating high-accuracy meshes is time-consuming, we take 50 shapes from each dataset to form 100 shapes for quantitative evaluation. + +Evaluation metrics. For quantitative evaluations, we follow the metrics that are commonly used in previous methods [33, 59], including symmetric Chamfer Distance (CD), Normal Consistency (NC), Edge Chamfer Distance (ECD). Details of computing these metrics are given in the supplemental materials. Additionally, we also report the number of generated primitives, $\# p$ , as a measure of how easy the output CAD results are to edit. + +# 5.2. Comparison on CAD Reconstruction + +We thoroughly compare our method with two types of primitive-based CAD reconstruction methods that output editable CAD models, including two CSG-like methods (i.e., UCSG-Net [19], CSG-Stump [33]) and two cylinder decomposition counterpart (i.e., point2Cyl [46]), ExtrudeNet [34]. For each method, we adopt the implementation provided by the corresponding authors, and use the same training strategy for training and fine-tuning. For CSG-Stump, we set the number of intersection nodes to 64, making it output a comparable number of primitives to other methods. Those methods provide a plethora of comparisons to other techniques and establish themselves as state-of-the-art. Note that for point2Cyl, we only report its results on Fusion 360 dataset, as the ABC dataset does not provide the labels needed to train point2Cyl. + +Quantitative results on the ABC and Fusion 360 datasets are reported in Table 1 and Table 2, respectively. It can be + +![](images/2e831fc7b15c6d7986cfe8bdbfda7c461815dc702822dea46ec98ad517cb10fd.jpg) +Figure 5. Visual comparison between reconstruction results on ABC dataset. + +seen that the proposed SECAD-Net outperforms both kinds of methods on all evaluation metrics while still generating a relatively small number of primitives. Fig. 5 and Fig. 6 display several qualitative comparison results. For fairness, all the reconstructed CAD models are visualized using marching cubes (MC) with 256 resolution. Visually as shown in the figures, our method achieves much better geometry and topological fidelity with more accurate structures (e.g., holes, junctions) and sharper features. + +# 5.3. CAD Generation via Sketch Interpolation + +Although without ground truth labels as guidance, SECAD-Net can learn plausible 2D sketches from raw 3D shapes. Thanks to the implicit sketch representation, we are able to generate different CAD variations when a pair of shapes is interpolated in the complete and continuous sketch latent space, as shown in Fig. 7. The results suggest that the generated sketch is gradually transformed even if the pair of shapes have significantly different structures, and we draw two further conclusions: (1) the predicted position of each extrusion box is relatively deterministic, although the input shape is different (see the left and right column sketches in the leftmost group); (2) when an extrusion box does not contain a shape, our SK-head does not generate a sketch, making the network output an adaptive number of cylinders (see the middle column sketches of the leftmost and the rightmost groups). + +![](images/a4b9b7be7df895b025b8cc6511770be79bfd077128697089dd40c836cbdd3945.jpg) +Figure 6. Visual comparison between reconstruction results on Fusion 360 dataset. + +Table 3. Ablation study on network design and sketch loss. We adopted setting (e) in the final model. + +
Settings(a)(b)(c)(d)(e)
Nsh14444
Nlay22244
Ncyl44844
Lsketch✓✓✓×✓
CD↓2.6270.9931.5040.3360.330
ECD↓1.7540.8821.0980.7720.724
NC↑0.7130.8350.7610.8630.863
+ +# 5.4. Ablations + +We perform ablation studies to carefully analyze the efficiency of major components of our designed model. All quantitative metrics are measured on the ABC dataset. + +Effect of network design and sketch loss. We first examine the effect of the number of components/parameters in SECAD-Net, including the number of SK-heads $(N_{sh})$ , the number of fully connected layers $(N_{lay})$ in each SK-head, and the number of output cylinders $(N_{cyl})$ . Then we show the necessity of the sketch loss by deactivating it to train the + +![](images/60a82da82e2ceb5b2f4842af712cc46a844d7cf30e569537f7dec8812c9e875b.jpg) +Figure 7. For each example, we encode the sketches of top and bottom shapes in latent vector space and then linearly interpolate the corresponding latent codes. + +Table 4. Ablation study on sketch representation. + +
RepresentationCD↓ECD↓NC↑#P↓
Box primitives0.5230.9820.8255.38
BSP0.6120.8380.8525.84
SK-head (Ours)0.3300.7240.8634.30
+ +network. The quantified results are presented in Table 3. Settings (a), (b), and (c) show that reducing the number of SK-heads or increasing the number of cylinder outputs will damage the model prediction accuracy. Settings (b), (d), and (e) show that increasing the number of MLP layers in SK-head or enabling $\mathcal{L}_{\text {sketch }}$ will improve the prediction accuracy. + +Effect of implicit sketch representation. To assess the efficiency of neural implicit sketch representation, we adopt two other classical shape representations, namely binary space partitioning (BSP [8]) and box-like primitives, to compare with our SK-head in SECAD-Net. For BSP, we set the number of output convex shapes to 8, each containing 12 partitions. The assembly method is consistent with [8] to + +![](images/bc6c5ae9c9e12a9d8dab39b75285c4adc6d596c0d3c38b4b388d2551890e005e.jpg) +Figure 8. Visual comparison results for ablation study on sketch representation. + +![](images/182685481d978c3ace4fe0da18b3f9e6353e165a7f849dd85b6f22ac34433edc.jpg) +Figure 9. SECAD-Net can aid in more applications. Left: the results of single-view reconstruction. Right: a subsequent CAD editing by changing the predicted cylinder primitives. + +represent 2D sketches. For box-like primitives, 24 rectangles are predicted. We divide them into two subsets in half, take the union operation separately, and subtract the other from one of the union results. The numerical and visual comparison results are shown in Table 4 and Fig. 8, respectively. It can be seen that our implicit field can represent the smoothest shape while obtaining the best reconstruction results. + +# 5.5. Other Applications + +By replacing the voxel encoder, SECAD-Net is flexible to reconstruct CAD models from other input shape representations, e.g., images and point clouds. Fig. 9 shows the results of SECAD-Net in solving single-view reconstruction (SVR) task. Following the training strategy of previous work [8, 9], we first use voxel data to complete the training of the 3D auto-encoding task, and then train an image encoder with the feature encoding of each shape as the target. The voxels and input images used for the SVR task are obtained directly from Fusion 360. Replacing more input representations, while feasible and meaningful, is not the focus of this paper and we leave it to future research. + +Finally, the parameters of both 2D sketches and 3D cylinders are available, thus the CAD results output from SECAD-Net can be directly loaded into existing CAD software for further editing. As shown in the right side of Fig. 9, interpretable CAD variations can be produced via specific editing operations, such as sketch-level curve editing, primitive-level displacement, rotation, scaling, and Boolean operations between primitives. + +# 6. Conclusion and Future Work + +We have presented a novel neural network that successively learns shape sketch and extrusion without any expensive annotations of shape segmentation and labels as the supervision. Our approach is able to learn smooth sketches, followed by the differentiable extrusion to reconstruct CAD models that are close to the ground truth. We evaluate SECAD-Net using diverse CAD datasets and demonstrate the advantages of our approach by ablation studies and comparing it to the state-of-the-art methods. We further demonstrate our method's applicability in single-image CAD reconstruction. Additionally, the CAD shapes generated by our approach can be directly fed into off-the-shelf CAD software for sketch-level or cylinder primitive-level editing. + +In future work, we plan to extend our approach to learn more CAD-related operations such as revolve, bevel, and sweep. Besides, we find that current deep learning models perform poorly on datasets with large differences in shape geometry and structure. Therefore, another promising direction is to explore how to improve the generalization of neural networks and enhance the realism of the generated shapes by learning structural and topological information. + +Acknowledgments. We thank the anonymous reviewer for their valuable suggestions. This work is partially funded by the National Natural Science Foundation of China (U22B2034, 62172416, U21A20515, 62172415), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022131). + +# References + +[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. In International conference on machine learning, pages 40-49. PMLR, 2018. 1 +[2] Matan Atzmon and Yaron Lipman. SAL: Sign agnostic learning of shapes from raw data. 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SECAD-Net for CAD reconstruction. Starting from a voxel grid (top), SECAD-Net learns Sketch-Extrude operations to reconstruct CAD models (bottom), without any supervision of part segmentation and sketch labels." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 402, + 192, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 402, + 192, + 414 + ], + "spans": [ + { + "bbox": [ + 143, + 402, + 192, + 414 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 428, + 290, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 290, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 290, + 693 + ], + "type": "text", + "content": "Reverse engineering CAD models from raw geometry is a classic but strenuous research problem. Previous learning-based methods rely heavily on labels due to the supervised design patterns or reconstruct CAD shapes that are not easily editable. In this work, we introduce SECAD-Net, an end-to-end neural network aimed at reconstructing compact and easy-to-edit CAD models in a self-supervised manner. Drawing inspiration from the modeling language that is most commonly used in modern CAD software, we propose to learn 2D sketches and 3D extrusion parameters from raw shapes, from which a set of extrusion cylinders can be generated by extruding each sketch from a 2D plane into a 3D body. By incorporating the Boolean operation (i.e., union), these cylinders can be combined to closely approximate the target geometry. We advocate the use of implicit fields for sketch representation, which allows for creating CAD variations by interpolating latent codes in the sketch latent space. Extensive experiments on both ABC and Fusion 360 datasets demonstrate the effectiveness of our method, and show superiority over state-of-the-art alternatives including the closely related method for supervised CAD reconstruction. We further apply our ap" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 403, + 547, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 547, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 547, + 439 + ], + "type": "text", + "content": "proach to CAD editing and single-view CAD reconstruction. Code will be released at https://github.com/BunnySoCrazy/SECAD-Net." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 464, + 387, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 387, + 477 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 387, + 477 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 581 + ], + "type": "text", + "content": "CAD reconstruction is one of the most sought-after geometric modeling technologies, which plays a substantial role in reverse engineering in case of the original design document is missing or the CAD model of a real object is not available. It empowers users to reproduce CAD models from other representations and supports the designer to create new variations to facilitate various engineering and manufacturing applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 714 + ], + "type": "text", + "content": "The advance in 3D scanning technologies has promoted the paradigm shift from time-consuming and laborious manual dimensions to automatic CAD reconstruction. A typical line of works [3,6,35,47] first reconstructs a polygon mesh from the scanned point cloud, then followed by mesh segmentation and primitive extraction to obtain a boundary representation (B-rep). Finally, a CAD shape parser is applied to convert the B-rep into a sequence of modeling operations. Recently, inspired by the substantial success of point set learning [1, 32, 49] and deep 3D representations [9,28,30], a number of methods have exploited neural" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 223, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 223, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 223, + 713 + ], + "type": "text", + "content": "*Corresponding author: jianwei.guo@nlpr.ia.ac.cn" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16816" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "networks to improve the above pipeline, e.g., detecting and fitting primitives to raw point clouds directly [25, 27, 40]. A few works (e.g., CSG-Net [39], UCSG-Net [19], and CSG-Stump [33]) further parse point cloud inputs into a constructive solid geometry (CSG) tree by predicting a set of primitives that are then combined with Boolean operations. Although achieving encouraging compact representation, they only output a set of simple primitives with limited types (e.g., planes, cylinders, spheres), which restricts their representation capability for reconstructing complex and more general 3D shapes. CAPRI-Net [59] introduces quadric surface primitives and the difference operation based on BSP-Net [8] to produce complicated convex and concave shapes via a CSG tree. However, controlling the implicit equation and parameters of quadric primitives is difficult for designers to edit the reconstructed models. Thus, the editability of those methods is quite limited." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 502 + ], + "type": "text", + "content": "In this paper, we develop a novel and versatile deep neural framework, named SECAD-Net, to reconstruct high-quality and editable CAD models. Our approach is inspired by the observation that a CAD model is usually designed as a command sequence of operations [7, 38, 50, 51, 57], i.e., a set of planar 2D sketches are first drawn then extruded into 3D solid shapes for Boolean operations to create the final model. At the heart of our approach is to learn the sketch and extrude modeling operations, rather than CSG with parametric primitives. To determine the position and axis of each sketch plane, SECAD-Net first learns multiple extrusion boxes to decompose the entire shape into multiple local regions. Afterward, for the local profile in each box, we utilize a fully connected network to learn the implicit representation of the sketch. An extrusion operator is then designed to calculate the implicit expression of the cylinders according to the predicted sketch and extrusion parameters. We finally apply a union operation to assemble all extrusion cylinders into the final CAD model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 502, + 289, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 289, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 289, + 587 + ], + "type": "text", + "content": "Benefiting from our representation, our approach is flexible and efficient to construct a wide range of 3D shapes. As the predictions of our method are fully interpretable, it allows users to express their ideas to create variations or improve the design by operating on 2D sketches or 3D cylinders intuitively. To summarize, our work makes the following contributions:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 592, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 592, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 592, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 58, + 592, + 287, + 641 + ], + "type": "text", + "content": "- We present a novel deep neural network for reverse engineering CAD models with self-supervision, leading to faithful reconstructions that closely approximate the target geometry." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 647, + 287, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 647, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 58, + 647, + 287, + 683 + ], + "type": "text", + "content": "- SECAD-Net is capable of learning implicit sketches and differentiable extrusions from raw 3D shapes without the guidance of ground truth sketch labels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 288, + 714 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the superiority of SECAD-Net through comprehensive comparisons. We" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "content": "also showcase its immediate applications to CAD interpolation, editing, and single-view reconstruction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 107, + 391, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 107, + 391, + 119 + ], + "spans": [ + { + "bbox": [ + 306, + 107, + 391, + 119 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 127, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 127, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 127, + 545, + 354 + ], + "type": "text", + "content": "Neural implicit representation. 3D shapes can be represented either explicitly (e.g., point sets, voxels, meshes) or implicitly (e.g., signed-distance functions, indicator functions), each of them comes with its own advantages and drawbacks. Recently, there is an explosion of neural implicit representations [9, 28, 30] that allow for generating detail-rich 3D shapes by predicting the underlying signed distance fields. Thanks to the ability to learn priors over shapes, many deep implicit works have been proposed to solve various 3D tasks, such as shape representation and completion [2, 10, 42], image-based 3D reconstruction [45, 52, 58], shape abstraction [16, 44] and novel view synthesis [12, 29]. Theoretically, any of the above shape representations can be used to represent sketches. However, primitive-based methods usually suppress the ability cap of shape representation. In this work, we choose to fit an implicit sketch representation using a neural network, and show its superiority over other representations (e.g., BSP [8]) in the ablation study, see Sec. 5.4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 355, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 545, + 498 + ], + "type": "text", + "content": "Reverse engineering CAD reconstruction. Over the past decades, reverse engineering has been extensively studied; it aims at converting measured data (a surface mesh or a point cloud) into solid 3D models that can be further edited and manufactured by industries. Traditional approaches addressing this problem consist of the following tasks: (1) segmentation of the point clouds/meshes [5,41,60], (2) fitting of parametric primitives to segmented regions [11, 36, 55], (3) finishing operations for CAD modeling [4, 24]. Important drawbacks of these conventional methods are the time-consuming process and the requirement of a skilled operator to guide the reconstruction [6]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "With the release of several large-scale CAD datasets (e.g., ABC [21], Fusion 360 [50]), SketchGraphs [37]), numerous approaches have explored deep learning to address primitive segmentation/detection [25, 56], parametric curve or surface inference from point clouds [17, 27, 31, 40, 48] or B-rep models [18, 23]. However, by only outputting individual curves or surfaces, these methods lack the CAD modeling operations that are needed to build solid models. Focusing on CAD generation rather than reconstruction task as ours, some approaches propose deep generative models that predict sequences of CAD modeling operations to produce CAD designs [26, 50, 51, 53, 54]. Aiming at CAD reconstruction involving inverse CSG modeling [15], CSGNet [39] first develops a neural model that parses a shape into a sequence of CSG operations. More recent works follow the line of CSG parsing by advancing the inference without any supervision [19], or improving representation capability with a three-layer reformulation of the classic" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16817" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 545, + 202 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 202 + ], + "type": "image", + "image_path": "11aba17092ac48e580551f23216bf6e7e5299f8ef332fdd603cb9027cd6fcaed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": "Figure 2. Network architecture for SECAD-Net: The embedding " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": " encoded from the voxel input is first fed to the extrusion box head to predict extrusion boxes. It is also sent to the sketch head network to calculate the sketch SDF " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{sk}}^i" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": " after concatenating with the linear transformed sampling point. " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{cyl}}^i" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": " stands for the SDF of the cylinder, which is acquired by extruding " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{sk}}^i" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": " with height " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "h_i" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": ". Then we convert " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{cyl}}^i" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": " to occupancy of cylinder " + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{O}}_i" + }, + { + "bbox": [ + 46, + 214, + 548, + 262 + ], + "type": "text", + "content": " and finally obtain the complete shape by union all the occupancies." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 281, + 287, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 353 + ], + "type": "text", + "content": "CSG-tree [33], or handling richer geometric and topological variations by introducing quadric surface primitives [59]. While achieving high-quality reconstruction, CSG tends to combine a large number of shape primitives that are not as flexible as the extrusions of 2D sketches and are also not easily user edited to control the final geometry." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 289, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 594 + ], + "type": "text", + "content": "Motivated by modern design tools, supervised methods are proposed [22, 46] utilizing the sketch-extrude procedural models and learning 2D sketches that can be extruded to 3D shapes. In contrast to their reliance on 2D labels, SECAD-Net is trained in a self-supervised manner. Most closely related to our work is ExtrudeNet [34]. SECAD-Net distinguishes itself from ExtrudeNet in several significant aspects: i) Following the traditional reconstruction process, ExtrudeNet first predicts the parameters of Bézier curves and then converts them into SDFs. In contrast, we jumped out of this paradigm and directly used neural networks to predict the 2D implicit fields of the profiles. ii) ExtrudeNet adopts closed Bézier curves to avoid self-intersection in sketches. This makes ExtrudeNet can only predict star-shaped profiles, which limits the expressive power of their CAD shapes. Our method does not impose any restrictions on the shape of the profile, thus having greater flexibility in shape expression. iii) To pursue the reconstruction effect, ExtrudeNet relies on a larger number of primitives, while our method is able to predict more compact CAD shapes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 605, + 235, + 618 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 235, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 235, + 618 + ], + "type": "text", + "content": "3. Problem Statement and Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 625, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 287, + 662 + ], + "type": "text", + "content": "In this section, we present an overview of the proposed approach. To precisely explain our techniques, we first provide the definition of several related terminologies (Fig. 3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 134, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 134, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 134, + 682 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Definition 1 (Loop, Profile and Sketch) In CAD terminology, a sketch is represented by a collection of geometric" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 279, + 545, + 376 + ], + "blocks": [ + { + "bbox": [ + 307, + 279, + 545, + 376 + ], + "lines": [ + { + "bbox": [ + 307, + 279, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 307, + 279, + 545, + 376 + ], + "type": "image", + "image_path": "7c8a862f7f54ac6d221647cc07f5bca000ea160b1a330cef40046863790a015d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 386, + 546, + 419 + ], + "lines": [ + { + "bbox": [ + 305, + 386, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 305, + 386, + 546, + 419 + ], + "type": "text", + "content": "Figure 3. Definitions of CAD terminologies used in this paper. Note that the axis of the sketch plane in the figure is the same as the z-axis in the extrusion box." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 442, + 547, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 547, + 491 + ], + "type": "text", + "content": "primitives. By referring to a closed curve as a loop and an enclosed region composed of one or multiple inner/outer loops as a profile, we define a sketch as the collection of one profile and its loops." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "text", + "content": "Definition 2 (Sketch plane and Extrusion box) A sketch plane is a finite plane with width " + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "text", + "content": " and length " + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "text", + "content": ", containing one or more sketches with the same extrusion height " + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "text", + "content": ". Then we define an extrusion box as a cuboid with the sketch plane as the base and " + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "inline_equation", + "content": "2h" + }, + { + "bbox": [ + 304, + 503, + 547, + 564 + ], + "type": "text", + "content": " as the height." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 576, + 547, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 576, + 547, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 576, + 547, + 660 + ], + "type": "text", + "content": "Definition 3 (Cylinder primitive and Cylinder) In this work, a cylinder refers to the shape obtained by extruding a sketch, and a cylinder primitive is obtained by performing an extrude operation on a closed area formed by a loop. A cylinder may contain one cylinder primitive or be obtained from several cylinder primitives through the Difference operation used in CSG modeling." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 670, + 373, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 373, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 373, + 681 + ], + "type": "text", + "content": "3.2. Overview" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 715 + ], + "type": "text", + "content": "We formulate the problem of CAD reconstruction as sketch and extrude inference: taking an input 3D shape," + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16818" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": "SECAD-Net aims to reconstruct the CAD model by predicting a set of geometric proxies that are decomposed to sketch-extrude operations. The overall pipeline of SECAD-Net is visualized in Fig. 2. Given a 3D voxel model, we first map it into a latent feature embedding " + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": " by using an encoder based on a 3D convolutional network. An extrusion box head network is then applied to predict the parameters of the sketch planes from " + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": ". We employ " + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": " sketch head network to independently learn " + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": " 2D signed distance fields (SDFs) as the implicit representation of a sketch. Next, we design a differentiable extrusion operator to calculate the SDF of the 3D cylinder primitives corresponding to the sketches. Finally, an occupancy transformation operation and a union operation transform the multiple SDFs into the full 3D reconstructed shape as the output of the network." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 261, + 103, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 103, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 103, + 273 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 281, + 189, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 189, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 189, + 294 + ], + "type": "text", + "content": "4.1. Sketch-Extrude Inferring" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 287, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 371 + ], + "type": "text", + "content": "We apply a standard 3D CNN encoder to extract a shape code " + }, + { + "bbox": [ + 46, + 300, + 287, + 371 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 300, + 287, + 371 + ], + "type": "text", + "content": " with size 256 from the input voxel. The code is then passed to the proposed SECAD-Net to output the sketch and extrusion cylinder parameters. Below we introduce the main modules of SECAD-Net following the order of data transmission during prediction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": "Extrusion box prediction. We first apply a fully connected layer to predict the parameters of the extrusion boxes. Taking the feature encoding " + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": " as input, a decoder, refereed to sketch box head, outputs a set of sketch boxes " + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{B} = \\{\\mathbf{s}_i,\\mathbf{c}_i,\\mathbf{r}_i\\mid i\\in N\\}" + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": " describes the 2D size (i.e., length and width) of the box, " + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": " represents the predicted position of the box's center, and " + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_i\\in \\mathbb{R}^4" + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": " is the rotation quaternion. The positive z-axis of the extrusion box determines the axial direction " + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 46, + 371, + 287, + 502 + ], + "type": "text", + "content": " of the sketch plane, and the height of the extrusion box is twice the height of the extrude operation (see Fig. 3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "content": "2D sketch inference. The sketches in each sketch plane depict the shape contained within the sketch box. Inspired by the recent neural implicit shapes [2, 46], we encode the shape of each sketch into a sketch latent space. To this end, we first project the 3D sampling points w.r.t the corresponding occupancy value onto the sketch plane along the axis " + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "content": ". A sketch head network (SK-head) then computes the signed distance from each sampling point to the sketch contour. The distance is negative for points in the sketch and positive for points outside. Each SK-head contains " + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "inline_equation", + "content": "N_{lay}" + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "content": " layers of fully connected layers, with softplus activation functions used between layers, and we clamp the output distance to [-1,1] in the last layer. Each 2D point is concatenated with the feature encoding " + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "content": " as a global condition before being fed into the SK-head. Regarding the " + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "content": "-th SK-head as an implicit function " + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "inline_equation", + "content": "f_i" + }, + { + "bbox": [ + 46, + 502, + 288, + 694 + ], + "type": "text", + "content": ", then formally we get:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 133, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 133, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {S}} _ {\\mathbf {s k}} ^ {i} = f _ {i} \\left(\\mathbf {x} _ {i} ^ {t}, \\mathbf {z}\\right), \\tag {1}", + "image_path": "96b5e63fcbbf2b70fa02868a9043b97326629114208c055cf23168aba016896c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^t" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " is the result of a linear transformation of the sampling points contained in the " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "-th extrusion box, which can be expressed as " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_i^{-1}(\\mathbf{x}_i - \\mathbf{c}_i)" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{sk}}^i" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " represents the signed distance field of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "-th sketch plane." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": "Differentiable extrusion. Next, we calculate the SDF of a cylinder based on the 2D distance field and the extrusion height " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ". We denote " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " as the volume between two hyperplanes " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^u" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^l" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^u" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^l" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " are the upper and lower surfaces on which the cylinder is located. Similarly, we define " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " as the volume inside the infinite cylinder where the side of the cylinder is located. The implicit field of the " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": "-th cylinder, " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{cyl}}^i" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ", is equal to one of the following cases: (1) the distance from a point " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^u" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^l" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ", when " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\Omega \\cap \\Psi^\\complement" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ", where superscript " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\complement" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " stands for complement; (2) " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{sk}}^i" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ", when " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": "; (3) the distance from " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " to the intersection curves of the cylinder and hyperplanes, when " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi^\\complement" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": "; (4) the maximum distance between " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\hat{S}_{\\mathrm{sk}}^i" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " and the point to " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^u" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "p^l" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ", when " + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\Omega^\\complement \\cap \\Psi" + }, + { + "bbox": [ + 304, + 120, + 546, + 304 + ], + "type": "text", + "content": ". The sub-formulas for each case are as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 308, + 545, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 545, + 380 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {S}} _ {\\mathrm {c y l}} ^ {i} = \\left\\{ \\begin{array}{l l} \\max \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right) & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} \\leq 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| \\leq h _ {i}\\right) \\\\ \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} \\leq 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| > h _ {i}\\right) \\\\ \\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} > 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| \\leq h _ {i}\\right) \\\\ \\left\\| \\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right) \\right\\| _ {2} & , \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i} > 0\\right) \\wedge \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| > h _ {i}\\right) \\end{array} \\right. \\tag {2}", + "image_path": "16912a8062a9407307b067b5bdc9f23b01e7090a799e95c9b7fd5d15b16db696.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 380, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 404 + ], + "type": "text", + "content": "Combining the above four sub-formulas with the max and min operations, the following result is obtained:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 328, + 408, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 408, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 328, + 408, + 545, + 447 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {S} _ {\\mathrm {c y l}} ^ {i} = \\min \\left(\\max \\left(\\hat {S} _ {\\mathrm {s k}} ^ {i}, \\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}\\right), 0\\right) \\\\ + \\left. \\left\\| m a x \\left(\\hat {\\mathcal {S}} _ {\\mathrm {s k}} ^ {i}, 0\\right), m a x \\left(\\left| \\mathbf {x} _ {i _ {z}} \\right| - h _ {i}, 0\\right) \\right\\| _ {2} \\right. \\tag {3} \\\\ \\end{array}", + "image_path": "2cb5c3ce65607e39db124d5be0d6c0fd8ce384d6b30e024d7b9232cdfa375c9c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 450, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 510 + ], + "type": "text", + "content": "Occupancy conversion and assembly. The occupancy function represents points inside the shape as 1 and points outside the shape as 0, which can be transformed by SDF. Following [13, 33], we use the Sigmoid function to perform differentiable transformation operations:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 370, + 514, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 514, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 370, + 514, + 545, + 529 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {O}} _ {i} = \\operatorname {S i g m o i d} (- \\eta \\cdot \\hat {\\mathcal {S}} _ {\\mathrm {c y l}} ^ {i}). \\tag {4}", + "image_path": "b6c0c506c91c4b4598765731d1c98c4a1e14a6ec9da51ff58803efce254e7aa3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 534, + 546, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 678 + ], + "type": "text", + "content": "We finally assemble the occupancy " + }, + { + "bbox": [ + 304, + 534, + 546, + 678 + ], + "type": "inline_equation", + "content": "\\hat{O}_i" + }, + { + "bbox": [ + 304, + 534, + 546, + 678 + ], + "type": "text", + "content": " of each cylinder to obtain the reconstructed shape. In order to express complex shapes, many works use intersection, union, and difference operations in CSG in the assembly stage [8,19,33,59]. In contrast to them, we only use the union operation, because the extrusion cylinders can naturally represent concave shapes. This helps us avoid designing intricate loss functions or employing multi-stage training strategies without losing the flexibility of reconstructing shape representations. We adopt the Softmax to compute the union operation as it is shown to be effective in avoiding vanishing gradients [33]:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 349, + 683, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 683, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 349, + 683, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\hat {\\mathcal {O}} _ {t o t a l} = \\sum_ {i} ^ {N} \\operatorname {S o f t m a x} (\\varphi \\cdot \\hat {\\mathcal {O}} _ {i}) \\cdot \\hat {\\mathcal {O}} _ {i}, \\tag {5}", + "image_path": "9b4b27f9bd149bc27366b5f1c9158d42f055f2d54a150d613d787737ac2b9c28.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16819" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "type": "text", + "content": " is the modulating coefficient and " + }, + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{O}}_{total}" + }, + { + "bbox": [ + 47, + 71, + 287, + 97 + ], + "type": "text", + "content": " is the occupancy representation of the final reconstructed shape." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 103, + 136, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 103, + 136, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 136, + 114 + ], + "type": "text", + "content": "4.2. Loss Function" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "type": "text", + "content": "We train SECAD-Net in a self-supervised fashion through the minimization of the sum of two objective terms. The supervision signal is mainly quantified by the reconstruction loss, which measures the mean squared error between the predicted shape occupancy " + }, + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{O}}_{total}" + }, + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "type": "text", + "content": " and the ground truth " + }, + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_{total}^{*}" + }, + { + "bbox": [ + 47, + 121, + 287, + 194 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 89, + 201, + 287, + 222 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 201, + 287, + 222 + ], + "spans": [ + { + "bbox": [ + 89, + 201, + 287, + 222 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c o n}} = \\mathbb {E} _ {x \\in \\mathbf {X}} \\left[ \\left(\\hat {\\mathcal {O}} _ {\\text {t o t a l}} - \\mathcal {O} _ {\\text {t o t a l}} ^ {*}\\right) ^ {2} \\right], \\tag {6}", + "image_path": "6fdf0c229d82c1be70ed933899437ca810ed46e50a00941045a1a097e8d1d885.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 228, + 282, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 282, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 282, + 240 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 228, + 282, + 240 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 228, + 282, + 240 + ], + "type": "text", + "content": " is a randomly sampled point in the shape volume." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": "However, we find that applying only " + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{recon}}" + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": " makes the network always learn fragmented cylinders. To tackle this problem, we design a 2D sketch loss to facilitate the network to learn the axis of the sketch plane and the complete profile. Specifically, each sketch plane cuts the voxel model to form an occupancy cross-section " + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_{cs}^{i^*}" + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": ". We project the 3D sampling points inside the " + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": "-th extrusion box " + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^i" + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": " onto the sketch plane along the axial direction, and calculate the difference between the occupancy value of the projected points " + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{O}}_{proj}" + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": " and ground truth " + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_{cs}^{i^*}" + }, + { + "bbox": [ + 46, + 240, + 287, + 361 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 368, + 287, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 368, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 85, + 368, + 287, + 400 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s k e t c h}} = \\sum_ {i = 1} ^ {N} \\mathbb {E} _ {x \\in \\mathcal {B} ^ {i}} \\left[ \\left(\\hat {\\mathcal {O}} _ {\\text {p r o j}} ^ {i} - \\mathcal {O} _ {\\text {c s}} ^ {i ^ {*}}\\right) ^ {2} \\right]. \\tag {7}", + "image_path": "3632e830f76b2fddaf2cebcf894a6745cbb4545194f9d274a6a19d56057dcf4a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 407, + 286, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 286, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 286, + 430 + ], + "type": "text", + "content": "The overall objective of SECAD-Net is defined as the combination of the above two terms:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 112, + 441, + 287, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 441, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 112, + 441, + 287, + 453 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {r e c o n}} + \\lambda \\mathcal {L} _ {\\text {s k e t c h}}, \\tag {8}", + "image_path": "be33f8ff8c1e62d7c2bb9ffc4425c1f5ebee1eed19e70e682649aa5d3968c508.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 461, + 160, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 461, + 160, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 461, + 160, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 461, + 160, + 472 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 461, + 160, + 472 + ], + "type": "text", + "content": " is a balance factor." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 479, + 167, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 167, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 167, + 491 + ], + "type": "text", + "content": "4.3. CAD Reconstruction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 653 + ], + "type": "text", + "content": "The output of SECAD-Net during the training phase is an implicit occupancy function of the 3D shape. In the prediction stage, we reconstruct CAD models by using sketch-extrude operations instead of the marching cubes method. Sketch and extrusion. To convert a 2D implicit field (Fig. 4 (a)) in the sketch latent space into an editable sketch, we input uniform 2D sampling points to the SK-head, and attach the implicit value to the position of the sampling point to obtain an explicit image-like 2D profile (Fig. 4 (b)). We then use the Teh-Chin chain approximation [43] to extract the contours of the profiles and the hierarchical relationships between them. We further apply Dierckx's fitting [14] to convert the contours into closed B-splines (Fig. 4 (c))." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "After extruding each sketch to get the cylinder primitives according to half the height of " + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{B}^i" + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": ", we assemble cylinder primitives into cylinders by alternately performing union or difference operations according to the hierarchical relationship between contours (primitive at hierarchy 0 difference" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 380, + 145 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 380, + 145 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 380, + 145 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 380, + 145 + ], + "type": "image", + "image_path": "f43568e8d49bcec6a03058a1063c8adb639ba2d141ae98d180614909fc77aca3.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 148, + 364, + 155 + ], + "lines": [ + { + "bbox": [ + 323, + 148, + 364, + 155 + ], + "spans": [ + { + "bbox": [ + 323, + 148, + 364, + 155 + ], + "type": "text", + "content": "(a) Implicit Field" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 383, + 70, + 459, + 146 + ], + "blocks": [ + { + "bbox": [ + 383, + 70, + 459, + 146 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 459, + 146 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 459, + 146 + ], + "type": "image", + "image_path": "3d162500a42b2569680b9764fe087b8773c77c5001d225e8e9378bcc1eb2642c.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 377, + 148, + 464, + 156 + ], + "lines": [ + { + "bbox": [ + 377, + 148, + 464, + 156 + ], + "spans": [ + { + "bbox": [ + 377, + 148, + 464, + 156 + ], + "type": "text", + "content": "(b) Sample Points with Occupancy" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 463, + 71, + 544, + 145 + ], + "blocks": [ + { + "bbox": [ + 463, + 71, + 544, + 145 + ], + "lines": [ + { + "bbox": [ + 463, + 71, + 544, + 145 + ], + "spans": [ + { + "bbox": [ + 463, + 71, + 544, + 145 + ], + "type": "image", + "image_path": "b959cc0e8ec1e50a7b16e45c01195b1235bde5a33a8c7444c6093b7fe1db6ca7.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 475, + 148, + 538, + 155 + ], + "lines": [ + { + "bbox": [ + 475, + 148, + 538, + 155 + ], + "spans": [ + { + "bbox": [ + 475, + 148, + 538, + 155 + ], + "type": "text", + "content": "(c) Fitted Sketch Splines" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 164, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 305, + 164, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 305, + 164, + 545, + 186 + ], + "type": "text", + "content": "Figure 4. Illustration of converting 2D implicit sketches into the closed B-splines." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 232 + ], + "type": "text", + "content": "primitives at hierarchy 1 in the case of Fig. 4). Finally, we take the union of all cylinders to obtain the CAD model." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 232, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 316 + ], + "type": "text", + "content": "Post-processing. We take two post-processing operations to clean up overlapping and shredded shapes in the result. First, for any two cylinders, when their overlapping coefficient is greater than 0.95, the smaller of them is discarded. Second, we delete all cylinders whose height is less than 0.01 in the reconstruction result. We demonstrate our final reconstructions in Fig. 5 and Fig. 6." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 324, + 438, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 324, + 438, + 337 + ], + "spans": [ + { + "bbox": [ + 305, + 324, + 438, + 337 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "text", + "content": "SECAD-Net is implemented in PyTorch and trained on a TITAN RTX GPU from NVIDIA®. We train our model using an Adam optimizer [20] with learning rate " + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "text", + "content": " and beta parameters (0.5, 0.99). We set both the number of MLP layers in the sketch head network and the number of output cylinders to 4. For hyper-parameters in Eq. 4, Eq. 5 and Eq. 8, we set " + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\eta = 150" + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\varphi = 25" + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\lambda = 0.01" + }, + { + "bbox": [ + 304, + 343, + 545, + 499 + ], + "type": "text", + "content": " in default, which generally works well in our experiments. Employing a similar training strategy to [59], we first pretrain SECAD-Net on the training datasets for 1,000 epochs using batch size 24, which takes about 8 hours, and finetuning on each test shape for 300 epochs, which takes about 3 minutes per shape." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 510, + 430, + 523 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 510, + 430, + 523 + ], + "spans": [ + { + "bbox": [ + 305, + 510, + 430, + 523 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 531, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 601 + ], + "type": "text", + "content": "In this section, we examine the performance of SECAD-Net on the ABC dataset [21] and Fusion 360 Gallery [50]. Through extensive comparisons and ablation studies, we demonstrate the effectiveness of our approach and show its superiority over state-of-the-art reference approaches for CAD reconstruction." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 611, + 355, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 355, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 355, + 624 + ], + "type": "text", + "content": "5.1. Setup" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Dataset preparation. For the ABC dataset, the voxel grids and sampling point data are provided by [59]. We use 5,000 groups of data for training and 1,000 for testing. For Fusion 360, which does not contain available voxels, we first randomly select 6,000 meshes, then discretize them into internally filled voxels. The train-test split is the same as ABC. We obtain sampling points with the corresponding occu" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16820" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 101, + 287, + 169 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "type": "text", + "content": "Table 1. Quantitative comparison between reconstruction results on ABC dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 101, + 287, + 169 + ], + "lines": [ + { + "bbox": [ + 48, + 101, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 48, + 101, + 287, + 169 + ], + "type": "table", + "html": "
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]1.8491.2550.82012.84
CSG-Stump [33]4.0310.7540.82817.18
ExtrudeNet [34]0.4710.9140.85214.46
Ours0.3300.7240.8634.30
", + "image_path": "0dd610fde718182c52591725fd32ae0469b3b44f8d46ff575a999ee74a963d08.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 211, + 287, + 291 + ], + "blocks": [ + { + "bbox": [ + 47, + 180, + 287, + 202 + ], + "lines": [ + { + "bbox": [ + 47, + 180, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 287, + 202 + ], + "type": "text", + "content": "Table 2. Quantitative comparison between reconstruction results on Fusion 360 dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 211, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 48, + 211, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 48, + 211, + 287, + 291 + ], + "type": "table", + "html": "
MethodsCD↓ECD↓NC↑#P↓
UCSG-Net [19]2.9505.2770.77010.84
CSG-Stump [33]2.7814.5900.74412.08
Point2Cyl [46]13.88914.6570.6692.76
ExtrudeNet [34]2.2633.5580.81915.72
Ours2.0523.2820.8035.44
", + "image_path": "c2d4eb0b5e8637306509967df8436c07382166d90c21d79e639557eb83c84226.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 312, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 384 + ], + "type": "text", + "content": "pancy value following [9]. The resolution of voxel shapes is " + }, + { + "bbox": [ + 46, + 312, + 287, + 384 + ], + "type": "inline_equation", + "content": "64^3" + }, + { + "bbox": [ + 46, + 312, + 287, + 384 + ], + "type": "text", + "content": " for both datasets, and the number of sampling points is 8,192. Considering that fine-tuning each method and generating high-accuracy meshes is time-consuming, we take 50 shapes from each dataset to form 100 shapes for quantitative evaluation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 384, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 480 + ], + "type": "text", + "content": "Evaluation metrics. For quantitative evaluations, we follow the metrics that are commonly used in previous methods [33, 59], including symmetric Chamfer Distance (CD), Normal Consistency (NC), Edge Chamfer Distance (ECD). Details of computing these metrics are given in the supplemental materials. Additionally, we also report the number of generated primitives, " + }, + { + "bbox": [ + 46, + 384, + 287, + 480 + ], + "type": "inline_equation", + "content": "\\# p" + }, + { + "bbox": [ + 46, + 384, + 287, + 480 + ], + "type": "text", + "content": ", as a measure of how easy the output CAD results are to edit." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 491, + 242, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 242, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 242, + 502 + ], + "type": "text", + "content": "5.2. Comparison on CAD Reconstruction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 688 + ], + "type": "text", + "content": "We thoroughly compare our method with two types of primitive-based CAD reconstruction methods that output editable CAD models, including two CSG-like methods (i.e., UCSG-Net [19], CSG-Stump [33]) and two cylinder decomposition counterpart (i.e., point2Cyl [46]), ExtrudeNet [34]. For each method, we adopt the implementation provided by the corresponding authors, and use the same training strategy for training and fine-tuning. For CSG-Stump, we set the number of intersection nodes to 64, making it output a comparable number of primitives to other methods. Those methods provide a plethora of comparisons to other techniques and establish themselves as state-of-the-art. Note that for point2Cyl, we only report its results on Fusion 360 dataset, as the ABC dataset does not provide the labels needed to train point2Cyl." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Quantitative results on the ABC and Fusion 360 datasets are reported in Table 1 and Table 2, respectively. It can be" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 545, + 335 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 545, + 335 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 545, + 335 + ], + "type": "image", + "image_path": "2e831fc7b15c6d7986cfe8bdbfda7c461815dc702822dea46ec98ad517cb10fd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 343, + 545, + 365 + ], + "lines": [ + { + "bbox": [ + 306, + 343, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 343, + 545, + 365 + ], + "type": "text", + "content": "Figure 5. Visual comparison between reconstruction results on ABC dataset." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 495 + ], + "type": "text", + "content": "seen that the proposed SECAD-Net outperforms both kinds of methods on all evaluation metrics while still generating a relatively small number of primitives. Fig. 5 and Fig. 6 display several qualitative comparison results. For fairness, all the reconstructed CAD models are visualized using marching cubes (MC) with 256 resolution. Visually as shown in the figures, our method achieves much better geometry and topological fidelity with more accurate structures (e.g., holes, junctions) and sharper features." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 503, + 523, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 523, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 523, + 516 + ], + "type": "text", + "content": "5.3. CAD Generation via Sketch Interpolation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Although without ground truth labels as guidance, SECAD-Net can learn plausible 2D sketches from raw 3D shapes. Thanks to the implicit sketch representation, we are able to generate different CAD variations when a pair of shapes is interpolated in the complete and continuous sketch latent space, as shown in Fig. 7. The results suggest that the generated sketch is gradually transformed even if the pair of shapes have significantly different structures, and we draw two further conclusions: (1) the predicted position of each extrusion box is relatively deterministic, although the input shape is different (see the left and right column sketches in the leftmost group); (2) when an extrusion box does not contain a shape, our SK-head does not generate a sketch, making the network output an adaptive number of cylinders (see the middle column sketches of the leftmost and the rightmost groups)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16821" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 289, + 388 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 289, + 388 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 289, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 289, + 388 + ], + "type": "image", + "image_path": "a4b9b7be7df895b025b8cc6511770be79bfd077128697089dd40c836cbdd3945.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 398, + 288, + 420 + ], + "lines": [ + { + "bbox": [ + 46, + 398, + 288, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 288, + 420 + ], + "type": "text", + "content": "Figure 6. Visual comparison between reconstruction results on Fusion 360 dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 463, + 287, + 567 + ], + "blocks": [ + { + "bbox": [ + 46, + 432, + 287, + 454 + ], + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 454 + ], + "type": "text", + "content": "Table 3. Ablation study on network design and sketch loss. We adopted setting (e) in the final model." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 463, + 287, + 567 + ], + "lines": [ + { + "bbox": [ + 48, + 463, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 48, + 463, + 287, + 567 + ], + "type": "table", + "html": "
Settings(a)(b)(c)(d)(e)
Nsh14444
Nlay22244
Ncyl44844
Lsketch✓✓✓×✓
CD↓2.6270.9931.5040.3360.330
ECD↓1.7540.8821.0980.7720.724
NC↑0.7130.8350.7610.8630.863
", + "image_path": "7db4df0a90ab7cd8a0b3791d847d1f287376a6bbaf63e63d3bfa4d625f898790.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 115, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 115, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 115, + 598 + ], + "type": "text", + "content": "5.4. Ablations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 640 + ], + "type": "text", + "content": "We perform ablation studies to carefully analyze the efficiency of major components of our designed model. All quantitative metrics are measured on the ABC dataset." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Effect of network design and sketch loss. We first examine the effect of the number of components/parameters in SECAD-Net, including the number of SK-heads " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "(N_{sh})" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": ", the number of fully connected layers " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "(N_{lay})" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": " in each SK-head, and the number of output cylinders " + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "inline_equation", + "content": "(N_{cyl})" + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": ". Then we show the necessity of the sketch loss by deactivating it to train the" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 305, + 70, + 544, + 390 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 544, + 390 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 544, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 544, + 390 + ], + "type": "image", + "image_path": "60a82da82e2ceb5b2f4842af712cc46a844d7cf30e569537f7dec8812c9e875b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "type": "text", + "content": "Figure 7. For each example, we encode the sketches of top and bottom shapes in latent vector space and then linearly interpolate the corresponding latent codes." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 467, + 545, + 522 + ], + "blocks": [ + { + "bbox": [ + 335, + 448, + 515, + 459 + ], + "lines": [ + { + "bbox": [ + 335, + 448, + 515, + 459 + ], + "spans": [ + { + "bbox": [ + 335, + 448, + 515, + 459 + ], + "type": "text", + "content": "Table 4. Ablation study on sketch representation." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 467, + 545, + 522 + ], + "lines": [ + { + "bbox": [ + 307, + 467, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 307, + 467, + 545, + 522 + ], + "type": "table", + "html": "
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", + "image_path": "5b223a8c592fcec07fd668be0b27954bb4e9e7dd2ef99fb66ac5e882532e7536.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": "network. The quantified results are presented in Table 3. Settings (a), (b), and (c) show that reducing the number of SK-heads or increasing the number of cylinder outputs will damage the model prediction accuracy. Settings (b), (d), and (e) show that increasing the number of MLP layers in SK-head or enabling " + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {sketch }}" + }, + { + "bbox": [ + 304, + 544, + 545, + 628 + ], + "type": "text", + "content": " will improve the prediction accuracy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 546, + 714 + ], + "type": "text", + "content": "Effect of implicit sketch representation. To assess the efficiency of neural implicit sketch representation, we adopt two other classical shape representations, namely binary space partitioning (BSP [8]) and box-like primitives, to compare with our SK-head in SECAD-Net. For BSP, we set the number of output convex shapes to 8, each containing 12 partitions. The assembly method is consistent with [8] to" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16822" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 287, + 244 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 287, + 244 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 287, + 244 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 287, + 244 + ], + "type": "image", + "image_path": "bc6c5ae9c9e12a9d8dab39b75285c4adc6d596c0d3c38b4b388d2551890e005e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 251, + 288, + 275 + ], + "lines": [ + { + "bbox": [ + 47, + 251, + 288, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 288, + 275 + ], + "type": "text", + "content": "Figure 8. Visual comparison results for ablation study on sketch representation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 296, + 287, + 542 + ], + "blocks": [ + { + "bbox": [ + 50, + 296, + 287, + 542 + ], + "lines": [ + { + "bbox": [ + 50, + 296, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 50, + 296, + 287, + 542 + ], + "type": "image", + "image_path": "182685481d978c3ace4fe0da18b3f9e6353e165a7f849dd85b6f22ac34433edc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 552, + 288, + 586 + ], + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 586 + ], + "type": "text", + "content": "Figure 9. SECAD-Net can aid in more applications. Left: the results of single-view reconstruction. Right: a subsequent CAD editing by changing the predicted cylinder primitives." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 617, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 712 + ], + "type": "text", + "content": "represent 2D sketches. For box-like primitives, 24 rectangles are predicted. We divide them into two subsets in half, take the union operation separately, and subtract the other from one of the union results. The numerical and visual comparison results are shown in Table 4 and Fig. 8, respectively. It can be seen that our implicit field can represent the smoothest shape while obtaining the best reconstruction results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 419, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 419, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 419, + 85 + ], + "type": "text", + "content": "5.5. Other Applications" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 92, + 545, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 545, + 236 + ], + "type": "text", + "content": "By replacing the voxel encoder, SECAD-Net is flexible to reconstruct CAD models from other input shape representations, e.g., images and point clouds. Fig. 9 shows the results of SECAD-Net in solving single-view reconstruction (SVR) task. Following the training strategy of previous work [8, 9], we first use voxel data to complete the training of the 3D auto-encoding task, and then train an image encoder with the feature encoding of each shape as the target. The voxels and input images used for the SVR task are obtained directly from Fusion 360. Replacing more input representations, while feasible and meaningful, is not the focus of this paper and we leave it to future research." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 238, + 546, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 546, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 546, + 334 + ], + "type": "text", + "content": "Finally, the parameters of both 2D sketches and 3D cylinders are available, thus the CAD results output from SECAD-Net can be directly loaded into existing CAD software for further editing. As shown in the right side of Fig. 9, interpretable CAD variations can be produced via specific editing operations, such as sketch-level curve editing, primitive-level displacement, rotation, scaling, and Boolean operations between primitives." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 352, + 471, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 471, + 364 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 471, + 364 + ], + "type": "text", + "content": "6. Conclusion and Future Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 374, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 529 + ], + "type": "text", + "content": "We have presented a novel neural network that successively learns shape sketch and extrusion without any expensive annotations of shape segmentation and labels as the supervision. Our approach is able to learn smooth sketches, followed by the differentiable extrusion to reconstruct CAD models that are close to the ground truth. We evaluate SECAD-Net using diverse CAD datasets and demonstrate the advantages of our approach by ablation studies and comparing it to the state-of-the-art methods. We further demonstrate our method's applicability in single-image CAD reconstruction. Additionally, the CAD shapes generated by our approach can be directly fed into off-the-shelf CAD software for sketch-level or cylinder primitive-level editing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 532, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 546, + 628 + ], + "type": "text", + "content": "In future work, we plan to extend our approach to learn more CAD-related operations such as revolve, bevel, and sweep. Besides, we find that current deep learning models perform poorly on datasets with large differences in shape geometry and structure. Therefore, another promising direction is to explore how to improve the generalization of neural networks and enhance the realism of the generated shapes by learning structural and topological information." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. We thank the anonymous reviewer for their valuable suggestions. This work is partially funded by the National Natural Science Foundation of China (U22B2034, 62172416, U21A20515, 62172415), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022131)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16823" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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Graph., 28(8):2879-2894, 2022. 2" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16826" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SFD2_ Semantic-Guided Feature Detection and Description/6efa713f-1ae0-4651-bc92-c61912feb28d_content_list.json b/2023/SFD2_ Semantic-Guided Feature Detection and Description/6efa713f-1ae0-4651-bc92-c61912feb28d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3bf35f9042aa7d447fbec135f9eb1f6861f63b18 --- /dev/null +++ b/2023/SFD2_ Semantic-Guided Feature Detection and Description/6efa713f-1ae0-4651-bc92-c61912feb28d_content_list.json @@ -0,0 +1,1569 @@ +[ + { + "type": "text", + "text": "SFD2: Semantic-guided Feature Detection and Description", + "text_level": 1, + "bbox": [ + 187, + 130, + 781, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fei Xue Ignas Budvytis Roberto Cipolla University of Cambridge", + "bbox": [ + 303, + 180, + 665, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{fx221, ib255, rc10001} $@$ cam.ac.uk", + "bbox": [ + 370, + 218, + 593, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual localization is a fundamental task for various applications including autonomous driving and robotics. Prior methods focus on extracting large amounts of often redundant locally reliable features, resulting in limited efficiency and accuracy, especially in large-scale environments under challenging conditions. Instead, we propose to extract globally reliable features by implicitly embedding high-level semantics into both the detection and description processes. Specifically, our semantic-aware detector is able to detect keypoints from reliable regions (e.g. building, traffic lane) and suppress unreliable areas (e.g. sky, car) implicitly instead of relying on explicit semantic labels. This boosts the accuracy of keypoint matching by reducing the number of features sensitive to appearance changes and avoiding the need of additional segmentation networks at test time. Moreover, our descriptors are augmented with semantics and have stronger discriminative ability, providing more inliers at test time. Particularly, experiments on long-term large-scale visual localization Aachen DayNight and RobotCar-Seasons datasets demonstrate that our model outperforms previous local features and gives competitive accuracy to advanced matchers but is about 2 and 3 times faster when using $2k$ and $4k$ keypoints, respectively. Code is available at https://github.com/feixue94/sfd2.", + "bbox": [ + 75, + 300, + 473, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 693, + 209, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual localization is key to various applications including autonomous driving and robotics. Structure-based algorithms [54, 57, 64, 69, 73, 79] involving mapping and localization processes still dominate in large-scale localization. Traditionally, handcrafted features (e.g. SIFT [3, 35], ORB [53]) are widely used. However, these features are mainly based on statistics of gradients of local patches and thus are prone to appearance changes such as illumination and season variations in the long-term visual localization task. With the success of CNNs, learning-based features [14, 16, 37, 45, 51, 76, 81] are introduced to replace handcrafted ones and have achieved excellent performance.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f6e7685d36555c3f5fa3c09b9c4229a7a3aa87352b41537c0b6f0a00456fb68a.jpg", + "image_caption": [ + "Figure 1. Overview of our framework. Our model implicitly incorporates semantics into the detection and description processes with guidance of an off-the-shelf segmentation network during the training process. Semantic- and feature-aware guidance are adopted to enhance its ability of embedding semantic information." + ], + "image_footnote": [], + "bbox": [ + 540, + 266, + 854, + 407 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With massive data for training, these methods should be able to automatically extract keypoints from more reliable regions (e.g. building, traffic lane) by focusing on discriminative features [64]. Nevertheless, due to the lack of explicit semantic signals for training, their ability of selecting globally reliable keypoints is limited, as shown in Fig. 2 (detailed analysis is provided in Sec. B.1 in the supplementary material). Therefore, they prefer to extract locally reliable features from objects including those which are not useful for long-term localization (e.g. sky, tree, car), leading to limited accuracy, as demonstrated in Table 2.", + "bbox": [ + 496, + 520, + 893, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, advanced matchers based on sparse keypoints [8, 55, 65] or dense pixels [9, 18, 19, 33, 40, 47, 67, 74] are proposed to enhance keypoint/pixel-wise matching and have obtained remarkable accuracy. Yet, they have quadratic time complexity due to the attention and correlation volume computation. Moreover, advanced matchers rely on spatial connections of keypoints and perform image-wise matching as opposed to fast point-wise matching, so they take much longer time than nearest neighbor matching (NN) in both mapping and localization processes because of a large number of image pairs (much larger than the number of images) [8]. Alternatively, some works leverage semantics [64, 73, 79] to filter unstable features to eliminate wrong correspondences and report close even better accu", + "bbox": [ + 496, + 689, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5206", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "racy than advanced matchers [79]. However, they require additional segmentation networks to provide semantic labels at test time and are fragile to segmentation errors.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instead, we implicitly incorporate semantics into a local feature model, allowing it to extract robust features automatically from a single network in an end-to-end fashion. In the training process, as shown in Fig. 1, we provide explicit semantics as supervision to guide the detection and description behaviors. Specifically, in the detection process, unlike most previous methods [14, 16, 32, 37, 51] adopting exhaustive detection, we employ a semantic-aware detection loss to encourage our detector to favor features from reliable objects (e.g. building, traffic lane) and suppress those from unreliable objects (e.g. sky). In the description process, rather than utilizing triplet loss widely used for descriptor learning [16, 41], we employ a semantic-aware description loss consisting of two terms: inter- and intra-class losses. The inter-class loss embeds semantics into descriptors by enforcing features with the same label to be close and those with different labels to be far. The intra-class loss, which is a soft-ranking loss [23], operates on features in each class independently and differentiates these features from objects of the same label. Such use of soft-ranking loss avoids the conflict with inter-class loss and retains the diversity of features in each class (e.g. features from buildings usually have larger diversity than those from traffic lights). With semantic-aware descriptor loss, our model is capable of producing descriptors with stronger discriminative ability. Benefiting from implicit semantic embedding, our method avoids using additional segmentation networks at test time and is less fragile to segmentation errors.", + "bbox": [ + 75, + 137, + 472, + 559 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As the local feature network is much simpler than typical segmentation networks e.g. UperNet [10], we also adopt an additional feature-consistency loss on the encoder to enhance its ability of learning semantic information. To avoid using costly to obtain ground-truth labels, we train our model with outputs of an off-the-shelf segmentation network [11, 34], which has achieved SOTA performance on the scene parsing task [83], but other semantic segmentation networks (e.g. [10]) can also be used.", + "bbox": [ + 75, + 560, + 468, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An overview of our system is shown in Fig. 1. We embed semantics implicitly into the feature detection and description network via the feature-aware and semantic-aware guidance in the training process. At test time, our model produces semantic-aware features from a single network directly. We summarize contributions as follows:", + "bbox": [ + 75, + 696, + 468, + 787 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel feature network which implicitly incorporates semantics into detection and description processes at training time, enabling the model to produce semantic-aware features end-to-end at test time.", + "- We adopt a combination of semantic-aware and feature-aware guidance strategy to make the model" + ], + "bbox": [ + 93, + 799, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/255208525ae22918530d2a590b0df382fbae6ee4262d03c58f3baa94fcec71d1.jpg", + "image_caption": [ + "Figure 2. Locally reliable features. We show top 1k keypoints (reliability high→low: 1-250, 251-500, 501-750, 751-1000) of prior local features including SPP [14], D2Net [16], R2D2 [51], and ASLFeat [37]. They indiscriminatively give high reliability to patches with rich textures even from objects e.g. sky, tree, pedestrian and car, which are reliable for long-term localization (best view in color)." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 213 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "embed semantic information more effectively.", + "bbox": [ + 531, + 354, + 836, + 369 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our method outperforms previous local features on the long-term localization task and gives competitive accuracy to advanced matchers but has higher efficiency.", + "bbox": [ + 514, + 378, + 890, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Experiments show our method achieves a better tradeoff between accuracy and efficiency than advanced matchers [8, 55, 65] especially on devices with limited computing resources. We organize the rest of this paper as follows. In Sec. 2, we introduce related works. In Sec. 3, we describe our method in detail. We discuss experiments and limitations in Sec. 4 and Sec. 5 and conclude the paper in Sec. 6.", + "bbox": [ + 496, + 438, + 890, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 556, + 640, + 571 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we discuss related work on visual localization, feature extraction and matching, and knowledge distillation.", + "bbox": [ + 496, + 583, + 890, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual localization. Visual localization methods can be roughly categorized as image-based and structure-based. Image-based systems recover camera poses by finding the most similar one in the database with global features, e.g. NetVLAD [2], CRN [27]. Due to the limited number of images in the database, they can only give approximate poses. To obtain more precise poses, structure-based methods build a sparse 3D map via SfM and estimate the pose via PnP from 2D-3D correspondences [12,54,57,58,69,79]. Some other works have tried to predict the camera pose directly from images, e.g. PoseNet [28] and its variations [80], or regress scene coordinates [5-7,26]. However, the former have been proved to perform similar to image retrieval [61] and latter are hard to scale to large-scale scenes [31].", + "bbox": [ + 496, + 628, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Local features. Handcrafted features [3, 35, 53] have been investigated for decades and we refer readers a survey [38] for more details and focus on learned features. With the success of CNNs, learned features are proposed to", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5207", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "replace handcrafted descriptors [15,17,36,41-43,49,71,72], detectors [13,68,70], or both [14,16,32,37,51,76,81]. HardNet [41] focuses on metric learning by maximizing the distance between the closest positive and negative examples. Instead of using pixel-wise correspondences for training, CAPS [77], PoSFeat [32] and PUMP [50] utilize camera pose and local consistency of matches for supervision. SuperPoint (SPP) [14] takes keypoint detection as a supervised task, training detector from synthetic geometric shapes. D2-Net [16] uses local maxima across the channels as score map. R2D2 [51] considers both the repeatability and reliability and adopts the average precision loss [23] for descriptor training. ASLFeat [37] employs deformable CNNs to learn shape-aware dense features. As they focus mainly on local reliability of features, regardless of their superior accuracy to handcrafted features, their performance is limited in the long-term large-scale localization task. To further improve the accuracy, some works [22,46,75] learn to filter unstable keypoints with extra matching score, repeatability or semantic labels. Essentially different with these methods, our model detects and extracts semantic-aware features automatically in an end-to-end fashion. As a result, our features are able to produce more accurate localization results.", + "bbox": [ + 76, + 90, + 472, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Advanced matcher. As NN matching is unable to incorporate spatial connections of keypoints for matching, advanced matchers are proposed to enhance the accuracy by leveraging the spatial context of a set of keypoints [8, 55, 65] or an image patch [9, 18, 33, 52, 67, 84]. SuperGlue (SPG) [55] utilizes graph neural networks with attention mechanism to propagate information among keypoints. It produces impressive accuracy, whereas its time complexity is quadratic to the number of keypoints. This problem is partially mitigated by using seeded matching [8] and cluster matching [65], but the time is still thousands of times slower than NN matching. Dense matchers [9, 33, 52, 67] compute pixel-wise correspondence from correlation volumes, so they undergo the high time and memory cost as sparse matchers [8, 55, 65]. Moreover, advanced matchers operates on image pairs as opposed to keypoints, so considering the number of image pairs, systems with advanced matchers could be much slower in real applications, as analyzed in [8]. In this paper, we embed high-level semantic information into local features implicitly to enhance both feature detection and description, enabling our model with simple NN matching to yield comparable results to advanced matchers. Our work provides a good trade-off of time and accuracy especially on devices with limited computing resources.", + "bbox": [ + 76, + 443, + 472, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual semantic localization. Compared to local features, high-level semantics are more robust to appearance changes and have been widely used in visual localization [7, 25, 26, 30, 31, 44, 62-64, 66, 73, 78]. LLN [78] and SVL [63] use the discriminative landmarks for place recognition. ToDayGAN [1] transfers night images to day im", + "bbox": [ + 76, + 810, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ages with GAN [20]. MFC [30], SMC [73], SSM [64], and DASGIL [25] incorporate segmentation networks into a standard localization pipeline to reject semantically-inconsistent matches. More recently, LBR [79] learns to recognize global instances for both coarse and fine localization. In fine localization, it filters unstable features and conducts instance-wise matching, achieving close accuracy to advanced matchers [55]. Unlike these methods, which require additional models to provide explicit semantic labels at test time, we embed the semantic information into the network and produce semantic-aware features directly from a single network.", + "bbox": [ + 496, + 90, + 893, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Knowledge distillation. Knowledge distillation techniques have been widely used for tasks including model compression [54] and knowledge transfer [82]. Our usage of pseudo ground-truth local reliability and semantic labels predicted by off-the-shelf networks is more like a knowledge transfer task. In this paper, we focus mainly on how to effectively leverage the high-level semantics for low-level feature extraction.", + "bbox": [ + 496, + 272, + 893, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 405, + 591, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 1, our model consists of an encoder $\\mathcal{F}_{enc}$ and two decoders $\\mathcal{F}_{det}$ and $\\mathcal{F}_{desc}$ . $\\mathcal{F}_{enc}$ extracts high-level features $\\mathbf{X}$ from image $\\mathbf{I} \\in R^{3 \\times H \\times W}$ . $\\mathcal{F}_{det}$ predicts the reliability map $\\mathbf{S} \\in R^{H \\times W}$ and $\\mathcal{F}_{desc}$ produces descriptors $\\mathbf{X}_{desc} \\in R^{128 \\times \\frac{H}{4} \\times \\frac{W}{4}}$ . $H$ and $W$ are the height and width of the image. In this section, we give details about how to implicitly incorporate semantic information into our feature detection and description processes.", + "bbox": [ + 496, + 430, + 893, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Semantic-guided Feature Detection", + "text_level": 1, + "bbox": [ + 498, + 560, + 805, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The detector predicts the reliability map as $\\mathbf{S} = \\mathcal{F}_{\\text{det}}(\\mathbf{X})$ . Previously, the reliability map $\\mathbf{S}$ is defined by the richness of textures in patches (e.g. response to corners [14] or blobs [35]). Recently, learned local features [16, 32, 37, 51] define the reliability on the discriminative ability of descriptors. As shown in Fig. 2, these two definitions, however, only reveal the reliability of pixels at a local level but lack the stability at a global level. Instead, we redefine the reliability of features by taking both the local reliability $\\mathbf{S}_{\\text{rel}}$ and global stability $\\mathbf{S}_{\\text{sta}}$ into consideration.", + "bbox": [ + 496, + 583, + 893, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local reliability. Local reliability shows the robustness of a keypoint to appearance changes and viewpoint variations. Previous learning-based features adopt two strategies for reliable feature learning: learning from groundtruth corners [14] and learning from the discriminative ability of descriptors [16, 32, 37, 51]. We find that corners [14] are more robust compared to purely learned detectors, as shown in [50, 79], where SPP detector achieves better results when replacing other detectors. Therefore, following [54], we use the detection score $\\mathbf{S}_{rel}$ of SPP [14] as pseudo groundtruth, which is one of the best corner detectors. At the same time,", + "bbox": [ + 496, + 734, + 895, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5208", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/47d22b6221b867eb8fa373f4b9c7da05b058caaae06b65b9f01db9753b37a1d2.jpg", + "image_caption": [ + "Segmentation mask" + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 272, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9ebcdbcd766078747251f1195fb64e095d60b87d6f0087967b88db86ed267771.jpg", + "image_caption": [ + "Global stability map $\\mathbf{S}_{sta}$", + "Figure 3. Semantic-guided feature detection. From left to right: semantic segmentation mask predicted by [11, 34], stability map $\\mathbf{S}_{sta}$ generated according to Table 1, local reliability map $\\mathbf{S}_{rel}$ produced by SuperPoint [14], and the final global reliability map $\\mathbf{S}$ . Local reliability map gives very high score to clouds (red), trees (green), and pedestrians (pink) in addition to buildings, while the global reliability map removes unstable regions (sky, pedestrians), suppresses short-term objects (trees), and retains stable areas (buildings)." + ], + "image_footnote": [], + "bbox": [ + 272, + 90, + 464, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c7213f1f951ed5d51b2188df8f50e3df5791cb975af547cead5e7d1dd8aaf140.jpg", + "image_caption": [ + "Local reliability map $\\mathbf{S}_{rel}$" + ], + "image_footnote": [], + "bbox": [ + 464, + 90, + 653, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/680f21d426a2a43a10a1d861863f51545ae06bdb5369cc7421ee50f97139f793.jpg", + "image_caption": [ + "Global reliability map S", + "High", + "Low" + ], + "image_footnote": [], + "bbox": [ + 655, + 90, + 846, + 200 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "local reliability is slightly adjusted by the discriminative ability of descriptors in the training process (see Sec. 3.2).", + "bbox": [ + 75, + 306, + 467, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Global stability. The global stability of a pixel is assigned based on the semantic label which it belongs to. Specifically, we group all 120 semantic labels in ADE20k dataset [83], according to how they change over time, into four categories, denoted as Volatile, Dynamic, Short-term, and Long-term in Table 1. Volatile objects (e.g. sky, water) are constantly changing and are redundant for localization. Dynamic objects (e.g. car, pedestrian) are moving everyday and could cause localization error by introducing wrong matches. Short-term objects (e.g. tree) can be used for short-term localization tasks (e.g. VO/SLAM), yet they are sensitive to changes of illumination (low albedo) and season conditions. Long-term objects (e.g. building, traffic light) are resistant to aforementioned changes and are ideal for long-term localization.", + "bbox": [ + 75, + 339, + 467, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of directly filtering unstable features [64,73,79], we rerank features with stability values assigned empirically according to the extent of desired suppression. In detail, Long-term objects are robust for both short and long-term localization, so their stability value is set to 1.0. Short-term objects are useful for short-term localization, so we set their stability to 0.5. The stability value of Volatile and Dynamic categories is set to 0.1 as they are not useful for both short/long-term localization. Note that we set it to 0.1 rather than 0. Our reranking strategy encourages the model to use stable features preferentially and uses keypoints from other objects as compensation when insufficient stable keypoints can be found, increasing the robustness of our model to various tasks (e.g. feature matching, short-term localization). Fig. 3 shows stability map $\\mathbf{S}_{sta}$ transformed from Table 1. Our current global stability is assigned based on predefined semantic labels, but a learned one might provide better performance and deserves further exploration.", + "bbox": [ + 75, + 566, + 467, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic-guided detection. The global reliability map $\\mathbf{S}_{gt}$ is generated by multiplying the local reliability map $\\mathbf{S}_{rel}$ and global stability map, as $\\mathbf{S}_{gt} = \\mathbf{S}_{rel} \\odot \\mathbf{S}_{sta}$ ( $\\odot$ is element-wise multiplication). Fig. 3 shows that local re", + "bbox": [ + 76, + 839, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/1a7f1f4d5bae05625ecf1a1b326e84dba588f3198b0d62ba358844c3d7b7175b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryVolatileDynamicShort-termLong-termStability
sky, water✓0.1
vehicle, pedestrian✓0.1
plant, grass✓0.5
building, traffic light✓1.0
", + "bbox": [ + 500, + 305, + 895, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Stability map. Semantic labels are categorized into four groups denoted as Volatile, Dynamic, Short-term, and Long-term. Four categories are empirically assigned with different stability values according to their robustness to appearance changes.", + "bbox": [ + 498, + 393, + 890, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "liability map gives high score for all pixels with rich textures even those from the sky, pedestrians, and trees, which are useless for localization. However, the global reliability map considering both local reliability and global stability discards these sensitive features and suppresses short-term keypoints effectively. The detection loss is defined as:", + "bbox": [ + 498, + 473, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d e t} = B C E (\\mathbf {S}, \\mathbf {S} _ {g t}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 571, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $BCE$ denotes the binary cross-entropy loss.", + "bbox": [ + 500, + 598, + 836, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Semantic-guided Feature Description", + "text_level": 1, + "bbox": [ + 500, + 619, + 821, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also enhance the discriminative ability of descriptors by embedding semantics into them directly. Unlike previous descriptors [14, 37, 41, 50, 51, 77], which only differentiate keypoints based on local patch information, our descriptors enforce similarities of features in the same class while retain dissimilarities for intra-class matching. However, the two forces conflict with each other during the training process, because class-level discriminative ability needs to squeeze the space of descriptors in the same class and intra-class discriminative ability has to increase the space. A simple solution could be to set a hard margin for all classes (Fig. 4 left), but it would lead to the loss of objects' inner diversity (e.g., almost all traffic lights are similar but different buildings vary dramatically), which is indispensable for intra-class matching. To solve this problem, we design the inter-class and intra-class losses based on two different metrics (Fig. 4 right).", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5209", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/79d33826dfedc3abcea07f9ba3900e0276c1db9e2e09ca5824b845b1a0709bfe.jpg", + "image_caption": [ + "Figure 4. Semantic-guided feature description. Simply optimizing inter- and intra-class losses with hard margins may cause accuracy loss due to two conflicting forces (push forces of inter- and intra-class) (left). Instead, we optimize the intra-class force with a hard margin, but apply a soft ranking loss for inter-class force to avoid conflicts and retain the inner diversity of each object (right)." + ], + "image_footnote": [], + "bbox": [ + 89, + 87, + 459, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inter-class loss. We first enforce the semantic consistency of features by maximizing the Euclidean distance between descriptors with different labels. This allows features to find correspondences from candidates with the same labels, reducing the search space and thus improving the matching accuracy. We define the inter-class loss based on triplet loss with a hard margin to separate all possible positive and negative keypoints with different labels in a batch:", + "bbox": [ + 75, + 318, + 468, + 441 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i n t e r} = \\frac {1}{N} \\sum \\left(\\left| \\left| \\mathbf {x} _ {i} ^ {c _ {1}} - \\mathbf {x} _ {j} ^ {c _ {1}} \\right| \\right| _ {2} - \\left| \\left| \\mathbf {x} _ {i} ^ {c _ {1}} - \\mathbf {x} _ {k} ^ {c _ {2}} \\right| \\right| _ {2} + m\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 109, + 453, + 468, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_i^{c_1},\\mathbf{x}_j^{c_1}$ , and $\\mathbf{x}_k^{c_2}$ are vectorized descriptors with labels of $c_{1},c_{1}$ , and $c_{2}$ ( $c_{1}\\neq c_{2}$ ). $m$ is the margin and set to 1.0. This loss is conducted on features in the whole batch and $N$ is the total number of features in a batch.", + "bbox": [ + 76, + 481, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Intra-class loss. To make sure that the intra-class loss doesn't conflict with the inter-class loss, we relax the limitation of distances between descriptors with the same label. Instead of using triplet loss with hard margins, we adopt a soft ranking loss [23] by optimizing the rank of positive and negative samples rather than their distances. We use the same strategy as [51] to generate positive and negative samples for each feature $\\mathbf{x}_i^c$ from self and the other images respectively, but enforce both positive and negative samples to share the same class label $c$ as $\\mathbf{x}_i^c$ . By optimizing ranks of all samples rather than forcing a hard boundary between positive and negative pairs as the triplet loss with a hard margin does, the soft ranking loss also retains the diversity of features on objects in the same class, as shown in Fig. 4 (right). The ranking loss is based on the averaging precision (AP) loss [23, 51]:", + "bbox": [ + 75, + 542, + 472, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i n t r a} = \\frac {1}{C} \\sum_ {c = 1} ^ {C} \\frac {1}{N _ {c}} \\sum_ {i = 1} ^ {N _ {c}} \\left(1 - A P \\left(\\mathbf {x} _ {i} ^ {c}, \\mathbf {S} ^ {\\mathbf {x} _ {i} ^ {c}}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 797, + 468, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_i^c$ and $\\mathbf{S}^{\\mathbf{x}_i^c}$ are the query descriptor with label $c$ and corresponding predicted local reliability. $C$ and $N_{c}$ are the total number of classes and features in class $c$ . Note that the AP loss for sample $\\mathbf{x}_i^c$ is weighted by its reliability $\\mathbf{S}^{\\mathbf{x}_i^c}$ .", + "bbox": [ + 76, + 839, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8137ba745d207b1628e1222c0a8ac591a3ade817d0059a29e1c5832b450b9db1.jpg", + "image_caption": [ + "Figure 5. Architecture of our network. Features are $4 \\times$ down-sampling to save time and memory cost. Resblocks [24] are adopted to enhance the model's capacity. We enforce the consistency between outputs of the middle two layers of our encoder and features of the segmentation network to enhance the ability of our model to embed semantic information during the training process." + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 875, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our final descriptor loss $L_{desc}$ is the combination of $L_{inter}$ and $L_{intra}$ , balanced by $w_{inter}$ and $w_{intra}$ :", + "bbox": [ + 498, + 340, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {d e s c} = w _ {i n t e r} L _ {i n t e r} + w _ {i n t r a} L _ {i n t r a}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 383, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Implicit Feature Guidance", + "text_level": 1, + "bbox": [ + 500, + 417, + 740, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With semantic-aware detection and description losses, our model is able to learn semantic-aware features. However, compared with feature learning, semantic prediction is a more complicated task, requiring powerful encoders and aggregation layers [4, 34] for semantic-aware feature embedding. To further improve the ability of our model to embed semantic information, we take inspiration from current knowledge distillation tasks [21] and introduce a feature consistency loss on intermediate outputs of the first three layers of the encoder.", + "bbox": [ + 496, + 441, + 890, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 5 shows the architecture of our network. We take intermediate outputs of the encoder of ConvNeXt [34] as supervision signal and enforce $l_{1}$ loss on features of the middle 2 layers of our model:", + "bbox": [ + 496, + 592, + 890, + 654 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {f e a t} = \\frac {1}{2} \\sum_ {i = 1} ^ {2} | \\mathbf {X} _ {i} - \\mathbf {X} _ {i} ^ {\\text {C o n v N e X t}} |, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 662, + 890, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{X}_i$ and $\\mathbf{X}_i^{ConvNeXt}$ are features of the $i$ th layer in our model and ConvNeXt [34], respectively. The total loss $L_{total}$ is the combination of detection loss $L_{det}$ , description loss $L_{desc}$ , and feature consistency loss $L_{feat}$ with weights of $w_{det}, w_{desc}$ , and $w_{feat}$ :", + "bbox": [ + 496, + 714, + 890, + 792 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {t o t a l}} = w _ {\\text {d e t}} L _ {\\text {d e t}} + w _ {\\text {d e s c}} L _ {\\text {d e s c}} + w _ {\\text {f e a t}} L _ {\\text {f e a t}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 801, + 890, + 819 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 830, + 633, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first give implementation details. Then, we test our method on visual localization tasks in Sec. 4.1 and analyze the running time in Sec. 4.2. Finally, we perform an ablation", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5210", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/a7fac905f868d3732105ed1166ccabf65a1dcab9317c4659baff832f47d3aa12.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
CAS.v1.1 [57]85.3 / 92.2 / 97.939.8 / 49.0 / 64.3
CSL [69]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
CPF [12]76.7 / 88.6 / 95.833.7 / 48.0 / 62.2
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
SSSM [64]71.8 / 91.5 / 96.858.2 / 76.5 / 90.8
VLM [78]62.4 / 71.8 / 79.935.7 / 44.9 / 54.1
SMC [73]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
LBR [79]88.3 / 95.6 / 98.884.7 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
LSIFT [35]82.8 / 88.1 / 93.130.6 / 43.9 / 58.2
SPP [14]80.5 / 87.4 / 94.242.9 / 62.2 / 76.5
D2Net [16]84.8 / 92.6 / 97.584.7 / 90.8 / 96.9
R2D2 [51]76.5 / 90.8 / 100.0
SIFT+CAPS [35, 77]77.6 / 86.7 / 99.0
SPP+CAPS [14, 77]82.7 / 87.8 / 100.0
SPP+LISRD [14, 49]78.6 / 86.7 / 98.0
SPP+PUMP [14, 50]74.4 / 88.0 / 98.4
R2D2+PUMP [14, 50]73.3 / 86.9 / 98.4
R2D2+LLF [14, 68]72.4 / 90.8 / 99.0
SOSNet+D2D [70, 72]73.5 / 83.7 / 96.9
PoSFeat [32]81.6 / 90.8 / 100.0
ASLFeat [37]81.6 / 87.8 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
MENCNet [52]76.5 / 84.7 / 98.0
Dual-RCNet [33]79.6 / 88.8 / 100.0
PDCNet [74]80.6 / 87.8 / 100.0
DGCNet [40]22.9 / 49.8 / 84.714.3 / 37.8 / 79.6
Pixloc [56]84.7 / 94.2 / 98.881.6 / 93.9 / 100.0
AHM [18]47.8 / 72.2 / 91.330.6 / 53.1 / 78.6
S2DNet [19]84.5 / 90.3 / 95.374.5 / 82.7 / 94.9
Patch2Pix [84]84.6 / 92.1 / 96.582.7 / 92.9 / 99.0
SPP+SPG [14, 55]89.6 / 95.4 / 98.886.7 / 93.9 / 100.0
SPP+SGMNet [8, 14]86.8 / 94.2 / 97.783.7 / 91.8 / 99.0
SPP+ClusterGNN [14, 65]89.4 / 95.5 / 98.581.6 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
", + "bbox": [ + 81, + 88, + 467, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "study in Sec. 4.3. More implementation details, results and analysis are provided in the supplementary material.", + "bbox": [ + 76, + 563, + 468, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. We use the identical training dataset as R2D2 [51]. The training dataset consists of reference images in Aachen_v1.0 dataset [60] and web images. As R2D2 [51] and LBR [79], training images are augmented with style transfer. To mitigate segmentation uncertainties caused by style transfer, semantic labels of stylized images are generated from their corresponding normal images. The network is implemented in PyTorch [48] and trained using Adam [29] optimizer with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.99$ , batch size of 4, weight decay of $4\\times 10^{-4}$ on a single 3090Ti GPU for 40 epochs. The hyper-parameter $w_{intra}$ is set to 0.5, while $w_{inter}$ , $w_{det}$ , $w_{desc}$ , and $w_{feat}$ are set to 1.0.", + "bbox": [ + 75, + 594, + 468, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Long-term Large-scale Localization", + "text_level": 1, + "bbox": [ + 76, + 786, + 388, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We test our method on Aachen (v1.0 and v1.1) [59, 60] and RobotCar-Seasons (RoCaS) [39, 60] datasets under various illumination, season, and weather conditions. Aachen_v1.0 contains 4,328 reference and 922 (824 day, 98 night) query images captured around the Aachen city center. Aachen_v1.1 expands v1.0 by adding 2,369 refer", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6439810a3f914547d81d58716e6c8ba4945b513284271b706f630f53b8794ee3.jpg", + "table_caption": [ + "Table 2. Results on Aachen dataset [59,60]. The best and second best results are highlighted with bold and red fonts." + ], + "table_footnote": [], + "table_body": "
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
SLBR [79]89.1 / 96.1 / 99.377.0 / 90.1 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
HSIFT [35]72.2 / 78.4 / 81.719.4 / 23.0 / 27.2
SPP [14]87.9 / 93.6 / 96.870.2 / 84.8 / 93.7
D2Net [16]84.1 / 91.0 / 95.563.4 / 83.8 / 92.1
R2D2 [51]88.8 / 95.3 / 97.872.3 / 88.5 / 94.2
ASLFeat [37]88.0 / 95.4 / 98.270.7 / 84.3 / 94.2
CAPS+SIFT [35, 77]82.4 / 91.3 / 95.961.3 / 83.8 / 95.3
LISRD+SPP [14, 49]73.3 / 86.9 / 97.9
LLF+R2D2 [14, 68]71.2 / 81.2 / 94.2
PoSFeat [32]73.8 / 87.4 / 98.4
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
MSPP+SGMNet [8, 14]88.7 / 96.2 / 98.975.9 / 89.0 / 99.0
SPP+SPG [14, 55]89.8 / 96.1 / 99.477.0 / 90.6 / 100.0
Patch2Pix [84]86.4 / 93.0 / 97.572.3 / 88.5 / 97.9
LoFTER [67]88.7 / 95.6 / 99.078.5 / 90.6 / 99.0
ASpanFormer [9]89.4 / 95.6 / 99.077.5 / 91.6 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
", + "bbox": [ + 516, + 88, + 879, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Results on Aachen_v1.1 dataset [59,60]. The best and second best results are highlighted with bold and red fonts.", + "bbox": [ + 500, + 329, + 890, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ence and 93 night query images. RoCaS has 26,121 reference and 11,934 query images. It is challenging because of various conditions of day query images (rain, snow, dusk, winter) and poor lighting of night query images in suburban areas. We adopt the success ratio at error thresholds of $(2^{\\circ},0.25m)$ , $(5^{\\circ},0.5m)$ , $(10^{\\circ},5m)$ as metric. We additionally provide results on Extended CMU-Seasons dataset in the supplementary material.", + "bbox": [ + 496, + 386, + 890, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. Baselines include classic systems (C) e.g. AS_v1.1 [57], CSL [69], and CPF [12] and methods using semantics (S), e.g. LLN [78], SMC [73], SSM [64], DASGIL [25], ToDayGAN [1] and LBR [79]. We also compare our model with learned features [14, 16, 37, 50, 51, 77] (L). As prior methods [14, 16, 37, 50, 51, 77], we use HLoc [54] pipeline for reconstruction and mutual nearest matching (MNN). NetVLAD [2] is used to offer 50 and 20 candidates for Aachen and RoCaS datasets, respectively. We additionally compare our approach with advanced sparse/dense matchers (M) e.g., Superglue (SPG) [55], SGMNet [8], ClusterGNN [65] and ASpanFormer [9], LoFTER [67], Patch2Pix [84], Dual-RCNet [33]. Their results are obtained from the visual benchmark or original papers.", + "bbox": [ + 496, + 508, + 892, + 719 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with classic methods (C). As shown in Table 2 and 4, our model outperforms all classic methods. As most these methods use SIFT [35], they are more sensitive to weather and illumination changes than learned features.", + "bbox": [ + 496, + 720, + 890, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with methods using explicit semantics (S). By leveraging semantic labels to filter potentially wrong matches, these models achieve better performance for day and night images in Table 2 and 4 but require segmentation results at test time. Our model outperforms all other approaches (except LBR [79]). LBR [79] reports", + "bbox": [ + 496, + 782, + 890, + 873 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1https://www.visuallocalization.net/benchmark/", + "bbox": [ + 517, + 886, + 772, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5211", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/00309e5a33c722a06e5406255a4b9b37c311649997e3b8770380dcf1fb45ed3d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
GroupMethodday (2°, 0.25m)night (5°, 0.5m)night-rain (10°, 5m)
CAS [57]43.6 / 76.0 / 94.01.6 / 3.9 / 10.52.0 / 10.9 / 18.0
CSL [69]45.3 / 73.5 / 90.10.2 / 0.9 / 5.30.9 / 4.3 / 9.1
CPF [12]48.0 / 78.0 / 94.22.3 / 6.6 / 15.34.5 / 12.3 / 18.6
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
SSSM [64]54.5 / 81.6 / 96.710.0 / 23.7 / 45.414.5 / 33.2 / 47.5
VLM [78]7.9 / 30.0 / 85.911.9 / 26.0 / 55.015.7 / 34.5 / 60.5
SMC [73]50.3 / 79.3 / 95.26.2 / 18.5 / 44.38.0 / 26.4 / 46.4
DASGIL-FD [25]8.7 / 30.7 / 81.31.6 / 4.8 / 19.91.8 / 4.3 / 21.6
ToDayGAN [1, 16]52.2 / 80.1 / 95.916.4 / 43.2 / 73.324.1 / 50.5 / 74.1
LBR [79]56.7 / 81.7 / 98.224.9 / 62.3 / 86.147.5 / 73.4 / 90.0
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
LSIFT [35]53.5 / 77.6 / 92.67.8 / 13.9 / 22.19.5 / 14.5 / 17.0
SPP [14]56.5 / 81.5 / 97.116.9 / 41.6 / 71.522.0 / 45.0 / 68.0
D2Net [16]54.5 / 80.0 / 95.318.0 / 39.7 / 53.922.7 / 40.5 / 56.1
R2D2 [51]57.4 / 81.9 / 97.918.3 / 43.4 / 67.829.1 / 50.2 / 68.2
CAPS [77]56.0 / 81.5 / 96.521.9 / 54.3 / 86.827.0 / 58.9 / 85.9
ASLFeat [37]57.1 / 81.9 / 98.423.5 / 55.9 / 80.141.1 / 66.8 / 86.1
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
MSPP+SPG [14, 55]56.9 / 81.7 / 98.124.2 / 62.6 / 87.442.3 / 69.3 / 90.2
Pixloc [56]56.9 / 82.0 / 98.124.2 / 62.8 / 88.445.5 / 72.5 / 90.7
AHM [18]45.7 / 78.0 / 95.116.2 / 55.3 / 93.628.4 / 68.4 / 95.5
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
", + "bbox": [ + 78, + 88, + 472, + 366 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Results on RobotCar-Seasons dataset [39,59]. The best and second best results are highlighted with bold and red fonts.", + "bbox": [ + 76, + 376, + 470, + 405 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "excellent accuracy by selecting keypoints from buildings and performing instance-wise matching. Our method gives close results to LBR on day images but better performance on most night images, because our model does not require explicit semantic labels and is less fragile to segmentation errors especially for night images. LBR performs better than ours on night-train images in Table 4 because it is trained on augmented night rainy images, while our model is trained only on generated night images as R2D2.", + "bbox": [ + 75, + 431, + 468, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with learned features (L). Benefiting from training with massive data, learned features such as R2D2 [51], ASLFeat [37] and PoSFeat [32], outperform SIFT [3, 35]. As they extract keypoints indiscriminately, they are still more sensitive to appearance changes especially on night images than semantic-aware methods [79], as shown in Table 2 and 4. Our model extracts semantic-aware features directly, so it gives higher accuracy.", + "bbox": [ + 75, + 566, + 468, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with advanced matchers (M). In Table 2, 3 and 4, we also show the results of previous advanced matchers. We find that our approach outperforms the recent efficient variations of SPG [55] (e.g. SGMNet [8], ClusterGNN [65]) and gives competitive results to SPG, which achieves the best accuracy and is also the slowest method. Note that our model only uses the simple MNN for matching. We provide a detailed analysis of time and memory usage in Sec. 4.2 and argue that our method provides a good trade off between running time and accuracy especially on devices with limited computing resources.", + "bbox": [ + 75, + 688, + 468, + 854 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Robustness to the number of keypoints. We observe that most previous methods [16, 32, 37, 50, 51] extract keypoints with the number ranging from 10k (R2D2, ASLFeat)", + "bbox": [ + 76, + 854, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c44646f60e3f346f5221a311ab0cf7a49418b93ba9c2717787fbb4f3719d70a.jpg", + "image_caption": [ + "Figure 6. Influence of the number of keypoints. We report results of different number (from 4k to 1k) of keypoints on Aachen_v1.1 [59, 60] at error threshold of $(2^{\\circ}, 0.25m)$ ." + ], + "image_footnote": [], + "bbox": [ + 531, + 88, + 694, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/81961bf4112944786bd7035247ab67ceb1011d2b866cce479a49a883b49195e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 88, + 862, + 244 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to 40k (PosFeat) for evaluation. Although increasing the number improves the accuracy, it causes the time cost as well, which should be taken into consideration especially on devices with limited computing resources. In this experiment, we test the ability of previous and our methods of extracting fewer but more robust features by reducing the number of keypoints from 4k to 1k. Note that results of [14, 51, 55, 79] are from LBR [79] and results of ASLFeat [37] are obtained by running official source code.", + "bbox": [ + 496, + 324, + 890, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 6 shows that as the number of keypoints decreases, all previous features [14, 37, 51] undergo dramatic accuracy loss especially for night images. SPP+SPG and LBR perform more robust because of the global context or semantics. With implicitly embedded semantics, our feature outperforms R2D2, ASLFeat, and SPP especially on night images and gives competitive results to SPP+SPG and LBR.", + "bbox": [ + 496, + 460, + 890, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison. Fig. 7 shows the detection and matching results of query images under conditions of large illumination and season changes. Compared with prior features [14, 37, 51], which prefer keypoints from areas with rich textures, our method favors keypoints from objects robust for long-term localization (e.g. buildings). When insufficient keypoints can be found from stale regions, our model also uses keypoints from Short-term objects e.g. trees from compensation but assigns them with lower reliability. Besides, our feature gives more inliers for query images with large occlusions of trees and severe illumination changes.", + "bbox": [ + 496, + 566, + 892, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Running time analysis", + "text_level": 1, + "bbox": [ + 500, + 741, + 707, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5 demonstrates the test time of previous features [14, 37, 51, 79], matchers [8, 55], and our method. Our method (33.2ms) is faster than R2D2 (72.4ms) [51] and slower than SPP (13.1ms) [14], but has higher accuracy. Besides, our method is faster than LBR (9.2+30.1ms) [79], which uses explicit instances to filter keypoints and advanced matchers including SPP+SPG (13.1+52.2/146.5ms) [14, 55] and SPP+SGM (13.1+33.2/97.6ms) [8, 14]. As the matching method is ex", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5212", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e9f1efd44f84eb7643bbd7355a640ba9a7ab3523511b2794adaf0b7741e09e75.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison of detection and matching. Left→right: SPP [14], R2D2 [51], ASLFeat [37] and our method. Our model favors keypoints on stable areas (reliability high→low: 1-250, 251-500, 501-750, 751-1000) and gives more inliers." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 281, + 263 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0191b8133b7d76ad5596c5b813ea17a5e81798747fe9b6321341e19d68ed7ac9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 90, + 483, + 263 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/87c24bb13b58163a926ef653d5698b0b1cef9ad8cfeca5bc318bbbb7c03c72cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 686, + 263 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c35d60ed22c3c626d14df4f5cb2aea6d83304931c40c1160360916b4790b8fa2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 90, + 888, + 263 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fa7802482fb12feb1db125b275108155c2f6f022819951bf0222a073700d80ab.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelInput sizeRunning time (ms)
SPP [14]1024×102413.1
R2D2 [51]1024×102472.4
ASLFeat* [37]1024×1024112.3
LBR (feature) [79]1024×102430.1
LBR (segmentation) [79]256×2569.2
SPG [55]2k×2k, 4k×4k52.2, 146.5
SGMNet [8]2k×2k, 4k×4k85.5, 97.6
Ours1024×102433.2
", + "bbox": [ + 84, + 327, + 460, + 435 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tensively used for each image pair in mapping and localization processes, SPG/SGMNet are about 18.3/3.3 times slower than NN on Aachen dataset [59, 60] in the mapping process as discussed in [8]. Therefore, our approach could be a good trade off between accuracy and efficiency.", + "bbox": [ + 75, + 498, + 468, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 582, + 227, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 6, we verify the effectiveness of all components in our network by progressively adding the semantic detection (SD), description (SS), and feature consistency (SF) losses. We also compare results of SS loss with triplet and ranking as intra-class loss. Our baseline is trained with detection scores of SPP [14] as detector supervision and ap [23] loss for descriptor learning. After adding SD loss, the model performs better especially for night images. The accuracy is further improved by introducing SS loss because it augments the discriminative ability of descriptors with semantics. Compared to triplet loss with carefully tuned margin, ranking loss improves more accuracy as objects' inner diversity can be better retained by optimizing ranks of samples. SF loss enhances the network's ability of embedding semantic information, leading to further improvements.", + "bbox": [ + 75, + 604, + 470, + 833 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 76, + 844, + 199, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The first limitation is the hand-defined stability values. A learned stability map from training data could be more ro-", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3a0a045065c49c4ab58e74ac806ce66b7479ad498f2ab2bf0f56b832a6355a2d.jpg", + "table_caption": [ + "Table 5. Running time. We report test time of prior features [14, 37, 51], matchers [8, 55] and our method (*in TensorFlow)." + ], + "table_footnote": [], + "table_body": "
SDSSSFDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)Night
XXX85.4 / 93.6 / 97.971.2 / 84.3 / 98.4
✓XX87.3 / 94.3 / 97.872.8 / 88.5 / 99.5
X✓(triplet)X87.9 / 95.1 / 98.973.8 / 86.9 / 99.0
X✓(ranking)X87.9 / 95.3 / 98.774.9 / 89.5 / 99.0
✓✓X88.2 / 95.5 / 98.875.9 / 89.0 / 99.5
✓✓✓88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
", + "bbox": [ + 506, + 327, + 885, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation study. We test the efficacy of semantic detection (SD), semantic description (SS), and semantic feature consistency (SF) losses. The best results are highlighted.", + "bbox": [ + 498, + 435, + 892, + 479 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "bust and further improve the localization accuracy. Besides, semantic labels used in the paper are from ADE20K [83] and the number of these labels is limited. Fine grained semantic labels [31] from automatic segmentation might be more reliable in real applications. Moreover, this work focuses mainly on outdoor localization and may not work very well in indoor scenarios due to the significant differences of object classes. Better performance for indoor scenes can be achieved by retraining the model with redefined stability map for indoor objects.", + "bbox": [ + 496, + 507, + 892, + 659 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 676, + 627, + 693 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we implicitly incorporate semantic information into the feature detection and description processes, enabling the model to extract globally reliable features from a single network end-to-end. Specifically, we leverage outputs of an off-the-shelf semantic segmentation network as guidance and adopt a combination of semantic- and feature-aware guidance strategies to enhance the ability of embedding semantic information at training time. Experiments on large-scale visual localization datasets demonstrate that our method outperforms prior local features and gives competitive performance to advanced matchers but has higher efficiency. We argue that our approach could be a good tradeoff between accuracy and efficiency.", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5213", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Asha Anoosheh, Torsten Sattler, Radu Timofte, Marc Pollefeys, and Luc Van Gool. Night-to-day image translation for retrieval-based localization. In ICRA, 2019. 3, 6, 7", + "[2] Relja Arandjelovic, Petr Gronat, Akihiko Torii, Tomas Pajdla, and Josef Sivic. NetVLAD: CNN architecture for weakly supervised place recognition. 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In CVPR, 2021. 3, 6" + ], + "bbox": [ + 78, + 92, + 467, + 892 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5216", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SFD2_ Semantic-Guided Feature Detection and Description/6efa713f-1ae0-4651-bc92-c61912feb28d_model.json b/2023/SFD2_ Semantic-Guided Feature Detection and Description/6efa713f-1ae0-4651-bc92-c61912feb28d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f78641e07a64c1cdb8a17dec2078c9fe7a92f01a --- /dev/null +++ b/2023/SFD2_ Semantic-Guided Feature Detection and Description/6efa713f-1ae0-4651-bc92-c61912feb28d_model.json @@ -0,0 +1,2510 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.188, + 0.131, + 0.782, + 0.154 + ], + "angle": 0, + "content": "SFD2: Semantic-guided Feature Detection and Description" + }, + { + "type": "text", + "bbox": [ + 0.304, + 0.181, + 0.666, + 0.218 + ], + "angle": 0, + "content": "Fei Xue Ignas Budvytis Roberto Cipolla University of Cambridge" + }, + { + "type": "text", + "bbox": [ + 0.371, + 0.219, + 0.594, + 0.234 + ], + "angle": 0, + "content": "{fx221, ib255, rc10001} \\(@\\) cam.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.664 + ], + "angle": 0, + "content": "Visual localization is a fundamental task for various applications including autonomous driving and robotics. Prior methods focus on extracting large amounts of often redundant locally reliable features, resulting in limited efficiency and accuracy, especially in large-scale environments under challenging conditions. Instead, we propose to extract globally reliable features by implicitly embedding high-level semantics into both the detection and description processes. Specifically, our semantic-aware detector is able to detect keypoints from reliable regions (e.g. building, traffic lane) and suppress unreliable areas (e.g. sky, car) implicitly instead of relying on explicit semantic labels. This boosts the accuracy of keypoint matching by reducing the number of features sensitive to appearance changes and avoiding the need of additional segmentation networks at test time. Moreover, our descriptors are augmented with semantics and have stronger discriminative ability, providing more inliers at test time. Particularly, experiments on long-term large-scale visual localization Aachen DayNight and RobotCar-Seasons datasets demonstrate that our model outperforms previous local features and gives competitive accuracy to advanced matchers but is about 2 and 3 times faster when using \\(2k\\) and \\(4k\\) keypoints, respectively. Code is available at https://github.com/feixue94/sfd2." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.694, + 0.21, + 0.71 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Visual localization is key to various applications including autonomous driving and robotics. Structure-based algorithms [54, 57, 64, 69, 73, 79] involving mapping and localization processes still dominate in large-scale localization. Traditionally, handcrafted features (e.g. SIFT [3, 35], ORB [53]) are widely used. However, these features are mainly based on statistics of gradients of local patches and thus are prone to appearance changes such as illumination and season variations in the long-term visual localization task. With the success of CNNs, learning-based features [14, 16, 37, 45, 51, 76, 81] are introduced to replace handcrafted ones and have achieved excellent performance." + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.267, + 0.856, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.419, + 0.895, + 0.49 + ], + "angle": 0, + "content": "Figure 1. Overview of our framework. Our model implicitly incorporates semantics into the detection and description processes with guidance of an off-the-shelf segmentation network during the training process. Semantic- and feature-aware guidance are adopted to enhance its ability of embedding semantic information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.895, + 0.687 + ], + "angle": 0, + "content": "With massive data for training, these methods should be able to automatically extract keypoints from more reliable regions (e.g. building, traffic lane) by focusing on discriminative features [64]. Nevertheless, due to the lack of explicit semantic signals for training, their ability of selecting globally reliable keypoints is limited, as shown in Fig. 2 (detailed analysis is provided in Sec. B.1 in the supplementary material). Therefore, they prefer to extract locally reliable features from objects including those which are not useful for long-term localization (e.g. sky, tree, car), leading to limited accuracy, as demonstrated in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Recently, advanced matchers based on sparse keypoints [8, 55, 65] or dense pixels [9, 18, 19, 33, 40, 47, 67, 74] are proposed to enhance keypoint/pixel-wise matching and have obtained remarkable accuracy. Yet, they have quadratic time complexity due to the attention and correlation volume computation. Moreover, advanced matchers rely on spatial connections of keypoints and perform image-wise matching as opposed to fast point-wise matching, so they take much longer time than nearest neighbor matching (NN) in both mapping and localization processes because of a large number of image pairs (much larger than the number of images) [8]. Alternatively, some works leverage semantics [64, 73, 79] to filter unstable features to eliminate wrong correspondences and report close even better accu" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5206" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "racy than advanced matchers [79]. However, they require additional segmentation networks to provide semantic labels at test time and are fragile to segmentation errors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Instead, we implicitly incorporate semantics into a local feature model, allowing it to extract robust features automatically from a single network in an end-to-end fashion. In the training process, as shown in Fig. 1, we provide explicit semantics as supervision to guide the detection and description behaviors. Specifically, in the detection process, unlike most previous methods [14, 16, 32, 37, 51] adopting exhaustive detection, we employ a semantic-aware detection loss to encourage our detector to favor features from reliable objects (e.g. building, traffic lane) and suppress those from unreliable objects (e.g. sky). In the description process, rather than utilizing triplet loss widely used for descriptor learning [16, 41], we employ a semantic-aware description loss consisting of two terms: inter- and intra-class losses. The inter-class loss embeds semantics into descriptors by enforcing features with the same label to be close and those with different labels to be far. The intra-class loss, which is a soft-ranking loss [23], operates on features in each class independently and differentiates these features from objects of the same label. Such use of soft-ranking loss avoids the conflict with inter-class loss and retains the diversity of features in each class (e.g. features from buildings usually have larger diversity than those from traffic lights). With semantic-aware descriptor loss, our model is capable of producing descriptors with stronger discriminative ability. Benefiting from implicit semantic embedding, our method avoids using additional segmentation networks at test time and is less fragile to segmentation errors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.696 + ], + "angle": 0, + "content": "As the local feature network is much simpler than typical segmentation networks e.g. UperNet [10], we also adopt an additional feature-consistency loss on the encoder to enhance its ability of learning semantic information. To avoid using costly to obtain ground-truth labels, we train our model with outputs of an off-the-shelf segmentation network [11, 34], which has achieved SOTA performance on the scene parsing task [83], but other semantic segmentation networks (e.g. [10]) can also be used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.788 + ], + "angle": 0, + "content": "An overview of our system is shown in Fig. 1. We embed semantics implicitly into the feature detection and description network via the feature-aware and semantic-aware guidance in the training process. At test time, our model produces semantic-aware features from a single network directly. We summarize contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.8, + 0.468, + 0.859 + ], + "angle": 0, + "content": "- We propose a novel feature network which implicitly incorporates semantics into detection and description processes at training time, enabling the model to produce semantic-aware features end-to-end at test time." + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We adopt a combination of semantic-aware and feature-aware guidance strategy to make the model" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.8, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.226, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Figure 2. Locally reliable features. We show top 1k keypoints (reliability high→low: 1-250, 251-500, 501-750, 751-1000) of prior local features including SPP [14], D2Net [16], R2D2 [51], and ASLFeat [37]. They indiscriminatively give high reliability to patches with rich textures even from objects e.g. sky, tree, pedestrian and car, which are reliable for long-term localization (best view in color)." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.355, + 0.837, + 0.37 + ], + "angle": 0, + "content": "embed semantic information more effectively." + }, + { + "type": "text", + "bbox": [ + 0.516, + 0.38, + 0.892, + 0.426 + ], + "angle": 0, + "content": "- Our method outperforms previous local features on the long-term localization task and gives competitive accuracy to advanced matchers but has higher efficiency." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Experiments show our method achieves a better tradeoff between accuracy and efficiency than advanced matchers [8, 55, 65] especially on devices with limited computing resources. We organize the rest of this paper as follows. In Sec. 2, we introduce related works. In Sec. 3, we describe our method in detail. We discuss experiments and limitations in Sec. 4 and Sec. 5 and conclude the paper in Sec. 6." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.558, + 0.642, + 0.573 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.891, + 0.628 + ], + "angle": 0, + "content": "In this section, we discuss related work on visual localization, feature extraction and matching, and knowledge distillation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Visual localization. Visual localization methods can be roughly categorized as image-based and structure-based. Image-based systems recover camera poses by finding the most similar one in the database with global features, e.g. NetVLAD [2], CRN [27]. Due to the limited number of images in the database, they can only give approximate poses. To obtain more precise poses, structure-based methods build a sparse 3D map via SfM and estimate the pose via PnP from 2D-3D correspondences [12,54,57,58,69,79]. Some other works have tried to predict the camera pose directly from images, e.g. PoseNet [28] and its variations [80], or regress scene coordinates [5-7,26]. However, the former have been proved to perform similar to image retrieval [61] and latter are hard to scale to large-scale scenes [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Local features. Handcrafted features [3, 35, 53] have been investigated for decades and we refer readers a survey [38] for more details and focus on learned features. With the success of CNNs, learned features are proposed to" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5207" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.44 + ], + "angle": 0, + "content": "replace handcrafted descriptors [15,17,36,41-43,49,71,72], detectors [13,68,70], or both [14,16,32,37,51,76,81]. HardNet [41] focuses on metric learning by maximizing the distance between the closest positive and negative examples. Instead of using pixel-wise correspondences for training, CAPS [77], PoSFeat [32] and PUMP [50] utilize camera pose and local consistency of matches for supervision. SuperPoint (SPP) [14] takes keypoint detection as a supervised task, training detector from synthetic geometric shapes. D2-Net [16] uses local maxima across the channels as score map. R2D2 [51] considers both the repeatability and reliability and adopts the average precision loss [23] for descriptor training. ASLFeat [37] employs deformable CNNs to learn shape-aware dense features. As they focus mainly on local reliability of features, regardless of their superior accuracy to handcrafted features, their performance is limited in the long-term large-scale localization task. To further improve the accuracy, some works [22,46,75] learn to filter unstable keypoints with extra matching score, repeatability or semantic labels. Essentially different with these methods, our model detects and extracts semantic-aware features automatically in an end-to-end fashion. As a result, our features are able to produce more accurate localization results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.444, + 0.473, + 0.807 + ], + "angle": 0, + "content": "Advanced matcher. As NN matching is unable to incorporate spatial connections of keypoints for matching, advanced matchers are proposed to enhance the accuracy by leveraging the spatial context of a set of keypoints [8, 55, 65] or an image patch [9, 18, 33, 52, 67, 84]. SuperGlue (SPG) [55] utilizes graph neural networks with attention mechanism to propagate information among keypoints. It produces impressive accuracy, whereas its time complexity is quadratic to the number of keypoints. This problem is partially mitigated by using seeded matching [8] and cluster matching [65], but the time is still thousands of times slower than NN matching. Dense matchers [9, 33, 52, 67] compute pixel-wise correspondence from correlation volumes, so they undergo the high time and memory cost as sparse matchers [8, 55, 65]. Moreover, advanced matchers operates on image pairs as opposed to keypoints, so considering the number of image pairs, systems with advanced matchers could be much slower in real applications, as analyzed in [8]. In this paper, we embed high-level semantic information into local features implicitly to enhance both feature detection and description, enabling our model with simple NN matching to yield comparable results to advanced matchers. Our work provides a good trade-off of time and accuracy especially on devices with limited computing resources." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Visual semantic localization. Compared to local features, high-level semantics are more robust to appearance changes and have been widely used in visual localization [7, 25, 26, 30, 31, 44, 62-64, 66, 73, 78]. LLN [78] and SVL [63] use the discriminative landmarks for place recognition. ToDayGAN [1] transfers night images to day im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.272 + ], + "angle": 0, + "content": "ages with GAN [20]. MFC [30], SMC [73], SSM [64], and DASGIL [25] incorporate segmentation networks into a standard localization pipeline to reject semantically-inconsistent matches. More recently, LBR [79] learns to recognize global instances for both coarse and fine localization. In fine localization, it filters unstable features and conducts instance-wise matching, achieving close accuracy to advanced matchers [55]. Unlike these methods, which require additional models to provide explicit semantic labels at test time, we embed the semantic information into the network and produce semantic-aware features directly from a single network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.895, + 0.395 + ], + "angle": 0, + "content": "Knowledge distillation. Knowledge distillation techniques have been widely used for tasks including model compression [54] and knowledge transfer [82]. Our usage of pseudo ground-truth local reliability and semantic labels predicted by off-the-shelf networks is more like a knowledge transfer task. In this paper, we focus mainly on how to effectively leverage the high-level semantics for low-level feature extraction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.406, + 0.593, + 0.422 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.895, + 0.553 + ], + "angle": 0, + "content": "As shown in Fig. 1, our model consists of an encoder \\(\\mathcal{F}_{enc}\\) and two decoders \\(\\mathcal{F}_{det}\\) and \\(\\mathcal{F}_{desc}\\). \\(\\mathcal{F}_{enc}\\) extracts high-level features \\(\\mathbf{X}\\) from image \\(\\mathbf{I} \\in R^{3 \\times H \\times W}\\). \\(\\mathcal{F}_{det}\\) predicts the reliability map \\(\\mathbf{S} \\in R^{H \\times W}\\) and \\(\\mathcal{F}_{desc}\\) produces descriptors \\(\\mathbf{X}_{desc} \\in R^{128 \\times \\frac{H}{4} \\times \\frac{W}{4}}\\). \\(H\\) and \\(W\\) are the height and width of the image. In this section, we give details about how to implicitly incorporate semantic information into our feature detection and description processes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.561, + 0.807, + 0.577 + ], + "angle": 0, + "content": "3.1. Semantic-guided Feature Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.735 + ], + "angle": 0, + "content": "The detector predicts the reliability map as \\(\\mathbf{S} = \\mathcal{F}_{\\text{det}}(\\mathbf{X})\\). Previously, the reliability map \\(\\mathbf{S}\\) is defined by the richness of textures in patches (e.g. response to corners [14] or blobs [35]). Recently, learned local features [16, 32, 37, 51] define the reliability on the discriminative ability of descriptors. As shown in Fig. 2, these two definitions, however, only reveal the reliability of pixels at a local level but lack the stability at a global level. Instead, we redefine the reliability of features by taking both the local reliability \\(\\mathbf{S}_{\\text{rel}}\\) and global stability \\(\\mathbf{S}_{\\text{sta}}\\) into consideration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.736, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Local reliability. Local reliability shows the robustness of a keypoint to appearance changes and viewpoint variations. Previous learning-based features adopt two strategies for reliable feature learning: learning from groundtruth corners [14] and learning from the discriminative ability of descriptors [16, 32, 37, 51]. We find that corners [14] are more robust compared to purely learned detectors, as shown in [50, 79], where SPP detector achieves better results when replacing other detectors. Therefore, following [54], we use the detection score \\(\\mathbf{S}_{rel}\\) of SPP [14] as pseudo groundtruth, which is one of the best corner detectors. At the same time," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5208" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.273, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.203, + 0.228, + 0.214 + ], + "angle": 0, + "content": "Segmentation mask" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.091, + 0.465, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.203, + 0.432, + 0.215 + ], + "angle": 0, + "content": "Global stability map \\(\\mathbf{S}_{sta}\\)" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.091, + 0.655, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.496, + 0.203, + 0.622, + 0.214 + ], + "angle": 0, + "content": "Local reliability map \\(\\mathbf{S}_{rel}\\)" + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.091, + 0.848, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.203, + 0.812, + 0.214 + ], + "angle": 0, + "content": "Global reliability map S" + }, + { + "type": "image_caption", + "bbox": [ + 0.859, + 0.092, + 0.889, + 0.104 + ], + "angle": 0, + "content": "High" + }, + { + "type": "image_caption", + "bbox": [ + 0.862, + 0.186, + 0.887, + 0.195 + ], + "angle": 0, + "content": "Low" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.226, + 0.894, + 0.282 + ], + "angle": 0, + "content": "Figure 3. Semantic-guided feature detection. From left to right: semantic segmentation mask predicted by [11, 34], stability map \\(\\mathbf{S}_{sta}\\) generated according to Table 1, local reliability map \\(\\mathbf{S}_{rel}\\) produced by SuperPoint [14], and the final global reliability map \\(\\mathbf{S}\\). Local reliability map gives very high score to clouds (red), trees (green), and pedestrians (pink) in addition to buildings, while the global reliability map removes unstable regions (sky, pedestrians), suppresses short-term objects (trees), and retains stable areas (buildings)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.308, + 0.468, + 0.339 + ], + "angle": 0, + "content": "local reliability is slightly adjusted by the discriminative ability of descriptors in the training process (see Sec. 3.2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.468, + 0.566 + ], + "angle": 0, + "content": "Global stability. The global stability of a pixel is assigned based on the semantic label which it belongs to. Specifically, we group all 120 semantic labels in ADE20k dataset [83], according to how they change over time, into four categories, denoted as Volatile, Dynamic, Short-term, and Long-term in Table 1. Volatile objects (e.g. sky, water) are constantly changing and are redundant for localization. Dynamic objects (e.g. car, pedestrian) are moving everyday and could cause localization error by introducing wrong matches. Short-term objects (e.g. tree) can be used for short-term localization tasks (e.g. VO/SLAM), yet they are sensitive to changes of illumination (low albedo) and season conditions. Long-term objects (e.g. building, traffic light) are resistant to aforementioned changes and are ideal for long-term localization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.468, + 0.839 + ], + "angle": 0, + "content": "Instead of directly filtering unstable features [64,73,79], we rerank features with stability values assigned empirically according to the extent of desired suppression. In detail, Long-term objects are robust for both short and long-term localization, so their stability value is set to 1.0. Short-term objects are useful for short-term localization, so we set their stability to 0.5. The stability value of Volatile and Dynamic categories is set to 0.1 as they are not useful for both short/long-term localization. Note that we set it to 0.1 rather than 0. Our reranking strategy encourages the model to use stable features preferentially and uses keypoints from other objects as compensation when insufficient stable keypoints can be found, increasing the robustness of our model to various tasks (e.g. feature matching, short-term localization). Fig. 3 shows stability map \\(\\mathbf{S}_{sta}\\) transformed from Table 1. Our current global stability is assigned based on predefined semantic labels, but a learned one might provide better performance and deserves further exploration." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Semantic-guided detection. The global reliability map \\(\\mathbf{S}_{gt}\\) is generated by multiplying the local reliability map \\(\\mathbf{S}_{rel}\\) and global stability map, as \\(\\mathbf{S}_{gt} = \\mathbf{S}_{rel} \\odot \\mathbf{S}_{sta}\\) (\\(\\odot\\) is element-wise multiplication). Fig. 3 shows that local re" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.306, + 0.897, + 0.38 + ], + "angle": 0, + "content": "
CategoryVolatileDynamicShort-termLong-termStability
sky, water✓0.1
vehicle, pedestrian✓0.1
plant, grass✓0.5
building, traffic light✓1.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.394, + 0.892, + 0.451 + ], + "angle": 0, + "content": "Table 1. Stability map. Semantic labels are categorized into four groups denoted as Volatile, Dynamic, Short-term, and Long-term. Four categories are empirically assigned with different stability values according to their robustness to appearance changes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.474, + 0.892, + 0.565 + ], + "angle": 0, + "content": "liability map gives high score for all pixels with rich textures even those from the sky, pedestrians, and trees, which are useless for localization. However, the global reliability map considering both local reliability and global stability discards these sensitive features and suppresses short-term keypoints effectively. The detection loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.573, + 0.891, + 0.59 + ], + "angle": 0, + "content": "\\[\nL _ {d e t} = B C E (\\mathbf {S}, \\mathbf {S} _ {g t}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.599, + 0.837, + 0.614 + ], + "angle": 0, + "content": "where \\( BCE \\) denotes the binary cross-entropy loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.822, + 0.637 + ], + "angle": 0, + "content": "3.2. Semantic-guided Feature Description" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also enhance the discriminative ability of descriptors by embedding semantics into them directly. Unlike previous descriptors [14, 37, 41, 50, 51, 77], which only differentiate keypoints based on local patch information, our descriptors enforce similarities of features in the same class while retain dissimilarities for intra-class matching. However, the two forces conflict with each other during the training process, because class-level discriminative ability needs to squeeze the space of descriptors in the same class and intra-class discriminative ability has to increase the space. A simple solution could be to set a hard margin for all classes (Fig. 4 left), but it would lead to the loss of objects' inner diversity (e.g., almost all traffic lights are similar but different buildings vary dramatically), which is indispensable for intra-class matching. To solve this problem, we design the inter-class and intra-class losses based on two different metrics (Fig. 4 right)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5209" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.088, + 0.46, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.21, + 0.473, + 0.296 + ], + "angle": 0, + "content": "Figure 4. Semantic-guided feature description. Simply optimizing inter- and intra-class losses with hard margins may cause accuracy loss due to two conflicting forces (push forces of inter- and intra-class) (left). Instead, we optimize the intra-class force with a hard margin, but apply a soft ranking loss for inter-class force to avoid conflicts and retain the inner diversity of each object (right)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Inter-class loss. We first enforce the semantic consistency of features by maximizing the Euclidean distance between descriptors with different labels. This allows features to find correspondences from candidates with the same labels, reducing the search space and thus improving the matching accuracy. We define the inter-class loss based on triplet loss with a hard margin to separate all possible positive and negative keypoints with different labels in a batch:" + }, + { + "type": "equation", + "bbox": [ + 0.111, + 0.454, + 0.47, + 0.478 + ], + "angle": 0, + "content": "\\[\nL _ {i n t e r} = \\frac {1}{N} \\sum \\left(\\left| \\left| \\mathbf {x} _ {i} ^ {c _ {1}} - \\mathbf {x} _ {j} ^ {c _ {1}} \\right| \\right| _ {2} - \\left| \\left| \\mathbf {x} _ {i} ^ {c _ {1}} - \\mathbf {x} _ {k} ^ {c _ {2}} \\right| \\right| _ {2} + m\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.482, + 0.47, + 0.543 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_i^{c_1},\\mathbf{x}_j^{c_1}\\), and \\(\\mathbf{x}_k^{c_2}\\) are vectorized descriptors with labels of \\(c_{1},c_{1}\\), and \\(c_{2}\\) (\\(c_{1}\\neq c_{2}\\)). \\(m\\) is the margin and set to 1.0. This loss is conducted on features in the whole batch and \\(N\\) is the total number of features in a batch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.543, + 0.473, + 0.786 + ], + "angle": 0, + "content": "Intra-class loss. To make sure that the intra-class loss doesn't conflict with the inter-class loss, we relax the limitation of distances between descriptors with the same label. Instead of using triplet loss with hard margins, we adopt a soft ranking loss [23] by optimizing the rank of positive and negative samples rather than their distances. We use the same strategy as [51] to generate positive and negative samples for each feature \\(\\mathbf{x}_i^c\\) from self and the other images respectively, but enforce both positive and negative samples to share the same class label \\(c\\) as \\(\\mathbf{x}_i^c\\). By optimizing ranks of all samples rather than forcing a hard boundary between positive and negative pairs as the triplet loss with a hard margin does, the soft ranking loss also retains the diversity of features on objects in the same class, as shown in Fig. 4 (right). The ranking loss is based on the averaging precision (AP) loss [23, 51]:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.799, + 0.47, + 0.834 + ], + "angle": 0, + "content": "\\[\nL _ {i n t r a} = \\frac {1}{C} \\sum_ {c = 1} ^ {C} \\frac {1}{N _ {c}} \\sum_ {i = 1} ^ {N _ {c}} \\left(1 - A P \\left(\\mathbf {x} _ {i} ^ {c}, \\mathbf {S} ^ {\\mathbf {x} _ {i} ^ {c}}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_i^c\\) and \\(\\mathbf{S}^{\\mathbf{x}_i^c}\\) are the query descriptor with label \\(c\\) and corresponding predicted local reliability. \\(C\\) and \\(N_{c}\\) are the total number of classes and features in class \\(c\\). Note that the AP loss for sample \\(\\mathbf{x}_i^c\\) is weighted by its reliability \\(\\mathbf{S}^{\\mathbf{x}_i^c}\\)." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.091, + 0.877, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.233, + 0.895, + 0.318 + ], + "angle": 0, + "content": "Figure 5. Architecture of our network. Features are \\(4 \\times\\) down-sampling to save time and memory cost. Resblocks [24] are adopted to enhance the model's capacity. We enforce the consistency between outputs of the middle two layers of our encoder and features of the segmentation network to enhance the ability of our model to embed semantic information during the training process." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.342, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Our final descriptor loss \\( L_{desc} \\) is the combination of \\( L_{inter} \\) and \\( L_{intra} \\), balanced by \\( w_{inter} \\) and \\( w_{intra} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.384, + 0.892, + 0.4 + ], + "angle": 0, + "content": "\\[\nL _ {d e s c} = w _ {i n t e r} L _ {i n t e r} + w _ {i n t r a} L _ {i n t r a}. \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.419, + 0.741, + 0.435 + ], + "angle": 0, + "content": "3.3. Implicit Feature Guidance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.592 + ], + "angle": 0, + "content": "With semantic-aware detection and description losses, our model is able to learn semantic-aware features. However, compared with feature learning, semantic prediction is a more complicated task, requiring powerful encoders and aggregation layers [4, 34] for semantic-aware feature embedding. To further improve the ability of our model to embed semantic information, we take inspiration from current knowledge distillation tasks [21] and introduce a feature consistency loss on intermediate outputs of the first three layers of the encoder." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Fig. 5 shows the architecture of our network. We take intermediate outputs of the encoder of ConvNeXt [34] as supervision signal and enforce \\( l_{1} \\) loss on features of the middle 2 layers of our model:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.664, + 0.892, + 0.705 + ], + "angle": 0, + "content": "\\[\nL _ {f e a t} = \\frac {1}{2} \\sum_ {i = 1} ^ {2} | \\mathbf {X} _ {i} - \\mathbf {X} _ {i} ^ {\\text {C o n v N e X t}} |, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.715, + 0.892, + 0.793 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}_i\\) and \\(\\mathbf{X}_i^{ConvNeXt}\\) are features of the \\(i\\)th layer in our model and ConvNeXt [34], respectively. The total loss \\(L_{total}\\) is the combination of detection loss \\(L_{det}\\), description loss \\(L_{desc}\\), and feature consistency loss \\(L_{feat}\\) with weights of \\(w_{det}, w_{desc}\\), and \\(w_{feat}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.803, + 0.892, + 0.82 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {t o t a l}} = w _ {\\text {d e t}} L _ {\\text {d e t}} + w _ {\\text {d e s c}} L _ {\\text {d e s c}} + w _ {\\text {f e a t}} L _ {\\text {f e a t}}. \\tag {6}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.634, + 0.848 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We first give implementation details. Then, we test our method on visual localization tasks in Sec. 4.1 and analyze the running time in Sec. 4.2. Finally, we perform an ablation" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5210" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.497 + ], + "angle": 0, + "content": "
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
CAS.v1.1 [57]85.3 / 92.2 / 97.939.8 / 49.0 / 64.3
CSL [69]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
CPF [12]76.7 / 88.6 / 95.833.7 / 48.0 / 62.2
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
SSSM [64]71.8 / 91.5 / 96.858.2 / 76.5 / 90.8
VLM [78]62.4 / 71.8 / 79.935.7 / 44.9 / 54.1
SMC [73]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
LBR [79]88.3 / 95.6 / 98.884.7 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
LSIFT [35]82.8 / 88.1 / 93.130.6 / 43.9 / 58.2
SPP [14]80.5 / 87.4 / 94.242.9 / 62.2 / 76.5
D2Net [16]84.8 / 92.6 / 97.584.7 / 90.8 / 96.9
R2D2 [51]76.5 / 90.8 / 100.0
SIFT+CAPS [35, 77]77.6 / 86.7 / 99.0
SPP+CAPS [14, 77]82.7 / 87.8 / 100.0
SPP+LISRD [14, 49]78.6 / 86.7 / 98.0
SPP+PUMP [14, 50]74.4 / 88.0 / 98.4
R2D2+PUMP [14, 50]73.3 / 86.9 / 98.4
R2D2+LLF [14, 68]72.4 / 90.8 / 99.0
SOSNet+D2D [70, 72]73.5 / 83.7 / 96.9
PoSFeat [32]81.6 / 90.8 / 100.0
ASLFeat [37]81.6 / 87.8 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
MENCNet [52]76.5 / 84.7 / 98.0
Dual-RCNet [33]79.6 / 88.8 / 100.0
PDCNet [74]80.6 / 87.8 / 100.0
DGCNet [40]22.9 / 49.8 / 84.714.3 / 37.8 / 79.6
Pixloc [56]84.7 / 94.2 / 98.881.6 / 93.9 / 100.0
AHM [18]47.8 / 72.2 / 91.330.6 / 53.1 / 78.6
S2DNet [19]84.5 / 90.3 / 95.374.5 / 82.7 / 94.9
Patch2Pix [84]84.6 / 92.1 / 96.582.7 / 92.9 / 99.0
SPP+SPG [14, 55]89.6 / 95.4 / 98.886.7 / 93.9 / 100.0
SPP+SGMNet [8, 14]86.8 / 94.2 / 97.783.7 / 91.8 / 99.0
SPP+ClusterGNN [14, 65]89.4 / 95.5 / 98.581.6 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.507, + 0.472, + 0.537 + ], + "angle": 0, + "content": "Table 2. Results on Aachen dataset [59,60]. The best and second best results are highlighted with bold and red fonts." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.564, + 0.47, + 0.594 + ], + "angle": 0, + "content": "study in Sec. 4.3. More implementation details, results and analysis are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.777 + ], + "angle": 0, + "content": "Implementation. We use the identical training dataset as R2D2 [51]. The training dataset consists of reference images in Aachen_v1.0 dataset [60] and web images. As R2D2 [51] and LBR [79], training images are augmented with style transfer. To mitigate segmentation uncertainties caused by style transfer, semantic labels of stylized images are generated from their corresponding normal images. The network is implemented in PyTorch [48] and trained using Adam [29] optimizer with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.99\\), batch size of 4, weight decay of \\(4\\times 10^{-4}\\) on a single 3090Ti GPU for 40 epochs. The hyper-parameter \\(w_{intra}\\) is set to 0.5, while \\(w_{inter}\\), \\(w_{det}\\), \\(w_{desc}\\), and \\(w_{feat}\\) are set to 1.0." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.39, + 0.803 + ], + "angle": 0, + "content": "4.1. Long-term Large-scale Localization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We test our method on Aachen (v1.0 and v1.1) [59, 60] and RobotCar-Seasons (RoCaS) [39, 60] datasets under various illumination, season, and weather conditions. Aachen_v1.0 contains 4,328 reference and 922 (824 day, 98 night) query images captured around the Aachen city center. Aachen_v1.1 expands v1.0 by adding 2,369 refer" + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.089, + 0.88, + 0.321 + ], + "angle": 0, + "content": "
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
SLBR [79]89.1 / 96.1 / 99.377.0 / 90.1 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
HSIFT [35]72.2 / 78.4 / 81.719.4 / 23.0 / 27.2
SPP [14]87.9 / 93.6 / 96.870.2 / 84.8 / 93.7
D2Net [16]84.1 / 91.0 / 95.563.4 / 83.8 / 92.1
R2D2 [51]88.8 / 95.3 / 97.872.3 / 88.5 / 94.2
ASLFeat [37]88.0 / 95.4 / 98.270.7 / 84.3 / 94.2
CAPS+SIFT [35, 77]82.4 / 91.3 / 95.961.3 / 83.8 / 95.3
LISRD+SPP [14, 49]73.3 / 86.9 / 97.9
LLF+R2D2 [14, 68]71.2 / 81.2 / 94.2
PoSFeat [32]73.8 / 87.4 / 98.4
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
MSPP+SGMNet [8, 14]88.7 / 96.2 / 98.975.9 / 89.0 / 99.0
SPP+SPG [14, 55]89.8 / 96.1 / 99.477.0 / 90.6 / 100.0
Patch2Pix [84]86.4 / 93.0 / 97.572.3 / 88.5 / 97.9
LoFTER [67]88.7 / 95.6 / 99.078.5 / 90.6 / 99.0
ASpanFormer [9]89.4 / 95.6 / 99.077.5 / 91.6 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.33, + 0.892, + 0.358 + ], + "angle": 0, + "content": "Table 3. Results on Aachen_v1.1 dataset [59,60]. The best and second best results are highlighted with bold and red fonts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.508 + ], + "angle": 0, + "content": "ence and 93 night query images. RoCaS has 26,121 reference and 11,934 query images. It is challenging because of various conditions of day query images (rain, snow, dusk, winter) and poor lighting of night query images in suburban areas. We adopt the success ratio at error thresholds of \\((2^{\\circ},0.25m)\\), \\((5^{\\circ},0.5m)\\), \\((10^{\\circ},5m)\\) as metric. We additionally provide results on Extended CMU-Seasons dataset in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.893, + 0.72 + ], + "angle": 0, + "content": "Baselines. Baselines include classic systems (C) e.g. AS_v1.1 [57], CSL [69], and CPF [12] and methods using semantics (S), e.g. LLN [78], SMC [73], SSM [64], DASGIL [25], ToDayGAN [1] and LBR [79]. We also compare our model with learned features [14, 16, 37, 50, 51, 77] (L). As prior methods [14, 16, 37, 50, 51, 77], we use HLoc [54] pipeline for reconstruction and mutual nearest matching (MNN). NetVLAD [2] is used to offer 50 and 20 candidates for Aachen and RoCaS datasets, respectively. We additionally compare our approach with advanced sparse/dense matchers (M) e.g., Superglue (SPG) [55], SGMNet [8], ClusterGNN [65] and ASpanFormer [9], LoFTER [67], Patch2Pix [84], Dual-RCNet [33]. Their results are obtained from the visual benchmark or original papers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.722, + 0.892, + 0.782 + ], + "angle": 0, + "content": "Comparison with classic methods (C). As shown in Table 2 and 4, our model outperforms all classic methods. As most these methods use SIFT [35], they are more sensitive to weather and illumination changes than learned features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Comparison with methods using explicit semantics (S). By leveraging semantic labels to filter potentially wrong matches, these models achieve better performance for day and night images in Table 2 and 4 but require segmentation results at test time. Our model outperforms all other approaches (except LBR [79]). LBR [79] reports" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.774, + 0.9 + ], + "angle": 0, + "content": "1https://www.visuallocalization.net/benchmark/" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5211" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.473, + 0.367 + ], + "angle": 0, + "content": "
GroupMethodday (2°, 0.25m)night (5°, 0.5m)night-rain (10°, 5m)
CAS [57]43.6 / 76.0 / 94.01.6 / 3.9 / 10.52.0 / 10.9 / 18.0
CSL [69]45.3 / 73.5 / 90.10.2 / 0.9 / 5.30.9 / 4.3 / 9.1
CPF [12]48.0 / 78.0 / 94.22.3 / 6.6 / 15.34.5 / 12.3 / 18.6
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
SSSM [64]54.5 / 81.6 / 96.710.0 / 23.7 / 45.414.5 / 33.2 / 47.5
VLM [78]7.9 / 30.0 / 85.911.9 / 26.0 / 55.015.7 / 34.5 / 60.5
SMC [73]50.3 / 79.3 / 95.26.2 / 18.5 / 44.38.0 / 26.4 / 46.4
DASGIL-FD [25]8.7 / 30.7 / 81.31.6 / 4.8 / 19.91.8 / 4.3 / 21.6
ToDayGAN [1, 16]52.2 / 80.1 / 95.916.4 / 43.2 / 73.324.1 / 50.5 / 74.1
LBR [79]56.7 / 81.7 / 98.224.9 / 62.3 / 86.147.5 / 73.4 / 90.0
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
LSIFT [35]53.5 / 77.6 / 92.67.8 / 13.9 / 22.19.5 / 14.5 / 17.0
SPP [14]56.5 / 81.5 / 97.116.9 / 41.6 / 71.522.0 / 45.0 / 68.0
D2Net [16]54.5 / 80.0 / 95.318.0 / 39.7 / 53.922.7 / 40.5 / 56.1
R2D2 [51]57.4 / 81.9 / 97.918.3 / 43.4 / 67.829.1 / 50.2 / 68.2
CAPS [77]56.0 / 81.5 / 96.521.9 / 54.3 / 86.827.0 / 58.9 / 85.9
ASLFeat [37]57.1 / 81.9 / 98.423.5 / 55.9 / 80.141.1 / 66.8 / 86.1
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
MSPP+SPG [14, 55]56.9 / 81.7 / 98.124.2 / 62.6 / 87.442.3 / 69.3 / 90.2
Pixloc [56]56.9 / 82.0 / 98.124.2 / 62.8 / 88.445.5 / 72.5 / 90.7
AHM [18]45.7 / 78.0 / 95.116.2 / 55.3 / 93.628.4 / 68.4 / 95.5
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.377, + 0.471, + 0.406 + ], + "angle": 0, + "content": "Table 4. Results on RobotCar-Seasons dataset [39,59]. The best and second best results are highlighted with bold and red fonts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.568 + ], + "angle": 0, + "content": "excellent accuracy by selecting keypoints from buildings and performing instance-wise matching. Our method gives close results to LBR on day images but better performance on most night images, because our model does not require explicit semantic labels and is less fragile to segmentation errors especially for night images. LBR performs better than ours on night-train images in Table 4 because it is trained on augmented night rainy images, while our model is trained only on generated night images as R2D2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Comparison with learned features (L). Benefiting from training with massive data, learned features such as R2D2 [51], ASLFeat [37] and PoSFeat [32], outperform SIFT [3, 35]. As they extract keypoints indiscriminately, they are still more sensitive to appearance changes especially on night images than semantic-aware methods [79], as shown in Table 2 and 4. Our model extracts semantic-aware features directly, so it gives higher accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Comparison with advanced matchers (M). In Table 2, 3 and 4, we also show the results of previous advanced matchers. We find that our approach outperforms the recent efficient variations of SPG [55] (e.g. SGMNet [8], ClusterGNN [65]) and gives competitive results to SPG, which achieves the best accuracy and is also the slowest method. Note that our model only uses the simple MNN for matching. We provide a detailed analysis of time and memory usage in Sec. 4.2 and argue that our method provides a good trade off between running time and accuracy especially on devices with limited computing resources." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Robustness to the number of keypoints. We observe that most previous methods [16, 32, 37, 50, 51] extract keypoints with the number ranging from 10k (R2D2, ASLFeat)" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.089, + 0.695, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.089, + 0.864, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.256, + 0.894, + 0.299 + ], + "angle": 0, + "content": "Figure 6. Influence of the number of keypoints. We report results of different number (from 4k to 1k) of keypoints on Aachen_v1.1 [59, 60] at error threshold of \\((2^{\\circ}, 0.25m)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.461 + ], + "angle": 0, + "content": "to 40k (PosFeat) for evaluation. Although increasing the number improves the accuracy, it causes the time cost as well, which should be taken into consideration especially on devices with limited computing resources. In this experiment, we test the ability of previous and our methods of extracting fewer but more robust features by reducing the number of keypoints from 4k to 1k. Note that results of [14, 51, 55, 79] are from LBR [79] and results of ASLFeat [37] are obtained by running official source code." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Fig. 6 shows that as the number of keypoints decreases, all previous features [14, 37, 51] undergo dramatic accuracy loss especially for night images. SPP+SPG and LBR perform more robust because of the global context or semantics. With implicitly embedded semantics, our feature outperforms R2D2, ASLFeat, and SPP especially on night images and gives competitive results to SPP+SPG and LBR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.893, + 0.734 + ], + "angle": 0, + "content": "Qualitative comparison. Fig. 7 shows the detection and matching results of query images under conditions of large illumination and season changes. Compared with prior features [14, 37, 51], which prefer keypoints from areas with rich textures, our method favors keypoints from objects robust for long-term localization (e.g. buildings). When insufficient keypoints can be found from stale regions, our model also uses keypoints from Short-term objects e.g. trees from compensation but assigns them with lower reliability. Besides, our feature gives more inliers for query images with large occlusions of trees and severe illumination changes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.708, + 0.758 + ], + "angle": 0, + "content": "4.2. Running time analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Table 5 demonstrates the test time of previous features [14, 37, 51, 79], matchers [8, 55], and our method. Our method (33.2ms) is faster than R2D2 (72.4ms) [51] and slower than SPP (13.1ms) [14], but has higher accuracy. Besides, our method is faster than LBR (9.2+30.1ms) [79], which uses explicit instances to filter keypoints and advanced matchers including SPP+SPG (13.1+52.2/146.5ms) [14, 55] and SPP+SGM (13.1+33.2/97.6ms) [8, 14]. As the matching method is ex" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5212" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.282, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.091, + 0.484, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.091, + 0.687, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.091, + 0.89, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.275, + 0.894, + 0.307 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison of detection and matching. Left→right: SPP [14], R2D2 [51], ASLFeat [37] and our method. Our model favors keypoints on stable areas (reliability high→low: 1-250, 251-500, 501-750, 751-1000) and gives more inliers." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.328, + 0.462, + 0.436 + ], + "angle": 0, + "content": "
ModelInput sizeRunning time (ms)
SPP [14]1024×102413.1
R2D2 [51]1024×102472.4
ASLFeat* [37]1024×1024112.3
LBR (feature) [79]1024×102430.1
LBR (segmentation) [79]256×2569.2
SPG [55]2k×2k, 4k×4k52.2, 146.5
SGMNet [8]2k×2k, 4k×4k85.5, 97.6
Ours1024×102433.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.446, + 0.47, + 0.475 + ], + "angle": 0, + "content": "Table 5. Running time. We report test time of prior features [14, 37, 51], matchers [8, 55] and our method (*in TensorFlow)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.576 + ], + "angle": 0, + "content": "tensively used for each image pair in mapping and localization processes, SPG/SGMNet are about 18.3/3.3 times slower than NN on Aachen dataset [59, 60] in the mapping process as discussed in [8]. Therefore, our approach could be a good trade off between accuracy and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.583, + 0.228, + 0.599 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.471, + 0.834 + ], + "angle": 0, + "content": "In Table 6, we verify the effectiveness of all components in our network by progressively adding the semantic detection (SD), description (SS), and feature consistency (SF) losses. We also compare results of SS loss with triplet and ranking as intra-class loss. Our baseline is trained with detection scores of SPP [14] as detector supervision and ap [23] loss for descriptor learning. After adding SD loss, the model performs better especially for night images. The accuracy is further improved by introducing SS loss because it augments the discriminative ability of descriptors with semantics. Compared to triplet loss with carefully tuned margin, ranking loss improves more accuracy as objects' inner diversity can be better retained by optimizing ranks of samples. SF loss enhances the network's ability of embedding semantic information, leading to further improvements." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.2, + 0.861 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The first limitation is the hand-defined stability values. A learned stability map from training data could be more ro-" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.328, + 0.887, + 0.426 + ], + "angle": 0, + "content": "
SDSSSFDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)Night
XXX85.4 / 93.6 / 97.971.2 / 84.3 / 98.4
✓XX87.3 / 94.3 / 97.872.8 / 88.5 / 99.5
X✓(triplet)X87.9 / 95.1 / 98.973.8 / 86.9 / 99.0
X✓(ranking)X87.9 / 95.3 / 98.774.9 / 89.5 / 99.0
✓✓X88.2 / 95.5 / 98.875.9 / 89.0 / 99.5
✓✓✓88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.436, + 0.893, + 0.48 + ], + "angle": 0, + "content": "Table 6. Ablation study. We test the efficacy of semantic detection (SD), semantic description (SS), and semantic feature consistency (SF) losses. The best results are highlighted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.893, + 0.66 + ], + "angle": 0, + "content": "bust and further improve the localization accuracy. Besides, semantic labels used in the paper are from ADE20K [83] and the number of these labels is limited. Fine grained semantic labels [31] from automatic segmentation might be more reliable in real applications. Moreover, this work focuses mainly on outdoor localization and may not work very well in indoor scenarios due to the significant differences of object classes. Better performance for indoor scenes can be achieved by retraining the model with redefined stability map for indoor objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.678, + 0.628, + 0.694 + ], + "angle": 0, + "content": "6. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we implicitly incorporate semantic information into the feature detection and description processes, enabling the model to extract globally reliable features from a single network end-to-end. Specifically, we leverage outputs of an off-the-shelf semantic segmentation network as guidance and adopt a combination of semantic- and feature-aware guidance strategies to enhance the ability of embedding semantic information at training time. Experiments on large-scale visual localization datasets demonstrate that our method outperforms prior local features and gives competitive performance to advanced matchers but has higher efficiency. We argue that our approach could be a good tradeoff between accuracy and efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5213" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Asha Anoosheh, Torsten Sattler, Radu Timofte, Marc Pollefeys, and Luc Van Gool. Night-to-day image translation for retrieval-based localization. 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Prior methods focus on extracting large amounts of often redundant locally reliable features, resulting in limited efficiency and accuracy, especially in large-scale environments under challenging conditions. Instead, we propose to extract globally reliable features by implicitly embedding high-level semantics into both the detection and description processes. Specifically, our semantic-aware detector is able to detect keypoints from reliable regions (e.g. building, traffic lane) and suppress unreliable areas (e.g. sky, car) implicitly instead of relying on explicit semantic labels. This boosts the accuracy of keypoint matching by reducing the number of features sensitive to appearance changes and avoiding the need of additional segmentation networks at test time. Moreover, our descriptors are augmented with semantics and have stronger discriminative ability, providing more inliers at test time. Particularly, experiments on long-term large-scale visual localization Aachen DayNight and RobotCar-Seasons datasets demonstrate that our model outperforms previous local features and gives competitive accuracy to advanced matchers but is about 2 and 3 times faster when using $2k$ and $4k$ keypoints, respectively. Code is available at https://github.com/feixue94/sfd2. + +# 1. Introduction + +Visual localization is key to various applications including autonomous driving and robotics. Structure-based algorithms [54, 57, 64, 69, 73, 79] involving mapping and localization processes still dominate in large-scale localization. Traditionally, handcrafted features (e.g. SIFT [3, 35], ORB [53]) are widely used. However, these features are mainly based on statistics of gradients of local patches and thus are prone to appearance changes such as illumination and season variations in the long-term visual localization task. With the success of CNNs, learning-based features [14, 16, 37, 45, 51, 76, 81] are introduced to replace handcrafted ones and have achieved excellent performance. + +![](images/f6e7685d36555c3f5fa3c09b9c4229a7a3aa87352b41537c0b6f0a00456fb68a.jpg) +Figure 1. Overview of our framework. Our model implicitly incorporates semantics into the detection and description processes with guidance of an off-the-shelf segmentation network during the training process. Semantic- and feature-aware guidance are adopted to enhance its ability of embedding semantic information. + +With massive data for training, these methods should be able to automatically extract keypoints from more reliable regions (e.g. building, traffic lane) by focusing on discriminative features [64]. Nevertheless, due to the lack of explicit semantic signals for training, their ability of selecting globally reliable keypoints is limited, as shown in Fig. 2 (detailed analysis is provided in Sec. B.1 in the supplementary material). Therefore, they prefer to extract locally reliable features from objects including those which are not useful for long-term localization (e.g. sky, tree, car), leading to limited accuracy, as demonstrated in Table 2. + +Recently, advanced matchers based on sparse keypoints [8, 55, 65] or dense pixels [9, 18, 19, 33, 40, 47, 67, 74] are proposed to enhance keypoint/pixel-wise matching and have obtained remarkable accuracy. Yet, they have quadratic time complexity due to the attention and correlation volume computation. Moreover, advanced matchers rely on spatial connections of keypoints and perform image-wise matching as opposed to fast point-wise matching, so they take much longer time than nearest neighbor matching (NN) in both mapping and localization processes because of a large number of image pairs (much larger than the number of images) [8]. Alternatively, some works leverage semantics [64, 73, 79] to filter unstable features to eliminate wrong correspondences and report close even better accu + +racy than advanced matchers [79]. However, they require additional segmentation networks to provide semantic labels at test time and are fragile to segmentation errors. + +Instead, we implicitly incorporate semantics into a local feature model, allowing it to extract robust features automatically from a single network in an end-to-end fashion. In the training process, as shown in Fig. 1, we provide explicit semantics as supervision to guide the detection and description behaviors. Specifically, in the detection process, unlike most previous methods [14, 16, 32, 37, 51] adopting exhaustive detection, we employ a semantic-aware detection loss to encourage our detector to favor features from reliable objects (e.g. building, traffic lane) and suppress those from unreliable objects (e.g. sky). In the description process, rather than utilizing triplet loss widely used for descriptor learning [16, 41], we employ a semantic-aware description loss consisting of two terms: inter- and intra-class losses. The inter-class loss embeds semantics into descriptors by enforcing features with the same label to be close and those with different labels to be far. The intra-class loss, which is a soft-ranking loss [23], operates on features in each class independently and differentiates these features from objects of the same label. Such use of soft-ranking loss avoids the conflict with inter-class loss and retains the diversity of features in each class (e.g. features from buildings usually have larger diversity than those from traffic lights). With semantic-aware descriptor loss, our model is capable of producing descriptors with stronger discriminative ability. Benefiting from implicit semantic embedding, our method avoids using additional segmentation networks at test time and is less fragile to segmentation errors. + +As the local feature network is much simpler than typical segmentation networks e.g. UperNet [10], we also adopt an additional feature-consistency loss on the encoder to enhance its ability of learning semantic information. To avoid using costly to obtain ground-truth labels, we train our model with outputs of an off-the-shelf segmentation network [11, 34], which has achieved SOTA performance on the scene parsing task [83], but other semantic segmentation networks (e.g. [10]) can also be used. + +An overview of our system is shown in Fig. 1. We embed semantics implicitly into the feature detection and description network via the feature-aware and semantic-aware guidance in the training process. At test time, our model produces semantic-aware features from a single network directly. We summarize contributions as follows: + +- We propose a novel feature network which implicitly incorporates semantics into detection and description processes at training time, enabling the model to produce semantic-aware features end-to-end at test time. +- We adopt a combination of semantic-aware and feature-aware guidance strategy to make the model + +![](images/255208525ae22918530d2a590b0df382fbae6ee4262d03c58f3baa94fcec71d1.jpg) +Figure 2. Locally reliable features. We show top 1k keypoints (reliability high→low: 1-250, 251-500, 501-750, 751-1000) of prior local features including SPP [14], D2Net [16], R2D2 [51], and ASLFeat [37]. They indiscriminatively give high reliability to patches with rich textures even from objects e.g. sky, tree, pedestrian and car, which are reliable for long-term localization (best view in color). + +embed semantic information more effectively. + +- Our method outperforms previous local features on the long-term localization task and gives competitive accuracy to advanced matchers but has higher efficiency. + +Experiments show our method achieves a better tradeoff between accuracy and efficiency than advanced matchers [8, 55, 65] especially on devices with limited computing resources. We organize the rest of this paper as follows. In Sec. 2, we introduce related works. In Sec. 3, we describe our method in detail. We discuss experiments and limitations in Sec. 4 and Sec. 5 and conclude the paper in Sec. 6. + +# 2. Related Work + +In this section, we discuss related work on visual localization, feature extraction and matching, and knowledge distillation. + +Visual localization. Visual localization methods can be roughly categorized as image-based and structure-based. Image-based systems recover camera poses by finding the most similar one in the database with global features, e.g. NetVLAD [2], CRN [27]. Due to the limited number of images in the database, they can only give approximate poses. To obtain more precise poses, structure-based methods build a sparse 3D map via SfM and estimate the pose via PnP from 2D-3D correspondences [12,54,57,58,69,79]. Some other works have tried to predict the camera pose directly from images, e.g. PoseNet [28] and its variations [80], or regress scene coordinates [5-7,26]. However, the former have been proved to perform similar to image retrieval [61] and latter are hard to scale to large-scale scenes [31]. + +Local features. Handcrafted features [3, 35, 53] have been investigated for decades and we refer readers a survey [38] for more details and focus on learned features. With the success of CNNs, learned features are proposed to + +replace handcrafted descriptors [15,17,36,41-43,49,71,72], detectors [13,68,70], or both [14,16,32,37,51,76,81]. HardNet [41] focuses on metric learning by maximizing the distance between the closest positive and negative examples. Instead of using pixel-wise correspondences for training, CAPS [77], PoSFeat [32] and PUMP [50] utilize camera pose and local consistency of matches for supervision. SuperPoint (SPP) [14] takes keypoint detection as a supervised task, training detector from synthetic geometric shapes. D2-Net [16] uses local maxima across the channels as score map. R2D2 [51] considers both the repeatability and reliability and adopts the average precision loss [23] for descriptor training. ASLFeat [37] employs deformable CNNs to learn shape-aware dense features. As they focus mainly on local reliability of features, regardless of their superior accuracy to handcrafted features, their performance is limited in the long-term large-scale localization task. To further improve the accuracy, some works [22,46,75] learn to filter unstable keypoints with extra matching score, repeatability or semantic labels. Essentially different with these methods, our model detects and extracts semantic-aware features automatically in an end-to-end fashion. As a result, our features are able to produce more accurate localization results. + +Advanced matcher. As NN matching is unable to incorporate spatial connections of keypoints for matching, advanced matchers are proposed to enhance the accuracy by leveraging the spatial context of a set of keypoints [8, 55, 65] or an image patch [9, 18, 33, 52, 67, 84]. SuperGlue (SPG) [55] utilizes graph neural networks with attention mechanism to propagate information among keypoints. It produces impressive accuracy, whereas its time complexity is quadratic to the number of keypoints. This problem is partially mitigated by using seeded matching [8] and cluster matching [65], but the time is still thousands of times slower than NN matching. Dense matchers [9, 33, 52, 67] compute pixel-wise correspondence from correlation volumes, so they undergo the high time and memory cost as sparse matchers [8, 55, 65]. Moreover, advanced matchers operates on image pairs as opposed to keypoints, so considering the number of image pairs, systems with advanced matchers could be much slower in real applications, as analyzed in [8]. In this paper, we embed high-level semantic information into local features implicitly to enhance both feature detection and description, enabling our model with simple NN matching to yield comparable results to advanced matchers. Our work provides a good trade-off of time and accuracy especially on devices with limited computing resources. + +Visual semantic localization. Compared to local features, high-level semantics are more robust to appearance changes and have been widely used in visual localization [7, 25, 26, 30, 31, 44, 62-64, 66, 73, 78]. LLN [78] and SVL [63] use the discriminative landmarks for place recognition. ToDayGAN [1] transfers night images to day im + +ages with GAN [20]. MFC [30], SMC [73], SSM [64], and DASGIL [25] incorporate segmentation networks into a standard localization pipeline to reject semantically-inconsistent matches. More recently, LBR [79] learns to recognize global instances for both coarse and fine localization. In fine localization, it filters unstable features and conducts instance-wise matching, achieving close accuracy to advanced matchers [55]. Unlike these methods, which require additional models to provide explicit semantic labels at test time, we embed the semantic information into the network and produce semantic-aware features directly from a single network. + +Knowledge distillation. Knowledge distillation techniques have been widely used for tasks including model compression [54] and knowledge transfer [82]. Our usage of pseudo ground-truth local reliability and semantic labels predicted by off-the-shelf networks is more like a knowledge transfer task. In this paper, we focus mainly on how to effectively leverage the high-level semantics for low-level feature extraction. + +# 3. Method + +As shown in Fig. 1, our model consists of an encoder $\mathcal{F}_{enc}$ and two decoders $\mathcal{F}_{det}$ and $\mathcal{F}_{desc}$ . $\mathcal{F}_{enc}$ extracts high-level features $\mathbf{X}$ from image $\mathbf{I} \in R^{3 \times H \times W}$ . $\mathcal{F}_{det}$ predicts the reliability map $\mathbf{S} \in R^{H \times W}$ and $\mathcal{F}_{desc}$ produces descriptors $\mathbf{X}_{desc} \in R^{128 \times \frac{H}{4} \times \frac{W}{4}}$ . $H$ and $W$ are the height and width of the image. In this section, we give details about how to implicitly incorporate semantic information into our feature detection and description processes. + +# 3.1. Semantic-guided Feature Detection + +The detector predicts the reliability map as $\mathbf{S} = \mathcal{F}_{\text{det}}(\mathbf{X})$ . Previously, the reliability map $\mathbf{S}$ is defined by the richness of textures in patches (e.g. response to corners [14] or blobs [35]). Recently, learned local features [16, 32, 37, 51] define the reliability on the discriminative ability of descriptors. As shown in Fig. 2, these two definitions, however, only reveal the reliability of pixels at a local level but lack the stability at a global level. Instead, we redefine the reliability of features by taking both the local reliability $\mathbf{S}_{\text{rel}}$ and global stability $\mathbf{S}_{\text{sta}}$ into consideration. + +Local reliability. Local reliability shows the robustness of a keypoint to appearance changes and viewpoint variations. Previous learning-based features adopt two strategies for reliable feature learning: learning from groundtruth corners [14] and learning from the discriminative ability of descriptors [16, 32, 37, 51]. We find that corners [14] are more robust compared to purely learned detectors, as shown in [50, 79], where SPP detector achieves better results when replacing other detectors. Therefore, following [54], we use the detection score $\mathbf{S}_{rel}$ of SPP [14] as pseudo groundtruth, which is one of the best corner detectors. At the same time, + +![](images/47d22b6221b867eb8fa373f4b9c7da05b058caaae06b65b9f01db9753b37a1d2.jpg) +Segmentation mask + +![](images/9ebcdbcd766078747251f1195fb64e095d60b87d6f0087967b88db86ed267771.jpg) +Global stability map $\mathbf{S}_{sta}$ +Figure 3. Semantic-guided feature detection. From left to right: semantic segmentation mask predicted by [11, 34], stability map $\mathbf{S}_{sta}$ generated according to Table 1, local reliability map $\mathbf{S}_{rel}$ produced by SuperPoint [14], and the final global reliability map $\mathbf{S}$ . Local reliability map gives very high score to clouds (red), trees (green), and pedestrians (pink) in addition to buildings, while the global reliability map removes unstable regions (sky, pedestrians), suppresses short-term objects (trees), and retains stable areas (buildings). + +![](images/c7213f1f951ed5d51b2188df8f50e3df5791cb975af547cead5e7d1dd8aaf140.jpg) +Local reliability map $\mathbf{S}_{rel}$ + +![](images/680f21d426a2a43a10a1d861863f51545ae06bdb5369cc7421ee50f97139f793.jpg) +Global reliability map S +High +Low + +local reliability is slightly adjusted by the discriminative ability of descriptors in the training process (see Sec. 3.2). + +Global stability. The global stability of a pixel is assigned based on the semantic label which it belongs to. Specifically, we group all 120 semantic labels in ADE20k dataset [83], according to how they change over time, into four categories, denoted as Volatile, Dynamic, Short-term, and Long-term in Table 1. Volatile objects (e.g. sky, water) are constantly changing and are redundant for localization. Dynamic objects (e.g. car, pedestrian) are moving everyday and could cause localization error by introducing wrong matches. Short-term objects (e.g. tree) can be used for short-term localization tasks (e.g. VO/SLAM), yet they are sensitive to changes of illumination (low albedo) and season conditions. Long-term objects (e.g. building, traffic light) are resistant to aforementioned changes and are ideal for long-term localization. + +Instead of directly filtering unstable features [64,73,79], we rerank features with stability values assigned empirically according to the extent of desired suppression. In detail, Long-term objects are robust for both short and long-term localization, so their stability value is set to 1.0. Short-term objects are useful for short-term localization, so we set their stability to 0.5. The stability value of Volatile and Dynamic categories is set to 0.1 as they are not useful for both short/long-term localization. Note that we set it to 0.1 rather than 0. Our reranking strategy encourages the model to use stable features preferentially and uses keypoints from other objects as compensation when insufficient stable keypoints can be found, increasing the robustness of our model to various tasks (e.g. feature matching, short-term localization). Fig. 3 shows stability map $\mathbf{S}_{sta}$ transformed from Table 1. Our current global stability is assigned based on predefined semantic labels, but a learned one might provide better performance and deserves further exploration. + +Semantic-guided detection. The global reliability map $\mathbf{S}_{gt}$ is generated by multiplying the local reliability map $\mathbf{S}_{rel}$ and global stability map, as $\mathbf{S}_{gt} = \mathbf{S}_{rel} \odot \mathbf{S}_{sta}$ ( $\odot$ is element-wise multiplication). Fig. 3 shows that local re + +
CategoryVolatileDynamicShort-termLong-termStability
sky, water✓0.1
vehicle, pedestrian✓0.1
plant, grass✓0.5
building, traffic light✓1.0
+ +Table 1. Stability map. Semantic labels are categorized into four groups denoted as Volatile, Dynamic, Short-term, and Long-term. Four categories are empirically assigned with different stability values according to their robustness to appearance changes. + +liability map gives high score for all pixels with rich textures even those from the sky, pedestrians, and trees, which are useless for localization. However, the global reliability map considering both local reliability and global stability discards these sensitive features and suppresses short-term keypoints effectively. The detection loss is defined as: + +$$ +L _ {d e t} = B C E (\mathbf {S}, \mathbf {S} _ {g t}), \tag {1} +$$ + +where $BCE$ denotes the binary cross-entropy loss. + +# 3.2. Semantic-guided Feature Description + +We also enhance the discriminative ability of descriptors by embedding semantics into them directly. Unlike previous descriptors [14, 37, 41, 50, 51, 77], which only differentiate keypoints based on local patch information, our descriptors enforce similarities of features in the same class while retain dissimilarities for intra-class matching. However, the two forces conflict with each other during the training process, because class-level discriminative ability needs to squeeze the space of descriptors in the same class and intra-class discriminative ability has to increase the space. A simple solution could be to set a hard margin for all classes (Fig. 4 left), but it would lead to the loss of objects' inner diversity (e.g., almost all traffic lights are similar but different buildings vary dramatically), which is indispensable for intra-class matching. To solve this problem, we design the inter-class and intra-class losses based on two different metrics (Fig. 4 right). + +![](images/79d33826dfedc3abcea07f9ba3900e0276c1db9e2e09ca5824b845b1a0709bfe.jpg) +Figure 4. Semantic-guided feature description. Simply optimizing inter- and intra-class losses with hard margins may cause accuracy loss due to two conflicting forces (push forces of inter- and intra-class) (left). Instead, we optimize the intra-class force with a hard margin, but apply a soft ranking loss for inter-class force to avoid conflicts and retain the inner diversity of each object (right). + +Inter-class loss. We first enforce the semantic consistency of features by maximizing the Euclidean distance between descriptors with different labels. This allows features to find correspondences from candidates with the same labels, reducing the search space and thus improving the matching accuracy. We define the inter-class loss based on triplet loss with a hard margin to separate all possible positive and negative keypoints with different labels in a batch: + +$$ +L _ {i n t e r} = \frac {1}{N} \sum \left(\left| \left| \mathbf {x} _ {i} ^ {c _ {1}} - \mathbf {x} _ {j} ^ {c _ {1}} \right| \right| _ {2} - \left| \left| \mathbf {x} _ {i} ^ {c _ {1}} - \mathbf {x} _ {k} ^ {c _ {2}} \right| \right| _ {2} + m\right), \tag {2} +$$ + +where $\mathbf{x}_i^{c_1},\mathbf{x}_j^{c_1}$ , and $\mathbf{x}_k^{c_2}$ are vectorized descriptors with labels of $c_{1},c_{1}$ , and $c_{2}$ ( $c_{1}\neq c_{2}$ ). $m$ is the margin and set to 1.0. This loss is conducted on features in the whole batch and $N$ is the total number of features in a batch. + +Intra-class loss. To make sure that the intra-class loss doesn't conflict with the inter-class loss, we relax the limitation of distances between descriptors with the same label. Instead of using triplet loss with hard margins, we adopt a soft ranking loss [23] by optimizing the rank of positive and negative samples rather than their distances. We use the same strategy as [51] to generate positive and negative samples for each feature $\mathbf{x}_i^c$ from self and the other images respectively, but enforce both positive and negative samples to share the same class label $c$ as $\mathbf{x}_i^c$ . By optimizing ranks of all samples rather than forcing a hard boundary between positive and negative pairs as the triplet loss with a hard margin does, the soft ranking loss also retains the diversity of features on objects in the same class, as shown in Fig. 4 (right). The ranking loss is based on the averaging precision (AP) loss [23, 51]: + +$$ +L _ {i n t r a} = \frac {1}{C} \sum_ {c = 1} ^ {C} \frac {1}{N _ {c}} \sum_ {i = 1} ^ {N _ {c}} \left(1 - A P \left(\mathbf {x} _ {i} ^ {c}, \mathbf {S} ^ {\mathbf {x} _ {i} ^ {c}}\right)\right), \tag {3} +$$ + +where $\mathbf{x}_i^c$ and $\mathbf{S}^{\mathbf{x}_i^c}$ are the query descriptor with label $c$ and corresponding predicted local reliability. $C$ and $N_{c}$ are the total number of classes and features in class $c$ . Note that the AP loss for sample $\mathbf{x}_i^c$ is weighted by its reliability $\mathbf{S}^{\mathbf{x}_i^c}$ . + +![](images/8137ba745d207b1628e1222c0a8ac591a3ade817d0059a29e1c5832b450b9db1.jpg) +Figure 5. Architecture of our network. Features are $4 \times$ down-sampling to save time and memory cost. Resblocks [24] are adopted to enhance the model's capacity. We enforce the consistency between outputs of the middle two layers of our encoder and features of the segmentation network to enhance the ability of our model to embed semantic information during the training process. + +Our final descriptor loss $L_{desc}$ is the combination of $L_{inter}$ and $L_{intra}$ , balanced by $w_{inter}$ and $w_{intra}$ : + +$$ +L _ {d e s c} = w _ {i n t e r} L _ {i n t e r} + w _ {i n t r a} L _ {i n t r a}. \tag {4} +$$ + +# 3.3. Implicit Feature Guidance + +With semantic-aware detection and description losses, our model is able to learn semantic-aware features. However, compared with feature learning, semantic prediction is a more complicated task, requiring powerful encoders and aggregation layers [4, 34] for semantic-aware feature embedding. To further improve the ability of our model to embed semantic information, we take inspiration from current knowledge distillation tasks [21] and introduce a feature consistency loss on intermediate outputs of the first three layers of the encoder. + +Fig. 5 shows the architecture of our network. We take intermediate outputs of the encoder of ConvNeXt [34] as supervision signal and enforce $l_{1}$ loss on features of the middle 2 layers of our model: + +$$ +L _ {f e a t} = \frac {1}{2} \sum_ {i = 1} ^ {2} | \mathbf {X} _ {i} - \mathbf {X} _ {i} ^ {\text {C o n v N e X t}} |, \tag {5} +$$ + +where $\mathbf{X}_i$ and $\mathbf{X}_i^{ConvNeXt}$ are features of the $i$ th layer in our model and ConvNeXt [34], respectively. The total loss $L_{total}$ is the combination of detection loss $L_{det}$ , description loss $L_{desc}$ , and feature consistency loss $L_{feat}$ with weights of $w_{det}, w_{desc}$ , and $w_{feat}$ : + +$$ +L _ {\text {t o t a l}} = w _ {\text {d e t}} L _ {\text {d e t}} + w _ {\text {d e s c}} L _ {\text {d e s c}} + w _ {\text {f e a t}} L _ {\text {f e a t}}. \tag {6} +$$ + +# 4. Experiments + +We first give implementation details. Then, we test our method on visual localization tasks in Sec. 4.1 and analyze the running time in Sec. 4.2. Finally, we perform an ablation + +
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
CAS.v1.1 [57]85.3 / 92.2 / 97.939.8 / 49.0 / 64.3
CSL [69]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
CPF [12]76.7 / 88.6 / 95.833.7 / 48.0 / 62.2
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
SSSM [64]71.8 / 91.5 / 96.858.2 / 76.5 / 90.8
VLM [78]62.4 / 71.8 / 79.935.7 / 44.9 / 54.1
SMC [73]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
LBR [79]88.3 / 95.6 / 98.884.7 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
LSIFT [35]82.8 / 88.1 / 93.130.6 / 43.9 / 58.2
SPP [14]80.5 / 87.4 / 94.242.9 / 62.2 / 76.5
D2Net [16]84.8 / 92.6 / 97.584.7 / 90.8 / 96.9
R2D2 [51]76.5 / 90.8 / 100.0
SIFT+CAPS [35, 77]77.6 / 86.7 / 99.0
SPP+CAPS [14, 77]82.7 / 87.8 / 100.0
SPP+LISRD [14, 49]78.6 / 86.7 / 98.0
SPP+PUMP [14, 50]74.4 / 88.0 / 98.4
R2D2+PUMP [14, 50]73.3 / 86.9 / 98.4
R2D2+LLF [14, 68]72.4 / 90.8 / 99.0
SOSNet+D2D [70, 72]73.5 / 83.7 / 96.9
PoSFeat [32]81.6 / 90.8 / 100.0
ASLFeat [37]81.6 / 87.8 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
MENCNet [52]76.5 / 84.7 / 98.0
Dual-RCNet [33]79.6 / 88.8 / 100.0
PDCNet [74]80.6 / 87.8 / 100.0
DGCNet [40]22.9 / 49.8 / 84.714.3 / 37.8 / 79.6
Pixloc [56]84.7 / 94.2 / 98.881.6 / 93.9 / 100.0
AHM [18]47.8 / 72.2 / 91.330.6 / 53.1 / 78.6
S2DNet [19]84.5 / 90.3 / 95.374.5 / 82.7 / 94.9
Patch2Pix [84]84.6 / 92.1 / 96.582.7 / 92.9 / 99.0
SPP+SPG [14, 55]89.6 / 95.4 / 98.886.7 / 93.9 / 100.0
SPP+SGMNet [8, 14]86.8 / 94.2 / 97.783.7 / 91.8 / 99.0
SPP+ClusterGNN [14, 65]89.4 / 95.5 / 98.581.6 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
+ +study in Sec. 4.3. More implementation details, results and analysis are provided in the supplementary material. + +Implementation. We use the identical training dataset as R2D2 [51]. The training dataset consists of reference images in Aachen_v1.0 dataset [60] and web images. As R2D2 [51] and LBR [79], training images are augmented with style transfer. To mitigate segmentation uncertainties caused by style transfer, semantic labels of stylized images are generated from their corresponding normal images. The network is implemented in PyTorch [48] and trained using Adam [29] optimizer with $\beta_{1} = 0.9$ , $\beta_{2} = 0.99$ , batch size of 4, weight decay of $4\times 10^{-4}$ on a single 3090Ti GPU for 40 epochs. The hyper-parameter $w_{intra}$ is set to 0.5, while $w_{inter}$ , $w_{det}$ , $w_{desc}$ , and $w_{feat}$ are set to 1.0. + +# 4.1. Long-term Large-scale Localization + +We test our method on Aachen (v1.0 and v1.1) [59, 60] and RobotCar-Seasons (RoCaS) [39, 60] datasets under various illumination, season, and weather conditions. Aachen_v1.0 contains 4,328 reference and 922 (824 day, 98 night) query images captured around the Aachen city center. Aachen_v1.1 expands v1.0 by adding 2,369 refer + +Table 2. Results on Aachen dataset [59,60]. The best and second best results are highlighted with bold and red fonts. + +
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
SLBR [79]89.1 / 96.1 / 99.377.0 / 90.1 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
HSIFT [35]72.2 / 78.4 / 81.719.4 / 23.0 / 27.2
SPP [14]87.9 / 93.6 / 96.870.2 / 84.8 / 93.7
D2Net [16]84.1 / 91.0 / 95.563.4 / 83.8 / 92.1
R2D2 [51]88.8 / 95.3 / 97.872.3 / 88.5 / 94.2
ASLFeat [37]88.0 / 95.4 / 98.270.7 / 84.3 / 94.2
CAPS+SIFT [35, 77]82.4 / 91.3 / 95.961.3 / 83.8 / 95.3
LISRD+SPP [14, 49]73.3 / 86.9 / 97.9
LLF+R2D2 [14, 68]71.2 / 81.2 / 94.2
PoSFeat [32]73.8 / 87.4 / 98.4
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
MSPP+SGMNet [8, 14]88.7 / 96.2 / 98.975.9 / 89.0 / 99.0
SPP+SPG [14, 55]89.8 / 96.1 / 99.477.0 / 90.6 / 100.0
Patch2Pix [84]86.4 / 93.0 / 97.572.3 / 88.5 / 97.9
LoFTER [67]88.7 / 95.6 / 99.078.5 / 90.6 / 99.0
ASpanFormer [9]89.4 / 95.6 / 99.077.5 / 91.6 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
+ +Table 3. Results on Aachen_v1.1 dataset [59,60]. The best and second best results are highlighted with bold and red fonts. + +ence and 93 night query images. RoCaS has 26,121 reference and 11,934 query images. It is challenging because of various conditions of day query images (rain, snow, dusk, winter) and poor lighting of night query images in suburban areas. We adopt the success ratio at error thresholds of $(2^{\circ},0.25m)$ , $(5^{\circ},0.5m)$ , $(10^{\circ},5m)$ as metric. We additionally provide results on Extended CMU-Seasons dataset in the supplementary material. + +Baselines. Baselines include classic systems (C) e.g. AS_v1.1 [57], CSL [69], and CPF [12] and methods using semantics (S), e.g. LLN [78], SMC [73], SSM [64], DASGIL [25], ToDayGAN [1] and LBR [79]. We also compare our model with learned features [14, 16, 37, 50, 51, 77] (L). As prior methods [14, 16, 37, 50, 51, 77], we use HLoc [54] pipeline for reconstruction and mutual nearest matching (MNN). NetVLAD [2] is used to offer 50 and 20 candidates for Aachen and RoCaS datasets, respectively. We additionally compare our approach with advanced sparse/dense matchers (M) e.g., Superglue (SPG) [55], SGMNet [8], ClusterGNN [65] and ASpanFormer [9], LoFTER [67], Patch2Pix [84], Dual-RCNet [33]. Their results are obtained from the visual benchmark or original papers. + +Comparison with classic methods (C). As shown in Table 2 and 4, our model outperforms all classic methods. As most these methods use SIFT [35], they are more sensitive to weather and illumination changes than learned features. + +Comparison with methods using explicit semantics (S). By leveraging semantic labels to filter potentially wrong matches, these models achieve better performance for day and night images in Table 2 and 4 but require segmentation results at test time. Our model outperforms all other approaches (except LBR [79]). LBR [79] reports + +
GroupMethodday (2°, 0.25m)night (5°, 0.5m)night-rain (10°, 5m)
CAS [57]43.6 / 76.0 / 94.01.6 / 3.9 / 10.52.0 / 10.9 / 18.0
CSL [69]45.3 / 73.5 / 90.10.2 / 0.9 / 5.30.9 / 4.3 / 9.1
CPF [12]48.0 / 78.0 / 94.22.3 / 6.6 / 15.34.5 / 12.3 / 18.6
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
SSSM [64]54.5 / 81.6 / 96.710.0 / 23.7 / 45.414.5 / 33.2 / 47.5
VLM [78]7.9 / 30.0 / 85.911.9 / 26.0 / 55.015.7 / 34.5 / 60.5
SMC [73]50.3 / 79.3 / 95.26.2 / 18.5 / 44.38.0 / 26.4 / 46.4
DASGIL-FD [25]8.7 / 30.7 / 81.31.6 / 4.8 / 19.91.8 / 4.3 / 21.6
ToDayGAN [1, 16]52.2 / 80.1 / 95.916.4 / 43.2 / 73.324.1 / 50.5 / 74.1
LBR [79]56.7 / 81.7 / 98.224.9 / 62.3 / 86.147.5 / 73.4 / 90.0
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
LSIFT [35]53.5 / 77.6 / 92.67.8 / 13.9 / 22.19.5 / 14.5 / 17.0
SPP [14]56.5 / 81.5 / 97.116.9 / 41.6 / 71.522.0 / 45.0 / 68.0
D2Net [16]54.5 / 80.0 / 95.318.0 / 39.7 / 53.922.7 / 40.5 / 56.1
R2D2 [51]57.4 / 81.9 / 97.918.3 / 43.4 / 67.829.1 / 50.2 / 68.2
CAPS [77]56.0 / 81.5 / 96.521.9 / 54.3 / 86.827.0 / 58.9 / 85.9
ASLFeat [37]57.1 / 81.9 / 98.423.5 / 55.9 / 80.141.1 / 66.8 / 86.1
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
MSPP+SPG [14, 55]56.9 / 81.7 / 98.124.2 / 62.6 / 87.442.3 / 69.3 / 90.2
Pixloc [56]56.9 / 82.0 / 98.124.2 / 62.8 / 88.445.5 / 72.5 / 90.7
AHM [18]45.7 / 78.0 / 95.116.2 / 55.3 / 93.628.4 / 68.4 / 95.5
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
+ +Table 4. Results on RobotCar-Seasons dataset [39,59]. The best and second best results are highlighted with bold and red fonts. + +excellent accuracy by selecting keypoints from buildings and performing instance-wise matching. Our method gives close results to LBR on day images but better performance on most night images, because our model does not require explicit semantic labels and is less fragile to segmentation errors especially for night images. LBR performs better than ours on night-train images in Table 4 because it is trained on augmented night rainy images, while our model is trained only on generated night images as R2D2. + +Comparison with learned features (L). Benefiting from training with massive data, learned features such as R2D2 [51], ASLFeat [37] and PoSFeat [32], outperform SIFT [3, 35]. As they extract keypoints indiscriminately, they are still more sensitive to appearance changes especially on night images than semantic-aware methods [79], as shown in Table 2 and 4. Our model extracts semantic-aware features directly, so it gives higher accuracy. + +Comparison with advanced matchers (M). In Table 2, 3 and 4, we also show the results of previous advanced matchers. We find that our approach outperforms the recent efficient variations of SPG [55] (e.g. SGMNet [8], ClusterGNN [65]) and gives competitive results to SPG, which achieves the best accuracy and is also the slowest method. Note that our model only uses the simple MNN for matching. We provide a detailed analysis of time and memory usage in Sec. 4.2 and argue that our method provides a good trade off between running time and accuracy especially on devices with limited computing resources. + +Robustness to the number of keypoints. We observe that most previous methods [16, 32, 37, 50, 51] extract keypoints with the number ranging from 10k (R2D2, ASLFeat) + +![](images/2c44646f60e3f346f5221a311ab0cf7a49418b93ba9c2717787fbb4f3719d70a.jpg) +Figure 6. Influence of the number of keypoints. We report results of different number (from 4k to 1k) of keypoints on Aachen_v1.1 [59, 60] at error threshold of $(2^{\circ}, 0.25m)$ . + +![](images/81961bf4112944786bd7035247ab67ceb1011d2b866cce479a49a883b49195e0.jpg) + +to 40k (PosFeat) for evaluation. Although increasing the number improves the accuracy, it causes the time cost as well, which should be taken into consideration especially on devices with limited computing resources. In this experiment, we test the ability of previous and our methods of extracting fewer but more robust features by reducing the number of keypoints from 4k to 1k. Note that results of [14, 51, 55, 79] are from LBR [79] and results of ASLFeat [37] are obtained by running official source code. + +Fig. 6 shows that as the number of keypoints decreases, all previous features [14, 37, 51] undergo dramatic accuracy loss especially for night images. SPP+SPG and LBR perform more robust because of the global context or semantics. With implicitly embedded semantics, our feature outperforms R2D2, ASLFeat, and SPP especially on night images and gives competitive results to SPP+SPG and LBR. + +Qualitative comparison. Fig. 7 shows the detection and matching results of query images under conditions of large illumination and season changes. Compared with prior features [14, 37, 51], which prefer keypoints from areas with rich textures, our method favors keypoints from objects robust for long-term localization (e.g. buildings). When insufficient keypoints can be found from stale regions, our model also uses keypoints from Short-term objects e.g. trees from compensation but assigns them with lower reliability. Besides, our feature gives more inliers for query images with large occlusions of trees and severe illumination changes. + +# 4.2. Running time analysis + +Table 5 demonstrates the test time of previous features [14, 37, 51, 79], matchers [8, 55], and our method. Our method (33.2ms) is faster than R2D2 (72.4ms) [51] and slower than SPP (13.1ms) [14], but has higher accuracy. Besides, our method is faster than LBR (9.2+30.1ms) [79], which uses explicit instances to filter keypoints and advanced matchers including SPP+SPG (13.1+52.2/146.5ms) [14, 55] and SPP+SGM (13.1+33.2/97.6ms) [8, 14]. As the matching method is ex + +![](images/e9f1efd44f84eb7643bbd7355a640ba9a7ab3523511b2794adaf0b7741e09e75.jpg) +Figure 7. Qualitative comparison of detection and matching. Left→right: SPP [14], R2D2 [51], ASLFeat [37] and our method. Our model favors keypoints on stable areas (reliability high→low: 1-250, 251-500, 501-750, 751-1000) and gives more inliers. + +![](images/0191b8133b7d76ad5596c5b813ea17a5e81798747fe9b6321341e19d68ed7ac9.jpg) + +![](images/87c24bb13b58163a926ef653d5698b0b1cef9ad8cfeca5bc318bbbb7c03c72cc.jpg) + +![](images/c35d60ed22c3c626d14df4f5cb2aea6d83304931c40c1160360916b4790b8fa2.jpg) + +
ModelInput sizeRunning time (ms)
SPP [14]1024×102413.1
R2D2 [51]1024×102472.4
ASLFeat* [37]1024×1024112.3
LBR (feature) [79]1024×102430.1
LBR (segmentation) [79]256×2569.2
SPG [55]2k×2k, 4k×4k52.2, 146.5
SGMNet [8]2k×2k, 4k×4k85.5, 97.6
Ours1024×102433.2
+ +tensively used for each image pair in mapping and localization processes, SPG/SGMNet are about 18.3/3.3 times slower than NN on Aachen dataset [59, 60] in the mapping process as discussed in [8]. Therefore, our approach could be a good trade off between accuracy and efficiency. + +# 4.3. Ablation study + +In Table 6, we verify the effectiveness of all components in our network by progressively adding the semantic detection (SD), description (SS), and feature consistency (SF) losses. We also compare results of SS loss with triplet and ranking as intra-class loss. Our baseline is trained with detection scores of SPP [14] as detector supervision and ap [23] loss for descriptor learning. After adding SD loss, the model performs better especially for night images. The accuracy is further improved by introducing SS loss because it augments the discriminative ability of descriptors with semantics. Compared to triplet loss with carefully tuned margin, ranking loss improves more accuracy as objects' inner diversity can be better retained by optimizing ranks of samples. SF loss enhances the network's ability of embedding semantic information, leading to further improvements. + +# 5. Limitations + +The first limitation is the hand-defined stability values. A learned stability map from training data could be more ro- + +Table 5. Running time. We report test time of prior features [14, 37, 51], matchers [8, 55] and our method (*in TensorFlow). + +
SDSSSFDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)Night
XXX85.4 / 93.6 / 97.971.2 / 84.3 / 98.4
✓XX87.3 / 94.3 / 97.872.8 / 88.5 / 99.5
X✓(triplet)X87.9 / 95.1 / 98.973.8 / 86.9 / 99.0
X✓(ranking)X87.9 / 95.3 / 98.774.9 / 89.5 / 99.0
✓✓X88.2 / 95.5 / 98.875.9 / 89.0 / 99.5
✓✓✓88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
+ +Table 6. Ablation study. We test the efficacy of semantic detection (SD), semantic description (SS), and semantic feature consistency (SF) losses. The best results are highlighted. + +bust and further improve the localization accuracy. Besides, semantic labels used in the paper are from ADE20K [83] and the number of these labels is limited. Fine grained semantic labels [31] from automatic segmentation might be more reliable in real applications. Moreover, this work focuses mainly on outdoor localization and may not work very well in indoor scenarios due to the significant differences of object classes. Better performance for indoor scenes can be achieved by retraining the model with redefined stability map for indoor objects. + +# 6. Conclusions + +In this paper, we implicitly incorporate semantic information into the feature detection and description processes, enabling the model to extract globally reliable features from a single network end-to-end. 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Knowledge as priors: Cross-modal knowledge generalization for datasets without superior knowledge. In CVPR, 2020. 3 +[83] Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. IJCV, 2019. 2, 4, 8 +[84] Qunjie Zhou, Torsten Sattler, and Laura Leal-Taixe. Patch2pix: Epipolar-guided pixel-level correspondences. In CVPR, 2021. 3, 6 \ No newline at end of file diff --git a/2023/SFD2_ Semantic-Guided Feature Detection and Description/images.zip b/2023/SFD2_ Semantic-Guided Feature Detection and Description/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e843d29be71729476006da48c871d24d05295f9f --- /dev/null +++ b/2023/SFD2_ Semantic-Guided Feature Detection and Description/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7ce8d6475e5ea46cf254e306ab8f7034809bf44839fd459dcf902cca72b9876f +size 775795 diff --git a/2023/SFD2_ Semantic-Guided Feature Detection and Description/layout.json b/2023/SFD2_ Semantic-Guided Feature Detection and Description/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..0aadf14a07e794e048064fe2ca779e53b40ae1de --- /dev/null +++ b/2023/SFD2_ Semantic-Guided Feature Detection and Description/layout.json @@ -0,0 +1,9263 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 115, + 103, + 478, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 103, + 478, + 121 + ], + "spans": [ + { + "bbox": [ + 115, + 103, + 478, + 121 + ], + "type": "text", + "content": "SFD2: Semantic-guided Feature Detection and Description" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 186, + 143, + 407, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 186, + 143, + 407, + 172 + ], + "spans": [ + { + "bbox": [ + 186, + 143, + 407, + 172 + ], + "type": "text", + "content": "Fei Xue Ignas Budvytis Roberto Cipolla University of Cambridge" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 227, + 173, + 363, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 227, + 173, + 363, + 185 + ], + "spans": [ + { + "bbox": [ + 227, + 173, + 363, + 185 + ], + "type": "text", + "content": "{fx221, ib255, rc10001} " + }, + { + "bbox": [ + 227, + 173, + 363, + 185 + ], + "type": "inline_equation", + "content": "@" + }, + { + "bbox": [ + 227, + 173, + 363, + 185 + ], + "type": "text", + "content": " cam.ac.uk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "type": "text", + "content": "Visual localization is a fundamental task for various applications including autonomous driving and robotics. Prior methods focus on extracting large amounts of often redundant locally reliable features, resulting in limited efficiency and accuracy, especially in large-scale environments under challenging conditions. Instead, we propose to extract globally reliable features by implicitly embedding high-level semantics into both the detection and description processes. Specifically, our semantic-aware detector is able to detect keypoints from reliable regions (e.g. building, traffic lane) and suppress unreliable areas (e.g. sky, car) implicitly instead of relying on explicit semantic labels. This boosts the accuracy of keypoint matching by reducing the number of features sensitive to appearance changes and avoiding the need of additional segmentation networks at test time. Moreover, our descriptors are augmented with semantics and have stronger discriminative ability, providing more inliers at test time. Particularly, experiments on long-term large-scale visual localization Aachen DayNight and RobotCar-Seasons datasets demonstrate that our model outperforms previous local features and gives competitive accuracy to advanced matchers but is about 2 and 3 times faster when using " + }, + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "type": "inline_equation", + "content": "2k" + }, + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "type": "inline_equation", + "content": "4k" + }, + { + "bbox": [ + 46, + 238, + 290, + 525 + ], + "type": "text", + "content": " keypoints, respectively. Code is available at https://github.com/feixue94/sfd2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 549, + 128, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 128, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 128, + 562 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Visual localization is key to various applications including autonomous driving and robotics. Structure-based algorithms [54, 57, 64, 69, 73, 79] involving mapping and localization processes still dominate in large-scale localization. Traditionally, handcrafted features (e.g. SIFT [3, 35], ORB [53]) are widely used. However, these features are mainly based on statistics of gradients of local patches and thus are prone to appearance changes such as illumination and season variations in the long-term visual localization task. With the success of CNNs, learning-based features [14, 16, 37, 45, 51, 76, 81] are introduced to replace handcrafted ones and have achieved excellent performance." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 331, + 211, + 523, + 323 + ], + "blocks": [ + { + "bbox": [ + 331, + 211, + 523, + 323 + ], + "lines": [ + { + "bbox": [ + 331, + 211, + 523, + 323 + ], + "spans": [ + { + "bbox": [ + 331, + 211, + 523, + 323 + ], + "type": "image", + "image_path": "f6e7685d36555c3f5fa3c09b9c4229a7a3aa87352b41537c0b6f0a00456fb68a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 331, + 547, + 388 + ], + "lines": [ + { + "bbox": [ + 305, + 331, + 547, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 547, + 388 + ], + "type": "text", + "content": "Figure 1. Overview of our framework. Our model implicitly incorporates semantics into the detection and description processes with guidance of an off-the-shelf segmentation network during the training process. Semantic- and feature-aware guidance are adopted to enhance its ability of embedding semantic information." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 412, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 547, + 544 + ], + "type": "text", + "content": "With massive data for training, these methods should be able to automatically extract keypoints from more reliable regions (e.g. building, traffic lane) by focusing on discriminative features [64]. Nevertheless, due to the lack of explicit semantic signals for training, their ability of selecting globally reliable keypoints is limited, as shown in Fig. 2 (detailed analysis is provided in Sec. B.1 in the supplementary material). Therefore, they prefer to extract locally reliable features from objects including those which are not useful for long-term localization (e.g. sky, tree, car), leading to limited accuracy, as demonstrated in Table 2." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 548, + 714 + ], + "type": "text", + "content": "Recently, advanced matchers based on sparse keypoints [8, 55, 65] or dense pixels [9, 18, 19, 33, 40, 47, 67, 74] are proposed to enhance keypoint/pixel-wise matching and have obtained remarkable accuracy. Yet, they have quadratic time complexity due to the attention and correlation volume computation. Moreover, advanced matchers rely on spatial connections of keypoints and perform image-wise matching as opposed to fast point-wise matching, so they take much longer time than nearest neighbor matching (NN) in both mapping and localization processes because of a large number of image pairs (much larger than the number of images) [8]. Alternatively, some works leverage semantics [64, 73, 79] to filter unstable features to eliminate wrong correspondences and report close even better accu" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5206" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "racy than advanced matchers [79]. However, they require additional segmentation networks to provide semantic labels at test time and are fragile to segmentation errors." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 289, + 443 + ], + "type": "text", + "content": "Instead, we implicitly incorporate semantics into a local feature model, allowing it to extract robust features automatically from a single network in an end-to-end fashion. In the training process, as shown in Fig. 1, we provide explicit semantics as supervision to guide the detection and description behaviors. Specifically, in the detection process, unlike most previous methods [14, 16, 32, 37, 51] adopting exhaustive detection, we employ a semantic-aware detection loss to encourage our detector to favor features from reliable objects (e.g. building, traffic lane) and suppress those from unreliable objects (e.g. sky). In the description process, rather than utilizing triplet loss widely used for descriptor learning [16, 41], we employ a semantic-aware description loss consisting of two terms: inter- and intra-class losses. The inter-class loss embeds semantics into descriptors by enforcing features with the same label to be close and those with different labels to be far. The intra-class loss, which is a soft-ranking loss [23], operates on features in each class independently and differentiates these features from objects of the same label. Such use of soft-ranking loss avoids the conflict with inter-class loss and retains the diversity of features in each class (e.g. features from buildings usually have larger diversity than those from traffic lights). With semantic-aware descriptor loss, our model is capable of producing descriptors with stronger discriminative ability. Benefiting from implicit semantic embedding, our method avoids using additional segmentation networks at test time and is less fragile to segmentation errors." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 444, + 287, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 551 + ], + "type": "text", + "content": "As the local feature network is much simpler than typical segmentation networks e.g. UperNet [10], we also adopt an additional feature-consistency loss on the encoder to enhance its ability of learning semantic information. To avoid using costly to obtain ground-truth labels, we train our model with outputs of an off-the-shelf segmentation network [11, 34], which has achieved SOTA performance on the scene parsing task [83], but other semantic segmentation networks (e.g. [10]) can also be used." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 552, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 624 + ], + "type": "text", + "content": "An overview of our system is shown in Fig. 1. We embed semantics implicitly into the feature detection and description network via the feature-aware and semantic-aware guidance in the training process. At test time, our model produces semantic-aware features from a single network directly. We summarize contributions as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 57, + 633, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 57, + 633, + 286, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 633, + 286, + 680 + ], + "spans": [ + { + "bbox": [ + 57, + 633, + 286, + 680 + ], + "type": "text", + "content": "- We propose a novel feature network which implicitly incorporates semantics into detection and description processes at training time, enabling the model to produce semantic-aware features end-to-end at test time." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 57, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 689, + 286, + 713 + ], + "type": "text", + "content": "- We adopt a combination of semantic-aware and feature-aware guidance strategy to make the model" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 169 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 169 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 169 + ], + "type": "image", + "image_path": "255208525ae22918530d2a590b0df382fbae6ee4262d03c58f3baa94fcec71d1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 178, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 258 + ], + "type": "text", + "content": "Figure 2. Locally reliable features. We show top 1k keypoints (reliability high→low: 1-250, 251-500, 501-750, 751-1000) of prior local features including SPP [14], D2Net [16], R2D2 [51], and ASLFeat [37]. They indiscriminatively give high reliability to patches with rich textures even from objects e.g. sky, tree, pedestrian and car, which are reliable for long-term localization (best view in color)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 325, + 281, + 512, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 281, + 512, + 293 + ], + "spans": [ + { + "bbox": [ + 325, + 281, + 512, + 293 + ], + "type": "text", + "content": "embed semantic information more effectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 300, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 300, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 315, + 300, + 545, + 337 + ], + "type": "text", + "content": "- Our method outperforms previous local features on the long-term localization task and gives competitive accuracy to advanced matchers but has higher efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 347, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 431 + ], + "type": "text", + "content": "Experiments show our method achieves a better tradeoff between accuracy and efficiency than advanced matchers [8, 55, 65] especially on devices with limited computing resources. We organize the rest of this paper as follows. In Sec. 2, we introduce related works. In Sec. 3, we describe our method in detail. We discuss experiments and limitations in Sec. 4 and Sec. 5 and conclude the paper in Sec. 6." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 441, + 392, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 392, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 392, + 453 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 462, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 497 + ], + "type": "text", + "content": "In this section, we discuss related work on visual localization, feature extraction and matching, and knowledge distillation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": "Visual localization. Visual localization methods can be roughly categorized as image-based and structure-based. Image-based systems recover camera poses by finding the most similar one in the database with global features, e.g. NetVLAD [2], CRN [27]. Due to the limited number of images in the database, they can only give approximate poses. To obtain more precise poses, structure-based methods build a sparse 3D map via SfM and estimate the pose via PnP from 2D-3D correspondences [12,54,57,58,69,79]. Some other works have tried to predict the camera pose directly from images, e.g. PoseNet [28] and its variations [80], or regress scene coordinates [5-7,26]. However, the former have been proved to perform similar to image retrieval [61] and latter are hard to scale to large-scale scenes [31]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Local features. Handcrafted features [3, 35, 53] have been investigated for decades and we refer readers a survey [38] for more details and focus on learned features. With the success of CNNs, learned features are proposed to" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5207" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 348 + ], + "type": "text", + "content": "replace handcrafted descriptors [15,17,36,41-43,49,71,72], detectors [13,68,70], or both [14,16,32,37,51,76,81]. HardNet [41] focuses on metric learning by maximizing the distance between the closest positive and negative examples. Instead of using pixel-wise correspondences for training, CAPS [77], PoSFeat [32] and PUMP [50] utilize camera pose and local consistency of matches for supervision. SuperPoint (SPP) [14] takes keypoint detection as a supervised task, training detector from synthetic geometric shapes. D2-Net [16] uses local maxima across the channels as score map. R2D2 [51] considers both the repeatability and reliability and adopts the average precision loss [23] for descriptor training. ASLFeat [37] employs deformable CNNs to learn shape-aware dense features. As they focus mainly on local reliability of features, regardless of their superior accuracy to handcrafted features, their performance is limited in the long-term large-scale localization task. To further improve the accuracy, some works [22,46,75] learn to filter unstable keypoints with extra matching score, repeatability or semantic labels. Essentially different with these methods, our model detects and extracts semantic-aware features automatically in an end-to-end fashion. As a result, our features are able to produce more accurate localization results." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 351, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 289, + 639 + ], + "type": "text", + "content": "Advanced matcher. As NN matching is unable to incorporate spatial connections of keypoints for matching, advanced matchers are proposed to enhance the accuracy by leveraging the spatial context of a set of keypoints [8, 55, 65] or an image patch [9, 18, 33, 52, 67, 84]. SuperGlue (SPG) [55] utilizes graph neural networks with attention mechanism to propagate information among keypoints. It produces impressive accuracy, whereas its time complexity is quadratic to the number of keypoints. This problem is partially mitigated by using seeded matching [8] and cluster matching [65], but the time is still thousands of times slower than NN matching. Dense matchers [9, 33, 52, 67] compute pixel-wise correspondence from correlation volumes, so they undergo the high time and memory cost as sparse matchers [8, 55, 65]. Moreover, advanced matchers operates on image pairs as opposed to keypoints, so considering the number of image pairs, systems with advanced matchers could be much slower in real applications, as analyzed in [8]. In this paper, we embed high-level semantic information into local features implicitly to enhance both feature detection and description, enabling our model with simple NN matching to yield comparable results to advanced matchers. Our work provides a good trade-off of time and accuracy especially on devices with limited computing resources." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 288, + 715 + ], + "type": "text", + "content": "Visual semantic localization. Compared to local features, high-level semantics are more robust to appearance changes and have been widely used in visual localization [7, 25, 26, 30, 31, 44, 62-64, 66, 73, 78]. LLN [78] and SVL [63] use the discriminative landmarks for place recognition. ToDayGAN [1] transfers night images to day im" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": "ages with GAN [20]. MFC [30], SMC [73], SSM [64], and DASGIL [25] incorporate segmentation networks into a standard localization pipeline to reject semantically-inconsistent matches. More recently, LBR [79] learns to recognize global instances for both coarse and fine localization. In fine localization, it filters unstable features and conducts instance-wise matching, achieving close accuracy to advanced matchers [55]. Unlike these methods, which require additional models to provide explicit semantic labels at test time, we embed the semantic information into the network and produce semantic-aware features directly from a single network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 216, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 547, + 312 + ], + "type": "text", + "content": "Knowledge distillation. Knowledge distillation techniques have been widely used for tasks including model compression [54] and knowledge transfer [82]. Our usage of pseudo ground-truth local reliability and semantic labels predicted by off-the-shelf networks is more like a knowledge transfer task. In this paper, we focus mainly on how to effectively leverage the high-level semantics for low-level feature extraction." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 321, + 362, + 334 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 321, + 362, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 321, + 362, + 334 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": "As shown in Fig. 1, our model consists of an encoder " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{enc}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " and two decoders " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{det}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{desc}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{enc}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " extracts high-level features " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " from image " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in R^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{det}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " predicts the reliability map " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{S} \\in R^{H \\times W}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{desc}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " produces descriptors " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{desc} \\in R^{128 \\times \\frac{H}{4} \\times \\frac{W}{4}}" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 341, + 547, + 437 + ], + "type": "text", + "content": " are the height and width of the image. In this section, we give details about how to implicitly incorporate semantic information into our feature detection and description processes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 444, + 493, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 493, + 456 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 493, + 456 + ], + "type": "text", + "content": "3.1. Semantic-guided Feature Detection" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "text", + "content": "The detector predicts the reliability map as " + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{S} = \\mathcal{F}_{\\text{det}}(\\mathbf{X})" + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "text", + "content": ". Previously, the reliability map " + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "text", + "content": " is defined by the richness of textures in patches (e.g. response to corners [14] or blobs [35]). Recently, learned local features [16, 32, 37, 51] define the reliability on the discriminative ability of descriptors. As shown in Fig. 2, these two definitions, however, only reveal the reliability of pixels at a local level but lack the stability at a global level. Instead, we redefine the reliability of features by taking both the local reliability " + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{\\text{rel}}" + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "text", + "content": " and global stability " + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{\\text{sta}}" + }, + { + "bbox": [ + 304, + 462, + 547, + 582 + ], + "type": "text", + "content": " into consideration." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "type": "text", + "content": "Local reliability. Local reliability shows the robustness of a keypoint to appearance changes and viewpoint variations. Previous learning-based features adopt two strategies for reliable feature learning: learning from groundtruth corners [14] and learning from the discriminative ability of descriptors [16, 32, 37, 51]. We find that corners [14] are more robust compared to purely learned detectors, as shown in [50, 79], where SPP detector achieves better results when replacing other detectors. Therefore, following [54], we use the detection score " + }, + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{rel}" + }, + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "type": "text", + "content": " of SPP [14] as pseudo groundtruth, which is one of the best corner detectors. 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Semantic-guided feature detection. From left to right: semantic segmentation mask predicted by [11, 34], stability map " + }, + { + "bbox": [ + 46, + 178, + 547, + 223 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{sta}" + }, + { + "bbox": [ + 46, + 178, + 547, + 223 + ], + "type": "text", + "content": " generated according to Table 1, local reliability map " + }, + { + "bbox": [ + 46, + 178, + 547, + 223 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{rel}" + }, + { + "bbox": [ + 46, + 178, + 547, + 223 + ], + "type": "text", + "content": " produced by SuperPoint [14], and the final global reliability map " + }, + { + "bbox": [ + 46, + 178, + 547, + 223 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 46, + 178, + 547, + 223 + ], + "type": "text", + "content": ". Local reliability map gives very high score to clouds (red), trees (green), and pedestrians (pink) in addition to buildings, while the global reliability map removes unstable regions (sky, pedestrians), suppresses short-term objects (trees), and retains stable areas (buildings)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 284, + 72, + 400, + 159 + ], + "blocks": [ + { + "bbox": [ + 284, + 72, + 400, + 159 + ], + "lines": [ + { + "bbox": [ + 284, + 72, + 400, + 159 + ], + "spans": [ + { + "bbox": [ + 284, + 72, + 400, + 159 + ], + "type": "image", + "image_path": "c7213f1f951ed5d51b2188df8f50e3df5791cb975af547cead5e7d1dd8aaf140.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 303, + 160, + 380, + 169 + ], + "lines": [ + { + "bbox": [ + 303, + 160, + 380, + 169 + ], + "spans": [ + { + "bbox": [ + 303, + 160, + 380, + 169 + ], + "type": "text", + "content": "Local reliability map " + }, + { + "bbox": [ + 303, + 160, + 380, + 169 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{rel}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 401, + 72, + 518, + 159 + ], + "blocks": [ + { + "bbox": [ + 401, + 72, + 518, + 159 + ], + "lines": [ + { + "bbox": [ + 401, + 72, + 518, + 159 + ], + "spans": [ + { + "bbox": [ + 401, + 72, + 518, + 159 + ], + "type": "image", + "image_path": "680f21d426a2a43a10a1d861863f51545ae06bdb5369cc7421ee50f97139f793.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 160, + 496, + 169 + ], + "lines": [ + { + "bbox": [ + 422, + 160, + 496, + 169 + ], + "spans": [ + { + "bbox": [ + 422, + 160, + 496, + 169 + ], + "type": "text", + "content": "Global reliability map S" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 525, + 72, + 544, + 82 + ], + "lines": [ + { + "bbox": [ + 525, + 72, + 544, + 82 + ], + "spans": [ + { + "bbox": [ + 525, + 72, + 544, + 82 + ], + "type": "text", + "content": "High" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 527, + 147, + 542, + 154 + ], + "lines": [ + { + "bbox": [ + 527, + 147, + 542, + 154 + ], + "spans": [ + { + "bbox": [ + 527, + 147, + 542, + 154 + ], + "type": "text", + "content": "Low" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 243, + 286, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 243, + 286, + 268 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 286, + 268 + ], + "type": "text", + "content": "local reliability is slightly adjusted by the discriminative ability of descriptors in the training process (see Sec. 3.2)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 269, + 286, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 286, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 286, + 448 + ], + "type": "text", + "content": "Global stability. The global stability of a pixel is assigned based on the semantic label which it belongs to. Specifically, we group all 120 semantic labels in ADE20k dataset [83], according to how they change over time, into four categories, denoted as Volatile, Dynamic, Short-term, and Long-term in Table 1. Volatile objects (e.g. sky, water) are constantly changing and are redundant for localization. Dynamic objects (e.g. car, pedestrian) are moving everyday and could cause localization error by introducing wrong matches. Short-term objects (e.g. tree) can be used for short-term localization tasks (e.g. VO/SLAM), yet they are sensitive to changes of illumination (low albedo) and season conditions. Long-term objects (e.g. building, traffic light) are resistant to aforementioned changes and are ideal for long-term localization." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 449, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 286, + 664 + ], + "type": "text", + "content": "Instead of directly filtering unstable features [64,73,79], we rerank features with stability values assigned empirically according to the extent of desired suppression. In detail, Long-term objects are robust for both short and long-term localization, so their stability value is set to 1.0. Short-term objects are useful for short-term localization, so we set their stability to 0.5. The stability value of Volatile and Dynamic categories is set to 0.1 as they are not useful for both short/long-term localization. Note that we set it to 0.1 rather than 0. Our reranking strategy encourages the model to use stable features preferentially and uses keypoints from other objects as compensation when insufficient stable keypoints can be found, increasing the robustness of our model to various tasks (e.g. feature matching, short-term localization). Fig. 3 shows stability map " + }, + { + "bbox": [ + 46, + 449, + 286, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{sta}" + }, + { + "bbox": [ + 46, + 449, + 286, + 664 + ], + "type": "text", + "content": " transformed from Table 1. Our current global stability is assigned based on predefined semantic labels, but a learned one might provide better performance and deserves further exploration." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": "Semantic-guided detection. The global reliability map " + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{gt}" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": " is generated by multiplying the local reliability map " + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{rel}" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": " and global stability map, as " + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_{gt} = \\mathbf{S}_{rel} \\odot \\mathbf{S}_{sta}" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 665, + 286, + 713 + ], + "type": "text", + "content": " is element-wise multiplication). Fig. 3 shows that local re" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 306, + 242, + 548, + 300 + ], + "blocks": [ + { + "bbox": [ + 306, + 242, + 548, + 300 + ], + "lines": [ + { + "bbox": [ + 306, + 242, + 548, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 548, + 300 + ], + "type": "table", + "html": "
CategoryVolatileDynamicShort-termLong-termStability
sky, water✓0.1
vehicle, pedestrian✓0.1
plant, grass✓0.5
building, traffic light✓1.0
", + "image_path": "1a7f1f4d5bae05625ecf1a1b326e84dba588f3198b0d62ba358844c3d7b7175b.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 312, + 545, + 357 + ], + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 357 + ], + "type": "text", + "content": "Table 1. Stability map. Semantic labels are categorized into four groups denoted as Volatile, Dynamic, Short-term, and Long-term. Four categories are empirically assigned with different stability values according to their robustness to appearance changes." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 375, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 375, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 545, + 447 + ], + "type": "text", + "content": "liability map gives high score for all pixels with rich textures even those from the sky, pedestrians, and trees, which are useless for localization. However, the global reliability map considering both local reliability and global stability discards these sensitive features and suppresses short-term keypoints effectively. The detection loss is defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 378, + 453, + 545, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 453, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 378, + 453, + 545, + 467 + ], + "type": "interline_equation", + "content": "L _ {d e t} = B C E (\\mathbf {S}, \\mathbf {S} _ {g t}), \\tag {1}", + "image_path": "1c94494ccbfa68a0afc13e0a91d467e81408741e271fb82b51342ffb27201c5d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 474, + 512, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 512, + 486 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 512, + 486 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 474, + 512, + 486 + ], + "type": "inline_equation", + "content": "BCE" + }, + { + "bbox": [ + 306, + 474, + 512, + 486 + ], + "type": "text", + "content": " denotes the binary cross-entropy loss." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 491, + 503, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 503, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 503, + 504 + ], + "type": "text", + "content": "3.2. Semantic-guided Feature Description" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "We also enhance the discriminative ability of descriptors by embedding semantics into them directly. Unlike previous descriptors [14, 37, 41, 50, 51, 77], which only differentiate keypoints based on local patch information, our descriptors enforce similarities of features in the same class while retain dissimilarities for intra-class matching. However, the two forces conflict with each other during the training process, because class-level discriminative ability needs to squeeze the space of descriptors in the same class and intra-class discriminative ability has to increase the space. A simple solution could be to set a hard margin for all classes (Fig. 4 left), but it would lead to the loss of objects' inner diversity (e.g., almost all traffic lights are similar but different buildings vary dramatically), which is indispensable for intra-class matching. To solve this problem, we design the inter-class and intra-class losses based on two different metrics (Fig. 4 right)." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5209" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 69, + 281, + 159 + ], + "blocks": [ + { + "bbox": [ + 55, + 69, + 281, + 159 + ], + "lines": [ + { + "bbox": [ + 55, + 69, + 281, + 159 + ], + "spans": [ + { + "bbox": [ + 55, + 69, + 281, + 159 + ], + "type": "image", + "image_path": "79d33826dfedc3abcea07f9ba3900e0276c1db9e2e09ca5824b845b1a0709bfe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 166, + 289, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 166, + 289, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 289, + 234 + ], + "type": "text", + "content": "Figure 4. Semantic-guided feature description. Simply optimizing inter- and intra-class losses with hard margins may cause accuracy loss due to two conflicting forces (push forces of inter- and intra-class) (left). Instead, we optimize the intra-class force with a hard margin, but apply a soft ranking loss for inter-class force to avoid conflicts and retain the inner diversity of each object (right)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 252, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 287, + 350 + ], + "type": "text", + "content": "Inter-class loss. We first enforce the semantic consistency of features by maximizing the Euclidean distance between descriptors with different labels. This allows features to find correspondences from candidates with the same labels, reducing the search space and thus improving the matching accuracy. We define the inter-class loss based on triplet loss with a hard margin to separate all possible positive and negative keypoints with different labels in a batch:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 67, + 359, + 287, + 378 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 359, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 67, + 359, + 287, + 378 + ], + "type": "interline_equation", + "content": "L _ {i n t e r} = \\frac {1}{N} \\sum \\left(\\left| \\left| \\mathbf {x} _ {i} ^ {c _ {1}} - \\mathbf {x} _ {j} ^ {c _ {1}} \\right| \\right| _ {2} - \\left| \\left| \\mathbf {x} _ {i} ^ {c _ {1}} - \\mathbf {x} _ {k} ^ {c _ {2}} \\right| \\right| _ {2} + m\\right), \\tag {2}", + "image_path": "523907f92165be2d7b888467b8148ec1ee8da9d3bef227f7f45c88b54818d65a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^{c_1},\\mathbf{x}_j^{c_1}" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_k^{c_2}" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": " are vectorized descriptors with labels of " + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "c_{1},c_{1}" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "c_{2}" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "c_{1}\\neq c_{2}" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": "). " + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": " is the margin and set to 1.0. This loss is conducted on features in the whole batch and " + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 381, + 287, + 430 + ], + "type": "text", + "content": " is the total number of features in a batch." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "text", + "content": "Intra-class loss. To make sure that the intra-class loss doesn't conflict with the inter-class loss, we relax the limitation of distances between descriptors with the same label. Instead of using triplet loss with hard margins, we adopt a soft ranking loss [23] by optimizing the rank of positive and negative samples rather than their distances. We use the same strategy as [51] to generate positive and negative samples for each feature " + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^c" + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "text", + "content": " from self and the other images respectively, but enforce both positive and negative samples to share the same class label " + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^c" + }, + { + "bbox": [ + 46, + 430, + 289, + 622 + ], + "type": "text", + "content": ". By optimizing ranks of all samples rather than forcing a hard boundary between positive and negative pairs as the triplet loss with a hard margin does, the soft ranking loss also retains the diversity of features on objects in the same class, as shown in Fig. 4 (right). The ranking loss is based on the averaging precision (AP) loss [23, 51]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 87, + 632, + 287, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 632, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 87, + 632, + 287, + 660 + ], + "type": "interline_equation", + "content": "L _ {i n t r a} = \\frac {1}{C} \\sum_ {c = 1} ^ {C} \\frac {1}{N _ {c}} \\sum_ {i = 1} ^ {N _ {c}} \\left(1 - A P \\left(\\mathbf {x} _ {i} ^ {c}, \\mathbf {S} ^ {\\mathbf {x} _ {i} ^ {c}}\\right)\\right), \\tag {3}", + "image_path": "994c2ea435ec601d9239df761d1fb5b5e7f00ee4a657662e832b645065bd84f7.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^c" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^{\\mathbf{x}_i^c}" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": " are the query descriptor with label " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": " and corresponding predicted local reliability. " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": " are the total number of classes and features in class " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": ". Note that the AP loss for sample " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^c" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": " is weighted by its reliability " + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{S}^{\\mathbf{x}_i^c}" + }, + { + "bbox": [ + 47, + 665, + 289, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 536, + 175 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 536, + 175 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 536, + 175 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 536, + 175 + ], + "type": "image", + "image_path": "8137ba745d207b1628e1222c0a8ac591a3ade817d0059a29e1c5832b450b9db1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 184, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 304, + 184, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 547, + 251 + ], + "type": "text", + "content": "Figure 5. Architecture of our network. Features are " + }, + { + "bbox": [ + 304, + 184, + 547, + 251 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 304, + 184, + 547, + 251 + ], + "type": "text", + "content": " down-sampling to save time and memory cost. Resblocks [24] are adopted to enhance the model's capacity. We enforce the consistency between outputs of the middle two layers of our encoder and features of the segmentation network to enhance the ability of our model to embed semantic information during the training process." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "content": "Our final descriptor loss " + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "inline_equation", + "content": "L_{desc}" + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "content": " is the combination of " + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "inline_equation", + "content": "L_{inter}" + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "inline_equation", + "content": "L_{intra}" + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "content": ", balanced by " + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "inline_equation", + "content": "w_{inter}" + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "inline_equation", + "content": "w_{intra}" + }, + { + "bbox": [ + 305, + 270, + 545, + 295 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 346, + 304, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 304, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 346, + 304, + 545, + 316 + ], + "type": "interline_equation", + "content": "L _ {d e s c} = w _ {i n t e r} L _ {i n t e r} + w _ {i n t r a} L _ {i n t r a}. \\tag {4}", + "image_path": "37e475d91f89e03db15210e3b3db694c32cc8d8659a8395c14adda61f775e53a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 331, + 453, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 453, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 453, + 344 + ], + "type": "text", + "content": "3.3. Implicit Feature Guidance" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 350, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 468 + ], + "type": "text", + "content": "With semantic-aware detection and description losses, our model is able to learn semantic-aware features. However, compared with feature learning, semantic prediction is a more complicated task, requiring powerful encoders and aggregation layers [4, 34] for semantic-aware feature embedding. To further improve the ability of our model to embed semantic information, we take inspiration from current knowledge distillation tasks [21] and introduce a feature consistency loss on intermediate outputs of the first three layers of the encoder." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": "Fig. 5 shows the architecture of our network. We take intermediate outputs of the encoder of ConvNeXt [34] as supervision signal and enforce " + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 304, + 469, + 545, + 518 + ], + "type": "text", + "content": " loss on features of the middle 2 layers of our model:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 352, + 525, + 545, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 525, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 352, + 525, + 545, + 558 + ], + "type": "interline_equation", + "content": "L _ {f e a t} = \\frac {1}{2} \\sum_ {i = 1} ^ {2} | \\mathbf {X} _ {i} - \\mathbf {X} _ {i} ^ {\\text {C o n v N e X t}} |, \\tag {5}", + "image_path": "778d1be09c8bbe67eea82fb29c73f1f8d1b35112dbe1b4a7ab15bca9f6d4a07f.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i^{ConvNeXt}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": " are features of the " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": "th layer in our model and ConvNeXt [34], respectively. The total loss " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "L_{total}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": " is the combination of detection loss " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "L_{det}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": ", description loss " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "L_{desc}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": ", and feature consistency loss " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "L_{feat}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": " with weights of " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "w_{det}, w_{desc}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "inline_equation", + "content": "w_{feat}" + }, + { + "bbox": [ + 304, + 566, + 545, + 628 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 321, + 635, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 635, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 321, + 635, + 545, + 649 + ], + "type": "interline_equation", + "content": "L _ {\\text {t o t a l}} = w _ {\\text {d e t}} L _ {\\text {d e t}} + w _ {\\text {d e s c}} L _ {\\text {d e s c}} + w _ {\\text {f e a t}} L _ {\\text {f e a t}}. \\tag {6}", + "image_path": "ae2c260cf89bd8b16772fa61823f5a2093c755755ceb239ab0d1ab82617b8b4b.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 388, + 671 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": "We first give implementation details. Then, we test our method on visual localization tasks in Sec. 4.1 and analyze the running time in Sec. 4.2. Finally, we perform an ablation" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5210" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 393 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 393 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 393 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 393 + ], + "type": "table", + "html": "
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
CAS.v1.1 [57]85.3 / 92.2 / 97.939.8 / 49.0 / 64.3
CSL [69]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
CPF [12]76.7 / 88.6 / 95.833.7 / 48.0 / 62.2
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
SSSM [64]71.8 / 91.5 / 96.858.2 / 76.5 / 90.8
VLM [78]62.4 / 71.8 / 79.935.7 / 44.9 / 54.1
SMC [73]52.3 / 80.0 / 94.329.6 / 40.8 / 56.1
LBR [79]88.3 / 95.6 / 98.884.7 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
LSIFT [35]82.8 / 88.1 / 93.130.6 / 43.9 / 58.2
SPP [14]80.5 / 87.4 / 94.242.9 / 62.2 / 76.5
D2Net [16]84.8 / 92.6 / 97.584.7 / 90.8 / 96.9
R2D2 [51]76.5 / 90.8 / 100.0
SIFT+CAPS [35, 77]77.6 / 86.7 / 99.0
SPP+CAPS [14, 77]82.7 / 87.8 / 100.0
SPP+LISRD [14, 49]78.6 / 86.7 / 98.0
SPP+PUMP [14, 50]74.4 / 88.0 / 98.4
R2D2+PUMP [14, 50]73.3 / 86.9 / 98.4
R2D2+LLF [14, 68]72.4 / 90.8 / 99.0
SOSNet+D2D [70, 72]73.5 / 83.7 / 96.9
PoSFeat [32]81.6 / 90.8 / 100.0
ASLFeat [37]81.6 / 87.8 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
MENCNet [52]76.5 / 84.7 / 98.0
Dual-RCNet [33]79.6 / 88.8 / 100.0
PDCNet [74]80.6 / 87.8 / 100.0
DGCNet [40]22.9 / 49.8 / 84.714.3 / 37.8 / 79.6
Pixloc [56]84.7 / 94.2 / 98.881.6 / 93.9 / 100.0
AHM [18]47.8 / 72.2 / 91.330.6 / 53.1 / 78.6
S2DNet [19]84.5 / 90.3 / 95.374.5 / 82.7 / 94.9
Patch2Pix [84]84.6 / 92.1 / 96.582.7 / 92.9 / 99.0
SPP+SPG [14, 55]89.6 / 95.4 / 98.886.7 / 93.9 / 100.0
SPP+SGMNet [8, 14]86.8 / 94.2 / 97.783.7 / 91.8 / 99.0
SPP+ClusterGNN [14, 65]89.4 / 95.5 / 98.581.6 / 93.9 / 100.0
Ours88.2 / 96.0 / 98.787.8 / 94.9 / 100.0
", + "image_path": "a7fac905f868d3732105ed1166ccabf65a1dcab9317c4659baff832f47d3aa12.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 446, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 287, + 470 + ], + "type": "text", + "content": "study in Sec. 4.3. More implementation details, results and analysis are provided in the supplementary material." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": "Implementation. We use the identical training dataset as R2D2 [51]. The training dataset consists of reference images in Aachen_v1.0 dataset [60] and web images. As R2D2 [51] and LBR [79], training images are augmented with style transfer. To mitigate segmentation uncertainties caused by style transfer, semantic labels of stylized images are generated from their corresponding normal images. The network is implemented in PyTorch [48] and trained using Adam [29] optimizer with " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.99" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": ", batch size of 4, weight decay of " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "4\\times 10^{-4}" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": " on a single 3090Ti GPU for 40 epochs. The hyper-parameter " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "w_{intra}" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": " is set to 0.5, while " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "w_{inter}" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "w_{det}" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "w_{desc}" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "inline_equation", + "content": "w_{feat}" + }, + { + "bbox": [ + 46, + 471, + 287, + 615 + ], + "type": "text", + "content": " are set to 1.0." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 623, + 238, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 238, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 238, + 635 + ], + "type": "text", + "content": "4.1. Long-term Large-scale Localization" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "We test our method on Aachen (v1.0 and v1.1) [59, 60] and RobotCar-Seasons (RoCaS) [39, 60] datasets under various illumination, season, and weather conditions. Aachen_v1.0 contains 4,328 reference and 922 (824 day, 98 night) query images captured around the Aachen city center. Aachen_v1.1 expands v1.0 by adding 2,369 refer" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 316, + 70, + 538, + 254 + ], + "blocks": [ + { + "bbox": [ + 47, + 401, + 288, + 425 + ], + "lines": [ + { + "bbox": [ + 47, + 401, + 288, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 288, + 425 + ], + "type": "text", + "content": "Table 2. Results on Aachen dataset [59,60]. The best and second best results are highlighted with bold and red fonts." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 70, + 538, + 254 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 538, + 254 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 538, + 254 + ], + "type": "table", + "html": "
GroupMethodDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)
SLBR [79]89.1 / 96.1 / 99.377.0 / 90.1 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
HSIFT [35]72.2 / 78.4 / 81.719.4 / 23.0 / 27.2
SPP [14]87.9 / 93.6 / 96.870.2 / 84.8 / 93.7
D2Net [16]84.1 / 91.0 / 95.563.4 / 83.8 / 92.1
R2D2 [51]88.8 / 95.3 / 97.872.3 / 88.5 / 94.2
ASLFeat [37]88.0 / 95.4 / 98.270.7 / 84.3 / 94.2
CAPS+SIFT [35, 77]82.4 / 91.3 / 95.961.3 / 83.8 / 95.3
LISRD+SPP [14, 49]73.3 / 86.9 / 97.9
LLF+R2D2 [14, 68]71.2 / 81.2 / 94.2
PoSFeat [32]73.8 / 87.4 / 98.4
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
MSPP+SGMNet [8, 14]88.7 / 96.2 / 98.975.9 / 89.0 / 99.0
SPP+SPG [14, 55]89.8 / 96.1 / 99.477.0 / 90.6 / 100.0
Patch2Pix [84]86.4 / 93.0 / 97.572.3 / 88.5 / 97.9
LoFTER [67]88.7 / 95.6 / 99.078.5 / 90.6 / 99.0
ASpanFormer [9]89.4 / 95.6 / 99.077.5 / 91.6 / 99.5
Ours88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
", + "image_path": "6439810a3f914547d81d58716e6c8ba4945b513284271b706f630f53b8794ee3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 261, + 545, + 283 + ], + "lines": [ + { + "bbox": [ + 306, + 261, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 545, + 283 + ], + "type": "text", + "content": "Table 3. Results on Aachen_v1.1 dataset [59,60]. The best and second best results are highlighted with bold and red fonts." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "text", + "content": "ence and 93 night query images. RoCaS has 26,121 reference and 11,934 query images. It is challenging because of various conditions of day query images (rain, snow, dusk, winter) and poor lighting of night query images in suburban areas. We adopt the success ratio at error thresholds of " + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "inline_equation", + "content": "(2^{\\circ},0.25m)" + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "inline_equation", + "content": "(5^{\\circ},0.5m)" + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "inline_equation", + "content": "(10^{\\circ},5m)" + }, + { + "bbox": [ + 304, + 306, + 545, + 402 + ], + "type": "text", + "content": " as metric. We additionally provide results on Extended CMU-Seasons dataset in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 403, + 546, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 546, + 570 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 546, + 570 + ], + "type": "text", + "content": "Baselines. Baselines include classic systems (C) e.g. AS_v1.1 [57], CSL [69], and CPF [12] and methods using semantics (S), e.g. LLN [78], SMC [73], SSM [64], DASGIL [25], ToDayGAN [1] and LBR [79]. We also compare our model with learned features [14, 16, 37, 50, 51, 77] (L). As prior methods [14, 16, 37, 50, 51, 77], we use HLoc [54] pipeline for reconstruction and mutual nearest matching (MNN). NetVLAD [2] is used to offer 50 and 20 candidates for Aachen and RoCaS datasets, respectively. We additionally compare our approach with advanced sparse/dense matchers (M) e.g., Superglue (SPG) [55], SGMNet [8], ClusterGNN [65] and ASpanFormer [9], LoFTER [67], Patch2Pix [84], Dual-RCNet [33]. Their results are obtained from the visual benchmark or original papers." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 571, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 571, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 571, + 545, + 619 + ], + "type": "text", + "content": "Comparison with classic methods (C). As shown in Table 2 and 4, our model outperforms all classic methods. As most these methods use SIFT [35], they are more sensitive to weather and illumination changes than learned features." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 545, + 692 + ], + "type": "text", + "content": "Comparison with methods using explicit semantics (S). By leveraging semantic labels to filter potentially wrong matches, these models achieve better performance for day and night images in Table 2 and 4 but require segmentation results at test time. Our model outperforms all other approaches (except LBR [79]). LBR [79] reports" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 473, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 473, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 473, + 712 + ], + "type": "text", + "content": "1https://www.visuallocalization.net/benchmark/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5211" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 289, + 290 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 290 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 290 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 290 + ], + "type": "table", + "html": "
GroupMethodday (2°, 0.25m)night (5°, 0.5m)night-rain (10°, 5m)
CAS [57]43.6 / 76.0 / 94.01.6 / 3.9 / 10.52.0 / 10.9 / 18.0
CSL [69]45.3 / 73.5 / 90.10.2 / 0.9 / 5.30.9 / 4.3 / 9.1
CPF [12]48.0 / 78.0 / 94.22.3 / 6.6 / 15.34.5 / 12.3 / 18.6
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
SSSM [64]54.5 / 81.6 / 96.710.0 / 23.7 / 45.414.5 / 33.2 / 47.5
VLM [78]7.9 / 30.0 / 85.911.9 / 26.0 / 55.015.7 / 34.5 / 60.5
SMC [73]50.3 / 79.3 / 95.26.2 / 18.5 / 44.38.0 / 26.4 / 46.4
DASGIL-FD [25]8.7 / 30.7 / 81.31.6 / 4.8 / 19.91.8 / 4.3 / 21.6
ToDayGAN [1, 16]52.2 / 80.1 / 95.916.4 / 43.2 / 73.324.1 / 50.5 / 74.1
LBR [79]56.7 / 81.7 / 98.224.9 / 62.3 / 86.147.5 / 73.4 / 90.0
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
LSIFT [35]53.5 / 77.6 / 92.67.8 / 13.9 / 22.19.5 / 14.5 / 17.0
SPP [14]56.5 / 81.5 / 97.116.9 / 41.6 / 71.522.0 / 45.0 / 68.0
D2Net [16]54.5 / 80.0 / 95.318.0 / 39.7 / 53.922.7 / 40.5 / 56.1
R2D2 [51]57.4 / 81.9 / 97.918.3 / 43.4 / 67.829.1 / 50.2 / 68.2
CAPS [77]56.0 / 81.5 / 96.521.9 / 54.3 / 86.827.0 / 58.9 / 85.9
ASLFeat [37]57.1 / 81.9 / 98.423.5 / 55.9 / 80.141.1 / 66.8 / 86.1
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
MSPP+SPG [14, 55]56.9 / 81.7 / 98.124.2 / 62.6 / 87.442.3 / 69.3 / 90.2
Pixloc [56]56.9 / 82.0 / 98.124.2 / 62.8 / 88.445.5 / 72.5 / 90.7
AHM [18]45.7 / 78.0 / 95.116.2 / 55.3 / 93.628.4 / 68.4 / 95.5
Ours56.9 / 81.6 / 97.427.6 / 66.2 / 90.243.0 / 71.1 / 90.0
", + "image_path": "00309e5a33c722a06e5406255a4b9b37c311649997e3b8770380dcf1fb45ed3d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 298, + 288, + 321 + ], + "lines": [ + { + "bbox": [ + 47, + 298, + 288, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 288, + 321 + ], + "type": "text", + "content": "Table 4. Results on RobotCar-Seasons dataset [39,59]. The best and second best results are highlighted with bold and red fonts." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 342, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 449 + ], + "type": "text", + "content": "excellent accuracy by selecting keypoints from buildings and performing instance-wise matching. Our method gives close results to LBR on day images but better performance on most night images, because our model does not require explicit semantic labels and is less fragile to segmentation errors especially for night images. LBR performs better than ours on night-train images in Table 4 because it is trained on augmented night rainy images, while our model is trained only on generated night images as R2D2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": "Comparison with learned features (L). Benefiting from training with massive data, learned features such as R2D2 [51], ASLFeat [37] and PoSFeat [32], outperform SIFT [3, 35]. As they extract keypoints indiscriminately, they are still more sensitive to appearance changes especially on night images than semantic-aware methods [79], as shown in Table 2 and 4. Our model extracts semantic-aware features directly, so it gives higher accuracy." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 677 + ], + "type": "text", + "content": "Comparison with advanced matchers (M). In Table 2, 3 and 4, we also show the results of previous advanced matchers. We find that our approach outperforms the recent efficient variations of SPG [55] (e.g. SGMNet [8], ClusterGNN [65]) and gives competitive results to SPG, which achieves the best accuracy and is also the slowest method. Note that our model only uses the simple MNN for matching. We provide a detailed analysis of time and memory usage in Sec. 4.2 and argue that our method provides a good trade off between running time and accuracy especially on devices with limited computing resources." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 714 + ], + "type": "text", + "content": "Robustness to the number of keypoints. We observe that most previous methods [16, 32, 37, 50, 51] extract keypoints with the number ranging from 10k (R2D2, ASLFeat)" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 325, + 70, + 425, + 194 + ], + "blocks": [ + { + "bbox": [ + 325, + 70, + 425, + 194 + ], + "lines": [ + { + "bbox": [ + 325, + 70, + 425, + 194 + ], + "spans": [ + { + "bbox": [ + 325, + 70, + 425, + 194 + ], + "type": "image", + "image_path": "2c44646f60e3f346f5221a311ab0cf7a49418b93ba9c2717787fbb4f3719d70a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 202, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 305, + 202, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 202, + 547, + 236 + ], + "type": "text", + "content": "Figure 6. Influence of the number of keypoints. We report results of different number (from 4k to 1k) of keypoints on Aachen_v1.1 [59, 60] at error threshold of " + }, + { + "bbox": [ + 305, + 202, + 547, + 236 + ], + "type": "inline_equation", + "content": "(2^{\\circ}, 0.25m)" + }, + { + "bbox": [ + 305, + 202, + 547, + 236 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 430, + 70, + 528, + 194 + ], + "blocks": [ + { + "bbox": [ + 430, + 70, + 528, + 194 + ], + "lines": [ + { + "bbox": [ + 430, + 70, + 528, + 194 + ], + "spans": [ + { + "bbox": [ + 430, + 70, + 528, + 194 + ], + "type": "image", + "image_path": "81961bf4112944786bd7035247ab67ceb1011d2b866cce479a49a883b49195e0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 257, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 365 + ], + "type": "text", + "content": "to 40k (PosFeat) for evaluation. Although increasing the number improves the accuracy, it causes the time cost as well, which should be taken into consideration especially on devices with limited computing resources. In this experiment, we test the ability of previous and our methods of extracting fewer but more robust features by reducing the number of keypoints from 4k to 1k. Note that results of [14, 51, 55, 79] are from LBR [79] and results of ASLFeat [37] are obtained by running official source code." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 365, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 449 + ], + "type": "text", + "content": "Fig. 6 shows that as the number of keypoints decreases, all previous features [14, 37, 51] undergo dramatic accuracy loss especially for night images. SPP+SPG and LBR perform more robust because of the global context or semantics. With implicitly embedded semantics, our feature outperforms R2D2, ASLFeat, and SPP especially on night images and gives competitive results to SPP+SPG and LBR." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 449, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 581 + ], + "type": "text", + "content": "Qualitative comparison. Fig. 7 shows the detection and matching results of query images under conditions of large illumination and season changes. Compared with prior features [14, 37, 51], which prefer keypoints from areas with rich textures, our method favors keypoints from objects robust for long-term localization (e.g. buildings). When insufficient keypoints can be found from stale regions, our model also uses keypoints from Short-term objects e.g. trees from compensation but assigns them with lower reliability. Besides, our feature gives more inliers for query images with large occlusions of trees and severe illumination changes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 587, + 433, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 433, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 433, + 600 + ], + "type": "text", + "content": "4.2. Running time analysis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Table 5 demonstrates the test time of previous features [14, 37, 51, 79], matchers [8, 55], and our method. Our method (33.2ms) is faster than R2D2 (72.4ms) [51] and slower than SPP (13.1ms) [14], but has higher accuracy. Besides, our method is faster than LBR (9.2+30.1ms) [79], which uses explicit instances to filter keypoints and advanced matchers including SPP+SPG (13.1+52.2/146.5ms) [14, 55] and SPP+SGM (13.1+33.2/97.6ms) [8, 14]. As the matching method is ex" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5212" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 172, + 209 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 172, + 209 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 172, + 209 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 172, + 209 + ], + "type": "image", + "image_path": "e9f1efd44f84eb7643bbd7355a640ba9a7ab3523511b2794adaf0b7741e09e75.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 217, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 547, + 243 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison of detection and matching. Left→right: SPP [14], R2D2 [51], ASLFeat [37] and our method. Our model favors keypoints on stable areas (reliability high→low: 1-250, 251-500, 501-750, 751-1000) and gives more inliers." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 72, + 296, + 209 + ], + "blocks": [ + { + "bbox": [ + 173, + 72, + 296, + 209 + ], + "lines": [ + { + "bbox": [ + 173, + 72, + 296, + 209 + ], + "spans": [ + { + "bbox": [ + 173, + 72, + 296, + 209 + ], + "type": "image", + "image_path": "0191b8133b7d76ad5596c5b813ea17a5e81798747fe9b6321341e19d68ed7ac9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 298, + 72, + 420, + 209 + ], + "blocks": [ + { + "bbox": [ + 298, + 72, + 420, + 209 + ], + "lines": [ + { + "bbox": [ + 298, + 72, + 420, + 209 + ], + "spans": [ + { + "bbox": [ + 298, + 72, + 420, + 209 + ], + "type": "image", + "image_path": "87c24bb13b58163a926ef653d5698b0b1cef9ad8cfeca5bc318bbbb7c03c72cc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 422, + 72, + 544, + 209 + ], + "blocks": [ + { + "bbox": [ + 422, + 72, + 544, + 209 + ], + "lines": [ + { + "bbox": [ + 422, + 72, + 544, + 209 + ], + "spans": [ + { + "bbox": [ + 422, + 72, + 544, + 209 + ], + "type": "image", + "image_path": "c35d60ed22c3c626d14df4f5cb2aea6d83304931c40c1160360916b4790b8fa2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 52, + 259, + 282, + 345 + ], + "blocks": [ + { + "bbox": [ + 52, + 259, + 282, + 345 + ], + "lines": [ + { + "bbox": [ + 52, + 259, + 282, + 345 + ], + "spans": [ + { + "bbox": [ + 52, + 259, + 282, + 345 + ], + "type": "table", + "html": "
ModelInput sizeRunning time (ms)
SPP [14]1024×102413.1
R2D2 [51]1024×102472.4
ASLFeat* [37]1024×1024112.3
LBR (feature) [79]1024×102430.1
LBR (segmentation) [79]256×2569.2
SPG [55]2k×2k, 4k×4k52.2, 146.5
SGMNet [8]2k×2k, 4k×4k85.5, 97.6
Ours1024×102433.2
", + "image_path": "fa7802482fb12feb1db125b275108155c2f6f022819951bf0222a073700d80ab.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 395, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 456 + ], + "type": "text", + "content": "tensively used for each image pair in mapping and localization processes, SPG/SGMNet are about 18.3/3.3 times slower than NN on Aachen dataset [59, 60] in the mapping process as discussed in [8]. Therefore, our approach could be a good trade off between accuracy and efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 461, + 139, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 461, + 139, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 461, + 139, + 474 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 479, + 288, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 660 + ], + "type": "text", + "content": "In Table 6, we verify the effectiveness of all components in our network by progressively adding the semantic detection (SD), description (SS), and feature consistency (SF) losses. We also compare results of SS loss with triplet and ranking as intra-class loss. Our baseline is trained with detection scores of SPP [14] as detector supervision and ap [23] loss for descriptor learning. After adding SD loss, the model performs better especially for night images. The accuracy is further improved by introducing SS loss because it augments the discriminative ability of descriptors with semantics. Compared to triplet loss with carefully tuned margin, ranking loss improves more accuracy as objects' inner diversity can be better retained by optimizing ranks of samples. SF loss enhances the network's ability of embedding semantic information, leading to further improvements." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 669, + 122, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 122, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 122, + 681 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "The first limitation is the hand-defined stability values. A learned stability map from training data could be more ro-" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 310, + 259, + 542, + 337 + ], + "blocks": [ + { + "bbox": [ + 47, + 353, + 287, + 376 + ], + "lines": [ + { + "bbox": [ + 47, + 353, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 287, + 376 + ], + "type": "text", + "content": "Table 5. Running time. We report test time of prior features [14, 37, 51], matchers [8, 55] and our method (*in TensorFlow)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 259, + 542, + 337 + ], + "lines": [ + { + "bbox": [ + 310, + 259, + 542, + 337 + ], + "spans": [ + { + "bbox": [ + 310, + 259, + 542, + 337 + ], + "type": "table", + "html": "
SDSSSFDay (2°, 0.25m)/(5°, 0.5m)/(10°, 5m)Night
XXX85.4 / 93.6 / 97.971.2 / 84.3 / 98.4
✓XX87.3 / 94.3 / 97.872.8 / 88.5 / 99.5
X✓(triplet)X87.9 / 95.1 / 98.973.8 / 86.9 / 99.0
X✓(ranking)X87.9 / 95.3 / 98.774.9 / 89.5 / 99.0
✓✓X88.2 / 95.5 / 98.875.9 / 89.0 / 99.5
✓✓✓88.2 / 96.0 / 98.778.0 / 92.1 / 99.5
", + "image_path": "3a0a045065c49c4ab58e74ac806ce66b7479ad498f2ab2bf0f56b832a6355a2d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 345, + 546, + 380 + ], + "lines": [ + { + "bbox": [ + 305, + 345, + 546, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 345, + 546, + 380 + ], + "type": "text", + "content": "Table 6. Ablation study. We test the efficacy of semantic detection (SD), semantic description (SS), and semantic feature consistency (SF) losses. The best results are highlighted." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 402, + 546, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 546, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 546, + 522 + ], + "type": "text", + "content": "bust and further improve the localization accuracy. Besides, semantic labels used in the paper are from ADE20K [83] and the number of these labels is limited. Fine grained semantic labels [31] from automatic segmentation might be more reliable in real applications. Moreover, this work focuses mainly on outdoor localization and may not work very well in indoor scenarios due to the significant differences of object classes. Better performance for indoor scenes can be achieved by retraining the model with redefined stability map for indoor objects." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 536, + 384, + 549 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 536, + 384, + 549 + ], + "spans": [ + { + "bbox": [ + 306, + 536, + 384, + 549 + ], + "type": "text", + "content": "6. Conclusions" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we implicitly incorporate semantic information into the feature detection and description processes, enabling the model to extract globally reliable features from a single network end-to-end. Specifically, we leverage outputs of an off-the-shelf semantic segmentation network as guidance and adopt a combination of semantic- and feature-aware guidance strategies to enhance the ability of embedding semantic information at training time. Experiments on large-scale visual localization datasets demonstrate that our method outperforms prior local features and gives competitive performance to advanced matchers but has higher efficiency. We argue that our approach could be a good tradeoff between accuracy and efficiency." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5213" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Asha Anoosheh, Torsten Sattler, Radu Timofte, Marc Pollefeys, and Luc Van Gool. 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In CVPR, 2021. 3, 6" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5216" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SGLoc_ Scene Geometry Encoding for Outdoor LiDAR Localization/56c4bde5-7fa2-4496-a50a-885b12091caa_content_list.json b/2023/SGLoc_ Scene Geometry Encoding for Outdoor LiDAR Localization/56c4bde5-7fa2-4496-a50a-885b12091caa_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..02594d0da39472b4c30cc7be0f977dad655645a1 --- /dev/null +++ b/2023/SGLoc_ Scene Geometry Encoding for Outdoor LiDAR Localization/56c4bde5-7fa2-4496-a50a-885b12091caa_content_list.json @@ -0,0 +1,1971 @@ +[ + { + "type": "text", + "text": "SGLoc: Scene Geometry Encoding for Outdoor LiDAR Localization", + "text_level": 1, + "bbox": [ + 138, + 130, + 828, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wen Li $^{1,2*}$ Shangshu Yu $^{1,2*}$ Cheng Wang $^{1,2\\dagger}$ Guosheng Hu $^{3}$ Siqi Shen $^{1,2}$ Chenglu Wen $^{1,2}$", + "bbox": [ + 106, + 179, + 861, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China $^{2}$ Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, School of Informatics, Xiamen University, China $^{3}$ Oosto, Belfast, UK", + "bbox": [ + 106, + 198, + 861, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 303, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "LiDAR-based absolute pose regression estimates the global pose through a deep network in an end-to-end manner, achieving impressive results in learning-based localization. However, the accuracy of existing methods still has room to improve due to the difficulty of effectively encoding the scene geometry and the unsatisfactory quality of the data. In this work, we propose a novel LiDAR localization framework, SGLoc, which decouples the pose estimation to point cloud correspondence regression and pose estimation via this correspondence. This decoupling effectively encodes the scene geometry because the decoupled correspondence regression step greatly preserves the scene geometry, leading to significant performance improvement. Apart from this decoupling, we also design a tri-scale spatial feature aggregation module and inter-geometric consistency constraint loss to effectively capture scene geometry. Moreover, we empirically find that the ground truth might be noisy due to GPS/INS measuring errors, greatly reducing the pose estimation performance. Thus, we propose a pose quality evaluation and enhancement method to measure and correct the ground truth pose. Extensive experiments on the Oxford Radar RobotCar and NCLT datasets demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art regression-based localization methods by $68.5\\%$ and $67.6\\%$ on position accuracy, respectively.", + "bbox": [ + 76, + 335, + 473, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 744, + 209, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Estimating the position and orientation of LiDAR from point clouds is a fundamental component of many applications in computer vision, e.g., autonomous driving, virtual reality, and augmented reality.", + "bbox": [ + 76, + 771, + 468, + 830 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contemporary state-of-the-art LiDAR-based localization methods explicitly use maps, which match the query point", + "bbox": [ + 76, + 832, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/48da2a67e01883c3383fa5bd20d43768b1a02685c4b94e2eb4a382e2eda7ada8.jpg", + "image_caption": [ + "Figure 1. LiDAR Localization results of our method and PosePN++ [51] (state-of-the-art method) in urban (left) and school (right) scenes from Oxford Radar RobotCar [2] and NCLT [34] datasets. The star indicates the starting position." + ], + "image_footnote": [], + "bbox": [ + 501, + 301, + 681, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e1bd0e578c82de888b89d2e8b364988a11a9ddbd3511247bd34ca88db909e32a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 301, + 890, + 433 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cloud with a pre-built 3D map [18, 23, 27, 49]. However, these methods usually require expensive 3D map storage and communication. One alternative is the regression-based approach, absolute pose regression (APR), which directly estimates the poses in the inference stage without maps [8, 24, 25, 40, 45]. APR methods typically use a CNN to encode the scene feature and a multi-layer perceptron to regress the pose. Compared to map-based methods, APR does not need to store the pre-built maps, accordingly reducing communications.", + "bbox": [ + 496, + 507, + 893, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For (1), APR networks learn highly abstract global scene representations, which allow the network to classify the scene effectively [25]. However, the global features usually cannot encode detailed scene geometry, which is the key to achieving an accurate pose estimation [10, 11, 38, 39]. Prior efforts have tried to minimize the relative pose or photometric errors to add geometry constraints by pose graph optimization (PGO) [4, 21] or novel view synthesis (NVS) [10, 11]. However, this introduces additional computations, limiting its wide applications. For (2), we empirically find current large-scale outdoor datasets suffer from various errors in the data due to GPS/INS measuring errors. It affects the APR learning process and makes it difficult to evaluate the localization results accurately. To our knowledge, the impact of data quality on localization has not been carefully investigated in the existing literature.", + "bbox": [ + 496, + 657, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 875, + 207, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 96, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "9286", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper proposes a novel framework, SGLoc, which can (1) effectively capture the scene geometry; In addition, we propose a data pre-processing method, Pose Quality Evaluation and Enhancement (PQEE), which can (2) improve data quality. (1) Existing APR methods conduct end-to-end regression from the point cloud in LiDAR coordinate to pose. Unlike them, SGLoc decouples this process to (a) regression from the point cloud in LiDAR coordinate to world coordinate and (b) pose estimation via the point cloud correspondence in LiDAR and world coordinate using RANSAC [17]. Importantly, step (a) can effectively preserve the scene geometry, which is key for pose estimation [10, 11, 38, 39]. To achieve high accuracy in step (a), we design a Tri-scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to effectively capture scene geometry. (2) We empirically find that pose errors in the data greatly degrade the pose estimation performance. For example, the ground truth pose obtained by GPS/INS suffers from measuring errors. To address this problem, we proposed a PQEE method which can measure the errors in the pose and correct them afterward. We conduct extensive experiments on Oxford Radar RobotCar [2] and NCLT [34] datasets, and results show that our method has great advantages over the state-of-the-art, as demonstrated in Fig. 1.", + "bbox": [ + 76, + 90, + 472, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 96, + 469, + 421, + 482 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences, which can effectively capture scene geometry, leading to significant performance improvement.", + "- We propose a novel Tri-Scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to further improve the encoding of scene geometry.", + "- We propose a generalized pose quality evaluation and enhancement (PQEE) method to measure and correct the pose errors in the localization data, improving $34.2\\% / 16.8\\%$ on position and orientation for existing LiDAR localization methods.", + "- Extensive experiments demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art LiDAR localization methods by $68.1\\%$ on position accuracy. In addition, to our knowledge, we are the first to reduce the error to the level of the sub-meter on some trajectories." + ], + "bbox": [ + 96, + 484, + 468, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 792, + 218, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Map-based Localization", + "text_level": 1, + "bbox": [ + 76, + 816, + 299, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Map-based methods aim to match the query point cloud with a pre-built 3D map, which can be classified into retrieval-based [18, 27, 30, 44, 49] and registration-based methods [14, 16, 20, 32, 37, 47]. Retrieval-based methods", + "bbox": [ + 76, + 839, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cast localization as a place recognition problem, which finds the most similar point cloud in the database. Registration-based localization performs fine matching between the query point cloud and the pred-built map. DCP [47] is an impressive work investigating geometry correspondences generated by weighted calculation for pose estimation. Unlike this, SGLoc directly regresses the correspondences. In addition, Some methods combine both retrieval and registration techniques to achieve better localization accuracy in dense urban areas [9, 12, 50, 52]. However, the high cost of 3D map storage and communication limits the widespread application of map-based methods.", + "bbox": [ + 496, + 90, + 893, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Regression-based Localization", + "text_level": 1, + "bbox": [ + 500, + 285, + 769, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, in camera localization, the scene coordinate regression method has been designed, which regresses 2D-3D correspondences and estimates the pose with PnP-RANSAC [4,6,7,22,54]. While these methods have shown impressive results in small and medium-sized scenes, e.g., 7-Scenes [42], they do not scale well to large scenes [5]. HSCNet attempts to solve this problem by conditioning discrete location labels around each pixel [28], but it still cannot be applied to large-scale outdoor scenes, e.g., the street scene in the Cambridge landmark dataset [25], which covers an area of about $5\\mathrm{hm}^2$ .", + "bbox": [ + 496, + 309, + 893, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Absolute pose regression. APR methods typically use the same basic pipeline: first, extracting high-level features using a CNN and then using these features to regress the 6-DoF pose. PoseNet [25] originally defines this task using a modified GoogleNet [43] to regress camera poses. Successors of PoseNet have focused on improving the framework through model architecture and loss function. E-PoseNet [33] proposes a translation and rotation equivariant CNN that directly induces representations of camera motions into the feature space. PAE [41] uses the pose auto-encoders framework to significantly reduce model parameters. However, the above methods learn highly abstract global scene representations, leading to various wrong predictions due to the lack of effective scene geometry encoding.", + "bbox": [ + 496, + 477, + 893, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent research suggests scene geometry is key to accurate pose estimation [10, 11, 38, 39]. Geometric PoseNet [24] investigates geometric loss for learning to regress position and orientation simultaneously with scene geometry. MapNet [8] adds pairwise geometric constraints between video frames using additional VO algorithms. AtLoc [45] utilizes a self-attention mechanism to adaptively focus on the import targets in the scene. MS-Transformer [40] proposes a transformer-based method to learn robust features. DirectPoseNet [11] adapts additional photometric loss by comparing the query image with NVS on the predicted pose. DFNet [10] explores a direct matching scheme in feature space, leading to a more robust performance than DirectPoseNet. However, these methods require auxiliary algo", + "bbox": [ + 496, + 689, + 895, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "9287", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a73edaff36b80adab289edf23ccf2765d99bcd627b37c1e258b8c3551d8b1cd8.jpg", + "image_caption": [ + "(1) Point cloud correspondence regression", + "Legend" + ], + "image_footnote": [ + "3D coordinates" + ], + "bbox": [ + 116, + 109, + 841, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c5b0fd8bcdb3ff59b582dfc2f60d885757ba9468a6a31a5964009aaa00d57fa0.jpg", + "image_caption": [ + "(2) 6-DoF pose estimation", + "Figure 2. Overview of the proposed framework including point cloud correspondence regression (top row) and 6-DoF pose estimation (bottom row). $F_{1}$ , $F_{2}$ , and $F_{3}$ are the extracted feature maps with different receptive fields." + ], + "image_footnote": [ + "Point features", + "Aggregated feature", + "$\\mathbb{X}$ Pose Hypotheses", + "Final Estimate" + ], + "bbox": [ + 117, + 247, + 648, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "rithms, e.g., PGO, NVS, introducing additional computations. Unlike these methods, we decouple the pose estimation process to (1) regression point cloud correspondence and (2) pose estimate via the correspondence using RANSAC. Through step (1), scene geometry can be effectively encoded without additional computations.", + "bbox": [ + 75, + 402, + 470, + 492 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, LiDAR-based APR methods, e.g., PointLoc [46], PoseSOE [51], and PosePN++ [51], have shown impressive performance on large-scale outdoor datasets because the point cloud is robust to illumination changes and rich in geometric information. However, effectively encoding scene geometry remains quite challenging.", + "bbox": [ + 75, + 493, + 470, + 584 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 599, + 168, + 614 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recent APR methods have achieved impressive results in localization. However, they do not effectively encode the scene geometry and measure the data quality, leading to the accuracy still having room to improve. In this paper, we propose SGLoc and a Pose Quality Evaluation Enhancement (PQEE) method to address these problems. Sec. 3.1 elaborates SGLoc, which can effectively capture the scene geometry. Then, a PQEE method (Sec. 3.2) is proposed to measure and correct the pose errors in the data.", + "bbox": [ + 75, + 625, + 468, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.SGLoc", + "text_level": 1, + "bbox": [ + 76, + 770, + 166, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now introduce the proposed SGLoc, as shown in Fig. 2, which can be divided into (1) point cloud correspondence regression: convert the Raw LiDAR Point Cloud (RPC) to its corresponding Point Cloud in World coordinate frame (WPC) and (2) 6-DoF pose estimation: estimate pose via matching RPC and WPC. In this work, we design a sparse-convolution-based FCN [15,31] to implement SGLoc,", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "which contains a feature extractor, a Tri-Scale Spatial Feature Aggregation (TSFA) module, and a regressor. The feature extractor and regressor generate feature maps with different receptive fields and achieve point cloud correspondence via regression, respectively. The TSFA module and intergeometric consistency constraint (IGCC) loss are proposed to effectively capture scene geometry.", + "bbox": [ + 496, + 402, + 893, + 508 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "**Framework.** Here we formulate the framework of SGLoc. Given the query point cloud $P_{t} \\in \\mathbb{R}^{N \\times 3}$ , we aim to estimate its global 6-DoF pose $\\mathbf{p}$ . Each pose $\\mathbf{p} = [\\mathbf{x}, \\mathbf{q}]$ is represented by a position vector $\\mathbf{x} \\in \\mathbb{R}^3$ and an orientation vector $\\mathbf{q} \\in \\mathbb{R}^r$ (e.g., a 4D unit quaternion or a 3D Euler angle). Hence, we first define the query point cloud pose $\\mathbf{p}$ as the transformation that maps 3D points in LiDAR coordinate frame, denoted as $\\mathbf{l}$ , to 3D points in world coordinate frame, denoted as $\\mathbf{w}$ , i.e.", + "bbox": [ + 496, + 508, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} = T l _ {i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 658, + 637, + 890, + 652 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $i$ denotes the point index in the query point cloud; $T$ is a $4 \\times 4$ matrix representation of the pose $\\mathbf{p}$ .", + "bbox": [ + 496, + 659, + 890, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then, we denote the complete set of scene coordinates with a global pose for the query point cloud as $\\mathcal{V}$ , i.e., $y_{i} \\in \\mathcal{V}$ . As shown in Fig. 2, (1) for point cloud correspondence regression, we utilize a neural network to learn a function $\\mathcal{F}: \\mathcal{V} = \\mathcal{F}(P_t)$ . (2) Regarding 6-DoF pose estimation during inference, we utilize the RANSAC algorithm to select $M$ group from the predicted correspondence $\\mathcal{V}$ , and optimize the energy function as follows:", + "bbox": [ + 496, + 689, + 890, + 809 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT ^ {\\prime} = \\arg \\min _ {T} \\sum_ {i} ^ {| M |} \\| T l _ {i} - w _ {i} \\| _ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 813, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $M$ is set to 3; $i$ denotes the point index; $T^{\\prime}$ is the estimated transformation matrix. Then, $T^{\\prime}$ can be used to calculate the above energy function of each correspondence", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "9288", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/57dffb77d13a6cb50b3dc257de79f4b65eee352dd47fb1db539256483d8d6c19.jpg", + "image_caption": [ + "Figure 3. Tri-Scale Spatial Feature Aggregation (TSFA) Module." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 468, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in $\\mathcal{V}$ to filter outliers. The above process will be repeated until convergence. Finally, the estimated $T^{\\prime}$ can easily be converted into a vectorized pose.", + "bbox": [ + 75, + 309, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is worth noting that during training, SGLoc only requires the input point cloud and the pose, which allows for effective scene geometry encoding by minimizing correspondence distance without any additional computations.", + "bbox": [ + 75, + 354, + 470, + 415 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tri-scale spatial feature aggregation. As described above, SGLoc estimates the pose via the regressed correspondence $\\mathcal{V}$ . Therefore, the spatial details in network features are critical to localization accuracy. To effectively capture the spatial details at shallow layers, inspired by the attention mechanism [19, 29, 53], we introduce a Tri-Scale Spatial Feature Aggregation (TSFA) module.", + "bbox": [ + 75, + 415, + 470, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2, the TSFA module takes the low-level features $F_{1}$ and $F_{2}$ and high-level feature $F_{3}$ as the input. We elaborate the architecture of TSFA module in Fig. 3. For convenience, we refer $F_{1}' = \\mathcal{H}(\\mathcal{D}(\\mathcal{H}(F_{1})), F_{2}' = \\mathcal{H}(\\mathcal{D}(\\mathcal{H}(F_{2}))$ and $F_{3}' = \\mathcal{H}(F_{3})$ ), where $\\mathcal{D}$ indicates the down-sampling and $\\mathcal{H}$ denotes the convolution followed by a batch normalization and a ReLU activation function. We first squeeze the channels of the features $(F_{1}, F_{2}, F_{3})$ to 1. Then, we conduct the addition operation and sigmoid activation to obtain the spatial attention mask, which can adaptively enhance spatial details. Finally, we apply dot product and concatenation to achieve a powerful feature with rich spatial details and structure information. The output can be expressed as:", + "bbox": [ + 75, + 521, + 472, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {o} = \\left[ \\sigma \\left(F _ {1} ^ {\\prime} + F _ {3} ^ {\\prime}\\right) \\odot F _ {1}, \\sigma \\left(F _ {2} ^ {\\prime} + F _ {3} ^ {\\prime}\\right) \\odot F _ {2}, F _ {3} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 739, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma$ is the sigmoid function; $\\odot$ is dot product; $[\\cdot]$ denotes the concatenation.", + "bbox": [ + 75, + 763, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inter-geometric consistency constraint. Training the network with $l1$ loss $(\\mathcal{L}_{L1})$ can effectively minimize the distance between the predicted and the ground truth scene coordinates. However, the above constraint is a node-wise loss, which supervises each correspondence individually. This is unfavorable for learning scene geometry. Inspired by spatial compatibility [1, 13], which assumes that two correspondences", + "bbox": [ + 75, + 795, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Pseudocode for PQEE method", + "text_level": 1, + "bbox": [ + 498, + 90, + 792, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: Raw point cloud set $P_r$ and pose set $T_r$ ; Standard point cloud set $P_s$ and pose set $T_s$", + "bbox": [ + 498, + 107, + 890, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: Pose error $E'$ ; Quality enhanced pose set $T_r'$", + "bbox": [ + 500, + 137, + 852, + 152 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initialization: Build submaps $M_r = \\{M_{r_1}, \\ldots, M_{r_n}\\}$ by $P_r$ and $T_r$ ; Build submaps $M_s = \\{M_{s_1}, \\ldots, M_{s_m}\\}$ by $P_s$ and $T_s$ ; $E \\gets 0$ ; $N \\gets 0$", + "bbox": [ + 500, + 152, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: for all $M_{r_i} \\in M_r$ do", + "2: Search $M_{r_i}$ 's nearest $M_{s_j}$", + "3: Register to obtain correspondences $\\mathcal{C}$ and $T_{ij}$", + "4: $T_{r_i}' \\gets T_{ij}T_{s_i}$", + "5: for all $C_k \\in C$ do", + "6: Calculate the Euclidean distance $d_{k}$", + "7: $E\\gets E + d_{k}$", + "8: $N\\gets N + 1$", + "9: return $E / N$ , $T_r'$" + ], + "bbox": [ + 509, + 200, + 849, + 337 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "have a higher score if the difference of spatial distance between them, we propose an Inter-Geometric Consistency Constraint (IGCC) loss to well learn scene geometry:", + "bbox": [ + 496, + 366, + 893, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I G C C} = \\frac {1}{| \\mathcal {Y} | ^ {2}} \\sum_ {i, j} \\| d _ {i, j} - d _ {i, j} ^ {*} \\| _ {1}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 412, + 890, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d_{i,j}^{*} = \\| y_{i}^{*} - y_{j}^{*}\\|_{1}$ is the ground truth inter-geometric consistency value. This constraint supervises the pairwise distance between the correspondences, serving as a complement to the node-wise supervision.", + "bbox": [ + 496, + 452, + 893, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss function. During training, the point cloud with global poses predicted by the network $\\mathcal{F}$ is optimized by $\\mathcal{L}_{L1}$ and $\\mathcal{L}_{IGCC}$ . For $\\mathcal{L}_{L1}$ , we minimize the average plain Euclidean distance between the predicted scene coordinates $y_{i}$ , and the ground truth of scene coordinates $y_{i}^{*}$ :", + "bbox": [ + 496, + 513, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L 1} = \\frac {1}{| \\mathcal {Y} |} \\sum_ {y _ {i} \\in \\mathcal {Y}} \\| y _ {i} - y _ {i} ^ {*} \\| _ {1}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 590, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The aforementioned $\\mathcal{L}_{IGCC}$ works with $\\mathcal{L}_{L1}$ to come up with the final loss:", + "bbox": [ + 496, + 628, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {L 1} + \\lambda \\mathcal {L} _ {I G C C}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 666, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyper-parameter to balance the two constraints.", + "bbox": [ + 496, + 686, + 893, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Pose Quality Evaluation and Enhancement", + "text_level": 1, + "bbox": [ + 500, + 710, + 864, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For localization, a high-quality dataset should precisely provide the same position values in the same position on different days. However, existing large-scale outdoor datasets do not satisfy this requirement since various pose errors in the data caused by GPS/INS measuring errors. We empirically find these inaccuracies significantly degrade localization accuracy. Therefore, we propose a Pose Quality Evaluation and Enhancement (PQEE) method to measure and correct pose errors in the data, see Alg. 1.", + "bbox": [ + 496, + 734, + 893, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first build submaps from point clouds and poses provided by datasets. Then, for each submap of the raw point", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "9289", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/90010f32b8cf0dc5bae745d7c9a8b3b7b979640a85ffe6f8df001d9f37da516b.jpg", + "image_caption": [ + "(a)PNVLAD" + ], + "image_footnote": [], + "bbox": [ + 102, + 95, + 282, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e5423cb17478dfb3058ef2a4622a143c1e900e5939e9488c0c4687179f757ff0.jpg", + "image_caption": [ + "(b) DCP" + ], + "image_footnote": [], + "bbox": [ + 295, + 95, + 473, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/268b7240e741cb181ada7f13b87afe534f16bc2494d269f1ec031d1bbc9aa587.jpg", + "image_caption": [ + "(c) PosePN" + ], + "image_footnote": [], + "bbox": [ + 490, + 95, + 669, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/58cfccdf59ba8d7db651f090db936565e0a6babdf2e375ef0350ef4156a22294.jpg", + "image_caption": [ + "(d) PosePN++" + ], + "image_footnote": [], + "bbox": [ + 684, + 95, + 861, + 196 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d94bc72c99d2b637aa8e5ecefe72ea931085de7e714971efab0376a152da1ebd.jpg", + "image_caption": [ + "(e) PoseSOE" + ], + "image_footnote": [], + "bbox": [ + 102, + 215, + 282, + 316 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a4899a1570f7b9a5f6b3507fa62a74518237fa0d7a26ae85c1c8464e170adb6a.jpg", + "image_caption": [ + "(f) PoseMinkLoc" + ], + "image_footnote": [], + "bbox": [ + 295, + 215, + 473, + 316 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b5a9b7ffb59944be312063e26181380a6b8a2e957d09202d98b9df77fbf9bb23.jpg", + "image_caption": [ + "(g) PointLoc" + ], + "image_footnote": [], + "bbox": [ + 486, + 215, + 671, + 316 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/239c77ba2e1d7f24a1fb3537f53a0d4b7ebe75104299ca087c5cb101bc0ff812.jpg", + "image_caption": [ + "(h) SGLoc" + ], + "image_footnote": [], + "bbox": [ + 684, + 215, + 861, + 316 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/87073f0deae97f074b1d431aa1c653b6e8e005a3d6621a3cab6b27f83c244d39.jpg", + "image_caption": [ + "(i) PNVLAD" + ], + "image_footnote": [], + "bbox": [ + 102, + 335, + 282, + 436 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/63b70b9f182311b4204207211bb1c8ba6dc8a1e3bcb33f40207e3867ba81725f.jpg", + "image_caption": [ + "(j) DCP" + ], + "image_footnote": [], + "bbox": [ + 295, + 335, + 473, + 436 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e8d0e6eac27821690801ceab857d8d628755af49467c3dc75a0cd0b7b93453e9.jpg", + "image_caption": [ + "(k) PosePN" + ], + "image_footnote": [], + "bbox": [ + 490, + 335, + 669, + 436 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a88032463498dd1198dfb9f7b839b57b53e20685c7ea078b4851e6ac04b92571.jpg", + "image_caption": [ + "(1) PosePN++" + ], + "image_footnote": [], + "bbox": [ + 684, + 335, + 861, + 436 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cbe62be5f8b56dfa0bb84befbe7acd3bc5429eb1d9c850ee0f905fb471e53bbb.jpg", + "image_caption": [ + "(m) PoseSOE" + ], + "image_footnote": [], + "bbox": [ + 102, + 457, + 282, + 558 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/646c1f73f678b590ef2b74787fc54e32a0ab9ec0808257a7e39cfabc13092cf1.jpg", + "image_caption": [ + "(n) PoseMinkLoc" + ], + "image_footnote": [], + "bbox": [ + 295, + 457, + 473, + 558 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/501bbf1371e9af3133c22551e8e6d0598f43096337bb658fa6f40a86b5301567.jpg", + "image_caption": [ + "(o) PointLoc", + "Figure 4. Trajectories of the baselines and the proposed method on the Oxford (top) and NCLT (bottom) datasets. The ground truth and predictions are shown in black and red, respectively. The star indicates the starting position." + ], + "image_footnote": [], + "bbox": [ + 490, + 457, + 669, + 558 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fcf2d54f75968b599896a44cf44da6c30f956e1cb50ff14084c56589ef320695.jpg", + "image_caption": [ + "(p) SGLoc" + ], + "image_footnote": [], + "bbox": [ + 684, + 457, + 861, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cloud, we search for its nearest submap in the standard point cloud, which is a pre-specified day of data, using the provided pose. The submaps are then registered to obtain the correspondence and transformation matrix, which can be used to evaluate and enhance the quality of the pose.", + "bbox": [ + 75, + 619, + 470, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Submaps building. The trajectory is divided into segments based on the prespecified distance to generate the sub-point cloud set. Then, we build the local submap according to Eq. (1), where the position of this submap is defined as the average position of the contained point cloud.", + "bbox": [ + 75, + 698, + 468, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Registration. For each submap $M_{r_i}$ , we search for its nearest submap $M_{s_j}$ based on position. Then, the ICP algorithm [3] is used to align the pair of submaps to obtain correspondence $\\mathcal{C}$ and relative transformation matrix $T_{ij}$ .", + "bbox": [ + 75, + 776, + 470, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pose evaluation and refinement. We calculate the average Euclidean distance between the correspondences of all submaps for pose quality evaluation. For pose refinement, the $T_{ij}$ is used to transform the pose of all point clouds in the", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$M_{ri}$ to correct pose errors in the data. The algorithm results are convincing when the transformed pose error is below the pre-specified threshold.", + "bbox": [ + 498, + 619, + 890, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 674, + 632, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 500, + 696, + 596, + 713 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benchmark datasets. We conduct experiments on two large-scale benchmark datasets. Oxford Radar RobotCar [2] (Oxford) is an urban scene localization dataset that contains over 32 repetitions traversals of a center Oxford route (about $10\\mathrm{km}$ , $200\\mathrm{hm}^2$ ). The dataset contains different weather, traffic, and lighting conditions. The point cloud is collected by dual Velodyne HDL-32E LiDAR. Ground truth pose is generated by the interpolations of INS. We use the data of 11-14-02-26, 14-12-05-52, 14-14-48-55, and 18-15-20-12 as the training set. The data of 15-13-06-37, 17-13-26-39, 17-14-03-00, and 18-14-14-42 are used as the test data.", + "bbox": [ + 496, + 718, + 893, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NCLT [34] dataset is collected by sensors on a Segway", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "9290", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/655421844bde8438492340abcf28d5e716b34c866a09807eb8eda7cbf22e8a01.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Oxford dataset
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
15-13-06-3718.14m, 3.28°16.04m, 4.54°14.32m, 3.06°9.59m, 1.92°7.59m, 1.94°11.20m, 2.62°12.42m, 2.26°3.01m, 1.91°
17-13-26-3924.57m, 3.08°16.22m, 3.56°16.97m, 2.49°10.66m, 1.92°10.39m, 2.08°14.24m, 2.42°13.14m, 2.50°4.07m, 2.07°
17-14-03-0019.93m, 3.13°14.87m, 3.45°13.48m, 2.60°9.01m, 1.51°9.21m, 2.12°12.35m, 2.46°12.91m, 1.92°3.37m, 1.89°
18-14-14-4215.59m, 2.63°12.97m, 3.99°9.14m, 1.78°8.44m, 1.71°7.27m, 1.87°10.06m, 2.15°11.31m, 1.98°2.12m, 1.66°
Average19.56m, 3.03°15.03m, 3.89°13.48m, 2.48°9.43m, 1.77°8.62m, 2.00°11.96m, 2.41°12.45m, 2.17°3.14m, 1.88°
Quality-enhanced Oxford dataset
15-13-06-3710.90m, 2.49°10.61m, 2.56°9.47m, 2.80°4.54m, 1.83°4.17m, 1.76°6.77m, 1.84°10.75m, 2.36°1.79m, 1.67°
17-13-26-3914.60m, 2.46°11.44m, 2.14°12.98m, 2.35°6.44m, 1.78°6.16m, 1.81°8.84m, 1.84°11.07m, 2.21°1.81m, 1.76°
17-14-03-0011.28m, 2.21°10.90m, 2.01°8.64m, 2.19°4.89m, 1.55°5.42m, 1.87°8.08m, 1.69°11.53m, 1.92°1.33m, 1.59°
18-14-14-429.00m, 1.90°9.51m, 2.08°6.26m, 1.64°4.64m, 1.61°4.16m, 1.70°6.56m, 2.06°9.82m, 2.07°1.19m, 1.39°
Average11.45m, 2.27°10.62m, 2.20°9.34m, 2.25°5.13m, 1.69°4.98m, 1.79°7.56m, 1.86°10.79m, 2.14°1.53m, 1.60°
", + "bbox": [ + 99, + 89, + 866, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Position error (m) and orientation error $\\left( {}^{ \\circ }\\right)$ for various methods on the Oxford and quality-enhanced Oxford datasets.", + "bbox": [ + 114, + 250, + 852, + 263 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3ab5609ef78b11a41c67b205b2ffddcf91a698820bc4eb657bc8395f7ef1fa0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 107, + 265, + 284, + 369 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/956411dbd4634bc06373c1415af3eae518a7335eb490c4688d5cbe9779b4356d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 299, + 266, + 473, + 369 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b66c8cc249877e66461eab706cf6aa849c8111db0e2219b46cfebc24091d7ed1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 266, + 669, + 369 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4ab67521b1b2a1c0da03e757a1915bad9e97f485692deb0b49eccf4f4f530862.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 266, + 861, + 369 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/761907881d84cd0f626ac066cb0761363b0e7cb95d42bd0704f2f5e5f5c7c0e1.jpg", + "image_caption": [ + "Figure 5. Cumulative distributions of the position errors (m) on the Oxford and quality-enhanced Oxford dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value." + ], + "image_footnote": [ + "PNVLAD DCP PosePN PosePN++ PoseMinkLoc PointLoc SGLoc" + ], + "bbox": [ + 106, + 373, + 279, + 489 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/998d5413a6fcce8f4ff9d54f035b69182021f8120aa43ae7aeb44e9ba64d731a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 373, + 473, + 489 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a9d0cc6a10ece4bfa4e71be4cdf3201a05a57b5582c72080d2fded92809c456.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 373, + 669, + 489 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ace40c87772aec7ea13b0ad045eca21208f87c14708791ed4fd75113d3ab8fd8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 373, + 861, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "robotic platform on the University of Michigan's North Campus. The dataset contains 27 traversals, where each traversal is nearly $5.5\\mathrm{km}$ and covers $45\\mathrm{hm}^2$ . The point cloud is gathered by a Velodyne HDL-32E LiDAR. The 6-DoF ground truth pose is obtained by SLAM. The data of 2012-01-22, 2012-02-02, 2012-02-18, and 2012-05-11 are treated as the training set, and the data of 2012-02-12, 2012-02-19, 2012-03-31, and 2012-05-26 are used as the test set. More details about datasets can be found in the supplementary.", + "bbox": [ + 75, + 554, + 470, + 689 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. The proposed SGLoc is implemented with PyTorch [35] and Minkowski Engine [15]. We run our code on a PC equipped with an Intel (R) Xeon (R) Silver 4214R CPU, 64GB of RAM, and a single NVIDIA RTX 3090 GPU. During training, we employ an Adam optimizer [26] with an initial learning rate of 0.001. The weight $\\lambda$ is set to 1 for all datasets. On the Oxford dataset, we use the point cloud from the left LiDAR and set the voxel size to $0.2\\mathrm{m}$ . On the NCLT dataset, the voxel size is $0.25\\mathrm{m}$ . The TSFA module uses feature maps from the 3rd, 5th, and 8th convolution blocks with 128, 256, and 512 dimensions, respectively. Each convolution block consists of two convolution layers and a residual connection.", + "bbox": [ + 75, + 689, + 470, + 885 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. To validate the performance of SGLoc, we com", + "bbox": [ + 76, + 885, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "pare it with several state-of-the-art learning-based LiDAR localization approaches. PointNetVLAD (PNVLAD) [44] is a large-scale point cloud retrieval-based method, and DCP [47] is a point cloud registration approach which employs PointNet [36] and DGCNN [48] as the embedding network. PNVLAD and DCP use the same configuration as PointLoc [46]. PosePN [51], PosePN++ [51], PoseSOE [51], PoseMinkLoc [51], and PointLoc are LiDAR-based localization framework that uses a single-frame point cloud for absolute pose regression.", + "bbox": [ + 496, + 554, + 893, + 704 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results of pose quality evaluation and enhancement. On the Oxford and NCLT datasets, the data of 14-14-48-55 and 2012-02-18 are selected as the standard, respectively. We set the distance of the trajectory segments to build sub-maps to $20\\mathrm{m}$ and the voxel size to $0.1\\mathrm{m}$ to reduce the duplicate points. Registration is considered successful when the root-mean-square error of correspondence is below $1\\mathrm{m}$ . The evaluated pose error of Oxford and NCLT datasets are $3.24\\mathrm{m}$ and $0.25\\mathrm{m}$ , respectively. Obviously, the ground truth poses in the data of NCLT is accurate. However, the pose of the Oxford dataset has various errors. Therefore, we perform quality enhancement on the Oxford dataset and obtain the enhanced pose with errors of $0.91\\mathrm{m}$ .", + "bbox": [ + 496, + 704, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "9291", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/070a3a86dcdc512235101c85d8d4c15a95b21f6da393b26637edfdb24b5a6529.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
2012-02-127.75m, 6.49°9.84m, 6.84°9.45m, 7.47°4.97m, 3.75°13.09m, 8.05°6.24m, 5.03°7.23m, 4.88°1.20m, 3.08°
2012-02-197.47m, 5.49°8.27m, 5.16°6.15m, 5.05°3.68m, 2.65°6.16m, 4.51°4.87m, 3.94°6.31m, 3.89°1.20m, 3.05°
2012-03-316.98m, 5.67°8.94m, 5.96°5.79m, 5.28°4.35m, 3.38°5.24m, 4.56°4.23m, 4.03°6.71m, 4.32°1.12m, 3.28°
2012-05-2614.34m, 7.93°15.62m, 7.99°13.47m, 7.77°9.59m, 4.49°12.60m, 7.67°10.32m, 6.52°10.02m, 5.32°3.81m, 4.74°
Average9.14m, 6.40°10.67m, 6.49°8.72m, 6.39°5.65m, 3.57°9.27m, 6.20°6.42m, 4.88°7.57m, 4.60°1.83m, 3.54°
", + "bbox": [ + 99, + 88, + 867, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a452ba50ba31e04308acecd78f472b1180c3bf585148e7c3702a7894235db7cc.jpg", + "image_caption": [ + "Figure 6. Cumulative distributions of the position errors (m) on the NCLT dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value." + ], + "image_footnote": [ + "PNVLAD DCP PosePN PosePN++ PoseSOE PoseMinkLoc PointLoc SGLoc" + ], + "bbox": [ + 102, + 186, + 277, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e5e9e027be59466163958615e341d678bf8e3fecdb6e3f267429ed6812e13328.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 300, + 186, + 473, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/22b34fd30e7aaffae80994ea2f4da7ea0a396e0787f8ae5346c080c8bd168b45.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 498, + 186, + 671, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a2dd08e7269b71ce96aace13e70eebfbdfa80fce944521073925ca818c60e58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 186, + 857, + 304 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Localization Results", + "text_level": 1, + "bbox": [ + 76, + 362, + 267, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Localization on the Oxford dataset. We first evaluate the proposed SGLoc on the Oxford dataset, as shown in Tab. 1. We report the mean position and orientation errors over the full test trajectories. The proposed framework achieves a mean error of $3.14\\mathrm{m} / 1.88^{\\circ}$ , outperforming all competitors. Specifically, compared to PoseSOE, it improves by $63.6\\%$ and $6\\%$ on position and orientation, respectively.", + "bbox": [ + 75, + 383, + 470, + 488 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further evaluate the proposed SGLoc on the quality-enhanced Oxford dataset, as shown in Tab. 2. Clearly, the mean position and orientation errors of all methods are significantly degraded compared to Tab. 1, illustrating the effectiveness and generalizability of the proposed PQEE method. SGLoc achieves a mean error of $1.53\\mathrm{m} / 1.60^{\\circ}$ , surpassing other methods by a large margin. Specifically, it improves PoseSOE by $69.3\\% / 10.6\\%$ . These results demonstrate that the proposed SGLoc can perform localization well in large-scale outdoor scenes.", + "bbox": [ + 75, + 489, + 470, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The first two rows in Fig. 4 illustrate the predicted trajectories on 17-14-03-00. The trajectory of SGLoc closely overlaps with the ground truth, demonstrating its accuracy. Fig. 5 shows the cumulative distributions of position errors on different trajectories. SGLoc achieves the desired performance, indicating that it effectively captures the scene geometry, leading to improved accuracy.", + "bbox": [ + 75, + 642, + 470, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Localization on the NCLT dataset. Then, we evaluate the proposed SGLoc on the NCLT dataset. Tab. 2 summarizes the results of all methods with mean position and orientation errors. Apparently, SGLoc significantly outperforms the existing methods with a mean error of $1.83\\mathrm{m} / 3.54^{\\circ}$ . Our approach improves by $67.6\\%$ on position compared to PosePN++. It should be explained that there are more outliers on 2012-05-26 due to the various differences between the test and training trajectories.", + "bbox": [ + 75, + 748, + 470, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The last two rows of Fig. 4 show the predicted trajectory", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8fa17baa1432b6c691f73253e32741bbda07c4710e966e22cdb812aca982739e.jpg", + "table_caption": [ + "Table 2. Position error (m) and orientation error $\\left( {}^{ \\circ }\\right)$ for various methods on the NCLT dataset." + ], + "table_footnote": [], + "table_body": "
15-13-06-3717-13-26-3917-14-03-0018-14-14-42
SGLoc w/o PGO1.79m, 1.67°1.81m, 1.75°1.33m, 1.59°1.19m, 1.39°
SGLoc w/ PGO1.58m, 1.10°1.56m, 1.16°1.10m, 1.18°0.99m, 1.04°
2012-02-122012-02-192012-03-312012-05-26
SGLoc w/o PGO1.20m, 3.08°1.20m, 3.05°1.12m, 3.28°3.81m, 4.74°
SGLoc w/ PGO0.88m, 2.35°0.85m, 2.06°0.79m, 2.34°3.25m, 3.52°
", + "bbox": [ + 503, + 361, + 888, + 431 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Localization results of SGLoc with PGO on the quality-enhanced Oxford and NCLT datasets.", + "bbox": [ + 498, + 434, + 893, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of 2012-03-31. Our prediction is closer to the ground truth and smoother than the competitors. The cumulative distributions of position errors are shown in Fig. 6, demonstrating the promising performance of the proposed SGLoc. It means that SGLoc can capture the scene geometry more efficiently compared to existing LiDAR-based localization methods.", + "bbox": [ + 496, + 472, + 893, + 564 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Localization Accuracy at Sub-meter Level", + "text_level": 1, + "bbox": [ + 500, + 573, + 859, + 589 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Similar to MapNet [8], we utilize PGO as post-processing to further improve localization results. As shown in Tab. 3, our method has further improved in accuracy with PGO. Specifically, the SGLoc achieves accuracy at the sub-meter level on 18-14-14-42 of the quality-enhanced Oxford dataset. Moreover, in all scenes of the NCLT dataset (except 2012-05-26), the mean error of SGLoc is $0.84\\mathrm{m} / 2.25^{\\circ}$ . To our knowledge, SGLoc is the first regression-based method to reduce the error to the level of the sub-meter on some trajectories, which bridges the gaps in practical applications. For more results, please refer to the supplementary.", + "bbox": [ + 496, + 595, + 893, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 771, + 653, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation on PQEE. As shown in Tab. 4, the proposed method outperforms the vanilla model without proposed modules by $43.5\\% /14.9\\%$ . Moreover, the performance of PQEE is significantly enhanced with or without IGCC or TSFA. For instance, PQEE considerably surpasses that without PQEE under IGCC and TSFA, achieving a mean error of $1.53\\mathrm{m} / 1.60^{\\circ}$ vs. $3.14\\mathrm{m} / 1.88^{\\circ}$ .", + "bbox": [ + 496, + 794, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "9292", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ff74e261b052dfc037af6a4e31e9f3abff5f999010bbcd8d0bf44c8fccbb83de.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
IGCCTSFAOxford w/o PQEEOxford w/ PQEENCLT
13.95m/2.89°2.23m/2.46°2.73m/5.19°
2✓3.46m/2.67°2.12m/2.32°2.62m/5.11°
3✓3.23m/2.10°1.68m/1.67°1.98m/3.51°
4✓✓3.14m/1.88°1.53m/1.60°1.83m/3.54°
", + "bbox": [ + 81, + 88, + 467, + 161 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on IGCC. We further conduct ablation experiments to demonstrate the importance of IGCC loss. In Tab. 4, the comparison between Row 1 and Row 2 shows the module notably improves accuracy. On the Oxford dataset, compared to the vanilla model, IGCC obtains a $12.4\\% /7.6\\%$ improvement. On the NCLT dataset, IGCC also leads to improvements. Furthermore, IGCC improves localization accuracy compared to the method with TSFA only. This demonstrates the proposed design is helpful for capturing the scene geometry.", + "bbox": [ + 75, + 191, + 468, + 343 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation on TSFA. The TSFA results are reported in Row 3 of Tab. 4. On the Oxford and NCLT dataset, compared to the results in Row 1, it yields an average $23.5\\% / 30.6\\%$ improvement on position and orientation. This significant improvement verifies that the proposed TSFA module can further improve the encoding of scene geometry.", + "bbox": [ + 75, + 343, + 470, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Runtime", + "text_level": 1, + "bbox": [ + 76, + 439, + 181, + 454 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the Oxford and NCLT datasets, the LiDAR scan rate is $20\\mathrm{Hz}$ and $10\\mathrm{Hz}$ , respectively. Therefore, the real-time performance here means that the running time of each scanning data is less than 50ms and 100ms, respectively. Tab. 5 shows the running time on the Oxford and NCLT dataset. On the Oxford dataset, SGLoc takes a running time of 38ms per frame, with the correspondence regression stage consuming 25ms and the pose estimation stage consuming 13ms. On the NCLT dataset, the running times are 75ms, 41ms, and 34ms, respectively. Note that the running time of PNVLAD, DCP, PosePN, and PoseMinkLoc are less than 10ms due to the simplicity of their networks. Therefore, Our SGLoc can achieve real-time localization and is very competitive with these methods, but the performance of SGLoc is much better.", + "bbox": [ + 75, + 460, + 472, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 76, + 679, + 191, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "LiDAR localization in large-scale outdoor scenes is a critical component of autonomous driving. However, existing APR methods still face challenges in effectively encoding scene geometry and dealing with unsatisfactory data quality, resulting in suboptimal accuracy. To overcome these challenges, we propose SGLoc and PQEE, which significantly improves accuracy. Compared to previous work, SGLoc stands out due to the following differences.", + "bbox": [ + 75, + 703, + 470, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Difference between SGLoc and DSAC++. Camera coordinate regression (DSAC++ [5]) predicts 2D-3D correspondences, to our knowledge, SGLoc is the first work to regress 3D-3D point correspondences. Though both DSAC++ and our SGLoc use regression, we address different problems.", + "bbox": [ + 75, + 824, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3c426c3ed673cfde1927a459cce603bddb454577fa8c3c2fe70b1b4023f6b78a.jpg", + "image_caption": [ + "Figure 7. Ground truth poses in the data on the Oxford (left) and quality-enhanced Oxford (right) dataset. The green trajectory indicates the prespecified standard data." + ], + "image_footnote": [], + "bbox": [ + 506, + 85, + 689, + 180 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b5e0c55f66493ee05449068ffb6ccea3532580f668e32e8d80257299f31f344e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 85, + 880, + 181 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/d3047202b5ceaa7586a518bc1751bb7eda4dda85877c7a485f50378265f48f55.jpg", + "table_caption": [ + "Table 4. Ablation study on the Oxford and NCLT datasets." + ], + "table_footnote": [], + "table_body": "
MethodsPNVLADDCPPosePNPosePN+PoseSOEPoseMinkLocPointLocSGLoc
Oxford6ms3ms2ms111ms244ms8ms625ms38ms
NCLT6ms3ms2ms108ms230ms8ms614ms75ms
", + "bbox": [ + 503, + 231, + 890, + 265 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Runtime (ms) of different methods on the Oxford and NCLT datasets.", + "bbox": [ + 496, + 268, + 890, + 296 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We summarize the differences. (1) SGLoc learns rigid transformations instead of affine transformations that require the intrinsics of the query camera; (2) Our methods' ground truth correspondences generation requires only input point clouds and poses, which can be deployed efficiently in online training; (3) SGLoc can be applied to large-scale outdoor scenes covering about $200\\mathrm{hm}^2$ .", + "bbox": [ + 496, + 306, + 893, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Difference between PQEE and point cloud registration. We empirically find existing large-scale outdoor datasets cannot precisely provide the same position values (bad quality) in the same position on different days, as shown in Fig. 7. More importantly, we find this degraded data quality can significantly decrease the localization accuracy. We hope this new finding can inspire researchers to work on this new source of performance degradation. Based on this new finding, we propose PQEE, which aligns and fuses standard/raw data in LiDAR localization. It uses point cloud registration, but the purpose differs from conventional point cloud registration.", + "bbox": [ + 496, + 414, + 893, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 603, + 617, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a novel regression-based framework, SGLoc, for LiDAR localization. SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences. The core component of SGLoc is the first step, which effectively encodes scene geometry, leading to significant performance improvement. To achieve high accuracy in this step, we propose the TSFA module and IGCC loss to improve the encoding of scene geometry. Moreover, to increase the data quality and localization accuracy, the PQEE method is designed to measure and correct the ground truth pose errors in the localization data. Extensive experimental results verify the great effectiveness of our method.", + "bbox": [ + 496, + 627, + 893, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work was partially supported by the open fund of PDL (2022-KJWPDL-12, WDZC20215250113), by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003).", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "9293", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongkai Chen, Lei Li, Zeyu Hu, Hongbo Fu, and Chiew-Lan Tai. Pointdsc: Robust point cloud registration using deep spatial consistency. 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In CVPR, pages 4919-4928, 2020. 2" + ], + "bbox": [ + 501, + 90, + 893, + 375 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "9295", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SGLoc_ Scene Geometry Encoding for Outdoor LiDAR Localization/56c4bde5-7fa2-4496-a50a-885b12091caa_model.json b/2023/SGLoc_ Scene Geometry Encoding for Outdoor LiDAR Localization/56c4bde5-7fa2-4496-a50a-885b12091caa_model.json new file mode 100644 index 0000000000000000000000000000000000000000..890c46dd29e38ed787c760cef4aaa56383ffdd92 --- /dev/null +++ b/2023/SGLoc_ Scene Geometry Encoding for Outdoor LiDAR Localization/56c4bde5-7fa2-4496-a50a-885b12091caa_model.json @@ -0,0 +1,2882 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.14, + 0.131, + 0.83, + 0.152 + ], + "angle": 0, + "content": "SGLoc: Scene Geometry Encoding for Outdoor LiDAR Localization" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.18, + 0.862, + 0.199 + ], + "angle": 0, + "content": "Wen Li\\(^{1,2*}\\) Shangshu Yu\\(^{1,2*}\\) Cheng Wang\\(^{1,2\\dagger}\\) Guosheng Hu\\(^{3}\\) Siqi Shen\\(^{1,2}\\) Chenglu Wen\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.199, + 0.862, + 0.27 + ], + "angle": 0, + "content": "\\(^{1}\\) Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University, China \\(^{2}\\) Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, School of Informatics, Xiamen University, China \\(^{3}\\) Oosto, Belfast, UK" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.304, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.474, + 0.716 + ], + "angle": 0, + "content": "LiDAR-based absolute pose regression estimates the global pose through a deep network in an end-to-end manner, achieving impressive results in learning-based localization. However, the accuracy of existing methods still has room to improve due to the difficulty of effectively encoding the scene geometry and the unsatisfactory quality of the data. In this work, we propose a novel LiDAR localization framework, SGLoc, which decouples the pose estimation to point cloud correspondence regression and pose estimation via this correspondence. This decoupling effectively encodes the scene geometry because the decoupled correspondence regression step greatly preserves the scene geometry, leading to significant performance improvement. Apart from this decoupling, we also design a tri-scale spatial feature aggregation module and inter-geometric consistency constraint loss to effectively capture scene geometry. Moreover, we empirically find that the ground truth might be noisy due to GPS/INS measuring errors, greatly reducing the pose estimation performance. Thus, we propose a pose quality evaluation and enhancement method to measure and correct the ground truth pose. Extensive experiments on the Oxford Radar RobotCar and NCLT datasets demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art regression-based localization methods by \\(68.5\\%\\) and \\(67.6\\%\\) on position accuracy, respectively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.745, + 0.21, + 0.761 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.772, + 0.47, + 0.832 + ], + "angle": 0, + "content": "Estimating the position and orientation of LiDAR from point clouds is a fundamental component of many applications in computer vision, e.g., autonomous driving, virtual reality, and augmented reality." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.833, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Contemporary state-of-the-art LiDAR-based localization methods explicitly use maps, which match the query point" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.303, + 0.683, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.303, + 0.892, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.441, + 0.894, + 0.498 + ], + "angle": 0, + "content": "Figure 1. LiDAR Localization results of our method and PosePN++ [51] (state-of-the-art method) in urban (left) and school (right) scenes from Oxford Radar RobotCar [2] and NCLT [34] datasets. The star indicates the starting position." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.895, + 0.658 + ], + "angle": 0, + "content": "cloud with a pre-built 3D map [18, 23, 27, 49]. However, these methods usually require expensive 3D map storage and communication. One alternative is the regression-based approach, absolute pose regression (APR), which directly estimates the poses in the inference stage without maps [8, 24, 25, 40, 45]. APR methods typically use a CNN to encode the scene feature and a multi-layer perceptron to regress the pose. Compared to map-based methods, APR does not need to store the pre-built maps, accordingly reducing communications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.896, + 0.902 + ], + "angle": 0, + "content": "For (1), APR networks learn highly abstract global scene representations, which allow the network to classify the scene effectively [25]. However, the global features usually cannot encode detailed scene geometry, which is the key to achieving an accurate pose estimation [10, 11, 38, 39]. Prior efforts have tried to minimize the relative pose or photometric errors to add geometry constraints by pose graph optimization (PGO) [4, 21] or novel view synthesis (NVS) [10, 11]. However, this introduces additional computations, limiting its wide applications. For (2), we empirically find current large-scale outdoor datasets suffer from various errors in the data due to GPS/INS measuring errors. It affects the APR learning process and makes it difficult to evaluate the localization results accurately. To our knowledge, the impact of data quality on localization has not been carefully investigated in the existing literature." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.208, + 0.888 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.222, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9286" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.468 + ], + "angle": 0, + "content": "This paper proposes a novel framework, SGLoc, which can (1) effectively capture the scene geometry; In addition, we propose a data pre-processing method, Pose Quality Evaluation and Enhancement (PQEE), which can (2) improve data quality. (1) Existing APR methods conduct end-to-end regression from the point cloud in LiDAR coordinate to pose. Unlike them, SGLoc decouples this process to (a) regression from the point cloud in LiDAR coordinate to world coordinate and (b) pose estimation via the point cloud correspondence in LiDAR and world coordinate using RANSAC [17]. Importantly, step (a) can effectively preserve the scene geometry, which is key for pose estimation [10, 11, 38, 39]. To achieve high accuracy in step (a), we design a Tri-scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to effectively capture scene geometry. (2) We empirically find that pose errors in the data greatly degrade the pose estimation performance. For example, the ground truth pose obtained by GPS/INS suffers from measuring errors. To address this problem, we proposed a PQEE method which can measure the errors in the pose and correct them afterward. We conduct extensive experiments on Oxford Radar RobotCar [2] and NCLT [34] datasets, and results show that our method has great advantages over the state-of-the-art, as demonstrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.47, + 0.423, + 0.483 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.486, + 0.47, + 0.56 + ], + "angle": 0, + "content": "- SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences, which can effectively capture scene geometry, leading to significant performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.564, + 0.47, + 0.623 + ], + "angle": 0, + "content": "- We propose a novel Tri-Scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to further improve the encoding of scene geometry." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.627, + 0.47, + 0.7 + ], + "angle": 0, + "content": "- We propose a generalized pose quality evaluation and enhancement (PQEE) method to measure and correct the pose errors in the localization data, improving \\(34.2\\% / 16.8\\%\\) on position and orientation for existing LiDAR localization methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.705, + 0.47, + 0.779 + ], + "angle": 0, + "content": "- Extensive experiments demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art LiDAR localization methods by \\(68.1\\%\\) on position accuracy. In addition, to our knowledge, we are the first to reduce the error to the level of the sub-meter on some trajectories." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.486, + 0.47, + 0.779 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.793, + 0.22, + 0.808 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.818, + 0.3, + 0.833 + ], + "angle": 0, + "content": "2.1. Map-based Localization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Map-based methods aim to match the query point cloud with a pre-built 3D map, which can be classified into retrieval-based [18, 27, 30, 44, 49] and registration-based methods [14, 16, 20, 32, 37, 47]. Retrieval-based methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.273 + ], + "angle": 0, + "content": "cast localization as a place recognition problem, which finds the most similar point cloud in the database. Registration-based localization performs fine matching between the query point cloud and the pred-built map. DCP [47] is an impressive work investigating geometry correspondences generated by weighted calculation for pose estimation. Unlike this, SGLoc directly regresses the correspondences. In addition, Some methods combine both retrieval and registration techniques to achieve better localization accuracy in dense urban areas [9, 12, 50, 52]. However, the high cost of 3D map storage and communication limits the widespread application of map-based methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.286, + 0.771, + 0.302 + ], + "angle": 0, + "content": "2.2. Regression-based Localization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.895, + 0.475 + ], + "angle": 0, + "content": "Recently, in camera localization, the scene coordinate regression method has been designed, which regresses 2D-3D correspondences and estimates the pose with PnP-RANSAC [4,6,7,22,54]. While these methods have shown impressive results in small and medium-sized scenes, e.g., 7-Scenes [42], they do not scale well to large scenes [5]. HSCNet attempts to solve this problem by conditioning discrete location labels around each pixel [28], but it still cannot be applied to large-scale outdoor scenes, e.g., the street scene in the Cambridge landmark dataset [25], which covers an area of about \\(5\\mathrm{hm}^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.895, + 0.689 + ], + "angle": 0, + "content": "Absolute pose regression. APR methods typically use the same basic pipeline: first, extracting high-level features using a CNN and then using these features to regress the 6-DoF pose. PoseNet [25] originally defines this task using a modified GoogleNet [43] to regress camera poses. Successors of PoseNet have focused on improving the framework through model architecture and loss function. E-PoseNet [33] proposes a translation and rotation equivariant CNN that directly induces representations of camera motions into the feature space. PAE [41] uses the pose auto-encoders framework to significantly reduce model parameters. However, the above methods learn highly abstract global scene representations, leading to various wrong predictions due to the lack of effective scene geometry encoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Recent research suggests scene geometry is key to accurate pose estimation [10, 11, 38, 39]. Geometric PoseNet [24] investigates geometric loss for learning to regress position and orientation simultaneously with scene geometry. MapNet [8] adds pairwise geometric constraints between video frames using additional VO algorithms. AtLoc [45] utilizes a self-attention mechanism to adaptively focus on the import targets in the scene. MS-Transformer [40] proposes a transformer-based method to learn robust features. DirectPoseNet [11] adapts additional photometric loss by comparing the query image with NVS on the predicted pose. DFNet [10] explores a direct matching scheme in feature space, leading to a more robust performance than DirectPoseNet. However, these methods require auxiliary algo" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9287" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.127, + 0.095, + 0.388, + 0.109 + ], + "angle": 0, + "content": "(1) Point cloud correspondence regression" + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.111, + 0.842, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.233, + 0.289, + 0.246 + ], + "angle": 0, + "content": "(2) 6-DoF pose estimation" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.248, + 0.65, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.233, + 0.755, + 0.246 + ], + "angle": 0, + "content": "Legend" + }, + { + "type": "image_footnote", + "bbox": [ + 0.699, + 0.253, + 0.802, + 0.265 + ], + "angle": 0, + "content": "3D coordinates" + }, + { + "type": "image_footnote", + "bbox": [ + 0.701, + 0.271, + 0.793, + 0.283 + ], + "angle": 0, + "content": "Point features" + }, + { + "type": "image_footnote", + "bbox": [ + 0.701, + 0.289, + 0.821, + 0.302 + ], + "angle": 0, + "content": "Aggregated feature" + }, + { + "type": "image_footnote", + "bbox": [ + 0.698, + 0.31, + 0.809, + 0.324 + ], + "angle": 0, + "content": "\\(\\mathbb{X}\\) Pose Hypotheses" + }, + { + "type": "image_footnote", + "bbox": [ + 0.698, + 0.332, + 0.797, + 0.345 + ], + "angle": 0, + "content": "Final Estimate" + }, + { + "type": "list", + "bbox": [ + 0.698, + 0.253, + 0.821, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.894, + 0.391 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed framework including point cloud correspondence regression (top row) and 6-DoF pose estimation (bottom row). \\( F_{1} \\), \\( F_{2} \\), and \\( F_{3} \\) are the extracted feature maps with different receptive fields." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.471, + 0.493 + ], + "angle": 0, + "content": "rithms, e.g., PGO, NVS, introducing additional computations. Unlike these methods, we decouple the pose estimation process to (1) regression point cloud correspondence and (2) pose estimate via the correspondence using RANSAC. Through step (1), scene geometry can be effectively encoded without additional computations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.472, + 0.585 + ], + "angle": 0, + "content": "Recently, LiDAR-based APR methods, e.g., PointLoc [46], PoseSOE [51], and PosePN++ [51], have shown impressive performance on large-scale outdoor datasets because the point cloud is robust to illumination changes and rich in geometric information. However, effectively encoding scene geometry remains quite challenging." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.6, + 0.169, + 0.615 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.47, + 0.761 + ], + "angle": 0, + "content": "Recent APR methods have achieved impressive results in localization. However, they do not effectively encode the scene geometry and measure the data quality, leading to the accuracy still having room to improve. In this paper, we propose SGLoc and a Pose Quality Evaluation Enhancement (PQEE) method to address these problems. Sec. 3.1 elaborates SGLoc, which can effectively capture the scene geometry. Then, a PQEE method (Sec. 3.2) is proposed to measure and correct the pose errors in the data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.168, + 0.787 + ], + "angle": 0, + "content": "3.1.SGLoc" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We now introduce the proposed SGLoc, as shown in Fig. 2, which can be divided into (1) point cloud correspondence regression: convert the Raw LiDAR Point Cloud (RPC) to its corresponding Point Cloud in World coordinate frame (WPC) and (2) 6-DoF pose estimation: estimate pose via matching RPC and WPC. In this work, we design a sparse-convolution-based FCN [15,31] to implement SGLoc," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.895, + 0.509 + ], + "angle": 0, + "content": "which contains a feature extractor, a Tri-Scale Spatial Feature Aggregation (TSFA) module, and a regressor. The feature extractor and regressor generate feature maps with different receptive fields and achieve point cloud correspondence via regression, respectively. The TSFA module and intergeometric consistency constraint (IGCC) loss are proposed to effectively capture scene geometry." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.63 + ], + "angle": 0, + "content": "**Framework.** Here we formulate the framework of SGLoc. Given the query point cloud \\( P_{t} \\in \\mathbb{R}^{N \\times 3} \\), we aim to estimate its global 6-DoF pose \\( \\mathbf{p} \\). Each pose \\( \\mathbf{p} = [\\mathbf{x}, \\mathbf{q}] \\) is represented by a position vector \\( \\mathbf{x} \\in \\mathbb{R}^3 \\) and an orientation vector \\( \\mathbf{q} \\in \\mathbb{R}^r \\) (e.g., a 4D unit quaternion or a 3D Euler angle). Hence, we first define the query point cloud pose \\( \\mathbf{p} \\) as the transformation that maps 3D points in LiDAR coordinate frame, denoted as \\( \\mathbf{l} \\), to 3D points in world coordinate frame, denoted as \\( \\mathbf{w} \\), i.e." + }, + { + "type": "equation", + "bbox": [ + 0.66, + 0.638, + 0.892, + 0.653 + ], + "angle": 0, + "content": "\\[\nw _ {i} = T l _ {i}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.891, + 0.69 + ], + "angle": 0, + "content": "where \\(i\\) denotes the point index in the query point cloud; \\(T\\) is a \\(4 \\times 4\\) matrix representation of the pose \\(\\mathbf{p}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Then, we denote the complete set of scene coordinates with a global pose for the query point cloud as \\(\\mathcal{V}\\), i.e., \\(y_{i} \\in \\mathcal{V}\\). As shown in Fig. 2, (1) for point cloud correspondence regression, we utilize a neural network to learn a function \\(\\mathcal{F}: \\mathcal{V} = \\mathcal{F}(P_t)\\). (2) Regarding 6-DoF pose estimation during inference, we utilize the RANSAC algorithm to select \\(M\\) group from the predicted correspondence \\(\\mathcal{V}\\), and optimize the energy function as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.814, + 0.892, + 0.855 + ], + "angle": 0, + "content": "\\[\nT ^ {\\prime} = \\arg \\min _ {T} \\sum_ {i} ^ {| M |} \\| T l _ {i} - w _ {i} \\| _ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(M\\) is set to 3; \\(i\\) denotes the point index; \\(T^{\\prime}\\) is the estimated transformation matrix. Then, \\(T^{\\prime}\\) can be used to calculate the above energy function of each correspondence" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9288" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.089, + 0.469, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.281, + 0.466, + 0.295 + ], + "angle": 0, + "content": "Figure 3. Tri-Scale Spatial Feature Aggregation (TSFA) Module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.47, + 0.356 + ], + "angle": 0, + "content": "in \\(\\mathcal{V}\\) to filter outliers. The above process will be repeated until convergence. Finally, the estimated \\(T^{\\prime}\\) can easily be converted into a vectorized pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.472, + 0.416 + ], + "angle": 0, + "content": "It is worth noting that during training, SGLoc only requires the input point cloud and the pose, which allows for effective scene geometry encoding by minimizing correspondence distance without any additional computations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.472, + 0.522 + ], + "angle": 0, + "content": "Tri-scale spatial feature aggregation. As described above, SGLoc estimates the pose via the regressed correspondence \\(\\mathcal{V}\\). Therefore, the spatial details in network features are critical to localization accuracy. To effectively capture the spatial details at shallow layers, inspired by the attention mechanism [19, 29, 53], we introduce a Tri-Scale Spatial Feature Aggregation (TSFA) module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.473, + 0.735 + ], + "angle": 0, + "content": "As shown in Fig. 2, the TSFA module takes the low-level features \\( F_{1} \\) and \\( F_{2} \\) and high-level feature \\( F_{3} \\) as the input. We elaborate the architecture of TSFA module in Fig. 3. For convenience, we refer \\( F_{1}' = \\mathcal{H}(\\mathcal{D}(\\mathcal{H}(F_{1})), F_{2}' = \\mathcal{H}(\\mathcal{D}(\\mathcal{H}(F_{2})) \\) and \\( F_{3}' = \\mathcal{H}(F_{3}) \\)), where \\( \\mathcal{D} \\) indicates the down-sampling and \\( \\mathcal{H} \\) denotes the convolution followed by a batch normalization and a ReLU activation function. We first squeeze the channels of the features \\( (F_{1}, F_{2}, F_{3}) \\) to 1. Then, we conduct the addition operation and sigmoid activation to obtain the spatial attention mask, which can adaptively enhance spatial details. Finally, we apply dot product and concatenation to achieve a powerful feature with rich spatial details and structure information. The output can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.74, + 0.47, + 0.759 + ], + "angle": 0, + "content": "\\[\nF _ {o} = \\left[ \\sigma \\left(F _ {1} ^ {\\prime} + F _ {3} ^ {\\prime}\\right) \\odot F _ {1}, \\sigma \\left(F _ {2} ^ {\\prime} + F _ {3} ^ {\\prime}\\right) \\odot F _ {2}, F _ {3} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.794 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is the sigmoid function; \\(\\odot\\) is dot product; \\([\\cdot]\\) denotes the concatenation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Inter-geometric consistency constraint. Training the network with \\( l1 \\) loss \\( (\\mathcal{L}_{L1}) \\) can effectively minimize the distance between the predicted and the ground truth scene coordinates. However, the above constraint is a node-wise loss, which supervises each correspondence individually. This is unfavorable for learning scene geometry. Inspired by spatial compatibility [1, 13], which assumes that two correspondences" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.794, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Pseudocode for PQEE method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.108, + 0.892, + 0.138 + ], + "angle": 0, + "content": "Input: Raw point cloud set \\( P_r \\) and pose set \\( T_r \\); Standard point cloud set \\( P_s \\) and pose set \\( T_s \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.138, + 0.854, + 0.153 + ], + "angle": 0, + "content": "Output: Pose error \\( E' \\); Quality enhanced pose set \\( T_r' \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.153, + 0.892, + 0.198 + ], + "angle": 0, + "content": "Initialization: Build submaps \\( M_r = \\{M_{r_1}, \\ldots, M_{r_n}\\} \\) by \\( P_r \\) and \\( T_r \\); Build submaps \\( M_s = \\{M_{s_1}, \\ldots, M_{s_m}\\} \\) by \\( P_s \\) and \\( T_s \\); \\( E \\gets 0 \\); \\( N \\gets 0 \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.201, + 0.672, + 0.216 + ], + "angle": 0, + "content": "1: for all \\( M_{r_i} \\in M_r \\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.217, + 0.726, + 0.232 + ], + "angle": 0, + "content": "2: Search \\( M_{r_i} \\)'s nearest \\( M_{s_j} \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.232, + 0.85, + 0.247 + ], + "angle": 0, + "content": "3: Register to obtain correspondences \\(\\mathcal{C}\\) and \\(T_{ij}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.247, + 0.646, + 0.262 + ], + "angle": 0, + "content": "4: \\( T_{r_i}' \\gets T_{ij}T_{s_i} \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.263, + 0.678, + 0.276 + ], + "angle": 0, + "content": "5: for all \\(C_k \\in C\\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.277, + 0.813, + 0.291 + ], + "angle": 0, + "content": "6: Calculate the Euclidean distance \\( d_{k} \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.292, + 0.668, + 0.306 + ], + "angle": 0, + "content": "7: \\(E\\gets E + d_{k}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.308, + 0.664, + 0.32 + ], + "angle": 0, + "content": "8: \\(N\\gets N + 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.323, + 0.642, + 0.338 + ], + "angle": 0, + "content": "9: return \\( E / N \\), \\( T_r' \\)" + }, + { + "type": "list", + "bbox": [ + 0.511, + 0.201, + 0.85, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.894, + 0.413 + ], + "angle": 0, + "content": "have a higher score if the difference of spatial distance between them, we propose an Inter-Geometric Consistency Constraint (IGCC) loss to well learn scene geometry:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.414, + 0.892, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I G C C} = \\frac {1}{| \\mathcal {Y} | ^ {2}} \\sum_ {i, j} \\| d _ {i, j} - d _ {i, j} ^ {*} \\| _ {1}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.894, + 0.514 + ], + "angle": 0, + "content": "where \\( d_{i,j}^{*} = \\| y_{i}^{*} - y_{j}^{*}\\|_{1} \\) is the ground truth inter-geometric consistency value. This constraint supervises the pairwise distance between the correspondences, serving as a complement to the node-wise supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Loss function. During training, the point cloud with global poses predicted by the network \\(\\mathcal{F}\\) is optimized by \\(\\mathcal{L}_{L1}\\) and \\(\\mathcal{L}_{IGCC}\\). For \\(\\mathcal{L}_{L1}\\), we minimize the average plain Euclidean distance between the predicted scene coordinates \\(y_{i}\\), and the ground truth of scene coordinates \\(y_{i}^{*}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.591, + 0.892, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L 1} = \\frac {1}{| \\mathcal {Y} |} \\sum_ {y _ {i} \\in \\mathcal {Y}} \\| y _ {i} - y _ {i} ^ {*} \\| _ {1}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.658 + ], + "angle": 0, + "content": "The aforementioned \\(\\mathcal{L}_{IGCC}\\) works with \\(\\mathcal{L}_{L1}\\) to come up with the final loss:" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.667, + 0.892, + 0.683 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {L 1} + \\lambda \\mathcal {L} _ {I G C C}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.894, + 0.704 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyper-parameter to balance the two constraints." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.866, + 0.728 + ], + "angle": 0, + "content": "3.2. Pose Quality Evaluation and Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.871 + ], + "angle": 0, + "content": "For localization, a high-quality dataset should precisely provide the same position values in the same position on different days. However, existing large-scale outdoor datasets do not satisfy this requirement since various pose errors in the data caused by GPS/INS measuring errors. We empirically find these inaccuracies significantly degrade localization accuracy. Therefore, we propose a Pose Quality Evaluation and Enhancement (PQEE) method to measure and correct pose errors in the data, see Alg. 1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We first build submaps from point clouds and poses provided by datasets. Then, for each submap of the raw point" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9289" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.096, + 0.283, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.2, + 0.233, + 0.212 + ], + "angle": 0, + "content": "(a)PNVLAD" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.097, + 0.475, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.2, + 0.413, + 0.212 + ], + "angle": 0, + "content": "(b) DCP" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.097, + 0.671, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.2, + 0.615, + 0.212 + ], + "angle": 0, + "content": "(c) PosePN" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.097, + 0.862, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.2, + 0.815, + 0.212 + ], + "angle": 0, + "content": "(d) PosePN++" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.216, + 0.283, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.164, + 0.319, + 0.231, + 0.331 + ], + "angle": 0, + "content": "(e) PoseSOE" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.216, + 0.475, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.346, + 0.319, + 0.434, + 0.331 + ], + "angle": 0, + "content": "(f) PoseMinkLoc" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.216, + 0.672, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.32, + 0.619, + 0.332 + ], + "angle": 0, + "content": "(g) PointLoc" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.216, + 0.862, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.319, + 0.798, + 0.331 + ], + "angle": 0, + "content": "(h) SGLoc" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.336, + 0.283, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.163, + 0.442, + 0.231, + 0.454 + ], + "angle": 0, + "content": "(i) PNVLAD" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.336, + 0.475, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.369, + 0.442, + 0.411, + 0.454 + ], + "angle": 0, + "content": "(j) DCP" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.336, + 0.671, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.555, + 0.442, + 0.615, + 0.454 + ], + "angle": 0, + "content": "(k) PosePN" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.336, + 0.862, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.442, + 0.813, + 0.454 + ], + "angle": 0, + "content": "(1) PosePN++" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.458, + 0.283, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.562, + 0.233, + 0.574 + ], + "angle": 0, + "content": "(m) PoseSOE" + }, + { + "type": "image", + "bbox": [ + 0.297, + 0.458, + 0.475, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.562, + 0.435, + 0.574 + ], + "angle": 0, + "content": "(n) PoseMinkLoc" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.458, + 0.671, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.562, + 0.618, + 0.574 + ], + "angle": 0, + "content": "(o) PointLoc" + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.458, + 0.862, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.562, + 0.805, + 0.574 + ], + "angle": 0, + "content": "(p) SGLoc" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.58, + 0.894, + 0.608 + ], + "angle": 0, + "content": "Figure 4. Trajectories of the baselines and the proposed method on the Oxford (top) and NCLT (bottom) datasets. The ground truth and predictions are shown in black and red, respectively. The star indicates the starting position." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.471, + 0.696 + ], + "angle": 0, + "content": "cloud, we search for its nearest submap in the standard point cloud, which is a pre-specified day of data, using the provided pose. The submaps are then registered to obtain the correspondence and transformation matrix, which can be used to evaluate and enhance the quality of the pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.699, + 0.47, + 0.775 + ], + "angle": 0, + "content": "Submaps building. The trajectory is divided into segments based on the prespecified distance to generate the sub-point cloud set. Then, we build the local submap according to Eq. (1), where the position of this submap is defined as the average position of the contained point cloud." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.777, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Registration. For each submap \\( M_{r_i} \\), we search for its nearest submap \\( M_{s_j} \\) based on position. Then, the ICP algorithm [3] is used to align the pair of submaps to obtain correspondence \\( \\mathcal{C} \\) and relative transformation matrix \\( T_{ij} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Pose evaluation and refinement. We calculate the average Euclidean distance between the correspondences of all submaps for pose quality evaluation. For pose refinement, the \\( T_{ij} \\) is used to transform the pose of all point clouds in the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.62, + 0.892, + 0.666 + ], + "angle": 0, + "content": "\\(M_{ri}\\) to correct pose errors in the data. The algorithm results are convincing when the transformed pose error is below the pre-specified threshold." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.675, + 0.633, + 0.693 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.698, + 0.598, + 0.714 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.894, + 0.884 + ], + "angle": 0, + "content": "Benchmark datasets. We conduct experiments on two large-scale benchmark datasets. Oxford Radar RobotCar [2] (Oxford) is an urban scene localization dataset that contains over 32 repetitions traversals of a center Oxford route (about \\(10\\mathrm{km}\\), \\(200\\mathrm{hm}^2\\)). The dataset contains different weather, traffic, and lighting conditions. The point cloud is collected by dual Velodyne HDL-32E LiDAR. Ground truth pose is generated by the interpolations of INS. We use the data of 11-14-02-26, 14-12-05-52, 14-14-48-55, and 18-15-20-12 as the training set. The data of 15-13-06-37, 17-13-26-39, 17-14-03-00, and 18-14-14-42 are used as the test data." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "NCLT [34] dataset is collected by sensors on a Segway" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9290" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.09, + 0.867, + 0.25 + ], + "angle": 0, + "content": "
Oxford dataset
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
15-13-06-3718.14m, 3.28°16.04m, 4.54°14.32m, 3.06°9.59m, 1.92°7.59m, 1.94°11.20m, 2.62°12.42m, 2.26°3.01m, 1.91°
17-13-26-3924.57m, 3.08°16.22m, 3.56°16.97m, 2.49°10.66m, 1.92°10.39m, 2.08°14.24m, 2.42°13.14m, 2.50°4.07m, 2.07°
17-14-03-0019.93m, 3.13°14.87m, 3.45°13.48m, 2.60°9.01m, 1.51°9.21m, 2.12°12.35m, 2.46°12.91m, 1.92°3.37m, 1.89°
18-14-14-4215.59m, 2.63°12.97m, 3.99°9.14m, 1.78°8.44m, 1.71°7.27m, 1.87°10.06m, 2.15°11.31m, 1.98°2.12m, 1.66°
Average19.56m, 3.03°15.03m, 3.89°13.48m, 2.48°9.43m, 1.77°8.62m, 2.00°11.96m, 2.41°12.45m, 2.17°3.14m, 1.88°
Quality-enhanced Oxford dataset
15-13-06-3710.90m, 2.49°10.61m, 2.56°9.47m, 2.80°4.54m, 1.83°4.17m, 1.76°6.77m, 1.84°10.75m, 2.36°1.79m, 1.67°
17-13-26-3914.60m, 2.46°11.44m, 2.14°12.98m, 2.35°6.44m, 1.78°6.16m, 1.81°8.84m, 1.84°11.07m, 2.21°1.81m, 1.76°
17-14-03-0011.28m, 2.21°10.90m, 2.01°8.64m, 2.19°4.89m, 1.55°5.42m, 1.87°8.08m, 1.69°11.53m, 1.92°1.33m, 1.59°
18-14-14-429.00m, 1.90°9.51m, 2.08°6.26m, 1.64°4.64m, 1.61°4.16m, 1.70°6.56m, 2.06°9.82m, 2.07°1.19m, 1.39°
Average11.45m, 2.27°10.62m, 2.20°9.34m, 2.25°5.13m, 1.69°4.98m, 1.79°7.56m, 1.86°10.79m, 2.14°1.53m, 1.60°
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.251, + 0.854, + 0.264 + ], + "angle": 0, + "content": "Table 1. Position error (m) and orientation error \\( \\left( {}^{ \\circ }\\right) \\) for various methods on the Oxford and quality-enhanced Oxford datasets." + }, + { + "type": "image", + "bbox": [ + 0.108, + 0.266, + 0.285, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.267, + 0.474, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.267, + 0.671, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.267, + 0.862, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.374, + 0.281, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.374, + 0.474, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.374, + 0.671, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.374, + 0.862, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.111, + 0.495, + 0.855, + 0.508 + ], + "angle": 0, + "content": "PNVLAD DCP PosePN PosePN++ PoseMinkLoc PointLoc SGLoc" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.511, + 0.891, + 0.539 + ], + "angle": 0, + "content": "Figure 5. Cumulative distributions of the position errors (m) on the Oxford and quality-enhanced Oxford dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.471, + 0.69 + ], + "angle": 0, + "content": "robotic platform on the University of Michigan's North Campus. The dataset contains 27 traversals, where each traversal is nearly \\(5.5\\mathrm{km}\\) and covers \\(45\\mathrm{hm}^2\\). The point cloud is gathered by a Velodyne HDL-32E LiDAR. The 6-DoF ground truth pose is obtained by SLAM. The data of 2012-01-22, 2012-02-02, 2012-02-18, and 2012-05-11 are treated as the training set, and the data of 2012-02-12, 2012-02-19, 2012-03-31, and 2012-05-26 are used as the test set. More details about datasets can be found in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.472, + 0.886 + ], + "angle": 0, + "content": "Implementation details. The proposed SGLoc is implemented with PyTorch [35] and Minkowski Engine [15]. We run our code on a PC equipped with an Intel (R) Xeon (R) Silver 4214R CPU, 64GB of RAM, and a single NVIDIA RTX 3090 GPU. During training, we employ an Adam optimizer [26] with an initial learning rate of 0.001. The weight \\(\\lambda\\) is set to 1 for all datasets. On the Oxford dataset, we use the point cloud from the left LiDAR and set the voxel size to \\(0.2\\mathrm{m}\\). On the NCLT dataset, the voxel size is \\(0.25\\mathrm{m}\\). The TSFA module uses feature maps from the 3rd, 5th, and 8th convolution blocks with 128, 256, and 512 dimensions, respectively. Each convolution block consists of two convolution layers and a residual connection." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Baselines. To validate the performance of SGLoc, we com" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.555, + 0.895, + 0.705 + ], + "angle": 0, + "content": "pare it with several state-of-the-art learning-based LiDAR localization approaches. PointNetVLAD (PNVLAD) [44] is a large-scale point cloud retrieval-based method, and DCP [47] is a point cloud registration approach which employs PointNet [36] and DGCNN [48] as the embedding network. PNVLAD and DCP use the same configuration as PointLoc [46]. PosePN [51], PosePN++ [51], PoseSOE [51], PoseMinkLoc [51], and PointLoc are LiDAR-based localization framework that uses a single-frame point cloud for absolute pose regression." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Results of pose quality evaluation and enhancement. On the Oxford and NCLT datasets, the data of 14-14-48-55 and 2012-02-18 are selected as the standard, respectively. We set the distance of the trajectory segments to build sub-maps to \\(20\\mathrm{m}\\) and the voxel size to \\(0.1\\mathrm{m}\\) to reduce the duplicate points. Registration is considered successful when the root-mean-square error of correspondence is below \\(1\\mathrm{m}\\). The evaluated pose error of Oxford and NCLT datasets are \\(3.24\\mathrm{m}\\) and \\(0.25\\mathrm{m}\\), respectively. Obviously, the ground truth poses in the data of NCLT is accurate. However, the pose of the Oxford dataset has various errors. Therefore, we perform quality enhancement on the Oxford dataset and obtain the enhanced pose with errors of \\(0.91\\mathrm{m}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "9291" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.868, + 0.169 + ], + "angle": 0, + "content": "
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
2012-02-127.75m, 6.49°9.84m, 6.84°9.45m, 7.47°4.97m, 3.75°13.09m, 8.05°6.24m, 5.03°7.23m, 4.88°1.20m, 3.08°
2012-02-197.47m, 5.49°8.27m, 5.16°6.15m, 5.05°3.68m, 2.65°6.16m, 4.51°4.87m, 3.94°6.31m, 3.89°1.20m, 3.05°
2012-03-316.98m, 5.67°8.94m, 5.96°5.79m, 5.28°4.35m, 3.38°5.24m, 4.56°4.23m, 4.03°6.71m, 4.32°1.12m, 3.28°
2012-05-2614.34m, 7.93°15.62m, 7.99°13.47m, 7.77°9.59m, 4.49°12.60m, 7.67°10.32m, 6.52°10.02m, 5.32°3.81m, 4.74°
Average9.14m, 6.40°10.67m, 6.49°8.72m, 6.39°5.65m, 3.57°9.27m, 6.20°6.42m, 4.88°7.57m, 4.60°1.83m, 3.54°
" + }, + { + "type": "table_caption", + "bbox": [ + 0.206, + 0.17, + 0.761, + 0.182 + ], + "angle": 0, + "content": "Table 2. Position error (m) and orientation error \\( \\left( {}^{ \\circ }\\right) \\) for various methods on the NCLT dataset." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.187, + 0.278, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.187, + 0.475, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.187, + 0.673, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.187, + 0.858, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.108, + 0.308, + 0.852, + 0.321 + ], + "angle": 0, + "content": "PNVLAD DCP PosePN PosePN++ PoseSOE PoseMinkLoc PointLoc SGLoc" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.324, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Figure 6. Cumulative distributions of the position errors (m) on the NCLT dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.363, + 0.269, + 0.378 + ], + "angle": 0, + "content": "4.2. Localization Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.471, + 0.489 + ], + "angle": 0, + "content": "Localization on the Oxford dataset. We first evaluate the proposed SGLoc on the Oxford dataset, as shown in Tab. 1. We report the mean position and orientation errors over the full test trajectories. The proposed framework achieves a mean error of \\(3.14\\mathrm{m} / 1.88^{\\circ}\\), outperforming all competitors. Specifically, compared to PoseSOE, it improves by \\(63.6\\%\\) and \\(6\\%\\) on position and orientation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.471, + 0.641 + ], + "angle": 0, + "content": "We further evaluate the proposed SGLoc on the quality-enhanced Oxford dataset, as shown in Tab. 2. Clearly, the mean position and orientation errors of all methods are significantly degraded compared to Tab. 1, illustrating the effectiveness and generalizability of the proposed PQEE method. SGLoc achieves a mean error of \\(1.53\\mathrm{m} / 1.60^{\\circ}\\), surpassing other methods by a large margin. Specifically, it improves PoseSOE by \\(69.3\\% / 10.6\\%\\). These results demonstrate that the proposed SGLoc can perform localization well in large-scale outdoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.471, + 0.748 + ], + "angle": 0, + "content": "The first two rows in Fig. 4 illustrate the predicted trajectories on 17-14-03-00. The trajectory of SGLoc closely overlaps with the ground truth, demonstrating its accuracy. Fig. 5 shows the cumulative distributions of position errors on different trajectories. SGLoc achieves the desired performance, indicating that it effectively captures the scene geometry, leading to improved accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.471, + 0.884 + ], + "angle": 0, + "content": "Localization on the NCLT dataset. Then, we evaluate the proposed SGLoc on the NCLT dataset. Tab. 2 summarizes the results of all methods with mean position and orientation errors. Apparently, SGLoc significantly outperforms the existing methods with a mean error of \\(1.83\\mathrm{m} / 3.54^{\\circ}\\). Our approach improves by \\(67.6\\%\\) on position compared to PosePN++. It should be explained that there are more outliers on 2012-05-26 due to the various differences between the test and training trajectories." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The last two rows of Fig. 4 show the predicted trajectory" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.362, + 0.89, + 0.433 + ], + "angle": 0, + "content": "
15-13-06-3717-13-26-3917-14-03-0018-14-14-42
SGLoc w/o PGO1.79m, 1.67°1.81m, 1.75°1.33m, 1.59°1.19m, 1.39°
SGLoc w/ PGO1.58m, 1.10°1.56m, 1.16°1.10m, 1.18°0.99m, 1.04°
2012-02-122012-02-192012-03-312012-05-26
SGLoc w/o PGO1.20m, 3.08°1.20m, 3.05°1.12m, 3.28°3.81m, 4.74°
SGLoc w/ PGO0.88m, 2.35°0.85m, 2.06°0.79m, 2.34°3.25m, 3.52°
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.435, + 0.894, + 0.462 + ], + "angle": 0, + "content": "Table 3. Localization results of SGLoc with PGO on the quality-enhanced Oxford and NCLT datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.894, + 0.565 + ], + "angle": 0, + "content": "of 2012-03-31. Our prediction is closer to the ground truth and smoother than the competitors. The cumulative distributions of position errors are shown in Fig. 6, demonstrating the promising performance of the proposed SGLoc. It means that SGLoc can capture the scene geometry more efficiently compared to existing LiDAR-based localization methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.86, + 0.59 + ], + "angle": 0, + "content": "4.3. Localization Accuracy at Sub-meter Level" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.895, + 0.764 + ], + "angle": 0, + "content": "Similar to MapNet [8], we utilize PGO as post-processing to further improve localization results. As shown in Tab. 3, our method has further improved in accuracy with PGO. Specifically, the SGLoc achieves accuracy at the sub-meter level on 18-14-14-42 of the quality-enhanced Oxford dataset. Moreover, in all scenes of the NCLT dataset (except 2012-05-26), the mean error of SGLoc is \\(0.84\\mathrm{m} / 2.25^{\\circ}\\). To our knowledge, SGLoc is the first regression-based method to reduce the error to the level of the sub-meter on some trajectories, which bridges the gaps in practical applications. For more results, please refer to the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.655, + 0.789 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.9 + ], + "angle": 0, + "content": "Ablation on PQEE. As shown in Tab. 4, the proposed method outperforms the vanilla model without proposed modules by \\(43.5\\% /14.9\\%\\). Moreover, the performance of PQEE is significantly enhanced with or without IGCC or TSFA. For instance, PQEE considerably surpasses that without PQEE under IGCC and TSFA, achieving a mean error of \\(1.53\\mathrm{m} / 1.60^{\\circ}\\) vs. \\(3.14\\mathrm{m} / 1.88^{\\circ}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9292" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.162 + ], + "angle": 0, + "content": "
IGCCTSFAOxford w/o PQEEOxford w/ PQEENCLT
13.95m/2.89°2.23m/2.46°2.73m/5.19°
2✓3.46m/2.67°2.12m/2.32°2.62m/5.11°
3✓3.23m/2.10°1.68m/1.67°1.98m/3.51°
4✓✓3.14m/1.88°1.53m/1.60°1.83m/3.54°
" + }, + { + "type": "table_caption", + "bbox": [ + 0.099, + 0.167, + 0.446, + 0.181 + ], + "angle": 0, + "content": "Table 4. Ablation study on the Oxford and NCLT datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.192, + 0.47, + 0.344 + ], + "angle": 0, + "content": "Ablation on IGCC. We further conduct ablation experiments to demonstrate the importance of IGCC loss. In Tab. 4, the comparison between Row 1 and Row 2 shows the module notably improves accuracy. On the Oxford dataset, compared to the vanilla model, IGCC obtains a \\(12.4\\% /7.6\\%\\) improvement. On the NCLT dataset, IGCC also leads to improvements. Furthermore, IGCC improves localization accuracy compared to the method with TSFA only. This demonstrates the proposed design is helpful for capturing the scene geometry." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.344, + 0.471, + 0.435 + ], + "angle": 0, + "content": "Ablation on TSFA. The TSFA results are reported in Row 3 of Tab. 4. On the Oxford and NCLT dataset, compared to the results in Row 1, it yields an average \\(23.5\\% / 30.6\\%\\) improvement on position and orientation. This significant improvement verifies that the proposed TSFA module can further improve the encoding of scene geometry." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.44, + 0.182, + 0.455 + ], + "angle": 0, + "content": "4.5. Runtime" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.473, + 0.673 + ], + "angle": 0, + "content": "For the Oxford and NCLT datasets, the LiDAR scan rate is \\(20\\mathrm{Hz}\\) and \\(10\\mathrm{Hz}\\), respectively. Therefore, the real-time performance here means that the running time of each scanning data is less than 50ms and 100ms, respectively. Tab. 5 shows the running time on the Oxford and NCLT dataset. On the Oxford dataset, SGLoc takes a running time of 38ms per frame, with the correspondence regression stage consuming 25ms and the pose estimation stage consuming 13ms. On the NCLT dataset, the running times are 75ms, 41ms, and 34ms, respectively. Note that the running time of PNVLAD, DCP, PosePN, and PoseMinkLoc are less than 10ms due to the simplicity of their networks. Therefore, Our SGLoc can achieve real-time localization and is very competitive with these methods, but the performance of SGLoc is much better." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.192, + 0.696 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.825 + ], + "angle": 0, + "content": "LiDAR localization in large-scale outdoor scenes is a critical component of autonomous driving. However, existing APR methods still face challenges in effectively encoding scene geometry and dealing with unsatisfactory data quality, resulting in suboptimal accuracy. To overcome these challenges, we propose SGLoc and PQEE, which significantly improves accuracy. Compared to previous work, SGLoc stands out due to the following differences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Difference between SGLoc and DSAC++. Camera coordinate regression (DSAC++ [5]) predicts 2D-3D correspondences, to our knowledge, SGLoc is the first work to regress 3D-3D point correspondences. Though both DSAC++ and our SGLoc use regression, we address different problems." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.087, + 0.691, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.087, + 0.882, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.185, + 0.895, + 0.227 + ], + "angle": 0, + "content": "Figure 7. Ground truth poses in the data on the Oxford (left) and quality-enhanced Oxford (right) dataset. The green trajectory indicates the prespecified standard data." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.232, + 0.892, + 0.266 + ], + "angle": 0, + "content": "
MethodsPNVLADDCPPosePNPosePN+PoseSOEPoseMinkLocPointLocSGLoc
Oxford6ms3ms2ms111ms244ms8ms625ms38ms
NCLT6ms3ms2ms108ms230ms8ms614ms75ms
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.297 + ], + "angle": 0, + "content": "Table 5. Runtime (ms) of different methods on the Oxford and NCLT datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.895, + 0.413 + ], + "angle": 0, + "content": "We summarize the differences. (1) SGLoc learns rigid transformations instead of affine transformations that require the intrinsics of the query camera; (2) Our methods' ground truth correspondences generation requires only input point clouds and poses, which can be deployed efficiently in online training; (3) SGLoc can be applied to large-scale outdoor scenes covering about \\(200\\mathrm{hm}^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.895, + 0.596 + ], + "angle": 0, + "content": "Difference between PQEE and point cloud registration. We empirically find existing large-scale outdoor datasets cannot precisely provide the same position values (bad quality) in the same position on different days, as shown in Fig. 7. More importantly, we find this degraded data quality can significantly decrease the localization accuracy. We hope this new finding can inspire researchers to work on this new source of performance degradation. Based on this new finding, we propose PQEE, which aligns and fuses standard/raw data in LiDAR localization. It uses point cloud registration, but the purpose differs from conventional point cloud registration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.619, + 0.62 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.824 + ], + "angle": 0, + "content": "We propose a novel regression-based framework, SGLoc, for LiDAR localization. SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences. The core component of SGLoc is the first step, which effectively encodes scene geometry, leading to significant performance improvement. To achieve high accuracy in this step, we propose the TSFA module and IGCC loss to improve the encoding of scene geometry. Moreover, to increase the data quality and localization accuracy, the PQEE method is designed to measure and correct the ground truth pose errors in the localization data. Extensive experimental results verify the great effectiveness of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements This work was partially supported by the open fund of PDL (2022-KJWPDL-12, WDZC20215250113), by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "9293" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongkai Chen, Lei Li, Zeyu Hu, Hongbo Fu, and Chiew-Lan Tai. Pointdsc: Robust point cloud registration using deep spatial consistency. 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However, the accuracy of existing methods still has room to improve due to the difficulty of effectively encoding the scene geometry and the unsatisfactory quality of the data. In this work, we propose a novel LiDAR localization framework, SGLoc, which decouples the pose estimation to point cloud correspondence regression and pose estimation via this correspondence. This decoupling effectively encodes the scene geometry because the decoupled correspondence regression step greatly preserves the scene geometry, leading to significant performance improvement. Apart from this decoupling, we also design a tri-scale spatial feature aggregation module and inter-geometric consistency constraint loss to effectively capture scene geometry. Moreover, we empirically find that the ground truth might be noisy due to GPS/INS measuring errors, greatly reducing the pose estimation performance. Thus, we propose a pose quality evaluation and enhancement method to measure and correct the ground truth pose. Extensive experiments on the Oxford Radar RobotCar and NCLT datasets demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art regression-based localization methods by $68.5\%$ and $67.6\%$ on position accuracy, respectively. + +# 1. Introduction + +Estimating the position and orientation of LiDAR from point clouds is a fundamental component of many applications in computer vision, e.g., autonomous driving, virtual reality, and augmented reality. + +Contemporary state-of-the-art LiDAR-based localization methods explicitly use maps, which match the query point + +![](images/48da2a67e01883c3383fa5bd20d43768b1a02685c4b94e2eb4a382e2eda7ada8.jpg) +Figure 1. LiDAR Localization results of our method and PosePN++ [51] (state-of-the-art method) in urban (left) and school (right) scenes from Oxford Radar RobotCar [2] and NCLT [34] datasets. The star indicates the starting position. + +![](images/e1bd0e578c82de888b89d2e8b364988a11a9ddbd3511247bd34ca88db909e32a.jpg) + +cloud with a pre-built 3D map [18, 23, 27, 49]. However, these methods usually require expensive 3D map storage and communication. One alternative is the regression-based approach, absolute pose regression (APR), which directly estimates the poses in the inference stage without maps [8, 24, 25, 40, 45]. APR methods typically use a CNN to encode the scene feature and a multi-layer perceptron to regress the pose. Compared to map-based methods, APR does not need to store the pre-built maps, accordingly reducing communications. + +For (1), APR networks learn highly abstract global scene representations, which allow the network to classify the scene effectively [25]. However, the global features usually cannot encode detailed scene geometry, which is the key to achieving an accurate pose estimation [10, 11, 38, 39]. Prior efforts have tried to minimize the relative pose or photometric errors to add geometry constraints by pose graph optimization (PGO) [4, 21] or novel view synthesis (NVS) [10, 11]. However, this introduces additional computations, limiting its wide applications. For (2), we empirically find current large-scale outdoor datasets suffer from various errors in the data due to GPS/INS measuring errors. It affects the APR learning process and makes it difficult to evaluate the localization results accurately. To our knowledge, the impact of data quality on localization has not been carefully investigated in the existing literature. + +This paper proposes a novel framework, SGLoc, which can (1) effectively capture the scene geometry; In addition, we propose a data pre-processing method, Pose Quality Evaluation and Enhancement (PQEE), which can (2) improve data quality. (1) Existing APR methods conduct end-to-end regression from the point cloud in LiDAR coordinate to pose. Unlike them, SGLoc decouples this process to (a) regression from the point cloud in LiDAR coordinate to world coordinate and (b) pose estimation via the point cloud correspondence in LiDAR and world coordinate using RANSAC [17]. Importantly, step (a) can effectively preserve the scene geometry, which is key for pose estimation [10, 11, 38, 39]. To achieve high accuracy in step (a), we design a Tri-scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to effectively capture scene geometry. (2) We empirically find that pose errors in the data greatly degrade the pose estimation performance. For example, the ground truth pose obtained by GPS/INS suffers from measuring errors. To address this problem, we proposed a PQEE method which can measure the errors in the pose and correct them afterward. We conduct extensive experiments on Oxford Radar RobotCar [2] and NCLT [34] datasets, and results show that our method has great advantages over the state-of-the-art, as demonstrated in Fig. 1. + +Our contributions can be summarized as follows: + +- SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences, which can effectively capture scene geometry, leading to significant performance improvement. +- We propose a novel Tri-Scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to further improve the encoding of scene geometry. +- We propose a generalized pose quality evaluation and enhancement (PQEE) method to measure and correct the pose errors in the localization data, improving $34.2\% / 16.8\%$ on position and orientation for existing LiDAR localization methods. +- Extensive experiments demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art LiDAR localization methods by $68.1\%$ on position accuracy. In addition, to our knowledge, we are the first to reduce the error to the level of the sub-meter on some trajectories. + +# 2. Related Work + +# 2.1. Map-based Localization + +Map-based methods aim to match the query point cloud with a pre-built 3D map, which can be classified into retrieval-based [18, 27, 30, 44, 49] and registration-based methods [14, 16, 20, 32, 37, 47]. Retrieval-based methods + +cast localization as a place recognition problem, which finds the most similar point cloud in the database. Registration-based localization performs fine matching between the query point cloud and the pred-built map. DCP [47] is an impressive work investigating geometry correspondences generated by weighted calculation for pose estimation. Unlike this, SGLoc directly regresses the correspondences. In addition, Some methods combine both retrieval and registration techniques to achieve better localization accuracy in dense urban areas [9, 12, 50, 52]. However, the high cost of 3D map storage and communication limits the widespread application of map-based methods. + +# 2.2. Regression-based Localization + +Recently, in camera localization, the scene coordinate regression method has been designed, which regresses 2D-3D correspondences and estimates the pose with PnP-RANSAC [4,6,7,22,54]. While these methods have shown impressive results in small and medium-sized scenes, e.g., 7-Scenes [42], they do not scale well to large scenes [5]. HSCNet attempts to solve this problem by conditioning discrete location labels around each pixel [28], but it still cannot be applied to large-scale outdoor scenes, e.g., the street scene in the Cambridge landmark dataset [25], which covers an area of about $5\mathrm{hm}^2$ . + +Absolute pose regression. APR methods typically use the same basic pipeline: first, extracting high-level features using a CNN and then using these features to regress the 6-DoF pose. PoseNet [25] originally defines this task using a modified GoogleNet [43] to regress camera poses. Successors of PoseNet have focused on improving the framework through model architecture and loss function. E-PoseNet [33] proposes a translation and rotation equivariant CNN that directly induces representations of camera motions into the feature space. PAE [41] uses the pose auto-encoders framework to significantly reduce model parameters. However, the above methods learn highly abstract global scene representations, leading to various wrong predictions due to the lack of effective scene geometry encoding. + +Recent research suggests scene geometry is key to accurate pose estimation [10, 11, 38, 39]. Geometric PoseNet [24] investigates geometric loss for learning to regress position and orientation simultaneously with scene geometry. MapNet [8] adds pairwise geometric constraints between video frames using additional VO algorithms. AtLoc [45] utilizes a self-attention mechanism to adaptively focus on the import targets in the scene. MS-Transformer [40] proposes a transformer-based method to learn robust features. DirectPoseNet [11] adapts additional photometric loss by comparing the query image with NVS on the predicted pose. DFNet [10] explores a direct matching scheme in feature space, leading to a more robust performance than DirectPoseNet. However, these methods require auxiliary algo + +(1) Point cloud correspondence regression +Legend +![](images/a73edaff36b80adab289edf23ccf2765d99bcd627b37c1e258b8c3551d8b1cd8.jpg) +3D coordinates + +(2) 6-DoF pose estimation +Figure 2. Overview of the proposed framework including point cloud correspondence regression (top row) and 6-DoF pose estimation (bottom row). $F_{1}$ , $F_{2}$ , and $F_{3}$ are the extracted feature maps with different receptive fields. +![](images/c5b0fd8bcdb3ff59b582dfc2f60d885757ba9468a6a31a5964009aaa00d57fa0.jpg) +Point features +Aggregated feature +$\mathbb{X}$ Pose Hypotheses +Final Estimate + +rithms, e.g., PGO, NVS, introducing additional computations. Unlike these methods, we decouple the pose estimation process to (1) regression point cloud correspondence and (2) pose estimate via the correspondence using RANSAC. Through step (1), scene geometry can be effectively encoded without additional computations. + +Recently, LiDAR-based APR methods, e.g., PointLoc [46], PoseSOE [51], and PosePN++ [51], have shown impressive performance on large-scale outdoor datasets because the point cloud is robust to illumination changes and rich in geometric information. However, effectively encoding scene geometry remains quite challenging. + +# 3. Method + +Recent APR methods have achieved impressive results in localization. However, they do not effectively encode the scene geometry and measure the data quality, leading to the accuracy still having room to improve. In this paper, we propose SGLoc and a Pose Quality Evaluation Enhancement (PQEE) method to address these problems. Sec. 3.1 elaborates SGLoc, which can effectively capture the scene geometry. Then, a PQEE method (Sec. 3.2) is proposed to measure and correct the pose errors in the data. + +# 3.1.SGLoc + +We now introduce the proposed SGLoc, as shown in Fig. 2, which can be divided into (1) point cloud correspondence regression: convert the Raw LiDAR Point Cloud (RPC) to its corresponding Point Cloud in World coordinate frame (WPC) and (2) 6-DoF pose estimation: estimate pose via matching RPC and WPC. In this work, we design a sparse-convolution-based FCN [15,31] to implement SGLoc, + +which contains a feature extractor, a Tri-Scale Spatial Feature Aggregation (TSFA) module, and a regressor. The feature extractor and regressor generate feature maps with different receptive fields and achieve point cloud correspondence via regression, respectively. The TSFA module and intergeometric consistency constraint (IGCC) loss are proposed to effectively capture scene geometry. + +**Framework.** Here we formulate the framework of SGLoc. Given the query point cloud $P_{t} \in \mathbb{R}^{N \times 3}$ , we aim to estimate its global 6-DoF pose $\mathbf{p}$ . Each pose $\mathbf{p} = [\mathbf{x}, \mathbf{q}]$ is represented by a position vector $\mathbf{x} \in \mathbb{R}^3$ and an orientation vector $\mathbf{q} \in \mathbb{R}^r$ (e.g., a 4D unit quaternion or a 3D Euler angle). Hence, we first define the query point cloud pose $\mathbf{p}$ as the transformation that maps 3D points in LiDAR coordinate frame, denoted as $\mathbf{l}$ , to 3D points in world coordinate frame, denoted as $\mathbf{w}$ , i.e. + +$$ +w _ {i} = T l _ {i}, \tag {1} +$$ + +where $i$ denotes the point index in the query point cloud; $T$ is a $4 \times 4$ matrix representation of the pose $\mathbf{p}$ . + +Then, we denote the complete set of scene coordinates with a global pose for the query point cloud as $\mathcal{V}$ , i.e., $y_{i} \in \mathcal{V}$ . As shown in Fig. 2, (1) for point cloud correspondence regression, we utilize a neural network to learn a function $\mathcal{F}: \mathcal{V} = \mathcal{F}(P_t)$ . (2) Regarding 6-DoF pose estimation during inference, we utilize the RANSAC algorithm to select $M$ group from the predicted correspondence $\mathcal{V}$ , and optimize the energy function as follows: + +$$ +T ^ {\prime} = \arg \min _ {T} \sum_ {i} ^ {| M |} \| T l _ {i} - w _ {i} \| _ {2}, \tag {2} +$$ + +where $M$ is set to 3; $i$ denotes the point index; $T^{\prime}$ is the estimated transformation matrix. Then, $T^{\prime}$ can be used to calculate the above energy function of each correspondence + +![](images/57dffb77d13a6cb50b3dc257de79f4b65eee352dd47fb1db539256483d8d6c19.jpg) +Figure 3. Tri-Scale Spatial Feature Aggregation (TSFA) Module. + +in $\mathcal{V}$ to filter outliers. The above process will be repeated until convergence. Finally, the estimated $T^{\prime}$ can easily be converted into a vectorized pose. + +It is worth noting that during training, SGLoc only requires the input point cloud and the pose, which allows for effective scene geometry encoding by minimizing correspondence distance without any additional computations. + +Tri-scale spatial feature aggregation. As described above, SGLoc estimates the pose via the regressed correspondence $\mathcal{V}$ . Therefore, the spatial details in network features are critical to localization accuracy. To effectively capture the spatial details at shallow layers, inspired by the attention mechanism [19, 29, 53], we introduce a Tri-Scale Spatial Feature Aggregation (TSFA) module. + +As shown in Fig. 2, the TSFA module takes the low-level features $F_{1}$ and $F_{2}$ and high-level feature $F_{3}$ as the input. We elaborate the architecture of TSFA module in Fig. 3. For convenience, we refer $F_{1}' = \mathcal{H}(\mathcal{D}(\mathcal{H}(F_{1})), F_{2}' = \mathcal{H}(\mathcal{D}(\mathcal{H}(F_{2}))$ and $F_{3}' = \mathcal{H}(F_{3})$ ), where $\mathcal{D}$ indicates the down-sampling and $\mathcal{H}$ denotes the convolution followed by a batch normalization and a ReLU activation function. We first squeeze the channels of the features $(F_{1}, F_{2}, F_{3})$ to 1. Then, we conduct the addition operation and sigmoid activation to obtain the spatial attention mask, which can adaptively enhance spatial details. Finally, we apply dot product and concatenation to achieve a powerful feature with rich spatial details and structure information. The output can be expressed as: + +$$ +F _ {o} = \left[ \sigma \left(F _ {1} ^ {\prime} + F _ {3} ^ {\prime}\right) \odot F _ {1}, \sigma \left(F _ {2} ^ {\prime} + F _ {3} ^ {\prime}\right) \odot F _ {2}, F _ {3} \right], \tag {3} +$$ + +where $\sigma$ is the sigmoid function; $\odot$ is dot product; $[\cdot]$ denotes the concatenation. + +Inter-geometric consistency constraint. Training the network with $l1$ loss $(\mathcal{L}_{L1})$ can effectively minimize the distance between the predicted and the ground truth scene coordinates. However, the above constraint is a node-wise loss, which supervises each correspondence individually. This is unfavorable for learning scene geometry. Inspired by spatial compatibility [1, 13], which assumes that two correspondences + +# Algorithm 1 Pseudocode for PQEE method + +Input: Raw point cloud set $P_r$ and pose set $T_r$ ; Standard point cloud set $P_s$ and pose set $T_s$ + +Output: Pose error $E'$ ; Quality enhanced pose set $T_r'$ + +Initialization: Build submaps $M_r = \{M_{r_1}, \ldots, M_{r_n}\}$ by $P_r$ and $T_r$ ; Build submaps $M_s = \{M_{s_1}, \ldots, M_{s_m}\}$ by $P_s$ and $T_s$ ; $E \gets 0$ ; $N \gets 0$ + +1: for all $M_{r_i} \in M_r$ do +2: Search $M_{r_i}$ 's nearest $M_{s_j}$ +3: Register to obtain correspondences $\mathcal{C}$ and $T_{ij}$ +4: $T_{r_i}' \gets T_{ij}T_{s_i}$ +5: for all $C_k \in C$ do +6: Calculate the Euclidean distance $d_{k}$ +7: $E\gets E + d_{k}$ +8: $N\gets N + 1$ +9: return $E / N$ , $T_r'$ + +have a higher score if the difference of spatial distance between them, we propose an Inter-Geometric Consistency Constraint (IGCC) loss to well learn scene geometry: + +$$ +\mathcal {L} _ {I G C C} = \frac {1}{| \mathcal {Y} | ^ {2}} \sum_ {i, j} \| d _ {i, j} - d _ {i, j} ^ {*} \| _ {1}, \tag {4} +$$ + +where $d_{i,j}^{*} = \| y_{i}^{*} - y_{j}^{*}\|_{1}$ is the ground truth inter-geometric consistency value. This constraint supervises the pairwise distance between the correspondences, serving as a complement to the node-wise supervision. + +Loss function. During training, the point cloud with global poses predicted by the network $\mathcal{F}$ is optimized by $\mathcal{L}_{L1}$ and $\mathcal{L}_{IGCC}$ . For $\mathcal{L}_{L1}$ , we minimize the average plain Euclidean distance between the predicted scene coordinates $y_{i}$ , and the ground truth of scene coordinates $y_{i}^{*}$ : + +$$ +\mathcal {L} _ {L 1} = \frac {1}{| \mathcal {Y} |} \sum_ {y _ {i} \in \mathcal {Y}} \| y _ {i} - y _ {i} ^ {*} \| _ {1}. \tag {5} +$$ + +The aforementioned $\mathcal{L}_{IGCC}$ works with $\mathcal{L}_{L1}$ to come up with the final loss: + +$$ +\mathcal {L} = \mathcal {L} _ {L 1} + \lambda \mathcal {L} _ {I G C C}, \tag {6} +$$ + +where $\lambda$ is a hyper-parameter to balance the two constraints. + +# 3.2. Pose Quality Evaluation and Enhancement + +For localization, a high-quality dataset should precisely provide the same position values in the same position on different days. However, existing large-scale outdoor datasets do not satisfy this requirement since various pose errors in the data caused by GPS/INS measuring errors. We empirically find these inaccuracies significantly degrade localization accuracy. Therefore, we propose a Pose Quality Evaluation and Enhancement (PQEE) method to measure and correct pose errors in the data, see Alg. 1. + +We first build submaps from point clouds and poses provided by datasets. Then, for each submap of the raw point + +![](images/90010f32b8cf0dc5bae745d7c9a8b3b7b979640a85ffe6f8df001d9f37da516b.jpg) +(a)PNVLAD + +![](images/e5423cb17478dfb3058ef2a4622a143c1e900e5939e9488c0c4687179f757ff0.jpg) +(b) DCP + +![](images/268b7240e741cb181ada7f13b87afe534f16bc2494d269f1ec031d1bbc9aa587.jpg) +(c) PosePN + +![](images/58cfccdf59ba8d7db651f090db936565e0a6babdf2e375ef0350ef4156a22294.jpg) +(d) PosePN++ + +![](images/d94bc72c99d2b637aa8e5ecefe72ea931085de7e714971efab0376a152da1ebd.jpg) +(e) PoseSOE + +![](images/a4899a1570f7b9a5f6b3507fa62a74518237fa0d7a26ae85c1c8464e170adb6a.jpg) +(f) PoseMinkLoc + +![](images/b5a9b7ffb59944be312063e26181380a6b8a2e957d09202d98b9df77fbf9bb23.jpg) +(g) PointLoc + +![](images/239c77ba2e1d7f24a1fb3537f53a0d4b7ebe75104299ca087c5cb101bc0ff812.jpg) +(h) SGLoc + +![](images/87073f0deae97f074b1d431aa1c653b6e8e005a3d6621a3cab6b27f83c244d39.jpg) +(i) PNVLAD + +![](images/63b70b9f182311b4204207211bb1c8ba6dc8a1e3bcb33f40207e3867ba81725f.jpg) +(j) DCP + +![](images/e8d0e6eac27821690801ceab857d8d628755af49467c3dc75a0cd0b7b93453e9.jpg) +(k) PosePN + +![](images/a88032463498dd1198dfb9f7b839b57b53e20685c7ea078b4851e6ac04b92571.jpg) +(1) PosePN++ + +![](images/cbe62be5f8b56dfa0bb84befbe7acd3bc5429eb1d9c850ee0f905fb471e53bbb.jpg) +(m) PoseSOE + +![](images/646c1f73f678b590ef2b74787fc54e32a0ab9ec0808257a7e39cfabc13092cf1.jpg) +(n) PoseMinkLoc + +![](images/501bbf1371e9af3133c22551e8e6d0598f43096337bb658fa6f40a86b5301567.jpg) +(o) PointLoc +Figure 4. Trajectories of the baselines and the proposed method on the Oxford (top) and NCLT (bottom) datasets. The ground truth and predictions are shown in black and red, respectively. The star indicates the starting position. + +![](images/fcf2d54f75968b599896a44cf44da6c30f956e1cb50ff14084c56589ef320695.jpg) +(p) SGLoc + +cloud, we search for its nearest submap in the standard point cloud, which is a pre-specified day of data, using the provided pose. The submaps are then registered to obtain the correspondence and transformation matrix, which can be used to evaluate and enhance the quality of the pose. + +Submaps building. The trajectory is divided into segments based on the prespecified distance to generate the sub-point cloud set. Then, we build the local submap according to Eq. (1), where the position of this submap is defined as the average position of the contained point cloud. + +Registration. For each submap $M_{r_i}$ , we search for its nearest submap $M_{s_j}$ based on position. Then, the ICP algorithm [3] is used to align the pair of submaps to obtain correspondence $\mathcal{C}$ and relative transformation matrix $T_{ij}$ . + +Pose evaluation and refinement. We calculate the average Euclidean distance between the correspondences of all submaps for pose quality evaluation. For pose refinement, the $T_{ij}$ is used to transform the pose of all point clouds in the + +$M_{ri}$ to correct pose errors in the data. The algorithm results are convincing when the transformed pose error is below the pre-specified threshold. + +# 4. Experiments + +# 4.1. Settings + +Benchmark datasets. We conduct experiments on two large-scale benchmark datasets. Oxford Radar RobotCar [2] (Oxford) is an urban scene localization dataset that contains over 32 repetitions traversals of a center Oxford route (about $10\mathrm{km}$ , $200\mathrm{hm}^2$ ). The dataset contains different weather, traffic, and lighting conditions. The point cloud is collected by dual Velodyne HDL-32E LiDAR. Ground truth pose is generated by the interpolations of INS. We use the data of 11-14-02-26, 14-12-05-52, 14-14-48-55, and 18-15-20-12 as the training set. The data of 15-13-06-37, 17-13-26-39, 17-14-03-00, and 18-14-14-42 are used as the test data. + +NCLT [34] dataset is collected by sensors on a Segway + +
Oxford dataset
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
15-13-06-3718.14m, 3.28°16.04m, 4.54°14.32m, 3.06°9.59m, 1.92°7.59m, 1.94°11.20m, 2.62°12.42m, 2.26°3.01m, 1.91°
17-13-26-3924.57m, 3.08°16.22m, 3.56°16.97m, 2.49°10.66m, 1.92°10.39m, 2.08°14.24m, 2.42°13.14m, 2.50°4.07m, 2.07°
17-14-03-0019.93m, 3.13°14.87m, 3.45°13.48m, 2.60°9.01m, 1.51°9.21m, 2.12°12.35m, 2.46°12.91m, 1.92°3.37m, 1.89°
18-14-14-4215.59m, 2.63°12.97m, 3.99°9.14m, 1.78°8.44m, 1.71°7.27m, 1.87°10.06m, 2.15°11.31m, 1.98°2.12m, 1.66°
Average19.56m, 3.03°15.03m, 3.89°13.48m, 2.48°9.43m, 1.77°8.62m, 2.00°11.96m, 2.41°12.45m, 2.17°3.14m, 1.88°
Quality-enhanced Oxford dataset
15-13-06-3710.90m, 2.49°10.61m, 2.56°9.47m, 2.80°4.54m, 1.83°4.17m, 1.76°6.77m, 1.84°10.75m, 2.36°1.79m, 1.67°
17-13-26-3914.60m, 2.46°11.44m, 2.14°12.98m, 2.35°6.44m, 1.78°6.16m, 1.81°8.84m, 1.84°11.07m, 2.21°1.81m, 1.76°
17-14-03-0011.28m, 2.21°10.90m, 2.01°8.64m, 2.19°4.89m, 1.55°5.42m, 1.87°8.08m, 1.69°11.53m, 1.92°1.33m, 1.59°
18-14-14-429.00m, 1.90°9.51m, 2.08°6.26m, 1.64°4.64m, 1.61°4.16m, 1.70°6.56m, 2.06°9.82m, 2.07°1.19m, 1.39°
Average11.45m, 2.27°10.62m, 2.20°9.34m, 2.25°5.13m, 1.69°4.98m, 1.79°7.56m, 1.86°10.79m, 2.14°1.53m, 1.60°
+ +Table 1. Position error (m) and orientation error $\left( {}^{ \circ }\right)$ for various methods on the Oxford and quality-enhanced Oxford datasets. + +![](images/3ab5609ef78b11a41c67b205b2ffddcf91a698820bc4eb657bc8395f7ef1fa0a.jpg) + +![](images/956411dbd4634bc06373c1415af3eae518a7335eb490c4688d5cbe9779b4356d.jpg) + +![](images/b66c8cc249877e66461eab706cf6aa849c8111db0e2219b46cfebc24091d7ed1.jpg) + +![](images/4ab67521b1b2a1c0da03e757a1915bad9e97f485692deb0b49eccf4f4f530862.jpg) + +Figure 5. Cumulative distributions of the position errors (m) on the Oxford and quality-enhanced Oxford dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value. +![](images/761907881d84cd0f626ac066cb0761363b0e7cb95d42bd0704f2f5e5f5c7c0e1.jpg) +PNVLAD DCP PosePN PosePN++ PoseMinkLoc PointLoc SGLoc + +![](images/998d5413a6fcce8f4ff9d54f035b69182021f8120aa43ae7aeb44e9ba64d731a.jpg) + +![](images/0a9d0cc6a10ece4bfa4e71be4cdf3201a05a57b5582c72080d2fded92809c456.jpg) + +![](images/ace40c87772aec7ea13b0ad045eca21208f87c14708791ed4fd75113d3ab8fd8.jpg) + +robotic platform on the University of Michigan's North Campus. The dataset contains 27 traversals, where each traversal is nearly $5.5\mathrm{km}$ and covers $45\mathrm{hm}^2$ . The point cloud is gathered by a Velodyne HDL-32E LiDAR. The 6-DoF ground truth pose is obtained by SLAM. The data of 2012-01-22, 2012-02-02, 2012-02-18, and 2012-05-11 are treated as the training set, and the data of 2012-02-12, 2012-02-19, 2012-03-31, and 2012-05-26 are used as the test set. More details about datasets can be found in the supplementary. + +Implementation details. The proposed SGLoc is implemented with PyTorch [35] and Minkowski Engine [15]. We run our code on a PC equipped with an Intel (R) Xeon (R) Silver 4214R CPU, 64GB of RAM, and a single NVIDIA RTX 3090 GPU. During training, we employ an Adam optimizer [26] with an initial learning rate of 0.001. The weight $\lambda$ is set to 1 for all datasets. On the Oxford dataset, we use the point cloud from the left LiDAR and set the voxel size to $0.2\mathrm{m}$ . On the NCLT dataset, the voxel size is $0.25\mathrm{m}$ . The TSFA module uses feature maps from the 3rd, 5th, and 8th convolution blocks with 128, 256, and 512 dimensions, respectively. Each convolution block consists of two convolution layers and a residual connection. + +Baselines. To validate the performance of SGLoc, we com + +pare it with several state-of-the-art learning-based LiDAR localization approaches. PointNetVLAD (PNVLAD) [44] is a large-scale point cloud retrieval-based method, and DCP [47] is a point cloud registration approach which employs PointNet [36] and DGCNN [48] as the embedding network. PNVLAD and DCP use the same configuration as PointLoc [46]. PosePN [51], PosePN++ [51], PoseSOE [51], PoseMinkLoc [51], and PointLoc are LiDAR-based localization framework that uses a single-frame point cloud for absolute pose regression. + +Results of pose quality evaluation and enhancement. On the Oxford and NCLT datasets, the data of 14-14-48-55 and 2012-02-18 are selected as the standard, respectively. We set the distance of the trajectory segments to build sub-maps to $20\mathrm{m}$ and the voxel size to $0.1\mathrm{m}$ to reduce the duplicate points. Registration is considered successful when the root-mean-square error of correspondence is below $1\mathrm{m}$ . The evaluated pose error of Oxford and NCLT datasets are $3.24\mathrm{m}$ and $0.25\mathrm{m}$ , respectively. Obviously, the ground truth poses in the data of NCLT is accurate. However, the pose of the Oxford dataset has various errors. Therefore, we perform quality enhancement on the Oxford dataset and obtain the enhanced pose with errors of $0.91\mathrm{m}$ . + +
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
2012-02-127.75m, 6.49°9.84m, 6.84°9.45m, 7.47°4.97m, 3.75°13.09m, 8.05°6.24m, 5.03°7.23m, 4.88°1.20m, 3.08°
2012-02-197.47m, 5.49°8.27m, 5.16°6.15m, 5.05°3.68m, 2.65°6.16m, 4.51°4.87m, 3.94°6.31m, 3.89°1.20m, 3.05°
2012-03-316.98m, 5.67°8.94m, 5.96°5.79m, 5.28°4.35m, 3.38°5.24m, 4.56°4.23m, 4.03°6.71m, 4.32°1.12m, 3.28°
2012-05-2614.34m, 7.93°15.62m, 7.99°13.47m, 7.77°9.59m, 4.49°12.60m, 7.67°10.32m, 6.52°10.02m, 5.32°3.81m, 4.74°
Average9.14m, 6.40°10.67m, 6.49°8.72m, 6.39°5.65m, 3.57°9.27m, 6.20°6.42m, 4.88°7.57m, 4.60°1.83m, 3.54°
+ +Figure 6. Cumulative distributions of the position errors (m) on the NCLT dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value. +![](images/a452ba50ba31e04308acecd78f472b1180c3bf585148e7c3702a7894235db7cc.jpg) +PNVLAD DCP PosePN PosePN++ PoseSOE PoseMinkLoc PointLoc SGLoc + +![](images/e5e9e027be59466163958615e341d678bf8e3fecdb6e3f267429ed6812e13328.jpg) + +![](images/22b34fd30e7aaffae80994ea2f4da7ea0a396e0787f8ae5346c080c8bd168b45.jpg) + +![](images/5a2dd08e7269b71ce96aace13e70eebfbdfa80fce944521073925ca818c60e58.jpg) + +# 4.2. Localization Results + +Localization on the Oxford dataset. We first evaluate the proposed SGLoc on the Oxford dataset, as shown in Tab. 1. We report the mean position and orientation errors over the full test trajectories. The proposed framework achieves a mean error of $3.14\mathrm{m} / 1.88^{\circ}$ , outperforming all competitors. Specifically, compared to PoseSOE, it improves by $63.6\%$ and $6\%$ on position and orientation, respectively. + +We further evaluate the proposed SGLoc on the quality-enhanced Oxford dataset, as shown in Tab. 2. Clearly, the mean position and orientation errors of all methods are significantly degraded compared to Tab. 1, illustrating the effectiveness and generalizability of the proposed PQEE method. SGLoc achieves a mean error of $1.53\mathrm{m} / 1.60^{\circ}$ , surpassing other methods by a large margin. Specifically, it improves PoseSOE by $69.3\% / 10.6\%$ . These results demonstrate that the proposed SGLoc can perform localization well in large-scale outdoor scenes. + +The first two rows in Fig. 4 illustrate the predicted trajectories on 17-14-03-00. The trajectory of SGLoc closely overlaps with the ground truth, demonstrating its accuracy. Fig. 5 shows the cumulative distributions of position errors on different trajectories. SGLoc achieves the desired performance, indicating that it effectively captures the scene geometry, leading to improved accuracy. + +Localization on the NCLT dataset. Then, we evaluate the proposed SGLoc on the NCLT dataset. Tab. 2 summarizes the results of all methods with mean position and orientation errors. Apparently, SGLoc significantly outperforms the existing methods with a mean error of $1.83\mathrm{m} / 3.54^{\circ}$ . Our approach improves by $67.6\%$ on position compared to PosePN++. It should be explained that there are more outliers on 2012-05-26 due to the various differences between the test and training trajectories. + +The last two rows of Fig. 4 show the predicted trajectory + +Table 2. Position error (m) and orientation error $\left( {}^{ \circ }\right)$ for various methods on the NCLT dataset. + +
15-13-06-3717-13-26-3917-14-03-0018-14-14-42
SGLoc w/o PGO1.79m, 1.67°1.81m, 1.75°1.33m, 1.59°1.19m, 1.39°
SGLoc w/ PGO1.58m, 1.10°1.56m, 1.16°1.10m, 1.18°0.99m, 1.04°
2012-02-122012-02-192012-03-312012-05-26
SGLoc w/o PGO1.20m, 3.08°1.20m, 3.05°1.12m, 3.28°3.81m, 4.74°
SGLoc w/ PGO0.88m, 2.35°0.85m, 2.06°0.79m, 2.34°3.25m, 3.52°
+ +Table 3. Localization results of SGLoc with PGO on the quality-enhanced Oxford and NCLT datasets. + +of 2012-03-31. Our prediction is closer to the ground truth and smoother than the competitors. The cumulative distributions of position errors are shown in Fig. 6, demonstrating the promising performance of the proposed SGLoc. It means that SGLoc can capture the scene geometry more efficiently compared to existing LiDAR-based localization methods. + +# 4.3. Localization Accuracy at Sub-meter Level + +Similar to MapNet [8], we utilize PGO as post-processing to further improve localization results. As shown in Tab. 3, our method has further improved in accuracy with PGO. Specifically, the SGLoc achieves accuracy at the sub-meter level on 18-14-14-42 of the quality-enhanced Oxford dataset. Moreover, in all scenes of the NCLT dataset (except 2012-05-26), the mean error of SGLoc is $0.84\mathrm{m} / 2.25^{\circ}$ . To our knowledge, SGLoc is the first regression-based method to reduce the error to the level of the sub-meter on some trajectories, which bridges the gaps in practical applications. For more results, please refer to the supplementary. + +# 4.4. Ablation Study + +Ablation on PQEE. As shown in Tab. 4, the proposed method outperforms the vanilla model without proposed modules by $43.5\% /14.9\%$ . Moreover, the performance of PQEE is significantly enhanced with or without IGCC or TSFA. For instance, PQEE considerably surpasses that without PQEE under IGCC and TSFA, achieving a mean error of $1.53\mathrm{m} / 1.60^{\circ}$ vs. $3.14\mathrm{m} / 1.88^{\circ}$ . + +
IGCCTSFAOxford w/o PQEEOxford w/ PQEENCLT
13.95m/2.89°2.23m/2.46°2.73m/5.19°
2✓3.46m/2.67°2.12m/2.32°2.62m/5.11°
3✓3.23m/2.10°1.68m/1.67°1.98m/3.51°
4✓✓3.14m/1.88°1.53m/1.60°1.83m/3.54°
+ +Ablation on IGCC. We further conduct ablation experiments to demonstrate the importance of IGCC loss. In Tab. 4, the comparison between Row 1 and Row 2 shows the module notably improves accuracy. On the Oxford dataset, compared to the vanilla model, IGCC obtains a $12.4\% /7.6\%$ improvement. On the NCLT dataset, IGCC also leads to improvements. Furthermore, IGCC improves localization accuracy compared to the method with TSFA only. This demonstrates the proposed design is helpful for capturing the scene geometry. + +Ablation on TSFA. The TSFA results are reported in Row 3 of Tab. 4. On the Oxford and NCLT dataset, compared to the results in Row 1, it yields an average $23.5\% / 30.6\%$ improvement on position and orientation. This significant improvement verifies that the proposed TSFA module can further improve the encoding of scene geometry. + +# 4.5. Runtime + +For the Oxford and NCLT datasets, the LiDAR scan rate is $20\mathrm{Hz}$ and $10\mathrm{Hz}$ , respectively. Therefore, the real-time performance here means that the running time of each scanning data is less than 50ms and 100ms, respectively. Tab. 5 shows the running time on the Oxford and NCLT dataset. On the Oxford dataset, SGLoc takes a running time of 38ms per frame, with the correspondence regression stage consuming 25ms and the pose estimation stage consuming 13ms. On the NCLT dataset, the running times are 75ms, 41ms, and 34ms, respectively. Note that the running time of PNVLAD, DCP, PosePN, and PoseMinkLoc are less than 10ms due to the simplicity of their networks. Therefore, Our SGLoc can achieve real-time localization and is very competitive with these methods, but the performance of SGLoc is much better. + +# 5. Discussion + +LiDAR localization in large-scale outdoor scenes is a critical component of autonomous driving. However, existing APR methods still face challenges in effectively encoding scene geometry and dealing with unsatisfactory data quality, resulting in suboptimal accuracy. To overcome these challenges, we propose SGLoc and PQEE, which significantly improves accuracy. Compared to previous work, SGLoc stands out due to the following differences. + +Difference between SGLoc and DSAC++. Camera coordinate regression (DSAC++ [5]) predicts 2D-3D correspondences, to our knowledge, SGLoc is the first work to regress 3D-3D point correspondences. Though both DSAC++ and our SGLoc use regression, we address different problems. + +![](images/3c426c3ed673cfde1927a459cce603bddb454577fa8c3c2fe70b1b4023f6b78a.jpg) +Figure 7. Ground truth poses in the data on the Oxford (left) and quality-enhanced Oxford (right) dataset. The green trajectory indicates the prespecified standard data. + +![](images/b5e0c55f66493ee05449068ffb6ccea3532580f668e32e8d80257299f31f344e.jpg) + +Table 4. Ablation study on the Oxford and NCLT datasets. + +
MethodsPNVLADDCPPosePNPosePN+PoseSOEPoseMinkLocPointLocSGLoc
Oxford6ms3ms2ms111ms244ms8ms625ms38ms
NCLT6ms3ms2ms108ms230ms8ms614ms75ms
+ +Table 5. Runtime (ms) of different methods on the Oxford and NCLT datasets. + +We summarize the differences. (1) SGLoc learns rigid transformations instead of affine transformations that require the intrinsics of the query camera; (2) Our methods' ground truth correspondences generation requires only input point clouds and poses, which can be deployed efficiently in online training; (3) SGLoc can be applied to large-scale outdoor scenes covering about $200\mathrm{hm}^2$ . + +Difference between PQEE and point cloud registration. We empirically find existing large-scale outdoor datasets cannot precisely provide the same position values (bad quality) in the same position on different days, as shown in Fig. 7. More importantly, we find this degraded data quality can significantly decrease the localization accuracy. We hope this new finding can inspire researchers to work on this new source of performance degradation. Based on this new finding, we propose PQEE, which aligns and fuses standard/raw data in LiDAR localization. It uses point cloud registration, but the purpose differs from conventional point cloud registration. + +# 6. Conclusion + +We propose a novel regression-based framework, SGLoc, for LiDAR localization. SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences. The core component of SGLoc is the first step, which effectively encodes scene geometry, leading to significant performance improvement. To achieve high accuracy in this step, we propose the TSFA module and IGCC loss to improve the encoding of scene geometry. Moreover, to increase the data quality and localization accuracy, the PQEE method is designed to measure and correct the ground truth pose errors in the localization data. Extensive experimental results verify the great effectiveness of our method. + +Acknowledgements This work was partially supported by the open fund of PDL (2022-KJWPDL-12, WDZC20215250113), by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003). + +# References + +[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongkai Chen, Lei Li, Zeyu Hu, Hongbo Fu, and Chiew-Lan Tai. Pointdsc: Robust point cloud registration using deep spatial consistency. In CVPR, pages 15859-15869, 2021. 4 +[2] Dan Barnes, Matthew Gadd, Paul Murcutt, Paul Newman, and Ingmar Posner. The oxford radar robotcar dataset: A radar extension to the oxford robotcar dataset. In ICRA, pages 6433-6438, 2020. 1, 2, 5 +[3] Paul J Besl and Neil D McKay. Method for registration of 3-d shapes. 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However, the accuracy of existing methods still has room to improve due to the difficulty of effectively encoding the scene geometry and the unsatisfactory quality of the data. In this work, we propose a novel LiDAR localization framework, SGLoc, which decouples the pose estimation to point cloud correspondence regression and pose estimation via this correspondence. This decoupling effectively encodes the scene geometry because the decoupled correspondence regression step greatly preserves the scene geometry, leading to significant performance improvement. Apart from this decoupling, we also design a tri-scale spatial feature aggregation module and inter-geometric consistency constraint loss to effectively capture scene geometry. Moreover, we empirically find that the ground truth might be noisy due to GPS/INS measuring errors, greatly reducing the pose estimation performance. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 611, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 287, + 658 + ], + "type": "text", + "content": "Estimating the position and orientation of LiDAR from point clouds is a fundamental component of many applications in computer vision, e.g., autonomous driving, virtual reality, and augmented reality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 659, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 287, + 684 + ], + "type": "text", + "content": "Contemporary state-of-the-art LiDAR-based localization methods explicitly use maps, which match the query point" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 239, + 417, + 343 + ], + "blocks": [ + { + "bbox": [ + 307, + 239, + 417, + 343 + ], + "lines": [ + { + "bbox": [ + 307, + 239, + 417, + 343 + ], + "spans": [ + { + "bbox": [ + 307, + 239, + 417, + 343 + ], + "type": "image", + "image_path": "48da2a67e01883c3383fa5bd20d43768b1a02685c4b94e2eb4a382e2eda7ada8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 349, + 547, + 394 + ], + "lines": [ + { + "bbox": [ + 305, + 349, + 547, + 394 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 547, + 394 + ], + "type": "text", + "content": "Figure 1. LiDAR Localization results of our method and PosePN++ [51] (state-of-the-art method) in urban (left) and school (right) scenes from Oxford Radar RobotCar [2] and NCLT [34] datasets. The star indicates the starting position." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 424, + 239, + 545, + 343 + ], + "blocks": [ + { + "bbox": [ + 424, + 239, + 545, + 343 + ], + "lines": [ + { + "bbox": [ + 424, + 239, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 424, + 239, + 545, + 343 + ], + "type": "image", + "image_path": "e1bd0e578c82de888b89d2e8b364988a11a9ddbd3511247bd34ca88db909e32a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 402, + 547, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 521 + ], + "type": "text", + "content": "cloud with a pre-built 3D map [18, 23, 27, 49]. However, these methods usually require expensive 3D map storage and communication. One alternative is the regression-based approach, absolute pose regression (APR), which directly estimates the poses in the inference stage without maps [8, 24, 25, 40, 45]. APR methods typically use a CNN to encode the scene feature and a multi-layer perceptron to regress the pose. Compared to map-based methods, APR does not need to store the pre-built maps, accordingly reducing communications." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "type": "text", + "content": "For (1), APR networks learn highly abstract global scene representations, which allow the network to classify the scene effectively [25]. However, the global features usually cannot encode detailed scene geometry, which is the key to achieving an accurate pose estimation [10, 11, 38, 39]. Prior efforts have tried to minimize the relative pose or photometric errors to add geometry constraints by pose graph optimization (PGO) [4, 21] or novel view synthesis (NVS) [10, 11]. However, this introduces additional computations, limiting its wide applications. For (2), we empirically find current large-scale outdoor datasets suffer from various errors in the data due to GPS/INS measuring errors. It affects the APR learning process and makes it difficult to evaluate the localization results accurately. To our knowledge, the impact of data quality on localization has not been carefully investigated in the existing literature." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 127, + 703 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9286" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 370 + ], + "type": "text", + "content": "This paper proposes a novel framework, SGLoc, which can (1) effectively capture the scene geometry; In addition, we propose a data pre-processing method, Pose Quality Evaluation and Enhancement (PQEE), which can (2) improve data quality. (1) Existing APR methods conduct end-to-end regression from the point cloud in LiDAR coordinate to pose. Unlike them, SGLoc decouples this process to (a) regression from the point cloud in LiDAR coordinate to world coordinate and (b) pose estimation via the point cloud correspondence in LiDAR and world coordinate using RANSAC [17]. Importantly, step (a) can effectively preserve the scene geometry, which is key for pose estimation [10, 11, 38, 39]. To achieve high accuracy in step (a), we design a Tri-scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to effectively capture scene geometry. (2) We empirically find that pose errors in the data greatly degrade the pose estimation performance. For example, the ground truth pose obtained by GPS/INS suffers from measuring errors. To address this problem, we proposed a PQEE method which can measure the errors in the pose and correct them afterward. We conduct extensive experiments on Oxford Radar RobotCar [2] and NCLT [34] datasets, and results show that our method has great advantages over the state-of-the-art, as demonstrated in Fig. 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 372, + 258, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 372, + 258, + 382 + ], + "spans": [ + { + "bbox": [ + 59, + 372, + 258, + 382 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 384, + 287, + 616 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 59, + 384, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 384, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 59, + 384, + 287, + 443 + ], + "type": "text", + "content": "- SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences, which can effectively capture scene geometry, leading to significant performance improvement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 446, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 446, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 59, + 446, + 287, + 493 + ], + "type": "text", + "content": "- We propose a novel Tri-Scale Spatial Feature Aggregation (TSFA) module and an Inter-Geometric Consistency Constraint (IGCC) loss to further improve the encoding of scene geometry." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 496, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 496, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 59, + 496, + 287, + 554 + ], + "type": "text", + "content": "- We propose a generalized pose quality evaluation and enhancement (PQEE) method to measure and correct the pose errors in the localization data, improving " + }, + { + "bbox": [ + 59, + 496, + 287, + 554 + ], + "type": "inline_equation", + "content": "34.2\\% / 16.8\\%" + }, + { + "bbox": [ + 59, + 496, + 287, + 554 + ], + "type": "text", + "content": " on position and orientation for existing LiDAR localization methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 558, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 558, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 59, + 558, + 287, + 616 + ], + "type": "text", + "content": "- Extensive experiments demonstrate the effectiveness of SGLoc, which outperforms state-of-the-art LiDAR localization methods by " + }, + { + "bbox": [ + 59, + 558, + 287, + 616 + ], + "type": "inline_equation", + "content": "68.1\\%" + }, + { + "bbox": [ + 59, + 558, + 287, + 616 + ], + "type": "text", + "content": " on position accuracy. In addition, to our knowledge, we are the first to reduce the error to the level of the sub-meter on some trajectories." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 628, + 134, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 134, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 134, + 639 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 647, + 183, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 183, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 183, + 659 + ], + "type": "text", + "content": "2.1. Map-based Localization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 713 + ], + "type": "text", + "content": "Map-based methods aim to match the query point cloud with a pre-built 3D map, which can be classified into retrieval-based [18, 27, 30, 44, 49] and registration-based methods [14, 16, 20, 32, 37, 47]. Retrieval-based methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": "cast localization as a place recognition problem, which finds the most similar point cloud in the database. Registration-based localization performs fine matching between the query point cloud and the pred-built map. DCP [47] is an impressive work investigating geometry correspondences generated by weighted calculation for pose estimation. Unlike this, SGLoc directly regresses the correspondences. In addition, Some methods combine both retrieval and registration techniques to achieve better localization accuracy in dense urban areas [9, 12, 50, 52]. However, the high cost of 3D map storage and communication limits the widespread application of map-based methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 226, + 471, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 226, + 471, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 226, + 471, + 239 + ], + "type": "text", + "content": "2.2. Regression-based Localization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 245, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 547, + 376 + ], + "type": "text", + "content": "Recently, in camera localization, the scene coordinate regression method has been designed, which regresses 2D-3D correspondences and estimates the pose with PnP-RANSAC [4,6,7,22,54]. While these methods have shown impressive results in small and medium-sized scenes, e.g., 7-Scenes [42], they do not scale well to large scenes [5]. HSCNet attempts to solve this problem by conditioning discrete location labels around each pixel [28], but it still cannot be applied to large-scale outdoor scenes, e.g., the street scene in the Cambridge landmark dataset [25], which covers an area of about " + }, + { + "bbox": [ + 304, + 245, + 547, + 376 + ], + "type": "inline_equation", + "content": "5\\mathrm{hm}^2" + }, + { + "bbox": [ + 304, + 245, + 547, + 376 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 378, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 547, + 545 + ], + "type": "text", + "content": "Absolute pose regression. APR methods typically use the same basic pipeline: first, extracting high-level features using a CNN and then using these features to regress the 6-DoF pose. PoseNet [25] originally defines this task using a modified GoogleNet [43] to regress camera poses. Successors of PoseNet have focused on improving the framework through model architecture and loss function. E-PoseNet [33] proposes a translation and rotation equivariant CNN that directly induces representations of camera motions into the feature space. PAE [41] uses the pose auto-encoders framework to significantly reduce model parameters. However, the above methods learn highly abstract global scene representations, leading to various wrong predictions due to the lack of effective scene geometry encoding." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 546, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 548, + 713 + ], + "type": "text", + "content": "Recent research suggests scene geometry is key to accurate pose estimation [10, 11, 38, 39]. Geometric PoseNet [24] investigates geometric loss for learning to regress position and orientation simultaneously with scene geometry. MapNet [8] adds pairwise geometric constraints between video frames using additional VO algorithms. AtLoc [45] utilizes a self-attention mechanism to adaptively focus on the import targets in the scene. MS-Transformer [40] proposes a transformer-based method to learn robust features. DirectPoseNet [11] adapts additional photometric loss by comparing the query image with NVS on the predicted pose. DFNet [10] explores a direct matching scheme in feature space, leading to a more robust performance than DirectPoseNet. However, these methods require auxiliary algo" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9287" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 87, + 515, + 178 + ], + "blocks": [ + { + "bbox": [ + 77, + 75, + 237, + 86 + ], + "lines": [ + { + "bbox": [ + 77, + 75, + 237, + 86 + ], + "spans": [ + { + "bbox": [ + 77, + 75, + 237, + 86 + ], + "type": "text", + "content": "(1) Point cloud correspondence regression" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 71, + 87, + 515, + 178 + ], + "lines": [ + { + "bbox": [ + 71, + 87, + 515, + 178 + ], + "spans": [ + { + "bbox": [ + 71, + 87, + 515, + 178 + ], + "type": "image", + "image_path": "a73edaff36b80adab289edf23ccf2765d99bcd627b37c1e258b8c3551d8b1cd8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 431, + 184, + 462, + 194 + ], + "lines": [ + { + "bbox": [ + 431, + 184, + 462, + 194 + ], + "spans": [ + { + "bbox": [ + 431, + 184, + 462, + 194 + ], + "type": "text", + "content": "Legend" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 200, + 490, + 209 + ], + "lines": [ + { + "bbox": [ + 427, + 200, + 490, + 209 + ], + "spans": [ + { + "bbox": [ + 427, + 200, + 490, + 209 + ], + "type": "text", + "content": "3D coordinates" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 72, + 196, + 397, + 279 + ], + "blocks": [ + { + "bbox": [ + 78, + 184, + 176, + 194 + ], + "lines": [ + { + "bbox": [ + 78, + 184, + 176, + 194 + ], + "spans": [ + { + "bbox": [ + 78, + 184, + 176, + 194 + ], + "type": "text", + "content": "(2) 6-DoF pose estimation" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 72, + 196, + 397, + 279 + ], + "lines": [ + { + "bbox": [ + 72, + 196, + 397, + 279 + ], + "spans": [ + { + "bbox": [ + 72, + 196, + 397, + 279 + ], + "type": "image", + "image_path": "c5b0fd8bcdb3ff59b582dfc2f60d885757ba9468a6a31a5964009aaa00d57fa0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 214, + 485, + 224 + ], + "lines": [ + { + "bbox": [ + 429, + 214, + 485, + 224 + ], + "spans": [ + { + "bbox": [ + 429, + 214, + 485, + 224 + ], + "type": "text", + "content": "Point features" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 429, + 228, + 502, + 239 + ], + "lines": [ + { + "bbox": [ + 429, + 228, + 502, + 239 + ], + "spans": [ + { + "bbox": [ + 429, + 228, + 502, + 239 + ], + "type": "text", + "content": "Aggregated feature" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 427, + 245, + 495, + 256 + ], + "lines": [ + { + "bbox": [ + 427, + 245, + 495, + 256 + ], + "spans": [ + { + "bbox": [ + 427, + 245, + 495, + 256 + ], + "type": "inline_equation", + "content": "\\mathbb{X}" + }, + { + "bbox": [ + 427, + 245, + 495, + 256 + ], + "type": "text", + "content": " Pose Hypotheses" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 427, + 262, + 487, + 273 + ], + "lines": [ + { + "bbox": [ + 427, + 262, + 487, + 273 + ], + "spans": [ + { + "bbox": [ + 427, + 262, + 487, + 273 + ], + "type": "text", + "content": "Final Estimate" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed framework including point cloud correspondence regression (top row) and 6-DoF pose estimation (bottom row). " + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "inline_equation", + "content": "F_{3}" + }, + { + "bbox": [ + 46, + 287, + 547, + 309 + ], + "type": "text", + "content": " are the extracted feature maps with different receptive fields." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 319, + 288, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 288, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 288, + 390 + ], + "type": "text", + "content": "rithms, e.g., PGO, NVS, introducing additional computations. Unlike these methods, we decouple the pose estimation process to (1) regression point cloud correspondence and (2) pose estimate via the correspondence using RANSAC. Through step (1), scene geometry can be effectively encoded without additional computations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 391, + 288, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 288, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 288, + 463 + ], + "type": "text", + "content": "Recently, LiDAR-based APR methods, e.g., PointLoc [46], PoseSOE [51], and PosePN++ [51], have shown impressive performance on large-scale outdoor datasets because the point cloud is robust to illumination changes and rich in geometric information. However, effectively encoding scene geometry remains quite challenging." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 475, + 103, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 103, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 103, + 487 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 495, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 602 + ], + "type": "text", + "content": "Recent APR methods have achieved impressive results in localization. However, they do not effectively encode the scene geometry and measure the data quality, leading to the accuracy still having room to improve. In this paper, we propose SGLoc and a Pose Quality Evaluation Enhancement (PQEE) method to address these problems. Sec. 3.1 elaborates SGLoc, which can effectively capture the scene geometry. Then, a PQEE method (Sec. 3.2) is proposed to measure and correct the pose errors in the data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 610, + 102, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 102, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 102, + 623 + ], + "type": "text", + "content": "3.1.SGLoc" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "We now introduce the proposed SGLoc, as shown in Fig. 2, which can be divided into (1) point cloud correspondence regression: convert the Raw LiDAR Point Cloud (RPC) to its corresponding Point Cloud in World coordinate frame (WPC) and (2) 6-DoF pose estimation: estimate pose via matching RPC and WPC. In this work, we design a sparse-convolution-based FCN [15,31] to implement SGLoc," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 547, + 403 + ], + "type": "text", + "content": "which contains a feature extractor, a Tri-Scale Spatial Feature Aggregation (TSFA) module, and a regressor. The feature extractor and regressor generate feature maps with different receptive fields and achieve point cloud correspondence via regression, respectively. The TSFA module and intergeometric consistency constraint (IGCC) loss are proposed to effectively capture scene geometry." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": "**Framework.** Here we formulate the framework of SGLoc. Given the query point cloud " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "P_{t} \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": ", we aim to estimate its global 6-DoF pose " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": ". Each pose " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = [\\mathbf{x}, \\mathbf{q}]" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": " is represented by a position vector " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": " and an orientation vector " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{q} \\in \\mathbb{R}^r" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": " (e.g., a 4D unit quaternion or a 3D Euler angle). Hence, we first define the query point cloud pose " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": " as the transformation that maps 3D points in LiDAR coordinate frame, denoted as " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{l}" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": ", to 3D points in world coordinate frame, denoted as " + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 403, + 545, + 498 + ], + "type": "text", + "content": ", i.e." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 403, + 505, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 403, + 505, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 403, + 505, + 545, + 517 + ], + "type": "interline_equation", + "content": "w _ {i} = T l _ {i}, \\tag {1}", + "image_path": "7a8c99f19fbf9598dca673bd11a43aa0459efb4609e254dab75040ee78cc042e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "text", + "content": " denotes the point index in the query point cloud; " + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "inline_equation", + "content": "4 \\times 4" + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "text", + "content": " matrix representation of the pose " + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 522, + 545, + 546 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": "Then, we denote the complete set of scene coordinates with a global pose for the query point cloud as " + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "inline_equation", + "content": "y_{i} \\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": ". As shown in Fig. 2, (1) for point cloud correspondence regression, we utilize a neural network to learn a function " + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{F}: \\mathcal{V} = \\mathcal{F}(P_t)" + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": ". (2) Regarding 6-DoF pose estimation during inference, we utilize the RANSAC algorithm to select " + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": " group from the predicted correspondence " + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 546, + 545, + 641 + ], + "type": "text", + "content": ", and optimize the energy function as follows:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 359, + 644, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 644, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 359, + 644, + 545, + 677 + ], + "type": "interline_equation", + "content": "T ^ {\\prime} = \\arg \\min _ {T} \\sum_ {i} ^ {| M |} \\| T l _ {i} - w _ {i} \\| _ {2}, \\tag {2}", + "image_path": "174d8a1aee0b9ef8447962cd0ed7759efc9e2e9c5b598223b0e3f0c65f48235f.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " is set to 3; " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " denotes the point index; " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "T^{\\prime}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " is the estimated transformation matrix. Then, " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "T^{\\prime}" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " can be used to calculate the above energy function of each correspondence" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9288" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 287, + 220 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 287, + 220 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 287, + 220 + ], + "type": "image", + "image_path": "57dffb77d13a6cb50b3dc257de79f4b65eee352dd47fb1db539256483d8d6c19.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 222, + 285, + 233 + ], + "lines": [ + { + "bbox": [ + 48, + 222, + 285, + 233 + ], + "spans": [ + { + "bbox": [ + 48, + 222, + 285, + 233 + ], + "type": "text", + "content": "Figure 3. Tri-Scale Spatial Feature Aggregation (TSFA) Module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "type": "text", + "content": "in " + }, + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "type": "text", + "content": " to filter outliers. The above process will be repeated until convergence. Finally, the estimated " + }, + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "type": "inline_equation", + "content": "T^{\\prime}" + }, + { + "bbox": [ + 46, + 245, + 287, + 281 + ], + "type": "text", + "content": " can easily be converted into a vectorized pose." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 288, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 288, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 288, + 329 + ], + "type": "text", + "content": "It is worth noting that during training, SGLoc only requires the input point cloud and the pose, which allows for effective scene geometry encoding by minimizing correspondence distance without any additional computations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": "Tri-scale spatial feature aggregation. As described above, SGLoc estimates the pose via the regressed correspondence " + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 329, + 288, + 413 + ], + "type": "text", + "content": ". Therefore, the spatial details in network features are critical to localization accuracy. To effectively capture the spatial details at shallow layers, inspired by the attention mechanism [19, 29, 53], we introduce a Tri-Scale Spatial Feature Aggregation (TSFA) module." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": "As shown in Fig. 2, the TSFA module takes the low-level features " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " and high-level feature " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "F_{3}" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " as the input. We elaborate the architecture of TSFA module in Fig. 3. For convenience, we refer " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "F_{1}' = \\mathcal{H}(\\mathcal{D}(\\mathcal{H}(F_{1})), F_{2}' = \\mathcal{H}(\\mathcal{D}(\\mathcal{H}(F_{2}))" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "F_{3}' = \\mathcal{H}(F_{3})" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": "), where " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " indicates the down-sampling and " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " denotes the convolution followed by a batch normalization and a ReLU activation function. We first squeeze the channels of the features " + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "inline_equation", + "content": "(F_{1}, F_{2}, F_{3})" + }, + { + "bbox": [ + 46, + 413, + 289, + 582 + ], + "type": "text", + "content": " to 1. Then, we conduct the addition operation and sigmoid activation to obtain the spatial attention mask, which can adaptively enhance spatial details. Finally, we apply dot product and concatenation to achieve a powerful feature with rich spatial details and structure information. The output can be expressed as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 586, + 287, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 586, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 62, + 586, + 287, + 601 + ], + "type": "interline_equation", + "content": "F _ {o} = \\left[ \\sigma \\left(F _ {1} ^ {\\prime} + F _ {3} ^ {\\prime}\\right) \\odot F _ {1}, \\sigma \\left(F _ {2} ^ {\\prime} + F _ {3} ^ {\\prime}\\right) \\odot F _ {2}, F _ {3} \\right], \\tag {3}", + "image_path": "be909f20a33d4aea47fffedac1da5ad0db319f2886f8a7e1e82779ae1bd09c83.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "content": " is the sigmoid function; " + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "content": " is dot product; " + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "inline_equation", + "content": "[\\cdot]" + }, + { + "bbox": [ + 46, + 605, + 287, + 628 + ], + "type": "text", + "content": " denotes the concatenation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": "Inter-geometric consistency constraint. Training the network with " + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": " loss " + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{L1})" + }, + { + "bbox": [ + 46, + 630, + 289, + 714 + ], + "type": "text", + "content": " can effectively minimize the distance between the predicted and the ground truth scene coordinates. However, the above constraint is a node-wise loss, which supervises each correspondence individually. This is unfavorable for learning scene geometry. Inspired by spatial compatibility [1, 13], which assumes that two correspondences" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 485, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 485, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 485, + 83 + ], + "type": "text", + "content": "Algorithm 1 Pseudocode for PQEE method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "content": "Input: Raw point cloud set " + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "content": " and pose set " + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "T_r" + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "content": "; Standard point cloud set " + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "P_s" + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "text", + "content": " and pose set " + }, + { + "bbox": [ + 305, + 85, + 545, + 109 + ], + "type": "inline_equation", + "content": "T_s" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 109, + 522, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 109, + 522, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 109, + 522, + 121 + ], + "type": "text", + "content": "Output: Pose error " + }, + { + "bbox": [ + 306, + 109, + 522, + 121 + ], + "type": "inline_equation", + "content": "E'" + }, + { + "bbox": [ + 306, + 109, + 522, + 121 + ], + "type": "text", + "content": "; Quality enhanced pose set " + }, + { + "bbox": [ + 306, + 109, + 522, + 121 + ], + "type": "inline_equation", + "content": "T_r'" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "text", + "content": "Initialization: Build submaps " + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "inline_equation", + "content": "M_r = \\{M_{r_1}, \\ldots, M_{r_n}\\}" + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "inline_equation", + "content": "P_r" + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "inline_equation", + "content": "T_r" + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": "text", + "content": "; Build submaps " + }, + { + "bbox": [ + 306, + 121, + 545, + 156 + ], + "type": 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Trajectories of the baselines and the proposed method on the Oxford (top) and NCLT (bottom) datasets. The ground truth and predictions are shown in black and red, respectively. The star indicates the starting position." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 419, + 362, + 527, + 442 + ], + "blocks": [ + { + "bbox": [ + 419, + 362, + 527, + 442 + ], + "lines": [ + { + "bbox": [ + 419, + 362, + 527, + 442 + ], + "spans": [ + { + "bbox": [ + 419, + 362, + 527, + 442 + ], + "type": "image", + "image_path": "fcf2d54f75968b599896a44cf44da6c30f956e1cb50ff14084c56589ef320695.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 459, + 445, + 492, + 454 + ], + "lines": [ + { + "bbox": [ + 459, + 445, + 492, + 454 + ], + "spans": [ + { + "bbox": [ + 459, + 445, + 492, + 454 + ], + "type": "text", + "content": "(p) SGLoc" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_caption" + } + ], + "index": 30 + }, + { + "bbox": [ + 46, + 491, + 288, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 288, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 288, + 551 + ], + "type": "text", + "content": "cloud, we search for its nearest submap in the standard point cloud, which is a pre-specified day of data, using the provided pose. The submaps are then registered to obtain the correspondence and transformation matrix, which can be used to evaluate and enhance the quality of the pose." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 553, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 553, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 553, + 287, + 613 + ], + "type": "text", + "content": "Submaps building. The trajectory is divided into segments based on the prespecified distance to generate the sub-point cloud set. Then, we build the local submap according to Eq. (1), where the position of this submap is defined as the average position of the contained point cloud." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "text", + "content": "Registration. For each submap " + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "inline_equation", + "content": "M_{r_i}" + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "text", + "content": ", we search for its nearest submap " + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "inline_equation", + "content": "M_{s_j}" + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "text", + "content": " based on position. Then, the ICP algorithm [3] is used to align the pair of submaps to obtain correspondence " + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "text", + "content": " and relative transformation matrix " + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "inline_equation", + "content": "T_{ij}" + }, + { + "bbox": [ + 46, + 615, + 288, + 664 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Pose evaluation and refinement. We calculate the average Euclidean distance between the correspondences of all submaps for pose quality evaluation. For pose refinement, the " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "T_{ij}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " is used to transform the pose of all point clouds in the" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 305, + 491, + 545, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 545, + 527 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 545, + 527 + ], + "type": "inline_equation", + "content": "M_{ri}" + }, + { + "bbox": [ + 305, + 491, + 545, + 527 + ], + "type": "text", + "content": " to correct pose errors in the data. The algorithm results are convincing when the transformed pose error is below the pre-specified threshold." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 534, + 387, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 387, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 387, + 548 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 552, + 365, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 365, + 565 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 365, + 565 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "type": "text", + "content": "Benchmark datasets. We conduct experiments on two large-scale benchmark datasets. Oxford Radar RobotCar [2] (Oxford) is an urban scene localization dataset that contains over 32 repetitions traversals of a center Oxford route (about " + }, + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "type": "inline_equation", + "content": "10\\mathrm{km}" + }, + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "type": "inline_equation", + "content": "200\\mathrm{hm}^2" + }, + { + "bbox": [ + 304, + 569, + 547, + 700 + ], + "type": "text", + "content": "). The dataset contains different weather, traffic, and lighting conditions. The point cloud is collected by dual Velodyne HDL-32E LiDAR. Ground truth pose is generated by the interpolations of INS. We use the data of 11-14-02-26, 14-12-05-52, 14-14-48-55, and 18-15-20-12 as the training set. The data of 15-13-06-37, 17-13-26-39, 17-14-03-00, and 18-14-14-42 are used as the test data." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "NCLT [34] dataset is collected by sensors on a Segway" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9290" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 71, + 530, + 198 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 530, + 198 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 530, + 198 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 530, + 198 + ], + "type": "table", + "html": "
Oxford dataset
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
15-13-06-3718.14m, 3.28°16.04m, 4.54°14.32m, 3.06°9.59m, 1.92°7.59m, 1.94°11.20m, 2.62°12.42m, 2.26°3.01m, 1.91°
17-13-26-3924.57m, 3.08°16.22m, 3.56°16.97m, 2.49°10.66m, 1.92°10.39m, 2.08°14.24m, 2.42°13.14m, 2.50°4.07m, 2.07°
17-14-03-0019.93m, 3.13°14.87m, 3.45°13.48m, 2.60°9.01m, 1.51°9.21m, 2.12°12.35m, 2.46°12.91m, 1.92°3.37m, 1.89°
18-14-14-4215.59m, 2.63°12.97m, 3.99°9.14m, 1.78°8.44m, 1.71°7.27m, 1.87°10.06m, 2.15°11.31m, 1.98°2.12m, 1.66°
Average19.56m, 3.03°15.03m, 3.89°13.48m, 2.48°9.43m, 1.77°8.62m, 2.00°11.96m, 2.41°12.45m, 2.17°3.14m, 1.88°
Quality-enhanced Oxford dataset
15-13-06-3710.90m, 2.49°10.61m, 2.56°9.47m, 2.80°4.54m, 1.83°4.17m, 1.76°6.77m, 1.84°10.75m, 2.36°1.79m, 1.67°
17-13-26-3914.60m, 2.46°11.44m, 2.14°12.98m, 2.35°6.44m, 1.78°6.16m, 1.81°8.84m, 1.84°11.07m, 2.21°1.81m, 1.76°
17-14-03-0011.28m, 2.21°10.90m, 2.01°8.64m, 2.19°4.89m, 1.55°5.42m, 1.87°8.08m, 1.69°11.53m, 1.92°1.33m, 1.59°
18-14-14-429.00m, 1.90°9.51m, 2.08°6.26m, 1.64°4.64m, 1.61°4.16m, 1.70°6.56m, 2.06°9.82m, 2.07°1.19m, 1.39°
Average11.45m, 2.27°10.62m, 2.20°9.34m, 2.25°5.13m, 1.69°4.98m, 1.79°7.56m, 1.86°10.79m, 2.14°1.53m, 1.60°
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Position error (m) and orientation error " + }, + { + "bbox": [ + 70, + 198, + 522, + 209 + ], + "type": "inline_equation", + "content": "\\left( {}^{ \\circ }\\right)" + }, + { + "bbox": [ + 70, + 198, + 522, + 209 + ], + "type": "text", + "content": " for various methods on the Oxford and quality-enhanced Oxford datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 66, + 210, + 174, + 293 + ], + "blocks": [ + { + "bbox": [ + 66, + 210, + 174, + 293 + ], + "lines": [ + { + "bbox": [ + 66, + 210, + 174, + 293 + ], + "spans": [ + { + "bbox": [ + 66, + 210, + 174, + 293 + ], + "type": "image", + "image_path": "3ab5609ef78b11a41c67b205b2ffddcf91a698820bc4eb657bc8395f7ef1fa0a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 183, + 211, + 290, + 293 + ], + "blocks": [ + { + "bbox": [ + 183, + 211, + 290, + 293 + ], + "lines": [ + { + "bbox": [ + 183, + 211, + 290, + 293 + ], + "spans": [ + { + "bbox": [ + 183, + 211, + 290, + 293 + ], + "type": "image", + "image_path": "956411dbd4634bc06373c1415af3eae518a7335eb490c4688d5cbe9779b4356d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 303, + 211, + 410, + 293 + ], + "blocks": [ + { + "bbox": [ + 303, + 211, + 410, + 293 + ], + "lines": [ + { + "bbox": [ + 303, + 211, + 410, + 293 + ], + "spans": [ + { + "bbox": [ + 303, + 211, + 410, + 293 + ], + "type": "image", + "image_path": "b66c8cc249877e66461eab706cf6aa849c8111db0e2219b46cfebc24091d7ed1.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 421, + 211, + 527, + 293 + ], + "blocks": [ + { + "bbox": [ + 421, + 211, + 527, + 293 + ], + "lines": [ + { + "bbox": [ + 421, + 211, + 527, + 293 + ], + "spans": [ + { + "bbox": [ + 421, + 211, + 527, + 293 + ], + "type": "image", + "image_path": "4ab67521b1b2a1c0da03e757a1915bad9e97f485692deb0b49eccf4f4f530862.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 65, + 296, + 171, + 388 + ], + "blocks": [ + { + "bbox": [ + 65, + 296, + 171, + 388 + ], + "lines": [ + { + "bbox": [ + 65, + 296, + 171, + 388 + ], + "spans": [ + { + "bbox": [ + 65, + 296, + 171, + 388 + ], + "type": "image", + "image_path": "761907881d84cd0f626ac066cb0761363b0e7cb95d42bd0704f2f5e5f5c7c0e1.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 392, + 523, + 402 + ], + "lines": [ + { + "bbox": [ + 67, + 392, + 523, + 402 + ], + "spans": [ + { + "bbox": [ + 67, + 392, + 523, + 402 + ], + "type": "text", + "content": "PNVLAD DCP PosePN PosePN++ PoseMinkLoc PointLoc SGLoc" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 404, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 46, + 404, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 545, + 426 + ], + "type": "text", + "content": "Figure 5. Cumulative distributions of the position errors (m) on the Oxford and quality-enhanced Oxford dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 184, + 296, + 290, + 388 + ], + "blocks": [ + { + "bbox": [ + 184, + 296, + 290, + 388 + ], + "lines": [ + { + "bbox": [ + 184, + 296, + 290, + 388 + ], + "spans": [ + { + "bbox": [ + 184, + 296, + 290, + 388 + ], + "type": "image", + "image_path": "998d5413a6fcce8f4ff9d54f035b69182021f8120aa43ae7aeb44e9ba64d731a.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 303, + 296, + 410, + 388 + ], + "blocks": [ + { + "bbox": [ + 303, + 296, + 410, + 388 + ], + "lines": [ + { + "bbox": [ + 303, + 296, + 410, + 388 + ], + "spans": [ + { + "bbox": [ + 303, + 296, + 410, + 388 + ], + "type": "image", + "image_path": "0a9d0cc6a10ece4bfa4e71be4cdf3201a05a57b5582c72080d2fded92809c456.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 421, + 296, + 527, + 388 + ], + "blocks": [ + { + "bbox": [ + 421, + 296, + 527, + 388 + ], + "lines": [ + { + "bbox": [ + 421, + 296, + 527, + 388 + ], + "spans": [ + { + "bbox": [ + 421, + 296, + 527, + 388 + ], + "type": "image", + "image_path": "ace40c87772aec7ea13b0ad045eca21208f87c14708791ed4fd75113d3ab8fd8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "type": "text", + "content": "robotic platform on the University of Michigan's North Campus. The dataset contains 27 traversals, where each traversal is nearly " + }, + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "type": "inline_equation", + "content": "5.5\\mathrm{km}" + }, + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "type": "text", + "content": " and covers " + }, + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "type": "inline_equation", + "content": "45\\mathrm{hm}^2" + }, + { + "bbox": [ + 46, + 439, + 288, + 546 + ], + "type": "text", + "content": ". The point cloud is gathered by a Velodyne HDL-32E LiDAR. The 6-DoF ground truth pose is obtained by SLAM. The data of 2012-01-22, 2012-02-02, 2012-02-18, and 2012-05-11 are treated as the training set, and the data of 2012-02-12, 2012-02-19, 2012-03-31, and 2012-05-26 are used as the test set. More details about datasets can be found in the supplementary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "text", + "content": "Implementation details. The proposed SGLoc is implemented with PyTorch [35] and Minkowski Engine [15]. We run our code on a PC equipped with an Intel (R) Xeon (R) Silver 4214R CPU, 64GB of RAM, and a single NVIDIA RTX 3090 GPU. During training, we employ an Adam optimizer [26] with an initial learning rate of 0.001. The weight " + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "text", + "content": " is set to 1 for all datasets. On the Oxford dataset, we use the point cloud from the left LiDAR and set the voxel size to " + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "inline_equation", + "content": "0.2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "text", + "content": ". On the NCLT dataset, the voxel size is " + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "inline_equation", + "content": "0.25\\mathrm{m}" + }, + { + "bbox": [ + 46, + 546, + 288, + 701 + ], + "type": "text", + "content": ". The TSFA module uses feature maps from the 3rd, 5th, and 8th convolution blocks with 128, 256, and 512 dimensions, respectively. Each convolution block consists of two convolution layers and a residual connection." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 713 + ], + "type": "text", + "content": "Baselines. To validate the performance of SGLoc, we com" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 439, + 547, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 439, + 547, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 439, + 547, + 558 + ], + "type": "text", + "content": "pare it with several state-of-the-art learning-based LiDAR localization approaches. PointNetVLAD (PNVLAD) [44] is a large-scale point cloud retrieval-based method, and DCP [47] is a point cloud registration approach which employs PointNet [36] and DGCNN [48] as the embedding network. PNVLAD and DCP use the same configuration as PointLoc [46]. PosePN [51], PosePN++ [51], PoseSOE [51], PoseMinkLoc [51], and PointLoc are LiDAR-based localization framework that uses a single-frame point cloud for absolute pose regression." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "Results of pose quality evaluation and enhancement. On the Oxford and NCLT datasets, the data of 14-14-48-55 and 2012-02-18 are selected as the standard, respectively. We set the distance of the trajectory segments to build sub-maps to " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "20\\mathrm{m}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " and the voxel size to " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{m}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " to reduce the duplicate points. Registration is considered successful when the root-mean-square error of correspondence is below " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "1\\mathrm{m}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": ". The evaluated pose error of Oxford and NCLT datasets are " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "3.24\\mathrm{m}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "0.25\\mathrm{m}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": ", respectively. Obviously, the ground truth poses in the data of NCLT is accurate. However, the pose of the Oxford dataset has various errors. Therefore, we perform quality enhancement on the Oxford dataset and obtain the enhanced pose with errors of " + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "inline_equation", + "content": "0.91\\mathrm{m}" + }, + { + "bbox": [ + 304, + 558, + 547, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "9291" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 531, + 133 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 531, + 133 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 531, + 133 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 531, + 133 + ], + "type": "table", + "html": "
MethodsPNVLADDCPPosePNPosePN++PoseSOEPoseMinkLocPointLocSGLoc
2012-02-127.75m, 6.49°9.84m, 6.84°9.45m, 7.47°4.97m, 3.75°13.09m, 8.05°6.24m, 5.03°7.23m, 4.88°1.20m, 3.08°
2012-02-197.47m, 5.49°8.27m, 5.16°6.15m, 5.05°3.68m, 2.65°6.16m, 4.51°4.87m, 3.94°6.31m, 3.89°1.20m, 3.05°
2012-03-316.98m, 5.67°8.94m, 5.96°5.79m, 5.28°4.35m, 3.38°5.24m, 4.56°4.23m, 4.03°6.71m, 4.32°1.12m, 3.28°
2012-05-2614.34m, 7.93°15.62m, 7.99°13.47m, 7.77°9.59m, 4.49°12.60m, 7.67°10.32m, 6.52°10.02m, 5.32°3.81m, 4.74°
Average9.14m, 6.40°10.67m, 6.49°8.72m, 6.39°5.65m, 3.57°9.27m, 6.20°6.42m, 4.88°7.57m, 4.60°1.83m, 3.54°
", + "image_path": "070a3a86dcdc512235101c85d8d4c15a95b21f6da393b26637edfdb24b5a6529.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 63, + 148, + 170, + 242 + ], + "blocks": [ + { + "bbox": [ + 63, + 148, + 170, + 242 + ], + "lines": [ + { + "bbox": [ + 63, + 148, + 170, + 242 + ], + "spans": [ + { + "bbox": [ + 63, + 148, + 170, + 242 + ], + "type": "image", + "image_path": "a452ba50ba31e04308acecd78f472b1180c3bf585148e7c3702a7894235db7cc.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 243, + 521, + 254 + ], + "lines": [ + { + "bbox": [ + 66, + 243, + 521, + 254 + ], + "spans": [ + { + "bbox": [ + 66, + 243, + 521, + 254 + ], + "type": "text", + "content": "PNVLAD DCP PosePN PosePN++ PoseSOE PoseMinkLoc PointLoc SGLoc" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 256, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 545, + 278 + ], + "type": "text", + "content": "Figure 6. Cumulative distributions of the position errors (m) on the NCLT dataset. The x-axis is the position error, and the y-axis is the percentage of point clouds with errors less than the value." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 184, + 148, + 290, + 241 + ], + "blocks": [ + { + "bbox": [ + 184, + 148, + 290, + 241 + ], + "lines": [ + { + "bbox": [ + 184, + 148, + 290, + 241 + ], + "spans": [ + { + "bbox": [ + 184, + 148, + 290, + 241 + ], + "type": "image", + "image_path": "e5e9e027be59466163958615e341d678bf8e3fecdb6e3f267429ed6812e13328.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 305, + 148, + 411, + 241 + ], + "blocks": [ + { + "bbox": [ + 305, + 148, + 411, + 241 + ], + "lines": [ + { + "bbox": [ + 305, + 148, + 411, + 241 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 411, + 241 + ], + "type": "image", + "image_path": "22b34fd30e7aaffae80994ea2f4da7ea0a396e0787f8ae5346c080c8bd168b45.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 420, + 148, + 525, + 241 + ], + "blocks": [ + { + "bbox": [ + 420, + 148, + 525, + 241 + ], + "lines": [ + { + "bbox": [ + 420, + 148, + 525, + 241 + ], + "spans": [ + { + "bbox": [ + 420, + 148, + 525, + 241 + ], + "type": "image", + "image_path": "5a2dd08e7269b71ce96aace13e70eebfbdfa80fce944521073925ca818c60e58.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 287, + 164, + 299 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 287, + 164, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 164, + 299 + ], + "type": "text", + "content": "4.2. Localization Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "text", + "content": "Localization on the Oxford dataset. We first evaluate the proposed SGLoc on the Oxford dataset, as shown in Tab. 1. We report the mean position and orientation errors over the full test trajectories. The proposed framework achieves a mean error of " + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "inline_equation", + "content": "3.14\\mathrm{m} / 1.88^{\\circ}" + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "text", + "content": ", outperforming all competitors. Specifically, compared to PoseSOE, it improves by " + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "inline_equation", + "content": "63.6\\%" + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 46, + 304, + 288, + 387 + ], + "type": "text", + "content": " on position and orientation, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "type": "text", + "content": "We further evaluate the proposed SGLoc on the quality-enhanced Oxford dataset, as shown in Tab. 2. Clearly, the mean position and orientation errors of all methods are significantly degraded compared to Tab. 1, illustrating the effectiveness and generalizability of the proposed PQEE method. SGLoc achieves a mean error of " + }, + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "type": "inline_equation", + "content": "1.53\\mathrm{m} / 1.60^{\\circ}" + }, + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "type": "text", + "content": ", surpassing other methods by a large margin. Specifically, it improves PoseSOE by " + }, + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "type": "inline_equation", + "content": "69.3\\% / 10.6\\%" + }, + { + "bbox": [ + 46, + 388, + 288, + 507 + ], + "type": "text", + "content": ". These results demonstrate that the proposed SGLoc can perform localization well in large-scale outdoor scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 509, + 288, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 288, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 288, + 592 + ], + "type": "text", + "content": "The first two rows in Fig. 4 illustrate the predicted trajectories on 17-14-03-00. The trajectory of SGLoc closely overlaps with the ground truth, demonstrating its accuracy. Fig. 5 shows the cumulative distributions of position errors on different trajectories. SGLoc achieves the desired performance, indicating that it effectively captures the scene geometry, leading to improved accuracy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "type": "text", + "content": "Localization on the NCLT dataset. Then, we evaluate the proposed SGLoc on the NCLT dataset. Tab. 2 summarizes the results of all methods with mean position and orientation errors. Apparently, SGLoc significantly outperforms the existing methods with a mean error of " + }, + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "type": "inline_equation", + "content": "1.83\\mathrm{m} / 3.54^{\\circ}" + }, + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "type": "text", + "content": ". Our approach improves by " + }, + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "type": "inline_equation", + "content": "67.6\\%" + }, + { + "bbox": [ + 46, + 593, + 288, + 700 + ], + "type": "text", + "content": " on position compared to PosePN++. It should be explained that there are more outliers on 2012-05-26 due to the various differences between the test and training trajectories." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "The last two rows of Fig. 4 show the predicted trajectory" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 308, + 286, + 544, + 342 + ], + "blocks": [ + { + "bbox": [ + 126, + 134, + 465, + 144 + ], + "lines": [ + { + "bbox": [ + 126, + 134, + 465, + 144 + ], + "spans": [ + { + "bbox": [ + 126, + 134, + 465, + 144 + ], + "type": "text", + "content": "Table 2. Position error (m) and orientation error " + }, + { + "bbox": [ + 126, + 134, + 465, + 144 + ], + "type": "inline_equation", + "content": "\\left( {}^{ \\circ }\\right)" + }, + { + "bbox": [ + 126, + 134, + 465, + 144 + ], + "type": "text", + "content": " for various methods on the NCLT dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 286, + 544, + 342 + ], + "lines": [ + { + "bbox": [ + 308, + 286, + 544, + 342 + ], + "spans": [ + { + "bbox": [ + 308, + 286, + 544, + 342 + ], + "type": "table", + "html": "
15-13-06-3717-13-26-3917-14-03-0018-14-14-42
SGLoc w/o PGO1.79m, 1.67°1.81m, 1.75°1.33m, 1.59°1.19m, 1.39°
SGLoc w/ PGO1.58m, 1.10°1.56m, 1.16°1.10m, 1.18°0.99m, 1.04°
2012-02-122012-02-192012-03-312012-05-26
SGLoc w/o PGO1.20m, 3.08°1.20m, 3.05°1.12m, 3.28°3.81m, 4.74°
SGLoc w/ PGO0.88m, 2.35°0.85m, 2.06°0.79m, 2.34°3.25m, 3.52°
", + "image_path": "8fa17baa1432b6c691f73253e32741bbda07c4710e966e22cdb812aca982739e.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 344, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 305, + 344, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 344, + 547, + 365 + ], + "type": "text", + "content": "Table 3. Localization results of SGLoc with PGO on the quality-enhanced Oxford and NCLT datasets." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 374, + 547, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 547, + 447 + ], + "type": "text", + "content": "of 2012-03-31. Our prediction is closer to the ground truth and smoother than the competitors. The cumulative distributions of position errors are shown in Fig. 6, demonstrating the promising performance of the proposed SGLoc. It means that SGLoc can capture the scene geometry more efficiently compared to existing LiDAR-based localization methods." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 454, + 526, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 526, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 526, + 467 + ], + "type": "text", + "content": "4.3. Localization Accuracy at Sub-meter Level" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 472, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 547, + 605 + ], + "type": "text", + "content": "Similar to MapNet [8], we utilize PGO as post-processing to further improve localization results. As shown in Tab. 3, our method has further improved in accuracy with PGO. Specifically, the SGLoc achieves accuracy at the sub-meter level on 18-14-14-42 of the quality-enhanced Oxford dataset. Moreover, in all scenes of the NCLT dataset (except 2012-05-26), the mean error of SGLoc is " + }, + { + "bbox": [ + 304, + 472, + 547, + 605 + ], + "type": "inline_equation", + "content": "0.84\\mathrm{m} / 2.25^{\\circ}" + }, + { + "bbox": [ + 304, + 472, + 547, + 605 + ], + "type": "text", + "content": ". To our knowledge, SGLoc is the first regression-based method to reduce the error to the level of the sub-meter on some trajectories, which bridges the gaps in practical applications. For more results, please refer to the supplementary." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "text", + "content": "Ablation on PQEE. As shown in Tab. 4, the proposed method outperforms the vanilla model without proposed modules by " + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "inline_equation", + "content": "43.5\\% /14.9\\%" + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "text", + "content": ". Moreover, the performance of PQEE is significantly enhanced with or without IGCC or TSFA. For instance, PQEE considerably surpasses that without PQEE under IGCC and TSFA, achieving a mean error of " + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "inline_equation", + "content": "1.53\\mathrm{m} / 1.60^{\\circ}" + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "inline_equation", + "content": "3.14\\mathrm{m} / 1.88^{\\circ}" + }, + { + "bbox": [ + 304, + 629, + 547, + 712 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9292" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 128 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 128 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 128 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 128 + ], + "type": "table", + "html": "
IGCCTSFAOxford w/o PQEEOxford w/ PQEENCLT
13.95m/2.89°2.23m/2.46°2.73m/5.19°
2✓3.46m/2.67°2.12m/2.32°2.62m/5.11°
3✓3.23m/2.10°1.68m/1.67°1.98m/3.51°
4✓✓3.14m/1.88°1.53m/1.60°1.83m/3.54°
", + "image_path": "ff74e261b052dfc037af6a4e31e9f3abff5f999010bbcd8d0bf44c8fccbb83de.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 152, + 287, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 152, + 287, + 272 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 287, + 272 + ], + "type": "text", + "content": "Ablation on IGCC. We further conduct ablation experiments to demonstrate the importance of IGCC loss. In Tab. 4, the comparison between Row 1 and Row 2 shows the module notably improves accuracy. On the Oxford dataset, compared to the vanilla model, IGCC obtains a " + }, + { + "bbox": [ + 46, + 152, + 287, + 272 + ], + "type": "inline_equation", + "content": "12.4\\% /7.6\\%" + }, + { + "bbox": [ + 46, + 152, + 287, + 272 + ], + "type": "text", + "content": " improvement. On the NCLT dataset, IGCC also leads to improvements. Furthermore, IGCC improves localization accuracy compared to the method with TSFA only. This demonstrates the proposed design is helpful for capturing the scene geometry." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 272, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 272, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 272, + 288, + 344 + ], + "type": "text", + "content": "Ablation on TSFA. The TSFA results are reported in Row 3 of Tab. 4. On the Oxford and NCLT dataset, compared to the results in Row 1, it yields an average " + }, + { + "bbox": [ + 46, + 272, + 288, + 344 + ], + "type": "inline_equation", + "content": "23.5\\% / 30.6\\%" + }, + { + "bbox": [ + 46, + 272, + 288, + 344 + ], + "type": "text", + "content": " improvement on position and orientation. This significant improvement verifies that the proposed TSFA module can further improve the encoding of scene geometry." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 348, + 111, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 111, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 111, + 360 + ], + "type": "text", + "content": "4.5. Runtime" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "type": "text", + "content": "For the Oxford and NCLT datasets, the LiDAR scan rate is " + }, + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "type": "inline_equation", + "content": "20\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 365, + 289, + 533 + ], + "type": "text", + "content": ", respectively. Therefore, the real-time performance here means that the running time of each scanning data is less than 50ms and 100ms, respectively. Tab. 5 shows the running time on the Oxford and NCLT dataset. On the Oxford dataset, SGLoc takes a running time of 38ms per frame, with the correspondence regression stage consuming 25ms and the pose estimation stage consuming 13ms. On the NCLT dataset, the running times are 75ms, 41ms, and 34ms, respectively. Note that the running time of PNVLAD, DCP, PosePN, and PoseMinkLoc are less than 10ms due to the simplicity of their networks. Therefore, Our SGLoc can achieve real-time localization and is very competitive with these methods, but the performance of SGLoc is much better." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 538, + 117, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 117, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 117, + 551 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 288, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 653 + ], + "type": "text", + "content": "LiDAR localization in large-scale outdoor scenes is a critical component of autonomous driving. However, existing APR methods still face challenges in effectively encoding scene geometry and dealing with unsatisfactory data quality, resulting in suboptimal accuracy. To overcome these challenges, we propose SGLoc and PQEE, which significantly improves accuracy. Compared to previous work, SGLoc stands out due to the following differences." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 714 + ], + "type": "text", + "content": "Difference between SGLoc and DSAC++. Camera coordinate regression (DSAC++ [5]) predicts 2D-3D correspondences, to our knowledge, SGLoc is the first work to regress 3D-3D point correspondences. Though both DSAC++ and our SGLoc use regression, we address different problems." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 68, + 422, + 143 + ], + "blocks": [ + { + "bbox": [ + 310, + 68, + 422, + 143 + ], + "lines": [ + { + "bbox": [ + 310, + 68, + 422, + 143 + ], + "spans": [ + { + "bbox": [ + 310, + 68, + 422, + 143 + ], + "type": "image", + "image_path": "3c426c3ed673cfde1927a459cce603bddb454577fa8c3c2fe70b1b4023f6b78a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 146, + 547, + 179 + ], + "lines": [ + { + "bbox": [ + 304, + 146, + 547, + 179 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 547, + 179 + ], + "type": "text", + "content": "Figure 7. Ground truth poses in the data on the Oxford (left) and quality-enhanced Oxford (right) dataset. The green trajectory indicates the prespecified standard data." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 426, + 68, + 539, + 144 + ], + "blocks": [ + { + "bbox": [ + 426, + 68, + 539, + 144 + ], + "lines": [ + { + "bbox": [ + 426, + 68, + 539, + 144 + ], + "spans": [ + { + "bbox": [ + 426, + 68, + 539, + 144 + ], + "type": "image", + "image_path": "b5e0c55f66493ee05449068ffb6ccea3532580f668e32e8d80257299f31f344e.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 308, + 183, + 545, + 210 + ], + "blocks": [ + { + "bbox": [ + 60, + 132, + 272, + 143 + ], + "lines": [ + { + "bbox": [ + 60, + 132, + 272, + 143 + ], + "spans": [ + { + "bbox": [ + 60, + 132, + 272, + 143 + ], + "type": "text", + "content": "Table 4. Ablation study on the Oxford and NCLT datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 183, + 545, + 210 + ], + "lines": [ + { + "bbox": [ + 308, + 183, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 308, + 183, + 545, + 210 + ], + "type": "table", + "html": "
MethodsPNVLADDCPPosePNPosePN+PoseSOEPoseMinkLocPointLocSGLoc
Oxford6ms3ms2ms111ms244ms8ms625ms38ms
NCLT6ms3ms2ms108ms230ms8ms614ms75ms
", + "image_path": "d3047202b5ceaa7586a518bc1751bb7eda4dda85877c7a485f50378265f48f55.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 213, + 545, + 235 + ], + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 235 + ], + "type": "text", + "content": "Table 5. Runtime (ms) of different methods on the Oxford and NCLT datasets." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": "We summarize the differences. (1) SGLoc learns rigid transformations instead of affine transformations that require the intrinsics of the query camera; (2) Our methods' ground truth correspondences generation requires only input point clouds and poses, which can be deployed efficiently in online training; (3) SGLoc can be applied to large-scale outdoor scenes covering about " + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "inline_equation", + "content": "200\\mathrm{hm}^2" + }, + { + "bbox": [ + 304, + 243, + 547, + 327 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 328, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 547, + 472 + ], + "type": "text", + "content": "Difference between PQEE and point cloud registration. We empirically find existing large-scale outdoor datasets cannot precisely provide the same position values (bad quality) in the same position on different days, as shown in Fig. 7. More importantly, we find this degraded data quality can significantly decrease the localization accuracy. We hope this new finding can inspire researchers to work on this new source of performance degradation. Based on this new finding, we propose PQEE, which aligns and fuses standard/raw data in LiDAR localization. It uses point cloud registration, but the purpose differs from conventional point cloud registration." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 478, + 378, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 378, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 378, + 491 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 497, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 652 + ], + "type": "text", + "content": "We propose a novel regression-based framework, SGLoc, for LiDAR localization. SGLoc is the first work to decouple LiDAR localization into point cloud correspondences regression and pose estimation via predicted correspondences. The core component of SGLoc is the first step, which effectively encodes scene geometry, leading to significant performance improvement. To achieve high accuracy in this step, we propose the TSFA module and IGCC loss to improve the encoding of scene geometry. Moreover, to increase the data quality and localization accuracy, the PQEE method is designed to measure and correct the ground truth pose errors in the localization data. Extensive experimental results verify the great effectiveness of our method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements This work was partially supported by the open fund of PDL (2022-KJWPDL-12, WDZC20215250113), by the FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "9293" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Xuyang Bai, Zixin Luo, Lei Zhou, Hongkai Chen, Lei Li, Zeyu Hu, Hongbo Fu, and Chiew-Lan Tai. 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In CVPR, pages 4919-4928, 2020. 2" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "9295" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SHS-Net_ Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds/b88f2048-c087-4b9c-9601-f88e3009b262_content_list.json b/2023/SHS-Net_ Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds/b88f2048-c087-4b9c-9601-f88e3009b262_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e7296dfc99c01c28a6dfb08cdc367a86a9808d22 --- /dev/null +++ b/2023/SHS-Net_ Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds/b88f2048-c087-4b9c-9601-f88e3009b262_content_list.json @@ -0,0 +1,2122 @@ +[ + { + "type": "text", + "text": "SHS-Net: Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds", + "text_level": 1, + "bbox": [ + 89, + 128, + 880, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qing Li $^{1}$ Huifang Feng $^{2}$ Kanle Shi $^{3}$ Yue Gao $^{1}$ Yi Fang $^{4}$ Yu-Shen Liu $^{1}$ * Zhizhong Han $^{5}$", + "bbox": [ + 223, + 202, + 743, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1School of Software, BNRist, Tsinghua University, Beijing, China", + "bbox": [ + 243, + 239, + 725, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Informatics, Xiamen University, Xiamen, China $^{3}$ Kuaishou Technology, Beijing, China", + "bbox": [ + 119, + 256, + 849, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{4}$ Center for Artificial Intelligence and Robotics, New York University Abu Dhabi, Abu Dhabi, UAE", + "bbox": [ + 125, + 273, + 844, + 291 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{5}$ Department of Computer Science, Wayne State University, Detroit, USA", + "bbox": [ + 217, + 292, + 751, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{leoqli, gaoyue, liuyushen}@tsinghua.edu.cn fenghuifang@stu.xmu.edu.cn", + "bbox": [ + 166, + 311, + 800, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "shikanle@kuaishou.com yfang@nyu.edu h312h@wayne.edu", + "bbox": [ + 240, + 330, + 723, + 344 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 378, + 313, + 395 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are available at https://github.com/LeoQLi/SHS-Net.", + "bbox": [ + 75, + 412, + 473, + 821 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/db4de02ce8ecdb85d23f3d699e759061f29b14204e99ed2d3fa8510bab7b9ba9.jpg", + "image_caption": [ + "Figure 1. We propose SHS-Net to estimate oriented normals directly from point clouds. In contrast, previous studies usually achieve this process through a two-stage paradigm using different algorithms, i.e., (1) unoriented normal estimation (e.g., PCA [19], AdaFit [59] and HSurf-Net [32]) and (2) normal orientation (e.g., MST [19], QPBO [45] and ODP [38])." + ], + "image_footnote": [], + "bbox": [ + 501, + 376, + 890, + 505 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 614, + 633, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In computer vision and graphics, estimating normals for point clouds is a prerequisite for many techniques. As an important geometric property of point clouds, normals with consistent orientation, i.e., oriented normals, clearly reveal the geometric structures and make significant contributions in downstream applications, such as rendering and surface reconstruction [24-26]. Generally, the estimation of oriented normals requires a two-stage paradigm (see Fig. 1): (1) the unoriented normal estimation from the local neighbors of the query point, (2) the normal orientation to make the normal directions to be globally consistent, e.g., facing outward of the surface. While unoriented normals can be estimated by plane or surface fitting of the local neighborhood, determining whether the normals are facing outward or inward is ambiguous. In recent years, many excellent algorithms [5, 29, 31, 32, 59] have been proposed for unoriented normal estimation, while there are few methods that", + "bbox": [ + 496, + 643, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The corresponding author is Yu-Shen Liu. This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data.", + "bbox": [ + 75, + 849, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13591", + "bbox": [ + 480, + 944, + 517, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "have reliable performance for normal orientation or directly estimating oriented normals. Estimating oriented normals from point clouds with noise, density variations, and complex geometries in an end-to-end manner is still a challenge.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The classic normal orientation methods rely on simple greedy propagation, which selects a seed point as the start and diffuses its normal orientation to the adjacent points via a minimum spanning tree (MST) [19, 27]. These methods are limited by error accumulation, where an incorrect orientation may degenerate all subsequent steps during the iterative propagation. Furthermore, they heavily rely on a smooth and clean assumption, which makes them easily fail in the presence of sharp edges or corners, density variations and noise. Meanwhile, their accuracy is sensitive to the neighborhood size of propagation. For example, a large size is usually used to smooth out outliers and noise, but can also erroneously include nearby surfaces. Considering that local information is usually not sufficient to guarantee robust orientation, some improved methods [22, 38, 45, 46, 49, 53] try to formulate the propagation process as a global energy optimization by introducing various constraints. Since their constraints are mainly derived from local consistency, the defects are inevitably inherited, and they also suffer from cumulative errors. Moreover, their data-specific parameters are difficult to generalize to new input types and topologies.", + "bbox": [ + 75, + 154, + 470, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Different from the propagation-based methods, which only consider the adjacent orientation, the volume-based approaches exploit volumetric representation, such as signed distance functions [35, 40] and variational formulations [2, 21, 48]. They aim to divide the space into interior/exterior and determine whether point normals are facing inward or outward. Despite improvements in accuracy and robustness, these methods cannot scale to large point clouds due to their computational complexity. In general, propagation-based methods have difficulty with sharp features, while volume-based methods have difficulty with open surfaces. Furthermore, the above-mentioned methods are usually complex and require a two-stage operation, their performance heavily depends on the parameter tuning in each separated stage. Recently, several learning-based methods [17, 18, 50] have been proposed to deliver oriented normals from point clouds and have exhibited promising performance. Since they focus on learning an accurate local feature descriptor and do not fully explore the relationship between the surface normal orientation and the underlying surface, their performance cannot be guaranteed across different noise levels and geometric structures.", + "bbox": [ + 75, + 474, + 470, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose to estimate oriented normals from point clouds by implicitly learning signed hyper surfaces, which are represented by MLP layers to interpret the geometric property in a high-dimensional feature space. We learn this new geometry representation from both local and global shape properties to directly estimate normals with", + "bbox": [ + 73, + 810, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "consistent orientation in an end-to-end manner. The insight of our method is that determining a globally consistent normal orientation should require global context to eliminate the ambiguity from local since orientation is not a local property. We evaluate our method by conducting a series of qualitative and quantitative experiments on a range of point clouds with different sampling densities, noise levels, thin and sharp structures.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows.", + "bbox": [ + 517, + 213, + 879, + 226 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new technique to represent point cloud geometric properties as signed hyper surfaces in a high-dimensional feature space.", + "- We show that the signed hyper surfaces can be used to estimate normals with consistent orientations directly from point clouds, rather than through a two-stage paradigm.", + "- We experimentally demonstrate that our method is able to estimate normals with high accuracy and achieves the state-of-the-art results in both unoriented and oriented normal estimation." + ], + "bbox": [ + 500, + 229, + 890, + 377 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 406, + 640, + 421 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unoriented Normal Estimation. Over the past few decades, many algorithms have been proposed for point cloud normal estimation, such as the classic Principle Component Analysis (PCA) [19] and its improvements [1, 20, 28, 39, 43], Voronoi-based paradigms [2, 3, 13, 36], and variants based on complex surface [4, 10, 16, 30, 41]. These methods are usually sensitive to noise and have limited accuracy even with heavy fine-tuned parameters. More recently, learning-based methods have been proposed to improve performance in this area and can be mainly divided into two categories: regression-based and surface fitting-based. The regression-based methods try to directly predict normals from structured data [8, 34, 44] or raw point clouds [6, 17, 18, 32, 33, 55-57] in a data-driven manner. Among them, HSurf-Net [32] achieves good performance by learning hyper surfaces from local patches, but the learned surfaces have no sign and cannot determine the normal orientation. The surface fitting-based methods integrate the traditional surface fitting techniques, such as plane fitting [9, 29] and jet fitting [5, 31, 54, 58, 59], into the end of the learning pipeline. They usually carefully design a network to predict point-wise weights, and then use a weighted surface formulation to solve the fitted surface normal. The normals estimated by the above methods randomly face both sides of the surface and cannot be used in many downstream applications without normal orientation.", + "bbox": [ + 496, + 431, + 890, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Consistent Normal Orientation. To make the unoriented normals have consistent orientations, early approaches mainly focus on local consistency and use the orientation propagation strategy upon a minimum spanning tree (MST) to let the adjacent points have the same orientations, such", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13592", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c737c2753d2fa077f56d92404a5c968cc7571c65049d8d4371b2093bcdba402e.jpg", + "image_caption": [ + "Figure 2. The learning pipeline of the signed hyper surfaces for oriented normal estimation." + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 872, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "as the pioneering work of [19] and its improved methods [22, 45, 46, 49, 53]. These methods have many limitations in real applications as we introduced earlier. ODP [38] aims to achieve global consistency by introducing a dipole propagation strategy across the partitioned patches, but its robustness may suffer from the patch partition. On the contrary, some alternative approaches propose to solve the consistent normal orientation through volumetric representation. They are usually developed for reconstructing surfaces from unoriented points by various techniques, such as signed distance functions [35, 40], variational formulations [2, 21, 48], visibility [11, 23], isvalue constraints [51] and active contours [52]. Recently, a few works [17, 18, 50] explore to predict oriented normals through end-to-end deep networks. These methods focus on learning a general mapping from point clouds to normals and neglect the underlying surface distribution for normal orientation, leading to a sub-optimal solution.", + "bbox": [ + 75, + 271, + 473, + 544 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 566, + 204, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In mathematics, an explicit representation in Euclidean space expresses the $z$ coordinate of a point $p$ in terms of the $x$ and $y$ , i.e., $z = f(x,y)$ . Such a surface is called an explicit surface, also called a height field. Another symmetric representation is $F(x,y,z) = 0$ , where $F$ implicitly defines a locus called an implicit surface, also called a scalar field [7]. The implicit surface is a zero iso-surface of $F$ , i.e., the point set $\\{p \\in \\mathbb{R}^3 : F(p) = 0\\}$ is a surface implicitly defined by $F$ . The explicit surface is usually used in surface fitting-based normal estimation, such as jet fitting [10], while the implicit surface is widely used in surface reconstruction. Generally, an explicit surface, i.e., $z = f(x,y)$ , can always be rewritten as an implicit surface, i.e., $F(x,y,z) = z - f(x,y) = 0$ . These two surface representations have the same tangent plane at a given point, where the normal is defined. See supplementary for details.", + "bbox": [ + 75, + 595, + 468, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Explicit Surface Fitting. We employ the widely used $n$ -jet surface model [10] to briefly review the explicit surface fitting for normal estimation. It represents the surface by a polynomial function $J_{n}:\\mathbb{R}^{2}\\to \\mathbb{R}$ , which maps a coordinate", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1590ae8503229a4771ae6e288f7c7535cf05364599439849ac2f4039aa5819c9.jpg", + "image_caption": [ + "Figure 3. Feature encoding network in patch and shape encoding." + ], + "image_footnote": [], + "bbox": [ + 501, + 268, + 890, + 328 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$(x,y)$ to its height $z$ in the tangent space by", + "bbox": [ + 500, + 363, + 790, + 378 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz = J _ {\\alpha , n} (x, y) = \\sum_ {k = 0} ^ {n} \\sum_ {j = 0} ^ {k} \\alpha_ {k - j, j} x ^ {k - j} y ^ {j}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 387, + 890, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha$ is the coefficient vector that defines the surface function. In order to find the optimal solution, the least squares approximation strategy is usually adopted to minimize the sum of the square errors between the (ground-truth) height and the jet value over a point set $\\{p_i\\}_{i=1}^N$ ,", + "bbox": [ + 496, + 438, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nJ _ {\\alpha , n} ^ {*} = \\underset {\\alpha} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| z _ {i} - J _ {\\alpha , n} \\left(x _ {i}, y _ {i}\\right) \\| ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 522, + 890, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "If $\\alpha = (\\alpha_{0,0},\\alpha_{1,0},\\alpha_{0,1},\\dots ,\\alpha_{0,n})$ is solved, then the normal at point $p$ on the fitted surface is computed by", + "bbox": [ + 498, + 571, + 890, + 602 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {n} _ {p} = h (\\alpha) = (- \\alpha_ {1, 0}, - \\alpha_ {0, 1}, 1) / \\sqrt {1 + \\alpha_ {1 , 0} ^ {2} + \\alpha_ {0 , 1} ^ {2}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 612, + 890, + 636 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implicit Surface Learning. In recent years, many learning-based approaches have been proposed to represent surfaces by implicit functions, such as signed distance function (SDF) [42] and occupancy function [37]. The signed (or oriented) distance function is the shortest distance of a given point $p = (x_0, y_0, z_0)$ to the closest surface $S$ in a metric space, with the sign determined by whether the point is inside $(F(p) < 0)$ or outside $(F(p) > 0)$ of the surface. The underlying surface is implicitly represented by the isosurface of $F(p) = 0$ . In the surface reconstruction task, a deep network is usually adopted to encode a 3D shape into a latent code, which is fed into a decoder together with query points to predict signed distances. If an implicit surface function is continuous and differentiable, the formula of tangent plane at a regular point $p$ (gradient is non-null) is $F_x(p)(x - x_0) + F_y(p)(y - y_0) + F_z(p)(z - z_0) = 0$ and its normal (i.e., perpendicular) is $\\mathbf{n}_p = \\nabla F(p) / \\| \\nabla F(p) \\|$ .", + "bbox": [ + 496, + 643, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13593", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 89, + 169, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we propose to implicitly learn signed hyper surfaces in the feature space for estimating oriented normals. In the following sections, we first introduce the representation of signed hyper surfaces by combining the characteristics of the above two surface representations. Then, we design an attention-weighted normal prediction module to solve the oriented normals of query points from signed hyper surfaces. Finally, we introduce how to learn this new surface representation from patch encoding and shape encoding using our designed loss functions.", + "bbox": [ + 75, + 114, + 472, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Signed Hyper Surface", + "text_level": 1, + "bbox": [ + 76, + 273, + 284, + 290 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We formulate the surface function $F(x,y,z) = z - f(x,y) = 0$ as a more general format $F(z_{1},z_{2}) = z_{1} - z_{2} = 0$ . Similarly, the signed hyper surface is implicitly learned by taking the latent encodings of point clouds as inputs and outputting an approximation of the surface in feature space,", + "bbox": [ + 76, + 297, + 468, + 375 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\pmb {S}} (\\chi) \\approx \\mathcal {E} _ {\\theta} (\\chi | z _ {1}, z _ {2}), z _ {1} = e _ {\\varphi} (\\pmb {P} _ {\\chi} ^ {1}), z _ {2} = e _ {\\psi} (\\pmb {P} _ {\\chi} ^ {2}), (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 393, + 468, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{E}$ is implemented by a neural network with parameter $\\theta$ that is conditioned on two latent vectors $z_{1}, z_{2} \\in \\mathbb{R}^{c}$ , which are extracted from point clouds by encoders $e_{\\varphi}$ and $e_{\\psi}$ , respectively. $P_{\\chi}^{1}$ and $P_{\\chi}^{2}$ are subsample sets of the raw point cloud $\\mathcal{P}$ , e.g., point patches around a given point $\\chi$ .", + "bbox": [ + 76, + 419, + 468, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to existing unoriented normal estimation methods [5, 17, 32, 59], we use a local patch $\\pmb{p}_q$ to capture the local geometry for accurately describing the surface pattern around a query point $q$ ,", + "bbox": [ + 75, + 494, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\boldsymbol {p}} ^ {\\mathbf {n}} (q) = \\mathcal {E} _ {\\theta} ^ {\\mathbf {n}} (q | z _ {q} ^ {\\mathbf {n}}), z _ {q} ^ {\\mathbf {n}} = e _ {\\varphi} (\\boldsymbol {p} _ {q}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 561, + 468, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the interior/exterior of a surface cannot be determined reliably from a local patch, we take a global subsample set $P_{q}$ from the point cloud $\\mathcal{P}$ to provide additional information to estimate the sign at point $q$ ,", + "bbox": [ + 76, + 587, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\boldsymbol {P}} ^ {s} (q) = \\operatorname {s g n} \\left(g ^ {s} (q)\\right) = \\operatorname {s g n} \\left(\\mathcal {E} _ {\\theta} ^ {s} \\left(q \\mid z _ {q} ^ {s}\\right)\\right), z _ {q} ^ {s} = e _ {\\psi} (\\boldsymbol {P} _ {q}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 654, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\operatorname{sgn}(\\cdot)$ is a signum function, $g^{s}(q)$ denotes the logarithm of the probability that $q$ has a positive sign. Thus, the signed hyper surface function at point $q$ is formulated as", + "bbox": [ + 75, + 686, + 468, + 733 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\boldsymbol {S}} (q) = f _ {\\boldsymbol {p}} ^ {\\mathbf {n}} (q) \\cdot f _ {\\boldsymbol {P}} ^ {s} (q) = \\mathcal {E} _ {\\theta} ^ {\\mathbf {n}, s} \\left(q \\mid z _ {q} ^ {\\mathbf {n}}, z _ {q} ^ {s}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 739, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from the surface reconstruction task that learns SDF by representing a surface as the zero-set of the SDF, we do not learn a distance field of points with respect to the underlying surface.", + "bbox": [ + 75, + 763, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Oriented Normal Estimation", + "text_level": 1, + "bbox": [ + 76, + 832, + 334, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To simplify notations, we denote $\\mathcal{E}_{\\theta}^{\\mathbf{n},s}(q|z_q^{\\mathbf{n}},z_q^s)$ as $S_{\\theta}(\\mathcal{X},\\mathcal{Y})$ , where $z_{q}^{\\mathbf{n}} = \\mathcal{X}\\in \\mathbb{R}^{c}$ and $z_{q}^{s} = \\mathcal{Y}\\in \\mathbb{R}^{c}$ are high dimensional latent vectors. According to the explicit surface", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2873ebc5d63558efca4f8e66b9a72d9a9c3e2dabfb52d6fb1b189f511931d450.jpg", + "image_caption": [ + "Figure 4. Attention-weighted normal prediction module $\\mathcal{H}(\\cdot)$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "fitting, we formulate the signed hyper surface $S_{\\theta}:\\mathbb{R}^{2c}\\to$ $\\mathbb{R}^c$ as a feature-based polynomial function [32]", + "bbox": [ + 498, + 212, + 890, + 243 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\theta , \\mu} (\\mathcal {X}, \\mathcal {Y}) = \\sum_ {k = 0} ^ {\\mu} \\sum_ {j = 0} ^ {k} \\theta_ {k - j, j} \\mathbf {x} _ {k - j} \\mathbf {y} _ {j} = \\theta [ \\mathcal {X}: \\mathcal {Y} ], \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 251, + 890, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $[ : ]$ means the feature fusion through concatenation, $\\mu$ denotes the number of fused items.", + "bbox": [ + 498, + 301, + 890, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to Eq. (2), the bivariate function $S_{\\theta, \\mu}(\\mathcal{X}, \\mathcal{Y})$ aims to map a feature pair $(\\mathcal{X}_i, \\mathcal{Y}_i)$ to their ground-truth value $\\mathcal{Z}_i = \\hat{S}(\\mathcal{X}_i, \\mathcal{Y}_i) \\in \\mathbb{R}^c$ in the feature space, i.e.,", + "bbox": [ + 498, + 330, + 890, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\mathcal {Z} _ {i} - \\mathcal {S} _ {\\theta , \\mu} (\\mathcal {X} _ {i}, \\mathcal {Y} _ {i}) \\| ^ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 385, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To solve the oriented normal $\\vec{\\mathbf{n}}$ from signed hyper surfaces, we introduce a normal prediction module $\\mathcal{H}(\\cdot)$ , thus", + "bbox": [ + 498, + 434, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\mathcal {H} \\left(\\mathcal {Z} _ {i}\\right) - \\mathcal {H} \\left(\\mathcal {S} _ {\\theta , \\mu} \\left(\\mathcal {X} _ {i}, \\mathcal {Y} _ {i}\\right)\\right) \\| ^ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 468, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, the oriented normal is optimized by", + "bbox": [ + 500, + 510, + 792, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\hat {\\vec {\\mathbf {n}}} _ {i} - \\vec {\\mathbf {n}} _ {i} \\| ^ {2}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 529, + 890, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attention-weighted Normal Prediction $\\mathcal{H}(\\cdot):\\mathbb{R}^c\\to \\mathbb{R}^4$ As shown in Fig. 4, we use an attention mechanism to recover the oriented normal $\\vec{\\bf{n}}_q$ of the query point $q$ from $c$ dimensional fused surface embedding $z_{q}$", + "bbox": [ + 498, + 571, + 890, + 635 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\dot {\\mathbf {n}} _ {q}, s\\right) = \\mathcal {O} \\left(\\mathcal {V} \\left(o _ {q}\\right) \\otimes \\operatorname {M A X} \\left\\{\\operatorname {s o f t m a x} _ {\\mathcal {N} _ {q}} \\left(\\mathcal {Q} _ {j} \\left(o _ {q}\\right) _ {j = 1} ^ {m}\\right) \\right\\}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 640, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $o_q = \\tau \\cdot z_q$ , $\\tau = \\mathrm{sigmoid}(\\mathcal{I}(z_q))$ . $\\mathcal{O}, \\mathcal{V}, \\mathcal{Q}$ and $\\mathcal{I}$ are MLPs. $m = 64$ is the feature dimension size. First, a multi-head strategy is adopted to deliver $m$ relative weights $\\mathcal{Q}_j(o_q)$ , which are normalized by softmax over neighbors $\\mathcal{N}_q$ into positive interpolation weights. Then, the feature maxpooling MAX{\\cdot} is performed to produce attention weights for each point. Meanwhile, the feature embedding $o_q$ is refined through another branch $\\mathcal{V}$ and modulated as the weighted sum through matrix multiplication. Finally, the normal and its sign (i.e., orientation) $\\vec{\\mathbf{n}}_q = (\\mathbf{n}_q \\in \\mathbb{R}^3, s \\in \\mathbb{R})$ is predicted as a 4D vector by $\\mathcal{O}$ , and $\\mathbf{n}_q = \\dot{\\mathbf{n}}_q / \\| \\dot{\\mathbf{n}}_q \\|$ .", + "bbox": [ + 498, + 672, + 890, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Feature Encoding", + "text_level": 1, + "bbox": [ + 500, + 847, + 671, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Patch Encoding. Given a neighborhood point patch $\\pmb{p}_q$ of the query point, our local latent code extraction layer $\\mathcal{F}$ is", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13594", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/08bd3f1cd3eb2a9b7e1308416958619c644ecb5cea5387d61e973d95b4461b5d.jpg", + "image_caption": [ + "Point Cloud", + "PCPNet" + ], + "image_footnote": [], + "bbox": [ + 101, + 103, + 153, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/73c26e8ade43df8567210864e6c994793356600629fc6576283e5317fba44b92.jpg", + "image_caption": [ + "PCA+MST", + "AdaFit+MST" + ], + "image_footnote": [], + "bbox": [ + 183, + 103, + 243, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7501406e26cad6d8a669427662b106fb2bc5a10f8fa78606e40f586cfa063fec.jpg", + "image_caption": [ + "PCA+ODP", + "AdaFit+ODP" + ], + "image_footnote": [], + "bbox": [ + 277, + 103, + 338, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/44c2fa255c2897617bdb379b44f08095af441cc83c2a02de233b8778d1dbb634.jpg", + "image_caption": [ + "PCA+QPBO", + "AdaFit+QPBO" + ], + "image_footnote": [], + "bbox": [ + 367, + 103, + 426, + 222 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/41784a8d7ebbd5165af477d7cc2aaeba1050454ea058d51fc405e886d6bf75c9.jpg", + "image_caption": [ + "Point Cloud", + "PCPNet" + ], + "image_footnote": [], + "bbox": [ + 454, + 102, + 553, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d9424a819ace7212fc79845de49e2116581933240abd31a462a75976cec5d5dc.jpg", + "image_caption": [ + "PCA+MST" + ], + "image_footnote": [], + "bbox": [ + 555, + 102, + 648, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/17cd2f153f0d81f1b10a2928825207fe53d4a148d1d85506ce4b3718c33c1aec.jpg", + "image_caption": [ + "PCA+ODP", + "AdaFit+ODP" + ], + "image_footnote": [], + "bbox": [ + 651, + 102, + 746, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e6ce11bd700f7090bd2f946ec8a59da2b8cc11f8eb499cc020995b78d943e3f4.jpg", + "image_caption": [ + "PCA+QPBO", + "AdaFit+QPBO" + ], + "image_footnote": [], + "bbox": [ + 750, + 102, + 843, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/36cb026d7d268291cfe42210117837a738360f7db60524d317f3f7f0a42d5c60.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 102, + 238, + 153, + 358 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/91d9b2c91c9904570b83f498e50d8fd7bc559809ba62125236cb478be9ee6271.jpg", + "image_caption": [ + "Figure 5. Visualization of the oriented normal error on datasets PCPNet (left) and FamousShape (right). The angle error is mapped to a heatmap ranging from $0^{\\circ}$ to $180^{\\circ}$ . The purple color indicates the same direction as the ground-truth, while the red color is the opposite." + ], + "image_footnote": [], + "bbox": [ + 102, + 371, + 153, + 491 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f4b8bc4b1c2e5122f6325a662c31bfa3fd97d30e41552bfc4fe922b04b78c4ae.jpg", + "image_caption": [ + "HSurf-Net+MST" + ], + "image_footnote": [], + "bbox": [ + 171, + 238, + 238, + 358 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/60ffd13777ef740ca8099dc15d5ba1ddcba842e07567b8e1098a663cfcc2ddc0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 371, + 238, + 491 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/47dbeda3e199710dfeb50b41ccab2fd67037fbda516d4a9218b02b64ab097768.jpg", + "image_caption": [ + "HSurf-Net+ODP" + ], + "image_footnote": [], + "bbox": [ + 281, + 238, + 328, + 358 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d4fd29d55d429eb7cbc31a51b486df751f1b376d08d629f4efe52834e42e2dff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 371, + 328, + 491 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3d532b2e468bc832910e2d5f36276825ef397c3c8ae4d78c9761b842e1669373.jpg", + "image_caption": [ + "HSurf-Net+QPBO" + ], + "image_footnote": [], + "bbox": [ + 354, + 238, + 423, + 358 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/daeadce6623735a16c1adf2d717b87bb6ac2e86fdcbf256ede233921f7692002.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 371, + 423, + 491 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e22dfb37c1b065c5d06aad18ad91fc70963be333d6c5c1fbc53145effedbf911.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 238, + 550, + 356 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e0071a850b04129d8ad9240c70f688b4fb1aeca1689728442af58b28ee7c7979.jpg", + "image_caption": [ + "AdaFit+MST" + ], + "image_footnote": [], + "bbox": [ + 555, + 238, + 650, + 354 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1e7431cd5cdd47140b259dfa1233636a9250e38efc69008744a929698a30234a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 238, + 746, + 354 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1829f08c9edbe249349cd704b3d6244115fe769002ac2480ceb1aa34aa0e1fb2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 238, + 843, + 354 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ef7e56bd933662303049323c36413c6478cc92faba1fd814709a6909f4172b98.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 454, + 371, + 552, + 489 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/329e253a9f6332a883bdbab05cb26ed00badb533c4771e410e2aa961c16b92f2.jpg", + "image_caption": [ + "HSurf-Net+MST" + ], + "image_footnote": [], + "bbox": [ + 553, + 371, + 650, + 489 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7bdaf2444cba56ea005ce9e43789ab30d5ae5444e1d8b0f08ae9541227d85d62.jpg", + "image_caption": [ + "HSurf-Net+ODP" + ], + "image_footnote": [], + "bbox": [ + 651, + 371, + 746, + 489 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/eff814e6a2a87db7e469e41086cd3c24bb7213a7b5a321e7f7f91114a2737831.jpg", + "image_caption": [ + "HSurf-Net+QPBO" + ], + "image_footnote": [], + "bbox": [ + 748, + 371, + 843, + 489 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c26f4d540aa4581666fa8b137f64c8e0699479c77969ea3951ea9ff3750e03fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 834, + 412, + 867, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "formulated as", + "bbox": [ + 76, + 534, + 171, + 546 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\dot {z} _ {i} ^ {\\mathbf {n}} = \\mathcal {A} \\left(\\mathcal {B} \\left(\\operatorname {M A X} \\left\\{\\mathcal {C} \\left(w _ {j} \\cdot z _ {j} ^ {\\mathbf {n}}\\right) \\right\\} _ {j = 1} ^ {N _ {l}}\\right), z _ {i} ^ {\\mathbf {n}}\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 554, + 468, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $i = 1,\\dots ,N_{l + 1},l$ is the neighborhood scale index and $N_{l + 1}\\leqslant N_l$ . $z_{i}^{\\mathbf{n}} = \\mathcal{D}(p_{i}),p_{i}\\in \\pmb{p}_{q}$ is the per-point feature in the patch. $\\mathcal{A},\\mathcal{B},\\mathcal{C}$ and $\\mathcal{D}$ are MLPs. MAX{} denotes the feature maxpooling over $N_{l}$ -nearest neighbors of the query point $q$ . $w$ is a distance-based weight given by", + "bbox": [ + 75, + 588, + 468, + 665 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {j} = \\frac {\\beta_ {j}}{\\sum_ {i = 1} ^ {N} \\beta_ {i}}, \\beta_ {i} = \\operatorname {s i g m o i d} \\left(\\gamma_ {1} - \\gamma_ {2} \\| p _ {i} - q \\| _ {2}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 666, + 468, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma_{1}$ and $\\gamma_{2}$ are learnable parameters with an initial value of 1.0. The weight $w$ makes the layer focus on the point $p_i$ which is closer to the query point $q$ . As shown in Fig. 3, we stack two layers $\\mathcal{F}$ to form a block, which is further stacked to build our patch feature encoder $e_{\\varphi}$ .", + "bbox": [ + 75, + 703, + 468, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Shape Encoding. Since the global subsample set $P_{q} = \\{p_{i}\\}_{i=1}^{N_{P}}$ can be seen as a patch with points distributed globally on the shape surface, we adopt a similar network architecture with the patch feature encoder to get the global latent code $z_{q}^{s}$ . To obtain $P_{q}$ , we use a probability-based sampling strategy [14], which brings more points closer to the query point $q$ . It samples points according to a density gradient that decreases with increasing distance from the", + "bbox": [ + 75, + 777, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "point $q$ . Moreover, we find that adding more points from random sampling brings better results. Then, the gradient of a point is calculated by", + "bbox": [ + 496, + 534, + 890, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nv \\left(p _ {i}\\right) = \\left\\{ \\begin{array}{l} {\\left[ 1 - 1. 5 \\frac {\\left\\| p _ {i} - q \\right\\| _ {2}}{\\operatorname* {m a x} _ {p _ {j} \\in \\mathcal {P}} \\left\\| p _ {j} - q \\right\\| _ {2}} \\right] _ {0. 0 5} ^ {1}} \\\\ 1 \\quad \\text {i f} i \\in \\mathcal {R} \\end{array} \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 580, + 890, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\left[\\cdot\\right]_{0.05}^{1}$ indicates value clamping. $\\mathcal{R}$ is a random sample index set of $\\mathcal{P}$ with $N_P / 1.5$ items. Finally, the sampling probability of a point $p_i \\in \\mathcal{P}$ is $\\rho(p_i) = v(p_i) / \\sum_{p_j \\in \\mathcal{P}} v(p_j)$ .", + "bbox": [ + 496, + 640, + 890, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature Fusion. In order to allow each point in the local patch to have global information and determine the normal orientation, we first use the maxpooling and repetition operation to make the output global latent code has the same dimension as the local latent code. Then, the two kinds of codes are fused by concatenation, i.e., $[z_q^{\\mathbf{n}}:z_q^s ]$ in Eq. (8).", + "bbox": [ + 496, + 689, + 890, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Loss Functions", + "text_level": 1, + "bbox": [ + 500, + 795, + 651, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the query point $q$ , we constrain its unoriented normal and normal sign (i.e., orientation), respectively. To learn an accurate unoriented normal, we employ the ground-truth $\\hat{\\mathbf{n}}_q$ to calculate a normal vector $\\sin$ loss [5]", + "bbox": [ + 496, + 821, + 890, + 881 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\sin} = \\left\\| \\mathbf {n} _ {q} \\times \\hat {\\mathbf {n}} _ {q} \\right\\|. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 885, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13595", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/eca6956298b54c64f5e029afdecf2e04d62367decd501f8c3d2b73610d484465.jpg", + "table_caption": [ + "Table 1. Unoriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted or unavailable." + ], + "table_footnote": [], + "table_body": "
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientStripeGradient
Jet [10]12.3512.8418.3327.6813.3913.1316.2920.1120.5731.3445.1918.8218.6925.79
PCA [19]12.2912.8718.3827.5213.6612.8116.2519.9020.6031.3345.0019.8418.5425.87
PCPNet [17]9.6411.5118.2722.8411.7313.4614.5818.4721.0732.6039.9318.1419.5024.95
Zhou et al.* [57]8.6710.4917.6224.1410.2910.6613.62-------
Nesti-Net [6]7.0610.2417.7722.318.648.9512.4911.6016.8031.6139.2212.3311.7720.55
Lenssen et al. [29]6.729.9517.1821.967.737.5111.8411.6216.9730.6239.4311.2110.7620.10
DeepFit [5]6.519.2116.7323.127.927.3111.8011.2116.3929.8439.9511.8410.5419.96
MTRNet* [9]6.439.6917.0822.238.396.8911.78-------
Refine-Net [56]5.929.0416.5222.197.707.2011.43-------
Zhang et al.* [54]5.659.1916.7822.936.686.2911.259.8316.1329.8139.819.729.1919.08
Zhou et al.* [58]5.909.1016.5022.086.796.4011.13-------
AdaFit [59]5.199.0516.4521.946.015.9010.769.0915.7829.7838.748.528.5718.41
GraphFit [31]5.218.9616.1221.716.305.8610.698.9115.7329.3738.679.108.6218.40
HSurf-Net [32]4.178.7816.2521.614.984.8610.117.5915.6429.4338.547.637.4017.70
Ours3.958.5516.1321.534.914.679.967.4115.3429.3338.567.747.2817.61
", + "bbox": [ + 81, + 104, + 885, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the normal orientation, we adopt the binary cross entropy $H$ [14] to calculate a sign classification loss", + "bbox": [ + 75, + 347, + 468, + 378 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s g n} = H \\left(\\sigma \\left(g ^ {s} (q)\\right), [ f _ {\\boldsymbol {S}} (q) > 0 ]\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 380, + 468, + 404 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\sigma$ is a logistic function that converts the sign into its probabilities. $[f_S(q) > 0]$ is 1 if the estimated normal faces the outward of surface $S$ and 0 otherwise. Our method achieves a significant performance boost by dividing the oriented normal estimation into unoriented normal regression and its sign classification, instead of directly regressing the oriented normals of query points (see Sec. 5.3).", + "bbox": [ + 75, + 406, + 468, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To make the model also pay attention to neighbor points $p_i \\in p_q$ , we compute a weighted mean square error (MSE)", + "bbox": [ + 75, + 512, + 468, + 544 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m s e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tau_ {i} \\| \\vec {\\mathbf {n}} _ {i} - \\hat {\\vec {\\mathbf {n}}} _ {i} \\| ^ {2}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 547, + 468, + 585 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where the neighborhood point normals $\\vec{\\mathbf{n}} = \\delta (z_q)$ are predicted from the surface embedding $z_{q}$ by an MLP layer $\\delta :\\mathbb{R}^c\\to \\mathbb{R}^3$ . Moreover, we add a loss term according to coplanarity [54] to facilitate the learning of $\\tau$ in Eq.(12),", + "bbox": [ + 75, + 589, + 468, + 651 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\tau} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\tau_ {i} - \\hat {\\tau} _ {i}\\right) ^ {2}, \\hat {\\tau} _ {i} = \\exp \\left(- \\frac {\\left(p _ {i} \\cdot \\hat {\\mathbf {n}} _ {q}\\right) ^ {2}}{\\xi^ {2}}\\right), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 652, + 468, + 693 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\xi = \\max (0.05^2, 0.3\\sum_{i=1}^{N}(p_i \\cdot \\hat{\\mathbf{n}}_q)^2 / N)$ . In summary, our final training loss for oriented normal estimation is", + "bbox": [ + 75, + 696, + 468, + 729 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\sin} + \\lambda_ {2} \\mathcal {L} _ {s g n} + \\lambda_ {3} \\mathcal {L} _ {m s e} + \\lambda_ {4} \\mathcal {L} _ {\\tau}, \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 741, + 468, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_1 = 0.1$ , $\\lambda_2 = 0.1$ , $\\lambda_3 = 0.5$ and $\\lambda_4 = 1.0$ are factors.", + "bbox": [ + 76, + 770, + 465, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 799, + 209, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. We only train our network model on the PCPNet shape dataset [17], which provides the groundtruth normals with consistent orientation (outward of the surface). We follow the same train/test data split and data processing as in [5, 17, 32, 59]. For patch encoding, we", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "randomly select a query point from the shape point cloud and search its 700 neighbors to form a patch. For shape encoding, we sample $N_P = 1200$ points from the shape point cloud according to the sampling probability. The Adam optimizer is adopted with an initial learning rate of $9 \\times 10^{-4}$ which is decayed to $1/5$ of the latest value at epochs $\\{400, 600, 800\\}$ . The model is trained on an NVIDIA 2080 Ti GPU with a batch size of 145 and epochs of 800.", + "bbox": [ + 496, + 347, + 890, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. Due to the lack of relevant datasets and the relatively simple test shapes of the PCPNet dataset [17], we further collect shapes with complex structures from other public datasets, such as the Famous dataset [14] and the Stanford 3D Scanning Repository [12]. We follow the same preprocessing steps as the PCPNet dataset to conduct data augmentation, e.g., adding Gaussian noise with different levels (0.12%, 0.6% and 1.2%) and uneven sampling (stripe and gradient). The ground-truth oriented normals are extracted from mesh data and used for evaluation. We call this dataset FamousShape and it is available along with our code.", + "bbox": [ + 496, + 469, + 892, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We use the angle Root Mean Squared Error (RMSE) to evaluate the estimated normals and the Area Under the Curve (AUC) to show the error distribution [17, 32, 59]. Note that for the baseline methods, we flip their oriented normals if more than half of the normals face inward.", + "bbox": [ + 496, + 637, + 890, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Unoriented Normal Comparison", + "text_level": 1, + "bbox": [ + 500, + 724, + 785, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We directly use our oriented normal estimation results to compare with baseline methods that are designed for estimating unoriented normals, such as the traditional methods PCA [19] and Jet [10], the learning-based surface fitting methods DeepFit [5] and AdaFit [59], and the learning-based regression methods Nesti-Net [6] and HSurf-Net [32]. As shown in Table 1, we report quantitative comparison results with the baselines in terms of normal angle RMSE on two datasets, PCPNet and FamousShape. On the PCPNet dataset, our method achieves the best perfor", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13596", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/99616098176e411dfc511ff2506ed50eb2b9c1734af6794dcd9e05ca89fdaae7.jpg", + "table_caption": [ + "Table 2. Oriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted." + ], + "table_footnote": [], + "table_body": "
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientNone0.12%0.6%1.2%StripeGradient
PCA [19]+MST [19]19.0530.2031.7639.6427.1123.3828.5235.8841.6738.0960.1631.6935.4040.48
PCA [19]+QPBO [45]18.5521.6130.9439.5423.0025.4626.5232.2539.3941.8061.9136.6935.8241.31
PCA [19]+ODP [38]28.9625.8634.9151.5228.7023.0032.1630.4731.2941.6584.0039.4130.7242.92
AdaFit [59]+MST [19]27.6743.6948.8354.3936.1840.4641.8743.1239.3362.2860.2745.5742.0048.76
AdaFit [59]+QPBO [45]26.4124.1740.3148.7627.7431.5633.1627.5537.6069.5662.7727.8629.1942.42
AdaFit [59]+ODP [38]26.3724.8635.4451.8826.4520.5730.9341.7539.1944.3172.9145.0942.3747.60
HSurf-Net [32]+MST [19]29.8244.4950.4755.4740.5443.1543.9954.0242.6768.3765.9152.5253.9656.24
HSurf-Net [32]+QPBO [45]30.3432.3444.0851.7133.4640.4938.7441.6241.0667.4162.0445.5943.8350.26
HSurf-Net [32]+ODP [38]26.9124.8535.8751.7526.9120.1631.0743.7743.7446.9172.7045.0943.9849.37
PCPNet [17]33.3434.2240.5444.4637.9535.4437.6640.5141.0946.6754.3640.5444.2644.57
DPGO* [50]23.7925.1935.6643.8928.9929.3331.14-------
Ours10.2813.2325.4035.5116.4017.9219.7921.6325.9641.1452.6726.3928.9732.79
", + "bbox": [ + 84, + 103, + 883, + 303 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/98e40ada0bae2eb1fa7d3a87c1b5ee79567b361f75a47a62c175cee81dc8cdb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 310, + 284, + 441 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/370202fa3dc66097bd1a0d16d1c70370b50569be47fed56d2d829c8ce792ed28.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 311, + 464, + 440 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/39d71f38630d934925f5467d1ebe4832cca2f5205bc631d0f58c33e83afe4035.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 448, + 282, + 578 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5deb392f42ab2856ecc24e91cd46bc4f82291b8e9795bf466f6b60a323eee4e6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 448, + 464, + 577 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0c5e57e267af7d9c56d8e16871b41bc3943cc95e9b5631c7fdf0241e9cfb5938.jpg", + "image_caption": [ + "Figure 6. Oriented normal AUC on the PCPNet dataset. It shows the percentage of correctly estimated normals (PGP) for a given angle threshold. Our method has the best value for all thresholds." + ], + "image_footnote": [], + "bbox": [ + 81, + 585, + 285, + 734 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/722cb46b2e7d2064ad0ea76fb12f8a20f48d0ad33cd965fc9e071f29b90043d8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 295, + 585, + 467, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mance under all noise levels and density variations. On our FamousShape dataset, our method achieves the best performance under most metrics and has the best average result.", + "bbox": [ + 75, + 792, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Oriented Normal Comparison", + "text_level": 1, + "bbox": [ + 76, + 847, + 344, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our approach for oriented normal estimation with various baseline methods, such as PCPNet [17]", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and DPGO [50]. In addition, we choose three unoriented normal estimation methods (PCA [19], AdaFit [59] and HSurf-Net [32]) and three normal orientation methods (MST [19], QPBO [45] and ODP [38]), and make different combinations of them to form two-stage pipelines for estimating oriented normals, such as PCA+MST. Among the baselines, PCA is a widely used traditional method, AdaFit is a representative surface fitting-based method, and HSurf-Net is a regression-based method and has the state-of-the-art performance for unoriented normal estimation. We use the original implementation of QPBO and ODP, and the implementation of MST in [47]. In Table 2, we show quantitative comparison results on datasets PCPNet and FamousShape. We can see that our method provides the most accurate normals under almost all noise levels and density variations for both datasets, and achieves huge performance gains in terms of average results compared to all baselines. From the experimental results, we find that the propagation-based normal orientation methods have significantly varied results when dealing with unoriented normal inputs from different estimation methods, such as PCA+MST and AdaFit+MST. A visual comparison of the normal errors is shown in Fig. 5. The error distributions of various methods are illustrated in Fig. 6.", + "bbox": [ + 496, + 311, + 890, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "KITTI Dataset. To verify the generalization ability of our method on LiDAR point clouds of outdoor scenes, we test directly on the KITTI dataset [15] with the model trained on the PCPNet dataset. We only report qualitative results on this dataset as it does not provide the ground-truth normals. In Fig. 7, we use the Poisson surface reconstruction algorithm [26] to generate surfaces using oriented normals estimated by different methods. As can be seen, compared to the baselines, our estimated normals facilitate the algorithm to reconstruct surfaces that can more accurately depict the spatial structure and distribution of real scenes.", + "bbox": [ + 496, + 674, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 847, + 663, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We provide ablation results for oriented normal estimation in Table 3 (a)-(d), which are discussed as follows.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13597", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/316ef18965c705128b51c072b331db04e2fd3fc0f496b23c6ee985c06099d31a.jpg", + "table_caption": [ + "Table 3. Ablation studies for oriented normals on the PCPNet dataset. The last column is the average results under the unoriented metric." + ], + "table_footnote": [], + "table_body": "
AblationFeat. Enco.Module HLossPoint Samp.NoiseDensityOriented AverageUnoriented Average
None0.12%0.6%1.2%StripeGradient
(a)w/o patch encoding✓✓✓35.1942.2355.5961.3838.9241.4945.8018.83
w/o shape encoding✓✓✓69.7264.3781.8777.0774.8490.3576.3714.94
w/o weight w✓✓✓11.1514.3226.4936.0317.9926.0322.0010.48
(b)w/o module H✓✓✓12.0814.5325.8735.8818.4531.8423.1110.24
(c)w/o Lsin, Lsgn✓✓✓23.8625.5534.1342.4832.4241.3033.2920.23
(d)w/o density gradient✓✓✓12.1018.2528.0538.1519.7928.0924.0710.00
w/o random sample✓✓✓11.0113.7925.6435.8617.2225.7121.549.94
ζ=1/2✓✓✓10.9914.0425.6635.7817.7337.8223.679.92
ζ=1/3✓✓✓13.2715.4226.8237.1617.5228.1123.059.95
NP=1100✓✓✓10.6714.2125.5435.9716.8026.9821.699.99
NP=1300✓✓✓12.4414.5325.9335.7918.4019.8521.169.98
Final✓✓✓✓10.2813.2325.4035.5116.4017.9219.799.96
", + "bbox": [ + 81, + 104, + 885, + 287 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9780287067785ff440e957ed23f9742dba9cd2968d18c81f47356b5fae7a38c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 290, + 279, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9f01062237c7a78ef05e5f5f46cfe997c2980dd8cf9e1f9ad3cfd2523ec1e57c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 290, + 483, + 385 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/713ad495d6dfecb3d47361f07898cd82c7927285d86a499e9a53d8fbd9f5a26e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 290, + 684, + 385 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f9fdf56d2de51d42844623b67d0369640e0e4badf1e3c4ae460f179ee668fcbc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 291, + 888, + 385 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1497df6178be2c1d742355ddbcea5367ba6b79130eea20753eb4827df47dc1a2.jpg", + "image_caption": [ + "Figure 7. Street surfaces reconstructed using estimated normals on the KITTI dataset. The raw point cloud is colored with height values." + ], + "image_footnote": [], + "bbox": [ + 80, + 385, + 279, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/79fde2768b5c6a09c5a50d9c5fd63ed4f0cc47d67658fd385ced42906506fba3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 385, + 483, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0958ee212169dfeb536c73bc330db8dc4c0f44e245973c22efd7177d5f386b4f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 385, + 684, + 479 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8179c472dd14486ad46823799dce38343b2458dfc5afb81fd60c0fb4e3415991.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 386, + 888, + 479 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(a) Feature Encoding. (1) We realize the oriented normal estimation without using the patch encoding or the shape encoding. (2) The distance-based weight $w$ is not used in both patch encoding and shape encoding.", + "(b) Module $\\mathcal{H}$ . The attention-weighted normal prediction module $\\mathcal{H}$ is replaced with simple MLP layers.", + "(c) Loss $\\mathcal{L}_{\\text{sin}}, \\mathcal{L}_{\\text{sgn}}$ . In our pipeline, we regress the unoriented normal and its sign of the query point $q$ , and constrain them in loss functions $\\mathcal{L}_{\\text{sin}}$ and $\\mathcal{L}_{\\text{sgn}}$ , respectively. Here, we alternatively directly predict the oriented normal $\\vec{\\mathbf{n}}_q$ from surface embedding and compute its MSE loss.", + "(d) Point Sampling. In the shape encoding, we obtain a global point set $P_{q}$ by a probability-based sampling strategy as in Eq. (15), which includes density gradient term and random sample term. The point set $P_{q}$ includes $N_{P} = 1200$ points, and the ratio of randomly sampled points is $\\zeta = 1/1.5$ . (1) We only adopt one of the two terms in Eq. (15) for point sampling, e.g., 'w/o density gradient' means all points are randomly sampled. (2) The ratio $\\zeta$ is changed to $1/2$ and $1/3$ . (3) The number $N_{P}$ is set to 1100 and 1300." + ], + "bbox": [ + 75, + 513, + 468, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "From Table 3, we can conclude that both patch encoding and shape encoding are vital for learning accurate oriented and unoriented normals in our pipeline. The adoption of the weight $w$ and the attention-weighted normal prediction module $\\mathcal{H}$ effectively improves the algorithm's perfor", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mance. Compared to directly predicting the oriented normal $\\vec{\\mathbf{n}}_q$ , solving it separately by learning signed hyper surface is significantly better. The combination of the density gradient term and the random sample term in sampling can produce better results than either one alone. The proportion and number of points in the sampling of shape encoding have a significant positive effect on oriented normals, but very little on unoriented normals.", + "bbox": [ + 496, + 513, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we formulate the oriented normal estimation of point clouds as the learning of signed hyper surfaces. We first review the explicit surface fitting and the implicit surface learning, and derive the formulation of the signed hyper surfaces from their inspiration. Then, we propose to use an attention-weighted normal prediction module to recover the normal and its sign of the query point from the embedding of the signed hyper surfaces. Finally, we introduce how such surfaces can be learned from the patch encoding and shape encoding using the designed loss functions. We conduct extensive evaluation and ablation experiments to report the state-of-the-art performance and justify the effectiveness of our designs. We show that the oriented normal estimation is tightly coupled with the surface reconstruction, which is an area to be explored in future work.", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13598", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin, and Claudio T Silva. Point set surfaces. In Proceedings Visualization, 2001. VIS'01., pages 21-29. IEEE, 2001. 2", + "[2] Pierre Alliez, David Cohen-Steiner, Yiying Tong, and Mathieu Desbrun. Voronoi-based variational reconstruction of unoriented point sets. In Symposium on Geometry Processing, volume 7, pages 39–48, 2007. 2, 3", + "[3] Nina Amenta and Marshall Bern. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6118-6127, 2021. 1, 2, 4, 6, 7" + ], + "bbox": [ + 501, + 92, + 890, + 897 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13600", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SHS-Net_ Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds/b88f2048-c087-4b9c-9601-f88e3009b262_model.json b/2023/SHS-Net_ Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds/b88f2048-c087-4b9c-9601-f88e3009b262_model.json new file mode 100644 index 0000000000000000000000000000000000000000..721e0c36ede689952db98ef88923d2585c4d99c3 --- /dev/null +++ b/2023/SHS-Net_ Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds/b88f2048-c087-4b9c-9601-f88e3009b262_model.json @@ -0,0 +1,2992 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.09, + 0.13, + 0.882, + 0.175 + ], + "angle": 0, + "content": "SHS-Net: Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds" + }, + { + "type": "text", + "bbox": [ + 0.224, + 0.203, + 0.744, + 0.24 + ], + "angle": 0, + "content": "Qing Li\\(^{1}\\) Huifang Feng\\(^{2}\\) Kanle Shi\\(^{3}\\) Yue Gao\\(^{1}\\) Yi Fang\\(^{4}\\) Yu-Shen Liu\\(^{1}\\)* Zhizhong Han\\(^{5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.24, + 0.726, + 0.257 + ], + "angle": 0, + "content": "1School of Software, BNRist, Tsinghua University, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.257, + 0.85, + 0.275 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Informatics, Xiamen University, Xiamen, China \\(^{3}\\)Kuaishou Technology, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.126, + 0.275, + 0.845, + 0.292 + ], + "angle": 0, + "content": "\\(^{4}\\)Center for Artificial Intelligence and Robotics, New York University Abu Dhabi, Abu Dhabi, UAE" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.293, + 0.753, + 0.31 + ], + "angle": 0, + "content": "\\(^{5}\\)Department of Computer Science, Wayne State University, Detroit, USA" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.312, + 0.802, + 0.327 + ], + "angle": 0, + "content": "{leoqli, gaoyue, liuyushen}@tsinghua.edu.cn fenghuifang@stu.xmu.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.331, + 0.725, + 0.345 + ], + "angle": 0, + "content": "shikanle@kuaishou.com yfang@nyu.edu h312h@wayne.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.38, + 0.314, + 0.396 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.474, + 0.822 + ], + "angle": 0, + "content": "We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are available at https://github.com/LeoQLi/SHS-Net." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.377, + 0.892, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.513, + 0.895, + 0.598 + ], + "angle": 0, + "content": "Figure 1. We propose SHS-Net to estimate oriented normals directly from point clouds. In contrast, previous studies usually achieve this process through a two-stage paradigm using different algorithms, i.e., (1) unoriented normal estimation (e.g., PCA [19], AdaFit [59] and HSurf-Net [32]) and (2) normal orientation (e.g., MST [19], QPBO [45] and ODP [38])." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.615, + 0.634, + 0.631 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In computer vision and graphics, estimating normals for point clouds is a prerequisite for many techniques. As an important geometric property of point clouds, normals with consistent orientation, i.e., oriented normals, clearly reveal the geometric structures and make significant contributions in downstream applications, such as rendering and surface reconstruction [24-26]. Generally, the estimation of oriented normals requires a two-stage paradigm (see Fig. 1): (1) the unoriented normal estimation from the local neighbors of the query point, (2) the normal orientation to make the normal directions to be globally consistent, e.g., facing outward of the surface. While unoriented normals can be estimated by plane or surface fitting of the local neighborhood, determining whether the normals are facing outward or inward is ambiguous. In recent years, many excellent algorithms [5, 29, 31, 32, 59] have been proposed for unoriented normal estimation, while there are few methods that" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.851, + 0.471, + 0.903 + ], + "angle": 0, + "content": "*The corresponding author is Yu-Shen Liu. This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "13591" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "have reliable performance for normal orientation or directly estimating oriented normals. Estimating oriented normals from point clouds with noise, density variations, and complex geometries in an end-to-end manner is still a challenge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.155, + 0.471, + 0.473 + ], + "angle": 0, + "content": "The classic normal orientation methods rely on simple greedy propagation, which selects a seed point as the start and diffuses its normal orientation to the adjacent points via a minimum spanning tree (MST) [19, 27]. These methods are limited by error accumulation, where an incorrect orientation may degenerate all subsequent steps during the iterative propagation. Furthermore, they heavily rely on a smooth and clean assumption, which makes them easily fail in the presence of sharp edges or corners, density variations and noise. Meanwhile, their accuracy is sensitive to the neighborhood size of propagation. For example, a large size is usually used to smooth out outliers and noise, but can also erroneously include nearby surfaces. Considering that local information is usually not sufficient to guarantee robust orientation, some improved methods [22, 38, 45, 46, 49, 53] try to formulate the propagation process as a global energy optimization by introducing various constraints. Since their constraints are mainly derived from local consistency, the defects are inevitably inherited, and they also suffer from cumulative errors. Moreover, their data-specific parameters are difficult to generalize to new input types and topologies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.471, + 0.807 + ], + "angle": 0, + "content": "Different from the propagation-based methods, which only consider the adjacent orientation, the volume-based approaches exploit volumetric representation, such as signed distance functions [35, 40] and variational formulations [2, 21, 48]. They aim to divide the space into interior/exterior and determine whether point normals are facing inward or outward. Despite improvements in accuracy and robustness, these methods cannot scale to large point clouds due to their computational complexity. In general, propagation-based methods have difficulty with sharp features, while volume-based methods have difficulty with open surfaces. Furthermore, the above-mentioned methods are usually complex and require a two-stage operation, their performance heavily depends on the parameter tuning in each separated stage. Recently, several learning-based methods [17, 18, 50] have been proposed to deliver oriented normals from point clouds and have exhibited promising performance. Since they focus on learning an accurate local feature descriptor and do not fully explore the relationship between the surface normal orientation and the underlying surface, their performance cannot be guaranteed across different noise levels and geometric structures." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this work, we propose to estimate oriented normals from point clouds by implicitly learning signed hyper surfaces, which are represented by MLP layers to interpret the geometric property in a high-dimensional feature space. We learn this new geometry representation from both local and global shape properties to directly estimate normals with" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "consistent orientation in an end-to-end manner. The insight of our method is that determining a globally consistent normal orientation should require global context to eliminate the ambiguity from local since orientation is not a local property. We evaluate our method by conducting a series of qualitative and quantitative experiments on a range of point clouds with different sampling densities, noise levels, thin and sharp structures." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.214, + 0.88, + 0.227 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.23, + 0.891, + 0.273 + ], + "angle": 0, + "content": "- We introduce a new technique to represent point cloud geometric properties as signed hyper surfaces in a high-dimensional feature space." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.275, + 0.891, + 0.319 + ], + "angle": 0, + "content": "- We show that the signed hyper surfaces can be used to estimate normals with consistent orientations directly from point clouds, rather than through a two-stage paradigm." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.32, + 0.891, + 0.378 + ], + "angle": 0, + "content": "- We experimentally demonstrate that our method is able to estimate normals with high accuracy and achieves the state-of-the-art results in both unoriented and oriented normal estimation." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.23, + 0.891, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.407, + 0.642, + 0.422 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.433, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Unoriented Normal Estimation. Over the past few decades, many algorithms have been proposed for point cloud normal estimation, such as the classic Principle Component Analysis (PCA) [19] and its improvements [1, 20, 28, 39, 43], Voronoi-based paradigms [2, 3, 13, 36], and variants based on complex surface [4, 10, 16, 30, 41]. These methods are usually sensitive to noise and have limited accuracy even with heavy fine-tuned parameters. More recently, learning-based methods have been proposed to improve performance in this area and can be mainly divided into two categories: regression-based and surface fitting-based. The regression-based methods try to directly predict normals from structured data [8, 34, 44] or raw point clouds [6, 17, 18, 32, 33, 55-57] in a data-driven manner. Among them, HSurf-Net [32] achieves good performance by learning hyper surfaces from local patches, but the learned surfaces have no sign and cannot determine the normal orientation. The surface fitting-based methods integrate the traditional surface fitting techniques, such as plane fitting [9, 29] and jet fitting [5, 31, 54, 58, 59], into the end of the learning pipeline. They usually carefully design a network to predict point-wise weights, and then use a weighted surface formulation to solve the fitted surface normal. The normals estimated by the above methods randomly face both sides of the surface and cannot be used in many downstream applications without normal orientation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Consistent Normal Orientation. To make the unoriented normals have consistent orientations, early approaches mainly focus on local consistency and use the orientation propagation strategy upon a minimum spanning tree (MST) to let the adjacent points have the same orientations, such" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13592" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.873, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.242, + 0.757, + 0.258 + ], + "angle": 0, + "content": "Figure 2. The learning pipeline of the signed hyper surfaces for oriented normal estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.272, + 0.474, + 0.545 + ], + "angle": 0, + "content": "as the pioneering work of [19] and its improved methods [22, 45, 46, 49, 53]. These methods have many limitations in real applications as we introduced earlier. ODP [38] aims to achieve global consistency by introducing a dipole propagation strategy across the partitioned patches, but its robustness may suffer from the patch partition. On the contrary, some alternative approaches propose to solve the consistent normal orientation through volumetric representation. They are usually developed for reconstructing surfaces from unoriented points by various techniques, such as signed distance functions [35, 40], variational formulations [2, 21, 48], visibility [11, 23], isvalue constraints [51] and active contours [52]. Recently, a few works [17, 18, 50] explore to predict oriented normals through end-to-end deep networks. These methods focus on learning a general mapping from point clouds to normals and neglect the underlying surface distribution for normal orientation, leading to a sub-optimal solution." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.567, + 0.205, + 0.584 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.596, + 0.47, + 0.839 + ], + "angle": 0, + "content": "In mathematics, an explicit representation in Euclidean space expresses the \\(z\\) coordinate of a point \\(p\\) in terms of the \\(x\\) and \\(y\\), i.e., \\(z = f(x,y)\\). Such a surface is called an explicit surface, also called a height field. Another symmetric representation is \\(F(x,y,z) = 0\\), where \\(F\\) implicitly defines a locus called an implicit surface, also called a scalar field [7]. The implicit surface is a zero iso-surface of \\(F\\), i.e., the point set \\(\\{p \\in \\mathbb{R}^3 : F(p) = 0\\}\\) is a surface implicitly defined by \\(F\\). The explicit surface is usually used in surface fitting-based normal estimation, such as jet fitting [10], while the implicit surface is widely used in surface reconstruction. Generally, an explicit surface, i.e., \\(z = f(x,y)\\), can always be rewritten as an implicit surface, i.e., \\(F(x,y,z) = z - f(x,y) = 0\\). These two surface representations have the same tangent plane at a given point, where the normal is defined. See supplementary for details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Explicit Surface Fitting. We employ the widely used \\( n \\)-jet surface model [10] to briefly review the explicit surface fitting for normal estimation. It represents the surface by a polynomial function \\( J_{n}:\\mathbb{R}^{2}\\to \\mathbb{R} \\), which maps a coordinate" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.269, + 0.892, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.501, + 0.336, + 0.892, + 0.351 + ], + "angle": 0, + "content": "Figure 3. Feature encoding network in patch and shape encoding." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.364, + 0.792, + 0.38 + ], + "angle": 0, + "content": "\\((x,y)\\) to its height \\(z\\) in the tangent space by" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.388, + 0.892, + 0.43 + ], + "angle": 0, + "content": "\\[\nz = J _ {\\alpha , n} (x, y) = \\sum_ {k = 0} ^ {n} \\sum_ {j = 0} ^ {k} \\alpha_ {k - j, j} x ^ {k - j} y ^ {j}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.515 + ], + "angle": 0, + "content": "where \\(\\alpha\\) is the coefficient vector that defines the surface function. In order to find the optimal solution, the least squares approximation strategy is usually adopted to minimize the sum of the square errors between the (ground-truth) height and the jet value over a point set \\(\\{p_i\\}_{i=1}^N\\)," + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.523, + 0.892, + 0.565 + ], + "angle": 0, + "content": "\\[\nJ _ {\\alpha , n} ^ {*} = \\underset {\\alpha} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| z _ {i} - J _ {\\alpha , n} \\left(x _ {i}, y _ {i}\\right) \\| ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.891, + 0.603 + ], + "angle": 0, + "content": "If \\(\\alpha = (\\alpha_{0,0},\\alpha_{1,0},\\alpha_{0,1},\\dots ,\\alpha_{0,n})\\) is solved, then the normal at point \\(p\\) on the fitted surface is computed by" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.613, + 0.892, + 0.637 + ], + "angle": 0, + "content": "\\[\n\\mathbf {n} _ {p} = h (\\alpha) = (- \\alpha_ {1, 0}, - \\alpha_ {0, 1}, 1) / \\sqrt {1 + \\alpha_ {1 , 0} ^ {2} + \\alpha_ {0 , 1} ^ {2}}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Implicit Surface Learning. In recent years, many learning-based approaches have been proposed to represent surfaces by implicit functions, such as signed distance function (SDF) [42] and occupancy function [37]. The signed (or oriented) distance function is the shortest distance of a given point \\( p = (x_0, y_0, z_0) \\) to the closest surface \\( S \\) in a metric space, with the sign determined by whether the point is inside \\( (F(p) < 0) \\) or outside \\( (F(p) > 0) \\) of the surface. The underlying surface is implicitly represented by the isosurface of \\( F(p) = 0 \\). In the surface reconstruction task, a deep network is usually adopted to encode a 3D shape into a latent code, which is fed into a decoder together with query points to predict signed distances. If an implicit surface function is continuous and differentiable, the formula of tangent plane at a regular point \\( p \\) (gradient is non-null) is \\( F_x(p)(x - x_0) + F_y(p)(y - y_0) + F_z(p)(z - z_0) = 0 \\) and its normal (i.e., perpendicular) is \\( \\mathbf{n}_p = \\nabla F(p) / \\| \\nabla F(p) \\| \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13593" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.17, + 0.105 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.473, + 0.268 + ], + "angle": 0, + "content": "As shown in Fig. 2, we propose to implicitly learn signed hyper surfaces in the feature space for estimating oriented normals. In the following sections, we first introduce the representation of signed hyper surfaces by combining the characteristics of the above two surface representations. Then, we design an attention-weighted normal prediction module to solve the oriented normals of query points from signed hyper surfaces. Finally, we introduce how to learn this new surface representation from patch encoding and shape encoding using our designed loss functions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.274, + 0.285, + 0.291 + ], + "angle": 0, + "content": "4.1. Signed Hyper Surface" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.298, + 0.47, + 0.375 + ], + "angle": 0, + "content": "We formulate the surface function \\( F(x,y,z) = z - f(x,y) = 0 \\) as a more general format \\( F(z_{1},z_{2}) = z_{1} - z_{2} = 0 \\). Similarly, the signed hyper surface is implicitly learned by taking the latent encodings of point clouds as inputs and outputting an approximation of the surface in feature space," + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.395, + 0.47, + 0.415 + ], + "angle": 0, + "content": "\\[\nf _ {\\pmb {S}} (\\chi) \\approx \\mathcal {E} _ {\\theta} (\\chi | z _ {1}, z _ {2}), z _ {1} = e _ {\\varphi} (\\pmb {P} _ {\\chi} ^ {1}), z _ {2} = e _ {\\psi} (\\pmb {P} _ {\\chi} ^ {2}), (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.42, + 0.469, + 0.496 + ], + "angle": 0, + "content": "where \\(\\mathcal{E}\\) is implemented by a neural network with parameter \\(\\theta\\) that is conditioned on two latent vectors \\(z_{1}, z_{2} \\in \\mathbb{R}^{c}\\), which are extracted from point clouds by encoders \\(e_{\\varphi}\\) and \\(e_{\\psi}\\), respectively. \\(P_{\\chi}^{1}\\) and \\(P_{\\chi}^{2}\\) are subsample sets of the raw point cloud \\(\\mathcal{P}\\), e.g., point patches around a given point \\(\\chi\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.469, + 0.557 + ], + "angle": 0, + "content": "Similar to existing unoriented normal estimation methods [5, 17, 32, 59], we use a local patch \\(\\pmb{p}_q\\) to capture the local geometry for accurately describing the surface pattern around a query point \\(q\\)," + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.563, + 0.469, + 0.583 + ], + "angle": 0, + "content": "\\[\nf _ {\\boldsymbol {p}} ^ {\\mathbf {n}} (q) = \\mathcal {E} _ {\\theta} ^ {\\mathbf {n}} (q | z _ {q} ^ {\\mathbf {n}}), z _ {q} ^ {\\mathbf {n}} = e _ {\\varphi} (\\boldsymbol {p} _ {q}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.588, + 0.47, + 0.649 + ], + "angle": 0, + "content": "Since the interior/exterior of a surface cannot be determined reliably from a local patch, we take a global subsample set \\( P_{q} \\) from the point cloud \\( \\mathcal{P} \\) to provide additional information to estimate the sign at point \\( q \\)," + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.655, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\nf _ {\\boldsymbol {P}} ^ {s} (q) = \\operatorname {s g n} \\left(g ^ {s} (q)\\right) = \\operatorname {s g n} \\left(\\mathcal {E} _ {\\theta} ^ {s} \\left(q \\mid z _ {q} ^ {s}\\right)\\right), z _ {q} ^ {s} = e _ {\\psi} (\\boldsymbol {P} _ {q}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.734 + ], + "angle": 0, + "content": "where \\(\\operatorname{sgn}(\\cdot)\\) is a signum function, \\(g^{s}(q)\\) denotes the logarithm of the probability that \\(q\\) has a positive sign. Thus, the signed hyper surface function at point \\(q\\) is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.74, + 0.469, + 0.759 + ], + "angle": 0, + "content": "\\[\nf _ {\\boldsymbol {S}} (q) = f _ {\\boldsymbol {p}} ^ {\\mathbf {n}} (q) \\cdot f _ {\\boldsymbol {P}} ^ {s} (q) = \\mathcal {E} _ {\\theta} ^ {\\mathbf {n}, s} \\left(q \\mid z _ {q} ^ {\\mathbf {n}}, z _ {q} ^ {s}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.826 + ], + "angle": 0, + "content": "Different from the surface reconstruction task that learns SDF by representing a surface as the zero-set of the SDF, we do not learn a distance field of points with respect to the underlying surface." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.336, + 0.848 + ], + "angle": 0, + "content": "4.2. Oriented Normal Estimation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.855, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To simplify notations, we denote \\(\\mathcal{E}_{\\theta}^{\\mathbf{n},s}(q|z_q^{\\mathbf{n}},z_q^s)\\) as \\(S_{\\theta}(\\mathcal{X},\\mathcal{Y})\\), where \\(z_{q}^{\\mathbf{n}} = \\mathcal{X}\\in \\mathbb{R}^{c}\\) and \\(z_{q}^{s} = \\mathcal{Y}\\in \\mathbb{R}^{c}\\) are high dimensional latent vectors. According to the explicit surface" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.189, + 0.88, + 0.204 + ], + "angle": 0, + "content": "Figure 4. Attention-weighted normal prediction module \\(\\mathcal{H}(\\cdot)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.213, + 0.892, + 0.244 + ], + "angle": 0, + "content": "fitting, we formulate the signed hyper surface \\(S_{\\theta}:\\mathbb{R}^{2c}\\to\\) \\(\\mathbb{R}^c\\) as a feature-based polynomial function [32]" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.252, + 0.892, + 0.295 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\theta , \\mu} (\\mathcal {X}, \\mathcal {Y}) = \\sum_ {k = 0} ^ {\\mu} \\sum_ {j = 0} ^ {k} \\theta_ {k - j, j} \\mathbf {x} _ {k - j} \\mathbf {y} _ {j} = \\theta [ \\mathcal {X}: \\mathcal {Y} ], \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.302, + 0.891, + 0.331 + ], + "angle": 0, + "content": "where \\([ : ]\\) means the feature fusion through concatenation, \\(\\mu\\) denotes the number of fused items." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.332, + 0.892, + 0.379 + ], + "angle": 0, + "content": "Similar to Eq. (2), the bivariate function \\(S_{\\theta, \\mu}(\\mathcal{X}, \\mathcal{Y})\\) aims to map a feature pair \\((\\mathcal{X}_i, \\mathcal{Y}_i)\\) to their ground-truth value \\(\\mathcal{Z}_i = \\hat{S}(\\mathcal{X}_i, \\mathcal{Y}_i) \\in \\mathbb{R}^c\\) in the feature space, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.386, + 0.892, + 0.428 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\mathcal {Z} _ {i} - \\mathcal {S} _ {\\theta , \\mu} (\\mathcal {X} _ {i}, \\mathcal {Y} _ {i}) \\| ^ {2}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.435, + 0.892, + 0.466 + ], + "angle": 0, + "content": "To solve the oriented normal \\(\\vec{\\mathbf{n}}\\) from signed hyper surfaces, we introduce a normal prediction module \\(\\mathcal{H}(\\cdot)\\), thus" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.469, + 0.892, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\mathcal {H} \\left(\\mathcal {Z} _ {i}\\right) - \\mathcal {H} \\left(\\mathcal {S} _ {\\theta , \\mu} \\left(\\mathcal {X} _ {i}, \\mathcal {Y} _ {i}\\right)\\right) \\| ^ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.511, + 0.794, + 0.527 + ], + "angle": 0, + "content": "Finally, the oriented normal is optimized by" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.53, + 0.892, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\hat {\\vec {\\mathbf {n}}} _ {i} - \\vec {\\mathbf {n}} _ {i} \\| ^ {2}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Attention-weighted Normal Prediction \\(\\mathcal{H}(\\cdot):\\mathbb{R}^c\\to \\mathbb{R}^4\\) As shown in Fig. 4, we use an attention mechanism to recover the oriented normal \\(\\vec{\\bf{n}}_q\\) of the query point \\(q\\) from \\(c\\) dimensional fused surface embedding \\(z_{q}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.641, + 0.892, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\left(\\dot {\\mathbf {n}} _ {q}, s\\right) = \\mathcal {O} \\left(\\mathcal {V} \\left(o _ {q}\\right) \\otimes \\operatorname {M A X} \\left\\{\\operatorname {s o f t m a x} _ {\\mathcal {N} _ {q}} \\left(\\mathcal {Q} _ {j} \\left(o _ {q}\\right) _ {j = 1} ^ {m}\\right) \\right\\}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.673, + 0.892, + 0.842 + ], + "angle": 0, + "content": "where \\(o_q = \\tau \\cdot z_q\\), \\(\\tau = \\mathrm{sigmoid}(\\mathcal{I}(z_q))\\). \\(\\mathcal{O}, \\mathcal{V}, \\mathcal{Q}\\) and \\(\\mathcal{I}\\) are MLPs. \\(m = 64\\) is the feature dimension size. First, a multi-head strategy is adopted to deliver \\(m\\) relative weights \\(\\mathcal{Q}_j(o_q)\\), which are normalized by softmax over neighbors \\(\\mathcal{N}_q\\) into positive interpolation weights. Then, the feature maxpooling MAX{\\cdot} is performed to produce attention weights for each point. Meanwhile, the feature embedding \\(o_q\\) is refined through another branch \\(\\mathcal{V}\\) and modulated as the weighted sum through matrix multiplication. Finally, the normal and its sign (i.e., orientation) \\(\\vec{\\mathbf{n}}_q = (\\mathbf{n}_q \\in \\mathbb{R}^3, s \\in \\mathbb{R})\\) is predicted as a 4D vector by \\(\\mathcal{O}\\), and \\(\\mathbf{n}_q = \\dot{\\mathbf{n}}_q / \\| \\dot{\\mathbf{n}}_q \\|\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.673, + 0.864 + ], + "angle": 0, + "content": "4.3. Feature Encoding" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Patch Encoding. Given a neighborhood point patch \\( \\pmb{p}_q \\) of the query point, our local latent code extraction layer \\( \\mathcal{F} \\) is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13594" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.089, + 0.165, + 0.102 + ], + "angle": 0, + "content": "Point Cloud" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.104, + 0.155, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.226, + 0.152, + 0.236 + ], + "angle": 0, + "content": "PCPNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.089, + 0.246, + 0.102 + ], + "angle": 0, + "content": "PCA+MST" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.104, + 0.244, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.18, + 0.226, + 0.252, + 0.237 + ], + "angle": 0, + "content": "AdaFit+MST" + }, + 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0.645, + 0.371 + ], + "angle": 0, + "content": "HSurf-Net+MST" + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.239, + 0.747, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.654, + 0.36, + 0.743, + 0.371 + ], + "angle": 0, + "content": "HSurf-Net+ODP" + }, + { + "type": "image", + "bbox": [ + 0.75, + 0.239, + 0.844, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.36, + 0.843, + 0.371 + ], + "angle": 0, + "content": "HSurf-Net+QPBO" + }, + { + "type": "image", + "bbox": [ + 0.455, + 0.372, + 0.553, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.372, + 0.651, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.372, + 0.747, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.749, + 0.372, + 0.844, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.835, + 0.413, + 0.868, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.494, + 0.893, + 0.522 + ], + "angle": 0, + "content": "Figure 5. Visualization of the oriented normal error on datasets PCPNet (left) and FamousShape (right). The angle error is mapped to a heatmap ranging from \\(0^{\\circ}\\) to \\(180^{\\circ}\\). The purple color indicates the same direction as the ground-truth, while the red color is the opposite." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.535, + 0.173, + 0.547 + ], + "angle": 0, + "content": "formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.555, + 0.47, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\dot {z} _ {i} ^ {\\mathbf {n}} = \\mathcal {A} \\left(\\mathcal {B} \\left(\\operatorname {M A X} \\left\\{\\mathcal {C} \\left(w _ {j} \\cdot z _ {j} ^ {\\mathbf {n}}\\right) \\right\\} _ {j = 1} ^ {N _ {l}}\\right), z _ {i} ^ {\\mathbf {n}}\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.666 + ], + "angle": 0, + "content": "where \\(i = 1,\\dots ,N_{l + 1},l\\) is the neighborhood scale index and \\(N_{l + 1}\\leqslant N_l\\). \\(z_{i}^{\\mathbf{n}} = \\mathcal{D}(p_{i}),p_{i}\\in \\pmb{p}_{q}\\) is the per-point feature in the patch. \\(\\mathcal{A},\\mathcal{B},\\mathcal{C}\\) and \\(\\mathcal{D}\\) are MLPs. MAX{} denotes the feature maxpooling over \\(N_{l}\\)-nearest neighbors of the query point \\(q\\). \\(w\\) is a distance-based weight given by" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.667, + 0.469, + 0.702 + ], + "angle": 0, + "content": "\\[\nw _ {j} = \\frac {\\beta_ {j}}{\\sum_ {i = 1} ^ {N} \\beta_ {i}}, \\beta_ {i} = \\operatorname {s i g m o i d} \\left(\\gamma_ {1} - \\gamma_ {2} \\| p _ {i} - q \\| _ {2}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.469, + 0.779 + ], + "angle": 0, + "content": "where \\(\\gamma_{1}\\) and \\(\\gamma_{2}\\) are learnable parameters with an initial value of 1.0. The weight \\(w\\) makes the layer focus on the point \\(p_i\\) which is closer to the query point \\(q\\). As shown in Fig. 3, we stack two layers \\(\\mathcal{F}\\) to form a block, which is further stacked to build our patch feature encoder \\(e_{\\varphi}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Shape Encoding. Since the global subsample set \\( P_{q} = \\{p_{i}\\}_{i=1}^{N_{P}} \\) can be seen as a patch with points distributed globally on the shape surface, we adopt a similar network architecture with the patch feature encoder to get the global latent code \\( z_{q}^{s} \\). To obtain \\( P_{q} \\), we use a probability-based sampling strategy [14], which brings more points closer to the query point \\( q \\). It samples points according to a density gradient that decreases with increasing distance from the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.58 + ], + "angle": 0, + "content": "point \\( q \\). Moreover, we find that adding more points from random sampling brings better results. Then, the gradient of a point is calculated by" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.582, + 0.892, + 0.638 + ], + "angle": 0, + "content": "\\[\nv \\left(p _ {i}\\right) = \\left\\{ \\begin{array}{l} {\\left[ 1 - 1. 5 \\frac {\\left\\| p _ {i} - q \\right\\| _ {2}}{\\operatorname* {m a x} _ {p _ {j} \\in \\mathcal {P}} \\left\\| p _ {j} - q \\right\\| _ {2}} \\right] _ {0. 0 5} ^ {1}} \\\\ 1 \\quad \\text {i f} i \\in \\mathcal {R} \\end{array} \\right. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.892, + 0.689 + ], + "angle": 0, + "content": "where \\(\\left[\\cdot\\right]_{0.05}^{1}\\) indicates value clamping. \\(\\mathcal{R}\\) is a random sample index set of \\(\\mathcal{P}\\) with \\(N_P / 1.5\\) items. Finally, the sampling probability of a point \\(p_i \\in \\mathcal{P}\\) is \\(\\rho(p_i) = v(p_i) / \\sum_{p_j \\in \\mathcal{P}} v(p_j)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.892, + 0.782 + ], + "angle": 0, + "content": "Feature Fusion. In order to allow each point in the local patch to have global information and determine the normal orientation, we first use the maxpooling and repetition operation to make the output global latent code has the same dimension as the local latent code. Then, the two kinds of codes are fused by concatenation, i.e., \\([z_q^{\\mathbf{n}}:z_q^s ]\\) in Eq. (8)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.796, + 0.652, + 0.81 + ], + "angle": 0, + "content": "4.4. Loss Functions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.822, + 0.892, + 0.882 + ], + "angle": 0, + "content": "For the query point \\(q\\), we constrain its unoriented normal and normal sign (i.e., orientation), respectively. To learn an accurate unoriented normal, we employ the ground-truth \\(\\hat{\\mathbf{n}}_q\\) to calculate a normal vector \\(\\sin\\) loss [5]" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.886, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\sin} = \\left\\| \\mathbf {n} _ {q} \\times \\hat {\\mathbf {n}} _ {q} \\right\\|. \\tag {16}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13595" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.89, + 0.103 + ], + "angle": 0, + "content": "Table 1. Unoriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted or unavailable." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.106, + 0.887, + 0.34 + ], + "angle": 0, + "content": "
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientStripeGradient
Jet [10]12.3512.8418.3327.6813.3913.1316.2920.1120.5731.3445.1918.8218.6925.79
PCA [19]12.2912.8718.3827.5213.6612.8116.2519.9020.6031.3345.0019.8418.5425.87
PCPNet [17]9.6411.5118.2722.8411.7313.4614.5818.4721.0732.6039.9318.1419.5024.95
Zhou et al.* [57]8.6710.4917.6224.1410.2910.6613.62-------
Nesti-Net [6]7.0610.2417.7722.318.648.9512.4911.6016.8031.6139.2212.3311.7720.55
Lenssen et al. [29]6.729.9517.1821.967.737.5111.8411.6216.9730.6239.4311.2110.7620.10
DeepFit [5]6.519.2116.7323.127.927.3111.8011.2116.3929.8439.9511.8410.5419.96
MTRNet* [9]6.439.6917.0822.238.396.8911.78-------
Refine-Net [56]5.929.0416.5222.197.707.2011.43-------
Zhang et al.* [54]5.659.1916.7822.936.686.2911.259.8316.1329.8139.819.729.1919.08
Zhou et al.* [58]5.909.1016.5022.086.796.4011.13-------
AdaFit [59]5.199.0516.4521.946.015.9010.769.0915.7829.7838.748.528.5718.41
GraphFit [31]5.218.9616.1221.716.305.8610.698.9115.7329.3738.679.108.6218.40
HSurf-Net [32]4.178.7816.2521.614.984.8610.117.5915.6429.4338.547.637.4017.70
Ours3.958.5516.1321.534.914.679.967.4115.3429.3338.567.747.2817.61
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.379 + ], + "angle": 0, + "content": "For the normal orientation, we adopt the binary cross entropy \\( H \\) [14] to calculate a sign classification loss" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.381, + 0.47, + 0.405 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s g n} = H \\left(\\sigma \\left(g ^ {s} (q)\\right), [ f _ {\\boldsymbol {S}} (q) > 0 ]\\right), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.469, + 0.514 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is a logistic function that converts the sign into its probabilities. \\([f_S(q) > 0]\\) is 1 if the estimated normal faces the outward of surface \\(S\\) and 0 otherwise. Our method achieves a significant performance boost by dividing the oriented normal estimation into unoriented normal regression and its sign classification, instead of directly regressing the oriented normals of query points (see Sec. 5.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.469, + 0.545 + ], + "angle": 0, + "content": "To make the model also pay attention to neighbor points \\( p_i \\in p_q \\), we compute a weighted mean square error (MSE)" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.548, + 0.47, + 0.587 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m s e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tau_ {i} \\| \\vec {\\mathbf {n}} _ {i} - \\hat {\\vec {\\mathbf {n}}} _ {i} \\| ^ {2}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.652 + ], + "angle": 0, + "content": "where the neighborhood point normals \\(\\vec{\\mathbf{n}} = \\delta (z_q)\\) are predicted from the surface embedding \\(z_{q}\\) by an MLP layer \\(\\delta :\\mathbb{R}^c\\to \\mathbb{R}^3\\) . Moreover, we add a loss term according to coplanarity [54] to facilitate the learning of \\(\\tau\\) in Eq.(12)," + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.654, + 0.469, + 0.694 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\tau} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\tau_ {i} - \\hat {\\tau} _ {i}\\right) ^ {2}, \\hat {\\tau} _ {i} = \\exp \\left(- \\frac {\\left(p _ {i} \\cdot \\hat {\\mathbf {n}} _ {q}\\right) ^ {2}}{\\xi^ {2}}\\right), \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.469, + 0.73 + ], + "angle": 0, + "content": "where \\(\\xi = \\max (0.05^2, 0.3\\sum_{i=1}^{N}(p_i \\cdot \\hat{\\mathbf{n}}_q)^2 / N)\\). In summary, our final training loss for oriented normal estimation is" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.742, + 0.469, + 0.759 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\sin} + \\lambda_ {2} \\mathcal {L} _ {s g n} + \\lambda_ {3} \\mathcal {L} _ {m s e} + \\lambda_ {4} \\mathcal {L} _ {\\tau}, \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.771, + 0.466, + 0.786 + ], + "angle": 0, + "content": "where \\(\\lambda_1 = 0.1\\), \\(\\lambda_2 = 0.1\\), \\(\\lambda_3 = 0.5\\) and \\(\\lambda_4 = 1.0\\) are factors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.21, + 0.817 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Implementation. We only train our network model on the PCPNet shape dataset [17], which provides the groundtruth normals with consistent orientation (outward of the surface). We follow the same train/test data split and data processing as in [5, 17, 32, 59]. For patch encoding, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.469 + ], + "angle": 0, + "content": "randomly select a query point from the shape point cloud and search its 700 neighbors to form a patch. For shape encoding, we sample \\( N_P = 1200 \\) points from the shape point cloud according to the sampling probability. The Adam optimizer is adopted with an initial learning rate of \\( 9 \\times 10^{-4} \\) which is decayed to \\( 1/5 \\) of the latest value at epochs \\( \\{400, 600, 800\\} \\). The model is trained on an NVIDIA 2080 Ti GPU with a batch size of 145 and epochs of 800." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.893, + 0.636 + ], + "angle": 0, + "content": "Dataset. Due to the lack of relevant datasets and the relatively simple test shapes of the PCPNet dataset [17], we further collect shapes with complex structures from other public datasets, such as the Famous dataset [14] and the Stanford 3D Scanning Repository [12]. We follow the same preprocessing steps as the PCPNet dataset to conduct data augmentation, e.g., adding Gaussian noise with different levels (0.12%, 0.6% and 1.2%) and uneven sampling (stripe and gradient). The ground-truth oriented normals are extracted from mesh data and used for evaluation. We call this dataset FamousShape and it is available along with our code." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Metrics. We use the angle Root Mean Squared Error (RMSE) to evaluate the estimated normals and the Area Under the Curve (AUC) to show the error distribution [17, 32, 59]. Note that for the baseline methods, we flip their oriented normals if more than half of the normals face inward." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.787, + 0.742 + ], + "angle": 0, + "content": "5.1. Unoriented Normal Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We directly use our oriented normal estimation results to compare with baseline methods that are designed for estimating unoriented normals, such as the traditional methods PCA [19] and Jet [10], the learning-based surface fitting methods DeepFit [5] and AdaFit [59], and the learning-based regression methods Nesti-Net [6] and HSurf-Net [32]. As shown in Table 1, we report quantitative comparison results with the baselines in terms of normal angle RMSE on two datasets, PCPNet and FamousShape. On the PCPNet dataset, our method achieves the best perfor" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13596" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.127, + 0.09, + 0.843, + 0.103 + ], + "angle": 0, + "content": "Table 2. Oriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.104, + 0.884, + 0.304 + ], + "angle": 0, + "content": "
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientNone0.12%0.6%1.2%StripeGradient
PCA [19]+MST [19]19.0530.2031.7639.6427.1123.3828.5235.8841.6738.0960.1631.6935.4040.48
PCA [19]+QPBO [45]18.5521.6130.9439.5423.0025.4626.5232.2539.3941.8061.9136.6935.8241.31
PCA [19]+ODP [38]28.9625.8634.9151.5228.7023.0032.1630.4731.2941.6584.0039.4130.7242.92
AdaFit [59]+MST [19]27.6743.6948.8354.3936.1840.4641.8743.1239.3362.2860.2745.5742.0048.76
AdaFit [59]+QPBO [45]26.4124.1740.3148.7627.7431.5633.1627.5537.6069.5662.7727.8629.1942.42
AdaFit [59]+ODP [38]26.3724.8635.4451.8826.4520.5730.9341.7539.1944.3172.9145.0942.3747.60
HSurf-Net [32]+MST [19]29.8244.4950.4755.4740.5443.1543.9954.0242.6768.3765.9152.5253.9656.24
HSurf-Net [32]+QPBO [45]30.3432.3444.0851.7133.4640.4938.7441.6241.0667.4162.0445.5943.8350.26
HSurf-Net [32]+ODP [38]26.9124.8535.8751.7526.9120.1631.0743.7743.7446.9172.7045.0943.9849.37
PCPNet [17]33.3434.2240.5444.4637.9535.4437.6640.5141.0946.6754.3640.5444.2644.57
DPGO* [50]23.7925.1935.6643.8928.9929.3331.14-------
Ours10.2813.2325.4035.5116.4017.9219.7921.6325.9641.1452.6726.3928.9732.79
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.311, + 0.285, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.312, + 0.465, + 0.441 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.449, + 0.284, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.449, + 0.465, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.586, + 0.287, + 0.735 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.296, + 0.586, + 0.468, + 0.735 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.738, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Figure 6. Oriented normal AUC on the PCPNet dataset. It shows the percentage of correctly estimated normals (PGP) for a given angle threshold. Our method has the best value for all thresholds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.47, + 0.84 + ], + "angle": 0, + "content": "mance under all noise levels and density variations. On our FamousShape dataset, our method achieves the best performance under most metrics and has the best average result." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.345, + 0.865 + ], + "angle": 0, + "content": "5.2. Oriented Normal Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We compare our approach for oriented normal estimation with various baseline methods, such as PCPNet [17]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.675 + ], + "angle": 0, + "content": "and DPGO [50]. In addition, we choose three unoriented normal estimation methods (PCA [19], AdaFit [59] and HSurf-Net [32]) and three normal orientation methods (MST [19], QPBO [45] and ODP [38]), and make different combinations of them to form two-stage pipelines for estimating oriented normals, such as PCA+MST. Among the baselines, PCA is a widely used traditional method, AdaFit is a representative surface fitting-based method, and HSurf-Net is a regression-based method and has the state-of-the-art performance for unoriented normal estimation. We use the original implementation of QPBO and ODP, and the implementation of MST in [47]. In Table 2, we show quantitative comparison results on datasets PCPNet and FamousShape. We can see that our method provides the most accurate normals under almost all noise levels and density variations for both datasets, and achieves huge performance gains in terms of average results compared to all baselines. From the experimental results, we find that the propagation-based normal orientation methods have significantly varied results when dealing with unoriented normal inputs from different estimation methods, such as PCA+MST and AdaFit+MST. A visual comparison of the normal errors is shown in Fig. 5. The error distributions of various methods are illustrated in Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.84 + ], + "angle": 0, + "content": "KITTI Dataset. To verify the generalization ability of our method on LiDAR point clouds of outdoor scenes, we test directly on the KITTI dataset [15] with the model trained on the PCPNet dataset. We only report qualitative results on this dataset as it does not provide the ground-truth normals. In Fig. 7, we use the Poisson surface reconstruction algorithm [26] to generate surfaces using oriented normals estimated by different methods. As can be seen, compared to the baselines, our estimated normals facilitate the algorithm to reconstruct surfaces that can more accurately depict the spatial structure and distribution of real scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.665, + 0.862 + ], + "angle": 0, + "content": "5.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We provide ablation results for oriented normal estimation in Table 3 (a)-(d), which are discussed as follows." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13597" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.09, + 0.887, + 0.103 + ], + "angle": 0, + "content": "Table 3. Ablation studies for oriented normals on the PCPNet dataset. The last column is the average results under the unoriented metric." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.106, + 0.887, + 0.289 + ], + "angle": 0, + "content": "
AblationFeat. Enco.Module HLossPoint Samp.NoiseDensityOriented AverageUnoriented Average
None0.12%0.6%1.2%StripeGradient
(a)w/o patch encoding✓✓✓35.1942.2355.5961.3838.9241.4945.8018.83
w/o shape encoding✓✓✓69.7264.3781.8777.0774.8490.3576.3714.94
w/o weight w✓✓✓11.1514.3226.4936.0317.9926.0322.0010.48
(b)w/o module H✓✓✓12.0814.5325.8735.8818.4531.8423.1110.24
(c)w/o Lsin, Lsgn✓✓✓23.8625.5534.1342.4832.4241.3033.2920.23
(d)w/o density gradient✓✓✓12.1018.2528.0538.1519.7928.0924.0710.00
w/o random sample✓✓✓11.0113.7925.6435.8617.2225.7121.549.94
ζ=1/2✓✓✓10.9914.0425.6635.7817.7337.8223.679.92
ζ=1/3✓✓✓13.2715.4226.8237.1617.5228.1123.059.95
NP=1100✓✓✓10.6714.2125.5435.9716.8026.9821.699.99
NP=1300✓✓✓12.4414.5325.9335.7918.4019.8521.169.98
Final✓✓✓✓10.2813.2325.4035.5116.4017.9219.799.96
" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.291, + 0.28, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.291, + 0.484, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.291, + 0.685, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.292, + 0.889, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.386, + 0.281, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.386, + 0.485, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.386, + 0.686, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.387, + 0.889, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.484, + 0.886, + 0.499 + ], + "angle": 0, + "content": "Figure 7. Street surfaces reconstructed using estimated normals on the KITTI dataset. The raw point cloud is colored with height values." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.469, + 0.575 + ], + "angle": 0, + "content": "(a) Feature Encoding. (1) We realize the oriented normal estimation without using the patch encoding or the shape encoding. (2) The distance-based weight \\( w \\) is not used in both patch encoding and shape encoding." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.577, + 0.469, + 0.608 + ], + "angle": 0, + "content": "(b) Module \\(\\mathcal{H}\\). The attention-weighted normal prediction module \\(\\mathcal{H}\\) is replaced with simple MLP layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.469, + 0.685 + ], + "angle": 0, + "content": "(c) Loss \\(\\mathcal{L}_{\\text{sin}}, \\mathcal{L}_{\\text{sgn}}\\). In our pipeline, we regress the unoriented normal and its sign of the query point \\(q\\), and constrain them in loss functions \\(\\mathcal{L}_{\\text{sin}}\\) and \\(\\mathcal{L}_{\\text{sgn}}\\), respectively. Here, we alternatively directly predict the oriented normal \\(\\vec{\\mathbf{n}}_q\\) from surface embedding and compute its MSE loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.469, + 0.824 + ], + "angle": 0, + "content": "(d) Point Sampling. In the shape encoding, we obtain a global point set \\( P_{q} \\) by a probability-based sampling strategy as in Eq. (15), which includes density gradient term and random sample term. The point set \\( P_{q} \\) includes \\( N_{P} = 1200 \\) points, and the ratio of randomly sampled points is \\( \\zeta = 1/1.5 \\). (1) We only adopt one of the two terms in Eq. (15) for point sampling, e.g., 'w/o density gradient' means all points are randomly sampled. (2) The ratio \\( \\zeta \\) is changed to \\( 1/2 \\) and \\( 1/3 \\). (3) The number \\( N_{P} \\) is set to 1100 and 1300." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.515, + 0.469, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "From Table 3, we can conclude that both patch encoding and shape encoding are vital for learning accurate oriented and unoriented normals in our pipeline. The adoption of the weight \\( w \\) and the attention-weighted normal prediction module \\( \\mathcal{H} \\) effectively improves the algorithm's perfor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.635 + ], + "angle": 0, + "content": "mance. Compared to directly predicting the oriented normal \\(\\vec{\\mathbf{n}}_q\\), solving it separately by learning signed hyper surface is significantly better. The combination of the density gradient term and the random sample term in sampling can produce better results than either one alone. The proportion and number of points in the sampling of shape encoding have a significant positive effect on oriented normals, but very little on unoriented normals." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.619, + 0.665 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this work, we formulate the oriented normal estimation of point clouds as the learning of signed hyper surfaces. We first review the explicit surface fitting and the implicit surface learning, and derive the formulation of the signed hyper surfaces from their inspiration. Then, we propose to use an attention-weighted normal prediction module to recover the normal and its sign of the query point from the embedding of the signed hyper surfaces. Finally, we introduce how such surfaces can be learned from the patch encoding and shape encoding using the designed loss functions. We conduct extensive evaluation and ablation experiments to report the state-of-the-art performance and justify the effectiveness of our designs. We show that the oriented normal estimation is tightly coupled with the surface reconstruction, which is an area to be explored in future work." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13598" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Marc Alexa, Johannes Behr, Daniel Cohen-Or, Shachar Fleishman, David Levin, and Claudio T Silva. Point set surfaces. In Proceedings Visualization, 2001. VIS'01., pages 21-29. 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Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are available at https://github.com/LeoQLi/SHS-Net. + +![](images/db4de02ce8ecdb85d23f3d699e759061f29b14204e99ed2d3fa8510bab7b9ba9.jpg) +Figure 1. We propose SHS-Net to estimate oriented normals directly from point clouds. In contrast, previous studies usually achieve this process through a two-stage paradigm using different algorithms, i.e., (1) unoriented normal estimation (e.g., PCA [19], AdaFit [59] and HSurf-Net [32]) and (2) normal orientation (e.g., MST [19], QPBO [45] and ODP [38]). + +# 1. Introduction + +In computer vision and graphics, estimating normals for point clouds is a prerequisite for many techniques. As an important geometric property of point clouds, normals with consistent orientation, i.e., oriented normals, clearly reveal the geometric structures and make significant contributions in downstream applications, such as rendering and surface reconstruction [24-26]. Generally, the estimation of oriented normals requires a two-stage paradigm (see Fig. 1): (1) the unoriented normal estimation from the local neighbors of the query point, (2) the normal orientation to make the normal directions to be globally consistent, e.g., facing outward of the surface. While unoriented normals can be estimated by plane or surface fitting of the local neighborhood, determining whether the normals are facing outward or inward is ambiguous. In recent years, many excellent algorithms [5, 29, 31, 32, 59] have been proposed for unoriented normal estimation, while there are few methods that + +have reliable performance for normal orientation or directly estimating oriented normals. Estimating oriented normals from point clouds with noise, density variations, and complex geometries in an end-to-end manner is still a challenge. + +The classic normal orientation methods rely on simple greedy propagation, which selects a seed point as the start and diffuses its normal orientation to the adjacent points via a minimum spanning tree (MST) [19, 27]. These methods are limited by error accumulation, where an incorrect orientation may degenerate all subsequent steps during the iterative propagation. Furthermore, they heavily rely on a smooth and clean assumption, which makes them easily fail in the presence of sharp edges or corners, density variations and noise. Meanwhile, their accuracy is sensitive to the neighborhood size of propagation. For example, a large size is usually used to smooth out outliers and noise, but can also erroneously include nearby surfaces. Considering that local information is usually not sufficient to guarantee robust orientation, some improved methods [22, 38, 45, 46, 49, 53] try to formulate the propagation process as a global energy optimization by introducing various constraints. Since their constraints are mainly derived from local consistency, the defects are inevitably inherited, and they also suffer from cumulative errors. Moreover, their data-specific parameters are difficult to generalize to new input types and topologies. + +Different from the propagation-based methods, which only consider the adjacent orientation, the volume-based approaches exploit volumetric representation, such as signed distance functions [35, 40] and variational formulations [2, 21, 48]. They aim to divide the space into interior/exterior and determine whether point normals are facing inward or outward. Despite improvements in accuracy and robustness, these methods cannot scale to large point clouds due to their computational complexity. In general, propagation-based methods have difficulty with sharp features, while volume-based methods have difficulty with open surfaces. Furthermore, the above-mentioned methods are usually complex and require a two-stage operation, their performance heavily depends on the parameter tuning in each separated stage. Recently, several learning-based methods [17, 18, 50] have been proposed to deliver oriented normals from point clouds and have exhibited promising performance. Since they focus on learning an accurate local feature descriptor and do not fully explore the relationship between the surface normal orientation and the underlying surface, their performance cannot be guaranteed across different noise levels and geometric structures. + +In this work, we propose to estimate oriented normals from point clouds by implicitly learning signed hyper surfaces, which are represented by MLP layers to interpret the geometric property in a high-dimensional feature space. We learn this new geometry representation from both local and global shape properties to directly estimate normals with + +consistent orientation in an end-to-end manner. The insight of our method is that determining a globally consistent normal orientation should require global context to eliminate the ambiguity from local since orientation is not a local property. We evaluate our method by conducting a series of qualitative and quantitative experiments on a range of point clouds with different sampling densities, noise levels, thin and sharp structures. + +Our main contributions can be summarized as follows. + +- We introduce a new technique to represent point cloud geometric properties as signed hyper surfaces in a high-dimensional feature space. +- We show that the signed hyper surfaces can be used to estimate normals with consistent orientations directly from point clouds, rather than through a two-stage paradigm. +- We experimentally demonstrate that our method is able to estimate normals with high accuracy and achieves the state-of-the-art results in both unoriented and oriented normal estimation. + +# 2. Related Work + +Unoriented Normal Estimation. Over the past few decades, many algorithms have been proposed for point cloud normal estimation, such as the classic Principle Component Analysis (PCA) [19] and its improvements [1, 20, 28, 39, 43], Voronoi-based paradigms [2, 3, 13, 36], and variants based on complex surface [4, 10, 16, 30, 41]. These methods are usually sensitive to noise and have limited accuracy even with heavy fine-tuned parameters. More recently, learning-based methods have been proposed to improve performance in this area and can be mainly divided into two categories: regression-based and surface fitting-based. The regression-based methods try to directly predict normals from structured data [8, 34, 44] or raw point clouds [6, 17, 18, 32, 33, 55-57] in a data-driven manner. Among them, HSurf-Net [32] achieves good performance by learning hyper surfaces from local patches, but the learned surfaces have no sign and cannot determine the normal orientation. The surface fitting-based methods integrate the traditional surface fitting techniques, such as plane fitting [9, 29] and jet fitting [5, 31, 54, 58, 59], into the end of the learning pipeline. They usually carefully design a network to predict point-wise weights, and then use a weighted surface formulation to solve the fitted surface normal. The normals estimated by the above methods randomly face both sides of the surface and cannot be used in many downstream applications without normal orientation. + +Consistent Normal Orientation. To make the unoriented normals have consistent orientations, early approaches mainly focus on local consistency and use the orientation propagation strategy upon a minimum spanning tree (MST) to let the adjacent points have the same orientations, such + +![](images/c737c2753d2fa077f56d92404a5c968cc7571c65049d8d4371b2093bcdba402e.jpg) +Figure 2. The learning pipeline of the signed hyper surfaces for oriented normal estimation. + +as the pioneering work of [19] and its improved methods [22, 45, 46, 49, 53]. These methods have many limitations in real applications as we introduced earlier. ODP [38] aims to achieve global consistency by introducing a dipole propagation strategy across the partitioned patches, but its robustness may suffer from the patch partition. On the contrary, some alternative approaches propose to solve the consistent normal orientation through volumetric representation. They are usually developed for reconstructing surfaces from unoriented points by various techniques, such as signed distance functions [35, 40], variational formulations [2, 21, 48], visibility [11, 23], isvalue constraints [51] and active contours [52]. Recently, a few works [17, 18, 50] explore to predict oriented normals through end-to-end deep networks. These methods focus on learning a general mapping from point clouds to normals and neglect the underlying surface distribution for normal orientation, leading to a sub-optimal solution. + +# 3. Preliminary + +In mathematics, an explicit representation in Euclidean space expresses the $z$ coordinate of a point $p$ in terms of the $x$ and $y$ , i.e., $z = f(x,y)$ . Such a surface is called an explicit surface, also called a height field. Another symmetric representation is $F(x,y,z) = 0$ , where $F$ implicitly defines a locus called an implicit surface, also called a scalar field [7]. The implicit surface is a zero iso-surface of $F$ , i.e., the point set $\{p \in \mathbb{R}^3 : F(p) = 0\}$ is a surface implicitly defined by $F$ . The explicit surface is usually used in surface fitting-based normal estimation, such as jet fitting [10], while the implicit surface is widely used in surface reconstruction. Generally, an explicit surface, i.e., $z = f(x,y)$ , can always be rewritten as an implicit surface, i.e., $F(x,y,z) = z - f(x,y) = 0$ . These two surface representations have the same tangent plane at a given point, where the normal is defined. See supplementary for details. + +Explicit Surface Fitting. We employ the widely used $n$ -jet surface model [10] to briefly review the explicit surface fitting for normal estimation. It represents the surface by a polynomial function $J_{n}:\mathbb{R}^{2}\to \mathbb{R}$ , which maps a coordinate + +![](images/1590ae8503229a4771ae6e288f7c7535cf05364599439849ac2f4039aa5819c9.jpg) +Figure 3. Feature encoding network in patch and shape encoding. + +$(x,y)$ to its height $z$ in the tangent space by + +$$ +z = J _ {\alpha , n} (x, y) = \sum_ {k = 0} ^ {n} \sum_ {j = 0} ^ {k} \alpha_ {k - j, j} x ^ {k - j} y ^ {j}, \tag {1} +$$ + +where $\alpha$ is the coefficient vector that defines the surface function. In order to find the optimal solution, the least squares approximation strategy is usually adopted to minimize the sum of the square errors between the (ground-truth) height and the jet value over a point set $\{p_i\}_{i=1}^N$ , + +$$ +J _ {\alpha , n} ^ {*} = \underset {\alpha} {\operatorname {a r g m i n}} \sum_ {i = 1} ^ {N} \| z _ {i} - J _ {\alpha , n} \left(x _ {i}, y _ {i}\right) \| ^ {2}. \tag {2} +$$ + +If $\alpha = (\alpha_{0,0},\alpha_{1,0},\alpha_{0,1},\dots ,\alpha_{0,n})$ is solved, then the normal at point $p$ on the fitted surface is computed by + +$$ +\mathbf {n} _ {p} = h (\alpha) = (- \alpha_ {1, 0}, - \alpha_ {0, 1}, 1) / \sqrt {1 + \alpha_ {1 , 0} ^ {2} + \alpha_ {0 , 1} ^ {2}}. \tag {3} +$$ + +Implicit Surface Learning. In recent years, many learning-based approaches have been proposed to represent surfaces by implicit functions, such as signed distance function (SDF) [42] and occupancy function [37]. The signed (or oriented) distance function is the shortest distance of a given point $p = (x_0, y_0, z_0)$ to the closest surface $S$ in a metric space, with the sign determined by whether the point is inside $(F(p) < 0)$ or outside $(F(p) > 0)$ of the surface. The underlying surface is implicitly represented by the isosurface of $F(p) = 0$ . In the surface reconstruction task, a deep network is usually adopted to encode a 3D shape into a latent code, which is fed into a decoder together with query points to predict signed distances. If an implicit surface function is continuous and differentiable, the formula of tangent plane at a regular point $p$ (gradient is non-null) is $F_x(p)(x - x_0) + F_y(p)(y - y_0) + F_z(p)(z - z_0) = 0$ and its normal (i.e., perpendicular) is $\mathbf{n}_p = \nabla F(p) / \| \nabla F(p) \|$ . + +# 4. Method + +As shown in Fig. 2, we propose to implicitly learn signed hyper surfaces in the feature space for estimating oriented normals. In the following sections, we first introduce the representation of signed hyper surfaces by combining the characteristics of the above two surface representations. Then, we design an attention-weighted normal prediction module to solve the oriented normals of query points from signed hyper surfaces. Finally, we introduce how to learn this new surface representation from patch encoding and shape encoding using our designed loss functions. + +# 4.1. Signed Hyper Surface + +We formulate the surface function $F(x,y,z) = z - f(x,y) = 0$ as a more general format $F(z_{1},z_{2}) = z_{1} - z_{2} = 0$ . Similarly, the signed hyper surface is implicitly learned by taking the latent encodings of point clouds as inputs and outputting an approximation of the surface in feature space, + +$$ +f _ {\pmb {S}} (\chi) \approx \mathcal {E} _ {\theta} (\chi | z _ {1}, z _ {2}), z _ {1} = e _ {\varphi} (\pmb {P} _ {\chi} ^ {1}), z _ {2} = e _ {\psi} (\pmb {P} _ {\chi} ^ {2}), (4) +$$ + +where $\mathcal{E}$ is implemented by a neural network with parameter $\theta$ that is conditioned on two latent vectors $z_{1}, z_{2} \in \mathbb{R}^{c}$ , which are extracted from point clouds by encoders $e_{\varphi}$ and $e_{\psi}$ , respectively. $P_{\chi}^{1}$ and $P_{\chi}^{2}$ are subsample sets of the raw point cloud $\mathcal{P}$ , e.g., point patches around a given point $\chi$ . + +Similar to existing unoriented normal estimation methods [5, 17, 32, 59], we use a local patch $\pmb{p}_q$ to capture the local geometry for accurately describing the surface pattern around a query point $q$ , + +$$ +f _ {\boldsymbol {p}} ^ {\mathbf {n}} (q) = \mathcal {E} _ {\theta} ^ {\mathbf {n}} (q | z _ {q} ^ {\mathbf {n}}), z _ {q} ^ {\mathbf {n}} = e _ {\varphi} (\boldsymbol {p} _ {q}). \tag {5} +$$ + +Since the interior/exterior of a surface cannot be determined reliably from a local patch, we take a global subsample set $P_{q}$ from the point cloud $\mathcal{P}$ to provide additional information to estimate the sign at point $q$ , + +$$ +f _ {\boldsymbol {P}} ^ {s} (q) = \operatorname {s g n} \left(g ^ {s} (q)\right) = \operatorname {s g n} \left(\mathcal {E} _ {\theta} ^ {s} \left(q \mid z _ {q} ^ {s}\right)\right), z _ {q} ^ {s} = e _ {\psi} (\boldsymbol {P} _ {q}), \tag {6} +$$ + +where $\operatorname{sgn}(\cdot)$ is a signum function, $g^{s}(q)$ denotes the logarithm of the probability that $q$ has a positive sign. Thus, the signed hyper surface function at point $q$ is formulated as + +$$ +f _ {\boldsymbol {S}} (q) = f _ {\boldsymbol {p}} ^ {\mathbf {n}} (q) \cdot f _ {\boldsymbol {P}} ^ {s} (q) = \mathcal {E} _ {\theta} ^ {\mathbf {n}, s} \left(q \mid z _ {q} ^ {\mathbf {n}}, z _ {q} ^ {s}\right). \tag {7} +$$ + +Different from the surface reconstruction task that learns SDF by representing a surface as the zero-set of the SDF, we do not learn a distance field of points with respect to the underlying surface. + +# 4.2. Oriented Normal Estimation + +To simplify notations, we denote $\mathcal{E}_{\theta}^{\mathbf{n},s}(q|z_q^{\mathbf{n}},z_q^s)$ as $S_{\theta}(\mathcal{X},\mathcal{Y})$ , where $z_{q}^{\mathbf{n}} = \mathcal{X}\in \mathbb{R}^{c}$ and $z_{q}^{s} = \mathcal{Y}\in \mathbb{R}^{c}$ are high dimensional latent vectors. According to the explicit surface + +![](images/2873ebc5d63558efca4f8e66b9a72d9a9c3e2dabfb52d6fb1b189f511931d450.jpg) +Figure 4. Attention-weighted normal prediction module $\mathcal{H}(\cdot)$ . + +fitting, we formulate the signed hyper surface $S_{\theta}:\mathbb{R}^{2c}\to$ $\mathbb{R}^c$ as a feature-based polynomial function [32] + +$$ +\mathcal {S} _ {\theta , \mu} (\mathcal {X}, \mathcal {Y}) = \sum_ {k = 0} ^ {\mu} \sum_ {j = 0} ^ {k} \theta_ {k - j, j} \mathbf {x} _ {k - j} \mathbf {y} _ {j} = \theta [ \mathcal {X}: \mathcal {Y} ], \tag {8} +$$ + +where $[ : ]$ means the feature fusion through concatenation, $\mu$ denotes the number of fused items. + +Similar to Eq. (2), the bivariate function $S_{\theta, \mu}(\mathcal{X}, \mathcal{Y})$ aims to map a feature pair $(\mathcal{X}_i, \mathcal{Y}_i)$ to their ground-truth value $\mathcal{Z}_i = \hat{S}(\mathcal{X}_i, \mathcal{Y}_i) \in \mathbb{R}^c$ in the feature space, i.e., + +$$ +\mathcal {S} _ {\theta , \mu} ^ {*} = \underset {\theta , \mu} {\operatorname {a r g m i n}} \sum_ {i = 1} ^ {N} \| \mathcal {Z} _ {i} - \mathcal {S} _ {\theta , \mu} (\mathcal {X} _ {i}, \mathcal {Y} _ {i}) \| ^ {2}. \tag {9} +$$ + +To solve the oriented normal $\vec{\mathbf{n}}$ from signed hyper surfaces, we introduce a normal prediction module $\mathcal{H}(\cdot)$ , thus + +$$ +\mathcal {S} _ {\theta , \mu} ^ {*} = \underset {\theta , \mu} {\operatorname {a r g m i n}} \sum_ {i = 1} ^ {N} \| \mathcal {H} \left(\mathcal {Z} _ {i}\right) - \mathcal {H} \left(\mathcal {S} _ {\theta , \mu} \left(\mathcal {X} _ {i}, \mathcal {Y} _ {i}\right)\right) \| ^ {2}. \tag {10} +$$ + +Finally, the oriented normal is optimized by + +$$ +\mathcal {S} _ {\theta , \mu} ^ {*} = \underset {\theta , \mu} {\operatorname {a r g m i n}} \sum_ {i = 1} ^ {N} \| \hat {\vec {\mathbf {n}}} _ {i} - \vec {\mathbf {n}} _ {i} \| ^ {2}. \tag {11} +$$ + +Attention-weighted Normal Prediction $\mathcal{H}(\cdot):\mathbb{R}^c\to \mathbb{R}^4$ As shown in Fig. 4, we use an attention mechanism to recover the oriented normal $\vec{\bf{n}}_q$ of the query point $q$ from $c$ dimensional fused surface embedding $z_{q}$ + +$$ +\left(\dot {\mathbf {n}} _ {q}, s\right) = \mathcal {O} \left(\mathcal {V} \left(o _ {q}\right) \otimes \operatorname {M A X} \left\{\operatorname {s o f t m a x} _ {\mathcal {N} _ {q}} \left(\mathcal {Q} _ {j} \left(o _ {q}\right) _ {j = 1} ^ {m}\right) \right\}\right), \tag {12} +$$ + +where $o_q = \tau \cdot z_q$ , $\tau = \mathrm{sigmoid}(\mathcal{I}(z_q))$ . $\mathcal{O}, \mathcal{V}, \mathcal{Q}$ and $\mathcal{I}$ are MLPs. $m = 64$ is the feature dimension size. First, a multi-head strategy is adopted to deliver $m$ relative weights $\mathcal{Q}_j(o_q)$ , which are normalized by softmax over neighbors $\mathcal{N}_q$ into positive interpolation weights. Then, the feature maxpooling MAX{\cdot} is performed to produce attention weights for each point. Meanwhile, the feature embedding $o_q$ is refined through another branch $\mathcal{V}$ and modulated as the weighted sum through matrix multiplication. Finally, the normal and its sign (i.e., orientation) $\vec{\mathbf{n}}_q = (\mathbf{n}_q \in \mathbb{R}^3, s \in \mathbb{R})$ is predicted as a 4D vector by $\mathcal{O}$ , and $\mathbf{n}_q = \dot{\mathbf{n}}_q / \| \dot{\mathbf{n}}_q \|$ . + +# 4.3. Feature Encoding + +Patch Encoding. Given a neighborhood point patch $\pmb{p}_q$ of the query point, our local latent code extraction layer $\mathcal{F}$ is + +![](images/08bd3f1cd3eb2a9b7e1308416958619c644ecb5cea5387d61e973d95b4461b5d.jpg) +Point Cloud +PCPNet + +![](images/73c26e8ade43df8567210864e6c994793356600629fc6576283e5317fba44b92.jpg) +PCA+MST +AdaFit+MST + +![](images/7501406e26cad6d8a669427662b106fb2bc5a10f8fa78606e40f586cfa063fec.jpg) +PCA+ODP +AdaFit+ODP + +![](images/44c2fa255c2897617bdb379b44f08095af441cc83c2a02de233b8778d1dbb634.jpg) +PCA+QPBO +AdaFit+QPBO + +![](images/41784a8d7ebbd5165af477d7cc2aaeba1050454ea058d51fc405e886d6bf75c9.jpg) +Point Cloud +PCPNet + +![](images/d9424a819ace7212fc79845de49e2116581933240abd31a462a75976cec5d5dc.jpg) +PCA+MST + +![](images/17cd2f153f0d81f1b10a2928825207fe53d4a148d1d85506ce4b3718c33c1aec.jpg) +PCA+ODP +AdaFit+ODP + +![](images/e6ce11bd700f7090bd2f946ec8a59da2b8cc11f8eb499cc020995b78d943e3f4.jpg) +PCA+QPBO +AdaFit+QPBO + +![](images/36cb026d7d268291cfe42210117837a738360f7db60524d317f3f7f0a42d5c60.jpg) +Ours + +![](images/91d9b2c91c9904570b83f498e50d8fd7bc559809ba62125236cb478be9ee6271.jpg) +Figure 5. Visualization of the oriented normal error on datasets PCPNet (left) and FamousShape (right). The angle error is mapped to a heatmap ranging from $0^{\circ}$ to $180^{\circ}$ . The purple color indicates the same direction as the ground-truth, while the red color is the opposite. + +![](images/f4b8bc4b1c2e5122f6325a662c31bfa3fd97d30e41552bfc4fe922b04b78c4ae.jpg) +HSurf-Net+MST + +![](images/60ffd13777ef740ca8099dc15d5ba1ddcba842e07567b8e1098a663cfcc2ddc0.jpg) + +![](images/47dbeda3e199710dfeb50b41ccab2fd67037fbda516d4a9218b02b64ab097768.jpg) +HSurf-Net+ODP + +![](images/d4fd29d55d429eb7cbc31a51b486df751f1b376d08d629f4efe52834e42e2dff.jpg) + +![](images/3d532b2e468bc832910e2d5f36276825ef397c3c8ae4d78c9761b842e1669373.jpg) +HSurf-Net+QPBO + +![](images/daeadce6623735a16c1adf2d717b87bb6ac2e86fdcbf256ede233921f7692002.jpg) + +![](images/e22dfb37c1b065c5d06aad18ad91fc70963be333d6c5c1fbc53145effedbf911.jpg) + +![](images/e0071a850b04129d8ad9240c70f688b4fb1aeca1689728442af58b28ee7c7979.jpg) +AdaFit+MST + +![](images/1e7431cd5cdd47140b259dfa1233636a9250e38efc69008744a929698a30234a.jpg) + +![](images/1829f08c9edbe249349cd704b3d6244115fe769002ac2480ceb1aa34aa0e1fb2.jpg) + +![](images/ef7e56bd933662303049323c36413c6478cc92faba1fd814709a6909f4172b98.jpg) +Ours + +![](images/329e253a9f6332a883bdbab05cb26ed00badb533c4771e410e2aa961c16b92f2.jpg) +HSurf-Net+MST + +![](images/7bdaf2444cba56ea005ce9e43789ab30d5ae5444e1d8b0f08ae9541227d85d62.jpg) +HSurf-Net+ODP + +![](images/eff814e6a2a87db7e469e41086cd3c24bb7213a7b5a321e7f7f91114a2737831.jpg) +HSurf-Net+QPBO + +![](images/c26f4d540aa4581666fa8b137f64c8e0699479c77969ea3951ea9ff3750e03fe.jpg) + +formulated as + +$$ +\dot {z} _ {i} ^ {\mathbf {n}} = \mathcal {A} \left(\mathcal {B} \left(\operatorname {M A X} \left\{\mathcal {C} \left(w _ {j} \cdot z _ {j} ^ {\mathbf {n}}\right) \right\} _ {j = 1} ^ {N _ {l}}\right), z _ {i} ^ {\mathbf {n}}\right), \tag {13} +$$ + +where $i = 1,\dots ,N_{l + 1},l$ is the neighborhood scale index and $N_{l + 1}\leqslant N_l$ . $z_{i}^{\mathbf{n}} = \mathcal{D}(p_{i}),p_{i}\in \pmb{p}_{q}$ is the per-point feature in the patch. $\mathcal{A},\mathcal{B},\mathcal{C}$ and $\mathcal{D}$ are MLPs. MAX{} denotes the feature maxpooling over $N_{l}$ -nearest neighbors of the query point $q$ . $w$ is a distance-based weight given by + +$$ +w _ {j} = \frac {\beta_ {j}}{\sum_ {i = 1} ^ {N} \beta_ {i}}, \beta_ {i} = \operatorname {s i g m o i d} \left(\gamma_ {1} - \gamma_ {2} \| p _ {i} - q \| _ {2}\right), \tag {14} +$$ + +where $\gamma_{1}$ and $\gamma_{2}$ are learnable parameters with an initial value of 1.0. The weight $w$ makes the layer focus on the point $p_i$ which is closer to the query point $q$ . As shown in Fig. 3, we stack two layers $\mathcal{F}$ to form a block, which is further stacked to build our patch feature encoder $e_{\varphi}$ . + +Shape Encoding. Since the global subsample set $P_{q} = \{p_{i}\}_{i=1}^{N_{P}}$ can be seen as a patch with points distributed globally on the shape surface, we adopt a similar network architecture with the patch feature encoder to get the global latent code $z_{q}^{s}$ . To obtain $P_{q}$ , we use a probability-based sampling strategy [14], which brings more points closer to the query point $q$ . It samples points according to a density gradient that decreases with increasing distance from the + +point $q$ . Moreover, we find that adding more points from random sampling brings better results. Then, the gradient of a point is calculated by + +$$ +v \left(p _ {i}\right) = \left\{ \begin{array}{l} {\left[ 1 - 1. 5 \frac {\left\| p _ {i} - q \right\| _ {2}}{\operatorname* {m a x} _ {p _ {j} \in \mathcal {P}} \left\| p _ {j} - q \right\| _ {2}} \right] _ {0. 0 5} ^ {1}} \\ 1 \quad \text {i f} i \in \mathcal {R} \end{array} \right. \tag {15} +$$ + +where $\left[\cdot\right]_{0.05}^{1}$ indicates value clamping. $\mathcal{R}$ is a random sample index set of $\mathcal{P}$ with $N_P / 1.5$ items. Finally, the sampling probability of a point $p_i \in \mathcal{P}$ is $\rho(p_i) = v(p_i) / \sum_{p_j \in \mathcal{P}} v(p_j)$ . + +Feature Fusion. In order to allow each point in the local patch to have global information and determine the normal orientation, we first use the maxpooling and repetition operation to make the output global latent code has the same dimension as the local latent code. Then, the two kinds of codes are fused by concatenation, i.e., $[z_q^{\mathbf{n}}:z_q^s ]$ in Eq. (8). + +# 4.4. Loss Functions + +For the query point $q$ , we constrain its unoriented normal and normal sign (i.e., orientation), respectively. To learn an accurate unoriented normal, we employ the ground-truth $\hat{\mathbf{n}}_q$ to calculate a normal vector $\sin$ loss [5] + +$$ +\mathcal {L} _ {\sin} = \left\| \mathbf {n} _ {q} \times \hat {\mathbf {n}} _ {q} \right\|. \tag {16} +$$ + +Table 1. Unoriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted or unavailable. + +
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientStripeGradient
Jet [10]12.3512.8418.3327.6813.3913.1316.2920.1120.5731.3445.1918.8218.6925.79
PCA [19]12.2912.8718.3827.5213.6612.8116.2519.9020.6031.3345.0019.8418.5425.87
PCPNet [17]9.6411.5118.2722.8411.7313.4614.5818.4721.0732.6039.9318.1419.5024.95
Zhou et al.* [57]8.6710.4917.6224.1410.2910.6613.62-------
Nesti-Net [6]7.0610.2417.7722.318.648.9512.4911.6016.8031.6139.2212.3311.7720.55
Lenssen et al. [29]6.729.9517.1821.967.737.5111.8411.6216.9730.6239.4311.2110.7620.10
DeepFit [5]6.519.2116.7323.127.927.3111.8011.2116.3929.8439.9511.8410.5419.96
MTRNet* [9]6.439.6917.0822.238.396.8911.78-------
Refine-Net [56]5.929.0416.5222.197.707.2011.43-------
Zhang et al.* [54]5.659.1916.7822.936.686.2911.259.8316.1329.8139.819.729.1919.08
Zhou et al.* [58]5.909.1016.5022.086.796.4011.13-------
AdaFit [59]5.199.0516.4521.946.015.9010.769.0915.7829.7838.748.528.5718.41
GraphFit [31]5.218.9616.1221.716.305.8610.698.9115.7329.3738.679.108.6218.40
HSurf-Net [32]4.178.7816.2521.614.984.8610.117.5915.6429.4338.547.637.4017.70
Ours3.958.5516.1321.534.914.679.967.4115.3429.3338.567.747.2817.61
+ +For the normal orientation, we adopt the binary cross entropy $H$ [14] to calculate a sign classification loss + +$$ +\mathcal {L} _ {s g n} = H \left(\sigma \left(g ^ {s} (q)\right), [ f _ {\boldsymbol {S}} (q) > 0 ]\right), \tag {17} +$$ + +where $\sigma$ is a logistic function that converts the sign into its probabilities. $[f_S(q) > 0]$ is 1 if the estimated normal faces the outward of surface $S$ and 0 otherwise. Our method achieves a significant performance boost by dividing the oriented normal estimation into unoriented normal regression and its sign classification, instead of directly regressing the oriented normals of query points (see Sec. 5.3). + +To make the model also pay attention to neighbor points $p_i \in p_q$ , we compute a weighted mean square error (MSE) + +$$ +\mathcal {L} _ {m s e} = \frac {1}{N} \sum_ {i = 1} ^ {N} \tau_ {i} \| \vec {\mathbf {n}} _ {i} - \hat {\vec {\mathbf {n}}} _ {i} \| ^ {2}, \tag {18} +$$ + +where the neighborhood point normals $\vec{\mathbf{n}} = \delta (z_q)$ are predicted from the surface embedding $z_{q}$ by an MLP layer $\delta :\mathbb{R}^c\to \mathbb{R}^3$ . Moreover, we add a loss term according to coplanarity [54] to facilitate the learning of $\tau$ in Eq.(12), + +$$ +\mathcal {L} _ {\tau} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left(\tau_ {i} - \hat {\tau} _ {i}\right) ^ {2}, \hat {\tau} _ {i} = \exp \left(- \frac {\left(p _ {i} \cdot \hat {\mathbf {n}} _ {q}\right) ^ {2}}{\xi^ {2}}\right), \tag {19} +$$ + +where $\xi = \max (0.05^2, 0.3\sum_{i=1}^{N}(p_i \cdot \hat{\mathbf{n}}_q)^2 / N)$ . In summary, our final training loss for oriented normal estimation is + +$$ +\mathcal {L} = \lambda_ {1} \mathcal {L} _ {\sin} + \lambda_ {2} \mathcal {L} _ {s g n} + \lambda_ {3} \mathcal {L} _ {m s e} + \lambda_ {4} \mathcal {L} _ {\tau}, \tag {20} +$$ + +where $\lambda_1 = 0.1$ , $\lambda_2 = 0.1$ , $\lambda_3 = 0.5$ and $\lambda_4 = 1.0$ are factors. + +# 5. Experiments + +Implementation. We only train our network model on the PCPNet shape dataset [17], which provides the groundtruth normals with consistent orientation (outward of the surface). We follow the same train/test data split and data processing as in [5, 17, 32, 59]. For patch encoding, we + +randomly select a query point from the shape point cloud and search its 700 neighbors to form a patch. For shape encoding, we sample $N_P = 1200$ points from the shape point cloud according to the sampling probability. The Adam optimizer is adopted with an initial learning rate of $9 \times 10^{-4}$ which is decayed to $1/5$ of the latest value at epochs $\{400, 600, 800\}$ . The model is trained on an NVIDIA 2080 Ti GPU with a batch size of 145 and epochs of 800. + +Dataset. Due to the lack of relevant datasets and the relatively simple test shapes of the PCPNet dataset [17], we further collect shapes with complex structures from other public datasets, such as the Famous dataset [14] and the Stanford 3D Scanning Repository [12]. We follow the same preprocessing steps as the PCPNet dataset to conduct data augmentation, e.g., adding Gaussian noise with different levels (0.12%, 0.6% and 1.2%) and uneven sampling (stripe and gradient). The ground-truth oriented normals are extracted from mesh data and used for evaluation. We call this dataset FamousShape and it is available along with our code. + +Metrics. We use the angle Root Mean Squared Error (RMSE) to evaluate the estimated normals and the Area Under the Curve (AUC) to show the error distribution [17, 32, 59]. Note that for the baseline methods, we flip their oriented normals if more than half of the normals face inward. + +# 5.1. Unoriented Normal Comparison + +We directly use our oriented normal estimation results to compare with baseline methods that are designed for estimating unoriented normals, such as the traditional methods PCA [19] and Jet [10], the learning-based surface fitting methods DeepFit [5] and AdaFit [59], and the learning-based regression methods Nesti-Net [6] and HSurf-Net [32]. As shown in Table 1, we report quantitative comparison results with the baselines in terms of normal angle RMSE on two datasets, PCPNet and FamousShape. On the PCPNet dataset, our method achieves the best perfor + +Table 2. Oriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted. + +
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientNone0.12%0.6%1.2%StripeGradient
PCA [19]+MST [19]19.0530.2031.7639.6427.1123.3828.5235.8841.6738.0960.1631.6935.4040.48
PCA [19]+QPBO [45]18.5521.6130.9439.5423.0025.4626.5232.2539.3941.8061.9136.6935.8241.31
PCA [19]+ODP [38]28.9625.8634.9151.5228.7023.0032.1630.4731.2941.6584.0039.4130.7242.92
AdaFit [59]+MST [19]27.6743.6948.8354.3936.1840.4641.8743.1239.3362.2860.2745.5742.0048.76
AdaFit [59]+QPBO [45]26.4124.1740.3148.7627.7431.5633.1627.5537.6069.5662.7727.8629.1942.42
AdaFit [59]+ODP [38]26.3724.8635.4451.8826.4520.5730.9341.7539.1944.3172.9145.0942.3747.60
HSurf-Net [32]+MST [19]29.8244.4950.4755.4740.5443.1543.9954.0242.6768.3765.9152.5253.9656.24
HSurf-Net [32]+QPBO [45]30.3432.3444.0851.7133.4640.4938.7441.6241.0667.4162.0445.5943.8350.26
HSurf-Net [32]+ODP [38]26.9124.8535.8751.7526.9120.1631.0743.7743.7446.9172.7045.0943.9849.37
PCPNet [17]33.3434.2240.5444.4637.9535.4437.6640.5141.0946.6754.3640.5444.2644.57
DPGO* [50]23.7925.1935.6643.8928.9929.3331.14-------
Ours10.2813.2325.4035.5116.4017.9219.7921.6325.9641.1452.6726.3928.9732.79
+ +![](images/98e40ada0bae2eb1fa7d3a87c1b5ee79567b361f75a47a62c175cee81dc8cdb3.jpg) + +![](images/370202fa3dc66097bd1a0d16d1c70370b50569be47fed56d2d829c8ce792ed28.jpg) + +![](images/39d71f38630d934925f5467d1ebe4832cca2f5205bc631d0f58c33e83afe4035.jpg) + +![](images/5deb392f42ab2856ecc24e91cd46bc4f82291b8e9795bf466f6b60a323eee4e6.jpg) + +![](images/0c5e57e267af7d9c56d8e16871b41bc3943cc95e9b5631c7fdf0241e9cfb5938.jpg) +Figure 6. Oriented normal AUC on the PCPNet dataset. It shows the percentage of correctly estimated normals (PGP) for a given angle threshold. Our method has the best value for all thresholds. + +![](images/722cb46b2e7d2064ad0ea76fb12f8a20f48d0ad33cd965fc9e071f29b90043d8.jpg) + +mance under all noise levels and density variations. On our FamousShape dataset, our method achieves the best performance under most metrics and has the best average result. + +# 5.2. Oriented Normal Comparison + +We compare our approach for oriented normal estimation with various baseline methods, such as PCPNet [17] + +and DPGO [50]. In addition, we choose three unoriented normal estimation methods (PCA [19], AdaFit [59] and HSurf-Net [32]) and three normal orientation methods (MST [19], QPBO [45] and ODP [38]), and make different combinations of them to form two-stage pipelines for estimating oriented normals, such as PCA+MST. Among the baselines, PCA is a widely used traditional method, AdaFit is a representative surface fitting-based method, and HSurf-Net is a regression-based method and has the state-of-the-art performance for unoriented normal estimation. We use the original implementation of QPBO and ODP, and the implementation of MST in [47]. In Table 2, we show quantitative comparison results on datasets PCPNet and FamousShape. We can see that our method provides the most accurate normals under almost all noise levels and density variations for both datasets, and achieves huge performance gains in terms of average results compared to all baselines. From the experimental results, we find that the propagation-based normal orientation methods have significantly varied results when dealing with unoriented normal inputs from different estimation methods, such as PCA+MST and AdaFit+MST. A visual comparison of the normal errors is shown in Fig. 5. The error distributions of various methods are illustrated in Fig. 6. + +KITTI Dataset. To verify the generalization ability of our method on LiDAR point clouds of outdoor scenes, we test directly on the KITTI dataset [15] with the model trained on the PCPNet dataset. We only report qualitative results on this dataset as it does not provide the ground-truth normals. In Fig. 7, we use the Poisson surface reconstruction algorithm [26] to generate surfaces using oriented normals estimated by different methods. As can be seen, compared to the baselines, our estimated normals facilitate the algorithm to reconstruct surfaces that can more accurately depict the spatial structure and distribution of real scenes. + +# 5.3. Ablation Studies + +We provide ablation results for oriented normal estimation in Table 3 (a)-(d), which are discussed as follows. + +Table 3. Ablation studies for oriented normals on the PCPNet dataset. The last column is the average results under the unoriented metric. + +
AblationFeat. Enco.Module HLossPoint Samp.NoiseDensityOriented AverageUnoriented Average
None0.12%0.6%1.2%StripeGradient
(a)w/o patch encoding✓✓✓35.1942.2355.5961.3838.9241.4945.8018.83
w/o shape encoding✓✓✓69.7264.3781.8777.0774.8490.3576.3714.94
w/o weight w✓✓✓11.1514.3226.4936.0317.9926.0322.0010.48
(b)w/o module H✓✓✓12.0814.5325.8735.8818.4531.8423.1110.24
(c)w/o Lsin, Lsgn✓✓✓23.8625.5534.1342.4832.4241.3033.2920.23
(d)w/o density gradient✓✓✓12.1018.2528.0538.1519.7928.0924.0710.00
w/o random sample✓✓✓11.0113.7925.6435.8617.2225.7121.549.94
ζ=1/2✓✓✓10.9914.0425.6635.7817.7337.8223.679.92
ζ=1/3✓✓✓13.2715.4226.8237.1617.5228.1123.059.95
NP=1100✓✓✓10.6714.2125.5435.9716.8026.9821.699.99
NP=1300✓✓✓12.4414.5325.9335.7918.4019.8521.169.98
Final✓✓✓✓10.2813.2325.4035.5116.4017.9219.799.96
+ +![](images/9780287067785ff440e957ed23f9742dba9cd2968d18c81f47356b5fae7a38c0.jpg) + +![](images/9f01062237c7a78ef05e5f5f46cfe997c2980dd8cf9e1f9ad3cfd2523ec1e57c.jpg) + +![](images/713ad495d6dfecb3d47361f07898cd82c7927285d86a499e9a53d8fbd9f5a26e.jpg) + +![](images/f9fdf56d2de51d42844623b67d0369640e0e4badf1e3c4ae460f179ee668fcbc.jpg) + +![](images/1497df6178be2c1d742355ddbcea5367ba6b79130eea20753eb4827df47dc1a2.jpg) +Figure 7. Street surfaces reconstructed using estimated normals on the KITTI dataset. The raw point cloud is colored with height values. + +![](images/79fde2768b5c6a09c5a50d9c5fd63ed4f0cc47d67658fd385ced42906506fba3.jpg) + +![](images/0958ee212169dfeb536c73bc330db8dc4c0f44e245973c22efd7177d5f386b4f.jpg) + +![](images/8179c472dd14486ad46823799dce38343b2458dfc5afb81fd60c0fb4e3415991.jpg) + +(a) Feature Encoding. (1) We realize the oriented normal estimation without using the patch encoding or the shape encoding. (2) The distance-based weight $w$ is not used in both patch encoding and shape encoding. +(b) Module $\mathcal{H}$ . The attention-weighted normal prediction module $\mathcal{H}$ is replaced with simple MLP layers. +(c) Loss $\mathcal{L}_{\text{sin}}, \mathcal{L}_{\text{sgn}}$ . In our pipeline, we regress the unoriented normal and its sign of the query point $q$ , and constrain them in loss functions $\mathcal{L}_{\text{sin}}$ and $\mathcal{L}_{\text{sgn}}$ , respectively. Here, we alternatively directly predict the oriented normal $\vec{\mathbf{n}}_q$ from surface embedding and compute its MSE loss. +(d) Point Sampling. In the shape encoding, we obtain a global point set $P_{q}$ by a probability-based sampling strategy as in Eq. (15), which includes density gradient term and random sample term. The point set $P_{q}$ includes $N_{P} = 1200$ points, and the ratio of randomly sampled points is $\zeta = 1/1.5$ . (1) We only adopt one of the two terms in Eq. (15) for point sampling, e.g., 'w/o density gradient' means all points are randomly sampled. (2) The ratio $\zeta$ is changed to $1/2$ and $1/3$ . (3) The number $N_{P}$ is set to 1100 and 1300. + +From Table 3, we can conclude that both patch encoding and shape encoding are vital for learning accurate oriented and unoriented normals in our pipeline. The adoption of the weight $w$ and the attention-weighted normal prediction module $\mathcal{H}$ effectively improves the algorithm's perfor + +mance. Compared to directly predicting the oriented normal $\vec{\mathbf{n}}_q$ , solving it separately by learning signed hyper surface is significantly better. The combination of the density gradient term and the random sample term in sampling can produce better results than either one alone. The proportion and number of points in the sampling of shape encoding have a significant positive effect on oriented normals, but very little on unoriented normals. + +# 6. Conclusion + +In this work, we formulate the oriented normal estimation of point clouds as the learning of signed hyper surfaces. We first review the explicit surface fitting and the implicit surface learning, and derive the formulation of the signed hyper surfaces from their inspiration. Then, we propose to use an attention-weighted normal prediction module to recover the normal and its sign of the query point from the embedding of the signed hyper surfaces. Finally, we introduce how such surfaces can be learned from the patch encoding and shape encoding using the designed loss functions. We conduct extensive evaluation and ablation experiments to report the state-of-the-art performance and justify the effectiveness of our designs. 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"Department of Computer Science, Wayne State University, Detroit, USA" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 102, + 247, + 490, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 247, + 490, + 258 + ], + "spans": [ + { + "bbox": [ + 102, + 247, + 490, + 258 + ], + "type": "text", + "content": "{leoqli, gaoyue, liuyushen}@tsinghua.edu.cn fenghuifang@stu.xmu.edu.cn" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 147, + 262, + 443, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 262, + 443, + 273 + ], + "spans": [ + { + "bbox": [ + 147, + 262, + 443, + 273 + ], + "type": "text", + "content": "shikanle@kuaishou.com yfang@nyu.edu h312h@wayne.edu" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 300, + 192, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 300, + 192, + 313 + ], + "spans": [ + { + "bbox": [ + 143, + 300, + 192, + 313 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 327, + 290, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 290, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 290, + 651 + ], + "type": "text", + "content": "We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are available at https://github.com/LeoQLi/SHS-Net." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 307, + 298, + 545, + 400 + ], + "blocks": [ + { + "bbox": [ + 307, + 298, + 545, + 400 + ], + "lines": [ + { + "bbox": [ + 307, + 298, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 307, + 298, + 545, + 400 + ], + "type": "image", + "image_path": "db4de02ce8ecdb85d23f3d699e759061f29b14204e99ed2d3fa8510bab7b9ba9.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 406, + 547, + 473 + ], + "lines": [ + { + "bbox": [ + 305, + 406, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 547, + 473 + ], + "type": "text", + "content": "Figure 1. We propose SHS-Net to estimate oriented normals directly from point clouds. In contrast, previous studies usually achieve this process through a two-stage paradigm using different algorithms, i.e., (1) unoriented normal estimation (e.g., PCA [19], AdaFit [59] and HSurf-Net [32]) and (2) normal orientation (e.g., MST [19], QPBO [45] and ODP [38])." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 487, + 388, + 499 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 388, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 388, + 499 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 713 + ], + "type": "text", + "content": "In computer vision and graphics, estimating normals for point clouds is a prerequisite for many techniques. As an important geometric property of point clouds, normals with consistent orientation, i.e., oriented normals, clearly reveal the geometric structures and make significant contributions in downstream applications, such as rendering and surface reconstruction [24-26]. Generally, the estimation of oriented normals requires a two-stage paradigm (see Fig. 1): (1) the unoriented normal estimation from the local neighbors of the query point, (2) the normal orientation to make the normal directions to be globally consistent, e.g., facing outward of the surface. While unoriented normals can be estimated by plane or surface fitting of the local neighborhood, determining whether the normals are facing outward or inward is ambiguous. In recent years, many excellent algorithms [5, 29, 31, 32, 59] have been proposed for unoriented normal estimation, while there are few methods that" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 673, + 288, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 673, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 288, + 715 + ], + "type": "text", + "content": "*The corresponding author is Yu-Shen Liu. This work was supported by National Key R&D Program of China (2022YFC3800600), the National Natural Science Foundation of China (62272263, 62072268), and in part by Tsinghua-Kuaishou Institute of Future Media Data." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 758 + ], + "type": "text", + "content": "13591" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "have reliable performance for normal orientation or directly estimating oriented normals. Estimating oriented normals from point clouds with noise, density variations, and complex geometries in an end-to-end manner is still a challenge." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 122, + 288, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 122, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 122, + 288, + 374 + ], + "type": "text", + "content": "The classic normal orientation methods rely on simple greedy propagation, which selects a seed point as the start and diffuses its normal orientation to the adjacent points via a minimum spanning tree (MST) [19, 27]. These methods are limited by error accumulation, where an incorrect orientation may degenerate all subsequent steps during the iterative propagation. Furthermore, they heavily rely on a smooth and clean assumption, which makes them easily fail in the presence of sharp edges or corners, density variations and noise. Meanwhile, their accuracy is sensitive to the neighborhood size of propagation. For example, a large size is usually used to smooth out outliers and noise, but can also erroneously include nearby surfaces. Considering that local information is usually not sufficient to guarantee robust orientation, some improved methods [22, 38, 45, 46, 49, 53] try to formulate the propagation process as a global energy optimization by introducing various constraints. Since their constraints are mainly derived from local consistency, the defects are inevitably inherited, and they also suffer from cumulative errors. Moreover, their data-specific parameters are difficult to generalize to new input types and topologies." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 376, + 288, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 639 + ], + "type": "text", + "content": "Different from the propagation-based methods, which only consider the adjacent orientation, the volume-based approaches exploit volumetric representation, such as signed distance functions [35, 40] and variational formulations [2, 21, 48]. They aim to divide the space into interior/exterior and determine whether point normals are facing inward or outward. Despite improvements in accuracy and robustness, these methods cannot scale to large point clouds due to their computational complexity. In general, propagation-based methods have difficulty with sharp features, while volume-based methods have difficulty with open surfaces. Furthermore, the above-mentioned methods are usually complex and require a two-stage operation, their performance heavily depends on the parameter tuning in each separated stage. Recently, several learning-based methods [17, 18, 50] have been proposed to deliver oriented normals from point clouds and have exhibited promising performance. Since they focus on learning an accurate local feature descriptor and do not fully explore the relationship between the surface normal orientation and the underlying surface, their performance cannot be guaranteed across different noise levels and geometric structures." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 45, + 642, + 287, + 714 + ], + "type": "text", + "content": "In this work, we propose to estimate oriented normals from point clouds by implicitly learning signed hyper surfaces, which are represented by MLP layers to interpret the geometric property in a high-dimensional feature space. We learn this new geometry representation from both local and global shape properties to directly estimate normals with" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "consistent orientation in an end-to-end manner. The insight of our method is that determining a globally consistent normal orientation should require global context to eliminate the ambiguity from local since orientation is not a local property. We evaluate our method by conducting a series of qualitative and quantitative experiments on a range of point clouds with different sampling densities, noise levels, thin and sharp structures." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 169, + 538, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 169, + 538, + 179 + ], + "spans": [ + { + "bbox": [ + 317, + 169, + 538, + 179 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 182, + 545, + 299 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 306, + 182, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 182, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 182, + 545, + 216 + ], + "type": "text", + "content": "- We introduce a new technique to represent point cloud geometric properties as signed hyper surfaces in a high-dimensional feature space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 217, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 545, + 252 + ], + "type": "text", + "content": "- We show that the signed hyper surfaces can be used to estimate normals with consistent orientations directly from point clouds, rather than through a two-stage paradigm." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 253, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 253, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 306, + 253, + 545, + 299 + ], + "type": "text", + "content": "- We experimentally demonstrate that our method is able to estimate normals with high accuracy and achieves the state-of-the-art results in both unoriented and oriented normal estimation." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 322, + 392, + 334 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 322, + 392, + 334 + ], + "spans": [ + { + "bbox": [ + 306, + 322, + 392, + 334 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 342, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 545, + 652 + ], + "type": "text", + "content": "Unoriented Normal Estimation. Over the past few decades, many algorithms have been proposed for point cloud normal estimation, such as the classic Principle Component Analysis (PCA) [19] and its improvements [1, 20, 28, 39, 43], Voronoi-based paradigms [2, 3, 13, 36], and variants based on complex surface [4, 10, 16, 30, 41]. These methods are usually sensitive to noise and have limited accuracy even with heavy fine-tuned parameters. More recently, learning-based methods have been proposed to improve performance in this area and can be mainly divided into two categories: regression-based and surface fitting-based. The regression-based methods try to directly predict normals from structured data [8, 34, 44] or raw point clouds [6, 17, 18, 32, 33, 55-57] in a data-driven manner. Among them, HSurf-Net [32] achieves good performance by learning hyper surfaces from local patches, but the learned surfaces have no sign and cannot determine the normal orientation. The surface fitting-based methods integrate the traditional surface fitting techniques, such as plane fitting [9, 29] and jet fitting [5, 31, 54, 58, 59], into the end of the learning pipeline. They usually carefully design a network to predict point-wise weights, and then use a weighted surface formulation to solve the fitted surface normal. The normals estimated by the above methods randomly face both sides of the surface and cannot be used in many downstream applications without normal orientation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Consistent Normal Orientation. To make the unoriented normals have consistent orientations, early approaches mainly focus on local consistency and use the orientation propagation strategy upon a minimum spanning tree (MST) to let the adjacent points have the same orientations, such" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13592" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 534, + 190 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 534, + 190 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 534, + 190 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 534, + 190 + ], + "type": "image", + "image_path": "c737c2753d2fa077f56d92404a5c968cc7571c65049d8d4371b2093bcdba402e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 129, + 191, + 463, + 204 + ], + "lines": [ + { + "bbox": [ + 129, + 191, + 463, + 204 + ], + "spans": [ + { + "bbox": [ + 129, + 191, + 463, + 204 + ], + "type": "text", + "content": "Figure 2. The learning pipeline of the signed hyper surfaces for oriented normal estimation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 215, + 290, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 215, + 290, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 215, + 290, + 431 + ], + "type": "text", + "content": "as the pioneering work of [19] and its improved methods [22, 45, 46, 49, 53]. These methods have many limitations in real applications as we introduced earlier. ODP [38] aims to achieve global consistency by introducing a dipole propagation strategy across the partitioned patches, but its robustness may suffer from the patch partition. On the contrary, some alternative approaches propose to solve the consistent normal orientation through volumetric representation. They are usually developed for reconstructing surfaces from unoriented points by various techniques, such as signed distance functions [35, 40], variational formulations [2, 21, 48], visibility [11, 23], isvalue constraints [51] and active contours [52]. Recently, a few works [17, 18, 50] explore to predict oriented normals through end-to-end deep networks. These methods focus on learning a general mapping from point clouds to normals and neglect the underlying surface distribution for normal orientation, leading to a sub-optimal solution." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 449, + 125, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 125, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 125, + 462 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": "In mathematics, an explicit representation in Euclidean space expresses the " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": " coordinate of a point " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": " in terms of the " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "z = f(x,y)" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ". Such a surface is called an explicit surface, also called a height field. Another symmetric representation is " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "F(x,y,z) = 0" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": " implicitly defines a locus called an implicit surface, also called a scalar field [7]. The implicit surface is a zero iso-surface of " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ", i.e., the point set " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\{p \\in \\mathbb{R}^3 : F(p) = 0\\}" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": " is a surface implicitly defined by " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ". The explicit surface is usually used in surface fitting-based normal estimation, such as jet fitting [10], while the implicit surface is widely used in surface reconstruction. Generally, an explicit surface, i.e., " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "z = f(x,y)" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ", can always be rewritten as an implicit surface, i.e., " + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "inline_equation", + "content": "F(x,y,z) = z - f(x,y) = 0" + }, + { + "bbox": [ + 46, + 472, + 287, + 664 + ], + "type": "text", + "content": ". These two surface representations have the same tangent plane at a given point, where the normal is defined. See supplementary for details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Explicit Surface Fitting. We employ the widely used " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "-jet surface model [10] to briefly review the explicit surface fitting for normal estimation. It represents the surface by a polynomial function " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "J_{n}:\\mathbb{R}^{2}\\to \\mathbb{R}" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": ", which maps a coordinate" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 213, + 545, + 260 + ], + "blocks": [ + { + "bbox": [ + 307, + 213, + 545, + 260 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 545, + 260 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 545, + 260 + ], + "type": "image", + "image_path": "1590ae8503229a4771ae6e288f7c7535cf05364599439849ac2f4039aa5819c9.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 266, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 306, + 266, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 545, + 277 + ], + "type": "text", + "content": "Figure 3. Feature encoding network in patch and shape encoding." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 288, + 484, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 288, + 484, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 288, + 484, + 300 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 306, + 288, + 484, + 300 + ], + "type": "text", + "content": " to its height " + }, + { + "bbox": [ + 306, + 288, + 484, + 300 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 306, + 288, + 484, + 300 + ], + "type": "text", + "content": " in the tangent space by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 341, + 307, + 545, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 307, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 341, + 307, + 545, + 340 + ], + "type": "interline_equation", + "content": "z = J _ {\\alpha , n} (x, y) = \\sum_ {k = 0} ^ {n} \\sum_ {j = 0} ^ {k} \\alpha_ {k - j, j} x ^ {k - j} y ^ {j}, \\tag {1}", + "image_path": "afc92f41bec64f313a8ddb1f87dff027be56e2b08c44275abbe10906b92d0af1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "text", + "content": " is the coefficient vector that defines the surface function. In order to find the optimal solution, the least squares approximation strategy is usually adopted to minimize the sum of the square errors between the (ground-truth) height and the jet value over a point set " + }, + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "inline_equation", + "content": "\\{p_i\\}_{i=1}^N" + }, + { + "bbox": [ + 304, + 347, + 545, + 407 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 341, + 414, + 545, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 414, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 341, + 414, + 545, + 447 + ], + "type": "interline_equation", + "content": "J _ {\\alpha , n} ^ {*} = \\underset {\\alpha} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| z _ {i} - J _ {\\alpha , n} \\left(x _ {i}, y _ {i}\\right) \\| ^ {2}. \\tag {2}", + "image_path": "45374dc1c77825be346967da15b66189d1de2227afbb4805138cb312327035db.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": "If " + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "inline_equation", + "content": "\\alpha = (\\alpha_{0,0},\\alpha_{1,0},\\alpha_{0,1},\\dots ,\\alpha_{0,n})" + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": " is solved, then the normal at point " + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 453, + 545, + 477 + ], + "type": "text", + "content": " on the fitted surface is computed by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 485, + 545, + 504 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 485, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 310, + 485, + 545, + 504 + ], + "type": "interline_equation", + "content": "\\mathbf {n} _ {p} = h (\\alpha) = (- \\alpha_ {1, 0}, - \\alpha_ {0, 1}, 1) / \\sqrt {1 + \\alpha_ {1 , 0} ^ {2} + \\alpha_ {0 , 1} ^ {2}}. \\tag {3}", + "image_path": "38bc258321c806c3fe94264821e0217e698334fc4a1b6a1a27fbfe48fb6b265a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": "Implicit Surface Learning. In recent years, many learning-based approaches have been proposed to represent surfaces by implicit functions, such as signed distance function (SDF) [42] and occupancy function [37]. The signed (or oriented) distance function is the shortest distance of a given point " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "p = (x_0, y_0, z_0)" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": " to the closest surface " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": " in a metric space, with the sign determined by whether the point is inside " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "(F(p) < 0)" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": " or outside " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "(F(p) > 0)" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": " of the surface. The underlying surface is implicitly represented by the isosurface of " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "F(p) = 0" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": ". In the surface reconstruction task, a deep network is usually adopted to encode a 3D shape into a latent code, which is fed into a decoder together with query points to predict signed distances. If an implicit surface function is continuous and differentiable, the formula of tangent plane at a regular point " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": " (gradient is non-null) is " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "F_x(p)(x - x_0) + F_y(p)(y - y_0) + F_z(p)(z - z_0) = 0" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": " and its normal (i.e., perpendicular) is " + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_p = \\nabla F(p) / \\| \\nabla F(p) \\|" + }, + { + "bbox": [ + 304, + 510, + 546, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13593" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 104, + 83 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 289, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 289, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 289, + 212 + ], + "type": "text", + "content": "As shown in Fig. 2, we propose to implicitly learn signed hyper surfaces in the feature space for estimating oriented normals. In the following sections, we first introduce the representation of signed hyper surfaces by combining the characteristics of the above two surface representations. Then, we design an attention-weighted normal prediction module to solve the oriented normals of query points from signed hyper surfaces. Finally, we introduce how to learn this new surface representation from patch encoding and shape encoding using our designed loss functions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 217, + 174, + 230 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 174, + 230 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 174, + 230 + ], + "type": "text", + "content": "4.1. Signed Hyper Surface" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "type": "text", + "content": "We formulate the surface function " + }, + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "type": "inline_equation", + "content": "F(x,y,z) = z - f(x,y) = 0" + }, + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "type": "text", + "content": " as a more general format " + }, + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "type": "inline_equation", + "content": "F(z_{1},z_{2}) = z_{1} - z_{2} = 0" + }, + { + "bbox": [ + 47, + 236, + 287, + 297 + ], + "type": "text", + "content": ". Similarly, the signed hyper surface is implicitly learned by taking the latent encodings of point clouds as inputs and outputting an approximation of the surface in feature space," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 53, + 312, + 287, + 328 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 312, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 53, + 312, + 287, + 328 + ], + "type": "interline_equation", + "content": "f _ {\\pmb {S}} (\\chi) \\approx \\mathcal {E} _ {\\theta} (\\chi | z _ {1}, z _ {2}), z _ {1} = e _ {\\varphi} (\\pmb {P} _ {\\chi} ^ {1}), z _ {2} = e _ {\\psi} (\\pmb {P} _ {\\chi} ^ {2}), (4)", + "image_path": "6d2b107a3250779c66636f3fe2714cad24a8875bef37131e74a69f7d3c09fd12.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": " is implemented by a neural network with parameter " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": " that is conditioned on two latent vectors " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "z_{1}, z_{2} \\in \\mathbb{R}^{c}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": ", which are extracted from point clouds by encoders " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "e_{\\varphi}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "e_{\\psi}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "P_{\\chi}^{1}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "P_{\\chi}^{2}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": " are subsample sets of the raw point cloud " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": ", e.g., point patches around a given point " + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 47, + 332, + 287, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": "Similar to existing unoriented normal estimation methods [5, 17, 32, 59], we use a local patch " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\pmb{p}_q" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " to capture the local geometry for accurately describing the surface pattern around a query point " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 96, + 445, + 287, + 461 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 445, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 96, + 445, + 287, + 461 + ], + "type": "interline_equation", + "content": "f _ {\\boldsymbol {p}} ^ {\\mathbf {n}} (q) = \\mathcal {E} _ {\\theta} ^ {\\mathbf {n}} (q | z _ {q} ^ {\\mathbf {n}}), z _ {q} ^ {\\mathbf {n}} = e _ {\\varphi} (\\boldsymbol {p} _ {q}). \\tag {5}", + "image_path": "3a81006962fdfd741f68f24fecdedcedde7696989b3d07cc498daa74da62f91f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "text", + "content": "Since the interior/exterior of a surface cannot be determined reliably from a local patch, we take a global subsample set " + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "inline_equation", + "content": "P_{q}" + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "text", + "content": " from the point cloud " + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "text", + "content": " to provide additional information to estimate the sign at point " + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 47, + 465, + 287, + 514 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 518, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 518, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 56, + 518, + 287, + 544 + ], + "type": "interline_equation", + "content": "f _ {\\boldsymbol {P}} ^ {s} (q) = \\operatorname {s g n} \\left(g ^ {s} (q)\\right) = \\operatorname {s g n} \\left(\\mathcal {E} _ {\\theta} ^ {s} \\left(q \\mid z _ {q} ^ {s}\\right)\\right), z _ {q} ^ {s} = e _ {\\psi} (\\boldsymbol {P} _ {q}), \\tag {6}", + "image_path": "bccc373544500c8754d3648b16fbc58dd3b9e477d5482c1dc6a416a9a0a02ada.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\operatorname{sgn}(\\cdot)" + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "text", + "content": " is a signum function, " + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "g^{s}(q)" + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "text", + "content": " denotes the logarithm of the probability that " + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "text", + "content": " has a positive sign. Thus, the signed hyper surface function at point " + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 544, + 287, + 581 + ], + "type": "text", + "content": " is formulated as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 82, + 586, + 287, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 586, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 82, + 586, + 287, + 601 + ], + "type": "interline_equation", + "content": "f _ {\\boldsymbol {S}} (q) = f _ {\\boldsymbol {p}} ^ {\\mathbf {n}} (q) \\cdot f _ {\\boldsymbol {P}} ^ {s} (q) = \\mathcal {E} _ {\\theta} ^ {\\mathbf {n}, s} \\left(q \\mid z _ {q} ^ {\\mathbf {n}}, z _ {q} ^ {s}\\right). \\tag {7}", + "image_path": "d8be5335b061a38ea92757643822d0173dc68219f743be8c2d68aeb5eb526f65.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "content": "Different from the surface reconstruction task that learns SDF by representing a surface as the zero-set of the SDF, we do not learn a distance field of points with respect to the underlying surface." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 659, + 205, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 205, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 205, + 671 + ], + "type": "text", + "content": "4.2. Oriented Normal Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "To simplify notations, we denote " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\theta}^{\\mathbf{n},s}(q|z_q^{\\mathbf{n}},z_q^s)" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "S_{\\theta}(\\mathcal{X},\\mathcal{Y})" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "z_{q}^{\\mathbf{n}} = \\mathcal{X}\\in \\mathbb{R}^{c}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "z_{q}^{s} = \\mathcal{Y}\\in \\mathbb{R}^{c}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " are high dimensional latent vectors. According to the explicit surface" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 145 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 145 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 145 + ], + "type": "image", + "image_path": "2873ebc5d63558efca4f8e66b9a72d9a9c3e2dabfb52d6fb1b189f511931d450.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 149, + 538, + 161 + ], + "lines": [ + { + "bbox": [ + 312, + 149, + 538, + 161 + ], + "spans": [ + { + "bbox": [ + 312, + 149, + 538, + 161 + ], + "type": "text", + "content": "Figure 4. Attention-weighted normal prediction module " + }, + { + "bbox": [ + 312, + 149, + 538, + 161 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot)" + }, + { + "bbox": [ + 312, + 149, + 538, + 161 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 168, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 168, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 545, + 193 + ], + "type": "text", + "content": "fitting, we formulate the signed hyper surface " + }, + { + "bbox": [ + 305, + 168, + 545, + 193 + ], + "type": "inline_equation", + "content": "S_{\\theta}:\\mathbb{R}^{2c}\\to" + }, + { + "bbox": [ + 305, + 168, + 545, + 193 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^c" + }, + { + "bbox": [ + 305, + 168, + 545, + 193 + ], + "type": "text", + "content": " as a feature-based polynomial function [32]" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 199, + 545, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 199, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 315, + 199, + 545, + 233 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\theta , \\mu} (\\mathcal {X}, \\mathcal {Y}) = \\sum_ {k = 0} ^ {\\mu} \\sum_ {j = 0} ^ {k} \\theta_ {k - j, j} \\mathbf {x} _ {k - j} \\mathbf {y} _ {j} = \\theta [ \\mathcal {X}: \\mathcal {Y} ], \\tag {8}", + "image_path": "745c9fd792eadf7aaf268231d173643426215bb0153f946eb80b1d1a090b1a6a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "type": "inline_equation", + "content": "[ : ]" + }, + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "type": "text", + "content": " means the feature fusion through concatenation, " + }, + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 305, + 239, + 545, + 262 + ], + "type": "text", + "content": " denotes the number of fused items." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "text", + "content": "Similar to Eq. (2), the bivariate function " + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "inline_equation", + "content": "S_{\\theta, \\mu}(\\mathcal{X}, \\mathcal{Y})" + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "text", + "content": " aims to map a feature pair " + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "inline_equation", + "content": "(\\mathcal{X}_i, \\mathcal{Y}_i)" + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "text", + "content": " to their ground-truth value " + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\mathcal{Z}_i = \\hat{S}(\\mathcal{X}_i, \\mathcal{Y}_i) \\in \\mathbb{R}^c" + }, + { + "bbox": [ + 305, + 262, + 545, + 300 + ], + "type": "text", + "content": " in the feature space, i.e.," + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 339, + 305, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 305, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 339, + 305, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\mathcal {Z} _ {i} - \\mathcal {S} _ {\\theta , \\mu} (\\mathcal {X} _ {i}, \\mathcal {Y} _ {i}) \\| ^ {2}. \\tag {9}", + "image_path": "370a16c841626f7ad7130e20d33345bf2d20037a77aad5d796e010fd0c67816e.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "type": "text", + "content": "To solve the oriented normal " + }, + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\vec{\\mathbf{n}}" + }, + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "type": "text", + "content": " from signed hyper surfaces, we introduce a normal prediction module " + }, + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot)" + }, + { + "bbox": [ + 305, + 344, + 545, + 369 + ], + "type": "text", + "content": ", thus" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 371, + 545, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 371, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 313, + 371, + 545, + 403 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\mathcal {H} \\left(\\mathcal {Z} _ {i}\\right) - \\mathcal {H} \\left(\\mathcal {S} _ {\\theta , \\mu} \\left(\\mathcal {X} _ {i}, \\mathcal {Y} _ {i}\\right)\\right) \\| ^ {2}. \\tag {10}", + "image_path": "ecd5abcde005b5e4951049e6191915b733d401a8da12984d7064091052e21d77.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 404, + 485, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 404, + 485, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 404, + 485, + 417 + ], + "type": "text", + "content": "Finally, the oriented normal is optimized by" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 359, + 419, + 545, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 419, + 545, + 452 + ], + "spans": [ + { + "bbox": [ + 359, + 419, + 545, + 452 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\theta , \\mu} ^ {*} = \\underset {\\theta , \\mu} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {N} \\| \\hat {\\vec {\\mathbf {n}}} _ {i} - 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MAX{} denotes the feature maxpooling over " + }, + { + "bbox": [ + 46, + 466, + 287, + 527 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 46, + 466, + 287, + 527 + ], + "type": "text", + "content": "-nearest neighbors of the query point " + }, + { + "bbox": [ + 46, + 466, + 287, + 527 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 466, + 287, + 527 + ], + "type": "text", + "content": ". 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The weight " + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "content": " makes the layer focus on the point " + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "content": " which is closer to the query point " + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "content": ". As shown in Fig. 3, we stack two layers " + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "content": " to form a block, which is further stacked to build our patch feature encoder " + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "inline_equation", + "content": "e_{\\varphi}" + }, + { + "bbox": [ + 46, + 557, + 287, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "text", + "content": "Shape Encoding. Since the global subsample set " + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_{q} = \\{p_{i}\\}_{i=1}^{N_{P}}" + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "text", + "content": " can be seen as a patch with points distributed globally on the shape surface, we adopt a similar network architecture with the patch feature encoder to get the global latent code " + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "inline_equation", + "content": "z_{q}^{s}" + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "text", + "content": ". To obtain " + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "inline_equation", + "content": "P_{q}" + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "text", + "content": ", we use a probability-based sampling strategy [14], which brings more points closer to the query point " + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 616, + 287, + 714 + ], + "type": "text", + "content": ". It samples points according to a density gradient that decreases with increasing distance from the" + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 423, + 545, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 459 + ], + "type": "text", + "content": "point " + }, + { + "bbox": [ + 304, + 423, + 545, + 459 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 423, + 545, + 459 + ], + "type": "text", + "content": ". Moreover, we find that adding more points from random sampling brings better results. Then, the gradient of a point is calculated by" + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 323, + 460, + 545, + 505 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 460, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 323, + 460, + 545, + 505 + ], + "type": "interline_equation", + "content": "v \\left(p _ {i}\\right) = \\left\\{ \\begin{array}{l} {\\left[ 1 - 1. 5 \\frac {\\left\\| p _ {i} - q \\right\\| _ {2}}{\\operatorname* {m a x} _ {p _ {j} \\in \\mathcal {P}} \\left\\| p _ {j} - q \\right\\| _ {2}} \\right] _ {0. 0 5} ^ {1}} \\\\ 1 \\quad \\text {i f} i \\in \\mathcal {R} \\end{array} \\right. \\tag {15}", + "image_path": "a7b0d62d22e892b1523b23410fa5c86c0b4be40f75c72b521090a700de2e66b4.jpg" + } + ] + } + ], + "index": 57 + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\left[\\cdot\\right]_{0.05}^{1}" + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": " indicates value clamping. " + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": " is a random sample index set of " + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "inline_equation", + "content": "N_P / 1.5" + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": " items. Finally, the sampling probability of a point " + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "inline_equation", + "content": "p_i \\in \\mathcal{P}" + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "inline_equation", + "content": "\\rho(p_i) = v(p_i) / \\sum_{p_j \\in \\mathcal{P}} v(p_j)" + }, + { + "bbox": [ + 304, + 507, + 545, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 304, + 546, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 619 + ], + "type": "text", + "content": "Feature Fusion. In order to allow each point in the local patch to have global information and determine the normal orientation, we first use the maxpooling and repetition operation to make the output global latent code has the same dimension as the local latent code. Then, the two kinds of codes are fused by concatenation, i.e., " + }, + { + "bbox": [ + 304, + 546, + 545, + 619 + ], + "type": "inline_equation", + "content": "[z_q^{\\mathbf{n}}:z_q^s ]" + }, + { + "bbox": [ + 304, + 546, + 545, + 619 + ], + "type": "text", + "content": " in Eq. (8)." + } + ] + } + ], + "index": 59 + }, + { + "bbox": [ + 306, + 630, + 399, + 641 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 399, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 399, + 641 + ], + "type": "text", + "content": "4.4. Loss Functions" + } + ] + } + ], + "index": 60 + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "text", + "content": "For the query point " + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "text", + "content": ", we constrain its unoriented normal and normal sign (i.e., orientation), respectively. To learn an accurate unoriented normal, we employ the ground-truth " + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{n}}_q" + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "text", + "content": " to calculate a normal vector " + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "inline_equation", + "content": "\\sin" + }, + { + "bbox": [ + 304, + 651, + 545, + 698 + ], + "type": "text", + "content": " loss [5]" + } + ] + } + ], + "index": 61 + }, + { + "bbox": [ + 384, + 701, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 701, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 384, + 701, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\sin} = \\left\\| \\mathbf {n} _ {q} \\times \\hat {\\mathbf {n}} _ {q} \\right\\|. \\tag {16}", + "image_path": "44b08765f4a4517184c4a55d659facdacf0c4e2352eb3c077e6ce9ebff4e56c1.jpg" + } + ] + } + ], + "index": 62 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13595" + } + ] + } + ], + "index": 63 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 83, + 542, + 269 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 544, + 81 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 544, + 81 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 544, + 81 + ], + "type": "text", + "content": "Table 1. Unoriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted or unavailable." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 83, + 542, + 269 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 542, + 269 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 542, + 269 + ], + "type": "table", + "html": "
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientStripeGradient
Jet [10]12.3512.8418.3327.6813.3913.1316.2920.1120.5731.3445.1918.8218.6925.79
PCA [19]12.2912.8718.3827.5213.6612.8116.2519.9020.6031.3345.0019.8418.5425.87
PCPNet [17]9.6411.5118.2722.8411.7313.4614.5818.4721.0732.6039.9318.1419.5024.95
Zhou et al.* [57]8.6710.4917.6224.1410.2910.6613.62-------
Nesti-Net [6]7.0610.2417.7722.318.648.9512.4911.6016.8031.6139.2212.3311.7720.55
Lenssen et al. [29]6.729.9517.1821.967.737.5111.8411.6216.9730.6239.4311.2110.7620.10
DeepFit [5]6.519.2116.7323.127.927.3111.8011.2116.3929.8439.9511.8410.5419.96
MTRNet* [9]6.439.6917.0822.238.396.8911.78-------
Refine-Net [56]5.929.0416.5222.197.707.2011.43-------
Zhang et al.* [54]5.659.1916.7822.936.686.2911.259.8316.1329.8139.819.729.1919.08
Zhou et al.* [58]5.909.1016.5022.086.796.4011.13-------
AdaFit [59]5.199.0516.4521.946.015.9010.769.0915.7829.7838.748.528.5718.41
GraphFit [31]5.218.9616.1221.716.305.8610.698.9115.7329.3738.679.108.6218.40
HSurf-Net [32]4.178.7816.2521.614.984.8610.117.5915.6429.4338.547.637.4017.70
Ours3.958.5516.1321.534.914.679.967.4115.3429.3338.567.747.2817.61
", + "image_path": "eca6956298b54c64f5e029afdecf2e04d62367decd501f8c3d2b73610d484465.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 275, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 300 + ], + "type": "text", + "content": "For the normal orientation, we adopt the binary cross entropy " + }, + { + "bbox": [ + 46, + 275, + 287, + 300 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 275, + 287, + 300 + ], + "type": "text", + "content": " [14] to calculate a sign classification loss" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 301, + 287, + 320 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 301, + 287, + 320 + ], + "spans": [ + { + "bbox": [ + 91, + 301, + 287, + 320 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s g n} = H \\left(\\sigma \\left(g ^ {s} (q)\\right), [ f _ {\\boldsymbol {S}} (q) > 0 ]\\right), \\tag {17}", + "image_path": "2c0cfef2b40d2de967e0c914c9ed9df19f70c26b36358d9ea6ac166709b1c08a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "text", + "content": " is a logistic function that converts the sign into its probabilities. " + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "inline_equation", + "content": "[f_S(q) > 0]" + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "text", + "content": " is 1 if the estimated normal faces the outward of surface " + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 322, + 287, + 407 + ], + "type": "text", + "content": " and 0 otherwise. Our method achieves a significant performance boost by dividing the oriented normal estimation into unoriented normal regression and its sign classification, instead of directly regressing the oriented normals of query points (see Sec. 5.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 406, + 287, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 431 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 431 + ], + "type": "text", + "content": "To make the model also pay attention to neighbor points " + }, + { + "bbox": [ + 46, + 406, + 287, + 431 + ], + "type": "inline_equation", + "content": "p_i \\in p_q" + }, + { + "bbox": [ + 46, + 406, + 287, + 431 + ], + "type": "text", + "content": ", we compute a weighted mean square error (MSE)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 434, + 287, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 434, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 287, + 464 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m s e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tau_ {i} \\| \\vec {\\mathbf {n}} _ {i} - \\hat {\\vec {\\mathbf {n}}} _ {i} \\| ^ {2}, \\tag {18}", + "image_path": "f41dacb8c632aeece4385b83288c31518ed01b6e724bc26ba6c91043fb664f87.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "text", + "content": "where the neighborhood point normals " + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\vec{\\mathbf{n}} = \\delta (z_q)" + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "text", + "content": " are predicted from the surface embedding " + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "inline_equation", + "content": "z_{q}" + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "text", + "content": " by an MLP layer " + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\delta :\\mathbb{R}^c\\to \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "text", + "content": " . Moreover, we add a loss term according to coplanarity [54] to facilitate the learning of " + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 467, + 287, + 516 + ], + "type": "text", + "content": " in Eq.(12)," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 517, + 287, + 549 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 517, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 53, + 517, + 287, + 549 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\tau} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\left(\\tau_ {i} - \\hat {\\tau} _ {i}\\right) ^ {2}, \\hat {\\tau} _ {i} = \\exp \\left(- \\frac {\\left(p _ {i} \\cdot \\hat {\\mathbf {n}} _ {q}\\right) ^ {2}}{\\xi^ {2}}\\right), \\tag {19}", + "image_path": "199d96adc73239ec246686d690c08e7daa21fffc87622c4161ff12b22d043861.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 552, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 578 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 552, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\xi = \\max (0.05^2, 0.3\\sum_{i=1}^{N}(p_i \\cdot \\hat{\\mathbf{n}}_q)^2 / N)" + }, + { + "bbox": [ + 46, + 552, + 287, + 578 + ], + "type": "text", + "content": ". In summary, our final training loss for oriented normal estimation is" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 69, + 587, + 287, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 587, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 69, + 587, + 287, + 601 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\sin} + \\lambda_ {2} \\mathcal {L} _ {s g n} + \\lambda_ {3} \\mathcal {L} _ {m s e} + \\lambda_ {4} \\mathcal {L} _ {\\tau}, \\tag {20}", + "image_path": "74ceb1d4980ba61bc926f6f92397335882b8f03db674aaa6e979d4d228fd4ae9.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "inline_equation", + "content": "\\lambda_1 = 0.1" + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "inline_equation", + "content": "\\lambda_2 = 0.1" + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "inline_equation", + "content": "\\lambda_3 = 0.5" + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "inline_equation", + "content": "\\lambda_4 = 1.0" + }, + { + "bbox": [ + 47, + 610, + 285, + 622 + ], + "type": "text", + "content": " are factors." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 633, + 128, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 128, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 128, + 647 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Implementation. We only train our network model on the PCPNet shape dataset [17], which provides the groundtruth normals with consistent orientation (outward of the surface). We follow the same train/test data split and data processing as in [5, 17, 32, 59]. For patch encoding, we" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "text", + "content": "randomly select a query point from the shape point cloud and search its 700 neighbors to form a patch. For shape encoding, we sample " + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "inline_equation", + "content": "N_P = 1200" + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "text", + "content": " points from the shape point cloud according to the sampling probability. The Adam optimizer is adopted with an initial learning rate of " + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "inline_equation", + "content": "9 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "text", + "content": " which is decayed to " + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "inline_equation", + "content": "1/5" + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "text", + "content": " of the latest value at epochs " + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "inline_equation", + "content": "\\{400, 600, 800\\}" + }, + { + "bbox": [ + 304, + 275, + 545, + 371 + ], + "type": "text", + "content": ". The model is trained on an NVIDIA 2080 Ti GPU with a batch size of 145 and epochs of 800." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 372, + 546, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 546, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 546, + 503 + ], + "type": "text", + "content": "Dataset. Due to the lack of relevant datasets and the relatively simple test shapes of the PCPNet dataset [17], we further collect shapes with complex structures from other public datasets, such as the Famous dataset [14] and the Stanford 3D Scanning Repository [12]. We follow the same preprocessing steps as the PCPNet dataset to conduct data augmentation, e.g., adding Gaussian noise with different levels (0.12%, 0.6% and 1.2%) and uneven sampling (stripe and gradient). The ground-truth oriented normals are extracted from mesh data and used for evaluation. We call this dataset FamousShape and it is available along with our code." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 505, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 545, + 564 + ], + "type": "text", + "content": "Metrics. We use the angle Root Mean Squared Error (RMSE) to evaluate the estimated normals and the Area Under the Curve (AUC) to show the error distribution [17, 32, 59]. Note that for the baseline methods, we flip their oriented normals if more than half of the normals face inward." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 574, + 481, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 481, + 587 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 481, + 587 + ], + "type": "text", + "content": "5.1. Unoriented Normal Comparison" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "We directly use our oriented normal estimation results to compare with baseline methods that are designed for estimating unoriented normals, such as the traditional methods PCA [19] and Jet [10], the learning-based surface fitting methods DeepFit [5] and AdaFit [59], and the learning-based regression methods Nesti-Net [6] and HSurf-Net [32]. As shown in Table 1, we report quantitative comparison results with the baselines in terms of normal angle RMSE on two datasets, PCPNet and FamousShape. On the PCPNet dataset, our method achieves the best perfor" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13596" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 82, + 541, + 240 + ], + "blocks": [ + { + "bbox": [ + 77, + 71, + 515, + 81 + ], + "lines": [ + { + "bbox": [ + 77, + 71, + 515, + 81 + ], + "spans": [ + { + "bbox": [ + 77, + 71, + 515, + 81 + ], + "type": "text", + "content": "Table 2. Oriented normal RMSE results on datasets PCPNet and FamousShape. * means the source code is uncompleted." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 82, + 541, + 240 + ], + "lines": [ + { + "bbox": [ + 52, + 82, + 541, + 240 + ], + "spans": [ + { + "bbox": [ + 52, + 82, + 541, + 240 + ], + "type": "table", + "html": "
CategoryPCPNet DatasetFamousShape Dataset
NoiseDensityAverageNoiseDensityAverage
None0.12%0.6%1.2%StripeGradientNone0.12%0.6%1.2%StripeGradient
PCA [19]+MST [19]19.0530.2031.7639.6427.1123.3828.5235.8841.6738.0960.1631.6935.4040.48
PCA [19]+QPBO [45]18.5521.6130.9439.5423.0025.4626.5232.2539.3941.8061.9136.6935.8241.31
PCA [19]+ODP [38]28.9625.8634.9151.5228.7023.0032.1630.4731.2941.6584.0039.4130.7242.92
AdaFit [59]+MST [19]27.6743.6948.8354.3936.1840.4641.8743.1239.3362.2860.2745.5742.0048.76
AdaFit [59]+QPBO [45]26.4124.1740.3148.7627.7431.5633.1627.5537.6069.5662.7727.8629.1942.42
AdaFit [59]+ODP [38]26.3724.8635.4451.8826.4520.5730.9341.7539.1944.3172.9145.0942.3747.60
HSurf-Net [32]+MST [19]29.8244.4950.4755.4740.5443.1543.9954.0242.6768.3765.9152.5253.9656.24
HSurf-Net [32]+QPBO [45]30.3432.3444.0851.7133.4640.4938.7441.6241.0667.4162.0445.5943.8350.26
HSurf-Net [32]+ODP [38]26.9124.8535.8751.7526.9120.1631.0743.7743.7446.9172.7045.0943.9849.37
PCPNet [17]33.3434.2240.5444.4637.9535.4437.6640.5141.0946.6754.3640.5444.2644.57
DPGO* [50]23.7925.1935.6643.8928.9929.3331.14-------
Ours10.2813.2325.4035.5116.4017.9219.7921.6325.9641.1452.6726.3928.9732.79
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Oriented normal AUC on the PCPNet dataset. It shows the percentage of correctly estimated normals (PGP) for a given angle threshold. Our method has the best value for all thresholds." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 181, + 464, + 286, + 582 + ], + "blocks": [ + { + "bbox": [ + 181, + 464, + 286, + 582 + ], + "lines": [ + { + "bbox": [ + 181, + 464, + 286, + 582 + ], + "spans": [ + { + "bbox": [ + 181, + 464, + 286, + 582 + ], + "type": "image", + "image_path": "722cb46b2e7d2064ad0ea76fb12f8a20f48d0ad33cd965fc9e071f29b90043d8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 628, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 665 + ], + "type": "text", + "content": "mance under all noise levels and density variations. On our FamousShape dataset, our method achieves the best performance under most metrics and has the best average result." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 211, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 211, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 211, + 685 + ], + "type": "text", + "content": "5.2. Oriented Normal Comparison" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "We compare our approach for oriented normal estimation with various baseline methods, such as PCPNet [17]" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 247, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 534 + ], + "type": "text", + "content": "and DPGO [50]. In addition, we choose three unoriented normal estimation methods (PCA [19], AdaFit [59] and HSurf-Net [32]) and three normal orientation methods (MST [19], QPBO [45] and ODP [38]), and make different combinations of them to form two-stage pipelines for estimating oriented normals, such as PCA+MST. Among the baselines, PCA is a widely used traditional method, AdaFit is a representative surface fitting-based method, and HSurf-Net is a regression-based method and has the state-of-the-art performance for unoriented normal estimation. We use the original implementation of QPBO and ODP, and the implementation of MST in [47]. In Table 2, we show quantitative comparison results on datasets PCPNet and FamousShape. We can see that our method provides the most accurate normals under almost all noise levels and density variations for both datasets, and achieves huge performance gains in terms of average results compared to all baselines. From the experimental results, we find that the propagation-based normal orientation methods have significantly varied results when dealing with unoriented normal inputs from different estimation methods, such as PCA+MST and AdaFit+MST. A visual comparison of the normal errors is shown in Fig. 5. The error distributions of various methods are illustrated in Fig. 6." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 665 + ], + "type": "text", + "content": "KITTI Dataset. To verify the generalization ability of our method on LiDAR point clouds of outdoor scenes, we test directly on the KITTI dataset [15] with the model trained on the PCPNet dataset. We only report qualitative results on this dataset as it does not provide the ground-truth normals. In Fig. 7, we use the Poisson surface reconstruction algorithm [26] to generate surfaces using oriented normals estimated by different methods. As can be seen, compared to the baselines, our estimated normals facilitate the algorithm to reconstruct surfaces that can more accurately depict the spatial structure and distribution of real scenes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 671, + 406, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 406, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 406, + 682 + ], + "type": "text", + "content": "5.3. Ablation Studies" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "We provide ablation results for oriented normal estimation in Table 3 (a)-(d), which are discussed as follows." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13597" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 83, + 542, + 228 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 542, + 81 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 542, + 81 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 542, + 81 + ], + "type": "text", + "content": "Table 3. Ablation studies for oriented normals on the PCPNet dataset. The last column is the average results under the unoriented metric." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 83, + 542, + 228 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 542, + 228 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 542, + 228 + ], + "type": "table", + "html": "
AblationFeat. Enco.Module HLossPoint Samp.NoiseDensityOriented AverageUnoriented Average
None0.12%0.6%1.2%StripeGradient
(a)w/o patch encoding✓✓✓35.1942.2355.5961.3838.9241.4945.8018.83
w/o shape encoding✓✓✓69.7264.3781.8777.0774.8490.3576.3714.94
w/o weight w✓✓✓11.1514.3226.4936.0317.9926.0322.0010.48
(b)w/o module H✓✓✓12.0814.5325.8735.8818.4531.8423.1110.24
(c)w/o Lsin, Lsgn✓✓✓23.8625.5534.1342.4832.4241.3033.2920.23
(d)w/o density gradient✓✓✓12.1018.2528.0538.1519.7928.0924.0710.00
w/o random sample✓✓✓11.0113.7925.6435.8617.2225.7121.549.94
ζ=1/2✓✓✓10.9914.0425.6635.7817.7337.8223.679.92
ζ=1/3✓✓✓13.2715.4226.8237.1617.5228.1123.059.95
NP=1100✓✓✓10.6714.2125.5435.9716.8026.9821.699.99
NP=1300✓✓✓12.4414.5325.9335.7918.4019.8521.169.98
Final✓✓✓✓10.2813.2325.4035.5116.4017.9219.799.96
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Street surfaces reconstructed using estimated normals on the KITTI dataset. The raw point cloud is colored with height values." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 173, + 305, + 296, + 380 + ], + "blocks": [ + { + "bbox": [ + 173, + 305, + 296, + 380 + ], + "lines": [ + { + "bbox": [ + 173, + 305, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 173, + 305, + 296, + 380 + ], + "type": "image", + "image_path": "79fde2768b5c6a09c5a50d9c5fd63ed4f0cc47d67658fd385ced42906506fba3.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 298, + 305, + 419, + 380 + ], + "blocks": [ + { + "bbox": [ + 298, + 305, + 419, + 380 + ], + "lines": [ + { + "bbox": [ + 298, + 305, + 419, + 380 + ], + "spans": [ + { + "bbox": [ + 298, + 305, + 419, + 380 + ], + "type": "image", + "image_path": "0958ee212169dfeb536c73bc330db8dc4c0f44e245973c22efd7177d5f386b4f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 421, + 306, + 544, + 380 + ], + "blocks": [ + { + "bbox": [ + 421, + 306, + 544, + 380 + ], + "lines": [ + { + "bbox": [ + 421, + 306, + 544, + 380 + ], + "spans": [ + { + "bbox": [ + 421, + 306, + 544, + 380 + ], + "type": "image", + "image_path": "8179c472dd14486ad46823799dce38343b2458dfc5afb81fd60c0fb4e3415991.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 407, + 287, + 652 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 46, + 407, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 455 + ], + "type": "text", + "content": "(a) Feature Encoding. (1) We realize the oriented normal estimation without using the patch encoding or the shape encoding. (2) The distance-based weight " + }, + { + "bbox": [ + 46, + 407, + 287, + 455 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 407, + 287, + 455 + ], + "type": "text", + "content": " is not used in both patch encoding and shape encoding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "type": "text", + "content": "(b) Module " + }, + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "type": "text", + "content": ". The attention-weighted normal prediction module " + }, + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 47, + 456, + 287, + 481 + ], + "type": "text", + "content": " is replaced with simple MLP layers." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "content": "(c) Loss " + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{sin}}, \\mathcal{L}_{\\text{sgn}}" + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "content": ". In our pipeline, we regress the unoriented normal and its sign of the query point " + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "content": ", and constrain them in loss functions " + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{sin}}" + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{sgn}}" + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "content": ", respectively. Here, we alternatively directly predict the oriented normal " + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\vec{\\mathbf{n}}_q" + }, + { + "bbox": [ + 46, + 483, + 287, + 542 + ], + "type": "text", + "content": " from surface embedding and compute its MSE loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": "(d) Point Sampling. In the shape encoding, we obtain a global point set " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "P_{q}" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " by a probability-based sampling strategy as in Eq. (15), which includes density gradient term and random sample term. The point set " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "P_{q}" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " includes " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "N_{P} = 1200" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " points, and the ratio of randomly sampled points is " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\zeta = 1/1.5" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": ". (1) We only adopt one of the two terms in Eq. (15) for point sampling, e.g., 'w/o density gradient' means all points are randomly sampled. (2) The ratio " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\zeta" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " is changed to " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "1/3" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": ". (3) The number " + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "inline_equation", + "content": "N_{P}" + }, + { + "bbox": [ + 46, + 544, + 287, + 652 + ], + "type": "text", + "content": " is set to 1100 and 1300." + } + ] + } + ], + "index": 14 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "From Table 3, we can conclude that both patch encoding and shape encoding are vital for learning accurate oriented and unoriented normals in our pipeline. The adoption of the weight " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " and the attention-weighted normal prediction module " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " effectively improves the algorithm's perfor" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 407, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 502 + ], + "type": "text", + "content": "mance. Compared to directly predicting the oriented normal " + }, + { + "bbox": [ + 304, + 407, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\vec{\\mathbf{n}}_q" + }, + { + "bbox": [ + 304, + 407, + 545, + 502 + ], + "type": "text", + "content": ", solving it separately by learning signed hyper surface is significantly better. The combination of the density gradient term and the random sample term in sampling can produce better results than either one alone. The proportion and number of points in the sampling of shape encoding have a significant positive effect on oriented normals, but very little on unoriented normals." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "In this work, we formulate the oriented normal estimation of point clouds as the learning of signed hyper surfaces. We first review the explicit surface fitting and the implicit surface learning, and derive the formulation of the signed hyper surfaces from their inspiration. Then, we propose to use an attention-weighted normal prediction module to recover the normal and its sign of the query point from the embedding of the signed hyper surfaces. Finally, we introduce how such surfaces can be learned from the patch encoding and shape encoding using the designed loss functions. We conduct extensive evaluation and ablation experiments to report the state-of-the-art performance and justify the effectiveness of our designs. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6118-6127, 2021. 1, 2, 4, 6, 7" + } + ] + } + ], + "index": 30 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13600" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/a369b37c-8e06-4d08-a268-de9d54816ab4_content_list.json b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/a369b37c-8e06-4d08-a268-de9d54816ab4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1ec9f5b19ab26dd5b9325a5efc5a8307030e639e --- /dev/null +++ b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/a369b37c-8e06-4d08-a268-de9d54816ab4_content_list.json @@ -0,0 +1,1676 @@ +[ + { + "type": "text", + "text": "SIEDOB: Semantic Image Editing by Disentangling Object and Background", + "text_level": 1, + "bbox": [ + 99, + 130, + 870, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wuyang Luo1 Su Yang1* Xinjian Zhang1 Weishan Zhang2", + "bbox": [ + 181, + 179, + 785, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University $\\{\\mathrm{wyluol8, suyang}\\} @$ fudan.edu.cn", + "bbox": [ + 150, + 200, + 816, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ School of Computer Science and Technology, China University of Petroleum", + "bbox": [ + 251, + 234, + 714, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic image editing provides users with a flexible tool to modify a given image guided by a corresponding segmentation map. In this task, the features of the foreground objects and the backgrounds are quite different. However, all previous methods handle backgrounds and objects as a whole using a monolithic model. Consequently, they remain limited in processing content-rich images and suffer from generating unrealistic objects and texture-inconsistent backgrounds. To address this issue, we propose a novel paradigm, Semantic Image Editing by Disentangling Object and Background (SIEDOB), the core idea of which is to explicitly leverages several heterogeneous subnetworks for objects and backgrounds. First, SIEDOB disassembles the edited input into background regions and instance-level objects. Then, we feed them into the dedicated generators. Finally, all synthesized parts are embedded in their original locations and utilize a fusion network to obtain a harmonized result. Moreover, to produce high-quality edited images, we propose some innovative designs, including Semantic-Aware Self-Propagation Module, Boundary-Anchored Patch Discriminator, and Style-Diversity Object Generator; and integrate them into SIEDOB. We conduct extensive experiments on Cityscapes and ADE20K-Room datasets and exhibit that our method remarkably outperforms the baselines, especially in synthesizing realistic and diverse objects and texture-consistent backgrounds. Code is available at https://github.com/WuyangLuo/SIEDOB.", + "bbox": [ + 75, + 318, + 473, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 772, + 209, + 787 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic image editing has recently gained significant traction due to its diverse applications, including adding, altering, or removing objects and controllably inpainting, outpainting, or repainting images. Existing methods have made impressive progress benefiting from Generative Adversar", + "bbox": [ + 75, + 799, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/30487b7cf41b1266705405421c3a9f99d8a21c9cdb7aaaba0fb77538eb48356d.jpg", + "image_caption": [ + "Input", + "Figure 1. Existing methods struggle to deal with the compound of backgrounds and several overlapping objects in a complex scene. They generate distorted objects and texturally inconsistent backgrounds. The proposed method can cope well with this input." + ], + "image_footnote": [], + "bbox": [ + 501, + 286, + 576, + 348 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0f2de8aa00d06b6b5e014fc172f07b6e7d0492d19bea5711f061029177bc0a3a.jpg", + "image_caption": [ + "SESAME" + ], + "image_footnote": [], + "bbox": [ + 578, + 287, + 643, + 348 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a43d5e018e9cf5c784c7784f8c47c2e15054689029a7ba77268503854fdc263e.jpg", + "image_caption": [ + "ASSET" + ], + "image_footnote": [], + "bbox": [ + 655, + 287, + 730, + 348 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/017a320a31007088c62f021b15bce4e09bdc7a6c5df8a53bb0f647c17813bcb0.jpg", + "image_caption": [ + "SPMPGAN" + ], + "image_footnote": [], + "bbox": [ + 733, + 287, + 816, + 348 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9e7ef790385c50673b34613a0de540fdd83ae8bfe624054e32871b8f4af22408.jpg", + "image_caption": [ + "SIEDOB" + ], + "image_footnote": [], + "bbox": [ + 816, + 287, + 895, + 348 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ial Networks (GAN) [5, 14] and have demonstrated promising results in relatively content-simple scenes, such as landscapes. However, they still suffer from inferior results for content-rich images with multiple discrepant objects, such as cityscapes or indoor rooms. This paper aims to improve editing performance in complex real-world scenes.", + "bbox": [ + 496, + 458, + 892, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "When image editing experts deal with a complex task, they decompose the input image into multiple independent and disparate elements and handle them with different skills. For example, when editing a photo with a congested road, they process the cars and pedestrians individually and then fill in the background. Inspired by this spirit, we propose a heterogeneous editing model, which mimics the experience of human experts and explicitly splits the compound content into two distinct components: Backgrounds and objects. The background has no regular shape and may span a large area. More importantly, the re-generated background's texture and the existing area must be consistent. Foregrounds objects are class-specific and appear anywhere with various scales. Due to the significant differences between the two components, it is necessary to disentangle them from the input and process them with different networks.", + "bbox": [ + 496, + 551, + 893, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several recent works [23, 28, 32] have been dedicated to this task. SESAME [32] proposes a new pair of generator and discriminator based on the cGAN framework [31], which generates edited content through a single-shot inference. ASSET [23] builds a transformer-based architecture with a sparse attention mechanism and synthesizes", + "bbox": [ + 496, + 809, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Corresponding author", + "bbox": [ + 99, + 886, + 233, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1868", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "edited regions relying on a codebook generated by VQ-GAN [4]. SPMPGAN [28] proposes a coarse-to-fine generator equipped with style-preserved modulation layers to retain style consistency between edited regions and context. These methods effectively enhance the ability of a monolithic model to handle the entire input. However, they deal with backgrounds and objects equally using the same generator, which causes them to produce inferior results. Figure 1 demonstrates an example. To tackle this limitation, we present a novel framework, Semantic Image Editing by Disentangling Object and Background (SIEDOB), to generate backgrounds and foreground objects separately, which can achieve two goals: Synthesizing texture-consistent backgrounds and generating photorealistic and diverse objects.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SIEDOB first disassembles the edited image into background regions and instance-level objects, then employs different generators to synthesize the corresponding content, and finally aggregates generated objects with backgrounds via a fusion network. In this way, we decouple our task into several more feasible subtasks and handle different components using dedicated sub-models.", + "bbox": [ + 75, + 318, + 472, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generating texture-consistent backgrounds with known context is not trivial since backgrounds may cross a sizeable spatial area in an image and have no regular shape. We propose a pair of boosted generator and discriminator to address this problem. Specifically, we propose Semantic-Aware Self-Propagation Module (SASPM) to help the generator efficiently transfer the semantic-wise features of known regions to generated regions. Moreover, to further enhance texture consistency, we design a Boundary-Anchored Patch Discriminator to force the generator to pay more attention to local textures of editing fringe.", + "bbox": [ + 75, + 426, + 472, + 593 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our task, depending on the scenario, the edited object may be requested to be inpainted or generated. If an object is partially visible, it undergoes a lightweight inpainting network. Otherwise, we employ a Style-Diversity Object Generator to obtain multi-modal results based on a style bank. After generating the backgrounds and all objects, we re-integrate them into a whole. However, the separate generation may lead to sudden boundaries and dissonance between objects and surroundings. To tackle this problem, we utilize a simple fusion network that predicts the residual value for each pixel to harmonize outputs.", + "bbox": [ + 75, + 594, + 472, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 96, + 761, + 459, + 776 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a new solution for semantic image editing, named SIEDOB, which can handle complex scenes by decoupling the generation of backgrounds and objects.", + "- We propose Semantic-Aware Self-Propagation Module and Boundary-Anchored Patch Discriminator to facilitate texture-consistent background generation." + ], + "bbox": [ + 96, + 794, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a Style-Diversity Object Generator that can generate diverse and realistic object images from masks.", + "- Extensive experiments on two benchmarks indicate that our method can generate texture-consistent results and deal with crowded objects well." + ], + "bbox": [ + 517, + 90, + 890, + 191 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 215, + 650, + 232 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Semantic Image Editing", + "text_level": 1, + "bbox": [ + 500, + 241, + 720, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic image editing refers to modifying a given image by manipulating a corresponding segmentation map and keeping the context coherent. This approach provides powerful editing capabilities, such as adding and removing objects, modifying shapes, and re-painting backgrounds. Compared to several related tasks, including semantic image synthesis [14, 33, 40, 42, 51] and image inpainting [13, 30, 45, 46, 48], semantic image editing has not been fully exploited due to its difficulty in generating realistic objects and texture-consistent backgrounds simultaneously. A few recent works are devoted to semantic image editing [10, 23, 28, 32]. HIM [10] is an early exploration that only operates on a single object using a two-stage network. SESAME [32] introduces a new pair of generators and discriminators to improve the quality of the generated results. Moreover, SESAME adopts a more flexible workflow that can respond to various image editing requirements of users. ASSET [23] proposes a novel transformer-based approach modeling long-range dependencies, enabling high-resolution image editing. SPMPGAN [28] presents a stylepreserved modulation technique and builds a progressive architecture that solves the style inconsistency problem in semantic image editing. These methods all consider semantic image editing as a global generation problem. Thus, they use a single model to process all elements of the edited image equally. In this work, we propose a decoupled framework to handle objects and backgrounds separately using heterogeneous generators, demonstrating more promising results.", + "bbox": [ + 496, + 263, + 890, + 702 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Image Synthesis via Heterogeneous Generators", + "text_level": 1, + "bbox": [ + 500, + 710, + 890, + 727 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For a wide variety of image generation tasks, most approaches impose monolithic generators on the entire image, including unsupervised image generation [17, 18, 35], image-to-image translation [29, 33, 42, 51], image inpainting [24, 45, 46], and image editing [15, 26]. They share the same network structure and weights to generate all the content without specialized submodels for different semantic regions or classes. Other methods use different architectures or weights to generate different image elements to improve generation quality for different components. For example, they employ multiple local branches specialized", + "bbox": [ + 496, + 734, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1869", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a520e55eedef2ec936a76064268613b6015452860abe51033691bcbd5ca87948.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed method. To reduce the complexity of modeling the entire edited region, we use a heterogeneous model to synthesize foreground objects and backgrounds separately, which contains three components: (1) Background generation, (2) object generation, (3) fusion network." + ], + "image_footnote": [], + "bbox": [ + 116, + 93, + 851, + 276 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for different parts [6, 9, 11, 21], decoupling content and style [12, 20, 27], generating foreground and a single foreground object separately [39, 43], enhancing local generation [1, 37], or having separate modules for different semantic categories [22, 40]. However, these methods are developed for pure image generation or translation tasks where their input is noises, categories, segmentation maps, or full images. Therefore, they only need to synthesize simple but visually plausible results to fool the discriminator. Semantic image editing is a more challenging task, and its difficulty lies in keeping coherence between edited and known regions. In this paper, we propose a heterogeneous framework that utilizes different sub-models for foreground objects and backgrounds to improve their generation quality concurrently.", + "bbox": [ + 75, + 358, + 472, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 602, + 250, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to edit a given image $I \\in \\mathbb{R}^{H \\times W \\times 3}$ guided by a user-provided segmentation map $S \\in \\mathbb{L}^{H \\times W \\times L}$ within an edited region defined by a mask map $M \\in \\mathbb{B}^{H \\times W \\times 1}$ whose value is 0 in the non-edited region and 1 in the edited region. Here $H, W,$ and $L$ denote the height, width, and number of semantic categories, respectively. The edited region of $I$ is erased as input $I_e = I \\times (1 - M)$ . We create a background mask $M_B$ and all instance-level object masks $\\{M_c^q\\}$ in the edited region based on the segmentation map. Here, $c \\in \\mathcal{C}, \\mathcal{C}$ is a pre-defined set of considered foreground categories, and $M_c^q$ is the $q$ -th instance that falls into the category $c$ . The background mask $M_B$ is composed of the remaining pixels. Thus, we can disassemble the input image $I_e$ to the background and objects according to $M_B$ and $\\{M_c^q\\}$ . Then we generate the background and objects separately using the respective generators. Finally, we integrate all generated content via a fusion network. The workflow is depicted in Figure 2.", + "bbox": [ + 75, + 627, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background Generation", + "text_level": 1, + "bbox": [ + 500, + 357, + 723, + 373 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For image editing, the background usually needs to be partially generated to fill the space, such as sky or ground. Therefore, generating style-consistent texture patterns in edited regions is critical and challenging since the generated background and the known region coexist. In addition, an image's background may be across a distant spatial distance and have no regular shape. Efficiently and accurately transferring feature styles from known to edited regions is vital for generating texture-consistent results. To this end, we propose a Semantic-Aware Self-Propagation Module (SASPM), which explicitly extracts semantic-wise feature codes from feature maps and propagates them to the corresponding regions at the same layer. Furthermore, we employ a Boundary-Anchored Patch Discriminator to enforce the generator to focus on local textures at the editing boundary.", + "bbox": [ + 496, + 382, + 890, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed background generator $G_B$ is shown in 3(c). We feed the disassembled background region into $G_B$ as the input: $I_B = I_e \\times M_B$ . $G_B$ follows an encoder-decoder structure. The encoder is composed of several successive GatedConv layers [46] with stride two, and the decoder contains corresponding GatedConv layers with upsampling and several SASPM.", + "bbox": [ + 496, + 626, + 890, + 731 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic-Aware Self-Propagation Modules (SASPM)", + "text_level": 1, + "bbox": [ + 500, + 732, + 864, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SASPM aims at propagating features of known regions to edited regions in a semantic-aware manner. Taking the sky area as an example shown in Figure 3(a)(b), a SASPM is divided into two steps. First, we extract the semantic-aware feature code by computing the average of the known sky area. Then, the feature code is broadcast into the entire sky area according to the corresponding semantic mask. SASPM can transfer the feature codes of each semantic label at the same feature level without the constraint of the receptive field. Formally, let $F \\in \\mathbb{R}^{H \\times W \\times C}$ denote a feature", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1870", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/120748f2853b389a798d0269d7daea07b8bda625d18727b070e66ae496a030b0.jpg", + "image_caption": [ + "Edited Image" + ], + "image_footnote": [], + "bbox": [ + 124, + 90, + 220, + 166 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8019a467d5375c0bb2d67b642132b6cfaaeb112e061de05f93a916550a9f141a.jpg", + "image_caption": [ + "Known Sky Region" + ], + "image_footnote": [], + "bbox": [ + 227, + 90, + 325, + 165 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7bcc9d39fb308da4882ed9e1f3b8366c211dcf6e80e51a273defa796a7bc7109.jpg", + "image_caption": [ + "Entire Sky Region" + ], + "image_footnote": [], + "bbox": [ + 331, + 90, + 428, + 165 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/69bb4166ff601b1e007588aaffa1e7970acbd87838286fc2a778a2208ac73933.jpg", + "image_caption": [ + "(a) A semantic category (sky) spans the known region and the edited region" + ], + "image_footnote": [], + "bbox": [ + 106, + 186, + 436, + 292 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5d82832549abf79be95adf14fad0fb07d3e3b5375157f0b8589a993aa935750a.jpg", + "image_caption": [ + "Figure 3. (a) A background category, such as sky, may span known and edited regions. We want to transfer the features from the known region to the generated region in a semantic-aware fashion. (b) The principle of SASPM. We extract the feature code for each background category from the known region and then propagate it to the entire region. (c) The architecture of our background generator." + ], + "image_footnote": [], + "bbox": [ + 102, + 297, + 444, + 410 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "map in front of a SASPM. $H$ , $W$ are the spatial dimension and $C$ is the number of channels. Let $U \\in \\mathbb{R}^{L \\times C}$ represent $L$ feature codes extracted from the known region, and the feature codes of non-background classes are set to zero. We generate a code map $P$ based on the segmentation map $S \\in \\mathbb{L}^{H \\times W \\times L}$ through a matrix multiplication to spatially broadcast the feature codes into the corresponding semantic region:", + "bbox": [ + 75, + 545, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP = S \\otimes U \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 681, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, $P \\in \\mathbb{R}^{H \\times W \\times C}$ is restored to the spatial dimension filled with the category-specific feature codes. Finally, we propagate $P$ into the original $F$ using a modulation operation following SPADE [33]. Specifically, we learn two parameters $\\gamma_{P} \\in \\mathbb{R}^{H \\times W \\times C}$ and $\\beta_{P} \\in \\mathbb{R}^{H \\times W \\times C}$ from $P$ to modulate $F$ :", + "bbox": [ + 75, + 700, + 468, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {P} = \\operatorname {R e L U} \\left(\\gamma_ {P} \\odot I N (\\operatorname {C o n v} (F)) \\oplus \\beta_ {P}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 815, + 468, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where $Conv(\\cdot), IN(\\cdot)$ , and $ReLU(\\cdot)$ denote Convolutional Layer, Instance Normalization, and ReLU activation function, respectively. $\\odot$ and $\\oplus$ are element-wise multiplication and addition.", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fc63ece7463334a8406e112aa21d3c25a692e10326d28ccb3d81281af51c8ce8.jpg", + "image_caption": [ + "Figure 4. Boundary-Anchored Patch Discriminator $D_{BAP}$ takes in four real image patches or fake image patches of random size. All patches are centered on the boundary of the edited region enclosed by the red line." + ], + "image_footnote": [], + "bbox": [ + 529, + 92, + 857, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Boundary-Anchored Patch Discriminator", + "text_level": 1, + "bbox": [ + 500, + 369, + 784, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We employ two discriminators for our background generator: (1) A global discriminator used by previous works [28]; (2) a novel Boundary-Anchored Patch Discriminator $D_{BAP}$ . We introduce $D_{BAP}$ to enforce the generator to pay attention to local texture across the fringe of the edited area. We expect $D_{BAP}$ can capture known and generated textures simultaneously to facilitate texture-consistent results. To this end, we randomly select several central points anchored on the boundary of the edited region to crop patches from real or generated images, as shown in Figure 4. Thus, the fake patches contain both real and fake textures, so $D_{BAP}$ can distinguish between true and false through texture consistency.", + "bbox": [ + 498, + 383, + 890, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training objective of $G_{B}$ is comprised of L1 Distance Loss $\\mathcal{L}_1$ , Perceptual Loss $\\mathcal{L}_{\\mathrm{P}}$ [16], Global Adversarial Loss $\\mathcal{L}_{GAN}^{G}$ , and Local Patch Adversarial Loss $\\mathcal{L}_{GAN}^{L}$ :", + "bbox": [ + 498, + 580, + 890, + 628 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {B} = \\mathcal {L} _ {1} + \\lambda_ {P B} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} ^ {G} + \\lambda_ {G A N} ^ {L} \\mathcal {L} _ {G A N} ^ {L} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 652, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where $\\mathcal{L}_1$ and $\\mathcal{L}_{\\mathrm{P}}$ force the generated results to be closer to the ground truth in RGB space and VGG space [38]. $\\mathcal{L}_{GAN}^{G}$ and $\\mathcal{L}_{GAN}^{L}$ are applied to global images and local patches, respectively. All adversarial losses in this work are associated with a SNPatchGAN Discriminator [46] using the hinge version [2].", + "bbox": [ + 498, + 684, + 890, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Object Generation", + "text_level": 1, + "bbox": [ + 500, + 786, + 679, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our task involves dealing with two scenarios: Inpainting or generating an object—the former aims at completing an object based on its visible part. The latter synthesizes an inexistent object from its mask with an arbitrary appearance. Unlike handling all objects at once, cropping each edited object and independently generating them allows", + "bbox": [ + 498, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1871", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9df297a83bcfe686387a088e7b3368ca4248b459a5d1d0dc3e27db9b48149cc1.jpg", + "image_caption": [ + "(a) Extract Style Map" + ], + "image_footnote": [], + "bbox": [ + 127, + 89, + 467, + 189 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e713369a55511ca4f1c2dd6f5e369788af1123539258239af564c1f1aa5b5e35.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 97, + 841, + 189 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ab7f21e920b2e18c5da3c5e44c6d70166f65b7e54adba50e40b38c4a3ea92208.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 129, + 199, + 480, + 323 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8f157caf5091613a43948abb26c140d155894275dac9575eb7f958c7fdddef78.jpg", + "image_caption": [ + "Figure 5. (a) How to extract style maps? During training, we extract their style codes from ground truth images or randomly sampled images and then generate style maps by broadcasting. During inference, we sample a class-specific style code directly from the style bank. (b) The structure of Semantic-Style Normalization Module (SSNM). (c) We build a Style-Diversity Object Generator equipped with SSNM." + ], + "image_footnote": [], + "bbox": [ + 504, + 199, + 836, + 323 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "us to use aligned input images with the same size, which is beneficial for generating high-quality results. Specifically, we crop all objects $\\{Crop(I_e)_c^q\\}$ from the edited region based on object masks $\\{M_c^q\\}$ . We leverage a two-way model to handle the different scenarios. One way is a lightweight inpainting network $G_{OI}$ to complete objects. $G_{OI}$ is a UNet-like [36] network and its training objective is: $\\mathcal{L}_{GI} = \\mathcal{L}_1 + \\lambda_{PI}\\mathcal{L}_{\\mathrm{P}} + \\mathcal{L}_{GAN}$ . $\\mathcal{L}_1$ , $\\mathcal{L}_{\\mathrm{P}}$ , and $\\mathcal{L}_{GAN}$ are the same as the terms in Equation 6. The other way is the proposed Style-Diversity Object Generator $G_{OG}$ for the multi-modal generation. Note that all categories of objects share $G_{OI}$ and $G_{OG}$ .", + "bbox": [ + 75, + 407, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Style-Diversity Object Generator", + "text_level": 1, + "bbox": [ + 76, + 601, + 299, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$G_{OG}$ generates a class-specific image from a one-hot segmentation map $M_{sem} \\in \\mathbb{L}^{H \\times W \\times K}$ created by the corresponding object mask $M_c^q$ . $K$ is the number of the predefined foreground class set. Motivated by disentanglement learning [12, 20, 27], we utilize style information to control the appearance of results for multi-modal generation. Specifically, we sample an image from the training set with the same class label and extract its style code $W \\in \\mathbb{R}^{128}$ by a style encoder $E_s$ . Then we generate a style map $M_{style} \\in \\mathbb{R}^{H \\times W \\times 128}$ via broadcasting the style code according to $M_c^q$ , as illustrated in Figure 5(a). At this point, we have acquired a semantic map $M_{sem}$ and a style map $M_{style}$ . The next is how to decode them back to a style-controlled object image. To this end, we design a Semantic-Style Normalization Module (SSNM) to integrate the style and semantic information, as shown in Figure 5(b). We first inject the semantic information into the input feature maps $F \\in \\mathbb{R}^{H \\times W \\times C}$ :", + "bbox": [ + 75, + 628, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {s e m} = R e L U \\left(\\gamma_ {c} \\odot I N (C o n v (F)) \\oplus \\beta_ {c}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 434, + 890, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where two normalization parameters, $\\gamma_c \\in \\mathbb{R}^{H \\times W \\times C}$ and $\\beta_c \\in \\mathbb{R}^{H \\times W \\times C}$ are learned from $M_{sem}$ . Similarly, the style information is injected by:", + "bbox": [ + 498, + 460, + 890, + 507 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {O} = \\operatorname {R e L U} \\left(\\gamma_ {s} \\odot I N \\left(\\operatorname {C o n v} \\left(F _ {\\text {s e m}}\\right)\\right) \\oplus \\beta_ {s}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 534, + 890, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where two normalization parameters $\\gamma_s \\in \\mathbb{R}^{H \\times W \\times C}$ and $\\beta_s \\in \\mathbb{R}^{H \\times W \\times C}$ are learned from $M_{style}$ .", + "bbox": [ + 498, + 560, + 888, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During training, for each sample, we take the ground truth image $I^{gt}$ and a randomly sampled image $I^s$ as the style images to generate two results $R^{gt}$ and $R^s$ . We employ the following objective function to optimize $G_{OG}$ :", + "bbox": [ + 496, + 592, + 890, + 652 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {G O} = \\mathcal {L} _ {1} + \\lambda_ {P O} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} + \\mathcal {L} _ {\\mathrm {S C C}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 667, + 890, + 683 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\mathcal{L}_1$ is only applied to $R^{gt}$ . $\\mathcal{L}_{\\mathrm{P}}$ , $\\mathcal{L}_{GAN}$ , and $\\mathcal{L}_{\\mathrm{SCC}}$ are imposed on all results. We introduce Style Cycle-Consistency Loss $\\mathcal{L}_{\\mathrm{SCC}}$ to force the generator to produce style-consistent results with style images.", + "bbox": [ + 496, + 689, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S C C} = 1 - \\cos \\left(\\frac {E _ {S} ^ {\\prime} (R)}{\\| E _ {S} ^ {\\prime} (R) \\| _ {2}}, \\frac {E _ {s} ^ {\\prime} \\left(I ^ {s t y l e}\\right)}{\\| E _ {S} ^ {\\prime} \\left(I ^ {s t y l e}\\right) \\| _ {2}}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 772, + 890, + 813 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where $I^{style}$ is the style image and $R$ is the generated result. $E_s'(\\cdot)$ is a style encoder with the same structure as $E_s$ . $\\cos(\\cdot, \\cdot)$ represents the cosine similarity of two vectors.", + "bbox": [ + 496, + 824, + 888, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Previous image translation methods [12, 20] achieve multi-modal generation by adding Gaussian noise during", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1872", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/dbdb21abf6f497cb65f4964d6d93a2d17ca2df6315cb6860a508d4bf55257fbb.jpg", + "image_caption": [ + "Figure 6. Structure of Fusion Network. The red line indicates the skip connection." + ], + "image_footnote": [], + "bbox": [ + 106, + 90, + 449, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "inference. We find that noise leads to low-quality results and limited diversity. To solve this problem, we replace the noise with a style bank. Precisely, once training is done, we extract all style codes from the training set by the trained $E_{s}$ and save them for building a class-aware style bank. During inference, we randomly sample different style codes from the style bank to generate different results. It is worth mentioning that our approach does not increase any additional computational overhead compared to adding noise.", + "bbox": [ + 75, + 252, + 470, + 390 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Fusion Network", + "text_level": 1, + "bbox": [ + 76, + 398, + 236, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After generating all backgrounds and objects, we embed them into their original positions to obtain a composited image. However, this preliminary result may be discordant since each object is generated independently without accounting for context. We employ a fusion network $F$ to harmonize the objects with the surroundings, as shown in Figure 6. $F$ learns an offset value for each pixel via a skip connection [7,36] to produce the final results. We use Perceptual Loss and Adversarial Loss to optimize $F$ :", + "bbox": [ + 75, + 421, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {F} = \\lambda_ {P F} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 574, + 468, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 603, + 209, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We conduct experiments on two datasets, Cityscapes and ADE20K-Room, used in [28, 32]. Cityscapes [3] contains complex street scene images in German cities. ADE20K-Room is a subset of ADE20K [50] consisting of indoor scene images. We train and test our model at $256 \\times 256$ resolution.", + "bbox": [ + 75, + 628, + 468, + 717 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. We use free-form, extension, and outpainting masks following [28]. Similar to the previous work [22], we choose those frequently-appearing categories as the foreground class set, (car, person) for Cityscapes and (bed, chest, lamp, chair, table) for ADE20K-Room. All sub-networks are independently trained using ADAM optimizers [19] for both the generator and the discriminators with momentum $\\beta_{1} = 0.5$ and $\\beta_{2} = 0.999$ , and the learning rates for the generator and the discriminators are set to 0.0001 and 0.0004, respectively. For training $D_{BAP}$ , we randomly crop 4 square patches with the size ranging from $96 \\times 96$ to $160 \\times 160$ . We set balance coefficients:", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9d32725e08e59a925b7210909fdfd27a6a7782c77512c960b2580fa2a81536ad.jpg", + "image_caption": [ + "Figure 7. Visual comparisons with state-of-the-art methods. Our method is effective in generating texture-consistent backgrounds and photo-realistic objects." + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 897, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\lambda_{PB} = \\lambda_{PI} = \\lambda_{PO} = \\lambda_{PF} = 10$ and $\\lambda_{GAN}^{L} = 0.2$ . The proposed method is implemented with Pytorch 1.10 [34], and all experiments are performed on a single NVIDIA RTX 3090 GPU.", + "bbox": [ + 498, + 378, + 890, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare the proposed methods with the state-of-the-art semantic image editing methods, including HIM [10], SESAME [32], ASSET [23], SPMPGAN [28]. We also introduce two additional methods [40, 48] as baselines to investigate related work more widely. LGGAN [40] learns a map from segmentation maps to photo-realistic images using global image-level and class-specific generators. Co-Mod [48] demonstrates impressive results in semantic image generation and image inpainting. We change their input to be the same as our task.", + "bbox": [ + 498, + 440, + 890, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Qualitative evaluation", + "text_level": 1, + "bbox": [ + 500, + 602, + 705, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We demonstrate a visual comparison of the competing methods, as shown in Figure 7. We observe that the results produced by the proposed SIEDOB are visually better than existing methods in two aspects: (1) Our method can well handle dense objects overlapping each other, e.g., in the second and third rows. However, other methods produce distorted and inseparable results. (2) Our method generate texture-consistent content between edited regions and known regions both on background and objects, e.g., the red cars in the first row and the curtain in the fourth row. The performance improvement benefits from our disentangling generation strategy and carefully designed sub-networks.", + "bbox": [ + 496, + 625, + 890, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative evaluation", + "text_level": 1, + "bbox": [ + 500, + 816, + 718, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1 lists the quantitative results with three different mask types. Following previous works, we use three metrics: FID [8], LPIPS [47], and mean Intersection-over-Union (mIoU). FID is introduced to assess the fidelity of the", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1873", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9ae2ba8e214b30fd6c01af4fae69e24792b407cbb86a6367bf91e23bbcbf177f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
M.MethodCityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
F.LGGAN15.290.09458.6224.740.09727.68
Co-Mod15.880.09756.5027.370.11127.52
HIM15.580.09358.9928.640.13328.04
SESAME12.890.08258.8821.730.10127.50
ASSET13.670.09858.1230.630.12626.02
SPMPGAN11.900.08458.8018.830.09028.22
SIEDOB11.070.07759.4117.610.08929.72
E.LGGAN26.010.17558.3737.090.21327.91
Co-Mod29.270.18856.4438.610.23127.13
HIM25.200.18058.9140.690.23927.61
SESAME20.300.16859.0836.430.21127.62
ASSET21.990.18658.0138.170.26127.03
SPMPGAN19.460.16759.1032.920.19927.73
SIEDOB19.200.15959.6331.660.19129.52
O.LGGAN39.120.25458.7749.070.33427.69
Co-Mod50.290.26455.3951.450.32526.54
HIM36.270.25258.9954.510.33728.19
SESAME28.270.23758.7547.720.30527.40
ASSET30.600.24058.9157.280.33127.18
SPMPGAN27.630.23358.5341.520.28827.85
SIEDOB27.900.22159.3741.070.27528.94
", + "bbox": [ + 106, + 88, + 442, + 330 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/959b326a4d92691901f8dc707900ccf82d765bf65c3a1a7a285622e42a096bbd.jpg", + "image_caption": [ + "Figure 8. Visual results of addition objects." + ], + "image_footnote": [], + "bbox": [ + 80, + 412, + 475, + 555 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8d900b17b0ac95b34a0fce4b8935a77175922410e2e7535e07f0affa0a3d304.jpg", + "image_caption": [ + "Figure 9. Multi-modal generation results." + ], + "image_footnote": [], + "bbox": [ + 86, + 599, + 460, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "results by computing the Wasserstein-2 distance between the distributions of the synthesized and real images. LPIPS evaluates the similarity between the generated image and the ground truth in a pairwise manner. mIoU measures the alignment of semantic labels between the generated results and input segmentation maps. We use solid models to obtain segmentation maps: HRNet [41] for ADE20K-Room, and DRN-D-105 [44] for Cityscapes. Our method outperforms the other methods under different metrics and mask settings.", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d163ed507081c000ed4f0508e2d0a0715ae08f360eb04e206e2b8bacf14a900.jpg", + "image_caption": [ + "Figure 10. Out-of-distribution editing. Our method can add cars in the middle of the road or on the sidewalk, which do not exist in the training dataset." + ], + "image_footnote": [], + "bbox": [ + 532, + 89, + 859, + 146 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ff3c082e736ff4cf1c210f3adc90f9dbb7a21298233a1bf3c53b2a31c3076ae6.jpg", + "table_caption": [ + "Table 1. Quantitative comparison with other methods. M., F., E., and O. represent Mask Type, Free-Form Mask, Extension Mask, and Outpainting Mask, respectively. (↑: Higher is better; ↓: Lower is better)" + ], + "table_footnote": [], + "table_body": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑Div↑FID↓LPIPS↓mIoU↑Div↑
LGGAN7.690.02757.01-24.490.17130.05-
Co-Mod7.790.02956.290.003021.090.11830.630.0145
HIM6.920.02858.71-29.100.23230.58-
SESAME6.670.02458.79-18.010.11730.89-
ASSET6.740.02556.020.005227.680.20929.790.0337
SPMPGAN6.590.02158.60-17.210.11530.58-
SIEDOB6.290.02058.880.005516.320.11031.040.0362
", + "bbox": [ + 501, + 215, + 895, + 316 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/407572744bce5d40734ce8f0dd8c12afe16386270a4c9725c2adbd4a86770bf6.jpg", + "table_caption": [ + "Table 2. Quantitative results of object addition." + ], + "table_footnote": [], + "table_body": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o SASPM14.110.08559.4320.030.09129.02
w/o DBAP12.680.08159.4919.140.08329.21
Full model12.150.07959.5118.720.08129.30
", + "bbox": [ + 537, + 356, + 854, + 415 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Quantitative study on SASPM and ${D}_{BAP}$ .", + "bbox": [ + 542, + 426, + 846, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Addition Object", + "text_level": 1, + "bbox": [ + 500, + 467, + 660, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adding a new object to the given image is an essential ability of semantic image editing. The visual results are shown in Figure 8. In this experiment, we randomly select an instance of each test image and create a rectangular mask encircling the object. The proposed method can generate realistic objects with crisp edges. Adding an object to the edited area that does not exist originally should have diverse results. Some previous methods [23,48] have multimodal generation capabilities. We sample two results from all methods, as shown in Figure 9. Our method achieves a higher diversity than other models because the previous methods only exert a global influence on the generation process; in contrast, our model independently generates each object using different class-aware style codes. The quantitative results listed in Table 2 also indicate the superiority of our method. Here, the Diversity score (Div) is calculated as the average LPIPS distance between pairs of randomly sampled results for all test images, as also done in [25,49]. Moreover, our model can hallucinate images that do not exist in the dataset's distribution, as shown in Figure 10.", + "bbox": [ + 496, + 489, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 801, + 651, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of SASPM and Boundary-Anchored Patch Discriminator. We investigate the contributions of the proposed SASPM and $D_{BAP}$ to the generation of texture-consistent background. To exclude the interference of the foreground, we create mask maps that only include back", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1874", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1a254f04485e719ba8b864cb7c69f361655f77749411273125f566e839b0b3fd.jpg", + "image_caption": [ + "Figure 11. Ablation analysis on SASPM and $D_{BAP}$ for synthesizing texture-consistent backgrounds." + ], + "image_footnote": [], + "bbox": [ + 125, + 89, + 423, + 190 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/df025af410496ed61eff8d13d7b18c17ac5af7c29f79df022c640be048eaef31.jpg", + "image_caption": [ + "Figure 12. Ablation study of object generation." + ], + "image_footnote": [], + "bbox": [ + 89, + 253, + 455, + 328 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ground regions in this study. We remove all SASPM (\"w/o SASPM\") or $D_{BAP}$ (\"w/o $D_{BAP}$ ) from our model as two baselines. The visual results are shown in Figure 11 and prove that SASPM and $D_{BAP}$ can help the background generator effectively alleviate texture inconsistencies. Vanilla convolutional layers have limited receptive fields and no ability to locate where edited or known regions are. SASPM explicitly transfers features from known regions to edited regions with the same semantic labels across distant spatial distances. $D_{BAP}$ forces the generator to pay more attention to local textures on editing boundaries rather than just global images. Quantitative results are listed in Table 3.", + "bbox": [ + 75, + 385, + 468, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Style-Diversity Object Generator. To verify the benefit of $\\mathcal{L}_{\\mathrm{SCC}}$ and the style bank, we set up two baselines: (1) Dropping out $\\mathcal{L}_{\\mathrm{SCC}}$ (\"w/o $\\mathcal{L}_{\\mathrm{SCC}}$ ). (2) Replacing the style codes with noise vectors (\"w Noise\"). Figure 12 shows some visual results. If we drop out $\\mathcal{L}_{\\mathrm{SCC}}$ , the generated image's style may not be consistent with the style image. If we produce multi-modal results by injecting noise, it leads to a loss of fidelity and diversity. This is because Gaussian noise is semantics-free, while style code is category-specific and provides controllability. The quantitative results are listed in Table 4.", + "bbox": [ + 75, + 566, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Separate Generation. We remove the object generator and the fusion network but keep other components unchanged to obtain a baseline (w/o Separation) and increase its channel number for a fair comparison. Qualitative and quantitative comparisons can be found in Figure 13 and Table 5, respectively. In this experiment, we employ the masks used in object addition. The visual comparison shows that the separate generation paradigm significantly improves performance for objects with complicated surroundings.", + "bbox": [ + 75, + 734, + 467, + 883 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of Fusion Network. Fusion network can", + "bbox": [ + 76, + 885, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3b39a7e3ce2ae4e0e8154ab3f3935bce0533c29a7ad3d905c0d86dfe02ef87c1.jpg", + "image_caption": [ + "Figure 13. Visual analysis on disentangled generation and fusion network." + ], + "image_footnote": [], + "bbox": [ + 526, + 89, + 866, + 186 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ca55dcefe4907aa6ea81d666b1cb00d7883177abd1a6bd8bc390b77bc59afc5b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
classw/o LSCCw NoiseGOG
FID↓Div↑FID↓Div↑FID↓Div↑
car123.820.103173.570.090118.320.115
person238.100.079307.110.052219.200.098
bed227.180.303395.330.210239.780.372
chest192.120.217273.100.113149.290.229
lamp121.010.195153.940.129112.500.218
chair168.010.274207.350.177163.140.289
table211.390.141289.550.091201.320.143
", + "bbox": [ + 560, + 239, + 831, + 340 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/24ec05ff95d86cf16382f0fc559a7715c22833e79cc5ae1ee9c7d0fd8a0c8a70.jpg", + "table_caption": [ + "Table 4. Quantitative results of different objects." + ], + "table_footnote": [], + "table_body": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o Separation6.780.02956.4321.970.18030.32
w/o Fusion6.730.02758.6819.190.13130.80
w/o Skip6.410.02258.7617.890.11830.96
Full model6.290.02058.8816.320.11031.04
", + "bbox": [ + 532, + 378, + 859, + 450 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Quantitative studies of separate generation paradigm and fusion network.", + "bbox": [ + 498, + 460, + 890, + 487 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "eliminate abrupt boundaries between generated objects and backgrounds. Removing the fusion network ( $w/o$ Fusion) or not using the skip connection ( $w/o$ Skip) will degrade the performance, which are qualitatively and quantitatively demonstrated in Figure 13 and Table 5.", + "bbox": [ + 496, + 513, + 890, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Limitations", + "text_level": 1, + "bbox": [ + 500, + 603, + 756, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes a novel paradigm for semantic image editing, named SIEDOB. Its core idea is that since the characteristics of foreground objects and backgrounds are dramatically different, we design a heterogeneous model to handle them separately. To this end, we present SASPM and Boundary-Anchored Patch Discriminator to facilitate the generation of texture-consistent backgrounds and employ a Style-Diversity Object Generator to produce high-quality and diverse objects. Extensive experimental results demonstrate the superiority of our method. However, our method has some limitations. Some foreground categories are very rare in the dataset, so we cannot obtain enough data for training. In addition, object generation is hard to produce satisfactory results when an object is with an extreme pose or large-scale occlusion.", + "bbox": [ + 496, + 628, + 890, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work is supported by State Grid Corporation of China (Grant No. 5500-202011091A-0-0-00).", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1875", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Deblina Bhattacharjee, Seungryong Kim, Guillaume Vizier, and Mathieu Salzmann. Dunit: Detection-based unsupervised image-to-image translation. 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Sean: Image synthesis with semantic region-adaptive nor" + ], + "bbox": [ + 501, + 92, + 890, + 901 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "1877", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "malization. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5104-5113, 2020. 2", + "bbox": [ + 109, + 90, + 470, + 133 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1878", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/a369b37c-8e06-4d08-a268-de9d54816ab4_model.json b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/a369b37c-8e06-4d08-a268-de9d54816ab4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a1e3b58b2f386e669eaede2f06634f5550de038e --- /dev/null +++ b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/a369b37c-8e06-4d08-a268-de9d54816ab4_model.json @@ -0,0 +1,2400 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.1, + 0.131, + 0.872, + 0.154 + ], + "angle": 0, + "content": "SIEDOB: Semantic Image Editing by Disentangling Object and Background" + }, + { + "type": "text", + "bbox": [ + 0.183, + 0.18, + 0.787, + 0.2 + ], + "angle": 0, + "content": "Wuyang Luo1 Su Yang1* Xinjian Zhang1 Weishan Zhang2" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.201, + 0.817, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University \\(\\{\\mathrm{wyluol8, suyang}\\} @\\)fudan.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.252, + 0.236, + 0.715, + 0.251 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Computer Science and Technology, China University of Petroleum" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.743 + ], + "angle": 0, + "content": "Semantic image editing provides users with a flexible tool to modify a given image guided by a corresponding segmentation map. In this task, the features of the foreground objects and the backgrounds are quite different. However, all previous methods handle backgrounds and objects as a whole using a monolithic model. Consequently, they remain limited in processing content-rich images and suffer from generating unrealistic objects and texture-inconsistent backgrounds. To address this issue, we propose a novel paradigm, Semantic Image Editing by Disentangling Object and Background (SIEDOB), the core idea of which is to explicitly leverages several heterogeneous subnetworks for objects and backgrounds. First, SIEDOB disassembles the edited input into background regions and instance-level objects. Then, we feed them into the dedicated generators. Finally, all synthesized parts are embedded in their original locations and utilize a fusion network to obtain a harmonized result. Moreover, to produce high-quality edited images, we propose some innovative designs, including Semantic-Aware Self-Propagation Module, Boundary-Anchored Patch Discriminator, and Style-Diversity Object Generator; and integrate them into SIEDOB. We conduct extensive experiments on Cityscapes and ADE20K-Room datasets and exhibit that our method remarkably outperforms the baselines, especially in synthesizing realistic and diverse objects and texture-consistent backgrounds. Code is available at https://github.com/WuyangLuo/SIEDOB." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.773, + 0.21, + 0.789 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Semantic image editing has recently gained significant traction due to its diverse applications, including adding, altering, or removing objects and controllably inpainting, outpainting, or repainting images. Existing methods have made impressive progress benefiting from Generative Adversar" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.287, + 0.578, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.349, + 0.555, + 0.358 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.58, + 0.288, + 0.644, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.349, + 0.641, + 0.358 + ], + "angle": 0, + "content": "SESAME" + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.288, + 0.731, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.349, + 0.714, + 0.358 + ], + "angle": 0, + "content": "ASSET" + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.288, + 0.817, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.751, + 0.349, + 0.802, + 0.358 + ], + "angle": 0, + "content": "SPMPGAN" + }, + { + "type": "image", + "bbox": [ + 0.818, + 0.288, + 0.897, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.836, + 0.349, + 0.876, + 0.358 + ], + "angle": 0, + "content": "SIEDOB" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.372, + 0.895, + 0.43 + ], + "angle": 0, + "content": "Figure 1. Existing methods struggle to deal with the compound of backgrounds and several overlapping objects in a complex scene. They generate distorted objects and texturally inconsistent backgrounds. The proposed method can cope well with this input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.893, + 0.55 + ], + "angle": 0, + "content": "ial Networks (GAN) [5, 14] and have demonstrated promising results in relatively content-simple scenes, such as landscapes. However, they still suffer from inferior results for content-rich images with multiple discrepant objects, such as cityscapes or indoor rooms. This paper aims to improve editing performance in complex real-world scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.895, + 0.807 + ], + "angle": 0, + "content": "When image editing experts deal with a complex task, they decompose the input image into multiple independent and disparate elements and handle them with different skills. For example, when editing a photo with a congested road, they process the cars and pedestrians individually and then fill in the background. Inspired by this spirit, we propose a heterogeneous editing model, which mimics the experience of human experts and explicitly splits the compound content into two distinct components: Backgrounds and objects. The background has no regular shape and may span a large area. More importantly, the re-generated background's texture and the existing area must be consistent. Foregrounds objects are class-specific and appear anywhere with various scales. Due to the significant differences between the two components, it is necessary to disentangle them from the input and process them with different networks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Several recent works [23, 28, 32] have been dedicated to this task. SESAME [32] proposes a new pair of generator and discriminator based on the cGAN framework [31], which generates edited content through a single-shot inference. ASSET [23] builds a transformer-based architecture with a sparse attention mechanism and synthesizes" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.234, + 0.9 + ], + "angle": 0, + "content": "Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1868" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "edited regions relying on a codebook generated by VQ-GAN [4]. SPMPGAN [28] proposes a coarse-to-fine generator equipped with style-preserved modulation layers to retain style consistency between edited regions and context. These methods effectively enhance the ability of a monolithic model to handle the entire input. However, they deal with backgrounds and objects equally using the same generator, which causes them to produce inferior results. Figure 1 demonstrates an example. To tackle this limitation, we present a novel framework, Semantic Image Editing by Disentangling Object and Background (SIEDOB), to generate backgrounds and foreground objects separately, which can achieve two goals: Synthesizing texture-consistent backgrounds and generating photorealistic and diverse objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.426 + ], + "angle": 0, + "content": "SIEDOB first disassembles the edited image into background regions and instance-level objects, then employs different generators to synthesize the corresponding content, and finally aggregates generated objects with backgrounds via a fusion network. In this way, we decouple our task into several more feasible subtasks and handle different components using dedicated sub-models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.473, + 0.594 + ], + "angle": 0, + "content": "Generating texture-consistent backgrounds with known context is not trivial since backgrounds may cross a sizeable spatial area in an image and have no regular shape. We propose a pair of boosted generator and discriminator to address this problem. Specifically, we propose Semantic-Aware Self-Propagation Module (SASPM) to help the generator efficiently transfer the semantic-wise features of known regions to generated regions. Moreover, to further enhance texture consistency, we design a Boundary-Anchored Patch Discriminator to force the generator to pay more attention to local textures of editing fringe." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.473, + 0.761 + ], + "angle": 0, + "content": "In our task, depending on the scenario, the edited object may be requested to be inpainted or generated. If an object is partially visible, it undergoes a lightweight inpainting network. Otherwise, we employ a Style-Diversity Object Generator to obtain multi-modal results based on a style bank. After generating the backgrounds and all objects, we re-integrate them into a whole. However, the separate generation may lead to sudden boundaries and dissonance between objects and surroundings. To tackle this problem, we utilize a simple fusion network that predicts the residual value for each pixel to harmonize outputs." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.762, + 0.46, + 0.777 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.795, + 0.468, + 0.84 + ], + "angle": 0, + "content": "- We propose a new solution for semantic image editing, named SIEDOB, which can handle complex scenes by decoupling the generation of backgrounds and objects." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- We propose Semantic-Aware Self-Propagation Module and Boundary-Anchored Patch Discriminator to facilitate texture-consistent background generation." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "- We propose a Style-Diversity Object Generator that can generate diverse and realistic object images from masks." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.147, + 0.892, + 0.192 + ], + "angle": 0, + "content": "- Extensive experiments on two benchmarks indicate that our method can generate texture-consistent results and deal with crowded objects well." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.217, + 0.651, + 0.233 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.242, + 0.722, + 0.259 + ], + "angle": 0, + "content": "2.1. Semantic Image Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.265, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Semantic image editing refers to modifying a given image by manipulating a corresponding segmentation map and keeping the context coherent. This approach provides powerful editing capabilities, such as adding and removing objects, modifying shapes, and re-painting backgrounds. Compared to several related tasks, including semantic image synthesis [14, 33, 40, 42, 51] and image inpainting [13, 30, 45, 46, 48], semantic image editing has not been fully exploited due to its difficulty in generating realistic objects and texture-consistent backgrounds simultaneously. A few recent works are devoted to semantic image editing [10, 23, 28, 32]. HIM [10] is an early exploration that only operates on a single object using a two-stage network. SESAME [32] introduces a new pair of generators and discriminators to improve the quality of the generated results. Moreover, SESAME adopts a more flexible workflow that can respond to various image editing requirements of users. ASSET [23] proposes a novel transformer-based approach modeling long-range dependencies, enabling high-resolution image editing. SPMPGAN [28] presents a stylepreserved modulation technique and builds a progressive architecture that solves the style inconsistency problem in semantic image editing. These methods all consider semantic image editing as a global generation problem. Thus, they use a single model to process all elements of the edited image equally. In this work, we propose a decoupled framework to handle objects and backgrounds separately using heterogeneous generators, demonstrating more promising results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.892, + 0.728 + ], + "angle": 0, + "content": "2.2. Image Synthesis via Heterogeneous Generators" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.903 + ], + "angle": 0, + "content": "For a wide variety of image generation tasks, most approaches impose monolithic generators on the entire image, including unsupervised image generation [17, 18, 35], image-to-image translation [29, 33, 42, 51], image inpainting [24, 45, 46], and image editing [15, 26]. They share the same network structure and weights to generate all the content without specialized submodels for different semantic regions or classes. Other methods use different architectures or weights to generate different image elements to improve generation quality for different components. For example, they employ multiple local branches specialized" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1869" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.117, + 0.094, + 0.852, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.29, + 0.895, + 0.335 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed method. To reduce the complexity of modeling the entire edited region, we use a heterogeneous model to synthesize foreground objects and backgrounds separately, which contains three components: (1) Background generation, (2) object generation, (3) fusion network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.473, + 0.587 + ], + "angle": 0, + "content": "for different parts [6, 9, 11, 21], decoupling content and style [12, 20, 27], generating foreground and a single foreground object separately [39, 43], enhancing local generation [1, 37], or having separate modules for different semantic categories [22, 40]. However, these methods are developed for pure image generation or translation tasks where their input is noises, categories, segmentation maps, or full images. Therefore, they only need to synthesize simple but visually plausible results to fool the discriminator. Semantic image editing is a more challenging task, and its difficulty lies in keeping coherence between edited and known regions. In this paper, we propose a heterogeneous framework that utilizes different sub-models for foreground objects and backgrounds to improve their generation quality concurrently." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.603, + 0.251, + 0.62 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our goal is to edit a given image \\( I \\in \\mathbb{R}^{H \\times W \\times 3} \\) guided by a user-provided segmentation map \\( S \\in \\mathbb{L}^{H \\times W \\times L} \\) within an edited region defined by a mask map \\( M \\in \\mathbb{B}^{H \\times W \\times 1} \\) whose value is 0 in the non-edited region and 1 in the edited region. Here \\( H, W, \\) and \\( L \\) denote the height, width, and number of semantic categories, respectively. The edited region of \\( I \\) is erased as input \\( I_e = I \\times (1 - M) \\). We create a background mask \\( M_B \\) and all instance-level object masks \\( \\{M_c^q\\} \\) in the edited region based on the segmentation map. Here, \\( c \\in \\mathcal{C}, \\mathcal{C} \\) is a pre-defined set of considered foreground categories, and \\( M_c^q \\) is the \\( q \\)-th instance that falls into the category \\( c \\). The background mask \\( M_B \\) is composed of the remaining pixels. Thus, we can disassemble the input image \\( I_e \\) to the background and objects according to \\( M_B \\) and \\( \\{M_c^q\\} \\). Then we generate the background and objects separately using the respective generators. Finally, we integrate all generated content via a fusion network. The workflow is depicted in Figure 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.358, + 0.724, + 0.374 + ], + "angle": 0, + "content": "3.1. Background Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.625 + ], + "angle": 0, + "content": "For image editing, the background usually needs to be partially generated to fill the space, such as sky or ground. Therefore, generating style-consistent texture patterns in edited regions is critical and challenging since the generated background and the known region coexist. In addition, an image's background may be across a distant spatial distance and have no regular shape. Efficiently and accurately transferring feature styles from known to edited regions is vital for generating texture-consistent results. To this end, we propose a Semantic-Aware Self-Propagation Module (SASPM), which explicitly extracts semantic-wise feature codes from feature maps and propagates them to the corresponding regions at the same layer. Furthermore, we employ a Boundary-Anchored Patch Discriminator to enforce the generator to focus on local textures at the editing boundary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.732 + ], + "angle": 0, + "content": "The proposed background generator \\( G_B \\) is shown in 3(c). We feed the disassembled background region into \\( G_B \\) as the input: \\( I_B = I_e \\times M_B \\). \\( G_B \\) follows an encoder-decoder structure. The encoder is composed of several successive GatedConv layers [46] with stride two, and the decoder contains corresponding GatedConv layers with upsampling and several SASPM." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.733, + 0.866, + 0.749 + ], + "angle": 0, + "content": "Semantic-Aware Self-Propagation Modules (SASPM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SASPM aims at propagating features of known regions to edited regions in a semantic-aware manner. Taking the sky area as an example shown in Figure 3(a)(b), a SASPM is divided into two steps. First, we extract the semantic-aware feature code by computing the average of the known sky area. Then, the feature code is broadcast into the entire sky area according to the corresponding semantic mask. SASPM can transfer the feature codes of each semantic label at the same feature level without the constraint of the receptive field. Formally, let \\( F \\in \\mathbb{R}^{H \\times W \\times C} \\) denote a feature" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1870" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.091, + 0.222, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.15, + 0.168, + 0.195, + 0.174 + ], + "angle": 0, + "content": "Edited Image" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.091, + 0.326, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.167, + 0.309, + 0.174 + ], + "angle": 0, + "content": "Known Sky Region" + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.091, + 0.429, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.35, + 0.167, + 0.411, + 0.174 + ], + "angle": 0, + "content": "Entire Sky Region" + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.176, + 0.424, + 0.186 + ], + "angle": 0, + "content": "(a) A semantic category (sky) spans the known region and the edited region" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.188, + 0.437, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.298, + 0.445, + 0.411 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.425, + 0.471, + 0.522 + ], + "angle": 0, + "content": "Figure 3. (a) A background category, such as sky, may span known and edited regions. We want to transfer the features from the known region to the generated region in a semantic-aware fashion. (b) The principle of SASPM. We extract the feature code for each background category from the known region and then propagate it to the entire region. (c) The architecture of our background generator." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.469, + 0.668 + ], + "angle": 0, + "content": "map in front of a SASPM. \\(H\\), \\(W\\) are the spatial dimension and \\(C\\) is the number of channels. Let \\(U \\in \\mathbb{R}^{L \\times C}\\) represent \\(L\\) feature codes extracted from the known region, and the feature codes of non-background classes are set to zero. We generate a code map \\(P\\) based on the segmentation map \\(S \\in \\mathbb{L}^{H \\times W \\times L}\\) through a matrix multiplication to spatially broadcast the feature codes into the corresponding semantic region:" + }, + { + "type": "equation", + "bbox": [ + 0.232, + 0.682, + 0.469, + 0.697 + ], + "angle": 0, + "content": "\\[\nP = S \\otimes U \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.469, + 0.791 + ], + "angle": 0, + "content": "Thus, \\(P \\in \\mathbb{R}^{H \\times W \\times C}\\) is restored to the spatial dimension filled with the category-specific feature codes. Finally, we propagate \\(P\\) into the original \\(F\\) using a modulation operation following SPADE [33]. Specifically, we learn two parameters \\(\\gamma_{P} \\in \\mathbb{R}^{H \\times W \\times C}\\) and \\(\\beta_{P} \\in \\mathbb{R}^{H \\times W \\times C}\\) from \\(P\\) to modulate \\(F\\):" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.816, + 0.469, + 0.833 + ], + "angle": 0, + "content": "\\[\nF _ {P} = \\operatorname {R e L U} \\left(\\gamma_ {P} \\odot I N (\\operatorname {C o n v} (F)) \\oplus \\beta_ {P}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Where \\(Conv(\\cdot), IN(\\cdot)\\), and \\(ReLU(\\cdot)\\) denote Convolutional Layer, Instance Normalization, and ReLU activation function, respectively. \\(\\odot\\) and \\(\\oplus\\) are element-wise multiplication and addition." + }, + { + "type": "image", + "bbox": [ + 0.53, + 0.093, + 0.858, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.285, + 0.892, + 0.341 + ], + "angle": 0, + "content": "Figure 4. Boundary-Anchored Patch Discriminator \\( D_{BAP} \\) takes in four real image patches or fake image patches of random size. All patches are centered on the boundary of the edited region enclosed by the red line." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.37, + 0.785, + 0.384 + ], + "angle": 0, + "content": "Boundary-Anchored Patch Discriminator" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.581 + ], + "angle": 0, + "content": "We employ two discriminators for our background generator: (1) A global discriminator used by previous works [28]; (2) a novel Boundary-Anchored Patch Discriminator \\(D_{BAP}\\). We introduce \\(D_{BAP}\\) to enforce the generator to pay attention to local texture across the fringe of the edited area. We expect \\(D_{BAP}\\) can capture known and generated textures simultaneously to facilitate texture-consistent results. To this end, we randomly select several central points anchored on the boundary of the edited region to crop patches from real or generated images, as shown in Figure 4. Thus, the fake patches contain both real and fake textures, so \\(D_{BAP}\\) can distinguish between true and false through texture consistency." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.891, + 0.629 + ], + "angle": 0, + "content": "The training objective of \\( G_{B} \\) is comprised of L1 Distance Loss \\( \\mathcal{L}_1 \\), Perceptual Loss \\( \\mathcal{L}_{\\mathrm{P}} \\) [16], Global Adversarial Loss \\( \\mathcal{L}_{GAN}^{G} \\), and Local Patch Adversarial Loss \\( \\mathcal{L}_{GAN}^{L} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.654, + 0.891, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {B} = \\mathcal {L} _ {1} + \\lambda_ {P B} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} ^ {G} + \\lambda_ {G A N} ^ {L} \\mathcal {L} _ {G A N} ^ {L} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.685, + 0.891, + 0.776 + ], + "angle": 0, + "content": "Where \\(\\mathcal{L}_1\\) and \\(\\mathcal{L}_{\\mathrm{P}}\\) force the generated results to be closer to the ground truth in RGB space and VGG space [38]. \\(\\mathcal{L}_{GAN}^{G}\\) and \\(\\mathcal{L}_{GAN}^{L}\\) are applied to global images and local patches, respectively. All adversarial losses in this work are associated with a SNPatchGAN Discriminator [46] using the hinge version [2]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.681, + 0.803 + ], + "angle": 0, + "content": "3.2. Object Generation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our task involves dealing with two scenarios: Inpainting or generating an object—the former aims at completing an object based on its visible part. The latter synthesizes an inexistent object from its mask with an arbitrary appearance. Unlike handling all objects at once, cropping each edited object and independently generating them allows" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1871" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.09, + 0.468, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.463, + 0.189, + 0.55, + 0.198 + ], + "angle": 0, + "content": "(a) Extract Style Map" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.098, + 0.842, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.13, + 0.2, + 0.482, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.2, + 0.837, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.339, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Figure 5. (a) How to extract style maps? During training, we extract their style codes from ground truth images or randomly sampled images and then generate style maps by broadcasting. During inference, we sample a class-specific style code directly from the style bank. (b) The structure of Semantic-Style Normalization Module (SSNM). (c) We build a Style-Diversity Object Generator equipped with SSNM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.47, + 0.59 + ], + "angle": 0, + "content": "us to use aligned input images with the same size, which is beneficial for generating high-quality results. Specifically, we crop all objects \\(\\{Crop(I_e)_c^q\\}\\) from the edited region based on object masks \\(\\{M_c^q\\}\\). We leverage a two-way model to handle the different scenarios. One way is a lightweight inpainting network \\(G_{OI}\\) to complete objects. \\(G_{OI}\\) is a UNet-like [36] network and its training objective is: \\(\\mathcal{L}_{GI} = \\mathcal{L}_1 + \\lambda_{PI}\\mathcal{L}_{\\mathrm{P}} + \\mathcal{L}_{GAN}\\). \\(\\mathcal{L}_1\\), \\(\\mathcal{L}_{\\mathrm{P}}\\), and \\(\\mathcal{L}_{GAN}\\) are the same as the terms in Equation 6. The other way is the proposed Style-Diversity Object Generator \\(G_{OG}\\) for the multi-modal generation. Note that all categories of objects share \\(G_{OI}\\) and \\(G_{OG}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.3, + 0.617 + ], + "angle": 0, + "content": "Style-Diversity Object Generator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.9 + ], + "angle": 0, + "content": "\\(G_{OG}\\) generates a class-specific image from a one-hot segmentation map \\(M_{sem} \\in \\mathbb{L}^{H \\times W \\times K}\\) created by the corresponding object mask \\(M_c^q\\). \\(K\\) is the number of the predefined foreground class set. Motivated by disentanglement learning [12, 20, 27], we utilize style information to control the appearance of results for multi-modal generation. Specifically, we sample an image from the training set with the same class label and extract its style code \\(W \\in \\mathbb{R}^{128}\\) by a style encoder \\(E_s\\). Then we generate a style map \\(M_{style} \\in \\mathbb{R}^{H \\times W \\times 128}\\) via broadcasting the style code according to \\(M_c^q\\), as illustrated in Figure 5(a). At this point, we have acquired a semantic map \\(M_{sem}\\) and a style map \\(M_{style}\\). The next is how to decode them back to a style-controlled object image. To this end, we design a Semantic-Style Normalization Module (SSNM) to integrate the style and semantic information, as shown in Figure 5(b). We first inject the semantic information into the input feature maps \\(F \\in \\mathbb{R}^{H \\times W \\times C}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.435, + 0.891, + 0.452 + ], + "angle": 0, + "content": "\\[\nF _ {s e m} = R e L U \\left(\\gamma_ {c} \\odot I N (C o n v (F)) \\oplus \\beta_ {c}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.891, + 0.508 + ], + "angle": 0, + "content": "Where two normalization parameters, \\(\\gamma_c \\in \\mathbb{R}^{H \\times W \\times C}\\) and \\(\\beta_c \\in \\mathbb{R}^{H \\times W \\times C}\\) are learned from \\(M_{sem}\\). Similarly, the style information is injected by:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.535, + 0.891, + 0.551 + ], + "angle": 0, + "content": "\\[\nF _ {O} = \\operatorname {R e L U} \\left(\\gamma_ {s} \\odot I N \\left(\\operatorname {C o n v} \\left(F _ {\\text {s e m}}\\right)\\right) \\oplus \\beta_ {s}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.561, + 0.89, + 0.592 + ], + "angle": 0, + "content": "Where two normalization parameters \\(\\gamma_s \\in \\mathbb{R}^{H \\times W \\times C}\\) and \\(\\beta_s \\in \\mathbb{R}^{H \\times W \\times C}\\) are learned from \\(M_{style}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.891, + 0.654 + ], + "angle": 0, + "content": "During training, for each sample, we take the ground truth image \\( I^{gt} \\) and a randomly sampled image \\( I^s \\) as the style images to generate two results \\( R^{gt} \\) and \\( R^s \\). We employ the following objective function to optimize \\( G_{OG} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.668, + 0.891, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {G O} = \\mathcal {L} _ {1} + \\lambda_ {P O} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} + \\mathcal {L} _ {\\mathrm {S C C}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.891, + 0.751 + ], + "angle": 0, + "content": "Here, \\(\\mathcal{L}_1\\) is only applied to \\(R^{gt}\\). \\(\\mathcal{L}_{\\mathrm{P}}\\), \\(\\mathcal{L}_{GAN}\\), and \\(\\mathcal{L}_{\\mathrm{SCC}}\\) are imposed on all results. We introduce Style Cycle-Consistency Loss \\(\\mathcal{L}_{\\mathrm{SCC}}\\) to force the generator to produce style-consistent results with style images." + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.773, + 0.891, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S C C} = 1 - \\cos \\left(\\frac {E _ {S} ^ {\\prime} (R)}{\\| E _ {S} ^ {\\prime} (R) \\| _ {2}}, \\frac {E _ {s} ^ {\\prime} \\left(I ^ {s t y l e}\\right)}{\\| E _ {S} ^ {\\prime} \\left(I ^ {s t y l e}\\right) \\| _ {2}}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.89, + 0.87 + ], + "angle": 0, + "content": "Where \\(I^{style}\\) is the style image and \\(R\\) is the generated result. \\(E_s'(\\cdot)\\) is a style encoder with the same structure as \\(E_s\\). \\(\\cos(\\cdot, \\cdot)\\) represents the cosine similarity of two vectors." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Previous image translation methods [12, 20] achieve multi-modal generation by adding Gaussian noise during" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1872" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.092, + 0.45, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.198, + 0.47, + 0.227 + ], + "angle": 0, + "content": "Figure 6. Structure of Fusion Network. The red line indicates the skip connection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.471, + 0.391 + ], + "angle": 0, + "content": "inference. We find that noise leads to low-quality results and limited diversity. To solve this problem, we replace the noise with a style bank. Precisely, once training is done, we extract all style codes from the training set by the trained \\( E_{s} \\) and save them for building a class-aware style bank. During inference, we randomly sample different style codes from the style bank to generate different results. It is worth mentioning that our approach does not increase any additional computational overhead compared to adding noise." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.238, + 0.415 + ], + "angle": 0, + "content": "3.3. Fusion Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.47, + 0.558 + ], + "angle": 0, + "content": "After generating all backgrounds and objects, we embed them into their original positions to obtain a composited image. However, this preliminary result may be discordant since each object is generated independently without accounting for context. We employ a fusion network \\( F \\) to harmonize the objects with the surroundings, as shown in Figure 6. \\( F \\) learns an offset value for each pixel via a skip connection [7,36] to produce the final results. We use Perceptual Loss and Adversarial Loss to optimize \\( F \\):" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.575, + 0.469, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {F} = \\lambda_ {P F} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.21, + 0.621 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.718 + ], + "angle": 0, + "content": "Datasets. We conduct experiments on two datasets, Cityscapes and ADE20K-Room, used in [28, 32]. Cityscapes [3] contains complex street scene images in German cities. ADE20K-Room is a subset of ADE20K [50] consisting of indoor scene images. We train and test our model at \\(256 \\times 256\\) resolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. We use free-form, extension, and outpainting masks following [28]. Similar to the previous work [22], we choose those frequently-appearing categories as the foreground class set, (car, person) for Cityscapes and (bed, chest, lamp, chair, table) for ADE20K-Room. All sub-networks are independently trained using ADAM optimizers [19] for both the generator and the discriminators with momentum \\(\\beta_{1} = 0.5\\) and \\(\\beta_{2} = 0.999\\), and the learning rates for the generator and the discriminators are set to 0.0001 and 0.0004, respectively. For training \\(D_{BAP}\\), we randomly crop 4 square patches with the size ranging from \\(96 \\times 96\\) to \\(160 \\times 160\\). We set balance coefficients:" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.898, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.312, + 0.892, + 0.355 + ], + "angle": 0, + "content": "Figure 7. Visual comparisons with state-of-the-art methods. Our method is effective in generating texture-consistent backgrounds and photo-realistic objects." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.38, + 0.892, + 0.44 + ], + "angle": 0, + "content": "\\(\\lambda_{PB} = \\lambda_{PI} = \\lambda_{PO} = \\lambda_{PF} = 10\\) and \\(\\lambda_{GAN}^{L} = 0.2\\). The proposed method is implemented with Pytorch 1.10 [34], and all experiments are performed on a single NVIDIA RTX 3090 GPU." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.441, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Baselines. We compare the proposed methods with the state-of-the-art semantic image editing methods, including HIM [10], SESAME [32], ASSET [23], SPMPGAN [28]. We also introduce two additional methods [40, 48] as baselines to investigate related work more widely. LGGAN [40] learns a map from segmentation maps to photo-realistic images using global image-level and class-specific generators. Co-Mod [48] demonstrates impressive results in semantic image generation and image inpainting. We change their input to be the same as our task." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.706, + 0.619 + ], + "angle": 0, + "content": "4.1. Qualitative evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.807 + ], + "angle": 0, + "content": "We demonstrate a visual comparison of the competing methods, as shown in Figure 7. We observe that the results produced by the proposed SIEDOB are visually better than existing methods in two aspects: (1) Our method can well handle dense objects overlapping each other, e.g., in the second and third rows. However, other methods produce distorted and inseparable results. (2) Our method generate texture-consistent content between edited regions and known regions both on background and objects, e.g., the red cars in the first row and the curtain in the fourth row. The performance improvement benefits from our disentangling generation strategy and carefully designed sub-networks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.719, + 0.833 + ], + "angle": 0, + "content": "4.2. Quantitative evaluation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Table 1 lists the quantitative results with three different mask types. Following previous works, we use three metrics: FID [8], LPIPS [47], and mean Intersection-over-Union (mIoU). FID is introduced to assess the fidelity of the" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1873" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.107, + 0.089, + 0.444, + 0.332 + ], + "angle": 0, + "content": "
M.MethodCityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
F.LGGAN15.290.09458.6224.740.09727.68
Co-Mod15.880.09756.5027.370.11127.52
HIM15.580.09358.9928.640.13328.04
SESAME12.890.08258.8821.730.10127.50
ASSET13.670.09858.1230.630.12626.02
SPMPGAN11.900.08458.8018.830.09028.22
SIEDOB11.070.07759.4117.610.08929.72
E.LGGAN26.010.17558.3737.090.21327.91
Co-Mod29.270.18856.4438.610.23127.13
HIM25.200.18058.9140.690.23927.61
SESAME20.300.16859.0836.430.21127.62
ASSET21.990.18658.0138.170.26127.03
SPMPGAN19.460.16759.1032.920.19927.73
SIEDOB19.200.15959.6331.660.19129.52
O.LGGAN39.120.25458.7749.070.33427.69
Co-Mod50.290.26455.3951.450.32526.54
HIM36.270.25258.9954.510.33728.19
SESAME28.270.23758.7547.720.30527.40
ASSET30.600.24058.9157.280.33127.18
SPMPGAN27.630.23358.5341.520.28827.85
SIEDOB27.900.22159.3741.070.27528.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.341, + 0.472, + 0.397 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison with other methods. M., F., E., and O. represent Mask Type, Free-Form Mask, Extension Mask, and Outpainting Mask, respectively. (↑: Higher is better; ↓: Lower is better)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.413, + 0.477, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.568, + 0.402, + 0.582 + ], + "angle": 0, + "content": "Figure 8. Visual results of addition objects." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.6, + 0.462, + 0.696 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.708, + 0.396, + 0.722 + ], + "angle": 0, + "content": "Figure 9. Multi-modal generation results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "results by computing the Wasserstein-2 distance between the distributions of the synthesized and real images. LPIPS evaluates the similarity between the generated image and the ground truth in a pairwise manner. mIoU measures the alignment of semantic labels between the generated results and input segmentation maps. We use solid models to obtain segmentation maps: HRNet [41] for ADE20K-Room, and DRN-D-105 [44] for Cityscapes. Our method outperforms the other methods under different metrics and mask settings." + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.09, + 0.861, + 0.147 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.16, + 0.892, + 0.203 + ], + "angle": 0, + "content": "Figure 10. Out-of-distribution editing. Our method can add cars in the middle of the road or on the sidewalk, which do not exist in the training dataset." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.216, + 0.897, + 0.318 + ], + "angle": 0, + "content": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑Div↑FID↓LPIPS↓mIoU↑Div↑
LGGAN7.690.02757.01-24.490.17130.05-
Co-Mod7.790.02956.290.003021.090.11830.630.0145
HIM6.920.02858.71-29.100.23230.58-
SESAME6.670.02458.79-18.010.11730.89-
ASSET6.740.02556.020.005227.680.20929.790.0337
SPMPGAN6.590.02158.60-17.210.11530.58-
SIEDOB6.290.02058.880.005516.320.11031.040.0362
" + }, + { + "type": "table_caption", + "bbox": [ + 0.555, + 0.33, + 0.835, + 0.343 + ], + "angle": 0, + "content": "Table 2. Quantitative results of object addition." + }, + { + "type": "table", + "bbox": [ + 0.539, + 0.357, + 0.855, + 0.416 + ], + "angle": 0, + "content": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o SASPM14.110.08559.4320.030.09129.02
w/o DBAP12.680.08159.4919.140.08329.21
Full model12.150.07959.5118.720.08129.30
" + }, + { + "type": "table_caption", + "bbox": [ + 0.544, + 0.427, + 0.847, + 0.44 + ], + "angle": 0, + "content": "Table 3. Quantitative study on SASPM and \\( {D}_{BAP} \\) ." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.661, + 0.484 + ], + "angle": 0, + "content": "4.3. Addition Object" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.491, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Adding a new object to the given image is an essential ability of semantic image editing. The visual results are shown in Figure 8. In this experiment, we randomly select an instance of each test image and create a rectangular mask encircling the object. The proposed method can generate realistic objects with crisp edges. Adding an object to the edited area that does not exist originally should have diverse results. Some previous methods [23,48] have multimodal generation capabilities. We sample two results from all methods, as shown in Figure 9. Our method achieves a higher diversity than other models because the previous methods only exert a global influence on the generation process; in contrast, our model independently generates each object using different class-aware style codes. The quantitative results listed in Table 2 also indicate the superiority of our method. Here, the Diversity score (Div) is calculated as the average LPIPS distance between pairs of randomly sampled results for all test images, as also done in [25,49]. Moreover, our model can hallucinate images that do not exist in the dataset's distribution, as shown in Figure 10." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.653, + 0.818 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of SASPM and Boundary-Anchored Patch Discriminator. We investigate the contributions of the proposed SASPM and \\(D_{BAP}\\) to the generation of texture-consistent background. To exclude the interference of the foreground, we create mask maps that only include back" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1874" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.09, + 0.424, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.205, + 0.468, + 0.234 + ], + "angle": 0, + "content": "Figure 11. Ablation analysis on SASPM and \\(D_{BAP}\\) for synthesizing texture-consistent backgrounds." + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.254, + 0.456, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.344, + 0.414, + 0.358 + ], + "angle": 0, + "content": "Figure 12. Ablation study of object generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.47, + 0.567 + ], + "angle": 0, + "content": "ground regions in this study. We remove all SASPM (\"w/o SASPM\") or \\(D_{BAP}\\) (\"w/o \\(D_{BAP}\\)) from our model as two baselines. The visual results are shown in Figure 11 and prove that SASPM and \\(D_{BAP}\\) can help the background generator effectively alleviate texture inconsistencies. Vanilla convolutional layers have limited receptive fields and no ability to locate where edited or known regions are. SASPM explicitly transfers features from known regions to edited regions with the same semantic labels across distant spatial distances. \\(D_{BAP}\\) forces the generator to pay more attention to local textures on editing boundaries rather than just global images. Quantitative results are listed in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Effectiveness of Style-Diversity Object Generator. To verify the benefit of \\(\\mathcal{L}_{\\mathrm{SCC}}\\) and the style bank, we set up two baselines: (1) Dropping out \\(\\mathcal{L}_{\\mathrm{SCC}}\\) (\"w/o \\(\\mathcal{L}_{\\mathrm{SCC}}\\)). (2) Replacing the style codes with noise vectors (\"w Noise\"). Figure 12 shows some visual results. If we drop out \\(\\mathcal{L}_{\\mathrm{SCC}}\\), the generated image's style may not be consistent with the style image. If we produce multi-modal results by injecting noise, it leads to a loss of fidelity and diversity. This is because Gaussian noise is semantics-free, while style code is category-specific and provides controllability. The quantitative results are listed in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Effectiveness of Separate Generation. We remove the object generator and the fusion network but keep other components unchanged to obtain a baseline (w/o Separation) and increase its channel number for a fair comparison. Qualitative and quantitative comparisons can be found in Figure 13 and Table 5, respectively. In this experiment, we employ the masks used in object addition. The visual comparison shows that the separate generation paradigm significantly improves performance for objects with complicated surroundings." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Effectiveness of Fusion Network. Fusion network can" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.09, + 0.867, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.2, + 0.892, + 0.226 + ], + "angle": 0, + "content": "Figure 13. Visual analysis on disentangled generation and fusion network." + }, + { + "type": "table", + "bbox": [ + 0.561, + 0.241, + 0.832, + 0.342 + ], + "angle": 0, + "content": "
classw/o LSCCw NoiseGOG
FID↓Div↑FID↓Div↑FID↓Div↑
car123.820.103173.570.090118.320.115
person238.100.079307.110.052219.200.098
bed227.180.303395.330.210239.780.372
chest192.120.217273.100.113149.290.229
lamp121.010.195153.940.129112.500.218
chair168.010.274207.350.177163.140.289
table211.390.141289.550.091201.320.143
" + }, + { + "type": "table_caption", + "bbox": [ + 0.551, + 0.353, + 0.839, + 0.368 + ], + "angle": 0, + "content": "Table 4. Quantitative results of different objects." + }, + { + "type": "table", + "bbox": [ + 0.533, + 0.38, + 0.86, + 0.451 + ], + "angle": 0, + "content": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o Separation6.780.02956.4321.970.18030.32
w/o Fusion6.730.02758.6819.190.13130.80
w/o Skip6.410.02258.7617.890.11830.96
Full model6.290.02058.8816.320.11031.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.462, + 0.892, + 0.488 + ], + "angle": 0, + "content": "Table 5. Quantitative studies of separate generation paradigm and fusion network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.59 + ], + "angle": 0, + "content": "eliminate abrupt boundaries between generated objects and backgrounds. Removing the fusion network (\\(w/o\\) Fusion) or not using the skip connection (\\(w/o\\) Skip) will degrade the performance, which are qualitatively and quantitatively demonstrated in Figure 13 and Table 5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.757, + 0.62 + ], + "angle": 0, + "content": "5. Conclusion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.854 + ], + "angle": 0, + "content": "This paper proposes a novel paradigm for semantic image editing, named SIEDOB. Its core idea is that since the characteristics of foreground objects and backgrounds are dramatically different, we design a heterogeneous model to handle them separately. To this end, we present SASPM and Boundary-Anchored Patch Discriminator to facilitate the generation of texture-consistent backgrounds and employ a Style-Diversity Object Generator to produce high-quality and diverse objects. Extensive experimental results demonstrate the superiority of our method. However, our method has some limitations. Some foreground categories are very rare in the dataset, so we cannot obtain enough data for training. In addition, object generation is hard to produce satisfactory results when an object is with an extreme pose or large-scale occlusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement This work is supported by State Grid Corporation of China (Grant No. 5500-202011091A-0-0-00)." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1875" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.186 + ], + "angle": 0, + "content": "[1] Deblina Bhattacharjee, Seungryong Kim, Guillaume Vizier, and Mathieu Salzmann. Dunit: Detection-based unsupervised image-to-image translation. 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In this task, the features of the foreground objects and the backgrounds are quite different. However, all previous methods handle backgrounds and objects as a whole using a monolithic model. Consequently, they remain limited in processing content-rich images and suffer from generating unrealistic objects and texture-inconsistent backgrounds. To address this issue, we propose a novel paradigm, Semantic Image Editing by Disentangling Object and Background (SIEDOB), the core idea of which is to explicitly leverages several heterogeneous subnetworks for objects and backgrounds. First, SIEDOB disassembles the edited input into background regions and instance-level objects. Then, we feed them into the dedicated generators. Finally, all synthesized parts are embedded in their original locations and utilize a fusion network to obtain a harmonized result. Moreover, to produce high-quality edited images, we propose some innovative designs, including Semantic-Aware Self-Propagation Module, Boundary-Anchored Patch Discriminator, and Style-Diversity Object Generator; and integrate them into SIEDOB. We conduct extensive experiments on Cityscapes and ADE20K-Room datasets and exhibit that our method remarkably outperforms the baselines, especially in synthesizing realistic and diverse objects and texture-consistent backgrounds. Code is available at https://github.com/WuyangLuo/SIEDOB. + +# 1. Introduction + +Semantic image editing has recently gained significant traction due to its diverse applications, including adding, altering, or removing objects and controllably inpainting, outpainting, or repainting images. Existing methods have made impressive progress benefiting from Generative Adversar + +![](images/30487b7cf41b1266705405421c3a9f99d8a21c9cdb7aaaba0fb77538eb48356d.jpg) +Input +Figure 1. Existing methods struggle to deal with the compound of backgrounds and several overlapping objects in a complex scene. They generate distorted objects and texturally inconsistent backgrounds. The proposed method can cope well with this input. + +![](images/0f2de8aa00d06b6b5e014fc172f07b6e7d0492d19bea5711f061029177bc0a3a.jpg) +SESAME + +![](images/a43d5e018e9cf5c784c7784f8c47c2e15054689029a7ba77268503854fdc263e.jpg) +ASSET + +![](images/017a320a31007088c62f021b15bce4e09bdc7a6c5df8a53bb0f647c17813bcb0.jpg) +SPMPGAN + +![](images/9e7ef790385c50673b34613a0de540fdd83ae8bfe624054e32871b8f4af22408.jpg) +SIEDOB + +ial Networks (GAN) [5, 14] and have demonstrated promising results in relatively content-simple scenes, such as landscapes. However, they still suffer from inferior results for content-rich images with multiple discrepant objects, such as cityscapes or indoor rooms. This paper aims to improve editing performance in complex real-world scenes. + +When image editing experts deal with a complex task, they decompose the input image into multiple independent and disparate elements and handle them with different skills. For example, when editing a photo with a congested road, they process the cars and pedestrians individually and then fill in the background. Inspired by this spirit, we propose a heterogeneous editing model, which mimics the experience of human experts and explicitly splits the compound content into two distinct components: Backgrounds and objects. The background has no regular shape and may span a large area. More importantly, the re-generated background's texture and the existing area must be consistent. Foregrounds objects are class-specific and appear anywhere with various scales. Due to the significant differences between the two components, it is necessary to disentangle them from the input and process them with different networks. + +Several recent works [23, 28, 32] have been dedicated to this task. SESAME [32] proposes a new pair of generator and discriminator based on the cGAN framework [31], which generates edited content through a single-shot inference. ASSET [23] builds a transformer-based architecture with a sparse attention mechanism and synthesizes + +edited regions relying on a codebook generated by VQ-GAN [4]. SPMPGAN [28] proposes a coarse-to-fine generator equipped with style-preserved modulation layers to retain style consistency between edited regions and context. These methods effectively enhance the ability of a monolithic model to handle the entire input. However, they deal with backgrounds and objects equally using the same generator, which causes them to produce inferior results. Figure 1 demonstrates an example. To tackle this limitation, we present a novel framework, Semantic Image Editing by Disentangling Object and Background (SIEDOB), to generate backgrounds and foreground objects separately, which can achieve two goals: Synthesizing texture-consistent backgrounds and generating photorealistic and diverse objects. + +SIEDOB first disassembles the edited image into background regions and instance-level objects, then employs different generators to synthesize the corresponding content, and finally aggregates generated objects with backgrounds via a fusion network. In this way, we decouple our task into several more feasible subtasks and handle different components using dedicated sub-models. + +Generating texture-consistent backgrounds with known context is not trivial since backgrounds may cross a sizeable spatial area in an image and have no regular shape. We propose a pair of boosted generator and discriminator to address this problem. Specifically, we propose Semantic-Aware Self-Propagation Module (SASPM) to help the generator efficiently transfer the semantic-wise features of known regions to generated regions. Moreover, to further enhance texture consistency, we design a Boundary-Anchored Patch Discriminator to force the generator to pay more attention to local textures of editing fringe. + +In our task, depending on the scenario, the edited object may be requested to be inpainted or generated. If an object is partially visible, it undergoes a lightweight inpainting network. Otherwise, we employ a Style-Diversity Object Generator to obtain multi-modal results based on a style bank. After generating the backgrounds and all objects, we re-integrate them into a whole. However, the separate generation may lead to sudden boundaries and dissonance between objects and surroundings. To tackle this problem, we utilize a simple fusion network that predicts the residual value for each pixel to harmonize outputs. + +Our main contributions can be summarized as follows: + +- We propose a new solution for semantic image editing, named SIEDOB, which can handle complex scenes by decoupling the generation of backgrounds and objects. +- We propose Semantic-Aware Self-Propagation Module and Boundary-Anchored Patch Discriminator to facilitate texture-consistent background generation. + +- We propose a Style-Diversity Object Generator that can generate diverse and realistic object images from masks. +- Extensive experiments on two benchmarks indicate that our method can generate texture-consistent results and deal with crowded objects well. + +# 2. Related Works + +# 2.1. Semantic Image Editing + +Semantic image editing refers to modifying a given image by manipulating a corresponding segmentation map and keeping the context coherent. This approach provides powerful editing capabilities, such as adding and removing objects, modifying shapes, and re-painting backgrounds. Compared to several related tasks, including semantic image synthesis [14, 33, 40, 42, 51] and image inpainting [13, 30, 45, 46, 48], semantic image editing has not been fully exploited due to its difficulty in generating realistic objects and texture-consistent backgrounds simultaneously. A few recent works are devoted to semantic image editing [10, 23, 28, 32]. HIM [10] is an early exploration that only operates on a single object using a two-stage network. SESAME [32] introduces a new pair of generators and discriminators to improve the quality of the generated results. Moreover, SESAME adopts a more flexible workflow that can respond to various image editing requirements of users. ASSET [23] proposes a novel transformer-based approach modeling long-range dependencies, enabling high-resolution image editing. SPMPGAN [28] presents a stylepreserved modulation technique and builds a progressive architecture that solves the style inconsistency problem in semantic image editing. These methods all consider semantic image editing as a global generation problem. Thus, they use a single model to process all elements of the edited image equally. In this work, we propose a decoupled framework to handle objects and backgrounds separately using heterogeneous generators, demonstrating more promising results. + +# 2.2. Image Synthesis via Heterogeneous Generators + +For a wide variety of image generation tasks, most approaches impose monolithic generators on the entire image, including unsupervised image generation [17, 18, 35], image-to-image translation [29, 33, 42, 51], image inpainting [24, 45, 46], and image editing [15, 26]. They share the same network structure and weights to generate all the content without specialized submodels for different semantic regions or classes. Other methods use different architectures or weights to generate different image elements to improve generation quality for different components. For example, they employ multiple local branches specialized + +![](images/a520e55eedef2ec936a76064268613b6015452860abe51033691bcbd5ca87948.jpg) +Figure 2. Overview of the proposed method. To reduce the complexity of modeling the entire edited region, we use a heterogeneous model to synthesize foreground objects and backgrounds separately, which contains three components: (1) Background generation, (2) object generation, (3) fusion network. + +for different parts [6, 9, 11, 21], decoupling content and style [12, 20, 27], generating foreground and a single foreground object separately [39, 43], enhancing local generation [1, 37], or having separate modules for different semantic categories [22, 40]. However, these methods are developed for pure image generation or translation tasks where their input is noises, categories, segmentation maps, or full images. Therefore, they only need to synthesize simple but visually plausible results to fool the discriminator. Semantic image editing is a more challenging task, and its difficulty lies in keeping coherence between edited and known regions. In this paper, we propose a heterogeneous framework that utilizes different sub-models for foreground objects and backgrounds to improve their generation quality concurrently. + +# 3. Proposed Method + +Our goal is to edit a given image $I \in \mathbb{R}^{H \times W \times 3}$ guided by a user-provided segmentation map $S \in \mathbb{L}^{H \times W \times L}$ within an edited region defined by a mask map $M \in \mathbb{B}^{H \times W \times 1}$ whose value is 0 in the non-edited region and 1 in the edited region. Here $H, W,$ and $L$ denote the height, width, and number of semantic categories, respectively. The edited region of $I$ is erased as input $I_e = I \times (1 - M)$ . We create a background mask $M_B$ and all instance-level object masks $\{M_c^q\}$ in the edited region based on the segmentation map. Here, $c \in \mathcal{C}, \mathcal{C}$ is a pre-defined set of considered foreground categories, and $M_c^q$ is the $q$ -th instance that falls into the category $c$ . The background mask $M_B$ is composed of the remaining pixels. Thus, we can disassemble the input image $I_e$ to the background and objects according to $M_B$ and $\{M_c^q\}$ . Then we generate the background and objects separately using the respective generators. Finally, we integrate all generated content via a fusion network. The workflow is depicted in Figure 2. + +# 3.1. Background Generation + +For image editing, the background usually needs to be partially generated to fill the space, such as sky or ground. Therefore, generating style-consistent texture patterns in edited regions is critical and challenging since the generated background and the known region coexist. In addition, an image's background may be across a distant spatial distance and have no regular shape. Efficiently and accurately transferring feature styles from known to edited regions is vital for generating texture-consistent results. To this end, we propose a Semantic-Aware Self-Propagation Module (SASPM), which explicitly extracts semantic-wise feature codes from feature maps and propagates them to the corresponding regions at the same layer. Furthermore, we employ a Boundary-Anchored Patch Discriminator to enforce the generator to focus on local textures at the editing boundary. + +The proposed background generator $G_B$ is shown in 3(c). We feed the disassembled background region into $G_B$ as the input: $I_B = I_e \times M_B$ . $G_B$ follows an encoder-decoder structure. The encoder is composed of several successive GatedConv layers [46] with stride two, and the decoder contains corresponding GatedConv layers with upsampling and several SASPM. + +# Semantic-Aware Self-Propagation Modules (SASPM) + +SASPM aims at propagating features of known regions to edited regions in a semantic-aware manner. Taking the sky area as an example shown in Figure 3(a)(b), a SASPM is divided into two steps. First, we extract the semantic-aware feature code by computing the average of the known sky area. Then, the feature code is broadcast into the entire sky area according to the corresponding semantic mask. SASPM can transfer the feature codes of each semantic label at the same feature level without the constraint of the receptive field. Formally, let $F \in \mathbb{R}^{H \times W \times C}$ denote a feature + +![](images/120748f2853b389a798d0269d7daea07b8bda625d18727b070e66ae496a030b0.jpg) +Edited Image + +![](images/8019a467d5375c0bb2d67b642132b6cfaaeb112e061de05f93a916550a9f141a.jpg) +Known Sky Region + +![](images/7bcc9d39fb308da4882ed9e1f3b8366c211dcf6e80e51a273defa796a7bc7109.jpg) +Entire Sky Region + +![](images/69bb4166ff601b1e007588aaffa1e7970acbd87838286fc2a778a2208ac73933.jpg) +(a) A semantic category (sky) spans the known region and the edited region + +![](images/5d82832549abf79be95adf14fad0fb07d3e3b5375157f0b8589a993aa935750a.jpg) +Figure 3. (a) A background category, such as sky, may span known and edited regions. We want to transfer the features from the known region to the generated region in a semantic-aware fashion. (b) The principle of SASPM. We extract the feature code for each background category from the known region and then propagate it to the entire region. (c) The architecture of our background generator. + +map in front of a SASPM. $H$ , $W$ are the spatial dimension and $C$ is the number of channels. Let $U \in \mathbb{R}^{L \times C}$ represent $L$ feature codes extracted from the known region, and the feature codes of non-background classes are set to zero. We generate a code map $P$ based on the segmentation map $S \in \mathbb{L}^{H \times W \times L}$ through a matrix multiplication to spatially broadcast the feature codes into the corresponding semantic region: + +$$ +P = S \otimes U \tag {1} +$$ + +Thus, $P \in \mathbb{R}^{H \times W \times C}$ is restored to the spatial dimension filled with the category-specific feature codes. Finally, we propagate $P$ into the original $F$ using a modulation operation following SPADE [33]. Specifically, we learn two parameters $\gamma_{P} \in \mathbb{R}^{H \times W \times C}$ and $\beta_{P} \in \mathbb{R}^{H \times W \times C}$ from $P$ to modulate $F$ : + +$$ +F _ {P} = \operatorname {R e L U} \left(\gamma_ {P} \odot I N (\operatorname {C o n v} (F)) \oplus \beta_ {P}\right) \tag {2} +$$ + +Where $Conv(\cdot), IN(\cdot)$ , and $ReLU(\cdot)$ denote Convolutional Layer, Instance Normalization, and ReLU activation function, respectively. $\odot$ and $\oplus$ are element-wise multiplication and addition. + +![](images/fc63ece7463334a8406e112aa21d3c25a692e10326d28ccb3d81281af51c8ce8.jpg) +Figure 4. Boundary-Anchored Patch Discriminator $D_{BAP}$ takes in four real image patches or fake image patches of random size. All patches are centered on the boundary of the edited region enclosed by the red line. + +# Boundary-Anchored Patch Discriminator + +We employ two discriminators for our background generator: (1) A global discriminator used by previous works [28]; (2) a novel Boundary-Anchored Patch Discriminator $D_{BAP}$ . We introduce $D_{BAP}$ to enforce the generator to pay attention to local texture across the fringe of the edited area. We expect $D_{BAP}$ can capture known and generated textures simultaneously to facilitate texture-consistent results. To this end, we randomly select several central points anchored on the boundary of the edited region to crop patches from real or generated images, as shown in Figure 4. Thus, the fake patches contain both real and fake textures, so $D_{BAP}$ can distinguish between true and false through texture consistency. + +The training objective of $G_{B}$ is comprised of L1 Distance Loss $\mathcal{L}_1$ , Perceptual Loss $\mathcal{L}_{\mathrm{P}}$ [16], Global Adversarial Loss $\mathcal{L}_{GAN}^{G}$ , and Local Patch Adversarial Loss $\mathcal{L}_{GAN}^{L}$ : + +$$ +\mathcal {L} _ {B} = \mathcal {L} _ {1} + \lambda_ {P B} \mathcal {L} _ {\mathrm {P}} + \mathcal {L} _ {G A N} ^ {G} + \lambda_ {G A N} ^ {L} \mathcal {L} _ {G A N} ^ {L} \tag {3} +$$ + +Where $\mathcal{L}_1$ and $\mathcal{L}_{\mathrm{P}}$ force the generated results to be closer to the ground truth in RGB space and VGG space [38]. $\mathcal{L}_{GAN}^{G}$ and $\mathcal{L}_{GAN}^{L}$ are applied to global images and local patches, respectively. All adversarial losses in this work are associated with a SNPatchGAN Discriminator [46] using the hinge version [2]. + +# 3.2. Object Generation + +Our task involves dealing with two scenarios: Inpainting or generating an object—the former aims at completing an object based on its visible part. The latter synthesizes an inexistent object from its mask with an arbitrary appearance. Unlike handling all objects at once, cropping each edited object and independently generating them allows + +![](images/9df297a83bcfe686387a088e7b3368ca4248b459a5d1d0dc3e27db9b48149cc1.jpg) +(a) Extract Style Map + +![](images/e713369a55511ca4f1c2dd6f5e369788af1123539258239af564c1f1aa5b5e35.jpg) + +![](images/ab7f21e920b2e18c5da3c5e44c6d70166f65b7e54adba50e40b38c4a3ea92208.jpg) + +![](images/8f157caf5091613a43948abb26c140d155894275dac9575eb7f958c7fdddef78.jpg) +Figure 5. (a) How to extract style maps? During training, we extract their style codes from ground truth images or randomly sampled images and then generate style maps by broadcasting. During inference, we sample a class-specific style code directly from the style bank. (b) The structure of Semantic-Style Normalization Module (SSNM). (c) We build a Style-Diversity Object Generator equipped with SSNM. + +us to use aligned input images with the same size, which is beneficial for generating high-quality results. Specifically, we crop all objects $\{Crop(I_e)_c^q\}$ from the edited region based on object masks $\{M_c^q\}$ . We leverage a two-way model to handle the different scenarios. One way is a lightweight inpainting network $G_{OI}$ to complete objects. $G_{OI}$ is a UNet-like [36] network and its training objective is: $\mathcal{L}_{GI} = \mathcal{L}_1 + \lambda_{PI}\mathcal{L}_{\mathrm{P}} + \mathcal{L}_{GAN}$ . $\mathcal{L}_1$ , $\mathcal{L}_{\mathrm{P}}$ , and $\mathcal{L}_{GAN}$ are the same as the terms in Equation 6. The other way is the proposed Style-Diversity Object Generator $G_{OG}$ for the multi-modal generation. Note that all categories of objects share $G_{OI}$ and $G_{OG}$ . + +# Style-Diversity Object Generator + +$G_{OG}$ generates a class-specific image from a one-hot segmentation map $M_{sem} \in \mathbb{L}^{H \times W \times K}$ created by the corresponding object mask $M_c^q$ . $K$ is the number of the predefined foreground class set. Motivated by disentanglement learning [12, 20, 27], we utilize style information to control the appearance of results for multi-modal generation. Specifically, we sample an image from the training set with the same class label and extract its style code $W \in \mathbb{R}^{128}$ by a style encoder $E_s$ . Then we generate a style map $M_{style} \in \mathbb{R}^{H \times W \times 128}$ via broadcasting the style code according to $M_c^q$ , as illustrated in Figure 5(a). At this point, we have acquired a semantic map $M_{sem}$ and a style map $M_{style}$ . The next is how to decode them back to a style-controlled object image. To this end, we design a Semantic-Style Normalization Module (SSNM) to integrate the style and semantic information, as shown in Figure 5(b). We first inject the semantic information into the input feature maps $F \in \mathbb{R}^{H \times W \times C}$ : + +$$ +F _ {s e m} = R e L U \left(\gamma_ {c} \odot I N (C o n v (F)) \oplus \beta_ {c}\right) \tag {4} +$$ + +Where two normalization parameters, $\gamma_c \in \mathbb{R}^{H \times W \times C}$ and $\beta_c \in \mathbb{R}^{H \times W \times C}$ are learned from $M_{sem}$ . Similarly, the style information is injected by: + +$$ +F _ {O} = \operatorname {R e L U} \left(\gamma_ {s} \odot I N \left(\operatorname {C o n v} \left(F _ {\text {s e m}}\right)\right) \oplus \beta_ {s}\right) \tag {5} +$$ + +Where two normalization parameters $\gamma_s \in \mathbb{R}^{H \times W \times C}$ and $\beta_s \in \mathbb{R}^{H \times W \times C}$ are learned from $M_{style}$ . + +During training, for each sample, we take the ground truth image $I^{gt}$ and a randomly sampled image $I^s$ as the style images to generate two results $R^{gt}$ and $R^s$ . We employ the following objective function to optimize $G_{OG}$ : + +$$ +\mathcal {L} _ {G O} = \mathcal {L} _ {1} + \lambda_ {P O} \mathcal {L} _ {\mathrm {P}} + \mathcal {L} _ {G A N} + \mathcal {L} _ {\mathrm {S C C}} \tag {6} +$$ + +Here, $\mathcal{L}_1$ is only applied to $R^{gt}$ . $\mathcal{L}_{\mathrm{P}}$ , $\mathcal{L}_{GAN}$ , and $\mathcal{L}_{\mathrm{SCC}}$ are imposed on all results. We introduce Style Cycle-Consistency Loss $\mathcal{L}_{\mathrm{SCC}}$ to force the generator to produce style-consistent results with style images. + +$$ +\mathcal {L} _ {S C C} = 1 - \cos \left(\frac {E _ {S} ^ {\prime} (R)}{\| E _ {S} ^ {\prime} (R) \| _ {2}}, \frac {E _ {s} ^ {\prime} \left(I ^ {s t y l e}\right)}{\| E _ {S} ^ {\prime} \left(I ^ {s t y l e}\right) \| _ {2}}\right) \tag {7} +$$ + +Where $I^{style}$ is the style image and $R$ is the generated result. $E_s'(\cdot)$ is a style encoder with the same structure as $E_s$ . $\cos(\cdot, \cdot)$ represents the cosine similarity of two vectors. + +Previous image translation methods [12, 20] achieve multi-modal generation by adding Gaussian noise during + +![](images/dbdb21abf6f497cb65f4964d6d93a2d17ca2df6315cb6860a508d4bf55257fbb.jpg) +Figure 6. Structure of Fusion Network. The red line indicates the skip connection. + +inference. We find that noise leads to low-quality results and limited diversity. To solve this problem, we replace the noise with a style bank. Precisely, once training is done, we extract all style codes from the training set by the trained $E_{s}$ and save them for building a class-aware style bank. During inference, we randomly sample different style codes from the style bank to generate different results. It is worth mentioning that our approach does not increase any additional computational overhead compared to adding noise. + +# 3.3. Fusion Network + +After generating all backgrounds and objects, we embed them into their original positions to obtain a composited image. However, this preliminary result may be discordant since each object is generated independently without accounting for context. We employ a fusion network $F$ to harmonize the objects with the surroundings, as shown in Figure 6. $F$ learns an offset value for each pixel via a skip connection [7,36] to produce the final results. We use Perceptual Loss and Adversarial Loss to optimize $F$ : + +$$ +\mathcal {L} _ {F} = \lambda_ {P F} \mathcal {L} _ {\mathrm {P}} + \mathcal {L} _ {G A N} \tag {8} +$$ + +# 4. Experiments + +Datasets. We conduct experiments on two datasets, Cityscapes and ADE20K-Room, used in [28, 32]. Cityscapes [3] contains complex street scene images in German cities. ADE20K-Room is a subset of ADE20K [50] consisting of indoor scene images. We train and test our model at $256 \times 256$ resolution. + +Implementation Details. We use free-form, extension, and outpainting masks following [28]. Similar to the previous work [22], we choose those frequently-appearing categories as the foreground class set, (car, person) for Cityscapes and (bed, chest, lamp, chair, table) for ADE20K-Room. All sub-networks are independently trained using ADAM optimizers [19] for both the generator and the discriminators with momentum $\beta_{1} = 0.5$ and $\beta_{2} = 0.999$ , and the learning rates for the generator and the discriminators are set to 0.0001 and 0.0004, respectively. For training $D_{BAP}$ , we randomly crop 4 square patches with the size ranging from $96 \times 96$ to $160 \times 160$ . We set balance coefficients: + +![](images/9d32725e08e59a925b7210909fdfd27a6a7782c77512c960b2580fa2a81536ad.jpg) +Figure 7. Visual comparisons with state-of-the-art methods. Our method is effective in generating texture-consistent backgrounds and photo-realistic objects. + +$\lambda_{PB} = \lambda_{PI} = \lambda_{PO} = \lambda_{PF} = 10$ and $\lambda_{GAN}^{L} = 0.2$ . The proposed method is implemented with Pytorch 1.10 [34], and all experiments are performed on a single NVIDIA RTX 3090 GPU. + +Baselines. We compare the proposed methods with the state-of-the-art semantic image editing methods, including HIM [10], SESAME [32], ASSET [23], SPMPGAN [28]. We also introduce two additional methods [40, 48] as baselines to investigate related work more widely. LGGAN [40] learns a map from segmentation maps to photo-realistic images using global image-level and class-specific generators. Co-Mod [48] demonstrates impressive results in semantic image generation and image inpainting. We change their input to be the same as our task. + +# 4.1. Qualitative evaluation + +We demonstrate a visual comparison of the competing methods, as shown in Figure 7. We observe that the results produced by the proposed SIEDOB are visually better than existing methods in two aspects: (1) Our method can well handle dense objects overlapping each other, e.g., in the second and third rows. However, other methods produce distorted and inseparable results. (2) Our method generate texture-consistent content between edited regions and known regions both on background and objects, e.g., the red cars in the first row and the curtain in the fourth row. The performance improvement benefits from our disentangling generation strategy and carefully designed sub-networks. + +# 4.2. Quantitative evaluation + +Table 1 lists the quantitative results with three different mask types. Following previous works, we use three metrics: FID [8], LPIPS [47], and mean Intersection-over-Union (mIoU). FID is introduced to assess the fidelity of the + +
M.MethodCityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
F.LGGAN15.290.09458.6224.740.09727.68
Co-Mod15.880.09756.5027.370.11127.52
HIM15.580.09358.9928.640.13328.04
SESAME12.890.08258.8821.730.10127.50
ASSET13.670.09858.1230.630.12626.02
SPMPGAN11.900.08458.8018.830.09028.22
SIEDOB11.070.07759.4117.610.08929.72
E.LGGAN26.010.17558.3737.090.21327.91
Co-Mod29.270.18856.4438.610.23127.13
HIM25.200.18058.9140.690.23927.61
SESAME20.300.16859.0836.430.21127.62
ASSET21.990.18658.0138.170.26127.03
SPMPGAN19.460.16759.1032.920.19927.73
SIEDOB19.200.15959.6331.660.19129.52
O.LGGAN39.120.25458.7749.070.33427.69
Co-Mod50.290.26455.3951.450.32526.54
HIM36.270.25258.9954.510.33728.19
SESAME28.270.23758.7547.720.30527.40
ASSET30.600.24058.9157.280.33127.18
SPMPGAN27.630.23358.5341.520.28827.85
SIEDOB27.900.22159.3741.070.27528.94
+ +![](images/959b326a4d92691901f8dc707900ccf82d765bf65c3a1a7a285622e42a096bbd.jpg) +Figure 8. Visual results of addition objects. + +![](images/e8d900b17b0ac95b34a0fce4b8935a77175922410e2e7535e07f0affa0a3d304.jpg) +Figure 9. Multi-modal generation results. + +results by computing the Wasserstein-2 distance between the distributions of the synthesized and real images. LPIPS evaluates the similarity between the generated image and the ground truth in a pairwise manner. mIoU measures the alignment of semantic labels between the generated results and input segmentation maps. We use solid models to obtain segmentation maps: HRNet [41] for ADE20K-Room, and DRN-D-105 [44] for Cityscapes. Our method outperforms the other methods under different metrics and mask settings. + +![](images/7d163ed507081c000ed4f0508e2d0a0715ae08f360eb04e206e2b8bacf14a900.jpg) +Figure 10. Out-of-distribution editing. Our method can add cars in the middle of the road or on the sidewalk, which do not exist in the training dataset. + +Table 1. Quantitative comparison with other methods. M., F., E., and O. represent Mask Type, Free-Form Mask, Extension Mask, and Outpainting Mask, respectively. (↑: Higher is better; ↓: Lower is better) + +
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑Div↑FID↓LPIPS↓mIoU↑Div↑
LGGAN7.690.02757.01-24.490.17130.05-
Co-Mod7.790.02956.290.003021.090.11830.630.0145
HIM6.920.02858.71-29.100.23230.58-
SESAME6.670.02458.79-18.010.11730.89-
ASSET6.740.02556.020.005227.680.20929.790.0337
SPMPGAN6.590.02158.60-17.210.11530.58-
SIEDOB6.290.02058.880.005516.320.11031.040.0362
+ +Table 2. Quantitative results of object addition. + +
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o SASPM14.110.08559.4320.030.09129.02
w/o DBAP12.680.08159.4919.140.08329.21
Full model12.150.07959.5118.720.08129.30
+ +Table 3. Quantitative study on SASPM and ${D}_{BAP}$ . + +# 4.3. Addition Object + +Adding a new object to the given image is an essential ability of semantic image editing. The visual results are shown in Figure 8. In this experiment, we randomly select an instance of each test image and create a rectangular mask encircling the object. The proposed method can generate realistic objects with crisp edges. Adding an object to the edited area that does not exist originally should have diverse results. Some previous methods [23,48] have multimodal generation capabilities. We sample two results from all methods, as shown in Figure 9. Our method achieves a higher diversity than other models because the previous methods only exert a global influence on the generation process; in contrast, our model independently generates each object using different class-aware style codes. The quantitative results listed in Table 2 also indicate the superiority of our method. Here, the Diversity score (Div) is calculated as the average LPIPS distance between pairs of randomly sampled results for all test images, as also done in [25,49]. Moreover, our model can hallucinate images that do not exist in the dataset's distribution, as shown in Figure 10. + +# 4.4. Ablation Study + +Effectiveness of SASPM and Boundary-Anchored Patch Discriminator. We investigate the contributions of the proposed SASPM and $D_{BAP}$ to the generation of texture-consistent background. To exclude the interference of the foreground, we create mask maps that only include back + +![](images/1a254f04485e719ba8b864cb7c69f361655f77749411273125f566e839b0b3fd.jpg) +Figure 11. Ablation analysis on SASPM and $D_{BAP}$ for synthesizing texture-consistent backgrounds. + +![](images/df025af410496ed61eff8d13d7b18c17ac5af7c29f79df022c640be048eaef31.jpg) +Figure 12. Ablation study of object generation. + +ground regions in this study. We remove all SASPM ("w/o SASPM") or $D_{BAP}$ ("w/o $D_{BAP}$ ) from our model as two baselines. The visual results are shown in Figure 11 and prove that SASPM and $D_{BAP}$ can help the background generator effectively alleviate texture inconsistencies. Vanilla convolutional layers have limited receptive fields and no ability to locate where edited or known regions are. SASPM explicitly transfers features from known regions to edited regions with the same semantic labels across distant spatial distances. $D_{BAP}$ forces the generator to pay more attention to local textures on editing boundaries rather than just global images. Quantitative results are listed in Table 3. + +Effectiveness of Style-Diversity Object Generator. To verify the benefit of $\mathcal{L}_{\mathrm{SCC}}$ and the style bank, we set up two baselines: (1) Dropping out $\mathcal{L}_{\mathrm{SCC}}$ ("w/o $\mathcal{L}_{\mathrm{SCC}}$ ). (2) Replacing the style codes with noise vectors ("w Noise"). Figure 12 shows some visual results. If we drop out $\mathcal{L}_{\mathrm{SCC}}$ , the generated image's style may not be consistent with the style image. If we produce multi-modal results by injecting noise, it leads to a loss of fidelity and diversity. This is because Gaussian noise is semantics-free, while style code is category-specific and provides controllability. The quantitative results are listed in Table 4. + +Effectiveness of Separate Generation. We remove the object generator and the fusion network but keep other components unchanged to obtain a baseline (w/o Separation) and increase its channel number for a fair comparison. Qualitative and quantitative comparisons can be found in Figure 13 and Table 5, respectively. In this experiment, we employ the masks used in object addition. The visual comparison shows that the separate generation paradigm significantly improves performance for objects with complicated surroundings. + +Effectiveness of Fusion Network. Fusion network can + +![](images/3b39a7e3ce2ae4e0e8154ab3f3935bce0533c29a7ad3d905c0d86dfe02ef87c1.jpg) +Figure 13. Visual analysis on disentangled generation and fusion network. + +
classw/o LSCCw NoiseGOG
FID↓Div↑FID↓Div↑FID↓Div↑
car123.820.103173.570.090118.320.115
person238.100.079307.110.052219.200.098
bed227.180.303395.330.210239.780.372
chest192.120.217273.100.113149.290.229
lamp121.010.195153.940.129112.500.218
chair168.010.274207.350.177163.140.289
table211.390.141289.550.091201.320.143
+ +Table 4. Quantitative results of different objects. + +
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o Separation6.780.02956.4321.970.18030.32
w/o Fusion6.730.02758.6819.190.13130.80
w/o Skip6.410.02258.7617.890.11830.96
Full model6.290.02058.8816.320.11031.04
+ +Table 5. Quantitative studies of separate generation paradigm and fusion network. + +eliminate abrupt boundaries between generated objects and backgrounds. Removing the fusion network ( $w/o$ Fusion) or not using the skip connection ( $w/o$ Skip) will degrade the performance, which are qualitatively and quantitatively demonstrated in Figure 13 and Table 5. + +# 5. Conclusion and Limitations + +This paper proposes a novel paradigm for semantic image editing, named SIEDOB. Its core idea is that since the characteristics of foreground objects and backgrounds are dramatically different, we design a heterogeneous model to handle them separately. To this end, we present SASPM and Boundary-Anchored Patch Discriminator to facilitate the generation of texture-consistent backgrounds and employ a Style-Diversity Object Generator to produce high-quality and diverse objects. Extensive experimental results demonstrate the superiority of our method. However, our method has some limitations. Some foreground categories are very rare in the dataset, so we cannot obtain enough data for training. In addition, object generation is hard to produce satisfactory results when an object is with an extreme pose or large-scale occlusion. + +Acknowledgement This work is supported by State Grid Corporation of China (Grant No. 5500-202011091A-0-0-00). + +# References + +[1] Deblina Bhattacharjee, Seungryong Kim, Guillaume Vizier, and Mathieu Salzmann. Dunit: Detection-based unsupervised image-to-image translation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4787-4796, 2020. 3 +[2] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. arXiv preprint arXiv:1809.11096, 2018. 4 +[3] Marius Cordts, Mohamed Omran, Sebastian Ramos, Timo Rehfeld, Markus Enzweiler, Rodrigo Benenson, Uwe Franke, Stefan Roth, and Bernt Schiele. The cityscapes dataset for semantic urban scene understanding. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5104-5113, 2020. 2 \ No newline at end of file diff --git a/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/images.zip b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..10ab21934e5b72faecd77bd3e5a29c3ce505bfd8 --- /dev/null +++ b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8f82acb61c6336d526040cfb32d100489d22dd37739ef28cba30b8a9e7014680 +size 714876 diff --git a/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/layout.json b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c15de708825c28da5b86ad3ecf3c6f580071ac88 --- /dev/null +++ b/2023/SIEDOB_ Semantic Image Editing by Disentangling Object and Background/layout.json @@ -0,0 +1,9982 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 61, + 103, + 533, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 103, + 533, + 121 + ], + "spans": [ + { + "bbox": [ + 61, + 103, + 533, + 121 + ], + "type": "text", + "content": "SIEDOB: Semantic Image Editing by Disentangling Object and Background" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 142, + 481, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 142, + 481, + 158 + ], + "spans": [ + { + "bbox": [ + 111, + 142, + 481, + 158 + ], + "type": "text", + "content": "Wuyang Luo1 Su Yang1* Xinjian Zhang1 Weishan Zhang2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 92, + 159, + 500, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 159, + 500, + 185 + ], + "spans": [ + { + "bbox": [ + 92, + 159, + 500, + 185 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 92, + 159, + 500, + 185 + ], + "type": "text", + "content": "Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University " + }, + { + "bbox": [ + 92, + 159, + 500, + 185 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{wyluol8, suyang}\\} @" + }, + { + "bbox": [ + 92, + 159, + 500, + 185 + ], + "type": "text", + "content": "fudan.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 154, + 186, + 437, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 154, + 186, + 437, + 198 + ], + "spans": [ + { + "bbox": [ + 154, + 186, + 437, + 198 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 154, + 186, + 437, + 198 + ], + "type": "text", + "content": "School of Computer Science and Technology, China University of Petroleum" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 252, + 290, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 588 + ], + "type": "text", + "content": "Semantic image editing provides users with a flexible tool to modify a given image guided by a corresponding segmentation map. In this task, the features of the foreground objects and the backgrounds are quite different. However, all previous methods handle backgrounds and objects as a whole using a monolithic model. Consequently, they remain limited in processing content-rich images and suffer from generating unrealistic objects and texture-inconsistent backgrounds. To address this issue, we propose a novel paradigm, Semantic Image Editing by Disentangling Object and Background (SIEDOB), the core idea of which is to explicitly leverages several heterogeneous subnetworks for objects and backgrounds. First, SIEDOB disassembles the edited input into background regions and instance-level objects. Then, we feed them into the dedicated generators. Finally, all synthesized parts are embedded in their original locations and utilize a fusion network to obtain a harmonized result. 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Existing methods struggle to deal with the compound of backgrounds and several overlapping objects in a complex scene. They generate distorted objects and texturally inconsistent backgrounds. 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However, they still suffer from inferior results for content-rich images with multiple discrepant objects, such as cityscapes or indoor rooms. This paper aims to improve editing performance in complex real-world scenes." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 437, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 639 + ], + "type": "text", + "content": "When image editing experts deal with a complex task, they decompose the input image into multiple independent and disparate elements and handle them with different skills. For example, when editing a photo with a congested road, they process the cars and pedestrians individually and then fill in the background. Inspired by this spirit, we propose a heterogeneous editing model, which mimics the experience of human experts and explicitly splits the compound content into two distinct components: Backgrounds and objects. The background has no regular shape and may span a large area. More importantly, the re-generated background's texture and the existing area must be consistent. Foregrounds objects are class-specific and appear anywhere with various scales. Due to the significant differences between the two components, it is necessary to disentangle them from the input and process them with different networks." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "content": "Several recent works [23, 28, 32] have been dedicated to this task. SESAME [32] proposes a new pair of generator and discriminator based on the cGAN framework [31], which generates edited content through a single-shot inference. ASSET [23] builds a transformer-based architecture with a sparse attention mechanism and synthesizes" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 143, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 143, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 143, + 712 + ], + "type": "text", + "content": "Corresponding author" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1868" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "edited regions relying on a codebook generated by VQ-GAN [4]. SPMPGAN [28] proposes a coarse-to-fine generator equipped with style-preserved modulation layers to retain style consistency between edited regions and context. These methods effectively enhance the ability of a monolithic model to handle the entire input. However, they deal with backgrounds and objects equally using the same generator, which causes them to produce inferior results. Figure 1 demonstrates an example. To tackle this limitation, we present a novel framework, Semantic Image Editing by Disentangling Object and Background (SIEDOB), to generate backgrounds and foreground objects separately, which can achieve two goals: Synthesizing texture-consistent backgrounds and generating photorealistic and diverse objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 252, + 289, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 337 + ], + "type": "text", + "content": "SIEDOB first disassembles the edited image into background regions and instance-level objects, then employs different generators to synthesize the corresponding content, and finally aggregates generated objects with backgrounds via a fusion network. In this way, we decouple our task into several more feasible subtasks and handle different components using dedicated sub-models." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 338, + 289, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 289, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 289, + 470 + ], + "type": "text", + "content": "Generating texture-consistent backgrounds with known context is not trivial since backgrounds may cross a sizeable spatial area in an image and have no regular shape. We propose a pair of boosted generator and discriminator to address this problem. Specifically, we propose Semantic-Aware Self-Propagation Module (SASPM) to help the generator efficiently transfer the semantic-wise features of known regions to generated regions. Moreover, to further enhance texture consistency, we design a Boundary-Anchored Patch Discriminator to force the generator to pay more attention to local textures of editing fringe." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 471, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 289, + 602 + ], + "type": "text", + "content": "In our task, depending on the scenario, the edited object may be requested to be inpainted or generated. If an object is partially visible, it undergoes a lightweight inpainting network. Otherwise, we employ a Style-Diversity Object Generator to obtain multi-modal results based on a style bank. After generating the backgrounds and all objects, we re-integrate them into a whole. However, the separate generation may lead to sudden boundaries and dissonance between objects and surroundings. To tackle this problem, we utilize a simple fusion network that predicts the residual value for each pixel to harmonize outputs." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 603, + 281, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 603, + 281, + 615 + ], + "spans": [ + { + "bbox": [ + 59, + 603, + 281, + 615 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 629, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 59, + 629, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 629, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 59, + 629, + 286, + 665 + ], + "type": "text", + "content": "- We propose a new solution for semantic image editing, named SIEDOB, which can handle complex scenes by decoupling the generation of backgrounds and objects." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 677, + 286, + 713 + ], + "type": "text", + "content": "- We propose Semantic-Aware Self-Propagation Module and Boundary-Anchored Patch Discriminator to facilitate texture-consistent background generation." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 317, + 72, + 545, + 152 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 107 + ], + "type": "text", + "content": "- We propose a Style-Diversity Object Generator that can generate diverse and realistic object images from masks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 116, + 545, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 116, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 317, + 116, + 545, + 152 + ], + "type": "text", + "content": "- Extensive experiments on two benchmarks indicate that our method can generate texture-consistent results and deal with crowded objects well." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 171, + 398, + 184 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 171, + 398, + 184 + ], + "spans": [ + { + "bbox": [ + 306, + 171, + 398, + 184 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 191, + 441, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 191, + 441, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 191, + 441, + 205 + ], + "type": "text", + "content": "2.1. Semantic Image Editing" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 209, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 556 + ], + "type": "text", + "content": "Semantic image editing refers to modifying a given image by manipulating a corresponding segmentation map and keeping the context coherent. This approach provides powerful editing capabilities, such as adding and removing objects, modifying shapes, and re-painting backgrounds. Compared to several related tasks, including semantic image synthesis [14, 33, 40, 42, 51] and image inpainting [13, 30, 45, 46, 48], semantic image editing has not been fully exploited due to its difficulty in generating realistic objects and texture-consistent backgrounds simultaneously. A few recent works are devoted to semantic image editing [10, 23, 28, 32]. HIM [10] is an early exploration that only operates on a single object using a two-stage network. SESAME [32] introduces a new pair of generators and discriminators to improve the quality of the generated results. Moreover, SESAME adopts a more flexible workflow that can respond to various image editing requirements of users. ASSET [23] proposes a novel transformer-based approach modeling long-range dependencies, enabling high-resolution image editing. SPMPGAN [28] presents a stylepreserved modulation technique and builds a progressive architecture that solves the style inconsistency problem in semantic image editing. These methods all consider semantic image editing as a global generation problem. Thus, they use a single model to process all elements of the edited image equally. In this work, we propose a decoupled framework to handle objects and backgrounds separately using heterogeneous generators, demonstrating more promising results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 563, + 545, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 545, + 576 + ], + "type": "text", + "content": "2.2. Image Synthesis via Heterogeneous Generators" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "type": "text", + "content": "For a wide variety of image generation tasks, most approaches impose monolithic generators on the entire image, including unsupervised image generation [17, 18, 35], image-to-image translation [29, 33, 42, 51], image inpainting [24, 45, 46], and image editing [15, 26]. They share the same network structure and weights to generate all the content without specialized submodels for different semantic regions or classes. Other methods use different architectures or weights to generate different image elements to improve generation quality for different components. For example, they employ multiple local branches specialized" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1869" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 71, + 74, + 521, + 219 + ], + "blocks": [ + { + "bbox": [ + 71, + 74, + 521, + 219 + ], + "lines": [ + { + "bbox": [ + 71, + 74, + 521, + 219 + ], + "spans": [ + { + "bbox": [ + 71, + 74, + 521, + 219 + ], + "type": "image", + "image_path": "a520e55eedef2ec936a76064268613b6015452860abe51033691bcbd5ca87948.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 229, + 547, + 265 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 547, + 265 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 547, + 265 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed method. To reduce the complexity of modeling the entire edited region, we use a heterogeneous model to synthesize foreground objects and backgrounds separately, which contains three components: (1) Background generation, (2) object generation, (3) fusion network." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 284, + 289, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 289, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 289, + 464 + ], + "type": "text", + "content": "for different parts [6, 9, 11, 21], decoupling content and style [12, 20, 27], generating foreground and a single foreground object separately [39, 43], enhancing local generation [1, 37], or having separate modules for different semantic categories [22, 40]. However, these methods are developed for pure image generation or translation tasks where their input is noises, categories, segmentation maps, or full images. Therefore, they only need to synthesize simple but visually plausible results to fool the discriminator. Semantic image editing is a more challenging task, and its difficulty lies in keeping coherence between edited and known regions. In this paper, we propose a heterogeneous framework that utilizes different sub-models for foreground objects and backgrounds to improve their generation quality concurrently." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 477, + 153, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 153, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 153, + 491 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": "Our goal is to edit a given image " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " guided by a user-provided segmentation map " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{L}^{H \\times W \\times L}" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " within an edited region defined by a mask map " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{B}^{H \\times W \\times 1}" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " whose value is 0 in the non-edited region and 1 in the edited region. Here " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "H, W," + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " denote the height, width, and number of semantic categories, respectively. The edited region of " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " is erased as input " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "I_e = I \\times (1 - M)" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": ". We create a background mask " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_B" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " and all instance-level object masks " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{M_c^q\\}" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " in the edited region based on the segmentation map. Here, " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "c \\in \\mathcal{C}, \\mathcal{C}" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " is a pre-defined set of considered foreground categories, and " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_c^q" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": "-th instance that falls into the category " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": ". The background mask " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_B" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " is composed of the remaining pixels. Thus, we can disassemble the input image " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "I_e" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " to the background and objects according to " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_B" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{M_c^q\\}" + }, + { + "bbox": [ + 46, + 497, + 289, + 715 + ], + "type": "text", + "content": ". Then we generate the background and objects separately using the respective generators. Finally, we integrate all generated content via a fusion network. The workflow is depicted in Figure 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 283, + 443, + 296 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 283, + 443, + 296 + ], + "spans": [ + { + "bbox": [ + 306, + 283, + 443, + 296 + ], + "type": "text", + "content": "3.1. Background Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 303, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 495 + ], + "type": "text", + "content": "For image editing, the background usually needs to be partially generated to fill the space, such as sky or ground. Therefore, generating style-consistent texture patterns in edited regions is critical and challenging since the generated background and the known region coexist. In addition, an image's background may be across a distant spatial distance and have no regular shape. Efficiently and accurately transferring feature styles from known to edited regions is vital for generating texture-consistent results. To this end, we propose a Semantic-Aware Self-Propagation Module (SASPM), which explicitly extracts semantic-wise feature codes from feature maps and propagates them to the corresponding regions at the same layer. Furthermore, we employ a Boundary-Anchored Patch Discriminator to enforce the generator to focus on local textures at the editing boundary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "text", + "content": "The proposed background generator " + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "inline_equation", + "content": "G_B" + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "text", + "content": " is shown in 3(c). We feed the disassembled background region into " + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "inline_equation", + "content": "G_B" + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "text", + "content": " as the input: " + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "inline_equation", + "content": "I_B = I_e \\times M_B" + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "inline_equation", + "content": "G_B" + }, + { + "bbox": [ + 304, + 496, + 545, + 579 + ], + "type": "text", + "content": " follows an encoder-decoder structure. The encoder is composed of several successive GatedConv layers [46] with stride two, and the decoder contains corresponding GatedConv layers with upsampling and several SASPM." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 580, + 529, + 593 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 580, + 529, + 593 + ], + "spans": [ + { + "bbox": [ + 306, + 580, + 529, + 593 + ], + "type": "text", + "content": "Semantic-Aware Self-Propagation Modules (SASPM)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "SASPM aims at propagating features of known regions to edited regions in a semantic-aware manner. Taking the sky area as an example shown in Figure 3(a)(b), a SASPM is divided into two steps. First, we extract the semantic-aware feature code by computing the average of the known sky area. Then, the feature code is broadcast into the entire sky area according to the corresponding semantic mask. SASPM can transfer the feature codes of each semantic label at the same feature level without the constraint of the receptive field. Formally, let " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " denote a feature" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1870" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 72, + 135, + 132 + ], + "blocks": [ + { + "bbox": [ + 76, + 72, + 135, + 132 + ], + "lines": [ + { + "bbox": [ + 76, + 72, + 135, + 132 + ], + "spans": [ + { + "bbox": [ + 76, + 72, + 135, + 132 + ], + "type": "image", + "image_path": "120748f2853b389a798d0269d7daea07b8bda625d18727b070e66ae496a030b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 91, + 133, + 119, + 137 + ], + "lines": [ + { + "bbox": [ + 91, + 133, + 119, + 137 + ], + "spans": [ + { + "bbox": [ + 91, + 133, + 119, + 137 + ], + "type": "text", + "content": "Edited Image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 139, + 72, + 199, + 131 + ], + "blocks": [ + { + "bbox": [ + 139, + 72, + 199, + 131 + ], + "lines": [ + { + "bbox": [ + 139, + 72, + 199, + 131 + ], + "spans": [ + { + "bbox": [ + 139, + 72, + 199, + 131 + ], + "type": "image", + "image_path": "8019a467d5375c0bb2d67b642132b6cfaaeb112e061de05f93a916550a9f141a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 132, + 189, + 137 + ], + "lines": [ + { + "bbox": [ + 149, + 132, + 189, + 137 + ], + "spans": [ + { + "bbox": [ + 149, + 132, + 189, + 137 + ], + "type": "text", + "content": "Known Sky Region" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 203, + 72, + 262, + 131 + ], + "blocks": [ + { + "bbox": [ + 203, + 72, + 262, + 131 + ], + "lines": [ + { + "bbox": [ + 203, + 72, + 262, + 131 + ], + "spans": [ + { + "bbox": [ + 203, + 72, + 262, + 131 + ], + "type": "image", + "image_path": "7bcc9d39fb308da4882ed9e1f3b8366c211dcf6e80e51a273defa796a7bc7109.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 214, + 132, + 251, + 137 + ], + "lines": [ + { + "bbox": [ + 214, + 132, + 251, + 137 + ], + "spans": [ + { + "bbox": [ + 214, + 132, + 251, + 137 + ], + "type": "text", + "content": "Entire Sky Region" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 65, + 148, + 267, + 232 + ], + "blocks": [ + { + "bbox": [ + 77, + 139, + 259, + 147 + ], + "lines": [ + { + "bbox": [ + 77, + 139, + 259, + 147 + ], + "spans": [ + { + "bbox": [ + 77, + 139, + 259, + 147 + ], + "type": "text", + "content": "(a) A semantic category (sky) spans the known region and the edited region" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 65, + 148, + 267, + 232 + ], + "lines": [ + { + "bbox": [ + 65, + 148, + 267, + 232 + ], + "spans": [ + { + "bbox": [ + 65, + 148, + 267, + 232 + ], + "type": "image", + "image_path": "69bb4166ff601b1e007588aaffa1e7970acbd87838286fc2a778a2208ac73933.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 63, + 236, + 272, + 325 + ], + "blocks": [ + { + "bbox": [ + 63, + 236, + 272, + 325 + ], + "lines": [ + { + "bbox": [ + 63, + 236, + 272, + 325 + ], + "spans": [ + { + "bbox": [ + 63, + 236, + 272, + 325 + ], + "type": "image", + "image_path": "5d82832549abf79be95adf14fad0fb07d3e3b5375157f0b8589a993aa935750a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 336, + 288, + 413 + ], + "lines": [ + { + "bbox": [ + 46, + 336, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 288, + 413 + ], + "type": "text", + "content": "Figure 3. (a) A background category, such as sky, may span known and edited regions. We want to transfer the features from the known region to the generated region in a semantic-aware fashion. (b) The principle of SASPM. We extract the feature code for each background category from the known region and then propagate it to the entire region. (c) The architecture of our background generator." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": "map in front of a SASPM. " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": " are the spatial dimension and " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": " is the number of channels. Let " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "U \\in \\mathbb{R}^{L \\times C}" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": " represent " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": " feature codes extracted from the known region, and the feature codes of non-background classes are set to zero. We generate a code map " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": " based on the segmentation map " + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "inline_equation", + "content": "S \\in \\mathbb{L}^{H \\times W \\times L}" + }, + { + "bbox": [ + 46, + 432, + 287, + 529 + ], + "type": "text", + "content": " through a matrix multiplication to spatially broadcast the feature codes into the corresponding semantic region:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 540, + 287, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 540, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 141, + 540, + 287, + 552 + ], + "type": "interline_equation", + "content": "P = S \\otimes U \\tag {1}", + "image_path": "e6c0d0a16c6aa777cefd2989e799917338d20989b131eba403a9360505953d8b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": "Thus, " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "P \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " is restored to the spatial dimension filled with the category-specific feature codes. Finally, we propagate " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " into the original " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " using a modulation operation following SPADE [33]. Specifically, we learn two parameters " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\gamma_{P} \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "\\beta_{P} \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": " to modulate " + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 555, + 287, + 626 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 79, + 646, + 287, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 646, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 79, + 646, + 287, + 659 + ], + "type": "interline_equation", + "content": "F _ {P} = \\operatorname {R e L U} \\left(\\gamma_ {P} \\odot I N (\\operatorname {C o n v} (F)) \\oplus \\beta_ {P}\\right) \\tag {2}", + "image_path": "3afd59583e30682d11c5a667de6e8b0c4d0fe6eaca0ef0dd499e8449978fdfb0.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "Conv(\\cdot), IN(\\cdot)" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "ReLU(\\cdot)" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": " denote Convolutional Layer, Instance Normalization, and ReLU activation function, respectively. " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": " are element-wise multiplication and addition." + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 324, + 73, + 525, + 213 + ], + "blocks": [ + { + "bbox": [ + 324, + 73, + 525, + 213 + ], + "lines": [ + { + "bbox": [ + 324, + 73, + 525, + 213 + ], + "spans": [ + { + "bbox": [ + 324, + 73, + 525, + 213 + ], + "type": "image", + "image_path": "fc63ece7463334a8406e112aa21d3c25a692e10326d28ccb3d81281af51c8ce8.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 225, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 305, + 225, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 225, + 545, + 270 + ], + "type": "text", + "content": "Figure 4. Boundary-Anchored Patch Discriminator " + }, + { + "bbox": [ + 305, + 225, + 545, + 270 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 305, + 225, + 545, + 270 + ], + "type": "text", + "content": " takes in four real image patches or fake image patches of random size. All patches are centered on the boundary of the edited region enclosed by the red line." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 293, + 480, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 480, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 480, + 304 + ], + "type": "text", + "content": "Boundary-Anchored Patch Discriminator" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": "We employ two discriminators for our background generator: (1) A global discriminator used by previous works [28]; (2) a novel Boundary-Anchored Patch Discriminator " + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": ". We introduce " + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": " to enforce the generator to pay attention to local texture across the fringe of the edited area. We expect " + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": " can capture known and generated textures simultaneously to facilitate texture-consistent results. To this end, we randomly select several central points anchored on the boundary of the edited region to crop patches from real or generated images, as shown in Figure 4. Thus, the fake patches contain both real and fake textures, so " + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": " can distinguish between true and false through texture consistency." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "content": "The training objective of " + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "inline_equation", + "content": "G_{B}" + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "content": " is comprised of L1 Distance Loss " + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "content": ", Perceptual Loss " + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{P}}" + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "content": " [16], Global Adversarial Loss " + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}^{G}" + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "content": ", and Local Patch Adversarial Loss " + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}^{L}" + }, + { + "bbox": [ + 305, + 460, + 545, + 498 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 331, + 517, + 545, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 517, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 331, + 517, + 545, + 533 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {B} = \\mathcal {L} _ {1} + \\lambda_ {P B} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} ^ {G} + \\lambda_ {G A N} ^ {L} \\mathcal {L} _ {G A N} ^ {L} \\tag {3}", + "image_path": "4451934ed73ddb9ca3345ea53d0da561c86da67243acb508691ab10f5bfbb901.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{P}}" + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "text", + "content": " force the generated results to be closer to the ground truth in RGB space and VGG space [38]. " + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}^{G}" + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}^{L}" + }, + { + "bbox": [ + 305, + 542, + 545, + 614 + ], + "type": "text", + "content": " are applied to global images and local patches, respectively. All adversarial losses in this work are associated with a SNPatchGAN Discriminator [46] using the hinge version [2]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 623, + 416, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 416, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 416, + 635 + ], + "type": "text", + "content": "3.2. Object Generation" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 642, + 545, + 713 + ], + "type": "text", + "content": "Our task involves dealing with two scenarios: Inpainting or generating an object—the former aims at completing an object based on its visible part. The latter synthesizes an inexistent object from its mask with an arbitrary appearance. Unlike handling all objects at once, cropping each edited object and independently generating them allows" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1871" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 71, + 286, + 150 + ], + "blocks": [ + { + "bbox": [ + 78, + 71, + 286, + 150 + ], + "lines": [ + { + "bbox": [ + 78, + 71, + 286, + 150 + ], + "spans": [ + { + "bbox": [ + 78, + 71, + 286, + 150 + ], + "type": "image", + "image_path": "9df297a83bcfe686387a088e7b3368ca4248b459a5d1d0dc3e27db9b48149cc1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 283, + 149, + 336, + 156 + ], + "lines": [ + { + "bbox": [ + 283, + 149, + 336, + 156 + ], + "spans": [ + { + "bbox": [ + 283, + 149, + 336, + 156 + ], + "type": "text", + "content": "(a) Extract Style Map" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 310, + 77, + 515, + 150 + ], + "blocks": [ + { + "bbox": [ + 310, + 77, + 515, + 150 + ], + "lines": [ + { + "bbox": [ + 310, + 77, + 515, + 150 + ], + "spans": [ + { + "bbox": [ + 310, + 77, + 515, + 150 + ], + "type": "image", + "image_path": "e713369a55511ca4f1c2dd6f5e369788af1123539258239af564c1f1aa5b5e35.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 79, + 158, + 294, + 256 + ], + "blocks": [ + { + "bbox": [ + 79, + 158, + 294, + 256 + ], + "lines": [ + { + "bbox": [ + 79, + 158, + 294, + 256 + ], + "spans": [ + { + "bbox": [ + 79, + 158, + 294, + 256 + ], + "type": "image", + "image_path": "ab7f21e920b2e18c5da3c5e44c6d70166f65b7e54adba50e40b38c4a3ea92208.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 309, + 158, + 512, + 256 + ], + "blocks": [ + { + "bbox": [ + 309, + 158, + 512, + 256 + ], + "lines": [ + { + "bbox": [ + 309, + 158, + 512, + 256 + ], + "spans": [ + { + "bbox": [ + 309, + 158, + 512, + 256 + ], + "type": "image", + "image_path": "8f157caf5091613a43948abb26c140d155894275dac9575eb7f958c7fdddef78.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 268, + 545, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 268, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 545, + 301 + ], + "type": "text", + "content": "Figure 5. (a) How to extract style maps? During training, we extract their style codes from ground truth images or randomly sampled images and then generate style maps by broadcasting. During inference, we sample a class-specific style code directly from the style bank. (b) The structure of Semantic-Style Normalization Module (SSNM). (c) We build a Style-Diversity Object Generator equipped with SSNM." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": "us to use aligned input images with the same size, which is beneficial for generating high-quality results. Specifically, we crop all objects " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\{Crop(I_e)_c^q\\}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " from the edited region based on object masks " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\{M_c^q\\}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": ". We leverage a two-way model to handle the different scenarios. One way is a lightweight inpainting network " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "G_{OI}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " to complete objects. " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "G_{OI}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " is a UNet-like [36] network and its training objective is: " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GI} = \\mathcal{L}_1 + \\lambda_{PI}\\mathcal{L}_{\\mathrm{P}} + \\mathcal{L}_{GAN}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{P}}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " are the same as the terms in Equation 6. The other way is the proposed Style-Diversity Object Generator " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "G_{OG}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " for the multi-modal generation. Note that all categories of objects share " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "G_{OI}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "inline_equation", + "content": "G_{OG}" + }, + { + "bbox": [ + 46, + 323, + 287, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 476, + 183, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 183, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 183, + 488 + ], + "type": "text", + "content": "Style-Diversity Object Generator" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "G_{OG}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": " generates a class-specific image from a one-hot segmentation map " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "M_{sem} \\in \\mathbb{L}^{H \\times W \\times K}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": " created by the corresponding object mask " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "M_c^q" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": " is the number of the predefined foreground class set. Motivated by disentanglement learning [12, 20, 27], we utilize style information to control the appearance of results for multi-modal generation. Specifically, we sample an image from the training set with the same class label and extract its style code " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "W \\in \\mathbb{R}^{128}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": " by a style encoder " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "E_s" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": ". Then we generate a style map " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "M_{style} \\in \\mathbb{R}^{H \\times W \\times 128}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": " via broadcasting the style code according to " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "M_c^q" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": ", as illustrated in Figure 5(a). At this point, we have acquired a semantic map " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "M_{sem}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": " and a style map " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "M_{style}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": ". The next is how to decode them back to a style-controlled object image. To this end, we design a Semantic-Style Normalization Module (SSNM) to integrate the style and semantic information, as shown in Figure 5(b). We first inject the semantic information into the input feature maps " + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 498, + 287, + 712 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 336, + 344, + 545, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 344, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 336, + 344, + 545, + 357 + ], + "type": "interline_equation", + "content": "F _ {s e m} = R e L U \\left(\\gamma_ {c} \\odot I N (C o n v (F)) \\oplus \\beta_ {c}\\right) \\tag {4}", + "image_path": "ddc35fba6127f6f64eb76e4e8cee341c94ae7d4b17afb93687d2c08d2d668385.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "text", + "content": "Where two normalization parameters, " + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\gamma_c \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "inline_equation", + "content": "\\beta_c \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "text", + "content": " are learned from " + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "inline_equation", + "content": "M_{sem}" + }, + { + "bbox": [ + 305, + 365, + 545, + 402 + ], + "type": "text", + "content": ". Similarly, the style information is injected by:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 333, + 423, + 545, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 423, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 333, + 423, + 545, + 436 + ], + "type": "interline_equation", + "content": "F _ {O} = \\operatorname {R e L U} \\left(\\gamma_ {s} \\odot I N \\left(\\operatorname {C o n v} \\left(F _ {\\text {s e m}}\\right)\\right) \\oplus \\beta_ {s}\\right) \\tag {5}", + "image_path": "eaa50c8488fbcc716910a8f5745bc1d9aa9c4b06c52fe15087f854168af709db.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "text", + "content": "Where two normalization parameters " + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "inline_equation", + "content": "\\gamma_s \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "inline_equation", + "content": "\\beta_s \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "text", + "content": " are learned from " + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "inline_equation", + "content": "M_{style}" + }, + { + "bbox": [ + 305, + 444, + 544, + 468 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "content": "During training, for each sample, we take the ground truth image " + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "inline_equation", + "content": "I^{gt}" + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "content": " and a randomly sampled image " + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "inline_equation", + "content": "I^s" + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "content": " as the style images to generate two results " + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "inline_equation", + "content": "R^{gt}" + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "inline_equation", + "content": "R^s" + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "content": ". We employ the following objective function to optimize " + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "inline_equation", + "content": "G_{OG}" + }, + { + "bbox": [ + 304, + 469, + 545, + 517 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 343, + 529, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 529, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 343, + 529, + 545, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {G O} = \\mathcal {L} _ {1} + \\lambda_ {P O} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} + \\mathcal {L} _ {\\mathrm {S C C}} \\tag {6}", + "image_path": "aaff3c401bab3ddddbb40b066faf812322b7bf902d0ce9ffd2d8c27bc7559004.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": " is only applied to " + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "R^{gt}" + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{P}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}" + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCC}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": " are imposed on all results. We introduce Style Cycle-Consistency Loss " + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCC}}" + }, + { + "bbox": [ + 304, + 546, + 545, + 594 + ], + "type": "text", + "content": " to force the generator to produce style-consistent results with style images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 318, + 612, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 612, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 318, + 612, + 545, + 644 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S C C} = 1 - \\cos \\left(\\frac {E _ {S} ^ {\\prime} (R)}{\\| E _ {S} ^ {\\prime} (R) \\| _ {2}}, \\frac {E _ {s} ^ {\\prime} \\left(I ^ {s t y l e}\\right)}{\\| E _ {S} ^ {\\prime} \\left(I ^ {s t y l e}\\right) \\| _ {2}}\\right) \\tag {7}", + "image_path": "2c653770fd6a6f154fe428ed580dcb2fce684406b3f201fd7cb2a4b533b335f7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "inline_equation", + "content": "I^{style}" + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "content": " is the style image and " + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "content": " is the generated result. " + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "inline_equation", + "content": "E_s'(\\cdot)" + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "content": " is a style encoder with the same structure as " + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "inline_equation", + "content": "E_s" + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "inline_equation", + "content": "\\cos(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 653, + 544, + 689 + ], + "type": "text", + "content": " represents the cosine similarity of two vectors." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Previous image translation methods [12, 20] achieve multi-modal generation by adding Gaussian noise during" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1872" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 72, + 275, + 144 + ], + "blocks": [ + { + "bbox": [ + 65, + 72, + 275, + 144 + ], + "lines": [ + { + "bbox": [ + 65, + 72, + 275, + 144 + ], + "spans": [ + { + "bbox": [ + 65, + 72, + 275, + 144 + ], + "type": "image", + "image_path": "dbdb21abf6f497cb65f4964d6d93a2d17ca2df6315cb6860a508d4bf55257fbb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 156, + 287, + 179 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 179 + ], + "type": "text", + "content": "Figure 6. Structure of Fusion Network. The red line indicates the skip connection." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 200, + 288, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 288, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 288, + 309 + ], + "type": "text", + "content": "inference. We find that noise leads to low-quality results and limited diversity. To solve this problem, we replace the noise with a style bank. Precisely, once training is done, we extract all style codes from the training set by the trained " + }, + { + "bbox": [ + 46, + 200, + 288, + 309 + ], + "type": "inline_equation", + "content": "E_{s}" + }, + { + "bbox": [ + 46, + 200, + 288, + 309 + ], + "type": "text", + "content": " and save them for building a class-aware style bank. During inference, we randomly sample different style codes from the style bank to generate different results. It is worth mentioning that our approach does not increase any additional computational overhead compared to adding noise." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 316, + 145, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 145, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 145, + 328 + ], + "type": "text", + "content": "3.3. Fusion Network" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "text", + "content": "After generating all backgrounds and objects, we embed them into their original positions to obtain a composited image. However, this preliminary result may be discordant since each object is generated independently without accounting for context. We employ a fusion network " + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "text", + "content": " to harmonize the objects with the surroundings, as shown in Figure 6. " + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "text", + "content": " learns an offset value for each pixel via a skip connection [7,36] to produce the final results. We use Perceptual Loss and Adversarial Loss to optimize " + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 334, + 287, + 441 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 455, + 287, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 455, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 116, + 455, + 287, + 467 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {F} = \\lambda_ {P F} \\mathcal {L} _ {\\mathrm {P}} + \\mathcal {L} _ {G A N} \\tag {8}", + "image_path": "323e7334eb67b2ef6be7147674a599fb8df87f1beb08cf13984619d72a7c0503.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 478, + 128, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 128, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 128, + 491 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 568 + ], + "type": "text", + "content": "Datasets. We conduct experiments on two datasets, Cityscapes and ADE20K-Room, used in [28, 32]. Cityscapes [3] contains complex street scene images in German cities. ADE20K-Room is a subset of ADE20K [50] consisting of indoor scene images. We train and test our model at " + }, + { + "bbox": [ + 46, + 498, + 287, + 568 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 498, + 287, + 568 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Implementation Details. We use free-form, extension, and outpainting masks following [28]. Similar to the previous work [22], we choose those frequently-appearing categories as the foreground class set, (car, person) for Cityscapes and (bed, chest, lamp, chair, table) for ADE20K-Room. All sub-networks are independently trained using ADAM optimizers [19] for both the generator and the discriminators with momentum " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.5" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ", and the learning rates for the generator and the discriminators are set to 0.0001 and 0.0004, respectively. For training " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ", we randomly crop 4 square patches with the size ranging from " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "96 \\times 96" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "160 \\times 160" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ". We set balance coefficients:" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 549, + 236 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 549, + 236 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 549, + 236 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 549, + 236 + ], + "type": "image", + "image_path": "9d32725e08e59a925b7210909fdfd27a6a7782c77512c960b2580fa2a81536ad.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 247, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 305, + 247, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 545, + 281 + ], + "type": "text", + "content": "Figure 7. Visual comparisons with state-of-the-art methods. Our method is effective in generating texture-consistent backgrounds and photo-realistic objects." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\lambda_{PB} = \\lambda_{PI} = \\lambda_{PO} = \\lambda_{PF} = 10" + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "inline_equation", + "content": "\\lambda_{GAN}^{L} = 0.2" + }, + { + "bbox": [ + 305, + 300, + 545, + 348 + ], + "type": "text", + "content": ". The proposed method is implemented with Pytorch 1.10 [34], and all experiments are performed on a single NVIDIA RTX 3090 GPU." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 349, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 545, + 469 + ], + "type": "text", + "content": "Baselines. We compare the proposed methods with the state-of-the-art semantic image editing methods, including HIM [10], SESAME [32], ASSET [23], SPMPGAN [28]. We also introduce two additional methods [40, 48] as baselines to investigate related work more widely. LGGAN [40] learns a map from segmentation maps to photo-realistic images using global image-level and class-specific generators. Co-Mod [48] demonstrates impressive results in semantic image generation and image inpainting. We change their input to be the same as our task." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 477, + 432, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 432, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 432, + 490 + ], + "type": "text", + "content": "4.1. Qualitative evaluation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 495, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 639 + ], + "type": "text", + "content": "We demonstrate a visual comparison of the competing methods, as shown in Figure 7. We observe that the results produced by the proposed SIEDOB are visually better than existing methods in two aspects: (1) Our method can well handle dense objects overlapping each other, e.g., in the second and third rows. However, other methods produce distorted and inseparable results. (2) Our method generate texture-consistent content between edited regions and known regions both on background and objects, e.g., the red cars in the first row and the curtain in the fourth row. The performance improvement benefits from our disentangling generation strategy and carefully designed sub-networks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 647, + 440, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 440, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 440, + 659 + ], + "type": "text", + "content": "4.2. Quantitative evaluation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Table 1 lists the quantitative results with three different mask types. Following previous works, we use three metrics: FID [8], LPIPS [47], and mean Intersection-over-Union (mIoU). FID is introduced to assess the fidelity of the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1873" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 70, + 271, + 262 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 271, + 262 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 271, + 262 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 271, + 262 + ], + "type": "table", + "html": "
M.MethodCityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
F.LGGAN15.290.09458.6224.740.09727.68
Co-Mod15.880.09756.5027.370.11127.52
HIM15.580.09358.9928.640.13328.04
SESAME12.890.08258.8821.730.10127.50
ASSET13.670.09858.1230.630.12626.02
SPMPGAN11.900.08458.8018.830.09028.22
SIEDOB11.070.07759.4117.610.08929.72
E.LGGAN26.010.17558.3737.090.21327.91
Co-Mod29.270.18856.4438.610.23127.13
HIM25.200.18058.9140.690.23927.61
SESAME20.300.16859.0836.430.21127.62
ASSET21.990.18658.0138.170.26127.03
SPMPGAN19.460.16759.1032.920.19927.73
SIEDOB19.200.15959.6331.660.19129.52
O.LGGAN39.120.25458.7749.070.33427.69
Co-Mod50.290.26455.3951.450.32526.54
HIM36.270.25258.9954.510.33728.19
SESAME28.270.23758.7547.720.30527.40
ASSET30.600.24058.9157.280.33127.18
SPMPGAN27.630.23358.5341.520.28827.85
SIEDOB27.900.22159.3741.070.27528.94
", + "image_path": "9ae2ba8e214b30fd6c01af4fae69e24792b407cbb86a6367bf91e23bbcbf177f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 49, + 327, + 291, + 440 + ], + "blocks": [ + { + "bbox": [ + 49, + 327, + 291, + 440 + ], + "lines": [ + { + "bbox": [ + 49, + 327, + 291, + 440 + ], + "spans": [ + { + "bbox": [ + 49, + 327, + 291, + 440 + ], + "type": "image", + "image_path": "959b326a4d92691901f8dc707900ccf82d765bf65c3a1a7a285622e42a096bbd.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 449, + 246, + 460 + ], + "lines": [ + { + "bbox": [ + 88, + 449, + 246, + 460 + ], + "spans": [ + { + "bbox": [ + 88, + 449, + 246, + 460 + ], + "type": "text", + "content": "Figure 8. Visual results of addition objects." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 53, + 475, + 282, + 551 + ], + "blocks": [ + { + "bbox": [ + 53, + 475, + 282, + 551 + ], + "lines": [ + { + "bbox": [ + 53, + 475, + 282, + 551 + ], + "spans": [ + { + "bbox": [ + 53, + 475, + 282, + 551 + ], + "type": "image", + "image_path": "e8d900b17b0ac95b34a0fce4b8935a77175922410e2e7535e07f0affa0a3d304.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 91, + 560, + 242, + 571 + ], + "lines": [ + { + "bbox": [ + 91, + 560, + 242, + 571 + ], + "spans": [ + { + "bbox": [ + 91, + 560, + 242, + 571 + ], + "type": "text", + "content": "Figure 9. Multi-modal generation results." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "results by computing the Wasserstein-2 distance between the distributions of the synthesized and real images. LPIPS evaluates the similarity between the generated image and the ground truth in a pairwise manner. mIoU measures the alignment of semantic labels between the generated results and input segmentation maps. We use solid models to obtain segmentation maps: HRNet [41] for ADE20K-Room, and DRN-D-105 [44] for Cityscapes. Our method outperforms the other methods under different metrics and mask settings." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 326, + 71, + 526, + 116 + ], + "blocks": [ + { + "bbox": [ + 326, + 71, + 526, + 116 + ], + "lines": [ + { + "bbox": [ + 326, + 71, + 526, + 116 + ], + "spans": [ + { + "bbox": [ + 326, + 71, + 526, + 116 + ], + "type": "image", + "image_path": "7d163ed507081c000ed4f0508e2d0a0715ae08f360eb04e206e2b8bacf14a900.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 126, + 545, + 160 + ], + "lines": [ + { + "bbox": [ + 305, + 126, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 305, + 126, + 545, + 160 + ], + "type": "text", + "content": "Figure 10. Out-of-distribution editing. Our method can add cars in the middle of the road or on the sidewalk, which do not exist in the training dataset." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 171, + 548, + 251 + ], + "blocks": [ + { + "bbox": [ + 47, + 270, + 288, + 314 + ], + "lines": [ + { + "bbox": [ + 47, + 270, + 288, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 270, + 288, + 314 + ], + "type": "text", + "content": "Table 1. Quantitative comparison with other methods. M., F., E., and O. represent Mask Type, Free-Form Mask, Extension Mask, and Outpainting Mask, respectively. (↑: Higher is better; ↓: Lower is better)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 171, + 548, + 251 + ], + "lines": [ + { + "bbox": [ + 307, + 171, + 548, + 251 + ], + "spans": [ + { + "bbox": [ + 307, + 171, + 548, + 251 + ], + "type": "table", + "html": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑Div↑FID↓LPIPS↓mIoU↑Div↑
LGGAN7.690.02757.01-24.490.17130.05-
Co-Mod7.790.02956.290.003021.090.11830.630.0145
HIM6.920.02858.71-29.100.23230.58-
SESAME6.670.02458.79-18.010.11730.89-
ASSET6.740.02556.020.005227.680.20929.790.0337
SPMPGAN6.590.02158.60-17.210.11530.58-
SIEDOB6.290.02058.880.005516.320.11031.040.0362
", + "image_path": "ff3c082e736ff4cf1c210f3adc90f9dbb7a21298233a1bf3c53b2a31c3076ae6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 329, + 282, + 523, + 329 + ], + "blocks": [ + { + "bbox": [ + 339, + 261, + 511, + 271 + ], + "lines": [ + { + "bbox": [ + 339, + 261, + 511, + 271 + ], + "spans": [ + { + "bbox": [ + 339, + 261, + 511, + 271 + ], + "type": "text", + "content": "Table 2. Quantitative results of object addition." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 329, + 282, + 523, + 329 + ], + "lines": [ + { + "bbox": [ + 329, + 282, + 523, + 329 + ], + "spans": [ + { + "bbox": [ + 329, + 282, + 523, + 329 + ], + "type": "table", + "html": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o SASPM14.110.08559.4320.030.09129.02
w/o DBAP12.680.08159.4919.140.08329.21
Full model12.150.07959.5118.720.08129.30
", + "image_path": "407572744bce5d40734ce8f0dd8c12afe16386270a4c9725c2adbd4a86770bf6.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 332, + 338, + 518, + 348 + ], + "lines": [ + { + "bbox": [ + 332, + 338, + 518, + 348 + ], + "spans": [ + { + "bbox": [ + 332, + 338, + 518, + 348 + ], + "type": "text", + "content": "Table 3. Quantitative study on SASPM and " + }, + { + "bbox": [ + 332, + 338, + 518, + 348 + ], + "type": "inline_equation", + "content": "{D}_{BAP}" + }, + { + "bbox": [ + 332, + 338, + 518, + 348 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 370, + 404, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 404, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 404, + 383 + ], + "type": "text", + "content": "4.3. Addition Object" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 388, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 628 + ], + "type": "text", + "content": "Adding a new object to the given image is an essential ability of semantic image editing. The visual results are shown in Figure 8. In this experiment, we randomly select an instance of each test image and create a rectangular mask encircling the object. The proposed method can generate realistic objects with crisp edges. Adding an object to the edited area that does not exist originally should have diverse results. Some previous methods [23,48] have multimodal generation capabilities. We sample two results from all methods, as shown in Figure 9. Our method achieves a higher diversity than other models because the previous methods only exert a global influence on the generation process; in contrast, our model independently generates each object using different class-aware style codes. The quantitative results listed in Table 2 also indicate the superiority of our method. Here, the Diversity score (Div) is calculated as the average LPIPS distance between pairs of randomly sampled results for all test images, as also done in [25,49]. Moreover, our model can hallucinate images that do not exist in the dataset's distribution, as shown in Figure 10." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 635, + 399, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 399, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 399, + 647 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Effectiveness of SASPM and Boundary-Anchored Patch Discriminator. We investigate the contributions of the proposed SASPM and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " to the generation of texture-consistent background. To exclude the interference of the foreground, we create mask maps that only include back" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1874" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 71, + 259, + 151 + ], + "blocks": [ + { + "bbox": [ + 77, + 71, + 259, + 151 + ], + "lines": [ + { + "bbox": [ + 77, + 71, + 259, + 151 + ], + "spans": [ + { + "bbox": [ + 77, + 71, + 259, + 151 + ], + "type": "image", + "image_path": "1a254f04485e719ba8b864cb7c69f361655f77749411273125f566e839b0b3fd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 162, + 286, + 185 + ], + "lines": [ + { + "bbox": [ + 47, + 162, + 286, + 185 + ], + "spans": [ + { + "bbox": [ + 47, + 162, + 286, + 185 + ], + "type": "text", + "content": "Figure 11. Ablation analysis on SASPM and " + }, + { + "bbox": [ + 47, + 162, + 286, + 185 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 47, + 162, + 286, + 185 + ], + "type": "text", + "content": " for synthesizing texture-consistent backgrounds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 201, + 279, + 260 + ], + "blocks": [ + { + "bbox": [ + 55, + 201, + 279, + 260 + ], + "lines": [ + { + "bbox": [ + 55, + 201, + 279, + 260 + ], + "spans": [ + { + "bbox": [ + 55, + 201, + 279, + 260 + ], + "type": "image", + "image_path": "df025af410496ed61eff8d13d7b18c17ac5af7c29f79df022c640be048eaef31.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 272, + 253, + 283 + ], + "lines": [ + { + "bbox": [ + 81, + 272, + 253, + 283 + ], + "spans": [ + { + "bbox": [ + 81, + 272, + 253, + 283 + ], + "type": "text", + "content": "Figure 12. Ablation study of object generation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "text", + "content": "ground regions in this study. We remove all SASPM (\"w/o SASPM\") or " + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "text", + "content": " (\"w/o " + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "text", + "content": ") from our model as two baselines. The visual results are shown in Figure 11 and prove that SASPM and " + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "text", + "content": " can help the background generator effectively alleviate texture inconsistencies. Vanilla convolutional layers have limited receptive fields and no ability to locate where edited or known regions are. SASPM explicitly transfers features from known regions to edited regions with the same semantic labels across distant spatial distances. " + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "inline_equation", + "content": "D_{BAP}" + }, + { + "bbox": [ + 46, + 305, + 287, + 449 + ], + "type": "text", + "content": " forces the generator to pay more attention to local textures on editing boundaries rather than just global images. Quantitative results are listed in Table 3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "text", + "content": "Effectiveness of Style-Diversity Object Generator. To verify the benefit of " + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCC}}" + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "text", + "content": " and the style bank, we set up two baselines: (1) Dropping out " + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCC}}" + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "text", + "content": " (\"w/o " + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCC}}" + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "text", + "content": "). (2) Replacing the style codes with noise vectors (\"w Noise\"). Figure 12 shows some visual results. If we drop out " + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCC}}" + }, + { + "bbox": [ + 46, + 449, + 287, + 581 + ], + "type": "text", + "content": ", the generated image's style may not be consistent with the style image. If we produce multi-modal results by injecting noise, it leads to a loss of fidelity and diversity. This is because Gaussian noise is semantics-free, while style code is category-specific and provides controllability. The quantitative results are listed in Table 4." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 700 + ], + "type": "text", + "content": "Effectiveness of Separate Generation. We remove the object generator and the fusion network but keep other components unchanged to obtain a baseline (w/o Separation) and increase its channel number for a fair comparison. Qualitative and quantitative comparisons can be found in Figure 13 and Table 5, respectively. In this experiment, we employ the masks used in object addition. The visual comparison shows that the separate generation paradigm significantly improves performance for objects with complicated surroundings." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "type": "text", + "content": "Effectiveness of Fusion Network. Fusion network can" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 322, + 71, + 530, + 148 + ], + "blocks": [ + { + "bbox": [ + 322, + 71, + 530, + 148 + ], + "lines": [ + { + "bbox": [ + 322, + 71, + 530, + 148 + ], + "spans": [ + { + "bbox": [ + 322, + 71, + 530, + 148 + ], + "type": "image", + "image_path": "3b39a7e3ce2ae4e0e8154ab3f3935bce0533c29a7ad3d905c0d86dfe02ef87c1.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 158, + 545, + 178 + ], + "lines": [ + { + "bbox": [ + 305, + 158, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 545, + 178 + ], + "type": "text", + "content": "Figure 13. Visual analysis on disentangled generation and fusion network." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 343, + 190, + 509, + 270 + ], + "blocks": [ + { + "bbox": [ + 343, + 190, + 509, + 270 + ], + "lines": [ + { + "bbox": [ + 343, + 190, + 509, + 270 + ], + "spans": [ + { + "bbox": [ + 343, + 190, + 509, + 270 + ], + "type": "table", + "html": "
classw/o LSCCw NoiseGOG
FID↓Div↑FID↓Div↑FID↓Div↑
car123.820.103173.570.090118.320.115
person238.100.079307.110.052219.200.098
bed227.180.303395.330.210239.780.372
chest192.120.217273.100.113149.290.229
lamp121.010.195153.940.129112.500.218
chair168.010.274207.350.177163.140.289
table211.390.141289.550.091201.320.143
", + "image_path": "ca55dcefe4907aa6ea81d666b1cb00d7883177abd1a6bd8bc390b77bc59afc5b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 326, + 300, + 526, + 357 + ], + "blocks": [ + { + "bbox": [ + 337, + 279, + 513, + 291 + ], + "lines": [ + { + "bbox": [ + 337, + 279, + 513, + 291 + ], + "spans": [ + { + "bbox": [ + 337, + 279, + 513, + 291 + ], + "type": "text", + "content": "Table 4. Quantitative results of different objects." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 300, + 526, + 357 + ], + "lines": [ + { + "bbox": [ + 326, + 300, + 526, + 357 + ], + "spans": [ + { + "bbox": [ + 326, + 300, + 526, + 357 + ], + "type": "table", + "html": "
CityscapesADE20K-Room
FID↓LPIPS↓mIoU↑FID↓LPIPS↓mIoU↑
w/o Separation6.780.02956.4321.970.18030.32
w/o Fusion6.730.02758.6819.190.13130.80
w/o Skip6.410.02258.7617.890.11830.96
Full model6.290.02058.8816.320.11031.04
", + "image_path": "24ec05ff95d86cf16382f0fc559a7715c22833e79cc5ae1ee9c7d0fd8a0c8a70.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 365, + 545, + 386 + ], + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 386 + ], + "type": "text", + "content": "Table 5. Quantitative studies of separate generation paradigm and fusion network." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "type": "text", + "content": "eliminate abrupt boundaries between generated objects and backgrounds. Removing the fusion network (" + }, + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "type": "text", + "content": " Fusion) or not using the skip connection (" + }, + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "type": "inline_equation", + "content": "w/o" + }, + { + "bbox": [ + 304, + 407, + 545, + 467 + ], + "type": "text", + "content": " Skip) will degrade the performance, which are qualitatively and quantitatively demonstrated in Figure 13 and Table 5." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 478, + 463, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 463, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 463, + 491 + ], + "type": "text", + "content": "5. Conclusion and Limitations" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "text", + "content": "This paper proposes a novel paradigm for semantic image editing, named SIEDOB. Its core idea is that since the characteristics of foreground objects and backgrounds are dramatically different, we design a heterogeneous model to handle them separately. To this end, we present SASPM and Boundary-Anchored Patch Discriminator to facilitate the generation of texture-consistent backgrounds and employ a Style-Diversity Object Generator to produce high-quality and diverse objects. Extensive experimental results demonstrate the superiority of our method. However, our method has some limitations. Some foreground categories are very rare in the dataset, so we cannot obtain enough data for training. In addition, object generation is hard to produce satisfactory results when an object is with an extreme pose or large-scale occlusion." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement This work is supported by State Grid Corporation of China (Grant No. 5500-202011091A-0-0-00)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1875" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 147 + ], + "type": "text", + "content": "[1] Deblina Bhattacharjee, Seungryong Kim, Guillaume Vizier, and Mathieu Salzmann. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5104-5113, 2020. 2" + } + ] + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1878" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SIM_ Semantic-Aware Instance Mask Generation for Box-Supervised Instance Segmentation/884f8e5b-a009-4236-8afe-619abfb36ed7_content_list.json b/2023/SIM_ Semantic-Aware Instance Mask Generation for Box-Supervised Instance Segmentation/884f8e5b-a009-4236-8afe-619abfb36ed7_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..5f2db793719df464cbe58c4a35a1caac867a1bf6 --- /dev/null +++ b/2023/SIM_ Semantic-Aware Instance Mask Generation for Box-Supervised Instance Segmentation/884f8e5b-a009-4236-8afe-619abfb36ed7_content_list.json @@ -0,0 +1,1798 @@ +[ + { + "type": "text", + "text": "SIM: Semantic-aware Instance Mask Generation for Box-Supervised Instance Segmentation", + "text_level": 1, + "bbox": [ + 218, + 130, + 751, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ruihuang Li\\* Chenhang He\\*, Yabin Zhang, Shuai Li, Liyi Chen, Lei Zhang† The Hong Kong Polytechnic University", + "bbox": [ + 153, + 202, + 821, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{csrhli, cshe, cslzhang}@comp.polyu.edu.hk", + "bbox": [ + 292, + 241, + 671, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Weakly supervised instance segmentation using only bounding box annotations has recently attracted much research attention. Most of the current efforts leverage low-level image features as extra supervision without explicitly exploiting the high-level semantic information of the objects, which will become ineffective when the foreground objects have similar appearances to the background or other objects nearby. We propose a new box-supervised instance segmentation approach by developing a Semantic-aware Instance Mask (SIM) generation paradigm. Instead of heavily relying on local pair-wise affinities among neighboring pixels, we construct a group of category-wise feature centroids as prototypes to identify foreground objects and assign them semantic-level pseudo labels. Considering that the semantic-aware prototypes cannot distinguish different instances of the same semantics, we propose a self-correction mechanism to rectify the falsely activated regions while enhancing the correct ones. Furthermore, to handle the occlusions between objects, we tailor the Copy-Paste operation for the weakly-supervised instance segmentation task to augment challenging training data. Extensive experimental results demonstrate the superiority of our proposed SIM approach over other state-of-the-art methods. The source code: https://github.com/1slrh/SIM.", + "bbox": [ + 75, + 323, + 473, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 717, + 209, + 732 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instance segmentation is among the fundamental tasks of computer vision, with many applications in autonomous driving, image editing, human-computer interaction, etc. The performance of instance segmentation has been improved significantly along with the advances in deep learning [6, 12, 34, 38]. However, training robust segmentation networks requires a large number of data with pixel-wise annotations, which consumes intensive human labor and", + "bbox": [ + 75, + 743, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e7b55cdab11cec2704654a2e0d28616c26781e5e519bc377a779d03a43b918dc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 290, + 630, + 357 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/126defbd4dba9001d58aa1d3abf4b65d047ab02bfc118f74b70ef672f5539bb5.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 632, + 291, + 756, + 356 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6fb346b4accf13f3aea7ec8605f5fbf5e3bd4417dc5544579b0548dc1f3f1da8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 291, + 885, + 356 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f22389ff0fdc9965a9d95ab54cf0aa288a2e736f355d4b669bbc97cffbd3fd4.jpg", + "image_caption": [ + "Figure 1. The pipeline of Semantic-aware Instance Mask (SIM) generation method. (a) shows the mask prediction produced by using only low-level affinity supervision, where the foreground heavily blends with background. (b) and (c) show the semantic-aware masks obtained with our constructed prototypes, which perceive the entity of objects but are unable to separate different instances of the same semantics. (d) shows the final instance pseudo mask rectified by our proposed self-correction module." + ], + "image_footnote": [], + "bbox": [ + 506, + 366, + 630, + 428 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/59983af5365473104c668a01c6203609f14e17c59d392107802a7a1c4d9bc2f1.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 630, + 366, + 754, + 428 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c87aec056c41cc216753e4fd695840207fb849ec642d97dbc12abbe99075a8e8.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 759, + 366, + 883, + 428 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "resources. To reduce the reliance on dense annotations, weakly-supervised instance segmentation based on cheap supervisions, such as bounding boxes [14,21,36], points [8] and image-level labels [1,18], has recently attracted increasing research attention.", + "bbox": [ + 496, + 582, + 890, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we focus on box-supervised instance segmentation (BSIS), where the bounding boxes provide coarse supervised information for pixel-wise prediction task. To provide pixel-wise supervision, conventional methods [10, 19] usually leverage off-the-shelf proposal techniques, such as MCG [30] and GrabCut [31], to create pseudo instance masks. However, the training pipelines of these methods with multiple iterative steps are cumbersome. Several recent works [14, 36] enable end-to-end training by taking pairwise affinities among pixels as extra supervision. Though these methods have achieved promising performance, they heavily depend on low-level image features, such as color pairs [36], and simply assume that the proximal pixels with similar colors are likely to have the same label. This leads to confusion when foreground objects have similar appearances to the background or other ob-", + "bbox": [ + 496, + 659, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*denotes the equal contribution, †denotes the corresponding author. This work is supported by the Hong Kong RGC RIF grant (R5001-18).", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7193", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jects nearby, as shown in Fig. 1 (a). It is thus error-prone to use only low-level image cues for supervision since they are weak to represent the inherent structure of objects.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by the fact that high-level semantic information can reveal intrinsic properties of object instances and hence provide effective supervision for segmentation model training, we propose a novel Semantic-aware Instance Mask generation method, namely SIM, to explicitly exploit the semantic information of objects. To distinguish proximal pixels with similar color but different semantics (please refer to Fig. 1 (a)), we construct a group of representative dataset-level prototypes, i.e., the feature centroids of different classes, to perform foreground/background segmentation, producing semantic-aware pseudo masks (see Fig. 1 (b)). These prototypes abstracted from massive training data can capture the structural information of objects, enabling more comprehensive semantic pattern understanding, which is complementary to affinity supervision of pairwise neighboring pixels. However, as shown in Fig. 1 (c), these prototypes are unable to separate the instances of the same semantics, especially for overlapping objects. We consequently develop a self-correction mechanism to rectify the false positives while enhancing the confidence of true-positive foreground objects, resulting in more precise instance-aware pseudo masks, as shown in Fig. 1 (d).", + "bbox": [ + 75, + 136, + 470, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "It is worth mentioning that our generated pseudo masks could co-evolve with the segmentation model without cumbersome iterative training procedures in previous methods [10, 21]. In addition, considering that the existing weakly-supervised instance segmentation methods only provide very limited supervision for rare categories and overlapping objects due to the lack of ground truth masks, we propose an online weakly-supervised Copy-Paste approach to create a combinatorial number of augmented training samples. Overall, the major contributions of this work can be summarized as follows:", + "bbox": [ + 75, + 469, + 468, + 633 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel BSIS framework is presented by developing a semantic-aware instance mask generation mechanism. Specifically, we construct a group of representative prototypes to explore the intrinsic properties of object instances and identify complete entities, which produces more reliable supervision than low-level features.", + "- A self-correction module is designed to rectify the semantic-aware pseudo masks to be instance-aware. The falsely activated regions will be reduced, and the correct ones will be boosted, enabling more stable training and progressively improving the segmentation results.", + "- We tailor the Copy-Paste operation for weakly-supervised segmentation tasks in order to create more occlusion patterns and more challenging training data. The overall framework can be trained in an end-to-end manner. Extensive experiments demonstrate the superiority of our method over other state-of-the-art methods." + ], + "bbox": [ + 75, + 640, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instance Segmentation (IS) is a fundamental task in computer vision fields, which aims to predict the pixel-wise mask for each instance of interest in an image. Many top performing IS methods [6, 15, 25, 42] follow the Mask R-CNN meta-architecture [12], which splits the IS task into two consecutive stages and performs segmentation on the extracted region proposals. Single-stage IS methods have also been rapidly developed during the past few years. YOLACT [3] and BlendMask [5] employ fine-grained FPN features rather than the RoI-aligned features for mask prediction. However, they still need crop operation for object localization. Some methods segment each instance in a fully convolutional manner without resorting to the detection results. For example, CondInst [34] and SOLO [38] employ instance-aware conditional convolutions and dynamically generate convolution kernels to segment different objects. Universal architectures [7, 41] have emerged with DETR [4] and show that end-to-end set prediction architecture is general enough for any segmentation task. Despite the promising performance, these methods heavily rely on expensive pixel-wise mask annotation, which restricts their usability in many practical applications.", + "bbox": [ + 496, + 114, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Weakly-Supervised Instance Segmentation (WSIS) with weak annotations is a more attractive yet challenging task. Some works attempt to achieve high-quality segmentation with box-level annotations [14, 17, 21, 36] or image-level annotations [1, 18]. Khoreva et al. [17] employ box supervisory training data for WSIS. However, the proposed method relies on the region proposal techniques, such as GrabCut [31] and MCG [30], to generate pseudo masks in an offline manner. Other recent methods [21, 37] also focus on generating instance labels by using an independent network, which require either extra salient data [38] or some post-processing methods [21]. This inevitably leads to a complicated training pipeline.", + "bbox": [ + 496, + 446, + 890, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve a simple yet effective training pipeline, BBTP [14] formulates WSIS as a multiple-instance learning problem and introduces a structural constraint to maintain the unity of estimated masks. BoxInst [36] builds upon an efficient CondInst [34] framework, and enforces the proximal pixels with similar colors to have the same label through a pairwise loss. Despite the promising performance, these methods depend heavily on local color supervision while neglecting the global structure of the entire object. Different from these methods, our proposed method provides more reliable supervision by leveraging high-level semantic information, which is beneficial for capturing the intrinsic structures of objects.", + "bbox": [ + 496, + 643, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pseudo Mask Generation. A widely adopted technique in conventional weakly-supervised semantic segmentation methods is Class Activation Map (CAM) [44], which aims to obtain an object localization map from class labels. How-", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7194", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7f0961fe6ded960d0036a6fcf77741460ca85f29ae9daacfefcfbcd2d3269b0b.jpg", + "image_caption": [ + "Figure 2. The framework of our proposed Semantic-aware Instance Mask (SIM) generation method. The model contains the main segmentation network $\\mathcal{F}_{seg}$ and its momentum-updated version $\\mathcal{F}_{seg}^{\\prime}$ . Given an image $X$ , we first pass it through $\\mathcal{F}_{seg}$ and $\\mathcal{F}_{seg}^{\\prime}$ to obtain the corresponding mask features $Z$ and $Z^{\\prime}$ . The prototypes are then updated as the moving average of feature cluster centroids. Next, we obtain the semantic probability map $M_{\\mathrm{S}}$ by measuring the distance between prototypes and mask features $Z^{\\prime}$ . After that, the falsely activated instances in $M_{\\mathrm{S}}$ are rectified by the instance probability map $M_{1}$ , which is obtained by integrating different positive masks of the same ground truth object. Finally, we obtain the pseudo mask $\\hat{M}$ by selecting highly-confident pixels with two thresholds." + ], + "image_footnote": [], + "bbox": [ + 99, + 85, + 872, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ever, CAM only identifies the most discriminative object regions and suffers from the problem of limited activation area [2,13,16,32]. Given that bounding boxes could provide the location information of objects in an image, BBAM [21] employs an object detector to produce a bounding box attribute map, which serves as a pseudo ground truth mask. As a more lightweight approach, self-training-based methods [22, 43, 48, 49] select high-scoring predictions on unlabeled data as pseudo labels for training. The idea of assigning labels based on prototypes has also been explored in semantic segmentation [22, 45, 46]. In this work, the prototype technique is adapted to capture the global structure of objects with the same semantics, reducing the noise caused by low-level feature supervision.", + "bbox": [ + 75, + 459, + 472, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 685, + 169, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 710, + 187, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the setting of box-supervised instance segmentation (BSIS), we are given a set of box annotated training data $\\mathcal{D} = \\{X_n, Y_n, B_n\\}_{n=1}^N$ , where $N$ is the number of images. Besides, $Y_n = \\{y_n^k\\}_{k=1}^K$ and $B_n = \\{b_n^k\\}_{k=1}^K$ denote the class-level and box-level annotations, where $K$ is the number of instances in the image $X_n$ , $y_n^k \\in \\{1, \\dots, C\\}$ represents the category label of the $k$ -th object in the $n$ -th image, and $b_n^k$ specifies its corresponding location.", + "bbox": [ + 75, + 734, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The overview of our method is shown in Fig. 2, where the proposed SIM module is highlighted in the green dotted box. We choose CondInst [34] and Mask2Former [7]", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "as the basic segmentation networks due to their simplicity and effectiveness. Instead of only relying on local pair-wise affinities among pixels as supervision [14,36], we employ a group of semantic-level prototypes to capture global structural information of objects, and produce semantic probability map $M_{\\mathrm{S}}$ by computing the distances between each pixel-wise feature vector and all prototypes. Since these prototypes are unable to separate different objects of the same semantics, we propose a self-correction mechanism to deactivate falsely estimated objects by using an instance probability map $M_{\\mathrm{I}}$ . This map can be obtained by integrating different positive masks corresponding to the same instance with an IoU-based weighting strategy. Finally, we employ two thresholds to select confident predictions as pseudo ground truths $\\hat{M}$ , and use them for training the segmentation network $\\mathcal{F}_{seg}$ .", + "bbox": [ + 496, + 459, + 890, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Semantic-aware Instance Mask Generation", + "text_level": 1, + "bbox": [ + 500, + 714, + 867, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Pseudo Semantic Map", + "text_level": 1, + "bbox": [ + 500, + 738, + 709, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Low-level image features, such as colors, intensity, edges, blobs, etc., could provide useful guidance to identify the object boundaries in an image. However, these features vary significantly with illuminations, motion blurs, and noises. Thus it is error-prone to take only low-level features as supervision for BSIS when object instances are heavily blended with the background. To address this issue, we attempt to explore the intrinsic structures of objects as semantic guidance to provide more robust supervision for BSIS", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7195", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "model training.", + "bbox": [ + 76, + 90, + 181, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We construct a group of representative prototypes to model the structural information of objects, and use them to generate semantic-aware pseudo masks. Considering that a single prototype is insufficient to capture the intra-class variance, we employ multiple prototypes [29, 45] to represent the objects in a category. Specifically, we extract $L$ prototypes (i.e., sub-centers) from each class $c \\in \\{1, \\dots, C\\}$ , denoted by $P_{c} = \\{p_{1}^{c}, \\dots, p_{L}^{c}\\}$ , to depict different characteristics of the same category. Given an input image $I \\in \\mathbb{R}^{h \\times w \\times 3}$ , we first pass it through the segmentation model $\\mathcal{F}_{seg}$ to obtain the feature map $Z \\in \\mathbb{R}^{H \\times W \\times D}$ , and normalize it with $z_{i} = \\frac{z_{i}}{||z_{i}||_{2}}$ , where $z_{i}$ denotes the $i$ -th feature vector of $Z$ with length $D$ . Unlike semantic segmentation, which predicts only one mask for each input image, we predict a variable number of masks depending on the number of categories in the image. To this end, we compute the semantic probability map corresponding to the $c$ -th category, denoted by $M_{\\mathrm{S}}^{c} \\in \\mathbb{R}^{H \\times W}$ , using the following formula:", + "bbox": [ + 75, + 108, + 473, + 395 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {\\mathrm {S}, i} ^ {c} = \\sigma \\left(\\max \\{\\frac {\\langle z _ {i} , p _ {l} ^ {c} \\rangle}{\\tau} \\} _ {l = 1} ^ {L}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 407, + 468, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\langle \\cdot \\rangle$ computes the cosine similarity between two $\\ell_2$ -normalized feature vectors. The sigmoid function $\\sigma (\\cdot)$ converts the feature distance to the probability that the pixel belongs to the $l$ -th sub-center, and $\\tau$ controls the concentration level of representations. Once computed, we assign these semantic probability maps to different objects according to their class labels $Y_{n}$ .", + "bbox": [ + 75, + 449, + 468, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-prototype update. We update the prototypes on-the-fly with the moving average of cluster centroids computed in previous mini-batches. Specifically, given an image $X_{n}$ and its corresponding pseudo mask $\\hat{M}$ , we obtain the pixelwise cluster assignments $Q$ of the $c$ -th category by optimizing the following objective function:", + "bbox": [ + 75, + 556, + 468, + 647 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {Q \\in \\mathbb {Q}} \\operatorname {T r} \\left(Q ^ {T} P _ {c} ^ {T} Z\\right) + \\varepsilon H (Q), \\quad s. t. Q \\in \\mathbb {Q}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 659, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\mathbb{Q} := \\{Q \\in \\mathbb{R}_+^{L \\times N_c} | Q\\mathbf{1}_{N_c} = r, Q^T\\mathbf{1}_L = h\\}$ .", + "bbox": [ + 101, + 686, + 426, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above formula is an instance of the optimal transport problem [9], where $Q = \\frac{1}{N_c} [q_1, \\dots, q_{N_c}]$ represents the transport assignment and is restricted to be a probability matrix with the constraint $\\mathbb{Q}$ . $N_c$ is the number of pixels belonging to the $c$ -th category, $H$ denotes the entropy function with $H(Q) = -\\sum_{ij} Q_{ij} \\log Q_{ij}$ , and $\\varepsilon$ controls the smoothness of distribution. $r = \\frac{1}{L} \\mathbf{1}_L$ and $h = \\frac{1}{N_c} \\mathbf{1}_{N_c}$ are the marginal projections of $Q$ onto its rows and columns, respectively, where $\\mathbf{1}_L$ and $\\mathbf{1}_{N_c}$ represent the vectors of ones of dimension $L$ and $N_c$ .", + "bbox": [ + 75, + 715, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By formulating the cluster assignment as an optimal transport problem, the optimization of Eq. 2 concerning $Q$", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1036247a50e5d4a60acd37f3f1740bd0cff0f483b5b0636832b7841fb4181be2.jpg", + "image_caption": [ + "Figure 3. (a) The mask quality varies much across different positive samples. (b) The instance-aware masks $M_{1}$ obtained by using positive mask weighting strategy." + ], + "image_footnote": [], + "bbox": [ + 513, + 89, + 883, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "can be solved in linear time by the Sinkhorn-Knopp algorithm [9]:", + "bbox": [ + 498, + 272, + 890, + 301 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ ^ {*} = \\operatorname {d i a g} (u) \\exp \\left(\\frac {P _ {c} ^ {T} Z}{\\varepsilon}\\right) \\operatorname {d i a g} (v), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 311, + 890, + 344 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $u \\in \\mathbb{R}^L$ and $v \\in \\mathbb{R}^{N_c}$ are two renormalization vectors. Finally, we update the prototypes as the moving average of cluster centroids. Particularly, in each iteration $t$ , the prototype is estimated as:", + "bbox": [ + 498, + 353, + 890, + 414 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. p _ {l} ^ {c} \\right| _ {t} = \\gamma \\cdot \\left. p _ {l} ^ {c} \\right| _ {t - 1} + (1 - \\gamma) \\cdot p _ {n, l} ^ {c}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 425, + 890, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda \\in [0,1]$ is the momentum coefficient. $p_{n,l}^{c}$ denotes the $l$ -th sub-center of the $c$ -th class in image $X_{n}$ , which is computed by:", + "bbox": [ + 498, + 453, + 890, + 500 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {n, l} ^ {c} = \\frac {\\sum_ {i} ^ {N _ {c}} z _ {i} \\cdot \\mathbb {1} \\left(Q _ {i , l} = 1\\right)}{\\sum_ {i} ^ {N _ {c}} \\mathbb {1} \\left(Q _ {i , l} = 1\\right)}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 508, + 890, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}$ is an indicator function, being 1 if $Q_{i,l} = 1$", + "bbox": [ + 498, + 556, + 846, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remarks on prototypes. The pairwise loss used in [36] explores pixel-to-pixel correlations, which provide local supervision but can not ensure the global consistency of objects with the same semantics. In contrast, the prototypes explore pixel-to-center relations, which could ensure the integrity of objects and provide more reliable supervision. Besides, since the prototypes are abstracted from massive training data, they could reveal the intrinsic properties of objects and filter out image-specific noise and outliers. In addition, we treat different categories equally and set the same number of prototypes for each category, which is potentially beneficial for identifying long-tailed objects.", + "bbox": [ + 496, + 571, + 890, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Self-Correction", + "text_level": 1, + "bbox": [ + 500, + 771, + 661, + 785 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Though the pseudo semantic masks $M_{\\mathrm{S}}$ could provide more reliable supervision from a global perspective, they could not distinguish different objects of the same semantics, especially when there exist overlaps or occlusions among objects. To overcome this limitation, we propose a simple yet effective self-correction module, which could upgrade the semantic-aware masks $M_{\\mathrm{S}}$ to be instance-aware.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7196", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Positive mask weighting. Let us first revisit some properties of anchor-free detectors such as FCOS [35]. In these works, anchors denote the dense feature points, and positive samples represent the anchors located in the center/bbox region of each object. These methods assign multiple positive samples, which have high enough Intersection over Union (IoU) with ground truth $(gt)$ box, to each object. However, the quality of masks produced by different positive samples varies significantly, as shown in Fig. 3 (a). Those ambiguous anchors, i.e., anchors that are taken as positive samples for multiple $gt$ objects simultaneously (red dots in Fig. 3), could not separate overlapping objects of the same semantics. Based on these observations, we propose a positive mask weighting strategy to integrate different masks according to their quality, resulting in a high-quality instance-aware mask $M_{\\mathrm{I}}$ . In specific, we define a metric of mask quality based on the IoU between predicted and $gt$ boxes:", + "bbox": [ + 76, + 90, + 472, + 349 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {p o s} = e ^ {\\mu \\cdot I o U}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 357, + 468, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mu$ controls the relative gaps between different weights. Each weight $w_{pos}$ is then normalized by the sum of weights for all positive samples. As can be seen in Fig. 3 (b), the pseudo instance masks $M_{\\mathrm{I}}$ could better separate different objects and provide more accurate supervision.", + "bbox": [ + 76, + 386, + 468, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pseudo mask loss. By employing $M_{\\mathrm{I}}$ , the falsely activated objects or pixels in $M_{\\mathrm{S}}$ could be suppressed, while the confidence of foreground objects could be enhanced. The rectification process is conducted as follows:", + "bbox": [ + 76, + 460, + 470, + 522 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {M} _ {p r o b} ^ {k, i} = (1 - \\alpha) \\cdot M _ {\\mathrm {S}} ^ {k, i} + \\alpha \\cdot M _ {\\mathrm {I}} ^ {k, i}, \\qquad (7)\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 529, + 468, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{M}_{prob}^{k,i}$ represents the $i$ -th pixel of the $k$ -th pseudo probability map, and $\\alpha \\in [0,1]$ controls the intensity of modulation. Finally, we set two thresholds $\\tau_{\\mathrm{high}}$ and $\\tau_{\\mathrm{low}}$ to select highly-confident foreground and background predictions as pseudo labels, resulting in $\\hat{M}$ . The pseudosupervised mask loss is defined by:", + "bbox": [ + 76, + 561, + 472, + 655 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p s e u d o} = \\frac {1}{N _ {p o s}} \\sum_ {k} ^ {N _ {p o s}} \\ell_ {m a s k} (M _ {p r e d}, \\hat {M} _ {k}, W), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 665, + 468, + 708 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the mask loss $\\ell_{mask}$ consists of two terms: binary cross-entropy loss $\\ell_{bce}$ and dice loss [28] $\\ell_{dice}$ . $\\hat{M}_k$ denotes the pseudo mask of the $k$ -th positive sample. $W$ is a binary weight mask that neglects ambiguous regions by using $\\tau_{\\mathrm{high}}$ and $\\tau_{\\mathrm{low}}$ , i.e., $W^i = 0$ , if $\\tau_{\\mathrm{low}} < \\hat{M}_{prob}^i < \\tau_{\\mathrm{high}}$ .", + "bbox": [ + 76, + 717, + 468, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Online Weakly-Supervised Copy-Paste", + "text_level": 1, + "bbox": [ + 76, + 801, + 411, + 818 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Object-aware Copy-Paste is a simple yet effective way to improve the data efficiency. However, Copy-Paste has rarely been explored for weakly-supervised instance segmentation. It is natural to employ pseudo masks as the guidance to cut object instances from an image $X$ . To achieve", + "bbox": [ + 76, + 824, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2b8b5c1ed61426d9e90617a5a0da64b0839c7ba1a480b008d97e9e491f5aa5b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 88, + 607, + 137 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/accdaf1c427ec215e34d463882f2d1854bce4bf71e9a1a34e564d5cb4c2955bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 88, + 697, + 137 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b07c5ec0818cbb579aeafec8138294d8ff7c06f2e76fed0431d59d90137c1fd1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 88, + 787, + 137 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/79c9106de779b635b3ad1395cefbe450f7c5b5376973e4fdc4b35ba487fd39c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 790, + 88, + 877, + 137 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5502e128cdaade468dc0ace73fb39f8a748e23735e317f52654c6786fab08540.jpg", + "image_caption": [ + "X", + "Figure 4. Examples of online weakly-supervised Copy-Paste. We use $\\hat{M}'$ to extract instances from $X'$ and paste them onto $X$ , resulting in new training data $X_{paste}$ ." + ], + "image_footnote": [], + "bbox": [ + 514, + 138, + 607, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2f1d4817975d17c3f552218c245c96912f6de577f941499e6720e1079d073f28.jpg", + "image_caption": [ + "X" + ], + "image_footnote": [], + "bbox": [ + 612, + 138, + 697, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d4461c9bca9af60c190763db973efebc97d7926177dd706c5a03c0d5e666b25b.jpg", + "image_caption": [ + "$X_{\\text{paste}}$" + ], + "image_footnote": [], + "bbox": [ + 702, + 138, + 787, + 234 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cc1162b3f177a6e334501aeace4c4f72b6569af6eba6aa198d90c1db2a3c78cf.jpg", + "image_caption": [ + "M" + ], + "image_footnote": [], + "bbox": [ + 792, + 138, + 877, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "online Copy-Paste, we set up a first-in-first-out memory bank $\\mathcal{M}$ to store training samples and their corresponding pseudo masks from preceding mini-batches, which ensures that the pseudo masks in $\\mathcal{M}$ could be updated on-the-fly.", + "bbox": [ + 496, + 316, + 890, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each training iteration, we randomly sample an image $\\{X', Y', B', \\hat{M}', S'\\}$ from $\\mathcal{M}$ and extract a subset of instances from $X'$ based on importance sampling, where $S'$ measures the importance of instances (please refer to supplemental materials for more details), so that instances with higher-quality masks are more likely to be selected. We paste the extracted objects onto input image $\\{X, Y, B\\}$ , and adjust the annotations accordingly, i.e., we remove fully occluded objects and update the masks and bounding boxes of partially occluded objects. Finally, we compute the mask loss only on the pasted instances:", + "bbox": [ + 496, + 376, + 892, + 542 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p a s t e} = \\sum_ {k} \\mathbb {1} _ {p a s t e} \\left[ \\ell_ {m a s k} \\left(M _ {p r e d} ^ {k}, \\hat {M} ^ {\\prime k}\\right) \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 550, + 890, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{1}_{\\text{paste}}$ is the indicator function, being 1 if the $k$ -th instance is copied from $X'$ .", + "bbox": [ + 498, + 588, + 890, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Objective Function", + "text_level": 1, + "bbox": [ + 500, + 626, + 684, + 642 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 2, we employ a momentum encoder to stabilize the pseudo mask generation process. The parameters of the segmentation model are updated by optimizing the following loss function $\\mathcal{L}_{seg}$ :", + "bbox": [ + 496, + 648, + 893, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s e g}} = \\mathcal {L} _ {\\text {l o w l e v e l}} + \\lambda_ {1} \\mathcal {L} _ {\\text {p s e u d o}} + \\lambda_ {2} \\mathcal {L} _ {\\text {p a s t e}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 718, + 890, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are two trade-off parameters. $\\mathcal{L}_{lowlevel}$ denotes low-level pairwise supervision defined in Box-Inst [36]. $\\mathcal{L}_{lowlevel}$ and $\\mathcal{L}_{pseudo}$ provide complementary supervision from local and global perspectives, respectively, and work together to bridge the performance gap between box-supervised and fully-supervised settings.", + "bbox": [ + 496, + 742, + 890, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 844, + 633, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on COCO [24] and PASCAL VOC [11] datasets. The model is trained on train2017,", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7197", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9111fa3310f6575bcb72afb83bbfee017bb2c242ab9e23b122cedc41c0459793.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
methodbackbonesche.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
fully-supervisedMask R-CNN [12]ResNet-101-FPN3×37.559.340.221.139.648.3
YOLACT-700 [3]ResNet-101-FPN4.5×31.250.632.812.133.347.1
PolarMask [40]ResNet-101-FPN2×32.153.733.114.733.845.3
SOLOv2 [38]ResNet-101-FPN3×39.760.742.917.342.957.4
CondInst [34]ResNet-101-FPN3×39.160.942.021.541.750.9
\\( Mask2Fomer^† \\)[7]ResNet-101-MSDefomAttn50e44.2--23.847.766.7
box-supervised\\( BBTP^† \\)[14]ResNet-101-FPN1×21.145.517.211.222.029.8
BBAM [21]ResNet-101-FPN1×25.750.023.3---
\\( BoxCaseg^‡ \\)[37]ResNet-101-FPN1×30.954.330.812.132.846.3
SIM (Ours)ResNet-101-FPN1×34.056.835.017.236.845.5
BoxLevelSet [23]ResNet-101-FPN3×33.456.834.115.236.846.8
BoxInst [36]ResNet-101-FPN3×33.256.533.616.235.345.1
SIM (Ours)ResNet-101-FPN3×35.358.936.418.438.047.5
BoxLevelSet [23]ResNet-DCN-101-BiFPN3×35.459.136.716.838.551.3
BoxInst [36]ResNet-DCN-101-BiFPN3×35.059.335.617.137.248.9
SIM (Ours)ResNet-DCN-101-BiFPN3×37.461.838.618.640.251.6
BoxInst [36]Swin-B-FPN3×37.963.239.020.041.253.1
SIM (Ours)Swin-B-FPN3×40.266.941.321.143.556.0
\\( BoxInst^† \\)[36]Mask2Former-ResNet-10150e35.759.836.416.638.555.4
\\( SIM^† \\)(Ours)Mask2Former-ResNet-10150e37.462.238.717.641.356.6
", + "bbox": [ + 174, + 88, + 802, + 373 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which contains about 115k images from 80 categories with only box annotations. We use val2017 (5k images) for ablation study and test-dev2017 (20k images) for comparisons with other methods.", + "bbox": [ + 75, + 436, + 470, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 508, + 294, + 525 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt CondInst [34] and Mask2Former [7] as our baseline. For CondInst, the backbone with FPN is pretrained on ImageNet. The training and testing details follow CondInst1 implemented with Detectron2 [39] unless specified. The model is warmed-up for 10k iterations with the projection loss and pairwise loss proposed in [36], and then trained for 80k iterations by adding our pseudo supervision loss and Copy-Paste loss with batch size 16 on 8 TITAN RTX GPUs. When ResNet is used as the backbone, our model is trained with SGDM optimizer. The initial learning rate is set to 0.01, and reduced by a factor of 10 at steps 60k and 80k, respectively. When SwinT [26] is used as the backbone, we adopt the AdamW [27] optimizer and set the initial learning rate to 0.0001. For Mask2Former, we follow its baseline settings2 and replace the original pixelwise mask loss with our designed loss terms. The length of the memory bank is set to 100, and we extract a quarter of the instances from each image with $1 \\sim 3$ instances per image. The momentum used to update networks and prototypes is set to 0.9999 and 0.999, respectively. The modulation intensity $\\alpha$ is empirically set to 0.5. Besides, $\\lambda_1$ , $\\lambda_2$ , $\\mu$ , and $\\tau$ are empirically set to 0.5, 1, 5, and 0.1, respectively.", + "bbox": [ + 73, + 532, + 470, + 864 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e9f2a120883ca8cc91fe38cfafd16c2fa57a1f65feb55f9e73345f4d21b69940.jpg", + "table_caption": [ + "Table 1. Comparisons between SIM and state-of-the-art methods on the COCO test-dev split. Symbol “†” means that the results are evaluated on the COCO val split, and “‡” denotes that BoxCaseg is trained with both box and salient object supervisions." + ], + "table_footnote": [], + "table_body": "
methodsbackboneAP\\( AP_{50} \\)\\( AP_{75} \\)
GrabCut* [31]ResNet-10119.038.817.0
SDI [17]VGG-16-44.816.3
BBTP [14]ResNet-10123.154.117.1
BBTP w/ CRF [14]ResNet-10127.559.121.9
BBAM [21]ResNet-101-63.731.8
BoxInst [36]ResNet-5034.359.134.2
BoxInst [36]ResNet-10136.561.437.0
DiscoBox [20]ResNet-50-59.835.5
DiscoBox [20]ResNet-101-62.237.5
BoxLevelSet [23]ResNet-5036.364.235.9
BoxLevelSet [23]ResNet-10138.366.338.7
SIM (Ours)ResNet-5036.765.535.6
SIM (Ours)ResNet-10138.667.138.3
", + "bbox": [ + 524, + 435, + 870, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Performance comparison on Pascal VOC val2012 split. Symbol “*” denotes that the results are copied from BoxInst.", + "bbox": [ + 498, + 637, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparisons with State-of-the-Arts", + "text_level": 1, + "bbox": [ + 498, + 680, + 812, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare the proposed SIM with state-of-the-art BSIS methods on the COCO [24] dataset. The fully supervised methods are also compared as a reference. As shown in Tab. 1, SIM outperforms BoxInst [36] and BoxLevelSet [23] by $1.6\\%$ and $1.4\\%$ AP with the ResNet-101-FPN backbone and $3\\times$ training schedule. This is because we employ dataset-level prototypes to exploit the semantic information of objects while filtering out trivial image-specific noises. It can also be seen that our SIM method produces impressive results on small objects, largely outperforming BoxInst and BoxLevelSet by $2.8\\%$ AP and $1.8\\%$ AP with ResNet-101-FPN backbone, respectively. This can be attributed to the proposed Copy-Paste", + "bbox": [ + 496, + 703, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{1}$ https://github.com/aim-uofa/AdelaiDe", + "bbox": [ + 94, + 875, + 303, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^{2}$ https://github.com/facebookresearch/Mask2Former", + "bbox": [ + 96, + 887, + 372, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7198", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/68888243df38156010be93a537f12ab46c77125c4ed51c7f4451647772b08f0e.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 91, + 88, + 254, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/12b11f945c9a42a629cc02b36ad643e0a8f71e1f75f91680a11eac9948182dd0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 256, + 88, + 421, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ff00f8e2d2fae8dab5bb7b9f70c97506d6375dc8cbb139da096d5e2014daa2a.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 423, + 88, + 570, + 174 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/001bde20a63c5525cb62f3fc1700285eed8517e9c94d88552615e250623416df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 89, + 717, + 174 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5bf8fb601b40bd4e44d867d9dc8da2ea88568e36475fd2b8b15b764aba93dfb.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 722, + 88, + 799, + 174 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bf8e2d0e9f28e02ce7a97b88bcb814da2e0c9d17ec2c3bb9a934feff532962eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 800, + 88, + 875, + 174 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c9679ede0f96c4e3f51bf487157d7302eed90e100416390d8f0493cf7fcddcbe.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 91, + 185, + 254, + 268 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17c7b0bdc36dc5e4acda977ac2a07ea344cc23808a4938ea24f2f2c2d9e2ef2d.jpg", + "image_caption": [ + "Figure 5. Qualitative results of BoxInst (in the red box) and our method (in the blue box) on COCO val2017." + ], + "image_footnote": [], + "bbox": [ + 254, + 185, + 419, + 268 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d35c6c434b18382176c455a4cffe02471adc723b8fb412c88f2264d24ab1bdb.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 423, + 185, + 570, + 268 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/803201f26d5bcd5bf1ba3457524f30b8dd3c9cf9e40a06dc054c85bcfcf792c4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 185, + 717, + 268 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6de9859ff037bc10c6a81d77b302b8253cef0a5f083a49a83892d37828baf546.jpg", + "image_caption": [ + "(f)" + ], + "image_footnote": [], + "bbox": [ + 722, + 185, + 799, + 268 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "operation, which creates many challenging training data of small hard objects. BoxInst lags behind on large objects due to the lack of semantic guidance. BoxLevelSet has lower performance on small objects because small objects lack rich features for level set evolution. By using stronger backbones with BiFPN [33] and DCN [47], the performance can be further boosted to $37.4\\%$ AP. By taking Swin transformer [26] as backbone [26], the proposed SIM could surpass BoxInst by $1.7\\%$ AP, attaining $39.6\\%$ AP. In addition, we also validate the effectiveness of our method on the query-based baseline, i.e., Mask2Former [7]. Our method achieves consistent improvement and outperforms BoxInst by $1.7\\%$ AP.", + "bbox": [ + 75, + 318, + 468, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 2 reports the segmentation results on the Pascal VOC [11] dataset. Our method outperforms BoxInst [36] by $2.4\\%$ and $2.1\\%$ AP with ResNet-50 and ResNet-101 backbones, respectively. BoxLevelSet [23] achieves comparable performance since the level set model could evolve the precise contour of objects, which is beneficial for large objects.", + "bbox": [ + 75, + 518, + 468, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative Results", + "text_level": 1, + "bbox": [ + 76, + 631, + 259, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 5 shows the qualitative segmentation results of our method and BoxInst on COCO val split. We have the following observations. First, according to (a), by leveraging the semantic-level supervision, our method is able to segment foreground instances that heavily tangle with background or other objects with similar appearances, because the prototypes explore global structural information of objects and could reduce the noise brought by using only local pair-wise affinity supervision. Second, as can be seen in (b) (c), our method could better separate overlapping instances of the same semantics since we introduce the self-correction module to reduce the falsely activated instances while enhancing the correct ones. Third, as shown in (d) and (f), benefiting from the abstraction of prototypes from massive training data, our method is able to perceive the whole entity of object instances and produce better segmentation results.", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/af2760ab84c149418fe40c74fcc87be69b19cc5976919edc55fcf6fb5b5c1cbd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
\\( \\mathcal{L}_{pseudo} \\)\\( \\mathcal{L}_{paste} \\)AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
baseline30.752.231.113.833.145.7
✓31.954.032.614.734.747.4
✓✓32.254.033.015.834.548.3
", + "bbox": [ + 519, + 316, + 870, + 375 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/abf0a5e0ddc993537f474b49ab5cafc5386c11850bdaaffa9509b130a78252eb.jpg", + "table_caption": [ + "Table 3. The Mask AP on COCO val2017 split by applying different loss terms." + ], + "table_footnote": [], + "table_body": "
αAPAP50AP75APSAPMAPL
030.552.730.614.133.344.8
0.331.353.131.915.134.046.1
0.532.254.033.015.834.548.3
0.732.054.032.415.734.447.9
131.453.032.315.034.247.0
", + "bbox": [ + 522, + 415, + 867, + 493 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/11c6a869e52fa2d9ef4e94de54c483ed1971f18e6a258461e5be033f438b2eae.jpg", + "table_caption": [ + "Table 4. Effect of modulation intensity $\\alpha$ ." + ], + "table_footnote": [], + "table_body": "
# prototypesAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
L=131.653.132.415.334.046.9
L=532.053.632.915.734.547.4
L=1032.254.033.015.834.548.3
L=5032.253.933.215.934.348.7
", + "bbox": [ + 522, + 520, + 867, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Effect of the number of prototypes $L$ per category.", + "bbox": [ + 519, + 589, + 870, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 619, + 653, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct ablation studies on the COCO dataset, with ResNet-50-FPN backbone and $1 \\times$ training schedule, to investigate the role of each component in our framework. The Mask AP on COCO val split is reported.", + "bbox": [ + 498, + 642, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Contribution of the two losses. Tab. 3 shows the contributions of the two loss terms, i.e., $\\mathcal{L}_{pseudo}$ and $\\mathcal{L}_{paste}$ . The baseline is BoxInst [36], which resorts to the color similarity between proximal pixels as supervision. The proposed pseudo mask loss improves the performance by $1.2\\%$ AP, especially on large objects ( $1.7\\%$ AP). This demonstrates that by introducing the semantic-aware instance mask generation paradigm, our method could distinguish not only proximal pixels with similar colors but also overlapping objects of the same semantics. Besides, the online weakly-supervised Copy-Paste loss brings a further improvement of $0.3\\%$ AP, while the performance on small objects $\\mathrm{AP}_S$ is largely improved by $1.1\\%$ AP.", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7199", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8cdf8a3b0f989148495e193712527fc40c5a84a0d43e67e5be2134f88f08ae2b.jpg", + "image_caption": [ + "Figure 6. Visualizations of pseudo semantic masks $M_{\\mathrm{S}}$ , pseudo instance masks $M_{\\mathrm{I}}$ , and final pseudo masks $\\hat{M}$" + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 490, + 250 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2bde7cc1f959124e3ac7ef4a6273ec0932bc2d7bca1a0948404c08997e8a6b22.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 89, + 895, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/66a2014ef133ebf250fd243eb50cc11b3fc3a07bd54492d3a276a2b702f77c31.jpg", + "image_caption": [ + "Figure 7. Visualizations of weights for different positive samples." + ], + "image_footnote": [], + "bbox": [ + 89, + 282, + 455, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the modulation intensity. We use the instance-aware pseudo probability map $M_{\\mathrm{I}}$ to modulate the semantic-aware map $M_{\\mathrm{S}}$ by using a parameter $\\alpha$ . Tab. 4 shows the results by setting $\\alpha$ to different values. One can draw a conclusion that the integration of semantic mask $M_{\\mathrm{S}}$ and instance mask $M_{\\mathrm{I}}$ leads to better results than any of them. Specifically, $M_{\\mathrm{S}}$ facilitates more holistic object pattern understanding by exploring the semantic information from the entire dataset, while $M_{\\mathrm{I}}$ rectifies the falsely activated objects in $M_{\\mathrm{S}}$ and improves the reliability of pseudo masks. Removing the self-correction module, i.e., setting $\\alpha$ to 0, will lead to an obvious performance drop by $1.7\\%$ AP. This is not surprising because the semantic mask contains certain noisy supervision caused by the falsely activated objects and pixels. On the other hand, training without semantic masks, i.e., setting $\\alpha$ to 1, will decrease the segmentation performance by $0.8\\%$ AP.", + "bbox": [ + 75, + 537, + 467, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Semantic masks vs. instance masks. We explore the complementarity of $M_{\\mathrm{S}}$ and $M_{\\mathrm{I}}$ by visualizing them in Fig. 6. As can be seen in (b-d), $M_{\\mathrm{S}}$ could distinguish object instances that have similar appearances but different semantics from the background and other objects. In comparison, from (a) (e-f), we see that $M_{\\mathrm{I}}$ is good at distinguishing different instances of the same semantics, which are employed", + "bbox": [ + 75, + 795, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to suppress the falsely activated instances in $M_{\\mathrm{S}}$ . They work together to produce more reliable supervision for training.", + "bbox": [ + 496, + 282, + 890, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualizations of weights. To further understand the effect of the positive mask weighting strategy, we show the visualizations of weights assigned to different positive samples in Fig. 7. It can be seen that large weights are mainly located in the central regions of foreground objects and far from other objects, while the small ones are located in ambiguous regions, such as overlapping regions between different objects and junctions between foreground and background. This weighting strategy facilitates generating higher-quality supervision and reducing the falsely activated instances. More analyses about this weighting strategy are provided in supplemental files.", + "bbox": [ + 496, + 315, + 890, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of the number of prototypes per category. We set multiple prototypes per category to better model intra-class variation. Tab. 5 reports the segmentation results w.r.t. different number of prototypes per category. The baseline attains $31.6\\%$ AP by representing each category with one prototype. There is a clear performance improvement (about $0.4\\%$ AP) by increasing the number of prototypes to 5; however, the performance reaches saturation when $L$ is more than 10. We set $L$ as 10 to trade off accuracy and cost.", + "bbox": [ + 496, + 496, + 890, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed a novel SIM method for box-supervised instance segmentation. To alleviate the limitations of pairwise affinity supervision from low-level image features, we explored high-level image semantic contexts by extracting a group of representative prototypes from the dataset and using them to segment foreground objects from background. To rectify the possible false positive instances in semantic masks, we introduced extra supervision by integrating mask predictions of different positive samples in a weighted manner. Furthermore, we devised an online weakly-supervised Copy-Paste method to create challenging training data by equipping a continuously updated memory bank to store historical images with pseudo masks. Both the qualitative and quantitative experiments demonstrated the superior performance of our SIM method over state-of-the-arts.", + "bbox": [ + 496, + 674, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7200", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2209-2218, 2019. 1, 2", + "[2] Jiwoon Ahn and Suha Kwak. Learning pixel-level semantic affinity with image-level supervision for weakly supervised semantic segmentation. 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In" + ], + "bbox": [ + 503, + 92, + 890, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7202", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + }, + { + "type": "header", + "text": "Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5982-5991, 2019. 3", + "bbox": [ + 109, + 92, + 468, + 119 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7203", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SIM_ Semantic-Aware Instance Mask Generation for Box-Supervised Instance Segmentation/884f8e5b-a009-4236-8afe-619abfb36ed7_model.json b/2023/SIM_ Semantic-Aware Instance Mask Generation for Box-Supervised Instance Segmentation/884f8e5b-a009-4236-8afe-619abfb36ed7_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7183512dfed626f0ee725ae1a89e43b19975538b --- /dev/null +++ b/2023/SIM_ Semantic-Aware Instance Mask Generation for Box-Supervised Instance Segmentation/884f8e5b-a009-4236-8afe-619abfb36ed7_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.219, + 0.131, + 0.753, + 0.177 + ], + "angle": 0, + "content": "SIM: Semantic-aware Instance Mask Generation for Box-Supervised Instance Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.203, + 0.823, + 0.24 + ], + "angle": 0, + "content": "Ruihuang Li\\* Chenhang He\\*, Yabin Zhang, Shuai Li, Liyi Chen, Lei Zhang† The Hong Kong Polytechnic University" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.242, + 0.673, + 0.258 + ], + "angle": 0, + "content": "{csrhli, cshe, cslzhang}@comp.polyu.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.687 + ], + "angle": 0, + "content": "Weakly supervised instance segmentation using only bounding box annotations has recently attracted much research attention. Most of the current efforts leverage low-level image features as extra supervision without explicitly exploiting the high-level semantic information of the objects, which will become ineffective when the foreground objects have similar appearances to the background or other objects nearby. We propose a new box-supervised instance segmentation approach by developing a Semantic-aware Instance Mask (SIM) generation paradigm. Instead of heavily relying on local pair-wise affinities among neighboring pixels, we construct a group of category-wise feature centroids as prototypes to identify foreground objects and assign them semantic-level pseudo labels. Considering that the semantic-aware prototypes cannot distinguish different instances of the same semantics, we propose a self-correction mechanism to rectify the falsely activated regions while enhancing the correct ones. Furthermore, to handle the occlusions between objects, we tailor the Copy-Paste operation for the weakly-supervised instance segmentation task to augment challenging training data. Extensive experimental results demonstrate the superiority of our proposed SIM approach over other state-of-the-art methods. The source code: https://github.com/1slrh/SIM." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.718, + 0.21, + 0.733 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Instance segmentation is among the fundamental tasks of computer vision, with many applications in autonomous driving, image editing, human-computer interaction, etc. The performance of instance segmentation has been improved significantly along with the advances in deep learning [6, 12, 34, 38]. However, training robust segmentation networks requires a large number of data with pixel-wise annotations, which consumes intensive human labor and" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.291, + 0.632, + 0.358 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.292, + 0.757, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.292, + 0.886, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.358, + 0.702, + 0.366 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.367, + 0.631, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.367, + 0.756, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.431, + 0.701, + 0.44 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.367, + 0.885, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.815, + 0.431, + 0.83, + 0.44 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.443, + 0.895, + 0.555 + ], + "angle": 0, + "content": "Figure 1. The pipeline of Semantic-aware Instance Mask (SIM) generation method. (a) shows the mask prediction produced by using only low-level affinity supervision, where the foreground heavily blends with background. (b) and (c) show the semantic-aware masks obtained with our constructed prototypes, which perceive the entity of objects but are unable to separate different instances of the same semantics. (d) shows the final instance pseudo mask rectified by our proposed self-correction module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.658 + ], + "angle": 0, + "content": "resources. To reduce the reliance on dense annotations, weakly-supervised instance segmentation based on cheap supervisions, such as bounding boxes [14,21,36], points [8] and image-level labels [1,18], has recently attracted increasing research attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In this paper, we focus on box-supervised instance segmentation (BSIS), where the bounding boxes provide coarse supervised information for pixel-wise prediction task. To provide pixel-wise supervision, conventional methods [10, 19] usually leverage off-the-shelf proposal techniques, such as MCG [30] and GrabCut [31], to create pseudo instance masks. However, the training pipelines of these methods with multiple iterative steps are cumbersome. Several recent works [14, 36] enable end-to-end training by taking pairwise affinities among pixels as extra supervision. Though these methods have achieved promising performance, they heavily depend on low-level image features, such as color pairs [36], and simply assume that the proximal pixels with similar colors are likely to have the same label. This leads to confusion when foreground objects have similar appearances to the background or other ob-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "*denotes the equal contribution, †denotes the corresponding author. This work is supported by the Hong Kong RGC RIF grant (R5001-18)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7193" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "jects nearby, as shown in Fig. 1 (a). It is thus error-prone to use only low-level image cues for supervision since they are weak to represent the inherent structure of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.469 + ], + "angle": 0, + "content": "Motivated by the fact that high-level semantic information can reveal intrinsic properties of object instances and hence provide effective supervision for segmentation model training, we propose a novel Semantic-aware Instance Mask generation method, namely SIM, to explicitly exploit the semantic information of objects. To distinguish proximal pixels with similar color but different semantics (please refer to Fig. 1 (a)), we construct a group of representative dataset-level prototypes, i.e., the feature centroids of different classes, to perform foreground/background segmentation, producing semantic-aware pseudo masks (see Fig. 1 (b)). These prototypes abstracted from massive training data can capture the structural information of objects, enabling more comprehensive semantic pattern understanding, which is complementary to affinity supervision of pairwise neighboring pixels. However, as shown in Fig. 1 (c), these prototypes are unable to separate the instances of the same semantics, especially for overlapping objects. We consequently develop a self-correction mechanism to rectify the false positives while enhancing the confidence of true-positive foreground objects, resulting in more precise instance-aware pseudo masks, as shown in Fig. 1 (d)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.635 + ], + "angle": 0, + "content": "It is worth mentioning that our generated pseudo masks could co-evolve with the segmentation model without cumbersome iterative training procedures in previous methods [10, 21]. In addition, considering that the existing weakly-supervised instance segmentation methods only provide very limited supervision for rare categories and overlapping objects due to the lack of ground truth masks, we propose an online weakly-supervised Copy-Paste approach to create a combinatorial number of augmented training samples. Overall, the major contributions of this work can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.732 + ], + "angle": 0, + "content": "- A novel BSIS framework is presented by developing a semantic-aware instance mask generation mechanism. Specifically, we construct a group of representative prototypes to explore the intrinsic properties of object instances and identify complete entities, which produces more reliable supervision than low-level features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.809 + ], + "angle": 0, + "content": "- A self-correction module is designed to rectify the semantic-aware pseudo masks to be instance-aware. The falsely activated regions will be reduced, and the correct ones will be boosted, enabling more stable training and progressively improving the segmentation results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.9 + ], + "angle": 0, + "content": "- We tailor the Copy-Paste operation for weakly-supervised segmentation tasks in order to create more occlusion patterns and more challenging training data. The overall framework can be trained in an end-to-end manner. Extensive experiments demonstrate the superiority of our method over other state-of-the-art methods." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.447 + ], + "angle": 0, + "content": "Instance Segmentation (IS) is a fundamental task in computer vision fields, which aims to predict the pixel-wise mask for each instance of interest in an image. Many top performing IS methods [6, 15, 25, 42] follow the Mask R-CNN meta-architecture [12], which splits the IS task into two consecutive stages and performs segmentation on the extracted region proposals. Single-stage IS methods have also been rapidly developed during the past few years. YOLACT [3] and BlendMask [5] employ fine-grained FPN features rather than the RoI-aligned features for mask prediction. However, they still need crop operation for object localization. Some methods segment each instance in a fully convolutional manner without resorting to the detection results. For example, CondInst [34] and SOLO [38] employ instance-aware conditional convolutions and dynamically generate convolution kernels to segment different objects. Universal architectures [7, 41] have emerged with DETR [4] and show that end-to-end set prediction architecture is general enough for any segmentation task. Despite the promising performance, these methods heavily rely on expensive pixel-wise mask annotation, which restricts their usability in many practical applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Weakly-Supervised Instance Segmentation (WSIS) with weak annotations is a more attractive yet challenging task. Some works attempt to achieve high-quality segmentation with box-level annotations [14, 17, 21, 36] or image-level annotations [1, 18]. Khoreva et al. [17] employ box supervisory training data for WSIS. However, the proposed method relies on the region proposal techniques, such as GrabCut [31] and MCG [30], to generate pseudo masks in an offline manner. Other recent methods [21, 37] also focus on generating instance labels by using an independent network, which require either extra salient data [38] or some post-processing methods [21]. This inevitably leads to a complicated training pipeline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.84 + ], + "angle": 0, + "content": "To achieve a simple yet effective training pipeline, BBTP [14] formulates WSIS as a multiple-instance learning problem and introduces a structural constraint to maintain the unity of estimated masks. BoxInst [36] builds upon an efficient CondInst [34] framework, and enforces the proximal pixels with similar colors to have the same label through a pairwise loss. Despite the promising performance, these methods depend heavily on local color supervision while neglecting the global structure of the entire object. Different from these methods, our proposed method provides more reliable supervision by leveraging high-level semantic information, which is beneficial for capturing the intrinsic structures of objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Pseudo Mask Generation. A widely adopted technique in conventional weakly-supervised semantic segmentation methods is Class Activation Map (CAM) [44], which aims to obtain an object localization map from class labels. How-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7194" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.087, + 0.873, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.362, + 0.895, + 0.447 + ], + "angle": 0, + "content": "Figure 2. The framework of our proposed Semantic-aware Instance Mask (SIM) generation method. The model contains the main segmentation network \\(\\mathcal{F}_{seg}\\) and its momentum-updated version \\(\\mathcal{F}_{seg}^{\\prime}\\). Given an image \\(X\\), we first pass it through \\(\\mathcal{F}_{seg}\\) and \\(\\mathcal{F}_{seg}^{\\prime}\\) to obtain the corresponding mask features \\(Z\\) and \\(Z^{\\prime}\\). The prototypes are then updated as the moving average of feature cluster centroids. Next, we obtain the semantic probability map \\(M_{\\mathrm{S}}\\) by measuring the distance between prototypes and mask features \\(Z^{\\prime}\\). After that, the falsely activated instances in \\(M_{\\mathrm{S}}\\) are rectified by the instance probability map \\(M_{1}\\), which is obtained by integrating different positive masks of the same ground truth object. Finally, we obtain the pseudo mask \\(\\hat{M}\\) by selecting highly-confident pixels with two thresholds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.673 + ], + "angle": 0, + "content": "ever, CAM only identifies the most discriminative object regions and suffers from the problem of limited activation area [2,13,16,32]. Given that bounding boxes could provide the location information of objects in an image, BBAM [21] employs an object detector to produce a bounding box attribute map, which serves as a pseudo ground truth mask. As a more lightweight approach, self-training-based methods [22, 43, 48, 49] select high-scoring predictions on unlabeled data as pseudo labels for training. The idea of assigning labels based on prototypes has also been explored in semantic segmentation [22, 45, 46]. In this work, the prototype technique is adapted to capture the global structure of objects with the same semantics, reducing the noise caused by low-level feature supervision." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.686, + 0.17, + 0.701 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.711, + 0.188, + 0.725 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.856 + ], + "angle": 0, + "content": "In the setting of box-supervised instance segmentation (BSIS), we are given a set of box annotated training data \\(\\mathcal{D} = \\{X_n, Y_n, B_n\\}_{n=1}^N\\), where \\(N\\) is the number of images. Besides, \\(Y_n = \\{y_n^k\\}_{k=1}^K\\) and \\(B_n = \\{b_n^k\\}_{k=1}^K\\) denote the class-level and box-level annotations, where \\(K\\) is the number of instances in the image \\(X_n\\), \\(y_n^k \\in \\{1, \\dots, C\\}\\) represents the category label of the \\(k\\)-th object in the \\(n\\)-th image, and \\(b_n^k\\) specifies its corresponding location." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The overview of our method is shown in Fig. 2, where the proposed SIM module is highlighted in the green dotted box. We choose CondInst [34] and Mask2Former [7]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.892, + 0.703 + ], + "angle": 0, + "content": "as the basic segmentation networks due to their simplicity and effectiveness. Instead of only relying on local pair-wise affinities among pixels as supervision [14,36], we employ a group of semantic-level prototypes to capture global structural information of objects, and produce semantic probability map \\( M_{\\mathrm{S}} \\) by computing the distances between each pixel-wise feature vector and all prototypes. Since these prototypes are unable to separate different objects of the same semantics, we propose a self-correction mechanism to deactivate falsely estimated objects by using an instance probability map \\( M_{\\mathrm{I}} \\). This map can be obtained by integrating different positive masks corresponding to the same instance with an IoU-based weighting strategy. Finally, we employ two thresholds to select confident predictions as pseudo ground truths \\( \\hat{M} \\), and use them for training the segmentation network \\( \\mathcal{F}_{seg} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.715, + 0.869, + 0.73 + ], + "angle": 0, + "content": "3.2. Semantic-aware Instance Mask Generation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.71, + 0.755 + ], + "angle": 0, + "content": "3.2.1 Pseudo Semantic Map" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Low-level image features, such as colors, intensity, edges, blobs, etc., could provide useful guidance to identify the object boundaries in an image. However, these features vary significantly with illuminations, motion blurs, and noises. Thus it is error-prone to take only low-level features as supervision for BSIS when object instances are heavily blended with the background. To address this issue, we attempt to explore the intrinsic structures of objects as semantic guidance to provide more robust supervision for BSIS" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7195" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.182, + 0.107 + ], + "angle": 0, + "content": "model training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.109, + 0.474, + 0.396 + ], + "angle": 0, + "content": "We construct a group of representative prototypes to model the structural information of objects, and use them to generate semantic-aware pseudo masks. Considering that a single prototype is insufficient to capture the intra-class variance, we employ multiple prototypes [29, 45] to represent the objects in a category. Specifically, we extract \\(L\\) prototypes (i.e., sub-centers) from each class \\(c \\in \\{1, \\dots, C\\}\\), denoted by \\(P_{c} = \\{p_{1}^{c}, \\dots, p_{L}^{c}\\}\\), to depict different characteristics of the same category. Given an input image \\(I \\in \\mathbb{R}^{h \\times w \\times 3}\\), we first pass it through the segmentation model \\(\\mathcal{F}_{seg}\\) to obtain the feature map \\(Z \\in \\mathbb{R}^{H \\times W \\times D}\\), and normalize it with \\(z_{i} = \\frac{z_{i}}{||z_{i}||_{2}}\\), where \\(z_{i}\\) denotes the \\(i\\)-th feature vector of \\(Z\\) with length \\(D\\). Unlike semantic segmentation, which predicts only one mask for each input image, we predict a variable number of masks depending on the number of categories in the image. To this end, we compute the semantic probability map corresponding to the \\(c\\)-th category, denoted by \\(M_{\\mathrm{S}}^{c} \\in \\mathbb{R}^{H \\times W}\\), using the following formula:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.408, + 0.47, + 0.437 + ], + "angle": 0, + "content": "\\[\nM _ {\\mathrm {S}, i} ^ {c} = \\sigma \\left(\\max \\{\\frac {\\langle z _ {i} , p _ {l} ^ {c} \\rangle}{\\tau} \\} _ {l = 1} ^ {L}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.555 + ], + "angle": 0, + "content": "where \\(\\langle \\cdot \\rangle\\) computes the cosine similarity between two \\(\\ell_2\\)-normalized feature vectors. The sigmoid function \\(\\sigma (\\cdot)\\) converts the feature distance to the probability that the pixel belongs to the \\(l\\)-th sub-center, and \\(\\tau\\) controls the concentration level of representations. Once computed, we assign these semantic probability maps to different objects according to their class labels \\(Y_{n}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.557, + 0.47, + 0.648 + ], + "angle": 0, + "content": "Multi-prototype update. We update the prototypes on-the-fly with the moving average of cluster centroids computed in previous mini-batches. Specifically, given an image \\( X_{n} \\) and its corresponding pseudo mask \\( \\hat{M} \\), we obtain the pixelwise cluster assignments \\( Q \\) of the \\( c \\)-th category by optimizing the following objective function:" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.66, + 0.47, + 0.688 + ], + "angle": 0, + "content": "\\[\n\\max _ {Q \\in \\mathbb {Q}} \\operatorname {T r} \\left(Q ^ {T} P _ {c} ^ {T} Z\\right) + \\varepsilon H (Q), \\quad s. t. Q \\in \\mathbb {Q}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.687, + 0.427, + 0.704 + ], + "angle": 0, + "content": "with \\(\\mathbb{Q} := \\{Q \\in \\mathbb{R}_+^{L \\times N_c} | Q\\mathbf{1}_{N_c} = r, Q^T\\mathbf{1}_L = h\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.47, + 0.869 + ], + "angle": 0, + "content": "The above formula is an instance of the optimal transport problem [9], where \\( Q = \\frac{1}{N_c} [q_1, \\dots, q_{N_c}] \\) represents the transport assignment and is restricted to be a probability matrix with the constraint \\( \\mathbb{Q} \\). \\( N_c \\) is the number of pixels belonging to the \\( c \\)-th category, \\( H \\) denotes the entropy function with \\( H(Q) = -\\sum_{ij} Q_{ij} \\log Q_{ij} \\), and \\( \\varepsilon \\) controls the smoothness of distribution. \\( r = \\frac{1}{L} \\mathbf{1}_L \\) and \\( h = \\frac{1}{N_c} \\mathbf{1}_{N_c} \\) are the marginal projections of \\( Q \\) onto its rows and columns, respectively, where \\( \\mathbf{1}_L \\) and \\( \\mathbf{1}_{N_c} \\) represent the vectors of ones of dimension \\( L \\) and \\( N_c \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "By formulating the cluster assignment as an optimal transport problem, the optimization of Eq. 2 concerning \\( Q \\)" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.09, + 0.885, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.218, + 0.892, + 0.26 + ], + "angle": 0, + "content": "Figure 3. (a) The mask quality varies much across different positive samples. (b) The instance-aware masks \\( M_{1} \\) obtained by using positive mask weighting strategy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.273, + 0.892, + 0.303 + ], + "angle": 0, + "content": "can be solved in linear time by the Sinkhorn-Knopp algorithm [9]:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.312, + 0.892, + 0.345 + ], + "angle": 0, + "content": "\\[\nQ ^ {*} = \\operatorname {d i a g} (u) \\exp \\left(\\frac {P _ {c} ^ {T} Z}{\\varepsilon}\\right) \\operatorname {d i a g} (v), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.354, + 0.892, + 0.415 + ], + "angle": 0, + "content": "where \\( u \\in \\mathbb{R}^L \\) and \\( v \\in \\mathbb{R}^{N_c} \\) are two renormalization vectors. Finally, we update the prototypes as the moving average of cluster centroids. Particularly, in each iteration \\( t \\), the prototype is estimated as:" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.426, + 0.892, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\left. p _ {l} ^ {c} \\right| _ {t} = \\gamma \\cdot \\left. p _ {l} ^ {c} \\right| _ {t - 1} + (1 - \\gamma) \\cdot p _ {n, l} ^ {c}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.454, + 0.892, + 0.5 + ], + "angle": 0, + "content": "where \\(\\lambda \\in [0,1]\\) is the momentum coefficient. \\(p_{n,l}^{c}\\) denotes the \\(l\\)-th sub-center of the \\(c\\)-th class in image \\(X_{n}\\), which is computed by:" + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.51, + 0.892, + 0.549 + ], + "angle": 0, + "content": "\\[\np _ {n, l} ^ {c} = \\frac {\\sum_ {i} ^ {N _ {c}} z _ {i} \\cdot \\mathbb {1} \\left(Q _ {i , l} = 1\\right)}{\\sum_ {i} ^ {N _ {c}} \\mathbb {1} \\left(Q _ {i , l} = 1\\right)}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.557, + 0.848, + 0.573 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}\\) is an indicator function, being 1 if \\(Q_{i,l} = 1\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.754 + ], + "angle": 0, + "content": "Remarks on prototypes. The pairwise loss used in [36] explores pixel-to-pixel correlations, which provide local supervision but can not ensure the global consistency of objects with the same semantics. In contrast, the prototypes explore pixel-to-center relations, which could ensure the integrity of objects and provide more reliable supervision. Besides, since the prototypes are abstracted from massive training data, they could reveal the intrinsic properties of objects and filter out image-specific noise and outliers. In addition, we treat different categories equally and set the same number of prototypes for each category, which is potentially beneficial for identifying long-tailed objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.662, + 0.786 + ], + "angle": 0, + "content": "3.2.2 Self-Correction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Though the pseudo semantic masks \\( M_{\\mathrm{S}} \\) could provide more reliable supervision from a global perspective, they could not distinguish different objects of the same semantics, especially when there exist overlaps or occlusions among objects. To overcome this limitation, we propose a simple yet effective self-correction module, which could upgrade the semantic-aware masks \\( M_{\\mathrm{S}} \\) to be instance-aware." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7196" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.351 + ], + "angle": 0, + "content": "Positive mask weighting. Let us first revisit some properties of anchor-free detectors such as FCOS [35]. In these works, anchors denote the dense feature points, and positive samples represent the anchors located in the center/bbox region of each object. These methods assign multiple positive samples, which have high enough Intersection over Union (IoU) with ground truth \\((gt)\\) box, to each object. However, the quality of masks produced by different positive samples varies significantly, as shown in Fig. 3 (a). Those ambiguous anchors, i.e., anchors that are taken as positive samples for multiple \\(gt\\) objects simultaneously (red dots in Fig. 3), could not separate overlapping objects of the same semantics. Based on these observations, we propose a positive mask weighting strategy to integrate different masks according to their quality, resulting in a high-quality instance-aware mask \\(M_{\\mathrm{I}}\\). In specific, we define a metric of mask quality based on the IoU between predicted and \\(gt\\) boxes:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.358, + 0.47, + 0.378 + ], + "angle": 0, + "content": "\\[\nw _ {p o s} = e ^ {\\mu \\cdot I o U}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.387, + 0.47, + 0.462 + ], + "angle": 0, + "content": "where \\(\\mu\\) controls the relative gaps between different weights. Each weight \\(w_{pos}\\) is then normalized by the sum of weights for all positive samples. As can be seen in Fig. 3 (b), the pseudo instance masks \\(M_{\\mathrm{I}}\\) could better separate different objects and provide more accurate supervision." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.462, + 0.472, + 0.523 + ], + "angle": 0, + "content": "Pseudo mask loss. By employing \\( M_{\\mathrm{I}} \\), the falsely activated objects or pixels in \\( M_{\\mathrm{S}} \\) could be suppressed, while the confidence of foreground objects could be enhanced. The rectification process is conducted as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.53, + 0.47, + 0.554 + ], + "angle": 0, + "content": "\\[\n\\hat {M} _ {p r o b} ^ {k, i} = (1 - \\alpha) \\cdot M _ {\\mathrm {S}} ^ {k, i} + \\alpha \\cdot M _ {\\mathrm {I}} ^ {k, i}, \\qquad (7)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.563, + 0.473, + 0.656 + ], + "angle": 0, + "content": "where \\(\\hat{M}_{prob}^{k,i}\\) represents the \\(i\\)-th pixel of the \\(k\\)-th pseudo probability map, and \\(\\alpha \\in [0,1]\\) controls the intensity of modulation. Finally, we set two thresholds \\(\\tau_{\\mathrm{high}}\\) and \\(\\tau_{\\mathrm{low}}\\) to select highly-confident foreground and background predictions as pseudo labels, resulting in \\(\\hat{M}\\). The pseudosupervised mask loss is defined by:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.666, + 0.47, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p s e u d o} = \\frac {1}{N _ {p o s}} \\sum_ {k} ^ {N _ {p o s}} \\ell_ {m a s k} (M _ {p r e d}, \\hat {M} _ {k}, W), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.718, + 0.47, + 0.795 + ], + "angle": 0, + "content": "where the mask loss \\(\\ell_{mask}\\) consists of two terms: binary cross-entropy loss \\(\\ell_{bce}\\) and dice loss [28] \\(\\ell_{dice}\\). \\(\\hat{M}_k\\) denotes the pseudo mask of the \\(k\\)-th positive sample. \\(W\\) is a binary weight mask that neglects ambiguous regions by using \\(\\tau_{\\mathrm{high}}\\) and \\(\\tau_{\\mathrm{low}}\\), i.e., \\(W^i = 0\\), if \\(\\tau_{\\mathrm{low}} < \\hat{M}_{prob}^i < \\tau_{\\mathrm{high}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.802, + 0.412, + 0.819 + ], + "angle": 0, + "content": "3.3. Online Weakly-Supervised Copy-Paste" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Object-aware Copy-Paste is a simple yet effective way to improve the data efficiency. However, Copy-Paste has rarely been explored for weakly-supervised instance segmentation. It is natural to employ pseudo masks as the guidance to cut object instances from an image \\( X \\). To achieve" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.089, + 0.609, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.089, + 0.698, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.089, + 0.788, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.792, + 0.089, + 0.879, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.14, + 0.609, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.236, + 0.567, + 0.245 + ], + "angle": 0, + "content": "X" + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.14, + 0.698, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.236, + 0.661, + 0.245 + ], + "angle": 0, + "content": "X" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.14, + 0.788, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.236, + 0.766, + 0.246 + ], + "angle": 0, + "content": "\\(X_{\\text{paste}}\\)" + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.14, + 0.879, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.828, + 0.236, + 0.843, + 0.245 + ], + "angle": 0, + "content": "M" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.257, + 0.894, + 0.3 + ], + "angle": 0, + "content": "Figure 4. Examples of online weakly-supervised Copy-Paste. We use \\(\\hat{M}'\\) to extract instances from \\(X'\\) and paste them onto \\(X\\), resulting in new training data \\(X_{paste}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.892, + 0.377 + ], + "angle": 0, + "content": "online Copy-Paste, we set up a first-in-first-out memory bank \\(\\mathcal{M}\\) to store training samples and their corresponding pseudo masks from preceding mini-batches, which ensures that the pseudo masks in \\(\\mathcal{M}\\) could be updated on-the-fly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.893, + 0.543 + ], + "angle": 0, + "content": "For each training iteration, we randomly sample an image \\(\\{X', Y', B', \\hat{M}', S'\\}\\) from \\(\\mathcal{M}\\) and extract a subset of instances from \\(X'\\) based on importance sampling, where \\(S'\\) measures the importance of instances (please refer to supplemental materials for more details), so that instances with higher-quality masks are more likely to be selected. We paste the extracted objects onto input image \\(\\{X, Y, B\\}\\), and adjust the annotations accordingly, i.e., we remove fully occluded objects and update the masks and bounding boxes of partially occluded objects. Finally, we compute the mask loss only on the pasted instances:" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.551, + 0.892, + 0.582 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p a s t e} = \\sum_ {k} \\mathbb {1} _ {p a s t e} \\left[ \\ell_ {m a s k} \\left(M _ {p r e d} ^ {k}, \\hat {M} ^ {\\prime k}\\right) \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.589, + 0.892, + 0.62 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}_{\\text{paste}}\\) is the indicator function, being 1 if the \\(k\\)-th instance is copied from \\(X'\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.627, + 0.685, + 0.643 + ], + "angle": 0, + "content": "3.4. Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.894, + 0.711 + ], + "angle": 0, + "content": "As shown in Fig. 2, we employ a momentum encoder to stabilize the pseudo mask generation process. The parameters of the segmentation model are updated by optimizing the following loss function \\(\\mathcal{L}_{seg}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.719, + 0.892, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s e g}} = \\mathcal {L} _ {\\text {l o w l e v e l}} + \\lambda_ {1} \\mathcal {L} _ {\\text {p s e u d o}} + \\lambda_ {2} \\mathcal {L} _ {\\text {p a s t e}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.892, + 0.834 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are two trade-off parameters. \\(\\mathcal{L}_{lowlevel}\\) denotes low-level pairwise supervision defined in Box-Inst [36]. \\(\\mathcal{L}_{lowlevel}\\) and \\(\\mathcal{L}_{pseudo}\\) provide complementary supervision from local and global perspectives, respectively, and work together to bridge the performance gap between box-supervised and fully-supervised settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.634, + 0.863 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We conduct experiments on COCO [24] and PASCAL VOC [11] datasets. The model is trained on train2017," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7197" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.175, + 0.089, + 0.803, + 0.374 + ], + "angle": 0, + "content": "
methodbackbonesche.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
fully-supervisedMask R-CNN [12]ResNet-101-FPN3×37.559.340.221.139.648.3
YOLACT-700 [3]ResNet-101-FPN4.5×31.250.632.812.133.347.1
PolarMask [40]ResNet-101-FPN2×32.153.733.114.733.845.3
SOLOv2 [38]ResNet-101-FPN3×39.760.742.917.342.957.4
CondInst [34]ResNet-101-FPN3×39.160.942.021.541.750.9
\\( Mask2Fomer^† \\)[7]ResNet-101-MSDefomAttn50e44.2--23.847.766.7
box-supervised\\( BBTP^† \\)[14]ResNet-101-FPN1×21.145.517.211.222.029.8
BBAM [21]ResNet-101-FPN1×25.750.023.3---
\\( BoxCaseg^‡ \\)[37]ResNet-101-FPN1×30.954.330.812.132.846.3
SIM (Ours)ResNet-101-FPN1×34.056.835.017.236.845.5
BoxLevelSet [23]ResNet-101-FPN3×33.456.834.115.236.846.8
BoxInst [36]ResNet-101-FPN3×33.256.533.616.235.345.1
SIM (Ours)ResNet-101-FPN3×35.358.936.418.438.047.5
BoxLevelSet [23]ResNet-DCN-101-BiFPN3×35.459.136.716.838.551.3
BoxInst [36]ResNet-DCN-101-BiFPN3×35.059.335.617.137.248.9
SIM (Ours)ResNet-DCN-101-BiFPN3×37.461.838.618.640.251.6
BoxInst [36]Swin-B-FPN3×37.963.239.020.041.253.1
SIM (Ours)Swin-B-FPN3×40.266.941.321.143.556.0
\\( BoxInst^† \\)[36]Mask2Former-ResNet-10150e35.759.836.416.638.555.4
\\( SIM^† \\)(Ours)Mask2Former-ResNet-10150e37.462.238.717.641.356.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.383, + 0.893, + 0.414 + ], + "angle": 0, + "content": "Table 1. Comparisons between SIM and state-of-the-art methods on the COCO test-dev split. Symbol “†” means that the results are evaluated on the COCO val split, and “‡” denotes that BoxCaseg is trained with both box and salient object supervisions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.471, + 0.5 + ], + "angle": 0, + "content": "which contains about 115k images from 80 categories with only box annotations. We use val2017 (5k images) for ablation study and test-dev2017 (20k images) for comparisons with other methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.509, + 0.295, + 0.526 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.533, + 0.471, + 0.866 + ], + "angle": 0, + "content": "We adopt CondInst [34] and Mask2Former [7] as our baseline. For CondInst, the backbone with FPN is pretrained on ImageNet. The training and testing details follow CondInst1 implemented with Detectron2 [39] unless specified. The model is warmed-up for 10k iterations with the projection loss and pairwise loss proposed in [36], and then trained for 80k iterations by adding our pseudo supervision loss and Copy-Paste loss with batch size 16 on 8 TITAN RTX GPUs. When ResNet is used as the backbone, our model is trained with SGDM optimizer. The initial learning rate is set to 0.01, and reduced by a factor of 10 at steps 60k and 80k, respectively. When SwinT [26] is used as the backbone, we adopt the AdamW [27] optimizer and set the initial learning rate to 0.0001. For Mask2Former, we follow its baseline settings2 and replace the original pixelwise mask loss with our designed loss terms. The length of the memory bank is set to 100, and we extract a quarter of the instances from each image with \\(1 \\sim 3\\) instances per image. The momentum used to update networks and prototypes is set to 0.9999 and 0.999, respectively. The modulation intensity \\(\\alpha\\) is empirically set to 0.5. Besides, \\(\\lambda_1\\), \\(\\lambda_2\\), \\(\\mu\\), and \\(\\tau\\) are empirically set to 0.5, 1, 5, and 0.1, respectively." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.436, + 0.872, + 0.628 + ], + "angle": 0, + "content": "
methodsbackboneAP\\( AP_{50} \\)\\( AP_{75} \\)
GrabCut* [31]ResNet-10119.038.817.0
SDI [17]VGG-16-44.816.3
BBTP [14]ResNet-10123.154.117.1
BBTP w/ CRF [14]ResNet-10127.559.121.9
BBAM [21]ResNet-101-63.731.8
BoxInst [36]ResNet-5034.359.134.2
BoxInst [36]ResNet-10136.561.437.0
DiscoBox [20]ResNet-50-59.835.5
DiscoBox [20]ResNet-101-62.237.5
BoxLevelSet [23]ResNet-5036.364.235.9
BoxLevelSet [23]ResNet-10138.366.338.7
SIM (Ours)ResNet-5036.765.535.6
SIM (Ours)ResNet-10138.667.138.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.668 + ], + "angle": 0, + "content": "Table 2. Performance comparison on Pascal VOC val2012 split. Symbol “*” denotes that the results are copied from BoxInst." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.681, + 0.813, + 0.698 + ], + "angle": 0, + "content": "4.2. Comparisons with State-of-the-Arts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We compare the proposed SIM with state-of-the-art BSIS methods on the COCO [24] dataset. The fully supervised methods are also compared as a reference. As shown in Tab. 1, SIM outperforms BoxInst [36] and BoxLevelSet [23] by \\(1.6\\%\\) and \\(1.4\\%\\) AP with the ResNet-101-FPN backbone and \\(3\\times\\) training schedule. This is because we employ dataset-level prototypes to exploit the semantic information of objects while filtering out trivial image-specific noises. It can also be seen that our SIM method produces impressive results on small objects, largely outperforming BoxInst and BoxLevelSet by \\(2.8\\%\\) AP and \\(1.8\\%\\) AP with ResNet-101-FPN backbone, respectively. This can be attributed to the proposed Copy-Paste" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.305, + 0.888 + ], + "angle": 0, + "content": "\\(^{1}\\)https://github.com/aim-uofa/AdelaiDe" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.373, + 0.9 + ], + "angle": 0, + "content": "\\(^{2}\\)https://github.com/facebookresearch/Mask2Former" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.373, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7198" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.089, + 0.255, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.257, + 0.089, + 0.422, + 0.174 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.249, + 0.175, + 0.265, + 0.185 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.424, + 0.089, + 0.571, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.567, + 0.176, + 0.581, + 0.185 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.09, + 0.718, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.089, + 0.8, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.801, + 0.089, + 0.876, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.176, + 0.81, + 0.185 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.186, + 0.256, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.256, + 0.186, + 0.421, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.249, + 0.271, + 0.266, + 0.281 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.424, + 0.186, + 0.571, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.186, + 0.718, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.271, + 0.581, + 0.281 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.186, + 0.8, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.797, + 0.27, + 0.81, + 0.28 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.285, + 0.813, + 0.299 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of BoxInst (in the red box) and our method (in the blue box) on COCO val2017." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.47, + 0.516 + ], + "angle": 0, + "content": "operation, which creates many challenging training data of small hard objects. BoxInst lags behind on large objects due to the lack of semantic guidance. BoxLevelSet has lower performance on small objects because small objects lack rich features for level set evolution. By using stronger backbones with BiFPN [33] and DCN [47], the performance can be further boosted to \\(37.4\\%\\) AP. By taking Swin transformer [26] as backbone [26], the proposed SIM could surpass BoxInst by \\(1.7\\%\\) AP, attaining \\(39.6\\%\\) AP. In addition, we also validate the effectiveness of our method on the query-based baseline, i.e., Mask2Former [7]. Our method achieves consistent improvement and outperforms BoxInst by \\(1.7\\%\\) AP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.611 + ], + "angle": 0, + "content": "Tab. 2 reports the segmentation results on the Pascal VOC [11] dataset. Our method outperforms BoxInst [36] by \\(2.4\\%\\) and \\(2.1\\%\\) AP with ResNet-50 and ResNet-101 backbones, respectively. BoxLevelSet [23] achieves comparable performance since the level set model could evolve the precise contour of objects, which is beneficial for large objects." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.632, + 0.26, + 0.648 + ], + "angle": 0, + "content": "4.3. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Fig. 5 shows the qualitative segmentation results of our method and BoxInst on COCO val split. We have the following observations. First, according to (a), by leveraging the semantic-level supervision, our method is able to segment foreground instances that heavily tangle with background or other objects with similar appearances, because the prototypes explore global structural information of objects and could reduce the noise brought by using only local pair-wise affinity supervision. Second, as can be seen in (b) (c), our method could better separate overlapping instances of the same semantics since we introduce the self-correction module to reduce the falsely activated instances while enhancing the correct ones. Third, as shown in (d) and (f), benefiting from the abstraction of prototypes from massive training data, our method is able to perceive the whole entity of object instances and produce better segmentation results." + }, + { + "type": "table", + "bbox": [ + 0.52, + 0.317, + 0.871, + 0.375 + ], + "angle": 0, + "content": "
\\( \\mathcal{L}_{pseudo} \\)\\( \\mathcal{L}_{paste} \\)AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
baseline30.752.231.113.833.145.7
✓31.954.032.614.734.747.4
✓✓32.254.033.015.834.548.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.378, + 0.891, + 0.404 + ], + "angle": 0, + "content": "Table 3. The Mask AP on COCO val2017 split by applying different loss terms." + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.416, + 0.868, + 0.494 + ], + "angle": 0, + "content": "
αAPAP50AP75APSAPMAPL
030.552.730.614.133.344.8
0.331.353.131.915.134.046.1
0.532.254.033.015.834.548.3
0.732.054.032.415.734.447.9
131.453.032.315.034.247.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.571, + 0.497, + 0.82, + 0.51 + ], + "angle": 0, + "content": "Table 4. Effect of modulation intensity \\( \\alpha \\) ." + }, + { + "type": "table", + "bbox": [ + 0.524, + 0.521, + 0.869, + 0.587 + ], + "angle": 0, + "content": "
# prototypesAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
L=131.653.132.415.334.046.9
L=532.053.632.915.734.547.4
L=1032.254.033.015.834.548.3
L=5032.253.933.215.934.348.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.59, + 0.871, + 0.604 + ], + "angle": 0, + "content": "Table 5. Effect of the number of prototypes \\( L \\) per category." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.62, + 0.654, + 0.636 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.643, + 0.892, + 0.704 + ], + "angle": 0, + "content": "We conduct ablation studies on the COCO dataset, with ResNet-50-FPN backbone and \\(1 \\times\\) training schedule, to investigate the role of each component in our framework. The Mask AP on COCO val split is reported." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Contribution of the two losses. Tab. 3 shows the contributions of the two loss terms, i.e., \\(\\mathcal{L}_{pseudo}\\) and \\(\\mathcal{L}_{paste}\\). The baseline is BoxInst [36], which resorts to the color similarity between proximal pixels as supervision. The proposed pseudo mask loss improves the performance by \\(1.2\\%\\) AP, especially on large objects (\\(1.7\\%\\) AP). This demonstrates that by introducing the semantic-aware instance mask generation paradigm, our method could distinguish not only proximal pixels with similar colors but also overlapping objects of the same semantics. Besides, the online weakly-supervised Copy-Paste loss brings a further improvement of \\(0.3\\%\\) AP, while the performance on small objects \\(\\mathrm{AP}_S\\) is largely improved by \\(1.1\\%\\) AP." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7199" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.491, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.09, + 0.897, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.154, + 0.251, + 0.813, + 0.266 + ], + "angle": 0, + "content": "Figure 6. Visualizations of pseudo semantic masks \\(M_{\\mathrm{S}}\\) , pseudo instance masks \\(M_{\\mathrm{I}}\\) , and final pseudo masks \\(\\hat{M}\\)" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.283, + 0.456, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.51, + 0.467, + 0.525 + ], + "angle": 0, + "content": "Figure 7. Visualizations of weights for different positive samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.468, + 0.793 + ], + "angle": 0, + "content": "Effect of the modulation intensity. We use the instance-aware pseudo probability map \\( M_{\\mathrm{I}} \\) to modulate the semantic-aware map \\( M_{\\mathrm{S}} \\) by using a parameter \\( \\alpha \\). Tab. 4 shows the results by setting \\( \\alpha \\) to different values. One can draw a conclusion that the integration of semantic mask \\( M_{\\mathrm{S}} \\) and instance mask \\( M_{\\mathrm{I}} \\) leads to better results than any of them. Specifically, \\( M_{\\mathrm{S}} \\) facilitates more holistic object pattern understanding by exploring the semantic information from the entire dataset, while \\( M_{\\mathrm{I}} \\) rectifies the falsely activated objects in \\( M_{\\mathrm{S}} \\) and improves the reliability of pseudo masks. Removing the self-correction module, i.e., setting \\( \\alpha \\) to 0, will lead to an obvious performance drop by \\( 1.7\\% \\) AP. This is not surprising because the semantic mask contains certain noisy supervision caused by the falsely activated objects and pixels. On the other hand, training without semantic masks, i.e., setting \\( \\alpha \\) to 1, will decrease the segmentation performance by \\( 0.8\\% \\) AP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Semantic masks vs. instance masks. We explore the complementarity of \\( M_{\\mathrm{S}} \\) and \\( M_{\\mathrm{I}} \\) by visualizing them in Fig. 6. As can be seen in (b-d), \\( M_{\\mathrm{S}} \\) could distinguish object instances that have similar appearances but different semantics from the background and other objects. In comparison, from (a) (e-f), we see that \\( M_{\\mathrm{I}} \\) is good at distinguishing different instances of the same semantics, which are employed" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.315 + ], + "angle": 0, + "content": "to suppress the falsely activated instances in \\( M_{\\mathrm{S}} \\). They work together to produce more reliable supervision for training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.495 + ], + "angle": 0, + "content": "Visualizations of weights. To further understand the effect of the positive mask weighting strategy, we show the visualizations of weights assigned to different positive samples in Fig. 7. It can be seen that large weights are mainly located in the central regions of foreground objects and far from other objects, while the small ones are located in ambiguous regions, such as overlapping regions between different objects and junctions between foreground and background. This weighting strategy facilitates generating higher-quality supervision and reducing the falsely activated instances. More analyses about this weighting strategy are provided in supplemental files." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.633 + ], + "angle": 0, + "content": "Effect of the number of prototypes per category. We set multiple prototypes per category to better model intra-class variation. Tab. 5 reports the segmentation results w.r.t. different number of prototypes per category. The baseline attains \\(31.6\\%\\) AP by representing each category with one prototype. There is a clear performance improvement (about \\(0.4\\%\\) AP) by increasing the number of prototypes to 5; however, the performance reaches saturation when \\(L\\) is more than 10. We set \\(L\\) as 10 to trade off accuracy and cost." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.618, + 0.664 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We proposed a novel SIM method for box-supervised instance segmentation. To alleviate the limitations of pairwise affinity supervision from low-level image features, we explored high-level image semantic contexts by extracting a group of representative prototypes from the dataset and using them to segment foreground objects from background. To rectify the possible false positive instances in semantic masks, we introduced extra supervision by integrating mask predictions of different positive samples in a weighted manner. Furthermore, we devised an online weakly-supervised Copy-Paste method to create challenging training data by equipping a continuously updated memory bank to store historical images with pseudo masks. Both the qualitative and quantitative experiments demonstrated the superior performance of our SIM method over state-of-the-arts." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7200" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2209-2218, 2019. 1, 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.257 + ], + "angle": 0, + "content": "[2] Jiwoon Ahn and Suha Kwak. Learning pixel-level semantic affinity with image-level supervision for weakly supervised semantic segmentation. 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Most of the current efforts leverage low-level image features as extra supervision without explicitly exploiting the high-level semantic information of the objects, which will become ineffective when the foreground objects have similar appearances to the background or other objects nearby. We propose a new box-supervised instance segmentation approach by developing a Semantic-aware Instance Mask (SIM) generation paradigm. Instead of heavily relying on local pair-wise affinities among neighboring pixels, we construct a group of category-wise feature centroids as prototypes to identify foreground objects and assign them semantic-level pseudo labels. Considering that the semantic-aware prototypes cannot distinguish different instances of the same semantics, we propose a self-correction mechanism to rectify the falsely activated regions while enhancing the correct ones. Furthermore, to handle the occlusions between objects, we tailor the Copy-Paste operation for the weakly-supervised instance segmentation task to augment challenging training data. Extensive experimental results demonstrate the superiority of our proposed SIM approach over other state-of-the-art methods. The source code: https://github.com/1slrh/SIM. + +# 1. Introduction + +Instance segmentation is among the fundamental tasks of computer vision, with many applications in autonomous driving, image editing, human-computer interaction, etc. The performance of instance segmentation has been improved significantly along with the advances in deep learning [6, 12, 34, 38]. However, training robust segmentation networks requires a large number of data with pixel-wise annotations, which consumes intensive human labor and + +![](images/e7b55cdab11cec2704654a2e0d28616c26781e5e519bc377a779d03a43b918dc.jpg) + +![](images/126defbd4dba9001d58aa1d3abf4b65d047ab02bfc118f74b70ef672f5539bb5.jpg) +(a) + +![](images/6fb346b4accf13f3aea7ec8605f5fbf5e3bd4417dc5544579b0548dc1f3f1da8.jpg) + +![](images/8f22389ff0fdc9965a9d95ab54cf0aa288a2e736f355d4b669bbc97cffbd3fd4.jpg) +Figure 1. The pipeline of Semantic-aware Instance Mask (SIM) generation method. (a) shows the mask prediction produced by using only low-level affinity supervision, where the foreground heavily blends with background. (b) and (c) show the semantic-aware masks obtained with our constructed prototypes, which perceive the entity of objects but are unable to separate different instances of the same semantics. (d) shows the final instance pseudo mask rectified by our proposed self-correction module. + +![](images/59983af5365473104c668a01c6203609f14e17c59d392107802a7a1c4d9bc2f1.jpg) +(c) + +![](images/c87aec056c41cc216753e4fd695840207fb849ec642d97dbc12abbe99075a8e8.jpg) +(d) + +resources. To reduce the reliance on dense annotations, weakly-supervised instance segmentation based on cheap supervisions, such as bounding boxes [14,21,36], points [8] and image-level labels [1,18], has recently attracted increasing research attention. + +In this paper, we focus on box-supervised instance segmentation (BSIS), where the bounding boxes provide coarse supervised information for pixel-wise prediction task. To provide pixel-wise supervision, conventional methods [10, 19] usually leverage off-the-shelf proposal techniques, such as MCG [30] and GrabCut [31], to create pseudo instance masks. However, the training pipelines of these methods with multiple iterative steps are cumbersome. Several recent works [14, 36] enable end-to-end training by taking pairwise affinities among pixels as extra supervision. Though these methods have achieved promising performance, they heavily depend on low-level image features, such as color pairs [36], and simply assume that the proximal pixels with similar colors are likely to have the same label. This leads to confusion when foreground objects have similar appearances to the background or other ob- + +jects nearby, as shown in Fig. 1 (a). It is thus error-prone to use only low-level image cues for supervision since they are weak to represent the inherent structure of objects. + +Motivated by the fact that high-level semantic information can reveal intrinsic properties of object instances and hence provide effective supervision for segmentation model training, we propose a novel Semantic-aware Instance Mask generation method, namely SIM, to explicitly exploit the semantic information of objects. To distinguish proximal pixels with similar color but different semantics (please refer to Fig. 1 (a)), we construct a group of representative dataset-level prototypes, i.e., the feature centroids of different classes, to perform foreground/background segmentation, producing semantic-aware pseudo masks (see Fig. 1 (b)). These prototypes abstracted from massive training data can capture the structural information of objects, enabling more comprehensive semantic pattern understanding, which is complementary to affinity supervision of pairwise neighboring pixels. However, as shown in Fig. 1 (c), these prototypes are unable to separate the instances of the same semantics, especially for overlapping objects. We consequently develop a self-correction mechanism to rectify the false positives while enhancing the confidence of true-positive foreground objects, resulting in more precise instance-aware pseudo masks, as shown in Fig. 1 (d). + +It is worth mentioning that our generated pseudo masks could co-evolve with the segmentation model without cumbersome iterative training procedures in previous methods [10, 21]. In addition, considering that the existing weakly-supervised instance segmentation methods only provide very limited supervision for rare categories and overlapping objects due to the lack of ground truth masks, we propose an online weakly-supervised Copy-Paste approach to create a combinatorial number of augmented training samples. Overall, the major contributions of this work can be summarized as follows: + +- A novel BSIS framework is presented by developing a semantic-aware instance mask generation mechanism. Specifically, we construct a group of representative prototypes to explore the intrinsic properties of object instances and identify complete entities, which produces more reliable supervision than low-level features. +- A self-correction module is designed to rectify the semantic-aware pseudo masks to be instance-aware. The falsely activated regions will be reduced, and the correct ones will be boosted, enabling more stable training and progressively improving the segmentation results. +- We tailor the Copy-Paste operation for weakly-supervised segmentation tasks in order to create more occlusion patterns and more challenging training data. The overall framework can be trained in an end-to-end manner. Extensive experiments demonstrate the superiority of our method over other state-of-the-art methods. + +# 2. Related Work + +Instance Segmentation (IS) is a fundamental task in computer vision fields, which aims to predict the pixel-wise mask for each instance of interest in an image. Many top performing IS methods [6, 15, 25, 42] follow the Mask R-CNN meta-architecture [12], which splits the IS task into two consecutive stages and performs segmentation on the extracted region proposals. Single-stage IS methods have also been rapidly developed during the past few years. YOLACT [3] and BlendMask [5] employ fine-grained FPN features rather than the RoI-aligned features for mask prediction. However, they still need crop operation for object localization. Some methods segment each instance in a fully convolutional manner without resorting to the detection results. For example, CondInst [34] and SOLO [38] employ instance-aware conditional convolutions and dynamically generate convolution kernels to segment different objects. Universal architectures [7, 41] have emerged with DETR [4] and show that end-to-end set prediction architecture is general enough for any segmentation task. Despite the promising performance, these methods heavily rely on expensive pixel-wise mask annotation, which restricts their usability in many practical applications. + +Weakly-Supervised Instance Segmentation (WSIS) with weak annotations is a more attractive yet challenging task. Some works attempt to achieve high-quality segmentation with box-level annotations [14, 17, 21, 36] or image-level annotations [1, 18]. Khoreva et al. [17] employ box supervisory training data for WSIS. However, the proposed method relies on the region proposal techniques, such as GrabCut [31] and MCG [30], to generate pseudo masks in an offline manner. Other recent methods [21, 37] also focus on generating instance labels by using an independent network, which require either extra salient data [38] or some post-processing methods [21]. This inevitably leads to a complicated training pipeline. + +To achieve a simple yet effective training pipeline, BBTP [14] formulates WSIS as a multiple-instance learning problem and introduces a structural constraint to maintain the unity of estimated masks. BoxInst [36] builds upon an efficient CondInst [34] framework, and enforces the proximal pixels with similar colors to have the same label through a pairwise loss. Despite the promising performance, these methods depend heavily on local color supervision while neglecting the global structure of the entire object. Different from these methods, our proposed method provides more reliable supervision by leveraging high-level semantic information, which is beneficial for capturing the intrinsic structures of objects. + +Pseudo Mask Generation. A widely adopted technique in conventional weakly-supervised semantic segmentation methods is Class Activation Map (CAM) [44], which aims to obtain an object localization map from class labels. How- + +![](images/7f0961fe6ded960d0036a6fcf77741460ca85f29ae9daacfefcfbcd2d3269b0b.jpg) +Figure 2. The framework of our proposed Semantic-aware Instance Mask (SIM) generation method. The model contains the main segmentation network $\mathcal{F}_{seg}$ and its momentum-updated version $\mathcal{F}_{seg}^{\prime}$ . Given an image $X$ , we first pass it through $\mathcal{F}_{seg}$ and $\mathcal{F}_{seg}^{\prime}$ to obtain the corresponding mask features $Z$ and $Z^{\prime}$ . The prototypes are then updated as the moving average of feature cluster centroids. Next, we obtain the semantic probability map $M_{\mathrm{S}}$ by measuring the distance between prototypes and mask features $Z^{\prime}$ . After that, the falsely activated instances in $M_{\mathrm{S}}$ are rectified by the instance probability map $M_{1}$ , which is obtained by integrating different positive masks of the same ground truth object. Finally, we obtain the pseudo mask $\hat{M}$ by selecting highly-confident pixels with two thresholds. + +ever, CAM only identifies the most discriminative object regions and suffers from the problem of limited activation area [2,13,16,32]. Given that bounding boxes could provide the location information of objects in an image, BBAM [21] employs an object detector to produce a bounding box attribute map, which serves as a pseudo ground truth mask. As a more lightweight approach, self-training-based methods [22, 43, 48, 49] select high-scoring predictions on unlabeled data as pseudo labels for training. The idea of assigning labels based on prototypes has also been explored in semantic segmentation [22, 45, 46]. In this work, the prototype technique is adapted to capture the global structure of objects with the same semantics, reducing the noise caused by low-level feature supervision. + +# 3. Method + +# 3.1. Overview + +In the setting of box-supervised instance segmentation (BSIS), we are given a set of box annotated training data $\mathcal{D} = \{X_n, Y_n, B_n\}_{n=1}^N$ , where $N$ is the number of images. Besides, $Y_n = \{y_n^k\}_{k=1}^K$ and $B_n = \{b_n^k\}_{k=1}^K$ denote the class-level and box-level annotations, where $K$ is the number of instances in the image $X_n$ , $y_n^k \in \{1, \dots, C\}$ represents the category label of the $k$ -th object in the $n$ -th image, and $b_n^k$ specifies its corresponding location. + +The overview of our method is shown in Fig. 2, where the proposed SIM module is highlighted in the green dotted box. We choose CondInst [34] and Mask2Former [7] + +as the basic segmentation networks due to their simplicity and effectiveness. Instead of only relying on local pair-wise affinities among pixels as supervision [14,36], we employ a group of semantic-level prototypes to capture global structural information of objects, and produce semantic probability map $M_{\mathrm{S}}$ by computing the distances between each pixel-wise feature vector and all prototypes. Since these prototypes are unable to separate different objects of the same semantics, we propose a self-correction mechanism to deactivate falsely estimated objects by using an instance probability map $M_{\mathrm{I}}$ . This map can be obtained by integrating different positive masks corresponding to the same instance with an IoU-based weighting strategy. Finally, we employ two thresholds to select confident predictions as pseudo ground truths $\hat{M}$ , and use them for training the segmentation network $\mathcal{F}_{seg}$ . + +# 3.2. Semantic-aware Instance Mask Generation + +# 3.2.1 Pseudo Semantic Map + +Low-level image features, such as colors, intensity, edges, blobs, etc., could provide useful guidance to identify the object boundaries in an image. However, these features vary significantly with illuminations, motion blurs, and noises. Thus it is error-prone to take only low-level features as supervision for BSIS when object instances are heavily blended with the background. To address this issue, we attempt to explore the intrinsic structures of objects as semantic guidance to provide more robust supervision for BSIS + +model training. + +We construct a group of representative prototypes to model the structural information of objects, and use them to generate semantic-aware pseudo masks. Considering that a single prototype is insufficient to capture the intra-class variance, we employ multiple prototypes [29, 45] to represent the objects in a category. Specifically, we extract $L$ prototypes (i.e., sub-centers) from each class $c \in \{1, \dots, C\}$ , denoted by $P_{c} = \{p_{1}^{c}, \dots, p_{L}^{c}\}$ , to depict different characteristics of the same category. Given an input image $I \in \mathbb{R}^{h \times w \times 3}$ , we first pass it through the segmentation model $\mathcal{F}_{seg}$ to obtain the feature map $Z \in \mathbb{R}^{H \times W \times D}$ , and normalize it with $z_{i} = \frac{z_{i}}{||z_{i}||_{2}}$ , where $z_{i}$ denotes the $i$ -th feature vector of $Z$ with length $D$ . Unlike semantic segmentation, which predicts only one mask for each input image, we predict a variable number of masks depending on the number of categories in the image. To this end, we compute the semantic probability map corresponding to the $c$ -th category, denoted by $M_{\mathrm{S}}^{c} \in \mathbb{R}^{H \times W}$ , using the following formula: + +$$ +M _ {\mathrm {S}, i} ^ {c} = \sigma \left(\max \{\frac {\langle z _ {i} , p _ {l} ^ {c} \rangle}{\tau} \} _ {l = 1} ^ {L}\right), \tag {1} +$$ + +where $\langle \cdot \rangle$ computes the cosine similarity between two $\ell_2$ -normalized feature vectors. The sigmoid function $\sigma (\cdot)$ converts the feature distance to the probability that the pixel belongs to the $l$ -th sub-center, and $\tau$ controls the concentration level of representations. Once computed, we assign these semantic probability maps to different objects according to their class labels $Y_{n}$ . + +Multi-prototype update. We update the prototypes on-the-fly with the moving average of cluster centroids computed in previous mini-batches. Specifically, given an image $X_{n}$ and its corresponding pseudo mask $\hat{M}$ , we obtain the pixelwise cluster assignments $Q$ of the $c$ -th category by optimizing the following objective function: + +$$ +\max _ {Q \in \mathbb {Q}} \operatorname {T r} \left(Q ^ {T} P _ {c} ^ {T} Z\right) + \varepsilon H (Q), \quad s. t. Q \in \mathbb {Q}, \tag {2} +$$ + +with $\mathbb{Q} := \{Q \in \mathbb{R}_+^{L \times N_c} | Q\mathbf{1}_{N_c} = r, Q^T\mathbf{1}_L = h\}$ . + +The above formula is an instance of the optimal transport problem [9], where $Q = \frac{1}{N_c} [q_1, \dots, q_{N_c}]$ represents the transport assignment and is restricted to be a probability matrix with the constraint $\mathbb{Q}$ . $N_c$ is the number of pixels belonging to the $c$ -th category, $H$ denotes the entropy function with $H(Q) = -\sum_{ij} Q_{ij} \log Q_{ij}$ , and $\varepsilon$ controls the smoothness of distribution. $r = \frac{1}{L} \mathbf{1}_L$ and $h = \frac{1}{N_c} \mathbf{1}_{N_c}$ are the marginal projections of $Q$ onto its rows and columns, respectively, where $\mathbf{1}_L$ and $\mathbf{1}_{N_c}$ represent the vectors of ones of dimension $L$ and $N_c$ . + +By formulating the cluster assignment as an optimal transport problem, the optimization of Eq. 2 concerning $Q$ + +![](images/1036247a50e5d4a60acd37f3f1740bd0cff0f483b5b0636832b7841fb4181be2.jpg) +Figure 3. (a) The mask quality varies much across different positive samples. (b) The instance-aware masks $M_{1}$ obtained by using positive mask weighting strategy. + +can be solved in linear time by the Sinkhorn-Knopp algorithm [9]: + +$$ +Q ^ {*} = \operatorname {d i a g} (u) \exp \left(\frac {P _ {c} ^ {T} Z}{\varepsilon}\right) \operatorname {d i a g} (v), \tag {3} +$$ + +where $u \in \mathbb{R}^L$ and $v \in \mathbb{R}^{N_c}$ are two renormalization vectors. Finally, we update the prototypes as the moving average of cluster centroids. Particularly, in each iteration $t$ , the prototype is estimated as: + +$$ +\left. p _ {l} ^ {c} \right| _ {t} = \gamma \cdot \left. p _ {l} ^ {c} \right| _ {t - 1} + (1 - \gamma) \cdot p _ {n, l} ^ {c}, \tag {4} +$$ + +where $\lambda \in [0,1]$ is the momentum coefficient. $p_{n,l}^{c}$ denotes the $l$ -th sub-center of the $c$ -th class in image $X_{n}$ , which is computed by: + +$$ +p _ {n, l} ^ {c} = \frac {\sum_ {i} ^ {N _ {c}} z _ {i} \cdot \mathbb {1} \left(Q _ {i , l} = 1\right)}{\sum_ {i} ^ {N _ {c}} \mathbb {1} \left(Q _ {i , l} = 1\right)}, \tag {5} +$$ + +where $\mathbb{1}$ is an indicator function, being 1 if $Q_{i,l} = 1$ + +Remarks on prototypes. The pairwise loss used in [36] explores pixel-to-pixel correlations, which provide local supervision but can not ensure the global consistency of objects with the same semantics. In contrast, the prototypes explore pixel-to-center relations, which could ensure the integrity of objects and provide more reliable supervision. Besides, since the prototypes are abstracted from massive training data, they could reveal the intrinsic properties of objects and filter out image-specific noise and outliers. In addition, we treat different categories equally and set the same number of prototypes for each category, which is potentially beneficial for identifying long-tailed objects. + +# 3.2.2 Self-Correction + +Though the pseudo semantic masks $M_{\mathrm{S}}$ could provide more reliable supervision from a global perspective, they could not distinguish different objects of the same semantics, especially when there exist overlaps or occlusions among objects. To overcome this limitation, we propose a simple yet effective self-correction module, which could upgrade the semantic-aware masks $M_{\mathrm{S}}$ to be instance-aware. + +Positive mask weighting. Let us first revisit some properties of anchor-free detectors such as FCOS [35]. In these works, anchors denote the dense feature points, and positive samples represent the anchors located in the center/bbox region of each object. These methods assign multiple positive samples, which have high enough Intersection over Union (IoU) with ground truth $(gt)$ box, to each object. However, the quality of masks produced by different positive samples varies significantly, as shown in Fig. 3 (a). Those ambiguous anchors, i.e., anchors that are taken as positive samples for multiple $gt$ objects simultaneously (red dots in Fig. 3), could not separate overlapping objects of the same semantics. Based on these observations, we propose a positive mask weighting strategy to integrate different masks according to their quality, resulting in a high-quality instance-aware mask $M_{\mathrm{I}}$ . In specific, we define a metric of mask quality based on the IoU between predicted and $gt$ boxes: + +$$ +w _ {p o s} = e ^ {\mu \cdot I o U}, \tag {6} +$$ + +where $\mu$ controls the relative gaps between different weights. Each weight $w_{pos}$ is then normalized by the sum of weights for all positive samples. As can be seen in Fig. 3 (b), the pseudo instance masks $M_{\mathrm{I}}$ could better separate different objects and provide more accurate supervision. + +Pseudo mask loss. By employing $M_{\mathrm{I}}$ , the falsely activated objects or pixels in $M_{\mathrm{S}}$ could be suppressed, while the confidence of foreground objects could be enhanced. The rectification process is conducted as follows: + +$$ +\hat {M} _ {p r o b} ^ {k, i} = (1 - \alpha) \cdot M _ {\mathrm {S}} ^ {k, i} + \alpha \cdot M _ {\mathrm {I}} ^ {k, i}, \qquad (7) +$$ + +where $\hat{M}_{prob}^{k,i}$ represents the $i$ -th pixel of the $k$ -th pseudo probability map, and $\alpha \in [0,1]$ controls the intensity of modulation. Finally, we set two thresholds $\tau_{\mathrm{high}}$ and $\tau_{\mathrm{low}}$ to select highly-confident foreground and background predictions as pseudo labels, resulting in $\hat{M}$ . The pseudosupervised mask loss is defined by: + +$$ +\mathcal {L} _ {p s e u d o} = \frac {1}{N _ {p o s}} \sum_ {k} ^ {N _ {p o s}} \ell_ {m a s k} (M _ {p r e d}, \hat {M} _ {k}, W), \tag {8} +$$ + +where the mask loss $\ell_{mask}$ consists of two terms: binary cross-entropy loss $\ell_{bce}$ and dice loss [28] $\ell_{dice}$ . $\hat{M}_k$ denotes the pseudo mask of the $k$ -th positive sample. $W$ is a binary weight mask that neglects ambiguous regions by using $\tau_{\mathrm{high}}$ and $\tau_{\mathrm{low}}$ , i.e., $W^i = 0$ , if $\tau_{\mathrm{low}} < \hat{M}_{prob}^i < \tau_{\mathrm{high}}$ . + +# 3.3. Online Weakly-Supervised Copy-Paste + +Object-aware Copy-Paste is a simple yet effective way to improve the data efficiency. However, Copy-Paste has rarely been explored for weakly-supervised instance segmentation. It is natural to employ pseudo masks as the guidance to cut object instances from an image $X$ . To achieve + +![](images/2b8b5c1ed61426d9e90617a5a0da64b0839c7ba1a480b008d97e9e491f5aa5b4.jpg) + +![](images/accdaf1c427ec215e34d463882f2d1854bce4bf71e9a1a34e564d5cb4c2955bd.jpg) + +![](images/b07c5ec0818cbb579aeafec8138294d8ff7c06f2e76fed0431d59d90137c1fd1.jpg) + +![](images/79c9106de779b635b3ad1395cefbe450f7c5b5376973e4fdc4b35ba487fd39c0.jpg) + +![](images/5502e128cdaade468dc0ace73fb39f8a748e23735e317f52654c6786fab08540.jpg) +X +Figure 4. Examples of online weakly-supervised Copy-Paste. We use $\hat{M}'$ to extract instances from $X'$ and paste them onto $X$ , resulting in new training data $X_{paste}$ . + +![](images/2f1d4817975d17c3f552218c245c96912f6de577f941499e6720e1079d073f28.jpg) +X + +![](images/d4461c9bca9af60c190763db973efebc97d7926177dd706c5a03c0d5e666b25b.jpg) +$X_{\text{paste}}$ + +![](images/cc1162b3f177a6e334501aeace4c4f72b6569af6eba6aa198d90c1db2a3c78cf.jpg) +M + +online Copy-Paste, we set up a first-in-first-out memory bank $\mathcal{M}$ to store training samples and their corresponding pseudo masks from preceding mini-batches, which ensures that the pseudo masks in $\mathcal{M}$ could be updated on-the-fly. + +For each training iteration, we randomly sample an image $\{X', Y', B', \hat{M}', S'\}$ from $\mathcal{M}$ and extract a subset of instances from $X'$ based on importance sampling, where $S'$ measures the importance of instances (please refer to supplemental materials for more details), so that instances with higher-quality masks are more likely to be selected. We paste the extracted objects onto input image $\{X, Y, B\}$ , and adjust the annotations accordingly, i.e., we remove fully occluded objects and update the masks and bounding boxes of partially occluded objects. Finally, we compute the mask loss only on the pasted instances: + +$$ +\mathcal {L} _ {p a s t e} = \sum_ {k} \mathbb {1} _ {p a s t e} \left[ \ell_ {m a s k} \left(M _ {p r e d} ^ {k}, \hat {M} ^ {\prime k}\right) \right], \tag {9} +$$ + +where $\mathbb{1}_{\text{paste}}$ is the indicator function, being 1 if the $k$ -th instance is copied from $X'$ . + +# 3.4. Objective Function + +As shown in Fig. 2, we employ a momentum encoder to stabilize the pseudo mask generation process. The parameters of the segmentation model are updated by optimizing the following loss function $\mathcal{L}_{seg}$ : + +$$ +\mathcal {L} _ {\text {s e g}} = \mathcal {L} _ {\text {l o w l e v e l}} + \lambda_ {1} \mathcal {L} _ {\text {p s e u d o}} + \lambda_ {2} \mathcal {L} _ {\text {p a s t e}}, \tag {10} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are two trade-off parameters. $\mathcal{L}_{lowlevel}$ denotes low-level pairwise supervision defined in Box-Inst [36]. $\mathcal{L}_{lowlevel}$ and $\mathcal{L}_{pseudo}$ provide complementary supervision from local and global perspectives, respectively, and work together to bridge the performance gap between box-supervised and fully-supervised settings. + +# 4. Experiments + +We conduct experiments on COCO [24] and PASCAL VOC [11] datasets. The model is trained on train2017, + +
methodbackbonesche.AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
fully-supervisedMask R-CNN [12]ResNet-101-FPN3×37.559.340.221.139.648.3
YOLACT-700 [3]ResNet-101-FPN4.5×31.250.632.812.133.347.1
PolarMask [40]ResNet-101-FPN2×32.153.733.114.733.845.3
SOLOv2 [38]ResNet-101-FPN3×39.760.742.917.342.957.4
CondInst [34]ResNet-101-FPN3×39.160.942.021.541.750.9
\( Mask2Fomer^† \)[7]ResNet-101-MSDefomAttn50e44.2--23.847.766.7
box-supervised\( BBTP^† \)[14]ResNet-101-FPN1×21.145.517.211.222.029.8
BBAM [21]ResNet-101-FPN1×25.750.023.3---
\( BoxCaseg^‡ \)[37]ResNet-101-FPN1×30.954.330.812.132.846.3
SIM (Ours)ResNet-101-FPN1×34.056.835.017.236.845.5
BoxLevelSet [23]ResNet-101-FPN3×33.456.834.115.236.846.8
BoxInst [36]ResNet-101-FPN3×33.256.533.616.235.345.1
SIM (Ours)ResNet-101-FPN3×35.358.936.418.438.047.5
BoxLevelSet [23]ResNet-DCN-101-BiFPN3×35.459.136.716.838.551.3
BoxInst [36]ResNet-DCN-101-BiFPN3×35.059.335.617.137.248.9
SIM (Ours)ResNet-DCN-101-BiFPN3×37.461.838.618.640.251.6
BoxInst [36]Swin-B-FPN3×37.963.239.020.041.253.1
SIM (Ours)Swin-B-FPN3×40.266.941.321.143.556.0
\( BoxInst^† \)[36]Mask2Former-ResNet-10150e35.759.836.416.638.555.4
\( SIM^† \)(Ours)Mask2Former-ResNet-10150e37.462.238.717.641.356.6
+ +which contains about 115k images from 80 categories with only box annotations. We use val2017 (5k images) for ablation study and test-dev2017 (20k images) for comparisons with other methods. + +# 4.1. Implementation Details + +We adopt CondInst [34] and Mask2Former [7] as our baseline. For CondInst, the backbone with FPN is pretrained on ImageNet. The training and testing details follow CondInst1 implemented with Detectron2 [39] unless specified. The model is warmed-up for 10k iterations with the projection loss and pairwise loss proposed in [36], and then trained for 80k iterations by adding our pseudo supervision loss and Copy-Paste loss with batch size 16 on 8 TITAN RTX GPUs. When ResNet is used as the backbone, our model is trained with SGDM optimizer. The initial learning rate is set to 0.01, and reduced by a factor of 10 at steps 60k and 80k, respectively. When SwinT [26] is used as the backbone, we adopt the AdamW [27] optimizer and set the initial learning rate to 0.0001. For Mask2Former, we follow its baseline settings2 and replace the original pixelwise mask loss with our designed loss terms. The length of the memory bank is set to 100, and we extract a quarter of the instances from each image with $1 \sim 3$ instances per image. The momentum used to update networks and prototypes is set to 0.9999 and 0.999, respectively. The modulation intensity $\alpha$ is empirically set to 0.5. Besides, $\lambda_1$ , $\lambda_2$ , $\mu$ , and $\tau$ are empirically set to 0.5, 1, 5, and 0.1, respectively. + +Table 1. Comparisons between SIM and state-of-the-art methods on the COCO test-dev split. Symbol “†” means that the results are evaluated on the COCO val split, and “‡” denotes that BoxCaseg is trained with both box and salient object supervisions. + +
methodsbackboneAP\( AP_{50} \)\( AP_{75} \)
GrabCut* [31]ResNet-10119.038.817.0
SDI [17]VGG-16-44.816.3
BBTP [14]ResNet-10123.154.117.1
BBTP w/ CRF [14]ResNet-10127.559.121.9
BBAM [21]ResNet-101-63.731.8
BoxInst [36]ResNet-5034.359.134.2
BoxInst [36]ResNet-10136.561.437.0
DiscoBox [20]ResNet-50-59.835.5
DiscoBox [20]ResNet-101-62.237.5
BoxLevelSet [23]ResNet-5036.364.235.9
BoxLevelSet [23]ResNet-10138.366.338.7
SIM (Ours)ResNet-5036.765.535.6
SIM (Ours)ResNet-10138.667.138.3
+ +Table 2. Performance comparison on Pascal VOC val2012 split. Symbol “*” denotes that the results are copied from BoxInst. + +# 4.2. Comparisons with State-of-the-Arts + +We compare the proposed SIM with state-of-the-art BSIS methods on the COCO [24] dataset. The fully supervised methods are also compared as a reference. As shown in Tab. 1, SIM outperforms BoxInst [36] and BoxLevelSet [23] by $1.6\%$ and $1.4\%$ AP with the ResNet-101-FPN backbone and $3\times$ training schedule. This is because we employ dataset-level prototypes to exploit the semantic information of objects while filtering out trivial image-specific noises. It can also be seen that our SIM method produces impressive results on small objects, largely outperforming BoxInst and BoxLevelSet by $2.8\%$ AP and $1.8\%$ AP with ResNet-101-FPN backbone, respectively. This can be attributed to the proposed Copy-Paste + +![](images/68888243df38156010be93a537f12ab46c77125c4ed51c7f4451647772b08f0e.jpg) +(a) + +![](images/12b11f945c9a42a629cc02b36ad643e0a8f71e1f75f91680a11eac9948182dd0.jpg) + +![](images/0ff00f8e2d2fae8dab5bb7b9f70c97506d6375dc8cbb139da096d5e2014daa2a.jpg) +(b) + +![](images/001bde20a63c5525cb62f3fc1700285eed8517e9c94d88552615e250623416df.jpg) + +![](images/a5bf8fb601b40bd4e44d867d9dc8da2ea88568e36475fd2b8b15b764aba93dfb.jpg) +(c) + +![](images/bf8e2d0e9f28e02ce7a97b88bcb814da2e0c9d17ec2c3bb9a934feff532962eb.jpg) + +![](images/c9679ede0f96c4e3f51bf487157d7302eed90e100416390d8f0493cf7fcddcbe.jpg) +(d) + +![](images/17c7b0bdc36dc5e4acda977ac2a07ea344cc23808a4938ea24f2f2c2d9e2ef2d.jpg) +Figure 5. Qualitative results of BoxInst (in the red box) and our method (in the blue box) on COCO val2017. + +![](images/9d35c6c434b18382176c455a4cffe02471adc723b8fb412c88f2264d24ab1bdb.jpg) +(e) + +![](images/803201f26d5bcd5bf1ba3457524f30b8dd3c9cf9e40a06dc054c85bcfcf792c4.jpg) + +![](images/6de9859ff037bc10c6a81d77b302b8253cef0a5f083a49a83892d37828baf546.jpg) +(f) + +operation, which creates many challenging training data of small hard objects. BoxInst lags behind on large objects due to the lack of semantic guidance. BoxLevelSet has lower performance on small objects because small objects lack rich features for level set evolution. By using stronger backbones with BiFPN [33] and DCN [47], the performance can be further boosted to $37.4\%$ AP. By taking Swin transformer [26] as backbone [26], the proposed SIM could surpass BoxInst by $1.7\%$ AP, attaining $39.6\%$ AP. In addition, we also validate the effectiveness of our method on the query-based baseline, i.e., Mask2Former [7]. Our method achieves consistent improvement and outperforms BoxInst by $1.7\%$ AP. + +Tab. 2 reports the segmentation results on the Pascal VOC [11] dataset. Our method outperforms BoxInst [36] by $2.4\%$ and $2.1\%$ AP with ResNet-50 and ResNet-101 backbones, respectively. BoxLevelSet [23] achieves comparable performance since the level set model could evolve the precise contour of objects, which is beneficial for large objects. + +# 4.3. Qualitative Results + +Fig. 5 shows the qualitative segmentation results of our method and BoxInst on COCO val split. We have the following observations. First, according to (a), by leveraging the semantic-level supervision, our method is able to segment foreground instances that heavily tangle with background or other objects with similar appearances, because the prototypes explore global structural information of objects and could reduce the noise brought by using only local pair-wise affinity supervision. Second, as can be seen in (b) (c), our method could better separate overlapping instances of the same semantics since we introduce the self-correction module to reduce the falsely activated instances while enhancing the correct ones. Third, as shown in (d) and (f), benefiting from the abstraction of prototypes from massive training data, our method is able to perceive the whole entity of object instances and produce better segmentation results. + +
\( \mathcal{L}_{pseudo} \)\( \mathcal{L}_{paste} \)AP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
baseline30.752.231.113.833.145.7
✓31.954.032.614.734.747.4
✓✓32.254.033.015.834.548.3
+ +Table 3. The Mask AP on COCO val2017 split by applying different loss terms. + +
αAPAP50AP75APSAPMAPL
030.552.730.614.133.344.8
0.331.353.131.915.134.046.1
0.532.254.033.015.834.548.3
0.732.054.032.415.734.447.9
131.453.032.315.034.247.0
+ +Table 4. Effect of modulation intensity $\alpha$ . + +
# prototypesAP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)
L=131.653.132.415.334.046.9
L=532.053.632.915.734.547.4
L=1032.254.033.015.834.548.3
L=5032.253.933.215.934.348.7
+ +Table 5. Effect of the number of prototypes $L$ per category. + +# 4.4. Ablation Study + +We conduct ablation studies on the COCO dataset, with ResNet-50-FPN backbone and $1 \times$ training schedule, to investigate the role of each component in our framework. The Mask AP on COCO val split is reported. + +Contribution of the two losses. Tab. 3 shows the contributions of the two loss terms, i.e., $\mathcal{L}_{pseudo}$ and $\mathcal{L}_{paste}$ . The baseline is BoxInst [36], which resorts to the color similarity between proximal pixels as supervision. The proposed pseudo mask loss improves the performance by $1.2\%$ AP, especially on large objects ( $1.7\%$ AP). This demonstrates that by introducing the semantic-aware instance mask generation paradigm, our method could distinguish not only proximal pixels with similar colors but also overlapping objects of the same semantics. Besides, the online weakly-supervised Copy-Paste loss brings a further improvement of $0.3\%$ AP, while the performance on small objects $\mathrm{AP}_S$ is largely improved by $1.1\%$ AP. + +![](images/8cdf8a3b0f989148495e193712527fc40c5a84a0d43e67e5be2134f88f08ae2b.jpg) +Figure 6. Visualizations of pseudo semantic masks $M_{\mathrm{S}}$ , pseudo instance masks $M_{\mathrm{I}}$ , and final pseudo masks $\hat{M}$ + +![](images/2bde7cc1f959124e3ac7ef4a6273ec0932bc2d7bca1a0948404c08997e8a6b22.jpg) + +![](images/66a2014ef133ebf250fd243eb50cc11b3fc3a07bd54492d3a276a2b702f77c31.jpg) +Figure 7. Visualizations of weights for different positive samples. + +Effect of the modulation intensity. We use the instance-aware pseudo probability map $M_{\mathrm{I}}$ to modulate the semantic-aware map $M_{\mathrm{S}}$ by using a parameter $\alpha$ . Tab. 4 shows the results by setting $\alpha$ to different values. One can draw a conclusion that the integration of semantic mask $M_{\mathrm{S}}$ and instance mask $M_{\mathrm{I}}$ leads to better results than any of them. Specifically, $M_{\mathrm{S}}$ facilitates more holistic object pattern understanding by exploring the semantic information from the entire dataset, while $M_{\mathrm{I}}$ rectifies the falsely activated objects in $M_{\mathrm{S}}$ and improves the reliability of pseudo masks. Removing the self-correction module, i.e., setting $\alpha$ to 0, will lead to an obvious performance drop by $1.7\%$ AP. This is not surprising because the semantic mask contains certain noisy supervision caused by the falsely activated objects and pixels. On the other hand, training without semantic masks, i.e., setting $\alpha$ to 1, will decrease the segmentation performance by $0.8\%$ AP. + +Semantic masks vs. instance masks. We explore the complementarity of $M_{\mathrm{S}}$ and $M_{\mathrm{I}}$ by visualizing them in Fig. 6. As can be seen in (b-d), $M_{\mathrm{S}}$ could distinguish object instances that have similar appearances but different semantics from the background and other objects. In comparison, from (a) (e-f), we see that $M_{\mathrm{I}}$ is good at distinguishing different instances of the same semantics, which are employed + +to suppress the falsely activated instances in $M_{\mathrm{S}}$ . They work together to produce more reliable supervision for training. + +Visualizations of weights. To further understand the effect of the positive mask weighting strategy, we show the visualizations of weights assigned to different positive samples in Fig. 7. It can be seen that large weights are mainly located in the central regions of foreground objects and far from other objects, while the small ones are located in ambiguous regions, such as overlapping regions between different objects and junctions between foreground and background. This weighting strategy facilitates generating higher-quality supervision and reducing the falsely activated instances. More analyses about this weighting strategy are provided in supplemental files. + +Effect of the number of prototypes per category. We set multiple prototypes per category to better model intra-class variation. Tab. 5 reports the segmentation results w.r.t. different number of prototypes per category. The baseline attains $31.6\%$ AP by representing each category with one prototype. There is a clear performance improvement (about $0.4\%$ AP) by increasing the number of prototypes to 5; however, the performance reaches saturation when $L$ is more than 10. We set $L$ as 10 to trade off accuracy and cost. + +# 5. Conclusion + +We proposed a novel SIM method for box-supervised instance segmentation. To alleviate the limitations of pairwise affinity supervision from low-level image features, we explored high-level image semantic contexts by extracting a group of representative prototypes from the dataset and using them to segment foreground objects from background. To rectify the possible false positive instances in semantic masks, we introduced extra supervision by integrating mask predictions of different positive samples in a weighted manner. Furthermore, we devised an online weakly-supervised Copy-Paste method to create challenging training data by equipping a continuously updated memory bank to store historical images with pseudo masks. Both the qualitative and quantitative experiments demonstrated the superior performance of our SIM method over state-of-the-arts. + +# References + +[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. Weakly supervised learning of instance segmentation with inter-pixel relations. 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Most of the current efforts leverage low-level image features as extra supervision without explicitly exploiting the high-level semantic information of the objects, which will become ineffective when the foreground objects have similar appearances to the background or other objects nearby. We propose a new box-supervised instance segmentation approach by developing a Semantic-aware Instance Mask (SIM) generation paradigm. Instead of heavily relying on local pair-wise affinities among neighboring pixels, we construct a group of category-wise feature centroids as prototypes to identify foreground objects and assign them semantic-level pseudo labels. Considering that the semantic-aware prototypes cannot distinguish different instances of the same semantics, we propose a self-correction mechanism to rectify the falsely activated regions while enhancing the correct ones. Furthermore, to handle the occlusions between objects, we tailor the Copy-Paste operation for the weakly-supervised instance segmentation task to augment challenging training data. Extensive experimental results demonstrate the superiority of our proposed SIM approach over other state-of-the-art methods. The source code: https://github.com/1slrh/SIM." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 568, + 128, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 128, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 128, + 580 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 589, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 684 + ], + "type": "text", + "content": "Instance segmentation is among the fundamental tasks of computer vision, with many applications in autonomous driving, image editing, human-computer interaction, etc. The performance of instance segmentation has been improved significantly along with the advances in deep learning [6, 12, 34, 38]. 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The pipeline of Semantic-aware Instance Mask (SIM) generation method. (a) shows the mask prediction produced by using only low-level affinity supervision, where the foreground heavily blends with background. (b) and (c) show the semantic-aware masks obtained with our constructed prototypes, which perceive the entity of objects but are unable to separate different instances of the same semantics. (d) shows the final instance pseudo mask rectified by our proposed self-correction module." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 386, + 290, + 462, + 339 + ], + "blocks": [ + { + "bbox": [ + 386, + 290, + 462, + 339 + ], + "lines": [ + { + "bbox": [ + 386, + 290, + 462, + 339 + ], + "spans": [ + { + "bbox": [ + 386, + 290, + 462, + 339 + ], + "type": "image", + "image_path": "59983af5365473104c668a01c6203609f14e17c59d392107802a7a1c4d9bc2f1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 420, + 341, + 429, + 348 + ], + "lines": [ + { + "bbox": [ + 420, + 341, + 429, + 348 + ], + "spans": [ + { + "bbox": [ + 420, + 341, + 429, + 348 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 465, + 290, + 541, + 339 + ], + "blocks": [ + { + "bbox": [ + 465, + 290, + 541, + 339 + ], + "lines": [ + { + "bbox": [ + 465, + 290, + 541, + 339 + ], + "spans": [ + { + "bbox": [ + 465, + 290, + 541, + 339 + ], + "type": "image", + "image_path": "c87aec056c41cc216753e4fd695840207fb849ec642d97dbc12abbe99075a8e8.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 498, + 341, + 507, + 348 + ], + "lines": [ + { + "bbox": [ + 498, + 341, + 507, + 348 + ], + "spans": [ + { + "bbox": [ + 498, + 341, + 507, + 348 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 521 + ], + "type": "text", + "content": "resources. To reduce the reliance on dense annotations, weakly-supervised instance segmentation based on cheap supervisions, such as bounding boxes [14,21,36], points [8] and image-level labels [1,18], has recently attracted increasing research attention." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 546, + 713 + ], + "type": "text", + "content": "In this paper, we focus on box-supervised instance segmentation (BSIS), where the bounding boxes provide coarse supervised information for pixel-wise prediction task. To provide pixel-wise supervision, conventional methods [10, 19] usually leverage off-the-shelf proposal techniques, such as MCG [30] and GrabCut [31], to create pseudo instance masks. However, the training pipelines of these methods with multiple iterative steps are cumbersome. Several recent works [14, 36] enable end-to-end training by taking pairwise affinities among pixels as extra supervision. Though these methods have achieved promising performance, they heavily depend on low-level image features, such as color pairs [36], and simply assume that the proximal pixels with similar colors are likely to have the same label. This leads to confusion when foreground objects have similar appearances to the background or other ob-" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "*denotes the equal contribution, †denotes the corresponding author. This work is supported by the Hong Kong RGC RIF grant (R5001-18)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7193" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "jects nearby, as shown in Fig. 1 (a). It is thus error-prone to use only low-level image cues for supervision since they are weak to represent the inherent structure of objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 371 + ], + "type": "text", + "content": "Motivated by the fact that high-level semantic information can reveal intrinsic properties of object instances and hence provide effective supervision for segmentation model training, we propose a novel Semantic-aware Instance Mask generation method, namely SIM, to explicitly exploit the semantic information of objects. To distinguish proximal pixels with similar color but different semantics (please refer to Fig. 1 (a)), we construct a group of representative dataset-level prototypes, i.e., the feature centroids of different classes, to perform foreground/background segmentation, producing semantic-aware pseudo masks (see Fig. 1 (b)). These prototypes abstracted from massive training data can capture the structural information of objects, enabling more comprehensive semantic pattern understanding, which is complementary to affinity supervision of pairwise neighboring pixels. However, as shown in Fig. 1 (c), these prototypes are unable to separate the instances of the same semantics, especially for overlapping objects. We consequently develop a self-correction mechanism to rectify the false positives while enhancing the confidence of true-positive foreground objects, resulting in more precise instance-aware pseudo masks, as shown in Fig. 1 (d)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 372, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 502 + ], + "type": "text", + "content": "It is worth mentioning that our generated pseudo masks could co-evolve with the segmentation model without cumbersome iterative training procedures in previous methods [10, 21]. In addition, considering that the existing weakly-supervised instance segmentation methods only provide very limited supervision for rare categories and overlapping objects due to the lack of ground truth masks, we propose an online weakly-supervised Copy-Paste approach to create a combinatorial number of augmented training samples. Overall, the major contributions of this work can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 507, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 46, + 507, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 579 + ], + "type": "text", + "content": "- A novel BSIS framework is presented by developing a semantic-aware instance mask generation mechanism. Specifically, we construct a group of representative prototypes to explore the intrinsic properties of object instances and identify complete entities, which produces more reliable supervision than low-level features." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 580, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 640 + ], + "type": "text", + "content": "- A self-correction module is designed to rectify the semantic-aware pseudo masks to be instance-aware. The falsely activated regions will be reduced, and the correct ones will be boosted, enabling more stable training and progressively improving the segmentation results." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": "- We tailor the Copy-Paste operation for weakly-supervised segmentation tasks in order to create more occlusion patterns and more challenging training data. The overall framework can be trained in an end-to-end manner. Extensive experiments demonstrate the superiority of our method over other state-of-the-art methods." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 91, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 354 + ], + "type": "text", + "content": "Instance Segmentation (IS) is a fundamental task in computer vision fields, which aims to predict the pixel-wise mask for each instance of interest in an image. Many top performing IS methods [6, 15, 25, 42] follow the Mask R-CNN meta-architecture [12], which splits the IS task into two consecutive stages and performs segmentation on the extracted region proposals. Single-stage IS methods have also been rapidly developed during the past few years. YOLACT [3] and BlendMask [5] employ fine-grained FPN features rather than the RoI-aligned features for mask prediction. However, they still need crop operation for object localization. Some methods segment each instance in a fully convolutional manner without resorting to the detection results. For example, CondInst [34] and SOLO [38] employ instance-aware conditional convolutions and dynamically generate convolution kernels to segment different objects. Universal architectures [7, 41] have emerged with DETR [4] and show that end-to-end set prediction architecture is general enough for any segmentation task. Despite the promising performance, these methods heavily rely on expensive pixel-wise mask annotation, which restricts their usability in many practical applications." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 354, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 510 + ], + "type": "text", + "content": "Weakly-Supervised Instance Segmentation (WSIS) with weak annotations is a more attractive yet challenging task. Some works attempt to achieve high-quality segmentation with box-level annotations [14, 17, 21, 36] or image-level annotations [1, 18]. Khoreva et al. [17] employ box supervisory training data for WSIS. However, the proposed method relies on the region proposal techniques, such as GrabCut [31] and MCG [30], to generate pseudo masks in an offline manner. Other recent methods [21, 37] also focus on generating instance labels by using an independent network, which require either extra salient data [38] or some post-processing methods [21]. This inevitably leads to a complicated training pipeline." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 510, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 665 + ], + "type": "text", + "content": "To achieve a simple yet effective training pipeline, BBTP [14] formulates WSIS as a multiple-instance learning problem and introduces a structural constraint to maintain the unity of estimated masks. BoxInst [36] builds upon an efficient CondInst [34] framework, and enforces the proximal pixels with similar colors to have the same label through a pairwise loss. Despite the promising performance, these methods depend heavily on local color supervision while neglecting the global structure of the entire object. Different from these methods, our proposed method provides more reliable supervision by leveraging high-level semantic information, which is beneficial for capturing the intrinsic structures of objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Pseudo Mask Generation. A widely adopted technique in conventional weakly-supervised semantic segmentation methods is Class Activation Map (CAM) [44], which aims to obtain an object localization map from class labels. How-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7194" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 68, + 534, + 277 + ], + "blocks": [ + { + "bbox": [ + 61, + 68, + 534, + 277 + ], + "lines": [ + { + "bbox": [ + 61, + 68, + 534, + 277 + ], + "spans": [ + { + "bbox": [ + 61, + 68, + 534, + 277 + ], + "type": "image", + "image_path": "7f0961fe6ded960d0036a6fcf77741460ca85f29ae9daacfefcfbcd2d3269b0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": "Figure 2. The framework of our proposed Semantic-aware Instance Mask (SIM) generation method. The model contains the main segmentation network " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{seg}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " and its momentum-updated version " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{seg}^{\\prime}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": ". Given an image " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": ", we first pass it through " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{seg}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{seg}^{\\prime}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " to obtain the corresponding mask features " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "Z^{\\prime}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": ". The prototypes are then updated as the moving average of feature cluster centroids. Next, we obtain the semantic probability map " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " by measuring the distance between prototypes and mask features " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "Z^{\\prime}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": ". After that, the falsely activated instances in " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " are rectified by the instance probability map " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "M_{1}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": ", which is obtained by integrating different positive masks of the same ground truth object. Finally, we obtain the pseudo mask " + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 46, + 286, + 547, + 354 + ], + "type": "text", + "content": " by selecting highly-confident pixels with two thresholds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 364, + 289, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 533 + ], + "type": "text", + "content": "ever, CAM only identifies the most discriminative object regions and suffers from the problem of limited activation area [2,13,16,32]. Given that bounding boxes could provide the location information of objects in an image, BBAM [21] employs an object detector to produce a bounding box attribute map, which serves as a pseudo ground truth mask. As a more lightweight approach, self-training-based methods [22, 43, 48, 49] select high-scoring predictions on unlabeled data as pseudo labels for training. The idea of assigning labels based on prototypes has also been explored in semantic segmentation [22, 45, 46]. In this work, the prototype technique is adapted to capture the global structure of objects with the same semantics, reducing the noise caused by low-level feature supervision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 543, + 104, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 543, + 104, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 543, + 104, + 555 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 563, + 115, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 115, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 115, + 574 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": "In the setting of box-supervised instance segmentation (BSIS), we are given a set of box annotated training data " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{X_n, Y_n, B_n\\}_{n=1}^N" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " is the number of images. Besides, " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "Y_n = \\{y_n^k\\}_{k=1}^K" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "B_n = \\{b_n^k\\}_{k=1}^K" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " denote the class-level and box-level annotations, where " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " is the number of instances in the image " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "X_n" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "y_n^k \\in \\{1, \\dots, C\\}" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " represents the category label of the " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": "-th object in the " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": "-th image, and " + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "inline_equation", + "content": "b_n^k" + }, + { + "bbox": [ + 46, + 582, + 287, + 677 + ], + "type": "text", + "content": " specifies its corresponding location." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "The overview of our method is shown in Fig. 2, where the proposed SIM module is highlighted in the green dotted box. We choose CondInst [34] and Mask2Former [7]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "text", + "content": "as the basic segmentation networks due to their simplicity and effectiveness. Instead of only relying on local pair-wise affinities among pixels as supervision [14,36], we employ a group of semantic-level prototypes to capture global structural information of objects, and produce semantic probability map " + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "text", + "content": " by computing the distances between each pixel-wise feature vector and all prototypes. Since these prototypes are unable to separate different objects of the same semantics, we propose a self-correction mechanism to deactivate falsely estimated objects by using an instance probability map " + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "text", + "content": ". This map can be obtained by integrating different positive masks corresponding to the same instance with an IoU-based weighting strategy. Finally, we employ two thresholds to select confident predictions as pseudo ground truths " + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "text", + "content": ", and use them for training the segmentation network " + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{seg}" + }, + { + "bbox": [ + 304, + 364, + 545, + 556 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 566, + 531, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 566, + 531, + 578 + ], + "spans": [ + { + "bbox": [ + 306, + 566, + 531, + 578 + ], + "type": "text", + "content": "3.2. Semantic-aware Instance Mask Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 585, + 434, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 434, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 434, + 597 + ], + "type": "text", + "content": "3.2.1 Pseudo Semantic Map" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "Low-level image features, such as colors, intensity, edges, blobs, etc., could provide useful guidance to identify the object boundaries in an image. However, these features vary significantly with illuminations, motion blurs, and noises. Thus it is error-prone to take only low-level features as supervision for BSIS when object instances are heavily blended with the background. To address this issue, we attempt to explore the intrinsic structures of objects as semantic guidance to provide more robust supervision for BSIS" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7195" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 111, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 111, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 111, + 84 + ], + "type": "text", + "content": "model training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": "We construct a group of representative prototypes to model the structural information of objects, and use them to generate semantic-aware pseudo masks. Considering that a single prototype is insufficient to capture the intra-class variance, we employ multiple prototypes [29, 45] to represent the objects in a category. Specifically, we extract " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": " prototypes (i.e., sub-centers) from each class " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "c \\in \\{1, \\dots, C\\}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "P_{c} = \\{p_{1}^{c}, \\dots, p_{L}^{c}\\}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ", to depict different characteristics of the same category. Given an input image " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{h \\times w \\times 3}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ", we first pass it through the segmentation model " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{seg}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": " to obtain the feature map " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "Z \\in \\mathbb{R}^{H \\times W \\times D}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ", and normalize it with " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "z_{i} = \\frac{z_{i}}{||z_{i}||_{2}}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "z_{i}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": "-th feature vector of " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": " with length " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ". Unlike semantic segmentation, which predicts only one mask for each input image, we predict a variable number of masks depending on the number of categories in the image. To this end, we compute the semantic probability map corresponding to the " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": "-th category, denoted by " + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}^{c} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 86, + 290, + 313 + ], + "type": "text", + "content": ", using the following formula:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 323, + 287, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 323, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 104, + 323, + 287, + 346 + ], + "type": "interline_equation", + "content": "M _ {\\mathrm {S}, i} ^ {c} = \\sigma \\left(\\max \\{\\frac {\\langle z _ {i} , p _ {l} ^ {c} \\rangle}{\\tau} \\} _ {l = 1} ^ {L}\\right), \\tag {1}", + "image_path": "899fbbb5433adb8422da43709521a236455f164837f7089dc70f5c97443e6642.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\langle \\cdot \\rangle" + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": " computes the cosine similarity between two " + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": "-normalized feature vectors. The sigmoid function " + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\sigma (\\cdot)" + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": " converts the feature distance to the probability that the pixel belongs to the " + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": "-th sub-center, and " + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": " controls the concentration level of representations. Once computed, we assign these semantic probability maps to different objects according to their class labels " + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "inline_equation", + "content": "Y_{n}" + }, + { + "bbox": [ + 46, + 356, + 287, + 439 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": "Multi-prototype update. We update the prototypes on-the-fly with the moving average of cluster centroids computed in previous mini-batches. Specifically, given an image " + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "inline_equation", + "content": "X_{n}" + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": " and its corresponding pseudo mask " + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": ", we obtain the pixelwise cluster assignments " + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 441, + 287, + 513 + ], + "type": "text", + "content": "-th category by optimizing the following objective function:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 80, + 522, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 522, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 80, + 522, + 287, + 544 + ], + "type": "interline_equation", + "content": "\\max _ {Q \\in \\mathbb {Q}} \\operatorname {T r} \\left(Q ^ {T} P _ {c} ^ {T} Z\\right) + \\varepsilon H (Q), \\quad s. t. Q \\in \\mathbb {Q}, \\tag {2}", + "image_path": "145834155db9b96efdd90b1e6db69e90816c31f4a1d348554095c2e8f81048a9.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 62, + 544, + 261, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 544, + 261, + 557 + ], + "spans": [ + { + "bbox": [ + 62, + 544, + 261, + 557 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 62, + 544, + 261, + 557 + ], + "type": "inline_equation", + "content": "\\mathbb{Q} := \\{Q \\in \\mathbb{R}_+^{L \\times N_c} | Q\\mathbf{1}_{N_c} = r, Q^T\\mathbf{1}_L = h\\}" + }, + { + "bbox": [ + 62, + 544, + 261, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": "The above formula is an instance of the optimal transport problem [9], where " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "Q = \\frac{1}{N_c} [q_1, \\dots, q_{N_c}]" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " represents the transport assignment and is restricted to be a probability matrix with the constraint " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbb{Q}" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " is the number of pixels belonging to the " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": "-th category, " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " denotes the entropy function with " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "H(Q) = -\\sum_{ij} Q_{ij} \\log Q_{ij}" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " controls the smoothness of distribution. " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "r = \\frac{1}{L} \\mathbf{1}_L" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "h = \\frac{1}{N_c} \\mathbf{1}_{N_c}" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " are the marginal projections of " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " onto its rows and columns, respectively, where " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{1}_L" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\mathbf{1}_{N_c}" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " represent the vectors of ones of dimension " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "inline_equation", + "content": "N_c" + }, + { + "bbox": [ + 46, + 567, + 287, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "By formulating the cluster assignment as an optimal transport problem, the optimization of Eq. 2 concerning " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "Q" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 314, + 71, + 541, + 170 + ], + "blocks": [ + { + "bbox": [ + 314, + 71, + 541, + 170 + ], + "lines": [ + { + "bbox": [ + 314, + 71, + 541, + 170 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 541, + 170 + ], + "type": "image", + "image_path": "1036247a50e5d4a60acd37f3f1740bd0cff0f483b5b0636832b7841fb4181be2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 172, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 305, + 172, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 172, + 545, + 205 + ], + "type": "text", + "content": "Figure 3. (a) The mask quality varies much across different positive samples. (b) The instance-aware masks " + }, + { + "bbox": [ + 305, + 172, + 545, + 205 + ], + "type": "inline_equation", + "content": "M_{1}" + }, + { + "bbox": [ + 305, + 172, + 545, + 205 + ], + "type": "text", + "content": " obtained by using positive mask weighting strategy." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 216, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 216, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 216, + 545, + 239 + ], + "type": "text", + "content": "can be solved in linear time by the Sinkhorn-Knopp algorithm [9]:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 352, + 247, + 545, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 247, + 545, + 273 + ], + "spans": [ + { + "bbox": [ + 352, + 247, + 545, + 273 + ], + "type": "interline_equation", + "content": "Q ^ {*} = \\operatorname {d i a g} (u) \\exp \\left(\\frac {P _ {c} ^ {T} Z}{\\varepsilon}\\right) \\operatorname {d i a g} (v), \\tag {3}", + "image_path": "0f870f360b1d14270e296e7670778ef6c5295e032acacd413598a879e158f943.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "inline_equation", + "content": "u \\in \\mathbb{R}^L" + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "inline_equation", + "content": "v \\in \\mathbb{R}^{N_c}" + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "text", + "content": " are two renormalization vectors. Finally, we update the prototypes as the moving average of cluster centroids. Particularly, in each iteration " + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 280, + 545, + 328 + ], + "type": "text", + "content": ", the prototype is estimated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 356, + 337, + 545, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 337, + 545, + 352 + ], + "spans": [ + { + "bbox": [ + 356, + 337, + 545, + 352 + ], + "type": "interline_equation", + "content": "\\left. p _ {l} ^ {c} \\right| _ {t} = \\gamma \\cdot \\left. p _ {l} ^ {c} \\right| _ {t - 1} + (1 - \\gamma) \\cdot p _ {n, l} ^ {c}, \\tag {4}", + "image_path": "773b9a4389223985802c6ea266faab2a9f3a7fc0a9af050a57f75602c7beacd7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "inline_equation", + "content": "\\lambda \\in [0,1]" + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "content": " is the momentum coefficient. " + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "inline_equation", + "content": "p_{n,l}^{c}" + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "content": "-th sub-center of the " + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "content": "-th class in image " + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "inline_equation", + "content": "X_{n}" + }, + { + "bbox": [ + 305, + 359, + 545, + 396 + ], + "type": "text", + "content": ", which is computed by:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 363, + 403, + 545, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 403, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 363, + 403, + 545, + 434 + ], + "type": "interline_equation", + "content": "p _ {n, l} ^ {c} = \\frac {\\sum_ {i} ^ {N _ {c}} z _ {i} \\cdot \\mathbb {1} \\left(Q _ {i , l} = 1\\right)}{\\sum_ {i} ^ {N _ {c}} \\mathbb {1} \\left(Q _ {i , l} = 1\\right)}, \\tag {5}", + "image_path": "5b1b0eac28fb587211c7ae593026ea95c1f5b9bbe01bc78d5c96eddff9a63f4d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 441, + 518, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 441, + 518, + 453 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 518, + 453 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 441, + 518, + 453 + ], + "type": "inline_equation", + "content": "\\mathbb{1}" + }, + { + "bbox": [ + 305, + 441, + 518, + 453 + ], + "type": "text", + "content": " is an indicator function, being 1 if " + }, + { + "bbox": [ + 305, + 441, + 518, + 453 + ], + "type": "inline_equation", + "content": "Q_{i,l} = 1" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 453, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 597 + ], + "type": "text", + "content": "Remarks on prototypes. The pairwise loss used in [36] explores pixel-to-pixel correlations, which provide local supervision but can not ensure the global consistency of objects with the same semantics. In contrast, the prototypes explore pixel-to-center relations, which could ensure the integrity of objects and provide more reliable supervision. Besides, since the prototypes are abstracted from massive training data, they could reveal the intrinsic properties of objects and filter out image-specific noise and outliers. In addition, we treat different categories equally and set the same number of prototypes for each category, which is potentially beneficial for identifying long-tailed objects." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 611, + 405, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 405, + 622 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 405, + 622 + ], + "type": "text", + "content": "3.2.2 Self-Correction" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Though the pseudo semantic masks " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " could provide more reliable supervision from a global perspective, they could not distinguish different objects of the same semantics, especially when there exist overlaps or occlusions among objects. To overcome this limitation, we propose a simple yet effective self-correction module, which could upgrade the semantic-aware masks " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " to be instance-aware." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7196" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": "Positive mask weighting. Let us first revisit some properties of anchor-free detectors such as FCOS [35]. In these works, anchors denote the dense feature points, and positive samples represent the anchors located in the center/bbox region of each object. These methods assign multiple positive samples, which have high enough Intersection over Union (IoU) with ground truth " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "(gt)" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": " box, to each object. However, the quality of masks produced by different positive samples varies significantly, as shown in Fig. 3 (a). Those ambiguous anchors, i.e., anchors that are taken as positive samples for multiple " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": " objects simultaneously (red dots in Fig. 3), could not separate overlapping objects of the same semantics. Based on these observations, we propose a positive mask weighting strategy to integrate different masks according to their quality, resulting in a high-quality instance-aware mask " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": ". In specific, we define a metric of mask quality based on the IoU between predicted and " + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "gt" + }, + { + "bbox": [ + 47, + 72, + 289, + 277 + ], + "type": "text", + "content": " boxes:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 134, + 283, + 287, + 299 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 283, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 134, + 283, + 287, + 299 + ], + "type": "interline_equation", + "content": "w _ {p o s} = e ^ {\\mu \\cdot I o U}, \\tag {6}", + "image_path": "8c5c67fe07f704cfa2cd55fd6d80033a9be8cba0cfeddafde8d8fb07c7089159.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "text", + "content": " controls the relative gaps between different weights. Each weight " + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "inline_equation", + "content": "w_{pos}" + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "text", + "content": " is then normalized by the sum of weights for all positive samples. As can be seen in Fig. 3 (b), the pseudo instance masks " + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 47, + 306, + 287, + 365 + ], + "type": "text", + "content": " could better separate different objects and provide more accurate supervision." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "type": "text", + "content": "Pseudo mask loss. By employing " + }, + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "type": "text", + "content": ", the falsely activated objects or pixels in " + }, + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 47, + 365, + 288, + 414 + ], + "type": "text", + "content": " could be suppressed, while the confidence of foreground objects could be enhanced. The rectification process is conducted as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 419, + 287, + 438 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 419, + 287, + 438 + ], + "spans": [ + { + "bbox": [ + 91, + 419, + 287, + 438 + ], + "type": "interline_equation", + "content": "\\hat {M} _ {p r o b} ^ {k, i} = (1 - \\alpha) \\cdot M _ {\\mathrm {S}} ^ {k, i} + \\alpha \\cdot M _ {\\mathrm {I}} ^ {k, i}, \\qquad (7)", + "image_path": "9e54282e198d0350c469e62579f70130b7623adde3c2745cb707d7e0fe35b814.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "\\hat{M}_{prob}^{k,i}" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": "-th pixel of the " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": "-th pseudo probability map, and " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "\\alpha \\in [0,1]" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": " controls the intensity of modulation. Finally, we set two thresholds " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{high}}" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{low}}" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": " to select highly-confident foreground and background predictions as pseudo labels, resulting in " + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 47, + 445, + 289, + 519 + ], + "type": "text", + "content": ". 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" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\hat{M}_k" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": " denotes the pseudo mask of the " + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": "-th positive sample. " + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": " is a binary weight mask that neglects ambiguous regions by using " + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{high}}" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{low}}" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "W^i = 0" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": ", if " + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{low}} < \\hat{M}_{prob}^i < \\tau_{\\mathrm{high}}" + }, + { + "bbox": [ + 47, + 568, + 287, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 635, + 252, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 252, + 648 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 252, + 648 + ], + "type": "text", + "content": "3.3. 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We use " + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "inline_equation", + "content": "\\hat{M}'" + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "text", + "content": " to extract instances from " + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "text", + "content": " and paste them onto " + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "text", + "content": ", resulting in new training data " + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "inline_equation", + "content": "X_{paste}" + }, + { + "bbox": [ + 305, + 203, + 547, + 237 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 375, + 110, 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430 + ], + "type": "text", + "content": " based on importance sampling, where " + }, + { + "bbox": [ + 304, + 298, + 546, + 430 + ], + "type": "inline_equation", + "content": "S'" + }, + { + "bbox": [ + 304, + 298, + 546, + 430 + ], + "type": "text", + "content": " measures the importance of instances (please refer to supplemental materials for more details), so that instances with higher-quality masks are more likely to be selected. We paste the extracted objects onto input image " + }, + { + "bbox": [ + 304, + 298, + 546, + 430 + ], + "type": "inline_equation", + "content": "\\{X, Y, B\\}" + }, + { + "bbox": [ + 304, + 298, + 546, + 430 + ], + "type": "text", + "content": ", and adjust the annotations accordingly, i.e., we remove fully occluded objects and update the masks and bounding boxes of partially occluded objects. Finally, we compute the mask loss only on the pasted instances:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 339, + 436, + 545, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 436, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 339, + 436, + 545, + 460 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p a s t e} = \\sum_ {k} \\mathbb {1} _ {p a s t e} \\left[ \\ell_ {m a s k} \\left(M _ {p r e d} ^ {k}, \\hat {M} ^ {\\prime k}\\right) \\right], \\tag {9}", + "image_path": "94e9198cb5032403fcebf77bdfc39f2a65601a5589c1b1b347a982a303a588ec.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_{\\text{paste}}" + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "content": " is the indicator function, being 1 if the " + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "content": "-th instance is copied from " + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 496, + 419, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 496, + 419, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 419, + 509 + ], + "type": "text", + "content": "3.4. Objective Function" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 514, + 547, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 563 + ], + "type": "text", + "content": "As shown in Fig. 2, we employ a momentum encoder to stabilize the pseudo mask generation process. The parameters of the segmentation model are updated by optimizing the following loss function " + }, + { + "bbox": [ + 304, + 514, + 547, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{seg}" + }, + { + "bbox": [ + 304, + 514, + 547, + 563 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 328, + 569, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 569, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 328, + 569, + 545, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s e g}} = \\mathcal {L} _ {\\text {l o w l e v e l}} + \\lambda_ {1} \\mathcal {L} _ {\\text {p s e u d o}} + \\lambda_ {2} \\mathcal {L} _ {\\text {p a s t e}}, \\tag {10}", + "image_path": "754f661d0a62db909e81e4c17e331e0a7255910a60191fee853512218f6c5d7c.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "content": " are two trade-off parameters. " + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{lowlevel}" + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "content": " denotes low-level pairwise supervision defined in Box-Inst [36]. " + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{lowlevel}" + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pseudo}" + }, + { + "bbox": [ + 304, + 588, + 545, + 660 + ], + "type": "text", + "content": " provide complementary supervision from local and global perspectives, respectively, and work together to bridge the performance gap between box-supervised and fully-supervised settings." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 669, + 388, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 388, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 388, + 683 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "We conduct experiments on COCO [24] and PASCAL VOC [11] datasets. The model is trained on train2017," + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7197" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 107, + 70, + 491, + 296 + ], + "blocks": [ + { + "bbox": [ + 107, + 70, + 491, + 296 + ], + "lines": [ + { + "bbox": [ + 107, + 70, + 491, + 296 + ], + "spans": [ + { + "bbox": [ + 107, + 70, + 491, + 296 + ], + "type": "table", + "html": "
methodbackbonesche.AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
fully-supervisedMask R-CNN [12]ResNet-101-FPN3×37.559.340.221.139.648.3
YOLACT-700 [3]ResNet-101-FPN4.5×31.250.632.812.133.347.1
PolarMask [40]ResNet-101-FPN2×32.153.733.114.733.845.3
SOLOv2 [38]ResNet-101-FPN3×39.760.742.917.342.957.4
CondInst [34]ResNet-101-FPN3×39.160.942.021.541.750.9
\\( Mask2Fomer^† \\)[7]ResNet-101-MSDefomAttn50e44.2--23.847.766.7
box-supervised\\( BBTP^† \\)[14]ResNet-101-FPN1×21.145.517.211.222.029.8
BBAM [21]ResNet-101-FPN1×25.750.023.3---
\\( BoxCaseg^‡ \\)[37]ResNet-101-FPN1×30.954.330.812.132.846.3
SIM (Ours)ResNet-101-FPN1×34.056.835.017.236.845.5
BoxLevelSet [23]ResNet-101-FPN3×33.456.834.115.236.846.8
BoxInst [36]ResNet-101-FPN3×33.256.533.616.235.345.1
SIM (Ours)ResNet-101-FPN3×35.358.936.418.438.047.5
BoxLevelSet [23]ResNet-DCN-101-BiFPN3×35.459.136.716.838.551.3
BoxInst [36]ResNet-DCN-101-BiFPN3×35.059.335.617.137.248.9
SIM (Ours)ResNet-DCN-101-BiFPN3×37.461.838.618.640.251.6
BoxInst [36]Swin-B-FPN3×37.963.239.020.041.253.1
SIM (Ours)Swin-B-FPN3×40.266.941.321.143.556.0
\\( BoxInst^† \\)[36]Mask2Former-ResNet-10150e35.759.836.416.638.555.4
\\( SIM^† \\)(Ours)Mask2Former-ResNet-10150e37.462.238.717.641.356.6
", + "image_path": "9111fa3310f6575bcb72afb83bbfee017bb2c242ab9e23b122cedc41c0459793.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 346, + 288, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 288, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 288, + 396 + ], + "type": "text", + "content": "which contains about 115k images from 80 categories with only box annotations. We use val2017 (5k images) for ablation study and test-dev2017 (20k images) for comparisons with other methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 403, + 180, + 416 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 180, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 180, + 416 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "spans": [ + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": "We adopt CondInst [34] and Mask2Former [7] as our baseline. For CondInst, the backbone with FPN is pretrained on ImageNet. The training and testing details follow CondInst1 implemented with Detectron2 [39] unless specified. The model is warmed-up for 10k iterations with the projection loss and pairwise loss proposed in [36], and then trained for 80k iterations by adding our pseudo supervision loss and Copy-Paste loss with batch size 16 on 8 TITAN RTX GPUs. When ResNet is used as the backbone, our model is trained with SGDM optimizer. The initial learning rate is set to 0.01, and reduced by a factor of 10 at steps 60k and 80k, respectively. When SwinT [26] is used as the backbone, we adopt the AdamW [27] optimizer and set the initial learning rate to 0.0001. For Mask2Former, we follow its baseline settings2 and replace the original pixelwise mask loss with our designed loss terms. The length of the memory bank is set to 100, and we extract a quarter of the instances from each image with " + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "inline_equation", + "content": "1 \\sim 3" + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": " instances per image. The momentum used to update networks and prototypes is set to 0.9999 and 0.999, respectively. The modulation intensity " + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": " is empirically set to 0.5. Besides, " + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\lambda_1" + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\lambda_2" + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 45, + 422, + 288, + 685 + ], + "type": "text", + "content": " are empirically set to 0.5, 1, 5, and 0.1, respectively." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 321, + 345, + 533, + 497 + ], + "blocks": [ + { + "bbox": [ + 46, + 303, + 546, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 546, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 546, + 327 + ], + "type": "text", + "content": "Table 1. Comparisons between SIM and state-of-the-art methods on the COCO test-dev split. Symbol “†” means that the results are evaluated on the COCO val split, and “‡” denotes that BoxCaseg is trained with both box and salient object supervisions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 345, + 533, + 497 + ], + "lines": [ + { + "bbox": [ + 321, + 345, + 533, + 497 + ], + "spans": [ + { + "bbox": [ + 321, + 345, + 533, + 497 + ], + "type": "table", + "html": "
methodsbackboneAP\\( AP_{50} \\)\\( AP_{75} \\)
GrabCut* [31]ResNet-10119.038.817.0
SDI [17]VGG-16-44.816.3
BBTP [14]ResNet-10123.154.117.1
BBTP w/ CRF [14]ResNet-10127.559.121.9
BBAM [21]ResNet-101-63.731.8
BoxInst [36]ResNet-5034.359.134.2
BoxInst [36]ResNet-10136.561.437.0
DiscoBox [20]ResNet-50-59.835.5
DiscoBox [20]ResNet-101-62.237.5
BoxLevelSet [23]ResNet-5036.364.235.9
BoxLevelSet [23]ResNet-10138.366.338.7
SIM (Ours)ResNet-5036.765.535.6
SIM (Ours)ResNet-10138.667.138.3
", + "image_path": "e9f2a120883ca8cc91fe38cfafd16c2fa57a1f65feb55f9e73345f4d21b69940.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 505, + 545, + 529 + ], + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 529 + ], + "type": "text", + "content": "Table 2. Performance comparison on Pascal VOC val2012 split. Symbol “*” denotes that the results are copied from BoxInst." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 539, + 497, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 497, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 497, + 552 + ], + "type": "text", + "content": "4.2. Comparisons with State-of-the-Arts" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": "We compare the proposed SIM with state-of-the-art BSIS methods on the COCO [24] dataset. The fully supervised methods are also compared as a reference. As shown in Tab. 1, SIM outperforms BoxInst [36] and BoxLevelSet [23] by " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " AP with the ResNet-101-FPN backbone and " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "3\\times" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " training schedule. This is because we employ dataset-level prototypes to exploit the semantic information of objects while filtering out trivial image-specific noises. It can also be seen that our SIM method produces impressive results on small objects, largely outperforming BoxInst and BoxLevelSet by " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " AP and " + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 304, + 557, + 545, + 715 + ], + "type": "text", + "content": " AP with ResNet-101-FPN backbone, respectively. 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BoxInst lags behind on large objects due to the lack of semantic guidance. BoxLevelSet has lower performance on small objects because small objects lack rich features for level set evolution. By using stronger backbones with BiFPN [33] and DCN [47], the performance can be further boosted to " + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "inline_equation", + "content": "37.4\\%" + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "text", + "content": " AP. By taking Swin transformer [26] as backbone [26], the proposed SIM could surpass BoxInst by " + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "text", + "content": " AP, attaining " + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "inline_equation", + "content": "39.6\\%" + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "text", + "content": " AP. In addition, we also validate the effectiveness of our method on the query-based baseline, i.e., Mask2Former [7]. Our method achieves consistent improvement and outperforms BoxInst by " + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 46, + 252, + 287, + 408 + ], + "type": "text", + "content": " AP." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "type": "text", + "content": "Tab. 2 reports the segmentation results on the Pascal VOC [11] dataset. Our method outperforms BoxInst [36] by " + }, + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 46, + 411, + 287, + 483 + ], + "type": "text", + "content": " AP with ResNet-50 and ResNet-101 backbones, respectively. BoxLevelSet [23] achieves comparable performance since the level set model could evolve the precise contour of objects, which is beneficial for large objects." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 500, + 159, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 500, + 159, + 513 + ], + "spans": [ + { + "bbox": [ + 47, + 500, + 159, + 513 + ], + "type": "text", + "content": "4.3. Qualitative Results" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "Fig. 5 shows the qualitative segmentation results of our method and BoxInst on COCO val split. We have the following observations. First, according to (a), by leveraging the semantic-level supervision, our method is able to segment foreground instances that heavily tangle with background or other objects with similar appearances, because the prototypes explore global structural information of objects and could reduce the noise brought by using only local pair-wise affinity supervision. Second, as can be seen in (b) (c), our method could better separate overlapping instances of the same semantics since we introduce the self-correction module to reduce the falsely activated instances while enhancing the correct ones. Third, as shown in (d) and (f), benefiting from the abstraction of prototypes from massive training data, our method is able to perceive the whole entity of object instances and produce better segmentation results." + } + ] + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 318, + 251, + 533, + 297 + ], + "blocks": [ + { + "bbox": [ + 318, + 251, + 533, + 297 + ], + "lines": [ + { + "bbox": [ + 318, + 251, + 533, + 297 + ], + "spans": [ + { + "bbox": [ + 318, + 251, + 533, + 297 + ], + "type": "table", + "html": "
\\( \\mathcal{L}_{pseudo} \\)\\( \\mathcal{L}_{paste} \\)AP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
baseline30.752.231.113.833.145.7
✓31.954.032.614.734.747.4
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αAPAP50AP75APSAPMAPL
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# prototypesAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)
L=131.653.132.415.334.046.9
L=532.053.632.915.734.547.4
L=1032.254.033.015.834.548.3
L=5032.253.933.215.934.348.7
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Tab. 3 shows the contributions of the two loss terms, i.e., " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pseudo}" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{paste}" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": ". The baseline is BoxInst [36], which resorts to the color similarity between proximal pixels as supervision. The proposed pseudo mask loss improves the performance by " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " AP, especially on large objects (" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " AP). This demonstrates that by introducing the semantic-aware instance mask generation paradigm, our method could distinguish not only proximal pixels with similar colors but also overlapping objects of the same semantics. Besides, the online weakly-supervised Copy-Paste loss brings a further improvement of " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " AP, while the performance on small objects " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_S" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " is largely improved by " + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "inline_equation", + "content": "1.1\\%" + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": " AP." + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7199" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 300, + 198 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 300, + 198 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 300, + 198 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 300, + 198 + ], + "type": "image", + "image_path": "8cdf8a3b0f989148495e193712527fc40c5a84a0d43e67e5be2134f88f08ae2b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "lines": [ + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "spans": [ + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "type": "text", + "content": "Figure 6. Visualizations of pseudo semantic masks " + }, + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "type": "text", + "content": " , pseudo instance masks " + }, + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "type": "text", + "content": " , and final pseudo masks " + }, + { + "bbox": [ + 94, + 198, + 497, + 210 + ], + "type": "inline_equation", + "content": "\\hat{M}" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 301, + 71, + 548, + 196 + ], + "blocks": [ + { + "bbox": [ + 301, + 71, + 548, + 196 + ], + "lines": [ + { + "bbox": [ + 301, + 71, + 548, + 196 + ], + "spans": [ + { + "bbox": [ + 301, + 71, + 548, + 196 + ], + "type": "image", + "image_path": "2bde7cc1f959124e3ac7ef4a6273ec0932bc2d7bca1a0948404c08997e8a6b22.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 224, + 279, + 398 + ], + "blocks": [ + { + "bbox": [ + 55, + 224, + 279, + 398 + ], + "lines": [ + { + "bbox": [ + 55, + 224, + 279, + 398 + ], + "spans": [ + { + "bbox": [ + 55, + 224, + 279, + 398 + ], + "type": "image", + "image_path": "66a2014ef133ebf250fd243eb50cc11b3fc3a07bd54492d3a276a2b702f77c31.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 403, + 285, + 415 + ], + "lines": [ + { + "bbox": [ + 47, + 403, + 285, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 285, + 415 + ], + "type": "text", + "content": "Figure 7. Visualizations of weights for different positive samples." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": "Effect of the modulation intensity. We use the instance-aware pseudo probability map " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " to modulate the semantic-aware map " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " by using a parameter " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": ". Tab. 4 shows the results by setting " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " to different values. One can draw a conclusion that the integration of semantic mask " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " and instance mask " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " leads to better results than any of them. Specifically, " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " facilitates more holistic object pattern understanding by exploring the semantic information from the entire dataset, while " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " rectifies the falsely activated objects in " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " and improves the reliability of pseudo masks. Removing the self-correction module, i.e., setting " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " to 0, will lead to an obvious performance drop by " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " AP. This is not surprising because the semantic mask contains certain noisy supervision caused by the falsely activated objects and pixels. On the other hand, training without semantic masks, i.e., setting " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " to 1, will decrease the segmentation performance by " + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 46, + 426, + 286, + 628 + ], + "type": "text", + "content": " AP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": "Semantic masks vs. instance masks. We explore the complementarity of " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " by visualizing them in Fig. 6. As can be seen in (b-d), " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " could distinguish object instances that have similar appearances but different semantics from the background and other objects. In comparison, from (a) (e-f), we see that " + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 630, + 286, + 713 + ], + "type": "text", + "content": " is good at distinguishing different instances of the same semantics, which are employed" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 224, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 249 + ], + "type": "text", + "content": "to suppress the falsely activated instances in " + }, + { + "bbox": [ + 304, + 224, + 545, + 249 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{S}}" + }, + { + "bbox": [ + 304, + 224, + 545, + 249 + ], + "type": "text", + "content": ". They work together to produce more reliable supervision for training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 250, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 545, + 392 + ], + "type": "text", + "content": "Visualizations of weights. To further understand the effect of the positive mask weighting strategy, we show the visualizations of weights assigned to different positive samples in Fig. 7. It can be seen that large weights are mainly located in the central regions of foreground objects and far from other objects, while the small ones are located in ambiguous regions, such as overlapping regions between different objects and junctions between foreground and background. This weighting strategy facilitates generating higher-quality supervision and reducing the falsely activated instances. More analyses about this weighting strategy are provided in supplemental files." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "text", + "content": "Effect of the number of prototypes per category. We set multiple prototypes per category to better model intra-class variation. Tab. 5 reports the segmentation results w.r.t. different number of prototypes per category. The baseline attains " + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "inline_equation", + "content": "31.6\\%" + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "text", + "content": " AP by representing each category with one prototype. There is a clear performance improvement (about " + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "text", + "content": " AP) by increasing the number of prototypes to 5; however, the performance reaches saturation when " + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "text", + "content": " is more than 10. We set " + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 393, + 545, + 501 + ], + "type": "text", + "content": " as 10 to trade off accuracy and cost." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 514, + 378, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 525 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 712 + ], + "type": "text", + "content": "We proposed a novel SIM method for box-supervised instance segmentation. To alleviate the limitations of pairwise affinity supervision from low-level image features, we explored high-level image semantic contexts by extracting a group of representative prototypes from the dataset and using them to segment foreground objects from background. To rectify the possible false positive instances in semantic masks, we introduced extra supervision by integrating mask predictions of different positive samples in a weighted manner. Furthermore, we devised an online weakly-supervised Copy-Paste method to create challenging training data by equipping a continuously updated memory bank to store historical images with pseudo masks. Both the qualitative and quantitative experiments demonstrated the superior performance of our SIM method over state-of-the-arts." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7200" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Jiwoon Ahn, Sunghyun Cho, and Suha Kwak. 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In" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7202" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + }, + { + "para_blocks": [], + "discarded_blocks": [ + { + "bbox": [ + 67, + 73, + 287, + 95 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 73, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 67, + 73, + 287, + 95 + ], + "type": "text", + "content": "Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5982-5991, 2019. 3" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "text", + "content": "7203" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/9e4aea54-e956-45c7-8e0d-e18b2b0dde98_content_list.json b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/9e4aea54-e956-45c7-8e0d-e18b2b0dde98_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..bf83a3ea06111ff1ad41ff4342b965f1f8dae266 --- /dev/null +++ b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/9e4aea54-e956-45c7-8e0d-e18b2b0dde98_content_list.json @@ -0,0 +1,2439 @@ +[ + { + "type": "text", + "text": "SINE: SIngle Image Editing with Text-to-Image Diffusion Models", + "text_level": 1, + "bbox": [ + 151, + 130, + 818, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhixing Zhang", + "bbox": [ + 122, + 179, + 251, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ligong Han", + "bbox": [ + 285, + 179, + 390, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Arnab Ghosh", + "bbox": [ + 428, + 180, + 542, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dimitris Metaxas1", + "bbox": [ + 584, + 180, + 728, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jian Ren", + "bbox": [ + 766, + 180, + 844, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Rutgers University $^{2}$ Snap Inc.", + "bbox": [ + 330, + 198, + 627, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 250, + 313, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent works on diffusion models have demonstrated a strong capability for conditioning image generation, e.g., text-guided image synthesis. Such success inspires many efforts trying to use large-scale pre-trained diffusion models for tackling a challenging problem—real image editing. Works conducted in this area learn a unique textual token corresponding to several images containing the same object. However, under many circumstances, only one image is available, such as the painting of the Girl with a Pearl Earring. Using existing works on fine-tuning the pretrained diffusion models with a single image causes severe overfitting issues. The information leakage from the pretrained diffusion models makes editing can not keep the same content as the given image while creating new features depicted by the language guidance. This work aims to address the problem of single-image editing. We propose a novel model-based guidance built upon the classifier-free guidance so that the knowledge from the model trained on a single image can be distilled into the pre-trained diffusion model, enabling content creation even with one given image. Additionally, we propose a patch-based fine-tuning that can effectively help the model generate images of arbitrary resolution. We provide extensive experiments to validate the design choices of our approach and show promising editing capabilities, including changing style, content addition, and object manipulation. Our code is made publicly available here.", + "bbox": [ + 75, + 282, + 472, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 722, + 207, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Automatic real image editing is an exciting direction, enabling content generation and creation with minimal effort. Although many works have been conducted in this area, achieving high-fidelity semantic manipulation on an image is still a challenging problem for the generative models, considering the target image might be out of the training data distribution [4, 11, 25, 26, 32, 58, 59]. The recently introduced large-scale text-to-image models, e.g., DALL-E 2 [37], Imagen [42], Parti [55], and StableDiffusion [39], can perform high-quality and diverse image generation with", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4473db6967966510f908112ae0fe0c7bb78546190cc147e946dfdf826dc4f5c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 250, + 565, + 297 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/352273be6c2aff332a4a822ac67e7b28d285929e39000f8165c2c6d7564ebba5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 570, + 250, + 620, + 297 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e9c527720118609eca22387f085b8165ebe0e27c171fc027446fd68eb627034e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 250, + 694, + 297 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b0e052b18dac938e485dac492c788c57a19386e68ce98d730968bcda528cbfb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 250, + 758, + 297 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"....super- hero cape", + "bbox": [ + 700, + 300, + 758, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/357cf2d0f4a1daae8f1ab7248aa552c922ddf5ed6e8a01ab86da0729d7a531d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 250, + 883, + 297 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"...super- hero cape", + "bbox": [ + 700, + 300, + 758, + 306 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8eb6a3b5a84c472c5f2df5e3d30d6149a0dfcbfb04c0aceefa5c7e2da6305cef.jpg", + "image_caption": [ + "Source Image", + "Source Image", + "Figure 1. With only one real image, i.e., Source Image, our method is able to manipulate and generate the content in various ways, such as changing style, adding context, modifying the object, and enlarging the resolution, through guidance from the text prompt." + ], + "image_footnote": [], + "bbox": [ + 501, + 306, + 565, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e617549f197f219fadeb206b50a9ab6084d651b67a78c0e2b3f184d124720bf8.jpg", + "image_caption": [ + "sculpture", + "Source Image", + ".covered by snow" + ], + "image_footnote": [], + "bbox": [ + 566, + 306, + 687, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c93c3c63a831182fa3baf26c17fa0d1e822da042d51fa8aa3ca976610e8673d8.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 696, + 306, + 758, + 354 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a98daf320862c44f342cee5c7e67b667912e0be136a6c17e2d6632fa255425dd.jpg", + "image_caption": [ + "\"coffee machine...\" \"coffee maker...\"", + "in snow", + "blossom street" + ], + "image_footnote": [], + "bbox": [ + 763, + 306, + 883, + 354 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "natural language guidance. The success of these works has inspired many subsequent efforts to leverage the pre-trained large-scale models for real image editing [10, 15, 20, 40]. They show that, with properly designed prompts and a limited number of fine-tuning steps, the text-to-image models can manipulate a given subject with text guidance.", + "bbox": [ + 496, + 460, + 890, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On the downside, the recent text-guided editing works that build upon the diffusion models suffer several limitations. First, the fine-tuning process might lead to the pretrained large-scale model overfit on the real image, which degrades the synthesized images' quality when editing. To tackle these issues, methods like using multiple images with the same content and applying regularization terms on the same object have been introduced [4, 40]. However, querying multiple images with identical content or object might not be an available choice; for instance, there is only one painting for Girl with a Pearl Earring. Directly editing the single image brings information leakage from the pretrained large-scale models, generating images with different content (examples in Fig. 5); therefore, the application scenarios of these methods are greatly constrained. Second, these works lack a reasonable understanding of the object geometry for the edited image. Thus, generating images with different spatial size as the training data cause undesired artifacts, e.g., repeated objects, and incorrectly modified geometry (examples in Fig. 5). Such drawbacks restrict applying these methods for generating images with an arbitrary resolution, e.g., synthesizing high-resolution images from a single photo of a castle (as in Fig. 4), again limiting", + "bbox": [ + 496, + 553, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6027", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the usage of these methods.", + "bbox": [ + 76, + 90, + 261, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present SINE, a framework utilizing pre-trained text-to-image diffusion models for SINgle image Editing and content manipulation. We build our approach based upon existing text-guided image generation approaches [10, 40] and propose the following novel techniques to solve overfitting issues on content and geometry, and language drift [28, 31]:", + "bbox": [ + 75, + 106, + 467, + 212 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- First, by appropriately modifying the classifier-free guidance [22], we introduce model-based classifier-free guidance that utilizes the diffusion model to provide the score guidance for content and structure. Taking advantage of the step-by-step sampling process used in diffusion models, we use the model fine-tuned on a single image to plant a content \"seed\" at the early stage of the denoising process and allow the pre-trained large-scale text-to-image model to edit creatively conditioned with the language guidance at a later stage.", + "- Second, to decouple the correlation between pixel position and content, we propose a patch-based fine-tuning strategy, enabling generation on arbitrary resolution." + ], + "bbox": [ + 78, + 222, + 467, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With a text descriptor describing the content that is aimed to be manipulated and language guidance depicting the desired output, our approach can edit the single unique image to the targeted domain with details preserved in arbitrary resolution. The output image keeps the structure and background intact while having features well-aligned with the target language guidance. As shown in Fig. 1, trained on a painting Girl with a Pearl Earring with resolution as $512 \\times 512$ , we can sample an image of a sculpture of the girl at the resolution of $640 \\times 512$ with the identity features preserved. Moreover, our method can successfully handle various edits such as style transfer, content addition, and object manipulation (more examples in Fig. 3). We hope our method can further boost creative content creation by opening the door to editing arbitrary images.", + "bbox": [ + 75, + 438, + 467, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 679, + 217, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-guided image synthesis has drawn considerable attention in the generative model context [1, 2, 6, 12, 14, 16-19, 34, 35, 38, 50, 53-56, 60]. The recent development of diffusion models [21, 46, 47, 49] introduced new solutions to this problem and produced impressive results [33, 37, 39, 42]. With the significant improvement of these models, rather than training a large-scale text-to-image model from scratch, a leading line of works focuses on taking advantage of the existing pre-trained model and manipulating images according to given natural language guidance [3, 10, 20, 24, 29, 40]. In these works, studies explore text-based interfaces for image editing [1, 3, 35], style transfer [27, 30], and generator domain adaption [11, 25, 48].", + "bbox": [ + 75, + 704, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The development of the diffusion model provides a giant and flexible design space for this task. Many works utilize pre-trained diffusion models as generative priors and are training-free. ILVR [7] guides the denoising process by replacing the low-frequency part of the sample with that of the target reference image. SDEdit [32] applies the diffusion process first on an image or a user-created semantic map and then conducts the denoising procedure conditioned with the desired output. Blended diffusion [3] performs language-guided inpainting with a given mask.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another line of research showed great potential and semantic editing ability of fine-tuning. DiffusionCLIP [25] leverages the CLIP [36] model to provide gradients for image manipulation and deliver impressive results on style transfer. Textual-Inversion [10] and DreamBooth [40] fine-tune the text embedding or the full diffusion model using a few personalized images (typically $3 \\sim 5$ ) to synthesize images of the same object in a novel context. These methods, however, either drastically change the layout of the original image when dealing with a single image or can not fully leverage the generalization ability of the pre-trained model for editing due to overfitting or language drift. Notably, Prompt-to-Prompt [20] controls the editing of synthesized images by manipulating the cross-attention maps; however, its editing ability is limited when applied to real images. Imagic [24], while delivering realistic results, requires fine-tuning process on each editing prompt for each image, leading to longer inference time.", + "bbox": [ + 496, + 242, + 890, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This work introduces a solution to achieve image fidelity and text alignment simultaneously. Our method can perform high-quality semantic editing globally and locally on one single image. On the other hand, previous works lack an understanding of the object geometry of the edited image. When editing the image at an arbitrary resolution, the artifacts in the results will be obvious. Prior works have investigated generating images at arbitrary resolution using positional encoding as inductive bias [41, 52, 52] so that the correlation between content and position can be eliminated. Anyres-GAN [5] adopt a patch training mechanism to leverage high-resolution data to help the generation of images in the low-resolution domain. We propose a patch-based fine-tuning method to achieve arbitrary resolution editing.", + "bbox": [ + 496, + 513, + 890, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 739, + 596, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For one arbitrary in-the-wild image, our goal is to edit the image via language while preserving the maximal amount of details from the original image. To do so, we leverage the generalization ability of pre-trained large-scale text-to-image models [39]. An intuitive approach is to fine-tune the diffusion models with the single image and text description, similar to DreamBooth [40]. Ideally, it should provide a model that can reconstruct the input image using the given text descriptor and synthesize new images when", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6028", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "given other language guidance. Unfortunately, we find the model can easily overfit the single trained image and its corresponding text description. Thus, although the fine-tuned model can still reconstruct the input image perfectly, it can no longer synthesize diverse images according to the given language guidance (as shown in Fig. 5). Moreover, it struggles to generate arbitrary resolution images due to the lack of positional information (as in Fig. 4).", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To solve the above issues, we propose a test-time model-based classifier-free guidance and a patch-based fine-tuning technique. An overview of our method is illustrated in Fig. 2. In the following sections, we review the backbone model used in our approach (Sec. 3.1). Then, we describe how to overcome the overfitting problem with model-based guidance (Sec. 3.2). Lastly, we present how to address the problem of limited resolution generation (Sec. 3.3).", + "bbox": [ + 75, + 212, + 473, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Language-Guided Diffusion Models", + "text_level": 1, + "bbox": [ + 76, + 342, + 390, + 357 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use the latent diffusion models (LDMs) [39] trained on a large-scale dataset as our base model and implement the proposed approaches by fine-tuning the pre-trained model. LDMs is a class of Denoising Diffusion Probabilistic Models (DDPMs) [21] that contains an auto-encoder trained on images, and a diffusion model learned on the latent space constructed by the auto-encoder. The encoder $\\mathcal{E}$ encodes a given image $\\mathcal{I} \\in \\mathbb{R}^{H \\times W \\times 3}$ to a latent representation $\\mathbf{z}$ , such that $\\mathbf{z} = \\mathcal{E}(\\mathcal{I})$ . The decoder $\\mathcal{D}$ reconstructs the estimated image $\\tilde{\\mathcal{I}}$ from the latent, such that $\\tilde{\\mathcal{I}} = \\mathcal{D}(\\mathbf{z})$ and $\\tilde{\\mathcal{I}} \\approx \\mathcal{I}$ . The diffusion model is trained to produce latent codes within the pre-trained latent space. The most intriguing property of LDMs is that the diffusion model can be conditioned on class labels, images, and text prompt. The conditional LDM is learned as follows:", + "bbox": [ + 75, + 364, + 473, + 592 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {L D M} := \\mathbb {E} _ {\\mathcal {E} (\\mathcal {I}), y, \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {z} _ {t}, t, \\boldsymbol {\\tau} _ {\\theta} (y)) \\| _ {\\mathbf {2}} ^ {2} \\right], \\quad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 599, + 468, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t$ is the time step, $\\mathbf{z}_t$ is the latent noised to time $t$ , $\\epsilon$ is the unscaled noise sample, $\\epsilon_{\\theta}$ is the denoising model, $y$ is the conditioning input, and $\\tau_{\\theta}$ maps $y$ to a conditioning vector. During training time, $\\epsilon_{\\theta}$ and $\\tau_{\\theta}$ are jointly optimized. A random noise tensor is sampled and denoised at inference time based on the conditioning input, e.g., text prompt, to produce a new latent. Inspired by DreamBooth [40], we construct the text prompt for fine-tuning a single image as \"a photo/painting of a [*] [class noun]\", where \"[*]\" is a unique identifier and \"[class noun]\" is a coarse class descriptor (e.g., \"castle\", \"lake\", \"car\", etc.).", + "bbox": [ + 75, + 626, + 472, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Model-Based Classifier-Free Guidance", + "text_level": 1, + "bbox": [ + 76, + 801, + 410, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "With the above-presented LDMs, we introduce our approach, inspired by classifier-free guidance, to overcome overfitting when fine-tuning LDMs with one image.", + "bbox": [ + 75, + 825, + 468, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Classifier-free guidance [22] is a technique widely adopted by prior text-to-image diffusion models [39, 42]. A single", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/10d7bf218339218e4056f5f911416fc38ce1fb9abfdafc040b7dd111226e1e1c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 95, + 880, + 284 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/75f085c3287505c4744b9df41e91aae613af74fecde4e53aedcd37a169fecd53.jpg", + "image_caption": [ + "Figure 2. Overview of our method. (a) Given a source image, we first randomly crop it into patches and get the corresponding latent code $\\mathbf{z}$ with the pre-trained encoder. At fine-tune time, the denoising model, $\\epsilon_{\\theta}$ , takes three inputs: noisy latent $\\mathbf{z}_T$ , language condition $\\mathbf{c}$ , and positional embedding for the area where the noisy latent is obtained. (b) During sampling, we give additional language guidance about the target domain to edit the image. Also, we sample a noisy latent code $\\mathbf{z}_T$ with the dimension corresponding to the desired output resolution. Language conditioning for $\\epsilon_{\\theta}$ and $\\mathbf{c}$ are given by pre-trained language encoder $\\tau_{\\theta}$ with the target language guidance. While for the fine-tuned diffusion model, $\\hat{\\epsilon}_{\\theta}$ , in addition to the language conditioning $\\hat{\\mathbf{c}}$ , we also input the positional embedding for the whole image. We employ a linear combination between the score calculated by each model for the first $K$ steps and inference only on pre-trained $\\epsilon_{\\theta}$ after." + ], + "image_footnote": [], + "bbox": [ + 508, + 287, + 880, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "diffusion model is trained using conditional and unconditional objectives by randomly dropping the condition during training. When sampling, a linear combination of the conditional and unconditional score estimation is used:", + "bbox": [ + 496, + 728, + 892, + 789 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {e}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) = w \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) + (1 - w) \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 799, + 890, + 815 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(\\mathbf{z}_t,\\mathbf{c})$ and $\\epsilon_{\\theta}(\\mathbf{z}_t)$ are the conditional and unconditional $\\epsilon$ -predictions, $\\mathbf{c}$ is the conditioning vector generated by $\\tau_{\\theta}$ , and $w$ is the weight for the guidance. The predication is performed using the Tweedie's formula [8], namely, $(\\mathbf{z}_t - \\sigma_t\\tilde{\\epsilon}_{\\theta}) / \\alpha_t$ , where $\\alpha_{t}$ and $\\sigma_{t}$ are functions of", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6029", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$t$ that affect the sampling quality.", + "bbox": [ + 76, + 90, + 297, + 106 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since we only have one image as the training data, e.g., painting of Mona Lisa, and one corresponding text descriptor of that image, the diffusion model suffers from overfitting, and severe language drifts after fine-tuning [40]. As a result, the fine-tuned model fails to synthesize images containing features from other language guidance. The overfitting issue might be due to only one repeated prompt used during fine-tuning, making other text prompts no longer accurate enough to control editing (see examples in Fig. 6).", + "bbox": [ + 75, + 107, + 467, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model-based classifier-free guidance. Existing \"personalized\" text-guided real image editing works only use one fine-tuned model for image generation and editing [10, 20, 40], ignoring the capacity of pre-trained large-scale text-to-image models. Instead, to alleviate the overfitting of the fine-tuned model, we leverage the pre-trained text-to-image model for image generation with the provided language guidance and use the fine-tuned model to provide content features in a fashion of combining scores from the two models, similar to classifier-free guidance.", + "bbox": [ + 75, + 244, + 467, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, let $\\hat{\\epsilon}_{\\theta}$ denote the fine-tuned denoising model, and $\\epsilon_{\\theta}$ denote the pre-trained text-to-image model. During sampling, at specified steps, we use our fine-tuned model to guide the pre-trained one by using a linear combination of the scores from each model. Thus, the score estimation in Eqn. 2 becomes:", + "bbox": [ + 75, + 396, + 467, + 486 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) = w \\left(v \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) + (1 - v) \\hat {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\hat {\\mathbf {c}}\\right)\\right) \\tag {3} \\\\ + (1 - w) \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 500, + 467, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $v$ stands for the model guidance weight, $\\hat{\\mathbf{c}}$ is the language guidance token obtained from the fine-tuned diffusion model with the text prompt used during fine-tuning, and $\\mathbf{c}$ is the target language conditioning obtained from the target prompt.", + "bbox": [ + 75, + 545, + 467, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To prevent artifacts from the over-fitted model and maintain the fidelity of the generated image, we propose to sample using Eqn. 3 with $t > K$ and sample using Eqn. 2 for $t \\leq K$ . From $K$ to 0, the denoising process only depends on the pre-trained model. Following this approach, we can fully leverage the generalization ability of the pre-trained model (examples in Fig. 6). Also note that this method could be generalized to include multiple prompts or even multiple modalities.", + "bbox": [ + 75, + 621, + 467, + 757 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Patch-Based Fine-Tuning", + "text_level": 1, + "bbox": [ + 76, + 770, + 307, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With model-based classifier-free guidance, we are able to edit and manipulate a single image with given language guidance. Here, we further show how to improve the finetuning process for a single training image so that the finetuned model can better understand the content and geometry of the image. Thus, it can provide better content guidance for the large-scale text-to-image model during the sampling", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "time and unleash the potential for generating arbitrary-resolution images [9].", + "bbox": [ + 498, + 90, + 888, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Limited-resolution generation. We first review the limitations of the current fine-tuning process. Given an input image $\\mathcal{I}$ with resolution as $H\\times W$ , we can obtain a downsampled latent code $\\mathbf{z}$ from the pre-trained encoder. Since the text-to-image diffusion model is pre-trained at a fixed resolution, i.e., $p\\times p$ , we need to resize the input image to a corresponding resolution $sp\\times sp$ , where $s$ represents the scaling factor of the encoder, to match the resolution for reducing the fine-tuning cost. In essence, prior knowledge of the correlation between the position and content information is learned by the diffusion model. Thus, when sampling from a higher-resolution noise tensor, the generated latent code leads to artifacts like duplicates or position shifting (visual examples in Fig. 5). To tackle such drawbacks, we propose a simple yet effective fine-tuning method.", + "bbox": [ + 496, + 121, + 890, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Patch-based fine-tuning. Inspired by Chai et al. [5], we treat our single training image as a function on coordinate for each pixel, bounded in $[0,H]\\times [0,W]$ . The diffusion model still generates latent code at the fixed resolution $p\\times p$ , but each latent code corresponds to a sub-area in the image. We denote the sub-area as $\\mathbf{v} = [h_1,w_1,h_2,w_2]$ where $(h_1,w_1)\\in [0,H]\\times [0,W]$ and $(h_2,w_2)\\in (h_1,H]\\times (w_1,W]$ indicate the top-left and bottom-right coordinates of the area, respectively. During fine-tuning, we sample patches from the image with different $\\mathbf{v}$ and resize the patches to resolution $sp$ . We denote the resulted patch as $\\mathcal{I}(F(\\mathbf{v}))\\in \\mathbb{R}^{sp\\times sp\\times 3}$ , where $F$ is the normalization and Fourier embedding [23] of the specific area. The encoded latent code of the patch is $\\mathbf{z_v} = \\mathcal{E}(\\mathcal{I}(F(\\mathbf{v})))$ . Our model uses the normalized Fourier embedding as an input to make the model learn the position-content correlation. Formally, our diffusion model is defined as $\\hat{\\epsilon}_{\\theta}(\\mathbf{z}_t,t,\\tau_{\\theta}(y),F(\\mathbf{v}))$ .", + "bbox": [ + 496, + 348, + 890, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After fine-tuning, the model can generate latent code at different resolutions by giving the positional information directly to the model. The arbitrary resolution image editing is conducted by feeding two inputs to the model: the positional embedding of the whole image; and a randomly sampled noisy latent with the dimension corresponding to the resolution we want. When sampling in an arbitrary resolution, the model can still keep the structure of the original image intact (examples in Fig. 4). It is worth noting that with or without the correct position encoding, our framework still naturally permits retargeting, i.e., maintaining the aspect ratio of salient objects, like SinGAN [44], InGAN [45], and Drop-the-GAN [13].", + "bbox": [ + 496, + 604, + 890, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 815, + 630, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Implementation Details While our method can be generally applied to different frameworks, we implement it based on the recently released text-to-image LDM, Stable Diffusion [39]. The pre-trained model was trained on $512 \\times 512$", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6030", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f34c956731ecece0480bee50f95cc1769eee653ee8c13ef44fa6d2e0a151d8b9.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 202, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/854217ca5e3aea56c9eb9fef4474b9599f29467598ec6e59c99023acefa0a278.jpg", + "image_caption": [ + "\"A painting of a grassland in the style of Vincent Van Gogh\"" + ], + "image_footnote": [], + "bbox": [ + 210, + 88, + 334, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c6a80a5a77689b01a2fb52bd260c37f836d92041b574ea71c32c1abdc149320c.jpg", + "image_caption": [ + "\"A photo of a grassland in thunderstorm\"" + ], + "image_footnote": [], + "bbox": [ + 344, + 89, + 468, + 184 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/727433d7d560b4c7bdbd3b1238bb1fd810fd9f4c42b28945ceec114181fc9437.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 202, + 202, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ff5d2a089f273753ad1fa52a640ceb3b41ab10dfa8b51242cb4137827a26793d.jpg", + "image_caption": [ + "\"A photo of a panda with the Eiffel Tower in the background.\"" + ], + "image_footnote": [], + "bbox": [ + 210, + 202, + 334, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/13ab2f4ef893fd5c08df4bfd009bdedf14fb39f7b4a0b106a06886d4cc979443.jpg", + "image_caption": [ + "\"A photo of a panda on desert\"" + ], + "image_footnote": [], + "bbox": [ + 344, + 202, + 468, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0e0d62ea9e1e1a9808f5b1d26950e3a1b98c0d8115c6ac0210591b1e6827fdae.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 314, + 202, + 407 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2e2e4af7c4237b53f5ffd5309513d59ff299e651737cfed38d63d4274f5985f8.jpg", + "image_caption": [ + "\"A sculpture of a horse'" + ], + "image_footnote": [], + "bbox": [ + 210, + 314, + 334, + 407 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8cfac96062fb1fb92f29b89413f256f22b4c9cda59f45d19d82235ca97afb32c.jpg", + "image_caption": [ + "\"A cartoon of a horse\"" + ], + "image_footnote": [], + "bbox": [ + 344, + 314, + 468, + 407 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d6fec66843ef989d41043cafa266b93a6c34f505e74371ec5b4ccd8237ffc96e.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 80, + 425, + 202, + 520 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/94d7d7ff586fe361466cacfad66558df44f168d8fde5ed73fde2407b57fe6871.jpg", + "image_caption": [ + "A painting of a girl in the style of Vincent Van Gogh" + ], + "image_footnote": [], + "bbox": [ + 210, + 425, + 334, + 518 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b9ba6ca735fd630ed46f5e2b4a322bf44966463eb1ed4d6803955806ca576563.jpg", + "image_caption": [ + "A painting of a girl in the style of Leonardo da Vinci" + ], + "image_footnote": [], + "bbox": [ + 344, + 425, + 468, + 518 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d405e70c3c8f7e7b7b14e8e2c06a27682ed640cf4060c0bb310b27113e57073d.jpg", + "image_caption": [ + "Source Image", + "Figure 3. Editing on single source image from various domains. We employ our method on various images and edit them with two target prompts at $512 \\times 512$ resolution. We show the wide range of edits our approach can be used, including but not limited to style transfer, content add-on, posture change, breed change, etc." + ], + "image_footnote": [], + "bbox": [ + 80, + 537, + 202, + 631 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/327877203c031c6f8519af4b0957bbaa4533b3d0310245bc087da64bc4292051.jpg", + "image_caption": [ + "\"A photo of a Husky in ocean" + ], + "image_footnote": [], + "bbox": [ + 210, + 536, + 334, + 630 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/80caa11582c13bcff91c45afe1f3afe124b24fa52ce5b77c42a1f5693920c7e8.jpg", + "image_caption": [ + "\"A cartoon of a dog on grass" + ], + "image_footnote": [], + "bbox": [ + 344, + 536, + 468, + 631 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/db008e4f146691913ee3c35dfdd4070fa504cf313b627e78683523e755a5e7c0.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 493, + 89, + 616, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/90004821aebaa50973b2b507afae692ac61d53d4216835dfbc644ea48a159af9.jpg", + "image_caption": [ + "A painting of a teddy bear in the style of street painting" + ], + "image_footnote": [], + "bbox": [ + 625, + 89, + 748, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/037b81f3b2ea405fd79577f89f615ae024672f54ca9fc24b8f2376e648256f22.jpg", + "image_caption": [ + "\"A cartoon of a teddy bear" + ], + "image_footnote": [], + "bbox": [ + 756, + 89, + 880, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8d26b0681765f3e77e48c6bdacfe50ca673a088f248f92fd7070813fa96f0fbe.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 493, + 202, + 616, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/39d3b7b7d56090c4739b3e3a3f729f0110d2153190c6d5bab5f69683c426155b.jpg", + "image_caption": [ + "A photo of a tree covered by snow" + ], + "image_footnote": [], + "bbox": [ + 625, + 202, + 748, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7090ff21cbf110aea1b68bbcd1cdeee006fc8b1225fbadc7e6764026b3f4d741.jpg", + "image_caption": [ + "\"A photo of a tree on fire.\"" + ], + "image_footnote": [], + "bbox": [ + 756, + 200, + 880, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0674a845cdd635365acb05fd88180b8ecedf6aad26f3b9f7d1d8e5487824df59.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 493, + 313, + 616, + 407 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/031a2995fbd9e734df9f84c2954530f0be8c84d94a958b2c95ad496b3beb2324.jpg", + "image_caption": [ + "\"modern art painting of a vase\"" + ], + "image_footnote": [], + "bbox": [ + 625, + 313, + 748, + 407 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/71c48181f4cfa9044b95217eb6c7cd3d8b7c530b3dd7aec04f14cbc755c92c64.jpg", + "image_caption": [ + "painting of a vase in the style of Vincent Van Gogh" + ], + "image_footnote": [], + "bbox": [ + 756, + 313, + 880, + 407 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/967a7935475ea0855e0fa53a7bc03035d3f624b1661eff0947cabe622d98076d.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 493, + 425, + 616, + 518 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/af30fe703138d50ec9e42599135fb38daa2f93f6822e04a19a3bae521a045831.jpg", + "image_caption": [ + "\"A photo of a building covered by snow\"" + ], + "image_footnote": [], + "bbox": [ + 625, + 425, + 748, + 518 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1f9a5e2a35098ca76215bbb7638485c42c14fed678e8ce783f5f6ec193b9142e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 425, + 880, + 518 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/77ccb2b730429ffaafd624cc36c69f9136bfe2d66321f5c451c38eb3e957d6c9.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 493, + 536, + 616, + 631 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/98359eb6a6e51b5bb0781de43c430f2461a0b729601dee841afdab83e4e8b6ac.jpg", + "image_caption": [ + "A photo of a jumping cat" + ], + "image_footnote": [], + "bbox": [ + 625, + 536, + 748, + 631 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/44f2c898f91cb85608ba4568c94cd02507f9e4a80976d0cca6467311f1d9393a.jpg", + "image_caption": [ + "\"A photo of a cyberpunk building.\"", + "\"A photo of a cat wearing a red hat\"" + ], + "image_footnote": [], + "bbox": [ + 756, + 536, + 880, + 631 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "images from LAION dataset [43]. The spatial size of the latent code from the pre-trained model is $64 \\times 64$ .", + "bbox": [ + 75, + 724, + 468, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For patch-based fine-tuning, we randomly crop images to patches with height and width uniformly in the range of $[0.1H, H] \\times [0.1W, W]$ and resize them to $512 \\times 512$ . Experiments are conducted using $1 \\times$ RTX 8000 GPU with a batch size of 1. The base learning rate is set to $1 \\times 10^{-6}$ . The number of time steps for the diffusion model, $T$ , is 1000. Experiments without and with patch-based fine-tuning are created after 800 and 10,000 optimization steps, respectively. Unless otherwise noted, we adopt other hyperparam-", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "eter choices from Stable Diffusion [39], and the results are generated with image resolution $512 \\times 512$ and with latent dimension $64 \\times 64$ . For sampling parameters, we choose $K = 400$ and $v = 0.7$ .", + "bbox": [ + 498, + 724, + 890, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Qualitative Evaluation", + "text_level": 1, + "bbox": [ + 500, + 795, + 709, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To better understand various approaches, we collect images from a wide range of domains, i.e., free-to-use high-resolution images from Flickr $^1$ and Unsplash $^2$ . During fine", + "bbox": [ + 498, + 819, + 890, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1 https://www.flickr.com/", + "bbox": [ + 517, + 875, + 651, + 887 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2https://unsplash.com/", + "bbox": [ + 519, + 887, + 640, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6031", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ed2602eb596955db2800c2cd67ed525d440c94721540502c5701ca37181537f1.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 83, + 157, + 174, + 227 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/baeb93a3a9467749fb5d3b425806360757e4d161dbed652cf19ebe12651b5916.jpg", + "image_caption": [], + "image_footnote": [ + "a) \"a castle in the style of Minecraft\" (512×1024)" + ], + "bbox": [ + 187, + 89, + 460, + 227 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/299a06c29139e399cd7955779924083f6a2949b49d5e87a29e35f37617edc4e5.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 83, + 335, + 174, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d00049e1355d763bc627d0066b09e34381872eec8255a58d57b029b570548992.jpg", + "image_caption": [ + "Figure 4. Arbitrary resolution editing. Our method achieves higher-resolution image editing without artifacts like duplicates, even on ones that change the height-width ratio drastically." + ], + "image_footnote": [ + "b) \"a Chinese painting of a castle\" $(512\\times 512)$", + "c) \"painting of a castle in the style of Hokusai\" (512×768)", + "d) \"pixel art of a castle\" $(512\\times 768)$", + "a) \"traditional Chinese painting of a lake\" $(1024\\times 512)$", + "b) \"a watercolor painting of a lake of a lake\" $(512\\times 512)$", + "c) \"an impressionism painting of a lake\" $(512\\times 512)$", + "d) \"painting of a lake ... Vincent Van Gogh\" $(512\\times 1024)$" + ], + "bbox": [ + 192, + 268, + 460, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tuning, we apply a coarse class descriptor to the content we want to preserve, e.g., dog, cat, castle, etc. After optimization, we edit each image with diverse editing prompts. We randomly generate 4 edit results for each image and editing prompt and choose the best one (such a process is also applied to other comparison methods). Our work shows impressive editing ability when applied to various images with different language guidance.", + "bbox": [ + 75, + 521, + 467, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As presented in Fig. 3, using the model-based classifier-free guidance (Sec. 3.2) enables us to apply various editing via text prompts on the single real images. Each image has two text prompts describing different features we want to edit, e.g., image style, background content, the texture of the content, etc. Our method can edit the related features while keeping the content intact. We further show our editing results on arbitrary resolution generation in Fig. 4. For each source image, we edit it with different prompts at various resolutions. As can be seen, our patch-based fine-tuning schedule (Sec. 3.3) successfully preserves the original portion and geometry features of the single source image, even on highly challenging resolution such as $512 \\times 1024$ .", + "bbox": [ + 75, + 642, + 467, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 847, + 215, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method to concurrent leading techniques, Textual-Inversion [10] and DreamBooth [40], that", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "can be used for single-image editing. Considering no official implementation has been released for DreamBooth, we adopt an unofficial but well-adopted and highly competitive implementation based on Stable Diffusion [39, 51]. We compare these techniques strictly according to the detailed guidance provided with the implementations.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 5 shows the comparison results. As can be noticed, our method maintains the fidelity of the images while applying changes as desired. Furthermore, our approach has high authenticity and structural integrity even for higher-resolution editing. For example, in the last row of Fig. 5, when the target prompt is “... standing on grass”, our method generates results by modifying the texture of the land on which the dog stands with other features intact. However, other methods result in a dramatic change in the structure of the whole image. Moreover, in the second row, when modifying the painting Mona Lisa, both Dream-Booth [40] and Textual-Inversion [10] fail to edit the image. Our work also shows clear advantages over the approaches on training-free editorings, such as ILVR [7], SDEdit [32], and Prompt-to-prompt [20], with the qualitative comparisons presented in the supplementary materials.", + "bbox": [ + 496, + 181, + 892, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Analysis", + "text_level": 1, + "bbox": [ + 500, + 436, + 671, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Patch-based fine-tuning. In Fig. 5, we show the results of editing images in higher resolution when fine-tuned without or with the proposed patch-based fine-tuning technique (w/o pos vs. w/ pos). When sampling at a higher resolution, as in the right part of Fig. 5, the denoising model fine-tuned without the patch-based training mechanism performs poorly. In the first row, the castle towers get duplicated to meet the resolution, and in the third row, the bench gets stretched disproportionately. In essence, our patch-based fine-tuning technique enables the diffusion model to leverage the super-resolution ability of the decoder and edit images at arbitrary resolution during testing time.", + "bbox": [ + 496, + 460, + 890, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis of model-based classifier-free guidance. We generate editing results by directly sampling from the fine-tuned model using Eqn. 2. We fine-tune the model without the patch-based schedule for 800 steps to retain more generalization ability. In this case, the model can perfectly reconstruct the source image while preserving as much editing ability as possible. We denote the setting as w/o gudiance. Using the same fine-tuned model, we conduct experiments under model-based classifier-free guidance, denoted as $w/$ guidance. As shown in Fig. 6, sampling without our model-based classifier-free guidance fails to react to the prompt, while our method can successfully edit images to match the target language guidance. We further analyze $K$ and $v$ in model-based classifier-free guidance.", + "bbox": [ + 496, + 643, + 892, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis on guidance step $K$ in Sec. 3.2. In Fig. 7, we show our results on editing with different settings of $K$ . We conduct this set of experiments by editing one single", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6032", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c947fdaf5a0056d2564f2732369fcce3fcfe6910e456a4ca3b04805b4ee00817.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 92, + 161, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6a0b4a9e74725309591d6648683692e03b74f316c24442dfa85e6d6962e6c26a.jpg", + "image_caption": [ + "DreamBooth" + ], + "image_footnote": [ + "\"Painting of a castle in the style of Vincent Van Gogh\" (H = 512, W = 512)" + ], + "bbox": [ + 176, + 103, + 256, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5309a48bedb1af578143cad60c14d30f8f1218524577e24f7d8dc73495f29111.jpg", + "image_caption": [ + "Textual-Inversion" + ], + "image_footnote": [], + "bbox": [ + 264, + 103, + 346, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/55fbba9591a6f438f71fcfccf22b5f7281a81fcd77b1bad2215e9732b9f2ea90.jpg", + "image_caption": [ + "Ours (w/o pos)" + ], + "image_footnote": [], + "bbox": [ + 352, + 103, + 433, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f41a89368d9d27791389fd5136c9a25b27b0a3e8a51eb653117bf7926b97ddde.jpg", + "image_caption": [ + "Ours (w/ pos)" + ], + "image_footnote": [], + "bbox": [ + 442, + 103, + 522, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa446fbb7385d891128b08b8cc2bb84e3fddab8536e80d748848ca62c5ed73d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 181, + 161, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0217a26c494f0ecd07becffe96fefebb24e9fdff245734613532b3c150d2ac2b.jpg", + "image_caption": [], + "image_footnote": [ + "\"Oil painting of a lady in the style of Pierre-Auguste Renoir\" (H = 512, W = 512)" + ], + "bbox": [ + 178, + 181, + 256, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d1464c1c47842cd598a989af36af96868904e216ed20955d7dc846bef5af7b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 181, + 344, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ca99e132445b3c41f3d9586b13bd571d95e969555638d111fffc92595362251a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 181, + 433, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b71be9b70290fb39ff6b333026d8c53cde3202d58aed94ba188b3b0f5e4ee7a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 442, + 181, + 521, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/beaf3796f7f20eafc75d629f1f8f19342dde18abebc006aeb48d2c8b6176fa34.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 258, + 161, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a66dbf82e5f3490e22fd54ce620582d75d4c6e6d638a44d1d16d730dbf092a85.jpg", + "image_caption": [], + "image_footnote": [ + "\"A children's drawing of a bench\" $(H = 512, W = 512)$" + ], + "bbox": [ + 178, + 258, + 256, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0263b2c6ebf7e11559065709cf407e5f5fbcdfac692e28a5a9fa051611d64b12.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 258, + 344, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/715de4845f822e8a4c35cf5630dc18f83b95530b0835f8eb572b3aca00a85fc5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 258, + 433, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8fbe6aa27e0b2cd0f9d025ee1f149fdeb520a7c00feac82965eed13027e8e378.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 442, + 258, + 521, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef35aeffa1b8e1449f1bfe7c7dbffe267b3c7770f10b49ad1d75076b70d00608.jpg", + "image_caption": [ + "Figure 5. Comparisons of various methods. We compare our method to DreamBooth [40] and Textual-Inversion [10]. We adopt default hyper-parameters for both methods provided in their paper or code. On the left part of the figure, we edit at the resolution same as training time. On the right part, we edit the source image at a higher resolution. Our work successfully edits the image as required while preserving the details of the source images. We also compare our method without and with the patch-based fine-tuning mechanism (w/o pos vs. w/ pos). When editing at a fixed resolution, two settings perform equally, while at a higher resolution, the patch-based fine-tuning method successfully prevents artifacts." + ], + "image_footnote": [], + "bbox": [ + 83, + 335, + 161, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f35ff5b697327ab8b884e82ed7840bac4737b2d3437ac9aa4fde33f4129527a2.jpg", + "image_caption": [], + "image_footnote": [ + "\"A dog standing on grass\" $(H = 512, W = 512)$" + ], + "bbox": [ + 178, + 335, + 256, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1b855bfef3d57512dd15d17b37fa4307509ad09c5dbbdb75b4a189cb7704cfba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 335, + 344, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7ae117f047cf219c88a585f33e341b567cecd81b669b73c60653622126ad931.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 335, + 433, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a341c9b31eb2a7ccd81d2b7865e2235451e6d29d80d3d24ec7643f002876166b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 442, + 335, + 521, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/53f8571aee97d9dc7e1e7dd6d8863585c0ae2383f103100e09804df7ac6d6514.jpg", + "image_caption": [ + "DreamBooth" + ], + "image_footnote": [], + "bbox": [ + 540, + 103, + 619, + 161 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/81c28e3c577f220da029d8ec0f1cbf640f2204365fe2fc0cb02257cb20d7472e.jpg", + "image_caption": [ + "Textual-Inversion" + ], + "image_footnote": [ + "\"A photo of a castle covered by snow\" (H = 512, W = 768)" + ], + "bbox": [ + 627, + 103, + 707, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/02ccfc9831a0efd15a7b0531b574459bcbacc3b474921cdd900754b3c03f51e7.jpg", + "image_caption": [ + "Ours (w/o pos)" + ], + "image_footnote": [], + "bbox": [ + 720, + 103, + 797, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a84dccf4f81a86cf1599249f8c5ae93758ea4f35b4c6ca4e5b5a170df4db9027.jpg", + "image_caption": [ + "Ours (w/ pos)" + ], + "image_footnote": [], + "bbox": [ + 808, + 103, + 887, + 165 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e2ad47382b41af81b87c5b7a9bb8244d4fabda5e614bffc8f078642ab045dc28.jpg", + "image_caption": [], + "image_footnote": [ + "\"A sculpture of a lady in the style of Michelangelo\" (H = 768, W = 768)" + ], + "bbox": [ + 540, + 181, + 619, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d80a5ca8782f4c2ab0c8528a22b5120f4f3354c3d3aebcb4fde86b0ac1ce031e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 181, + 707, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/664adee6144509d39e0213b1be31cca48d3326f2954c5fb18ce8578e2e3f045a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 181, + 797, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d541ce1edc14d76778521f8c488db6f3039348bebb262e51319cc01c3feadbeb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 808, + 181, + 887, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/19913a7bb39cabf785b393c8b25185be2edccc96ed865b43c4201c57492a3d1e.jpg", + "image_caption": [], + "image_footnote": [ + "\"A bench in a desert\" $(H = 768, W = 768)$" + ], + "bbox": [ + 540, + 258, + 620, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ea34e3ba4b91929d954525062579635d8387a8261987c9d5e0b06aeb7a1471d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 258, + 707, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c0eb0ee17493708c363c7c30aa2b37933921aebb5ee2a53c5f37219be97d6c18.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 258, + 797, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/07553382286977f2fff32ad0d1001a475fd2df706d0b9768e3af95924dd7ff78.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 808, + 258, + 887, + 319 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1ba48ee90a91967fb2dc5ecfbea174620a43613620ef1011dd8a7610b6216f3.jpg", + "image_caption": [], + "image_footnote": [ + "\"A sculpture of a dog in the style of Michelangelo\" (H = 768, W = 768)" + ], + "bbox": [ + 540, + 335, + 620, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ec5ab8589f4c2a4ae367afc69fc706579fc8edbaa40c0025654b17ef8192aee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 335, + 707, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/57da8c66ceab9852322b64528e1a41dfba79398852b45b37b761f8184435c482.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 335, + 797, + 395 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3231fd8adfb249921ccf5216eecdb2d689b060569b8201ebc725663c2933066f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 808, + 335, + 887, + 395 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "image with the same language guidance at $768 \\times 768$ resolution. We set $v = 0.7$ . When $K = 0$ , the model-based classifier-free guidance is applied for each step of the denoising process. Since the generalization ability of the finetuned model is limited, in this case, the model fails to apply the desired property to the single source image. When $K = 1,000$ , the model-based classifier-free guidance is not applied to any step. Thus, the structure of the image is not preserved, and the generated result becomes a random sample of the pre-trained model.", + "bbox": [ + 75, + 525, + 468, + 675 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further show the quantitative results Fig. 8a. We repeat the abovementioned procedure over different $K$ and randomly sample 20 images for each $K$ . We calculate two metrics. To understand the editing result, the image fidelity that is measured by the LPIPS [57] distance between the original and the edited image. The text alignment calculated by the CLIP [36] score to understand the alignment between our generated images and target text. As can be seen, the image fidelity drops with the increase of $K$ , indicating more details provided by the pre-trained model instead of the fine-tuned one. The text alignment measurement improves since the more details generated by the pre-trained model, the better editing results align with the target domain. To preserve the edit result's authenticity and fidelity", + "bbox": [ + 75, + 689, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to the source image, we set $K$ as 400.", + "bbox": [ + 500, + 525, + 750, + 539 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis on guidance weight $v$ in Sec. 3.2. We further study the impact of the guidance weight $(v)$ in Fig. 9. We set $K = 400$ and resolution as $768 \\times 768$ for each edit and use the same random seed to generate the result. As can be observed, the value of $v$ controls the fidelity of the edit result. However, since the pre-trained model is trained at the resolution $512 \\times 512$ , the generated image contains many artifacts. When $v = 1$ , the synthesized image entirely depends on the results from the pre-trained model. Additionally, we conduct quantitative experiments with LPIPS score measuring the image fidelity and CLIP score for the text alignment in Fig. 8b. When $v$ is close to 1, the fidelity decreases while the edited feature decreases. When $v$ is close to 0, the model relies mainly on the fine-tuned model for the output when $t > K$ . However, since the fine-tuned model contains poor generalization ability, there is a significant amount of artifacts in the generated results, which leads to a poor LPIPS score. We choose 0.7 for each edit in this work as a trade-off between fidelity and creativity.", + "bbox": [ + 496, + 546, + 890, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Other analysis. We defer the analysis of model-based classifier-free guidance with multiple inputs and fine-tuning without coarse class descriptor or prior-preservation loss to the supplementary materials.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6033", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/90f534f999e88f363c477524a0eb11becd0299fcd740328700a677264f574267.jpg", + "image_caption": [ + "Figure 6. Analysis of model-based classifier-free guidance. Directly sampling with target text using the fine-tuned model (w/o guidance) fails to generate images corresponding to the text prompt. In contrast, the model-based classifier-free guidance (w/guidance) can synthesize high-fidelity images." + ], + "image_footnote": [], + "bbox": [ + 89, + 92, + 441, + 422 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9ef6ed5843aed5e0b14d7c68e5cbc0e0f04b915456501bac7a075bc49af76ab4.jpg", + "image_caption": [ + "Figure 7. Analysis on guidance step $K$ . Varying $K$ , we can decide the steps where the model-based guidance is applied, which controls the details from the source image and edits to be applied." + ], + "image_footnote": [], + "bbox": [ + 81, + 517, + 450, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 768, + 194, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work introduces SINE, a method for single-image editing. With only one image and a brief description of the object in the image, our approach can enable a wide range of editing for arbitrary resolution, followed by the information depicted in the language guidance. To achieve such results, we leverage the pre-trained large-scale text-to-image diffusion model. Specifically, we first fine-tune the", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/173ebaa8fb8c9f632db85910b95167c737500f2053da3a6548e64b9cfcd213e2.jpg", + "image_caption": [ + "(a) Number of steps of the guidance." + ], + "image_footnote": [], + "bbox": [ + 501, + 99, + 694, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6a5237881aad305a35274db6c15a2fd63d7a37f4fdc1f543594b1eaba9b7af86.jpg", + "image_caption": [ + "(b) Weight of the guidance." + ], + "image_footnote": [], + "bbox": [ + 697, + 99, + 887, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/83543c2ea4ff0034c2fce5208d8470457121f20e592318496ad056c71188f4b9.jpg", + "image_caption": [ + "Figure 8. Trade-off between fidelity and alignment with target text. We calculate the CLIP score [36] (a higher CLIP score indicates a better alignment between the edit result and target text) and 1-LPIPS score [57] (showing the fidelity between edit results and source image, the higher, the better).", + "Figure 9. Analysis of score interpolation. Varying $v$ with the same random seed gets editing results with various qualities." + ], + "image_footnote": [], + "bbox": [ + 501, + 297, + 870, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "pre-trained model with our patch-based fine-tuning method until it overfits the single image. Then, during sampling time, we use the overfitted model to guide the pre-trained diffusion model for image synthesis, which maintains the fidelity of the results while taking advantage of the generalization ability of the pre-trained model. Compared with other methods, our approach has a better geometrical understanding of the image and thus can conduct complex editing to the images besides style transfer.", + "bbox": [ + 496, + 618, + 890, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, in some cases where confusing editing guidance is given for the diffusion model, e.g., a chair-shaped dog, our method could fail. In cases where drastic changes are to be applied, e.g., changing a dog to a tiger in the same posture, there are also noticeable artifacts. We show more examples in the supplementary materials.", + "bbox": [ + 496, + 753, + 890, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "One future direction is improving the fidelity of the editing results, which could be achieved by alleviating the overfitting problem of the fine-tuned model.", + "bbox": [ + 496, + 845, + 890, + 890 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6034", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. Clip2stylegan: Unsupervised extraction of stylegan edit directions. In ACM SIGGRAPH 2022 Conference Proceedings, pages 1-9, 2022. 2", + "[2] Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019. 2" + ], + "bbox": [ + 78, + 92, + 468, + 556 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6037", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/9e4aea54-e956-45c7-8e0d-e18b2b0dde98_model.json b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/9e4aea54-e956-45c7-8e0d-e18b2b0dde98_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b92372c805ce6d79eebc5c227814ee6ee9fbc053 --- /dev/null +++ b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/9e4aea54-e956-45c7-8e0d-e18b2b0dde98_model.json @@ -0,0 +1,3632 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.152, + 0.131, + 0.819, + 0.154 + ], + "angle": 0, + "content": "SINE: SIngle Image Editing with Text-to-Image Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.18, + 0.252, + 0.201 + ], + "angle": 0, + "content": "Zhixing Zhang" + }, + { + "type": "text", + "bbox": [ + 0.287, + 0.18, + 0.392, + 0.199 + ], + "angle": 0, + "content": "Ligong Han" + }, + { + "type": "text", + "bbox": [ + 0.429, + 0.181, + 0.543, + 0.199 + ], + "angle": 0, + "content": "Arnab Ghosh" + }, + { + "type": "text", + "bbox": [ + 0.585, + 0.181, + 0.73, + 0.198 + ], + "angle": 0, + "content": "Dimitris Metaxas1" + }, + { + "type": "text", + "bbox": [ + 0.767, + 0.181, + 0.845, + 0.197 + ], + "angle": 0, + "content": "Jian Ren" + }, + { + "type": "text", + "bbox": [ + 0.331, + 0.199, + 0.628, + 0.218 + ], + "angle": 0, + "content": "\\(^{1}\\)Rutgers University \\(^{2}\\)Snap Inc." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.251, + 0.314, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.473, + 0.692 + ], + "angle": 0, + "content": "Recent works on diffusion models have demonstrated a strong capability for conditioning image generation, e.g., text-guided image synthesis. Such success inspires many efforts trying to use large-scale pre-trained diffusion models for tackling a challenging problem—real image editing. Works conducted in this area learn a unique textual token corresponding to several images containing the same object. However, under many circumstances, only one image is available, such as the painting of the Girl with a Pearl Earring. Using existing works on fine-tuning the pretrained diffusion models with a single image causes severe overfitting issues. The information leakage from the pretrained diffusion models makes editing can not keep the same content as the given image while creating new features depicted by the language guidance. This work aims to address the problem of single-image editing. We propose a novel model-based guidance built upon the classifier-free guidance so that the knowledge from the model trained on a single image can be distilled into the pre-trained diffusion model, enabling content creation even with one given image. Additionally, we propose a patch-based fine-tuning that can effectively help the model generate images of arbitrary resolution. We provide extensive experiments to validate the design choices of our approach and show promising editing capabilities, including changing style, content addition, and object manipulation. Our code is made publicly available here." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.723, + 0.208, + 0.739 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Automatic real image editing is an exciting direction, enabling content generation and creation with minimal effort. Although many works have been conducted in this area, achieving high-fidelity semantic manipulation on an image is still a challenging problem for the generative models, considering the target image might be out of the training data distribution [4, 11, 25, 26, 32, 58, 59]. The recently introduced large-scale text-to-image models, e.g., DALL-E 2 [37], Imagen [42], Parti [55], and StableDiffusion [39], can perform high-quality and diverse image generation with" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.25, + 0.566, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.301, + 0.558, + 0.308 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.251, + 0.621, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.586, + 0.301, + 0.615, + 0.308 + ], + "angle": 0, + "content": "sculpture" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.251, + 0.696, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.301, + 0.687, + 0.308 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.251, + 0.759, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.301, + 0.759, + 0.308 + ], + "angle": 0, + "content": "\"....super- hero cape" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.251, + 0.885, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.301, + 0.759, + 0.308 + ], + "angle": 0, + "content": "\"...super- hero cape" + }, + { + "type": "image_caption", + "bbox": [ + 0.764, + 0.301, + 0.884, + 0.308 + ], + "angle": 0, + "content": "\"coffee machine...\" \"coffee maker...\"" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.308, + 0.566, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.356, + 0.557, + 0.364 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.308, + 0.689, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.356, + 0.658, + 0.363 + ], + "angle": 0, + "content": ".covered by snow" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.308, + 0.759, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.356, + 0.75, + 0.363 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.308, + 0.885, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.356, + 0.808, + 0.363 + ], + "angle": 0, + "content": "in snow" + }, + { + "type": "image_caption", + "bbox": [ + 0.834, + 0.356, + 0.878, + 0.363 + ], + "angle": 0, + "content": "blossom street" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Figure 1. With only one real image, i.e., Source Image, our method is able to manipulate and generate the content in various ways, such as changing style, adding context, modifying the object, and enlarging the resolution, through guidance from the text prompt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.552 + ], + "angle": 0, + "content": "natural language guidance. The success of these works has inspired many subsequent efforts to leverage the pre-trained large-scale models for real image editing [10, 15, 20, 40]. They show that, with properly designed prompts and a limited number of fine-tuning steps, the text-to-image models can manipulate a given subject with text guidance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.893, + 0.903 + ], + "angle": 0, + "content": "On the downside, the recent text-guided editing works that build upon the diffusion models suffer several limitations. First, the fine-tuning process might lead to the pretrained large-scale model overfit on the real image, which degrades the synthesized images' quality when editing. To tackle these issues, methods like using multiple images with the same content and applying regularization terms on the same object have been introduced [4, 40]. However, querying multiple images with identical content or object might not be an available choice; for instance, there is only one painting for Girl with a Pearl Earring. Directly editing the single image brings information leakage from the pretrained large-scale models, generating images with different content (examples in Fig. 5); therefore, the application scenarios of these methods are greatly constrained. Second, these works lack a reasonable understanding of the object geometry for the edited image. Thus, generating images with different spatial size as the training data cause undesired artifacts, e.g., repeated objects, and incorrectly modified geometry (examples in Fig. 5). Such drawbacks restrict applying these methods for generating images with an arbitrary resolution, e.g., synthesizing high-resolution images from a single photo of a castle (as in Fig. 4), again limiting" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6027" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.262, + 0.106 + ], + "angle": 0, + "content": "the usage of these methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.468, + 0.213 + ], + "angle": 0, + "content": "In this work, we present SINE, a framework utilizing pre-trained text-to-image diffusion models for SINgle image Editing and content manipulation. We build our approach based upon existing text-guided image generation approaches [10, 40] and propose the following novel techniques to solve overfitting issues on content and geometry, and language drift [28, 31]:" + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.223, + 0.468, + 0.375 + ], + "angle": 0, + "content": "- First, by appropriately modifying the classifier-free guidance [22], we introduce model-based classifier-free guidance that utilizes the diffusion model to provide the score guidance for content and structure. Taking advantage of the step-by-step sampling process used in diffusion models, we use the model fine-tuned on a single image to plant a content \"seed\" at the early stage of the denoising process and allow the pre-trained large-scale text-to-image model to edit creatively conditioned with the language guidance at a later stage." + }, + { + "type": "text", + "bbox": [ + 0.08, + 0.384, + 0.468, + 0.43 + ], + "angle": 0, + "content": "- Second, to decouple the correlation between pixel position and content, we propose a patch-based fine-tuning strategy, enabling generation on arbitrary resolution." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.223, + 0.468, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.468, + 0.665 + ], + "angle": 0, + "content": "With a text descriptor describing the content that is aimed to be manipulated and language guidance depicting the desired output, our approach can edit the single unique image to the targeted domain with details preserved in arbitrary resolution. The output image keeps the structure and background intact while having features well-aligned with the target language guidance. As shown in Fig. 1, trained on a painting Girl with a Pearl Earring with resolution as \\(512 \\times 512\\), we can sample an image of a sculpture of the girl at the resolution of \\(640 \\times 512\\) with the identity features preserved. Moreover, our method can successfully handle various edits such as style transfer, content addition, and object manipulation (more examples in Fig. 3). We hope our method can further boost creative content creation by opening the door to editing arbitrary images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.218, + 0.695 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Text-guided image synthesis has drawn considerable attention in the generative model context [1, 2, 6, 12, 14, 16-19, 34, 35, 38, 50, 53-56, 60]. The recent development of diffusion models [21, 46, 47, 49] introduced new solutions to this problem and produced impressive results [33, 37, 39, 42]. With the significant improvement of these models, rather than training a large-scale text-to-image model from scratch, a leading line of works focuses on taking advantage of the existing pre-trained model and manipulating images according to given natural language guidance [3, 10, 20, 24, 29, 40]. In these works, studies explore text-based interfaces for image editing [1, 3, 35], style transfer [27, 30], and generator domain adaption [11, 25, 48]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "The development of the diffusion model provides a giant and flexible design space for this task. Many works utilize pre-trained diffusion models as generative priors and are training-free. ILVR [7] guides the denoising process by replacing the low-frequency part of the sample with that of the target reference image. SDEdit [32] applies the diffusion process first on an image or a user-created semantic map and then conducts the denoising procedure conditioned with the desired output. Blended diffusion [3] performs language-guided inpainting with a given mask." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.514 + ], + "angle": 0, + "content": "Another line of research showed great potential and semantic editing ability of fine-tuning. DiffusionCLIP [25] leverages the CLIP [36] model to provide gradients for image manipulation and deliver impressive results on style transfer. Textual-Inversion [10] and DreamBooth [40] fine-tune the text embedding or the full diffusion model using a few personalized images (typically \\(3 \\sim 5\\)) to synthesize images of the same object in a novel context. These methods, however, either drastically change the layout of the original image when dealing with a single image or can not fully leverage the generalization ability of the pre-trained model for editing due to overfitting or language drift. Notably, Prompt-to-Prompt [20] controls the editing of synthesized images by manipulating the cross-attention maps; however, its editing ability is limited when applied to real images. Imagic [24], while delivering realistic results, requires fine-tuning process on each editing prompt for each image, leading to longer inference time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.727 + ], + "angle": 0, + "content": "This work introduces a solution to achieve image fidelity and text alignment simultaneously. Our method can perform high-quality semantic editing globally and locally on one single image. On the other hand, previous works lack an understanding of the object geometry of the edited image. When editing the image at an arbitrary resolution, the artifacts in the results will be obvious. Prior works have investigated generating images at arbitrary resolution using positional encoding as inductive bias [41, 52, 52] so that the correlation between content and position can be eliminated. Anyres-GAN [5] adopt a patch training mechanism to leverage high-resolution data to help the generation of images in the low-resolution domain. We propose a patch-based fine-tuning method to achieve arbitrary resolution editing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.598, + 0.755 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For one arbitrary in-the-wild image, our goal is to edit the image via language while preserving the maximal amount of details from the original image. To do so, we leverage the generalization ability of pre-trained large-scale text-to-image models [39]. An intuitive approach is to fine-tune the diffusion models with the single image and text description, similar to DreamBooth [40]. Ideally, it should provide a model that can reconstruct the input image using the given text descriptor and synthesize new images when" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6028" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "given other language guidance. Unfortunately, we find the model can easily overfit the single trained image and its corresponding text description. Thus, although the fine-tuned model can still reconstruct the input image perfectly, it can no longer synthesize diverse images according to the given language guidance (as shown in Fig. 5). Moreover, it struggles to generate arbitrary resolution images due to the lack of positional information (as in Fig. 4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.474, + 0.336 + ], + "angle": 0, + "content": "To solve the above issues, we propose a test-time model-based classifier-free guidance and a patch-based fine-tuning technique. An overview of our method is illustrated in Fig. 2. In the following sections, we review the backbone model used in our approach (Sec. 3.1). Then, we describe how to overcome the overfitting problem with model-based guidance (Sec. 3.2). Lastly, we present how to address the problem of limited resolution generation (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.343, + 0.391, + 0.358 + ], + "angle": 0, + "content": "3.1. Language-Guided Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.474, + 0.593 + ], + "angle": 0, + "content": "We use the latent diffusion models (LDMs) [39] trained on a large-scale dataset as our base model and implement the proposed approaches by fine-tuning the pre-trained model. LDMs is a class of Denoising Diffusion Probabilistic Models (DDPMs) [21] that contains an auto-encoder trained on images, and a diffusion model learned on the latent space constructed by the auto-encoder. The encoder \\(\\mathcal{E}\\) encodes a given image \\(\\mathcal{I} \\in \\mathbb{R}^{H \\times W \\times 3}\\) to a latent representation \\(\\mathbf{z}\\), such that \\(\\mathbf{z} = \\mathcal{E}(\\mathcal{I})\\). The decoder \\(\\mathcal{D}\\) reconstructs the estimated image \\(\\tilde{\\mathcal{I}}\\) from the latent, such that \\(\\tilde{\\mathcal{I}} = \\mathcal{D}(\\mathbf{z})\\) and \\(\\tilde{\\mathcal{I}} \\approx \\mathcal{I}\\). The diffusion model is trained to produce latent codes within the pre-trained latent space. The most intriguing property of LDMs is that the diffusion model can be conditioned on class labels, images, and text prompt. The conditional LDM is learned as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.601, + 0.47, + 0.62 + ], + "angle": 0, + "content": "\\[\nL _ {L D M} := \\mathbb {E} _ {\\mathcal {E} (\\mathcal {I}), y, \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {z} _ {t}, t, \\boldsymbol {\\tau} _ {\\theta} (y)) \\| _ {\\mathbf {2}} ^ {2} \\right], \\quad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.473, + 0.795 + ], + "angle": 0, + "content": "where \\(t\\) is the time step, \\(\\mathbf{z}_t\\) is the latent noised to time \\(t\\), \\(\\epsilon\\) is the unscaled noise sample, \\(\\epsilon_{\\theta}\\) is the denoising model, \\(y\\) is the conditioning input, and \\(\\tau_{\\theta}\\) maps \\(y\\) to a conditioning vector. During training time, \\(\\epsilon_{\\theta}\\) and \\(\\tau_{\\theta}\\) are jointly optimized. A random noise tensor is sampled and denoised at inference time based on the conditioning input, e.g., text prompt, to produce a new latent. Inspired by DreamBooth [40], we construct the text prompt for fine-tuning a single image as \"a photo/painting of a [*] [class noun]\", where \"[*]\" is a unique identifier and \"[class noun]\" is a coarse class descriptor (e.g., \"castle\", \"lake\", \"car\", etc.)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.411, + 0.817 + ], + "angle": 0, + "content": "3.2. Model-Based Classifier-Free Guidance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.871 + ], + "angle": 0, + "content": "With the above-presented LDMs, we introduce our approach, inspired by classifier-free guidance, to overcome overfitting when fine-tuning LDMs with one image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Classifier-free guidance [22] is a technique widely adopted by prior text-to-image diffusion models [39, 42]. A single" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.097, + 0.882, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.289, + 0.882, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.5, + 0.895, + 0.709 + ], + "angle": 0, + "content": "Figure 2. Overview of our method. (a) Given a source image, we first randomly crop it into patches and get the corresponding latent code \\(\\mathbf{z}\\) with the pre-trained encoder. At fine-tune time, the denoising model, \\(\\epsilon_{\\theta}\\), takes three inputs: noisy latent \\(\\mathbf{z}_T\\), language condition \\(\\mathbf{c}\\), and positional embedding for the area where the noisy latent is obtained. (b) During sampling, we give additional language guidance about the target domain to edit the image. Also, we sample a noisy latent code \\(\\mathbf{z}_T\\) with the dimension corresponding to the desired output resolution. Language conditioning for \\(\\epsilon_{\\theta}\\) and \\(\\mathbf{c}\\) are given by pre-trained language encoder \\(\\tau_{\\theta}\\) with the target language guidance. While for the fine-tuned diffusion model, \\(\\hat{\\epsilon}_{\\theta}\\), in addition to the language conditioning \\(\\hat{\\mathbf{c}}\\), we also input the positional embedding for the whole image. We employ a linear combination between the score calculated by each model for the first \\(K\\) steps and inference only on pre-trained \\(\\epsilon_{\\theta}\\) after." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.893, + 0.79 + ], + "angle": 0, + "content": "diffusion model is trained using conditional and unconditional objectives by randomly dropping the condition during training. When sampling, a linear combination of the conditional and unconditional score estimation is used:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.8, + 0.892, + 0.816 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {e}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) = w \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) + (1 - w) \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(\\mathbf{z}_t,\\mathbf{c})\\) and \\(\\epsilon_{\\theta}(\\mathbf{z}_t)\\) are the conditional and unconditional \\(\\epsilon\\)-predictions, \\(\\mathbf{c}\\) is the conditioning vector generated by \\(\\tau_{\\theta}\\), and \\(w\\) is the weight for the guidance. The predication is performed using the Tweedie's formula [8], namely, \\((\\mathbf{z}_t - \\sigma_t\\tilde{\\epsilon}_{\\theta}) / \\alpha_t\\), where \\(\\alpha_{t}\\) and \\(\\sigma_{t}\\) are functions of" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6029" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.299, + 0.107 + ], + "angle": 0, + "content": "\\(t\\) that affect the sampling quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.468, + 0.244 + ], + "angle": 0, + "content": "Since we only have one image as the training data, e.g., painting of Mona Lisa, and one corresponding text descriptor of that image, the diffusion model suffers from overfitting, and severe language drifts after fine-tuning [40]. As a result, the fine-tuned model fails to synthesize images containing features from other language guidance. The overfitting issue might be due to only one repeated prompt used during fine-tuning, making other text prompts no longer accurate enough to control editing (see examples in Fig. 6)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.468, + 0.395 + ], + "angle": 0, + "content": "Model-based classifier-free guidance. Existing \"personalized\" text-guided real image editing works only use one fine-tuned model for image generation and editing [10, 20, 40], ignoring the capacity of pre-trained large-scale text-to-image models. Instead, to alleviate the overfitting of the fine-tuned model, we leverage the pre-trained text-to-image model for image generation with the provided language guidance and use the fine-tuned model to provide content features in a fashion of combining scores from the two models, similar to classifier-free guidance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.468, + 0.487 + ], + "angle": 0, + "content": "Specifically, let \\(\\hat{\\epsilon}_{\\theta}\\) denote the fine-tuned denoising model, and \\(\\epsilon_{\\theta}\\) denote the pre-trained text-to-image model. During sampling, at specified steps, we use our fine-tuned model to guide the pre-trained one by using a linear combination of the scores from each model. Thus, the score estimation in Eqn. 2 becomes:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.501, + 0.468, + 0.533 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) = w \\left(v \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) + (1 - v) \\hat {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\hat {\\mathbf {c}}\\right)\\right) \\tag {3} \\\\ + (1 - w) \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.468, + 0.621 + ], + "angle": 0, + "content": "where \\( v \\) stands for the model guidance weight, \\( \\hat{\\mathbf{c}} \\) is the language guidance token obtained from the fine-tuned diffusion model with the text prompt used during fine-tuning, and \\( \\mathbf{c} \\) is the target language conditioning obtained from the target prompt." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.468, + 0.758 + ], + "angle": 0, + "content": "To prevent artifacts from the over-fitted model and maintain the fidelity of the generated image, we propose to sample using Eqn. 3 with \\( t > K \\) and sample using Eqn. 2 for \\( t \\leq K \\). From \\( K \\) to 0, the denoising process only depends on the pre-trained model. Following this approach, we can fully leverage the generalization ability of the pre-trained model (examples in Fig. 6). Also note that this method could be generalized to include multiple prompts or even multiple modalities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.308, + 0.787 + ], + "angle": 0, + "content": "3.3. Patch-Based Fine-Tuning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "With model-based classifier-free guidance, we are able to edit and manipulate a single image with given language guidance. Here, we further show how to improve the finetuning process for a single training image so that the finetuned model can better understand the content and geometry of the image. Thus, it can provide better content guidance for the large-scale text-to-image model during the sampling" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.122 + ], + "angle": 0, + "content": "time and unleash the potential for generating arbitrary-resolution images [9]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.348 + ], + "angle": 0, + "content": "Limited-resolution generation. We first review the limitations of the current fine-tuning process. Given an input image \\(\\mathcal{I}\\) with resolution as \\(H\\times W\\), we can obtain a downsampled latent code \\(\\mathbf{z}\\) from the pre-trained encoder. Since the text-to-image diffusion model is pre-trained at a fixed resolution, i.e., \\(p\\times p\\), we need to resize the input image to a corresponding resolution \\(sp\\times sp\\), where \\(s\\) represents the scaling factor of the encoder, to match the resolution for reducing the fine-tuning cost. In essence, prior knowledge of the correlation between the position and content information is learned by the diffusion model. Thus, when sampling from a higher-resolution noise tensor, the generated latent code leads to artifacts like duplicates or position shifting (visual examples in Fig. 5). To tackle such drawbacks, we propose a simple yet effective fine-tuning method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.605 + ], + "angle": 0, + "content": "Patch-based fine-tuning. Inspired by Chai et al. [5], we treat our single training image as a function on coordinate for each pixel, bounded in \\([0,H]\\times [0,W]\\). The diffusion model still generates latent code at the fixed resolution \\(p\\times p\\), but each latent code corresponds to a sub-area in the image. We denote the sub-area as \\(\\mathbf{v} = [h_1,w_1,h_2,w_2]\\) where \\((h_1,w_1)\\in [0,H]\\times [0,W]\\) and \\((h_2,w_2)\\in (h_1,H]\\times (w_1,W]\\) indicate the top-left and bottom-right coordinates of the area, respectively. During fine-tuning, we sample patches from the image with different \\(\\mathbf{v}\\) and resize the patches to resolution \\(sp\\). We denote the resulted patch as \\(\\mathcal{I}(F(\\mathbf{v}))\\in \\mathbb{R}^{sp\\times sp\\times 3}\\), where \\(F\\) is the normalization and Fourier embedding [23] of the specific area. The encoded latent code of the patch is \\(\\mathbf{z_v} = \\mathcal{E}(\\mathcal{I}(F(\\mathbf{v})))\\). Our model uses the normalized Fourier embedding as an input to make the model learn the position-content correlation. Formally, our diffusion model is defined as \\(\\hat{\\epsilon}_{\\theta}(\\mathbf{z}_t,t,\\tau_{\\theta}(y),F(\\mathbf{v}))\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.801 + ], + "angle": 0, + "content": "After fine-tuning, the model can generate latent code at different resolutions by giving the positional information directly to the model. The arbitrary resolution image editing is conducted by feeding two inputs to the model: the positional embedding of the whole image; and a randomly sampled noisy latent with the dimension corresponding to the resolution we want. When sampling in an arbitrary resolution, the model can still keep the structure of the original image intact (examples in Fig. 4). It is worth noting that with or without the correct position encoding, our framework still naturally permits retargeting, i.e., maintaining the aspect ratio of salient objects, like SinGAN [44], InGAN [45], and Drop-the-GAN [13]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.632, + 0.832 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implementation Details While our method can be generally applied to different frameworks, we implement it based on the recently released text-to-image LDM, Stable Diffusion [39]. The pre-trained model was trained on \\(512 \\times 512\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "6030" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.203, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.186, + 0.183, + 0.197 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.336, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.185, + 0.333, + 0.201 + ], + "angle": 0, + "content": "\"A painting of a grassland in the style of Vincent Van Gogh\"" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.09, + 0.469, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.185, + 0.456, + 0.201 + ], + "angle": 0, + "content": "\"A photo of a grassland in thunderstorm\"" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.203, + 0.203, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.298, + 0.182, + 0.31 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.203, + 0.335, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.298, + 0.334, + 0.313 + ], + "angle": 0, + "content": "\"A photo of a panda with the Eiffel Tower in the background.\"" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.203, + 0.469, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.298, + 0.45, + 0.312 + ], + "angle": 0, + "content": "\"A photo of a panda on desert\"" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.315, + 0.203, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.409, + 0.183, + 0.42 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.315, + 0.335, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.232, + 0.409, + 0.318, + 0.417 + ], + "angle": 0, + "content": "\"A sculpture of a horse'" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.315, + 0.469, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.369, + 0.409, + 0.451, + 0.416 + ], + "angle": 0, + "content": "\"A cartoon of a horse\"" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.426, + 0.203, + 0.521 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.522, + 0.182, + 0.533 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.426, + 0.335, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.521, + 0.324, + 0.536 + ], + "angle": 0, + "content": "A painting of a girl in the style of Vincent Van Gogh" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.426, + 0.469, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.521, + 0.456, + 0.536 + ], + "angle": 0, + "content": "A painting of a girl in the style of Leonardo da Vinci" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.538, + 0.203, + 0.632 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.633, + 0.183, + 0.644 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.537, + 0.335, + 0.631 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.632, + 0.328, + 0.64 + ], + "angle": 0, + "content": "\"A photo of a Husky in ocean" + }, + { + "type": "image", + "bbox": [ + 0.346, + 0.537, + 0.469, + 0.632 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.633, + 0.459, + 0.64 + ], + "angle": 0, + "content": "\"A cartoon of a dog on grass" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.09, + 0.617, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.186, + 0.596, + 0.197 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.09, + 0.749, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.185, + 0.744, + 0.201 + ], + "angle": 0, + "content": "A painting of a teddy bear in the style of street painting" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.09, + 0.881, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.185, + 0.867, + 0.192 + ], + "angle": 0, + "content": "\"A cartoon of a teddy bear" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.203, + 0.617, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.298, + 0.595, + 0.31 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.203, + 0.749, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.298, + 0.741, + 0.311 + ], + "angle": 0, + "content": "A photo of a tree covered by snow" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.202, + 0.881, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.298, + 0.867, + 0.304 + ], + "angle": 0, + "content": "\"A photo of a tree on fire.\"" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.314, + 0.617, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.41, + 0.595, + 0.42 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.314, + 0.749, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.409, + 0.734, + 0.423 + ], + "angle": 0, + "content": "\"modern art painting of a vase\"" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.314, + 0.881, + 0.408 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.761, + 0.409, + 0.869, + 0.424 + ], + "angle": 0, + "content": "painting of a vase in the style of Vincent Van Gogh" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.426, + 0.617, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.522, + 0.595, + 0.533 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.426, + 0.749, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.521, + 0.745, + 0.536 + ], + "angle": 0, + "content": "\"A photo of a building covered by snow\"" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.426, + 0.881, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.521, + 0.863, + 0.537 + ], + "angle": 0, + "content": "\"A photo of a cyberpunk building.\"" + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.537, + 0.617, + 0.632 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.633, + 0.595, + 0.643 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.537, + 0.749, + 0.632 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.633, + 0.733, + 0.64 + ], + "angle": 0, + "content": "A photo of a jumping cat" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.537, + 0.881, + 0.632 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.773, + 0.633, + 0.872, + 0.647 + ], + "angle": 0, + "content": "\"A photo of a cat wearing a red hat\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.664, + 0.892, + 0.706 + ], + "angle": 0, + "content": "Figure 3. Editing on single source image from various domains. We employ our method on various images and edit them with two target prompts at \\(512 \\times 512\\) resolution. We show the wide range of edits our approach can be used, including but not limited to style transfer, content add-on, posture change, breed change, etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.469, + 0.756 + ], + "angle": 0, + "content": "images from LAION dataset [43]. The spatial size of the latent code from the pre-trained model is \\(64 \\times 64\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "For patch-based fine-tuning, we randomly crop images to patches with height and width uniformly in the range of \\([0.1H, H] \\times [0.1W, W]\\) and resize them to \\(512 \\times 512\\). Experiments are conducted using \\(1 \\times\\) RTX 8000 GPU with a batch size of 1. The base learning rate is set to \\(1 \\times 10^{-6}\\). The number of time steps for the diffusion model, \\(T\\), is 1000. Experiments without and with patch-based fine-tuning are created after 800 and 10,000 optimization steps, respectively. Unless otherwise noted, we adopt other hyperparam-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.726, + 0.892, + 0.786 + ], + "angle": 0, + "content": "eter choices from Stable Diffusion [39], and the results are generated with image resolution \\(512 \\times 512\\) and with latent dimension \\(64 \\times 64\\). For sampling parameters, we choose \\(K = 400\\) and \\(v = 0.7\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.796, + 0.71, + 0.812 + ], + "angle": 0, + "content": "4.1. Qualitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.82, + 0.892, + 0.866 + ], + "angle": 0, + "content": "To better understand various approaches, we collect images from a wide range of domains, i.e., free-to-use high-resolution images from Flickr\\(^1\\) and Unsplash\\(^2\\). During fine" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.875, + 0.652, + 0.888 + ], + "angle": 0, + "content": "1 https://www.flickr.com/" + }, + { + "type": "page_footnote", + "bbox": [ + 0.52, + 0.888, + 0.641, + 0.901 + ], + "angle": 0, + "content": "2https://unsplash.com/" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.875, + 0.652, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6031" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.158, + 0.175, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.229, + 0.172, + 0.241 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.188, + 0.09, + 0.462, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.192, + 0.229, + 0.408, + 0.237 + ], + "angle": 0, + "content": "a) \"a castle in the style of Minecraft\" (512×1024)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.192, + 0.237, + 0.391, + 0.247 + ], + "angle": 0, + "content": "b) \"a Chinese painting of a castle\" \\((512\\times 512)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.192, + 0.247, + 0.439, + 0.257 + ], + "angle": 0, + "content": "c) \"painting of a castle in the style of Hokusai\" (512×768)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.192, + 0.257, + 0.346, + 0.266 + ], + "angle": 0, + "content": "d) \"pixel art of a castle\" \\((512\\times 768)\\)" + }, + { + "type": "list", + "bbox": [ + 0.192, + 0.229, + 0.439, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.337, + 0.175, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.408, + 0.171, + 0.42 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.269, + 0.462, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.193, + 0.407, + 0.428, + 0.416 + ], + "angle": 0, + "content": "a) \"traditional Chinese painting of a lake\" \\((1024\\times 512)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.193, + 0.416, + 0.432, + 0.425 + ], + "angle": 0, + "content": "b) \"a watercolor painting of a lake of a lake\" \\((512\\times 512)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.193, + 0.425, + 0.414, + 0.435 + ], + "angle": 0, + "content": "c) \"an impressionism painting of a lake\" \\((512\\times 512)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.193, + 0.435, + 0.435, + 0.444 + ], + "angle": 0, + "content": "d) \"painting of a lake ... Vincent Van Gogh\" \\((512\\times 1024)\\)" + }, + { + "type": "list", + "bbox": [ + 0.193, + 0.407, + 0.435, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.46, + 0.47, + 0.502 + ], + "angle": 0, + "content": "Figure 4. Arbitrary resolution editing. Our method achieves higher-resolution image editing without artifacts like duplicates, even on ones that change the height-width ratio drastically." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.468, + 0.642 + ], + "angle": 0, + "content": "tuning, we apply a coarse class descriptor to the content we want to preserve, e.g., dog, cat, castle, etc. After optimization, we edit each image with diverse editing prompts. We randomly generate 4 edit results for each image and editing prompt and choose the best one (such a process is also applied to other comparison methods). Our work shows impressive editing ability when applied to various images with different language guidance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.468, + 0.839 + ], + "angle": 0, + "content": "As presented in Fig. 3, using the model-based classifier-free guidance (Sec. 3.2) enables us to apply various editing via text prompts on the single real images. Each image has two text prompts describing different features we want to edit, e.g., image style, background content, the texture of the content, etc. Our method can edit the related features while keeping the content intact. We further show our editing results on arbitrary resolution generation in Fig. 4. For each source image, we edit it with different prompts at various resolutions. As can be seen, our patch-based fine-tuning schedule (Sec. 3.3) successfully preserves the original portion and geometry features of the single source image, even on highly challenging resolution such as \\(512 \\times 1024\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.216, + 0.864 + ], + "angle": 0, + "content": "4.2. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We compare our method to concurrent leading techniques, Textual-Inversion [10] and DreamBooth [40], that" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "can be used for single-image editing. Considering no official implementation has been released for DreamBooth, we adopt an unofficial but well-adopted and highly competitive implementation based on Stable Diffusion [39, 51]. We compare these techniques strictly according to the detailed guidance provided with the implementations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.893, + 0.426 + ], + "angle": 0, + "content": "Fig. 5 shows the comparison results. As can be noticed, our method maintains the fidelity of the images while applying changes as desired. Furthermore, our approach has high authenticity and structural integrity even for higher-resolution editing. For example, in the last row of Fig. 5, when the target prompt is “... standing on grass”, our method generates results by modifying the texture of the land on which the dog stands with other features intact. However, other methods result in a dramatic change in the structure of the whole image. Moreover, in the second row, when modifying the painting Mona Lisa, both Dream-Booth [40] and Textual-Inversion [10] fail to edit the image. Our work also shows clear advantages over the approaches on training-free editorings, such as ILVR [7], SDEdit [32], and Prompt-to-prompt [20], with the qualitative comparisons presented in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.437, + 0.673, + 0.453 + ], + "angle": 0, + "content": "4.3. Ablation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Patch-based fine-tuning. In Fig. 5, we show the results of editing images in higher resolution when fine-tuned without or with the proposed patch-based fine-tuning technique (w/o pos vs. w/ pos). When sampling at a higher resolution, as in the right part of Fig. 5, the denoising model fine-tuned without the patch-based training mechanism performs poorly. In the first row, the castle towers get duplicated to meet the resolution, and in the third row, the bench gets stretched disproportionately. In essence, our patch-based fine-tuning technique enables the diffusion model to leverage the super-resolution ability of the decoder and edit images at arbitrary resolution during testing time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.893, + 0.854 + ], + "angle": 0, + "content": "Analysis of model-based classifier-free guidance. We generate editing results by directly sampling from the fine-tuned model using Eqn. 2. We fine-tune the model without the patch-based schedule for 800 steps to retain more generalization ability. In this case, the model can perfectly reconstruct the source image while preserving as much editing ability as possible. We denote the setting as w/o gudiance. Using the same fine-tuned model, we conduct experiments under model-based classifier-free guidance, denoted as \\(w/\\) guidance. As shown in Fig. 6, sampling without our model-based classifier-free guidance fails to react to the prompt, while our method can successfully edit images to match the target language guidance. We further analyze \\(K\\) and \\(v\\) in model-based classifier-free guidance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Analysis on guidance step \\(K\\) in Sec. 3.2. In Fig. 7, we show our results on editing with different settings of \\(K\\). We conduct this set of experiments by editing one single" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6032" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.093, + 0.162, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.184, + 0.094, + 0.248, + 0.103 + ], + "angle": 0, + "content": "DreamBooth" + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.104, + 0.258, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.265, + 0.094, + 0.348, + 0.103 + ], + "angle": 0, + "content": "Textual-Inversion" + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.104, + 0.347, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.358, + 0.094, + 0.429, + 0.103 + ], + "angle": 0, + "content": "Ours (w/o pos)" + }, + { + "type": "image", + "bbox": [ + 0.354, + 0.104, + 0.434, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.45, + 0.094, + 0.514, + 0.103 + ], + "angle": 0, + "content": "Ours (w/ pos)" + }, + { + "type": "image", + "bbox": [ + 0.443, + 0.104, + 0.523, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.186, + 0.167, + 0.475, + 0.176 + ], + "angle": 0, + "content": "\"Painting of a castle in the style of Vincent Van Gogh\" (H = 512, W = 512)" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.183, + 0.163, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.183, + 0.257, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.183, + 0.346, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.183, + 0.434, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.443, + 0.183, + 0.522, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.186, + 0.244, + 0.5, + 0.254 + ], + "angle": 0, + "content": "\"Oil painting of a lady in the style of Pierre-Auguste Renoir\" (H = 512, W = 512)" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.259, + 0.163, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.259, + 0.257, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.259, + 0.346, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.259, + 0.434, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.443, + 0.259, + 0.522, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.187, + 0.321, + 0.399, + 0.33 + ], + "angle": 0, + "content": "\"A children's drawing of a bench\" \\((H = 512, W = 512)\\)" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.336, + 0.163, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.336, + 0.257, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.266, + 0.336, + 0.346, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.336, + 0.434, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.443, + 0.336, + 0.522, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.186, + 0.397, + 0.37, + 0.407 + ], + "angle": 0, + "content": "\"A dog standing on grass\" \\((H = 512, W = 512)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.094, + 0.61, + 0.103 + ], + "angle": 0, + "content": "DreamBooth" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.104, + 0.62, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.094, + 0.71, + 0.103 + ], + "angle": 0, + "content": "Textual-Inversion" + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.104, + 0.709, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.094, + 0.795, + 0.103 + ], + "angle": 0, + "content": "Ours (w/o pos)" + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.104, + 0.799, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.815, + 0.094, + 0.88, + 0.103 + ], + "angle": 0, + "content": "Ours (w/ pos)" + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.104, + 0.888, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.546, + 0.167, + 0.776, + 0.176 + ], + "angle": 0, + "content": "\"A photo of a castle covered by snow\" (H = 512, W = 768)" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.183, + 0.62, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.183, + 0.708, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.183, + 0.798, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.183, + 0.888, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.547, + 0.244, + 0.825, + 0.254 + ], + "angle": 0, + "content": "\"A sculpture of a lady in the style of Michelangelo\" (H = 768, W = 768)" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.259, + 0.621, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.259, + 0.709, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.259, + 0.798, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.26, + 0.888, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.547, + 0.321, + 0.715, + 0.33 + ], + "angle": 0, + "content": "\"A bench in a desert\" \\((H = 768, W = 768)\\)" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.336, + 0.621, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.336, + 0.709, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.336, + 0.798, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.81, + 0.336, + 0.888, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.547, + 0.397, + 0.821, + 0.406 + ], + "angle": 0, + "content": "\"A sculpture of a dog in the style of Michelangelo\" (H = 768, W = 768)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.421, + 0.894, + 0.505 + ], + "angle": 0, + "content": "Figure 5. Comparisons of various methods. We compare our method to DreamBooth [40] and Textual-Inversion [10]. We adopt default hyper-parameters for both methods provided in their paper or code. On the left part of the figure, we edit at the resolution same as training time. On the right part, we edit the source image at a higher resolution. Our work successfully edits the image as required while preserving the details of the source images. We also compare our method without and with the patch-based fine-tuning mechanism (w/o pos vs. w/ pos). When editing at a fixed resolution, two settings perform equally, while at a higher resolution, the patch-based fine-tuning method successfully prevents artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.47, + 0.676 + ], + "angle": 0, + "content": "image with the same language guidance at \\(768 \\times 768\\) resolution. We set \\(v = 0.7\\). When \\(K = 0\\), the model-based classifier-free guidance is applied for each step of the denoising process. Since the generalization ability of the finetuned model is limited, in this case, the model fails to apply the desired property to the single source image. When \\(K = 1,000\\), the model-based classifier-free guidance is not applied to any step. Thus, the structure of the image is not preserved, and the generated result becomes a random sample of the pre-trained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We further show the quantitative results Fig. 8a. We repeat the abovementioned procedure over different \\( K \\) and randomly sample 20 images for each \\( K \\). We calculate two metrics. To understand the editing result, the image fidelity that is measured by the LPIPS [57] distance between the original and the edited image. The text alignment calculated by the CLIP [36] score to understand the alignment between our generated images and target text. As can be seen, the image fidelity drops with the increase of \\( K \\), indicating more details provided by the pre-trained model instead of the fine-tuned one. The text alignment measurement improves since the more details generated by the pre-trained model, the better editing results align with the target domain. To preserve the edit result's authenticity and fidelity" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.526, + 0.75, + 0.54 + ], + "angle": 0, + "content": "to the source image, we set \\(K\\) as 400." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.835 + ], + "angle": 0, + "content": "Analysis on guidance weight \\( v \\) in Sec. 3.2. We further study the impact of the guidance weight \\( (v) \\) in Fig. 9. We set \\( K = 400 \\) and resolution as \\( 768 \\times 768 \\) for each edit and use the same random seed to generate the result. As can be observed, the value of \\( v \\) controls the fidelity of the edit result. However, since the pre-trained model is trained at the resolution \\( 512 \\times 512 \\), the generated image contains many artifacts. When \\( v = 1 \\), the synthesized image entirely depends on the results from the pre-trained model. Additionally, we conduct quantitative experiments with LPIPS score measuring the image fidelity and CLIP score for the text alignment in Fig. 8b. When \\( v \\) is close to 1, the fidelity decreases while the edited feature decreases. When \\( v \\) is close to 0, the model relies mainly on the fine-tuned model for the output when \\( t > K \\). However, since the fine-tuned model contains poor generalization ability, there is a significant amount of artifacts in the generated results, which leads to a poor LPIPS score. We choose 0.7 for each edit in this work as a trade-off between fidelity and creativity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Other analysis. We defer the analysis of model-based classifier-free guidance with multiple inputs and fine-tuning without coarse class descriptor or prior-preservation loss to the supplementary materials." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "6033" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.093, + 0.442, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.439, + 0.47, + 0.509 + ], + "angle": 0, + "content": "Figure 6. Analysis of model-based classifier-free guidance. Directly sampling with target text using the fine-tuned model (w/o guidance) fails to generate images corresponding to the text prompt. In contrast, the model-based classifier-free guidance (w/guidance) can synthesize high-fidelity images." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.518, + 0.452, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.706, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Figure 7. Analysis on guidance step \\( K \\). Varying \\( K \\), we can decide the steps where the model-based guidance is applied, which controls the details from the source image and edits to be applied." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.769, + 0.196, + 0.785 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "This work introduces SINE, a method for single-image editing. With only one image and a brief description of the object in the image, our approach can enable a wide range of editing for arbitrary resolution, followed by the information depicted in the language guidance. To achieve such results, we leverage the pre-trained large-scale text-to-image diffusion model. Specifically, we first fine-tune the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.1, + 0.695, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.203, + 0.695, + 0.216 + ], + "angle": 0, + "content": "(a) Number of steps of the guidance." + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.1, + 0.888, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.203, + 0.866, + 0.216 + ], + "angle": 0, + "content": "(b) Weight of the guidance." + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.221, + 0.892, + 0.291 + ], + "angle": 0, + "content": "Figure 8. Trade-off between fidelity and alignment with target text. We calculate the CLIP score [36] (a higher CLIP score indicates a better alignment between the edit result and target text) and 1-LPIPS score [57] (showing the fidelity between edit results and source image, the higher, the better)." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.298, + 0.871, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.585, + 0.891, + 0.613 + ], + "angle": 0, + "content": "Figure 9. Analysis of score interpolation. Varying \\( v \\) with the same random seed gets editing results with various qualities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.755 + ], + "angle": 0, + "content": "pre-trained model with our patch-based fine-tuning method until it overfits the single image. Then, during sampling time, we use the overfitted model to guide the pre-trained diffusion model for image synthesis, which maintains the fidelity of the results while taking advantage of the generalization ability of the pre-trained model. Compared with other methods, our approach has a better geometrical understanding of the image and thus can conduct complex editing to the images besides style transfer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.892, + 0.846 + ], + "angle": 0, + "content": "However, in some cases where confusing editing guidance is given for the diffusion model, e.g., a chair-shaped dog, our method could fail. In cases where drastic changes are to be applied, e.g., changing a dog to a tiger in the same posture, there are also noticeable artifacts. We show more examples in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.846, + 0.891, + 0.891 + ], + "angle": 0, + "content": "One future direction is improving the fidelity of the editing results, which could be achieved by alleviating the overfitting problem of the fine-tuned model." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6034" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. Clip2stylegan: Unsupervised extraction of stylegan edit directions. 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Such success inspires many efforts trying to use large-scale pre-trained diffusion models for tackling a challenging problem—real image editing. Works conducted in this area learn a unique textual token corresponding to several images containing the same object. However, under many circumstances, only one image is available, such as the painting of the Girl with a Pearl Earring. Using existing works on fine-tuning the pretrained diffusion models with a single image causes severe overfitting issues. The information leakage from the pretrained diffusion models makes editing can not keep the same content as the given image while creating new features depicted by the language guidance. This work aims to address the problem of single-image editing. We propose a novel model-based guidance built upon the classifier-free guidance so that the knowledge from the model trained on a single image can be distilled into the pre-trained diffusion model, enabling content creation even with one given image. Additionally, we propose a patch-based fine-tuning that can effectively help the model generate images of arbitrary resolution. We provide extensive experiments to validate the design choices of our approach and show promising editing capabilities, including changing style, content addition, and object manipulation. Our code is made publicly available here. + +# 1. Introduction + +Automatic real image editing is an exciting direction, enabling content generation and creation with minimal effort. Although many works have been conducted in this area, achieving high-fidelity semantic manipulation on an image is still a challenging problem for the generative models, considering the target image might be out of the training data distribution [4, 11, 25, 26, 32, 58, 59]. The recently introduced large-scale text-to-image models, e.g., DALL-E 2 [37], Imagen [42], Parti [55], and StableDiffusion [39], can perform high-quality and diverse image generation with + +![](images/4473db6967966510f908112ae0fe0c7bb78546190cc147e946dfdf826dc4f5c7.jpg) + +![](images/352273be6c2aff332a4a822ac67e7b28d285929e39000f8165c2c6d7564ebba5.jpg) + +![](images/e9c527720118609eca22387f085b8165ebe0e27c171fc027446fd68eb627034e.jpg) + +![](images/0b0e052b18dac938e485dac492c788c57a19386e68ce98d730968bcda528cbfb.jpg) + +"....super- hero cape + +![](images/357cf2d0f4a1daae8f1ab7248aa552c922ddf5ed6e8a01ab86da0729d7a531d3.jpg) + +"...super- hero cape + +![](images/8eb6a3b5a84c472c5f2df5e3d30d6149a0dfcbfb04c0aceefa5c7e2da6305cef.jpg) +Source Image +Source Image +Figure 1. With only one real image, i.e., Source Image, our method is able to manipulate and generate the content in various ways, such as changing style, adding context, modifying the object, and enlarging the resolution, through guidance from the text prompt. + +![](images/e617549f197f219fadeb206b50a9ab6084d651b67a78c0e2b3f184d124720bf8.jpg) +sculpture +Source Image +.covered by snow + +![](images/c93c3c63a831182fa3baf26c17fa0d1e822da042d51fa8aa3ca976610e8673d8.jpg) +Source Image + +![](images/a98daf320862c44f342cee5c7e67b667912e0be136a6c17e2d6632fa255425dd.jpg) +"coffee machine..." "coffee maker..." +in snow +blossom street + +natural language guidance. The success of these works has inspired many subsequent efforts to leverage the pre-trained large-scale models for real image editing [10, 15, 20, 40]. They show that, with properly designed prompts and a limited number of fine-tuning steps, the text-to-image models can manipulate a given subject with text guidance. + +On the downside, the recent text-guided editing works that build upon the diffusion models suffer several limitations. First, the fine-tuning process might lead to the pretrained large-scale model overfit on the real image, which degrades the synthesized images' quality when editing. To tackle these issues, methods like using multiple images with the same content and applying regularization terms on the same object have been introduced [4, 40]. However, querying multiple images with identical content or object might not be an available choice; for instance, there is only one painting for Girl with a Pearl Earring. Directly editing the single image brings information leakage from the pretrained large-scale models, generating images with different content (examples in Fig. 5); therefore, the application scenarios of these methods are greatly constrained. Second, these works lack a reasonable understanding of the object geometry for the edited image. Thus, generating images with different spatial size as the training data cause undesired artifacts, e.g., repeated objects, and incorrectly modified geometry (examples in Fig. 5). Such drawbacks restrict applying these methods for generating images with an arbitrary resolution, e.g., synthesizing high-resolution images from a single photo of a castle (as in Fig. 4), again limiting + +the usage of these methods. + +In this work, we present SINE, a framework utilizing pre-trained text-to-image diffusion models for SINgle image Editing and content manipulation. We build our approach based upon existing text-guided image generation approaches [10, 40] and propose the following novel techniques to solve overfitting issues on content and geometry, and language drift [28, 31]: + +- First, by appropriately modifying the classifier-free guidance [22], we introduce model-based classifier-free guidance that utilizes the diffusion model to provide the score guidance for content and structure. Taking advantage of the step-by-step sampling process used in diffusion models, we use the model fine-tuned on a single image to plant a content "seed" at the early stage of the denoising process and allow the pre-trained large-scale text-to-image model to edit creatively conditioned with the language guidance at a later stage. +- Second, to decouple the correlation between pixel position and content, we propose a patch-based fine-tuning strategy, enabling generation on arbitrary resolution. + +With a text descriptor describing the content that is aimed to be manipulated and language guidance depicting the desired output, our approach can edit the single unique image to the targeted domain with details preserved in arbitrary resolution. The output image keeps the structure and background intact while having features well-aligned with the target language guidance. As shown in Fig. 1, trained on a painting Girl with a Pearl Earring with resolution as $512 \times 512$ , we can sample an image of a sculpture of the girl at the resolution of $640 \times 512$ with the identity features preserved. Moreover, our method can successfully handle various edits such as style transfer, content addition, and object manipulation (more examples in Fig. 3). We hope our method can further boost creative content creation by opening the door to editing arbitrary images. + +# 2. Related Work + +Text-guided image synthesis has drawn considerable attention in the generative model context [1, 2, 6, 12, 14, 16-19, 34, 35, 38, 50, 53-56, 60]. The recent development of diffusion models [21, 46, 47, 49] introduced new solutions to this problem and produced impressive results [33, 37, 39, 42]. With the significant improvement of these models, rather than training a large-scale text-to-image model from scratch, a leading line of works focuses on taking advantage of the existing pre-trained model and manipulating images according to given natural language guidance [3, 10, 20, 24, 29, 40]. In these works, studies explore text-based interfaces for image editing [1, 3, 35], style transfer [27, 30], and generator domain adaption [11, 25, 48]. + +The development of the diffusion model provides a giant and flexible design space for this task. Many works utilize pre-trained diffusion models as generative priors and are training-free. ILVR [7] guides the denoising process by replacing the low-frequency part of the sample with that of the target reference image. SDEdit [32] applies the diffusion process first on an image or a user-created semantic map and then conducts the denoising procedure conditioned with the desired output. Blended diffusion [3] performs language-guided inpainting with a given mask. + +Another line of research showed great potential and semantic editing ability of fine-tuning. DiffusionCLIP [25] leverages the CLIP [36] model to provide gradients for image manipulation and deliver impressive results on style transfer. Textual-Inversion [10] and DreamBooth [40] fine-tune the text embedding or the full diffusion model using a few personalized images (typically $3 \sim 5$ ) to synthesize images of the same object in a novel context. These methods, however, either drastically change the layout of the original image when dealing with a single image or can not fully leverage the generalization ability of the pre-trained model for editing due to overfitting or language drift. Notably, Prompt-to-Prompt [20] controls the editing of synthesized images by manipulating the cross-attention maps; however, its editing ability is limited when applied to real images. Imagic [24], while delivering realistic results, requires fine-tuning process on each editing prompt for each image, leading to longer inference time. + +This work introduces a solution to achieve image fidelity and text alignment simultaneously. Our method can perform high-quality semantic editing globally and locally on one single image. On the other hand, previous works lack an understanding of the object geometry of the edited image. When editing the image at an arbitrary resolution, the artifacts in the results will be obvious. Prior works have investigated generating images at arbitrary resolution using positional encoding as inductive bias [41, 52, 52] so that the correlation between content and position can be eliminated. Anyres-GAN [5] adopt a patch training mechanism to leverage high-resolution data to help the generation of images in the low-resolution domain. We propose a patch-based fine-tuning method to achieve arbitrary resolution editing. + +# 3. Methods + +For one arbitrary in-the-wild image, our goal is to edit the image via language while preserving the maximal amount of details from the original image. To do so, we leverage the generalization ability of pre-trained large-scale text-to-image models [39]. An intuitive approach is to fine-tune the diffusion models with the single image and text description, similar to DreamBooth [40]. Ideally, it should provide a model that can reconstruct the input image using the given text descriptor and synthesize new images when + +given other language guidance. Unfortunately, we find the model can easily overfit the single trained image and its corresponding text description. Thus, although the fine-tuned model can still reconstruct the input image perfectly, it can no longer synthesize diverse images according to the given language guidance (as shown in Fig. 5). Moreover, it struggles to generate arbitrary resolution images due to the lack of positional information (as in Fig. 4). + +To solve the above issues, we propose a test-time model-based classifier-free guidance and a patch-based fine-tuning technique. An overview of our method is illustrated in Fig. 2. In the following sections, we review the backbone model used in our approach (Sec. 3.1). Then, we describe how to overcome the overfitting problem with model-based guidance (Sec. 3.2). Lastly, we present how to address the problem of limited resolution generation (Sec. 3.3). + +# 3.1. Language-Guided Diffusion Models + +We use the latent diffusion models (LDMs) [39] trained on a large-scale dataset as our base model and implement the proposed approaches by fine-tuning the pre-trained model. LDMs is a class of Denoising Diffusion Probabilistic Models (DDPMs) [21] that contains an auto-encoder trained on images, and a diffusion model learned on the latent space constructed by the auto-encoder. The encoder $\mathcal{E}$ encodes a given image $\mathcal{I} \in \mathbb{R}^{H \times W \times 3}$ to a latent representation $\mathbf{z}$ , such that $\mathbf{z} = \mathcal{E}(\mathcal{I})$ . The decoder $\mathcal{D}$ reconstructs the estimated image $\tilde{\mathcal{I}}$ from the latent, such that $\tilde{\mathcal{I}} = \mathcal{D}(\mathbf{z})$ and $\tilde{\mathcal{I}} \approx \mathcal{I}$ . The diffusion model is trained to produce latent codes within the pre-trained latent space. The most intriguing property of LDMs is that the diffusion model can be conditioned on class labels, images, and text prompt. The conditional LDM is learned as follows: + +$$ +L _ {L D M} := \mathbb {E} _ {\mathcal {E} (\mathcal {I}), y, \boldsymbol {\epsilon} \sim \mathcal {N} (0, 1), t} \left[ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} (\mathbf {z} _ {t}, t, \boldsymbol {\tau} _ {\theta} (y)) \| _ {\mathbf {2}} ^ {2} \right], \quad (1) +$$ + +where $t$ is the time step, $\mathbf{z}_t$ is the latent noised to time $t$ , $\epsilon$ is the unscaled noise sample, $\epsilon_{\theta}$ is the denoising model, $y$ is the conditioning input, and $\tau_{\theta}$ maps $y$ to a conditioning vector. During training time, $\epsilon_{\theta}$ and $\tau_{\theta}$ are jointly optimized. A random noise tensor is sampled and denoised at inference time based on the conditioning input, e.g., text prompt, to produce a new latent. Inspired by DreamBooth [40], we construct the text prompt for fine-tuning a single image as "a photo/painting of a [*] [class noun]", where "[*]" is a unique identifier and "[class noun]" is a coarse class descriptor (e.g., "castle", "lake", "car", etc.). + +# 3.2. Model-Based Classifier-Free Guidance + +With the above-presented LDMs, we introduce our approach, inspired by classifier-free guidance, to overcome overfitting when fine-tuning LDMs with one image. + +Classifier-free guidance [22] is a technique widely adopted by prior text-to-image diffusion models [39, 42]. A single + +![](images/10d7bf218339218e4056f5f911416fc38ce1fb9abfdafc040b7dd111226e1e1c.jpg) + +![](images/75f085c3287505c4744b9df41e91aae613af74fecde4e53aedcd37a169fecd53.jpg) +Figure 2. Overview of our method. (a) Given a source image, we first randomly crop it into patches and get the corresponding latent code $\mathbf{z}$ with the pre-trained encoder. At fine-tune time, the denoising model, $\epsilon_{\theta}$ , takes three inputs: noisy latent $\mathbf{z}_T$ , language condition $\mathbf{c}$ , and positional embedding for the area where the noisy latent is obtained. (b) During sampling, we give additional language guidance about the target domain to edit the image. Also, we sample a noisy latent code $\mathbf{z}_T$ with the dimension corresponding to the desired output resolution. Language conditioning for $\epsilon_{\theta}$ and $\mathbf{c}$ are given by pre-trained language encoder $\tau_{\theta}$ with the target language guidance. While for the fine-tuned diffusion model, $\hat{\epsilon}_{\theta}$ , in addition to the language conditioning $\hat{\mathbf{c}}$ , we also input the positional embedding for the whole image. We employ a linear combination between the score calculated by each model for the first $K$ steps and inference only on pre-trained $\epsilon_{\theta}$ after. + +diffusion model is trained using conditional and unconditional objectives by randomly dropping the condition during training. When sampling, a linear combination of the conditional and unconditional score estimation is used: + +$$ +\tilde {\mathbf {e}} _ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c}\right) = w \boldsymbol {\epsilon} _ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c}\right) + (1 - w) \boldsymbol {\epsilon} _ {\theta} \left(\mathbf {z} _ {t}\right), \tag {2} +$$ + +where $\epsilon_{\theta}(\mathbf{z}_t,\mathbf{c})$ and $\epsilon_{\theta}(\mathbf{z}_t)$ are the conditional and unconditional $\epsilon$ -predictions, $\mathbf{c}$ is the conditioning vector generated by $\tau_{\theta}$ , and $w$ is the weight for the guidance. The predication is performed using the Tweedie's formula [8], namely, $(\mathbf{z}_t - \sigma_t\tilde{\epsilon}_{\theta}) / \alpha_t$ , where $\alpha_{t}$ and $\sigma_{t}$ are functions of + +$t$ that affect the sampling quality. + +Since we only have one image as the training data, e.g., painting of Mona Lisa, and one corresponding text descriptor of that image, the diffusion model suffers from overfitting, and severe language drifts after fine-tuning [40]. As a result, the fine-tuned model fails to synthesize images containing features from other language guidance. The overfitting issue might be due to only one repeated prompt used during fine-tuning, making other text prompts no longer accurate enough to control editing (see examples in Fig. 6). + +Model-based classifier-free guidance. Existing "personalized" text-guided real image editing works only use one fine-tuned model for image generation and editing [10, 20, 40], ignoring the capacity of pre-trained large-scale text-to-image models. Instead, to alleviate the overfitting of the fine-tuned model, we leverage the pre-trained text-to-image model for image generation with the provided language guidance and use the fine-tuned model to provide content features in a fashion of combining scores from the two models, similar to classifier-free guidance. + +Specifically, let $\hat{\epsilon}_{\theta}$ denote the fine-tuned denoising model, and $\epsilon_{\theta}$ denote the pre-trained text-to-image model. During sampling, at specified steps, we use our fine-tuned model to guide the pre-trained one by using a linear combination of the scores from each model. Thus, the score estimation in Eqn. 2 becomes: + +$$ +\begin{array}{l} \tilde {\boldsymbol {\epsilon}} _ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c}\right) = w \left(v \boldsymbol {\epsilon} _ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c}\right) + (1 - v) \hat {\boldsymbol {\epsilon}} _ {\theta} \left(\mathbf {z} _ {t}, \hat {\mathbf {c}}\right)\right) \tag {3} \\ + (1 - w) \epsilon_ {\theta} \left(\mathbf {z} _ {t}\right), \\ \end{array} +$$ + +where $v$ stands for the model guidance weight, $\hat{\mathbf{c}}$ is the language guidance token obtained from the fine-tuned diffusion model with the text prompt used during fine-tuning, and $\mathbf{c}$ is the target language conditioning obtained from the target prompt. + +To prevent artifacts from the over-fitted model and maintain the fidelity of the generated image, we propose to sample using Eqn. 3 with $t > K$ and sample using Eqn. 2 for $t \leq K$ . From $K$ to 0, the denoising process only depends on the pre-trained model. Following this approach, we can fully leverage the generalization ability of the pre-trained model (examples in Fig. 6). Also note that this method could be generalized to include multiple prompts or even multiple modalities. + +# 3.3. Patch-Based Fine-Tuning + +With model-based classifier-free guidance, we are able to edit and manipulate a single image with given language guidance. Here, we further show how to improve the finetuning process for a single training image so that the finetuned model can better understand the content and geometry of the image. Thus, it can provide better content guidance for the large-scale text-to-image model during the sampling + +time and unleash the potential for generating arbitrary-resolution images [9]. + +Limited-resolution generation. We first review the limitations of the current fine-tuning process. Given an input image $\mathcal{I}$ with resolution as $H\times W$ , we can obtain a downsampled latent code $\mathbf{z}$ from the pre-trained encoder. Since the text-to-image diffusion model is pre-trained at a fixed resolution, i.e., $p\times p$ , we need to resize the input image to a corresponding resolution $sp\times sp$ , where $s$ represents the scaling factor of the encoder, to match the resolution for reducing the fine-tuning cost. In essence, prior knowledge of the correlation between the position and content information is learned by the diffusion model. Thus, when sampling from a higher-resolution noise tensor, the generated latent code leads to artifacts like duplicates or position shifting (visual examples in Fig. 5). To tackle such drawbacks, we propose a simple yet effective fine-tuning method. + +Patch-based fine-tuning. Inspired by Chai et al. [5], we treat our single training image as a function on coordinate for each pixel, bounded in $[0,H]\times [0,W]$ . The diffusion model still generates latent code at the fixed resolution $p\times p$ , but each latent code corresponds to a sub-area in the image. We denote the sub-area as $\mathbf{v} = [h_1,w_1,h_2,w_2]$ where $(h_1,w_1)\in [0,H]\times [0,W]$ and $(h_2,w_2)\in (h_1,H]\times (w_1,W]$ indicate the top-left and bottom-right coordinates of the area, respectively. During fine-tuning, we sample patches from the image with different $\mathbf{v}$ and resize the patches to resolution $sp$ . We denote the resulted patch as $\mathcal{I}(F(\mathbf{v}))\in \mathbb{R}^{sp\times sp\times 3}$ , where $F$ is the normalization and Fourier embedding [23] of the specific area. The encoded latent code of the patch is $\mathbf{z_v} = \mathcal{E}(\mathcal{I}(F(\mathbf{v})))$ . Our model uses the normalized Fourier embedding as an input to make the model learn the position-content correlation. Formally, our diffusion model is defined as $\hat{\epsilon}_{\theta}(\mathbf{z}_t,t,\tau_{\theta}(y),F(\mathbf{v}))$ . + +After fine-tuning, the model can generate latent code at different resolutions by giving the positional information directly to the model. The arbitrary resolution image editing is conducted by feeding two inputs to the model: the positional embedding of the whole image; and a randomly sampled noisy latent with the dimension corresponding to the resolution we want. When sampling in an arbitrary resolution, the model can still keep the structure of the original image intact (examples in Fig. 4). It is worth noting that with or without the correct position encoding, our framework still naturally permits retargeting, i.e., maintaining the aspect ratio of salient objects, like SinGAN [44], InGAN [45], and Drop-the-GAN [13]. + +# 4. Experiments + +Implementation Details While our method can be generally applied to different frameworks, we implement it based on the recently released text-to-image LDM, Stable Diffusion [39]. The pre-trained model was trained on $512 \times 512$ + +![](images/f34c956731ecece0480bee50f95cc1769eee653ee8c13ef44fa6d2e0a151d8b9.jpg) +Source Image + +![](images/854217ca5e3aea56c9eb9fef4474b9599f29467598ec6e59c99023acefa0a278.jpg) +"A painting of a grassland in the style of Vincent Van Gogh" + +![](images/c6a80a5a77689b01a2fb52bd260c37f836d92041b574ea71c32c1abdc149320c.jpg) +"A photo of a grassland in thunderstorm" + +![](images/727433d7d560b4c7bdbd3b1238bb1fd810fd9f4c42b28945ceec114181fc9437.jpg) +Source Image + +![](images/ff5d2a089f273753ad1fa52a640ceb3b41ab10dfa8b51242cb4137827a26793d.jpg) +"A photo of a panda with the Eiffel Tower in the background." + +![](images/13ab2f4ef893fd5c08df4bfd009bdedf14fb39f7b4a0b106a06886d4cc979443.jpg) +"A photo of a panda on desert" + +![](images/0e0d62ea9e1e1a9808f5b1d26950e3a1b98c0d8115c6ac0210591b1e6827fdae.jpg) +Source Image + +![](images/2e2e4af7c4237b53f5ffd5309513d59ff299e651737cfed38d63d4274f5985f8.jpg) +"A sculpture of a horse' + +![](images/8cfac96062fb1fb92f29b89413f256f22b4c9cda59f45d19d82235ca97afb32c.jpg) +"A cartoon of a horse" + +![](images/d6fec66843ef989d41043cafa266b93a6c34f505e74371ec5b4ccd8237ffc96e.jpg) +Source Image + +![](images/94d7d7ff586fe361466cacfad66558df44f168d8fde5ed73fde2407b57fe6871.jpg) +A painting of a girl in the style of Vincent Van Gogh + +![](images/b9ba6ca735fd630ed46f5e2b4a322bf44966463eb1ed4d6803955806ca576563.jpg) +A painting of a girl in the style of Leonardo da Vinci + +![](images/d405e70c3c8f7e7b7b14e8e2c06a27682ed640cf4060c0bb310b27113e57073d.jpg) +Source Image +Figure 3. Editing on single source image from various domains. We employ our method on various images and edit them with two target prompts at $512 \times 512$ resolution. We show the wide range of edits our approach can be used, including but not limited to style transfer, content add-on, posture change, breed change, etc. + +![](images/327877203c031c6f8519af4b0957bbaa4533b3d0310245bc087da64bc4292051.jpg) +"A photo of a Husky in ocean + +![](images/80caa11582c13bcff91c45afe1f3afe124b24fa52ce5b77c42a1f5693920c7e8.jpg) +"A cartoon of a dog on grass + +![](images/db008e4f146691913ee3c35dfdd4070fa504cf313b627e78683523e755a5e7c0.jpg) +Source Image + +![](images/90004821aebaa50973b2b507afae692ac61d53d4216835dfbc644ea48a159af9.jpg) +A painting of a teddy bear in the style of street painting + +![](images/037b81f3b2ea405fd79577f89f615ae024672f54ca9fc24b8f2376e648256f22.jpg) +"A cartoon of a teddy bear + +![](images/8d26b0681765f3e77e48c6bdacfe50ca673a088f248f92fd7070813fa96f0fbe.jpg) +Source Image + +![](images/39d3b7b7d56090c4739b3e3a3f729f0110d2153190c6d5bab5f69683c426155b.jpg) +A photo of a tree covered by snow + +![](images/7090ff21cbf110aea1b68bbcd1cdeee006fc8b1225fbadc7e6764026b3f4d741.jpg) +"A photo of a tree on fire." + +![](images/0674a845cdd635365acb05fd88180b8ecedf6aad26f3b9f7d1d8e5487824df59.jpg) +Source Image + +![](images/031a2995fbd9e734df9f84c2954530f0be8c84d94a958b2c95ad496b3beb2324.jpg) +"modern art painting of a vase" + +![](images/71c48181f4cfa9044b95217eb6c7cd3d8b7c530b3dd7aec04f14cbc755c92c64.jpg) +painting of a vase in the style of Vincent Van Gogh + +![](images/967a7935475ea0855e0fa53a7bc03035d3f624b1661eff0947cabe622d98076d.jpg) +Source Image + +![](images/af30fe703138d50ec9e42599135fb38daa2f93f6822e04a19a3bae521a045831.jpg) +"A photo of a building covered by snow" + +![](images/1f9a5e2a35098ca76215bbb7638485c42c14fed678e8ce783f5f6ec193b9142e.jpg) + +![](images/77ccb2b730429ffaafd624cc36c69f9136bfe2d66321f5c451c38eb3e957d6c9.jpg) +Source Image + +![](images/98359eb6a6e51b5bb0781de43c430f2461a0b729601dee841afdab83e4e8b6ac.jpg) +A photo of a jumping cat + +![](images/44f2c898f91cb85608ba4568c94cd02507f9e4a80976d0cca6467311f1d9393a.jpg) +"A photo of a cyberpunk building." +"A photo of a cat wearing a red hat" + +images from LAION dataset [43]. The spatial size of the latent code from the pre-trained model is $64 \times 64$ . + +For patch-based fine-tuning, we randomly crop images to patches with height and width uniformly in the range of $[0.1H, H] \times [0.1W, W]$ and resize them to $512 \times 512$ . Experiments are conducted using $1 \times$ RTX 8000 GPU with a batch size of 1. The base learning rate is set to $1 \times 10^{-6}$ . The number of time steps for the diffusion model, $T$ , is 1000. Experiments without and with patch-based fine-tuning are created after 800 and 10,000 optimization steps, respectively. Unless otherwise noted, we adopt other hyperparam- + +eter choices from Stable Diffusion [39], and the results are generated with image resolution $512 \times 512$ and with latent dimension $64 \times 64$ . For sampling parameters, we choose $K = 400$ and $v = 0.7$ . + +# 4.1. Qualitative Evaluation + +To better understand various approaches, we collect images from a wide range of domains, i.e., free-to-use high-resolution images from Flickr $^1$ and Unsplash $^2$ . During fine + +![](images/ed2602eb596955db2800c2cd67ed525d440c94721540502c5701ca37181537f1.jpg) +Source Image + +![](images/baeb93a3a9467749fb5d3b425806360757e4d161dbed652cf19ebe12651b5916.jpg) +a) "a castle in the style of Minecraft" (512×1024) + +![](images/299a06c29139e399cd7955779924083f6a2949b49d5e87a29e35f37617edc4e5.jpg) +Source Image + +Figure 4. Arbitrary resolution editing. Our method achieves higher-resolution image editing without artifacts like duplicates, even on ones that change the height-width ratio drastically. +![](images/d00049e1355d763bc627d0066b09e34381872eec8255a58d57b029b570548992.jpg) +b) "a Chinese painting of a castle" $(512\times 512)$ +c) "painting of a castle in the style of Hokusai" (512×768) +d) "pixel art of a castle" $(512\times 768)$ +a) "traditional Chinese painting of a lake" $(1024\times 512)$ +b) "a watercolor painting of a lake of a lake" $(512\times 512)$ +c) "an impressionism painting of a lake" $(512\times 512)$ +d) "painting of a lake ... Vincent Van Gogh" $(512\times 1024)$ + +tuning, we apply a coarse class descriptor to the content we want to preserve, e.g., dog, cat, castle, etc. After optimization, we edit each image with diverse editing prompts. We randomly generate 4 edit results for each image and editing prompt and choose the best one (such a process is also applied to other comparison methods). Our work shows impressive editing ability when applied to various images with different language guidance. + +As presented in Fig. 3, using the model-based classifier-free guidance (Sec. 3.2) enables us to apply various editing via text prompts on the single real images. Each image has two text prompts describing different features we want to edit, e.g., image style, background content, the texture of the content, etc. Our method can edit the related features while keeping the content intact. We further show our editing results on arbitrary resolution generation in Fig. 4. For each source image, we edit it with different prompts at various resolutions. As can be seen, our patch-based fine-tuning schedule (Sec. 3.3) successfully preserves the original portion and geometry features of the single source image, even on highly challenging resolution such as $512 \times 1024$ . + +# 4.2. Comparisons + +We compare our method to concurrent leading techniques, Textual-Inversion [10] and DreamBooth [40], that + +can be used for single-image editing. Considering no official implementation has been released for DreamBooth, we adopt an unofficial but well-adopted and highly competitive implementation based on Stable Diffusion [39, 51]. We compare these techniques strictly according to the detailed guidance provided with the implementations. + +Fig. 5 shows the comparison results. As can be noticed, our method maintains the fidelity of the images while applying changes as desired. Furthermore, our approach has high authenticity and structural integrity even for higher-resolution editing. For example, in the last row of Fig. 5, when the target prompt is “... standing on grass”, our method generates results by modifying the texture of the land on which the dog stands with other features intact. However, other methods result in a dramatic change in the structure of the whole image. Moreover, in the second row, when modifying the painting Mona Lisa, both Dream-Booth [40] and Textual-Inversion [10] fail to edit the image. Our work also shows clear advantages over the approaches on training-free editorings, such as ILVR [7], SDEdit [32], and Prompt-to-prompt [20], with the qualitative comparisons presented in the supplementary materials. + +# 4.3. Ablation Analysis + +Patch-based fine-tuning. In Fig. 5, we show the results of editing images in higher resolution when fine-tuned without or with the proposed patch-based fine-tuning technique (w/o pos vs. w/ pos). When sampling at a higher resolution, as in the right part of Fig. 5, the denoising model fine-tuned without the patch-based training mechanism performs poorly. In the first row, the castle towers get duplicated to meet the resolution, and in the third row, the bench gets stretched disproportionately. In essence, our patch-based fine-tuning technique enables the diffusion model to leverage the super-resolution ability of the decoder and edit images at arbitrary resolution during testing time. + +Analysis of model-based classifier-free guidance. We generate editing results by directly sampling from the fine-tuned model using Eqn. 2. We fine-tune the model without the patch-based schedule for 800 steps to retain more generalization ability. In this case, the model can perfectly reconstruct the source image while preserving as much editing ability as possible. We denote the setting as w/o gudiance. Using the same fine-tuned model, we conduct experiments under model-based classifier-free guidance, denoted as $w/$ guidance. As shown in Fig. 6, sampling without our model-based classifier-free guidance fails to react to the prompt, while our method can successfully edit images to match the target language guidance. We further analyze $K$ and $v$ in model-based classifier-free guidance. + +Analysis on guidance step $K$ in Sec. 3.2. In Fig. 7, we show our results on editing with different settings of $K$ . We conduct this set of experiments by editing one single + +![](images/c947fdaf5a0056d2564f2732369fcce3fcfe6910e456a4ca3b04805b4ee00817.jpg) + +DreamBooth +![](images/6a0b4a9e74725309591d6648683692e03b74f316c24442dfa85e6d6962e6c26a.jpg) +"Painting of a castle in the style of Vincent Van Gogh" (H = 512, W = 512) + +![](images/5309a48bedb1af578143cad60c14d30f8f1218524577e24f7d8dc73495f29111.jpg) +Textual-Inversion + +![](images/55fbba9591a6f438f71fcfccf22b5f7281a81fcd77b1bad2215e9732b9f2ea90.jpg) +Ours (w/o pos) + +![](images/f41a89368d9d27791389fd5136c9a25b27b0a3e8a51eb653117bf7926b97ddde.jpg) +Ours (w/ pos) + +![](images/fa446fbb7385d891128b08b8cc2bb84e3fddab8536e80d748848ca62c5ed73d6.jpg) + +![](images/0217a26c494f0ecd07becffe96fefebb24e9fdff245734613532b3c150d2ac2b.jpg) +"Oil painting of a lady in the style of Pierre-Auguste Renoir" (H = 512, W = 512) + +![](images/8d1464c1c47842cd598a989af36af96868904e216ed20955d7dc846bef5af7b2.jpg) + +![](images/ca99e132445b3c41f3d9586b13bd571d95e969555638d111fffc92595362251a.jpg) + +![](images/b71be9b70290fb39ff6b333026d8c53cde3202d58aed94ba188b3b0f5e4ee7a3.jpg) + +![](images/beaf3796f7f20eafc75d629f1f8f19342dde18abebc006aeb48d2c8b6176fa34.jpg) + +![](images/a66dbf82e5f3490e22fd54ce620582d75d4c6e6d638a44d1d16d730dbf092a85.jpg) +"A children's drawing of a bench" $(H = 512, W = 512)$ + +![](images/0263b2c6ebf7e11559065709cf407e5f5fbcdfac692e28a5a9fa051611d64b12.jpg) + +![](images/715de4845f822e8a4c35cf5630dc18f83b95530b0835f8eb572b3aca00a85fc5.jpg) + +![](images/8fbe6aa27e0b2cd0f9d025ee1f149fdeb520a7c00feac82965eed13027e8e378.jpg) + +![](images/ef35aeffa1b8e1449f1bfe7c7dbffe267b3c7770f10b49ad1d75076b70d00608.jpg) +Figure 5. Comparisons of various methods. We compare our method to DreamBooth [40] and Textual-Inversion [10]. We adopt default hyper-parameters for both methods provided in their paper or code. On the left part of the figure, we edit at the resolution same as training time. On the right part, we edit the source image at a higher resolution. Our work successfully edits the image as required while preserving the details of the source images. We also compare our method without and with the patch-based fine-tuning mechanism (w/o pos vs. w/ pos). When editing at a fixed resolution, two settings perform equally, while at a higher resolution, the patch-based fine-tuning method successfully prevents artifacts. + +![](images/f35ff5b697327ab8b884e82ed7840bac4737b2d3437ac9aa4fde33f4129527a2.jpg) +"A dog standing on grass" $(H = 512, W = 512)$ + +![](images/1b855bfef3d57512dd15d17b37fa4307509ad09c5dbbdb75b4a189cb7704cfba.jpg) + +![](images/a7ae117f047cf219c88a585f33e341b567cecd81b669b73c60653622126ad931.jpg) + +![](images/a341c9b31eb2a7ccd81d2b7865e2235451e6d29d80d3d24ec7643f002876166b.jpg) + +![](images/53f8571aee97d9dc7e1e7dd6d8863585c0ae2383f103100e09804df7ac6d6514.jpg) +DreamBooth + +Textual-Inversion +![](images/81c28e3c577f220da029d8ec0f1cbf640f2204365fe2fc0cb02257cb20d7472e.jpg) +"A photo of a castle covered by snow" (H = 512, W = 768) + +![](images/02ccfc9831a0efd15a7b0531b574459bcbacc3b474921cdd900754b3c03f51e7.jpg) +Ours (w/o pos) + +![](images/a84dccf4f81a86cf1599249f8c5ae93758ea4f35b4c6ca4e5b5a170df4db9027.jpg) +Ours (w/ pos) + +![](images/e2ad47382b41af81b87c5b7a9bb8244d4fabda5e614bffc8f078642ab045dc28.jpg) +"A sculpture of a lady in the style of Michelangelo" (H = 768, W = 768) + +![](images/d80a5ca8782f4c2ab0c8528a22b5120f4f3354c3d3aebcb4fde86b0ac1ce031e.jpg) + +![](images/664adee6144509d39e0213b1be31cca48d3326f2954c5fb18ce8578e2e3f045a.jpg) + +![](images/d541ce1edc14d76778521f8c488db6f3039348bebb262e51319cc01c3feadbeb.jpg) + +![](images/19913a7bb39cabf785b393c8b25185be2edccc96ed865b43c4201c57492a3d1e.jpg) +"A bench in a desert" $(H = 768, W = 768)$ + +![](images/7ea34e3ba4b91929d954525062579635d8387a8261987c9d5e0b06aeb7a1471d.jpg) + +![](images/c0eb0ee17493708c363c7c30aa2b37933921aebb5ee2a53c5f37219be97d6c18.jpg) + +![](images/07553382286977f2fff32ad0d1001a475fd2df706d0b9768e3af95924dd7ff78.jpg) + +![](images/e1ba48ee90a91967fb2dc5ecfbea174620a43613620ef1011dd8a7610b6216f3.jpg) +"A sculpture of a dog in the style of Michelangelo" (H = 768, W = 768) + +![](images/8ec5ab8589f4c2a4ae367afc69fc706579fc8edbaa40c0025654b17ef8192aee.jpg) + +![](images/57da8c66ceab9852322b64528e1a41dfba79398852b45b37b761f8184435c482.jpg) + +![](images/3231fd8adfb249921ccf5216eecdb2d689b060569b8201ebc725663c2933066f.jpg) + +image with the same language guidance at $768 \times 768$ resolution. We set $v = 0.7$ . When $K = 0$ , the model-based classifier-free guidance is applied for each step of the denoising process. Since the generalization ability of the finetuned model is limited, in this case, the model fails to apply the desired property to the single source image. When $K = 1,000$ , the model-based classifier-free guidance is not applied to any step. Thus, the structure of the image is not preserved, and the generated result becomes a random sample of the pre-trained model. + +We further show the quantitative results Fig. 8a. We repeat the abovementioned procedure over different $K$ and randomly sample 20 images for each $K$ . We calculate two metrics. To understand the editing result, the image fidelity that is measured by the LPIPS [57] distance between the original and the edited image. The text alignment calculated by the CLIP [36] score to understand the alignment between our generated images and target text. As can be seen, the image fidelity drops with the increase of $K$ , indicating more details provided by the pre-trained model instead of the fine-tuned one. The text alignment measurement improves since the more details generated by the pre-trained model, the better editing results align with the target domain. To preserve the edit result's authenticity and fidelity + +to the source image, we set $K$ as 400. + +Analysis on guidance weight $v$ in Sec. 3.2. We further study the impact of the guidance weight $(v)$ in Fig. 9. We set $K = 400$ and resolution as $768 \times 768$ for each edit and use the same random seed to generate the result. As can be observed, the value of $v$ controls the fidelity of the edit result. However, since the pre-trained model is trained at the resolution $512 \times 512$ , the generated image contains many artifacts. When $v = 1$ , the synthesized image entirely depends on the results from the pre-trained model. Additionally, we conduct quantitative experiments with LPIPS score measuring the image fidelity and CLIP score for the text alignment in Fig. 8b. When $v$ is close to 1, the fidelity decreases while the edited feature decreases. When $v$ is close to 0, the model relies mainly on the fine-tuned model for the output when $t > K$ . However, since the fine-tuned model contains poor generalization ability, there is a significant amount of artifacts in the generated results, which leads to a poor LPIPS score. We choose 0.7 for each edit in this work as a trade-off between fidelity and creativity. + +Other analysis. We defer the analysis of model-based classifier-free guidance with multiple inputs and fine-tuning without coarse class descriptor or prior-preservation loss to the supplementary materials. + +![](images/90f534f999e88f363c477524a0eb11becd0299fcd740328700a677264f574267.jpg) +Figure 6. Analysis of model-based classifier-free guidance. Directly sampling with target text using the fine-tuned model (w/o guidance) fails to generate images corresponding to the text prompt. In contrast, the model-based classifier-free guidance (w/guidance) can synthesize high-fidelity images. + +![](images/9ef6ed5843aed5e0b14d7c68e5cbc0e0f04b915456501bac7a075bc49af76ab4.jpg) +Figure 7. Analysis on guidance step $K$ . Varying $K$ , we can decide the steps where the model-based guidance is applied, which controls the details from the source image and edits to be applied. + +# 5. Conclusion + +This work introduces SINE, a method for single-image editing. With only one image and a brief description of the object in the image, our approach can enable a wide range of editing for arbitrary resolution, followed by the information depicted in the language guidance. To achieve such results, we leverage the pre-trained large-scale text-to-image diffusion model. Specifically, we first fine-tune the + +![](images/173ebaa8fb8c9f632db85910b95167c737500f2053da3a6548e64b9cfcd213e2.jpg) +(a) Number of steps of the guidance. + +![](images/6a5237881aad305a35274db6c15a2fd63d7a37f4fdc1f543594b1eaba9b7af86.jpg) +(b) Weight of the guidance. + +![](images/83543c2ea4ff0034c2fce5208d8470457121f20e592318496ad056c71188f4b9.jpg) +Figure 8. Trade-off between fidelity and alignment with target text. We calculate the CLIP score [36] (a higher CLIP score indicates a better alignment between the edit result and target text) and 1-LPIPS score [57] (showing the fidelity between edit results and source image, the higher, the better). +Figure 9. Analysis of score interpolation. Varying $v$ with the same random seed gets editing results with various qualities. + +pre-trained model with our patch-based fine-tuning method until it overfits the single image. Then, during sampling time, we use the overfitted model to guide the pre-trained diffusion model for image synthesis, which maintains the fidelity of the results while taking advantage of the generalization ability of the pre-trained model. Compared with other methods, our approach has a better geometrical understanding of the image and thus can conduct complex editing to the images besides style transfer. + +However, in some cases where confusing editing guidance is given for the diffusion model, e.g., a chair-shaped dog, our method could fail. In cases where drastic changes are to be applied, e.g., changing a dog to a tiger in the same posture, there are also noticeable artifacts. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019. 2 \ No newline at end of file diff --git a/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/images.zip b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..80d8e03ac6c60a75aa4138951e65c5e404e2eed0 --- /dev/null +++ b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e6460ef448a590faadb2ca5c27497dc233f14a94386d35d2ff9b398cb21b35a5 +size 918667 diff --git a/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/layout.json b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..3d55a60737041c89aa589a62c35d7f408043354d --- /dev/null +++ b/2023/SINE_ SINgle Image Editing With Text-to-Image Diffusion Models/layout.json @@ -0,0 +1,14053 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 93, + 103, + 501, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 103, + 501, + 121 + ], + "spans": [ + { + "bbox": [ + 93, + 103, + 501, + 121 + ], + "type": "text", + "content": "SINE: SIngle Image Editing with Text-to-Image Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 75, + 142, + 154, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 142, + 154, + 159 + ], + "spans": [ + { + "bbox": [ + 75, + 142, + 154, + 159 + ], + "type": "text", + "content": "Zhixing Zhang" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 175, + 142, + 239, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 175, + 142, + 239, + 157 + ], + "spans": [ + { + "bbox": [ + 175, + 142, + 239, + 157 + ], + "type": "text", + "content": "Ligong Han" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 262, + 143, + 332, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 262, + 143, + 332, + 157 + ], + "spans": [ + { + "bbox": [ + 262, + 143, + 332, + 157 + ], + "type": "text", + "content": "Arnab Ghosh" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 358, + 143, + 446, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 143, + 446, + 156 + ], + "spans": [ + { + "bbox": [ + 358, + 143, + 446, + 156 + ], + "type": "text", + "content": "Dimitris Metaxas1" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 469, + 143, + 517, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 469, + 143, + 517, + 156 + ], + "spans": [ + { + "bbox": [ + 469, + 143, + 517, + 156 + ], + "type": "text", + "content": "Jian Ren" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 202, + 157, + 384, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 202, + 157, + 384, + 172 + ], + "spans": [ + { + "bbox": [ + 202, + 157, + 384, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 202, + 157, + 384, + 172 + ], + "type": "text", + "content": "Rutgers University " + }, + { + "bbox": [ + 202, + 157, + 384, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 202, + 157, + 384, + 172 + ], + "type": "text", + "content": "Snap Inc." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 198, + 192, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 198, + 192, + 211 + ], + "spans": [ + { + "bbox": [ + 143, + 198, + 192, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 224, + 289, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 289, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 289, + 548 + ], + "type": "text", + "content": "Recent works on diffusion models have demonstrated a strong capability for conditioning image generation, e.g., text-guided image synthesis. Such success inspires many efforts trying to use large-scale pre-trained diffusion models for tackling a challenging problem—real image editing. Works conducted in this area learn a unique textual token corresponding to several images containing the same object. However, under many circumstances, only one image is available, such as the painting of the Girl with a Pearl Earring. Using existing works on fine-tuning the pretrained diffusion models with a single image causes severe overfitting issues. The information leakage from the pretrained diffusion models makes editing can not keep the same content as the given image while creating new features depicted by the language guidance. This work aims to address the problem of single-image editing. 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The success of these works has inspired many subsequent efforts to leverage the pre-trained large-scale models for real image editing [10, 15, 20, 40]. They show that, with properly designed prompts and a limited number of fine-tuning steps, the text-to-image models can manipulate a given subject with text guidance." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 438, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 546, + 715 + ], + "type": "text", + "content": "On the downside, the recent text-guided editing works that build upon the diffusion models suffer several limitations. First, the fine-tuning process might lead to the pretrained large-scale model overfit on the real image, which degrades the synthesized images' quality when editing. To tackle these issues, methods like using multiple images with the same content and applying regularization terms on the same object have been introduced [4, 40]. However, querying multiple images with identical content or object might not be an available choice; for instance, there is only one painting for Girl with a Pearl Earring. Directly editing the single image brings information leakage from the pretrained large-scale models, generating images with different content (examples in Fig. 5); therefore, the application scenarios of these methods are greatly constrained. Second, these works lack a reasonable understanding of the object geometry for the edited image. Thus, generating images with different spatial size as the training data cause undesired artifacts, e.g., repeated objects, and incorrectly modified geometry (examples in Fig. 5). Such drawbacks restrict applying these methods for generating images with an arbitrary resolution, e.g., synthesizing high-resolution images from a single photo of a castle (as in Fig. 4), again limiting" + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6027" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 160, + 83 + ], + "type": "text", + "content": "the usage of these methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 286, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 286, + 168 + ], + "type": "text", + "content": "In this work, we present SINE, a framework utilizing pre-trained text-to-image diffusion models for SINgle image Editing and content manipulation. We build our approach based upon existing text-guided image generation approaches [10, 40] and propose the following novel techniques to solve overfitting issues on content and geometry, and language drift [28, 31]:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 176, + 286, + 340 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 48, + 176, + 286, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 176, + 286, + 297 + ], + "spans": [ + { + "bbox": [ + 48, + 176, + 286, + 297 + ], + "type": "text", + "content": "- First, by appropriately modifying the classifier-free guidance [22], we introduce model-based classifier-free guidance that utilizes the diffusion model to provide the score guidance for content and structure. Taking advantage of the step-by-step sampling process used in diffusion models, we use the model fine-tuned on a single image to plant a content \"seed\" at the early stage of the denoising process and allow the pre-trained large-scale text-to-image model to edit creatively conditioned with the language guidance at a later stage." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 304, + 286, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 304, + 286, + 340 + ], + "spans": [ + { + "bbox": [ + 48, + 304, + 286, + 340 + ], + "type": "text", + "content": "- Second, to decouple the correlation between pixel position and content, we propose a patch-based fine-tuning strategy, enabling generation on arbitrary resolution." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "type": "text", + "content": "With a text descriptor describing the content that is aimed to be manipulated and language guidance depicting the desired output, our approach can edit the single unique image to the targeted domain with details preserved in arbitrary resolution. The output image keeps the structure and background intact while having features well-aligned with the target language guidance. As shown in Fig. 1, trained on a painting Girl with a Pearl Earring with resolution as " + }, + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "type": "text", + "content": ", we can sample an image of a sculpture of the girl at the resolution of " + }, + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "type": "inline_equation", + "content": "640 \\times 512" + }, + { + "bbox": [ + 46, + 347, + 286, + 526 + ], + "type": "text", + "content": " with the identity features preserved. Moreover, our method can successfully handle various edits such as style transfer, content addition, and object manipulation (more examples in Fig. 3). We hope our method can further boost creative content creation by opening the door to editing arbitrary images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 538, + 133, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 133, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 133, + 550 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": "Text-guided image synthesis has drawn considerable attention in the generative model context [1, 2, 6, 12, 14, 16-19, 34, 35, 38, 50, 53-56, 60]. The recent development of diffusion models [21, 46, 47, 49] introduced new solutions to this problem and produced impressive results [33, 37, 39, 42]. With the significant improvement of these models, rather than training a large-scale text-to-image model from scratch, a leading line of works focuses on taking advantage of the existing pre-trained model and manipulating images according to given natural language guidance [3, 10, 20, 24, 29, 40]. In these works, studies explore text-based interfaces for image editing [1, 3, 35], style transfer [27, 30], and generator domain adaption [11, 25, 48]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "The development of the diffusion model provides a giant and flexible design space for this task. Many works utilize pre-trained diffusion models as generative priors and are training-free. ILVR [7] guides the denoising process by replacing the low-frequency part of the sample with that of the target reference image. SDEdit [32] applies the diffusion process first on an image or a user-created semantic map and then conducts the denoising procedure conditioned with the desired output. Blended diffusion [3] performs language-guided inpainting with a given mask." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 192, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 407 + ], + "type": "text", + "content": "Another line of research showed great potential and semantic editing ability of fine-tuning. DiffusionCLIP [25] leverages the CLIP [36] model to provide gradients for image manipulation and deliver impressive results on style transfer. Textual-Inversion [10] and DreamBooth [40] fine-tune the text embedding or the full diffusion model using a few personalized images (typically " + }, + { + "bbox": [ + 304, + 192, + 545, + 407 + ], + "type": "inline_equation", + "content": "3 \\sim 5" + }, + { + "bbox": [ + 304, + 192, + 545, + 407 + ], + "type": "text", + "content": ") to synthesize images of the same object in a novel context. These methods, however, either drastically change the layout of the original image when dealing with a single image or can not fully leverage the generalization ability of the pre-trained model for editing due to overfitting or language drift. Notably, Prompt-to-Prompt [20] controls the editing of synthesized images by manipulating the cross-attention maps; however, its editing ability is limited when applied to real images. Imagic [24], while delivering realistic results, requires fine-tuning process on each editing prompt for each image, leading to longer inference time." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 407, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 575 + ], + "type": "text", + "content": "This work introduces a solution to achieve image fidelity and text alignment simultaneously. Our method can perform high-quality semantic editing globally and locally on one single image. On the other hand, previous works lack an understanding of the object geometry of the edited image. When editing the image at an arbitrary resolution, the artifacts in the results will be obvious. Prior works have investigated generating images at arbitrary resolution using positional encoding as inductive bias [41, 52, 52] so that the correlation between content and position can be eliminated. Anyres-GAN [5] adopt a patch training mechanism to leverage high-resolution data to help the generation of images in the low-resolution domain. We propose a patch-based fine-tuning method to achieve arbitrary resolution editing." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 586, + 365, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 365, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 365, + 597 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "For one arbitrary in-the-wild image, our goal is to edit the image via language while preserving the maximal amount of details from the original image. To do so, we leverage the generalization ability of pre-trained large-scale text-to-image models [39]. An intuitive approach is to fine-tune the diffusion models with the single image and text description, similar to DreamBooth [40]. Ideally, it should provide a model that can reconstruct the input image using the given text descriptor and synthesize new images when" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6028" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "given other language guidance. Unfortunately, we find the model can easily overfit the single trained image and its corresponding text description. Thus, although the fine-tuned model can still reconstruct the input image perfectly, it can no longer synthesize diverse images according to the given language guidance (as shown in Fig. 5). Moreover, it struggles to generate arbitrary resolution images due to the lack of positional information (as in Fig. 4)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 290, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 290, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 290, + 266 + ], + "type": "text", + "content": "To solve the above issues, we propose a test-time model-based classifier-free guidance and a patch-based fine-tuning technique. An overview of our method is illustrated in Fig. 2. In the following sections, we review the backbone model used in our approach (Sec. 3.1). Then, we describe how to overcome the overfitting problem with model-based guidance (Sec. 3.2). Lastly, we present how to address the problem of limited resolution generation (Sec. 3.3)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 271, + 239, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 239, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 239, + 283 + ], + "type": "text", + "content": "3.1. Language-Guided Diffusion Models" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": "We use the latent diffusion models (LDMs) [39] trained on a large-scale dataset as our base model and implement the proposed approaches by fine-tuning the pre-trained model. LDMs is a class of Denoising Diffusion Probabilistic Models (DDPMs) [21] that contains an auto-encoder trained on images, and a diffusion model learned on the latent space constructed by the auto-encoder. The encoder " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": " encodes a given image " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{I} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": " to a latent representation " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\mathbf{z} = \\mathcal{E}(\\mathcal{I})" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": ". The decoder " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": " reconstructs the estimated image " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{I}}" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": " from the latent, such that " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{I}} = \\mathcal{D}(\\mathbf{z})" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{I}} \\approx \\mathcal{I}" + }, + { + "bbox": [ + 46, + 289, + 290, + 469 + ], + "type": "text", + "content": ". The diffusion model is trained to produce latent codes within the pre-trained latent space. The most intriguing property of LDMs is that the diffusion model can be conditioned on class labels, images, and text prompt. The conditional LDM is learned as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 55, + 475, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 475, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 55, + 475, + 287, + 491 + ], + "type": "interline_equation", + "content": "L _ {L D M} := \\mathbb {E} _ {\\mathcal {E} (\\mathcal {I}), y, \\boldsymbol {\\epsilon} \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\theta} (\\mathbf {z} _ {t}, t, \\boldsymbol {\\tau} _ {\\theta} (y)) \\| _ {\\mathbf {2}} ^ {2} \\right], \\quad (1)", + "image_path": "4d00c75fdfe7d45d36f4620e8ce28483a10789b83d664fc74eb0645983911e53.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " is the time step, " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " is the latent noised to time " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " is the unscaled noise sample, " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " is the denoising model, " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " is the conditioning input, and " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " maps " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " to a conditioning vector. During training time, " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 46, + 496, + 289, + 629 + ], + "type": "text", + "content": " are jointly optimized. A random noise tensor is sampled and denoised at inference time based on the conditioning input, e.g., text prompt, to produce a new latent. Inspired by DreamBooth [40], we construct the text prompt for fine-tuning a single image as \"a photo/painting of a [*] [class noun]\", where \"[*]\" is a unique identifier and \"[class noun]\" is a coarse class descriptor (e.g., \"castle\", \"lake\", \"car\", etc.)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 251, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 251, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 251, + 647 + ], + "type": "text", + "content": "3.2. Model-Based Classifier-Free Guidance" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "type": "text", + "content": "With the above-presented LDMs, we introduce our approach, inspired by classifier-free guidance, to overcome overfitting when fine-tuning LDMs with one image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "Classifier-free guidance [22] is a technique widely adopted by prior text-to-image diffusion models [39, 42]. A single" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 76, + 539, + 225 + ], + "blocks": [ + { + "bbox": [ + 310, + 76, + 539, + 225 + ], + "lines": [ + { + "bbox": [ + 310, + 76, + 539, + 225 + ], + "spans": [ + { + "bbox": [ + 310, + 76, + 539, + 225 + ], + "type": "image", + "image_path": "10d7bf218339218e4056f5f911416fc38ce1fb9abfdafc040b7dd111226e1e1c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 311, + 228, + 539, + 384 + ], + "blocks": [ + { + "bbox": [ + 311, + 228, + 539, + 384 + ], + "lines": [ + { + "bbox": [ + 311, + 228, + 539, + 384 + ], + "spans": [ + { + "bbox": [ + 311, + 228, + 539, + 384 + ], + "type": "image", + "image_path": "75f085c3287505c4744b9df41e91aae613af74fecde4e53aedcd37a169fecd53.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": "Figure 2. Overview of our method. (a) Given a source image, we first randomly crop it into patches and get the corresponding latent code " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " with the pre-trained encoder. At fine-tune time, the denoising model, " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": ", takes three inputs: noisy latent " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": ", language condition " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": ", and positional embedding for the area where the noisy latent is obtained. (b) During sampling, we give additional language guidance about the target domain to edit the image. Also, we sample a noisy latent code " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_T" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " with the dimension corresponding to the desired output resolution. Language conditioning for " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " are given by pre-trained language encoder " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " with the target language guidance. While for the fine-tuned diffusion model, " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{\\theta}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": ", in addition to the language conditioning " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": ", we also input the positional embedding for the whole image. We employ a linear combination between the score calculated by each model for the first " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " steps and inference only on pre-trained " + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 304, + 396, + 547, + 561 + ], + "type": "text", + "content": " after." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 577, + 546, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 546, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 546, + 625 + ], + "type": "text", + "content": "diffusion model is trained using conditional and unconditional objectives by randomly dropping the condition during training. When sampling, a linear combination of the conditional and unconditional score estimation is used:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 344, + 633, + 545, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 633, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 344, + 633, + 545, + 646 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {e}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) = w \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) + (1 - w) \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\tag {2}", + "image_path": "dff2ee28acf4ff8c6c04983562d80f97dc01736dc28814ba61596cd90d9ed506.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t,\\mathbf{c})" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t)" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " are the conditional and unconditional " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "-predictions, " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " is the conditioning vector generated by " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " is the weight for the guidance. The predication is performed using the Tweedie's formula [8], namely, " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_t - \\sigma_t\\tilde{\\epsilon}_{\\theta}) / \\alpha_t" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\sigma_{t}" + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": " are functions of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6029" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 182, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 182, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 182, + 84 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 72, + 182, + 84 + ], + "type": "text", + "content": " that affect the sampling quality." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 286, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 286, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 286, + 193 + ], + "type": "text", + "content": "Since we only have one image as the training data, e.g., painting of Mona Lisa, and one corresponding text descriptor of that image, the diffusion model suffers from overfitting, and severe language drifts after fine-tuning [40]. As a result, the fine-tuned model fails to synthesize images containing features from other language guidance. The overfitting issue might be due to only one repeated prompt used during fine-tuning, making other text prompts no longer accurate enough to control editing (see examples in Fig. 6)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 194, + 286, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 286, + 312 + ], + "type": "text", + "content": "Model-based classifier-free guidance. Existing \"personalized\" text-guided real image editing works only use one fine-tuned model for image generation and editing [10, 20, 40], ignoring the capacity of pre-trained large-scale text-to-image models. Instead, to alleviate the overfitting of the fine-tuned model, we leverage the pre-trained text-to-image model for image generation with the provided language guidance and use the fine-tuned model to provide content features in a fashion of combining scores from the two models, similar to classifier-free guidance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "type": "text", + "content": "Specifically, let " + }, + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{\\theta}" + }, + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "type": "text", + "content": " denote the fine-tuned denoising model, and " + }, + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 314, + 286, + 385 + ], + "type": "text", + "content": " denote the pre-trained text-to-image model. During sampling, at specified steps, we use our fine-tuned model to guide the pre-trained one by using a linear combination of the scores from each model. Thus, the score estimation in Eqn. 2 becomes:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 81, + 396, + 286, + 422 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 396, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 81, + 396, + 286, + 422 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) = w \\left(v \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c}\\right) + (1 - v) \\hat {\\boldsymbol {\\epsilon}} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\hat {\\mathbf {c}}\\right)\\right) \\tag {3} \\\\ + (1 - w) \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right), \\\\ \\end{array}", + "image_path": "025e84af959746fa2a7ec21d8d8382854b1a8c2dca7a9e967c69edd2e0f29b2f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "text", + "content": " stands for the model guidance weight, " + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}" + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "text", + "content": " is the language guidance token obtained from the fine-tuned diffusion model with the text prompt used during fine-tuning, and " + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 432, + 286, + 491 + ], + "type": "text", + "content": " is the target language conditioning obtained from the target prompt." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "text", + "content": "To prevent artifacts from the over-fitted model and maintain the fidelity of the generated image, we propose to sample using Eqn. 3 with " + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "inline_equation", + "content": "t > K" + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "text", + "content": " and sample using Eqn. 2 for " + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "inline_equation", + "content": "t \\leq K" + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "text", + "content": ". From " + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 492, + 286, + 600 + ], + "type": "text", + "content": " to 0, the denoising process only depends on the pre-trained model. Following this approach, we can fully leverage the generalization ability of the pre-trained model (examples in Fig. 6). Also note that this method could be generalized to include multiple prompts or even multiple modalities." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 610, + 188, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 188, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 188, + 623 + ], + "type": "text", + "content": "3.3. Patch-Based Fine-Tuning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "With model-based classifier-free guidance, we are able to edit and manipulate a single image with given language guidance. Here, we further show how to improve the finetuning process for a single training image so that the finetuned model can better understand the content and geometry of the image. Thus, it can provide better content guidance for the large-scale text-to-image model during the sampling" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": "time and unleash the potential for generating arbitrary-resolution images [9]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": "Limited-resolution generation. We first review the limitations of the current fine-tuning process. Given an input image " + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": " with resolution as " + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "inline_equation", + "content": "H\\times W" + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": ", we can obtain a downsampled latent code " + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": " from the pre-trained encoder. Since the text-to-image diffusion model is pre-trained at a fixed resolution, i.e., " + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "inline_equation", + "content": "p\\times p" + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": ", we need to resize the input image to a corresponding resolution " + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "inline_equation", + "content": "sp\\times sp" + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 96, + 545, + 275 + ], + "type": "text", + "content": " represents the scaling factor of the encoder, to match the resolution for reducing the fine-tuning cost. In essence, prior knowledge of the correlation between the position and content information is learned by the diffusion model. Thus, when sampling from a higher-resolution noise tensor, the generated latent code leads to artifacts like duplicates or position shifting (visual examples in Fig. 5). To tackle such drawbacks, we propose a simple yet effective fine-tuning method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": "Patch-based fine-tuning. Inspired by Chai et al. [5], we treat our single training image as a function on coordinate for each pixel, bounded in " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "[0,H]\\times [0,W]" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": ". The diffusion model still generates latent code at the fixed resolution " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "p\\times p" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": ", but each latent code corresponds to a sub-area in the image. We denote the sub-area as " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{v} = [h_1,w_1,h_2,w_2]" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "(h_1,w_1)\\in [0,H]\\times [0,W]" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "(h_2,w_2)\\in (h_1,H]\\times (w_1,W]" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": " indicate the top-left and bottom-right coordinates of the area, respectively. During fine-tuning, we sample patches from the image with different " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": " and resize the patches to resolution " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "sp" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": ". We denote the resulted patch as " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(F(\\mathbf{v}))\\in \\mathbb{R}^{sp\\times sp\\times 3}" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": " is the normalization and Fourier embedding [23] of the specific area. The encoded latent code of the patch is " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathbf{z_v} = \\mathcal{E}(\\mathcal{I}(F(\\mathbf{v})))" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": ". Our model uses the normalized Fourier embedding as an input to make the model learn the position-content correlation. Formally, our diffusion model is defined as " + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}_{\\theta}(\\mathbf{z}_t,t,\\tau_{\\theta}(y),F(\\mathbf{v}))" + }, + { + "bbox": [ + 304, + 276, + 545, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 479, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 634 + ], + "type": "text", + "content": "After fine-tuning, the model can generate latent code at different resolutions by giving the positional information directly to the model. The arbitrary resolution image editing is conducted by feeding two inputs to the model: the positional embedding of the whole image; and a randomly sampled noisy latent with the dimension corresponding to the resolution we want. When sampling in an arbitrary resolution, the model can still keep the structure of the original image intact (examples in Fig. 4). It is worth noting that with or without the correct position encoding, our framework still naturally permits retargeting, i.e., maintaining the aspect ratio of salient objects, like SinGAN [44], InGAN [45], and Drop-the-GAN [13]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 646, + 386, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 386, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 386, + 658 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Implementation Details While our method can be generally applied to different frameworks, we implement it based on the recently released text-to-image LDM, Stable Diffusion [39]. The pre-trained model was trained on " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "512 \\times 512" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6030" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 124, + 146 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 124, + 146 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 124, + 146 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 124, + 146 + ], + "type": "image", + "image_path": "f34c956731ecece0480bee50f95cc1769eee653ee8c13ef44fa6d2e0a151d8b9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + 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The spatial size of the latent code from the pre-trained model is " + }, + { + "bbox": [ + 46, + 574, + 287, + 598 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 574, + 287, + 598 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 61 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "For patch-based fine-tuning, we randomly crop images to patches with height and width uniformly in the range of " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "[0.1H, H] \\times [0.1W, W]" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " and resize them to " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". Experiments are conducted using " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " RTX 8000 GPU with a batch size of 1. The base learning rate is set to " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". The number of time steps for the diffusion model, " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", is 1000. Experiments without and with patch-based fine-tuning are created after 800 and 10,000 optimization steps, respectively. Unless otherwise noted, we adopt other hyperparam-" + } + ] + } + ], + "index": 62 + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": "eter choices from Stable Diffusion [39], and the results are generated with image resolution " + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": " and with latent dimension " + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": ". For sampling parameters, we choose " + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "inline_equation", + "content": "K = 400" + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "inline_equation", + "content": "v = 0.7" + }, + { + "bbox": [ + 305, + 574, + 545, + 622 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 63 + }, + { + "bbox": [ + 306, + 630, + 434, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 434, + 643 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 434, + 643 + ], + "type": "text", + "content": "4.1. Qualitative Evaluation" + } + ] + } + ], + "index": 64 + }, + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "type": "text", + "content": "To better understand various approaches, we collect images from a wide range of domains, i.e., free-to-use high-resolution images from Flickr" + }, + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "type": "text", + "content": " and Unsplash" + }, + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 305, + 649, + 545, + 685 + ], + "type": "text", + "content": ". During fine" + } + ] + } + ], + "index": 65 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 693, + 399, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 693, + 399, + 703 + ], + "spans": [ + { + "bbox": [ + 317, + 693, + 399, + 703 + ], + "type": "text", + "content": "1 https://www.flickr.com/" + } + ] + } + ], + "index": 66 + }, + { + "bbox": [ + 318, + 703, + 392, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 703, + 392, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 703, + 392, + 713 + ], + "type": "text", + "content": "2https://unsplash.com/" + } + ] + } + ], + "index": 67 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6031" + } + ] + } + ], + "index": 69 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 125, + 107, + 180 + ], + "blocks": [ + { + "bbox": [ + 51, + 125, + 107, + 180 + ], + "lines": [ + { + "bbox": [ + 51, + 125, + 107, + 180 + ], + "spans": [ + { + "bbox": [ + 51, + 125, + 107, + 180 + ], + "type": "image", + "image_path": "ed2602eb596955db2800c2cd67ed525d440c94721540502c5701ca37181537f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 53, + 181, + 105, + 190 + ], + "lines": [ + { + "bbox": [ + 53, + 181, + 105, + 190 + ], + "spans": [ + { + "bbox": [ + 53, + 181, + 105, + 190 + ], + "type": "text", + "content": "Source Image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 115, + 71, + 282, + 180 + ], + "blocks": [ + { + "bbox": [ + 115, + 71, + 282, + 180 + ], + "lines": [ + { + "bbox": [ + 115, + 71, + 282, + 180 + ], + "spans": [ + { + 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"type": "text", + "content": "c) \"painting of a castle in the style of Hokusai\" (512×768)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 117, + 203, + 211, + 210 + ], + "lines": [ + { + "bbox": [ + 117, + 203, + 211, + 210 + ], + "spans": [ + { + "bbox": [ + 117, + 203, + 211, + 210 + ], + "type": "text", + "content": "d) \"pixel art of a castle\" " + }, + { + "bbox": [ + 117, + 203, + 211, + 210 + ], + "type": "inline_equation", + "content": "(512\\times 768)" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 118, + 213, + 282, + 322 + ], + "lines": [ + { + "bbox": [ + 118, + 213, + 282, + 322 + ], + "spans": [ + { + "bbox": [ + 118, + 213, + 282, + 322 + ], + "type": "image", + "image_path": "d00049e1355d763bc627d0066b09e34381872eec8255a58d57b029b570548992.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 118, + 322, + 261, + 329 + ], + "lines": [ + { + "bbox": [ + 118, + 322, + 261, + 329 + ], + "spans": [ + { + "bbox": [ + 118, + 322, + 261, + 329 + ], + "type": "text", + "content": "a) \"traditional Chinese painting of a lake\" " + }, + { + "bbox": [ + 118, + 322, + 261, + 329 + ], + "type": "inline_equation", + "content": "(1024\\times 512)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 118, + 329, + 264, + 336 + ], + "lines": [ + { + "bbox": [ + 118, + 329, + 264, + 336 + ], + "spans": [ + { + "bbox": [ + 118, + 329, + 264, + 336 + ], + "type": "text", + "content": "b) \"a watercolor painting of a lake of a lake\" " + }, + { + "bbox": [ + 118, + 329, + 264, + 336 + ], + "type": "inline_equation", + "content": "(512\\times 512)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 118, + 336, + 253, + 344 + ], + "lines": [ + { + "bbox": [ + 118, + 336, + 253, + 344 + ], + "spans": [ + { + "bbox": [ + 118, + 336, + 253, + 344 + ], + "type": "text", + "content": "c) \"an impressionism painting of a lake\" " + }, + { + "bbox": [ + 118, + 336, + 253, + 344 + ], + "type": "inline_equation", + "content": "(512\\times 512)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 118, + 344, + 266, + 351 + ], + "lines": [ + { + "bbox": [ + 118, + 344, + 266, + 351 + ], + "spans": [ + { + "bbox": [ + 118, + 344, + 266, + 351 + ], + "type": "text", + "content": "d) \"painting of a lake ... Vincent Van Gogh\" " + }, + { + "bbox": [ + 118, + 344, + 266, + 351 + ], + "type": "inline_equation", + "content": "(512\\times 1024)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 364, + 287, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 364, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 287, + 397 + ], + "type": "text", + "content": "Figure 4. Arbitrary resolution editing. Our method achieves higher-resolution image editing without artifacts like duplicates, even on ones that change the height-width ratio drastically." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 286, + 508 + ], + "type": "text", + "content": "tuning, we apply a coarse class descriptor to the content we want to preserve, e.g., dog, cat, castle, etc. After optimization, we edit each image with diverse editing prompts. We randomly generate 4 edit results for each image and editing prompt and choose the best one (such a process is also applied to other comparison methods). Our work shows impressive editing ability when applied to various images with different language guidance." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 509, + 286, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 286, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 286, + 664 + ], + "type": "text", + "content": "As presented in Fig. 3, using the model-based classifier-free guidance (Sec. 3.2) enables us to apply various editing via text prompts on the single real images. Each image has two text prompts describing different features we want to edit, e.g., image style, background content, the texture of the content, etc. Our method can edit the related features while keeping the content intact. We further show our editing results on arbitrary resolution generation in Fig. 4. For each source image, we edit it with different prompts at various resolutions. As can be seen, our patch-based fine-tuning schedule (Sec. 3.3) successfully preserves the original portion and geometry features of the single source image, even on highly challenging resolution such as " + }, + { + "bbox": [ + 46, + 509, + 286, + 664 + ], + "type": "inline_equation", + "content": "512 \\times 1024" + }, + { + "bbox": [ + 46, + 509, + 286, + 664 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 671, + 132, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 132, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 132, + 684 + ], + "type": "text", + "content": "4.2. Comparisons" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "We compare our method to concurrent leading techniques, Textual-Inversion [10] and DreamBooth [40], that" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "can be used for single-image editing. Considering no official implementation has been released for DreamBooth, we adopt an unofficial but well-adopted and highly competitive implementation based on Stable Diffusion [39, 51]. We compare these techniques strictly according to the detailed guidance provided with the implementations." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 144, + 546, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 337 + ], + "type": "text", + "content": "Fig. 5 shows the comparison results. As can be noticed, our method maintains the fidelity of the images while applying changes as desired. Furthermore, our approach has high authenticity and structural integrity even for higher-resolution editing. For example, in the last row of Fig. 5, when the target prompt is “... standing on grass”, our method generates results by modifying the texture of the land on which the dog stands with other features intact. However, other methods result in a dramatic change in the structure of the whole image. Moreover, in the second row, when modifying the painting Mona Lisa, both Dream-Booth [40] and Textual-Inversion [10] fail to edit the image. Our work also shows clear advantages over the approaches on training-free editorings, such as ILVR [7], SDEdit [32], and Prompt-to-prompt [20], with the qualitative comparisons presented in the supplementary materials." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 346, + 411, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 411, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 411, + 358 + ], + "type": "text", + "content": "4.3. Ablation Analysis" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 365, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 509 + ], + "type": "text", + "content": "Patch-based fine-tuning. In Fig. 5, we show the results of editing images in higher resolution when fine-tuned without or with the proposed patch-based fine-tuning technique (w/o pos vs. w/ pos). When sampling at a higher resolution, as in the right part of Fig. 5, the denoising model fine-tuned without the patch-based training mechanism performs poorly. In the first row, the castle towers get duplicated to meet the resolution, and in the third row, the bench gets stretched disproportionately. In essence, our patch-based fine-tuning technique enables the diffusion model to leverage the super-resolution ability of the decoder and edit images at arbitrary resolution during testing time." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "content": "Analysis of model-based classifier-free guidance. We generate editing results by directly sampling from the fine-tuned model using Eqn. 2. We fine-tune the model without the patch-based schedule for 800 steps to retain more generalization ability. In this case, the model can perfectly reconstruct the source image while preserving as much editing ability as possible. We denote the setting as w/o gudiance. Using the same fine-tuned model, we conduct experiments under model-based classifier-free guidance, denoted as " + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "inline_equation", + "content": "w/" + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "content": " guidance. As shown in Fig. 6, sampling without our model-based classifier-free guidance fails to react to the prompt, while our method can successfully edit images to match the target language guidance. We further analyze " + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 510, + 546, + 676 + ], + "type": "text", + "content": " in model-based classifier-free guidance." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Analysis on guidance step " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": " in Sec. 3.2. In Fig. 7, we show our results on editing with different settings of " + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": ". 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22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 333, + 547, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 333, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 547, + 399 + ], + "type": "text", + "content": "Figure 5. Comparisons of various methods. We compare our method to DreamBooth [40] and Textual-Inversion [10]. We adopt default hyper-parameters for both methods provided in their paper or code. On the left part of the figure, we edit at the resolution same as training time. On the right part, we edit the source image at a higher resolution. Our work successfully edits the image as required while preserving the details of the source images. We also compare our method without and with the patch-based fine-tuning mechanism (w/o pos vs. w/ pos). When editing at a fixed resolution, two settings perform equally, while at a higher resolution, the patch-based fine-tuning method successfully prevents artifacts." + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 109, + 266, + 157, + 313 + ], + "blocks": [ + { + "bbox": [ + 109, + 266, + 157, + 313 + ], + "lines": [ + { + "bbox": [ + 109, + 266, + 157, + 313 + ], + "spans": [ + { + "bbox": [ + 109, + 266, + 157, + 313 + ], + "type": "image", + "image_path": "f35ff5b697327ab8b884e82ed7840bac4737b2d3437ac9aa4fde33f4129527a2.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 113, + 314, + 226, + 322 + ], + "lines": [ + { + "bbox": [ + 113, + 314, + 226, + 322 + ], + "spans": [ + { + "bbox": [ + 113, + 314, + 226, + 322 + ], + "type": "text", + "content": "\"A dog standing on grass\" " + }, + { + "bbox": [ + 113, + 314, + 226, + 322 + ], + "type": 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We set " + }, + { + "bbox": [ + 46, + 416, + 287, + 535 + ], + "type": "inline_equation", + "content": "v = 0.7" + }, + { + "bbox": [ + 46, + 416, + 287, + 535 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 46, + 416, + 287, + 535 + ], + "type": "inline_equation", + "content": "K = 0" + }, + { + "bbox": [ + 46, + 416, + 287, + 535 + ], + "type": "text", + "content": ", the model-based classifier-free guidance is applied for each step of the denoising process. Since the generalization ability of the finetuned model is limited, in this case, the model fails to apply the desired property to the single source image. When " + }, + { + "bbox": [ + 46, + 416, + 287, + 535 + ], + "type": "inline_equation", + "content": "K = 1,000" + }, + { + "bbox": [ + 46, + 416, + 287, + 535 + ], + "type": "text", + "content": ", the model-based classifier-free guidance is not applied to any step. Thus, the structure of the image is not preserved, and the generated result becomes a random sample of the pre-trained model." + } + ] + } + ], + "index": 53 + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": "We further show the quantitative results Fig. 8a. We repeat the abovementioned procedure over different " + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": " and randomly sample 20 images for each " + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": ". We calculate two metrics. To understand the editing result, the image fidelity that is measured by the LPIPS [57] distance between the original and the edited image. The text alignment calculated by the CLIP [36] score to understand the alignment between our generated images and target text. As can be seen, the image fidelity drops with the increase of " + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 546, + 288, + 713 + ], + "type": "text", + "content": ", indicating more details provided by the pre-trained model instead of the fine-tuned one. The text alignment measurement improves since the more details generated by the pre-trained model, the better editing results align with the target domain. To preserve the edit result's authenticity and fidelity" + } + ] + } + ], + "index": 54 + }, + { + "bbox": [ + 306, + 416, + 459, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 416, + 459, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 416, + 459, + 427 + ], + "type": "text", + "content": "to the source image, we set " + }, + { + "bbox": [ + 306, + 416, + 459, + 427 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 416, + 459, + 427 + ], + "type": "text", + "content": " as 400." + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": "Analysis on guidance weight " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " in Sec. 3.2. We further study the impact of the guidance weight " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "(v)" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " in Fig. 9. We set " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "K = 400" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " and resolution as " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "768 \\times 768" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " for each edit and use the same random seed to generate the result. As can be observed, the value of " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " controls the fidelity of the edit result. However, since the pre-trained model is trained at the resolution " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": ", the generated image contains many artifacts. When " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "v = 1" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": ", the synthesized image entirely depends on the results from the pre-trained model. Additionally, we conduct quantitative experiments with LPIPS score measuring the image fidelity and CLIP score for the text alignment in Fig. 8b. When " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " is close to 1, the fidelity decreases while the edited feature decreases. When " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": " is close to 0, the model relies mainly on the fine-tuned model for the output when " + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "inline_equation", + "content": "t > K" + }, + { + "bbox": [ + 304, + 433, + 545, + 661 + ], + "type": "text", + "content": ". However, since the fine-tuned model contains poor generalization ability, there is a significant amount of artifacts in the generated results, which leads to a poor LPIPS score. We choose 0.7 for each edit in this work as a trade-off between fidelity and creativity." + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Other analysis. We defer the analysis of model-based classifier-free guidance with multiple inputs and fine-tuning without coarse class descriptor or prior-preservation loss to the supplementary materials." + } + ] + } + ], + "index": 57 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6033" + } + ] + } + ], + "index": 58 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 73, + 270, + 335 + ], + "blocks": [ + { + "bbox": [ + 55, + 73, + 270, + 335 + ], + "lines": [ + { + "bbox": [ + 55, + 73, + 270, + 335 + ], + "spans": [ + { + "bbox": [ + 55, + 73, + 270, + 335 + ], + "type": "image", + "image_path": "90f534f999e88f363c477524a0eb11becd0299fcd740328700a677264f574267.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 347, + 287, + 403 + ], + "lines": [ + { + "bbox": [ + 47, + 347, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 287, + 403 + ], + "type": "text", + "content": "Figure 6. Analysis of model-based classifier-free guidance. Directly sampling with target text using the fine-tuned model (w/o guidance) fails to generate images corresponding to the text prompt. In contrast, the model-based classifier-free guidance (w/guidance) can synthesize high-fidelity images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 410, + 276, + 548 + ], + "blocks": [ + { + "bbox": [ + 50, + 410, + 276, + 548 + ], + "lines": [ + { + "bbox": [ + 50, + 410, + 276, + 548 + ], + "spans": [ + { + "bbox": [ + 50, + 410, + 276, + 548 + ], + "type": "image", + "image_path": "9ef6ed5843aed5e0b14d7c68e5cbc0e0f04b915456501bac7a075bc49af76ab4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "lines": [ + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "type": "text", + "content": "Figure 7. Analysis on guidance step " + }, + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "type": "text", + "content": ". Varying " + }, + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 559, + 287, + 593 + ], + "type": "text", + "content": ", we can decide the steps where the model-based guidance is applied, which controls the details from the source image and edits to be applied." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 609, + 119, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 119, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 119, + 621 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "This work introduces SINE, a method for single-image editing. With only one image and a brief description of the object in the image, our approach can enable a wide range of editing for arbitrary resolution, followed by the information depicted in the language guidance. To achieve such results, we leverage the pre-trained large-scale text-to-image diffusion model. Specifically, we first fine-tune the" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 79, + 425, + 159 + ], + "blocks": [ + { + "bbox": [ + 307, + 79, + 425, + 159 + ], + "lines": [ + { + "bbox": [ + 307, + 79, + 425, + 159 + ], + "spans": [ + { + "bbox": [ + 307, + 79, + 425, + 159 + ], + "type": "image", + "image_path": "173ebaa8fb8c9f632db85910b95167c737500f2053da3a6548e64b9cfcd213e2.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 308, + 160, + 425, + 171 + ], + "lines": [ + { + "bbox": [ + 308, + 160, + 425, + 171 + ], + "spans": [ + { + "bbox": [ + 308, + 160, + 425, + 171 + ], + "type": "text", + "content": "(a) Number of steps of the guidance." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 427, + 79, + 543, + 159 + ], + "blocks": [ + { + "bbox": [ + 427, + 79, + 543, + 159 + ], + "lines": [ + { + "bbox": [ + 427, + 79, + 543, + 159 + ], + "spans": [ + { + "bbox": [ + 427, + 79, + 543, + 159 + ], + "type": "image", + "image_path": "6a5237881aad305a35274db6c15a2fd63d7a37f4fdc1f543594b1eaba9b7af86.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 441, + 160, + 529, + 171 + ], + "lines": [ + { + "bbox": [ + 441, + 160, + 529, + 171 + ], + "spans": [ + { + "bbox": [ + 441, + 160, + 529, + 171 + ], + "type": "text", + "content": "(b) Weight of the guidance." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 236, + 533, + 450 + ], + "blocks": [ + { + "bbox": [ + 306, + 175, + 545, + 230 + ], + "lines": [ + { + "bbox": [ + 306, + 175, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 545, + 230 + ], + "type": "text", + "content": "Figure 8. Trade-off between fidelity and alignment with target text. We calculate the CLIP score [36] (a higher CLIP score indicates a better alignment between the edit result and target text) and 1-LPIPS score [57] (showing the fidelity between edit results and source image, the higher, the better)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 236, + 533, + 450 + ], + "lines": [ + { + "bbox": [ + 307, + 236, + 533, + 450 + ], + "spans": [ + { + "bbox": [ + 307, + 236, + 533, + 450 + ], + "type": "image", + "image_path": "83543c2ea4ff0034c2fce5208d8470457121f20e592318496ad056c71188f4b9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 463, + 545, + 485 + ], + "lines": [ + { + "bbox": [ + 306, + 463, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 306, + 463, + 545, + 485 + ], + "type": "text", + "content": "Figure 9. Analysis of score interpolation. Varying " + }, + { + "bbox": [ + 306, + 463, + 545, + 485 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 306, + 463, + 545, + 485 + ], + "type": "text", + "content": " with the same random seed gets editing results with various qualities." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 490, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 597 + ], + "type": "text", + "content": "pre-trained model with our patch-based fine-tuning method until it overfits the single image. Then, during sampling time, we use the overfitted model to guide the pre-trained diffusion model for image synthesis, which maintains the fidelity of the results while taking advantage of the generalization ability of the pre-trained model. Compared with other methods, our approach has a better geometrical understanding of the image and thus can conduct complex editing to the images besides style transfer." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 597, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 545, + 670 + ], + "type": "text", + "content": "However, in some cases where confusing editing guidance is given for the diffusion model, e.g., a chair-shaped dog, our method could fail. In cases where drastic changes are to be applied, e.g., changing a dog to a tiger in the same posture, there are also noticeable artifacts. We show more examples in the supplementary materials." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 670, + 545, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 670, + 545, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 670, + 545, + 705 + ], + "type": "text", + "content": "One future direction is improving the fidelity of the editing results, which could be achieved by alleviating the overfitting problem of the fine-tuned model." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6034" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Rameen Abdal, Peihao Zhu, John Femiani, Niloy Mitra, and Peter Wonka. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 5802-5810, 2019. 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6037" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/98bd5d41-9994-4c5a-92c8-200bf021b945_content_list.json b/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/98bd5d41-9994-4c5a-92c8-200bf021b945_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..658f06e819ec95b98261fe00c22482b55dcb5a07 --- /dev/null +++ b/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/98bd5d41-9994-4c5a-92c8-200bf021b945_content_list.json @@ -0,0 +1,3220 @@ +[ + { + "type": "text", + "text": "SINE: Semantic-driven Image-based NeRF Editing with Prior-guided Editing Field", + "text_level": 1, + "bbox": [ + 225, + 66, + 743, + 112 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chong Bao $^{1*}$ Yinda Zhang $^{2*}$ Bangbang Yang $^{1*}$ Tianxing Fan $^{1}$ \nZesong Yang $^{1}$ Hujun Bao $^{1}$ Guofeng Zhang $^{1\\dagger}$ Zhaopeng Cui $^{1\\dagger}$ $^{1}$ State Key Lab of CAD&CG, Zhejiang University $^{2}$ Google https://zju3dv.github.io/sine/", + "bbox": [ + 217, + 119, + 756, + 193 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4757b30ae703efa5bbf6b1197c945b6a540dbb6f7a90bd46cf99b80b6be23427.jpg", + "image_caption": [ + "Figure 1. We propose a novel semantic-driven image-based editing approach, which allows users to edit a photo-realistic NeRF with a single-view image or with text prompts, and renders edited novel views with vivid details and multi-view consistency." + ], + "image_footnote": [], + "bbox": [ + 84, + 199, + 423, + 371 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7f6dd04e1bca8e5f7a5560cbfebecae4177f0ffd26c55a0b3cf5d73c0aee71c0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 424, + 199, + 888, + 371 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 412, + 313, + 428 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the great success in 2D editing using user-friendly tools, such as Photoshop, semantic strokes, or even text prompts, similar capabilities in 3D areas are still limited, either relying on 3D modeling skills or allowing editing within only a few categories. In this paper, we present a novel semantic-driven NeRF editing approach, which enables users to edit a neural radiance field with a single image, and faithfully delivers edited novel views with high fidelity and multi-view consistency. To achieve this goal, we propose a prior-guided editing field to encode fine-grained geometric and texture editing in 3D space, and develop a series of techniques to aid the editing process, including cyclic constraints with a proxy mesh to facilitate geometric supervision, a color compositing mechanism to stabilize semantic-driven texture editing, and a feature-cluster-based regularization to preserve the irrelevant content unchanged. Extensive experiments and editing examples on both real-world and synthetic data demonstrate that our method achieves photo-realistic 3D editing using only a single edited image, pushing the bound of semantic-driven editing in 3D real-world scenes.", + "bbox": [ + 73, + 441, + 473, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 763, + 209, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semantic-driven editing approaches, such as stroke-based scene editing [34, 39, 66], text-driven image synthesis and editing [1, 50, 53], and attribute-based face editing [27, 60], have greatly improved the ease of artistic creation. However, despite the great success of 2D image edit", + "bbox": [ + 75, + 787, + 468, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing and neural rendering techniques [14, 42], similar editing abilities in the 3D area are still limited: (1) they require laborious annotation such as image masks [27, 71] and mesh vertices [69, 74] to achieve the desired manipulation; (2) they conduct global style transfer [12, 13, 16, 20, 75] while ignoring the semantic meaning of each object part (e.g., windows and tires of a vehicle should be textured differently); (3) they can edit on categories by learning a textured 3D latent representation (e.g., 3D-aware GANs with faces and cars etc.) [6, 8, 9, 17, 45, 56, 59, 60], or at a coarse level [35, 64] with basic color assignment or object-level disentanglement [30], but struggle to conduct texture editing on objects with photo-realistic textures or out-of-distribution characteristics.", + "bbox": [ + 500, + 412, + 892, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Based on this observation, we believe that, on the way toward semantic-driven 3D editing, the following properties should be ensured. First, the operation of editing should be effortless, i.e., users can edit 3D scenes on a single 2D image in convenient ways, e.g., using off-the-shelf tools such as GAN-based editing [28, 34], text-driven editing [1, 53], Photoshop, or even a downloaded Internet image without pixel-wise alignment, rather than steering 3D modeling software with specific knowledge [69], or repeatedly editing from multi-view images. Second, the editing method should be applicable to real-world scenes or objects and preserve vivid appearances, which is beyond existing 3D-aware generative models [8, 9] due to the limited categories and insufficient data diversity on real-world objects.", + "bbox": [ + 496, + 627, + 892, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To fulfill this goal, we propose a novel Semantic-driven Image-based Editing approach for Neural radiance field in real-world scenes, named SINE. Specifically, our method allows users to edit a neural radiance field with a sin-", + "bbox": [ + 496, + 839, + 893, + 898 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Authors contributed equally.", + "bbox": [ + 94, + 875, + 253, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 96, + 887, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20919", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "gle image, i.e., either by changing a rendered image using off-the-shelf image editing tools or providing an image for texture transferring (see Sec. 4.4), and then delivers edited novel views with consistent semantic meaning. Unlike previous works that directly fine-tune the existing NeRF model [30, 35, 64], SINE learns a prior-guided editing field to encode geometric and texture changes over the original 3D scene (see Fig. 2), thus enabling fine-grained editing ability. By leveraging guidance from existing neural priors (shape prior models [15] and Vision Transformer models [7], etc.), SINE can directly perform semantic-driven editing on photo-realistic scenes without pre-training a category-level latent space. For example, in Fig. 1, users can stretch a car's back or change all four tires to cookies by only editing a single image, and can even cooperate with text-prompts editing [1] to modify a specific object of a scene with vivid appearances.", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, even when guided with neural priors, editing NeRF from a single image with multi-view consistency and accuracy is still challenging. (1) The generic NeRF does not necessarily provide an explicit surface or signed distance field, such that it cannot directly work with shape priors [15]. Therefore, we propose to use cyclic constraints with a proxy mesh to represent the edited NeRF's geometry, which facilitates guided editing using coarse shape prior. (2) Learning a coordinate-based 3D editing field using a single edited view is not sufficient to capture fine-grained details, and applying semantic supervision [7, 52] directly to the editing field leads to sub-optimal convergence (see Sec. 4.5). To tackle these challenges, we propose a color compositing mechanism by first rendering the template NeRF color and modification color individually, and then deferred blending them to yield the edited view, which significantly improves semantic-driven texture editing. (3) Ideally, a user's editing should only affect the desired regions while maintaining other parts untouched. However, in semantic-driven editing, the prior losses require taking the full shape or image as input, which leads to appearance or shape drifting at the undesired area. To precisely control the editing while excluding irrelevant parts from being affected, we generate feature clusters of the editing area using the ViT-based feature field [7, 30], and use these clusters to distinguish whether a location is allowed to be edited or should remain unchanged.", + "bbox": [ + 75, + 351, + 472, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the contributions of our paper are as follows. (1) We propose a novel semantic-driven image-based NeRF editing approach, called SINE, which allows users to edit a neural radiance field simply on just a single view of the rendering. SINE leverages a prior-guided editing field to encode fine-grained geometry and texture changes over the given pre-trained NeRF, thus delivering multi-view consistent edited views with high fidelity. (2) To achieve semantic editing functionality, we develop a series of techniques,", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "including cyclic constraints with a proxy mesh for geometric editing, the color compositing mechanism to enhance texture editing, and the feature-cluster-based regularization to control the affected editing area and maintain irrelevant parts unchanged. (3) Experiments and editing examples on both real-world/synthetic and object-centric/unbounded $360^{\\circ}$ scenes data demonstrate superior editing capabilities and quality with effortless operations.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 498, + 220, + 650, + 237 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural rendering with external priors. Neural rendering techniques aim at rendering novel views with high-quality [42] or controllable properties [27, 48] by learning from 2D photo capture. Recently, NeRF [42] achieves photo-realistic rendering with volume rendering and inspires many works, including surface reconstruction [31,65, 73], scene editing [4, 18, 67, 70, 71] and generation [22, 51], inverse rendering [5, 76], SLAM [72, 77], etc. For learning from few-shot images [23] or 3D inpainting [43], NeRF's variants use hand-crafted losses [44] or large language-image models [23, 68] as external priors. However, due to insufficient 3D supervision, such methods cannot reconstruct accurate geometry and only produce visually plausible results. Besides, some works [21, 32, 40] use the symmetric assumption to reconstruct category-level objects (e.g., cars, chairs) but cannot generalize on complex scenes. Neural 2D & 3D scene editing. With the development of neural networks, semantic-driven 2D photo editing allows user editing in various friendly ways, such as controlling attribute of faces [19, 28], stroke-based editing [34, 39, 66], sketch-to-image generation [11, 55], image-to-image texture transferring [62], or text-driven image generation [53] and editing [29]. Nevertheless, in 3D scene editing, similar capabilities are still limited due to the high demand for multi-view consistency. Existing approaches either rely on laborious annotation [27, 69, 71, 74], only support object deformation or translation [30, 61, 63, 74], or only perform global style transfer [12, 13, 16, 20, 75] without strong semantic meaning. Recently, 3D-aware GANs [8, 9, 17, 24, 45, 56, 59] and semantic NeRF editing [35, 64] learn a latent space of the category and enable editing via latent code control. However, the quality and editing ability of these methods mainly depend on the dataset (e.g., human faces [59, 60] or objects in ShapeNet [10]), and they cannot generalize to objects with rich appearances or out-of-distribution features [1]. In contrast, our method allows for semantic-driven editing directly on the given photo-realistic NeRF, and uses a prior-guided editing field to learn fine-grained editing from only a single image.", + "bbox": [ + 496, + 243, + 893, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 844, + 591, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first formulate the goal of our semantic NeRF editing task as follows. As illustrated in the left part of Fig. 2,", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "footer", + "text": "20920", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6b6466b8e020a4b36c5de6daa64f71298661f1549e2791f5cd7b0f7bba140247.jpg", + "image_caption": [ + "Figure 2. Overview. We encode geometric and texture changes over the original template NeRF with a prior-guided editing field, where the geometric modification field $F_{\\Delta G}$ transformed the edited space query $\\mathbf{x}$ into the template space $\\mathbf{x}'$ , and the texture modification field $F_{\\Delta T}$ encodes modification colors $\\mathbf{m}'$ . Then, we render deformed template image $\\hat{I}_o$ and color modification image $\\hat{I}_m$ with all the queries, and use a color compositing layer to blend $\\hat{I}_o$ and $\\hat{I}_m$ into the edited view $\\hat{I}$ ." + ], + "image_footnote": [], + "bbox": [ + 93, + 66, + 294, + 271 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/083065336e39a14d99352c688140f11033cbd5234bec460e9fe15d54eedb2203.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 297, + 66, + 651, + 271 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9543a069156a473733ebcd87c90a98efebcc98b957fc288a4d196293c134a780.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 655, + 68, + 877, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "given a pre-trained NeRF of a photo-realistic scene (named template NeRF), we aim at editing the template NeRF using only a single-view 2D image, and then produce novel views with consistent semantic meaning (see Sec. 4.3 and Sec. 4.4). Note that naively fine-tuning on the edited single view cannot obtain satisfactory results due to the spatial ambiguity and lack of multi-view supervision (see Sec. 4.2). Therefore, we propose to use a novel prior-guided editing field to encode fine-grained changes (Sec. 3.1) in 3D space, which leverages geometry and texture priors to guide the learning of semantic-driven editing (Sec. 3.2 and Sec. 3.3). Besides, to precisely control the editing area while maintaining other parts unchanged, we design editing regularization with feature cluster-based semantic masking (Sec. 3.4).", + "bbox": [ + 75, + 339, + 473, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. SINE Rendering Pipeline", + "text_level": 1, + "bbox": [ + 76, + 563, + 308, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, we use a dedicated editing field to encode geometry and texture changes over the pre-trained template NeRF. The editing field consists of an implicit geometric modification field $F_{\\Delta G}$ and a texture modification field $F_{\\Delta T}$ , where $F_{\\Delta G}$ deforms the query points from the observed edited space to the original template space, as $\\mathbf{x}' \\coloneqq F_{\\Delta G}(\\mathbf{x})$ , and $F_{\\Delta T}$ encodes the modification color $\\mathbf{m}'$ , as $\\mathbf{m}' \\coloneqq F_{\\Delta T}(\\mathbf{x})$ . Specifically, for each sampled query point $\\{\\mathbf{x}_i | i = 1, \\dots, N\\}$ along the ray $r$ with view direction $d$ , we first obtain the deformed points $\\mathbf{x}'$ (in template space) and modification color $\\mathbf{m}'$ , and feed $\\mathbf{x}'$ and $d$ to the template NeRF to obtain the density $\\delta'$ and template colors $\\mathbf{c}'$ . Then, we perform dual volume rendering both on edited fields and template NeRF following the quadrature rules [38,42], which is defined as:", + "bbox": [ + 75, + 585, + 470, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {C} _ {o} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} \\mathbf {c} _ {i} ^ {\\prime}, \\quad \\hat {C} _ {e} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} \\mathbf {m} _ {i} ^ {\\prime}, \\tag {1} \\\\ T _ {i} = \\exp \\left(- \\sum_ {j = 1} ^ {i - 1} \\sigma^ {\\prime} _ {j} \\delta_ {j}\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 811, + 468, + 904 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{i} = 1 - \\exp (-\\sigma^{\\prime}_{i}\\delta_{i})$ , and $\\delta_{i}$ is the distance between adjacent samples along the ray. In this way, we obtain the deformed template image $\\hat{I}_o$ from the template NeRF's pixel color $\\hat{C}_o(\\boldsymbol {r})$ and color modification image $\\hat{I}_m$ from the modification color $\\hat{C}_e(\\boldsymbol {r})$ . Finally, we apply the color compositing layer (see Sec. 3.3) to blend $\\hat{I}_o$ and $\\hat{I}_m$ into the resulting edited views $\\hat{I}$ .", + "bbox": [ + 496, + 338, + 890, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Prior-Guided Geometric Editing", + "text_level": 1, + "bbox": [ + 500, + 449, + 785, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we explain how to learn $F_{\\Delta G}(\\mathbf{x})$ with the geometric prior.", + "bbox": [ + 496, + 467, + 890, + 497 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Shape prior constraint on the edited NeRF. We leverage geometric prior models, such as neural implicit shape representation [15, 46] or depth prediction [3], to mitigate the ambiguity of geometric editing based on editing from a single perspective. (1) For objects within a certain shape category (e.g., cars, airplanes), we use DIF [15], in which the implicit SDF field and the prior mesh $\\hat{M}_P$ can be generated with the condition of an estimizable latent code $\\hat{\\mathbf{z}}$ . We force the edited NeRF's geometry $\\hat{M}_E$ to be explainable by a pre-trained DIF model with the geometric prior loss:", + "bbox": [ + 496, + 498, + 890, + 648 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal{L}_{gp} = \\min_{\\hat{\\mathbf{z}}}\\bigl(\\sum_{\\mathbf{p}^{\\prime}\\in \\hat{M}_{E}}f_{\\mathrm{SDF}}(\\hat{\\mathbf{z}},\\mathbf{p}^{\\prime}) + \\lambda ||\\hat{\\mathbf{z}} ||_{2}^{2}\\bigr) \\\\ + \\sum_ {\\mathbf {p} _ {i} ^ {\\prime} \\in \\hat {M} _ {E}} \\min _ {\\mathbf {p} _ {t} \\in \\hat {M} _ {P}} | | \\mathbf {p} _ {i} ^ {\\prime} - \\mathbf {p} _ {t} | | _ {2} ^ {2} \\tag {2} \\\\ + \\sum_ {\\mathbf {p} _ {i} \\in \\hat {M} _ {P}} \\min _ {\\mathbf {p} _ {t} ^ {\\prime} \\in \\hat {M} _ {E}} | | \\mathbf {p} _ {i} - \\mathbf {p} _ {t} ^ {\\prime} | | _ {2} ^ {2}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 651, + 890, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first term encourages the sampled surface points on the edited NeRF's geometry $\\hat{M}_E$ to lie on the manifold of DIF's latent space with an SDF loss $f_{\\mathrm{SDF}}$ and the latent code regularization [15]. The last two terms are Chamfer constraints, which enforce the $\\hat{M}_E$ close to the DIF's periodically updated prior mesh $\\hat{M}_P$ [36] by minimizing the closest surface points. (2) For objects without a category-level prior, we can build a finalized shape prior $\\hat{M}_P$ beforehand. Practically, we find 3D deforming vertices with 2D correspond", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20921", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "dence [26] and monocular depth prediction [3], and use ARAP [57] to deform the proxy triangle mesh $M_{\\Theta}$ to $\\hat{M}_P$ . Then, we can inherit the Chamfer loss term in Eq. (2) for prior-guided supervision.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Representing edited NeRF's geometry as a deformed proxy mesh. The edited NeRF has no explicit surface definition or SDF field to directly apply the geometric prior loss (Eq. (2)). Therefore, to obtain the edited mesh surface $\\hat{M}_E$ , as illustrated in Fig. 3 (a), we first fit the template NeRF geometry with a proxy mesh $M_{\\Theta}$ [36, 65], and then learn a forward modification field $F_{\\Delta G}^{\\prime}$ to warp the template proxy mesh to the edited space. $F_{\\Delta G}^{\\prime}$ is an inverse of the editing field $F_{\\Delta G}$ , which maps from the template space to the query space [33, 41], as $\\mathbf{x} \\coloneqq F_{\\Delta G}^{\\prime}(\\mathbf{x}^{\\prime})$ , and can be supervised using a cycle loss $\\mathcal{L}_{\\mathrm{cyc}}$ (see the supplementary material for details). Note that the deformed mesh proxy might not reflect fine-grained details of the specific shape identity. It facilitates applying shape priors to the edited field and provides essential guidance during geometric editing.", + "bbox": [ + 75, + 155, + 470, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning geometric editing with users' 2D editing. The goal of geometric editing is to deform the given NeRF according to the edited target image while satisfying semantic properties. To this end, apart from the geometric prior loss in Eq. (2), we add the following geometric editing loss in two folds. (1) We encourage the edited NeRF to satisfy the user's edited image by directly supervising rendering colors and opacity on $N_{r}$ rays, which is defined as:", + "bbox": [ + 75, + 386, + 468, + 507 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {g t}} = \\frac {1}{| N _ {r} |} \\sum_ {\\boldsymbol {r} \\in N _ {r}} \\left\\| \\hat {C} (\\boldsymbol {r}) - C _ {t} (\\boldsymbol {r}) \\right\\| _ {2} ^ {2} + \\operatorname {B C E} \\left(\\hat {O} (\\boldsymbol {r}), O _ {e} (\\boldsymbol {r})\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 508, + 467, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The first photometric loss term encourages the rendered color $\\hat{C}(\\boldsymbol{r})$ close to the edited target color $C_t(\\boldsymbol{r})$ . The second silhouette loss term enforces the rendered opacity $\\hat{O}(\\boldsymbol{r})$ close to the edited object's silhouette $O_e(\\boldsymbol{r})$ (derived from users' editing tools) by minimizing the binary cross-entropy loss, where $\\hat{O}(\\boldsymbol{r}) = \\sum_{i=1}^{N} T_i \\alpha_i$ . (2) To obtain a spatially smooth deformation and mitigate overfitting to the mesh's surface points, inspired by previous works [15, 48, 49], we also add deformation regularization as:", + "bbox": [ + 75, + 561, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {g r}} = \\frac {1}{M} \\sum_ {i = 1} ^ {N} | | \\nabla F _ {\\Delta G} (\\mathbf {p} _ {i}) | | _ {2} + | | F _ {\\Delta G} (\\mathbf {p} _ {i}) - F _ {\\Delta G} (\\mathbf {p} _ {i} + \\epsilon) | | _ {1}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 700, + 470, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the first term penalizes the spatial gradient of the geometric editing, and the second term encourages the editing to be smooth under a mild 3D positional jitter $\\epsilon$ .", + "bbox": [ + 75, + 753, + 468, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall geometric editing loss is defined as:", + "bbox": [ + 96, + 803, + 413, + 816 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {g e o}} = \\lambda_ {\\mathrm {g p}} \\mathcal {L} _ {\\mathrm {g p}} + \\mathcal {L} _ {\\mathrm {g t}} + \\lambda_ {\\mathrm {g r}} \\mathcal {L} _ {\\mathrm {g r}} + \\lambda_ {\\mathrm {c y c}} \\mathcal {L} _ {\\mathrm {c y c}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 820, + 468, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we set $\\lambda_{\\mathrm{gp}} = 0.03$ , $\\lambda_{\\mathrm{gr}} = 0.1$ and $\\lambda_{\\mathrm{cyc}} = 10$ . Intuitively, the geometric editing loss $\\mathcal{L}_{\\mathrm{geo}}$ jointly optimizes edited NeRF's geometry $\\hat{M}_E$ and the latent shape code $\\hat{\\mathbf{z}}$ (for category-level objects) to best fit the user's 2D editing", + "bbox": [ + 75, + 838, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9cc630d15ac491cd3bea4b97b80638ed782d59fa8df1558b7ff42408b765262b.jpg", + "image_caption": [ + "(a) Geometric Prior Guidance" + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 890, + 239 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bd665c5fc612d82114b96ab2dbda1388b11068361743e2d09845343d1e4eb9bd.jpg", + "image_caption": [ + "(b) Texture Prior Guidance", + "Figure 3. We leverage geometric [3, 15] and texture [7, 62] priors to guide the learning of semantic-driven NeRF editing." + ], + "image_footnote": [], + "bbox": [ + 513, + 252, + 887, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "while maintaining shape prior's semantic properties (i.e., shape symmetry or physical conformity).", + "bbox": [ + 498, + 417, + 890, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Prior-Guided Texture Editing", + "text_level": 1, + "bbox": [ + 500, + 454, + 764, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Semantic texture prior supervision. In our task, users only conduct editing on a single image, but we hope to naturally propagate editing effects to multi-views with semantic meaning (see Fig. 1). Therefore, we need to utilize semantic texture supervision that supports transferring the editing to the given NeRF across views, rather than using a pixel-aligned photometric loss. Inspired by Tumanyan et al. [62], we use a pre-trained ViT model [7] as the semantic texture prior, and apply the texture transferring loss in a multi-view manner as illustrated in Fig. 3 (b), which is defined as:", + "bbox": [ + 496, + 472, + 890, + 623 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {t e x}} = \\left| \\left| t _ {\\mathrm {C L S}} \\left(I _ {t}\\right) - t _ {\\mathrm {C L S}} (\\hat {I}) \\right| \\right| _ {2} + \\left| \\left| S \\left(\\hat {I} _ {o}\\right) - S (\\hat {I}) \\right| \\right| _ {F}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 625, + 890, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I_{t}$ is the user's edited image, $\\hat{I}_o$ and $\\hat{I}$ are the template image and edited image as introduced in Sec. 3.1. $t_{\\mathrm{CLS}}(\\cdot)$ and $S(\\cdot)$ are the extracted deepest CLS token and the structural self-similarity defined by Tumanyan et al. [62]. Essentially, this loss encourages $\\hat{I}_o$ and $\\hat{I}$ to share a similar spatial structure, and $\\hat{I}_t$ and $\\hat{I}$ to contain similar image cues.", + "bbox": [ + 496, + 643, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoupled rendering with color compositing layer. To achieve texture modification, a naive approach is to directly add the modification color $\\mathbf{m}'$ from the editing field to the template NeRF's radiance color $\\mathbf{c}'$ during volume rendering. However, we find it suffers from sub-optimal convergence when cooperating with texture transferring loss (see Sec. 4.5), since NeRF struggles to learn the global-consistent appearance under the variational supervisory as shown in Fig. 8(a). To tackle this issue, we re-design the rendering pipeline in a decoupled manner. As shown in Fig. 2, we first render the deformed template image $\\hat{I}_o$ with", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "20922", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "template NeRF and the color modification $\\hat{I}_m$ with $F_{\\Delta T}$ , and then use a 2D CNN-based color compositing layer to deferred blend the modification $\\hat{I}_m$ into the template image $\\hat{I}_o$ , which yields final edited view $\\hat{I}$ . Intuitively, the coordinate-based editing field can encode fine-grained details from photometric constraints but cannot easily learn from coarse semantic supervision, while the proposed color compositing layer can reduce the difficulty by using easy-to-learn CNN layers before applying texture transferring loss. Besides, it also learns view-dependent effects from the semantic prior, making the rendering results more realistic (e.g., the shining diamond effect in Fig. 1).", + "bbox": [ + 75, + 89, + 472, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Editing Regularization", + "text_level": 1, + "bbox": [ + 76, + 277, + 289, + 294 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Feature-cluster-based semantic masking. To precisely edit the desired region while preserving other content unchanged, inspired by previous works [30, 61, 63], we learn a distilled feature field with DINO-ViT [7] to reconstruct scenes/objects with semantic features. However, existing semantic field decomposing approaches [30, 61] are limited to the query-based similarity and require all the editing to be finalized on the 3D field, which is not compatible with our color compositing mechanism. Therefore, we leverage users' editing silhouette $M_e$ to generate several feature clusters from the distilled feature map, and compute semantic masks $\\hat{M}_e$ using the closest cosine similarity to cluster centers with a threshold, which will be served for image-based editing regularization.", + "bbox": [ + 75, + 297, + 472, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regularization on geometric and texture editing. With the semantic masks that indicate the editing area, we can apply editing regularization to the geometric and texture editing, i.e., by enforcing the rendered pixels and the queries at the irrelevant part unchanged, which is defined as:", + "bbox": [ + 75, + 510, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\sum_ {\\mathbf {x} \\in \\hat {I} \\backslash \\hat {M} _ {e}} | | F _ {\\Delta G} (\\mathbf {x}) | | _ {1} + \\sum_ {\\mathbf {r} \\in \\hat {I} \\backslash \\hat {M} _ {e}} | | \\hat {C} (\\mathbf {r}) - \\hat {C} _ {o} (\\mathbf {r}) | | _ {2} ^ {2}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 585, + 468, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the sampled points $\\mathbf{x}$ and rays $\\pmb{r}$ are both from the background area of the computed semantic masks $\\hat{M}_e$ .", + "bbox": [ + 75, + 623, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 669, + 209, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 689, + 179, + 704 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate SINE on both real-world/synthetic and object/scene datasets, including real-world car dataset [54], PhotoShape datasets (synthetic chairs) [47], “pinecone”, “vasedeck”, and “garden” from NeRF real-world $360^{\\circ}$ scenes [2, 42], “chairs” and “hotdog” from NeRF photorealistic synthetic data [42], bird status from DTU [25] dataset, and “airplane” from BlenderSwap [37]. Please refer to the supplementary material for more details.", + "bbox": [ + 75, + 708, + 468, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Semantic-driven vs. Manual Editing", + "text_level": 1, + "bbox": [ + 76, + 835, + 393, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first clarify the difference between our semantic-driven NeRF editing and manual NeRF editing (e.g., NeuMesh [69], NeRF-Editing [74]). As illustrated in Fig. 4", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/00b2a3a7996e634dfba593e61178554da045b44b5fa5e44132d810006385f57d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 89, + 651, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8e806e0d27e68bbce4a20e09e3737ead8a5cd0113226b7c3eb147e044b569626.jpg", + "image_caption": [], + "image_footnote": [ + "(a) Image-based geometric editing vs. manual geometric editing" + ], + "bbox": [ + 509, + 157, + 647, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c0aff3aafb90d47429330e757e64f38e1b609f0db2b6d2d99842aa11fa5d795c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 90, + 880, + 157 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/95697844db0c365cfbb70a8b6282014b14a1712e07105fb4621e4f2317aadefe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 157, + 880, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a05d4a6bb8ed670eb451a506d8a190338fa7990de7662f72aebe7cb625ff715a.jpg", + "image_caption": [ + "Figure 4. We show the difference between our semantic-driven image-based NeRF editing and manual NeRF editing [69]." + ], + "image_footnote": [ + "(b) Semantic-driven texture editing vs. naive single-view fine-tuning" + ], + "bbox": [ + 514, + 237, + 620, + 334 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1df8ee0517e4cc4a6929f1fa7eb0240f1e1e2c567c2030a5503ca699834e3085.jpg", + "image_caption": [ + "Single-View Fine-Tuning" + ], + "image_footnote": [], + "bbox": [ + 674, + 243, + 771, + 276 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c1e2ca55be06ca1afbb7b7154af7ca3f0afa32376041420796a0dc023a22d940.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 243, + 883, + 286 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d617a3a6cc07c05e8c3a536ce36903f7654410f3b474073b7bfd545b41813cec.jpg", + "image_caption": [ + "Semantic-driven Editing" + ], + "image_footnote": [], + "bbox": [ + 676, + 297, + 771, + 334 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c365d14a17b7f4b03d81c00635e21a3e84c7b22dd2de37ba6479043b54961e7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 787, + 297, + 883, + 334 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(a), our method provides much more effortless ways than manual approaches. For example, they require 3D modeling skills to bind the skeleton of the mesh using Blender [69], or drive models [74] with Mixamo poses [58], while our method can easily achieve similar geometric editing with only a single-view image. Besides, naively fine-tuning NeRF on a single-view with a pixel-aligned photometric loss like NeuMesh [69] would only modify visible regions, which leads to inconsistent novel view rendering (e.g., in Fig. 4 (b), the car edited by single-view fine-tuning would expose unpainted red part). On the contrary, our method leverages semantic priors [7] to naturally edit objects with multi-view consistency, which does not require pixel-wise alignment and enables texture transferring between objects with different shapes (see cars and chairs in Fig. 6 (a)).", + "bbox": [ + 496, + 380, + 892, + 607 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Semantic-driven Geometric Editing", + "text_level": 1, + "bbox": [ + 500, + 609, + 808, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We first show our geometric editing results in Fig. 5 (a), where the objects can be faithfully deformed according to users' 2D editing (e.g., the airplane with warped wings [37], green chair with bent legs [42] and deformed bird status [25]). For the usage of geometry prior, we use a pre-trained DIF [15] model for cars [54], chairs [47] and planes [37], and use ARAP-based shape priors for general objects without a category-level prior (i.e., toy in Fig. 4 (a), green chair with unusual shape and status in Fig. 5 (a), etc.). Then, we compare our method with EG3D [9], a 3D-aware generative model that learns a latent representation of category-level objects, and EditNeRF [35], a NeRF variant that supports object editing with single-view user interaction. In addition to editing comparisons, we also used PSNR, SSIM, and LPIPS [42] to measure the edited rendering quality on synthetic cars and chairs. For the geometric editing on EG3D, we first conduct 3D GAN inversion to obtain the style code with multi-view images (same input", + "bbox": [ + 496, + 628, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20923", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/230f95a35f2d224ec7e6b704a74f4cd55db56ed17a3f12a7b47449e520e22cd0.jpg", + "image_caption": [ + "2D User Editing" + ], + "image_footnote": [], + "bbox": [ + 86, + 99, + 191, + 157 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c5791413423123aaf786983df5080c4e7cebfea18fe2a9590db15c3b25c4a4e5.jpg", + "image_caption": [ + "Our Rendering" + ], + "image_footnote": [], + "bbox": [ + 191, + 101, + 276, + 156 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/39471ac650f95fd6b1e3b7ea8828564b2f51c16eae9867f84dc764a26bc43d64.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 107, + 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As shown in Fig. 5 (b), we conduct different editing operations on four cars from CalWare $360^{\\circ}$ datasets with DIF shape prior [15], i.e., enlarging/shrinking tires/back. Due to the difficulty of learning a latent textured 3D representation and the limitation of data diversity, 3D-aware generative models like EG3D cannot produce rendering results with fine-grained details, which also results in lower evaluation metrics. For the Photoshape [47], EditNeRF [35] does not provide edited GT images, so we regenerate all testing cases using Blender, which is more challenging than the original ones. Then, we evaluate EditNeRF [35] by fine-tuning the pre-trained models on specific chairs from the PhotoShape dataset. As shown in Fig. 5 (c), EditNeRF produces more blurry rendering results than ours, and cannot achieve satisfactory results with single-view editing (e.g., multi-view inconsistent chair back in the first row, and unmodified or blurry shapes in the third and fourth rows). By contrast, our method consistently delivers high-fidelity rendering results and achieves reliable editing capability by leveraging geometric priors [3, 15]. This demonstrates that, for seman", + "bbox": [ + 76, + 574, + 468, + 891 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tic geometric NeRF editing, learning a prior-guided editing field like ours can maintain better visual quality and achieve greater generalization ability than pre-training a textured 3D generative model or latent model.", + "bbox": [ + 500, + 574, + 890, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Semantic-driven Texture Editing", + "text_level": 1, + "bbox": [ + 500, + 640, + 785, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our semantic texture editing ability on both objects (cars from CalWare $360^{\\circ}$ , chairs from PhotoShape [47]) and unbounded $360^{\\circ}$ scenes [2, 42]. Since our method only requires a single image as editing input, we exhibit several editing functionalities as shown in Fig. 6. Users can edit by assigning new textures on the car using Photoshop (adding sea wave windows in Fig. 6 (a)), using a downloaded Internet image with different shapes as a reference (transferring textures of cars and chairs in Fig. 6 (a)). Moreover, we cooperate SINE with off-the-shelf text-prompts editing methods [1] by using a single text-edited image as the target, which enables to change the object's appearance in the $360^{\\circ}$ scene with vivid effects (e.g., shiny plastic round table or burning pinecone in Fig.6 (b)) while preserving background unchanged. It is noteworthy that our method does not pre-train a latent model within a spe", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20924", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9f6013af96e4e6d3e36a1eab974612e9cb69c6ff54b39e441c900ed99edaa7bb.jpg", + "image_caption": [ + "Source" + ], + "image_footnote": [], + "bbox": [ + 83, + 94, + 163, + 123 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9f50d2d886e017968106686d34aecb68975534020e684c4b6699bc93fc2f7cac.jpg", + "image_caption": [ + "Target (from Internet)" + ], + "image_footnote": [], + "bbox": [ + 158, + 98, + 277, + 123 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c3eb6e35b352085c9bbd607a7d8bf963b4a17d0b8fbc7cd43bc0ddfff0766727.jpg", + "image_caption": [ + "Source" + ], + "image_footnote": [], + "bbox": [ + 98, + 140, + 142, + 186 + ], + "page_idx": 6 + }, + 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"Silver Car" + ], + "image_footnote": [], + "bbox": [ + 84, + 239, + 161, + 267 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d91f536febc42fc3d794b9822346ce91b73be5d87940336655e40df5daf462e.jpg", + "image_caption": [ + "\"Ice Sculpture Car\"" + ], + "image_footnote": [], + "bbox": [ + 189, + 234, + 313, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b74c21ee87e97930c81336c23321543e6bc47785581b0ac17aa9945a9b21ca83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 364, + 234, + 493, + 284 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/705701fa43dbd8064621866dc869effd125802e81d1d413bd425e7c43cc1f34f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 346, + 297, + 524, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6eb1f942c155174d69a113772b7805c7f2bcb9890dcb58634eb4bf05d53c5bd8.jpg", + "image_caption": [ + "(a) Texture editing with users' target images" + ], + "image_footnote": [], + "bbox": [ + 557, + 233, + 673, + 284 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aa0731624c123f0875e634d6efdf893aea29a983d4edddb2827cb2d8f192d17d.jpg", + "image_caption": [ + "\"Swarovski Blue Crystal Car\"", + "\"Snowy Vasedeck\"" + ], + "image_footnote": [], + "bbox": [ + 527, + 297, + 704, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e53b964850819022f994334aaa284e094fca9d4553279ca0c9beace2c71bebb2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 718, + 234, + 848, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f2bc11cb98222f22d890af4c9ea849008a3c0d29bcf638aa2e1c0644e3c387b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 297, + 885, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/70ed9e63f3ad9ea8c33c73a699659eccd08059a4076d0b06c2c585d69b518245.jpg", + "image_caption": [ + "Vasedeck" + ], + "image_footnote": [], + "bbox": [ + 83, + 323, + 161, + 369 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/71bfabe5e97747339d9b6a3f2370f31659c5649d06d184aa89c1f36630ba8420.jpg", + "image_caption": [ + "\"Stained Glass Vasedeck\"" + ], + "image_footnote": [], + "bbox": [ + 166, + 299, + 343, + 383 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 346, + 299, + 524, + 383 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4ad3f8889d1377c41daaf29c2f6e21443f7c1c4a8d22a715f4e948e1d1450d48.jpg", + "image_caption": [ + "\"Kid's Plasticine Round Table\"" + ], + "image_footnote": [], + "bbox": [ + 527, + 402, + 704, + 473 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/822855b80d7e63f89b377d66e43f6f2111ccd45beecb75c971fac8eacb8133ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 402, + 885, + 473 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16e771a007157ad13daa0d9257ac84227408c9d4a4788e485854d4ad0bcc2536.jpg", + "image_caption": [ + "Garden" + ], + "image_footnote": [], + "bbox": [ + 83, + 425, + 161, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/49b181905a634b5daf5061ae5c2efbdabbd2a0c47a14bc0ff87af613a1ff2b25.jpg", + "image_caption": [ + "\"Plastic Round Table\"" + ], + "image_footnote": [], + "bbox": [ + 166, + 402, + 343, + 473 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d49847b1abb9001e61eae4e13417a56699865882fc63bcc885e607fda11d53a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 346, + 402, + 522, + 473 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2411e62de124afd99ba8a629eade06d9f1c0ce51e66b17e51c5da0573ea19941.jpg", + "image_caption": [ + "\"Burning", + "Rendering" + ], + "image_footnote": [], + "bbox": [ + 527, + 494, + 704, + 580 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44e8c88d08c1363c9b522237b58108be52356ef90194abe37bc06b79e14f6656.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 494, + 885, + 580 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b72f1751f1d24959b7d31acd3ab9ee6396a7a0cc11a732569b0a05c439a3fc41.jpg", + "image_caption": [ + "Pinecone" + ], + "image_footnote": [], + "bbox": [ + 83, + 518, + 161, + 564 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0400218bfb67c49117270644a7f4d5e5ee059a92c6dde5bca668e3900904ea1.jpg", + "image_caption": [ + "\"Golden Pinecone\"" + ], + "image_footnote": [], + "bbox": [ + 166, + 494, + 343, + 580 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad4067351809715d950789130b4719cd93121ce17e77160abe94a643056be6e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 88, + 645, + 210, + 695 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2d5daab57c6b1ae89d621d9688b62d158013bb9aeb5560280f2e48e27fbb2de1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 648, + 310, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/91397635fb27eab0662e41368a7379d2b6362e3d846bc5ff0449d2d859ea527d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 313, + 648, + 419, + 691 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cac615dff18645cbfa1ae8055c4109fceb15961a676aa629c941dae6cf7727fc.jpg", + "image_caption": [ + "(b) Texture editing with text-prompts", + "Figure 6. We show our texture editing results when given users' target images and cooperating with text-prompt-based editing methods [1]." + ], + "image_footnote": [], + "bbox": [ + 421, + 640, + 537, + 698 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c502f58d00c4b188035499ff774ed96ba4142492f804a3de3a3581a61c4c440f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 540, + 640, + 653, + 696 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed2f6a3a23200853084e587a6f8a807041abc41b4a4b952c8eed0e85fcff0794.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 640, + 769, + 696 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/606e9ef5519efde8822135d7a6758d3a98d1ac2f33a11611529212340c1059eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 640, + 887, + 696 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d76959ba05c0e08ab9fcc6b68cba0bcbd6df19ebe6994d729bad27d23ecd057e.jpg", + "image_caption": [ + "Source / Target" + ], + "image_footnote": [], + "bbox": [ + 89, + 699, + 205, + 753 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/17bde7e124391893735242d25134eac7af8f7aa9a181b962c1892b2c08653610.jpg", + "image_caption": [ + "ARF" + ], + "image_footnote": [], + "bbox": [ + 214, + 710, + 313, + 760 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/01a6a13711abdfeaf8c22007db5a367bfc3b22dd45d173f86e39abf2d529fce2.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 320, + 710, + 419, + 761 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c528a47139befef008148f190a0062ae5881d156778f92efa15280a500cd3e42.jpg", + "image_caption": [ + "Source / Target", + "(a) Comparison of texture editing with target images." + ], + "image_footnote": [], + "bbox": [ + 424, + 702, + 537, + 766 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/963e2ec43661165bb41a50fbeec8bf7a1d507a11696b23677726c887dc83d552.jpg", + "image_caption": [ + "ARF" + ], + "image_footnote": [], + "bbox": [ + 540, + 700, + 653, + 766 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ad733432b4e4e5ca53bb52c473af572508015e9ec3d8239c8e09f454e18fee2.jpg", + "image_caption": [ + "CLIP-NeRF", + "(b) Comparison of texture editing with text-prompts.", + "Figure 7. We compare our texture editing with ARF [75] and CLIP-NeRF [64] on the real-world cars [54] and $360^{\\circ}$ [2,42] scene dataset." + ], + "image_footnote": [], + "bbox": [ + 656, + 700, + 771, + 767 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef702d8ff9fd901e5d214a05c71a8646fd7d457c1056c647226c0a474321742f.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 774, + 700, + 887, + 766 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cific category like cars or chairs, yet still transfers texture between objects with correct semantic meaning, e.g., the texture styles of chair legs and cloths in the edited views are precisely matched to the target images in Fig. 6 (a). Besides, we also compare our methods with ARF [75], a", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "NeRF stylization method that also takes a single reference image as input, and CLIP-NeRF [64], which supports text-driven NeRF editing using the large language model [52]. As demonstrated in Fig. 7, ARF globally changes appearance colors to the given target images but fails to produce", + "bbox": [ + 498, + 824, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20925", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/efdcdabc31f9a46a28b0596a7b5f114d164bb50fb502435285ddf47ed4a2a448.jpg", + "image_caption": [ + "(a) Ablation studies of color compositing mechanism.", + "(b) Ablation studies of editing regularization." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/86c4f409705d0802ba663a145a1caeafc59949a2db2e8baadd235ddf1fa67467.jpg", + "image_caption": [ + "Figure 8. We analyze the effectiveness of the color compositing mechanism and editing regularization in texture editing.", + "Figure 9. We inspect the efficacy of the geometric prior constraint and editing regularization in geometric editing." + ], + "image_footnote": [], + "bbox": [ + 83, + 238, + 468, + 435 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fine-grained details (e.g., cookie tires in Fig. 7 (a)). For CLIP-NeRF, since it directly fine-tunes NeRF's color layers, the results only show color/hue adjustment on the original scene (e.g., in Fig. 7, the round table turns gray instead of a realistic silver texture, the vasedeck turns blue instead of a shining diamond). Thanks to the prior-guided editing field, our method learns more fine-grained editing details than the others, and achieves texture editing with consistent semantic meaning to the given target images (e.g., similar appearance to the Tesla's cybertruck in Fig. 7 (a)), and delivers rich appearance details and vivid effects (e.g., silver texture and shining diamond effects in Fig. 7 (b)).", + "bbox": [ + 75, + 470, + 468, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "User study. We also perform user studies to compare our texture editing (including target-image-based editing and text-prompts editing as Fig. 7) with ARF [75] and CLIP-NeRF [64] on 43 cases with 30 users. The results show that users prefer our methods $(89.5\\% / 83.3\\%)$ to ARF $(10.4\\% / 7.4\\%)$ and CLIP-NeRF $(9.3\\%)$ . Please refer to the supplementary material for more details.", + "bbox": [ + 75, + 652, + 470, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 761, + 241, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Geometric prior constraints. We first analyze the effectiveness of geometric prior constraints (Sec. 3.2) by ablating geometric prior loss (Eq. (2)) in Fig. 9 (i.e., deforming cars and airplanes with DIF shape prior, and adding plates with general shape prior). As shown in Fig. 9 (b), when learning without geometric prior constraints, the object will be distorted when rendered from other views (e.g., collapsed car back, twisted airplanes, and warped hotdog plates). By ap-", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "plying geometric prior constraints, we successfully mitigate the geometric ambiguity for single-image-based editing and produce plausible rendering results from novel views.", + "bbox": [ + 496, + 239, + 890, + 285 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Color compositing mechanism. We then inspect the efficacy of the color compositing mechanism (Sec. 3.3) by disabling the texture modification field $F_{\\Delta T}$ and the color compositing layer in turn. As demonstrated in Fig. 8 (a), when learning texture editing without $F_{\\Delta T}$ , the rendered edited object can show a similar global appearance to the target, but lose vivid local patterns (e.g., gray and white grains and blue shininess). When ablating the color compositing layers, the editing effect might not be properly applied to every part of the object (e.g., the uncovered gray part of the car's front). When all the compositing mechanism is enabled, we successfully learn NeRF editing with fine-grained local patterns and globally similar appearance.", + "bbox": [ + 496, + 286, + 892, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Editing regularization. We finally evaluate the editing regularization (Sec. 3.4) in geometric and texture editing by ablating regularization loss (Eq. (7)). As shown in Fig. 9 (c) and Fig. 8 (b), when learning editing without regularization, the irrelevant part would be inevitably changed (e.g., bent car's front and airplane's head in Fig. 9 (c), a spurious cookie at the car's front and snowy background in Fig. 8 (b)). By adding editing regularization, we can modify the user-desired objects precisely while preserving other content unchanged.", + "bbox": [ + 496, + 482, + 892, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Please refer to the supplementary material for more experiments (e.g., ablation on more loss terms, visualization of color composition layer, discussion with external supervision, etc.).", + "bbox": [ + 496, + 633, + 890, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 707, + 617, + 722 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a novel semantic-driven NeRF editing approach, which supports editing a photo-realistic template NeRF with a single user-edited image, and delivers edited novel views with high-fidelity and multi-view consistency. As a limitation, our approach does not support editing with topology changes, which can be future work. Besides, our method assumes users' editing to be semantically meaningful, so we cannot use target images with meaningless random paintings.", + "bbox": [ + 496, + 731, + 890, + 867 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment. This work was partially supported by NSF of China (No. 62102356).", + "bbox": [ + 496, + 868, + 890, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20926", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. arXiv preprint arXiv:2204.02491, 2022. 1, 2, 6, 7", + "[2] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.227, + 0.067, + 0.745, + 0.113 + ], + "angle": 0, + "content": "SINE: Semantic-driven Image-based NeRF Editing with Prior-guided Editing Field" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.121, + 0.757, + 0.194 + ], + "angle": 0, + "content": "Chong Bao\\(^{1*}\\) Yinda Zhang\\(^{2*}\\) Bangbang Yang\\(^{1*}\\) Tianxing Fan\\(^{1}\\) \nZesong Yang\\(^{1}\\) Hujun Bao\\(^{1}\\) Guofeng Zhang\\(^{1\\dagger}\\) Zhaopeng Cui\\(^{1\\dagger}\\) \n\\(^{1}\\)State Key Lab of CAD&CG, Zhejiang University \\(^{2}\\)Google https://zju3dv.github.io/sine/" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.2, + 0.424, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.426, + 0.2, + 0.889, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.372, + 0.893, + 0.402 + ], + "angle": 0, + "content": "Figure 1. We propose a novel semantic-driven image-based editing approach, which allows users to edit a photo-realistic NeRF with a single-view image or with text prompts, and renders edited novel views with vivid details and multi-view consistency." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.413, + 0.314, + 0.429 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.443, + 0.474, + 0.76 + ], + "angle": 0, + "content": "Despite the great success in 2D editing using user-friendly tools, such as Photoshop, semantic strokes, or even text prompts, similar capabilities in 3D areas are still limited, either relying on 3D modeling skills or allowing editing within only a few categories. In this paper, we present a novel semantic-driven NeRF editing approach, which enables users to edit a neural radiance field with a single image, and faithfully delivers edited novel views with high fidelity and multi-view consistency. To achieve this goal, we propose a prior-guided editing field to encode fine-grained geometric and texture editing in 3D space, and develop a series of techniques to aid the editing process, including cyclic constraints with a proxy mesh to facilitate geometric supervision, a color compositing mechanism to stabilize semantic-driven texture editing, and a feature-cluster-based regularization to preserve the irrelevant content unchanged. Extensive experiments and editing examples on both real-world and synthetic data demonstrate that our method achieves photo-realistic 3D editing using only a single edited image, pushing the bound of semantic-driven editing in 3D real-world scenes." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.764, + 0.21, + 0.78 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.789, + 0.47, + 0.867 + ], + "angle": 0, + "content": "Semantic-driven editing approaches, such as stroke-based scene editing [34, 39, 66], text-driven image synthesis and editing [1, 50, 53], and attribute-based face editing [27, 60], have greatly improved the ease of artistic creation. However, despite the great success of 2D image edit" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.414, + 0.893, + 0.626 + ], + "angle": 0, + "content": "ing and neural rendering techniques [14, 42], similar editing abilities in the 3D area are still limited: (1) they require laborious annotation such as image masks [27, 71] and mesh vertices [69, 74] to achieve the desired manipulation; (2) they conduct global style transfer [12, 13, 16, 20, 75] while ignoring the semantic meaning of each object part (e.g., windows and tires of a vehicle should be textured differently); (3) they can edit on categories by learning a textured 3D latent representation (e.g., 3D-aware GANs with faces and cars etc.) [6, 8, 9, 17, 45, 56, 59, 60], or at a coarse level [35, 64] with basic color assignment or object-level disentanglement [30], but struggle to conduct texture editing on objects with photo-realistic textures or out-of-distribution characteristics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.84 + ], + "angle": 0, + "content": "Based on this observation, we believe that, on the way toward semantic-driven 3D editing, the following properties should be ensured. First, the operation of editing should be effortless, i.e., users can edit 3D scenes on a single 2D image in convenient ways, e.g., using off-the-shelf tools such as GAN-based editing [28, 34], text-driven editing [1, 53], Photoshop, or even a downloaded Internet image without pixel-wise alignment, rather than steering 3D modeling software with specific knowledge [69], or repeatedly editing from multi-view images. Second, the editing method should be applicable to real-world scenes or objects and preserve vivid appearances, which is beyond existing 3D-aware generative models [8, 9] due to the limited categories and insufficient data diversity on real-world objects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.9 + ], + "angle": 0, + "content": "To fulfill this goal, we propose a novel Semantic-driven Image-based Editing approach for Neural radiance field in real-world scenes, named SINE. Specifically, our method allows users to edit a neural radiance field with a sin-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.254, + 0.888 + ], + "angle": 0, + "content": "*Authors contributed equally." + }, + { + "type": "page_footnote", + "bbox": [ + 0.098, + 0.888, + 0.227, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.254, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20919" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.35 + ], + "angle": 0, + "content": "gle image, i.e., either by changing a rendered image using off-the-shelf image editing tools or providing an image for texture transferring (see Sec. 4.4), and then delivers edited novel views with consistent semantic meaning. Unlike previous works that directly fine-tune the existing NeRF model [30, 35, 64], SINE learns a prior-guided editing field to encode geometric and texture changes over the original 3D scene (see Fig. 2), thus enabling fine-grained editing ability. By leveraging guidance from existing neural priors (shape prior models [15] and Vision Transformer models [7], etc.), SINE can directly perform semantic-driven editing on photo-realistic scenes without pre-training a category-level latent space. For example, in Fig. 1, users can stretch a car's back or change all four tires to cookies by only editing a single image, and can even cooperate with text-prompts editing [1] to modify a specific object of a scene with vivid appearances." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.761 + ], + "angle": 0, + "content": "However, even when guided with neural priors, editing NeRF from a single image with multi-view consistency and accuracy is still challenging. (1) The generic NeRF does not necessarily provide an explicit surface or signed distance field, such that it cannot directly work with shape priors [15]. Therefore, we propose to use cyclic constraints with a proxy mesh to represent the edited NeRF's geometry, which facilitates guided editing using coarse shape prior. (2) Learning a coordinate-based 3D editing field using a single edited view is not sufficient to capture fine-grained details, and applying semantic supervision [7, 52] directly to the editing field leads to sub-optimal convergence (see Sec. 4.5). To tackle these challenges, we propose a color compositing mechanism by first rendering the template NeRF color and modification color individually, and then deferred blending them to yield the edited view, which significantly improves semantic-driven texture editing. (3) Ideally, a user's editing should only affect the desired regions while maintaining other parts untouched. However, in semantic-driven editing, the prior losses require taking the full shape or image as input, which leads to appearance or shape drifting at the undesired area. To precisely control the editing while excluding irrelevant parts from being affected, we generate feature clusters of the editing area using the ViT-based feature field [7, 30], and use these clusters to distinguish whether a location is allowed to be edited or should remain unchanged." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In summary, the contributions of our paper are as follows. (1) We propose a novel semantic-driven image-based NeRF editing approach, called SINE, which allows users to edit a neural radiance field simply on just a single view of the rendering. SINE leverages a prior-guided editing field to encode fine-grained geometry and texture changes over the given pre-trained NeRF, thus delivering multi-view consistent edited views with high fidelity. (2) To achieve semantic editing functionality, we develop a series of techniques," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "including cyclic constraints with a proxy mesh for geometric editing, the color compositing mechanism to enhance texture editing, and the feature-cluster-based regularization to control the affected editing area and maintain irrelevant parts unchanged. (3) Experiments and editing examples on both real-world/synthetic and object-centric/unbounded \\(360^{\\circ}\\) scenes data demonstrate superior editing capabilities and quality with effortless operations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.222, + 0.651, + 0.238 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.895, + 0.835 + ], + "angle": 0, + "content": "Neural rendering with external priors. Neural rendering techniques aim at rendering novel views with high-quality [42] or controllable properties [27, 48] by learning from 2D photo capture. Recently, NeRF [42] achieves photo-realistic rendering with volume rendering and inspires many works, including surface reconstruction [31,65, 73], scene editing [4, 18, 67, 70, 71] and generation [22, 51], inverse rendering [5, 76], SLAM [72, 77], etc. For learning from few-shot images [23] or 3D inpainting [43], NeRF's variants use hand-crafted losses [44] or large language-image models [23, 68] as external priors. However, due to insufficient 3D supervision, such methods cannot reconstruct accurate geometry and only produce visually plausible results. Besides, some works [21, 32, 40] use the symmetric assumption to reconstruct category-level objects (e.g., cars, chairs) but cannot generalize on complex scenes. Neural 2D & 3D scene editing. With the development of neural networks, semantic-driven 2D photo editing allows user editing in various friendly ways, such as controlling attribute of faces [19, 28], stroke-based editing [34, 39, 66], sketch-to-image generation [11, 55], image-to-image texture transferring [62], or text-driven image generation [53] and editing [29]. Nevertheless, in 3D scene editing, similar capabilities are still limited due to the high demand for multi-view consistency. Existing approaches either rely on laborious annotation [27, 69, 71, 74], only support object deformation or translation [30, 61, 63, 74], or only perform global style transfer [12, 13, 16, 20, 75] without strong semantic meaning. Recently, 3D-aware GANs [8, 9, 17, 24, 45, 56, 59] and semantic NeRF editing [35, 64] learn a latent space of the category and enable editing via latent code control. However, the quality and editing ability of these methods mainly depend on the dataset (e.g., human faces [59, 60] or objects in ShapeNet [10]), and they cannot generalize to objects with rich appearances or out-of-distribution features [1]. In contrast, our method allows for semantic-driven editing directly on the given photo-realistic NeRF, and uses a prior-guided editing field to learn fine-grained editing from only a single image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.593, + 0.861 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We first formulate the goal of our semantic NeRF editing task as follows. As illustrated in the left part of Fig. 2," + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20920" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.094, + 0.068, + 0.295, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.299, + 0.068, + 0.653, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.656, + 0.069, + 0.878, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.276, + 0.894, + 0.332 + ], + "angle": 0, + "content": "Figure 2. Overview. We encode geometric and texture changes over the original template NeRF with a prior-guided editing field, where the geometric modification field \\( F_{\\Delta G} \\) transformed the edited space query \\( \\mathbf{x} \\) into the template space \\( \\mathbf{x}' \\), and the texture modification field \\( F_{\\Delta T} \\) encodes modification colors \\( \\mathbf{m}' \\). Then, we render deformed template image \\( \\hat{I}_o \\) and color modification image \\( \\hat{I}_m \\) with all the queries, and use a color compositing layer to blend \\( \\hat{I}_o \\) and \\( \\hat{I}_m \\) into the edited view \\( \\hat{I} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.474, + 0.552 + ], + "angle": 0, + "content": "given a pre-trained NeRF of a photo-realistic scene (named template NeRF), we aim at editing the template NeRF using only a single-view 2D image, and then produce novel views with consistent semantic meaning (see Sec. 4.3 and Sec. 4.4). Note that naively fine-tuning on the edited single view cannot obtain satisfactory results due to the spatial ambiguity and lack of multi-view supervision (see Sec. 4.2). Therefore, we propose to use a novel prior-guided editing field to encode fine-grained changes (Sec. 3.1) in 3D space, which leverages geometry and texture priors to guide the learning of semantic-driven editing (Sec. 3.2 and Sec. 3.3). Besides, to precisely control the editing area while maintaining other parts unchanged, we design editing regularization with feature cluster-based semantic masking (Sec. 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.564, + 0.31, + 0.581 + ], + "angle": 0, + "content": "3.1. SINE Rendering Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.471, + 0.812 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, we use a dedicated editing field to encode geometry and texture changes over the pre-trained template NeRF. The editing field consists of an implicit geometric modification field \\( F_{\\Delta G} \\) and a texture modification field \\( F_{\\Delta T} \\), where \\( F_{\\Delta G} \\) deforms the query points from the observed edited space to the original template space, as \\( \\mathbf{x}' \\coloneqq F_{\\Delta G}(\\mathbf{x}) \\), and \\( F_{\\Delta T} \\) encodes the modification color \\( \\mathbf{m}' \\), as \\( \\mathbf{m}' \\coloneqq F_{\\Delta T}(\\mathbf{x}) \\). Specifically, for each sampled query point \\( \\{\\mathbf{x}_i | i = 1, \\dots, N\\} \\) along the ray \\( r \\) with view direction \\( d \\), we first obtain the deformed points \\( \\mathbf{x}' \\) (in template space) and modification color \\( \\mathbf{m}' \\), and feed \\( \\mathbf{x}' \\) and \\( d \\) to the template NeRF to obtain the density \\( \\delta' \\) and template colors \\( \\mathbf{c}' \\). Then, we perform dual volume rendering both on edited fields and template NeRF following the quadrature rules [38,42], which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.813, + 0.47, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {C} _ {o} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} \\mathbf {c} _ {i} ^ {\\prime}, \\quad \\hat {C} _ {e} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} \\mathbf {m} _ {i} ^ {\\prime}, \\tag {1} \\\\ T _ {i} = \\exp \\left(- \\sum_ {j = 1} ^ {i - 1} \\sigma^ {\\prime} _ {j} \\delta_ {j}\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.892, + 0.446 + ], + "angle": 0, + "content": "where \\(\\alpha_{i} = 1 - \\exp (-\\sigma^{\\prime}_{i}\\delta_{i})\\), and \\(\\delta_{i}\\) is the distance between adjacent samples along the ray. In this way, we obtain the deformed template image \\(\\hat{I}_o\\) from the template NeRF's pixel color \\(\\hat{C}_o(\\boldsymbol {r})\\) and color modification image \\(\\hat{I}_m\\) from the modification color \\(\\hat{C}_e(\\boldsymbol {r})\\). Finally, we apply the color compositing layer (see Sec. 3.3) to blend \\(\\hat{I}_o\\) and \\(\\hat{I}_m\\) into the resulting edited views \\(\\hat{I}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.787, + 0.466 + ], + "angle": 0, + "content": "3.2. Prior-Guided Geometric Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.891, + 0.498 + ], + "angle": 0, + "content": "In this section, we explain how to learn \\( F_{\\Delta G}(\\mathbf{x}) \\) with the geometric prior." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.65 + ], + "angle": 0, + "content": "Shape prior constraint on the edited NeRF. We leverage geometric prior models, such as neural implicit shape representation [15, 46] or depth prediction [3], to mitigate the ambiguity of geometric editing based on editing from a single perspective. (1) For objects within a certain shape category (e.g., cars, airplanes), we use DIF [15], in which the implicit SDF field and the prior mesh \\(\\hat{M}_P\\) can be generated with the condition of an estimizable latent code \\(\\hat{\\mathbf{z}}\\). We force the edited NeRF's geometry \\(\\hat{M}_E\\) to be explainable by a pre-trained DIF model with the geometric prior loss:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.652, + 0.891, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal{L}_{gp} = \\min_{\\hat{\\mathbf{z}}}\\bigl(\\sum_{\\mathbf{p}^{\\prime}\\in \\hat{M}_{E}}f_{\\mathrm{SDF}}(\\hat{\\mathbf{z}},\\mathbf{p}^{\\prime}) + \\lambda ||\\hat{\\mathbf{z}} ||_{2}^{2}\\bigr) \\\\ + \\sum_ {\\mathbf {p} _ {i} ^ {\\prime} \\in \\hat {M} _ {E}} \\min _ {\\mathbf {p} _ {t} \\in \\hat {M} _ {P}} | | \\mathbf {p} _ {i} ^ {\\prime} - \\mathbf {p} _ {t} | | _ {2} ^ {2} \\tag {2} \\\\ + \\sum_ {\\mathbf {p} _ {i} \\in \\hat {M} _ {P}} \\min _ {\\mathbf {p} _ {t} ^ {\\prime} \\in \\hat {M} _ {E}} | | \\mathbf {p} _ {i} - \\mathbf {p} _ {t} ^ {\\prime} | | _ {2} ^ {2}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The first term encourages the sampled surface points on the edited NeRF's geometry \\(\\hat{M}_E\\) to lie on the manifold of DIF's latent space with an SDF loss \\(f_{\\mathrm{SDF}}\\) and the latent code regularization [15]. The last two terms are Chamfer constraints, which enforce the \\(\\hat{M}_E\\) close to the DIF's periodically updated prior mesh \\(\\hat{M}_P\\) [36] by minimizing the closest surface points. (2) For objects without a category-level prior, we can build a finalized shape prior \\(\\hat{M}_P\\) beforehand. Practically, we find 3D deforming vertices with 2D correspond" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20921" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "dence [26] and monocular depth prediction [3], and use ARAP [57] to deform the proxy triangle mesh \\( M_{\\Theta} \\) to \\( \\hat{M}_P \\). Then, we can inherit the Chamfer loss term in Eq. (2) for prior-guided supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.156, + 0.471, + 0.384 + ], + "angle": 0, + "content": "Representing edited NeRF's geometry as a deformed proxy mesh. The edited NeRF has no explicit surface definition or SDF field to directly apply the geometric prior loss (Eq. (2)). Therefore, to obtain the edited mesh surface \\(\\hat{M}_E\\), as illustrated in Fig. 3 (a), we first fit the template NeRF geometry with a proxy mesh \\(M_{\\Theta}\\) [36, 65], and then learn a forward modification field \\(F_{\\Delta G}^{\\prime}\\) to warp the template proxy mesh to the edited space. \\(F_{\\Delta G}^{\\prime}\\) is an inverse of the editing field \\(F_{\\Delta G}\\), which maps from the template space to the query space [33, 41], as \\(\\mathbf{x} \\coloneqq F_{\\Delta G}^{\\prime}(\\mathbf{x}^{\\prime})\\), and can be supervised using a cycle loss \\(\\mathcal{L}_{\\mathrm{cyc}}\\) (see the supplementary material for details). Note that the deformed mesh proxy might not reflect fine-grained details of the specific shape identity. It facilitates applying shape priors to the edited field and provides essential guidance during geometric editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.508 + ], + "angle": 0, + "content": "Learning geometric editing with users' 2D editing. The goal of geometric editing is to deform the given NeRF according to the edited target image while satisfying semantic properties. To this end, apart from the geometric prior loss in Eq. (2), we add the following geometric editing loss in two folds. (1) We encourage the edited NeRF to satisfy the user's edited image by directly supervising rendering colors and opacity on \\( N_{r} \\) rays, which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.51, + 0.468, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {g t}} = \\frac {1}{| N _ {r} |} \\sum_ {\\boldsymbol {r} \\in N _ {r}} \\left\\| \\hat {C} (\\boldsymbol {r}) - C _ {t} (\\boldsymbol {r}) \\right\\| _ {2} ^ {2} + \\operatorname {B C E} \\left(\\hat {O} (\\boldsymbol {r}), O _ {e} (\\boldsymbol {r})\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.698 + ], + "angle": 0, + "content": "The first photometric loss term encourages the rendered color \\(\\hat{C}(\\boldsymbol{r})\\) close to the edited target color \\(C_t(\\boldsymbol{r})\\). The second silhouette loss term enforces the rendered opacity \\(\\hat{O}(\\boldsymbol{r})\\) close to the edited object's silhouette \\(O_e(\\boldsymbol{r})\\) (derived from users' editing tools) by minimizing the binary cross-entropy loss, where \\(\\hat{O}(\\boldsymbol{r}) = \\sum_{i=1}^{N} T_i \\alpha_i\\). (2) To obtain a spatially smooth deformation and mitigate overfitting to the mesh's surface points, inspired by previous works [15, 48, 49], we also add deformation regularization as:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.701, + 0.472, + 0.753 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {g r}} = \\frac {1}{M} \\sum_ {i = 1} ^ {N} | | \\nabla F _ {\\Delta G} (\\mathbf {p} _ {i}) | | _ {2} + | | F _ {\\Delta G} (\\mathbf {p} _ {i}) - F _ {\\Delta G} (\\mathbf {p} _ {i} + \\epsilon) | | _ {1}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.8 + ], + "angle": 0, + "content": "where the first term penalizes the spatial gradient of the geometric editing, and the second term encourages the editing to be smooth under a mild 3D positional jitter \\(\\epsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.804, + 0.414, + 0.818 + ], + "angle": 0, + "content": "The overall geometric editing loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.821, + 0.469, + 0.838 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {g e o}} = \\lambda_ {\\mathrm {g p}} \\mathcal {L} _ {\\mathrm {g p}} + \\mathcal {L} _ {\\mathrm {g t}} + \\lambda_ {\\mathrm {g r}} \\mathcal {L} _ {\\mathrm {g r}} + \\lambda_ {\\mathrm {c y c}} \\mathcal {L} _ {\\mathrm {c y c}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.839, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where we set \\(\\lambda_{\\mathrm{gp}} = 0.03\\), \\(\\lambda_{\\mathrm{gr}} = 0.1\\) and \\(\\lambda_{\\mathrm{cyc}} = 10\\). Intuitively, the geometric editing loss \\(\\mathcal{L}_{\\mathrm{geo}}\\) jointly optimizes edited NeRF's geometry \\(\\hat{M}_E\\) and the latent shape code \\(\\hat{\\mathbf{z}}\\) (for category-level objects) to best fit the user's 2D editing" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.091, + 0.892, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.609, + 0.24, + 0.788, + 0.251 + ], + "angle": 0, + "content": "(a) Geometric Prior Guidance" + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.253, + 0.888, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.371, + 0.771, + 0.382 + ], + "angle": 0, + "content": "(b) Texture Prior Guidance" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.382, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Figure 3. We leverage geometric [3, 15] and texture [7, 62] priors to guide the learning of semantic-driven NeRF editing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.418, + 0.891, + 0.45 + ], + "angle": 0, + "content": "while maintaining shape prior's semantic properties (i.e., shape symmetry or physical conformity)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.455, + 0.766, + 0.47 + ], + "angle": 0, + "content": "3.3. Prior-Guided Texture Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Semantic texture prior supervision. In our task, users only conduct editing on a single image, but we hope to naturally propagate editing effects to multi-views with semantic meaning (see Fig. 1). Therefore, we need to utilize semantic texture supervision that supports transferring the editing to the given NeRF across views, rather than using a pixel-aligned photometric loss. Inspired by Tumanyan et al. [62], we use a pre-trained ViT model [7] as the semantic texture prior, and apply the texture transferring loss in a multi-view manner as illustrated in Fig. 3 (b), which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.625, + 0.892, + 0.643 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {t e x}} = \\left| \\left| t _ {\\mathrm {C L S}} \\left(I _ {t}\\right) - t _ {\\mathrm {C L S}} (\\hat {I}) \\right| \\right| _ {2} + \\left| \\left| S \\left(\\hat {I} _ {o}\\right) - S (\\hat {I}) \\right| \\right| _ {F}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.735 + ], + "angle": 0, + "content": "where \\(I_{t}\\) is the user's edited image, \\(\\hat{I}_o\\) and \\(\\hat{I}\\) are the template image and edited image as introduced in Sec. 3.1. \\(t_{\\mathrm{CLS}}(\\cdot)\\) and \\(S(\\cdot)\\) are the extracted deepest CLS token and the structural self-similarity defined by Tumanyan et al. [62]. Essentially, this loss encourages \\(\\hat{I}_o\\) and \\(\\hat{I}\\) to share a similar spatial structure, and \\(\\hat{I}_t\\) and \\(\\hat{I}\\) to contain similar image cues." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Decoupled rendering with color compositing layer. To achieve texture modification, a naive approach is to directly add the modification color \\(\\mathbf{m}'\\) from the editing field to the template NeRF's radiance color \\(\\mathbf{c}'\\) during volume rendering. However, we find it suffers from sub-optimal convergence when cooperating with texture transferring loss (see Sec. 4.5), since NeRF struggles to learn the global-consistent appearance under the variational supervisory as shown in Fig. 8(a). To tackle this issue, we re-design the rendering pipeline in a decoupled manner. As shown in Fig. 2, we first render the deformed template image \\(\\hat{I}_o\\) with" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20922" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.473, + 0.273 + ], + "angle": 0, + "content": "template NeRF and the color modification \\(\\hat{I}_m\\) with \\(F_{\\Delta T}\\), and then use a 2D CNN-based color compositing layer to deferred blend the modification \\(\\hat{I}_m\\) into the template image \\(\\hat{I}_o\\), which yields final edited view \\(\\hat{I}\\). Intuitively, the coordinate-based editing field can encode fine-grained details from photometric constraints but cannot easily learn from coarse semantic supervision, while the proposed color compositing layer can reduce the difficulty by using easy-to-learn CNN layers before applying texture transferring loss. Besides, it also learns view-dependent effects from the semantic prior, making the rendering results more realistic (e.g., the shining diamond effect in Fig. 1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.279, + 0.29, + 0.295 + ], + "angle": 0, + "content": "3.4. Editing Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.299, + 0.473, + 0.51 + ], + "angle": 0, + "content": "Feature-cluster-based semantic masking. To precisely edit the desired region while preserving other content unchanged, inspired by previous works [30, 61, 63], we learn a distilled feature field with DINO-ViT [7] to reconstruct scenes/objects with semantic features. However, existing semantic field decomposing approaches [30, 61] are limited to the query-based similarity and require all the editing to be finalized on the 3D field, which is not compatible with our color compositing mechanism. Therefore, we leverage users' editing silhouette \\( M_e \\) to generate several feature clusters from the distilled feature map, and compute semantic masks \\( \\hat{M}_e \\) using the closest cosine similarity to cluster centers with a threshold, which will be served for image-based editing regularization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.511, + 0.47, + 0.586 + ], + "angle": 0, + "content": "Regularization on geometric and texture editing. With the semantic masks that indicate the editing area, we can apply editing regularization to the geometric and texture editing, i.e., by enforcing the rendered pixels and the queries at the irrelevant part unchanged, which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.587, + 0.47, + 0.623 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\sum_ {\\mathbf {x} \\in \\hat {I} \\backslash \\hat {M} _ {e}} | | F _ {\\Delta G} (\\mathbf {x}) | | _ {1} + \\sum_ {\\mathbf {r} \\in \\hat {I} \\backslash \\hat {M} _ {e}} | | \\hat {C} (\\mathbf {r}) - \\hat {C} _ {o} (\\mathbf {r}) | | _ {2} ^ {2}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.655 + ], + "angle": 0, + "content": "where the sampled points \\(\\mathbf{x}\\) and rays \\(\\pmb{r}\\) are both from the background area of the computed semantic masks \\(\\hat{M}_e\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.67, + 0.21, + 0.687 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.69, + 0.18, + 0.705 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.831 + ], + "angle": 0, + "content": "We evaluate SINE on both real-world/synthetic and object/scene datasets, including real-world car dataset [54], PhotoShape datasets (synthetic chairs) [47], “pinecone”, “vasedeck”, and “garden” from NeRF real-world \\(360^{\\circ}\\) scenes [2, 42], “chairs” and “hotdog” from NeRF photorealistic synthetic data [42], bird status from DTU [25] dataset, and “airplane” from BlenderSwap [37]. Please refer to the supplementary material for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.837, + 0.395, + 0.853 + ], + "angle": 0, + "content": "4.2. Semantic-driven vs. Manual Editing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We first clarify the difference between our semantic-driven NeRF editing and manual NeRF editing (e.g., NeuMesh [69], NeRF-Editing [74]). As illustrated in Fig. 4" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.09, + 0.652, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.159, + 0.648, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.091, + 0.882, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.159, + 0.882, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.534, + 0.221, + 0.856, + 0.234 + ], + "angle": 0, + "content": "(a) Image-based geometric editing vs. manual geometric editing" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.238, + 0.621, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.249, + 0.676, + 0.274 + ], + "angle": 0, + "content": "Single-View Fine-Tuning" + }, + { + "type": "image", + "bbox": [ + 0.676, + 0.244, + 0.772, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.244, + 0.884, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.624, + 0.295, + 0.685, + 0.319 + ], + "angle": 0, + "content": "Semantic-driven Editing" + }, + { + "type": "image", + "bbox": [ + 0.677, + 0.298, + 0.772, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.298, + 0.884, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.52, + 0.337, + 0.867, + 0.349 + ], + "angle": 0, + "content": "(b) Semantic-driven texture editing vs. naive single-view fine-tuning" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.35, + 0.892, + 0.377 + ], + "angle": 0, + "content": "Figure 4. We show the difference between our semantic-driven image-based NeRF editing and manual NeRF editing [69]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.893, + 0.608 + ], + "angle": 0, + "content": "(a), our method provides much more effortless ways than manual approaches. For example, they require 3D modeling skills to bind the skeleton of the mesh using Blender [69], or drive models [74] with Mixamo poses [58], while our method can easily achieve similar geometric editing with only a single-view image. Besides, naively fine-tuning NeRF on a single-view with a pixel-aligned photometric loss like NeuMesh [69] would only modify visible regions, which leads to inconsistent novel view rendering (e.g., in Fig. 4 (b), the car edited by single-view fine-tuning would expose unpainted red part). On the contrary, our method leverages semantic priors [7] to naturally edit objects with multi-view consistency, which does not require pixel-wise alignment and enables texture transferring between objects with different shapes (see cars and chairs in Fig. 6 (a))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.611, + 0.81, + 0.627 + ], + "angle": 0, + "content": "4.3. Semantic-driven Geometric Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We first show our geometric editing results in Fig. 5 (a), where the objects can be faithfully deformed according to users' 2D editing (e.g., the airplane with warped wings [37], green chair with bent legs [42] and deformed bird status [25]). For the usage of geometry prior, we use a pre-trained DIF [15] model for cars [54], chairs [47] and planes [37], and use ARAP-based shape priors for general objects without a category-level prior (i.e., toy in Fig. 4 (a), green chair with unusual shape and status in Fig. 5 (a), etc.). Then, we compare our method with EG3D [9], a 3D-aware generative model that learns a latent representation of category-level objects, and EditNeRF [35], a NeRF variant that supports object editing with single-view user interaction. In addition to editing comparisons, we also used PSNR, SSIM, and LPIPS [42] to measure the edited rendering quality on synthetic cars and chairs. For the geometric editing on EG3D, we first conduct 3D GAN inversion to obtain the style code with multi-view images (same input" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20923" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.101, + 0.192, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.16, + 0.18, + 0.171 + ], + "angle": 0, + "content": "2D User Editing" + }, + { + "type": "image", + "bbox": [ + 0.192, + 0.102, + 0.277, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.237, + 0.16, + 0.311, + 0.171 + ], + "angle": 0, + "content": "Our Rendering" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.108, + 0.372, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.379, + 0.092, + 0.45, + 0.155 + ], + "angle": 0, + "content": null + }, + { + "type": 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+ { + "type": "image", + "bbox": [ + 0.846, + 0.347, + 0.887, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.845, + 0.383, + 0.887, + 0.417 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.846, + 0.427, + 0.887, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.846, + 0.464, + 0.887, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.823, + 0.507, + 0.848, + 0.515 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.521, + 0.885, + 0.529 + ], + "angle": 0, + "content": "24.96/0.94/0.06" + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.534, + 0.454, + 0.545 + ], + "angle": 0, + "content": "(b) Comparison with EG3D on the real-world car dataset." + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.534, + 0.882, + 0.545 + ], + "angle": 0, + "content": "(c) Comparison with EditNeRF on the PhotoShape dataset." + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.547, + 0.866, + 0.56 + ], + "angle": 0, + "content": "Figure 5. We compare the geometric editing with EG3D [9] and EditNeRF [35] on the real-world cars [54] and PhotoShape [47]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.575, + 0.47, + 0.892 + ], + "angle": 0, + "content": "as ours), and then fine-tune the code on the target images. As shown in Fig. 5 (b), we conduct different editing operations on four cars from CalWare \\(360^{\\circ}\\) datasets with DIF shape prior [15], i.e., enlarging/shrinking tires/back. Due to the difficulty of learning a latent textured 3D representation and the limitation of data diversity, 3D-aware generative models like EG3D cannot produce rendering results with fine-grained details, which also results in lower evaluation metrics. For the Photoshape [47], EditNeRF [35] does not provide edited GT images, so we regenerate all testing cases using Blender, which is more challenging than the original ones. Then, we evaluate EditNeRF [35] by fine-tuning the pre-trained models on specific chairs from the PhotoShape dataset. As shown in Fig. 5 (c), EditNeRF produces more blurry rendering results than ours, and cannot achieve satisfactory results with single-view editing (e.g., multi-view inconsistent chair back in the first row, and unmodified or blurry shapes in the third and fourth rows). By contrast, our method consistently delivers high-fidelity rendering results and achieves reliable editing capability by leveraging geometric priors [3, 15]. This demonstrates that, for seman" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.575, + 0.891, + 0.635 + ], + "angle": 0, + "content": "tic geometric NeRF editing, learning a prior-guided editing field like ours can maintain better visual quality and achieve greater generalization ability than pre-training a textured 3D generative model or latent model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.641, + 0.787, + 0.657 + ], + "angle": 0, + "content": "4.4. Semantic-driven Texture Editing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate our semantic texture editing ability on both objects (cars from CalWare \\(360^{\\circ}\\), chairs from PhotoShape [47]) and unbounded \\(360^{\\circ}\\) scenes [2, 42]. Since our method only requires a single image as editing input, we exhibit several editing functionalities as shown in Fig. 6. Users can edit by assigning new textures on the car using Photoshop (adding sea wave windows in Fig. 6 (a)), using a downloaded Internet image with different shapes as a reference (transferring textures of cars and chairs in Fig. 6 (a)). Moreover, we cooperate SINE with off-the-shelf text-prompts editing methods [1] by using a single text-edited image as the target, which enables to change the object's appearance in the \\(360^{\\circ}\\) scene with vivid effects (e.g., shiny plastic round table or burning pinecone in Fig.6 (b)) while preserving background unchanged. It is noteworthy that our method does not pre-train a latent model within a spe" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20924" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.095, + 0.164, + 0.124 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.128, + 0.143, + 0.138 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.099, + 0.279, + 0.124 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.128, + 0.293, + 0.138 + ], + "angle": 0, + "content": "Target (from Internet)" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.141, + 0.143, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.19, + 0.142, + 0.2 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image", + "bbox": [ + 0.161, + 0.141, + 0.207, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.19, + 0.218, + 0.201 + ], + "angle": 0, + "content": "Target" + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.202, + 0.218, + 0.212 + ], + "angle": 0, + "content": "(from Internet)" + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.141, + 0.314, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.24, + 0.19, + 0.302, + 0.201 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.096, + 0.376, + 0.126 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.128, + 0.416, + 0.139 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.141, + 0.377, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.096, + 0.47, + 0.126 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.13, + 0.416, + 0.139 + ], + "angle": 0, + "content": "ering" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.141, + 0.477, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.403, + 0.19, + 0.465, + 0.201 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.213, + 0.614, + 0.227 + ], + "angle": 0, + "content": "(a) Texture editing with users' target images" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.092, + 0.576, + 0.125 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.592, + 0.092, + 0.681, + 0.125 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.128, + 0.548, + 0.139 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.128, + 0.7, + 0.139 + ], + "angle": 0, + "content": "Target (User Editing)" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.141, + 0.548, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.19, + 0.549, + 0.2 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image", + "bbox": [ + 0.554, + 0.141, + 0.606, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.19, + 0.606, + 0.201 + ], + "angle": 0, + "content": "Target" + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.202, + 0.622, + 0.212 + ], + "angle": 0, + "content": "(from Internet)" + }, + { + "type": "image", + "bbox": [ + 0.619, + 0.142, + 0.707, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.631, + 0.19, + 0.693, + 0.201 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.092, + 0.772, + 0.126 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.128, + 0.808, + 0.139 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.141, + 0.774, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.785, + 0.092, + 0.869, + 0.126 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.128, + 0.808, + 0.139 + ], + "angle": 0, + "content": "ring" + }, + { + "type": "image", + "bbox": [ + 0.786, + 0.141, + 0.876, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.19, + 0.862, + 0.201 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.241, + 0.163, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.092, + 0.271, + 0.154, + 0.282 + ], + "angle": 0, + "content": "Silver Car" + }, + { + "type": "image", + "bbox": [ + 0.191, + 0.235, + 0.314, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.283, + 0.286, + 0.399, + 0.297 + ], + "angle": 0, + "content": "\"Ice Sculpture Car\"" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.236, + 0.495, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.348, + 0.298, + 0.525, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.27, + 0.387, + 0.422, + 0.398 + ], + "angle": 0, + "content": "\"Stained Glass Vasedeck\"" + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.234, + 0.674, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.623, + 0.286, + 0.796, + 0.298 + ], + "angle": 0, + "content": "\"Swarovski Blue Crystal Car\"" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.298, + 0.705, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.654, + 0.387, + 0.762, + 0.398 + ], + "angle": 0, + "content": "\"Snowy Vasedeck\"" + }, + { + "type": "image", + "bbox": [ + 0.719, + 0.235, + 0.849, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.298, + 0.887, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.324, + 0.163, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.374, + 0.151, + 0.385 + ], + "angle": 0, + "content": "Vasedeck" + }, + { + "type": "image", + "bbox": [ + 0.167, + 0.3, + 0.344, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.348, + 0.3, + 0.525, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.404, + 0.705, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.618, + 0.477, + 0.797, + 0.489 + ], + "angle": 0, + "content": "\"Kid's Plasticine Round Table\"" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.404, + 0.886, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.426, + 0.163, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.469, + 0.145, + 0.48 + ], + "angle": 0, + "content": "Garden" + }, + { + "type": "image", + "bbox": [ + 0.167, + 0.404, + 0.344, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.281, + 0.477, + 0.41, + 0.489 + ], + "angle": 0, + "content": "\"Plastic Round Table\"" + }, + { + "type": "image", + "bbox": [ + 0.348, + 0.404, + 0.524, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.496, + 0.705, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.65, + 0.585, + 0.704, + 0.596 + ], + "angle": 0, + "content": "\"Burning" + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.496, + 0.886, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.52, + 0.163, + 0.565 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.569, + 0.151, + 0.579 + ], + "angle": 0, + "content": "Pinecone" + }, + { + "type": "image", + "bbox": [ + 0.168, + 0.495, + 0.344, + 0.582 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.585, + 0.401, + 0.595 + ], + "angle": 0, + "content": "\"Golden Pinecone\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.491, + 0.599, + 0.554, + 0.61 + ], + "angle": 0, + "content": "Rendering" + }, + { + "type": "image_caption", + "bbox": [ + 0.413, + 0.611, + 0.633, + 0.623 + ], + "angle": 0, + "content": "(b) Texture editing with text-prompts" + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.624, + 0.891, + 0.637 + ], + "angle": 0, + "content": "Figure 6. We show our texture editing results when given users' target images and cooperating with text-prompt-based editing methods [1]." + }, + { + "type": "image", + "bbox": [ + 0.089, + 0.646, + 0.211, + 0.696 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.203, + 0.649, + 0.311, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.649, + 0.421, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.423, + 0.641, + 0.538, + 0.699 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.641, + 0.655, + 0.698 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.641, + 0.771, + 0.698 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.641, + 0.888, + 0.698 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.7, + 0.206, + 0.755 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.768, + 0.195, + 0.779 + ], + "angle": 0, + "content": "Source / Target" + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.711, + 0.315, + 0.761 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.249, + 0.768, + 0.278, + 0.778 + ], + "angle": 0, + "content": "ARF" + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.711, + 0.421, + 0.762 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.348, + 0.768, + 0.377, + 0.778 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.425, + 0.703, + 0.538, + 0.767 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.442, + 0.768, + 0.527, + 0.779 + ], + "angle": 0, + "content": "Source / Target" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.702, + 0.655, + 0.767 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.592, + 0.768, + 0.619, + 0.778 + ], + "angle": 0, + "content": "ARF" + }, + { + "type": "image", + "bbox": [ + 0.658, + 0.702, + 0.772, + 0.768 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.768, + 0.75, + 0.778 + ], + "angle": 0, + "content": "CLIP-NeRF" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.702, + 0.888, + 0.767 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.768, + 0.848, + 0.778 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.782, + 0.416, + 0.796 + ], + "angle": 0, + "content": "(a) Comparison of texture editing with target images." + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.782, + 0.834, + 0.796 + ], + "angle": 0, + "content": "(b) Comparison of texture editing with text-prompts." + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.797, + 0.888, + 0.811 + ], + "angle": 0, + "content": "Figure 7. We compare our texture editing with ARF [75] and CLIP-NeRF [64] on the real-world cars [54] and \\(360^{\\circ}\\) [2,42] scene dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.9 + ], + "angle": 0, + "content": "cific category like cars or chairs, yet still transfers texture between objects with correct semantic meaning, e.g., the texture styles of chair legs and cloths in the edited views are precisely matched to the target images in Fig. 6 (a). Besides, we also compare our methods with ARF [75], a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "NeRF stylization method that also takes a single reference image as input, and CLIP-NeRF [64], which supports text-driven NeRF editing using the large language model [52]. As demonstrated in Fig. 7, ARF globally changes appearance colors to the given target images but fails to produce" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20925" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.202, + 0.453, + 0.213 + ], + "angle": 0, + "content": "(a) Ablation studies of color compositing mechanism." + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.202, + 0.816, + 0.214 + ], + "angle": 0, + "content": "(b) Ablation studies of editing regularization." + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.214, + 0.838, + 0.227 + ], + "angle": 0, + "content": "Figure 8. We analyze the effectiveness of the color compositing mechanism and editing regularization in texture editing." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.239, + 0.47, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.438, + 0.47, + 0.465 + ], + "angle": 0, + "content": "Figure 9. We inspect the efficacy of the geometric prior constraint and editing regularization in geometric editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.47, + 0.652 + ], + "angle": 0, + "content": "fine-grained details (e.g., cookie tires in Fig. 7 (a)). For CLIP-NeRF, since it directly fine-tunes NeRF's color layers, the results only show color/hue adjustment on the original scene (e.g., in Fig. 7, the round table turns gray instead of a realistic silver texture, the vasedeck turns blue instead of a shining diamond). Thanks to the prior-guided editing field, our method learns more fine-grained editing details than the others, and achieves texture editing with consistent semantic meaning to the given target images (e.g., similar appearance to the Tesla's cybertruck in Fig. 7 (a)), and delivers rich appearance details and vivid effects (e.g., silver texture and shining diamond effects in Fig. 7 (b))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.471, + 0.758 + ], + "angle": 0, + "content": "User study. We also perform user studies to compare our texture editing (including target-image-based editing and text-prompts editing as Fig. 7) with ARF [75] and CLIP-NeRF [64] on 43 cases with 30 users. The results show that users prefer our methods \\((89.5\\% / 83.3\\%)\\) to ARF \\((10.4\\% / 7.4\\%)\\) and CLIP-NeRF \\((9.3\\%)\\). Please refer to the supplementary material for more details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.762, + 0.242, + 0.777 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Geometric prior constraints. We first analyze the effectiveness of geometric prior constraints (Sec. 3.2) by ablating geometric prior loss (Eq. (2)) in Fig. 9 (i.e., deforming cars and airplanes with DIF shape prior, and adding plates with general shape prior). As shown in Fig. 9 (b), when learning without geometric prior constraints, the object will be distorted when rendered from other views (e.g., collapsed car back, twisted airplanes, and warped hotdog plates). By ap-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.241, + 0.892, + 0.286 + ], + "angle": 0, + "content": "plying geometric prior constraints, we successfully mitigate the geometric ambiguity for single-image-based editing and produce plausible rendering results from novel views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.893, + 0.482 + ], + "angle": 0, + "content": "Color compositing mechanism. We then inspect the efficacy of the color compositing mechanism (Sec. 3.3) by disabling the texture modification field \\( F_{\\Delta T} \\) and the color compositing layer in turn. As demonstrated in Fig. 8 (a), when learning texture editing without \\( F_{\\Delta T} \\), the rendered edited object can show a similar global appearance to the target, but lose vivid local patterns (e.g., gray and white grains and blue shininess). When ablating the color compositing layers, the editing effect might not be properly applied to every part of the object (e.g., the uncovered gray part of the car's front). When all the compositing mechanism is enabled, we successfully learn NeRF editing with fine-grained local patterns and globally similar appearance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.893, + 0.633 + ], + "angle": 0, + "content": "Editing regularization. We finally evaluate the editing regularization (Sec. 3.4) in geometric and texture editing by ablating regularization loss (Eq. (7)). As shown in Fig. 9 (c) and Fig. 8 (b), when learning editing without regularization, the irrelevant part would be inevitably changed (e.g., bent car's front and airplane's head in Fig. 9 (c), a spurious cookie at the car's front and snowy background in Fig. 8 (b)). By adding editing regularization, we can modify the user-desired objects precisely while preserving other content unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.892, + 0.693 + ], + "angle": 0, + "content": "Please refer to the supplementary material for more experiments (e.g., ablation on more loss terms, visualization of color composition layer, discussion with external supervision, etc.)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.708, + 0.619, + 0.723 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.868 + ], + "angle": 0, + "content": "We have proposed a novel semantic-driven NeRF editing approach, which supports editing a photo-realistic template NeRF with a single user-edited image, and delivers edited novel views with high-fidelity and multi-view consistency. As a limitation, our approach does not support editing with topology changes, which can be future work. Besides, our method assumes users' editing to be semantically meaningful, so we cannot use target images with meaningless random paintings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.869, + 0.892, + 0.898 + ], + "angle": 0, + "content": "Acknowledgment. This work was partially supported by NSF of China (No. 62102356)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20926" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. arXiv preprint arXiv:2204.02491, 2022. 1, 2, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Jonathan T. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12786-12796, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.866 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20929" + } + ] +] \ No newline at end of file diff --git a/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/98bd5d41-9994-4c5a-92c8-200bf021b945_origin.pdf b/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/98bd5d41-9994-4c5a-92c8-200bf021b945_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..56a0f087b9d5cf54ea4f9e1313e4ec948ff5e7a0 --- /dev/null +++ b/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/98bd5d41-9994-4c5a-92c8-200bf021b945_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0d6b191dd0b6b970f719035c2f8bc9ef2fe7863216bf9f5200a66cb19aaeca2b +size 6480898 diff --git a/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/full.md b/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/full.md new file mode 100644 index 0000000000000000000000000000000000000000..dd2c0b167b0d93404196dc5e27a583bb5559b082 --- /dev/null +++ b/2023/SINE_ Semantic-Driven Image-Based NeRF Editing With Prior-Guided Editing Field/full.md @@ -0,0 +1,617 @@ +# SINE: Semantic-driven Image-based NeRF Editing with Prior-guided Editing Field + +Chong Bao $^{1*}$ Yinda Zhang $^{2*}$ Bangbang Yang $^{1*}$ Tianxing Fan $^{1}$ +Zesong Yang $^{1}$ Hujun Bao $^{1}$ Guofeng Zhang $^{1\dagger}$ Zhaopeng Cui $^{1\dagger}$ $^{1}$ State Key Lab of CAD&CG, Zhejiang University $^{2}$ Google https://zju3dv.github.io/sine/ + +![](images/4757b30ae703efa5bbf6b1197c945b6a540dbb6f7a90bd46cf99b80b6be23427.jpg) +Figure 1. We propose a novel semantic-driven image-based editing approach, which allows users to edit a photo-realistic NeRF with a single-view image or with text prompts, and renders edited novel views with vivid details and multi-view consistency. + +![](images/7f6dd04e1bca8e5f7a5560cbfebecae4177f0ffd26c55a0b3cf5d73c0aee71c0.jpg) + +# Abstract + +Despite the great success in 2D editing using user-friendly tools, such as Photoshop, semantic strokes, or even text prompts, similar capabilities in 3D areas are still limited, either relying on 3D modeling skills or allowing editing within only a few categories. In this paper, we present a novel semantic-driven NeRF editing approach, which enables users to edit a neural radiance field with a single image, and faithfully delivers edited novel views with high fidelity and multi-view consistency. To achieve this goal, we propose a prior-guided editing field to encode fine-grained geometric and texture editing in 3D space, and develop a series of techniques to aid the editing process, including cyclic constraints with a proxy mesh to facilitate geometric supervision, a color compositing mechanism to stabilize semantic-driven texture editing, and a feature-cluster-based regularization to preserve the irrelevant content unchanged. Extensive experiments and editing examples on both real-world and synthetic data demonstrate that our method achieves photo-realistic 3D editing using only a single edited image, pushing the bound of semantic-driven editing in 3D real-world scenes. + +# 1. Introduction + +Semantic-driven editing approaches, such as stroke-based scene editing [34, 39, 66], text-driven image synthesis and editing [1, 50, 53], and attribute-based face editing [27, 60], have greatly improved the ease of artistic creation. However, despite the great success of 2D image edit + +ing and neural rendering techniques [14, 42], similar editing abilities in the 3D area are still limited: (1) they require laborious annotation such as image masks [27, 71] and mesh vertices [69, 74] to achieve the desired manipulation; (2) they conduct global style transfer [12, 13, 16, 20, 75] while ignoring the semantic meaning of each object part (e.g., windows and tires of a vehicle should be textured differently); (3) they can edit on categories by learning a textured 3D latent representation (e.g., 3D-aware GANs with faces and cars etc.) [6, 8, 9, 17, 45, 56, 59, 60], or at a coarse level [35, 64] with basic color assignment or object-level disentanglement [30], but struggle to conduct texture editing on objects with photo-realistic textures or out-of-distribution characteristics. + +Based on this observation, we believe that, on the way toward semantic-driven 3D editing, the following properties should be ensured. First, the operation of editing should be effortless, i.e., users can edit 3D scenes on a single 2D image in convenient ways, e.g., using off-the-shelf tools such as GAN-based editing [28, 34], text-driven editing [1, 53], Photoshop, or even a downloaded Internet image without pixel-wise alignment, rather than steering 3D modeling software with specific knowledge [69], or repeatedly editing from multi-view images. Second, the editing method should be applicable to real-world scenes or objects and preserve vivid appearances, which is beyond existing 3D-aware generative models [8, 9] due to the limited categories and insufficient data diversity on real-world objects. + +To fulfill this goal, we propose a novel Semantic-driven Image-based Editing approach for Neural radiance field in real-world scenes, named SINE. Specifically, our method allows users to edit a neural radiance field with a sin- + +gle image, i.e., either by changing a rendered image using off-the-shelf image editing tools or providing an image for texture transferring (see Sec. 4.4), and then delivers edited novel views with consistent semantic meaning. Unlike previous works that directly fine-tune the existing NeRF model [30, 35, 64], SINE learns a prior-guided editing field to encode geometric and texture changes over the original 3D scene (see Fig. 2), thus enabling fine-grained editing ability. By leveraging guidance from existing neural priors (shape prior models [15] and Vision Transformer models [7], etc.), SINE can directly perform semantic-driven editing on photo-realistic scenes without pre-training a category-level latent space. For example, in Fig. 1, users can stretch a car's back or change all four tires to cookies by only editing a single image, and can even cooperate with text-prompts editing [1] to modify a specific object of a scene with vivid appearances. + +However, even when guided with neural priors, editing NeRF from a single image with multi-view consistency and accuracy is still challenging. (1) The generic NeRF does not necessarily provide an explicit surface or signed distance field, such that it cannot directly work with shape priors [15]. Therefore, we propose to use cyclic constraints with a proxy mesh to represent the edited NeRF's geometry, which facilitates guided editing using coarse shape prior. (2) Learning a coordinate-based 3D editing field using a single edited view is not sufficient to capture fine-grained details, and applying semantic supervision [7, 52] directly to the editing field leads to sub-optimal convergence (see Sec. 4.5). To tackle these challenges, we propose a color compositing mechanism by first rendering the template NeRF color and modification color individually, and then deferred blending them to yield the edited view, which significantly improves semantic-driven texture editing. (3) Ideally, a user's editing should only affect the desired regions while maintaining other parts untouched. However, in semantic-driven editing, the prior losses require taking the full shape or image as input, which leads to appearance or shape drifting at the undesired area. To precisely control the editing while excluding irrelevant parts from being affected, we generate feature clusters of the editing area using the ViT-based feature field [7, 30], and use these clusters to distinguish whether a location is allowed to be edited or should remain unchanged. + +In summary, the contributions of our paper are as follows. (1) We propose a novel semantic-driven image-based NeRF editing approach, called SINE, which allows users to edit a neural radiance field simply on just a single view of the rendering. SINE leverages a prior-guided editing field to encode fine-grained geometry and texture changes over the given pre-trained NeRF, thus delivering multi-view consistent edited views with high fidelity. (2) To achieve semantic editing functionality, we develop a series of techniques, + +including cyclic constraints with a proxy mesh for geometric editing, the color compositing mechanism to enhance texture editing, and the feature-cluster-based regularization to control the affected editing area and maintain irrelevant parts unchanged. (3) Experiments and editing examples on both real-world/synthetic and object-centric/unbounded $360^{\circ}$ scenes data demonstrate superior editing capabilities and quality with effortless operations. + +# 2. Related Works + +Neural rendering with external priors. Neural rendering techniques aim at rendering novel views with high-quality [42] or controllable properties [27, 48] by learning from 2D photo capture. Recently, NeRF [42] achieves photo-realistic rendering with volume rendering and inspires many works, including surface reconstruction [31,65, 73], scene editing [4, 18, 67, 70, 71] and generation [22, 51], inverse rendering [5, 76], SLAM [72, 77], etc. For learning from few-shot images [23] or 3D inpainting [43], NeRF's variants use hand-crafted losses [44] or large language-image models [23, 68] as external priors. However, due to insufficient 3D supervision, such methods cannot reconstruct accurate geometry and only produce visually plausible results. Besides, some works [21, 32, 40] use the symmetric assumption to reconstruct category-level objects (e.g., cars, chairs) but cannot generalize on complex scenes. Neural 2D & 3D scene editing. With the development of neural networks, semantic-driven 2D photo editing allows user editing in various friendly ways, such as controlling attribute of faces [19, 28], stroke-based editing [34, 39, 66], sketch-to-image generation [11, 55], image-to-image texture transferring [62], or text-driven image generation [53] and editing [29]. Nevertheless, in 3D scene editing, similar capabilities are still limited due to the high demand for multi-view consistency. Existing approaches either rely on laborious annotation [27, 69, 71, 74], only support object deformation or translation [30, 61, 63, 74], or only perform global style transfer [12, 13, 16, 20, 75] without strong semantic meaning. Recently, 3D-aware GANs [8, 9, 17, 24, 45, 56, 59] and semantic NeRF editing [35, 64] learn a latent space of the category and enable editing via latent code control. However, the quality and editing ability of these methods mainly depend on the dataset (e.g., human faces [59, 60] or objects in ShapeNet [10]), and they cannot generalize to objects with rich appearances or out-of-distribution features [1]. In contrast, our method allows for semantic-driven editing directly on the given photo-realistic NeRF, and uses a prior-guided editing field to learn fine-grained editing from only a single image. + +# 3. Method + +We first formulate the goal of our semantic NeRF editing task as follows. As illustrated in the left part of Fig. 2, + +![](images/6b6466b8e020a4b36c5de6daa64f71298661f1549e2791f5cd7b0f7bba140247.jpg) +Figure 2. Overview. We encode geometric and texture changes over the original template NeRF with a prior-guided editing field, where the geometric modification field $F_{\Delta G}$ transformed the edited space query $\mathbf{x}$ into the template space $\mathbf{x}'$ , and the texture modification field $F_{\Delta T}$ encodes modification colors $\mathbf{m}'$ . Then, we render deformed template image $\hat{I}_o$ and color modification image $\hat{I}_m$ with all the queries, and use a color compositing layer to blend $\hat{I}_o$ and $\hat{I}_m$ into the edited view $\hat{I}$ . + +![](images/083065336e39a14d99352c688140f11033cbd5234bec460e9fe15d54eedb2203.jpg) + +![](images/9543a069156a473733ebcd87c90a98efebcc98b957fc288a4d196293c134a780.jpg) + +given a pre-trained NeRF of a photo-realistic scene (named template NeRF), we aim at editing the template NeRF using only a single-view 2D image, and then produce novel views with consistent semantic meaning (see Sec. 4.3 and Sec. 4.4). Note that naively fine-tuning on the edited single view cannot obtain satisfactory results due to the spatial ambiguity and lack of multi-view supervision (see Sec. 4.2). Therefore, we propose to use a novel prior-guided editing field to encode fine-grained changes (Sec. 3.1) in 3D space, which leverages geometry and texture priors to guide the learning of semantic-driven editing (Sec. 3.2 and Sec. 3.3). Besides, to precisely control the editing area while maintaining other parts unchanged, we design editing regularization with feature cluster-based semantic masking (Sec. 3.4). + +# 3.1. SINE Rendering Pipeline + +As illustrated in Fig. 2, we use a dedicated editing field to encode geometry and texture changes over the pre-trained template NeRF. The editing field consists of an implicit geometric modification field $F_{\Delta G}$ and a texture modification field $F_{\Delta T}$ , where $F_{\Delta G}$ deforms the query points from the observed edited space to the original template space, as $\mathbf{x}' \coloneqq F_{\Delta G}(\mathbf{x})$ , and $F_{\Delta T}$ encodes the modification color $\mathbf{m}'$ , as $\mathbf{m}' \coloneqq F_{\Delta T}(\mathbf{x})$ . Specifically, for each sampled query point $\{\mathbf{x}_i | i = 1, \dots, N\}$ along the ray $r$ with view direction $d$ , we first obtain the deformed points $\mathbf{x}'$ (in template space) and modification color $\mathbf{m}'$ , and feed $\mathbf{x}'$ and $d$ to the template NeRF to obtain the density $\delta'$ and template colors $\mathbf{c}'$ . Then, we perform dual volume rendering both on edited fields and template NeRF following the quadrature rules [38,42], which is defined as: + +$$ +\begin{array}{l} \hat {C} _ {o} (\boldsymbol {r}) = \sum_ {i = 1} ^ {N} T _ {i} \alpha_ {i} \mathbf {c} _ {i} ^ {\prime}, \quad \hat {C} _ {e} (\boldsymbol {r}) = \sum_ {i = 1} ^ {N} T _ {i} \alpha_ {i} \mathbf {m} _ {i} ^ {\prime}, \tag {1} \\ T _ {i} = \exp \left(- \sum_ {j = 1} ^ {i - 1} \sigma^ {\prime} _ {j} \delta_ {j}\right), \\ \end{array} +$$ + +where $\alpha_{i} = 1 - \exp (-\sigma^{\prime}_{i}\delta_{i})$ , and $\delta_{i}$ is the distance between adjacent samples along the ray. In this way, we obtain the deformed template image $\hat{I}_o$ from the template NeRF's pixel color $\hat{C}_o(\boldsymbol {r})$ and color modification image $\hat{I}_m$ from the modification color $\hat{C}_e(\boldsymbol {r})$ . Finally, we apply the color compositing layer (see Sec. 3.3) to blend $\hat{I}_o$ and $\hat{I}_m$ into the resulting edited views $\hat{I}$ . + +# 3.2. Prior-Guided Geometric Editing + +In this section, we explain how to learn $F_{\Delta G}(\mathbf{x})$ with the geometric prior. + +Shape prior constraint on the edited NeRF. We leverage geometric prior models, such as neural implicit shape representation [15, 46] or depth prediction [3], to mitigate the ambiguity of geometric editing based on editing from a single perspective. (1) For objects within a certain shape category (e.g., cars, airplanes), we use DIF [15], in which the implicit SDF field and the prior mesh $\hat{M}_P$ can be generated with the condition of an estimizable latent code $\hat{\mathbf{z}}$ . We force the edited NeRF's geometry $\hat{M}_E$ to be explainable by a pre-trained DIF model with the geometric prior loss: + +$$ +\begin{array}{l} \mathcal{L}_{gp} = \min_{\hat{\mathbf{z}}}\bigl(\sum_{\mathbf{p}^{\prime}\in \hat{M}_{E}}f_{\mathrm{SDF}}(\hat{\mathbf{z}},\mathbf{p}^{\prime}) + \lambda ||\hat{\mathbf{z}} ||_{2}^{2}\bigr) \\ + \sum_ {\mathbf {p} _ {i} ^ {\prime} \in \hat {M} _ {E}} \min _ {\mathbf {p} _ {t} \in \hat {M} _ {P}} | | \mathbf {p} _ {i} ^ {\prime} - \mathbf {p} _ {t} | | _ {2} ^ {2} \tag {2} \\ + \sum_ {\mathbf {p} _ {i} \in \hat {M} _ {P}} \min _ {\mathbf {p} _ {t} ^ {\prime} \in \hat {M} _ {E}} | | \mathbf {p} _ {i} - \mathbf {p} _ {t} ^ {\prime} | | _ {2} ^ {2}. \\ \end{array} +$$ + +The first term encourages the sampled surface points on the edited NeRF's geometry $\hat{M}_E$ to lie on the manifold of DIF's latent space with an SDF loss $f_{\mathrm{SDF}}$ and the latent code regularization [15]. The last two terms are Chamfer constraints, which enforce the $\hat{M}_E$ close to the DIF's periodically updated prior mesh $\hat{M}_P$ [36] by minimizing the closest surface points. (2) For objects without a category-level prior, we can build a finalized shape prior $\hat{M}_P$ beforehand. Practically, we find 3D deforming vertices with 2D correspond + +dence [26] and monocular depth prediction [3], and use ARAP [57] to deform the proxy triangle mesh $M_{\Theta}$ to $\hat{M}_P$ . Then, we can inherit the Chamfer loss term in Eq. (2) for prior-guided supervision. + +Representing edited NeRF's geometry as a deformed proxy mesh. The edited NeRF has no explicit surface definition or SDF field to directly apply the geometric prior loss (Eq. (2)). Therefore, to obtain the edited mesh surface $\hat{M}_E$ , as illustrated in Fig. 3 (a), we first fit the template NeRF geometry with a proxy mesh $M_{\Theta}$ [36, 65], and then learn a forward modification field $F_{\Delta G}^{\prime}$ to warp the template proxy mesh to the edited space. $F_{\Delta G}^{\prime}$ is an inverse of the editing field $F_{\Delta G}$ , which maps from the template space to the query space [33, 41], as $\mathbf{x} \coloneqq F_{\Delta G}^{\prime}(\mathbf{x}^{\prime})$ , and can be supervised using a cycle loss $\mathcal{L}_{\mathrm{cyc}}$ (see the supplementary material for details). Note that the deformed mesh proxy might not reflect fine-grained details of the specific shape identity. It facilitates applying shape priors to the edited field and provides essential guidance during geometric editing. + +Learning geometric editing with users' 2D editing. The goal of geometric editing is to deform the given NeRF according to the edited target image while satisfying semantic properties. To this end, apart from the geometric prior loss in Eq. (2), we add the following geometric editing loss in two folds. (1) We encourage the edited NeRF to satisfy the user's edited image by directly supervising rendering colors and opacity on $N_{r}$ rays, which is defined as: + +$$ +\mathcal {L} _ {\mathrm {g t}} = \frac {1}{| N _ {r} |} \sum_ {\boldsymbol {r} \in N _ {r}} \left\| \hat {C} (\boldsymbol {r}) - C _ {t} (\boldsymbol {r}) \right\| _ {2} ^ {2} + \operatorname {B C E} \left(\hat {O} (\boldsymbol {r}), O _ {e} (\boldsymbol {r})\right). \tag {3} +$$ + +The first photometric loss term encourages the rendered color $\hat{C}(\boldsymbol{r})$ close to the edited target color $C_t(\boldsymbol{r})$ . The second silhouette loss term enforces the rendered opacity $\hat{O}(\boldsymbol{r})$ close to the edited object's silhouette $O_e(\boldsymbol{r})$ (derived from users' editing tools) by minimizing the binary cross-entropy loss, where $\hat{O}(\boldsymbol{r}) = \sum_{i=1}^{N} T_i \alpha_i$ . (2) To obtain a spatially smooth deformation and mitigate overfitting to the mesh's surface points, inspired by previous works [15, 48, 49], we also add deformation regularization as: + +$$ +\mathcal {L} _ {\mathrm {g r}} = \frac {1}{M} \sum_ {i = 1} ^ {N} | | \nabla F _ {\Delta G} (\mathbf {p} _ {i}) | | _ {2} + | | F _ {\Delta G} (\mathbf {p} _ {i}) - F _ {\Delta G} (\mathbf {p} _ {i} + \epsilon) | | _ {1}, \tag {4} +$$ + +where the first term penalizes the spatial gradient of the geometric editing, and the second term encourages the editing to be smooth under a mild 3D positional jitter $\epsilon$ . + +The overall geometric editing loss is defined as: + +$$ +\mathcal {L} _ {\mathrm {g e o}} = \lambda_ {\mathrm {g p}} \mathcal {L} _ {\mathrm {g p}} + \mathcal {L} _ {\mathrm {g t}} + \lambda_ {\mathrm {g r}} \mathcal {L} _ {\mathrm {g r}} + \lambda_ {\mathrm {c y c}} \mathcal {L} _ {\mathrm {c y c}}, \tag {5} +$$ + +where we set $\lambda_{\mathrm{gp}} = 0.03$ , $\lambda_{\mathrm{gr}} = 0.1$ and $\lambda_{\mathrm{cyc}} = 10$ . Intuitively, the geometric editing loss $\mathcal{L}_{\mathrm{geo}}$ jointly optimizes edited NeRF's geometry $\hat{M}_E$ and the latent shape code $\hat{\mathbf{z}}$ (for category-level objects) to best fit the user's 2D editing + +![](images/9cc630d15ac491cd3bea4b97b80638ed782d59fa8df1558b7ff42408b765262b.jpg) +(a) Geometric Prior Guidance + +![](images/bd665c5fc612d82114b96ab2dbda1388b11068361743e2d09845343d1e4eb9bd.jpg) +(b) Texture Prior Guidance +Figure 3. We leverage geometric [3, 15] and texture [7, 62] priors to guide the learning of semantic-driven NeRF editing. + +while maintaining shape prior's semantic properties (i.e., shape symmetry or physical conformity). + +# 3.3. Prior-Guided Texture Editing + +Semantic texture prior supervision. In our task, users only conduct editing on a single image, but we hope to naturally propagate editing effects to multi-views with semantic meaning (see Fig. 1). Therefore, we need to utilize semantic texture supervision that supports transferring the editing to the given NeRF across views, rather than using a pixel-aligned photometric loss. Inspired by Tumanyan et al. [62], we use a pre-trained ViT model [7] as the semantic texture prior, and apply the texture transferring loss in a multi-view manner as illustrated in Fig. 3 (b), which is defined as: + +$$ +\mathcal {L} _ {\mathrm {t e x}} = \left| \left| t _ {\mathrm {C L S}} \left(I _ {t}\right) - t _ {\mathrm {C L S}} (\hat {I}) \right| \right| _ {2} + \left| \left| S \left(\hat {I} _ {o}\right) - S (\hat {I}) \right| \right| _ {F}, \tag {6} +$$ + +where $I_{t}$ is the user's edited image, $\hat{I}_o$ and $\hat{I}$ are the template image and edited image as introduced in Sec. 3.1. $t_{\mathrm{CLS}}(\cdot)$ and $S(\cdot)$ are the extracted deepest CLS token and the structural self-similarity defined by Tumanyan et al. [62]. Essentially, this loss encourages $\hat{I}_o$ and $\hat{I}$ to share a similar spatial structure, and $\hat{I}_t$ and $\hat{I}$ to contain similar image cues. + +Decoupled rendering with color compositing layer. To achieve texture modification, a naive approach is to directly add the modification color $\mathbf{m}'$ from the editing field to the template NeRF's radiance color $\mathbf{c}'$ during volume rendering. However, we find it suffers from sub-optimal convergence when cooperating with texture transferring loss (see Sec. 4.5), since NeRF struggles to learn the global-consistent appearance under the variational supervisory as shown in Fig. 8(a). To tackle this issue, we re-design the rendering pipeline in a decoupled manner. As shown in Fig. 2, we first render the deformed template image $\hat{I}_o$ with + +template NeRF and the color modification $\hat{I}_m$ with $F_{\Delta T}$ , and then use a 2D CNN-based color compositing layer to deferred blend the modification $\hat{I}_m$ into the template image $\hat{I}_o$ , which yields final edited view $\hat{I}$ . Intuitively, the coordinate-based editing field can encode fine-grained details from photometric constraints but cannot easily learn from coarse semantic supervision, while the proposed color compositing layer can reduce the difficulty by using easy-to-learn CNN layers before applying texture transferring loss. Besides, it also learns view-dependent effects from the semantic prior, making the rendering results more realistic (e.g., the shining diamond effect in Fig. 1). + +# 3.4. Editing Regularization + +Feature-cluster-based semantic masking. To precisely edit the desired region while preserving other content unchanged, inspired by previous works [30, 61, 63], we learn a distilled feature field with DINO-ViT [7] to reconstruct scenes/objects with semantic features. However, existing semantic field decomposing approaches [30, 61] are limited to the query-based similarity and require all the editing to be finalized on the 3D field, which is not compatible with our color compositing mechanism. Therefore, we leverage users' editing silhouette $M_e$ to generate several feature clusters from the distilled feature map, and compute semantic masks $\hat{M}_e$ using the closest cosine similarity to cluster centers with a threshold, which will be served for image-based editing regularization. + +Regularization on geometric and texture editing. With the semantic masks that indicate the editing area, we can apply editing regularization to the geometric and texture editing, i.e., by enforcing the rendered pixels and the queries at the irrelevant part unchanged, which is defined as: + +$$ +\mathcal {L} _ {\text {r e g}} = \sum_ {\mathbf {x} \in \hat {I} \backslash \hat {M} _ {e}} | | F _ {\Delta G} (\mathbf {x}) | | _ {1} + \sum_ {\mathbf {r} \in \hat {I} \backslash \hat {M} _ {e}} | | \hat {C} (\mathbf {r}) - \hat {C} _ {o} (\mathbf {r}) | | _ {2} ^ {2}, \tag {7} +$$ + +where the sampled points $\mathbf{x}$ and rays $\pmb{r}$ are both from the background area of the computed semantic masks $\hat{M}_e$ . + +# 4. Experiments + +# 4.1. Datasets + +We evaluate SINE on both real-world/synthetic and object/scene datasets, including real-world car dataset [54], PhotoShape datasets (synthetic chairs) [47], “pinecone”, “vasedeck”, and “garden” from NeRF real-world $360^{\circ}$ scenes [2, 42], “chairs” and “hotdog” from NeRF photorealistic synthetic data [42], bird status from DTU [25] dataset, and “airplane” from BlenderSwap [37]. Please refer to the supplementary material for more details. + +# 4.2. Semantic-driven vs. Manual Editing + +We first clarify the difference between our semantic-driven NeRF editing and manual NeRF editing (e.g., NeuMesh [69], NeRF-Editing [74]). As illustrated in Fig. 4 + +![](images/00b2a3a7996e634dfba593e61178554da045b44b5fa5e44132d810006385f57d.jpg) + +![](images/8e806e0d27e68bbce4a20e09e3737ead8a5cd0113226b7c3eb147e044b569626.jpg) +(a) Image-based geometric editing vs. manual geometric editing + +![](images/c0aff3aafb90d47429330e757e64f38e1b609f0db2b6d2d99842aa11fa5d795c.jpg) + +![](images/95697844db0c365cfbb70a8b6282014b14a1712e07105fb4621e4f2317aadefe.jpg) + +Figure 4. We show the difference between our semantic-driven image-based NeRF editing and manual NeRF editing [69]. +![](images/a05d4a6bb8ed670eb451a506d8a190338fa7990de7662f72aebe7cb625ff715a.jpg) +(b) Semantic-driven texture editing vs. naive single-view fine-tuning + +![](images/1df8ee0517e4cc4a6929f1fa7eb0240f1e1e2c567c2030a5503ca699834e3085.jpg) +Single-View Fine-Tuning + +![](images/c1e2ca55be06ca1afbb7b7154af7ca3f0afa32376041420796a0dc023a22d940.jpg) + +![](images/d617a3a6cc07c05e8c3a536ce36903f7654410f3b474073b7bfd545b41813cec.jpg) +Semantic-driven Editing + +![](images/c365d14a17b7f4b03d81c00635e21a3e84c7b22dd2de37ba6479043b54961e7d.jpg) + +(a), our method provides much more effortless ways than manual approaches. For example, they require 3D modeling skills to bind the skeleton of the mesh using Blender [69], or drive models [74] with Mixamo poses [58], while our method can easily achieve similar geometric editing with only a single-view image. Besides, naively fine-tuning NeRF on a single-view with a pixel-aligned photometric loss like NeuMesh [69] would only modify visible regions, which leads to inconsistent novel view rendering (e.g., in Fig. 4 (b), the car edited by single-view fine-tuning would expose unpainted red part). On the contrary, our method leverages semantic priors [7] to naturally edit objects with multi-view consistency, which does not require pixel-wise alignment and enables texture transferring between objects with different shapes (see cars and chairs in Fig. 6 (a)). + +# 4.3. Semantic-driven Geometric Editing + +We first show our geometric editing results in Fig. 5 (a), where the objects can be faithfully deformed according to users' 2D editing (e.g., the airplane with warped wings [37], green chair with bent legs [42] and deformed bird status [25]). For the usage of geometry prior, we use a pre-trained DIF [15] model for cars [54], chairs [47] and planes [37], and use ARAP-based shape priors for general objects without a category-level prior (i.e., toy in Fig. 4 (a), green chair with unusual shape and status in Fig. 5 (a), etc.). Then, we compare our method with EG3D [9], a 3D-aware generative model that learns a latent representation of category-level objects, and EditNeRF [35], a NeRF variant that supports object editing with single-view user interaction. In addition to editing comparisons, we also used PSNR, SSIM, and LPIPS [42] to measure the edited rendering quality on synthetic cars and chairs. For the geometric editing on EG3D, we first conduct 3D GAN inversion to obtain the style code with multi-view images (same input + +![](images/230f95a35f2d224ec7e6b704a74f4cd55db56ed17a3f12a7b47449e520e22cd0.jpg) +2D User Editing + +![](images/c5791413423123aaf786983df5080c4e7cebfea18fe2a9590db15c3b25c4a4e5.jpg) +Our Rendering + +![](images/39471ac650f95fd6b1e3b7ea8828564b2f51c16eae9867f84dc764a26bc43d64.jpg) + +![](images/d1c9d2b32d19b935c225af0b17c7cdb800b48905dc7cc99a73800367be3a5ed4.jpg) +2D User Editing + +![](images/d5a699509c242bdbdcbd0ca157e1a0e1714548b46b525f9f5bbbf6befe281f06.jpg) + +![](images/0ede81e58e1ece1d0844222068c825e06e69d286fca0baee1445925a7cbd5ade.jpg) + +![](images/ded11cc462ef8c14617ad536958cbf9fd3c69a76d7abd94026ca78c4abf3cb22.jpg) +2D User Editing + +![](images/b24b842be12b9e333dd51dcc6bfe562dad09d0e0bf8f61384633667fe326858e.jpg) +Our Rendering + +![](images/d81474256c9d987bc89bbc1cc283b13d651f62dfea3ca79f461d2ae843417c19.jpg) + +![](images/4a9fa013780cc560c379c26b9d65abe37e4404f95884e3060625ee87dd3dc6b0.jpg) + +![](images/66c4d3cc91dcd61c3b20a50b7fc2c13b13a69975bd23dd59dfc70a2ec44fc7bd.jpg) + +![](images/7e01fe8486a0bd22440875d210bd73250506f590088aac5e291122188537215f.jpg) + +![](images/8f9791ab8027fab1710c811adac2235a688c4b13fa017de46df49ca60bde6a10.jpg) + +![](images/bebd64182a6f6245397be0e37693d3840a6d47665972e81ee75bd993031ff62a.jpg) + +![](images/d523633e7a42470809211e60719780aded1c85924b86f8e2352a1a0d90670ab5.jpg) + +![](images/efd8207d79e55431ade4c4f018c84c9dabe59f4205ff1f38e54a47ba8fd94ce8.jpg) + +![](images/9b0893981802e5cd15b2ad5696d94f2567d1fefd59bad8fb21bf55ccd37056c1.jpg) +(a) Our geometric editing results. + +![](images/968a95f5a73c40257848c042de1a0551903cd117e3ba41392167998a7984c497.jpg) + +![](images/fdcca1835355c596ff3fa79de71a066d2fb7d07a14bce86373599d2f4c3749c7.jpg) + +![](images/939488bf3f49b09a46d847df10e7b04767ede242a75b6ec7cba49d6674b77bab.jpg) + +![](images/43523217a24588e5bcaab5f9cf02fc6c946d2871c29c38d7a1e82c6560d72924.jpg) + +![](images/10349956f6a4bc8ddfdfa6563b8971dcc9a19a69edf94e5d5b8a55dc2d85dfe2.jpg) + +![](images/35ea50ba63d5c7f783366711d7440f87fdaa525778a6035a7193137cb42d5d92.jpg) + +![](images/3a7d8f8182a117b3d4a14b20aa90bbdd4d8a0297084b06eb4ec0ce018ebc02cf.jpg) + +![](images/7ad5f401b21f9b58a463b3975d11ed987aa25a1a8ff72f92d1881b5ca668870e.jpg) + +![](images/eef9d362611d24e81e51b54a1873dffa8cca22f260c73fb71c95bcd898ac8afd.jpg) + +![](images/ef759fbeb0a9840c230a41d7e9636609f6ef43f1ac971b419dd58637214f13ec.jpg) + +![](images/15a0dc22a581f9fdf4116aae6f62452e84184dedebb619dd68893a0e9e8dfce7.jpg) + +![](images/f295b1ab5e0e57497d34ce695d6d496416e5be9087393355ca2d82033096cc47.jpg) + +![](images/2c3e4cf3fdde84ae89cb5620a54492a1d6e8410e0de00b01573a498e9d7c1354.jpg) + +![](images/7d8d2b430929d3473228a2771bf091863fa4da1e18962056a770c3075f14cec5.jpg) + +![](images/09f190270d4dfe50b6aa7556d3851f91a7b5dcbb0345823e0dca1a85645803f0.jpg) + +![](images/81fa109d9e99cc4ae75ac58e9ded1fbb021b4f8892ee37a71c64fc4b71fc522b.jpg) + +![](images/88d6b8788cb80b47d03b8de24b68344c7d31293bd94f43abf28d5f48ee6fd854.jpg) + +![](images/0f5a04b87fde27a893795c4b99e55350353fa6bd798aa82ca7c80ed30fa7b871.jpg) + +![](images/0043f47e2b08a79638d96df283cd6b89f1af40f7f858ab4784fc7b06080e8f52.jpg) + +![](images/1a6c1d4609a68f6e13fd5ccf8396e62e279f2e9026f3b8ccd2284a9cd2b62c9a.jpg) + +![](images/5dffa7f504c308e2e074c56054cbac05f6b286ddd3c292d5d9a7d82553a8119a.jpg) + +![](images/8bf0eede5e7408bf4f950cb806b031e7379ecb7d45f0fe06c71d9f7a05d6b3dc.jpg) + +![](images/04f9e8cbc36831cea4014428255b6a33aed6c2a540c1352ea3cfb8fe9aa785ca.jpg) + +![](images/4d4ad0dcee44f7c30bb5ae0515e6800ea21daebf84c498972fad55771c8f6b9e.jpg) + +![](images/be8a1865b08f0a68c15f1d2905d1b8004464657c139cad0224d478bc69b491b7.jpg) + +![](images/7becbceb4df72a4e9abfa42308249e5c37fbf7bae1702995226e2a5ae2730309.jpg) +Source + +![](images/73544559b6a5381a37a025059c9d2c012118ebd1254566babe4cae010bf3236c.jpg) + +![](images/c3b14c60975c538357527884df519760f96920316613839d62b283a61dfb415b.jpg) +2D Editing +PNSR↑/SSIM↑/LPIPS↓ +(b) Comparison with EG3D on the real-world car dataset. +Figure 5. We compare the geometric editing with EG3D [9] and EditNeRF [35] on the real-world cars [54] and PhotoShape [47]. + +![](images/2480b8ba48e49c92a9dfa94af7d5d74ca80bc74e6fdc7acf0590347d9e990553.jpg) + +![](images/ecfdb361a3039c4fd994c76c673851b732c1dfb6b3279a99b6a4fbcb3ad5d2dc.jpg) +EG3D + +![](images/e5c88614f12c3c7a8a6c357af1c08263874dd8bc2e17f847f7e211ff0bd085d2.jpg) + +![](images/0472bdee7c360474b51e4df9abd01cc3fd3efa55dee44f0a37ce4d5d6c2696f2.jpg) +18.66/0.87/0.10 + +![](images/62749577d8853344e07cb4a9979afdad78a58310bc295b93cd8ac948b1c557c5.jpg) + +![](images/ec37f9e175c66139bc2b357cd26543ed9f19eb4f897ca845daf725ebd475b701.jpg) +Ours +33.99/0.98/0.01 + +![](images/a2631435a7bb11fb237454c758320231e7a85811746b1b86e43ca407586cd3d6.jpg) + +![](images/8a3639cd386e6a7493fe3d1598dab8304369aa5ceb60e9d05671a770f2ac0e26.jpg) + +![](images/b251efedf11e01a94a9a8b36e71ec804b7786eff52728eccb809b0fe6addb1dd.jpg) + +![](images/99ca793ca781c79675d15a13f9e786745745dd23edb28f2edffe331bf15856d1.jpg) + +![](images/a88f15311b3b787a34b4d830a48d7775416b7c21207c8b110b00fb0e8350ba56.jpg) + +![](images/fda3e2e02ef476ab27c3a3f5fca715580603f2e6f716124fec3f187d4761ab3e.jpg) + +![](images/2d7da71235e9c7cdf34308192c9772c7c6ac61cc2d07a9375537e1c7d6420d98.jpg) + +![](images/19ac12d8becbaefafe08bdef7d17f2a764175cee780304cef251cc4a863dc1c8.jpg) + +![](images/acd053fc8c054ae3769cd8ad3d7b7177ecf97fb3815d5b055afdc868d1643be8.jpg) + +![](images/1e49ccf247050a2c7886809eab1affa81c86483307eb7e0d685d08a047d390bd.jpg) + +![](images/ccf6a912a8c4353038ff6b7d444746e4d94718ecf21b28f34621d20eb57026eb.jpg) + +![](images/c658272faa9df9ceb33b3fa177b9f004631cbc83ebbca2f6b2c182d17bddde99.jpg) + +![](images/f133ed58e571c8c40c0b81b4b4b78414d32d9ac6abdc7feeaba56becfd346388.jpg) + +![](images/7940da28c046bee281fb2dc00d237f1aeb56f42a59bc89ebf72fa0beb3d304d0.jpg) + +![](images/1fd317009391ecf924c28dd9876cc1d8983617e8f400ab5e11e795125a107259.jpg) + +![](images/de21b9400200690facb76ce3d5a58964521c67ccdb95f5290a06f21041c57a9a.jpg) + +![](images/53ffdafd0608d96637a6d092567bf17a9e8ac54594f0499d8b28102023533848.jpg) + +![](images/a0584c0eb986834b19f5159dd3d59f82ed052e84242bf2de9f510d70ae1ff951.jpg) + +![](images/f5d028b6a466adaba6b1078b08394d2257ca65eebea2bc6008f498b82e2f29c0.jpg) + +![](images/5dcd4f321e98b1f940b4666d93de33c8bd434ea38f3604e18f12ab2a3ef212a2.jpg) + +![](images/2fcc22437376253464331ae3cba56ec7528f01f1fcebad2859f95cfde4d89aad.jpg) + +![](images/37aac6e0f31c8e201169e52be7c29855f7e369f6c650f58c0710b0648073a287.jpg) + +![](images/77c4b3487c00d22bbd3cf0950749ed6d145dc3546b33062ca2ab9781e79cc60c.jpg) + +![](images/de86718f928a058c53cd39469ee8791deff90b622262563a87dd5c2a2a62e676.jpg) + +![](images/29866d1344c91e5135941dbf69665968fce22eb90d4c3e5d0c193ade7e764078.jpg) +Ours +24.96/0.94/0.06 +(c) Comparison with EditNeRF on the PhotoShape dataset. + +as ours), and then fine-tune the code on the target images. As shown in Fig. 5 (b), we conduct different editing operations on four cars from CalWare $360^{\circ}$ datasets with DIF shape prior [15], i.e., enlarging/shrinking tires/back. Due to the difficulty of learning a latent textured 3D representation and the limitation of data diversity, 3D-aware generative models like EG3D cannot produce rendering results with fine-grained details, which also results in lower evaluation metrics. For the Photoshape [47], EditNeRF [35] does not provide edited GT images, so we regenerate all testing cases using Blender, which is more challenging than the original ones. Then, we evaluate EditNeRF [35] by fine-tuning the pre-trained models on specific chairs from the PhotoShape dataset. As shown in Fig. 5 (c), EditNeRF produces more blurry rendering results than ours, and cannot achieve satisfactory results with single-view editing (e.g., multi-view inconsistent chair back in the first row, and unmodified or blurry shapes in the third and fourth rows). By contrast, our method consistently delivers high-fidelity rendering results and achieves reliable editing capability by leveraging geometric priors [3, 15]. This demonstrates that, for seman + +tic geometric NeRF editing, learning a prior-guided editing field like ours can maintain better visual quality and achieve greater generalization ability than pre-training a textured 3D generative model or latent model. + +# 4.4. Semantic-driven Texture Editing + +We evaluate our semantic texture editing ability on both objects (cars from CalWare $360^{\circ}$ , chairs from PhotoShape [47]) and unbounded $360^{\circ}$ scenes [2, 42]. Since our method only requires a single image as editing input, we exhibit several editing functionalities as shown in Fig. 6. Users can edit by assigning new textures on the car using Photoshop (adding sea wave windows in Fig. 6 (a)), using a downloaded Internet image with different shapes as a reference (transferring textures of cars and chairs in Fig. 6 (a)). Moreover, we cooperate SINE with off-the-shelf text-prompts editing methods [1] by using a single text-edited image as the target, which enables to change the object's appearance in the $360^{\circ}$ scene with vivid effects (e.g., shiny plastic round table or burning pinecone in Fig.6 (b)) while preserving background unchanged. It is noteworthy that our method does not pre-train a latent model within a spe + +![](images/9f6013af96e4e6d3e36a1eab974612e9cb69c6ff54b39e441c900ed99edaa7bb.jpg) +Source + +![](images/9f50d2d886e017968106686d34aecb68975534020e684c4b6699bc93fc2f7cac.jpg) +Target (from Internet) + +![](images/c3eb6e35b352085c9bbd607a7d8bf963b4a17d0b8fbc7cd43bc0ddfff0766727.jpg) +Source + +![](images/388646ccb368270f6cde881d5054d0d55636153a29cf7376c24dfcd852e8bb4d.jpg) +Target + +![](images/5008004cf297156815867fa43bb4fc81c9a255862f8a0039f9232f6e63ba0b1c.jpg) +(from Internet) +Rendering + +![](images/19247f28a1d4f6f53d2fc62c1af9a9f17f57a1c2e6078e35d4628ffb2dae361a.jpg) + +![](images/9d219741a869cd9f602d57d7cd944b02bbee1bb51ae450788fd573908641822d.jpg) +Rendering + +![](images/6843269970a4980ea5103f5bc790485cc3aae9a96885e6aa130d57552994b736.jpg) + +ering + +![](images/b1a578750da0bc884114e13222dca8e58f778841a41242df4b76e5b9cb9450f4.jpg) +Rendering + +![](images/b10828e49b4d0519f16a6d5de3e5154a570257f1706b005526b46ac99e993335.jpg) + +![](images/6ddd54cd939698b2d0af9b10b43cbe6911ca1266c49d6d08f42ab83e6be8c3b1.jpg) + +![](images/b66425739d8c0e3d2061975f76999a484fca8f7ee24fcbc879985cc1102f3315.jpg) +Source +Source + +![](images/4538d92e3bbc384bf6362c1e0a8fbcba1081808d06ef6ee678e54528601b956b.jpg) +Target (User Editing) +Target +(from Internet) + +![](images/a5219d3ff8caca58345ef4794a26e5581583cc462c98d9ad21dee50a984c1daf.jpg) +Rendering + +![](images/b3029dc2f469d7ee6b971d38a0edde3db65ddfd51d0e3d2860ce689b776a6698.jpg) + +![](images/d30f42bfb711de4251d138ab970018e29bdfc1e208aed0016b2f084083f90cbe.jpg) +Rendering + +![](images/9db20aa8199798924e90edf332011dd42c9141d63ff41ec3d1b1c693d77064f9.jpg) + +ring + +![](images/956831fbebfb93de69580ec5f834fdb2812745b3df4bdc3c4f07c5ef9390ee27.jpg) +Rendering + +![](images/8033eadcd4bf2f89579136ee9b74d3eb6a6fbfb98a51c5532e7927eb8059c8bf.jpg) +Silver Car + +![](images/8d91f536febc42fc3d794b9822346ce91b73be5d87940336655e40df5daf462e.jpg) +"Ice Sculpture Car" + +![](images/b74c21ee87e97930c81336c23321543e6bc47785581b0ac17aa9945a9b21ca83.jpg) + +![](images/705701fa43dbd8064621866dc869effd125802e81d1d413bd425e7c43cc1f34f.jpg) + +![](images/6eb1f942c155174d69a113772b7805c7f2bcb9890dcb58634eb4bf05d53c5bd8.jpg) +(a) Texture editing with users' target images + +![](images/aa0731624c123f0875e634d6efdf893aea29a983d4edddb2827cb2d8f192d17d.jpg) +"Swarovski Blue Crystal Car" +"Snowy Vasedeck" + +![](images/e53b964850819022f994334aaa284e094fca9d4553279ca0c9beace2c71bebb2.jpg) + +![](images/4f2bc11cb98222f22d890af4c9ea849008a3c0d29bcf638aa2e1c0644e3c387b.jpg) + +![](images/70ed9e63f3ad9ea8c33c73a699659eccd08059a4076d0b06c2c585d69b518245.jpg) +Vasedeck + +![](images/71bfabe5e97747339d9b6a3f2370f31659c5649d06d184aa89c1f36630ba8420.jpg) +"Stained Glass Vasedeck" + +![](images/4ad3f8889d1377c41daaf29c2f6e21443f7c1c4a8d22a715f4e948e1d1450d48.jpg) +"Kid's Plasticine Round Table" + +![](images/822855b80d7e63f89b377d66e43f6f2111ccd45beecb75c971fac8eacb8133ee.jpg) + +![](images/16e771a007157ad13daa0d9257ac84227408c9d4a4788e485854d4ad0bcc2536.jpg) +Garden + +![](images/49b181905a634b5daf5061ae5c2efbdabbd2a0c47a14bc0ff87af613a1ff2b25.jpg) +"Plastic Round Table" + +![](images/d49847b1abb9001e61eae4e13417a56699865882fc63bcc885e607fda11d53a8.jpg) + +![](images/2411e62de124afd99ba8a629eade06d9f1c0ce51e66b17e51c5da0573ea19941.jpg) +"Burning +Rendering + +![](images/44e8c88d08c1363c9b522237b58108be52356ef90194abe37bc06b79e14f6656.jpg) + +![](images/b72f1751f1d24959b7d31acd3ab9ee6396a7a0cc11a732569b0a05c439a3fc41.jpg) +Pinecone + +![](images/e0400218bfb67c49117270644a7f4d5e5ee059a92c6dde5bca668e3900904ea1.jpg) +"Golden Pinecone" + +![](images/ad4067351809715d950789130b4719cd93121ce17e77160abe94a643056be6e0.jpg) + +![](images/2d5daab57c6b1ae89d621d9688b62d158013bb9aeb5560280f2e48e27fbb2de1.jpg) + +![](images/91397635fb27eab0662e41368a7379d2b6362e3d846bc5ff0449d2d859ea527d.jpg) + +![](images/cac615dff18645cbfa1ae8055c4109fceb15961a676aa629c941dae6cf7727fc.jpg) +(b) Texture editing with text-prompts +Figure 6. We show our texture editing results when given users' target images and cooperating with text-prompt-based editing methods [1]. + +![](images/c502f58d00c4b188035499ff774ed96ba4142492f804a3de3a3581a61c4c440f.jpg) + +![](images/ed2f6a3a23200853084e587a6f8a807041abc41b4a4b952c8eed0e85fcff0794.jpg) + +![](images/606e9ef5519efde8822135d7a6758d3a98d1ac2f33a11611529212340c1059eb.jpg) + +![](images/d76959ba05c0e08ab9fcc6b68cba0bcbd6df19ebe6994d729bad27d23ecd057e.jpg) +Source / Target + +![](images/17bde7e124391893735242d25134eac7af8f7aa9a181b962c1892b2c08653610.jpg) +ARF + +![](images/01a6a13711abdfeaf8c22007db5a367bfc3b22dd45d173f86e39abf2d529fce2.jpg) +Ours + +![](images/c528a47139befef008148f190a0062ae5881d156778f92efa15280a500cd3e42.jpg) +Source / Target +(a) Comparison of texture editing with target images. + +![](images/963e2ec43661165bb41a50fbeec8bf7a1d507a11696b23677726c887dc83d552.jpg) +ARF + +![](images/8ad733432b4e4e5ca53bb52c473af572508015e9ec3d8239c8e09f454e18fee2.jpg) +CLIP-NeRF +(b) Comparison of texture editing with text-prompts. +Figure 7. We compare our texture editing with ARF [75] and CLIP-NeRF [64] on the real-world cars [54] and $360^{\circ}$ [2,42] scene dataset. + +![](images/ef702d8ff9fd901e5d214a05c71a8646fd7d457c1056c647226c0a474321742f.jpg) +Ours + +cific category like cars or chairs, yet still transfers texture between objects with correct semantic meaning, e.g., the texture styles of chair legs and cloths in the edited views are precisely matched to the target images in Fig. 6 (a). Besides, we also compare our methods with ARF [75], a + +NeRF stylization method that also takes a single reference image as input, and CLIP-NeRF [64], which supports text-driven NeRF editing using the large language model [52]. As demonstrated in Fig. 7, ARF globally changes appearance colors to the given target images but fails to produce + +![](images/efdcdabc31f9a46a28b0596a7b5f114d164bb50fb502435285ddf47ed4a2a448.jpg) +(a) Ablation studies of color compositing mechanism. +(b) Ablation studies of editing regularization. + +![](images/86c4f409705d0802ba663a145a1caeafc59949a2db2e8baadd235ddf1fa67467.jpg) +Figure 8. We analyze the effectiveness of the color compositing mechanism and editing regularization in texture editing. +Figure 9. We inspect the efficacy of the geometric prior constraint and editing regularization in geometric editing. + +fine-grained details (e.g., cookie tires in Fig. 7 (a)). For CLIP-NeRF, since it directly fine-tunes NeRF's color layers, the results only show color/hue adjustment on the original scene (e.g., in Fig. 7, the round table turns gray instead of a realistic silver texture, the vasedeck turns blue instead of a shining diamond). Thanks to the prior-guided editing field, our method learns more fine-grained editing details than the others, and achieves texture editing with consistent semantic meaning to the given target images (e.g., similar appearance to the Tesla's cybertruck in Fig. 7 (a)), and delivers rich appearance details and vivid effects (e.g., silver texture and shining diamond effects in Fig. 7 (b)). + +User study. We also perform user studies to compare our texture editing (including target-image-based editing and text-prompts editing as Fig. 7) with ARF [75] and CLIP-NeRF [64] on 43 cases with 30 users. The results show that users prefer our methods $(89.5\% / 83.3\%)$ to ARF $(10.4\% / 7.4\%)$ and CLIP-NeRF $(9.3\%)$ . Please refer to the supplementary material for more details. + +# 4.5. Ablation Studies + +Geometric prior constraints. We first analyze the effectiveness of geometric prior constraints (Sec. 3.2) by ablating geometric prior loss (Eq. (2)) in Fig. 9 (i.e., deforming cars and airplanes with DIF shape prior, and adding plates with general shape prior). As shown in Fig. 9 (b), when learning without geometric prior constraints, the object will be distorted when rendered from other views (e.g., collapsed car back, twisted airplanes, and warped hotdog plates). By ap- + +plying geometric prior constraints, we successfully mitigate the geometric ambiguity for single-image-based editing and produce plausible rendering results from novel views. + +Color compositing mechanism. We then inspect the efficacy of the color compositing mechanism (Sec. 3.3) by disabling the texture modification field $F_{\Delta T}$ and the color compositing layer in turn. As demonstrated in Fig. 8 (a), when learning texture editing without $F_{\Delta T}$ , the rendered edited object can show a similar global appearance to the target, but lose vivid local patterns (e.g., gray and white grains and blue shininess). When ablating the color compositing layers, the editing effect might not be properly applied to every part of the object (e.g., the uncovered gray part of the car's front). When all the compositing mechanism is enabled, we successfully learn NeRF editing with fine-grained local patterns and globally similar appearance. + +Editing regularization. We finally evaluate the editing regularization (Sec. 3.4) in geometric and texture editing by ablating regularization loss (Eq. (7)). As shown in Fig. 9 (c) and Fig. 8 (b), when learning editing without regularization, the irrelevant part would be inevitably changed (e.g., bent car's front and airplane's head in Fig. 9 (c), a spurious cookie at the car's front and snowy background in Fig. 8 (b)). By adding editing regularization, we can modify the user-desired objects precisely while preserving other content unchanged. + +Please refer to the supplementary material for more experiments (e.g., ablation on more loss terms, visualization of color composition layer, discussion with external supervision, etc.). + +# 5. Conclusion + +We have proposed a novel semantic-driven NeRF editing approach, which supports editing a photo-realistic template NeRF with a single user-edited image, and delivers edited novel views with high-fidelity and multi-view consistency. As a limitation, our approach does not support editing with topology changes, which can be future work. Besides, our method assumes users' editing to be semantically meaningful, so we cannot use target images with meaningless random paintings. + +Acknowledgment. This work was partially supported by NSF of China (No. 62102356). + +# References + +[1] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. 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We propose a novel semantic-driven image-based editing approach, which allows users to edit a photo-realistic NeRF with a single-view image or with text prompts, and renders edited novel views with vivid details and multi-view consistency." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 260, + 158, + 544, + 294 + ], + "blocks": [ + { + "bbox": [ + 260, + 158, + 544, + 294 + ], + "lines": [ + { + "bbox": [ + 260, + 158, + 544, + 294 + ], + "spans": [ + { + "bbox": [ + 260, + 158, + 544, + 294 + ], + "type": "image", + "image_path": "7f6dd04e1bca8e5f7a5560cbfebecae4177f0ffd26c55a0b3cf5d73c0aee71c0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 327, + 192, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 327, + 192, + 339 + ], + "spans": [ + { + "bbox": [ + 143, + 327, + 192, + 339 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 350, + 290, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 350, + 290, + 601 + ], + "spans": [ + { + "bbox": [ + 45, + 350, + 290, + 601 + ], + "type": "text", + "content": "Despite the great success in 2D editing using user-friendly tools, such as Photoshop, semantic strokes, or even text prompts, similar capabilities in 3D areas are still limited, either relying on 3D modeling skills or allowing editing within only a few categories. In this paper, we present a novel semantic-driven NeRF editing approach, which enables users to edit a neural radiance field with a single image, and faithfully delivers edited novel views with high fidelity and multi-view consistency. To achieve this goal, we propose a prior-guided editing field to encode fine-grained geometric and texture editing in 3D space, and develop a series of techniques to aid the editing process, including cyclic constraints with a proxy mesh to facilitate geometric supervision, a color compositing mechanism to stabilize semantic-driven texture editing, and a feature-cluster-based regularization to preserve the irrelevant content unchanged. Extensive experiments and editing examples on both real-world and synthetic data demonstrate that our method achieves photo-realistic 3D editing using only a single edited image, pushing the bound of semantic-driven editing in 3D real-world scenes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 605, + 128, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 128, + 617 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 128, + 617 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 624, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 287, + 686 + ], + "type": "text", + "content": "Semantic-driven editing approaches, such as stroke-based scene editing [34, 39, 66], text-driven image synthesis and editing [1, 50, 53], and attribute-based face editing [27, 60], have greatly improved the ease of artistic creation. However, despite the great success of 2D image edit" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 327, + 546, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 546, + 495 + ], + "type": "text", + "content": "ing and neural rendering techniques [14, 42], similar editing abilities in the 3D area are still limited: (1) they require laborious annotation such as image masks [27, 71] and mesh vertices [69, 74] to achieve the desired manipulation; (2) they conduct global style transfer [12, 13, 16, 20, 75] while ignoring the semantic meaning of each object part (e.g., windows and tires of a vehicle should be textured differently); (3) they can edit on categories by learning a textured 3D latent representation (e.g., 3D-aware GANs with faces and cars etc.) [6, 8, 9, 17, 45, 56, 59, 60], or at a coarse level [35, 64] with basic color assignment or object-level disentanglement [30], but struggle to conduct texture editing on objects with photo-realistic textures or out-of-distribution characteristics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 546, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 665 + ], + "type": "text", + "content": "Based on this observation, we believe that, on the way toward semantic-driven 3D editing, the following properties should be ensured. First, the operation of editing should be effortless, i.e., users can edit 3D scenes on a single 2D image in convenient ways, e.g., using off-the-shelf tools such as GAN-based editing [28, 34], text-driven editing [1, 53], Photoshop, or even a downloaded Internet image without pixel-wise alignment, rather than steering 3D modeling software with specific knowledge [69], or repeatedly editing from multi-view images. Second, the editing method should be applicable to real-world scenes or objects and preserve vivid appearances, which is beyond existing 3D-aware generative models [8, 9] due to the limited categories and insufficient data diversity on real-world objects." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "content": "To fulfill this goal, we propose a novel Semantic-driven Image-based Editing approach for Neural radiance field in real-world scenes, named SINE. Specifically, our method allows users to edit a neural radiance field with a sin-" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 155, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 155, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 155, + 703 + ], + "type": "text", + "content": "*Authors contributed equally." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20919" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "gle image, i.e., either by changing a rendered image using off-the-shelf image editing tools or providing an image for texture transferring (see Sec. 4.4), and then delivers edited novel views with consistent semantic meaning. Unlike previous works that directly fine-tune the existing NeRF model [30, 35, 64], SINE learns a prior-guided editing field to encode geometric and texture changes over the original 3D scene (see Fig. 2), thus enabling fine-grained editing ability. By leveraging guidance from existing neural priors (shape prior models [15] and Vision Transformer models [7], etc.), SINE can directly perform semantic-driven editing on photo-realistic scenes without pre-training a category-level latent space. For example, in Fig. 1, users can stretch a car's back or change all four tires to cookies by only editing a single image, and can even cooperate with text-prompts editing [1] to modify a specific object of a scene with vivid appearances." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 278, + 289, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 289, + 602 + ], + "type": "text", + "content": "However, even when guided with neural priors, editing NeRF from a single image with multi-view consistency and accuracy is still challenging. (1) The generic NeRF does not necessarily provide an explicit surface or signed distance field, such that it cannot directly work with shape priors [15]. Therefore, we propose to use cyclic constraints with a proxy mesh to represent the edited NeRF's geometry, which facilitates guided editing using coarse shape prior. (2) Learning a coordinate-based 3D editing field using a single edited view is not sufficient to capture fine-grained details, and applying semantic supervision [7, 52] directly to the editing field leads to sub-optimal convergence (see Sec. 4.5). To tackle these challenges, we propose a color compositing mechanism by first rendering the template NeRF color and modification color individually, and then deferred blending them to yield the edited view, which significantly improves semantic-driven texture editing. (3) Ideally, a user's editing should only affect the desired regions while maintaining other parts untouched. However, in semantic-driven editing, the prior losses require taking the full shape or image as input, which leads to appearance or shape drifting at the undesired area. To precisely control the editing while excluding irrelevant parts from being affected, we generate feature clusters of the editing area using the ViT-based feature field [7, 30], and use these clusters to distinguish whether a location is allowed to be edited or should remain unchanged." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "In summary, the contributions of our paper are as follows. (1) We propose a novel semantic-driven image-based NeRF editing approach, called SINE, which allows users to edit a neural radiance field simply on just a single view of the rendering. SINE leverages a prior-guided editing field to encode fine-grained geometry and texture changes over the given pre-trained NeRF, thus delivering multi-view consistent edited views with high fidelity. (2) To achieve semantic editing functionality, we develop a series of techniques," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "including cyclic constraints with a proxy mesh for geometric editing, the color compositing mechanism to enhance texture editing, and the feature-cluster-based regularization to control the affected editing area and maintain irrelevant parts unchanged. (3) Experiments and editing examples on both real-world/synthetic and object-centric/unbounded " + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": " scenes data demonstrate superior editing capabilities and quality with effortless operations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 175, + 398, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 175, + 398, + 188 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 398, + 188 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 193, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 547, + 661 + ], + "type": "text", + "content": "Neural rendering with external priors. Neural rendering techniques aim at rendering novel views with high-quality [42] or controllable properties [27, 48] by learning from 2D photo capture. Recently, NeRF [42] achieves photo-realistic rendering with volume rendering and inspires many works, including surface reconstruction [31,65, 73], scene editing [4, 18, 67, 70, 71] and generation [22, 51], inverse rendering [5, 76], SLAM [72, 77], etc. For learning from few-shot images [23] or 3D inpainting [43], NeRF's variants use hand-crafted losses [44] or large language-image models [23, 68] as external priors. However, due to insufficient 3D supervision, such methods cannot reconstruct accurate geometry and only produce visually plausible results. Besides, some works [21, 32, 40] use the symmetric assumption to reconstruct category-level objects (e.g., cars, chairs) but cannot generalize on complex scenes. Neural 2D & 3D scene editing. With the development of neural networks, semantic-driven 2D photo editing allows user editing in various friendly ways, such as controlling attribute of faces [19, 28], stroke-based editing [34, 39, 66], sketch-to-image generation [11, 55], image-to-image texture transferring [62], or text-driven image generation [53] and editing [29]. Nevertheless, in 3D scene editing, similar capabilities are still limited due to the high demand for multi-view consistency. Existing approaches either rely on laborious annotation [27, 69, 71, 74], only support object deformation or translation [30, 61, 63, 74], or only perform global style transfer [12, 13, 16, 20, 75] without strong semantic meaning. Recently, 3D-aware GANs [8, 9, 17, 24, 45, 56, 59] and semantic NeRF editing [35, 64] learn a latent space of the category and enable editing via latent code control. However, the quality and editing ability of these methods mainly depend on the dataset (e.g., human faces [59, 60] or objects in ShapeNet [10]), and they cannot generalize to objects with rich appearances or out-of-distribution features [1]. In contrast, our method allows for semantic-driven editing directly on the given photo-realistic NeRF, and uses a prior-guided editing field to learn fine-grained editing from only a single image." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 669, + 362, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 362, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 362, + 681 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "We first formulate the goal of our semantic NeRF editing task as follows. As illustrated in the left part of Fig. 2," + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20920" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 57, + 53, + 180, + 215 + ], + "blocks": [ + { + "bbox": [ + 57, + 53, + 180, + 215 + ], + "lines": [ + { + "bbox": [ + 57, + 53, + 180, + 215 + ], + "spans": [ + { + "bbox": [ + 57, + 53, + 180, + 215 + ], + "type": "image", + "image_path": "6b6466b8e020a4b36c5de6daa64f71298661f1549e2791f5cd7b0f7bba140247.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": "Figure 2. Overview. We encode geometric and texture changes over the original template NeRF with a prior-guided editing field, where the geometric modification field " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " transformed the edited space query " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " into the template space " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": ", and the texture modification field " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "F_{\\Delta T}" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " encodes modification colors " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\mathbf{m}'" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": ". Then, we render deformed template image " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " and color modification image " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\hat{I}_m" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " with all the queries, and use a color compositing layer to blend " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\hat{I}_m" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": " into the edited view " + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 46, + 218, + 547, + 262 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 182, + 53, + 399, + 215 + ], + "blocks": [ + { + "bbox": [ + 182, + 53, + 399, + 215 + ], + "lines": [ + { + "bbox": [ + 182, + 53, + 399, + 215 + ], + "spans": [ + { + "bbox": [ + 182, + 53, + 399, + 215 + ], + "type": "image", + "image_path": "083065336e39a14d99352c688140f11033cbd5234bec460e9fe15d54eedb2203.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 401, + 54, + 537, + 215 + ], + "blocks": [ + { + "bbox": [ + 401, + 54, + 537, + 215 + ], + "lines": [ + { + "bbox": [ + 401, + 54, + 537, + 215 + ], + "spans": [ + { + "bbox": [ + 401, + 54, + 537, + 215 + ], + "type": "image", + "image_path": "9543a069156a473733ebcd87c90a98efebcc98b957fc288a4d196293c134a780.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 269, + 290, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 290, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 290, + 437 + ], + "type": "text", + "content": "given a pre-trained NeRF of a photo-realistic scene (named template NeRF), we aim at editing the template NeRF using only a single-view 2D image, and then produce novel views with consistent semantic meaning (see Sec. 4.3 and Sec. 4.4). Note that naively fine-tuning on the edited single view cannot obtain satisfactory results due to the spatial ambiguity and lack of multi-view supervision (see Sec. 4.2). Therefore, we propose to use a novel prior-guided editing field to encode fine-grained changes (Sec. 3.1) in 3D space, which leverages geometry and texture priors to guide the learning of semantic-driven editing (Sec. 3.2 and Sec. 3.3). Besides, to precisely control the editing area while maintaining other parts unchanged, we design editing regularization with feature cluster-based semantic masking (Sec. 3.4)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 446, + 189, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 189, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 189, + 460 + ], + "type": "text", + "content": "3.1. SINE Rendering Pipeline" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": "As illustrated in Fig. 2, we use a dedicated editing field to encode geometry and texture changes over the pre-trained template NeRF. The editing field consists of an implicit geometric modification field " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " and a texture modification field " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "F_{\\Delta T}" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " deforms the query points from the observed edited space to the original template space, as " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{x}' \\coloneqq F_{\\Delta G}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "F_{\\Delta T}" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " encodes the modification color " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{m}'" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ", as " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{m}' \\coloneqq F_{\\Delta T}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ". Specifically, for each sampled query point " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_i | i = 1, \\dots, N\\}" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " along the ray " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " with view direction " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ", we first obtain the deformed points " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " (in template space) and modification color " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{m}'" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ", and feed " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{x}'" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " to the template NeRF to obtain the density " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\delta'" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": " and template colors " + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{c}'" + }, + { + "bbox": [ + 46, + 464, + 288, + 643 + ], + "type": "text", + "content": ". Then, we perform dual volume rendering both on edited fields and template NeRF following the quadrature rules [38,42], which is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 73, + 643, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 643, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 73, + 643, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {C} _ {o} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} \\mathbf {c} _ {i} ^ {\\prime}, \\quad \\hat {C} _ {e} (\\boldsymbol {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\alpha_ {i} \\mathbf {m} _ {i} ^ {\\prime}, \\tag {1} \\\\ T _ {i} = \\exp \\left(- \\sum_ {j = 1} ^ {i - 1} \\sigma^ {\\prime} _ {j} \\delta_ {j}\\right), \\\\ \\end{array}", + "image_path": "88b5c858e1ff1ecbdae10bb47b257b77ce90ea52398c1784b968fbb9afa248ac.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\alpha_{i} = 1 - \\exp (-\\sigma^{\\prime}_{i}\\delta_{i})" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": " is the distance between adjacent samples along the ray. In this way, we obtain the deformed template image " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": " from the template NeRF's pixel color " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{C}_o(\\boldsymbol {r})" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": " and color modification image " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{I}_m" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": " from the modification color " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{C}_e(\\boldsymbol {r})" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": ". Finally, we apply the color compositing layer (see Sec. 3.3) to blend " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{I}_m" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": " into the resulting edited views " + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 268, + 545, + 353 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 356, + 481, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 481, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 481, + 369 + ], + "type": "text", + "content": "3.2. Prior-Guided Geometric Editing" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 370, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 394 + ], + "type": "text", + "content": "In this section, we explain how to learn " + }, + { + "bbox": [ + 304, + 370, + 545, + 394 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 370, + 545, + 394 + ], + "type": "text", + "content": " with the geometric prior." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "text", + "content": "Shape prior constraint on the edited NeRF. We leverage geometric prior models, such as neural implicit shape representation [15, 46] or depth prediction [3], to mitigate the ambiguity of geometric editing based on editing from a single perspective. (1) For objects within a certain shape category (e.g., cars, airplanes), we use DIF [15], in which the implicit SDF field and the prior mesh " + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\hat{M}_P" + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "text", + "content": " can be generated with the condition of an estimizable latent code " + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "text", + "content": ". We force the edited NeRF's geometry " + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\hat{M}_E" + }, + { + "bbox": [ + 304, + 395, + 545, + 514 + ], + "type": "text", + "content": " to be explainable by a pre-trained DIF model with the geometric prior loss:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 516, + 545, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 516, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 347, + 516, + 545, + 604 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal{L}_{gp} = \\min_{\\hat{\\mathbf{z}}}\\bigl(\\sum_{\\mathbf{p}^{\\prime}\\in \\hat{M}_{E}}f_{\\mathrm{SDF}}(\\hat{\\mathbf{z}},\\mathbf{p}^{\\prime}) + \\lambda ||\\hat{\\mathbf{z}} ||_{2}^{2}\\bigr) \\\\ + \\sum_ {\\mathbf {p} _ {i} ^ {\\prime} \\in \\hat {M} _ {E}} \\min _ {\\mathbf {p} _ {t} \\in \\hat {M} _ {P}} | | \\mathbf {p} _ {i} ^ {\\prime} - \\mathbf {p} _ {t} | | _ {2} ^ {2} \\tag {2} \\\\ + \\sum_ {\\mathbf {p} _ {i} \\in \\hat {M} _ {P}} \\min _ {\\mathbf {p} _ {t} ^ {\\prime} \\in \\hat {M} _ {E}} | | \\mathbf {p} _ {i} - \\mathbf {p} _ {t} ^ {\\prime} | | _ {2} ^ {2}. \\\\ \\end{array}", + "image_path": "2f00448f2685f65c26a78fc6dcd8a8bd0e9b1dcb59238c6088640196d62765cd.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "The first term encourages the sampled surface points on the edited NeRF's geometry " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{M}_E" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " to lie on the manifold of DIF's latent space with an SDF loss " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{SDF}}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " and the latent code regularization [15]. The last two terms are Chamfer constraints, which enforce the " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{M}_E" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " close to the DIF's periodically updated prior mesh " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{M}_P" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " [36] by minimizing the closest surface points. (2) For objects without a category-level prior, we can build a finalized shape prior " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{M}_P" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " beforehand. Practically, we find 3D deforming vertices with 2D correspond" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20921" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "dence [26] and monocular depth prediction [3], and use ARAP [57] to deform the proxy triangle mesh " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "M_{\\Theta}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\hat{M}_P" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ". Then, we can inherit the Chamfer loss term in Eq. (2) for prior-guided supervision." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": "Representing edited NeRF's geometry as a deformed proxy mesh. The edited NeRF has no explicit surface definition or SDF field to directly apply the geometric prior loss (Eq. (2)). Therefore, to obtain the edited mesh surface " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "\\hat{M}_E" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": ", as illustrated in Fig. 3 (a), we first fit the template NeRF geometry with a proxy mesh " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "M_{\\Theta}" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": " [36, 65], and then learn a forward modification field " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}^{\\prime}" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": " to warp the template proxy mesh to the edited space. " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}^{\\prime}" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": " is an inverse of the editing field " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "F_{\\Delta G}" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": ", which maps from the template space to the query space [33, 41], as " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\coloneqq F_{\\Delta G}^{\\prime}(\\mathbf{x}^{\\prime})" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": ", and can be supervised using a cycle loss " + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cyc}}" + }, + { + "bbox": [ + 46, + 123, + 288, + 304 + ], + "type": "text", + "content": " (see the supplementary material for details). Note that the deformed mesh proxy might not reflect fine-grained details of the specific shape identity. It facilitates applying shape priors to the edited field and provides essential guidance during geometric editing." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 306, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 402 + ], + "type": "text", + "content": "Learning geometric editing with users' 2D editing. The goal of geometric editing is to deform the given NeRF according to the edited target image while satisfying semantic properties. To this end, apart from the geometric prior loss in Eq. (2), we add the following geometric editing loss in two folds. (1) We encourage the edited NeRF to satisfy the user's edited image by directly supervising rendering colors and opacity on " + }, + { + "bbox": [ + 46, + 306, + 287, + 402 + ], + "type": "inline_equation", + "content": "N_{r}" + }, + { + "bbox": [ + 46, + 306, + 287, + 402 + ], + "type": "text", + "content": " rays, which is defined as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 403, + 286, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 286, + 442 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {g t}} = \\frac {1}{| N _ {r} |} \\sum_ {\\boldsymbol {r} \\in N _ {r}} \\left\\| \\hat {C} (\\boldsymbol {r}) - C _ {t} (\\boldsymbol {r}) \\right\\| _ {2} ^ {2} + \\operatorname {B C E} \\left(\\hat {O} (\\boldsymbol {r}), O _ {e} (\\boldsymbol {r})\\right). \\tag {3}", + "image_path": "03a5c4abb57b8dac85d89c1122958245cb39b4c1616b052f48755630e187e990.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "content": "The first photometric loss term encourages the rendered color " + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\hat{C}(\\boldsymbol{r})" + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "content": " close to the edited target color " + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "inline_equation", + "content": "C_t(\\boldsymbol{r})" + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "content": ". The second silhouette loss term enforces the rendered opacity " + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\hat{O}(\\boldsymbol{r})" + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "content": " close to the edited object's silhouette " + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "inline_equation", + "content": "O_e(\\boldsymbol{r})" + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "content": " (derived from users' editing tools) by minimizing the binary cross-entropy loss, where " + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\hat{O}(\\boldsymbol{r}) = \\sum_{i=1}^{N} T_i \\alpha_i" + }, + { + "bbox": [ + 46, + 445, + 287, + 552 + ], + "type": "text", + "content": ". (2) To obtain a spatially smooth deformation and mitigate overfitting to the mesh's surface points, inspired by previous works [15, 48, 49], we also add deformation regularization as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 555, + 288, + 596 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 288, + 596 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 288, + 596 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {g r}} = \\frac {1}{M} \\sum_ {i = 1} ^ {N} | | \\nabla F _ {\\Delta G} (\\mathbf {p} _ {i}) | | _ {2} + | | F _ {\\Delta G} (\\mathbf {p} _ {i}) - F _ {\\Delta G} (\\mathbf {p} _ {i} + \\epsilon) | | _ {1}, \\tag {4}", + "image_path": "8909283a68ee3fc4f1b36df7a9692dd7c55b897640693fb9d6a12e8697c820ae.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "type": "text", + "content": "where the first term penalizes the spatial gradient of the geometric editing, and the second term encourages the editing to be smooth under a mild 3D positional jitter " + }, + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 597, + 287, + 633 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 636, + 253, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 636, + 253, + 647 + ], + "spans": [ + { + "bbox": [ + 59, + 636, + 253, + 647 + ], + "type": "text", + "content": "The overall geometric editing loss is defined as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 81, + 650, + 287, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 650, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 81, + 650, + 287, + 663 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {g e o}} = \\lambda_ {\\mathrm {g p}} \\mathcal {L} _ {\\mathrm {g p}} + \\mathcal {L} _ {\\mathrm {g t}} + \\lambda_ {\\mathrm {g r}} \\mathcal {L} _ {\\mathrm {g r}} + \\lambda_ {\\mathrm {c y c}} \\mathcal {L} _ {\\mathrm {c y c}}, \\tag {5}", + "image_path": "613f10dde0a3ebc5aec5d5b02212daa8960142bcd9269ae0ea4fbdfcaddf1a5b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": "where we set " + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{gp}} = 0.03" + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{gr}} = 0.1" + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{cyc}} = 10" + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": ". Intuitively, the geometric editing loss " + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{geo}}" + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": " jointly optimizes edited NeRF's geometry " + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{M}_E" + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": " and the latent shape code " + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}" + }, + { + "bbox": [ + 46, + 664, + 287, + 714 + ], + "type": "text", + "content": " (for category-level objects) to best fit the user's 2D editing" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 190 + ], + "type": "image", + "image_path": "9cc630d15ac491cd3bea4b97b80638ed782d59fa8df1558b7ff42408b765262b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 372, + 190, + 482, + 198 + ], + "lines": [ + { + "bbox": [ + 372, + 190, + 482, + 198 + ], + "spans": [ + { + "bbox": [ + 372, + 190, + 482, + 198 + ], + "type": "text", + "content": "(a) Geometric Prior Guidance" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 314, + 200, + 543, + 292 + ], + "blocks": [ + { + "bbox": [ + 314, + 200, + 543, + 292 + ], + "lines": [ + { + "bbox": [ + 314, + 200, + 543, + 292 + ], + "spans": [ + { + "bbox": [ + 314, + 200, + 543, + 292 + ], + "type": "image", + "image_path": "bd665c5fc612d82114b96ab2dbda1388b11068361743e2d09845343d1e4eb9bd.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 293, + 471, + 302 + ], + "lines": [ + { + "bbox": [ + 371, + 293, + 471, + 302 + ], + "spans": [ + { + "bbox": [ + 371, + 293, + 471, + 302 + ], + "type": "text", + "content": "(b) Texture Prior Guidance" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 302, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 305, + 302, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 545, + 324 + ], + "type": "text", + "content": "Figure 3. We leverage geometric [3, 15] and texture [7, 62] priors to guide the learning of semantic-driven NeRF editing." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 331, + 545, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 356 + ], + "type": "text", + "content": "while maintaining shape prior's semantic properties (i.e., shape symmetry or physical conformity)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 360, + 468, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 468, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 468, + 372 + ], + "type": "text", + "content": "3.3. Prior-Guided Texture Editing" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "type": "text", + "content": "Semantic texture prior supervision. In our task, users only conduct editing on a single image, but we hope to naturally propagate editing effects to multi-views with semantic meaning (see Fig. 1). Therefore, we need to utilize semantic texture supervision that supports transferring the editing to the given NeRF across views, rather than using a pixel-aligned photometric loss. Inspired by Tumanyan et al. [62], we use a pre-trained ViT model [7] as the semantic texture prior, and apply the texture transferring loss in a multi-view manner as illustrated in Fig. 3 (b), which is defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 495, + 545, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 495, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 315, + 495, + 545, + 509 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {t e x}} = \\left| \\left| t _ {\\mathrm {C L S}} \\left(I _ {t}\\right) - t _ {\\mathrm {C L S}} (\\hat {I}) \\right| \\right| _ {2} + \\left| \\left| S \\left(\\hat {I} _ {o}\\right) - S (\\hat {I}) \\right| \\right| _ {F}, \\tag {6}", + "image_path": "c6b86d356e299d3ffe3a47640afccf754933cca6cf8dc8ace754b620ae5a603b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " is the user's edited image, " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " are the template image and edited image as introduced in Sec. 3.1. " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "t_{\\mathrm{CLS}}(\\cdot)" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " are the extracted deepest CLS token and the structural self-similarity defined by Tumanyan et al. [62]. Essentially, this loss encourages " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " to share a similar spatial structure, and " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{I}_t" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 304, + 510, + 545, + 582 + ], + "type": "text", + "content": " to contain similar image cues." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Decoupled rendering with color compositing layer. To achieve texture modification, a naive approach is to directly add the modification color " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{m}'" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " from the editing field to the template NeRF's radiance color " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{c}'" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " during volume rendering. However, we find it suffers from sub-optimal convergence when cooperating with texture transferring loss (see Sec. 4.5), since NeRF struggles to learn the global-consistent appearance under the variational supervisory as shown in Fig. 8(a). To tackle this issue, we re-design the rendering pipeline in a decoupled manner. As shown in Fig. 2, we first render the deformed template image " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " with" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20922" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "content": "template NeRF and the color modification " + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\hat{I}_m" + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "inline_equation", + "content": "F_{\\Delta T}" + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "content": ", and then use a 2D CNN-based color compositing layer to deferred blend the modification " + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\hat{I}_m" + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "content": " into the template image " + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\hat{I}_o" + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "content": ", which yields final edited view " + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 46, + 71, + 289, + 216 + ], + "type": "text", + "content": ". Intuitively, the coordinate-based editing field can encode fine-grained details from photometric constraints but cannot easily learn from coarse semantic supervision, while the proposed color compositing layer can reduce the difficulty by using easy-to-learn CNN layers before applying texture transferring loss. Besides, it also learns view-dependent effects from the semantic prior, making the rendering results more realistic (e.g., the shining diamond effect in Fig. 1)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 220, + 177, + 233 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 220, + 177, + 233 + ], + "spans": [ + { + "bbox": [ + 47, + 220, + 177, + 233 + ], + "type": "text", + "content": "3.4. Editing Regularization" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "type": "text", + "content": "Feature-cluster-based semantic masking. To precisely edit the desired region while preserving other content unchanged, inspired by previous works [30, 61, 63], we learn a distilled feature field with DINO-ViT [7] to reconstruct scenes/objects with semantic features. However, existing semantic field decomposing approaches [30, 61] are limited to the query-based similarity and require all the editing to be finalized on the 3D field, which is not compatible with our color compositing mechanism. Therefore, we leverage users' editing silhouette " + }, + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "type": "inline_equation", + "content": "M_e" + }, + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "type": "text", + "content": " to generate several feature clusters from the distilled feature map, and compute semantic masks " + }, + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "type": "inline_equation", + "content": "\\hat{M}_e" + }, + { + "bbox": [ + 46, + 236, + 289, + 403 + ], + "type": "text", + "content": " using the closest cosine similarity to cluster centers with a threshold, which will be served for image-based editing regularization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 287, + 464 + ], + "type": "text", + "content": "Regularization on geometric and texture editing. With the semantic masks that indicate the editing area, we can apply editing regularization to the geometric and texture editing, i.e., by enforcing the rendered pixels and the queries at the irrelevant part unchanged, which is defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 464, + 287, + 493 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 464, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 61, + 464, + 287, + 493 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} = \\sum_ {\\mathbf {x} \\in \\hat {I} \\backslash \\hat {M} _ {e}} | | F _ {\\Delta G} (\\mathbf {x}) | | _ {1} + \\sum_ {\\mathbf {r} \\in \\hat {I} \\backslash \\hat {M} _ {e}} | | \\hat {C} (\\mathbf {r}) - \\hat {C} _ {o} (\\mathbf {r}) | | _ {2} ^ {2}, \\tag {7}", + "image_path": "a75593059cd0e9ccb33408cd60d0b66e9dbb3b99f2b6d1984e87bb7eda4e59d3.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "text", + "content": "where the sampled points " + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "text", + "content": " and rays " + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\pmb{r}" + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "text", + "content": " are both from the background area of the computed semantic masks " + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\hat{M}_e" + }, + { + "bbox": [ + 46, + 494, + 287, + 518 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 530, + 128, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 128, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 128, + 544 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 546, + 110, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 110, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 110, + 558 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 561, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 658 + ], + "type": "text", + "content": "We evaluate SINE on both real-world/synthetic and object/scene datasets, including real-world car dataset [54], PhotoShape datasets (synthetic chairs) [47], “pinecone”, “vasedeck”, and “garden” from NeRF real-world " + }, + { + "bbox": [ + 46, + 561, + 287, + 658 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 561, + 287, + 658 + ], + "type": "text", + "content": " scenes [2, 42], “chairs” and “hotdog” from NeRF photorealistic synthetic data [42], bird status from DTU [25] dataset, and “airplane” from BlenderSwap [37]. Please refer to the supplementary material for more details." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 662, + 241, + 675 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 241, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 241, + 675 + ], + "type": "text", + "content": "4.2. Semantic-driven vs. Manual Editing" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "We first clarify the difference between our semantic-driven NeRF editing and manual NeRF editing (e.g., NeuMesh [69], NeRF-Editing [74]). As illustrated in Fig. 4" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 312, + 71, + 399, + 125 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 399, + 125 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 399, + 125 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 399, + 125 + ], + "type": "image", + "image_path": "00b2a3a7996e634dfba593e61178554da045b44b5fa5e44132d810006385f57d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 312, + 125, + 396, + 175 + ], + "blocks": [ + { + "bbox": [ + 312, + 125, + 396, + 175 + ], + "lines": [ + { + "bbox": [ + 312, + 125, + 396, + 175 + ], + "spans": [ + { + "bbox": [ + 312, + 125, + 396, + 175 + ], + "type": "image", + "image_path": "8e806e0d27e68bbce4a20e09e3737ead8a5cd0113226b7c3eb147e044b569626.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 175, + 523, + 185 + ], + "lines": [ + { + "bbox": [ + 326, + 175, + 523, + 185 + ], + "spans": [ + { + "bbox": [ + 326, + 175, + 523, + 185 + ], + "type": "text", + "content": "(a) Image-based geometric editing vs. manual geometric editing" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 416, + 72, + 539, + 125 + ], + "blocks": [ + { + "bbox": [ + 416, + 72, + 539, + 125 + ], + "lines": [ + { + "bbox": [ + 416, + 72, + 539, + 125 + ], + "spans": [ + { + "bbox": [ + 416, + 72, + 539, + 125 + ], + "type": "image", + "image_path": "c0aff3aafb90d47429330e757e64f38e1b609f0db2b6d2d99842aa11fa5d795c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 416, + 125, + 539, + 175 + ], + "blocks": [ + { + "bbox": [ + 416, + 125, + 539, + 175 + ], + "lines": [ + { + "bbox": [ + 416, + 125, + 539, + 175 + ], + "spans": [ + { + "bbox": [ + 416, + 125, + 539, + 175 + ], + "type": "image", + "image_path": "95697844db0c365cfbb70a8b6282014b14a1712e07105fb4621e4f2317aadefe.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 315, + 188, + 380, + 265 + ], + "blocks": [ + { + "bbox": [ + 315, + 188, + 380, + 265 + ], + "lines": [ + { + "bbox": [ + 315, + 188, + 380, + 265 + ], + "spans": [ + { + "bbox": [ + 315, + 188, + 380, + 265 + ], + "type": "image", + "image_path": "a05d4a6bb8ed670eb451a506d8a190338fa7990de7662f72aebe7cb625ff715a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 266, + 530, + 276 + ], + "lines": [ + { + "bbox": [ + 318, + 266, + 530, + 276 + ], + "spans": [ + { + "bbox": [ + 318, + 266, + 530, + 276 + ], + "type": "text", + "content": "(b) Semantic-driven texture editing vs. naive single-view fine-tuning" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 305, + 277, + 545, + 298 + ], + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 298 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 298 + ], + "type": "text", + "content": "Figure 4. We show the difference between our semantic-driven image-based NeRF editing and manual NeRF editing [69]." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 413, + 193, + 472, + 219 + ], + "blocks": [ + { + "bbox": [ + 381, + 197, + 413, + 217 + ], + "lines": [ + { + "bbox": [ + 381, + 197, + 413, + 217 + ], + "spans": [ + { + "bbox": [ + 381, + 197, + 413, + 217 + ], + "type": "text", + "content": "Single-View Fine-Tuning" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 413, + 193, + 472, + 219 + ], + "lines": [ + { + "bbox": [ + 413, + 193, + 472, + 219 + ], + "spans": [ + { + "bbox": [ + 413, + 193, + 472, + 219 + ], + "type": "image", + "image_path": "1df8ee0517e4cc4a6929f1fa7eb0240f1e1e2c567c2030a5503ca699834e3085.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 481, + 193, + 541, + 227 + ], + "blocks": [ + { + "bbox": [ + 481, + 193, + 541, + 227 + ], + "lines": [ + { + "bbox": [ + 481, + 193, + 541, + 227 + ], + "spans": [ + { + "bbox": [ + 481, + 193, + 541, + 227 + ], + "type": "image", + "image_path": "c1e2ca55be06ca1afbb7b7154af7ca3f0afa32376041420796a0dc023a22d940.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 414, + 236, + 472, + 265 + ], + "blocks": [ + { + "bbox": [ + 381, + 233, + 419, + 252 + ], + "lines": [ + { + "bbox": [ + 381, + 233, + 419, + 252 + ], + "spans": [ + { + "bbox": [ + 381, + 233, + 419, + 252 + ], + "type": "text", + "content": "Semantic-driven Editing" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 414, + 236, + 472, + 265 + ], + "lines": [ + { + "bbox": [ + 414, + 236, + 472, + 265 + ], + "spans": [ + { + "bbox": [ + 414, + 236, + 472, + 265 + ], + "type": "image", + "image_path": "d617a3a6cc07c05e8c3a536ce36903f7654410f3b474073b7bfd545b41813cec.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 482, + 236, + 541, + 265 + ], + "blocks": [ + { + "bbox": [ + 482, + 236, + 541, + 265 + ], + "lines": [ + { + "bbox": [ + 482, + 236, + 541, + 265 + ], + "spans": [ + { + "bbox": [ + 482, + 236, + 541, + 265 + ], + "type": "image", + "image_path": "c365d14a17b7f4b03d81c00635e21a3e84c7b22dd2de37ba6479043b54961e7d.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 301, + 546, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 546, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 546, + 481 + ], + "type": "text", + "content": "(a), our method provides much more effortless ways than manual approaches. For example, they require 3D modeling skills to bind the skeleton of the mesh using Blender [69], or drive models [74] with Mixamo poses [58], while our method can easily achieve similar geometric editing with only a single-view image. Besides, naively fine-tuning NeRF on a single-view with a pixel-aligned photometric loss like NeuMesh [69] would only modify visible regions, which leads to inconsistent novel view rendering (e.g., in Fig. 4 (b), the car edited by single-view fine-tuning would expose unpainted red part). On the contrary, our method leverages semantic priors [7] to naturally edit objects with multi-view consistency, which does not require pixel-wise alignment and enables texture transferring between objects with different shapes (see cars and chairs in Fig. 6 (a))." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 483, + 495, + 496 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 495, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 495, + 496 + ], + "type": "text", + "content": "4.3. 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Then, we compare our method with EG3D [9], a 3D-aware generative model that learns a latent representation of category-level objects, and EditNeRF [35], a NeRF variant that supports object editing with single-view user interaction. In addition to editing comparisons, we also used PSNR, SSIM, and LPIPS [42] to measure the edited rendering quality on synthetic cars and chairs. 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As shown in Fig. 5 (b), we conduct different editing operations on four cars from CalWare " + }, + { + "bbox": [ + 47, + 455, + 287, + 706 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 455, + 287, + 706 + ], + "type": "text", + "content": " datasets with DIF shape prior [15], i.e., enlarging/shrinking tires/back. Due to the difficulty of learning a latent textured 3D representation and the limitation of data diversity, 3D-aware generative models like EG3D cannot produce rendering results with fine-grained details, which also results in lower evaluation metrics. For the Photoshape [47], EditNeRF [35] does not provide edited GT images, so we regenerate all testing cases using Blender, which is more challenging than the original ones. Then, we evaluate EditNeRF [35] by fine-tuning the pre-trained models on specific chairs from the PhotoShape dataset. As shown in Fig. 5 (c), EditNeRF produces more blurry rendering results than ours, and cannot achieve satisfactory results with single-view editing (e.g., multi-view inconsistent chair back in the first row, and unmodified or blurry shapes in the third and fourth rows). By contrast, our method consistently delivers high-fidelity rendering results and achieves reliable editing capability by leveraging geometric priors [3, 15]. This demonstrates that, for seman" + } + ] + } + ], + "index": 94 + }, + { + "bbox": [ + 306, + 455, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 545, + 502 + ], + "type": "text", + "content": "tic geometric NeRF editing, learning a prior-guided editing field like ours can maintain better visual quality and achieve greater generalization ability than pre-training a textured 3D generative model or latent model." + } + ] + } + ], + "index": 95 + }, + { + "bbox": [ + 306, + 507, + 481, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 507, + 481, + 520 + ], + "spans": [ + { + "bbox": [ + 306, + 507, + 481, + 520 + ], + "type": "text", + "content": "4.4. 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Users can edit by assigning new textures on the car using Photoshop (adding sea wave windows in Fig. 6 (a)), using a downloaded Internet image with different shapes as a reference (transferring textures of cars and chairs in Fig. 6 (a)). Moreover, we cooperate SINE with off-the-shelf text-prompts editing methods [1] by using a single text-edited image as the target, which enables to change the object's appearance in the " + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": " scene with vivid effects (e.g., shiny plastic round table or burning pinecone in Fig.6 (b)) while preserving background unchanged. 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We show our texture editing results when given users' target images and cooperating with text-prompt-based editing methods [1]." + } + ] + } + ], + "index": 71, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 258, + 507, + 329, + 553 + ], + "lines": [ + { + "bbox": [ + 258, + 507, + 329, + 553 + ], + "spans": [ + { + "bbox": [ + 258, + 507, + 329, + 553 + ], + "type": "image", + "image_path": "cac615dff18645cbfa1ae8055c4109fceb15961a676aa629c941dae6cf7727fc.jpg" + } + ] + } + ], + "index": 75, + "angle": 0, + "type": "image_body" + } + ], + "index": 75 + }, + { + "type": "image", + "bbox": [ + 331, + 507, + 400, + 552 + ], + "blocks": [ + { + "bbox": [ + 331, + 507, + 400, + 552 + ], + "lines": [ + { + "bbox": [ + 331, + 507, + 400, + 552 + ], + "spans": [ + { + "bbox": [ + 331, + 507, + 400, + 552 + ], + "type": "image", + "image_path": "c502f58d00c4b188035499ff774ed96ba4142492f804a3de3a3581a61c4c440f.jpg" + } + ] + } + ], + "index": 76, + "angle": 0, + "type": 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We compare our texture editing with ARF [75] and CLIP-NeRF [64] on the real-world cars [54] and " + }, + { + "bbox": [ + 47, + 631, + 543, + 642 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 631, + 543, + 642 + ], + "type": "text", + "content": " [2,42] scene dataset." + } + ] + } + ], + "index": 95, + "angle": 0, + "type": "image_caption" + } + ], + "index": 89 + }, + { + "type": "image", + "bbox": [ + 474, + 555, + 543, + 607 + ], + "blocks": [ + { + "bbox": [ + 474, + 555, + 543, + 607 + ], + "lines": [ + { + "bbox": [ + 474, + 555, + 543, + 607 + ], + "spans": [ + { + "bbox": [ + 474, + 555, + 543, + 607 + ], + "type": "image", + "image_path": "ef702d8ff9fd901e5d214a05c71a8646fd7d457c1056c647226c0a474321742f.jpg" + } + ] + } + ], + "index": 91, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 608, + 518, + 616 + ], + "lines": [ + { + "bbox": [ + 501, + 608, + 518, + 616 + ], + "spans": [ + { + "bbox": [ + 501, + 608, + 518, + 616 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 92, + "angle": 0, + "type": "image_caption" + } + ], + "index": 91 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "cific category like cars or chairs, yet still transfers texture between objects with correct semantic meaning, e.g., the texture styles of chair legs and cloths in the edited views are precisely matched to the target images in Fig. 6 (a). Besides, we also compare our methods with ARF [75], a" + } + ] + } + ], + "index": 96 + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "NeRF stylization method that also takes a single reference image as input, and CLIP-NeRF [64], which supports text-driven NeRF editing using the large language model [52]. As demonstrated in Fig. 7, ARF globally changes appearance colors to the given target images but fails to produce" + } + ] + } + ], + "index": 97 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "20925" + } + ] + } + ], + "index": 98 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 158 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 158 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 158 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 158 + ], + "type": "image", + "image_path": "efdcdabc31f9a46a28b0596a7b5f114d164bb50fb502435285ddf47ed4a2a448.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 159, + 277, + 168 + ], + "lines": [ + { + "bbox": [ + 111, + 159, + 277, + 168 + ], + "spans": [ + { + "bbox": [ + 111, + 159, + 277, + 168 + ], + "type": "text", + "content": "(a) Ablation studies of color compositing mechanism." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 359, + 159, + 499, + 169 + ], + "lines": [ + { + "bbox": [ + 359, + 159, + 499, + 169 + ], + "spans": [ + { + "bbox": [ + 359, + 159, + 499, + 169 + ], + "type": "text", + "content": "(b) Ablation studies of editing regularization." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 189, + 287, + 345 + ], + "blocks": [ + { + "bbox": [ + 78, + 169, + 512, + 179 + ], + "lines": [ + { + "bbox": [ + 78, + 169, + 512, + 179 + ], + "spans": [ + { + "bbox": [ + 78, + 169, + 512, + 179 + ], + "type": "text", + "content": "Figure 8. We analyze the effectiveness of the color compositing mechanism and editing regularization in texture editing." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 189, + 287, + 345 + ], + "lines": [ + { + "bbox": [ + 51, + 189, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 51, + 189, + 287, + 345 + ], + "type": "image", + "image_path": "86c4f409705d0802ba663a145a1caeafc59949a2db2e8baadd235ddf1fa67467.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 346, + 287, + 368 + ], + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 368 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 368 + ], + "type": "text", + "content": "Figure 9. We inspect the efficacy of the geometric prior constraint and editing regularization in geometric editing." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 373, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 516 + ], + "type": "text", + "content": "fine-grained details (e.g., cookie tires in Fig. 7 (a)). For CLIP-NeRF, since it directly fine-tunes NeRF's color layers, the results only show color/hue adjustment on the original scene (e.g., in Fig. 7, the round table turns gray instead of a realistic silver texture, the vasedeck turns blue instead of a shining diamond). Thanks to the prior-guided editing field, our method learns more fine-grained editing details than the others, and achieves texture editing with consistent semantic meaning to the given target images (e.g., similar appearance to the Tesla's cybertruck in Fig. 7 (a)), and delivers rich appearance details and vivid effects (e.g., silver texture and shining diamond effects in Fig. 7 (b))." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "text", + "content": "User study. We also perform user studies to compare our texture editing (including target-image-based editing and text-prompts editing as Fig. 7) with ARF [75] and CLIP-NeRF [64] on 43 cases with 30 users. The results show that users prefer our methods " + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "inline_equation", + "content": "(89.5\\% / 83.3\\%)" + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "text", + "content": " to ARF " + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "inline_equation", + "content": "(10.4\\% / 7.4\\%)" + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "text", + "content": " and CLIP-NeRF " + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "inline_equation", + "content": "(9.3\\%)" + }, + { + "bbox": [ + 46, + 517, + 288, + 600 + ], + "type": "text", + "content": ". Please refer to the supplementary material for more details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 603, + 148, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 603, + 148, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 603, + 148, + 615 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Geometric prior constraints. We first analyze the effectiveness of geometric prior constraints (Sec. 3.2) by ablating geometric prior loss (Eq. (2)) in Fig. 9 (i.e., deforming cars and airplanes with DIF shape prior, and adding plates with general shape prior). As shown in Fig. 9 (b), when learning without geometric prior constraints, the object will be distorted when rendered from other views (e.g., collapsed car back, twisted airplanes, and warped hotdog plates). By ap-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 304, + 190, + 545, + 226 + ], + "type": "text", + "content": "plying geometric prior constraints, we successfully mitigate the geometric ambiguity for single-image-based editing and produce plausible rendering results from novel views." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "type": "text", + "content": "Color compositing mechanism. We then inspect the efficacy of the color compositing mechanism (Sec. 3.3) by disabling the texture modification field " + }, + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "type": "inline_equation", + "content": "F_{\\Delta T}" + }, + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "type": "text", + "content": " and the color compositing layer in turn. As demonstrated in Fig. 8 (a), when learning texture editing without " + }, + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "type": "inline_equation", + "content": "F_{\\Delta T}" + }, + { + "bbox": [ + 304, + 227, + 546, + 381 + ], + "type": "text", + "content": ", the rendered edited object can show a similar global appearance to the target, but lose vivid local patterns (e.g., gray and white grains and blue shininess). When ablating the color compositing layers, the editing effect might not be properly applied to every part of the object (e.g., the uncovered gray part of the car's front). When all the compositing mechanism is enabled, we successfully learn NeRF editing with fine-grained local patterns and globally similar appearance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 382, + 546, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 546, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 546, + 501 + ], + "type": "text", + "content": "Editing regularization. We finally evaluate the editing regularization (Sec. 3.4) in geometric and texture editing by ablating regularization loss (Eq. (7)). As shown in Fig. 9 (c) and Fig. 8 (b), when learning editing without regularization, the irrelevant part would be inevitably changed (e.g., bent car's front and airplane's head in Fig. 9 (c), a spurious cookie at the car's front and snowy background in Fig. 8 (b)). By adding editing regularization, we can modify the user-desired objects precisely while preserving other content unchanged." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 502, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 548 + ], + "type": "text", + "content": "Please refer to the supplementary material for more experiments (e.g., ablation on more loss terms, visualization of color composition layer, discussion with external supervision, etc.)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 560, + 378, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 378, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 378, + 572 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 579, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 687 + ], + "type": "text", + "content": "We have proposed a novel semantic-driven NeRF editing approach, which supports editing a photo-realistic template NeRF with a single user-edited image, and delivers edited novel views with high-fidelity and multi-view consistency. As a limitation, our approach does not support editing with topology changes, which can be future work. Besides, our method assumes users' editing to be semantically meaningful, so we cannot use target images with meaningless random paintings." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 688, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 688, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 688, + 545, + 711 + ], + "type": "text", + "content": "Acknowledgment. This work was partially supported by NSF of China (No. 62102356)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20926" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 12786-12796, 2022. 2" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20929" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_content_list.json b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..eb84a8eaa8c1e879cfaef84c3b02d0e8bf58da4d --- /dev/null +++ b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_content_list.json @@ -0,0 +1,1553 @@ +[ + { + "type": "text", + "text": "SLACK: Stable Learning of Augmentations with Cold-start and KL regularization", + "text_level": 1, + "bbox": [ + 264, + 130, + 707, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Juliette Marrie1,2", + "bbox": [ + 163, + 202, + 305, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Michael Arbel", + "bbox": [ + 351, + 203, + 475, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diane Larlus", + "bbox": [ + 524, + 203, + 638, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Julien Mairal", + "bbox": [ + 686, + 203, + 800, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK", + "bbox": [ + 129, + 238, + 586, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Naver Labs Europe", + "bbox": [ + 635, + 238, + 834, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Data augmentation is known to improve the generalization capabilities of neural networks, provided that the set of transformations is chosen with care, a selection often performed manually. Automatic data augmentation aims at automating this process. However, most recent approaches still rely on some prior information; they start from a small pool of manually-selected default transformations that are either used to pretrain the network or forced to be part of the policy learned by the automatic data augmentation algorithm. In this paper, we propose to directly learn the augmentation policy without leveraging such prior knowledge. The resulting bilevel optimization problem becomes more challenging due to the larger search space and the inherent instability of bilevel optimization algorithms. To mitigate these issues (i) we follow a successive cold-start strategy with a Kullback-Leibler regularization, and (ii) we parameterize magnitudes as continuous distributions. Our approach leads to competitive results on standard benchmarks despite a more challenging setting, and generalizes beyond natural images.1", + "bbox": [ + 75, + 323, + 473, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 654, + 209, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Data augmentation, which encourages predictions to be stable with respect to particular image transformations, has become an essential component in visual recognition systems. While the data augmentation process is conceptually simple, choosing the optimal set of image transformations for a given task or dataset is challenging. For instance, designing a good set for ImageNet [4] or even CIFAR-10/100 [13] has been the result of a long-standing research effort. Whereas data augmentation strategies that have been chosen by hand for ImageNet have been used successfully for many recognition tasks involving natural images, they may fail to generalize to other domains such as medical imaging, remote sensing or hyperspectral imaging.", + "bbox": [ + 75, + 680, + 470, + 877 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This has motivated automating the design of data augmentation strategies [10, 12, 14-16, 19, 27, 31]. Those are often represented as a stochastic policy that randomly draws a combination of transformations along with their magnitudes from a large predefined set, each time an image is sampled. The goal becomes to learn strategies that effectively compose multiple transformations, which is a challenging task given the large search space of augmentations.", + "bbox": [ + 500, + 292, + 890, + 412 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A natural framework for learning the parameters of this policy is that of bilevel optimization. Intuitively, one looks for the best possible policy such that a neural network trained with this policy on a training set (inner problem) generalizes well on a distinct validation set (outer problem). Optimizing the resulting formulation is challenging as the outer problem depends on the solution of the inner problem. Classical techniques for solving this bilevel problem, such as unrolled optimization, can become highly unstable as the network weights become progressively suboptimal for the current policy during the learning process.", + "bbox": [ + 496, + 414, + 892, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Moreover, augmentations are often non-differentiable in the parameters of the policy, thus requiring techniques other than direct differentiation, such as Bayesian optimization [15], gradient approximations (e.g. RELAX [7]), or the score method / REINFORCE [28] algorithm. While these techniques bypass the differentiability issues, they can suffer from large bias or variance. As a result, learning augmentation policies is a difficult problem whose challenges are exacerbated by the inherent instability of the optimization techniques developed to solve bilevel problems, such as unrolled optimization [1].", + "bbox": [ + 496, + 582, + 893, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A standard way to improve stability and make the automatic data augmentation problem simpler is to reduce the search space. This is often achieved by learning the policy on top of \"default\" transformations such as Cutout [5], random cropping and resizing, or color jittering, all known to be well-suited to natural images which compose standard benchmarks such as CIFAR or ImageNet, or by discarding transformations known to be harmful such as Invert. Fixing some of the transformations and removing others mitigate the challenges inherent to learning a compo", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1Project page: https://europe.naverlabs.com/slack", + "bbox": [ + 94, + 886, + 359, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24306", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba85ba473cfca554dd1086a4f79486a24aa734681f21bd49b3e3fb5503639458.jpg", + "image_caption": [ + "Figure 1. For different domains of the DomainNet dataset [21] (one per line), we show an image from that domain (left) and that image transformed using the three most likely (middle) and the three least likely (right) augmentations for that domain, as estimated by SLACK." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 883, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sition of transformations. TrivialAugment [19] also shows that state-of-the-art results can be achieved on these previous benchmarks simply by directly applying the policy classically used for initializing auto-augmentation models, up to minor modifications. Moreover, all methods rely on carefully chosen ranges that constraint the transformation's magnitudes. Despite its effectiveness, manually selecting default transformations and magnitude ranges restricts the applicability of such policies to natural images and prevents generalisation to other domains.", + "bbox": [ + 75, + 414, + 468, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, our goal is to choose augmentation strategies without relying on default transformations nor on hand-selected magnitude ranges known to suit common benchmarks. To achieve this objective, we first introduce a simple interpretable model for the augmentation policies which allows learning both the frequency by which a given augmentation is selected and the magnitude by which it is applied. Then, we propose a method for learning these augmentation policies by solving a bilevel optimization problem. Our method relies on the REINFORCE technique for computing the gradient of the policy and on unrolled optimization for learning the policy, both of which can result in instabilities and yield high variance estimates.", + "bbox": [ + 75, + 566, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these issues, we introduce an efficient multistage algorithm with a cold-start strategy and a Kullback-Leibler (KL) regularization that are designed to improve the stability of the process for learning the data augmentation policy. More precisely, the algorithm first pre-trains a network with a data augmentation policy uniformly sampling over all transformations. Then, each stage uses a \"cold-start\" strategy by restarting from the pre-trained network and performs incremental updates of the current policy.", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This multi-stage approach with cold start prevents the network from becoming progressively suboptimal as the policy is updated using unrolled optimization. The KL regularization defines a trust region for the policy to compensate for the possibly high variance of gradient estimates obtained using the REINFORCE technique and encourages exploration during training, preventing collapse to trivial solutions. This regularization is inspired by proximal point algorithms in convex optimization [22], which have also been successful in reinforcement learning tasks [23].", + "bbox": [ + 496, + 414, + 892, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By combining the regularized multi-stage approach with our interpretable model of the augmentation policies, we obtained the proposed SLACK method, which stands for Stable Learning of Augmentations with Cold-start and Kullback-Leibler regularization. SLACK is an efficient data augmentation learning method that is able to address the challenging bilevel optimization problem of learning a stochastic data augmentation policy without relying strongly on prior knowledge. Figure 1 illustrates the transformations found by SLACK to be most important / detrimental on a dataset of different domains including nonnatural images.", + "bbox": [ + 496, + 566, + 892, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our contribution is threefold. (i) We propose a simple and interpretable model of the policies which allows learning both frequency and magnitudes of the augmentations. (ii) We propose a regularized multi-stage strategy to improve the stability of the bilevel optimization algorithm used for solving the data augmentation learning problem. (iii) We evaluate our method on challenging experimental settings, and show that it finds competitive augmentation strategies on natural images without resorting to prior information and generalizes to other domains.", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24307", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The choice of image transformation (also known as data augmentation) has become central in the design of computer vision pipelines. To remove the burden of manual selection, automatic data augmentation strategies have been proposed [20, 26]. AutoAugment [2], one of the earliest methods, uses for instance a recurrent neural network for designing the augmentation policy. Because such an approach requires retraining a prediction model at each iteration, it is prohibitively slow, and more efficient alternatives have been proposed. They aim at reducing the training cost using, e.g., population-based training [12], Bayesian optimization [15], and more recently, gradient-based approaches based on bilevel optimization [9, 10, 14, 15, 18, 27, 30], relying on various gradient estimation techniques such as RELAX [7] or the Score method [28]. While the former is inherently biased, the latter is theoretically exact, but has a high variance when approximated in the context of stochastic optimization. Therefore, these approximations may lead to diverging gradient updates. Our method alleviates this by introducing a KL regularization that defines a trust-region for the policy.", + "bbox": [ + 75, + 118, + 472, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Automatic augmentation using prior knowledge. Most previous works learn augmentations using a small network learned on a subset of the dataset of interest, before retraining the prediction model on a larger network using the full (augmented) data. This choice is appealing to recent gradient-based methods [9, 14] as the search phase for an augmentation policy is often reduced to minutes. Nevertheless, [10, 30] have observed that policies found with such a reduced setup may be suboptimal compared to approaches exploiting full datasets for training both the augmentation policy and the prediction model. This observation was confirmed in [3], which shows that a naive grid search could actually yield state-of-the-art results when directly training on the full-size network and the full data. These results are however obtained at the expense of using strong prior knowledge: augmentation policies are applied on top of default transformations that are manually and independently chosen for each benchmark. Lately, [19] has shown that with a few additional careful choices regarding the augmentation policies, applying a single random transformation on top of the default ones could lead to state-of-the-art results.", + "bbox": [ + 75, + 428, + 472, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To avoid relying on default augmentations, DeepAA [31] has recently proposed a greedy approach that is able to learn these transformations. Yet, learning is performed after a \"pre-training\" phase leveraging the usual default transformations. Moreover, while such a greedy approach simplifies the search procedure and reduces its stochasticity, the resulting computational cost is high. Instead, our approach improves stability and allows directly learning the joint probability of sampling multiple transformations, reducing the search time twofold compared to DeepAA.", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b0f5998908ae6f25ea0a6265b402027faa394ff0984f025d578a54628e55c3ca.jpg", + "image_caption": [ + "Figure 2. Overview of our proposed SLACK method. We learn a data augmentation policy parameterized by $\\phi$ using bilevel optimization. The inner loop finds the optimal network parameter $\\theta^{*}$ on images from $\\mathcal{D}_{\\mathrm{train}}$ . The outer loop trains on a disjoint set of images $\\mathcal{D}_{\\mathrm{val}}$ using this network and finds the optimal transformation parameters $\\phi$ . The method is enhanced with i) a cold-start strategy that structures the learning into rounds which share $\\phi$ but restart the network from the pretrained one, and ii) a KL regularization." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 893, + 289 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 439, + 591, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method, SLACK, defines an augmentation policy, which is a probabilistic model for generating data augmentations. The goal is to learn the parameters of this augmentation policy so as to improve the performance of the trained classifier on a held-out dataset. We first describe the augmentation policy (Sec. 3.1) and then formalize the problem of learning data augmentations with bilevel optimization (Sec. 3.2). We then describe our approach for solving such a bilevel optimization problem, which aims at stabilizing the optimization (Sec. 3.3).", + "bbox": [ + 496, + 465, + 893, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Stochastic data augmentations policy", + "text_level": 1, + "bbox": [ + 500, + 628, + 821, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An augmentation function $\\tau$ transforms an image $x$ into another augmented image $\\tau(x)$ of the same dimensions. We consider composite augmentations obtained by combining simpler augmentations selected from a finite set $S = \\{s_1, \\ldots, s_N\\}$ of $N$ candidate elementary transformations, such as rotations, translations, shearing, etc. Each elementary transformation depends on a magnitude parameter $m$ that controls the strength of the transformations, for instance, the angle by which an image is rotated. Magnitudes are normalized to be in the unit interval [0, 1].", + "bbox": [ + 496, + 654, + 893, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Augmentation policy. We define the augmentation policy as a probabilistic model $p_{\\phi}$ that generates composite augmentations given some parameter $\\phi$ to be learned. The model generates an augmentation in three steps: (1) it samples $K$ elementary transformations $t_1,\\ldots ,t_K$ from $\\mathcal{S}$ according to a categorical distribution $p_{\\pi}$ of parameter $\\pi$ , (2)", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24308", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "it samples values for the magnitudes $m_{1},\\ldots ,m_{K}$ for each of the selected elementary transformations $t_k$ according to a smoothed uniform distribution $p_\\mu$ of parameter $\\mu$ and (3) it composes the $K$ elementary transformations to obtain the composite augmentation, with each $t_k$ applied using its corresponding magnitude $m_{k}$ . Therefore, the augmentation policy $p_{\\phi}(\\tau)$ takes the form", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\phi} (\\tau) = \\prod_ {i = 1} ^ {K} p _ {\\pi} \\left(t _ {i}\\right) p _ {\\mu} \\left(m _ {i} \\mid t _ {i}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 209, + 468, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the parameters $\\phi = (\\pi, \\mu)$ are learned jointly. Next, we describe the sampling of the transformations and of their magnitudes.", + "bbox": [ + 76, + 262, + 468, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sampling transformations. We sample elementary transformations $t_k$ with replacement from a categorical distribution $\\mathrm{Cat}_{\\pi_k}$ of dimension $N$ parameterized by a logit vector $\\pi_k \\coloneqq (\\pi_{k,n})_{1 \\leq n \\leq N}$ . The probability $p_{\\pi}(t_1, \\ldots, t_K)$ of sampling the $K$ transformations is given by:", + "bbox": [ + 76, + 311, + 468, + 387 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\pi} \\left(t _ {1}, \\dots , t _ {K}\\right) = \\Pi_ {k = 1} ^ {K} \\operatorname {C a t} _ {\\pi_ {k}} \\left(t _ {k}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 398, + 468, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we collect all logits to form a parameter matrix $\\pi$ of size $K\\times N$ . These parameters are learned.", + "bbox": [ + 76, + 428, + 468, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sampling magnitudes. The magnitudes of each elementary transformation $s_i$ in $S$ are sampled from a smoothed uniform distribution between $[0, \\mu_i]$ whose upper-bound $\\mu_i$ is learned. More precisely, the distribution's density is defined as", + "bbox": [ + 76, + 462, + 468, + 536 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mu_ {i}} (m _ {i}) = \\frac {1}{\\mu_ {i}} \\int_ {0} ^ {\\mu_ {i}} \\mathcal {N} (m _ {i}, \\sigma) (u) d u,\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 545, + 395, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(m_i,\\sigma)$ is the Gaussian distribution of mean $m_{i}$ and deviation $\\sigma$ . The density $p_{\\mu_i}(m_i)$ approximates the uniform distribution $\\frac{1}{\\mu_i}\\mathbf{1}_{[0,\\mu_i]}$ as the deviation $\\sigma$ approaches 0. In practice, we set $\\sigma = 0.1$ as we found it to achieve a good trade-off between smoothing and approximation.", + "bbox": [ + 76, + 589, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Why a uniform distribution? We ran some ablations on previous methods (see supplementary) which suggest that a uniform sampling works on par with more elaborate sampling strategies, and that the magnitude range has more impact on the results.", + "bbox": [ + 76, + 670, + 468, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Bilevel formulation for policy search", + "text_level": 1, + "bbox": [ + 76, + 756, + 393, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We consider a prediction task, such as predicting the class $y$ of some natural image $x$ using a model $f_{\\theta}(x)$ with parameter $\\theta$ . We are interested in finding the best policy parameter $\\phi$ so that the prediction model $f_{\\theta}$ , when trained using such policy on a training set $\\mathcal{D}$ of input/output pairs $(x,y)$ , generalizes well on the test set $\\mathcal{D}_{\\mathrm{test}}$ . The problem naturally decomposes in two phases. During the search phase, the optimal augmentation policy $p_{\\phi}$ is learned on $\\mathcal{D}$ .", + "bbox": [ + 76, + 780, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "During the evaluation phase, the model is re-trained on $\\mathcal{D}$ using $p_{\\phi}$ and is then evaluated on $\\mathcal{D}_{\\mathrm{test}}$ . The evaluation phase is performed using standard optimization methods. However, the search phase requires solving a complex optimization problem that we describe next.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Search phase as a bilevel problem. The search phase naturally writes as a bilevel problem involving two interdependent losses: a lower-level loss $\\mathcal{L}_{\\mathrm{train}}(\\theta, \\phi)$ for learning an optimal model parameter $\\theta^{\\star}(\\phi)$ obtained using the augmentation policy $p_{\\phi}$ and an upper-level loss $\\mathcal{F}(\\phi)$ for learning the policy parameter $\\phi$ by evaluating the optimal model with parameter $\\theta^{\\star}(\\phi)$ . Each of these objectives is evaluated on two separate splits of the available data $\\mathcal{D}$ : a training split $\\mathcal{D}_{\\mathrm{train}}$ for the lower-level loss and a validation split $\\mathcal{D}_{\\mathrm{val}}$ for the upper-level loss. Below, we describe both losses.", + "bbox": [ + 496, + 170, + 890, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lower-level loss. We first introduce the training loss $\\ell_{\\mathrm{train}}(\\theta, \\tau)$ when only a fixed augmentation $\\tau$ is used:", + "bbox": [ + 500, + 325, + 890, + 357 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {\\text {t r a i n}} (\\theta , \\tau) := \\mathbb {E} _ {(x, y) \\sim \\mathcal {D} _ {\\text {t r a i n}}} [ \\ell (y, f _ {\\theta} (\\tau (x))) ],\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 369, + 836, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $(x,y)$ is an (image, label) pair drawn from $\\mathcal{D}_{\\mathrm{train}}$ and $\\ell$ is a pointwise prediction loss (e.g. cross-entropy). We then define the training loss $\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)$ for an augmentation policy $p_{\\phi}$ by taking the expectation of $\\ell_{\\mathrm{train}}(\\theta ,\\tau)$ over augmentations $\\tau$ sampled according to the policy $p_{\\phi}$ :", + "bbox": [ + 496, + 398, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t r a i n}} (\\theta , \\phi) := \\mathbb {E} _ {\\tau \\sim p _ {\\phi}} \\left[ \\ell_ {\\text {t r a i n}} (\\theta , \\tau) \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 488, + 810, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, for a given policy $p_{\\phi}$ , the goal is to learn the optimal model parameter $\\theta^{\\star}(\\phi)$ by minimizing $\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)$ over $\\theta$", + "bbox": [ + 496, + 517, + 890, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Upper-level loss. We first denote by $\\mathcal{L}_{\\mathrm{val}}(\\theta)$ the validation loss for a given model of parameter $\\theta$ :", + "bbox": [ + 496, + 551, + 890, + 582 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {v a l}} (\\theta) := \\mathbb {E} _ {(x, y) \\sim \\mathcal {D} _ {\\text {v a l}}} [ \\ell (y, f _ {\\theta} (x)) ].\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 595, + 815, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The validation loss $\\mathcal{L}_{\\mathrm{val}}(\\theta)$ is computed over the validation set $\\mathcal{D}_{\\mathrm{val}}$ without applying any augmentation and thus provides a proxy for the performance on the test dataset. We then define the upper-level loss to be the validation loss of an optimal model $\\theta^{\\star}(\\phi)$ learned using a policy $p_{\\phi}$ :", + "bbox": [ + 496, + 625, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} (\\phi) := \\mathcal {L} _ {\\text {v a l}} \\left(\\theta^ {*} (\\phi)\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 713, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While optimizing the lower-level loss is relatively standard, minimizing the upper-level loss $\\mathcal{F}$ is more challenging due to the complex dependence of the optimal model parameter $\\theta^{\\star}(\\phi)$ on the policy. Next, we describe our proposed algorithm for solving the bilevel problem.", + "bbox": [ + 496, + 744, + 890, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. SLACK algorithm", + "text_level": 1, + "bbox": [ + 500, + 830, + 678, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose Algorithm 1 for learning the optimal policy during the search phase. SLACK first pre-trains the prediction model using the objective $\\mathcal{L}_{\\mathrm{train}}(\\theta, \\phi_{\\mathrm{uniform}})$ for an", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24309", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "initial policy parametrized by $\\phi_{\\mathrm{uniform}}$ which samples uniformly among all elementary transformations. It then performs $n_{\\mathrm{rounds}}$ rounds to update the parameters $\\theta$ and $\\phi$ jointly using a bilevel optimization algorithm. This approach is reminiscent of the one of AutoAugment (AA) [3] that fully re-trains the network for each policy update. Yet, it is several orders of magnitude faster than AA, as it benefits from pre-training and from our bilevel optimization.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SLACK relies on two strategies to ensure the stability of the parameter updates during each round: a cold-start strategy for the prediction model and an anchoring strategy for the policy. The cold-start initializes the prediction model at the beginning of each round using a pre-trained model $\\theta_0$ . Anchoring is achieved by encouraging the current policy to remain close to some anchor policy $p_{\\tilde{\\phi}}$ . We set $\\tilde{\\phi}$ to the current policy parameter $\\phi$ at the beginning of each round. During the first $n_{\\mathrm{retrain}}$ steps of each round, the algorithm only updates the model parameter using a stochastic estimate $\\hat{g}_{\\theta}$ of $\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)$ while maintaining the policy fixed. Then for the last $n_{\\mathrm{total}} - n_{\\mathrm{retrain}}$ steps, the algorithm alternates between model updates and policy updates. The policy updates aim to minimize the sum of the upper-level objective $\\mathcal{F}$ and an anchoring $d(p_{\\phi},p_{\\tilde{\\phi}})\\coloneqq \\mathrm{KL}(p_{\\pi},p_{\\tilde{\\pi}})$ encouraging the policy $p_{\\phi}$ to remain close to the anchor policy $p_{\\tilde{\\phi}}$ . These updates are obtained using a stochastic estimate $\\hat{G}_{\\phi}$ along with the exact gradient of the KL regularization which admits a closed-form expression. Next we explain how we estimate the gradients $\\hat{g}_{\\theta}$ and $\\hat{G}_{\\phi}$ and discuss the effect of cold-start and KL-regularization.", + "bbox": [ + 75, + 210, + 473, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 SLACK", + "text_level": 1, + "bbox": [ + 78, + 547, + 222, + 561 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Initialize policy parameter $\\phi \\gets \\phi_{\\mathrm{uniform}}$", + "2: Pre-training: $\\theta_0\\gets$ optimize $(\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi))$", + "3: for $i \\in \\{1, \\dots, n_{\\text{rounds}}\\}$ do", + "4: Cold-start: $\\theta \\gets \\theta_0$ .", + "5: Update anchor policy: $\\tilde{\\phi} \\gets \\phi$ .", + "6: for $j\\in \\{1,\\dots,n_{\\mathrm{total}}\\}$ do", + "7: Compute stochastic gradient $\\hat{g}_{\\theta}\\approx \\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)$", + "8: Update $\\theta$ : $\\theta \\gets \\theta - \\eta \\hat{g}_{\\theta}$ .", + "9: if $j > n_{\\mathrm{retrain}}$ then", + "10: Compute stochastic gradient $\\hat{G}_{\\phi}\\approx \\nabla_{\\phi}\\mathcal{F}(\\phi)$", + "11: Update $\\phi$ : $\\phi \\gets \\phi - \\alpha (\\hat{G}_{\\phi} + \\lambda \\nabla_{\\phi} d(p_{\\phi}, p_{\\phi}^{\\prime}))$ .", + "12: end if", + "13: end for", + "14: end for" + ], + "bbox": [ + 81, + 566, + 403, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gradient estimation. Algorithm 1 requires estimating the gradient of $\\mathcal{F}(\\phi)$ , which is challenging given the complex dependence of the upper-level loss on the policy $p_{\\phi}$ through the optimal model parameter $\\theta^{\\star}(\\phi)$ learned using such a policy. In line with previous works [9, 14, 18, 27], we approximate the optimal model parameter $\\theta^{*}(\\phi)$ with a simpler function $\\hat{\\theta} (\\phi)$ that is easier to compute:", + "bbox": [ + 75, + 761, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\theta} (\\phi): = \\theta - \\eta \\nabla_ {\\theta} \\mathcal {L} _ {\\text {t r a i n}} (\\theta , \\phi). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 878, + 468, + 896 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Eq. (4) corresponds to one gradient step to optimize the lower-level loss starting from the current parameter $\\theta$ and $\\phi$ and using step-size $\\eta > 0$ . By keeping track of the dependence in $\\phi$ and exploiting the fact that the augmentation policy $p_{\\phi}$ has a score $\\nabla_{\\phi} \\log p_{\\phi}(\\tau)$ that can be computed explicitly using Eq. (1), we can use the REINFORCE/Score method [6] to derive a closed-form expression for $\\nabla_{\\phi} \\hat{\\theta}(\\phi)$ which will serve for approximating the gradient of $\\mathcal{F}$ :", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\phi} \\hat {\\theta} (\\phi) = - \\eta \\mathbb {E} _ {\\tau \\sim p _ {\\phi}} \\left[ \\nabla_ {\\theta} \\ell_ {\\text {t r a i n}} (\\theta , \\tau) \\nabla_ {\\phi} \\log p _ {\\phi} (\\tau) ^ {\\top} \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 222, + 870, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we approximate the upper-level loss $\\mathcal{F}(\\phi)$ with a simpler function $\\hat{\\mathcal{F}} (\\phi)\\coloneqq \\mathcal{L}_{\\mathrm{val}}(\\hat{\\theta} (\\phi))$ and the gradient $\\nabla_{\\phi}\\mathcal{F}(\\phi)$ with $\\nabla_{\\phi}\\hat{\\mathcal{F}} (\\phi)$ which is obtained using the chain rule:", + "bbox": [ + 496, + 252, + 890, + 301 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\phi} \\mathcal {F} (\\phi) \\approx \\nabla_ {\\phi} \\hat {\\mathcal {F}} (\\phi) = \\nabla_ {\\theta} \\mathcal {L} _ {\\text {v a l}} \\left(\\hat {\\theta} (\\phi)\\right) ^ {\\top} \\nabla_ {\\phi} \\hat {\\theta} (\\phi). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 313, + 890, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The above expression requires only first-order derivatives and matrix-vector products, which is amenable to efficient implementation using automatic differentiation softwares.", + "bbox": [ + 496, + 343, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Stochastic gradient estimates. In practice, we replace all expectations by estimates on a batch of data and sampled augmentations. More precisely, to compute the approximation $\\hat{g}_{\\theta}$ to $\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)$ , we sample $B_{\\mathrm{aug}}$ augmentations from $p_{\\phi}$ and then apply each of them to a batch of training data $B_{\\mathrm{train}}$ from $\\mathcal{D}_{\\mathrm{train}}$ . Using the same batch of data and augmentation, we approximate $\\hat{\\theta} (\\phi)$ and $\\nabla_{\\phi}\\hat{\\theta} (\\phi)$ appearing in Eq. (5). Finally, we use a batch $B_{\\mathrm{val}}$ of data from $\\mathcal{D}_{\\mathrm{val}}$ to estimate $\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{val}}(\\hat{\\theta} (\\phi))$ and compute $\\hat{G}_{\\phi}$ , which is a stochastic estimate of $\\nabla_{\\phi}\\hat{\\mathcal{F}} (\\phi)$ in Eq. (5).", + "bbox": [ + 496, + 392, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cold-start. The cold-start strategy allows to re-train the model at each round with the current augmentation policy starting from the pre-trained model. This approach is closer to the original bilevel formulation which implies finding an optimal prediction model for each policy. Initializing with a pre-trained model yields computational gain as fewer iterations are needed to optimize the model. We could instead use a warm-start strategy which initializes the model at each round with the learned model at the previous round. Yet we experimentally observe that such approach progressively leads to overfitting and degrades the quality of the learned policies (see supplementary).", + "bbox": [ + 496, + 549, + 890, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Anchoring using KL regularization. We experimentally found that adding an anchoring $d(p_{\\phi}, p_{\\tilde{\\phi}}) \\coloneqq \\mathrm{KL}(p_{\\pi}, p_{\\tilde{\\pi}})$ with strength parameter $\\lambda$ when updating the policy prevents the algorithm from collapsing towards trivial policies. The anchoring affects only the categorical distribution $p_{\\pi}$ . For the magnitudes $p_{\\mu}$ , we did not use anchoring as it is ill-defined for a uniform distribution. Instead, we simply used smaller step-sizes. Our approach takes inspiration from Proximal Policy Optimization [23] used in the context of reinforcement learning which is known to improve policy search.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24310", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 90, + 209, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we first briefly describe our experimental setup (Sec 4.1). Then we evaluate our approach on several standard benchmarks composed of natural images (Sec 4.2) as well as on a benchmark with other domains (Sec 4.3). We finally report some ablation studies (Sec 4.4).", + "bbox": [ + 75, + 114, + 468, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 199, + 264, + 215 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Benchmarks.** We first evaluate our model on three standard benchmarks, CIFAR10 [13], CIFAR100 [13] and ImageNet-100 [25], all composed of natural images. To study how well our method generalizes beyond natural images, we also evaluate on the DomainNet dataset [21], which contains 345 classes for 6 different domains. To ensure our protocol uses a similar number of training images for each domain, we use a reduced set of 50,000 training images for the two largest domains (real, quickdraw) and leave the remaining images for testing. For the other domains, we isolate $20\\%$ of the data for testing.", + "bbox": [ + 75, + 224, + 468, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Architectures. CIFAR10/100 are evaluated with two architectures that are standard for automatic data augmentation: WideResNet-40x2 and WideResNet-28x10 [29]. Unlike previous works whose search phase is only conducted with the smaller WideResNet-40x2, we search and evaluate with the same architecture, as we found it to be better (see Sec. 4.4). ImageNet-100 and DomainNet are evaluated with a ResNet-18 [11] architecture.", + "bbox": [ + 75, + 395, + 468, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Transformation space. Our data augmentation search space is composed of the standard pool of 15 transformations: Identity, ShearX, ShearY, TranslateX, TranslateY, Rotate, AutoContrast, Equalize, Invert, Solarize, Posterize, Contrast, Brightness, Sharpness, Color. We add to this pool the transformations that previous methods usually apply by default: Cutout and RandomCrop for CIFAR, RandomResizeCrop for ImageNet, Grayscale for DomainNet. Following standard practice, when RandomResizeCrop is sampled, it is always applied first. We learn the range of its scale parameter. We do not add ColorJitter that is also applied by default in prior work for ImageNet, as it is already a mix of Brightness, Contrast and Color. However we add Hue, which is one component of ColorJitter and never applied by default. Following prior work, the magnitudes are mapped to [0,1]. After mapping, $\\mu$ is initialized at 0.75 to favour exploration (see details in supplementary). We also uniformly sample magnitudes for Cutout and RandomCrop, whereas their value is hand-picked in prior work. Since the datasets are horizontally symmetric, we follow common practice and apply flip by default.", + "bbox": [ + 75, + 518, + 468, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Policy search. We apply a train/val split of 0.5/0.5, meaning that half of the data is used to train the model parameters while the other half is used to learn the augmentation policy. Pre-training is done in the same setting as the evaluation", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(see next paragraph), except that we train only with the train data in the train/val split of the search phase. We use SGD with momentum for the optimization of the validation and training losses. For the latter, we use the same weight decay as for the final policy evaluation. We sample 8 different augmentations for computing the expectation that is needed for the stochastic gradient estimate, as detailed in Sec. 3.3.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Policy evaluation. We evaluate our models following the framework of TrivialAugment [19]. The corresponding hyperparameters can be found in the supplementary. We evaluate each policy with 4 independent runs, meaning that our results are averaged over a total of $4 \\times 4 = 16$ evaluations. Our Uniform policy (corresponding to SLACK's initialization) and our reported results on TrivialAugment are evaluated with 8 independent runs. We also report a confidence interval which contains the true mean with probability $p = 95\\%$ , under the assumption of normally distributed accuracies.", + "bbox": [ + 496, + 200, + 892, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with the state of the art", + "text_level": 1, + "bbox": [ + 498, + 375, + 815, + 392 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method with a Uniform augmentation policy as well as many previous approaches for data augmentation, including AutoAugment (AA) [2], Fast AutoAugment (FastAA) [15], Differentiable Automatic Data Augmentation (DADA) [14], RandAugment (RA) [3], Teach Augment [24], UniformAugment [20], TrivialAugment (TA) [19], and Deep AutoAugment (DeepAA) [31].", + "bbox": [ + 496, + 398, + 890, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each method, we indicate the total number of composed transformations, and the number of hard-coded transformations among those (Tables 1 and 2). For SLACK, we evaluate the policies obtained from 4 independent search runs (each with 4 different train/val splits) to assess the robustness of our approach. We follow the same process when reproducing DeepAA on CIFAR10/100. Note that all previous methods use a single run for search, before evaluating the policy with one or multiple runs. We report $95\\%$ confidence intervals for those evaluating with multiple runs.", + "bbox": [ + 496, + 505, + 890, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The supplementary provides qualitative results showing the evolution of the probability distributions over the transformations and the final estimated policies for all datasets.", + "bbox": [ + 496, + 656, + 890, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR. In Table 1, we observe that, despite not hard-coding Cutout and RandomCrop in our policy, our method is competitive on both CIFAR10 and CIFAR100.", + "bbox": [ + 496, + 704, + 890, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We found that, in general, Cutout and Rotate are selected with a high probability, while the Invert transformation is systematically discarded (see supplementary). This is consistent with the choices made in practice by prior work of adding/removing these transformations manually.", + "bbox": [ + 496, + 750, + 890, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We observe a mismatch between DeepAA's reported results [31], and those we obtain when evaluating their approach on multiple search runs, using the author's code and following their recommendations. This is likely due to the stochasticity of the search procedure.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24311", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3a009396541c2083ef9cf351ee91ba45fd6fcce6f6aabe23a2bcc9887780a3be.jpg", + "table_caption": [], + "table_footnote": [ + "*: DeepAA uses hard-coded transformations for pre-training. **: DeepAA learns random flipping unlike other baselines. † We evaluate the policies found from 4 independent search runs as we do for SLACK, using the code from the authors and following their recommendations." + ], + "table_body": "
# AugmentationsCIFAR10CIFAR100
TotalHard-codedWRN-40-2WRN-28-10WRN-40-2WRN-28-10
AA [2]4296.397.479.382.9
FastAA [15]4296.497.379.482.7
DADA [14]4296.497.379.182.5
RA [3]42-97.3-83.3
TeachA [24]42-97.5-83.2
UniformAugment [17]4296.2597.3379.0182.82
TA (Wide) [19]3296.32 ± .0597.46 ± .0679.86 ± .1984.33 ± .17
Uniform policy3096.12 ± .0897.26 ± .0778.79 ± .2582.82 ± .24
DeepAA [31]6**0*-97.56 ± .14-84.02 ± .18
DeepAA (reproduced)†6**0*96.25 ± .1197.27 ± .1179.26 ± .3583.38 ± .33
SLACK (Ours)3096.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
", + "bbox": [ + 178, + 88, + 794, + 272 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/85bc785631feea07305bf7e587f56b3d82ad659b10a107bdde86e34b18aa9779.jpg", + "table_caption": [ + "Table 1. Test accuracies on CIFAR10 and CIFAR100. For SLACK and DeepAA (reproduced) we conduct 4 independent searches, and evaluate each policy with 4 evaluation runs, meaning that we report averages over 16 evaluations. TA and DeepAA are also evaluated with multiple evaluation runs. Results for the remaining methods are reported from the corresponding papers and based on a single run." + ], + "table_footnote": [], + "table_body": "
# AugmentationsImageNet-100
TotalHard-codedResNet18
TA (RA) [19]†5485.87 ± .30
TA (Wide) [19]†5486.39 ± .18
Uniform policy3085.78 ± .32
SLACK3086.06 ± .11
", + "bbox": [ + 106, + 390, + 442, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Test accuracies on ImageNet-100.", + "bbox": [ + 143, + 503, + 401, + 517 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ImageNet-100. Results for ImageNet-100 are reported in Table 2. We compare SLACK to our Uniform policy and to TrivialAugment (RA) and (Wide) variants, the latter using larger magnitude ranges for its random transformation. SLACK's results lie in between both variants and improve over our Uniform policy.", + "bbox": [ + 75, + 546, + 468, + 637 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Interestingly, for ImageNet-100, we found that RandomResizeCrop is not favoured during the search phase (see supplementary), suggesting that it is not critical for ImageNet-100. Instead the performance gap between TA (Wide) and TA (RA) suggest that harder transformations are key to a better performance for this dataset.", + "bbox": [ + 75, + 637, + 468, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Beyond natural images", + "text_level": 1, + "bbox": [ + 76, + 739, + 290, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the DomainNet dataset, we compare SLACK to a Uniform policy, to the augmentations used by DomainBed [8] for domain generalization, and to the TrivialAugment (RA) and (Wide) methods with their ImageNet and CIFAR default settings. Results can be found in Table 3.", + "bbox": [ + 75, + 763, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DomainBed uses the same default transformations as TA ImageNet together with Grayscale, but with smaller magnitudes and unlike TA, does not add a random transformation. Yet it strongly overfits and performs much lower than TA.", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This suggests that augmentations well suited for domain generalization do not perform well on the individual tasks. TA (Wide) ImageNet consistently outperforms all other TA flavors. This further justifies the need to learn the magnitude range and to eliminate any manual range selection process.", + "bbox": [ + 496, + 393, + 890, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SLACK is a close second, yet it learns the policy end-to-end. The learned policies are illustrated as pie charts in Fig. 3. The slices represent the probability $\\pi$ over the different transformations while their radius represent the corresponding magnitudes. They differ from a domain to another, suggesting that the gain compared to the initialization (i.e. Uniform policy) results from SLACK's ability to learn and adapt to each domain.", + "bbox": [ + 496, + 469, + 890, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation study", + "text_level": 1, + "bbox": [ + 498, + 598, + 648, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we evaluate our contributions and main design choices: the network architecture used for search, the KL regularization, and the benefits of learning $\\pi$ and $\\mu$ . More ablations can be found in the supplementary. Note that hyperparameters are adjusted to each baseline included in the comparison, to make them as competitive as possible.", + "bbox": [ + 496, + 621, + 890, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Network architecture for search. In prior works, the search phase (when there is one) is conducted on the smaller WideResNet-40x2 architecture for CIFAR10 and CIFAR100, and the learned policy is evaluated for both WideResNet-40x2 and WideResNet-28x10. Table 4 shows that for SLACK, searching directly with WideResNet-28x10 gives the best results for that architecture.", + "bbox": [ + 496, + 715, + 890, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "KL regularization. We compare SLACK with a flavor that does not apply KL-regularization. For the latter, we reduce the outer learning rate so that the augmentation policies with and without regularization evolve at similar speeds. Results in Table 5 show that our regularization is beneficial.", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24312", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5e2180c55934da24852a412e121c2442f409294ce3d59cc88667521f2e9d2db8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
# AugmentationsReal-50kQuickdraw-50kInforgraphSketchPaintingClipartAverage
TotalHard-coded
\\( DomainBed^† \\)5562.54 ± .1566.54 ± .9126.76 ± .3659.54 ± .3758.31 ± .2566.23 ± .1057.23 ± .18
\\( TA (RA) ImageNet^† \\)5470.85 ± .1367.85 ± .0735.24 ± .1965.63 ± .1164.75 ± .1870.29 ± .1862.43 ± .05
\\( TA (Wide) ImageNet^† \\)5471.56 ± .0768.60 ± .0535.44 ± .3366.21 ± .1665.15 ± .2071.19 ± .1963.03 ± .07
\\( TA (RA) CIFAR^† \\)3270.28 ± .0868.35 ± .0733.85 ± .2164.13 ± .1264.73 ± .1770.33 ± .2161.94 ± .05
\\( TA (Wide) CIFAR^† \\)3271.12 ± .1069.29 ± .0534.21 ± .2965.52 ± .2564.81 ± .1471.01 ± .2162.66 ± .07
Uniform policy3070.37 ± .0868.27 ± .0634.11 ± .2165.22 ± .1763.97 ± .2472.26 ± .1462.37 ± .06
SLACK (ours)3071.00 ± .1368.14 ± .1134.78 ± .1865.41 ± .1664.83 ± .1272.65 ± .2062.80 ± .06
", + "bbox": [ + 101, + 88, + 866, + 210 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d5131b5c03d33bf63ceaed729b8d64b4e7047c2692f1776c6d8e78cb412d13a6.jpg", + "image_caption": [ + "Figure 3. Policies found on DomainNet for the best search split. Gray circle: initial magnitude upper-bounds. Radius of each pie: learned upper-bounds. Size of each pie: probability of each transformation, averaged over the three composite distributions. Transformations which are parameter-free, AutoContrast, Equalize, Grayscale, and Invert, are displayed with maximal magnitude upper-bound." + ], + "image_footnote": [], + "bbox": [ + 86, + 243, + 346, + 463 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/80e5898d173dd775d932a15034785dae799096d087c6d95ca8586097481d44fa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 244, + 609, + 460 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47e3e1f1ad2eb18a94fa6626e4a7cbd91a579a003703508d4f466edef76b38ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 244, + 872, + 463 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/511678c86cc2b4c234f718e5f7ab7250675f104396997065b304e8e401106aa6.jpg", + "table_caption": [ + "Table 3. Test accuracies on DomainNet." + ], + "table_footnote": [], + "table_body": "
Search architectureCIFAR10CIFAR100
WRN-40-297.43 ± .0483.94 ± .20
WRN-28-10 (ours)97.46 ± .0684.08 ± .16
", + "bbox": [ + 142, + 532, + 405, + 579 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/206f01f975b7c115a044c382d8fe54a2076d5f2d62f7ca54ff115989fffb5e7a.jpg", + "table_caption": [ + "Table 4. CIFAR10/100 accuracy evaluated with WRN-28-10: impact of using a smaller architecture for the search phase." + ], + "table_footnote": [], + "table_body": "
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
without KL96.27 ± .0597.06 ± .1179.61 ± .1383.79 ± .19
with KL (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
", + "bbox": [ + 78, + 633, + 475, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Joint learning of $\\pi$ and $\\mu$ . Lastly, we study how beneficial jointly learning our augmentation parameters is compared to the initial Uniform policy and to a setting where only $\\pi$ or $\\mu$ is learned. Results can be found in Table 6.", + "bbox": [ + 75, + 751, + 468, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 828, + 194, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we address the task of automatic data augmentation. Considering the more challenging bilevel optimization problem that arises when the search space is not", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bde3e8ffdf29f160409f32a73a7f59a5ef835e0d8b789d587f1a68b779fc79e0.jpg", + "table_caption": [ + "Table 5. CIFAR10/100 accuracy with/without KL regularization." + ], + "table_footnote": [], + "table_body": "
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
Uniform policy96.22 ± .1097.38 ± .0579.07 ± .2483.26 ± .17
μ only96.20 ± .0897.42 ± .0579.22 ± .1783.57 ± .18
π only96.22 ± .0997.35 ± .0479.36 ± .1183.45 ± .15
π and μ (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
", + "bbox": [ + 504, + 532, + 890, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. CIFAR10/100 accuracy when only learning part of the policy parameters", + "bbox": [ + 498, + 625, + 890, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "reduced with default transformations, our proposed SLACK method tackles the resulting stability issues thanks to a multi-stage approach based on cold-start, coupled with a KL-regularization. Combined, they allow to reduce the variance of the gradient estimate and to better control the optimization process. We have experimentally observed that our method performs on par with recent approaches leveraging prior knowledge. It has also proved versatile enough to select domain-specific transformations when confronted to non-natural images.", + "bbox": [ + 496, + 683, + 890, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by ANR 3IA MIAI@Grenoble Alpes (ANR-19-P3IA-0003) and performed using HPC resources from GENCI-IDRIS (Grant 2022-AD011013343).", + "bbox": [ + 496, + 839, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24313", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael Arbel and Julien Mairal. Non-convex bilevel games with critical point selection maps. preprint arXiv:2207.04888, 2022. 1", + "[2] Ekin D Cubuk, Barret Zoph, Dandelion Mane, Vijay Vasudevan, and Quoc V Le. Autoaugment: Learning augmentation policies from data. arXiv preprint arXiv:1805.09501, 2018. 3, 6, 7", + "[3] Ekin Dogus Cubuk, Barret Zoph, Jon Shlens, and Quoc Le. RandAugment: Practical automated data augmentation with a reduced search space. 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Yan, D. Lin, and W. Ouyang. Online hyper-parameter learning for autoaugmentation strategy. In Proc. ICCV, 2019. 1", + "[17] Tom Ching LingChen, Ava Khonsari, Amirreza Lashkari, Mina Rafi Nazari, Jaspreet Singh Sambee, and Mario A Nascimento. Uniformaugment: A search-free probabilistic data augmentation approach. arXiv preprint arXiv:2003.14348, 2020. 7" + ], + "bbox": [ + 78, + 114, + 468, + 898 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[18] Aoming Liu, Zehao Huang, Zhiwu Huang, and Naiyan Wang. Direct differentiable augmentation search. In Proc. ICCV, 2021. 3, 5", + "[19] Samuel G. Müller and Frank Hutter. TrivialAugment: tuning-free yet state-of-the-art data augmentation. In Proc. ICCV, 2021. 1, 2, 3, 6, 7", + "[20] Mattis Paulin, Jérôme Revaud, Zaid Harchaoui, Florent Perronnin, and Cordelia Schmid. Transformation pursuit for image classification. In Proc. 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ICLR, 2022. 1, 3, 6, 7" + ], + "bbox": [ + 501, + 92, + 890, + 689 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "24314", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_model.json b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6b71f9f861843a3b147e3c319b0c07765aa1c010 --- /dev/null +++ b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_model.json @@ -0,0 +1,2033 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.265, + 0.131, + 0.709, + 0.177 + ], + "angle": 0, + "content": "SLACK: Stable Learning of Augmentations with Cold-start and KL regularization" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.203, + 0.306, + 0.221 + ], + "angle": 0, + "content": "Juliette Marrie1,2" + }, + { + "type": "text", + "bbox": [ + 0.352, + 0.204, + 0.477, + 0.221 + ], + "angle": 0, + "content": "Michael Arbel" + }, + { + "type": "text", + "bbox": [ + 0.526, + 0.204, + 0.64, + 0.221 + ], + "angle": 0, + "content": "Diane Larlus" + }, + { + "type": "text", + "bbox": [ + 0.687, + 0.204, + 0.802, + 0.221 + ], + "angle": 0, + "content": "Julien Mairal" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.239, + 0.588, + 0.257 + ], + "angle": 0, + "content": "1 Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK" + }, + { + "type": "text", + "bbox": [ + 0.637, + 0.239, + 0.835, + 0.258 + ], + "angle": 0, + "content": "\\(^{2}\\) Naver Labs Europe" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.626 + ], + "angle": 0, + "content": "Data augmentation is known to improve the generalization capabilities of neural networks, provided that the set of transformations is chosen with care, a selection often performed manually. Automatic data augmentation aims at automating this process. However, most recent approaches still rely on some prior information; they start from a small pool of manually-selected default transformations that are either used to pretrain the network or forced to be part of the policy learned by the automatic data augmentation algorithm. In this paper, we propose to directly learn the augmentation policy without leveraging such prior knowledge. The resulting bilevel optimization problem becomes more challenging due to the larger search space and the inherent instability of bilevel optimization algorithms. To mitigate these issues (i) we follow a successive cold-start strategy with a Kullback-Leibler regularization, and (ii) we parameterize magnitudes as continuous distributions. Our approach leads to competitive results on standard benchmarks despite a more challenging setting, and generalizes beyond natural images.1" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.655, + 0.21, + 0.672 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.471, + 0.878 + ], + "angle": 0, + "content": "Data augmentation, which encourages predictions to be stable with respect to particular image transformations, has become an essential component in visual recognition systems. While the data augmentation process is conceptually simple, choosing the optimal set of image transformations for a given task or dataset is challenging. For instance, designing a good set for ImageNet [4] or even CIFAR-10/100 [13] has been the result of a long-standing research effort. Whereas data augmentation strategies that have been chosen by hand for ImageNet have been used successfully for many recognition tasks involving natural images, they may fail to generalize to other domains such as medical imaging, remote sensing or hyperspectral imaging." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.892, + 0.414 + ], + "angle": 0, + "content": "This has motivated automating the design of data augmentation strategies [10, 12, 14-16, 19, 27, 31]. Those are often represented as a stochastic policy that randomly draws a combination of transformations along with their magnitudes from a large predefined set, each time an image is sampled. The goal becomes to learn strategies that effectively compose multiple transformations, which is a challenging task given the large search space of augmentations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.893, + 0.583 + ], + "angle": 0, + "content": "A natural framework for learning the parameters of this policy is that of bilevel optimization. Intuitively, one looks for the best possible policy such that a neural network trained with this policy on a training set (inner problem) generalizes well on a distinct validation set (outer problem). Optimizing the resulting formulation is challenging as the outer problem depends on the solution of the inner problem. Classical techniques for solving this bilevel problem, such as unrolled optimization, can become highly unstable as the network weights become progressively suboptimal for the current policy during the learning process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.895, + 0.749 + ], + "angle": 0, + "content": "Moreover, augmentations are often non-differentiable in the parameters of the policy, thus requiring techniques other than direct differentiation, such as Bayesian optimization [15], gradient approximations (e.g. RELAX [7]), or the score method / REINFORCE [28] algorithm. While these techniques bypass the differentiability issues, they can suffer from large bias or variance. As a result, learning augmentation policies is a difficult problem whose challenges are exacerbated by the inherent instability of the optimization techniques developed to solve bilevel problems, such as unrolled optimization [1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "A standard way to improve stability and make the automatic data augmentation problem simpler is to reduce the search space. This is often achieved by learning the policy on top of \"default\" transformations such as Cutout [5], random cropping and resizing, or color jittering, all known to be well-suited to natural images which compose standard benchmarks such as CIFAR or ImageNet, or by discarding transformations known to be harmful such as Invert. Fixing some of the transformations and removing others mitigate the challenges inherent to learning a compo" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.361, + 0.902 + ], + "angle": 0, + "content": "1Project page: https://europe.naverlabs.com/slack" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24306" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.885, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.361, + 0.893, + 0.391 + ], + "angle": 0, + "content": "Figure 1. For different domains of the DomainNet dataset [21] (one per line), we show an image from that domain (left) and that image transformed using the three most likely (middle) and the three least likely (right) augmentations for that domain, as estimated by SLACK." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.47, + 0.567 + ], + "angle": 0, + "content": "sition of transformations. TrivialAugment [19] also shows that state-of-the-art results can be achieved on these previous benchmarks simply by directly applying the policy classically used for initializing auto-augmentation models, up to minor modifications. Moreover, all methods rely on carefully chosen ranges that constraint the transformation's magnitudes. Despite its effectiveness, manually selecting default transformations and magnitude ranges restricts the applicability of such policies to natural images and prevents generalisation to other domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.764 + ], + "angle": 0, + "content": "In this paper, our goal is to choose augmentation strategies without relying on default transformations nor on hand-selected magnitude ranges known to suit common benchmarks. To achieve this objective, we first introduce a simple interpretable model for the augmentation policies which allows learning both the frequency by which a given augmentation is selected and the magnitude by which it is applied. Then, we propose a method for learning these augmentation policies by solving a bilevel optimization problem. Our method relies on the REINFORCE technique for computing the gradient of the policy and on unrolled optimization for learning the policy, both of which can result in instabilities and yield high variance estimates." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To address these issues, we introduce an efficient multistage algorithm with a cold-start strategy and a Kullback-Leibler (KL) regularization that are designed to improve the stability of the process for learning the data augmentation policy. More precisely, the algorithm first pre-trains a network with a data augmentation policy uniformly sampling over all transformations. Then, each stage uses a \"cold-start\" strategy by restarting from the pre-trained network and performs incremental updates of the current policy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.893, + 0.567 + ], + "angle": 0, + "content": "This multi-stage approach with cold start prevents the network from becoming progressively suboptimal as the policy is updated using unrolled optimization. The KL regularization defines a trust region for the policy to compensate for the possibly high variance of gradient estimates obtained using the REINFORCE technique and encourages exploration during training, preventing collapse to trivial solutions. This regularization is inspired by proximal point algorithms in convex optimization [22], which have also been successful in reinforcement learning tasks [23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.893, + 0.749 + ], + "angle": 0, + "content": "By combining the regularized multi-stage approach with our interpretable model of the augmentation policies, we obtained the proposed SLACK method, which stands for Stable Learning of Augmentations with Cold-start and Kullback-Leibler regularization. SLACK is an efficient data augmentation learning method that is able to address the challenging bilevel optimization problem of learning a stochastic data augmentation policy without relying strongly on prior knowledge. Figure 1 illustrates the transformations found by SLACK to be most important / detrimental on a dataset of different domains including nonnatural images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To summarize, our contribution is threefold. (i) We propose a simple and interpretable model of the policies which allows learning both frequency and magnitudes of the augmentations. (ii) We propose a regularized multi-stage strategy to improve the stability of the bilevel optimization algorithm used for solving the data augmentation learning problem. (iii) We evaluate our method on challenging experimental settings, and show that it finds competitive augmentation strategies on natural images without resorting to prior information and generalizes to other domains." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24307" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.119, + 0.473, + 0.422 + ], + "angle": 0, + "content": "The choice of image transformation (also known as data augmentation) has become central in the design of computer vision pipelines. To remove the burden of manual selection, automatic data augmentation strategies have been proposed [20, 26]. AutoAugment [2], one of the earliest methods, uses for instance a recurrent neural network for designing the augmentation policy. Because such an approach requires retraining a prediction model at each iteration, it is prohibitively slow, and more efficient alternatives have been proposed. They aim at reducing the training cost using, e.g., population-based training [12], Bayesian optimization [15], and more recently, gradient-based approaches based on bilevel optimization [9, 10, 14, 15, 18, 27, 30], relying on various gradient estimation techniques such as RELAX [7] or the Score method [28]. While the former is inherently biased, the latter is theoretically exact, but has a high variance when approximated in the context of stochastic optimization. Therefore, these approximations may lead to diverging gradient updates. Our method alleviates this by introducing a KL regularization that defines a trust-region for the policy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.473, + 0.746 + ], + "angle": 0, + "content": "Automatic augmentation using prior knowledge. Most previous works learn augmentations using a small network learned on a subset of the dataset of interest, before retraining the prediction model on a larger network using the full (augmented) data. This choice is appealing to recent gradient-based methods [9, 14] as the search phase for an augmentation policy is often reduced to minutes. Nevertheless, [10, 30] have observed that policies found with such a reduced setup may be suboptimal compared to approaches exploiting full datasets for training both the augmentation policy and the prediction model. This observation was confirmed in [3], which shows that a naive grid search could actually yield state-of-the-art results when directly training on the full-size network and the full data. These results are however obtained at the expense of using strong prior knowledge: augmentation policies are applied on top of default transformations that are manually and independently chosen for each benchmark. Lately, [19] has shown that with a few additional careful choices regarding the augmentation policies, applying a single random transformation on top of the default ones could lead to state-of-the-art results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To avoid relying on default augmentations, DeepAA [31] has recently proposed a greedy approach that is able to learn these transformations. Yet, learning is performed after a \"pre-training\" phase leveraging the usual default transformations. Moreover, while such a greedy approach simplifies the search procedure and reduces its stochasticity, the resulting computational cost is high. Instead, our approach improves stability and allows directly learning the joint probability of sampling multiple transformations, reducing the search time twofold compared to DeepAA." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.895, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.301, + 0.895, + 0.414 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed SLACK method. We learn a data augmentation policy parameterized by \\(\\phi\\) using bilevel optimization. The inner loop finds the optimal network parameter \\(\\theta^{*}\\) on images from \\(\\mathcal{D}_{\\mathrm{train}}\\). The outer loop trains on a disjoint set of images \\(\\mathcal{D}_{\\mathrm{val}}\\) using this network and finds the optimal transformation parameters \\(\\phi\\). The method is enhanced with i) a cold-start strategy that structures the learning into rounds which share \\(\\phi\\) but restart the network from the pretrained one, and ii) a KL regularization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.593, + 0.456 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.895, + 0.619 + ], + "angle": 0, + "content": "Our method, SLACK, defines an augmentation policy, which is a probabilistic model for generating data augmentations. The goal is to learn the parameters of this augmentation policy so as to improve the performance of the trained classifier on a held-out dataset. We first describe the augmentation policy (Sec. 3.1) and then formalize the problem of learning data augmentations with bilevel optimization (Sec. 3.2). We then describe our approach for solving such a bilevel optimization problem, which aims at stabilizing the optimization (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.63, + 0.822, + 0.648 + ], + "angle": 0, + "content": "3.1. Stochastic data augmentations policy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.894, + 0.807 + ], + "angle": 0, + "content": "An augmentation function \\(\\tau\\) transforms an image \\(x\\) into another augmented image \\(\\tau(x)\\) of the same dimensions. We consider composite augmentations obtained by combining simpler augmentations selected from a finite set \\(S = \\{s_1, \\ldots, s_N\\}\\) of \\(N\\) candidate elementary transformations, such as rotations, translations, shearing, etc. Each elementary transformation depends on a magnitude parameter \\(m\\) that controls the strength of the transformations, for instance, the angle by which an image is rotated. Magnitudes are normalized to be in the unit interval [0, 1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Augmentation policy. We define the augmentation policy as a probabilistic model \\(p_{\\phi}\\) that generates composite augmentations given some parameter \\(\\phi\\) to be learned. The model generates an augmentation in three steps: (1) it samples \\(K\\) elementary transformations \\(t_1,\\ldots ,t_K\\) from \\(\\mathcal{S}\\) according to a categorical distribution \\(p_{\\pi}\\) of parameter \\(\\pi\\), (2)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24308" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "it samples values for the magnitudes \\(m_{1},\\ldots ,m_{K}\\) for each of the selected elementary transformations \\(t_k\\) according to a smoothed uniform distribution \\(p_\\mu\\) of parameter \\(\\mu\\) and (3) it composes the \\(K\\) elementary transformations to obtain the composite augmentation, with each \\(t_k\\) applied using its corresponding magnitude \\(m_{k}\\). Therefore, the augmentation policy \\(p_{\\phi}(\\tau)\\) takes the form" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.21, + 0.47, + 0.252 + ], + "angle": 0, + "content": "\\[\np _ {\\phi} (\\tau) = \\prod_ {i = 1} ^ {K} p _ {\\pi} \\left(t _ {i}\\right) p _ {\\mu} \\left(m _ {i} \\mid t _ {i}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.263, + 0.47, + 0.308 + ], + "angle": 0, + "content": "where the parameters \\(\\phi = (\\pi, \\mu)\\) are learned jointly. Next, we describe the sampling of the transformations and of their magnitudes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.312, + 0.47, + 0.388 + ], + "angle": 0, + "content": "Sampling transformations. We sample elementary transformations \\( t_k \\) with replacement from a categorical distribution \\( \\mathrm{Cat}_{\\pi_k} \\) of dimension \\( N \\) parameterized by a logit vector \\( \\pi_k \\coloneqq (\\pi_{k,n})_{1 \\leq n \\leq N} \\). The probability \\( p_{\\pi}(t_1, \\ldots, t_K) \\) of sampling the \\( K \\) transformations is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.399, + 0.47, + 0.418 + ], + "angle": 0, + "content": "\\[\np _ {\\pi} \\left(t _ {1}, \\dots , t _ {K}\\right) = \\Pi_ {k = 1} ^ {K} \\operatorname {C a t} _ {\\pi_ {k}} \\left(t _ {k}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.429, + 0.47, + 0.459 + ], + "angle": 0, + "content": "where we collect all logits to form a parameter matrix \\(\\pi\\) of size \\(K\\times N\\). These parameters are learned." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.463, + 0.469, + 0.537 + ], + "angle": 0, + "content": "Sampling magnitudes. The magnitudes of each elementary transformation \\( s_i \\) in \\( S \\) are sampled from a smoothed uniform distribution between \\( [0, \\mu_i] \\) whose upper-bound \\( \\mu_i \\) is learned. More precisely, the distribution's density is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.546, + 0.397, + 0.58 + ], + "angle": 0, + "content": "\\[\np _ {\\mu_ {i}} (m _ {i}) = \\frac {1}{\\mu_ {i}} \\int_ {0} ^ {\\mu_ {i}} \\mathcal {N} (m _ {i}, \\sigma) (u) d u,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.59, + 0.469, + 0.668 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(m_i,\\sigma)\\) is the Gaussian distribution of mean \\(m_{i}\\) and deviation \\(\\sigma\\). The density \\(p_{\\mu_i}(m_i)\\) approximates the uniform distribution \\(\\frac{1}{\\mu_i}\\mathbf{1}_{[0,\\mu_i]}\\) as the deviation \\(\\sigma\\) approaches 0. In practice, we set \\(\\sigma = 0.1\\) as we found it to achieve a good trade-off between smoothing and approximation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.671, + 0.469, + 0.747 + ], + "angle": 0, + "content": "Why a uniform distribution? We ran some ablations on previous methods (see supplementary) which suggest that a uniform sampling works on par with more elaborate sampling strategies, and that the magnitude range has more impact on the results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.394, + 0.773 + ], + "angle": 0, + "content": "3.2. Bilevel formulation for policy search" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We consider a prediction task, such as predicting the class \\(y\\) of some natural image \\(x\\) using a model \\(f_{\\theta}(x)\\) with parameter \\(\\theta\\). We are interested in finding the best policy parameter \\(\\phi\\) so that the prediction model \\(f_{\\theta}\\), when trained using such policy on a training set \\(\\mathcal{D}\\) of input/output pairs \\((x,y)\\), generalizes well on the test set \\(\\mathcal{D}_{\\mathrm{test}}\\). The problem naturally decomposes in two phases. During the search phase, the optimal augmentation policy \\(p_{\\phi}\\) is learned on \\(\\mathcal{D}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "During the evaluation phase, the model is re-trained on \\(\\mathcal{D}\\) using \\(p_{\\phi}\\) and is then evaluated on \\(\\mathcal{D}_{\\mathrm{test}}\\). The evaluation phase is performed using standard optimization methods. However, the search phase requires solving a complex optimization problem that we describe next." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.171, + 0.892, + 0.322 + ], + "angle": 0, + "content": "Search phase as a bilevel problem. The search phase naturally writes as a bilevel problem involving two interdependent losses: a lower-level loss \\(\\mathcal{L}_{\\mathrm{train}}(\\theta, \\phi)\\) for learning an optimal model parameter \\(\\theta^{\\star}(\\phi)\\) obtained using the augmentation policy \\(p_{\\phi}\\) and an upper-level loss \\(\\mathcal{F}(\\phi)\\) for learning the policy parameter \\(\\phi\\) by evaluating the optimal model with parameter \\(\\theta^{\\star}(\\phi)\\). Each of these objectives is evaluated on two separate splits of the available data \\(\\mathcal{D}\\): a training split \\(\\mathcal{D}_{\\mathrm{train}}\\) for the lower-level loss and a validation split \\(\\mathcal{D}_{\\mathrm{val}}\\) for the upper-level loss. Below, we describe both losses." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.327, + 0.892, + 0.358 + ], + "angle": 0, + "content": "Lower-level loss. We first introduce the training loss \\(\\ell_{\\mathrm{train}}(\\theta, \\tau)\\) when only a fixed augmentation \\(\\tau\\) is used:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.37, + 0.838, + 0.388 + ], + "angle": 0, + "content": "\\[\n\\ell_ {\\text {t r a i n}} (\\theta , \\tau) := \\mathbb {E} _ {(x, y) \\sim \\mathcal {D} _ {\\text {t r a i n}}} [ \\ell (y, f _ {\\theta} (\\tau (x))) ],\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.476 + ], + "angle": 0, + "content": "where \\((x,y)\\) is an (image, label) pair drawn from \\(\\mathcal{D}_{\\mathrm{train}}\\) and \\(\\ell\\) is a pointwise prediction loss (e.g. cross-entropy). We then define the training loss \\(\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)\\) for an augmentation policy \\(p_{\\phi}\\) by taking the expectation of \\(\\ell_{\\mathrm{train}}(\\theta ,\\tau)\\) over augmentations \\(\\tau\\) sampled according to the policy \\(p_{\\phi}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.489, + 0.811, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t r a i n}} (\\theta , \\phi) := \\mathbb {E} _ {\\tau \\sim p _ {\\phi}} \\left[ \\ell_ {\\text {t r a i n}} (\\theta , \\tau) \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.549 + ], + "angle": 0, + "content": "Hence, for a given policy \\(p_{\\phi}\\), the goal is to learn the optimal model parameter \\(\\theta^{\\star}(\\phi)\\) by minimizing \\(\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)\\) over \\(\\theta\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Upper-level loss. We first denote by \\(\\mathcal{L}_{\\mathrm{val}}(\\theta)\\) the validation loss for a given model of parameter \\(\\theta\\):" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.596, + 0.816, + 0.614 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {v a l}} (\\theta) := \\mathbb {E} _ {(x, y) \\sim \\mathcal {D} _ {\\text {v a l}}} [ \\ell (y, f _ {\\theta} (x)) ].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.702 + ], + "angle": 0, + "content": "The validation loss \\(\\mathcal{L}_{\\mathrm{val}}(\\theta)\\) is computed over the validation set \\(\\mathcal{D}_{\\mathrm{val}}\\) without applying any augmentation and thus provides a proxy for the performance on the test dataset. We then define the upper-level loss to be the validation loss of an optimal model \\(\\theta^{\\star}(\\phi)\\) learned using a policy \\(p_{\\phi}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.714, + 0.892, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} (\\phi) := \\mathcal {L} _ {\\text {v a l}} \\left(\\theta^ {*} (\\phi)\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.745, + 0.892, + 0.821 + ], + "angle": 0, + "content": "While optimizing the lower-level loss is relatively standard, minimizing the upper-level loss \\(\\mathcal{F}\\) is more challenging due to the complex dependence of the optimal model parameter \\(\\theta^{\\star}(\\phi)\\) on the policy. Next, we describe our proposed algorithm for solving the bilevel problem." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.679, + 0.848 + ], + "angle": 0, + "content": "3.3. SLACK algorithm" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We propose Algorithm 1 for learning the optimal policy during the search phase. SLACK first pre-trains the prediction model using the objective \\(\\mathcal{L}_{\\mathrm{train}}(\\theta, \\phi_{\\mathrm{uniform}})\\) for an" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24309" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "initial policy parametrized by \\(\\phi_{\\mathrm{uniform}}\\) which samples uniformly among all elementary transformations. It then performs \\(n_{\\mathrm{rounds}}\\) rounds to update the parameters \\(\\theta\\) and \\(\\phi\\) jointly using a bilevel optimization algorithm. This approach is reminiscent of the one of AutoAugment (AA) [3] that fully re-trains the network for each policy update. Yet, it is several orders of magnitude faster than AA, as it benefits from pre-training and from our bilevel optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.212, + 0.474, + 0.534 + ], + "angle": 0, + "content": "SLACK relies on two strategies to ensure the stability of the parameter updates during each round: a cold-start strategy for the prediction model and an anchoring strategy for the policy. The cold-start initializes the prediction model at the beginning of each round using a pre-trained model \\(\\theta_0\\). Anchoring is achieved by encouraging the current policy to remain close to some anchor policy \\(p_{\\tilde{\\phi}}\\). We set \\(\\tilde{\\phi}\\) to the current policy parameter \\(\\phi\\) at the beginning of each round. During the first \\(n_{\\mathrm{retrain}}\\) steps of each round, the algorithm only updates the model parameter using a stochastic estimate \\(\\hat{g}_{\\theta}\\) of \\(\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)\\) while maintaining the policy fixed. Then for the last \\(n_{\\mathrm{total}} - n_{\\mathrm{retrain}}\\) steps, the algorithm alternates between model updates and policy updates. The policy updates aim to minimize the sum of the upper-level objective \\(\\mathcal{F}\\) and an anchoring \\(d(p_{\\phi},p_{\\tilde{\\phi}})\\coloneqq \\mathrm{KL}(p_{\\pi},p_{\\tilde{\\pi}})\\) encouraging the policy \\(p_{\\phi}\\) to remain close to the anchor policy \\(p_{\\tilde{\\phi}}\\). These updates are obtained using a stochastic estimate \\(\\hat{G}_{\\phi}\\) along with the exact gradient of the KL regularization which admits a closed-form expression. Next we explain how we estimate the gradients \\(\\hat{g}_{\\theta}\\) and \\(\\hat{G}_{\\phi}\\) and discuss the effect of cold-start and KL-regularization." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.549, + 0.223, + 0.563 + ], + "angle": 0, + "content": "Algorithm 1 SLACK" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.567, + 0.332, + 0.58 + ], + "angle": 0, + "content": "1: Initialize policy parameter \\(\\phi \\gets \\phi_{\\mathrm{uniform}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.58, + 0.355, + 0.593 + ], + "angle": 0, + "content": "2: Pre-training: \\(\\theta_0\\gets\\) optimize \\((\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi))\\)" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.593, + 0.246, + 0.605 + ], + "angle": 0, + "content": "3: for \\( i \\in \\{1, \\dots, n_{\\text{rounds}}\\} \\) do" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.605, + 0.229, + 0.616 + ], + "angle": 0, + "content": "4: Cold-start: \\(\\theta \\gets \\theta_0\\)." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.616, + 0.289, + 0.628 + ], + "angle": 0, + "content": "5: Update anchor policy: \\(\\tilde{\\phi} \\gets \\phi\\)." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.628, + 0.255, + 0.64 + ], + "angle": 0, + "content": "6: for \\(j\\in \\{1,\\dots,n_{\\mathrm{total}}\\}\\) do" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.64, + 0.398, + 0.652 + ], + "angle": 0, + "content": "7: Compute stochastic gradient \\(\\hat{g}_{\\theta}\\approx \\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)\\)" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.652, + 0.268, + 0.664 + ], + "angle": 0, + "content": "8: Update \\(\\theta\\): \\(\\theta \\gets \\theta - \\eta \\hat{g}_{\\theta}\\)." + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.664, + 0.239, + 0.676 + ], + "angle": 0, + "content": "9: if \\( j > n_{\\mathrm{retrain}} \\) then" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.676, + 0.393, + 0.688 + ], + "angle": 0, + "content": "10: Compute stochastic gradient \\(\\hat{G}_{\\phi}\\approx \\nabla_{\\phi}\\mathcal{F}(\\phi)\\)" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.689, + 0.405, + 0.703 + ], + "angle": 0, + "content": "11: Update \\(\\phi\\): \\(\\phi \\gets \\phi - \\alpha (\\hat{G}_{\\phi} + \\lambda \\nabla_{\\phi} d(p_{\\phi}, p_{\\phi}^{\\prime}))\\)." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.703, + 0.171, + 0.714 + ], + "angle": 0, + "content": "12: end if" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.715, + 0.162, + 0.726 + ], + "angle": 0, + "content": "13: end for" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.727, + 0.146, + 0.738 + ], + "angle": 0, + "content": "14: end for" + }, + { + "type": "list", + "bbox": [ + 0.082, + 0.567, + 0.405, + 0.738 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Gradient estimation. Algorithm 1 requires estimating the gradient of \\(\\mathcal{F}(\\phi)\\), which is challenging given the complex dependence of the upper-level loss on the policy \\(p_{\\phi}\\) through the optimal model parameter \\(\\theta^{\\star}(\\phi)\\) learned using such a policy. In line with previous works [9, 14, 18, 27], we approximate the optimal model parameter \\(\\theta^{*}(\\phi)\\) with a simpler function \\(\\hat{\\theta} (\\phi)\\) that is easier to compute:" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.88, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\hat {\\theta} (\\phi): = \\theta - \\eta \\nabla_ {\\theta} \\mathcal {L} _ {\\text {t r a i n}} (\\theta , \\phi). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "Eq. (4) corresponds to one gradient step to optimize the lower-level loss starting from the current parameter \\(\\theta\\) and \\(\\phi\\) and using step-size \\(\\eta > 0\\). By keeping track of the dependence in \\(\\phi\\) and exploiting the fact that the augmentation policy \\(p_{\\phi}\\) has a score \\(\\nabla_{\\phi} \\log p_{\\phi}(\\tau)\\) that can be computed explicitly using Eq. (1), we can use the REINFORCE/Score method [6] to derive a closed-form expression for \\(\\nabla_{\\phi} \\hat{\\theta}(\\phi)\\) which will serve for approximating the gradient of \\(\\mathcal{F}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.223, + 0.871, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\phi} \\hat {\\theta} (\\phi) = - \\eta \\mathbb {E} _ {\\tau \\sim p _ {\\phi}} \\left[ \\nabla_ {\\theta} \\ell_ {\\text {t r a i n}} (\\theta , \\tau) \\nabla_ {\\phi} \\log p _ {\\phi} (\\tau) ^ {\\top} \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Then, we approximate the upper-level loss \\(\\mathcal{F}(\\phi)\\) with a simpler function \\(\\hat{\\mathcal{F}} (\\phi)\\coloneqq \\mathcal{L}_{\\mathrm{val}}(\\hat{\\theta} (\\phi))\\) and the gradient \\(\\nabla_{\\phi}\\mathcal{F}(\\phi)\\) with \\(\\nabla_{\\phi}\\hat{\\mathcal{F}} (\\phi)\\) which is obtained using the chain rule:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.314, + 0.892, + 0.333 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\phi} \\mathcal {F} (\\phi) \\approx \\nabla_ {\\phi} \\hat {\\mathcal {F}} (\\phi) = \\nabla_ {\\theta} \\mathcal {L} _ {\\text {v a l}} \\left(\\hat {\\theta} (\\phi)\\right) ^ {\\top} \\nabla_ {\\phi} \\hat {\\theta} (\\phi). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.39 + ], + "angle": 0, + "content": "The above expression requires only first-order derivatives and matrix-vector products, which is amenable to efficient implementation using automatic differentiation softwares." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Stochastic gradient estimates. In practice, we replace all expectations by estimates on a batch of data and sampled augmentations. More precisely, to compute the approximation \\(\\hat{g}_{\\theta}\\) to \\(\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)\\), we sample \\(B_{\\mathrm{aug}}\\) augmentations from \\(p_{\\phi}\\) and then apply each of them to a batch of training data \\(B_{\\mathrm{train}}\\) from \\(\\mathcal{D}_{\\mathrm{train}}\\). Using the same batch of data and augmentation, we approximate \\(\\hat{\\theta} (\\phi)\\) and \\(\\nabla_{\\phi}\\hat{\\theta} (\\phi)\\) appearing in Eq. (5). Finally, we use a batch \\(B_{\\mathrm{val}}\\) of data from \\(\\mathcal{D}_{\\mathrm{val}}\\) to estimate \\(\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{val}}(\\hat{\\theta} (\\phi))\\) and compute \\(\\hat{G}_{\\phi}\\), which is a stochastic estimate of \\(\\nabla_{\\phi}\\hat{\\mathcal{F}} (\\phi)\\) in Eq. (5)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Cold-start. The cold-start strategy allows to re-train the model at each round with the current augmentation policy starting from the pre-trained model. This approach is closer to the original bilevel formulation which implies finding an optimal prediction model for each policy. Initializing with a pre-trained model yields computational gain as fewer iterations are needed to optimize the model. We could instead use a warm-start strategy which initializes the model at each round with the learned model at the previous round. Yet we experimentally observe that such approach progressively leads to overfitting and degrades the quality of the learned policies (see supplementary)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Anchoring using KL regularization. We experimentally found that adding an anchoring \\( d(p_{\\phi}, p_{\\tilde{\\phi}}) \\coloneqq \\mathrm{KL}(p_{\\pi}, p_{\\tilde{\\pi}}) \\) with strength parameter \\( \\lambda \\) when updating the policy prevents the algorithm from collapsing towards trivial policies. The anchoring affects only the categorical distribution \\( p_{\\pi} \\). For the magnitudes \\( p_{\\mu} \\), we did not use anchoring as it is ill-defined for a uniform distribution. Instead, we simply used smaller step-sizes. Our approach takes inspiration from Proximal Policy Optimization [23] used in the context of reinforcement learning which is known to improve policy search." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24310" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.21, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.192 + ], + "angle": 0, + "content": "In this section, we first briefly describe our experimental setup (Sec 4.1). Then we evaluate our approach on several standard benchmarks composed of natural images (Sec 4.2) as well as on a benchmark with other domains (Sec 4.3). We finally report some ablation studies (Sec 4.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.2, + 0.266, + 0.216 + ], + "angle": 0, + "content": "4.1. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.226, + 0.47, + 0.392 + ], + "angle": 0, + "content": "**Benchmarks.** We first evaluate our model on three standard benchmarks, CIFAR10 [13], CIFAR100 [13] and ImageNet-100 [25], all composed of natural images. To study how well our method generalizes beyond natural images, we also evaluate on the DomainNet dataset [21], which contains 345 classes for 6 different domains. To ensure our protocol uses a similar number of training images for each domain, we use a reduced set of 50,000 training images for the two largest domains (real, quickdraw) and leave the remaining images for testing. For the other domains, we isolate \\(20\\%\\) of the data for testing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.47, + 0.517 + ], + "angle": 0, + "content": "Architectures. CIFAR10/100 are evaluated with two architectures that are standard for automatic data augmentation: WideResNet-40x2 and WideResNet-28x10 [29]. Unlike previous works whose search phase is only conducted with the smaller WideResNet-40x2, we search and evaluate with the same architecture, as we found it to be better (see Sec. 4.4). ImageNet-100 and DomainNet are evaluated with a ResNet-18 [11] architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.838 + ], + "angle": 0, + "content": "Transformation space. Our data augmentation search space is composed of the standard pool of 15 transformations: Identity, ShearX, ShearY, TranslateX, TranslateY, Rotate, AutoContrast, Equalize, Invert, Solarize, Posterize, Contrast, Brightness, Sharpness, Color. We add to this pool the transformations that previous methods usually apply by default: Cutout and RandomCrop for CIFAR, RandomResizeCrop for ImageNet, Grayscale for DomainNet. Following standard practice, when RandomResizeCrop is sampled, it is always applied first. We learn the range of its scale parameter. We do not add ColorJitter that is also applied by default in prior work for ImageNet, as it is already a mix of Brightness, Contrast and Color. However we add Hue, which is one component of ColorJitter and never applied by default. Following prior work, the magnitudes are mapped to [0,1]. After mapping, \\(\\mu\\) is initialized at 0.75 to favour exploration (see details in supplementary). We also uniformly sample magnitudes for Cutout and RandomCrop, whereas their value is hand-picked in prior work. Since the datasets are horizontally symmetric, we follow common practice and apply flip by default." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Policy search. We apply a train/val split of 0.5/0.5, meaning that half of the data is used to train the model parameters while the other half is used to learn the augmentation policy. Pre-training is done in the same setting as the evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "(see next paragraph), except that we train only with the train data in the train/val split of the search phase. We use SGD with momentum for the optimization of the validation and training losses. For the latter, we use the same weight decay as for the final policy evaluation. We sample 8 different augmentations for computing the expectation that is needed for the stochastic gradient estimate, as detailed in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.201, + 0.893, + 0.366 + ], + "angle": 0, + "content": "Policy evaluation. We evaluate our models following the framework of TrivialAugment [19]. The corresponding hyperparameters can be found in the supplementary. We evaluate each policy with 4 independent runs, meaning that our results are averaged over a total of \\(4 \\times 4 = 16\\) evaluations. Our Uniform policy (corresponding to SLACK's initialization) and our reported results on TrivialAugment are evaluated with 8 independent runs. We also report a confidence interval which contains the true mean with probability \\(p = 95\\%\\), under the assumption of normally distributed accuracies." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.376, + 0.816, + 0.393 + ], + "angle": 0, + "content": "4.2. Comparison with the state of the art" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.505 + ], + "angle": 0, + "content": "We compare our method with a Uniform augmentation policy as well as many previous approaches for data augmentation, including AutoAugment (AA) [2], Fast AutoAugment (FastAA) [15], Differentiable Automatic Data Augmentation (DADA) [14], RandAugment (RA) [3], Teach Augment [24], UniformAugment [20], TrivialAugment (TA) [19], and Deep AutoAugment (DeepAA) [31]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.656 + ], + "angle": 0, + "content": "For each method, we indicate the total number of composed transformations, and the number of hard-coded transformations among those (Tables 1 and 2). For SLACK, we evaluate the policies obtained from 4 independent search runs (each with 4 different train/val splits) to assess the robustness of our approach. We follow the same process when reproducing DeepAA on CIFAR10/100. Note that all previous methods use a single run for search, before evaluating the policy with one or multiple runs. We report \\(95\\%\\) confidence intervals for those evaluating with multiple runs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.701 + ], + "angle": 0, + "content": "The supplementary provides qualitative results showing the evolution of the probability distributions over the transformations and the final estimated policies for all datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.75 + ], + "angle": 0, + "content": "CIFAR. In Table 1, we observe that, despite not hard-coding Cutout and RandomCrop in our policy, our method is competitive on both CIFAR10 and CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.826 + ], + "angle": 0, + "content": "We found that, in general, Cutout and Rotate are selected with a high probability, while the Invert transformation is systematically discarded (see supplementary). This is consistent with the choices made in practice by prior work of adding/removing these transformations manually." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We observe a mismatch between DeepAA's reported results [31], and those we obtain when evaluating their approach on multiple search runs, using the author's code and following their recommendations. This is likely due to the stochasticity of the search procedure." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24311" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.179, + 0.089, + 0.795, + 0.273 + ], + "angle": 0, + "content": "
# AugmentationsCIFAR10CIFAR100
TotalHard-codedWRN-40-2WRN-28-10WRN-40-2WRN-28-10
AA [2]4296.397.479.382.9
FastAA [15]4296.497.379.482.7
DADA [14]4296.497.379.182.5
RA [3]42-97.3-83.3
TeachA [24]42-97.5-83.2
UniformAugment [17]4296.2597.3379.0182.82
TA (Wide) [19]3296.32 ± .0597.46 ± .0679.86 ± .1984.33 ± .17
Uniform policy3096.12 ± .0897.26 ± .0778.79 ± .2582.82 ± .24
DeepAA [31]6**0*-97.56 ± .14-84.02 ± .18
DeepAA (reproduced)†6**0*96.25 ± .1197.27 ± .1179.26 ± .3583.38 ± .33
SLACK (Ours)3096.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.282, + 0.895, + 0.326 + ], + "angle": 0, + "content": "Table 1. Test accuracies on CIFAR10 and CIFAR100. For SLACK and DeepAA (reproduced) we conduct 4 independent searches, and evaluate each policy with 4 evaluation runs, meaning that we report averages over 16 evaluations. TA and DeepAA are also evaluated with multiple evaluation runs. Results for the remaining methods are reported from the corresponding papers and based on a single run." + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.332, + 0.89, + 0.358 + ], + "angle": 0, + "content": "*: DeepAA uses hard-coded transformations for pre-training. **: DeepAA learns random flipping unlike other baselines. † We evaluate the policies found from 4 independent search runs as we do for SLACK, using the code from the authors and following their recommendations." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.391, + 0.443, + 0.495 + ], + "angle": 0, + "content": "
# AugmentationsImageNet-100
TotalHard-codedResNet18
TA (RA) [19]†5485.87 ± .30
TA (Wide) [19]†5486.39 ± .18
Uniform policy3085.78 ± .32
SLACK3086.06 ± .11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.145, + 0.505, + 0.402, + 0.518 + ], + "angle": 0, + "content": "Table 2. Test accuracies on ImageNet-100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.638 + ], + "angle": 0, + "content": "ImageNet-100. Results for ImageNet-100 are reported in Table 2. We compare SLACK to our Uniform policy and to TrivialAugment (RA) and (Wide) variants, the latter using larger magnitude ranges for its random transformation. SLACK's results lie in between both variants and improve over our Uniform policy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.729 + ], + "angle": 0, + "content": "Interestingly, for ImageNet-100, we found that RandomResizeCrop is not favoured during the search phase (see supplementary), suggesting that it is not critical for ImageNet-100. Instead the performance gap between TA (Wide) and TA (RA) suggest that harder transformations are key to a better performance for this dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.291, + 0.758 + ], + "angle": 0, + "content": "4.3. Beyond natural images" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.84 + ], + "angle": 0, + "content": "For the DomainNet dataset, we compare SLACK to a Uniform policy, to the augmentations used by DomainBed [8] for domain generalization, and to the TrivialAugment (RA) and (Wide) methods with their ImageNet and CIFAR default settings. Results can be found in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "DomainBed uses the same default transformations as TA ImageNet together with Grayscale, but with smaller magnitudes and unlike TA, does not add a random transformation. Yet it strongly overfits and performs much lower than TA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.47 + ], + "angle": 0, + "content": "This suggests that augmentations well suited for domain generalization do not perform well on the individual tasks. TA (Wide) ImageNet consistently outperforms all other TA flavors. This further justifies the need to learn the magnitude range and to eliminate any manual range selection process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.591 + ], + "angle": 0, + "content": "SLACK is a close second, yet it learns the policy end-to-end. The learned policies are illustrated as pie charts in Fig. 3. The slices represent the probability \\(\\pi\\) over the different transformations while their radius represent the corresponding magnitudes. They differ from a domain to another, suggesting that the gain compared to the initialization (i.e. Uniform policy) results from SLACK's ability to learn and adapt to each domain." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.599, + 0.65, + 0.615 + ], + "angle": 0, + "content": "4.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.713 + ], + "angle": 0, + "content": "In this section, we evaluate our contributions and main design choices: the network architecture used for search, the KL regularization, and the benefits of learning \\(\\pi\\) and \\(\\mu\\). More ablations can be found in the supplementary. Note that hyperparameters are adjusted to each baseline included in the comparison, to make them as competitive as possible." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Network architecture for search. In prior works, the search phase (when there is one) is conducted on the smaller WideResNet-40x2 architecture for CIFAR10 and CIFAR100, and the learned policy is evaluated for both WideResNet-40x2 and WideResNet-28x10. Table 4 shows that for SLACK, searching directly with WideResNet-28x10 gives the best results for that architecture." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "KL regularization. We compare SLACK with a flavor that does not apply KL-regularization. For the latter, we reduce the outer learning rate so that the augmentation policies with and without regularization evolve at similar speeds. Results in Table 5 show that our regularization is beneficial." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24312" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.867, + 0.212 + ], + "angle": 0, + "content": "
# AugmentationsReal-50kQuickdraw-50kInforgraphSketchPaintingClipartAverage
TotalHard-coded
\\( DomainBed^† \\)5562.54 ± .1566.54 ± .9126.76 ± .3659.54 ± .3758.31 ± .2566.23 ± .1057.23 ± .18
\\( TA (RA) ImageNet^† \\)5470.85 ± .1367.85 ± .0735.24 ± .1965.63 ± .1164.75 ± .1870.29 ± .1862.43 ± .05
\\( TA (Wide) ImageNet^† \\)5471.56 ± .0768.60 ± .0535.44 ± .3366.21 ± .1665.15 ± .2071.19 ± .1963.03 ± .07
\\( TA (RA) CIFAR^† \\)3270.28 ± .0868.35 ± .0733.85 ± .2164.13 ± .1264.73 ± .1770.33 ± .2161.94 ± .05
\\( TA (Wide) CIFAR^† \\)3271.12 ± .1069.29 ± .0534.21 ± .2965.52 ± .2564.81 ± .1471.01 ± .2162.66 ± .07
Uniform policy3070.37 ± .0868.27 ± .0634.11 ± .2165.22 ± .1763.97 ± .2472.26 ± .1462.37 ± .06
SLACK (ours)3071.00 ± .1368.14 ± .1134.78 ± .1865.41 ± .1664.83 ± .1272.65 ± .2062.80 ± .06
" + }, + { + "type": "table_caption", + "bbox": [ + 0.365, + 0.218, + 0.604, + 0.23 + ], + "angle": 0, + "content": "Table 3. Test accuracies on DomainNet." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.244, + 0.348, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.245, + 0.61, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.245, + 0.874, + 0.464 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.468, + 0.893, + 0.511 + ], + "angle": 0, + "content": "Figure 3. Policies found on DomainNet for the best search split. Gray circle: initial magnitude upper-bounds. Radius of each pie: learned upper-bounds. Size of each pie: probability of each transformation, averaged over the three composite distributions. Transformations which are parameter-free, AutoContrast, Equalize, Grayscale, and Invert, are displayed with maximal magnitude upper-bound." + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.533, + 0.406, + 0.58 + ], + "angle": 0, + "content": "
Search architectureCIFAR10CIFAR100
WRN-40-297.43 ± .0483.94 ± .20
WRN-28-10 (ours)97.46 ± .0684.08 ± .16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.591, + 0.47, + 0.62 + ], + "angle": 0, + "content": "Table 4. CIFAR10/100 accuracy evaluated with WRN-28-10: impact of using a smaller architecture for the search phase." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.635, + 0.477, + 0.699 + ], + "angle": 0, + "content": "
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
without KL96.27 ± .0597.06 ± .1179.61 ± .1383.79 ± .19
with KL (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.709, + 0.466, + 0.723 + ], + "angle": 0, + "content": "Table 5. CIFAR10/100 accuracy with/without KL regularization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.752, + 0.47, + 0.813 + ], + "angle": 0, + "content": "Joint learning of \\(\\pi\\) and \\(\\mu\\). Lastly, we study how beneficial jointly learning our augmentation parameters is compared to the initial Uniform policy and to a setting where only \\(\\pi\\) or \\(\\mu\\) is learned. Results can be found in Table 6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.829, + 0.196, + 0.845 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In this paper, we address the task of automatic data augmentation. Considering the more challenging bilevel optimization problem that arises when the search space is not" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.533, + 0.892, + 0.616 + ], + "angle": 0, + "content": "
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
Uniform policy96.22 ± .1097.38 ± .0579.07 ± .2483.26 ± .17
μ only96.20 ± .0897.42 ± .0579.22 ± .1783.57 ± .18
π only96.22 ± .0997.35 ± .0479.36 ± .1183.45 ± .15
π and μ (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.625, + 0.892, + 0.654 + ], + "angle": 0, + "content": "Table 6. CIFAR10/100 accuracy when only learning part of the policy parameters" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.892, + 0.836 + ], + "angle": 0, + "content": "reduced with default transformations, our proposed SLACK method tackles the resulting stability issues thanks to a multi-stage approach based on cold-start, coupled with a KL-regularization. Combined, they allow to reduce the variance of the gradient estimate and to better control the optimization process. We have experimentally observed that our method performs on par with recent approaches leveraging prior knowledge. It has also proved versatile enough to select domain-specific transformations when confronted to non-natural images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.9 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by ANR 3IA MIAI@Grenoble Alpes (ANR-19-P3IA-0003) and performed using HPC resources from GENCI-IDRIS (Grant 2022-AD011013343)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24313" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Michael Arbel and Julien Mairal. Non-convex bilevel games with critical point selection maps. preprint arXiv:2207.04888, 2022. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.47, + 0.213 + ], + "angle": 0, + "content": "[2] Ekin D Cubuk, Barret Zoph, Dandelion Mane, Vijay Vasudevan, and Quoc V Le. 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ICLR, 2022. 1, 3, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.69 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24314" + } + ] +] \ No newline at end of file diff --git a/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_origin.pdf b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2aaa5a9eeca3af2c07720906520d77b01d4cff27 --- /dev/null +++ b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/13983024-bdf8-451a-82ba-7c4e7f6f3424_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1425cd7ce920951c1d963f2b68eae3ec36e314a7397bf571f0dc28a5d8ad5c38 +size 3786288 diff --git a/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/full.md b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4ffbe48a783d6e849cda9da1abdfb2a6faa4d138 --- /dev/null +++ b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/full.md @@ -0,0 +1,310 @@ +# SLACK: Stable Learning of Augmentations with Cold-start and KL regularization + +Juliette Marrie1,2 + +Michael Arbel + +Diane Larlus + +Julien Mairal + +1 Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK + +$^{2}$ Naver Labs Europe + +# Abstract + +Data augmentation is known to improve the generalization capabilities of neural networks, provided that the set of transformations is chosen with care, a selection often performed manually. Automatic data augmentation aims at automating this process. However, most recent approaches still rely on some prior information; they start from a small pool of manually-selected default transformations that are either used to pretrain the network or forced to be part of the policy learned by the automatic data augmentation algorithm. In this paper, we propose to directly learn the augmentation policy without leveraging such prior knowledge. The resulting bilevel optimization problem becomes more challenging due to the larger search space and the inherent instability of bilevel optimization algorithms. To mitigate these issues (i) we follow a successive cold-start strategy with a Kullback-Leibler regularization, and (ii) we parameterize magnitudes as continuous distributions. Our approach leads to competitive results on standard benchmarks despite a more challenging setting, and generalizes beyond natural images.1 + +# 1. Introduction + +Data augmentation, which encourages predictions to be stable with respect to particular image transformations, has become an essential component in visual recognition systems. While the data augmentation process is conceptually simple, choosing the optimal set of image transformations for a given task or dataset is challenging. For instance, designing a good set for ImageNet [4] or even CIFAR-10/100 [13] has been the result of a long-standing research effort. Whereas data augmentation strategies that have been chosen by hand for ImageNet have been used successfully for many recognition tasks involving natural images, they may fail to generalize to other domains such as medical imaging, remote sensing or hyperspectral imaging. + +This has motivated automating the design of data augmentation strategies [10, 12, 14-16, 19, 27, 31]. Those are often represented as a stochastic policy that randomly draws a combination of transformations along with their magnitudes from a large predefined set, each time an image is sampled. The goal becomes to learn strategies that effectively compose multiple transformations, which is a challenging task given the large search space of augmentations. + +A natural framework for learning the parameters of this policy is that of bilevel optimization. Intuitively, one looks for the best possible policy such that a neural network trained with this policy on a training set (inner problem) generalizes well on a distinct validation set (outer problem). Optimizing the resulting formulation is challenging as the outer problem depends on the solution of the inner problem. Classical techniques for solving this bilevel problem, such as unrolled optimization, can become highly unstable as the network weights become progressively suboptimal for the current policy during the learning process. + +Moreover, augmentations are often non-differentiable in the parameters of the policy, thus requiring techniques other than direct differentiation, such as Bayesian optimization [15], gradient approximations (e.g. RELAX [7]), or the score method / REINFORCE [28] algorithm. While these techniques bypass the differentiability issues, they can suffer from large bias or variance. As a result, learning augmentation policies is a difficult problem whose challenges are exacerbated by the inherent instability of the optimization techniques developed to solve bilevel problems, such as unrolled optimization [1]. + +A standard way to improve stability and make the automatic data augmentation problem simpler is to reduce the search space. This is often achieved by learning the policy on top of "default" transformations such as Cutout [5], random cropping and resizing, or color jittering, all known to be well-suited to natural images which compose standard benchmarks such as CIFAR or ImageNet, or by discarding transformations known to be harmful such as Invert. Fixing some of the transformations and removing others mitigate the challenges inherent to learning a compo + +![](images/ba85ba473cfca554dd1086a4f79486a24aa734681f21bd49b3e3fb5503639458.jpg) +Figure 1. For different domains of the DomainNet dataset [21] (one per line), we show an image from that domain (left) and that image transformed using the three most likely (middle) and the three least likely (right) augmentations for that domain, as estimated by SLACK. + +sition of transformations. TrivialAugment [19] also shows that state-of-the-art results can be achieved on these previous benchmarks simply by directly applying the policy classically used for initializing auto-augmentation models, up to minor modifications. Moreover, all methods rely on carefully chosen ranges that constraint the transformation's magnitudes. Despite its effectiveness, manually selecting default transformations and magnitude ranges restricts the applicability of such policies to natural images and prevents generalisation to other domains. + +In this paper, our goal is to choose augmentation strategies without relying on default transformations nor on hand-selected magnitude ranges known to suit common benchmarks. To achieve this objective, we first introduce a simple interpretable model for the augmentation policies which allows learning both the frequency by which a given augmentation is selected and the magnitude by which it is applied. Then, we propose a method for learning these augmentation policies by solving a bilevel optimization problem. Our method relies on the REINFORCE technique for computing the gradient of the policy and on unrolled optimization for learning the policy, both of which can result in instabilities and yield high variance estimates. + +To address these issues, we introduce an efficient multistage algorithm with a cold-start strategy and a Kullback-Leibler (KL) regularization that are designed to improve the stability of the process for learning the data augmentation policy. More precisely, the algorithm first pre-trains a network with a data augmentation policy uniformly sampling over all transformations. Then, each stage uses a "cold-start" strategy by restarting from the pre-trained network and performs incremental updates of the current policy. + +This multi-stage approach with cold start prevents the network from becoming progressively suboptimal as the policy is updated using unrolled optimization. The KL regularization defines a trust region for the policy to compensate for the possibly high variance of gradient estimates obtained using the REINFORCE technique and encourages exploration during training, preventing collapse to trivial solutions. This regularization is inspired by proximal point algorithms in convex optimization [22], which have also been successful in reinforcement learning tasks [23]. + +By combining the regularized multi-stage approach with our interpretable model of the augmentation policies, we obtained the proposed SLACK method, which stands for Stable Learning of Augmentations with Cold-start and Kullback-Leibler regularization. SLACK is an efficient data augmentation learning method that is able to address the challenging bilevel optimization problem of learning a stochastic data augmentation policy without relying strongly on prior knowledge. Figure 1 illustrates the transformations found by SLACK to be most important / detrimental on a dataset of different domains including nonnatural images. + +To summarize, our contribution is threefold. (i) We propose a simple and interpretable model of the policies which allows learning both frequency and magnitudes of the augmentations. (ii) We propose a regularized multi-stage strategy to improve the stability of the bilevel optimization algorithm used for solving the data augmentation learning problem. (iii) We evaluate our method on challenging experimental settings, and show that it finds competitive augmentation strategies on natural images without resorting to prior information and generalizes to other domains. + +# 2. Related Work + +The choice of image transformation (also known as data augmentation) has become central in the design of computer vision pipelines. To remove the burden of manual selection, automatic data augmentation strategies have been proposed [20, 26]. AutoAugment [2], one of the earliest methods, uses for instance a recurrent neural network for designing the augmentation policy. Because such an approach requires retraining a prediction model at each iteration, it is prohibitively slow, and more efficient alternatives have been proposed. They aim at reducing the training cost using, e.g., population-based training [12], Bayesian optimization [15], and more recently, gradient-based approaches based on bilevel optimization [9, 10, 14, 15, 18, 27, 30], relying on various gradient estimation techniques such as RELAX [7] or the Score method [28]. While the former is inherently biased, the latter is theoretically exact, but has a high variance when approximated in the context of stochastic optimization. Therefore, these approximations may lead to diverging gradient updates. Our method alleviates this by introducing a KL regularization that defines a trust-region for the policy. + +Automatic augmentation using prior knowledge. Most previous works learn augmentations using a small network learned on a subset of the dataset of interest, before retraining the prediction model on a larger network using the full (augmented) data. This choice is appealing to recent gradient-based methods [9, 14] as the search phase for an augmentation policy is often reduced to minutes. Nevertheless, [10, 30] have observed that policies found with such a reduced setup may be suboptimal compared to approaches exploiting full datasets for training both the augmentation policy and the prediction model. This observation was confirmed in [3], which shows that a naive grid search could actually yield state-of-the-art results when directly training on the full-size network and the full data. These results are however obtained at the expense of using strong prior knowledge: augmentation policies are applied on top of default transformations that are manually and independently chosen for each benchmark. Lately, [19] has shown that with a few additional careful choices regarding the augmentation policies, applying a single random transformation on top of the default ones could lead to state-of-the-art results. + +To avoid relying on default augmentations, DeepAA [31] has recently proposed a greedy approach that is able to learn these transformations. Yet, learning is performed after a "pre-training" phase leveraging the usual default transformations. Moreover, while such a greedy approach simplifies the search procedure and reduces its stochasticity, the resulting computational cost is high. Instead, our approach improves stability and allows directly learning the joint probability of sampling multiple transformations, reducing the search time twofold compared to DeepAA. + +![](images/b0f5998908ae6f25ea0a6265b402027faa394ff0984f025d578a54628e55c3ca.jpg) +Figure 2. Overview of our proposed SLACK method. We learn a data augmentation policy parameterized by $\phi$ using bilevel optimization. The inner loop finds the optimal network parameter $\theta^{*}$ on images from $\mathcal{D}_{\mathrm{train}}$ . The outer loop trains on a disjoint set of images $\mathcal{D}_{\mathrm{val}}$ using this network and finds the optimal transformation parameters $\phi$ . The method is enhanced with i) a cold-start strategy that structures the learning into rounds which share $\phi$ but restart the network from the pretrained one, and ii) a KL regularization. + +# 3. Method + +Our method, SLACK, defines an augmentation policy, which is a probabilistic model for generating data augmentations. The goal is to learn the parameters of this augmentation policy so as to improve the performance of the trained classifier on a held-out dataset. We first describe the augmentation policy (Sec. 3.1) and then formalize the problem of learning data augmentations with bilevel optimization (Sec. 3.2). We then describe our approach for solving such a bilevel optimization problem, which aims at stabilizing the optimization (Sec. 3.3). + +# 3.1. Stochastic data augmentations policy + +An augmentation function $\tau$ transforms an image $x$ into another augmented image $\tau(x)$ of the same dimensions. We consider composite augmentations obtained by combining simpler augmentations selected from a finite set $S = \{s_1, \ldots, s_N\}$ of $N$ candidate elementary transformations, such as rotations, translations, shearing, etc. Each elementary transformation depends on a magnitude parameter $m$ that controls the strength of the transformations, for instance, the angle by which an image is rotated. Magnitudes are normalized to be in the unit interval [0, 1]. + +Augmentation policy. We define the augmentation policy as a probabilistic model $p_{\phi}$ that generates composite augmentations given some parameter $\phi$ to be learned. The model generates an augmentation in three steps: (1) it samples $K$ elementary transformations $t_1,\ldots ,t_K$ from $\mathcal{S}$ according to a categorical distribution $p_{\pi}$ of parameter $\pi$ , (2) + +it samples values for the magnitudes $m_{1},\ldots ,m_{K}$ for each of the selected elementary transformations $t_k$ according to a smoothed uniform distribution $p_\mu$ of parameter $\mu$ and (3) it composes the $K$ elementary transformations to obtain the composite augmentation, with each $t_k$ applied using its corresponding magnitude $m_{k}$ . Therefore, the augmentation policy $p_{\phi}(\tau)$ takes the form + +$$ +p _ {\phi} (\tau) = \prod_ {i = 1} ^ {K} p _ {\pi} \left(t _ {i}\right) p _ {\mu} \left(m _ {i} \mid t _ {i}\right), \tag {1} +$$ + +where the parameters $\phi = (\pi, \mu)$ are learned jointly. Next, we describe the sampling of the transformations and of their magnitudes. + +Sampling transformations. We sample elementary transformations $t_k$ with replacement from a categorical distribution $\mathrm{Cat}_{\pi_k}$ of dimension $N$ parameterized by a logit vector $\pi_k \coloneqq (\pi_{k,n})_{1 \leq n \leq N}$ . The probability $p_{\pi}(t_1, \ldots, t_K)$ of sampling the $K$ transformations is given by: + +$$ +p _ {\pi} \left(t _ {1}, \dots , t _ {K}\right) = \Pi_ {k = 1} ^ {K} \operatorname {C a t} _ {\pi_ {k}} \left(t _ {k}\right), \tag {2} +$$ + +where we collect all logits to form a parameter matrix $\pi$ of size $K\times N$ . These parameters are learned. + +Sampling magnitudes. The magnitudes of each elementary transformation $s_i$ in $S$ are sampled from a smoothed uniform distribution between $[0, \mu_i]$ whose upper-bound $\mu_i$ is learned. More precisely, the distribution's density is defined as + +$$ +p _ {\mu_ {i}} (m _ {i}) = \frac {1}{\mu_ {i}} \int_ {0} ^ {\mu_ {i}} \mathcal {N} (m _ {i}, \sigma) (u) d u, +$$ + +where $\mathcal{N}(m_i,\sigma)$ is the Gaussian distribution of mean $m_{i}$ and deviation $\sigma$ . The density $p_{\mu_i}(m_i)$ approximates the uniform distribution $\frac{1}{\mu_i}\mathbf{1}_{[0,\mu_i]}$ as the deviation $\sigma$ approaches 0. In practice, we set $\sigma = 0.1$ as we found it to achieve a good trade-off between smoothing and approximation. + +Why a uniform distribution? We ran some ablations on previous methods (see supplementary) which suggest that a uniform sampling works on par with more elaborate sampling strategies, and that the magnitude range has more impact on the results. + +# 3.2. Bilevel formulation for policy search + +We consider a prediction task, such as predicting the class $y$ of some natural image $x$ using a model $f_{\theta}(x)$ with parameter $\theta$ . We are interested in finding the best policy parameter $\phi$ so that the prediction model $f_{\theta}$ , when trained using such policy on a training set $\mathcal{D}$ of input/output pairs $(x,y)$ , generalizes well on the test set $\mathcal{D}_{\mathrm{test}}$ . The problem naturally decomposes in two phases. During the search phase, the optimal augmentation policy $p_{\phi}$ is learned on $\mathcal{D}$ . + +During the evaluation phase, the model is re-trained on $\mathcal{D}$ using $p_{\phi}$ and is then evaluated on $\mathcal{D}_{\mathrm{test}}$ . The evaluation phase is performed using standard optimization methods. However, the search phase requires solving a complex optimization problem that we describe next. + +Search phase as a bilevel problem. The search phase naturally writes as a bilevel problem involving two interdependent losses: a lower-level loss $\mathcal{L}_{\mathrm{train}}(\theta, \phi)$ for learning an optimal model parameter $\theta^{\star}(\phi)$ obtained using the augmentation policy $p_{\phi}$ and an upper-level loss $\mathcal{F}(\phi)$ for learning the policy parameter $\phi$ by evaluating the optimal model with parameter $\theta^{\star}(\phi)$ . Each of these objectives is evaluated on two separate splits of the available data $\mathcal{D}$ : a training split $\mathcal{D}_{\mathrm{train}}$ for the lower-level loss and a validation split $\mathcal{D}_{\mathrm{val}}$ for the upper-level loss. Below, we describe both losses. + +Lower-level loss. We first introduce the training loss $\ell_{\mathrm{train}}(\theta, \tau)$ when only a fixed augmentation $\tau$ is used: + +$$ +\ell_ {\text {t r a i n}} (\theta , \tau) := \mathbb {E} _ {(x, y) \sim \mathcal {D} _ {\text {t r a i n}}} [ \ell (y, f _ {\theta} (\tau (x))) ], +$$ + +where $(x,y)$ is an (image, label) pair drawn from $\mathcal{D}_{\mathrm{train}}$ and $\ell$ is a pointwise prediction loss (e.g. cross-entropy). We then define the training loss $\mathcal{L}_{\mathrm{train}}(\theta ,\phi)$ for an augmentation policy $p_{\phi}$ by taking the expectation of $\ell_{\mathrm{train}}(\theta ,\tau)$ over augmentations $\tau$ sampled according to the policy $p_{\phi}$ : + +$$ +\mathcal {L} _ {\text {t r a i n}} (\theta , \phi) := \mathbb {E} _ {\tau \sim p _ {\phi}} \left[ \ell_ {\text {t r a i n}} (\theta , \tau) \right]. +$$ + +Hence, for a given policy $p_{\phi}$ , the goal is to learn the optimal model parameter $\theta^{\star}(\phi)$ by minimizing $\mathcal{L}_{\mathrm{train}}(\theta ,\phi)$ over $\theta$ + +Upper-level loss. We first denote by $\mathcal{L}_{\mathrm{val}}(\theta)$ the validation loss for a given model of parameter $\theta$ : + +$$ +\mathcal {L} _ {\text {v a l}} (\theta) := \mathbb {E} _ {(x, y) \sim \mathcal {D} _ {\text {v a l}}} [ \ell (y, f _ {\theta} (x)) ]. +$$ + +The validation loss $\mathcal{L}_{\mathrm{val}}(\theta)$ is computed over the validation set $\mathcal{D}_{\mathrm{val}}$ without applying any augmentation and thus provides a proxy for the performance on the test dataset. We then define the upper-level loss to be the validation loss of an optimal model $\theta^{\star}(\phi)$ learned using a policy $p_{\phi}$ : + +$$ +\mathcal {F} (\phi) := \mathcal {L} _ {\text {v a l}} \left(\theta^ {*} (\phi)\right). \tag {3} +$$ + +While optimizing the lower-level loss is relatively standard, minimizing the upper-level loss $\mathcal{F}$ is more challenging due to the complex dependence of the optimal model parameter $\theta^{\star}(\phi)$ on the policy. Next, we describe our proposed algorithm for solving the bilevel problem. + +# 3.3. SLACK algorithm + +We propose Algorithm 1 for learning the optimal policy during the search phase. SLACK first pre-trains the prediction model using the objective $\mathcal{L}_{\mathrm{train}}(\theta, \phi_{\mathrm{uniform}})$ for an + +initial policy parametrized by $\phi_{\mathrm{uniform}}$ which samples uniformly among all elementary transformations. It then performs $n_{\mathrm{rounds}}$ rounds to update the parameters $\theta$ and $\phi$ jointly using a bilevel optimization algorithm. This approach is reminiscent of the one of AutoAugment (AA) [3] that fully re-trains the network for each policy update. Yet, it is several orders of magnitude faster than AA, as it benefits from pre-training and from our bilevel optimization. + +SLACK relies on two strategies to ensure the stability of the parameter updates during each round: a cold-start strategy for the prediction model and an anchoring strategy for the policy. The cold-start initializes the prediction model at the beginning of each round using a pre-trained model $\theta_0$ . Anchoring is achieved by encouraging the current policy to remain close to some anchor policy $p_{\tilde{\phi}}$ . We set $\tilde{\phi}$ to the current policy parameter $\phi$ at the beginning of each round. During the first $n_{\mathrm{retrain}}$ steps of each round, the algorithm only updates the model parameter using a stochastic estimate $\hat{g}_{\theta}$ of $\nabla_{\theta}\mathcal{L}_{\mathrm{train}}(\theta ,\phi)$ while maintaining the policy fixed. Then for the last $n_{\mathrm{total}} - n_{\mathrm{retrain}}$ steps, the algorithm alternates between model updates and policy updates. The policy updates aim to minimize the sum of the upper-level objective $\mathcal{F}$ and an anchoring $d(p_{\phi},p_{\tilde{\phi}})\coloneqq \mathrm{KL}(p_{\pi},p_{\tilde{\pi}})$ encouraging the policy $p_{\phi}$ to remain close to the anchor policy $p_{\tilde{\phi}}$ . These updates are obtained using a stochastic estimate $\hat{G}_{\phi}$ along with the exact gradient of the KL regularization which admits a closed-form expression. Next we explain how we estimate the gradients $\hat{g}_{\theta}$ and $\hat{G}_{\phi}$ and discuss the effect of cold-start and KL-regularization. + +# Algorithm 1 SLACK + +1: Initialize policy parameter $\phi \gets \phi_{\mathrm{uniform}}$ +2: Pre-training: $\theta_0\gets$ optimize $(\mathcal{L}_{\mathrm{train}}(\theta ,\phi))$ +3: for $i \in \{1, \dots, n_{\text{rounds}}\}$ do +4: Cold-start: $\theta \gets \theta_0$ . +5: Update anchor policy: $\tilde{\phi} \gets \phi$ . +6: for $j\in \{1,\dots,n_{\mathrm{total}}\}$ do +7: Compute stochastic gradient $\hat{g}_{\theta}\approx \nabla_{\theta}\mathcal{L}_{\mathrm{train}}(\theta ,\phi)$ +8: Update $\theta$ : $\theta \gets \theta - \eta \hat{g}_{\theta}$ . +9: if $j > n_{\mathrm{retrain}}$ then +10: Compute stochastic gradient $\hat{G}_{\phi}\approx \nabla_{\phi}\mathcal{F}(\phi)$ +11: Update $\phi$ : $\phi \gets \phi - \alpha (\hat{G}_{\phi} + \lambda \nabla_{\phi} d(p_{\phi}, p_{\phi}^{\prime}))$ . +12: end if +13: end for +14: end for + +Gradient estimation. Algorithm 1 requires estimating the gradient of $\mathcal{F}(\phi)$ , which is challenging given the complex dependence of the upper-level loss on the policy $p_{\phi}$ through the optimal model parameter $\theta^{\star}(\phi)$ learned using such a policy. In line with previous works [9, 14, 18, 27], we approximate the optimal model parameter $\theta^{*}(\phi)$ with a simpler function $\hat{\theta} (\phi)$ that is easier to compute: + +$$ +\hat {\theta} (\phi): = \theta - \eta \nabla_ {\theta} \mathcal {L} _ {\text {t r a i n}} (\theta , \phi). \tag {4} +$$ + +Eq. (4) corresponds to one gradient step to optimize the lower-level loss starting from the current parameter $\theta$ and $\phi$ and using step-size $\eta > 0$ . By keeping track of the dependence in $\phi$ and exploiting the fact that the augmentation policy $p_{\phi}$ has a score $\nabla_{\phi} \log p_{\phi}(\tau)$ that can be computed explicitly using Eq. (1), we can use the REINFORCE/Score method [6] to derive a closed-form expression for $\nabla_{\phi} \hat{\theta}(\phi)$ which will serve for approximating the gradient of $\mathcal{F}$ : + +$$ +\nabla_ {\phi} \hat {\theta} (\phi) = - \eta \mathbb {E} _ {\tau \sim p _ {\phi}} \left[ \nabla_ {\theta} \ell_ {\text {t r a i n}} (\theta , \tau) \nabla_ {\phi} \log p _ {\phi} (\tau) ^ {\top} \right]. +$$ + +Then, we approximate the upper-level loss $\mathcal{F}(\phi)$ with a simpler function $\hat{\mathcal{F}} (\phi)\coloneqq \mathcal{L}_{\mathrm{val}}(\hat{\theta} (\phi))$ and the gradient $\nabla_{\phi}\mathcal{F}(\phi)$ with $\nabla_{\phi}\hat{\mathcal{F}} (\phi)$ which is obtained using the chain rule: + +$$ +\nabla_ {\phi} \mathcal {F} (\phi) \approx \nabla_ {\phi} \hat {\mathcal {F}} (\phi) = \nabla_ {\theta} \mathcal {L} _ {\text {v a l}} \left(\hat {\theta} (\phi)\right) ^ {\top} \nabla_ {\phi} \hat {\theta} (\phi). \tag {5} +$$ + +The above expression requires only first-order derivatives and matrix-vector products, which is amenable to efficient implementation using automatic differentiation softwares. + +Stochastic gradient estimates. In practice, we replace all expectations by estimates on a batch of data and sampled augmentations. More precisely, to compute the approximation $\hat{g}_{\theta}$ to $\nabla_{\theta}\mathcal{L}_{\mathrm{train}}(\theta ,\phi)$ , we sample $B_{\mathrm{aug}}$ augmentations from $p_{\phi}$ and then apply each of them to a batch of training data $B_{\mathrm{train}}$ from $\mathcal{D}_{\mathrm{train}}$ . Using the same batch of data and augmentation, we approximate $\hat{\theta} (\phi)$ and $\nabla_{\phi}\hat{\theta} (\phi)$ appearing in Eq. (5). Finally, we use a batch $B_{\mathrm{val}}$ of data from $\mathcal{D}_{\mathrm{val}}$ to estimate $\nabla_{\theta}\mathcal{L}_{\mathrm{val}}(\hat{\theta} (\phi))$ and compute $\hat{G}_{\phi}$ , which is a stochastic estimate of $\nabla_{\phi}\hat{\mathcal{F}} (\phi)$ in Eq. (5). + +Cold-start. The cold-start strategy allows to re-train the model at each round with the current augmentation policy starting from the pre-trained model. This approach is closer to the original bilevel formulation which implies finding an optimal prediction model for each policy. Initializing with a pre-trained model yields computational gain as fewer iterations are needed to optimize the model. We could instead use a warm-start strategy which initializes the model at each round with the learned model at the previous round. Yet we experimentally observe that such approach progressively leads to overfitting and degrades the quality of the learned policies (see supplementary). + +Anchoring using KL regularization. We experimentally found that adding an anchoring $d(p_{\phi}, p_{\tilde{\phi}}) \coloneqq \mathrm{KL}(p_{\pi}, p_{\tilde{\pi}})$ with strength parameter $\lambda$ when updating the policy prevents the algorithm from collapsing towards trivial policies. The anchoring affects only the categorical distribution $p_{\pi}$ . For the magnitudes $p_{\mu}$ , we did not use anchoring as it is ill-defined for a uniform distribution. Instead, we simply used smaller step-sizes. Our approach takes inspiration from Proximal Policy Optimization [23] used in the context of reinforcement learning which is known to improve policy search. + +# 4. Experiments + +In this section, we first briefly describe our experimental setup (Sec 4.1). Then we evaluate our approach on several standard benchmarks composed of natural images (Sec 4.2) as well as on a benchmark with other domains (Sec 4.3). We finally report some ablation studies (Sec 4.4). + +# 4.1. Experimental setup + +**Benchmarks.** We first evaluate our model on three standard benchmarks, CIFAR10 [13], CIFAR100 [13] and ImageNet-100 [25], all composed of natural images. To study how well our method generalizes beyond natural images, we also evaluate on the DomainNet dataset [21], which contains 345 classes for 6 different domains. To ensure our protocol uses a similar number of training images for each domain, we use a reduced set of 50,000 training images for the two largest domains (real, quickdraw) and leave the remaining images for testing. For the other domains, we isolate $20\%$ of the data for testing. + +Architectures. CIFAR10/100 are evaluated with two architectures that are standard for automatic data augmentation: WideResNet-40x2 and WideResNet-28x10 [29]. Unlike previous works whose search phase is only conducted with the smaller WideResNet-40x2, we search and evaluate with the same architecture, as we found it to be better (see Sec. 4.4). ImageNet-100 and DomainNet are evaluated with a ResNet-18 [11] architecture. + +Transformation space. Our data augmentation search space is composed of the standard pool of 15 transformations: Identity, ShearX, ShearY, TranslateX, TranslateY, Rotate, AutoContrast, Equalize, Invert, Solarize, Posterize, Contrast, Brightness, Sharpness, Color. We add to this pool the transformations that previous methods usually apply by default: Cutout and RandomCrop for CIFAR, RandomResizeCrop for ImageNet, Grayscale for DomainNet. Following standard practice, when RandomResizeCrop is sampled, it is always applied first. We learn the range of its scale parameter. We do not add ColorJitter that is also applied by default in prior work for ImageNet, as it is already a mix of Brightness, Contrast and Color. However we add Hue, which is one component of ColorJitter and never applied by default. Following prior work, the magnitudes are mapped to [0,1]. After mapping, $\mu$ is initialized at 0.75 to favour exploration (see details in supplementary). We also uniformly sample magnitudes for Cutout and RandomCrop, whereas their value is hand-picked in prior work. Since the datasets are horizontally symmetric, we follow common practice and apply flip by default. + +Policy search. We apply a train/val split of 0.5/0.5, meaning that half of the data is used to train the model parameters while the other half is used to learn the augmentation policy. Pre-training is done in the same setting as the evaluation + +(see next paragraph), except that we train only with the train data in the train/val split of the search phase. We use SGD with momentum for the optimization of the validation and training losses. For the latter, we use the same weight decay as for the final policy evaluation. We sample 8 different augmentations for computing the expectation that is needed for the stochastic gradient estimate, as detailed in Sec. 3.3. + +Policy evaluation. We evaluate our models following the framework of TrivialAugment [19]. The corresponding hyperparameters can be found in the supplementary. We evaluate each policy with 4 independent runs, meaning that our results are averaged over a total of $4 \times 4 = 16$ evaluations. Our Uniform policy (corresponding to SLACK's initialization) and our reported results on TrivialAugment are evaluated with 8 independent runs. We also report a confidence interval which contains the true mean with probability $p = 95\%$ , under the assumption of normally distributed accuracies. + +# 4.2. Comparison with the state of the art + +We compare our method with a Uniform augmentation policy as well as many previous approaches for data augmentation, including AutoAugment (AA) [2], Fast AutoAugment (FastAA) [15], Differentiable Automatic Data Augmentation (DADA) [14], RandAugment (RA) [3], Teach Augment [24], UniformAugment [20], TrivialAugment (TA) [19], and Deep AutoAugment (DeepAA) [31]. + +For each method, we indicate the total number of composed transformations, and the number of hard-coded transformations among those (Tables 1 and 2). For SLACK, we evaluate the policies obtained from 4 independent search runs (each with 4 different train/val splits) to assess the robustness of our approach. We follow the same process when reproducing DeepAA on CIFAR10/100. Note that all previous methods use a single run for search, before evaluating the policy with one or multiple runs. We report $95\%$ confidence intervals for those evaluating with multiple runs. + +The supplementary provides qualitative results showing the evolution of the probability distributions over the transformations and the final estimated policies for all datasets. + +CIFAR. In Table 1, we observe that, despite not hard-coding Cutout and RandomCrop in our policy, our method is competitive on both CIFAR10 and CIFAR100. + +We found that, in general, Cutout and Rotate are selected with a high probability, while the Invert transformation is systematically discarded (see supplementary). This is consistent with the choices made in practice by prior work of adding/removing these transformations manually. + +We observe a mismatch between DeepAA's reported results [31], and those we obtain when evaluating their approach on multiple search runs, using the author's code and following their recommendations. This is likely due to the stochasticity of the search procedure. + +
# AugmentationsCIFAR10CIFAR100
TotalHard-codedWRN-40-2WRN-28-10WRN-40-2WRN-28-10
AA [2]4296.397.479.382.9
FastAA [15]4296.497.379.482.7
DADA [14]4296.497.379.182.5
RA [3]42-97.3-83.3
TeachA [24]42-97.5-83.2
UniformAugment [17]4296.2597.3379.0182.82
TA (Wide) [19]3296.32 ± .0597.46 ± .0679.86 ± .1984.33 ± .17
Uniform policy3096.12 ± .0897.26 ± .0778.79 ± .2582.82 ± .24
DeepAA [31]6**0*-97.56 ± .14-84.02 ± .18
DeepAA (reproduced)†6**0*96.25 ± .1197.27 ± .1179.26 ± .3583.38 ± .33
SLACK (Ours)3096.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
+ +*: DeepAA uses hard-coded transformations for pre-training. **: DeepAA learns random flipping unlike other baselines. † We evaluate the policies found from 4 independent search runs as we do for SLACK, using the code from the authors and following their recommendations. + +Table 1. Test accuracies on CIFAR10 and CIFAR100. For SLACK and DeepAA (reproduced) we conduct 4 independent searches, and evaluate each policy with 4 evaluation runs, meaning that we report averages over 16 evaluations. TA and DeepAA are also evaluated with multiple evaluation runs. Results for the remaining methods are reported from the corresponding papers and based on a single run. + +
# AugmentationsImageNet-100
TotalHard-codedResNet18
TA (RA) [19]†5485.87 ± .30
TA (Wide) [19]†5486.39 ± .18
Uniform policy3085.78 ± .32
SLACK3086.06 ± .11
+ +Table 2. Test accuracies on ImageNet-100. + +ImageNet-100. Results for ImageNet-100 are reported in Table 2. We compare SLACK to our Uniform policy and to TrivialAugment (RA) and (Wide) variants, the latter using larger magnitude ranges for its random transformation. SLACK's results lie in between both variants and improve over our Uniform policy. + +Interestingly, for ImageNet-100, we found that RandomResizeCrop is not favoured during the search phase (see supplementary), suggesting that it is not critical for ImageNet-100. Instead the performance gap between TA (Wide) and TA (RA) suggest that harder transformations are key to a better performance for this dataset. + +# 4.3. Beyond natural images + +For the DomainNet dataset, we compare SLACK to a Uniform policy, to the augmentations used by DomainBed [8] for domain generalization, and to the TrivialAugment (RA) and (Wide) methods with their ImageNet and CIFAR default settings. Results can be found in Table 3. + +DomainBed uses the same default transformations as TA ImageNet together with Grayscale, but with smaller magnitudes and unlike TA, does not add a random transformation. Yet it strongly overfits and performs much lower than TA. + +This suggests that augmentations well suited for domain generalization do not perform well on the individual tasks. TA (Wide) ImageNet consistently outperforms all other TA flavors. This further justifies the need to learn the magnitude range and to eliminate any manual range selection process. + +SLACK is a close second, yet it learns the policy end-to-end. The learned policies are illustrated as pie charts in Fig. 3. The slices represent the probability $\pi$ over the different transformations while their radius represent the corresponding magnitudes. They differ from a domain to another, suggesting that the gain compared to the initialization (i.e. Uniform policy) results from SLACK's ability to learn and adapt to each domain. + +# 4.4. Ablation study + +In this section, we evaluate our contributions and main design choices: the network architecture used for search, the KL regularization, and the benefits of learning $\pi$ and $\mu$ . More ablations can be found in the supplementary. Note that hyperparameters are adjusted to each baseline included in the comparison, to make them as competitive as possible. + +Network architecture for search. In prior works, the search phase (when there is one) is conducted on the smaller WideResNet-40x2 architecture for CIFAR10 and CIFAR100, and the learned policy is evaluated for both WideResNet-40x2 and WideResNet-28x10. Table 4 shows that for SLACK, searching directly with WideResNet-28x10 gives the best results for that architecture. + +KL regularization. We compare SLACK with a flavor that does not apply KL-regularization. For the latter, we reduce the outer learning rate so that the augmentation policies with and without regularization evolve at similar speeds. Results in Table 5 show that our regularization is beneficial. + +
# AugmentationsReal-50kQuickdraw-50kInforgraphSketchPaintingClipartAverage
TotalHard-coded
\( DomainBed^† \)5562.54 ± .1566.54 ± .9126.76 ± .3659.54 ± .3758.31 ± .2566.23 ± .1057.23 ± .18
\( TA (RA) ImageNet^† \)5470.85 ± .1367.85 ± .0735.24 ± .1965.63 ± .1164.75 ± .1870.29 ± .1862.43 ± .05
\( TA (Wide) ImageNet^† \)5471.56 ± .0768.60 ± .0535.44 ± .3366.21 ± .1665.15 ± .2071.19 ± .1963.03 ± .07
\( TA (RA) CIFAR^† \)3270.28 ± .0868.35 ± .0733.85 ± .2164.13 ± .1264.73 ± .1770.33 ± .2161.94 ± .05
\( TA (Wide) CIFAR^† \)3271.12 ± .1069.29 ± .0534.21 ± .2965.52 ± .2564.81 ± .1471.01 ± .2162.66 ± .07
Uniform policy3070.37 ± .0868.27 ± .0634.11 ± .2165.22 ± .1763.97 ± .2472.26 ± .1462.37 ± .06
SLACK (ours)3071.00 ± .1368.14 ± .1134.78 ± .1865.41 ± .1664.83 ± .1272.65 ± .2062.80 ± .06
+ +![](images/d5131b5c03d33bf63ceaed729b8d64b4e7047c2692f1776c6d8e78cb412d13a6.jpg) +Figure 3. Policies found on DomainNet for the best search split. Gray circle: initial magnitude upper-bounds. Radius of each pie: learned upper-bounds. Size of each pie: probability of each transformation, averaged over the three composite distributions. Transformations which are parameter-free, AutoContrast, Equalize, Grayscale, and Invert, are displayed with maximal magnitude upper-bound. + +![](images/80e5898d173dd775d932a15034785dae799096d087c6d95ca8586097481d44fa.jpg) + +![](images/47e3e1f1ad2eb18a94fa6626e4a7cbd91a579a003703508d4f466edef76b38ef.jpg) + +Table 3. Test accuracies on DomainNet. + +
Search architectureCIFAR10CIFAR100
WRN-40-297.43 ± .0483.94 ± .20
WRN-28-10 (ours)97.46 ± .0684.08 ± .16
+ +Table 4. CIFAR10/100 accuracy evaluated with WRN-28-10: impact of using a smaller architecture for the search phase. + +
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
without KL96.27 ± .0597.06 ± .1179.61 ± .1383.79 ± .19
with KL (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
+ +Joint learning of $\pi$ and $\mu$ . Lastly, we study how beneficial jointly learning our augmentation parameters is compared to the initial Uniform policy and to a setting where only $\pi$ or $\mu$ is learned. Results can be found in Table 6. + +# 5. Conclusion + +In this paper, we address the task of automatic data augmentation. Considering the more challenging bilevel optimization problem that arises when the search space is not + +Table 5. CIFAR10/100 accuracy with/without KL regularization. + +
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
Uniform policy96.22 ± .1097.38 ± .0579.07 ± .2483.26 ± .17
μ only96.20 ± .0897.42 ± .0579.22 ± .1783.57 ± .18
π only96.22 ± .0997.35 ± .0479.36 ± .1183.45 ± .15
π and μ (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
+ +Table 6. CIFAR10/100 accuracy when only learning part of the policy parameters + +reduced with default transformations, our proposed SLACK method tackles the resulting stability issues thanks to a multi-stage approach based on cold-start, coupled with a KL-regularization. Combined, they allow to reduce the variance of the gradient estimate and to better control the optimization process. We have experimentally observed that our method performs on par with recent approaches leveraging prior knowledge. It has also proved versatile enough to select domain-specific transformations when confronted to non-natural images. + +Acknowledgments. This work was supported by ANR 3IA MIAI@Grenoble Alpes (ANR-19-P3IA-0003) and performed using HPC resources from GENCI-IDRIS (Grant 2022-AD011013343). + +# References + +[1] Michael Arbel and Julien Mairal. 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ICLR, 2022. 1, 3, 6, 7 \ No newline at end of file diff --git a/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/images.zip b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..522bdba7ea1389e7eda3c9489ba5348125f1bc36 --- /dev/null +++ b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3579c3300ba4c2627ac6d8c28ea27f91037d137048e9b11722702575cbe825be +size 493365 diff --git a/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/layout.json b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..88edd5bd91569517b0ee0b4d8ac0f7e702bf0116 --- /dev/null +++ b/2023/SLACK_ Stable Learning of Augmentations With Cold-Start and KL Regularization/layout.json @@ -0,0 +1,9635 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 162, + 103, + 433, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 103, + 433, + 140 + ], + "spans": [ + { + "bbox": [ + 162, + 103, + 433, + 140 + ], + "type": "text", + "content": "SLACK: Stable Learning of Augmentations with Cold-start and KL regularization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 160, + 187, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 160, + 187, + 175 + ], + "spans": [ + { + "bbox": [ + 100, + 160, + 187, + 175 + ], + "type": "text", + "content": "Juliette Marrie1,2" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 215, + 161, + 291, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 215, + 161, + 291, + 175 + ], + "spans": [ + { + "bbox": [ + 215, + 161, + 291, + 175 + ], + "type": "text", + "content": "Michael Arbel" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 321, + 161, + 391, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 161, + 391, + 175 + ], + "spans": [ + { + "bbox": [ + 321, + 161, + 391, + 175 + ], + "type": "text", + "content": "Diane Larlus" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 420, + 161, + 490, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 420, + 161, + 490, + 175 + ], + "spans": [ + { + "bbox": [ + 420, + 161, + 490, + 175 + ], + "type": "text", + "content": "Julien Mairal" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 79, + 189, + 359, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 189, + 359, + 203 + ], + "spans": [ + { + "bbox": [ + 79, + 189, + 359, + 203 + ], + "type": "text", + "content": "1 Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 389, + 189, + 511, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 189, + 511, + 204 + ], + "spans": [ + { + "bbox": [ + 389, + 189, + 511, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 389, + 189, + 511, + 204 + ], + "type": "text", + "content": " Naver Labs Europe" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 256, + 290, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 495 + ], + "type": "text", + "content": "Data augmentation is known to improve the generalization capabilities of neural networks, provided that the set of transformations is chosen with care, a selection often performed manually. Automatic data augmentation aims at automating this process. However, most recent approaches still rely on some prior information; they start from a small pool of manually-selected default transformations that are either used to pretrain the network or forced to be part of the policy learned by the automatic data augmentation algorithm. In this paper, we propose to directly learn the augmentation policy without leveraging such prior knowledge. The resulting bilevel optimization problem becomes more challenging due to the larger search space and the inherent instability of bilevel optimization algorithms. To mitigate these issues (i) we follow a successive cold-start strategy with a Kullback-Leibler regularization, and (ii) we parameterize magnitudes as continuous distributions. Our approach leads to competitive results on standard benchmarks despite a more challenging setting, and generalizes beyond natural images.1" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 518, + 128, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 518, + 128, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 518, + 128, + 532 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 539, + 288, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 288, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 288, + 695 + ], + "type": "text", + "content": "Data augmentation, which encourages predictions to be stable with respect to particular image transformations, has become an essential component in visual recognition systems. While the data augmentation process is conceptually simple, choosing the optimal set of image transformations for a given task or dataset is challenging. For instance, designing a good set for ImageNet [4] or even CIFAR-10/100 [13] has been the result of a long-standing research effort. Whereas data augmentation strategies that have been chosen by hand for ImageNet have been used successfully for many recognition tasks involving natural images, they may fail to generalize to other domains such as medical imaging, remote sensing or hyperspectral imaging." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 232, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 545, + 327 + ], + "type": "text", + "content": "This has motivated automating the design of data augmentation strategies [10, 12, 14-16, 19, 27, 31]. Those are often represented as a stochastic policy that randomly draws a combination of transformations along with their magnitudes from a large predefined set, each time an image is sampled. The goal becomes to learn strategies that effectively compose multiple transformations, which is a challenging task given the large search space of augmentations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 328, + 546, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 546, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 546, + 461 + ], + "type": "text", + "content": "A natural framework for learning the parameters of this policy is that of bilevel optimization. Intuitively, one looks for the best possible policy such that a neural network trained with this policy on a training set (inner problem) generalizes well on a distinct validation set (outer problem). Optimizing the resulting formulation is challenging as the outer problem depends on the solution of the inner problem. Classical techniques for solving this bilevel problem, such as unrolled optimization, can become highly unstable as the network weights become progressively suboptimal for the current policy during the learning process." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 461, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 547, + 593 + ], + "type": "text", + "content": "Moreover, augmentations are often non-differentiable in the parameters of the policy, thus requiring techniques other than direct differentiation, such as Bayesian optimization [15], gradient approximations (e.g. RELAX [7]), or the score method / REINFORCE [28] algorithm. While these techniques bypass the differentiability issues, they can suffer from large bias or variance. As a result, learning augmentation policies is a difficult problem whose challenges are exacerbated by the inherent instability of the optimization techniques developed to solve bilevel problems, such as unrolled optimization [1]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "A standard way to improve stability and make the automatic data augmentation problem simpler is to reduce the search space. This is often achieved by learning the policy on top of \"default\" transformations such as Cutout [5], random cropping and resizing, or color jittering, all known to be well-suited to natural images which compose standard benchmarks such as CIFAR or ImageNet, or by discarding transformations known to be harmful such as Invert. Fixing some of the transformations and removing others mitigate the challenges inherent to learning a compo" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "type": "text", + "content": "1Project page: https://europe.naverlabs.com/slack" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24306" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 541, + 277 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 541, + 277 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 541, + 277 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 541, + 277 + ], + "type": "image", + "image_path": "ba85ba473cfca554dd1086a4f79486a24aa734681f21bd49b3e3fb5503639458.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 546, + 309 + ], + "type": "text", + "content": "Figure 1. For different domains of the DomainNet dataset [21] (one per line), we show an image from that domain (left) and that image transformed using the three most likely (middle) and the three least likely (right) augmentations for that domain, as estimated by SLACK." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 287, + 449 + ], + "type": "text", + "content": "sition of transformations. TrivialAugment [19] also shows that state-of-the-art results can be achieved on these previous benchmarks simply by directly applying the policy classically used for initializing auto-augmentation models, up to minor modifications. Moreover, all methods rely on carefully chosen ranges that constraint the transformation's magnitudes. Despite its effectiveness, manually selecting default transformations and magnitude ranges restricts the applicability of such policies to natural images and prevents generalisation to other domains." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 605 + ], + "type": "text", + "content": "In this paper, our goal is to choose augmentation strategies without relying on default transformations nor on hand-selected magnitude ranges known to suit common benchmarks. To achieve this objective, we first introduce a simple interpretable model for the augmentation policies which allows learning both the frequency by which a given augmentation is selected and the magnitude by which it is applied. Then, we propose a method for learning these augmentation policies by solving a bilevel optimization problem. Our method relies on the REINFORCE technique for computing the gradient of the policy and on unrolled optimization for learning the policy, both of which can result in instabilities and yield high variance estimates." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "To address these issues, we introduce an efficient multistage algorithm with a cold-start strategy and a Kullback-Leibler (KL) regularization that are designed to improve the stability of the process for learning the data augmentation policy. More precisely, the algorithm first pre-trains a network with a data augmentation policy uniformly sampling over all transformations. Then, each stage uses a \"cold-start\" strategy by restarting from the pre-trained network and performs incremental updates of the current policy." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 328, + 546, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 546, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 546, + 449 + ], + "type": "text", + "content": "This multi-stage approach with cold start prevents the network from becoming progressively suboptimal as the policy is updated using unrolled optimization. The KL regularization defines a trust region for the policy to compensate for the possibly high variance of gradient estimates obtained using the REINFORCE technique and encourages exploration during training, preventing collapse to trivial solutions. This regularization is inspired by proximal point algorithms in convex optimization [22], which have also been successful in reinforcement learning tasks [23]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 449, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 593 + ], + "type": "text", + "content": "By combining the regularized multi-stage approach with our interpretable model of the augmentation policies, we obtained the proposed SLACK method, which stands for Stable Learning of Augmentations with Cold-start and Kullback-Leibler regularization. SLACK is an efficient data augmentation learning method that is able to address the challenging bilevel optimization problem of learning a stochastic data augmentation policy without relying strongly on prior knowledge. Figure 1 illustrates the transformations found by SLACK to be most important / detrimental on a dataset of different domains including nonnatural images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "To summarize, our contribution is threefold. (i) We propose a simple and interpretable model of the policies which allows learning both frequency and magnitudes of the augmentations. (ii) We propose a regularized multi-stage strategy to improve the stability of the bilevel optimization algorithm used for solving the data augmentation learning problem. (iii) We evaluate our method on challenging experimental settings, and show that it finds competitive augmentation strategies on natural images without resorting to prior information and generalizes to other domains." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24307" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 94, + 289, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 94, + 289, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 94, + 289, + 334 + ], + "type": "text", + "content": "The choice of image transformation (also known as data augmentation) has become central in the design of computer vision pipelines. To remove the burden of manual selection, automatic data augmentation strategies have been proposed [20, 26]. AutoAugment [2], one of the earliest methods, uses for instance a recurrent neural network for designing the augmentation policy. Because such an approach requires retraining a prediction model at each iteration, it is prohibitively slow, and more efficient alternatives have been proposed. They aim at reducing the training cost using, e.g., population-based training [12], Bayesian optimization [15], and more recently, gradient-based approaches based on bilevel optimization [9, 10, 14, 15, 18, 27, 30], relying on various gradient estimation techniques such as RELAX [7] or the Score method [28]. While the former is inherently biased, the latter is theoretically exact, but has a high variance when approximated in the context of stochastic optimization. Therefore, these approximations may lead to diverging gradient updates. Our method alleviates this by introducing a KL regularization that defines a trust-region for the policy." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 339, + 289, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 289, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 289, + 590 + ], + "type": "text", + "content": "Automatic augmentation using prior knowledge. Most previous works learn augmentations using a small network learned on a subset of the dataset of interest, before retraining the prediction model on a larger network using the full (augmented) data. This choice is appealing to recent gradient-based methods [9, 14] as the search phase for an augmentation policy is often reduced to minutes. Nevertheless, [10, 30] have observed that policies found with such a reduced setup may be suboptimal compared to approaches exploiting full datasets for training both the augmentation policy and the prediction model. This observation was confirmed in [3], which shows that a naive grid search could actually yield state-of-the-art results when directly training on the full-size network and the full data. These results are however obtained at the expense of using strong prior knowledge: augmentation policies are applied on top of default transformations that are manually and independently chosen for each benchmark. Lately, [19] has shown that with a few additional careful choices regarding the augmentation policies, applying a single random transformation on top of the default ones could lead to state-of-the-art results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "To avoid relying on default augmentations, DeepAA [31] has recently proposed a greedy approach that is able to learn these transformations. Yet, learning is performed after a \"pre-training\" phase leveraging the usual default transformations. Moreover, while such a greedy approach simplifies the search procedure and reduces its stochasticity, the resulting computational cost is high. Instead, our approach improves stability and allows directly learning the joint probability of sampling multiple transformations, reducing the search time twofold compared to DeepAA." + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 547, + 229 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 547, + 229 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 547, + 229 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 547, + 229 + ], + "type": "image", + "image_path": "b0f5998908ae6f25ea0a6265b402027faa394ff0984f025d578a54628e55c3ca.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed SLACK method. We learn a data augmentation policy parameterized by " + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": " using bilevel optimization. The inner loop finds the optimal network parameter " + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\theta^{*}" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": " on images from " + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": ". The outer loop trains on a disjoint set of images " + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{val}}" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": " using this network and finds the optimal transformation parameters " + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": ". The method is enhanced with i) a cold-start strategy that structures the learning into rounds which share " + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 238, + 547, + 327 + ], + "type": "text", + "content": " but restart the network from the pretrained one, and ii) a KL regularization." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 348, + 362, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 362, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 362, + 361 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 369, + 547, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 547, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 547, + 490 + ], + "type": "text", + "content": "Our method, SLACK, defines an augmentation policy, which is a probabilistic model for generating data augmentations. The goal is to learn the parameters of this augmentation policy so as to improve the performance of the trained classifier on a held-out dataset. We first describe the augmentation policy (Sec. 3.1) and then formalize the problem of learning data augmentations with bilevel optimization (Sec. 3.2). We then describe our approach for solving such a bilevel optimization problem, which aims at stabilizing the optimization (Sec. 3.3)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 498, + 503, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 503, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 503, + 513 + ], + "type": "text", + "content": "3.1. Stochastic data augmentations policy" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": "An augmentation function " + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": " transforms an image " + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": " into another augmented image " + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\tau(x)" + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": " of the same dimensions. We consider composite augmentations obtained by combining simpler augmentations selected from a finite set " + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "inline_equation", + "content": "S = \\{s_1, \\ldots, s_N\\}" + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": " candidate elementary transformations, such as rotations, translations, shearing, etc. Each elementary transformation depends on a magnitude parameter " + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 518, + 547, + 639 + ], + "type": "text", + "content": " that controls the strength of the transformations, for instance, the angle by which an image is rotated. Magnitudes are normalized to be in the unit interval [0, 1]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Augmentation policy. We define the augmentation policy as a probabilistic model " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " that generates composite augmentations given some parameter " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " to be learned. The model generates an augmentation in three steps: (1) it samples " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " elementary transformations " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "t_1,\\ldots ,t_K" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " according to a categorical distribution " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "p_{\\pi}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " of parameter " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": ", (2)" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24308" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "it samples values for the magnitudes " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "m_{1},\\ldots ,m_{K}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " for each of the selected elementary transformations " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " according to a smoothed uniform distribution " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "p_\\mu" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " of parameter " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " and (3) it composes the " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " elementary transformations to obtain the composite augmentation, with each " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " applied using its corresponding magnitude " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "m_{k}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": ". Therefore, the augmentation policy " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "p_{\\phi}(\\tau)" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " takes the form" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 166, + 287, + 199 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 166, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 104, + 166, + 287, + 199 + ], + "type": "interline_equation", + "content": "p _ {\\phi} (\\tau) = \\prod_ {i = 1} ^ {K} p _ {\\pi} \\left(t _ {i}\\right) p _ {\\mu} \\left(m _ {i} \\mid t _ {i}\\right), \\tag {1}", + "image_path": "11c412418a40e88e2faf2278355757a4ecea0532c09928d6e4e4f4d67083b139.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "type": "text", + "content": "where the parameters " + }, + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "type": "inline_equation", + "content": "\\phi = (\\pi, \\mu)" + }, + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "type": "text", + "content": " are learned jointly. Next, we describe the sampling of the transformations and of their magnitudes." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": "Sampling transformations. We sample elementary transformations " + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": " with replacement from a categorical distribution " + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "inline_equation", + "content": "\\mathrm{Cat}_{\\pi_k}" + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": " of dimension " + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": " parameterized by a logit vector " + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "inline_equation", + "content": "\\pi_k \\coloneqq (\\pi_{k,n})_{1 \\leq n \\leq N}" + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": ". The probability " + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "inline_equation", + "content": "p_{\\pi}(t_1, \\ldots, t_K)" + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": " of sampling the " + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 247, + 287, + 307 + ], + "type": "text", + "content": " transformations is given by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 95, + 316, + 287, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 316, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 95, + 316, + 287, + 331 + ], + "type": "interline_equation", + "content": "p _ {\\pi} \\left(t _ {1}, \\dots , t _ {K}\\right) = \\Pi_ {k = 1} ^ {K} \\operatorname {C a t} _ {\\pi_ {k}} \\left(t _ {k}\\right), \\tag {2}", + "image_path": "462785f8692df9d0f75e4dc6221d861adfb47b8d3014968376399c8fbb43129a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "type": "text", + "content": "where we collect all logits to form a parameter matrix " + }, + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "type": "inline_equation", + "content": "K\\times N" + }, + { + "bbox": [ + 47, + 339, + 287, + 363 + ], + "type": "text", + "content": ". These parameters are learned." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "text", + "content": "Sampling magnitudes. The magnitudes of each elementary transformation " + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "text", + "content": " are sampled from a smoothed uniform distribution between " + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "inline_equation", + "content": "[0, \\mu_i]" + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "text", + "content": " whose upper-bound " + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\mu_i" + }, + { + "bbox": [ + 47, + 366, + 287, + 425 + ], + "type": "text", + "content": " is learned. More precisely, the distribution's density is defined as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 91, + 432, + 242, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 432, + 242, + 459 + ], + "spans": [ + { + "bbox": [ + 91, + 432, + 242, + 459 + ], + "type": "interline_equation", + "content": "p _ {\\mu_ {i}} (m _ {i}) = \\frac {1}{\\mu_ {i}} \\int_ {0} ^ {\\mu_ {i}} \\mathcal {N} (m _ {i}, \\sigma) (u) d u,", + "image_path": "412f340e90a3231ddf352b1975596a98cb0a1e66becaabeda7288bfaa4b02518.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(m_i,\\sigma)" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": " is the Gaussian distribution of mean " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": " and deviation " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": ". The density " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "p_{\\mu_i}(m_i)" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": " approximates the uniform distribution " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\mu_i}\\mathbf{1}_{[0,\\mu_i]}" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": " as the deviation " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": " approaches 0. In practice, we set " + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\sigma = 0.1" + }, + { + "bbox": [ + 47, + 467, + 287, + 529 + ], + "type": "text", + "content": " as we found it to achieve a good trade-off between smoothing and approximation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 531, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 531, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 531, + 287, + 591 + ], + "type": "text", + "content": "Why a uniform distribution? We ran some ablations on previous methods (see supplementary) which suggest that a uniform sampling works on par with more elaborate sampling strategies, and that the magnitude range has more impact on the results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 599, + 241, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 241, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 241, + 612 + ], + "type": "text", + "content": "3.2. Bilevel formulation for policy search" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": "We consider a prediction task, such as predicting the class " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": " of some natural image " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": " using a model " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}(x)" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": " with parameter " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": ". We are interested in finding the best policy parameter " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": " so that the prediction model " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": ", when trained using such policy on a training set " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": " of input/output pairs " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": ", generalizes well on the test set " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{test}}" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": ". The problem naturally decomposes in two phases. During the search phase, the optimal augmentation policy " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": " is learned on " + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 618, + 287, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "During the evaluation phase, the model is re-trained on " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " using " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " and is then evaluated on " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{test}}" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": ". The evaluation phase is performed using standard optimization methods. However, the search phase requires solving a complex optimization problem that we describe next." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": "Search phase as a bilevel problem. The search phase naturally writes as a bilevel problem involving two interdependent losses: a lower-level loss " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{train}}(\\theta, \\phi)" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " for learning an optimal model parameter " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\theta^{\\star}(\\phi)" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " obtained using the augmentation policy " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " and an upper-level loss " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\phi)" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " for learning the policy parameter " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " by evaluating the optimal model with parameter " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\theta^{\\star}(\\phi)" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": ". Each of these objectives is evaluated on two separate splits of the available data " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": ": a training split " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " for the lower-level loss and a validation split " + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{val}}" + }, + { + "bbox": [ + 304, + 135, + 545, + 255 + ], + "type": "text", + "content": " for the upper-level loss. Below, we describe both losses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "type": "text", + "content": "Lower-level loss. We first introduce the training loss " + }, + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "type": "inline_equation", + "content": "\\ell_{\\mathrm{train}}(\\theta, \\tau)" + }, + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "type": "text", + "content": " when only a fixed augmentation " + }, + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 306, + 258, + 545, + 283 + ], + "type": "text", + "content": " is used:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 337, + 293, + 512, + 307 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 293, + 512, + 307 + ], + "spans": [ + { + "bbox": [ + 337, + 293, + 512, + 307 + ], + "type": "interline_equation", + "content": "\\ell_ {\\text {t r a i n}} (\\theta , \\tau) := \\mathbb {E} _ {(x, y) \\sim \\mathcal {D} _ {\\text {t r a i n}}} [ \\ell (y, f _ {\\theta} (\\tau (x))) ],", + "image_path": "da827a7bf9c1d73f90d279a0b4f0cab6ffa244d75e5bcca8888260230b0f3712.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " is an (image, label) pair drawn from " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " is a pointwise prediction loss (e.g. cross-entropy). We then define the training loss " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " for an augmentation policy " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " by taking the expectation of " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\ell_{\\mathrm{train}}(\\theta ,\\tau)" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " over augmentations " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " sampled according to the policy " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 355, + 387, + 496, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 387, + 496, + 400 + ], + "spans": [ + { + "bbox": [ + 355, + 387, + 496, + 400 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t r a i n}} (\\theta , \\phi) := \\mathbb {E} _ {\\tau \\sim p _ {\\phi}} \\left[ \\ell_ {\\text {t r a i n}} (\\theta , \\tau) \\right].", + "image_path": "338821e135c979ba65a56b588d7404852dc4dcf0db9b61fae1b0d0f4a03de0dd.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "text", + "content": "Hence, for a given policy " + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "text", + "content": ", the goal is to learn the optimal model parameter " + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\theta^{\\star}(\\phi)" + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "text", + "content": " by minimizing " + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)" + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "text", + "content": " over " + }, + { + "bbox": [ + 304, + 410, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\theta" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "type": "text", + "content": "Upper-level loss. We first denote by " + }, + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{val}}(\\theta)" + }, + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "type": "text", + "content": " the validation loss for a given model of parameter " + }, + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 437, + 545, + 461 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 472, + 499, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 472, + 499, + 486 + ], + "spans": [ + { + "bbox": [ + 351, + 472, + 499, + 486 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {v a l}} (\\theta) := \\mathbb {E} _ {(x, y) \\sim \\mathcal {D} _ {\\text {v a l}}} [ \\ell (y, f _ {\\theta} (x)) ].", + "image_path": "447be29bd3765945167c383f9d2abedae592df12a28f1cd7b4e4ab4693a2e593.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": "The validation loss " + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{val}}(\\theta)" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": " is computed over the validation set " + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{val}}" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": " without applying any augmentation and thus provides a proxy for the performance on the test dataset. We then define the upper-level loss to be the validation loss of an optimal model " + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\theta^{\\star}(\\phi)" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": " learned using a policy " + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 495, + 545, + 555 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 380, + 565, + 545, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 565, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 380, + 565, + 545, + 578 + ], + "type": "interline_equation", + "content": "\\mathcal {F} (\\phi) := \\mathcal {L} _ {\\text {v a l}} \\left(\\theta^ {*} (\\phi)\\right). \\tag {3}", + "image_path": "a97734508131e08eeef7758899da372179ad9ca6e432bd8f6028928b16679735.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "type": "text", + "content": "While optimizing the lower-level loss is relatively standard, minimizing the upper-level loss " + }, + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "type": "text", + "content": " is more challenging due to the complex dependence of the optimal model parameter " + }, + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "type": "inline_equation", + "content": "\\theta^{\\star}(\\phi)" + }, + { + "bbox": [ + 304, + 590, + 545, + 650 + ], + "type": "text", + "content": " on the policy. Next, we describe our proposed algorithm for solving the bilevel problem." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 658, + 415, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 415, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 415, + 671 + ], + "type": "text", + "content": "3.3. SLACK algorithm" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "We propose Algorithm 1 for learning the optimal policy during the search phase. SLACK first pre-trains the prediction model using the objective " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{train}}(\\theta, \\phi_{\\mathrm{uniform}})" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " for an" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24309" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "initial policy parametrized by " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{uniform}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " which samples uniformly among all elementary transformations. It then performs " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{rounds}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " rounds to update the parameters " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": " jointly using a bilevel optimization algorithm. This approach is reminiscent of the one of AutoAugment (AA) [3] that fully re-trains the network for each policy update. Yet, it is several orders of magnitude faster than AA, as it benefits from pre-training and from our bilevel optimization." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": "SLACK relies on two strategies to ensure the stability of the parameter updates during each round: a cold-start strategy for the prediction model and an anchoring strategy for the policy. The cold-start initializes the prediction model at the beginning of each round using a pre-trained model " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\theta_0" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": ". Anchoring is achieved by encouraging the current policy to remain close to some anchor policy " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "p_{\\tilde{\\phi}}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\tilde{\\phi}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " to the current policy parameter " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " at the beginning of each round. During the first " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{retrain}}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " steps of each round, the algorithm only updates the model parameter using a stochastic estimate " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\hat{g}_{\\theta}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " while maintaining the policy fixed. Then for the last " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "n_{\\mathrm{total}} - n_{\\mathrm{retrain}}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " steps, the algorithm alternates between model updates and policy updates. The policy updates aim to minimize the sum of the upper-level objective " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " and an anchoring " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "d(p_{\\phi},p_{\\tilde{\\phi}})\\coloneqq \\mathrm{KL}(p_{\\pi},p_{\\tilde{\\pi}})" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " encouraging the policy " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " to remain close to the anchor policy " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "p_{\\tilde{\\phi}}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": ". These updates are obtained using a stochastic estimate " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\hat{G}_{\\phi}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " along with the exact gradient of the KL regularization which admits a closed-form expression. Next we explain how we estimate the gradients " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\hat{g}_{\\theta}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "inline_equation", + "content": "\\hat{G}_{\\phi}" + }, + { + "bbox": [ + 46, + 167, + 290, + 422 + ], + "type": "text", + "content": " and discuss the effect of cold-start and KL-regularization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 48, + 434, + 136, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 434, + 136, + 445 + ], + "spans": [ + { + "bbox": [ + 48, + 434, + 136, + 445 + ], + "type": "text", + "content": "Algorithm 1 SLACK" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 449, + 247, + 584 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 50, + 449, + 203, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 449, + 203, + 459 + ], + "spans": [ + { + "bbox": [ + 50, + 449, + 203, + 459 + ], + "type": "text", + "content": "1: Initialize policy parameter " + }, + { + "bbox": [ + 50, + 449, + 203, + 459 + ], + "type": "inline_equation", + "content": "\\phi \\gets \\phi_{\\mathrm{uniform}}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 50, + 459, + 217, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 459, + 217, + 469 + ], + "spans": [ + { + "bbox": [ + 50, + 459, + 217, + 469 + ], + "type": "text", + "content": "2: Pre-training: " + }, + { + "bbox": [ + 50, + 459, + 217, + 469 + ], + "type": "inline_equation", + "content": "\\theta_0\\gets" + }, + { + "bbox": [ + 50, + 459, + 217, + 469 + ], + "type": "text", + "content": " optimize " + }, + { + "bbox": [ + 50, + 459, + 217, + 469 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi))" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 469, + 150, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 469, + 150, + 479 + ], + "spans": [ + { + "bbox": [ + 51, + 469, + 150, + 479 + ], + "type": "text", + "content": "3: for " + }, + { + "bbox": [ + 51, + 469, + 150, + 479 + ], + "type": "inline_equation", + "content": "i \\in \\{1, \\dots, n_{\\text{rounds}}\\}" + }, + { + "bbox": [ + 51, + 469, + 150, + 479 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 479, + 140, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 479, + 140, + 487 + ], + "spans": [ + { + "bbox": [ + 51, + 479, + 140, + 487 + ], + "type": "text", + "content": "4: Cold-start: " + }, + { + "bbox": [ + 51, + 479, + 140, + 487 + ], + "type": "inline_equation", + "content": "\\theta \\gets \\theta_0" + }, + { + "bbox": [ + 51, + 479, + 140, + 487 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 487, + 176, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 487, + 176, + 497 + ], + "spans": [ + { + "bbox": [ + 51, + 487, + 176, + 497 + ], + "type": "text", + "content": "5: Update anchor policy: " + }, + { + "bbox": [ + 51, + 487, + 176, + 497 + ], + "type": "inline_equation", + "content": "\\tilde{\\phi} \\gets \\phi" + }, + { + "bbox": [ + 51, + 487, + 176, + 497 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 497, + 156, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 497, + 156, + 506 + ], + "spans": [ + { + "bbox": [ + 51, + 497, + 156, + 506 + ], + "type": "text", + "content": "6: for " + }, + { + "bbox": [ + 51, + 497, + 156, + 506 + ], + "type": "inline_equation", + "content": "j\\in \\{1,\\dots,n_{\\mathrm{total}}\\}" + }, + { + "bbox": [ + 51, + 497, + 156, + 506 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 51, + 506, + 243, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 506, + 243, + 516 + ], + "spans": [ + { + "bbox": [ + 51, + 506, + 243, + 516 + ], + "type": "text", + "content": "7: Compute stochastic gradient " + }, + { + "bbox": [ + 51, + 506, + 243, + 516 + ], + "type": "inline_equation", + "content": "\\hat{g}_{\\theta}\\approx \\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "spans": [ + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "type": "text", + "content": "8: Update " + }, + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "type": "inline_equation", + "content": "\\theta \\gets \\theta - \\eta \\hat{g}_{\\theta}" + }, + { + "bbox": [ + 51, + 516, + 164, + 525 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 51, + 525, + 146, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 525, + 146, + 535 + ], + "spans": [ + { + "bbox": [ + 51, + 525, + 146, + 535 + ], + "type": "text", + "content": "9: if " + }, + { + "bbox": [ + 51, + 525, + 146, + 535 + ], + "type": "inline_equation", + "content": "j > n_{\\mathrm{retrain}}" + }, + { + "bbox": [ + 51, + 525, + 146, + 535 + ], + "type": "text", + "content": " then" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 50, + 535, + 240, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 535, + 240, + 544 + ], + "spans": [ + { + "bbox": [ + 50, + 535, + 240, + 544 + ], + "type": "text", + "content": "10: Compute stochastic gradient " + }, + { + "bbox": [ + 50, + 535, + 240, + 544 + ], + "type": "inline_equation", + "content": "\\hat{G}_{\\phi}\\approx \\nabla_{\\phi}\\mathcal{F}(\\phi)" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "spans": [ + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "type": "text", + "content": "11: Update " + }, + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "type": "inline_equation", + "content": "\\phi \\gets \\phi - \\alpha (\\hat{G}_{\\phi} + \\lambda \\nabla_{\\phi} d(p_{\\phi}, p_{\\phi}^{\\prime}))" + }, + { + "bbox": [ + 50, + 545, + 247, + 556 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 50, + 556, + 104, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 556, + 104, + 565 + ], + "spans": [ + { + "bbox": [ + 50, + 556, + 104, + 565 + ], + "type": "text", + "content": "12: end if" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 50, + 566, + 99, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 566, + 99, + 574 + ], + "spans": [ + { + "bbox": [ + 50, + 566, + 99, + 574 + ], + "type": "text", + "content": "13: end for" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 50, + 575, + 89, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 575, + 89, + 584 + ], + "spans": [ + { + "bbox": [ + 50, + 575, + 89, + 584 + ], + "type": "text", + "content": "14: end for" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "content": "Gradient estimation. Algorithm 1 requires estimating the gradient of " + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\phi)" + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "content": ", which is challenging given the complex dependence of the upper-level loss on the policy " + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "content": " through the optimal model parameter " + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\theta^{\\star}(\\phi)" + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "content": " learned using such a policy. In line with previous works [9, 14, 18, 27], we approximate the optimal model parameter " + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\theta^{*}(\\phi)" + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "content": " with a simpler function " + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\hat{\\theta} (\\phi)" + }, + { + "bbox": [ + 46, + 603, + 287, + 689 + ], + "type": "text", + "content": " that is easier to compute:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 696, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 696, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\hat {\\theta} (\\phi): = \\theta - \\eta \\nabla_ {\\theta} \\mathcal {L} _ {\\text {t r a i n}} (\\theta , \\phi). \\tag {4}", + "image_path": "21adbf68e3eb2062b3885a61340da076a4429028d7ebe30fbe35a0afdd91c65f.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "Eq. (4) corresponds to one gradient step to optimize the lower-level loss starting from the current parameter " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and using step-size " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\eta > 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ". By keeping track of the dependence in " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " and exploiting the fact that the augmentation policy " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " has a score " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\nabla_{\\phi} \\log p_{\\phi}(\\tau)" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " that can be computed explicitly using Eq. (1), we can use the REINFORCE/Score method [6] to derive a closed-form expression for " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\nabla_{\\phi} \\hat{\\theta}(\\phi)" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": " which will serve for approximating the gradient of " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 317, + 176, + 533, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 176, + 533, + 192 + ], + "spans": [ + { + "bbox": [ + 317, + 176, + 533, + 192 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\phi} \\hat {\\theta} (\\phi) = - \\eta \\mathbb {E} _ {\\tau \\sim p _ {\\phi}} \\left[ \\nabla_ {\\theta} \\ell_ {\\text {t r a i n}} (\\theta , \\tau) \\nabla_ {\\phi} \\log p _ {\\phi} (\\tau) ^ {\\top} \\right].", + "image_path": "02fcf7bbc53b02261e0dbb3202f5e3960e0aa11760171a31295e2bd70dda34ed.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "text", + "content": "Then, we approximate the upper-level loss " + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\phi)" + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "text", + "content": " with a simpler function " + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{F}} (\\phi)\\coloneqq \\mathcal{L}_{\\mathrm{val}}(\\hat{\\theta} (\\phi))" + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "text", + "content": " and the gradient " + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\nabla_{\\phi}\\mathcal{F}(\\phi)" + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\nabla_{\\phi}\\hat{\\mathcal{F}} (\\phi)" + }, + { + "bbox": [ + 304, + 200, + 545, + 239 + ], + "type": "text", + "content": " which is obtained using the chain rule:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 321, + 248, + 545, + 263 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 248, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 321, + 248, + 545, + 263 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\phi} \\mathcal {F} (\\phi) \\approx \\nabla_ {\\phi} \\hat {\\mathcal {F}} (\\phi) = \\nabla_ {\\theta} \\mathcal {L} _ {\\text {v a l}} \\left(\\hat {\\theta} (\\phi)\\right) ^ {\\top} \\nabla_ {\\phi} \\hat {\\theta} (\\phi). \\tag {5}", + "image_path": "5de188b12f8b6734990455cca951a60bb9d5ab5bee304197b2a9f65726986503.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 272, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 308 + ], + "type": "text", + "content": "The above expression requires only first-order derivatives and matrix-vector products, which is amenable to efficient implementation using automatic differentiation softwares." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": "Stochastic gradient estimates. In practice, we replace all expectations by estimates on a batch of data and sampled augmentations. More precisely, to compute the approximation " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\hat{g}_{\\theta}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{train}}(\\theta ,\\phi)" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": ", we sample " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "B_{\\mathrm{aug}}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " augmentations from " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "p_{\\phi}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " and then apply each of them to a batch of training data " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "B_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": ". Using the same batch of data and augmentation, we approximate " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\hat{\\theta} (\\phi)" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\nabla_{\\phi}\\hat{\\theta} (\\phi)" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " appearing in Eq. (5). Finally, we use a batch " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "B_{\\mathrm{val}}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " of data from " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathrm{val}}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " to estimate " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\nabla_{\\theta}\\mathcal{L}_{\\mathrm{val}}(\\hat{\\theta} (\\phi))" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " and compute " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\hat{G}_{\\phi}" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": ", which is a stochastic estimate of " + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "inline_equation", + "content": "\\nabla_{\\phi}\\hat{\\mathcal{F}} (\\phi)" + }, + { + "bbox": [ + 304, + 311, + 545, + 433 + ], + "type": "text", + "content": " in Eq. (5)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 435, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 579 + ], + "type": "text", + "content": "Cold-start. The cold-start strategy allows to re-train the model at each round with the current augmentation policy starting from the pre-trained model. This approach is closer to the original bilevel formulation which implies finding an optimal prediction model for each policy. Initializing with a pre-trained model yields computational gain as fewer iterations are needed to optimize the model. We could instead use a warm-start strategy which initializes the model at each round with the learned model at the previous round. Yet we experimentally observe that such approach progressively leads to overfitting and degrades the quality of the learned policies (see supplementary)." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Anchoring using KL regularization. We experimentally found that adding an anchoring " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "d(p_{\\phi}, p_{\\tilde{\\phi}}) \\coloneqq \\mathrm{KL}(p_{\\pi}, p_{\\tilde{\\pi}})" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " with strength parameter " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " when updating the policy prevents the algorithm from collapsing towards trivial policies. The anchoring affects only the categorical distribution " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{\\pi}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ". For the magnitudes " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{\\mu}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ", we did not use anchoring as it is ill-defined for a uniform distribution. Instead, we simply used smaller step-sizes. Our approach takes inspiration from Proximal Policy Optimization [23] used in the context of reinforcement learning which is known to improve policy search." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24310" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 128, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 152 + ], + "type": "text", + "content": "In this section, we first briefly describe our experimental setup (Sec 4.1). Then we evaluate our approach on several standard benchmarks composed of natural images (Sec 4.2) as well as on a benchmark with other domains (Sec 4.3). We finally report some ablation studies (Sec 4.4)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 158, + 162, + 171 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 158, + 162, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 158, + 162, + 171 + ], + "type": "text", + "content": "4.1. Experimental setup" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 178, + 287, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 178, + 287, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 287, + 310 + ], + "type": "text", + "content": "**Benchmarks.** We first evaluate our model on three standard benchmarks, CIFAR10 [13], CIFAR100 [13] and ImageNet-100 [25], all composed of natural images. To study how well our method generalizes beyond natural images, we also evaluate on the DomainNet dataset [21], which contains 345 classes for 6 different domains. To ensure our protocol uses a similar number of training images for each domain, we use a reduced set of 50,000 training images for the two largest domains (real, quickdraw) and leave the remaining images for testing. For the other domains, we isolate " + }, + { + "bbox": [ + 46, + 178, + 287, + 310 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 178, + 287, + 310 + ], + "type": "text", + "content": " of the data for testing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 313, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 287, + 409 + ], + "type": "text", + "content": "Architectures. CIFAR10/100 are evaluated with two architectures that are standard for automatic data augmentation: WideResNet-40x2 and WideResNet-28x10 [29]. Unlike previous works whose search phase is only conducted with the smaller WideResNet-40x2, we search and evaluate with the same architecture, as we found it to be better (see Sec. 4.4). ImageNet-100 and DomainNet are evaluated with a ResNet-18 [11] architecture." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "type": "text", + "content": "Transformation space. Our data augmentation search space is composed of the standard pool of 15 transformations: Identity, ShearX, ShearY, TranslateX, TranslateY, Rotate, AutoContrast, Equalize, Invert, Solarize, Posterize, Contrast, Brightness, Sharpness, Color. We add to this pool the transformations that previous methods usually apply by default: Cutout and RandomCrop for CIFAR, RandomResizeCrop for ImageNet, Grayscale for DomainNet. Following standard practice, when RandomResizeCrop is sampled, it is always applied first. We learn the range of its scale parameter. We do not add ColorJitter that is also applied by default in prior work for ImageNet, as it is already a mix of Brightness, Contrast and Color. However we add Hue, which is one component of ColorJitter and never applied by default. Following prior work, the magnitudes are mapped to [0,1]. After mapping, " + }, + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 411, + 287, + 663 + ], + "type": "text", + "content": " is initialized at 0.75 to favour exploration (see details in supplementary). We also uniformly sample magnitudes for Cutout and RandomCrop, whereas their value is hand-picked in prior work. Since the datasets are horizontally symmetric, we follow common practice and apply flip by default." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Policy search. We apply a train/val split of 0.5/0.5, meaning that half of the data is used to train the model parameters while the other half is used to learn the augmentation policy. Pre-training is done in the same setting as the evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "(see next paragraph), except that we train only with the train data in the train/val split of the search phase. We use SGD with momentum for the optimization of the validation and training losses. For the latter, we use the same weight decay as for the final policy evaluation. We sample 8 different augmentations for computing the expectation that is needed for the stochastic gradient estimate, as detailed in Sec. 3.3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "type": "text", + "content": "Policy evaluation. We evaluate our models following the framework of TrivialAugment [19]. The corresponding hyperparameters can be found in the supplementary. We evaluate each policy with 4 independent runs, meaning that our results are averaged over a total of " + }, + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "type": "inline_equation", + "content": "4 \\times 4 = 16" + }, + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "type": "text", + "content": " evaluations. Our Uniform policy (corresponding to SLACK's initialization) and our reported results on TrivialAugment are evaluated with 8 independent runs. We also report a confidence interval which contains the true mean with probability " + }, + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "type": "inline_equation", + "content": "p = 95\\%" + }, + { + "bbox": [ + 304, + 159, + 546, + 289 + ], + "type": "text", + "content": ", under the assumption of normally distributed accuracies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 297, + 499, + 311 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 499, + 311 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 499, + 311 + ], + "type": "text", + "content": "4.2. Comparison with the state of the art" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": "We compare our method with a Uniform augmentation policy as well as many previous approaches for data augmentation, including AutoAugment (AA) [2], Fast AutoAugment (FastAA) [15], Differentiable Automatic Data Augmentation (DADA) [14], RandAugment (RA) [3], Teach Augment [24], UniformAugment [20], TrivialAugment (TA) [19], and Deep AutoAugment (DeepAA) [31]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 400, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 519 + ], + "type": "text", + "content": "For each method, we indicate the total number of composed transformations, and the number of hard-coded transformations among those (Tables 1 and 2). For SLACK, we evaluate the policies obtained from 4 independent search runs (each with 4 different train/val splits) to assess the robustness of our approach. We follow the same process when reproducing DeepAA on CIFAR10/100. Note that all previous methods use a single run for search, before evaluating the policy with one or multiple runs. We report " + }, + { + "bbox": [ + 304, + 400, + 545, + 519 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 400, + 545, + 519 + ], + "type": "text", + "content": " confidence intervals for those evaluating with multiple runs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 520, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 555 + ], + "type": "text", + "content": "The supplementary provides qualitative results showing the evolution of the probability distributions over the transformations and the final estimated policies for all datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 594 + ], + "type": "text", + "content": "CIFAR. In Table 1, we observe that, despite not hard-coding Cutout and RandomCrop in our policy, our method is competitive on both CIFAR10 and CIFAR100." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 654 + ], + "type": "text", + "content": "We found that, in general, Cutout and Rotate are selected with a high probability, while the Invert transformation is systematically discarded (see supplementary). This is consistent with the choices made in practice by prior work of adding/removing these transformations manually." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We observe a mismatch between DeepAA's reported results [31], and those we obtain when evaluating their approach on multiple search runs, using the author's code and following their recommendations. This is likely due to the stochasticity of the search procedure." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24311" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 109, + 70, + 486, + 216 + ], + "blocks": [ + { + "bbox": [ + 109, + 70, + 486, + 216 + ], + "lines": [ + { + "bbox": [ + 109, + 70, + 486, + 216 + ], + "spans": [ + { + "bbox": [ + 109, + 70, + 486, + 216 + ], + "type": "table", + "html": "
# AugmentationsCIFAR10CIFAR100
TotalHard-codedWRN-40-2WRN-28-10WRN-40-2WRN-28-10
AA [2]4296.397.479.382.9
FastAA [15]4296.497.379.482.7
DADA [14]4296.497.379.182.5
RA [3]42-97.3-83.3
TeachA [24]42-97.5-83.2
UniformAugment [17]4296.2597.3379.0182.82
TA (Wide) [19]3296.32 ± .0597.46 ± .0679.86 ± .1984.33 ± .17
Uniform policy3096.12 ± .0897.26 ± .0778.79 ± .2582.82 ± .24
DeepAA [31]6**0*-97.56 ± .14-84.02 ± .18
DeepAA (reproduced)†6**0*96.25 ± .1197.27 ± .1179.26 ± .3583.38 ± .33
SLACK (Ours)3096.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
", + "image_path": "3a009396541c2083ef9cf351ee91ba45fd6fcce6f6aabe23a2bcc9887780a3be.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 262, + 544, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 544, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 544, + 283 + ], + "type": "text", + "content": "*: DeepAA uses hard-coded transformations for pre-training. **: DeepAA learns random flipping unlike other baselines. † We evaluate the policies found from 4 independent search runs as we do for SLACK, using the code from the authors and following their recommendations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 65, + 309, + 271, + 392 + ], + "blocks": [ + { + "bbox": [ + 46, + 223, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 223, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 547, + 258 + ], + "type": "text", + "content": "Table 1. Test accuracies on CIFAR10 and CIFAR100. For SLACK and DeepAA (reproduced) we conduct 4 independent searches, and evaluate each policy with 4 evaluation runs, meaning that we report averages over 16 evaluations. TA and DeepAA are also evaluated with multiple evaluation runs. Results for the remaining methods are reported from the corresponding papers and based on a single run." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 309, + 271, + 392 + ], + "lines": [ + { + "bbox": [ + 65, + 309, + 271, + 392 + ], + "spans": [ + { + "bbox": [ + 65, + 309, + 271, + 392 + ], + "type": "table", + "html": "
# AugmentationsImageNet-100
TotalHard-codedResNet18
TA (RA) [19]†5485.87 ± .30
TA (Wide) [19]†5486.39 ± .18
Uniform policy3085.78 ± .32
SLACK3086.06 ± .11
", + "image_path": "85bc785631feea07305bf7e587f56b3d82ad659b10a107bdde86e34b18aa9779.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 399, + 246, + 410 + ], + "lines": [ + { + "bbox": [ + 88, + 399, + 246, + 410 + ], + "spans": [ + { + "bbox": [ + 88, + 399, + 246, + 410 + ], + "type": "text", + "content": "Table 2. Test accuracies on ImageNet-100." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 433, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 505 + ], + "type": "text", + "content": "ImageNet-100. Results for ImageNet-100 are reported in Table 2. We compare SLACK to our Uniform policy and to TrivialAugment (RA) and (Wide) variants, the latter using larger magnitude ranges for its random transformation. SLACK's results lie in between both variants and improve over our Uniform policy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 505, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 577 + ], + "type": "text", + "content": "Interestingly, for ImageNet-100, we found that RandomResizeCrop is not favoured during the search phase (see supplementary), suggesting that it is not critical for ImageNet-100. Instead the performance gap between TA (Wide) and TA (RA) suggest that harder transformations are key to a better performance for this dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 586, + 178, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 178, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 178, + 600 + ], + "type": "text", + "content": "4.3. Beyond natural images" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 665 + ], + "type": "text", + "content": "For the DomainNet dataset, we compare SLACK to a Uniform policy, to the augmentations used by DomainBed [8] for domain generalization, and to the TrivialAugment (RA) and (Wide) methods with their ImageNet and CIFAR default settings. Results can be found in Table 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "DomainBed uses the same default transformations as TA ImageNet together with Grayscale, but with smaller magnitudes and unlike TA, does not add a random transformation. Yet it strongly overfits and performs much lower than TA." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 312, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 372 + ], + "type": "text", + "content": "This suggests that augmentations well suited for domain generalization do not perform well on the individual tasks. TA (Wide) ImageNet consistently outperforms all other TA flavors. This further justifies the need to learn the magnitude range and to eliminate any manual range selection process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "type": "text", + "content": "SLACK is a close second, yet it learns the policy end-to-end. The learned policies are illustrated as pie charts in Fig. 3. The slices represent the probability " + }, + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 372, + 545, + 468 + ], + "type": "text", + "content": " over the different transformations while their radius represent the corresponding magnitudes. They differ from a domain to another, suggesting that the gain compared to the initialization (i.e. Uniform policy) results from SLACK's ability to learn and adapt to each domain." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 474, + 397, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 397, + 487 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 397, + 487 + ], + "type": "text", + "content": "4.4. Ablation study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "type": "text", + "content": "In this section, we evaluate our contributions and main design choices: the network architecture used for search, the KL regularization, and the benefits of learning " + }, + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 492, + 545, + 564 + ], + "type": "text", + "content": ". More ablations can be found in the supplementary. Note that hyperparameters are adjusted to each baseline included in the comparison, to make them as competitive as possible." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 651 + ], + "type": "text", + "content": "Network architecture for search. In prior works, the search phase (when there is one) is conducted on the smaller WideResNet-40x2 architecture for CIFAR10 and CIFAR100, and the learned policy is evaluated for both WideResNet-40x2 and WideResNet-28x10. Table 4 shows that for SLACK, searching directly with WideResNet-28x10 gives the best results for that architecture." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "KL regularization. We compare SLACK with a flavor that does not apply KL-regularization. For the latter, we reduce the outer learning rate so that the augmentation policies with and without regularization evolve at similar speeds. Results in Table 5 show that our regularization is beneficial." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24312" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 530, + 167 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 530, + 167 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 530, + 167 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 530, + 167 + ], + "type": "table", + "html": "
# AugmentationsReal-50kQuickdraw-50kInforgraphSketchPaintingClipartAverage
TotalHard-coded
\\( DomainBed^† \\)5562.54 ± .1566.54 ± .9126.76 ± .3659.54 ± .3758.31 ± .2566.23 ± .1057.23 ± .18
\\( TA (RA) ImageNet^† \\)5470.85 ± .1367.85 ± .0735.24 ± .1965.63 ± .1164.75 ± .1870.29 ± .1862.43 ± .05
\\( TA (Wide) ImageNet^† \\)5471.56 ± .0768.60 ± .0535.44 ± .3366.21 ± .1665.15 ± .2071.19 ± .1963.03 ± .07
\\( TA (RA) CIFAR^† \\)3270.28 ± .0868.35 ± .0733.85 ± .2164.13 ± .1264.73 ± .1770.33 ± .2161.94 ± .05
\\( TA (Wide) CIFAR^† \\)3271.12 ± .1069.29 ± .0534.21 ± .2965.52 ± .2564.81 ± .1471.01 ± .2162.66 ± .07
Uniform policy3070.37 ± .0868.27 ± .0634.11 ± .2165.22 ± .1763.97 ± .2472.26 ± .1462.37 ± .06
SLACK (ours)3071.00 ± .1368.14 ± .1134.78 ± .1865.41 ± .1664.83 ± .1272.65 ± .2062.80 ± .06
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Search architectureCIFAR10CIFAR100
WRN-40-297.43 ± .0483.94 ± .20
WRN-28-10 (ours)97.46 ± .0684.08 ± .16
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SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
without KL96.27 ± .0597.06 ± .1179.61 ± .1383.79 ± .19
with KL (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
", + "image_path": "206f01f975b7c115a044c382d8fe54a2076d5f2d62f7ca54ff115989fffb5e7a.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "text", + "content": "Joint learning of " + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "text", + "content": ". Lastly, we study how beneficial jointly learning our augmentation parameters is compared to the initial Uniform policy and to a setting where only " + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 595, + 287, + 643 + ], + "type": "text", + "content": " is learned. Results can be found in Table 6." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 656, + 119, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 119, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 119, + 669 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "In this paper, we address the task of automatic data augmentation. Considering the more challenging bilevel optimization problem that arises when the search space is not" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 309, + 422, + 545, + 487 + ], + "blocks": [ + { + "bbox": [ + 48, + 561, + 285, + 572 + ], + "lines": [ + { + "bbox": [ + 48, + 561, + 285, + 572 + ], + "spans": [ + { + "bbox": [ + 48, + 561, + 285, + 572 + ], + "type": "text", + "content": "Table 5. CIFAR10/100 accuracy with/without KL regularization." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 422, + 545, + 487 + ], + "lines": [ + { + "bbox": [ + 309, + 422, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 309, + 422, + 545, + 487 + ], + "type": "table", + "html": "
SLACK variantCIFAR10CIFAR100
WRN-40-2WRN-28-10WRN-40-2WRN-28-10
Uniform policy96.22 ± .1097.38 ± .0579.07 ± .2483.26 ± .17
μ only96.20 ± .0897.42 ± .0579.22 ± .1783.57 ± .18
π only96.22 ± .0997.35 ± .0479.36 ± .1183.45 ± .15
π and μ (ours)96.29 ± .0897.46 ± .0679.87 ± .1184.08 ± .16
", + "image_path": "bde3e8ffdf29f160409f32a73a7f59a5ef835e0d8b789d587f1a68b779fc79e0.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 495, + 545, + 517 + ], + "lines": [ + { + "bbox": [ + 305, + 495, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 545, + 517 + ], + "type": "text", + "content": "Table 6. CIFAR10/100 accuracy when only learning part of the policy parameters" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 541, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 545, + 662 + ], + "type": "text", + "content": "reduced with default transformations, our proposed SLACK method tackles the resulting stability issues thanks to a multi-stage approach based on cold-start, coupled with a KL-regularization. Combined, they allow to reduce the variance of the gradient estimate and to better control the optimization process. We have experimentally observed that our method performs on par with recent approaches leveraging prior knowledge. It has also proved versatile enough to select domain-specific transformations when confronted to non-natural images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by ANR 3IA MIAI@Grenoble Alpes (ANR-19-P3IA-0003) and performed using HPC resources from GENCI-IDRIS (Grant 2022-AD011013343)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24313" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Michael Arbel and Julien Mairal. 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Using the head-mounted LiDAR and camera to scan the IMUs wearer, we construct SLOPER4D, a large scene-aware dataset for global 4D human pose estimation in urban environments." + ], + "image_footnote": [], + "bbox": [ + 287, + 330, + 870, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 625, + 313, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present SLOPER4D, a novel scene-aware dataset collected in large urban environments to facilitate the research of global human pose estimation (GHPE) with human-scene interaction in the wild. Employing a head-mounted device integrated with a LiDAR and camera, we record 12 human subjects' activities over 10 diverse urban scenes from an egocentric view. Frame-wise annotations for 2D key points, 3D pose parameters, and global translations are provided, together with reconstructed scene point clouds. To obtain accurate 3D ground truth in such large dynamic scenes, we propose a joint optimization method to fit local SMPL meshes to the scene and fine-tune the camera calibration during dynamic motions frame by frame, resulting in plausible and scene-natural 3D human poses. Even", + "bbox": [ + 73, + 657, + 468, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tually, SLOPER4D consists of 15 sequences of human motions, each of which has a trajectory length of more than 200 meters (up to 1,300 meters) and covers an area of more than $200\\mathrm{m}^2$ (up to $30,000\\mathrm{m}^2$ ), including more than 100k LiDAR frames, 300k video frames, and 500k IMU-based motion frames. With SLOPER4D, we provide a detailed and thorough analysis of two critical tasks, including camera-based 3D HPE and LiDAR-based 3D HPE in urban environments, and benchmark a new task, GHPE. The in-depth analysis demonstrates SLOPER4D poses significant challenges to existing methods and produces great research opportunities. The dataset and code are released at http://www.lidarhumanmotion.net/sloper4d/.", + "bbox": [ + 500, + 625, + 890, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 829, + 630, + 844 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Urban-level human motion capture is attracting more and more attention, which targets acquiring consecutive fine-grained human pose representations, such as 3D skeletons", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "682", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "and parametric mesh models, with accurate global locations in the physical world. It is essential for human action recognition, social-behavioral analysis, and scene perception and further benefits many downstream applications, including Augmented/Virtual Reality, simulation, autonomous driving, smart city, sociology, etc. However, capturing extra large-scale dynamic scenes and annotating detailed 3D representations for humans with diverse poses is not trivial.", + "bbox": [ + 75, + 90, + 470, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Over the past decades, a large number of datasets and benchmarks have been proposed and have greatly promoted the research in 3D human pose estimation (HPE). They can be divided into two main categories according to the capture environment. The first class usually leverages marker-based systems [16, 33, 45], cameras [14, 59, 60], or RGB-D sensors [13, 64] to capture human local poses in constrained environments. However, the optical system is sensitive to light and lacks depth information, making it unstable in outdoor scenes and difficult to provide global translations, and the RGB-D sensor has limited range and could not work outdoors. The second class [39, 49] attempts to take advantage of body-mounted IMUs to capture occlusion-free 3D poses in free environments. However, IMUs suffer from severe drift for long-term capturing, resulting in misalignments with the human body. Then, some methods exploit additional sensors, such as RGB camera [17], RGB-D camera [46, 57, 67], or LiDAR [27] to alleviate the problem and make obvious improvement. However, they all focus on HPE without considering the scene constraints, which are limited in reconstructing human-scene integrated digital urban and human-scene natural interactions.", + "bbox": [ + 75, + 214, + 473, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To capture human pose and related static scenes simultaneously, some studies use wearable IMUs and body-mounted camera [12] or LiDAR [5] to register the human in large real scenarios and they are promising for capturing human-involved real-world scenes. However, human pose and scene are decoupled in these works due to the ego view, where auxiliary visual sensors are used for collecting the scene data while IMUs are utilized for obtaining the 3D pose. Different from them, we propose a novel setting for human-scene capture with wearable IMUs and global-view LiDAR and camera, which can provide multi-modal data for more accurate 3D HPE.", + "bbox": [ + 75, + 550, + 470, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a huge scene-aware dataset for sequential human pose estimation in urban environments, named SLOPER4D. To our knowledge, it is the first urban-level 3D HPE dataset with multi-modal capture data, including calibrated and synchronized IMU measurements, LiDAR point clouds, and images for each subject. Moreover, the dataset provides rich annotations, including 3D poses, SMPL [32] models and locations in the world coordinate system, 2D poses and bounding boxes in the image coordinate system, and reconstructed 3D scene mesh. In particular, we propose a joint optimization method for", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "obtaining accurate and natural human motion representations by utilizing multi-sensor complementation and scene constraints, which also benefit global localization and camera calibration in the dynamic acquisition process. Furthermore, SLOPER4D consists of over 15 sequences in 10 scenes, including library, commercial street, coastal runway, football field, landscape garden, etc., with up to $30\\mathrm{k}$ $m^2$ area size and $200\\sim 1,000m$ trajectory length for each sequence. By providing multi-modal capture data and diverse human-scene-related annotations, SLOPER4D opens a new door to benchmark urban-level HPE.", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct extensive experiments to show the superiority of our joint optimization approach for acquiring high-quality 3D pose annotations. Additionally, based on our proposed new dataset, we benchmark two critical tasks: camera-based 3D HPE and LiDAR-based 3D HPE, as well as provide benchmarks for GHPE.", + "bbox": [ + 496, + 257, + 890, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 517, + 348, + 821, + 361 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations.", + "- We propose an effective joint optimization method for acquiring accurate human motions in both local and global by integrating LiDAR SLAM results, IMU poses, and scene constraints.", + "- We benchmark two HPE tasks as well as a GHPE task on SLOPER4D, demonstrating its potential of promoting urban-level 3D HPE research." + ], + "bbox": [ + 517, + 366, + 890, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 550, + 640, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. 3D Human Motion Datasets", + "text_level": 1, + "bbox": [ + 500, + 575, + 751, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many datasets have been proposed with different sensors and setups to facilitate the research on 3D human pose estimation. The H3.6M [16] is a large-size dataset providing synchronized video with optical-based MoCap in studio environments. To perform markerless capture in different indoor scenes, PROX [13] uses an RGB-D sensor to scan a single person. EgoBody [64] uses multiple RGB-D sensors to pre-scan the room and scan the interacting persons. LiDARHuman26M [27] can capture long-range human motions with static LiDAR and IMUs. However, they are limited to static environments, human activities, and interactions. 3DPW [49] is the first dataset providing 3D annotations in the wild which uses a single hand-held RGB camera to optimize human pose from IMUs for a certain period of frames. It doesn't provide accurate global translation and 3D scenes. HPS [12] reconstructs the human body pose using IMUs and self-localizes it with a head-mounted camera in large 3D scenes, but it heavily relies on the pre-built map. HSC4D [5] removes the reliance on the pre-built map and achieves global human motion capture in large scenes.", + "bbox": [ + 496, + 598, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "683", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/b0b82f21ab7a2fe965a1ab877212887ea9a196bb40b53261fa6a1b36c286398c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetIn the wildGlobal3D ScenePoint cloudVideoIMU# Scene# Area size (m2)# Subject# Frame
H3.6M [16]X✓XX✓X-12113.6M
3DPW [49]✓XXX✓✓-< 300751k
PROX [13]X✓✓X✓X12< 302020k
HPS [12]✓✓✓X✓*✓8< 1,00077k
HSC4D [5]✓✓✓✓*X✓5< 5,000210k
LH26M [27]XXX✓✓✓-< 20013184k
EgoBody [64]X✓✓X✓X15< 5020153k
SLOPER4D✓✓✓✓✓✓10< 30,00012100k
", + "bbox": [ + 98, + 88, + 874, + 232 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1. Comparisons with existing datasets. \"Global\" denotes to human poses with global translation. The \"area size\" is estimated with the published data. The * indicates the data modality is only used for human self-localization rather than for human-related data.", + "bbox": [ + 75, + 236, + 893, + 265 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, the camera in HPS and the LiDAR in HSC4D are only used to perceive the environment rather than capture human data. With the scene-aware dataset we proposed for global human pose estimation, we can benchmark the 3D HPE in the wild with the LiDAR or camera modalities.", + "bbox": [ + 75, + 276, + 470, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Human Localization and Scene Mapping", + "text_level": 1, + "bbox": [ + 76, + 361, + 428, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Human self-localization aims at estimating the 6-DoF of the human subject in global coordinates. The image-based methods [21, 37, 52] regress locations directly from a single image with a pre-built map. The scene-specific property makes them hard to generalize to unseen scenes. LiDAR is widely used in Simultaneous Localization and Mapping (SLAM) [4, 28, 41, 62] due to its robustness and low drift. To address the drift problem and improve robustness in dynamic motions, RGB cameras [40, 44, 63], IMU [10, 36, 42], or both [6, 43, 68], have been integrated with the mapping task. Most attention has been paid to autonomous driving [9] [23] or robotics from the third-person view and they usually do not focus on humans. To achieve self-localization, LiDAR is designed as backpacked [20, 31, 54] and handheld [2]. To efficiently capture human motions and reconstruct urban scenes, we utilize LiDAR with a built-in IMU (different from the IMUs for motion capture) and propose a pipeline for constructing multi-modal data. This approach provides accurate information on human motions at both local and global levels, as well as enables mapping in large outdoor environments.", + "bbox": [ + 73, + 383, + 470, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Global 3D Human Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 710, + 382, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most studies recover human meshes in camera coordinate [26, 66] or root-relative poses [18, 24, 25]. Recovering global human motions in unconstrained scenes is a challenging topic in computer vision and has gained more and more research interest in recent years. IMU sensors are widely used in commercial [38, 39] and research activities [15, 48, 51], and are attached to body limbs to capture human motions in studio-environments. But it suffers severe drift in the wild. Some methods rely on additional RGB [8, 34, 49, 50] or pre-scan maps [12], or LiDAR [5] to complement the IMUs in large-scale scenes. Based on", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "human-scene interaction, some work proposed scene-aware solutions using static cameras [14, 60] to obtain accurate and scene-natural human motions. 4DCapture [30] uses a dynamic head-mounted camera to self-localize and reconstruct the scene with the Struct From Motion method. However, it often fails when the illumination changes in the wild. MOVER [60] uses a single camera to optimize the 3D objects in a static scene, resulting in better 3D scene reconstruction and human motions. GLAMR [61] uses global trajectory predictions to constrain both human motions and dynamic camera poses, achieving state-of-the-art results on inthe-wild videos. However, it lacks a benchmark for quantitatively comparing different HPE methods on a global level. To deal with this limitation, we propose SLOPER4D, the first large-scale urban-level human pose dataset with rich 2D/3D annotations.", + "bbox": [ + 496, + 276, + 893, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. SLOPER4D Dataset", + "text_level": 1, + "bbox": [ + 498, + 532, + 694, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SLOPER4D collects scene-aware 4D human data with our body-worn capturing system in urban scenes. In this section, we first introduce the data acquisition in Sec. 3.1, second, we detail the data construction and annotation process in Sec. 3.2, then we introduce the global optimization-based Sec. 3.3 method to obtain high quality both 3D/2D data, finally, we compare our dataset in Sec. 3.4 with the existing datasets and highlight our novelty.", + "bbox": [ + 496, + 559, + 893, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Data Acquisition", + "text_level": 1, + "bbox": [ + 500, + 691, + 666, + 708 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hardware setup. As shown in Fig. 1, during the data collection procedure, the scanning person follows the performer (IMUs wearer) and scans him with a LiDAR and a camera on the helmet. Additionally, Fig. 2 shows the hardware details of our capturing system. Regarding the sensor module, the 128-beams Ouster-os1 LiDAR and the DJI-Action2 camera are rigidly installed on the helmet. To capture raw human motions, we use Noitom's inertial MoCap product, PN Studio, to attach 17 wireless IMUs to the IMU wearer's body limbs, torso, and head. The camera's field of view (FOV) is $116^{\\circ} \\times 84^{\\circ}$ and the LiDAR's FOV is $360^{\\circ} \\times 45^{\\circ}$ . To make the performer within the LiDAR's FOV", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "684", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d9c3d5862253826f16f29b745c027ee5d28526a7f241e730f31bb73b395fddf9.jpg", + "image_caption": [ + "Figure 2. Our capturing system's hardware details. The sensor module includes a LiDAR, a camera, and 17 body-attached IMU sensors. The storage module consists of a NUC11, a receiver, and a battery in the backpack." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 460, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "as much as possible, we tilt the LiDAR down around $45^{\\circ}$ . Regarding the storage module, the scanning person's backpack places a wireless IMU data receiver, a 24V battery, and an Intel NUC11. The mini-computer NUC11 stores IMU data from the wireless receiver and point clouds from LiDAR in real-time. Videos are stored locally in the camera. The LiDAR and NUC11 are both powered by the battery.", + "bbox": [ + 75, + 388, + 467, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Coordinate systems. Let's define three coordinate systems: 1) IMU coordinate system $\\{I\\}$ : the origin is at LiDAR wearer's spine base at the starting time, and the $X / Y / Z$ axis is pointing left/upward/forward of the human. 2) LiDAR Coordinate system $\\{L\\}$ : the origin is at the center of the LiDAR, and the $X / Y / Z$ axis is pointing right/forward/upward of the LiDAR. 3) Global/World coordinate system $\\{W\\}$ : the origin is on the floor of the LiDAR wearer's starting position, and the $X / Y / Z$ axis is pointing right/forward/upward of the LiDAR wearer.", + "bbox": [ + 75, + 500, + 467, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Calibration. Following the setup in [53], we use a chessboard to calibrate the camera intrinsic $K_{in}$ and introduces a terrestrial laser scanner (TLS) to obtain accurate camera extrinsic parameter, $K_{ex}$ . Due to the LiDAR point cloud being too sparse, we manually choose the corresponding points both on the 2D image and the TLS map registered to the point cloud, and then we solve the perspective-n-point (PnP) problem to obtain $K_{in}$ . For every 3D scene, the calibration $R_{WL}$ , which transforms $\\{L\\}$ to $\\{W\\}$ is manually set to make the ground's $z$ -axis upward and height to zero for the starting position. By using singular value decomposition, the calibration $R_{WI}$ , which transforms $\\{I\\}$ to $\\{W\\}$ , is calculated through the similarity between IMU trajectory and LiDAR trajectory on the XY plane.", + "bbox": [ + 75, + 655, + 467, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Synchronization. The synchronization of data from multiple sensors in human subject data is achieved through peak", + "bbox": [ + 75, + 869, + 467, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "detection. Before and after the capture, the subject is asked to perform jumps. Then the peak height time in IMU is automatically detected and the peak times in the LiDAR and camera data are manually identified. Finally, all modalities are aligned by the peaks and downsampled to match the LiDAR frame rate of $20\\mathrm{Hz}$ .", + "bbox": [ + 498, + 90, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Data Processing", + "text_level": 1, + "bbox": [ + 500, + 193, + 660, + 209 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D pose detection. We use Detectron [56] to detect and Deepsort [55] to track humans in videos. However, the tracking often fails due to the IMUs wearer entering/exiting the field of view or occlusions. To solve this problem, we manually assign the same ID for the tracked person in a video sequence. As for 3D point cloud reference, we project them on images according to the $K_{ex}$ . However, due to the jitter brought by dynamic motions, the camera and the Li-DAR are not perfectly rigidly connected. Thus, $K_{ex}$ will be further optimized in Sec. 3.3.", + "bbox": [ + 498, + 220, + 890, + 372 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LiDAR-inertial localization and mapping. The LiDAR-only method often fails in mapping because of the dynamic head rotation and crowded urban environments. Incorporating an IMU can compensate for motion distortion in a LiDAR scan $p^L$ and provide an accurate initial pose. Using a LiDAR with an integrated IMU, and by combining Kalman filter-based lidar-inertial odometry [58] with factor graph-based loop closure optimization [7] [22], we successfully estimate the ego-motion of LiDAR and build the global consistency 3D scene map with n frame point clouds $P_{1:n}^{L} = \\{p_{1}^{L},\\dots ,p_{n}^{L}\\}$ . To provide accurate scene constrain in Sec. 3.3, we utilize the VDB-Fusion [47] to generate a clean scene mesh $S$ that excludes moving objects.", + "bbox": [ + 498, + 376, + 890, + 573 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "IMUs pose estimation. We use SMPL [32] to represent the human body motion $M^{I} = \\varPhi(\\theta^{I}, t^{I}, \\beta) \\in \\mathbb{R}^{6890 \\times 3}$ in IMU coordinate space $\\{I\\}$ , where pose parameter $\\Theta_{1:n}^{I} = \\{\\theta_{1}^{I}, \\dots, \\theta_{n}^{I}\\} \\in \\mathbb{R}^{72 \\times n}$ is composed of pelvis joint's orientation $R_{1:n}^{I} = \\{r_{1}^{I}, \\dots, r_{n}^{I}\\} \\in \\mathbb{R}^{3 \\times n}$ and the other 23 joints' rotation relative to their parent joint. The $T_{1:n}^{I} = \\{t_{1}^{I}, \\dots, r_{n}^{I}\\} \\in \\mathbb{R}^{3 \\times n}$ is the pelvis joint's translation and $\\beta \\in \\mathbb{R}^{10}$ is a constant value representing a person's body shape. $T$ and $\\Theta$ are estimated by the commercial MoCap product, while $\\beta$ is obtained by using IPNet [3] to fit the scanned model captured by an iPhone13 Promax. Since the IMU are accurate locally but drift globally, $T^{I}$ is used for raw calibration of the $\\{I\\}$ to $\\{W\\}$ , and the initial global motion $M = M^{W} = R^{WI}M^{I}$ will be further optimized.", + "bbox": [ + 498, + 577, + 890, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Data Optimization", + "text_level": 1, + "bbox": [ + 500, + 801, + 679, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To obtain precise and scene-plausible human motion $M$ in the world coordinate system, we use scene geometry $S$ with several physico-based terms to perform joint optimizations to find the optimal motion $M^{*}$ that minimize $\\mathcal{L}$ . In a k-frame segment, the optimization is written as:", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "685", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/04ccb905610d26d59ac5e51fe2ff0258171dd73c88349a464f2064cefc6aa1d1.jpg", + "image_caption": [ + "Figure 3. The pipeline of the dataset construction. The capturing system simultaneously collects multimodal data, including LiDAR, camera, and IMU data. Then they are further processed. A joint optimization approach with multiple loss terms is then employed to optimize motion locally and globally. As a result, we obtain rich 2D/3D annotations with accurate global motion and scene information." + ], + "image_footnote": [], + "bbox": [ + 83, + 87, + 472, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/76285f66060c4561ad9dc45d47c7a6fe6ab9c965ff24ce6cbaedf22c18c873c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 477, + 88, + 676, + 422 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ea40a3c9dca492023d2dc292ca2a0b49d3c4fc99b42942540f313fb4866d392f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 681, + 88, + 880, + 422 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM _ {1: k} ^ {*} = \\arg \\min _ {M _ {1: k}} \\mathcal {L} (M _ {1: k}, \\boldsymbol {S}),\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 482, + 303, + 505 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {s m t} + \\lambda_ {s c} \\mathcal {L} _ {s c} + \\lambda_ {p r i} \\mathcal {L} _ {p r i} + \\lambda_ {m 2 p} \\mathcal {L} _ {m 2 p}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 507, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s m t} = \\lambda_ {\\text {t r a n s}} \\mathcal {L} _ {\\text {t r a n s}} + \\lambda_ {\\text {o r i t}} \\mathcal {L} _ {\\text {o r i t}} + \\lambda_ {j t s} \\mathcal {L} _ {j t s},\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 530, + 421, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{smt}$ is a smoothness term, which consists of a translation loss $\\mathcal{L}_{trans}$ , an orientation loss $\\mathcal{L}_{orit}$ , and a joints loss $\\mathcal{L}_{jts}$ . $\\mathcal{L}_{sc}$ is a scene-aware-contact term, $\\mathcal{L}_{pri}$ is a pose prior term, and $\\mathcal{L}_{m2p}$ is a mesh-to-points term. The $\\lambda_{sc}, \\lambda_{pri}, \\lambda_{trans}, \\lambda_{orit}, \\lambda_{jts}$ , and $\\lambda_{m2p}$ are loss terms' coefficients. $\\mathcal{L}$ is minimized with a gradient descent algorithm.", + "bbox": [ + 76, + 553, + 468, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Smoothness term. The objective of this term is to minimize the acceleration of the pelvis joint, the accelerations of the other 23 pelvis-relative joints, which is denoted as $J_{1:k} = \\{j_1,\\dots ,j_k\\} \\in \\mathbb{R}^{69\\times k}$ , and the angular velocity of all joints to smooth human movements.", + "bbox": [ + 76, + 647, + 468, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Scene-aware contact term. we compare the movement of every foot vertices in IMU motions $M_{k}^{I}$ and label the foot as stable if its velocity is less than $0.1 \\, m/s^2$ . Finally, the Chamfer Distance (CD) between this foot and its closest surface is expressed as the scene contact loss $\\mathcal{L}_{sc}$ .", + "bbox": [ + 75, + 727, + 470, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pose prior term. The poses estimated by IMUs are roughly accurate but will likely cause some misalignments to the end of the body limb due to the accumulating error. Hence, $\\mathcal{L}_{\\text {prior }}$ is used to constrain the $\\Theta$ close to the initial value at the beginning of the optimization.", + "bbox": [ + 75, + 806, + 468, + 881 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Mesh-to-points term. The point cloud $p^L$ from the mov", + "bbox": [ + 76, + 885, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ing LiDAR provides strong prior depth information. However, though the SMPL mesh is watertight and complete, the human points are sparse and partial, which makes the registration methods such as ICP, not ideal as expected. To address this issue, we propose a viewpoint-based mesh-to-point loss function $\\mathcal{L}_{m2p}$ . First, we remove the hidden SMPL mesh faces from the LiDAR's viewpoint. Then we sample points, denoted as $P_{1:k}^{\\prime} = \\{p_{1}^{\\prime},\\dots ,p_{k}^{\\prime}\\}$ , from the remaining faces by LiDAR resolution. The loss is defined as the Chamfer Distance from $P_{1:k}^{\\prime}$ to $P_{1:k}$ .", + "bbox": [ + 496, + 488, + 890, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All loss terms functions are detailed as follows:", + "bbox": [ + 519, + 643, + 834, + 657 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t r a n s} = \\frac {1}{k - 2} \\sum_ {i = 1} ^ {k - 2} \\| t _ {i + 2} - 2 t _ {i + 1} + t _ {i} \\| _ {2} ^ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 681, + 838, + 722 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {j t s} = \\frac {1}{k - 2} \\sum_ {i = 1} ^ {k - 2} \\| \\mathcal {J} _ {i + 2} - 2 \\mathcal {J} _ {i + 1} + \\mathcal {J} _ {i} \\| _ {2} ^ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 724, + 823, + 767 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o r i t}} = \\frac {1}{k - 1} \\sum_ {i = 1} ^ {k - 1} \\| r _ {i + 1} - r _ {i} \\| _ {2} ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 770, + 890, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p r i} = \\frac {1}{k} \\sum_ {i = 1} ^ {k} \\| \\theta_ {i} - R ^ {W I} \\theta_ {i} ^ {I} \\| _ {2} ^ {2},\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 814, + 761, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m 2 p} = \\frac {1}{k} \\sum_ {i = 1} ^ {k} \\sum_ {\\hat {p ^ {\\prime}} \\in p _ {i} ^ {\\prime}} \\frac {1}{| p _ {i} ^ {\\prime} |} \\min _ {\\hat {p} \\in p _ {i}} \\| \\hat {p} - \\hat {p ^ {\\prime}} \\| _ {2} ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 859, + 828, + 904 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "686", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ef098b021f375666ddff575fc506701a85afc40d4312063b785bdcf20ccf84bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 90, + 486, + 263 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/86cf44f94a386a2517ad9562bfe004d8c857dee158b09df98acb986915400084.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 90, + 883, + 263 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9fa2b9dfe264a43fb76fbaabb17243c8c627e5d3e00ec9a1c57c6e11684ad35d.jpg", + "image_caption": [ + "Figure 4. The diverse scenes and activities of our dataset. The images in the left column are our reconstructed scenes with human trajectories overlaid on them. The right images are the SMPL meshes overlaid on images / point clouds / scenes." + ], + "image_footnote": [], + "bbox": [ + 83, + 265, + 486, + 438 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/afa4bf9ca6b3318db4901c9d382de52267a23ecb48884a91f913ad028a9b4db0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 265, + 883, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Camera extrinsic optimization. We aim to optimize extrinsic parameters $K_{ex}$ for every frame by minimizing the $\\mathcal{L}_{cam}$ , which comprises of the keypoints loss $\\mathcal{L}_{kpt}$ and the bounding box loss $\\mathcal{L}_{box}$ . The $\\mathcal{L}_{kpt}$ measures the mean square error between the 2D human keypoints $kpt^{2d}$ in the image and the 3D human keypoints $kpt^{3d}$ of the optimized SMPL model projected to the image with $K_{ex}$ ; the $\\mathcal{L}_{box}$ computes the Intersection over Union loss between the 2D human bounding box $box^{2d}$ in the image and the 3D human bounding box $box^{3d}$ projected to the image with $K_{ex}$ .", + "bbox": [ + 75, + 491, + 468, + 642 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nK _ {e x} ^ {*} = \\arg \\min _ {K _ {e x} \\in S E (3)} \\mathcal {L} _ {c a m} (K _ {e x}),\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 647, + 380, + 670 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c a m} = \\lambda_ {k p t} \\mathcal {L} _ {k p t} \\left(k p t ^ {3 d}, k p t ^ {2 d}, K _ {e x}\\right) + \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 672, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {b o x} \\mathcal {L} _ {b o x} \\left(b o x ^ {3 d}, b o x ^ {2 d}, K _ {e x}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 694, + 398, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{kpt}$ and $\\lambda_{box}$ are constant coefficients.", + "bbox": [ + 76, + 719, + 382, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Dataset Comparison", + "text_level": 1, + "bbox": [ + 76, + 741, + 269, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SLOPER4D is the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations for GHPE. The head-mounted LiDAR and camera are utilized to simultaneously record the IMU-wearer's activities, including running outside, playing football, visiting, reading, climbing/descending stairs, discussing, borrowing a book, greeting, etc. The dataset consists of 15 sequences from 12 human subjects in 10 locations. There are a total of $100\\mathrm{k}$ LiDAR frames, $300\\mathrm{k}$ video", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "frames, and 500k IMU-based motion frames captured over a total distance of more than $8km$ and an area of up to $30,000m^2$ . The results of our dataset are shown in Fig. 4.", + "bbox": [ + 498, + 491, + 890, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For the captured person, we provide the segmentation of 3D points from LiDAR frames and 2D bounding boxes from images synchronized with LiDAR. We also provide 3D pose annotations with SMPL format. Compared to other datasets Tab. 1, it is worth mentioning that SLOPER4D provides the 3D scene reconstructions and accurate global translation annotations, allowing us to quantitatively study the scene-aware global pose estimation from both LiDAR and monocular videos. In addition to the dense 3D point cloud map reconstructed from the LiDAR, SLOPER4D provides the high-precision colorful point cloud map from a Terrestrial Laser Scanner (Trimble TX5) for better visualization and map comparison.", + "bbox": [ + 496, + 537, + 892, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 752, + 633, + 770 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we first evaluate SLOPER4D Dataset qualitatively, indicating that our dataset is solid enough to benchmark new tasks. Then we perform a cross-dataset evaluation to further assess our dataset's novelty on two tasks: LiDAR-based 3D HPE and camera-based 3D HPE. Finally, we introduce the new benchmark, GHPE, and perform experiments on GLAMR. More quantitative evaluations and experiments are in the supplementary material.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "687", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fbb75deec27903f44dedf109f36eb64ccb51ecb64e98f0e4cc5980d12c14992d.jpg", + "image_caption": [ + "Figure 5. Comparison between our optimization results (red SMPL) and the ICP results (green SMPL). It shows the red SMPL aligns better with the cyan human points than the green SMPL." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 460, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dbdbd32f01d1bf40adce58c6a94b4aafe4d31f01e600cb1c73a31f99e0902694.jpg", + "image_caption": [ + "Figure 6. The comparison before (left) and after (right) extrinsic optimization by projecting the point clouds (upper) and SMPL (lower) are projected onto the image." + ], + "image_footnote": [], + "bbox": [ + 78, + 287, + 460, + 457 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training/Test splits. We split our data into training and test sets for LiDAR/Camera-based pose estimation. The training set of SLOPER4D contains eleven sequences of data with a total of 80k LiDAR frames and corresponding RGB frames. The test set has four sequences of data with around 20k LiDAR frames and corresponding RGB frames. For global pose estimation, we select three challenging scenarios for evaluation. The first one is a single-person football training scenario with highly dynamic motions. The second one is running along a coastal runway. The third one is a garden tour involving daily motions.", + "bbox": [ + 75, + 517, + 468, + 683 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation metrics. For 3D HPE, we employ Mean per joint position error (MPJPE) and Procrustes-aligned MPJPE (PA-MPJPE) for evaluation. MPJPE is the mean euclidean distance between the ground-truth and predicted joints. PA-MPJPE first aligns the predicted joints to the ground-truth joints by carrying out rigid transformation based on Procrustes analysis and then calculates MPJPE. For global trajectory evaluation, we utilize Absolute Trajectory Error (ATE) and the Relative Pose (the pose refers to orientation here) Error (RPE) in visual SLAM systems [11], where the ATE is well-suited for measuring the global localization and, in contrast, the RPE is suitable for measuring the system's drift, for example, the drift per second. Global MPJPE (G-MPJPE) is MPJPE calculated by placing the", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SMPL model in the global coordinates.", + "bbox": [ + 498, + 90, + 759, + 106 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative evaluation. For the human pose qualitative evaluation, we project the SMPL to the image and visualize the 3D human with corresponding LiDAR points in 3D space (shown in Fig. 4). The results demonstrate that the 3D human mesh aligns well with 3D environments and 2D images. As a large-scale urban-level human pose dataset, SLOPER4D provides multi-modal capture data and rich human-scene annotations, as well as diverse challenging human activities in large scenes. To evaluate our optimization method, we first compare our method with the results from ICP. As shown in Fig. 5, the scene-aware constraints and human mesh-to-points constraint efficiently optimize the local poses, global translation, and even the orientation error from IMU. To show the effectiveness of the camera extrinsic optimization, we report the results in Fig. 6. The 2D projecting error was visually lowered after optimization.", + "bbox": [ + 496, + 109, + 893, + 351 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Cross-Dataset Evaluation", + "text_level": 1, + "bbox": [ + 500, + 361, + 732, + 375 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ac3ee26f7c22d2b09f00ba4b7cb00e5ae198a95c5c825002029fe34367c73cc7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Test TrainLH26MOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
LH26M79.367.0228.7149.9
Ours212.3128.386.165.1
LH26M + Ours85.572.079.260.1
", + "bbox": [ + 501, + 393, + 890, + 457 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/02d3326f481190f291363e05c13ca41e10ffb8b5aecae9000954bbbacdb698e8.jpg", + "table_caption": [ + "(a) LiDAR-based 3D pose estimation with LiDARCap [27]." + ], + "table_footnote": [], + "table_body": "
Test Train3DPWOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
VIBE [24]93.556.5102.566.2
Ours + AMASS124.366.886.652.4
w. 3DPW83.052.090.058.3
HbryIK [26]88.749.3104.957.0
w. Ours87.349.267.644.2
w. 3DPW71.341.875.850.0
w. 3DPW + Ours76.446.766.242.8
", + "bbox": [ + 501, + 479, + 890, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(b) Camera-based 3D pose estimation.", + "bbox": [ + 594, + 590, + 795, + 602 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Cross-dataset evaluation results with different modalities. The LH26M in (a) refers to LiDARHuman26M dataset from LiDARcap. VIBE is pre-trained on AMASS [33], MPI-INF-3DHP [35] InstaVariety [19], PoseTrack [1], PennAction [65]. HbryIK is pre-trained on H36M, MPI-INF-3DHP, MSCOCO [29]", + "bbox": [ + 496, + 611, + 890, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate root-relative 3D human pose estimation with different modalities, namely the LiDAR and the camera. 3DPW is an in-the-wild human motion dataset that is most related to us. With VIBE, we cross-evaluated our dataset's camera modal by using 3DPW. LiDARHuman26M is a lidar-based dataset for long-range human pose estimation. We can cross-evaluate our dataset's LiDAR modal with it. Tab. 2(a) shows the evaluation results on LiDAR-based 3D pose estimation task and Tab. 2(b) shows the results on camera-based 3D pose estimation. Taking the results from Tab. 2(a), for example, when the model is trained from another dataset only, the errors are the largest. But the error will be further reduced by around $60\\%$ when training on LiDARHuman26M and our dataset together. It", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "688", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "suggests a domain gap exists between different LiDAR sensors, and both datasets complement each other. The results of another task show that the pre-trained VIBE model generalizes better on 3DPW than on our dataset. But the error on 3DPW increases when finetuned on our dataset, while the error decreases on our dataset. This suggests that the pre-trained model complements SLOPER4D better than the opposite. Comparing the results across different modalities, the error on our dataset from the method trained on mixed LiDAR point cloud datasets is $13\\%$ lower than the method trained on the images.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Benchmark on Global Human Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 265, + 468, + 279 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6ec0a646892b6d691bd5fba50a2ca95e58ae21de0064757ff51b110a13e9c82d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SequenceMetricRMSE ↓meanstd.max
FootballATE3.262.851.5811.83
Running001ATE29.4825.5514.7256.07
Garden001ATE2.862.571.266.55
FootballRPE0.080.060.051.34
Running001RPE0.400.350.191.04
Garden001RPE0.060.040.040.71
", + "bbox": [ + 93, + 285, + 454, + 392 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f1141d6ae8680c3d74c3cfb3eed0fe766c72be70d271110d3c8e00dc9c745d98.jpg", + "table_caption": [ + "Table 3. Global trajectory evaluation of GLAMR. Unit: $m$ ." + ], + "table_footnote": [], + "table_body": "
SequenceScaleMPJPE ↓PA-MPJPE ↓G-MPJPE ↓
Football11.83264.6118.55268.7
Running00156.07652.1119.632329.3
Garden0016.55139.486.34407.0
", + "bbox": [ + 84, + 424, + 460, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. GHPE results from GLAMR. Unit: mm.", + "bbox": [ + 124, + 492, + 421, + 505 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b3db3b305a3a55fddfa5f97dbfa47cd2f0ab450d82362e7ea0c297f26e4f5ab6.jpg", + "image_caption": [ + "Figure 7. The ATE error $(m)$ mapped on the GT trajectory. The color represents the error according to the color bar." + ], + "image_footnote": [], + "bbox": [ + 81, + 517, + 460, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this subsection, we benchmark the GHPE task of GLAMR [61] on SLOPER4D. GLAMR is a global occlusion-aware method for 3D global human mesh recovery from dynamic monocular cameras. For the scale uncertainty of the monocular camera, we compute the affine matrix from the estimated trajectory to the ground truth trajectory and rotate, translate and scale the estimated trajectory before error computation.", + "bbox": [ + 75, + 750, + 467, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 reports the global trajectory error with ATE and RPE, Tab. 4 reports the global human pose metric, and", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Fig. 7 shows the ATE error mapped on GT trajectory. Comparing the results on the three scenes, the football and Garden001 have a significantly lower RPE in the global scene. In comparison, GLAMR performs the worst on the running scene, with an ATE's RMSE of $29.48\\mathrm{m}$ . This scene has the largest area size and the highest human pace. GLAMR achieves a low PA-MPJPE of $86.3\\mathrm{mm}$ on Garden001, a sequence with daily walking and visiting motions. It's the first time that we have tested the GPHE on such large outdoor scenes. GLAMR achieves relatively better results on daily human motion while performing worse on high-dynamic activities in the wild. The interesting point is that the trajectory tendency is pretty similar to the reference, even in dynamic football training motions, which demonstrates the ability of GLAMR to be a baseline. It is expected that more research will focus on GHPE in real-world interactive scenarios, and the experiments show our SLOPER4D's potential to promote urban-level GHPE research.", + "bbox": [ + 496, + 90, + 890, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussions", + "text_level": 1, + "bbox": [ + 500, + 388, + 620, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. Firstly, SLOPER4D is limited to single-person capture though it perceives multiple-person data. Secondly, the camera and LiDAR are not synchronized online, causing tedious offline work if the camera loses frames even with a low time offset ( $< 50~ms$ ). Finally, texture information from the camera is not fully exploited for color and texture reconstruction of scenes and humans. In our future work, we will propose an online synchronization algorithm and extend our work to multiple-person capturing.", + "bbox": [ + 496, + 420, + 890, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusions. We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations. Based on our proposed new dataset, we benchmark two critical tasks, camera-based 3D HPE and LiDAR-based 3D HPE. SLOPER4D also benchmarks the GHPE task. The results demonstrate the potential of SLOPER4D in boosting the development of these areas. Our work contributes to extending motion capture to large global scenes based on the current methods and datasets. We hope this work will foster future creation and interaction in urban environments.", + "bbox": [ + 496, + 564, + 890, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported in part by the Natural Science Foundation of China (No.62171393), the Fundamental Research Funds for the Central Universities (No.20720220064), FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003), and NSFC (No.62206173). We thank Zhiyong Wang for helping us incorporate FAST-LIO2 into our mapping system. 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IEEE, 2019. 3" + ], + "bbox": [ + 501, + 92, + 893, + 386 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "692", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SLOPER4D_ A Scene-Aware Dataset for Global 4D Human Pose Estimation in Urban Environments/6eb8c194-2d4e-4f05-826e-be6c8b0450e0_model.json b/2023/SLOPER4D_ A Scene-Aware Dataset for Global 4D Human Pose Estimation in Urban Environments/6eb8c194-2d4e-4f05-826e-be6c8b0450e0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..17521488a07cc0a066e471ec51bcd4faf28c50e8 --- /dev/null +++ b/2023/SLOPER4D_ A Scene-Aware Dataset for Global 4D Human Pose Estimation in Urban Environments/6eb8c194-2d4e-4f05-826e-be6c8b0450e0_model.json @@ -0,0 +1,2477 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.089, + 0.131, + 0.882, + 0.175 + ], + "angle": 0, + "content": "SLOPER4D: A Scene-Aware Dataset for Global 4D Human Pose Estimation in Urban Environments" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.202, + 0.21, + 0.221 + ], + "angle": 0, + "content": "Yudi Dai\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.222, + 0.287, + 0.24 + ], + "angle": 0, + "content": "Hongwei Yi4" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.204, + 0.362, + 0.221 + ], + "angle": 0, + "content": "Yitai Lin1,2" + }, + { + "type": "text", + "bbox": [ + 0.35, + 0.222, + 0.445, + 0.24 + ], + "angle": 0, + "content": "Siqi Shen1,2" + }, + { + "type": "text", + "bbox": [ + 0.424, + 0.204, + 0.531, + 0.222 + ], + "angle": 0, + "content": "Xiping Lin1,2" + }, + { + "type": "text", + "bbox": [ + 0.592, + 0.204, + 0.726, + 0.222 + ], + "angle": 0, + "content": "Chenglu Wen\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.782, + 0.204, + 0.851, + 0.221 + ], + "angle": 0, + "content": "Lan \\(\\mathbf{X}\\mathbf{u}^3\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.222, + 0.604, + 0.239 + ], + "angle": 0, + "content": "Yuexin Ma" + }, + { + "type": "text", + "bbox": [ + 0.667, + 0.222, + 0.788, + 0.24 + ], + "angle": 0, + "content": "Cheng Wang\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.246, + 0.834, + 0.265 + ], + "angle": 0, + "content": "\\(^{1}\\) Fujian Key Laboratory of Sensing and Computing for Smart Cities, Xiamen University" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.265, + 0.88, + 0.283 + ], + "angle": 0, + "content": "\\(^{2}\\) Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education" + }, + { + "type": "text", + "bbox": [ + 0.28, + 0.283, + 0.69, + 0.299 + ], + "angle": 0, + "content": "of China, School of Informatics, Xiamen University" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.299, + 0.369, + 0.318 + ], + "angle": 0, + "content": "\\(^{3}\\)ShanghaiTech University, China" + }, + { + "type": "text", + "bbox": [ + 0.421, + 0.3, + 0.86, + 0.318 + ], + "angle": 0, + "content": "4Max Planck Institute for Intelligent Systems, Germany" + }, + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.339, + 0.262, + 0.351 + ], + "angle": 0, + "content": "LiDAR Camera IMUs" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.353, + 0.278, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.132, + 0.562, + 0.248, + 0.575 + ], + "angle": 0, + "content": "Capturing System" + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.332, + 0.871, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.474, + 0.562, + 0.686, + 0.574 + ], + "angle": 0, + "content": "Global Human Motion and Scene" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.583, + 0.89, + 0.613 + ], + "angle": 0, + "content": "Figure 1. Using the head-mounted LiDAR and camera to scan the IMUs wearer, we construct SLOPER4D, a large scene-aware dataset for global 4D human pose estimation in urban environments." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.625, + 0.314, + 0.64 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.659, + 0.47, + 0.87 + ], + "angle": 0, + "content": "We present SLOPER4D, a novel scene-aware dataset collected in large urban environments to facilitate the research of global human pose estimation (GHPE) with human-scene interaction in the wild. Employing a head-mounted device integrated with a LiDAR and camera, we record 12 human subjects' activities over 10 diverse urban scenes from an egocentric view. Frame-wise annotations for 2D key points, 3D pose parameters, and global translations are provided, together with reconstructed scene point clouds. To obtain accurate 3D ground truth in such large dynamic scenes, we propose a joint optimization method to fit local SMPL meshes to the scene and fine-tune the camera calibration during dynamic motions frame by frame, resulting in plausible and scene-natural 3D human poses. Even" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.626, + 0.892, + 0.822 + ], + "angle": 0, + "content": "tually, SLOPER4D consists of 15 sequences of human motions, each of which has a trajectory length of more than 200 meters (up to 1,300 meters) and covers an area of more than \\(200\\mathrm{m}^2\\) (up to \\(30,000\\mathrm{m}^2\\)), including more than 100k LiDAR frames, 300k video frames, and 500k IMU-based motion frames. With SLOPER4D, we provide a detailed and thorough analysis of two critical tasks, including camera-based 3D HPE and LiDAR-based 3D HPE in urban environments, and benchmark a new task, GHPE. The in-depth analysis demonstrates SLOPER4D poses significant challenges to existing methods and produces great research opportunities. The dataset and code are released at http://www.lidarhumanmotion.net/sloper4d/." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.83, + 0.631, + 0.845 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Urban-level human motion capture is attracting more and more attention, which targets acquiring consecutive fine-grained human pose representations, such as 3D skeletons" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "682" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.212 + ], + "angle": 0, + "content": "and parametric mesh models, with accurate global locations in the physical world. It is essential for human action recognition, social-behavioral analysis, and scene perception and further benefits many downstream applications, including Augmented/Virtual Reality, simulation, autonomous driving, smart city, sociology, etc. However, capturing extra large-scale dynamic scenes and annotating detailed 3D representations for humans with diverse poses is not trivial." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.474, + 0.548 + ], + "angle": 0, + "content": "Over the past decades, a large number of datasets and benchmarks have been proposed and have greatly promoted the research in 3D human pose estimation (HPE). They can be divided into two main categories according to the capture environment. The first class usually leverages marker-based systems [16, 33, 45], cameras [14, 59, 60], or RGB-D sensors [13, 64] to capture human local poses in constrained environments. However, the optical system is sensitive to light and lacks depth information, making it unstable in outdoor scenes and difficult to provide global translations, and the RGB-D sensor has limited range and could not work outdoors. The second class [39, 49] attempts to take advantage of body-mounted IMUs to capture occlusion-free 3D poses in free environments. However, IMUs suffer from severe drift for long-term capturing, resulting in misalignments with the human body. Then, some methods exploit additional sensors, such as RGB camera [17], RGB-D camera [46, 57, 67], or LiDAR [27] to alleviate the problem and make obvious improvement. However, they all focus on HPE without considering the scene constraints, which are limited in reconstructing human-scene integrated digital urban and human-scene natural interactions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.471, + 0.732 + ], + "angle": 0, + "content": "To capture human pose and related static scenes simultaneously, some studies use wearable IMUs and body-mounted camera [12] or LiDAR [5] to register the human in large real scenarios and they are promising for capturing human-involved real-world scenes. However, human pose and scene are decoupled in these works due to the ego view, where auxiliary visual sensors are used for collecting the scene data while IMUs are utilized for obtaining the 3D pose. Different from them, we propose a novel setting for human-scene capture with wearable IMUs and global-view LiDAR and camera, which can provide multi-modal data for more accurate 3D HPE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a huge scene-aware dataset for sequential human pose estimation in urban environments, named SLOPER4D. To our knowledge, it is the first urban-level 3D HPE dataset with multi-modal capture data, including calibrated and synchronized IMU measurements, LiDAR point clouds, and images for each subject. Moreover, the dataset provides rich annotations, including 3D poses, SMPL [32] models and locations in the world coordinate system, 2D poses and bounding boxes in the image coordinate system, and reconstructed 3D scene mesh. In particular, we propose a joint optimization method for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "obtaining accurate and natural human motion representations by utilizing multi-sensor complementation and scene constraints, which also benefit global localization and camera calibration in the dynamic acquisition process. Furthermore, SLOPER4D consists of over 15 sequences in 10 scenes, including library, commercial street, coastal runway, football field, landscape garden, etc., with up to \\(30\\mathrm{k}\\) \\(m^2\\) area size and \\(200\\sim 1,000m\\) trajectory length for each sequence. By providing multi-modal capture data and diverse human-scene-related annotations, SLOPER4D opens a new door to benchmark urban-level HPE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.348 + ], + "angle": 0, + "content": "We conduct extensive experiments to show the superiority of our joint optimization approach for acquiring high-quality 3D pose annotations. Additionally, based on our proposed new dataset, we benchmark two critical tasks: camera-based 3D HPE and LiDAR-based 3D HPE, as well as provide benchmarks for GHPE." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.349, + 0.822, + 0.362 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.367, + 0.892, + 0.41 + ], + "angle": 0, + "content": "- We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.422, + 0.892, + 0.481 + ], + "angle": 0, + "content": "- We propose an effective joint optimization method for acquiring accurate human motions in both local and global by integrating LiDAR SLAM results, IMU poses, and scene constraints." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.492, + 0.892, + 0.537 + ], + "angle": 0, + "content": "- We benchmark two HPE tasks as well as a GHPE task on SLOPER4D, demonstrating its potential of promoting urban-level 3D HPE research." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.367, + 0.892, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.642, + 0.567 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.576, + 0.752, + 0.591 + ], + "angle": 0, + "content": "2.1. 3D Human Motion Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Many datasets have been proposed with different sensors and setups to facilitate the research on 3D human pose estimation. The H3.6M [16] is a large-size dataset providing synchronized video with optical-based MoCap in studio environments. To perform markerless capture in different indoor scenes, PROX [13] uses an RGB-D sensor to scan a single person. EgoBody [64] uses multiple RGB-D sensors to pre-scan the room and scan the interacting persons. LiDARHuman26M [27] can capture long-range human motions with static LiDAR and IMUs. However, they are limited to static environments, human activities, and interactions. 3DPW [49] is the first dataset providing 3D annotations in the wild which uses a single hand-held RGB camera to optimize human pose from IMUs for a certain period of frames. It doesn't provide accurate global translation and 3D scenes. HPS [12] reconstructs the human body pose using IMUs and self-localizes it with a head-mounted camera in large 3D scenes, but it heavily relies on the pre-built map. HSC4D [5] removes the reliance on the pre-built map and achieves global human motion capture in large scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "683" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.089, + 0.875, + 0.233 + ], + "angle": 0, + "content": "
DatasetIn the wildGlobal3D ScenePoint cloudVideoIMU# Scene# Area size (m2)# Subject# Frame
H3.6M [16]X✓XX✓X-12113.6M
3DPW [49]✓XXX✓✓-< 300751k
PROX [13]X✓✓X✓X12< 302020k
HPS [12]✓✓✓X✓*✓8< 1,00077k
HSC4D [5]✓✓✓✓*X✓5< 5,000210k
LH26M [27]XXX✓✓✓-< 20013184k
EgoBody [64]X✓✓X✓X15< 5020153k
SLOPER4D✓✓✓✓✓✓10< 30,00012100k
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.237, + 0.894, + 0.266 + ], + "angle": 0, + "content": "Table 1. Comparisons with existing datasets. \"Global\" denotes to human poses with global translation. The \"area size\" is estimated with the published data. The * indicates the data modality is only used for human self-localization rather than for human-related data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.471, + 0.353 + ], + "angle": 0, + "content": "However, the camera in HPS and the LiDAR in HSC4D are only used to perceive the environment rather than capture human data. With the scene-aware dataset we proposed for global human pose estimation, we can benchmark the 3D HPE in the wild with the LiDAR or camera modalities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.362, + 0.429, + 0.379 + ], + "angle": 0, + "content": "2.2. Human Localization and Scene Mapping" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.385, + 0.471, + 0.702 + ], + "angle": 0, + "content": "Human self-localization aims at estimating the 6-DoF of the human subject in global coordinates. The image-based methods [21, 37, 52] regress locations directly from a single image with a pre-built map. The scene-specific property makes them hard to generalize to unseen scenes. LiDAR is widely used in Simultaneous Localization and Mapping (SLAM) [4, 28, 41, 62] due to its robustness and low drift. To address the drift problem and improve robustness in dynamic motions, RGB cameras [40, 44, 63], IMU [10, 36, 42], or both [6, 43, 68], have been integrated with the mapping task. Most attention has been paid to autonomous driving [9] [23] or robotics from the third-person view and they usually do not focus on humans. To achieve self-localization, LiDAR is designed as backpacked [20, 31, 54] and handheld [2]. To efficiently capture human motions and reconstruct urban scenes, we utilize LiDAR with a built-in IMU (different from the IMUs for motion capture) and propose a pipeline for constructing multi-modal data. This approach provides accurate information on human motions at both local and global levels, as well as enables mapping in large outdoor environments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.383, + 0.727 + ], + "angle": 0, + "content": "2.3. Global 3D Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Most studies recover human meshes in camera coordinate [26, 66] or root-relative poses [18, 24, 25]. Recovering global human motions in unconstrained scenes is a challenging topic in computer vision and has gained more and more research interest in recent years. IMU sensors are widely used in commercial [38, 39] and research activities [15, 48, 51], and are attached to body limbs to capture human motions in studio-environments. But it suffers severe drift in the wild. Some methods rely on additional RGB [8, 34, 49, 50] or pre-scan maps [12], or LiDAR [5] to complement the IMUs in large-scale scenes. Based on" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.895, + 0.519 + ], + "angle": 0, + "content": "human-scene interaction, some work proposed scene-aware solutions using static cameras [14, 60] to obtain accurate and scene-natural human motions. 4DCapture [30] uses a dynamic head-mounted camera to self-localize and reconstruct the scene with the Struct From Motion method. However, it often fails when the illumination changes in the wild. MOVER [60] uses a single camera to optimize the 3D objects in a static scene, resulting in better 3D scene reconstruction and human motions. GLAMR [61] uses global trajectory predictions to constrain both human motions and dynamic camera poses, achieving state-of-the-art results on inthe-wild videos. However, it lacks a benchmark for quantitatively comparing different HPE methods on a global level. To deal with this limitation, we propose SLOPER4D, the first large-scale urban-level human pose dataset with rich 2D/3D annotations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.534, + 0.696, + 0.55 + ], + "angle": 0, + "content": "3. SLOPER4D Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.894, + 0.683 + ], + "angle": 0, + "content": "SLOPER4D collects scene-aware 4D human data with our body-worn capturing system in urban scenes. In this section, we first introduce the data acquisition in Sec. 3.1, second, we detail the data construction and annotation process in Sec. 3.2, then we introduce the global optimization-based Sec. 3.3 method to obtain high quality both 3D/2D data, finally, we compare our dataset in Sec. 3.4 with the existing datasets and highlight our novelty." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.692, + 0.667, + 0.709 + ], + "angle": 0, + "content": "3.1. Data Acquisition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Hardware setup. As shown in Fig. 1, during the data collection procedure, the scanning person follows the performer (IMUs wearer) and scans him with a LiDAR and a camera on the helmet. Additionally, Fig. 2 shows the hardware details of our capturing system. Regarding the sensor module, the 128-beams Ouster-os1 LiDAR and the DJI-Action2 camera are rigidly installed on the helmet. To capture raw human motions, we use Noitom's inertial MoCap product, PN Studio, to attach 17 wireless IMUs to the IMU wearer's body limbs, torso, and head. The camera's field of view (FOV) is \\(116^{\\circ} \\times 84^{\\circ}\\) and the LiDAR's FOV is \\(360^{\\circ} \\times 45^{\\circ}\\). To make the performer within the LiDAR's FOV" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "684" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.462, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.47, + 0.386 + ], + "angle": 0, + "content": "Figure 2. Our capturing system's hardware details. The sensor module includes a LiDAR, a camera, and 17 body-attached IMU sensors. The storage module consists of a NUC11, a receiver, and a battery in the backpack." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.39, + 0.468, + 0.496 + ], + "angle": 0, + "content": "as much as possible, we tilt the LiDAR down around \\(45^{\\circ}\\). Regarding the storage module, the scanning person's backpack places a wireless IMU data receiver, a 24V battery, and an Intel NUC11. The mini-computer NUC11 stores IMU data from the wireless receiver and point clouds from LiDAR in real-time. Videos are stored locally in the camera. The LiDAR and NUC11 are both powered by the battery." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.468, + 0.651 + ], + "angle": 0, + "content": "Coordinate systems. Let's define three coordinate systems: 1) IMU coordinate system \\(\\{I\\}\\): the origin is at LiDAR wearer's spine base at the starting time, and the \\(X / Y / Z\\) axis is pointing left/upward/forward of the human. 2) LiDAR Coordinate system \\(\\{L\\}\\): the origin is at the center of the LiDAR, and the \\(X / Y / Z\\) axis is pointing right/forward/upward of the LiDAR. 3) Global/World coordinate system \\(\\{W\\}\\): the origin is on the floor of the LiDAR wearer's starting position, and the \\(X / Y / Z\\) axis is pointing right/forward/upward of the LiDAR wearer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.468, + 0.867 + ], + "angle": 0, + "content": "Calibration. Following the setup in [53], we use a chessboard to calibrate the camera intrinsic \\( K_{in} \\) and introduces a terrestrial laser scanner (TLS) to obtain accurate camera extrinsic parameter, \\( K_{ex} \\). Due to the LiDAR point cloud being too sparse, we manually choose the corresponding points both on the 2D image and the TLS map registered to the point cloud, and then we solve the perspective-n-point (PnP) problem to obtain \\( K_{in} \\). For every 3D scene, the calibration \\( R_{WL} \\), which transforms \\( \\{L\\} \\) to \\( \\{W\\} \\) is manually set to make the ground's \\( z \\)-axis upward and height to zero for the starting position. By using singular value decomposition, the calibration \\( R_{WI} \\), which transforms \\( \\{I\\} \\) to \\( \\{W\\} \\), is calculated through the similarity between IMU trajectory and LiDAR trajectory on the XY plane." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Synchronization. The synchronization of data from multiple sensors in human subject data is achieved through peak" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "detection. Before and after the capture, the subject is asked to perform jumps. Then the peak height time in IMU is automatically detected and the peak times in the LiDAR and camera data are manually identified. Finally, all modalities are aligned by the peaks and downsampled to match the LiDAR frame rate of \\(20\\mathrm{Hz}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.194, + 0.661, + 0.21 + ], + "angle": 0, + "content": "3.2. Data Processing" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.222, + 0.892, + 0.373 + ], + "angle": 0, + "content": "2D pose detection. We use Detectron [56] to detect and Deepsort [55] to track humans in videos. However, the tracking often fails due to the IMUs wearer entering/exiting the field of view or occlusions. To solve this problem, we manually assign the same ID for the tracked person in a video sequence. As for 3D point cloud reference, we project them on images according to the \\( K_{ex} \\). However, due to the jitter brought by dynamic motions, the camera and the Li-DAR are not perfectly rigidly connected. Thus, \\( K_{ex} \\) will be further optimized in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.377, + 0.892, + 0.574 + ], + "angle": 0, + "content": "LiDAR-inertial localization and mapping. The LiDAR-only method often fails in mapping because of the dynamic head rotation and crowded urban environments. Incorporating an IMU can compensate for motion distortion in a LiDAR scan \\( p^L \\) and provide an accurate initial pose. Using a LiDAR with an integrated IMU, and by combining Kalman filter-based lidar-inertial odometry [58] with factor graph-based loop closure optimization [7] [22], we successfully estimate the ego-motion of LiDAR and build the global consistency 3D scene map with n frame point clouds \\( P_{1:n}^{L} = \\{p_{1}^{L},\\dots ,p_{n}^{L}\\} \\). To provide accurate scene constrain in Sec. 3.3, we utilize the VDB-Fusion [47] to generate a clean scene mesh \\( S \\) that excludes moving objects." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.578, + 0.892, + 0.79 + ], + "angle": 0, + "content": "IMUs pose estimation. We use SMPL [32] to represent the human body motion \\( M^{I} = \\varPhi(\\theta^{I}, t^{I}, \\beta) \\in \\mathbb{R}^{6890 \\times 3} \\) in IMU coordinate space \\( \\{I\\} \\), where pose parameter \\( \\Theta_{1:n}^{I} = \\{\\theta_{1}^{I}, \\dots, \\theta_{n}^{I}\\} \\in \\mathbb{R}^{72 \\times n} \\) is composed of pelvis joint's orientation \\( R_{1:n}^{I} = \\{r_{1}^{I}, \\dots, r_{n}^{I}\\} \\in \\mathbb{R}^{3 \\times n} \\) and the other 23 joints' rotation relative to their parent joint. The \\( T_{1:n}^{I} = \\{t_{1}^{I}, \\dots, r_{n}^{I}\\} \\in \\mathbb{R}^{3 \\times n} \\) is the pelvis joint's translation and \\( \\beta \\in \\mathbb{R}^{10} \\) is a constant value representing a person's body shape. \\( T \\) and \\( \\Theta \\) are estimated by the commercial MoCap product, while \\( \\beta \\) is obtained by using IPNet [3] to fit the scanned model captured by an iPhone13 Promax. Since the IMU are accurate locally but drift globally, \\( T^{I} \\) is used for raw calibration of the \\( \\{I\\} \\) to \\( \\{W\\} \\), and the initial global motion \\( M = M^{W} = R^{WI}M^{I} \\) will be further optimized." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.681, + 0.818 + ], + "angle": 0, + "content": "3.3. Data Optimization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To obtain precise and scene-plausible human motion \\(M\\) in the world coordinate system, we use scene geometry \\(S\\) with several physico-based terms to perform joint optimizations to find the optimal motion \\(M^{*}\\) that minimize \\(\\mathcal{L}\\). In a k-frame segment, the optimization is written as:" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "685" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.473, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.478, + 0.089, + 0.677, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.089, + 0.882, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.431, + 0.894, + 0.475 + ], + "angle": 0, + "content": "Figure 3. The pipeline of the dataset construction. The capturing system simultaneously collects multimodal data, including LiDAR, camera, and IMU data. Then they are further processed. A joint optimization approach with multiple loss terms is then employed to optimize motion locally and globally. As a result, we obtain rich 2D/3D annotations with accurate global motion and scene information." + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.483, + 0.305, + 0.506 + ], + "angle": 0, + "content": "\\[\nM _ {1: k} ^ {*} = \\arg \\min _ {M _ {1: k}} \\mathcal {L} (M _ {1: k}, \\boldsymbol {S}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.508, + 0.469, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {s m t} + \\lambda_ {s c} \\mathcal {L} _ {s c} + \\lambda_ {p r i} \\mathcal {L} _ {p r i} + \\lambda_ {m 2 p} \\mathcal {L} _ {m 2 p}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.531, + 0.422, + 0.549 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s m t} = \\lambda_ {\\text {t r a n s}} \\mathcal {L} _ {\\text {t r a n s}} + \\lambda_ {\\text {o r i t}} \\mathcal {L} _ {\\text {o r i t}} + \\lambda_ {j t s} \\mathcal {L} _ {j t s},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.47, + 0.645 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{smt}\\) is a smoothness term, which consists of a translation loss \\(\\mathcal{L}_{trans}\\), an orientation loss \\(\\mathcal{L}_{orit}\\), and a joints loss \\(\\mathcal{L}_{jts}\\). \\(\\mathcal{L}_{sc}\\) is a scene-aware-contact term, \\(\\mathcal{L}_{pri}\\) is a pose prior term, and \\(\\mathcal{L}_{m2p}\\) is a mesh-to-points term. The \\(\\lambda_{sc}, \\lambda_{pri}, \\lambda_{trans}, \\lambda_{orit}, \\lambda_{jts}\\), and \\(\\lambda_{m2p}\\) are loss terms' coefficients. \\(\\mathcal{L}\\) is minimized with a gradient descent algorithm." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.47, + 0.724 + ], + "angle": 0, + "content": "Smoothness term. The objective of this term is to minimize the acceleration of the pelvis joint, the accelerations of the other 23 pelvis-relative joints, which is denoted as \\( J_{1:k} = \\{j_1,\\dots ,j_k\\} \\in \\mathbb{R}^{69\\times k} \\), and the angular velocity of all joints to smooth human movements." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.471, + 0.804 + ], + "angle": 0, + "content": "Scene-aware contact term. we compare the movement of every foot vertices in IMU motions \\( M_{k}^{I} \\) and label the foot as stable if its velocity is less than \\( 0.1 \\, m/s^2 \\). Finally, the Chamfer Distance (CD) between this foot and its closest surface is expressed as the scene contact loss \\( \\mathcal{L}_{sc} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.807, + 0.47, + 0.882 + ], + "angle": 0, + "content": "Pose prior term. The poses estimated by IMUs are roughly accurate but will likely cause some misalignments to the end of the body limb due to the accumulating error. Hence, \\(\\mathcal{L}_{\\text {prior }}\\) is used to constrain the \\(\\Theta\\) close to the initial value at the beginning of the optimization." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Mesh-to-points term. The point cloud \\(p^L\\) from the mov" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.641 + ], + "angle": 0, + "content": "ing LiDAR provides strong prior depth information. However, though the SMPL mesh is watertight and complete, the human points are sparse and partial, which makes the registration methods such as ICP, not ideal as expected. To address this issue, we propose a viewpoint-based mesh-to-point loss function \\(\\mathcal{L}_{m2p}\\). First, we remove the hidden SMPL mesh faces from the LiDAR's viewpoint. Then we sample points, denoted as \\(P_{1:k}^{\\prime} = \\{p_{1}^{\\prime},\\dots ,p_{k}^{\\prime}\\}\\), from the remaining faces by LiDAR resolution. The loss is defined as the Chamfer Distance from \\(P_{1:k}^{\\prime}\\) to \\(P_{1:k}\\)." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.645, + 0.835, + 0.659 + ], + "angle": 0, + "content": "All loss terms functions are detailed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.682, + 0.839, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t r a n s} = \\frac {1}{k - 2} \\sum_ {i = 1} ^ {k - 2} \\| t _ {i + 2} - 2 t _ {i + 1} + t _ {i} \\| _ {2} ^ {2},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.726, + 0.824, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {j t s} = \\frac {1}{k - 2} \\sum_ {i = 1} ^ {k - 2} \\| \\mathcal {J} _ {i + 2} - 2 \\mathcal {J} _ {i + 1} + \\mathcal {J} _ {i} \\| _ {2} ^ {2},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.771, + 0.892, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o r i t}} = \\frac {1}{k - 1} \\sum_ {i = 1} ^ {k - 1} \\| r _ {i + 1} - r _ {i} \\| _ {2} ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.815, + 0.763, + 0.856 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p r i} = \\frac {1}{k} \\sum_ {i = 1} ^ {k} \\| \\theta_ {i} - R ^ {W I} \\theta_ {i} ^ {I} \\| _ {2} ^ {2},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.554, + 0.86, + 0.83, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m 2 p} = \\frac {1}{k} \\sum_ {i = 1} ^ {k} \\sum_ {\\hat {p ^ {\\prime}} \\in p _ {i} ^ {\\prime}} \\frac {1}{| p _ {i} ^ {\\prime} |} \\min _ {\\hat {p} \\in p _ {i}} \\| \\hat {p} - \\hat {p ^ {\\prime}} \\| _ {2} ^ {2}.\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "686" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.487, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.092, + 0.885, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.266, + 0.487, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.266, + 0.885, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.448, + 0.893, + 0.476 + ], + "angle": 0, + "content": "Figure 4. The diverse scenes and activities of our dataset. The images in the left column are our reconstructed scenes with human trajectories overlaid on them. The right images are the SMPL meshes overlaid on images / point clouds / scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.643 + ], + "angle": 0, + "content": "Camera extrinsic optimization. We aim to optimize extrinsic parameters \\( K_{ex} \\) for every frame by minimizing the \\( \\mathcal{L}_{cam} \\), which comprises of the keypoints loss \\( \\mathcal{L}_{kpt} \\) and the bounding box loss \\( \\mathcal{L}_{box} \\). The \\( \\mathcal{L}_{kpt} \\) measures the mean square error between the 2D human keypoints \\( kpt^{2d} \\) in the image and the 3D human keypoints \\( kpt^{3d} \\) of the optimized SMPL model projected to the image with \\( K_{ex} \\); the \\( \\mathcal{L}_{box} \\) computes the Intersection over Union loss between the 2D human bounding box \\( box^{2d} \\) in the image and the 3D human bounding box \\( box^{3d} \\) projected to the image with \\( K_{ex} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.648, + 0.382, + 0.671 + ], + "angle": 0, + "content": "\\[\nK _ {e x} ^ {*} = \\arg \\min _ {K _ {e x} \\in S E (3)} \\mathcal {L} _ {c a m} (K _ {e x}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.674, + 0.469, + 0.693 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c a m} = \\lambda_ {k p t} \\mathcal {L} _ {k p t} \\left(k p t ^ {3 d}, k p t ^ {2 d}, K _ {e x}\\right) + \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.695, + 0.399, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {b o x} \\mathcal {L} _ {b o x} \\left(b o x ^ {3 d}, b o x ^ {2 d}, K _ {e x}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.383, + 0.735 + ], + "angle": 0, + "content": "where \\(\\lambda_{kpt}\\) and \\(\\lambda_{box}\\) are constant coefficients." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.271, + 0.759 + ], + "angle": 0, + "content": "3.4. Dataset Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "SLOPER4D is the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations for GHPE. The head-mounted LiDAR and camera are utilized to simultaneously record the IMU-wearer's activities, including running outside, playing football, visiting, reading, climbing/descending stairs, discussing, borrowing a book, greeting, etc. The dataset consists of 15 sequences from 12 human subjects in 10 locations. There are a total of \\(100\\mathrm{k}\\) LiDAR frames, \\(300\\mathrm{k}\\) video" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.492, + 0.892, + 0.537 + ], + "angle": 0, + "content": "frames, and 500k IMU-based motion frames captured over a total distance of more than \\(8km\\) and an area of up to \\(30,000m^2\\). The results of our dataset are shown in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.893, + 0.736 + ], + "angle": 0, + "content": "For the captured person, we provide the segmentation of 3D points from LiDAR frames and 2D bounding boxes from images synchronized with LiDAR. We also provide 3D pose annotations with SMPL format. Compared to other datasets Tab. 1, it is worth mentioning that SLOPER4D provides the 3D scene reconstructions and accurate global translation annotations, allowing us to quantitatively study the scene-aware global pose estimation from both LiDAR and monocular videos. In addition to the dense 3D point cloud map reconstructed from the LiDAR, SLOPER4D provides the high-precision colorful point cloud map from a Terrestrial Laser Scanner (Trimble TX5) for better visualization and map comparison." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.753, + 0.634, + 0.771 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we first evaluate SLOPER4D Dataset qualitatively, indicating that our dataset is solid enough to benchmark new tasks. Then we perform a cross-dataset evaluation to further assess our dataset's novelty on two tasks: LiDAR-based 3D HPE and camera-based 3D HPE. Finally, we introduce the new benchmark, GHPE, and perform experiments on GLAMR. More quantitative evaluations and experiments are in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "687" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.462, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.24, + 0.47, + 0.283 + ], + "angle": 0, + "content": "Figure 5. Comparison between our optimization results (red SMPL) and the ICP results (green SMPL). It shows the red SMPL aligns better with the cyan human points than the green SMPL." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.289, + 0.462, + 0.458 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.46, + 0.469, + 0.502 + ], + "angle": 0, + "content": "Figure 6. The comparison before (left) and after (right) extrinsic optimization by projecting the point clouds (upper) and SMPL (lower) are projected onto the image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.47, + 0.684 + ], + "angle": 0, + "content": "Training/Test splits. We split our data into training and test sets for LiDAR/Camera-based pose estimation. The training set of SLOPER4D contains eleven sequences of data with a total of 80k LiDAR frames and corresponding RGB frames. The test set has four sequences of data with around 20k LiDAR frames and corresponding RGB frames. For global pose estimation, we select three challenging scenarios for evaluation. The first one is a single-person football training scenario with highly dynamic motions. The second one is running along a coastal runway. The third one is a garden tour involving daily motions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Evaluation metrics. For 3D HPE, we employ Mean per joint position error (MPJPE) and Procrustes-aligned MPJPE (PA-MPJPE) for evaluation. MPJPE is the mean euclidean distance between the ground-truth and predicted joints. PA-MPJPE first aligns the predicted joints to the ground-truth joints by carrying out rigid transformation based on Procrustes analysis and then calculates MPJPE. For global trajectory evaluation, we utilize Absolute Trajectory Error (ATE) and the Relative Pose (the pose refers to orientation here) Error (RPE) in visual SLAM systems [11], where the ATE is well-suited for measuring the global localization and, in contrast, the RPE is suitable for measuring the system's drift, for example, the drift per second. Global MPJPE (G-MPJPE) is MPJPE calculated by placing the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.761, + 0.107 + ], + "angle": 0, + "content": "SMPL model in the global coordinates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.11, + 0.895, + 0.352 + ], + "angle": 0, + "content": "Qualitative evaluation. For the human pose qualitative evaluation, we project the SMPL to the image and visualize the 3D human with corresponding LiDAR points in 3D space (shown in Fig. 4). The results demonstrate that the 3D human mesh aligns well with 3D environments and 2D images. As a large-scale urban-level human pose dataset, SLOPER4D provides multi-modal capture data and rich human-scene annotations, as well as diverse challenging human activities in large scenes. To evaluate our optimization method, we first compare our method with the results from ICP. As shown in Fig. 5, the scene-aware constraints and human mesh-to-points constraint efficiently optimize the local poses, global translation, and even the orientation error from IMU. To show the effectiveness of the camera extrinsic optimization, we report the results in Fig. 6. The 2D projecting error was visually lowered after optimization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.362, + 0.733, + 0.376 + ], + "angle": 0, + "content": "4.1. Cross-Dataset Evaluation" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.395, + 0.892, + 0.458 + ], + "angle": 0, + "content": "
Test TrainLH26MOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
LH26M79.367.0228.7149.9
Ours212.3128.386.165.1
LH26M + Ours85.572.079.260.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.539, + 0.458, + 0.854, + 0.47 + ], + "angle": 0, + "content": "(a) LiDAR-based 3D pose estimation with LiDARCap [27]." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.48, + 0.892, + 0.592 + ], + "angle": 0, + "content": "
Test Train3DPWOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
VIBE [24]93.556.5102.566.2
Ours + AMASS124.366.886.652.4
w. 3DPW83.052.090.058.3
HbryIK [26]88.749.3104.957.0
w. Ours87.349.267.644.2
w. 3DPW71.341.875.850.0
w. 3DPW + Ours76.446.766.242.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.595, + 0.592, + 0.797, + 0.603 + ], + "angle": 0, + "content": "(b) Camera-based 3D pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.682 + ], + "angle": 0, + "content": "Table 2. Cross-dataset evaluation results with different modalities. The LH26M in (a) refers to LiDARHuman26M dataset from LiDARcap. VIBE is pre-trained on AMASS [33], MPI-INF-3DHP [35] InstaVariety [19], PoseTrack [1], PennAction [65]. HbryIK is pre-trained on H36M, MPI-INF-3DHP, MSCOCO [29]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We evaluate root-relative 3D human pose estimation with different modalities, namely the LiDAR and the camera. 3DPW is an in-the-wild human motion dataset that is most related to us. With VIBE, we cross-evaluated our dataset's camera modal by using 3DPW. LiDARHuman26M is a lidar-based dataset for long-range human pose estimation. We can cross-evaluate our dataset's LiDAR modal with it. Tab. 2(a) shows the evaluation results on LiDAR-based 3D pose estimation task and Tab. 2(b) shows the results on camera-based 3D pose estimation. Taking the results from Tab. 2(a), for example, when the model is trained from another dataset only, the errors are the largest. But the error will be further reduced by around \\(60\\%\\) when training on LiDARHuman26M and our dataset together. It" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "688" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "suggests a domain gap exists between different LiDAR sensors, and both datasets complement each other. The results of another task show that the pre-trained VIBE model generalizes better on 3DPW than on our dataset. But the error on 3DPW increases when finetuned on our dataset, while the error decreases on our dataset. This suggests that the pre-trained model complements SLOPER4D better than the opposite. Comparing the results across different modalities, the error on our dataset from the method trained on mixed LiDAR point cloud datasets is \\(13\\%\\) lower than the method trained on the images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.266, + 0.47, + 0.28 + ], + "angle": 0, + "content": "4.2. Benchmark on Global Human Pose Estimation" + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.286, + 0.455, + 0.393 + ], + "angle": 0, + "content": "
SequenceMetricRMSE ↓meanstd.max
FootballATE3.262.851.5811.83
Running001ATE29.4825.5514.7256.07
Garden001ATE2.862.571.266.55
FootballRPE0.080.060.051.34
Running001RPE0.400.350.191.04
Garden001RPE0.060.040.040.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.396, + 0.449, + 0.41 + ], + "angle": 0, + "content": "Table 3. Global trajectory evaluation of GLAMR. Unit: \\( m \\) ." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.425, + 0.462, + 0.489 + ], + "angle": 0, + "content": "
SequenceScaleMPJPE ↓PA-MPJPE ↓G-MPJPE ↓
Football11.83264.6118.55268.7
Running00156.07652.1119.632329.3
Garden0016.55139.486.34407.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.125, + 0.493, + 0.422, + 0.506 + ], + "angle": 0, + "content": "Table 4. GHPE results from GLAMR. Unit: mm." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.518, + 0.462, + 0.706 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.712, + 0.47, + 0.741 + ], + "angle": 0, + "content": "Figure 7. The ATE error \\((m)\\) mapped on the GT trajectory. The color represents the error according to the color bar." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.87 + ], + "angle": 0, + "content": "In this subsection, we benchmark the GHPE task of GLAMR [61] on SLOPER4D. GLAMR is a global occlusion-aware method for 3D global human mesh recovery from dynamic monocular cameras. For the scale uncertainty of the monocular camera, we compute the affine matrix from the estimated trajectory to the ground truth trajectory and rotate, translate and scale the estimated trajectory before error computation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Tab. 3 reports the global trajectory error with ATE and RPE, Tab. 4 reports the global human pose metric, and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Fig. 7 shows the ATE error mapped on GT trajectory. Comparing the results on the three scenes, the football and Garden001 have a significantly lower RPE in the global scene. In comparison, GLAMR performs the worst on the running scene, with an ATE's RMSE of \\(29.48\\mathrm{m}\\). This scene has the largest area size and the highest human pace. GLAMR achieves a low PA-MPJPE of \\(86.3\\mathrm{mm}\\) on Garden001, a sequence with daily walking and visiting motions. It's the first time that we have tested the GPHE on such large outdoor scenes. GLAMR achieves relatively better results on daily human motion while performing worse on high-dynamic activities in the wild. The interesting point is that the trajectory tendency is pretty similar to the reference, even in dynamic football training motions, which demonstrates the ability of GLAMR to be a baseline. It is expected that more research will focus on GHPE in real-world interactive scenarios, and the experiments show our SLOPER4D's potential to promote urban-level GHPE research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.389, + 0.622, + 0.404 + ], + "angle": 0, + "content": "5. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.892, + 0.558 + ], + "angle": 0, + "content": "Limitations. Firstly, SLOPER4D is limited to single-person capture though it perceives multiple-person data. Secondly, the camera and LiDAR are not synchronized online, causing tedious offline work if the camera loses frames even with a low time offset (\\(< 50~ms\\)). Finally, texture information from the camera is not fully exploited for color and texture reconstruction of scenes and humans. In our future work, we will propose an online synchronization algorithm and extend our work to multiple-person capturing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Conclusions. We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations. Based on our proposed new dataset, we benchmark two critical tasks, camera-based 3D HPE and LiDAR-based 3D HPE. SLOPER4D also benchmarks the GHPE task. The results demonstrate the potential of SLOPER4D in boosting the development of these areas. Our work contributes to extending motion capture to large global scenes based on the current methods and datasets. We hope this work will foster future creation and interaction in urban environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported in part by the Natural Science Foundation of China (No.62171393), the Fundamental Research Funds for the Central Universities (No.20720220064), FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003), and NSFC (No.62206173). We thank Zhiyong Wang for helping us incorporate FAST-LIO2 into our mapping system. 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Using the head-mounted LiDAR and camera to scan the IMUs wearer, we construct SLOPER4D, a large scene-aware dataset for global 4D human pose estimation in urban environments. + +# Abstract + +We present SLOPER4D, a novel scene-aware dataset collected in large urban environments to facilitate the research of global human pose estimation (GHPE) with human-scene interaction in the wild. Employing a head-mounted device integrated with a LiDAR and camera, we record 12 human subjects' activities over 10 diverse urban scenes from an egocentric view. Frame-wise annotations for 2D key points, 3D pose parameters, and global translations are provided, together with reconstructed scene point clouds. To obtain accurate 3D ground truth in such large dynamic scenes, we propose a joint optimization method to fit local SMPL meshes to the scene and fine-tune the camera calibration during dynamic motions frame by frame, resulting in plausible and scene-natural 3D human poses. Even + +tually, SLOPER4D consists of 15 sequences of human motions, each of which has a trajectory length of more than 200 meters (up to 1,300 meters) and covers an area of more than $200\mathrm{m}^2$ (up to $30,000\mathrm{m}^2$ ), including more than 100k LiDAR frames, 300k video frames, and 500k IMU-based motion frames. With SLOPER4D, we provide a detailed and thorough analysis of two critical tasks, including camera-based 3D HPE and LiDAR-based 3D HPE in urban environments, and benchmark a new task, GHPE. The in-depth analysis demonstrates SLOPER4D poses significant challenges to existing methods and produces great research opportunities. The dataset and code are released at http://www.lidarhumanmotion.net/sloper4d/. + +# 1. Introduction + +Urban-level human motion capture is attracting more and more attention, which targets acquiring consecutive fine-grained human pose representations, such as 3D skeletons + +and parametric mesh models, with accurate global locations in the physical world. It is essential for human action recognition, social-behavioral analysis, and scene perception and further benefits many downstream applications, including Augmented/Virtual Reality, simulation, autonomous driving, smart city, sociology, etc. However, capturing extra large-scale dynamic scenes and annotating detailed 3D representations for humans with diverse poses is not trivial. + +Over the past decades, a large number of datasets and benchmarks have been proposed and have greatly promoted the research in 3D human pose estimation (HPE). They can be divided into two main categories according to the capture environment. The first class usually leverages marker-based systems [16, 33, 45], cameras [14, 59, 60], or RGB-D sensors [13, 64] to capture human local poses in constrained environments. However, the optical system is sensitive to light and lacks depth information, making it unstable in outdoor scenes and difficult to provide global translations, and the RGB-D sensor has limited range and could not work outdoors. The second class [39, 49] attempts to take advantage of body-mounted IMUs to capture occlusion-free 3D poses in free environments. However, IMUs suffer from severe drift for long-term capturing, resulting in misalignments with the human body. Then, some methods exploit additional sensors, such as RGB camera [17], RGB-D camera [46, 57, 67], or LiDAR [27] to alleviate the problem and make obvious improvement. However, they all focus on HPE without considering the scene constraints, which are limited in reconstructing human-scene integrated digital urban and human-scene natural interactions. + +To capture human pose and related static scenes simultaneously, some studies use wearable IMUs and body-mounted camera [12] or LiDAR [5] to register the human in large real scenarios and they are promising for capturing human-involved real-world scenes. However, human pose and scene are decoupled in these works due to the ego view, where auxiliary visual sensors are used for collecting the scene data while IMUs are utilized for obtaining the 3D pose. Different from them, we propose a novel setting for human-scene capture with wearable IMUs and global-view LiDAR and camera, which can provide multi-modal data for more accurate 3D HPE. + +In this paper, we propose a huge scene-aware dataset for sequential human pose estimation in urban environments, named SLOPER4D. To our knowledge, it is the first urban-level 3D HPE dataset with multi-modal capture data, including calibrated and synchronized IMU measurements, LiDAR point clouds, and images for each subject. Moreover, the dataset provides rich annotations, including 3D poses, SMPL [32] models and locations in the world coordinate system, 2D poses and bounding boxes in the image coordinate system, and reconstructed 3D scene mesh. In particular, we propose a joint optimization method for + +obtaining accurate and natural human motion representations by utilizing multi-sensor complementation and scene constraints, which also benefit global localization and camera calibration in the dynamic acquisition process. Furthermore, SLOPER4D consists of over 15 sequences in 10 scenes, including library, commercial street, coastal runway, football field, landscape garden, etc., with up to $30\mathrm{k}$ $m^2$ area size and $200\sim 1,000m$ trajectory length for each sequence. By providing multi-modal capture data and diverse human-scene-related annotations, SLOPER4D opens a new door to benchmark urban-level HPE. + +We conduct extensive experiments to show the superiority of our joint optimization approach for acquiring high-quality 3D pose annotations. Additionally, based on our proposed new dataset, we benchmark two critical tasks: camera-based 3D HPE and LiDAR-based 3D HPE, as well as provide benchmarks for GHPE. + +Our contributions are summarized as follows: + +- We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations. +- We propose an effective joint optimization method for acquiring accurate human motions in both local and global by integrating LiDAR SLAM results, IMU poses, and scene constraints. +- We benchmark two HPE tasks as well as a GHPE task on SLOPER4D, demonstrating its potential of promoting urban-level 3D HPE research. + +# 2. Related Work + +# 2.1. 3D Human Motion Datasets + +Many datasets have been proposed with different sensors and setups to facilitate the research on 3D human pose estimation. The H3.6M [16] is a large-size dataset providing synchronized video with optical-based MoCap in studio environments. To perform markerless capture in different indoor scenes, PROX [13] uses an RGB-D sensor to scan a single person. EgoBody [64] uses multiple RGB-D sensors to pre-scan the room and scan the interacting persons. LiDARHuman26M [27] can capture long-range human motions with static LiDAR and IMUs. However, they are limited to static environments, human activities, and interactions. 3DPW [49] is the first dataset providing 3D annotations in the wild which uses a single hand-held RGB camera to optimize human pose from IMUs for a certain period of frames. It doesn't provide accurate global translation and 3D scenes. HPS [12] reconstructs the human body pose using IMUs and self-localizes it with a head-mounted camera in large 3D scenes, but it heavily relies on the pre-built map. HSC4D [5] removes the reliance on the pre-built map and achieves global human motion capture in large scenes. + +
DatasetIn the wildGlobal3D ScenePoint cloudVideoIMU# Scene# Area size (m2)# Subject# Frame
H3.6M [16]X✓XX✓X-12113.6M
3DPW [49]✓XXX✓✓-< 300751k
PROX [13]X✓✓X✓X12< 302020k
HPS [12]✓✓✓X✓*✓8< 1,00077k
HSC4D [5]✓✓✓✓*X✓5< 5,000210k
LH26M [27]XXX✓✓✓-< 20013184k
EgoBody [64]X✓✓X✓X15< 5020153k
SLOPER4D✓✓✓✓✓✓10< 30,00012100k
+ +Table 1. Comparisons with existing datasets. "Global" denotes to human poses with global translation. The "area size" is estimated with the published data. The * indicates the data modality is only used for human self-localization rather than for human-related data. + +However, the camera in HPS and the LiDAR in HSC4D are only used to perceive the environment rather than capture human data. With the scene-aware dataset we proposed for global human pose estimation, we can benchmark the 3D HPE in the wild with the LiDAR or camera modalities. + +# 2.2. Human Localization and Scene Mapping + +Human self-localization aims at estimating the 6-DoF of the human subject in global coordinates. The image-based methods [21, 37, 52] regress locations directly from a single image with a pre-built map. The scene-specific property makes them hard to generalize to unseen scenes. LiDAR is widely used in Simultaneous Localization and Mapping (SLAM) [4, 28, 41, 62] due to its robustness and low drift. To address the drift problem and improve robustness in dynamic motions, RGB cameras [40, 44, 63], IMU [10, 36, 42], or both [6, 43, 68], have been integrated with the mapping task. Most attention has been paid to autonomous driving [9] [23] or robotics from the third-person view and they usually do not focus on humans. To achieve self-localization, LiDAR is designed as backpacked [20, 31, 54] and handheld [2]. To efficiently capture human motions and reconstruct urban scenes, we utilize LiDAR with a built-in IMU (different from the IMUs for motion capture) and propose a pipeline for constructing multi-modal data. This approach provides accurate information on human motions at both local and global levels, as well as enables mapping in large outdoor environments. + +# 2.3. Global 3D Human Pose Estimation + +Most studies recover human meshes in camera coordinate [26, 66] or root-relative poses [18, 24, 25]. Recovering global human motions in unconstrained scenes is a challenging topic in computer vision and has gained more and more research interest in recent years. IMU sensors are widely used in commercial [38, 39] and research activities [15, 48, 51], and are attached to body limbs to capture human motions in studio-environments. But it suffers severe drift in the wild. Some methods rely on additional RGB [8, 34, 49, 50] or pre-scan maps [12], or LiDAR [5] to complement the IMUs in large-scale scenes. Based on + +human-scene interaction, some work proposed scene-aware solutions using static cameras [14, 60] to obtain accurate and scene-natural human motions. 4DCapture [30] uses a dynamic head-mounted camera to self-localize and reconstruct the scene with the Struct From Motion method. However, it often fails when the illumination changes in the wild. MOVER [60] uses a single camera to optimize the 3D objects in a static scene, resulting in better 3D scene reconstruction and human motions. GLAMR [61] uses global trajectory predictions to constrain both human motions and dynamic camera poses, achieving state-of-the-art results on inthe-wild videos. However, it lacks a benchmark for quantitatively comparing different HPE methods on a global level. To deal with this limitation, we propose SLOPER4D, the first large-scale urban-level human pose dataset with rich 2D/3D annotations. + +# 3. SLOPER4D Dataset + +SLOPER4D collects scene-aware 4D human data with our body-worn capturing system in urban scenes. In this section, we first introduce the data acquisition in Sec. 3.1, second, we detail the data construction and annotation process in Sec. 3.2, then we introduce the global optimization-based Sec. 3.3 method to obtain high quality both 3D/2D data, finally, we compare our dataset in Sec. 3.4 with the existing datasets and highlight our novelty. + +# 3.1. Data Acquisition + +Hardware setup. As shown in Fig. 1, during the data collection procedure, the scanning person follows the performer (IMUs wearer) and scans him with a LiDAR and a camera on the helmet. Additionally, Fig. 2 shows the hardware details of our capturing system. Regarding the sensor module, the 128-beams Ouster-os1 LiDAR and the DJI-Action2 camera are rigidly installed on the helmet. To capture raw human motions, we use Noitom's inertial MoCap product, PN Studio, to attach 17 wireless IMUs to the IMU wearer's body limbs, torso, and head. The camera's field of view (FOV) is $116^{\circ} \times 84^{\circ}$ and the LiDAR's FOV is $360^{\circ} \times 45^{\circ}$ . To make the performer within the LiDAR's FOV + +![](images/d9c3d5862253826f16f29b745c027ee5d28526a7f241e730f31bb73b395fddf9.jpg) +Figure 2. Our capturing system's hardware details. The sensor module includes a LiDAR, a camera, and 17 body-attached IMU sensors. The storage module consists of a NUC11, a receiver, and a battery in the backpack. + +as much as possible, we tilt the LiDAR down around $45^{\circ}$ . Regarding the storage module, the scanning person's backpack places a wireless IMU data receiver, a 24V battery, and an Intel NUC11. The mini-computer NUC11 stores IMU data from the wireless receiver and point clouds from LiDAR in real-time. Videos are stored locally in the camera. The LiDAR and NUC11 are both powered by the battery. + +Coordinate systems. Let's define three coordinate systems: 1) IMU coordinate system $\{I\}$ : the origin is at LiDAR wearer's spine base at the starting time, and the $X / Y / Z$ axis is pointing left/upward/forward of the human. 2) LiDAR Coordinate system $\{L\}$ : the origin is at the center of the LiDAR, and the $X / Y / Z$ axis is pointing right/forward/upward of the LiDAR. 3) Global/World coordinate system $\{W\}$ : the origin is on the floor of the LiDAR wearer's starting position, and the $X / Y / Z$ axis is pointing right/forward/upward of the LiDAR wearer. + +Calibration. Following the setup in [53], we use a chessboard to calibrate the camera intrinsic $K_{in}$ and introduces a terrestrial laser scanner (TLS) to obtain accurate camera extrinsic parameter, $K_{ex}$ . Due to the LiDAR point cloud being too sparse, we manually choose the corresponding points both on the 2D image and the TLS map registered to the point cloud, and then we solve the perspective-n-point (PnP) problem to obtain $K_{in}$ . For every 3D scene, the calibration $R_{WL}$ , which transforms $\{L\}$ to $\{W\}$ is manually set to make the ground's $z$ -axis upward and height to zero for the starting position. By using singular value decomposition, the calibration $R_{WI}$ , which transforms $\{I\}$ to $\{W\}$ , is calculated through the similarity between IMU trajectory and LiDAR trajectory on the XY plane. + +Synchronization. The synchronization of data from multiple sensors in human subject data is achieved through peak + +detection. Before and after the capture, the subject is asked to perform jumps. Then the peak height time in IMU is automatically detected and the peak times in the LiDAR and camera data are manually identified. Finally, all modalities are aligned by the peaks and downsampled to match the LiDAR frame rate of $20\mathrm{Hz}$ . + +# 3.2. Data Processing + +2D pose detection. We use Detectron [56] to detect and Deepsort [55] to track humans in videos. However, the tracking often fails due to the IMUs wearer entering/exiting the field of view or occlusions. To solve this problem, we manually assign the same ID for the tracked person in a video sequence. As for 3D point cloud reference, we project them on images according to the $K_{ex}$ . However, due to the jitter brought by dynamic motions, the camera and the Li-DAR are not perfectly rigidly connected. Thus, $K_{ex}$ will be further optimized in Sec. 3.3. + +LiDAR-inertial localization and mapping. The LiDAR-only method often fails in mapping because of the dynamic head rotation and crowded urban environments. Incorporating an IMU can compensate for motion distortion in a LiDAR scan $p^L$ and provide an accurate initial pose. Using a LiDAR with an integrated IMU, and by combining Kalman filter-based lidar-inertial odometry [58] with factor graph-based loop closure optimization [7] [22], we successfully estimate the ego-motion of LiDAR and build the global consistency 3D scene map with n frame point clouds $P_{1:n}^{L} = \{p_{1}^{L},\dots ,p_{n}^{L}\}$ . To provide accurate scene constrain in Sec. 3.3, we utilize the VDB-Fusion [47] to generate a clean scene mesh $S$ that excludes moving objects. + +IMUs pose estimation. We use SMPL [32] to represent the human body motion $M^{I} = \varPhi(\theta^{I}, t^{I}, \beta) \in \mathbb{R}^{6890 \times 3}$ in IMU coordinate space $\{I\}$ , where pose parameter $\Theta_{1:n}^{I} = \{\theta_{1}^{I}, \dots, \theta_{n}^{I}\} \in \mathbb{R}^{72 \times n}$ is composed of pelvis joint's orientation $R_{1:n}^{I} = \{r_{1}^{I}, \dots, r_{n}^{I}\} \in \mathbb{R}^{3 \times n}$ and the other 23 joints' rotation relative to their parent joint. The $T_{1:n}^{I} = \{t_{1}^{I}, \dots, r_{n}^{I}\} \in \mathbb{R}^{3 \times n}$ is the pelvis joint's translation and $\beta \in \mathbb{R}^{10}$ is a constant value representing a person's body shape. $T$ and $\Theta$ are estimated by the commercial MoCap product, while $\beta$ is obtained by using IPNet [3] to fit the scanned model captured by an iPhone13 Promax. Since the IMU are accurate locally but drift globally, $T^{I}$ is used for raw calibration of the $\{I\}$ to $\{W\}$ , and the initial global motion $M = M^{W} = R^{WI}M^{I}$ will be further optimized. + +# 3.3. Data Optimization + +To obtain precise and scene-plausible human motion $M$ in the world coordinate system, we use scene geometry $S$ with several physico-based terms to perform joint optimizations to find the optimal motion $M^{*}$ that minimize $\mathcal{L}$ . In a k-frame segment, the optimization is written as: + +![](images/04ccb905610d26d59ac5e51fe2ff0258171dd73c88349a464f2064cefc6aa1d1.jpg) +Figure 3. The pipeline of the dataset construction. The capturing system simultaneously collects multimodal data, including LiDAR, camera, and IMU data. Then they are further processed. A joint optimization approach with multiple loss terms is then employed to optimize motion locally and globally. As a result, we obtain rich 2D/3D annotations with accurate global motion and scene information. + +![](images/76285f66060c4561ad9dc45d47c7a6fe6ab9c965ff24ce6cbaedf22c18c873c8.jpg) + +![](images/ea40a3c9dca492023d2dc292ca2a0b49d3c4fc99b42942540f313fb4866d392f.jpg) + +$$ +M _ {1: k} ^ {*} = \arg \min _ {M _ {1: k}} \mathcal {L} (M _ {1: k}, \boldsymbol {S}), +$$ + +$$ +\mathcal {L} = \mathcal {L} _ {s m t} + \lambda_ {s c} \mathcal {L} _ {s c} + \lambda_ {p r i} \mathcal {L} _ {p r i} + \lambda_ {m 2 p} \mathcal {L} _ {m 2 p}, \tag {1} +$$ + +$$ +\mathcal {L} _ {s m t} = \lambda_ {\text {t r a n s}} \mathcal {L} _ {\text {t r a n s}} + \lambda_ {\text {o r i t}} \mathcal {L} _ {\text {o r i t}} + \lambda_ {j t s} \mathcal {L} _ {j t s}, +$$ + +where $\mathcal{L}_{smt}$ is a smoothness term, which consists of a translation loss $\mathcal{L}_{trans}$ , an orientation loss $\mathcal{L}_{orit}$ , and a joints loss $\mathcal{L}_{jts}$ . $\mathcal{L}_{sc}$ is a scene-aware-contact term, $\mathcal{L}_{pri}$ is a pose prior term, and $\mathcal{L}_{m2p}$ is a mesh-to-points term. The $\lambda_{sc}, \lambda_{pri}, \lambda_{trans}, \lambda_{orit}, \lambda_{jts}$ , and $\lambda_{m2p}$ are loss terms' coefficients. $\mathcal{L}$ is minimized with a gradient descent algorithm. + +Smoothness term. The objective of this term is to minimize the acceleration of the pelvis joint, the accelerations of the other 23 pelvis-relative joints, which is denoted as $J_{1:k} = \{j_1,\dots ,j_k\} \in \mathbb{R}^{69\times k}$ , and the angular velocity of all joints to smooth human movements. + +Scene-aware contact term. we compare the movement of every foot vertices in IMU motions $M_{k}^{I}$ and label the foot as stable if its velocity is less than $0.1 \, m/s^2$ . Finally, the Chamfer Distance (CD) between this foot and its closest surface is expressed as the scene contact loss $\mathcal{L}_{sc}$ . + +Pose prior term. The poses estimated by IMUs are roughly accurate but will likely cause some misalignments to the end of the body limb due to the accumulating error. Hence, $\mathcal{L}_{\text {prior }}$ is used to constrain the $\Theta$ close to the initial value at the beginning of the optimization. + +Mesh-to-points term. The point cloud $p^L$ from the mov + +ing LiDAR provides strong prior depth information. However, though the SMPL mesh is watertight and complete, the human points are sparse and partial, which makes the registration methods such as ICP, not ideal as expected. To address this issue, we propose a viewpoint-based mesh-to-point loss function $\mathcal{L}_{m2p}$ . First, we remove the hidden SMPL mesh faces from the LiDAR's viewpoint. Then we sample points, denoted as $P_{1:k}^{\prime} = \{p_{1}^{\prime},\dots ,p_{k}^{\prime}\}$ , from the remaining faces by LiDAR resolution. The loss is defined as the Chamfer Distance from $P_{1:k}^{\prime}$ to $P_{1:k}$ . + +All loss terms functions are detailed as follows: + +$$ +\mathcal {L} _ {t r a n s} = \frac {1}{k - 2} \sum_ {i = 1} ^ {k - 2} \| t _ {i + 2} - 2 t _ {i + 1} + t _ {i} \| _ {2} ^ {2}, +$$ + +$$ +\mathcal {L} _ {j t s} = \frac {1}{k - 2} \sum_ {i = 1} ^ {k - 2} \| \mathcal {J} _ {i + 2} - 2 \mathcal {J} _ {i + 1} + \mathcal {J} _ {i} \| _ {2} ^ {2}, +$$ + +$$ +\mathcal {L} _ {\text {o r i t}} = \frac {1}{k - 1} \sum_ {i = 1} ^ {k - 1} \| r _ {i + 1} - r _ {i} \| _ {2} ^ {2}, \tag {2} +$$ + +$$ +\mathcal {L} _ {p r i} = \frac {1}{k} \sum_ {i = 1} ^ {k} \| \theta_ {i} - R ^ {W I} \theta_ {i} ^ {I} \| _ {2} ^ {2}, +$$ + +$$ +\mathcal {L} _ {m 2 p} = \frac {1}{k} \sum_ {i = 1} ^ {k} \sum_ {\hat {p ^ {\prime}} \in p _ {i} ^ {\prime}} \frac {1}{| p _ {i} ^ {\prime} |} \min _ {\hat {p} \in p _ {i}} \| \hat {p} - \hat {p ^ {\prime}} \| _ {2} ^ {2}. +$$ + +![](images/ef098b021f375666ddff575fc506701a85afc40d4312063b785bdcf20ccf84bc.jpg) + +![](images/86cf44f94a386a2517ad9562bfe004d8c857dee158b09df98acb986915400084.jpg) + +![](images/9fa2b9dfe264a43fb76fbaabb17243c8c627e5d3e00ec9a1c57c6e11684ad35d.jpg) +Figure 4. The diverse scenes and activities of our dataset. The images in the left column are our reconstructed scenes with human trajectories overlaid on them. The right images are the SMPL meshes overlaid on images / point clouds / scenes. + +![](images/afa4bf9ca6b3318db4901c9d382de52267a23ecb48884a91f913ad028a9b4db0.jpg) + +Camera extrinsic optimization. We aim to optimize extrinsic parameters $K_{ex}$ for every frame by minimizing the $\mathcal{L}_{cam}$ , which comprises of the keypoints loss $\mathcal{L}_{kpt}$ and the bounding box loss $\mathcal{L}_{box}$ . The $\mathcal{L}_{kpt}$ measures the mean square error between the 2D human keypoints $kpt^{2d}$ in the image and the 3D human keypoints $kpt^{3d}$ of the optimized SMPL model projected to the image with $K_{ex}$ ; the $\mathcal{L}_{box}$ computes the Intersection over Union loss between the 2D human bounding box $box^{2d}$ in the image and the 3D human bounding box $box^{3d}$ projected to the image with $K_{ex}$ . + +$$ +K _ {e x} ^ {*} = \arg \min _ {K _ {e x} \in S E (3)} \mathcal {L} _ {c a m} (K _ {e x}), +$$ + +$$ +\mathcal {L} _ {c a m} = \lambda_ {k p t} \mathcal {L} _ {k p t} \left(k p t ^ {3 d}, k p t ^ {2 d}, K _ {e x}\right) + \tag {3} +$$ + +$$ +\lambda_ {b o x} \mathcal {L} _ {b o x} \left(b o x ^ {3 d}, b o x ^ {2 d}, K _ {e x}\right), +$$ + +where $\lambda_{kpt}$ and $\lambda_{box}$ are constant coefficients. + +# 3.4. Dataset Comparison + +SLOPER4D is the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations for GHPE. The head-mounted LiDAR and camera are utilized to simultaneously record the IMU-wearer's activities, including running outside, playing football, visiting, reading, climbing/descending stairs, discussing, borrowing a book, greeting, etc. The dataset consists of 15 sequences from 12 human subjects in 10 locations. There are a total of $100\mathrm{k}$ LiDAR frames, $300\mathrm{k}$ video + +frames, and 500k IMU-based motion frames captured over a total distance of more than $8km$ and an area of up to $30,000m^2$ . The results of our dataset are shown in Fig. 4. + +For the captured person, we provide the segmentation of 3D points from LiDAR frames and 2D bounding boxes from images synchronized with LiDAR. We also provide 3D pose annotations with SMPL format. Compared to other datasets Tab. 1, it is worth mentioning that SLOPER4D provides the 3D scene reconstructions and accurate global translation annotations, allowing us to quantitatively study the scene-aware global pose estimation from both LiDAR and monocular videos. In addition to the dense 3D point cloud map reconstructed from the LiDAR, SLOPER4D provides the high-precision colorful point cloud map from a Terrestrial Laser Scanner (Trimble TX5) for better visualization and map comparison. + +# 4. Experiments + +In this section, we first evaluate SLOPER4D Dataset qualitatively, indicating that our dataset is solid enough to benchmark new tasks. Then we perform a cross-dataset evaluation to further assess our dataset's novelty on two tasks: LiDAR-based 3D HPE and camera-based 3D HPE. Finally, we introduce the new benchmark, GHPE, and perform experiments on GLAMR. More quantitative evaluations and experiments are in the supplementary material. + +![](images/fbb75deec27903f44dedf109f36eb64ccb51ecb64e98f0e4cc5980d12c14992d.jpg) +Figure 5. Comparison between our optimization results (red SMPL) and the ICP results (green SMPL). It shows the red SMPL aligns better with the cyan human points than the green SMPL. + +![](images/dbdbd32f01d1bf40adce58c6a94b4aafe4d31f01e600cb1c73a31f99e0902694.jpg) +Figure 6. The comparison before (left) and after (right) extrinsic optimization by projecting the point clouds (upper) and SMPL (lower) are projected onto the image. + +Training/Test splits. We split our data into training and test sets for LiDAR/Camera-based pose estimation. The training set of SLOPER4D contains eleven sequences of data with a total of 80k LiDAR frames and corresponding RGB frames. The test set has four sequences of data with around 20k LiDAR frames and corresponding RGB frames. For global pose estimation, we select three challenging scenarios for evaluation. The first one is a single-person football training scenario with highly dynamic motions. The second one is running along a coastal runway. The third one is a garden tour involving daily motions. + +Evaluation metrics. For 3D HPE, we employ Mean per joint position error (MPJPE) and Procrustes-aligned MPJPE (PA-MPJPE) for evaluation. MPJPE is the mean euclidean distance between the ground-truth and predicted joints. PA-MPJPE first aligns the predicted joints to the ground-truth joints by carrying out rigid transformation based on Procrustes analysis and then calculates MPJPE. For global trajectory evaluation, we utilize Absolute Trajectory Error (ATE) and the Relative Pose (the pose refers to orientation here) Error (RPE) in visual SLAM systems [11], where the ATE is well-suited for measuring the global localization and, in contrast, the RPE is suitable for measuring the system's drift, for example, the drift per second. Global MPJPE (G-MPJPE) is MPJPE calculated by placing the + +SMPL model in the global coordinates. + +Qualitative evaluation. For the human pose qualitative evaluation, we project the SMPL to the image and visualize the 3D human with corresponding LiDAR points in 3D space (shown in Fig. 4). The results demonstrate that the 3D human mesh aligns well with 3D environments and 2D images. As a large-scale urban-level human pose dataset, SLOPER4D provides multi-modal capture data and rich human-scene annotations, as well as diverse challenging human activities in large scenes. To evaluate our optimization method, we first compare our method with the results from ICP. As shown in Fig. 5, the scene-aware constraints and human mesh-to-points constraint efficiently optimize the local poses, global translation, and even the orientation error from IMU. To show the effectiveness of the camera extrinsic optimization, we report the results in Fig. 6. The 2D projecting error was visually lowered after optimization. + +# 4.1. Cross-Dataset Evaluation + +
Test TrainLH26MOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
LH26M79.367.0228.7149.9
Ours212.3128.386.165.1
LH26M + Ours85.572.079.260.1
+ +(a) LiDAR-based 3D pose estimation with LiDARCap [27]. + +
Test Train3DPWOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
VIBE [24]93.556.5102.566.2
Ours + AMASS124.366.886.652.4
w. 3DPW83.052.090.058.3
HbryIK [26]88.749.3104.957.0
w. Ours87.349.267.644.2
w. 3DPW71.341.875.850.0
w. 3DPW + Ours76.446.766.242.8
+ +(b) Camera-based 3D pose estimation. + +Table 2. Cross-dataset evaluation results with different modalities. The LH26M in (a) refers to LiDARHuman26M dataset from LiDARcap. VIBE is pre-trained on AMASS [33], MPI-INF-3DHP [35] InstaVariety [19], PoseTrack [1], PennAction [65]. HbryIK is pre-trained on H36M, MPI-INF-3DHP, MSCOCO [29] + +We evaluate root-relative 3D human pose estimation with different modalities, namely the LiDAR and the camera. 3DPW is an in-the-wild human motion dataset that is most related to us. With VIBE, we cross-evaluated our dataset's camera modal by using 3DPW. LiDARHuman26M is a lidar-based dataset for long-range human pose estimation. We can cross-evaluate our dataset's LiDAR modal with it. Tab. 2(a) shows the evaluation results on LiDAR-based 3D pose estimation task and Tab. 2(b) shows the results on camera-based 3D pose estimation. Taking the results from Tab. 2(a), for example, when the model is trained from another dataset only, the errors are the largest. But the error will be further reduced by around $60\%$ when training on LiDARHuman26M and our dataset together. It + +suggests a domain gap exists between different LiDAR sensors, and both datasets complement each other. The results of another task show that the pre-trained VIBE model generalizes better on 3DPW than on our dataset. But the error on 3DPW increases when finetuned on our dataset, while the error decreases on our dataset. This suggests that the pre-trained model complements SLOPER4D better than the opposite. Comparing the results across different modalities, the error on our dataset from the method trained on mixed LiDAR point cloud datasets is $13\%$ lower than the method trained on the images. + +# 4.2. Benchmark on Global Human Pose Estimation + +
SequenceMetricRMSE ↓meanstd.max
FootballATE3.262.851.5811.83
Running001ATE29.4825.5514.7256.07
Garden001ATE2.862.571.266.55
FootballRPE0.080.060.051.34
Running001RPE0.400.350.191.04
Garden001RPE0.060.040.040.71
+ +Table 3. Global trajectory evaluation of GLAMR. Unit: $m$ . + +
SequenceScaleMPJPE ↓PA-MPJPE ↓G-MPJPE ↓
Football11.83264.6118.55268.7
Running00156.07652.1119.632329.3
Garden0016.55139.486.34407.0
+ +Table 4. GHPE results from GLAMR. Unit: mm. + +![](images/b3db3b305a3a55fddfa5f97dbfa47cd2f0ab450d82362e7ea0c297f26e4f5ab6.jpg) +Figure 7. The ATE error $(m)$ mapped on the GT trajectory. The color represents the error according to the color bar. + +In this subsection, we benchmark the GHPE task of GLAMR [61] on SLOPER4D. GLAMR is a global occlusion-aware method for 3D global human mesh recovery from dynamic monocular cameras. For the scale uncertainty of the monocular camera, we compute the affine matrix from the estimated trajectory to the ground truth trajectory and rotate, translate and scale the estimated trajectory before error computation. + +Tab. 3 reports the global trajectory error with ATE and RPE, Tab. 4 reports the global human pose metric, and + +Fig. 7 shows the ATE error mapped on GT trajectory. Comparing the results on the three scenes, the football and Garden001 have a significantly lower RPE in the global scene. In comparison, GLAMR performs the worst on the running scene, with an ATE's RMSE of $29.48\mathrm{m}$ . This scene has the largest area size and the highest human pace. GLAMR achieves a low PA-MPJPE of $86.3\mathrm{mm}$ on Garden001, a sequence with daily walking and visiting motions. It's the first time that we have tested the GPHE on such large outdoor scenes. GLAMR achieves relatively better results on daily human motion while performing worse on high-dynamic activities in the wild. The interesting point is that the trajectory tendency is pretty similar to the reference, even in dynamic football training motions, which demonstrates the ability of GLAMR to be a baseline. It is expected that more research will focus on GHPE in real-world interactive scenarios, and the experiments show our SLOPER4D's potential to promote urban-level GHPE research. + +# 5. Discussions + +Limitations. Firstly, SLOPER4D is limited to single-person capture though it perceives multiple-person data. Secondly, the camera and LiDAR are not synchronized online, causing tedious offline work if the camera loses frames even with a low time offset ( $< 50~ms$ ). Finally, texture information from the camera is not fully exploited for color and texture reconstruction of scenes and humans. In our future work, we will propose an online synchronization algorithm and extend our work to multiple-person capturing. + +Conclusions. We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations. Based on our proposed new dataset, we benchmark two critical tasks, camera-based 3D HPE and LiDAR-based 3D HPE. SLOPER4D also benchmarks the GHPE task. The results demonstrate the potential of SLOPER4D in boosting the development of these areas. Our work contributes to extending motion capture to large global scenes based on the current methods and datasets. We hope this work will foster future creation and interaction in urban environments. + +Acknowledgements. This work was supported in part by the Natural Science Foundation of China (No.62171393), the Fundamental Research Funds for the Central Universities (No.20720220064), FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003), and NSFC (No.62206173). We thank Zhiyong Wang for helping us incorporate FAST-LIO2 into our mapping system. We also acknowledge support from Shanghai Frontiers Science Center of Human-centered Artificial Intelligence (ShangHAI). + +# References + +[1] Mykhaylo Andriluka, Umar Iqbal, Eldar Insafutdinov, Leonid Pishchulin, Anton Milan, Juergen Gall, and Bernt Schiele. Posetrack: A benchmark for human pose estimation and tracking. 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Using the head-mounted LiDAR and camera to scan the IMUs wearer, we construct SLOPER4D, a large scene-aware dataset for global 4D human pose estimation in urban environments." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 143, + 495, + 192, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 495, + 192, + 506 + ], + "spans": [ + { + "bbox": [ + 143, + 495, + 192, + 506 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 45, + 521, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 521, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 45, + 521, + 287, + 689 + ], + "type": "text", + "content": "We present SLOPER4D, a novel scene-aware dataset collected in large urban environments to facilitate the research of global human pose estimation (GHPE) with human-scene interaction in the wild. Employing a head-mounted device integrated with a LiDAR and camera, we record 12 human subjects' activities over 10 diverse urban scenes from an egocentric view. Frame-wise annotations for 2D key points, 3D pose parameters, and global translations are provided, together with reconstructed scene point clouds. To obtain accurate 3D ground truth in such large dynamic scenes, we propose a joint optimization method to fit local SMPL meshes to the scene and fine-tune the camera calibration during dynamic motions frame by frame, resulting in plausible and scene-natural 3D human poses. Even" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "type": "text", + "content": "tually, SLOPER4D consists of 15 sequences of human motions, each of which has a trajectory length of more than 200 meters (up to 1,300 meters) and covers an area of more than " + }, + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "type": "inline_equation", + "content": "200\\mathrm{m}^2" + }, + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "type": "text", + "content": " (up to " + }, + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "type": "inline_equation", + "content": "30,000\\mathrm{m}^2" + }, + { + "bbox": [ + 306, + 495, + 545, + 651 + ], + "type": "text", + "content": "), including more than 100k LiDAR frames, 300k video frames, and 500k IMU-based motion frames. With SLOPER4D, we provide a detailed and thorough analysis of two critical tasks, including camera-based 3D HPE and LiDAR-based 3D HPE in urban environments, and benchmark a new task, GHPE. The in-depth analysis demonstrates SLOPER4D poses significant challenges to existing methods and produces great research opportunities. The dataset and code are released at http://www.lidarhumanmotion.net/sloper4d/." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 657, + 386, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 386, + 669 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 386, + 669 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "Urban-level human motion capture is attracting more and more attention, which targets acquiring consecutive fine-grained human pose representations, such as 3D skeletons" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "682" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "content": "and parametric mesh models, with accurate global locations in the physical world. It is essential for human action recognition, social-behavioral analysis, and scene perception and further benefits many downstream applications, including Augmented/Virtual Reality, simulation, autonomous driving, smart city, sociology, etc. However, capturing extra large-scale dynamic scenes and annotating detailed 3D representations for humans with diverse poses is not trivial." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 170, + 290, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 290, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 290, + 434 + ], + "type": "text", + "content": "Over the past decades, a large number of datasets and benchmarks have been proposed and have greatly promoted the research in 3D human pose estimation (HPE). They can be divided into two main categories according to the capture environment. The first class usually leverages marker-based systems [16, 33, 45], cameras [14, 59, 60], or RGB-D sensors [13, 64] to capture human local poses in constrained environments. However, the optical system is sensitive to light and lacks depth information, making it unstable in outdoor scenes and difficult to provide global translations, and the RGB-D sensor has limited range and could not work outdoors. The second class [39, 49] attempts to take advantage of body-mounted IMUs to capture occlusion-free 3D poses in free environments. However, IMUs suffer from severe drift for long-term capturing, resulting in misalignments with the human body. Then, some methods exploit additional sensors, such as RGB camera [17], RGB-D camera [46, 57, 67], or LiDAR [27] to alleviate the problem and make obvious improvement. However, they all focus on HPE without considering the scene constraints, which are limited in reconstructing human-scene integrated digital urban and human-scene natural interactions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 436, + 288, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 288, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 288, + 579 + ], + "type": "text", + "content": "To capture human pose and related static scenes simultaneously, some studies use wearable IMUs and body-mounted camera [12] or LiDAR [5] to register the human in large real scenarios and they are promising for capturing human-involved real-world scenes. However, human pose and scene are decoupled in these works due to the ego view, where auxiliary visual sensors are used for collecting the scene data while IMUs are utilized for obtaining the 3D pose. Different from them, we propose a novel setting for human-scene capture with wearable IMUs and global-view LiDAR and camera, which can provide multi-modal data for more accurate 3D HPE." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "In this paper, we propose a huge scene-aware dataset for sequential human pose estimation in urban environments, named SLOPER4D. To our knowledge, it is the first urban-level 3D HPE dataset with multi-modal capture data, including calibrated and synchronized IMU measurements, LiDAR point clouds, and images for each subject. Moreover, the dataset provides rich annotations, including 3D poses, SMPL [32] models and locations in the world coordinate system, 2D poses and bounding boxes in the image coordinate system, and reconstructed 3D scene mesh. In particular, we propose a joint optimization method for" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "obtaining accurate and natural human motion representations by utilizing multi-sensor complementation and scene constraints, which also benefit global localization and camera calibration in the dynamic acquisition process. Furthermore, SLOPER4D consists of over 15 sequences in 10 scenes, including library, commercial street, coastal runway, football field, landscape garden, etc., with up to " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "30\\mathrm{k}" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "m^2" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " area size and " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "200\\sim 1,000m" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " trajectory length for each sequence. By providing multi-modal capture data and diverse human-scene-related annotations, SLOPER4D opens a new door to benchmark urban-level HPE." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 204, + 545, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 275 + ], + "type": "text", + "content": "We conduct extensive experiments to show the superiority of our joint optimization approach for acquiring high-quality 3D pose annotations. Additionally, based on our proposed new dataset, we benchmark two critical tasks: camera-based 3D HPE and LiDAR-based 3D HPE, as well as provide benchmarks for GHPE." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 276, + 503, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 276, + 503, + 286 + ], + "spans": [ + { + "bbox": [ + 317, + 276, + 503, + 286 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 290, + 545, + 425 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 290, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 290, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 317, + 290, + 545, + 324 + ], + "type": "text", + "content": "- We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 334, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 334, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 334, + 545, + 380 + ], + "type": "text", + "content": "- We propose an effective joint optimization method for acquiring accurate human motions in both local and global by integrating LiDAR SLAM results, IMU poses, and scene constraints." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 389, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 389, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 317, + 389, + 545, + 425 + ], + "type": "text", + "content": "- We benchmark two HPE tasks as well as a GHPE task on SLOPER4D, demonstrating its potential of promoting urban-level 3D HPE research." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 436, + 392, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 392, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 392, + 449 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 456, + 460, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 460, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 460, + 468 + ], + "type": "text", + "content": "2.1. 3D Human Motion Datasets" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 715 + ], + "type": "text", + "content": "Many datasets have been proposed with different sensors and setups to facilitate the research on 3D human pose estimation. The H3.6M [16] is a large-size dataset providing synchronized video with optical-based MoCap in studio environments. To perform markerless capture in different indoor scenes, PROX [13] uses an RGB-D sensor to scan a single person. EgoBody [64] uses multiple RGB-D sensors to pre-scan the room and scan the interacting persons. LiDARHuman26M [27] can capture long-range human motions with static LiDAR and IMUs. However, they are limited to static environments, human activities, and interactions. 3DPW [49] is the first dataset providing 3D annotations in the wild which uses a single hand-held RGB camera to optimize human pose from IMUs for a certain period of frames. It doesn't provide accurate global translation and 3D scenes. HPS [12] reconstructs the human body pose using IMUs and self-localizes it with a head-mounted camera in large 3D scenes, but it heavily relies on the pre-built map. HSC4D [5] removes the reliance on the pre-built map and achieves global human motion capture in large scenes." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "683" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 70, + 535, + 184 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 535, + 184 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 535, + 184 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 535, + 184 + ], + "type": "table", + "html": "
DatasetIn the wildGlobal3D ScenePoint cloudVideoIMU# Scene# Area size (m2)# Subject# Frame
H3.6M [16]X✓XX✓X-12113.6M
3DPW [49]✓XXX✓✓-< 300751k
PROX [13]X✓✓X✓X12< 302020k
HPS [12]✓✓✓X✓*✓8< 1,00077k
HSC4D [5]✓✓✓✓*X✓5< 5,000210k
LH26M [27]XXX✓✓✓-< 20013184k
EgoBody [64]X✓✓X✓X15< 5020153k
SLOPER4D✓✓✓✓✓✓10< 30,00012100k
", + "image_path": "b0b82f21ab7a2fe965a1ab877212887ea9a196bb40b53261fa6a1b36c286398c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 187, + 547, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 547, + 210 + ], + "type": "text", + "content": "Table 1. Comparisons with existing datasets. \"Global\" denotes to human poses with global translation. The \"area size\" is estimated with the published data. The * indicates the data modality is only used for human self-localization rather than for human-related data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 219, + 288, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 288, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 288, + 279 + ], + "type": "text", + "content": "However, the camera in HPS and the LiDAR in HSC4D are only used to perceive the environment rather than capture human data. With the scene-aware dataset we proposed for global human pose estimation, we can benchmark the 3D HPE in the wild with the LiDAR or camera modalities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 286, + 262, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 286, + 262, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 286, + 262, + 300 + ], + "type": "text", + "content": "2.2. Human Localization and Scene Mapping" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 304, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 304, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 45, + 304, + 288, + 555 + ], + "type": "text", + "content": "Human self-localization aims at estimating the 6-DoF of the human subject in global coordinates. The image-based methods [21, 37, 52] regress locations directly from a single image with a pre-built map. The scene-specific property makes them hard to generalize to unseen scenes. LiDAR is widely used in Simultaneous Localization and Mapping (SLAM) [4, 28, 41, 62] due to its robustness and low drift. To address the drift problem and improve robustness in dynamic motions, RGB cameras [40, 44, 63], IMU [10, 36, 42], or both [6, 43, 68], have been integrated with the mapping task. Most attention has been paid to autonomous driving [9] [23] or robotics from the third-person view and they usually do not focus on humans. To achieve self-localization, LiDAR is designed as backpacked [20, 31, 54] and handheld [2]. To efficiently capture human motions and reconstruct urban scenes, we utilize LiDAR with a built-in IMU (different from the IMUs for motion capture) and propose a pipeline for constructing multi-modal data. This approach provides accurate information on human motions at both local and global levels, as well as enables mapping in large outdoor environments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 563, + 234, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 234, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 234, + 575 + ], + "type": "text", + "content": "2.3. Global 3D Human Pose Estimation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Most studies recover human meshes in camera coordinate [26, 66] or root-relative poses [18, 24, 25]. Recovering global human motions in unconstrained scenes is a challenging topic in computer vision and has gained more and more research interest in recent years. IMU sensors are widely used in commercial [38, 39] and research activities [15, 48, 51], and are attached to body limbs to capture human motions in studio-environments. But it suffers severe drift in the wild. Some methods rely on additional RGB [8, 34, 49, 50] or pre-scan maps [12], or LiDAR [5] to complement the IMUs in large-scale scenes. Based on" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 219, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 547, + 411 + ], + "type": "text", + "content": "human-scene interaction, some work proposed scene-aware solutions using static cameras [14, 60] to obtain accurate and scene-natural human motions. 4DCapture [30] uses a dynamic head-mounted camera to self-localize and reconstruct the scene with the Struct From Motion method. However, it often fails when the illumination changes in the wild. MOVER [60] uses a single camera to optimize the 3D objects in a static scene, resulting in better 3D scene reconstruction and human motions. GLAMR [61] uses global trajectory predictions to constrain both human motions and dynamic camera poses, achieving state-of-the-art results on inthe-wild videos. However, it lacks a benchmark for quantitatively comparing different HPE methods on a global level. To deal with this limitation, we propose SLOPER4D, the first large-scale urban-level human pose dataset with rich 2D/3D annotations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 422, + 425, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 425, + 435 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 425, + 435 + ], + "type": "text", + "content": "3. SLOPER4D Dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 443, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 547, + 540 + ], + "type": "text", + "content": "SLOPER4D collects scene-aware 4D human data with our body-worn capturing system in urban scenes. In this section, we first introduce the data acquisition in Sec. 3.1, second, we detail the data construction and annotation process in Sec. 3.2, then we introduce the global optimization-based Sec. 3.3 method to obtain high quality both 3D/2D data, finally, we compare our dataset in Sec. 3.4 with the existing datasets and highlight our novelty." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 548, + 408, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 408, + 561 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 408, + 561 + ], + "type": "text", + "content": "3.1. Data Acquisition" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Hardware setup. As shown in Fig. 1, during the data collection procedure, the scanning person follows the performer (IMUs wearer) and scans him with a LiDAR and a camera on the helmet. Additionally, Fig. 2 shows the hardware details of our capturing system. Regarding the sensor module, the 128-beams Ouster-os1 LiDAR and the DJI-Action2 camera are rigidly installed on the helmet. To capture raw human motions, we use Noitom's inertial MoCap product, PN Studio, to attach 17 wireless IMUs to the IMU wearer's body limbs, torso, and head. The camera's field of view (FOV) is " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "116^{\\circ} \\times 84^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and the LiDAR's FOV is " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ} \\times 45^{\\circ}" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ". To make the performer within the LiDAR's FOV" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "684" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 282, + 255 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 282, + 255 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 282, + 255 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 282, + 255 + ], + "type": "image", + "image_path": "d9c3d5862253826f16f29b745c027ee5d28526a7f241e730f31bb73b395fddf9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 260, + 287, + 305 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 287, + 305 + ], + "type": "text", + "content": "Figure 2. Our capturing system's hardware details. The sensor module includes a LiDAR, a camera, and 17 body-attached IMU sensors. The storage module consists of a NUC11, a receiver, and a battery in the backpack." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 308, + 286, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 286, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 286, + 392 + ], + "type": "text", + "content": "as much as possible, we tilt the LiDAR down around " + }, + { + "bbox": [ + 46, + 308, + 286, + 392 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 46, + 308, + 286, + 392 + ], + "type": "text", + "content": ". Regarding the storage module, the scanning person's backpack places a wireless IMU data receiver, a 24V battery, and an Intel NUC11. The mini-computer NUC11 stores IMU data from the wireless receiver and point clouds from LiDAR in real-time. Videos are stored locally in the camera. The LiDAR and NUC11 are both powered by the battery." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": "Coordinate systems. Let's define three coordinate systems: 1) IMU coordinate system " + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "inline_equation", + "content": "\\{I\\}" + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": ": the origin is at LiDAR wearer's spine base at the starting time, and the " + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "inline_equation", + "content": "X / Y / Z" + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": " axis is pointing left/upward/forward of the human. 2) LiDAR Coordinate system " + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "inline_equation", + "content": "\\{L\\}" + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": ": the origin is at the center of the LiDAR, and the " + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "inline_equation", + "content": "X / Y / Z" + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": " axis is pointing right/forward/upward of the LiDAR. 3) Global/World coordinate system " + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "inline_equation", + "content": "\\{W\\}" + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": ": the origin is on the floor of the LiDAR wearer's starting position, and the " + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "inline_equation", + "content": "X / Y / Z" + }, + { + "bbox": [ + 46, + 396, + 286, + 515 + ], + "type": "text", + "content": " axis is pointing right/forward/upward of the LiDAR wearer." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": "Calibration. Following the setup in [53], we use a chessboard to calibrate the camera intrinsic " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "K_{in}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": " and introduces a terrestrial laser scanner (TLS) to obtain accurate camera extrinsic parameter, " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "K_{ex}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": ". Due to the LiDAR point cloud being too sparse, we manually choose the corresponding points both on the 2D image and the TLS map registered to the point cloud, and then we solve the perspective-n-point (PnP) problem to obtain " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "K_{in}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": ". For every 3D scene, the calibration " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "R_{WL}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": ", which transforms " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "\\{L\\}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "\\{W\\}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": " is manually set to make the ground's " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": "-axis upward and height to zero for the starting position. By using singular value decomposition, the calibration " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "R_{WI}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": ", which transforms " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "\\{I\\}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "inline_equation", + "content": "\\{W\\}" + }, + { + "bbox": [ + 46, + 519, + 286, + 686 + ], + "type": "text", + "content": ", is calculated through the similarity between IMU trajectory and LiDAR trajectory on the XY plane." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "content": "Synchronization. The synchronization of data from multiple sensors in human subject data is achieved through peak" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": "detection. Before and after the capture, the subject is asked to perform jumps. Then the peak height time in IMU is automatically detected and the peak times in the LiDAR and camera data are manually identified. Finally, all modalities are aligned by the peaks and downsampled to match the LiDAR frame rate of " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "20\\mathrm{Hz}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 153, + 404, + 166 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 153, + 404, + 166 + ], + "spans": [ + { + "bbox": [ + 306, + 153, + 404, + 166 + ], + "type": "text", + "content": "3.2. Data Processing" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "type": "text", + "content": "2D pose detection. We use Detectron [56] to detect and Deepsort [55] to track humans in videos. However, the tracking often fails due to the IMUs wearer entering/exiting the field of view or occlusions. To solve this problem, we manually assign the same ID for the tracked person in a video sequence. As for 3D point cloud reference, we project them on images according to the " + }, + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "type": "inline_equation", + "content": "K_{ex}" + }, + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "type": "text", + "content": ". However, due to the jitter brought by dynamic motions, the camera and the Li-DAR are not perfectly rigidly connected. Thus, " + }, + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "type": "inline_equation", + "content": "K_{ex}" + }, + { + "bbox": [ + 305, + 175, + 545, + 295 + ], + "type": "text", + "content": " will be further optimized in Sec. 3.3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "text", + "content": "LiDAR-inertial localization and mapping. The LiDAR-only method often fails in mapping because of the dynamic head rotation and crowded urban environments. Incorporating an IMU can compensate for motion distortion in a LiDAR scan " + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "inline_equation", + "content": "p^L" + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "text", + "content": " and provide an accurate initial pose. Using a LiDAR with an integrated IMU, and by combining Kalman filter-based lidar-inertial odometry [58] with factor graph-based loop closure optimization [7] [22], we successfully estimate the ego-motion of LiDAR and build the global consistency 3D scene map with n frame point clouds " + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "inline_equation", + "content": "P_{1:n}^{L} = \\{p_{1}^{L},\\dots ,p_{n}^{L}\\}" + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "text", + "content": ". To provide accurate scene constrain in Sec. 3.3, we utilize the VDB-Fusion [47] to generate a clean scene mesh " + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 298, + 545, + 454 + ], + "type": "text", + "content": " that excludes moving objects." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": "IMUs pose estimation. We use SMPL [32] to represent the human body motion " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "M^{I} = \\varPhi(\\theta^{I}, t^{I}, \\beta) \\in \\mathbb{R}^{6890 \\times 3}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " in IMU coordinate space " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\{I\\}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": ", where pose parameter " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\Theta_{1:n}^{I} = \\{\\theta_{1}^{I}, \\dots, \\theta_{n}^{I}\\} \\in \\mathbb{R}^{72 \\times n}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " is composed of pelvis joint's orientation " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "R_{1:n}^{I} = \\{r_{1}^{I}, \\dots, r_{n}^{I}\\} \\in \\mathbb{R}^{3 \\times n}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " and the other 23 joints' rotation relative to their parent joint. The " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "T_{1:n}^{I} = \\{t_{1}^{I}, \\dots, r_{n}^{I}\\} \\in \\mathbb{R}^{3 \\times n}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " is the pelvis joint's translation and " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{10}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " is a constant value representing a person's body shape. " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " are estimated by the commercial MoCap product, while " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " is obtained by using IPNet [3] to fit the scanned model captured by an iPhone13 Promax. Since the IMU are accurate locally but drift globally, " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "T^{I}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " is used for raw calibration of the " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\{I\\}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\{W\\}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": ", and the initial global motion " + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "inline_equation", + "content": "M = M^{W} = R^{WI}M^{I}" + }, + { + "bbox": [ + 305, + 457, + 545, + 625 + ], + "type": "text", + "content": " will be further optimized." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 635, + 416, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 416, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 416, + 647 + ], + "type": "text", + "content": "3.3. Data Optimization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "To obtain precise and scene-plausible human motion " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " in the world coordinate system, we use scene geometry " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " with several physico-based terms to perform joint optimizations to find the optimal motion " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "M^{*}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " that minimize " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": ". In a k-frame segment, the optimization is written as:" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "685" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 289, + 335 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 289, + 335 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 289, + 335 + ], + "type": "image", + "image_path": "04ccb905610d26d59ac5e51fe2ff0258171dd73c88349a464f2064cefc6aa1d1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 341, + 547, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 341, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 547, + 376 + ], + "type": "text", + "content": "Figure 3. The pipeline of the dataset construction. The capturing system simultaneously collects multimodal data, including LiDAR, camera, and IMU data. Then they are further processed. A joint optimization approach with multiple loss terms is then employed to optimize motion locally and globally. As a result, we obtain rich 2D/3D annotations with accurate global motion and scene information." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 292, + 70, + 414, + 335 + ], + "blocks": [ + { + "bbox": [ + 292, + 70, + 414, + 335 + ], + "lines": [ + { + "bbox": [ + 292, + 70, + 414, + 335 + ], + "spans": [ + { + "bbox": [ + 292, + 70, + 414, + 335 + ], + "type": "image", + "image_path": "76285f66060c4561ad9dc45d47c7a6fe6ab9c965ff24ce6cbaedf22c18c873c8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 417, + 70, + 539, + 335 + ], + "blocks": [ + { + "bbox": [ + 417, + 70, + 539, + 335 + ], + "lines": [ + { + "bbox": [ + 417, + 70, + 539, + 335 + ], + "spans": [ + { + "bbox": [ + 417, + 70, + 539, + 335 + ], + "type": "image", + "image_path": "ea40a3c9dca492023d2dc292ca2a0b49d3c4fc99b42942540f313fb4866d392f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 382, + 186, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 382, + 186, + 400 + ], + "spans": [ + { + "bbox": [ + 64, + 382, + 186, + 400 + ], + "type": "interline_equation", + "content": "M _ {1: k} ^ {*} = \\arg \\min _ {M _ {1: k}} \\mathcal {L} (M _ {1: k}, \\boldsymbol {S}),", + "image_path": "87a8b731154bfeab762c4360f9941f2efd100eaeaead5e462ae563bd109b0b7b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 64, + 402, + 287, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 402, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 64, + 402, + 287, + 418 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {s m t} + \\lambda_ {s c} \\mathcal {L} _ {s c} + \\lambda_ {p r i} \\mathcal {L} _ {p r i} + \\lambda_ {m 2 p} \\mathcal {L} _ {m 2 p}, \\tag {1}", + "image_path": "3f250086d75da7bb532f686a240d093a429ea243968133bf85c9d3903426b52b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 420, + 258, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 420, + 258, + 434 + ], + "spans": [ + { + "bbox": [ + 64, + 420, + 258, + 434 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s m t} = \\lambda_ {\\text {t r a n s}} \\mathcal {L} _ {\\text {t r a n s}} + \\lambda_ {\\text {o r i t}} \\mathcal {L} _ {\\text {o r i t}} + \\lambda_ {j t s} \\mathcal {L} _ {j t s},", + "image_path": "e9e4ea8fa817e0a227d247d34335a9ab2d215955614cc5d98bb5b54f84318a1a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{smt}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": " is a smoothness term, which consists of a translation loss " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{trans}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": ", an orientation loss " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{orit}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": ", and a joints loss " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{jts}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sc}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": " is a scene-aware-contact term, " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{pri}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": " is a pose prior term, and " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{m2p}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": " is a mesh-to-points term. The " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\lambda_{sc}, \\lambda_{pri}, \\lambda_{trans}, \\lambda_{orit}, \\lambda_{jts}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\lambda_{m2p}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": " are loss terms' coefficients. " + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 438, + 287, + 510 + ], + "type": "text", + "content": " is minimized with a gradient descent algorithm." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "text", + "content": "Smoothness term. The objective of this term is to minimize the acceleration of the pelvis joint, the accelerations of the other 23 pelvis-relative joints, which is denoted as " + }, + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "inline_equation", + "content": "J_{1:k} = \\{j_1,\\dots ,j_k\\} \\in \\mathbb{R}^{69\\times k}" + }, + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "text", + "content": ", and the angular velocity of all joints to smooth human movements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "text", + "content": "Scene-aware contact term. we compare the movement of every foot vertices in IMU motions " + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "inline_equation", + "content": "M_{k}^{I}" + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "text", + "content": " and label the foot as stable if its velocity is less than " + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "inline_equation", + "content": "0.1 \\, m/s^2" + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "text", + "content": ". Finally, the Chamfer Distance (CD) between this foot and its closest surface is expressed as the scene contact loss " + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sc}" + }, + { + "bbox": [ + 46, + 576, + 288, + 636 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "type": "text", + "content": "Pose prior term. The poses estimated by IMUs are roughly accurate but will likely cause some misalignments to the end of the body limb due to the accumulating error. Hence, " + }, + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text {prior }}" + }, + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "type": "text", + "content": " is used to constrain the " + }, + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 639, + 287, + 698 + ], + "type": "text", + "content": " close to the initial value at the beginning of the optimization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": "Mesh-to-points term. The point cloud " + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "inline_equation", + "content": "p^L" + }, + { + "bbox": [ + 47, + 701, + 287, + 714 + ], + "type": "text", + "content": " from the mov" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "text", + "content": "ing LiDAR provides strong prior depth information. However, though the SMPL mesh is watertight and complete, the human points are sparse and partial, which makes the registration methods such as ICP, not ideal as expected. To address this issue, we propose a viewpoint-based mesh-to-point loss function " + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{m2p}" + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "text", + "content": ". First, we remove the hidden SMPL mesh faces from the LiDAR's viewpoint. Then we sample points, denoted as " + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "inline_equation", + "content": "P_{1:k}^{\\prime} = \\{p_{1}^{\\prime},\\dots ,p_{k}^{\\prime}\\}" + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "text", + "content": ", from the remaining faces by LiDAR resolution. The loss is defined as the Chamfer Distance from " + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "inline_equation", + "content": "P_{1:k}^{\\prime}" + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "inline_equation", + "content": "P_{1:k}" + }, + { + "bbox": [ + 304, + 387, + 545, + 507 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 510, + 511, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 510, + 511, + 521 + ], + "spans": [ + { + "bbox": [ + 318, + 510, + 511, + 521 + ], + "type": "text", + "content": "All loss terms functions are detailed as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 338, + 540, + 513, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 540, + 513, + 572 + ], + "spans": [ + { + "bbox": [ + 338, + 540, + 513, + 572 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t r a n s} = \\frac {1}{k - 2} \\sum_ {i = 1} ^ {k - 2} \\| t _ {i + 2} - 2 t _ {i + 1} + t _ {i} \\| _ {2} ^ {2},", + "image_path": "abffb983585554982b9568edbde83c8840f331dffe8c4536d642f1b5ed3e9705.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 338, + 574, + 504, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 574, + 504, + 608 + ], + "spans": [ + { + "bbox": [ + 338, + 574, + 504, + 608 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {j t s} = \\frac {1}{k - 2} \\sum_ {i = 1} ^ {k - 2} \\| \\mathcal {J} _ {i + 2} - 2 \\mathcal {J} _ {i + 1} + \\mathcal {J} _ {i} \\| _ {2} ^ {2},", + "image_path": "5f76bc266a508ea175d4d2b11ea27e747c884f90ea40d88f6b21b1986a3523b0.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 338, + 610, + 545, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 610, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 338, + 610, + 545, + 643 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o r i t}} = \\frac {1}{k - 1} \\sum_ {i = 1} ^ {k - 1} \\| r _ {i + 1} - r _ {i} \\| _ {2} ^ {2}, \\tag {2}", + "image_path": "f20eb23e8f5c30618d80d5752ece58958e77793e2576336b9a15f6620c70d4ae.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 339, + 645, + 466, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 645, + 466, + 677 + ], + "spans": [ + { + "bbox": [ + 339, + 645, + 466, + 677 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p r i} = \\frac {1}{k} \\sum_ {i = 1} ^ {k} \\| \\theta_ {i} - R ^ {W I} \\theta_ {i} ^ {I} \\| _ {2} ^ {2},", + "image_path": "a4adf38335e198e4ce6b9ad5810667ed5f337cedac83c927af8ec060cf5d1976.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 339, + 681, + 507, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 681, + 507, + 716 + ], + "spans": [ + { + "bbox": [ + 339, + 681, + 507, + 716 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m 2 p} = \\frac {1}{k} \\sum_ {i = 1} ^ {k} \\sum_ {\\hat {p ^ {\\prime}} \\in p _ {i} ^ {\\prime}} \\frac {1}{| p _ {i} ^ {\\prime} |} \\min _ {\\hat {p} \\in p _ {i}} \\| \\hat {p} - \\hat {p ^ {\\prime}} \\| _ {2} ^ {2}.", + "image_path": "26ef9990619b6043f9589ef5ed7fb0da9d10f587f54bfa2be95fa6bca673ae3f.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "686" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 298, + 209 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 298, + 209 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 298, + 209 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 298, + 209 + ], + "type": "image", + "image_path": "ef098b021f375666ddff575fc506701a85afc40d4312063b785bdcf20ccf84bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 72, + 541, + 209 + ], + "blocks": [ + { + "bbox": [ + 298, + 72, + 541, + 209 + ], + "lines": [ + { + "bbox": [ + 298, + 72, + 541, + 209 + ], + "spans": [ + { + "bbox": [ + 298, + 72, + 541, + 209 + ], + "type": "image", + "image_path": "86cf44f94a386a2517ad9562bfe004d8c857dee158b09df98acb986915400084.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 51, + 210, + 298, + 347 + ], + "blocks": [ + { + "bbox": [ + 51, + 210, + 298, + 347 + ], + "lines": [ + { + "bbox": [ + 51, + 210, + 298, + 347 + ], + "spans": [ + { + "bbox": [ + 51, + 210, + 298, + 347 + ], + "type": "image", + "image_path": "9fa2b9dfe264a43fb76fbaabb17243c8c627e5d3e00ec9a1c57c6e11684ad35d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 354, + 546, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 354, + 546, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 546, + 376 + ], + "type": "text", + "content": "Figure 4. The diverse scenes and activities of our dataset. The images in the left column are our reconstructed scenes with human trajectories overlaid on them. The right images are the SMPL meshes overlaid on images / point clouds / scenes." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 210, + 541, + 348 + ], + "blocks": [ + { + "bbox": [ + 298, + 210, + 541, + 348 + ], + "lines": [ + { + "bbox": [ + 298, + 210, + 541, + 348 + ], + "spans": [ + { + "bbox": [ + 298, + 210, + 541, + 348 + ], + "type": "image", + "image_path": "afa4bf9ca6b3318db4901c9d382de52267a23ecb48884a91f913ad028a9b4db0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": "Camera extrinsic optimization. We aim to optimize extrinsic parameters " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "K_{ex}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " for every frame by minimizing the " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cam}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": ", which comprises of the keypoints loss " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kpt}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " and the bounding box loss " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{box}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{kpt}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " measures the mean square error between the 2D human keypoints " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "kpt^{2d}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " in the image and the 3D human keypoints " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "kpt^{3d}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " of the optimized SMPL model projected to the image with " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "K_{ex}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": "; the " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{box}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " computes the Intersection over Union loss between the 2D human bounding box " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "box^{2d}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " in the image and the 3D human bounding box " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "box^{3d}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": " projected to the image with " + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "inline_equation", + "content": "K_{ex}" + }, + { + "bbox": [ + 46, + 389, + 287, + 509 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 513, + 233, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 513, + 233, + 531 + ], + "spans": [ + { + "bbox": [ + 91, + 513, + 233, + 531 + ], + "type": "interline_equation", + "content": "K _ {e x} ^ {*} = \\arg \\min _ {K _ {e x} \\in S E (3)} \\mathcal {L} _ {c a m} (K _ {e x}),", + "image_path": "06a571ad98016309edfcc96c2831e7e6d8e1508686c61c234468128155ef7af6.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 87, + 533, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 533, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 87, + 533, + 287, + 548 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c a m} = \\lambda_ {k p t} \\mathcal {L} _ {k p t} \\left(k p t ^ {3 d}, k p t ^ {2 d}, K _ {e x}\\right) + \\tag {3}", + "image_path": "90f49562994338ac231e953b8cda46aa534634fdcc4fb152d70e593348575924.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 121, + 550, + 244, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 550, + 244, + 564 + ], + "spans": [ + { + "bbox": [ + 121, + 550, + 244, + 564 + ], + "type": "interline_equation", + "content": "\\lambda_ {b o x} \\mathcal {L} _ {b o x} \\left(b o x ^ {3 d}, b o x ^ {2 d}, K _ {e x}\\right),", + "image_path": "252209e3221d9a28cbd73199834938fa5684beee1be0112e74b18636430a06a0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "type": "inline_equation", + "content": "\\lambda_{kpt}" + }, + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "type": "inline_equation", + "content": "\\lambda_{box}" + }, + { + "bbox": [ + 47, + 570, + 234, + 582 + ], + "type": "text", + "content": " are constant coefficients." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 587, + 165, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 165, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 165, + 601 + ], + "type": "text", + "content": "3.4. Dataset Comparison" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "SLOPER4D is the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations for GHPE. The head-mounted LiDAR and camera are utilized to simultaneously record the IMU-wearer's activities, including running outside, playing football, visiting, reading, climbing/descending stairs, discussing, borrowing a book, greeting, etc. The dataset consists of 15 sequences from 12 human subjects in 10 locations. There are a total of " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "100\\mathrm{k}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " LiDAR frames, " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "300\\mathrm{k}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " video" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "type": "text", + "content": "frames, and 500k IMU-based motion frames captured over a total distance of more than " + }, + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "type": "inline_equation", + "content": "8km" + }, + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "type": "text", + "content": " and an area of up to " + }, + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "type": "inline_equation", + "content": "30,000m^2" + }, + { + "bbox": [ + 305, + 389, + 545, + 425 + ], + "type": "text", + "content": ". The results of our dataset are shown in Fig. 4." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 582 + ], + "type": "text", + "content": "For the captured person, we provide the segmentation of 3D points from LiDAR frames and 2D bounding boxes from images synchronized with LiDAR. We also provide 3D pose annotations with SMPL format. Compared to other datasets Tab. 1, it is worth mentioning that SLOPER4D provides the 3D scene reconstructions and accurate global translation annotations, allowing us to quantitatively study the scene-aware global pose estimation from both LiDAR and monocular videos. In addition to the dense 3D point cloud map reconstructed from the LiDAR, SLOPER4D provides the high-precision colorful point cloud map from a Terrestrial Laser Scanner (Trimble TX5) for better visualization and map comparison." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 596, + 388, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 596, + 388, + 610 + ], + "spans": [ + { + "bbox": [ + 306, + 596, + 388, + 610 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "In this section, we first evaluate SLOPER4D Dataset qualitatively, indicating that our dataset is solid enough to benchmark new tasks. Then we perform a cross-dataset evaluation to further assess our dataset's novelty on two tasks: LiDAR-based 3D HPE and camera-based 3D HPE. Finally, we introduce the new benchmark, GHPE, and perform experiments on GLAMR. More quantitative evaluations and experiments are in the supplementary material." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "687" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 282, + 183 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 282, + 183 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 282, + 183 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 282, + 183 + ], + "type": "image", + "image_path": "fbb75deec27903f44dedf109f36eb64ccb51ecb64e98f0e4cc5980d12c14992d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 190, + 287, + 224 + ], + "lines": [ + { + "bbox": [ + 47, + 190, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 190, + 287, + 224 + ], + "type": "text", + "content": "Figure 5. Comparison between our optimization results (red SMPL) and the ICP results (green SMPL). It shows the red SMPL aligns better with the cyan human points than the green SMPL." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 228, + 282, + 362 + ], + "blocks": [ + { + "bbox": [ + 48, + 228, + 282, + 362 + ], + "lines": [ + { + "bbox": [ + 48, + 228, + 282, + 362 + ], + "spans": [ + { + "bbox": [ + 48, + 228, + 282, + 362 + ], + "type": "image", + "image_path": "dbdbd32f01d1bf40adce58c6a94b4aafe4d31f01e600cb1c73a31f99e0902694.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 364, + 287, + 397 + ], + "lines": [ + { + "bbox": [ + 47, + 364, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 364, + 287, + 397 + ], + "type": "text", + "content": "Figure 6. The comparison before (left) and after (right) extrinsic optimization by projecting the point clouds (upper) and SMPL (lower) are projected onto the image." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 410, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 541 + ], + "type": "text", + "content": "Training/Test splits. We split our data into training and test sets for LiDAR/Camera-based pose estimation. The training set of SLOPER4D contains eleven sequences of data with a total of 80k LiDAR frames and corresponding RGB frames. The test set has four sequences of data with around 20k LiDAR frames and corresponding RGB frames. For global pose estimation, we select three challenging scenarios for evaluation. The first one is a single-person football training scenario with highly dynamic motions. The second one is running along a coastal runway. The third one is a garden tour involving daily motions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "Evaluation metrics. For 3D HPE, we employ Mean per joint position error (MPJPE) and Procrustes-aligned MPJPE (PA-MPJPE) for evaluation. MPJPE is the mean euclidean distance between the ground-truth and predicted joints. PA-MPJPE first aligns the predicted joints to the ground-truth joints by carrying out rigid transformation based on Procrustes analysis and then calculates MPJPE. For global trajectory evaluation, we utilize Absolute Trajectory Error (ATE) and the Relative Pose (the pose refers to orientation here) Error (RPE) in visual SLAM systems [11], where the ATE is well-suited for measuring the global localization and, in contrast, the RPE is suitable for measuring the system's drift, for example, the drift per second. Global MPJPE (G-MPJPE) is MPJPE calculated by placing the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 465, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 465, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 465, + 84 + ], + "type": "text", + "content": "SMPL model in the global coordinates." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 87, + 547, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 87, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 87, + 547, + 278 + ], + "type": "text", + "content": "Qualitative evaluation. For the human pose qualitative evaluation, we project the SMPL to the image and visualize the 3D human with corresponding LiDAR points in 3D space (shown in Fig. 4). The results demonstrate that the 3D human mesh aligns well with 3D environments and 2D images. As a large-scale urban-level human pose dataset, SLOPER4D provides multi-modal capture data and rich human-scene annotations, as well as diverse challenging human activities in large scenes. To evaluate our optimization method, we first compare our method with the results from ICP. As shown in Fig. 5, the scene-aware constraints and human mesh-to-points constraint efficiently optimize the local poses, global translation, and even the orientation error from IMU. To show the effectiveness of the camera extrinsic optimization, we report the results in Fig. 6. The 2D projecting error was visually lowered after optimization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 286, + 448, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 286, + 448, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 286, + 448, + 297 + ], + "type": "text", + "content": "4.1. Cross-Dataset Evaluation" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 312, + 545, + 362 + ], + "blocks": [ + { + "bbox": [ + 307, + 312, + 545, + 362 + ], + "lines": [ + { + "bbox": [ + 307, + 312, + 545, + 362 + ], + "spans": [ + { + "bbox": [ + 307, + 312, + 545, + 362 + ], + "type": "table", + "html": "
Test TrainLH26MOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
LH26M79.367.0228.7149.9
Ours212.3128.386.165.1
LH26M + Ours85.572.079.260.1
", + "image_path": "ac3ee26f7c22d2b09f00ba4b7cb00e5ae198a95c5c825002029fe34367c73cc7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 380, + 545, + 468 + ], + "blocks": [ + { + "bbox": [ + 329, + 362, + 522, + 372 + ], + "lines": [ + { + "bbox": [ + 329, + 362, + 522, + 372 + ], + "spans": [ + { + "bbox": [ + 329, + 362, + 522, + 372 + ], + "type": "text", + "content": "(a) LiDAR-based 3D pose estimation with LiDARCap [27]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 380, + 545, + 468 + ], + "lines": [ + { + "bbox": [ + 307, + 380, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 307, + 380, + 545, + 468 + ], + "type": "table", + "html": "
Test Train3DPWOurs
MPJPEPA-MPJPEMPJPEPA-MPJPE
VIBE [24]93.556.5102.566.2
Ours + AMASS124.366.886.652.4
w. 3DPW83.052.090.058.3
HbryIK [26]88.749.3104.957.0
w. Ours87.349.267.644.2
w. 3DPW71.341.875.850.0
w. 3DPW + Ours76.446.766.242.8
", + "image_path": "02d3326f481190f291363e05c13ca41e10ffb8b5aecae9000954bbbacdb698e8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 364, + 468, + 487, + 477 + ], + "lines": [ + { + "bbox": [ + 364, + 468, + 487, + 477 + ], + "spans": [ + { + "bbox": [ + 364, + 468, + 487, + 477 + ], + "type": "text", + "content": "(b) Camera-based 3D pose estimation." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 484, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 540 + ], + "type": "text", + "content": "Table 2. Cross-dataset evaluation results with different modalities. The LH26M in (a) refers to LiDARHuman26M dataset from LiDARcap. VIBE is pre-trained on AMASS [33], MPI-INF-3DHP [35] InstaVariety [19], PoseTrack [1], PennAction [65]. HbryIK is pre-trained on H36M, MPI-INF-3DHP, MSCOCO [29]" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "We evaluate root-relative 3D human pose estimation with different modalities, namely the LiDAR and the camera. 3DPW is an in-the-wild human motion dataset that is most related to us. With VIBE, we cross-evaluated our dataset's camera modal by using 3DPW. LiDARHuman26M is a lidar-based dataset for long-range human pose estimation. We can cross-evaluate our dataset's LiDAR modal with it. Tab. 2(a) shows the evaluation results on LiDAR-based 3D pose estimation task and Tab. 2(b) shows the results on camera-based 3D pose estimation. Taking the results from Tab. 2(a), for example, when the model is trained from another dataset only, the errors are the largest. But the error will be further reduced by around " + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": " when training on LiDARHuman26M and our dataset together. It" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "688" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "suggests a domain gap exists between different LiDAR sensors, and both datasets complement each other. The results of another task show that the pre-trained VIBE model generalizes better on 3DPW than on our dataset. But the error on 3DPW increases when finetuned on our dataset, while the error decreases on our dataset. This suggests that the pre-trained model complements SLOPER4D better than the opposite. Comparing the results across different modalities, the error on our dataset from the method trained on mixed LiDAR point cloud datasets is " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "13\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " lower than the method trained on the images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 210, + 287, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 287, + 221 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 287, + 221 + ], + "type": "text", + "content": "4.2. Benchmark on Global Human Pose Estimation" + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 57, + 226, + 278, + 311 + ], + "blocks": [ + { + "bbox": [ + 57, + 226, + 278, + 311 + ], + "lines": [ + { + "bbox": [ + 57, + 226, + 278, + 311 + ], + "spans": [ + { + "bbox": [ + 57, + 226, + 278, + 311 + ], + "type": "table", + "html": "
SequenceMetricRMSE ↓meanstd.max
FootballATE3.262.851.5811.83
Running001ATE29.4825.5514.7256.07
Garden001ATE2.862.571.266.55
FootballRPE0.080.060.051.34
Running001RPE0.400.350.191.04
Garden001RPE0.060.040.040.71
", + "image_path": "6ec0a646892b6d691bd5fba50a2ca95e58ae21de0064757ff51b110a13e9c82d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 52, + 336, + 282, + 387 + ], + "blocks": [ + { + "bbox": [ + 59, + 313, + 274, + 324 + ], + "lines": [ + { + "bbox": [ + 59, + 313, + 274, + 324 + ], + "spans": [ + { + "bbox": [ + 59, + 313, + 274, + 324 + ], + "type": "text", + "content": "Table 3. Global trajectory evaluation of GLAMR. Unit: " + }, + { + "bbox": [ + 59, + 313, + 274, + 324 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 59, + 313, + 274, + 324 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 336, + 282, + 387 + ], + "lines": [ + { + "bbox": [ + 52, + 336, + 282, + 387 + ], + "spans": [ + { + "bbox": [ + 52, + 336, + 282, + 387 + ], + "type": "table", + "html": "
SequenceScaleMPJPE ↓PA-MPJPE ↓G-MPJPE ↓
Football11.83264.6118.55268.7
Running00156.07652.1119.632329.3
Garden0016.55139.486.34407.0
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Unit: mm." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 410, + 282, + 559 + ], + "blocks": [ + { + "bbox": [ + 50, + 410, + 282, + 559 + ], + "lines": [ + { + "bbox": [ + 50, + 410, + 282, + 559 + ], + "spans": [ + { + "bbox": [ + 50, + 410, + 282, + 559 + ], + "type": "image", + "image_path": "b3db3b305a3a55fddfa5f97dbfa47cd2f0ab450d82362e7ea0c297f26e4f5ab6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 563, + 287, + 586 + ], + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 586 + ], + "type": "text", + "content": "Figure 7. The ATE error " + }, + { + "bbox": [ + 46, + 563, + 287, + 586 + ], + "type": "inline_equation", + "content": "(m)" + }, + { + "bbox": [ + 46, + 563, + 287, + 586 + ], + "type": "text", + "content": " mapped on the GT trajectory. The color represents the error according to the color bar." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 689 + ], + "type": "text", + "content": "In this subsection, we benchmark the GHPE task of GLAMR [61] on SLOPER4D. GLAMR is a global occlusion-aware method for 3D global human mesh recovery from dynamic monocular cameras. For the scale uncertainty of the monocular camera, we compute the affine matrix from the estimated trajectory to the ground truth trajectory and rotate, translate and scale the estimated trajectory before error computation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Tab. 3 reports the global trajectory error with ATE and RPE, Tab. 4 reports the global human pose metric, and" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": "Fig. 7 shows the ATE error mapped on GT trajectory. Comparing the results on the three scenes, the football and Garden001 have a significantly lower RPE in the global scene. In comparison, GLAMR performs the worst on the running scene, with an ATE's RMSE of " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "29.48\\mathrm{m}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": ". This scene has the largest area size and the highest human pace. GLAMR achieves a low PA-MPJPE of " + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "inline_equation", + "content": "86.3\\mathrm{mm}" + }, + { + "bbox": [ + 304, + 72, + 545, + 288 + ], + "type": "text", + "content": " on Garden001, a sequence with daily walking and visiting motions. It's the first time that we have tested the GPHE on such large outdoor scenes. GLAMR achieves relatively better results on daily human motion while performing worse on high-dynamic activities in the wild. The interesting point is that the trajectory tendency is pretty similar to the reference, even in dynamic football training motions, which demonstrates the ability of GLAMR to be a baseline. It is expected that more research will focus on GHPE in real-world interactive scenarios, and the experiments show our SLOPER4D's potential to promote urban-level GHPE research." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 308, + 380, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 308, + 380, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 308, + 380, + 319 + ], + "type": "text", + "content": "5. Discussions" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 333, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 545, + 441 + ], + "type": "text", + "content": "Limitations. Firstly, SLOPER4D is limited to single-person capture though it perceives multiple-person data. Secondly, the camera and LiDAR are not synchronized online, causing tedious offline work if the camera loses frames even with a low time offset (" + }, + { + "bbox": [ + 304, + 333, + 545, + 441 + ], + "type": "inline_equation", + "content": "< 50~ms" + }, + { + "bbox": [ + 304, + 333, + 545, + 441 + ], + "type": "text", + "content": "). Finally, texture information from the camera is not fully exploited for color and texture reconstruction of scenes and humans. In our future work, we will propose an online synchronization algorithm and extend our work to multiple-person capturing." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 447, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 579 + ], + "type": "text", + "content": "Conclusions. We propose the first large-scale urban-level human pose dataset with multi-modal capture data and rich human-scene annotations. Based on our proposed new dataset, we benchmark two critical tasks, camera-based 3D HPE and LiDAR-based 3D HPE. SLOPER4D also benchmarks the GHPE task. The results demonstrate the potential of SLOPER4D in boosting the development of these areas. Our work contributes to extending motion capture to large global scenes based on the current methods and datasets. We hope this work will foster future creation and interaction in urban environments." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 715 + ], + "type": "text", + "content": "Acknowledgements. This work was supported in part by the Natural Science Foundation of China (No.62171393), the Fundamental Research Funds for the Central Universities (No.20720220064), FuXiaQuan National Independent Innovation Demonstration Zone Collaborative Innovation Platform (No.3502ZCQXT2021003), and NSFC (No.62206173). We thank Zhiyong Wang for helping us incorporate FAST-LIO2 into our mapping system. We also acknowledge support from Shanghai Frontiers Science Center of Human-centered Artificial Intelligence (ShangHAI)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "689" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Mykhaylo Andriluka, Umar Iqbal, Eldar Insafutdinov, Leonid Pishchulin, Anton Milan, Juergen Gall, and Bernt Schiele. 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IEEE, 2019. 3" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "692" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_content_list.json b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..fac290ebcda9fb14462c58ece8cfaeea67906dc0 --- /dev/null +++ b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_content_list.json @@ -0,0 +1,1737 @@ +[ + { + "type": "text", + "text": "SMAE: Few-shot Learning for HDR Deghosting with Saturation-Aware Masked Autoencoders", + "text_level": 1, + "bbox": [ + 124, + 128, + 844, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qingsen Yan†1 Song Zhang†2 Weiye Chen†2 Hao Tang³ Yu Zhu¹", + "bbox": [ + 189, + 200, + 776, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jinqiu Sun $^{1}$ Luc Van Gool $^{3}$ Yanning Zhang $^{1*}$", + "bbox": [ + 290, + 220, + 684, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Northwestern Polytechnical University $^{2}$ Xidian University $^{3}$ CVL, ETH Zurich", + "bbox": [ + 150, + 239, + 813, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 312, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generating a high-quality High Dynamic Range (HDR) image from dynamic scenes has recently been extensively studied by exploiting Deep Neural Networks (DNNs). Most DNNs-based methods require a large amount of training data with ground truth, requiring tedious and time-consuming work. Few-shot HDR imaging aims to generate satisfactory images with limited data. However, it is difficult for modern DNNs to avoid overfitting when trained on only a few images. In this work, we propose a novel semi-supervised approach to realize few-shot HDR imaging via two stages of training, called SSHDR. Unlikely previous methods, directly recovering content and removing ghosts simultaneously, which is hard to achieve optimum, we first generate content of saturated regions with a self-supervised mechanism and then address ghosts via an iterative semi-supervised learning framework. Concretely, considering that saturated regions can be regarded as masking Low Dynamic Range (LDR) input regions, we design a Saturated Mask AutoEncoder (SMAE) to learn a robust feature representation and reconstruct a non-saturated HDR image. We also propose an adaptive pseudo-label selection strategy to pick high-quality HDR pseudo-labels in the second stage to avoid the effect of mislabeled samples. Experiments demonstrate that SSHDR outperforms state-of-the-art methods quantitatively and qualitatively within and across different datasets, achieving appealing HDR visualization with few labeled samples.", + "bbox": [ + 75, + 323, + 473, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 758, + 209, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Standard digital photography sensors are unable to capture the wide range of illumination present in natural scenes, resulting in Low Dynamic Range (LDR) images that often", + "bbox": [ + 75, + 784, + 468, + 830 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "*† The first three authors contributed equally to this work. This work was partially supported by NSFC (U19B2037, 61901384), Natural Science Basic Research Program of Shaanxi (2021JCW-03, 2023-JC-QN-0685), and National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology. Corresponding author: Yu Zhu.", + "bbox": [ + 75, + 838, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ae770f29fe0d77b7fa99b7f344fe67b31039282a8768363cf4545210445b745f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 290, + 576, + 324 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67c4779b1d49d793cad7a22e035bc602715af5b8e7a8ff9a31614b92aab07c8c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 289, + 794, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dc836e23247023ce32d6d1105c8366ed8fa8bc299fa438fba13f1fb6aad9230b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 797, + 290, + 843, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9119fe0482a0c0866255db4468ac120604e504925b8427a5629691c20c34dbb9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 799, + 327, + 844, + 363 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/268a45a03aa883d7a362057c529c2fcb568166115ba7dc793389cb9c26989018.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 846, + 290, + 890, + 325 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2ba0c236c4b42bf488f23dad188dcbc1e8ae80e6396d2afb4b7f2425f955fa08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 846, + 327, + 890, + 363 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4e5eafe4807f43f804c8e4bd1be140c4fde7270db3057b1e77806bbbd0e52095.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 846, + 366, + 890, + 402 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a5967468c55031fd71eeb2a7d0cf24973429b19ad7ac6ce205fa219d5cc67c27.jpg", + "image_caption": [ + "LDRs" + ], + "image_footnote": [], + "bbox": [ + 504, + 414, + 571, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f11641bc7dc13d15a157c1a01896f086ffcd49468a0f6503cc7fca12b9b4030b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 414, + 650, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d1fbbb9595be5f31734639d8778b7ce94acd25348f9de6476c067ce085f9f869.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 650, + 414, + 728, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3e387854f21812213115a85408740f1f4dcfae4f9fcc5d23845f674621a13c48.jpg", + "image_caption": [ + "LDR Patches" + ], + "image_footnote": [], + "bbox": [ + 728, + 414, + 810, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0cb375b1d717eb82c2a4fb617b843ed9f650037a27e2c129c2023bd1b51e548a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 810, + 414, + 890, + 459 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a186c3b538b54a9c700ec2479e360e58b36b99c9e1ead07f688ab540c781b7ce.jpg", + "image_caption": [ + "Sen", + "[24]", + "Figure 1. The proposed method generates high-quality images with few labeled samples when compared with several methods." + ], + "image_footnote": [], + "bbox": [ + 506, + 460, + 571, + 505 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b813d9767e45b072f4942aab66327c73c0b427fb8afe5454b030c25d6a31a1f3.jpg", + "image_caption": [ + "Kalantari", + "[9]", + "[31]" + ], + "image_footnote": [], + "bbox": [ + 571, + 460, + 650, + 505 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/85a6d071c2312b4dcc17f80ded69f438b5e2dce983c04ec092f52a07ef523ed2.jpg", + "image_caption": [ + "AHDR", + "ADNET", + "[14]" + ], + "image_footnote": [], + "bbox": [ + 650, + 460, + 730, + 505 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/452b95b3086597e56dd3e1c970e440e281ebdd0029ad6ba0ea8974bac7983153.jpg", + "image_caption": [ + "FSHDR", + "[22]", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 730, + 460, + 810, + 505 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/461c508d3cffe5ef88de37c961c85f14f92f94fc9677360c981c3593d09e1602.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 810, + 460, + 890, + 505 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "suffer from over or underexposed regions, which can damage the details of the scene. High Dynamic Range (HDR) imaging has been developed to address these limitations. This technique combines several LDR images with different exposures to generate an HDR image. While HDR imaging can effectively recover details in static scenes, it may produce ghosting artifacts when used with dynamic scenes or hand-held camera scenarios.", + "bbox": [ + 496, + 566, + 890, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Historically, various techniques have been suggested to address such issues, such as alignment-based methods [3,10,27,37], patch-based methods [8,15,24], and rejection-based methods [5, 11, 19, 20, 35, 40]. Two categories of alignment-based approaches exist: rigid alignment (e.g., homographies) that fail to address foreground motions, and non-rigid alignment (e.g., optical flow) that is error-prone. Patch-based techniques merge similar regions using patch-level alignment and produce superior results, but suffer from high complexity. Rejection-based methods aim to eliminate misaligned areas before fusing images, but may result in a loss of information in motion regions.", + "bbox": [ + 496, + 688, + 892, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As Deep Neural Networks (DNNs) become increasingly prevalent, the DNN-based HDR deghosting methods", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation.", + "bbox": [ + 236, + 0, + 807, + 18 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "Except for this watermark, it is identical to the accepted version;", + "bbox": [ + 323, + 16, + 722, + 30 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 292, + 31, + 753, + 45 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5775", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[9, 33, 36] achieve better visual results compared to traditional methods. However, these alignment approaches are error-prone and inevitably cause ghosting artifacts (see Figure 1 Kalantari's results). AHDR [31, 32] proposes spatial attention to suppress motion and saturation, which effectively alleviate misalignment problems. Based on AHDR, ADNET [14] proposes a dual branch architecture using spatial attention and PCD-alignment [29] to remove ghosting artifacts. All these above methods directly learn the complicated HDR mapping function with abundant HDR ground truth data. However, it's challenging to collect a large amount of HDR-labeled data. The reasons can be attributed to that 1) generating a ghost-free HDR ground truth sample requires an absolute static background, and 2) it is time-consuming and requires considerable manpower to do manual post-examination. This generates a new setting that only uses a few labeled data for HDR imaging.", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, FSHDR [22] attempts to generate a ghost-free HDR image with only few labeled data. They use a preliminary model trained with a large amount of unlabeled dynamic samples, and a few dynamic and static labeled samples to generate HDR pseudo-labels and synthesize artificial dynamic LDR inputs to improve the model performance of dynamic scenes further. This approach expects the model to handle both the saturation and the ghosting problems simultaneously, but it is hard to achieve under the condition of few labeled data, especially misaligned regions caused by saturation and motion (see Figure 1 FSHDR). In addition, FSHDR uses optical flow to forcibly synthesize dynamic LDR inputs from poorly generated HDR pseudo-labels, the errors in optical flow further intensify the degraded quality of artificial dynamic LDR images, resulting in an apparent distribution shift between LDR training and testing data, which hampers the performance of the network.", + "bbox": [ + 75, + 352, + 472, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The above analysis makes it very challenging to directly generate a high-quality and ghost-free HDR image with few labeled samples. A reasonable way is to address the saturation problems first and then cope with the ghosting problems with a few labeled samples. In this paper, we propose a semi-supervised approach for HDR deghosting, named SSHDR, which consists of two stages: self-supervised learning network for content completion and sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we pretrain a Saturated Mask AutoEncoder (SMAE), which learns the representation of HDR features to generate content of saturated regions by self-supervised learning. Specifically, considering that the saturated regions can be regarded as masking the short LDR input patches, inspired by [6], we randomly mask a high proportion of the short LDR input and expect the model to reconstruct a no-saturated HDR image from the remaining LDR patches in the first stage. This self-supervised approach allows the model to recover the saturated regions", + "bbox": [ + 75, + 613, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with the capability to effectively learn a robust representation for the HDR domain and map an LDR image to an HDR image. In the second stage, to prevent the overfitting problem with a few labeled training samples and make full use of the unlabeled samples, we iteratively train the model with a few labeled samples and a large amount of HDR pseudo-labels from unlabeled data. Based on the pretrained SMAE, a sample-quality-based iterative semi-supervised learning framework is proposed to address the ghosting artifacts. Considering the quality of pseudo-labels is uneven, we develop an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels (i.e., well-exposed, ghost-free) to avoid awful pseudo-labels hampering the optimization process. This selection strategy is guided by a few labeled samples and enhances the diversity of training samples in each epoch. The experiments demonstrate that our proposed approach can generate high-quality HDR images with few labeled samples and achieves state-of-the-art performance on individual and cross-public datasets. Our contributions can be summarized as follows:", + "bbox": [ + 496, + 90, + 893, + 393 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel and generalized HDR self-supervised pretraining model, which uses mask strategy to reconstruct an HDR image and addresses saturated problems from one LDR image.", + "- We propose a sample-quality-based semi-supervised training approach to select well-exposed and ghost-free HDR pseudo-labels, which improves ghost removal.", + "- We perform both qualitative and quantitative experiments, which show that our method achieves state-of-the-art results on individual and cross-public datasets." + ], + "bbox": [ + 500, + 393, + 890, + 545 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 561, + 640, + 577 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. HDR Deghosting Methods", + "text_level": 1, + "bbox": [ + 500, + 587, + 738, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The existing HDR deghosting methods include four categories: alignment-based method, patch-based method, rejection-based method, and CNN-based method.", + "bbox": [ + 496, + 611, + 890, + 656 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Alignment-based Method. Rigid or non-rigid registration is mainly used in alignment-based approaches. Bogoni [3] estimated flow vectors to align with the reference images. Kang et al. [10] utilized optical flow to align images in the luminance domain to remove ghosting artifacts. Tomaszewska et al. [27] used SIFT feature to perform global alignments. Since the dense correspondence computed by alignment methods are error-prone, they cannot handle large motion and occlusion.", + "bbox": [ + 496, + 657, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Rejection-based Method. Rejection-based methods detect and eliminate motion from static regions. Then they merge static inputs to get HDR images. Grosch et al. [5] estimated a motion map and used it to generate ghost-free HDR. Zhang et al. [40] obtained a motion weighting map using quality measurement on image gradients. Lee et al. [11] and Oh et al. [19] detected motion regions using rank min", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5776", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "imization. However, rejection-based methods remove the misalignment of regions. It will result in a lack of content in moving regions.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Patch-based Method. Patch-based methods use patch-level alignment to merge similar contents. Sen et al. [24] proposed a patch-based energy minimization approach that optimizes alignment and reconstruction simultaneously. Hu et al. [8] utilized a patch-match mechanism to produce aligned images. Although these methods have good performance, they suffer from high computational costs.", + "bbox": [ + 75, + 136, + 467, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CNN-based Method. Kalantari et al. [9] used a CNN network to fuse LDR images that are aligned with optical flow. Wu et al. [30] used homography to align the camera motion and reconstructed HDR images by CNN. Yan et al. [31] proposed an attention mechanism to suppress motion and saturation. Yan et al. [34] designed a nonlocal block to release the constraint of locality receptive field for global merging HDR. Niu et al. [18] proposed HDR-GAN to recover missing content using generative adversarial networks. Ye et al. [38] proposed multi-step feature fusion to generate ghost-free images. Liu et al. [14] utilized the PCD alignment subnetwork to remove ghosts. However, these methods require a large number of labeled samples, which is difficult to collect.", + "bbox": [ + 75, + 242, + 467, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Few-shot Learning (FSL)", + "text_level": 1, + "bbox": [ + 76, + 465, + 307, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Humans can successfully learn new ideas with relatively little supervision. Inspired by such ability, FSL aims to learn robust representations with few labeled samples. There are three main categories for FSL methods: databased category [1, 23, 25], which augment the experience with prior knowledge; model-based category [2, 17, 26], which shrinks the size of the hypothesis space using prior knowledge; algorithm-based category [4, 12, 39], which modifies the search for the optimal hypothesis using prior knowledge. For HDR deghosting, Prabhakar et al. [22] proposed a data-based category deghosting method, which uses artificial dynamic sequences synthesis for motion transfer. Still, it is hard to handle both the saturation and the ghosting problems simultaneously with few labeled data.", + "bbox": [ + 75, + 489, + 467, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 715, + 285, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Data Distribution", + "text_level": 1, + "bbox": [ + 76, + 739, + 248, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following the setting of few-shot HDR imaging [22], we utilize 1) $N$ dynamic unlabeled LDR samples $U = \\{L_1^U,\\dots ,L_N^U\\}$ , where each $L^U$ consists of three LDRs $(X_{1}^{U},X_{2}^{U},X_{3}^{U})$ with different exposures. 2) $M$ static labeled LDR samples $S = \\{L_1^S,\\dots ,L_M^S\\}$ , where each $L^S$ consists of three LDRs $(X_1^S,X_2^S,X_3^S)$ with different exposures and ground truth $Y^{S}$ . 3) $K$ dynamic labeled LDR samples $D = \\{L_1^D,\\dots ,L_K^D\\}$ , where each $L^D$ consists of three LDRs $(X_1^D,X_2^D,X_3^D)$ and ground truth $Y^{D}$ . Since it is difficult to", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "collect labeled samples, we set $K$ to be less than or equal to 5, and $M$ is fixed at 5. While it is easy to capture unlabeled samples, $N$ can be arbitrary.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Model Overview", + "text_level": 1, + "bbox": [ + 500, + 145, + 663, + 159 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generating a non-saturated and ghost-free HDR image with few labeled samples is challenging. It is a proper way to address saturated problems first and then handle ghosting problems. As shown in Figure 2, we propose a semi-supervised approach for HDR deghosting. Our approach consists of two stages: a self-supervised learning network for content completion and a sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we propose a multi-scale Transformer model based on self-supervised learning with a saturated-masked autoencoder to make it capable of recovering saturated regions. In a word, we randomly mask LDR patches and reconstruct non-saturated HDR images from the remaining LDR patches.", + "bbox": [ + 496, + 167, + 890, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the second stage, we propose a sample-quality-based iterative semi-supervised learning approach that learns to address ghosting problems. We finetune the pretrained model based on the first stage with a few labeled samples. Then, we iteratively train the model with labeled samples and unlabeled samples with pseudo-labels. Considering that the HDR pseudo-labels inevitably contain saturated and ghosting regions, which deteriorate the model performance, we propose an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process.", + "bbox": [ + 496, + 364, + 890, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Self-supervised Learning Stage", + "text_level": 1, + "bbox": [ + 500, + 540, + 774, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Input. Considering that there are more saturated regions in the medium $(X_2^U)$ and long exposure frames $(X_3^U)$ of unlabeled data $U$ , we first transform the short exposure frame $(X_1^U)$ into a new medium $(X_{2^{\\prime}}^{U})$ and long exposure frames $(X_{3^{\\prime}}^{U})$ by exposure adjustment,", + "bbox": [ + 498, + 564, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nX _ {i ^ {\\prime}} ^ {U} = \\operatorname {c l i p} \\left(\\left(\\frac {\\left(X _ {1} ^ {U}\\right) ^ {\\gamma} \\times t _ {i}}{t _ {1}}\\right) ^ {\\frac {1}{\\gamma}}\\right), \\quad i = 2, 3. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 651, + 890, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Then following previous work [9, 30], we map the LDR input images $X_{1}^{U}, X_{2'}^{U}, X_{3'}^{U}$ to HDR domain by gamma correction to get $H_{i}$ ,", + "bbox": [ + 498, + 694, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH _ {i ^ {\\prime}} = \\left(X _ {i ^ {\\prime}} ^ {U}\\right) ^ {\\gamma} / t _ {i}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 746, + 890, + 766 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Note that $X_{1'}^U = X_1^U$ , $t_i$ denotes the exposure time of LDR image $X_i$ , $\\gamma$ represents the gamma correction parameter, we set $\\gamma$ to 2.2. Then, we concatenate $X_{i'}$ and $H_{i'}$ along the channel dimension to get a 6-channel input $I_i = [X_{i'}, H_{i'}]$ , we subsequently mask the input $I_i$ patches to get $I_i'$ . Concretely, we divide the input into non-overlapping patches and randomly mask a subset of these patches with a high mask ratio (75%) (see Figure 3). Note that the patch size", + "bbox": [ + 496, + 776, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5777", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d4c38973c69615b4c75e303c0526dc60ea36e3dbaf5bc95ccd08bc54dd3f2dcb.jpg", + "image_caption": [ + "Figure 2. The overview of our framework." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 898, + 368 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6450e334fca0bab898d2f9e884551fc4b61bfe31a318cf92e6b1d9170cc48fe4.jpg", + "image_caption": [ + "Figure 3. The detailed procedure of Stage 1. To recover the saturated regions, we utilize the short exposure frame as input and ground truth." + ], + "image_footnote": [], + "bbox": [ + 76, + 392, + 472, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is $8 \\times 8$ . Considering that the masking strategy is another way to destruct the saturated regions, we intend the model to learn a robust representation to recover these saturated regions. Finally, $I' = \\{I_1', I_2', I_3'\\}$ is the input of the model.", + "bbox": [ + 75, + 551, + 468, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Model. Our SMAE self-supervised training-based multiscale Transformer consists of a feature extraction module, hallucination module, and Multi-Scale Residual Swin Transformer fusion Module (MSRSTM). The details in our model are included in the Appendix.", + "bbox": [ + 75, + 612, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hallucination Module. We first adopt three convolutional layers to extract shallow feature $F_{i}$ . Then, we divide the shallow feature $F_{i}$ into non-overlapping patches $\\overline{F_{i}}$ , and map each patch $\\overline{F_{i}}$ into query, keys and values. Subsequently, we calculate the similarity map between $\\overline{q}$ and $\\overline{k}$ , and perform the Softmax function to get the attention weight. Finally, we apply the attention weight to $\\overline{v}$ to get $F_{s}^{i}$ ,", + "bbox": [ + 75, + 688, + 468, + 810 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {q} = \\overline {{F _ {2}}} W _ {q}, \\quad \\bar {k _ {i}} = \\overline {{F _ {i}}} W _ {k}, \\quad \\bar {v _ {i}} = \\overline {{F _ {i}}} W _ {v}, \\quad i = 1, 3 \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 816, + 468, + 844 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {s} ^ {i} = \\mathrm {S o f t m a x} (\\overline {{q}} \\overline {{k _ {i}}} ^ {T} / \\sqrt {d} + b) \\overline {{v _ {i}}},\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 839, + 308, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $b$ represents a learnable position encoding, $d$ denotes the dimension of $\\overline{q}$ .", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "MSRSTM. To merge more information from different exposure regions, inspired by [13], we propose a MultiScale Residual Swin Transformer Module (MSRSTM). First, $F_{s}^{1}, F_{s}^{2}, F_{s}^{3}$ is concatenated along the channel dimension to get the input of MSRSTM. Note that $F_{s}^{2}$ denotes $F_{2}$ . Then, MSRSTM merges a long range of information from different exposure regions. MSRSTM consists of multiple multi-scale Swin Transformer layers (STL), a few convolutional layers, and a residual connection. Given the input feature $F_{out,i}^{N-1}$ of $i$ -th MSRSTM, the output $F_{out,i}^{N}$ of MSRSTM can be formulated as follows:", + "bbox": [ + 496, + 395, + 893, + 560 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {S T L, i} ^ {N} = \\operatorname {C o n v} \\left(\\left(\\operatorname {C o n c a t} \\left(S T L _ {i} ^ {N, l _ {1}} \\left(F _ {\\text {o u t}, i} ^ {N - 1}\\right), \\right. \\right. \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 561, + 893, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS T L _ {i} ^ {N, l _ {2}} \\left(F _ {o u t, i} ^ {N - 1}\\right), S T L _ {i} ^ {N, l _ {3}} \\left(F _ {o u t, i} ^ {N - 1}\\right)),\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 585, + 846, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {o u t, i} ^ {N} = \\operatorname {C o n v} \\left(F _ {S T L, i} ^ {N}\\right) + F _ {o u t, i} ^ {N - 1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 613, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $STL_{i}^{N,l_{j}}(\\cdot)$ represents the $N$ -th Swin Transformer layer of the $l_{j}$ scale in the $i$ -th MSRSTM, $F_{out,i}^{N-1}$ denotes the input feature of the $N$ -th Swin Transformer layer in the $i$ -th MSRSTM.", + "bbox": [ + 496, + 638, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss Function. Since unlabeled samples do not have HDR ground truth labels, we calculate the self-supervised loss in the LDR domain. We first use function $\\omega$ to transform the predicted HDR image $\\hat{Y}$ to short, medium, and long exposure LDR images $\\hat{Y}_i$ ,", + "bbox": [ + 496, + 700, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {Y} _ {i} = \\omega (\\hat {Y}) = (\\hat {Y} \\times t _ {i}) ^ {\\frac {1}{\\gamma}}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 781, + 890, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To recover the saturated regions, we transform the short exposure frame (since the predicted HDR in this stage is aligned to the short exposure frame) to new short, medium, and long exposure frames by ground truth generation. Then, we regard the new exposure frames as the ground truth $X_{i}^{GT}$ of the model,", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5778", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {i} ^ {G T} = \\left(\\frac {\\left(X _ {1} ^ {U}\\right) ^ {\\gamma} \\times t _ {i}}{t _ {1}}\\right) ^ {\\frac {1}{\\gamma}}, \\quad i = 1, 2, 3. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 87, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we calculate $L_{1}$ self-supervised loss between $\\hat{Y}_i$ and $X_i^{GT}$ , 3", + "bbox": [ + 76, + 130, + 468, + 161 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {S S L} = \\sum_ {i = 1} ^ {3} \\left| \\left| \\hat {Y} _ {i} - X _ {i} ^ {G T} \\right| \\right| _ {1}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 151, + 468, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Semi-supervised Learning Stage", + "text_level": 1, + "bbox": [ + 76, + 198, + 359, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finetune. At the beginning of this stage, to improve the saturated regions and further learn to handle ghosting regions, we first finetune the pretrained model with a few dynamic samples $D$ and static labeled samples $S$ . Here we apply $\\mu$ -law to map the linear domain image to the tonemapped domain image,", + "bbox": [ + 76, + 220, + 468, + 311 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT (x) = \\frac {\\log (1 + \\mu x)}{\\log (1 + \\mu)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 309, + 468, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T(x)$ is the tonemap function, $\\mu = 5000$ . Then we calculate the reconstruction loss $L_{recon}$ and perceptual loss $L_{percep}$ between the predicted HDR $\\hat{Y}_0^D, \\hat{Y}_0^S$ and ground truth HDR $Y_0^D, Y_0^S$ ,", + "bbox": [ + 76, + 349, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {r e c o n}} = \\left\\| T \\left(\\hat {Y} _ {0} ^ {D}\\right) - T \\left(Y _ {0} ^ {D}\\right) \\right\\| _ {1} + \\left\\| T \\left(\\hat {Y} _ {0} ^ {S}\\right) - T \\left(Y _ {0} ^ {S}\\right) \\right\\| _ {1}, (10) \\\\ L _ {p e r c e p} = \\left\\| \\phi_ {i, j} \\left(T \\left(\\hat {Y} _ {0} ^ {D}\\right)\\right) - \\phi_ {i, j} \\left(T \\left(Y _ {0} ^ {D}\\right)\\right) \\right\\| _ {1} (11) \\\\ + \\left| \\left| \\phi_ {i, j} \\left(T \\left(\\hat {Y} _ {0} ^ {S}\\right)\\right) - \\phi_ {i, j} \\left(T \\left(Y _ {0} ^ {S}\\right)\\right) \\right| \\right| _ {1}, \\\\ L _ {\\text {f i n e t u n e}} = L _ {\\text {r e c o n}} + \\lambda L _ {\\text {p e r c e p}}, (12) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 414, + 467, + 505 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi_{i,j}$ represents the $j$ -th convolutional layer and the $i$ -th max-pooling layer in VGG19, $\\lambda = 1e^{-2}$ .", + "bbox": [ + 76, + 508, + 468, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Iteration. To prevent the overfitting problem with a few labeled training samples and exploit unlabeled samples, we further generate the pseudo-labels $\\hat{Y}_t^U$ of unlabeled data. Concretely, we iteratively and adaptively train the model with a few dynamic and static samples $D$ and $S$ and a large number of unlabeled samples $U$ . Specifically, at timestep $t$ , we use model $N_t$ to predict the pseudo-labels $\\hat{Y}_t^U$ of unlabeled data. Then, we train the model $N_t$ with a few labeled and pseudo-labeled samples to get the model $N_{t+1}$ at timestep $t+1$ . Note that we use finetune model to generate unlabel HDR pseudo-labels $\\hat{Y}_0^U$ at timestep $t=0$ . Finally, at each timestep in the refinement stage, we calculate the reconstruction loss and perceptual loss as follows,", + "bbox": [ + 76, + 539, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {I t e r a t i o n} = L _ {r e c o n, t + 1} ^ {D} + L _ {r e c o n, t + 1} ^ {S} + \\sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {r e c o n, t + 1} ^ {U _ {i}} \\\\ + \\lambda \\left(L _ {\\text {p e r c e p}, t + 1} ^ {D} + L _ {\\text {p e r c e p}, t + 1} ^ {S} + \\sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {\\text {p e r c e p}, t + 1} ^ {U _ {i}}\\right), \\tag {13} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 741, + 483, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda = 1e^{-2}$ . $W_{t + 1}^{U_i}$ is the weight factor of unlabeled data $U_{i}$ . To get loss weight $W_{t + 1}^{U_i}$ , please refer to the next section in detail.", + "bbox": [ + 76, + 851, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "APSS. Since the HDR pseudo-labels inevitably contain saturated and ghosted samples, we propose an Adaptive Pseudo-labels Selection Strategy (APSS) to pick well-exposed and ghost-free HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process. Specifically, at timestep $t$ , we use model $N_{t}$ to predict HDR images with dynamic and static labeled samples $\\hat{Y}_t^D$ and $\\hat{Y}_t^S$ . Then we use function $\\omega$ to map the predicted HDR image to medium exposure image $\\tilde{Y}_t^{D\\cup S}$ and calculate the loss between $\\tilde{Y}_t^{D\\cup S}$ and original medium exposure LDR image $X_{2,t}^{D\\cup S}$ in well exposure regions to get $L_{select,t}^{D\\cup S}$ ,", + "bbox": [ + 498, + 90, + 890, + 258 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {s e l e c t}, t} ^ {D \\cup S} = | | \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {D}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {D}\\right)\\right) | | _ {1} \\tag {14} \\\\ + \\left\\| \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {S}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {S}\\right)\\right) \\right\\| _ {1}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 267, + 890, + 308 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\text{mask}(\\cdot)$ denotes masking the over and under-exposure regions. Subsequently, we sort all patches' losses, and adopt $\\sigma(\\cdot, \\cdot)$ function to get $\\beta$ percentile (85th) loss as a selection threshold $\\tau_t$ ,", + "bbox": [ + 498, + 319, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tau_ {t} = \\sigma \\left(L _ {\\text {s e l e c t}, t} ^ {D \\cup S}, \\beta\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 387, + 890, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, we use model $N_{t}$ to predict pseudo-labels $\\hat{Y}_t^U$ of unlabeled samples, similar to the operation of labeled data mentioned above. We then use $\\omega$ function to map $\\hat{Y}_t^U$ to medium exposure to get $\\hat{Y}_t^U$ and calculate the loss between $\\tilde{Y}_t^U$ and original medium exposure LDR image $X_{2,t}^{U}$ to get $L_{select,t}^{U} = \\{L_{select,t}^{U_1},L_{select,t}^{U_2},\\dots ,L_{select,t}^{U_N}\\}$ . If the current loss $L_{select,t}^{U_i}$ is greater than $\\tau_{t}$ , we consider the pseudo-label to be of poor quality, which has more saturated and ghosted regions. Then we will give a lower weight which tends to decay linearly in the next training iteration.", + "bbox": [ + 498, + 419, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s e l e c t}, t} ^ {U} = \\left\\| \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {U}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {U}\\right)\\right) \\right\\| _ {1}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 584, + 890, + 604 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nm _ {t} ^ {U} = \\max \\left(L _ {\\text {s e l e c t}, t} ^ {U}\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 614, + 890, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nW _ {t + 1} ^ {U _ {i}} = \\left\\{ \\begin{array}{l l} 1 & L _ {\\text {s e l e c t}, t} ^ {U _ {i}} \\leq \\tau_ {t} \\\\ \\frac {m _ {t} ^ {U} - L _ {\\text {s e l e c t} , t} ^ {U _ {i}}}{m _ {t} ^ {U} - \\tau_ {t}} & L _ {\\text {s e l e c t}, t} ^ {U _ {i}} > \\tau_ {t} \\end{array} \\right. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 652, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $X_{2,t}^{U}$ is the unlabeled medium exposure image in timestep $t$ , $m_t^U$ is the largest selection loss of unlabeled samples in timestep $t$ , $W_{t + 1}^{U_i}$ is the weight factor of $U_{i}$ smaple in the $t + 1$ training iteration.", + "bbox": [ + 498, + 707, + 890, + 770 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 784, + 630, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We train all the methods on two public datasets, Kalantari's [9] and Hu's dataset [7]. Kalantari's dataset includes 74 training samples and 15 testing samples. Three different LDR images in a sample are captured with exposure biases of $\\{-2,0, + 2\\}$ or $\\{-3,0, + 3\\}$ . Hu's dataset is captured at three exposure levels (i.e., $\\{-2,0, + 2\\}$ ). There are", + "bbox": [ + 498, + 809, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5779", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/47653c9857ac3e05bbe3107df4251da410df0a8bd75e243a5102e6ba8185bc7b.jpg", + "image_caption": [ + "Figure 4. Examples of Kalantari's [9] and Hu's [7] datasets (top row) and Tursun's [28] and Prabhakar's [21] datasets (bottom row). Note that we directly evaluate the methods on Tursun's and Prabhakar's datasets with the checkpoint trained on Kalantari's dataset." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 874, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "85 training samples and 15 testing samples in Hu's dataset. We train all comparison methods with the same set of images. Concretely, we randomly choose $K \\in \\{1, 5\\}$ dynamic labeled samples and $Q = 5$ static labeled samples for training in all methods. Furthermore, for each $K$ , we evaluate all methods for 5 runs denoted as 5-way in Table 1. In addition, since FSHDR [22] and our method exploit unlabeled samples, we also use the rest of the dataset samples as unlabeled data $U$ . Finally, to verify generalization performance, we evaluate all methods on Tursun's dataset [28] that does not have ground truth and Prabhakar's dataset [21].", + "bbox": [ + 75, + 648, + 472, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. We calculate five common metrics used for testing, i.e., PSNR-L, PSRN- $\\mu$ , SSIM-L, SSIM- $\\mu$ , and HDR-VDP-2 [16], where '-L' denotes linear domain, '- $\\mu$ ' denotes tonemapping domain.", + "bbox": [ + 76, + 820, + 468, + 881 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. The window size in MSRSTM is", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$2 \\times 2, 4 \\times 4$ and $8 \\times 8$ . In the training stage, we crop the 128 $\\times$ 128 patches with stride 64 for the training dataset. We use the Adam optimizer, and set the batch size and learning rate as 4 and 0.0005, receptively. And we set $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ , and $\\epsilon = 1e^{-8}$ in the Adam optimizer. We implement our model using PyTorch with 2 NVIDIA GeForce 3090 GPUs and train for 200 epochs.", + "bbox": [ + 498, + 648, + 890, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Comparison with State-of-the-art Methods", + "text_level": 1, + "bbox": [ + 498, + 768, + 864, + 784 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate our model, we carry out quantitative and qualitative experiments comparing with several state-of-the-art methods, including patch-based classical methods: Sen [24], Hu [8], and deep learning-based methods: Kalantari [9], DeepHDR [30], AHDRNet [31], ADNet [14], FSHDR [22]. We use the codes provided by the authors.", + "bbox": [ + 496, + 792, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on Kalantari's and Hu's Datasets. In Fig-", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5780", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/93c514fa1aaec198d4949fd6421c375dec06cc5c97da8131ec381a6f79bb2d3c.jpg", + "table_caption": [ + "Table 1. The evaluation results on Kalantari's [9] and Hu's [7] datasets. The best and the second best results are highlighted in Bold and Underline, respectively." + ], + "table_footnote": [], + "table_body": "
DatasetMetricSettingKalantariDeepHDRAHDRNetADNetFSHDROurs
KalantariPSNR-l5way-5shot39.37±0.1238.25±0.2940.61±0.1040.78±0.1541.39±0.1241.54±0.10
PSNR-μ39.86±0.1938.62±0.2741.05±0.3240.93±0.3841.40±0.1341.61±0.08
PSNR-l5way-1shot36.94±0.4436.67±0.6738.83±0.3938.96±0.3541.04±0.1141.14±0.11
PSNR-μ37.33±1.2137.01±1.6839.15±1.0439.08±1.0641.13±0.0741.25±0.05
HuPSNR-l5way-5shot41.36±0.2540.73±0.6646.37±0.7646.88±0.8147.13±0.1347.41±0.12
PSNR-μ38.95±0.1439.92±0.2243.42±0.4443.79±0.4843.98±0.2744.24±0.17
PSNR-l5way-1shot38.67±0.4337.82±0.8644.64±0.8044.75±0.8444.94±0.2345.04±0.16
PSNR-μ36.83±0.6238.49±1.0742.37±1.4242.41±1.2042.50±0.8742.55±0.44
", + "bbox": [ + 148, + 119, + 821, + 252 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/174bb6724a5a4405e964a56cc158290e3581d34b1b467d94874d7863189cae0a.jpg", + "table_caption": [ + "Table 2. Further evaluation results on Kalantari's [9], Hu's [7] and Prabhakar's datasets [21]. The best and the second best results are highlighted in Bold and Underline in each setting, respectively." + ], + "table_footnote": [], + "table_body": "
KalantariHu
PSNR-lPSNR-μSSIM-lSSIM-μHV2PSNR-lPSNR-μSSIM-lSSIM-μHV2
S1Sen38.5740.940.97110.978064.7133.5831.480.96340.953166.39
Hu30.8432.190.94080.963262.0536.9436.560.98770.982467.58
FSHDR40.9741.110.98640.982767.0842.1541.140.99040.989171.35
Ours (K=0)41.1241.200.98660.986867.1642.9941.300.99120.990372.18
S2Ours (K=1)41.1441.250.98660.986967.2045.0442.550.99380.992873.23
Ours (K=5)41.5441.610.98790.988067.3347.4144.240.99740.993674.49
S3Kalantari41.2241.850.98480.987266.2343.7641.600.99380.991472.94
DeepHDR40.9141.640.98630.985767.4241.2041.130.99410.987070.82
AHDRNet41.2341.870.98680.988967.5049.2245.760.99800.995675.04
ADNET41.3141.800.98710.988367.5750.3846.790.99870.994876.32
FSHDR41.7941.920.98760.985167.7049.5645.900.99840.994575.25
Ours41.6841.970.98890.989567.7750.3146.880.99880.995776.21
S4Kalantari25.8721.440.86100.917660.0010.2316.950.69030.834649.10
DeepHDR25.9221.430.85970.917060.0225.4820.860.92150.835466.83
AHDRNet26.6222.080.87370.923858.8911.4417.840.67320.838952.79
ADNET25.7621.390.86860.821760.3610.8618.090.69150.839949.28
FSHDR28.0322.010.87510.920360.5312.8219.370.74420.834755.34
Ours27.9122.450.87640.925261.0230.2921.560.94400.845667.07
S5Kalantari31.2433.100.95270.959363.9919.8218.630.76790.874259.50
DeepHDR30.7529.010.92440.922363.2619.8418.700.76980.875259.48
AHDRNet31.8433.490.95880.960664.4020.8020.510.82590.913659.79
ADNET31.0833.500.95360.963663.8820.7820.800.82680.917359.71
FSHDR32.7032.240.95530.946564.3720.2319.710.79290.902659.63
Ours32.7234.490.95860.971364.4520.6921.960.82570.920759.76
", + "bbox": [ + 155, + 282, + 810, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ure 4 (a) and (b), we compare our method with other state-of-the-art methods in the 5-shot scenario. Due to insufficient labeled samples, large motion, and saturation, most comparing methods suffer from color distortion and ghosting artifacts in these two datasets. Kalantari's method and DeepHDR produce undesirable artifacts and color distortion (see Figure 4 (a)(b)). There are two reasons behind that: misalignment of optical flow and homographies and the lack of labeled data. Although AHDRNet and ADNET are proposed to suppress motion and saturation with attention mechanisms, they cannot reconstruct ghost-free HDR images with few labeled samples. They also produce severe ghosting artifacts (see the red block in Figure 4 (a)(b)). FSHDR exploits unlabeled data to alleviate ghosts under the constraint of a few labeled samples, but it is difficult to handle both ghosting and saturation problems simultaneously. We can see that FSHDR still suffers from ghosting artifacts which leaves an obvious hand artifact in the car (see the red block in Figure 4 (a)). Thanks to the pro", + "bbox": [ + 75, + 609, + 472, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "posed SMAE and sample-quality-based iterative learning strategy, which first address the saturation problems using SMAE and then adaptively sample well-exposed and ghost-free pseudo-labels to handle ghosting problems, we can reconstruct ghost-free HDR images with only a few labeled samples.", + "bbox": [ + 496, + 609, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The quantitative results under the constraint of few shot scenarios on two dataset are shown in Table 1. We report means and $95\\%$ margin of variations for 5 and 1 shot cases across 5 runs. Our method achieves state-of-the-art performance on all metrics of two datasets, while most other methods perform poorly with only a few labeled samples. We show that our proposed method surpasses second-best method by 0.15db and 0.21db in terms of PSNR- $l$ and PSNR- $\\mu$ for 5way-5shot setting on Kalantari's dataset, and it also improves by 0.28db and 0.26db for 5way-5shot setting on Hu's dataset. For 5way-1shot setting, our method consistently outperforms other approaches on two datasets.", + "bbox": [ + 496, + 702, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition, as shown in Table 2, we further compare our", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5781", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5319d5c86d79528b67b9ce3b8bc6de547793e9de617d5b45a2f89001038df582.jpg", + "table_caption": [ + "Table 3. Ablation study of 5 shot scenario on Kalantari's dataset." + ], + "table_footnote": [], + "table_body": "
#ModelPSNR-lPSNR-μHDR-VDP-2
B1SSHDR41.5441.6167.33
B2Stage2Net41.3141.4367.21
B3w/o APSS41.4941.4567.29
B4AHDR*41.4841.5167.30
B5FSHDR*41.4141.4367.26
B6Vanilla-AHDR40.6141.0566.95
B7Vanilla-FSHHDR41.3941.4067.25
", + "bbox": [ + 114, + 106, + 429, + 218 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "method with major HDR deghosting approaches in zero-shot setting $S_{1}$ , few-shot setting $S_{2}$ , and fully supervised setting $S_{3}$ . Note that we use all the dynamic labeled samples without static and unlabeled samples for plain training in setting $S_{3}$ . Our zero-shot approach outperforms other methods in zero-shot setting on two datasets. It also outperforms some 5-shot and fully supervised methods in most metrics. Finally, our few-shot and fully supervised approaches achieve state-of-the-art performance among two datasets.", + "bbox": [ + 75, + 229, + 467, + 366 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation Generalization Across Different Datasets. We compare our method against other approaches on Kalantari's, Hu's, Tursun's, and Prabhakar's datasets to verify generalization performance. We directly evaluate the methods with the checkpoint trained on Kalantari's dataset and show the qualitative results on Tursun's and Prabhakar's datasets in Figure 4 (c)(d). More results are included in the Appendix. In Figure 4 (c), since the lady's motion is large, all the comparison methods cannot remove the ghosting artifacts. In Figure 4 (d), the comparison methods have obvious color distortion and ghosting artifacts on the floor and in the ceiling. It shows that other methods have poor generalization performance across different datasets. All these methods address both the saturation and ghosting problems simultaneously. They cannot learn a robust representation to reconstruct a high-quality HDR image. Thanks to our SMAE and sample-quality-based iterative learning strategy, we can learn a robust representation to recover saturated regions and remove ghosting artifacts.", + "bbox": [ + 75, + 366, + 467, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 2, setting $S_{4}$ denotes that we utilize the checkpoint trained on Kalantari's or Hu's dataset under 5 shot scenario to evaluate on Hu's or Kalantari's dataset reversely. Setting $S_{5}$ represents that we train on Kalantari's or Hu's dataset under 5 shot scenario and evaluate on Prabhakar's dataset. Our method achieves better numerical performance in terms of PSNR- $l$ and PSNR- $\\mu$ . It demonstrates that our method generalizes well across different datasets.", + "bbox": [ + 75, + 654, + 467, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 786, + 240, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation studies on Kalantari's dataset under the condition of 5 shot scenario across 5 runs and analyze the importance of each component. We use the following variants of our whole SSHDR model: 1) SSHDR: The full model of SSHDR network trained with two entire stages. 2) Stage2Net: The model only trained in the second", + "bbox": [ + 75, + 809, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7b867f3f671e1d0900228efd3f361124434e91241277c3050683e4cb2587e2b4.jpg", + "image_caption": [ + "Figure 5. Visual results of poor pseudo-labels." + ], + "image_footnote": [], + "bbox": [ + 521, + 88, + 870, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "stage without SMAE pre-training. 3) w/o APSS: The model trained with two stages without using sample-quality-based pseudo-labels selection strategy. 4) $\\text{AHDR}^*$ : The AHDR model is trained with our proposed two stages strategy. 5) $\\text{FSHDR}^*$ : Our model is trained with the FSHDR strategy. 6) Vanilla-AHDR: The vanilla AHDR model trained in 5 shot scenario. 7) Vanilla-FSHDR: The vanilla FSHDR model trained with 5 labeled samples.", + "bbox": [ + 496, + 271, + 890, + 392 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SMAE Pre-training. As shown in Table 3, the performance of Stage2Net is significantly decreased compared with SSHDR. Since the SMAE learns a robust representation to generate content of saturated regions, it helps to improve the saturated regions. In a word, it demonstrates that the SMAE pre-training stage is an effective mechanism.", + "bbox": [ + 496, + 393, + 890, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pseudo-labels Selection Strategy. Since the sample-quality-based pseudo-labels selection strategy can exclude saturated and ghosted samples (see Figure 5), the model can be guided in a correct optimization direction which is effective for ghost removal. When we remove the pseudolabels selection strategy, the performance of the model without APSS is dropped.", + "bbox": [ + 496, + 483, + 890, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Two Stages Strategy. In Table 3, we report the performance of $\\mathrm{AHDR}^*$ . It achieves a significant increment compared with the vanilla AHDR model, which demonstrates the effectiveness of the overall two stages strategy.", + "bbox": [ + 496, + 589, + 890, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Proposed Model Architecture. When we replace our two stages strategy with the FSHDR strategy, the numerical results increase compared with FSHDR. It shows that our proposed model architecture is also sound.", + "bbox": [ + 496, + 650, + 890, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 731, + 617, + 744 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a novel semi-supervised deghosting method for few-shot HDR problem via two stages of completing saturation and deghosting. In the first stage, a Saturated Mask AutoEncoder is proposed to learn a robust representation and reconstruct a non-saturated HDR image with a self-supervised mechanism. 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IEEE Transactions on Image Processing, 21(4):2318-2323, 2011. 1, 2" + ], + "bbox": [ + 78, + 90, + 468, + 868 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5784", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_model.json b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6d75218a561da3f6628a6e673816231f74d48fa8 --- /dev/null +++ b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_model.json @@ -0,0 +1,2310 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.02 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + }, + { + "type": "header", + "bbox": [ + 0.325, + 0.017, + 0.723, + 0.031 + ], + "angle": 0, + "content": "Except for this watermark, it is identical to the accepted version;" + }, + { + "type": "header", + "bbox": [ + 0.294, + 0.032, + 0.754, + 0.046 + ], + "angle": 0, + "content": "the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.125, + 0.13, + 0.846, + 0.175 + ], + "angle": 0, + "content": "SMAE: Few-shot Learning for HDR Deghosting with Saturation-Aware Masked Autoencoders" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.202, + 0.777, + 0.222 + ], + "angle": 0, + "content": "Qingsen Yan†1 Song Zhang†2 Weiye Chen†2 Hao Tang³ Yu Zhu¹" + }, + { + "type": "text", + "bbox": [ + 0.291, + 0.222, + 0.686, + 0.24 + ], + "angle": 0, + "content": "Jinqiu Sun\\(^{1}\\) Luc Van Gool\\(^{3}\\) Yanning Zhang\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.24, + 0.815, + 0.258 + ], + "angle": 0, + "content": "\\(^{1}\\)Northwestern Polytechnical University \\(^{2}\\)Xidian University \\(^{3}\\)CVL, ETH Zurich" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.313, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.732 + ], + "angle": 0, + "content": "Generating a high-quality High Dynamic Range (HDR) image from dynamic scenes has recently been extensively studied by exploiting Deep Neural Networks (DNNs). Most DNNs-based methods require a large amount of training data with ground truth, requiring tedious and time-consuming work. Few-shot HDR imaging aims to generate satisfactory images with limited data. However, it is difficult for modern DNNs to avoid overfitting when trained on only a few images. In this work, we propose a novel semi-supervised approach to realize few-shot HDR imaging via two stages of training, called SSHDR. Unlikely previous methods, directly recovering content and removing ghosts simultaneously, which is hard to achieve optimum, we first generate content of saturated regions with a self-supervised mechanism and then address ghosts via an iterative semi-supervised learning framework. Concretely, considering that saturated regions can be regarded as masking Low Dynamic Range (LDR) input regions, we design a Saturated Mask AutoEncoder (SMAE) to learn a robust feature representation and reconstruct a non-saturated HDR image. We also propose an adaptive pseudo-label selection strategy to pick high-quality HDR pseudo-labels in the second stage to avoid the effect of mislabeled samples. Experiments demonstrate that SSHDR outperforms state-of-the-art methods quantitatively and qualitatively within and across different datasets, achieving appealing HDR visualization with few labeled samples." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.76, + 0.21, + 0.775 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.785, + 0.47, + 0.832 + ], + "angle": 0, + "content": "Standard digital photography sensors are unable to capture the wide range of illumination present in natural scenes, resulting in Low Dynamic Range (LDR) images that often" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.839, + 0.47, + 0.902 + ], + "angle": 0, + "content": "*† The first three authors contributed equally to this work. This work was partially supported by NSFC (U19B2037, 61901384), Natural Science Basic Research Program of Shaanxi (2021JCW-03, 2023-JC-QN-0685), and National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology. Corresponding author: Yu Zhu." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.291, + 0.578, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.29, + 0.795, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.405, + 0.559, + 0.414 + ], + "angle": 0, + "content": "LDRs" + }, + { + "type": "image", + "bbox": [ + 0.799, + 0.291, + 0.844, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.8, + 0.328, + 0.845, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.848, + 0.291, + 0.891, + 0.326 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.848, + 0.328, + 0.892, + 0.364 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.848, + 0.367, + 0.892, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.809, + 0.405, + 0.862, + 0.414 + ], + "angle": 0, + "content": "LDR Patches" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.415, + 0.572, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.415, + 0.651, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.415, + 0.73, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.73, + 0.415, + 0.811, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.811, + 0.415, + 0.892, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.462, + 0.572, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.462, + 0.651, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.462, + 0.731, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.462, + 0.811, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.811, + 0.462, + 0.892, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.508, + 0.553, + 0.516 + ], + "angle": 0, + "content": "Sen" + }, + { + "type": "image_caption", + "bbox": [ + 0.535, + 0.516, + 0.553, + 0.525 + ], + "angle": 0, + "content": "[24]" + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.508, + 0.619, + 0.516 + ], + "angle": 0, + "content": "Kalantari" + }, + { + "type": "image_caption", + "bbox": [ + 0.591, + 0.516, + 0.605, + 0.525 + ], + "angle": 0, + "content": "[9]" + }, + { + "type": "image_caption", + "bbox": [ + 0.629, + 0.508, + 0.666, + 0.516 + ], + "angle": 0, + "content": "AHDR" + }, + { + "type": "image_caption", + "bbox": [ + 0.642, + 0.516, + 0.661, + 0.525 + ], + "angle": 0, + "content": "[31]" + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.508, + 0.722, + 0.516 + ], + "angle": 0, + "content": "ADNET" + }, + { + "type": "image_caption", + "bbox": [ + 0.696, + 0.516, + 0.715, + 0.525 + ], + "angle": 0, + "content": "[14]" + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.508, + 0.776, + 0.516 + ], + "angle": 0, + "content": "FSHDR" + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.516, + 0.768, + 0.525 + ], + "angle": 0, + "content": "[22]" + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.508, + 0.824, + 0.516 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.858, + 0.508, + 0.873, + 0.516 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.525, + 0.892, + 0.553 + ], + "angle": 0, + "content": "Figure 1. The proposed method generates high-quality images with few labeled samples when compared with several methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.687 + ], + "angle": 0, + "content": "suffer from over or underexposed regions, which can damage the details of the scene. High Dynamic Range (HDR) imaging has been developed to address these limitations. This technique combines several LDR images with different exposures to generate an HDR image. While HDR imaging can effectively recover details in static scenes, it may produce ghosting artifacts when used with dynamic scenes or hand-held camera scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Historically, various techniques have been suggested to address such issues, such as alignment-based methods [3,10,27,37], patch-based methods [8,15,24], and rejection-based methods [5, 11, 19, 20, 35, 40]. Two categories of alignment-based approaches exist: rigid alignment (e.g., homographies) that fail to address foreground motions, and non-rigid alignment (e.g., optical flow) that is error-prone. Patch-based techniques merge similar regions using patch-level alignment and produce superior results, but suffer from high complexity. Rejection-based methods aim to eliminate misaligned areas before fusing images, but may result in a loss of information in motion regions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As Deep Neural Networks (DNNs) become increasingly prevalent, the DNN-based HDR deghosting methods" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5775" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.35 + ], + "angle": 0, + "content": "[9, 33, 36] achieve better visual results compared to traditional methods. However, these alignment approaches are error-prone and inevitably cause ghosting artifacts (see Figure 1 Kalantari's results). AHDR [31, 32] proposes spatial attention to suppress motion and saturation, which effectively alleviate misalignment problems. Based on AHDR, ADNET [14] proposes a dual branch architecture using spatial attention and PCD-alignment [29] to remove ghosting artifacts. All these above methods directly learn the complicated HDR mapping function with abundant HDR ground truth data. However, it's challenging to collect a large amount of HDR-labeled data. The reasons can be attributed to that 1) generating a ghost-free HDR ground truth sample requires an absolute static background, and 2) it is time-consuming and requires considerable manpower to do manual post-examination. This generates a new setting that only uses a few labeled data for HDR imaging." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.61 + ], + "angle": 0, + "content": "Recently, FSHDR [22] attempts to generate a ghost-free HDR image with only few labeled data. They use a preliminary model trained with a large amount of unlabeled dynamic samples, and a few dynamic and static labeled samples to generate HDR pseudo-labels and synthesize artificial dynamic LDR inputs to improve the model performance of dynamic scenes further. This approach expects the model to handle both the saturation and the ghosting problems simultaneously, but it is hard to achieve under the condition of few labeled data, especially misaligned regions caused by saturation and motion (see Figure 1 FSHDR). In addition, FSHDR uses optical flow to forcibly synthesize dynamic LDR inputs from poorly generated HDR pseudo-labels, the errors in optical flow further intensify the degraded quality of artificial dynamic LDR images, resulting in an apparent distribution shift between LDR training and testing data, which hampers the performance of the network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "The above analysis makes it very challenging to directly generate a high-quality and ghost-free HDR image with few labeled samples. A reasonable way is to address the saturation problems first and then cope with the ghosting problems with a few labeled samples. In this paper, we propose a semi-supervised approach for HDR deghosting, named SSHDR, which consists of two stages: self-supervised learning network for content completion and sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we pretrain a Saturated Mask AutoEncoder (SMAE), which learns the representation of HDR features to generate content of saturated regions by self-supervised learning. Specifically, considering that the saturated regions can be regarded as masking the short LDR input patches, inspired by [6], we randomly mask a high proportion of the short LDR input and expect the model to reconstruct a no-saturated HDR image from the remaining LDR patches in the first stage. This self-supervised approach allows the model to recover the saturated regions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.394 + ], + "angle": 0, + "content": "with the capability to effectively learn a robust representation for the HDR domain and map an LDR image to an HDR image. In the second stage, to prevent the overfitting problem with a few labeled training samples and make full use of the unlabeled samples, we iteratively train the model with a few labeled samples and a large amount of HDR pseudo-labels from unlabeled data. Based on the pretrained SMAE, a sample-quality-based iterative semi-supervised learning framework is proposed to address the ghosting artifacts. Considering the quality of pseudo-labels is uneven, we develop an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels (i.e., well-exposed, ghost-free) to avoid awful pseudo-labels hampering the optimization process. This selection strategy is guided by a few labeled samples and enhances the diversity of training samples in each epoch. The experiments demonstrate that our proposed approach can generate high-quality HDR images with few labeled samples and achieves state-of-the-art performance on individual and cross-public datasets. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.395, + 0.892, + 0.455 + ], + "angle": 0, + "content": "- We propose a novel and generalized HDR self-supervised pretraining model, which uses mask strategy to reconstruct an HDR image and addresses saturated problems from one LDR image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.455, + 0.892, + 0.5 + ], + "angle": 0, + "content": "- We propose a sample-quality-based semi-supervised training approach to select well-exposed and ghost-free HDR pseudo-labels, which improves ghost removal." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.5, + 0.892, + 0.546 + ], + "angle": 0, + "content": "- We perform both qualitative and quantitative experiments, which show that our method achieves state-of-the-art results on individual and cross-public datasets." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.395, + 0.892, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.562, + 0.642, + 0.578 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.588, + 0.74, + 0.604 + ], + "angle": 0, + "content": "2.1. HDR Deghosting Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.657 + ], + "angle": 0, + "content": "The existing HDR deghosting methods include four categories: alignment-based method, patch-based method, rejection-based method, and CNN-based method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Alignment-based Method. Rigid or non-rigid registration is mainly used in alignment-based approaches. Bogoni [3] estimated flow vectors to align with the reference images. Kang et al. [10] utilized optical flow to align images in the luminance domain to remove ghosting artifacts. Tomaszewska et al. [27] used SIFT feature to perform global alignments. Since the dense correspondence computed by alignment methods are error-prone, they cannot handle large motion and occlusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Rejection-based Method. Rejection-based methods detect and eliminate motion from static regions. Then they merge static inputs to get HDR images. Grosch et al. [5] estimated a motion map and used it to generate ghost-free HDR. Zhang et al. [40] obtained a motion weighting map using quality measurement on image gradients. Lee et al. [11] and Oh et al. [19] detected motion regions using rank min" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5776" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "imization. However, rejection-based methods remove the misalignment of regions. It will result in a lack of content in moving regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.468, + 0.242 + ], + "angle": 0, + "content": "Patch-based Method. Patch-based methods use patch-level alignment to merge similar contents. Sen et al. [24] proposed a patch-based energy minimization approach that optimizes alignment and reconstruction simultaneously. Hu et al. [8] utilized a patch-match mechanism to produce aligned images. Although these methods have good performance, they suffer from high computational costs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.468, + 0.453 + ], + "angle": 0, + "content": "CNN-based Method. Kalantari et al. [9] used a CNN network to fuse LDR images that are aligned with optical flow. Wu et al. [30] used homography to align the camera motion and reconstructed HDR images by CNN. Yan et al. [31] proposed an attention mechanism to suppress motion and saturation. Yan et al. [34] designed a nonlocal block to release the constraint of locality receptive field for global merging HDR. Niu et al. [18] proposed HDR-GAN to recover missing content using generative adversarial networks. Ye et al. [38] proposed multi-step feature fusion to generate ghost-free images. Liu et al. [14] utilized the PCD alignment subnetwork to remove ghosts. However, these methods require a large number of labeled samples, which is difficult to collect." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.466, + 0.308, + 0.481 + ], + "angle": 0, + "content": "2.2. Few-shot Learning (FSL)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.468, + 0.701 + ], + "angle": 0, + "content": "Humans can successfully learn new ideas with relatively little supervision. Inspired by such ability, FSL aims to learn robust representations with few labeled samples. There are three main categories for FSL methods: databased category [1, 23, 25], which augment the experience with prior knowledge; model-based category [2, 17, 26], which shrinks the size of the hypothesis space using prior knowledge; algorithm-based category [4, 12, 39], which modifies the search for the optimal hypothesis using prior knowledge. For HDR deghosting, Prabhakar et al. [22] proposed a data-based category deghosting method, which uses artificial dynamic sequences synthesis for motion transfer. Still, it is hard to handle both the saturation and the ghosting problems simultaneously with few labeled data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.716, + 0.287, + 0.733 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.249, + 0.755 + ], + "angle": 0, + "content": "3.1. Data Distribution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Following the setting of few-shot HDR imaging [22], we utilize 1) \\(N\\) dynamic unlabeled LDR samples \\(U = \\{L_1^U,\\dots ,L_N^U\\}\\), where each \\(L^U\\) consists of three LDRs \\((X_{1}^{U},X_{2}^{U},X_{3}^{U})\\) with different exposures. 2) \\(M\\) static labeled LDR samples \\(S = \\{L_1^S,\\dots ,L_M^S\\}\\), where each \\(L^S\\) consists of three LDRs \\((X_1^S,X_2^S,X_3^S)\\) with different exposures and ground truth \\(Y^{S}\\). 3) \\(K\\) dynamic labeled LDR samples \\(D = \\{L_1^D,\\dots ,L_K^D\\}\\), where each \\(L^D\\) consists of three LDRs \\((X_1^D,X_2^D,X_3^D)\\) and ground truth \\(Y^{D}\\). Since it is difficult to" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "collect labeled samples, we set \\( K \\) to be less than or equal to 5, and \\( M \\) is fixed at 5. While it is easy to capture unlabeled samples, \\( N \\) can be arbitrary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.146, + 0.664, + 0.16 + ], + "angle": 0, + "content": "3.2. Model Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.169, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Generating a non-saturated and ghost-free HDR image with few labeled samples is challenging. It is a proper way to address saturated problems first and then handle ghosting problems. As shown in Figure 2, we propose a semi-supervised approach for HDR deghosting. Our approach consists of two stages: a self-supervised learning network for content completion and a sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we propose a multi-scale Transformer model based on self-supervised learning with a saturated-masked autoencoder to make it capable of recovering saturated regions. In a word, we randomly mask LDR patches and reconstruct non-saturated HDR images from the remaining LDR patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.532 + ], + "angle": 0, + "content": "In the second stage, we propose a sample-quality-based iterative semi-supervised learning approach that learns to address ghosting problems. We finetune the pretrained model based on the first stage with a few labeled samples. Then, we iteratively train the model with labeled samples and unlabeled samples with pseudo-labels. Considering that the HDR pseudo-labels inevitably contain saturated and ghosting regions, which deteriorate the model performance, we propose an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.541, + 0.776, + 0.557 + ], + "angle": 0, + "content": "3.3. Self-supervised Learning Stage" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.645 + ], + "angle": 0, + "content": "Input. Considering that there are more saturated regions in the medium \\((X_2^U)\\) and long exposure frames \\((X_3^U)\\) of unlabeled data \\(U\\), we first transform the short exposure frame \\((X_1^U)\\) into a new medium \\((X_{2^{\\prime}}^{U})\\) and long exposure frames \\((X_{3^{\\prime}}^{U})\\) by exposure adjustment," + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.652, + 0.892, + 0.685 + ], + "angle": 0, + "content": "\\[\nX _ {i ^ {\\prime}} ^ {U} = \\operatorname {c l i p} \\left(\\left(\\frac {\\left(X _ {1} ^ {U}\\right) ^ {\\gamma} \\times t _ {i}}{t _ {1}}\\right) ^ {\\frac {1}{\\gamma}}\\right), \\quad i = 2, 3. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.695, + 0.891, + 0.741 + ], + "angle": 0, + "content": "Then following previous work [9, 30], we map the LDR input images \\(X_{1}^{U}, X_{2'}^{U}, X_{3'}^{U}\\) to HDR domain by gamma correction to get \\(H_{i}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.636, + 0.747, + 0.891, + 0.767 + ], + "angle": 0, + "content": "\\[\nH _ {i ^ {\\prime}} = \\left(X _ {i ^ {\\prime}} ^ {U}\\right) ^ {\\gamma} / t _ {i}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.777, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Note that \\( X_{1'}^U = X_1^U \\), \\( t_i \\) denotes the exposure time of LDR image \\( X_i \\), \\( \\gamma \\) represents the gamma correction parameter, we set \\( \\gamma \\) to 2.2. Then, we concatenate \\( X_{i'} \\) and \\( H_{i'} \\) along the channel dimension to get a 6-channel input \\( I_i = [X_{i'}, H_{i'}] \\), we subsequently mask the input \\( I_i \\) patches to get \\( I_i' \\). Concretely, we divide the input into non-overlapping patches and randomly mask a subset of these patches with a high mask ratio (75%) (see Figure 3). Note that the patch size" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5777" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.899, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.358, + 0.37, + 0.611, + 0.383 + ], + "angle": 0, + "content": "Figure 2. The overview of our framework." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.393, + 0.473, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.498, + 0.47, + 0.54 + ], + "angle": 0, + "content": "Figure 3. The detailed procedure of Stage 1. To recover the saturated regions, we utilize the short exposure frame as input and ground truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.47, + 0.613 + ], + "angle": 0, + "content": "is \\(8 \\times 8\\). Considering that the masking strategy is another way to destruct the saturated regions, we intend the model to learn a robust representation to recover these saturated regions. Finally, \\(I' = \\{I_1', I_2', I_3'\\}\\) is the input of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Model. Our SMAE self-supervised training-based multiscale Transformer consists of a feature extraction module, hallucination module, and Multi-Scale Residual Swin Transformer fusion Module (MSRSTM). The details in our model are included in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.811 + ], + "angle": 0, + "content": "Hallucination Module. We first adopt three convolutional layers to extract shallow feature \\( F_{i} \\). Then, we divide the shallow feature \\( F_{i} \\) into non-overlapping patches \\( \\overline{F_{i}} \\), and map each patch \\( \\overline{F_{i}} \\) into query, keys and values. Subsequently, we calculate the similarity map between \\( \\overline{q} \\) and \\( \\overline{k} \\), and perform the Softmax function to get the attention weight. Finally, we apply the attention weight to \\( \\overline{v} \\) to get \\( F_{s}^{i} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.817, + 0.47, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\bar {q} = \\overline {{F _ {2}}} W _ {q}, \\quad \\bar {k _ {i}} = \\overline {{F _ {i}}} W _ {k}, \\quad \\bar {v _ {i}} = \\overline {{F _ {i}}} W _ {v}, \\quad i = 1, 3 \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.84, + 0.31, + 0.86 + ], + "angle": 0, + "content": "\\[\nF _ {s} ^ {i} = \\mathrm {S o f t m a x} (\\overline {{q}} \\overline {{k _ {i}}} ^ {T} / \\sqrt {d} + b) \\overline {{v _ {i}}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(b\\) represents a learnable position encoding, \\(d\\) denotes the dimension of \\(\\overline{q}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.895, + 0.561 + ], + "angle": 0, + "content": "MSRSTM. To merge more information from different exposure regions, inspired by [13], we propose a MultiScale Residual Swin Transformer Module (MSRSTM). First, \\( F_{s}^{1}, F_{s}^{2}, F_{s}^{3} \\) is concatenated along the channel dimension to get the input of MSRSTM. Note that \\( F_{s}^{2} \\) denotes \\( F_{2} \\). Then, MSRSTM merges a long range of information from different exposure regions. MSRSTM consists of multiple multi-scale Swin Transformer layers (STL), a few convolutional layers, and a residual connection. Given the input feature \\( F_{out,i}^{N-1} \\) of \\( i \\)-th MSRSTM, the output \\( F_{out,i}^{N} \\) of MSRSTM can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.563, + 0.895, + 0.592 + ], + "angle": 0, + "content": "\\[\nF _ {S T L, i} ^ {N} = \\operatorname {C o n v} \\left(\\left(\\operatorname {C o n c a t} \\left(S T L _ {i} ^ {N, l _ {1}} \\left(F _ {\\text {o u t}, i} ^ {N - 1}\\right), \\right. \\right. \\right.\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.587, + 0.847, + 0.606 + ], + "angle": 0, + "content": "\\[\nS T L _ {i} ^ {N, l _ {2}} \\left(F _ {o u t, i} ^ {N - 1}\\right), S T L _ {i} ^ {N, l _ {3}} \\left(F _ {o u t, i} ^ {N - 1}\\right)),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.614, + 0.892, + 0.634 + ], + "angle": 0, + "content": "\\[\nF _ {o u t, i} ^ {N} = \\operatorname {C o n v} \\left(F _ {S T L, i} ^ {N}\\right) + F _ {o u t, i} ^ {N - 1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.701 + ], + "angle": 0, + "content": "where \\(STL_{i}^{N,l_{j}}(\\cdot)\\) represents the \\(N\\)-th Swin Transformer layer of the \\(l_{j}\\) scale in the \\(i\\)-th MSRSTM, \\(F_{out,i}^{N-1}\\) denotes the input feature of the \\(N\\)-th Swin Transformer layer in the \\(i\\)-th MSRSTM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.892, + 0.778 + ], + "angle": 0, + "content": "Loss Function. Since unlabeled samples do not have HDR ground truth labels, we calculate the self-supervised loss in the LDR domain. We first use function \\(\\omega\\) to transform the predicted HDR image \\(\\hat{Y}\\) to short, medium, and long exposure LDR images \\(\\hat{Y}_i\\)," + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.782, + 0.892, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\hat {Y} _ {i} = \\omega (\\hat {Y}) = (\\hat {Y} \\times t _ {i}) ^ {\\frac {1}{\\gamma}}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To recover the saturated regions, we transform the short exposure frame (since the predicted HDR in this stage is aligned to the short exposure frame) to new short, medium, and long exposure frames by ground truth generation. Then, we regard the new exposure frames as the ground truth \\( X_{i}^{GT} \\) of the model," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5778" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.146, + 0.088, + 0.47, + 0.122 + ], + "angle": 0, + "content": "\\[\nX _ {i} ^ {G T} = \\left(\\frac {\\left(X _ {1} ^ {U}\\right) ^ {\\gamma} \\times t _ {i}}{t _ {1}}\\right) ^ {\\frac {1}{\\gamma}}, \\quad i = 1, 2, 3. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.131, + 0.47, + 0.162 + ], + "angle": 0, + "content": "Finally, we calculate \\(L_{1}\\) self-supervised loss between \\(\\hat{Y}_i\\) and \\(X_i^{GT}\\), 3" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.152, + 0.469, + 0.192 + ], + "angle": 0, + "content": "\\[\nL _ {S S L} = \\sum_ {i = 1} ^ {3} \\left| \\left| \\hat {Y} _ {i} - X _ {i} ^ {G T} \\right| \\right| _ {1}. \\tag {8}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.199, + 0.361, + 0.216 + ], + "angle": 0, + "content": "3.4. Semi-supervised Learning Stage" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.222, + 0.469, + 0.312 + ], + "angle": 0, + "content": "Finetune. At the beginning of this stage, to improve the saturated regions and further learn to handle ghosting regions, we first finetune the pretrained model with a few dynamic samples \\(D\\) and static labeled samples \\(S\\). Here we apply \\(\\mu\\)-law to map the linear domain image to the tonemapped domain image," + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.31, + 0.469, + 0.342 + ], + "angle": 0, + "content": "\\[\nT (x) = \\frac {\\log (1 + \\mu x)}{\\log (1 + \\mu)}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.35, + 0.469, + 0.412 + ], + "angle": 0, + "content": "where \\(T(x)\\) is the tonemap function, \\(\\mu = 5000\\). Then we calculate the reconstruction loss \\(L_{recon}\\) and perceptual loss \\(L_{percep}\\) between the predicted HDR \\(\\hat{Y}_0^D, \\hat{Y}_0^S\\) and ground truth HDR \\(Y_0^D, Y_0^S\\)," + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.415, + 0.468, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {r e c o n}} = \\left\\| T \\left(\\hat {Y} _ {0} ^ {D}\\right) - T \\left(Y _ {0} ^ {D}\\right) \\right\\| _ {1} + \\left\\| T \\left(\\hat {Y} _ {0} ^ {S}\\right) - T \\left(Y _ {0} ^ {S}\\right) \\right\\| _ {1}, (10) \\\\ L _ {p e r c e p} = \\left\\| \\phi_ {i, j} \\left(T \\left(\\hat {Y} _ {0} ^ {D}\\right)\\right) - \\phi_ {i, j} \\left(T \\left(Y _ {0} ^ {D}\\right)\\right) \\right\\| _ {1} (11) \\\\ + \\left| \\left| \\phi_ {i, j} \\left(T \\left(\\hat {Y} _ {0} ^ {S}\\right)\\right) - \\phi_ {i, j} \\left(T \\left(Y _ {0} ^ {S}\\right)\\right) \\right| \\right| _ {1}, \\\\ L _ {\\text {f i n e t u n e}} = L _ {\\text {r e c o n}} + \\lambda L _ {\\text {p e r c e p}}, (12) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.51, + 0.469, + 0.54 + ], + "angle": 0, + "content": "where \\(\\phi_{i,j}\\) represents the \\(j\\)-th convolutional layer and the \\(i\\)-th max-pooling layer in VGG19, \\(\\lambda = 1e^{-2}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.54, + 0.469, + 0.736 + ], + "angle": 0, + "content": "Iteration. To prevent the overfitting problem with a few labeled training samples and exploit unlabeled samples, we further generate the pseudo-labels \\(\\hat{Y}_t^U\\) of unlabeled data. Concretely, we iteratively and adaptively train the model with a few dynamic and static samples \\(D\\) and \\(S\\) and a large number of unlabeled samples \\(U\\). Specifically, at timestep \\(t\\), we use model \\(N_t\\) to predict the pseudo-labels \\(\\hat{Y}_t^U\\) of unlabeled data. Then, we train the model \\(N_t\\) with a few labeled and pseudo-labeled samples to get the model \\(N_{t+1}\\) at timestep \\(t+1\\). Note that we use finetune model to generate unlabel HDR pseudo-labels \\(\\hat{Y}_0^U\\) at timestep \\(t=0\\). Finally, at each timestep in the refinement stage, we calculate the reconstruction loss and perceptual loss as follows," + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.742, + 0.484, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {I t e r a t i o n} = L _ {r e c o n, t + 1} ^ {D} + L _ {r e c o n, t + 1} ^ {S} + \\sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {r e c o n, t + 1} ^ {U _ {i}} \\\\ + \\lambda \\left(L _ {\\text {p e r c e p}, t + 1} ^ {D} + L _ {\\text {p e r c e p}, t + 1} ^ {S} + \\sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {\\text {p e r c e p}, t + 1} ^ {U _ {i}}\\right), \\tag {13} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.852, + 0.469, + 0.9 + ], + "angle": 0, + "content": "where \\(\\lambda = 1e^{-2}\\). \\(W_{t + 1}^{U_i}\\) is the weight factor of unlabeled data \\(U_{i}\\). To get loss weight \\(W_{t + 1}^{U_i}\\), please refer to the next section in detail." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.26 + ], + "angle": 0, + "content": "APSS. Since the HDR pseudo-labels inevitably contain saturated and ghosted samples, we propose an Adaptive Pseudo-labels Selection Strategy (APSS) to pick well-exposed and ghost-free HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process. Specifically, at timestep \\( t \\), we use model \\( N_{t} \\) to predict HDR images with dynamic and static labeled samples \\( \\hat{Y}_t^D \\) and \\( \\hat{Y}_t^S \\). Then we use function \\( \\omega \\) to map the predicted HDR image to medium exposure image \\( \\tilde{Y}_t^{D\\cup S} \\) and calculate the loss between \\( \\tilde{Y}_t^{D\\cup S} \\) and original medium exposure LDR image \\( X_{2,t}^{D\\cup S} \\) in well exposure regions to get \\( L_{select,t}^{D\\cup S} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.268, + 0.892, + 0.309 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {s e l e c t}, t} ^ {D \\cup S} = | | \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {D}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {D}\\right)\\right) | | _ {1} \\tag {14} \\\\ + \\left\\| \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {S}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {S}\\right)\\right) \\right\\| _ {1}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.32, + 0.892, + 0.38 + ], + "angle": 0, + "content": "where \\( \\text{mask}(\\cdot) \\) denotes masking the over and under-exposure regions. Subsequently, we sort all patches' losses, and adopt \\( \\sigma(\\cdot, \\cdot) \\) function to get \\( \\beta \\) percentile (85th) loss as a selection threshold \\( \\tau_t \\)," + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.388, + 0.891, + 0.408 + ], + "angle": 0, + "content": "\\[\n\\tau_ {t} = \\sigma \\left(L _ {\\text {s e l e c t}, t} ^ {D \\cup S}, \\beta\\right). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.42, + 0.892, + 0.578 + ], + "angle": 0, + "content": "Furthermore, we use model \\(N_{t}\\) to predict pseudo-labels \\(\\hat{Y}_t^U\\) of unlabeled samples, similar to the operation of labeled data mentioned above. We then use \\(\\omega\\) function to map \\(\\hat{Y}_t^U\\) to medium exposure to get \\(\\hat{Y}_t^U\\) and calculate the loss between \\(\\tilde{Y}_t^U\\) and original medium exposure LDR image \\(X_{2,t}^{U}\\) to get \\(L_{select,t}^{U} = \\{L_{select,t}^{U_1},L_{select,t}^{U_2},\\dots ,L_{select,t}^{U_N}\\}\\). If the current loss \\(L_{select,t}^{U_i}\\) is greater than \\(\\tau_{t}\\), we consider the pseudo-label to be of poor quality, which has more saturated and ghosted regions. Then we will give a lower weight which tends to decay linearly in the next training iteration." + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.585, + 0.891, + 0.605 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s e l e c t}, t} ^ {U} = \\left\\| \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {U}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {U}\\right)\\right) \\right\\| _ {1}, \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.616, + 0.891, + 0.635 + ], + "angle": 0, + "content": "\\[\nm _ {t} ^ {U} = \\max \\left(L _ {\\text {s e l e c t}, t} ^ {U}\\right), \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.653, + 0.891, + 0.701 + ], + "angle": 0, + "content": "\\[\nW _ {t + 1} ^ {U _ {i}} = \\left\\{ \\begin{array}{l l} 1 & L _ {\\text {s e l e c t}, t} ^ {U _ {i}} \\leq \\tau_ {t} \\\\ \\frac {m _ {t} ^ {U} - L _ {\\text {s e l e c t} , t} ^ {U _ {i}}}{m _ {t} ^ {U} - \\tau_ {t}} & L _ {\\text {s e l e c t}, t} ^ {U _ {i}} > \\tau_ {t} \\end{array} \\right. \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.708, + 0.892, + 0.771 + ], + "angle": 0, + "content": "where \\(X_{2,t}^{U}\\) is the unlabeled medium exposure image in timestep \\(t\\), \\(m_t^U\\) is the largest selection loss of unlabeled samples in timestep \\(t\\), \\(W_{t + 1}^{U_i}\\) is the weight factor of \\(U_{i}\\) smaple in the \\(t + 1\\) training iteration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.632, + 0.802 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. We train all the methods on two public datasets, Kalantari's [9] and Hu's dataset [7]. Kalantari's dataset includes 74 training samples and 15 testing samples. Three different LDR images in a sample are captured with exposure biases of \\(\\{-2,0, + 2\\}\\) or \\(\\{-3,0, + 3\\}\\). Hu's dataset is captured at three exposure levels (i.e., \\(\\{-2,0, + 2\\}\\)). There are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5779" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.875, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.61, + 0.893, + 0.639 + ], + "angle": 0, + "content": "Figure 4. Examples of Kalantari's [9] and Hu's [7] datasets (top row) and Tursun's [28] and Prabhakar's [21] datasets (bottom row). Note that we directly evaluate the methods on Tursun's and Prabhakar's datasets with the checkpoint trained on Kalantari's dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.473, + 0.816 + ], + "angle": 0, + "content": "85 training samples and 15 testing samples in Hu's dataset. We train all comparison methods with the same set of images. Concretely, we randomly choose \\( K \\in \\{1, 5\\} \\) dynamic labeled samples and \\( Q = 5 \\) static labeled samples for training in all methods. Furthermore, for each \\( K \\), we evaluate all methods for 5 runs denoted as 5-way in Table 1. In addition, since FSHDR [22] and our method exploit unlabeled samples, we also use the rest of the dataset samples as unlabeled data \\( U \\). Finally, to verify generalization performance, we evaluate all methods on Tursun's dataset [28] that does not have ground truth and Prabhakar's dataset [21]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.821, + 0.47, + 0.882 + ], + "angle": 0, + "content": "Evaluation Metrics. We calculate five common metrics used for testing, i.e., PSNR-L, PSRN- \\(\\mu\\), SSIM-L, SSIM- \\(\\mu\\), and HDR-VDP-2 [16], where '-L' denotes linear domain, '-\\(\\mu\\) ' denotes tonemapping domain." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Implementation Details. The window size in MSRSTM is" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.65, + 0.892, + 0.756 + ], + "angle": 0, + "content": "\\(2 \\times 2, 4 \\times 4\\) and \\(8 \\times 8\\). In the training stage, we crop the 128 \\(\\times\\) 128 patches with stride 64 for the training dataset. We use the Adam optimizer, and set the batch size and learning rate as 4 and 0.0005, receptively. And we set \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\), and \\(\\epsilon = 1e^{-8}\\) in the Adam optimizer. We implement our model using PyTorch with 2 NVIDIA GeForce 3090 GPUs and train for 200 epochs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.769, + 0.866, + 0.785 + ], + "angle": 0, + "content": "4.1. Comparison with State-of-the-art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.794, + 0.892, + 0.884 + ], + "angle": 0, + "content": "To evaluate our model, we carry out quantitative and qualitative experiments comparing with several state-of-the-art methods, including patch-based classical methods: Sen [24], Hu [8], and deep learning-based methods: Kalantari [9], DeepHDR [30], AHDRNet [31], ADNet [14], FSHDR [22]. We use the codes provided by the authors." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Evaluation on Kalantari's and Hu's Datasets. In Fig-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5780" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 1. The evaluation results on Kalantari's [9] and Hu's [7] datasets. The best and the second best results are highlighted in Bold and Underline, respectively." + }, + { + "type": "table", + "bbox": [ + 0.149, + 0.121, + 0.823, + 0.253 + ], + "angle": 0, + "content": "
DatasetMetricSettingKalantariDeepHDRAHDRNetADNetFSHDROurs
KalantariPSNR-l5way-5shot39.37±0.1238.25±0.2940.61±0.1040.78±0.1541.39±0.1241.54±0.10
PSNR-μ39.86±0.1938.62±0.2741.05±0.3240.93±0.3841.40±0.1341.61±0.08
PSNR-l5way-1shot36.94±0.4436.67±0.6738.83±0.3938.96±0.3541.04±0.1141.14±0.11
PSNR-μ37.33±1.2137.01±1.6839.15±1.0439.08±1.0641.13±0.0741.25±0.05
HuPSNR-l5way-5shot41.36±0.2540.73±0.6646.37±0.7646.88±0.8147.13±0.1347.41±0.12
PSNR-μ38.95±0.1439.92±0.2243.42±0.4443.79±0.4843.98±0.2744.24±0.17
PSNR-l5way-1shot38.67±0.4337.82±0.8644.64±0.8044.75±0.8444.94±0.2345.04±0.16
PSNR-μ36.83±0.6238.49±1.0742.37±1.4242.41±1.2042.50±0.8742.55±0.44
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.256, + 0.895, + 0.283 + ], + "angle": 0, + "content": "Table 2. Further evaluation results on Kalantari's [9], Hu's [7] and Prabhakar's datasets [21]. The best and the second best results are highlighted in Bold and Underline in each setting, respectively." + }, + { + "type": "table", + "bbox": [ + 0.156, + 0.283, + 0.812, + 0.6 + ], + "angle": 0, + "content": "
KalantariHu
PSNR-lPSNR-μSSIM-lSSIM-μHV2PSNR-lPSNR-μSSIM-lSSIM-μHV2
S1Sen38.5740.940.97110.978064.7133.5831.480.96340.953166.39
Hu30.8432.190.94080.963262.0536.9436.560.98770.982467.58
FSHDR40.9741.110.98640.982767.0842.1541.140.99040.989171.35
Ours (K=0)41.1241.200.98660.986867.1642.9941.300.99120.990372.18
S2Ours (K=1)41.1441.250.98660.986967.2045.0442.550.99380.992873.23
Ours (K=5)41.5441.610.98790.988067.3347.4144.240.99740.993674.49
S3Kalantari41.2241.850.98480.987266.2343.7641.600.99380.991472.94
DeepHDR40.9141.640.98630.985767.4241.2041.130.99410.987070.82
AHDRNet41.2341.870.98680.988967.5049.2245.760.99800.995675.04
ADNET41.3141.800.98710.988367.5750.3846.790.99870.994876.32
FSHDR41.7941.920.98760.985167.7049.5645.900.99840.994575.25
Ours41.6841.970.98890.989567.7750.3146.880.99880.995776.21
S4Kalantari25.8721.440.86100.917660.0010.2316.950.69030.834649.10
DeepHDR25.9221.430.85970.917060.0225.4820.860.92150.835466.83
AHDRNet26.6222.080.87370.923858.8911.4417.840.67320.838952.79
ADNET25.7621.390.86860.821760.3610.8618.090.69150.839949.28
FSHDR28.0322.010.87510.920360.5312.8219.370.74420.834755.34
Ours27.9122.450.87640.925261.0230.2921.560.94400.845667.07
S5Kalantari31.2433.100.95270.959363.9919.8218.630.76790.874259.50
DeepHDR30.7529.010.92440.922363.2619.8418.700.76980.875259.48
AHDRNet31.8433.490.95880.960664.4020.8020.510.82590.913659.79
ADNET31.0833.500.95360.963663.8820.7820.800.82680.917359.71
FSHDR32.7032.240.95530.946564.3720.2319.710.79290.902659.63
Ours32.7234.490.95860.971364.4520.6921.960.82570.920759.76
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.473, + 0.899 + ], + "angle": 0, + "content": "ure 4 (a) and (b), we compare our method with other state-of-the-art methods in the 5-shot scenario. Due to insufficient labeled samples, large motion, and saturation, most comparing methods suffer from color distortion and ghosting artifacts in these two datasets. Kalantari's method and DeepHDR produce undesirable artifacts and color distortion (see Figure 4 (a)(b)). There are two reasons behind that: misalignment of optical flow and homographies and the lack of labeled data. Although AHDRNet and ADNET are proposed to suppress motion and saturation with attention mechanisms, they cannot reconstruct ghost-free HDR images with few labeled samples. They also produce severe ghosting artifacts (see the red block in Figure 4 (a)(b)). FSHDR exploits unlabeled data to alleviate ghosts under the constraint of a few labeled samples, but it is difficult to handle both ghosting and saturation problems simultaneously. We can see that FSHDR still suffers from ghosting artifacts which leaves an obvious hand artifact in the car (see the red block in Figure 4 (a)). Thanks to the pro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.701 + ], + "angle": 0, + "content": "posed SMAE and sample-quality-based iterative learning strategy, which first address the saturation problems using SMAE and then adaptively sample well-exposed and ghost-free pseudo-labels to handle ghosting problems, we can reconstruct ghost-free HDR images with only a few labeled samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.884 + ], + "angle": 0, + "content": "The quantitative results under the constraint of few shot scenarios on two dataset are shown in Table 1. We report means and \\(95\\%\\) margin of variations for 5 and 1 shot cases across 5 runs. Our method achieves state-of-the-art performance on all metrics of two datasets, while most other methods perform poorly with only a few labeled samples. We show that our proposed method surpasses second-best method by 0.15db and 0.21db in terms of PSNR- \\(l\\) and PSNR- \\(\\mu\\) for 5way-5shot setting on Kalantari's dataset, and it also improves by 0.28db and 0.26db for 5way-5shot setting on Hu's dataset. For 5way-1shot setting, our method consistently outperforms other approaches on two datasets." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In addition, as shown in Table 2, we further compare our" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5781" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.09, + 0.465, + 0.103 + ], + "angle": 0, + "content": "Table 3. Ablation study of 5 shot scenario on Kalantari's dataset." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.107, + 0.43, + 0.219 + ], + "angle": 0, + "content": "
#ModelPSNR-lPSNR-μHDR-VDP-2
B1SSHDR41.5441.6167.33
B2Stage2Net41.3141.4367.21
B3w/o APSS41.4941.4567.29
B4AHDR*41.4841.5167.30
B5FSHDR*41.4141.4367.26
B6Vanilla-AHDR40.6141.0566.95
B7Vanilla-FSHHDR41.3941.4067.25
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.468, + 0.367 + ], + "angle": 0, + "content": "method with major HDR deghosting approaches in zero-shot setting \\( S_{1} \\), few-shot setting \\( S_{2} \\), and fully supervised setting \\( S_{3} \\). Note that we use all the dynamic labeled samples without static and unlabeled samples for plain training in setting \\( S_{3} \\). Our zero-shot approach outperforms other methods in zero-shot setting on two datasets. It also outperforms some 5-shot and fully supervised methods in most metrics. Finally, our few-shot and fully supervised approaches achieve state-of-the-art performance among two datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.468, + 0.653 + ], + "angle": 0, + "content": "Evaluation Generalization Across Different Datasets. We compare our method against other approaches on Kalantari's, Hu's, Tursun's, and Prabhakar's datasets to verify generalization performance. We directly evaluate the methods with the checkpoint trained on Kalantari's dataset and show the qualitative results on Tursun's and Prabhakar's datasets in Figure 4 (c)(d). More results are included in the Appendix. In Figure 4 (c), since the lady's motion is large, all the comparison methods cannot remove the ghosting artifacts. In Figure 4 (d), the comparison methods have obvious color distortion and ghosting artifacts on the floor and in the ceiling. It shows that other methods have poor generalization performance across different datasets. All these methods address both the saturation and ghosting problems simultaneously. They cannot learn a robust representation to reconstruct a high-quality HDR image. Thanks to our SMAE and sample-quality-based iterative learning strategy, we can learn a robust representation to recover saturated regions and remove ghosting artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.468, + 0.775 + ], + "angle": 0, + "content": "In Table 2, setting \\( S_{4} \\) denotes that we utilize the checkpoint trained on Kalantari's or Hu's dataset under 5 shot scenario to evaluate on Hu's or Kalantari's dataset reversely. Setting \\( S_{5} \\) represents that we train on Kalantari's or Hu's dataset under 5 shot scenario and evaluate on Prabhakar's dataset. Our method achieves better numerical performance in terms of PSNR- \\( l \\) and PSNR- \\( \\mu \\). It demonstrates that our method generalizes well across different datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.241, + 0.801 + ], + "angle": 0, + "content": "4.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We conduct ablation studies on Kalantari's dataset under the condition of 5 shot scenario across 5 runs and analyze the importance of each component. We use the following variants of our whole SSHDR model: 1) SSHDR: The full model of SSHDR network trained with two entire stages. 2) Stage2Net: The model only trained in the second" + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.089, + 0.871, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.557, + 0.243, + 0.833, + 0.257 + ], + "angle": 0, + "content": "Figure 5. Visual results of poor pseudo-labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.272, + 0.892, + 0.393 + ], + "angle": 0, + "content": "stage without SMAE pre-training. 3) w/o APSS: The model trained with two stages without using sample-quality-based pseudo-labels selection strategy. 4) \\( \\text{AHDR}^* \\): The AHDR model is trained with our proposed two stages strategy. 5) \\( \\text{FSHDR}^* \\): Our model is trained with the FSHDR strategy. 6) Vanilla-AHDR: The vanilla AHDR model trained in 5 shot scenario. 7) Vanilla-FSHDR: The vanilla FSHDR model trained with 5 labeled samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.892, + 0.484 + ], + "angle": 0, + "content": "SMAE Pre-training. As shown in Table 3, the performance of Stage2Net is significantly decreased compared with SSHDR. Since the SMAE learns a robust representation to generate content of saturated regions, it helps to improve the saturated regions. In a word, it demonstrates that the SMAE pre-training stage is an effective mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.891, + 0.589 + ], + "angle": 0, + "content": "Pseudo-labels Selection Strategy. Since the sample-quality-based pseudo-labels selection strategy can exclude saturated and ghosted samples (see Figure 5), the model can be guided in a correct optimization direction which is effective for ghost removal. When we remove the pseudolabels selection strategy, the performance of the model without APSS is dropped." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.891, + 0.65 + ], + "angle": 0, + "content": "Two Stages Strategy. In Table 3, we report the performance of \\( \\mathrm{AHDR}^* \\). It achieves a significant increment compared with the vanilla AHDR model, which demonstrates the effectiveness of the overall two stages strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Proposed Model Architecture. When we replace our two stages strategy with the FSHDR strategy, the numerical results increase compared with FSHDR. It shows that our proposed model architecture is also sound." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.732, + 0.618, + 0.746 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We propose a novel semi-supervised deghosting method for few-shot HDR problem via two stages of completing saturation and deghosting. In the first stage, a Saturated Mask AutoEncoder is proposed to learn a robust representation and reconstruct a non-saturated HDR image with a self-supervised mechanism. In the second stage, we propose an adaptive pseudo-label selection strategy to avoid the effects of mistrabeled samples. Finally, our approach shows superiority over the existing state-of-the-art methods." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5782" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Sagie Benaim and Lior Wolf. One-shot unsupervised cross domain translation. Advances in neural information processing systems (NIPS), 31, 2018. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.213 + ], + "angle": 0, + "content": "[2] Luca Bertinetto, João F Henriques, Jack Valmadre, Philip Torr, and Andrea Vedaldi. Learning feed-forward one-shot learners. 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IEEE Transactions on Image Processing, 21(4):2318-2323, 2011. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.869 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5784" + } + ] +] \ No newline at end of file diff --git a/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_origin.pdf b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..15815d1ee27b29eb3125d0ae230d596088f3eac2 --- /dev/null +++ b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/1480ea63-f1bc-4488-8d0b-6bc8008633c3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5453e870445a3c914488ba4738c4965743e17bf61feb120339ed95fa95b8d4fe +size 4412541 diff --git a/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/full.md b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a9a9c7b0c9372a1058171a42fdc6ae2ee2141eb3 --- /dev/null +++ b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/full.md @@ -0,0 +1,356 @@ +# SMAE: Few-shot Learning for HDR Deghosting with Saturation-Aware Masked Autoencoders + +Qingsen Yan†1 Song Zhang†2 Weiye Chen†2 Hao Tang³ Yu Zhu¹ + +Jinqiu Sun $^{1}$ Luc Van Gool $^{3}$ Yanning Zhang $^{1*}$ + +$^{1}$ Northwestern Polytechnical University $^{2}$ Xidian University $^{3}$ CVL, ETH Zurich + +# Abstract + +Generating a high-quality High Dynamic Range (HDR) image from dynamic scenes has recently been extensively studied by exploiting Deep Neural Networks (DNNs). Most DNNs-based methods require a large amount of training data with ground truth, requiring tedious and time-consuming work. Few-shot HDR imaging aims to generate satisfactory images with limited data. However, it is difficult for modern DNNs to avoid overfitting when trained on only a few images. In this work, we propose a novel semi-supervised approach to realize few-shot HDR imaging via two stages of training, called SSHDR. Unlikely previous methods, directly recovering content and removing ghosts simultaneously, which is hard to achieve optimum, we first generate content of saturated regions with a self-supervised mechanism and then address ghosts via an iterative semi-supervised learning framework. Concretely, considering that saturated regions can be regarded as masking Low Dynamic Range (LDR) input regions, we design a Saturated Mask AutoEncoder (SMAE) to learn a robust feature representation and reconstruct a non-saturated HDR image. We also propose an adaptive pseudo-label selection strategy to pick high-quality HDR pseudo-labels in the second stage to avoid the effect of mislabeled samples. Experiments demonstrate that SSHDR outperforms state-of-the-art methods quantitatively and qualitatively within and across different datasets, achieving appealing HDR visualization with few labeled samples. + +# 1. Introduction + +Standard digital photography sensors are unable to capture the wide range of illumination present in natural scenes, resulting in Low Dynamic Range (LDR) images that often + +*† The first three authors contributed equally to this work. This work was partially supported by NSFC (U19B2037, 61901384), Natural Science Basic Research Program of Shaanxi (2021JCW-03, 2023-JC-QN-0685), and National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology. Corresponding author: Yu Zhu. + +![](images/ae770f29fe0d77b7fa99b7f344fe67b31039282a8768363cf4545210445b745f.jpg) + +![](images/67c4779b1d49d793cad7a22e035bc602715af5b8e7a8ff9a31614b92aab07c8c.jpg) + +![](images/dc836e23247023ce32d6d1105c8366ed8fa8bc299fa438fba13f1fb6aad9230b.jpg) + +![](images/9119fe0482a0c0866255db4468ac120604e504925b8427a5629691c20c34dbb9.jpg) + +![](images/268a45a03aa883d7a362057c529c2fcb568166115ba7dc793389cb9c26989018.jpg) + +![](images/2ba0c236c4b42bf488f23dad188dcbc1e8ae80e6396d2afb4b7f2425f955fa08.jpg) + +![](images/4e5eafe4807f43f804c8e4bd1be140c4fde7270db3057b1e77806bbbd0e52095.jpg) + +![](images/a5967468c55031fd71eeb2a7d0cf24973429b19ad7ac6ce205fa219d5cc67c27.jpg) +LDRs + +![](images/f11641bc7dc13d15a157c1a01896f086ffcd49468a0f6503cc7fca12b9b4030b.jpg) + +![](images/d1fbbb9595be5f31734639d8778b7ce94acd25348f9de6476c067ce085f9f869.jpg) + +![](images/3e387854f21812213115a85408740f1f4dcfae4f9fcc5d23845f674621a13c48.jpg) +LDR Patches + +![](images/0cb375b1d717eb82c2a4fb617b843ed9f650037a27e2c129c2023bd1b51e548a.jpg) + +![](images/a186c3b538b54a9c700ec2479e360e58b36b99c9e1ead07f688ab540c781b7ce.jpg) +Sen +[24] +Figure 1. The proposed method generates high-quality images with few labeled samples when compared with several methods. + +![](images/b813d9767e45b072f4942aab66327c73c0b427fb8afe5454b030c25d6a31a1f3.jpg) +Kalantari +[9] +[31] + +![](images/85a6d071c2312b4dcc17f80ded69f438b5e2dce983c04ec092f52a07ef523ed2.jpg) +AHDR +ADNET +[14] + +![](images/452b95b3086597e56dd3e1c970e440e281ebdd0029ad6ba0ea8974bac7983153.jpg) +FSHDR +[22] +Ours + +![](images/461c508d3cffe5ef88de37c961c85f14f92f94fc9677360c981c3593d09e1602.jpg) +GT + +suffer from over or underexposed regions, which can damage the details of the scene. High Dynamic Range (HDR) imaging has been developed to address these limitations. This technique combines several LDR images with different exposures to generate an HDR image. While HDR imaging can effectively recover details in static scenes, it may produce ghosting artifacts when used with dynamic scenes or hand-held camera scenarios. + +Historically, various techniques have been suggested to address such issues, such as alignment-based methods [3,10,27,37], patch-based methods [8,15,24], and rejection-based methods [5, 11, 19, 20, 35, 40]. Two categories of alignment-based approaches exist: rigid alignment (e.g., homographies) that fail to address foreground motions, and non-rigid alignment (e.g., optical flow) that is error-prone. Patch-based techniques merge similar regions using patch-level alignment and produce superior results, but suffer from high complexity. Rejection-based methods aim to eliminate misaligned areas before fusing images, but may result in a loss of information in motion regions. + +As Deep Neural Networks (DNNs) become increasingly prevalent, the DNN-based HDR deghosting methods + +[9, 33, 36] achieve better visual results compared to traditional methods. However, these alignment approaches are error-prone and inevitably cause ghosting artifacts (see Figure 1 Kalantari's results). AHDR [31, 32] proposes spatial attention to suppress motion and saturation, which effectively alleviate misalignment problems. Based on AHDR, ADNET [14] proposes a dual branch architecture using spatial attention and PCD-alignment [29] to remove ghosting artifacts. All these above methods directly learn the complicated HDR mapping function with abundant HDR ground truth data. However, it's challenging to collect a large amount of HDR-labeled data. The reasons can be attributed to that 1) generating a ghost-free HDR ground truth sample requires an absolute static background, and 2) it is time-consuming and requires considerable manpower to do manual post-examination. This generates a new setting that only uses a few labeled data for HDR imaging. + +Recently, FSHDR [22] attempts to generate a ghost-free HDR image with only few labeled data. They use a preliminary model trained with a large amount of unlabeled dynamic samples, and a few dynamic and static labeled samples to generate HDR pseudo-labels and synthesize artificial dynamic LDR inputs to improve the model performance of dynamic scenes further. This approach expects the model to handle both the saturation and the ghosting problems simultaneously, but it is hard to achieve under the condition of few labeled data, especially misaligned regions caused by saturation and motion (see Figure 1 FSHDR). In addition, FSHDR uses optical flow to forcibly synthesize dynamic LDR inputs from poorly generated HDR pseudo-labels, the errors in optical flow further intensify the degraded quality of artificial dynamic LDR images, resulting in an apparent distribution shift between LDR training and testing data, which hampers the performance of the network. + +The above analysis makes it very challenging to directly generate a high-quality and ghost-free HDR image with few labeled samples. A reasonable way is to address the saturation problems first and then cope with the ghosting problems with a few labeled samples. In this paper, we propose a semi-supervised approach for HDR deghosting, named SSHDR, which consists of two stages: self-supervised learning network for content completion and sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we pretrain a Saturated Mask AutoEncoder (SMAE), which learns the representation of HDR features to generate content of saturated regions by self-supervised learning. Specifically, considering that the saturated regions can be regarded as masking the short LDR input patches, inspired by [6], we randomly mask a high proportion of the short LDR input and expect the model to reconstruct a no-saturated HDR image from the remaining LDR patches in the first stage. This self-supervised approach allows the model to recover the saturated regions + +with the capability to effectively learn a robust representation for the HDR domain and map an LDR image to an HDR image. In the second stage, to prevent the overfitting problem with a few labeled training samples and make full use of the unlabeled samples, we iteratively train the model with a few labeled samples and a large amount of HDR pseudo-labels from unlabeled data. Based on the pretrained SMAE, a sample-quality-based iterative semi-supervised learning framework is proposed to address the ghosting artifacts. Considering the quality of pseudo-labels is uneven, we develop an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels (i.e., well-exposed, ghost-free) to avoid awful pseudo-labels hampering the optimization process. This selection strategy is guided by a few labeled samples and enhances the diversity of training samples in each epoch. The experiments demonstrate that our proposed approach can generate high-quality HDR images with few labeled samples and achieves state-of-the-art performance on individual and cross-public datasets. Our contributions can be summarized as follows: + +- We propose a novel and generalized HDR self-supervised pretraining model, which uses mask strategy to reconstruct an HDR image and addresses saturated problems from one LDR image. +- We propose a sample-quality-based semi-supervised training approach to select well-exposed and ghost-free HDR pseudo-labels, which improves ghost removal. +- We perform both qualitative and quantitative experiments, which show that our method achieves state-of-the-art results on individual and cross-public datasets. + +# 2. Related Work + +# 2.1. HDR Deghosting Methods + +The existing HDR deghosting methods include four categories: alignment-based method, patch-based method, rejection-based method, and CNN-based method. + +Alignment-based Method. Rigid or non-rigid registration is mainly used in alignment-based approaches. Bogoni [3] estimated flow vectors to align with the reference images. Kang et al. [10] utilized optical flow to align images in the luminance domain to remove ghosting artifacts. Tomaszewska et al. [27] used SIFT feature to perform global alignments. Since the dense correspondence computed by alignment methods are error-prone, they cannot handle large motion and occlusion. + +Rejection-based Method. Rejection-based methods detect and eliminate motion from static regions. Then they merge static inputs to get HDR images. Grosch et al. [5] estimated a motion map and used it to generate ghost-free HDR. Zhang et al. [40] obtained a motion weighting map using quality measurement on image gradients. Lee et al. [11] and Oh et al. [19] detected motion regions using rank min + +imization. However, rejection-based methods remove the misalignment of regions. It will result in a lack of content in moving regions. + +Patch-based Method. Patch-based methods use patch-level alignment to merge similar contents. Sen et al. [24] proposed a patch-based energy minimization approach that optimizes alignment and reconstruction simultaneously. Hu et al. [8] utilized a patch-match mechanism to produce aligned images. Although these methods have good performance, they suffer from high computational costs. + +CNN-based Method. Kalantari et al. [9] used a CNN network to fuse LDR images that are aligned with optical flow. Wu et al. [30] used homography to align the camera motion and reconstructed HDR images by CNN. Yan et al. [31] proposed an attention mechanism to suppress motion and saturation. Yan et al. [34] designed a nonlocal block to release the constraint of locality receptive field for global merging HDR. Niu et al. [18] proposed HDR-GAN to recover missing content using generative adversarial networks. Ye et al. [38] proposed multi-step feature fusion to generate ghost-free images. Liu et al. [14] utilized the PCD alignment subnetwork to remove ghosts. However, these methods require a large number of labeled samples, which is difficult to collect. + +# 2.2. Few-shot Learning (FSL) + +Humans can successfully learn new ideas with relatively little supervision. Inspired by such ability, FSL aims to learn robust representations with few labeled samples. There are three main categories for FSL methods: databased category [1, 23, 25], which augment the experience with prior knowledge; model-based category [2, 17, 26], which shrinks the size of the hypothesis space using prior knowledge; algorithm-based category [4, 12, 39], which modifies the search for the optimal hypothesis using prior knowledge. For HDR deghosting, Prabhakar et al. [22] proposed a data-based category deghosting method, which uses artificial dynamic sequences synthesis for motion transfer. Still, it is hard to handle both the saturation and the ghosting problems simultaneously with few labeled data. + +# 3. The Proposed Method + +# 3.1. Data Distribution + +Following the setting of few-shot HDR imaging [22], we utilize 1) $N$ dynamic unlabeled LDR samples $U = \{L_1^U,\dots ,L_N^U\}$ , where each $L^U$ consists of three LDRs $(X_{1}^{U},X_{2}^{U},X_{3}^{U})$ with different exposures. 2) $M$ static labeled LDR samples $S = \{L_1^S,\dots ,L_M^S\}$ , where each $L^S$ consists of three LDRs $(X_1^S,X_2^S,X_3^S)$ with different exposures and ground truth $Y^{S}$ . 3) $K$ dynamic labeled LDR samples $D = \{L_1^D,\dots ,L_K^D\}$ , where each $L^D$ consists of three LDRs $(X_1^D,X_2^D,X_3^D)$ and ground truth $Y^{D}$ . Since it is difficult to + +collect labeled samples, we set $K$ to be less than or equal to 5, and $M$ is fixed at 5. While it is easy to capture unlabeled samples, $N$ can be arbitrary. + +# 3.2. Model Overview + +Generating a non-saturated and ghost-free HDR image with few labeled samples is challenging. It is a proper way to address saturated problems first and then handle ghosting problems. As shown in Figure 2, we propose a semi-supervised approach for HDR deghosting. Our approach consists of two stages: a self-supervised learning network for content completion and a sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we propose a multi-scale Transformer model based on self-supervised learning with a saturated-masked autoencoder to make it capable of recovering saturated regions. In a word, we randomly mask LDR patches and reconstruct non-saturated HDR images from the remaining LDR patches. + +In the second stage, we propose a sample-quality-based iterative semi-supervised learning approach that learns to address ghosting problems. We finetune the pretrained model based on the first stage with a few labeled samples. Then, we iteratively train the model with labeled samples and unlabeled samples with pseudo-labels. Considering that the HDR pseudo-labels inevitably contain saturated and ghosting regions, which deteriorate the model performance, we propose an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process. + +# 3.3. Self-supervised Learning Stage + +Input. Considering that there are more saturated regions in the medium $(X_2^U)$ and long exposure frames $(X_3^U)$ of unlabeled data $U$ , we first transform the short exposure frame $(X_1^U)$ into a new medium $(X_{2^{\prime}}^{U})$ and long exposure frames $(X_{3^{\prime}}^{U})$ by exposure adjustment, + +$$ +X _ {i ^ {\prime}} ^ {U} = \operatorname {c l i p} \left(\left(\frac {\left(X _ {1} ^ {U}\right) ^ {\gamma} \times t _ {i}}{t _ {1}}\right) ^ {\frac {1}{\gamma}}\right), \quad i = 2, 3. \tag {1} +$$ + +Then following previous work [9, 30], we map the LDR input images $X_{1}^{U}, X_{2'}^{U}, X_{3'}^{U}$ to HDR domain by gamma correction to get $H_{i}$ , + +$$ +H _ {i ^ {\prime}} = \left(X _ {i ^ {\prime}} ^ {U}\right) ^ {\gamma} / t _ {i}. \tag {2} +$$ + +Note that $X_{1'}^U = X_1^U$ , $t_i$ denotes the exposure time of LDR image $X_i$ , $\gamma$ represents the gamma correction parameter, we set $\gamma$ to 2.2. Then, we concatenate $X_{i'}$ and $H_{i'}$ along the channel dimension to get a 6-channel input $I_i = [X_{i'}, H_{i'}]$ , we subsequently mask the input $I_i$ patches to get $I_i'$ . Concretely, we divide the input into non-overlapping patches and randomly mask a subset of these patches with a high mask ratio (75%) (see Figure 3). Note that the patch size + +![](images/d4c38973c69615b4c75e303c0526dc60ea36e3dbaf5bc95ccd08bc54dd3f2dcb.jpg) +Figure 2. The overview of our framework. + +![](images/6450e334fca0bab898d2f9e884551fc4b61bfe31a318cf92e6b1d9170cc48fe4.jpg) +Figure 3. The detailed procedure of Stage 1. To recover the saturated regions, we utilize the short exposure frame as input and ground truth. + +is $8 \times 8$ . Considering that the masking strategy is another way to destruct the saturated regions, we intend the model to learn a robust representation to recover these saturated regions. Finally, $I' = \{I_1', I_2', I_3'\}$ is the input of the model. + +Model. Our SMAE self-supervised training-based multiscale Transformer consists of a feature extraction module, hallucination module, and Multi-Scale Residual Swin Transformer fusion Module (MSRSTM). The details in our model are included in the Appendix. + +Hallucination Module. We first adopt three convolutional layers to extract shallow feature $F_{i}$ . Then, we divide the shallow feature $F_{i}$ into non-overlapping patches $\overline{F_{i}}$ , and map each patch $\overline{F_{i}}$ into query, keys and values. Subsequently, we calculate the similarity map between $\overline{q}$ and $\overline{k}$ , and perform the Softmax function to get the attention weight. Finally, we apply the attention weight to $\overline{v}$ to get $F_{s}^{i}$ , + +$$ +\bar {q} = \overline {{F _ {2}}} W _ {q}, \quad \bar {k _ {i}} = \overline {{F _ {i}}} W _ {k}, \quad \bar {v _ {i}} = \overline {{F _ {i}}} W _ {v}, \quad i = 1, 3 \tag {3} +$$ + +$$ +F _ {s} ^ {i} = \mathrm {S o f t m a x} (\overline {{q}} \overline {{k _ {i}}} ^ {T} / \sqrt {d} + b) \overline {{v _ {i}}}, +$$ + +where $b$ represents a learnable position encoding, $d$ denotes the dimension of $\overline{q}$ . + +MSRSTM. To merge more information from different exposure regions, inspired by [13], we propose a MultiScale Residual Swin Transformer Module (MSRSTM). First, $F_{s}^{1}, F_{s}^{2}, F_{s}^{3}$ is concatenated along the channel dimension to get the input of MSRSTM. Note that $F_{s}^{2}$ denotes $F_{2}$ . Then, MSRSTM merges a long range of information from different exposure regions. MSRSTM consists of multiple multi-scale Swin Transformer layers (STL), a few convolutional layers, and a residual connection. Given the input feature $F_{out,i}^{N-1}$ of $i$ -th MSRSTM, the output $F_{out,i}^{N}$ of MSRSTM can be formulated as follows: + +$$ +F _ {S T L, i} ^ {N} = \operatorname {C o n v} \left(\left(\operatorname {C o n c a t} \left(S T L _ {i} ^ {N, l _ {1}} \left(F _ {\text {o u t}, i} ^ {N - 1}\right), \right. \right. \right. +$$ + +$$ +S T L _ {i} ^ {N, l _ {2}} \left(F _ {o u t, i} ^ {N - 1}\right), S T L _ {i} ^ {N, l _ {3}} \left(F _ {o u t, i} ^ {N - 1}\right)), +$$ + +$$ +F _ {o u t, i} ^ {N} = \operatorname {C o n v} \left(F _ {S T L, i} ^ {N}\right) + F _ {o u t, i} ^ {N - 1}, \tag {5} +$$ + +where $STL_{i}^{N,l_{j}}(\cdot)$ represents the $N$ -th Swin Transformer layer of the $l_{j}$ scale in the $i$ -th MSRSTM, $F_{out,i}^{N-1}$ denotes the input feature of the $N$ -th Swin Transformer layer in the $i$ -th MSRSTM. + +Loss Function. Since unlabeled samples do not have HDR ground truth labels, we calculate the self-supervised loss in the LDR domain. We first use function $\omega$ to transform the predicted HDR image $\hat{Y}$ to short, medium, and long exposure LDR images $\hat{Y}_i$ , + +$$ +\hat {Y} _ {i} = \omega (\hat {Y}) = (\hat {Y} \times t _ {i}) ^ {\frac {1}{\gamma}}. \tag {6} +$$ + +To recover the saturated regions, we transform the short exposure frame (since the predicted HDR in this stage is aligned to the short exposure frame) to new short, medium, and long exposure frames by ground truth generation. Then, we regard the new exposure frames as the ground truth $X_{i}^{GT}$ of the model, + +$$ +X _ {i} ^ {G T} = \left(\frac {\left(X _ {1} ^ {U}\right) ^ {\gamma} \times t _ {i}}{t _ {1}}\right) ^ {\frac {1}{\gamma}}, \quad i = 1, 2, 3. \tag {7} +$$ + +Finally, we calculate $L_{1}$ self-supervised loss between $\hat{Y}_i$ and $X_i^{GT}$ , 3 + +$$ +L _ {S S L} = \sum_ {i = 1} ^ {3} \left| \left| \hat {Y} _ {i} - X _ {i} ^ {G T} \right| \right| _ {1}. \tag {8} +$$ + +# 3.4. Semi-supervised Learning Stage + +Finetune. At the beginning of this stage, to improve the saturated regions and further learn to handle ghosting regions, we first finetune the pretrained model with a few dynamic samples $D$ and static labeled samples $S$ . Here we apply $\mu$ -law to map the linear domain image to the tonemapped domain image, + +$$ +T (x) = \frac {\log (1 + \mu x)}{\log (1 + \mu)}, \tag {9} +$$ + +where $T(x)$ is the tonemap function, $\mu = 5000$ . Then we calculate the reconstruction loss $L_{recon}$ and perceptual loss $L_{percep}$ between the predicted HDR $\hat{Y}_0^D, \hat{Y}_0^S$ and ground truth HDR $Y_0^D, Y_0^S$ , + +$$ +\begin{array}{l} L _ {\text {r e c o n}} = \left\| T \left(\hat {Y} _ {0} ^ {D}\right) - T \left(Y _ {0} ^ {D}\right) \right\| _ {1} + \left\| T \left(\hat {Y} _ {0} ^ {S}\right) - T \left(Y _ {0} ^ {S}\right) \right\| _ {1}, (10) \\ L _ {p e r c e p} = \left\| \phi_ {i, j} \left(T \left(\hat {Y} _ {0} ^ {D}\right)\right) - \phi_ {i, j} \left(T \left(Y _ {0} ^ {D}\right)\right) \right\| _ {1} (11) \\ + \left| \left| \phi_ {i, j} \left(T \left(\hat {Y} _ {0} ^ {S}\right)\right) - \phi_ {i, j} \left(T \left(Y _ {0} ^ {S}\right)\right) \right| \right| _ {1}, \\ L _ {\text {f i n e t u n e}} = L _ {\text {r e c o n}} + \lambda L _ {\text {p e r c e p}}, (12) \\ \end{array} +$$ + +where $\phi_{i,j}$ represents the $j$ -th convolutional layer and the $i$ -th max-pooling layer in VGG19, $\lambda = 1e^{-2}$ . + +Iteration. To prevent the overfitting problem with a few labeled training samples and exploit unlabeled samples, we further generate the pseudo-labels $\hat{Y}_t^U$ of unlabeled data. Concretely, we iteratively and adaptively train the model with a few dynamic and static samples $D$ and $S$ and a large number of unlabeled samples $U$ . Specifically, at timestep $t$ , we use model $N_t$ to predict the pseudo-labels $\hat{Y}_t^U$ of unlabeled data. Then, we train the model $N_t$ with a few labeled and pseudo-labeled samples to get the model $N_{t+1}$ at timestep $t+1$ . Note that we use finetune model to generate unlabel HDR pseudo-labels $\hat{Y}_0^U$ at timestep $t=0$ . Finally, at each timestep in the refinement stage, we calculate the reconstruction loss and perceptual loss as follows, + +$$ +\begin{array}{l} L _ {I t e r a t i o n} = L _ {r e c o n, t + 1} ^ {D} + L _ {r e c o n, t + 1} ^ {S} + \sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {r e c o n, t + 1} ^ {U _ {i}} \\ + \lambda \left(L _ {\text {p e r c e p}, t + 1} ^ {D} + L _ {\text {p e r c e p}, t + 1} ^ {S} + \sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {\text {p e r c e p}, t + 1} ^ {U _ {i}}\right), \tag {13} \\ \end{array} +$$ + +where $\lambda = 1e^{-2}$ . $W_{t + 1}^{U_i}$ is the weight factor of unlabeled data $U_{i}$ . To get loss weight $W_{t + 1}^{U_i}$ , please refer to the next section in detail. + +APSS. Since the HDR pseudo-labels inevitably contain saturated and ghosted samples, we propose an Adaptive Pseudo-labels Selection Strategy (APSS) to pick well-exposed and ghost-free HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process. Specifically, at timestep $t$ , we use model $N_{t}$ to predict HDR images with dynamic and static labeled samples $\hat{Y}_t^D$ and $\hat{Y}_t^S$ . Then we use function $\omega$ to map the predicted HDR image to medium exposure image $\tilde{Y}_t^{D\cup S}$ and calculate the loss between $\tilde{Y}_t^{D\cup S}$ and original medium exposure LDR image $X_{2,t}^{D\cup S}$ in well exposure regions to get $L_{select,t}^{D\cup S}$ , + +$$ +\begin{array}{l} L _ {\text {s e l e c t}, t} ^ {D \cup S} = | | \operatorname {m a s k} \left(\omega \left(\hat {Y} _ {t} ^ {D}\right)\right) - \operatorname {m a s k} \left(\omega \left(X _ {2, t} ^ {D}\right)\right) | | _ {1} \tag {14} \\ + \left\| \operatorname {m a s k} \left(\omega \left(\hat {Y} _ {t} ^ {S}\right)\right) - \operatorname {m a s k} \left(\omega \left(X _ {2, t} ^ {S}\right)\right) \right\| _ {1}, \\ \end{array} +$$ + +where $\text{mask}(\cdot)$ denotes masking the over and under-exposure regions. Subsequently, we sort all patches' losses, and adopt $\sigma(\cdot, \cdot)$ function to get $\beta$ percentile (85th) loss as a selection threshold $\tau_t$ , + +$$ +\tau_ {t} = \sigma \left(L _ {\text {s e l e c t}, t} ^ {D \cup S}, \beta\right). \tag {15} +$$ + +Furthermore, we use model $N_{t}$ to predict pseudo-labels $\hat{Y}_t^U$ of unlabeled samples, similar to the operation of labeled data mentioned above. We then use $\omega$ function to map $\hat{Y}_t^U$ to medium exposure to get $\hat{Y}_t^U$ and calculate the loss between $\tilde{Y}_t^U$ and original medium exposure LDR image $X_{2,t}^{U}$ to get $L_{select,t}^{U} = \{L_{select,t}^{U_1},L_{select,t}^{U_2},\dots ,L_{select,t}^{U_N}\}$ . If the current loss $L_{select,t}^{U_i}$ is greater than $\tau_{t}$ , we consider the pseudo-label to be of poor quality, which has more saturated and ghosted regions. Then we will give a lower weight which tends to decay linearly in the next training iteration. + +$$ +L _ {\text {s e l e c t}, t} ^ {U} = \left\| \operatorname {m a s k} \left(\omega \left(\hat {Y} _ {t} ^ {U}\right)\right) - \operatorname {m a s k} \left(\omega \left(X _ {2, t} ^ {U}\right)\right) \right\| _ {1}, \tag {16} +$$ + +$$ +m _ {t} ^ {U} = \max \left(L _ {\text {s e l e c t}, t} ^ {U}\right), \tag {17} +$$ + +$$ +W _ {t + 1} ^ {U _ {i}} = \left\{ \begin{array}{l l} 1 & L _ {\text {s e l e c t}, t} ^ {U _ {i}} \leq \tau_ {t} \\ \frac {m _ {t} ^ {U} - L _ {\text {s e l e c t} , t} ^ {U _ {i}}}{m _ {t} ^ {U} - \tau_ {t}} & L _ {\text {s e l e c t}, t} ^ {U _ {i}} > \tau_ {t} \end{array} \right. \tag {18} +$$ + +where $X_{2,t}^{U}$ is the unlabeled medium exposure image in timestep $t$ , $m_t^U$ is the largest selection loss of unlabeled samples in timestep $t$ , $W_{t + 1}^{U_i}$ is the weight factor of $U_{i}$ smaple in the $t + 1$ training iteration. + +# 4. Experiments + +Datasets. We train all the methods on two public datasets, Kalantari's [9] and Hu's dataset [7]. Kalantari's dataset includes 74 training samples and 15 testing samples. Three different LDR images in a sample are captured with exposure biases of $\{-2,0, + 2\}$ or $\{-3,0, + 3\}$ . Hu's dataset is captured at three exposure levels (i.e., $\{-2,0, + 2\}$ ). There are + +![](images/47653c9857ac3e05bbe3107df4251da410df0a8bd75e243a5102e6ba8185bc7b.jpg) +Figure 4. Examples of Kalantari's [9] and Hu's [7] datasets (top row) and Tursun's [28] and Prabhakar's [21] datasets (bottom row). Note that we directly evaluate the methods on Tursun's and Prabhakar's datasets with the checkpoint trained on Kalantari's dataset. + +85 training samples and 15 testing samples in Hu's dataset. We train all comparison methods with the same set of images. Concretely, we randomly choose $K \in \{1, 5\}$ dynamic labeled samples and $Q = 5$ static labeled samples for training in all methods. Furthermore, for each $K$ , we evaluate all methods for 5 runs denoted as 5-way in Table 1. In addition, since FSHDR [22] and our method exploit unlabeled samples, we also use the rest of the dataset samples as unlabeled data $U$ . Finally, to verify generalization performance, we evaluate all methods on Tursun's dataset [28] that does not have ground truth and Prabhakar's dataset [21]. + +Evaluation Metrics. We calculate five common metrics used for testing, i.e., PSNR-L, PSRN- $\mu$ , SSIM-L, SSIM- $\mu$ , and HDR-VDP-2 [16], where '-L' denotes linear domain, '- $\mu$ ' denotes tonemapping domain. + +Implementation Details. The window size in MSRSTM is + +$2 \times 2, 4 \times 4$ and $8 \times 8$ . In the training stage, we crop the 128 $\times$ 128 patches with stride 64 for the training dataset. We use the Adam optimizer, and set the batch size and learning rate as 4 and 0.0005, receptively. And we set $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ , and $\epsilon = 1e^{-8}$ in the Adam optimizer. We implement our model using PyTorch with 2 NVIDIA GeForce 3090 GPUs and train for 200 epochs. + +# 4.1. Comparison with State-of-the-art Methods + +To evaluate our model, we carry out quantitative and qualitative experiments comparing with several state-of-the-art methods, including patch-based classical methods: Sen [24], Hu [8], and deep learning-based methods: Kalantari [9], DeepHDR [30], AHDRNet [31], ADNet [14], FSHDR [22]. We use the codes provided by the authors. + +Evaluation on Kalantari's and Hu's Datasets. In Fig- + +Table 1. The evaluation results on Kalantari's [9] and Hu's [7] datasets. The best and the second best results are highlighted in Bold and Underline, respectively. + +
DatasetMetricSettingKalantariDeepHDRAHDRNetADNetFSHDROurs
KalantariPSNR-l5way-5shot39.37±0.1238.25±0.2940.61±0.1040.78±0.1541.39±0.1241.54±0.10
PSNR-μ39.86±0.1938.62±0.2741.05±0.3240.93±0.3841.40±0.1341.61±0.08
PSNR-l5way-1shot36.94±0.4436.67±0.6738.83±0.3938.96±0.3541.04±0.1141.14±0.11
PSNR-μ37.33±1.2137.01±1.6839.15±1.0439.08±1.0641.13±0.0741.25±0.05
HuPSNR-l5way-5shot41.36±0.2540.73±0.6646.37±0.7646.88±0.8147.13±0.1347.41±0.12
PSNR-μ38.95±0.1439.92±0.2243.42±0.4443.79±0.4843.98±0.2744.24±0.17
PSNR-l5way-1shot38.67±0.4337.82±0.8644.64±0.8044.75±0.8444.94±0.2345.04±0.16
PSNR-μ36.83±0.6238.49±1.0742.37±1.4242.41±1.2042.50±0.8742.55±0.44
+ +Table 2. Further evaluation results on Kalantari's [9], Hu's [7] and Prabhakar's datasets [21]. The best and the second best results are highlighted in Bold and Underline in each setting, respectively. + +
KalantariHu
PSNR-lPSNR-μSSIM-lSSIM-μHV2PSNR-lPSNR-μSSIM-lSSIM-μHV2
S1Sen38.5740.940.97110.978064.7133.5831.480.96340.953166.39
Hu30.8432.190.94080.963262.0536.9436.560.98770.982467.58
FSHDR40.9741.110.98640.982767.0842.1541.140.99040.989171.35
Ours (K=0)41.1241.200.98660.986867.1642.9941.300.99120.990372.18
S2Ours (K=1)41.1441.250.98660.986967.2045.0442.550.99380.992873.23
Ours (K=5)41.5441.610.98790.988067.3347.4144.240.99740.993674.49
S3Kalantari41.2241.850.98480.987266.2343.7641.600.99380.991472.94
DeepHDR40.9141.640.98630.985767.4241.2041.130.99410.987070.82
AHDRNet41.2341.870.98680.988967.5049.2245.760.99800.995675.04
ADNET41.3141.800.98710.988367.5750.3846.790.99870.994876.32
FSHDR41.7941.920.98760.985167.7049.5645.900.99840.994575.25
Ours41.6841.970.98890.989567.7750.3146.880.99880.995776.21
S4Kalantari25.8721.440.86100.917660.0010.2316.950.69030.834649.10
DeepHDR25.9221.430.85970.917060.0225.4820.860.92150.835466.83
AHDRNet26.6222.080.87370.923858.8911.4417.840.67320.838952.79
ADNET25.7621.390.86860.821760.3610.8618.090.69150.839949.28
FSHDR28.0322.010.87510.920360.5312.8219.370.74420.834755.34
Ours27.9122.450.87640.925261.0230.2921.560.94400.845667.07
S5Kalantari31.2433.100.95270.959363.9919.8218.630.76790.874259.50
DeepHDR30.7529.010.92440.922363.2619.8418.700.76980.875259.48
AHDRNet31.8433.490.95880.960664.4020.8020.510.82590.913659.79
ADNET31.0833.500.95360.963663.8820.7820.800.82680.917359.71
FSHDR32.7032.240.95530.946564.3720.2319.710.79290.902659.63
Ours32.7234.490.95860.971364.4520.6921.960.82570.920759.76
+ +ure 4 (a) and (b), we compare our method with other state-of-the-art methods in the 5-shot scenario. Due to insufficient labeled samples, large motion, and saturation, most comparing methods suffer from color distortion and ghosting artifacts in these two datasets. Kalantari's method and DeepHDR produce undesirable artifacts and color distortion (see Figure 4 (a)(b)). There are two reasons behind that: misalignment of optical flow and homographies and the lack of labeled data. Although AHDRNet and ADNET are proposed to suppress motion and saturation with attention mechanisms, they cannot reconstruct ghost-free HDR images with few labeled samples. They also produce severe ghosting artifacts (see the red block in Figure 4 (a)(b)). FSHDR exploits unlabeled data to alleviate ghosts under the constraint of a few labeled samples, but it is difficult to handle both ghosting and saturation problems simultaneously. We can see that FSHDR still suffers from ghosting artifacts which leaves an obvious hand artifact in the car (see the red block in Figure 4 (a)). Thanks to the pro + +posed SMAE and sample-quality-based iterative learning strategy, which first address the saturation problems using SMAE and then adaptively sample well-exposed and ghost-free pseudo-labels to handle ghosting problems, we can reconstruct ghost-free HDR images with only a few labeled samples. + +The quantitative results under the constraint of few shot scenarios on two dataset are shown in Table 1. We report means and $95\%$ margin of variations for 5 and 1 shot cases across 5 runs. Our method achieves state-of-the-art performance on all metrics of two datasets, while most other methods perform poorly with only a few labeled samples. We show that our proposed method surpasses second-best method by 0.15db and 0.21db in terms of PSNR- $l$ and PSNR- $\mu$ for 5way-5shot setting on Kalantari's dataset, and it also improves by 0.28db and 0.26db for 5way-5shot setting on Hu's dataset. For 5way-1shot setting, our method consistently outperforms other approaches on two datasets. + +In addition, as shown in Table 2, we further compare our + +Table 3. Ablation study of 5 shot scenario on Kalantari's dataset. + +
#ModelPSNR-lPSNR-μHDR-VDP-2
B1SSHDR41.5441.6167.33
B2Stage2Net41.3141.4367.21
B3w/o APSS41.4941.4567.29
B4AHDR*41.4841.5167.30
B5FSHDR*41.4141.4367.26
B6Vanilla-AHDR40.6141.0566.95
B7Vanilla-FSHHDR41.3941.4067.25
+ +method with major HDR deghosting approaches in zero-shot setting $S_{1}$ , few-shot setting $S_{2}$ , and fully supervised setting $S_{3}$ . Note that we use all the dynamic labeled samples without static and unlabeled samples for plain training in setting $S_{3}$ . Our zero-shot approach outperforms other methods in zero-shot setting on two datasets. It also outperforms some 5-shot and fully supervised methods in most metrics. Finally, our few-shot and fully supervised approaches achieve state-of-the-art performance among two datasets. + +Evaluation Generalization Across Different Datasets. We compare our method against other approaches on Kalantari's, Hu's, Tursun's, and Prabhakar's datasets to verify generalization performance. We directly evaluate the methods with the checkpoint trained on Kalantari's dataset and show the qualitative results on Tursun's and Prabhakar's datasets in Figure 4 (c)(d). More results are included in the Appendix. In Figure 4 (c), since the lady's motion is large, all the comparison methods cannot remove the ghosting artifacts. In Figure 4 (d), the comparison methods have obvious color distortion and ghosting artifacts on the floor and in the ceiling. It shows that other methods have poor generalization performance across different datasets. All these methods address both the saturation and ghosting problems simultaneously. They cannot learn a robust representation to reconstruct a high-quality HDR image. Thanks to our SMAE and sample-quality-based iterative learning strategy, we can learn a robust representation to recover saturated regions and remove ghosting artifacts. + +In Table 2, setting $S_{4}$ denotes that we utilize the checkpoint trained on Kalantari's or Hu's dataset under 5 shot scenario to evaluate on Hu's or Kalantari's dataset reversely. Setting $S_{5}$ represents that we train on Kalantari's or Hu's dataset under 5 shot scenario and evaluate on Prabhakar's dataset. Our method achieves better numerical performance in terms of PSNR- $l$ and PSNR- $\mu$ . It demonstrates that our method generalizes well across different datasets. + +# 4.2. Ablation Studies + +We conduct ablation studies on Kalantari's dataset under the condition of 5 shot scenario across 5 runs and analyze the importance of each component. We use the following variants of our whole SSHDR model: 1) SSHDR: The full model of SSHDR network trained with two entire stages. 2) Stage2Net: The model only trained in the second + +![](images/7b867f3f671e1d0900228efd3f361124434e91241277c3050683e4cb2587e2b4.jpg) +Figure 5. Visual results of poor pseudo-labels. + +stage without SMAE pre-training. 3) w/o APSS: The model trained with two stages without using sample-quality-based pseudo-labels selection strategy. 4) $\text{AHDR}^*$ : The AHDR model is trained with our proposed two stages strategy. 5) $\text{FSHDR}^*$ : Our model is trained with the FSHDR strategy. 6) Vanilla-AHDR: The vanilla AHDR model trained in 5 shot scenario. 7) Vanilla-FSHDR: The vanilla FSHDR model trained with 5 labeled samples. + +SMAE Pre-training. As shown in Table 3, the performance of Stage2Net is significantly decreased compared with SSHDR. Since the SMAE learns a robust representation to generate content of saturated regions, it helps to improve the saturated regions. In a word, it demonstrates that the SMAE pre-training stage is an effective mechanism. + +Pseudo-labels Selection Strategy. Since the sample-quality-based pseudo-labels selection strategy can exclude saturated and ghosted samples (see Figure 5), the model can be guided in a correct optimization direction which is effective for ghost removal. When we remove the pseudolabels selection strategy, the performance of the model without APSS is dropped. + +Two Stages Strategy. In Table 3, we report the performance of $\mathrm{AHDR}^*$ . It achieves a significant increment compared with the vanilla AHDR model, which demonstrates the effectiveness of the overall two stages strategy. + +Proposed Model Architecture. When we replace our two stages strategy with the FSHDR strategy, the numerical results increase compared with FSHDR. It shows that our proposed model architecture is also sound. + +# 5. Conclusion + +We propose a novel semi-supervised deghosting method for few-shot HDR problem via two stages of completing saturation and deghosting. 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IEEE Transactions on Image Processing, 21(4):2318-2323, 2011. 1, 2 \ No newline at end of file diff --git a/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/images.zip b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..b1f8368a2fd84be8895b16696e8e457a7e3b2938 --- /dev/null +++ b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bd31fe6473a1a824d93c5f5d71b5fca77642b9bbe91eee63fd62856c8d53f441 +size 933824 diff --git a/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/layout.json b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..7e6956be920cfa48a460b2e70f7e4fec8af0b554 --- /dev/null +++ b/2023/SMAE_ Few-Shot Learning for HDR Deghosting With Saturation-Aware Masked Autoencoders/layout.json @@ -0,0 +1,10443 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 76, + 102, + 517, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 76, + 102, + 517, + 138 + ], + "spans": [ + { + "bbox": [ + 76, + 102, + 517, + 138 + ], + "type": "text", + "content": "SMAE: Few-shot Learning for HDR Deghosting with Saturation-Aware Masked Autoencoders" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 159, + 475, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 159, + 475, + 175 + ], + "spans": [ + { + "bbox": [ + 116, + 159, + 475, + 175 + ], + "type": "text", + "content": "Qingsen Yan†1 Song Zhang†2 Weiye Chen†2 Hao Tang³ Yu Zhu¹" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "spans": [ + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "text", + "content": "Jinqiu Sun" + }, + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "text", + "content": " Luc Van Gool" + }, + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "text", + "content": " Yanning Zhang" + }, + { + "bbox": [ + 178, + 175, + 419, + 190 + ], + "type": "inline_equation", + "content": "^{1*}" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "spans": [ + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "text", + "content": "Northwestern Polytechnical University " + }, + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "text", + "content": "Xidian University " + }, + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 92, + 190, + 498, + 204 + ], + "type": "text", + "content": "CVL, ETH Zurich" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 191, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 256, + 290, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 579 + ], + "type": "text", + "content": "Generating a high-quality High Dynamic Range (HDR) image from dynamic scenes has recently been extensively studied by exploiting Deep Neural Networks (DNNs). Most DNNs-based methods require a large amount of training data with ground truth, requiring tedious and time-consuming work. Few-shot HDR imaging aims to generate satisfactory images with limited data. However, it is difficult for modern DNNs to avoid overfitting when trained on only a few images. In this work, we propose a novel semi-supervised approach to realize few-shot HDR imaging via two stages of training, called SSHDR. Unlikely previous methods, directly recovering content and removing ghosts simultaneously, which is hard to achieve optimum, we first generate content of saturated regions with a self-supervised mechanism and then address ghosts via an iterative semi-supervised learning framework. Concretely, considering that saturated regions can be regarded as masking Low Dynamic Range (LDR) input regions, we design a Saturated Mask AutoEncoder (SMAE) to learn a robust feature representation and reconstruct a non-saturated HDR image. 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This work was partially supported by NSFC (U19B2037, 61901384), Natural Science Basic Research Program of Shaanxi (2021JCW-03, 2023-JC-QN-0685), and National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology. 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High Dynamic Range (HDR) imaging has been developed to address these limitations. This technique combines several LDR images with different exposures to generate an HDR image. While HDR imaging can effectively recover details in static scenes, it may produce ghosting artifacts when used with dynamic scenes or hand-held camera scenarios." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 304, + 545, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 689 + ], + "type": "text", + "content": "Historically, various techniques have been suggested to address such issues, such as alignment-based methods [3,10,27,37], patch-based methods [8,15,24], and rejection-based methods [5, 11, 19, 20, 35, 40]. Two categories of alignment-based approaches exist: rigid alignment (e.g., homographies) that fail to address foreground motions, and non-rigid alignment (e.g., optical flow) that is error-prone. Patch-based techniques merge similar regions using patch-level alignment and produce superior results, but suffer from high complexity. Rejection-based methods aim to eliminate misaligned areas before fusing images, but may result in a loss of information in motion regions." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "As Deep Neural Networks (DNNs) become increasingly prevalent, the DNN-based HDR deghosting methods" + } + ] + } + ], + "index": 47 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 15 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 15 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 15 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 198, + 13, + 442, + 24 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 198, + 13, + 442, + 24 + ], + "spans": [ + { + "bbox": [ + 198, + 13, + 442, + 24 + ], + "type": "text", + "content": "Except for this watermark, it is identical to the accepted version;" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 179, + 25, + 461, + 36 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 179, + 25, + 461, + 36 + ], + "spans": [ + { + "bbox": [ + 179, + 25, + 461, + 36 + ], + "type": "text", + "content": "the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5775" + } + ] + } + ], + "index": 48 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "[9, 33, 36] achieve better visual results compared to traditional methods. However, these alignment approaches are error-prone and inevitably cause ghosting artifacts (see Figure 1 Kalantari's results). AHDR [31, 32] proposes spatial attention to suppress motion and saturation, which effectively alleviate misalignment problems. Based on AHDR, ADNET [14] proposes a dual branch architecture using spatial attention and PCD-alignment [29] to remove ghosting artifacts. All these above methods directly learn the complicated HDR mapping function with abundant HDR ground truth data. However, it's challenging to collect a large amount of HDR-labeled data. The reasons can be attributed to that 1) generating a ghost-free HDR ground truth sample requires an absolute static background, and 2) it is time-consuming and requires considerable manpower to do manual post-examination. This generates a new setting that only uses a few labeled data for HDR imaging." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 483 + ], + "type": "text", + "content": "Recently, FSHDR [22] attempts to generate a ghost-free HDR image with only few labeled data. They use a preliminary model trained with a large amount of unlabeled dynamic samples, and a few dynamic and static labeled samples to generate HDR pseudo-labels and synthesize artificial dynamic LDR inputs to improve the model performance of dynamic scenes further. This approach expects the model to handle both the saturation and the ghosting problems simultaneously, but it is hard to achieve under the condition of few labeled data, especially misaligned regions caused by saturation and motion (see Figure 1 FSHDR). In addition, FSHDR uses optical flow to forcibly synthesize dynamic LDR inputs from poorly generated HDR pseudo-labels, the errors in optical flow further intensify the degraded quality of artificial dynamic LDR images, resulting in an apparent distribution shift between LDR training and testing data, which hampers the performance of the network." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 715 + ], + "type": "text", + "content": "The above analysis makes it very challenging to directly generate a high-quality and ghost-free HDR image with few labeled samples. A reasonable way is to address the saturation problems first and then cope with the ghosting problems with a few labeled samples. In this paper, we propose a semi-supervised approach for HDR deghosting, named SSHDR, which consists of two stages: self-supervised learning network for content completion and sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we pretrain a Saturated Mask AutoEncoder (SMAE), which learns the representation of HDR features to generate content of saturated regions by self-supervised learning. Specifically, considering that the saturated regions can be regarded as masking the short LDR input patches, inspired by [6], we randomly mask a high proportion of the short LDR input and expect the model to reconstruct a no-saturated HDR image from the remaining LDR patches in the first stage. This self-supervised approach allows the model to recover the saturated regions" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 312 + ], + "type": "text", + "content": "with the capability to effectively learn a robust representation for the HDR domain and map an LDR image to an HDR image. In the second stage, to prevent the overfitting problem with a few labeled training samples and make full use of the unlabeled samples, we iteratively train the model with a few labeled samples and a large amount of HDR pseudo-labels from unlabeled data. Based on the pretrained SMAE, a sample-quality-based iterative semi-supervised learning framework is proposed to address the ghosting artifacts. Considering the quality of pseudo-labels is uneven, we develop an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels (i.e., well-exposed, ghost-free) to avoid awful pseudo-labels hampering the optimization process. This selection strategy is guided by a few labeled samples and enhances the diversity of training samples in each epoch. The experiments demonstrate that our proposed approach can generate high-quality HDR images with few labeled samples and achieves state-of-the-art performance on individual and cross-public datasets. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 312, + 545, + 432 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 306, + 312, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 312, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 312, + 545, + 360 + ], + "type": "text", + "content": "- We propose a novel and generalized HDR self-supervised pretraining model, which uses mask strategy to reconstruct an HDR image and addresses saturated problems from one LDR image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "type": "text", + "content": "- We propose a sample-quality-based semi-supervised training approach to select well-exposed and ghost-free HDR pseudo-labels, which improves ghost removal." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 396, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 432 + ], + "type": "text", + "content": "- We perform both qualitative and quantitative experiments, which show that our method achieves state-of-the-art results on individual and cross-public datasets." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 445, + 392, + 457 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 392, + 457 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 392, + 457 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 465, + 452, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 465, + 452, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 465, + 452, + 478 + ], + "type": "text", + "content": "2.1. HDR Deghosting Methods" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 520 + ], + "type": "text", + "content": "The existing HDR deghosting methods include four categories: alignment-based method, patch-based method, rejection-based method, and CNN-based method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 628 + ], + "type": "text", + "content": "Alignment-based Method. Rigid or non-rigid registration is mainly used in alignment-based approaches. Bogoni [3] estimated flow vectors to align with the reference images. Kang et al. [10] utilized optical flow to align images in the luminance domain to remove ghosting artifacts. Tomaszewska et al. [27] used SIFT feature to perform global alignments. Since the dense correspondence computed by alignment methods are error-prone, they cannot handle large motion and occlusion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Rejection-based Method. Rejection-based methods detect and eliminate motion from static regions. Then they merge static inputs to get HDR images. Grosch et al. [5] estimated a motion map and used it to generate ghost-free HDR. Zhang et al. [40] obtained a motion weighting map using quality measurement on image gradients. Lee et al. [11] and Oh et al. [19] detected motion regions using rank min" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "text", + "content": "5776" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "imization. However, rejection-based methods remove the misalignment of regions. It will result in a lack of content in moving regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 286, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 286, + 191 + ], + "type": "text", + "content": "Patch-based Method. Patch-based methods use patch-level alignment to merge similar contents. Sen et al. [24] proposed a patch-based energy minimization approach that optimizes alignment and reconstruction simultaneously. Hu et al. [8] utilized a patch-match mechanism to produce aligned images. Although these methods have good performance, they suffer from high computational costs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 192, + 286, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 286, + 358 + ], + "type": "text", + "content": "CNN-based Method. Kalantari et al. [9] used a CNN network to fuse LDR images that are aligned with optical flow. Wu et al. [30] used homography to align the camera motion and reconstructed HDR images by CNN. Yan et al. [31] proposed an attention mechanism to suppress motion and saturation. Yan et al. [34] designed a nonlocal block to release the constraint of locality receptive field for global merging HDR. Niu et al. [18] proposed HDR-GAN to recover missing content using generative adversarial networks. Ye et al. [38] proposed multi-step feature fusion to generate ghost-free images. Liu et al. [14] utilized the PCD alignment subnetwork to remove ghosts. However, these methods require a large number of labeled samples, which is difficult to collect." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 369, + 188, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 188, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 188, + 380 + ], + "type": "text", + "content": "2.2. Few-shot Learning (FSL)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 286, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 286, + 555 + ], + "type": "text", + "content": "Humans can successfully learn new ideas with relatively little supervision. Inspired by such ability, FSL aims to learn robust representations with few labeled samples. There are three main categories for FSL methods: databased category [1, 23, 25], which augment the experience with prior knowledge; model-based category [2, 17, 26], which shrinks the size of the hypothesis space using prior knowledge; algorithm-based category [4, 12, 39], which modifies the search for the optimal hypothesis using prior knowledge. For HDR deghosting, Prabhakar et al. [22] proposed a data-based category deghosting method, which uses artificial dynamic sequences synthesis for motion transfer. Still, it is hard to handle both the saturation and the ghosting problems simultaneously with few labeled data." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 567, + 175, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 175, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 175, + 580 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 586, + 152, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 152, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 152, + 597 + ], + "type": "text", + "content": "3.1. Data Distribution" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Following the setting of few-shot HDR imaging [22], we utilize 1) " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " dynamic unlabeled LDR samples " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "U = \\{L_1^U,\\dots ,L_N^U\\}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "L^U" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " consists of three LDRs " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "(X_{1}^{U},X_{2}^{U},X_{3}^{U})" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " with different exposures. 2) " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " static labeled LDR samples " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "S = \\{L_1^S,\\dots ,L_M^S\\}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "L^S" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " consists of three LDRs " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "(X_1^S,X_2^S,X_3^S)" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " with different exposures and ground truth " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "Y^{S}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ". 3) " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " dynamic labeled LDR samples " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "D = \\{L_1^D,\\dots ,L_K^D\\}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "L^D" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " consists of three LDRs " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "(X_1^D,X_2^D,X_3^D)" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " and ground truth " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "Y^{D}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": ". Since it is difficult to" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "collect labeled samples, we set " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " to be less than or equal to 5, and " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " is fixed at 5. While it is easy to capture unlabeled samples, " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " can be arbitrary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 115, + 406, + 126 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 115, + 406, + 126 + ], + "spans": [ + { + "bbox": [ + 306, + 115, + 406, + 126 + ], + "type": "text", + "content": "3.2. Model Overview" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 133, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 289 + ], + "type": "text", + "content": "Generating a non-saturated and ghost-free HDR image with few labeled samples is challenging. It is a proper way to address saturated problems first and then handle ghosting problems. As shown in Figure 2, we propose a semi-supervised approach for HDR deghosting. Our approach consists of two stages: a self-supervised learning network for content completion and a sample-quality-based iterative semi-supervised learning for deghosting. In the first stage, we propose a multi-scale Transformer model based on self-supervised learning with a saturated-masked autoencoder to make it capable of recovering saturated regions. In a word, we randomly mask LDR patches and reconstruct non-saturated HDR images from the remaining LDR patches." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 289, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 421 + ], + "type": "text", + "content": "In the second stage, we propose a sample-quality-based iterative semi-supervised learning approach that learns to address ghosting problems. We finetune the pretrained model based on the first stage with a few labeled samples. Then, we iteratively train the model with labeled samples and unlabeled samples with pseudo-labels. Considering that the HDR pseudo-labels inevitably contain saturated and ghosting regions, which deteriorate the model performance, we propose an adaptive pseudo-labels selection strategy to pick high-quality HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 428, + 474, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 428, + 474, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 428, + 474, + 441 + ], + "type": "text", + "content": "3.3. Self-supervised Learning Stage" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": "Input. Considering that there are more saturated regions in the medium " + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "inline_equation", + "content": "(X_2^U)" + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": " and long exposure frames " + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "inline_equation", + "content": "(X_3^U)" + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": " of unlabeled data " + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": ", we first transform the short exposure frame " + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "inline_equation", + "content": "(X_1^U)" + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": " into a new medium " + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "inline_equation", + "content": "(X_{2^{\\prime}}^{U})" + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": " and long exposure frames " + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "inline_equation", + "content": "(X_{3^{\\prime}}^{U})" + }, + { + "bbox": [ + 305, + 447, + 545, + 510 + ], + "type": "text", + "content": " by exposure adjustment," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 343, + 516, + 545, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 516, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 343, + 516, + 545, + 542 + ], + "type": "interline_equation", + "content": "X _ {i ^ {\\prime}} ^ {U} = \\operatorname {c l i p} \\left(\\left(\\frac {\\left(X _ {1} ^ {U}\\right) ^ {\\gamma} \\times t _ {i}}{t _ {1}}\\right) ^ {\\frac {1}{\\gamma}}\\right), \\quad i = 2, 3. \\tag {1}", + "image_path": "7ebe43176e4e8983f7dcdf765d8cfe78077e1ddcf80c0d1f146b8cf984d34089.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "type": "text", + "content": "Then following previous work [9, 30], we map the LDR input images " + }, + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "type": "inline_equation", + "content": "X_{1}^{U}, X_{2'}^{U}, X_{3'}^{U}" + }, + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "type": "text", + "content": " to HDR domain by gamma correction to get " + }, + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "type": "inline_equation", + "content": "H_{i}" + }, + { + "bbox": [ + 305, + 550, + 545, + 586 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 389, + 591, + 545, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 591, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 389, + 591, + 545, + 607 + ], + "type": "interline_equation", + "content": "H _ {i ^ {\\prime}} = \\left(X _ {i ^ {\\prime}} ^ {U}\\right) ^ {\\gamma} / t _ {i}. \\tag {2}", + "image_path": "182656549f8fb1004e767bd8a40ddd383af019e1be81e95ff6f4963912a11c6b.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{1'}^U = X_1^U" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": " denotes the exposure time of LDR image " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_i" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": " represents the gamma correction parameter, we set " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": " to 2.2. Then, we concatenate " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "X_{i'}" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "H_{i'}" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": " along the channel dimension to get a 6-channel input " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_i = [X_{i'}, H_{i'}]" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": ", we subsequently mask the input " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": " patches to get " + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_i'" + }, + { + "bbox": [ + 304, + 615, + 545, + 713 + ], + "type": "text", + "content": ". Concretely, we divide the input into non-overlapping patches and randomly mask a subset of these patches with a high mask ratio (75%) (see Figure 3). Note that the patch size" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "5777" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 550, + 292 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 550, + 292 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 550, + 292 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 550, + 292 + ], + "type": "image", + "image_path": "d4c38973c69615b4c75e303c0526dc60ea36e3dbaf5bc95ccd08bc54dd3f2dcb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 219, + 293, + 373, + 303 + ], + "lines": [ + { + "bbox": [ + 219, + 293, + 373, + 303 + ], + "spans": [ + { + "bbox": [ + 219, + 293, + 373, + 303 + ], + "type": "text", + "content": "Figure 2. The overview of our framework." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 311, + 289, + 395 + ], + "blocks": [ + { + "bbox": [ + 47, + 311, + 289, + 395 + ], + "lines": [ + { + "bbox": [ + 47, + 311, + 289, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 311, + 289, + 395 + ], + "type": "image", + "image_path": "6450e334fca0bab898d2f9e884551fc4b61bfe31a318cf92e6b1d9170cc48fe4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 394, + 287, + 427 + ], + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 427 + ], + "type": "text", + "content": "Figure 3. The detailed procedure of Stage 1. To recover the saturated regions, we utilize the short exposure frame as input and ground truth." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "text", + "content": "is " + }, + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "text", + "content": ". Considering that the masking strategy is another way to destruct the saturated regions, we intend the model to learn a robust representation to recover these saturated regions. Finally, " + }, + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "inline_equation", + "content": "I' = \\{I_1', I_2', I_3'\\}" + }, + { + "bbox": [ + 46, + 437, + 287, + 485 + ], + "type": "text", + "content": " is the input of the model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 544 + ], + "type": "text", + "content": "Model. Our SMAE self-supervised training-based multiscale Transformer consists of a feature extraction module, hallucination module, and Multi-Scale Residual Swin Transformer fusion Module (MSRSTM). The details in our model are included in the Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": "Hallucination Module. We first adopt three convolutional layers to extract shallow feature " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": ". Then, we divide the shallow feature " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "F_{i}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": " into non-overlapping patches " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\overline{F_{i}}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": ", and map each patch " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\overline{F_{i}}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": " into query, keys and values. Subsequently, we calculate the similarity map between " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\overline{q}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\overline{k}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": ", and perform the Softmax function to get the attention weight. Finally, we apply the attention weight to " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "\\overline{v}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "inline_equation", + "content": "F_{s}^{i}" + }, + { + "bbox": [ + 46, + 545, + 287, + 642 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 647, + 287, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 647, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 56, + 647, + 287, + 669 + ], + "type": "interline_equation", + "content": "\\bar {q} = \\overline {{F _ {2}}} W _ {q}, \\quad \\bar {k _ {i}} = \\overline {{F _ {i}}} W _ {k}, \\quad \\bar {v _ {i}} = \\overline {{F _ {i}}} W _ {v}, \\quad i = 1, 3 \\tag {3}", + "image_path": "105d9610057869e4fb6d7065632161cf953c4d2fab45c7275975d141e2e95f0f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 53, + 665, + 189, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 665, + 189, + 681 + ], + "spans": [ + { + "bbox": [ + 53, + 665, + 189, + 681 + ], + "type": "interline_equation", + "content": "F _ {s} ^ {i} = \\mathrm {S o f t m a x} (\\overline {{q}} \\overline {{k _ {i}}} ^ {T} / \\sqrt {d} + b) \\overline {{v _ {i}}},", + "image_path": "2a7a3d72f82f960f904879b5b6cde64ebf84d2f1b8c4bbd15aba32a3a98fb568.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " represents a learnable position encoding, " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " denotes the dimension of " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\overline{q}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": "MSRSTM. To merge more information from different exposure regions, inspired by [13], we propose a MultiScale Residual Swin Transformer Module (MSRSTM). First, " + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "inline_equation", + "content": "F_{s}^{1}, F_{s}^{2}, F_{s}^{3}" + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": " is concatenated along the channel dimension to get the input of MSRSTM. Note that " + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "inline_equation", + "content": "F_{s}^{2}" + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": " denotes " + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": ". Then, MSRSTM merges a long range of information from different exposure regions. MSRSTM consists of multiple multi-scale Swin Transformer layers (STL), a few convolutional layers, and a residual connection. Given the input feature " + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "inline_equation", + "content": "F_{out,i}^{N-1}" + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": "-th MSRSTM, the output " + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "inline_equation", + "content": "F_{out,i}^{N}" + }, + { + "bbox": [ + 304, + 313, + 547, + 444 + ], + "type": "text", + "content": " of MSRSTM can be formulated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 333, + 445, + 547, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 445, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 333, + 445, + 547, + 468 + ], + "type": "interline_equation", + "content": "F _ {S T L, i} ^ {N} = \\operatorname {C o n v} \\left(\\left(\\operatorname {C o n c a t} \\left(S T L _ {i} ^ {N, l _ {1}} \\left(F _ {\\text {o u t}, i} ^ {N - 1}\\right), \\right. \\right. \\right.", + "image_path": "f9cc4f8edb4b7c36b84b556541bea7a59958d8a732ebdd271f5ea4a8cdc3cf4f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 365, + 464, + 518, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 464, + 518, + 479 + ], + "spans": [ + { + "bbox": [ + 365, + 464, + 518, + 479 + ], + "type": "interline_equation", + "content": "S T L _ {i} ^ {N, l _ {2}} \\left(F _ {o u t, i} ^ {N - 1}\\right), S T L _ {i} ^ {N, l _ {3}} \\left(F _ {o u t, i} ^ {N - 1}\\right)),", + "image_path": "cbc91703129bba205899c68231c97656b2177d53985f4fcb181aee594e77c5bd.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 355, + 486, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 486, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 355, + 486, + 545, + 502 + ], + "type": "interline_equation", + "content": "F _ {o u t, i} ^ {N} = \\operatorname {C o n v} \\left(F _ {S T L, i} ^ {N}\\right) + F _ {o u t, i} ^ {N - 1}, \\tag {5}", + "image_path": "1a6c84004eb088e3355774bc54314befeb93bc5b0d08bde303ada4f56fd93325.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "STL_{i}^{N,l_{j}}(\\cdot)" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "-th Swin Transformer layer of the " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "l_{j}" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": " scale in the " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "-th MSRSTM, " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "F_{out,i}^{N-1}" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": " denotes the input feature of the " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "-th Swin Transformer layer in the " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "-th MSRSTM." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "text", + "content": "Loss Function. Since unlabeled samples do not have HDR ground truth labels, we calculate the self-supervised loss in the LDR domain. We first use function " + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "text", + "content": " to transform the predicted HDR image " + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{Y}" + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "text", + "content": " to short, medium, and long exposure LDR images " + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\hat{Y}_i" + }, + { + "bbox": [ + 304, + 555, + 545, + 616 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 372, + 619, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 619, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 372, + 619, + 545, + 635 + ], + "type": "interline_equation", + "content": "\\hat {Y} _ {i} = \\omega (\\hat {Y}) = (\\hat {Y} \\times t _ {i}) ^ {\\frac {1}{\\gamma}}. \\tag {6}", + "image_path": "8d2772e31016900bb6cc6bd2d6e75681846d5016f60bb2d48627fedcb6c29494.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "To recover the saturated regions, we transform the short exposure frame (since the predicted HDR in this stage is aligned to the short exposure frame) to new short, medium, and long exposure frames by ground truth generation. Then, we regard the new exposure frames as the ground truth " + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "inline_equation", + "content": "X_{i}^{GT}" + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": " of the model," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5778" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 89, + 69, + 287, + 96 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 69, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 89, + 69, + 287, + 96 + ], + "type": "interline_equation", + "content": "X _ {i} ^ {G T} = \\left(\\frac {\\left(X _ {1} ^ {U}\\right) ^ {\\gamma} \\times t _ {i}}{t _ {1}}\\right) ^ {\\frac {1}{\\gamma}}, \\quad i = 1, 2, 3. \\tag {7}", + "image_path": "cbca75dcc16454746a965073562fe45423b423c394fc0938911382b0cac4db91.jpg" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "text", + "content": "Finally, we calculate " + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "text", + "content": " self-supervised loss between " + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "inline_equation", + "content": "\\hat{Y}_i" + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "inline_equation", + "content": "X_i^{GT}" + }, + { + "bbox": [ + 47, + 103, + 287, + 128 + ], + "type": "text", + "content": ", 3" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 108, + 120, + 287, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 120, + 287, + 152 + ], + "spans": [ + { + "bbox": [ + 108, + 120, + 287, + 152 + ], + "type": "interline_equation", + "content": "L _ {S S L} = \\sum_ {i = 1} ^ {3} \\left| \\left| \\hat {Y} _ {i} - X _ {i} ^ {G T} \\right| \\right| _ {1}. \\tag {8}", + "image_path": "5b61d3a7d7d96fdc866df82d3dd50295360f02170b77266a7f9867c6dd8c2d7b.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 157, + 220, + 171 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 157, + 220, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 157, + 220, + 171 + ], + "type": "text", + "content": "3.4. Semi-supervised Learning Stage" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "text", + "content": "Finetune. At the beginning of this stage, to improve the saturated regions and further learn to handle ghosting regions, we first finetune the pretrained model with a few dynamic samples " + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "text", + "content": " and static labeled samples " + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "text", + "content": ". Here we apply " + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 175, + 287, + 247 + ], + "type": "text", + "content": "-law to map the linear domain image to the tonemapped domain image," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 121, + 245, + 287, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 245, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 121, + 245, + 287, + 270 + ], + "type": "interline_equation", + "content": "T (x) = \\frac {\\log (1 + \\mu x)}{\\log (1 + \\mu)}, \\tag {9}", + "image_path": "99f957965719022085ed3653d57254e89c64459119c198e85a171bf3f43a82b3.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "T(x)" + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": " is the tonemap function, " + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\mu = 5000" + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": ". Then we calculate the reconstruction loss " + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "L_{recon}" + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": " and perceptual loss " + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "L_{percep}" + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": " between the predicted HDR " + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "\\hat{Y}_0^D, \\hat{Y}_0^S" + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": " and ground truth HDR " + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "Y_0^D, Y_0^S" + }, + { + "bbox": [ + 47, + 277, + 287, + 326 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 328, + 286, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 328, + 286, + 400 + ], + "spans": [ + { + "bbox": [ + 51, + 328, + 286, + 400 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {r e c o n}} = \\left\\| T \\left(\\hat {Y} _ {0} ^ {D}\\right) - T \\left(Y _ {0} ^ {D}\\right) \\right\\| _ {1} + \\left\\| T \\left(\\hat {Y} _ {0} ^ {S}\\right) - T \\left(Y _ {0} ^ {S}\\right) \\right\\| _ {1}, (10) \\\\ L _ {p e r c e p} = \\left\\| \\phi_ {i, j} \\left(T \\left(\\hat {Y} _ {0} ^ {D}\\right)\\right) - \\phi_ {i, j} \\left(T \\left(Y _ {0} ^ {D}\\right)\\right) \\right\\| _ {1} (11) \\\\ + \\left| \\left| \\phi_ {i, j} \\left(T \\left(\\hat {Y} _ {0} ^ {S}\\right)\\right) - \\phi_ {i, j} \\left(T \\left(Y _ {0} ^ {S}\\right)\\right) \\right| \\right| _ {1}, \\\\ L _ {\\text {f i n e t u n e}} = L _ {\\text {r e c o n}} + \\lambda L _ {\\text {p e r c e p}}, (12) \\\\ \\end{array}", + "image_path": "6bd2a5fd57a0bdc47bb1fccd7c5820db275a121895bf2dd2767062bc23bab0cc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\phi_{i,j}" + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "text", + "content": "-th convolutional layer and the " + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "text", + "content": "-th max-pooling layer in VGG19, " + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\lambda = 1e^{-2}" + }, + { + "bbox": [ + 47, + 403, + 287, + 427 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": "Iteration. To prevent the overfitting problem with a few labeled training samples and exploit unlabeled samples, we further generate the pseudo-labels " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^U" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " of unlabeled data. Concretely, we iteratively and adaptively train the model with a few dynamic and static samples " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " and a large number of unlabeled samples " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": ". Specifically, at timestep " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": ", we use model " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "N_t" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " to predict the pseudo-labels " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^U" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " of unlabeled data. Then, we train the model " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "N_t" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " with a few labeled and pseudo-labeled samples to get the model " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "N_{t+1}" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "t+1" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": ". Note that we use finetune model to generate unlabel HDR pseudo-labels " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "\\hat{Y}_0^U" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": " at timestep " + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "inline_equation", + "content": "t=0" + }, + { + "bbox": [ + 47, + 427, + 287, + 582 + ], + "type": "text", + "content": ". Finally, at each timestep in the refinement stage, we calculate the reconstruction loss and perceptual loss as follows," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 587, + 296, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 296, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 296, + 666 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {I t e r a t i o n} = L _ {r e c o n, t + 1} ^ {D} + L _ {r e c o n, t + 1} ^ {S} + \\sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {r e c o n, t + 1} ^ {U _ {i}} \\\\ + \\lambda \\left(L _ {\\text {p e r c e p}, t + 1} ^ {D} + L _ {\\text {p e r c e p}, t + 1} ^ {S} + \\sum_ {i = 1} ^ {N} W _ {t + 1} ^ {U _ {i}} L _ {\\text {p e r c e p}, t + 1} ^ {U _ {i}}\\right), \\tag {13} \\\\ \\end{array}", + "image_path": "0f5ab27b7e8a10cfca162ade751a002610f37af342d4ca77976ec03921cbeccb.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda = 1e^{-2}" + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "inline_equation", + "content": "W_{t + 1}^{U_i}" + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "text", + "content": " is the weight factor of unlabeled data " + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "inline_equation", + "content": "U_{i}" + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "text", + "content": ". To get loss weight " + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "inline_equation", + "content": "W_{t + 1}^{U_i}" + }, + { + "bbox": [ + 47, + 674, + 287, + 712 + ], + "type": "text", + "content": ", please refer to the next section in detail." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": "APSS. Since the HDR pseudo-labels inevitably contain saturated and ghosted samples, we propose an Adaptive Pseudo-labels Selection Strategy (APSS) to pick well-exposed and ghost-free HDR pseudo-labels to avoid awful pseudo-labels hampering the optimization process. Specifically, at timestep " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": ", we use model " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": " to predict HDR images with dynamic and static labeled samples " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^D" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^S" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": ". Then we use function " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": " to map the predicted HDR image to medium exposure image " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\tilde{Y}_t^{D\\cup S}" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": " and calculate the loss between " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "\\tilde{Y}_t^{D\\cup S}" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": " and original medium exposure LDR image " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "X_{2,t}^{D\\cup S}" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": " in well exposure regions to get " + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "inline_equation", + "content": "L_{select,t}^{D\\cup S}" + }, + { + "bbox": [ + 305, + 72, + 545, + 205 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 212, + 545, + 244 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 212, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 315, + 212, + 545, + 244 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {s e l e c t}, t} ^ {D \\cup S} = | | \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {D}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {D}\\right)\\right) | | _ {1} \\tag {14} \\\\ + \\left\\| \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {S}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {S}\\right)\\right) \\right\\| _ {1}, \\\\ \\end{array}", + "image_path": "b9ef889c9e64075f72131bd2aa9093d34e7652bf0598cd99d825eac5ff061834.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\text{mask}(\\cdot)" + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "text", + "content": " denotes masking the over and under-exposure regions. Subsequently, we sort all patches' losses, and adopt " + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot, \\cdot)" + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "text", + "content": " function to get " + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "text", + "content": " percentile (85th) loss as a selection threshold " + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "inline_equation", + "content": "\\tau_t" + }, + { + "bbox": [ + 305, + 253, + 545, + 300 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 383, + 307, + 545, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 307, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 383, + 307, + 545, + 323 + ], + "type": "interline_equation", + "content": "\\tau_ {t} = \\sigma \\left(L _ {\\text {s e l e c t}, t} ^ {D \\cup S}, \\beta\\right). \\tag {15}", + "image_path": "1830d7bc11f5342aa8a7491927705d5c3083b566fcca1232648b27a53d126034.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": "Furthermore, we use model " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " to predict pseudo-labels " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^U" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " of unlabeled samples, similar to the operation of labeled data mentioned above. We then use " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " function to map " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^U" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " to medium exposure to get " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\hat{Y}_t^U" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " and calculate the loss between " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\tilde{Y}_t^U" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " and original medium exposure LDR image " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "X_{2,t}^{U}" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " to get " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "L_{select,t}^{U} = \\{L_{select,t}^{U_1},L_{select,t}^{U_2},\\dots ,L_{select,t}^{U_N}\\}" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": ". If the current loss " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "L_{select,t}^{U_i}" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": " is greater than " + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\tau_{t}" + }, + { + "bbox": [ + 305, + 332, + 545, + 457 + ], + "type": "text", + "content": ", we consider the pseudo-label to be of poor quality, which has more saturated and ghosted regions. Then we will give a lower weight which tends to decay linearly in the next training iteration." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 463, + 545, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 463, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 315, + 463, + 545, + 479 + ], + "type": "interline_equation", + "content": "L _ {\\text {s e l e c t}, t} ^ {U} = \\left\\| \\operatorname {m a s k} \\left(\\omega \\left(\\hat {Y} _ {t} ^ {U}\\right)\\right) - \\operatorname {m a s k} \\left(\\omega \\left(X _ {2, t} ^ {U}\\right)\\right) \\right\\| _ {1}, \\tag {16}", + "image_path": "57e98208d7417c9704a4e90743394dc1710b7dceda0980f3db364cba35ab595c.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 378, + 487, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 487, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 378, + 487, + 545, + 502 + ], + "type": "interline_equation", + "content": "m _ {t} ^ {U} = \\max \\left(L _ {\\text {s e l e c t}, t} ^ {U}\\right), \\tag {17}", + "image_path": "6b553a49c339bc2b0fe50856ef88bc7b37a73d447c28ab9a43a63ba2383b00e1.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 342, + 517, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 517, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 342, + 517, + 545, + 555 + ], + "type": "interline_equation", + "content": "W _ {t + 1} ^ {U _ {i}} = \\left\\{ \\begin{array}{l l} 1 & L _ {\\text {s e l e c t}, t} ^ {U _ {i}} \\leq \\tau_ {t} \\\\ \\frac {m _ {t} ^ {U} - L _ {\\text {s e l e c t} , t} ^ {U _ {i}}}{m _ {t} ^ {U} - \\tau_ {t}} & L _ {\\text {s e l e c t}, t} ^ {U _ {i}} > \\tau_ {t} \\end{array} \\right. \\tag {18}", + "image_path": "354e31e19320afcb37f84ba1defad26bbcc15a39ce90cb481b561f9d8dd820eb.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "X_{2,t}^{U}" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": " is the unlabeled medium exposure image in timestep " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "m_t^U" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": " is the largest selection loss of unlabeled samples in timestep " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "W_{t + 1}^{U_i}" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": " is the weight factor of " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "U_{i}" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": " smaple in the " + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 305, + 560, + 545, + 610 + ], + "type": "text", + "content": " training iteration." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 621, + 386, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 386, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 386, + 635 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "text", + "content": "Datasets. We train all the methods on two public datasets, Kalantari's [9] and Hu's dataset [7]. Kalantari's dataset includes 74 training samples and 15 testing samples. Three different LDR images in a sample are captured with exposure biases of " + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{-2,0, + 2\\}" + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{-3,0, + 3\\}" + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "text", + "content": ". Hu's dataset is captured at three exposure levels (i.e., " + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{-2,0, + 2\\}" + }, + { + "bbox": [ + 305, + 641, + 545, + 713 + ], + "type": "text", + "content": "). There are" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5779" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 535, + 482 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 535, + 482 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 535, + 482 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 535, + 482 + ], + "type": "image", + "image_path": "47653c9857ac3e05bbe3107df4251da410df0a8bd75e243a5102e6ba8185bc7b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 483, + 546, + 506 + ], + "lines": [ + { + "bbox": [ + 46, + 483, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 546, + 506 + ], + "type": "text", + "content": "Figure 4. Examples of Kalantari's [9] and Hu's [7] datasets (top row) and Tursun's [28] and Prabhakar's [21] datasets (bottom row). Note that we directly evaluate the methods on Tursun's and Prabhakar's datasets with the checkpoint trained on Kalantari's dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": "85 training samples and 15 testing samples in Hu's dataset. We train all comparison methods with the same set of images. Concretely, we randomly choose " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "K \\in \\{1, 5\\}" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": " dynamic labeled samples and " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "Q = 5" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": " static labeled samples for training in all methods. Furthermore, for each " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": ", we evaluate all methods for 5 runs denoted as 5-way in Table 1. In addition, since FSHDR [22] and our method exploit unlabeled samples, we also use the rest of the dataset samples as unlabeled data " + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 46, + 514, + 289, + 646 + ], + "type": "text", + "content": ". Finally, to verify generalization performance, we evaluate all methods on Tursun's dataset [28] that does not have ground truth and Prabhakar's dataset [21]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "spans": [ + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "text", + "content": "Evaluation Metrics. We calculate five common metrics used for testing, i.e., PSNR-L, PSRN- " + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "text", + "content": ", SSIM-L, SSIM- " + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "text", + "content": ", and HDR-VDP-2 [16], where '-L' denotes linear domain, '-" + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 650, + 287, + 698 + ], + "type": "text", + "content": " ' denotes tonemapping domain." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "Implementation Details. The window size in MSRSTM is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "inline_equation", + "content": "2 \\times 2, 4 \\times 4" + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "content": ". In the training stage, we crop the 128 " + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "content": " 128 patches with stride 64 for the training dataset. We use the Adam optimizer, and set the batch size and learning rate as 4 and 0.0005, receptively. And we set " + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\epsilon = 1e^{-8}" + }, + { + "bbox": [ + 305, + 514, + 545, + 598 + ], + "type": "text", + "content": " in the Adam optimizer. We implement our model using PyTorch with 2 NVIDIA GeForce 3090 GPUs and train for 200 epochs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 609, + 529, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 529, + 621 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 529, + 621 + ], + "type": "text", + "content": "4.1. Comparison with State-of-the-art Methods" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 628, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 628, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 628, + 545, + 700 + ], + "type": "text", + "content": "To evaluate our model, we carry out quantitative and qualitative experiments comparing with several state-of-the-art methods, including patch-based classical methods: Sen [24], Hu [8], and deep learning-based methods: Kalantari [9], DeepHDR [30], AHDRNet [31], ADNet [14], FSHDR [22]. We use the codes provided by the authors." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Evaluation on Kalantari's and Hu's Datasets. In Fig-" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5780" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 91, + 95, + 503, + 200 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. The evaluation results on Kalantari's [9] and Hu's [7] datasets. The best and the second best results are highlighted in Bold and Underline, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 91, + 95, + 503, + 200 + ], + "lines": [ + { + "bbox": [ + 91, + 95, + 503, + 200 + ], + "spans": [ + { + "bbox": [ + 91, + 95, + 503, + 200 + ], + "type": "table", + "html": "
DatasetMetricSettingKalantariDeepHDRAHDRNetADNetFSHDROurs
KalantariPSNR-l5way-5shot39.37±0.1238.25±0.2940.61±0.1040.78±0.1541.39±0.1241.54±0.10
PSNR-μ39.86±0.1938.62±0.2741.05±0.3240.93±0.3841.40±0.1341.61±0.08
PSNR-l5way-1shot36.94±0.4436.67±0.6738.83±0.3938.96±0.3541.04±0.1141.14±0.11
PSNR-μ37.33±1.2137.01±1.6839.15±1.0439.08±1.0641.13±0.0741.25±0.05
HuPSNR-l5way-5shot41.36±0.2540.73±0.6646.37±0.7646.88±0.8147.13±0.1347.41±0.12
PSNR-μ38.95±0.1439.92±0.2243.42±0.4443.79±0.4843.98±0.2744.24±0.17
PSNR-l5way-1shot38.67±0.4337.82±0.8644.64±0.8044.75±0.8444.94±0.2345.04±0.16
PSNR-μ36.83±0.6238.49±1.0742.37±1.4242.41±1.2042.50±0.8742.55±0.44
", + "image_path": "93c514fa1aaec198d4949fd6421c375dec06cc5c97da8131ec381a6f79bb2d3c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 95, + 224, + 496, + 475 + ], + "blocks": [ + { + "bbox": [ + 46, + 202, + 547, + 224 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 547, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 547, + 224 + ], + "type": "text", + "content": "Table 2. Further evaluation results on Kalantari's [9], Hu's [7] and Prabhakar's datasets [21]. The best and the second best results are highlighted in Bold and Underline in each setting, respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 95, + 224, + 496, + 475 + ], + "lines": [ + { + "bbox": [ + 95, + 224, + 496, + 475 + ], + "spans": [ + { + "bbox": [ + 95, + 224, + 496, + 475 + ], + "type": "table", + "html": "
KalantariHu
PSNR-lPSNR-μSSIM-lSSIM-μHV2PSNR-lPSNR-μSSIM-lSSIM-μHV2
S1Sen38.5740.940.97110.978064.7133.5831.480.96340.953166.39
Hu30.8432.190.94080.963262.0536.9436.560.98770.982467.58
FSHDR40.9741.110.98640.982767.0842.1541.140.99040.989171.35
Ours (K=0)41.1241.200.98660.986867.1642.9941.300.99120.990372.18
S2Ours (K=1)41.1441.250.98660.986967.2045.0442.550.99380.992873.23
Ours (K=5)41.5441.610.98790.988067.3347.4144.240.99740.993674.49
S3Kalantari41.2241.850.98480.987266.2343.7641.600.99380.991472.94
DeepHDR40.9141.640.98630.985767.4241.2041.130.99410.987070.82
AHDRNet41.2341.870.98680.988967.5049.2245.760.99800.995675.04
ADNET41.3141.800.98710.988367.5750.3846.790.99870.994876.32
FSHDR41.7941.920.98760.985167.7049.5645.900.99840.994575.25
Ours41.6841.970.98890.989567.7750.3146.880.99880.995776.21
S4Kalantari25.8721.440.86100.917660.0010.2316.950.69030.834649.10
DeepHDR25.9221.430.85970.917060.0225.4820.860.92150.835466.83
AHDRNet26.6222.080.87370.923858.8911.4417.840.67320.838952.79
ADNET25.7621.390.86860.821760.3610.8618.090.69150.839949.28
FSHDR28.0322.010.87510.920360.5312.8219.370.74420.834755.34
Ours27.9122.450.87640.925261.0230.2921.560.94400.845667.07
S5Kalantari31.2433.100.95270.959363.9919.8218.630.76790.874259.50
DeepHDR30.7529.010.92440.922363.2619.8418.700.76980.875259.48
AHDRNet31.8433.490.95880.960664.4020.8020.510.82590.913659.79
ADNET31.0833.500.95360.963663.8820.7820.800.82680.917359.71
FSHDR32.7032.240.95530.946564.3720.2319.710.79290.902659.63
Ours32.7234.490.95860.971364.4520.6921.960.82570.920759.76
", + "image_path": "174bb6724a5a4405e964a56cc158290e3581d34b1b467d94874d7863189cae0a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 483, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 289, + 712 + ], + "type": "text", + "content": "ure 4 (a) and (b), we compare our method with other state-of-the-art methods in the 5-shot scenario. Due to insufficient labeled samples, large motion, and saturation, most comparing methods suffer from color distortion and ghosting artifacts in these two datasets. Kalantari's method and DeepHDR produce undesirable artifacts and color distortion (see Figure 4 (a)(b)). There are two reasons behind that: misalignment of optical flow and homographies and the lack of labeled data. Although AHDRNet and ADNET are proposed to suppress motion and saturation with attention mechanisms, they cannot reconstruct ghost-free HDR images with few labeled samples. They also produce severe ghosting artifacts (see the red block in Figure 4 (a)(b)). FSHDR exploits unlabeled data to alleviate ghosts under the constraint of a few labeled samples, but it is difficult to handle both ghosting and saturation problems simultaneously. We can see that FSHDR still suffers from ghosting artifacts which leaves an obvious hand artifact in the car (see the red block in Figure 4 (a)). Thanks to the pro" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 483, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 555 + ], + "type": "text", + "content": "posed SMAE and sample-quality-based iterative learning strategy, which first address the saturation problems using SMAE and then adaptively sample well-exposed and ghost-free pseudo-labels to handle ghosting problems, we can reconstruct ghost-free HDR images with only a few labeled samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "text", + "content": "The quantitative results under the constraint of few shot scenarios on two dataset are shown in Table 1. We report means and " + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "text", + "content": " margin of variations for 5 and 1 shot cases across 5 runs. Our method achieves state-of-the-art performance on all metrics of two datasets, while most other methods perform poorly with only a few labeled samples. We show that our proposed method surpasses second-best method by 0.15db and 0.21db in terms of PSNR- " + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "text", + "content": " and PSNR- " + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 556, + 545, + 700 + ], + "type": "text", + "content": " for 5way-5shot setting on Kalantari's dataset, and it also improves by 0.28db and 0.26db for 5way-5shot setting on Hu's dataset. For 5way-1shot setting, our method consistently outperforms other approaches on two datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "In addition, as shown in Table 2, we further compare our" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "5781" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 70, + 84, + 263, + 173 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 284, + 81 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 284, + 81 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 284, + 81 + ], + "type": "text", + "content": "Table 3. Ablation study of 5 shot scenario on Kalantari's dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 70, + 84, + 263, + 173 + ], + "lines": [ + { + "bbox": [ + 70, + 84, + 263, + 173 + ], + "spans": [ + { + "bbox": [ + 70, + 84, + 263, + 173 + ], + "type": "table", + "html": "
#ModelPSNR-lPSNR-μHDR-VDP-2
B1SSHDR41.5441.6167.33
B2Stage2Net41.3141.4367.21
B3w/o APSS41.4941.4567.29
B4AHDR*41.4841.5167.30
B5FSHDR*41.4141.4367.26
B6Vanilla-AHDR40.6141.0566.95
B7Vanilla-FSHHDR41.3941.4067.25
", + "image_path": "5319d5c86d79528b67b9ce3b8bc6de547793e9de617d5b45a2f89001038df582.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "text", + "content": "method with major HDR deghosting approaches in zero-shot setting " + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "inline_equation", + "content": "S_{1}" + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "text", + "content": ", few-shot setting " + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "inline_equation", + "content": "S_{2}" + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "text", + "content": ", and fully supervised setting " + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "inline_equation", + "content": "S_{3}" + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "text", + "content": ". Note that we use all the dynamic labeled samples without static and unlabeled samples for plain training in setting " + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "inline_equation", + "content": "S_{3}" + }, + { + "bbox": [ + 46, + 182, + 286, + 290 + ], + "type": "text", + "content": ". Our zero-shot approach outperforms other methods in zero-shot setting on two datasets. It also outperforms some 5-shot and fully supervised methods in most metrics. Finally, our few-shot and fully supervised approaches achieve state-of-the-art performance among two datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 290, + 286, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 286, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 286, + 517 + ], + "type": "text", + "content": "Evaluation Generalization Across Different Datasets. We compare our method against other approaches on Kalantari's, Hu's, Tursun's, and Prabhakar's datasets to verify generalization performance. We directly evaluate the methods with the checkpoint trained on Kalantari's dataset and show the qualitative results on Tursun's and Prabhakar's datasets in Figure 4 (c)(d). More results are included in the Appendix. In Figure 4 (c), since the lady's motion is large, all the comparison methods cannot remove the ghosting artifacts. In Figure 4 (d), the comparison methods have obvious color distortion and ghosting artifacts on the floor and in the ceiling. It shows that other methods have poor generalization performance across different datasets. All these methods address both the saturation and ghosting problems simultaneously. They cannot learn a robust representation to reconstruct a high-quality HDR image. Thanks to our SMAE and sample-quality-based iterative learning strategy, we can learn a robust representation to recover saturated regions and remove ghosting artifacts." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "text", + "content": "In Table 2, setting " + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "inline_equation", + "content": "S_{4}" + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "text", + "content": " denotes that we utilize the checkpoint trained on Kalantari's or Hu's dataset under 5 shot scenario to evaluate on Hu's or Kalantari's dataset reversely. Setting " + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "inline_equation", + "content": "S_{5}" + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "text", + "content": " represents that we train on Kalantari's or Hu's dataset under 5 shot scenario and evaluate on Prabhakar's dataset. Our method achieves better numerical performance in terms of PSNR- " + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "text", + "content": " and PSNR- " + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 518, + 286, + 613 + ], + "type": "text", + "content": ". It demonstrates that our method generalizes well across different datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 623, + 147, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 147, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 147, + 634 + ], + "type": "text", + "content": "4.2. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 286, + 713 + ], + "type": "text", + "content": "We conduct ablation studies on Kalantari's dataset under the condition of 5 shot scenario across 5 runs and analyze the importance of each component. We use the following variants of our whole SSHDR model: 1) SSHDR: The full model of SSHDR network trained with two entire stages. 2) Stage2Net: The model only trained in the second" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 319, + 70, + 533, + 191 + ], + "blocks": [ + { + "bbox": [ + 319, + 70, + 533, + 191 + ], + "lines": [ + { + "bbox": [ + 319, + 70, + 533, + 191 + ], + "spans": [ + { + "bbox": [ + 319, + 70, + 533, + 191 + ], + "type": "image", + "image_path": "7b867f3f671e1d0900228efd3f361124434e91241277c3050683e4cb2587e2b4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 192, + 509, + 203 + ], + "lines": [ + { + "bbox": [ + 340, + 192, + 509, + 203 + ], + "spans": [ + { + "bbox": [ + 340, + 192, + 509, + 203 + ], + "type": "text", + "content": "Figure 5. Visual results of poor pseudo-labels." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "type": "text", + "content": "stage without SMAE pre-training. 3) w/o APSS: The model trained with two stages without using sample-quality-based pseudo-labels selection strategy. 4) " + }, + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "type": "inline_equation", + "content": "\\text{AHDR}^*" + }, + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "type": "text", + "content": ": The AHDR model is trained with our proposed two stages strategy. 5) " + }, + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "type": "inline_equation", + "content": "\\text{FSHDR}^*" + }, + { + "bbox": [ + 304, + 215, + 545, + 311 + ], + "type": "text", + "content": ": Our model is trained with the FSHDR strategy. 6) Vanilla-AHDR: The vanilla AHDR model trained in 5 shot scenario. 7) Vanilla-FSHDR: The vanilla FSHDR model trained with 5 labeled samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 312, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 383 + ], + "type": "text", + "content": "SMAE Pre-training. As shown in Table 3, the performance of Stage2Net is significantly decreased compared with SSHDR. Since the SMAE learns a robust representation to generate content of saturated regions, it helps to improve the saturated regions. In a word, it demonstrates that the SMAE pre-training stage is an effective mechanism." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 383, + 545, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 466 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 466 + ], + "type": "text", + "content": "Pseudo-labels Selection Strategy. Since the sample-quality-based pseudo-labels selection strategy can exclude saturated and ghosted samples (see Figure 5), the model can be guided in a correct optimization direction which is effective for ghost removal. When we remove the pseudolabels selection strategy, the performance of the model without APSS is dropped." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 467, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 545, + 514 + ], + "type": "text", + "content": "Two Stages Strategy. In Table 3, we report the performance of " + }, + { + "bbox": [ + 304, + 467, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathrm{AHDR}^*" + }, + { + "bbox": [ + 304, + 467, + 545, + 514 + ], + "type": "text", + "content": ". It achieves a significant increment compared with the vanilla AHDR model, which demonstrates the effectiveness of the overall two stages strategy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 515, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 562 + ], + "type": "text", + "content": "Proposed Model Architecture. When we replace our two stages strategy with the FSHDR strategy, the numerical results increase compared with FSHDR. It shows that our proposed model architecture is also sound." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 579, + 378, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 579, + 378, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 579, + 378, + 590 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 712 + ], + "type": "text", + "content": "We propose a novel semi-supervised deghosting method for few-shot HDR problem via two stages of completing saturation and deghosting. In the first stage, a Saturated Mask AutoEncoder is proposed to learn a robust representation and reconstruct a non-saturated HDR image with a self-supervised mechanism. In the second stage, we propose an adaptive pseudo-label selection strategy to avoid the effects of mistrabeled samples. 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IEEE Transactions on Image Processing, 21(4):2318-2323, 2011. 1, 2" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5784" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SMOC-Net_ Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation/7ed77cdd-0ec8-4cc4-8097-ec9f36276521_content_list.json b/2023/SMOC-Net_ Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation/7ed77cdd-0ec8-4cc4-8097-ec9f36276521_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9b6fef8e35665394e4e5d6773b243826ea4d518f --- /dev/null +++ b/2023/SMOC-Net_ Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation/7ed77cdd-0ec8-4cc4-8097-ec9f36276521_content_list.json @@ -0,0 +1,1856 @@ +[ + { + "type": "text", + "text": "SMOC-Net: Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation", + "text_level": 1, + "bbox": [ + 99, + 128, + 870, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tao Tan $^{1,2}$ , Qialei Dong $^{1,2,3}$", + "bbox": [ + 374, + 202, + 594, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Artificial Intelligence, UCAS", + "bbox": [ + 323, + 220, + 645, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ State Key Laboratory of Multimodal Artificial Intelligence Systems, CASIA", + "bbox": [ + 181, + 238, + 787, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3Center for Excellence in Brain Science and Intelligence Technology, CAS", + "bbox": [ + 189, + 256, + 779, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tantao2022@ia.ac.cn, qldong@nlpr.ia.ac.cn, Corresponding author: Qiulei Dong", + "bbox": [ + 153, + 277, + 800, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, self-supervised 6D object pose estimation, where synthetic images with object poses (sometimes jointly with un-annotated real images) are used for training, has attracted much attention in computer vision. Some typical works in literature employ a time-consuming differentiable renderer for object pose prediction at the training stage, so that (i) their performances on real images are generally limited due to the gap between their rendered images and real images and (ii) their training process is computationally expensive. To address the two problems, we propose a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The proposed network is explored under a knowledge distillation framework, consisting of a teacher model and a student model. The teacher model contains a backbone estimation module for initial object pose estimation, and an object pose refiner for refining the initial object poses using a geometric constraint (called relative-pose constraint) derived from relative camera poses. The student model gains knowledge for object pose estimation from the teacher model by imposing the relative-pose constraint. Thanks to the relative-pose constraint, SMOC-Net could not only narrow the domain gap between synthetic and real data but also reduce the training cost. Experimental results on two public datasets demonstrate that SMOC-Net outperforms several state-of-the-art methods by a large margin while requiring much less training time than the differentiable-renderer-based methods.", + "bbox": [ + 75, + 358, + 472, + 796 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 828, + 209, + 844 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Monocular 6D object pose estimation is a challenging task in the computer vision field, which aims to estimate object poses from single images. According to whether real", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "images with ground-truth object poses are given for model training, the existing works for monocular object pose estimation in literature could be divided into two categories: fully-supervised methods [17, 35] which are trained by utilizing annotated real images with ground-truth object poses, and self-supervised methods [16, 34] which are trained by utilizing synthetic images with object poses (sometimes jointly with un-annotated real images). Since it is very time-consuming to obtain high-quality object poses as ground truth, self-supervised monocular object pose estimation has attracted increasing attention recently [16, 33, 39].", + "bbox": [ + 496, + 327, + 893, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some existing methods for self-supervised monocular object pose estimation [16, 31] use only synthetic images with object poses (which are generated via Blender [22] or some other rendering tools [24, 29]) for training. However, due to the domain gap between real and synthetic data, the performances of these self-supervised methods are significantly lower compared to the fully-supervised methods [22, 35]. Addressing this domain gap problem, a few recent self-supervised methods [33, 34, 39] jointly use synthetic images with object pose and un-annotated real images at their training stage, where a differentiable renderer [19] is introduced to provide a constraint on the difference between real and rendered images. Although these methods could alleviate the domain gap problem by utilizing the introduced differentiable renderer, they still have to be confronted with the following two problems: (i) There still exists a noticeable gap between real images and rendered images by the differentiable renderer, so that their performances on object pose estimation are still limited; (ii) Much time has to be spent on differentiable rendering during training, so that the training costs of these methods are quite heavy.", + "bbox": [ + 496, + 500, + 893, + 819 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address the above problems, this paper proposes a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The SMOC-Net is designed via the knowledge distillation technique, con", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21307", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sisting of a teacher model and a student model. Under the teacher model, a backbone pose estimation module is introduced to provide an initial estimation on the pose of the image object. Then, a geometric constraint (called relative-pose constraint) on object poses is mathematically derived from relative camera poses which are calculated by a typical structure from motion method (here, we straightforwardly use COLMAP [25, 26]), and a camera-posed-refiner is further explored to refine the initial object pose based on this constraint. The student model simply employs the same architecture as the backbone estimation module of the teacher model, and it learns knowledge from the teacher model by imposing the relative-pose constraint, so that it could estimate object poses as accurately and fast as possible. Once the proposed SMOC-Net has been trained, only its student model is used to predict the object pose from an arbitrary testing image.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In sum, the main contributions in this paper include:", + "bbox": [ + 96, + 348, + 442, + 362 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We design the relative-pose constraint on object poses under the knowledge distillation framework for self-supervised object pose estimation. And it could narrow the domain gap between synthetic and real data to some extent.", + "2. According to the designed relative-pose constraint, we explore the camera-pose-guided refiner, which is able to refine low-accuracy object poses effectively.", + "3. By jointly utilizing the camera-pose-guided refiner and the above object pose constraint, we propose the SMOC-Net for monocular 6D object pose estimation. Experimental results in Sec. 4 demonstrate that the proposed SMOC-Net does not only outperform several state-of-the-art methods when only synthetic images with object poses and un-annotated real images are used for training, but also perform better than three state-of-the-art fully-supervised methods on the public dataset LineMOD [8]." + ], + "bbox": [ + 75, + 363, + 467, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 617, + 218, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we review the existing fully-supervised and self-supervised methods for monocular 6D object pose estimation in literature, respectively.", + "bbox": [ + 76, + 642, + 468, + 688 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Fully-Supervised 6D Object Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 696, + 454, + 713 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fully-supervised object pose estimation methods use real RGB(D) images with object poses for training. Some early works directly regressed object pose with various Convolutional Neural Networks (CNNs) such as PoseCNN [37] and SSD-6D [13]. Xiang et al. [37] proposed the PoseCNN for 6D object pose estimation, which estimated the 3D translation by predicting the distance between object center in the image and the camera, and the 3D rotation was estimated by regressing a quaternion representation. Kehl et al. [13] proposed the SSD-6D, where rotation estimation was treated as a classification problem by discretizing the rotation space into classifiable viewpoint bins.", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For improving pose estimation accuracy further, many methods first established 2D-3D correspondences using CNNs, and then solved the object pose via Perspective-n-Point (PnP) algorithms. Keypoint-based methods [22, 28, 32] established correspondences by detecting keypoints in 2D images. Peng et al. [22] proposed a pixel level voting network (PVNet) by using the direction vector field to predict keypoints, which achieved good performance under severe truncation and occlusion. Song et al. [28] proposed the HybridPose by using hybrid representation such as keypoints, edge vectors, and symmetry correspondences. Some other methods predicted the corresponding 3D coordinates of each pixel in 2D images [17, 21, 40] or dense UV maps [41] to establish dense correspondences. Li et al. [17] proposed CDPN, which treated rotation and translation estimations as two different tasks. Rotation was calculated from dense correspondences, while translation was directly regressed from the target region. Hodan et al. [11] proposed EPOS, which represented the target object by compact surface fragments for better handling symmetries. To achieve end-to-end training, a Patch-PnP module consisting of CNNs and fully connected layers was proposed in [35]. Chen et al. [4] proposed an Epro-PnP module whose output was the probability density distribution of object pose and also achieved end-to-end training. Su et al. [30] proposed a discrete descriptor to represent the object surface densely, which was used to establish accurate and robust correspondences. Huang et al. [18] proposed to predict 3D object coordinates at 3D query points sampled in the camera frustum, which could efficiently handle occlusions. Shun et al. [12] utilized a deep texture rendering and differentiable Levenberg-Marquardt optimization to refine the object poses fast and accurately. Xu et al. [38] proposed a framework based on a recurrent neural network for object pose refinement, which was robust to erroneous initial poses and occlusions.", + "bbox": [ + 496, + 90, + 893, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Self-Supervised 6D Object Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 647, + 864, + 664 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To avoid the data annotation problem in fully-supervised object pose estimation, many self-supervised methods for object pose estimation have been proposed. Some self-supervised methods [16, 23, 31] only used synthetic images with object poses as training data. Sundermeyer et al. [31] proposed the AAE method by utilizing an auto-encoder, where only synthetic data was used for training. It employed a series of domain adaption techniques to reduce the domain gap between real and synthetic images. Rambach et al. [23] proposed to estimate object pose from synthetic single channel images, showing that proper representation could also reduce the domain gap. Li et al. [16] proposed SD-Pose, which preprocessed input images by multi-level semantic representations and achieved better performance.", + "bbox": [ + 496, + 672, + 890, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further narrow the domain gap, a few recent self", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21308", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3b8bbcc8ec36c1c94bf4b05ea54840015c6373f77c83a1c4f6c51f0d9b398e89.jpg", + "image_caption": [ + "Figure 1. Architecture of the proposed SMOC-Net. It consists of a teacher model and a student model. The teacher model consists of a backbone pose estimation module and a camera-pose-guided (C-P-G) refiner. The student model simply employs the same architecture as the backbone estimation module of the teacher model. For a set of multi-view real images $\\{I_1^{src},\\dots,I_n^{src}\\}$ , their corresponding camera poses $\\{P_{c1},\\dots,P_{cn}\\}$ are calculated by an SfM method (a). Then, a 2D object detector (Yolov4 [1]) is used to extract object regions from the input images, and a set of object patch pairs are obtained for self-supervised training. The predicted object poses $\\{P_{oi},P_{oj}\\}$ are self-supervised with camera poses $\\{P_{ci},P_{cj}\\}$ (b) and pseudo pose labels $\\{P_{oi}^*,P_{oj}^*\\}$ (c) that have been refined by the camera-pose-guided refiner (d)." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 874, + 372 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "supervised methods [33, 34, 39] jointly used synthetic images with object poses and un-annotated real images at their training stage. In [34], the network was first trained on synthetic data in a fully-supervised manner and then self-supervised with un-annotated real data by seeking a visually and geometrically optimal alignment between real images and rendered images by a differentiable renderer. But depth images were required during self-supervised training. Sock et al. [27] proposed a two-stage self-supervised method, which also used a differentiable renderer to establish pose consistency between rendered and real images. Beyond using image-level consistency for self-supervised pose estimation, Yang et al. [39] proposed a self-supervised network DSC-PoseNet based on dual-scale keypoint consistency. But it suffered dramatic performance degradation when there was occlusion. Wang et al. [33] revised [34] and proposed Self6D++, which used the pose estimation network GDR-Net [35] and noisy student training to improve accuracy and robustness. However, there still exists a gap between real images and rendered images by the differentiable renderer. And additionally, differentiable rendering is a computationally expensive process. Addressing these issues, this paper proposes a novel self-supervised object pose estimation by imposing a derived geometric constraint from camera poses, which would be described in detail in the following section.", + "bbox": [ + 75, + 506, + 472, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 503, + 635, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we propose the SMOC-Net for self-supervised monocular object pose estimation. Firstly, the architecture of the proposed SMOC-Net is introduced. Then, we present the derived geometric constraint from camera poses and the camera-pose-guided refiner respectively. Finally, the total loss function is described.", + "bbox": [ + 496, + 530, + 890, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Architecture", + "text_level": 1, + "bbox": [ + 498, + 633, + 635, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The SMOC-Net is explored under a knowledge distillation framework, which contains a teacher model and a student model, and its architecture is shown in Fig. 1. As seen from this figure, an object detector is firstly used for extracting the object regions in the input images, and we simply use Yolo-v4 [1] here as the object detector as done in some existing object pose estimation works [33, 35]. The teacher model consists of a backbone estimation module and a camera-pose-guided refiner. The backbone estimation module is used to calculate an initial object pose estimation, and we simply use the existing method GDR-Net [35] as the backbone estimation module here. The camera-pose-guided refiner is explored to refine the initial object pose obtained from the backbone estimation module, by utilizing a derived geometric constraint from relative camera poses (called relative-pose constraint). The student model", + "bbox": [ + 496, + 657, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21309", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bc1f2c704dca4d77b24dd7aa836eb1f72cdb9bad3c5ad6bfad6ac3daec4b018e.jpg", + "image_caption": [ + "Figure 2. World, object and camera coordinate systems. For a 3D point $P$ , its coordinates could be transformed from object/world coordinate systems to camera coordinate systems by corresponding absolute object/camera poses in the camera/world systems." + ], + "image_footnote": [], + "bbox": [ + 122, + 88, + 421, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "employs the same architecture as the backbone estimation module, and it gains knowledge from the teacher model by utilizing the same relative-pose constraint.", + "bbox": [ + 75, + 398, + 467, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the training stage, the proposed SMOC-Net is trained by utilizing both synthetic data [10] with labels and a set of un-annotated real multi-view images. Firstly, the backbone GDR-Net and the detector Yolo-v4 are trained singly by only utilizing the synthetic RGB data as done in [33, 34]. Then, the classic SfM (Structure from Motion) method COLMAP [5, 25, 26] is utilized to calculate the corresponding absolute camera poses from the training set of multiview real images, and the object detector is implemented for extracting object patches from the input real images. According to the calculated camera poses as well as the corresponding original real object patches, we could straightforwardly obtain a set of object patch pairs with pseudo relative camera poses (which could be calculated according to the obtained absolute camera poses). Next, unlike the existing works [33, 34, 39] that deal with each training image singly, the proposed method deals with pairs of training patches. Finally, the student model is trained with the set of augmented object patch pairs with pseudo relative poses for learning knowledge from the teacher model.", + "bbox": [ + 75, + 444, + 467, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At the testing stage, only the student module is used for predicting object pose from each monocular RGB image. In Sections 3.2 and 3.3, both the relative-pose constraint and the camera-pose-guided refiner would be introduced, respectively, in detail.", + "bbox": [ + 75, + 746, + 467, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Relative-Pose Constraint", + "text_level": 1, + "bbox": [ + 76, + 832, + 303, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a set of $N$ object patch pairs with the corresponding absolute camera poses in the world coordinate system, we could obtain a geometric constraint on the object relative", + "bbox": [ + 76, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "pose (called relative-posed constraint) for each patch pair as follows:", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For an arbitrary pair of object patches, without loss of generality, let $i$ and $j$ ( $i < j$ ; $i = 1, \\dots, N - 1$ ; $j = i + 1, \\dots, N$ ) denote the indices of the two patches. Then as shown in Fig. 2, for an arbitrary 3D object point, let $X_{ci}$ and $X_{cj}$ denote its coordinates in the two camera coordinate systems corresponding to the two input patches, and let $X_o$ and $X_w$ denote its coordinates in the object and world coordinate systems respectively.", + "bbox": [ + 498, + 121, + 890, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $[R_{oi}, t_{oi}]$ and $[R_{oj}, t_{oj}]$ represent the absolute object poses in the two camera systems. Then, we have", + "bbox": [ + 498, + 242, + 890, + 271 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {c i} = R _ {o i} X _ {o} + t _ {o i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 282, + 890, + 297 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {c j} = R _ {o j} X _ {o} + t _ {o j}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 301, + 890, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $[R_{ci}, t_{ci}]$ and $[R_{cj}, t_{cj}]$ represent the absolute camera poses in the world system, which are calculated by the SfM method COLMAP [5, 25]. It has to be pointed out that the calculated translations by COLMAP are not equal to the ground-truth translation, but up to a scale. Hence, we have", + "bbox": [ + 498, + 325, + 890, + 401 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {c i} = R _ {c i} X _ {w} + \\lambda t _ {c i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 411, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {c j} = R _ {c j} X _ {w} + \\lambda t _ {c j}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 430, + 890, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a scale factor. According to Eqn. (1) and Eqn. (3), we have", + "bbox": [ + 498, + 455, + 888, + 483 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {w} = R _ {c i} ^ {- 1} R _ {o i} X _ {o} + R _ {c i} ^ {- 1} \\left(t _ {o i} - \\lambda t _ {c i}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 493, + 890, + 511 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to Eqn. (2) and Eqn. (4), we have", + "bbox": [ + 500, + 520, + 795, + 535 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {w} = R _ {c j} ^ {- 1} R _ {o j} X _ {o} + R _ {c j} ^ {- 1} \\left(t _ {o j} - \\lambda t _ {c j}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 542, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to Eqn. (5) and Eqn. (6), we have", + "bbox": [ + 500, + 570, + 795, + 585 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {c i} ^ {- 1} R _ {o i} = R _ {c j} ^ {- 1} R _ {o j}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 593, + 890, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {c i} ^ {- 1} \\left(t _ {o i} - \\lambda t _ {c i}\\right) = R _ {c j} ^ {- 1} \\left(t _ {o j} - \\lambda t _ {c j}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 614, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Eqn. (7) could be rewritten as", + "bbox": [ + 500, + 642, + 699, + 656 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {o i} R _ {o j} ^ {- 1} = R _ {c i} R _ {c j} ^ {- 1}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 664, + 890, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Eqn. (8) could be rewritten as", + "bbox": [ + 500, + 691, + 699, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} = \\lambda \\left(R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 714, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To remove the scale factor $\\lambda$ , both sides of the Eqn. (10) are normalized as", + "bbox": [ + 498, + 741, + 890, + 770 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{| | R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} | | _ {2}} = \\frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{| | R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} | | _ {2}}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 776, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $||\\cdot ||_2$ is the $L_{2}$ norm. It is noted that once the camera poses $[R_{ci},t_{ci}]$ and $[R_{cj},t_{cj}]$ are known, Eqn. (9) and Eqn. (11) provide constraints on relative object rotation and translation respectively. Hence, they are used together as our relative-pose constraint.", + "bbox": [ + 498, + 824, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21310", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e3d85c0fb176e36c34ad2409e15e2ebe53cc6248cf8e757f6ceb5d6d35e625a0.jpg", + "image_caption": [ + "Figure 3. Architecture of the explored camera-pose-guided refiner. For a pair of 6D object poses $\\{P_{init - oi}^{*}, P_{init - oj}^{*}\\}$ , they are first refined by DeepIM [15]. The refined poses $\\{\\widetilde{P}_{oi}, \\widetilde{P}_{oj}\\}$ are then further updated using rotation increments and translation increments calculated according to the relative-pose constraint." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 472, + 231 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Camera-Pose-Guided Refiner", + "text_level": 1, + "bbox": [ + 76, + 335, + 341, + 351 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we propose an iterative object pose refiner (called camera-pose-guided refiner), and its architecture is shown in Fig. 3. Given a set of $N$ object patch pairs with the corresponding absolute camera poses in the world coordinate system, and their corresponding initial object poses are estimated by the teacher backbone estimation module. We could further refine the initial poses of each patch pair by utilizing the above relative-pose constraint as follows:", + "bbox": [ + 75, + 359, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At each iteration, the object poses are firstly refined by DeepIM [15], which is pre-trained on synthetic RGB data. Let $\\widetilde{P}_{oi} = [\\widetilde{R}_{oi},\\widetilde{t}_{oi}]$ and $\\widetilde{P}_{oj} = [\\widetilde{R}_{oj},\\widetilde{t}_{oj}]$ represent the refined absolute object poses of two input patches. Then, we further refine the absolute object rotations and translations of the two patches with the corresponding absolute camera poses, respectively.", + "bbox": [ + 75, + 481, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Rotation Refinement Let $R_{ij} = R_{ci}R_{cj}^{-1}$ denotes the relative camera rotation of two camera systems. In the rotation refinement, we seek to apply slight increments to the object rotations $\\{\\widetilde{R}_{oi},\\widetilde{R}_{oj}\\}$ . At each iteration, let $\\{\\Delta R_{oi},\\Delta R_{oj}\\}$ represent the referred slight increments. Then, the object rotations would be updated as $\\{\\widetilde{R}_{oi}\\Delta R_{oi},\\widetilde{R}_{oj}\\Delta R_{oj}\\}$ . According to the relative rotation constraint in Eqn. (9), we have the following constraint equation:", + "bbox": [ + 75, + 585, + 468, + 708 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta R _ {o i} ^ {- 1} \\Delta R _ {i j} \\Delta R _ {o j} = E, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 717, + 468, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Delta R_{ij} = \\widetilde{R}_{oi}^{-1}R_{ij}\\widetilde{R}_{oj}$ . This is an under-constrained equation whose solution is not unique, hence, an auxiliary condition $\\Delta R_{oi}^{-1} = \\Delta R_{oj}$ is introduced for guaranteeing a unique solution, considering that both the increments $\\Delta R_{oi}$ and $\\Delta R_{oj}$ at each iteration change slightly. Then, considering that Eqn. (12) is a nonlinear equation which is hard to solve, we compute the approximate solution by solving the following minimization problem:", + "bbox": [ + 75, + 744, + 470, + 868 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Delta R _ {o i}, \\Delta R _ {o j}} | | \\omega (\\Delta R _ {o i} ^ {- 1} \\Delta R _ {i j} \\Delta R _ {o j}) | | _ {2} ^ {2}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 877, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\omega(R)$ is the axis-angle representation of 3D rotation $R$ . Let $\\{\\Delta \\omega_{oi}, \\Delta \\omega_{oj}\\}$ denote the axis-angle representation of $\\{\\Delta R_{oi}, \\Delta R_{oj}\\}$ , and $\\Delta \\omega_{ij}$ denote the axis-angle representation of $\\Delta R_{ij}$ . The concatenation of $\\Delta \\omega_{oi}$ and $\\Delta \\omega_{oj}$ into a $6 \\times 1$ vector is denoted as $\\Delta \\Omega$ . Therefore, our problem is to solve the following minimization problem:", + "bbox": [ + 498, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Delta \\Omega} \\| r _ {i j} (\\Delta \\Omega) \\| _ {2} ^ {2}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 191, + 890, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 226, + 545, + 238 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nr _ {i j} (\\Delta \\Omega) = \\omega (R (- \\Delta \\omega_ {o i}) R (\\Delta \\omega_ {i j}) R (\\Delta \\omega_ {o j})). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 252, + 890, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by Avishek et al. [3], the above minimization problem is transformed to solve the following problem using quasi-Newton method:", + "bbox": [ + 498, + 280, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\Delta \\Omega} \\| r _ {i j} (\\mathbf {0}) + \\mathcal {J} r _ {i j} (\\mathbf {0}) ^ {T} \\Delta \\Omega \\| _ {2} ^ {2}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 335, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is equivalent to solve a linear system of equations:", + "bbox": [ + 500, + 369, + 846, + 385 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nJ r _ {i j} (\\mathbf {0}) ^ {T} \\Delta \\Omega = - r _ {i j} (\\mathbf {0}), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 395, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $Jr_{ij}(\\mathbf{0})$ is the Jacobian of $r_{ij}(\\Delta \\Omega)$ at the current point $\\Delta \\Omega = \\mathbf{0}$ , and", + "bbox": [ + 498, + 424, + 890, + 454 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} {J r _ {i j} (\\mathbf {0}) ^ {T}} \\approx {\\frac {| | \\Delta \\omega_ {i j} | | _ {2}}{2} \\cot (\\frac {| | \\Delta \\omega_ {i j} | | _ {2}}{2}) [ I - I ]} \\\\ \\approx [ I - I ]. \\tag {18} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 464, + 890, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the final approximate solution is", + "bbox": [ + 500, + 523, + 787, + 537 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\omega_ {o i} = - \\Delta \\omega_ {o j} = - \\frac {\\Delta \\omega_ {i j}}{2}, \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 549, + 890, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta R _ {o i} = \\Delta R _ {o j} ^ {- 1} = R \\left(- \\frac {\\Delta \\omega_ {i j}}{2}\\right). \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 580, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Translation Refinement In the translation refinement, we seek to apply slight increments to object translations $\\{\\widetilde{t}_{oi},\\widetilde{t}_{oj}\\}$ . At each iteration, let $\\{\\Delta t_{oi},\\Delta t_{oj}\\}$ represent the referred slight increments. Then, the object translations would be updated as $\\{\\widetilde{t}_{oi} + \\Delta t_{oi},\\widetilde{t}_{oj} + \\Delta t_{oj}\\}$ . According to the relative translation constraint in Eqn. (11), we have the following constraint equation:", + "bbox": [ + 500, + 619, + 890, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {R _ {c i} ^ {- 1} \\left(\\widetilde {t} _ {o i} + \\Delta t _ {o i}\\right) - R _ {c j} ^ {- 1} \\left(\\widetilde {t} _ {o j} + \\Delta t _ {o j}\\right)}{\\left| \\left| R _ {c i} ^ {- 1} \\left(\\widetilde {t} _ {o i} + \\Delta t _ {o i}\\right) - R _ {c j} ^ {- 1} \\left(\\widetilde {t} _ {o j} + \\Delta t _ {o j}\\right) \\right| \\right| _ {2}} - \\frac {t _ {i j}}{\\left| \\left| t _ {i j} \\right| \\right| _ {2}} = \\mathbf {0}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 734, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 787, + 544, + 800 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i j} = R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}. \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 800, + 890, + 820 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is approximate to solve the following linear system of equations:", + "bbox": [ + 498, + 825, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {R _ {c i} ^ {- 1} \\Delta t _ {o i} - R _ {c j} ^ {- 1} \\Delta t _ {o j}}{\\left| \\left| t _ {i j} ^ {*} \\right| \\right| _ {2}} + \\frac {t _ {i j} ^ {*}}{\\left| \\left| t _ {i j} ^ {*} \\right| \\right| _ {2}} - \\frac {t _ {i j}}{\\left| \\left| t _ {i j} \\right| \\right| _ {2}} = \\mathbf {0}, \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 864, + 890, + 904 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21311", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 92, + 124, + 104 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt _ {i j} ^ {*} = R _ {c i} ^ {- 1} \\widetilde {t} _ {o i} - R _ {c j} ^ {- 1} \\widetilde {t} _ {o j}. \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 116, + 468, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This is also an under-constrained equation, hence, an auxiliary condition $\\Delta t_{oi} = -\\Delta t_{oj}$ is introduced, considering that both the increments $\\Delta t_{oi}$ and $\\Delta t_{oj}$ at each iteration change slightly. So the final approximate solution is", + "bbox": [ + 76, + 147, + 468, + 208 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta t _ {o i} = - \\Delta t _ {o j} = \\left(R _ {c i} ^ {- 1} + R _ {c j} ^ {- 1}\\right) ^ {- 1} \\left(\\frac {\\left\\| t _ {i j} ^ {*} \\right\\| _ {2}}{\\left\\| t _ {i j} \\right\\| _ {2}} t _ {i j} - t _ {i j} ^ {*}\\right). \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 218, + 468, + 253 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, the absolute object poses are further updated by utilizing both rotation increments and translation increments. Let $P_{oi}^{*}$ and $P_{oj}^{*}$ represent the updated object poses. Then, we have", + "bbox": [ + 76, + 263, + 468, + 323 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nP _ {o i} ^ {*} = \\left[ \\widetilde {R} _ {o i} \\Delta R _ {o i}, \\widetilde {t} _ {o i} + \\Delta t _ {o i} \\right], \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 333, + 468, + 353 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nP _ {o j} ^ {*} = \\left[ \\widetilde {R} _ {o j} \\Delta R _ {o j}, \\widetilde {t} _ {o j} + \\Delta t _ {o j} \\right]. \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 354, + 468, + 376 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Loss Function", + "text_level": 1, + "bbox": [ + 76, + 386, + 220, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The total loss function $\\mathcal{L}_{\\text{self}}$ of the proposed SMOC-Net contains three loss terms: a rotation loss $\\mathcal{L}_{\\text{rot}}$ , a translation loss $\\mathcal{L}_{\\text{trans}}$ and a point matching loss $\\mathcal{L}_{\\text{pm}}^{\\text{pair}}$ .", + "bbox": [ + 76, + 409, + 468, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "According to the relative rotation constraint, the rotation loss is defined as", + "bbox": [ + 76, + 455, + 468, + 483 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r o t} = \\left| \\left| \\omega \\left(R _ {o j} R _ {o i} ^ {- 1} R _ {i j}\\right) \\right| \\right| _ {2}, \\tag {28}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 496, + 468, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $R_{ij} = R_{ci}R_{cj}^{-1}$", + "bbox": [ + 76, + 525, + 230, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "According to the relative translation constraint, the translation loss is defined by measuring the angle of two relative translation vectors as", + "bbox": [ + 76, + 542, + 468, + 585 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t r a n s}} = \\mathrm {a c o s} \\left(t _ {c, i j} \\cdot t _ {o, i j}\\right), \\tag {29}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 599, + 468, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathrm{acos}(\\cdot)$ is the arccos function and", + "bbox": [ + 76, + 627, + 344, + 642 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt _ {c, i j} = \\frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{\\left| \\left| R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} \\right| \\right| _ {2}}, \\tag {30}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 652, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt _ {o, i j} = \\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{\\left| \\left| R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} \\right| \\right| _ {2}}. \\tag {31}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 695, + 468, + 734 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inspired by [15, 33, 35], the point matching loss for geometrically aligning the predicted poses and the pseudo pose labels is used:", + "bbox": [ + 76, + 744, + 468, + 789 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p m} = \\min _ {R _ {o} \\in s y m X \\in \\mathcal {M}} \\operatorname {a v g} \\left| \\left| \\left(R _ {o} ^ {*} X + t _ {o} ^ {*}\\right) - \\left(R _ {o} X + t _ {o}\\right) \\right| \\right| _ {1}, \\tag {32}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 801, + 468, + 828 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $||\\cdot ||_1$ is the $L_{1}$ norm, $\\text{sym}$ is a pool of symmetric rotations including the given rotation to deal with symmetric objects following [21], $\\mathcal{M}$ represents the CAD object point cloud given in the evaluation datasets, $R_o$ , $(t_{ox}, t_{oy})$ and $t_{oz}$", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "are disentangled from $P_{o} = [R_{o}, t_{o}]$ , and $P_{o}^{*} = [R_{o}^{*}, t_{o}^{*}]$ denotes the pseudo pose label. Since the proposed method deals with pairs of training patches, the sum of two point matching losses is eventually used:", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p m} ^ {\\text {p a i r}} = \\mathcal {L} _ {p m, i} + \\mathcal {L} _ {p m, j}. \\tag {33}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 159, + 890, + 179 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accordingly, the total loss function $\\mathcal{L}_{self}$ is the weighted sum of the above three loss terms as", + "bbox": [ + 498, + 185, + 890, + 214 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s e l f} = \\mathcal {L} _ {r o t} + \\lambda_ {1} \\mathcal {L} _ {t r a n s} + \\lambda_ {2} \\mathcal {L} _ {p m} ^ {\\text {p a i r}}, \\tag {34}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 223, + 890, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are two weight parameters.", + "bbox": [ + 500, + 250, + 794, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 276, + 630, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 301, + 601, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Synthetic PBR Dataset [10] As the physically-based renderer has been proven to perform better than OpenGL renderers [13, 34], we use the synthetic PBR data from [10] to train the 2D object detector Yolov4 [1] and the backbone pose estimation module GDR-Net [35].", + "bbox": [ + 498, + 324, + 890, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LineMOD [8] is a standard benchmark for 6D object pose estimation, consisting of 13 sequences. And there are about $1.2\\mathrm{k}$ images in each sequence. As done in [13], we use $15\\%$ of images for training and the remaining for testing.", + "bbox": [ + 498, + 398, + 890, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Occluded-LineMOD [2] is generated from benchvise sequence of the LineMOD dataset, and it contains 1214 images. As done in [33], we sample data for testing using the BOP split [9] and use the remaining data for training.", + "bbox": [ + 498, + 460, + 890, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Metrics", + "text_level": 1, + "bbox": [ + 500, + 529, + 594, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the performance using the common Average Distance of Distinguishable Model Points (ADD) metric [8], which measures the distance between 3D object model point clouds transformed by the predicted pose and the corresponding ground-truth. A pose is considered correct when the distance is less than $10\\%$ of the diameter of a 3D model. ADD-S is used [37] for symmetric objects by computing the closest point distance.", + "bbox": [ + 498, + 551, + 890, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 681, + 715, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method is implemented by Pytorch, and all experiments are conducted on an NVIDIA 3080 GPU. The camera poses are calculated using a classic SfM method COLMAP [25,26,36] before training. We replace ResNet-34 [7] backbone of GDR-Net [35] with ResNeSt-50 [6] backbone as done in [33]. The learning rate is set to $10^{-4}$ . The strategy of pre-training with synthetic data is the same as [33]. During the self-supervised training, we train the student pose estimation network for 30 epochs using un-annotated real RGB data, and the batch size is set to 8. In each epoch, all $N$ training images are randomly divided into $N/2$ image pairs. During inference, only the student pose estimation network is used.", + "bbox": [ + 498, + 704, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21312", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/90254fec289e65cff1a2bde61d08f0a1e0fa35e375cae8685caf4cca9abf9725.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Training MannerMethodsTraining dataApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
Fully-supervisionDPOD [41]R53.395.290.094.160.497.466.099.693.864.999.888.171.482.6
PVNet [22]43.699.986.995.579.396.452.699.295.781.998.999.392.486.3
CDPN [17]64.497.891.795.583.896.266.899.799.685.897.997.990.889.9
Self-supervisionAAE [31]S4.222.932.937.018.724.85.981.046.218.235.161.236.332.6
MHP [20]11.966.222.459.826.944.68.355.754.615.560.8-34.438.8
DPOD [41]35.159.415.548.828.159.325.651.234.617.784.745.020.940.5
Self6D [34]S+R−+D38.975.236.965.657.967.019.699.094.116.277.968.250.158.9
Self6D++ [33]75.494.997.099.586.698.968.399.096.141.999.498.994.388.5
DSC-PoseNet [39]S+R−35.983.151.561.045.068.027.689.252.526.456.368.746.454.7
Self6D++ [33]76.091.697.199.885.698.856.591.092.235.499.597.491.885.6
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
", + "bbox": [ + 120, + 88, + 849, + 255 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5f7dc2ee73fcea268272d97af0302d8a99b34943235b018c6f97c71213b9a848.jpg", + "table_caption": [ + "Table 1. Comparison with state-of-the-art methods on LineMOD dataset. The table reports results for the Average Recall (%) of ADD(-S). All results except ours and DSC-PoseNet are copied from [33]. The best RGB based label-free method is marked in bold. R: annotated real RGB data. S: synthetic RGB data. $\\mathbb{R}^{-}$ : unannotated real RGB data. D: depth data." + ], + "table_footnote": [], + "table_body": "
MethodsTraining dataApeCanCatDrilDuckEb.GlueHolepMean
DPOD [41]S2.34.01.210.57.24.412.97.56.3
CDPN [17]20.015.116.45.022.236.127.924.020.8
CosyPose [14]44.069.942.167.547.824.460.017.546.7
Self6D [34]S+R-+D13.743.218.732.514.457.854.322.032.1
Self6D++ [33]59.496.560.892.030.651.188.638.364.7
DSC-PoseNet [39]S+R-13.915.119.440.56.938.924.016.321.9
Self6D++ [33]57.795.052.690.526.745.087.123.559.8
OURS60.094.559.193.037.248.389.325.063.3
", + "bbox": [ + 176, + 321, + 794, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison with state-of-the-art methods on Occluded-LineMOD dataset.", + "bbox": [ + 235, + 470, + 730, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparative Evaluation", + "text_level": 1, + "bbox": [ + 76, + 510, + 302, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons on LineMOD. Here, we evaluate the proposed SMOC-Net on the LineMOD dataset in comparison to some state-of-the-art methods, including three fully-supervised methods (DPOD [41], PVNet [22], CDPN [17]), three self-supervised methods that are trained with only synthetic data (AAE [31], MHP [20], DPOD [41]), one self-supervised method that is trained with both synthetic data and un-annotated real images (DSC-PoseNet [39]), and two self-supervised methods that are trained with synthetic data + un-annotated real images + depth images (Self6D [34], Self6D++ [33]). In addition, for a more comprehensive comparison, we also compare our method with Self6D++ [33] trained with synthetic data and un-annotated real images but without depth images. The corresponding results are reported in Table 1.", + "bbox": [ + 75, + 536, + 468, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As seen from Table 1, the fully-supervised methods DPOD, PVNet, CDPN perform better than most of the existing self-supervised methods in most cases, mainly because annotated real images with object poses are used for training these fully-supervised methods. Moreover, the proposed SMOC-Net achieves a better performance than all the comparative methods (regardless of whether these methods are trained in an either fully-supervised or self-supervised manner), because of the derived relative-pose", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "constraint and the designed camera-posed-refiner in SMOC-Net. These results demonstrate the effectiveness of the proposed method for 6D object pose estimation.", + "bbox": [ + 498, + 511, + 890, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons on Occluded-LineMOD. We evaluate the proposed SMOC-Net on the Occluded-LineMOD dataset where there exist many occlusions, in comparison to DPOD [41], CDPN [17], CosyPose [14], Self6D [34], Self6D++ [33], and DSC-PoseNet [39]. The corresponding results are reported in Table 2. As seen from this table, the overall average recalls of most of the comparative methods are lower than $60\\%$ or even lower. Among all the comparative methods, Self6D++ trained with 3 categories of data (synthetic, unannotated real images, and depth images) performs the best, mainly because it uses additional scene depth images at the training stage, which contain 3D spatial information and are more effective in capturing the 3D spatial relationship between adjacent objects. Moreover, the proposed SMOC-Net achieves a slightly lower performance than Self6D++ that is trained with 3 categories of data (synthetic, unannotated real images, and depth images). However, the SMOC-Net significantly outperforms Self6D++ that is trained without depth images in the same manner as SMOC-Net, and it also performs significantly better than the other comparative methods. These results demonstrate that the proposed method could effectively handle the oc", + "bbox": [ + 496, + 568, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21313", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1d82a17e163d1960ca40aa62c4d57cefeabceb65a08af99f9b4e160e7398ad3c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
w/o Lrot82.195.097.099.894.1100.072.698.599.340.399.996.295.290.0
w/o Ltrans84.392.995.999.893.999.777.098.798.747.5100.098.194.390.8
w/o refiner*88.396.096.699.792.8100.070.498.099.042.2100.097.394.390.4
OURS-50.799.489.597.280.098.726.381.191.241.998.898.964.477.5
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
", + "bbox": [ + 117, + 88, + 854, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7fb34a57e5ba78503a708c4d7add4fd62ecabada6abca38f529e78f48c1d8da7.jpg", + "image_caption": [ + "Figure 4. Visualized results on Occluded-LineMOD dataset. Top: results of DSC-PoseNet. Middle: results of Self6D++. Bottom: results of SMOC-Net. Red: the ground-truth object poses. Green: the results after self-supervised training." + ], + "image_footnote": [], + "bbox": [ + 127, + 239, + 419, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "clusion case. Fig. 4 illustrates the visualized results of Self6D++, DSC-PoseNet and SMOC-Net, which are all trained with synthetic data and un-annotated real images.", + "bbox": [ + 75, + 508, + 468, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 579, + 230, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the effects of the losses $\\mathcal{L}_{rot},\\mathcal{L}_{trans}$ and the camera-pose-guided refiner, we conduct the ablation study on LineMOD and the results are reported in Table 3.", + "bbox": [ + 75, + 607, + 468, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Firstly, we respectively disable the rotation loss $\\mathcal{L}_{rot}$ and the translation loss $\\mathcal{L}_{trans}$ . The corresponding models are denoted as w/o $\\mathcal{L}_{rot}$ and w/o $\\mathcal{L}_{trans}$ respectively. As shown in Table 3, the pose accuracy decreases when disabling each of them. These results demonstrate that both of the rotation loss and the translation loss are effective to improve the pose accuracy for our method. Then, we replace the proposed camera-pose-guided refiner with DeepIM [15], and the corresponding model is denoted as w/o refiner*. The performance of w/o refiner* is significantly lower than the complete SMOC-Net. In addition, we also train our model with only synthetic data, which is denoted as OUR-. The overall average recall of OUR $^{-}$ is much lower than the complete SMOC-Net, demonstrating that the proposed self-supervised object pose estimation method could significantly improve the pose accuracy.", + "bbox": [ + 75, + 657, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4d9da7f496f26b3e09c4fda9819280497fcd97d11cabdeaa8476d9840460b876.jpg", + "table_caption": [ + "Table 3. Ablation study on LineMOD dataset. Individual loss and pose refiner are evaluated on LineMOD. * : the proposed camera-posedguided refiner is replaced with DeepIM [15]. Ours: our results trained on synthetic data. The best results are marked in bold." + ], + "table_footnote": [], + "table_body": "
MethodTraining/Rendering Time (s)Total Time (s)
Self6D++ [33]37/291110
OURS8/-283
", + "bbox": [ + 514, + 239, + 879, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparison of the training times in one epoch and the total times on LineMOD.", + "bbox": [ + 498, + 303, + 890, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Comparison of Training Time", + "text_level": 1, + "bbox": [ + 500, + 354, + 766, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here, we compare our training time on the LineMOD dataset with Self6D++ [33], a state-of-the-art differentiable-renderer-based method.", + "bbox": [ + 498, + 378, + 890, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Both the training times in one epoch and the total times by the two methods are reported in Table 4. As seen in Table 4, the training time of Self6D++ in one epoch is 37 seconds, but Self6D++ spends 29 seconds on rendering, indicating that rendering is a main time-consuming part for such a differentiable-renderer-based method. Moreover, the training time of our method in one epoch is much less than Self6D++, and the total training time (for both SfM and network training) of our method is also much less than Self6D++. These results demonstrate the priority of the proposed method in model training.", + "bbox": [ + 496, + 422, + 892, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 603, + 617, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed the SMOC-Net for self-supervised monocular object pose estimation by utilizing the predicted camera poses from un-annotated real images. Unlike most of the existing self-supervised methods that rely on differentiable renderer for providing additional constraint on object pose prediction, the SMOC-Net utilizes the derived relative-pose constraint for boosting the performance on object pose estimation. We also propose a pose refiner for further refining the initial object pose with the derived relative-pose constraint. The experimental results on two public datasets demonstrate the effectiveness of the proposed method even when dealing with strong occlusions. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant Nos. U1805264 and 61991423), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB32050100), the Beijing Municipal Science and Technology Project (Grant No. Z211100011021004).", + "bbox": [ + 496, + 628, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21314", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. YOLOv4: Optimal Speed and Accuracy of Object Detection. arXiv preprint arXiv:2004.10934, 2020. 3, 6", + "[2] Eric Brachmann, Alexander Krull, Frank Michel, Stefan Gumhold, Jamie Shotton, and Carsten Rother. Learning 6D Object Pose Estimation Using 3D Object Coordinates. 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DSC-PoseNet: Learning 6DoF Object Pose Estimation via Dual-Scale Consistency. In CVPR, pages 3907-3916, 2021. 1, 3, 4, 7", + "[40] Xin Yu, Zheyu Zhuang, Piotr Koniusz, and Hongdong Li. 6DoF Object Pose Estimation via Differentiable Proxy Voting Loss. In CVPR, 2020. 2", + "[41] Sergey Zakharov, Ivan Shugurov, and Slobodan Ilic. Dpod: 6d pose object detector and refiner. In ICCV, pages 1941-1950, 2019. 2, 7" + ], + "bbox": [ + 78, + 90, + 468, + 670 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21316", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SMOC-Net_ Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation/7ed77cdd-0ec8-4cc4-8097-ec9f36276521_model.json b/2023/SMOC-Net_ Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation/7ed77cdd-0ec8-4cc4-8097-ec9f36276521_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ce8b560b05e4e1d61114171b3a23847e50b27860 --- /dev/null +++ b/2023/SMOC-Net_ Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation/7ed77cdd-0ec8-4cc4-8097-ec9f36276521_model.json @@ -0,0 +1,2288 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.1, + 0.13, + 0.872, + 0.175 + ], + "angle": 0, + "content": "SMOC-Net: Leveraging Camera Pose for Self-Supervised Monocular Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.375, + 0.203, + 0.596, + 0.221 + ], + "angle": 0, + "content": "Tao Tan\\(^{1,2}\\), Qialei Dong\\(^{1,2,3}\\)" + }, + { + "type": "text", + "bbox": [ + 0.325, + 0.221, + 0.646, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Artificial Intelligence, UCAS" + }, + { + "type": "text", + "bbox": [ + 0.182, + 0.239, + 0.788, + 0.257 + ], + "angle": 0, + "content": "\\(^{2}\\)State Key Laboratory of Multimodal Artificial Intelligence Systems, CASIA" + }, + { + "type": "text", + "bbox": [ + 0.19, + 0.257, + 0.78, + 0.275 + ], + "angle": 0, + "content": "3Center for Excellence in Brain Science and Intelligence Technology, CAS" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.278, + 0.802, + 0.293 + ], + "angle": 0, + "content": "tantao2022@ia.ac.cn, qldong@nlpr.ia.ac.cn, Corresponding author: Qiulei Dong" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.473, + 0.797 + ], + "angle": 0, + "content": "Recently, self-supervised 6D object pose estimation, where synthetic images with object poses (sometimes jointly with un-annotated real images) are used for training, has attracted much attention in computer vision. Some typical works in literature employ a time-consuming differentiable renderer for object pose prediction at the training stage, so that (i) their performances on real images are generally limited due to the gap between their rendered images and real images and (ii) their training process is computationally expensive. To address the two problems, we propose a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The proposed network is explored under a knowledge distillation framework, consisting of a teacher model and a student model. The teacher model contains a backbone estimation module for initial object pose estimation, and an object pose refiner for refining the initial object poses using a geometric constraint (called relative-pose constraint) derived from relative camera poses. The student model gains knowledge for object pose estimation from the teacher model by imposing the relative-pose constraint. Thanks to the relative-pose constraint, SMOC-Net could not only narrow the domain gap between synthetic and real data but also reduce the training cost. Experimental results on two public datasets demonstrate that SMOC-Net outperforms several state-of-the-art methods by a large margin while requiring much less training time than the differentiable-renderer-based methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.829, + 0.21, + 0.845 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Monocular 6D object pose estimation is a challenging task in the computer vision field, which aims to estimate object poses from single images. According to whether real" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.895, + 0.496 + ], + "angle": 0, + "content": "images with ground-truth object poses are given for model training, the existing works for monocular object pose estimation in literature could be divided into two categories: fully-supervised methods [17, 35] which are trained by utilizing annotated real images with ground-truth object poses, and self-supervised methods [16, 34] which are trained by utilizing synthetic images with object poses (sometimes jointly with un-annotated real images). Since it is very time-consuming to obtain high-quality object poses as ground truth, self-supervised monocular object pose estimation has attracted increasing attention recently [16, 33, 39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.895, + 0.82 + ], + "angle": 0, + "content": "Some existing methods for self-supervised monocular object pose estimation [16, 31] use only synthetic images with object poses (which are generated via Blender [22] or some other rendering tools [24, 29]) for training. However, due to the domain gap between real and synthetic data, the performances of these self-supervised methods are significantly lower compared to the fully-supervised methods [22, 35]. Addressing this domain gap problem, a few recent self-supervised methods [33, 34, 39] jointly use synthetic images with object pose and un-annotated real images at their training stage, where a differentiable renderer [19] is introduced to provide a constraint on the difference between real and rendered images. Although these methods could alleviate the domain gap problem by utilizing the introduced differentiable renderer, they still have to be confronted with the following two problems: (i) There still exists a noticeable gap between real images and rendered images by the differentiable renderer, so that their performances on object pose estimation are still limited; (ii) Much time has to be spent on differentiable rendering during training, so that the training costs of these methods are quite heavy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "To address the above problems, this paper proposes a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The SMOC-Net is designed via the knowledge distillation technique, con" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21307" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "sisting of a teacher model and a student model. Under the teacher model, a backbone pose estimation module is introduced to provide an initial estimation on the pose of the image object. Then, a geometric constraint (called relative-pose constraint) on object poses is mathematically derived from relative camera poses which are calculated by a typical structure from motion method (here, we straightforwardly use COLMAP [25, 26]), and a camera-posed-refiner is further explored to refine the initial object pose based on this constraint. The student model simply employs the same architecture as the backbone estimation module of the teacher model, and it learns knowledge from the teacher model by imposing the relative-pose constraint, so that it could estimate object poses as accurately and fast as possible. Once the proposed SMOC-Net has been trained, only its student model is used to predict the object pose from an arbitrary testing image." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.349, + 0.443, + 0.363 + ], + "angle": 0, + "content": "In sum, the main contributions in this paper include:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.468, + 0.422 + ], + "angle": 0, + "content": "1. We design the relative-pose constraint on object poses under the knowledge distillation framework for self-supervised object pose estimation. And it could narrow the domain gap between synthetic and real data to some extent." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.468, + 0.468 + ], + "angle": 0, + "content": "2. According to the designed relative-pose constraint, we explore the camera-pose-guided refiner, which is able to refine low-accuracy object poses effectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.468, + 0.604 + ], + "angle": 0, + "content": "3. By jointly utilizing the camera-pose-guided refiner and the above object pose constraint, we propose the SMOC-Net for monocular 6D object pose estimation. Experimental results in Sec. 4 demonstrate that the proposed SMOC-Net does not only outperform several state-of-the-art methods when only synthetic images with object poses and un-annotated real images are used for training, but also perform better than three state-of-the-art fully-supervised methods on the public dataset LineMOD [8]." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.364, + 0.468, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.618, + 0.22, + 0.634 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.643, + 0.47, + 0.689 + ], + "angle": 0, + "content": "In this section, we review the existing fully-supervised and self-supervised methods for monocular 6D object pose estimation in literature, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.455, + 0.714 + ], + "angle": 0, + "content": "2.1. Fully-Supervised 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Fully-supervised object pose estimation methods use real RGB(D) images with object poses for training. Some early works directly regressed object pose with various Convolutional Neural Networks (CNNs) such as PoseCNN [37] and SSD-6D [13]. Xiang et al. [37] proposed the PoseCNN for 6D object pose estimation, which estimated the 3D translation by predicting the distance between object center in the image and the camera, and the 3D rotation was estimated by regressing a quaternion representation. Kehl et al. [13] proposed the SSD-6D, where rotation estimation was treated as a classification problem by discretizing the rotation space into classifiable viewpoint bins." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.635 + ], + "angle": 0, + "content": "For improving pose estimation accuracy further, many methods first established 2D-3D correspondences using CNNs, and then solved the object pose via Perspective-n-Point (PnP) algorithms. Keypoint-based methods [22, 28, 32] established correspondences by detecting keypoints in 2D images. Peng et al. [22] proposed a pixel level voting network (PVNet) by using the direction vector field to predict keypoints, which achieved good performance under severe truncation and occlusion. Song et al. [28] proposed the HybridPose by using hybrid representation such as keypoints, edge vectors, and symmetry correspondences. Some other methods predicted the corresponding 3D coordinates of each pixel in 2D images [17, 21, 40] or dense UV maps [41] to establish dense correspondences. Li et al. [17] proposed CDPN, which treated rotation and translation estimations as two different tasks. Rotation was calculated from dense correspondences, while translation was directly regressed from the target region. Hodan et al. [11] proposed EPOS, which represented the target object by compact surface fragments for better handling symmetries. To achieve end-to-end training, a Patch-PnP module consisting of CNNs and fully connected layers was proposed in [35]. Chen et al. [4] proposed an Epro-PnP module whose output was the probability density distribution of object pose and also achieved end-to-end training. Su et al. [30] proposed a discrete descriptor to represent the object surface densely, which was used to establish accurate and robust correspondences. Huang et al. [18] proposed to predict 3D object coordinates at 3D query points sampled in the camera frustum, which could efficiently handle occlusions. Shun et al. [12] utilized a deep texture rendering and differentiable Levenberg-Marquardt optimization to refine the object poses fast and accurately. Xu et al. [38] proposed a framework based on a recurrent neural network for object pose refinement, which was robust to erroneous initial poses and occlusions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.866, + 0.665 + ], + "angle": 0, + "content": "2.2. Self-Supervised 6D Object Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.884 + ], + "angle": 0, + "content": "To avoid the data annotation problem in fully-supervised object pose estimation, many self-supervised methods for object pose estimation have been proposed. Some self-supervised methods [16, 23, 31] only used synthetic images with object poses as training data. Sundermeyer et al. [31] proposed the AAE method by utilizing an auto-encoder, where only synthetic data was used for training. It employed a series of domain adaption techniques to reduce the domain gap between real and synthetic images. Rambach et al. [23] proposed to estimate object pose from synthetic single channel images, showing that proper representation could also reduce the domain gap. Li et al. [16] proposed SD-Pose, which preprocessed input images by multi-level semantic representations and achieved better performance." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To further narrow the domain gap, a few recent self" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21308" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.875, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.893, + 0.48 + ], + "angle": 0, + "content": "Figure 1. Architecture of the proposed SMOC-Net. It consists of a teacher model and a student model. The teacher model consists of a backbone pose estimation module and a camera-pose-guided (C-P-G) refiner. The student model simply employs the same architecture as the backbone estimation module of the teacher model. For a set of multi-view real images \\(\\{I_1^{src},\\dots,I_n^{src}\\}\\), their corresponding camera poses \\(\\{P_{c1},\\dots,P_{cn}\\}\\) are calculated by an SfM method (a). Then, a 2D object detector (Yolov4 [1]) is used to extract object regions from the input images, and a set of object patch pairs are obtained for self-supervised training. The predicted object poses \\(\\{P_{oi},P_{oj}\\}\\) are self-supervised with camera poses \\(\\{P_{ci},P_{cj}\\}\\) (b) and pseudo pose labels \\(\\{P_{oi}^*,P_{oj}^*\\}\\) (c) that have been refined by the camera-pose-guided refiner (d)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.473, + 0.9 + ], + "angle": 0, + "content": "supervised methods [33, 34, 39] jointly used synthetic images with object poses and un-annotated real images at their training stage. In [34], the network was first trained on synthetic data in a fully-supervised manner and then self-supervised with un-annotated real data by seeking a visually and geometrically optimal alignment between real images and rendered images by a differentiable renderer. But depth images were required during self-supervised training. Sock et al. [27] proposed a two-stage self-supervised method, which also used a differentiable renderer to establish pose consistency between rendered and real images. Beyond using image-level consistency for self-supervised pose estimation, Yang et al. [39] proposed a self-supervised network DSC-PoseNet based on dual-scale keypoint consistency. But it suffered dramatic performance degradation when there was occlusion. Wang et al. [33] revised [34] and proposed Self6D++, which used the pose estimation network GDR-Net [35] and noisy student training to improve accuracy and robustness. However, there still exists a gap between real images and rendered images by the differentiable renderer. And additionally, differentiable rendering is a computationally expensive process. Addressing these issues, this paper proposes a novel self-supervised object pose estimation by imposing a derived geometric constraint from camera poses, which would be described in detail in the following section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.505, + 0.637, + 0.523 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.624 + ], + "angle": 0, + "content": "In this section, we propose the SMOC-Net for self-supervised monocular object pose estimation. Firstly, the architecture of the proposed SMOC-Net is introduced. Then, we present the derived geometric constraint from camera poses and the camera-pose-guided refiner respectively. Finally, the total loss function is described." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.635, + 0.636, + 0.65 + ], + "angle": 0, + "content": "3.1. Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.903 + ], + "angle": 0, + "content": "The SMOC-Net is explored under a knowledge distillation framework, which contains a teacher model and a student model, and its architecture is shown in Fig. 1. As seen from this figure, an object detector is firstly used for extracting the object regions in the input images, and we simply use Yolo-v4 [1] here as the object detector as done in some existing object pose estimation works [33, 35]. The teacher model consists of a backbone estimation module and a camera-pose-guided refiner. The backbone estimation module is used to calculate an initial object pose estimation, and we simply use the existing method GDR-Net [35] as the backbone estimation module here. The camera-pose-guided refiner is explored to refine the initial object pose obtained from the backbone estimation module, by utilizing a derived geometric constraint from relative camera poses (called relative-pose constraint). The student model" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21309" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.089, + 0.422, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.47, + 0.373 + ], + "angle": 0, + "content": "Figure 2. World, object and camera coordinate systems. For a 3D point \\( P \\), its coordinates could be transformed from object/world coordinate systems to camera coordinate systems by corresponding absolute object/camera poses in the camera/world systems." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.468, + 0.445 + ], + "angle": 0, + "content": "employs the same architecture as the backbone estimation module, and it gains knowledge from the teacher model by utilizing the same relative-pose constraint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.468, + 0.746 + ], + "angle": 0, + "content": "At the training stage, the proposed SMOC-Net is trained by utilizing both synthetic data [10] with labels and a set of un-annotated real multi-view images. Firstly, the backbone GDR-Net and the detector Yolo-v4 are trained singly by only utilizing the synthetic RGB data as done in [33, 34]. Then, the classic SfM (Structure from Motion) method COLMAP [5, 25, 26] is utilized to calculate the corresponding absolute camera poses from the training set of multiview real images, and the object detector is implemented for extracting object patches from the input real images. According to the calculated camera poses as well as the corresponding original real object patches, we could straightforwardly obtain a set of object patch pairs with pseudo relative camera poses (which could be calculated according to the obtained absolute camera poses). Next, unlike the existing works [33, 34, 39] that deal with each training image singly, the proposed method deals with pairs of training patches. Finally, the student model is trained with the set of augmented object patch pairs with pseudo relative poses for learning knowledge from the teacher model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.468, + 0.822 + ], + "angle": 0, + "content": "At the testing stage, only the student module is used for predicting object pose from each monocular RGB image. In Sections 3.2 and 3.3, both the relative-pose constraint and the camera-pose-guided refiner would be introduced, respectively, in detail." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.833, + 0.304, + 0.847 + ], + "angle": 0, + "content": "3.2. Relative-Pose Constraint" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Given a set of \\(N\\) object patch pairs with the corresponding absolute camera poses in the world coordinate system, we could obtain a geometric constraint on the object relative" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.891, + 0.12 + ], + "angle": 0, + "content": "pose (called relative-posed constraint) for each patch pair as follows:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.892, + 0.242 + ], + "angle": 0, + "content": "For an arbitrary pair of object patches, without loss of generality, let \\( i \\) and \\( j \\) (\\( i < j \\); \\( i = 1, \\dots, N - 1 \\); \\( j = i + 1, \\dots, N \\)) denote the indices of the two patches. Then as shown in Fig. 2, for an arbitrary 3D object point, let \\( X_{ci} \\) and \\( X_{cj} \\) denote its coordinates in the two camera coordinate systems corresponding to the two input patches, and let \\( X_o \\) and \\( X_w \\) denote its coordinates in the object and world coordinate systems respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.243, + 0.892, + 0.272 + ], + "angle": 0, + "content": "Let \\([R_{oi}, t_{oi}]\\) and \\([R_{oj}, t_{oj}]\\) represent the absolute object poses in the two camera systems. Then, we have" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.283, + 0.891, + 0.298 + ], + "angle": 0, + "content": "\\[\nX _ {c i} = R _ {o i} X _ {o} + t _ {o i}, \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.302, + 0.891, + 0.318 + ], + "angle": 0, + "content": "\\[\nX _ {c j} = R _ {o j} X _ {o} + t _ {o j}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.327, + 0.891, + 0.402 + ], + "angle": 0, + "content": "Let \\([R_{ci}, t_{ci}]\\) and \\([R_{cj}, t_{cj}]\\) represent the absolute camera poses in the world system, which are calculated by the SfM method COLMAP [5, 25]. It has to be pointed out that the calculated translations by COLMAP are not equal to the ground-truth translation, but up to a scale. Hence, we have" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.412, + 0.891, + 0.427 + ], + "angle": 0, + "content": "\\[\nX _ {c i} = R _ {c i} X _ {w} + \\lambda t _ {c i}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.431, + 0.891, + 0.447 + ], + "angle": 0, + "content": "\\[\nX _ {c j} = R _ {c j} X _ {w} + \\lambda t _ {c j}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.456, + 0.89, + 0.484 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a scale factor. According to Eqn. (1) and Eqn. (3), we have" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.494, + 0.891, + 0.512 + ], + "angle": 0, + "content": "\\[\nX _ {w} = R _ {c i} ^ {- 1} R _ {o i} X _ {o} + R _ {c i} ^ {- 1} \\left(t _ {o i} - \\lambda t _ {c i}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.521, + 0.797, + 0.536 + ], + "angle": 0, + "content": "According to Eqn. (2) and Eqn. (4), we have" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.544, + 0.891, + 0.563 + ], + "angle": 0, + "content": "\\[\nX _ {w} = R _ {c j} ^ {- 1} R _ {o j} X _ {o} + R _ {c j} ^ {- 1} \\left(t _ {o j} - \\lambda t _ {c j}\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.571, + 0.797, + 0.586 + ], + "angle": 0, + "content": "According to Eqn. (5) and Eqn. (6), we have" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.594, + 0.891, + 0.613 + ], + "angle": 0, + "content": "\\[\nR _ {c i} ^ {- 1} R _ {o i} = R _ {c j} ^ {- 1} R _ {o j}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.615, + 0.891, + 0.635 + ], + "angle": 0, + "content": "\\[\nR _ {c i} ^ {- 1} \\left(t _ {o i} - \\lambda t _ {c i}\\right) = R _ {c j} ^ {- 1} \\left(t _ {o j} - \\lambda t _ {c j}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.643, + 0.7, + 0.657 + ], + "angle": 0, + "content": "Eqn. (7) could be rewritten as" + }, + { + "type": "equation", + "bbox": [ + 0.626, + 0.665, + 0.891, + 0.685 + ], + "angle": 0, + "content": "\\[\nR _ {o i} R _ {o j} ^ {- 1} = R _ {c i} R _ {c j} ^ {- 1}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.693, + 0.7, + 0.707 + ], + "angle": 0, + "content": "Eqn. (8) could be rewritten as" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.715, + 0.891, + 0.735 + ], + "angle": 0, + "content": "\\[\nR _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} = \\lambda \\left(R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.742, + 0.891, + 0.771 + ], + "angle": 0, + "content": "To remove the scale factor \\(\\lambda\\), both sides of the Eqn. (10) are normalized as" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.777, + 0.891, + 0.818 + ], + "angle": 0, + "content": "\\[\n\\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{| | R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} | | _ {2}} = \\frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{| | R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} | | _ {2}}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.891, + 0.9 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_2\\) is the \\(L_{2}\\) norm. It is noted that once the camera poses \\([R_{ci},t_{ci}]\\) and \\([R_{cj},t_{cj}]\\) are known, Eqn. (9) and Eqn. (11) provide constraints on relative object rotation and translation respectively. Hence, they are used together as our relative-pose constraint." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21310" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.473, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.24, + 0.47, + 0.313 + ], + "angle": 0, + "content": "Figure 3. Architecture of the explored camera-pose-guided refiner. For a pair of 6D object poses \\(\\{P_{init - oi}^{*}, P_{init - oj}^{*}\\}\\), they are first refined by DeepIM [15]. The refined poses \\(\\{\\widetilde{P}_{oi}, \\widetilde{P}_{oj}\\}\\) are then further updated using rotation increments and translation increments calculated according to the relative-pose constraint." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.337, + 0.342, + 0.352 + ], + "angle": 0, + "content": "3.3. Camera-Pose-Guided Refiner" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.481 + ], + "angle": 0, + "content": "In this section, we propose an iterative object pose refiner (called camera-pose-guided refiner), and its architecture is shown in Fig. 3. Given a set of \\(N\\) object patch pairs with the corresponding absolute camera poses in the world coordinate system, and their corresponding initial object poses are estimated by the teacher backbone estimation module. We could further refine the initial poses of each patch pair by utilizing the above relative-pose constraint as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.47, + 0.587 + ], + "angle": 0, + "content": "At each iteration, the object poses are firstly refined by DeepIM [15], which is pre-trained on synthetic RGB data. Let \\(\\widetilde{P}_{oi} = [\\widetilde{R}_{oi},\\widetilde{t}_{oi}]\\) and \\(\\widetilde{P}_{oj} = [\\widetilde{R}_{oj},\\widetilde{t}_{oj}]\\) represent the refined absolute object poses of two input patches. Then, we further refine the absolute object rotations and translations of the two patches with the corresponding absolute camera poses, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.709 + ], + "angle": 0, + "content": "Rotation Refinement Let \\( R_{ij} = R_{ci}R_{cj}^{-1} \\) denotes the relative camera rotation of two camera systems. In the rotation refinement, we seek to apply slight increments to the object rotations \\( \\{\\widetilde{R}_{oi},\\widetilde{R}_{oj}\\} \\). At each iteration, let \\( \\{\\Delta R_{oi},\\Delta R_{oj}\\} \\) represent the referred slight increments. Then, the object rotations would be updated as \\( \\{\\widetilde{R}_{oi}\\Delta R_{oi},\\widetilde{R}_{oj}\\Delta R_{oj}\\} \\). According to the relative rotation constraint in Eqn. (9), we have the following constraint equation:" + }, + { + "type": "equation", + "bbox": [ + 0.191, + 0.718, + 0.47, + 0.737 + ], + "angle": 0, + "content": "\\[\n\\Delta R _ {o i} ^ {- 1} \\Delta R _ {i j} \\Delta R _ {o j} = E, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.471, + 0.869 + ], + "angle": 0, + "content": "where \\(\\Delta R_{ij} = \\widetilde{R}_{oi}^{-1}R_{ij}\\widetilde{R}_{oj}\\). This is an under-constrained equation whose solution is not unique, hence, an auxiliary condition \\(\\Delta R_{oi}^{-1} = \\Delta R_{oj}\\) is introduced for guaranteeing a unique solution, considering that both the increments \\(\\Delta R_{oi}\\) and \\(\\Delta R_{oj}\\) at each iteration change slightly. Then, considering that Eqn. (12) is a nonlinear equation which is hard to solve, we compute the approximate solution by solving the following minimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.878, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Delta R _ {o i}, \\Delta R _ {o j}} | | \\omega (\\Delta R _ {o i} ^ {- 1} \\Delta R _ {i j} \\Delta R _ {o j}) | | _ {2} ^ {2}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "where \\(\\omega(R)\\) is the axis-angle representation of 3D rotation \\(R\\). Let \\(\\{\\Delta \\omega_{oi}, \\Delta \\omega_{oj}\\}\\) denote the axis-angle representation of \\(\\{\\Delta R_{oi}, \\Delta R_{oj}\\}\\), and \\(\\Delta \\omega_{ij}\\) denote the axis-angle representation of \\(\\Delta R_{ij}\\). The concatenation of \\(\\Delta \\omega_{oi}\\) and \\(\\Delta \\omega_{oj}\\) into a \\(6 \\times 1\\) vector is denoted as \\(\\Delta \\Omega\\). Therefore, our problem is to solve the following minimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.635, + 0.193, + 0.892, + 0.216 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Delta \\Omega} \\| r _ {i j} (\\Delta \\Omega) \\| _ {2} ^ {2}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.227, + 0.547, + 0.239 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.253, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\nr _ {i j} (\\Delta \\Omega) = \\omega (R (- \\Delta \\omega_ {o i}) R (\\Delta \\omega_ {i j}) R (\\Delta \\omega_ {o j})). \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.281, + 0.892, + 0.326 + ], + "angle": 0, + "content": "Inspired by Avishek et al. [3], the above minimization problem is transformed to solve the following problem using quasi-Newton method:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.336, + 0.892, + 0.36 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\Delta \\Omega} \\| r _ {i j} (\\mathbf {0}) + \\mathcal {J} r _ {i j} (\\mathbf {0}) ^ {T} \\Delta \\Omega \\| _ {2} ^ {2}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.37, + 0.847, + 0.386 + ], + "angle": 0, + "content": "It is equivalent to solve a linear system of equations:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.396, + 0.892, + 0.414 + ], + "angle": 0, + "content": "\\[\nJ r _ {i j} (\\mathbf {0}) ^ {T} \\Delta \\Omega = - r _ {i j} (\\mathbf {0}), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.425, + 0.892, + 0.455 + ], + "angle": 0, + "content": "where \\( Jr_{ij}(\\mathbf{0}) \\) is the Jacobian of \\( r_{ij}(\\Delta \\Omega) \\) at the current point \\( \\Delta \\Omega = \\mathbf{0} \\), and" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.465, + 0.892, + 0.513 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} {J r _ {i j} (\\mathbf {0}) ^ {T}} \\approx {\\frac {| | \\Delta \\omega_ {i j} | | _ {2}}{2} \\cot (\\frac {| | \\Delta \\omega_ {i j} | | _ {2}}{2}) [ I - I ]} \\\\ \\approx [ I - I ]. \\tag {18} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.525, + 0.788, + 0.539 + ], + "angle": 0, + "content": "Therefore, the final approximate solution is" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.55, + 0.892, + 0.58 + ], + "angle": 0, + "content": "\\[\n\\Delta \\omega_ {o i} = - \\Delta \\omega_ {o j} = - \\frac {\\Delta \\omega_ {i j}}{2}, \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.581, + 0.892, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\Delta R _ {o i} = \\Delta R _ {o j} ^ {- 1} = R \\left(- \\frac {\\Delta \\omega_ {i j}}{2}\\right). \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.62, + 0.892, + 0.726 + ], + "angle": 0, + "content": "Translation Refinement In the translation refinement, we seek to apply slight increments to object translations \\(\\{\\widetilde{t}_{oi},\\widetilde{t}_{oj}\\}\\). At each iteration, let \\(\\{\\Delta t_{oi},\\Delta t_{oj}\\}\\) represent the referred slight increments. Then, the object translations would be updated as \\(\\{\\widetilde{t}_{oi} + \\Delta t_{oi},\\widetilde{t}_{oj} + \\Delta t_{oj}\\}\\). According to the relative translation constraint in Eqn. (11), we have the following constraint equation:" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.735, + 0.892, + 0.788 + ], + "angle": 0, + "content": "\\[\n\\frac {R _ {c i} ^ {- 1} \\left(\\widetilde {t} _ {o i} + \\Delta t _ {o i}\\right) - R _ {c j} ^ {- 1} \\left(\\widetilde {t} _ {o j} + \\Delta t _ {o j}\\right)}{\\left| \\left| R _ {c i} ^ {- 1} \\left(\\widetilde {t} _ {o i} + \\Delta t _ {o i}\\right) - R _ {c j} ^ {- 1} \\left(\\widetilde {t} _ {o j} + \\Delta t _ {o j}\\right) \\right| \\right| _ {2}} - \\frac {t _ {i j}}{\\left| \\left| t _ {i j} \\right| \\right| _ {2}} = \\mathbf {0}, \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.789, + 0.545, + 0.801 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.801, + 0.892, + 0.821 + ], + "angle": 0, + "content": "\\[\nt _ {i j} = R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}. \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.856 + ], + "angle": 0, + "content": "It is approximate to solve the following linear system of equations:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.866, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\frac {R _ {c i} ^ {- 1} \\Delta t _ {o i} - R _ {c j} ^ {- 1} \\Delta t _ {o j}}{\\left| \\left| t _ {i j} ^ {*} \\right| \\right| _ {2}} + \\frac {t _ {i j} ^ {*}}{\\left| \\left| t _ {i j} ^ {*} \\right| \\right| _ {2}} - \\frac {t _ {i j}}{\\left| \\left| t _ {i j} \\right| \\right| _ {2}} = \\mathbf {0}, \\tag {23}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21311" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.093, + 0.125, + 0.105 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.117, + 0.47, + 0.138 + ], + "angle": 0, + "content": "\\[\nt _ {i j} ^ {*} = R _ {c i} ^ {- 1} \\widetilde {t} _ {o i} - R _ {c j} ^ {- 1} \\widetilde {t} _ {o j}. \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.148, + 0.47, + 0.209 + ], + "angle": 0, + "content": "This is also an under-constrained equation, hence, an auxiliary condition \\(\\Delta t_{oi} = -\\Delta t_{oj}\\) is introduced, considering that both the increments \\(\\Delta t_{oi}\\) and \\(\\Delta t_{oj}\\) at each iteration change slightly. So the final approximate solution is" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.219, + 0.47, + 0.255 + ], + "angle": 0, + "content": "\\[\n\\Delta t _ {o i} = - \\Delta t _ {o j} = \\left(R _ {c i} ^ {- 1} + R _ {c j} ^ {- 1}\\right) ^ {- 1} \\left(\\frac {\\left\\| t _ {i j} ^ {*} \\right\\| _ {2}}{\\left\\| t _ {i j} \\right\\| _ {2}} t _ {i j} - t _ {i j} ^ {*}\\right). \\tag {25}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.264, + 0.47, + 0.324 + ], + "angle": 0, + "content": "Finally, the absolute object poses are further updated by utilizing both rotation increments and translation increments. Let \\( P_{oi}^{*} \\) and \\( P_{oj}^{*} \\) represent the updated object poses. Then, we have" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.334, + 0.469, + 0.354 + ], + "angle": 0, + "content": "\\[\nP _ {o i} ^ {*} = \\left[ \\widetilde {R} _ {o i} \\Delta R _ {o i}, \\widetilde {t} _ {o i} + \\Delta t _ {o i} \\right], \\tag {26}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.356, + 0.469, + 0.377 + ], + "angle": 0, + "content": "\\[\nP _ {o j} ^ {*} = \\left[ \\widetilde {R} _ {o j} \\Delta R _ {o j}, \\widetilde {t} _ {o j} + \\Delta t _ {o j} \\right]. \\tag {27}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.387, + 0.222, + 0.401 + ], + "angle": 0, + "content": "3.4. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.41, + 0.469, + 0.456 + ], + "angle": 0, + "content": "The total loss function \\(\\mathcal{L}_{\\text{self}}\\) of the proposed SMOC-Net contains three loss terms: a rotation loss \\(\\mathcal{L}_{\\text{rot}}\\), a translation loss \\(\\mathcal{L}_{\\text{trans}}\\) and a point matching loss \\(\\mathcal{L}_{\\text{pm}}^{\\text{pair}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.456, + 0.469, + 0.484 + ], + "angle": 0, + "content": "According to the relative rotation constraint, the rotation loss is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.497, + 0.469, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r o t} = \\left| \\left| \\omega \\left(R _ {o j} R _ {o i} ^ {- 1} R _ {i j}\\right) \\right| \\right| _ {2}, \\tag {28}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.526, + 0.231, + 0.543 + ], + "angle": 0, + "content": "where \\(R_{ij} = R_{ci}R_{cj}^{-1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.543, + 0.469, + 0.586 + ], + "angle": 0, + "content": "According to the relative translation constraint, the translation loss is defined by measuring the angle of two relative translation vectors as" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.6, + 0.469, + 0.618 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t r a n s}} = \\mathrm {a c o s} \\left(t _ {c, i j} \\cdot t _ {o, i j}\\right), \\tag {29}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.628, + 0.345, + 0.643 + ], + "angle": 0, + "content": "where \\( \\mathrm{acos}(\\cdot) \\) is the arccos function and" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.654, + 0.469, + 0.693 + ], + "angle": 0, + "content": "\\[\nt _ {c, i j} = \\frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{\\left| \\left| R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} \\right| \\right| _ {2}}, \\tag {30}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.696, + 0.469, + 0.735 + ], + "angle": 0, + "content": "\\[\nt _ {o, i j} = \\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{\\left| \\left| R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} \\right| \\right| _ {2}}. \\tag {31}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.746, + 0.469, + 0.79 + ], + "angle": 0, + "content": "Inspired by [15, 33, 35], the point matching loss for geometrically aligning the predicted poses and the pseudo pose labels is used:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.803, + 0.469, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p m} = \\min _ {R _ {o} \\in s y m X \\in \\mathcal {M}} \\operatorname {a v g} \\left| \\left| \\left(R _ {o} ^ {*} X + t _ {o} ^ {*}\\right) - \\left(R _ {o} X + t _ {o}\\right) \\right| \\right| _ {1}, \\tag {32}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(||\\cdot ||_1\\) is the \\(L_{1}\\) norm, \\(\\text{sym}\\) is a pool of symmetric rotations including the given rotation to deal with symmetric objects following [21], \\(\\mathcal{M}\\) represents the CAD object point cloud given in the evaluation datasets, \\(R_o\\), \\((t_{ox}, t_{oy})\\) and \\(t_{oz}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.152 + ], + "angle": 0, + "content": "are disentangled from \\( P_{o} = [R_{o}, t_{o}] \\), and \\( P_{o}^{*} = [R_{o}^{*}, t_{o}^{*}] \\) denotes the pseudo pose label. Since the proposed method deals with pairs of training patches, the sum of two point matching losses is eventually used:" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.16, + 0.892, + 0.18 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p m} ^ {\\text {p a i r}} = \\mathcal {L} _ {p m, i} + \\mathcal {L} _ {p m, j}. \\tag {33}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.186, + 0.892, + 0.215 + ], + "angle": 0, + "content": "Accordingly, the total loss function \\(\\mathcal{L}_{self}\\) is the weighted sum of the above three loss terms as" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.224, + 0.892, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s e l f} = \\mathcal {L} _ {r o t} + \\lambda_ {1} \\mathcal {L} _ {t r a n s} + \\lambda_ {2} \\mathcal {L} _ {p m} ^ {\\text {p a i r}}, \\tag {34}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.25, + 0.795, + 0.265 + ], + "angle": 0, + "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are two weight parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.277, + 0.632, + 0.294 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.302, + 0.602, + 0.316 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.325, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Synthetic PBR Dataset [10] As the physically-based renderer has been proven to perform better than OpenGL renderers [13, 34], we use the synthetic PBR data from [10] to train the 2D object detector Yolov4 [1] and the backbone pose estimation module GDR-Net [35]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.4, + 0.892, + 0.461 + ], + "angle": 0, + "content": "LineMOD [8] is a standard benchmark for 6D object pose estimation, consisting of 13 sequences. And there are about \\(1.2\\mathrm{k}\\) images in each sequence. As done in [13], we use \\(15\\%\\) of images for training and the remaining for testing." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.461, + 0.892, + 0.522 + ], + "angle": 0, + "content": "Occluded-LineMOD [2] is generated from benchvise sequence of the LineMOD dataset, and it contains 1214 images. As done in [33], we sample data for testing using the BOP split [9] and use the remaining data for training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.53, + 0.596, + 0.544 + ], + "angle": 0, + "content": "4.2. Metrics" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.674 + ], + "angle": 0, + "content": "We evaluate the performance using the common Average Distance of Distinguishable Model Points (ADD) metric [8], which measures the distance between 3D object model point clouds transformed by the predicted pose and the corresponding ground-truth. A pose is considered correct when the distance is less than \\(10\\%\\) of the diameter of a 3D model. ADD-S is used [37] for symmetric objects by computing the closest point distance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.717, + 0.698 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Our method is implemented by Pytorch, and all experiments are conducted on an NVIDIA 3080 GPU. The camera poses are calculated using a classic SfM method COLMAP [25,26,36] before training. We replace ResNet-34 [7] backbone of GDR-Net [35] with ResNeSt-50 [6] backbone as done in [33]. The learning rate is set to \\(10^{-4}\\). The strategy of pre-training with synthetic data is the same as [33]. During the self-supervised training, we train the student pose estimation network for 30 epochs using un-annotated real RGB data, and the batch size is set to 8. In each epoch, all \\(N\\) training images are randomly divided into \\(N/2\\) image pairs. During inference, only the student pose estimation network is used." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21312" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.122, + 0.089, + 0.85, + 0.256 + ], + "angle": 0, + "content": "
Training MannerMethodsTraining dataApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
Fully-supervisionDPOD [41]R53.395.290.094.160.497.466.099.693.864.999.888.171.482.6
PVNet [22]43.699.986.995.579.396.452.699.295.781.998.999.392.486.3
CDPN [17]64.497.891.795.583.896.266.899.799.685.897.997.990.889.9
Self-supervisionAAE [31]S4.222.932.937.018.724.85.981.046.218.235.161.236.332.6
MHP [20]11.966.222.459.826.944.68.355.754.615.560.8-34.438.8
DPOD [41]35.159.415.548.828.159.325.651.234.617.784.745.020.940.5
Self6D [34]S+R−+D38.975.236.965.657.967.019.699.094.116.277.968.250.158.9
Self6D++ [33]75.494.997.099.586.698.968.399.096.141.999.498.994.388.5
DSC-PoseNet [39]S+R−35.983.151.561.045.068.027.689.252.526.456.368.746.454.7
Self6D++ [33]76.091.697.199.885.698.856.591.092.235.499.597.491.885.6
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.267, + 0.892, + 0.309 + ], + "angle": 0, + "content": "Table 1. Comparison with state-of-the-art methods on LineMOD dataset. The table reports results for the Average Recall (%) of ADD(-S). All results except ours and DSC-PoseNet are copied from [33]. The best RGB based label-free method is marked in bold. R: annotated real RGB data. S: synthetic RGB data. \\(\\mathbb{R}^{-}\\) : unannotated real RGB data. D: depth data." + }, + { + "type": "table", + "bbox": [ + 0.177, + 0.323, + 0.795, + 0.461 + ], + "angle": 0, + "content": "
MethodsTraining dataApeCanCatDrilDuckEb.GlueHolepMean
DPOD [41]S2.34.01.210.57.24.412.97.56.3
CDPN [17]20.015.116.45.022.236.127.924.020.8
CosyPose [14]44.069.942.167.547.824.460.017.546.7
Self6D [34]S+R-+D13.743.218.732.514.457.854.322.032.1
Self6D++ [33]59.496.560.892.030.651.188.638.364.7
DSC-PoseNet [39]S+R-13.915.119.440.56.938.924.016.321.9
Self6D++ [33]57.795.052.690.526.745.087.123.559.8
OURS60.094.559.193.037.248.389.325.063.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.236, + 0.471, + 0.731, + 0.484 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art methods on Occluded-LineMOD dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.511, + 0.303, + 0.527 + ], + "angle": 0, + "content": "4.4. Comparative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Comparisons on LineMOD. Here, we evaluate the proposed SMOC-Net on the LineMOD dataset in comparison to some state-of-the-art methods, including three fully-supervised methods (DPOD [41], PVNet [22], CDPN [17]), three self-supervised methods that are trained with only synthetic data (AAE [31], MHP [20], DPOD [41]), one self-supervised method that is trained with both synthetic data and un-annotated real images (DSC-PoseNet [39]), and two self-supervised methods that are trained with synthetic data + un-annotated real images + depth images (Self6D [34], Self6D++ [33]). In addition, for a more comprehensive comparison, we also compare our method with Self6D++ [33] trained with synthetic data and un-annotated real images but without depth images. The corresponding results are reported in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "As seen from Table 1, the fully-supervised methods DPOD, PVNet, CDPN perform better than most of the existing self-supervised methods in most cases, mainly because annotated real images with object poses are used for training these fully-supervised methods. Moreover, the proposed SMOC-Net achieves a better performance than all the comparative methods (regardless of whether these methods are trained in an either fully-supervised or self-supervised manner), because of the derived relative-pose" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.512, + 0.892, + 0.558 + ], + "angle": 0, + "content": "constraint and the designed camera-posed-refiner in SMOC-Net. These results demonstrate the effectiveness of the proposed method for 6D object pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Comparisons on Occluded-LineMOD. We evaluate the proposed SMOC-Net on the Occluded-LineMOD dataset where there exist many occlusions, in comparison to DPOD [41], CDPN [17], CosyPose [14], Self6D [34], Self6D++ [33], and DSC-PoseNet [39]. The corresponding results are reported in Table 2. As seen from this table, the overall average recalls of most of the comparative methods are lower than \\(60\\%\\) or even lower. Among all the comparative methods, Self6D++ trained with 3 categories of data (synthetic, unannotated real images, and depth images) performs the best, mainly because it uses additional scene depth images at the training stage, which contain 3D spatial information and are more effective in capturing the 3D spatial relationship between adjacent objects. Moreover, the proposed SMOC-Net achieves a slightly lower performance than Self6D++ that is trained with 3 categories of data (synthetic, unannotated real images, and depth images). However, the SMOC-Net significantly outperforms Self6D++ that is trained without depth images in the same manner as SMOC-Net, and it also performs significantly better than the other comparative methods. These results demonstrate that the proposed method could effectively handle the oc" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21313" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.118, + 0.089, + 0.855, + 0.178 + ], + "angle": 0, + "content": "
MethodApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
w/o Lrot82.195.097.099.894.1100.072.698.599.340.399.996.295.290.0
w/o Ltrans84.392.995.999.893.999.777.098.798.747.5100.098.194.390.8
w/o refiner*88.396.096.699.792.8100.070.498.099.042.2100.097.394.390.4
OURS-50.799.489.597.280.098.726.381.191.241.998.898.964.477.5
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.188, + 0.892, + 0.217 + ], + "angle": 0, + "content": "Table 3. Ablation study on LineMOD dataset. Individual loss and pose refiner are evaluated on LineMOD. * : the proposed camera-posedguided refiner is replaced with DeepIM [15]. Ours: our results trained on synthetic data. The best results are marked in bold." + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.24, + 0.421, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.416, + 0.471, + 0.472 + ], + "angle": 0, + "content": "Figure 4. Visualized results on Occluded-LineMOD dataset. Top: results of DSC-PoseNet. Middle: results of Self6D++. Bottom: results of SMOC-Net. Red: the ground-truth object poses. Green: the results after self-supervised training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.556 + ], + "angle": 0, + "content": "clusion case. Fig. 4 illustrates the visualized results of Self6D++, DSC-PoseNet and SMOC-Net, which are all trained with synthetic data and un-annotated real images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.58, + 0.231, + 0.596 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.469, + 0.655 + ], + "angle": 0, + "content": "To evaluate the effects of the losses \\(\\mathcal{L}_{rot},\\mathcal{L}_{trans}\\) and the camera-pose-guided refiner, we conduct the ablation study on LineMOD and the results are reported in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Firstly, we respectively disable the rotation loss \\(\\mathcal{L}_{rot}\\) and the translation loss \\(\\mathcal{L}_{trans}\\). The corresponding models are denoted as w/o \\(\\mathcal{L}_{rot}\\) and w/o \\(\\mathcal{L}_{trans}\\) respectively. As shown in Table 3, the pose accuracy decreases when disabling each of them. These results demonstrate that both of the rotation loss and the translation loss are effective to improve the pose accuracy for our method. Then, we replace the proposed camera-pose-guided refiner with DeepIM [15], and the corresponding model is denoted as w/o refiner*. The performance of w/o refiner* is significantly lower than the complete SMOC-Net. In addition, we also train our model with only synthetic data, which is denoted as OUR-. The overall average recall of OUR\\(^{-}\\) is much lower than the complete SMOC-Net, demonstrating that the proposed self-supervised object pose estimation method could significantly improve the pose accuracy." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.24, + 0.88, + 0.294 + ], + "angle": 0, + "content": "
MethodTraining/Rendering Time (s)Total Time (s)
Self6D++ [33]37/291110
OURS8/-283
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Table 4. Comparison of the training times in one epoch and the total times on LineMOD." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.355, + 0.767, + 0.372 + ], + "angle": 0, + "content": "4.6. Comparison of Training Time" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.379, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Here, we compare our training time on the LineMOD dataset with Self6D++ [33], a state-of-the-art differentiable-renderer-based method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.424, + 0.893, + 0.59 + ], + "angle": 0, + "content": "Both the training times in one epoch and the total times by the two methods are reported in Table 4. As seen in Table 4, the training time of Self6D++ in one epoch is 37 seconds, but Self6D++ spends 29 seconds on rendering, indicating that rendering is a main time-consuming part for such a differentiable-renderer-based method. Moreover, the training time of our method in one epoch is much less than Self6D++, and the total training time (for both SfM and network training) of our method is also much less than Self6D++. These results demonstrate the priority of the proposed method in model training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.619, + 0.619 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we have proposed the SMOC-Net for self-supervised monocular object pose estimation by utilizing the predicted camera poses from un-annotated real images. Unlike most of the existing self-supervised methods that rely on differentiable renderer for providing additional constraint on object pose prediction, the SMOC-Net utilizes the derived relative-pose constraint for boosting the performance on object pose estimation. We also propose a pose refiner for further refining the initial object pose with the derived relative-pose constraint. The experimental results on two public datasets demonstrate the effectiveness of the proposed method even when dealing with strong occlusions. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant Nos. U1805264 and 61991423), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB32050100), the Beijing Municipal Science and Technology Project (Grant No. Z211100011021004)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21314" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. YOLOv4: Optimal Speed and Accuracy of Object Detection. arXiv preprint arXiv:2004.10934, 2020. 3, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.468, + 0.226 + ], + "angle": 0, + "content": "[2] Eric Brachmann, Alexander Krull, Frank Michel, Stefan Gumhold, Jamie Shotton, and Carsten Rother. 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Some typical works in literature employ a time-consuming differentiable renderer for object pose prediction at the training stage, so that (i) their performances on real images are generally limited due to the gap between their rendered images and real images and (ii) their training process is computationally expensive. To address the two problems, we propose a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The proposed network is explored under a knowledge distillation framework, consisting of a teacher model and a student model. The teacher model contains a backbone estimation module for initial object pose estimation, and an object pose refiner for refining the initial object poses using a geometric constraint (called relative-pose constraint) derived from relative camera poses. The student model gains knowledge for object pose estimation from the teacher model by imposing the relative-pose constraint. Thanks to the relative-pose constraint, SMOC-Net could not only narrow the domain gap between synthetic and real data but also reduce the training cost. Experimental results on two public datasets demonstrate that SMOC-Net outperforms several state-of-the-art methods by a large margin while requiring much less training time than the differentiable-renderer-based methods. + +# 1. Introduction + +Monocular 6D object pose estimation is a challenging task in the computer vision field, which aims to estimate object poses from single images. According to whether real + +images with ground-truth object poses are given for model training, the existing works for monocular object pose estimation in literature could be divided into two categories: fully-supervised methods [17, 35] which are trained by utilizing annotated real images with ground-truth object poses, and self-supervised methods [16, 34] which are trained by utilizing synthetic images with object poses (sometimes jointly with un-annotated real images). Since it is very time-consuming to obtain high-quality object poses as ground truth, self-supervised monocular object pose estimation has attracted increasing attention recently [16, 33, 39]. + +Some existing methods for self-supervised monocular object pose estimation [16, 31] use only synthetic images with object poses (which are generated via Blender [22] or some other rendering tools [24, 29]) for training. However, due to the domain gap between real and synthetic data, the performances of these self-supervised methods are significantly lower compared to the fully-supervised methods [22, 35]. Addressing this domain gap problem, a few recent self-supervised methods [33, 34, 39] jointly use synthetic images with object pose and un-annotated real images at their training stage, where a differentiable renderer [19] is introduced to provide a constraint on the difference between real and rendered images. Although these methods could alleviate the domain gap problem by utilizing the introduced differentiable renderer, they still have to be confronted with the following two problems: (i) There still exists a noticeable gap between real images and rendered images by the differentiable renderer, so that their performances on object pose estimation are still limited; (ii) Much time has to be spent on differentiable rendering during training, so that the training costs of these methods are quite heavy. + +To address the above problems, this paper proposes a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The SMOC-Net is designed via the knowledge distillation technique, con + +sisting of a teacher model and a student model. Under the teacher model, a backbone pose estimation module is introduced to provide an initial estimation on the pose of the image object. Then, a geometric constraint (called relative-pose constraint) on object poses is mathematically derived from relative camera poses which are calculated by a typical structure from motion method (here, we straightforwardly use COLMAP [25, 26]), and a camera-posed-refiner is further explored to refine the initial object pose based on this constraint. The student model simply employs the same architecture as the backbone estimation module of the teacher model, and it learns knowledge from the teacher model by imposing the relative-pose constraint, so that it could estimate object poses as accurately and fast as possible. Once the proposed SMOC-Net has been trained, only its student model is used to predict the object pose from an arbitrary testing image. + +In sum, the main contributions in this paper include: + +1. We design the relative-pose constraint on object poses under the knowledge distillation framework for self-supervised object pose estimation. And it could narrow the domain gap between synthetic and real data to some extent. +2. According to the designed relative-pose constraint, we explore the camera-pose-guided refiner, which is able to refine low-accuracy object poses effectively. +3. By jointly utilizing the camera-pose-guided refiner and the above object pose constraint, we propose the SMOC-Net for monocular 6D object pose estimation. Experimental results in Sec. 4 demonstrate that the proposed SMOC-Net does not only outperform several state-of-the-art methods when only synthetic images with object poses and un-annotated real images are used for training, but also perform better than three state-of-the-art fully-supervised methods on the public dataset LineMOD [8]. + +# 2. Related Work + +In this section, we review the existing fully-supervised and self-supervised methods for monocular 6D object pose estimation in literature, respectively. + +# 2.1. Fully-Supervised 6D Object Pose Estimation + +Fully-supervised object pose estimation methods use real RGB(D) images with object poses for training. Some early works directly regressed object pose with various Convolutional Neural Networks (CNNs) such as PoseCNN [37] and SSD-6D [13]. Xiang et al. [37] proposed the PoseCNN for 6D object pose estimation, which estimated the 3D translation by predicting the distance between object center in the image and the camera, and the 3D rotation was estimated by regressing a quaternion representation. Kehl et al. [13] proposed the SSD-6D, where rotation estimation was treated as a classification problem by discretizing the rotation space into classifiable viewpoint bins. + +For improving pose estimation accuracy further, many methods first established 2D-3D correspondences using CNNs, and then solved the object pose via Perspective-n-Point (PnP) algorithms. Keypoint-based methods [22, 28, 32] established correspondences by detecting keypoints in 2D images. Peng et al. [22] proposed a pixel level voting network (PVNet) by using the direction vector field to predict keypoints, which achieved good performance under severe truncation and occlusion. Song et al. [28] proposed the HybridPose by using hybrid representation such as keypoints, edge vectors, and symmetry correspondences. Some other methods predicted the corresponding 3D coordinates of each pixel in 2D images [17, 21, 40] or dense UV maps [41] to establish dense correspondences. Li et al. [17] proposed CDPN, which treated rotation and translation estimations as two different tasks. Rotation was calculated from dense correspondences, while translation was directly regressed from the target region. Hodan et al. [11] proposed EPOS, which represented the target object by compact surface fragments for better handling symmetries. To achieve end-to-end training, a Patch-PnP module consisting of CNNs and fully connected layers was proposed in [35]. Chen et al. [4] proposed an Epro-PnP module whose output was the probability density distribution of object pose and also achieved end-to-end training. Su et al. [30] proposed a discrete descriptor to represent the object surface densely, which was used to establish accurate and robust correspondences. Huang et al. [18] proposed to predict 3D object coordinates at 3D query points sampled in the camera frustum, which could efficiently handle occlusions. Shun et al. [12] utilized a deep texture rendering and differentiable Levenberg-Marquardt optimization to refine the object poses fast and accurately. Xu et al. [38] proposed a framework based on a recurrent neural network for object pose refinement, which was robust to erroneous initial poses and occlusions. + +# 2.2. Self-Supervised 6D Object Pose Estimation + +To avoid the data annotation problem in fully-supervised object pose estimation, many self-supervised methods for object pose estimation have been proposed. Some self-supervised methods [16, 23, 31] only used synthetic images with object poses as training data. Sundermeyer et al. [31] proposed the AAE method by utilizing an auto-encoder, where only synthetic data was used for training. It employed a series of domain adaption techniques to reduce the domain gap between real and synthetic images. Rambach et al. [23] proposed to estimate object pose from synthetic single channel images, showing that proper representation could also reduce the domain gap. Li et al. [16] proposed SD-Pose, which preprocessed input images by multi-level semantic representations and achieved better performance. + +To further narrow the domain gap, a few recent self + +![](images/3b8bbcc8ec36c1c94bf4b05ea54840015c6373f77c83a1c4f6c51f0d9b398e89.jpg) +Figure 1. Architecture of the proposed SMOC-Net. It consists of a teacher model and a student model. The teacher model consists of a backbone pose estimation module and a camera-pose-guided (C-P-G) refiner. The student model simply employs the same architecture as the backbone estimation module of the teacher model. For a set of multi-view real images $\{I_1^{src},\dots,I_n^{src}\}$ , their corresponding camera poses $\{P_{c1},\dots,P_{cn}\}$ are calculated by an SfM method (a). Then, a 2D object detector (Yolov4 [1]) is used to extract object regions from the input images, and a set of object patch pairs are obtained for self-supervised training. The predicted object poses $\{P_{oi},P_{oj}\}$ are self-supervised with camera poses $\{P_{ci},P_{cj}\}$ (b) and pseudo pose labels $\{P_{oi}^*,P_{oj}^*\}$ (c) that have been refined by the camera-pose-guided refiner (d). + +supervised methods [33, 34, 39] jointly used synthetic images with object poses and un-annotated real images at their training stage. In [34], the network was first trained on synthetic data in a fully-supervised manner and then self-supervised with un-annotated real data by seeking a visually and geometrically optimal alignment between real images and rendered images by a differentiable renderer. But depth images were required during self-supervised training. Sock et al. [27] proposed a two-stage self-supervised method, which also used a differentiable renderer to establish pose consistency between rendered and real images. Beyond using image-level consistency for self-supervised pose estimation, Yang et al. [39] proposed a self-supervised network DSC-PoseNet based on dual-scale keypoint consistency. But it suffered dramatic performance degradation when there was occlusion. Wang et al. [33] revised [34] and proposed Self6D++, which used the pose estimation network GDR-Net [35] and noisy student training to improve accuracy and robustness. However, there still exists a gap between real images and rendered images by the differentiable renderer. And additionally, differentiable rendering is a computationally expensive process. Addressing these issues, this paper proposes a novel self-supervised object pose estimation by imposing a derived geometric constraint from camera poses, which would be described in detail in the following section. + +# 3. Methodology + +In this section, we propose the SMOC-Net for self-supervised monocular object pose estimation. Firstly, the architecture of the proposed SMOC-Net is introduced. Then, we present the derived geometric constraint from camera poses and the camera-pose-guided refiner respectively. Finally, the total loss function is described. + +# 3.1. Architecture + +The SMOC-Net is explored under a knowledge distillation framework, which contains a teacher model and a student model, and its architecture is shown in Fig. 1. As seen from this figure, an object detector is firstly used for extracting the object regions in the input images, and we simply use Yolo-v4 [1] here as the object detector as done in some existing object pose estimation works [33, 35]. The teacher model consists of a backbone estimation module and a camera-pose-guided refiner. The backbone estimation module is used to calculate an initial object pose estimation, and we simply use the existing method GDR-Net [35] as the backbone estimation module here. The camera-pose-guided refiner is explored to refine the initial object pose obtained from the backbone estimation module, by utilizing a derived geometric constraint from relative camera poses (called relative-pose constraint). The student model + +![](images/bc1f2c704dca4d77b24dd7aa836eb1f72cdb9bad3c5ad6bfad6ac3daec4b018e.jpg) +Figure 2. World, object and camera coordinate systems. For a 3D point $P$ , its coordinates could be transformed from object/world coordinate systems to camera coordinate systems by corresponding absolute object/camera poses in the camera/world systems. + +employs the same architecture as the backbone estimation module, and it gains knowledge from the teacher model by utilizing the same relative-pose constraint. + +At the training stage, the proposed SMOC-Net is trained by utilizing both synthetic data [10] with labels and a set of un-annotated real multi-view images. Firstly, the backbone GDR-Net and the detector Yolo-v4 are trained singly by only utilizing the synthetic RGB data as done in [33, 34]. Then, the classic SfM (Structure from Motion) method COLMAP [5, 25, 26] is utilized to calculate the corresponding absolute camera poses from the training set of multiview real images, and the object detector is implemented for extracting object patches from the input real images. According to the calculated camera poses as well as the corresponding original real object patches, we could straightforwardly obtain a set of object patch pairs with pseudo relative camera poses (which could be calculated according to the obtained absolute camera poses). Next, unlike the existing works [33, 34, 39] that deal with each training image singly, the proposed method deals with pairs of training patches. Finally, the student model is trained with the set of augmented object patch pairs with pseudo relative poses for learning knowledge from the teacher model. + +At the testing stage, only the student module is used for predicting object pose from each monocular RGB image. In Sections 3.2 and 3.3, both the relative-pose constraint and the camera-pose-guided refiner would be introduced, respectively, in detail. + +# 3.2. Relative-Pose Constraint + +Given a set of $N$ object patch pairs with the corresponding absolute camera poses in the world coordinate system, we could obtain a geometric constraint on the object relative + +pose (called relative-posed constraint) for each patch pair as follows: + +For an arbitrary pair of object patches, without loss of generality, let $i$ and $j$ ( $i < j$ ; $i = 1, \dots, N - 1$ ; $j = i + 1, \dots, N$ ) denote the indices of the two patches. Then as shown in Fig. 2, for an arbitrary 3D object point, let $X_{ci}$ and $X_{cj}$ denote its coordinates in the two camera coordinate systems corresponding to the two input patches, and let $X_o$ and $X_w$ denote its coordinates in the object and world coordinate systems respectively. + +Let $[R_{oi}, t_{oi}]$ and $[R_{oj}, t_{oj}]$ represent the absolute object poses in the two camera systems. Then, we have + +$$ +X _ {c i} = R _ {o i} X _ {o} + t _ {o i}, \tag {1} +$$ + +$$ +X _ {c j} = R _ {o j} X _ {o} + t _ {o j}. \tag {2} +$$ + +Let $[R_{ci}, t_{ci}]$ and $[R_{cj}, t_{cj}]$ represent the absolute camera poses in the world system, which are calculated by the SfM method COLMAP [5, 25]. It has to be pointed out that the calculated translations by COLMAP are not equal to the ground-truth translation, but up to a scale. Hence, we have + +$$ +X _ {c i} = R _ {c i} X _ {w} + \lambda t _ {c i}, \tag {3} +$$ + +$$ +X _ {c j} = R _ {c j} X _ {w} + \lambda t _ {c j}, \tag {4} +$$ + +where $\lambda$ is a scale factor. According to Eqn. (1) and Eqn. (3), we have + +$$ +X _ {w} = R _ {c i} ^ {- 1} R _ {o i} X _ {o} + R _ {c i} ^ {- 1} \left(t _ {o i} - \lambda t _ {c i}\right). \tag {5} +$$ + +According to Eqn. (2) and Eqn. (4), we have + +$$ +X _ {w} = R _ {c j} ^ {- 1} R _ {o j} X _ {o} + R _ {c j} ^ {- 1} \left(t _ {o j} - \lambda t _ {c j}\right). \tag {6} +$$ + +According to Eqn. (5) and Eqn. (6), we have + +$$ +R _ {c i} ^ {- 1} R _ {o i} = R _ {c j} ^ {- 1} R _ {o j}, \tag {7} +$$ + +$$ +R _ {c i} ^ {- 1} \left(t _ {o i} - \lambda t _ {c i}\right) = R _ {c j} ^ {- 1} \left(t _ {o j} - \lambda t _ {c j}\right). \tag {8} +$$ + +Eqn. (7) could be rewritten as + +$$ +R _ {o i} R _ {o j} ^ {- 1} = R _ {c i} R _ {c j} ^ {- 1}. \tag {9} +$$ + +Eqn. (8) could be rewritten as + +$$ +R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} = \lambda \left(R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}\right). \tag {10} +$$ + +To remove the scale factor $\lambda$ , both sides of the Eqn. (10) are normalized as + +$$ +\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{| | R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} | | _ {2}} = \frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{| | R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} | | _ {2}}, \tag {11} +$$ + +where $||\cdot ||_2$ is the $L_{2}$ norm. It is noted that once the camera poses $[R_{ci},t_{ci}]$ and $[R_{cj},t_{cj}]$ are known, Eqn. (9) and Eqn. (11) provide constraints on relative object rotation and translation respectively. Hence, they are used together as our relative-pose constraint. + +![](images/e3d85c0fb176e36c34ad2409e15e2ebe53cc6248cf8e757f6ceb5d6d35e625a0.jpg) +Figure 3. Architecture of the explored camera-pose-guided refiner. For a pair of 6D object poses $\{P_{init - oi}^{*}, P_{init - oj}^{*}\}$ , they are first refined by DeepIM [15]. The refined poses $\{\widetilde{P}_{oi}, \widetilde{P}_{oj}\}$ are then further updated using rotation increments and translation increments calculated according to the relative-pose constraint. + +# 3.3. Camera-Pose-Guided Refiner + +In this section, we propose an iterative object pose refiner (called camera-pose-guided refiner), and its architecture is shown in Fig. 3. Given a set of $N$ object patch pairs with the corresponding absolute camera poses in the world coordinate system, and their corresponding initial object poses are estimated by the teacher backbone estimation module. We could further refine the initial poses of each patch pair by utilizing the above relative-pose constraint as follows: + +At each iteration, the object poses are firstly refined by DeepIM [15], which is pre-trained on synthetic RGB data. Let $\widetilde{P}_{oi} = [\widetilde{R}_{oi},\widetilde{t}_{oi}]$ and $\widetilde{P}_{oj} = [\widetilde{R}_{oj},\widetilde{t}_{oj}]$ represent the refined absolute object poses of two input patches. Then, we further refine the absolute object rotations and translations of the two patches with the corresponding absolute camera poses, respectively. + +Rotation Refinement Let $R_{ij} = R_{ci}R_{cj}^{-1}$ denotes the relative camera rotation of two camera systems. In the rotation refinement, we seek to apply slight increments to the object rotations $\{\widetilde{R}_{oi},\widetilde{R}_{oj}\}$ . At each iteration, let $\{\Delta R_{oi},\Delta R_{oj}\}$ represent the referred slight increments. Then, the object rotations would be updated as $\{\widetilde{R}_{oi}\Delta R_{oi},\widetilde{R}_{oj}\Delta R_{oj}\}$ . According to the relative rotation constraint in Eqn. (9), we have the following constraint equation: + +$$ +\Delta R _ {o i} ^ {- 1} \Delta R _ {i j} \Delta R _ {o j} = E, \tag {12} +$$ + +where $\Delta R_{ij} = \widetilde{R}_{oi}^{-1}R_{ij}\widetilde{R}_{oj}$ . This is an under-constrained equation whose solution is not unique, hence, an auxiliary condition $\Delta R_{oi}^{-1} = \Delta R_{oj}$ is introduced for guaranteeing a unique solution, considering that both the increments $\Delta R_{oi}$ and $\Delta R_{oj}$ at each iteration change slightly. Then, considering that Eqn. (12) is a nonlinear equation which is hard to solve, we compute the approximate solution by solving the following minimization problem: + +$$ +\min _ {\Delta R _ {o i}, \Delta R _ {o j}} | | \omega (\Delta R _ {o i} ^ {- 1} \Delta R _ {i j} \Delta R _ {o j}) | | _ {2} ^ {2}, \tag {13} +$$ + +where $\omega(R)$ is the axis-angle representation of 3D rotation $R$ . Let $\{\Delta \omega_{oi}, \Delta \omega_{oj}\}$ denote the axis-angle representation of $\{\Delta R_{oi}, \Delta R_{oj}\}$ , and $\Delta \omega_{ij}$ denote the axis-angle representation of $\Delta R_{ij}$ . The concatenation of $\Delta \omega_{oi}$ and $\Delta \omega_{oj}$ into a $6 \times 1$ vector is denoted as $\Delta \Omega$ . Therefore, our problem is to solve the following minimization problem: + +$$ +\min _ {\Delta \Omega} \| r _ {i j} (\Delta \Omega) \| _ {2} ^ {2}, \tag {14} +$$ + +where + +$$ +r _ {i j} (\Delta \Omega) = \omega (R (- \Delta \omega_ {o i}) R (\Delta \omega_ {i j}) R (\Delta \omega_ {o j})). \tag {15} +$$ + +Inspired by Avishek et al. [3], the above minimization problem is transformed to solve the following problem using quasi-Newton method: + +$$ +\min _ {\Delta \Omega} \| r _ {i j} (\mathbf {0}) + \mathcal {J} r _ {i j} (\mathbf {0}) ^ {T} \Delta \Omega \| _ {2} ^ {2}. \tag {16} +$$ + +It is equivalent to solve a linear system of equations: + +$$ +J r _ {i j} (\mathbf {0}) ^ {T} \Delta \Omega = - r _ {i j} (\mathbf {0}), \tag {17} +$$ + +where $Jr_{ij}(\mathbf{0})$ is the Jacobian of $r_{ij}(\Delta \Omega)$ at the current point $\Delta \Omega = \mathbf{0}$ , and + +$$ +\begin{array}{l} {J r _ {i j} (\mathbf {0}) ^ {T}} \approx {\frac {| | \Delta \omega_ {i j} | | _ {2}}{2} \cot (\frac {| | \Delta \omega_ {i j} | | _ {2}}{2}) [ I - I ]} \\ \approx [ I - I ]. \tag {18} \\ \end{array} +$$ + +Therefore, the final approximate solution is + +$$ +\Delta \omega_ {o i} = - \Delta \omega_ {o j} = - \frac {\Delta \omega_ {i j}}{2}, \tag {19} +$$ + +$$ +\Delta R _ {o i} = \Delta R _ {o j} ^ {- 1} = R \left(- \frac {\Delta \omega_ {i j}}{2}\right). \tag {20} +$$ + +Translation Refinement In the translation refinement, we seek to apply slight increments to object translations $\{\widetilde{t}_{oi},\widetilde{t}_{oj}\}$ . At each iteration, let $\{\Delta t_{oi},\Delta t_{oj}\}$ represent the referred slight increments. Then, the object translations would be updated as $\{\widetilde{t}_{oi} + \Delta t_{oi},\widetilde{t}_{oj} + \Delta t_{oj}\}$ . According to the relative translation constraint in Eqn. (11), we have the following constraint equation: + +$$ +\frac {R _ {c i} ^ {- 1} \left(\widetilde {t} _ {o i} + \Delta t _ {o i}\right) - R _ {c j} ^ {- 1} \left(\widetilde {t} _ {o j} + \Delta t _ {o j}\right)}{\left| \left| R _ {c i} ^ {- 1} \left(\widetilde {t} _ {o i} + \Delta t _ {o i}\right) - R _ {c j} ^ {- 1} \left(\widetilde {t} _ {o j} + \Delta t _ {o j}\right) \right| \right| _ {2}} - \frac {t _ {i j}}{\left| \left| t _ {i j} \right| \right| _ {2}} = \mathbf {0}, \tag {21} +$$ + +where + +$$ +t _ {i j} = R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}. \tag {22} +$$ + +It is approximate to solve the following linear system of equations: + +$$ +\frac {R _ {c i} ^ {- 1} \Delta t _ {o i} - R _ {c j} ^ {- 1} \Delta t _ {o j}}{\left| \left| t _ {i j} ^ {*} \right| \right| _ {2}} + \frac {t _ {i j} ^ {*}}{\left| \left| t _ {i j} ^ {*} \right| \right| _ {2}} - \frac {t _ {i j}}{\left| \left| t _ {i j} \right| \right| _ {2}} = \mathbf {0}, \tag {23} +$$ + +where + +$$ +t _ {i j} ^ {*} = R _ {c i} ^ {- 1} \widetilde {t} _ {o i} - R _ {c j} ^ {- 1} \widetilde {t} _ {o j}. \tag {24} +$$ + +This is also an under-constrained equation, hence, an auxiliary condition $\Delta t_{oi} = -\Delta t_{oj}$ is introduced, considering that both the increments $\Delta t_{oi}$ and $\Delta t_{oj}$ at each iteration change slightly. So the final approximate solution is + +$$ +\Delta t _ {o i} = - \Delta t _ {o j} = \left(R _ {c i} ^ {- 1} + R _ {c j} ^ {- 1}\right) ^ {- 1} \left(\frac {\left\| t _ {i j} ^ {*} \right\| _ {2}}{\left\| t _ {i j} \right\| _ {2}} t _ {i j} - t _ {i j} ^ {*}\right). \tag {25} +$$ + +Finally, the absolute object poses are further updated by utilizing both rotation increments and translation increments. Let $P_{oi}^{*}$ and $P_{oj}^{*}$ represent the updated object poses. Then, we have + +$$ +P _ {o i} ^ {*} = \left[ \widetilde {R} _ {o i} \Delta R _ {o i}, \widetilde {t} _ {o i} + \Delta t _ {o i} \right], \tag {26} +$$ + +$$ +P _ {o j} ^ {*} = \left[ \widetilde {R} _ {o j} \Delta R _ {o j}, \widetilde {t} _ {o j} + \Delta t _ {o j} \right]. \tag {27} +$$ + +# 3.4. Loss Function + +The total loss function $\mathcal{L}_{\text{self}}$ of the proposed SMOC-Net contains three loss terms: a rotation loss $\mathcal{L}_{\text{rot}}$ , a translation loss $\mathcal{L}_{\text{trans}}$ and a point matching loss $\mathcal{L}_{\text{pm}}^{\text{pair}}$ . + +According to the relative rotation constraint, the rotation loss is defined as + +$$ +\mathcal {L} _ {r o t} = \left| \left| \omega \left(R _ {o j} R _ {o i} ^ {- 1} R _ {i j}\right) \right| \right| _ {2}, \tag {28} +$$ + +where $R_{ij} = R_{ci}R_{cj}^{-1}$ + +According to the relative translation constraint, the translation loss is defined by measuring the angle of two relative translation vectors as + +$$ +\mathcal {L} _ {\text {t r a n s}} = \mathrm {a c o s} \left(t _ {c, i j} \cdot t _ {o, i j}\right), \tag {29} +$$ + +where $\mathrm{acos}(\cdot)$ is the arccos function and + +$$ +t _ {c, i j} = \frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{\left| \left| R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} \right| \right| _ {2}}, \tag {30} +$$ + +$$ +t _ {o, i j} = \frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{\left| \left| R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} \right| \right| _ {2}}. \tag {31} +$$ + +Inspired by [15, 33, 35], the point matching loss for geometrically aligning the predicted poses and the pseudo pose labels is used: + +$$ +\mathcal {L} _ {p m} = \min _ {R _ {o} \in s y m X \in \mathcal {M}} \operatorname {a v g} \left| \left| \left(R _ {o} ^ {*} X + t _ {o} ^ {*}\right) - \left(R _ {o} X + t _ {o}\right) \right| \right| _ {1}, \tag {32} +$$ + +where $||\cdot ||_1$ is the $L_{1}$ norm, $\text{sym}$ is a pool of symmetric rotations including the given rotation to deal with symmetric objects following [21], $\mathcal{M}$ represents the CAD object point cloud given in the evaluation datasets, $R_o$ , $(t_{ox}, t_{oy})$ and $t_{oz}$ + +are disentangled from $P_{o} = [R_{o}, t_{o}]$ , and $P_{o}^{*} = [R_{o}^{*}, t_{o}^{*}]$ denotes the pseudo pose label. Since the proposed method deals with pairs of training patches, the sum of two point matching losses is eventually used: + +$$ +\mathcal {L} _ {p m} ^ {\text {p a i r}} = \mathcal {L} _ {p m, i} + \mathcal {L} _ {p m, j}. \tag {33} +$$ + +Accordingly, the total loss function $\mathcal{L}_{self}$ is the weighted sum of the above three loss terms as + +$$ +\mathcal {L} _ {s e l f} = \mathcal {L} _ {r o t} + \lambda_ {1} \mathcal {L} _ {t r a n s} + \lambda_ {2} \mathcal {L} _ {p m} ^ {\text {p a i r}}, \tag {34} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are two weight parameters. + +# 4. Experiments + +# 4.1. Datasets + +Synthetic PBR Dataset [10] As the physically-based renderer has been proven to perform better than OpenGL renderers [13, 34], we use the synthetic PBR data from [10] to train the 2D object detector Yolov4 [1] and the backbone pose estimation module GDR-Net [35]. + +LineMOD [8] is a standard benchmark for 6D object pose estimation, consisting of 13 sequences. And there are about $1.2\mathrm{k}$ images in each sequence. As done in [13], we use $15\%$ of images for training and the remaining for testing. + +Occluded-LineMOD [2] is generated from benchvise sequence of the LineMOD dataset, and it contains 1214 images. As done in [33], we sample data for testing using the BOP split [9] and use the remaining data for training. + +# 4.2. Metrics + +We evaluate the performance using the common Average Distance of Distinguishable Model Points (ADD) metric [8], which measures the distance between 3D object model point clouds transformed by the predicted pose and the corresponding ground-truth. A pose is considered correct when the distance is less than $10\%$ of the diameter of a 3D model. ADD-S is used [37] for symmetric objects by computing the closest point distance. + +# 4.3. Implementation Details + +Our method is implemented by Pytorch, and all experiments are conducted on an NVIDIA 3080 GPU. The camera poses are calculated using a classic SfM method COLMAP [25,26,36] before training. We replace ResNet-34 [7] backbone of GDR-Net [35] with ResNeSt-50 [6] backbone as done in [33]. The learning rate is set to $10^{-4}$ . The strategy of pre-training with synthetic data is the same as [33]. During the self-supervised training, we train the student pose estimation network for 30 epochs using un-annotated real RGB data, and the batch size is set to 8. In each epoch, all $N$ training images are randomly divided into $N/2$ image pairs. During inference, only the student pose estimation network is used. + +
Training MannerMethodsTraining dataApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
Fully-supervisionDPOD [41]R53.395.290.094.160.497.466.099.693.864.999.888.171.482.6
PVNet [22]43.699.986.995.579.396.452.699.295.781.998.999.392.486.3
CDPN [17]64.497.891.795.583.896.266.899.799.685.897.997.990.889.9
Self-supervisionAAE [31]S4.222.932.937.018.724.85.981.046.218.235.161.236.332.6
MHP [20]11.966.222.459.826.944.68.355.754.615.560.8-34.438.8
DPOD [41]35.159.415.548.828.159.325.651.234.617.784.745.020.940.5
Self6D [34]S+R−+D38.975.236.965.657.967.019.699.094.116.277.968.250.158.9
Self6D++ [33]75.494.997.099.586.698.968.399.096.141.999.498.994.388.5
DSC-PoseNet [39]S+R−35.983.151.561.045.068.027.689.252.526.456.368.746.454.7
Self6D++ [33]76.091.697.199.885.698.856.591.092.235.499.597.491.885.6
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
+ +Table 1. Comparison with state-of-the-art methods on LineMOD dataset. The table reports results for the Average Recall (%) of ADD(-S). All results except ours and DSC-PoseNet are copied from [33]. The best RGB based label-free method is marked in bold. R: annotated real RGB data. S: synthetic RGB data. $\mathbb{R}^{-}$ : unannotated real RGB data. D: depth data. + +
MethodsTraining dataApeCanCatDrilDuckEb.GlueHolepMean
DPOD [41]S2.34.01.210.57.24.412.97.56.3
CDPN [17]20.015.116.45.022.236.127.924.020.8
CosyPose [14]44.069.942.167.547.824.460.017.546.7
Self6D [34]S+R-+D13.743.218.732.514.457.854.322.032.1
Self6D++ [33]59.496.560.892.030.651.188.638.364.7
DSC-PoseNet [39]S+R-13.915.119.440.56.938.924.016.321.9
Self6D++ [33]57.795.052.690.526.745.087.123.559.8
OURS60.094.559.193.037.248.389.325.063.3
+ +Table 2. Comparison with state-of-the-art methods on Occluded-LineMOD dataset. + +# 4.4. Comparative Evaluation + +Comparisons on LineMOD. Here, we evaluate the proposed SMOC-Net on the LineMOD dataset in comparison to some state-of-the-art methods, including three fully-supervised methods (DPOD [41], PVNet [22], CDPN [17]), three self-supervised methods that are trained with only synthetic data (AAE [31], MHP [20], DPOD [41]), one self-supervised method that is trained with both synthetic data and un-annotated real images (DSC-PoseNet [39]), and two self-supervised methods that are trained with synthetic data + un-annotated real images + depth images (Self6D [34], Self6D++ [33]). In addition, for a more comprehensive comparison, we also compare our method with Self6D++ [33] trained with synthetic data and un-annotated real images but without depth images. The corresponding results are reported in Table 1. + +As seen from Table 1, the fully-supervised methods DPOD, PVNet, CDPN perform better than most of the existing self-supervised methods in most cases, mainly because annotated real images with object poses are used for training these fully-supervised methods. Moreover, the proposed SMOC-Net achieves a better performance than all the comparative methods (regardless of whether these methods are trained in an either fully-supervised or self-supervised manner), because of the derived relative-pose + +constraint and the designed camera-posed-refiner in SMOC-Net. These results demonstrate the effectiveness of the proposed method for 6D object pose estimation. + +Comparisons on Occluded-LineMOD. We evaluate the proposed SMOC-Net on the Occluded-LineMOD dataset where there exist many occlusions, in comparison to DPOD [41], CDPN [17], CosyPose [14], Self6D [34], Self6D++ [33], and DSC-PoseNet [39]. The corresponding results are reported in Table 2. As seen from this table, the overall average recalls of most of the comparative methods are lower than $60\%$ or even lower. Among all the comparative methods, Self6D++ trained with 3 categories of data (synthetic, unannotated real images, and depth images) performs the best, mainly because it uses additional scene depth images at the training stage, which contain 3D spatial information and are more effective in capturing the 3D spatial relationship between adjacent objects. Moreover, the proposed SMOC-Net achieves a slightly lower performance than Self6D++ that is trained with 3 categories of data (synthetic, unannotated real images, and depth images). However, the SMOC-Net significantly outperforms Self6D++ that is trained without depth images in the same manner as SMOC-Net, and it also performs significantly better than the other comparative methods. These results demonstrate that the proposed method could effectively handle the oc + +
MethodApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
w/o Lrot82.195.097.099.894.1100.072.698.599.340.399.996.295.290.0
w/o Ltrans84.392.995.999.893.999.777.098.798.747.5100.098.194.390.8
w/o refiner*88.396.096.699.792.8100.070.498.099.042.2100.097.394.390.4
OURS-50.799.489.597.280.098.726.381.191.241.998.898.964.477.5
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
+ +![](images/7fb34a57e5ba78503a708c4d7add4fd62ecabada6abca38f529e78f48c1d8da7.jpg) +Figure 4. Visualized results on Occluded-LineMOD dataset. Top: results of DSC-PoseNet. Middle: results of Self6D++. Bottom: results of SMOC-Net. Red: the ground-truth object poses. Green: the results after self-supervised training. + +clusion case. Fig. 4 illustrates the visualized results of Self6D++, DSC-PoseNet and SMOC-Net, which are all trained with synthetic data and un-annotated real images. + +# 4.5. Ablation Study + +To evaluate the effects of the losses $\mathcal{L}_{rot},\mathcal{L}_{trans}$ and the camera-pose-guided refiner, we conduct the ablation study on LineMOD and the results are reported in Table 3. + +Firstly, we respectively disable the rotation loss $\mathcal{L}_{rot}$ and the translation loss $\mathcal{L}_{trans}$ . The corresponding models are denoted as w/o $\mathcal{L}_{rot}$ and w/o $\mathcal{L}_{trans}$ respectively. As shown in Table 3, the pose accuracy decreases when disabling each of them. These results demonstrate that both of the rotation loss and the translation loss are effective to improve the pose accuracy for our method. Then, we replace the proposed camera-pose-guided refiner with DeepIM [15], and the corresponding model is denoted as w/o refiner*. The performance of w/o refiner* is significantly lower than the complete SMOC-Net. In addition, we also train our model with only synthetic data, which is denoted as OUR-. The overall average recall of OUR $^{-}$ is much lower than the complete SMOC-Net, demonstrating that the proposed self-supervised object pose estimation method could significantly improve the pose accuracy. + +Table 3. Ablation study on LineMOD dataset. Individual loss and pose refiner are evaluated on LineMOD. * : the proposed camera-posedguided refiner is replaced with DeepIM [15]. Ours: our results trained on synthetic data. The best results are marked in bold. + +
MethodTraining/Rendering Time (s)Total Time (s)
Self6D++ [33]37/291110
OURS8/-283
+ +Table 4. Comparison of the training times in one epoch and the total times on LineMOD. + +# 4.6. Comparison of Training Time + +Here, we compare our training time on the LineMOD dataset with Self6D++ [33], a state-of-the-art differentiable-renderer-based method. + +Both the training times in one epoch and the total times by the two methods are reported in Table 4. As seen in Table 4, the training time of Self6D++ in one epoch is 37 seconds, but Self6D++ spends 29 seconds on rendering, indicating that rendering is a main time-consuming part for such a differentiable-renderer-based method. Moreover, the training time of our method in one epoch is much less than Self6D++, and the total training time (for both SfM and network training) of our method is also much less than Self6D++. These results demonstrate the priority of the proposed method in model training. + +# 5. Conclusion + +In this paper, we have proposed the SMOC-Net for self-supervised monocular object pose estimation by utilizing the predicted camera poses from un-annotated real images. Unlike most of the existing self-supervised methods that rely on differentiable renderer for providing additional constraint on object pose prediction, the SMOC-Net utilizes the derived relative-pose constraint for boosting the performance on object pose estimation. We also propose a pose refiner for further refining the initial object pose with the derived relative-pose constraint. The experimental results on two public datasets demonstrate the effectiveness of the proposed method even when dealing with strong occlusions. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant Nos. U1805264 and 61991423), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB32050100), the Beijing Municipal Science and Technology Project (Grant No. Z211100011021004). + +# References + +[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. YOLOv4: Optimal Speed and Accuracy of Object Detection. arXiv preprint arXiv:2004.10934, 2020. 3, 6 +[2] Eric Brachmann, Alexander Krull, Frank Michel, Stefan Gumhold, Jamie Shotton, and Carsten Rother. Learning 6D Object Pose Estimation Using 3D Object Coordinates. In ECCV, pages 536-551, 2014. 6 +[3] Avishek Chatterjee and Venu Madhav Govindu. Robust Relative Rotation Averaging. PAMI, 40(4):958-972, 2017. 5 +[4] Hansheng Chen, Pichao Wang, Fan Wang, Wei Tian, Lu Xiong, and Hao Li. EPro-PnP: Generalized end-to-end probabilistic perspective-n-points for monocular object pose estimation. In CVPR, pages 2781-2790, 2022. 2 +[5] Qiulei Dong, Xiang Gao, Hainan Cui, and Zhanyi Hu. 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Some typical works in literature employ a time-consuming differentiable renderer for object pose prediction at the training stage, so that (i) their performances on real images are generally limited due to the gap between their rendered images and real images and (ii) their training process is computationally expensive. To address the two problems, we propose a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The proposed network is explored under a knowledge distillation framework, consisting of a teacher model and a student model. The teacher model contains a backbone estimation module for initial object pose estimation, and an object pose refiner for refining the initial object poses using a geometric constraint (called relative-pose constraint) derived from relative camera poses. The student model gains knowledge for object pose estimation from the teacher model by imposing the relative-pose constraint. Thanks to the relative-pose constraint, SMOC-Net could not only narrow the domain gap between synthetic and real data but also reduce the training cost. Experimental results on two public datasets demonstrate that SMOC-Net outperforms several state-of-the-art methods by a large margin while requiring much less training time than the differentiable-renderer-based methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 656, + 128, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 128, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 128, + 669 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Monocular 6D object pose estimation is a challenging task in the computer vision field, which aims to estimate object poses from single images. According to whether real" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 259, + 547, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 547, + 392 + ], + "type": "text", + "content": "images with ground-truth object poses are given for model training, the existing works for monocular object pose estimation in literature could be divided into two categories: fully-supervised methods [17, 35] which are trained by utilizing annotated real images with ground-truth object poses, and self-supervised methods [16, 34] which are trained by utilizing synthetic images with object poses (sometimes jointly with un-annotated real images). Since it is very time-consuming to obtain high-quality object poses as ground truth, self-supervised monocular object pose estimation has attracted increasing attention recently [16, 33, 39]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 396, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 649 + ], + "type": "text", + "content": "Some existing methods for self-supervised monocular object pose estimation [16, 31] use only synthetic images with object poses (which are generated via Blender [22] or some other rendering tools [24, 29]) for training. However, due to the domain gap between real and synthetic data, the performances of these self-supervised methods are significantly lower compared to the fully-supervised methods [22, 35]. Addressing this domain gap problem, a few recent self-supervised methods [33, 34, 39] jointly use synthetic images with object pose and un-annotated real images at their training stage, where a differentiable renderer [19] is introduced to provide a constraint on the difference between real and rendered images. Although these methods could alleviate the domain gap problem by utilizing the introduced differentiable renderer, they still have to be confronted with the following two problems: (i) There still exists a noticeable gap between real images and rendered images by the differentiable renderer, so that their performances on object pose estimation are still limited; (ii) Much time has to be spent on differentiable rendering during training, so that the training costs of these methods are quite heavy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "To address the above problems, this paper proposes a novel Network for Self-supervised Monocular Object pose estimation by utilizing the predicted Camera poses from un-annotated real images, called SMOC-Net. The SMOC-Net is designed via the knowledge distillation technique, con" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21307" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "sisting of a teacher model and a student model. Under the teacher model, a backbone pose estimation module is introduced to provide an initial estimation on the pose of the image object. Then, a geometric constraint (called relative-pose constraint) on object poses is mathematically derived from relative camera poses which are calculated by a typical structure from motion method (here, we straightforwardly use COLMAP [25, 26]), and a camera-posed-refiner is further explored to refine the initial object pose based on this constraint. The student model simply employs the same architecture as the backbone estimation module of the teacher model, and it learns knowledge from the teacher model by imposing the relative-pose constraint, so that it could estimate object poses as accurately and fast as possible. Once the proposed SMOC-Net has been trained, only its student model is used to predict the object pose from an arbitrary testing image." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 276, + 271, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 276, + 271, + 287 + ], + "spans": [ + { + "bbox": [ + 59, + 276, + 271, + 287 + ], + "type": "text", + "content": "In sum, the main contributions in this paper include:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 286, + 478 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 288, + 286, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 286, + 334 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 286, + 334 + ], + "type": "text", + "content": "1. We design the relative-pose constraint on object poses under the knowledge distillation framework for self-supervised object pose estimation. And it could narrow the domain gap between synthetic and real data to some extent." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 335, + 286, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 286, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 286, + 370 + ], + "type": "text", + "content": "2. According to the designed relative-pose constraint, we explore the camera-pose-guided refiner, which is able to refine low-accuracy object poses effectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 371, + 286, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 286, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 286, + 478 + ], + "type": "text", + "content": "3. By jointly utilizing the camera-pose-guided refiner and the above object pose constraint, we propose the SMOC-Net for monocular 6D object pose estimation. Experimental results in Sec. 4 demonstrate that the proposed SMOC-Net does not only outperform several state-of-the-art methods when only synthetic images with object poses and un-annotated real images are used for training, but also perform better than three state-of-the-art fully-supervised methods on the public dataset LineMOD [8]." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 489, + 134, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 134, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 134, + 502 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 509, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 509, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 509, + 287, + 545 + ], + "type": "text", + "content": "In this section, we review the existing fully-supervised and self-supervised methods for monocular 6D object pose estimation in literature, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 552, + 278, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 278, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 278, + 565 + ], + "type": "text", + "content": "2.1. Fully-Supervised 6D Object Pose Estimation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Fully-supervised object pose estimation methods use real RGB(D) images with object poses for training. Some early works directly regressed object pose with various Convolutional Neural Networks (CNNs) such as PoseCNN [37] and SSD-6D [13]. Xiang et al. [37] proposed the PoseCNN for 6D object pose estimation, which estimated the 3D translation by predicting the distance between object center in the image and the camera, and the 3D rotation was estimated by regressing a quaternion representation. Kehl et al. [13] proposed the SSD-6D, where rotation estimation was treated as a classification problem by discretizing the rotation space into classifiable viewpoint bins." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 502 + ], + "type": "text", + "content": "For improving pose estimation accuracy further, many methods first established 2D-3D correspondences using CNNs, and then solved the object pose via Perspective-n-Point (PnP) algorithms. Keypoint-based methods [22, 28, 32] established correspondences by detecting keypoints in 2D images. Peng et al. [22] proposed a pixel level voting network (PVNet) by using the direction vector field to predict keypoints, which achieved good performance under severe truncation and occlusion. Song et al. [28] proposed the HybridPose by using hybrid representation such as keypoints, edge vectors, and symmetry correspondences. Some other methods predicted the corresponding 3D coordinates of each pixel in 2D images [17, 21, 40] or dense UV maps [41] to establish dense correspondences. Li et al. [17] proposed CDPN, which treated rotation and translation estimations as two different tasks. Rotation was calculated from dense correspondences, while translation was directly regressed from the target region. Hodan et al. [11] proposed EPOS, which represented the target object by compact surface fragments for better handling symmetries. To achieve end-to-end training, a Patch-PnP module consisting of CNNs and fully connected layers was proposed in [35]. Chen et al. [4] proposed an Epro-PnP module whose output was the probability density distribution of object pose and also achieved end-to-end training. Su et al. [30] proposed a discrete descriptor to represent the object surface densely, which was used to establish accurate and robust correspondences. Huang et al. [18] proposed to predict 3D object coordinates at 3D query points sampled in the camera frustum, which could efficiently handle occlusions. Shun et al. [12] utilized a deep texture rendering and differentiable Levenberg-Marquardt optimization to refine the object poses fast and accurately. Xu et al. [38] proposed a framework based on a recurrent neural network for object pose refinement, which was robust to erroneous initial poses and occlusions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 513, + 529, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 529, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 529, + 526 + ], + "type": "text", + "content": "2.2. Self-Supervised 6D Object Pose Estimation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 533, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 700 + ], + "type": "text", + "content": "To avoid the data annotation problem in fully-supervised object pose estimation, many self-supervised methods for object pose estimation have been proposed. Some self-supervised methods [16, 23, 31] only used synthetic images with object poses as training data. Sundermeyer et al. [31] proposed the AAE method by utilizing an auto-encoder, where only synthetic data was used for training. It employed a series of domain adaption techniques to reduce the domain gap between real and synthetic images. Rambach et al. [23] proposed to estimate object pose from synthetic single channel images, showing that proper representation could also reduce the domain gap. Li et al. [16] proposed SD-Pose, which preprocessed input images by multi-level semantic representations and achieved better performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "To further narrow the domain gap, a few recent self" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21308" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 535, + 295 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 535, + 295 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 535, + 295 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 535, + 295 + ], + "type": "image", + "image_path": "3b8bbcc8ec36c1c94bf4b05ea54840015c6373f77c83a1c4f6c51f0d9b398e89.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "text", + "content": "Figure 1. Architecture of the proposed SMOC-Net. It consists of a teacher model and a student model. The teacher model consists of a backbone pose estimation module and a camera-pose-guided (C-P-G) refiner. The student model simply employs the same architecture as the backbone estimation module of the teacher model. For a set of multi-view real images " + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "inline_equation", + "content": "\\{I_1^{src},\\dots,I_n^{src}\\}" + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "text", + "content": ", their corresponding camera poses " + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "inline_equation", + "content": "\\{P_{c1},\\dots,P_{cn}\\}" + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "text", + "content": " are calculated by an SfM method (a). Then, a 2D object detector (Yolov4 [1]) is used to extract object regions from the input images, and a set of object patch pairs are obtained for self-supervised training. The predicted object poses " + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "inline_equation", + "content": "\\{P_{oi},P_{oj}\\}" + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "text", + "content": " are self-supervised with camera poses " + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "inline_equation", + "content": "\\{P_{ci},P_{cj}\\}" + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "text", + "content": " (b) and pseudo pose labels " + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "inline_equation", + "content": "\\{P_{oi}^*,P_{oj}^*\\}" + }, + { + "bbox": [ + 46, + 303, + 546, + 380 + ], + "type": "text", + "content": " (c) that have been refined by the camera-pose-guided refiner (d)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 401, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 289, + 712 + ], + "type": "text", + "content": "supervised methods [33, 34, 39] jointly used synthetic images with object poses and un-annotated real images at their training stage. In [34], the network was first trained on synthetic data in a fully-supervised manner and then self-supervised with un-annotated real data by seeking a visually and geometrically optimal alignment between real images and rendered images by a differentiable renderer. But depth images were required during self-supervised training. Sock et al. [27] proposed a two-stage self-supervised method, which also used a differentiable renderer to establish pose consistency between rendered and real images. Beyond using image-level consistency for self-supervised pose estimation, Yang et al. [39] proposed a self-supervised network DSC-PoseNet based on dual-scale keypoint consistency. But it suffered dramatic performance degradation when there was occlusion. Wang et al. [33] revised [34] and proposed Self6D++, which used the pose estimation network GDR-Net [35] and noisy student training to improve accuracy and robustness. However, there still exists a gap between real images and rendered images by the differentiable renderer. And additionally, differentiable rendering is a computationally expensive process. Addressing these issues, this paper proposes a novel self-supervised object pose estimation by imposing a derived geometric constraint from camera poses, which would be described in detail in the following section." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 399, + 389, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 389, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 389, + 414 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 420, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 494 + ], + "type": "text", + "content": "In this section, we propose the SMOC-Net for self-supervised monocular object pose estimation. Firstly, the architecture of the proposed SMOC-Net is introduced. Then, we present the derived geometric constraint from camera poses and the camera-pose-guided refiner respectively. Finally, the total loss function is described." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 502, + 389, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 389, + 514 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 389, + 514 + ], + "type": "text", + "content": "3.1. Architecture" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 521, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 715 + ], + "type": "text", + "content": "The SMOC-Net is explored under a knowledge distillation framework, which contains a teacher model and a student model, and its architecture is shown in Fig. 1. As seen from this figure, an object detector is firstly used for extracting the object regions in the input images, and we simply use Yolo-v4 [1] here as the object detector as done in some existing object pose estimation works [33, 35]. The teacher model consists of a backbone estimation module and a camera-pose-guided refiner. The backbone estimation module is used to calculate an initial object pose estimation, and we simply use the existing method GDR-Net [35] as the backbone estimation module here. The camera-pose-guided refiner is explored to refine the initial object pose obtained from the backbone estimation module, by utilizing a derived geometric constraint from relative camera poses (called relative-pose constraint). The student model" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21309" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 70, + 258, + 242 + ], + "blocks": [ + { + "bbox": [ + 75, + 70, + 258, + 242 + ], + "lines": [ + { + "bbox": [ + 75, + 70, + 258, + 242 + ], + "spans": [ + { + "bbox": [ + 75, + 70, + 258, + 242 + ], + "type": "image", + "image_path": "bc1f2c704dca4d77b24dd7aa836eb1f72cdb9bad3c5ad6bfad6ac3daec4b018e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 287, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 295 + ], + "type": "text", + "content": "Figure 2. World, object and camera coordinate systems. For a 3D point " + }, + { + "bbox": [ + 46, + 251, + 287, + 295 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 251, + 287, + 295 + ], + "type": "text", + "content": ", its coordinates could be transformed from object/world coordinate systems to camera coordinate systems by corresponding absolute object/camera poses in the camera/world systems." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 316, + 286, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 286, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 286, + 352 + ], + "type": "text", + "content": "employs the same architecture as the backbone estimation module, and it gains knowledge from the teacher model by utilizing the same relative-pose constraint." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 286, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 286, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 286, + 590 + ], + "type": "text", + "content": "At the training stage, the proposed SMOC-Net is trained by utilizing both synthetic data [10] with labels and a set of un-annotated real multi-view images. Firstly, the backbone GDR-Net and the detector Yolo-v4 are trained singly by only utilizing the synthetic RGB data as done in [33, 34]. Then, the classic SfM (Structure from Motion) method COLMAP [5, 25, 26] is utilized to calculate the corresponding absolute camera poses from the training set of multiview real images, and the object detector is implemented for extracting object patches from the input real images. According to the calculated camera poses as well as the corresponding original real object patches, we could straightforwardly obtain a set of object patch pairs with pseudo relative camera poses (which could be calculated according to the obtained absolute camera poses). Next, unlike the existing works [33, 34, 39] that deal with each training image singly, the proposed method deals with pairs of training patches. Finally, the student model is trained with the set of augmented object patch pairs with pseudo relative poses for learning knowledge from the teacher model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 591, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 286, + 651 + ], + "type": "text", + "content": "At the testing stage, only the student module is used for predicting object pose from each monocular RGB image. In Sections 3.2 and 3.3, both the relative-pose constraint and the camera-pose-guided refiner would be introduced, respectively, in detail." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 659, + 186, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 186, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 186, + 670 + ], + "type": "text", + "content": "3.2. Relative-Pose Constraint" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": "Given a set of " + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 677, + 286, + 713 + ], + "type": "text", + "content": " object patch pairs with the corresponding absolute camera poses in the world coordinate system, we could obtain a geometric constraint on the object relative" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "pose (called relative-posed constraint) for each patch pair as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": "For an arbitrary pair of object patches, without loss of generality, let " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "i < j" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "i = 1, \\dots, N - 1" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "j = i + 1, \\dots, N" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": ") denote the indices of the two patches. Then as shown in Fig. 2, for an arbitrary 3D object point, let " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "X_{ci}" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "X_{cj}" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": " denote its coordinates in the two camera coordinate systems corresponding to the two input patches, and let " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "X_o" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "inline_equation", + "content": "X_w" + }, + { + "bbox": [ + 305, + 96, + 545, + 191 + ], + "type": "text", + "content": " denote its coordinates in the object and world coordinate systems respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "type": "inline_equation", + "content": "[R_{oi}, t_{oi}]" + }, + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "type": "inline_equation", + "content": "[R_{oj}, t_{oj}]" + }, + { + "bbox": [ + 305, + 192, + 545, + 215 + ], + "type": "text", + "content": " represent the absolute object poses in the two camera systems. Then, we have" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 382, + 224, + 545, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 224, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 382, + 224, + 545, + 236 + ], + "type": "interline_equation", + "content": "X _ {c i} = R _ {o i} X _ {o} + t _ {o i}, \\tag {1}", + "image_path": "9695d7375c309747204d726eceeb73e4141ad666552e0ebfeb566f2105b8f3f6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 382, + 239, + 545, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 239, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 382, + 239, + 545, + 251 + ], + "type": "interline_equation", + "content": "X _ {c j} = R _ {o j} X _ {o} + t _ {o j}. \\tag {2}", + "image_path": "40efd40ae575cd0454741e00f66784dea2c16494c36b421cf53a09560a42854c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "type": "inline_equation", + "content": "[R_{ci}, t_{ci}]" + }, + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "type": "inline_equation", + "content": "[R_{cj}, t_{cj}]" + }, + { + "bbox": [ + 305, + 258, + 545, + 318 + ], + "type": "text", + "content": " represent the absolute camera poses in the world system, which are calculated by the SfM method COLMAP [5, 25]. It has to be pointed out that the calculated translations by COLMAP are not equal to the ground-truth translation, but up to a scale. Hence, we have" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 379, + 326, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 326, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 379, + 326, + 545, + 338 + ], + "type": "interline_equation", + "content": "X _ {c i} = R _ {c i} X _ {w} + \\lambda t _ {c i}, \\tag {3}", + "image_path": "ef6dbb796b892a7908c7f0f7129ca659e9022bbeef328ed1db80dcfaacc36cb8.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 379, + 341, + 545, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 341, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 379, + 341, + 545, + 354 + ], + "type": "interline_equation", + "content": "X _ {c j} = R _ {c j} X _ {w} + \\lambda t _ {c j}, \\tag {4}", + "image_path": "8bbafbf55e31b84caee37cf1cef2eb5e284bf3ed070048352eb97342777f7bd1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 361, + 544, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 361, + 544, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 544, + 383 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 361, + 544, + 383 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 361, + 544, + 383 + ], + "type": "text", + "content": " is a scale factor. According to Eqn. (1) and Eqn. (3), we have" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 347, + 391, + 545, + 405 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 391, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 347, + 391, + 545, + 405 + ], + "type": "interline_equation", + "content": "X _ {w} = R _ {c i} ^ {- 1} R _ {o i} X _ {o} + R _ {c i} ^ {- 1} \\left(t _ {o i} - \\lambda t _ {c i}\\right). \\tag {5}", + "image_path": "84e017f07f25744fbbced6dfc158fb2e8c831e2349a94c61d68feb27d973e564.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 412, + 487, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 412, + 487, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 412, + 487, + 424 + ], + "type": "text", + "content": "According to Eqn. (2) and Eqn. (4), we have" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 345, + 430, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 430, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 345, + 430, + 545, + 445 + ], + "type": "interline_equation", + "content": "X _ {w} = R _ {c j} ^ {- 1} R _ {o j} X _ {o} + R _ {c j} ^ {- 1} \\left(t _ {o j} - \\lambda t _ {c j}\\right). \\tag {6}", + "image_path": "2b17cd4473254000bca871d2424d5217d7ab24d2bed8fd6e7de659c1c42a031f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 452, + 487, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 487, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 487, + 464 + ], + "type": "text", + "content": "According to Eqn. (5) and Eqn. (6), we have" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 382, + 470, + 545, + 485 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 470, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 382, + 470, + 545, + 485 + ], + "type": "interline_equation", + "content": "R _ {c i} ^ {- 1} R _ {o i} = R _ {c j} ^ {- 1} R _ {o j}, \\tag {7}", + "image_path": "c245bbd60d4f00ed14c730795ce2b41ffa669208b8d79ebce32e480c8283be39.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 350, + 487, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 487, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 350, + 487, + 545, + 502 + ], + "type": "interline_equation", + "content": "R _ {c i} ^ {- 1} \\left(t _ {o i} - \\lambda t _ {c i}\\right) = R _ {c j} ^ {- 1} \\left(t _ {o j} - \\lambda t _ {c j}\\right). \\tag {8}", + "image_path": "38c0b37afc71ba292933d4c7466e25ba8b962205212874c30fee5994b501ecbe.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 509, + 428, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 428, + 520 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 428, + 520 + ], + "type": "text", + "content": "Eqn. (7) could be rewritten as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 383, + 526, + 545, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 526, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 383, + 526, + 545, + 542 + ], + "type": "interline_equation", + "content": "R _ {o i} R _ {o j} ^ {- 1} = R _ {c i} R _ {c j} ^ {- 1}. \\tag {9}", + "image_path": "cf790eabcf78a7dd76d6f453e853f538d6678853f5a68068ff45bce789cb48ac.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 548, + 428, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 428, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 428, + 559 + ], + "type": "text", + "content": "Eqn. (8) could be rewritten as" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 330, + 566, + 545, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 566, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 330, + 566, + 545, + 582 + ], + "type": "interline_equation", + "content": "R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} = \\lambda \\left(R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}\\right). \\tag {10}", + "image_path": "823137d37e7884b6e9163bc1af8fabd2deb31d4a8173d0e286f6e72170c0fc2d.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "type": "text", + "content": "To remove the scale factor " + }, + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 587, + 545, + 610 + ], + "type": "text", + "content": ", both sides of the Eqn. (10) are normalized as" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 318, + 615, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 615, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 318, + 615, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{| | R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} | | _ {2}} = \\frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{| | R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} | | _ {2}}, \\tag {11}", + "image_path": "18c4bb83cccf53fec01fed91cee65ace014959947316875d9f14322e454b74e1.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "||\\cdot ||_2" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": " norm. It is noted that once the camera poses " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "[R_{ci},t_{ci}]" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "inline_equation", + "content": "[R_{cj},t_{cj}]" + }, + { + "bbox": [ + 305, + 653, + 545, + 712 + ], + "type": "text", + "content": " are known, Eqn. (9) and Eqn. (11) provide constraints on relative object rotation and translation respectively. Hence, they are used together as our relative-pose constraint." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21310" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 289, + 183 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 183 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 183 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 183 + ], + "type": "image", + "image_path": "e3d85c0fb176e36c34ad2409e15e2ebe53cc6248cf8e757f6ceb5d6d35e625a0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "type": "text", + "content": "Figure 3. Architecture of the explored camera-pose-guided refiner. For a pair of 6D object poses " + }, + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\{P_{init - oi}^{*}, P_{init - oj}^{*}\\}" + }, + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "type": "text", + "content": ", they are first refined by DeepIM [15]. The refined poses " + }, + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{P}_{oi}, \\widetilde{P}_{oj}\\}" + }, + { + "bbox": [ + 46, + 190, + 287, + 247 + ], + "type": "text", + "content": " are then further updated using rotation increments and translation increments calculated according to the relative-pose constraint." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 266, + 209, + 278 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 209, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 209, + 278 + ], + "type": "text", + "content": "3.3. Camera-Pose-Guided Refiner" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "text", + "content": "In this section, we propose an iterative object pose refiner (called camera-pose-guided refiner), and its architecture is shown in Fig. 3. Given a set of " + }, + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "text", + "content": " object patch pairs with the corresponding absolute camera poses in the world coordinate system, and their corresponding initial object poses are estimated by the teacher backbone estimation module. We could further refine the initial poses of each patch pair by utilizing the above relative-pose constraint as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "type": "text", + "content": "At each iteration, the object poses are firstly refined by DeepIM [15], which is pre-trained on synthetic RGB data. Let " + }, + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\widetilde{P}_{oi} = [\\widetilde{R}_{oi},\\widetilde{t}_{oi}]" + }, + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\widetilde{P}_{oj} = [\\widetilde{R}_{oj},\\widetilde{t}_{oj}]" + }, + { + "bbox": [ + 46, + 381, + 287, + 464 + ], + "type": "text", + "content": " represent the refined absolute object poses of two input patches. Then, we further refine the absolute object rotations and translations of the two patches with the corresponding absolute camera poses, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "text", + "content": "Rotation Refinement Let " + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "inline_equation", + "content": "R_{ij} = R_{ci}R_{cj}^{-1}" + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "text", + "content": " denotes the relative camera rotation of two camera systems. In the rotation refinement, we seek to apply slight increments to the object rotations " + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{R}_{oi},\\widetilde{R}_{oj}\\}" + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "text", + "content": ". At each iteration, let " + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "inline_equation", + "content": "\\{\\Delta R_{oi},\\Delta R_{oj}\\}" + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "text", + "content": " represent the referred slight increments. Then, the object rotations would be updated as " + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{R}_{oi}\\Delta R_{oi},\\widetilde{R}_{oj}\\Delta R_{oj}\\}" + }, + { + "bbox": [ + 46, + 464, + 287, + 561 + ], + "type": "text", + "content": ". According to the relative rotation constraint in Eqn. (9), we have the following constraint equation:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 568, + 287, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 568, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 116, + 568, + 287, + 583 + ], + "type": "interline_equation", + "content": "\\Delta R _ {o i} ^ {- 1} \\Delta R _ {i j} \\Delta R _ {o j} = E, \\tag {12}", + "image_path": "a0603daba8f376df8316a305272e957d35c3d533613f231bdc999b09af875601.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\Delta R_{ij} = \\widetilde{R}_{oi}^{-1}R_{ij}\\widetilde{R}_{oj}" + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "text", + "content": ". This is an under-constrained equation whose solution is not unique, hence, an auxiliary condition " + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\Delta R_{oi}^{-1} = \\Delta R_{oj}" + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "text", + "content": " is introduced for guaranteeing a unique solution, considering that both the increments " + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\Delta R_{oi}" + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\Delta R_{oj}" + }, + { + "bbox": [ + 46, + 590, + 288, + 688 + ], + "type": "text", + "content": " at each iteration change slightly. Then, considering that Eqn. (12) is a nonlinear equation which is hard to solve, we compute the approximate solution by solving the following minimization problem:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 695, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 695, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 91, + 695, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\min _ {\\Delta R _ {o i}, \\Delta R _ {o j}} | | \\omega (\\Delta R _ {o i} ^ {- 1} \\Delta R _ {i j} \\Delta R _ {o j}) | | _ {2} ^ {2}, \\tag {13}", + "image_path": "6dd4419c7de0c59127decbbf6c24640650a6ce97bfe4be3c9de6001462c3602c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\omega(R)" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " is the axis-angle representation of 3D rotation " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{\\Delta \\omega_{oi}, \\Delta \\omega_{oj}\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " denote the axis-angle representation of " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\{\\Delta R_{oi}, \\Delta R_{oj}\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\Delta \\omega_{ij}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " denote the axis-angle representation of " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\Delta R_{ij}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": ". The concatenation of " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\Delta \\omega_{oi}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\Delta \\omega_{oj}" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " into a " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "6 \\times 1" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": " vector is denoted as " + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\Delta \\Omega" + }, + { + "bbox": [ + 305, + 72, + 545, + 144 + ], + "type": "text", + "content": ". Therefore, our problem is to solve the following minimization problem:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 388, + 152, + 545, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 152, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 388, + 152, + 545, + 171 + ], + "type": "interline_equation", + "content": "\\min _ {\\Delta \\Omega} \\| r _ {i j} (\\Delta \\Omega) \\| _ {2} ^ {2}, \\tag {14}", + "image_path": "008066e11a316a901a7827061050a99513776d0992f7bacabf3daeaa6d99367c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 179, + 334, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 179, + 334, + 189 + ], + "spans": [ + { + "bbox": [ + 306, + 179, + 334, + 189 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 323, + 200, + 545, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 200, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 323, + 200, + 545, + 214 + ], + "type": "interline_equation", + "content": "r _ {i j} (\\Delta \\Omega) = \\omega (R (- \\Delta \\omega_ {o i}) R (\\Delta \\omega_ {i j}) R (\\Delta \\omega_ {o j})). \\tag {15}", + "image_path": "b8cb2f8765eb63d02af4dea022f1360a0735394224cf5754408fe36aeb38161e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 222, + 545, + 258 + ], + "type": "text", + "content": "Inspired by Avishek et al. [3], the above minimization problem is transformed to solve the following problem using quasi-Newton method:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 266, + 545, + 285 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 266, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 359, + 266, + 545, + 285 + ], + "type": "interline_equation", + "content": "\\min _ {\\Delta \\Omega} \\| r _ {i j} (\\mathbf {0}) + \\mathcal {J} r _ {i j} (\\mathbf {0}) ^ {T} \\Delta \\Omega \\| _ {2} ^ {2}. \\tag {16}", + "image_path": "909c5af2b4661d21b1e974048dd5a258300f64a679d09becab66ecd9ee6cf182.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 293, + 518, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 518, + 305 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 518, + 305 + ], + "type": "text", + "content": "It is equivalent to solve a linear system of equations:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 374, + 313, + 545, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 313, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 374, + 313, + 545, + 327 + ], + "type": "interline_equation", + "content": "J r _ {i j} (\\mathbf {0}) ^ {T} \\Delta \\Omega = - r _ {i j} (\\mathbf {0}), \\tag {17}", + "image_path": "282653047301f5385b7afe50f5e8fe0fb5d08499d994aab9f146374c179e6e89.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "inline_equation", + "content": "Jr_{ij}(\\mathbf{0})" + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "text", + "content": " is the Jacobian of " + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "inline_equation", + "content": "r_{ij}(\\Delta \\Omega)" + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "text", + "content": " at the current point " + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "inline_equation", + "content": "\\Delta \\Omega = \\mathbf{0}" + }, + { + "bbox": [ + 305, + 336, + 545, + 360 + ], + "type": "text", + "content": ", and" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 325, + 368, + 545, + 406 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 368, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 325, + 368, + 545, + 406 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} {J r _ {i j} (\\mathbf {0}) ^ {T}} \\approx {\\frac {| | \\Delta \\omega_ {i j} | | _ {2}}{2} \\cot (\\frac {| | \\Delta \\omega_ {i j} | | _ {2}}{2}) [ I - I ]} \\\\ \\approx [ I - I ]. \\tag {18} \\\\ \\end{array}", + "image_path": "3131c2ad6987e7291bb9949b235b17412ce7364fe9897e88fd193d2ab4eacb3c.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 415, + 482, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 415, + 482, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 415, + 482, + 426 + ], + "type": "text", + "content": "Therefore, the final approximate solution is" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 367, + 435, + 545, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 435, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 367, + 435, + 545, + 459 + ], + "type": "interline_equation", + "content": "\\Delta \\omega_ {o i} = - \\Delta \\omega_ {o j} = - \\frac {\\Delta \\omega_ {i j}}{2}, \\tag {19}", + "image_path": "42372fdaaf8a365d9dbb52cf7af5d0c2618efa7219dd19a60ae5e8f7489ecc80.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 361, + 460, + 545, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 460, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 361, + 460, + 545, + 483 + ], + "type": "interline_equation", + "content": "\\Delta R _ {o i} = \\Delta R _ {o j} ^ {- 1} = R \\left(- \\frac {\\Delta \\omega_ {i j}}{2}\\right). \\tag {20}", + "image_path": "2b990ad6c1e4f1022c2a8135ce7758e66e90fff6047f1ccb8e882cd7a09f7c27.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "text", + "content": "Translation Refinement In the translation refinement, we seek to apply slight increments to object translations " + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{t}_{oi},\\widetilde{t}_{oj}\\}" + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "text", + "content": ". At each iteration, let " + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\{\\Delta t_{oi},\\Delta t_{oj}\\}" + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "text", + "content": " represent the referred slight increments. Then, the object translations would be updated as " + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{t}_{oi} + \\Delta t_{oi},\\widetilde{t}_{oj} + \\Delta t_{oj}\\}" + }, + { + "bbox": [ + 306, + 491, + 545, + 574 + ], + "type": "text", + "content": ". According to the relative translation constraint in Eqn. (11), we have the following constraint equation:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 309, + 582, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 582, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 309, + 582, + 545, + 624 + ], + "type": "interline_equation", + "content": "\\frac {R _ {c i} ^ {- 1} \\left(\\widetilde {t} _ {o i} + \\Delta t _ {o i}\\right) - R _ {c j} ^ {- 1} \\left(\\widetilde {t} _ {o j} + \\Delta t _ {o j}\\right)}{\\left| \\left| R _ {c i} ^ {- 1} \\left(\\widetilde {t} _ {o i} + \\Delta t _ {o i}\\right) - R _ {c j} ^ {- 1} \\left(\\widetilde {t} _ {o j} + \\Delta t _ {o j}\\right) \\right| \\right| _ {2}} - \\frac {t _ {i j}}{\\left| \\left| t _ {i j} \\right| \\right| _ {2}} = \\mathbf {0}, \\tag {21}", + "image_path": "430cede89f34f63e27f10b1f371508caea15db8272c502049751c0627ce69857.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 624, + 333, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 624, + 333, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 624, + 333, + 634 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 375, + 634, + 545, + 650 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 634, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 375, + 634, + 545, + 650 + ], + "type": "interline_equation", + "content": "t _ {i j} = R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}. \\tag {22}", + "image_path": "bcecff700ffc64b2daab7a8660d6f12c591ce1a64f5ac2068402fe26377293e8.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 654, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 677 + ], + "type": "text", + "content": "It is approximate to solve the following linear system of equations:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 320, + 685, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 685, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 320, + 685, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\frac {R _ {c i} ^ {- 1} \\Delta t _ {o i} - R _ {c j} ^ {- 1} \\Delta t _ {o j}}{\\left| \\left| t _ {i j} ^ {*} \\right| \\right| _ {2}} + \\frac {t _ {i j} ^ {*}}{\\left| \\left| t _ {i j} ^ {*} \\right| \\right| _ {2}} - \\frac {t _ {i j}}{\\left| \\left| t _ {i j} \\right| \\right| _ {2}} = \\mathbf {0}, \\tag {23}", + "image_path": "58d2302488ad6a01c6d08df49d68c3c457df67b5bdd5ce96b359c4e809cac287.jpg" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21311" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 73, + 76, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 73, + 76, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 73, + 76, + 83 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 92, + 287, + 109 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 92, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 116, + 92, + 287, + 109 + ], + "type": "interline_equation", + "content": "t _ {i j} ^ {*} = R _ {c i} ^ {- 1} \\widetilde {t} _ {o i} - R _ {c j} ^ {- 1} \\widetilde {t} _ {o j}. \\tag {24}", + "image_path": "6313b64af5aff1999af014a4e4601d614acf46d8a5ac5aabb1063c2d5f44a7a7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "spans": [ + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": "This is also an under-constrained equation, hence, an auxiliary condition " + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "inline_equation", + "content": "\\Delta t_{oi} = -\\Delta t_{oj}" + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": " is introduced, considering that both the increments " + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "inline_equation", + "content": "\\Delta t_{oi}" + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "inline_equation", + "content": "\\Delta t_{oj}" + }, + { + "bbox": [ + 47, + 117, + 287, + 165 + ], + "type": "text", + "content": " at each iteration change slightly. So the final approximate solution is" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 52, + 173, + 287, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 173, + 287, + 201 + ], + "spans": [ + { + "bbox": [ + 52, + 173, + 287, + 201 + ], + "type": "interline_equation", + "content": "\\Delta t _ {o i} = - \\Delta t _ {o j} = \\left(R _ {c i} ^ {- 1} + R _ {c j} ^ {- 1}\\right) ^ {- 1} \\left(\\frac {\\left\\| t _ {i j} ^ {*} \\right\\| _ {2}}{\\left\\| t _ {i j} \\right\\| _ {2}} t _ {i j} - t _ {i j} ^ {*}\\right). \\tag {25}", + "image_path": "fb56dd820906fcb77a637a333f9a3d396fbd27a71ad77dca21aacca0fb99e011.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "type": "text", + "content": "Finally, the absolute object poses are further updated by utilizing both rotation increments and translation increments. Let " + }, + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "type": "inline_equation", + "content": "P_{oi}^{*}" + }, + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "type": "inline_equation", + "content": "P_{oj}^{*}" + }, + { + "bbox": [ + 47, + 209, + 287, + 256 + ], + "type": "text", + "content": " represent the updated object poses. Then, we have" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 264, + 287, + 280 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 264, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 104, + 264, + 287, + 280 + ], + "type": "interline_equation", + "content": "P _ {o i} ^ {*} = \\left[ \\widetilde {R} _ {o i} \\Delta R _ {o i}, \\widetilde {t} _ {o i} + \\Delta t _ {o i} \\right], \\tag {26}", + "image_path": "0966ff49fbcd76ca6fd712a2b6cf43a94c60bfd7a0adacbc8a8332baf9d33a58.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 281, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 281, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 104, + 281, + 287, + 298 + ], + "type": "interline_equation", + "content": "P _ {o j} ^ {*} = \\left[ \\widetilde {R} _ {o j} \\Delta R _ {o j}, \\widetilde {t} _ {o j} + \\Delta t _ {o j} \\right]. \\tag {27}", + "image_path": "879efb741db45d11ed115abcffbc4b167fb5602def3bea7dc19d3bc3d74ce675.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 306, + 135, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 135, + 317 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 135, + 317 + ], + "type": "text", + "content": "3.4. Loss Function" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "text", + "content": "The total loss function " + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{self}}" + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "text", + "content": " of the proposed SMOC-Net contains three loss terms: a rotation loss " + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{rot}}" + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "text", + "content": ", a translation loss " + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{trans}}" + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "text", + "content": " and a point matching loss " + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{pm}}^{\\text{pair}}" + }, + { + "bbox": [ + 47, + 324, + 287, + 361 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 361, + 287, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 383 + ], + "type": "text", + "content": "According to the relative rotation constraint, the rotation loss is defined as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 108, + 393, + 287, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 393, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 108, + 393, + 287, + 408 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r o t} = \\left| \\left| \\omega \\left(R _ {o j} R _ {o i} ^ {- 1} R _ {i j}\\right) \\right| \\right| _ {2}, \\tag {28}", + "image_path": "b3e45f8df306d80d9b74655be1f0896dd7d15586017dbbba820c3a1b7b557df1.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 416, + 141, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 141, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 141, + 430 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 416, + 141, + 430 + ], + "type": "inline_equation", + "content": "R_{ij} = R_{ci}R_{cj}^{-1}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 430, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 287, + 464 + ], + "type": "text", + "content": "According to the relative translation constraint, the translation loss is defined by measuring the angle of two relative translation vectors as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 110, + 475, + 287, + 489 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 475, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 110, + 475, + 287, + 489 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t r a n s}} = \\mathrm {a c o s} \\left(t _ {c, i j} \\cdot t _ {o, i j}\\right), \\tag {29}", + "image_path": "bf3a514c7c886fd42c55942c2d10d1b25f1b8b1838918deb9c282b12e644e452.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 497, + 211, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 497, + 211, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 497, + 211, + 509 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 497, + 211, + 509 + ], + "type": "inline_equation", + "content": "\\mathrm{acos}(\\cdot)" + }, + { + "bbox": [ + 47, + 497, + 211, + 509 + ], + "type": "text", + "content": " is the arccos function and" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 517, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 517, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 104, + 517, + 287, + 548 + ], + "type": "interline_equation", + "content": "t _ {c, i j} = \\frac {R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j}}{\\left| \\left| R _ {c i} ^ {- 1} t _ {c i} - R _ {c j} ^ {- 1} t _ {c j} \\right| \\right| _ {2}}, \\tag {30}", + "image_path": "2be8f086544ecb3851196dbbcc8e873bea26f805cc1759a88f328513477b41f9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 551, + 287, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 551, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 104, + 551, + 287, + 582 + ], + "type": "interline_equation", + "content": "t _ {o, i j} = \\frac {R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j}}{\\left| \\left| R _ {c i} ^ {- 1} t _ {o i} - R _ {c j} ^ {- 1} t _ {o j} \\right| \\right| _ {2}}. \\tag {31}", + "image_path": "84f82cec44c09b80eab6e2f6b02779196a49dadeedaebd72a93a1a6087efe609.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 287, + 625 + ], + "type": "text", + "content": "Inspired by [15, 33, 35], the point matching loss for geometrically aligning the predicted poses and the pseudo pose labels is used:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 52, + 635, + 287, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 635, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 52, + 635, + 287, + 656 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p m} = \\min _ {R _ {o} \\in s y m X \\in \\mathcal {M}} \\operatorname {a v g} \\left| \\left| \\left(R _ {o} ^ {*} X + t _ {o} ^ {*}\\right) - \\left(R _ {o} X + t _ {o}\\right) \\right| \\right| _ {1}, \\tag {32}", + "image_path": "6005a92e9ac67bc5ffaf773518f075df59eef65ec32bba2666b4f6cbb20abb77.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "||\\cdot ||_1" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " norm, " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\text{sym}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " is a pool of symmetric rotations including the given rotation to deal with symmetric objects following [21], " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " represents the CAD object point cloud given in the evaluation datasets, " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "R_o" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "(t_{ox}, t_{oy})" + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "t_{oz}" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "are disentangled from " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "P_{o} = [R_{o}, t_{o}]" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "P_{o}^{*} = [R_{o}^{*}, t_{o}^{*}]" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " denotes the pseudo pose label. Since the proposed method deals with pairs of training patches, the sum of two point matching losses is eventually used:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 375, + 126, + 545, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 126, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 375, + 126, + 545, + 142 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p m} ^ {\\text {p a i r}} = \\mathcal {L} _ {p m, i} + \\mathcal {L} _ {p m, j}. \\tag {33}", + "image_path": "ccfb5cc32cb561fd15e7a8bd67a80c7112caf17987bbac8389587387b9a78b37.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 147, + 545, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 147, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 305, + 147, + 545, + 170 + ], + "type": "text", + "content": "Accordingly, the total loss function " + }, + { + "bbox": [ + 305, + 147, + 545, + 170 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{self}" + }, + { + "bbox": [ + 305, + 147, + 545, + 170 + ], + "type": "text", + "content": " is the weighted sum of the above three loss terms as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 348, + 177, + 545, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 177, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 348, + 177, + 545, + 192 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s e l f} = \\mathcal {L} _ {r o t} + \\lambda_ {1} \\mathcal {L} _ {t r a n s} + \\lambda_ {2} \\mathcal {L} _ {p m} ^ {\\text {p a i r}}, \\tag {34}", + "image_path": "f5a9847fa5a237e59532e43ee881a06fa04e421c870d98dc55b912be02f23b6e.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "spans": [ + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 306, + 198, + 486, + 209 + ], + "type": "text", + "content": " are two weight parameters." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 219, + 386, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 219, + 386, + 232 + ], + "spans": [ + { + "bbox": [ + 306, + 219, + 386, + 232 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 239, + 368, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 239, + 368, + 250 + ], + "spans": [ + { + "bbox": [ + 306, + 239, + 368, + 250 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 257, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 257, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 257, + 545, + 316 + ], + "type": "text", + "content": "Synthetic PBR Dataset [10] As the physically-based renderer has been proven to perform better than OpenGL renderers [13, 34], we use the synthetic PBR data from [10] to train the 2D object detector Yolov4 [1] and the backbone pose estimation module GDR-Net [35]." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "type": "text", + "content": "LineMOD [8] is a standard benchmark for 6D object pose estimation, consisting of 13 sequences. And there are about " + }, + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "type": "inline_equation", + "content": "1.2\\mathrm{k}" + }, + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "type": "text", + "content": " images in each sequence. As done in [13], we use " + }, + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 305, + 316, + 545, + 365 + ], + "type": "text", + "content": " of images for training and the remaining for testing." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 365, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 413 + ], + "type": "text", + "content": "Occluded-LineMOD [2] is generated from benchvise sequence of the LineMOD dataset, and it contains 1214 images. As done in [33], we sample data for testing using the BOP split [9] and use the remaining data for training." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 419, + 364, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 419, + 364, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 419, + 364, + 430 + ], + "type": "text", + "content": "4.2. Metrics" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 437, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 533 + ], + "type": "text", + "content": "We evaluate the performance using the common Average Distance of Distinguishable Model Points (ADD) metric [8], which measures the distance between 3D object model point clouds transformed by the predicted pose and the corresponding ground-truth. A pose is considered correct when the distance is less than " + }, + { + "bbox": [ + 305, + 437, + 545, + 533 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 437, + 545, + 533 + ], + "type": "text", + "content": " of the diameter of a 3D model. ADD-S is used [37] for symmetric objects by computing the closest point distance." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 540, + 438, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 438, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 438, + 552 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "text", + "content": "Our method is implemented by Pytorch, and all experiments are conducted on an NVIDIA 3080 GPU. The camera poses are calculated using a classic SfM method COLMAP [25,26,36] before training. We replace ResNet-34 [7] backbone of GDR-Net [35] with ResNeSt-50 [6] backbone as done in [33]. The learning rate is set to " + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "text", + "content": ". The strategy of pre-training with synthetic data is the same as [33]. During the self-supervised training, we train the student pose estimation network for 30 epochs using un-annotated real RGB data, and the batch size is set to 8. In each epoch, all " + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "text", + "content": " training images are randomly divided into " + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "inline_equation", + "content": "N/2" + }, + { + "bbox": [ + 305, + 558, + 545, + 712 + ], + "type": "text", + "content": " image pairs. During inference, only the student pose estimation network is used." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21312" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 70, + 520, + 202 + ], + "blocks": [ + { + "bbox": [ + 74, + 70, + 520, + 202 + ], + "lines": [ + { + "bbox": [ + 74, + 70, + 520, + 202 + ], + "spans": [ + { + "bbox": [ + 74, + 70, + 520, + 202 + ], + "type": "table", + "html": "
Training MannerMethodsTraining dataApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
Fully-supervisionDPOD [41]R53.395.290.094.160.497.466.099.693.864.999.888.171.482.6
PVNet [22]43.699.986.995.579.396.452.699.295.781.998.999.392.486.3
CDPN [17]64.497.891.795.583.896.266.899.799.685.897.997.990.889.9
Self-supervisionAAE [31]S4.222.932.937.018.724.85.981.046.218.235.161.236.332.6
MHP [20]11.966.222.459.826.944.68.355.754.615.560.8-34.438.8
DPOD [41]35.159.415.548.828.159.325.651.234.617.784.745.020.940.5
Self6D [34]S+R−+D38.975.236.965.657.967.019.699.094.116.277.968.250.158.9
Self6D++ [33]75.494.997.099.586.698.968.399.096.141.999.498.994.388.5
DSC-PoseNet [39]S+R−35.983.151.561.045.068.027.689.252.526.456.368.746.454.7
Self6D++ [33]76.091.697.199.885.698.856.591.092.235.499.597.491.885.6
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
", + "image_path": "90254fec289e65cff1a2bde61d08f0a1e0fa35e375cae8685caf4cca9abf9725.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 108, + 255, + 486, + 365 + ], + "blocks": [ + { + "bbox": [ + 46, + 211, + 545, + 244 + ], + "lines": [ + { + "bbox": [ + 46, + 211, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 545, + 244 + ], + "type": "text", + "content": "Table 1. Comparison with state-of-the-art methods on LineMOD dataset. The table reports results for the Average Recall (%) of ADD(-S). All results except ours and DSC-PoseNet are copied from [33]. The best RGB based label-free method is marked in bold. R: annotated real RGB data. S: synthetic RGB data. " + }, + { + "bbox": [ + 46, + 211, + 545, + 244 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{-}" + }, + { + "bbox": [ + 46, + 211, + 545, + 244 + ], + "type": "text", + "content": " : unannotated real RGB data. D: depth data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 108, + 255, + 486, + 365 + ], + "lines": [ + { + "bbox": [ + 108, + 255, + 486, + 365 + ], + "spans": [ + { + "bbox": [ + 108, + 255, + 486, + 365 + ], + "type": "table", + "html": "
MethodsTraining dataApeCanCatDrilDuckEb.GlueHolepMean
DPOD [41]S2.34.01.210.57.24.412.97.56.3
CDPN [17]20.015.116.45.022.236.127.924.020.8
CosyPose [14]44.069.942.167.547.824.460.017.546.7
Self6D [34]S+R-+D13.743.218.732.514.457.854.322.032.1
Self6D++ [33]59.496.560.892.030.651.188.638.364.7
DSC-PoseNet [39]S+R-13.915.119.440.56.938.924.016.321.9
Self6D++ [33]57.795.052.690.526.745.087.123.559.8
OURS60.094.559.193.037.248.389.325.063.3
", + "image_path": "5f7dc2ee73fcea268272d97af0302d8a99b34943235b018c6f97c71213b9a848.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 144, + 373, + 447, + 383 + ], + "lines": [ + { + "bbox": [ + 144, + 373, + 447, + 383 + ], + "spans": [ + { + "bbox": [ + 144, + 373, + 447, + 383 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art methods on Occluded-LineMOD dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 404, + 185, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 404, + 185, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 404, + 185, + 417 + ], + "type": "text", + "content": "4.4. Comparative Evaluation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 425, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 604 + ], + "type": "text", + "content": "Comparisons on LineMOD. Here, we evaluate the proposed SMOC-Net on the LineMOD dataset in comparison to some state-of-the-art methods, including three fully-supervised methods (DPOD [41], PVNet [22], CDPN [17]), three self-supervised methods that are trained with only synthetic data (AAE [31], MHP [20], DPOD [41]), one self-supervised method that is trained with both synthetic data and un-annotated real images (DSC-PoseNet [39]), and two self-supervised methods that are trained with synthetic data + un-annotated real images + depth images (Self6D [34], Self6D++ [33]). In addition, for a more comprehensive comparison, we also compare our method with Self6D++ [33] trained with synthetic data and un-annotated real images but without depth images. The corresponding results are reported in Table 1." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "As seen from Table 1, the fully-supervised methods DPOD, PVNet, CDPN perform better than most of the existing self-supervised methods in most cases, mainly because annotated real images with object poses are used for training these fully-supervised methods. Moreover, the proposed SMOC-Net achieves a better performance than all the comparative methods (regardless of whether these methods are trained in an either fully-supervised or self-supervised manner), because of the derived relative-pose" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 305, + 405, + 545, + 441 + ], + "type": "text", + "content": "constraint and the designed camera-posed-refiner in SMOC-Net. These results demonstrate the effectiveness of the proposed method for 6D object pose estimation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "content": "Comparisons on Occluded-LineMOD. We evaluate the proposed SMOC-Net on the Occluded-LineMOD dataset where there exist many occlusions, in comparison to DPOD [41], CDPN [17], CosyPose [14], Self6D [34], Self6D++ [33], and DSC-PoseNet [39]. The corresponding results are reported in Table 2. As seen from this table, the overall average recalls of most of the comparative methods are lower than " + }, + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "content": " or even lower. Among all the comparative methods, Self6D++ trained with 3 categories of data (synthetic, unannotated real images, and depth images) performs the best, mainly because it uses additional scene depth images at the training stage, which contain 3D spatial information and are more effective in capturing the 3D spatial relationship between adjacent objects. Moreover, the proposed SMOC-Net achieves a slightly lower performance than Self6D++ that is trained with 3 categories of data (synthetic, unannotated real images, and depth images). However, the SMOC-Net significantly outperforms Self6D++ that is trained without depth images in the same manner as SMOC-Net, and it also performs significantly better than the other comparative methods. These results demonstrate that the proposed method could effectively handle the oc" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21313" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 72, + 70, + 523, + 140 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 523, + 140 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 523, + 140 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 523, + 140 + ], + "type": "table", + "html": "
MethodApeBv.CamCanCatDrilDuckEb.GlueHolepIronLampPhoneMean
w/o Lrot82.195.097.099.894.1100.072.698.599.340.399.996.295.290.0
w/o Ltrans84.392.995.999.893.999.777.098.798.747.5100.098.194.390.8
w/o refiner*88.396.096.699.792.8100.070.498.099.042.2100.097.394.390.4
OURS-50.799.489.597.280.098.726.381.191.241.998.898.964.477.5
OURS85.696.797.299.995.0100.076.098.399.245.699.998.994.091.3
", + "image_path": "1d82a17e163d1960ca40aa62c4d57cefeabceb65a08af99f9b4e160e7398ad3c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 78, + 190, + 257, + 321 + ], + "blocks": [ + { + "bbox": [ + 78, + 190, + 257, + 321 + ], + "lines": [ + { + "bbox": [ + 78, + 190, + 257, + 321 + ], + "spans": [ + { + "bbox": [ + 78, + 190, + 257, + 321 + ], + "type": "image", + "image_path": "7fb34a57e5ba78503a708c4d7add4fd62ecabada6abca38f529e78f48c1d8da7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 329, + 288, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 373 + ], + "type": "text", + "content": "Figure 4. Visualized results on Occluded-LineMOD dataset. Top: results of DSC-PoseNet. Middle: results of Self6D++. Bottom: results of SMOC-Net. Red: the ground-truth object poses. Green: the results after self-supervised training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 440 + ], + "type": "text", + "content": "clusion case. Fig. 4 illustrates the visualized results of Self6D++, DSC-PoseNet and SMOC-Net, which are all trained with synthetic data and un-annotated real images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 459, + 141, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 459, + 141, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 459, + 141, + 472 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "content": "To evaluate the effects of the losses " + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rot},\\mathcal{L}_{trans}" + }, + { + "bbox": [ + 46, + 481, + 287, + 518 + ], + "type": "text", + "content": " and the camera-pose-guided refiner, we conduct the ablation study on LineMOD and the results are reported in Table 3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "content": "Firstly, we respectively disable the rotation loss " + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rot}" + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "content": " and the translation loss " + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{trans}" + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "content": ". The corresponding models are denoted as w/o " + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rot}" + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "content": " and w/o " + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{trans}" + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "content": " respectively. As shown in Table 3, the pose accuracy decreases when disabling each of them. These results demonstrate that both of the rotation loss and the translation loss are effective to improve the pose accuracy for our method. Then, we replace the proposed camera-pose-guided refiner with DeepIM [15], and the corresponding model is denoted as w/o refiner*. The performance of w/o refiner* is significantly lower than the complete SMOC-Net. In addition, we also train our model with only synthetic data, which is denoted as OUR-. The overall average recall of OUR" + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "inline_equation", + "content": "^{-}" + }, + { + "bbox": [ + 46, + 521, + 287, + 715 + ], + "type": "text", + "content": " is much lower than the complete SMOC-Net, demonstrating that the proposed self-supervised object pose estimation method could significantly improve the pose accuracy." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 190, + 538, + 232 + ], + "blocks": [ + { + "bbox": [ + 46, + 148, + 545, + 171 + ], + "lines": [ + { + "bbox": [ + 46, + 148, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 545, + 171 + ], + "type": "text", + "content": "Table 3. Ablation study on LineMOD dataset. Individual loss and pose refiner are evaluated on LineMOD. * : the proposed camera-posedguided refiner is replaced with DeepIM [15]. Ours: our results trained on synthetic data. The best results are marked in bold." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 190, + 538, + 232 + ], + "lines": [ + { + "bbox": [ + 315, + 190, + 538, + 232 + ], + "spans": [ + { + "bbox": [ + 315, + 190, + 538, + 232 + ], + "type": "table", + "html": "
MethodTraining/Rendering Time (s)Total Time (s)
Self6D++ [33]37/291110
OURS8/-283
", + "image_path": "4d9da7f496f26b3e09c4fda9819280497fcd97d11cabdeaa8476d9840460b876.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 240, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 262 + ], + "type": "text", + "content": "Table 4. Comparison of the training times in one epoch and the total times on LineMOD." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 281, + 469, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 469, + 294 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 469, + 294 + ], + "type": "text", + "content": "4.6. Comparison of Training Time" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 545, + 334 + ], + "type": "text", + "content": "Here, we compare our training time on the LineMOD dataset with Self6D++ [33], a state-of-the-art differentiable-renderer-based method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 546, + 467 + ], + "type": "text", + "content": "Both the training times in one epoch and the total times by the two methods are reported in Table 4. As seen in Table 4, the training time of Self6D++ in one epoch is 37 seconds, but Self6D++ spends 29 seconds on rendering, indicating that rendering is a main time-consuming part for such a differentiable-renderer-based method. Moreover, the training time of our method in one epoch is much less than Self6D++, and the total training time (for both SfM and network training) of our method is also much less than Self6D++. These results demonstrate the priority of the proposed method in model training." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 478, + 378, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 378, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 378, + 490 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we have proposed the SMOC-Net for self-supervised monocular object pose estimation by utilizing the predicted camera poses from un-annotated real images. Unlike most of the existing self-supervised methods that rely on differentiable renderer for providing additional constraint on object pose prediction, the SMOC-Net utilizes the derived relative-pose constraint for boosting the performance on object pose estimation. We also propose a pose refiner for further refining the initial object pose with the derived relative-pose constraint. The experimental results on two public datasets demonstrate the effectiveness of the proposed method even when dealing with strong occlusions. Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant Nos. U1805264 and 61991423), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB32050100), the Beijing Municipal Science and Technology Project (Grant No. Z211100011021004)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21314" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao. 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In ICCV, pages 1941-1950, 2019. 2, 7" + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "21316" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_content_list.json b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..68ed8078814d22ab657ff455bdcfa907d8d9b187 --- /dev/null +++ b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_content_list.json @@ -0,0 +1,1904 @@ +[ + { + "type": "text", + "text": "SMPCov: Self-moving Point Representations for Continuous Convolution", + "text_level": 1, + "bbox": [ + 107, + 128, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sanghyeon Kim $^{1}$ Eunbyung Park $^{1,2*}$ $^{1}$ Department of Electrical and Computer Engineering, Sungkyunkwan University \n $^{2}$ Department of Artificial Intelligence, Sungkyunkwan University", + "bbox": [ + 163, + 179, + 805, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv", + "bbox": [ + 75, + 301, + 472, + 680 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 710, + 209, + 726 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There has been a recent surge of interest in representing the convolutional kernel as a function over a continuous input domain. It can easily handle irregularly sampled data both in time [1, 59] and space [61, 65], overcoming the drawbacks of the discrete convolution operating only on discretized sampled data with pre-defined resolutions and grids. With the progress in modeling and training continuous kernels, it has enjoyed great success in many practical scenarios, such as 3D point cloud classification and segmen", + "bbox": [ + 75, + 737, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tation [36,41,52,58,64], image super resolution [57], object tracking [10], to name a few. Furthermore, the recent trends of using large convolutional kernels with strong empirical results urge us to develop a more efficient way to implement it [13,32], and the continuous convolution will be a promising candidate because of its capability to readily construct arbitrarily large receptive fields [44, 45].", + "bbox": [ + 496, + 268, + 893, + 377 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the dominant approaches to modeling the continuous kernel is to use a particular type of neural network architecture, taking as inputs low-dimensional input coordinates and generating the kernel values [44, 45], known as neural fields [38, 49] or simply MLPs. Using neural fields to represent the kernels, we can query kernel values at arbitrary resolutions in parallel and construct the large kernels with a fixed parameter budget, as opposed to the conventional discrete convolutions requiring more parameters to enlarge receptive fields. Thanks to recent advances to overcome the spectral bias on training neural fields [49], they can also represent functions with high-frequency components, which enables learned kernels to capture fine details of input data.", + "bbox": [ + 496, + 378, + 893, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While promising in various tasks and applications, this approach has a few downsides. First, it incurs considerable computational burdens to already computation-heavy processes of training deep neural networks. Each training iteration involves multiple forward and backward passes of MLPs to generate kernels and update the parameters of MLPs. This additional complexity prevents it from being applied to large-scale problems, such as ImageNet-scale, since it needs deeper and wider MLP architectures to construct more complex kernels with more input and output channels. Although MLPs can generate larger sizes and numbers of kernels without adding more parameters, it has been known that the size of MLPs mainly determines the complexity of the functions they represent and, eventually, the performance of the CNNs.", + "bbox": [ + 496, + 595, + 895, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Furthermore, the kernels generated by an MLP depend heavily on the architectural priors. As a universal function approximator, a neural network with sufficient depth and width can express any continuous functions [25]. However, we have empirically observed strong evidence that the ar", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding authors", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10289", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chitecture of neural networks has played a significant role in many practical settings, suggesting that various architectural changes to the kernel-generating MLPs would significantly affect the performance of CNNs. Considering a large number of hyperparameters in training neural networks, adding more knobs to tune, e.g., activation functions, width, depth, and many architectural variations of MLPs., would not be a pragmatic solution for both machine learning researchers and practitioners.", + "bbox": [ + 75, + 90, + 470, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we aim to build continuous convolution kernels with negligible computational cost and minimal architectural priors. We propose to use moving point representations and implement infinite resolution by interpolating nearby moving points at arbitrary query locations. The moving points are the actual kernel parameters, and we connect the neighboring points to build continuous kernels. Recent techniques in neural fields literature inspire it, where they used grid or irregularly distributed points to represent features or quantities in questions (density or colors) for novel view synthesis [6, 50, 63, 66, 67]. The suggested approach only introduces minor computational costs (interpolation costs) and does not consist of neural networks (only point representations and interpolation kernels). Moreover, the spectral bias presented in training MLPs [43] does not exist in the suggested representation. Each point representation covers the local area of the input domain and is updated independently of each other, contrasted with MLPs, where updating each parameter would affect the entire input domain. Therefore, highly different values of nearby points can easily express high-frequency components of the function.", + "bbox": [ + 75, + 229, + 470, + 561 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The proposed method can also be more parameter efficient than the discrete convolution to construct the large kernels. Depending on the complexity of the kernels to be learned, a few numbers of points may be sufficient to cover a large receptive field (e.g., a unimodal function can be approximated by a single point). Many works have extensively exploited non-full ranks of the learned kernels to implement efficient convolutions or compress the models [32]. Our approach can likewise benefit from the presence of learned kernels with low-frequency components.", + "bbox": [ + 75, + 565, + 468, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct comprehensive experimental results to show the effectiveness of the proposed method. First, we demonstrate that moving point representations can approximate continuous functions very well in 1D and 2D function fitting experiments. Then, we test its ability to handle long-term dependencies on various sequential datasets. Finally, we also evaluate our model on 2D image data. Especially, we perform large-scale experiments on the ImageNet classification dataset (to our knowledge, it is the first attempt to use continuous convolution for such a large-scale problem). Our proposed method can be used as a drop-in replacement of convolution layers for all the above tasks without bells", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and whistles. The experimental results show that it consistently improves the performance of the prior arts.", + "bbox": [ + 498, + 90, + 890, + 122 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 500, + 135, + 645, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural fields and continuous convolution. Neural fields have recently emerged as an alternative neural network representation [49]. It is a field parameterized by a neural network, such as simple MLP, taking as low-dimensional coordinates input and generating quantity in questions. It has shown great success in various visual computing domains, such as novel view synthesis [38], 3D shape representation [37, 40], and data compression [17], to name a few. Since it is a function over a continuous input domain, it can produce outputs at arbitrary resolutions. Recent studies have exploited its continuous nature to model continuous kernels for CNNs [44, 45, 58]. [58] used an MLP architecture to implement the continuous kernel to handle irregularly sampled data, such as 3D point clouds. While successful, the descriptive power of the learned kernel is limited due to its bias toward learning low-frequency components. With the recent advances in overcoming the spectral bias [49], [45] has explored various activation functions to improve the performance of CNNs. To further improve, [44] proposed to learn the receptive field sizes and showed impressive performance on multiple tasks.", + "bbox": [ + 496, + 160, + 890, + 477 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also propose a method that can likewise be classified as a neural field. However, we implement a field without neural networks, using self-moving point representations and interpolation schemes. It significantly reduces the computational costs to compute the kernels during training compared to the conventional MLP-based methods. Furthermore, it removes the burden of numerous hyperparameter searches for a newly introduced neural network in the already complicated training procedure.", + "bbox": [ + 496, + 478, + 890, + 613 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Grid and point representations. Although MLP-based neural fields have succeeded in many tasks, they require substantial computational costs for training and inference, and the spectral bias presented in MLPs often degrades the performance. In order to reduce the computations and avoid the issues of using MLPs, classical grid-based representations have been adopted in the neural fields. Plenoxels [66] stores the coefficients of spherical harmonic in the 3D voxel structure and implements the infinite resolution via the interpolation methods, reducing the training time from days to minutes. Instant-NGP [39] further optimized the speed using a hash-based indexing algorithm. The combination of grid representations and MLPs has been extensively explored to find better solutions [6, 50].", + "bbox": [ + 496, + 613, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point representations have been recently suggested in neural fields to improve the shortcomings in grid-based representations, thanks to their flexibility and expressibility [63, 67]. They can generate outputs over a continuous input domain by interpolating neighboring points given a", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10290", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b454e824fac6acaa52a96315dd082ad4839d377c5eefe38d2e8943ce7b3a80b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 85, + 274, + 174 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/136124815209c9ed3e59d5ada63f91c00693466584c5963989b28c2b22e1ad53.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 339, + 85, + 591, + 175 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/54a805de77e88ee3e925eb04d9298226393faf1af58823f7dd98dc5dab133032.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 661, + 88, + 864, + 175 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5a28e083f89021db08bf615c23560bc5cc0591dd07833f9a53e2f4366529bcba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 186, + 245, + 277 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c3fa5883061529250fb77cb8fe4122653ea3ff782cc00a1a6be2285cbf3764c4.jpg", + "image_caption": [ + "Figure 1. A various methods for large kernel construction." + ], + "image_footnote": [], + "bbox": [ + 254, + 188, + 452, + 277 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f209bd801e10c314137a4609f4eeb4cb256fdab39285f826a66bb865c93e741.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 188, + 671, + 277 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b653ecc59508a8e5fc1d6471fe5c6116d8a89c4783ee6618498c8ef338e2e71e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 188, + 890, + 277 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "query point. It can be more accurate and parameter efficient than the grid-based ones since it can adaptively locate points, considering the complexity of functions, e.g., fewer points in low-frequency areas. Although our work is largely inspired by these works, 1. we repurpose the point representations to build continuous convolutional kernels, 2. we do not use MLPs that would introduce additional modeling complexity, 3. our method does not require complex initializations (or algorithms) to relocate points, such as depth-based initialization [63] and mask-based initialization [67].", + "bbox": [ + 75, + 315, + 468, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Large kernel convolution. Since the great success of VGG-style CNNs [24, 26, 48, 51] in ImageNet [12], we repeatedly apply small kernels (e.g., $3 \\times 3$ kernel) with deep layers to get a large receptive field and deal with long-term dependencies. With the massive success of transformers in the vision domain [15, 16, 34, 55], which have a large receptive field, recent studies have started to revisit the descriptive power of large kernels [13, 32, 35, 53]. RepLKNet [13] has shown we can increase the kernel size up to $31 \\times 31$ with the help of the reparameterization trick. More recently, SLaK [32] managed to scale the kernel size to $51 \\times 51$ and $61 \\times 61$ , showing improved performance with dynamic sparsity and low-rank factorization (Fig. 1-(b)). While promising, the number of parameters increases according to the kernel size, which is a major bottleneck in representing large kernels.", + "bbox": [ + 75, + 469, + 468, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The continuous kernel can construct large kernels with a fixed parameter budget (Fig. 1-(c)). CKConv [45] and FlexConv [44] have exploited this property and demonstrated that their method can model long-term dependencies by constructing large kernels on various datasets. However, they introduce a considerable amount of computations to the training process, and they have yet to perform largescale experiments, e.g., ImageNet. To the best of our knowledge, our approach is the first to conduct such a large-scale experiment using continuous convolution.", + "bbox": [ + 75, + 715, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "On the other hand, dilated convolutions [7, 8] can also be used to enlarge receptive fields with a small number of", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "parameters, and they also do not introduce additional computations during training (Fig. 1-(d)). Deformable convolutions [9] look similar to ours in terms of moving points arbitrarily (Fig. 1-(e)). However, they learn how to deform the kernels (or predict the offset) during inference. On the other hand, we adjust the locations of the point representations during training to find the optimal large kernels. A concurrent work suggests learning the offsets during training [23]. In contrast to ours, it is a discrete formulation, thus losing the benefits of continuous convolution. Furthermore, we adjust the receptive fields of each point representation separately, yielding more expressive representations.", + "bbox": [ + 496, + 315, + 890, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Continuous convolution for point clouds. There have been many continuous convolution approaches to handle 3D point cloud data, which is an important example of irregularly sampled data. PointNet [41] and PointNet++ [42] are pioneer works that use average pooling and $1 \\times 1$ convolution to aggregate features. [31, 33, 58, 60] leveraged MLPs to implement continuous convolution. KPCov [52] is also considered a continuous convolution and shares some similarities with ours (Fig. 1-f). They also used point representation and interpolation kernels for handling point clouds. However, their points are fixed over the training, unlike ours. They also proposed a deformable version, which requires additional neural networks to predict the offset of the kernel points.", + "bbox": [ + 496, + 501, + 892, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. SMPCov", + "text_level": 1, + "bbox": [ + 500, + 738, + 609, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Self-moving point representation", + "text_level": 1, + "bbox": [ + 500, + 767, + 787, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section describes the proposed self-moving point representation to represent a continuous function. Let $d$ be the size of the input coordinates dimension, e.g., 1 in timeseries data and 2 in the spatial domain. $\\mathsf{SMP}:\\mathbb{R}^d\\to \\mathbb{R}^{N_c}$ is a vector-valued function, mapping from the input coordinates to the output kernel vectors, where $N_{c}$ is a channel size. Given a query point $x\\in \\mathbb{R}^d$ , we define a continuous", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10291", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "kernel function as follows.", + "bbox": [ + 76, + 90, + 256, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S M P} (x; \\phi) = \\frac {1}{| \\mathcal {N} (x) |} \\sum_ {i \\in \\mathcal {N} (x)} g (x, p _ {i}, r _ {i}) w _ {i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 109, + 468, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\phi = \\{\\{p_i\\}_{i = 1}^{N_p},\\{w_i\\}_{i = 1}^{N_p},\\{r_i\\}_{i = 1}^{N_p}\\}$ is a set of learnable parameters, and $N_{p}$ is the number of points that are used to represent the function. $p_i\\in \\mathbb{R}^d$ is the coordinates of self-moving point representation $w_{i}\\in \\mathbb{R}^{N_{c}}$ , and each point representation also has a learnable radius, $r_i\\in \\mathbb{R}^+$ is a positive real number, which we implement it by clipping for numerical stability. We define a distance function $g:\\mathbb{R}^d\\times \\mathbb{R}^d\\times \\mathbb{R}^+\\to \\mathbb{R}$ as follows,", + "bbox": [ + 76, + 157, + 472, + 282 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng (x, p _ {i}, r _ {i}) = 1 - \\frac {\\| x - p _ {i} \\| _ {1}}{r _ {i}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 289, + 468, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\| \\cdot \\|_1$ is a L1 distance. $\\mathcal{N}(x)$ is a set of indices of neighboring points of a query coordinate $x$ , defined as $\\mathcal{N}(x) = \\{i | g(x, p_i, r_i) > 0, \\forall i\\}$ . Thus, points beyond a certain distance (depending on the radius) will not affect the query point. Hence, SMP generates output vectors by a weighted average of the nearby point representations. Note that all three parameters $\\{p_i\\}, \\{w_i\\}, \\{r_i\\}$ are jointly trained with the CNN model parameters, and the gradients w.r.t those parameters can be easily computed using an automatic differentiation library. As the name SMP suggests, the coordinates $\\{p_i\\}$ are updated during training, resulting in moving points representation.", + "bbox": [ + 75, + 328, + 468, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compared to a fixed-point representation, where $\\{p_i\\}$ are not trainable, ours can approximate complex functions more precisely. Since each point can move freely, more points can be gathered in high-frequency areas. On the other hand, few points can easily represent low-frequency components, resulting in more parameter-efficient representation. For example, a single point may be sufficient to approximate unimodal functions.", + "bbox": [ + 75, + 508, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. SMPConv", + "text_level": 1, + "bbox": [ + 76, + 638, + 191, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We leverage the suggested representation to implement a continuous convolution operator. In one dimensional case, $d = 1$ , a continuous convolution can be formulated as,", + "bbox": [ + 75, + 662, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(f * \\operatorname {S M P}) (x) = \\sum_ {c = 1} ^ {N _ {c}} \\int_ {\\mathbb {R}} f _ {c} (\\tau) \\operatorname {S M P} _ {c} (x - \\tau) d \\tau , \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 714, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f: \\mathbb{R} \\to \\mathbb{R}^{N_c}$ is a input function and the $f_{c}$ and $\\mathrm{SMP}_c$ denote the $c$ -th element of the inputs. The convolution operator generates a function, computing the filter responses by summing over entire $N_{c}$ channels. One SMP representation corresponds to a convolution operator, and multiple SMPs are used to implement one convolutional layer to generate multiple output channels. In contrast to the previous MLP-based continuous convolution, which uses one neural network for one convolutional layer, our approach has separate", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/612c5bbfabb25031f6971bddcfcac3f9897aa884f51c350565dad04606e34031.jpg", + "image_caption": [ + "(a) SMP (1D)" + ], + "image_footnote": [], + "bbox": [ + 519, + 88, + 736, + 218 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c2f4cfc3794999dac228bbf93e20fd08a02e9634c14c64cb03ca6cdb16cde6ea.jpg", + "image_caption": [ + "(b) SMP (2D)", + "Figure 2. Self-moving point representation. (a) SMP as a function of the one-dimensional input domain, and (b) SMP as a function of the two-dimensional input domain. 'C #1' means the first channel. Each channel shares the location of the points, whereas each channel has its own weight parameters." + ], + "image_footnote": [], + "bbox": [ + 743, + 88, + 882, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "parameters for each convolution filter in a layer. It gives more freedom to each filter and results in more descriptive power of the learned filter.", + "bbox": [ + 496, + 351, + 890, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As depicted in Fig. 2, the kernels of each filter share the position parameters. That is, each filter of one layer has its own position parameters. Although we could use different SMP for different channels. However, it will considerably increase the number of learnable parameters ( $\\{p_i\\}$ per channel), and we believe that locating points at the same location for a convolutional filter can be a reasonable prior, where a convolutional filter can focus on specific areas in the input domain.", + "bbox": [ + 496, + 397, + 892, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We leverage our continuous formulation to construct large kernels, motivated by the recent success of using them in many tasks. We can create arbitrary size large kernels by querying multiple discretized coordinates to SMP.", + "bbox": [ + 496, + 534, + 893, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Training", + "text_level": 1, + "bbox": [ + 500, + 604, + 604, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training a large kernel has been challenging and computationally heavy, and naive training practice has yet to show promising results. Recently, [13, 14] proposed a reparameterization trick to combine different-size kernels as a separate branch, resulting in improved performance and more stable training. We also applied the same trick to train CNNs with SMPConv.", + "bbox": [ + 496, + 628, + 890, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We empirically figured out that performance degradation occurs when the coordinates $\\{p_i\\}$ are forced to fit inside the kernel by clipping. Thus, we let the coordinates be freely updated during training.", + "bbox": [ + 496, + 734, + 890, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also found that the initialization of the parameters $\\phi$ matters. For point locations, $\\{p_i\\}$ , we randomly sample from a gaussian distribution with small $\\sigma$ . It initially locates the points in the center and gradually spreads out over the training process. We empirically found that this strategy yields more stable training, especially at the beginning of the training. We also initialized with small values", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10292", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/9be20a7b342a8610b38acbe6ebc684aa2fe88b234e66f45ea634d75294bf6b62.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodkParams.Time ↓Throughput ↑
Deformable [9]30.29M61.24390.7
51.37M157.31618.9
74.39M293.1882.3
FlexConv [44]330.67M92.91923.4
SMPConv330.49M40.14258.4
", + "bbox": [ + 93, + 94, + 459, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Training time (sec/epoch) and throughput (examples/sec) comparison with CIFAR10 on a single RTX3090 GPU. Both are tested with a batch size of 64 and input resolution of $32 \\times 32$ . The $k$ is kernel size. The time is the average training time of the first 10 epochs.", + "bbox": [ + 76, + 191, + 468, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $\\{r_i\\}$ , which each weight parameter firstly has a narrow sight. Over the course of training, $\\{r_i\\}$ also gradually increases if necessary.", + "bbox": [ + 76, + 289, + 468, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Efficiency", + "text_level": 1, + "bbox": [ + 76, + 344, + 191, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Assuming the size of a convolution filter is $C \\times N \\times N$ , where $C$ is the number of kernels and $N$ is the height and width of filter, $CN^2$ parameters are required in dense convolution (Fig. 1-(a)). Therefore, the number of parameters is proportional to kernel resolution $N \\times N$ . On the other hand, SMP needs $(1 + d + C)N_{p}$ parameters, where $d$ is the size of the input coordinates dimension, and $N_{p}$ is the number of weight points. We used $N_{p} \\ll N^{2}$ , so SMP is more efficient than dense convolution in terms of the number of parameters. Furthermore, as the number of parameters does not depend on kernel resolution, SMP can represent kernels of any size, such as large or continuous kernels with fixed budget parameters.", + "bbox": [ + 75, + 368, + 468, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Due to the point representations and interpolation schemes without supplementary neural networks, SMPConv has an advantage of computational complexity. On the other hand, the existing large kernel convolutions are computationally heavy. Deformable convolution (Fig. 1-(e)), for example, requires offset prediction networks and convolution with interpolated inputs during both training and inference, resulting in additional computation and parameter costs. Additionally, it relies on dense convolution, making it impractical to increase kernel size significantly. Similarly, MLP-based methods (Fig. 1-(c)) like FlexConv [44] leverage kernel generation neural network, and it also increases computational burdens. The results presented in Tab. 1 demonstrate that SMPConv outperforms the existing large kernel convolutions in terms of speed.", + "bbox": [ + 75, + 566, + 470, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 806, + 209, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Continuous function approximation", + "text_level": 1, + "bbox": [ + 76, + 830, + 387, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Firstly, we conducted a fitting experiment to validate that our self-moving point representation can work as an approximator for a continuous function. To do so, we used", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/973ff0d1afabaaf1182553d0edb99f42f125c0103fc43bd221328197ddf7638a.jpg", + "image_caption": [ + "$f_{a}(x,y) = \\cos (e^{y} / 0.5) + \\sin ((x^{2} - 0.5) / 5)$" + ], + "image_footnote": [], + "bbox": [ + 517, + 92, + 638, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/686e1067b02dab736e906306784a30d4bbb4d516f2799904222365fa7cd93778.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 650, + 95, + 740, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d42447effa1082f89058dc474dd779ecddd8a10b80d4924cddcd01fde659baef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 95, + 851, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/87ec7d9536c1db127ed4d93830cc35429d7769a5fc3414f103e85803b8798914.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 859, + 95, + 877, + 176 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/17e2fb7ef9adf14bb70e4f01325d91a24147aa5505d34666354d39be93b6dcf2.jpg", + "image_caption": [ + "$f_{b}(x,y) = \\cos (x + y) + \\sin (40x + 2y^{2}) / 5$" + ], + "image_footnote": [], + "bbox": [ + 517, + 194, + 635, + 277 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/549446d7608d7889f5400e98f089dad4a4227e3e60517ab949a9ce48e4694b69.jpg", + "image_caption": [ + "Figure 3. Comparison between the moving point and the fixed point representations through the fitting. Our proposed moving point representations can approximate given continuous functions with higher accuracy." + ], + "image_footnote": [], + "bbox": [ + 645, + 196, + 738, + 277 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ac8771fb52e211bf09d75d8e2eabd8455bc5afe700c865b26d6e83baaf8fb37a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 198, + 848, + 277 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2e8d34502bed68a330e14f91ab359c707ae5a75d9a49624bf3cd64d0d6040315.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 859, + 198, + 875, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "two sinusoidal-based functions as the ground truth. Given a function, SMP is optimized to represent the sampled function on a $51 \\times 51$ grid. In this experiment, we designed SMP with 204 points. The fitting result has been shown in Fig. 3. It demonstrates that our proposed method reasonably well approximates a given continuous function with fewer points. Additionally, we compared with the fixed point representation and observed that optimizing the position of points together helps to better approximate the function as the number of points is equal.", + "bbox": [ + 498, + 393, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Sequential data classification", + "text_level": 1, + "bbox": [ + 500, + 558, + 756, + 574 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To demonstrate that SMPConv can handle long-term dependencies well, we evaluated our method on various sequential data tasks, such as sequential image and time-series classification. To do so, we followed FlexTCN [44] to construct a SMPConv architecture for causal 1D CNN whose kernel size is same as the input sequence length. We substituted their parameterized kernels with ours without additional modifications. To maintain a similar number of network parameters, SMPConv contains 30 weight points in each SMP. To alleviate the computation burdens caused by the convolution with large kernels, we have considered exploiting the computations through a fast Fourier transform. More network and experimental details are in Appx. 1.1.", + "bbox": [ + 496, + 582, + 890, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sequential image. We tested our SMPConv on the 1D version of images from the datasets, sequential MNIST (sMNIST), permuted MNIST(pMNIST) [29], and sequential CIFAR10 (sCIFAR10) [4]. These datasets have long input sequence lengths, for example, 784 for sMNIST and pMNIST, and 1024 for sCIFAR10. Note that it is hard to model these datasets without proper kernel representations. As shown in Tab. 2, the proposed model has achieved state", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10293", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2cf8ba54ec13d53781c9b5fc810b4510b9c0d4eee6ade0c3b0d82fb969510911.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelParams.sMNISTpMNISTsCIFAR10
DilRNN [4]44k98.096.1-
LSTM [2]70k87.285.7-
GRU [2]70k96.287.3-
TCN [2]70k99.097.2-
r-LSTM [56]500k98.495.272.2
IndRNN [30]83k99.096.0-
TrellisNet [3]8M99.2098.1373.42
URLSTM [20]-99.2896.9671.00
HiPPO [18]0.5M-98.30-
coRNN [47]134k99.497.3-
CKCNN [45]98k99.3198.0062.25
LSSL [21]-99.5398.7684.65
S4 [19]-99.6398.7091.13
FlexTCN [44]375k99.6298.6380.82
Ours373k99.7599.1084.86
", + "bbox": [ + 93, + 93, + 455, + 301 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ea7b2c2ec95ff7e5deb16479008d48d91ac442759c6d48126a2459d482474be3.jpg", + "table_caption": [ + "Table 2. Sequential image classification results." + ], + "table_footnote": [], + "table_body": "
ModelParams.CTSCSC-raw
GRU-ODE [11]89k96.244.8~ 10.0
GRU-Δt [27]89k97.820.0~ 10.0
GRU-D [5]89k95.923.9~ 10.0
ODE-RNN [46]89k97.193.2~ 10.0
NCDE [27]89k98.888.5~ 10.0
CKCNN [45]100k99.5395.2771.66
LSSL [21]--93.58-
S4 [19]--93.9698.32
FlexTCN [44]373k99.5397.6791.73
Ours371k99.5397.4594.95
", + "bbox": [ + 94, + 354, + 455, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of-the-art results on both sMNIST and pMNIST. For sCIFAR10 dataset, our model has outperformed all the comparative models except S4 [19]. Compared with the FlexTCN, which has a similar network base, our model improved the accuracy by $4\\%$ . These results show that our proposed model is suitable and effective for sequential images.", + "bbox": [ + 75, + 577, + 468, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Time-series. We evaluated our model on time-series sequence datasets, character trajectories (CT) [1], and speech commands (SC) [59]. The results have been displayed in Tab. 3. In the relatively shorter MFCC features data, SM-PConv achieved test accuracy similar to FlexTCN. To validate that our proposed model can model extremely long sequences, we conducted experiments on the SC-raw dataset, which has a sequence length of 16000. Similar to the sequence image classification result, our model outperformed FlexTCN with a large margin of $+3\\%$ .", + "bbox": [ + 75, + 670, + 468, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Compared to other models, our SMPConv has achieved considerably better performance for both sequential image and time-series classification. It ensures that our kernel representation is capable of handling long-term dependencies even in the case of a limited number of parameters.", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e426c1583399579c20fe4d3aa3aa1d875c12afe098247a726b31889df2f88bcf.jpg", + "table_caption": [ + "Table 3. Time-series classification results." + ], + "table_footnote": [], + "table_body": "
ModelParams.Accuracy
ResNet-44 [24]660k92.9
CKCNN-16 [44]630k72.1
FlexNet-16 [44]670k92.2
Ours490k93.0
", + "bbox": [ + 553, + 95, + 838, + 175 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. 2D image classification on CIFAR10.", + "bbox": [ + 557, + 186, + 833, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Image classification", + "text_level": 1, + "bbox": [ + 500, + 226, + 686, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Image classification with the continuous kernel. We validated our SMPConv on a 2D image dataset, CIFAR10 [28], which is dominated by discrete convolutions, to show that the continuous kernel can capture spatial information as well. Similar to the experiments on sequential data, we followed the network design choice of FlexNet [44], where the kernel size is $33 \\times 33$ . More details are in Appx. 1.1.", + "bbox": [ + 496, + 250, + 890, + 369 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Tab. 4, our continuous kernel representation model slightly outperforms ResNet, a discrete $3 \\times 3$ convolution model, with a less number of parameters. It implies that our model is competitive and promising. Our model also showed better performance than MLP-based counterparts, CKCNN-16 and FlexNet-16, even when the parameters of ours were around $30\\%$ lesser. In addition, we have already identified the efficiency of our model in Tab. 1. These results suggest that our method is more suitable for kernel generation than MLP-based implicit formulations.", + "bbox": [ + 496, + 371, + 890, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Large scale image classification. Finally, we tested our SMPConv on a large-scale ImageNet dataset [12], which contains more than one million training images and 50,000 validation images. For such a large dataset, the convolution kernels should be carefully trained to model complex data relationships accurately. Through such an experiment, therefore, we can validate that our SMP can represent a descriptive convolution kernel.", + "bbox": [ + 496, + 522, + 890, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Firstly, we constructed large-scale variants of SMPConv architecture based on RepLKNet [13]. We replaced its discrete depth-wise separable convolution kernel with our SMP. In general, the larger the data and network, the larger the number of filters. To prevent excessive point position parameters depending on the number of filters, we shared the position of points over filters in large-scale settings. We empirically found that this position sharing has little effect on classification performance.", + "bbox": [ + 496, + 643, + 890, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We proposed two variants of our model, SMPConv-T and SMPConv-B. Thanks to our efficient large kernel, we adjusted the number of channels and blocks so that our variants have a similar number of parameters to the previous models. The number of blocks and channels for each stage is [2, 2, 8, 2] and [96, 192, 384, 768] for SMPConv-T and [2, 2, 20, 2] and [128, 256, 512, 1024] for SMPConv-B, respectively. In RepLKNet-31B, the number of blocks and", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10294", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4601cb83d88bdcf2a0b4c31fbc03a720bf18bc658e2e8820e9be0e8446c4f604.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelParams.FLOPsTop-1 Accuracy
ResNet-50 [24]26M4.1G76.5
ResNext-50-32x4d [62]25M4.3G77.6
ResMLP-S24 [54]30M6.0G79.4
DeiT-S [55]22M4.6G79.8
Swin-T [34]28M4.5G81.3
TNT-S [22]24M5.2G81.3
ConvNeXt-T [35]29M4.5G82.1
SLaK-T [32]30M5.0G82.5
SMPConv-T(ours)27M5.7G82.5
DeiT-Base/16 [55]87M17.6G81.8
Swin-B [34]88M15.4G83.5
ConvNeXt-B [35]89M15.4G83.8
SLaK-B [32]95M17.1G84.0
RepLKNet-31B [13]79M15.3G83.5
SMPConv-B(ours)80M16.6G83.8
", + "bbox": [ + 93, + 93, + 457, + 301 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/89e4432113f80916b6d6aa89ff2da307cfd7834e46c642c6064de3eee0df87e3.jpg", + "table_caption": [ + "Table 5. 2D image classification on ImageNet-1K." + ], + "table_footnote": [], + "table_body": "
ModelsradiuscoordinateAccuracy
A--90.92
B✓-91.35
C-✓92.47
SMPConv✓✓93.00
", + "bbox": [ + 114, + 347, + 434, + 429 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/96435581d61d6c51d80a96ba7c825f472ad4e4f79bf67200be11b49a1117f375.jpg", + "table_caption": [ + "Table 6. Ablation study on CIFAR10. A checkmark means that the component is a learnable. In case of SMPConv, for instance, both radius and coordinate are learnable parameters." + ], + "table_footnote": [], + "table_body": "
σ0.050.20.30.5
Accuracy93.0092.2491.8491.51
", + "bbox": [ + 117, + 503, + 429, + 537 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/aa62bf15d621bd5b6e7396c1910ba47e12bf97eef1f7462e01c937582d078ce1.jpg", + "table_caption": [ + "Table 7. Classification results on CIFAR10 with different standard deviation $\\sigma$ of point location sampling distribution." + ], + "table_footnote": [], + "table_body": "
r0.120.180.240.3
Accuracy93.0092.3692.0691.76
", + "bbox": [ + 117, + 598, + 429, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "channels for each stage is [2, 2, 18, 2] and [128, 256, 512, 1024]. More experimental details are provided in Appx. 1.2.", + "bbox": [ + 76, + 698, + 467, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As reported in Tab. 5, our models obtained competitive performance with fewer parameters than existing models. These results show that our kernel representation is promising for large-scale domains as well. Overall, our kernel representation is highly effective and descriptive.", + "bbox": [ + 75, + 744, + 467, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation", + "text_level": 1, + "bbox": [ + 76, + 830, + 181, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We performed various ablation studies with additional experiments on CIFAR10 image classification. First, we investigated the validity of learnable radius and coordinate. In", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/62ef5a50da84dacad2aa5a6a8e944bfc503b4fce700a0152fc97d7f034b78af8.jpg", + "table_caption": [ + "Table 8. Classification results on CIFAR10 with different initial radius $r$ ." + ], + "table_footnote": [], + "table_body": "
Np48163264
Params.250k330k490k809k1447k
Accuracy92.5692.2893.0092.8492.21
", + "bbox": [ + 511, + 95, + 882, + 147 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 9. Classification results on CIFAR10 with different number of moving points $N_{p}$ .", + "bbox": [ + 498, + 156, + 890, + 185 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 6, it showed that performance degradation occurs when either one or both components are set to non-learnable parameters. Remarkably, Model C, which set coordinate to trainable parameters, outperformed Model A by a considerable margin. Furthermore, Model B also had a slight performance gain. It suggests that even randomly distributed fixed weight points can increase their interpolation ability with trainable radius. These results indicate that training both coordinate and radius is valid.", + "bbox": [ + 496, + 212, + 890, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we identified the effect of the initial position of the points by varying the $\\sigma$ , a standard deviation of point location sampling distribution. In Tab. 7, we observed that a small $\\sigma$ value, indicating initial positions of the points are gathered in the center of the kernel, leads to higher accuracy. This is because it is difficult to train large kernels from the beginning of training. Thus, large kernels can be effectively trained by starting with small kernels and expanding the receptive fields through moving points.", + "bbox": [ + 496, + 349, + 892, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also found that larger initial radius degrades the model performance as shown in Tab. 8. The large radius results in a large initial kernel size, which makes initial training difficult. Furthermore, it is also challenging to train a large area of the kernel dependent on a single weight point which is not optimized in the early stages of training. Both Tab. 7 and Tab. 8 empirically show that our initialization methods for SMP are effective.", + "bbox": [ + 496, + 486, + 890, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As depicted in Tab. 9, we figured out that simply increasing the number of weight points $N_{p}$ does not help for performance. It implies that a small number of points are enough to represent a proper convolution filter. Since the performance is influenced by the number of points, our method is also required tuning like common neural networks. However, the performance difference between CKCNN and FlexNet in Tab. 4 shows that MLP-based methods are severely influenced by architectural settings. That is, they have extensive search space, such as depth, width, and activation function, so they typically require more tuning than our method. Moreover, the impact of the number of points is not particularly significant in that even the worst $(N_{p} = 64)$ slightly outperforms the FlexNet (acc=92.20).", + "bbox": [ + 496, + 608, + 892, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Visualization", + "text_level": 1, + "bbox": [ + 500, + 830, + 637, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we analyze our SMP by visualizing filters trained on CIFAR10. In the first column of Fig. 4, we can observe the trained weight points' position. In our method, point lo", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10295", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9e0a1798878334b894cf0a5d51929cd2666561aad866da9c808d232cf9b610d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 97, + 215, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/13f10b6608dc550736933f7d278c82d9bf6145c58e3fd36d804d26172b26a40d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 223, + 99, + 321, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3bf793a6435850132eadc421057732c73e6951104e23e150b9c5abf30378be9d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 331, + 101, + 429, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b15f30bcfcf8e758b206429b1eb07eb0a58937fcd68438194a3622b2033a803a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 439, + 101, + 535, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/da60f52c5c6f4db692ca1caa11c75da5a12d7d67f851cd46d7019abee884cbbb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 547, + 101, + 643, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1767b448133c5f9553ff93137fbc4d1c943476b4cc46e6c6d9fc88e8c65ea5ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 656, + 101, + 754, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db91d6cf51e8d98414cf46b18014bd854b455d77bee3b080245ff60d5cfce611.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 99, + 888, + 179 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cf5779d61bd5be33e4250baeb368724129b9903bd92ecc05158f331c704e0592.jpg", + "image_caption": [ + "points" + ], + "image_footnote": [], + "bbox": [ + 84, + 188, + 215, + 277 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/46c3c7aa9ba83d2b99a3c2f351a71a776f3eed2e90b552de98bd97f0f46ba175.jpg", + "image_caption": [ + "kernel 1" + ], + "image_footnote": [], + "bbox": [ + 223, + 191, + 321, + 270 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1b74387b6b4d4665d2152e4e85c343eed0c36c0579553f8bd8ca674668c831bf.jpg", + "image_caption": [ + "kernel 2" + ], + "image_footnote": [], + "bbox": [ + 331, + 191, + 429, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/064b0e148b5291b05fe84751cf7021a5faff96a1336d9d3ffd37b64dd6974636.jpg", + "image_caption": [ + "kernel 3" + ], + "image_footnote": [], + "bbox": [ + 439, + 191, + 537, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1e8d126b2924cfd22fb259df6418110630375f5437d1f61ff2fed2556fc90b97.jpg", + "image_caption": [ + "kernel 4" + ], + "image_footnote": [], + "bbox": [ + 547, + 191, + 645, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb5678ae102a304ece858d33923fbf1c75368840e572cb0838d7242982e492e7.jpg", + "image_caption": [ + "kernel 5" + ], + "image_footnote": [], + "bbox": [ + 656, + 191, + 754, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f3fd7aed893bc0175ca3f2005ac001b99fa9e575ed20f5080dc74f0a1d6c87bc.jpg", + "image_caption": [ + "kernel 6" + ], + "image_footnote": [], + "bbox": [ + 761, + 191, + 888, + 268 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8952a576dd706a68782b2567ce3b3726fcd7cf6022e86d386ce018e6b9fede13.jpg", + "image_caption": [ + "Figure 4. Visualization of kernels. Each row shows the location of points and first 6 kernels of a filter. For ease of visualization, the kernels are first subjected to the absolute value operation and then normalized to a range of [0,1].", + "(a) Layer 1", + "Figure 5. Normalized sum of the absolute value of trained filters. (a), (b), and (c) are top, middle, and bottom layers, respectively." + ], + "image_footnote": [], + "bbox": [ + 94, + 362, + 210, + 448 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/88eb384bcbd67e00289cdfd32becdaee6676bfe69d52ab394cdf41e8f671af11.jpg", + "image_caption": [ + "(b) Layer 8" + ], + "image_footnote": [], + "bbox": [ + 218, + 368, + 316, + 446 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/985c85d1e740ca467545e000607a61a1bba5826ea0a54333feca69c3d4aa252d.jpg", + "image_caption": [ + "(c) Layer 14" + ], + "image_footnote": [], + "bbox": [ + 331, + 368, + 454, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cations $p_i$ are mainly sampled near the center of the kernel for stable training. It shows that the points spread out for optimal kernel representation over the training process, as we argued, and thus the receptive fields are not limited to a small part. Also, we can figure out that there are square patterns caused by Eq. (2) in the kernels, where each square has its own area. This suggests that although the radius parameters are initialized with small values, the values are individually increased and optimized for each corresponding weight point during training.", + "bbox": [ + 75, + 527, + 467, + 678 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Observing visualized convolution kernel in Fig. 4, kernels from the same filter share the receptive fields. It allows a single filter to focus on the shared area. Furthermore, as illustrated in Fig. 5, SMPConv has large adaptive receptive fields which are not conventional square or rectangular shapes. This is because it consists of optimized filters with their own small and large receptive fields. Thus, our method can handle not only global information but also local details.", + "bbox": [ + 75, + 679, + 467, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and discussion", + "text_level": 1, + "bbox": [ + 76, + 829, + 320, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a method to build a continuous convolution. We propose using point representations, where each point has the weight parameters, coordinates, and ra", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "dius to learn. By connecting the points, we can implement a continuous function, which can be utilized to construct convolutional kernels. We have provided extensive experimental results, showing that drop-in replacement in the existing training pipeline without bells and whistles improved the performance by a safe margin. We also show that a continuous convolution can be effectively utilized in a large-scale experiment. We expect more research and development in this direction.", + "bbox": [ + 496, + 359, + 890, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although promising, there are many rooms to be improved. Due to the limited computational budget, we could not conduct sufficient experiments in the large-scale experiment. The experimental results provided in this manuscript resulted from a few runs. As trial and error are essential in the machine learning development process, we plan to find optimal configurations and training techniques to enhance the performance of the proposed method.", + "bbox": [ + 496, + 496, + 890, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also observed that the learned kernels often show sparse patterns depending on the tasks. It is well aligned with the success of dilated convolution or its variants, and our methods automatically learn proper sparsity during the training process on specific tasks. Adding prior knowledge through training and regularization techniques would further improve performance, especially for tasks requiring longer-term dependency modeling.", + "bbox": [ + 496, + 617, + 890, + 737 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 751, + 658, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank Usman Ali for valuable discussions. This research was supported by the Ministry of Science and ICT (MSIT) of Korea, under the National Research Foundation (NRF) grant (2022R1F1A1064184, 2022R1A4A3033571), Institute of Information and Communication Technology Planning Evaluation (IITP) grants for the AI Graduate School program (IITP-2019-0-00421), and the BK21 FOUR Project.", + "bbox": [ + 496, + 773, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10296", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. 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Differentiable point-based radiance fields for efficient view synthesis. arXiv preprint arXiv:2205.14330, 2022. 2, 3" + ], + "bbox": [ + 78, + 90, + 468, + 373 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10299", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_model.json b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b34da30ffb41a02a6d5b1855ee8a535b8ea06b29 --- /dev/null +++ b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_model.json @@ -0,0 +1,2708 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.13, + 0.862, + 0.154 + ], + "angle": 0, + "content": "SMPCov: Self-moving Point Representations for Continuous Convolution" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.18, + 0.806, + 0.235 + ], + "angle": 0, + "content": "Sanghyeon Kim\\(^{1}\\) Eunbyung Park\\(^{1,2*}\\) \n\\(^{1}\\)Department of Electrical and Computer Engineering, Sungkyunkwan University \n\\(^{2}\\)Department of Artificial Intelligence, Sungkyunkwan University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.473, + 0.681 + ], + "angle": 0, + "content": "Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.712, + 0.21, + 0.727 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.47, + 0.875 + ], + "angle": 0, + "content": "There has been a recent surge of interest in representing the convolutional kernel as a function over a continuous input domain. It can easily handle irregularly sampled data both in time [1, 59] and space [61, 65], overcoming the drawbacks of the discrete convolution operating only on discretized sampled data with pre-defined resolutions and grids. With the progress in modeling and training continuous kernels, it has enjoyed great success in many practical scenarios, such as 3D point cloud classification and segmen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.895, + 0.378 + ], + "angle": 0, + "content": "tation [36,41,52,58,64], image super resolution [57], object tracking [10], to name a few. Furthermore, the recent trends of using large convolutional kernels with strong empirical results urge us to develop a more efficient way to implement it [13,32], and the continuous convolution will be a promising candidate because of its capability to readily construct arbitrarily large receptive fields [44, 45]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.895, + 0.593 + ], + "angle": 0, + "content": "One of the dominant approaches to modeling the continuous kernel is to use a particular type of neural network architecture, taking as inputs low-dimensional input coordinates and generating the kernel values [44, 45], known as neural fields [38, 49] or simply MLPs. Using neural fields to represent the kernels, we can query kernel values at arbitrary resolutions in parallel and construct the large kernels with a fixed parameter budget, as opposed to the conventional discrete convolutions requiring more parameters to enlarge receptive fields. Thanks to recent advances to overcome the spectral bias on training neural fields [49], they can also represent functions with high-frequency components, which enables learned kernels to capture fine details of input data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.896, + 0.822 + ], + "angle": 0, + "content": "While promising in various tasks and applications, this approach has a few downsides. First, it incurs considerable computational burdens to already computation-heavy processes of training deep neural networks. Each training iteration involves multiple forward and backward passes of MLPs to generate kernels and update the parameters of MLPs. This additional complexity prevents it from being applied to large-scale problems, such as ImageNet-scale, since it needs deeper and wider MLP architectures to construct more complex kernels with more input and output channels. Although MLPs can generate larger sizes and numbers of kernels without adding more parameters, it has been known that the size of MLPs mainly determines the complexity of the functions they represent and, eventually, the performance of the CNNs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Furthermore, the kernels generated by an MLP depend heavily on the architectural priors. As a universal function approximator, a neural network with sufficient depth and width can express any continuous functions [25]. However, we have empirically observed strong evidence that the ar" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "*Corresponding authors" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10289" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.228 + ], + "angle": 0, + "content": "chitecture of neural networks has played a significant role in many practical settings, suggesting that various architectural changes to the kernel-generating MLPs would significantly affect the performance of CNNs. Considering a large number of hyperparameters in training neural networks, adding more knobs to tune, e.g., activation functions, width, depth, and many architectural variations of MLPs., would not be a pragmatic solution for both machine learning researchers and practitioners." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.471, + 0.562 + ], + "angle": 0, + "content": "In this paper, we aim to build continuous convolution kernels with negligible computational cost and minimal architectural priors. We propose to use moving point representations and implement infinite resolution by interpolating nearby moving points at arbitrary query locations. The moving points are the actual kernel parameters, and we connect the neighboring points to build continuous kernels. Recent techniques in neural fields literature inspire it, where they used grid or irregularly distributed points to represent features or quantities in questions (density or colors) for novel view synthesis [6, 50, 63, 66, 67]. The suggested approach only introduces minor computational costs (interpolation costs) and does not consist of neural networks (only point representations and interpolation kernels). Moreover, the spectral bias presented in training MLPs [43] does not exist in the suggested representation. Each point representation covers the local area of the input domain and is updated independently of each other, contrasted with MLPs, where updating each parameter would affect the entire input domain. Therefore, highly different values of nearby points can easily express high-frequency components of the function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.718 + ], + "angle": 0, + "content": "The proposed method can also be more parameter efficient than the discrete convolution to construct the large kernels. Depending on the complexity of the kernels to be learned, a few numbers of points may be sufficient to cover a large receptive field (e.g., a unimodal function can be approximated by a single point). Many works have extensively exploited non-full ranks of the learned kernels to implement efficient convolutions or compress the models [32]. Our approach can likewise benefit from the presence of learned kernels with low-frequency components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We conduct comprehensive experimental results to show the effectiveness of the proposed method. First, we demonstrate that moving point representations can approximate continuous functions very well in 1D and 2D function fitting experiments. Then, we test its ability to handle long-term dependencies on various sequential datasets. Finally, we also evaluate our model on 2D image data. Especially, we perform large-scale experiments on the ImageNet classification dataset (to our knowledge, it is the first attempt to use continuous convolution for such a large-scale problem). Our proposed method can be used as a drop-in replacement of convolution layers for all the above tasks without bells" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "and whistles. The experimental results show that it consistently improves the performance of the prior arts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.136, + 0.646, + 0.151 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.161, + 0.892, + 0.478 + ], + "angle": 0, + "content": "Neural fields and continuous convolution. Neural fields have recently emerged as an alternative neural network representation [49]. It is a field parameterized by a neural network, such as simple MLP, taking as low-dimensional coordinates input and generating quantity in questions. It has shown great success in various visual computing domains, such as novel view synthesis [38], 3D shape representation [37, 40], and data compression [17], to name a few. Since it is a function over a continuous input domain, it can produce outputs at arbitrary resolutions. Recent studies have exploited its continuous nature to model continuous kernels for CNNs [44, 45, 58]. [58] used an MLP architecture to implement the continuous kernel to handle irregularly sampled data, such as 3D point clouds. While successful, the descriptive power of the learned kernel is limited due to its bias toward learning low-frequency components. With the recent advances in overcoming the spectral bias [49], [45] has explored various activation functions to improve the performance of CNNs. To further improve, [44] proposed to learn the receptive field sizes and showed impressive performance on multiple tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.892, + 0.614 + ], + "angle": 0, + "content": "We also propose a method that can likewise be classified as a neural field. However, we implement a field without neural networks, using self-moving point representations and interpolation schemes. It significantly reduces the computational costs to compute the kernels during training compared to the conventional MLP-based methods. Furthermore, it removes the burden of numerous hyperparameter searches for a newly introduced neural network in the already complicated training procedure." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Grid and point representations. Although MLP-based neural fields have succeeded in many tasks, they require substantial computational costs for training and inference, and the spectral bias presented in MLPs often degrades the performance. In order to reduce the computations and avoid the issues of using MLPs, classical grid-based representations have been adopted in the neural fields. Plenoxels [66] stores the coefficients of spherical harmonic in the 3D voxel structure and implements the infinite resolution via the interpolation methods, reducing the training time from days to minutes. Instant-NGP [39] further optimized the speed using a hash-based indexing algorithm. The combination of grid representations and MLPs has been extensively explored to find better solutions [6, 50]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Point representations have been recently suggested in neural fields to improve the shortcomings in grid-based representations, thanks to their flexibility and expressibility [63, 67]. They can generate outputs over a continuous input domain by interpolating neighboring points given a" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10290" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.087, + 0.275, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.341, + 0.087, + 0.592, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.663, + 0.089, + 0.866, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.187, + 0.246, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.256, + 0.189, + 0.453, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.189, + 0.672, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.189, + 0.892, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.31, + 0.293, + 0.658, + 0.307 + ], + "angle": 0, + "content": "Figure 1. A various methods for large kernel construction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.316, + 0.47, + 0.466 + ], + "angle": 0, + "content": "query point. It can be more accurate and parameter efficient than the grid-based ones since it can adaptively locate points, considering the complexity of functions, e.g., fewer points in low-frequency areas. Although our work is largely inspired by these works, 1. we repurpose the point representations to build continuous convolutional kernels, 2. we do not use MLPs that would introduce additional modeling complexity, 3. our method does not require complex initializations (or algorithms) to relocate points, such as depth-based initialization [63] and mask-based initialization [67]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Large kernel convolution. Since the great success of VGG-style CNNs [24, 26, 48, 51] in ImageNet [12], we repeatedly apply small kernels (e.g., \\(3 \\times 3\\) kernel) with deep layers to get a large receptive field and deal with long-term dependencies. With the massive success of transformers in the vision domain [15, 16, 34, 55], which have a large receptive field, recent studies have started to revisit the descriptive power of large kernels [13, 32, 35, 53]. RepLKNet [13] has shown we can increase the kernel size up to \\(31 \\times 31\\) with the help of the reparameterization trick. More recently, SLaK [32] managed to scale the kernel size to \\(51 \\times 51\\) and \\(61 \\times 61\\), showing improved performance with dynamic sparsity and low-rank factorization (Fig. 1-(b)). While promising, the number of parameters increases according to the kernel size, which is a major bottleneck in representing large kernels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.469, + 0.867 + ], + "angle": 0, + "content": "The continuous kernel can construct large kernels with a fixed parameter budget (Fig. 1-(c)). CKConv [45] and FlexConv [44] have exploited this property and demonstrated that their method can model long-term dependencies by constructing large kernels on various datasets. However, they introduce a considerable amount of computations to the training process, and they have yet to perform largescale experiments, e.g., ImageNet. To the best of our knowledge, our approach is the first to conduct such a large-scale experiment using continuous convolution." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "On the other hand, dilated convolutions [7, 8] can also be used to enlarge receptive fields with a small number of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.892, + 0.497 + ], + "angle": 0, + "content": "parameters, and they also do not introduce additional computations during training (Fig. 1-(d)). Deformable convolutions [9] look similar to ours in terms of moving points arbitrarily (Fig. 1-(e)). However, they learn how to deform the kernels (or predict the offset) during inference. On the other hand, we adjust the locations of the point representations during training to find the optimal large kernels. A concurrent work suggests learning the offsets during training [23]. In contrast to ours, it is a discrete formulation, thus losing the benefits of continuous convolution. Furthermore, we adjust the receptive fields of each point representation separately, yielding more expressive representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.893, + 0.713 + ], + "angle": 0, + "content": "Continuous convolution for point clouds. There have been many continuous convolution approaches to handle 3D point cloud data, which is an important example of irregularly sampled data. PointNet [41] and PointNet++ [42] are pioneer works that use average pooling and \\(1 \\times 1\\) convolution to aggregate features. [31, 33, 58, 60] leveraged MLPs to implement continuous convolution. KPCov [52] is also considered a continuous convolution and shares some similarities with ours (Fig. 1-f). They also used point representation and interpolation kernels for handling point clouds. However, their points are fixed over the training, unlike ours. They also proposed a deformable version, which requires additional neural networks to predict the offset of the kernel points." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.61, + 0.755 + ], + "angle": 0, + "content": "3. SMPCov" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.788, + 0.784 + ], + "angle": 0, + "content": "3.1. Self-moving point representation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This section describes the proposed self-moving point representation to represent a continuous function. Let \\(d\\) be the size of the input coordinates dimension, e.g., 1 in timeseries data and 2 in the spatial domain. \\(\\mathsf{SMP}:\\mathbb{R}^d\\to \\mathbb{R}^{N_c}\\) is a vector-valued function, mapping from the input coordinates to the output kernel vectors, where \\(N_{c}\\) is a channel size. Given a query point \\(x\\in \\mathbb{R}^d\\), we define a continuous" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10291" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.258, + 0.106 + ], + "angle": 0, + "content": "kernel function as follows." + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.111, + 0.47, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S M P} (x; \\phi) = \\frac {1}{| \\mathcal {N} (x) |} \\sum_ {i \\in \\mathcal {N} (x)} g (x, p _ {i}, r _ {i}) w _ {i}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.159, + 0.473, + 0.283 + ], + "angle": 0, + "content": "where \\(\\phi = \\{\\{p_i\\}_{i = 1}^{N_p},\\{w_i\\}_{i = 1}^{N_p},\\{r_i\\}_{i = 1}^{N_p}\\}\\) is a set of learnable parameters, and \\(N_{p}\\) is the number of points that are used to represent the function. \\(p_i\\in \\mathbb{R}^d\\) is the coordinates of self-moving point representation \\(w_{i}\\in \\mathbb{R}^{N_{c}}\\) , and each point representation also has a learnable radius, \\(r_i\\in \\mathbb{R}^+\\) is a positive real number, which we implement it by clipping for numerical stability. We define a distance function \\(g:\\mathbb{R}^d\\times \\mathbb{R}^d\\times \\mathbb{R}^+\\to \\mathbb{R}\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.29, + 0.47, + 0.322 + ], + "angle": 0, + "content": "\\[\ng (x, p _ {i}, r _ {i}) = 1 - \\frac {\\| x - p _ {i} \\| _ {1}}{r _ {i}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.47, + 0.51 + ], + "angle": 0, + "content": "where \\( \\| \\cdot \\|_1 \\) is a L1 distance. \\( \\mathcal{N}(x) \\) is a set of indices of neighboring points of a query coordinate \\( x \\), defined as \\( \\mathcal{N}(x) = \\{i | g(x, p_i, r_i) > 0, \\forall i\\} \\). Thus, points beyond a certain distance (depending on the radius) will not affect the query point. Hence, SMP generates output vectors by a weighted average of the nearby point representations. Note that all three parameters \\( \\{p_i\\}, \\{w_i\\}, \\{r_i\\} \\) are jointly trained with the CNN model parameters, and the gradients w.r.t those parameters can be easily computed using an automatic differentiation library. As the name SMP suggests, the coordinates \\( \\{p_i\\} \\) are updated during training, resulting in moving points representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Compared to a fixed-point representation, where \\(\\{p_i\\}\\) are not trainable, ours can approximate complex functions more precisely. Since each point can move freely, more points can be gathered in high-frequency areas. On the other hand, few points can easily represent low-frequency components, resulting in more parameter-efficient representation. For example, a single point may be sufficient to approximate unimodal functions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.639, + 0.192, + 0.654 + ], + "angle": 0, + "content": "3.2. SMPConv" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.47, + 0.707 + ], + "angle": 0, + "content": "We leverage the suggested representation to implement a continuous convolution operator. In one dimensional case, \\(d = 1\\), a continuous convolution can be formulated as," + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.715, + 0.47, + 0.756 + ], + "angle": 0, + "content": "\\[\n(f * \\operatorname {S M P}) (x) = \\sum_ {c = 1} ^ {N _ {c}} \\int_ {\\mathbb {R}} f _ {c} (\\tau) \\operatorname {S M P} _ {c} (x - \\tau) d \\tau , \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\( f: \\mathbb{R} \\to \\mathbb{R}^{N_c} \\) is a input function and the \\( f_{c} \\) and \\( \\mathrm{SMP}_c \\) denote the \\( c \\)-th element of the inputs. The convolution operator generates a function, computing the filter responses by summing over entire \\( N_{c} \\) channels. One SMP representation corresponds to a convolution operator, and multiple SMPs are used to implement one convolutional layer to generate multiple output channels. In contrast to the previous MLP-based continuous convolution, which uses one neural network for one convolutional layer, our approach has separate" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.089, + 0.738, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.571, + 0.227, + 0.641, + 0.24 + ], + "angle": 0, + "content": "(a) SMP (1D)" + }, + { + "type": "image", + "bbox": [ + 0.745, + 0.089, + 0.883, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.226, + 0.847, + 0.239 + ], + "angle": 0, + "content": "(b) SMP (2D)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.255, + 0.894, + 0.326 + ], + "angle": 0, + "content": "Figure 2. Self-moving point representation. (a) SMP as a function of the one-dimensional input domain, and (b) SMP as a function of the two-dimensional input domain. 'C #1' means the first channel. Each channel shares the location of the points, whereas each channel has its own weight parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.397 + ], + "angle": 0, + "content": "parameters for each convolution filter in a layer. It gives more freedom to each filter and results in more descriptive power of the learned filter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.893, + 0.533 + ], + "angle": 0, + "content": "As depicted in Fig. 2, the kernels of each filter share the position parameters. That is, each filter of one layer has its own position parameters. Although we could use different SMP for different channels. However, it will considerably increase the number of learnable parameters (\\(\\{p_i\\}\\) per channel), and we believe that locating points at the same location for a convolutional filter can be a reasonable prior, where a convolutional filter can focus on specific areas in the input domain." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.894, + 0.595 + ], + "angle": 0, + "content": "We leverage our continuous formulation to construct large kernels, motivated by the recent success of using them in many tasks. We can create arbitrary size large kernels by querying multiple discretized coordinates to SMP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.605, + 0.621 + ], + "angle": 0, + "content": "3.3. Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Training a large kernel has been challenging and computationally heavy, and naive training practice has yet to show promising results. Recently, [13, 14] proposed a reparameterization trick to combine different-size kernels as a separate branch, resulting in improved performance and more stable training. We also applied the same trick to train CNNs with SMPConv." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.796 + ], + "angle": 0, + "content": "We empirically figured out that performance degradation occurs when the coordinates \\(\\{p_i\\}\\) are forced to fit inside the kernel by clipping. Thus, we let the coordinates be freely updated during training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also found that the initialization of the parameters \\(\\phi\\) matters. For point locations, \\(\\{p_i\\}\\), we randomly sample from a gaussian distribution with small \\(\\sigma\\). It initially locates the points in the center and gradually spreads out over the training process. We empirically found that this strategy yields more stable training, especially at the beginning of the training. We also initialized with small values" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10292" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.095, + 0.46, + 0.182 + ], + "angle": 0, + "content": "
MethodkParams.Time ↓Throughput ↑
Deformable [9]30.29M61.24390.7
51.37M157.31618.9
74.39M293.1882.3
FlexConv [44]330.67M92.91923.4
SMPConv330.49M40.14258.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.193, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Table 1. Training time (sec/epoch) and throughput (examples/sec) comparison with CIFAR10 on a single RTX3090 GPU. Both are tested with a batch size of 64 and input resolution of \\(32 \\times 32\\). The \\(k\\) is kernel size. The time is the average training time of the first 10 epochs." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.29, + 0.469, + 0.336 + ], + "angle": 0, + "content": "for \\(\\{r_i\\}\\), which each weight parameter firstly has a narrow sight. Over the course of training, \\(\\{r_i\\}\\) also gradually increases if necessary." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.345, + 0.192, + 0.361 + ], + "angle": 0, + "content": "3.4. Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.566 + ], + "angle": 0, + "content": "Assuming the size of a convolution filter is \\( C \\times N \\times N \\), where \\( C \\) is the number of kernels and \\( N \\) is the height and width of filter, \\( CN^2 \\) parameters are required in dense convolution (Fig. 1-(a)). Therefore, the number of parameters is proportional to kernel resolution \\( N \\times N \\). On the other hand, SMP needs \\( (1 + d + C)N_{p} \\) parameters, where \\( d \\) is the size of the input coordinates dimension, and \\( N_{p} \\) is the number of weight points. We used \\( N_{p} \\ll N^{2} \\), so SMP is more efficient than dense convolution in terms of the number of parameters. Furthermore, as the number of parameters does not depend on kernel resolution, SMP can represent kernels of any size, such as large or continuous kernels with fixed budget parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.471, + 0.793 + ], + "angle": 0, + "content": "Due to the point representations and interpolation schemes without supplementary neural networks, SMPConv has an advantage of computational complexity. On the other hand, the existing large kernel convolutions are computationally heavy. Deformable convolution (Fig. 1-(e)), for example, requires offset prediction networks and convolution with interpolated inputs during both training and inference, resulting in additional computation and parameter costs. Additionally, it relies on dense convolution, making it impractical to increase kernel size significantly. Similarly, MLP-based methods (Fig. 1-(c)) like FlexConv [44] leverage kernel generation neural network, and it also increases computational burdens. The results presented in Tab. 1 demonstrate that SMPConv outperforms the existing large kernel convolutions in terms of speed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.807, + 0.21, + 0.824 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.388, + 0.849 + ], + "angle": 0, + "content": "4.1. Continuous function approximation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Firstly, we conducted a fitting experiment to validate that our self-moving point representation can work as an approximator for a continuous function. To do so, we used" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.093, + 0.639, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.097, + 0.741, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.097, + 0.852, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.86, + 0.097, + 0.878, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.181, + 0.788, + 0.193 + ], + "angle": 0, + "content": "\\(f_{a}(x,y) = \\cos (e^{y} / 0.5) + \\sin ((x^{2} - 0.5) / 5)\\)" + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.195, + 0.637, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.198, + 0.739, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.199, + 0.849, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.86, + 0.199, + 0.877, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.605, + 0.283, + 0.785, + 0.295 + ], + "angle": 0, + "content": "\\(f_{b}(x,y) = \\cos (x + y) + \\sin (40x + 2y^{2}) / 5\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.31, + 0.892, + 0.366 + ], + "angle": 0, + "content": "Figure 3. Comparison between the moving point and the fixed point representations through the fitting. Our proposed moving point representations can approximate given continuous functions with higher accuracy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.547 + ], + "angle": 0, + "content": "two sinusoidal-based functions as the ground truth. Given a function, SMP is optimized to represent the sampled function on a \\(51 \\times 51\\) grid. In this experiment, we designed SMP with 204 points. The fitting result has been shown in Fig. 3. It demonstrates that our proposed method reasonably well approximates a given continuous function with fewer points. Additionally, we compared with the fixed point representation and observed that optimizing the position of points together helps to better approximate the function as the number of points is equal." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.757, + 0.575 + ], + "angle": 0, + "content": "4.2. Sequential data classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.78 + ], + "angle": 0, + "content": "To demonstrate that SMPConv can handle long-term dependencies well, we evaluated our method on various sequential data tasks, such as sequential image and time-series classification. To do so, we followed FlexTCN [44] to construct a SMPConv architecture for causal 1D CNN whose kernel size is same as the input sequence length. We substituted their parameterized kernels with ours without additional modifications. To maintain a similar number of network parameters, SMPConv contains 30 weight points in each SMP. To alleviate the computation burdens caused by the convolution with large kernels, we have considered exploiting the computations through a fast Fourier transform. More network and experimental details are in Appx. 1.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Sequential image. We tested our SMPConv on the 1D version of images from the datasets, sequential MNIST (sMNIST), permuted MNIST(pMNIST) [29], and sequential CIFAR10 (sCIFAR10) [4]. These datasets have long input sequence lengths, for example, 784 for sMNIST and pMNIST, and 1024 for sCIFAR10. Note that it is hard to model these datasets without proper kernel representations. As shown in Tab. 2, the proposed model has achieved state" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10293" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.094, + 0.457, + 0.303 + ], + "angle": 0, + "content": "
ModelParams.sMNISTpMNISTsCIFAR10
DilRNN [4]44k98.096.1-
LSTM [2]70k87.285.7-
GRU [2]70k96.287.3-
TCN [2]70k99.097.2-
r-LSTM [56]500k98.495.272.2
IndRNN [30]83k99.096.0-
TrellisNet [3]8M99.2098.1373.42
URLSTM [20]-99.2896.9671.00
HiPPO [18]0.5M-98.30-
coRNN [47]134k99.497.3-
CKCNN [45]98k99.3198.0062.25
LSSL [21]-99.5398.7684.65
S4 [19]-99.6398.7091.13
FlexTCN [44]375k99.6298.6380.82
Ours373k99.7599.1084.86
" + }, + { + "type": "table_caption", + "bbox": [ + 0.132, + 0.314, + 0.414, + 0.328 + ], + "angle": 0, + "content": "Table 2. Sequential image classification results." + }, + { + "type": "table", + "bbox": [ + 0.095, + 0.355, + 0.457, + 0.521 + ], + "angle": 0, + "content": "
ModelParams.CTSCSC-raw
GRU-ODE [11]89k96.244.8~ 10.0
GRU-Δt [27]89k97.820.0~ 10.0
GRU-D [5]89k95.923.9~ 10.0
ODE-RNN [46]89k97.193.2~ 10.0
NCDE [27]89k98.888.5~ 10.0
CKCNN [45]100k99.5395.2771.66
LSSL [21]--93.58-
S4 [19]--93.9698.32
FlexTCN [44]373k99.5397.6791.73
Ours371k99.5397.4594.95
" + }, + { + "type": "table_caption", + "bbox": [ + 0.148, + 0.532, + 0.398, + 0.545 + ], + "angle": 0, + "content": "Table 3. Time-series classification results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.469, + 0.669 + ], + "angle": 0, + "content": "of-the-art results on both sMNIST and pMNIST. For sCIFAR10 dataset, our model has outperformed all the comparative models except S4 [19]. Compared with the FlexTCN, which has a similar network base, our model improved the accuracy by \\(4\\%\\). These results show that our proposed model is suitable and effective for sequential images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.469, + 0.822 + ], + "angle": 0, + "content": "Time-series. We evaluated our model on time-series sequence datasets, character trajectories (CT) [1], and speech commands (SC) [59]. The results have been displayed in Tab. 3. In the relatively shorter MFCC features data, SM-PConv achieved test accuracy similar to FlexTCN. To validate that our proposed model can model extremely long sequences, we conducted experiments on the SC-raw dataset, which has a sequence length of 16000. Similar to the sequence image classification result, our model outperformed FlexTCN with a large margin of \\(+3\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.903 + ], + "angle": 0, + "content": "Compared to other models, our SMPConv has achieved considerably better performance for both sequential image and time-series classification. It ensures that our kernel representation is capable of handling long-term dependencies even in the case of a limited number of parameters." + }, + { + "type": "table", + "bbox": [ + 0.554, + 0.097, + 0.839, + 0.176 + ], + "angle": 0, + "content": "
ModelParams.Accuracy
ResNet-44 [24]660k92.9
CKCNN-16 [44]630k72.1
FlexNet-16 [44]670k92.2
Ours490k93.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.558, + 0.187, + 0.834, + 0.201 + ], + "angle": 0, + "content": "Table 4. 2D image classification on CIFAR10." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.227, + 0.687, + 0.243 + ], + "angle": 0, + "content": "4.3. Image classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.371 + ], + "angle": 0, + "content": "Image classification with the continuous kernel. We validated our SMPConv on a 2D image dataset, CIFAR10 [28], which is dominated by discrete convolutions, to show that the continuous kernel can capture spatial information as well. Similar to the experiments on sequential data, we followed the network design choice of FlexNet [44], where the kernel size is \\(33 \\times 33\\). More details are in Appx. 1.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.522 + ], + "angle": 0, + "content": "As shown in Tab. 4, our continuous kernel representation model slightly outperforms ResNet, a discrete \\(3 \\times 3\\) convolution model, with a less number of parameters. It implies that our model is competitive and promising. Our model also showed better performance than MLP-based counterparts, CKCNN-16 and FlexNet-16, even when the parameters of ours were around \\(30\\%\\) lesser. In addition, we have already identified the efficiency of our model in Tab. 1. These results suggest that our method is more suitable for kernel generation than MLP-based implicit formulations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Large scale image classification. Finally, we tested our SMPConv on a large-scale ImageNet dataset [12], which contains more than one million training images and 50,000 validation images. For such a large dataset, the convolution kernels should be carefully trained to model complex data relationships accurately. Through such an experiment, therefore, we can validate that our SMP can represent a descriptive convolution kernel." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Firstly, we constructed large-scale variants of SMPConv architecture based on RepLKNet [13]. We replaced its discrete depth-wise separable convolution kernel with our SMP. In general, the larger the data and network, the larger the number of filters. To prevent excessive point position parameters depending on the number of filters, we shared the position of points over filters in large-scale settings. We empirically found that this position sharing has little effect on classification performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We proposed two variants of our model, SMPConv-T and SMPConv-B. Thanks to our efficient large kernel, we adjusted the number of channels and blocks so that our variants have a similar number of parameters to the previous models. The number of blocks and channels for each stage is [2, 2, 8, 2] and [96, 192, 384, 768] for SMPConv-T and [2, 2, 20, 2] and [128, 256, 512, 1024] for SMPConv-B, respectively. In RepLKNet-31B, the number of blocks and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10294" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.094, + 0.459, + 0.303 + ], + "angle": 0, + "content": "
ModelParams.FLOPsTop-1 Accuracy
ResNet-50 [24]26M4.1G76.5
ResNext-50-32x4d [62]25M4.3G77.6
ResMLP-S24 [54]30M6.0G79.4
DeiT-S [55]22M4.6G79.8
Swin-T [34]28M4.5G81.3
TNT-S [22]24M5.2G81.3
ConvNeXt-T [35]29M4.5G82.1
SLaK-T [32]30M5.0G82.5
SMPConv-T(ours)27M5.7G82.5
DeiT-Base/16 [55]87M17.6G81.8
Swin-B [34]88M15.4G83.5
ConvNeXt-B [35]89M15.4G83.8
SLaK-B [32]95M17.1G84.0
RepLKNet-31B [13]79M15.3G83.5
SMPConv-B(ours)80M16.6G83.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.123, + 0.313, + 0.424, + 0.327 + ], + "angle": 0, + "content": "Table 5. 2D image classification on ImageNet-1K." + }, + { + "type": "table", + "bbox": [ + 0.115, + 0.348, + 0.435, + 0.43 + ], + "angle": 0, + "content": "
ModelsradiuscoordinateAccuracy
A--90.92
B✓-91.35
C-✓92.47
SMPConv✓✓93.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.482 + ], + "angle": 0, + "content": "Table 6. Ablation study on CIFAR10. A checkmark means that the component is a learnable. In case of SMPConv, for instance, both radius and coordinate are learnable parameters." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.504, + 0.43, + 0.539 + ], + "angle": 0, + "content": "
σ0.050.20.30.5
Accuracy93.0092.2491.8491.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.549, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Table 7. Classification results on CIFAR10 with different standard deviation \\( \\sigma \\) of point location sampling distribution." + }, + { + "type": "table", + "bbox": [ + 0.118, + 0.599, + 0.43, + 0.635 + ], + "angle": 0, + "content": "
r0.120.180.240.3
Accuracy93.0092.3692.0691.76
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.672 + ], + "angle": 0, + "content": "Table 8. Classification results on CIFAR10 with different initial radius \\( r \\) ." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.699, + 0.468, + 0.744 + ], + "angle": 0, + "content": "channels for each stage is [2, 2, 18, 2] and [128, 256, 512, 1024]. More experimental details are provided in Appx. 1.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.468, + 0.822 + ], + "angle": 0, + "content": "As reported in Tab. 5, our models obtained competitive performance with fewer parameters than existing models. These results show that our kernel representation is promising for large-scale domains as well. Overall, our kernel representation is highly effective and descriptive." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.182, + 0.847 + ], + "angle": 0, + "content": "4.4. Ablation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We performed various ablation studies with additional experiments on CIFAR10 image classification. First, we investigated the validity of learnable radius and coordinate. In" + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.097, + 0.883, + 0.148 + ], + "angle": 0, + "content": "
Np48163264
Params.250k330k490k809k1447k
Accuracy92.5692.2893.0092.8492.21
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.157, + 0.892, + 0.186 + ], + "angle": 0, + "content": "Table 9. Classification results on CIFAR10 with different number of moving points \\( N_{p} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.349 + ], + "angle": 0, + "content": "Tab. 6, it showed that performance degradation occurs when either one or both components are set to non-learnable parameters. Remarkably, Model C, which set coordinate to trainable parameters, outperformed Model A by a considerable margin. Furthermore, Model B also had a slight performance gain. It suggests that even randomly distributed fixed weight points can increase their interpolation ability with trainable radius. These results indicate that training both coordinate and radius is valid." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.893, + 0.487 + ], + "angle": 0, + "content": "Next, we identified the effect of the initial position of the points by varying the \\(\\sigma\\), a standard deviation of point location sampling distribution. In Tab. 7, we observed that a small \\(\\sigma\\) value, indicating initial positions of the points are gathered in the center of the kernel, leads to higher accuracy. This is because it is difficult to train large kernels from the beginning of training. Thus, large kernels can be effectively trained by starting with small kernels and expanding the receptive fields through moving points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.607 + ], + "angle": 0, + "content": "We also found that larger initial radius degrades the model performance as shown in Tab. 8. The large radius results in a large initial kernel size, which makes initial training difficult. Furthermore, it is also challenging to train a large area of the kernel dependent on a single weight point which is not optimized in the early stages of training. Both Tab. 7 and Tab. 8 empirically show that our initialization methods for SMP are effective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.893, + 0.821 + ], + "angle": 0, + "content": "As depicted in Tab. 9, we figured out that simply increasing the number of weight points \\( N_{p} \\) does not help for performance. It implies that a small number of points are enough to represent a proper convolution filter. Since the performance is influenced by the number of points, our method is also required tuning like common neural networks. However, the performance difference between CKCNN and FlexNet in Tab. 4 shows that MLP-based methods are severely influenced by architectural settings. That is, they have extensive search space, such as depth, width, and activation function, so they typically require more tuning than our method. Moreover, the impact of the number of points is not particularly significant in that even the worst \\( (N_{p} = 64) \\) slightly outperforms the FlexNet (acc=92.20)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.638, + 0.846 + ], + "angle": 0, + "content": "4.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Finally, we analyze our SMP by visualizing filters trained on CIFAR10. In the first column of Fig. 4, we can observe the trained weight points' position. In our method, point lo" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10295" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.098, + 0.216, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.101, + 0.323, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.102, + 0.43, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.44, + 0.102, + 0.537, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.548, + 0.102, + 0.645, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.102, + 0.755, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.1, + 0.889, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.189, + 0.216, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.281, + 0.177, + 0.29 + ], + "angle": 0, + "content": "points" + }, + { + "type": "image", + "bbox": [ + 0.224, + 0.193, + 0.323, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.256, + 0.28, + 0.293, + 0.289 + ], + "angle": 0, + "content": "kernel 1" + }, + { + "type": "image", + "bbox": [ + 0.332, + 0.193, + 0.43, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.365, + 0.28, + 0.403, + 0.289 + ], + "angle": 0, + "content": "kernel 2" + }, + { + "type": "image", + "bbox": [ + 0.44, + 0.193, + 0.538, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.47, + 0.28, + 0.508, + 0.289 + ], + "angle": 0, + "content": "kernel 3" + }, + { + "type": "image", + "bbox": [ + 0.548, + 0.193, + 0.646, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.28, + 0.615, + 0.289 + ], + "angle": 0, + "content": "kernel 4" + }, + { + "type": "image", + "bbox": [ + 0.657, + 0.193, + 0.755, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.686, + 0.28, + 0.724, + 0.289 + ], + "angle": 0, + "content": "kernel 5" + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.192, + 0.889, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.28, + 0.831, + 0.289 + ], + "angle": 0, + "content": "kernel 6" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.306, + 0.892, + 0.334 + ], + "angle": 0, + "content": "Figure 4. Visualization of kernels. Each row shows the location of points and first 6 kernels of a filter. For ease of visualization, the kernels are first subjected to the absolute value operation and then normalized to a range of [0,1]." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.363, + 0.212, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.449, + 0.174, + 0.458 + ], + "angle": 0, + "content": "(a) Layer 1" + }, + { + "type": "image", + "bbox": [ + 0.219, + 0.369, + 0.318, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.449, + 0.29, + 0.458 + ], + "angle": 0, + "content": "(b) Layer 8" + }, + { + "type": "image", + "bbox": [ + 0.333, + 0.369, + 0.455, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.359, + 0.449, + 0.408, + 0.458 + ], + "angle": 0, + "content": "(c) Layer 14" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.474, + 0.468, + 0.501 + ], + "angle": 0, + "content": "Figure 5. Normalized sum of the absolute value of trained filters. (a), (b), and (c) are top, middle, and bottom layers, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.468, + 0.679 + ], + "angle": 0, + "content": "cations \\( p_i \\) are mainly sampled near the center of the kernel for stable training. It shows that the points spread out for optimal kernel representation over the training process, as we argued, and thus the receptive fields are not limited to a small part. Also, we can figure out that there are square patterns caused by Eq. (2) in the kernels, where each square has its own area. This suggests that although the radius parameters are initialized with small values, the values are individually increased and optimized for each corresponding weight point during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.468, + 0.815 + ], + "angle": 0, + "content": "Observing visualized convolution kernel in Fig. 4, kernels from the same filter share the receptive fields. It allows a single filter to focus on the shared area. Furthermore, as illustrated in Fig. 5, SMPConv has large adaptive receptive fields which are not conventional square or rectangular shapes. This is because it consists of optimized filters with their own small and large receptive fields. Thus, our method can handle not only global information but also local details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.321, + 0.846 + ], + "angle": 0, + "content": "5. Conclusion and discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In this paper, we present a method to build a continuous convolution. We propose using point representations, where each point has the weight parameters, coordinates, and ra" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.495 + ], + "angle": 0, + "content": "dius to learn. By connecting the points, we can implement a continuous function, which can be utilized to construct convolutional kernels. We have provided extensive experimental results, showing that drop-in replacement in the existing training pipeline without bells and whistles improved the performance by a safe margin. We also show that a continuous convolution can be effectively utilized in a large-scale experiment. We expect more research and development in this direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.618 + ], + "angle": 0, + "content": "Although promising, there are many rooms to be improved. Due to the limited computational budget, we could not conduct sufficient experiments in the large-scale experiment. The experimental results provided in this manuscript resulted from a few runs. As trial and error are essential in the machine learning development process, we plan to find optimal configurations and training techniques to enhance the performance of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.738 + ], + "angle": 0, + "content": "We also observed that the learned kernels often show sparse patterns depending on the tasks. It is well aligned with the success of dilated convolution or its variants, and our methods automatically learn proper sparsity during the training process on specific tasks. Adding prior knowledge through training and regularization techniques would further improve performance, especially for tasks requiring longer-term dependency modeling." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.752, + 0.659, + 0.768 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.892, + 0.888 + ], + "angle": 0, + "content": "We thank Usman Ali for valuable discussions. This research was supported by the Ministry of Science and ICT (MSIT) of Korea, under the National Research Foundation (NRF) grant (2022R1F1A1064184, 2022R1A4A3033571), Institute of Information and Communication Technology Planning Evaluation (IITP) grants for the AI Graduate School program (IITP-2019-0-00421), and the BK21 FOUR Project." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10296" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. 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Differentiable point-based radiance fields for efficient view synthesis. arXiv preprint arXiv:2205.14330, 2022. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "10299" + } + ] +] \ No newline at end of file diff --git a/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_origin.pdf b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2204dc74e7f421fa9c5095e4e0585e7a7d0bd0d9 --- /dev/null +++ b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/a40d3fb1-72be-4c1d-a333-984a29892bca_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:492d9f1c00e2fb0daf8b334ad6b94b473b85554d3b97222bf10abbb15922e1ca +size 2896552 diff --git a/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/full.md b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/full.md new file mode 100644 index 0000000000000000000000000000000000000000..be824de95a8a4d09ea24247f1b9483f01314ebc9 --- /dev/null +++ b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/full.md @@ -0,0 +1,374 @@ +# SMPCov: Self-moving Point Representations for Continuous Convolution + +Sanghyeon Kim $^{1}$ Eunbyung Park $^{1,2*}$ $^{1}$ Department of Electrical and Computer Engineering, Sungkyunkwan University + $^{2}$ Department of Artificial Intelligence, Sungkyunkwan University + +# Abstract + +Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv + +# 1. Introduction + +There has been a recent surge of interest in representing the convolutional kernel as a function over a continuous input domain. It can easily handle irregularly sampled data both in time [1, 59] and space [61, 65], overcoming the drawbacks of the discrete convolution operating only on discretized sampled data with pre-defined resolutions and grids. With the progress in modeling and training continuous kernels, it has enjoyed great success in many practical scenarios, such as 3D point cloud classification and segmen + +tation [36,41,52,58,64], image super resolution [57], object tracking [10], to name a few. Furthermore, the recent trends of using large convolutional kernels with strong empirical results urge us to develop a more efficient way to implement it [13,32], and the continuous convolution will be a promising candidate because of its capability to readily construct arbitrarily large receptive fields [44, 45]. + +One of the dominant approaches to modeling the continuous kernel is to use a particular type of neural network architecture, taking as inputs low-dimensional input coordinates and generating the kernel values [44, 45], known as neural fields [38, 49] or simply MLPs. Using neural fields to represent the kernels, we can query kernel values at arbitrary resolutions in parallel and construct the large kernels with a fixed parameter budget, as opposed to the conventional discrete convolutions requiring more parameters to enlarge receptive fields. Thanks to recent advances to overcome the spectral bias on training neural fields [49], they can also represent functions with high-frequency components, which enables learned kernels to capture fine details of input data. + +While promising in various tasks and applications, this approach has a few downsides. First, it incurs considerable computational burdens to already computation-heavy processes of training deep neural networks. Each training iteration involves multiple forward and backward passes of MLPs to generate kernels and update the parameters of MLPs. This additional complexity prevents it from being applied to large-scale problems, such as ImageNet-scale, since it needs deeper and wider MLP architectures to construct more complex kernels with more input and output channels. Although MLPs can generate larger sizes and numbers of kernels without adding more parameters, it has been known that the size of MLPs mainly determines the complexity of the functions they represent and, eventually, the performance of the CNNs. + +Furthermore, the kernels generated by an MLP depend heavily on the architectural priors. As a universal function approximator, a neural network with sufficient depth and width can express any continuous functions [25]. However, we have empirically observed strong evidence that the ar + +chitecture of neural networks has played a significant role in many practical settings, suggesting that various architectural changes to the kernel-generating MLPs would significantly affect the performance of CNNs. Considering a large number of hyperparameters in training neural networks, adding more knobs to tune, e.g., activation functions, width, depth, and many architectural variations of MLPs., would not be a pragmatic solution for both machine learning researchers and practitioners. + +In this paper, we aim to build continuous convolution kernels with negligible computational cost and minimal architectural priors. We propose to use moving point representations and implement infinite resolution by interpolating nearby moving points at arbitrary query locations. The moving points are the actual kernel parameters, and we connect the neighboring points to build continuous kernels. Recent techniques in neural fields literature inspire it, where they used grid or irregularly distributed points to represent features or quantities in questions (density or colors) for novel view synthesis [6, 50, 63, 66, 67]. The suggested approach only introduces minor computational costs (interpolation costs) and does not consist of neural networks (only point representations and interpolation kernels). Moreover, the spectral bias presented in training MLPs [43] does not exist in the suggested representation. Each point representation covers the local area of the input domain and is updated independently of each other, contrasted with MLPs, where updating each parameter would affect the entire input domain. Therefore, highly different values of nearby points can easily express high-frequency components of the function. + +The proposed method can also be more parameter efficient than the discrete convolution to construct the large kernels. Depending on the complexity of the kernels to be learned, a few numbers of points may be sufficient to cover a large receptive field (e.g., a unimodal function can be approximated by a single point). Many works have extensively exploited non-full ranks of the learned kernels to implement efficient convolutions or compress the models [32]. Our approach can likewise benefit from the presence of learned kernels with low-frequency components. + +We conduct comprehensive experimental results to show the effectiveness of the proposed method. First, we demonstrate that moving point representations can approximate continuous functions very well in 1D and 2D function fitting experiments. Then, we test its ability to handle long-term dependencies on various sequential datasets. Finally, we also evaluate our model on 2D image data. Especially, we perform large-scale experiments on the ImageNet classification dataset (to our knowledge, it is the first attempt to use continuous convolution for such a large-scale problem). Our proposed method can be used as a drop-in replacement of convolution layers for all the above tasks without bells + +and whistles. The experimental results show that it consistently improves the performance of the prior arts. + +# 2. Related works + +Neural fields and continuous convolution. Neural fields have recently emerged as an alternative neural network representation [49]. It is a field parameterized by a neural network, such as simple MLP, taking as low-dimensional coordinates input and generating quantity in questions. It has shown great success in various visual computing domains, such as novel view synthesis [38], 3D shape representation [37, 40], and data compression [17], to name a few. Since it is a function over a continuous input domain, it can produce outputs at arbitrary resolutions. Recent studies have exploited its continuous nature to model continuous kernels for CNNs [44, 45, 58]. [58] used an MLP architecture to implement the continuous kernel to handle irregularly sampled data, such as 3D point clouds. While successful, the descriptive power of the learned kernel is limited due to its bias toward learning low-frequency components. With the recent advances in overcoming the spectral bias [49], [45] has explored various activation functions to improve the performance of CNNs. To further improve, [44] proposed to learn the receptive field sizes and showed impressive performance on multiple tasks. + +We also propose a method that can likewise be classified as a neural field. However, we implement a field without neural networks, using self-moving point representations and interpolation schemes. It significantly reduces the computational costs to compute the kernels during training compared to the conventional MLP-based methods. Furthermore, it removes the burden of numerous hyperparameter searches for a newly introduced neural network in the already complicated training procedure. + +Grid and point representations. Although MLP-based neural fields have succeeded in many tasks, they require substantial computational costs for training and inference, and the spectral bias presented in MLPs often degrades the performance. In order to reduce the computations and avoid the issues of using MLPs, classical grid-based representations have been adopted in the neural fields. Plenoxels [66] stores the coefficients of spherical harmonic in the 3D voxel structure and implements the infinite resolution via the interpolation methods, reducing the training time from days to minutes. Instant-NGP [39] further optimized the speed using a hash-based indexing algorithm. The combination of grid representations and MLPs has been extensively explored to find better solutions [6, 50]. + +Point representations have been recently suggested in neural fields to improve the shortcomings in grid-based representations, thanks to their flexibility and expressibility [63, 67]. They can generate outputs over a continuous input domain by interpolating neighboring points given a + +![](images/b454e824fac6acaa52a96315dd082ad4839d377c5eefe38d2e8943ce7b3a80b0.jpg) + +![](images/136124815209c9ed3e59d5ada63f91c00693466584c5963989b28c2b22e1ad53.jpg) + +![](images/54a805de77e88ee3e925eb04d9298226393faf1af58823f7dd98dc5dab133032.jpg) + +![](images/5a28e083f89021db08bf615c23560bc5cc0591dd07833f9a53e2f4366529bcba.jpg) + +![](images/c3fa5883061529250fb77cb8fe4122653ea3ff782cc00a1a6be2285cbf3764c4.jpg) +Figure 1. A various methods for large kernel construction. + +![](images/8f209bd801e10c314137a4609f4eeb4cb256fdab39285f826a66bb865c93e741.jpg) + +![](images/b653ecc59508a8e5fc1d6471fe5c6116d8a89c4783ee6618498c8ef338e2e71e.jpg) + +query point. It can be more accurate and parameter efficient than the grid-based ones since it can adaptively locate points, considering the complexity of functions, e.g., fewer points in low-frequency areas. Although our work is largely inspired by these works, 1. we repurpose the point representations to build continuous convolutional kernels, 2. we do not use MLPs that would introduce additional modeling complexity, 3. our method does not require complex initializations (or algorithms) to relocate points, such as depth-based initialization [63] and mask-based initialization [67]. + +Large kernel convolution. Since the great success of VGG-style CNNs [24, 26, 48, 51] in ImageNet [12], we repeatedly apply small kernels (e.g., $3 \times 3$ kernel) with deep layers to get a large receptive field and deal with long-term dependencies. With the massive success of transformers in the vision domain [15, 16, 34, 55], which have a large receptive field, recent studies have started to revisit the descriptive power of large kernels [13, 32, 35, 53]. RepLKNet [13] has shown we can increase the kernel size up to $31 \times 31$ with the help of the reparameterization trick. More recently, SLaK [32] managed to scale the kernel size to $51 \times 51$ and $61 \times 61$ , showing improved performance with dynamic sparsity and low-rank factorization (Fig. 1-(b)). While promising, the number of parameters increases according to the kernel size, which is a major bottleneck in representing large kernels. + +The continuous kernel can construct large kernels with a fixed parameter budget (Fig. 1-(c)). CKConv [45] and FlexConv [44] have exploited this property and demonstrated that their method can model long-term dependencies by constructing large kernels on various datasets. However, they introduce a considerable amount of computations to the training process, and they have yet to perform largescale experiments, e.g., ImageNet. To the best of our knowledge, our approach is the first to conduct such a large-scale experiment using continuous convolution. + +On the other hand, dilated convolutions [7, 8] can also be used to enlarge receptive fields with a small number of + +parameters, and they also do not introduce additional computations during training (Fig. 1-(d)). Deformable convolutions [9] look similar to ours in terms of moving points arbitrarily (Fig. 1-(e)). However, they learn how to deform the kernels (or predict the offset) during inference. On the other hand, we adjust the locations of the point representations during training to find the optimal large kernels. A concurrent work suggests learning the offsets during training [23]. In contrast to ours, it is a discrete formulation, thus losing the benefits of continuous convolution. Furthermore, we adjust the receptive fields of each point representation separately, yielding more expressive representations. + +Continuous convolution for point clouds. There have been many continuous convolution approaches to handle 3D point cloud data, which is an important example of irregularly sampled data. PointNet [41] and PointNet++ [42] are pioneer works that use average pooling and $1 \times 1$ convolution to aggregate features. [31, 33, 58, 60] leveraged MLPs to implement continuous convolution. KPCov [52] is also considered a continuous convolution and shares some similarities with ours (Fig. 1-f). They also used point representation and interpolation kernels for handling point clouds. However, their points are fixed over the training, unlike ours. They also proposed a deformable version, which requires additional neural networks to predict the offset of the kernel points. + +# 3. SMPCov + +# 3.1. Self-moving point representation + +This section describes the proposed self-moving point representation to represent a continuous function. Let $d$ be the size of the input coordinates dimension, e.g., 1 in timeseries data and 2 in the spatial domain. $\mathsf{SMP}:\mathbb{R}^d\to \mathbb{R}^{N_c}$ is a vector-valued function, mapping from the input coordinates to the output kernel vectors, where $N_{c}$ is a channel size. Given a query point $x\in \mathbb{R}^d$ , we define a continuous + +kernel function as follows. + +$$ +\operatorname {S M P} (x; \phi) = \frac {1}{| \mathcal {N} (x) |} \sum_ {i \in \mathcal {N} (x)} g (x, p _ {i}, r _ {i}) w _ {i}, \tag {1} +$$ + +where $\phi = \{\{p_i\}_{i = 1}^{N_p},\{w_i\}_{i = 1}^{N_p},\{r_i\}_{i = 1}^{N_p}\}$ is a set of learnable parameters, and $N_{p}$ is the number of points that are used to represent the function. $p_i\in \mathbb{R}^d$ is the coordinates of self-moving point representation $w_{i}\in \mathbb{R}^{N_{c}}$ , and each point representation also has a learnable radius, $r_i\in \mathbb{R}^+$ is a positive real number, which we implement it by clipping for numerical stability. We define a distance function $g:\mathbb{R}^d\times \mathbb{R}^d\times \mathbb{R}^+\to \mathbb{R}$ as follows, + +$$ +g (x, p _ {i}, r _ {i}) = 1 - \frac {\| x - p _ {i} \| _ {1}}{r _ {i}}, \tag {2} +$$ + +where $\| \cdot \|_1$ is a L1 distance. $\mathcal{N}(x)$ is a set of indices of neighboring points of a query coordinate $x$ , defined as $\mathcal{N}(x) = \{i | g(x, p_i, r_i) > 0, \forall i\}$ . Thus, points beyond a certain distance (depending on the radius) will not affect the query point. Hence, SMP generates output vectors by a weighted average of the nearby point representations. Note that all three parameters $\{p_i\}, \{w_i\}, \{r_i\}$ are jointly trained with the CNN model parameters, and the gradients w.r.t those parameters can be easily computed using an automatic differentiation library. As the name SMP suggests, the coordinates $\{p_i\}$ are updated during training, resulting in moving points representation. + +Compared to a fixed-point representation, where $\{p_i\}$ are not trainable, ours can approximate complex functions more precisely. Since each point can move freely, more points can be gathered in high-frequency areas. On the other hand, few points can easily represent low-frequency components, resulting in more parameter-efficient representation. For example, a single point may be sufficient to approximate unimodal functions. + +# 3.2. SMPConv + +We leverage the suggested representation to implement a continuous convolution operator. In one dimensional case, $d = 1$ , a continuous convolution can be formulated as, + +$$ +(f * \operatorname {S M P}) (x) = \sum_ {c = 1} ^ {N _ {c}} \int_ {\mathbb {R}} f _ {c} (\tau) \operatorname {S M P} _ {c} (x - \tau) d \tau , \tag {3} +$$ + +where $f: \mathbb{R} \to \mathbb{R}^{N_c}$ is a input function and the $f_{c}$ and $\mathrm{SMP}_c$ denote the $c$ -th element of the inputs. The convolution operator generates a function, computing the filter responses by summing over entire $N_{c}$ channels. One SMP representation corresponds to a convolution operator, and multiple SMPs are used to implement one convolutional layer to generate multiple output channels. In contrast to the previous MLP-based continuous convolution, which uses one neural network for one convolutional layer, our approach has separate + +![](images/612c5bbfabb25031f6971bddcfcac3f9897aa884f51c350565dad04606e34031.jpg) +(a) SMP (1D) + +![](images/c2f4cfc3794999dac228bbf93e20fd08a02e9634c14c64cb03ca6cdb16cde6ea.jpg) +(b) SMP (2D) +Figure 2. Self-moving point representation. (a) SMP as a function of the one-dimensional input domain, and (b) SMP as a function of the two-dimensional input domain. 'C #1' means the first channel. Each channel shares the location of the points, whereas each channel has its own weight parameters. + +parameters for each convolution filter in a layer. It gives more freedom to each filter and results in more descriptive power of the learned filter. + +As depicted in Fig. 2, the kernels of each filter share the position parameters. That is, each filter of one layer has its own position parameters. Although we could use different SMP for different channels. However, it will considerably increase the number of learnable parameters ( $\{p_i\}$ per channel), and we believe that locating points at the same location for a convolutional filter can be a reasonable prior, where a convolutional filter can focus on specific areas in the input domain. + +We leverage our continuous formulation to construct large kernels, motivated by the recent success of using them in many tasks. We can create arbitrary size large kernels by querying multiple discretized coordinates to SMP. + +# 3.3. Training + +Training a large kernel has been challenging and computationally heavy, and naive training practice has yet to show promising results. Recently, [13, 14] proposed a reparameterization trick to combine different-size kernels as a separate branch, resulting in improved performance and more stable training. We also applied the same trick to train CNNs with SMPConv. + +We empirically figured out that performance degradation occurs when the coordinates $\{p_i\}$ are forced to fit inside the kernel by clipping. Thus, we let the coordinates be freely updated during training. + +We also found that the initialization of the parameters $\phi$ matters. For point locations, $\{p_i\}$ , we randomly sample from a gaussian distribution with small $\sigma$ . It initially locates the points in the center and gradually spreads out over the training process. We empirically found that this strategy yields more stable training, especially at the beginning of the training. We also initialized with small values + +
MethodkParams.Time ↓Throughput ↑
Deformable [9]30.29M61.24390.7
51.37M157.31618.9
74.39M293.1882.3
FlexConv [44]330.67M92.91923.4
SMPConv330.49M40.14258.4
+ +Table 1. Training time (sec/epoch) and throughput (examples/sec) comparison with CIFAR10 on a single RTX3090 GPU. Both are tested with a batch size of 64 and input resolution of $32 \times 32$ . The $k$ is kernel size. The time is the average training time of the first 10 epochs. + +for $\{r_i\}$ , which each weight parameter firstly has a narrow sight. Over the course of training, $\{r_i\}$ also gradually increases if necessary. + +# 3.4. Efficiency + +Assuming the size of a convolution filter is $C \times N \times N$ , where $C$ is the number of kernels and $N$ is the height and width of filter, $CN^2$ parameters are required in dense convolution (Fig. 1-(a)). Therefore, the number of parameters is proportional to kernel resolution $N \times N$ . On the other hand, SMP needs $(1 + d + C)N_{p}$ parameters, where $d$ is the size of the input coordinates dimension, and $N_{p}$ is the number of weight points. We used $N_{p} \ll N^{2}$ , so SMP is more efficient than dense convolution in terms of the number of parameters. Furthermore, as the number of parameters does not depend on kernel resolution, SMP can represent kernels of any size, such as large or continuous kernels with fixed budget parameters. + +Due to the point representations and interpolation schemes without supplementary neural networks, SMPConv has an advantage of computational complexity. On the other hand, the existing large kernel convolutions are computationally heavy. Deformable convolution (Fig. 1-(e)), for example, requires offset prediction networks and convolution with interpolated inputs during both training and inference, resulting in additional computation and parameter costs. Additionally, it relies on dense convolution, making it impractical to increase kernel size significantly. Similarly, MLP-based methods (Fig. 1-(c)) like FlexConv [44] leverage kernel generation neural network, and it also increases computational burdens. The results presented in Tab. 1 demonstrate that SMPConv outperforms the existing large kernel convolutions in terms of speed. + +# 4. Experiments + +# 4.1. Continuous function approximation + +Firstly, we conducted a fitting experiment to validate that our self-moving point representation can work as an approximator for a continuous function. To do so, we used + +![](images/973ff0d1afabaaf1182553d0edb99f42f125c0103fc43bd221328197ddf7638a.jpg) +$f_{a}(x,y) = \cos (e^{y} / 0.5) + \sin ((x^{2} - 0.5) / 5)$ + +![](images/686e1067b02dab736e906306784a30d4bbb4d516f2799904222365fa7cd93778.jpg) + +![](images/d42447effa1082f89058dc474dd779ecddd8a10b80d4924cddcd01fde659baef.jpg) + +![](images/87ec7d9536c1db127ed4d93830cc35429d7769a5fc3414f103e85803b8798914.jpg) + +![](images/17e2fb7ef9adf14bb70e4f01325d91a24147aa5505d34666354d39be93b6dcf2.jpg) +$f_{b}(x,y) = \cos (x + y) + \sin (40x + 2y^{2}) / 5$ + +![](images/549446d7608d7889f5400e98f089dad4a4227e3e60517ab949a9ce48e4694b69.jpg) +Figure 3. Comparison between the moving point and the fixed point representations through the fitting. Our proposed moving point representations can approximate given continuous functions with higher accuracy. + +![](images/ac8771fb52e211bf09d75d8e2eabd8455bc5afe700c865b26d6e83baaf8fb37a.jpg) + +![](images/2e8d34502bed68a330e14f91ab359c707ae5a75d9a49624bf3cd64d0d6040315.jpg) + +two sinusoidal-based functions as the ground truth. Given a function, SMP is optimized to represent the sampled function on a $51 \times 51$ grid. In this experiment, we designed SMP with 204 points. The fitting result has been shown in Fig. 3. It demonstrates that our proposed method reasonably well approximates a given continuous function with fewer points. Additionally, we compared with the fixed point representation and observed that optimizing the position of points together helps to better approximate the function as the number of points is equal. + +# 4.2. Sequential data classification + +To demonstrate that SMPConv can handle long-term dependencies well, we evaluated our method on various sequential data tasks, such as sequential image and time-series classification. To do so, we followed FlexTCN [44] to construct a SMPConv architecture for causal 1D CNN whose kernel size is same as the input sequence length. We substituted their parameterized kernels with ours without additional modifications. To maintain a similar number of network parameters, SMPConv contains 30 weight points in each SMP. To alleviate the computation burdens caused by the convolution with large kernels, we have considered exploiting the computations through a fast Fourier transform. More network and experimental details are in Appx. 1.1. + +Sequential image. We tested our SMPConv on the 1D version of images from the datasets, sequential MNIST (sMNIST), permuted MNIST(pMNIST) [29], and sequential CIFAR10 (sCIFAR10) [4]. These datasets have long input sequence lengths, for example, 784 for sMNIST and pMNIST, and 1024 for sCIFAR10. Note that it is hard to model these datasets without proper kernel representations. As shown in Tab. 2, the proposed model has achieved state + +
ModelParams.sMNISTpMNISTsCIFAR10
DilRNN [4]44k98.096.1-
LSTM [2]70k87.285.7-
GRU [2]70k96.287.3-
TCN [2]70k99.097.2-
r-LSTM [56]500k98.495.272.2
IndRNN [30]83k99.096.0-
TrellisNet [3]8M99.2098.1373.42
URLSTM [20]-99.2896.9671.00
HiPPO [18]0.5M-98.30-
coRNN [47]134k99.497.3-
CKCNN [45]98k99.3198.0062.25
LSSL [21]-99.5398.7684.65
S4 [19]-99.6398.7091.13
FlexTCN [44]375k99.6298.6380.82
Ours373k99.7599.1084.86
+ +Table 2. Sequential image classification results. + +
ModelParams.CTSCSC-raw
GRU-ODE [11]89k96.244.8~ 10.0
GRU-Δt [27]89k97.820.0~ 10.0
GRU-D [5]89k95.923.9~ 10.0
ODE-RNN [46]89k97.193.2~ 10.0
NCDE [27]89k98.888.5~ 10.0
CKCNN [45]100k99.5395.2771.66
LSSL [21]--93.58-
S4 [19]--93.9698.32
FlexTCN [44]373k99.5397.6791.73
Ours371k99.5397.4594.95
+ +of-the-art results on both sMNIST and pMNIST. For sCIFAR10 dataset, our model has outperformed all the comparative models except S4 [19]. Compared with the FlexTCN, which has a similar network base, our model improved the accuracy by $4\%$ . These results show that our proposed model is suitable and effective for sequential images. + +Time-series. We evaluated our model on time-series sequence datasets, character trajectories (CT) [1], and speech commands (SC) [59]. The results have been displayed in Tab. 3. In the relatively shorter MFCC features data, SM-PConv achieved test accuracy similar to FlexTCN. To validate that our proposed model can model extremely long sequences, we conducted experiments on the SC-raw dataset, which has a sequence length of 16000. Similar to the sequence image classification result, our model outperformed FlexTCN with a large margin of $+3\%$ . + +Compared to other models, our SMPConv has achieved considerably better performance for both sequential image and time-series classification. It ensures that our kernel representation is capable of handling long-term dependencies even in the case of a limited number of parameters. + +Table 3. Time-series classification results. + +
ModelParams.Accuracy
ResNet-44 [24]660k92.9
CKCNN-16 [44]630k72.1
FlexNet-16 [44]670k92.2
Ours490k93.0
+ +Table 4. 2D image classification on CIFAR10. + +# 4.3. Image classification + +Image classification with the continuous kernel. We validated our SMPConv on a 2D image dataset, CIFAR10 [28], which is dominated by discrete convolutions, to show that the continuous kernel can capture spatial information as well. Similar to the experiments on sequential data, we followed the network design choice of FlexNet [44], where the kernel size is $33 \times 33$ . More details are in Appx. 1.1. + +As shown in Tab. 4, our continuous kernel representation model slightly outperforms ResNet, a discrete $3 \times 3$ convolution model, with a less number of parameters. It implies that our model is competitive and promising. Our model also showed better performance than MLP-based counterparts, CKCNN-16 and FlexNet-16, even when the parameters of ours were around $30\%$ lesser. In addition, we have already identified the efficiency of our model in Tab. 1. These results suggest that our method is more suitable for kernel generation than MLP-based implicit formulations. + +Large scale image classification. Finally, we tested our SMPConv on a large-scale ImageNet dataset [12], which contains more than one million training images and 50,000 validation images. For such a large dataset, the convolution kernels should be carefully trained to model complex data relationships accurately. Through such an experiment, therefore, we can validate that our SMP can represent a descriptive convolution kernel. + +Firstly, we constructed large-scale variants of SMPConv architecture based on RepLKNet [13]. We replaced its discrete depth-wise separable convolution kernel with our SMP. In general, the larger the data and network, the larger the number of filters. To prevent excessive point position parameters depending on the number of filters, we shared the position of points over filters in large-scale settings. We empirically found that this position sharing has little effect on classification performance. + +We proposed two variants of our model, SMPConv-T and SMPConv-B. Thanks to our efficient large kernel, we adjusted the number of channels and blocks so that our variants have a similar number of parameters to the previous models. The number of blocks and channels for each stage is [2, 2, 8, 2] and [96, 192, 384, 768] for SMPConv-T and [2, 2, 20, 2] and [128, 256, 512, 1024] for SMPConv-B, respectively. In RepLKNet-31B, the number of blocks and + +
ModelParams.FLOPsTop-1 Accuracy
ResNet-50 [24]26M4.1G76.5
ResNext-50-32x4d [62]25M4.3G77.6
ResMLP-S24 [54]30M6.0G79.4
DeiT-S [55]22M4.6G79.8
Swin-T [34]28M4.5G81.3
TNT-S [22]24M5.2G81.3
ConvNeXt-T [35]29M4.5G82.1
SLaK-T [32]30M5.0G82.5
SMPConv-T(ours)27M5.7G82.5
DeiT-Base/16 [55]87M17.6G81.8
Swin-B [34]88M15.4G83.5
ConvNeXt-B [35]89M15.4G83.8
SLaK-B [32]95M17.1G84.0
RepLKNet-31B [13]79M15.3G83.5
SMPConv-B(ours)80M16.6G83.8
+ +Table 5. 2D image classification on ImageNet-1K. + +
ModelsradiuscoordinateAccuracy
A--90.92
B✓-91.35
C-✓92.47
SMPConv✓✓93.00
+ +Table 6. Ablation study on CIFAR10. A checkmark means that the component is a learnable. In case of SMPConv, for instance, both radius and coordinate are learnable parameters. + +
σ0.050.20.30.5
Accuracy93.0092.2491.8491.51
+ +Table 7. Classification results on CIFAR10 with different standard deviation $\sigma$ of point location sampling distribution. + +
r0.120.180.240.3
Accuracy93.0092.3692.0691.76
+ +channels for each stage is [2, 2, 18, 2] and [128, 256, 512, 1024]. More experimental details are provided in Appx. 1.2. + +As reported in Tab. 5, our models obtained competitive performance with fewer parameters than existing models. These results show that our kernel representation is promising for large-scale domains as well. Overall, our kernel representation is highly effective and descriptive. + +# 4.4. Ablation + +We performed various ablation studies with additional experiments on CIFAR10 image classification. First, we investigated the validity of learnable radius and coordinate. In + +Table 8. Classification results on CIFAR10 with different initial radius $r$ . + +
Np48163264
Params.250k330k490k809k1447k
Accuracy92.5692.2893.0092.8492.21
+ +Table 9. Classification results on CIFAR10 with different number of moving points $N_{p}$ . + +Tab. 6, it showed that performance degradation occurs when either one or both components are set to non-learnable parameters. Remarkably, Model C, which set coordinate to trainable parameters, outperformed Model A by a considerable margin. Furthermore, Model B also had a slight performance gain. It suggests that even randomly distributed fixed weight points can increase their interpolation ability with trainable radius. These results indicate that training both coordinate and radius is valid. + +Next, we identified the effect of the initial position of the points by varying the $\sigma$ , a standard deviation of point location sampling distribution. In Tab. 7, we observed that a small $\sigma$ value, indicating initial positions of the points are gathered in the center of the kernel, leads to higher accuracy. This is because it is difficult to train large kernels from the beginning of training. Thus, large kernels can be effectively trained by starting with small kernels and expanding the receptive fields through moving points. + +We also found that larger initial radius degrades the model performance as shown in Tab. 8. The large radius results in a large initial kernel size, which makes initial training difficult. Furthermore, it is also challenging to train a large area of the kernel dependent on a single weight point which is not optimized in the early stages of training. Both Tab. 7 and Tab. 8 empirically show that our initialization methods for SMP are effective. + +As depicted in Tab. 9, we figured out that simply increasing the number of weight points $N_{p}$ does not help for performance. It implies that a small number of points are enough to represent a proper convolution filter. Since the performance is influenced by the number of points, our method is also required tuning like common neural networks. However, the performance difference between CKCNN and FlexNet in Tab. 4 shows that MLP-based methods are severely influenced by architectural settings. That is, they have extensive search space, such as depth, width, and activation function, so they typically require more tuning than our method. Moreover, the impact of the number of points is not particularly significant in that even the worst $(N_{p} = 64)$ slightly outperforms the FlexNet (acc=92.20). + +# 4.5. Visualization + +Finally, we analyze our SMP by visualizing filters trained on CIFAR10. In the first column of Fig. 4, we can observe the trained weight points' position. In our method, point lo + +![](images/9e0a1798878334b894cf0a5d51929cd2666561aad866da9c808d232cf9b610d5.jpg) + +![](images/13f10b6608dc550736933f7d278c82d9bf6145c58e3fd36d804d26172b26a40d.jpg) + +![](images/3bf793a6435850132eadc421057732c73e6951104e23e150b9c5abf30378be9d.jpg) + +![](images/b15f30bcfcf8e758b206429b1eb07eb0a58937fcd68438194a3622b2033a803a.jpg) + +![](images/da60f52c5c6f4db692ca1caa11c75da5a12d7d67f851cd46d7019abee884cbbb.jpg) + +![](images/1767b448133c5f9553ff93137fbc4d1c943476b4cc46e6c6d9fc88e8c65ea5ee.jpg) + +![](images/db91d6cf51e8d98414cf46b18014bd854b455d77bee3b080245ff60d5cfce611.jpg) + +![](images/cf5779d61bd5be33e4250baeb368724129b9903bd92ecc05158f331c704e0592.jpg) +points + +![](images/46c3c7aa9ba83d2b99a3c2f351a71a776f3eed2e90b552de98bd97f0f46ba175.jpg) +kernel 1 + +![](images/1b74387b6b4d4665d2152e4e85c343eed0c36c0579553f8bd8ca674668c831bf.jpg) +kernel 2 + +![](images/064b0e148b5291b05fe84751cf7021a5faff96a1336d9d3ffd37b64dd6974636.jpg) +kernel 3 + +![](images/1e8d126b2924cfd22fb259df6418110630375f5437d1f61ff2fed2556fc90b97.jpg) +kernel 4 + +![](images/cb5678ae102a304ece858d33923fbf1c75368840e572cb0838d7242982e492e7.jpg) +kernel 5 + +![](images/f3fd7aed893bc0175ca3f2005ac001b99fa9e575ed20f5080dc74f0a1d6c87bc.jpg) +kernel 6 + +![](images/8952a576dd706a68782b2567ce3b3726fcd7cf6022e86d386ce018e6b9fede13.jpg) +Figure 4. Visualization of kernels. Each row shows the location of points and first 6 kernels of a filter. For ease of visualization, the kernels are first subjected to the absolute value operation and then normalized to a range of [0,1]. +(a) Layer 1 +Figure 5. Normalized sum of the absolute value of trained filters. (a), (b), and (c) are top, middle, and bottom layers, respectively. + +![](images/88eb384bcbd67e00289cdfd32becdaee6676bfe69d52ab394cdf41e8f671af11.jpg) +(b) Layer 8 + +![](images/985c85d1e740ca467545e000607a61a1bba5826ea0a54333feca69c3d4aa252d.jpg) +(c) Layer 14 + +cations $p_i$ are mainly sampled near the center of the kernel for stable training. It shows that the points spread out for optimal kernel representation over the training process, as we argued, and thus the receptive fields are not limited to a small part. Also, we can figure out that there are square patterns caused by Eq. (2) in the kernels, where each square has its own area. This suggests that although the radius parameters are initialized with small values, the values are individually increased and optimized for each corresponding weight point during training. + +Observing visualized convolution kernel in Fig. 4, kernels from the same filter share the receptive fields. It allows a single filter to focus on the shared area. Furthermore, as illustrated in Fig. 5, SMPConv has large adaptive receptive fields which are not conventional square or rectangular shapes. This is because it consists of optimized filters with their own small and large receptive fields. Thus, our method can handle not only global information but also local details. + +# 5. Conclusion and discussion + +In this paper, we present a method to build a continuous convolution. We propose using point representations, where each point has the weight parameters, coordinates, and ra + +dius to learn. By connecting the points, we can implement a continuous function, which can be utilized to construct convolutional kernels. We have provided extensive experimental results, showing that drop-in replacement in the existing training pipeline without bells and whistles improved the performance by a safe margin. We also show that a continuous convolution can be effectively utilized in a large-scale experiment. We expect more research and development in this direction. + +Although promising, there are many rooms to be improved. Due to the limited computational budget, we could not conduct sufficient experiments in the large-scale experiment. The experimental results provided in this manuscript resulted from a few runs. As trial and error are essential in the machine learning development process, we plan to find optimal configurations and training techniques to enhance the performance of the proposed method. + +We also observed that the learned kernels often show sparse patterns depending on the tasks. It is well aligned with the success of dilated convolution or its variants, and our methods automatically learn proper sparsity during the training process on specific tasks. Adding prior knowledge through training and regularization techniques would further improve performance, especially for tasks requiring longer-term dependency modeling. + +# Acknowledgments + +We thank Usman Ali for valuable discussions. This research was supported by the Ministry of Science and ICT (MSIT) of Korea, under the National Research Foundation (NRF) grant (2022R1F1A1064184, 2022R1A4A3033571), Institute of Information and Communication Technology Planning Evaluation (IITP) grants for the AI Graduate School program (IITP-2019-0-00421), and the BK21 FOUR Project. + +# References + +[1] Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. The uea multivariate time series classification archive, 2018. arXiv preprint arXiv:1811.00075, 2018. 1, 6 +[2] Shaojie Bai, J Zico Kolter, and Vladlen Koltun. An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:1803.01271, 2018.6 +[3] Shaojie Bai, J Zico Kolter, and Vladlen Koltun. 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Spidercnn: Deep learning on point sets with parameterized convolutional filters. In ECCV, pages 87-102, 2018. 1 +[65] Li Yi, Vladimir G Kim, Duygu Ceylan, I-Chao Shen, Mengyan Yan, Hao Su, Cewu Lu, Qixing Huang, Alla Sheffer, and Leonidas Guibas. A scalable active framework for region annotation in 3d shape collections. ACM ToG, 35(6):1-12, 2016. 1 +[66] Alex Yu, Sara Fridovich-Keil, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. arXiv preprint arXiv:2112.05131, 2021. 2 +[67] Qiang Zhang, Seung-Hwan Baek, Szymon Rusinkiewicz, and Felix Heide. Differentiable point-based radiance fields for efficient view synthesis. arXiv preprint arXiv:2205.14330, 2022. 2, 3 \ No newline at end of file diff --git a/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/images.zip b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ec47cb858a6d10a3a49a3b9e6f1fb50e42a50b6a --- /dev/null +++ b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d36dbd15daa75933a1afa5d0cc96969042c06dd693f2e8ad1abf3a99aebaf82b +size 428154 diff --git a/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/layout.json b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fa495b36fe81393df176161d1e91ccfb43aa3f8d --- /dev/null +++ b/2023/SMPConv_ Self-Moving Point Representations for Continuous Convolution/layout.json @@ -0,0 +1,9882 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 66, + 102, + 527, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 102, + 527, + 121 + ], + "spans": [ + { + "bbox": [ + 66, + 102, + 527, + 121 + ], + "type": "text", + "content": "SMPCov: Self-moving Point Representations for Continuous Convolution" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "spans": [ + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "text", + "content": "Sanghyeon Kim" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "text", + "content": " Eunbyung Park" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "text", + "content": "Department of Electrical and Computer Engineering, Sungkyunkwan University \n" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 100, + 142, + 493, + 186 + ], + "type": "text", + "content": "Department of Artificial Intelligence, Sungkyunkwan University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 239, + 289, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 539 + ], + "type": "text", + "content": "Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 563, + 128, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 128, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 128, + 575 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 584, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 584, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 287, + 693 + ], + "type": "text", + "content": "There has been a recent surge of interest in representing the convolutional kernel as a function over a continuous input domain. It can easily handle irregularly sampled data both in time [1, 59] and space [61, 65], overcoming the drawbacks of the discrete convolution operating only on discretized sampled data with pre-defined resolutions and grids. With the progress in modeling and training continuous kernels, it has enjoyed great success in many practical scenarios, such as 3D point cloud classification and segmen" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 213, + 547, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 299 + ], + "type": "text", + "content": "tation [36,41,52,58,64], image super resolution [57], object tracking [10], to name a few. Furthermore, the recent trends of using large convolutional kernels with strong empirical results urge us to develop a more efficient way to implement it [13,32], and the continuous convolution will be a promising candidate because of its capability to readily construct arbitrarily large receptive fields [44, 45]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 300, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 547, + 469 + ], + "type": "text", + "content": "One of the dominant approaches to modeling the continuous kernel is to use a particular type of neural network architecture, taking as inputs low-dimensional input coordinates and generating the kernel values [44, 45], known as neural fields [38, 49] or simply MLPs. Using neural fields to represent the kernels, we can query kernel values at arbitrary resolutions in parallel and construct the large kernels with a fixed parameter budget, as opposed to the conventional discrete convolutions requiring more parameters to enlarge receptive fields. Thanks to recent advances to overcome the spectral bias on training neural fields [49], they can also represent functions with high-frequency components, which enables learned kernels to capture fine details of input data." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 472, + 548, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 548, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 548, + 651 + ], + "type": "text", + "content": "While promising in various tasks and applications, this approach has a few downsides. First, it incurs considerable computational burdens to already computation-heavy processes of training deep neural networks. Each training iteration involves multiple forward and backward passes of MLPs to generate kernels and update the parameters of MLPs. This additional complexity prevents it from being applied to large-scale problems, such as ImageNet-scale, since it needs deeper and wider MLP architectures to construct more complex kernels with more input and output channels. Although MLPs can generate larger sizes and numbers of kernels without adding more parameters, it has been known that the size of MLPs mainly determines the complexity of the functions they represent and, eventually, the performance of the CNNs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "Furthermore, the kernels generated by an MLP depend heavily on the architectural priors. As a universal function approximator, a neural network with sufficient depth and width can express any continuous functions [25]. However, we have empirically observed strong evidence that the ar" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "*Corresponding authors" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10289" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 180 + ], + "type": "text", + "content": "chitecture of neural networks has played a significant role in many practical settings, suggesting that various architectural changes to the kernel-generating MLPs would significantly affect the performance of CNNs. Considering a large number of hyperparameters in training neural networks, adding more knobs to tune, e.g., activation functions, width, depth, and many architectural variations of MLPs., would not be a pragmatic solution for both machine learning researchers and practitioners." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 182, + 288, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 288, + 445 + ], + "type": "text", + "content": "In this paper, we aim to build continuous convolution kernels with negligible computational cost and minimal architectural priors. We propose to use moving point representations and implement infinite resolution by interpolating nearby moving points at arbitrary query locations. The moving points are the actual kernel parameters, and we connect the neighboring points to build continuous kernels. Recent techniques in neural fields literature inspire it, where they used grid or irregularly distributed points to represent features or quantities in questions (density or colors) for novel view synthesis [6, 50, 63, 66, 67]. The suggested approach only introduces minor computational costs (interpolation costs) and does not consist of neural networks (only point representations and interpolation kernels). Moreover, the spectral bias presented in training MLPs [43] does not exist in the suggested representation. Each point representation covers the local area of the input domain and is updated independently of each other, contrasted with MLPs, where updating each parameter would affect the entire input domain. Therefore, highly different values of nearby points can easily express high-frequency components of the function." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 448, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 568 + ], + "type": "text", + "content": "The proposed method can also be more parameter efficient than the discrete convolution to construct the large kernels. Depending on the complexity of the kernels to be learned, a few numbers of points may be sufficient to cover a large receptive field (e.g., a unimodal function can be approximated by a single point). Many works have extensively exploited non-full ranks of the learned kernels to implement efficient convolutions or compress the models [32]. Our approach can likewise benefit from the presence of learned kernels with low-frequency components." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "We conduct comprehensive experimental results to show the effectiveness of the proposed method. First, we demonstrate that moving point representations can approximate continuous functions very well in 1D and 2D function fitting experiments. Then, we test its ability to handle long-term dependencies on various sequential datasets. Finally, we also evaluate our model on 2D image data. Especially, we perform large-scale experiments on the ImageNet classification dataset (to our knowledge, it is the first attempt to use continuous convolution for such a large-scale problem). Our proposed method can be used as a drop-in replacement of convolution layers for all the above tasks without bells" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 97 + ], + "type": "text", + "content": "and whistles. The experimental results show that it consistently improves the performance of the prior arts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 107, + 395, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 107, + 395, + 119 + ], + "spans": [ + { + "bbox": [ + 306, + 107, + 395, + 119 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 127, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 127, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 127, + 545, + 378 + ], + "type": "text", + "content": "Neural fields and continuous convolution. Neural fields have recently emerged as an alternative neural network representation [49]. It is a field parameterized by a neural network, such as simple MLP, taking as low-dimensional coordinates input and generating quantity in questions. It has shown great success in various visual computing domains, such as novel view synthesis [38], 3D shape representation [37, 40], and data compression [17], to name a few. Since it is a function over a continuous input domain, it can produce outputs at arbitrary resolutions. Recent studies have exploited its continuous nature to model continuous kernels for CNNs [44, 45, 58]. [58] used an MLP architecture to implement the continuous kernel to handle irregularly sampled data, such as 3D point clouds. While successful, the descriptive power of the learned kernel is limited due to its bias toward learning low-frequency components. With the recent advances in overcoming the spectral bias [49], [45] has explored various activation functions to improve the performance of CNNs. To further improve, [44] proposed to learn the receptive field sizes and showed impressive performance on multiple tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 379, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 545, + 486 + ], + "type": "text", + "content": "We also propose a method that can likewise be classified as a neural field. However, we implement a field without neural networks, using self-moving point representations and interpolation schemes. It significantly reduces the computational costs to compute the kernels during training compared to the conventional MLP-based methods. Furthermore, it removes the burden of numerous hyperparameter searches for a newly introduced neural network in the already complicated training procedure." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 486, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 653 + ], + "type": "text", + "content": "Grid and point representations. Although MLP-based neural fields have succeeded in many tasks, they require substantial computational costs for training and inference, and the spectral bias presented in MLPs often degrades the performance. In order to reduce the computations and avoid the issues of using MLPs, classical grid-based representations have been adopted in the neural fields. Plenoxels [66] stores the coefficients of spherical harmonic in the 3D voxel structure and implements the infinite resolution via the interpolation methods, reducing the training time from days to minutes. Instant-NGP [39] further optimized the speed using a hash-based indexing algorithm. The combination of grid representations and MLPs has been extensively explored to find better solutions [6, 50]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Point representations have been recently suggested in neural fields to improve the shortcomings in grid-based representations, thanks to their flexibility and expressibility [63, 67]. They can generate outputs over a continuous input domain by interpolating neighboring points given a" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10290" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 68, + 168, + 138 + ], + "blocks": [ + { + "bbox": [ + 61, + 68, + 168, + 138 + ], + "lines": [ + { + "bbox": [ + 61, + 68, + 168, + 138 + ], + "spans": [ + { + "bbox": [ + 61, + 68, + 168, + 138 + ], + "type": "image", + "image_path": "b454e824fac6acaa52a96315dd082ad4839d377c5eefe38d2e8943ce7b3a80b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 208, + 68, + 362, + 139 + ], + "blocks": [ + { + "bbox": [ + 208, + 68, + 362, + 139 + ], + "lines": [ + { + "bbox": [ + 208, + 68, + 362, + 139 + ], + "spans": [ + { + "bbox": [ + 208, + 68, + 362, + 139 + ], + "type": "image", + "image_path": "136124815209c9ed3e59d5ada63f91c00693466584c5963989b28c2b22e1ad53.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 405, + 70, + 529, + 139 + ], + "blocks": [ + { + "bbox": [ + 405, + 70, + 529, + 139 + ], + "lines": [ + { + "bbox": [ + 405, + 70, + 529, + 139 + ], + "spans": [ + { + "bbox": [ + 405, + 70, + 529, + 139 + ], + "type": "image", + "image_path": "54a805de77e88ee3e925eb04d9298226393faf1af58823f7dd98dc5dab133032.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 47, + 148, + 150, + 220 + ], + "blocks": [ + { + "bbox": [ + 47, + 148, + 150, + 220 + ], + "lines": [ + { + "bbox": [ + 47, + 148, + 150, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 150, + 220 + ], + "type": "image", + "image_path": "5a28e083f89021db08bf615c23560bc5cc0591dd07833f9a53e2f4366529bcba.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 156, + 149, + 277, + 220 + ], + "blocks": [ + { + "bbox": [ + 156, + 149, + 277, + 220 + ], + "lines": [ + { + "bbox": [ + 156, + 149, + 277, + 220 + ], + "spans": [ + { + "bbox": [ + 156, + 149, + 277, + 220 + ], + "type": "image", + "image_path": "c3fa5883061529250fb77cb8fe4122653ea3ff782cc00a1a6be2285cbf3764c4.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 189, + 232, + 402, + 243 + ], + "lines": [ + { + "bbox": [ + 189, + 232, + 402, + 243 + ], + "spans": [ + { + "bbox": [ + 189, + 232, + 402, + 243 + ], + "type": "text", + "content": "Figure 1. A various methods for large kernel construction." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 283, + 149, + 411, + 220 + ], + "blocks": [ + { + "bbox": [ + 283, + 149, + 411, + 220 + ], + "lines": [ + { + "bbox": [ + 283, + 149, + 411, + 220 + ], + "spans": [ + { + "bbox": [ + 283, + 149, + 411, + 220 + ], + "type": "image", + "image_path": "8f209bd801e10c314137a4609f4eeb4cb256fdab39285f826a66bb865c93e741.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 419, + 149, + 545, + 220 + ], + "blocks": [ + { + "bbox": [ + 419, + 149, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 419, + 149, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 419, + 149, + 545, + 220 + ], + "type": "image", + "image_path": "b653ecc59508a8e5fc1d6471fe5c6116d8a89c4783ee6618498c8ef338e2e71e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 250, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 250, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 287, + 369 + ], + "type": "text", + "content": "query point. It can be more accurate and parameter efficient than the grid-based ones since it can adaptively locate points, considering the complexity of functions, e.g., fewer points in low-frequency areas. Although our work is largely inspired by these works, 1. we repurpose the point representations to build continuous convolutional kernels, 2. we do not use MLPs that would introduce additional modeling complexity, 3. our method does not require complex initializations (or algorithms) to relocate points, such as depth-based initialization [63] and mask-based initialization [67]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "text", + "content": "Large kernel convolution. Since the great success of VGG-style CNNs [24, 26, 48, 51] in ImageNet [12], we repeatedly apply small kernels (e.g., " + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "text", + "content": " kernel) with deep layers to get a large receptive field and deal with long-term dependencies. With the massive success of transformers in the vision domain [15, 16, 34, 55], which have a large receptive field, recent studies have started to revisit the descriptive power of large kernels [13, 32, 35, 53]. RepLKNet [13] has shown we can increase the kernel size up to " + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "inline_equation", + "content": "31 \\times 31" + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "text", + "content": " with the help of the reparameterization trick. More recently, SLaK [32] managed to scale the kernel size to " + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "inline_equation", + "content": "51 \\times 51" + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "inline_equation", + "content": "61 \\times 61" + }, + { + "bbox": [ + 46, + 372, + 287, + 564 + ], + "type": "text", + "content": ", showing improved performance with dynamic sparsity and low-rank factorization (Fig. 1-(b)). While promising, the number of parameters increases according to the kernel size, which is a major bottleneck in representing large kernels." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 567, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 686 + ], + "type": "text", + "content": "The continuous kernel can construct large kernels with a fixed parameter budget (Fig. 1-(c)). CKConv [45] and FlexConv [44] have exploited this property and demonstrated that their method can model long-term dependencies by constructing large kernels on various datasets. However, they introduce a considerable amount of computations to the training process, and they have yet to perform largescale experiments, e.g., ImageNet. To the best of our knowledge, our approach is the first to conduct such a large-scale experiment using continuous convolution." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "On the other hand, dilated convolutions [7, 8] can also be used to enlarge receptive fields with a small number of" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 250, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 545, + 393 + ], + "type": "text", + "content": "parameters, and they also do not introduce additional computations during training (Fig. 1-(d)). Deformable convolutions [9] look similar to ours in terms of moving points arbitrarily (Fig. 1-(e)). However, they learn how to deform the kernels (or predict the offset) during inference. On the other hand, we adjust the locations of the point representations during training to find the optimal large kernels. A concurrent work suggests learning the offsets during training [23]. In contrast to ours, it is a discrete formulation, thus losing the benefits of continuous convolution. Furthermore, we adjust the receptive fields of each point representation separately, yielding more expressive representations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "type": "text", + "content": "Continuous convolution for point clouds. There have been many continuous convolution approaches to handle 3D point cloud data, which is an important example of irregularly sampled data. PointNet [41] and PointNet++ [42] are pioneer works that use average pooling and " + }, + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 397, + 546, + 564 + ], + "type": "text", + "content": " convolution to aggregate features. [31, 33, 58, 60] leveraged MLPs to implement continuous convolution. KPCov [52] is also considered a continuous convolution and shares some similarities with ours (Fig. 1-f). They also used point representation and interpolation kernels for handling point clouds. However, their points are fixed over the training, unlike ours. They also proposed a deformable version, which requires additional neural networks to predict the offset of the kernel points." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 585, + 373, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 373, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 373, + 597 + ], + "type": "text", + "content": "3. SMPCov" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 608, + 482, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 482, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 482, + 620 + ], + "type": "text", + "content": "3.1. Self-moving point representation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "This section describes the proposed self-moving point representation to represent a continuous function. Let " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " be the size of the input coordinates dimension, e.g., 1 in timeseries data and 2 in the spatial domain. " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathsf{SMP}:\\mathbb{R}^d\\to \\mathbb{R}^{N_c}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is a vector-valued function, mapping from the input coordinates to the output kernel vectors, where " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is a channel size. Given a query point " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "x\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", we define a continuous" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10291" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 157, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 157, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 157, + 83 + ], + "type": "text", + "content": "kernel function as follows." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 79, + 87, + 287, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 87, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 79, + 87, + 287, + 118 + ], + "type": "interline_equation", + "content": "\\operatorname {S M P} (x; \\phi) = \\frac {1}{| \\mathcal {N} (x) |} \\sum_ {i \\in \\mathcal {N} (x)} g (x, p _ {i}, r _ {i}) w _ {i}, \\tag {1}", + "image_path": "050347f4cefdfb1d4e89a07f2a33f4ecd80dc614145ea65cdd611716d4633ee3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "inline_equation", + "content": "\\phi = \\{\\{p_i\\}_{i = 1}^{N_p},\\{w_i\\}_{i = 1}^{N_p},\\{r_i\\}_{i = 1}^{N_p}\\}" + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": " is a set of learnable parameters, and " + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": " is the number of points that are used to represent the function. " + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "inline_equation", + "content": "p_i\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": " is the coordinates of self-moving point representation " + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "inline_equation", + "content": "w_{i}\\in \\mathbb{R}^{N_{c}}" + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": " , and each point representation also has a learnable radius, " + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "inline_equation", + "content": "r_i\\in \\mathbb{R}^+" + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": " is a positive real number, which we implement it by clipping for numerical stability. We define a distance function " + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "inline_equation", + "content": "g:\\mathbb{R}^d\\times \\mathbb{R}^d\\times \\mathbb{R}^+\\to \\mathbb{R}" + }, + { + "bbox": [ + 47, + 125, + 289, + 224 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 229, + 287, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 229, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 229, + 287, + 255 + ], + "type": "interline_equation", + "content": "g (x, p _ {i}, r _ {i}) = 1 - \\frac {\\| x - p _ {i} \\| _ {1}}{r _ {i}}, \\tag {2}", + "image_path": "5dce22fde3e3301e256acdf7ffceabf3343841267362908f968e98e8a7c0338a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|_1" + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": " is a L1 distance. " + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(x)" + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": " is a set of indices of neighboring points of a query coordinate " + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": ", defined as " + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(x) = \\{i | g(x, p_i, r_i) > 0, \\forall i\\}" + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": ". Thus, points beyond a certain distance (depending on the radius) will not affect the query point. Hence, SMP generates output vectors by a weighted average of the nearby point representations. Note that all three parameters " + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\{p_i\\}, \\{w_i\\}, \\{r_i\\}" + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": " are jointly trained with the CNN model parameters, and the gradients w.r.t those parameters can be easily computed using an automatic differentiation library. As the name SMP suggests, the coordinates " + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\{p_i\\}" + }, + { + "bbox": [ + 46, + 260, + 287, + 403 + ], + "type": "text", + "content": " are updated during training, resulting in moving points representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 403, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 499 + ], + "type": "text", + "content": "Compared to a fixed-point representation, where " + }, + { + "bbox": [ + 46, + 403, + 287, + 499 + ], + "type": "inline_equation", + "content": "\\{p_i\\}" + }, + { + "bbox": [ + 46, + 403, + 287, + 499 + ], + "type": "text", + "content": " are not trainable, ours can approximate complex functions more precisely. Since each point can move freely, more points can be gathered in high-frequency areas. On the other hand, few points can easily represent low-frequency components, resulting in more parameter-efficient representation. For example, a single point may be sufficient to approximate unimodal functions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 506, + 117, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 117, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 117, + 517 + ], + "type": "text", + "content": "3.2. SMPConv" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "type": "text", + "content": "We leverage the suggested representation to implement a continuous convolution operator. In one dimensional case, " + }, + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "type": "inline_equation", + "content": "d = 1" + }, + { + "bbox": [ + 46, + 525, + 287, + 559 + ], + "type": "text", + "content": ", a continuous convolution can be formulated as," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 73, + 566, + 287, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 566, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 73, + 566, + 287, + 598 + ], + "type": "interline_equation", + "content": "(f * \\operatorname {S M P}) (x) = \\sum_ {c = 1} ^ {N _ {c}} \\int_ {\\mathbb {R}} f _ {c} (\\tau) \\operatorname {S M P} _ {c} (x - \\tau) d \\tau , \\tag {3}", + "image_path": "eb7bda04f0a3768bf2cde7f16d57ac1d43ed6ac6d7210da4f7574b0c0426f76c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "f: \\mathbb{R} \\to \\mathbb{R}^{N_c}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " is a input function and the " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{c}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{SMP}_c" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "-th element of the inputs. The convolution operator generates a function, computing the filter responses by summing over entire " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " channels. One SMP representation corresponds to a convolution operator, and multiple SMPs are used to implement one convolutional layer to generate multiple output channels. In contrast to the previous MLP-based continuous convolution, which uses one neural network for one convolutional layer, our approach has separate" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 318, + 70, + 451, + 173 + ], + "blocks": [ + { + "bbox": [ + 318, + 70, + 451, + 173 + ], + "lines": [ + { + "bbox": [ + 318, + 70, + 451, + 173 + ], + "spans": [ + { + "bbox": [ + 318, + 70, + 451, + 173 + ], + "type": "image", + "image_path": "612c5bbfabb25031f6971bddcfcac3f9897aa884f51c350565dad04606e34031.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 349, + 179, + 392, + 190 + ], + "lines": [ + { + "bbox": [ + 349, + 179, + 392, + 190 + ], + "spans": [ + { + "bbox": [ + 349, + 179, + 392, + 190 + ], + "type": "text", + "content": "(a) SMP (1D)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 455, + 70, + 540, + 175 + ], + "blocks": [ + { + "bbox": [ + 455, + 70, + 540, + 175 + ], + "lines": [ + { + "bbox": [ + 455, + 70, + 540, + 175 + ], + "spans": [ + { + "bbox": [ + 455, + 70, + 540, + 175 + ], + "type": "image", + "image_path": "c2f4cfc3794999dac228bbf93e20fd08a02e9634c14c64cb03ca6cdb16cde6ea.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 475, + 178, + 518, + 189 + ], + "lines": [ + { + "bbox": [ + 475, + 178, + 518, + 189 + ], + "spans": [ + { + "bbox": [ + 475, + 178, + 518, + 189 + ], + "type": "text", + "content": "(b) SMP (2D)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 201, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 201, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 547, + 258 + ], + "type": "text", + "content": "Figure 2. Self-moving point representation. (a) SMP as a function of the one-dimensional input domain, and (b) SMP as a function of the two-dimensional input domain. 'C #1' means the first channel. Each channel shares the location of the points, whereas each channel has its own weight parameters." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 278, + 545, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 314 + ], + "type": "text", + "content": "parameters for each convolution filter in a layer. It gives more freedom to each filter and results in more descriptive power of the learned filter." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 315, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 546, + 422 + ], + "type": "text", + "content": "As depicted in Fig. 2, the kernels of each filter share the position parameters. That is, each filter of one layer has its own position parameters. Although we could use different SMP for different channels. However, it will considerably increase the number of learnable parameters (" + }, + { + "bbox": [ + 304, + 315, + 546, + 422 + ], + "type": "inline_equation", + "content": "\\{p_i\\}" + }, + { + "bbox": [ + 304, + 315, + 546, + 422 + ], + "type": "text", + "content": " per channel), and we believe that locating points at the same location for a convolutional filter can be a reasonable prior, where a convolutional filter can focus on specific areas in the input domain." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 423, + 547, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 547, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 547, + 471 + ], + "type": "text", + "content": "We leverage our continuous formulation to construct large kernels, motivated by the recent success of using them in many tasks. We can create arbitrary size large kernels by querying multiple discretized coordinates to SMP." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 479, + 370, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 370, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 370, + 491 + ], + "type": "text", + "content": "3.3. Training" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 581 + ], + "type": "text", + "content": "Training a large kernel has been challenging and computationally heavy, and naive training practice has yet to show promising results. Recently, [13, 14] proposed a reparameterization trick to combine different-size kernels as a separate branch, resulting in improved performance and more stable training. We also applied the same trick to train CNNs with SMPConv." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 630 + ], + "type": "text", + "content": "We empirically figured out that performance degradation occurs when the coordinates " + }, + { + "bbox": [ + 304, + 582, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\{p_i\\}" + }, + { + "bbox": [ + 304, + 582, + 545, + 630 + ], + "type": "text", + "content": " are forced to fit inside the kernel by clipping. Thus, we let the coordinates be freely updated during training." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "We also found that the initialization of the parameters " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " matters. For point locations, " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{p_i\\}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", we randomly sample from a gaussian distribution with small " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ". It initially locates the points in the center and gradually spreads out over the training process. We empirically found that this strategy yields more stable training, especially at the beginning of the training. We also initialized with small values" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10292" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 75, + 281, + 144 + ], + "blocks": [ + { + "bbox": [ + 57, + 75, + 281, + 144 + ], + "lines": [ + { + "bbox": [ + 57, + 75, + 281, + 144 + ], + "spans": [ + { + "bbox": [ + 57, + 75, + 281, + 144 + ], + "type": "table", + "html": "
MethodkParams.Time ↓Throughput ↑
Deformable [9]30.29M61.24390.7
51.37M157.31618.9
74.39M293.1882.3
FlexConv [44]330.67M92.91923.4
SMPConv330.49M40.14258.4
", + "image_path": "9be20a7b342a8610b38acbe6ebc684aa2fe88b234e66f45ea634d75294bf6b62.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "lines": [ + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "type": "text", + "content": "Table 1. Training time (sec/epoch) and throughput (examples/sec) comparison with CIFAR10 on a single RTX3090 GPU. Both are tested with a batch size of 64 and input resolution of " + }, + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 152, + 287, + 208 + ], + "type": "text", + "content": " is kernel size. The time is the average training time of the first 10 epochs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\{r_i\\}" + }, + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "type": "text", + "content": ", which each weight parameter firstly has a narrow sight. Over the course of training, " + }, + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\{r_i\\}" + }, + { + "bbox": [ + 47, + 229, + 287, + 266 + ], + "type": "text", + "content": " also gradually increases if necessary." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 273, + 117, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 117, + 285 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 117, + 285 + ], + "type": "text", + "content": "3.4. Efficiency" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": "Assuming the size of a convolution filter is " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "C \\times N \\times N" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": " is the number of kernels and " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": " is the height and width of filter, " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "CN^2" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": " parameters are required in dense convolution (Fig. 1-(a)). Therefore, the number of parameters is proportional to kernel resolution " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": ". On the other hand, SMP needs " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "(1 + d + C)N_{p}" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": " parameters, where " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": " is the size of the input coordinates dimension, and " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": " is the number of weight points. We used " + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "inline_equation", + "content": "N_{p} \\ll N^{2}" + }, + { + "bbox": [ + 46, + 292, + 287, + 448 + ], + "type": "text", + "content": ", so SMP is more efficient than dense convolution in terms of the number of parameters. Furthermore, as the number of parameters does not depend on kernel resolution, SMP can represent kernels of any size, such as large or continuous kernels with fixed budget parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 628 + ], + "type": "text", + "content": "Due to the point representations and interpolation schemes without supplementary neural networks, SMPConv has an advantage of computational complexity. On the other hand, the existing large kernel convolutions are computationally heavy. Deformable convolution (Fig. 1-(e)), for example, requires offset prediction networks and convolution with interpolated inputs during both training and inference, resulting in additional computation and parameter costs. Additionally, it relies on dense convolution, making it impractical to increase kernel size significantly. Similarly, MLP-based methods (Fig. 1-(c)) like FlexConv [44] leverage kernel generation neural network, and it also increases computational burdens. The results presented in Tab. 1 demonstrate that SMPConv outperforms the existing large kernel convolutions in terms of speed." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 639, + 128, + 652 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 639, + 128, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 639, + 128, + 652 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 237, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 237, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 237, + 672 + ], + "type": "text", + "content": "4.1. Continuous function approximation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Firstly, we conducted a fitting experiment to validate that our self-moving point representation can work as an approximator for a continuous function. To do so, we used" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 73, + 391, + 140 + ], + "blocks": [ + { + "bbox": [ + 317, + 73, + 391, + 140 + ], + "lines": [ + { + "bbox": [ + 317, + 73, + 391, + 140 + ], + "spans": [ + { + "bbox": [ + 317, + 73, + 391, + 140 + ], + "type": "image", + "image_path": "973ff0d1afabaaf1182553d0edb99f42f125c0103fc43bd221328197ddf7638a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 143, + 482, + 152 + ], + "lines": [ + { + "bbox": [ + 370, + 143, + 482, + 152 + ], + "spans": [ + { + "bbox": [ + 370, + 143, + 482, + 152 + ], + "type": "inline_equation", + "content": "f_{a}(x,y) = \\cos (e^{y} / 0.5) + \\sin ((x^{2} - 0.5) / 5)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 398, + 76, + 453, + 140 + ], + "blocks": [ + { + "bbox": [ + 398, + 76, + 453, + 140 + ], + "lines": [ + { + "bbox": [ + 398, + 76, + 453, + 140 + ], + "spans": [ + { + "bbox": [ + 398, + 76, + 453, + 140 + ], + "type": "image", + "image_path": "686e1067b02dab736e906306784a30d4bbb4d516f2799904222365fa7cd93778.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 465, + 76, + 521, + 140 + ], + "blocks": [ + { + "bbox": [ + 465, + 76, + 521, + 140 + ], + "lines": [ + { + "bbox": [ + 465, + 76, + 521, + 140 + ], + "spans": [ + { + "bbox": [ + 465, + 76, + 521, + 140 + ], + "type": "image", + "image_path": "d42447effa1082f89058dc474dd779ecddd8a10b80d4924cddcd01fde659baef.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 526, + 76, + 537, + 140 + ], + "blocks": [ + { + "bbox": [ + 526, + 76, + 537, + 140 + ], + "lines": [ + { + "bbox": [ + 526, + 76, + 537, + 140 + ], + "spans": [ + { + "bbox": [ + 526, + 76, + 537, + 140 + ], + "type": "image", + "image_path": "87ec7d9536c1db127ed4d93830cc35429d7769a5fc3414f103e85803b8798914.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 317, + 154, + 389, + 220 + ], + "blocks": [ + { + "bbox": [ + 317, + 154, + 389, + 220 + ], + "lines": [ + { + "bbox": [ + 317, + 154, + 389, + 220 + ], + "spans": [ + { + "bbox": [ + 317, + 154, + 389, + 220 + ], + "type": "image", + "image_path": "17e2fb7ef9adf14bb70e4f01325d91a24147aa5505d34666354d39be93b6dcf2.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 224, + 480, + 233 + ], + "lines": [ + { + "bbox": [ + 370, + 224, + 480, + 233 + ], + "spans": [ + { + "bbox": [ + 370, + 224, + 480, + 233 + ], + "type": "inline_equation", + "content": "f_{b}(x,y) = \\cos (x + y) + \\sin (40x + 2y^{2}) / 5" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 395, + 156, + 452, + 220 + ], + "blocks": [ + { + "bbox": [ + 395, + 156, + 452, + 220 + ], + "lines": [ + { + "bbox": [ + 395, + 156, + 452, + 220 + ], + "spans": [ + { + "bbox": [ + 395, + 156, + 452, + 220 + ], + "type": "image", + "image_path": "549446d7608d7889f5400e98f089dad4a4227e3e60517ab949a9ce48e4694b69.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 245, + 545, + 289 + ], + "lines": [ + { + "bbox": [ + 305, + 245, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 245, + 545, + 289 + ], + "type": "text", + "content": "Figure 3. Comparison between the moving point and the fixed point representations through the fitting. Our proposed moving point representations can approximate given continuous functions with higher accuracy." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 463, + 157, + 519, + 220 + ], + "blocks": [ + { + "bbox": [ + 463, + 157, + 519, + 220 + ], + "lines": [ + { + "bbox": [ + 463, + 157, + 519, + 220 + ], + "spans": [ + { + "bbox": [ + 463, + 157, + 519, + 220 + ], + "type": "image", + "image_path": "ac8771fb52e211bf09d75d8e2eabd8455bc5afe700c865b26d6e83baaf8fb37a.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 526, + 157, + 536, + 220 + ], + "blocks": [ + { + "bbox": [ + 526, + 157, + 536, + 220 + ], + "lines": [ + { + "bbox": [ + 526, + 157, + 536, + 220 + ], + "spans": [ + { + "bbox": [ + 526, + 157, + 536, + 220 + ], + "type": "image", + "image_path": "2e8d34502bed68a330e14f91ab359c707ae5a75d9a49624bf3cd64d0d6040315.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 312, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 433 + ], + "type": "text", + "content": "two sinusoidal-based functions as the ground truth. Given a function, SMP is optimized to represent the sampled function on a " + }, + { + "bbox": [ + 305, + 312, + 545, + 433 + ], + "type": "inline_equation", + "content": "51 \\times 51" + }, + { + "bbox": [ + 305, + 312, + 545, + 433 + ], + "type": "text", + "content": " grid. In this experiment, we designed SMP with 204 points. The fitting result has been shown in Fig. 3. It demonstrates that our proposed method reasonably well approximates a given continuous function with fewer points. Additionally, we compared with the fixed point representation and observed that optimizing the position of points together helps to better approximate the function as the number of points is equal." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 442, + 463, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 463, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 463, + 455 + ], + "type": "text", + "content": "4.2. Sequential data classification" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 461, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 617 + ], + "type": "text", + "content": "To demonstrate that SMPConv can handle long-term dependencies well, we evaluated our method on various sequential data tasks, such as sequential image and time-series classification. To do so, we followed FlexTCN [44] to construct a SMPConv architecture for causal 1D CNN whose kernel size is same as the input sequence length. We substituted their parameterized kernels with ours without additional modifications. To maintain a similar number of network parameters, SMPConv contains 30 weight points in each SMP. To alleviate the computation burdens caused by the convolution with large kernels, we have considered exploiting the computations through a fast Fourier transform. More network and experimental details are in Appx. 1.1." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Sequential image. We tested our SMPConv on the 1D version of images from the datasets, sequential MNIST (sMNIST), permuted MNIST(pMNIST) [29], and sequential CIFAR10 (sCIFAR10) [4]. These datasets have long input sequence lengths, for example, 784 for sMNIST and pMNIST, and 1024 for sCIFAR10. Note that it is hard to model these datasets without proper kernel representations. As shown in Tab. 2, the proposed model has achieved state" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10293" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 74, + 279, + 239 + ], + "blocks": [ + { + "bbox": [ + 57, + 74, + 279, + 239 + ], + "lines": [ + { + "bbox": [ + 57, + 74, + 279, + 239 + ], + "spans": [ + { + "bbox": [ + 57, + 74, + 279, + 239 + ], + "type": "table", + "html": "
ModelParams.sMNISTpMNISTsCIFAR10
DilRNN [4]44k98.096.1-
LSTM [2]70k87.285.7-
GRU [2]70k96.287.3-
TCN [2]70k99.097.2-
r-LSTM [56]500k98.495.272.2
IndRNN [30]83k99.096.0-
TrellisNet [3]8M99.2098.1373.42
URLSTM [20]-99.2896.9671.00
HiPPO [18]0.5M-98.30-
coRNN [47]134k99.497.3-
CKCNN [45]98k99.3198.0062.25
LSSL [21]-99.5398.7684.65
S4 [19]-99.6398.7091.13
FlexTCN [44]375k99.6298.6380.82
Ours373k99.7599.1084.86
", + "image_path": "2cf8ba54ec13d53781c9b5fc810b4510b9c0d4eee6ade0c3b0d82fb969510911.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 58, + 281, + 279, + 412 + ], + "blocks": [ + { + "bbox": [ + 80, + 248, + 253, + 259 + ], + "lines": [ + { + "bbox": [ + 80, + 248, + 253, + 259 + ], + "spans": [ + { + "bbox": [ + 80, + 248, + 253, + 259 + ], + "type": "text", + "content": "Table 2. Sequential image classification results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 58, + 281, + 279, + 412 + ], + "lines": [ + { + "bbox": [ + 58, + 281, + 279, + 412 + ], + "spans": [ + { + "bbox": [ + 58, + 281, + 279, + 412 + ], + "type": "table", + "html": "
ModelParams.CTSCSC-raw
GRU-ODE [11]89k96.244.8~ 10.0
GRU-Δt [27]89k97.820.0~ 10.0
GRU-D [5]89k95.923.9~ 10.0
ODE-RNN [46]89k97.193.2~ 10.0
NCDE [27]89k98.888.5~ 10.0
CKCNN [45]100k99.5395.2771.66
LSSL [21]--93.58-
S4 [19]--93.9698.32
FlexTCN [44]373k99.5397.6791.73
Ours371k99.5397.4594.95
", + "image_path": "ea7b2c2ec95ff7e5deb16479008d48d91ac442759c6d48126a2459d482474be3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 457, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 529 + ], + "type": "text", + "content": "of-the-art results on both sMNIST and pMNIST. For sCIFAR10 dataset, our model has outperformed all the comparative models except S4 [19]. Compared with the FlexTCN, which has a similar network base, our model improved the accuracy by " + }, + { + "bbox": [ + 46, + 457, + 287, + 529 + ], + "type": "inline_equation", + "content": "4\\%" + }, + { + "bbox": [ + 46, + 457, + 287, + 529 + ], + "type": "text", + "content": ". These results show that our proposed model is suitable and effective for sequential images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 531, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 287, + 651 + ], + "type": "text", + "content": "Time-series. We evaluated our model on time-series sequence datasets, character trajectories (CT) [1], and speech commands (SC) [59]. The results have been displayed in Tab. 3. In the relatively shorter MFCC features data, SM-PConv achieved test accuracy similar to FlexTCN. To validate that our proposed model can model extremely long sequences, we conducted experiments on the SC-raw dataset, which has a sequence length of 16000. Similar to the sequence image classification result, our model outperformed FlexTCN with a large margin of " + }, + { + "bbox": [ + 46, + 531, + 287, + 651 + ], + "type": "inline_equation", + "content": "+3\\%" + }, + { + "bbox": [ + 46, + 531, + 287, + 651 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Compared to other models, our SMPConv has achieved considerably better performance for both sequential image and time-series classification. It ensures that our kernel representation is capable of handling long-term dependencies even in the case of a limited number of parameters." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 339, + 76, + 513, + 139 + ], + "blocks": [ + { + "bbox": [ + 90, + 421, + 243, + 431 + ], + "lines": [ + { + "bbox": [ + 90, + 421, + 243, + 431 + ], + "spans": [ + { + "bbox": [ + 90, + 421, + 243, + 431 + ], + "type": "text", + "content": "Table 3. Time-series classification results." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 339, + 76, + 513, + 139 + ], + "lines": [ + { + "bbox": [ + 339, + 76, + 513, + 139 + ], + "spans": [ + { + "bbox": [ + 339, + 76, + 513, + 139 + ], + "type": "table", + "html": "
ModelParams.Accuracy
ResNet-44 [24]660k92.9
CKCNN-16 [44]630k72.1
FlexNet-16 [44]670k92.2
Ours490k93.0
", + "image_path": "e426c1583399579c20fe4d3aa3aa1d875c12afe098247a726b31889df2f88bcf.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 341, + 148, + 510, + 159 + ], + "lines": [ + { + "bbox": [ + 341, + 148, + 510, + 159 + ], + "spans": [ + { + "bbox": [ + 341, + 148, + 510, + 159 + ], + "type": "text", + "content": "Table 4. 2D image classification on CIFAR10." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 179, + 420, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 179, + 420, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 179, + 420, + 192 + ], + "type": "text", + "content": "4.3. Image classification" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "content": "Image classification with the continuous kernel. We validated our SMPConv on a 2D image dataset, CIFAR10 [28], which is dominated by discrete convolutions, to show that the continuous kernel can capture spatial information as well. Similar to the experiments on sequential data, we followed the network design choice of FlexNet [44], where the kernel size is " + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "inline_equation", + "content": "33 \\times 33" + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "content": ". More details are in Appx. 1.1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "text", + "content": "As shown in Tab. 4, our continuous kernel representation model slightly outperforms ResNet, a discrete " + }, + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "text", + "content": " convolution model, with a less number of parameters. It implies that our model is competitive and promising. Our model also showed better performance than MLP-based counterparts, CKCNN-16 and FlexNet-16, even when the parameters of ours were around " + }, + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 294, + 545, + 413 + ], + "type": "text", + "content": " lesser. In addition, we have already identified the efficiency of our model in Tab. 1. These results suggest that our method is more suitable for kernel generation than MLP-based implicit formulations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 414, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 510 + ], + "type": "text", + "content": "Large scale image classification. Finally, we tested our SMPConv on a large-scale ImageNet dataset [12], which contains more than one million training images and 50,000 validation images. For such a large dataset, the convolution kernels should be carefully trained to model complex data relationships accurately. Through such an experiment, therefore, we can validate that our SMP can represent a descriptive convolution kernel." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 617 + ], + "type": "text", + "content": "Firstly, we constructed large-scale variants of SMPConv architecture based on RepLKNet [13]. We replaced its discrete depth-wise separable convolution kernel with our SMP. In general, the larger the data and network, the larger the number of filters. To prevent excessive point position parameters depending on the number of filters, we shared the position of points over filters in large-scale settings. We empirically found that this position sharing has little effect on classification performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "We proposed two variants of our model, SMPConv-T and SMPConv-B. Thanks to our efficient large kernel, we adjusted the number of channels and blocks so that our variants have a similar number of parameters to the previous models. The number of blocks and channels for each stage is [2, 2, 8, 2] and [96, 192, 384, 768] for SMPConv-T and [2, 2, 20, 2] and [128, 256, 512, 1024] for SMPConv-B, respectively. In RepLKNet-31B, the number of blocks and" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10294" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 74, + 280, + 239 + ], + "blocks": [ + { + "bbox": [ + 57, + 74, + 280, + 239 + ], + "lines": [ + { + "bbox": [ + 57, + 74, + 280, + 239 + ], + "spans": [ + { + "bbox": [ + 57, + 74, + 280, + 239 + ], + "type": "table", + "html": "
ModelParams.FLOPsTop-1 Accuracy
ResNet-50 [24]26M4.1G76.5
ResNext-50-32x4d [62]25M4.3G77.6
ResMLP-S24 [54]30M6.0G79.4
DeiT-S [55]22M4.6G79.8
Swin-T [34]28M4.5G81.3
TNT-S [22]24M5.2G81.3
ConvNeXt-T [35]29M4.5G82.1
SLaK-T [32]30M5.0G82.5
SMPConv-T(ours)27M5.7G82.5
DeiT-Base/16 [55]87M17.6G81.8
Swin-B [34]88M15.4G83.5
ConvNeXt-B [35]89M15.4G83.8
SLaK-B [32]95M17.1G84.0
RepLKNet-31B [13]79M15.3G83.5
SMPConv-B(ours)80M16.6G83.8
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ModelsradiuscoordinateAccuracy
A--90.92
B✓-91.35
C-✓92.47
SMPConv✓✓93.00
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σ0.050.20.30.5
Accuracy93.0092.2491.8491.51
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r0.120.180.240.3
Accuracy93.0092.3692.0691.76
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Np48163264
Params.250k330k490k809k1447k
Accuracy92.5692.2893.0092.8492.21
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Classification results on CIFAR10 with different number of moving points " + }, + { + "bbox": [ + 305, + 124, + 545, + 147 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 305, + 124, + 545, + 147 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 168, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 276 + ], + "type": "text", + "content": "Tab. 6, it showed that performance degradation occurs when either one or both components are set to non-learnable parameters. Remarkably, Model C, which set coordinate to trainable parameters, outperformed Model A by a considerable margin. Furthermore, Model B also had a slight performance gain. It suggests that even randomly distributed fixed weight points can increase their interpolation ability with trainable radius. These results indicate that training both coordinate and radius is valid." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "type": "text", + "content": "Next, we identified the effect of the initial position of the points by varying the " + }, + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "type": "text", + "content": ", a standard deviation of point location sampling distribution. In Tab. 7, we observed that a small " + }, + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 277, + 546, + 385 + ], + "type": "text", + "content": " value, indicating initial positions of the points are gathered in the center of the kernel, leads to higher accuracy. This is because it is difficult to train large kernels from the beginning of training. Thus, large kernels can be effectively trained by starting with small kernels and expanding the receptive fields through moving points." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 385, + 545, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 480 + ], + "type": "text", + "content": "We also found that larger initial radius degrades the model performance as shown in Tab. 8. The large radius results in a large initial kernel size, which makes initial training difficult. Furthermore, it is also challenging to train a large area of the kernel dependent on a single weight point which is not optimized in the early stages of training. Both Tab. 7 and Tab. 8 empirically show that our initialization methods for SMP are effective." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "type": "text", + "content": "As depicted in Tab. 9, we figured out that simply increasing the number of weight points " + }, + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "type": "text", + "content": " does not help for performance. It implies that a small number of points are enough to represent a proper convolution filter. Since the performance is influenced by the number of points, our method is also required tuning like common neural networks. However, the performance difference between CKCNN and FlexNet in Tab. 4 shows that MLP-based methods are severely influenced by architectural settings. That is, they have extensive search space, such as depth, width, and activation function, so they typically require more tuning than our method. Moreover, the impact of the number of points is not particularly significant in that even the worst " + }, + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "type": "inline_equation", + "content": "(N_{p} = 64)" + }, + { + "bbox": [ + 304, + 482, + 546, + 650 + ], + "type": "text", + "content": " slightly outperforms the FlexNet (acc=92.20)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 658, + 390, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 390, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 390, + 670 + ], + "type": "text", + "content": "4.5. Visualization" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Finally, we analyze our SMP by visualizing filters trained on CIFAR10. In the first column of Fig. 4, we can observe the trained weight points' position. 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+ { + "bbox": [ + 46, + 242, + 545, + 264 + ], + "type": "text", + "content": "Figure 4. Visualization of kernels. Each row shows the location of points and first 6 kernels of a filter. For ease of visualization, the kernels are first subjected to the absolute value operation and then normalized to a range of [0,1]." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 287, + 129, + 355 + ], + "lines": [ + { + "bbox": [ + 58, + 287, + 129, + 355 + ], + "spans": [ + { + "bbox": [ + 58, + 287, + 129, + 355 + ], + "type": "image", + "image_path": "8952a576dd706a68782b2567ce3b3726fcd7cf6022e86d386ce018e6b9fede13.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 355, + 106, + 362 + ], + "lines": [ + { + "bbox": [ + 80, + 355, + 106, + 362 + ], + "spans": [ + { + "bbox": [ + 80, + 355, + 106, + 362 + ], + "type": "text", + "content": "(a) Layer 1" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 375, + 286, + 396 + ], + "lines": [ + { + "bbox": [ + 47, + 375, + 286, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 286, + 396 + ], + "type": "text", + "content": "Figure 5. Normalized sum of the absolute value of trained filters. (a), (b), and (c) are top, middle, and bottom layers, respectively." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 134, + 292, + 194, + 354 + ], + "blocks": [ + { + "bbox": [ + 134, + 292, + 194, + 354 + ], + "lines": [ + { + "bbox": [ + 134, + 292, + 194, + 354 + ], + "spans": [ + { + "bbox": [ + 134, + 292, + 194, + 354 + ], + "type": "image", + "image_path": "88eb384bcbd67e00289cdfd32becdaee6676bfe69d52ab394cdf41e8f671af11.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 149, + 355, + 177, + 362 + ], + "lines": [ + { + "bbox": [ + 149, + 355, + 177, + 362 + ], + "spans": [ + { + "bbox": [ + 149, + 355, + 177, + 362 + ], + "type": "text", + "content": "(b) Layer 8" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 203, + 292, + 278, + 354 + ], + "blocks": [ + { + "bbox": [ + 203, + 292, + 278, + 354 + ], + "lines": [ + { + "bbox": [ + 203, + 292, + 278, + 354 + ], + "spans": [ + { + "bbox": [ + 203, + 292, + 278, + 354 + ], + "type": "image", + "image_path": "985c85d1e740ca467545e000607a61a1bba5826ea0a54333feca69c3d4aa252d.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 219, + 355, + 249, + 362 + ], + "lines": [ + { + "bbox": [ + 219, + 355, + 249, + 362 + ], + "spans": [ + { + "bbox": [ + 219, + 355, + 249, + 362 + ], + "type": "text", + "content": "(c) Layer 14" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 418, + 286, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 286, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 286, + 537 + ], + "type": "text", + "content": "cations " + }, + { + "bbox": [ + 46, + 418, + 286, + 537 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 418, + 286, + 537 + ], + "type": "text", + "content": " are mainly sampled near the center of the kernel for stable training. It shows that the points spread out for optimal kernel representation over the training process, as we argued, and thus the receptive fields are not limited to a small part. Also, we can figure out that there are square patterns caused by Eq. (2) in the kernels, where each square has its own area. This suggests that although the radius parameters are initialized with small values, the values are individually increased and optimized for each corresponding weight point during training." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 538, + 286, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 538, + 286, + 645 + ], + "spans": [ + { + "bbox": [ + 46, + 538, + 286, + 645 + ], + "type": "text", + "content": "Observing visualized convolution kernel in Fig. 4, kernels from the same filter share the receptive fields. It allows a single filter to focus on the shared area. Furthermore, as illustrated in Fig. 5, SMPConv has large adaptive receptive fields which are not conventional square or rectangular shapes. This is because it consists of optimized filters with their own small and large receptive fields. Thus, our method can handle not only global information but also local details." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 657, + 196, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 196, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 196, + 670 + ], + "type": "text", + "content": "5. Conclusion and discussion" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "In this paper, we present a method to build a continuous convolution. We propose using point representations, where each point has the weight parameters, coordinates, and ra" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 285, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 392 + ], + "type": "text", + "content": "dius to learn. By connecting the points, we can implement a continuous function, which can be utilized to construct convolutional kernels. We have provided extensive experimental results, showing that drop-in replacement in the existing training pipeline without bells and whistles improved the performance by a safe margin. We also show that a continuous convolution can be effectively utilized in a large-scale experiment. We expect more research and development in this direction." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 393, + 545, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 489 + ], + "type": "text", + "content": "Although promising, there are many rooms to be improved. Due to the limited computational budget, we could not conduct sufficient experiments in the large-scale experiment. The experimental results provided in this manuscript resulted from a few runs. As trial and error are essential in the machine learning development process, we plan to find optimal configurations and training techniques to enhance the performance of the proposed method." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 489, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 545, + 584 + ], + "type": "text", + "content": "We also observed that the learned kernels often show sparse patterns depending on the tasks. It is well aligned with the success of dilated convolution or its variants, and our methods automatically learn proper sparsity during the training process on specific tasks. Adding prior knowledge through training and regularization techniques would further improve performance, especially for tasks requiring longer-term dependency modeling." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 595, + 403, + 608 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 595, + 403, + 608 + ], + "spans": [ + { + "bbox": [ + 306, + 595, + 403, + 608 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 613, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 703 + ], + "type": "text", + "content": "We thank Usman Ali for valuable discussions. This research was supported by the Ministry of Science and ICT (MSIT) of Korea, under the National Research Foundation (NRF) grant (2022R1F1A1064184, 2022R1A4A3033571), Institute of Information and Communication Technology Planning Evaluation (IITP) grants for the AI Graduate School program (IITP-2019-0-00421), and the BK21 FOUR Project." + } + ] + } + ], + "index": 37 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10296" + } + ] + } + ], + "index": 38 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. 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Differentiable point-based radiance fields for efficient view synthesis. arXiv preprint arXiv:2205.14330, 2022. 2, 3" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "10299" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/b6c29c1e-51a1-4935-bf5e-ec2e26810dec_content_list.json b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/b6c29c1e-51a1-4935-bf5e-ec2e26810dec_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..436141c694abbe0b2795ccc5981f9854512b0a8c --- /dev/null +++ b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/b6c29c1e-51a1-4935-bf5e-ec2e26810dec_content_list.json @@ -0,0 +1,1841 @@ +[ + { + "type": "text", + "text": "SOOD: Towards Semi-Supervised Oriented Object Detection", + "text_level": 1, + "bbox": [ + 176, + 130, + 794, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Wei Hua\\*, Dingkang Liang\\*, Jingyu Li, Xiaolong Liu, Zhikang Zou, Xiaoqing Ye, Xiang Bai", + "bbox": [ + 86, + 179, + 879, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Huazhong University of Science and Technology, {whua_hust, dkliang, xbai} @hust.edu.cn \n2Baidu Inc., China", + "bbox": [ + 122, + 214, + 848, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-Supervised Object Detection (SSOD), aiming to explore unlabeled data for boosting object detectors, has become an active task in recent years. However, existing SSOD approaches mainly focus on horizontal objects, leaving multi-oriented objects that are common in aerial images unexplored. This paper proposes a novel Semi-supervised Oriented Object Detection model, termed SOOD, built upon the mainstream pseudo-labeling framework. Towards oriented objects in aerial scenes, we design two loss functions to provide better supervision. Focusing on the orientations of objects, the first loss regularizes the consistency between each pseudo-label-prediction pair (includes a prediction and its corresponding pseudo label) with adaptive weights based on their orientation gap. Focusing on the layout of an image, the second loss regularizes the similarity and explicitly builds the many-to-many relation between the sets of pseudo-labels and predictions. Such a global consistency constraint can further boost semi-supervised learning. Our experiments show that when trained with the two proposed losses, SOOD surpasses the state-of-the-art SSOD methods under various settings on the DOTAv1.5 benchmark. The code will be available at https://github.com/HamPerdredes/SOOD.", + "bbox": [ + 76, + 318, + 473, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 698, + 209, + 714 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sufficient labeled data is essential for fully-supervised object detection. However, the data labeling process is time-consuming and expensive. Recently, Semi-Supervised Object Detection (SSOD), where object detectors are learned from labeled data as well as easy-to-obtain unlabeled data, has attracted increasing attention. Existing SSOD methods [16, 24, 44, 50] mainly focus on detecting objects with horizontal bounding boxes in general scenes. Nevertheless, in more complex scenes, such as aerial scenes, objects usu", + "bbox": [ + 75, + 724, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/826a5548f5459ca64255c3a713d1079ccce3a2b7e04c2361d46fc5f201049fdc.jpg", + "image_caption": [ + "(a) Arbitrary rotating objects" + ], + "image_footnote": [], + "bbox": [ + 509, + 286, + 689, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/09aa9cb227da62c57eef758c8ffe9dc814e1fbbe6afa1970fb52a16c5a54c16b.jpg", + "image_caption": [ + "(b) Small and dense objects", + "Figure 1. Arbitrary rotating (a), small and dense (b) objects are common in aerial scenes, which are often regularly arranged on the image. From a global perspective, this pattern indicates that an aerial can be regarded as a layout." + ], + "image_footnote": [], + "bbox": [ + 702, + 286, + 883, + 387 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ally need to be annotated with oriented bounding boxes. Considering the higher annotation cost of oriented boxes*, semi-supervised oriented object detection is worth studying.", + "bbox": [ + 496, + 513, + 890, + 560 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compared with general scenes, the main characteristics of objects in aerial scenes (or aerial objects for short) are three-fold: arbitrary orientations, small scales, and agglomeration, as shown in Fig. 1. The mainstream SSOD methods are based on the pseudo-labeling framework [3,35,36] consisting of a teacher model and a student model. The teacher model, an Exponential Moving Average (EMA) of the student model at historical training iterations, generates pseudo-labels for unlabeled images. Thus, the student model can learn from both labeled and unlabeled data. To extend the framework to oriented object detection, we think the following two aspects need to be addressed: 1) As orientation is an essential property of multi-oriented objects, how to use the orientation information when guiding the student with pseudo-labels is critical. 2) As aerial objects are often dense and regularly distributed in an image, we can utilize the layout to facilitate the learning of each pair instead of treating them individually.", + "bbox": [ + 496, + 561, + 892, + 833 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper proposes the first Semi-supervised Oriented", + "bbox": [ + 517, + 834, + 890, + 849 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. † Corresponding author. \nWork done when Dingkang Liang was an intern at Baidu.", + "bbox": [ + 94, + 875, + 405, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Annotation cost of an oriented box is about 36.5% (86$ vs. 63$ per 1k at 2022.11) more than a horizontal box according to https://cloud.google.com/ai-platform/data-labeling/pricing.", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15558", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Object Detection method, termed SOOD. Following [50], SOOD is built upon the dense pseudo-labeling framework, where the pseudo labels are filtered from the raw pixelwise predictions (including box coordinates and confidence scores). The key design is two simple yet effective losses that enforce the instance-level and set-level consistency between the student's and the teacher's predictions.", + "bbox": [ + 75, + 90, + 467, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To be specific, considering that the pseudo-label-prediction pairs are not equally informative, we propose the Rotation-aware Adaptive Weighting (RAW) loss. It utilizes the orientation gap of each pair, which reflects the difficulty of this sample in a way, to weight the corresponding loss dynamically. In this manner, we can softly pick those more useful supervision signals to guide the learning of the student. In addition, considering that the layout of an aerial image can potentially reflect components' overall status (e.g., objects' density and location distribution) and help the detection process, we propose the Global Consistency (GC) loss. It measures the similarity of the pseudo-labels and the predictions from a global perspective, which can alleviate the disturbance of noise in pseudo-labels and implicitly regularizes the mutual relations between different objects.", + "bbox": [ + 75, + 198, + 467, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We extensively evaluate SOOD under various settings on DOTA-v1.5, a popular aerial object detection benchmark. Our SOOD achieves consistent performance improvement when using $10\\%$ , $20\\%$ , $30\\%$ , and full of labeled data, compared with the state-of-the-art SSOD methods (using the same oriented object detector). The ablation study also verifies the effectiveness of the two losses.", + "bbox": [ + 75, + 424, + 467, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, this paper makes an early exploration of semi-supervised learning for oriented object detection. By analyzing the distinct characteristics of oriented objects from general objects, we propose two novel loss functions to adapt the pseudo-label framework to this task. We hope that this work can provide a good starting point for semi-supervised oriented object detection and serve as a simple yet strong baseline for future research.", + "bbox": [ + 75, + 529, + 467, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 76, + 664, + 220, + 679 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-Supervised Object Detection. In the past few years, semi-supervised learning (SSL) [2, 32] has achieved impressive performance in image classification. These works leverage unlabeled data by using pseudo-label [9,15,17,42], consistency regularization [2,36,41], data augmentation [4, 31] and even adversarial training [26]. Compared to semi-supervised image classification, SSOD requires instance-level predictions and additional bounding boxes regression sub-task, which makes it more challenging. In [28, 51], pseudo-labels are assembled from predictions of data with different augmentations. CSD [14] only utilizes the horizontal flipping augmentation and applies consistency loss to constrain the model, but the weak augmentation limits its performance. STAC [33] trains an object detect-", + "bbox": [ + 75, + 688, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion with labeled data and generates pseudo-labels on unlabeled data with this detector offline. After that, some studies [24,35,44,45] adopt EMA from Mean Teacher [36] to update the teacher model after each training iteration. ISMT [45] obtains more accurate pseudo-labels by fusing current pseudo-labels and history labels. Unbiased Teacher [24] replaces cross-entropy loss with focal loss [22] to solve the class-imbalance issue and filters pseudo-labels by threshold. Soft Teacher [44] uses the classification scores to adaptively weight the loss of each pseudo-box and proposes box jittering to select reliable pseudo-labels. Unbiased Teacher v2 [25] adopts an anchor-free detector and uses uncertainty predictions to select pseudo-labels for the regression branch. Dense Teacher [50] replaces postprocessed instance-level pseudo-labels with dense pixel-level pseudo-labels, which successfully removes the influence of thresholds and post-processing hyper-parameters. However, none of these works are designed for oriented object detection in aerial scenes. This paper aims to fill this blank and offer a starting point for future research.", + "bbox": [ + 496, + 90, + 890, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Orient Object Detection. Different from general object detectors [8, 23, 29, 30], oriented object detectors represent objects with Oriented Bounding Boxes (OBBs). Typical oriented objects include aerial objects and multi-oriented scene texts [12, 19, 20, 34]. In recent years, many oriented object detection methods have been proposed to boost the performance for this area. CSL [46] formulates the angle regression problem as a classification task to address the out-of-bound issue. $\\mathrm{R}^3\\mathrm{Det}$ [47] predicts Horizontal Bounding Boxes (HBBs) at the first stage to improve detection speed and align the feature in the second stage to predict oriented objects. Oriented R-CNN [43] proposes a concise multi-oriented region proposal network and uses the midpoint offsets to represent arbitrarily oriented objects. ReDet [12] proposes a Rotation-equivariant detector to extract rotation-invariant from rotation-equivariant for accurate aerial object detection. Oriented RepPoints [18] proposes a quality assessment module and samples assignment scheme for adaptive points learning, which can obtain non-axis features from neighboring objects and neglect background noises. Different from the above works that focus on the supervised paradigm, this paper makes an early exploration of semi-supervised oriented object detection, which can reduce the annotation cost and boost detectors with unlabeled data.", + "bbox": [ + 496, + 393, + 890, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 768, + 625, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we revisit the mainstream pseudolabeling paradigm in SSOD and Monge-Kantarovich optimal transport theory [27] as preliminary.", + "bbox": [ + 496, + 792, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Pseudo-labeling Paradigm", + "text_level": 1, + "bbox": [ + 500, + 847, + 736, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pseudo-labeling frameworks [25, 44, 50] inherited designs from the Mean Teacher [36] structure, which consists", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15559", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of two parts, i.e., a teacher model and a student model. The teacher model is an Exponential Moving Average (EMA) of the student model. They are learned iteratively by the following steps. 1) Generate pseudo-labels for the unlabeled data in a batch. The pseudo-labels are filtered from the teacher's predictions, e.g., the box coordinates and the classification scores. Meanwhile, the student makes predictions for both labeled and unlabeled data in the batch. 2) Compute loss for the student model's predictions. It consists of two parts, the unsupervised loss $\\mathcal{L}_u$ and supervised loss $\\mathcal{L}_s$ . They are computed for the unlabeled data with the pseudo-labels and the labeled data with the ground truth (GT) labels, respectively. The overall loss $\\mathcal{L}$ is the sum of them. 3) Update the parameters of the student model according to the overall loss. The teacher model is updated simultaneously in an EMA manner. In this way, based on the mutual learning mechanism, both models evolve as the training goes on.", + "bbox": [ + 75, + 90, + 472, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the sparsity of pseudo-labels, pseudo-labeling frameworks can be further categorized into sparse pseudolabeling [25, 44] and dense pseudo-labeling [50], termed SPL and DPL, respectively. The SPL selects the teacher's predictions after the post-processing operations, e.g., nonmaximum suppression and score filtering. It obtains sparse labels to supervise the student, e.g., bounding boxes and categories. The DPL directly samples the post-sigmoid log-its predicted by the teacher, which are dense and informative. Compared with SPL, DPL bypasses those lengthy post-processing methods, reserving more details from the teacher than its pseudo-box counterpart.", + "bbox": [ + 75, + 363, + 472, + 545 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Optimal Transport", + "text_level": 1, + "bbox": [ + 76, + 554, + 261, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Monge-Kantorovich Optimal Transport (OT) [27] aims to solve the problem of simultaneously moving items from one set to another set with minimum cost. It has been widely explored in various computer vision tasks [1, 7, 39, 49]. The mathematical formulations of OT are described as follows in detail.", + "bbox": [ + 75, + 578, + 468, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathbb{X} = \\{x_i|x_i\\in \\mathbb{R}^d\\}_{i}^{N}$ and $\\mathbb{Y} = \\{y_j|y_j\\in \\mathbb{R}^d\\}_{j}^{N}$ denote two sets of $N$ $d$ -dimensional vectors. Their discrete distributions $\\hat{\\mathbb{X}}$ and $\\hat{\\mathbb{Y}}$ are formulated as:", + "bbox": [ + 75, + 667, + 468, + 714 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbb {X}} = \\sum_ {i} ^ {N} \\hat {x} _ {i} \\delta_ {f _ {i}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 222, + 726, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbb {Y}} = \\sum_ {j} ^ {N} \\hat {y} _ {j} \\delta_ {g _ {j}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 757, + 468, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{x}}$ and $\\hat{\\mathbf{y}}$ are the discrete probability vectors, $\\delta$ is the Dirac delta function. Therefore, the OT cost is measured between these two probabilities, $\\hat{\\mathbf{x}}$ and $\\hat{\\mathbf{y}}$ . The possible transportation plans from $\\hat{\\mathbf{x}}$ to $\\hat{\\mathbf{y}}$ are formed as:", + "bbox": [ + 75, + 782, + 468, + 844 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {P} = \\left\\{\\boldsymbol {p} \\in \\mathbb {R} ^ {N \\times N} \\mid \\boldsymbol {p} \\mathbf {1} _ {N} = \\hat {\\mathbf {x}}, \\boldsymbol {p} ^ {T} \\mathbf {1} _ {N} = \\hat {\\mathbf {y}} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 854, + 468, + 873 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{1}_N$ is an $N$ -dimensional column vector whose values", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are all 1. The OT cost is then defined as:", + "bbox": [ + 500, + 90, + 769, + 104 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\omega_ {o t} (\\hat {\\mathbf {x}}, \\hat {\\mathbf {y}}) = \\min _ {\\boldsymbol {p} \\in \\boldsymbol {P}} \\left\\langle \\mathbf {C}, \\boldsymbol {p} \\right\\rangle , \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 119, + 890, + 141 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{C} \\in \\mathbb{R}^{N \\times N}$ represents the cost matrix between two sets, $\\langle \\cdot \\rangle$ represents inner product. In common, the OT problem is solved in its dual formulation", + "bbox": [ + 498, + 154, + 893, + 200 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {W} _ {o t} (\\hat {\\mathbf {x}}, \\hat {\\mathbf {y}}) = \\max _ {\\boldsymbol {\\lambda}, \\boldsymbol {\\mu} \\in \\mathbb {R} ^ {N}} \\left\\langle \\boldsymbol {\\lambda}, \\hat {\\mathbf {x}} \\right\\rangle + \\left\\langle \\boldsymbol {\\mu}, \\hat {\\mathbf {y}} \\right\\rangle , \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 210, + 890, + 238 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ns. t. \\lambda_ {i} + \\mu_ {j} \\leq \\mathbf {C} _ {i, j}, \\forall i, j,\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 239, + 823, + 253 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda$ and $\\mu$ are the solutions of the OT problem, which can be approximated in an iterative manner [5].", + "bbox": [ + 500, + 265, + 890, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 309, + 589, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 illustrates an overview of our proposed SOOD. Towards multi-oriented object detection in aerial images, we build our approach upon the popular dense pseudo-labeling framework [50], along with the Rotation-aware Adaptive Weighting (RAW) loss and the Global Consistency (GC) loss. In this section, we first describe the overall framework in Sec. 4.1. Then, we describe the key design of the proposed losses, RAW and GC, in the following Sec. 4.2 and Sec. 4.3, respectively.", + "bbox": [ + 498, + 335, + 893, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. The Overall Framework", + "text_level": 1, + "bbox": [ + 500, + 481, + 723, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Currently, the Dense Pseudo-Labeling (DPL) framework achieves the state-of-the-art in SSOD. Hence, we construct a DPL-based end-to-end baseline, including the supervised and unsupervised parts. For the supervised part, the student model is trained with labeled data in a regular manner. For the unsupervised part, we first obtain predicted boxes of the teacher after post-processing. These boxes indicate informative areas in the prediction map, where we randomly sample predictions, forming them as dense pseudo-labels $P^t$ . Note that we also select the predictions $P^s$ at the same correspondence positions from the student.", + "bbox": [ + 498, + 503, + 890, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use the oriented version of FCOS [37] as the teacher and student models. The basic unsupervised loss consists of three parts: classification loss, regression loss, and centerness loss, corresponding to the output of FCOS. We adopt smooth 11 loss for regression loss, binary cross-entropy loss for classification and center-ness loss. Based on these losses, we first perform adaptive weighting on them through RAW and further measure the global consistency between the teacher and the student via GC.", + "bbox": [ + 498, + 670, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Rotation-aware Adaptive Weighting Loss", + "text_level": 1, + "bbox": [ + 500, + 816, + 852, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Orientation is one essential property of an oriented object. As shown in Fig. 1, even if objects are dense and small, their orientations remain clear. Previous oriented object detection methods have already employed such a property by", + "bbox": [ + 498, + 840, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15560", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0f512317b9213522b0422f60b4681461d27690687049b8a033ba304091c8f64a.jpg", + "image_caption": [ + "Figure 2. The pipeline of the proposed SOOD. Each training batch consists of both labeled and unlabeled images. Note that the supervised part is hidden for simplicity. For the unsupervised part, we sample dense pseudo-labels from the teacher's prediction map and select the student's predictions at the same positions, obtaining a series of pseudo-label-prediction pairs. We dynamically weigh each pair's unsupervised loss by their orientation difference. Besides, we regard them as two discrete distributions, measuring their similarity in a many-to-many manner via a global consistency loss." + ], + "image_footnote": [], + "bbox": [ + 94, + 85, + 880, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "assembling it into loss calculation. However, these works are under the assumption that the angles of the labels are reliable. In this case, it is natural to strictly force the prediction close to the ground truth.", + "bbox": [ + 75, + 441, + 468, + 501 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unfortunately, the above assumption does not hold in the semi-supervised setting. In other words, the pseudolabels may be incorrect. Simply forcing the student to be close to the teacher may cause noise accumulation, harming the model's training process. Hence, we propose to utilize the orientation information softly. Intuitively, as orientation is essential but hard to be accurately predicted, the difference in rotation angles between a prediction and a pseudolabel can reflect the difficulty of the sample in a way. In other words, the orientation difference can be used to dynamically adjust the unsupervised loss. Therefore, we construct a rotation-aware modulating factor, similar to focal loss [22]. This factor can dynamically weight the loss of each pseudo-label-prediction pair by considering their orientation difference.", + "bbox": [ + 75, + 503, + 470, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the modulating factor $\\omega_{i}^{rot}$ of the $i$ -th pair is formed as:", + "bbox": [ + 76, + 729, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\omega_ {i} ^ {\\text {r o t}} = 1 + \\sigma_ {i}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 761, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {i} = \\alpha \\frac {\\left| r _ {i} ^ {t} - r _ {i} ^ {s} \\right|}{\\pi}, r _ {i} ^ {t}, r _ {i} ^ {s} \\in \\left[ - \\frac {\\pi}{2}, \\frac {\\pi}{2}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 787, + 468, + 818 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $r_i^t$ and $r_i^s$ are the $i$ -th pseudo-label's and prediction's rotation angle in radians, respectively. $\\alpha$ is a hyperparameter for adjusting orientation's importance, and we set it to 50 empirically. We add a constant to $\\sigma_i$ , maintaining the origin unsupervised loss when pseudo-label and", + "bbox": [ + 76, + 824, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "prediction have the same orientation. With the rotation-aware modulating factor, the overall rotation-aware adaptive weighting loss is formulated as:", + "bbox": [ + 498, + 441, + 890, + 488 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {R A W} = \\sum_ {i} ^ {N _ {p}} \\omega_ {i} ^ {\\text {r o t}} \\mathcal {L} _ {u} ^ {i}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 500, + 890, + 520 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N_{p}$ is the number of pseudo-labels and $\\mathcal{L}_u^i$ is the basic unsupervised loss of the $i$ -th pseudo-label-prediction pair. By using the rotation-aware modulating factor, the RAW loss makes better use of the orientation information and provides more informative guidance, potentially benefiting the semi-supervised learning process.", + "bbox": [ + 498, + 532, + 890, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Global Consistency Loss", + "text_level": 1, + "bbox": [ + 500, + 635, + 723, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Objects in an aerial image are usually dense and regularly distributed, as depicted in Fig. 1. Similar to texts in a document, the arrangement of the set of objects, i.e., the layout, encodes the mutual relations between them and the global pattern of the image. Ideally, the layout consistency between the student's and the teacher's predictions will be ensured if each pseudo-label-prediction pair is aligned. However, the latter condition is too strict and may hurt performance when there are noises in pseudo-labels. Therefore, it is reasonable to add the consistency between layouts as an additional relaxed optimization objective, encouraging the student to learn robust information from the teacher. In this way, the noise disturbance in pseudo-labels can be alleviated. Besides, the relations between different predicted instances from the student can also be regularized implicitly, which provides an additional guide to the student.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15561", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce the optimal transport cost [38] to measure the global similarity of layouts between the teacher's and the student's predictions, forming the global consistency loss. To be concrete, we denote the classification scores predicted by the teacher and the student by $\\mathbf{s}^t\\in \\mathbb{R}^{N_p\\times K}$ and $\\mathbf{s}^s\\in \\mathbb{R}^{N_p\\times K}$ respectively, where $K$ is the number of classes. Then, their global distributions, $\\mathbf{d}^t\\in \\mathbb{R}^{N_p}$ and $\\mathbf{d}^s\\in \\mathbb{R}^{N_p}$ can be formulated by", + "bbox": [ + 76, + 90, + 472, + 212 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {i} ^ {t} = e ^ {\\mathbf {s} _ {i, c (i)} ^ {t}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 222, + 468, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {i} ^ {s} = e ^ {\\mathbf {S} _ {i, c (i)} ^ {s}}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 227, + 251, + 468, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $c(i) = \\underset{j=1,\\ldots,K}{\\arg \\max} \\mathbf{s}_{i,j}^{t}$ is the index of the class with the largest score for the $i$ -th pseudo-label.", + "bbox": [ + 76, + 275, + 468, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The global consistency loss is defined as the OT problem's dual formulation", + "bbox": [ + 76, + 314, + 468, + 344 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {G C} \\left(\\mathbf {d} ^ {t}, \\mathbf {d} ^ {s}\\right) = \\left\\langle \\boldsymbol {\\lambda} ^ {*}, \\frac {\\mathbf {d} ^ {t}}{\\| \\mathbf {d} ^ {t} \\| _ {1}} \\right\\rangle + \\left\\langle \\boldsymbol {\\mu} ^ {*}, \\frac {\\mathbf {d} ^ {s}}{\\| \\mathbf {d} ^ {s} \\| _ {1}} \\right\\rangle , \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 351, + 468, + 386 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we normalize two distributions to form discrete probabilities, by dividing them to their sum. To construct the cost map for solving the OT problem, we consider both the spatial distance and the score difference of each possible matching pair. Specifically, for each prediction, we measure its matching cost with every pseudo-label as follows:", + "bbox": [ + 76, + 393, + 468, + 486 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i, j} = C _ {i, j} ^ {\\text {d i s t}} + C _ {i, j} ^ {\\text {s c o r e}}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 494, + 468, + 513 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i, j} ^ {\\text {d i s t}} = \\frac {\\left\\| \\mathbf {z} _ {i} ^ {t} - \\mathbf {z} _ {j} ^ {s} \\right\\| _ {2} ^ {2}}{\\max _ {1 < = a , b < = N _ {p}} \\left\\| \\mathbf {z} _ {a} ^ {t} - \\mathbf {z} _ {b} ^ {s} \\right\\| _ {2} ^ {2}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 523, + 468, + 560 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i, j} ^ {\\text {s c o r e}} = \\frac {\\left\\| \\mathbf {s} _ {i , c (i)} ^ {t} - \\mathbf {s} _ {j , c (j)} ^ {s} \\right\\| _ {1}}{\\max _ {1 < = a , b < = N _ {p}} \\left\\| \\mathbf {s} _ {a , c (a)} ^ {t} - \\mathbf {s} _ {b , c (b)} ^ {s} \\right\\| _ {1}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 565, + 468, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{z}_i^t$ and $\\mathbf{z}_j^s$ are 2D coordinates of the $i$ -th sample in the teacher and the $j_{th}$ sample in the student.", + "bbox": [ + 76, + 609, + 468, + 640 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We solve the OT problem by a fast Sinkhorn distances algorithm [5], obtaining the approximate solution $\\lambda^{*}$ and $\\mu^{*}$ . Based on the defined loss, its gradient with respect to $\\mathbf{d}^s$ is", + "bbox": [ + 76, + 641, + 468, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\partial \\mathcal {L} _ {G C} \\left(\\mathbf {d} ^ {t} , \\mathbf {d} ^ {s}\\right)}{\\partial \\mathbf {d} ^ {s}} = \\frac {\\boldsymbol {\\mu} ^ {*}}{\\| \\mathbf {d} ^ {s} \\| _ {1}} - \\frac {\\langle \\boldsymbol {\\mu} ^ {*} , \\mathbf {d} ^ {s} \\rangle}{\\| \\mathbf {d} ^ {s} \\| _ {1} ^ {2}}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 696, + 468, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The gradients can be back-propagated to update the model, enforcing the layout consistency in the framework. Although OT-based loss has been explored before [6,39,49], our goal of using OT is different. Specifically, they focus on utilizing OT to improve the model's generalizability [6, 39] or mitigate the matching constraint [49]. However, our GC aims to model the many-to-many relationship between the teacher and the student, which is complementary to the RAW. In addition, we adopt such a set-to-set matching to alleviate the error in pseudo-label assignment, providing a more loose but stable constraint.", + "bbox": [ + 76, + 734, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SOOD is trained with the proposed unsupervised losses, RAW and GC, for unlabeled data as well as the supervised loss for labeled data. The overall loss $\\mathcal{L}$ is defined as:", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\underbrace {\\mathcal {L} _ {R A W} + \\mathcal {L} _ {G C}} _ {\\mathcal {L} _ {u}} + \\mathcal {L} _ {s}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 148, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that the supervised loss is the same as defined in FCOS, our designs only modify the unsupervised part.", + "bbox": [ + 498, + 193, + 890, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 237, + 633, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on DOTA-v1.5, which is proposed at DOAI-2019†. It contains 2806 large aerial images and 402,089 annotated oriented objects. It includes three subsets: DOTA-v1.5-train, DOTA-v1.5-val and DOTA-v1.5-test, containing 1411, 458, and 937 images, respectively. The annotations of DOTA-v1.5-test is not released.", + "bbox": [ + 496, + 262, + 890, + 352 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "There are 16 categories in this dataset: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), Helicopter (HC) and Container crane (CC). Compared with DOTA-v1.0 [40], a previous version, DOTA-v1.5 contains more small instances (less than 10 pixels), which makes it more challenging.", + "bbox": [ + 496, + 353, + 890, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following conventions in SSOD, we consider two protocols, Partially Labeled Data and Fully Labeled Data, to validate the performance of a method on limited and abundant labeled data, respectively.", + "bbox": [ + 496, + 489, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Partially Labeled Data. We randomly sample $10\\%$ , $20\\%$ , and $30\\%$ images from DOTA-v1.5-train as labeled data and set the remaining images as unlabeled data. Following DOTA-v1.5-train's data distribution, we provide one fold for each data proportion.", + "bbox": [ + 496, + 549, + 890, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fully Labeled Data. We set DOTA-v1.5-train as labeled data and DOTA-v1.5-test as unlabeled data.", + "bbox": [ + 496, + 625, + 890, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For all experiments, we perform evaluation on DOTAv1.5-val and report the performance with the standard mean average precision (mAP) as the evaluation metrics.", + "bbox": [ + 496, + 655, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 709, + 715, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Without loss of generality, we take FCOS [37] as the representative anchor-free detector, and adopt ResNet-50 [13] with FPN [21] as the backbone for all our experiments. Following the previous works [11, 12, 40], we crop the original images into $1024 \\times 1024$ patches with a stride of 824, that is, the pixel overlap between two adjacent patches is 200. We utilize asymmetric data augmentation for unlabeled data. Specifically, we use strong augmentation for", + "bbox": [ + 496, + 732, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "†The 1st Workshop on Detecting Objects in Aerial Images in conjunction with IEEE CVPR 2019 https://captain-whu.github.io/DOAI2019/dataset.html", + "bbox": [ + 500, + 862, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15562", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5674f0088ab5c35a7c2f28756221e520443420728dce5e25fdcae1cadd8233bb.jpg", + "table_caption": [ + "Table 1. Experimental results on DOTA-v1.5 under the Partially Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS, respectively. Experiments are conducted on 10%, 20% and 30% labeled data settings." + ], + "table_footnote": [], + "table_body": "
SettingMethodPublication10%20%30%
SupervisedFaster R-CNN* [30]NeurIPS 201643.4351.3253.14
FCOS† [37]ICCV 201942.7850.1154.79
Semi-supervisedUnbiased Teacher* [24]ICLR 202144.5152.8053.33
Soft Teacher* [44]ICCV 202148.4654.8957.83
Dense Teacher† [50]ECCV 202246.9053.9357.86
SOOD† (ours)-48.6355.5859.23
", + "bbox": [ + 106, + 128, + 867, + 256 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bb87aeb61126b234b562fd01af1daf7015557146503d5b2eba3b26c6fd23c8ad.jpg", + "table_caption": [ + "Table 2. Experimental results on DOTA-v1.5 under the Fully Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS respectively. Numbers in font of the arrow indicate the supervised baseline." + ], + "table_footnote": [], + "table_body": "
MethodPublicationmAP
Unbiased Teacher* [24]ICLR 202166.12 → 1.27 → 64.85
Soft Teacher* [44]ICCV 202166.12 → +0.28 → 66.40
Dense Teacher† [50]ECCV 202265.46 → +0.92 → 66.38
SOOD† (ours)-65.46 → +2.24 → 67.70
", + "bbox": [ + 93, + 344, + 454, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the student model and weak augmentation for the teacher model. Random flipping is used for weak augmentation, while strong augmentation contains random flipping, color jittering, random grayscale, and random Gaussian blur. All models are trained for 180k iterations on 2 RTX3090 GPUs. With the SGD optimizer, the initial learning rate of 0.0025 is divided by 10 at 120k and 160k. The momentum and the weight decay are set to 0.9 and 0.0001, respectively. Each GPU takes 3 images as input, where the proportion between unlabeled and labeled data is set to 1:2. The pseudo-label sampling ratio is set as 0.25 by default. Following previous SSOD works [24, 50], we use the \"burn-in\" strategy to initialize the teacher model.", + "bbox": [ + 75, + 473, + 468, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 676, + 215, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare our method with the state-of-the-art SSOD methods [3, 24, 44] on DOTA-v1.5. For a fair comparison, we re-implement these methods on oriented object detectors with the same augmentation setting.", + "bbox": [ + 75, + 700, + 468, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Partially Labeled Data. We evaluate our method under different labeled data proportions, and the results are shown in Tab. 1. Our SOOD achieves state-of-the-art performance under all proportions. Specifically, it obtains 48.63, 55.58, and $59.23\\mathrm{mAP}$ on $10\\%$ , $20\\%$ , and $30\\%$ proportions, respectively, surpassing our supervised baseline by $+5.85$ , $+5.47$ , and $+4.44\\mathrm{mAP}$ . We also surpass the state-of-the-art anchor-free method Dense Teacher [50] by $+1.73$ , $+1.65$ , and $+1.37$ under various proportions. We provide two anchor-", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e773326d77cb241cdbef56418085cbd515b224c607ae4aa3b681d65edfe4a8f9.jpg", + "table_caption": [ + "Table 3. The effectiveness of SOOD on other methods under Fully Labeled Data setting. * means based on RetinaNet [22]. SOOD is able to generalize to other detectors and boost their performance." + ], + "table_footnote": [], + "table_body": "
DetectorPublicationMethodmAP
CFA [10]CVPR 2021Supervised Ours65.75\n67.07
KLD* [48]NeurIPS 2021Supervised Ours62.21\n64.62
", + "bbox": [ + 514, + 330, + 879, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "based methods for comparison, Unbiased Teacher [24] and Soft Teacher [44]. On $10\\%$ and $20\\%$ proportions, our SOOD achieves higher performance than Soft Teacher, even though our baseline is weaker than Soft Teacher's. Under $30\\%$ data proportion, our SOOD surpasses Soft Teacher and Unbiased Teacher by at least $1.40\\mathrm{mAP}$ .", + "bbox": [ + 496, + 455, + 890, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The qualitative results of our method compared with supervised baseline and Dense Teacher [50] are shown in Fig. 3. With the help of our RAW and GC, SOOD is able to exploit more potential semantic information from the unlabeled data, helping reduce false predictions and improve the detection quality.", + "bbox": [ + 496, + 547, + 890, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fully Labeled Data. We also compare our SOOD with the other SSOD methods [24, 44, 50] on fully labeled data setting. Since the reported methods are based on different detectors, we report the results of the compared methods and their baseline in Tab. 2. Our SOOD surpasses previous methods by at least 1.30 points. Compared to our baseline, we obtain $+2.24\\mathrm{mAP}$ improvement, which further demonstrates our method's ability to learn from unlabeled data. We notice that the performance of Unbiased Teacher [24] drops after adding unlabeled data. The reason might be that Unbiased Teacher does not apply unsupervised losses for bounding box regression, which is important for oriented object detection.", + "bbox": [ + 496, + 642, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Generalization on other detectors. To further validate the effectiveness of our method, we evaluate our method on other oriented object detectors, CFA [10] and KLD [48], under the Fully Labeled Data setting. As shown in Tab. 3,", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15563", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bc567d3996879f86dd793c77d83861cb6c05e206e8f1741901b99c26326c4f36.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 88, + 320, + 199 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/984242e64871c6107941d38bce8675d69ce81c321f14c2197aa406c456fa1ac2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 88, + 482, + 199 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/33da7ed33742af8cf8ae5b44761c549b0a859588da10cd40b557a024d8f2b049.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 88, + 645, + 199 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ccdacf9511ae816a962964d63b6b65f3f4dac30c0a8681bc8d52e5feaef923d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 88, + 810, + 199 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc755ab69477f580cd1ce4abf46632848a927156c7d3af40f57d1959b76c308d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 200, + 320, + 311 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3cde8da9260c8d59228e8e17a5f19d84f5841d70b883b908b6d783b12b34260c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 200, + 482, + 311 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6aa8eb3690788a292ffc206c6ad28fa89bf70dc13ba97391636105f67fa3cb55.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 200, + 645, + 311 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4655ed10059995dc8ad17e44f26ed320ea0048302c97ce2e1872ddbbbadaff35.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 200, + 810, + 311 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b34e5d5d28db04bb4f77863f1d4bc6e97eb7ffcb7ad1cfc478e202d8c0c77bf2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 158, + 311, + 320, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fede77dccc4221f6c3c4137ae06338a49b3f9b1e3a97790b5fa656e83a6ece21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 311, + 482, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c503127738af7902361d0d994799e7f4d334c5a74d6d9070f24aaa93b0c8b92b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 311, + 645, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e99757c2ef34706193b0e4fbd1de699d60ede3893898617e87ad04fc2e99a98a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 311, + 810, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/de72a0a76f3146e6a575d70760aef03f6551654f84f1d823d6cb9ddd4d1d9fab.jpg", + "image_caption": [ + "Figure 3. Some visualization examples from the DOTA-v1.5 dataset. From left to right, each column shows ground truth, results of the supervised baseline (rotated-FCOS [37]), Dense Teacher [3], and our SOOD. The green rectangles indicate predictions. The red dashed circle, solid red circle, and red arrow represent false negative, false positive, and inaccurate orientation prediction, respectively." + ], + "image_footnote": [], + "bbox": [ + 158, + 422, + 320, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/29b61592d2d788ee3385bca6bcbe210a28fbdcd95b3a9865a9e3f25e25898614.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 422, + 482, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/955d2cfeb89ff0a1ca6292eb4def76e815d54f7171b35f8adee0080053f4580d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 422, + 645, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8501eb0cf3a43a637b66f475acf8da7aec8c12d5b58946c0610cfca28bbb962.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 422, + 810, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "although CFA is a strong detector, our method still results in an improvement of $+1.32\\mathrm{mAP}$ and reaches 67.07 mAP. On the KLD detector, our method brings an improvement of $+2.41\\mathrm{mAP}$ . The above results validate the generalization ability of our method.", + "bbox": [ + 75, + 614, + 472, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 703, + 230, + 719 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we conduct extensive studies to validate our key designs. Unless specified, all the ablation experiments are performed using $10\\%$ of labeled data.", + "bbox": [ + 75, + 727, + 468, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The effect of each component. We study the effects of the proposed two losses, Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Note that our SOOD degrades to the vanilla dense pseudolabeling framework without these two losses. As shown in Tab. 4, both losses are proved effective and complementary under all three settings: RAW and GC can each bring performance gain, and the baseline is further improved when", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8e7a8353766506823e8b54b6a824c404eff27331e76709bd045c4f28fc8327be.jpg", + "table_caption": [ + "Table 4. The effects of Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Experiments are conducted on $10\\%$ , $20\\%$ and $30\\%$ labeled data settings." + ], + "table_footnote": [], + "table_body": "
SettingRAWGCmAP
10%20%30%
I--47.2454.0757.74
II✓-47.8255.2158.93
III-✓47.7154.7258.70
IV✓✓48.6355.5859.23
", + "bbox": [ + 513, + 657, + 879, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "equipped with two losses. It indicates that the local constraint built by RAW and the global constraint built by GC can benefit the semi-supervised learning process, boosting the model by constructing one-to-one and many-to-many relationships between the teacher and the student.", + "bbox": [ + 496, + 799, + 893, + 876 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The influence of sampling ratio. In this part, we discuss", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15564", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/003bb1e8efbff53a452073a1c591d3c90dfa5f12290085f3b3526bd6a4d2a7c0.jpg", + "table_caption": [ + "Table 5. The effect of the sampling ratio for instance-level dense pseudo-labeling. Experiments are conducted at $10\\%$ setting, and the method is equipped with both RAW and GC losses." + ], + "table_footnote": [], + "table_body": "
SettingSample RatiomAP
I0.12548.27
II0.2548.63
III0.547.91
IV1.047.69
", + "bbox": [ + 109, + 141, + 436, + 228 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/48b2bc72e14efa9434519a20c7c5e36f70eecc59af4326082c3aee4682f0502c.jpg", + "table_caption": [ + "Table 6. The effects of different compositions in the cost map of GC. Experiments are conducted at $10\\%$ setting, and the method is equipped with RAW loss. The results indicate that both distance and score are essential factors of the cost map." + ], + "table_footnote": [], + "table_body": "
SettingDistanceScoremAP
I--47.82
II-✓48.10
III✓-47.94
IV✓✓48.63
", + "bbox": [ + 80, + 308, + 468, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the influence of the ratios in sampling pseudo-labels. The results with different sampling ratios are shown in Tab. 5. The best performance, $48.36\\mathrm{mAP}$ , is achieved when the sample ratio is set to 0.25. Setting it to other values degrades the performance. We hypothesize that this value ensures a good balance between noises (e.g., false positives) and valid predictions (e.g., true positives). Increasing it will introduce more noise that harms the training process, while decreasing it leads to information loss and failure in learning the representation of objects.", + "bbox": [ + 75, + 420, + 468, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effect of different compositions in cost map of GC. Here, we study the effects of the spatial distance and the score difference when constructing the cost map of optimal transport in GC loss. The results of different settings are shown in Tab. 6. We get at most $+0.28$ mAP improvement when using only one of them, indicating that the information from only one side is inadequate for learning the global prior. When considering both the score difference and spatial distance, the performance gain brought by GC is further improved to $+0.81$ mAP. It indicates that the information from score difference and spatial distance are complementary. With their help, RAW can effectively model the many-to-many relationship between the teacher and the student, providing an informative guide to the model.", + "bbox": [ + 75, + 577, + 468, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The effect of RAW's hyper-parameter $\\alpha$ . Here, we study the influence of the hyper-parameter $\\alpha$ in RAW. As shown in Tab. 7, we set $\\alpha$ to 1.0 and get the performance of 47.77 mAP. As $\\alpha$ increases, the performance of our method improves when $\\alpha$ varies from 1 to 50. However, further increasing it to 100.0 slightly hurt the performance. Therefore, we set it to 50 by default. For this observation, we", + "bbox": [ + 75, + 795, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e3afadad26018b928e77d5c64f4ac892e10c7bd5fb993ff1c2372c997a5943bc.jpg", + "table_caption": [ + "Table 7. The effect of hyper-parameter $\\alpha$ in the RAW loss. Experiments are conducted at ${10}\\%$ setting,and the method is equipped with GC loss." + ], + "table_footnote": [], + "table_body": "
SettingαmAP
I147.77
II1047.87
III5048.63
IV10047.95
", + "bbox": [ + 563, + 142, + 831, + 229 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "conjecture that increasing the weight $\\alpha$ will enlarge the influence of orientation information, but also amplify the impact of teacher's inaccurate labels.", + "bbox": [ + 498, + 258, + 890, + 305 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Limitation and Discussion", + "text_level": 1, + "bbox": [ + 500, + 323, + 736, + 338 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although our method achieves satisfactory results on semi-supervised oriented object detection, the usage of aerial objects' characteristics is limited. Apart from orientation and global layout, many other properties of aerial objects should be considered, e.g., scale variations and large aspect ratios. Apart from that, we separately consider orientation and global layout by constructing two different constraints, which can be integrated into one unified module to utilize both information simultaneously. We also find that oriented objects and even complex objects wildly appear in other tasks, such as 3D object detection and text detection, leaving much room for further exploration.", + "bbox": [ + 496, + 349, + 893, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 551, + 619, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented an effective solution for semi-supervised oriented object detection, which is important but neglected. Focusing on oriented objects' characteristics in aerial scenes, we have designed two novel losses, rotation-aware adaptive weighting (RAW) loss and global consistency (GC) loss. The former considers the importance of rotation information for oriented objects, dynamically weighting each pseudo-label-prediction pair by their rotation difference. The latter introduces the global layout concept to SSOD, measuring the global similarity between the teacher and the student in a many-to-many manner. To validate the effectiveness of our method, we have conducted extensive experiments on the DOTA-v1.5 benchmark. Compared with state-of-the-art methods, SOOD achieves consistent performance improvement on partially and fully labeled data.", + "bbox": [ + 496, + 580, + 890, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the National Science Fund for Distinguished Young Scholars of China (Grant No.62225603) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206103).", + "bbox": [ + 496, + 825, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15565", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. In Proc. of Intl. Conf. on Machine Learning, pages 214-223. PMLR, 2017. 3", + "[2] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. 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In Proc. of IEEE Intl. Conf. on Computer Vision and Pattern Recognition, pages 10687-10698, 2020. 2", + "[43] Xingxing Xie, Gong Cheng, Jiabao Wang, Xiwen Yao, and Junwei Han. Oriented r-cnn for object detection. In Porc. of IEEE Intl. Conf. on Computer Vision, pages 3520-3529, 2021. 2", + "[44] Mengde Xu, Zheng Zhang, Han Hu, Jianfeng Wang, Lijuan Wang, Fangyun Wei, Xiang Bai, and Zicheng Liu. End-to-end semi-supervised object detection with soft teacher. In Porc. of IEEE Intl. Conf. on Computer Vision, pages 3060-3069, 2021. 1, 2, 3, 6", + "[45] Qize Yang, Xihan Wei, Biao Wang, Xian-Sheng Hua, and Lei Zhang. Interactive self-training with mean teachers for semi-supervised object detection. In Proc. of IEEE Intl. Conf. on Computer Vision and Pattern Recognition, pages 5941-5950, 2021. 2", + "[46] Xue Yang and Junchi Yan. On the arbitrary-oriented object detection: Classification based approaches revisited. International Journal of Computer Vision, 130(5):1340-1365, 2022. 2", + "[47] Xue Yang, Junchi Yan, Ziming Feng, and Tao He. R3det: Refined single-stage detector with feature refinement for rotating object. In Proc. of the AAAI Conf. on Artificial Intelligence, volume 35, pages 3163-3171, 2021. 2", + "[48] Xue Yang, Xiaojiang Yang, Jirui Yang, Qi Ming, Wentao Wang, Qi Tian, and Junchi Yan. Learning high-precision bounding box for rotated object detection via kullback-Leibler divergence. Proc. of Advances in Neural Information Processing Systems, 2021. 6", + "[49] Fangneng Zhan, Yingchen Yu, Kaiwen Cui, Gongjie Zhang, Shijian Lu, Jianxiong Pan, Changgong Zhang, Feiying Ma, Xuansong Xie, and Chunyan Miao. Unbalanced feature transport for exemplar-based image translation. In Proc. of IEEE Intl. Conf. on Computer Vision and Pattern Recognition, pages 15028-15038, 2021. 3, 5", + "[50] Hongyu Zhou, Zheng Ge, Songtao Liu, Weixin Mao, Zeming Li, Haiyan Yu, and Jian Sun. Dense teacher: Dense pseudolabels for semi-supervised object detection. In Proc. of European Conference on Computer Vision, 2022. 1, 2, 3, 6", + "[51] Barret Zoph, Golnaz Ghiasi, Tsung-Yi Lin, Yin Cui, Hanxiao Liu, Ekin Dogus Cubuk, and Quoc Le. Rethinking pretraining and self-training. Proc. of Advances in Neural Information Processing Systems, 33:3833-3845, 2020. 2" + ], + "bbox": [ + 501, + 92, + 890, + 726 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15567", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/b6c29c1e-51a1-4935-bf5e-ec2e26810dec_model.json b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/b6c29c1e-51a1-4935-bf5e-ec2e26810dec_model.json new file mode 100644 index 0000000000000000000000000000000000000000..6482af63d5d04f5469456d4c7e80bf0b397ab403 --- /dev/null +++ b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/b6c29c1e-51a1-4935-bf5e-ec2e26810dec_model.json @@ -0,0 +1,2398 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.177, + 0.131, + 0.795, + 0.154 + ], + "angle": 0, + "content": "SOOD: Towards Semi-Supervised Oriented Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.18, + 0.88, + 0.201 + ], + "angle": 0, + "content": "Wei Hua\\*, Dingkang Liang\\*, Jingyu Li, Xiaolong Liu, Zhikang Zou, Xiaoqing Ye, Xiang Bai" + }, + { + "type": "text", + "bbox": [ + 0.123, + 0.215, + 0.849, + 0.252 + ], + "angle": 0, + "content": "1Huazhong University of Science and Technology, {whua_hust, dkliang, xbai} @hust.edu.cn \n2Baidu Inc., China" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.668 + ], + "angle": 0, + "content": "Semi-Supervised Object Detection (SSOD), aiming to explore unlabeled data for boosting object detectors, has become an active task in recent years. However, existing SSOD approaches mainly focus on horizontal objects, leaving multi-oriented objects that are common in aerial images unexplored. This paper proposes a novel Semi-supervised Oriented Object Detection model, termed SOOD, built upon the mainstream pseudo-labeling framework. Towards oriented objects in aerial scenes, we design two loss functions to provide better supervision. Focusing on the orientations of objects, the first loss regularizes the consistency between each pseudo-label-prediction pair (includes a prediction and its corresponding pseudo label) with adaptive weights based on their orientation gap. Focusing on the layout of an image, the second loss regularizes the similarity and explicitly builds the many-to-many relation between the sets of pseudo-labels and predictions. Such a global consistency constraint can further boost semi-supervised learning. Our experiments show that when trained with the two proposed losses, SOOD surpasses the state-of-the-art SSOD methods under various settings on the DOTAv1.5 benchmark. The code will be available at https://github.com/HamPerdredes/SOOD." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.699, + 0.21, + 0.715 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.862 + ], + "angle": 0, + "content": "Sufficient labeled data is essential for fully-supervised object detection. However, the data labeling process is time-consuming and expensive. Recently, Semi-Supervised Object Detection (SSOD), where object detectors are learned from labeled data as well as easy-to-obtain unlabeled data, has attracted increasing attention. Existing SSOD methods [16, 24, 44, 50] mainly focus on detecting objects with horizontal bounding boxes in general scenes. Nevertheless, in more complex scenes, such as aerial scenes, objects usu" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.287, + 0.691, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.52, + 0.394, + 0.678, + 0.407 + ], + "angle": 0, + "content": "(a) Arbitrary rotating objects" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.287, + 0.884, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.394, + 0.869, + 0.407 + ], + "angle": 0, + "content": "(b) Small and dense objects" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.43, + 0.895, + 0.487 + ], + "angle": 0, + "content": "Figure 1. Arbitrary rotating (a), small and dense (b) objects are common in aerial scenes, which are often regularly arranged on the image. From a global perspective, this pattern indicates that an aerial can be regarded as a layout." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.561 + ], + "angle": 0, + "content": "ally need to be annotated with oriented bounding boxes. Considering the higher annotation cost of oriented boxes*, semi-supervised oriented object detection is worth studying." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.893, + 0.834 + ], + "angle": 0, + "content": "Compared with general scenes, the main characteristics of objects in aerial scenes (or aerial objects for short) are three-fold: arbitrary orientations, small scales, and agglomeration, as shown in Fig. 1. The mainstream SSOD methods are based on the pseudo-labeling framework [3,35,36] consisting of a teacher model and a student model. The teacher model, an Exponential Moving Average (EMA) of the student model at historical training iterations, generates pseudo-labels for unlabeled images. Thus, the student model can learn from both labeled and unlabeled data. To extend the framework to oriented object detection, we think the following two aspects need to be addressed: 1) As orientation is an essential property of multi-oriented objects, how to use the orientation information when guiding the student with pseudo-labels is critical. 2) As aerial objects are often dense and regularly distributed in an image, we can utilize the layout to facilitate the learning of each pair instead of treating them individually." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.835, + 0.892, + 0.851 + ], + "angle": 0, + "content": "This paper proposes the first Semi-supervised Oriented" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.406, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution. † Corresponding author. \nWork done when Dingkang Liang was an intern at Baidu." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "*Annotation cost of an oriented box is about 36.5% (86$ vs. 63$ per 1k at 2022.11) more than a horizontal box according to https://cloud.google.com/ai-platform/data-labeling/pricing." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15558" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.198 + ], + "angle": 0, + "content": "Object Detection method, termed SOOD. Following [50], SOOD is built upon the dense pseudo-labeling framework, where the pseudo labels are filtered from the raw pixelwise predictions (including box coordinates and confidence scores). The key design is two simple yet effective losses that enforce the instance-level and set-level consistency between the student's and the teacher's predictions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.468, + 0.424 + ], + "angle": 0, + "content": "To be specific, considering that the pseudo-label-prediction pairs are not equally informative, we propose the Rotation-aware Adaptive Weighting (RAW) loss. It utilizes the orientation gap of each pair, which reflects the difficulty of this sample in a way, to weight the corresponding loss dynamically. In this manner, we can softly pick those more useful supervision signals to guide the learning of the student. In addition, considering that the layout of an aerial image can potentially reflect components' overall status (e.g., objects' density and location distribution) and help the detection process, we propose the Global Consistency (GC) loss. It measures the similarity of the pseudo-labels and the predictions from a global perspective, which can alleviate the disturbance of noise in pseudo-labels and implicitly regularizes the mutual relations between different objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.468, + 0.528 + ], + "angle": 0, + "content": "We extensively evaluate SOOD under various settings on DOTA-v1.5, a popular aerial object detection benchmark. Our SOOD achieves consistent performance improvement when using \\(10\\%\\), \\(20\\%\\), \\(30\\%\\), and full of labeled data, compared with the state-of-the-art SSOD methods (using the same oriented object detector). The ablation study also verifies the effectiveness of the two losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.468, + 0.651 + ], + "angle": 0, + "content": "In summary, this paper makes an early exploration of semi-supervised learning for oriented object detection. By analyzing the distinct characteristics of oriented objects from general objects, we propose two novel loss functions to adapt the pseudo-label framework to this task. We hope that this work can provide a good starting point for semi-supervised oriented object detection and serve as a simple yet strong baseline for future research." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.222, + 0.68 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Semi-Supervised Object Detection. In the past few years, semi-supervised learning (SSL) [2, 32] has achieved impressive performance in image classification. These works leverage unlabeled data by using pseudo-label [9,15,17,42], consistency regularization [2,36,41], data augmentation [4, 31] and even adversarial training [26]. Compared to semi-supervised image classification, SSOD requires instance-level predictions and additional bounding boxes regression sub-task, which makes it more challenging. In [28, 51], pseudo-labels are assembled from predictions of data with different augmentations. CSD [14] only utilizes the horizontal flipping augmentation and applies consistency loss to constrain the model, but the weak augmentation limits its performance. STAC [33] trains an object detect-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.394 + ], + "angle": 0, + "content": "tion with labeled data and generates pseudo-labels on unlabeled data with this detector offline. After that, some studies [24,35,44,45] adopt EMA from Mean Teacher [36] to update the teacher model after each training iteration. ISMT [45] obtains more accurate pseudo-labels by fusing current pseudo-labels and history labels. Unbiased Teacher [24] replaces cross-entropy loss with focal loss [22] to solve the class-imbalance issue and filters pseudo-labels by threshold. Soft Teacher [44] uses the classification scores to adaptively weight the loss of each pseudo-box and proposes box jittering to select reliable pseudo-labels. Unbiased Teacher v2 [25] adopts an anchor-free detector and uses uncertainty predictions to select pseudo-labels for the regression branch. Dense Teacher [50] replaces postprocessed instance-level pseudo-labels with dense pixel-level pseudo-labels, which successfully removes the influence of thresholds and post-processing hyper-parameters. However, none of these works are designed for oriented object detection in aerial scenes. This paper aims to fill this blank and offer a starting point for future research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.756 + ], + "angle": 0, + "content": "Orient Object Detection. Different from general object detectors [8, 23, 29, 30], oriented object detectors represent objects with Oriented Bounding Boxes (OBBs). Typical oriented objects include aerial objects and multi-oriented scene texts [12, 19, 20, 34]. In recent years, many oriented object detection methods have been proposed to boost the performance for this area. CSL [46] formulates the angle regression problem as a classification task to address the out-of-bound issue. \\(\\mathrm{R}^3\\mathrm{Det}\\) [47] predicts Horizontal Bounding Boxes (HBBs) at the first stage to improve detection speed and align the feature in the second stage to predict oriented objects. Oriented R-CNN [43] proposes a concise multi-oriented region proposal network and uses the midpoint offsets to represent arbitrarily oriented objects. ReDet [12] proposes a Rotation-equivariant detector to extract rotation-invariant from rotation-equivariant for accurate aerial object detection. Oriented RepPoints [18] proposes a quality assessment module and samples assignment scheme for adaptive points learning, which can obtain non-axis features from neighboring objects and neglect background noises. Different from the above works that focus on the supervised paradigm, this paper makes an early exploration of semi-supervised oriented object detection, which can reduce the annotation cost and boost detectors with unlabeled data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.627, + 0.785 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.794, + 0.891, + 0.84 + ], + "angle": 0, + "content": "In this section, we revisit the mainstream pseudolabeling paradigm in SSOD and Monge-Kantarovich optimal transport theory [27] as preliminary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.738, + 0.864 + ], + "angle": 0, + "content": "3.1. Pseudo-labeling Paradigm" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Pseudo-labeling frameworks [25, 44, 50] inherited designs from the Mean Teacher [36] structure, which consists" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15559" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.363 + ], + "angle": 0, + "content": "of two parts, i.e., a teacher model and a student model. The teacher model is an Exponential Moving Average (EMA) of the student model. They are learned iteratively by the following steps. 1) Generate pseudo-labels for the unlabeled data in a batch. The pseudo-labels are filtered from the teacher's predictions, e.g., the box coordinates and the classification scores. Meanwhile, the student makes predictions for both labeled and unlabeled data in the batch. 2) Compute loss for the student model's predictions. It consists of two parts, the unsupervised loss \\(\\mathcal{L}_u\\) and supervised loss \\(\\mathcal{L}_s\\). They are computed for the unlabeled data with the pseudo-labels and the labeled data with the ground truth (GT) labels, respectively. The overall loss \\(\\mathcal{L}\\) is the sum of them. 3) Update the parameters of the student model according to the overall loss. The teacher model is updated simultaneously in an EMA manner. In this way, based on the mutual learning mechanism, both models evolve as the training goes on." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.546 + ], + "angle": 0, + "content": "Based on the sparsity of pseudo-labels, pseudo-labeling frameworks can be further categorized into sparse pseudolabeling [25, 44] and dense pseudo-labeling [50], termed SPL and DPL, respectively. The SPL selects the teacher's predictions after the post-processing operations, e.g., nonmaximum suppression and score filtering. It obtains sparse labels to supervise the student, e.g., bounding boxes and categories. The DPL directly samples the post-sigmoid log-its predicted by the teacher, which are dense and informative. Compared with SPL, DPL bypasses those lengthy post-processing methods, reserving more details from the teacher than its pseudo-box counterpart." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.555, + 0.262, + 0.572 + ], + "angle": 0, + "content": "3.2. Optimal Transport" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.668 + ], + "angle": 0, + "content": "The Monge-Kantorovich Optimal Transport (OT) [27] aims to solve the problem of simultaneously moving items from one set to another set with minimum cost. It has been widely explored in various computer vision tasks [1, 7, 39, 49]. The mathematical formulations of OT are described as follows in detail." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.47, + 0.715 + ], + "angle": 0, + "content": "Let \\(\\mathbb{X} = \\{x_i|x_i\\in \\mathbb{R}^d\\}_{i}^{N}\\) and \\(\\mathbb{Y} = \\{y_j|y_j\\in \\mathbb{R}^d\\}_{j}^{N}\\) denote two sets of \\(N\\) \\(d\\) -dimensional vectors. Their discrete distributions \\(\\hat{\\mathbb{X}}\\) and \\(\\hat{\\mathbb{Y}}\\) are formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.223, + 0.727, + 0.469, + 0.746 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbb {X}} = \\sum_ {i} ^ {N} \\hat {x} _ {i} \\delta_ {f _ {i}} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.222, + 0.758, + 0.469, + 0.779 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbb {Y}} = \\sum_ {j} ^ {N} \\hat {y} _ {j} \\delta_ {g _ {j}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.47, + 0.845 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{x}}\\) and \\(\\hat{\\mathbf{y}}\\) are the discrete probability vectors, \\(\\delta\\) is the Dirac delta function. Therefore, the OT cost is measured between these two probabilities, \\(\\hat{\\mathbf{x}}\\) and \\(\\hat{\\mathbf{y}}\\). The possible transportation plans from \\(\\hat{\\mathbf{x}}\\) to \\(\\hat{\\mathbf{y}}\\) are formed as:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.856, + 0.469, + 0.874 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {P} = \\left\\{\\boldsymbol {p} \\in \\mathbb {R} ^ {N \\times N} \\mid \\boldsymbol {p} \\mathbf {1} _ {N} = \\hat {\\mathbf {x}}, \\boldsymbol {p} ^ {T} \\mathbf {1} _ {N} = \\hat {\\mathbf {y}} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{1}_N\\) is an \\(N\\)-dimensional column vector whose values" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.771, + 0.106 + ], + "angle": 0, + "content": "are all 1. The OT cost is then defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.12, + 0.892, + 0.142 + ], + "angle": 0, + "content": "\\[\n\\omega_ {o t} (\\hat {\\mathbf {x}}, \\hat {\\mathbf {y}}) = \\min _ {\\boldsymbol {p} \\in \\boldsymbol {P}} \\left\\langle \\mathbf {C}, \\boldsymbol {p} \\right\\rangle , \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.155, + 0.894, + 0.201 + ], + "angle": 0, + "content": "where \\(\\mathbf{C} \\in \\mathbb{R}^{N \\times N}\\) represents the cost matrix between two sets, \\(\\langle \\cdot \\rangle\\) represents inner product. In common, the OT problem is solved in its dual formulation" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.212, + 0.892, + 0.239 + ], + "angle": 0, + "content": "\\[\n\\mathcal {W} _ {o t} (\\hat {\\mathbf {x}}, \\hat {\\mathbf {y}}) = \\max _ {\\boldsymbol {\\lambda}, \\boldsymbol {\\mu} \\in \\mathbb {R} ^ {N}} \\left\\langle \\boldsymbol {\\lambda}, \\hat {\\mathbf {x}} \\right\\rangle + \\left\\langle \\boldsymbol {\\mu}, \\hat {\\mathbf {y}} \\right\\rangle , \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.646, + 0.24, + 0.824, + 0.254 + ], + "angle": 0, + "content": "\\[\ns. t. \\lambda_ {i} + \\mu_ {j} \\leq \\mathbf {C} _ {i, j}, \\forall i, j,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.266, + 0.892, + 0.297 + ], + "angle": 0, + "content": "where \\(\\lambda\\) and \\(\\mu\\) are the solutions of the OT problem, which can be approximated in an iterative manner [5]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.31, + 0.591, + 0.326 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.336, + 0.894, + 0.472 + ], + "angle": 0, + "content": "Fig. 2 illustrates an overview of our proposed SOOD. Towards multi-oriented object detection in aerial images, we build our approach upon the popular dense pseudo-labeling framework [50], along with the Rotation-aware Adaptive Weighting (RAW) loss and the Global Consistency (GC) loss. In this section, we first describe the overall framework in Sec. 4.1. Then, we describe the key design of the proposed losses, RAW and GC, in the following Sec. 4.2 and Sec. 4.3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.482, + 0.724, + 0.496 + ], + "angle": 0, + "content": "4.1. The Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.505, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Currently, the Dense Pseudo-Labeling (DPL) framework achieves the state-of-the-art in SSOD. Hence, we construct a DPL-based end-to-end baseline, including the supervised and unsupervised parts. For the supervised part, the student model is trained with labeled data in a regular manner. For the unsupervised part, we first obtain predicted boxes of the teacher after post-processing. These boxes indicate informative areas in the prediction map, where we randomly sample predictions, forming them as dense pseudo-labels \\(P^t\\). Note that we also select the predictions \\(P^s\\) at the same correspondence positions from the student." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.671, + 0.892, + 0.807 + ], + "angle": 0, + "content": "We use the oriented version of FCOS [37] as the teacher and student models. The basic unsupervised loss consists of three parts: classification loss, regression loss, and centerness loss, corresponding to the output of FCOS. We adopt smooth 11 loss for regression loss, binary cross-entropy loss for classification and center-ness loss. Based on these losses, we first perform adaptive weighting on them through RAW and further measure the global consistency between the teacher and the student via GC." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.854, + 0.833 + ], + "angle": 0, + "content": "4.2. Rotation-aware Adaptive Weighting Loss" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Orientation is one essential property of an oriented object. As shown in Fig. 1, even if objects are dense and small, their orientations remain clear. Previous oriented object detection methods have already employed such a property by" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15560" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.087, + 0.881, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.895, + 0.417 + ], + "angle": 0, + "content": "Figure 2. The pipeline of the proposed SOOD. Each training batch consists of both labeled and unlabeled images. Note that the supervised part is hidden for simplicity. For the unsupervised part, we sample dense pseudo-labels from the teacher's prediction map and select the student's predictions at the same positions, obtaining a series of pseudo-label-prediction pairs. We dynamically weigh each pair's unsupervised loss by their orientation difference. Besides, we regard them as two discrete distributions, measuring their similarity in a many-to-many manner via a global consistency loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.502 + ], + "angle": 0, + "content": "assembling it into loss calculation. However, these works are under the assumption that the angles of the labels are reliable. In this case, it is natural to strictly force the prediction close to the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.471, + 0.729 + ], + "angle": 0, + "content": "Unfortunately, the above assumption does not hold in the semi-supervised setting. In other words, the pseudolabels may be incorrect. Simply forcing the student to be close to the teacher may cause noise accumulation, harming the model's training process. Hence, we propose to utilize the orientation information softly. Intuitively, as orientation is essential but hard to be accurately predicted, the difference in rotation angles between a prediction and a pseudolabel can reflect the difficulty of the sample in a way. In other words, the orientation difference can be used to dynamically adjust the unsupervised loss. Therefore, we construct a rotation-aware modulating factor, similar to focal loss [22]. This factor can dynamically weight the loss of each pseudo-label-prediction pair by considering their orientation difference." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.731, + 0.47, + 0.76 + ], + "angle": 0, + "content": "Specifically, the modulating factor \\(\\omega_{i}^{rot}\\) of the \\(i\\)-th pair is formed as:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.762, + 0.47, + 0.78 + ], + "angle": 0, + "content": "\\[\n\\omega_ {i} ^ {\\text {r o t}} = 1 + \\sigma_ {i}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.788, + 0.47, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {i} = \\alpha \\frac {\\left| r _ {i} ^ {t} - r _ {i} ^ {s} \\right|}{\\pi}, r _ {i} ^ {t}, r _ {i} ^ {s} \\in \\left[ - \\frac {\\pi}{2}, \\frac {\\pi}{2}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\( r_i^t \\) and \\( r_i^s \\) are the \\( i \\)-th pseudo-label's and prediction's rotation angle in radians, respectively. \\( \\alpha \\) is a hyperparameter for adjusting orientation's importance, and we set it to 50 empirically. We add a constant to \\( \\sigma_i \\), maintaining the origin unsupervised loss when pseudo-label and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.489 + ], + "angle": 0, + "content": "prediction have the same orientation. With the rotation-aware modulating factor, the overall rotation-aware adaptive weighting loss is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.501, + 0.892, + 0.521 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {R A W} = \\sum_ {i} ^ {N _ {p}} \\omega_ {i} ^ {\\text {r o t}} \\mathcal {L} _ {u} ^ {i}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.533, + 0.892, + 0.624 + ], + "angle": 0, + "content": "where \\(N_{p}\\) is the number of pseudo-labels and \\(\\mathcal{L}_u^i\\) is the basic unsupervised loss of the \\(i\\)-th pseudo-label-prediction pair. By using the rotation-aware modulating factor, the RAW loss makes better use of the orientation information and provides more informative guidance, potentially benefiting the semi-supervised learning process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.636, + 0.725, + 0.652 + ], + "angle": 0, + "content": "4.3. Global Consistency Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Objects in an aerial image are usually dense and regularly distributed, as depicted in Fig. 1. Similar to texts in a document, the arrangement of the set of objects, i.e., the layout, encodes the mutual relations between them and the global pattern of the image. Ideally, the layout consistency between the student's and the teacher's predictions will be ensured if each pseudo-label-prediction pair is aligned. However, the latter condition is too strict and may hurt performance when there are noises in pseudo-labels. Therefore, it is reasonable to add the consistency between layouts as an additional relaxed optimization objective, encouraging the student to learn robust information from the teacher. In this way, the noise disturbance in pseudo-labels can be alleviated. Besides, the relations between different predicted instances from the student can also be regularized implicitly, which provides an additional guide to the student." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15561" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "We introduce the optimal transport cost [38] to measure the global similarity of layouts between the teacher's and the student's predictions, forming the global consistency loss. To be concrete, we denote the classification scores predicted by the teacher and the student by \\(\\mathbf{s}^t\\in \\mathbb{R}^{N_p\\times K}\\) and \\(\\mathbf{s}^s\\in \\mathbb{R}^{N_p\\times K}\\) respectively, where \\(K\\) is the number of classes. Then, their global distributions, \\(\\mathbf{d}^t\\in \\mathbb{R}^{N_p}\\) and \\(\\mathbf{d}^s\\in \\mathbb{R}^{N_p}\\) can be formulated by" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.223, + 0.47, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {i} ^ {t} = e ^ {\\mathbf {s} _ {i, c (i)} ^ {t}}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.228, + 0.252, + 0.469, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {i} ^ {s} = e ^ {\\mathbf {S} _ {i, c (i)} ^ {s}}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.276, + 0.469, + 0.314 + ], + "angle": 0, + "content": "where \\( c(i) = \\underset{j=1,\\ldots,K}{\\arg \\max} \\mathbf{s}_{i,j}^{t} \\) is the index of the class with the largest score for the \\( i \\)-th pseudo-label." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.315, + 0.469, + 0.345 + ], + "angle": 0, + "content": "The global consistency loss is defined as the OT problem's dual formulation" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.352, + 0.469, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {G C} \\left(\\mathbf {d} ^ {t}, \\mathbf {d} ^ {s}\\right) = \\left\\langle \\boldsymbol {\\lambda} ^ {*}, \\frac {\\mathbf {d} ^ {t}}{\\| \\mathbf {d} ^ {t} \\| _ {1}} \\right\\rangle + \\left\\langle \\boldsymbol {\\mu} ^ {*}, \\frac {\\mathbf {d} ^ {s}}{\\| \\mathbf {d} ^ {s} \\| _ {1}} \\right\\rangle , \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.469, + 0.487 + ], + "angle": 0, + "content": "where we normalize two distributions to form discrete probabilities, by dividing them to their sum. To construct the cost map for solving the OT problem, we consider both the spatial distance and the score difference of each possible matching pair. Specifically, for each prediction, we measure its matching cost with every pseudo-label as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.495, + 0.469, + 0.515 + ], + "angle": 0, + "content": "\\[\nC _ {i, j} = C _ {i, j} ^ {\\text {d i s t}} + C _ {i, j} ^ {\\text {s c o r e}}, \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.524, + 0.469, + 0.561 + ], + "angle": 0, + "content": "\\[\nC _ {i, j} ^ {\\text {d i s t}} = \\frac {\\left\\| \\mathbf {z} _ {i} ^ {t} - \\mathbf {z} _ {j} ^ {s} \\right\\| _ {2} ^ {2}}{\\max _ {1 < = a , b < = N _ {p}} \\left\\| \\mathbf {z} _ {a} ^ {t} - \\mathbf {z} _ {b} ^ {s} \\right\\| _ {2} ^ {2}}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.566, + 0.469, + 0.605 + ], + "angle": 0, + "content": "\\[\nC _ {i, j} ^ {\\text {s c o r e}} = \\frac {\\left\\| \\mathbf {s} _ {i , c (i)} ^ {t} - \\mathbf {s} _ {j , c (j)} ^ {s} \\right\\| _ {1}}{\\max _ {1 < = a , b < = N _ {p}} \\left\\| \\mathbf {s} _ {a , c (a)} ^ {t} - \\mathbf {s} _ {b , c (b)} ^ {s} \\right\\| _ {1}}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.611, + 0.469, + 0.641 + ], + "angle": 0, + "content": "where \\(\\mathbf{z}_i^t\\) and \\(\\mathbf{z}_j^s\\) are 2D coordinates of the \\(i\\)-th sample in the teacher and the \\(j_{th}\\) sample in the student." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.642, + 0.469, + 0.698 + ], + "angle": 0, + "content": "We solve the OT problem by a fast Sinkhorn distances algorithm [5], obtaining the approximate solution \\(\\lambda^{*}\\) and \\(\\mu^{*}\\). Based on the defined loss, its gradient with respect to \\(\\mathbf{d}^s\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.698, + 0.469, + 0.731 + ], + "angle": 0, + "content": "\\[\n\\frac {\\partial \\mathcal {L} _ {G C} \\left(\\mathbf {d} ^ {t} , \\mathbf {d} ^ {s}\\right)}{\\partial \\mathbf {d} ^ {s}} = \\frac {\\boldsymbol {\\mu} ^ {*}}{\\| \\mathbf {d} ^ {s} \\| _ {1}} - \\frac {\\langle \\boldsymbol {\\mu} ^ {*} , \\mathbf {d} ^ {s} \\rangle}{\\| \\mathbf {d} ^ {s} \\| _ {1} ^ {2}}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.47, + 0.9 + ], + "angle": 0, + "content": "The gradients can be back-propagated to update the model, enforcing the layout consistency in the framework. Although OT-based loss has been explored before [6,39,49], our goal of using OT is different. Specifically, they focus on utilizing OT to improve the model's generalizability [6, 39] or mitigate the matching constraint [49]. However, our GC aims to model the many-to-many relationship between the teacher and the student, which is complementary to the RAW. In addition, we adopt such a set-to-set matching to alleviate the error in pseudo-label assignment, providing a more loose but stable constraint." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "SOOD is trained with the proposed unsupervised losses, RAW and GC, for unlabeled data as well as the supervised loss for labeled data. The overall loss \\(\\mathcal{L}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.149, + 0.892, + 0.183 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\underbrace {\\mathcal {L} _ {R A W} + \\mathcal {L} _ {G C}} _ {\\mathcal {L} _ {u}} + \\mathcal {L} _ {s}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.194, + 0.892, + 0.224 + ], + "angle": 0, + "content": "Note that the supervised loss is the same as defined in FCOS, our designs only modify the unsupervised part." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.238, + 0.634, + 0.254 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.263, + 0.892, + 0.353 + ], + "angle": 0, + "content": "We conduct experiments on DOTA-v1.5, which is proposed at DOAI-2019†. It contains 2806 large aerial images and 402,089 annotated oriented objects. It includes three subsets: DOTA-v1.5-train, DOTA-v1.5-val and DOTA-v1.5-test, containing 1411, 458, and 937 images, respectively. The annotations of DOTA-v1.5-test is not released." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.892, + 0.489 + ], + "angle": 0, + "content": "There are 16 categories in this dataset: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), Helicopter (HC) and Container crane (CC). Compared with DOTA-v1.0 [40], a previous version, DOTA-v1.5 contains more small instances (less than 10 pixels), which makes it more challenging." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.549 + ], + "angle": 0, + "content": "Following conventions in SSOD, we consider two protocols, Partially Labeled Data and Fully Labeled Data, to validate the performance of a method on limited and abundant labeled data, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Partially Labeled Data. We randomly sample \\(10\\%\\), \\(20\\%\\), and \\(30\\%\\) images from DOTA-v1.5-train as labeled data and set the remaining images as unlabeled data. Following DOTA-v1.5-train's data distribution, we provide one fold for each data proportion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.654 + ], + "angle": 0, + "content": "Fully Labeled Data. We set DOTA-v1.5-train as labeled data and DOTA-v1.5-test as unlabeled data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.701 + ], + "angle": 0, + "content": "For all experiments, we perform evaluation on DOTAv1.5-val and report the performance with the standard mean average precision (mAP) as the evaluation metrics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.717, + 0.726 + ], + "angle": 0, + "content": "5.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.855 + ], + "angle": 0, + "content": "Without loss of generality, we take FCOS [37] as the representative anchor-free detector, and adopt ResNet-50 [13] with FPN [21] as the backbone for all our experiments. Following the previous works [11, 12, 40], we crop the original images into \\(1024 \\times 1024\\) patches with a stride of 824, that is, the pixel overlap between two adjacent patches is 200. We utilize asymmetric data augmentation for unlabeled data. Specifically, we use strong augmentation for" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.9 + ], + "angle": 0, + "content": "†The 1st Workshop on Detecting Objects in Aerial Images in conjunction with IEEE CVPR 2019 https://captain-whu.github.io/DOAI2019/dataset.html" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15562" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 1. Experimental results on DOTA-v1.5 under the Partially Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS, respectively. Experiments are conducted on 10%, 20% and 30% labeled data settings." + }, + { + "type": "table", + "bbox": [ + 0.107, + 0.129, + 0.868, + 0.257 + ], + "angle": 0, + "content": "
SettingMethodPublication10%20%30%
SupervisedFaster R-CNN* [30]NeurIPS 201643.4351.3253.14
FCOS† [37]ICCV 201942.7850.1154.79
Semi-supervisedUnbiased Teacher* [24]ICLR 202144.5152.8053.33
Soft Teacher* [44]ICCV 202148.4654.8957.83
Dense Teacher† [50]ECCV 202246.9053.9357.86
SOOD† (ours)-48.6355.5859.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.278, + 0.472, + 0.335 + ], + "angle": 0, + "content": "Table 2. Experimental results on DOTA-v1.5 under the Fully Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS respectively. Numbers in font of the arrow indicate the supervised baseline." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.345, + 0.455, + 0.451 + ], + "angle": 0, + "content": "
MethodPublicationmAP
Unbiased Teacher* [24]ICLR 202166.12 → 1.27 → 64.85
Soft Teacher* [44]ICCV 202166.12 → +0.28 → 66.40
Dense Teacher† [50]ECCV 202265.46 → +0.92 → 66.38
SOOD† (ours)-65.46 → +2.24 → 67.70
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.669 + ], + "angle": 0, + "content": "the student model and weak augmentation for the teacher model. Random flipping is used for weak augmentation, while strong augmentation contains random flipping, color jittering, random grayscale, and random Gaussian blur. All models are trained for 180k iterations on 2 RTX3090 GPUs. With the SGD optimizer, the initial learning rate of 0.0025 is divided by 10 at 120k and 160k. The momentum and the weight decay are set to 0.9 and 0.0001, respectively. Each GPU takes 3 images as input, where the proportion between unlabeled and labeled data is set to 1:2. The pseudo-label sampling ratio is set as 0.25 by default. Following previous SSOD works [24, 50], we use the \"burn-in\" strategy to initialize the teacher model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.678, + 0.216, + 0.693 + ], + "angle": 0, + "content": "5.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.469, + 0.763 + ], + "angle": 0, + "content": "In this section, we compare our method with the state-of-the-art SSOD methods [3, 24, 44] on DOTA-v1.5. For a fair comparison, we re-implement these methods on oriented object detectors with the same augmentation setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Partially Labeled Data. We evaluate our method under different labeled data proportions, and the results are shown in Tab. 1. Our SOOD achieves state-of-the-art performance under all proportions. Specifically, it obtains 48.63, 55.58, and \\(59.23\\mathrm{mAP}\\) on \\(10\\%\\), \\(20\\%\\), and \\(30\\%\\) proportions, respectively, surpassing our supervised baseline by \\(+5.85\\), \\(+5.47\\), and \\(+4.44\\mathrm{mAP}\\). We also surpass the state-of-the-art anchor-free method Dense Teacher [50] by \\(+1.73\\), \\(+1.65\\), and \\(+1.37\\) under various proportions. We provide two anchor-" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.278, + 0.892, + 0.321 + ], + "angle": 0, + "content": "Table 3. The effectiveness of SOOD on other methods under Fully Labeled Data setting. * means based on RetinaNet [22]. SOOD is able to generalize to other detectors and boost their performance." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.331, + 0.88, + 0.43 + ], + "angle": 0, + "content": "
DetectorPublicationMethodmAP
CFA [10]CVPR 2021Supervised Ours65.75\n67.07
KLD* [48]NeurIPS 2021Supervised Ours62.21\n64.62
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.547 + ], + "angle": 0, + "content": "based methods for comparison, Unbiased Teacher [24] and Soft Teacher [44]. On \\(10\\%\\) and \\(20\\%\\) proportions, our SOOD achieves higher performance than Soft Teacher, even though our baseline is weaker than Soft Teacher's. Under \\(30\\%\\) data proportion, our SOOD surpasses Soft Teacher and Unbiased Teacher by at least \\(1.40\\mathrm{mAP}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.64 + ], + "angle": 0, + "content": "The qualitative results of our method compared with supervised baseline and Dense Teacher [50] are shown in Fig. 3. With the help of our RAW and GC, SOOD is able to exploit more potential semantic information from the unlabeled data, helping reduce false predictions and improve the detection quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Fully Labeled Data. We also compare our SOOD with the other SSOD methods [24, 44, 50] on fully labeled data setting. Since the reported methods are based on different detectors, we report the results of the compared methods and their baseline in Tab. 2. Our SOOD surpasses previous methods by at least 1.30 points. Compared to our baseline, we obtain \\(+2.24\\mathrm{mAP}\\) improvement, which further demonstrates our method's ability to learn from unlabeled data. We notice that the performance of Unbiased Teacher [24] drops after adding unlabeled data. The reason might be that Unbiased Teacher does not apply unsupervised losses for bounding box regression, which is important for oriented object detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Generalization on other detectors. To further validate the effectiveness of our method, we evaluate our method on other oriented object detectors, CFA [10] and KLD [48], under the Fully Labeled Data setting. As shown in Tab. 3," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15563" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.16, + 0.089, + 0.321, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.089, + 0.483, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.089, + 0.647, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.089, + 0.811, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.201, + 0.321, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.201, + 0.483, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.201, + 0.647, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.201, + 0.811, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.313, + 0.321, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.313, + 0.483, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.313, + 0.647, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.313, + 0.811, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.424, + 0.321, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.424, + 0.483, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.424, + 0.647, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.424, + 0.811, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.547, + 0.895, + 0.591 + ], + "angle": 0, + "content": "Figure 3. Some visualization examples from the DOTA-v1.5 dataset. From left to right, each column shows ground truth, results of the supervised baseline (rotated-FCOS [37]), Dense Teacher [3], and our SOOD. The green rectangles indicate predictions. The red dashed circle, solid red circle, and red arrow represent false negative, false positive, and inaccurate orientation prediction, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.473, + 0.692 + ], + "angle": 0, + "content": "although CFA is a strong detector, our method still results in an improvement of \\(+1.32\\mathrm{mAP}\\) and reaches 67.07 mAP. On the KLD detector, our method brings an improvement of \\(+2.41\\mathrm{mAP}\\). The above results validate the generalization ability of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.704, + 0.231, + 0.72 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.773 + ], + "angle": 0, + "content": "In this section, we conduct extensive studies to validate our key designs. Unless specified, all the ablation experiments are performed using \\(10\\%\\) of labeled data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The effect of each component. We study the effects of the proposed two losses, Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Note that our SOOD degrades to the vanilla dense pseudolabeling framework without these two losses. As shown in Tab. 4, both losses are proved effective and complementary under all three settings: RAW and GC can each bring performance gain, and the baseline is further improved when" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.656 + ], + "angle": 0, + "content": "Table 4. The effects of Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Experiments are conducted on \\(10\\%\\), \\(20\\%\\) and \\(30\\%\\) labeled data settings." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.659, + 0.88, + 0.768 + ], + "angle": 0, + "content": "
SettingRAWGCmAP
10%20%30%
I--47.2454.0757.74
II✓-47.8255.2158.93
III-✓47.7154.7258.70
IV✓✓48.6355.5859.23
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.895, + 0.877 + ], + "angle": 0, + "content": "equipped with two losses. It indicates that the local constraint built by RAW and the global constraint built by GC can benefit the semi-supervised learning process, boosting the model by constructing one-to-one and many-to-many relationships between the teacher and the student." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The influence of sampling ratio. In this part, we discuss" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15564" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.472, + 0.132 + ], + "angle": 0, + "content": "Table 5. The effect of the sampling ratio for instance-level dense pseudo-labeling. Experiments are conducted at \\(10\\%\\) setting, and the method is equipped with both RAW and GC losses." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.142, + 0.437, + 0.229 + ], + "angle": 0, + "content": "
SettingSample RatiomAP
I0.12548.27
II0.2548.63
III0.547.91
IV1.047.69
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.243, + 0.472, + 0.3 + ], + "angle": 0, + "content": "Table 6. The effects of different compositions in the cost map of GC. Experiments are conducted at \\(10\\%\\) setting, and the method is equipped with RAW loss. The results indicate that both distance and score are essential factors of the cost map." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.309, + 0.469, + 0.396 + ], + "angle": 0, + "content": "
SettingDistanceScoremAP
I--47.82
II-✓48.10
III✓-47.94
IV✓✓48.63
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.47, + 0.573 + ], + "angle": 0, + "content": "the influence of the ratios in sampling pseudo-labels. The results with different sampling ratios are shown in Tab. 5. The best performance, \\(48.36\\mathrm{mAP}\\), is achieved when the sample ratio is set to 0.25. Setting it to other values degrades the performance. We hypothesize that this value ensures a good balance between noises (e.g., false positives) and valid predictions (e.g., true positives). Increasing it will introduce more noise that harms the training process, while decreasing it leads to information loss and failure in learning the representation of objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.79 + ], + "angle": 0, + "content": "The effect of different compositions in cost map of GC. Here, we study the effects of the spatial distance and the score difference when constructing the cost map of optimal transport in GC loss. The results of different settings are shown in Tab. 6. We get at most \\(+0.28\\) mAP improvement when using only one of them, indicating that the information from only one side is inadequate for learning the global prior. When considering both the score difference and spatial distance, the performance gain brought by GC is further improved to \\(+0.81\\) mAP. It indicates that the information from score difference and spatial distance are complementary. With their help, RAW can effectively model the many-to-many relationship between the teacher and the student, providing an informative guide to the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The effect of RAW's hyper-parameter \\(\\alpha\\). Here, we study the influence of the hyper-parameter \\(\\alpha\\) in RAW. As shown in Tab. 7, we set \\(\\alpha\\) to 1.0 and get the performance of 47.77 mAP. As \\(\\alpha\\) increases, the performance of our method improves when \\(\\alpha\\) varies from 1 to 50. However, further increasing it to 100.0 slightly hurt the performance. Therefore, we set it to 50 by default. For this observation, we" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.132 + ], + "angle": 0, + "content": "Table 7. The effect of hyper-parameter \\( \\alpha \\) in the RAW loss. Experiments are conducted at \\( {10}\\% \\) setting,and the method is equipped with GC loss." + }, + { + "type": "table", + "bbox": [ + 0.564, + 0.143, + 0.832, + 0.23 + ], + "angle": 0, + "content": "
SettingαmAP
I147.77
II1047.87
III5048.63
IV10047.95
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.26, + 0.892, + 0.306 + ], + "angle": 0, + "content": "conjecture that increasing the weight \\(\\alpha\\) will enlarge the influence of orientation information, but also amplify the impact of teacher's inaccurate labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.324, + 0.738, + 0.339 + ], + "angle": 0, + "content": "5.4. Limitation and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.895, + 0.532 + ], + "angle": 0, + "content": "Although our method achieves satisfactory results on semi-supervised oriented object detection, the usage of aerial objects' characteristics is limited. Apart from orientation and global layout, many other properties of aerial objects should be considered, e.g., scale variations and large aspect ratios. Apart from that, we separately consider orientation and global layout by constructing two different constraints, which can be integrated into one unified module to utilize both information simultaneously. We also find that oriented objects and even complex objects wildly appear in other tasks, such as 3D object detection and text detection, leaving much room for further exploration." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.553, + 0.62, + 0.569 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.822 + ], + "angle": 0, + "content": "In this paper, we have presented an effective solution for semi-supervised oriented object detection, which is important but neglected. Focusing on oriented objects' characteristics in aerial scenes, we have designed two novel losses, rotation-aware adaptive weighting (RAW) loss and global consistency (GC) loss. The former considers the importance of rotation information for oriented objects, dynamically weighting each pseudo-label-prediction pair by their rotation difference. The latter introduces the global layout concept to SSOD, measuring the global similarity between the teacher and the student in a many-to-many manner. To validate the effectiveness of our method, we have conducted extensive experiments on the DOTA-v1.5 benchmark. Compared with state-of-the-art methods, SOOD achieves consistent performance improvement on partially and fully labeled data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the National Science Fund for Distinguished Young Scholars of China (Grant No.62225603) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206103)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15565" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.158 + ], + "angle": 0, + "content": "[1] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. In Proc. of Intl. Conf. on Machine Learning, pages 214-223. PMLR, 2017. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.471, + 0.226 + ], + "angle": 0, + "content": "[2] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. 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However, existing SSOD approaches mainly focus on horizontal objects, leaving multi-oriented objects that are common in aerial images unexplored. This paper proposes a novel Semi-supervised Oriented Object Detection model, termed SOOD, built upon the mainstream pseudo-labeling framework. Towards oriented objects in aerial scenes, we design two loss functions to provide better supervision. Focusing on the orientations of objects, the first loss regularizes the consistency between each pseudo-label-prediction pair (includes a prediction and its corresponding pseudo label) with adaptive weights based on their orientation gap. Focusing on the layout of an image, the second loss regularizes the similarity and explicitly builds the many-to-many relation between the sets of pseudo-labels and predictions. Such a global consistency constraint can further boost semi-supervised learning. Our experiments show that when trained with the two proposed losses, SOOD surpasses the state-of-the-art SSOD methods under various settings on the DOTAv1.5 benchmark. The code will be available at https://github.com/HamPerdredes/SOOD. + +# 1. Introduction + +Sufficient labeled data is essential for fully-supervised object detection. However, the data labeling process is time-consuming and expensive. Recently, Semi-Supervised Object Detection (SSOD), where object detectors are learned from labeled data as well as easy-to-obtain unlabeled data, has attracted increasing attention. Existing SSOD methods [16, 24, 44, 50] mainly focus on detecting objects with horizontal bounding boxes in general scenes. Nevertheless, in more complex scenes, such as aerial scenes, objects usu + +![](images/826a5548f5459ca64255c3a713d1079ccce3a2b7e04c2361d46fc5f201049fdc.jpg) +(a) Arbitrary rotating objects + +![](images/09aa9cb227da62c57eef758c8ffe9dc814e1fbbe6afa1970fb52a16c5a54c16b.jpg) +(b) Small and dense objects +Figure 1. Arbitrary rotating (a), small and dense (b) objects are common in aerial scenes, which are often regularly arranged on the image. From a global perspective, this pattern indicates that an aerial can be regarded as a layout. + +ally need to be annotated with oriented bounding boxes. Considering the higher annotation cost of oriented boxes*, semi-supervised oriented object detection is worth studying. + +Compared with general scenes, the main characteristics of objects in aerial scenes (or aerial objects for short) are three-fold: arbitrary orientations, small scales, and agglomeration, as shown in Fig. 1. The mainstream SSOD methods are based on the pseudo-labeling framework [3,35,36] consisting of a teacher model and a student model. The teacher model, an Exponential Moving Average (EMA) of the student model at historical training iterations, generates pseudo-labels for unlabeled images. Thus, the student model can learn from both labeled and unlabeled data. To extend the framework to oriented object detection, we think the following two aspects need to be addressed: 1) As orientation is an essential property of multi-oriented objects, how to use the orientation information when guiding the student with pseudo-labels is critical. 2) As aerial objects are often dense and regularly distributed in an image, we can utilize the layout to facilitate the learning of each pair instead of treating them individually. + +This paper proposes the first Semi-supervised Oriented + +Object Detection method, termed SOOD. Following [50], SOOD is built upon the dense pseudo-labeling framework, where the pseudo labels are filtered from the raw pixelwise predictions (including box coordinates and confidence scores). The key design is two simple yet effective losses that enforce the instance-level and set-level consistency between the student's and the teacher's predictions. + +To be specific, considering that the pseudo-label-prediction pairs are not equally informative, we propose the Rotation-aware Adaptive Weighting (RAW) loss. It utilizes the orientation gap of each pair, which reflects the difficulty of this sample in a way, to weight the corresponding loss dynamically. In this manner, we can softly pick those more useful supervision signals to guide the learning of the student. In addition, considering that the layout of an aerial image can potentially reflect components' overall status (e.g., objects' density and location distribution) and help the detection process, we propose the Global Consistency (GC) loss. It measures the similarity of the pseudo-labels and the predictions from a global perspective, which can alleviate the disturbance of noise in pseudo-labels and implicitly regularizes the mutual relations between different objects. + +We extensively evaluate SOOD under various settings on DOTA-v1.5, a popular aerial object detection benchmark. Our SOOD achieves consistent performance improvement when using $10\%$ , $20\%$ , $30\%$ , and full of labeled data, compared with the state-of-the-art SSOD methods (using the same oriented object detector). The ablation study also verifies the effectiveness of the two losses. + +In summary, this paper makes an early exploration of semi-supervised learning for oriented object detection. By analyzing the distinct characteristics of oriented objects from general objects, we propose two novel loss functions to adapt the pseudo-label framework to this task. We hope that this work can provide a good starting point for semi-supervised oriented object detection and serve as a simple yet strong baseline for future research. + +# 2. Related works + +Semi-Supervised Object Detection. In the past few years, semi-supervised learning (SSL) [2, 32] has achieved impressive performance in image classification. These works leverage unlabeled data by using pseudo-label [9,15,17,42], consistency regularization [2,36,41], data augmentation [4, 31] and even adversarial training [26]. Compared to semi-supervised image classification, SSOD requires instance-level predictions and additional bounding boxes regression sub-task, which makes it more challenging. In [28, 51], pseudo-labels are assembled from predictions of data with different augmentations. CSD [14] only utilizes the horizontal flipping augmentation and applies consistency loss to constrain the model, but the weak augmentation limits its performance. STAC [33] trains an object detect- + +tion with labeled data and generates pseudo-labels on unlabeled data with this detector offline. After that, some studies [24,35,44,45] adopt EMA from Mean Teacher [36] to update the teacher model after each training iteration. ISMT [45] obtains more accurate pseudo-labels by fusing current pseudo-labels and history labels. Unbiased Teacher [24] replaces cross-entropy loss with focal loss [22] to solve the class-imbalance issue and filters pseudo-labels by threshold. Soft Teacher [44] uses the classification scores to adaptively weight the loss of each pseudo-box and proposes box jittering to select reliable pseudo-labels. Unbiased Teacher v2 [25] adopts an anchor-free detector and uses uncertainty predictions to select pseudo-labels for the regression branch. Dense Teacher [50] replaces postprocessed instance-level pseudo-labels with dense pixel-level pseudo-labels, which successfully removes the influence of thresholds and post-processing hyper-parameters. However, none of these works are designed for oriented object detection in aerial scenes. This paper aims to fill this blank and offer a starting point for future research. + +Orient Object Detection. Different from general object detectors [8, 23, 29, 30], oriented object detectors represent objects with Oriented Bounding Boxes (OBBs). Typical oriented objects include aerial objects and multi-oriented scene texts [12, 19, 20, 34]. In recent years, many oriented object detection methods have been proposed to boost the performance for this area. CSL [46] formulates the angle regression problem as a classification task to address the out-of-bound issue. $\mathrm{R}^3\mathrm{Det}$ [47] predicts Horizontal Bounding Boxes (HBBs) at the first stage to improve detection speed and align the feature in the second stage to predict oriented objects. Oriented R-CNN [43] proposes a concise multi-oriented region proposal network and uses the midpoint offsets to represent arbitrarily oriented objects. ReDet [12] proposes a Rotation-equivariant detector to extract rotation-invariant from rotation-equivariant for accurate aerial object detection. Oriented RepPoints [18] proposes a quality assessment module and samples assignment scheme for adaptive points learning, which can obtain non-axis features from neighboring objects and neglect background noises. Different from the above works that focus on the supervised paradigm, this paper makes an early exploration of semi-supervised oriented object detection, which can reduce the annotation cost and boost detectors with unlabeled data. + +# 3. Preliminary + +In this section, we revisit the mainstream pseudolabeling paradigm in SSOD and Monge-Kantarovich optimal transport theory [27] as preliminary. + +# 3.1. Pseudo-labeling Paradigm + +Pseudo-labeling frameworks [25, 44, 50] inherited designs from the Mean Teacher [36] structure, which consists + +of two parts, i.e., a teacher model and a student model. The teacher model is an Exponential Moving Average (EMA) of the student model. They are learned iteratively by the following steps. 1) Generate pseudo-labels for the unlabeled data in a batch. The pseudo-labels are filtered from the teacher's predictions, e.g., the box coordinates and the classification scores. Meanwhile, the student makes predictions for both labeled and unlabeled data in the batch. 2) Compute loss for the student model's predictions. It consists of two parts, the unsupervised loss $\mathcal{L}_u$ and supervised loss $\mathcal{L}_s$ . They are computed for the unlabeled data with the pseudo-labels and the labeled data with the ground truth (GT) labels, respectively. The overall loss $\mathcal{L}$ is the sum of them. 3) Update the parameters of the student model according to the overall loss. The teacher model is updated simultaneously in an EMA manner. In this way, based on the mutual learning mechanism, both models evolve as the training goes on. + +Based on the sparsity of pseudo-labels, pseudo-labeling frameworks can be further categorized into sparse pseudolabeling [25, 44] and dense pseudo-labeling [50], termed SPL and DPL, respectively. The SPL selects the teacher's predictions after the post-processing operations, e.g., nonmaximum suppression and score filtering. It obtains sparse labels to supervise the student, e.g., bounding boxes and categories. The DPL directly samples the post-sigmoid log-its predicted by the teacher, which are dense and informative. Compared with SPL, DPL bypasses those lengthy post-processing methods, reserving more details from the teacher than its pseudo-box counterpart. + +# 3.2. Optimal Transport + +The Monge-Kantorovich Optimal Transport (OT) [27] aims to solve the problem of simultaneously moving items from one set to another set with minimum cost. It has been widely explored in various computer vision tasks [1, 7, 39, 49]. The mathematical formulations of OT are described as follows in detail. + +Let $\mathbb{X} = \{x_i|x_i\in \mathbb{R}^d\}_{i}^{N}$ and $\mathbb{Y} = \{y_j|y_j\in \mathbb{R}^d\}_{j}^{N}$ denote two sets of $N$ $d$ -dimensional vectors. Their discrete distributions $\hat{\mathbb{X}}$ and $\hat{\mathbb{Y}}$ are formulated as: + +$$ +\hat {\mathbb {X}} = \sum_ {i} ^ {N} \hat {x} _ {i} \delta_ {f _ {i}} \tag {1} +$$ + +$$ +\hat {\mathbb {Y}} = \sum_ {j} ^ {N} \hat {y} _ {j} \delta_ {g _ {j}}, \tag {2} +$$ + +where $\hat{\mathbf{x}}$ and $\hat{\mathbf{y}}$ are the discrete probability vectors, $\delta$ is the Dirac delta function. Therefore, the OT cost is measured between these two probabilities, $\hat{\mathbf{x}}$ and $\hat{\mathbf{y}}$ . The possible transportation plans from $\hat{\mathbf{x}}$ to $\hat{\mathbf{y}}$ are formed as: + +$$ +\boldsymbol {P} = \left\{\boldsymbol {p} \in \mathbb {R} ^ {N \times N} \mid \boldsymbol {p} \mathbf {1} _ {N} = \hat {\mathbf {x}}, \boldsymbol {p} ^ {T} \mathbf {1} _ {N} = \hat {\mathbf {y}} \right\}, \tag {3} +$$ + +where $\mathbf{1}_N$ is an $N$ -dimensional column vector whose values + +are all 1. The OT cost is then defined as: + +$$ +\omega_ {o t} (\hat {\mathbf {x}}, \hat {\mathbf {y}}) = \min _ {\boldsymbol {p} \in \boldsymbol {P}} \left\langle \mathbf {C}, \boldsymbol {p} \right\rangle , \tag {4} +$$ + +where $\mathbf{C} \in \mathbb{R}^{N \times N}$ represents the cost matrix between two sets, $\langle \cdot \rangle$ represents inner product. In common, the OT problem is solved in its dual formulation + +$$ +\mathcal {W} _ {o t} (\hat {\mathbf {x}}, \hat {\mathbf {y}}) = \max _ {\boldsymbol {\lambda}, \boldsymbol {\mu} \in \mathbb {R} ^ {N}} \left\langle \boldsymbol {\lambda}, \hat {\mathbf {x}} \right\rangle + \left\langle \boldsymbol {\mu}, \hat {\mathbf {y}} \right\rangle , \tag {5} +$$ + +$$ +s. t. \lambda_ {i} + \mu_ {j} \leq \mathbf {C} _ {i, j}, \forall i, j, +$$ + +where $\lambda$ and $\mu$ are the solutions of the OT problem, which can be approximated in an iterative manner [5]. + +# 4. Method + +Fig. 2 illustrates an overview of our proposed SOOD. Towards multi-oriented object detection in aerial images, we build our approach upon the popular dense pseudo-labeling framework [50], along with the Rotation-aware Adaptive Weighting (RAW) loss and the Global Consistency (GC) loss. In this section, we first describe the overall framework in Sec. 4.1. Then, we describe the key design of the proposed losses, RAW and GC, in the following Sec. 4.2 and Sec. 4.3, respectively. + +# 4.1. The Overall Framework + +Currently, the Dense Pseudo-Labeling (DPL) framework achieves the state-of-the-art in SSOD. Hence, we construct a DPL-based end-to-end baseline, including the supervised and unsupervised parts. For the supervised part, the student model is trained with labeled data in a regular manner. For the unsupervised part, we first obtain predicted boxes of the teacher after post-processing. These boxes indicate informative areas in the prediction map, where we randomly sample predictions, forming them as dense pseudo-labels $P^t$ . Note that we also select the predictions $P^s$ at the same correspondence positions from the student. + +We use the oriented version of FCOS [37] as the teacher and student models. The basic unsupervised loss consists of three parts: classification loss, regression loss, and centerness loss, corresponding to the output of FCOS. We adopt smooth 11 loss for regression loss, binary cross-entropy loss for classification and center-ness loss. Based on these losses, we first perform adaptive weighting on them through RAW and further measure the global consistency between the teacher and the student via GC. + +# 4.2. Rotation-aware Adaptive Weighting Loss + +Orientation is one essential property of an oriented object. As shown in Fig. 1, even if objects are dense and small, their orientations remain clear. Previous oriented object detection methods have already employed such a property by + +![](images/0f512317b9213522b0422f60b4681461d27690687049b8a033ba304091c8f64a.jpg) +Figure 2. The pipeline of the proposed SOOD. Each training batch consists of both labeled and unlabeled images. Note that the supervised part is hidden for simplicity. For the unsupervised part, we sample dense pseudo-labels from the teacher's prediction map and select the student's predictions at the same positions, obtaining a series of pseudo-label-prediction pairs. We dynamically weigh each pair's unsupervised loss by their orientation difference. Besides, we regard them as two discrete distributions, measuring their similarity in a many-to-many manner via a global consistency loss. + +assembling it into loss calculation. However, these works are under the assumption that the angles of the labels are reliable. In this case, it is natural to strictly force the prediction close to the ground truth. + +Unfortunately, the above assumption does not hold in the semi-supervised setting. In other words, the pseudolabels may be incorrect. Simply forcing the student to be close to the teacher may cause noise accumulation, harming the model's training process. Hence, we propose to utilize the orientation information softly. Intuitively, as orientation is essential but hard to be accurately predicted, the difference in rotation angles between a prediction and a pseudolabel can reflect the difficulty of the sample in a way. In other words, the orientation difference can be used to dynamically adjust the unsupervised loss. Therefore, we construct a rotation-aware modulating factor, similar to focal loss [22]. This factor can dynamically weight the loss of each pseudo-label-prediction pair by considering their orientation difference. + +Specifically, the modulating factor $\omega_{i}^{rot}$ of the $i$ -th pair is formed as: + +$$ +\omega_ {i} ^ {\text {r o t}} = 1 + \sigma_ {i}, \tag {6} +$$ + +$$ +\sigma_ {i} = \alpha \frac {\left| r _ {i} ^ {t} - r _ {i} ^ {s} \right|}{\pi}, r _ {i} ^ {t}, r _ {i} ^ {s} \in \left[ - \frac {\pi}{2}, \frac {\pi}{2}\right), \tag {7} +$$ + +where $r_i^t$ and $r_i^s$ are the $i$ -th pseudo-label's and prediction's rotation angle in radians, respectively. $\alpha$ is a hyperparameter for adjusting orientation's importance, and we set it to 50 empirically. We add a constant to $\sigma_i$ , maintaining the origin unsupervised loss when pseudo-label and + +prediction have the same orientation. With the rotation-aware modulating factor, the overall rotation-aware adaptive weighting loss is formulated as: + +$$ +\mathcal {L} _ {R A W} = \sum_ {i} ^ {N _ {p}} \omega_ {i} ^ {\text {r o t}} \mathcal {L} _ {u} ^ {i}, \tag {8} +$$ + +where $N_{p}$ is the number of pseudo-labels and $\mathcal{L}_u^i$ is the basic unsupervised loss of the $i$ -th pseudo-label-prediction pair. By using the rotation-aware modulating factor, the RAW loss makes better use of the orientation information and provides more informative guidance, potentially benefiting the semi-supervised learning process. + +# 4.3. Global Consistency Loss + +Objects in an aerial image are usually dense and regularly distributed, as depicted in Fig. 1. Similar to texts in a document, the arrangement of the set of objects, i.e., the layout, encodes the mutual relations between them and the global pattern of the image. Ideally, the layout consistency between the student's and the teacher's predictions will be ensured if each pseudo-label-prediction pair is aligned. However, the latter condition is too strict and may hurt performance when there are noises in pseudo-labels. Therefore, it is reasonable to add the consistency between layouts as an additional relaxed optimization objective, encouraging the student to learn robust information from the teacher. In this way, the noise disturbance in pseudo-labels can be alleviated. Besides, the relations between different predicted instances from the student can also be regularized implicitly, which provides an additional guide to the student. + +We introduce the optimal transport cost [38] to measure the global similarity of layouts between the teacher's and the student's predictions, forming the global consistency loss. To be concrete, we denote the classification scores predicted by the teacher and the student by $\mathbf{s}^t\in \mathbb{R}^{N_p\times K}$ and $\mathbf{s}^s\in \mathbb{R}^{N_p\times K}$ respectively, where $K$ is the number of classes. Then, their global distributions, $\mathbf{d}^t\in \mathbb{R}^{N_p}$ and $\mathbf{d}^s\in \mathbb{R}^{N_p}$ can be formulated by + +$$ +\mathbf {d} _ {i} ^ {t} = e ^ {\mathbf {s} _ {i, c (i)} ^ {t}}, \tag {9} +$$ + +$$ +\mathbf {d} _ {i} ^ {s} = e ^ {\mathbf {S} _ {i, c (i)} ^ {s}}, \tag {10} +$$ + +where $c(i) = \underset{j=1,\ldots,K}{\arg \max} \mathbf{s}_{i,j}^{t}$ is the index of the class with the largest score for the $i$ -th pseudo-label. + +The global consistency loss is defined as the OT problem's dual formulation + +$$ +\mathcal {L} _ {G C} \left(\mathbf {d} ^ {t}, \mathbf {d} ^ {s}\right) = \left\langle \boldsymbol {\lambda} ^ {*}, \frac {\mathbf {d} ^ {t}}{\| \mathbf {d} ^ {t} \| _ {1}} \right\rangle + \left\langle \boldsymbol {\mu} ^ {*}, \frac {\mathbf {d} ^ {s}}{\| \mathbf {d} ^ {s} \| _ {1}} \right\rangle , \tag {11} +$$ + +where we normalize two distributions to form discrete probabilities, by dividing them to their sum. To construct the cost map for solving the OT problem, we consider both the spatial distance and the score difference of each possible matching pair. Specifically, for each prediction, we measure its matching cost with every pseudo-label as follows: + +$$ +C _ {i, j} = C _ {i, j} ^ {\text {d i s t}} + C _ {i, j} ^ {\text {s c o r e}}, \tag {12} +$$ + +$$ +C _ {i, j} ^ {\text {d i s t}} = \frac {\left\| \mathbf {z} _ {i} ^ {t} - \mathbf {z} _ {j} ^ {s} \right\| _ {2} ^ {2}}{\max _ {1 < = a , b < = N _ {p}} \left\| \mathbf {z} _ {a} ^ {t} - \mathbf {z} _ {b} ^ {s} \right\| _ {2} ^ {2}}, \tag {13} +$$ + +$$ +C _ {i, j} ^ {\text {s c o r e}} = \frac {\left\| \mathbf {s} _ {i , c (i)} ^ {t} - \mathbf {s} _ {j , c (j)} ^ {s} \right\| _ {1}}{\max _ {1 < = a , b < = N _ {p}} \left\| \mathbf {s} _ {a , c (a)} ^ {t} - \mathbf {s} _ {b , c (b)} ^ {s} \right\| _ {1}}, \tag {14} +$$ + +where $\mathbf{z}_i^t$ and $\mathbf{z}_j^s$ are 2D coordinates of the $i$ -th sample in the teacher and the $j_{th}$ sample in the student. + +We solve the OT problem by a fast Sinkhorn distances algorithm [5], obtaining the approximate solution $\lambda^{*}$ and $\mu^{*}$ . Based on the defined loss, its gradient with respect to $\mathbf{d}^s$ is + +$$ +\frac {\partial \mathcal {L} _ {G C} \left(\mathbf {d} ^ {t} , \mathbf {d} ^ {s}\right)}{\partial \mathbf {d} ^ {s}} = \frac {\boldsymbol {\mu} ^ {*}}{\| \mathbf {d} ^ {s} \| _ {1}} - \frac {\langle \boldsymbol {\mu} ^ {*} , \mathbf {d} ^ {s} \rangle}{\| \mathbf {d} ^ {s} \| _ {1} ^ {2}}. \tag {15} +$$ + +The gradients can be back-propagated to update the model, enforcing the layout consistency in the framework. Although OT-based loss has been explored before [6,39,49], our goal of using OT is different. Specifically, they focus on utilizing OT to improve the model's generalizability [6, 39] or mitigate the matching constraint [49]. However, our GC aims to model the many-to-many relationship between the teacher and the student, which is complementary to the RAW. In addition, we adopt such a set-to-set matching to alleviate the error in pseudo-label assignment, providing a more loose but stable constraint. + +SOOD is trained with the proposed unsupervised losses, RAW and GC, for unlabeled data as well as the supervised loss for labeled data. The overall loss $\mathcal{L}$ is defined as: + +$$ +\mathcal {L} = \underbrace {\mathcal {L} _ {R A W} + \mathcal {L} _ {G C}} _ {\mathcal {L} _ {u}} + \mathcal {L} _ {s}. \tag {16} +$$ + +Note that the supervised loss is the same as defined in FCOS, our designs only modify the unsupervised part. + +# 5. Experiments + +We conduct experiments on DOTA-v1.5, which is proposed at DOAI-2019†. It contains 2806 large aerial images and 402,089 annotated oriented objects. It includes three subsets: DOTA-v1.5-train, DOTA-v1.5-val and DOTA-v1.5-test, containing 1411, 458, and 937 images, respectively. The annotations of DOTA-v1.5-test is not released. + +There are 16 categories in this dataset: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), Helicopter (HC) and Container crane (CC). Compared with DOTA-v1.0 [40], a previous version, DOTA-v1.5 contains more small instances (less than 10 pixels), which makes it more challenging. + +Following conventions in SSOD, we consider two protocols, Partially Labeled Data and Fully Labeled Data, to validate the performance of a method on limited and abundant labeled data, respectively. + +Partially Labeled Data. We randomly sample $10\%$ , $20\%$ , and $30\%$ images from DOTA-v1.5-train as labeled data and set the remaining images as unlabeled data. Following DOTA-v1.5-train's data distribution, we provide one fold for each data proportion. + +Fully Labeled Data. We set DOTA-v1.5-train as labeled data and DOTA-v1.5-test as unlabeled data. + +For all experiments, we perform evaluation on DOTAv1.5-val and report the performance with the standard mean average precision (mAP) as the evaluation metrics. + +# 5.1. Implementation Details + +Without loss of generality, we take FCOS [37] as the representative anchor-free detector, and adopt ResNet-50 [13] with FPN [21] as the backbone for all our experiments. Following the previous works [11, 12, 40], we crop the original images into $1024 \times 1024$ patches with a stride of 824, that is, the pixel overlap between two adjacent patches is 200. We utilize asymmetric data augmentation for unlabeled data. Specifically, we use strong augmentation for + +Table 1. Experimental results on DOTA-v1.5 under the Partially Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS, respectively. Experiments are conducted on 10%, 20% and 30% labeled data settings. + +
SettingMethodPublication10%20%30%
SupervisedFaster R-CNN* [30]NeurIPS 201643.4351.3253.14
FCOS† [37]ICCV 201942.7850.1154.79
Semi-supervisedUnbiased Teacher* [24]ICLR 202144.5152.8053.33
Soft Teacher* [44]ICCV 202148.4654.8957.83
Dense Teacher† [50]ECCV 202246.9053.9357.86
SOOD† (ours)-48.6355.5859.23
+ +Table 2. Experimental results on DOTA-v1.5 under the Fully Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS respectively. Numbers in font of the arrow indicate the supervised baseline. + +
MethodPublicationmAP
Unbiased Teacher* [24]ICLR 202166.12 → 1.27 → 64.85
Soft Teacher* [44]ICCV 202166.12 → +0.28 → 66.40
Dense Teacher† [50]ECCV 202265.46 → +0.92 → 66.38
SOOD† (ours)-65.46 → +2.24 → 67.70
+ +the student model and weak augmentation for the teacher model. Random flipping is used for weak augmentation, while strong augmentation contains random flipping, color jittering, random grayscale, and random Gaussian blur. All models are trained for 180k iterations on 2 RTX3090 GPUs. With the SGD optimizer, the initial learning rate of 0.0025 is divided by 10 at 120k and 160k. The momentum and the weight decay are set to 0.9 and 0.0001, respectively. Each GPU takes 3 images as input, where the proportion between unlabeled and labeled data is set to 1:2. The pseudo-label sampling ratio is set as 0.25 by default. Following previous SSOD works [24, 50], we use the "burn-in" strategy to initialize the teacher model. + +# 5.2. Main Results + +In this section, we compare our method with the state-of-the-art SSOD methods [3, 24, 44] on DOTA-v1.5. For a fair comparison, we re-implement these methods on oriented object detectors with the same augmentation setting. + +Partially Labeled Data. We evaluate our method under different labeled data proportions, and the results are shown in Tab. 1. Our SOOD achieves state-of-the-art performance under all proportions. Specifically, it obtains 48.63, 55.58, and $59.23\mathrm{mAP}$ on $10\%$ , $20\%$ , and $30\%$ proportions, respectively, surpassing our supervised baseline by $+5.85$ , $+5.47$ , and $+4.44\mathrm{mAP}$ . We also surpass the state-of-the-art anchor-free method Dense Teacher [50] by $+1.73$ , $+1.65$ , and $+1.37$ under various proportions. We provide two anchor- + +Table 3. The effectiveness of SOOD on other methods under Fully Labeled Data setting. * means based on RetinaNet [22]. SOOD is able to generalize to other detectors and boost their performance. + +
DetectorPublicationMethodmAP
CFA [10]CVPR 2021Supervised Ours65.75 +67.07
KLD* [48]NeurIPS 2021Supervised Ours62.21 +64.62
+ +based methods for comparison, Unbiased Teacher [24] and Soft Teacher [44]. On $10\%$ and $20\%$ proportions, our SOOD achieves higher performance than Soft Teacher, even though our baseline is weaker than Soft Teacher's. Under $30\%$ data proportion, our SOOD surpasses Soft Teacher and Unbiased Teacher by at least $1.40\mathrm{mAP}$ . + +The qualitative results of our method compared with supervised baseline and Dense Teacher [50] are shown in Fig. 3. With the help of our RAW and GC, SOOD is able to exploit more potential semantic information from the unlabeled data, helping reduce false predictions and improve the detection quality. + +Fully Labeled Data. We also compare our SOOD with the other SSOD methods [24, 44, 50] on fully labeled data setting. Since the reported methods are based on different detectors, we report the results of the compared methods and their baseline in Tab. 2. Our SOOD surpasses previous methods by at least 1.30 points. Compared to our baseline, we obtain $+2.24\mathrm{mAP}$ improvement, which further demonstrates our method's ability to learn from unlabeled data. We notice that the performance of Unbiased Teacher [24] drops after adding unlabeled data. The reason might be that Unbiased Teacher does not apply unsupervised losses for bounding box regression, which is important for oriented object detection. + +Generalization on other detectors. To further validate the effectiveness of our method, we evaluate our method on other oriented object detectors, CFA [10] and KLD [48], under the Fully Labeled Data setting. As shown in Tab. 3, + +![](images/bc567d3996879f86dd793c77d83861cb6c05e206e8f1741901b99c26326c4f36.jpg) + +![](images/984242e64871c6107941d38bce8675d69ce81c321f14c2197aa406c456fa1ac2.jpg) + +![](images/33da7ed33742af8cf8ae5b44761c549b0a859588da10cd40b557a024d8f2b049.jpg) + +![](images/ccdacf9511ae816a962964d63b6b65f3f4dac30c0a8681bc8d52e5feaef923d0.jpg) + +![](images/fc755ab69477f580cd1ce4abf46632848a927156c7d3af40f57d1959b76c308d.jpg) + +![](images/3cde8da9260c8d59228e8e17a5f19d84f5841d70b883b908b6d783b12b34260c.jpg) + +![](images/6aa8eb3690788a292ffc206c6ad28fa89bf70dc13ba97391636105f67fa3cb55.jpg) + +![](images/4655ed10059995dc8ad17e44f26ed320ea0048302c97ce2e1872ddbbbadaff35.jpg) + +![](images/b34e5d5d28db04bb4f77863f1d4bc6e97eb7ffcb7ad1cfc478e202d8c0c77bf2.jpg) + +![](images/fede77dccc4221f6c3c4137ae06338a49b3f9b1e3a97790b5fa656e83a6ece21.jpg) + +![](images/c503127738af7902361d0d994799e7f4d334c5a74d6d9070f24aaa93b0c8b92b.jpg) + +![](images/e99757c2ef34706193b0e4fbd1de699d60ede3893898617e87ad04fc2e99a98a.jpg) + +![](images/de72a0a76f3146e6a575d70760aef03f6551654f84f1d823d6cb9ddd4d1d9fab.jpg) +Figure 3. Some visualization examples from the DOTA-v1.5 dataset. From left to right, each column shows ground truth, results of the supervised baseline (rotated-FCOS [37]), Dense Teacher [3], and our SOOD. The green rectangles indicate predictions. The red dashed circle, solid red circle, and red arrow represent false negative, false positive, and inaccurate orientation prediction, respectively. + +![](images/29b61592d2d788ee3385bca6bcbe210a28fbdcd95b3a9865a9e3f25e25898614.jpg) + +![](images/955d2cfeb89ff0a1ca6292eb4def76e815d54f7171b35f8adee0080053f4580d.jpg) + +![](images/e8501eb0cf3a43a637b66f475acf8da7aec8c12d5b58946c0610cfca28bbb962.jpg) + +although CFA is a strong detector, our method still results in an improvement of $+1.32\mathrm{mAP}$ and reaches 67.07 mAP. On the KLD detector, our method brings an improvement of $+2.41\mathrm{mAP}$ . The above results validate the generalization ability of our method. + +# 5.3. Ablation Study + +In this section, we conduct extensive studies to validate our key designs. Unless specified, all the ablation experiments are performed using $10\%$ of labeled data. + +The effect of each component. We study the effects of the proposed two losses, Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Note that our SOOD degrades to the vanilla dense pseudolabeling framework without these two losses. As shown in Tab. 4, both losses are proved effective and complementary under all three settings: RAW and GC can each bring performance gain, and the baseline is further improved when + +Table 4. The effects of Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Experiments are conducted on $10\%$ , $20\%$ and $30\%$ labeled data settings. + +
SettingRAWGCmAP
10%20%30%
I--47.2454.0757.74
II✓-47.8255.2158.93
III-✓47.7154.7258.70
IV✓✓48.6355.5859.23
+ +equipped with two losses. It indicates that the local constraint built by RAW and the global constraint built by GC can benefit the semi-supervised learning process, boosting the model by constructing one-to-one and many-to-many relationships between the teacher and the student. + +The influence of sampling ratio. In this part, we discuss + +Table 5. The effect of the sampling ratio for instance-level dense pseudo-labeling. Experiments are conducted at $10\%$ setting, and the method is equipped with both RAW and GC losses. + +
SettingSample RatiomAP
I0.12548.27
II0.2548.63
III0.547.91
IV1.047.69
+ +Table 6. The effects of different compositions in the cost map of GC. Experiments are conducted at $10\%$ setting, and the method is equipped with RAW loss. The results indicate that both distance and score are essential factors of the cost map. + +
SettingDistanceScoremAP
I--47.82
II-✓48.10
III✓-47.94
IV✓✓48.63
+ +the influence of the ratios in sampling pseudo-labels. The results with different sampling ratios are shown in Tab. 5. The best performance, $48.36\mathrm{mAP}$ , is achieved when the sample ratio is set to 0.25. Setting it to other values degrades the performance. We hypothesize that this value ensures a good balance between noises (e.g., false positives) and valid predictions (e.g., true positives). Increasing it will introduce more noise that harms the training process, while decreasing it leads to information loss and failure in learning the representation of objects. + +The effect of different compositions in cost map of GC. Here, we study the effects of the spatial distance and the score difference when constructing the cost map of optimal transport in GC loss. The results of different settings are shown in Tab. 6. We get at most $+0.28$ mAP improvement when using only one of them, indicating that the information from only one side is inadequate for learning the global prior. When considering both the score difference and spatial distance, the performance gain brought by GC is further improved to $+0.81$ mAP. It indicates that the information from score difference and spatial distance are complementary. With their help, RAW can effectively model the many-to-many relationship between the teacher and the student, providing an informative guide to the model. + +The effect of RAW's hyper-parameter $\alpha$ . Here, we study the influence of the hyper-parameter $\alpha$ in RAW. As shown in Tab. 7, we set $\alpha$ to 1.0 and get the performance of 47.77 mAP. As $\alpha$ increases, the performance of our method improves when $\alpha$ varies from 1 to 50. However, further increasing it to 100.0 slightly hurt the performance. Therefore, we set it to 50 by default. For this observation, we + +Table 7. The effect of hyper-parameter $\alpha$ in the RAW loss. Experiments are conducted at ${10}\%$ setting,and the method is equipped with GC loss. + +
SettingαmAP
I147.77
II1047.87
III5048.63
IV10047.95
+ +conjecture that increasing the weight $\alpha$ will enlarge the influence of orientation information, but also amplify the impact of teacher's inaccurate labels. + +# 5.4. Limitation and Discussion + +Although our method achieves satisfactory results on semi-supervised oriented object detection, the usage of aerial objects' characteristics is limited. Apart from orientation and global layout, many other properties of aerial objects should be considered, e.g., scale variations and large aspect ratios. Apart from that, we separately consider orientation and global layout by constructing two different constraints, which can be integrated into one unified module to utilize both information simultaneously. We also find that oriented objects and even complex objects wildly appear in other tasks, such as 3D object detection and text detection, leaving much room for further exploration. + +# 6. Conclusion + +In this paper, we have presented an effective solution for semi-supervised oriented object detection, which is important but neglected. Focusing on oriented objects' characteristics in aerial scenes, we have designed two novel losses, rotation-aware adaptive weighting (RAW) loss and global consistency (GC) loss. The former considers the importance of rotation information for oriented objects, dynamically weighting each pseudo-label-prediction pair by their rotation difference. The latter introduces the global layout concept to SSOD, measuring the global similarity between the teacher and the student in a many-to-many manner. To validate the effectiveness of our method, we have conducted extensive experiments on the DOTA-v1.5 benchmark. Compared with state-of-the-art methods, SOOD achieves consistent performance improvement on partially and fully labeled data. + +Acknowledgements. 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Rethinking pretraining and self-training. Proc. of Advances in Neural Information Processing Systems, 33:3833-3845, 2020. 2 \ No newline at end of file diff --git a/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/images.zip b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f7a5e9b4e3f1db27a0fc7d10fc36dd244b466461 --- /dev/null +++ b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1c4a47711355085b6145f0232873b3530439a6bcaddfda1753b87c0b2cf783ad +size 500759 diff --git a/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/layout.json b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..393781db60558fc09b8bdd5c097f145f9cfecbbb --- /dev/null +++ b/2023/SOOD_ Towards Semi-Supervised Oriented Object Detection/layout.json @@ -0,0 +1,9314 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 108, + 103, + 486, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 103, + 486, + 121 + ], + "spans": [ + { + "bbox": [ + 108, + 103, + 486, + 121 + ], + "type": "text", + "content": "SOOD: Towards Semi-Supervised Oriented Object Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 142, + 538, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 142, + 538, + 159 + ], + "spans": [ + { + "bbox": [ + 53, + 142, + 538, + 159 + ], + "type": "text", + "content": "Wei Hua\\*, Dingkang Liang\\*, Jingyu Li, Xiaolong Liu, Zhikang Zou, Xiaoqing Ye, Xiang Bai" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 75, + 170, + 519, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 170, + 519, + 199 + ], + "spans": [ + { + "bbox": [ + 75, + 170, + 519, + 199 + ], + "type": "text", + "content": "1Huazhong University of Science and Technology, {whua_hust, dkliang, xbai} @hust.edu.cn \n2Baidu Inc., China" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 252, + 290, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 290, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 290, + 529 + ], + "type": "text", + "content": "Semi-Supervised Object Detection (SSOD), aiming to explore unlabeled data for boosting object detectors, has become an active task in recent years. However, existing SSOD approaches mainly focus on horizontal objects, leaving multi-oriented objects that are common in aerial images unexplored. This paper proposes a novel Semi-supervised Oriented Object Detection model, termed SOOD, built upon the mainstream pseudo-labeling framework. Towards oriented objects in aerial scenes, we design two loss functions to provide better supervision. Focusing on the orientations of objects, the first loss regularizes the consistency between each pseudo-label-prediction pair (includes a prediction and its corresponding pseudo label) with adaptive weights based on their orientation gap. Focusing on the layout of an image, the second loss regularizes the similarity and explicitly builds the many-to-many relation between the sets of pseudo-labels and predictions. Such a global consistency constraint can further boost semi-supervised learning. Our experiments show that when trained with the two proposed losses, SOOD surpasses the state-of-the-art SSOD methods under various settings on the DOTAv1.5 benchmark. The code will be available at https://github.com/HamPerdredes/SOOD." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 553, + 128, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 553, + 128, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 128, + 566 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 574, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 682 + ], + "type": "text", + "content": "Sufficient labeled data is essential for fully-supervised object detection. However, the data labeling process is time-consuming and expensive. Recently, Semi-Supervised Object Detection (SSOD), where object detectors are learned from labeled data as well as easy-to-obtain unlabeled data, has attracted increasing attention. Existing SSOD methods [16, 24, 44, 50] mainly focus on detecting objects with horizontal bounding boxes in general scenes. Nevertheless, in more complex scenes, such as aerial scenes, objects usu" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 227, + 422, + 307 + ], + "blocks": [ + { + "bbox": [ + 312, + 227, + 422, + 307 + ], + "lines": [ + { + "bbox": [ + 312, + 227, + 422, + 307 + ], + "spans": [ + { + "bbox": [ + 312, + 227, + 422, + 307 + ], + "type": "image", + "image_path": "826a5548f5459ca64255c3a713d1079ccce3a2b7e04c2361d46fc5f201049fdc.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 312, + 414, + 322 + ], + "lines": [ + { + "bbox": [ + 318, + 312, + 414, + 322 + ], + "spans": [ + { + "bbox": [ + 318, + 312, + 414, + 322 + ], + "type": "text", + "content": "(a) Arbitrary rotating objects" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 430, + 227, + 541, + 307 + ], + "blocks": [ + { + "bbox": [ + 430, + 227, + 541, + 307 + ], + "lines": [ + { + "bbox": [ + 430, + 227, + 541, + 307 + ], + "spans": [ + { + "bbox": [ + 430, + 227, + 541, + 307 + ], + "type": "image", + "image_path": "09aa9cb227da62c57eef758c8ffe9dc814e1fbbe6afa1970fb52a16c5a54c16b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 439, + 312, + 531, + 322 + ], + "lines": [ + { + "bbox": [ + 439, + 312, + 531, + 322 + ], + "spans": [ + { + "bbox": [ + 439, + 312, + 531, + 322 + ], + "type": "text", + "content": "(b) Small and dense objects" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 340, + 547, + 385 + ], + "lines": [ + { + "bbox": [ + 305, + 340, + 547, + 385 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 547, + 385 + ], + "type": "text", + "content": "Figure 1. Arbitrary rotating (a), small and dense (b) objects are common in aerial scenes, which are often regularly arranged on the image. From a global perspective, this pattern indicates that an aerial can be regarded as a layout." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 407, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 444 + ], + "type": "text", + "content": "ally need to be annotated with oriented bounding boxes. Considering the higher annotation cost of oriented boxes*, semi-supervised oriented object detection is worth studying." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 445, + 546, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 546, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 546, + 660 + ], + "type": "text", + "content": "Compared with general scenes, the main characteristics of objects in aerial scenes (or aerial objects for short) are three-fold: arbitrary orientations, small scales, and agglomeration, as shown in Fig. 1. The mainstream SSOD methods are based on the pseudo-labeling framework [3,35,36] consisting of a teacher model and a student model. The teacher model, an Exponential Moving Average (EMA) of the student model at historical training iterations, generates pseudo-labels for unlabeled images. Thus, the student model can learn from both labeled and unlabeled data. To extend the framework to oriented object detection, we think the following two aspects need to be addressed: 1) As orientation is an essential property of multi-oriented objects, how to use the orientation information when guiding the student with pseudo-labels is critical. 2) As aerial objects are often dense and regularly distributed in an image, we can utilize the layout to facilitate the learning of each pair instead of treating them individually." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 661, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 661, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 317, + 661, + 545, + 673 + ], + "type": "text", + "content": "This paper proposes the first Semi-supervised Oriented" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 248, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 248, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 248, + 713 + ], + "type": "text", + "content": "*Equal contribution. † Corresponding author. \nWork done when Dingkang Liang was an intern at Baidu." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "*Annotation cost of an oriented box is about 36.5% (86$ vs. 63$ per 1k at 2022.11) more than a horizontal box according to https://cloud.google.com/ai-platform/data-labeling/pricing." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15558" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 156 + ], + "type": "text", + "content": "Object Detection method, termed SOOD. Following [50], SOOD is built upon the dense pseudo-labeling framework, where the pseudo labels are filtered from the raw pixelwise predictions (including box coordinates and confidence scores). The key design is two simple yet effective losses that enforce the instance-level and set-level consistency between the student's and the teacher's predictions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 286, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 286, + 335 + ], + "type": "text", + "content": "To be specific, considering that the pseudo-label-prediction pairs are not equally informative, we propose the Rotation-aware Adaptive Weighting (RAW) loss. It utilizes the orientation gap of each pair, which reflects the difficulty of this sample in a way, to weight the corresponding loss dynamically. In this manner, we can softly pick those more useful supervision signals to guide the learning of the student. In addition, considering that the layout of an aerial image can potentially reflect components' overall status (e.g., objects' density and location distribution) and help the detection process, we propose the Global Consistency (GC) loss. It measures the similarity of the pseudo-labels and the predictions from a global perspective, which can alleviate the disturbance of noise in pseudo-labels and implicitly regularizes the mutual relations between different objects." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "text", + "content": "We extensively evaluate SOOD under various settings on DOTA-v1.5, a popular aerial object detection benchmark. Our SOOD achieves consistent performance improvement when using " + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 336, + 286, + 418 + ], + "type": "text", + "content": ", and full of labeled data, compared with the state-of-the-art SSOD methods (using the same oriented object detector). The ablation study also verifies the effectiveness of the two losses." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 419, + 286, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 286, + 515 + ], + "type": "text", + "content": "In summary, this paper makes an early exploration of semi-supervised learning for oriented object detection. By analyzing the distinct characteristics of oriented objects from general objects, we propose two novel loss functions to adapt the pseudo-label framework to this task. We hope that this work can provide a good starting point for semi-supervised oriented object detection and serve as a simple yet strong baseline for future research." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 526, + 135, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 135, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 135, + 538 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": "Semi-Supervised Object Detection. In the past few years, semi-supervised learning (SSL) [2, 32] has achieved impressive performance in image classification. These works leverage unlabeled data by using pseudo-label [9,15,17,42], consistency regularization [2,36,41], data augmentation [4, 31] and even adversarial training [26]. Compared to semi-supervised image classification, SSOD requires instance-level predictions and additional bounding boxes regression sub-task, which makes it more challenging. In [28, 51], pseudo-labels are assembled from predictions of data with different augmentations. CSD [14] only utilizes the horizontal flipping augmentation and applies consistency loss to constrain the model, but the weak augmentation limits its performance. STAC [33] trains an object detect-" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 312 + ], + "type": "text", + "content": "tion with labeled data and generates pseudo-labels on unlabeled data with this detector offline. After that, some studies [24,35,44,45] adopt EMA from Mean Teacher [36] to update the teacher model after each training iteration. ISMT [45] obtains more accurate pseudo-labels by fusing current pseudo-labels and history labels. Unbiased Teacher [24] replaces cross-entropy loss with focal loss [22] to solve the class-imbalance issue and filters pseudo-labels by threshold. Soft Teacher [44] uses the classification scores to adaptively weight the loss of each pseudo-box and proposes box jittering to select reliable pseudo-labels. Unbiased Teacher v2 [25] adopts an anchor-free detector and uses uncertainty predictions to select pseudo-labels for the regression branch. Dense Teacher [50] replaces postprocessed instance-level pseudo-labels with dense pixel-level pseudo-labels, which successfully removes the influence of thresholds and post-processing hyper-parameters. However, none of these works are designed for oriented object detection in aerial scenes. This paper aims to fill this blank and offer a starting point for future research." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 312, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 598 + ], + "type": "text", + "content": "Orient Object Detection. Different from general object detectors [8, 23, 29, 30], oriented object detectors represent objects with Oriented Bounding Boxes (OBBs). Typical oriented objects include aerial objects and multi-oriented scene texts [12, 19, 20, 34]. In recent years, many oriented object detection methods have been proposed to boost the performance for this area. CSL [46] formulates the angle regression problem as a classification task to address the out-of-bound issue. " + }, + { + "bbox": [ + 304, + 312, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\mathrm{R}^3\\mathrm{Det}" + }, + { + "bbox": [ + 304, + 312, + 545, + 598 + ], + "type": "text", + "content": " [47] predicts Horizontal Bounding Boxes (HBBs) at the first stage to improve detection speed and align the feature in the second stage to predict oriented objects. Oriented R-CNN [43] proposes a concise multi-oriented region proposal network and uses the midpoint offsets to represent arbitrarily oriented objects. ReDet [12] proposes a Rotation-equivariant detector to extract rotation-invariant from rotation-equivariant for accurate aerial object detection. Oriented RepPoints [18] proposes a quality assessment module and samples assignment scheme for adaptive points learning, which can obtain non-axis features from neighboring objects and neglect background noises. Different from the above works that focus on the supervised paradigm, this paper makes an early exploration of semi-supervised oriented object detection, which can reduce the annotation cost and boost detectors with unlabeled data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 609, + 383, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 383, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 383, + 621 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 628, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 628, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 628, + 545, + 665 + ], + "type": "text", + "content": "In this section, we revisit the mainstream pseudolabeling paradigm in SSOD and Monge-Kantarovich optimal transport theory [27] as preliminary." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 671, + 451, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 451, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 451, + 684 + ], + "type": "text", + "content": "3.1. Pseudo-labeling Paradigm" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Pseudo-labeling frameworks [25, 44, 50] inherited designs from the Mean Teacher [36] structure, which consists" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15559" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": "of two parts, i.e., a teacher model and a student model. The teacher model is an Exponential Moving Average (EMA) of the student model. They are learned iteratively by the following steps. 1) Generate pseudo-labels for the unlabeled data in a batch. The pseudo-labels are filtered from the teacher's predictions, e.g., the box coordinates and the classification scores. Meanwhile, the student makes predictions for both labeled and unlabeled data in the batch. 2) Compute loss for the student model's predictions. It consists of two parts, the unsupervised loss " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_u" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": " and supervised loss " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ". They are computed for the unlabeled data with the pseudo-labels and the labeled data with the ground truth (GT) labels, respectively. The overall loss " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": " is the sum of them. 3) Update the parameters of the student model according to the overall loss. The teacher model is updated simultaneously in an EMA manner. In this way, based on the mutual learning mechanism, both models evolve as the training goes on." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 289, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 432 + ], + "type": "text", + "content": "Based on the sparsity of pseudo-labels, pseudo-labeling frameworks can be further categorized into sparse pseudolabeling [25, 44] and dense pseudo-labeling [50], termed SPL and DPL, respectively. The SPL selects the teacher's predictions after the post-processing operations, e.g., nonmaximum suppression and score filtering. It obtains sparse labels to supervise the student, e.g., bounding boxes and categories. The DPL directly samples the post-sigmoid log-its predicted by the teacher, which are dense and informative. Compared with SPL, DPL bypasses those lengthy post-processing methods, reserving more details from the teacher than its pseudo-box counterpart." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 439, + 160, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 160, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 160, + 453 + ], + "type": "text", + "content": "3.2. Optimal Transport" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 458, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 529 + ], + "type": "text", + "content": "The Monge-Kantorovich Optimal Transport (OT) [27] aims to solve the problem of simultaneously moving items from one set to another set with minimum cost. It has been widely explored in various computer vision tasks [1, 7, 39, 49]. The mathematical formulations of OT are described as follows in detail." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "inline_equation", + "content": "\\mathbb{X} = \\{x_i|x_i\\in \\mathbb{R}^d\\}_{i}^{N}" + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "inline_equation", + "content": "\\mathbb{Y} = \\{y_j|y_j\\in \\mathbb{R}^d\\}_{j}^{N}" + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "content": " denote two sets of " + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "content": " -dimensional vectors. Their discrete distributions " + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbb{X}}" + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbb{Y}}" + }, + { + "bbox": [ + 46, + 529, + 287, + 566 + ], + "type": "text", + "content": " are formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 136, + 575, + 287, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 575, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 136, + 575, + 287, + 590 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbb {X}} = \\sum_ {i} ^ {N} \\hat {x} _ {i} \\delta_ {f _ {i}} \\tag {1}", + "image_path": "fcfa588a12231ec9317e436eb8527952d75b0fa2378934c4dfe133efbe24f61e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 135, + 600, + 287, + 616 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 600, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 135, + 600, + 287, + 616 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbb {Y}} = \\sum_ {j} ^ {N} \\hat {y} _ {j} \\delta_ {g _ {j}}, \\tag {2}", + "image_path": "9a70392f2ffe209e9ed605ddd6b71a74ddf7cb35caac8094e338f5f0e4ca9e80.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": " are the discrete probability vectors, " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": " is the Dirac delta function. Therefore, the OT cost is measured between these two probabilities, " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": ". The possible transportation plans from " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}}" + }, + { + "bbox": [ + 46, + 620, + 287, + 669 + ], + "type": "text", + "content": " are formed as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 80, + 677, + 287, + 692 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 677, + 287, + 692 + ], + "spans": [ + { + "bbox": [ + 80, + 677, + 287, + 692 + ], + "type": "interline_equation", + "content": "\\boldsymbol {P} = \\left\\{\\boldsymbol {p} \\in \\mathbb {R} ^ {N \\times N} \\mid \\boldsymbol {p} \\mathbf {1} _ {N} = \\hat {\\mathbf {x}}, \\boldsymbol {p} ^ {T} \\mathbf {1} _ {N} = \\hat {\\mathbf {y}} \\right\\}, \\tag {3}", + "image_path": "f727fa29c1e2b8fd7752c979974cb1074a27d7894e9951788280f04b7db9539d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{1}_N" + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": " is an " + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "-dimensional column vector whose values" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 471, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 471, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 471, + 83 + ], + "type": "text", + "content": "are all 1. The OT cost is then defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 375, + 95, + 545, + 112 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 95, + 545, + 112 + ], + "spans": [ + { + "bbox": [ + 375, + 95, + 545, + 112 + ], + "type": "interline_equation", + "content": "\\omega_ {o t} (\\hat {\\mathbf {x}}, \\hat {\\mathbf {y}}) = \\min _ {\\boldsymbol {p} \\in \\boldsymbol {P}} \\left\\langle \\mathbf {C}, \\boldsymbol {p} \\right\\rangle , \\tag {4}", + "image_path": "9eeaacc670de6b375a5528cd755421cc8ae20c029ce178b6a6f7ecbf7c373ae2.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "spans": [ + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "content": " represents the cost matrix between two sets, " + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "inline_equation", + "content": "\\langle \\cdot \\rangle" + }, + { + "bbox": [ + 305, + 122, + 547, + 159 + ], + "type": "text", + "content": " represents inner product. In common, the OT problem is solved in its dual formulation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 349, + 167, + 545, + 189 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 167, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 349, + 167, + 545, + 189 + ], + "type": "interline_equation", + "content": "\\mathcal {W} _ {o t} (\\hat {\\mathbf {x}}, \\hat {\\mathbf {y}}) = \\max _ {\\boldsymbol {\\lambda}, \\boldsymbol {\\mu} \\in \\mathbb {R} ^ {N}} \\left\\langle \\boldsymbol {\\lambda}, \\hat {\\mathbf {x}} \\right\\rangle + \\left\\langle \\boldsymbol {\\mu}, \\hat {\\mathbf {y}} \\right\\rangle , \\tag {5}", + "image_path": "1ba7256da9433713d683cb48ec6d3d95a81adda16a173b42438881e7f42b8c14.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 395, + 190, + 504, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 190, + 504, + 201 + ], + "spans": [ + { + "bbox": [ + 395, + 190, + 504, + 201 + ], + "type": "interline_equation", + "content": "s. t. \\lambda_ {i} + \\mu_ {j} \\leq \\mathbf {C} _ {i, j}, \\forall i, j,", + "image_path": "9d7558f46b4f973460ffece9ad6b018ee427c5044e04f355db68d0ba9eb465f2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 306, + 210, + 545, + 235 + ], + "type": "text", + "content": " are the solutions of the OT problem, which can be approximated in an iterative manner [5]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 245, + 361, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 245, + 361, + 258 + ], + "spans": [ + { + "bbox": [ + 306, + 245, + 361, + 258 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 266, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 547, + 373 + ], + "type": "text", + "content": "Fig. 2 illustrates an overview of our proposed SOOD. Towards multi-oriented object detection in aerial images, we build our approach upon the popular dense pseudo-labeling framework [50], along with the Rotation-aware Adaptive Weighting (RAW) loss and the Global Consistency (GC) loss. In this section, we first describe the overall framework in Sec. 4.1. Then, we describe the key design of the proposed losses, RAW and GC, in the following Sec. 4.2 and Sec. 4.3, respectively." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 381, + 443, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 443, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 443, + 392 + ], + "type": "text", + "content": "4.1. The Overall Framework" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "type": "text", + "content": "Currently, the Dense Pseudo-Labeling (DPL) framework achieves the state-of-the-art in SSOD. Hence, we construct a DPL-based end-to-end baseline, including the supervised and unsupervised parts. For the supervised part, the student model is trained with labeled data in a regular manner. For the unsupervised part, we first obtain predicted boxes of the teacher after post-processing. These boxes indicate informative areas in the prediction map, where we randomly sample predictions, forming them as dense pseudo-labels " + }, + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "type": "inline_equation", + "content": "P^t" + }, + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "type": "text", + "content": ". Note that we also select the predictions " + }, + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "type": "inline_equation", + "content": "P^s" + }, + { + "bbox": [ + 305, + 399, + 545, + 530 + ], + "type": "text", + "content": " at the same correspondence positions from the student." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 531, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 531, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 305, + 531, + 545, + 639 + ], + "type": "text", + "content": "We use the oriented version of FCOS [37] as the teacher and student models. The basic unsupervised loss consists of three parts: classification loss, regression loss, and centerness loss, corresponding to the output of FCOS. We adopt smooth 11 loss for regression loss, binary cross-entropy loss for classification and center-ness loss. Based on these losses, we first perform adaptive weighting on them through RAW and further measure the global consistency between the teacher and the student via GC." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 647, + 522, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 522, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 522, + 659 + ], + "type": "text", + "content": "4.2. Rotation-aware Adaptive Weighting Loss" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 666, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 714 + ], + "type": "text", + "content": "Orientation is one essential property of an oriented object. As shown in Fig. 1, even if objects are dense and small, their orientations remain clear. Previous oriented object detection methods have already employed such a property by" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15560" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 68, + 539, + 258 + ], + "blocks": [ + { + "bbox": [ + 58, + 68, + 539, + 258 + ], + "lines": [ + { + "bbox": [ + 58, + 68, + 539, + 258 + ], + "spans": [ + { + "bbox": [ + 58, + 68, + 539, + 258 + ], + "type": "image", + "image_path": "0f512317b9213522b0422f60b4681461d27690687049b8a033ba304091c8f64a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 547, + 330 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 547, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 547, + 330 + ], + "type": "text", + "content": "Figure 2. The pipeline of the proposed SOOD. Each training batch consists of both labeled and unlabeled images. Note that the supervised part is hidden for simplicity. For the unsupervised part, we sample dense pseudo-labels from the teacher's prediction map and select the student's predictions at the same positions, obtaining a series of pseudo-label-prediction pairs. We dynamically weigh each pair's unsupervised loss by their orientation difference. Besides, we regard them as two discrete distributions, measuring their similarity in a many-to-many manner via a global consistency loss." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 350, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 397 + ], + "type": "text", + "content": "assembling it into loss calculation. However, these works are under the assumption that the angles of the labels are reliable. In this case, it is natural to strictly force the prediction close to the ground truth." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 399, + 288, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 288, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 288, + 577 + ], + "type": "text", + "content": "Unfortunately, the above assumption does not hold in the semi-supervised setting. In other words, the pseudolabels may be incorrect. Simply forcing the student to be close to the teacher may cause noise accumulation, harming the model's training process. Hence, we propose to utilize the orientation information softly. Intuitively, as orientation is essential but hard to be accurately predicted, the difference in rotation angles between a prediction and a pseudolabel can reflect the difficulty of the sample in a way. In other words, the orientation difference can be used to dynamically adjust the unsupervised loss. Therefore, we construct a rotation-aware modulating factor, similar to focal loss [22]. This factor can dynamically weight the loss of each pseudo-label-prediction pair by considering their orientation difference." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "content": "Specifically, the modulating factor " + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\omega_{i}^{rot}" + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "content": " of the " + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 578, + 287, + 601 + ], + "type": "text", + "content": "-th pair is formed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 603, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 603, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 134, + 603, + 287, + 617 + ], + "type": "interline_equation", + "content": "\\omega_ {i} ^ {\\text {r o t}} = 1 + \\sigma_ {i}, \\tag {6}", + "image_path": "290e36b2f4a91c395f2792d8e613ca51be2a06a485d2f6443fa8ca5aa7a81651.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 93, + 624, + 287, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 624, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 93, + 624, + 287, + 648 + ], + "type": "interline_equation", + "content": "\\sigma_ {i} = \\alpha \\frac {\\left| r _ {i} ^ {t} - r _ {i} ^ {s} \\right|}{\\pi}, r _ {i} ^ {t}, r _ {i} ^ {s} \\in \\left[ - \\frac {\\pi}{2}, \\frac {\\pi}{2}\\right), \\tag {7}", + "image_path": "4b7381358f074d2d9d8ede5438ffa6124fd444820c11e8888646893d71e387b5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_i^t" + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "r_i^s" + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "content": "-th pseudo-label's and prediction's rotation angle in radians, respectively. " + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "content": " is a hyperparameter for adjusting orientation's importance, and we set it to 50 empirically. We add a constant to " + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_i" + }, + { + "bbox": [ + 47, + 653, + 288, + 714 + ], + "type": "text", + "content": ", maintaining the origin unsupervised loss when pseudo-label and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 350, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 387 + ], + "type": "text", + "content": "prediction have the same orientation. With the rotation-aware modulating factor, the overall rotation-aware adaptive weighting loss is formulated as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 376, + 396, + 545, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 396, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 376, + 396, + 545, + 412 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {R A W} = \\sum_ {i} ^ {N _ {p}} \\omega_ {i} ^ {\\text {r o t}} \\mathcal {L} _ {u} ^ {i}, \\tag {8}", + "image_path": "ca7e3f9a699d1993e01ccb5e793269e7d8377ab4198048f3645c56a4633a9fb8.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "text", + "content": " is the number of pseudo-labels and " + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_u^i" + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "text", + "content": " is the basic unsupervised loss of the " + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 422, + 545, + 494 + ], + "type": "text", + "content": "-th pseudo-label-prediction pair. By using the rotation-aware modulating factor, the RAW loss makes better use of the orientation information and provides more informative guidance, potentially benefiting the semi-supervised learning process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 503, + 443, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 443, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 443, + 516 + ], + "type": "text", + "content": "4.3. Global Consistency Loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Objects in an aerial image are usually dense and regularly distributed, as depicted in Fig. 1. Similar to texts in a document, the arrangement of the set of objects, i.e., the layout, encodes the mutual relations between them and the global pattern of the image. Ideally, the layout consistency between the student's and the teacher's predictions will be ensured if each pseudo-label-prediction pair is aligned. However, the latter condition is too strict and may hurt performance when there are noises in pseudo-labels. Therefore, it is reasonable to add the consistency between layouts as an additional relaxed optimization objective, encouraging the student to learn robust information from the teacher. In this way, the noise disturbance in pseudo-labels can be alleviated. Besides, the relations between different predicted instances from the student can also be regularized implicitly, which provides an additional guide to the student." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15561" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": "We introduce the optimal transport cost [38] to measure the global similarity of layouts between the teacher's and the student's predictions, forming the global consistency loss. To be concrete, we denote the classification scores predicted by the teacher and the student by " + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{s}^t\\in \\mathbb{R}^{N_p\\times K}" + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{s}^s\\in \\mathbb{R}^{N_p\\times K}" + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": " respectively, where " + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": " is the number of classes. Then, their global distributions, " + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{d}^t\\in \\mathbb{R}^{N_p}" + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{d}^s\\in \\mathbb{R}^{N_p}" + }, + { + "bbox": [ + 47, + 72, + 289, + 168 + ], + "type": "text", + "content": " can be formulated by" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 139, + 176, + 287, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 176, + 287, + 192 + ], + "spans": [ + { + "bbox": [ + 139, + 176, + 287, + 192 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {i} ^ {t} = e ^ {\\mathbf {s} _ {i, c (i)} ^ {t}}, \\tag {9}", + "image_path": "844bdc1821b3206c8e97f966271bbf7105b5c2d21545b48b857bfd9a1ce9835c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 139, + 199, + 287, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 139, + 199, + 287, + 214 + ], + "spans": [ + { + "bbox": [ + 139, + 199, + 287, + 214 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {i} ^ {s} = e ^ {\\mathbf {S} _ {i, c (i)} ^ {s}}, \\tag {10}", + "image_path": "197fca779ad7ec9add3cb8c4d05e862cdb1e7cd98c7b41ea7f17a5d446fdfed3.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "type": "inline_equation", + "content": "c(i) = \\underset{j=1,\\ldots,K}{\\arg \\max} \\mathbf{s}_{i,j}^{t}" + }, + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "type": "text", + "content": " is the index of the class with the largest score for the " + }, + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 218, + 287, + 248 + ], + "type": "text", + "content": "-th pseudo-label." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 249, + 287, + 273 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 249, + 287, + 273 + ], + "spans": [ + { + "bbox": [ + 47, + 249, + 287, + 273 + ], + "type": "text", + "content": "The global consistency loss is defined as the OT problem's dual formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 278, + 287, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 278, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 52, + 278, + 287, + 306 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {G C} \\left(\\mathbf {d} ^ {t}, \\mathbf {d} ^ {s}\\right) = \\left\\langle \\boldsymbol {\\lambda} ^ {*}, \\frac {\\mathbf {d} ^ {t}}{\\| \\mathbf {d} ^ {t} \\| _ {1}} \\right\\rangle + \\left\\langle \\boldsymbol {\\mu} ^ {*}, \\frac {\\mathbf {d} ^ {s}}{\\| \\mathbf {d} ^ {s} \\| _ {1}} \\right\\rangle , \\tag {11}", + "image_path": "a56845f7579ef78f9ad788db1ec0d7d551c5b0f063b8622e6f9523549e459866.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 312, + 287, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 287, + 385 + ], + "type": "text", + "content": "where we normalize two distributions to form discrete probabilities, by dividing them to their sum. To construct the cost map for solving the OT problem, we consider both the spatial distance and the score difference of each possible matching pair. Specifically, for each prediction, we measure its matching cost with every pseudo-label as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 117, + 392, + 287, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 392, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 117, + 392, + 287, + 407 + ], + "type": "interline_equation", + "content": "C _ {i, j} = C _ {i, j} ^ {\\text {d i s t}} + C _ {i, j} ^ {\\text {s c o r e}}, \\tag {12}", + "image_path": "bdf8fe5730df2dc436e5745e0b5385e9c07bac5a52c7892735d70a22c2be5ccf.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 86, + 415, + 287, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 415, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 86, + 415, + 287, + 444 + ], + "type": "interline_equation", + "content": "C _ {i, j} ^ {\\text {d i s t}} = \\frac {\\left\\| \\mathbf {z} _ {i} ^ {t} - \\mathbf {z} _ {j} ^ {s} \\right\\| _ {2} ^ {2}}{\\max _ {1 < = a , b < = N _ {p}} \\left\\| \\mathbf {z} _ {a} ^ {t} - \\mathbf {z} _ {b} ^ {s} \\right\\| _ {2} ^ {2}}, \\tag {13}", + "image_path": "2a685d137bfce98e1e5213941fcb7e8e1e887caca71e24deb4954007dcbc26d7.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 61, + 448, + 287, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 448, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 61, + 448, + 287, + 479 + ], + "type": "interline_equation", + "content": "C _ {i, j} ^ {\\text {s c o r e}} = \\frac {\\left\\| \\mathbf {s} _ {i , c (i)} ^ {t} - \\mathbf {s} _ {j , c (j)} ^ {s} \\right\\| _ {1}}{\\max _ {1 < = a , b < = N _ {p}} \\left\\| \\mathbf {s} _ {a , c (a)} ^ {t} - \\mathbf {s} _ {b , c (b)} ^ {s} \\right\\| _ {1}}, \\tag {14}", + "image_path": "468a106191baf1a72c69d5108dbdd7f90c0a0005f6245312bbf041eb2bb6c52a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^t" + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_j^s" + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "text", + "content": " are 2D coordinates of the " + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "text", + "content": "-th sample in the teacher and the " + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "inline_equation", + "content": "j_{th}" + }, + { + "bbox": [ + 47, + 483, + 287, + 507 + ], + "type": "text", + "content": " sample in the student." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "text", + "content": "We solve the OT problem by a fast Sinkhorn distances algorithm [5], obtaining the approximate solution " + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\lambda^{*}" + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mu^{*}" + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "text", + "content": ". Based on the defined loss, its gradient with respect to " + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{d}^s" + }, + { + "bbox": [ + 47, + 508, + 287, + 552 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 89, + 552, + 287, + 578 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 552, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 89, + 552, + 287, + 578 + ], + "type": "interline_equation", + "content": "\\frac {\\partial \\mathcal {L} _ {G C} \\left(\\mathbf {d} ^ {t} , \\mathbf {d} ^ {s}\\right)}{\\partial \\mathbf {d} ^ {s}} = \\frac {\\boldsymbol {\\mu} ^ {*}}{\\| \\mathbf {d} ^ {s} \\| _ {1}} - \\frac {\\langle \\boldsymbol {\\mu} ^ {*} , \\mathbf {d} ^ {s} \\rangle}{\\| \\mathbf {d} ^ {s} \\| _ {1} ^ {2}}. \\tag {15}", + "image_path": "f35e8cf4e7f9672b6a300fdf2ea22815eacd34b9462d840087b92fa843b27bf0.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 582, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 712 + ], + "type": "text", + "content": "The gradients can be back-propagated to update the model, enforcing the layout consistency in the framework. Although OT-based loss has been explored before [6,39,49], our goal of using OT is different. Specifically, they focus on utilizing OT to improve the model's generalizability [6, 39] or mitigate the matching constraint [49]. However, our GC aims to model the many-to-many relationship between the teacher and the student, which is complementary to the RAW. In addition, we adopt such a set-to-set matching to alleviate the error in pseudo-label assignment, providing a more loose but stable constraint." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "SOOD is trained with the proposed unsupervised losses, RAW and GC, for unlabeled data as well as the supervised loss for labeled data. The overall loss " + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 372, + 118, + 545, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 118, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 372, + 118, + 545, + 144 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\underbrace {\\mathcal {L} _ {R A W} + \\mathcal {L} _ {G C}} _ {\\mathcal {L} _ {u}} + \\mathcal {L} _ {s}. \\tag {16}", + "image_path": "ec518591f250b524780682e456d84e2a24b9bd0f9536f9e92cfdef1a527f8882.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 153, + 545, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 153, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 305, + 153, + 545, + 177 + ], + "type": "text", + "content": "Note that the supervised loss is the same as defined in FCOS, our designs only modify the unsupervised part." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 188, + 388, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 388, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 388, + 201 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 208, + 545, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 208, + 545, + 279 + ], + "spans": [ + { + "bbox": [ + 304, + 208, + 545, + 279 + ], + "type": "text", + "content": "We conduct experiments on DOTA-v1.5, which is proposed at DOAI-2019†. It contains 2806 large aerial images and 402,089 annotated oriented objects. It includes three subsets: DOTA-v1.5-train, DOTA-v1.5-val and DOTA-v1.5-test, containing 1411, 458, and 937 images, respectively. The annotations of DOTA-v1.5-test is not released." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 280, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 545, + 387 + ], + "type": "text", + "content": "There are 16 categories in this dataset: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), Helicopter (HC) and Container crane (CC). Compared with DOTA-v1.0 [40], a previous version, DOTA-v1.5 contains more small instances (less than 10 pixels), which makes it more challenging." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 434 + ], + "type": "text", + "content": "Following conventions in SSOD, we consider two protocols, Partially Labeled Data and Fully Labeled Data, to validate the performance of a method on limited and abundant labeled data, respectively." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "text", + "content": "Partially Labeled Data. We randomly sample " + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 435, + 545, + 494 + ], + "type": "text", + "content": " images from DOTA-v1.5-train as labeled data and set the remaining images as unlabeled data. Following DOTA-v1.5-train's data distribution, we provide one fold for each data proportion." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 495, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 517 + ], + "type": "text", + "content": "Fully Labeled Data. We set DOTA-v1.5-train as labeled data and DOTA-v1.5-test as unlabeled data." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 519, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 555 + ], + "type": "text", + "content": "For all experiments, we perform evaluation on DOTAv1.5-val and report the performance with the standard mean average precision (mAP) as the evaluation metrics." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 562, + 438, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 438, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 438, + 574 + ], + "type": "text", + "content": "5.1. Implementation Details" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 580, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 677 + ], + "type": "text", + "content": "Without loss of generality, we take FCOS [37] as the representative anchor-free detector, and adopt ResNet-50 [13] with FPN [21] as the backbone for all our experiments. Following the previous works [11, 12, 40], we crop the original images into " + }, + { + "bbox": [ + 304, + 580, + 545, + 677 + ], + "type": "inline_equation", + "content": "1024 \\times 1024" + }, + { + "bbox": [ + 304, + 580, + 545, + 677 + ], + "type": "text", + "content": " patches with a stride of 824, that is, the pixel overlap between two adjacent patches is 200. We utilize asymmetric data augmentation for unlabeled data. Specifically, we use strong augmentation for" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": "†The 1st Workshop on Detecting Objects in Aerial Images in conjunction with IEEE CVPR 2019 https://captain-whu.github.io/DOAI2019/dataset.html" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15562" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 65, + 102, + 531, + 203 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 1. Experimental results on DOTA-v1.5 under the Partially Labeled Data setting. * and † indicate our implementations with rotated-Faster-RCNN and rotated-FCOS, respectively. Experiments are conducted on 10%, 20% and 30% labeled data settings." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 65, + 102, + 531, + 203 + ], + "lines": [ + { + "bbox": [ + 65, + 102, + 531, + 203 + ], + "spans": [ + { + "bbox": [ + 65, + 102, + 531, + 203 + ], + "type": "table", + "html": "
SettingMethodPublication10%20%30%
SupervisedFaster R-CNN* [30]NeurIPS 201643.4351.3253.14
FCOS† [37]ICCV 201942.7850.1154.79
Semi-supervisedUnbiased Teacher* [24]ICLR 202144.5152.8053.33
Soft Teacher* [44]ICCV 202148.4654.8957.83
Dense Teacher† [50]ECCV 202246.9053.9357.86
SOOD† (ours)-48.6355.5859.23
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MethodPublicationmAP
Unbiased Teacher* [24]ICLR 202166.12 → 1.27 → 64.85
Soft Teacher* [44]ICCV 202166.12 → +0.28 → 66.40
Dense Teacher† [50]ECCV 202265.46 → +0.92 → 66.38
SOOD† (ours)-65.46 → +2.24 → 67.70
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The pseudo-label sampling ratio is set as 0.25 by default. Following previous SSOD works [24, 50], we use the \"burn-in\" strategy to initialize the teacher model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 536, + 132, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 132, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 132, + 548 + ], + "type": "text", + "content": "5.2. Main Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 555, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 604 + ], + "type": "text", + "content": "In this section, we compare our method with the state-of-the-art SSOD methods [3, 24, 44] on DOTA-v1.5. For a fair comparison, we re-implement these methods on oriented object detectors with the same augmentation setting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Partially Labeled Data. We evaluate our method under different labeled data proportions, and the results are shown in Tab. 1. Our SOOD achieves state-of-the-art performance under all proportions. Specifically, it obtains 48.63, 55.58, and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "59.23\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " proportions, respectively, surpassing our supervised baseline by " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "+5.85" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "+5.47" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "+4.44\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". We also surpass the state-of-the-art anchor-free method Dense Teacher [50] by " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "+1.73" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "+1.65" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "+1.37" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " under various proportions. We provide two anchor-" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 315, + 262, + 538, + 340 + ], + "blocks": [ + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 254 + ], + "type": "text", + "content": "Table 3. The effectiveness of SOOD on other methods under Fully Labeled Data setting. * means based on RetinaNet [22]. SOOD is able to generalize to other detectors and boost their performance." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 262, + 538, + 340 + ], + "lines": [ + { + "bbox": [ + 315, + 262, + 538, + 340 + ], + "spans": [ + { + "bbox": [ + 315, + 262, + 538, + 340 + ], + "type": "table", + "html": "
DetectorPublicationMethodmAP
CFA [10]CVPR 2021Supervised Ours65.75\n67.07
KLD* [48]NeurIPS 2021Supervised Ours62.21\n64.62
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On " + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "text", + "content": " proportions, our SOOD achieves higher performance than Soft Teacher, even though our baseline is weaker than Soft Teacher's. Under " + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "text", + "content": " data proportion, our SOOD surpasses Soft Teacher and Unbiased Teacher by at least " + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "inline_equation", + "content": "1.40\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 434, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 506 + ], + "type": "text", + "content": "The qualitative results of our method compared with supervised baseline and Dense Teacher [50] are shown in Fig. 3. With the help of our RAW and GC, SOOD is able to exploit more potential semantic information from the unlabeled data, helping reduce false predictions and improve the detection quality." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 509, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 664 + ], + "type": "text", + "content": "Fully Labeled Data. We also compare our SOOD with the other SSOD methods [24, 44, 50] on fully labeled data setting. Since the reported methods are based on different detectors, we report the results of the compared methods and their baseline in Tab. 2. Our SOOD surpasses previous methods by at least 1.30 points. Compared to our baseline, we obtain " + }, + { + "bbox": [ + 304, + 509, + 545, + 664 + ], + "type": "inline_equation", + "content": "+2.24\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 509, + 545, + 664 + ], + "type": "text", + "content": " improvement, which further demonstrates our method's ability to learn from unlabeled data. We notice that the performance of Unbiased Teacher [24] drops after adding unlabeled data. The reason might be that Unbiased Teacher does not apply unsupervised losses for bounding box regression, which is important for oriented object detection." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Generalization on other detectors. To further validate the effectiveness of our method, we evaluate our method on other oriented object detectors, CFA [10] and KLD [48], under the Fully Labeled Data setting. 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Some visualization examples from the DOTA-v1.5 dataset. From left to right, each column shows ground truth, results of the supervised baseline (rotated-FCOS [37]), Dense Teacher [3], and our SOOD. The green rectangles indicate predictions. The red dashed circle, solid red circle, and red arrow represent false negative, false positive, and inaccurate orientation prediction, respectively." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 197, + 335, + 295, + 423 + ], + "blocks": [ + { + "bbox": [ + 197, + 335, + 295, + 423 + ], + "lines": [ + { + "bbox": [ + 197, + 335, + 295, + 423 + ], + "spans": [ + { + "bbox": [ + 197, + 335, + 295, + 423 + ], + "type": "image", + "image_path": "29b61592d2d788ee3385bca6bcbe210a28fbdcd95b3a9865a9e3f25e25898614.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 297, + 335, + 395, + 423 + ], + "blocks": [ + { + "bbox": [ + 297, + 335, + 395, + 423 + ], + "lines": [ + { + "bbox": [ + 297, + 335, + 395, + 423 + ], + "spans": [ + { + "bbox": [ + 297, + 335, + 395, + 423 + ], + "type": "image", + "image_path": "955d2cfeb89ff0a1ca6292eb4def76e815d54f7171b35f8adee0080053f4580d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 397, + 335, + 496, + 423 + ], + "blocks": [ + { + "bbox": [ + 397, + 335, + 496, + 423 + ], + "lines": [ + { + "bbox": [ + 397, + 335, + 496, + 423 + ], + "spans": [ + { + "bbox": [ + 397, + 335, + 496, + 423 + ], + "type": "image", + "image_path": "e8501eb0cf3a43a637b66f475acf8da7aec8c12d5b58946c0610cfca28bbb962.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "type": "text", + "content": "although CFA is a strong detector, our method still results in an improvement of " + }, + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "type": "inline_equation", + "content": "+1.32\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "type": "text", + "content": " and reaches 67.07 mAP. On the KLD detector, our method brings an improvement of " + }, + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "type": "inline_equation", + "content": "+2.41\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 487, + 289, + 548 + ], + "type": "text", + "content": ". The above results validate the generalization ability of our method." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 557, + 141, + 570 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 141, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 141, + 570 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 576, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 287, + 612 + ], + "type": "text", + "content": "In this section, we conduct extensive studies to validate our key designs. Unless specified, all the ablation experiments are performed using " + }, + { + "bbox": [ + 46, + 576, + 287, + 612 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 576, + 287, + 612 + ], + "type": "text", + "content": " of labeled data." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "The effect of each component. We study the effects of the proposed two losses, Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Note that our SOOD degrades to the vanilla dense pseudolabeling framework without these two losses. As shown in Tab. 4, both losses are proved effective and complementary under all three settings: RAW and GC can each bring performance gain, and the baseline is further improved when" + } + ] + } + ], + "index": 20 + }, + { + "type": "table", + "bbox": [ + 314, + 521, + 538, + 608 + ], + "blocks": [ + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "text", + "content": "Table 4. The effects of Rotation-aware Adaptive Weighting (RAW) loss and Global Consistency (GC) loss. Experiments are conducted on " + }, + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 486, + 547, + 519 + ], + "type": "text", + "content": " labeled data settings." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 314, + 521, + 538, + 608 + ], + "lines": [ + { + "bbox": [ + 314, + 521, + 538, + 608 + ], + "spans": [ + { + "bbox": [ + 314, + 521, + 538, + 608 + ], + "type": "table", + "html": "
SettingRAWGCmAP
10%20%30%
I--47.2454.0757.74
II✓-47.8255.2158.93
III-✓47.7154.7258.70
IV✓✓48.6355.5859.23
", + "image_path": "8e7a8353766506823e8b54b6a824c404eff27331e76709bd045c4f28fc8327be.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_body" + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 547, + 694 + ], + "type": "text", + "content": "equipped with two losses. It indicates that the local constraint built by RAW and the global constraint built by GC can benefit the semi-supervised learning process, boosting the model by constructing one-to-one and many-to-many relationships between the teacher and the student." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "The influence of sampling ratio. In this part, we discuss" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15564" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 112, + 267, + 181 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": "Table 5. The effect of the sampling ratio for instance-level dense pseudo-labeling. Experiments are conducted at " + }, + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 47, + 70, + 288, + 104 + ], + "type": "text", + "content": " setting, and the method is equipped with both RAW and GC losses." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 67, + 112, + 267, + 181 + ], + "lines": [ + { + "bbox": [ + 67, + 112, + 267, + 181 + ], + "spans": [ + { + "bbox": [ + 67, + 112, + 267, + 181 + ], + "type": "table", + "html": "
SettingSample RatiomAP
I0.12548.27
II0.2548.63
III0.547.91
IV1.047.69
", + "image_path": "003bb1e8efbff53a452073a1c591d3c90dfa5f12290085f3b3526bd6a4d2a7c0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 244, + 287, + 313 + ], + "blocks": [ + { + "bbox": [ + 47, + 192, + 288, + 237 + ], + "lines": [ + { + "bbox": [ + 47, + 192, + 288, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 288, + 237 + ], + "type": "text", + "content": "Table 6. The effects of different compositions in the cost map of GC. Experiments are conducted at " + }, + { + "bbox": [ + 47, + 192, + 288, + 237 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 47, + 192, + 288, + 237 + ], + "type": "text", + "content": " setting, and the method is equipped with RAW loss. The results indicate that both distance and score are essential factors of the cost map." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 244, + 287, + 313 + ], + "lines": [ + { + "bbox": [ + 49, + 244, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 49, + 244, + 287, + 313 + ], + "type": "table", + "html": "
SettingDistanceScoremAP
I--47.82
II-✓48.10
III✓-47.94
IV✓✓48.63
", + "image_path": "48b2bc72e14efa9434519a20c7c5e36f70eecc59af4326082c3aee4682f0502c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 333, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 453 + ], + "type": "text", + "content": "the influence of the ratios in sampling pseudo-labels. The results with different sampling ratios are shown in Tab. 5. The best performance, " + }, + { + "bbox": [ + 46, + 333, + 287, + 453 + ], + "type": "inline_equation", + "content": "48.36\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 333, + 287, + 453 + ], + "type": "text", + "content": ", is achieved when the sample ratio is set to 0.25. Setting it to other values degrades the performance. We hypothesize that this value ensures a good balance between noises (e.g., false positives) and valid predictions (e.g., true positives). Increasing it will introduce more noise that harms the training process, while decreasing it leads to information loss and failure in learning the representation of objects." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "type": "text", + "content": "The effect of different compositions in cost map of GC. Here, we study the effects of the spatial distance and the score difference when constructing the cost map of optimal transport in GC loss. The results of different settings are shown in Tab. 6. We get at most " + }, + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "type": "inline_equation", + "content": "+0.28" + }, + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "type": "text", + "content": " mAP improvement when using only one of them, indicating that the information from only one side is inadequate for learning the global prior. When considering both the score difference and spatial distance, the performance gain brought by GC is further improved to " + }, + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "type": "inline_equation", + "content": "+0.81" + }, + { + "bbox": [ + 46, + 457, + 287, + 625 + ], + "type": "text", + "content": " mAP. It indicates that the information from score difference and spatial distance are complementary. With their help, RAW can effectively model the many-to-many relationship between the teacher and the student, providing an informative guide to the model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": "The effect of RAW's hyper-parameter " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": ". Here, we study the influence of the hyper-parameter " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": " in RAW. As shown in Tab. 7, we set " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": " to 1.0 and get the performance of 47.77 mAP. As " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": " increases, the performance of our method improves when " + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 630, + 287, + 715 + ], + "type": "text", + "content": " varies from 1 to 50. However, further increasing it to 100.0 slightly hurt the performance. Therefore, we set it to 50 by default. For this observation, we" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 345, + 113, + 509, + 182 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "type": "text", + "content": "Table 7. The effect of hyper-parameter " + }, + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 70, + 545, + 104 + ], + "type": "text", + "content": " in the RAW loss. 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Limitation and Discussion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 277, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 421 + ], + "type": "text", + "content": "Although our method achieves satisfactory results on semi-supervised oriented object detection, the usage of aerial objects' characteristics is limited. Apart from orientation and global layout, many other properties of aerial objects should be considered, e.g., scale variations and large aspect ratios. Apart from that, we separately consider orientation and global layout by constructing two different constraints, which can be integrated into one unified module to utilize both information simultaneously. We also find that oriented objects and even complex objects wildly appear in other tasks, such as 3D object detection and text detection, leaving much room for further exploration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 437, + 379, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 379, + 450 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 379, + 450 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 460, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 651 + ], + "type": "text", + "content": "In this paper, we have presented an effective solution for semi-supervised oriented object detection, which is important but neglected. Focusing on oriented objects' characteristics in aerial scenes, we have designed two novel losses, rotation-aware adaptive weighting (RAW) loss and global consistency (GC) loss. The former considers the importance of rotation information for oriented objects, dynamically weighting each pseudo-label-prediction pair by their rotation difference. The latter introduces the global layout concept to SSOD, measuring the global similarity between the teacher and the student in a many-to-many manner. To validate the effectiveness of our method, we have conducted extensive experiments on the DOTA-v1.5 benchmark. Compared with state-of-the-art methods, SOOD achieves consistent performance improvement on partially and fully labeled data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the National Science Fund for Distinguished Young Scholars of China (Grant No.62225603) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No.62206103)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15565" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 125 + ], + "type": "text", + "content": "[1] Martin Arjovsky, Soumith Chintala, and Léon Bottou. 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While showing impressive performance, it relies on the availability of dense input views with highly accurate camera poses, thus limiting its application in real-world scenarios. In this work, we introduce Sparse Pose Adjusting Radiance Field (SPARF), to address the challenge of novel-view synthesis given only few wide-baseline input images (as low as 3) with noisy camera poses. Our approach exploits multi-view geometry constraints in order to jointly learn the NeRF and refine the camera poses. By relying on pixel matches extracted between the input views, our multiview correspondence objective enforces the optimized scene and camera poses to converge to a global and geometrically accurate solution. Our depth consistency loss further encourages the reconstructed scene to be consistent from any viewpoint. Our approach sets a new state of the art in the sparse-view regime on multiple challenging datasets.", + "bbox": [ + 75, + 300, + 473, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 599, + 209, + 616 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Novel-view synthesis (NVS) has long been one of the most essential goals in computer vision. It refers to the task of rendering unseen viewpoints of a scene given a particular set of input images. NVS has recently gained tremendous popularity, in part due to the success of Neural Radiance Fields (NeRFs) [30]. NeRF encodes 3D scenes with a multi-layer perceptron (MLP) mapping 3D point locations to color and volume density and uses volume rendering to synthesize images. It has demonstrated remarkable abilities for high-fidelity view synthesis under two conditions: dense input views and highly accurate camera poses.", + "bbox": [ + 75, + 625, + 468, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Both these requirements however severely impede the usability of NeRFs in real-world applications. For instance, in AR/VR or autonomous driving, the input is inevitably much sparser, with only few images of any particular object or region available per scene. In such sparse-view scenario, NeRF rapidly overfits to the input views [11, 22, 32], lead", + "bbox": [ + 75, + 792, + 468, + 883 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/224da0dcb90d7d0a16ca29ced0c50e4290a8898a78ee36eaba68bbc5d104ec93.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 540, + 250, + 640, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/14e80a2451ca3145cb8def768ea9d3079562909594e5dbe5255db877d9738918.jpg", + "image_caption": [ + "Sparse input views" + ], + "image_footnote": [], + "bbox": [ + 643, + 251, + 743, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9a2850e436660ab0ef95ffb32f9a91db3a84d29638c1ef0e018aa33dadc219a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 251, + 846, + 309 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8e017f5f5c5fd2fb93175035c21faa0f00975b45dbe2cdb3cce96e8ecb6a64c3.jpg", + "image_caption": [ + "Ground-truth camera poses NeRF" + ], + "image_footnote": [], + "bbox": [ + 529, + 364, + 629, + 422 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/07d327833f34edace7a99005b188db41ce6cca6405a3610725b20e07111a8dc7.jpg", + "image_caption": [ + "Figure 1. Novel-view rendering from sparse images. We show the RGB (second row) and depth (last row) renderings from an unseen viewpoint under sparse settings (3 input views only). Even with ground-truth camera poses, NeRF [30] overfits to the training images, leading to degenerate geometry (almost constant depth). BARF [24], which can successfully handle noisy poses when dense views are available, struggles in the sparse regime. Our approach SPARF instead produces realistic novel-view renderings with accurate geometry, given only 3 input views with noisy poses." + ], + "image_footnote": [], + "bbox": [ + 529, + 425, + 630, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5f29f0f43f16e460b5b80dcf1562d6c99a9bb2732a8b954ad02aa65c4ec6a4d7.jpg", + "image_caption": [ + "Noisy camera poses" + ], + "image_footnote": [], + "bbox": [ + 674, + 330, + 699, + 348 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e9819ca4576daa9822b20b9cec7823d7d98ed41bfc137306be102287439a20de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 343, + 684, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8cc7d50bd0bc3e3c0e154a686596b95d3f35c619fcfb43b7fa7b5a0ce872b175.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 345, + 743, + 364 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c93ee580cfdadc24eeb4ceef087a0190e25fb78fde2aadb185476bb96e69c668.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 364, + 750, + 422 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba9ab2cc86ecec790d1908442c2c2b9ff81962d3b4d839a7accb38d875855348.jpg", + "image_caption": [ + "SPARF (Ours)" + ], + "image_footnote": [], + "bbox": [ + 756, + 364, + 854, + 422 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c949705b08ef3ddcb465b66daf4707232e93b12ac1f4f3d3f9895a20e67daa1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 425, + 750, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be174234a62f5c8253a138513fb01ffdda35c5a5d03ac0811cf009e9a2593491.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 425, + 856, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing to inconsistent reconstructions at best, and degenerate solutions at worst (Fig. 1 left). Moreover, the de-facto standard to estimate per-scene poses is to use an off-the-shelf Structure-from-Motion approach, such as COLMAP [37]. When provided with many input views, COLMAP can generally estimate accurate camera poses. Its performance nevertheless rapidly degrades when reducing the number of views, or increasing the baseline between the images [55].", + "bbox": [ + 496, + 626, + 893, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Multiple works focus on improving NeRF's performance in the sparse-view setting. One line of research [6,53] trains conditional neural field models on large-scale datasets. Alternative approaches instead propose various regularization on color and geometry for per-scene training [11, 19, 22, 32, 34]. Despite showing impressive results in the sparse scenario, all these approaches assume perfect camera poses as a pre-requisite. Unfortunately, estimating accurate camera poses for few wide-baseline images is challenging [55] and has spawned its own research direction [1, 7, 14-16, 28, 60],", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was conducted during an internship at Google.", + "bbox": [ + 107, + 890, + 416, + 902 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4190", + "bbox": [ + 480, + 946, + 514, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "hence making this assumption unrealistic.", + "bbox": [ + 76, + 90, + 354, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, multiple approaches attempt to reduce the dependency of NeRFs on highly accurate input camera poses. They rely on per-image training signals, such as a photometric [9, 24, 29, 48, 50] or silhouette loss [5, 23, 56], to jointly optimize the NeRF and the poses. However, in the sparse-view scenario where the 3D space is under-constrained, we observe that it is crucial to explicitly exploit the relation between the different training images and their underlying scene geometry, to enforce learning a global and geometrically accurate solution. This is not the case of previous works [5, 23, 24, 48, 50, 56], which hence fail to register the poses in the sparse regime. As shown in Fig. 1, middle for BARF [24], it leads to poor novel-view synthesis quality.", + "bbox": [ + 75, + 108, + 467, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose Sparse Pose Adjusting Radiance Field (SPARF), a joint pose-NeRF training strategy. Our approach produces realistic novel-view renderings given only few wide-baseline input images (as low as 3) with noisy camera poses (see Fig. 1 right). Crucially, it does not assume any prior on the scene or object shape. We introduce novel constraints derived from multi-view geometry [17] to drive and bound the NeRF-pose optimization. We first infer pixel correspondences relating the input views with a pre-trained matching model [43]. These pixel matches are utilized in our multi-view correspondence objective, which minimizes the re-projection error using the depth rendered by the NeRF and the current pose estimates. Through the explicit connection between the training views, the loss enforces convergence to a global and geometrically accurate pose/scene solution, consistent across all training views. We also propose the depth consistency loss to boost the rendering quality from novel viewpoints. By using the depth rendered from the training views to create pseudo-ground-truth depth for unseen viewing directions, it encourages the reconstructed scene to be consistent from any viewpoint. We extensively evaluate and compare our approach on the challenging DTU [20], LLFF [38], and Replica [39] datasets, setting a new state of the art on all three benchmarks.", + "bbox": [ + 75, + 305, + 467, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 686, + 218, + 702 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We review approaches focusing on few-shot novel view rendering as well as joint pose-NeRF refinement.", + "bbox": [ + 76, + 714, + 467, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Sparse input novel-view rendering: To circumvent the requirement of dense input views, a line of works [6,8,25,41, 46, 53] incorporates prior knowledge by pre-training conditional models of radiance fields on large posed multi-view datasets. Despite showing promising results on sparse input images, their generalization to out-of-distribution novel views remains a challenge. Multiple works [11, 19, 22, 32, 34] follow a different direction, focusing on per-scene training for few-shot novel view rendering. DietNeRF [19] compares CLIP [33] embeddings of rendered and training", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "views. InfoNeRF [22] penalizes the NeRF overfitting to limited input views with a ray entropy regularization. Similarly, Barron et al. [4] introduce a distortion loss, which encourages sparsity of the density in each ray. In RegNeRF, Niemeyer et al. [32] propose to regularize the geometry and appearance of rendered patches with a depth smoothness and normalizing flow objectives. Recently, a number of works [11, 34, 49, 54] incorporate depth priors to constraint the NeRF optimization. Notably, DS-NeRF [11] improves reconstruction accuracy by including additional sparse depth supervision. Related are also approaches that learn a signed distance function (SDF), aiming for accurate 3D reconstruction in the sparse-view scenario [26, 51]. However, all these works assume perfect poses as a prerequisite. We instead propose a novel training strategy leading to accurate geometry and novel-view renderings in the sparse regime, even when facing imperfect input poses.", + "bbox": [ + 496, + 90, + 890, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Joint NeRF and pose refinement: Several approaches attempt to reduce NeRF's reliance on highly accurate input camera poses [9,24,29,48,50]. BARF [24] and NeRF-- [48] jointly optimize the radiance field and camera parameters of initial noisy poses, relying on the photometric loss as the only training signal. SiNeRF [50] and GARF [9] propose different activation functions, easing the pose optimization. GNeRF [29] introduces a sequential training approach including a rough initial pose network that uses GAN-style training, thereby circumventing the need for initial pose estimates. SCNeRF [21] proposes a geometric loss minimizing the ray intersection re-projection error at previously extracted sparse correspondences to optimize over camera extrinsics and intrinsics. A number of works [5, 23, 52] also combine the photometric objective with a silhouette or mask loss, requiring accurate foreground segmentation, and limiting their applicability to objects. Related are also implicit SLAM systems [2, 40, 59], which progressively optimize over the geometry and camera estimates of an input RGB-D sequence. While previous works assume a dense coverage of the 3D space, Zhang et al. propose NeRS [56], which tackles the task of single object reconstruction by deforming a unit sphere over time while refining poses of few input views. However, NeRS is restricted to simple objects with a known shape prior. We instead assume access to only few wide-baseline RGB images with noisy pose estimates, without any prior on the scene or object shape.", + "bbox": [ + 496, + 353, + 890, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 777, + 637, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We first briefly introduce notation, the basics of NeRF representation, and camera operations.", + "bbox": [ + 496, + 805, + 890, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Camera pose: Let $P_{i}^{c2w} = \\left[R_{i}^{c2w}|\\mathbf{t}_{i}^{c2w}\\right] \\in SE(3)$ be the camera-to-world transform of camera $i$ , where $R_{i}^{c2w} \\in SO(3)$ and $\\mathbf{t}_{i}^{c2w} \\in \\mathbb{R}^{3}$ are the rotation and translation, respectively. We denote as $K \\in \\mathbb{R}^{3 \\times 3}$ the intrinsic matrix.", + "bbox": [ + 496, + 838, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4191", + "bbox": [ + 480, + 946, + 513, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the rest of the manuscript, we drop the superscript $^{c2w}$ . As a result, unless otherwise stated, $P = P^{c2w}$ and all 3D quantities are defined in the world coordinate system.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Camera projection: For any vector $\\mathbf{x} \\in \\mathbb{R}^l$ of dimension $l$ , $\\bar{\\mathbf{x}} \\in \\mathbb{R}^{l+1}$ corresponds to its homogeneous representation, i.e., $\\bar{\\mathbf{x}} = [\\mathbf{x}^T, 1]$ . We additionally define $\\pi$ to be the camera projection operator, which maps a 3D point in the camera coordinate frame $\\mathbf{x}^c \\in \\mathbb{R}^3$ to a pixel coordinate $\\mathbf{p} \\in \\mathbb{R}^2$ . Likewise, $\\pi^{-1}$ is defined to be the backprojection operator, which maps a pixel $\\mathbf{p}$ and depth $z$ to a 3D point $\\mathbf{x}^c$ .", + "bbox": [ + 75, + 138, + 467, + 244 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\pi \\left(\\mathbf {x} ^ {c}\\right) \\cong K \\mathbf {x} ^ {c}, \\quad \\pi^ {- 1} (\\mathbf {p}, z) = z K ^ {- 1} \\bar {\\mathbf {p}}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 255, + 468, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene representation: We adopt the NeRF [30] framework to represent the underlying 3D scene and image formation. A neural radiance field is a continuous function that maps a 3D location $\\mathbf{x} \\in \\mathbb{R}^3$ and a unit-norm ray viewing direction $\\mathbf{d} \\in \\mathbb{S}^2$ to an RGB color $\\mathbf{c} \\in [0,1]^3$ and volume density $\\sigma \\in \\mathbb{R}^+$ . It can be formulated as", + "bbox": [ + 75, + 284, + 468, + 375 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n[ \\mathbf {c}, \\sigma ] = F _ {\\theta} \\left(\\gamma_ {x} (\\mathbf {x}), \\gamma_ {d} (\\mathbf {d})\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 386, + 468, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $F$ is an MLP with parameters $\\theta$ , and $\\gamma: \\mathbb{R}^3 \\to \\mathbb{R}^{3+6L}$ is a positional encoding function with $L$ frequency bases.", + "bbox": [ + 75, + 409, + 467, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Volume rendering: Given a camera pose $P_{i}$ , each pixel coordinate $\\mathbf{p} \\in \\mathbb{R}^2$ determines a ray in the world coordinate system, whose origin is the camera center of projection $\\mathbf{o}_i = \\mathbf{t}_i$ and whose direction is defined as $\\mathbf{d}_{i,\\mathrm{p}} = R_i K_i^{-1} \\bar{\\mathbf{p}}$ . We can express a 3D point along the viewing ray associated with $\\mathbf{p}$ at depth $t$ as $\\mathbf{r}_{i,\\mathrm{p}}(t) = \\mathbf{o}_i + t \\mathbf{d}_{i,\\mathrm{p}}$ . To render the color $\\hat{\\mathbf{I}}_{i,\\mathrm{p}} \\in [0,1]^3$ at pixel $\\mathbf{p}$ , we sample $M$ discrete depth values $t_m$ along the ray within the near and far plane $[t_n, t_f]$ , and query the radiance field $F_\\theta(2)$ at the underlying 3D points. The corresponding predicted color and volume density values $\\{(\\mathbf{c}_m, \\sigma_m)\\}_{m=1}^M$ are then composited as,", + "bbox": [ + 75, + 443, + 468, + 612 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {I}} _ {i, \\mathbf {p}} = \\hat {I} (\\mathbf {p}; \\theta , P _ {i}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\mathbf {c} _ {m}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 623, + 468, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{m} = T_{m}\\left(1 - \\exp (-\\sigma_{m}\\delta_{m})\\right)$ (4)", + "bbox": [ + 133, + 667, + 468, + 684 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT _ {m} = \\exp \\left(- \\sum_ {m ^ {\\prime} = 1} ^ {m} \\sigma_ {m ^ {\\prime}} \\delta_ {m ^ {\\prime}}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 686, + 468, + 728 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$T_{m}$ denotes the accumulated transmittance along the ray from $t_n$ to $t_m$ , and $\\delta_{m} = t_{m + 1} - t_{m}$ is the distance between adjacent samples. Similarly, the approximate depth of the scene viewed from pixel $\\mathbf{p}$ is obtained as,", + "bbox": [ + 75, + 737, + 468, + 797 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {z} _ {i, \\mathrm {p}} = \\hat {z} (\\mathbf {p}; \\theta , P _ {i}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} t _ {m}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 808, + 468, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $\\hat{I}$ and $\\hat{z}$ denote the RGB and depth rendering functions. In practice, NeRF [30] trains two MLPs, a coarse network $F_{\\theta}^{c}$ and a fine network $F_{\\theta}^{f}$ , where the former is", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "used to guide sampling along the ray for the latter, thereby enabling more accurate estimation of (3)-(6).", + "bbox": [ + 498, + 90, + 888, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Photometric loss: Given a dataset of $n$ RGB images $\\mathcal{I} = \\{I_1, I_2, \\dots, I_n\\}$ of a scene associated with initial noisy poses $\\hat{\\mathcal{P}} = \\left\\{\\hat{P}_1, \\hat{P}_2, \\dots, \\hat{P}_n\\right\\}$ , previous approaches [9, 24, 48, 50] optimize the radiance field function $F_{\\theta}$ along with the camera pose estimates $\\hat{\\mathcal{P}}$ using a photometric loss as follows,", + "bbox": [ + 498, + 125, + 890, + 207 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p h o t o}} (\\theta , \\hat {\\mathcal {P}}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\sum_ {\\mathrm {p}} \\left\\| I _ {i} (\\mathbf {p}) - \\hat {I} (\\mathbf {p}; \\theta , \\hat {P} _ {i}) \\right\\| _ {2} ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 219, + 890, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While this works well with dense views, it fails in the sparse regime. We propose an approach to effectively refine the poses and train the neural field for this challenging scenario.", + "bbox": [ + 498, + 270, + 890, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 330, + 589, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This work addresses the challenge of novel view synthesis based on neural implicit representations, in the sparse-view regime. In particular, we assume access to only sparse input views with noisy camera pose estimates. The training image collection contains few images (as low as 3) and they present large viewpoint variations.", + "bbox": [ + 498, + 356, + 890, + 446 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This leads to two major challenges: (i) given only few input images, the NeRF model [30] instantly overfits to the training views without learning a meaningful 3D geometry, even with perfect input camera poses [19,22,32]. As shown in Fig. 1, this leads to degenerate novel view renderings, including for similar train/test viewing directions. The problem becomes amplified when considering noisy input camera poses. (ii) Previous pose-NeRF refinement approaches [5,9,24,48,50] were designed considering a dense coverage of the 3D space, i.e. many input views. They apply their training objectives, e.g. the photometric loss (7), on each training image independently. However, in the sparse-view regime, i.e. where the 3D space is under-constrained, such supervision is often too weak for the pose/NeRF system to converge to a globally consistent geometric solution. Failure to correctly register the training poses also leads to poor novel view rendering quality (see Fig. 1, 4).", + "bbox": [ + 496, + 446, + 890, + 703 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose SPARF, a simple, yet effective training strategy to jointly learn the scene representation and refine the initial training poses, tailored for the sparse-view scenario. As the prominent source of inspiration, we draw from well-established principles of multi-view geometry [17], which we adapt to the NeRF framework. In Sec. 4.1, we introduce our multi-view correspondence objective as the main driving signal for the joint pose-NeRF training. By relying on pixel correspondences between the training views, the loss enforces convergence to a global and accurate geometric solution consistent across all training views, thereby solving both challenges (i) and (ii). Moreover, in Sec. 4.2 we propose an additional term, i.e. the depth consistency loss,", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4192", + "bbox": [ + 480, + 946, + 514, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2b67d87eadaa314ce304ba9e93e3ed223d1d95982d7a83d85bc5a50ade5c73c5.jpg", + "image_caption": [ + "Figure 2. Our approach SPARF for joint pose-NeRF training given only few input images with noisy camera pose estimates. We first rely on a pre-trained dense correspondence network [43] to extract matches between the training views. Our multi-view correspondence loss (Sec. 4.1) minimizes the re-projection error between matches, i.e. it enforces each pixel of a particular training view to project to its matching pixel in another training view. We use the rendered NeRF depth (6) and the current pose estimates $\\hat{\\mathcal{P}}$ to backproject each pixel in 3D space. This constraint hence encourages the learned scene and pose estimates to converge to a global and accurate geometric solution, consistent across all training views. Our depth consistency loss (Sec. 4.2) further uses the rendered depths from the training viewpoints to create pseudo-depth supervision for unseen viewpoints, thereby encouraging the reconstructed scene to be consistent from any direction." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 880, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which encourages the learned scene geometry to be consistent across all viewpoints, including those for which no RGB supervision is available. In doing so, it boosts novel-view rendering quality, further tackling the overfitting problem (i). We present our final training strategy in Sec. 4.3 and visualize our approach in Fig. 2.", + "bbox": [ + 75, + 430, + 470, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Multi-View Correspondence Loss", + "text_level": 1, + "bbox": [ + 76, + 535, + 370, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Directly overfitting on the training images leads to a corrupted neural radiance field collapsing towards the provided views, even when assuming perfect camera poses [11, 19, 32]. With noisy input poses, the problem becomes amplified, making it impossible to use the photometric loss (7) as the main signal for the joint pose-NeRF training. We propose a training objective, the multi-view correspondence loss, to enforce learning a globally consistent 3D solution over the optimized scene geometry and camera poses.", + "bbox": [ + 75, + 560, + 468, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multi-view geometry constraint: We draw inspiration from principles of multi-view geometry [17]. We assume that given an image pair $(I_i, I_j)$ , we can obtain pairs of matching pixels $\\mathbf{p} \\in I_i$ and $\\mathbf{q} \\in I_j$ . We then compute estimates of the depth at both pixels $\\hat{z}_{i,\\mathfrak{p}} = \\hat{z}(\\mathbf{p}; \\theta, \\hat{P}_i)$ and $\\hat{z}_{j,\\mathfrak{q}} = \\hat{z}(\\mathbf{q}; \\theta, \\hat{P}_j)$ according to eq. (6). Principles of multiview geometry dictate that both pixels must backproject to the same 3D point in the world coordinate system. This is formulated as $\\hat{P}_j \\pi^{-1}(\\mathbf{q}, \\hat{z}_{j,\\mathfrak{q}}) = \\hat{P}_i \\pi^{-1}(\\mathbf{p}, \\hat{z}_{i,\\mathfrak{p}})$ . However, when translating this constraint into a training objective, the magnitude of the loss is subject to large variations depending on the scene scale and the initial camera poses, requiring a tedious tuning of the loss weighting.", + "bbox": [ + 75, + 700, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training objective: We instead project the 3D points back to image space, therefore minimizing the distance between pixels rather than directly in 3D space. We illustrate this objective in Fig. 2 (steps 1-2). For a randomly sampled training image pair $(I_i, I_j)$ , our multi-view correspondence objective is formulated as $\\mathcal{L}_{\\mathrm{MVCorr}}(\\theta, \\hat{\\mathcal{P}}) = \\sum_{\\mathrm{p} \\in \\mathcal{V}} \\mathcal{L}_{\\mathrm{p}}$ , where", + "bbox": [ + 496, + 430, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p}} = w _ {\\mathrm {p}} \\rho \\left(\\mathbf {q} - \\pi \\left(\\hat {P} _ {j} ^ {- 1} \\hat {P} _ {i} \\quad \\pi^ {- 1} (\\mathbf {p}, \\hat {z} (\\mathbf {p}; \\theta , \\hat {P} _ {i}))\\right)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 532, + 890, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $\\rho$ denotes the Huber loss function [18] and $w_{\\mathfrak{p}} \\in [0,1]$ is the confidence associated with the correspondence $(\\mathbf{p}, \\mathbf{q})$ , which we obtain as detailed below. We additionally define the set $\\mathcal{V} = \\{\\mathbf{p}: w_{\\mathfrak{p}} \\geq \\kappa\\}$ , where $\\kappa = 0.95$ . The homogenization operations were omitted for clarity.", + "bbox": [ + 496, + 564, + 890, + 640 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our loss serves two purposes. By connecting the training images through correspondences, our multi-view correspondence objective enforces the learned geometry and camera poses to converge to a solution geometrically consistent across all training images. This is unlike the photometric loss (7) which applies supervision on each training image independently. Moreover, the underlying constraint is only satisfied if the learned 3D points converge to the true reconstructed scene (up to a similarity). As such, the objective (8) provides direct supervision on the rendered depth (6), implicitly enforcing it to be close to the surface.", + "bbox": [ + 496, + 641, + 892, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Correspondence prediction: Any classical [27, 35] or learned [13,36,42,44,45] matching approach could be used to obtain the matches relating pairs of training views. We rely on a pre-trained dense correspondence regression network, in particular PDC-Net [43]. It predicts a match $\\mathbf{q}$ for each pixel $\\mathbf{p}$ , along with a confidence $w_{\\mathrm{p}}$ . We found", + "bbox": [ + 496, + 810, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4193", + "bbox": [ + 480, + 946, + 514, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the high number of accurate matches to be beneficial for our joint pose-NeRF refinement. Similar conclusions were derived in the context of dense versus sparse depth supervision [11,34]. The dense correspondence map also implicitly imposes a smoothness prior to the rendered depth. In suppl., we present results using a sparse matcher [12, 36] instead.", + "bbox": [ + 75, + 90, + 470, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Improving Geometry at Unobserved Views", + "text_level": 1, + "bbox": [ + 76, + 188, + 441, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The multi-view correspondence loss favors a global and geometrically accurate solution, consistent across all training images. Nevertheless, the reconstructed scene often still suffers from inconsistencies when seen from novel viewpoints. For those, no RGB supervision is available during training. We propose an additional training objective, the depth consistency loss, which encourages the learned geometry to be consistent from any viewing direction.", + "bbox": [ + 75, + 212, + 468, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Depth consistency loss: The main idea is to use the depth maps rendered from the training viewpoints to create pseudo-depth supervision for novel, unseen, viewpoints (Fig. 2, step 3). We sample a virtual pose $P_{un}$ , in practice obtained as an interpolation between the poses of two close-by training views. For a pixel $\\mathbf{p}$ in a sampled training image $I_i$ , $\\mathbf{r_p}^{un} = P_{un}^{-1}\\hat{P}_i\\pi^{-1}(\\mathbf{p},\\hat{z} (\\mathbf{p};\\theta ,\\hat{P}_i))$ is the corresponding 3D point in the coordinate system of the unseen view $P_{un}$ . $\\mathbf{y}\\in \\mathbb{R}^2$ denotes its pixel projection in view $P_{un}$ as $\\mathbf{y} = \\pi \\left(\\mathbf{r}_{\\mathrm{p}}^{un}\\right)$ , and $z_{\\mathrm{y}}$ is its projected depth in $P_{un}$ , i.e. $z_{\\mathrm{y}} = \\left[\\mathbf{r}_{\\mathrm{p}}^{un}\\right]_3$ , where $[\\cdot ]_3$ refers to taking the third coordinate of the vector. We formulate our depth consistency loss as,", + "bbox": [ + 75, + 335, + 468, + 520 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D C o n s}} (\\theta) = \\sum_ {\\mathrm {p}} \\gamma_ {\\mathrm {y}} \\rho \\left(z _ {\\mathrm {y}} - \\hat {z} (\\mathbf {y}; \\theta , P _ {u n})\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 525, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To account for occlusion and out-of-view projections in which (9) is invalid, we have included a visibility mask $\\gamma_{\\mathrm{y}} \\in [0,1]$ . We explain its definition in the section below.", + "bbox": [ + 75, + 563, + 468, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the pseudo-depth supervision $z_{\\mathrm{y}}$ is created from renderings, it is subject to errors. For this reason, we find it important to backpropagate through the pseudo-supervision $\\mathbf{y}$ and $z_{\\mathrm{y}}$ . Note that we however do not backpropagate through the pose estimate $\\hat{P}_i$ . Moreover, as verified experimentally in Tab. 2, our depth consistency objective (9) is complementary to our multi-view correspondence loss (8), the latter enforcing an accurate reconstructed geometry while the former ensures it is consistent from any viewpoint.", + "bbox": [ + 75, + 608, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visibility mask $\\gamma_{\\mathbf{y}}$ : We first exclude points if their pixel projections $\\mathbf{y}$ is outside of the virtual view, by setting the mask as $\\gamma_{\\mathrm{y}} = 0$ . The depth consistency loss is also invalid for pixels that are occluded by the reconstructed scene in the virtual view. To identify these occluded pixels, we follow the strategy of [10]. In particular, we check whether there are occupied regions on the ray between the camera center $\\mathbf{o}_{un}$ of $P_{un}$ and the 3D point $\\mathbf{r}_{un,\\mathbf{y}}(z_{\\mathbf{y}})$ at depth $z_{\\mathbf{y}}$ . We compute how occluded a 3D point is with its transmittance (5) in the unseen view, as $\\gamma_{\\mathrm{y}} = T_{un,z_{\\mathbf{y}}}$ . Intuitively, $\\gamma_{\\mathrm{y}}$", + "bbox": [ + 75, + 750, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is close to 1 if there is no point with a large density between the camera center $\\mathbf{o}_{un}$ and $\\mathbf{r}_{un,y}(z_y)$ , otherwise it is close to 0. Next, we present our overall training framework.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Training Framework", + "text_level": 1, + "bbox": [ + 498, + 145, + 697, + 162 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Staged training: Our final training objective is formulated as $\\mathcal{L}(\\theta, \\hat{\\mathcal{P}}) = \\mathcal{L}_{\\mathrm{photo}}(\\theta, \\hat{\\mathcal{P}}) + \\lambda_{\\mathrm{c}} \\mathcal{L}_{\\mathrm{MVCorr}}(\\theta, \\hat{\\mathcal{P}}) + \\lambda_{\\mathrm{d}} \\mathcal{L}_{\\mathrm{DCons}}(\\theta)$ , where $\\lambda_{\\mathrm{c}}$ and $\\lambda_{\\mathrm{d}}$ are predefined weighting factors. The training is split into two stages. In the first part, the pose estimates are trained jointly with the coarse MLP $F_{\\theta}^{c}$ . However, due to the exploration of the pose space at the early stages of training, the learned scene tends to showcase blurry surfaces. As a result, in the second training stage, we freeze the pose estimates and train both the coarse and fine networks $F_{\\theta}^{c}$ and $F_{\\theta}^{f}$ . This ensures that the fine network learns a sharp geometry, benefiting from the pre-trained coarse network. From a practical perspective, our training objectives can be integrated at a low computational cost, since the RGB or depth pixel renderings (3)-(6) can be shared between the three loss terms.", + "bbox": [ + 496, + 172, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Coarse-to-fine positional encoding: In BARF [24], Lin et al. propose to gradually activate the high-frequency components of the positional encodings (2) over the course of the optimization. We refer the reader to [24] for the exact formulation. While originally proposed in the context of pose refinement, we found that this strategy is also extremely beneficial in the sparse-view setting, even when the poses are fixed. It prevents the network from immediately overfitting to the training images, thereby avoiding the worst degenerate geometries. We therefore adopt this coarse-to-fine positional encoding approach as default.", + "bbox": [ + 496, + 402, + 892, + 569 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental Results", + "text_level": 1, + "bbox": [ + 498, + 582, + 705, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the proposed SPARF for novel-view rendering in the few-view setting, in particular when only three input views are available. Results with different numbers of views are provided in suppl. We extensively analyze our method and compare it to earlier approaches, setting a new state of the art on multiple datasets. Further results, visualizations, and implementation details are provided in suppl.", + "bbox": [ + 496, + 607, + 890, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 498, + 722, + 705, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and metrics: We report results on the DTU [20], LLFF [38] and Replica [39] datasets, for the challenging scenario of 3 input views. DTU is composed of complex object-level scenes with wide-baseline views spanning a half hemisphere. We adhere to the protocol of [53] and evaluate on their reported test split of 15 scenes. Following [32], we additionally evaluate all methods with the object masks applied to the rendered images, to avoid penalizing methods for incorrect background predictions. On LLFF, we follow community standards [30] and use every $8^{\\text{th}}$ image as", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4194", + "bbox": [ + 480, + 946, + 514, + 957 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/be61cba45dacaa5a323e69d8eb1b4eb6352172fe376faa32b28e92ca19abb372.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Comparison of different positional encoding strategies applied to NeRF [30] on DTU (3 views), using ground-truth poses. Results in $(\\cdot)$ are computed by masking the background." + ], + "table_body": "
MethodPSNR ↑SSIM ↑LPIPS ↓DE ↓
I Full PE [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)0.87
II Smaller MLP model9.03 (10.06)0.34 (0.65)0.68 (0.34)0.79
III No PE16.11 (18.40)0.68 (0.80)0.37 (0.24)0.30
IV CF PE [24] (Sec. 4.3)16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
", + "bbox": [ + 80, + 88, + 478, + 157 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the test set. We sample the training views evenly from the remaining images. For the Replica dataset, which depicts videos of room-scale indoor scenes, we subsample every $k^{th}$ frame, from which we randomly select a triplet of consecutive training images. As metrics, we report the average rotation and translation errors for pose registration, and PSNR, SSIM [47] and LPIPS [57] for view synthesis. On the DTU and Replica datasets, we additionally compare the rendered depth with the available ground-truth depth and compute the mean depth absolute error (DE).", + "bbox": [ + 75, + 215, + 468, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details: We train our approach for 100K iterations, which takes about 10 hours on a single A100 GPU. As pose parametrization, we adopt the continuous 6-vector representation [58] for the rotation and directly optimize the translation vector. We provide all training hyperparameters in the supplementary.", + "bbox": [ + 75, + 369, + 468, + 460 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Method Analysis", + "text_level": 1, + "bbox": [ + 76, + 469, + 243, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first perform a comprehensive analysis of our approach, on DTU [20], considering only 3 input views.", + "bbox": [ + 75, + 493, + 468, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Impact of positional encoding: Training on sparse input views using the standard NeRF [30] immediately overfits to the provided images, even with perfect poses. We noticed that the overfitting is largely due to the high-frequency positional encodings (PE), and thus experimented with different PE strategies. We present the results in Tab. 1. The standard NeRF (I) with high-frequency PE [30] leads to degenerate geometry and novel view renderings. In (II), using a simplified MLP makes little difference. While training without PE (III) largely prevents overfitting, the coarse-to-fine PE strategy [24] leads to the best result, as shown in (IV).", + "bbox": [ + 75, + 526, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablation study: In Tab. 2, we ablate the key components of our approach, here assuming fixed ground-truth poses and starting from NeRF with coarse-to-fine PE. Adding our multi-view correspondence loss (8) results in drastically better performance on all metrics. Including our depth", + "bbox": [ + 75, + 696, + 468, + 772 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e4598275caf3fcad2531e1bd3f8b203be70d45e41fb32552988005564101c6d8.jpg", + "table_caption": [], + "table_footnote": [ + "Table 2. Ablation study on the DTU dataset (3 views), with fixed ground-truth poses. Results in $(\\cdot)$ are computed by masking the background. All networks use the coarse-to-fine PE [24]." + ], + "table_body": "
MV-Corr (8)DCons (9)PSNR ↑SSIM ↑LPIPS ↓DE ↓
XX16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
X✓15.86 (18.91)0.71 (0.82)0.28 (0.14)0.20
✓X18.13 (20.81)0.77 (0.87)0.22 (0.10)0.10
✓✓18.30 (21.01)0.78 (0.87)0.21 (0.10)0.08
", + "bbox": [ + 81, + 784, + 470, + 849 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c9c1ec2eb336316dc44525589cd2468dfb2cd09acfdba68e0f2f52f149d4987c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 87, + 741, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a901ab2a76cfd7b8c914afe414e06be6c47655f3002061cdb70c67d2344d9395.jpg", + "image_caption": [ + "Figure 3. We compare two training objectives using ground-truth depth for pose-NeRF training in the sparse-view regime. In (A), a loss comparing for each training image the rendered depth (6) with the ground truth one, can learn locally perfect geometry (as highlighted by the dashed red rectangles). However, the NeRF/poses do not converge to a global solution, because the optimized poses and geometry of the different images are disjoint. Instead, supervising the learned 3D points of each training image to be equal to the ground-truth 3D points in (B) solves this issue, by enforcing the system to converge to a global (unique) geometric solution." + ], + "image_footnote": [], + "bbox": [ + 741, + 92, + 890, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "consistency module (9) further leads to a small improvement, achieving the best performance overall. Also note that our depth-consistency module (9) works best in collaboration with our multi-view correspondences loss (8) since the latter is needed to learn an accurate geometry.", + "bbox": [ + 496, + 409, + 890, + 486 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Intuition on pose-NeRF training losses: We first want to build an intuition on what loss might be suitable for joint pose-NeRF training in the sparse regime. To do so, we use ground-truth depth or 3D data in two alternative training losses, which we compare here. We illustrate this experiment in Fig. 3 and present results in Tab. 3, top part. As in previous work [24], for each scene of DTU [20], we synthetically perturb the ground-truth camera poses with $15\\%$ of additive gaussian noise. In (I), we train with an L1 loss comparing the rendered depth (6) with the ground-truth depth (Fig. 3A). Surprisingly, this loss struggles to refine the poses. Instead, in (II) we minimize the distance between the learned 3D points (rendered depth (6) backprojected to world frame) and the ground-truth 3D points, as illustrated in Fig. 3B. This training loss successfully registers the poses, resulting in drastically better novel-view rendering quality. As the main insight from this experiment, we hypothesize that, in the sparse-view regime, it is crucial to enforce an explicit geometric connection between the different training images and their underlying scene geometry. This is not the case in (I), where the depth loss favors per-image locally accurate geometry, but the NeRF/poses can converge to disconnected solutions for each training image.", + "bbox": [ + 496, + 489, + 892, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison of losses for pose-NeRF training: In Tab. 3 bottom part, we then compare our loss (8) to objectives commonly used for joint pose-NeRF training. The photometric loss (7) (III), even associated with a mask/silhouette", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4195", + "bbox": [ + 480, + 946, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ba8609afddf01c8336c00d91a075ac51915ce8307a45706e314afbea8ecd029f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LossesRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
I Photo. + L1 GT depth7.328.913.8 (14.0)0.54 (0.70)0.46 (0.27)0.17
II Photo. + L1 GT 3D points0.41.518.8 (20.3)0.75 (0.84)0.21 (0.11)0.07
III Photo. (7)10.351.510.7 (9.8)0.43 (0.62)0.59 (0.36)1.9
IV Photo. + mask loss [23,56]13.257.7----
V MVCorr (8)1.986.6---0.19
VI Photo. + MVCorr ((7)-(8))1.855.516.0 (17.8)0.68 (0.81)0.28 (0.14)0.13
", + "bbox": [ + 80, + 88, + 478, + 170 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "loss [5,23,56] in (IV), completely fails to register the poses, thus leading to poor novel-view synthesis performance. This is in line with our hypothesis that it is important to explicitly exploit the geometric relation between the training views for successful registration. Moreover, because the 3D space is under-constrained in the sparse-view regime, multiple neighboring poses can lead to similar mask losses. While our multi-view correspondence loss (8) alone (V) already drastically outperforms the photometric loss (III) in terms of pose and learned geometry (depth error), combining the two in (VI) leads to the best performance. This is because, through the correspondences, our approach favors a NeRF/pose solution consistent across all training images. Note that this version neither includes our depth consistency loss (9) (Sec. 4.2) nor our staged training (Sec. 4.3).", + "bbox": [ + 75, + 241, + 473, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparison to SOTA with Noisy Poses", + "text_level": 1, + "bbox": [ + 76, + 478, + 411, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Here, we evaluate SPARF, our joint pose and NeRF training approach. Results with different pose initialization schemes are presented in the supplementary.", + "bbox": [ + 75, + 501, + 468, + 547 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines: We compare to BARF [24], the state-of-the-art in pose-NeRF refinement when assuming dense input views. It is representative of a line of approaches [9, 24, 29, 48, 50] using the photometric loss (7) as the main signal. We also experiment with adding the depth regularization loss of [32] or the ray sparsity loss of [4] to BARF, which we denote as RegBARF and DistBARF respectively. We additionally compare to SCNeRF [21], which uses a geometric loss based on correspondences, minimizing the rays' intersection re-projection error. For a fair comparison, we integrate coarse-to-fine PE [24] (Sec. 4.3) in all methods.", + "bbox": [ + 75, + 549, + 468, + 717 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on DTU: Following [9, 24, 50], for each scene, we synthetically perturb the ground-truth camera poses with $15\\%$ of additive gaussian noise. The initial poses thus have", + "bbox": [ + 76, + 719, + 468, + 766 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ff61a0e371fc23e05f8d064f87f39d249ac6a31f4605991a3eaa2b07d15c9b51.jpg", + "table_caption": [ + "Table 3. Comparison of training objectives for joint pose-NeRF refinement on DTU [20] with initial noisy poses (3 views). Rotation errors are in degree and translation errors are multiplied by 100. Results in $(\\cdot)$ are computed by masking the background." + ], + "table_footnote": [], + "table_body": "
MethodRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
BARF [24]10.3351.510.71 (9.76)0.43 (0.62)0.59 (0.36)1.90
RegBARF [24, 32]11.2052.810.38 (9.20)0.45 (0.62)0.61 (0.38)2.33
DistBARF [4, 24]11.6955.79.50 (9.15)0.34 (0.76)0.67 (0.36)1.90
SCNeRF [21]3.4416.412.04 (11.71)0.45 (0.66)0.52 (0.30)0.85
SPARF (Ours)1.815.017.74 (18.92)0.71 (0.83)0.26 (0.13)0.12
", + "bbox": [ + 81, + 779, + 465, + 851 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Evaluation on DTU [20] (3 views) with noisy initial poses. Rotation errors are in $^\\circ$ and translation errors are multiplied by 100. Results in $(\\cdot)$ are computed by masking the background.", + "bbox": [ + 75, + 854, + 468, + 897 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f2778eae166540be155231eb9fcd908fbac9fcec6a712672fccf7409a8755fc7.jpg", + "image_caption": [ + "Figure 4. Novel-view rendering (RGB and depth). The input (not shown here) contains 3 images with initial noisy camera poses." + ], + "image_footnote": [], + "bbox": [ + 504, + 85, + 893, + 404 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "an average rotation and translation error of $15^{\\circ}$ and 70 respectively. We show initial and optimized poses in Fig. 5. From the results in Tab. 4 and Fig. 4A, we observe that BARF, RegBARF, and DistBARF completely fail to register the poses, leading to poor view-synthesis quality. SCNeRF's geometric loss performs better at registering the poses but the learned scene still suffers from many inconsistencies. This is because SCNeRF's loss [21] does not influence the learned radiance field function, and thus, cannot prevent the NeRF model from overfitting to the sparse input views. Since our multi-view correspondence loss (8) acts on both the camera pose estimates and the learned neural field by enforcing them to fit the correspondence constraint, it leads to an accurate reconstructed scene. Our approach SPARF hence significantly outperforms all others both in novel-view rendering quality and pose registration.", + "bbox": [ + 496, + 450, + 892, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on LLFF: The LLFF dataset consists of 8 complex forward-facing scenes. Following [24], we initialize all camera poses with the identity transformation and present results in Tab. 5. In [24], Lin et al. show that BARF almost perfectly registers the camera poses given dense input views. However, we show here that it strug", + "bbox": [ + 496, + 696, + 893, + 787 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/617619e6b033ad0ed5bd1b64120c02259088f5567e951c11022fcb18a44ca4a2.jpg", + "image_caption": [ + "Figure 5. Optimized poses on DTU with 3 input views. We compare the ground-truth poses (in pink) with the optimized ones (in blue). In the first column, the initial noisy poses are in blue." + ], + "image_footnote": [], + "bbox": [ + 500, + 800, + 893, + 852 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4196", + "bbox": [ + 482, + 946, + 514, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/50dc9588e9632b964d94f56afa4014c772e408bee3767ffb7df0c8692fcce2d9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Rot. (°) ↓Trans. (×100) ↓PSNR ↑SSIM ↑LPIPS ↓
BARF [24]2.0411.617.470.480.37
RegBARF [24, 32]1.525.018.570.520.36
DistBARF [4, 24]5.5926.514.690.340.49
SCNeRF [21]1.9311.417.100.450.40
SPARF (Ours)0.532.819.580.610.31
", + "bbox": [ + 78, + 88, + 464, + 164 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e7ccc6a1ed20f884e223a45d340030f61a73975ef9a4a28c2067d38ea2a64040.jpg", + "table_caption": [ + "Table 5. Evaluation on the forward-facing dataset LLFF [38] (3 views) starting from initial identity poses." + ], + "table_footnote": [], + "table_body": "
MethodRot (°) ↓Trans (×100) ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
G SPARF (Ours)Fixed GT poses26.430.880.130.39
F NeRF [30]Fixed poses obtained20.990.730.321.33
DS-NeRF [11]from COLMAP (run w.23.520.810.200.99
SPARF (Ours)PDC-Net [43] matches25.030.840.150.66
R BARF [24]3.3516.9620.730.720.300.84
RegBARF [24, 32]3.6620.8720.000.700.321.00
DistBARF [4, 24]2.367.7322.460.770.230.47
SCNeRF [21]0.654.1222.540.790.240.73
DS-NeRF [11]1.305.0424.750.830.200.69
SPARF (Ours)0.150.7626.980.880.130.36
", + "bbox": [ + 78, + 210, + 470, + 340 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "gles in the sparse-view setting, thereby severely impacting the accuracy of novel view synthesis. While adding the depth smoothness loss (RegBARF) improves results, our approach SPARF outperforms all previous works. A qualitative comparison is shown in Fig. 4B.", + "bbox": [ + 75, + 453, + 468, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results on Replica: To demonstrate that our approach is also applicable to non-forward-facing indoor scenes, we evaluate on the Replica dataset in Tab. 6 and Fig. 4C. As pose initialization, we use COLMAP [37] with improved matches, i.e. using PDC-Net [43]. The initial pose estimates thus have an average rotation and translation error of respectively $0.39^{\\circ}$ and 3.01. Comparing the top (G) and middle part (F) of Tab. 6, we show that even such a low initial error impacts the novel-view rendering quality when using fixed poses. In the bottom part (R), our pose-NeRF training strategy leads to the best results, matching the accuracy obtained by our approach with perfect poses (top row, G).", + "bbox": [ + 75, + 532, + 468, + 714 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Comparison to SOTA with Ground-Truth Poses", + "text_level": 1, + "bbox": [ + 76, + 722, + 468, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we show that our approach brings significant improvement in novel view rendering quality even when considering fixed ground-truth poses.", + "bbox": [ + 75, + 744, + 468, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Baselines: We compare to works specifically designed to tackle per-scene few-shot novel view rendering, namely DietNeRF [19], DS-NeRF [11], InfoNeRF [22] and RegNeRF [32], along with the standard NeRF [30] and MipNeRF [3]. For completeness, we also compare against a state-of-the-art conditional model, PixelNeRF [53], trained on DTU [20] and further finetuned per-scene on LLFF [38].", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c4866e03451d2f8f944ea844b1a1b6078180681217a4220f0d26a47d8ff2d11d.jpg", + "table_caption": [ + "Table 6. Evaluation on Replica [39] (3 views) with initial poses obtained by COLMAP [37, 43]. The initial rotation and translation errors are $0.39^{\\circ}$ and 3.01 respectively. In the middle part (F), these initial poses are fixed and used as \"pseudo-gt\". In the bottom part (R), the poses are refined along with training the NeRF. For comparison, in the top part (G), we use fixed ground-truth poses. The best and second-best results are in red and blue respectively." + ], + "table_footnote": [], + "table_body": "
MethodDTULLFF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [53]19.36 (18.00)0.70 (0.77)0.32 (0.23)7.930.270.68
PixelNeRF-ft [53]---16.170.440.51
MipNeRF [3]7.64 (8.68)0.23 (0.57)0.66 (0.35)14.620.350.50
NeRF [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)13.610.280.56
DietNeRF [19]10.01 (11.85)0.35 (0.63)0.57 (0.31)14.940.370.5
InfoNeRF [22]11.23 (-)0.44 (-)0.54 (-)---
RegNeRF [32]15.33 (18.89)0.62 (0.75)0.34 (0.19)19.080.590.34
DS-NeRF [11]16.52 (-)0.54 (-)0.48 (-)18.000.550.27
SPARF (Ours)18.30 (21.01)0.78 (0.87)0.21 (0.10)20.200.630.24
", + "bbox": [ + 503, + 89, + 893, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Evaluation on DTU [20] and LLFF [38] (3 views), with fixed ground-truth poses. Results in $(\\cdot)$ are computed by masking the background. Results of [3, 19, 32] are taken from [32]. The best and second-best results are in red and blue respectively.", + "bbox": [ + 498, + 220, + 890, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results: We present results on DTU and LLFF in Tab. 7. Compared to previous per-scene approaches [19,22,32] that only apply different regularization to the learned scene, our multi-view correspondence loss (8) provides a strong supervision on the rendered depth, implicitly encouraging it to be close to the true surface. Our depth consistency objective (9) further boosts the performance, by directly enforcing the learned scene to be consistent from any viewpoint. As a result, our approach SPARF performs best compared to all baselines on both datasets and for all metrics. The only exception is PSNR on the whole image compared to conditional model PixelNeRF [53]. This is because DTU has black backgrounds, where a wrong color prediction (like in Fig. 4A for SPARF) has a large impact on the PSNR value. For conditional models which rely on feature projections, it is easier to predict a correct background color. However, most real-world applications are more interested in accurately reconstructing the object of interest than the background. When evaluated only in the object region, our SPARF obtains 3.24dB higher PSNR than PixelNeRF.", + "bbox": [ + 496, + 289, + 890, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 604, + 617, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose SPARF, a joint pose-NeRF training strategy capable of producing realistic novel-view renderings given few wide-baseline input images with noisy camera pose estimates. By integrating two novel objectives inspired by multi-view geometry principles, we set a new state of the art on three challenging datasets.", + "bbox": [ + 496, + 630, + 890, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work: Our approach is only applicable to input image collections where each image has covisible regions with at least one other. Moreover, the performance of our method depends on the quality of the matching network. Filtering strategies or per-scene online refinement of the correspondence network thus appear as promising future directions. An interesting direction is also to refine the camera intrinsics and distortion parameters along with the extrinsics. Finally, using voxel grids to encode the radiance field [31] instead of an MLP could lead to faster convergence, and potentially even better results.", + "bbox": [ + 496, + 724, + 890, + 890 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4197", + "bbox": [ + 480, + 946, + 514, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Wei Wang 0108, Zheng Dang, Yinlin Hu, Pascal Fua, and Mathieu Salzmann. Backpropagation-friendly eigendecomposition. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d'Alché Buc, Edward A. 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In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, virtual, June 19-25, 2021, pages 32-42, 2021." + ], + "bbox": [ + 503, + 92, + 890, + 472 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4200", + "bbox": [ + 482, + 946, + 514, + 957 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SPARF_ Neural Radiance Fields From Sparse and Noisy Poses/9768904d-8df6-48f0-a9ea-13cb333d26ef_model.json b/2023/SPARF_ Neural Radiance Fields From Sparse and Noisy Poses/9768904d-8df6-48f0-a9ea-13cb333d26ef_model.json new file mode 100644 index 0000000000000000000000000000000000000000..43de01f858a34cf508a1b67e30ae33f2295c02ea --- /dev/null +++ b/2023/SPARF_ Neural Radiance Fields From Sparse and Noisy Poses/9768904d-8df6-48f0-a9ea-13cb333d26ef_model.json @@ -0,0 +1,2411 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.131, + 0.797, + 0.154 + ], + "angle": 0, + "content": "SPARF: Neural Radiance Fields from Sparse and Noisy Poses" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.18, + 0.868, + 0.217 + ], + "angle": 0, + "content": "Prune Truong\\(^{1,2*}\\) Marie-Julie Rakotosaona\\(^{2}\\) Fabian Manhardt\\(^{2}\\) Federico Tombari\\(^{2,3}\\) ETH Zurich \\({}^{2}\\)Google \\({}^{3}\\)Technical University of Munich" + }, + { + "type": "text", + "bbox": [ + 0.114, + 0.22, + 0.855, + 0.234 + ], + "angle": 0, + "content": "prune.truong@vision.ee.ethz.ch {mrukotosaona, fabianmanhardt, tombari}@google.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.573 + ], + "angle": 0, + "content": "Neural Radiance Field (NeRF) has recently emerged as a powerful representation to synthesize photorealistic novel views. While showing impressive performance, it relies on the availability of dense input views with highly accurate camera poses, thus limiting its application in real-world scenarios. In this work, we introduce Sparse Pose Adjusting Radiance Field (SPARF), to address the challenge of novel-view synthesis given only few wide-baseline input images (as low as 3) with noisy camera poses. Our approach exploits multi-view geometry constraints in order to jointly learn the NeRF and refine the camera poses. By relying on pixel matches extracted between the input views, our multiview correspondence objective enforces the optimized scene and camera poses to converge to a global and geometrically accurate solution. Our depth consistency loss further encourages the reconstructed scene to be consistent from any viewpoint. Our approach sets a new state of the art in the sparse-view regime on multiple challenging datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.601, + 0.21, + 0.617 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Novel-view synthesis (NVS) has long been one of the most essential goals in computer vision. It refers to the task of rendering unseen viewpoints of a scene given a particular set of input images. NVS has recently gained tremendous popularity, in part due to the success of Neural Radiance Fields (NeRFs) [30]. NeRF encodes 3D scenes with a multi-layer perceptron (MLP) mapping 3D point locations to color and volume density and uses volume rendering to synthesize images. It has demonstrated remarkable abilities for high-fidelity view synthesis under two conditions: dense input views and highly accurate camera poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Both these requirements however severely impede the usability of NeRFs in real-world applications. For instance, in AR/VR or autonomous driving, the input is inevitably much sparser, with only few images of any particular object or region available per scene. In such sparse-view scenario, NeRF rapidly overfits to the input views [11, 22, 32], lead" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.251, + 0.642, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.645, + 0.252, + 0.744, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.748, + 0.252, + 0.848, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.646, + 0.31, + 0.744, + 0.319 + ], + "angle": 0, + "content": "Sparse input views" + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.326, + 0.617, + 0.366 + ], + "angle": 0, + "content": "Ground-truth camera poses NeRF" + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.366, + 0.63, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.531, + 0.426, + 0.631, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.676, + 0.331, + 0.7, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.704, + 0.334, + 0.805, + 0.344 + ], + "angle": 0, + "content": "Noisy camera poses" + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.344, + 0.685, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.346, + 0.744, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.777, + 0.358, + 0.84, + 0.366 + ], + "angle": 0, + "content": "SPARF (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.366, + 0.751, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.366, + 0.856, + 0.423 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.653, + 0.426, + 0.751, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.426, + 0.857, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.489, + 0.892, + 0.614 + ], + "angle": 0, + "content": "Figure 1. Novel-view rendering from sparse images. We show the RGB (second row) and depth (last row) renderings from an unseen viewpoint under sparse settings (3 input views only). Even with ground-truth camera poses, NeRF [30] overfits to the training images, leading to degenerate geometry (almost constant depth). BARF [24], which can successfully handle noisy poses when dense views are available, struggles in the sparse regime. Our approach SPARF instead produces realistic novel-view renderings with accurate geometry, given only 3 input views with noisy poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.894, + 0.748 + ], + "angle": 0, + "content": "ing to inconsistent reconstructions at best, and degenerate solutions at worst (Fig. 1 left). Moreover, the de-facto standard to estimate per-scene poses is to use an off-the-shelf Structure-from-Motion approach, such as COLMAP [37]. When provided with many input views, COLMAP can generally estimate accurate camera poses. Its performance nevertheless rapidly degrades when reducing the number of views, or increasing the baseline between the images [55]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Multiple works focus on improving NeRF's performance in the sparse-view setting. One line of research [6,53] trains conditional neural field models on large-scale datasets. Alternative approaches instead propose various regularization on color and geometry for per-scene training [11, 19, 22, 32, 34]. Despite showing impressive results in the sparse scenario, all these approaches assume perfect camera poses as a pre-requisite. Unfortunately, estimating accurate camera poses for few wide-baseline images is challenging [55] and has spawned its own research direction [1, 7, 14-16, 28, 60]," + }, + { + "type": "page_footnote", + "bbox": [ + 0.108, + 0.891, + 0.417, + 0.904 + ], + "angle": 0, + "content": "*This work was conducted during an internship at Google." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4190" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.356, + 0.106 + ], + "angle": 0, + "content": "hence making this assumption unrealistic." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.109, + 0.468, + 0.304 + ], + "angle": 0, + "content": "Recently, multiple approaches attempt to reduce the dependency of NeRFs on highly accurate input camera poses. They rely on per-image training signals, such as a photometric [9, 24, 29, 48, 50] or silhouette loss [5, 23, 56], to jointly optimize the NeRF and the poses. However, in the sparse-view scenario where the 3D space is under-constrained, we observe that it is crucial to explicitly exploit the relation between the different training images and their underlying scene geometry, to enforce learning a global and geometrically accurate solution. This is not the case of previous works [5, 23, 24, 48, 50, 56], which hence fail to register the poses in the sparse regime. As shown in Fig. 1, middle for BARF [24], it leads to poor novel-view synthesis quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.468, + 0.668 + ], + "angle": 0, + "content": "We propose Sparse Pose Adjusting Radiance Field (SPARF), a joint pose-NeRF training strategy. Our approach produces realistic novel-view renderings given only few wide-baseline input images (as low as 3) with noisy camera poses (see Fig. 1 right). Crucially, it does not assume any prior on the scene or object shape. We introduce novel constraints derived from multi-view geometry [17] to drive and bound the NeRF-pose optimization. We first infer pixel correspondences relating the input views with a pre-trained matching model [43]. These pixel matches are utilized in our multi-view correspondence objective, which minimizes the re-projection error using the depth rendered by the NeRF and the current pose estimates. Through the explicit connection between the training views, the loss enforces convergence to a global and geometrically accurate pose/scene solution, consistent across all training views. We also propose the depth consistency loss to boost the rendering quality from novel viewpoints. By using the depth rendered from the training views to create pseudo-ground-truth depth for unseen viewing directions, it encourages the reconstructed scene to be consistent from any viewpoint. We extensively evaluate and compare our approach on the challenging DTU [20], LLFF [38], and Replica [39] datasets, setting a new state of the art on all three benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.687, + 0.219, + 0.703 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.468, + 0.744 + ], + "angle": 0, + "content": "We review approaches focusing on few-shot novel view rendering as well as joint pose-NeRF refinement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Sparse input novel-view rendering: To circumvent the requirement of dense input views, a line of works [6,8,25,41, 46, 53] incorporates prior knowledge by pre-training conditional models of radiance fields on large posed multi-view datasets. Despite showing promising results on sparse input images, their generalization to out-of-distribution novel views remains a challenge. Multiple works [11, 19, 22, 32, 34] follow a different direction, focusing on per-scene training for few-shot novel view rendering. DietNeRF [19] compares CLIP [33] embeddings of rendered and training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.349 + ], + "angle": 0, + "content": "views. InfoNeRF [22] penalizes the NeRF overfitting to limited input views with a ray entropy regularization. Similarly, Barron et al. [4] introduce a distortion loss, which encourages sparsity of the density in each ray. In RegNeRF, Niemeyer et al. [32] propose to regularize the geometry and appearance of rendered patches with a depth smoothness and normalizing flow objectives. Recently, a number of works [11, 34, 49, 54] incorporate depth priors to constraint the NeRF optimization. Notably, DS-NeRF [11] improves reconstruction accuracy by including additional sparse depth supervision. Related are also approaches that learn a signed distance function (SDF), aiming for accurate 3D reconstruction in the sparse-view scenario [26, 51]. However, all these works assume perfect poses as a prerequisite. We instead propose a novel training strategy leading to accurate geometry and novel-view renderings in the sparse regime, even when facing imperfect input poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Joint NeRF and pose refinement: Several approaches attempt to reduce NeRF's reliance on highly accurate input camera poses [9,24,29,48,50]. BARF [24] and NeRF-- [48] jointly optimize the radiance field and camera parameters of initial noisy poses, relying on the photometric loss as the only training signal. SiNeRF [50] and GARF [9] propose different activation functions, easing the pose optimization. GNeRF [29] introduces a sequential training approach including a rough initial pose network that uses GAN-style training, thereby circumventing the need for initial pose estimates. SCNeRF [21] proposes a geometric loss minimizing the ray intersection re-projection error at previously extracted sparse correspondences to optimize over camera extrinsics and intrinsics. A number of works [5, 23, 52] also combine the photometric objective with a silhouette or mask loss, requiring accurate foreground segmentation, and limiting their applicability to objects. Related are also implicit SLAM systems [2, 40, 59], which progressively optimize over the geometry and camera estimates of an input RGB-D sequence. While previous works assume a dense coverage of the 3D space, Zhang et al. propose NeRS [56], which tackles the task of single object reconstruction by deforming a unit sphere over time while refining poses of few input views. However, NeRS is restricted to simple objects with a known shape prior. We instead assume access to only few wide-baseline RGB images with noisy pose estimates, without any prior on the scene or object shape." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.779, + 0.638, + 0.794 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.806, + 0.891, + 0.835 + ], + "angle": 0, + "content": "We first briefly introduce notation, the basics of NeRF representation, and camera operations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.839, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Camera pose: Let \\( P_{i}^{c2w} = \\left[R_{i}^{c2w}|\\mathbf{t}_{i}^{c2w}\\right] \\in SE(3) \\) be the camera-to-world transform of camera \\( i \\), where \\( R_{i}^{c2w} \\in SO(3) \\) and \\( \\mathbf{t}_{i}^{c2w} \\in \\mathbb{R}^{3} \\) are the rotation and translation, respectively. We denote as \\( K \\in \\mathbb{R}^{3 \\times 3} \\) the intrinsic matrix." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.514, + 0.958 + ], + "angle": 0, + "content": "4191" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.137 + ], + "angle": 0, + "content": "For the rest of the manuscript, we drop the superscript \\( ^{c2w} \\). As a result, unless otherwise stated, \\( P = P^{c2w} \\) and all 3D quantities are defined in the world coordinate system." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.468, + 0.246 + ], + "angle": 0, + "content": "Camera projection: For any vector \\(\\mathbf{x} \\in \\mathbb{R}^l\\) of dimension \\(l\\), \\(\\bar{\\mathbf{x}} \\in \\mathbb{R}^{l+1}\\) corresponds to its homogeneous representation, i.e., \\(\\bar{\\mathbf{x}} = [\\mathbf{x}^T, 1]\\). We additionally define \\(\\pi\\) to be the camera projection operator, which maps a 3D point in the camera coordinate frame \\(\\mathbf{x}^c \\in \\mathbb{R}^3\\) to a pixel coordinate \\(\\mathbf{p} \\in \\mathbb{R}^2\\). Likewise, \\(\\pi^{-1}\\) is defined to be the backprojection operator, which maps a pixel \\(\\mathbf{p}\\) and depth \\(z\\) to a 3D point \\(\\mathbf{x}^c\\)." + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.256, + 0.469, + 0.274 + ], + "angle": 0, + "content": "\\[\n\\pi \\left(\\mathbf {x} ^ {c}\\right) \\cong K \\mathbf {x} ^ {c}, \\quad \\pi^ {- 1} (\\mathbf {p}, z) = z K ^ {- 1} \\bar {\\mathbf {p}}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.469, + 0.375 + ], + "angle": 0, + "content": "Scene representation: We adopt the NeRF [30] framework to represent the underlying 3D scene and image formation. A neural radiance field is a continuous function that maps a 3D location \\(\\mathbf{x} \\in \\mathbb{R}^3\\) and a unit-norm ray viewing direction \\(\\mathbf{d} \\in \\mathbb{S}^2\\) to an RGB color \\(\\mathbf{c} \\in [0,1]^3\\) and volume density \\(\\sigma \\in \\mathbb{R}^+\\). It can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.387, + 0.469, + 0.404 + ], + "angle": 0, + "content": "\\[\n[ \\mathbf {c}, \\sigma ] = F _ {\\theta} \\left(\\gamma_ {x} (\\mathbf {x}), \\gamma_ {d} (\\mathbf {d})\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.468, + 0.44 + ], + "angle": 0, + "content": "Here, \\(F\\) is an MLP with parameters \\(\\theta\\), and \\(\\gamma: \\mathbb{R}^3 \\to \\mathbb{R}^{3+6L}\\) is a positional encoding function with \\(L\\) frequency bases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.469, + 0.613 + ], + "angle": 0, + "content": "Volume rendering: Given a camera pose \\(P_{i}\\), each pixel coordinate \\(\\mathbf{p} \\in \\mathbb{R}^2\\) determines a ray in the world coordinate system, whose origin is the camera center of projection \\(\\mathbf{o}_i = \\mathbf{t}_i\\) and whose direction is defined as \\(\\mathbf{d}_{i,\\mathrm{p}} = R_i K_i^{-1} \\bar{\\mathbf{p}}\\). We can express a 3D point along the viewing ray associated with \\(\\mathbf{p}\\) at depth \\(t\\) as \\(\\mathbf{r}_{i,\\mathrm{p}}(t) = \\mathbf{o}_i + t \\mathbf{d}_{i,\\mathrm{p}}\\). To render the color \\(\\hat{\\mathbf{I}}_{i,\\mathrm{p}} \\in [0,1]^3\\) at pixel \\(\\mathbf{p}\\), we sample \\(M\\) discrete depth values \\(t_m\\) along the ray within the near and far plane \\([t_n, t_f]\\), and query the radiance field \\(F_\\theta(2)\\) at the underlying 3D points. The corresponding predicted color and volume density values \\(\\{(\\mathbf{c}_m, \\sigma_m)\\}_{m=1}^M\\) are then composited as," + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.624, + 0.469, + 0.665 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {I}} _ {i, \\mathbf {p}} = \\hat {I} (\\mathbf {p}; \\theta , P _ {i}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\mathbf {c} _ {m}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.135, + 0.668, + 0.469, + 0.685 + ], + "angle": 0, + "content": "where \\(\\alpha_{m} = T_{m}\\left(1 - \\exp (-\\sigma_{m}\\delta_{m})\\right)\\) (4)" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.688, + 0.469, + 0.729 + ], + "angle": 0, + "content": "\\[\nT _ {m} = \\exp \\left(- \\sum_ {m ^ {\\prime} = 1} ^ {m} \\sigma_ {m ^ {\\prime}} \\delta_ {m ^ {\\prime}}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.469, + 0.798 + ], + "angle": 0, + "content": "\\(T_{m}\\) denotes the accumulated transmittance along the ray from \\(t_n\\) to \\(t_m\\), and \\(\\delta_{m} = t_{m + 1} - t_{m}\\) is the distance between adjacent samples. Similarly, the approximate depth of the scene viewed from pixel \\(\\mathbf{p}\\) is obtained as," + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.809, + 0.469, + 0.85 + ], + "angle": 0, + "content": "\\[\n\\hat {z} _ {i, \\mathrm {p}} = \\hat {z} (\\mathbf {p}; \\theta , P _ {i}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} t _ {m}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Here, \\(\\hat{I}\\) and \\(\\hat{z}\\) denote the RGB and depth rendering functions. In practice, NeRF [30] trains two MLPs, a coarse network \\(F_{\\theta}^{c}\\) and a fine network \\(F_{\\theta}^{f}\\), where the former is" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.122 + ], + "angle": 0, + "content": "used to guide sampling along the ray for the latter, thereby enabling more accurate estimation of (3)-(6)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.126, + 0.892, + 0.208 + ], + "angle": 0, + "content": "Photometric loss: Given a dataset of \\( n \\) RGB images \\( \\mathcal{I} = \\{I_1, I_2, \\dots, I_n\\} \\) of a scene associated with initial noisy poses \\( \\hat{\\mathcal{P}} = \\left\\{\\hat{P}_1, \\hat{P}_2, \\dots, \\hat{P}_n\\right\\} \\), previous approaches [9, 24, 48, 50] optimize the radiance field function \\( F_{\\theta} \\) along with the camera pose estimates \\( \\hat{\\mathcal{P}} \\) using a photometric loss as follows," + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.22, + 0.892, + 0.26 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p h o t o}} (\\theta , \\hat {\\mathcal {P}}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\sum_ {\\mathrm {p}} \\left\\| I _ {i} (\\mathbf {p}) - \\hat {I} (\\mathbf {p}; \\theta , \\hat {P} _ {i}) \\right\\| _ {2} ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.271, + 0.892, + 0.317 + ], + "angle": 0, + "content": "While this works well with dense views, it fails in the sparse regime. We propose an approach to effectively refine the poses and train the neural field for this challenging scenario." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.331, + 0.59, + 0.347 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.357, + 0.892, + 0.447 + ], + "angle": 0, + "content": "This work addresses the challenge of novel view synthesis based on neural implicit representations, in the sparse-view regime. In particular, we assume access to only sparse input views with noisy camera pose estimates. The training image collection contains few images (as low as 3) and they present large viewpoint variations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.704 + ], + "angle": 0, + "content": "This leads to two major challenges: (i) given only few input images, the NeRF model [30] instantly overfits to the training views without learning a meaningful 3D geometry, even with perfect input camera poses [19,22,32]. As shown in Fig. 1, this leads to degenerate novel view renderings, including for similar train/test viewing directions. The problem becomes amplified when considering noisy input camera poses. (ii) Previous pose-NeRF refinement approaches [5,9,24,48,50] were designed considering a dense coverage of the 3D space, i.e. many input views. They apply their training objectives, e.g. the photometric loss (7), on each training image independently. However, in the sparse-view regime, i.e. where the 3D space is under-constrained, such supervision is often too weak for the pose/NeRF system to converge to a globally consistent geometric solution. Failure to correctly register the training poses also leads to poor novel view rendering quality (see Fig. 1, 4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose SPARF, a simple, yet effective training strategy to jointly learn the scene representation and refine the initial training poses, tailored for the sparse-view scenario. As the prominent source of inspiration, we draw from well-established principles of multi-view geometry [17], which we adapt to the NeRF framework. In Sec. 4.1, we introduce our multi-view correspondence objective as the main driving signal for the joint pose-NeRF training. By relying on pixel correspondences between the training views, the loss enforces convergence to a global and accurate geometric solution consistent across all training views, thereby solving both challenges (i) and (ii). Moreover, in Sec. 4.2 we propose an additional term, i.e. the depth consistency loss," + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4192" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.882, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.322, + 0.895, + 0.42 + ], + "angle": 0, + "content": "Figure 2. Our approach SPARF for joint pose-NeRF training given only few input images with noisy camera pose estimates. We first rely on a pre-trained dense correspondence network [43] to extract matches between the training views. Our multi-view correspondence loss (Sec. 4.1) minimizes the re-projection error between matches, i.e. it enforces each pixel of a particular training view to project to its matching pixel in another training view. We use the rendered NeRF depth (6) and the current pose estimates \\(\\hat{\\mathcal{P}}\\) to backproject each pixel in 3D space. This constraint hence encourages the learned scene and pose estimates to converge to a global and accurate geometric solution, consistent across all training views. Our depth consistency loss (Sec. 4.2) further uses the rendered depths from the training viewpoints to create pseudo-depth supervision for unseen viewpoints, thereby encouraging the reconstructed scene to be consistent from any direction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.471, + 0.522 + ], + "angle": 0, + "content": "which encourages the learned scene geometry to be consistent across all viewpoints, including those for which no RGB supervision is available. In doing so, it boosts novel-view rendering quality, further tackling the overfitting problem (i). We present our final training strategy in Sec. 4.3 and visualize our approach in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.536, + 0.371, + 0.552 + ], + "angle": 0, + "content": "4.1. Multi-View Correspondence Loss" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.697 + ], + "angle": 0, + "content": "Directly overfitting on the training images leads to a corrupted neural radiance field collapsing towards the provided views, even when assuming perfect camera poses [11, 19, 32]. With noisy input poses, the problem becomes amplified, making it impossible to use the photometric loss (7) as the main signal for the joint pose-NeRF training. We propose a training objective, the multi-view correspondence loss, to enforce learning a globally consistent 3D solution over the optimized scene geometry and camera poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Multi-view geometry constraint: We draw inspiration from principles of multi-view geometry [17]. We assume that given an image pair \\((I_i, I_j)\\), we can obtain pairs of matching pixels \\(\\mathbf{p} \\in I_i\\) and \\(\\mathbf{q} \\in I_j\\). We then compute estimates of the depth at both pixels \\(\\hat{z}_{i,\\mathfrak{p}} = \\hat{z}(\\mathbf{p}; \\theta, \\hat{P}_i)\\) and \\(\\hat{z}_{j,\\mathfrak{q}} = \\hat{z}(\\mathbf{q}; \\theta, \\hat{P}_j)\\) according to eq. (6). Principles of multiview geometry dictate that both pixels must backproject to the same 3D point in the world coordinate system. This is formulated as \\(\\hat{P}_j \\pi^{-1}(\\mathbf{q}, \\hat{z}_{j,\\mathfrak{q}}) = \\hat{P}_i \\pi^{-1}(\\mathbf{p}, \\hat{z}_{i,\\mathfrak{p}})\\). However, when translating this constraint into a training objective, the magnitude of the loss is subject to large variations depending on the scene scale and the initial camera poses, requiring a tedious tuning of the loss weighting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.527 + ], + "angle": 0, + "content": "Training objective: We instead project the 3D points back to image space, therefore minimizing the distance between pixels rather than directly in 3D space. We illustrate this objective in Fig. 2 (steps 1-2). For a randomly sampled training image pair \\((I_i, I_j)\\), our multi-view correspondence objective is formulated as \\(\\mathcal{L}_{\\mathrm{MVCorr}}(\\theta, \\hat{\\mathcal{P}}) = \\sum_{\\mathrm{p} \\in \\mathcal{V}} \\mathcal{L}_{\\mathrm{p}}\\), where" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.533, + 0.892, + 0.559 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p}} = w _ {\\mathrm {p}} \\rho \\left(\\mathbf {q} - \\pi \\left(\\hat {P} _ {j} ^ {- 1} \\hat {P} _ {i} \\quad \\pi^ {- 1} (\\mathbf {p}, \\hat {z} (\\mathbf {p}; \\theta , \\hat {P} _ {i}))\\right)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.892, + 0.641 + ], + "angle": 0, + "content": "Here \\(\\rho\\) denotes the Huber loss function [18] and \\(w_{\\mathfrak{p}} \\in [0,1]\\) is the confidence associated with the correspondence \\((\\mathbf{p}, \\mathbf{q})\\), which we obtain as detailed below. We additionally define the set \\(\\mathcal{V} = \\{\\mathbf{p}: w_{\\mathfrak{p}} \\geq \\kappa\\}\\), where \\(\\kappa = 0.95\\). The homogenization operations were omitted for clarity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.893, + 0.807 + ], + "angle": 0, + "content": "Our loss serves two purposes. By connecting the training images through correspondences, our multi-view correspondence objective enforces the learned geometry and camera poses to converge to a solution geometrically consistent across all training images. This is unlike the photometric loss (7) which applies supervision on each training image independently. Moreover, the underlying constraint is only satisfied if the learned 3D points converge to the true reconstructed scene (up to a similarity). As such, the objective (8) provides direct supervision on the rendered depth (6), implicitly enforcing it to be close to the surface." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Correspondence prediction: Any classical [27, 35] or learned [13,36,42,44,45] matching approach could be used to obtain the matches relating pairs of training views. We rely on a pre-trained dense correspondence regression network, in particular PDC-Net [43]. It predicts a match \\(\\mathbf{q}\\) for each pixel \\(\\mathbf{p}\\), along with a confidence \\(w_{\\mathrm{p}}\\). We found" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4193" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.184 + ], + "angle": 0, + "content": "the high number of accurate matches to be beneficial for our joint pose-NeRF refinement. Similar conclusions were derived in the context of dense versus sparse depth supervision [11,34]. The dense correspondence map also implicitly imposes a smoothness prior to the rendered depth. In suppl., we present results using a sparse matcher [12, 36] instead." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.189, + 0.442, + 0.206 + ], + "angle": 0, + "content": "4.2. Improving Geometry at Unobserved Views" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.333 + ], + "angle": 0, + "content": "The multi-view correspondence loss favors a global and geometrically accurate solution, consistent across all training images. Nevertheless, the reconstructed scene often still suffers from inconsistencies when seen from novel viewpoints. For those, no RGB supervision is available during training. We propose an additional training objective, the depth consistency loss, which encourages the learned geometry to be consistent from any viewing direction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.47, + 0.521 + ], + "angle": 0, + "content": "Depth consistency loss: The main idea is to use the depth maps rendered from the training viewpoints to create pseudo-depth supervision for novel, unseen, viewpoints (Fig. 2, step 3). We sample a virtual pose \\( P_{un} \\), in practice obtained as an interpolation between the poses of two close-by training views. For a pixel \\( \\mathbf{p} \\) in a sampled training image \\( I_i \\), \\( \\mathbf{r_p}^{un} = P_{un}^{-1}\\hat{P}_i\\pi^{-1}(\\mathbf{p},\\hat{z} (\\mathbf{p};\\theta ,\\hat{P}_i)) \\) is the corresponding 3D point in the coordinate system of the unseen view \\( P_{un} \\). \\( \\mathbf{y}\\in \\mathbb{R}^2 \\) denotes its pixel projection in view \\( P_{un} \\) as \\( \\mathbf{y} = \\pi \\left(\\mathbf{r}_{\\mathrm{p}}^{un}\\right) \\), and \\( z_{\\mathrm{y}} \\) is its projected depth in \\( P_{un} \\), i.e. \\( z_{\\mathrm{y}} = \\left[\\mathbf{r}_{\\mathrm{p}}^{un}\\right]_3 \\), where \\( [\\cdot ]_3 \\) refers to taking the third coordinate of the vector. We formulate our depth consistency loss as," + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.526, + 0.469, + 0.558 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {D C o n s}} (\\theta) = \\sum_ {\\mathrm {p}} \\gamma_ {\\mathrm {y}} \\rho \\left(z _ {\\mathrm {y}} - \\hat {z} (\\mathbf {y}; \\theta , P _ {u n})\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.469, + 0.609 + ], + "angle": 0, + "content": "To account for occlusion and out-of-view projections in which (9) is invalid, we have included a visibility mask \\(\\gamma_{\\mathrm{y}} \\in [0,1]\\). We explain its definition in the section below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.469, + 0.746 + ], + "angle": 0, + "content": "Since the pseudo-depth supervision \\( z_{\\mathrm{y}} \\) is created from renderings, it is subject to errors. For this reason, we find it important to backpropagate through the pseudo-supervision \\( \\mathbf{y} \\) and \\( z_{\\mathrm{y}} \\). Note that we however do not backpropagate through the pose estimate \\( \\hat{P}_i \\). Moreover, as verified experimentally in Tab. 2, our depth consistency objective (9) is complementary to our multi-view correspondence loss (8), the latter enforcing an accurate reconstructed geometry while the former ensures it is consistent from any viewpoint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.904 + ], + "angle": 0, + "content": "Visibility mask \\(\\gamma_{\\mathbf{y}}\\): We first exclude points if their pixel projections \\(\\mathbf{y}\\) is outside of the virtual view, by setting the mask as \\(\\gamma_{\\mathrm{y}} = 0\\). The depth consistency loss is also invalid for pixels that are occluded by the reconstructed scene in the virtual view. To identify these occluded pixels, we follow the strategy of [10]. In particular, we check whether there are occupied regions on the ray between the camera center \\(\\mathbf{o}_{un}\\) of \\(P_{un}\\) and the 3D point \\(\\mathbf{r}_{un,\\mathbf{y}}(z_{\\mathbf{y}})\\) at depth \\(z_{\\mathbf{y}}\\). We compute how occluded a 3D point is with its transmittance (5) in the unseen view, as \\(\\gamma_{\\mathrm{y}} = T_{un,z_{\\mathbf{y}}}\\). Intuitively, \\(\\gamma_{\\mathrm{y}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "is close to 1 if there is no point with a large density between the camera center \\(\\mathbf{o}_{un}\\) and \\(\\mathbf{r}_{un,y}(z_y)\\), otherwise it is close to 0. Next, we present our overall training framework." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.146, + 0.698, + 0.163 + ], + "angle": 0, + "content": "4.3. Training Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.173, + 0.892, + 0.399 + ], + "angle": 0, + "content": "Staged training: Our final training objective is formulated as \\(\\mathcal{L}(\\theta, \\hat{\\mathcal{P}}) = \\mathcal{L}_{\\mathrm{photo}}(\\theta, \\hat{\\mathcal{P}}) + \\lambda_{\\mathrm{c}} \\mathcal{L}_{\\mathrm{MVCorr}}(\\theta, \\hat{\\mathcal{P}}) + \\lambda_{\\mathrm{d}} \\mathcal{L}_{\\mathrm{DCons}}(\\theta)\\), where \\(\\lambda_{\\mathrm{c}}\\) and \\(\\lambda_{\\mathrm{d}}\\) are predefined weighting factors. The training is split into two stages. In the first part, the pose estimates are trained jointly with the coarse MLP \\(F_{\\theta}^{c}\\). However, due to the exploration of the pose space at the early stages of training, the learned scene tends to showcase blurry surfaces. As a result, in the second training stage, we freeze the pose estimates and train both the coarse and fine networks \\(F_{\\theta}^{c}\\) and \\(F_{\\theta}^{f}\\). This ensures that the fine network learns a sharp geometry, benefiting from the pre-trained coarse network. From a practical perspective, our training objectives can be integrated at a low computational cost, since the RGB or depth pixel renderings (3)-(6) can be shared between the three loss terms." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.893, + 0.57 + ], + "angle": 0, + "content": "Coarse-to-fine positional encoding: In BARF [24], Lin et al. propose to gradually activate the high-frequency components of the positional encodings (2) over the course of the optimization. We refer the reader to [24] for the exact formulation. While originally proposed in the context of pose refinement, we found that this strategy is also extremely beneficial in the sparse-view setting, even when the poses are fixed. It prevents the network from immediately overfitting to the training images, thereby avoiding the worst degenerate geometries. We therefore adopt this coarse-to-fine positional encoding approach as default." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.583, + 0.706, + 0.6 + ], + "angle": 0, + "content": "5. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.715 + ], + "angle": 0, + "content": "We evaluate the proposed SPARF for novel-view rendering in the few-view setting, in particular when only three input views are available. Results with different numbers of views are provided in suppl. We extensively analyze our method and compare it to earlier approaches, setting a new state of the art on multiple datasets. Further results, visualizations, and implementation details are provided in suppl." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.723, + 0.707, + 0.74 + ], + "angle": 0, + "content": "5.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets and metrics: We report results on the DTU [20], LLFF [38] and Replica [39] datasets, for the challenging scenario of 3 input views. DTU is composed of complex object-level scenes with wide-baseline views spanning a half hemisphere. We adhere to the protocol of [53] and evaluate on their reported test split of 15 scenes. Following [32], we additionally evaluate all methods with the object masks applied to the rendered images, to avoid penalizing methods for incorrect background predictions. On LLFF, we follow community standards [30] and use every \\(8^{\\text{th}}\\) image as" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4194" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.48, + 0.158 + ], + "angle": 0, + "content": "
MethodPSNR ↑SSIM ↑LPIPS ↓DE ↓
I Full PE [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)0.87
II Smaller MLP model9.03 (10.06)0.34 (0.65)0.68 (0.34)0.79
III No PE16.11 (18.40)0.68 (0.80)0.37 (0.24)0.30
IV CF PE [24] (Sec. 4.3)16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.161, + 0.47, + 0.203 + ], + "angle": 0, + "content": "Table 1. Comparison of different positional encoding strategies applied to NeRF [30] on DTU (3 views), using ground-truth poses. Results in \\((\\cdot)\\) are computed by masking the background." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.216, + 0.47, + 0.367 + ], + "angle": 0, + "content": "the test set. We sample the training views evenly from the remaining images. For the Replica dataset, which depicts videos of room-scale indoor scenes, we subsample every \\( k^{th} \\) frame, from which we randomly select a triplet of consecutive training images. As metrics, we report the average rotation and translation errors for pose registration, and PSNR, SSIM [47] and LPIPS [57] for view synthesis. On the DTU and Replica datasets, we additionally compare the rendered depth with the available ground-truth depth and compute the mean depth absolute error (DE)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.462 + ], + "angle": 0, + "content": "Implementation details: We train our approach for 100K iterations, which takes about 10 hours on a single A100 GPU. As pose parametrization, we adopt the continuous 6-vector representation [58] for the rotation and directly optimize the translation vector. We provide all training hyperparameters in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.47, + 0.245, + 0.485 + ], + "angle": 0, + "content": "5.2. Method Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.469, + 0.525 + ], + "angle": 0, + "content": "We first perform a comprehensive analysis of our approach, on DTU [20], considering only 3 input views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.693 + ], + "angle": 0, + "content": "Impact of positional encoding: Training on sparse input views using the standard NeRF [30] immediately overfits to the provided images, even with perfect poses. We noticed that the overfitting is largely due to the high-frequency positional encodings (PE), and thus experimented with different PE strategies. We present the results in Tab. 1. The standard NeRF (I) with high-frequency PE [30] leads to degenerate geometry and novel view renderings. In (II), using a simplified MLP makes little difference. While training without PE (III) largely prevents overfitting, the coarse-to-fine PE strategy [24] leads to the best result, as shown in (IV)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Ablation study: In Tab. 2, we ablate the key components of our approach, here assuming fixed ground-truth poses and starting from NeRF with coarse-to-fine PE. Adding our multi-view correspondence loss (8) results in drastically better performance on all metrics. Including our depth" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.785, + 0.472, + 0.851 + ], + "angle": 0, + "content": "
MV-Corr (8)DCons (9)PSNR ↑SSIM ↑LPIPS ↓DE ↓
XX16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
X✓15.86 (18.91)0.71 (0.82)0.28 (0.14)0.20
✓X18.13 (20.81)0.77 (0.87)0.22 (0.10)0.10
✓✓18.30 (21.01)0.78 (0.87)0.21 (0.10)0.08
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.855, + 0.47, + 0.897 + ], + "angle": 0, + "content": "Table 2. Ablation study on the DTU dataset (3 views), with fixed ground-truth poses. Results in \\((\\cdot)\\) are computed by masking the background. All networks use the coarse-to-fine PE [24]." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.742, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.742, + 0.093, + 0.892, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.26, + 0.894, + 0.399 + ], + "angle": 0, + "content": "Figure 3. We compare two training objectives using ground-truth depth for pose-NeRF training in the sparse-view regime. In (A), a loss comparing for each training image the rendered depth (6) with the ground truth one, can learn locally perfect geometry (as highlighted by the dashed red rectangles). However, the NeRF/poses do not converge to a global solution, because the optimized poses and geometry of the different images are disjoint. Instead, supervising the learned 3D points of each training image to be equal to the ground-truth 3D points in (B) solves this issue, by enforcing the system to converge to a global (unique) geometric solution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.487 + ], + "angle": 0, + "content": "consistency module (9) further leads to a small improvement, achieving the best performance overall. Also note that our depth-consistency module (9) works best in collaboration with our multi-view correspondences loss (8) since the latter is needed to learn an accurate geometry." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.838 + ], + "angle": 0, + "content": "Intuition on pose-NeRF training losses: We first want to build an intuition on what loss might be suitable for joint pose-NeRF training in the sparse regime. To do so, we use ground-truth depth or 3D data in two alternative training losses, which we compare here. We illustrate this experiment in Fig. 3 and present results in Tab. 3, top part. As in previous work [24], for each scene of DTU [20], we synthetically perturb the ground-truth camera poses with \\(15\\%\\) of additive gaussian noise. In (I), we train with an L1 loss comparing the rendered depth (6) with the ground-truth depth (Fig. 3A). Surprisingly, this loss struggles to refine the poses. Instead, in (II) we minimize the distance between the learned 3D points (rendered depth (6) backprojected to world frame) and the ground-truth 3D points, as illustrated in Fig. 3B. This training loss successfully registers the poses, resulting in drastically better novel-view rendering quality. As the main insight from this experiment, we hypothesize that, in the sparse-view regime, it is crucial to enforce an explicit geometric connection between the different training images and their underlying scene geometry. This is not the case in (I), where the depth loss favors per-image locally accurate geometry, but the NeRF/poses can converge to disconnected solutions for each training image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Comparison of losses for pose-NeRF training: In Tab. 3 bottom part, we then compare our loss (8) to objectives commonly used for joint pose-NeRF training. The photometric loss (7) (III), even associated with a mask/silhouette" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4195" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.48, + 0.171 + ], + "angle": 0, + "content": "
LossesRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
I Photo. + L1 GT depth7.328.913.8 (14.0)0.54 (0.70)0.46 (0.27)0.17
II Photo. + L1 GT 3D points0.41.518.8 (20.3)0.75 (0.84)0.21 (0.11)0.07
III Photo. (7)10.351.510.7 (9.8)0.43 (0.62)0.59 (0.36)1.9
IV Photo. + mask loss [23,56]13.257.7----
V MVCorr (8)1.986.6---0.19
VI Photo. + MVCorr ((7)-(8))1.855.516.0 (17.8)0.68 (0.81)0.28 (0.14)0.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.175, + 0.47, + 0.232 + ], + "angle": 0, + "content": "Table 3. Comparison of training objectives for joint pose-NeRF refinement on DTU [20] with initial noisy poses (3 views). Rotation errors are in degree and translation errors are multiplied by 100. Results in \\((\\cdot)\\) are computed by masking the background." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.474, + 0.471 + ], + "angle": 0, + "content": "loss [5,23,56] in (IV), completely fails to register the poses, thus leading to poor novel-view synthesis performance. This is in line with our hypothesis that it is important to explicitly exploit the geometric relation between the training views for successful registration. Moreover, because the 3D space is under-constrained in the sparse-view regime, multiple neighboring poses can lead to similar mask losses. While our multi-view correspondence loss (8) alone (V) already drastically outperforms the photometric loss (III) in terms of pose and learned geometry (depth error), combining the two in (VI) leads to the best performance. This is because, through the correspondences, our approach favors a NeRF/pose solution consistent across all training images. Note that this version neither includes our depth consistency loss (9) (Sec. 4.2) nor our staged training (Sec. 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.479, + 0.413, + 0.495 + ], + "angle": 0, + "content": "5.3. Comparison to SOTA with Noisy Poses" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.47, + 0.548 + ], + "angle": 0, + "content": "Here, we evaluate SPARF, our joint pose and NeRF training approach. Results with different pose initialization schemes are presented in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.718 + ], + "angle": 0, + "content": "Baselines: We compare to BARF [24], the state-of-the-art in pose-NeRF refinement when assuming dense input views. It is representative of a line of approaches [9, 24, 29, 48, 50] using the photometric loss (7) as the main signal. We also experiment with adding the depth regularization loss of [32] or the ray sparsity loss of [4] to BARF, which we denote as RegBARF and DistBARF respectively. We additionally compare to SCNeRF [21], which uses a geometric loss based on correspondences, minimizing the rays' intersection re-projection error. For a fair comparison, we integrate coarse-to-fine PE [24] (Sec. 4.3) in all methods." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.72, + 0.47, + 0.767 + ], + "angle": 0, + "content": "Results on DTU: Following [9, 24, 50], for each scene, we synthetically perturb the ground-truth camera poses with \\(15\\%\\) of additive gaussian noise. The initial poses thus have" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.78, + 0.466, + 0.852 + ], + "angle": 0, + "content": "
MethodRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
BARF [24]10.3351.510.71 (9.76)0.43 (0.62)0.59 (0.36)1.90
RegBARF [24, 32]11.2052.810.38 (9.20)0.45 (0.62)0.61 (0.38)2.33
DistBARF [4, 24]11.6955.79.50 (9.15)0.34 (0.76)0.67 (0.36)1.90
SCNeRF [21]3.4416.412.04 (11.71)0.45 (0.66)0.52 (0.30)0.85
SPARF (Ours)1.815.017.74 (18.92)0.71 (0.83)0.26 (0.13)0.12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.855, + 0.47, + 0.898 + ], + "angle": 0, + "content": "Table 4. Evaluation on DTU [20] (3 views) with noisy initial poses. Rotation errors are in \\(^\\circ\\) and translation errors are multiplied by 100. Results in \\((\\cdot)\\) are computed by masking the background." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.087, + 0.895, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.408, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Figure 4. Novel-view rendering (RGB and depth). The input (not shown here) contains 3 images with initial noisy camera poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.893, + 0.693 + ], + "angle": 0, + "content": "an average rotation and translation error of \\(15^{\\circ}\\) and 70 respectively. We show initial and optimized poses in Fig. 5. From the results in Tab. 4 and Fig. 4A, we observe that BARF, RegBARF, and DistBARF completely fail to register the poses, leading to poor view-synthesis quality. SCNeRF's geometric loss performs better at registering the poses but the learned scene still suffers from many inconsistencies. This is because SCNeRF's loss [21] does not influence the learned radiance field function, and thus, cannot prevent the NeRF model from overfitting to the sparse input views. Since our multi-view correspondence loss (8) acts on both the camera pose estimates and the learned neural field by enforcing them to fit the correspondence constraint, it leads to an accurate reconstructed scene. Our approach SPARF hence significantly outperforms all others both in novel-view rendering quality and pose registration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.697, + 0.894, + 0.789 + ], + "angle": 0, + "content": "Results on LLFF: The LLFF dataset consists of 8 complex forward-facing scenes. Following [24], we initialize all camera poses with the identity transformation and present results in Tab. 5. In [24], Lin et al. show that BARF almost perfectly registers the camera poses given dense input views. However, we show here that it strug" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.801, + 0.894, + 0.853 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.855, + 0.893, + 0.898 + ], + "angle": 0, + "content": "Figure 5. Optimized poses on DTU with 3 input views. We compare the ground-truth poses (in pink) with the optimized ones (in blue). In the first column, the initial noisy poses are in blue." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4196" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.465, + 0.165 + ], + "angle": 0, + "content": "
Rot. (°) ↓Trans. (×100) ↓PSNR ↑SSIM ↑LPIPS ↓
BARF [24]2.0411.617.470.480.37
RegBARF [24, 32]1.525.018.570.520.36
DistBARF [4, 24]5.5926.514.690.340.49
SCNeRF [21]1.9311.417.100.450.40
SPARF (Ours)0.532.819.580.610.31
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.17, + 0.468, + 0.198 + ], + "angle": 0, + "content": "Table 5. Evaluation on the forward-facing dataset LLFF [38] (3 views) starting from initial identity poses." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.211, + 0.472, + 0.342 + ], + "angle": 0, + "content": "
MethodRot (°) ↓Trans (×100) ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
G SPARF (Ours)Fixed GT poses26.430.880.130.39
F NeRF [30]Fixed poses obtained20.990.730.321.33
DS-NeRF [11]from COLMAP (run w.23.520.810.200.99
SPARF (Ours)PDC-Net [43] matches25.030.840.150.66
R BARF [24]3.3516.9620.730.720.300.84
RegBARF [24, 32]3.6620.8720.000.700.321.00
DistBARF [4, 24]2.367.7322.460.770.230.47
SCNeRF [21]0.654.1222.540.790.240.73
DS-NeRF [11]1.305.0424.750.830.200.69
SPARF (Ours)0.150.7626.980.880.130.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Table 6. Evaluation on Replica [39] (3 views) with initial poses obtained by COLMAP [37, 43]. The initial rotation and translation errors are \\(0.39^{\\circ}\\) and 3.01 respectively. In the middle part (F), these initial poses are fixed and used as \"pseudo-gt\". In the bottom part (R), the poses are refined along with training the NeRF. For comparison, in the top part (G), we use fixed ground-truth poses. The best and second-best results are in red and blue respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.469, + 0.53 + ], + "angle": 0, + "content": "gles in the sparse-view setting, thereby severely impacting the accuracy of novel view synthesis. While adding the depth smoothness loss (RegBARF) improves results, our approach SPARF outperforms all previous works. A qualitative comparison is shown in Fig. 4B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.469, + 0.715 + ], + "angle": 0, + "content": "Results on Replica: To demonstrate that our approach is also applicable to non-forward-facing indoor scenes, we evaluate on the Replica dataset in Tab. 6 and Fig. 4C. As pose initialization, we use COLMAP [37] with improved matches, i.e. using PDC-Net [43]. The initial pose estimates thus have an average rotation and translation error of respectively \\(0.39^{\\circ}\\) and 3.01. Comparing the top (G) and middle part (F) of Tab. 6, we show that even such a low initial error impacts the novel-view rendering quality when using fixed poses. In the bottom part (R), our pose-NeRF training strategy leads to the best results, matching the accuracy obtained by our approach with perfect poses (top row, G)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.469, + 0.739 + ], + "angle": 0, + "content": "5.4. Comparison to SOTA with Ground-Truth Poses" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.793 + ], + "angle": 0, + "content": "Finally, we show that our approach brings significant improvement in novel view rendering quality even when considering fixed ground-truth poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Baselines: We compare to works specifically designed to tackle per-scene few-shot novel view rendering, namely DietNeRF [19], DS-NeRF [11], InfoNeRF [22] and RegNeRF [32], along with the standard NeRF [30] and MipNeRF [3]. For completeness, we also compare against a state-of-the-art conditional model, PixelNeRF [53], trained on DTU [20] and further finetuned per-scene on LLFF [38]." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.09, + 0.895, + 0.216 + ], + "angle": 0, + "content": "
MethodDTULLFF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [53]19.36 (18.00)0.70 (0.77)0.32 (0.23)7.930.270.68
PixelNeRF-ft [53]---16.170.440.51
MipNeRF [3]7.64 (8.68)0.23 (0.57)0.66 (0.35)14.620.350.50
NeRF [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)13.610.280.56
DietNeRF [19]10.01 (11.85)0.35 (0.63)0.57 (0.31)14.940.370.5
InfoNeRF [22]11.23 (-)0.44 (-)0.54 (-)---
RegNeRF [32]15.33 (18.89)0.62 (0.75)0.34 (0.19)19.080.590.34
DS-NeRF [11]16.52 (-)0.54 (-)0.48 (-)18.000.550.27
SPARF (Ours)18.30 (21.01)0.78 (0.87)0.21 (0.10)20.200.630.24
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.222, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Table 7. Evaluation on DTU [20] and LLFF [38] (3 views), with fixed ground-truth poses. Results in \\((\\cdot)\\) are computed by masking the background. Results of [3, 19, 32] are taken from [32]. The best and second-best results are in red and blue respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Results: We present results on DTU and LLFF in Tab. 7. Compared to previous per-scene approaches [19,22,32] that only apply different regularization to the learned scene, our multi-view correspondence loss (8) provides a strong supervision on the rendered depth, implicitly encouraging it to be close to the true surface. Our depth consistency objective (9) further boosts the performance, by directly enforcing the learned scene to be consistent from any viewpoint. As a result, our approach SPARF performs best compared to all baselines on both datasets and for all metrics. The only exception is PSNR on the whole image compared to conditional model PixelNeRF [53]. This is because DTU has black backgrounds, where a wrong color prediction (like in Fig. 4A for SPARF) has a large impact on the PSNR value. For conditional models which rely on feature projections, it is easier to predict a correct background color. However, most real-world applications are more interested in accurately reconstructing the object of interest than the background. When evaluated only in the object region, our SPARF obtains 3.24dB higher PSNR than PixelNeRF." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.606, + 0.619, + 0.621 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.892, + 0.722 + ], + "angle": 0, + "content": "We propose SPARF, a joint pose-NeRF training strategy capable of producing realistic novel-view renderings given few wide-baseline input images with noisy camera pose estimates. By integrating two novel objectives inspired by multi-view geometry principles, we set a new state of the art on three challenging datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.725, + 0.892, + 0.891 + ], + "angle": 0, + "content": "Limitations and future work: Our approach is only applicable to input image collections where each image has covisible regions with at least one other. Moreover, the performance of our method depends on the quality of the matching network. Filtering strategies or per-scene online refinement of the correspondence network thus appear as promising future directions. An interesting direction is also to refine the camera intrinsics and distortion parameters along with the extrinsics. Finally, using voxel grids to encode the radiance field [31] instead of an MLP could lead to faster convergence, and potentially even better results." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.947, + 0.516, + 0.958 + ], + "angle": 0, + "content": "4197" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.239 + ], + "angle": 0, + "content": "[1] Wei Wang 0108, Zheng Dang, Yinlin Hu, Pascal Fua, and Mathieu Salzmann. Backpropagation-friendly eigendecomposition. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d'Alché Buc, Edward A. 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While showing impressive performance, it relies on the availability of dense input views with highly accurate camera poses, thus limiting its application in real-world scenarios. In this work, we introduce Sparse Pose Adjusting Radiance Field (SPARF), to address the challenge of novel-view synthesis given only few wide-baseline input images (as low as 3) with noisy camera poses. Our approach exploits multi-view geometry constraints in order to jointly learn the NeRF and refine the camera poses. By relying on pixel matches extracted between the input views, our multiview correspondence objective enforces the optimized scene and camera poses to converge to a global and geometrically accurate solution. Our depth consistency loss further encourages the reconstructed scene to be consistent from any viewpoint. Our approach sets a new state of the art in the sparse-view regime on multiple challenging datasets. + +# 1. Introduction + +Novel-view synthesis (NVS) has long been one of the most essential goals in computer vision. It refers to the task of rendering unseen viewpoints of a scene given a particular set of input images. NVS has recently gained tremendous popularity, in part due to the success of Neural Radiance Fields (NeRFs) [30]. NeRF encodes 3D scenes with a multi-layer perceptron (MLP) mapping 3D point locations to color and volume density and uses volume rendering to synthesize images. It has demonstrated remarkable abilities for high-fidelity view synthesis under two conditions: dense input views and highly accurate camera poses. + +Both these requirements however severely impede the usability of NeRFs in real-world applications. For instance, in AR/VR or autonomous driving, the input is inevitably much sparser, with only few images of any particular object or region available per scene. In such sparse-view scenario, NeRF rapidly overfits to the input views [11, 22, 32], lead + +![](images/224da0dcb90d7d0a16ca29ced0c50e4290a8898a78ee36eaba68bbc5d104ec93.jpg) + +![](images/14e80a2451ca3145cb8def768ea9d3079562909594e5dbe5255db877d9738918.jpg) +Sparse input views + +![](images/9a2850e436660ab0ef95ffb32f9a91db3a84d29638c1ef0e018aa33dadc219a7.jpg) + +![](images/8e017f5f5c5fd2fb93175035c21faa0f00975b45dbe2cdb3cce96e8ecb6a64c3.jpg) +Ground-truth camera poses NeRF + +![](images/07d327833f34edace7a99005b188db41ce6cca6405a3610725b20e07111a8dc7.jpg) +Figure 1. Novel-view rendering from sparse images. We show the RGB (second row) and depth (last row) renderings from an unseen viewpoint under sparse settings (3 input views only). Even with ground-truth camera poses, NeRF [30] overfits to the training images, leading to degenerate geometry (almost constant depth). BARF [24], which can successfully handle noisy poses when dense views are available, struggles in the sparse regime. Our approach SPARF instead produces realistic novel-view renderings with accurate geometry, given only 3 input views with noisy poses. + +![](images/5f29f0f43f16e460b5b80dcf1562d6c99a9bb2732a8b954ad02aa65c4ec6a4d7.jpg) +Noisy camera poses + +![](images/e9819ca4576daa9822b20b9cec7823d7d98ed41bfc137306be102287439a20de.jpg) + +![](images/8cc7d50bd0bc3e3c0e154a686596b95d3f35c619fcfb43b7fa7b5a0ce872b175.jpg) + +![](images/c93ee580cfdadc24eeb4ceef087a0190e25fb78fde2aadb185476bb96e69c668.jpg) + +![](images/ba9ab2cc86ecec790d1908442c2c2b9ff81962d3b4d839a7accb38d875855348.jpg) +SPARF (Ours) + +![](images/c949705b08ef3ddcb465b66daf4707232e93b12ac1f4f3d3f9895a20e67daa1b.jpg) + +![](images/be174234a62f5c8253a138513fb01ffdda35c5a5d03ac0811cf009e9a2593491.jpg) + +ing to inconsistent reconstructions at best, and degenerate solutions at worst (Fig. 1 left). Moreover, the de-facto standard to estimate per-scene poses is to use an off-the-shelf Structure-from-Motion approach, such as COLMAP [37]. When provided with many input views, COLMAP can generally estimate accurate camera poses. Its performance nevertheless rapidly degrades when reducing the number of views, or increasing the baseline between the images [55]. + +Multiple works focus on improving NeRF's performance in the sparse-view setting. One line of research [6,53] trains conditional neural field models on large-scale datasets. Alternative approaches instead propose various regularization on color and geometry for per-scene training [11, 19, 22, 32, 34]. Despite showing impressive results in the sparse scenario, all these approaches assume perfect camera poses as a pre-requisite. Unfortunately, estimating accurate camera poses for few wide-baseline images is challenging [55] and has spawned its own research direction [1, 7, 14-16, 28, 60], + +hence making this assumption unrealistic. + +Recently, multiple approaches attempt to reduce the dependency of NeRFs on highly accurate input camera poses. They rely on per-image training signals, such as a photometric [9, 24, 29, 48, 50] or silhouette loss [5, 23, 56], to jointly optimize the NeRF and the poses. However, in the sparse-view scenario where the 3D space is under-constrained, we observe that it is crucial to explicitly exploit the relation between the different training images and their underlying scene geometry, to enforce learning a global and geometrically accurate solution. This is not the case of previous works [5, 23, 24, 48, 50, 56], which hence fail to register the poses in the sparse regime. As shown in Fig. 1, middle for BARF [24], it leads to poor novel-view synthesis quality. + +We propose Sparse Pose Adjusting Radiance Field (SPARF), a joint pose-NeRF training strategy. Our approach produces realistic novel-view renderings given only few wide-baseline input images (as low as 3) with noisy camera poses (see Fig. 1 right). Crucially, it does not assume any prior on the scene or object shape. We introduce novel constraints derived from multi-view geometry [17] to drive and bound the NeRF-pose optimization. We first infer pixel correspondences relating the input views with a pre-trained matching model [43]. These pixel matches are utilized in our multi-view correspondence objective, which minimizes the re-projection error using the depth rendered by the NeRF and the current pose estimates. Through the explicit connection between the training views, the loss enforces convergence to a global and geometrically accurate pose/scene solution, consistent across all training views. We also propose the depth consistency loss to boost the rendering quality from novel viewpoints. By using the depth rendered from the training views to create pseudo-ground-truth depth for unseen viewing directions, it encourages the reconstructed scene to be consistent from any viewpoint. We extensively evaluate and compare our approach on the challenging DTU [20], LLFF [38], and Replica [39] datasets, setting a new state of the art on all three benchmarks. + +# 2. Related Work + +We review approaches focusing on few-shot novel view rendering as well as joint pose-NeRF refinement. + +Sparse input novel-view rendering: To circumvent the requirement of dense input views, a line of works [6,8,25,41, 46, 53] incorporates prior knowledge by pre-training conditional models of radiance fields on large posed multi-view datasets. Despite showing promising results on sparse input images, their generalization to out-of-distribution novel views remains a challenge. Multiple works [11, 19, 22, 32, 34] follow a different direction, focusing on per-scene training for few-shot novel view rendering. DietNeRF [19] compares CLIP [33] embeddings of rendered and training + +views. InfoNeRF [22] penalizes the NeRF overfitting to limited input views with a ray entropy regularization. Similarly, Barron et al. [4] introduce a distortion loss, which encourages sparsity of the density in each ray. In RegNeRF, Niemeyer et al. [32] propose to regularize the geometry and appearance of rendered patches with a depth smoothness and normalizing flow objectives. Recently, a number of works [11, 34, 49, 54] incorporate depth priors to constraint the NeRF optimization. Notably, DS-NeRF [11] improves reconstruction accuracy by including additional sparse depth supervision. Related are also approaches that learn a signed distance function (SDF), aiming for accurate 3D reconstruction in the sparse-view scenario [26, 51]. However, all these works assume perfect poses as a prerequisite. We instead propose a novel training strategy leading to accurate geometry and novel-view renderings in the sparse regime, even when facing imperfect input poses. + +Joint NeRF and pose refinement: Several approaches attempt to reduce NeRF's reliance on highly accurate input camera poses [9,24,29,48,50]. BARF [24] and NeRF-- [48] jointly optimize the radiance field and camera parameters of initial noisy poses, relying on the photometric loss as the only training signal. SiNeRF [50] and GARF [9] propose different activation functions, easing the pose optimization. GNeRF [29] introduces a sequential training approach including a rough initial pose network that uses GAN-style training, thereby circumventing the need for initial pose estimates. SCNeRF [21] proposes a geometric loss minimizing the ray intersection re-projection error at previously extracted sparse correspondences to optimize over camera extrinsics and intrinsics. A number of works [5, 23, 52] also combine the photometric objective with a silhouette or mask loss, requiring accurate foreground segmentation, and limiting their applicability to objects. Related are also implicit SLAM systems [2, 40, 59], which progressively optimize over the geometry and camera estimates of an input RGB-D sequence. While previous works assume a dense coverage of the 3D space, Zhang et al. propose NeRS [56], which tackles the task of single object reconstruction by deforming a unit sphere over time while refining poses of few input views. However, NeRS is restricted to simple objects with a known shape prior. We instead assume access to only few wide-baseline RGB images with noisy pose estimates, without any prior on the scene or object shape. + +# 3. Preliminaries + +We first briefly introduce notation, the basics of NeRF representation, and camera operations. + +Camera pose: Let $P_{i}^{c2w} = \left[R_{i}^{c2w}|\mathbf{t}_{i}^{c2w}\right] \in SE(3)$ be the camera-to-world transform of camera $i$ , where $R_{i}^{c2w} \in SO(3)$ and $\mathbf{t}_{i}^{c2w} \in \mathbb{R}^{3}$ are the rotation and translation, respectively. We denote as $K \in \mathbb{R}^{3 \times 3}$ the intrinsic matrix. + +For the rest of the manuscript, we drop the superscript $^{c2w}$ . As a result, unless otherwise stated, $P = P^{c2w}$ and all 3D quantities are defined in the world coordinate system. + +Camera projection: For any vector $\mathbf{x} \in \mathbb{R}^l$ of dimension $l$ , $\bar{\mathbf{x}} \in \mathbb{R}^{l+1}$ corresponds to its homogeneous representation, i.e., $\bar{\mathbf{x}} = [\mathbf{x}^T, 1]$ . We additionally define $\pi$ to be the camera projection operator, which maps a 3D point in the camera coordinate frame $\mathbf{x}^c \in \mathbb{R}^3$ to a pixel coordinate $\mathbf{p} \in \mathbb{R}^2$ . Likewise, $\pi^{-1}$ is defined to be the backprojection operator, which maps a pixel $\mathbf{p}$ and depth $z$ to a 3D point $\mathbf{x}^c$ . + +$$ +\pi \left(\mathbf {x} ^ {c}\right) \cong K \mathbf {x} ^ {c}, \quad \pi^ {- 1} (\mathbf {p}, z) = z K ^ {- 1} \bar {\mathbf {p}}. \tag {1} +$$ + +Scene representation: We adopt the NeRF [30] framework to represent the underlying 3D scene and image formation. A neural radiance field is a continuous function that maps a 3D location $\mathbf{x} \in \mathbb{R}^3$ and a unit-norm ray viewing direction $\mathbf{d} \in \mathbb{S}^2$ to an RGB color $\mathbf{c} \in [0,1]^3$ and volume density $\sigma \in \mathbb{R}^+$ . It can be formulated as + +$$ +[ \mathbf {c}, \sigma ] = F _ {\theta} \left(\gamma_ {x} (\mathbf {x}), \gamma_ {d} (\mathbf {d})\right). \tag {2} +$$ + +Here, $F$ is an MLP with parameters $\theta$ , and $\gamma: \mathbb{R}^3 \to \mathbb{R}^{3+6L}$ is a positional encoding function with $L$ frequency bases. + +Volume rendering: Given a camera pose $P_{i}$ , each pixel coordinate $\mathbf{p} \in \mathbb{R}^2$ determines a ray in the world coordinate system, whose origin is the camera center of projection $\mathbf{o}_i = \mathbf{t}_i$ and whose direction is defined as $\mathbf{d}_{i,\mathrm{p}} = R_i K_i^{-1} \bar{\mathbf{p}}$ . We can express a 3D point along the viewing ray associated with $\mathbf{p}$ at depth $t$ as $\mathbf{r}_{i,\mathrm{p}}(t) = \mathbf{o}_i + t \mathbf{d}_{i,\mathrm{p}}$ . To render the color $\hat{\mathbf{I}}_{i,\mathrm{p}} \in [0,1]^3$ at pixel $\mathbf{p}$ , we sample $M$ discrete depth values $t_m$ along the ray within the near and far plane $[t_n, t_f]$ , and query the radiance field $F_\theta(2)$ at the underlying 3D points. The corresponding predicted color and volume density values $\{(\mathbf{c}_m, \sigma_m)\}_{m=1}^M$ are then composited as, + +$$ +\hat {\mathbf {I}} _ {i, \mathbf {p}} = \hat {I} (\mathbf {p}; \theta , P _ {i}) = \sum_ {m = 1} ^ {M} \alpha_ {m} \mathbf {c} _ {m}, \tag {3} +$$ + +where $\alpha_{m} = T_{m}\left(1 - \exp (-\sigma_{m}\delta_{m})\right)$ (4) + +$$ +T _ {m} = \exp \left(- \sum_ {m ^ {\prime} = 1} ^ {m} \sigma_ {m ^ {\prime}} \delta_ {m ^ {\prime}}\right). \tag {5} +$$ + +$T_{m}$ denotes the accumulated transmittance along the ray from $t_n$ to $t_m$ , and $\delta_{m} = t_{m + 1} - t_{m}$ is the distance between adjacent samples. Similarly, the approximate depth of the scene viewed from pixel $\mathbf{p}$ is obtained as, + +$$ +\hat {z} _ {i, \mathrm {p}} = \hat {z} (\mathbf {p}; \theta , P _ {i}) = \sum_ {m = 1} ^ {M} \alpha_ {m} t _ {m}. \tag {6} +$$ + +Here, $\hat{I}$ and $\hat{z}$ denote the RGB and depth rendering functions. In practice, NeRF [30] trains two MLPs, a coarse network $F_{\theta}^{c}$ and a fine network $F_{\theta}^{f}$ , where the former is + +used to guide sampling along the ray for the latter, thereby enabling more accurate estimation of (3)-(6). + +Photometric loss: Given a dataset of $n$ RGB images $\mathcal{I} = \{I_1, I_2, \dots, I_n\}$ of a scene associated with initial noisy poses $\hat{\mathcal{P}} = \left\{\hat{P}_1, \hat{P}_2, \dots, \hat{P}_n\right\}$ , previous approaches [9, 24, 48, 50] optimize the radiance field function $F_{\theta}$ along with the camera pose estimates $\hat{\mathcal{P}}$ using a photometric loss as follows, + +$$ +\mathcal {L} _ {\mathrm {p h o t o}} (\theta , \hat {\mathcal {P}}) = \frac {1}{n} \sum_ {i = 1} ^ {n} \sum_ {\mathrm {p}} \left\| I _ {i} (\mathbf {p}) - \hat {I} (\mathbf {p}; \theta , \hat {P} _ {i}) \right\| _ {2} ^ {2}. \tag {7} +$$ + +While this works well with dense views, it fails in the sparse regime. We propose an approach to effectively refine the poses and train the neural field for this challenging scenario. + +# 4. Method + +This work addresses the challenge of novel view synthesis based on neural implicit representations, in the sparse-view regime. In particular, we assume access to only sparse input views with noisy camera pose estimates. The training image collection contains few images (as low as 3) and they present large viewpoint variations. + +This leads to two major challenges: (i) given only few input images, the NeRF model [30] instantly overfits to the training views without learning a meaningful 3D geometry, even with perfect input camera poses [19,22,32]. As shown in Fig. 1, this leads to degenerate novel view renderings, including for similar train/test viewing directions. The problem becomes amplified when considering noisy input camera poses. (ii) Previous pose-NeRF refinement approaches [5,9,24,48,50] were designed considering a dense coverage of the 3D space, i.e. many input views. They apply their training objectives, e.g. the photometric loss (7), on each training image independently. However, in the sparse-view regime, i.e. where the 3D space is under-constrained, such supervision is often too weak for the pose/NeRF system to converge to a globally consistent geometric solution. Failure to correctly register the training poses also leads to poor novel view rendering quality (see Fig. 1, 4). + +We propose SPARF, a simple, yet effective training strategy to jointly learn the scene representation and refine the initial training poses, tailored for the sparse-view scenario. As the prominent source of inspiration, we draw from well-established principles of multi-view geometry [17], which we adapt to the NeRF framework. In Sec. 4.1, we introduce our multi-view correspondence objective as the main driving signal for the joint pose-NeRF training. By relying on pixel correspondences between the training views, the loss enforces convergence to a global and accurate geometric solution consistent across all training views, thereby solving both challenges (i) and (ii). Moreover, in Sec. 4.2 we propose an additional term, i.e. the depth consistency loss, + +![](images/2b67d87eadaa314ce304ba9e93e3ed223d1d95982d7a83d85bc5a50ade5c73c5.jpg) +Figure 2. Our approach SPARF for joint pose-NeRF training given only few input images with noisy camera pose estimates. We first rely on a pre-trained dense correspondence network [43] to extract matches between the training views. Our multi-view correspondence loss (Sec. 4.1) minimizes the re-projection error between matches, i.e. it enforces each pixel of a particular training view to project to its matching pixel in another training view. We use the rendered NeRF depth (6) and the current pose estimates $\hat{\mathcal{P}}$ to backproject each pixel in 3D space. This constraint hence encourages the learned scene and pose estimates to converge to a global and accurate geometric solution, consistent across all training views. Our depth consistency loss (Sec. 4.2) further uses the rendered depths from the training viewpoints to create pseudo-depth supervision for unseen viewpoints, thereby encouraging the reconstructed scene to be consistent from any direction. + +which encourages the learned scene geometry to be consistent across all viewpoints, including those for which no RGB supervision is available. In doing so, it boosts novel-view rendering quality, further tackling the overfitting problem (i). We present our final training strategy in Sec. 4.3 and visualize our approach in Fig. 2. + +# 4.1. Multi-View Correspondence Loss + +Directly overfitting on the training images leads to a corrupted neural radiance field collapsing towards the provided views, even when assuming perfect camera poses [11, 19, 32]. With noisy input poses, the problem becomes amplified, making it impossible to use the photometric loss (7) as the main signal for the joint pose-NeRF training. We propose a training objective, the multi-view correspondence loss, to enforce learning a globally consistent 3D solution over the optimized scene geometry and camera poses. + +Multi-view geometry constraint: We draw inspiration from principles of multi-view geometry [17]. We assume that given an image pair $(I_i, I_j)$ , we can obtain pairs of matching pixels $\mathbf{p} \in I_i$ and $\mathbf{q} \in I_j$ . We then compute estimates of the depth at both pixels $\hat{z}_{i,\mathfrak{p}} = \hat{z}(\mathbf{p}; \theta, \hat{P}_i)$ and $\hat{z}_{j,\mathfrak{q}} = \hat{z}(\mathbf{q}; \theta, \hat{P}_j)$ according to eq. (6). Principles of multiview geometry dictate that both pixels must backproject to the same 3D point in the world coordinate system. This is formulated as $\hat{P}_j \pi^{-1}(\mathbf{q}, \hat{z}_{j,\mathfrak{q}}) = \hat{P}_i \pi^{-1}(\mathbf{p}, \hat{z}_{i,\mathfrak{p}})$ . However, when translating this constraint into a training objective, the magnitude of the loss is subject to large variations depending on the scene scale and the initial camera poses, requiring a tedious tuning of the loss weighting. + +Training objective: We instead project the 3D points back to image space, therefore minimizing the distance between pixels rather than directly in 3D space. We illustrate this objective in Fig. 2 (steps 1-2). For a randomly sampled training image pair $(I_i, I_j)$ , our multi-view correspondence objective is formulated as $\mathcal{L}_{\mathrm{MVCorr}}(\theta, \hat{\mathcal{P}}) = \sum_{\mathrm{p} \in \mathcal{V}} \mathcal{L}_{\mathrm{p}}$ , where + +$$ +\mathcal {L} _ {\mathrm {p}} = w _ {\mathrm {p}} \rho \left(\mathbf {q} - \pi \left(\hat {P} _ {j} ^ {- 1} \hat {P} _ {i} \quad \pi^ {- 1} (\mathbf {p}, \hat {z} (\mathbf {p}; \theta , \hat {P} _ {i}))\right)\right). \tag {8} +$$ + +Here $\rho$ denotes the Huber loss function [18] and $w_{\mathfrak{p}} \in [0,1]$ is the confidence associated with the correspondence $(\mathbf{p}, \mathbf{q})$ , which we obtain as detailed below. We additionally define the set $\mathcal{V} = \{\mathbf{p}: w_{\mathfrak{p}} \geq \kappa\}$ , where $\kappa = 0.95$ . The homogenization operations were omitted for clarity. + +Our loss serves two purposes. By connecting the training images through correspondences, our multi-view correspondence objective enforces the learned geometry and camera poses to converge to a solution geometrically consistent across all training images. This is unlike the photometric loss (7) which applies supervision on each training image independently. Moreover, the underlying constraint is only satisfied if the learned 3D points converge to the true reconstructed scene (up to a similarity). As such, the objective (8) provides direct supervision on the rendered depth (6), implicitly enforcing it to be close to the surface. + +Correspondence prediction: Any classical [27, 35] or learned [13,36,42,44,45] matching approach could be used to obtain the matches relating pairs of training views. We rely on a pre-trained dense correspondence regression network, in particular PDC-Net [43]. It predicts a match $\mathbf{q}$ for each pixel $\mathbf{p}$ , along with a confidence $w_{\mathrm{p}}$ . We found + +the high number of accurate matches to be beneficial for our joint pose-NeRF refinement. Similar conclusions were derived in the context of dense versus sparse depth supervision [11,34]. The dense correspondence map also implicitly imposes a smoothness prior to the rendered depth. In suppl., we present results using a sparse matcher [12, 36] instead. + +# 4.2. Improving Geometry at Unobserved Views + +The multi-view correspondence loss favors a global and geometrically accurate solution, consistent across all training images. Nevertheless, the reconstructed scene often still suffers from inconsistencies when seen from novel viewpoints. For those, no RGB supervision is available during training. We propose an additional training objective, the depth consistency loss, which encourages the learned geometry to be consistent from any viewing direction. + +Depth consistency loss: The main idea is to use the depth maps rendered from the training viewpoints to create pseudo-depth supervision for novel, unseen, viewpoints (Fig. 2, step 3). We sample a virtual pose $P_{un}$ , in practice obtained as an interpolation between the poses of two close-by training views. For a pixel $\mathbf{p}$ in a sampled training image $I_i$ , $\mathbf{r_p}^{un} = P_{un}^{-1}\hat{P}_i\pi^{-1}(\mathbf{p},\hat{z} (\mathbf{p};\theta ,\hat{P}_i))$ is the corresponding 3D point in the coordinate system of the unseen view $P_{un}$ . $\mathbf{y}\in \mathbb{R}^2$ denotes its pixel projection in view $P_{un}$ as $\mathbf{y} = \pi \left(\mathbf{r}_{\mathrm{p}}^{un}\right)$ , and $z_{\mathrm{y}}$ is its projected depth in $P_{un}$ , i.e. $z_{\mathrm{y}} = \left[\mathbf{r}_{\mathrm{p}}^{un}\right]_3$ , where $[\cdot ]_3$ refers to taking the third coordinate of the vector. We formulate our depth consistency loss as, + +$$ +\mathcal {L} _ {\mathrm {D C o n s}} (\theta) = \sum_ {\mathrm {p}} \gamma_ {\mathrm {y}} \rho \left(z _ {\mathrm {y}} - \hat {z} (\mathbf {y}; \theta , P _ {u n})\right). \tag {9} +$$ + +To account for occlusion and out-of-view projections in which (9) is invalid, we have included a visibility mask $\gamma_{\mathrm{y}} \in [0,1]$ . We explain its definition in the section below. + +Since the pseudo-depth supervision $z_{\mathrm{y}}$ is created from renderings, it is subject to errors. For this reason, we find it important to backpropagate through the pseudo-supervision $\mathbf{y}$ and $z_{\mathrm{y}}$ . Note that we however do not backpropagate through the pose estimate $\hat{P}_i$ . Moreover, as verified experimentally in Tab. 2, our depth consistency objective (9) is complementary to our multi-view correspondence loss (8), the latter enforcing an accurate reconstructed geometry while the former ensures it is consistent from any viewpoint. + +Visibility mask $\gamma_{\mathbf{y}}$ : We first exclude points if their pixel projections $\mathbf{y}$ is outside of the virtual view, by setting the mask as $\gamma_{\mathrm{y}} = 0$ . The depth consistency loss is also invalid for pixels that are occluded by the reconstructed scene in the virtual view. To identify these occluded pixels, we follow the strategy of [10]. In particular, we check whether there are occupied regions on the ray between the camera center $\mathbf{o}_{un}$ of $P_{un}$ and the 3D point $\mathbf{r}_{un,\mathbf{y}}(z_{\mathbf{y}})$ at depth $z_{\mathbf{y}}$ . We compute how occluded a 3D point is with its transmittance (5) in the unseen view, as $\gamma_{\mathrm{y}} = T_{un,z_{\mathbf{y}}}$ . Intuitively, $\gamma_{\mathrm{y}}$ + +is close to 1 if there is no point with a large density between the camera center $\mathbf{o}_{un}$ and $\mathbf{r}_{un,y}(z_y)$ , otherwise it is close to 0. Next, we present our overall training framework. + +# 4.3. Training Framework + +Staged training: Our final training objective is formulated as $\mathcal{L}(\theta, \hat{\mathcal{P}}) = \mathcal{L}_{\mathrm{photo}}(\theta, \hat{\mathcal{P}}) + \lambda_{\mathrm{c}} \mathcal{L}_{\mathrm{MVCorr}}(\theta, \hat{\mathcal{P}}) + \lambda_{\mathrm{d}} \mathcal{L}_{\mathrm{DCons}}(\theta)$ , where $\lambda_{\mathrm{c}}$ and $\lambda_{\mathrm{d}}$ are predefined weighting factors. The training is split into two stages. In the first part, the pose estimates are trained jointly with the coarse MLP $F_{\theta}^{c}$ . However, due to the exploration of the pose space at the early stages of training, the learned scene tends to showcase blurry surfaces. As a result, in the second training stage, we freeze the pose estimates and train both the coarse and fine networks $F_{\theta}^{c}$ and $F_{\theta}^{f}$ . This ensures that the fine network learns a sharp geometry, benefiting from the pre-trained coarse network. From a practical perspective, our training objectives can be integrated at a low computational cost, since the RGB or depth pixel renderings (3)-(6) can be shared between the three loss terms. + +Coarse-to-fine positional encoding: In BARF [24], Lin et al. propose to gradually activate the high-frequency components of the positional encodings (2) over the course of the optimization. We refer the reader to [24] for the exact formulation. While originally proposed in the context of pose refinement, we found that this strategy is also extremely beneficial in the sparse-view setting, even when the poses are fixed. It prevents the network from immediately overfitting to the training images, thereby avoiding the worst degenerate geometries. We therefore adopt this coarse-to-fine positional encoding approach as default. + +# 5. Experimental Results + +We evaluate the proposed SPARF for novel-view rendering in the few-view setting, in particular when only three input views are available. Results with different numbers of views are provided in suppl. We extensively analyze our method and compare it to earlier approaches, setting a new state of the art on multiple datasets. Further results, visualizations, and implementation details are provided in suppl. + +# 5.1. Experimental Settings + +Datasets and metrics: We report results on the DTU [20], LLFF [38] and Replica [39] datasets, for the challenging scenario of 3 input views. DTU is composed of complex object-level scenes with wide-baseline views spanning a half hemisphere. We adhere to the protocol of [53] and evaluate on their reported test split of 15 scenes. Following [32], we additionally evaluate all methods with the object masks applied to the rendered images, to avoid penalizing methods for incorrect background predictions. On LLFF, we follow community standards [30] and use every $8^{\text{th}}$ image as + +
MethodPSNR ↑SSIM ↑LPIPS ↓DE ↓
I Full PE [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)0.87
II Smaller MLP model9.03 (10.06)0.34 (0.65)0.68 (0.34)0.79
III No PE16.11 (18.40)0.68 (0.80)0.37 (0.24)0.30
IV CF PE [24] (Sec. 4.3)16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
+ +Table 1. Comparison of different positional encoding strategies applied to NeRF [30] on DTU (3 views), using ground-truth poses. Results in $(\cdot)$ are computed by masking the background. + +the test set. We sample the training views evenly from the remaining images. For the Replica dataset, which depicts videos of room-scale indoor scenes, we subsample every $k^{th}$ frame, from which we randomly select a triplet of consecutive training images. As metrics, we report the average rotation and translation errors for pose registration, and PSNR, SSIM [47] and LPIPS [57] for view synthesis. On the DTU and Replica datasets, we additionally compare the rendered depth with the available ground-truth depth and compute the mean depth absolute error (DE). + +Implementation details: We train our approach for 100K iterations, which takes about 10 hours on a single A100 GPU. As pose parametrization, we adopt the continuous 6-vector representation [58] for the rotation and directly optimize the translation vector. We provide all training hyperparameters in the supplementary. + +# 5.2. Method Analysis + +We first perform a comprehensive analysis of our approach, on DTU [20], considering only 3 input views. + +Impact of positional encoding: Training on sparse input views using the standard NeRF [30] immediately overfits to the provided images, even with perfect poses. We noticed that the overfitting is largely due to the high-frequency positional encodings (PE), and thus experimented with different PE strategies. We present the results in Tab. 1. The standard NeRF (I) with high-frequency PE [30] leads to degenerate geometry and novel view renderings. In (II), using a simplified MLP makes little difference. While training without PE (III) largely prevents overfitting, the coarse-to-fine PE strategy [24] leads to the best result, as shown in (IV). + +Ablation study: In Tab. 2, we ablate the key components of our approach, here assuming fixed ground-truth poses and starting from NeRF with coarse-to-fine PE. Adding our multi-view correspondence loss (8) results in drastically better performance on all metrics. Including our depth + +
MV-Corr (8)DCons (9)PSNR ↑SSIM ↑LPIPS ↓DE ↓
XX16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
X✓15.86 (18.91)0.71 (0.82)0.28 (0.14)0.20
✓X18.13 (20.81)0.77 (0.87)0.22 (0.10)0.10
✓✓18.30 (21.01)0.78 (0.87)0.21 (0.10)0.08
+ +Table 2. Ablation study on the DTU dataset (3 views), with fixed ground-truth poses. Results in $(\cdot)$ are computed by masking the background. All networks use the coarse-to-fine PE [24]. + +![](images/c9c1ec2eb336316dc44525589cd2468dfb2cd09acfdba68e0f2f52f149d4987c.jpg) + +![](images/a901ab2a76cfd7b8c914afe414e06be6c47655f3002061cdb70c67d2344d9395.jpg) +Figure 3. We compare two training objectives using ground-truth depth for pose-NeRF training in the sparse-view regime. In (A), a loss comparing for each training image the rendered depth (6) with the ground truth one, can learn locally perfect geometry (as highlighted by the dashed red rectangles). However, the NeRF/poses do not converge to a global solution, because the optimized poses and geometry of the different images are disjoint. Instead, supervising the learned 3D points of each training image to be equal to the ground-truth 3D points in (B) solves this issue, by enforcing the system to converge to a global (unique) geometric solution. + +consistency module (9) further leads to a small improvement, achieving the best performance overall. Also note that our depth-consistency module (9) works best in collaboration with our multi-view correspondences loss (8) since the latter is needed to learn an accurate geometry. + +Intuition on pose-NeRF training losses: We first want to build an intuition on what loss might be suitable for joint pose-NeRF training in the sparse regime. To do so, we use ground-truth depth or 3D data in two alternative training losses, which we compare here. We illustrate this experiment in Fig. 3 and present results in Tab. 3, top part. As in previous work [24], for each scene of DTU [20], we synthetically perturb the ground-truth camera poses with $15\%$ of additive gaussian noise. In (I), we train with an L1 loss comparing the rendered depth (6) with the ground-truth depth (Fig. 3A). Surprisingly, this loss struggles to refine the poses. Instead, in (II) we minimize the distance between the learned 3D points (rendered depth (6) backprojected to world frame) and the ground-truth 3D points, as illustrated in Fig. 3B. This training loss successfully registers the poses, resulting in drastically better novel-view rendering quality. As the main insight from this experiment, we hypothesize that, in the sparse-view regime, it is crucial to enforce an explicit geometric connection between the different training images and their underlying scene geometry. This is not the case in (I), where the depth loss favors per-image locally accurate geometry, but the NeRF/poses can converge to disconnected solutions for each training image. + +Comparison of losses for pose-NeRF training: In Tab. 3 bottom part, we then compare our loss (8) to objectives commonly used for joint pose-NeRF training. The photometric loss (7) (III), even associated with a mask/silhouette + +
LossesRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
I Photo. + L1 GT depth7.328.913.8 (14.0)0.54 (0.70)0.46 (0.27)0.17
II Photo. + L1 GT 3D points0.41.518.8 (20.3)0.75 (0.84)0.21 (0.11)0.07
III Photo. (7)10.351.510.7 (9.8)0.43 (0.62)0.59 (0.36)1.9
IV Photo. + mask loss [23,56]13.257.7----
V MVCorr (8)1.986.6---0.19
VI Photo. + MVCorr ((7)-(8))1.855.516.0 (17.8)0.68 (0.81)0.28 (0.14)0.13
+ +loss [5,23,56] in (IV), completely fails to register the poses, thus leading to poor novel-view synthesis performance. This is in line with our hypothesis that it is important to explicitly exploit the geometric relation between the training views for successful registration. Moreover, because the 3D space is under-constrained in the sparse-view regime, multiple neighboring poses can lead to similar mask losses. While our multi-view correspondence loss (8) alone (V) already drastically outperforms the photometric loss (III) in terms of pose and learned geometry (depth error), combining the two in (VI) leads to the best performance. This is because, through the correspondences, our approach favors a NeRF/pose solution consistent across all training images. Note that this version neither includes our depth consistency loss (9) (Sec. 4.2) nor our staged training (Sec. 4.3). + +# 5.3. Comparison to SOTA with Noisy Poses + +Here, we evaluate SPARF, our joint pose and NeRF training approach. Results with different pose initialization schemes are presented in the supplementary. + +Baselines: We compare to BARF [24], the state-of-the-art in pose-NeRF refinement when assuming dense input views. It is representative of a line of approaches [9, 24, 29, 48, 50] using the photometric loss (7) as the main signal. We also experiment with adding the depth regularization loss of [32] or the ray sparsity loss of [4] to BARF, which we denote as RegBARF and DistBARF respectively. We additionally compare to SCNeRF [21], which uses a geometric loss based on correspondences, minimizing the rays' intersection re-projection error. For a fair comparison, we integrate coarse-to-fine PE [24] (Sec. 4.3) in all methods. + +Results on DTU: Following [9, 24, 50], for each scene, we synthetically perturb the ground-truth camera poses with $15\%$ of additive gaussian noise. The initial poses thus have + +Table 3. Comparison of training objectives for joint pose-NeRF refinement on DTU [20] with initial noisy poses (3 views). Rotation errors are in degree and translation errors are multiplied by 100. Results in $(\cdot)$ are computed by masking the background. + +
MethodRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
BARF [24]10.3351.510.71 (9.76)0.43 (0.62)0.59 (0.36)1.90
RegBARF [24, 32]11.2052.810.38 (9.20)0.45 (0.62)0.61 (0.38)2.33
DistBARF [4, 24]11.6955.79.50 (9.15)0.34 (0.76)0.67 (0.36)1.90
SCNeRF [21]3.4416.412.04 (11.71)0.45 (0.66)0.52 (0.30)0.85
SPARF (Ours)1.815.017.74 (18.92)0.71 (0.83)0.26 (0.13)0.12
+ +Table 4. Evaluation on DTU [20] (3 views) with noisy initial poses. Rotation errors are in $^\circ$ and translation errors are multiplied by 100. Results in $(\cdot)$ are computed by masking the background. + +![](images/f2778eae166540be155231eb9fcd908fbac9fcec6a712672fccf7409a8755fc7.jpg) +Figure 4. Novel-view rendering (RGB and depth). The input (not shown here) contains 3 images with initial noisy camera poses. + +an average rotation and translation error of $15^{\circ}$ and 70 respectively. We show initial and optimized poses in Fig. 5. From the results in Tab. 4 and Fig. 4A, we observe that BARF, RegBARF, and DistBARF completely fail to register the poses, leading to poor view-synthesis quality. SCNeRF's geometric loss performs better at registering the poses but the learned scene still suffers from many inconsistencies. This is because SCNeRF's loss [21] does not influence the learned radiance field function, and thus, cannot prevent the NeRF model from overfitting to the sparse input views. Since our multi-view correspondence loss (8) acts on both the camera pose estimates and the learned neural field by enforcing them to fit the correspondence constraint, it leads to an accurate reconstructed scene. Our approach SPARF hence significantly outperforms all others both in novel-view rendering quality and pose registration. + +Results on LLFF: The LLFF dataset consists of 8 complex forward-facing scenes. Following [24], we initialize all camera poses with the identity transformation and present results in Tab. 5. In [24], Lin et al. show that BARF almost perfectly registers the camera poses given dense input views. However, we show here that it strug + +![](images/617619e6b033ad0ed5bd1b64120c02259088f5567e951c11022fcb18a44ca4a2.jpg) +Figure 5. Optimized poses on DTU with 3 input views. We compare the ground-truth poses (in pink) with the optimized ones (in blue). In the first column, the initial noisy poses are in blue. + +
Rot. (°) ↓Trans. (×100) ↓PSNR ↑SSIM ↑LPIPS ↓
BARF [24]2.0411.617.470.480.37
RegBARF [24, 32]1.525.018.570.520.36
DistBARF [4, 24]5.5926.514.690.340.49
SCNeRF [21]1.9311.417.100.450.40
SPARF (Ours)0.532.819.580.610.31
+ +Table 5. Evaluation on the forward-facing dataset LLFF [38] (3 views) starting from initial identity poses. + +
MethodRot (°) ↓Trans (×100) ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
G SPARF (Ours)Fixed GT poses26.430.880.130.39
F NeRF [30]Fixed poses obtained20.990.730.321.33
DS-NeRF [11]from COLMAP (run w.23.520.810.200.99
SPARF (Ours)PDC-Net [43] matches25.030.840.150.66
R BARF [24]3.3516.9620.730.720.300.84
RegBARF [24, 32]3.6620.8720.000.700.321.00
DistBARF [4, 24]2.367.7322.460.770.230.47
SCNeRF [21]0.654.1222.540.790.240.73
DS-NeRF [11]1.305.0424.750.830.200.69
SPARF (Ours)0.150.7626.980.880.130.36
+ +gles in the sparse-view setting, thereby severely impacting the accuracy of novel view synthesis. While adding the depth smoothness loss (RegBARF) improves results, our approach SPARF outperforms all previous works. A qualitative comparison is shown in Fig. 4B. + +Results on Replica: To demonstrate that our approach is also applicable to non-forward-facing indoor scenes, we evaluate on the Replica dataset in Tab. 6 and Fig. 4C. As pose initialization, we use COLMAP [37] with improved matches, i.e. using PDC-Net [43]. The initial pose estimates thus have an average rotation and translation error of respectively $0.39^{\circ}$ and 3.01. Comparing the top (G) and middle part (F) of Tab. 6, we show that even such a low initial error impacts the novel-view rendering quality when using fixed poses. In the bottom part (R), our pose-NeRF training strategy leads to the best results, matching the accuracy obtained by our approach with perfect poses (top row, G). + +# 5.4. Comparison to SOTA with Ground-Truth Poses + +Finally, we show that our approach brings significant improvement in novel view rendering quality even when considering fixed ground-truth poses. + +Baselines: We compare to works specifically designed to tackle per-scene few-shot novel view rendering, namely DietNeRF [19], DS-NeRF [11], InfoNeRF [22] and RegNeRF [32], along with the standard NeRF [30] and MipNeRF [3]. For completeness, we also compare against a state-of-the-art conditional model, PixelNeRF [53], trained on DTU [20] and further finetuned per-scene on LLFF [38]. + +Table 6. Evaluation on Replica [39] (3 views) with initial poses obtained by COLMAP [37, 43]. The initial rotation and translation errors are $0.39^{\circ}$ and 3.01 respectively. In the middle part (F), these initial poses are fixed and used as "pseudo-gt". In the bottom part (R), the poses are refined along with training the NeRF. For comparison, in the top part (G), we use fixed ground-truth poses. The best and second-best results are in red and blue respectively. + +
MethodDTULLFF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [53]19.36 (18.00)0.70 (0.77)0.32 (0.23)7.930.270.68
PixelNeRF-ft [53]---16.170.440.51
MipNeRF [3]7.64 (8.68)0.23 (0.57)0.66 (0.35)14.620.350.50
NeRF [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)13.610.280.56
DietNeRF [19]10.01 (11.85)0.35 (0.63)0.57 (0.31)14.940.370.5
InfoNeRF [22]11.23 (-)0.44 (-)0.54 (-)---
RegNeRF [32]15.33 (18.89)0.62 (0.75)0.34 (0.19)19.080.590.34
DS-NeRF [11]16.52 (-)0.54 (-)0.48 (-)18.000.550.27
SPARF (Ours)18.30 (21.01)0.78 (0.87)0.21 (0.10)20.200.630.24
+ +Table 7. Evaluation on DTU [20] and LLFF [38] (3 views), with fixed ground-truth poses. Results in $(\cdot)$ are computed by masking the background. Results of [3, 19, 32] are taken from [32]. The best and second-best results are in red and blue respectively. + +Results: We present results on DTU and LLFF in Tab. 7. Compared to previous per-scene approaches [19,22,32] that only apply different regularization to the learned scene, our multi-view correspondence loss (8) provides a strong supervision on the rendered depth, implicitly encouraging it to be close to the true surface. Our depth consistency objective (9) further boosts the performance, by directly enforcing the learned scene to be consistent from any viewpoint. As a result, our approach SPARF performs best compared to all baselines on both datasets and for all metrics. The only exception is PSNR on the whole image compared to conditional model PixelNeRF [53]. This is because DTU has black backgrounds, where a wrong color prediction (like in Fig. 4A for SPARF) has a large impact on the PSNR value. For conditional models which rely on feature projections, it is easier to predict a correct background color. However, most real-world applications are more interested in accurately reconstructing the object of interest than the background. When evaluated only in the object region, our SPARF obtains 3.24dB higher PSNR than PixelNeRF. + +# 6. Conclusion + +We propose SPARF, a joint pose-NeRF training strategy capable of producing realistic novel-view renderings given few wide-baseline input images with noisy camera pose estimates. By integrating two novel objectives inspired by multi-view geometry principles, we set a new state of the art on three challenging datasets. + +Limitations and future work: Our approach is only applicable to input image collections where each image has covisible regions with at least one other. Moreover, the performance of our method depends on the quality of the matching network. Filtering strategies or per-scene online refinement of the correspondence network thus appear as promising future directions. An interesting direction is also to refine the camera intrinsics and distortion parameters along with the extrinsics. Finally, using voxel grids to encode the radiance field [31] instead of an MLP could lead to faster convergence, and potentially even better results. + +# References + +[1] Wei Wang 0108, Zheng Dang, Yinlin Hu, Pascal Fua, and Mathieu Salzmann. Backpropagation-friendly eigendecomposition. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d'Alché Buc, Edward A. Fox, and Roman Garnett, editors, Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, 8-14 December 2019, Vancouver, BC, Canada, pages 3156-3164, 2019. 1 +[2] Dejan Azinovic, Ricardo Martin-Brualla, Dan B. 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While showing impressive performance, it relies on the availability of dense input views with highly accurate camera poses, thus limiting its application in real-world scenarios. In this work, we introduce Sparse Pose Adjusting Radiance Field (SPARF), to address the challenge of novel-view synthesis given only few wide-baseline input images (as low as 3) with noisy camera poses. Our approach exploits multi-view geometry constraints in order to jointly learn the NeRF and refine the camera poses. By relying on pixel matches extracted between the input views, our multiview correspondence objective enforces the optimized scene and camera poses to converge to a global and geometrically accurate solution. Our depth consistency loss further encourages the reconstructed scene to be consistent from any viewpoint. 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NeRF encodes 3D scenes with a multi-layer perceptron (MLP) mapping 3D point locations to color and volume density and uses volume rendering to synthesize images. It has demonstrated remarkable abilities for high-fidelity view synthesis under two conditions: dense input views and highly accurate camera poses." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 628, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 700 + ], + "type": "text", + "content": "Both these requirements however severely impede the usability of NeRFs in real-world applications. For instance, in AR/VR or autonomous driving, the input is inevitably much sparser, with only few images of any particular object or region available per scene. 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Novel-view rendering from sparse images. We show the RGB (second row) and depth (last row) renderings from an unseen viewpoint under sparse settings (3 input views only). Even with ground-truth camera poses, NeRF [30] overfits to the training images, leading to degenerate geometry (almost constant depth). BARF [24], which can successfully handle noisy poses when dense views are available, struggles in the sparse regime. 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Moreover, the de-facto standard to estimate per-scene poses is to use an off-the-shelf Structure-from-Motion approach, such as COLMAP [37]. When provided with many input views, COLMAP can generally estimate accurate camera poses. Its performance nevertheless rapidly degrades when reducing the number of views, or increasing the baseline between the images [55]." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "Multiple works focus on improving NeRF's performance in the sparse-view setting. One line of research [6,53] trains conditional neural field models on large-scale datasets. Alternative approaches instead propose various regularization on color and geometry for per-scene training [11, 19, 22, 32, 34]. Despite showing impressive results in the sparse scenario, all these approaches assume perfect camera poses as a pre-requisite. Unfortunately, estimating accurate camera poses for few wide-baseline images is challenging [55] and has spawned its own research direction [1, 7, 14-16, 28, 60]," + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 705, + 255, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 705, + 255, + 715 + ], + "spans": [ + { + "bbox": [ + 66, + 705, + 255, + 715 + ], + "type": "text", + "content": "*This work was conducted during an internship at Google." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "text", + "content": "4190" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 217, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 217, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 217, + 83 + ], + "type": "text", + "content": "hence making this assumption unrealistic." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 86, + 286, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 86, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 86, + 286, + 240 + ], + "type": "text", + "content": "Recently, multiple approaches attempt to reduce the dependency of NeRFs on highly accurate input camera poses. They rely on per-image training signals, such as a photometric [9, 24, 29, 48, 50] or silhouette loss [5, 23, 56], to jointly optimize the NeRF and the poses. However, in the sparse-view scenario where the 3D space is under-constrained, we observe that it is crucial to explicitly exploit the relation between the different training images and their underlying scene geometry, to enforce learning a global and geometrically accurate solution. This is not the case of previous works [5, 23, 24, 48, 50, 56], which hence fail to register the poses in the sparse regime. As shown in Fig. 1, middle for BARF [24], it leads to poor novel-view synthesis quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 242, + 286, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 286, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 286, + 529 + ], + "type": "text", + "content": "We propose Sparse Pose Adjusting Radiance Field (SPARF), a joint pose-NeRF training strategy. Our approach produces realistic novel-view renderings given only few wide-baseline input images (as low as 3) with noisy camera poses (see Fig. 1 right). Crucially, it does not assume any prior on the scene or object shape. We introduce novel constraints derived from multi-view geometry [17] to drive and bound the NeRF-pose optimization. We first infer pixel correspondences relating the input views with a pre-trained matching model [43]. These pixel matches are utilized in our multi-view correspondence objective, which minimizes the re-projection error using the depth rendered by the NeRF and the current pose estimates. Through the explicit connection between the training views, the loss enforces convergence to a global and geometrically accurate pose/scene solution, consistent across all training views. We also propose the depth consistency loss to boost the rendering quality from novel viewpoints. By using the depth rendered from the training views to create pseudo-ground-truth depth for unseen viewing directions, it encourages the reconstructed scene to be consistent from any viewpoint. We extensively evaluate and compare our approach on the challenging DTU [20], LLFF [38], and Replica [39] datasets, setting a new state of the art on all three benchmarks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 544, + 134, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 134, + 556 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 134, + 556 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 566, + 286, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 286, + 589 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 286, + 589 + ], + "type": "text", + "content": "We review approaches focusing on few-shot novel view rendering as well as joint pose-NeRF refinement." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Sparse input novel-view rendering: To circumvent the requirement of dense input views, a line of works [6,8,25,41, 46, 53] incorporates prior knowledge by pre-training conditional models of radiance fields on large posed multi-view datasets. Despite showing promising results on sparse input images, their generalization to out-of-distribution novel views remains a challenge. Multiple works [11, 19, 22, 32, 34] follow a different direction, focusing on per-scene training for few-shot novel view rendering. DietNeRF [19] compares CLIP [33] embeddings of rendered and training" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 276 + ], + "type": "text", + "content": "views. InfoNeRF [22] penalizes the NeRF overfitting to limited input views with a ray entropy regularization. Similarly, Barron et al. [4] introduce a distortion loss, which encourages sparsity of the density in each ray. In RegNeRF, Niemeyer et al. [32] propose to regularize the geometry and appearance of rendered patches with a depth smoothness and normalizing flow objectives. Recently, a number of works [11, 34, 49, 54] incorporate depth priors to constraint the NeRF optimization. Notably, DS-NeRF [11] improves reconstruction accuracy by including additional sparse depth supervision. Related are also approaches that learn a signed distance function (SDF), aiming for accurate 3D reconstruction in the sparse-view scenario [26, 51]. However, all these works assume perfect poses as a prerequisite. We instead propose a novel training strategy leading to accurate geometry and novel-view renderings in the sparse regime, even when facing imperfect input poses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 280, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 545, + 602 + ], + "type": "text", + "content": "Joint NeRF and pose refinement: Several approaches attempt to reduce NeRF's reliance on highly accurate input camera poses [9,24,29,48,50]. BARF [24] and NeRF-- [48] jointly optimize the radiance field and camera parameters of initial noisy poses, relying on the photometric loss as the only training signal. SiNeRF [50] and GARF [9] propose different activation functions, easing the pose optimization. GNeRF [29] introduces a sequential training approach including a rough initial pose network that uses GAN-style training, thereby circumventing the need for initial pose estimates. SCNeRF [21] proposes a geometric loss minimizing the ray intersection re-projection error at previously extracted sparse correspondences to optimize over camera extrinsics and intrinsics. A number of works [5, 23, 52] also combine the photometric objective with a silhouette or mask loss, requiring accurate foreground segmentation, and limiting their applicability to objects. Related are also implicit SLAM systems [2, 40, 59], which progressively optimize over the geometry and camera estimates of an input RGB-D sequence. While previous works assume a dense coverage of the 3D space, Zhang et al. propose NeRS [56], which tackles the task of single object reconstruction by deforming a unit sphere over time while refining poses of few input views. However, NeRS is restricted to simple objects with a known shape prior. We instead assume access to only few wide-baseline RGB images with noisy pose estimates, without any prior on the scene or object shape." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 616, + 390, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 390, + 628 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 390, + 628 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 638, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 638, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 638, + 545, + 661 + ], + "type": "text", + "content": "We first briefly introduce notation, the basics of NeRF representation, and camera operations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": "Camera pose: Let " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "P_{i}^{c2w} = \\left[R_{i}^{c2w}|\\mathbf{t}_{i}^{c2w}\\right] \\in SE(3)" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": " be the camera-to-world transform of camera " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "R_{i}^{c2w} \\in SO(3)" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{i}^{c2w} \\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": " are the rotation and translation, respectively. We denote as " + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "inline_equation", + "content": "K \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 304, + 664, + 545, + 713 + ], + "type": "text", + "content": " the intrinsic matrix." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 314, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 314, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 314, + 758 + ], + "type": "text", + "content": "4191" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "For the rest of the manuscript, we drop the superscript " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "^{c2w}" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": ". As a result, unless otherwise stated, " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "P = P^{c2w}" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " and all 3D quantities are defined in the world coordinate system." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": "Camera projection: For any vector " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^l" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " of dimension " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{x}} \\in \\mathbb{R}^{l+1}" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " corresponds to its homogeneous representation, i.e., " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{x}} = [\\mathbf{x}^T, 1]" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": ". We additionally define " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " to be the camera projection operator, which maps a 3D point in the camera coordinate frame " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^c \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " to a pixel coordinate " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": ". Likewise, " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\pi^{-1}" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " is defined to be the backprojection operator, which maps a pixel " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " and depth " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": " to a 3D point " + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^c" + }, + { + "bbox": [ + 46, + 110, + 286, + 194 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 80, + 202, + 287, + 217 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 202, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 80, + 202, + 287, + 217 + ], + "type": "interline_equation", + "content": "\\pi \\left(\\mathbf {x} ^ {c}\\right) \\cong K \\mathbf {x} ^ {c}, \\quad \\pi^ {- 1} (\\mathbf {p}, z) = z K ^ {- 1} \\bar {\\mathbf {p}}. \\tag {1}", + "image_path": "e3472e3a14c50d59aee490b66b27c7db9064bf06a7306cb249521e7b76c5a650.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "text", + "content": "Scene representation: We adopt the NeRF [30] framework to represent the underlying 3D scene and image formation. A neural radiance field is a continuous function that maps a 3D location " + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "text", + "content": " and a unit-norm ray viewing direction " + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{d} \\in \\mathbb{S}^2" + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "text", + "content": " to an RGB color " + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in [0,1]^3" + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "text", + "content": " and volume density " + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}^+" + }, + { + "bbox": [ + 46, + 225, + 287, + 297 + ], + "type": "text", + "content": ". It can be formulated as" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 306, + 287, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 306, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 110, + 306, + 287, + 319 + ], + "type": "interline_equation", + "content": "[ \\mathbf {c}, \\sigma ] = F _ {\\theta} \\left(\\gamma_ {x} (\\mathbf {x}), \\gamma_ {d} (\\mathbf {d})\\right). \\tag {2}", + "image_path": "52f875095a3b7890d250220a2d4ca3b791d07982215923d3558d0ba3bc658c5a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "text", + "content": " is an MLP with parameters " + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "inline_equation", + "content": "\\gamma: \\mathbb{R}^3 \\to \\mathbb{R}^{3+6L}" + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "text", + "content": " is a positional encoding function with " + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 324, + 286, + 348 + ], + "type": "text", + "content": " frequency bases." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": "Volume rendering: Given a camera pose " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "P_{i}" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": ", each pixel coordinate " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " determines a ray in the world coordinate system, whose origin is the camera center of projection " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_i = \\mathbf{t}_i" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " and whose direction is defined as " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_{i,\\mathrm{p}} = R_i K_i^{-1} \\bar{\\mathbf{p}}" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": ". We can express a 3D point along the viewing ray associated with " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " at depth " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{i,\\mathrm{p}}(t) = \\mathbf{o}_i + t \\mathbf{d}_{i,\\mathrm{p}}" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": ". To render the color " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{I}}_{i,\\mathrm{p}} \\in [0,1]^3" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " at pixel " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": ", we sample " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " discrete depth values " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "t_m" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " along the ray within the near and far plane " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "[t_n, t_f]" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": ", and query the radiance field " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "F_\\theta(2)" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " at the underlying 3D points. The corresponding predicted color and volume density values " + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{c}_m, \\sigma_m)\\}_{m=1}^M" + }, + { + "bbox": [ + 46, + 351, + 287, + 485 + ], + "type": "text", + "content": " are then composited as," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 494, + 287, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 494, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 116, + 494, + 287, + 526 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {I}} _ {i, \\mathbf {p}} = \\hat {I} (\\mathbf {p}; \\theta , P _ {i}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} \\mathbf {c} _ {m}, \\tag {3}", + "image_path": "a77a0cc9052461636cc83b934c85e5d4e869384b8361c145200e1279c237c072.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 82, + 529, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 529, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 82, + 529, + 287, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 82, + 529, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\alpha_{m} = T_{m}\\left(1 - \\exp (-\\sigma_{m}\\delta_{m})\\right)" + }, + { + "bbox": [ + 82, + 529, + 287, + 542 + ], + "type": "text", + "content": " (4)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 116, + 544, + 287, + 577 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 544, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 116, + 544, + 287, + 577 + ], + "type": "interline_equation", + "content": "T _ {m} = \\exp \\left(- \\sum_ {m ^ {\\prime} = 1} ^ {m} \\sigma_ {m ^ {\\prime}} \\delta_ {m ^ {\\prime}}\\right). \\tag {5}", + "image_path": "5fc4b3c507d131f467e0f5730c5b54659cdd9af813e8fb43d5abeeabafd42548.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "inline_equation", + "content": "T_{m}" + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "text", + "content": " denotes the accumulated transmittance along the ray from " + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "inline_equation", + "content": "t_m" + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\delta_{m} = t_{m + 1} - t_{m}" + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "text", + "content": " is the distance between adjacent samples. Similarly, the approximate depth of the scene viewed from pixel " + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 584, + 287, + 632 + ], + "type": "text", + "content": " is obtained as," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 99, + 640, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 640, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 99, + 640, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\hat {z} _ {i, \\mathrm {p}} = \\hat {z} (\\mathbf {p}; \\theta , P _ {i}) = \\sum_ {m = 1} ^ {M} \\alpha_ {m} t _ {m}. \\tag {6}", + "image_path": "477858ca6f638125d4cf1eb419528a23090c006a26fb335dfb69b2d213acf835.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{I}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{z}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " denote the RGB and depth rendering functions. In practice, NeRF [30] trains two MLPs, a coarse network " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "F_{\\theta}^{c}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " and a fine network " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "F_{\\theta}^{f}" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": ", where the former is" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": "used to guide sampling along the ray for the latter, thereby enabling more accurate estimation of (3)-(6)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "spans": [ + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "content": "Photometric loss: Given a dataset of " + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "content": " RGB images " + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{I_1, I_2, \\dots, I_n\\}" + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "content": " of a scene associated with initial noisy poses " + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}} = \\left\\{\\hat{P}_1, \\hat{P}_2, \\dots, \\hat{P}_n\\right\\}" + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "content": ", previous approaches [9, 24, 48, 50] optimize the radiance field function " + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "content": " along with the camera pose estimates " + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 305, + 99, + 545, + 164 + ], + "type": "text", + "content": " using a photometric loss as follows," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 174, + 545, + 205 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 174, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 317, + 174, + 545, + 205 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p h o t o}} (\\theta , \\hat {\\mathcal {P}}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\sum_ {\\mathrm {p}} \\left\\| I _ {i} (\\mathbf {p}) - \\hat {I} (\\mathbf {p}; \\theta , \\hat {P} _ {i}) \\right\\| _ {2} ^ {2}. \\tag {7}", + "image_path": "13ee1a2fdd4bd441ae7c4000a0bed28671c802d5afdee8a23a5e1bc50e82cc8b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 214, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 214, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 214, + 545, + 251 + ], + "type": "text", + "content": "While this works well with dense views, it fails in the sparse regime. We propose an approach to effectively refine the poses and train the neural field for this challenging scenario." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 262, + 361, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 361, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 361, + 274 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 545, + 354 + ], + "type": "text", + "content": "This work addresses the challenge of novel view synthesis based on neural implicit representations, in the sparse-view regime. In particular, we assume access to only sparse input views with noisy camera pose estimates. The training image collection contains few images (as low as 3) and they present large viewpoint variations." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 354, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 557 + ], + "type": "text", + "content": "This leads to two major challenges: (i) given only few input images, the NeRF model [30] instantly overfits to the training views without learning a meaningful 3D geometry, even with perfect input camera poses [19,22,32]. As shown in Fig. 1, this leads to degenerate novel view renderings, including for similar train/test viewing directions. The problem becomes amplified when considering noisy input camera poses. (ii) Previous pose-NeRF refinement approaches [5,9,24,48,50] were designed considering a dense coverage of the 3D space, i.e. many input views. They apply their training objectives, e.g. the photometric loss (7), on each training image independently. However, in the sparse-view regime, i.e. where the 3D space is under-constrained, such supervision is often too weak for the pose/NeRF system to converge to a globally consistent geometric solution. Failure to correctly register the training poses also leads to poor novel view rendering quality (see Fig. 1, 4)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "We propose SPARF, a simple, yet effective training strategy to jointly learn the scene representation and refine the initial training poses, tailored for the sparse-view scenario. As the prominent source of inspiration, we draw from well-established principles of multi-view geometry [17], which we adapt to the NeRF framework. In Sec. 4.1, we introduce our multi-view correspondence objective as the main driving signal for the joint pose-NeRF training. By relying on pixel correspondences between the training views, the loss enforces convergence to a global and accurate geometric solution consistent across all training views, thereby solving both challenges (i) and (ii). Moreover, in Sec. 4.2 we propose an additional term, i.e. the depth consistency loss," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "text", + "content": "4192" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 539, + 252 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 539, + 252 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 539, + 252 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 539, + 252 + ], + "type": "image", + "image_path": "2b67d87eadaa314ce304ba9e93e3ed223d1d95982d7a83d85bc5a50ade5c73c5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 255, + 547, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 547, + 332 + ], + "type": "text", + "content": "Figure 2. Our approach SPARF for joint pose-NeRF training given only few input images with noisy camera pose estimates. We first rely on a pre-trained dense correspondence network [43] to extract matches between the training views. Our multi-view correspondence loss (Sec. 4.1) minimizes the re-projection error between matches, i.e. it enforces each pixel of a particular training view to project to its matching pixel in another training view. We use the rendered NeRF depth (6) and the current pose estimates " + }, + { + "bbox": [ + 46, + 255, + 547, + 332 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 255, + 547, + 332 + ], + "type": "text", + "content": " to backproject each pixel in 3D space. This constraint hence encourages the learned scene and pose estimates to converge to a global and accurate geometric solution, consistent across all training views. Our depth consistency loss (Sec. 4.2) further uses the rendered depths from the training viewpoints to create pseudo-depth supervision for unseen viewpoints, thereby encouraging the reconstructed scene to be consistent from any direction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 341, + 288, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 288, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 288, + 413 + ], + "type": "text", + "content": "which encourages the learned scene geometry to be consistent across all viewpoints, including those for which no RGB supervision is available. In doing so, it boosts novel-view rendering quality, further tackling the overfitting problem (i). We present our final training strategy in Sec. 4.3 and visualize our approach in Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 424, + 227, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 227, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 227, + 437 + ], + "type": "text", + "content": "4.1. Multi-View Correspondence Loss" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 444, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 552 + ], + "type": "text", + "content": "Directly overfitting on the training images leads to a corrupted neural radiance field collapsing towards the provided views, even when assuming perfect camera poses [11, 19, 32]. With noisy input poses, the problem becomes amplified, making it impossible to use the photometric loss (7) as the main signal for the joint pose-NeRF training. We propose a training objective, the multi-view correspondence loss, to enforce learning a globally consistent 3D solution over the optimized scene geometry and camera poses." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": "Multi-view geometry constraint: We draw inspiration from principles of multi-view geometry [17]. We assume that given an image pair " + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "inline_equation", + "content": "(I_i, I_j)" + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": ", we can obtain pairs of matching pixels " + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p} \\in I_i" + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{q} \\in I_j" + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": ". We then compute estimates of the depth at both pixels " + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{z}_{i,\\mathfrak{p}} = \\hat{z}(\\mathbf{p}; \\theta, \\hat{P}_i)" + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{z}_{j,\\mathfrak{q}} = \\hat{z}(\\mathbf{q}; \\theta, \\hat{P}_j)" + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": " according to eq. (6). Principles of multiview geometry dictate that both pixels must backproject to the same 3D point in the world coordinate system. This is formulated as " + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{P}_j \\pi^{-1}(\\mathbf{q}, \\hat{z}_{j,\\mathfrak{q}}) = \\hat{P}_i \\pi^{-1}(\\mathbf{p}, \\hat{z}_{i,\\mathfrak{p}})" + }, + { + "bbox": [ + 46, + 555, + 288, + 715 + ], + "type": "text", + "content": ". However, when translating this constraint into a training objective, the magnitude of the loss is subject to large variations depending on the scene scale and the initial camera poses, requiring a tedious tuning of the loss weighting." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "type": "text", + "content": "Training objective: We instead project the 3D points back to image space, therefore minimizing the distance between pixels rather than directly in 3D space. We illustrate this objective in Fig. 2 (steps 1-2). For a randomly sampled training image pair " + }, + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "type": "inline_equation", + "content": "(I_i, I_j)" + }, + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "type": "text", + "content": ", our multi-view correspondence objective is formulated as " + }, + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MVCorr}}(\\theta, \\hat{\\mathcal{P}}) = \\sum_{\\mathrm{p} \\in \\mathcal{V}} \\mathcal{L}_{\\mathrm{p}}" + }, + { + "bbox": [ + 304, + 341, + 545, + 417 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 311, + 422, + 545, + 442 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 422, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 311, + 422, + 545, + 442 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p}} = w _ {\\mathrm {p}} \\rho \\left(\\mathbf {q} - \\pi \\left(\\hat {P} _ {j} ^ {- 1} \\hat {P} _ {i} \\quad \\pi^ {- 1} (\\mathbf {p}, \\hat {z} (\\mathbf {p}; \\theta , \\hat {P} _ {i}))\\right)\\right). \\tag {8}", + "image_path": "59d9a5cd698d57faeab5913292167309211fe74cb07bf230fcb78c162ce7f1ae.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "content": " denotes the Huber loss function [18] and " + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "inline_equation", + "content": "w_{\\mathfrak{p}} \\in [0,1]" + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "content": " is the confidence associated with the correspondence " + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}, \\mathbf{q})" + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "content": ", which we obtain as detailed below. We additionally define the set " + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\mathbf{p}: w_{\\mathfrak{p}} \\geq \\kappa\\}" + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\kappa = 0.95" + }, + { + "bbox": [ + 304, + 447, + 545, + 507 + ], + "type": "text", + "content": ". The homogenization operations were omitted for clarity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 508, + 546, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 546, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 546, + 639 + ], + "type": "text", + "content": "Our loss serves two purposes. By connecting the training images through correspondences, our multi-view correspondence objective enforces the learned geometry and camera poses to converge to a solution geometrically consistent across all training images. This is unlike the photometric loss (7) which applies supervision on each training image independently. Moreover, the underlying constraint is only satisfied if the learned 3D points converge to the true reconstructed scene (up to a similarity). As such, the objective (8) provides direct supervision on the rendered depth (6), implicitly enforcing it to be close to the surface." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": "Correspondence prediction: Any classical [27, 35] or learned [13,36,42,44,45] matching approach could be used to obtain the matches relating pairs of training views. We rely on a pre-trained dense correspondence regression network, in particular PDC-Net [43]. It predicts a match " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": " for each pixel " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": ", along with a confidence " + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{p}}" + }, + { + "bbox": [ + 304, + 642, + 547, + 715 + ], + "type": "text", + "content": ". We found" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "text", + "content": "4193" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 145 + ], + "type": "text", + "content": "the high number of accurate matches to be beneficial for our joint pose-NeRF refinement. Similar conclusions were derived in the context of dense versus sparse depth supervision [11,34]. The dense correspondence map also implicitly imposes a smoothness prior to the rendered depth. In suppl., we present results using a sparse matcher [12, 36] instead." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 149, + 270, + 163 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 149, + 270, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 149, + 270, + 163 + ], + "type": "text", + "content": "4.2. Improving Geometry at Unobserved Views" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 168, + 287, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 263 + ], + "type": "text", + "content": "The multi-view correspondence loss favors a global and geometrically accurate solution, consistent across all training images. Nevertheless, the reconstructed scene often still suffers from inconsistencies when seen from novel viewpoints. For those, no RGB supervision is available during training. We propose an additional training objective, the depth consistency loss, which encourages the learned geometry to be consistent from any viewing direction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": "Depth consistency loss: The main idea is to use the depth maps rendered from the training viewpoints to create pseudo-depth supervision for novel, unseen, viewpoints (Fig. 2, step 3). We sample a virtual pose " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "P_{un}" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": ", in practice obtained as an interpolation between the poses of two close-by training views. For a pixel " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": " in a sampled training image " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{r_p}^{un} = P_{un}^{-1}\\hat{P}_i\\pi^{-1}(\\mathbf{p},\\hat{z} (\\mathbf{p};\\theta ,\\hat{P}_i))" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": " is the corresponding 3D point in the coordinate system of the unseen view " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "P_{un}" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{y}\\in \\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": " denotes its pixel projection in view " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "P_{un}" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "\\mathbf{y} = \\pi \\left(\\mathbf{r}_{\\mathrm{p}}^{un}\\right)" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{y}}" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": " is its projected depth in " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "P_{un}" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{y}} = \\left[\\mathbf{r}_{\\mathrm{p}}^{un}\\right]_3" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "inline_equation", + "content": "[\\cdot ]_3" + }, + { + "bbox": [ + 46, + 266, + 287, + 412 + ], + "type": "text", + "content": " refers to taking the third coordinate of the vector. We formulate our depth consistency loss as," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 80, + 416, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 416, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 80, + 416, + 287, + 441 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {D C o n s}} (\\theta) = \\sum_ {\\mathrm {p}} \\gamma_ {\\mathrm {y}} \\rho \\left(z _ {\\mathrm {y}} - \\hat {z} (\\mathbf {y}; \\theta , P _ {u n})\\right). \\tag {9}", + "image_path": "94ab42d26290ec6e221e74f659fb8054c76245c6a986fce63fdb8fa2ee8700c3.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 446, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 482 + ], + "type": "text", + "content": "To account for occlusion and out-of-view projections in which (9) is invalid, we have included a visibility mask " + }, + { + "bbox": [ + 46, + 446, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathrm{y}} \\in [0,1]" + }, + { + "bbox": [ + 46, + 446, + 287, + 482 + ], + "type": "text", + "content": ". We explain its definition in the section below." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "text", + "content": "Since the pseudo-depth supervision " + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{y}}" + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "text", + "content": " is created from renderings, it is subject to errors. For this reason, we find it important to backpropagate through the pseudo-supervision " + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{y}}" + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "text", + "content": ". Note that we however do not backpropagate through the pose estimate " + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\hat{P}_i" + }, + { + "bbox": [ + 46, + 482, + 287, + 590 + ], + "type": "text", + "content": ". Moreover, as verified experimentally in Tab. 2, our depth consistency objective (9) is complementary to our multi-view correspondence loss (8), the latter enforcing an accurate reconstructed geometry while the former ensures it is consistent from any viewpoint." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": "Visibility mask " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathbf{y}}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": ": We first exclude points if their pixel projections " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " is outside of the virtual view, by setting the mask as " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathrm{y}} = 0" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": ". The depth consistency loss is also invalid for pixels that are occluded by the reconstructed scene in the virtual view. To identify these occluded pixels, we follow the strategy of [10]. In particular, we check whether there are occupied regions on the ray between the camera center " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_{un}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "P_{un}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " and the 3D point " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{un,\\mathbf{y}}(z_{\\mathbf{y}})" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": " at depth " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "z_{\\mathbf{y}}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": ". We compute how occluded a 3D point is with its transmittance (5) in the unseen view, as " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathrm{y}} = T_{un,z_{\\mathbf{y}}}" + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "text", + "content": ". Intuitively, " + }, + { + "bbox": [ + 46, + 594, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{\\mathrm{y}}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "is close to 1 if there is no point with a large density between the camera center " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_{un}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{r}_{un,y}(z_y)" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", otherwise it is close to 0. Next, we present our overall training framework." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 115, + 427, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 115, + 427, + 129 + ], + "spans": [ + { + "bbox": [ + 305, + 115, + 427, + 129 + ], + "type": "text", + "content": "4.3. Training Framework" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": "Staged training: Our final training objective is formulated as " + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\theta, \\hat{\\mathcal{P}}) = \\mathcal{L}_{\\mathrm{photo}}(\\theta, \\hat{\\mathcal{P}}) + \\lambda_{\\mathrm{c}} \\mathcal{L}_{\\mathrm{MVCorr}}(\\theta, \\hat{\\mathcal{P}}) + \\lambda_{\\mathrm{d}} \\mathcal{L}_{\\mathrm{DCons}}(\\theta)" + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{c}}" + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{d}}" + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": " are predefined weighting factors. The training is split into two stages. In the first part, the pose estimates are trained jointly with the coarse MLP " + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "inline_equation", + "content": "F_{\\theta}^{c}" + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": ". However, due to the exploration of the pose space at the early stages of training, the learned scene tends to showcase blurry surfaces. As a result, in the second training stage, we freeze the pose estimates and train both the coarse and fine networks " + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "inline_equation", + "content": "F_{\\theta}^{c}" + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "inline_equation", + "content": "F_{\\theta}^{f}" + }, + { + "bbox": [ + 304, + 137, + 545, + 316 + ], + "type": "text", + "content": ". This ensures that the fine network learns a sharp geometry, benefiting from the pre-trained coarse network. From a practical perspective, our training objectives can be integrated at a low computational cost, since the RGB or depth pixel renderings (3)-(6) can be shared between the three loss terms." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 319, + 546, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 546, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 546, + 451 + ], + "type": "text", + "content": "Coarse-to-fine positional encoding: In BARF [24], Lin et al. propose to gradually activate the high-frequency components of the positional encodings (2) over the course of the optimization. We refer the reader to [24] for the exact formulation. While originally proposed in the context of pose refinement, we found that this strategy is also extremely beneficial in the sparse-view setting, even when the poses are fixed. It prevents the network from immediately overfitting to the training images, thereby avoiding the worst degenerate geometries. We therefore adopt this coarse-to-fine positional encoding approach as default." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 461, + 432, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 461, + 432, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 461, + 432, + 475 + ], + "type": "text", + "content": "5. Experimental Results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 481, + 545, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 566 + ], + "type": "text", + "content": "We evaluate the proposed SPARF for novel-view rendering in the few-view setting, in particular when only three input views are available. Results with different numbers of views are provided in suppl. We extensively analyze our method and compare it to earlier approaches, setting a new state of the art on multiple datasets. Further results, visualizations, and implementation details are provided in suppl." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 572, + 432, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 572, + 432, + 586 + ], + "spans": [ + { + "bbox": [ + 305, + 572, + 432, + 586 + ], + "type": "text", + "content": "5.1. Experimental Settings" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Datasets and metrics: We report results on the DTU [20], LLFF [38] and Replica [39] datasets, for the challenging scenario of 3 input views. DTU is composed of complex object-level scenes with wide-baseline views spanning a half hemisphere. We adhere to the protocol of [53] and evaluate on their reported test split of 15 scenes. Following [32], we additionally evaluate all methods with the object masks applied to the rendered images, to avoid penalizing methods for incorrect background predictions. On LLFF, we follow community standards [30] and use every " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "8^{\\text{th}}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " image as" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "text", + "content": "4194" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 293, + 125 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 293, + 125 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 293, + 125 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 293, + 125 + ], + "type": "table", + "html": "
MethodPSNR ↑SSIM ↑LPIPS ↓DE ↓
I Full PE [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)0.87
II Smaller MLP model9.03 (10.06)0.34 (0.65)0.68 (0.34)0.79
III No PE16.11 (18.40)0.68 (0.80)0.37 (0.24)0.30
IV CF PE [24] (Sec. 4.3)16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
", + "image_path": "be61cba45dacaa5a323e69d8eb1b4eb6352172fe376faa32b28e92ca19abb372.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "lines": [ + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "spans": [ + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "type": "text", + "content": "Table 1. Comparison of different positional encoding strategies applied to NeRF [30] on DTU (3 views), using ground-truth poses. Results in " + }, + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 47, + 127, + 287, + 160 + ], + "type": "text", + "content": " are computed by masking the background." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 290 + ], + "type": "text", + "content": "the test set. We sample the training views evenly from the remaining images. For the Replica dataset, which depicts videos of room-scale indoor scenes, we subsample every " + }, + { + "bbox": [ + 46, + 171, + 287, + 290 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 171, + 287, + 290 + ], + "type": "text", + "content": " frame, from which we randomly select a triplet of consecutive training images. As metrics, we report the average rotation and translation errors for pose registration, and PSNR, SSIM [47] and LPIPS [57] for view synthesis. On the DTU and Replica datasets, we additionally compare the rendered depth with the available ground-truth depth and compute the mean depth absolute error (DE)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 365 + ], + "type": "text", + "content": "Implementation details: We train our approach for 100K iterations, which takes about 10 hours on a single A100 GPU. As pose parametrization, we adopt the continuous 6-vector representation [58] for the rotation and directly optimize the translation vector. We provide all training hyperparameters in the supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 372, + 149, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 149, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 149, + 384 + ], + "type": "text", + "content": "5.2. Method Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 391, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 287, + 415 + ], + "type": "text", + "content": "We first perform a comprehensive analysis of our approach, on DTU [20], considering only 3 input views." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 417, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 548 + ], + "type": "text", + "content": "Impact of positional encoding: Training on sparse input views using the standard NeRF [30] immediately overfits to the provided images, even with perfect poses. We noticed that the overfitting is largely due to the high-frequency positional encodings (PE), and thus experimented with different PE strategies. We present the results in Tab. 1. The standard NeRF (I) with high-frequency PE [30] leads to degenerate geometry and novel view renderings. In (II), using a simplified MLP makes little difference. While training without PE (III) largely prevents overfitting, the coarse-to-fine PE strategy [24] leads to the best result, as shown in (IV)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 552, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 612 + ], + "type": "text", + "content": "Ablation study: In Tab. 2, we ablate the key components of our approach, here assuming fixed ground-truth poses and starting from NeRF with coarse-to-fine PE. Adding our multi-view correspondence loss (8) results in drastically better performance on all metrics. Including our depth" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 50, + 621, + 288, + 673 + ], + "blocks": [ + { + "bbox": [ + 50, + 621, + 288, + 673 + ], + "lines": [ + { + "bbox": [ + 50, + 621, + 288, + 673 + ], + "spans": [ + { + "bbox": [ + 50, + 621, + 288, + 673 + ], + "type": "table", + "html": "
MV-Corr (8)DCons (9)PSNR ↑SSIM ↑LPIPS ↓DE ↓
XX16.27 (18.41)0.69 (0.81)0.29 (0.14)0.39
X✓15.86 (18.91)0.71 (0.82)0.28 (0.14)0.20
✓X18.13 (20.81)0.77 (0.87)0.22 (0.10)0.10
✓✓18.30 (21.01)0.78 (0.87)0.21 (0.10)0.08
", + "image_path": "e4598275caf3fcad2531e1bd3f8b203be70d45e41fb32552988005564101c6d8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "type": "text", + "content": "Table 2. Ablation study on the DTU dataset (3 views), with fixed ground-truth poses. Results in " + }, + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 46, + 677, + 287, + 710 + ], + "type": "text", + "content": " are computed by masking the background. All networks use the coarse-to-fine PE [24]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 454, + 204 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 454, + 204 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 454, + 204 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 454, + 204 + ], + "type": "image", + "image_path": "c9c1ec2eb336316dc44525589cd2468dfb2cd09acfdba68e0f2f52f149d4987c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 454, + 73, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 454, + 73, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 454, + 73, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 454, + 73, + 545, + 205 + ], + "type": "image", + "image_path": "a901ab2a76cfd7b8c914afe414e06be6c47655f3002061cdb70c67d2344d9395.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 205, + 547, + 316 + ], + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 316 + ], + "type": "text", + "content": "Figure 3. We compare two training objectives using ground-truth depth for pose-NeRF training in the sparse-view regime. In (A), a loss comparing for each training image the rendered depth (6) with the ground truth one, can learn locally perfect geometry (as highlighted by the dashed red rectangles). However, the NeRF/poses do not converge to a global solution, because the optimized poses and geometry of the different images are disjoint. Instead, supervising the learned 3D points of each training image to be equal to the ground-truth 3D points in (B) solves this issue, by enforcing the system to converge to a global (unique) geometric solution." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 324, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 385 + ], + "type": "text", + "content": "consistency module (9) further leads to a small improvement, achieving the best performance overall. Also note that our depth-consistency module (9) works best in collaboration with our multi-view correspondences loss (8) since the latter is needed to learn an accurate geometry." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 388, + 546, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 663 + ], + "type": "text", + "content": "Intuition on pose-NeRF training losses: We first want to build an intuition on what loss might be suitable for joint pose-NeRF training in the sparse regime. To do so, we use ground-truth depth or 3D data in two alternative training losses, which we compare here. We illustrate this experiment in Fig. 3 and present results in Tab. 3, top part. As in previous work [24], for each scene of DTU [20], we synthetically perturb the ground-truth camera poses with " + }, + { + "bbox": [ + 304, + 388, + 546, + 663 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 388, + 546, + 663 + ], + "type": "text", + "content": " of additive gaussian noise. In (I), we train with an L1 loss comparing the rendered depth (6) with the ground-truth depth (Fig. 3A). Surprisingly, this loss struggles to refine the poses. Instead, in (II) we minimize the distance between the learned 3D points (rendered depth (6) backprojected to world frame) and the ground-truth 3D points, as illustrated in Fig. 3B. This training loss successfully registers the poses, resulting in drastically better novel-view rendering quality. As the main insight from this experiment, we hypothesize that, in the sparse-view regime, it is crucial to enforce an explicit geometric connection between the different training images and their underlying scene geometry. This is not the case in (I), where the depth loss favors per-image locally accurate geometry, but the NeRF/poses can converge to disconnected solutions for each training image." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Comparison of losses for pose-NeRF training: In Tab. 3 bottom part, we then compare our loss (8) to objectives commonly used for joint pose-NeRF training. The photometric loss (7) (III), even associated with a mask/silhouette" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 750, + 315, + 758 + ], + "type": "text", + "content": "4195" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 293, + 135 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 293, + 135 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 293, + 135 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 293, + 135 + ], + "type": "table", + "html": "
LossesRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
I Photo. + L1 GT depth7.328.913.8 (14.0)0.54 (0.70)0.46 (0.27)0.17
II Photo. + L1 GT 3D points0.41.518.8 (20.3)0.75 (0.84)0.21 (0.11)0.07
III Photo. (7)10.351.510.7 (9.8)0.43 (0.62)0.59 (0.36)1.9
IV Photo. + mask loss [23,56]13.257.7----
V MVCorr (8)1.986.6---0.19
VI Photo. + MVCorr ((7)-(8))1.855.516.0 (17.8)0.68 (0.81)0.28 (0.14)0.13
", + "image_path": "ba8609afddf01c8336c00d91a075ac51915ce8307a45706e314afbea8ecd029f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 191, + 290, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 290, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 290, + 373 + ], + "type": "text", + "content": "loss [5,23,56] in (IV), completely fails to register the poses, thus leading to poor novel-view synthesis performance. This is in line with our hypothesis that it is important to explicitly exploit the geometric relation between the training views for successful registration. Moreover, because the 3D space is under-constrained in the sparse-view regime, multiple neighboring poses can lead to similar mask losses. While our multi-view correspondence loss (8) alone (V) already drastically outperforms the photometric loss (III) in terms of pose and learned geometry (depth error), combining the two in (VI) leads to the best performance. This is because, through the correspondences, our approach favors a NeRF/pose solution consistent across all training images. Note that this version neither includes our depth consistency loss (9) (Sec. 4.2) nor our staged training (Sec. 4.3)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 379, + 252, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 379, + 252, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 379, + 252, + 392 + ], + "type": "text", + "content": "5.3. Comparison to SOTA with Noisy Poses" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 397, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 287, + 434 + ], + "type": "text", + "content": "Here, we evaluate SPARF, our joint pose and NeRF training approach. Results with different pose initialization schemes are presented in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 435, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 568 + ], + "type": "text", + "content": "Baselines: We compare to BARF [24], the state-of-the-art in pose-NeRF refinement when assuming dense input views. It is representative of a line of approaches [9, 24, 29, 48, 50] using the photometric loss (7) as the main signal. We also experiment with adding the depth regularization loss of [32] or the ray sparsity loss of [4] to BARF, which we denote as RegBARF and DistBARF respectively. We additionally compare to SCNeRF [21], which uses a geometric loss based on correspondences, minimizing the rays' intersection re-projection error. For a fair comparison, we integrate coarse-to-fine PE [24] (Sec. 4.3) in all methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 570, + 287, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 607 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 607 + ], + "type": "text", + "content": "Results on DTU: Following [9, 24, 50], for each scene, we synthetically perturb the ground-truth camera poses with " + }, + { + "bbox": [ + 47, + 570, + 287, + 607 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 47, + 570, + 287, + 607 + ], + "type": "text", + "content": " of additive gaussian noise. The initial poses thus have" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 617, + 285, + 674 + ], + "blocks": [ + { + "bbox": [ + 47, + 138, + 287, + 183 + ], + "lines": [ + { + "bbox": [ + 47, + 138, + 287, + 183 + ], + "spans": [ + { + "bbox": [ + 47, + 138, + 287, + 183 + ], + "type": "text", + "content": "Table 3. Comparison of training objectives for joint pose-NeRF refinement on DTU [20] with initial noisy poses (3 views). Rotation errors are in degree and translation errors are multiplied by 100. Results in " + }, + { + "bbox": [ + 47, + 138, + 287, + 183 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 47, + 138, + 287, + 183 + ], + "type": "text", + "content": " are computed by masking the background." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 617, + 285, + 674 + ], + "lines": [ + { + "bbox": [ + 50, + 617, + 285, + 674 + ], + "spans": [ + { + "bbox": [ + 50, + 617, + 285, + 674 + ], + "type": "table", + "html": "
MethodRot. ↓Trans. ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
BARF [24]10.3351.510.71 (9.76)0.43 (0.62)0.59 (0.36)1.90
RegBARF [24, 32]11.2052.810.38 (9.20)0.45 (0.62)0.61 (0.38)2.33
DistBARF [4, 24]11.6955.79.50 (9.15)0.34 (0.76)0.67 (0.36)1.90
SCNeRF [21]3.4416.412.04 (11.71)0.45 (0.66)0.52 (0.30)0.85
SPARF (Ours)1.815.017.74 (18.92)0.71 (0.83)0.26 (0.13)0.12
", + "image_path": "ff61a0e371fc23e05f8d064f87f39d249ac6a31f4605991a3eaa2b07d15c9b51.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "type": "text", + "content": "Table 4. Evaluation on DTU [20] (3 views) with noisy initial poses. Rotation errors are in " + }, + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "type": "inline_equation", + "content": "^\\circ" + }, + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "type": "text", + "content": " and translation errors are multiplied by 100. Results in " + }, + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 46, + 677, + 287, + 711 + ], + "type": "text", + "content": " are computed by masking the background." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 309, + 68, + 547, + 320 + ], + "blocks": [ + { + "bbox": [ + 309, + 68, + 547, + 320 + ], + "lines": [ + { + "bbox": [ + 309, + 68, + 547, + 320 + ], + "spans": [ + { + "bbox": [ + 309, + 68, + 547, + 320 + ], + "type": "image", + "image_path": "f2778eae166540be155231eb9fcd908fbac9fcec6a712672fccf7409a8755fc7.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 323, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 546, + 346 + ], + "type": "text", + "content": "Figure 4. Novel-view rendering (RGB and depth). The input (not shown here) contains 3 images with initial noisy camera poses." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 357, + 546, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 546, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 546, + 548 + ], + "type": "text", + "content": "an average rotation and translation error of " + }, + { + "bbox": [ + 304, + 357, + 546, + 548 + ], + "type": "inline_equation", + "content": "15^{\\circ}" + }, + { + "bbox": [ + 304, + 357, + 546, + 548 + ], + "type": "text", + "content": " and 70 respectively. We show initial and optimized poses in Fig. 5. From the results in Tab. 4 and Fig. 4A, we observe that BARF, RegBARF, and DistBARF completely fail to register the poses, leading to poor view-synthesis quality. SCNeRF's geometric loss performs better at registering the poses but the learned scene still suffers from many inconsistencies. This is because SCNeRF's loss [21] does not influence the learned radiance field function, and thus, cannot prevent the NeRF model from overfitting to the sparse input views. Since our multi-view correspondence loss (8) acts on both the camera pose estimates and the learned neural field by enforcing them to fit the correspondence constraint, it leads to an accurate reconstructed scene. Our approach SPARF hence significantly outperforms all others both in novel-view rendering quality and pose registration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 552, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 552, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 552, + 547, + 624 + ], + "type": "text", + "content": "Results on LLFF: The LLFF dataset consists of 8 complex forward-facing scenes. Following [24], we initialize all camera poses with the identity transformation and present results in Tab. 5. In [24], Lin et al. show that BARF almost perfectly registers the camera poses given dense input views. However, we show here that it strug" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 306, + 634, + 547, + 675 + ], + "blocks": [ + { + "bbox": [ + 306, + 634, + 547, + 675 + ], + "lines": [ + { + "bbox": [ + 306, + 634, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 547, + 675 + ], + "type": "image", + "image_path": "617619e6b033ad0ed5bd1b64120c02259088f5567e951c11022fcb18a44ca4a2.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 677, + 546, + 711 + ], + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 711 + ], + "type": "text", + "content": "Figure 5. Optimized poses on DTU with 3 input views. We compare the ground-truth poses (in pink) with the optimized ones (in blue). In the first column, the initial noisy poses are in blue." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "text", + "content": "4196" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 284, + 130 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 284, + 130 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 284, + 130 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 284, + 130 + ], + "type": "table", + "html": "
Rot. (°) ↓Trans. (×100) ↓PSNR ↑SSIM ↑LPIPS ↓
BARF [24]2.0411.617.470.480.37
RegBARF [24, 32]1.525.018.570.520.36
DistBARF [4, 24]5.5926.514.690.340.49
SCNeRF [21]1.9311.417.100.450.40
SPARF (Ours)0.532.819.580.610.31
", + "image_path": "50dc9588e9632b964d94f56afa4014c772e408bee3767ffb7df0c8692fcce2d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 167, + 288, + 270 + ], + "blocks": [ + { + "bbox": [ + 47, + 134, + 286, + 156 + ], + "lines": [ + { + "bbox": [ + 47, + 134, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 134, + 286, + 156 + ], + "type": "text", + "content": "Table 5. Evaluation on the forward-facing dataset LLFF [38] (3 views) starting from initial identity poses." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 167, + 288, + 270 + ], + "lines": [ + { + "bbox": [ + 48, + 167, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 48, + 167, + 288, + 270 + ], + "type": "table", + "html": "
MethodRot (°) ↓Trans (×100) ↓PSNR ↑SSIM ↑LPIPS ↓DE ↓
G SPARF (Ours)Fixed GT poses26.430.880.130.39
F NeRF [30]Fixed poses obtained20.990.730.321.33
DS-NeRF [11]from COLMAP (run w.23.520.810.200.99
SPARF (Ours)PDC-Net [43] matches25.030.840.150.66
R BARF [24]3.3516.9620.730.720.300.84
RegBARF [24, 32]3.6620.8720.000.700.321.00
DistBARF [4, 24]2.367.7322.460.770.230.47
SCNeRF [21]0.654.1222.540.790.240.73
DS-NeRF [11]1.305.0424.750.830.200.69
SPARF (Ours)0.150.7626.980.880.130.36
", + "image_path": "e7ccc6a1ed20f884e223a45d340030f61a73975ef9a4a28c2067d38ea2a64040.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 359, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 287, + 419 + ], + "type": "text", + "content": "gles in the sparse-view setting, thereby severely impacting the accuracy of novel view synthesis. While adding the depth smoothness loss (RegBARF) improves results, our approach SPARF outperforms all previous works. A qualitative comparison is shown in Fig. 4B." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": "Results on Replica: To demonstrate that our approach is also applicable to non-forward-facing indoor scenes, we evaluate on the Replica dataset in Tab. 6 and Fig. 4C. As pose initialization, we use COLMAP [37] with improved matches, i.e. using PDC-Net [43]. The initial pose estimates thus have an average rotation and translation error of respectively " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "0.39^{\\circ}" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " and 3.01. Comparing the top (G) and middle part (F) of Tab. 6, we show that even such a low initial error impacts the novel-view rendering quality when using fixed poses. In the bottom part (R), our pose-NeRF training strategy leads to the best results, matching the accuracy obtained by our approach with perfect poses (top row, G)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 572, + 287, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 287, + 585 + ], + "type": "text", + "content": "5.4. Comparison to SOTA with Ground-Truth Poses" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 590, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 628 + ], + "type": "text", + "content": "Finally, we show that our approach brings significant improvement in novel view rendering quality even when considering fixed ground-truth poses." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Baselines: We compare to works specifically designed to tackle per-scene few-shot novel view rendering, namely DietNeRF [19], DS-NeRF [11], InfoNeRF [22] and RegNeRF [32], along with the standard NeRF [30] and MipNeRF [3]. For completeness, we also compare against a state-of-the-art conditional model, PixelNeRF [53], trained on DTU [20] and further finetuned per-scene on LLFF [38]." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 71, + 547, + 171 + ], + "blocks": [ + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "type": "text", + "content": "Table 6. Evaluation on Replica [39] (3 views) with initial poses obtained by COLMAP [37, 43]. The initial rotation and translation errors are " + }, + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "type": "inline_equation", + "content": "0.39^{\\circ}" + }, + { + "bbox": [ + 46, + 273, + 287, + 350 + ], + "type": "text", + "content": " and 3.01 respectively. In the middle part (F), these initial poses are fixed and used as \"pseudo-gt\". In the bottom part (R), the poses are refined along with training the NeRF. For comparison, in the top part (G), we use fixed ground-truth poses. The best and second-best results are in red and blue respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 71, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 308, + 71, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 308, + 71, + 547, + 171 + ], + "type": "table", + "html": "
MethodDTULLFF
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [53]19.36 (18.00)0.70 (0.77)0.32 (0.23)7.930.270.68
PixelNeRF-ft [53]---16.170.440.51
MipNeRF [3]7.64 (8.68)0.23 (0.57)0.66 (0.35)14.620.350.50
NeRF [30]8.41 (9.34)0.31 (0.63)0.71 (0.36)13.610.280.56
DietNeRF [19]10.01 (11.85)0.35 (0.63)0.57 (0.31)14.940.370.5
InfoNeRF [22]11.23 (-)0.44 (-)0.54 (-)---
RegNeRF [32]15.33 (18.89)0.62 (0.75)0.34 (0.19)19.080.590.34
DS-NeRF [11]16.52 (-)0.54 (-)0.48 (-)18.000.550.27
SPARF (Ours)18.30 (21.01)0.78 (0.87)0.21 (0.10)20.200.630.24
", + "image_path": "c4866e03451d2f8f944ea844b1a1b6078180681217a4220f0d26a47d8ff2d11d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 175, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 220 + ], + "type": "text", + "content": "Table 7. Evaluation on DTU [20] and LLFF [38] (3 views), with fixed ground-truth poses. Results in " + }, + { + "bbox": [ + 305, + 175, + 545, + 220 + ], + "type": "inline_equation", + "content": "(\\cdot)" + }, + { + "bbox": [ + 305, + 175, + 545, + 220 + ], + "type": "text", + "content": " are computed by masking the background. Results of [3, 19, 32] are taken from [32]. The best and second-best results are in red and blue respectively." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 229, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 545, + 469 + ], + "type": "text", + "content": "Results: We present results on DTU and LLFF in Tab. 7. Compared to previous per-scene approaches [19,22,32] that only apply different regularization to the learned scene, our multi-view correspondence loss (8) provides a strong supervision on the rendered depth, implicitly encouraging it to be close to the true surface. Our depth consistency objective (9) further boosts the performance, by directly enforcing the learned scene to be consistent from any viewpoint. As a result, our approach SPARF performs best compared to all baselines on both datasets and for all metrics. The only exception is PSNR on the whole image compared to conditional model PixelNeRF [53]. This is because DTU has black backgrounds, where a wrong color prediction (like in Fig. 4A for SPARF) has a large impact on the PSNR value. For conditional models which rely on feature projections, it is easier to predict a correct background color. However, most real-world applications are more interested in accurately reconstructing the object of interest than the background. When evaluated only in the object region, our SPARF obtains 3.24dB higher PSNR than PixelNeRF." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 479, + 378, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 378, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 378, + 491 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 499, + 545, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 545, + 571 + ], + "type": "text", + "content": "We propose SPARF, a joint pose-NeRF training strategy capable of producing realistic novel-view renderings given few wide-baseline input images with noisy camera pose estimates. By integrating two novel objectives inspired by multi-view geometry principles, we set a new state of the art on three challenging datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 574, + 545, + 705 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 705 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 705 + ], + "type": "text", + "content": "Limitations and future work: Our approach is only applicable to input image collections where each image has covisible regions with at least one other. Moreover, the performance of our method depends on the quality of the matching network. Filtering strategies or per-scene online refinement of the correspondence network thus appear as promising future directions. An interesting direction is also to refine the camera intrinsics and distortion parameters along with the extrinsics. 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Brostow, Moustapha Cissé, Giovanni Maria Farinella, and Tal Hassner, editors, Computer Vision - ECCV 2022 - 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceed" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 308, + 73, + 545, + 374 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 326, + 73, + 545, + 95 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 73, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 326, + 73, + 545, + 95 + ], + "type": "text", + "content": "ings, Part XXXI, volume 13691 of Lecture Notes in Computer Science, pages 592-611. Springer, 2022. 1" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 308, + 97, + 545, + 140 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 97, + 545, + 140 + ], + "spans": [ + { + "bbox": [ + 308, + 97, + 545, + 140 + ], + "type": "text", + "content": "[56] Jason Y. 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Computer Vision Foundation / IEEE, 2019. 6" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 308, + 263, + 545, + 318 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 263, + 545, + 318 + ], + "spans": [ + { + "bbox": [ + 308, + 263, + 545, + 318 + ], + "type": "text", + "content": "[59] Zihan Zhu, Songyou Peng, Viktor Larsson, Weiwei Xu, Hujun Bao, Zhaopeng Cui, Martin R. Oswald, and Marc Pollefeys. Nice-slam: Neural implicit scalable encoding for slam. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022. 2" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 308, + 319, + 545, + 374 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 319, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 308, + 319, + 545, + 374 + ], + "type": "text", + "content": "[60] Bingbing Zhuang and Manmohan Chandraker. Fusing the old with the new: Learning relative camera pose with geometry-guided uncertainty. In IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, virtual, June 19-25, 2021, pages 32-42, 2021." + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 750, + 315, + 758 + ], + "type": "text", + "content": "4200" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SPIn-NeRF_ Multiview Segmentation and Perceptual Inpainting With Neural Radiance Fields/a5f839e7-988d-4934-9aef-4c494df6e55a_content_list.json b/2023/SPIn-NeRF_ Multiview Segmentation and Perceptual Inpainting With Neural Radiance Fields/a5f839e7-988d-4934-9aef-4c494df6e55a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..aeccfc4bc3f70fed3a3cf2c77061996a7ab591f2 --- /dev/null +++ b/2023/SPIn-NeRF_ Multiview Segmentation and Perceptual Inpainting With Neural Radiance Fields/a5f839e7-988d-4934-9aef-4c494df6e55a_content_list.json @@ -0,0 +1,1582 @@ +[ + { + "type": "text", + "text": "SPIn-NeRF: Multiview Segmentation and Perceptual Inpainting with Neural Radiance Fields", + "text_level": 1, + "bbox": [ + 98, + 128, + 870, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ashkan Mirzaei $^{1,2}$ Tristan Aumentado-Armstrong $^{1,2,4}$ Konstantinos G. Derpanis $^{1,3,4}$ Jonathan Kelly $^{2}$ Marcus A. Brubaker $^{1,3,4}$ Igor Gilitschenski $^{2}$ Alex Levinshtein $^{1}$ $^{1}$ Samsung AI Centre Toronto $^{2}$ University of Toronto $^{3}$ York University $^{4}$ Vector Institute for AI {a.mirzaei,tristan.a}@partner.samsung.com, {jkelly,gilitschenski}@cs.toronto.edu {kosta,mab}@eecs.yorku.ca, alex.lev@samsung.com", + "bbox": [ + 109, + 200, + 859, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7153f095fb01c307fe410e1221cc3238b4506317aaa4d33dc4336ff5f0cc5721.jpg", + "image_caption": [ + "Figure 1. An example of the inputs and outputs of our 3D inpainting framework. In addition to the images captured from the scene and their corresponding camera parameters, users are tasked with providing a few points in a single image to indicate which object they wish to remove from the scene (upper-left inset). These sparse annotations are then automatically transferred to all other views, and utilized for multiview mask construction (upper-right inset). The resulting 3D-consistent mask is used in a perceptual optimization problem that results in 3D scene inpainting (lower row), with rendered depth from the optimized NeRF shown for each image as an inset." + ], + "image_footnote": [], + "bbox": [ + 81, + 327, + 888, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 585, + 313, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural Radiance Fields (NeRFs) have emerged as a popular approach for novel view synthesis. While NeRFs are quickly being adapted for a wider set of applications, intuitively editing NeRF scenes is still an open challenge. One important editing task is the removal of unwanted objects from a 3D scene, such that the replaced region is visually plausible and consistent with its context. We refer to this task as 3D inpainting. In 3D, solutions must be both consistent across multiple views and geometrically valid. In this paper, we propose a novel 3D inpainting method that addresses these challenges. Given a small set of posed images and sparse annotations in a single input image, our framework first rapidly obtains a 3D segmentation mask for a target object. Using the mask, a perceptual optimization-based approach is then introduced that leverages learned 2D image inpainters, distilling their information into 3D space, while ensuring view consistency. We also address the lack of a diverse benchmark for evaluating 3D scene", + "bbox": [ + 73, + 628, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": " inpainting methods by introducing a dataset comprised of challenging real-world scenes. In particular, our dataset contains views of the same scene with and without a target object, enabling more principled benchmarking of the 3D inpainting task. We first demonstrate the superiority of our approach on multiview segmentation, comparing to NeRF-based methods and 2D segmentation approaches. We then evaluate on the task of 3D inpainting, establishing state-of-the-art performance against other NeRF manipulation algorithms, as well as a strong 2D image inpainter baseline.", + "bbox": [ + 496, + 585, + 893, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 768, + 632, + 784 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural rendering methods, especially Neural Radiance Fields (NeRFs) [35], have recently emerged as a new modality for representing and reconstructing scenes [50], achieving impressive results for novel view synthesis. Substantial research effort continues to focus on formulating more efficient NeRFs (e.g., [6, 20, 43]), to make NeRFs more accessible in use-cases with more limited computa", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20669", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tional resources. As NeRFs become more widely accessible, the need for editing and manipulating the scenes represented by NeRFs will continue to grow. One notable editing application is removing objects and inpainting the 3D scene, analogous to the well-studied 2D image inpainting task [23]. However, several obstacles impede progress on this task, not only for the 3D inpainting process itself, but also in obtaining the input segmentation masks. First, NeRF scenes are implicitly encoded within the neural mapping weights, resulting in an entangled and uninterpretable representation that is non-trivial to manipulate (compared to, say, the explicit discretized form of 2D image arrays or meshes in 3D). Moreover, any attempt to inpaint a 3D scene must not only generate a perceptually realistic appearance in a single given view, but also preserve fundamental 3D properties, such as appearance consistency across views and geometric plausibility. Finally, to obtain masks for the target object, it is more intuitive for most end users to interact with 2D images, rather than 3D interfaces; however, requiring annotations of multiple images (and maintaining view-consistent segments) is burdensome to users. An appealing alternative is to expect only a minimal set of annotations for a single view. This motivates a method capable of obtaining a view-consistent 3D segmentation mask of the object (for use in inpainting) from single-view sparse annotations.", + "bbox": [ + 76, + 90, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we address these challenges with an integrated method that takes in multiview images of a scene, extracts a 3D mask with minimal user input, and fits a NeRF to the masked images, such that the target object is replaced with plausible 3D appearance and geometry. Existing interactive 2D segmentation methods do not consider the 3D aspects of the problem (e.g., [42]), while current NeRF-based approaches are unable to use sparse annotations [76] to perform well, or do not attain sufficient accuracy [44]. Similarly, while some current NeRF manipulation algorithms allow object removal, they do not attempt to provide perceptually realistic inpaintings of newly unveiled parts of space (e.g., [64]). To our knowledge, this is the first approach that handles both interactive multiview segmentation and full 3D inpainting in a single framework.", + "bbox": [ + 76, + 473, + 472, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our technique leverages off-the-shelf, 3D-unaware models for segmentation and inpainting, and transfers their outputs to 3D space in a view-consistent manner. Building on the (2D) interactive segmentation [8, 15, 33] literature, our framework starts from a small number of user-defined image points on a target object (and a few negative samples outside it). From these, our algorithm initializes masks with a video-based model [4], and lifts them into a coherent 3D segmentation via fitting a semantic NeRF [36, 76, 77]. Then, after applying a pretrained 2D inpainter [48] to the multiview image set, a customized NeRF fitting process is used to reconstruct the 3D inpainted scene, utilizing perceptual losses [72] to account for inconsistencies in the 2D", + "bbox": [ + 76, + 704, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "inpainted images, as well as inpainted depth images to regularize the geometry of the masked region. Overall, we provide a complete method, from object selection to novel view synthesis of the inpainted scenes, in a unified framework with minimal burden on the user, illustrated in Figure 1.", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the effectiveness of our approach through extensive qualitative and quantitative evaluations. In addition, we address the lack of a benchmark for comparing scene inpainting methods, and introduce a new dataset where the \"ground-truth inpaintings\" (i.e., real images of the scene without the object) are available as well.", + "bbox": [ + 496, + 167, + 893, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows: (i) a complete process for 3D scene manipulation, starting from object selection with minimal user interaction and ending with a 3D inpainted NeRF scene; (ii) to perform such selection, an extension of 2D segmentation models to the multiview case, capable of recovering 3D-consistent masks from sparse annotations; (iii) to ensure view-consistency and perceptual plausibility, a novel optimization-based formulation of 3D inpainting in NeRFs, which leverages 2D inpainters; and (iv) a new dataset for 3D object removal evaluation that includes corresponding object-free ground-truth.", + "bbox": [ + 496, + 257, + 893, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 436, + 640, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image Inpainting. Inpainting in 2D has received significant research attention [23]. While early techniques relied on patches [9, 16], recent neural methods optimize both perceptual realism and reconstruction (e.g., [22, 27, 48]). Various lines of research continue to be explored for improving visual fidelity, including adversarial training (e.g., [40, 73]), architectural advances (e.g., [27, 30, 62, 63]), pluralistic outputs (e.g., [73, 75]), multiscale processing (e.g., [21, 58, 69]), and perceptual metrics (e.g., [22, 48, 72]). Our work leverages LaMa [48], which applies frequency-domain transforms [7] inspired by transformers [11, 12]. Yet, none of these lift the problem into 3D; thus, inpainting multiple captures of a scene in a consistent manner remains an underexplored task. While there are some existing 3D-aware image inpainting algorithms, they either only partially operate in 3D [65], rely on reference images [74], or consider more limited scenarios [24]. In contrast, our method operates directly in 3D, via the multiview-based NeRF model.", + "bbox": [ + 496, + 462, + 893, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NeRF Manipulation. Representing scenes via volumetric rendering has recently become an important research direction [50]. Based on differentiable volume rendering [18,52] and positional encoding [13,49,53], NeRFs [35] have demonstrated remarkable performance in novel-view synthesis. Recent works have studied potential improvements in NeRF's training or rendering speed [5, 6, 17, 38, 47, 67], reconstruction quality [1, 2, 10, 29], and data requirements [28, 56, 59, 68]. However, manipulating NeRF scenes remains a challenge. Clip-NeRF [55], Object-NeRF [64], LaTeRF [36], and others [25, 32, 70] introduce approaches", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20670", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to alter and complete objects represented by NeRFs; however, their performance is limited to simple objects, rather than scenes with significant clutter and texture, or they focus on tasks other than general inpainting (e.g., recoloring or deforming). Most closely related to our method is NeRF-In [31], a concurrent unpublished work, which inpaints NeRF scenes with geometry and radiance priors from 2D image inpainters, but does not address inconsistency; instead, its use of a simple pixelwise loss relegates it to simply reducing the number of views used for fitting, which reduces final view synthesis quality. Similarly using a pixelwise loss, the concurrent Remove-NeRF model [60] reduces inconsistencies by excluding views based on an uncertainty mechanism. In contrast, our approach is able to inpaint NeRF representations of challenging real-world scenes by incorporating 2D information in a view-consistent manner, via a perceptual [72] training regime. This avoids over-constraints on the inpainting, which would normally lead to blurriness.", + "bbox": [ + 75, + 90, + 472, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background: Neural Radiance Fields", + "text_level": 1, + "bbox": [ + 76, + 390, + 413, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NeRFs [35] encode a 3D scene as a function, $f: (x,d) \\to (c,\\sigma)$ , that maps a 3D coordinate, $x$ , and a view direction, $d$ , to a color, $c$ , and density, $\\sigma$ . The function $f$ can be modelled in various ways (e.g., [35, 47]). For a ray, $r$ , the expected color is estimated by volumetric rendering via quadrature; the ray is divided into $N$ sections between $t_n$ and $t_f$ (the near and far bounds), with $t_i$ sampled from the $i$ -th section, to render the estimated color, $\\widehat{C}(r)$ :", + "bbox": [ + 75, + 415, + 470, + 539 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) c _ {i}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 547, + 468, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T_{i} = \\exp (-\\sum_{j = 1}^{i - 1}\\sigma_{j}\\delta_{j})$ is the transmittance, $\\delta_{i} = t_{i + 1} - t_{i}$ is the distance between two adjacent points, and $c_{i}$ and $\\sigma_{i}$ are the color and density at $t_i$ , respectively. For the rays passing through pixels of the training views, the ground-truth color $C_\\mathrm{GT}(r)$ is available, and the model is optimized using the reconstruction loss:", + "bbox": [ + 75, + 599, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e c}} = \\sum_ {r \\in \\mathcal {R}} \\| \\widehat {C} (r) - C _ {\\mathrm {G T}} (r) \\| ^ {2}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 700, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{R}$ is a ray batch sampled from the training views.", + "bbox": [ + 76, + 741, + 449, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 768, + 168, + 784 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a set of RGB images, $\\mathcal{I} = \\{I_i\\}_{i=1}^n$ , with corresponding 3D poses, $\\mathcal{G} = \\{G_i\\}_{i=1}^n$ , and camera intrinsic matrix, $K$ , our model expects one additional \"source\" view with sparse user annotations (i.e., a few points identifying the unwanted object). From these inputs, we produce a NeRF model of the scene, capable of synthesizing an inpainted image from any novel view. We begin by obtaining", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/de9bc58e0eb796c7686c40927dbb18fde0c811667643ffef0e678ea50d80c3c0.jpg", + "image_caption": [ + "Figure 2. Overview of our multiview segmentation architecture. As input, this network takes in a 3D coordinate, $x$ , and a view direction, $d$ , and returns view-independent density, $\\sigma(x)$ , objectness logit, $s(x)$ , and view-dependent color, $c(x, d)$ ." + ], + "image_footnote": [], + "bbox": [ + 511, + 90, + 877, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "an initial 3D mask from the single-view annotated source (§ 4.1.1), followed by fitting a semantic NeRF, to improve the consistency and quality of the mask (§ 4.1.2). Finally, in § 4.2 we describe our view-consistent inpainting method, which takes the views and recovered masks as inputs. Our approach leverages the outputs of 2D inpainters [48] as appearance and geometry priors to supervise the fitting of a new NeRF. Figure 1 illustrates our entire approach, including the inputs and outputs. Additional details are in our supplementary material.", + "bbox": [ + 496, + 279, + 890, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Multiview Segmentation", + "text_level": 1, + "bbox": [ + 500, + 439, + 723, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1.1 Mask Initialization", + "text_level": 1, + "bbox": [ + 500, + 462, + 687, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first describe how we initialize a rough 3D mask from single-view annotations. Denote the annotated source view as $I_{1}$ . The sparse information about the object and the source view are given to an interactive segmentation model [15] to estimate the initial source object mask, $\\widehat{M}_{1}$ . The training views are then treated as a video sequence and, along with $\\widehat{M}_{1}$ , given to a video instance segmentation model $V$ [4, 57], to compute $V(\\{I_i\\}_{i=1}^n, \\widehat{M}_1) = \\{\\widehat{M}_i\\}_{i=1}^n$ where $\\widehat{M}_i$ is the initial guess for the object mask for $I_i$ . The initial masks, $\\{\\widehat{M}_i\\}_{i=1}^n$ , are typically inaccurate around the boundaries, since the training views are not actually adjacent video frames, and video segmentation models are usually 3D-unaware. Hence, we use a semantic NeRF model [36, 76, 77] to resolve the inconsistencies and improve the masks (§ 4.1.2), thus obtaining the masks for each input view, $\\{M_i\\}_{i=1}^n$ , to use for inpainting (§ 4.2).", + "bbox": [ + 496, + 486, + 890, + 737 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1.2 NeRF-based Segmentation", + "text_level": 1, + "bbox": [ + 500, + 753, + 738, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our multiview segmentation module takes the input RGB images, $\\{I_i\\}_{i=1}^n$ , the corresponding camera intrinsic and extrinsic parameters, and the initial masks, $\\{\\widehat{M_i}\\}_{i=1}^n$ , and trains a semantic NeRF [76]. Figure 2 depicts the network used in the semantic NeRF; for a point, $x$ , and a view direction, $d$ , in addition to a density, $\\sigma(x)$ , and color, $c(x,d)$ , it returns a pre-sigmoid \"objectness\" logit, $s(x)$ . The objectness probability is then acquired as $p(x) = \\text{Sigmoid}(s(x))$ .", + "bbox": [ + 496, + 777, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20671", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We use Instant-NGP [3, 37, 38] as our NeRF architecture due to its fast convergence. The expected objectness logit, $\\widehat{S}(r)$ , associated with a ray, $r$ , is obtained by rendering the logits of the points on $r$ instead of their colors, with respect to the densities, in Eq. 1 [36]:", + "bbox": [ + 76, + 90, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {S} (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) s _ {i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 175, + 468, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where for simplicity, $s(r(t_i))$ is denoted by $s_i$ . The objectness probability of a ray, $\\widehat{P}(r) = \\text{Sigmoid}(\\widehat{S}(r))$ , is then supervised using the classification loss:", + "bbox": [ + 76, + 224, + 468, + 272 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c l f}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\operatorname {B C E} \\left(\\mathbb {1} _ {r \\in \\mathcal {R} _ {\\text {m a s k e d}}}, \\widehat {P} (r)\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 280, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{1}$ is the indicator function, BCE stands for the binary cross entropy loss, and $\\mathcal{R}_{\\mathrm{masked}}$ is the set of rays passing through pixels that are masked in $\\{\\widehat{M}_i\\}_{i=1}^n$ . During the calculation of the classification loss, $\\mathcal{L}_{\\mathrm{clf}}$ , the weights of the colors in the rendering equation (Eq. 1) are detached to limit the supervised updates to the logits; this prevents changes to the existing geometry, due to gradient updates altering the $\\sigma$ field. The geometry is supervised using a reconstruction loss, $\\mathcal{L}_{\\mathrm{rec}}$ , as in NeRF [35], via the given RGB images. The overall loss, used to supervise the NeRF-based multiview segmentation model, is then given by:", + "bbox": [ + 75, + 324, + 468, + 492 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {m v}} = \\mathcal {L} _ {\\mathrm {r e c}} + \\lambda_ {\\mathrm {c l f}} \\mathcal {L} _ {\\mathrm {c l f}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 502, + 468, + 517 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the classification weight, $\\lambda_{\\mathrm{clf}}$ , is a hyper-parameter. After optimization, 3D-consistent masks, $\\{M_i\\}_{i=1}^n$ , are obtained by thresholding the objectness probabilities and masking the pixels with probabilities greater than 0.5. Finally, we use two stages for optimization to further improve the masks; after obtaining the initial 3D mask, the masks are rendered from the training views, and are used to supervise a secondary multiview segmentation model as initial guesses (instead of the video segmentation outputs).", + "bbox": [ + 75, + 527, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Multiview Inpainting", + "text_level": 1, + "bbox": [ + 76, + 671, + 276, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 3 shows an overview of our view-consistent inpainting method. As the paucity of data precludes directly training a 3D inpainter, our method leverages existing 2D inpainters to obtain depth and appearance priors, which then supervise the fitting of a NeRF to the completed scene. This inpainted NeRF is trained using the following loss:", + "bbox": [ + 75, + 695, + 468, + 785 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n p}} = \\mathcal {L} ^ {\\prime} _ {\\text {r e c}} + \\lambda_ {\\mathrm {L P I P S}} \\mathcal {L} _ {\\mathrm {L P I P S}} + \\lambda_ {\\text {d e p t h}} \\mathcal {L} _ {\\text {d e p t h}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 794, + 468, + 811 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{rec}}^{\\prime}$ is the reconstruction loss for the unmasked pixels, and $\\mathcal{L}_{\\mathrm{LPIPS}}$ and $\\mathcal{L}_{\\mathrm{depth}}$ define the perceptual and depth losses (see below), with weights $\\lambda_{\\mathrm{LPIPS}}$ and $\\lambda_{\\mathrm{depth}}$ .", + "bbox": [ + 76, + 820, + 468, + 866 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d1fc40b4d477bb3fcf73a48a77163e871d638b49e799b3f3d21aa53f03b2677d.jpg", + "image_caption": [ + "Figure 3. Overview of our inpainting method. Using posed input images and their corresponding masks (upper- and lower-left insets), we obtain (i) an initial NeRF with the target object present and (ii) the set of inpainted input RGB images with the target object removed (but with view inconsistencies). The initial NeRF (i) is used to compute depth, which we inpaint to obtain depth images as geometric priors (upper-right inset). The inpainted RGB images (ii), which act as appearance priors, are used with the depth priors, to fit a 3D consistent NeRF to the inpainted scene. $^1$" + ], + "image_footnote": [], + "bbox": [ + 503, + 88, + 890, + 218 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.1 RGB Priors", + "text_level": 1, + "bbox": [ + 500, + 380, + 635, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our proposed view-consistent inpainting approach uses RGB inputs, $\\{I_i\\}_{i=1}^n$ , the camera intrinsic and extrinsic parameters, and corresponding object masks, $\\{M_i\\}_{i=1}^n$ , to fit a NeRF to the scene without the undesired object. To begin with, each image and mask pair, $(I_i, M_i)$ , is given to an image inpainter, INP, to obtain the inpainted RGB images, $\\{\\widetilde{I}_i\\}_{i=1}^n$ , where $\\widetilde{I}_i = \\mathrm{INP}(I_i, M_i)$ [48]. Since each view is inpainted independently, directly supervising a NeRF using the inpainted views leads to blurry results due to the 3D inconsistencies between each $\\widetilde{I}_i$ (see Figure 7). In this paper, instead of using mean squared error (MSE) to optimize the masked area, we propose the use of a perceptual loss, LPIPS [72], to optimize the masked parts of the images, while still using MSE for the unmasked parts, where no inpainting is needed. This loss is calculated as follows:", + "bbox": [ + 498, + 404, + 890, + 630 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {L P I P S}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\operatorname {L P I P S} (\\widehat {I _ {i}}, \\widetilde {I _ {i}}), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 641, + 890, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{B}$ is a batch of indices between 1 and $n$ , and $\\widehat{I}_i$ is the $i$ -th view rendered using NeRF. Our model for multiview inpainting and segmentation uses the same architecture (see Figure 2), except for the additional logit output, $s$ .", + "bbox": [ + 498, + 690, + 890, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2.2 Depth Priors", + "text_level": 1, + "bbox": [ + 500, + 771, + 643, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Even with the perceptual loss, the discrepancies between the inpainted views can incorrectly guide the model towards converging to degenerate geometries (e.g., 'foggy' geometry may form near the cameras, to explain the disparate per-view information). Thus, we use inpainted depth maps as additional guidance for the NeRF model, and detach the weights when calculating the perceptual loss and use the", + "bbox": [ + 498, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "$^{1}$ IBRNet images in Fig. 3,5,6,7 by Wang et al. available in IBRNet [56] under an Apache License 2.0.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "20672", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "perceptual loss to only fit the colors of the scene. For this purpose, we use a NeRF optimized on images that include the unwanted object, and render the depth maps, $\\{D_i\\}_{i=1}^n$ , corresponding to the training views. Depth maps are calculated by substituting the distance to the camera instead of the color of points into Eq. 1:", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) t _ {i}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 194, + 468, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The rendered depths are then given to an inpainter to obtain inpainted depth maps, $\\{\\widetilde{D}_i\\}_{i=1}^n$ , where $\\widetilde{D}_i$ is obtained as $\\widetilde{D}_i = \\mathrm{INP}(D_i, M_i)$ . We found that using LaMa [48] for depth inpainting, as in the RGB case, gave sufficiently high-quality results. Note that this is all calculated as a preprocessing step, and with a NeRF optimized on the original scene. This NeRF can be the same model used for multiview segmentation. If using another source for obtaining masks, such as human annotated masks, a new NeRF is fitted to the scene. These depth maps are then used to supervise the inpainted NeRF's geometry, via the $\\ell_2$ distance of its rendered depths, $\\widehat{D}_i$ , to the inpainted depths, $\\widetilde{D}_i$ :", + "bbox": [ + 75, + 246, + 472, + 431 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {d e p t h}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\left| \\widehat {D} (r) - \\widetilde {D} (r) \\right| ^ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 441, + 468, + 478 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\widehat{D}(r)$ and $\\widetilde{D}(r)$ are the depth values for a ray, $r$ .", + "bbox": [ + 76, + 489, + 437, + 508 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.3 Patch-based Optimization", + "text_level": 1, + "bbox": [ + 76, + 529, + 313, + 544 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Calculating the perceptual loss, Eq. 7, requires full input views to be rendered during the optimization. Since rendering each pixel necessitates multiple forward passes through the MLP, for high-resolution images, this is an expensive process, resulting in issues such as (i) the batch size, $|\\mathcal{B}|$ , has to be small to fit the rendered images and their corresponding computation graphs in memory, and (ii) slow optimization, even with batch sizes as small as $|\\mathcal{B}| = 1$ . A straightforward solution is to render a downsized image and compare it to the downsized version of the inpainted images; however, this leads to a loss of information if the downsizing factor is large. Following image-based works (e.g., SinGAN [46] and DPNN [14]), and 3D works (e.g., ARF [71]), we perform the computations on a patch-basis; instead of rendering complete views, we render batches of smaller patches, and compare them with their counterparts in the inpainted images based on the perceptual loss. Only patches inside the bounding box of the object mask are used. For fitting the unmasked areas, recall that $\\mathcal{L}_{\\mathrm{rec}}'$ (Eq. 6) simply alters $\\mathcal{L}_{\\mathrm{rec}}$ (Eq. 2) to sample rays only from unmasked pixels. By separating the perceptual and reconstruction losses, we prevent inconsistency within the mask, while avoiding unnecessary changes to the rest of the scene.", + "bbox": [ + 75, + 551, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/96fed5a9841afc84b0c07073c10646bfebab901b73afad90cb04847e99f7ef5e.jpg", + "image_caption": [ + "60 Input Views + Camera Poses" + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 632, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/69d07eec86b6a8ee5f1dcb1133c4a131d4ac682e405b3c208e7e7fa6152057de.jpg", + "image_caption": [ + "Human-Annotated Object Masks" + ], + "image_footnote": [], + "bbox": [ + 632, + 88, + 758, + 200 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/81908990a5ff11a8ee34ccf93e07a2743312537e8c813277dfb4a610405da77d.jpg", + "image_caption": [ + "40 GT Views + Camera Poses", + "Figure 4. Scenes from our dataset. Columns: input view (left), corresponding target object mask (middle), and a ground-truth view without the target object, from a different camera pose (right). Rows: different scenes; see supplement for examples of all scenes." + ], + "image_footnote": [], + "bbox": [ + 759, + 88, + 888, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2.4 Mask Refinement", + "text_level": 1, + "bbox": [ + 500, + 306, + 676, + 320 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, we consider further leveraging the multiview data to guide the image inpainter. In particular, parts of the training images that are currently being generated by the 2D image inpainter might be visible in other views; in such cases, there is no need to hallucinate those details, since they can be retrieved from the other views. To prevent such unnecessary inpaintings, we propose a mask refinement approach: for each source image, depth, and mask tuple, $(I_s, D_s, M_s)$ , we substitute pixels in $I_s$ and $D_s$ that are visible from at least one other view, to shrink the source mask, $M_s$ . After this refinement step, only parts of $I_s$ and $D_s$ that are occluded by the undesired object in all of the training views will remain masked. As a result, the image inpainter has to fill in a smaller area, resulting in improved inpaintings. Please see our supplementary material for details.", + "bbox": [ + 496, + 330, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 571, + 633, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. To evaluate multiview segmentation (MVSeg), we adopt real-world scenes from LLFF [34], NeRF-360 [35], NeRF-Supervision [66], and Shiny [61]. For multiview (MV) inpainting, in addition to providing qualitative results on scenes from IBRNet [56], we address the need for a standard benchmark including ground-truth captures of scenes without the unwanted object as test views, and introduce a dataset containing 10 real-world forward-facing scenes with human annotated object masks. For each scene, we provide 60 training images with the object and 40 test images without the object. This dataset is further suitable for evaluating tasks such as real-time 3D inpainting, unsupervised 3D segmentation, and video inpainting. Figure 4 shows sample views from two scenes of our dataset.", + "bbox": [ + 496, + 598, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Metrics. To evaluate our segmentation model, we use the accuracy of the predictions (pixel-wise) and the intersection over union (IoU) metric. For MV inpainting, we follow the image-to-image literature [48] and report the average learned perceptual image patch similarity (LPIPS) [72], and the average Fréchet inception distance (FID) [19] between", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20673", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3a1daa75ba6d30c38977c4af582eaaa3b5dee49759887d872d0c5ddc480382e9.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation of multiview segmentation models, for the task of transferring the source mask to other views." + ], + "table_footnote": [], + "table_body": "
MethodAcc.↑IoU↑
Proj. + Grab Cut [45] (2D)91.0846.61
Proj. + EdgeFlow [15] (2D)96.8481.63
Semantic NeRF [76] (only source mask)94.6375.13
Proj. + EdgeFlow [15] + Semantic NeRF [76]97.2683.95
Feature Field Distillation [26]97.3783.07
Video Segmentation [4,57]98.4388.34
Ours98.8590.96
Ours (two-stage)98.9191.66
", + "bbox": [ + 81, + 127, + 464, + 252 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the distribution of the ground-truth test views and model outputs. Since our focus is the inpainting, we only calculate the LPIPS and FID inside the bounding box of the object mask (using our MVSeg model, we can render the object mask from the test views that do not contain the object).", + "bbox": [ + 75, + 277, + 468, + 352 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multiview Segmentation Baselines. For MVSeg, one category of baselines is projection-based approaches: the source mask is projected into the other views using the scene geometry from a NeRF. This gives us an incomplete mask in the other views. Then, a variety of interactive segmentation approaches are applied to the incomplete masks, propagating them to obtain complete object masks: Proj. + Grab Cut [45] and Proj. + EdgeFlow [15]. In addition, we consider Proj. + EdgeFlow + Semantic NeRF, where an additional Semantic NeRF [76] is fitted to make the outputs 3D consistent. Another baseline [26] is a representative of the concurrent works on distilling 2D pixel-level features to 3D scenes [51] and post-processing them for obtaining segmentation masks. As a baseline for video-segmentation [57], we compare to Dino [4] since it does not rely on temporally close neighboring frames.", + "bbox": [ + 75, + 353, + 468, + 593 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multiview Inpainting Baselines. Masked NeRF only uses the unmasked pixels to optimize a NeRF. Object NeRF [64] filters the unwanted points in 3D without explicitly inpainting the missing regions. No code is available for NeRF-In [31], so we use our own implementation of their model, with slight modifications (we use LaMa [48] as the inpainter). In addition, we compare our results to LaMa [48] as a representative of state-of-the-art 2D inpainters. To enable fair comparison between the NeRF-based 3D models (which, in addition to inpainting, have to synthesize novel views), we compare to LaMa by (i) fitting a NeRF on the views with the object $^2$ , (ii) rendering the test views from the fitted NeRF, and (iii) passing these rendered images to LaMa. Finally, for reference and as an ideal \"gold standard\" 3D inpainting baseline, we fit a NeRF on the ground-truth test images, use the optimized NeRF to render the test-views, and then compare the rendered results to the ground-truth. We provide these results for completeness, as", + "bbox": [ + 75, + 594, + 468, + 864 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a85587c6df13fd196487ac86c3f28694edcc4f6e85c8d02e2106bc264d63597f.jpg", + "table_caption": [ + "Table 2. Quantitative evaluation of our inpainting method, using human-annotated object masks." + ], + "table_footnote": [], + "table_body": "
MethodLPIPS↓FID↓
Ideal0.4079100.25
LaMa (2D) [48]0.5369174.61
Object NeRF [64]0.6829271.80
Masked NeRF [35]0.6030294.69
NeRF-In [31]0.5699238.33
NeRF-In [31] (Single)0.4884183.23
Ours (no geo. inpainting)0.4952200.34
Ours0.4654156.64
Ours (Refined RGB/Depth)0.4664163.79
Ours (Refined RGB)0.4529147.31
", + "bbox": [ + 524, + 127, + 864, + 299 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "an upper-bound on the best possible results one can expect to obtain when using the same NeRF architecture.", + "bbox": [ + 498, + 324, + 890, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Results", + "text_level": 1, + "bbox": [ + 500, + 363, + 591, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multiview Segmentation. We first evaluate our MVSeg model without any inpainting. In this experiment, we assume that the sparse image points are already given to an off-the-shelf interactive segmentation model, and that the source mask is available. Thus, the task is to transfer the source mask to other views. Table 1 shows that our model outperforms all of the 2D (3D-inconsistent) and 3D-consistent baselines. In addition, our two-stage optimization helps to further improve the obtained masks.", + "bbox": [ + 496, + 386, + 890, + 522 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitatively, Figure 5 compares the results of our segmentation model with the outputs of Neural Volumetric Object Selection (NVOS) [44] and video segmentation [4, 57]. Compared to the coarse edges of the 3D-unaware video segmentation model, our model reduces noise and improves consistency across views. Although NVOS uses scribbles, rather than the sparse points used in our model, our MVSeg visually outperforms NVOS. Since the NVOS code base is not available, we reproduce the published qualitative results for NVOS [44] (see supplemental for more examples).", + "bbox": [ + 496, + 523, + 890, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multiview Inpainting. Our dataset is used for quantitative evaluation of our proposed inpainting method against the baselines. Table 2 shows the comparison of our MV inpainting method with the baselines, assuming that the object masks from all of the views are given. The \"ideal\" row is not a baseline, but rather a NeRF fitted to the ground-truth test views (views of the scene without the object). While this is only one instantiation of the many possible inpainted scenes, it provides a convenient measure of the best performance one might reasonably expect in this scenario. Overall, our method significantly outperforms the alternative 2D and 3D inpainting approaches. Although our model uses a 2D image inpainter's [48] outputs to obtain a view-consistent inpainted NeRF, it is able to use this ensemble of MV information, in addition to the priors encoded by", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "2Since the test views that do not contain the object should not be available to the model during the inference.", + "bbox": [ + 76, + 875, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20674", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/44b53cf8f3bd72b7bc6277454ba08e2fd17b5ba58bc26f209c36ce64094a19a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 218, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9545002d4b03125c60a72c26ea5ead46ad88f52142c1df27f2ebd599c5ba6ea3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 220, + 88, + 352, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/004ec54ac2cceac7c049f0193529bc6e54d19103a7173ee63024ce93c790ca58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 88, + 486, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7b95d02db97acf0a334df2a462b93ca71ddd02b66fb2510ef8f72298dd8cffcf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 88, + 620, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16edcc29221911979934e5936b26b5e88ba270df269cea8606635c278809def1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 88, + 751, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4cbc90b7c3c77f27b8554ffd933923f340c3b2491b529343bd5b8bbc4e809970.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 751, + 88, + 887, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1ee66a64e2a1f288b665bbf52100b094793455cfb1bc740ff22d38d91a54d90f.jpg", + "image_caption": [ + "Input View", + "Figure 5. A qualitative comparison of our multiview segmentation model against Neural Volumetric Object Selection (NVOS) [44] (reproduced from original paper), video segmentation [4], and the human-annotated masks (GT). Our two-stage approach refers to running our multiview segmentation model twice, with the output of the first run as the initialization of the second (see § 4.1.2). Our method is less noisy than NVOS, which also misses some pieces of the target (e.g., the lowest flower in the bottom row), but captures more details than the video segmentation alone (e.g., the blurred edges of the flowers). Our two-stage approach helps fill in some missing aspects of the one-stage output. Please see our supplement for additional qualitative examples." + ], + "image_footnote": [], + "bbox": [ + 83, + 167, + 220, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e9ecf9214f822bf0e2ec0bd5b47b39ec6e7903115e498987403b8dcd67a04a7e.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 220, + 167, + 352, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/92c0f7046bb31d23a3bc7f983fcbf433e146a1d65f7ca1bfe0ec0c47e5681da1.jpg", + "image_caption": [ + "NVOS" + ], + "image_footnote": [], + "bbox": [ + 352, + 167, + 486, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8428c2fd4315ee981652331d47228b77bbf066b898f2515775d84c245633cb35.jpg", + "image_caption": [ + "Video Segmentation (2D)" + ], + "image_footnote": [], + "bbox": [ + 486, + 167, + 620, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c3e1c53c869a12ee1c1bbda771c30f5f541d9c42e176ee9f06817e2f43a01196.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 620, + 167, + 751, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ef80005f9d36aaee6ddcc593a234efa812da36645b9862efba2107b3aef3e652.jpg", + "image_caption": [ + "Ours (Two-Stage)" + ], + "image_footnote": [], + "bbox": [ + 751, + 167, + 885, + 244 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4bdb65f4533e490f6a5e14cd16b4e24d10b559a7da18d7fd1dcfc3bbd5803944.jpg", + "table_caption": [ + "Table 3. Quantitative evaluation of our inpainting method, using the outputs of our multiview segmentation model." + ], + "table_footnote": [], + "table_body": "
MethodLPIPS↓FID↓
LaMa (2D) [48]0.5439169.92
Object NeRF [64]0.6679286.55
Masked NeRF [35]0.6340332.70
NeRF-In [31]0.5858240.27
NeRF-In [31] (Single)0.5054176.27
Ours0.4662140.56
", + "bbox": [ + 117, + 414, + 424, + 525 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the perceptual loss function, to outperform the 2D inpainter. Table 2 further shows that removing geometry guidance impairs the inpainted scene quality.", + "bbox": [ + 75, + 551, + 468, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We display qualitative results of our MV inpainting method in Figure 6, showing that it can reconstruct a view-consistent scene with detailed textures, including coherent view-dependent radiance for both shiny and non-shiny surfaces. In addition, in Figure 7, we provide a visual comparison to the unpublished concurrent work NeRF-In [31], which has the second-lowest error. We observe that a NeRF-In model fitted to all of the inpainted views results in blurry outputs. Alternatively, using a single inpainted view for supervising the masked region leads to artifacts in further views, due to the lack of supervision for the view-dependent radiance, as well as the poor extrapolation capabilities of the network. In contrast, our perceptual approach relaxes the exact reconstruction constraints in the masked region, thus preventing blurriness despite using all of the images, while avoiding artifacts caused by single-view supervision.", + "bbox": [ + 75, + 598, + 468, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 shows that refinement provides a small but significant boost in inpainting quality, due to smaller masks requiring less hallucination from the inpainter. Yet, empirically, refinement only subtly trims the masks (reducing", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b3447f0d67e81d0c560111e5443fc520537effd669f9420fbf12ff95e1311652.jpg", + "table_caption": [ + "Table 4. Evaluation of our 3D inpainting method across input view number (upper half) and mask dilation level (lower half)." + ], + "table_footnote": [], + "table_body": "
Input Views10204060
LPIPS↓0.47260.47130.46670.4654
FID↓171.19172.63158.02156.64
Dilation452550
LPIPS↓0.61020.53690.46540.4904
FID↓283.01230.03156.64164.66
", + "bbox": [ + 511, + 414, + 879, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mean masked area by $4.74\\%$ on our dataset), as the camera has limited movement during data collection, to ensure similarity between the training and testing views. Further, due to noisy NeRF geometries projecting incorrect values, refining depths lowers performance, whereas refining colours alone achieves our best results.", + "bbox": [ + 496, + 536, + 890, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "So far, our experiments examine the performance of our MVSeg and MV inpainting independently; however, one can combine them to remove objects from NeRF scenes with minimal user interaction. Table 3 shows that using the output masks of our MVSeg model, instead of using the human-annotated object masks, results in a subtle decrease in the inpainting quality. However, our model with MVSegs still outperforms other methods, even when they are fitted on human-annotated segmentations.", + "bbox": [ + 496, + 627, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Variations and Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 771, + 782, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Number of Input Views. Limiting the number of input views is a standard approach employed in the literature to modulate the reconstruction quality of NeRFs [54]. Table 4 shows that the performance of our inpainter degrades with fewer inputs. Thus, we argue that as better-quality NeRFs are introduced, our approach, which is agnostic to the underlying NeRF model, can readily benefit.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20675", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e4f0bbe17f35d00eab93a74f2443363d56da1bc53620245230b854aedf13628.jpg", + "image_caption": [ + "Figure 6. Visualizations of our view-consistent inpainting results. Upper rows per inset show NeRF renderings of the original scene from novel views, with the first image also displaying the associated mask. Lower rows show the corresponding inpainted view. Notice that the synthesized views maintain consistency with each other; however, view-dependent effects still remain (e.g., the lighting on the uncovered part of the piano). Please see our supplement for additional scenes, and our project website with videos for better visualization." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 885, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b03e48a6b91c30330e8288251e54bdcf103f83e532d7f086403dfca44cdc5013.jpg", + "image_caption": [ + "Figure 7. Qualitative comparisons with other baselines. Columns: novel views of the scene, synthesized by a NeRF (on the unmasked images), NeRF-In, NeRF-In (with a single masked training image), and our approach. NeRF-In is significantly more blurry, while NeRF-In (single) tends to have difficulty with details closer to the edge of the mask boundary (zoom into boxes for examples)." + ], + "image_footnote": [], + "bbox": [ + 81, + 474, + 465, + 713 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Importance of Accurate Masks. Here, we examine the impact of accurate masks on inpainting, via variable dilations of the object masks with a $5 \\times 5$ kernel. Larger masks lead to relying more on the view-inconsistent outputs and", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "hallucinations of the 2D inpainters, while smaller masks may permit parts of the unwanted object's edges to remain and confuse the 2D inpainter. A subtle dilation is also useful for reducing the effect of shadows. This balance between over-masking and under-masking is demonstrated in Table 4, with five dilation iterations found to be optimal and therefore used for all other experiments.", + "bbox": [ + 498, + 478, + 890, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 601, + 619, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a novel approach to inpaint NeRF scenes, which enforces viewpoint consistency based on image and geometric priors, given a single-view object mask. In addition, we provided a multiview segmentation method that simplifies the annotation process by using a set of sparse pixel-level clicks on (and around) the undesired object and translating them into a 3D mask that can be rendered from novel views. We provided experiments to show the effectiveness of our segmentation and inpainting methods. The main limitation of our work is the assumption of semantically consistent image priors, potentially only differing in terms of textures. Finally, we introduce a dataset that not only addresses the lack of challenging benchmarks for multiview inpainting, but which we believe can assist future advances in this new line of research.", + "bbox": [ + 496, + 628, + 890, + 852 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was conducted at Samsung AI Centre Toronto and it was funded by Mitacs and Samsung Research, Samsung Electronics Co., Ltd.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20676", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. 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In arXiv, 2021. 2, 3" + ], + "bbox": [ + 78, + 90, + 468, + 773 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20679", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SPIn-NeRF_ Multiview Segmentation and Perceptual Inpainting With Neural Radiance Fields/a5f839e7-988d-4934-9aef-4c494df6e55a_model.json b/2023/SPIn-NeRF_ Multiview Segmentation and Perceptual Inpainting With Neural Radiance Fields/a5f839e7-988d-4934-9aef-4c494df6e55a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..52a2c890af2d8489fb189e32f7d708ea68c57c91 --- /dev/null +++ b/2023/SPIn-NeRF_ Multiview Segmentation and Perceptual Inpainting With Neural Radiance Fields/a5f839e7-988d-4934-9aef-4c494df6e55a_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.13, + 0.872, + 0.175 + ], + "angle": 0, + "content": "SPIn-NeRF: Multiview Segmentation and Perceptual Inpainting with Neural Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.11, + 0.202, + 0.861, + 0.294 + ], + "angle": 0, + "content": "Ashkan Mirzaei\\(^{1,2}\\) Tristan Aumentado-Armstrong\\(^{1,2,4}\\) Konstantinos G. Derpanis\\(^{1,3,4}\\) Jonathan Kelly\\(^{2}\\) Marcus A. Brubaker\\(^{1,3,4}\\) Igor Gilitschenski\\(^{2}\\) Alex Levinshtein\\(^{1}\\) \n\\(^{1}\\)Samsung AI Centre Toronto \\(^{2}\\)University of Toronto \\(^{3}\\)York University \\(^{4}\\)Vector Institute for AI {a.mirzaei,tristan.a}@partner.samsung.com, {jkelly,gilitschenski}@cs.toronto.edu {kosta,mab}@eecs.yorku.ca, alex.lev@samsung.com" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.328, + 0.889, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.503, + 0.893, + 0.574 + ], + "angle": 0, + "content": "Figure 1. An example of the inputs and outputs of our 3D inpainting framework. In addition to the images captured from the scene and their corresponding camera parameters, users are tasked with providing a few points in a single image to indicate which object they wish to remove from the scene (upper-left inset). These sparse annotations are then automatically transferred to all other views, and utilized for multiview mask construction (upper-right inset). The resulting 3D-consistent mask is used in a perceptual optimization problem that results in 3D scene inpainting (lower row), with rendered depth from the optimized NeRF shown for each image as an inset." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.586, + 0.314, + 0.601 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.629, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Neural Radiance Fields (NeRFs) have emerged as a popular approach for novel view synthesis. While NeRFs are quickly being adapted for a wider set of applications, intuitively editing NeRF scenes is still an open challenge. One important editing task is the removal of unwanted objects from a 3D scene, such that the replaced region is visually plausible and consistent with its context. We refer to this task as 3D inpainting. In 3D, solutions must be both consistent across multiple views and geometrically valid. In this paper, we propose a novel 3D inpainting method that addresses these challenges. Given a small set of posed images and sparse annotations in a single input image, our framework first rapidly obtains a 3D segmentation mask for a target object. Using the mask, a perceptual optimization-based approach is then introduced that leverages learned 2D image inpainters, distilling their information into 3D space, while ensuring view consistency. We also address the lack of a diverse benchmark for evaluating 3D scene" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.587, + 0.895, + 0.74 + ], + "angle": 0, + "content": " inpainting methods by introducing a dataset comprised of challenging real-world scenes. In particular, our dataset contains views of the same scene with and without a target object, enabling more principled benchmarking of the 3D inpainting task. We first demonstrate the superiority of our approach on multiview segmentation, comparing to NeRF-based methods and 2D segmentation approaches. We then evaluate on the task of 3D inpainting, establishing state-of-the-art performance against other NeRF manipulation algorithms, as well as a strong 2D image inpainter baseline." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.769, + 0.633, + 0.785 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Neural rendering methods, especially Neural Radiance Fields (NeRFs) [35], have recently emerged as a new modality for representing and reconstructing scenes [50], achieving impressive results for novel view synthesis. Substantial research effort continues to focus on formulating more efficient NeRFs (e.g., [6, 20, 43]), to make NeRFs more accessible in use-cases with more limited computa" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20669" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.471 + ], + "angle": 0, + "content": "tional resources. As NeRFs become more widely accessible, the need for editing and manipulating the scenes represented by NeRFs will continue to grow. One notable editing application is removing objects and inpainting the 3D scene, analogous to the well-studied 2D image inpainting task [23]. However, several obstacles impede progress on this task, not only for the 3D inpainting process itself, but also in obtaining the input segmentation masks. First, NeRF scenes are implicitly encoded within the neural mapping weights, resulting in an entangled and uninterpretable representation that is non-trivial to manipulate (compared to, say, the explicit discretized form of 2D image arrays or meshes in 3D). Moreover, any attempt to inpaint a 3D scene must not only generate a perceptually realistic appearance in a single given view, but also preserve fundamental 3D properties, such as appearance consistency across views and geometric plausibility. Finally, to obtain masks for the target object, it is more intuitive for most end users to interact with 2D images, rather than 3D interfaces; however, requiring annotations of multiple images (and maintaining view-consistent segments) is burdensome to users. An appealing alternative is to expect only a minimal set of annotations for a single view. This motivates a method capable of obtaining a view-consistent 3D segmentation mask of the object (for use in inpainting) from single-view sparse annotations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.473, + 0.702 + ], + "angle": 0, + "content": "In this paper, we address these challenges with an integrated method that takes in multiview images of a scene, extracts a 3D mask with minimal user input, and fits a NeRF to the masked images, such that the target object is replaced with plausible 3D appearance and geometry. Existing interactive 2D segmentation methods do not consider the 3D aspects of the problem (e.g., [42]), while current NeRF-based approaches are unable to use sparse annotations [76] to perform well, or do not attain sufficient accuracy [44]. Similarly, while some current NeRF manipulation algorithms allow object removal, they do not attempt to provide perceptually realistic inpaintings of newly unveiled parts of space (e.g., [64]). To our knowledge, this is the first approach that handles both interactive multiview segmentation and full 3D inpainting in a single framework." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our technique leverages off-the-shelf, 3D-unaware models for segmentation and inpainting, and transfers their outputs to 3D space in a view-consistent manner. Building on the (2D) interactive segmentation [8, 15, 33] literature, our framework starts from a small number of user-defined image points on a target object (and a few negative samples outside it). From these, our algorithm initializes masks with a video-based model [4], and lifts them into a coherent 3D segmentation via fitting a semantic NeRF [36, 76, 77]. Then, after applying a pretrained 2D inpainter [48] to the multiview image set, a customized NeRF fitting process is used to reconstruct the 3D inpainted scene, utilizing perceptual losses [72] to account for inconsistencies in the 2D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "inpainted images, as well as inpainted depth images to regularize the geometry of the masked region. Overall, we provide a complete method, from object selection to novel view synthesis of the inpainted scenes, in a unified framework with minimal burden on the user, illustrated in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.895, + 0.258 + ], + "angle": 0, + "content": "We demonstrate the effectiveness of our approach through extensive qualitative and quantitative evaluations. In addition, we address the lack of a benchmark for comparing scene inpainting methods, and introduce a new dataset where the \"ground-truth inpaintings\" (i.e., real images of the scene without the object) are available as well." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.895, + 0.426 + ], + "angle": 0, + "content": "In summary, our contributions are as follows: (i) a complete process for 3D scene manipulation, starting from object selection with minimal user interaction and ending with a 3D inpainted NeRF scene; (ii) to perform such selection, an extension of 2D segmentation models to the multiview case, capable of recovering 3D-consistent masks from sparse annotations; (iii) to ensure view-consistency and perceptual plausibility, a novel optimization-based formulation of 3D inpainting in NeRFs, which leverages 2D inpainters; and (iv) a new dataset for 3D object removal evaluation that includes corresponding object-free ground-truth." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.438, + 0.642, + 0.453 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.895, + 0.735 + ], + "angle": 0, + "content": "Image Inpainting. Inpainting in 2D has received significant research attention [23]. While early techniques relied on patches [9, 16], recent neural methods optimize both perceptual realism and reconstruction (e.g., [22, 27, 48]). Various lines of research continue to be explored for improving visual fidelity, including adversarial training (e.g., [40, 73]), architectural advances (e.g., [27, 30, 62, 63]), pluralistic outputs (e.g., [73, 75]), multiscale processing (e.g., [21, 58, 69]), and perceptual metrics (e.g., [22, 48, 72]). Our work leverages LaMa [48], which applies frequency-domain transforms [7] inspired by transformers [11, 12]. Yet, none of these lift the problem into 3D; thus, inpainting multiple captures of a scene in a consistent manner remains an underexplored task. While there are some existing 3D-aware image inpainting algorithms, they either only partially operate in 3D [65], rely on reference images [74], or consider more limited scenarios [24]. In contrast, our method operates directly in 3D, via the multiview-based NeRF model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "NeRF Manipulation. Representing scenes via volumetric rendering has recently become an important research direction [50]. Based on differentiable volume rendering [18,52] and positional encoding [13,49,53], NeRFs [35] have demonstrated remarkable performance in novel-view synthesis. Recent works have studied potential improvements in NeRF's training or rendering speed [5, 6, 17, 38, 47, 67], reconstruction quality [1, 2, 10, 29], and data requirements [28, 56, 59, 68]. However, manipulating NeRF scenes remains a challenge. Clip-NeRF [55], Object-NeRF [64], LaTeRF [36], and others [25, 32, 70] introduce approaches" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20670" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.381 + ], + "angle": 0, + "content": "to alter and complete objects represented by NeRFs; however, their performance is limited to simple objects, rather than scenes with significant clutter and texture, or they focus on tasks other than general inpainting (e.g., recoloring or deforming). Most closely related to our method is NeRF-In [31], a concurrent unpublished work, which inpaints NeRF scenes with geometry and radiance priors from 2D image inpainters, but does not address inconsistency; instead, its use of a simple pixelwise loss relegates it to simply reducing the number of views used for fitting, which reduces final view synthesis quality. Similarly using a pixelwise loss, the concurrent Remove-NeRF model [60] reduces inconsistencies by excluding views based on an uncertainty mechanism. In contrast, our approach is able to inpaint NeRF representations of challenging real-world scenes by incorporating 2D information in a view-consistent manner, via a perceptual [72] training regime. This avoids over-constraints on the inpainting, which would normally lead to blurriness." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.391, + 0.414, + 0.409 + ], + "angle": 0, + "content": "3. Background: Neural Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.471, + 0.54 + ], + "angle": 0, + "content": "NeRFs [35] encode a 3D scene as a function, \\( f: (x,d) \\to (c,\\sigma) \\), that maps a 3D coordinate, \\( x \\), and a view direction, \\( d \\), to a color, \\( c \\), and density, \\( \\sigma \\). The function \\( f \\) can be modelled in various ways (e.g., [35, 47]). For a ray, \\( r \\), the expected color is estimated by volumetric rendering via quadrature; the ray is divided into \\( N \\) sections between \\( t_n \\) and \\( t_f \\) (the near and far bounds), with \\( t_i \\) sampled from the \\( i \\)-th section, to render the estimated color, \\( \\widehat{C}(r) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.549, + 0.47, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) c _ {i}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.47, + 0.693 + ], + "angle": 0, + "content": "where \\( T_{i} = \\exp (-\\sum_{j = 1}^{i - 1}\\sigma_{j}\\delta_{j}) \\) is the transmittance, \\( \\delta_{i} = t_{i + 1} - t_{i} \\) is the distance between two adjacent points, and \\( c_{i} \\) and \\( \\sigma_{i} \\) are the color and density at \\( t_i \\), respectively. For the rays passing through pixels of the training views, the ground-truth color \\( C_\\mathrm{GT}(r) \\) is available, and the model is optimized using the reconstruction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.701, + 0.469, + 0.734 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r e c}} = \\sum_ {r \\in \\mathcal {R}} \\| \\widehat {C} (r) - C _ {\\mathrm {G T}} (r) \\| ^ {2}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.742, + 0.45, + 0.758 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}\\) is a ray batch sampled from the training views." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.169, + 0.785 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Given a set of RGB images, \\(\\mathcal{I} = \\{I_i\\}_{i=1}^n\\), with corresponding 3D poses, \\(\\mathcal{G} = \\{G_i\\}_{i=1}^n\\), and camera intrinsic matrix, \\(K\\), our model expects one additional \"source\" view with sparse user annotations (i.e., a few points identifying the unwanted object). From these inputs, we produce a NeRF model of the scene, capable of synthesizing an inpainted image from any novel view. We begin by obtaining" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.092, + 0.878, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.199, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Figure 2. Overview of our multiview segmentation architecture. As input, this network takes in a 3D coordinate, \\( x \\), and a view direction, \\( d \\), and returns view-independent density, \\( \\sigma(x) \\), objectness logit, \\( s(x) \\), and view-dependent color, \\( c(x, d) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.432 + ], + "angle": 0, + "content": "an initial 3D mask from the single-view annotated source (§ 4.1.1), followed by fitting a semantic NeRF, to improve the consistency and quality of the mask (§ 4.1.2). Finally, in § 4.2 we describe our view-consistent inpainting method, which takes the views and recovered masks as inputs. Our approach leverages the outputs of 2D inpainters [48] as appearance and geometry priors to supervise the fitting of a new NeRF. Figure 1 illustrates our entire approach, including the inputs and outputs. Additional details are in our supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.44, + 0.724, + 0.457 + ], + "angle": 0, + "content": "4.1. Multiview Segmentation" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.463, + 0.688, + 0.478 + ], + "angle": 0, + "content": "4.1.1 Mask Initialization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.738 + ], + "angle": 0, + "content": "We first describe how we initialize a rough 3D mask from single-view annotations. Denote the annotated source view as \\( I_{1} \\). The sparse information about the object and the source view are given to an interactive segmentation model [15] to estimate the initial source object mask, \\( \\widehat{M}_{1} \\). The training views are then treated as a video sequence and, along with \\( \\widehat{M}_{1} \\), given to a video instance segmentation model \\( V \\) [4, 57], to compute \\( V(\\{I_i\\}_{i=1}^n, \\widehat{M}_1) = \\{\\widehat{M}_i\\}_{i=1}^n \\) where \\( \\widehat{M}_i \\) is the initial guess for the object mask for \\( I_i \\). The initial masks, \\( \\{\\widehat{M}_i\\}_{i=1}^n \\), are typically inaccurate around the boundaries, since the training views are not actually adjacent video frames, and video segmentation models are usually 3D-unaware. Hence, we use a semantic NeRF model [36, 76, 77] to resolve the inconsistencies and improve the masks (§ 4.1.2), thus obtaining the masks for each input view, \\( \\{M_i\\}_{i=1}^n \\), to use for inpainting (§ 4.2)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.74, + 0.77 + ], + "angle": 0, + "content": "4.1.2 NeRF-based Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Our multiview segmentation module takes the input RGB images, \\(\\{I_i\\}_{i=1}^n\\), the corresponding camera intrinsic and extrinsic parameters, and the initial masks, \\(\\{\\widehat{M_i}\\}_{i=1}^n\\), and trains a semantic NeRF [76]. Figure 2 depicts the network used in the semantic NeRF; for a point, \\(x\\), and a view direction, \\(d\\), in addition to a density, \\(\\sigma(x)\\), and color, \\(c(x,d)\\), it returns a pre-sigmoid \"objectness\" logit, \\(s(x)\\). The objectness probability is then acquired as \\(p(x) = \\text{Sigmoid}(s(x))\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20671" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.168 + ], + "angle": 0, + "content": "We use Instant-NGP [3, 37, 38] as our NeRF architecture due to its fast convergence. The expected objectness logit, \\(\\widehat{S}(r)\\), associated with a ray, \\(r\\), is obtained by rendering the logits of the points on \\(r\\) instead of their colors, with respect to the densities, in Eq. 1 [36]:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.176, + 0.469, + 0.217 + ], + "angle": 0, + "content": "\\[\n\\widehat {S} (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) s _ {i}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.226, + 0.469, + 0.273 + ], + "angle": 0, + "content": "where for simplicity, \\( s(r(t_i)) \\) is denoted by \\( s_i \\). The objectness probability of a ray, \\( \\widehat{P}(r) = \\text{Sigmoid}(\\widehat{S}(r)) \\), is then supervised using the classification loss:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.281, + 0.469, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c l f}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\operatorname {B C E} \\left(\\mathbb {1} _ {r \\in \\mathcal {R} _ {\\text {m a s k e d}}}, \\widehat {P} (r)\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.325, + 0.469, + 0.493 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}\\) is the indicator function, BCE stands for the binary cross entropy loss, and \\(\\mathcal{R}_{\\mathrm{masked}}\\) is the set of rays passing through pixels that are masked in \\(\\{\\widehat{M}_i\\}_{i=1}^n\\). During the calculation of the classification loss, \\(\\mathcal{L}_{\\mathrm{clf}}\\), the weights of the colors in the rendering equation (Eq. 1) are detached to limit the supervised updates to the logits; this prevents changes to the existing geometry, due to gradient updates altering the \\(\\sigma\\) field. The geometry is supervised using a reconstruction loss, \\(\\mathcal{L}_{\\mathrm{rec}}\\), as in NeRF [35], via the given RGB images. The overall loss, used to supervise the NeRF-based multiview segmentation model, is then given by:" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.503, + 0.469, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {m v}} = \\mathcal {L} _ {\\mathrm {r e c}} + \\lambda_ {\\mathrm {c l f}} \\mathcal {L} _ {\\mathrm {c l f}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.469, + 0.664 + ], + "angle": 0, + "content": "where the classification weight, \\(\\lambda_{\\mathrm{clf}}\\), is a hyper-parameter. After optimization, 3D-consistent masks, \\(\\{M_i\\}_{i=1}^n\\), are obtained by thresholding the objectness probabilities and masking the pixels with probabilities greater than 0.5. Finally, we use two stages for optimization to further improve the masks; after obtaining the initial 3D mask, the masks are rendered from the training views, and are used to supervise a secondary multiview segmentation model as initial guesses (instead of the video segmentation outputs)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.672, + 0.277, + 0.689 + ], + "angle": 0, + "content": "4.2. Multiview Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.469, + 0.786 + ], + "angle": 0, + "content": "Figure 3 shows an overview of our view-consistent inpainting method. As the paucity of data precludes directly training a 3D inpainter, our method leverages existing 2D inpainters to obtain depth and appearance priors, which then supervise the fitting of a NeRF to the completed scene. This inpainted NeRF is trained using the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.795, + 0.469, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n p}} = \\mathcal {L} ^ {\\prime} _ {\\text {r e c}} + \\lambda_ {\\mathrm {L P I P S}} \\mathcal {L} _ {\\mathrm {L P I P S}} + \\lambda_ {\\text {d e p t h}} \\mathcal {L} _ {\\text {d e p t h}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.821, + 0.469, + 0.867 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{rec}}^{\\prime}\\) is the reconstruction loss for the unmasked pixels, and \\(\\mathcal{L}_{\\mathrm{LPIPS}}\\) and \\(\\mathcal{L}_{\\mathrm{depth}}\\) define the perceptual and depth losses (see below), with weights \\(\\lambda_{\\mathrm{LPIPS}}\\) and \\(\\lambda_{\\mathrm{depth}}\\)." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.089, + 0.891, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.229, + 0.892, + 0.355 + ], + "angle": 0, + "content": "Figure 3. Overview of our inpainting method. Using posed input images and their corresponding masks (upper- and lower-left insets), we obtain (i) an initial NeRF with the target object present and (ii) the set of inpainted input RGB images with the target object removed (but with view inconsistencies). The initial NeRF (i) is used to compute depth, which we inpaint to obtain depth images as geometric priors (upper-right inset). The inpainted RGB images (ii), which act as appearance priors, are used with the depth priors, to fit a 3D consistent NeRF to the inpainted scene.\\(^1\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.381, + 0.637, + 0.394 + ], + "angle": 0, + "content": "4.2.1 RGB Priors" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.405, + 0.892, + 0.631 + ], + "angle": 0, + "content": "Our proposed view-consistent inpainting approach uses RGB inputs, \\(\\{I_i\\}_{i=1}^n\\), the camera intrinsic and extrinsic parameters, and corresponding object masks, \\(\\{M_i\\}_{i=1}^n\\), to fit a NeRF to the scene without the undesired object. To begin with, each image and mask pair, \\((I_i, M_i)\\), is given to an image inpainter, INP, to obtain the inpainted RGB images, \\(\\{\\widetilde{I}_i\\}_{i=1}^n\\), where \\(\\widetilde{I}_i = \\mathrm{INP}(I_i, M_i)\\) [48]. Since each view is inpainted independently, directly supervising a NeRF using the inpainted views leads to blurry results due to the 3D inconsistencies between each \\(\\widetilde{I}_i\\) (see Figure 7). In this paper, instead of using mean squared error (MSE) to optimize the masked area, we propose the use of a perceptual loss, LPIPS [72], to optimize the masked parts of the images, while still using MSE for the unmasked parts, where no inpainting is needed. This loss is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.588, + 0.642, + 0.891, + 0.678 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {L P I P S}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\operatorname {L P I P S} (\\widehat {I _ {i}}, \\widetilde {I _ {i}}), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.691, + 0.891, + 0.753 + ], + "angle": 0, + "content": "where \\(\\mathcal{B}\\) is a batch of indices between 1 and \\(n\\), and \\(\\widehat{I}_i\\) is the \\(i\\)-th view rendered using NeRF. Our model for multiview inpainting and segmentation uses the same architecture (see Figure 2), except for the additional logit output, \\(s\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.644, + 0.787 + ], + "angle": 0, + "content": "4.2.2 Depth Priors" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Even with the perceptual loss, the discrepancies between the inpainted views can incorrectly guide the model towards converging to degenerate geometries (e.g., 'foggy' geometry may form near the cameras, to explain the disparate per-view information). Thus, we use inpainted depth maps as additional guidance for the NeRF model, and detach the weights when calculating the perceptual loss and use the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "\\(^{1}\\)IBRNet images in Fig. 3,5,6,7 by Wang et al. available in IBRNet [56] under an Apache License 2.0." + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20672" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "perceptual loss to only fit the colors of the scene. For this purpose, we use a NeRF optimized on images that include the unwanted object, and render the depth maps, \\(\\{D_i\\}_{i=1}^n\\), corresponding to the training views. Depth maps are calculated by substituting the distance to the camera instead of the color of points into Eq. 1:" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.195, + 0.47, + 0.236 + ], + "angle": 0, + "content": "\\[\nD (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) t _ {i}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.473, + 0.432 + ], + "angle": 0, + "content": "The rendered depths are then given to an inpainter to obtain inpainted depth maps, \\(\\{\\widetilde{D}_i\\}_{i=1}^n\\), where \\(\\widetilde{D}_i\\) is obtained as \\(\\widetilde{D}_i = \\mathrm{INP}(D_i, M_i)\\). We found that using LaMa [48] for depth inpainting, as in the RGB case, gave sufficiently high-quality results. Note that this is all calculated as a preprocessing step, and with a NeRF optimized on the original scene. This NeRF can be the same model used for multiview segmentation. If using another source for obtaining masks, such as human annotated masks, a new NeRF is fitted to the scene. These depth maps are then used to supervise the inpainted NeRF's geometry, via the \\(\\ell_2\\) distance of its rendered depths, \\(\\widehat{D}_i\\), to the inpainted depths, \\(\\widetilde{D}_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.442, + 0.47, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {d e p t h}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\left| \\widehat {D} (r) - \\widetilde {D} (r) \\right| ^ {2}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.491, + 0.438, + 0.51 + ], + "angle": 0, + "content": "where \\(\\widehat{D}(r)\\) and \\(\\widetilde{D}(r)\\) are the depth values for a ray, \\(r\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.53, + 0.315, + 0.545 + ], + "angle": 0, + "content": "4.2.3 Patch-based Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Calculating the perceptual loss, Eq. 7, requires full input views to be rendered during the optimization. Since rendering each pixel necessitates multiple forward passes through the MLP, for high-resolution images, this is an expensive process, resulting in issues such as (i) the batch size, \\( |\\mathcal{B}| \\), has to be small to fit the rendered images and their corresponding computation graphs in memory, and (ii) slow optimization, even with batch sizes as small as \\( |\\mathcal{B}| = 1 \\). A straightforward solution is to render a downsized image and compare it to the downsized version of the inpainted images; however, this leads to a loss of information if the downsizing factor is large. Following image-based works (e.g., SinGAN [46] and DPNN [14]), and 3D works (e.g., ARF [71]), we perform the computations on a patch-basis; instead of rendering complete views, we render batches of smaller patches, and compare them with their counterparts in the inpainted images based on the perceptual loss. Only patches inside the bounding box of the object mask are used. For fitting the unmasked areas, recall that \\( \\mathcal{L}_{\\mathrm{rec}}' \\) (Eq. 6) simply alters \\( \\mathcal{L}_{\\mathrm{rec}} \\) (Eq. 2) to sample rays only from unmasked pixels. By separating the perceptual and reconstruction losses, we prevent inconsistency within the mask, while avoiding unnecessary changes to the rest of the scene." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.633, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.203, + 0.632, + 0.212 + ], + "angle": 0, + "content": "60 Input Views + Camera Poses" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.089, + 0.759, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.203, + 0.758, + 0.212 + ], + "angle": 0, + "content": "Human-Annotated Object Masks" + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.089, + 0.889, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.203, + 0.882, + 0.212 + ], + "angle": 0, + "content": "40 GT Views + Camera Poses" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.224, + 0.892, + 0.28 + ], + "angle": 0, + "content": "Figure 4. Scenes from our dataset. Columns: input view (left), corresponding target object mask (middle), and a ground-truth view without the target object, from a different camera pose (right). Rows: different scenes; see supplement for examples of all scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.307, + 0.678, + 0.321 + ], + "angle": 0, + "content": "4.2.4 Mask Refinement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.331, + 0.892, + 0.558 + ], + "angle": 0, + "content": "Here, we consider further leveraging the multiview data to guide the image inpainter. In particular, parts of the training images that are currently being generated by the 2D image inpainter might be visible in other views; in such cases, there is no need to hallucinate those details, since they can be retrieved from the other views. To prevent such unnecessary inpaintings, we propose a mask refinement approach: for each source image, depth, and mask tuple, \\((I_s, D_s, M_s)\\), we substitute pixels in \\(I_s\\) and \\(D_s\\) that are visible from at least one other view, to shrink the source mask, \\(M_s\\). After this refinement step, only parts of \\(I_s\\) and \\(D_s\\) that are occluded by the undesired object in all of the training views will remain masked. As a result, the image inpainter has to fill in a smaller area, resulting in improved inpaintings. Please see our supplementary material for details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.573, + 0.634, + 0.59 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Dataset. To evaluate multiview segmentation (MVSeg), we adopt real-world scenes from LLFF [34], NeRF-360 [35], NeRF-Supervision [66], and Shiny [61]. For multiview (MV) inpainting, in addition to providing qualitative results on scenes from IBRNet [56], we address the need for a standard benchmark including ground-truth captures of scenes without the unwanted object as test views, and introduce a dataset containing 10 real-world forward-facing scenes with human annotated object masks. For each scene, we provide 60 training images with the object and 40 test images without the object. This dataset is further suitable for evaluating tasks such as real-time 3D inpainting, unsupervised 3D segmentation, and video inpainting. Figure 4 shows sample views from two scenes of our dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Metrics. To evaluate our segmentation model, we use the accuracy of the predictions (pixel-wise) and the intersection over union (IoU) metric. For MV inpainting, we follow the image-to-image literature [48] and report the average learned perceptual image patch similarity (LPIPS) [72], and the average Fréchet inception distance (FID) [19] between" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20673" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation of multiview segmentation models, for the task of transferring the source mask to other views." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.128, + 0.465, + 0.253 + ], + "angle": 0, + "content": "
MethodAcc.↑IoU↑
Proj. + Grab Cut [45] (2D)91.0846.61
Proj. + EdgeFlow [15] (2D)96.8481.63
Semantic NeRF [76] (only source mask)94.6375.13
Proj. + EdgeFlow [15] + Semantic NeRF [76]97.2683.95
Feature Field Distillation [26]97.3783.07
Video Segmentation [4,57]98.4388.34
Ours98.8590.96
Ours (two-stage)98.9191.66
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.47, + 0.353 + ], + "angle": 0, + "content": "the distribution of the ground-truth test views and model outputs. Since our focus is the inpainting, we only calculate the LPIPS and FID inside the bounding box of the object mask (using our MVSeg model, we can render the object mask from the test views that do not contain the object)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.47, + 0.594 + ], + "angle": 0, + "content": "Multiview Segmentation Baselines. For MVSeg, one category of baselines is projection-based approaches: the source mask is projected into the other views using the scene geometry from a NeRF. This gives us an incomplete mask in the other views. Then, a variety of interactive segmentation approaches are applied to the incomplete masks, propagating them to obtain complete object masks: Proj. + Grab Cut [45] and Proj. + EdgeFlow [15]. In addition, we consider Proj. + EdgeFlow + Semantic NeRF, where an additional Semantic NeRF [76] is fitted to make the outputs 3D consistent. Another baseline [26] is a representative of the concurrent works on distilling 2D pixel-level features to 3D scenes [51] and post-processing them for obtaining segmentation masks. As a baseline for video-segmentation [57], we compare to Dino [4] since it does not rely on temporally close neighboring frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Multiview Inpainting Baselines. Masked NeRF only uses the unmasked pixels to optimize a NeRF. Object NeRF [64] filters the unwanted points in 3D without explicitly inpainting the missing regions. No code is available for NeRF-In [31], so we use our own implementation of their model, with slight modifications (we use LaMa [48] as the inpainter). In addition, we compare our results to LaMa [48] as a representative of state-of-the-art 2D inpainters. To enable fair comparison between the NeRF-based 3D models (which, in addition to inpainting, have to synthesize novel views), we compare to LaMa by (i) fitting a NeRF on the views with the object\\(^2\\), (ii) rendering the test views from the fitted NeRF, and (iii) passing these rendered images to LaMa. Finally, for reference and as an ideal \"gold standard\" 3D inpainting baseline, we fit a NeRF on the ground-truth test images, use the optimized NeRF to render the test-views, and then compare the rendered results to the ground-truth. We provide these results for completeness, as" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluation of our inpainting method, using human-annotated object masks." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.128, + 0.865, + 0.3 + ], + "angle": 0, + "content": "
MethodLPIPS↓FID↓
Ideal0.4079100.25
LaMa (2D) [48]0.5369174.61
Object NeRF [64]0.6829271.80
Masked NeRF [35]0.6030294.69
NeRF-In [31]0.5699238.33
NeRF-In [31] (Single)0.4884183.23
Ours (no geo. inpainting)0.4952200.34
Ours0.4654156.64
Ours (Refined RGB/Depth)0.4664163.79
Ours (Refined RGB)0.4529147.31
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.325, + 0.892, + 0.355 + ], + "angle": 0, + "content": "an upper-bound on the best possible results one can expect to obtain when using the same NeRF architecture." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.364, + 0.593, + 0.379 + ], + "angle": 0, + "content": "5.1. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.387, + 0.892, + 0.523 + ], + "angle": 0, + "content": "Multiview Segmentation. We first evaluate our MVSeg model without any inpainting. In this experiment, we assume that the sparse image points are already given to an off-the-shelf interactive segmentation model, and that the source mask is available. Thus, the task is to transfer the source mask to other views. Table 1 shows that our model outperforms all of the 2D (3D-inconsistent) and 3D-consistent baselines. In addition, our two-stage optimization helps to further improve the obtained masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Qualitatively, Figure 5 compares the results of our segmentation model with the outputs of Neural Volumetric Object Selection (NVOS) [44] and video segmentation [4, 57]. Compared to the coarse edges of the 3D-unaware video segmentation model, our model reduces noise and improves consistency across views. Although NVOS uses scribbles, rather than the sparse points used in our model, our MVSeg visually outperforms NVOS. Since the NVOS code base is not available, we reproduce the published qualitative results for NVOS [44] (see supplemental for more examples)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Multiview Inpainting. Our dataset is used for quantitative evaluation of our proposed inpainting method against the baselines. Table 2 shows the comparison of our MV inpainting method with the baselines, assuming that the object masks from all of the views are given. The \"ideal\" row is not a baseline, but rather a NeRF fitted to the ground-truth test views (views of the scene without the object). While this is only one instantiation of the many possible inpainted scenes, it provides a convenient measure of the best performance one might reasonably expect in this scenario. Overall, our method significantly outperforms the alternative 2D and 3D inpainting approaches. Although our model uses a 2D image inpainter's [48] outputs to obtain a view-consistent inpainted NeRF, it is able to use this ensemble of MV information, in addition to the priors encoded by" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.9 + ], + "angle": 0, + "content": "2Since the test views that do not contain the object should not be available to the model during the inference." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20674" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.22, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.089, + 0.353, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.089, + 0.487, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.089, + 0.621, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.089, + 0.753, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.089, + 0.888, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.168, + 0.221, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.246, + 0.182, + 0.256 + ], + "angle": 0, + "content": "Input View" + }, + { + "type": "image", + "bbox": [ + 0.222, + 0.168, + 0.353, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.278, + 0.246, + 0.296, + 0.255 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.168, + 0.487, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.403, + 0.246, + 0.439, + 0.256 + ], + "angle": 0, + "content": "NVOS" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.168, + 0.622, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.49, + 0.246, + 0.622, + 0.257 + ], + "angle": 0, + "content": "Video Segmentation (2D)" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.168, + 0.753, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.675, + 0.246, + 0.704, + 0.256 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.168, + 0.887, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.246, + 0.868, + 0.257 + ], + "angle": 0, + "content": "Ours (Two-Stage)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.268, + 0.895, + 0.352 + ], + "angle": 0, + "content": "Figure 5. A qualitative comparison of our multiview segmentation model against Neural Volumetric Object Selection (NVOS) [44] (reproduced from original paper), video segmentation [4], and the human-annotated masks (GT). Our two-stage approach refers to running our multiview segmentation model twice, with the output of the first run as the initialization of the second (see § 4.1.2). Our method is less noisy than NVOS, which also misses some pieces of the target (e.g., the lowest flower in the bottom row), but captures more details than the video segmentation alone (e.g., the blurred edges of the flowers). Our two-stage approach helps fill in some missing aspects of the one-stage output. Please see our supplement for additional qualitative examples." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.377, + 0.471, + 0.406 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation of our inpainting method, using the outputs of our multiview segmentation model." + }, + { + "type": "table", + "bbox": [ + 0.119, + 0.415, + 0.426, + 0.526 + ], + "angle": 0, + "content": "
MethodLPIPS↓FID↓
LaMa (2D) [48]0.5439169.92
Object NeRF [64]0.6679286.55
Masked NeRF [35]0.6340332.70
NeRF-In [31]0.5858240.27
NeRF-In [31] (Single)0.5054176.27
Ours0.4662140.56
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.598 + ], + "angle": 0, + "content": "the perceptual loss function, to outperform the 2D inpainter. Table 2 further shows that removing geometry guidance impairs the inpainted scene quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.84 + ], + "angle": 0, + "content": "We display qualitative results of our MV inpainting method in Figure 6, showing that it can reconstruct a view-consistent scene with detailed textures, including coherent view-dependent radiance for both shiny and non-shiny surfaces. In addition, in Figure 7, we provide a visual comparison to the unpublished concurrent work NeRF-In [31], which has the second-lowest error. We observe that a NeRF-In model fitted to all of the inpainted views results in blurry outputs. Alternatively, using a single inpainted view for supervising the masked region leads to artifacts in further views, due to the lack of supervision for the view-dependent radiance, as well as the poor extrapolation capabilities of the network. In contrast, our perceptual approach relaxes the exact reconstruction constraints in the masked region, thus preventing blurriness despite using all of the images, while avoiding artifacts caused by single-view supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Table 2 shows that refinement provides a small but significant boost in inpainting quality, due to smaller masks requiring less hallucination from the inpainter. Yet, empirically, refinement only subtly trims the masks (reducing" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.377, + 0.892, + 0.406 + ], + "angle": 0, + "content": "Table 4. Evaluation of our 3D inpainting method across input view number (upper half) and mask dilation level (lower half)." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.415, + 0.88, + 0.513 + ], + "angle": 0, + "content": "
Input Views10204060
LPIPS↓0.47260.47130.46670.4654
FID↓171.19172.63158.02156.64
Dilation452550
LPIPS↓0.61020.53690.46540.4904
FID↓283.01230.03156.64164.66
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.627 + ], + "angle": 0, + "content": "mean masked area by \\(4.74\\%\\) on our dataset), as the camera has limited movement during data collection, to ensure similarity between the training and testing views. Further, due to noisy NeRF geometries projecting incorrect values, refining depths lowers performance, whereas refining colours alone achieves our best results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.764 + ], + "angle": 0, + "content": "So far, our experiments examine the performance of our MVSeg and MV inpainting independently; however, one can combine them to remove objects from NeRF scenes with minimal user interaction. Table 3 shows that using the output masks of our MVSeg model, instead of using the human-annotated object masks, results in a subtle decrease in the inpainting quality. However, our model with MVSegs still outperforms other methods, even when they are fitted on human-annotated segmentations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.783, + 0.788 + ], + "angle": 0, + "content": "5.2. Variations and Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Number of Input Views. Limiting the number of input views is a standard approach employed in the literature to modulate the reconstruction quality of NeRFs [54]. Table 4 shows that the performance of our inpainter degrades with fewer inputs. Thus, we argue that as better-quality NeRFs are introduced, our approach, which is agnostic to the underlying NeRF model, can readily benefit." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20675" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.887, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.396, + 0.895, + 0.455 + ], + "angle": 0, + "content": "Figure 6. Visualizations of our view-consistent inpainting results. Upper rows per inset show NeRF renderings of the original scene from novel views, with the first image also displaying the associated mask. Lower rows show the corresponding inpainted view. Notice that the synthesized views maintain consistency with each other; however, view-dependent effects still remain (e.g., the lighting on the uncovered part of the piano). Please see our supplement for additional scenes, and our project website with videos for better visualization." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.476, + 0.467, + 0.714 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.726, + 0.471, + 0.81 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparisons with other baselines. Columns: novel views of the scene, synthesized by a NeRF (on the unmasked images), NeRF-In, NeRF-In (with a single masked training image), and our approach. NeRF-In is significantly more blurry, while NeRF-In (single) tends to have difficulty with details closer to the edge of the mask boundary (zoom into boxes for examples)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Importance of Accurate Masks. Here, we examine the impact of accurate masks on inpainting, via variable dilations of the object masks with a \\(5 \\times 5\\) kernel. Larger masks lead to relying more on the view-inconsistent outputs and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.585 + ], + "angle": 0, + "content": "hallucinations of the 2D inpainters, while smaller masks may permit parts of the unwanted object's edges to remain and confuse the 2D inpainter. A subtle dilation is also useful for reducing the effect of shadows. This balance between over-masking and under-masking is demonstrated in Table 4, with five dilation iterations found to be optimal and therefore used for all other experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.602, + 0.62, + 0.617 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.853 + ], + "angle": 0, + "content": "In this paper, we presented a novel approach to inpaint NeRF scenes, which enforces viewpoint consistency based on image and geometric priors, given a single-view object mask. In addition, we provided a multiview segmentation method that simplifies the annotation process by using a set of sparse pixel-level clicks on (and around) the undesired object and translating them into a 3D mask that can be rendered from novel views. We provided experiments to show the effectiveness of our segmentation and inpainting methods. The main limitation of our work is the assumption of semantically consistent image priors, potentially only differing in terms of textures. Finally, we introduce a dataset that not only addresses the lack of challenging benchmarks for multiview inpainting, but which we believe can assist future advances in this new line of research." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was conducted at Samsung AI Centre Toronto and it was funded by Mitacs and Samsung Research, Samsung Electronics Co., Ltd." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20676" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. Mip-NeRF: A multiscale representation for antiailiasing neural radiance fields. ICCV, 2021. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.47, + 0.213 + ], + "angle": 0, + "content": "[2] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. 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Derpanis $^{1,3,4}$ Jonathan Kelly $^{2}$ Marcus A. Brubaker $^{1,3,4}$ Igor Gilitschenski $^{2}$ Alex Levinshtein $^{1}$ $^{1}$ Samsung AI Centre Toronto $^{2}$ University of Toronto $^{3}$ York University $^{4}$ Vector Institute for AI {a.mirzaei,tristan.a}@partner.samsung.com, {jkelly,gilitschenski}@cs.toronto.edu {kosta,mab}@eecs.yorku.ca, alex.lev@samsung.com + +![](images/7153f095fb01c307fe410e1221cc3238b4506317aaa4d33dc4336ff5f0cc5721.jpg) +Figure 1. An example of the inputs and outputs of our 3D inpainting framework. In addition to the images captured from the scene and their corresponding camera parameters, users are tasked with providing a few points in a single image to indicate which object they wish to remove from the scene (upper-left inset). These sparse annotations are then automatically transferred to all other views, and utilized for multiview mask construction (upper-right inset). The resulting 3D-consistent mask is used in a perceptual optimization problem that results in 3D scene inpainting (lower row), with rendered depth from the optimized NeRF shown for each image as an inset. + +# Abstract + +Neural Radiance Fields (NeRFs) have emerged as a popular approach for novel view synthesis. While NeRFs are quickly being adapted for a wider set of applications, intuitively editing NeRF scenes is still an open challenge. One important editing task is the removal of unwanted objects from a 3D scene, such that the replaced region is visually plausible and consistent with its context. We refer to this task as 3D inpainting. In 3D, solutions must be both consistent across multiple views and geometrically valid. In this paper, we propose a novel 3D inpainting method that addresses these challenges. Given a small set of posed images and sparse annotations in a single input image, our framework first rapidly obtains a 3D segmentation mask for a target object. Using the mask, a perceptual optimization-based approach is then introduced that leverages learned 2D image inpainters, distilling their information into 3D space, while ensuring view consistency. We also address the lack of a diverse benchmark for evaluating 3D scene + +inpainting methods by introducing a dataset comprised of challenging real-world scenes. In particular, our dataset contains views of the same scene with and without a target object, enabling more principled benchmarking of the 3D inpainting task. We first demonstrate the superiority of our approach on multiview segmentation, comparing to NeRF-based methods and 2D segmentation approaches. We then evaluate on the task of 3D inpainting, establishing state-of-the-art performance against other NeRF manipulation algorithms, as well as a strong 2D image inpainter baseline. + +# 1. Introduction + +Neural rendering methods, especially Neural Radiance Fields (NeRFs) [35], have recently emerged as a new modality for representing and reconstructing scenes [50], achieving impressive results for novel view synthesis. Substantial research effort continues to focus on formulating more efficient NeRFs (e.g., [6, 20, 43]), to make NeRFs more accessible in use-cases with more limited computa + +tional resources. As NeRFs become more widely accessible, the need for editing and manipulating the scenes represented by NeRFs will continue to grow. One notable editing application is removing objects and inpainting the 3D scene, analogous to the well-studied 2D image inpainting task [23]. However, several obstacles impede progress on this task, not only for the 3D inpainting process itself, but also in obtaining the input segmentation masks. First, NeRF scenes are implicitly encoded within the neural mapping weights, resulting in an entangled and uninterpretable representation that is non-trivial to manipulate (compared to, say, the explicit discretized form of 2D image arrays or meshes in 3D). Moreover, any attempt to inpaint a 3D scene must not only generate a perceptually realistic appearance in a single given view, but also preserve fundamental 3D properties, such as appearance consistency across views and geometric plausibility. Finally, to obtain masks for the target object, it is more intuitive for most end users to interact with 2D images, rather than 3D interfaces; however, requiring annotations of multiple images (and maintaining view-consistent segments) is burdensome to users. An appealing alternative is to expect only a minimal set of annotations for a single view. This motivates a method capable of obtaining a view-consistent 3D segmentation mask of the object (for use in inpainting) from single-view sparse annotations. + +In this paper, we address these challenges with an integrated method that takes in multiview images of a scene, extracts a 3D mask with minimal user input, and fits a NeRF to the masked images, such that the target object is replaced with plausible 3D appearance and geometry. Existing interactive 2D segmentation methods do not consider the 3D aspects of the problem (e.g., [42]), while current NeRF-based approaches are unable to use sparse annotations [76] to perform well, or do not attain sufficient accuracy [44]. Similarly, while some current NeRF manipulation algorithms allow object removal, they do not attempt to provide perceptually realistic inpaintings of newly unveiled parts of space (e.g., [64]). To our knowledge, this is the first approach that handles both interactive multiview segmentation and full 3D inpainting in a single framework. + +Our technique leverages off-the-shelf, 3D-unaware models for segmentation and inpainting, and transfers their outputs to 3D space in a view-consistent manner. Building on the (2D) interactive segmentation [8, 15, 33] literature, our framework starts from a small number of user-defined image points on a target object (and a few negative samples outside it). From these, our algorithm initializes masks with a video-based model [4], and lifts them into a coherent 3D segmentation via fitting a semantic NeRF [36, 76, 77]. Then, after applying a pretrained 2D inpainter [48] to the multiview image set, a customized NeRF fitting process is used to reconstruct the 3D inpainted scene, utilizing perceptual losses [72] to account for inconsistencies in the 2D + +inpainted images, as well as inpainted depth images to regularize the geometry of the masked region. Overall, we provide a complete method, from object selection to novel view synthesis of the inpainted scenes, in a unified framework with minimal burden on the user, illustrated in Figure 1. + +We demonstrate the effectiveness of our approach through extensive qualitative and quantitative evaluations. In addition, we address the lack of a benchmark for comparing scene inpainting methods, and introduce a new dataset where the "ground-truth inpaintings" (i.e., real images of the scene without the object) are available as well. + +In summary, our contributions are as follows: (i) a complete process for 3D scene manipulation, starting from object selection with minimal user interaction and ending with a 3D inpainted NeRF scene; (ii) to perform such selection, an extension of 2D segmentation models to the multiview case, capable of recovering 3D-consistent masks from sparse annotations; (iii) to ensure view-consistency and perceptual plausibility, a novel optimization-based formulation of 3D inpainting in NeRFs, which leverages 2D inpainters; and (iv) a new dataset for 3D object removal evaluation that includes corresponding object-free ground-truth. + +# 2. Related Work + +Image Inpainting. Inpainting in 2D has received significant research attention [23]. While early techniques relied on patches [9, 16], recent neural methods optimize both perceptual realism and reconstruction (e.g., [22, 27, 48]). Various lines of research continue to be explored for improving visual fidelity, including adversarial training (e.g., [40, 73]), architectural advances (e.g., [27, 30, 62, 63]), pluralistic outputs (e.g., [73, 75]), multiscale processing (e.g., [21, 58, 69]), and perceptual metrics (e.g., [22, 48, 72]). Our work leverages LaMa [48], which applies frequency-domain transforms [7] inspired by transformers [11, 12]. Yet, none of these lift the problem into 3D; thus, inpainting multiple captures of a scene in a consistent manner remains an underexplored task. While there are some existing 3D-aware image inpainting algorithms, they either only partially operate in 3D [65], rely on reference images [74], or consider more limited scenarios [24]. In contrast, our method operates directly in 3D, via the multiview-based NeRF model. + +NeRF Manipulation. Representing scenes via volumetric rendering has recently become an important research direction [50]. Based on differentiable volume rendering [18,52] and positional encoding [13,49,53], NeRFs [35] have demonstrated remarkable performance in novel-view synthesis. Recent works have studied potential improvements in NeRF's training or rendering speed [5, 6, 17, 38, 47, 67], reconstruction quality [1, 2, 10, 29], and data requirements [28, 56, 59, 68]. However, manipulating NeRF scenes remains a challenge. Clip-NeRF [55], Object-NeRF [64], LaTeRF [36], and others [25, 32, 70] introduce approaches + +to alter and complete objects represented by NeRFs; however, their performance is limited to simple objects, rather than scenes with significant clutter and texture, or they focus on tasks other than general inpainting (e.g., recoloring or deforming). Most closely related to our method is NeRF-In [31], a concurrent unpublished work, which inpaints NeRF scenes with geometry and radiance priors from 2D image inpainters, but does not address inconsistency; instead, its use of a simple pixelwise loss relegates it to simply reducing the number of views used for fitting, which reduces final view synthesis quality. Similarly using a pixelwise loss, the concurrent Remove-NeRF model [60] reduces inconsistencies by excluding views based on an uncertainty mechanism. In contrast, our approach is able to inpaint NeRF representations of challenging real-world scenes by incorporating 2D information in a view-consistent manner, via a perceptual [72] training regime. This avoids over-constraints on the inpainting, which would normally lead to blurriness. + +# 3. Background: Neural Radiance Fields + +NeRFs [35] encode a 3D scene as a function, $f: (x,d) \to (c,\sigma)$ , that maps a 3D coordinate, $x$ , and a view direction, $d$ , to a color, $c$ , and density, $\sigma$ . The function $f$ can be modelled in various ways (e.g., [35, 47]). For a ray, $r$ , the expected color is estimated by volumetric rendering via quadrature; the ray is divided into $N$ sections between $t_n$ and $t_f$ (the near and far bounds), with $t_i$ sampled from the $i$ -th section, to render the estimated color, $\widehat{C}(r)$ : + +$$ +\hat {C} (r) = \sum_ {i = 1} ^ {N} T _ {i} \left(1 - \exp \left(- \sigma_ {i} \delta_ {i}\right)\right) c _ {i}, \tag {1} +$$ + +where $T_{i} = \exp (-\sum_{j = 1}^{i - 1}\sigma_{j}\delta_{j})$ is the transmittance, $\delta_{i} = t_{i + 1} - t_{i}$ is the distance between two adjacent points, and $c_{i}$ and $\sigma_{i}$ are the color and density at $t_i$ , respectively. For the rays passing through pixels of the training views, the ground-truth color $C_\mathrm{GT}(r)$ is available, and the model is optimized using the reconstruction loss: + +$$ +\mathcal {L} _ {\mathrm {r e c}} = \sum_ {r \in \mathcal {R}} \| \widehat {C} (r) - C _ {\mathrm {G T}} (r) \| ^ {2}, \tag {2} +$$ + +where $\mathcal{R}$ is a ray batch sampled from the training views. + +# 4. Method + +Given a set of RGB images, $\mathcal{I} = \{I_i\}_{i=1}^n$ , with corresponding 3D poses, $\mathcal{G} = \{G_i\}_{i=1}^n$ , and camera intrinsic matrix, $K$ , our model expects one additional "source" view with sparse user annotations (i.e., a few points identifying the unwanted object). From these inputs, we produce a NeRF model of the scene, capable of synthesizing an inpainted image from any novel view. We begin by obtaining + +![](images/de9bc58e0eb796c7686c40927dbb18fde0c811667643ffef0e678ea50d80c3c0.jpg) +Figure 2. Overview of our multiview segmentation architecture. As input, this network takes in a 3D coordinate, $x$ , and a view direction, $d$ , and returns view-independent density, $\sigma(x)$ , objectness logit, $s(x)$ , and view-dependent color, $c(x, d)$ . + +an initial 3D mask from the single-view annotated source (§ 4.1.1), followed by fitting a semantic NeRF, to improve the consistency and quality of the mask (§ 4.1.2). Finally, in § 4.2 we describe our view-consistent inpainting method, which takes the views and recovered masks as inputs. Our approach leverages the outputs of 2D inpainters [48] as appearance and geometry priors to supervise the fitting of a new NeRF. Figure 1 illustrates our entire approach, including the inputs and outputs. Additional details are in our supplementary material. + +# 4.1. Multiview Segmentation + +# 4.1.1 Mask Initialization + +We first describe how we initialize a rough 3D mask from single-view annotations. Denote the annotated source view as $I_{1}$ . The sparse information about the object and the source view are given to an interactive segmentation model [15] to estimate the initial source object mask, $\widehat{M}_{1}$ . The training views are then treated as a video sequence and, along with $\widehat{M}_{1}$ , given to a video instance segmentation model $V$ [4, 57], to compute $V(\{I_i\}_{i=1}^n, \widehat{M}_1) = \{\widehat{M}_i\}_{i=1}^n$ where $\widehat{M}_i$ is the initial guess for the object mask for $I_i$ . The initial masks, $\{\widehat{M}_i\}_{i=1}^n$ , are typically inaccurate around the boundaries, since the training views are not actually adjacent video frames, and video segmentation models are usually 3D-unaware. Hence, we use a semantic NeRF model [36, 76, 77] to resolve the inconsistencies and improve the masks (§ 4.1.2), thus obtaining the masks for each input view, $\{M_i\}_{i=1}^n$ , to use for inpainting (§ 4.2). + +# 4.1.2 NeRF-based Segmentation + +Our multiview segmentation module takes the input RGB images, $\{I_i\}_{i=1}^n$ , the corresponding camera intrinsic and extrinsic parameters, and the initial masks, $\{\widehat{M_i}\}_{i=1}^n$ , and trains a semantic NeRF [76]. Figure 2 depicts the network used in the semantic NeRF; for a point, $x$ , and a view direction, $d$ , in addition to a density, $\sigma(x)$ , and color, $c(x,d)$ , it returns a pre-sigmoid "objectness" logit, $s(x)$ . The objectness probability is then acquired as $p(x) = \text{Sigmoid}(s(x))$ . + +We use Instant-NGP [3, 37, 38] as our NeRF architecture due to its fast convergence. The expected objectness logit, $\widehat{S}(r)$ , associated with a ray, $r$ , is obtained by rendering the logits of the points on $r$ instead of their colors, with respect to the densities, in Eq. 1 [36]: + +$$ +\widehat {S} (r) = \sum_ {i = 1} ^ {N} T _ {i} \left(1 - \exp \left(- \sigma_ {i} \delta_ {i}\right)\right) s _ {i}, \tag {3} +$$ + +where for simplicity, $s(r(t_i))$ is denoted by $s_i$ . The objectness probability of a ray, $\widehat{P}(r) = \text{Sigmoid}(\widehat{S}(r))$ , is then supervised using the classification loss: + +$$ +\mathcal {L} _ {\mathrm {c l f}} = \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} \operatorname {B C E} \left(\mathbb {1} _ {r \in \mathcal {R} _ {\text {m a s k e d}}}, \widehat {P} (r)\right), \tag {4} +$$ + +where $\mathbb{1}$ is the indicator function, BCE stands for the binary cross entropy loss, and $\mathcal{R}_{\mathrm{masked}}$ is the set of rays passing through pixels that are masked in $\{\widehat{M}_i\}_{i=1}^n$ . During the calculation of the classification loss, $\mathcal{L}_{\mathrm{clf}}$ , the weights of the colors in the rendering equation (Eq. 1) are detached to limit the supervised updates to the logits; this prevents changes to the existing geometry, due to gradient updates altering the $\sigma$ field. The geometry is supervised using a reconstruction loss, $\mathcal{L}_{\mathrm{rec}}$ , as in NeRF [35], via the given RGB images. The overall loss, used to supervise the NeRF-based multiview segmentation model, is then given by: + +$$ +\mathcal {L} _ {\mathrm {m v}} = \mathcal {L} _ {\mathrm {r e c}} + \lambda_ {\mathrm {c l f}} \mathcal {L} _ {\mathrm {c l f}}, \tag {5} +$$ + +where the classification weight, $\lambda_{\mathrm{clf}}$ , is a hyper-parameter. After optimization, 3D-consistent masks, $\{M_i\}_{i=1}^n$ , are obtained by thresholding the objectness probabilities and masking the pixels with probabilities greater than 0.5. Finally, we use two stages for optimization to further improve the masks; after obtaining the initial 3D mask, the masks are rendered from the training views, and are used to supervise a secondary multiview segmentation model as initial guesses (instead of the video segmentation outputs). + +# 4.2. Multiview Inpainting + +Figure 3 shows an overview of our view-consistent inpainting method. As the paucity of data precludes directly training a 3D inpainter, our method leverages existing 2D inpainters to obtain depth and appearance priors, which then supervise the fitting of a NeRF to the completed scene. This inpainted NeRF is trained using the following loss: + +$$ +\mathcal {L} _ {\text {i n p}} = \mathcal {L} ^ {\prime} _ {\text {r e c}} + \lambda_ {\mathrm {L P I P S}} \mathcal {L} _ {\mathrm {L P I P S}} + \lambda_ {\text {d e p t h}} \mathcal {L} _ {\text {d e p t h}}, \tag {6} +$$ + +where $\mathcal{L}_{\mathrm{rec}}^{\prime}$ is the reconstruction loss for the unmasked pixels, and $\mathcal{L}_{\mathrm{LPIPS}}$ and $\mathcal{L}_{\mathrm{depth}}$ define the perceptual and depth losses (see below), with weights $\lambda_{\mathrm{LPIPS}}$ and $\lambda_{\mathrm{depth}}$ . + +![](images/d1fc40b4d477bb3fcf73a48a77163e871d638b49e799b3f3d21aa53f03b2677d.jpg) +Figure 3. Overview of our inpainting method. Using posed input images and their corresponding masks (upper- and lower-left insets), we obtain (i) an initial NeRF with the target object present and (ii) the set of inpainted input RGB images with the target object removed (but with view inconsistencies). The initial NeRF (i) is used to compute depth, which we inpaint to obtain depth images as geometric priors (upper-right inset). The inpainted RGB images (ii), which act as appearance priors, are used with the depth priors, to fit a 3D consistent NeRF to the inpainted scene. $^1$ + +# 4.2.1 RGB Priors + +Our proposed view-consistent inpainting approach uses RGB inputs, $\{I_i\}_{i=1}^n$ , the camera intrinsic and extrinsic parameters, and corresponding object masks, $\{M_i\}_{i=1}^n$ , to fit a NeRF to the scene without the undesired object. To begin with, each image and mask pair, $(I_i, M_i)$ , is given to an image inpainter, INP, to obtain the inpainted RGB images, $\{\widetilde{I}_i\}_{i=1}^n$ , where $\widetilde{I}_i = \mathrm{INP}(I_i, M_i)$ [48]. Since each view is inpainted independently, directly supervising a NeRF using the inpainted views leads to blurry results due to the 3D inconsistencies between each $\widetilde{I}_i$ (see Figure 7). In this paper, instead of using mean squared error (MSE) to optimize the masked area, we propose the use of a perceptual loss, LPIPS [72], to optimize the masked parts of the images, while still using MSE for the unmasked parts, where no inpainting is needed. This loss is calculated as follows: + +$$ +\mathcal {L} _ {\mathrm {L P I P S}} = \frac {1}{| \mathcal {B} |} \sum_ {i \in \mathcal {B}} \operatorname {L P I P S} (\widehat {I _ {i}}, \widetilde {I _ {i}}), \tag {7} +$$ + +where $\mathcal{B}$ is a batch of indices between 1 and $n$ , and $\widehat{I}_i$ is the $i$ -th view rendered using NeRF. Our model for multiview inpainting and segmentation uses the same architecture (see Figure 2), except for the additional logit output, $s$ . + +# 4.2.2 Depth Priors + +Even with the perceptual loss, the discrepancies between the inpainted views can incorrectly guide the model towards converging to degenerate geometries (e.g., 'foggy' geometry may form near the cameras, to explain the disparate per-view information). Thus, we use inpainted depth maps as additional guidance for the NeRF model, and detach the weights when calculating the perceptual loss and use the + +perceptual loss to only fit the colors of the scene. For this purpose, we use a NeRF optimized on images that include the unwanted object, and render the depth maps, $\{D_i\}_{i=1}^n$ , corresponding to the training views. Depth maps are calculated by substituting the distance to the camera instead of the color of points into Eq. 1: + +$$ +D (r) = \sum_ {i = 1} ^ {N} T _ {i} \left(1 - \exp \left(- \sigma_ {i} \delta_ {i}\right)\right) t _ {i}. \tag {8} +$$ + +The rendered depths are then given to an inpainter to obtain inpainted depth maps, $\{\widetilde{D}_i\}_{i=1}^n$ , where $\widetilde{D}_i$ is obtained as $\widetilde{D}_i = \mathrm{INP}(D_i, M_i)$ . We found that using LaMa [48] for depth inpainting, as in the RGB case, gave sufficiently high-quality results. Note that this is all calculated as a preprocessing step, and with a NeRF optimized on the original scene. This NeRF can be the same model used for multiview segmentation. If using another source for obtaining masks, such as human annotated masks, a new NeRF is fitted to the scene. These depth maps are then used to supervise the inpainted NeRF's geometry, via the $\ell_2$ distance of its rendered depths, $\widehat{D}_i$ , to the inpainted depths, $\widetilde{D}_i$ : + +$$ +\mathcal {L} _ {\text {d e p t h}} = \frac {1}{| \mathcal {R} |} \sum_ {r \in \mathcal {R}} \left| \widehat {D} (r) - \widetilde {D} (r) \right| ^ {2}, \tag {9} +$$ + +where $\widehat{D}(r)$ and $\widetilde{D}(r)$ are the depth values for a ray, $r$ . + +# 4.2.3 Patch-based Optimization + +Calculating the perceptual loss, Eq. 7, requires full input views to be rendered during the optimization. Since rendering each pixel necessitates multiple forward passes through the MLP, for high-resolution images, this is an expensive process, resulting in issues such as (i) the batch size, $|\mathcal{B}|$ , has to be small to fit the rendered images and their corresponding computation graphs in memory, and (ii) slow optimization, even with batch sizes as small as $|\mathcal{B}| = 1$ . A straightforward solution is to render a downsized image and compare it to the downsized version of the inpainted images; however, this leads to a loss of information if the downsizing factor is large. Following image-based works (e.g., SinGAN [46] and DPNN [14]), and 3D works (e.g., ARF [71]), we perform the computations on a patch-basis; instead of rendering complete views, we render batches of smaller patches, and compare them with their counterparts in the inpainted images based on the perceptual loss. Only patches inside the bounding box of the object mask are used. For fitting the unmasked areas, recall that $\mathcal{L}_{\mathrm{rec}}'$ (Eq. 6) simply alters $\mathcal{L}_{\mathrm{rec}}$ (Eq. 2) to sample rays only from unmasked pixels. By separating the perceptual and reconstruction losses, we prevent inconsistency within the mask, while avoiding unnecessary changes to the rest of the scene. + +![](images/96fed5a9841afc84b0c07073c10646bfebab901b73afad90cb04847e99f7ef5e.jpg) +60 Input Views + Camera Poses + +![](images/69d07eec86b6a8ee5f1dcb1133c4a131d4ac682e405b3c208e7e7fa6152057de.jpg) +Human-Annotated Object Masks + +![](images/81908990a5ff11a8ee34ccf93e07a2743312537e8c813277dfb4a610405da77d.jpg) +40 GT Views + Camera Poses +Figure 4. Scenes from our dataset. Columns: input view (left), corresponding target object mask (middle), and a ground-truth view without the target object, from a different camera pose (right). Rows: different scenes; see supplement for examples of all scenes. + +# 4.2.4 Mask Refinement + +Here, we consider further leveraging the multiview data to guide the image inpainter. In particular, parts of the training images that are currently being generated by the 2D image inpainter might be visible in other views; in such cases, there is no need to hallucinate those details, since they can be retrieved from the other views. To prevent such unnecessary inpaintings, we propose a mask refinement approach: for each source image, depth, and mask tuple, $(I_s, D_s, M_s)$ , we substitute pixels in $I_s$ and $D_s$ that are visible from at least one other view, to shrink the source mask, $M_s$ . After this refinement step, only parts of $I_s$ and $D_s$ that are occluded by the undesired object in all of the training views will remain masked. As a result, the image inpainter has to fill in a smaller area, resulting in improved inpaintings. Please see our supplementary material for details. + +# 5. Experiments + +Dataset. To evaluate multiview segmentation (MVSeg), we adopt real-world scenes from LLFF [34], NeRF-360 [35], NeRF-Supervision [66], and Shiny [61]. For multiview (MV) inpainting, in addition to providing qualitative results on scenes from IBRNet [56], we address the need for a standard benchmark including ground-truth captures of scenes without the unwanted object as test views, and introduce a dataset containing 10 real-world forward-facing scenes with human annotated object masks. For each scene, we provide 60 training images with the object and 40 test images without the object. This dataset is further suitable for evaluating tasks such as real-time 3D inpainting, unsupervised 3D segmentation, and video inpainting. Figure 4 shows sample views from two scenes of our dataset. + +Metrics. To evaluate our segmentation model, we use the accuracy of the predictions (pixel-wise) and the intersection over union (IoU) metric. For MV inpainting, we follow the image-to-image literature [48] and report the average learned perceptual image patch similarity (LPIPS) [72], and the average Fréchet inception distance (FID) [19] between + +Table 1. Quantitative evaluation of multiview segmentation models, for the task of transferring the source mask to other views. + +
MethodAcc.↑IoU↑
Proj. + Grab Cut [45] (2D)91.0846.61
Proj. + EdgeFlow [15] (2D)96.8481.63
Semantic NeRF [76] (only source mask)94.6375.13
Proj. + EdgeFlow [15] + Semantic NeRF [76]97.2683.95
Feature Field Distillation [26]97.3783.07
Video Segmentation [4,57]98.4388.34
Ours98.8590.96
Ours (two-stage)98.9191.66
+ +the distribution of the ground-truth test views and model outputs. Since our focus is the inpainting, we only calculate the LPIPS and FID inside the bounding box of the object mask (using our MVSeg model, we can render the object mask from the test views that do not contain the object). + +Multiview Segmentation Baselines. For MVSeg, one category of baselines is projection-based approaches: the source mask is projected into the other views using the scene geometry from a NeRF. This gives us an incomplete mask in the other views. Then, a variety of interactive segmentation approaches are applied to the incomplete masks, propagating them to obtain complete object masks: Proj. + Grab Cut [45] and Proj. + EdgeFlow [15]. In addition, we consider Proj. + EdgeFlow + Semantic NeRF, where an additional Semantic NeRF [76] is fitted to make the outputs 3D consistent. Another baseline [26] is a representative of the concurrent works on distilling 2D pixel-level features to 3D scenes [51] and post-processing them for obtaining segmentation masks. As a baseline for video-segmentation [57], we compare to Dino [4] since it does not rely on temporally close neighboring frames. + +Multiview Inpainting Baselines. Masked NeRF only uses the unmasked pixels to optimize a NeRF. Object NeRF [64] filters the unwanted points in 3D without explicitly inpainting the missing regions. No code is available for NeRF-In [31], so we use our own implementation of their model, with slight modifications (we use LaMa [48] as the inpainter). In addition, we compare our results to LaMa [48] as a representative of state-of-the-art 2D inpainters. To enable fair comparison between the NeRF-based 3D models (which, in addition to inpainting, have to synthesize novel views), we compare to LaMa by (i) fitting a NeRF on the views with the object $^2$ , (ii) rendering the test views from the fitted NeRF, and (iii) passing these rendered images to LaMa. Finally, for reference and as an ideal "gold standard" 3D inpainting baseline, we fit a NeRF on the ground-truth test images, use the optimized NeRF to render the test-views, and then compare the rendered results to the ground-truth. We provide these results for completeness, as + +Table 2. Quantitative evaluation of our inpainting method, using human-annotated object masks. + +
MethodLPIPS↓FID↓
Ideal0.4079100.25
LaMa (2D) [48]0.5369174.61
Object NeRF [64]0.6829271.80
Masked NeRF [35]0.6030294.69
NeRF-In [31]0.5699238.33
NeRF-In [31] (Single)0.4884183.23
Ours (no geo. inpainting)0.4952200.34
Ours0.4654156.64
Ours (Refined RGB/Depth)0.4664163.79
Ours (Refined RGB)0.4529147.31
+ +an upper-bound on the best possible results one can expect to obtain when using the same NeRF architecture. + +# 5.1. Results + +Multiview Segmentation. We first evaluate our MVSeg model without any inpainting. In this experiment, we assume that the sparse image points are already given to an off-the-shelf interactive segmentation model, and that the source mask is available. Thus, the task is to transfer the source mask to other views. Table 1 shows that our model outperforms all of the 2D (3D-inconsistent) and 3D-consistent baselines. In addition, our two-stage optimization helps to further improve the obtained masks. + +Qualitatively, Figure 5 compares the results of our segmentation model with the outputs of Neural Volumetric Object Selection (NVOS) [44] and video segmentation [4, 57]. Compared to the coarse edges of the 3D-unaware video segmentation model, our model reduces noise and improves consistency across views. Although NVOS uses scribbles, rather than the sparse points used in our model, our MVSeg visually outperforms NVOS. Since the NVOS code base is not available, we reproduce the published qualitative results for NVOS [44] (see supplemental for more examples). + +Multiview Inpainting. Our dataset is used for quantitative evaluation of our proposed inpainting method against the baselines. Table 2 shows the comparison of our MV inpainting method with the baselines, assuming that the object masks from all of the views are given. The "ideal" row is not a baseline, but rather a NeRF fitted to the ground-truth test views (views of the scene without the object). While this is only one instantiation of the many possible inpainted scenes, it provides a convenient measure of the best performance one might reasonably expect in this scenario. Overall, our method significantly outperforms the alternative 2D and 3D inpainting approaches. Although our model uses a 2D image inpainter's [48] outputs to obtain a view-consistent inpainted NeRF, it is able to use this ensemble of MV information, in addition to the priors encoded by + +![](images/44b53cf8f3bd72b7bc6277454ba08e2fd17b5ba58bc26f209c36ce64094a19a6.jpg) + +![](images/9545002d4b03125c60a72c26ea5ead46ad88f52142c1df27f2ebd599c5ba6ea3.jpg) + +![](images/004ec54ac2cceac7c049f0193529bc6e54d19103a7173ee63024ce93c790ca58.jpg) + +![](images/7b95d02db97acf0a334df2a462b93ca71ddd02b66fb2510ef8f72298dd8cffcf.jpg) + +![](images/16edcc29221911979934e5936b26b5e88ba270df269cea8606635c278809def1.jpg) + +![](images/4cbc90b7c3c77f27b8554ffd933923f340c3b2491b529343bd5b8bbc4e809970.jpg) + +![](images/1ee66a64e2a1f288b665bbf52100b094793455cfb1bc740ff22d38d91a54d90f.jpg) +Input View +Figure 5. A qualitative comparison of our multiview segmentation model against Neural Volumetric Object Selection (NVOS) [44] (reproduced from original paper), video segmentation [4], and the human-annotated masks (GT). Our two-stage approach refers to running our multiview segmentation model twice, with the output of the first run as the initialization of the second (see § 4.1.2). Our method is less noisy than NVOS, which also misses some pieces of the target (e.g., the lowest flower in the bottom row), but captures more details than the video segmentation alone (e.g., the blurred edges of the flowers). Our two-stage approach helps fill in some missing aspects of the one-stage output. Please see our supplement for additional qualitative examples. + +![](images/e9ecf9214f822bf0e2ec0bd5b47b39ec6e7903115e498987403b8dcd67a04a7e.jpg) +GT + +![](images/92c0f7046bb31d23a3bc7f983fcbf433e146a1d65f7ca1bfe0ec0c47e5681da1.jpg) +NVOS + +![](images/8428c2fd4315ee981652331d47228b77bbf066b898f2515775d84c245633cb35.jpg) +Video Segmentation (2D) + +![](images/c3e1c53c869a12ee1c1bbda771c30f5f541d9c42e176ee9f06817e2f43a01196.jpg) +Ours + +![](images/ef80005f9d36aaee6ddcc593a234efa812da36645b9862efba2107b3aef3e652.jpg) +Ours (Two-Stage) + +Table 3. Quantitative evaluation of our inpainting method, using the outputs of our multiview segmentation model. + +
MethodLPIPS↓FID↓
LaMa (2D) [48]0.5439169.92
Object NeRF [64]0.6679286.55
Masked NeRF [35]0.6340332.70
NeRF-In [31]0.5858240.27
NeRF-In [31] (Single)0.5054176.27
Ours0.4662140.56
+ +the perceptual loss function, to outperform the 2D inpainter. Table 2 further shows that removing geometry guidance impairs the inpainted scene quality. + +We display qualitative results of our MV inpainting method in Figure 6, showing that it can reconstruct a view-consistent scene with detailed textures, including coherent view-dependent radiance for both shiny and non-shiny surfaces. In addition, in Figure 7, we provide a visual comparison to the unpublished concurrent work NeRF-In [31], which has the second-lowest error. We observe that a NeRF-In model fitted to all of the inpainted views results in blurry outputs. Alternatively, using a single inpainted view for supervising the masked region leads to artifacts in further views, due to the lack of supervision for the view-dependent radiance, as well as the poor extrapolation capabilities of the network. In contrast, our perceptual approach relaxes the exact reconstruction constraints in the masked region, thus preventing blurriness despite using all of the images, while avoiding artifacts caused by single-view supervision. + +Table 2 shows that refinement provides a small but significant boost in inpainting quality, due to smaller masks requiring less hallucination from the inpainter. Yet, empirically, refinement only subtly trims the masks (reducing + +Table 4. Evaluation of our 3D inpainting method across input view number (upper half) and mask dilation level (lower half). + +
Input Views10204060
LPIPS↓0.47260.47130.46670.4654
FID↓171.19172.63158.02156.64
Dilation452550
LPIPS↓0.61020.53690.46540.4904
FID↓283.01230.03156.64164.66
+ +mean masked area by $4.74\%$ on our dataset), as the camera has limited movement during data collection, to ensure similarity between the training and testing views. Further, due to noisy NeRF geometries projecting incorrect values, refining depths lowers performance, whereas refining colours alone achieves our best results. + +So far, our experiments examine the performance of our MVSeg and MV inpainting independently; however, one can combine them to remove objects from NeRF scenes with minimal user interaction. Table 3 shows that using the output masks of our MVSeg model, instead of using the human-annotated object masks, results in a subtle decrease in the inpainting quality. However, our model with MVSegs still outperforms other methods, even when they are fitted on human-annotated segmentations. + +# 5.2. Variations and Ablation Studies + +Number of Input Views. Limiting the number of input views is a standard approach employed in the literature to modulate the reconstruction quality of NeRFs [54]. Table 4 shows that the performance of our inpainter degrades with fewer inputs. Thus, we argue that as better-quality NeRFs are introduced, our approach, which is agnostic to the underlying NeRF model, can readily benefit. + +![](images/8e4f0bbe17f35d00eab93a74f2443363d56da1bc53620245230b854aedf13628.jpg) +Figure 6. Visualizations of our view-consistent inpainting results. Upper rows per inset show NeRF renderings of the original scene from novel views, with the first image also displaying the associated mask. Lower rows show the corresponding inpainted view. Notice that the synthesized views maintain consistency with each other; however, view-dependent effects still remain (e.g., the lighting on the uncovered part of the piano). Please see our supplement for additional scenes, and our project website with videos for better visualization. + +![](images/b03e48a6b91c30330e8288251e54bdcf103f83e532d7f086403dfca44cdc5013.jpg) +Figure 7. Qualitative comparisons with other baselines. Columns: novel views of the scene, synthesized by a NeRF (on the unmasked images), NeRF-In, NeRF-In (with a single masked training image), and our approach. NeRF-In is significantly more blurry, while NeRF-In (single) tends to have difficulty with details closer to the edge of the mask boundary (zoom into boxes for examples). + +Importance of Accurate Masks. Here, we examine the impact of accurate masks on inpainting, via variable dilations of the object masks with a $5 \times 5$ kernel. Larger masks lead to relying more on the view-inconsistent outputs and + +hallucinations of the 2D inpainters, while smaller masks may permit parts of the unwanted object's edges to remain and confuse the 2D inpainter. A subtle dilation is also useful for reducing the effect of shadows. This balance between over-masking and under-masking is demonstrated in Table 4, with five dilation iterations found to be optimal and therefore used for all other experiments. + +# 6. Conclusion + +In this paper, we presented a novel approach to inpaint NeRF scenes, which enforces viewpoint consistency based on image and geometric priors, given a single-view object mask. In addition, we provided a multiview segmentation method that simplifies the annotation process by using a set of sparse pixel-level clicks on (and around) the undesired object and translating them into a 3D mask that can be rendered from novel views. We provided experiments to show the effectiveness of our segmentation and inpainting methods. The main limitation of our work is the assumption of semantically consistent image priors, potentially only differing in terms of textures. Finally, we introduce a dataset that not only addresses the lack of challenging benchmarks for multiview inpainting, but which we believe can assist future advances in this new line of research. + +Acknowledgments. This work was conducted at Samsung AI Centre Toronto and it was funded by Mitacs and Samsung Research, Samsung Electronics Co., Ltd. + +# References + +[1] Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. Mip-NeRF: A multiscale representation for antiailiasing neural radiance fields. ICCV, 2021. 2 +[2] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. CVPR, 2022. 2 +[3] Yash Bhalgat. Hashnerf-pytorch. https://github.com/yashbhalgat/HashNeRF-pytorch/, 2022. 4, 13 +[4] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. 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An example of the inputs and outputs of our 3D inpainting framework. In addition to the images captured from the scene and their corresponding camera parameters, users are tasked with providing a few points in a single image to indicate which object they wish to remove from the scene (upper-left inset). These sparse annotations are then automatically transferred to all other views, and utilized for multiview mask construction (upper-right inset). The resulting 3D-consistent mask is used in a perceptual optimization problem that results in 3D scene inpainting (lower row), with rendered depth from the optimized NeRF shown for each image as an inset." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 464, + 192, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 464, + 192, + 475 + ], + "spans": [ + { + "bbox": [ + 143, + 464, + 192, + 475 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 45, + 498, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 498, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 288, + 713 + ], + "type": "text", + "content": "Neural Radiance Fields (NeRFs) have emerged as a popular approach for novel view synthesis. While NeRFs are quickly being adapted for a wider set of applications, intuitively editing NeRF scenes is still an open challenge. One important editing task is the removal of unwanted objects from a 3D scene, such that the replaced region is visually plausible and consistent with its context. We refer to this task as 3D inpainting. In 3D, solutions must be both consistent across multiple views and geometrically valid. In this paper, we propose a novel 3D inpainting method that addresses these challenges. Given a small set of posed images and sparse annotations in a single input image, our framework first rapidly obtains a 3D segmentation mask for a target object. Using the mask, a perceptual optimization-based approach is then introduced that leverages learned 2D image inpainters, distilling their information into 3D space, while ensuring view consistency. We also address the lack of a diverse benchmark for evaluating 3D scene" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 464, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 586 + ], + "type": "text", + "content": " inpainting methods by introducing a dataset comprised of challenging real-world scenes. In particular, our dataset contains views of the same scene with and without a target object, enabling more principled benchmarking of the 3D inpainting task. We first demonstrate the superiority of our approach on multiview segmentation, comparing to NeRF-based methods and 2D segmentation approaches. We then evaluate on the task of 3D inpainting, establishing state-of-the-art performance against other NeRF manipulation algorithms, as well as a strong 2D image inpainter baseline." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 609, + 387, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 387, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 387, + 621 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "Neural rendering methods, especially Neural Radiance Fields (NeRFs) [35], have recently emerged as a new modality for representing and reconstructing scenes [50], achieving impressive results for novel view synthesis. Substantial research effort continues to focus on formulating more efficient NeRFs (e.g., [6, 20, 43]), to make NeRFs more accessible in use-cases with more limited computa" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20669" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "type": "text", + "content": "tional resources. As NeRFs become more widely accessible, the need for editing and manipulating the scenes represented by NeRFs will continue to grow. One notable editing application is removing objects and inpainting the 3D scene, analogous to the well-studied 2D image inpainting task [23]. However, several obstacles impede progress on this task, not only for the 3D inpainting process itself, but also in obtaining the input segmentation masks. First, NeRF scenes are implicitly encoded within the neural mapping weights, resulting in an entangled and uninterpretable representation that is non-trivial to manipulate (compared to, say, the explicit discretized form of 2D image arrays or meshes in 3D). Moreover, any attempt to inpaint a 3D scene must not only generate a perceptually realistic appearance in a single given view, but also preserve fundamental 3D properties, such as appearance consistency across views and geometric plausibility. Finally, to obtain masks for the target object, it is more intuitive for most end users to interact with 2D images, rather than 3D interfaces; however, requiring annotations of multiple images (and maintaining view-consistent segments) is burdensome to users. An appealing alternative is to expect only a minimal set of annotations for a single view. This motivates a method capable of obtaining a view-consistent 3D segmentation mask of the object (for use in inpainting) from single-view sparse annotations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 375, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 289, + 555 + ], + "type": "text", + "content": "In this paper, we address these challenges with an integrated method that takes in multiview images of a scene, extracts a 3D mask with minimal user input, and fits a NeRF to the masked images, such that the target object is replaced with plausible 3D appearance and geometry. Existing interactive 2D segmentation methods do not consider the 3D aspects of the problem (e.g., [42]), while current NeRF-based approaches are unable to use sparse annotations [76] to perform well, or do not attain sufficient accuracy [44]. Similarly, while some current NeRF manipulation algorithms allow object removal, they do not attempt to provide perceptually realistic inpaintings of newly unveiled parts of space (e.g., [64]). To our knowledge, this is the first approach that handles both interactive multiview segmentation and full 3D inpainting in a single framework." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 289, + 715 + ], + "type": "text", + "content": "Our technique leverages off-the-shelf, 3D-unaware models for segmentation and inpainting, and transfers their outputs to 3D space in a view-consistent manner. Building on the (2D) interactive segmentation [8, 15, 33] literature, our framework starts from a small number of user-defined image points on a target object (and a few negative samples outside it). From these, our algorithm initializes masks with a video-based model [4], and lifts them into a coherent 3D segmentation via fitting a semantic NeRF [36, 76, 77]. Then, after applying a pretrained 2D inpainter [48] to the multiview image set, a customized NeRF fitting process is used to reconstruct the 3D inpainted scene, utilizing perceptual losses [72] to account for inconsistencies in the 2D" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "inpainted images, as well as inpainted depth images to regularize the geometry of the masked region. Overall, we provide a complete method, from object selection to novel view synthesis of the inpainted scenes, in a unified framework with minimal burden on the user, illustrated in Figure 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 133, + 547, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 204 + ], + "type": "text", + "content": "We demonstrate the effectiveness of our approach through extensive qualitative and quantitative evaluations. In addition, we address the lack of a benchmark for comparing scene inpainting methods, and introduce a new dataset where the \"ground-truth inpaintings\" (i.e., real images of the scene without the object) are available as well." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 204, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 547, + 337 + ], + "type": "text", + "content": "In summary, our contributions are as follows: (i) a complete process for 3D scene manipulation, starting from object selection with minimal user interaction and ending with a 3D inpainted NeRF scene; (ii) to perform such selection, an extension of 2D segmentation models to the multiview case, capable of recovering 3D-consistent masks from sparse annotations; (iii) to ensure view-consistency and perceptual plausibility, a novel optimization-based formulation of 3D inpainting in NeRFs, which leverages 2D inpainters; and (iv) a new dataset for 3D object removal evaluation that includes corresponding object-free ground-truth." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 346, + 392, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 392, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 392, + 358 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 366, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 547, + 582 + ], + "type": "text", + "content": "Image Inpainting. Inpainting in 2D has received significant research attention [23]. While early techniques relied on patches [9, 16], recent neural methods optimize both perceptual realism and reconstruction (e.g., [22, 27, 48]). Various lines of research continue to be explored for improving visual fidelity, including adversarial training (e.g., [40, 73]), architectural advances (e.g., [27, 30, 62, 63]), pluralistic outputs (e.g., [73, 75]), multiscale processing (e.g., [21, 58, 69]), and perceptual metrics (e.g., [22, 48, 72]). Our work leverages LaMa [48], which applies frequency-domain transforms [7] inspired by transformers [11, 12]. Yet, none of these lift the problem into 3D; thus, inpainting multiple captures of a scene in a consistent manner remains an underexplored task. While there are some existing 3D-aware image inpainting algorithms, they either only partially operate in 3D [65], rely on reference images [74], or consider more limited scenarios [24]. In contrast, our method operates directly in 3D, via the multiview-based NeRF model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "NeRF Manipulation. Representing scenes via volumetric rendering has recently become an important research direction [50]. Based on differentiable volume rendering [18,52] and positional encoding [13,49,53], NeRFs [35] have demonstrated remarkable performance in novel-view synthesis. Recent works have studied potential improvements in NeRF's training or rendering speed [5, 6, 17, 38, 47, 67], reconstruction quality [1, 2, 10, 29], and data requirements [28, 56, 59, 68]. However, manipulating NeRF scenes remains a challenge. Clip-NeRF [55], Object-NeRF [64], LaTeRF [36], and others [25, 32, 70] introduce approaches" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20670" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 301 + ], + "type": "text", + "content": "to alter and complete objects represented by NeRFs; however, their performance is limited to simple objects, rather than scenes with significant clutter and texture, or they focus on tasks other than general inpainting (e.g., recoloring or deforming). Most closely related to our method is NeRF-In [31], a concurrent unpublished work, which inpaints NeRF scenes with geometry and radiance priors from 2D image inpainters, but does not address inconsistency; instead, its use of a simple pixelwise loss relegates it to simply reducing the number of views used for fitting, which reduces final view synthesis quality. Similarly using a pixelwise loss, the concurrent Remove-NeRF model [60] reduces inconsistencies by excluding views based on an uncertainty mechanism. In contrast, our approach is able to inpaint NeRF representations of challenging real-world scenes by incorporating 2D information in a view-consistent manner, via a perceptual [72] training regime. This avoids over-constraints on the inpainting, which would normally lead to blurriness." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 309, + 253, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 309, + 253, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 309, + 253, + 323 + ], + "type": "text", + "content": "3. Background: Neural Radiance Fields" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": "NeRFs [35] encode a 3D scene as a function, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "f: (x,d) \\to (c,\\sigma)" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ", that maps a 3D coordinate, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ", and a view direction, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ", to a color, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ", and density, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ". The function " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": " can be modelled in various ways (e.g., [35, 47]). For a ray, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ", the expected color is estimated by volumetric rendering via quadrature; the ray is divided into " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": " sections between " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "t_f" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": " (the near and far bounds), with " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": " sampled from the " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": "-th section, to render the estimated color, " + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "inline_equation", + "content": "\\widehat{C}(r)" + }, + { + "bbox": [ + 46, + 329, + 288, + 427 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 434, + 287, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 434, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 94, + 434, + 287, + 467 + ], + "type": "interline_equation", + "content": "\\hat {C} (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) c _ {i}, \\tag {1}", + "image_path": "816bea430e9e8babd13aacf4c7b7fce95fab25c207c8403f557b03b0e7487791.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "inline_equation", + "content": "T_{i} = \\exp (-\\sum_{j = 1}^{i - 1}\\sigma_{j}\\delta_{j})" + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": " is the transmittance, " + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\delta_{i} = t_{i + 1} - t_{i}" + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": " is the distance between two adjacent points, and " + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": " are the color and density at " + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": ", respectively. For the rays passing through pixels of the training views, the ground-truth color " + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "inline_equation", + "content": "C_\\mathrm{GT}(r)" + }, + { + "bbox": [ + 46, + 475, + 287, + 548 + ], + "type": "text", + "content": " is available, and the model is optimized using the reconstruction loss:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 555, + 287, + 581 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 555, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 102, + 555, + 287, + 581 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r e c}} = \\sum_ {r \\in \\mathcal {R}} \\| \\widehat {C} (r) - C _ {\\mathrm {G T}} (r) \\| ^ {2}, \\tag {2}", + "image_path": "c71a272eb3912620fbfe95a64c5ef83a8f383894d972dcfb4109d34bed3a164f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 587, + 275, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 275, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 275, + 600 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 587, + 275, + 600 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 587, + 275, + 600 + ], + "type": "text", + "content": " is a ray batch sampled from the training views." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 609, + 103, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 103, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 103, + 621 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Given a set of RGB images, " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{I} = \\{I_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": ", with corresponding 3D poses, " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{G_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": ", and camera intrinsic matrix, " + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": ", our model expects one additional \"source\" view with sparse user annotations (i.e., a few points identifying the unwanted object). From these inputs, we produce a NeRF model of the scene, capable of synthesizing an inpainted image from any novel view. We begin by obtaining" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 313, + 72, + 537, + 144 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 537, + 144 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 537, + 144 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 537, + 144 + ], + "type": "image", + "image_path": "de9bc58e0eb796c7686c40927dbb18fde0c811667643ffef0e678ea50d80c3c0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "text", + "content": "Figure 2. Overview of our multiview segmentation architecture. As input, this network takes in a 3D coordinate, " + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "text", + "content": ", and a view direction, " + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "text", + "content": ", and returns view-independent density, " + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "inline_equation", + "content": "\\sigma(x)" + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "text", + "content": ", objectness logit, " + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "inline_equation", + "content": "s(x)" + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "text", + "content": ", and view-dependent color, " + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "inline_equation", + "content": "c(x, d)" + }, + { + "bbox": [ + 305, + 157, + 545, + 202 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 221, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 545, + 342 + ], + "type": "text", + "content": "an initial 3D mask from the single-view annotated source (§ 4.1.1), followed by fitting a semantic NeRF, to improve the consistency and quality of the mask (§ 4.1.2). Finally, in § 4.2 we describe our view-consistent inpainting method, which takes the views and recovered masks as inputs. Our approach leverages the outputs of 2D inpainters [48] as appearance and geometry priors to supervise the fitting of a new NeRF. Figure 1 illustrates our entire approach, including the inputs and outputs. Additional details are in our supplementary material." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 348, + 443, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 443, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 443, + 361 + ], + "type": "text", + "content": "4.1. Multiview Segmentation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 366, + 421, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 366, + 421, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 366, + 421, + 378 + ], + "type": "text", + "content": "4.1.1 Mask Initialization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": "We first describe how we initialize a rough 3D mask from single-view annotations. Denote the annotated source view as " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": ". The sparse information about the object and the source view are given to an interactive segmentation model [15] to estimate the initial source object mask, " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\widehat{M}_{1}" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": ". The training views are then treated as a video sequence and, along with " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\widehat{M}_{1}" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": ", given to a video instance segmentation model " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": " [4, 57], to compute " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "V(\\{I_i\\}_{i=1}^n, \\widehat{M}_1) = \\{\\widehat{M}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\widehat{M}_i" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": " is the initial guess for the object mask for " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "I_i" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": ". The initial masks, " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\{\\widehat{M}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": ", are typically inaccurate around the boundaries, since the training views are not actually adjacent video frames, and video segmentation models are usually 3D-unaware. Hence, we use a semantic NeRF model [36, 76, 77] to resolve the inconsistencies and improve the masks (§ 4.1.2), thus obtaining the masks for each input view, " + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "inline_equation", + "content": "\\{M_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 385, + 545, + 584 + ], + "type": "text", + "content": ", to use for inpainting (§ 4.2)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 597, + 452, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 452, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 452, + 609 + ], + "type": "text", + "content": "4.1.2 NeRF-based Segmentation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": "Our multiview segmentation module takes the input RGB images, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ", the corresponding camera intrinsic and extrinsic parameters, and the initial masks, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\{\\widehat{M_i}\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ", and trains a semantic NeRF [76]. Figure 2 depicts the network used in the semantic NeRF; for a point, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ", and a view direction, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ", in addition to a density, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\sigma(x)" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ", and color, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "c(x,d)" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ", it returns a pre-sigmoid \"objectness\" logit, " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "s(x)" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": ". The objectness probability is then acquired as " + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "inline_equation", + "content": "p(x) = \\text{Sigmoid}(s(x))" + }, + { + "bbox": [ + 304, + 616, + 545, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20671" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": "We use Instant-NGP [3, 37, 38] as our NeRF architecture due to its fast convergence. The expected objectness logit, " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\widehat{S}(r)" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": ", associated with a ray, " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": ", is obtained by rendering the logits of the points on " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " instead of their colors, with respect to the densities, in Eq. 1 [36]:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 94, + 139, + 287, + 171 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 139, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 94, + 139, + 287, + 171 + ], + "type": "interline_equation", + "content": "\\widehat {S} (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) s _ {i}, \\tag {3}", + "image_path": "442be788da398653c9d56a3667ae9a3e25532a4225ec2688c926a019f88c9d79.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "text", + "content": "where for simplicity, " + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "inline_equation", + "content": "s(r(t_i))" + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "text", + "content": " is denoted by " + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "inline_equation", + "content": "s_i" + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "text", + "content": ". The objectness probability of a ray, " + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "inline_equation", + "content": "\\widehat{P}(r) = \\text{Sigmoid}(\\widehat{S}(r))" + }, + { + "bbox": [ + 47, + 178, + 287, + 216 + ], + "type": "text", + "content": ", is then supervised using the classification loss:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 86, + 222, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 222, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 86, + 222, + 287, + 251 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c l f}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\operatorname {B C E} \\left(\\mathbb {1} _ {r \\in \\mathcal {R} _ {\\text {m a s k e d}}}, \\widehat {P} (r)\\right), \\tag {4}", + "image_path": "51dd18b67f117fb4c04a7b2ea50ee0775b7201f5abb8f6b9c4559f1cb47adcc7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\mathbb{1}" + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": " is the indicator function, BCE stands for the binary cross entropy loss, and " + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_{\\mathrm{masked}}" + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": " is the set of rays passing through pixels that are masked in " + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\{\\widehat{M}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": ". During the calculation of the classification loss, " + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{clf}}" + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": ", the weights of the colors in the rendering equation (Eq. 1) are detached to limit the supervised updates to the logits; this prevents changes to the existing geometry, due to gradient updates altering the " + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": " field. The geometry is supervised using a reconstruction loss, " + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 257, + 287, + 390 + ], + "type": "text", + "content": ", as in NeRF [35], via the given RGB images. The overall loss, used to supervise the NeRF-based multiview segmentation model, is then given by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 121, + 398, + 287, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 398, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 121, + 398, + 287, + 410 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {m v}} = \\mathcal {L} _ {\\mathrm {r e c}} + \\lambda_ {\\mathrm {c l f}} \\mathcal {L} _ {\\mathrm {c l f}}, \\tag {5}", + "image_path": "49df470f79347914c3125a8350b8ff1fda6d29d9b9d9b657fda02934c002be8e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "text", + "content": "where the classification weight, " + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{clf}}" + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "text", + "content": ", is a hyper-parameter. After optimization, 3D-consistent masks, " + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "inline_equation", + "content": "\\{M_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 418, + 287, + 525 + ], + "type": "text", + "content": ", are obtained by thresholding the objectness probabilities and masking the pixels with probabilities greater than 0.5. Finally, we use two stages for optimization to further improve the masks; after obtaining the initial 3D mask, the masks are rendered from the training views, and are used to supervise a secondary multiview segmentation model as initial guesses (instead of the video segmentation outputs)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 532, + 169, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 169, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 169, + 545 + ], + "type": "text", + "content": "4.2. Multiview Inpainting" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 551, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 622 + ], + "type": "text", + "content": "Figure 3 shows an overview of our view-consistent inpainting method. As the paucity of data precludes directly training a 3D inpainter, our method leverages existing 2D inpainters to obtain depth and appearance priors, which then supervise the fitting of a NeRF to the completed scene. This inpainted NeRF is trained using the following loss:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 80, + 629, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 629, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 80, + 629, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n p}} = \\mathcal {L} ^ {\\prime} _ {\\text {r e c}} + \\lambda_ {\\mathrm {L P I P S}} \\mathcal {L} _ {\\mathrm {L P I P S}} + \\lambda_ {\\text {d e p t h}} \\mathcal {L} _ {\\text {d e p t h}}, \\tag {6}", + "image_path": "e212ba3a7c2288123e8685fbd4ca411e907c0881b13633d912e0a3dc0b61387a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}^{\\prime}" + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "content": " is the reconstruction loss for the unmasked pixels, and " + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{LPIPS}}" + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{depth}}" + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "content": " define the perceptual and depth losses (see below), with weights " + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{LPIPS}}" + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{depth}}" + }, + { + "bbox": [ + 47, + 650, + 287, + 686 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 308, + 70, + 545, + 173 + ], + "blocks": [ + { + "bbox": [ + 308, + 70, + 545, + 173 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 545, + 173 + ], + "type": "image", + "image_path": "d1fc40b4d477bb3fcf73a48a77163e871d638b49e799b3f3d21aa53f03b2677d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 181, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 305, + 181, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 305, + 181, + 545, + 281 + ], + "type": "text", + "content": "Figure 3. Overview of our inpainting method. Using posed input images and their corresponding masks (upper- and lower-left insets), we obtain (i) an initial NeRF with the target object present and (ii) the set of inpainted input RGB images with the target object removed (but with view inconsistencies). The initial NeRF (i) is used to compute depth, which we inpaint to obtain depth images as geometric priors (upper-right inset). The inpainted RGB images (ii), which act as appearance priors, are used with the depth priors, to fit a 3D consistent NeRF to the inpainted scene." + }, + { + "bbox": [ + 305, + 181, + 545, + 281 + ], + "type": "inline_equation", + "content": "^1" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 301, + 389, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 389, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 389, + 312 + ], + "type": "text", + "content": "4.2.1 RGB Priors" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": "Our proposed view-consistent inpainting approach uses RGB inputs, " + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\{I_i\\}_{i=1}^n" + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": ", the camera intrinsic and extrinsic parameters, and corresponding object masks, " + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\{M_i\\}_{i=1}^n" + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": ", to fit a NeRF to the scene without the undesired object. To begin with, each image and mask pair, " + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "inline_equation", + "content": "(I_i, M_i)" + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": ", is given to an image inpainter, INP, to obtain the inpainted RGB images, " + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{I}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_i = \\mathrm{INP}(I_i, M_i)" + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": " [48]. Since each view is inpainted independently, directly supervising a NeRF using the inpainted views leads to blurry results due to the 3D inconsistencies between each " + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_i" + }, + { + "bbox": [ + 305, + 320, + 545, + 499 + ], + "type": "text", + "content": " (see Figure 7). In this paper, instead of using mean squared error (MSE) to optimize the masked area, we propose the use of a perceptual loss, LPIPS [72], to optimize the masked parts of the images, while still using MSE for the unmasked parts, where no inpainting is needed. This loss is calculated as follows:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 359, + 508, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 508, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 359, + 508, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {L P I P S}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {i \\in \\mathcal {B}} \\operatorname {L P I P S} (\\widehat {I _ {i}}, \\widetilde {I _ {i}}), \\tag {7}", + "image_path": "685e18fedd7d3da594a622a4ae39955388d6c8b897f460a1fea09cda1c40d54c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "content": " is a batch of indices between 1 and " + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "inline_equation", + "content": "\\widehat{I}_i" + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "content": "-th view rendered using NeRF. Our model for multiview inpainting and segmentation uses the same architecture (see Figure 2), except for the additional logit output, " + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 305, + 547, + 545, + 596 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 611, + 394, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 394, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 394, + 623 + ], + "type": "text", + "content": "4.2.2 Depth Priors" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": "Even with the perceptual loss, the discrepancies between the inpainted views can incorrectly guide the model towards converging to degenerate geometries (e.g., 'foggy' geometry may form near the cameras, to explain the disparate per-view information). Thus, we use inpainted depth maps as additional guidance for the NeRF model, and detach the weights when calculating the perceptual loss and use the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "IBRNet images in Fig. 3,5,6,7 by Wang et al. available in IBRNet [56] under an Apache License 2.0." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20672" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "perceptual loss to only fit the colors of the scene. For this purpose, we use a NeRF optimized on images that include the unwanted object, and render the depth maps, " + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "inline_equation", + "content": "\\{D_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": ", corresponding to the training views. Depth maps are calculated by substituting the distance to the camera instead of the color of points into Eq. 1:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 94, + 154, + 287, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 154, + 287, + 186 + ], + "spans": [ + { + "bbox": [ + 94, + 154, + 287, + 186 + ], + "type": "interline_equation", + "content": "D (r) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) t _ {i}. \\tag {8}", + "image_path": "6eb1c3de6ed64de4a76e943f075a2a44cb9ab0dc7ecd889192127d295ddd8484.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": "The rendered depths are then given to an inpainter to obtain inpainted depth maps, " + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{D}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_i" + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": " is obtained as " + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_i = \\mathrm{INP}(D_i, M_i)" + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": ". We found that using LaMa [48] for depth inpainting, as in the RGB case, gave sufficiently high-quality results. Note that this is all calculated as a preprocessing step, and with a NeRF optimized on the original scene. This NeRF can be the same model used for multiview segmentation. If using another source for obtaining masks, such as human annotated masks, a new NeRF is fitted to the scene. These depth maps are then used to supervise the inpainted NeRF's geometry, via the " + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": " distance of its rendered depths, " + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\widehat{D}_i" + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": ", to the inpainted depths, " + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_i" + }, + { + "bbox": [ + 46, + 195, + 289, + 342 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 350, + 287, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 350, + 287, + 379 + ], + "spans": [ + { + "bbox": [ + 94, + 350, + 287, + 379 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {d e p t h}} = \\frac {1}{| \\mathcal {R} |} \\sum_ {r \\in \\mathcal {R}} \\left| \\widehat {D} (r) - \\widetilde {D} (r) \\right| ^ {2}, \\tag {9}", + "image_path": "07cd5250c9a37ce3ac8fc20c5d9d63de0fdcb1e1f85f1e0184687d0205431a68.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "inline_equation", + "content": "\\widehat{D}(r)" + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "inline_equation", + "content": "\\widetilde{D}(r)" + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "text", + "content": " are the depth values for a ray, " + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 388, + 268, + 403 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 419, + 192, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 419, + 192, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 419, + 192, + 431 + ], + "type": "text", + "content": "4.2.3 Patch-based Optimization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "content": "Calculating the perceptual loss, Eq. 7, requires full input views to be rendered during the optimization. Since rendering each pixel necessitates multiple forward passes through the MLP, for high-resolution images, this is an expensive process, resulting in issues such as (i) the batch size, " + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "inline_equation", + "content": "|\\mathcal{B}|" + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "content": ", has to be small to fit the rendered images and their corresponding computation graphs in memory, and (ii) slow optimization, even with batch sizes as small as " + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "inline_equation", + "content": "|\\mathcal{B}| = 1" + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "content": ". A straightforward solution is to render a downsized image and compare it to the downsized version of the inpainted images; however, this leads to a loss of information if the downsizing factor is large. Following image-based works (e.g., SinGAN [46] and DPNN [14]), and 3D works (e.g., ARF [71]), we perform the computations on a patch-basis; instead of rendering complete views, we render batches of smaller patches, and compare them with their counterparts in the inpainted images based on the perceptual loss. Only patches inside the bounding box of the object mask are used. For fitting the unmasked areas, recall that " + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}'" + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "content": " (Eq. 6) simply alters " + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 437, + 289, + 715 + ], + "type": "text", + "content": " (Eq. 2) to sample rays only from unmasked pixels. By separating the perceptual and reconstruction losses, we prevent inconsistency within the mask, while avoiding unnecessary changes to the rest of the scene." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 387, + 159 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 387, + 159 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 387, + 159 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 387, + 159 + ], + "type": "image", + "image_path": "96fed5a9841afc84b0c07073c10646bfebab901b73afad90cb04847e99f7ef5e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 160, + 386, + 167 + ], + "lines": [ + { + "bbox": [ + 310, + 160, + 386, + 167 + ], + "spans": [ + { + "bbox": [ + 310, + 160, + 386, + 167 + ], + "type": "text", + "content": "60 Input Views + Camera Poses" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 387, + 70, + 464, + 159 + ], + "blocks": [ + { + "bbox": [ + 387, + 70, + 464, + 159 + ], + "lines": [ + { + "bbox": [ + 387, + 70, + 464, + 159 + ], + "spans": [ + { + "bbox": [ + 387, + 70, + 464, + 159 + ], + "type": "image", + "image_path": "69d07eec86b6a8ee5f1dcb1133c4a131d4ac682e405b3c208e7e7fa6152057de.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 387, + 160, + 463, + 167 + ], + "lines": [ + { + "bbox": [ + 387, + 160, + 463, + 167 + ], + "spans": [ + { + "bbox": [ + 387, + 160, + 463, + 167 + ], + "type": "text", + "content": "Human-Annotated Object Masks" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 465, + 70, + 544, + 159 + ], + "blocks": [ + { + "bbox": [ + 465, + 70, + 544, + 159 + ], + "lines": [ + { + "bbox": [ + 465, + 70, + 544, + 159 + ], + "spans": [ + { + "bbox": [ + 465, + 70, + 544, + 159 + ], + "type": "image", + "image_path": "81908990a5ff11a8ee34ccf93e07a2743312537e8c813277dfb4a610405da77d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 160, + 539, + 167 + ], + "lines": [ + { + "bbox": [ + 468, + 160, + 539, + 167 + ], + "spans": [ + { + "bbox": [ + 468, + 160, + 539, + 167 + ], + "type": "text", + "content": "40 GT Views + Camera Poses" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "lines": [ + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "spans": [ + { + "bbox": [ + 305, + 177, + 545, + 221 + ], + "type": "text", + "content": "Figure 4. Scenes from our dataset. Columns: input view (left), corresponding target object mask (middle), and a ground-truth view without the target object, from a different camera pose (right). Rows: different scenes; see supplement for examples of all scenes." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 243, + 414, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 243, + 414, + 254 + ], + "spans": [ + { + "bbox": [ + 306, + 243, + 414, + 254 + ], + "type": "text", + "content": "4.2.4 Mask Refinement" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": "Here, we consider further leveraging the multiview data to guide the image inpainter. In particular, parts of the training images that are currently being generated by the 2D image inpainter might be visible in other views; in such cases, there is no need to hallucinate those details, since they can be retrieved from the other views. To prevent such unnecessary inpaintings, we propose a mask refinement approach: for each source image, depth, and mask tuple, " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "(I_s, D_s, M_s)" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": ", we substitute pixels in " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "I_s" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "D_s" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": " that are visible from at least one other view, to shrink the source mask, " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "M_s" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": ". After this refinement step, only parts of " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "I_s" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "inline_equation", + "content": "D_s" + }, + { + "bbox": [ + 304, + 262, + 545, + 441 + ], + "type": "text", + "content": " that are occluded by the undesired object in all of the training views will remain masked. As a result, the image inpainter has to fill in a smaller area, resulting in improved inpaintings. Please see our supplementary material for details." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 453, + 388, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 453, + 388, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 453, + 388, + 467 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 641 + ], + "type": "text", + "content": "Dataset. To evaluate multiview segmentation (MVSeg), we adopt real-world scenes from LLFF [34], NeRF-360 [35], NeRF-Supervision [66], and Shiny [61]. For multiview (MV) inpainting, in addition to providing qualitative results on scenes from IBRNet [56], we address the need for a standard benchmark including ground-truth captures of scenes without the unwanted object as test views, and introduce a dataset containing 10 real-world forward-facing scenes with human annotated object masks. For each scene, we provide 60 training images with the object and 40 test images without the object. This dataset is further suitable for evaluating tasks such as real-time 3D inpainting, unsupervised 3D segmentation, and video inpainting. Figure 4 shows sample views from two scenes of our dataset." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Metrics. To evaluate our segmentation model, we use the accuracy of the predictions (pixel-wise) and the intersection over union (IoU) metric. For MV inpainting, we follow the image-to-image literature [48] and report the average learned perceptual image patch similarity (LPIPS) [72], and the average Fréchet inception distance (FID) [19] between" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20673" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 101, + 284, + 200 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation of multiview segmentation models, for the task of transferring the source mask to other views." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 101, + 284, + 200 + ], + "lines": [ + { + "bbox": [ + 50, + 101, + 284, + 200 + ], + "spans": [ + { + "bbox": [ + 50, + 101, + 284, + 200 + ], + "type": "table", + "html": "
MethodAcc.↑IoU↑
Proj. + Grab Cut [45] (2D)91.0846.61
Proj. + EdgeFlow [15] (2D)96.8481.63
Semantic NeRF [76] (only source mask)94.6375.13
Proj. + EdgeFlow [15] + Semantic NeRF [76]97.2683.95
Feature Field Distillation [26]97.3783.07
Video Segmentation [4,57]98.4388.34
Ours98.8590.96
Ours (two-stage)98.9191.66
", + "image_path": "3a1daa75ba6d30c38977c4af582eaaa3b5dee49759887d872d0c5ddc480382e9.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 220, + 287, + 279 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 279 + ], + "type": "text", + "content": "the distribution of the ground-truth test views and model outputs. Since our focus is the inpainting, we only calculate the LPIPS and FID inside the bounding box of the object mask (using our MVSeg model, we can render the object mask from the test views that do not contain the object)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 280, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 287, + 470 + ], + "type": "text", + "content": "Multiview Segmentation Baselines. For MVSeg, one category of baselines is projection-based approaches: the source mask is projected into the other views using the scene geometry from a NeRF. This gives us an incomplete mask in the other views. Then, a variety of interactive segmentation approaches are applied to the incomplete masks, propagating them to obtain complete object masks: Proj. + Grab Cut [45] and Proj. + EdgeFlow [15]. In addition, we consider Proj. + EdgeFlow + Semantic NeRF, where an additional Semantic NeRF [76] is fitted to make the outputs 3D consistent. Another baseline [26] is a representative of the concurrent works on distilling 2D pixel-level features to 3D scenes [51] and post-processing them for obtaining segmentation masks. As a baseline for video-segmentation [57], we compare to Dino [4] since it does not rely on temporally close neighboring frames." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 471, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 685 + ], + "type": "text", + "content": "Multiview Inpainting Baselines. Masked NeRF only uses the unmasked pixels to optimize a NeRF. Object NeRF [64] filters the unwanted points in 3D without explicitly inpainting the missing regions. No code is available for NeRF-In [31], so we use our own implementation of their model, with slight modifications (we use LaMa [48] as the inpainter). In addition, we compare our results to LaMa [48] as a representative of state-of-the-art 2D inpainters. To enable fair comparison between the NeRF-based 3D models (which, in addition to inpainting, have to synthesize novel views), we compare to LaMa by (i) fitting a NeRF on the views with the object" + }, + { + "bbox": [ + 46, + 471, + 287, + 685 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 471, + 287, + 685 + ], + "type": "text", + "content": ", (ii) rendering the test views from the fitted NeRF, and (iii) passing these rendered images to LaMa. Finally, for reference and as an ideal \"gold standard\" 3D inpainting baseline, we fit a NeRF on the ground-truth test images, use the optimized NeRF to render the test-views, and then compare the rendered results to the ground-truth. We provide these results for completeness, as" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 321, + 101, + 529, + 237 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 2. Quantitative evaluation of our inpainting method, using human-annotated object masks." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 101, + 529, + 237 + ], + "lines": [ + { + "bbox": [ + 321, + 101, + 529, + 237 + ], + "spans": [ + { + "bbox": [ + 321, + 101, + 529, + 237 + ], + "type": "table", + "html": "
MethodLPIPS↓FID↓
Ideal0.4079100.25
LaMa (2D) [48]0.5369174.61
Object NeRF [64]0.6829271.80
Masked NeRF [35]0.6030294.69
NeRF-In [31]0.5699238.33
NeRF-In [31] (Single)0.4884183.23
Ours (no geo. inpainting)0.4952200.34
Ours0.4654156.64
Ours (Refined RGB/Depth)0.4664163.79
Ours (Refined RGB)0.4529147.31
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Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 306, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 306, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 306, + 545, + 414 + ], + "type": "text", + "content": "Multiview Segmentation. We first evaluate our MVSeg model without any inpainting. In this experiment, we assume that the sparse image points are already given to an off-the-shelf interactive segmentation model, and that the source mask is available. Thus, the task is to transfer the source mask to other views. Table 1 shows that our model outperforms all of the 2D (3D-inconsistent) and 3D-consistent baselines. In addition, our two-stage optimization helps to further improve the obtained masks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 415, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 533 + ], + "type": "text", + "content": "Qualitatively, Figure 5 compares the results of our segmentation model with the outputs of Neural Volumetric Object Selection (NVOS) [44] and video segmentation [4, 57]. Compared to the coarse edges of the 3D-unaware video segmentation model, our model reduces noise and improves consistency across views. Although NVOS uses scribbles, rather than the sparse points used in our model, our MVSeg visually outperforms NVOS. Since the NVOS code base is not available, we reproduce the published qualitative results for NVOS [44] (see supplemental for more examples)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Multiview Inpainting. Our dataset is used for quantitative evaluation of our proposed inpainting method against the baselines. Table 2 shows the comparison of our MV inpainting method with the baselines, assuming that the object masks from all of the views are given. The \"ideal\" row is not a baseline, but rather a NeRF fitted to the ground-truth test views (views of the scene without the object). While this is only one instantiation of the many possible inpainted scenes, it provides a convenient measure of the best performance one might reasonably expect in this scenario. Overall, our method significantly outperforms the alternative 2D and 3D inpainting approaches. Although our model uses a 2D image inpainter's [48] outputs to obtain a view-consistent inpainted NeRF, it is able to use this ensemble of MV information, in addition to the priors encoded by" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": "2Since the test views that do not contain the object should not be available to the model during the inference." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20674" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 134, + 132 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 134, + 132 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 134, + 132 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 134, + 132 + ], + "type": "image", + "image_path": "44b53cf8f3bd72b7bc6277454ba08e2fd17b5ba58bc26f209c36ce64094a19a6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 135, + 70, + 216, + 133 + ], + "blocks": [ + { + "bbox": [ + 135, + 70, + 216, + 133 + ], + "lines": [ + { + "bbox": [ + 135, + 70, + 216, + 133 + ], + "spans": [ + { + "bbox": [ + 135, + 70, + 216, + 133 + ], + "type": "image", + "image_path": "9545002d4b03125c60a72c26ea5ead46ad88f52142c1df27f2ebd599c5ba6ea3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 216, + 70, + 298, + 133 + ], + "blocks": [ + { + "bbox": [ + 216, + 70, + 298, + 133 + ], + "lines": [ + { + "bbox": [ + 216, + 70, + 298, + 133 + ], + "spans": [ + { + "bbox": [ + 216, + 70, + 298, + 133 + ], + "type": "image", + "image_path": "004ec54ac2cceac7c049f0193529bc6e54d19103a7173ee63024ce93c790ca58.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 298, + 70, + 380, + 133 + ], + "blocks": [ + { + "bbox": [ + 298, + 70, + 380, + 133 + ], + "lines": [ + { + "bbox": [ + 298, + 70, + 380, + 133 + ], + "spans": [ + { + "bbox": [ + 298, + 70, + 380, + 133 + ], + "type": "image", + "image_path": "7b95d02db97acf0a334df2a462b93ca71ddd02b66fb2510ef8f72298dd8cffcf.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 380, + 70, + 460, + 133 + ], + "blocks": [ + { + "bbox": [ + 380, + 70, + 460, + 133 + ], + "lines": [ + { + "bbox": [ + 380, + 70, + 460, + 133 + ], + "spans": [ + { + "bbox": [ + 380, + 70, + 460, + 133 + ], + "type": "image", + "image_path": "16edcc29221911979934e5936b26b5e88ba270df269cea8606635c278809def1.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 460, + 70, + 543, + 133 + ], + "blocks": [ + { + "bbox": [ + 460, + 70, + 543, + 133 + ], + "lines": [ + { + "bbox": [ + 460, + 70, + 543, + 133 + ], + "spans": [ + { + "bbox": [ + 460, + 70, + 543, + 133 + ], + "type": "image", + "image_path": "4cbc90b7c3c77f27b8554ffd933923f340c3b2491b529343bd5b8bbc4e809970.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 51, + 133, + 135, + 194 + ], + "blocks": [ + { + "bbox": [ + 51, + 133, + 135, + 194 + ], + "lines": [ + { + "bbox": [ + 51, + 133, + 135, + 194 + ], + "spans": [ + { + "bbox": [ + 51, + 133, + 135, + 194 + ], + "type": "image", + "image_path": "1ee66a64e2a1f288b665bbf52100b094793455cfb1bc740ff22d38d91a54d90f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 194, + 111, + 202 + ], + "lines": [ + { + "bbox": [ + 75, + 194, + 111, + 202 + ], + "spans": [ + { + "bbox": [ + 75, + 194, + 111, + 202 + ], + "type": "text", + "content": "Input View" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 212, + 547, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 212, + 547, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 547, + 278 + ], + "type": "text", + "content": "Figure 5. A qualitative comparison of our multiview segmentation model against Neural Volumetric Object Selection (NVOS) [44] (reproduced from original paper), video segmentation [4], and the human-annotated masks (GT). Our two-stage approach refers to running our multiview segmentation model twice, with the output of the first run as the initialization of the second (see § 4.1.2). Our method is less noisy than NVOS, which also misses some pieces of the target (e.g., the lowest flower in the bottom row), but captures more details than the video segmentation alone (e.g., the blurred edges of the flowers). Our two-stage approach helps fill in some missing aspects of the one-stage output. Please see our supplement for additional qualitative examples." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 135, + 133, + 216, + 194 + ], + "blocks": [ + { + "bbox": [ + 135, + 133, + 216, + 194 + ], + "lines": [ + { + "bbox": [ + 135, + 133, + 216, + 194 + ], + "spans": [ + { + "bbox": [ + 135, + 133, + 216, + 194 + ], + "type": "image", + "image_path": "e9ecf9214f822bf0e2ec0bd5b47b39ec6e7903115e498987403b8dcd67a04a7e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 170, + 194, + 181, + 201 + ], + "lines": [ + { + "bbox": [ + 170, + 194, + 181, + 201 + ], + "spans": [ + { + "bbox": [ + 170, + 194, + 181, + 201 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 216, + 133, + 298, + 194 + ], + "blocks": [ + { + "bbox": [ + 216, + 133, + 298, + 194 + ], + "lines": [ + { + "bbox": [ + 216, + 133, + 298, + 194 + ], + "spans": [ + { + "bbox": [ + 216, + 133, + 298, + 194 + ], + "type": "image", + "image_path": "92c0f7046bb31d23a3bc7f983fcbf433e146a1d65f7ca1bfe0ec0c47e5681da1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 246, + 194, + 268, + 202 + ], + "lines": [ + { + "bbox": [ + 246, + 194, + 268, + 202 + ], + "spans": [ + { + "bbox": [ + 246, + 194, + 268, + 202 + ], + "type": "text", + "content": "NVOS" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 298, + 133, + 380, + 194 + ], + "blocks": [ + { + "bbox": [ + 298, + 133, + 380, + 194 + ], + "lines": [ + { + "bbox": [ + 298, + 133, + 380, + 194 + ], + "spans": [ + { + "bbox": [ + 298, + 133, + 380, + 194 + ], + "type": "image", + "image_path": "8428c2fd4315ee981652331d47228b77bbf066b898f2515775d84c245633cb35.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 299, + 194, + 380, + 203 + ], + "lines": [ + { + "bbox": [ + 299, + 194, + 380, + 203 + ], + "spans": [ + { + "bbox": [ + 299, + 194, + 380, + 203 + ], + "type": "text", + "content": "Video Segmentation (2D)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 380, + 133, + 460, + 194 + ], + "blocks": [ + { + "bbox": [ + 380, + 133, + 460, + 194 + ], + "lines": [ + { + "bbox": [ + 380, + 133, + 460, + 194 + ], + "spans": [ + { + "bbox": [ + 380, + 133, + 460, + 194 + ], + "type": "image", + "image_path": "c3e1c53c869a12ee1c1bbda771c30f5f541d9c42e176ee9f06817e2f43a01196.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 413, + 194, + 430, + 202 + ], + "lines": [ + { + "bbox": [ + 413, + 194, + 430, + 202 + ], + "spans": [ + { + "bbox": [ + 413, + 194, + 430, + 202 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 460, + 133, + 542, + 194 + ], + "blocks": [ + { + "bbox": [ + 460, + 133, + 542, + 194 + ], + "lines": [ + { + "bbox": [ + 460, + 133, + 542, + 194 + ], + "spans": [ + { + "bbox": [ + 460, + 133, + 542, + 194 + ], + "type": "image", + "image_path": "ef80005f9d36aaee6ddcc593a234efa812da36645b9862efba2107b3aef3e652.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 194, + 531, + 203 + ], + "lines": [ + { + "bbox": [ + 473, + 194, + 531, + 203 + ], + "spans": [ + { + "bbox": [ + 473, + 194, + 531, + 203 + ], + "type": "text", + "content": "Ours (Two-Stage)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 72, + 328, + 260, + 416 + ], + "blocks": [ + { + "bbox": [ + 47, + 298, + 288, + 321 + ], + "lines": [ + { + "bbox": [ + 47, + 298, + 288, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 298, + 288, + 321 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation of our inpainting method, using the outputs of our multiview segmentation model." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 72, + 328, + 260, + 416 + ], + "lines": [ + { + "bbox": [ + 72, + 328, + 260, + 416 + ], + "spans": [ + { + "bbox": [ + 72, + 328, + 260, + 416 + ], + "type": "table", + "html": "
MethodLPIPS↓FID↓
LaMa (2D) [48]0.5439169.92
Object NeRF [64]0.6679286.55
Masked NeRF [35]0.6340332.70
NeRF-In [31]0.5858240.27
NeRF-In [31] (Single)0.5054176.27
Ours0.4662140.56
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Input Views10204060
LPIPS↓0.47260.47130.46670.4654
FID↓171.19172.63158.02156.64
Dilation452550
LPIPS↓0.61020.53690.46540.4904
FID↓283.01230.03156.64164.66
", + "image_path": "b3447f0d67e81d0c560111e5443fc520537effd669f9420fbf12ff95e1311652.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": "mean masked area by " + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "inline_equation", + "content": "4.74\\%" + }, + { + "bbox": [ + 304, + 425, + 545, + 496 + ], + "type": "text", + "content": " on our dataset), as the camera has limited movement during data collection, to ensure similarity between the training and testing views. Further, due to noisy NeRF geometries projecting incorrect values, refining depths lowers performance, whereas refining colours alone achieves our best results." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 605 + ], + "type": "text", + "content": "So far, our experiments examine the performance of our MVSeg and MV inpainting independently; however, one can combine them to remove objects from NeRF scenes with minimal user interaction. Table 3 shows that using the output masks of our MVSeg model, instead of using the human-annotated object masks, results in a subtle decrease in the inpainting quality. However, our model with MVSegs still outperforms other methods, even when they are fitted on human-annotated segmentations." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 611, + 479, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 479, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 479, + 624 + ], + "type": "text", + "content": "5.2. Variations and Ablation Studies" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Number of Input Views. Limiting the number of input views is a standard approach employed in the literature to modulate the reconstruction quality of NeRFs [54]. Table 4 shows that the performance of our inpainter degrades with fewer inputs. Thus, we argue that as better-quality NeRFs are introduced, our approach, which is agnostic to the underlying NeRF model, can readily benefit." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20675" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 542, + 304 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 542, + 304 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 542, + 304 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 542, + 304 + ], + "type": "image", + "image_path": "8e4f0bbe17f35d00eab93a74f2443363d56da1bc53620245230b854aedf13628.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 313, + 547, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 313, + 547, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 547, + 360 + ], + "type": "text", + "content": "Figure 6. Visualizations of our view-consistent inpainting results. Upper rows per inset show NeRF renderings of the original scene from novel views, with the first image also displaying the associated mask. Lower rows show the corresponding inpainted view. Notice that the synthesized views maintain consistency with each other; however, view-dependent effects still remain (e.g., the lighting on the uncovered part of the piano). Please see our supplement for additional scenes, and our project website with videos for better visualization." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 376, + 285, + 565 + ], + "blocks": [ + { + "bbox": [ + 50, + 376, + 285, + 565 + ], + "lines": [ + { + "bbox": [ + 50, + 376, + 285, + 565 + ], + "spans": [ + { + "bbox": [ + 50, + 376, + 285, + 565 + ], + "type": "image", + "image_path": "b03e48a6b91c30330e8288251e54bdcf103f83e532d7f086403dfca44cdc5013.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 574, + 288, + 641 + ], + "lines": [ + { + "bbox": [ + 46, + 574, + 288, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 288, + 641 + ], + "type": "text", + "content": "Figure 7. Qualitative comparisons with other baselines. Columns: novel views of the scene, synthesized by a NeRF (on the unmasked images), NeRF-In, NeRF-In (with a single masked training image), and our approach. NeRF-In is significantly more blurry, while NeRF-In (single) tends to have difficulty with details closer to the edge of the mask boundary (zoom into boxes for examples)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Importance of Accurate Masks. Here, we examine the impact of accurate masks on inpainting, via variable dilations of the object masks with a " + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": " kernel. Larger masks lead to relying more on the view-inconsistent outputs and" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 379, + 545, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 463 + ], + "type": "text", + "content": "hallucinations of the 2D inpainters, while smaller masks may permit parts of the unwanted object's edges to remain and confuse the 2D inpainter. A subtle dilation is also useful for reducing the effect of shadows. This balance between over-masking and under-masking is demonstrated in Table 4, with five dilation iterations found to be optimal and therefore used for all other experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 476, + 379, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 476, + 379, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 476, + 379, + 488 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 498, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 675 + ], + "type": "text", + "content": "In this paper, we presented a novel approach to inpaint NeRF scenes, which enforces viewpoint consistency based on image and geometric priors, given a single-view object mask. In addition, we provided a multiview segmentation method that simplifies the annotation process by using a set of sparse pixel-level clicks on (and around) the undesired object and translating them into a 3D mask that can be rendered from novel views. We provided experiments to show the effectiveness of our segmentation and inpainting methods. The main limitation of our work is the assumption of semantically consistent image priors, potentially only differing in terms of textures. Finally, we introduce a dataset that not only addresses the lack of challenging benchmarks for multiview inpainting, but which we believe can assist future advances in this new line of research." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. 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Yuille Chaoyi Zhang Weidong Cai Zongwei Zhou\\*", + "bbox": [ + 238, + 179, + 730, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Sydney 2Johns Hopkins University", + "bbox": [ + 279, + 223, + 691, + 243 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "GitHub: https://github.com/tiangexiang/SQUID", + "bbox": [ + 339, + 250, + 624, + 265 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 300, + 312, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. To exploit this structured information, we propose the use of Space-aware Memory Queues for In-painting and Detecting anomalies from radiography images (abbreviated as SQUID). We show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, it can identify anomalies (unseen/modified patterns) in the image. SQUID surpasses 13 state-of-the-art methods in unsupervised anomaly detection by at least 5 points on two chest X-ray benchmark datasets measured by the Area Under the Curve (AUC). Additionally, we have created a new dataset (DigitAnatomy), which synthesizes the spatial correlation and consistent shape in chest anatomy. We hope DigitAnatomy can prompt the development, evaluation, and interpretability of anomaly detection methods.", + "bbox": [ + 75, + 333, + 473, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 621, + 209, + 636 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision tasks in photographic imaging and radiography imaging are different. For example, when identifying objects in photographic images, we assume translation invariance—a cat is a cat no matter if it appears on the left or right of the image. In radiography imaging, on the other hand, the relative location and orientation of a structure are important characteristics that allow the identification of normal anatomy and pathological conditions [20,83]. Since radiography imaging protocols assess patients in a fairly consistent orientation, the generated images have great similarity across various patients, equipment manufacturers, and facility locations (see examples in Figure 1d). The consistent and recurrent anatomy facilitates the analysis of numerous critical problems and should be considered a significant advantage for radiography imaging [85]. Several investiga", + "bbox": [ + 75, + 647, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/205d91ce4f2c6f59d8b7f416d7fac0a80d3a9a02a87b3d6daec91504dcff3f5f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 309, + 545, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2f30b215ba4cfc47e30e9009f87663287a0d59840596d6c61a9d1943628ef04e.jpg", + "image_caption": [ + "Normal", + "(a) Crowded Scenes" + ], + "image_footnote": [], + "bbox": [ + 545, + 299, + 594, + 382 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/81ccd7120ced9ef690bf3af4a31c795bc5debffb6569fdaa472d44ad779ab5e8.jpg", + "image_caption": [ + "Abnormal" + ], + "image_footnote": [], + "bbox": [ + 594, + 299, + 663, + 382 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7534d595057c1871b069fba406728c03bdf10cd7f196b012da3b1b670be58864.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 409, + 547, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c74328b1521685c56f574820832d28069ee5f2bdae9d401e0eb37801cebe753f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 547, + 409, + 594, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/645ecb157e543a92c01f82fc834009755f777baa336230ca73096505d07e6932.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 409, + 642, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/00637016774841bc7bcc50cb996faa06da59b1747a84c60730e404530ce0a919.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 642, + 409, + 689, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6606254a668178a46dcf81215df3f52cf08b54e5cc1aaad213ab87ff10bbc879.jpg", + "image_caption": [ + "(c) Digit Anatomy" + ], + "image_footnote": [], + "bbox": [ + 501, + 445, + 547, + 479 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b64d7cac19c94ec579db7e0c6cc5743fd18a6e666b82b745b6bceb3be192a428.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 547, + 445, + 594, + 479 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/40eff3f564226e1bc174a768c29c5b275130749493ebc39871a2f8df09af046b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 594, + 445, + 642, + 479 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d44ced5fd33b78f239660a6286f89f0a0450d3edca0f1f3325f6618916035db2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 642, + 445, + 691, + 479 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c87854999d7b394b8d8100cba8dc83733948e886350c07f55420168cce71b40d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 309, + 745, + 344 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f60dd840d0aa4f33c7e2e0a709e8bd1ef5b4fbae44c31de235e42d0f7437515b.jpg", + "image_caption": [ + "Normal", + "Textures" + ], + "image_footnote": [], + "bbox": [ + 745, + 299, + 792, + 382 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ea362f90c650fd05816f83b11986818801f9f9ad53c24dd62f7ebe1e9380b450.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 792, + 299, + 887, + 344 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/44ea51ec0b085119d68c3db7b4af304963858bef932a8f6337780a0e8c74bf31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 794, + 345, + 841, + 382 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dc83a0fca15980ff0808f2e92b9da92388434952f42d849bc0853e65b278cba2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 841, + 345, + 887, + 382 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/56b9d251f375913a6c003777014d24f7050b82af3d555a79cd0d146874769ce0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 745, + 406, + 794, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fe757925fc92338a2fbf7cc75220dc8762403d439d8d8d1064358902d832af41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 794, + 407, + 841, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e4ad243b2f38c30f78a908531b7dd5ffcdb93bf450fa031453dfe67fe2a025be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 841, + 407, + 888, + 444 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7b1915e5a3b28ddbf0ec2449d647272fa32b694076aae4cf8d000f2fce714166.jpg", + "image_caption": [ + "(d) Chest Anatomy", + "Figure 1. Anomaly detection in radiography images can be both easier and harder than in photographic images. It is easier because radiography images are spatially structured due to consistent imaging protocols. It is harder because anomalies in radiography images are subtle and require medical expertise to annotate." + ], + "image_footnote": [], + "bbox": [ + 794, + 445, + 841, + 483 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dfa87e794c8533597b5b8c7674fd6961bb3c88ba02ebac891b6805470ec1a315.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 841, + 445, + 888, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions have demonstrated the value of this prior knowledge in enhancing Deep Nets' performance by adding location features, modifying objective functions, and constraining coordinates relative to landmarks in images [3,47,49,69,86]. Our work seeks to answer this critical question: Can we exploit consistent anatomical patterns and their spatial information to strengthen Deep Nets' detection of anomalies from radiography images without manual annotation?", + "bbox": [ + 496, + 609, + 890, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unsupervised anomaly detection only uses healthy images for model training and requires no other annotations such as disease diagnosis or localization [5]. As many as $80\\%$ of clinical errors occur when the radiologist misses the abnormality in the first place [7]. The impact of anomaly detection is to reduce that $80\\%$ by clearly pointing out to radiologists that there exists a suspicious lesion and then having them look at the scan in depth. Unlike previous anomaly detection methods, we formulate the task as an in-painting task to exploit the anatomical consistency in appearance, position, and layout across radiography images. Specif", + "bbox": [ + 496, + 734, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Zongwei Zhou (zzhou82@jh.edu)", + "bbox": [ + 94, + 886, + 405, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23890", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ically, we propose _Space-aware Memory Queues for Inpainting and Detecting anomalies from radiography images (abbreviated as _SQUID). During training, our model can dynamically maintain a visual pattern dictionary by taxonomizing recurrent anatomical patterns based on their spatial locations. Due to the consistency in anatomy, the same body region across healthy images is expected to express similar visual patterns, which makes the total number of unique patterns manageable. During inference, since anomaly patterns do not exist in the dictionary, the generated radiography image is expected to be unrealistic if an anomaly is present. As a result, the model can identify the anomaly by discriminating the quality of the in-painting task. The success of anomaly detection has two basic assumptions [89]: first, anomalies only occur rarely in the data; second, anomalies differ from the normal patterns significantly.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We have conducted experiments on two large-scale, publicly available radiography imaging datasets. Our SQUID is significantly superior to predominant methods in unsupervised anomaly detection by over 5 points on the ZhangLab dataset [32]; remarkably, we have demonstrated a 10-point improvement over 13 recent unsupervised anomaly detection methods on the Stanford CheXpert dataset [29]. In addition, we have created a new dataset (DigitAnatomy) to elucidate spatial correlation and consistent shape of the chest anatomy in radiography (see Figure 1c). DigitAnatomy is dedicated to easing the development, evaluation, and interpretability of anomaly detection methods. The qualitative visualization clearly shows the superiority of our SQUID over the current state-of-the-art methods.", + "bbox": [ + 75, + 333, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions include: (I) the best performing unsupervised anomaly detection method for chest radiography imaging; (II) a synthetic dataset to promote anomaly detection research; (III) SQUID overcomes limitations in dominant unsupervised anomaly detection methods [1, 17, 35, 61, 82] by inventing Space-aware Memory Queue (§3.2), and Feature-level In-painting (§3.3).", + "bbox": [ + 75, + 544, + 472, + 650 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 660, + 218, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Anomaly detection in natural imaging. Anomaly detection is the task of identifying rare events that deviate from the distribution of normal data [52]. Early attempts include one-class SVM [64], dictionary learning [81], and sparse coding [11]. Due to the lack of sufficient samples of anomalies, later works typically formulate anomaly detection as an unsupervised learning problem [13, 26, 27, 37, 38, 42, 57, 67, 90]. These can be roughly categorized into reconstruction-based and density-based methods. Reconstruction-based methods train a model (e.g. Auto-Encoder) to recover the original inputs [9, 66, 71, 77, 87, 88] and identify anomalies by analyzing reconstruction errors. Density-based methods predict anomalies by estimating the normal data distribution (e.g. via VAEs [35] or GANs [2, 61, 62]). However,", + "bbox": [ + 75, + 688, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the learned distribution for normal images by these methods cannot explain the possible abnormalities. In this paper, we address these limitations by maintaining a visual pattern memory from homogeneous medical images. Several other previous works investigated the use of image inpainting for anomaly detection, i.e. parts of the input image are masked out, and the model is trained to recover the missing parts in a self-supervised way [22, 40, 51, 56, 79]. There are also plenty of works on detecting anomalies in video sequences [15, 45, 46]. Bergmann et al. [6] and Salehi et al. [59] proposed similar student-teacher networks, whereas our method utilizes such a structure to distillate input-aware features only, and the teacher network is completely disabled during inference.", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Anomaly detection in medical imaging. Anomaly detection in the medical domain is usually approached on a per-pathology basis. Supervised learning based methods [5, 44, 63] are commonly adopted to detect specific types of abnormalities, such as lesions [91], pathologies [33], tumors [4], and nodules [84]. Recent unsupervised methods have been proposed to detect anomalies in general [5, 25, 66]. With the help of GANs, anomaly detection can be achieved with weak annotations. In AnoGAN [62], the discriminator was heavily over-fitted to the normal image distribution to detect the anomaly. Subsequently, f-AnoGAN [61] was proposed to improve computational efficiency. Marimont et al. [50] designed an auto-decoder network to fit the distribution of normal images. The spatial coordinates and anomaly probabilities are mapped over a proxy for different tissue types. Han et al. [21] proposed a two-step GAN-based framework for detecting anomalies in MRI slices as well. However, their method relies on a voxel-wise representation for the 3D MRI sequences, which is impossible in our task. Most recently, a hybrid framework SALAD [82] was proposed that combines GAN with self-supervised techniques. Normal images are first augmented to carry the forged anomaly through pixel corruption and pixel shuffling. The fake abnormal images, along with the original normal ones, are fed to the GAN for learning more robust feature representations. However, these approaches demand strong prior knowledge and assumptions about the anomaly type to make the augmentation effective. Differing from photographic images, radiography imaging protocols produce images with consistent anatomical patterns, which are much more challenging to detect due to subtle imaging clues and overlapping anatomic structures (Figure 1). Unlike most existing works, we present a novel method that explicitly harnesses the radiography images' properties, dramatically improving the performance in anomaly detection from radiography images.", + "bbox": [ + 496, + 306, + 893, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Memory networks. Incorporating memory modules into neural networks has been demonstrated to be effective for many tasks [8, 16, 31, 36, 39]. Adopting Memory Matrix", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23891", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/90fa828be64669b491d7387f8a1304a0890d7e91f8a5071590df1889b5f40d3c.jpg", + "image_caption": [ + "Figure 2. SQUID. We divide an input image into $N \\times N$ non-overlapping patches and feed them into the encoder for feature extraction. Two generators will be trained to reconstruct the original image. Along with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically via a novel Memory Queue (§3.2); The teacher generator directly uses the features extracted by the encoder; the student generator uses the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm. We employ a discriminator to assess whether the image reconstructed by the student generator is real or fake. Once trained, it can also be used to detect anomalies in test images (§3.4)." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 893, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "for unsupervised anomaly detection was first proposed in MemAE [17]. In addition to auto-encoding (AE), an extra Memory Matrix was introduced between the encoder and the decoder to capture normal feature patterns during training. The matrix is jointly optimized along with the AE and hence learns an essential basis to be able to assemble normal patterns. Based on this paradigm, Park et al. [53] introduced a non-learnable memory module that can be updated with inputs. Note that although our proposed Memory Queue also does not require any gradients, our method differs significantly in its usage purpose and updating rules. Considering the extra memory usage in existing methods, Lv et al. [48] proposed a dynamic prototype unit that encodes normal dynamics on the fly, while consuming little additional memory. In this paper, we overcome the limitations of the Memory Matrix and propose an effective yet efficient Memory Queue for unsupervised anomaly detection in radiography images.", + "bbox": [ + 75, + 434, + 472, + 708 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. SQUID", + "text_level": 1, + "bbox": [ + 76, + 722, + 171, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview (Figure 2)", + "text_level": 1, + "bbox": [ + 76, + 750, + 267, + 766 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Feature extraction. We divide the input image into $N \\times N$ non-overlapping patches and feed them into an encoder for feature extraction. The extracted features will be used for image reconstruction. Practically, the encoder can be any backbone architectures [14,70]; we adopt basic Convolutions and Pooling layers in this work for simplicity.", + "(2) Image reconstruction. We introduce teacher and student generators to reconstruct the original image. Along" + ], + "bbox": [ + 76, + 773, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically as a Memory Queue (§3.2). Specifically, the teacher generator directly reconstructs the image using the features extracted by the encoder (essentially an auto-encoder [58]). The student generator, on the other hand, using the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm [28] at all of the up-sampling levels. The objective of the student generator is to reconstruct a normal image from the augmented features, which will then be used for anomaly discrimination (§3.4); while the teacher generator serves as a regularizer that prevents the student from constantly generating the same normal image.", + "bbox": [ + 496, + 434, + 893, + 647 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(3) Anomaly discrimination. Following the adversarial learning [61, 62], we employ a discriminator to assess whether the generated image is real or fake. Only the student generator will receive the gradient derived from the discriminator. The two generators and the discriminator are competing against each other until they converge to an equilibrium. Once trained, the discriminator can be used to detect anomalies in test images (§3.4).", + "bbox": [ + 496, + 648, + 893, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Inventing Memory Queue as Dictionary", + "text_level": 1, + "bbox": [ + 498, + 781, + 841, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivation. The Memory Matrix was introduced by Gong et al. [17] and has since been widely adopted in unsupervised anomaly detection [18, 45, 78]. To forge a \"normal\" appearance, features are augmented by weighted averaging", + "bbox": [ + 496, + 804, + 893, + 867 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1We disabled the backpropagation between the teacher and encoder by stop-gradient [23] and showed its empirical benefit in Table 2.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23892", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7a80bc98057cd58a0942a47bc621b2eae3f0333c7f1a2bea0860882901b45111.jpg", + "image_caption": [ + "Memory Matrix", + "Similarity" + ], + "image_footnote": [], + "bbox": [ + 78, + 104, + 261, + 165 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/696e901fdc12e3aa14de9ac7abb83daca7daa1866b4adf1d9f2f0462864d6b77.jpg", + "image_caption": [ + "Space-aware Memory", + "Figure 3. Space-aware memory. For unique encoding of location information, we restrict each patch to be only accessible by a non-overlapping region in the memory." + ], + "image_footnote": [], + "bbox": [ + 281, + 104, + 483, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the similar patterns in Memory Matrix. This augmentation is, however, applied to the features extracted from the whole image, discarding the spatial information in images. Therefore, the Memory Matrix in its current form cannot perceive the anatomical consistency as in radiography images.", + "bbox": [ + 75, + 244, + 468, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Space-aware memory. To harness the spatial information, we pass the divided small patches, instead of the whole image, into the model. These patches are associated with unique location identifiers of the original image. We seek to build the relationship between the patch location and memory region, by restricting the search space in Memory Matrix to the patch-corresponded non-overlapping segments only. That is, a patch at a particular location can only access a corresponding segment in the whole Memory Matrix (illustrated in Figure 3). We refer to this new strategy as \"space-aware memory\" because it enables explicit encoding of the spatial information into Memory Matrix. Space-aware memory can also accelerate the augmentation speed compared with [17] as it no longer goes through the entire Memory Matrix to assemble similar features.", + "bbox": [ + 75, + 321, + 468, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Memory queue. In learning-based Memory Matrix [17], \"normal patterns\" are forged by combining learned basis in the matrix. However, there is always a distribution discrepancy between the basic combinations and the actual image features. This disparity makes it hard for the subsequent image generation. To address this issue, we propose a Memory Queue to store real image features during model training, therefore presenting an identical distribution to the image features. Specifically, it directly copies previously seen features into a queue structure during training2. Once trained, Memory Queue can be used as a dictionary of normal anatomical patterns. In Figure 4, we show t-SNE visualizations to validate that the learned basis in Memory Matrix (blue dots) distributes differently from the actual image features of the training set (gray dots). In contrast, the stored image features in our Memory Queue (red dots) are", + "bbox": [ + 75, + 551, + 468, + 794 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c7c791b1ffeb49a78dbfe5fabb08a0d44a03edce9edf7a08bcc4e12fd03e455d.jpg", + "image_caption": [ + "Figure 4. t-SNE visualizations of patterns in Memory Matrix, Memory Queue, and patch features of the training samples [73]. Patterns in the Memory Matrix are far away from the distribution of patch features, while patterns in the Memory Queue (as copies of previously seen features) share a similar distribution." + ], + "image_footnote": [], + "bbox": [ + 500, + 85, + 893, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "in an identical distribution to the actual ones.", + "bbox": [ + 498, + 292, + 797, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gumbel shrinkage. Controlling the number of activated patterns in the memory has proven to be advantageous for anomaly detection [17, 19]. However, setting a hard shrinkage threshold fails to adapt to cases where no suitable entries can be found in the memory. One natural workaround is to activate the top- $k$ similar patterns in the memory. However, this strategy restricts the gradient flow to only the top- $k$ memory entries, while the rest inactivated ones could not receive any gradients and be updated as expected. To extend gradients to all patterns in the memory, inspired by Jang [30], we present a Gumbel Shrinkage schema:", + "bbox": [ + 496, + 310, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} ^ {\\prime} = \\operatorname {s g} (\\operatorname {h s} (\\mathbf {w}, \\operatorname {t o p k} (\\mathbf {w})) - \\phi (\\mathbf {w})) + \\phi (\\mathbf {w}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 489, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{w}$ denotes the similarity between the image features and entries in Memory, $sg(\\cdot)$ the stop-gradient operation, $\\mathrm{hs}(\\cdot ,t)$ the hard shrinkage operator with threshold $t$ , and $\\phi (\\cdot)$ the Softmax function. In the forward pass, Gumbel Shrinkage ensures the combination of the top- $k$ most similar entries in the memory; During the back-propagation, Gumbel Shrinkage essentially functions as Softmax. We apply Gumbel Shrinkage to both Memory Queue and Memory Matrix in our framework.", + "bbox": [ + 496, + 520, + 892, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Formulating Anomaly Detection as In-painting", + "text_level": 1, + "bbox": [ + 498, + 665, + 890, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivation. Image in-painting [41, 54] was initially proposed to recover corrupted image regions with neighboring context. Following the above intuition, we propose to achieve anomaly detection via in-painting anomalous radiography patterns into healthy ones. When in-painting pixels in the image space, recovered regions have been usually seen to associate with boundary artifacts, particularly when using Deep Nets [43]. These undesired artifacts are responsible for numerous false positives when formulating anomaly detection as a pixel-level in-painting task [66, 87]. To alleviate this issue, we achieve the in-painting task at the feature level instead. Latent features are better invariant to pixel-level noise, rotation, and translation, therefore are more suitable for subsequent anomaly detection.", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "In practice, copying features into the queue at every training iteration demands considerable computational time. Supposing $N$ patterns in the queue and $M$ training iterations, the sampling strategy in [17] demands an $\\mathcal{O}(NM)$ time complexity. We implement it more efficiently: at each iteration, the current batch of features will be copied into the queue for only once (Figure 5c), yielding a linear complexity of $\\mathcal{O}(M + cM)$ with the copy-and-paste operation in a constant time $c$ . We follow the first-in-first-out (FIFO) paradigm to update the queue continuously.", + "bbox": [ + 75, + 803, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23893", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2ca2e402bfb3f8c9a3c7cf7523307b4490abcb7e84887935739b7e8f3355cc46.jpg", + "image_caption": [ + "(a) Augment $\\mathcal{F}$ to $\\mathcal{N}$" + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 321, + 195 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/70f20ab0d6930d05ba9a2a31bb5c6a32e560d47f3da42e914af31c43ca45e6b0.jpg", + "image_caption": [ + "(b) Aggregate $\\mathcal{F}$ and $\\mathcal{N}$" + ], + "image_footnote": [], + "bbox": [ + 375, + 128, + 647, + 195 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3e3a5cb10861939d12f19c15632d2581ba234cfcdd8ba6365acf13502ee1b7ea.jpg", + "image_caption": [ + "(c) Copy $\\mathcal{F}$ to Memory Queue", + "Figure 5. Three-step workflow of our in-painting block. (a) Each non-overlapping patch feature $\\mathcal{F}$ is queried to a unique region in Memory Queue, and the most similar items are assembled to $\\mathcal{N}$ . (b) Each center patch feature $\\mathcal{F}$ and its eight neighbors $\\mathcal{N}$ are used as query and key/value, respectively, to a Transformer layer for in-painting. (c) Each Memory Queue region copies its corresponding patch features $\\mathcal{F}$ into the memory by maintaining a pointer. Note that this step is only performed during training." + ], + "image_footnote": [], + "bbox": [ + 702, + 85, + 888, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In-painting block. We integrate our Memory Queue inside a novel in-painting block to perform feature-space in-painting. The block starts with a Memory Queue that augments $w \\times h$ non-overlapping patch features $\\mathcal{F}_{\\{(1,1), \\dots, (w,h)\\}}$ into their most similar \"normal\" patterns $\\mathcal{N}_{\\{(1,1), \\dots, (w,h)\\}}$ (Figure 5a). Since $\\mathcal{N}$ is assembled by features extracted from previous training data, $\\mathcal{N}$ is not subject to the current input image. To recap the characteristics of the input image, we aggregate both patch features $\\mathcal{F}$ and their augmented features $\\mathcal{N}$ using a transformer block [74]. In details, for each patch $\\mathcal{F}_{i,j}$ , its spatially adjacent eight augmented ones $\\mathcal{N}_{\\{(i-1,j-1), \\dots, (i+1,j+1)\\}}$ are used as conditions to refine $\\mathcal{F}_{i,j}$ (Figure 5b). The query token of the transformer block is flattened $\\mathcal{F}_{(i,j)} \\in \\mathcal{R}^{1 \\times *}$ and key/value tokens are $\\mathcal{N}_{\\{(i-1,j-1), \\dots, (i+1,j+1)\\}} \\in \\mathcal{R}^{8 \\times *}$ . At the start and the end of our in-painting block, we apply an extra pair of point-wise convolutions $(1 \\times 1$ convolutional kernel) [24].", + "bbox": [ + 75, + 309, + 472, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Masked shortcut. We employ a shortcut within the inpainting block to better aggregate features and ease optimization. Our empirical study shows that a direct residual connection downgrades the effectiveness of the in-painting block (Appendix B). Inspired by Xiang et al. [76], we utilize a random binary mask to gate shortcut features during training (Figure 5b). As such, given the input patch features $\\mathcal{F}$ , the output of the in-painting block is obtained by:", + "bbox": [ + 75, + 570, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} ^ {\\prime} = (1 - \\delta) \\cdot \\mathcal {F} + \\delta \\cdot \\text {i n p a i n t} (\\mathcal {F}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 702, + 468, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{inpaint}(\\cdot)$ is the designed in-painting block, $\\delta \\sim$ Bernoulli $(\\rho)$ is a binary variable with $\\rho$ the gating probability. After obtaining $\\mathcal{F}'$ at each training step, the originally $\\mathcal{F}$ are then copied to update the memory (Figure 5c). During inference, we disable the shortcut completely such that $\\mathcal{F}' = \\mathrm{inpaint}(\\mathcal{F})$ for deterministic predictions.", + "bbox": [ + 76, + 731, + 468, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Anomaly Discrimination", + "text_level": 1, + "bbox": [ + 76, + 832, + 303, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our discriminator can detect anomalies by assessing the quality of the reconstructions—normal if realistic; abnormal otherwise. It is because the generator was trained on", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "normal images, so Memory Queues only store normal patterns. During inference, since abnormal patterns were never present in Memory Queues, the reconstructed image is expected to appear unrealistic.", + "bbox": [ + 496, + 309, + 890, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our in-painting block focuses on augmenting any patch feature (either normal or abnormal) into similar \"normal\" features. The student generator then reconstructs a \"normal\" image based on the \"normal\" features. The teacher generator is used to prevent the student from generating the same image regardless of inputs. Once trained, the semantic (rather than pixel-level) difference between the input and the student generator's reconstructed image is expected to be small if normal and big otherwise. We, therefore, delegate the optimized discriminator network for alerting anomalies perceptually. For better clarification, we note the encoder, teacher generator, student generator, and discriminator as $\\mathbf{E}$ , $\\mathbf{G}_{\\mathrm{t}}$ , $\\mathbf{G}_{\\mathrm{s}}$ , and $\\mathbf{D}$ . An anomaly score $A$ can be computed through: $A = \\phi \\left( \\frac{\\mathbf{D}(\\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I})) - \\mu}{\\sigma} \\right)$ , where $\\phi (\\cdot)$ is the Sigmoid function, $\\mu$ and $\\sigma$ are the mean and standard deviation of anomaly scores calculated on training samples.", + "bbox": [ + 496, + 372, + 892, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 632, + 643, + 646 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SQUID is optimized by five loss functions. The mean square error (MSE) between input and reconstructed images is used for both teacher and student generators. Concretely, $\\mathcal{L}_{\\mathrm{t}} = (\\mathbf{I} - \\mathbf{G}_{\\mathrm{t}}(\\mathbf{E}(\\mathbf{I}))^{2}$ and $\\mathcal{L}_{\\mathrm{s}} = (\\mathbf{I} - \\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I})))^{2}$ for the teacher and student generators, respectively, where $\\mathbf{I}$ denotes the input image. Following the knowledge distillation paradigm, we apply a distance constraint between the teacher and student generators to all levels of features: $\\mathcal{L}_{\\mathrm{dist}} = \\sum_{i=1}^{l} (\\mathcal{F}_{\\mathrm{t}}^{i} - \\mathcal{F}_{\\mathrm{s}}^{i})^{2}$ , where $l$ is the level of features used for knowledge distillation, $\\mathcal{F}_{\\mathrm{t}}$ and $\\mathcal{F}_{\\mathrm{s}}$ are the intermediate features in the teacher and student generators, respectively. In addition, we employ an adversarial loss (similar to DCGAN [55]) to improve the quality of the image generated by the student generator. Specifically, the following equation is minimized: $\\mathcal{L}_{\\mathrm{gen}} = \\log(1 - \\mathbf{D}(\\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I}))))$ . The discriminator seeks to maximize the average of the proba", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23894", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ab12043032b7c0df511708b290d28466efd4de2775e427cce995851b9ac9e3ee.jpg", + "image_caption": [ + "Input SQUID f-AnoGAN Ganomly MemAE", + "Figure 6. Reconstruction results on DigitAnatomy. Our feature-level in-painting is more robust to amplified noise and pixel variance than the existing pixel-level in-painting methods. More visualization can be found in Appendix D." + ], + "image_footnote": [], + "bbox": [ + 83, + 97, + 468, + 337 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "bility for real images and the inverted probability for fake images: $\\mathcal{L}_{\\mathrm{dis}} = \\log (\\mathbf{D}(\\mathbf{I})) + \\log (1 - \\mathbf{D}(\\mathbf{G}_s(\\mathbf{E}(\\mathbf{I}))))$ . In summary, SQUID is trained to minimize the generative loss terms $(\\lambda_{\\mathrm{t}}\\mathcal{L}_{\\mathrm{t}} + \\lambda_{\\mathrm{s}}\\mathcal{L}_{\\mathrm{s}} + \\lambda_{\\mathrm{dist}}\\mathcal{L}_{\\mathrm{dist}} + \\lambda_{\\mathrm{gen}}\\mathcal{L}_{\\mathrm{gen}})$ and to maximize the discriminative loss term $(\\lambda_{\\mathrm{dis}}\\mathcal{L}_{\\mathrm{dis}})$", + "bbox": [ + 75, + 429, + 468, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 518, + 209, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. New Benchmark", + "text_level": 1, + "bbox": [ + 76, + 542, + 241, + 558 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DigitAnatomy. We have created a synthetic dataset to verify our main idea, wherein the human anatomy is translated into Arabic digits one to nine in an in-grid placement (see examples in Figure 1 and Figure 6). The images containing digits in the correct order are considered \"normal\"; otherwise, they are considered \"abnormal\". The types of simulated abnormalities include missing, misordered, flipped, and zero digit(s). DigitAnatomy is particularly advantageous for radiography imaging for three reasons. First, it simulates two unique properties of radiography images, i.e. spatial correlation and consistent shape. Second, annotating radiography images demands specialized expertise, but digits are easier for problem debugging. Third, the ground truth of the simulated anomaly is readily accessible in DigitAnatomy, whereas it is hard to collect sufficient examples for each abnormal type in radiography images. The pseudocode for creating DigitAnatomy is in Appendix C.", + "bbox": [ + 75, + 566, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Public Benchmarks", + "text_level": 1, + "bbox": [ + 76, + 832, + 264, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ZhangLab Chest X-ray [32]. This dataset contains healthy and pneumonia (as anomaly) images, officially split into training and testing sets. The training set consists of 1,349", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/be63930eb63c33fe497a8a3d3293c78b869b9605dd1b1b66c28143fe70217e14.jpg", + "table_caption": [ + "Table 1. Benchmark results on the test sets of the two datasets." + ], + "table_footnote": [], + "table_body": "
ZhangLabRef & YearAUC (%)Acc (%)F1 (%)
Auto-Encoder-59.963.477.2
VAE [35]Arxiv'1361.864.077.4
Ganomaly [1]ACCV'1878.070.079.0
f-AnoGAN [61]MIA'1975.574.081.0
MemAE [17]ICCV'1977.8±1.456.5±1.182.6±0.9
MNAD [53]CVPR'2077.3±0.973.6±0.779.3±1.1
SALAD [82]TMI'2182.7±0.875.9±0.982.1±0.3
CutPaste [40]CVPR'2173.6±3.964.0±6.572.3±8.9
PANDA [56]CVPR'2165.7±1.365.4±1.966.3±1.2
M-KD [59]CVPR'2174.1±2.669.1±0.262.3±8.4
IF 2D [50]MICCAI'2181.0±2.876.4±0.282.2±2.7
PaDiM [12]ICPR'2171.4±3.472.9±2.480.7±1.2
IGD [10]AAAI'2273.4±1.974.0±2.280.9±1.3
SQUID-87.6±1.580.3±1.384.7±0.8
CheXpertRef & YearAUC (%)Acc (%)F1 (%)
Ganomaly [1]ACCV'1868.9±1.465.7±0.265.1±1.9
f-AnoGAN [61]MIA'1965.8±3.363.7±1.859.4±3.8
MemAE [17]ICCV'1954.3±4.055.6±1.453.3±7.0
CutPaste [40]CVPR'2165.5±2.262.7±2.060.3±4.6
PANDA [56]CVPR'2168.6±0.966.4±2.865.3±1.5
M-KD [59]CVPR'2169.8±1.666.0±2.563.6±5.7
SQUID-78.1±5.171.9±3.875.9±5.7
", + "bbox": [ + 503, + 113, + 890, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "normal and 3,883 abnormal images; the testing set has 234 normal and 390 abnormal images. We randomly separate 200 images (100 normal and 100 abnormal) from the training set as the validation set for hyper-parameter tuning. We resized all the images to $128 \\times 128$ .", + "bbox": [ + 496, + 388, + 890, + 463 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stanford CheXpert [29]. We conducted evaluations on the front-view PA images in the CheXpert dataset, which account for a total of 12 different anomalies. In all front-view PA images, there are 5,249 normal and 23,671 abnormal images for training; 250 normal and 250 abnormal images (with at least 10 images per disease type) from the training set were used for testing. We used the same hyperparameters found in the ZhangLab experiments.", + "bbox": [ + 496, + 468, + 890, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Baselines and Metrics", + "text_level": 1, + "bbox": [ + 500, + 599, + 705, + 614 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We considered a total number of 13 major baselines for direct comparison: Auto-Encoder, VAE [35]—the classic UAD methods; Ganomaly [1], f-AnoGAN [61], IF [50], SALAD [82]—the current state of the arts for medical imaging; and MemAE [17], CutPaste [40], M-KD [60], PANDA [56], PaDiM [12], IGD [10]—the most recent UAD methods. We evaluated performance using standard metrics: Receiver Operating Characteristic (ROC) curve, Area Under the ROC Curve (AUC), Accuracy (Acc), and F1-score (F1). Unless explicitly specified, we trained all models from scratch for at least three times independently.", + "bbox": [ + 496, + 623, + 890, + 790 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 800, + 717, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We utilized common data augmentation strategies such as random translation within the $[-0.05, + 0.05]$ range and a random scaling of [0.95, 1.05]. The Adam [34] optimizer was used with a batch size of 16 and a weight decay of $1e-5$ . The learning rate was initially set to $1e-4$ for both the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23895", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ad0e095a5b4e480aed8e5529570a545981c947c81a0bfc8cb54dbeb8cf22bc8b.jpg", + "image_caption": [ + "(a) ZhangLab Chest X-ray" + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 272, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a2f96c851ff4585b54ca76f11e5e1f16a15ba1ff48f1d68a1aca71a544c7a464.jpg", + "image_caption": [ + "(b) Stanford CheXpert", + "Figure 7. ROC curves comparison on the two datasets." + ], + "image_footnote": [], + "bbox": [ + 272, + 87, + 467, + 243 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "generator and the discriminator and then decayed to $2e - 5$ in 1000 epochs following the cosine annealing scheduler. The discriminator is trained at every iteration, while the generator is trained every two iterations. We set loss weights as $\\lambda_{\\mathrm{t}} = 0.01$ , $\\lambda_{\\mathrm{s}} = 10$ , $\\lambda_{\\mathrm{dist}} = 0.001$ , $\\lambda_{\\mathrm{gen}} = 0.005$ , and $\\lambda_{\\mathrm{dis}} = 0.005$ . We divide the input images in $2\\times 2$ non-overlapping patches, fix the shortcut mask probability at $\\rho = 95\\%$ , and activate only the top 5 similar patterns in the Gumbel Shrinkage. The impact of these hyper-parameters is studied in §5.3. The architectures of our generators and discriminator are detailed in Appendix A.", + "bbox": [ + 75, + 308, + 472, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 489, + 163, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Interpreting SQUID on DigitAnatomy", + "text_level": 1, + "bbox": [ + 76, + 513, + 397, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 6 presents qualitative results on DigitAnatomy to examine the capability of image reconstruction and to interpret the mistakes made by existing methods [1, 17, 61]. We deliberately inject anomalies (e.g. novel, misordered, missing digits) into normal images (highlighted in light blue) and test if the model can reconstruct their normal counterparts. To raise the task difficulty, we also assess the reconstruction quality from a blank image (as an extreme case). In general, the images reconstructed by our SQUID carry more meaningful and indicative information than other baseline methods. It is mainly attributed to our space-aware memory, with which the resulting dictionary is associated with unique patterns as well as their spatial information. Once an anomaly arises (e.g. missing digit), the in-painting block will augment the abnormal feature to its normal counterpart by assembling top- $k$ most similar patterns from the dictionary. Other methods, however, do not possess this ability, so they reconstruct defective images. For instance, GAN-based methods (f-AnoGAN and Ganomly) tend to reconstruct an exemplar image averaged from the training examples. MemAE performs relatively better due to its Memory Matrix, but it does not work well for the anomaly of missing digits and completely fails on the extreme anomaly attack.", + "bbox": [ + 75, + 537, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3bb0486a2fa9b461c57ac7498adda6a57df77c832e6bef77f07b07d855d11b10.jpg", + "image_caption": [ + "Figure 8. Reconstruction results of SQUID on the two datasets, associated with the corresponding anomaly scores (defined in §3.4). A larger score indicates a higher probability of being abnormal. More visualization can be found in Appendix D." + ], + "image_footnote": [], + "bbox": [ + 500, + 85, + 718, + 199 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce8e6af5e3ef78038d1ceddf6d7bb2172985d84a278bb9a1e72f0bb842535c4c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 725, + 85, + 893, + 199 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Benchmarking SQUID on Chest Radiography", + "text_level": 1, + "bbox": [ + 498, + 291, + 883, + 308 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our SQUID was mainly evaluated on two large-scale benchmarks: ZhangLab Chest X-ray and Stanford CheXpert and compared with a wide range of state-of-the-art counterparts. According to Table 1, SQUID achieves the most promising result on all metrics for both datasets. Specifically, SQUID outperforms the runner-up counterparts by at least $5\\%$ in AUC, $5\\%$ in Accuracy. The highest F1 scores SQUID achieved, along with the ROC curves shown in Figure 7, demonstrate that our method yields the best trade-off between sensitivity and specificity. Overall, the significant improvements observed with SQUID proved the effectiveness of our proposed techniques in this work. In Figure 8, we visualize the reconstruction results of SQUID on exemplary normal and abnormal images in the two datasets. For normal cases, SQUID can easily find a similar match in Memory Queue, achieving the reconstruction smoothly. For abnormal cases, the contradiction will arise by imposing forged normal patterns into the abnormal features. In this way, the generated images will vary significantly from the input, which will then be captured by the discriminator. We plot the heatmap of the discriminator (using Grad-CAM [65]) to indicate the most likely regions to appear anomalous. As a result, the reconstructed healthy images yield much lower anomaly scores than the diseased ones, validating the effectiveness of SQUID.", + "bbox": [ + 496, + 316, + 892, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Limitation. We found SQUID in its current form, is not able to localize anomalies at the pixel level precisely. It is understandable because our SQUID is an unsupervised method, requiring zero manual annotation for normal/abnormal images, unlike [60, 68, 72, 75, 80]. Those methods that compute pixel-level residuals for anomaly detection suffer from amplified noise in the input and reconstructed output. Our in-painting strategy, however, is performed at the feature level and is more robust to pixel-level variance.", + "bbox": [ + 496, + 698, + 893, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablating Key Properties in SQUID", + "text_level": 1, + "bbox": [ + 498, + 845, + 799, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Component study. We examine the impact of components in SQUID by taking each one of them out of the entire", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23896", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b9afb66b5ced512b2cb419284b5590b2df105ba24b03cc8129d50a0850e9bcf6.jpg", + "table_caption": [ + "Table 2. Performance benefits from all the components in SQUID." + ], + "table_footnote": [], + "table_body": "
MethodAUC (%)Acc (%)F1 (%)
w/o Space-aware Memory77.6±0.575.5±0.582.5±0.6
w/o In-painting Block80.9±2.175.8±1.581.6±1.3
w/o Gumbel Shrinkage81.1±0.977.6±0.981.3±0.8
w/o Knowledge Distillation81.2±0.875.2±0.781.3±0.8
w/o Stop Gradient81.7±4.376.7±2.882.5±1.6
w/o Memory Queue82.5±1.178.6±0.981.7±1.1
w/o Masked Shortcuts82.5±1.376.4±0.882.3±1.1
w/o Decoder Memory82.9±1.277.4±1.181.2±0.5
Full SQUID87.6±1.580.3±1.384.7±0.8
", + "bbox": [ + 76, + 112, + 467, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/37f5c8885ba1eb2a0012385273bc7d51195e38ead1473d3cc5002fb8e2148c2e.jpg", + "image_caption": [ + "Figure 9. Hyper-parameter ablations." + ], + "image_footnote": [], + "bbox": [ + 76, + 234, + 468, + 415 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "framework. Table 2 shows that each component accounts for at least $5\\%$ performance gain. The space-aware memory $(+10.0\\%)$ and in-painting block $(+6.7\\%)$ are the top 2 most significant contributors, which underline our motivation and justification of the method development ( $\\S 3.2$ and $\\S 3.3$ ). Although replacing Memory Queue with Memory Matrix could maintain a decent result (only dropped $5.1\\%$ ), our Memory Queue presents a more trustworthy recovery of \"normal\" patterns in the image than Memory Matrix (MemAE [17]), evidenced by Figure 6.", + "bbox": [ + 75, + 469, + 468, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyper-parameter robustness. After selecting the best hyper-parameters on the validation set, we here report the inference results on the testing set to study the robustness of different hyper-parameters in Figure 9. When input images are divided into a single patch, space-aware settings are not triggered, therefore yielding the worst performance. Although the spatial structures are relatively stable in most chest radiography, certain deviations can still be observed. Therefore, with small patches, object parts in one patch can easily appear in adjacent patches and be misdetected as anomalies. The number of topK activations in Gumbel softmax also impacts the performances. According to the AUC vs. the number of patterns in each Memory Queue region, we found that a small number of items is sufficient to support normal pattern querying in local regions. The best result is achieved by merely 200 items per region. When the item number exceeds 500 per region, AUC scores begin to drop continuously. AUC vs. the mask probability $\\rho$ was", + "bbox": [ + 75, + 628, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fad4a9bf1f9fce94045372cfa6d9fb751d67e6df6acc8a2f6b540b3bcb13654c.jpg", + "image_caption": [ + "Figure 10. Results of mixing normal/abnormal training samples." + ], + "image_footnote": [], + "bbox": [ + 500, + 87, + 890, + 161 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "further plotted to verify that enabling a limited number of feature skips $(\\rho = 95\\%)$ yields the best AUC score. The effectiveness of the in-painting will severely deteriorate if more features are allowed to be skipped $(\\rho < 90\\%)$ .", + "bbox": [ + 496, + 212, + 893, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Disease-free training requirement? Unsupervised methods for medical anomaly detection are uncommon because the so-called UAD methods are not \"unsupervised\"—they must be trained on disease-free images only (e.g. [5]). In practice, cleaning up disease-free images relies on manual annotation (essentially, image-level healthy/diseased labels). With disease-free sample ratio in the training set ranging from $100\\%$ to $50\\%$ , we have compared the robustness of SQUID with three competitive baselines (CutPaste [40], PANDA [56] and M-KD [60]). Figure 10 remarks that our proposed memory queue can tolerate the disease/healthy training ratio up to $50\\%$ by automatically omitting minority anatomical patterns. In contrast, CutPaste drops significantly as the percentage of normal images decreases; PANDA and M-KD can maintain the performance due to the use of pre-trained features. Interestingly, M-KD with mixed data even outperforms its vanilla training setting, although with considerable fluctuations.", + "bbox": [ + 496, + 276, + 892, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 561, + 617, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present SQUID for unsupervised anomaly detection from radiography images. Qualitatively, we show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, SQUID can identify anomalies accurately. Quantitatively, SQUID is superior to predominant methods by over 5 points AUC on the ZhangLab dataset and 10 points AUC on the Stanford CheXpert dataset. The outstanding results are attributable to our observation: Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. We synthesized the DigitAnatomy dataset to resemble key attributes of chest anatomy in radiography images for prompting future method development.", + "bbox": [ + 496, + 587, + 892, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. 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PhD thesis, Arizona State University, 2021. 1" + ], + "bbox": [ + 78, + 92, + 467, + 898 + ], + "page_idx": 11 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[86] Zongwei Zhou, Jae Shin, Ruibin Feng, R Todd Hurst, Christopher B Kendall, and Jianming Liang. Integrating active learning and transfer learning for carotid intima-media thickness video interpretation. Journal of digital imaging, 32(2):290-299, 2019. 1", + "[87] Zongwei Zhou, Vatsal Sodha, Jiaxuan Pang, Michael B Gotway, and Jianming Liang. Models genesis. Medical image analysis, 67:101840, 2021. 2, 4, 13", + "[88] Zongwei Zhou, Vatsal Sodha, Md Mahfuzur Rahman Siddiquee, Ruibin Feng, Nima Tajbakhsh, Michael B Gotway, and Jianming Liang. Models genesis: Generic autodidactic models for 3d medical image analysis. In International conference on medical image computing and computer-assisted intervention, pages 384-393. Springer, 2019. 2", + "[89] Arthur Zimek and Erich Schubert. Outlier detection. 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Springer, 2011. 2" + ], + "bbox": [ + 503, + 92, + 890, + 470 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "23901", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/c1d458f7-f8ad-480d-9ab9-60ca7bc1a759_model.json b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/c1d458f7-f8ad-480d-9ab9-60ca7bc1a759_model.json new file mode 100644 index 0000000000000000000000000000000000000000..94eee97b5dd01f0ee1df5617169f4a54f2286653 --- /dev/null +++ b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/c1d458f7-f8ad-480d-9ab9-60ca7bc1a759_model.json @@ -0,0 +1,2875 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.123, + 0.131, + 0.846, + 0.153 + ], + "angle": 0, + "content": "SQUID: Deep Feature In-Painting for Unsupervised Anomaly Detection" + }, + { + "type": "text", + "bbox": [ + 0.239, + 0.18, + 0.731, + 0.218 + ], + "angle": 0, + "content": "Tiang Xiang Yixiao Zhang Yongyi Lu Alan L. Yuille Chaoyi Zhang Weidong Cai Zongwei Zhou\\*" + }, + { + "type": "text", + "bbox": [ + 0.28, + 0.224, + 0.692, + 0.244 + ], + "angle": 0, + "content": "1University of Sydney 2Johns Hopkins University" + }, + { + "type": "text", + "bbox": [ + 0.34, + 0.251, + 0.625, + 0.266 + ], + "angle": 0, + "content": "GitHub: https://github.com/tiangexiang/SQUID" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.301, + 0.313, + 0.317 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.474, + 0.592 + ], + "angle": 0, + "content": "Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. To exploit this structured information, we propose the use of Space-aware Memory Queues for In-painting and Detecting anomalies from radiography images (abbreviated as SQUID). We show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, it can identify anomalies (unseen/modified patterns) in the image. SQUID surpasses 13 state-of-the-art methods in unsupervised anomaly detection by at least 5 points on two chest X-ray benchmark datasets measured by the Area Under the Curve (AUC). Additionally, we have created a new dataset (DigitAnatomy), which synthesizes the spatial correlation and consistent shape in chest anatomy. We hope DigitAnatomy can prompt the development, evaluation, and interpretability of anomaly detection methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.622, + 0.21, + 0.637 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.648, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Vision tasks in photographic imaging and radiography imaging are different. For example, when identifying objects in photographic images, we assume translation invariance—a cat is a cat no matter if it appears on the left or right of the image. In radiography imaging, on the other hand, the relative location and orientation of a structure are important characteristics that allow the identification of normal anatomy and pathological conditions [20,83]. Since radiography imaging protocols assess patients in a fairly consistent orientation, the generated images have great similarity across various patients, equipment manufacturers, and facility locations (see examples in Figure 1d). The consistent and recurrent anatomy facilitates the analysis of numerous critical problems and should be considered a significant advantage for radiography imaging [85]. Several investiga" + }, + { + "type": "image_caption", + "bbox": [ + 0.53, + 0.3, + 0.566, + 0.309 + ], + "angle": 0, + "content": "Normal" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.31, + 0.547, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.3, + 0.596, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.3, + 0.665, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.543, + 0.386, + 0.649, + 0.397 + ], + "angle": 0, + "content": "(a) Crowded Scenes" + }, + { + "type": "image_caption", + "bbox": [ + 0.621, + 0.3, + 0.665, + 0.309 + ], + "angle": 0, + "content": "Abnormal" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.41, + 0.548, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.548, + 0.41, + 0.596, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.41, + 0.643, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.643, + 0.41, + 0.691, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.446, + 0.548, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.548, + 0.446, + 0.596, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.596, + 0.446, + 0.643, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.643, + 0.446, + 0.692, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.486, + 0.643, + 0.498 + ], + "angle": 0, + "content": "(c) Digit Anatomy" + }, + { + "type": "image_caption", + "bbox": [ + 0.73, + 0.3, + 0.765, + 0.308 + ], + "angle": 0, + "content": "Normal" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.31, + 0.746, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.746, + 0.3, + 0.794, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.794, + 0.3, + 0.888, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.385, + 0.794, + 0.397 + ], + "angle": 0, + "content": "Textures" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.346, + 0.842, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.842, + 0.346, + 0.888, + 0.383 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.746, + 0.407, + 0.795, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.409, + 0.842, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.842, + 0.409, + 0.889, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.446, + 0.842, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.842, + 0.446, + 0.889, + 0.484 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.744, + 0.486, + 0.844, + 0.498 + ], + "angle": 0, + "content": "(d) Chest Anatomy" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.508, + 0.892, + 0.579 + ], + "angle": 0, + "content": "Figure 1. Anomaly detection in radiography images can be both easier and harder than in photographic images. It is easier because radiography images are spatially structured due to consistent imaging protocols. It is harder because anomalies in radiography images are subtle and require medical expertise to annotate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.732 + ], + "angle": 0, + "content": "tions have demonstrated the value of this prior knowledge in enhancing Deep Nets' performance by adding location features, modifying objective functions, and constraining coordinates relative to landmarks in images [3,47,49,69,86]. Our work seeks to answer this critical question: Can we exploit consistent anatomical patterns and their spatial information to strengthen Deep Nets' detection of anomalies from radiography images without manual annotation?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Unsupervised anomaly detection only uses healthy images for model training and requires no other annotations such as disease diagnosis or localization [5]. As many as \\(80\\%\\) of clinical errors occur when the radiologist misses the abnormality in the first place [7]. The impact of anomaly detection is to reduce that \\(80\\%\\) by clearly pointing out to radiologists that there exists a suspicious lesion and then having them look at the scan in depth. Unlike previous anomaly detection methods, we formulate the task as an in-painting task to exploit the anatomical consistency in appearance, position, and layout across radiography images. Specif" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.406, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author: Zongwei Zhou (zzhou82@jh.edu)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23890" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "ically, we propose _Space-aware Memory Queues for Inpainting and Detecting anomalies from radiography images (abbreviated as _SQUID). During training, our model can dynamically maintain a visual pattern dictionary by taxonomizing recurrent anatomical patterns based on their spatial locations. Due to the consistency in anatomy, the same body region across healthy images is expected to express similar visual patterns, which makes the total number of unique patterns manageable. During inference, since anomaly patterns do not exist in the dictionary, the generated radiography image is expected to be unrealistic if an anomaly is present. As a result, the model can identify the anomaly by discriminating the quality of the in-painting task. The success of anomaly detection has two basic assumptions [89]: first, anomalies only occur rarely in the data; second, anomalies differ from the normal patterns significantly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.473, + 0.544 + ], + "angle": 0, + "content": "We have conducted experiments on two large-scale, publicly available radiography imaging datasets. Our SQUID is significantly superior to predominant methods in unsupervised anomaly detection by over 5 points on the ZhangLab dataset [32]; remarkably, we have demonstrated a 10-point improvement over 13 recent unsupervised anomaly detection methods on the Stanford CheXpert dataset [29]. In addition, we have created a new dataset (DigitAnatomy) to elucidate spatial correlation and consistent shape of the chest anatomy in radiography (see Figure 1c). DigitAnatomy is dedicated to easing the development, evaluation, and interpretability of anomaly detection methods. The qualitative visualization clearly shows the superiority of our SQUID over the current state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.545, + 0.473, + 0.651 + ], + "angle": 0, + "content": "In summary, our contributions include: (I) the best performing unsupervised anomaly detection method for chest radiography imaging; (II) a synthetic dataset to promote anomaly detection research; (III) SQUID overcomes limitations in dominant unsupervised anomaly detection methods [1, 17, 35, 61, 82] by inventing Space-aware Memory Queue (§3.2), and Feature-level In-painting (§3.3)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.661, + 0.22, + 0.679 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Anomaly detection in natural imaging. Anomaly detection is the task of identifying rare events that deviate from the distribution of normal data [52]. Early attempts include one-class SVM [64], dictionary learning [81], and sparse coding [11]. Due to the lack of sufficient samples of anomalies, later works typically formulate anomaly detection as an unsupervised learning problem [13, 26, 27, 37, 38, 42, 57, 67, 90]. These can be roughly categorized into reconstruction-based and density-based methods. Reconstruction-based methods train a model (e.g. Auto-Encoder) to recover the original inputs [9, 66, 71, 77, 87, 88] and identify anomalies by analyzing reconstruction errors. Density-based methods predict anomalies by estimating the normal data distribution (e.g. via VAEs [35] or GANs [2, 61, 62]). However," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "the learned distribution for normal images by these methods cannot explain the possible abnormalities. In this paper, we address these limitations by maintaining a visual pattern memory from homogeneous medical images. Several other previous works investigated the use of image inpainting for anomaly detection, i.e. parts of the input image are masked out, and the model is trained to recover the missing parts in a self-supervised way [22, 40, 51, 56, 79]. There are also plenty of works on detecting anomalies in video sequences [15, 45, 46]. Bergmann et al. [6] and Salehi et al. [59] proposed similar student-teacher networks, whereas our method utilizes such a structure to distillate input-aware features only, and the teacher network is completely disabled during inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.895, + 0.852 + ], + "angle": 0, + "content": "Anomaly detection in medical imaging. Anomaly detection in the medical domain is usually approached on a per-pathology basis. Supervised learning based methods [5, 44, 63] are commonly adopted to detect specific types of abnormalities, such as lesions [91], pathologies [33], tumors [4], and nodules [84]. Recent unsupervised methods have been proposed to detect anomalies in general [5, 25, 66]. With the help of GANs, anomaly detection can be achieved with weak annotations. In AnoGAN [62], the discriminator was heavily over-fitted to the normal image distribution to detect the anomaly. Subsequently, f-AnoGAN [61] was proposed to improve computational efficiency. Marimont et al. [50] designed an auto-decoder network to fit the distribution of normal images. The spatial coordinates and anomaly probabilities are mapped over a proxy for different tissue types. Han et al. [21] proposed a two-step GAN-based framework for detecting anomalies in MRI slices as well. However, their method relies on a voxel-wise representation for the 3D MRI sequences, which is impossible in our task. Most recently, a hybrid framework SALAD [82] was proposed that combines GAN with self-supervised techniques. Normal images are first augmented to carry the forged anomaly through pixel corruption and pixel shuffling. The fake abnormal images, along with the original normal ones, are fed to the GAN for learning more robust feature representations. However, these approaches demand strong prior knowledge and assumptions about the anomaly type to make the augmentation effective. Differing from photographic images, radiography imaging protocols produce images with consistent anatomical patterns, which are much more challenging to detect due to subtle imaging clues and overlapping anatomic structures (Figure 1). Unlike most existing works, we present a novel method that explicitly harnesses the radiography images' properties, dramatically improving the performance in anomaly detection from radiography images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Memory networks. Incorporating memory modules into neural networks has been demonstrated to be effective for many tasks [8, 16, 31, 36, 39]. Adopting Memory Matrix" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "23891" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.088, + 0.895, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.896, + 0.41 + ], + "angle": 0, + "content": "Figure 2. SQUID. We divide an input image into \\( N \\times N \\) non-overlapping patches and feed them into the encoder for feature extraction. Two generators will be trained to reconstruct the original image. Along with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically via a novel Memory Queue (§3.2); The teacher generator directly uses the features extracted by the encoder; the student generator uses the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm. We employ a discriminator to assess whether the image reconstructed by the student generator is real or fake. Once trained, it can also be used to detect anomalies in test images (§3.4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.473, + 0.709 + ], + "angle": 0, + "content": "for unsupervised anomaly detection was first proposed in MemAE [17]. In addition to auto-encoding (AE), an extra Memory Matrix was introduced between the encoder and the decoder to capture normal feature patterns during training. The matrix is jointly optimized along with the AE and hence learns an essential basis to be able to assemble normal patterns. Based on this paradigm, Park et al. [53] introduced a non-learnable memory module that can be updated with inputs. Note that although our proposed Memory Queue also does not require any gradients, our method differs significantly in its usage purpose and updating rules. Considering the extra memory usage in existing methods, Lv et al. [48] proposed a dynamic prototype unit that encodes normal dynamics on the fly, while consuming little additional memory. In this paper, we overcome the limitations of the Memory Matrix and propose an effective yet efficient Memory Queue for unsupervised anomaly detection in radiography images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.172, + 0.74 + ], + "angle": 0, + "content": "3. SQUID" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.75, + 0.268, + 0.767 + ], + "angle": 0, + "content": "3.1. Overview (Figure 2)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.774, + 0.47, + 0.866 + ], + "angle": 0, + "content": "(1) Feature extraction. We divide the input image into \\( N \\times N \\) non-overlapping patches and feed them into an encoder for feature extraction. The extracted features will be used for image reconstruction. Practically, the encoder can be any backbone architectures [14,70]; we adopt basic Convolutions and Pooling layers in this work for simplicity." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "(2) Image reconstruction. We introduce teacher and student generators to reconstruct the original image. Along" + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.774, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.895, + 0.648 + ], + "angle": 0, + "content": "with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically as a Memory Queue (§3.2). Specifically, the teacher generator directly reconstructs the image using the features extracted by the encoder (essentially an auto-encoder [58]). The student generator, on the other hand, using the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm [28] at all of the up-sampling levels. The objective of the student generator is to reconstruct a normal image from the augmented features, which will then be used for anomaly discrimination (§3.4); while the teacher generator serves as a regularizer that prevents the student from constantly generating the same normal image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.894, + 0.773 + ], + "angle": 0, + "content": "(3) Anomaly discrimination. Following the adversarial learning [61, 62], we employ a discriminator to assess whether the generated image is real or fake. Only the student generator will receive the gradient derived from the discriminator. The two generators and the discriminator are competing against each other until they converge to an equilibrium. Once trained, the discriminator can be used to detect anomalies in test images (§3.4)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.782, + 0.842, + 0.799 + ], + "angle": 0, + "content": "3.2. Inventing Memory Queue as Dictionary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.805, + 0.895, + 0.868 + ], + "angle": 0, + "content": "Motivation. The Memory Matrix was introduced by Gong et al. [17] and has since been widely adopted in unsupervised anomaly detection [18, 45, 78]. To forge a \"normal\" appearance, features are augmented by weighted averaging" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1We disabled the backpropagation between the teacher and encoder by stop-gradient [23] and showed its empirical benefit in Table 2." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23892" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.088, + 0.19, + 0.1 + ], + "angle": 0, + "content": "Memory Matrix" + }, + { + "type": "image_caption", + "bbox": [ + 0.211, + 0.089, + 0.266, + 0.1 + ], + "angle": 0, + "content": "Similarity" + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.089, + 0.408, + 0.1 + ], + "angle": 0, + "content": "Space-aware Memory" + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.105, + 0.262, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.105, + 0.484, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.177, + 0.47, + 0.219 + ], + "angle": 0, + "content": "Figure 3. Space-aware memory. For unique encoding of location information, we restrict each patch to be only accessible by a non-overlapping region in the memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.245, + 0.469, + 0.32 + ], + "angle": 0, + "content": "the similar patterns in Memory Matrix. This augmentation is, however, applied to the features extracted from the whole image, discarding the spatial information in images. Therefore, the Memory Matrix in its current form cannot perceive the anatomical consistency as in radiography images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.323, + 0.47, + 0.549 + ], + "angle": 0, + "content": "Space-aware memory. To harness the spatial information, we pass the divided small patches, instead of the whole image, into the model. These patches are associated with unique location identifiers of the original image. We seek to build the relationship between the patch location and memory region, by restricting the search space in Memory Matrix to the patch-corresponded non-overlapping segments only. That is, a patch at a particular location can only access a corresponding segment in the whole Memory Matrix (illustrated in Figure 3). We refer to this new strategy as \"space-aware memory\" because it enables explicit encoding of the spatial information into Memory Matrix. Space-aware memory can also accelerate the augmentation speed compared with [17] as it no longer goes through the entire Memory Matrix to assemble similar features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Memory queue. In learning-based Memory Matrix [17], \"normal patterns\" are forged by combining learned basis in the matrix. However, there is always a distribution discrepancy between the basic combinations and the actual image features. This disparity makes it hard for the subsequent image generation. To address this issue, we propose a Memory Queue to store real image features during model training, therefore presenting an identical distribution to the image features. Specifically, it directly copies previously seen features into a queue structure during training2. Once trained, Memory Queue can be used as a dictionary of normal anatomical patterns. In Figure 4, we show t-SNE visualizations to validate that the learned basis in Memory Matrix (blue dots) distributes differently from the actual image features of the training set (gray dots). In contrast, the stored image features in our Memory Queue (red dots) are" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.087, + 0.895, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.197, + 0.894, + 0.268 + ], + "angle": 0, + "content": "Figure 4. t-SNE visualizations of patterns in Memory Matrix, Memory Queue, and patch features of the training samples [73]. Patterns in the Memory Matrix are far away from the distribution of patch features, while patterns in the Memory Queue (as copies of previously seen features) share a similar distribution." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.293, + 0.798, + 0.307 + ], + "angle": 0, + "content": "in an identical distribution to the actual ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.892, + 0.478 + ], + "angle": 0, + "content": "Gumbel shrinkage. Controlling the number of activated patterns in the memory has proven to be advantageous for anomaly detection [17, 19]. However, setting a hard shrinkage threshold fails to adapt to cases where no suitable entries can be found in the memory. One natural workaround is to activate the top-\\(k\\) similar patterns in the memory. However, this strategy restricts the gradient flow to only the top-\\(k\\) memory entries, while the rest inactivated ones could not receive any gradients and be updated as expected. To extend gradients to all patterns in the memory, inspired by Jang [30], we present a Gumbel Shrinkage schema:" + }, + { + "type": "equation", + "bbox": [ + 0.539, + 0.491, + 0.892, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} ^ {\\prime} = \\operatorname {s g} (\\operatorname {h s} (\\mathbf {w}, \\operatorname {t o p k} (\\mathbf {w})) - \\phi (\\mathbf {w})) + \\phi (\\mathbf {w}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.893, + 0.656 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}\\) denotes the similarity between the image features and entries in Memory, \\(sg(\\cdot)\\) the stop-gradient operation, \\(\\mathrm{hs}(\\cdot ,t)\\) the hard shrinkage operator with threshold \\(t\\), and \\(\\phi (\\cdot)\\) the Softmax function. In the forward pass, Gumbel Shrinkage ensures the combination of the top- \\(k\\) most similar entries in the memory; During the back-propagation, Gumbel Shrinkage essentially functions as Softmax. We apply Gumbel Shrinkage to both Memory Queue and Memory Matrix in our framework." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.666, + 0.892, + 0.683 + ], + "angle": 0, + "content": "3.3. Formulating Anomaly Detection as In-painting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Motivation. Image in-painting [41, 54] was initially proposed to recover corrupted image regions with neighboring context. Following the above intuition, we propose to achieve anomaly detection via in-painting anomalous radiography patterns into healthy ones. When in-painting pixels in the image space, recovered regions have been usually seen to associate with boundary artifacts, particularly when using Deep Nets [43]. These undesired artifacts are responsible for numerous false positives when formulating anomaly detection as a pixel-level in-painting task [66, 87]. To alleviate this issue, we achieve the in-painting task at the feature level instead. Latent features are better invariant to pixel-level noise, rotation, and translation, therefore are more suitable for subsequent anomaly detection." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In practice, copying features into the queue at every training iteration demands considerable computational time. Supposing \\(N\\) patterns in the queue and \\(M\\) training iterations, the sampling strategy in [17] demands an \\(\\mathcal{O}(NM)\\) time complexity. We implement it more efficiently: at each iteration, the current batch of features will be copied into the queue for only once (Figure 5c), yielding a linear complexity of \\(\\mathcal{O}(M + cM)\\) with the copy-and-paste operation in a constant time \\(c\\). We follow the first-in-first-out (FIFO) paradigm to update the queue continuously." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23893" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.322, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.141, + 0.205, + 0.255, + 0.218 + ], + "angle": 0, + "content": "(a) Augment \\(\\mathcal{F}\\) to \\(\\mathcal{N}\\)" + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.129, + 0.648, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.418, + 0.205, + 0.546, + 0.218 + ], + "angle": 0, + "content": "(b) Aggregate \\(\\mathcal{F}\\) and \\(\\mathcal{N}\\)" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.087, + 0.889, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.731, + 0.205, + 0.892, + 0.218 + ], + "angle": 0, + "content": "(c) Copy \\(\\mathcal{F}\\) to Memory Queue" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.227, + 0.894, + 0.285 + ], + "angle": 0, + "content": "Figure 5. Three-step workflow of our in-painting block. (a) Each non-overlapping patch feature \\(\\mathcal{F}\\) is queried to a unique region in Memory Queue, and the most similar items are assembled to \\(\\mathcal{N}\\). (b) Each center patch feature \\(\\mathcal{F}\\) and its eight neighbors \\(\\mathcal{N}\\) are used as query and key/value, respectively, to a Transformer layer for in-painting. (c) Each Memory Queue region copies its corresponding patch features \\(\\mathcal{F}\\) into the memory by maintaining a pointer. Note that this step is only performed during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.473, + 0.568 + ], + "angle": 0, + "content": "In-painting block. We integrate our Memory Queue inside a novel in-painting block to perform feature-space in-painting. The block starts with a Memory Queue that augments \\( w \\times h \\) non-overlapping patch features \\( \\mathcal{F}_{\\{(1,1), \\dots, (w,h)\\}} \\) into their most similar \"normal\" patterns \\( \\mathcal{N}_{\\{(1,1), \\dots, (w,h)\\}} \\) (Figure 5a). Since \\( \\mathcal{N} \\) is assembled by features extracted from previous training data, \\( \\mathcal{N} \\) is not subject to the current input image. To recap the characteristics of the input image, we aggregate both patch features \\( \\mathcal{F} \\) and their augmented features \\( \\mathcal{N} \\) using a transformer block [74]. In details, for each patch \\( \\mathcal{F}_{i,j} \\), its spatially adjacent eight augmented ones \\( \\mathcal{N}_{\\{(i-1,j-1), \\dots, (i+1,j+1)\\}} \\) are used as conditions to refine \\( \\mathcal{F}_{i,j} \\) (Figure 5b). The query token of the transformer block is flattened \\( \\mathcal{F}_{(i,j)} \\in \\mathcal{R}^{1 \\times *} \\) and key/value tokens are \\( \\mathcal{N}_{\\{(i-1,j-1), \\dots, (i+1,j+1)\\}} \\in \\mathcal{R}^{8 \\times *} \\). At the start and the end of our in-painting block, we apply an extra pair of point-wise convolutions \\( (1 \\times 1 \\) convolutional kernel) [24]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.571, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Masked shortcut. We employ a shortcut within the inpainting block to better aggregate features and ease optimization. Our empirical study shows that a direct residual connection downgrades the effectiveness of the in-painting block (Appendix B). Inspired by Xiang et al. [76], we utilize a random binary mask to gate shortcut features during training (Figure 5b). As such, given the input patch features \\(\\mathcal{F}\\), the output of the in-painting block is obtained by:" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.703, + 0.47, + 0.721 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} ^ {\\prime} = (1 - \\delta) \\cdot \\mathcal {F} + \\delta \\cdot \\text {i n p a i n t} (\\mathcal {F}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.732, + 0.47, + 0.824 + ], + "angle": 0, + "content": "where \\(\\mathrm{inpaint}(\\cdot)\\) is the designed in-painting block, \\(\\delta \\sim\\) Bernoulli \\((\\rho)\\) is a binary variable with \\(\\rho\\) the gating probability. After obtaining \\(\\mathcal{F}'\\) at each training step, the originally \\(\\mathcal{F}\\) are then copied to update the memory (Figure 5c). During inference, we disable the shortcut completely such that \\(\\mathcal{F}' = \\mathrm{inpaint}(\\mathcal{F})\\) for deterministic predictions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.304, + 0.849 + ], + "angle": 0, + "content": "3.4. Anomaly Discrimination" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Our discriminator can detect anomalies by assessing the quality of the reconstructions—normal if realistic; abnormal otherwise. It is because the generator was trained on" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.37 + ], + "angle": 0, + "content": "normal images, so Memory Queues only store normal patterns. During inference, since abnormal patterns were never present in Memory Queues, the reconstructed image is expected to appear unrealistic." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.893, + 0.617 + ], + "angle": 0, + "content": "Our in-painting block focuses on augmenting any patch feature (either normal or abnormal) into similar \"normal\" features. The student generator then reconstructs a \"normal\" image based on the \"normal\" features. The teacher generator is used to prevent the student from generating the same image regardless of inputs. Once trained, the semantic (rather than pixel-level) difference between the input and the student generator's reconstructed image is expected to be small if normal and big otherwise. We, therefore, delegate the optimized discriminator network for alerting anomalies perceptually. For better clarification, we note the encoder, teacher generator, student generator, and discriminator as \\(\\mathbf{E}\\), \\(\\mathbf{G}_{\\mathrm{t}}\\), \\(\\mathbf{G}_{\\mathrm{s}}\\), and \\(\\mathbf{D}\\). An anomaly score \\(A\\) can be computed through: \\(A = \\phi \\left( \\frac{\\mathbf{D}(\\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I})) - \\mu}{\\sigma} \\right)\\), where \\(\\phi (\\cdot)\\) is the Sigmoid function, \\(\\mu\\) and \\(\\sigma\\) are the mean and standard deviation of anomaly scores calculated on training samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.645, + 0.647 + ], + "angle": 0, + "content": "3.5. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.901 + ], + "angle": 0, + "content": "SQUID is optimized by five loss functions. The mean square error (MSE) between input and reconstructed images is used for both teacher and student generators. Concretely, \\(\\mathcal{L}_{\\mathrm{t}} = (\\mathbf{I} - \\mathbf{G}_{\\mathrm{t}}(\\mathbf{E}(\\mathbf{I}))^{2}\\) and \\(\\mathcal{L}_{\\mathrm{s}} = (\\mathbf{I} - \\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I})))^{2}\\) for the teacher and student generators, respectively, where \\(\\mathbf{I}\\) denotes the input image. Following the knowledge distillation paradigm, we apply a distance constraint between the teacher and student generators to all levels of features: \\(\\mathcal{L}_{\\mathrm{dist}} = \\sum_{i=1}^{l} (\\mathcal{F}_{\\mathrm{t}}^{i} - \\mathcal{F}_{\\mathrm{s}}^{i})^{2}\\), where \\(l\\) is the level of features used for knowledge distillation, \\(\\mathcal{F}_{\\mathrm{t}}\\) and \\(\\mathcal{F}_{\\mathrm{s}}\\) are the intermediate features in the teacher and student generators, respectively. In addition, we employ an adversarial loss (similar to DCGAN [55]) to improve the quality of the image generated by the student generator. Specifically, the following equation is minimized: \\(\\mathcal{L}_{\\mathrm{gen}} = \\log(1 - \\mathbf{D}(\\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I}))))\\). The discriminator seeks to maximize the average of the proba" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23894" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.172, + 0.089, + 0.46, + 0.098 + ], + "angle": 0, + "content": "Input SQUID f-AnoGAN Ganomly MemAE" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.098, + 0.47, + 0.338 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Figure 6. Reconstruction results on DigitAnatomy. Our feature-level in-painting is more robust to amplified noise and pixel variance than the existing pixel-level in-painting methods. More visualization can be found in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.507 + ], + "angle": 0, + "content": "bility for real images and the inverted probability for fake images: \\(\\mathcal{L}_{\\mathrm{dis}} = \\log (\\mathbf{D}(\\mathbf{I})) + \\log (1 - \\mathbf{D}(\\mathbf{G}_s(\\mathbf{E}(\\mathbf{I}))))\\) . In summary, SQUID is trained to minimize the generative loss terms \\((\\lambda_{\\mathrm{t}}\\mathcal{L}_{\\mathrm{t}} + \\lambda_{\\mathrm{s}}\\mathcal{L}_{\\mathrm{s}} + \\lambda_{\\mathrm{dist}}\\mathcal{L}_{\\mathrm{dist}} + \\lambda_{\\mathrm{gen}}\\mathcal{L}_{\\mathrm{gen}})\\) and to maximize the discriminative loss term \\((\\lambda_{\\mathrm{dis}}\\mathcal{L}_{\\mathrm{dis}})\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.519, + 0.21, + 0.536 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.242, + 0.559 + ], + "angle": 0, + "content": "4.1. New Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.825 + ], + "angle": 0, + "content": "DigitAnatomy. We have created a synthetic dataset to verify our main idea, wherein the human anatomy is translated into Arabic digits one to nine in an in-grid placement (see examples in Figure 1 and Figure 6). The images containing digits in the correct order are considered \"normal\"; otherwise, they are considered \"abnormal\". The types of simulated abnormalities include missing, misordered, flipped, and zero digit(s). DigitAnatomy is particularly advantageous for radiography imaging for three reasons. First, it simulates two unique properties of radiography images, i.e. spatial correlation and consistent shape. Second, annotating radiography images demands specialized expertise, but digits are easier for problem debugging. Third, the ground truth of the simulated anomaly is readily accessible in DigitAnatomy, whereas it is hard to collect sufficient examples for each abnormal type in radiography images. The pseudocode for creating DigitAnatomy is in Appendix C." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.265, + 0.848 + ], + "angle": 0, + "content": "4.2. Public Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "ZhangLab Chest X-ray [32]. This dataset contains healthy and pneumonia (as anomaly) images, officially split into training and testing sets. The training set consists of 1,349" + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.09, + 0.882, + 0.103 + ], + "angle": 0, + "content": "Table 1. Benchmark results on the test sets of the two datasets." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.114, + 0.891, + 0.361 + ], + "angle": 0, + "content": "
ZhangLabRef & YearAUC (%)Acc (%)F1 (%)
Auto-Encoder-59.963.477.2
VAE [35]Arxiv'1361.864.077.4
Ganomaly [1]ACCV'1878.070.079.0
f-AnoGAN [61]MIA'1975.574.081.0
MemAE [17]ICCV'1977.8±1.456.5±1.182.6±0.9
MNAD [53]CVPR'2077.3±0.973.6±0.779.3±1.1
SALAD [82]TMI'2182.7±0.875.9±0.982.1±0.3
CutPaste [40]CVPR'2173.6±3.964.0±6.572.3±8.9
PANDA [56]CVPR'2165.7±1.365.4±1.966.3±1.2
M-KD [59]CVPR'2174.1±2.669.1±0.262.3±8.4
IF 2D [50]MICCAI'2181.0±2.876.4±0.282.2±2.7
PaDiM [12]ICPR'2171.4±3.472.9±2.480.7±1.2
IGD [10]AAAI'2273.4±1.974.0±2.280.9±1.3
SQUID-87.6±1.580.3±1.384.7±0.8
CheXpertRef & YearAUC (%)Acc (%)F1 (%)
Ganomaly [1]ACCV'1868.9±1.465.7±0.265.1±1.9
f-AnoGAN [61]MIA'1965.8±3.363.7±1.859.4±3.8
MemAE [17]ICCV'1954.3±4.055.6±1.453.3±7.0
CutPaste [40]CVPR'2165.5±2.262.7±2.060.3±4.6
PANDA [56]CVPR'2168.6±0.966.4±2.865.3±1.5
M-KD [59]CVPR'2169.8±1.666.0±2.563.6±5.7
SQUID-78.1±5.171.9±3.875.9±5.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.389, + 0.892, + 0.464 + ], + "angle": 0, + "content": "normal and 3,883 abnormal images; the testing set has 234 normal and 390 abnormal images. We randomly separate 200 images (100 normal and 100 abnormal) from the training set as the validation set for hyper-parameter tuning. We resized all the images to \\(128 \\times 128\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.591 + ], + "angle": 0, + "content": "Stanford CheXpert [29]. We conducted evaluations on the front-view PA images in the CheXpert dataset, which account for a total of 12 different anomalies. In all front-view PA images, there are 5,249 normal and 23,671 abnormal images for training; 250 normal and 250 abnormal images (with at least 10 images per disease type) from the training set were used for testing. We used the same hyperparameters found in the ZhangLab experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.601, + 0.706, + 0.616 + ], + "angle": 0, + "content": "4.3. Baselines and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.791 + ], + "angle": 0, + "content": "We considered a total number of 13 major baselines for direct comparison: Auto-Encoder, VAE [35]—the classic UAD methods; Ganomaly [1], f-AnoGAN [61], IF [50], SALAD [82]—the current state of the arts for medical imaging; and MemAE [17], CutPaste [40], M-KD [60], PANDA [56], PaDiM [12], IGD [10]—the most recent UAD methods. We evaluated performance using standard metrics: Receiver Operating Characteristic (ROC) curve, Area Under the ROC Curve (AUC), Accuracy (Acc), and F1-score (F1). Unless explicitly specified, we trained all models from scratch for at least three times independently." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.718, + 0.817 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We utilized common data augmentation strategies such as random translation within the \\([-0.05, + 0.05]\\) range and a random scaling of [0.95, 1.05]. The Adam [34] optimizer was used with a batch size of 16 and a weight decay of \\(1e-5\\). The learning rate was initially set to \\(1e-4\\) for both the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23895" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.273, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.246, + 0.247, + 0.256 + ], + "angle": 0, + "content": "(a) ZhangLab Chest X-ray" + }, + { + "type": "image", + "bbox": [ + 0.273, + 0.088, + 0.468, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.246, + 0.43, + 0.256 + ], + "angle": 0, + "content": "(b) Stanford CheXpert" + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.267, + 0.435, + 0.281 + ], + "angle": 0, + "content": "Figure 7. ROC curves comparison on the two datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.473, + 0.476 + ], + "angle": 0, + "content": "generator and the discriminator and then decayed to \\(2e - 5\\) in 1000 epochs following the cosine annealing scheduler. The discriminator is trained at every iteration, while the generator is trained every two iterations. We set loss weights as \\(\\lambda_{\\mathrm{t}} = 0.01\\), \\(\\lambda_{\\mathrm{s}} = 10\\), \\(\\lambda_{\\mathrm{dist}} = 0.001\\), \\(\\lambda_{\\mathrm{gen}} = 0.005\\), and \\(\\lambda_{\\mathrm{dis}} = 0.005\\). We divide the input images in \\(2\\times 2\\) non-overlapping patches, fix the shortcut mask probability at \\(\\rho = 95\\%\\), and activate only the top 5 similar patterns in the Gumbel Shrinkage. The impact of these hyper-parameters is studied in §5.3. The architectures of our generators and discriminator are detailed in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.49, + 0.164, + 0.505 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.398, + 0.532 + ], + "angle": 0, + "content": "5.1. Interpreting SQUID on DigitAnatomy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Figure 6 presents qualitative results on DigitAnatomy to examine the capability of image reconstruction and to interpret the mistakes made by existing methods [1, 17, 61]. We deliberately inject anomalies (e.g. novel, misordered, missing digits) into normal images (highlighted in light blue) and test if the model can reconstruct their normal counterparts. To raise the task difficulty, we also assess the reconstruction quality from a blank image (as an extreme case). In general, the images reconstructed by our SQUID carry more meaningful and indicative information than other baseline methods. It is mainly attributed to our space-aware memory, with which the resulting dictionary is associated with unique patterns as well as their spatial information. Once an anomaly arises (e.g. missing digit), the in-painting block will augment the abnormal feature to its normal counterpart by assembling top-\\(k\\) most similar patterns from the dictionary. Other methods, however, do not possess this ability, so they reconstruct defective images. For instance, GAN-based methods (f-AnoGAN and Ganomly) tend to reconstruct an exemplar image averaged from the training examples. MemAE performs relatively better due to its Memory Matrix, but it does not work well for the anomaly of missing digits and completely fails on the extreme anomaly attack." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.087, + 0.72, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.727, + 0.087, + 0.895, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.209, + 0.892, + 0.266 + ], + "angle": 0, + "content": "Figure 8. Reconstruction results of SQUID on the two datasets, associated with the corresponding anomaly scores (defined in §3.4). A larger score indicates a higher probability of being abnormal. More visualization can be found in Appendix D." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.292, + 0.884, + 0.309 + ], + "angle": 0, + "content": "5.2. Benchmarking SQUID on Chest Radiography" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.317, + 0.893, + 0.694 + ], + "angle": 0, + "content": "Our SQUID was mainly evaluated on two large-scale benchmarks: ZhangLab Chest X-ray and Stanford CheXpert and compared with a wide range of state-of-the-art counterparts. According to Table 1, SQUID achieves the most promising result on all metrics for both datasets. Specifically, SQUID outperforms the runner-up counterparts by at least \\(5\\%\\) in AUC, \\(5\\%\\) in Accuracy. The highest F1 scores SQUID achieved, along with the ROC curves shown in Figure 7, demonstrate that our method yields the best trade-off between sensitivity and specificity. Overall, the significant improvements observed with SQUID proved the effectiveness of our proposed techniques in this work. In Figure 8, we visualize the reconstruction results of SQUID on exemplary normal and abnormal images in the two datasets. For normal cases, SQUID can easily find a similar match in Memory Queue, achieving the reconstruction smoothly. For abnormal cases, the contradiction will arise by imposing forged normal patterns into the abnormal features. In this way, the generated images will vary significantly from the input, which will then be captured by the discriminator. We plot the heatmap of the discriminator (using Grad-CAM [65]) to indicate the most likely regions to appear anomalous. As a result, the reconstructed healthy images yield much lower anomaly scores than the diseased ones, validating the effectiveness of SQUID." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.895, + 0.835 + ], + "angle": 0, + "content": "Limitation. We found SQUID in its current form, is not able to localize anomalies at the pixel level precisely. It is understandable because our SQUID is an unsupervised method, requiring zero manual annotation for normal/abnormal images, unlike [60, 68, 72, 75, 80]. Those methods that compute pixel-level residuals for anomaly detection suffer from amplified noise in the input and reconstructed output. Our in-painting strategy, however, is performed at the feature level and is more robust to pixel-level variance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.847, + 0.8, + 0.863 + ], + "angle": 0, + "content": "5.3. Ablating Key Properties in SQUID" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Component study. We examine the impact of components in SQUID by taking each one of them out of the entire" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23896" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.089, + 0.468, + 0.103 + ], + "angle": 0, + "content": "Table 2. Performance benefits from all the components in SQUID." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.113, + 0.468, + 0.221 + ], + "angle": 0, + "content": "
MethodAUC (%)Acc (%)F1 (%)
w/o Space-aware Memory77.6±0.575.5±0.582.5±0.6
w/o In-painting Block80.9±2.175.8±1.581.6±1.3
w/o Gumbel Shrinkage81.1±0.977.6±0.981.3±0.8
w/o Knowledge Distillation81.2±0.875.2±0.781.3±0.8
w/o Stop Gradient81.7±4.376.7±2.882.5±1.6
w/o Memory Queue82.5±1.178.6±0.981.7±1.1
w/o Masked Shortcuts82.5±1.376.4±0.882.3±1.1
w/o Decoder Memory82.9±1.277.4±1.181.2±0.5
Full SQUID87.6±1.580.3±1.384.7±0.8
" + }, + { + "type": "image", + "bbox": [ + 0.077, + 0.235, + 0.47, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.425, + 0.383, + 0.439 + ], + "angle": 0, + "content": "Figure 9. Hyper-parameter ablations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.47, + 0.47, + 0.622 + ], + "angle": 0, + "content": "framework. Table 2 shows that each component accounts for at least \\(5\\%\\) performance gain. The space-aware memory \\((+10.0\\%)\\) and in-painting block \\((+6.7\\%)\\) are the top 2 most significant contributors, which underline our motivation and justification of the method development (\\(\\S 3.2\\) and \\(\\S 3.3\\)). Although replacing Memory Queue with Memory Matrix could maintain a decent result (only dropped \\(5.1\\%\\)), our Memory Queue presents a more trustworthy recovery of \"normal\" patterns in the image than Memory Matrix (MemAE [17]), evidenced by Figure 6." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Hyper-parameter robustness. After selecting the best hyper-parameters on the validation set, we here report the inference results on the testing set to study the robustness of different hyper-parameters in Figure 9. When input images are divided into a single patch, space-aware settings are not triggered, therefore yielding the worst performance. Although the spatial structures are relatively stable in most chest radiography, certain deviations can still be observed. Therefore, with small patches, object parts in one patch can easily appear in adjacent patches and be misdetected as anomalies. The number of topK activations in Gumbel softmax also impacts the performances. According to the AUC vs. the number of patterns in each Memory Queue region, we found that a small number of items is sufficient to support normal pattern querying in local regions. The best result is achieved by merely 200 items per region. When the item number exceeds 500 per region, AUC scores begin to drop continuously. AUC vs. the mask probability \\(\\rho\\) was" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.088, + 0.892, + 0.162 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.172, + 0.886, + 0.187 + ], + "angle": 0, + "content": "Figure 10. Results of mixing normal/abnormal training samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.894, + 0.274 + ], + "angle": 0, + "content": "further plotted to verify that enabling a limited number of feature skips \\((\\rho = 95\\%)\\) yields the best AUC score. The effectiveness of the in-painting will severely deteriorate if more features are allowed to be skipped \\((\\rho < 90\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.277, + 0.893, + 0.549 + ], + "angle": 0, + "content": "Disease-free training requirement? Unsupervised methods for medical anomaly detection are uncommon because the so-called UAD methods are not \"unsupervised\"—they must be trained on disease-free images only (e.g. [5]). In practice, cleaning up disease-free images relies on manual annotation (essentially, image-level healthy/diseased labels). With disease-free sample ratio in the training set ranging from \\(100\\%\\) to \\(50\\%\\), we have compared the robustness of SQUID with three competitive baselines (CutPaste [40], PANDA [56] and M-KD [60]). Figure 10 remarks that our proposed memory queue can tolerate the disease/healthy training ratio up to \\(50\\%\\) by automatically omitting minority anatomical patterns. In contrast, CutPaste drops significantly as the percentage of normal images decreases; PANDA and M-KD can maintain the performance due to the use of pre-trained features. Interestingly, M-KD with mixed data even outperforms its vanilla training setting, although with considerable fluctuations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.562, + 0.619, + 0.577 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.893, + 0.8 + ], + "angle": 0, + "content": "We present SQUID for unsupervised anomaly detection from radiography images. Qualitatively, we show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, SQUID can identify anomalies accurately. Quantitatively, SQUID is superior to predominant methods by over 5 points AUC on the ZhangLab dataset and 10 points AUC on the Stanford CheXpert dataset. The outstanding results are attributable to our observation: Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. We synthesized the DigitAnatomy dataset to resemble key attributes of chest anatomy in radiography images for prompting future method development." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.806, + 0.894, + 0.898 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. We appreciate the constructive suggestions from Yingda Xia, Yixiao Zhang, Jessica Han, Yingwei Li, Bowen Li, Huiyu Wang, Adam Kortylewski, and Sonomi Oyagi." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23897" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Samet Akcay, Amir Atapour-Abarghouei, and Toby P Breckon. Ganomaly: Semi-supervised anomaly detection via adversarial training. In Asian conference on computer vision, pages 622–637. Springer, 2018. 2, 6, 7, 14, 15" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Varghese Alex, Mohammed Safwan KP, Sai Saketh Chennamsetty, and Ganapathy Krishnamurthi. Generative adversarial networks for brain lesion detection. 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Springer, 2011. 2" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23901" + } + ] +] \ No newline at end of file diff --git a/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/c1d458f7-f8ad-480d-9ab9-60ca7bc1a759_origin.pdf b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/c1d458f7-f8ad-480d-9ab9-60ca7bc1a759_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a4c52897fca10a2bbaff58cebfb65ef5c102ad4a --- /dev/null +++ b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/c1d458f7-f8ad-480d-9ab9-60ca7bc1a759_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3d546a2e0301020f8311a5d2af748e47f772c4fc7741af19023dfa4ba9821461 +size 8496115 diff --git a/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/full.md b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c6e4927e8970b173387bda73364ca33ee1f15548 --- /dev/null +++ b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/full.md @@ -0,0 +1,357 @@ +# SQUID: Deep Feature In-Painting for Unsupervised Anomaly Detection + +Tiang Xiang Yixiao Zhang Yongyi Lu Alan L. Yuille Chaoyi Zhang Weidong Cai Zongwei Zhou\* + +1University of Sydney 2Johns Hopkins University + +GitHub: https://github.com/tiangexiang/SQUID + +# Abstract + +Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. To exploit this structured information, we propose the use of Space-aware Memory Queues for In-painting and Detecting anomalies from radiography images (abbreviated as SQUID). We show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, it can identify anomalies (unseen/modified patterns) in the image. SQUID surpasses 13 state-of-the-art methods in unsupervised anomaly detection by at least 5 points on two chest X-ray benchmark datasets measured by the Area Under the Curve (AUC). Additionally, we have created a new dataset (DigitAnatomy), which synthesizes the spatial correlation and consistent shape in chest anatomy. We hope DigitAnatomy can prompt the development, evaluation, and interpretability of anomaly detection methods. + +# 1. Introduction + +Vision tasks in photographic imaging and radiography imaging are different. For example, when identifying objects in photographic images, we assume translation invariance—a cat is a cat no matter if it appears on the left or right of the image. In radiography imaging, on the other hand, the relative location and orientation of a structure are important characteristics that allow the identification of normal anatomy and pathological conditions [20,83]. Since radiography imaging protocols assess patients in a fairly consistent orientation, the generated images have great similarity across various patients, equipment manufacturers, and facility locations (see examples in Figure 1d). The consistent and recurrent anatomy facilitates the analysis of numerous critical problems and should be considered a significant advantage for radiography imaging [85]. Several investiga + +![](images/205d91ce4f2c6f59d8b7f416d7fac0a80d3a9a02a87b3d6daec91504dcff3f5f.jpg) + +![](images/2f30b215ba4cfc47e30e9009f87663287a0d59840596d6c61a9d1943628ef04e.jpg) +Normal +(a) Crowded Scenes + +![](images/81ccd7120ced9ef690bf3af4a31c795bc5debffb6569fdaa472d44ad779ab5e8.jpg) +Abnormal + +![](images/7534d595057c1871b069fba406728c03bdf10cd7f196b012da3b1b670be58864.jpg) + +![](images/c74328b1521685c56f574820832d28069ee5f2bdae9d401e0eb37801cebe753f.jpg) + +![](images/645ecb157e543a92c01f82fc834009755f777baa336230ca73096505d07e6932.jpg) + +![](images/00637016774841bc7bcc50cb996faa06da59b1747a84c60730e404530ce0a919.jpg) + +![](images/6606254a668178a46dcf81215df3f52cf08b54e5cc1aaad213ab87ff10bbc879.jpg) +(c) Digit Anatomy + +![](images/b64d7cac19c94ec579db7e0c6cc5743fd18a6e666b82b745b6bceb3be192a428.jpg) + +![](images/40eff3f564226e1bc174a768c29c5b275130749493ebc39871a2f8df09af046b.jpg) + +![](images/d44ced5fd33b78f239660a6286f89f0a0450d3edca0f1f3325f6618916035db2.jpg) + +![](images/c87854999d7b394b8d8100cba8dc83733948e886350c07f55420168cce71b40d.jpg) + +![](images/f60dd840d0aa4f33c7e2e0a709e8bd1ef5b4fbae44c31de235e42d0f7437515b.jpg) +Normal +Textures + +![](images/ea362f90c650fd05816f83b11986818801f9f9ad53c24dd62f7ebe1e9380b450.jpg) + +![](images/44ea51ec0b085119d68c3db7b4af304963858bef932a8f6337780a0e8c74bf31.jpg) + +![](images/dc83a0fca15980ff0808f2e92b9da92388434952f42d849bc0853e65b278cba2.jpg) + +![](images/56b9d251f375913a6c003777014d24f7050b82af3d555a79cd0d146874769ce0.jpg) + +![](images/fe757925fc92338a2fbf7cc75220dc8762403d439d8d8d1064358902d832af41.jpg) + +![](images/e4ad243b2f38c30f78a908531b7dd5ffcdb93bf450fa031453dfe67fe2a025be.jpg) + +![](images/7b1915e5a3b28ddbf0ec2449d647272fa32b694076aae4cf8d000f2fce714166.jpg) +(d) Chest Anatomy +Figure 1. Anomaly detection in radiography images can be both easier and harder than in photographic images. It is easier because radiography images are spatially structured due to consistent imaging protocols. It is harder because anomalies in radiography images are subtle and require medical expertise to annotate. + +![](images/dfa87e794c8533597b5b8c7674fd6961bb3c88ba02ebac891b6805470ec1a315.jpg) + +tions have demonstrated the value of this prior knowledge in enhancing Deep Nets' performance by adding location features, modifying objective functions, and constraining coordinates relative to landmarks in images [3,47,49,69,86]. Our work seeks to answer this critical question: Can we exploit consistent anatomical patterns and their spatial information to strengthen Deep Nets' detection of anomalies from radiography images without manual annotation? + +Unsupervised anomaly detection only uses healthy images for model training and requires no other annotations such as disease diagnosis or localization [5]. As many as $80\%$ of clinical errors occur when the radiologist misses the abnormality in the first place [7]. The impact of anomaly detection is to reduce that $80\%$ by clearly pointing out to radiologists that there exists a suspicious lesion and then having them look at the scan in depth. Unlike previous anomaly detection methods, we formulate the task as an in-painting task to exploit the anatomical consistency in appearance, position, and layout across radiography images. Specif + +ically, we propose _Space-aware Memory Queues for Inpainting and Detecting anomalies from radiography images (abbreviated as _SQUID). During training, our model can dynamically maintain a visual pattern dictionary by taxonomizing recurrent anatomical patterns based on their spatial locations. Due to the consistency in anatomy, the same body region across healthy images is expected to express similar visual patterns, which makes the total number of unique patterns manageable. During inference, since anomaly patterns do not exist in the dictionary, the generated radiography image is expected to be unrealistic if an anomaly is present. As a result, the model can identify the anomaly by discriminating the quality of the in-painting task. The success of anomaly detection has two basic assumptions [89]: first, anomalies only occur rarely in the data; second, anomalies differ from the normal patterns significantly. + +We have conducted experiments on two large-scale, publicly available radiography imaging datasets. Our SQUID is significantly superior to predominant methods in unsupervised anomaly detection by over 5 points on the ZhangLab dataset [32]; remarkably, we have demonstrated a 10-point improvement over 13 recent unsupervised anomaly detection methods on the Stanford CheXpert dataset [29]. In addition, we have created a new dataset (DigitAnatomy) to elucidate spatial correlation and consistent shape of the chest anatomy in radiography (see Figure 1c). DigitAnatomy is dedicated to easing the development, evaluation, and interpretability of anomaly detection methods. The qualitative visualization clearly shows the superiority of our SQUID over the current state-of-the-art methods. + +In summary, our contributions include: (I) the best performing unsupervised anomaly detection method for chest radiography imaging; (II) a synthetic dataset to promote anomaly detection research; (III) SQUID overcomes limitations in dominant unsupervised anomaly detection methods [1, 17, 35, 61, 82] by inventing Space-aware Memory Queue (§3.2), and Feature-level In-painting (§3.3). + +# 2. Related Work + +Anomaly detection in natural imaging. Anomaly detection is the task of identifying rare events that deviate from the distribution of normal data [52]. Early attempts include one-class SVM [64], dictionary learning [81], and sparse coding [11]. Due to the lack of sufficient samples of anomalies, later works typically formulate anomaly detection as an unsupervised learning problem [13, 26, 27, 37, 38, 42, 57, 67, 90]. These can be roughly categorized into reconstruction-based and density-based methods. Reconstruction-based methods train a model (e.g. Auto-Encoder) to recover the original inputs [9, 66, 71, 77, 87, 88] and identify anomalies by analyzing reconstruction errors. Density-based methods predict anomalies by estimating the normal data distribution (e.g. via VAEs [35] or GANs [2, 61, 62]). However, + +the learned distribution for normal images by these methods cannot explain the possible abnormalities. In this paper, we address these limitations by maintaining a visual pattern memory from homogeneous medical images. Several other previous works investigated the use of image inpainting for anomaly detection, i.e. parts of the input image are masked out, and the model is trained to recover the missing parts in a self-supervised way [22, 40, 51, 56, 79]. There are also plenty of works on detecting anomalies in video sequences [15, 45, 46]. Bergmann et al. [6] and Salehi et al. [59] proposed similar student-teacher networks, whereas our method utilizes such a structure to distillate input-aware features only, and the teacher network is completely disabled during inference. + +Anomaly detection in medical imaging. Anomaly detection in the medical domain is usually approached on a per-pathology basis. Supervised learning based methods [5, 44, 63] are commonly adopted to detect specific types of abnormalities, such as lesions [91], pathologies [33], tumors [4], and nodules [84]. Recent unsupervised methods have been proposed to detect anomalies in general [5, 25, 66]. With the help of GANs, anomaly detection can be achieved with weak annotations. In AnoGAN [62], the discriminator was heavily over-fitted to the normal image distribution to detect the anomaly. Subsequently, f-AnoGAN [61] was proposed to improve computational efficiency. Marimont et al. [50] designed an auto-decoder network to fit the distribution of normal images. The spatial coordinates and anomaly probabilities are mapped over a proxy for different tissue types. Han et al. [21] proposed a two-step GAN-based framework for detecting anomalies in MRI slices as well. However, their method relies on a voxel-wise representation for the 3D MRI sequences, which is impossible in our task. Most recently, a hybrid framework SALAD [82] was proposed that combines GAN with self-supervised techniques. Normal images are first augmented to carry the forged anomaly through pixel corruption and pixel shuffling. The fake abnormal images, along with the original normal ones, are fed to the GAN for learning more robust feature representations. However, these approaches demand strong prior knowledge and assumptions about the anomaly type to make the augmentation effective. Differing from photographic images, radiography imaging protocols produce images with consistent anatomical patterns, which are much more challenging to detect due to subtle imaging clues and overlapping anatomic structures (Figure 1). Unlike most existing works, we present a novel method that explicitly harnesses the radiography images' properties, dramatically improving the performance in anomaly detection from radiography images. + +Memory networks. Incorporating memory modules into neural networks has been demonstrated to be effective for many tasks [8, 16, 31, 36, 39]. Adopting Memory Matrix + +![](images/90fa828be64669b491d7387f8a1304a0890d7e91f8a5071590df1889b5f40d3c.jpg) +Figure 2. SQUID. We divide an input image into $N \times N$ non-overlapping patches and feed them into the encoder for feature extraction. Two generators will be trained to reconstruct the original image. Along with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically via a novel Memory Queue (§3.2); The teacher generator directly uses the features extracted by the encoder; the student generator uses the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm. We employ a discriminator to assess whether the image reconstructed by the student generator is real or fake. Once trained, it can also be used to detect anomalies in test images (§3.4). + +for unsupervised anomaly detection was first proposed in MemAE [17]. In addition to auto-encoding (AE), an extra Memory Matrix was introduced between the encoder and the decoder to capture normal feature patterns during training. The matrix is jointly optimized along with the AE and hence learns an essential basis to be able to assemble normal patterns. Based on this paradigm, Park et al. [53] introduced a non-learnable memory module that can be updated with inputs. Note that although our proposed Memory Queue also does not require any gradients, our method differs significantly in its usage purpose and updating rules. Considering the extra memory usage in existing methods, Lv et al. [48] proposed a dynamic prototype unit that encodes normal dynamics on the fly, while consuming little additional memory. In this paper, we overcome the limitations of the Memory Matrix and propose an effective yet efficient Memory Queue for unsupervised anomaly detection in radiography images. + +# 3. SQUID + +# 3.1. Overview (Figure 2) + +(1) Feature extraction. We divide the input image into $N \times N$ non-overlapping patches and feed them into an encoder for feature extraction. The extracted features will be used for image reconstruction. Practically, the encoder can be any backbone architectures [14,70]; we adopt basic Convolutions and Pooling layers in this work for simplicity. +(2) Image reconstruction. We introduce teacher and student generators to reconstruct the original image. Along + +with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically as a Memory Queue (§3.2). Specifically, the teacher generator directly reconstructs the image using the features extracted by the encoder (essentially an auto-encoder [58]). The student generator, on the other hand, using the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm [28] at all of the up-sampling levels. The objective of the student generator is to reconstruct a normal image from the augmented features, which will then be used for anomaly discrimination (§3.4); while the teacher generator serves as a regularizer that prevents the student from constantly generating the same normal image. + +(3) Anomaly discrimination. Following the adversarial learning [61, 62], we employ a discriminator to assess whether the generated image is real or fake. Only the student generator will receive the gradient derived from the discriminator. The two generators and the discriminator are competing against each other until they converge to an equilibrium. Once trained, the discriminator can be used to detect anomalies in test images (§3.4). + +# 3.2. Inventing Memory Queue as Dictionary + +Motivation. The Memory Matrix was introduced by Gong et al. [17] and has since been widely adopted in unsupervised anomaly detection [18, 45, 78]. To forge a "normal" appearance, features are augmented by weighted averaging + +![](images/7a80bc98057cd58a0942a47bc621b2eae3f0333c7f1a2bea0860882901b45111.jpg) +Memory Matrix +Similarity + +![](images/696e901fdc12e3aa14de9ac7abb83daca7daa1866b4adf1d9f2f0462864d6b77.jpg) +Space-aware Memory +Figure 3. Space-aware memory. For unique encoding of location information, we restrict each patch to be only accessible by a non-overlapping region in the memory. + +the similar patterns in Memory Matrix. This augmentation is, however, applied to the features extracted from the whole image, discarding the spatial information in images. Therefore, the Memory Matrix in its current form cannot perceive the anatomical consistency as in radiography images. + +Space-aware memory. To harness the spatial information, we pass the divided small patches, instead of the whole image, into the model. These patches are associated with unique location identifiers of the original image. We seek to build the relationship between the patch location and memory region, by restricting the search space in Memory Matrix to the patch-corresponded non-overlapping segments only. That is, a patch at a particular location can only access a corresponding segment in the whole Memory Matrix (illustrated in Figure 3). We refer to this new strategy as "space-aware memory" because it enables explicit encoding of the spatial information into Memory Matrix. Space-aware memory can also accelerate the augmentation speed compared with [17] as it no longer goes through the entire Memory Matrix to assemble similar features. + +Memory queue. In learning-based Memory Matrix [17], "normal patterns" are forged by combining learned basis in the matrix. However, there is always a distribution discrepancy between the basic combinations and the actual image features. This disparity makes it hard for the subsequent image generation. To address this issue, we propose a Memory Queue to store real image features during model training, therefore presenting an identical distribution to the image features. Specifically, it directly copies previously seen features into a queue structure during training2. Once trained, Memory Queue can be used as a dictionary of normal anatomical patterns. In Figure 4, we show t-SNE visualizations to validate that the learned basis in Memory Matrix (blue dots) distributes differently from the actual image features of the training set (gray dots). In contrast, the stored image features in our Memory Queue (red dots) are + +![](images/c7c791b1ffeb49a78dbfe5fabb08a0d44a03edce9edf7a08bcc4e12fd03e455d.jpg) +Figure 4. t-SNE visualizations of patterns in Memory Matrix, Memory Queue, and patch features of the training samples [73]. Patterns in the Memory Matrix are far away from the distribution of patch features, while patterns in the Memory Queue (as copies of previously seen features) share a similar distribution. + +in an identical distribution to the actual ones. + +Gumbel shrinkage. Controlling the number of activated patterns in the memory has proven to be advantageous for anomaly detection [17, 19]. However, setting a hard shrinkage threshold fails to adapt to cases where no suitable entries can be found in the memory. One natural workaround is to activate the top- $k$ similar patterns in the memory. However, this strategy restricts the gradient flow to only the top- $k$ memory entries, while the rest inactivated ones could not receive any gradients and be updated as expected. To extend gradients to all patterns in the memory, inspired by Jang [30], we present a Gumbel Shrinkage schema: + +$$ +\mathbf {w} ^ {\prime} = \operatorname {s g} (\operatorname {h s} (\mathbf {w}, \operatorname {t o p k} (\mathbf {w})) - \phi (\mathbf {w})) + \phi (\mathbf {w}), \tag {1} +$$ + +where $\mathbf{w}$ denotes the similarity between the image features and entries in Memory, $sg(\cdot)$ the stop-gradient operation, $\mathrm{hs}(\cdot ,t)$ the hard shrinkage operator with threshold $t$ , and $\phi (\cdot)$ the Softmax function. In the forward pass, Gumbel Shrinkage ensures the combination of the top- $k$ most similar entries in the memory; During the back-propagation, Gumbel Shrinkage essentially functions as Softmax. We apply Gumbel Shrinkage to both Memory Queue and Memory Matrix in our framework. + +# 3.3. Formulating Anomaly Detection as In-painting + +Motivation. Image in-painting [41, 54] was initially proposed to recover corrupted image regions with neighboring context. Following the above intuition, we propose to achieve anomaly detection via in-painting anomalous radiography patterns into healthy ones. When in-painting pixels in the image space, recovered regions have been usually seen to associate with boundary artifacts, particularly when using Deep Nets [43]. These undesired artifacts are responsible for numerous false positives when formulating anomaly detection as a pixel-level in-painting task [66, 87]. To alleviate this issue, we achieve the in-painting task at the feature level instead. Latent features are better invariant to pixel-level noise, rotation, and translation, therefore are more suitable for subsequent anomaly detection. + +![](images/2ca2e402bfb3f8c9a3c7cf7523307b4490abcb7e84887935739b7e8f3355cc46.jpg) +(a) Augment $\mathcal{F}$ to $\mathcal{N}$ + +![](images/70f20ab0d6930d05ba9a2a31bb5c6a32e560d47f3da42e914af31c43ca45e6b0.jpg) +(b) Aggregate $\mathcal{F}$ and $\mathcal{N}$ + +![](images/3e3a5cb10861939d12f19c15632d2581ba234cfcdd8ba6365acf13502ee1b7ea.jpg) +(c) Copy $\mathcal{F}$ to Memory Queue +Figure 5. Three-step workflow of our in-painting block. (a) Each non-overlapping patch feature $\mathcal{F}$ is queried to a unique region in Memory Queue, and the most similar items are assembled to $\mathcal{N}$ . (b) Each center patch feature $\mathcal{F}$ and its eight neighbors $\mathcal{N}$ are used as query and key/value, respectively, to a Transformer layer for in-painting. (c) Each Memory Queue region copies its corresponding patch features $\mathcal{F}$ into the memory by maintaining a pointer. Note that this step is only performed during training. + +In-painting block. We integrate our Memory Queue inside a novel in-painting block to perform feature-space in-painting. The block starts with a Memory Queue that augments $w \times h$ non-overlapping patch features $\mathcal{F}_{\{(1,1), \dots, (w,h)\}}$ into their most similar "normal" patterns $\mathcal{N}_{\{(1,1), \dots, (w,h)\}}$ (Figure 5a). Since $\mathcal{N}$ is assembled by features extracted from previous training data, $\mathcal{N}$ is not subject to the current input image. To recap the characteristics of the input image, we aggregate both patch features $\mathcal{F}$ and their augmented features $\mathcal{N}$ using a transformer block [74]. In details, for each patch $\mathcal{F}_{i,j}$ , its spatially adjacent eight augmented ones $\mathcal{N}_{\{(i-1,j-1), \dots, (i+1,j+1)\}}$ are used as conditions to refine $\mathcal{F}_{i,j}$ (Figure 5b). The query token of the transformer block is flattened $\mathcal{F}_{(i,j)} \in \mathcal{R}^{1 \times *}$ and key/value tokens are $\mathcal{N}_{\{(i-1,j-1), \dots, (i+1,j+1)\}} \in \mathcal{R}^{8 \times *}$ . At the start and the end of our in-painting block, we apply an extra pair of point-wise convolutions $(1 \times 1$ convolutional kernel) [24]. + +Masked shortcut. We employ a shortcut within the inpainting block to better aggregate features and ease optimization. Our empirical study shows that a direct residual connection downgrades the effectiveness of the in-painting block (Appendix B). Inspired by Xiang et al. [76], we utilize a random binary mask to gate shortcut features during training (Figure 5b). As such, given the input patch features $\mathcal{F}$ , the output of the in-painting block is obtained by: + +$$ +\mathcal {F} ^ {\prime} = (1 - \delta) \cdot \mathcal {F} + \delta \cdot \text {i n p a i n t} (\mathcal {F}), \tag {2} +$$ + +where $\mathrm{inpaint}(\cdot)$ is the designed in-painting block, $\delta \sim$ Bernoulli $(\rho)$ is a binary variable with $\rho$ the gating probability. After obtaining $\mathcal{F}'$ at each training step, the originally $\mathcal{F}$ are then copied to update the memory (Figure 5c). During inference, we disable the shortcut completely such that $\mathcal{F}' = \mathrm{inpaint}(\mathcal{F})$ for deterministic predictions. + +# 3.4. Anomaly Discrimination + +Our discriminator can detect anomalies by assessing the quality of the reconstructions—normal if realistic; abnormal otherwise. It is because the generator was trained on + +normal images, so Memory Queues only store normal patterns. During inference, since abnormal patterns were never present in Memory Queues, the reconstructed image is expected to appear unrealistic. + +Our in-painting block focuses on augmenting any patch feature (either normal or abnormal) into similar "normal" features. The student generator then reconstructs a "normal" image based on the "normal" features. The teacher generator is used to prevent the student from generating the same image regardless of inputs. Once trained, the semantic (rather than pixel-level) difference between the input and the student generator's reconstructed image is expected to be small if normal and big otherwise. We, therefore, delegate the optimized discriminator network for alerting anomalies perceptually. For better clarification, we note the encoder, teacher generator, student generator, and discriminator as $\mathbf{E}$ , $\mathbf{G}_{\mathrm{t}}$ , $\mathbf{G}_{\mathrm{s}}$ , and $\mathbf{D}$ . An anomaly score $A$ can be computed through: $A = \phi \left( \frac{\mathbf{D}(\mathbf{G}_{\mathrm{s}}(\mathbf{E}(\mathbf{I})) - \mu}{\sigma} \right)$ , where $\phi (\cdot)$ is the Sigmoid function, $\mu$ and $\sigma$ are the mean and standard deviation of anomaly scores calculated on training samples. + +# 3.5. Loss Function + +SQUID is optimized by five loss functions. The mean square error (MSE) between input and reconstructed images is used for both teacher and student generators. Concretely, $\mathcal{L}_{\mathrm{t}} = (\mathbf{I} - \mathbf{G}_{\mathrm{t}}(\mathbf{E}(\mathbf{I}))^{2}$ and $\mathcal{L}_{\mathrm{s}} = (\mathbf{I} - \mathbf{G}_{\mathrm{s}}(\mathbf{E}(\mathbf{I})))^{2}$ for the teacher and student generators, respectively, where $\mathbf{I}$ denotes the input image. Following the knowledge distillation paradigm, we apply a distance constraint between the teacher and student generators to all levels of features: $\mathcal{L}_{\mathrm{dist}} = \sum_{i=1}^{l} (\mathcal{F}_{\mathrm{t}}^{i} - \mathcal{F}_{\mathrm{s}}^{i})^{2}$ , where $l$ is the level of features used for knowledge distillation, $\mathcal{F}_{\mathrm{t}}$ and $\mathcal{F}_{\mathrm{s}}$ are the intermediate features in the teacher and student generators, respectively. In addition, we employ an adversarial loss (similar to DCGAN [55]) to improve the quality of the image generated by the student generator. Specifically, the following equation is minimized: $\mathcal{L}_{\mathrm{gen}} = \log(1 - \mathbf{D}(\mathbf{G}_{\mathrm{s}}(\mathbf{E}(\mathbf{I}))))$ . The discriminator seeks to maximize the average of the proba + +![](images/ab12043032b7c0df511708b290d28466efd4de2775e427cce995851b9ac9e3ee.jpg) +Input SQUID f-AnoGAN Ganomly MemAE +Figure 6. Reconstruction results on DigitAnatomy. Our feature-level in-painting is more robust to amplified noise and pixel variance than the existing pixel-level in-painting methods. More visualization can be found in Appendix D. + +bility for real images and the inverted probability for fake images: $\mathcal{L}_{\mathrm{dis}} = \log (\mathbf{D}(\mathbf{I})) + \log (1 - \mathbf{D}(\mathbf{G}_s(\mathbf{E}(\mathbf{I}))))$ . In summary, SQUID is trained to minimize the generative loss terms $(\lambda_{\mathrm{t}}\mathcal{L}_{\mathrm{t}} + \lambda_{\mathrm{s}}\mathcal{L}_{\mathrm{s}} + \lambda_{\mathrm{dist}}\mathcal{L}_{\mathrm{dist}} + \lambda_{\mathrm{gen}}\mathcal{L}_{\mathrm{gen}})$ and to maximize the discriminative loss term $(\lambda_{\mathrm{dis}}\mathcal{L}_{\mathrm{dis}})$ + +# 4. Experiments + +# 4.1. New Benchmark + +DigitAnatomy. We have created a synthetic dataset to verify our main idea, wherein the human anatomy is translated into Arabic digits one to nine in an in-grid placement (see examples in Figure 1 and Figure 6). The images containing digits in the correct order are considered "normal"; otherwise, they are considered "abnormal". The types of simulated abnormalities include missing, misordered, flipped, and zero digit(s). DigitAnatomy is particularly advantageous for radiography imaging for three reasons. First, it simulates two unique properties of radiography images, i.e. spatial correlation and consistent shape. Second, annotating radiography images demands specialized expertise, but digits are easier for problem debugging. Third, the ground truth of the simulated anomaly is readily accessible in DigitAnatomy, whereas it is hard to collect sufficient examples for each abnormal type in radiography images. The pseudocode for creating DigitAnatomy is in Appendix C. + +# 4.2. Public Benchmarks + +ZhangLab Chest X-ray [32]. This dataset contains healthy and pneumonia (as anomaly) images, officially split into training and testing sets. The training set consists of 1,349 + +Table 1. Benchmark results on the test sets of the two datasets. + +
ZhangLabRef & YearAUC (%)Acc (%)F1 (%)
Auto-Encoder-59.963.477.2
VAE [35]Arxiv'1361.864.077.4
Ganomaly [1]ACCV'1878.070.079.0
f-AnoGAN [61]MIA'1975.574.081.0
MemAE [17]ICCV'1977.8±1.456.5±1.182.6±0.9
MNAD [53]CVPR'2077.3±0.973.6±0.779.3±1.1
SALAD [82]TMI'2182.7±0.875.9±0.982.1±0.3
CutPaste [40]CVPR'2173.6±3.964.0±6.572.3±8.9
PANDA [56]CVPR'2165.7±1.365.4±1.966.3±1.2
M-KD [59]CVPR'2174.1±2.669.1±0.262.3±8.4
IF 2D [50]MICCAI'2181.0±2.876.4±0.282.2±2.7
PaDiM [12]ICPR'2171.4±3.472.9±2.480.7±1.2
IGD [10]AAAI'2273.4±1.974.0±2.280.9±1.3
SQUID-87.6±1.580.3±1.384.7±0.8
CheXpertRef & YearAUC (%)Acc (%)F1 (%)
Ganomaly [1]ACCV'1868.9±1.465.7±0.265.1±1.9
f-AnoGAN [61]MIA'1965.8±3.363.7±1.859.4±3.8
MemAE [17]ICCV'1954.3±4.055.6±1.453.3±7.0
CutPaste [40]CVPR'2165.5±2.262.7±2.060.3±4.6
PANDA [56]CVPR'2168.6±0.966.4±2.865.3±1.5
M-KD [59]CVPR'2169.8±1.666.0±2.563.6±5.7
SQUID-78.1±5.171.9±3.875.9±5.7
+ +normal and 3,883 abnormal images; the testing set has 234 normal and 390 abnormal images. We randomly separate 200 images (100 normal and 100 abnormal) from the training set as the validation set for hyper-parameter tuning. We resized all the images to $128 \times 128$ . + +Stanford CheXpert [29]. We conducted evaluations on the front-view PA images in the CheXpert dataset, which account for a total of 12 different anomalies. In all front-view PA images, there are 5,249 normal and 23,671 abnormal images for training; 250 normal and 250 abnormal images (with at least 10 images per disease type) from the training set were used for testing. We used the same hyperparameters found in the ZhangLab experiments. + +# 4.3. Baselines and Metrics + +We considered a total number of 13 major baselines for direct comparison: Auto-Encoder, VAE [35]—the classic UAD methods; Ganomaly [1], f-AnoGAN [61], IF [50], SALAD [82]—the current state of the arts for medical imaging; and MemAE [17], CutPaste [40], M-KD [60], PANDA [56], PaDiM [12], IGD [10]—the most recent UAD methods. We evaluated performance using standard metrics: Receiver Operating Characteristic (ROC) curve, Area Under the ROC Curve (AUC), Accuracy (Acc), and F1-score (F1). Unless explicitly specified, we trained all models from scratch for at least three times independently. + +# 4.4. Implementation Details + +We utilized common data augmentation strategies such as random translation within the $[-0.05, + 0.05]$ range and a random scaling of [0.95, 1.05]. The Adam [34] optimizer was used with a batch size of 16 and a weight decay of $1e-5$ . The learning rate was initially set to $1e-4$ for both the + +![](images/ad0e095a5b4e480aed8e5529570a545981c947c81a0bfc8cb54dbeb8cf22bc8b.jpg) +(a) ZhangLab Chest X-ray + +![](images/a2f96c851ff4585b54ca76f11e5e1f16a15ba1ff48f1d68a1aca71a544c7a464.jpg) +(b) Stanford CheXpert +Figure 7. ROC curves comparison on the two datasets. + +generator and the discriminator and then decayed to $2e - 5$ in 1000 epochs following the cosine annealing scheduler. The discriminator is trained at every iteration, while the generator is trained every two iterations. We set loss weights as $\lambda_{\mathrm{t}} = 0.01$ , $\lambda_{\mathrm{s}} = 10$ , $\lambda_{\mathrm{dist}} = 0.001$ , $\lambda_{\mathrm{gen}} = 0.005$ , and $\lambda_{\mathrm{dis}} = 0.005$ . We divide the input images in $2\times 2$ non-overlapping patches, fix the shortcut mask probability at $\rho = 95\%$ , and activate only the top 5 similar patterns in the Gumbel Shrinkage. The impact of these hyper-parameters is studied in §5.3. The architectures of our generators and discriminator are detailed in Appendix A. + +# 5. Results + +# 5.1. Interpreting SQUID on DigitAnatomy + +Figure 6 presents qualitative results on DigitAnatomy to examine the capability of image reconstruction and to interpret the mistakes made by existing methods [1, 17, 61]. We deliberately inject anomalies (e.g. novel, misordered, missing digits) into normal images (highlighted in light blue) and test if the model can reconstruct their normal counterparts. To raise the task difficulty, we also assess the reconstruction quality from a blank image (as an extreme case). In general, the images reconstructed by our SQUID carry more meaningful and indicative information than other baseline methods. It is mainly attributed to our space-aware memory, with which the resulting dictionary is associated with unique patterns as well as their spatial information. Once an anomaly arises (e.g. missing digit), the in-painting block will augment the abnormal feature to its normal counterpart by assembling top- $k$ most similar patterns from the dictionary. Other methods, however, do not possess this ability, so they reconstruct defective images. For instance, GAN-based methods (f-AnoGAN and Ganomly) tend to reconstruct an exemplar image averaged from the training examples. MemAE performs relatively better due to its Memory Matrix, but it does not work well for the anomaly of missing digits and completely fails on the extreme anomaly attack. + +![](images/3bb0486a2fa9b461c57ac7498adda6a57df77c832e6bef77f07b07d855d11b10.jpg) +Figure 8. Reconstruction results of SQUID on the two datasets, associated with the corresponding anomaly scores (defined in §3.4). A larger score indicates a higher probability of being abnormal. More visualization can be found in Appendix D. + +![](images/ce8e6af5e3ef78038d1ceddf6d7bb2172985d84a278bb9a1e72f0bb842535c4c.jpg) + +# 5.2. Benchmarking SQUID on Chest Radiography + +Our SQUID was mainly evaluated on two large-scale benchmarks: ZhangLab Chest X-ray and Stanford CheXpert and compared with a wide range of state-of-the-art counterparts. According to Table 1, SQUID achieves the most promising result on all metrics for both datasets. Specifically, SQUID outperforms the runner-up counterparts by at least $5\%$ in AUC, $5\%$ in Accuracy. The highest F1 scores SQUID achieved, along with the ROC curves shown in Figure 7, demonstrate that our method yields the best trade-off between sensitivity and specificity. Overall, the significant improvements observed with SQUID proved the effectiveness of our proposed techniques in this work. In Figure 8, we visualize the reconstruction results of SQUID on exemplary normal and abnormal images in the two datasets. For normal cases, SQUID can easily find a similar match in Memory Queue, achieving the reconstruction smoothly. For abnormal cases, the contradiction will arise by imposing forged normal patterns into the abnormal features. In this way, the generated images will vary significantly from the input, which will then be captured by the discriminator. We plot the heatmap of the discriminator (using Grad-CAM [65]) to indicate the most likely regions to appear anomalous. As a result, the reconstructed healthy images yield much lower anomaly scores than the diseased ones, validating the effectiveness of SQUID. + +Limitation. We found SQUID in its current form, is not able to localize anomalies at the pixel level precisely. It is understandable because our SQUID is an unsupervised method, requiring zero manual annotation for normal/abnormal images, unlike [60, 68, 72, 75, 80]. Those methods that compute pixel-level residuals for anomaly detection suffer from amplified noise in the input and reconstructed output. Our in-painting strategy, however, is performed at the feature level and is more robust to pixel-level variance. + +# 5.3. Ablating Key Properties in SQUID + +Component study. We examine the impact of components in SQUID by taking each one of them out of the entire + +Table 2. Performance benefits from all the components in SQUID. + +
MethodAUC (%)Acc (%)F1 (%)
w/o Space-aware Memory77.6±0.575.5±0.582.5±0.6
w/o In-painting Block80.9±2.175.8±1.581.6±1.3
w/o Gumbel Shrinkage81.1±0.977.6±0.981.3±0.8
w/o Knowledge Distillation81.2±0.875.2±0.781.3±0.8
w/o Stop Gradient81.7±4.376.7±2.882.5±1.6
w/o Memory Queue82.5±1.178.6±0.981.7±1.1
w/o Masked Shortcuts82.5±1.376.4±0.882.3±1.1
w/o Decoder Memory82.9±1.277.4±1.181.2±0.5
Full SQUID87.6±1.580.3±1.384.7±0.8
+ +![](images/37f5c8885ba1eb2a0012385273bc7d51195e38ead1473d3cc5002fb8e2148c2e.jpg) +Figure 9. Hyper-parameter ablations. + +framework. Table 2 shows that each component accounts for at least $5\%$ performance gain. The space-aware memory $(+10.0\%)$ and in-painting block $(+6.7\%)$ are the top 2 most significant contributors, which underline our motivation and justification of the method development ( $\S 3.2$ and $\S 3.3$ ). Although replacing Memory Queue with Memory Matrix could maintain a decent result (only dropped $5.1\%$ ), our Memory Queue presents a more trustworthy recovery of "normal" patterns in the image than Memory Matrix (MemAE [17]), evidenced by Figure 6. + +Hyper-parameter robustness. After selecting the best hyper-parameters on the validation set, we here report the inference results on the testing set to study the robustness of different hyper-parameters in Figure 9. When input images are divided into a single patch, space-aware settings are not triggered, therefore yielding the worst performance. Although the spatial structures are relatively stable in most chest radiography, certain deviations can still be observed. Therefore, with small patches, object parts in one patch can easily appear in adjacent patches and be misdetected as anomalies. The number of topK activations in Gumbel softmax also impacts the performances. According to the AUC vs. the number of patterns in each Memory Queue region, we found that a small number of items is sufficient to support normal pattern querying in local regions. The best result is achieved by merely 200 items per region. When the item number exceeds 500 per region, AUC scores begin to drop continuously. AUC vs. the mask probability $\rho$ was + +![](images/fad4a9bf1f9fce94045372cfa6d9fb751d67e6df6acc8a2f6b540b3bcb13654c.jpg) +Figure 10. Results of mixing normal/abnormal training samples. + +further plotted to verify that enabling a limited number of feature skips $(\rho = 95\%)$ yields the best AUC score. The effectiveness of the in-painting will severely deteriorate if more features are allowed to be skipped $(\rho < 90\%)$ . + +Disease-free training requirement? Unsupervised methods for medical anomaly detection are uncommon because the so-called UAD methods are not "unsupervised"—they must be trained on disease-free images only (e.g. [5]). In practice, cleaning up disease-free images relies on manual annotation (essentially, image-level healthy/diseased labels). With disease-free sample ratio in the training set ranging from $100\%$ to $50\%$ , we have compared the robustness of SQUID with three competitive baselines (CutPaste [40], PANDA [56] and M-KD [60]). Figure 10 remarks that our proposed memory queue can tolerate the disease/healthy training ratio up to $50\%$ by automatically omitting minority anatomical patterns. In contrast, CutPaste drops significantly as the percentage of normal images decreases; PANDA and M-KD can maintain the performance due to the use of pre-trained features. Interestingly, M-KD with mixed data even outperforms its vanilla training setting, although with considerable fluctuations. + +# 6. Conclusion + +We present SQUID for unsupervised anomaly detection from radiography images. Qualitatively, we show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, SQUID can identify anomalies accurately. Quantitatively, SQUID is superior to predominant methods by over 5 points AUC on the ZhangLab dataset and 10 points AUC on the Stanford CheXpert dataset. The outstanding results are attributable to our observation: Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. We synthesized the DigitAnatomy dataset to resemble key attributes of chest anatomy in radiography images for prompting future method development. + +Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. We appreciate the constructive suggestions from Yingda Xia, Yixiao Zhang, Jessica Han, Yingwei Li, Bowen Li, Huiyu Wang, Adam Kortylewski, and Sonomi Oyagi. + +# References + +[1] Samet Akcay, Amir Atapour-Abarghouei, and Toby P Breckon. Ganomaly: Semi-supervised anomaly detection via adversarial training. In Asian conference on computer vision, pages 622–637. 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Springer, 2011. 2 \ No newline at end of file diff --git a/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/images.zip b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4a776876b82a508f294c35397fb5016e93075612 --- /dev/null +++ b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a6dd6d6bd2ee7c1e1b71e557573c0154aff6d417236d6fc1083d02fb0fc7fa3e +size 542186 diff --git a/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/layout.json b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..42adcb17811769bf68a7d3ac99cbf8463fdb9fa3 --- /dev/null +++ b/2023/SQUID_ Deep Feature In-Painting for Unsupervised Anomaly Detection/layout.json @@ -0,0 +1,10832 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 75, + 103, + 517, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 103, + 517, + 121 + ], + "spans": [ + { + "bbox": [ + 75, + 103, + 517, + 121 + ], + "type": "text", + "content": "SQUID: Deep Feature In-Painting for Unsupervised Anomaly Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 146, + 142, + 447, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 146, + 142, + 447, + 172 + ], + "spans": [ + { + "bbox": [ + 146, + 142, + 447, + 172 + ], + "type": "text", + "content": "Tiang Xiang Yixiao Zhang Yongyi Lu Alan L. 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+ 394 + ], + "lines": [ + { + "bbox": [ + 455, + 384, + 516, + 394 + ], + "spans": [ + { + "bbox": [ + 455, + 384, + 516, + 394 + ], + "type": "text", + "content": "(d) Chest Anatomy" + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 402, + 545, + 458 + ], + "lines": [ + { + "bbox": [ + 305, + 402, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 402, + 545, + 458 + ], + "type": "text", + "content": "Figure 1. Anomaly detection in radiography images can be both easier and harder than in photographic images. It is easier because radiography images are spatially structured due to consistent imaging protocols. It is harder because anomalies in radiography images are subtle and require medical expertise to annotate." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 515, + 353, + 544, + 383 + ], + "blocks": [ + { + "bbox": [ + 515, + 353, + 544, + 383 + ], + "lines": [ + { + "bbox": [ + 515, + 353, + 544, + 383 + ], + "spans": [ + { + "bbox": [ + 515, + 353, + 544, + 383 + ], + "type": "image", + "image_path": "dfa87e794c8533597b5b8c7674fd6961bb3c88ba02ebac891b6805470ec1a315.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": "tions have demonstrated the value of this prior knowledge in enhancing Deep Nets' performance by adding location features, modifying objective functions, and constraining coordinates relative to landmarks in images [3,47,49,69,86]. Our work seeks to answer this critical question: Can we exploit consistent anatomical patterns and their spatial information to strengthen Deep Nets' detection of anomalies from radiography images without manual annotation?" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": "Unsupervised anomaly detection only uses healthy images for model training and requires no other annotations such as disease diagnosis or localization [5]. As many as " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": " of clinical errors occur when the radiologist misses the abnormality in the first place [7]. The impact of anomaly detection is to reduce that " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": " by clearly pointing out to radiologists that there exists a suspicious lesion and then having them look at the scan in depth. Unlike previous anomaly detection methods, we formulate the task as an in-painting task to exploit the anatomical consistency in appearance, position, and layout across radiography images. Specif" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 248, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 248, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 248, + 712 + ], + "type": "text", + "content": "*Corresponding author: Zongwei Zhou (zzhou82@jh.edu)" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23890" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "ically, we propose _Space-aware Memory Queues for Inpainting and Detecting anomalies from radiography images (abbreviated as _SQUID). During training, our model can dynamically maintain a visual pattern dictionary by taxonomizing recurrent anatomical patterns based on their spatial locations. Due to the consistency in anatomy, the same body region across healthy images is expected to express similar visual patterns, which makes the total number of unique patterns manageable. During inference, since anomaly patterns do not exist in the dictionary, the generated radiography image is expected to be unrealistic if an anomaly is present. As a result, the model can identify the anomaly by discriminating the quality of the in-painting task. The success of anomaly detection has two basic assumptions [89]: first, anomalies only occur rarely in the data; second, anomalies differ from the normal patterns significantly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 289, + 430 + ], + "type": "text", + "content": "We have conducted experiments on two large-scale, publicly available radiography imaging datasets. Our SQUID is significantly superior to predominant methods in unsupervised anomaly detection by over 5 points on the ZhangLab dataset [32]; remarkably, we have demonstrated a 10-point improvement over 13 recent unsupervised anomaly detection methods on the Stanford CheXpert dataset [29]. In addition, we have created a new dataset (DigitAnatomy) to elucidate spatial correlation and consistent shape of the chest anatomy in radiography (see Figure 1c). DigitAnatomy is dedicated to easing the development, evaluation, and interpretability of anomaly detection methods. The qualitative visualization clearly shows the superiority of our SQUID over the current state-of-the-art methods." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 431, + 289, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 431, + 289, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 431, + 289, + 515 + ], + "type": "text", + "content": "In summary, our contributions include: (I) the best performing unsupervised anomaly detection method for chest radiography imaging; (II) a synthetic dataset to promote anomaly detection research; (III) SQUID overcomes limitations in dominant unsupervised anomaly detection methods [1, 17, 35, 61, 82] by inventing Space-aware Memory Queue (§3.2), and Feature-level In-painting (§3.3)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 523, + 134, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 134, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 134, + 537 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "Anomaly detection in natural imaging. Anomaly detection is the task of identifying rare events that deviate from the distribution of normal data [52]. Early attempts include one-class SVM [64], dictionary learning [81], and sparse coding [11]. Due to the lack of sufficient samples of anomalies, later works typically formulate anomaly detection as an unsupervised learning problem [13, 26, 27, 37, 38, 42, 57, 67, 90]. These can be roughly categorized into reconstruction-based and density-based methods. Reconstruction-based methods train a model (e.g. Auto-Encoder) to recover the original inputs [9, 66, 71, 77, 87, 88] and identify anomalies by analyzing reconstruction errors. Density-based methods predict anomalies by estimating the normal data distribution (e.g. via VAEs [35] or GANs [2, 61, 62]). However," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "the learned distribution for normal images by these methods cannot explain the possible abnormalities. In this paper, we address these limitations by maintaining a visual pattern memory from homogeneous medical images. Several other previous works investigated the use of image inpainting for anomaly detection, i.e. parts of the input image are masked out, and the model is trained to recover the missing parts in a self-supervised way [22, 40, 51, 56, 79]. There are also plenty of works on detecting anomalies in video sequences [15, 45, 46]. Bergmann et al. [6] and Salehi et al. [59] proposed similar student-teacher networks, whereas our method utilizes such a structure to distillate input-aware features only, and the teacher network is completely disabled during inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 243, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 674 + ], + "type": "text", + "content": "Anomaly detection in medical imaging. Anomaly detection in the medical domain is usually approached on a per-pathology basis. Supervised learning based methods [5, 44, 63] are commonly adopted to detect specific types of abnormalities, such as lesions [91], pathologies [33], tumors [4], and nodules [84]. Recent unsupervised methods have been proposed to detect anomalies in general [5, 25, 66]. With the help of GANs, anomaly detection can be achieved with weak annotations. In AnoGAN [62], the discriminator was heavily over-fitted to the normal image distribution to detect the anomaly. Subsequently, f-AnoGAN [61] was proposed to improve computational efficiency. Marimont et al. [50] designed an auto-decoder network to fit the distribution of normal images. The spatial coordinates and anomaly probabilities are mapped over a proxy for different tissue types. Han et al. [21] proposed a two-step GAN-based framework for detecting anomalies in MRI slices as well. However, their method relies on a voxel-wise representation for the 3D MRI sequences, which is impossible in our task. Most recently, a hybrid framework SALAD [82] was proposed that combines GAN with self-supervised techniques. Normal images are first augmented to carry the forged anomaly through pixel corruption and pixel shuffling. The fake abnormal images, along with the original normal ones, are fed to the GAN for learning more robust feature representations. However, these approaches demand strong prior knowledge and assumptions about the anomaly type to make the augmentation effective. Differing from photographic images, radiography imaging protocols produce images with consistent anatomical patterns, which are much more challenging to detect due to subtle imaging clues and overlapping anatomic structures (Figure 1). Unlike most existing works, we present a novel method that explicitly harnesses the radiography images' properties, dramatically improving the performance in anomaly detection from radiography images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Memory networks. Incorporating memory modules into neural networks has been demonstrated to be effective for many tasks [8, 16, 31, 36, 39]. Adopting Memory Matrix" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "23891" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 547, + 250 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 547, + 250 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 547, + 250 + ], + "type": "image", + "image_path": "90fa828be64669b491d7387f8a1304a0890d7e91f8a5071590df1889b5f40d3c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 257, + 548, + 324 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 548, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 548, + 324 + ], + "type": "text", + "content": "Figure 2. SQUID. We divide an input image into " + }, + { + "bbox": [ + 46, + 257, + 548, + 324 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 46, + 257, + 548, + 324 + ], + "type": "text", + "content": " non-overlapping patches and feed them into the encoder for feature extraction. Two generators will be trained to reconstruct the original image. Along with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically via a novel Memory Queue (§3.2); The teacher generator directly uses the features extracted by the encoder; the student generator uses the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm. We employ a discriminator to assess whether the image reconstructed by the student generator is real or fake. Once trained, it can also be used to detect anomalies in test images (§3.4)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 344, + 289, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 344, + 289, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 289, + 561 + ], + "type": "text", + "content": "for unsupervised anomaly detection was first proposed in MemAE [17]. In addition to auto-encoding (AE), an extra Memory Matrix was introduced between the encoder and the decoder to capture normal feature patterns during training. The matrix is jointly optimized along with the AE and hence learns an essential basis to be able to assemble normal patterns. Based on this paradigm, Park et al. [53] introduced a non-learnable memory module that can be updated with inputs. Note that although our proposed Memory Queue also does not require any gradients, our method differs significantly in its usage purpose and updating rules. Considering the extra memory usage in existing methods, Lv et al. [48] proposed a dynamic prototype unit that encodes normal dynamics on the fly, while consuming little additional memory. In this paper, we overcome the limitations of the Memory Matrix and propose an effective yet efficient Memory Queue for unsupervised anomaly detection in radiography images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 572, + 105, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 105, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 105, + 586 + ], + "type": "text", + "content": "3. SQUID" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 594, + 164, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 164, + 607 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 164, + 607 + ], + "type": "text", + "content": "3.1. Overview (Figure 2)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 613, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 613, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 685 + ], + "type": "text", + "content": "(1) Feature extraction. We divide the input image into " + }, + { + "bbox": [ + 47, + 613, + 287, + 685 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 47, + 613, + 287, + 685 + ], + "type": "text", + "content": " non-overlapping patches and feed them into an encoder for feature extraction. The extracted features will be used for image reconstruction. Practically, the encoder can be any backbone architectures [14,70]; we adopt basic Convolutions and Pooling layers in this work for simplicity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "(2) Image reconstruction. We introduce teacher and student generators to reconstruct the original image. Along" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 344, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 547, + 513 + ], + "type": "text", + "content": "with the reconstruction, a dictionary of anatomical patterns will be created and updated dynamically as a Memory Queue (§3.2). Specifically, the teacher generator directly reconstructs the image using the features extracted by the encoder (essentially an auto-encoder [58]). The student generator, on the other hand, using the features augmented by our in-painting block (§3.3). The teacher and student generators are coupled through a knowledge distillation paradigm [28] at all of the up-sampling levels. The objective of the student generator is to reconstruct a normal image from the augmented features, which will then be used for anomaly discrimination (§3.4); while the teacher generator serves as a regularizer that prevents the student from constantly generating the same normal image." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 514, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 612 + ], + "type": "text", + "content": "(3) Anomaly discrimination. Following the adversarial learning [61, 62], we employ a discriminator to assess whether the generated image is real or fake. Only the student generator will receive the gradient derived from the discriminator. The two generators and the discriminator are competing against each other until they converge to an equilibrium. Once trained, the discriminator can be used to detect anomalies in test images (§3.4)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 619, + 515, + 632 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 619, + 515, + 632 + ], + "spans": [ + { + "bbox": [ + 305, + 619, + 515, + 632 + ], + "type": "text", + "content": "3.2. Inventing Memory Queue as Dictionary" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 637, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 637, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 637, + 547, + 687 + ], + "type": "text", + "content": "Motivation. The Memory Matrix was introduced by Gong et al. [17] and has since been widely adopted in unsupervised anomaly detection [18, 45, 78]. To forge a \"normal\" appearance, features are augmented by weighted averaging" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1We disabled the backpropagation between the teacher and encoder by stop-gradient [23] and showed its empirical benefit in Table 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23892" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 83, + 160, + 131 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 116, + 79 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 116, + 79 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 116, + 79 + ], + "type": "text", + "content": "Memory Matrix" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 129, + 70, + 162, + 79 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 162, + 79 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 162, + 79 + ], + "type": "text", + "content": "Similarity" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 83, + 160, + 131 + ], + "lines": [ + { + "bbox": [ + 48, + 83, + 160, + 131 + ], + "spans": [ + { + "bbox": [ + 48, + 83, + 160, + 131 + ], + "type": "image", + "image_path": "7a80bc98057cd58a0942a47bc621b2eae3f0333c7f1a2bea0860882901b45111.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 172, + 83, + 296, + 132 + ], + "blocks": [ + { + "bbox": [ + 172, + 70, + 249, + 79 + ], + "lines": [ + { + "bbox": [ + 172, + 70, + 249, + 79 + ], + "spans": [ + { + "bbox": [ + 172, + 70, + 249, + 79 + ], + "type": "text", + "content": "Space-aware Memory" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 172, + 83, + 296, + 132 + ], + "lines": [ + { + "bbox": [ + 172, + 83, + 296, + 132 + ], + "spans": [ + { + "bbox": [ + 172, + 83, + 296, + 132 + ], + "type": "image", + "image_path": "696e901fdc12e3aa14de9ac7abb83daca7daa1866b4adf1d9f2f0462864d6b77.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "type": "text", + "content": "Figure 3. Space-aware memory. For unique encoding of location information, we restrict each patch to be only accessible by a non-overlapping region in the memory." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 194, + 287, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 253 + ], + "type": "text", + "content": "the similar patterns in Memory Matrix. This augmentation is, however, applied to the features extracted from the whole image, discarding the spatial information in images. Therefore, the Memory Matrix in its current form cannot perceive the anatomical consistency as in radiography images." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 255, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 287, + 434 + ], + "type": "text", + "content": "Space-aware memory. To harness the spatial information, we pass the divided small patches, instead of the whole image, into the model. These patches are associated with unique location identifiers of the original image. We seek to build the relationship between the patch location and memory region, by restricting the search space in Memory Matrix to the patch-corresponded non-overlapping segments only. That is, a patch at a particular location can only access a corresponding segment in the whole Memory Matrix (illustrated in Figure 3). We refer to this new strategy as \"space-aware memory\" because it enables explicit encoding of the spatial information into Memory Matrix. Space-aware memory can also accelerate the augmentation speed compared with [17] as it no longer goes through the entire Memory Matrix to assemble similar features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 437, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 629 + ], + "type": "text", + "content": "Memory queue. In learning-based Memory Matrix [17], \"normal patterns\" are forged by combining learned basis in the matrix. However, there is always a distribution discrepancy between the basic combinations and the actual image features. This disparity makes it hard for the subsequent image generation. To address this issue, we propose a Memory Queue to store real image features during model training, therefore presenting an identical distribution to the image features. Specifically, it directly copies previously seen features into a queue structure during training2. Once trained, Memory Queue can be used as a dictionary of normal anatomical patterns. In Figure 4, we show t-SNE visualizations to validate that the learned basis in Memory Matrix (blue dots) distributes differently from the actual image features of the training set (gray dots). In contrast, the stored image features in our Memory Queue (red dots) are" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 306, + 68, + 547, + 148 + ], + "blocks": [ + { + "bbox": [ + 306, + 68, + 547, + 148 + ], + "lines": [ + { + "bbox": [ + 306, + 68, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 306, + 68, + 547, + 148 + ], + "type": "image", + "image_path": "c7c791b1ffeb49a78dbfe5fabb08a0d44a03edce9edf7a08bcc4e12fd03e455d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 156, + 547, + 212 + ], + "lines": [ + { + "bbox": [ + 304, + 156, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 547, + 212 + ], + "type": "text", + "content": "Figure 4. t-SNE visualizations of patterns in Memory Matrix, Memory Queue, and patch features of the training samples [73]. Patterns in the Memory Matrix are far away from the distribution of patch features, while patterns in the Memory Queue (as copies of previously seen features) share a similar distribution." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 232, + 488, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 488, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 488, + 243 + ], + "type": "text", + "content": "in an identical distribution to the actual ones." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "type": "text", + "content": "Gumbel shrinkage. Controlling the number of activated patterns in the memory has proven to be advantageous for anomaly detection [17, 19]. However, setting a hard shrinkage threshold fails to adapt to cases where no suitable entries can be found in the memory. One natural workaround is to activate the top-" + }, + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "type": "text", + "content": " similar patterns in the memory. However, this strategy restricts the gradient flow to only the top-" + }, + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 246, + 545, + 378 + ], + "type": "text", + "content": " memory entries, while the rest inactivated ones could not receive any gradients and be updated as expected. To extend gradients to all patterns in the memory, inspired by Jang [30], we present a Gumbel Shrinkage schema:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 329, + 388, + 545, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 388, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 329, + 388, + 545, + 403 + ], + "type": "interline_equation", + "content": "\\mathbf {w} ^ {\\prime} = \\operatorname {s g} (\\operatorname {h s} (\\mathbf {w}, \\operatorname {t o p k} (\\mathbf {w})) - \\phi (\\mathbf {w})) + \\phi (\\mathbf {w}), \\tag {1}", + "image_path": "b5c643f8bb064ed37f2dd7cdacde44c3cb405f6939228bbad8bf9c73cc0d81ee.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": " denotes the similarity between the image features and entries in Memory, " + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "inline_equation", + "content": "sg(\\cdot)" + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": " the stop-gradient operation, " + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\mathrm{hs}(\\cdot ,t)" + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": " the hard shrinkage operator with threshold " + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": " the Softmax function. In the forward pass, Gumbel Shrinkage ensures the combination of the top- " + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 412, + 546, + 519 + ], + "type": "text", + "content": " most similar entries in the memory; During the back-propagation, Gumbel Shrinkage essentially functions as Softmax. We apply Gumbel Shrinkage to both Memory Queue and Memory Matrix in our framework." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 527, + 545, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 527, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 305, + 527, + 545, + 540 + ], + "type": "text", + "content": "3.3. Formulating Anomaly Detection as In-painting" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Motivation. Image in-painting [41, 54] was initially proposed to recover corrupted image regions with neighboring context. Following the above intuition, we propose to achieve anomaly detection via in-painting anomalous radiography patterns into healthy ones. When in-painting pixels in the image space, recovered regions have been usually seen to associate with boundary artifacts, particularly when using Deep Nets [43]. These undesired artifacts are responsible for numerous false positives when formulating anomaly detection as a pixel-level in-painting task [66, 87]. To alleviate this issue, we achieve the in-painting task at the feature level instead. Latent features are better invariant to pixel-level noise, rotation, and translation, therefore are more suitable for subsequent anomaly detection." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "text", + "content": "In practice, copying features into the queue at every training iteration demands considerable computational time. Supposing " + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "text", + "content": " patterns in the queue and " + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "text", + "content": " training iterations, the sampling strategy in [17] demands an " + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(NM)" + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "text", + "content": " time complexity. We implement it more efficiently: at each iteration, the current batch of features will be copied into the queue for only once (Figure 5c), yielding a linear complexity of " + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(M + cM)" + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "text", + "content": " with the copy-and-paste operation in a constant time " + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 636, + 287, + 713 + ], + "type": "text", + "content": ". We follow the first-in-first-out (FIFO) paradigm to update the queue continuously." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23893" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 197, + 155 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 197, + 155 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 197, + 155 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 197, + 155 + ], + "type": "image", + "image_path": "2ca2e402bfb3f8c9a3c7cf7523307b4490abcb7e84887935739b7e8f3355cc46.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 86, + 162, + 156, + 172 + ], + "lines": [ + { + "bbox": [ + 86, + 162, + 156, + 172 + ], + "spans": [ + { + "bbox": [ + 86, + 162, + 156, + 172 + ], + "type": "text", + "content": "(a) Augment " + }, + { + "bbox": [ + 86, + 162, + 156, + 172 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 86, + 162, + 156, + 172 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 86, + 162, + 156, + 172 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 230, + 102, + 396, + 155 + ], + "blocks": [ + { + "bbox": [ + 230, + 102, + 396, + 155 + ], + "lines": [ + { + "bbox": [ + 230, + 102, + 396, + 155 + ], + "spans": [ + { + "bbox": [ + 230, + 102, + 396, + 155 + ], + "type": "image", + "image_path": "70f20ab0d6930d05ba9a2a31bb5c6a32e560d47f3da42e914af31c43ca45e6b0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 255, + 162, + 334, + 172 + ], + "lines": [ + { + "bbox": [ + 255, + 162, + 334, + 172 + ], + "spans": [ + { + "bbox": [ + 255, + 162, + 334, + 172 + ], + "type": "text", + "content": "(b) Aggregate " + }, + { + "bbox": [ + 255, + 162, + 334, + 172 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 255, + 162, + 334, + 172 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 255, + 162, + 334, + 172 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 430, + 68, + 544, + 156 + ], + "blocks": [ + { + "bbox": [ + 430, + 68, + 544, + 156 + ], + "lines": [ + { + "bbox": [ + 430, + 68, + 544, + 156 + ], + "spans": [ + { + "bbox": [ + 430, + 68, + 544, + 156 + ], + "type": "image", + "image_path": "3e3a5cb10861939d12f19c15632d2581ba234cfcdd8ba6365acf13502ee1b7ea.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 447, + 162, + 545, + 172 + ], + "lines": [ + { + "bbox": [ + 447, + 162, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 447, + 162, + 545, + 172 + ], + "type": "text", + "content": "(c) Copy " + }, + { + "bbox": [ + 447, + 162, + 545, + 172 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 447, + 162, + 545, + 172 + ], + "type": "text", + "content": " to Memory Queue" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "lines": [ + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "spans": [ + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "text", + "content": "Figure 5. Three-step workflow of our in-painting block. (a) Each non-overlapping patch feature " + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "text", + "content": " is queried to a unique region in Memory Queue, and the most similar items are assembled to " + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "text", + "content": ". (b) Each center patch feature " + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "text", + "content": " and its eight neighbors " + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "text", + "content": " are used as query and key/value, respectively, to a Transformer layer for in-painting. (c) Each Memory Queue region copies its corresponding patch features " + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 45, + 179, + 547, + 225 + ], + "type": "text", + "content": " into the memory by maintaining a pointer. Note that this step is only performed during training." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": "In-painting block. We integrate our Memory Queue inside a novel in-painting block to perform feature-space in-painting. The block starts with a Memory Queue that augments " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "w \\times h" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " non-overlapping patch features " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\{(1,1), \\dots, (w,h)\\}}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " into their most similar \"normal\" patterns " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\{(1,1), \\dots, (w,h)\\}}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " (Figure 5a). Since " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " is assembled by features extracted from previous training data, " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " is not subject to the current input image. To recap the characteristics of the input image, we aggregate both patch features " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " and their augmented features " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " using a transformer block [74]. In details, for each patch " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{i,j}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": ", its spatially adjacent eight augmented ones " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\{(i-1,j-1), \\dots, (i+1,j+1)\\}}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " are used as conditions to refine " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{i,j}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " (Figure 5b). The query token of the transformer block is flattened " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{(i,j)} \\in \\mathcal{R}^{1 \\times *}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " and key/value tokens are " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\{(i-1,j-1), \\dots, (i+1,j+1)\\}} \\in \\mathcal{R}^{8 \\times *}" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": ". At the start and the end of our in-painting block, we apply an extra pair of point-wise convolutions " + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "inline_equation", + "content": "(1 \\times 1" + }, + { + "bbox": [ + 46, + 245, + 289, + 449 + ], + "type": "text", + "content": " convolutional kernel) [24]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "type": "text", + "content": "Masked shortcut. We employ a shortcut within the inpainting block to better aggregate features and ease optimization. Our empirical study shows that a direct residual connection downgrades the effectiveness of the in-painting block (Appendix B). Inspired by Xiang et al. [76], we utilize a random binary mask to gate shortcut features during training (Figure 5b). As such, given the input patch features " + }, + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 452, + 287, + 548 + ], + "type": "text", + "content": ", the output of the in-painting block is obtained by:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 88, + 556, + 287, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 556, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 88, + 556, + 287, + 571 + ], + "type": "interline_equation", + "content": "\\mathcal {F} ^ {\\prime} = (1 - \\delta) \\cdot \\mathcal {F} + \\delta \\cdot \\text {i n p a i n t} (\\mathcal {F}), \\tag {2}", + "image_path": "45c59938a87cb7ff5e83be6965f90cf76632b62f0b9e297d6d425e7f0987eb35.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathrm{inpaint}(\\cdot)" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " is the designed in-painting block, " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\delta \\sim" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " Bernoulli " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "(\\rho)" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " is a binary variable with " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " the gating probability. After obtaining " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}'" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " at each training step, the originally " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " are then copied to update the memory (Figure 5c). During inference, we disable the shortcut completely such that " + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "inline_equation", + "content": "\\mathcal{F}' = \\mathrm{inpaint}(\\mathcal{F})" + }, + { + "bbox": [ + 47, + 579, + 287, + 652 + ], + "type": "text", + "content": " for deterministic predictions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 659, + 186, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 186, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 186, + 672 + ], + "type": "text", + "content": "3.4. Anomaly Discrimination" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Our discriminator can detect anomalies by assessing the quality of the reconstructions—normal if realistic; abnormal otherwise. It is because the generator was trained on" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 245, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 293 + ], + "type": "text", + "content": "normal images, so Memory Queues only store normal patterns. During inference, since abnormal patterns were never present in Memory Queues, the reconstructed image is expected to appear unrealistic." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": "Our in-painting block focuses on augmenting any patch feature (either normal or abnormal) into similar \"normal\" features. The student generator then reconstructs a \"normal\" image based on the \"normal\" features. The teacher generator is used to prevent the student from generating the same image regardless of inputs. Once trained, the semantic (rather than pixel-level) difference between the input and the student generator's reconstructed image is expected to be small if normal and big otherwise. We, therefore, delegate the optimized discriminator network for alerting anomalies perceptually. For better clarification, we note the encoder, teacher generator, student generator, and discriminator as " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{\\mathrm{t}}" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_{\\mathrm{s}}" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": ". An anomaly score " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": " can be computed through: " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "A = \\phi \\left( \\frac{\\mathbf{D}(\\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I})) - \\mu}{\\sigma} \\right)" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\phi (\\cdot)" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": " is the Sigmoid function, " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 295, + 546, + 488 + ], + "type": "text", + "content": " are the mean and standard deviation of anomaly scores calculated on training samples." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 501, + 394, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 394, + 512 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 394, + 512 + ], + "type": "text", + "content": "3.5. Loss Function" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "SQUID is optimized by five loss functions. The mean square error (MSE) between input and reconstructed images is used for both teacher and student generators. Concretely, " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{t}} = (\\mathbf{I} - \\mathbf{G}_{\\mathrm{t}}(\\mathbf{E}(\\mathbf{I}))^{2}" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{s}} = (\\mathbf{I} - \\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I})))^{2}" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " for the teacher and student generators, respectively, where " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " denotes the input image. Following the knowledge distillation paradigm, we apply a distance constraint between the teacher and student generators to all levels of features: " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}} = \\sum_{i=1}^{l} (\\mathcal{F}_{\\mathrm{t}}^{i} - \\mathcal{F}_{\\mathrm{s}}^{i})^{2}" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " is the level of features used for knowledge distillation, " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{t}}" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{s}}" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " are the intermediate features in the teacher and student generators, respectively. In addition, we employ an adversarial loss (similar to DCGAN [55]) to improve the quality of the image generated by the student generator. Specifically, the following equation is minimized: " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{gen}} = \\log(1 - \\mathbf{D}(\\mathbf{G}_{\\mathrm{s}}(\\mathbf{E}(\\mathbf{I}))))" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": ". The discriminator seeks to maximize the average of the proba" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23894" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 77, + 287, + 267 + ], + "blocks": [ + { + "bbox": [ + 105, + 70, + 281, + 77 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 281, + 77 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 281, + 77 + ], + "type": "text", + "content": "Input SQUID f-AnoGAN Ganomly MemAE" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 77, + 287, + 267 + ], + "lines": [ + { + "bbox": [ + 51, + 77, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 51, + 77, + 287, + 267 + ], + "type": "image", + "image_path": "ab12043032b7c0df511708b290d28466efd4de2775e427cce995851b9ac9e3ee.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 276, + 287, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 321 + ], + "type": "text", + "content": "Figure 6. Reconstruction results on DigitAnatomy. Our feature-level in-painting is more robust to amplified noise and pixel variance than the existing pixel-level in-painting methods. More visualization can be found in Appendix D." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "text", + "content": "bility for real images and the inverted probability for fake images: " + }, + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dis}} = \\log (\\mathbf{D}(\\mathbf{I})) + \\log (1 - \\mathbf{D}(\\mathbf{G}_s(\\mathbf{E}(\\mathbf{I}))))" + }, + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "text", + "content": " . In summary, SQUID is trained to minimize the generative loss terms " + }, + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "inline_equation", + "content": "(\\lambda_{\\mathrm{t}}\\mathcal{L}_{\\mathrm{t}} + \\lambda_{\\mathrm{s}}\\mathcal{L}_{\\mathrm{s}} + \\lambda_{\\mathrm{dist}}\\mathcal{L}_{\\mathrm{dist}} + \\lambda_{\\mathrm{gen}}\\mathcal{L}_{\\mathrm{gen}})" + }, + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "text", + "content": " and to maximize the discriminative loss term " + }, + { + "bbox": [ + 46, + 340, + 287, + 401 + ], + "type": "inline_equation", + "content": "(\\lambda_{\\mathrm{dis}}\\mathcal{L}_{\\mathrm{dis}})" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 411, + 128, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 128, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 128, + 424 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 430, + 148, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 148, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 148, + 442 + ], + "type": "text", + "content": "4.1. New Benchmark" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 449, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 653 + ], + "type": "text", + "content": "DigitAnatomy. We have created a synthetic dataset to verify our main idea, wherein the human anatomy is translated into Arabic digits one to nine in an in-grid placement (see examples in Figure 1 and Figure 6). The images containing digits in the correct order are considered \"normal\"; otherwise, they are considered \"abnormal\". The types of simulated abnormalities include missing, misordered, flipped, and zero digit(s). DigitAnatomy is particularly advantageous for radiography imaging for three reasons. First, it simulates two unique properties of radiography images, i.e. spatial correlation and consistent shape. Second, annotating radiography images demands specialized expertise, but digits are easier for problem debugging. Third, the ground truth of the simulated anomaly is readily accessible in DigitAnatomy, whereas it is hard to collect sufficient examples for each abnormal type in radiography images. The pseudocode for creating DigitAnatomy is in Appendix C." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 659, + 162, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 162, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 162, + 671 + ], + "type": "text", + "content": "4.2. Public Benchmarks" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "ZhangLab Chest X-ray [32]. This dataset contains healthy and pneumonia (as anomaly) images, officially split into training and testing sets. The training set consists of 1,349" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 308, + 90, + 545, + 285 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 539, + 81 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 539, + 81 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 539, + 81 + ], + "type": "text", + "content": "Table 1. Benchmark results on the test sets of the two datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 90, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 308, + 90, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 308, + 90, + 545, + 285 + ], + "type": "table", + "html": "
ZhangLabRef & YearAUC (%)Acc (%)F1 (%)
Auto-Encoder-59.963.477.2
VAE [35]Arxiv'1361.864.077.4
Ganomaly [1]ACCV'1878.070.079.0
f-AnoGAN [61]MIA'1975.574.081.0
MemAE [17]ICCV'1977.8±1.456.5±1.182.6±0.9
MNAD [53]CVPR'2077.3±0.973.6±0.779.3±1.1
SALAD [82]TMI'2182.7±0.875.9±0.982.1±0.3
CutPaste [40]CVPR'2173.6±3.964.0±6.572.3±8.9
PANDA [56]CVPR'2165.7±1.365.4±1.966.3±1.2
M-KD [59]CVPR'2174.1±2.669.1±0.262.3±8.4
IF 2D [50]MICCAI'2181.0±2.876.4±0.282.2±2.7
PaDiM [12]ICPR'2171.4±3.472.9±2.480.7±1.2
IGD [10]AAAI'2273.4±1.974.0±2.280.9±1.3
SQUID-87.6±1.580.3±1.384.7±0.8
CheXpertRef & YearAUC (%)Acc (%)F1 (%)
Ganomaly [1]ACCV'1868.9±1.465.7±0.265.1±1.9
f-AnoGAN [61]MIA'1965.8±3.363.7±1.859.4±3.8
MemAE [17]ICCV'1954.3±4.055.6±1.453.3±7.0
CutPaste [40]CVPR'2165.5±2.262.7±2.060.3±4.6
PANDA [56]CVPR'2168.6±0.966.4±2.865.3±1.5
M-KD [59]CVPR'2169.8±1.666.0±2.563.6±5.7
SQUID-78.1±5.171.9±3.875.9±5.7
", + "image_path": "be63930eb63c33fe497a8a3d3293c78b869b9605dd1b1b66c28143fe70217e14.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 308, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 367 + ], + "type": "text", + "content": "normal and 3,883 abnormal images; the testing set has 234 normal and 390 abnormal images. We randomly separate 200 images (100 normal and 100 abnormal) from the training set as the validation set for hyper-parameter tuning. We resized all the images to " + }, + { + "bbox": [ + 304, + 308, + 545, + 367 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 308, + 545, + 367 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 371, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 545, + 468 + ], + "type": "text", + "content": "Stanford CheXpert [29]. We conducted evaluations on the front-view PA images in the CheXpert dataset, which account for a total of 12 different anomalies. In all front-view PA images, there are 5,249 normal and 23,671 abnormal images for training; 250 normal and 250 abnormal images (with at least 10 images per disease type) from the training set were used for testing. We used the same hyperparameters found in the ZhangLab experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 475, + 432, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 432, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 432, + 487 + ], + "type": "text", + "content": "4.3. Baselines and Metrics" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 494, + 545, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 626 + ], + "type": "text", + "content": "We considered a total number of 13 major baselines for direct comparison: Auto-Encoder, VAE [35]—the classic UAD methods; Ganomaly [1], f-AnoGAN [61], IF [50], SALAD [82]—the current state of the arts for medical imaging; and MemAE [17], CutPaste [40], M-KD [60], PANDA [56], PaDiM [12], IGD [10]—the most recent UAD methods. We evaluated performance using standard metrics: Receiver Operating Characteristic (ROC) curve, Area Under the ROC Curve (AUC), Accuracy (Acc), and F1-score (F1). Unless explicitly specified, we trained all models from scratch for at least three times independently." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 634, + 439, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 439, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 439, + 647 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We utilized common data augmentation strategies such as random translation within the " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "[-0.05, + 0.05]" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " range and a random scaling of [0.95, 1.05]. The Adam [34] optimizer was used with a batch size of 16 and a weight decay of " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "1e-5" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": ". The learning rate was initially set to " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "1e-4" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " for both the" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23895" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 167, + 192 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 167, + 192 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 167, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 167, + 192 + ], + "type": "image", + "image_path": "ad0e095a5b4e480aed8e5529570a545981c947c81a0bfc8cb54dbeb8cf22bc8b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 78, + 194, + 151, + 202 + ], + "lines": [ + { + "bbox": [ + 78, + 194, + 151, + 202 + ], + "spans": [ + { + "bbox": [ + 78, + 194, + 151, + 202 + ], + "type": "text", + "content": "(a) ZhangLab Chest X-ray" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 69, + 286, + 193 + ], + "blocks": [ + { + "bbox": [ + 167, + 69, + 286, + 193 + ], + "lines": [ + { + "bbox": [ + 167, + 69, + 286, + 193 + ], + "spans": [ + { + "bbox": [ + 167, + 69, + 286, + 193 + ], + "type": "image", + "image_path": "a2f96c851ff4585b54ca76f11e5e1f16a15ba1ff48f1d68a1aca71a544c7a464.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 194, + 263, + 202 + ], + "lines": [ + { + "bbox": [ + 198, + 194, + 263, + 202 + ], + "spans": [ + { + "bbox": [ + 198, + 194, + 263, + 202 + ], + "type": "text", + "content": "(b) Stanford CheXpert" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 67, + 211, + 266, + 222 + ], + "lines": [ + { + "bbox": [ + 67, + 211, + 266, + 222 + ], + "spans": [ + { + "bbox": [ + 67, + 211, + 266, + 222 + ], + "type": "text", + "content": "Figure 7. ROC curves comparison on the two datasets." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": "generator and the discriminator and then decayed to " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "2e - 5" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": " in 1000 epochs following the cosine annealing scheduler. The discriminator is trained at every iteration, while the generator is trained every two iterations. We set loss weights as " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{t}} = 0.01" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{s}} = 10" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{dist}} = 0.001" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{gen}} = 0.005" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{dis}} = 0.005" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": ". We divide the input images in " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "2\\times 2" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": " non-overlapping patches, fix the shortcut mask probability at " + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "inline_equation", + "content": "\\rho = 95\\%" + }, + { + "bbox": [ + 46, + 244, + 289, + 376 + ], + "type": "text", + "content": ", and activate only the top 5 similar patterns in the Gumbel Shrinkage. The impact of these hyper-parameters is studied in §5.3. The architectures of our generators and discriminator are detailed in Appendix A." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 388, + 100, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 100, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 100, + 399 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 407, + 243, + 421 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 243, + 421 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 243, + 421 + ], + "type": "text", + "content": "5.1. Interpreting SQUID on DigitAnatomy" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": "Figure 6 presents qualitative results on DigitAnatomy to examine the capability of image reconstruction and to interpret the mistakes made by existing methods [1, 17, 61]. We deliberately inject anomalies (e.g. novel, misordered, missing digits) into normal images (highlighted in light blue) and test if the model can reconstruct their normal counterparts. To raise the task difficulty, we also assess the reconstruction quality from a blank image (as an extreme case). In general, the images reconstructed by our SQUID carry more meaningful and indicative information than other baseline methods. It is mainly attributed to our space-aware memory, with which the resulting dictionary is associated with unique patterns as well as their spatial information. Once an anomaly arises (e.g. missing digit), the in-painting block will augment the abnormal feature to its normal counterpart by assembling top-" + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": " most similar patterns from the dictionary. Other methods, however, do not possess this ability, so they reconstruct defective images. For instance, GAN-based methods (f-AnoGAN and Ganomly) tend to reconstruct an exemplar image averaged from the training examples. MemAE performs relatively better due to its Memory Matrix, but it does not work well for the anomaly of missing digits and completely fails on the extreme anomaly attack." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 306, + 68, + 440, + 158 + ], + "blocks": [ + { + "bbox": [ + 306, + 68, + 440, + 158 + ], + "lines": [ + { + "bbox": [ + 306, + 68, + 440, + 158 + ], + "spans": [ + { + "bbox": [ + 306, + 68, + 440, + 158 + ], + "type": "image", + "image_path": "3bb0486a2fa9b461c57ac7498adda6a57df77c832e6bef77f07b07d855d11b10.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 165, + 545, + 210 + ], + "lines": [ + { + "bbox": [ + 305, + 165, + 545, + 210 + ], + "spans": [ + { + "bbox": [ + 305, + 165, + 545, + 210 + ], + "type": "text", + "content": "Figure 8. Reconstruction results of SQUID on the two datasets, associated with the corresponding anomaly scores (defined in §3.4). A larger score indicates a higher probability of being abnormal. More visualization can be found in Appendix D." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 444, + 68, + 547, + 158 + ], + "blocks": [ + { + "bbox": [ + 444, + 68, + 547, + 158 + ], + "lines": [ + { + "bbox": [ + 444, + 68, + 547, + 158 + ], + "spans": [ + { + "bbox": [ + 444, + 68, + 547, + 158 + ], + "type": "image", + "image_path": "ce8e6af5e3ef78038d1ceddf6d7bb2172985d84a278bb9a1e72f0bb842535c4c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 231, + 541, + 244 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 541, + 244 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 541, + 244 + ], + "type": "text", + "content": "5.2. Benchmarking SQUID on Chest Radiography" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "type": "text", + "content": "Our SQUID was mainly evaluated on two large-scale benchmarks: ZhangLab Chest X-ray and Stanford CheXpert and compared with a wide range of state-of-the-art counterparts. According to Table 1, SQUID achieves the most promising result on all metrics for both datasets. Specifically, SQUID outperforms the runner-up counterparts by at least " + }, + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "type": "text", + "content": " in AUC, " + }, + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 251, + 546, + 549 + ], + "type": "text", + "content": " in Accuracy. The highest F1 scores SQUID achieved, along with the ROC curves shown in Figure 7, demonstrate that our method yields the best trade-off between sensitivity and specificity. Overall, the significant improvements observed with SQUID proved the effectiveness of our proposed techniques in this work. In Figure 8, we visualize the reconstruction results of SQUID on exemplary normal and abnormal images in the two datasets. For normal cases, SQUID can easily find a similar match in Memory Queue, achieving the reconstruction smoothly. For abnormal cases, the contradiction will arise by imposing forged normal patterns into the abnormal features. In this way, the generated images will vary significantly from the input, which will then be captured by the discriminator. We plot the heatmap of the discriminator (using Grad-CAM [65]) to indicate the most likely regions to appear anomalous. As a result, the reconstructed healthy images yield much lower anomaly scores than the diseased ones, validating the effectiveness of SQUID." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 553, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 547, + 661 + ], + "type": "text", + "content": "Limitation. We found SQUID in its current form, is not able to localize anomalies at the pixel level precisely. It is understandable because our SQUID is an unsupervised method, requiring zero manual annotation for normal/abnormal images, unlike [60, 68, 72, 75, 80]. Those methods that compute pixel-level residuals for anomaly detection suffer from amplified noise in the input and reconstructed output. Our in-painting strategy, however, is performed at the feature level and is more robust to pixel-level variance." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 670, + 489, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 670, + 489, + 683 + ], + "spans": [ + { + "bbox": [ + 305, + 670, + 489, + 683 + ], + "type": "text", + "content": "5.3. Ablating Key Properties in SQUID" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Component study. We examine the impact of components in SQUID by taking each one of them out of the entire" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23896" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 89, + 286, + 175 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 286, + 81 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 286, + 81 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 286, + 81 + ], + "type": "text", + "content": "Table 2. Performance benefits from all the components in SQUID." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 89, + 286, + 175 + ], + "lines": [ + { + "bbox": [ + 47, + 89, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 47, + 89, + 286, + 175 + ], + "type": "table", + "html": "
MethodAUC (%)Acc (%)F1 (%)
w/o Space-aware Memory77.6±0.575.5±0.582.5±0.6
w/o In-painting Block80.9±2.175.8±1.581.6±1.3
w/o Gumbel Shrinkage81.1±0.977.6±0.981.3±0.8
w/o Knowledge Distillation81.2±0.875.2±0.781.3±0.8
w/o Stop Gradient81.7±4.376.7±2.882.5±1.6
w/o Memory Queue82.5±1.178.6±0.981.7±1.1
w/o Masked Shortcuts82.5±1.376.4±0.882.3±1.1
w/o Decoder Memory82.9±1.277.4±1.181.2±0.5
Full SQUID87.6±1.580.3±1.384.7±0.8
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Hyper-parameter ablations." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": "framework. Table 2 shows that each component accounts for at least " + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": " performance gain. The space-aware memory " + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "inline_equation", + "content": "(+10.0\\%)" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": " and in-painting block " + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "inline_equation", + "content": "(+6.7\\%)" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": " are the top 2 most significant contributors, which underline our motivation and justification of the method development (" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\S 3.2" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "inline_equation", + "content": "\\S 3.3" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": "). Although replacing Memory Queue with Memory Matrix could maintain a decent result (only dropped " + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 46, + 372, + 287, + 492 + ], + "type": "text", + "content": "), our Memory Queue presents a more trustworthy recovery of \"normal\" patterns in the image than Memory Matrix (MemAE [17]), evidenced by Figure 6." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": "Hyper-parameter robustness. After selecting the best hyper-parameters on the validation set, we here report the inference results on the testing set to study the robustness of different hyper-parameters in Figure 9. When input images are divided into a single patch, space-aware settings are not triggered, therefore yielding the worst performance. Although the spatial structures are relatively stable in most chest radiography, certain deviations can still be observed. Therefore, with small patches, object parts in one patch can easily appear in adjacent patches and be misdetected as anomalies. The number of topK activations in Gumbel softmax also impacts the performances. According to the AUC vs. the number of patterns in each Memory Queue region, we found that a small number of items is sufficient to support normal pattern querying in local regions. The best result is achieved by merely 200 items per region. When the item number exceeds 500 per region, AUC scores begin to drop continuously. AUC vs. the mask probability " + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 498, + 288, + 714 + ], + "type": "text", + "content": " was" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 306, + 69, + 545, + 128 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 545, + 128 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 545, + 128 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 545, + 128 + ], + "type": "image", + "image_path": "fad4a9bf1f9fce94045372cfa6d9fb751d67e6df6acc8a2f6b540b3bcb13654c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 308, + 136, + 542, + 148 + ], + "lines": [ + { + "bbox": [ + 308, + 136, + 542, + 148 + ], + "spans": [ + { + "bbox": [ + 308, + 136, + 542, + 148 + ], + "type": "text", + "content": "Figure 10. Results of mixing normal/abnormal training samples." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "type": "text", + "content": "further plotted to verify that enabling a limited number of feature skips " + }, + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "type": "inline_equation", + "content": "(\\rho = 95\\%)" + }, + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "type": "text", + "content": " yields the best AUC score. The effectiveness of the in-painting will severely deteriorate if more features are allowed to be skipped " + }, + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "type": "inline_equation", + "content": "(\\rho < 90\\%)" + }, + { + "bbox": [ + 304, + 168, + 547, + 217 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "text", + "content": "Disease-free training requirement? Unsupervised methods for medical anomaly detection are uncommon because the so-called UAD methods are not \"unsupervised\"—they must be trained on disease-free images only (e.g. [5]). In practice, cleaning up disease-free images relies on manual annotation (essentially, image-level healthy/diseased labels). With disease-free sample ratio in the training set ranging from " + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "text", + "content": ", we have compared the robustness of SQUID with three competitive baselines (CutPaste [40], PANDA [56] and M-KD [60]). Figure 10 remarks that our proposed memory queue can tolerate the disease/healthy training ratio up to " + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 219, + 546, + 434 + ], + "type": "text", + "content": " by automatically omitting minority anatomical patterns. In contrast, CutPaste drops significantly as the percentage of normal images decreases; PANDA and M-KD can maintain the performance due to the use of pre-trained features. Interestingly, M-KD with mixed data even outperforms its vanilla training setting, although with considerable fluctuations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 445, + 378, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 378, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 378, + 456 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 465, + 546, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 546, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 546, + 633 + ], + "type": "text", + "content": "We present SQUID for unsupervised anomaly detection from radiography images. Qualitatively, we show that SQUID can taxonomize the ingrained anatomical structures into recurrent patterns; and in the inference, SQUID can identify anomalies accurately. Quantitatively, SQUID is superior to predominant methods by over 5 points AUC on the ZhangLab dataset and 10 points AUC on the Stanford CheXpert dataset. The outstanding results are attributable to our observation: Radiography imaging protocols focus on particular body regions, therefore producing images of great similarity and yielding recurrent anatomical structures across patients. We synthesized the DigitAnatomy dataset to resemble key attributes of chest anatomy in radiography images for prompting future method development." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 638, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 638, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 638, + 547, + 711 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and partially by the Patrick J. McGovern Foundation Award. 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Springer, 2011. 2" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23901" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_content_list.json b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1dcc358413d72f1556dd9e3c1e3ce9cdebd29676 --- /dev/null +++ b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_content_list.json @@ -0,0 +1,1589 @@ +[ + { + "type": "text", + "text": "STAR Loss: Reducing Semantic Ambiguity in Facial Landmark Detection", + "text_level": 1, + "bbox": [ + 112, + 130, + 859, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhenglin Zhou $^{1*}$ , Huaxia Li $^{2*}$ , Hong Liu $^{3*}$ , Nanyang Wang $^{2}$ , Gang Yu $^{2}$ , Rongrong Ji $^{1\\dagger}$", + "bbox": [ + 129, + 179, + 841, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University. 2 Tencent PCG. 3 National Institute of Information. zhenglinzhou@stu.xmu.edu.cn, {haroldzcli, cageswang, skicyyu}@tencent.com, hliu@nii.ac.jp, rrji@xmu.edu.cn", + "bbox": [ + 101, + 200, + 870, + 265 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 313, + 320 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, deep learning-based facial landmark detection has achieved significant improvement. However, the semantic ambiguity problem degrades detection performance. Specifically, the semantic ambiguity causes inconsistent annotation and negatively affects the model's convergence, leading to worse accuracy and instability prediction. To solve this problem, we propose a Self-adaptTive Ambiguity Reduction (STAR) loss by exploiting the properties of semantic ambiguity. We find that semantic ambiguity results in the anisotropic predicted distribution, which inspires us to use predicted distribution to represent semantic ambiguity. Based on this, we design the STAR loss that measures the anisotropism of the predicted distribution. Compared with the standard regression loss, STAR loss is encouraged to be small when the predicted distribution is anisotropic and thus adaptively mitigates the impact of semantic ambiguity. Moreover, we propose two kinds of eigenvalue restriction methods that could avoid both distribution's abnormal change and the model's premature convergence. Finally, the comprehensive experiments demonstrate that STAR loss outperforms the state-of-the-art methods on three benchmarks, i.e., COFW, 300W, and WFLW, with negligible computation overhead. Code is at https://github.com/ZhenglinZhou/STAR", + "bbox": [ + 76, + 335, + 473, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 724, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Facial landmark detection, which aims to locate a group of pre-defined facial landmarks from images [48, 51, 56], is a fundamental problem for many downstream tasks, including face verification [12], face synthetic [1], and 3D face reconstruction [10, 13, 17, 46].", + "bbox": [ + 75, + 750, + 468, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Thanks to the development of Convolutional Neural Networks (CNNs) [20, 36, 39], facial landmark detection has", + "bbox": [ + 76, + 825, + 468, + 856 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/376a97a868bff121914e5521fc5c0f51c1497fcfc56d236f34539bd882178579.jpg", + "image_caption": [ + "Figure 1. The impact of semantic ambiguity. We visualize the outputs of five models trained with the same architecture under the same experimental setting. (1) The first row shows the predicted facial landmarks for Mr. Tony Stark, marked as red points. And the green point refers to the corresponding mean value. (2) The second row shows the results of predicted probability distribution (i.e., heatmap) from one of the trained models." + ], + "image_footnote": [], + "bbox": [ + 501, + 303, + 888, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "improved significantly. At first, coordinate regression methods [3, 16, 33, 47] are proposed to learn the transformation between CNN features and landmark locations via fully connected layers. Recently, the research focus has been the heatmap regression methods, which have shown superiority over coordinate regression methods. The heatmap regression methods [21, 24, 48] predict an intermediate heatmap for each landmark and decode the coordinates from the heatmap. But, the commonly used decoder, Argmax [55], is not differentiable and suffers from quantization error. Recently, some solutions have been proposed [38, 53], and the focus is on the differentiable expectation decoder: soft-Argmax [32]. With the help of soft-Argmax, the heatmap regression method has the advantage of end-to-end training. So the training loss is mainly composed of a regression loss (such as $\\mathcal{L}_2$ ), which makes the model prediction fit the manual annotation.", + "bbox": [ + 496, + 609, + 893, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the manual annotation suffers from the semantic ambiguity problem [16, 21, 30]. Specifically, some fa", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 94, + 862, + 222, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. This work was done when Zhenglin Zhou was an enrn at Tencent PCG.", + "bbox": [ + 94, + 875, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15475", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5f442f303f7270149a35b6f9a49be996ebdd238cf7c4dc03ac41e5f284023596.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 88, + 861, + 196 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/01510269ddd119b3bc03f16aa6b60d0b18afd9a9c03f6b08fbb95f884dae9fad.jpg", + "image_caption": [ + "Figure 2. The overview of our framework. We use a four stacked Hourglasses (HGs) Network. To mitigate the impact of semantic ambiguity, the STAR loss is applied to each HG module. (Best view in color.)" + ], + "image_footnote": [], + "bbox": [ + 84, + 205, + 540, + 313 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9e45aeb75e216d7239eeadae54d64b63940ecab5b8bf28206f571d9c193a6f82.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 545, + 205, + 885, + 313 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cial landmarks, especially landmarks located on face contour, do not have a clear and accurate definition. For example, the contour landmarks are defined to evenly distribute around the face contour without a clear definition of the positions [30]. It makes human annotators confused about the position, and it is inevitable to induce inconsistent and imprecise annotations. Thus, we argue that the regression loss will be misled by ambiguous annotations and degrade the model's convergence and performance. As shown in Figure 1, training the neural network with ambiguous annotations makes the predictions for facial contour landmarks unstable and inaccurate, which will hurt the downstream task [15]. The key problem is to design a new regression loss that mitigates the impact of semantic ambiguity.", + "bbox": [ + 75, + 368, + 472, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a novel self-adaptive ambiguity reduction method, STAR loss, by fully exploiting semantic ambiguity. To this end, we explore the impact of semantic ambiguity on the heatmap. Typically, the distribution normalization loss forces the predicted probability distribution to resemble an isotropic Gaussian distribution [32]. However, as shown in Figure 1, compared with the isotropic distribution of the eye corner point, the predicted distribution of the facial contour point is anisotropic. The main difference between the two landmarks is semantic ambiguity, which is more severe in the contour point. We infer that the semantic ambiguity is related to the anisotropic distribution. When the predicted distribution of one facial landmark is anisotropic, this facial landmark has severe semantic ambiguity (leading to model unconvergence), so it is necessary to reduce its impact.", + "bbox": [ + 75, + 582, + 468, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we begin our story by introducing a customized principal component analysis (PCA) that can process the discrete probability distribution, which contains three steps: weighted mean estimation, unbiased weighted covariance estimation, and eigen-decomposition. We de", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "compose a group of predicted distributions and visualize the corresponding principal components. The visualization results show that the first principal component is along with the face contour. Meanwhile, the ambiguous direction for contour landmarks is aligned with the face contour. Therefore, we infer that their first principal component direction is highly consistent with their ambiguity direction.", + "bbox": [ + 496, + 368, + 892, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "According to this new observation, we design our STAR loss, which decomposes the prediction error into two principal component directions and divides it by the corresponding energy value. For a facial landmark with anisotropic predicted distribution, the energy of the first principal component is higher than the second. In this way, the error in the first principal component direction can be adaptively suppressed, thereby alleviating the impact of ambiguity annotation on training. However, we find this initial version of STAR loss suffers an abnormal energy increase, leading to premature convergence. To solve this problem, we find that the anomaly results from that the model tends to increase the energy to minimize STAR loss. As a result, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decreasing abnormally.", + "bbox": [ + 496, + 476, + 893, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate the STAR loss on three widely-used benchmarks, i.e., COFW [5], 300W [35] and WFLW [48]. Experiments show that STAR loss indeed helps deep models achieve competitive performance compared to state-of-the-art methods. Code will be released for reproduction.", + "bbox": [ + 496, + 703, + 893, + 780 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 797, + 640, + 814 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "At early stages, facial landmark detection is based on statistic models such as Active Appearance Models [8,31], Constrained Local Models [9], and 3D Morphable Models [2]. Recently, with the development of CNN, deep learning methods have achieved state-of-the-art performance in", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15476", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "facial landmark detection [21, 29, 51, 53], which mainly includes two main branches: coordinate regression method and heatmap regression method.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Coordinate Regression Method. Coordinate regression methods [18, 56, 58] utilize fully connected (FC) layers to learn the transformation between CNN features and landmark coordinates. However, coordinate regression methods commonly require a huge number of samples for training, which constrains performance improvements. To this end, many works address this issue from different perspectives - e.g., style transfer [14, 34], semi-supervised learning [3, 15], and virtual data [47]. To further improve the performance, both MDM [41] and RAR [52] use cascaded recurrent networks to sequentially refine the landmark estimation. SDFL [29] and SDL [27] introduce graph constraint through graph convolutional network (GCN). SLPT [50] and RePFromer [26] learn an adaptive inherent relation based on the attention mechanism.", + "bbox": [ + 75, + 138, + 468, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Heatmap Regression Method. Heatmap regression methods output an intermediate heatmap for each landmark and take the landmark with the highest intensity as the optimal output. The stacked hourglass network [55], U-Net [11], and HRNet [44] are commonly used to generate the high-quality heatmap. However, heatmap regression methods usually suffer from quantization error since the heatmap is commonly much smaller than the input image. Many works are proposed to mitigate the error, including better heatmap generation [4, 16], mapping construction from heatmap to coordinates [24, 32], coordinates further refinement [4, 38, 53]. Furthermore, many works [21, 45, 48] use facial boundary as the structure constraint to further improve the performance. HSLE [60] automatically constructs a hierarchical structure for learning robust facial landmark detection. LUVLi [24] estimates both the uncertainty and visibility of predicted landmarks. And FaRL [57] proposes the general facial representation learning.", + "bbox": [ + 75, + 368, + 470, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic Ambiguity in Facial Landmark Detection. There exist several works [15, 16, 21, 24, 30, 48] addressing semantic ambiguity problems on facial landmark detection. SBR [16] uses the coherency of optical flow between adjacent frames as supervision but is sensitive to illumination and occlusion. LAB [48] uses facial boundary lines as the structure constraint, which is practical but computationally expensive. Moreover, SA [30] proposes a latent variable optimization strategy to find semantically consistent annotations and alleviate random noise during the training stage. However, the complex training strategy limits its application. Closely related to our work is ADNet [21], which presents two key modules, i.e., Anisotropic Direction Loss (ADL) and Anisotropic Attention Module (AAM), to handle the ambiguous annotations problem. Among them, ADL imposes more constraints in normal direction for landmarks on facial boundaries, but the direction and constraint", + "bbox": [ + 75, + 643, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "weight is hand-crafted so that such coarse-grained design degrades its performance.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 132, + 625, + 150 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We briefly introduce the pipeline of current widely-used regression methods below.", + "bbox": [ + 498, + 157, + 890, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown at the top of Figure 2, the basic model of the regression method is stacked of four Hourglasses Networks (HGs) [56]. Each HG generates $N$ heatmaps, where $N$ is the number of pre-defined facial landmarks. The normalized heatmap can be viewed as the probability distribution over the predicted facial landmarks. The predicted coordinates are decoded from the heatmap by a soft-Argmax [32].", + "bbox": [ + 496, + 188, + 890, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, given a discrete probability distribution $h$ , we define the value $h_i$ as the probability of the predicted landmark locating at $y_i \\in \\mathbb{R}^2$ . The expectation coordinate $\\mu$ is decoded by soft-Argmax:", + "bbox": [ + 496, + 294, + 890, + 354 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu = \\text {s o f t - A r g m a x} (h) = \\sum_ {i} h _ {i} y _ {i}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 361, + 890, + 392 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on these predicted coordinates, we can use the regression loss to learn the parameter of the model. The regression loss can be viewed as a distance $d(\\cdot)$ between predicted coordinates $\\mu$ and manual annotations $y_{t}$ . And $l1$ -distance, $l2$ -distance, smooth- $l1$ distance, and Wing distance [18] are widely used. So, the regression loss can be formulated as follows:", + "bbox": [ + 496, + 398, + 890, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e g} = d \\left(y _ {t} - \\mu\\right) = d \\left(y _ {t} - \\sum_ {i} h _ {i} y _ {i}\\right). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 508, + 890, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The manual annotations suffer from the semantic ambiguity problem. As shown in the gray box of Figure 2, the key to this problem lies in the regression loss.", + "bbox": [ + 496, + 546, + 890, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 602, + 589, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The semantic ambiguity problem degrades detection performance considerably. To handle this problem, we design a novel STAR loss, which is influenced by predicted distribution. Specifically, STAR loss is encouraged to be small when the predicted distribution is anisotropic. To represent the shape of the predicted distribution, we first introduce a customized PCA applied to the discrete probability distribution. Then, we visualize the results of PCA computed on the predicted distribution and discuss the relevance between its first principal component and the semantic ambiguity. Based on this, we present the STAR loss in detail, which adaptively suppresses the prediction error in the first principal component direction to mitigate the impact of ambiguity annotation during the training phase.", + "bbox": [ + 496, + 628, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Analysis of the Semantic Ambiguity", + "text_level": 1, + "bbox": [ + 500, + 847, + 805, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The PCA of Discrete Probability Distribution. We first design a customized PCA applied to the discrete", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15477", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/de660ebb60a08bf2679d9ff1e2b04c2b125f3f6ac83d5c1c533389e11eab5c9c.jpg", + "image_caption": [ + "Figure 3. The visualization of the PCA results. The yellow and blue arrows indicate the predicted discrete distribution's first and second principal components, respectively. The length of the arrow is the corresponding eigenvalues. We use the $(\\lambda_1 / \\lambda_2)$ to formulate the ambiguity, which is represented by the shading of the blue ellipse. (Best view in color.)" + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "probability distribution, which is composed of two steps: (1) Approximate the means and covariance matrix; (2) Compute the eigen-decomposition of the covariance matrix.", + "bbox": [ + 75, + 364, + 468, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "STEP 1: similar to the weighted mean in Eq.(1), the weighted covariance matrix is given by:", + "bbox": [ + 76, + 411, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma_ {b} = \\frac {\\sum_ {i} h _ {i} \\left(y _ {i} - \\mu\\right) ^ {T} \\left(y _ {i} - \\mu\\right)}{V _ {1}}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 452, + 468, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V_{1} = \\sum_{i}h_{i}$ . To approximate more precisely, we determine a correction factor to yield an unbiased estimator. The correction factor is $(1 - V_2 / V_1^2)$ , where $V_{2} = \\sum_{i}h_{i}^{2}$ . So, the unbiased weighted estimate of the covariance matrix, with Bessel's correction, is given by Eq.(4). And we commonly use $\\Sigma = \\Sigma_{ub}$ .", + "bbox": [ + 75, + 498, + 472, + 590 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma_ {u b} = \\frac {\\sum_ {i} h _ {i} (y _ {i} - \\mu) ^ {T} (y _ {i} - \\mu)}{V _ {1} - (V _ {2} / V _ {1})}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 599, + 468, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "STEP 2: we compute the eigen-decomposition of covariance matrix, which can be formulated as below:", + "bbox": [ + 76, + 647, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma = V L V ^ {- 1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 222, + 688, + 468, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $V = \\left[v_{1},v_{2}\\right]\\in \\mathbb{R}^{2\\times 2}$ is the eigenvectors matrix, and $L = diag(\\lambda_1,\\lambda_2)\\in \\mathbb{R}^{2\\times 2}$ is the corresponding eigenvalues matrix. We refer $(v_{1},\\lambda_{1})$ and $(v_{2},\\lambda_{2})$ to represent the first and second principal component, respectively.", + "bbox": [ + 76, + 717, + 468, + 780 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discussion of Relevance. In Figure 3, we visualize the PCA results of predicted discrete probability distribution (More visualization can be found in supplementary materials). On the one hand, a significant feature of the contour landmarks is that their first principal component is along with the face contour. Meanwhile, as discussed above, the ambiguity direction for the contour landmarks is also along with the face contour. That is, for landmarks with an", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "anisotropic predicted distribution, the first principal component direction is highly consistent with their ambiguity direction. On the other hand, we visualize the elliptical eccentricity $(\\lambda_1 / \\lambda_2)$ by the shading of blue. Compared with the near-white eye corner, the color of the contour point is blue. It indicates that eccentricity is higher when the ambiguity is more severe. We further infer that the corresponding energy can represent the ambiguity intensity. Because the energy indicates the variance along with the corresponding direction of the principal component. Meanwhile, the high variance in an anisotropic predicted distribution mainly results from inconsistent annotation caused by semantic ambiguity. Based on these two observations, we introduce STAR loss.", + "bbox": [ + 496, + 90, + 892, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. STAR Loss", + "text_level": 1, + "bbox": [ + 500, + 299, + 624, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed STAR loss belongs to a self-adaptive ambiguity reduction regression loss. And we realize it by an ambiguity-guided decomposition. Meanwhile, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decrease abnormally.", + "bbox": [ + 496, + 323, + 890, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ambiguity-guided Decomposition. Following the motivations above, STAR loss decomposes the prediction error into the two principal component directions and divides by the corresponding energy value to reduce ambiguity effect self-adaptively. Thus, the STAR loss can be formulated as:", + "bbox": [ + 496, + 398, + 892, + 476 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {S T A R} \\left(y _ {t}, \\mu , d\\right) = \\frac {1}{\\sqrt {\\lambda_ {1}}} d \\left(v _ {1} ^ {T} \\left(y _ {t} - \\mu\\right)\\right) \\tag {6} \\\\ + \\frac {1}{\\sqrt {\\lambda_ {2}}} d (v _ {2} ^ {T} (y _ {t} - \\mu)), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 487, + 890, + 553 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $v_{1}^{T}$ and $v_{2}^{T}$ project the prediction error $(y_{t} - \\mu)$ according to ambiguity directions, $\\lambda_{1}$ and $\\lambda_{2}$ adaptively imposes constraint, and $d$ denotes the distance function. Because the decomposition operation does not affect the error metric, STAR loss can be used with an arbitrary distance function and benefits from their improvement, such as smooth- $l1$ , Wing [18], Awing [45], etc.", + "bbox": [ + 496, + 565, + 890, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Take an anisotropic distribution as an example where the $\\lambda_{1}$ is much larger than $\\lambda_{2}$ . The $\\mathcal{L}_{STAR}$ results in a small prediction error in the direction of the first principal component $v_{1}$ . It makes the model pay less attention to the prediction error in the diction of $v_{1}$ , which is mainly caused by inconsistent manual annotation. As a result, with the help of $\\mathcal{L}_{STAR}$ , the detection model can mitigate the impact of semantic ambiguity, leading to better convergence.", + "bbox": [ + 496, + 672, + 892, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Eigenvalue Restriction. According to our experiments, we find an abnormal increase of the eigenvalue $\\lambda_{i}$ that leads to the model's premature convergence. To solve this problem, we consider the main reason is that the eigenvalue $\\lambda$ is a denominator in $\\mathcal{L}_{STAR}$ . To minimize $\\mathcal{L}_{STAR}$ , the model tends to increase the eigenvalue $\\lambda_{i}$ . Therefore, we propose two kinds of restriction on the eigenvalue to avoid $\\mathcal{L}_{STAR}$", + "bbox": [ + 496, + 795, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15478", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4b9f59b68c1d3713c138abed727e727f6090195195579cd55da51228b49268b7.jpg", + "image_caption": [ + "Figure 4. The NME results of different distance functions with varying input image resolution in WFLW. The blue and red lines indicate the distance function without and with STAR loss, respectively." + ], + "image_footnote": [], + "bbox": [ + 81, + 101, + 277, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/af731285c73689cb512cda2ec106aae836521504938665a34ba5c6519167c345.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 101, + 478, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1143169f3da3a8362f82315a8c3b19550894873a3446c23179af907044b993a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 101, + 676, + 210 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/23b9d7c74e7f5028ec8d1681c68ac7c921d27dcaca0f5618b7109e4cf8968089.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 676, + 101, + 875, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "decrease abnormally. The first one is a loss restriction term, namely value restriction, which is formulated as below:", + "bbox": [ + 75, + 277, + 467, + 306 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {v a l u e}} = \\frac {\\lambda_ {1} + \\lambda_ {2}}{2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 319, + 468, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It directly restricts the abnormal increase of the eigenvalue. On the other hand, we propose to detach the gradient of eigenvalue and eigenvectors, namely detach restriction. It cuts off the backpropagation from eigenvalue and eigenvectors so that they act as constant values in STAR loss. Thus, STAR loss could use them but not directly affect the shape of the predicted distribution. The ablation study shows that both restrictions help mitigate the abnormal increase problem. And we use the value restriction as the default setting unless mentioned.", + "bbox": [ + 75, + 356, + 468, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 522, + 209, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we present the experiment settings, including training details, model setup, dataset, and evaluation metrics. Second, we investigate the benefits of STAR loss with extensive experiments. Third, we discuss the relationship between STAR Loss and related works.", + "bbox": [ + 75, + 547, + 468, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 76, + 635, + 269, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data Augmentation. We use the same data augmentation strategy in [21] for all experiments. The input image is generated in two steps: (1) Crop the face regions and resize them into $256 \\times 256$ . (2) Perform augmentations with random rotation $(18^{\\circ})$ , random scaling $(\\pm 10\\%)$ , random crop $(\\pm 5\\%)$ , random gray $(20\\%)$ , random blur $(30\\%)$ , random occlusion $(40\\%)$ and random horizontal flip $(50\\%)$ .", + "bbox": [ + 75, + 657, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Setup of Model. We use a four-stacked hourglass model as the backbone. The recursive step in HG is set to 3. Each hourglass module outputs a $64 \\times 64$ feature map. We follow the training strategy introduces in [21]. Specifically, we employed an Adam optimizer and an initial learning rate of $1 \\times 10^{-3}$ . We train the model for 500 epochs and reduce the learning rate by 10 at each epoch of 200, 350, and 450. The model was trained on four GPUs (32GB NVIDIA Tesla V100), where the batch size of each GPU is 16. We", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "also study some commonly used tricks that can further improve the performance, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21].", + "bbox": [ + 496, + 277, + 890, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on three commonly used public datasets including COFW [5], 300W [35], WFLW [48]. Meanwhile, we use a video-based dataset, 300VW [7,37,42], to make a cross-dataset validation. In detail, COFW contains 1,345 training images and 507 testing images with 29 landmarks. 300W contains 3,148 training images and 689 test images. All images are labeled with 68 landmarks. We use the common setting on 300-W, where the test set is split into the common (554 images) and challenge (135 images) sets. WFLW is currently the most used dataset in facial landmark detection, which contains 7,500 training images and 2,500 test images with 98 landmarks. 300VW: we use the test sets to validate the model trained on 300W. It provides three test sets: Category-A (well-lit, 31 videos with 62,135 frames), Category-B (mild unconstrained, 19 videos with 32,805 videos), and Category-C (challenging, 14 videos with 26,338 frames).", + "bbox": [ + 496, + 323, + 892, + 578 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We use three commonly used evaluation metrics: Normalized Mean Error (NME), Failure Rate (FR), and Area Under Curve (AUC), to evaluate the landmark detection performance. Specifically, (1) NME: we use the inter-ocular distance in 300W, WFLW dataset, and the inter-pupils distance in COFW dataset for normalization; (2) FR: we set the thresholds by $10\\%$ for WFLW; (3) AUC: we set the thresholds by $10\\%$ for WFLW.", + "bbox": [ + 496, + 579, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Accuracy Evaluation", + "text_level": 1, + "bbox": [ + 500, + 710, + 696, + 726 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compared our STAR loss against 14 state-of-the-art baselines (as reported in Table 1). We design two interesting experiments on 300W, including within-dataset validation and cross-dataset validation. First, the results of within-dataset validation are shown in Table 1. Our method can achieve state-of-the-art performance on all test sets. Primarily, we have a 0.2 improvement in the challenge subset compared with the state-of-the-art methods. Second, for cross-dataset validation, the model is trained on 300W and evaluated on 300VW. Meanwhile, the results of cross-dataset validation are shown in Table 2. We evaluate different dis", + "bbox": [ + 496, + 734, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15479", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/390d2a67476ff0dcf1fc8ec9841c6ad950370cdd4766b41a75208e2429804242.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneParam. (M)WFLW-FullCOFW (NME)300W (NME)
(NME)(FR10%)(AUC10%)FullComm.Chal.
LAB [48]Hourglass12.265.277.560.532-3.492.985.19
Wing [18]ResNet-50254.996.000.5505.44---
DeCaFa [11]U-Net104.624.840.563-3.392.935.26
HRNet [44]HRNet-W189.74.64.64--3.322.875.15
Awing [45]Hourglass25.14.362.840.5724.943.072.724.52
AVS + SAN [33]ITN-CPM-4.394.080.591-3.863.216.46
DAG [28]HRNet-W18-4.213.040.589-3.042.624.77
LUVLi [24]DU-Net-4.373.120.577-3.232.765.16
ADNet [21]Hourglass13.374.142.720.6024.682.932.534.58
HIH [53]Hourglass22.684.082.600.6054.633.092.654.89
PIPNet [22]ResNet-10145.74.31---3.192.784.89
SLPT [50]HRNet-W18C-lite9.984.142.760.5954.793.172.754.90
DTLD [25]ResNet-1813.34.082.76--2.962.594.50
RePFormer [26]ResNet-101-4.11---3.01--
Ours (smooth-l1 distance)Hourglass13.374.022.320.6054.622.872.524.32
", + "bbox": [ + 83, + 88, + 888, + 375 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8dd2f77bd7fce177bb3c5105610ac7858f966ab7be5948fda43b00838f9f4013.jpg", + "table_caption": [ + "Table 1. Comparing with state-of-the-art methods on COFW, 300W and WFLW. The best and second best results are marked in colors of red and blue, respectively. We mainly report NME score on COFW, 300W, and WFLW. On WFLW, we also report the FR and AUC, whose thresholds are both set to $10\\%$ ." + ], + "table_footnote": [], + "table_body": "
wo./w.Category-ACategory-BCategory-C
l14.08/4.083.33/3.378.71/8.55
l24.16/3.963.48/3.358.44/8.27
smooth-l14.00/3.973.40/3.398.69/8.42
", + "bbox": [ + 83, + 431, + 460, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tance functions combined with STAR loss. The results show that our method achieves an average improvement of 0.2 in Category-C. Notably, the subset Category-C is the most challenging one, where the video frames are blurred and with strong occlusions. We observe a significant improvement in the challenge test of both within-dataset and cross-dataset validation, which verifies the effectiveness of our method. Meanwhile, our method achieves state-of-the-art performance in the COFW dataset.", + "bbox": [ + 75, + 578, + 468, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The WFLW is a very challenging benchmark because it contains many images under adverse conditions such as pose, make-up, illumination, blur, and expression. We report the results in Table 1, where our method still achieves the best results. In detail, our STAR loss achieves an improvement of 0.06, 0.28 in NME, and $\\mathrm{FR}_{10\\%}$ metrics of the full test set, respectively, when compared to the state-of-the-art methods. Compared with the increase in COFW and 300-W datasets, the improvement achieved by STAR loss in the WFLW dataset is sufficient. We conclude that STAR loss has a better performance over a big dataset, i.e., the proposed STAR loss will mitigate the effect of annotation", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d1959204d86eb8b21d6925f794a22f3f225a590f19d44cff1534cd247aa5448a.jpg", + "table_caption": [ + "Table 2. The cross-dataset validations with different distance functions. We train all modes on 300W with or without using STAR loss, and we report the NME scores on 300VW." + ], + "table_footnote": [], + "table_body": "
wo./w.l1smooth-l1l2Wing
COFW
basic5.00/4.765.02/4.785.59/4.894.94/4.79
+DR4.78/4.704.76/4.705.06/4.734.76/4.67
+AAM5.01/4.774.88/4.625.44/4.774.95/4.70
300W
basic3.13/2.983.12/3.003.45/3.053.12/3.02
+DR3.04/2.943.02/2.963.20/2.993.04/2.96
+AAM2.97/2.892.93/2.873.08/2.912.93/2.88
WFLW
basic4.35/4.164.34/4.174.79/4.314.32/4.17
+DR4.17/4.134.18/4.104.29/4.214.18/4.12
+AAM4.19/4.054.14/4.024.37/4.114.15/4.05
", + "bbox": [ + 524, + 431, + 867, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. The robustness analysis on COFW, 300W, and WFLW. We report the NME score for basic model trained with or without using our STAR loss. We also study the influence of two widely used tricks, like DR and AAM.", + "bbox": [ + 498, + 636, + 890, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "error and benefit from the large amounts of noise data.", + "bbox": [ + 500, + 705, + 857, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 729, + 653, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation on Different Distance Functions. To investigate the effect of the distance function, we test the STAR loss with the commonly used distance function, such as $l1$ -distance, $l2$ distance, smooth- $l1$ distance, and Wing distance [18] in COFW, 300W and WFLW dataset, respectively. Note that the smooth- $l1$ distance used here is formulated as below:", + "bbox": [ + 496, + 752, + 890, + 857 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l l} \\frac {0 . 5}{s} \\left(y _ {t} - \\mu\\right) ^ {2}, & \\left| y _ {t} - \\mu \\right| < s \\\\ \\left| y _ {t} - \\mu \\right| - 0. 5 s, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 864, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15480", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d8b8716861a2cfffc0361279ea9c067b3a963e958e8543c90487e6e06f8a212d.jpg", + "image_caption": [ + "l1", + "$\\mathcal{L}_{STAR}(l1)$", + "Figure 5. Qualitative results of different distance functions w.o/w. STAR loss on WFLW dataset. Green and red points represent the predicted and ground-truth points, respectively. The yellow circles indicate the clear failures, which are solved with the help of STAR loss. (Best view in color and zoom in.)" + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 277, + 316 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ebe2eaddf9b6a31915c22836e9ae146661a42a604bbd3cc6142078a8dc83e5c1.jpg", + "image_caption": [ + "12", + "$\\mathcal{L}_{STAR}(l2)$" + ], + "image_footnote": [], + "bbox": [ + 281, + 90, + 480, + 316 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/55da0cdfd3e4a8eb044308952442f6145a4fa2c12668678eccb7e3e2dd12dca9.jpg", + "image_caption": [ + "smooth-11", + "$\\mathcal{L}_{STAR}$ (smooth-l1)" + ], + "image_footnote": [], + "bbox": [ + 486, + 89, + 684, + 316 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/784918e6cd66641ff080dc4ada4e5c64398f8f155e45854d7c96a507e308a105.jpg", + "image_caption": [ + "Wing", + "$\\mathcal{L}_{STAR}$ (Wing)" + ], + "image_footnote": [], + "bbox": [ + 691, + 89, + 888, + 316 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $s$ is a threshold that is usually set as $s = 0.01$ . We refer to the regression loss defined in Eq.(2) as a baseline. The results are shown in Table 3. Compared with the baseline, STAR loss can achieve an average improvement of 0.34, 0.19, and 0.25 on COFW, 300W, and WFLW among different distance functions, respectively, with negligible computational. Meanwhile, we find that STAR loss has a significant effect when combined with $l2$ -distance.", + "bbox": [ + 75, + 406, + 468, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Moreover, we visualize the failure cases of different distance functions with and without STAR loss on WFLW dataset. As shown in Figure 5, the results with STAR exhibits better structural constraints. We infer that STAR works as a label regularization, which helps the model avoid over-fitting ambiguity annotation and pay more attention to the relation between landmarks.", + "bbox": [ + 75, + 531, + 468, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation on Different Distribution Normalization. We evaluate our proposed STAR loss with different distribution normalizations, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]. DR is a stricter regularization that forces the heatmap to resemble a Gaussian distribution. AAM is an attention module that learns a point-edge heatmap as an attention mask and forces the heatmap to resemble a mixture of Gaussian distribution and adjacent boundary [24] distribution. In DR, we use Jensen-Shannon divergence as the divergence measure and set the Gaussian $\\sigma$ equals to 1.0. Regarding AAM, we follow the setting in paper [21].", + "bbox": [ + 75, + 640, + 468, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 3, both of them have a positive effect: (1) In the WFLW dataset, STAR loss achieve an average improvement of 0.07 and 0.16 on DR and AAM, respectively; (2) In the COFW dataset, the improvement is 0.14 and 0.35, respectively; (3) In the 300W dataset, the improvement is", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/03fd08072fe4620005b08380bc5592039971e22a84312d08d901ca6159499367.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
w12351020
NME4.174.204.184.184.184.20
", + "bbox": [ + 522, + 404, + 870, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. The analysis of $w$ . We report the NME scores for STAR loss with smooth- $l_{1}$ distance with the varying $w$ on WFLW.", + "bbox": [ + 500, + 441, + 890, + 469 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "0.11 and 0.09, respectively; We observe that the AAM is better suited to STAR loss because the boundary information in AAM further helps. And the best results among the three datasets are taken with the combination of smooth- $l$ 1 distance, AAM, and STAR loss, which refers to the default model setup in accuracy evaluation. Notice that the model used for visualization in Figure 1, and Figure 3 is trained with the combination of $\\mathcal{L}_2$ and DR.", + "bbox": [ + 496, + 491, + 890, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation on Different Input Image Resolution. We investigate the influence of different input image resolutions (64px, 128px, and 256px). The results are shown in Figure 4, STAR loss has a positive effect on all input image resolution. Specifically, STAR loss can achieve an average improvement of 0.20, 0.30, and 0.25 in 64px, 128px, and 256px among different distance functions, respectively. Notice that the baseline with STAR loss in 128px is equal to or better than the baseline in 256px. It means that STAR loss is not very sensitive to the input image size, which encourages using STAR loss in a small model.", + "bbox": [ + 496, + 613, + 892, + 777 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation on Different Restrictions. Firstly, we investigate the value restriction and discuss the effect of its weight $w$ in STAR loss. As shown in Table 4, STAR loss is not sensitive to $w$ , and we choose $w = 1$ as the default setting in our experiments. Then, we analyze the detach restriction. As shown in Table 5, the restriction is essential, and the effect of detach restriction is comparable with the value restriction. This observation indicates that the improvement", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15481", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e326b0eb0413dab7c2399acbec4eb36ee25a5221b39ce2db080bd0153c06ed6c.jpg", + "image_caption": [ + "Figure 6. The variance distribution. We visualize the variance statistic of five models trained under the same experimental setting with and without STAR loss. The red and blue lines indicate the corresponding mean value of $l2$ distance function with and without STAR loss, respectively." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 464, + 255 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is mainly contributed by STAR loss but not the value restriction term.", + "bbox": [ + 75, + 348, + 468, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation on Stability. We evaluate the effect of STAR loss on stability. To quantitatively analyze the stability, we design a toy experiment: 1) train $N = 5$ models under the same experimental setting with and without STAR loss, respectively; 2) count the variance of $N$ models' predictions on the WFLW test set. As shown in Figure 6, the predictions of models trained with our STAR loss distribute more intensively within a small variance range. Meanwhile, the mean value of prediction variances drops from 0.79 to 0.69. It indicates that STAR loss does mitigate the impact of ambiguous annotations and makes prediction more stable.", + "bbox": [ + 75, + 378, + 468, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Discussion with Related Solutions", + "text_level": 1, + "bbox": [ + 76, + 558, + 372, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ADL vs. STAR Loss. In ADNet [21], Huang et al. introduce an Anisotropic Direction Loss (ADL), which imposes strong constraints in the normal direction and weak constraints in the tangent direction for landmarks on the facial boundary. The normal direction is calculated by the slope from its adjacent points, and the constraint strength is a hyperparameter. We argue that the hand-crafted design degrades its performance. Compared with it, STAR loss estimates the direction and constraint weight via PCA of heatmaps, which is a fine-grained and self-adaptive scheme. Then, we replaced ADL with STAR in ADNet and adopted the same setup for a fair comparison. As shown in Table 6, STAR loss brings further improvements of 0.12, 0.28, 0.08, 0.07, 0.13, 0.11, 0.10 in NME in full WFLW and six sub-categories, respectively. Besides, STAR is plug-and-play for heatmap-based methods with an arbitrary number of landmarks without extra direction computation design.", + "bbox": [ + 75, + 582, + 468, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "LUVLi Loss v.s. STAR Loss. LUVLi [24] introduces an uncertainty-based loss (e.g., Gaussian Log-Likelihood (GLL)) to facial landmark detection. The GLL consists of a Mahalanobis distance and a regularization term. As dis", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0325d7db5597cb76bdb2e55f76d442283ebd4991fa59e9eaec1026df9c1b605e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
WFLWbasic+AAM
baseline4.344.14
wo. restriction4.604.61
w. value restriction4.174.02
w. detach restriction4.204.05
", + "bbox": [ + 558, + 88, + 834, + 167 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/86ed9f8371090cd91ad58d9cb242252bed186babf58a0e69c72beff953ceecc6.jpg", + "table_caption": [ + "Table 5. The analysis of restriction method. We report the NME scores for STAR loss (smooth- $l1$ distance) without and with different restriction methods on WFLW." + ], + "table_footnote": [], + "table_body": "
WFLWFullPoseExp.Ill.Make.Occl.Blur
ADL [21]4.146.964.384.094.055.064.79
STAR4.026.764.273.973.844.804.58
", + "bbox": [ + 501, + 232, + 890, + 270 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. The comparison between ADL and STAR loss.", + "bbox": [ + 527, + 272, + 861, + 286 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cussed in Sec. 5.3, the value restriction is unnecessary for STAR loss. So, we mainly compare the Mahalanobis distance with $\\mathcal{L}_{STAR}$ by a toy experiment: replace $\\mathcal{L}_{STAR}$ with Mahalanobis distance and adopt the same setup for a fair comparison. The experiment shows that replacing $\\mathcal{L}_{STAR}$ with Mahalanobis can take 4.32 in NME in WFLW. However, our $\\mathcal{L}_{STAR}$ takes 4.17, which has a further 0.15 NME improvement in WFLW. So, compared with LUVLi, STAR is lighter and better: 1) propose the heatmap-based covariance estimation, simplifying model structure; 2) design the loss function from the perspective of ambiguity reduction, thus achieving significant performance gain.", + "bbox": [ + 496, + 319, + 890, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 532, + 617, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We study the semantic ambiguity problem in facial landmark detection and propose a self-adaptive ambiguity reduction method, STAR loss. We first observe that the predicted distribution can represent semantic ambiguity. Then we use PCA to indicate the character of the predicted distribution and indirectly formulate the direction and intensity of semantic ambiguity. Based on this, STAR loss adaptively suppresses the prediction error in the ambiguity direction to mitigate the impact of ambiguity annotation in training. With the help of STAR loss, our method achieves state-of-the-art performance on three benchmarks.", + "bbox": [ + 496, + 561, + 890, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This work was supported in part by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001) and the Grant-in-Aid for JSPS Fellows Grant (No. 21F20377).", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15482", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jianmin Bao, Dong Chen, Fang Wen, Houqiang Li, and Gang Hua. Towards open-set identity preserving face synthesis. 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In CVPR, 2019. 3" + ], + "bbox": [ + 501, + 92, + 890, + 544 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15484", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_model.json b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2aea66847b086d9604364e202537e412d59cf02c --- /dev/null +++ b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_model.json @@ -0,0 +1,2321 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.131, + 0.861, + 0.154 + ], + "angle": 0, + "content": "STAR Loss: Reducing Semantic Ambiguity in Facial Landmark Detection" + }, + { + "type": "text", + "bbox": [ + 0.13, + 0.18, + 0.843, + 0.2 + ], + "angle": 0, + "content": "Zhenglin Zhou\\(^{1*}\\), Huaxia Li\\(^{2*}\\), Hong Liu\\(^{3*}\\), Nanyang Wang\\(^{2}\\), Gang Yu\\(^{2}\\), Rongrong Ji\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.102, + 0.201, + 0.871, + 0.266 + ], + "angle": 0, + "content": "1 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University. 2 Tencent PCG. 3 National Institute of Information. zhenglinzhou@stu.xmu.edu.cn, {haroldzcli, cageswang, skicyyu}@tencent.com, hliu@nii.ac.jp, rrji@xmu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.336, + 0.474, + 0.699 + ], + "angle": 0, + "content": "Recently, deep learning-based facial landmark detection has achieved significant improvement. However, the semantic ambiguity problem degrades detection performance. Specifically, the semantic ambiguity causes inconsistent annotation and negatively affects the model's convergence, leading to worse accuracy and instability prediction. To solve this problem, we propose a Self-adaptTive Ambiguity Reduction (STAR) loss by exploiting the properties of semantic ambiguity. We find that semantic ambiguity results in the anisotropic predicted distribution, which inspires us to use predicted distribution to represent semantic ambiguity. Based on this, we design the STAR loss that measures the anisotropism of the predicted distribution. Compared with the standard regression loss, STAR loss is encouraged to be small when the predicted distribution is anisotropic and thus adaptively mitigates the impact of semantic ambiguity. Moreover, we propose two kinds of eigenvalue restriction methods that could avoid both distribution's abnormal change and the model's premature convergence. Finally, the comprehensive experiments demonstrate that STAR loss outperforms the state-of-the-art methods on three benchmarks, i.e., COFW, 300W, and WFLW, with negligible computation overhead. Code is at https://github.com/ZhenglinZhou/STAR" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.725, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.47, + 0.826 + ], + "angle": 0, + "content": "Facial landmark detection, which aims to locate a group of pre-defined facial landmarks from images [48, 51, 56], is a fundamental problem for many downstream tasks, including face verification [12], face synthetic [1], and 3D face reconstruction [10, 13, 17, 46]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.47, + 0.857 + ], + "angle": 0, + "content": "Thanks to the development of Convolutional Neural Networks (CNNs) [20, 36, 39], facial landmark detection has" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.304, + 0.889, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.491, + 0.895, + 0.588 + ], + "angle": 0, + "content": "Figure 1. The impact of semantic ambiguity. We visualize the outputs of five models trained with the same architecture under the same experimental setting. (1) The first row shows the predicted facial landmarks for Mr. Tony Stark, marked as red points. And the green point refers to the corresponding mean value. (2) The second row shows the results of predicted probability distribution (i.e., heatmap) from one of the trained models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.895, + 0.867 + ], + "angle": 0, + "content": "improved significantly. At first, coordinate regression methods [3, 16, 33, 47] are proposed to learn the transformation between CNN features and landmark locations via fully connected layers. Recently, the research focus has been the heatmap regression methods, which have shown superiority over coordinate regression methods. The heatmap regression methods [21, 24, 48] predict an intermediate heatmap for each landmark and decode the coordinates from the heatmap. But, the commonly used decoder, Argmax [55], is not differentiable and suffers from quantization error. Recently, some solutions have been proposed [38, 53], and the focus is on the differentiable expectation decoder: soft-Argmax [32]. With the help of soft-Argmax, the heatmap regression method has the advantage of end-to-end training. So the training loss is mainly composed of a regression loss (such as \\(\\mathcal{L}_2\\)), which makes the model prediction fit the manual annotation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.895, + 0.902 + ], + "angle": 0, + "content": "However, the manual annotation suffers from the semantic ambiguity problem [16, 21, 30]. Specifically, some fa" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.863, + 0.223, + 0.876 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.876, + 0.469, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution. This work was done when Zhenglin Zhou was an enrn at Tencent PCG." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.863, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15475" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.862, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.206, + 0.541, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.547, + 0.206, + 0.887, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.326, + 0.893, + 0.357 + ], + "angle": 0, + "content": "Figure 2. The overview of our framework. We use a four stacked Hourglasses (HGs) Network. To mitigate the impact of semantic ambiguity, the STAR loss is applied to each HG module. (Best view in color.)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.473, + 0.581 + ], + "angle": 0, + "content": "cial landmarks, especially landmarks located on face contour, do not have a clear and accurate definition. For example, the contour landmarks are defined to evenly distribute around the face contour without a clear definition of the positions [30]. It makes human annotators confused about the position, and it is inevitable to induce inconsistent and imprecise annotations. Thus, we argue that the regression loss will be misled by ambiguous annotations and degrade the model's convergence and performance. As shown in Figure 1, training the neural network with ambiguous annotations makes the predictions for facial contour landmarks unstable and inaccurate, which will hurt the downstream task [15]. The key problem is to design a new regression loss that mitigates the impact of semantic ambiguity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.824 + ], + "angle": 0, + "content": "In this paper, we propose a novel self-adaptive ambiguity reduction method, STAR loss, by fully exploiting semantic ambiguity. To this end, we explore the impact of semantic ambiguity on the heatmap. Typically, the distribution normalization loss forces the predicted probability distribution to resemble an isotropic Gaussian distribution [32]. However, as shown in Figure 1, compared with the isotropic distribution of the eye corner point, the predicted distribution of the facial contour point is anisotropic. The main difference between the two landmarks is semantic ambiguity, which is more severe in the contour point. We infer that the semantic ambiguity is related to the anisotropic distribution. When the predicted distribution of one facial landmark is anisotropic, this facial landmark has severe semantic ambiguity (leading to model unconvergence), so it is necessary to reduce its impact." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To this end, we begin our story by introducing a customized principal component analysis (PCA) that can process the discrete probability distribution, which contains three steps: weighted mean estimation, unbiased weighted covariance estimation, and eigen-decomposition. We de" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.893, + 0.476 + ], + "angle": 0, + "content": "compose a group of predicted distributions and visualize the corresponding principal components. The visualization results show that the first principal component is along with the face contour. Meanwhile, the ambiguous direction for contour landmarks is aligned with the face contour. Therefore, we infer that their first principal component direction is highly consistent with their ambiguity direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.895, + 0.702 + ], + "angle": 0, + "content": "According to this new observation, we design our STAR loss, which decomposes the prediction error into two principal component directions and divides it by the corresponding energy value. For a facial landmark with anisotropic predicted distribution, the energy of the first principal component is higher than the second. In this way, the error in the first principal component direction can be adaptively suppressed, thereby alleviating the impact of ambiguity annotation on training. However, we find this initial version of STAR loss suffers an abnormal energy increase, leading to premature convergence. To solve this problem, we find that the anomaly results from that the model tends to increase the energy to minimize STAR loss. As a result, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decreasing abnormally." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.781 + ], + "angle": 0, + "content": "We evaluate the STAR loss on three widely-used benchmarks, i.e., COFW [5], 300W [35] and WFLW [48]. Experiments show that STAR loss indeed helps deep models achieve competitive performance compared to state-of-the-art methods. Code will be released for reproduction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.642, + 0.815 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "At early stages, facial landmark detection is based on statistic models such as Active Appearance Models [8,31], Constrained Local Models [9], and 3D Morphable Models [2]. Recently, with the development of CNN, deep learning methods have achieved state-of-the-art performance in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15476" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "facial landmark detection [21, 29, 51, 53], which mainly includes two main branches: coordinate regression method and heatmap regression method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.14, + 0.47, + 0.365 + ], + "angle": 0, + "content": "Coordinate Regression Method. Coordinate regression methods [18, 56, 58] utilize fully connected (FC) layers to learn the transformation between CNN features and landmark coordinates. However, coordinate regression methods commonly require a huge number of samples for training, which constrains performance improvements. To this end, many works address this issue from different perspectives - e.g., style transfer [14, 34], semi-supervised learning [3, 15], and virtual data [47]. To further improve the performance, both MDM [41] and RAR [52] use cascaded recurrent networks to sequentially refine the landmark estimation. SDFL [29] and SDL [27] introduce graph constraint through graph convolutional network (GCN). SLPT [50] and RePFromer [26] learn an adaptive inherent relation based on the attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.471, + 0.642 + ], + "angle": 0, + "content": "Heatmap Regression Method. Heatmap regression methods output an intermediate heatmap for each landmark and take the landmark with the highest intensity as the optimal output. The stacked hourglass network [55], U-Net [11], and HRNet [44] are commonly used to generate the high-quality heatmap. However, heatmap regression methods usually suffer from quantization error since the heatmap is commonly much smaller than the input image. Many works are proposed to mitigate the error, including better heatmap generation [4, 16], mapping construction from heatmap to coordinates [24, 32], coordinates further refinement [4, 38, 53]. Furthermore, many works [21, 45, 48] use facial boundary as the structure constraint to further improve the performance. HSLE [60] automatically constructs a hierarchical structure for learning robust facial landmark detection. LUVLi [24] estimates both the uncertainty and visibility of predicted landmarks. And FaRL [57] proposes the general facial representation learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Semantic Ambiguity in Facial Landmark Detection. There exist several works [15, 16, 21, 24, 30, 48] addressing semantic ambiguity problems on facial landmark detection. SBR [16] uses the coherency of optical flow between adjacent frames as supervision but is sensitive to illumination and occlusion. LAB [48] uses facial boundary lines as the structure constraint, which is practical but computationally expensive. Moreover, SA [30] proposes a latent variable optimization strategy to find semantically consistent annotations and alleviate random noise during the training stage. However, the complex training strategy limits its application. Closely related to our work is ADNet [21], which presents two key modules, i.e., Anisotropic Direction Loss (ADL) and Anisotropic Attention Module (AAM), to handle the ambiguous annotations problem. Among them, ADL imposes more constraints in normal direction for landmarks on facial boundaries, but the direction and constraint" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "weight is hand-crafted so that such coarse-grained design degrades its performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.133, + 0.627, + 0.151 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.159, + 0.892, + 0.188 + ], + "angle": 0, + "content": "We briefly introduce the pipeline of current widely-used regression methods below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.189, + 0.892, + 0.295 + ], + "angle": 0, + "content": "As shown at the top of Figure 2, the basic model of the regression method is stacked of four Hourglasses Networks (HGs) [56]. Each HG generates \\(N\\) heatmaps, where \\(N\\) is the number of pre-defined facial landmarks. The normalized heatmap can be viewed as the probability distribution over the predicted facial landmarks. The predicted coordinates are decoded from the heatmap by a soft-Argmax [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.356 + ], + "angle": 0, + "content": "Formally, given a discrete probability distribution \\( h \\), we define the value \\( h_i \\) as the probability of the predicted landmark locating at \\( y_i \\in \\mathbb{R}^2 \\). The expectation coordinate \\( \\mu \\) is decoded by soft-Argmax:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.362, + 0.892, + 0.393 + ], + "angle": 0, + "content": "\\[\n\\mu = \\text {s o f t - A r g m a x} (h) = \\sum_ {i} h _ {i} y _ {i}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.504 + ], + "angle": 0, + "content": "Based on these predicted coordinates, we can use the regression loss to learn the parameter of the model. The regression loss can be viewed as a distance \\( d(\\cdot) \\) between predicted coordinates \\( \\mu \\) and manual annotations \\( y_{t} \\). And \\( l1 \\)-distance, \\( l2 \\)-distance, smooth- \\( l1 \\) distance, and Wing distance [18] are widely used. So, the regression loss can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.509, + 0.892, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e g} = d \\left(y _ {t} - \\mu\\right) = d \\left(y _ {t} - \\sum_ {i} h _ {i} y _ {i}\\right). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.592 + ], + "angle": 0, + "content": "The manual annotations suffer from the semantic ambiguity problem. As shown in the gray box of Figure 2, the key to this problem lies in the regression loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.603, + 0.591, + 0.619 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.84 + ], + "angle": 0, + "content": "The semantic ambiguity problem degrades detection performance considerably. To handle this problem, we design a novel STAR loss, which is influenced by predicted distribution. Specifically, STAR loss is encouraged to be small when the predicted distribution is anisotropic. To represent the shape of the predicted distribution, we first introduce a customized PCA applied to the discrete probability distribution. Then, we visualize the results of PCA computed on the predicted distribution and discuss the relevance between its first principal component and the semantic ambiguity. Based on this, we present the STAR loss in detail, which adaptively suppresses the prediction error in the first principal component direction to mitigate the impact of ambiguity annotation during the training phase." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.807, + 0.865 + ], + "angle": 0, + "content": "4.1. Analysis of the Semantic Ambiguity" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The PCA of Discrete Probability Distribution. We first design a customized PCA applied to the discrete" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15477" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.346 + ], + "angle": 0, + "content": "Figure 3. The visualization of the PCA results. The yellow and blue arrows indicate the predicted discrete distribution's first and second principal components, respectively. The length of the arrow is the corresponding eigenvalues. We use the \\((\\lambda_1 / \\lambda_2)\\) to formulate the ambiguity, which is represented by the shading of the blue ellipse. (Best view in color.)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.412 + ], + "angle": 0, + "content": "probability distribution, which is composed of two steps: (1) Approximate the means and covariance matrix; (2) Compute the eigen-decomposition of the covariance matrix." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.47, + 0.443 + ], + "angle": 0, + "content": "STEP 1: similar to the weighted mean in Eq.(1), the weighted covariance matrix is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.453, + 0.47, + 0.488 + ], + "angle": 0, + "content": "\\[\n\\Sigma_ {b} = \\frac {\\sum_ {i} h _ {i} \\left(y _ {i} - \\mu\\right) ^ {T} \\left(y _ {i} - \\mu\\right)}{V _ {1}}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.473, + 0.592 + ], + "angle": 0, + "content": "where \\( V_{1} = \\sum_{i}h_{i} \\). To approximate more precisely, we determine a correction factor to yield an unbiased estimator. The correction factor is \\( (1 - V_2 / V_1^2) \\), where \\( V_{2} = \\sum_{i}h_{i}^{2} \\). So, the unbiased weighted estimate of the covariance matrix, with Bessel's correction, is given by Eq.(4). And we commonly use \\( \\Sigma = \\Sigma_{ub} \\)." + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.601, + 0.47, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\Sigma_ {u b} = \\frac {\\sum_ {i} h _ {i} (y _ {i} - \\mu) ^ {T} (y _ {i} - \\mu)}{V _ {1} - (V _ {2} / V _ {1})}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.47, + 0.678 + ], + "angle": 0, + "content": "STEP 2: we compute the eigen-decomposition of covariance matrix, which can be formulated as below:" + }, + { + "type": "equation", + "bbox": [ + 0.223, + 0.689, + 0.47, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\Sigma = V L V ^ {- 1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.718, + 0.47, + 0.781 + ], + "angle": 0, + "content": "where \\(V = \\left[v_{1},v_{2}\\right]\\in \\mathbb{R}^{2\\times 2}\\) is the eigenvectors matrix, and \\(L = diag(\\lambda_1,\\lambda_2)\\in \\mathbb{R}^{2\\times 2}\\) is the corresponding eigenvalues matrix. We refer \\((v_{1},\\lambda_{1})\\) and \\((v_{2},\\lambda_{2})\\) to represent the first and second principal component, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Discussion of Relevance. In Figure 3, we visualize the PCA results of predicted discrete probability distribution (More visualization can be found in supplementary materials). On the one hand, a significant feature of the contour landmarks is that their first principal component is along with the face contour. Meanwhile, as discussed above, the ambiguity direction for the contour landmarks is also along with the face contour. That is, for landmarks with an" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.289 + ], + "angle": 0, + "content": "anisotropic predicted distribution, the first principal component direction is highly consistent with their ambiguity direction. On the other hand, we visualize the elliptical eccentricity \\((\\lambda_1 / \\lambda_2)\\) by the shading of blue. Compared with the near-white eye corner, the color of the contour point is blue. It indicates that eccentricity is higher when the ambiguity is more severe. We further infer that the corresponding energy can represent the ambiguity intensity. Because the energy indicates the variance along with the corresponding direction of the principal component. Meanwhile, the high variance in an anisotropic predicted distribution mainly results from inconsistent annotation caused by semantic ambiguity. Based on these two observations, we introduce STAR loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.3, + 0.625, + 0.315 + ], + "angle": 0, + "content": "4.2. STAR Loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.892, + 0.4 + ], + "angle": 0, + "content": "The proposed STAR loss belongs to a self-adaptive ambiguity reduction regression loss. And we realize it by an ambiguity-guided decomposition. Meanwhile, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decrease abnormally." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.893, + 0.477 + ], + "angle": 0, + "content": "Ambiguity-guided Decomposition. Following the motivations above, STAR loss decomposes the prediction error into the two principal component directions and divides by the corresponding energy value to reduce ambiguity effect self-adaptively. Thus, the STAR loss can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.488, + 0.892, + 0.554 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {S T A R} \\left(y _ {t}, \\mu , d\\right) = \\frac {1}{\\sqrt {\\lambda_ {1}}} d \\left(v _ {1} ^ {T} \\left(y _ {t} - \\mu\\right)\\right) \\tag {6} \\\\ + \\frac {1}{\\sqrt {\\lambda_ {2}}} d (v _ {2} ^ {T} (y _ {t} - \\mu)), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.674 + ], + "angle": 0, + "content": "where \\( v_{1}^{T} \\) and \\( v_{2}^{T} \\) project the prediction error \\( (y_{t} - \\mu) \\) according to ambiguity directions, \\( \\lambda_{1} \\) and \\( \\lambda_{2} \\) adaptively imposes constraint, and \\( d \\) denotes the distance function. Because the decomposition operation does not affect the error metric, STAR loss can be used with an arbitrary distance function and benefits from their improvement, such as smooth- \\( l1 \\), Wing [18], Awing [45], etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.795 + ], + "angle": 0, + "content": "Take an anisotropic distribution as an example where the \\(\\lambda_{1}\\) is much larger than \\(\\lambda_{2}\\). The \\(\\mathcal{L}_{STAR}\\) results in a small prediction error in the direction of the first principal component \\(v_{1}\\). It makes the model pay less attention to the prediction error in the diction of \\(v_{1}\\), which is mainly caused by inconsistent manual annotation. As a result, with the help of \\(\\mathcal{L}_{STAR}\\), the detection model can mitigate the impact of semantic ambiguity, leading to better convergence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Eigenvalue Restriction. According to our experiments, we find an abnormal increase of the eigenvalue \\(\\lambda_{i}\\) that leads to the model's premature convergence. To solve this problem, we consider the main reason is that the eigenvalue \\(\\lambda\\) is a denominator in \\(\\mathcal{L}_{STAR}\\). To minimize \\(\\mathcal{L}_{STAR}\\), the model tends to increase the eigenvalue \\(\\lambda_{i}\\). Therefore, we propose two kinds of restriction on the eigenvalue to avoid \\(\\mathcal{L}_{STAR}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15478" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.102, + 0.278, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.102, + 0.48, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.481, + 0.102, + 0.678, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.102, + 0.876, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.892, + 0.264 + ], + "angle": 0, + "content": "Figure 4. The NME results of different distance functions with varying input image resolution in WFLW. The blue and red lines indicate the distance function without and with STAR loss, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.278, + 0.468, + 0.308 + ], + "angle": 0, + "content": "decrease abnormally. The first one is a loss restriction term, namely value restriction, which is formulated as below:" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.32, + 0.47, + 0.351 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {v a l u e}} = \\frac {\\lambda_ {1} + \\lambda_ {2}}{2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.507 + ], + "angle": 0, + "content": "It directly restricts the abnormal increase of the eigenvalue. On the other hand, we propose to detach the gradient of eigenvalue and eigenvectors, namely detach restriction. It cuts off the backpropagation from eigenvalue and eigenvectors so that they act as constant values in STAR loss. Thus, STAR loss could use them but not directly affect the shape of the predicted distribution. The ablation study shows that both restrictions help mitigate the abnormal increase problem. And we use the value restriction as the default setting unless mentioned." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.523, + 0.21, + 0.54 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.469, + 0.624 + ], + "angle": 0, + "content": "First, we present the experiment settings, including training details, model setup, dataset, and evaluation metrics. Second, we investigate the benefits of STAR loss with extensive experiments. Third, we discuss the relationship between STAR Loss and related works." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.271, + 0.652 + ], + "angle": 0, + "content": "5.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.469, + 0.764 + ], + "angle": 0, + "content": "Data Augmentation. We use the same data augmentation strategy in [21] for all experiments. The input image is generated in two steps: (1) Crop the face regions and resize them into \\(256 \\times 256\\). (2) Perform augmentations with random rotation \\((18^{\\circ})\\), random scaling \\((\\pm 10\\%)\\), random crop \\((\\pm 5\\%)\\), random gray \\((20\\%)\\), random blur \\((30\\%)\\), random occlusion \\((40\\%)\\) and random horizontal flip \\((50\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The Setup of Model. We use a four-stacked hourglass model as the backbone. The recursive step in HG is set to 3. Each hourglass module outputs a \\(64 \\times 64\\) feature map. We follow the training strategy introduces in [21]. Specifically, we employed an Adam optimizer and an initial learning rate of \\(1 \\times 10^{-3}\\). We train the model for 500 epochs and reduce the learning rate by 10 at each epoch of 200, 350, and 450. The model was trained on four GPUs (32GB NVIDIA Tesla V100), where the batch size of each GPU is 16. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.278, + 0.892, + 0.323 + ], + "angle": 0, + "content": "also study some commonly used tricks that can further improve the performance, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.324, + 0.893, + 0.579 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on three commonly used public datasets including COFW [5], 300W [35], WFLW [48]. Meanwhile, we use a video-based dataset, 300VW [7,37,42], to make a cross-dataset validation. In detail, COFW contains 1,345 training images and 507 testing images with 29 landmarks. 300W contains 3,148 training images and 689 test images. All images are labeled with 68 landmarks. We use the common setting on 300-W, where the test set is split into the common (554 images) and challenge (135 images) sets. WFLW is currently the most used dataset in facial landmark detection, which contains 7,500 training images and 2,500 test images with 98 landmarks. 300VW: we use the test sets to validate the model trained on 300W. It provides three test sets: Category-A (well-lit, 31 videos with 62,135 frames), Category-B (mild unconstrained, 19 videos with 32,805 videos), and Category-C (challenging, 14 videos with 26,338 frames)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Evaluation Metrics. We use three commonly used evaluation metrics: Normalized Mean Error (NME), Failure Rate (FR), and Area Under Curve (AUC), to evaluate the landmark detection performance. Specifically, (1) NME: we use the inter-ocular distance in 300W, WFLW dataset, and the inter-pupils distance in COFW dataset for normalization; (2) FR: we set the thresholds by \\(10\\%\\) for WFLW; (3) AUC: we set the thresholds by \\(10\\%\\) for WFLW." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.711, + 0.697, + 0.727 + ], + "angle": 0, + "content": "5.2. Accuracy Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We compared our STAR loss against 14 state-of-the-art baselines (as reported in Table 1). We design two interesting experiments on 300W, including within-dataset validation and cross-dataset validation. First, the results of within-dataset validation are shown in Table 1. Our method can achieve state-of-the-art performance on all test sets. Primarily, we have a 0.2 improvement in the challenge subset compared with the state-of-the-art methods. Second, for cross-dataset validation, the model is trained on 300W and evaluated on 300VW. Meanwhile, the results of cross-dataset validation are shown in Table 2. We evaluate different dis" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15479" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.89, + 0.375 + ], + "angle": 0, + "content": "
MethodBackboneParam. (M)WFLW-FullCOFW (NME)300W (NME)
(NME)(FR10%)(AUC10%)FullComm.Chal.
LAB [48]Hourglass12.265.277.560.532-3.492.985.19
Wing [18]ResNet-50254.996.000.5505.44---
DeCaFa [11]U-Net104.624.840.563-3.392.935.26
HRNet [44]HRNet-W189.74.64.64--3.322.875.15
Awing [45]Hourglass25.14.362.840.5724.943.072.724.52
AVS + SAN [33]ITN-CPM-4.394.080.591-3.863.216.46
DAG [28]HRNet-W18-4.213.040.589-3.042.624.77
LUVLi [24]DU-Net-4.373.120.577-3.232.765.16
ADNet [21]Hourglass13.374.142.720.6024.682.932.534.58
HIH [53]Hourglass22.684.082.600.6054.633.092.654.89
PIPNet [22]ResNet-10145.74.31---3.192.784.89
SLPT [50]HRNet-W18C-lite9.984.142.760.5954.793.172.754.90
DTLD [25]ResNet-1813.34.082.76--2.962.594.50
RePFormer [26]ResNet-101-4.11---3.01--
Ours (smooth-l1 distance)Hourglass13.374.022.320.6054.622.872.524.32
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.379, + 0.893, + 0.42 + ], + "angle": 0, + "content": "Table 1. Comparing with state-of-the-art methods on COFW, 300W and WFLW. The best and second best results are marked in colors of red and blue, respectively. We mainly report NME score on COFW, 300W, and WFLW. On WFLW, we also report the FR and AUC, whose thresholds are both set to \\(10\\%\\)." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.433, + 0.462, + 0.509 + ], + "angle": 0, + "content": "
wo./w.Category-ACategory-BCategory-C
l14.08/4.083.33/3.378.71/8.55
l24.16/3.963.48/3.358.44/8.27
smooth-l14.00/3.973.40/3.398.69/8.42
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.556 + ], + "angle": 0, + "content": "Table 2. The cross-dataset validations with different distance functions. We train all modes on 300W with or without using STAR loss, and we report the NME scores on 300VW." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.47, + 0.716 + ], + "angle": 0, + "content": "tance functions combined with STAR loss. The results show that our method achieves an average improvement of 0.2 in Category-C. Notably, the subset Category-C is the most challenging one, where the video frames are blurred and with strong occlusions. We observe a significant improvement in the challenge test of both within-dataset and cross-dataset validation, which verifies the effectiveness of our method. Meanwhile, our method achieves state-of-the-art performance in the COFW dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "The WFLW is a very challenging benchmark because it contains many images under adverse conditions such as pose, make-up, illumination, blur, and expression. We report the results in Table 1, where our method still achieves the best results. In detail, our STAR loss achieves an improvement of 0.06, 0.28 in NME, and \\(\\mathrm{FR}_{10\\%}\\) metrics of the full test set, respectively, when compared to the state-of-the-art methods. Compared with the increase in COFW and 300-W datasets, the improvement achieved by STAR loss in the WFLW dataset is sufficient. We conclude that STAR loss has a better performance over a big dataset, i.e., the proposed STAR loss will mitigate the effect of annotation" + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.433, + 0.869, + 0.635 + ], + "angle": 0, + "content": "
wo./w.l1smooth-l1l2Wing
COFW
basic5.00/4.765.02/4.785.59/4.894.94/4.79
+DR4.78/4.704.76/4.705.06/4.734.76/4.67
+AAM5.01/4.774.88/4.625.44/4.774.95/4.70
300W
basic3.13/2.983.12/3.003.45/3.053.12/3.02
+DR3.04/2.943.02/2.963.20/2.993.04/2.96
+AAM2.97/2.892.93/2.873.08/2.912.93/2.88
WFLW
basic4.35/4.164.34/4.174.79/4.314.32/4.17
+DR4.17/4.134.18/4.104.29/4.214.18/4.12
+AAM4.19/4.054.14/4.024.37/4.114.15/4.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.637, + 0.892, + 0.692 + ], + "angle": 0, + "content": "Table 3. The robustness analysis on COFW, 300W, and WFLW. We report the NME score for basic model trained with or without using our STAR loss. We also study the influence of two widely used tricks, like DR and AAM." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.707, + 0.859, + 0.722 + ], + "angle": 0, + "content": "error and benefit from the large amounts of noise data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.73, + 0.655, + 0.746 + ], + "angle": 0, + "content": "5.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Evaluation on Different Distance Functions. To investigate the effect of the distance function, we test the STAR loss with the commonly used distance function, such as \\( l1 \\)-distance, \\( l2 \\) distance, smooth- \\( l1 \\) distance, and Wing distance [18] in COFW, 300W and WFLW dataset, respectively. Note that the smooth- \\( l1 \\) distance used here is formulated as below:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.865, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l l} \\frac {0 . 5}{s} \\left(y _ {t} - \\mu\\right) ^ {2}, & \\left| y _ {t} - \\mu \\right| < s \\\\ \\left| y _ {t} - \\mu \\right| - 0. 5 s, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15480" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.278, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.122, + 0.321, + 0.137, + 0.332 + ], + "angle": 0, + "content": "l1" + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.32, + 0.261, + 0.335 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{STAR}(l1)\\)" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.091, + 0.481, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.321, + 0.331, + 0.332 + ], + "angle": 0, + "content": "12" + }, + { + "type": "image_caption", + "bbox": [ + 0.385, + 0.321, + 0.453, + 0.335 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{STAR}(l2)\\)" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.09, + 0.686, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.323, + 0.563, + 0.332 + ], + "angle": 0, + "content": "smooth-11" + }, + { + "type": "image_caption", + "bbox": [ + 0.587, + 0.321, + 0.685, + 0.334 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{STAR}\\) (smooth-l1)" + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.09, + 0.89, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.319, + 0.764, + 0.333 + ], + "angle": 0, + "content": "Wing" + }, + { + "type": "image_caption", + "bbox": [ + 0.799, + 0.319, + 0.885, + 0.333 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{STAR}\\) (Wing)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.345, + 0.893, + 0.386 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of different distance functions w.o/w. STAR loss on WFLW dataset. Green and red points represent the predicted and ground-truth points, respectively. The yellow circles indicate the clear failures, which are solved with the help of STAR loss. (Best view in color and zoom in.)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.469, + 0.527 + ], + "angle": 0, + "content": "where \\( s \\) is a threshold that is usually set as \\( s = 0.01 \\). We refer to the regression loss defined in Eq.(2) as a baseline. The results are shown in Table 3. Compared with the baseline, STAR loss can achieve an average improvement of 0.34, 0.19, and 0.25 on COFW, 300W, and WFLW among different distance functions, respectively, with negligible computational. Meanwhile, we find that STAR loss has a significant effect when combined with \\( l2 \\)-distance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.469, + 0.636 + ], + "angle": 0, + "content": "Moreover, we visualize the failure cases of different distance functions with and without STAR loss on WFLW dataset. As shown in Figure 5, the results with STAR exhibits better structural constraints. We infer that STAR works as a label regularization, which helps the model avoid over-fitting ambiguity annotation and pay more attention to the relation between landmarks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.469, + 0.822 + ], + "angle": 0, + "content": "Evaluation on Different Distribution Normalization. We evaluate our proposed STAR loss with different distribution normalizations, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]. DR is a stricter regularization that forces the heatmap to resemble a Gaussian distribution. AAM is an attention module that learns a point-edge heatmap as an attention mask and forces the heatmap to resemble a mixture of Gaussian distribution and adjacent boundary [24] distribution. In DR, we use Jensen-Shannon divergence as the divergence measure and set the Gaussian \\(\\sigma\\) equals to 1.0. Regarding AAM, we follow the setting in paper [21]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In Table 3, both of them have a positive effect: (1) In the WFLW dataset, STAR loss achieve an average improvement of 0.07 and 0.16 on DR and AAM, respectively; (2) In the COFW dataset, the improvement is 0.14 and 0.35, respectively; (3) In the 300W dataset, the improvement is" + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.405, + 0.871, + 0.437 + ], + "angle": 0, + "content": "
w12351020
NME4.174.204.184.184.184.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.442, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Table 4. The analysis of \\( w \\). We report the NME scores for STAR loss with smooth-\\( l_{1} \\) distance with the varying \\( w \\) on WFLW." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.612 + ], + "angle": 0, + "content": "0.11 and 0.09, respectively; We observe that the AAM is better suited to STAR loss because the boundary information in AAM further helps. And the best results among the three datasets are taken with the combination of smooth-\\(l\\)1 distance, AAM, and STAR loss, which refers to the default model setup in accuracy evaluation. Notice that the model used for visualization in Figure 1, and Figure 3 is trained with the combination of \\(\\mathcal{L}_2\\) and DR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Evaluation on Different Input Image Resolution. We investigate the influence of different input image resolutions (64px, 128px, and 256px). The results are shown in Figure 4, STAR loss has a positive effect on all input image resolution. Specifically, STAR loss can achieve an average improvement of 0.20, 0.30, and 0.25 in 64px, 128px, and 256px among different distance functions, respectively. Notice that the baseline with STAR loss in 128px is equal to or better than the baseline in 256px. It means that STAR loss is not very sensitive to the input image size, which encourages using STAR loss in a small model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Evaluation on Different Restrictions. Firstly, we investigate the value restriction and discuss the effect of its weight \\( w \\) in STAR loss. As shown in Table 4, STAR loss is not sensitive to \\( w \\), and we choose \\( w = 1 \\) as the default setting in our experiments. Then, we analyze the detach restriction. As shown in Table 5, the restriction is essential, and the effect of detach restriction is comparable with the value restriction. This observation indicates that the improvement" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15481" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.092, + 0.465, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.263, + 0.47, + 0.334 + ], + "angle": 0, + "content": "Figure 6. The variance distribution. We visualize the variance statistic of five models trained under the same experimental setting with and without STAR loss. The red and blue lines indicate the corresponding mean value of \\( l2 \\) distance function with and without STAR loss, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.469, + 0.379 + ], + "angle": 0, + "content": "is mainly contributed by STAR loss but not the value restriction term." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.547 + ], + "angle": 0, + "content": "Evaluation on Stability. We evaluate the effect of STAR loss on stability. To quantitatively analyze the stability, we design a toy experiment: 1) train \\( N = 5 \\) models under the same experimental setting with and without STAR loss, respectively; 2) count the variance of \\( N \\) models' predictions on the WFLW test set. As shown in Figure 6, the predictions of models trained with our STAR loss distribute more intensively within a small variance range. Meanwhile, the mean value of prediction variances drops from 0.79 to 0.69. It indicates that STAR loss does mitigate the impact of ambiguous annotations and makes prediction more stable." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.373, + 0.573 + ], + "angle": 0, + "content": "5.4. Discussion with Related Solutions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.839 + ], + "angle": 0, + "content": "ADL vs. STAR Loss. In ADNet [21], Huang et al. introduce an Anisotropic Direction Loss (ADL), which imposes strong constraints in the normal direction and weak constraints in the tangent direction for landmarks on the facial boundary. The normal direction is calculated by the slope from its adjacent points, and the constraint strength is a hyperparameter. We argue that the hand-crafted design degrades its performance. Compared with it, STAR loss estimates the direction and constraint weight via PCA of heatmaps, which is a fine-grained and self-adaptive scheme. Then, we replaced ADL with STAR in ADNet and adopted the same setup for a fair comparison. As shown in Table 6, STAR loss brings further improvements of 0.12, 0.28, 0.08, 0.07, 0.13, 0.11, 0.10 in NME in full WFLW and six sub-categories, respectively. Besides, STAR is plug-and-play for heatmap-based methods with an arbitrary number of landmarks without extra direction computation design." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "LUVLi Loss v.s. STAR Loss. LUVLi [24] introduces an uncertainty-based loss (e.g., Gaussian Log-Likelihood (GLL)) to facial landmark detection. The GLL consists of a Mahalanobis distance and a regularization term. As dis" + }, + { + "type": "table", + "bbox": [ + 0.559, + 0.089, + 0.835, + 0.168 + ], + "angle": 0, + "content": "
WFLWbasic+AAM
baseline4.344.14
wo. restriction4.604.61
w. value restriction4.174.02
w. detach restriction4.204.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.172, + 0.892, + 0.214 + ], + "angle": 0, + "content": "Table 5. The analysis of restriction method. We report the NME scores for STAR loss (smooth- \\(l1\\) distance) without and with different restriction methods on WFLW." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.233, + 0.892, + 0.271 + ], + "angle": 0, + "content": "
WFLWFullPoseExp.Ill.Make.Occl.Blur
ADL [21]4.146.964.384.094.055.064.79
STAR4.026.764.273.973.844.804.58
" + }, + { + "type": "table_caption", + "bbox": [ + 0.529, + 0.273, + 0.862, + 0.287 + ], + "angle": 0, + "content": "Table 6. The comparison between ADL and STAR loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.502 + ], + "angle": 0, + "content": "cussed in Sec. 5.3, the value restriction is unnecessary for STAR loss. So, we mainly compare the Mahalanobis distance with \\(\\mathcal{L}_{STAR}\\) by a toy experiment: replace \\(\\mathcal{L}_{STAR}\\) with Mahalanobis distance and adopt the same setup for a fair comparison. The experiment shows that replacing \\(\\mathcal{L}_{STAR}\\) with Mahalanobis can take 4.32 in NME in WFLW. However, our \\(\\mathcal{L}_{STAR}\\) takes 4.17, which has a further 0.15 NME improvement in WFLW. So, compared with LUVLi, STAR is lighter and better: 1) propose the heatmap-based covariance estimation, simplifying model structure; 2) design the loss function from the perspective of ambiguity reduction, thus achieving significant performance gain." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.533, + 0.619, + 0.547 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.73 + ], + "angle": 0, + "content": "We study the semantic ambiguity problem in facial landmark detection and propose a self-adaptive ambiguity reduction method, STAR loss. We first observe that the predicted distribution can represent semantic ambiguity. Then we use PCA to indicate the character of the predicted distribution and indirectly formulate the direction and intensity of semantic ambiguity. Based on this, STAR loss adaptively suppresses the prediction error in the ambiguity direction to mitigate the impact of ambiguity annotation in training. With the help of STAR loss, our method achieves state-of-the-art performance on three benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement. This work was supported in part by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001) and the Grant-in-Aid for JSPS Fellows Grant (No. 21F20377)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15482" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Jianmin Bao, Dong Chen, Fang Wen, Houqiang Li, and Gang Hua. Towards open-set identity preserving face synthesis. 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In CVPR, 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15484" + } + ] +] \ No newline at end of file diff --git a/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_origin.pdf b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..87ab7c4a38edaac08ea71110c61edce518bba74f --- /dev/null +++ b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/fb30f024-6bbe-44bb-baaf-0659043475bc_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0006ec3f12de0083b03254e1cc74afc4b612bb6fdb7ba565fd6ba889ae8a6a76 +size 5559859 diff --git a/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/full.md b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7839db89dbececbb09a51e2b964bf77e0f0f87cd --- /dev/null +++ b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/full.md @@ -0,0 +1,323 @@ +# STAR Loss: Reducing Semantic Ambiguity in Facial Landmark Detection + +Zhenglin Zhou $^{1*}$ , Huaxia Li $^{2*}$ , Hong Liu $^{3*}$ , Nanyang Wang $^{2}$ , Gang Yu $^{2}$ , Rongrong Ji $^{1\dagger}$ + +1 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University. 2 Tencent PCG. 3 National Institute of Information. zhenglinzhou@stu.xmu.edu.cn, {haroldzcli, cageswang, skicyyu}@tencent.com, hliu@nii.ac.jp, rrji@xmu.edu.cn + +# Abstract + +Recently, deep learning-based facial landmark detection has achieved significant improvement. However, the semantic ambiguity problem degrades detection performance. Specifically, the semantic ambiguity causes inconsistent annotation and negatively affects the model's convergence, leading to worse accuracy and instability prediction. To solve this problem, we propose a Self-adaptTive Ambiguity Reduction (STAR) loss by exploiting the properties of semantic ambiguity. We find that semantic ambiguity results in the anisotropic predicted distribution, which inspires us to use predicted distribution to represent semantic ambiguity. Based on this, we design the STAR loss that measures the anisotropism of the predicted distribution. Compared with the standard regression loss, STAR loss is encouraged to be small when the predicted distribution is anisotropic and thus adaptively mitigates the impact of semantic ambiguity. Moreover, we propose two kinds of eigenvalue restriction methods that could avoid both distribution's abnormal change and the model's premature convergence. Finally, the comprehensive experiments demonstrate that STAR loss outperforms the state-of-the-art methods on three benchmarks, i.e., COFW, 300W, and WFLW, with negligible computation overhead. Code is at https://github.com/ZhenglinZhou/STAR + +# 1. Introduction + +Facial landmark detection, which aims to locate a group of pre-defined facial landmarks from images [48, 51, 56], is a fundamental problem for many downstream tasks, including face verification [12], face synthetic [1], and 3D face reconstruction [10, 13, 17, 46]. + +Thanks to the development of Convolutional Neural Networks (CNNs) [20, 36, 39], facial landmark detection has + +![](images/376a97a868bff121914e5521fc5c0f51c1497fcfc56d236f34539bd882178579.jpg) +Figure 1. The impact of semantic ambiguity. We visualize the outputs of five models trained with the same architecture under the same experimental setting. (1) The first row shows the predicted facial landmarks for Mr. Tony Stark, marked as red points. And the green point refers to the corresponding mean value. (2) The second row shows the results of predicted probability distribution (i.e., heatmap) from one of the trained models. + +improved significantly. At first, coordinate regression methods [3, 16, 33, 47] are proposed to learn the transformation between CNN features and landmark locations via fully connected layers. Recently, the research focus has been the heatmap regression methods, which have shown superiority over coordinate regression methods. The heatmap regression methods [21, 24, 48] predict an intermediate heatmap for each landmark and decode the coordinates from the heatmap. But, the commonly used decoder, Argmax [55], is not differentiable and suffers from quantization error. Recently, some solutions have been proposed [38, 53], and the focus is on the differentiable expectation decoder: soft-Argmax [32]. With the help of soft-Argmax, the heatmap regression method has the advantage of end-to-end training. So the training loss is mainly composed of a regression loss (such as $\mathcal{L}_2$ ), which makes the model prediction fit the manual annotation. + +However, the manual annotation suffers from the semantic ambiguity problem [16, 21, 30]. Specifically, some fa + +![](images/5f442f303f7270149a35b6f9a49be996ebdd238cf7c4dc03ac41e5f284023596.jpg) + +![](images/01510269ddd119b3bc03f16aa6b60d0b18afd9a9c03f6b08fbb95f884dae9fad.jpg) +Figure 2. The overview of our framework. We use a four stacked Hourglasses (HGs) Network. To mitigate the impact of semantic ambiguity, the STAR loss is applied to each HG module. (Best view in color.) + +![](images/9e45aeb75e216d7239eeadae54d64b63940ecab5b8bf28206f571d9c193a6f82.jpg) + +cial landmarks, especially landmarks located on face contour, do not have a clear and accurate definition. For example, the contour landmarks are defined to evenly distribute around the face contour without a clear definition of the positions [30]. It makes human annotators confused about the position, and it is inevitable to induce inconsistent and imprecise annotations. Thus, we argue that the regression loss will be misled by ambiguous annotations and degrade the model's convergence and performance. As shown in Figure 1, training the neural network with ambiguous annotations makes the predictions for facial contour landmarks unstable and inaccurate, which will hurt the downstream task [15]. The key problem is to design a new regression loss that mitigates the impact of semantic ambiguity. + +In this paper, we propose a novel self-adaptive ambiguity reduction method, STAR loss, by fully exploiting semantic ambiguity. To this end, we explore the impact of semantic ambiguity on the heatmap. Typically, the distribution normalization loss forces the predicted probability distribution to resemble an isotropic Gaussian distribution [32]. However, as shown in Figure 1, compared with the isotropic distribution of the eye corner point, the predicted distribution of the facial contour point is anisotropic. The main difference between the two landmarks is semantic ambiguity, which is more severe in the contour point. We infer that the semantic ambiguity is related to the anisotropic distribution. When the predicted distribution of one facial landmark is anisotropic, this facial landmark has severe semantic ambiguity (leading to model unconvergence), so it is necessary to reduce its impact. + +To this end, we begin our story by introducing a customized principal component analysis (PCA) that can process the discrete probability distribution, which contains three steps: weighted mean estimation, unbiased weighted covariance estimation, and eigen-decomposition. We de + +compose a group of predicted distributions and visualize the corresponding principal components. The visualization results show that the first principal component is along with the face contour. Meanwhile, the ambiguous direction for contour landmarks is aligned with the face contour. Therefore, we infer that their first principal component direction is highly consistent with their ambiguity direction. + +According to this new observation, we design our STAR loss, which decomposes the prediction error into two principal component directions and divides it by the corresponding energy value. For a facial landmark with anisotropic predicted distribution, the energy of the first principal component is higher than the second. In this way, the error in the first principal component direction can be adaptively suppressed, thereby alleviating the impact of ambiguity annotation on training. However, we find this initial version of STAR loss suffers an abnormal energy increase, leading to premature convergence. To solve this problem, we find that the anomaly results from that the model tends to increase the energy to minimize STAR loss. As a result, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decreasing abnormally. + +We evaluate the STAR loss on three widely-used benchmarks, i.e., COFW [5], 300W [35] and WFLW [48]. Experiments show that STAR loss indeed helps deep models achieve competitive performance compared to state-of-the-art methods. Code will be released for reproduction. + +# 2. Related Work + +At early stages, facial landmark detection is based on statistic models such as Active Appearance Models [8,31], Constrained Local Models [9], and 3D Morphable Models [2]. Recently, with the development of CNN, deep learning methods have achieved state-of-the-art performance in + +facial landmark detection [21, 29, 51, 53], which mainly includes two main branches: coordinate regression method and heatmap regression method. + +Coordinate Regression Method. Coordinate regression methods [18, 56, 58] utilize fully connected (FC) layers to learn the transformation between CNN features and landmark coordinates. However, coordinate regression methods commonly require a huge number of samples for training, which constrains performance improvements. To this end, many works address this issue from different perspectives - e.g., style transfer [14, 34], semi-supervised learning [3, 15], and virtual data [47]. To further improve the performance, both MDM [41] and RAR [52] use cascaded recurrent networks to sequentially refine the landmark estimation. SDFL [29] and SDL [27] introduce graph constraint through graph convolutional network (GCN). SLPT [50] and RePFromer [26] learn an adaptive inherent relation based on the attention mechanism. + +Heatmap Regression Method. Heatmap regression methods output an intermediate heatmap for each landmark and take the landmark with the highest intensity as the optimal output. The stacked hourglass network [55], U-Net [11], and HRNet [44] are commonly used to generate the high-quality heatmap. However, heatmap regression methods usually suffer from quantization error since the heatmap is commonly much smaller than the input image. Many works are proposed to mitigate the error, including better heatmap generation [4, 16], mapping construction from heatmap to coordinates [24, 32], coordinates further refinement [4, 38, 53]. Furthermore, many works [21, 45, 48] use facial boundary as the structure constraint to further improve the performance. HSLE [60] automatically constructs a hierarchical structure for learning robust facial landmark detection. LUVLi [24] estimates both the uncertainty and visibility of predicted landmarks. And FaRL [57] proposes the general facial representation learning. + +Semantic Ambiguity in Facial Landmark Detection. There exist several works [15, 16, 21, 24, 30, 48] addressing semantic ambiguity problems on facial landmark detection. SBR [16] uses the coherency of optical flow between adjacent frames as supervision but is sensitive to illumination and occlusion. LAB [48] uses facial boundary lines as the structure constraint, which is practical but computationally expensive. Moreover, SA [30] proposes a latent variable optimization strategy to find semantically consistent annotations and alleviate random noise during the training stage. However, the complex training strategy limits its application. Closely related to our work is ADNet [21], which presents two key modules, i.e., Anisotropic Direction Loss (ADL) and Anisotropic Attention Module (AAM), to handle the ambiguous annotations problem. Among them, ADL imposes more constraints in normal direction for landmarks on facial boundaries, but the direction and constraint + +weight is hand-crafted so that such coarse-grained design degrades its performance. + +# 3. Preliminary + +We briefly introduce the pipeline of current widely-used regression methods below. + +As shown at the top of Figure 2, the basic model of the regression method is stacked of four Hourglasses Networks (HGs) [56]. Each HG generates $N$ heatmaps, where $N$ is the number of pre-defined facial landmarks. The normalized heatmap can be viewed as the probability distribution over the predicted facial landmarks. The predicted coordinates are decoded from the heatmap by a soft-Argmax [32]. + +Formally, given a discrete probability distribution $h$ , we define the value $h_i$ as the probability of the predicted landmark locating at $y_i \in \mathbb{R}^2$ . The expectation coordinate $\mu$ is decoded by soft-Argmax: + +$$ +\mu = \text {s o f t - A r g m a x} (h) = \sum_ {i} h _ {i} y _ {i}. \tag {1} +$$ + +Based on these predicted coordinates, we can use the regression loss to learn the parameter of the model. The regression loss can be viewed as a distance $d(\cdot)$ between predicted coordinates $\mu$ and manual annotations $y_{t}$ . And $l1$ -distance, $l2$ -distance, smooth- $l1$ distance, and Wing distance [18] are widely used. So, the regression loss can be formulated as follows: + +$$ +\mathcal {L} _ {r e g} = d \left(y _ {t} - \mu\right) = d \left(y _ {t} - \sum_ {i} h _ {i} y _ {i}\right). \tag {2} +$$ + +The manual annotations suffer from the semantic ambiguity problem. As shown in the gray box of Figure 2, the key to this problem lies in the regression loss. + +# 4. Method + +The semantic ambiguity problem degrades detection performance considerably. To handle this problem, we design a novel STAR loss, which is influenced by predicted distribution. Specifically, STAR loss is encouraged to be small when the predicted distribution is anisotropic. To represent the shape of the predicted distribution, we first introduce a customized PCA applied to the discrete probability distribution. Then, we visualize the results of PCA computed on the predicted distribution and discuss the relevance between its first principal component and the semantic ambiguity. Based on this, we present the STAR loss in detail, which adaptively suppresses the prediction error in the first principal component direction to mitigate the impact of ambiguity annotation during the training phase. + +# 4.1. Analysis of the Semantic Ambiguity + +The PCA of Discrete Probability Distribution. We first design a customized PCA applied to the discrete + +![](images/de660ebb60a08bf2679d9ff1e2b04c2b125f3f6ac83d5c1c533389e11eab5c9c.jpg) +Figure 3. The visualization of the PCA results. The yellow and blue arrows indicate the predicted discrete distribution's first and second principal components, respectively. The length of the arrow is the corresponding eigenvalues. We use the $(\lambda_1 / \lambda_2)$ to formulate the ambiguity, which is represented by the shading of the blue ellipse. (Best view in color.) + +probability distribution, which is composed of two steps: (1) Approximate the means and covariance matrix; (2) Compute the eigen-decomposition of the covariance matrix. + +STEP 1: similar to the weighted mean in Eq.(1), the weighted covariance matrix is given by: + +$$ +\Sigma_ {b} = \frac {\sum_ {i} h _ {i} \left(y _ {i} - \mu\right) ^ {T} \left(y _ {i} - \mu\right)}{V _ {1}}, \tag {3} +$$ + +where $V_{1} = \sum_{i}h_{i}$ . To approximate more precisely, we determine a correction factor to yield an unbiased estimator. The correction factor is $(1 - V_2 / V_1^2)$ , where $V_{2} = \sum_{i}h_{i}^{2}$ . So, the unbiased weighted estimate of the covariance matrix, with Bessel's correction, is given by Eq.(4). And we commonly use $\Sigma = \Sigma_{ub}$ . + +$$ +\Sigma_ {u b} = \frac {\sum_ {i} h _ {i} (y _ {i} - \mu) ^ {T} (y _ {i} - \mu)}{V _ {1} - (V _ {2} / V _ {1})}. \tag {4} +$$ + +STEP 2: we compute the eigen-decomposition of covariance matrix, which can be formulated as below: + +$$ +\Sigma = V L V ^ {- 1}, \tag {5} +$$ + +where $V = \left[v_{1},v_{2}\right]\in \mathbb{R}^{2\times 2}$ is the eigenvectors matrix, and $L = diag(\lambda_1,\lambda_2)\in \mathbb{R}^{2\times 2}$ is the corresponding eigenvalues matrix. We refer $(v_{1},\lambda_{1})$ and $(v_{2},\lambda_{2})$ to represent the first and second principal component, respectively. + +Discussion of Relevance. In Figure 3, we visualize the PCA results of predicted discrete probability distribution (More visualization can be found in supplementary materials). On the one hand, a significant feature of the contour landmarks is that their first principal component is along with the face contour. Meanwhile, as discussed above, the ambiguity direction for the contour landmarks is also along with the face contour. That is, for landmarks with an + +anisotropic predicted distribution, the first principal component direction is highly consistent with their ambiguity direction. On the other hand, we visualize the elliptical eccentricity $(\lambda_1 / \lambda_2)$ by the shading of blue. Compared with the near-white eye corner, the color of the contour point is blue. It indicates that eccentricity is higher when the ambiguity is more severe. We further infer that the corresponding energy can represent the ambiguity intensity. Because the energy indicates the variance along with the corresponding direction of the principal component. Meanwhile, the high variance in an anisotropic predicted distribution mainly results from inconsistent annotation caused by semantic ambiguity. Based on these two observations, we introduce STAR loss. + +# 4.2. STAR Loss + +The proposed STAR loss belongs to a self-adaptive ambiguity reduction regression loss. And we realize it by an ambiguity-guided decomposition. Meanwhile, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decrease abnormally. + +Ambiguity-guided Decomposition. Following the motivations above, STAR loss decomposes the prediction error into the two principal component directions and divides by the corresponding energy value to reduce ambiguity effect self-adaptively. Thus, the STAR loss can be formulated as: + +$$ +\begin{array}{l} \mathcal {L} _ {S T A R} \left(y _ {t}, \mu , d\right) = \frac {1}{\sqrt {\lambda_ {1}}} d \left(v _ {1} ^ {T} \left(y _ {t} - \mu\right)\right) \tag {6} \\ + \frac {1}{\sqrt {\lambda_ {2}}} d (v _ {2} ^ {T} (y _ {t} - \mu)), \\ \end{array} +$$ + +where $v_{1}^{T}$ and $v_{2}^{T}$ project the prediction error $(y_{t} - \mu)$ according to ambiguity directions, $\lambda_{1}$ and $\lambda_{2}$ adaptively imposes constraint, and $d$ denotes the distance function. Because the decomposition operation does not affect the error metric, STAR loss can be used with an arbitrary distance function and benefits from their improvement, such as smooth- $l1$ , Wing [18], Awing [45], etc. + +Take an anisotropic distribution as an example where the $\lambda_{1}$ is much larger than $\lambda_{2}$ . The $\mathcal{L}_{STAR}$ results in a small prediction error in the direction of the first principal component $v_{1}$ . It makes the model pay less attention to the prediction error in the diction of $v_{1}$ , which is mainly caused by inconsistent manual annotation. As a result, with the help of $\mathcal{L}_{STAR}$ , the detection model can mitigate the impact of semantic ambiguity, leading to better convergence. + +Eigenvalue Restriction. According to our experiments, we find an abnormal increase of the eigenvalue $\lambda_{i}$ that leads to the model's premature convergence. To solve this problem, we consider the main reason is that the eigenvalue $\lambda$ is a denominator in $\mathcal{L}_{STAR}$ . To minimize $\mathcal{L}_{STAR}$ , the model tends to increase the eigenvalue $\lambda_{i}$ . Therefore, we propose two kinds of restriction on the eigenvalue to avoid $\mathcal{L}_{STAR}$ + +![](images/4b9f59b68c1d3713c138abed727e727f6090195195579cd55da51228b49268b7.jpg) +Figure 4. The NME results of different distance functions with varying input image resolution in WFLW. The blue and red lines indicate the distance function without and with STAR loss, respectively. + +![](images/af731285c73689cb512cda2ec106aae836521504938665a34ba5c6519167c345.jpg) + +![](images/1143169f3da3a8362f82315a8c3b19550894873a3446c23179af907044b993a0.jpg) + +![](images/23b9d7c74e7f5028ec8d1681c68ac7c921d27dcaca0f5618b7109e4cf8968089.jpg) + +decrease abnormally. The first one is a loss restriction term, namely value restriction, which is formulated as below: + +$$ +\mathcal {L} _ {\text {v a l u e}} = \frac {\lambda_ {1} + \lambda_ {2}}{2}. \tag {7} +$$ + +It directly restricts the abnormal increase of the eigenvalue. On the other hand, we propose to detach the gradient of eigenvalue and eigenvectors, namely detach restriction. It cuts off the backpropagation from eigenvalue and eigenvectors so that they act as constant values in STAR loss. Thus, STAR loss could use them but not directly affect the shape of the predicted distribution. The ablation study shows that both restrictions help mitigate the abnormal increase problem. And we use the value restriction as the default setting unless mentioned. + +# 5. Experiments + +First, we present the experiment settings, including training details, model setup, dataset, and evaluation metrics. Second, we investigate the benefits of STAR loss with extensive experiments. Third, we discuss the relationship between STAR Loss and related works. + +# 5.1. Experiment Settings + +Data Augmentation. We use the same data augmentation strategy in [21] for all experiments. The input image is generated in two steps: (1) Crop the face regions and resize them into $256 \times 256$ . (2) Perform augmentations with random rotation $(18^{\circ})$ , random scaling $(\pm 10\%)$ , random crop $(\pm 5\%)$ , random gray $(20\%)$ , random blur $(30\%)$ , random occlusion $(40\%)$ and random horizontal flip $(50\%)$ . + +The Setup of Model. We use a four-stacked hourglass model as the backbone. The recursive step in HG is set to 3. Each hourglass module outputs a $64 \times 64$ feature map. We follow the training strategy introduces in [21]. Specifically, we employed an Adam optimizer and an initial learning rate of $1 \times 10^{-3}$ . We train the model for 500 epochs and reduce the learning rate by 10 at each epoch of 200, 350, and 450. The model was trained on four GPUs (32GB NVIDIA Tesla V100), where the batch size of each GPU is 16. We + +also study some commonly used tricks that can further improve the performance, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]. + +Datasets. We evaluate our method on three commonly used public datasets including COFW [5], 300W [35], WFLW [48]. Meanwhile, we use a video-based dataset, 300VW [7,37,42], to make a cross-dataset validation. In detail, COFW contains 1,345 training images and 507 testing images with 29 landmarks. 300W contains 3,148 training images and 689 test images. All images are labeled with 68 landmarks. We use the common setting on 300-W, where the test set is split into the common (554 images) and challenge (135 images) sets. WFLW is currently the most used dataset in facial landmark detection, which contains 7,500 training images and 2,500 test images with 98 landmarks. 300VW: we use the test sets to validate the model trained on 300W. It provides three test sets: Category-A (well-lit, 31 videos with 62,135 frames), Category-B (mild unconstrained, 19 videos with 32,805 videos), and Category-C (challenging, 14 videos with 26,338 frames). + +Evaluation Metrics. We use three commonly used evaluation metrics: Normalized Mean Error (NME), Failure Rate (FR), and Area Under Curve (AUC), to evaluate the landmark detection performance. Specifically, (1) NME: we use the inter-ocular distance in 300W, WFLW dataset, and the inter-pupils distance in COFW dataset for normalization; (2) FR: we set the thresholds by $10\%$ for WFLW; (3) AUC: we set the thresholds by $10\%$ for WFLW. + +# 5.2. Accuracy Evaluation + +We compared our STAR loss against 14 state-of-the-art baselines (as reported in Table 1). We design two interesting experiments on 300W, including within-dataset validation and cross-dataset validation. First, the results of within-dataset validation are shown in Table 1. Our method can achieve state-of-the-art performance on all test sets. Primarily, we have a 0.2 improvement in the challenge subset compared with the state-of-the-art methods. Second, for cross-dataset validation, the model is trained on 300W and evaluated on 300VW. Meanwhile, the results of cross-dataset validation are shown in Table 2. We evaluate different dis + +
MethodBackboneParam. (M)WFLW-FullCOFW (NME)300W (NME)
(NME)(FR10%)(AUC10%)FullComm.Chal.
LAB [48]Hourglass12.265.277.560.532-3.492.985.19
Wing [18]ResNet-50254.996.000.5505.44---
DeCaFa [11]U-Net104.624.840.563-3.392.935.26
HRNet [44]HRNet-W189.74.64.64--3.322.875.15
Awing [45]Hourglass25.14.362.840.5724.943.072.724.52
AVS + SAN [33]ITN-CPM-4.394.080.591-3.863.216.46
DAG [28]HRNet-W18-4.213.040.589-3.042.624.77
LUVLi [24]DU-Net-4.373.120.577-3.232.765.16
ADNet [21]Hourglass13.374.142.720.6024.682.932.534.58
HIH [53]Hourglass22.684.082.600.6054.633.092.654.89
PIPNet [22]ResNet-10145.74.31---3.192.784.89
SLPT [50]HRNet-W18C-lite9.984.142.760.5954.793.172.754.90
DTLD [25]ResNet-1813.34.082.76--2.962.594.50
RePFormer [26]ResNet-101-4.11---3.01--
Ours (smooth-l1 distance)Hourglass13.374.022.320.6054.622.872.524.32
+ +Table 1. Comparing with state-of-the-art methods on COFW, 300W and WFLW. The best and second best results are marked in colors of red and blue, respectively. We mainly report NME score on COFW, 300W, and WFLW. On WFLW, we also report the FR and AUC, whose thresholds are both set to $10\%$ . + +
wo./w.Category-ACategory-BCategory-C
l14.08/4.083.33/3.378.71/8.55
l24.16/3.963.48/3.358.44/8.27
smooth-l14.00/3.973.40/3.398.69/8.42
+ +tance functions combined with STAR loss. The results show that our method achieves an average improvement of 0.2 in Category-C. Notably, the subset Category-C is the most challenging one, where the video frames are blurred and with strong occlusions. We observe a significant improvement in the challenge test of both within-dataset and cross-dataset validation, which verifies the effectiveness of our method. Meanwhile, our method achieves state-of-the-art performance in the COFW dataset. + +The WFLW is a very challenging benchmark because it contains many images under adverse conditions such as pose, make-up, illumination, blur, and expression. We report the results in Table 1, where our method still achieves the best results. In detail, our STAR loss achieves an improvement of 0.06, 0.28 in NME, and $\mathrm{FR}_{10\%}$ metrics of the full test set, respectively, when compared to the state-of-the-art methods. Compared with the increase in COFW and 300-W datasets, the improvement achieved by STAR loss in the WFLW dataset is sufficient. We conclude that STAR loss has a better performance over a big dataset, i.e., the proposed STAR loss will mitigate the effect of annotation + +Table 2. The cross-dataset validations with different distance functions. We train all modes on 300W with or without using STAR loss, and we report the NME scores on 300VW. + +
wo./w.l1smooth-l1l2Wing
COFW
basic5.00/4.765.02/4.785.59/4.894.94/4.79
+DR4.78/4.704.76/4.705.06/4.734.76/4.67
+AAM5.01/4.774.88/4.625.44/4.774.95/4.70
300W
basic3.13/2.983.12/3.003.45/3.053.12/3.02
+DR3.04/2.943.02/2.963.20/2.993.04/2.96
+AAM2.97/2.892.93/2.873.08/2.912.93/2.88
WFLW
basic4.35/4.164.34/4.174.79/4.314.32/4.17
+DR4.17/4.134.18/4.104.29/4.214.18/4.12
+AAM4.19/4.054.14/4.024.37/4.114.15/4.05
+ +Table 3. The robustness analysis on COFW, 300W, and WFLW. We report the NME score for basic model trained with or without using our STAR loss. We also study the influence of two widely used tricks, like DR and AAM. + +error and benefit from the large amounts of noise data. + +# 5.3. Ablation Study + +Evaluation on Different Distance Functions. To investigate the effect of the distance function, we test the STAR loss with the commonly used distance function, such as $l1$ -distance, $l2$ distance, smooth- $l1$ distance, and Wing distance [18] in COFW, 300W and WFLW dataset, respectively. Note that the smooth- $l1$ distance used here is formulated as below: + +$$ +\left\{ \begin{array}{l l} \frac {0 . 5}{s} \left(y _ {t} - \mu\right) ^ {2}, & \left| y _ {t} - \mu \right| < s \\ \left| y _ {t} - \mu \right| - 0. 5 s, & \text {o t h e r w i s e} \end{array} , \right. \tag {8} +$$ + +![](images/d8b8716861a2cfffc0361279ea9c067b3a963e958e8543c90487e6e06f8a212d.jpg) +l1 +$\mathcal{L}_{STAR}(l1)$ +Figure 5. Qualitative results of different distance functions w.o/w. STAR loss on WFLW dataset. Green and red points represent the predicted and ground-truth points, respectively. The yellow circles indicate the clear failures, which are solved with the help of STAR loss. (Best view in color and zoom in.) + +![](images/ebe2eaddf9b6a31915c22836e9ae146661a42a604bbd3cc6142078a8dc83e5c1.jpg) +12 +$\mathcal{L}_{STAR}(l2)$ + +![](images/55da0cdfd3e4a8eb044308952442f6145a4fa2c12668678eccb7e3e2dd12dca9.jpg) +smooth-11 +$\mathcal{L}_{STAR}$ (smooth-l1) + +![](images/784918e6cd66641ff080dc4ada4e5c64398f8f155e45854d7c96a507e308a105.jpg) +Wing +$\mathcal{L}_{STAR}$ (Wing) + +where $s$ is a threshold that is usually set as $s = 0.01$ . We refer to the regression loss defined in Eq.(2) as a baseline. The results are shown in Table 3. Compared with the baseline, STAR loss can achieve an average improvement of 0.34, 0.19, and 0.25 on COFW, 300W, and WFLW among different distance functions, respectively, with negligible computational. Meanwhile, we find that STAR loss has a significant effect when combined with $l2$ -distance. + +Moreover, we visualize the failure cases of different distance functions with and without STAR loss on WFLW dataset. As shown in Figure 5, the results with STAR exhibits better structural constraints. We infer that STAR works as a label regularization, which helps the model avoid over-fitting ambiguity annotation and pay more attention to the relation between landmarks. + +Evaluation on Different Distribution Normalization. We evaluate our proposed STAR loss with different distribution normalizations, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]. DR is a stricter regularization that forces the heatmap to resemble a Gaussian distribution. AAM is an attention module that learns a point-edge heatmap as an attention mask and forces the heatmap to resemble a mixture of Gaussian distribution and adjacent boundary [24] distribution. In DR, we use Jensen-Shannon divergence as the divergence measure and set the Gaussian $\sigma$ equals to 1.0. Regarding AAM, we follow the setting in paper [21]. + +In Table 3, both of them have a positive effect: (1) In the WFLW dataset, STAR loss achieve an average improvement of 0.07 and 0.16 on DR and AAM, respectively; (2) In the COFW dataset, the improvement is 0.14 and 0.35, respectively; (3) In the 300W dataset, the improvement is + +
w12351020
NME4.174.204.184.184.184.20
+ +Table 4. The analysis of $w$ . We report the NME scores for STAR loss with smooth- $l_{1}$ distance with the varying $w$ on WFLW. + +0.11 and 0.09, respectively; We observe that the AAM is better suited to STAR loss because the boundary information in AAM further helps. And the best results among the three datasets are taken with the combination of smooth- $l$ 1 distance, AAM, and STAR loss, which refers to the default model setup in accuracy evaluation. Notice that the model used for visualization in Figure 1, and Figure 3 is trained with the combination of $\mathcal{L}_2$ and DR. + +Evaluation on Different Input Image Resolution. We investigate the influence of different input image resolutions (64px, 128px, and 256px). The results are shown in Figure 4, STAR loss has a positive effect on all input image resolution. Specifically, STAR loss can achieve an average improvement of 0.20, 0.30, and 0.25 in 64px, 128px, and 256px among different distance functions, respectively. Notice that the baseline with STAR loss in 128px is equal to or better than the baseline in 256px. It means that STAR loss is not very sensitive to the input image size, which encourages using STAR loss in a small model. + +Evaluation on Different Restrictions. Firstly, we investigate the value restriction and discuss the effect of its weight $w$ in STAR loss. As shown in Table 4, STAR loss is not sensitive to $w$ , and we choose $w = 1$ as the default setting in our experiments. Then, we analyze the detach restriction. As shown in Table 5, the restriction is essential, and the effect of detach restriction is comparable with the value restriction. This observation indicates that the improvement + +![](images/e326b0eb0413dab7c2399acbec4eb36ee25a5221b39ce2db080bd0153c06ed6c.jpg) +Figure 6. The variance distribution. We visualize the variance statistic of five models trained under the same experimental setting with and without STAR loss. The red and blue lines indicate the corresponding mean value of $l2$ distance function with and without STAR loss, respectively. + +is mainly contributed by STAR loss but not the value restriction term. + +Evaluation on Stability. We evaluate the effect of STAR loss on stability. To quantitatively analyze the stability, we design a toy experiment: 1) train $N = 5$ models under the same experimental setting with and without STAR loss, respectively; 2) count the variance of $N$ models' predictions on the WFLW test set. As shown in Figure 6, the predictions of models trained with our STAR loss distribute more intensively within a small variance range. Meanwhile, the mean value of prediction variances drops from 0.79 to 0.69. It indicates that STAR loss does mitigate the impact of ambiguous annotations and makes prediction more stable. + +# 5.4. Discussion with Related Solutions + +ADL vs. STAR Loss. In ADNet [21], Huang et al. introduce an Anisotropic Direction Loss (ADL), which imposes strong constraints in the normal direction and weak constraints in the tangent direction for landmarks on the facial boundary. The normal direction is calculated by the slope from its adjacent points, and the constraint strength is a hyperparameter. We argue that the hand-crafted design degrades its performance. Compared with it, STAR loss estimates the direction and constraint weight via PCA of heatmaps, which is a fine-grained and self-adaptive scheme. Then, we replaced ADL with STAR in ADNet and adopted the same setup for a fair comparison. As shown in Table 6, STAR loss brings further improvements of 0.12, 0.28, 0.08, 0.07, 0.13, 0.11, 0.10 in NME in full WFLW and six sub-categories, respectively. Besides, STAR is plug-and-play for heatmap-based methods with an arbitrary number of landmarks without extra direction computation design. + +LUVLi Loss v.s. STAR Loss. LUVLi [24] introduces an uncertainty-based loss (e.g., Gaussian Log-Likelihood (GLL)) to facial landmark detection. The GLL consists of a Mahalanobis distance and a regularization term. As dis + +
WFLWbasic+AAM
baseline4.344.14
wo. restriction4.604.61
w. value restriction4.174.02
w. detach restriction4.204.05
+ +Table 5. The analysis of restriction method. We report the NME scores for STAR loss (smooth- $l1$ distance) without and with different restriction methods on WFLW. + +
WFLWFullPoseExp.Ill.Make.Occl.Blur
ADL [21]4.146.964.384.094.055.064.79
STAR4.026.764.273.973.844.804.58
+ +Table 6. The comparison between ADL and STAR loss. + +cussed in Sec. 5.3, the value restriction is unnecessary for STAR loss. So, we mainly compare the Mahalanobis distance with $\mathcal{L}_{STAR}$ by a toy experiment: replace $\mathcal{L}_{STAR}$ with Mahalanobis distance and adopt the same setup for a fair comparison. The experiment shows that replacing $\mathcal{L}_{STAR}$ with Mahalanobis can take 4.32 in NME in WFLW. However, our $\mathcal{L}_{STAR}$ takes 4.17, which has a further 0.15 NME improvement in WFLW. So, compared with LUVLi, STAR is lighter and better: 1) propose the heatmap-based covariance estimation, simplifying model structure; 2) design the loss function from the perspective of ambiguity reduction, thus achieving significant performance gain. + +# 6. Conclusion + +We study the semantic ambiguity problem in facial landmark detection and propose a self-adaptive ambiguity reduction method, STAR loss. We first observe that the predicted distribution can represent semantic ambiguity. Then we use PCA to indicate the character of the predicted distribution and indirectly formulate the direction and intensity of semantic ambiguity. Based on this, STAR loss adaptively suppresses the prediction error in the ambiguity direction to mitigate the impact of ambiguity annotation in training. With the help of STAR loss, our method achieves state-of-the-art performance on three benchmarks. + +Acknowledgement. This work was supported in part by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001) and the Grant-in-Aid for JSPS Fellows Grant (No. 21F20377). + +# References + +[1] Jianmin Bao, Dong Chen, Fang Wen, Houqiang Li, and Gang Hua. Towards open-set identity preserving face synthesis. In CVPR, 2018. 1 +[2] Volker Blanz and Thomas Vetter. Face recognition based on fitting a 3d morphable model. TPAMI, 2003. 2 +[3] Bjorn Browatzki and Christian Wallraven. 3fabrec: Fast few-shot face alignment by reconstruction. In CVPR, 2020. 1, 3 +[4] Adrian Bulat, Enrique Sanchez, and Georgios Tzimiropoulos. 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Supervised descent method and its applications to face alignment. In CVPR, 2013. 12, 13 +[55] Jing Yang, Qingshan Liu, and Kaihua Zhang. Stacked hourglass network for robust facial landmark localisation. In CVPR, 2017. 1, 3 +[56] Zhanpeng Zhang, Ping Luo, Chen Change Loy, and Xiaou Tang. Facial landmark detection by deep multi-task learning. In ECCV, 2014. 1, 3, 12 +[57] Yinglin Zheng, Hao Yang, Ting Zhang, Jianmin Bao, Dongdong Chen, Yangyu Huang, Lu Yuan, Dong Chen, Ming Zeng, and Fang Wen. General facial representation learning in a visual-linguistic manner. In CVPR, 2021. 3 +[58] Erjin Zhou, Haoqiang Fan, Zhimin Cao, Yuning Jiang, and Qi Yin. Extensive facial landmark localization with coarse-to-fine convolutional network cascade. In ICCVW, 2013. 3 +[59] Shizhan Zhu, Cheng Li, Chen Change Loy, and Xiaou Tang. Face alignment by coarse-to-fine shape searching. In CVPR, 2015. 12, 13 +[60] Xu Zou, Sheng Zhong, Luxin Yan, Xiangyun Zhao, Jiahuan Zhou, and Ying Wu. Learning robust facial landmark detection via hierarchical structured ensemble. In CVPR, 2019. 3 \ No newline at end of file diff --git a/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/images.zip b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c1c8a73ff1f6357afab18b392fbbcddd1b7ff711 --- /dev/null +++ b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:72ad585c3cdabe485c652e0e3e386af28a2fa7558a3475623bb61c6c725255f0 +size 588123 diff --git a/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/layout.json b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..69f1afecf4aaa3c572f109cc2717a2f830145f77 --- /dev/null +++ b/2023/STAR Loss_ Reducing Semantic Ambiguity in Facial Landmark Detection/layout.json @@ -0,0 +1,8878 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 69, + 103, + 526, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 103, + 526, + 121 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 526, + 121 + ], + "type": "text", + "content": "STAR Loss: Reducing Semantic Ambiguity in Facial Landmark Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "spans": [ + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "content": "Zhenglin Zhou" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "content": ", Huaxia Li" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "content": ", Hong Liu" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "inline_equation", + "content": "^{3*}" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "content": ", Nanyang Wang" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "content": ", Gang Yu" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "text", + "content": ", Rongrong Ji" + }, + { + "bbox": [ + 79, + 142, + 515, + 158 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 159, + 533, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 159, + 533, + 210 + ], + "spans": [ + { + "bbox": [ + 62, + 159, + 533, + 210 + ], + "type": "text", + "content": "1 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University. 2 Tencent PCG. 3 National Institute of Information. zhenglinzhou@stu.xmu.edu.cn, {haroldzcli, cageswang, skicyyu}@tencent.com, hliu@nii.ac.jp, rrji@xmu.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "spans": [ + { + "bbox": [ + 143, + 241, + 192, + 254 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 266, + 290, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 290, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 290, + 553 + ], + "type": "text", + "content": "Recently, deep learning-based facial landmark detection has achieved significant improvement. However, the semantic ambiguity problem degrades detection performance. Specifically, the semantic ambiguity causes inconsistent annotation and negatively affects the model's convergence, leading to worse accuracy and instability prediction. To solve this problem, we propose a Self-adaptTive Ambiguity Reduction (STAR) loss by exploiting the properties of semantic ambiguity. We find that semantic ambiguity results in the anisotropic predicted distribution, which inspires us to use predicted distribution to represent semantic ambiguity. Based on this, we design the STAR loss that measures the anisotropism of the predicted distribution. Compared with the standard regression loss, STAR loss is encouraged to be small when the predicted distribution is anisotropic and thus adaptively mitigates the impact of semantic ambiguity. Moreover, we propose two kinds of eigenvalue restriction methods that could avoid both distribution's abnormal change and the model's premature convergence. Finally, the comprehensive experiments demonstrate that STAR loss outperforms the state-of-the-art methods on three benchmarks, i.e., COFW, 300W, and WFLW, with negligible computation overhead. Code is at https://github.com/ZhenglinZhou/STAR" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 654 + ], + "type": "text", + "content": "Facial landmark detection, which aims to locate a group of pre-defined facial landmarks from images [48, 51, 56], is a fundamental problem for many downstream tasks, including face verification [12], face synthetic [1], and 3D face reconstruction [10, 13, 17, 46]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 678 + ], + "type": "text", + "content": "Thanks to the development of Convolutional Neural Networks (CNNs) [20, 36, 39], facial landmark detection has" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 240, + 544, + 380 + ], + "blocks": [ + { + "bbox": [ + 307, + 240, + 544, + 380 + ], + "lines": [ + { + "bbox": [ + 307, + 240, + 544, + 380 + ], + "spans": [ + { + "bbox": [ + 307, + 240, + 544, + 380 + ], + "type": "image", + "image_path": "376a97a868bff121914e5521fc5c0f51c1497fcfc56d236f34539bd882178579.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 388, + 547, + 465 + ], + "lines": [ + { + "bbox": [ + 305, + 388, + 547, + 465 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 547, + 465 + ], + "type": "text", + "content": "Figure 1. The impact of semantic ambiguity. We visualize the outputs of five models trained with the same architecture under the same experimental setting. (1) The first row shows the predicted facial landmarks for Mr. Tony Stark, marked as red points. And the green point refers to the corresponding mean value. (2) The second row shows the results of predicted probability distribution (i.e., heatmap) from one of the trained models." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "text", + "content": "improved significantly. At first, coordinate regression methods [3, 16, 33, 47] are proposed to learn the transformation between CNN features and landmark locations via fully connected layers. Recently, the research focus has been the heatmap regression methods, which have shown superiority over coordinate regression methods. The heatmap regression methods [21, 24, 48] predict an intermediate heatmap for each landmark and decode the coordinates from the heatmap. But, the commonly used decoder, Argmax [55], is not differentiable and suffers from quantization error. Recently, some solutions have been proposed [38, 53], and the focus is on the differentiable expectation decoder: soft-Argmax [32]. With the help of soft-Argmax, the heatmap regression method has the advantage of end-to-end training. So the training loss is mainly composed of a regression loss (such as " + }, + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 304, + 483, + 547, + 686 + ], + "type": "text", + "content": "), which makes the model prediction fit the manual annotation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "However, the manual annotation suffers from the semantic ambiguity problem [16, 21, 30]. Specifically, some fa" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 683, + 136, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 136, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 136, + 693 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 58, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 287, + 712 + ], + "type": "text", + "content": "*Equal contribution. This work was done when Zhenglin Zhou was an enrn at Tencent PCG." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15475" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 527, + 156 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 527, + 156 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 527, + 156 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 527, + 156 + ], + "type": "image", + "image_path": "5f442f303f7270149a35b6f9a49be996ebdd238cf7c4dc03ac41e5f284023596.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 163, + 331, + 248 + ], + "blocks": [ + { + "bbox": [ + 52, + 163, + 331, + 248 + ], + "lines": [ + { + "bbox": [ + 52, + 163, + 331, + 248 + ], + "spans": [ + { + "bbox": [ + 52, + 163, + 331, + 248 + ], + "type": "image", + "image_path": "01510269ddd119b3bc03f16aa6b60d0b18afd9a9c03f6b08fbb95f884dae9fad.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 546, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 546, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 546, + 282 + ], + "type": "text", + "content": "Figure 2. The overview of our framework. We use a four stacked Hourglasses (HGs) Network. To mitigate the impact of semantic ambiguity, the STAR loss is applied to each HG module. (Best view in color.)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 334, + 163, + 542, + 248 + ], + "blocks": [ + { + "bbox": [ + 334, + 163, + 542, + 248 + ], + "lines": [ + { + "bbox": [ + 334, + 163, + 542, + 248 + ], + "spans": [ + { + "bbox": [ + 334, + 163, + 542, + 248 + ], + "type": "image", + "image_path": "9e45aeb75e216d7239eeadae54d64b63940ecab5b8bf28206f571d9c193a6f82.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "type": "text", + "content": "cial landmarks, especially landmarks located on face contour, do not have a clear and accurate definition. For example, the contour landmarks are defined to evenly distribute around the face contour without a clear definition of the positions [30]. It makes human annotators confused about the position, and it is inevitable to induce inconsistent and imprecise annotations. Thus, we argue that the regression loss will be misled by ambiguous annotations and degrade the model's convergence and performance. As shown in Figure 1, training the neural network with ambiguous annotations makes the predictions for facial contour landmarks unstable and inaccurate, which will hurt the downstream task [15]. The key problem is to design a new regression loss that mitigates the impact of semantic ambiguity." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 461, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 652 + ], + "type": "text", + "content": "In this paper, we propose a novel self-adaptive ambiguity reduction method, STAR loss, by fully exploiting semantic ambiguity. To this end, we explore the impact of semantic ambiguity on the heatmap. Typically, the distribution normalization loss forces the predicted probability distribution to resemble an isotropic Gaussian distribution [32]. However, as shown in Figure 1, compared with the isotropic distribution of the eye corner point, the predicted distribution of the facial contour point is anisotropic. The main difference between the two landmarks is semantic ambiguity, which is more severe in the contour point. We infer that the semantic ambiguity is related to the anisotropic distribution. When the predicted distribution of one facial landmark is anisotropic, this facial landmark has severe semantic ambiguity (leading to model unconvergence), so it is necessary to reduce its impact." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "To this end, we begin our story by introducing a customized principal component analysis (PCA) that can process the discrete probability distribution, which contains three steps: weighted mean estimation, unbiased weighted covariance estimation, and eigen-decomposition. We de" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 292, + 546, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 546, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 546, + 376 + ], + "type": "text", + "content": "compose a group of predicted distributions and visualize the corresponding principal components. The visualization results show that the first principal component is along with the face contour. Meanwhile, the ambiguous direction for contour landmarks is aligned with the face contour. Therefore, we infer that their first principal component direction is highly consistent with their ambiguity direction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 377, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 547, + 555 + ], + "type": "text", + "content": "According to this new observation, we design our STAR loss, which decomposes the prediction error into two principal component directions and divides it by the corresponding energy value. For a facial landmark with anisotropic predicted distribution, the energy of the first principal component is higher than the second. In this way, the error in the first principal component direction can be adaptively suppressed, thereby alleviating the impact of ambiguity annotation on training. However, we find this initial version of STAR loss suffers an abnormal energy increase, leading to premature convergence. To solve this problem, we find that the anomaly results from that the model tends to increase the energy to minimize STAR loss. As a result, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decreasing abnormally." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 557, + 547, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 618 + ], + "type": "text", + "content": "We evaluate the STAR loss on three widely-used benchmarks, i.e., COFW [5], 300W [35] and WFLW [48]. Experiments show that STAR loss indeed helps deep models achieve competitive performance compared to state-of-the-art methods. Code will be released for reproduction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 632, + 392, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 392, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 392, + 645 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "At early stages, facial landmark detection is based on statistic models such as Active Appearance Models [8,31], Constrained Local Models [9], and 3D Morphable Models [2]. Recently, with the development of CNN, deep learning methods have achieved state-of-the-art performance in" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15476" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "facial landmark detection [21, 29, 51, 53], which mainly includes two main branches: coordinate regression method and heatmap regression method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 110, + 287, + 289 + ], + "type": "text", + "content": "Coordinate Regression Method. Coordinate regression methods [18, 56, 58] utilize fully connected (FC) layers to learn the transformation between CNN features and landmark coordinates. However, coordinate regression methods commonly require a huge number of samples for training, which constrains performance improvements. To this end, many works address this issue from different perspectives - e.g., style transfer [14, 34], semi-supervised learning [3, 15], and virtual data [47]. To further improve the performance, both MDM [41] and RAR [52] use cascaded recurrent networks to sequentially refine the landmark estimation. SDFL [29] and SDL [27] introduce graph constraint through graph convolutional network (GCN). SLPT [50] and RePFromer [26] learn an adaptive inherent relation based on the attention mechanism." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 292, + 288, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 288, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 288, + 508 + ], + "type": "text", + "content": "Heatmap Regression Method. Heatmap regression methods output an intermediate heatmap for each landmark and take the landmark with the highest intensity as the optimal output. The stacked hourglass network [55], U-Net [11], and HRNet [44] are commonly used to generate the high-quality heatmap. However, heatmap regression methods usually suffer from quantization error since the heatmap is commonly much smaller than the input image. Many works are proposed to mitigate the error, including better heatmap generation [4, 16], mapping construction from heatmap to coordinates [24, 32], coordinates further refinement [4, 38, 53]. Furthermore, many works [21, 45, 48] use facial boundary as the structure constraint to further improve the performance. HSLE [60] automatically constructs a hierarchical structure for learning robust facial landmark detection. LUVLi [24] estimates both the uncertainty and visibility of predicted landmarks. And FaRL [57] proposes the general facial representation learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 713 + ], + "type": "text", + "content": "Semantic Ambiguity in Facial Landmark Detection. There exist several works [15, 16, 21, 24, 30, 48] addressing semantic ambiguity problems on facial landmark detection. SBR [16] uses the coherency of optical flow between adjacent frames as supervision but is sensitive to illumination and occlusion. LAB [48] uses facial boundary lines as the structure constraint, which is practical but computationally expensive. Moreover, SA [30] proposes a latent variable optimization strategy to find semantically consistent annotations and alleviate random noise during the training stage. However, the complex training strategy limits its application. Closely related to our work is ADNet [21], which presents two key modules, i.e., Anisotropic Direction Loss (ADL) and Anisotropic Attention Module (AAM), to handle the ambiguous annotations problem. Among them, ADL imposes more constraints in normal direction for landmarks on facial boundaries, but the direction and constraint" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "weight is hand-crafted so that such coarse-grained design degrades its performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 105, + 383, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 105, + 383, + 119 + ], + "spans": [ + { + "bbox": [ + 306, + 105, + 383, + 119 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 125, + 545, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 125, + 545, + 148 + ], + "spans": [ + { + "bbox": [ + 305, + 125, + 545, + 148 + ], + "type": "text", + "content": "We briefly introduce the pipeline of current widely-used regression methods below." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "text", + "content": "As shown at the top of Figure 2, the basic model of the regression method is stacked of four Hourglasses Networks (HGs) [56]. Each HG generates " + }, + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "text", + "content": " heatmaps, where " + }, + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 149, + 545, + 233 + ], + "type": "text", + "content": " is the number of pre-defined facial landmarks. The normalized heatmap can be viewed as the probability distribution over the predicted facial landmarks. The predicted coordinates are decoded from the heatmap by a soft-Argmax [32]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "text", + "content": "Formally, given a discrete probability distribution " + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "text", + "content": ", we define the value " + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "inline_equation", + "content": "h_i" + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "text", + "content": " as the probability of the predicted landmark locating at " + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "inline_equation", + "content": "y_i \\in \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "text", + "content": ". The expectation coordinate " + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 233, + 545, + 281 + ], + "type": "text", + "content": " is decoded by soft-Argmax:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 357, + 286, + 545, + 311 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 286, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 357, + 286, + 545, + 311 + ], + "type": "interline_equation", + "content": "\\mu = \\text {s o f t - A r g m a x} (h) = \\sum_ {i} h _ {i} y _ {i}. \\tag {1}", + "image_path": "918d7ccf582a301c941949dc7053f412e753576df7f8aea578f7e019248c0adf.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": "Based on these predicted coordinates, we can use the regression loss to learn the parameter of the model. The regression loss can be viewed as a distance " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "d(\\cdot)" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": " between predicted coordinates " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": " and manual annotations " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": ". And " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": "-distance, " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "l2" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": "-distance, smooth- " + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 304, + 316, + 545, + 399 + ], + "type": "text", + "content": " distance, and Wing distance [18] are widely used. So, the regression loss can be formulated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 346, + 403, + 545, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 403, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 346, + 403, + 545, + 428 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e g} = d \\left(y _ {t} - \\mu\\right) = d \\left(y _ {t} - \\sum_ {i} h _ {i} y _ {i}\\right). \\tag {2}", + "image_path": "938c14bdfd2436ea1d0bdf34f9d0efe01326390460c2fbc8bbd75595188d2d77.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 468 + ], + "type": "text", + "content": "The manual annotations suffer from the semantic ambiguity problem. As shown in the gray box of Figure 2, the key to this problem lies in the regression loss." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 477, + 361, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 361, + 490 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 361, + 490 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 665 + ], + "type": "text", + "content": "The semantic ambiguity problem degrades detection performance considerably. To handle this problem, we design a novel STAR loss, which is influenced by predicted distribution. Specifically, STAR loss is encouraged to be small when the predicted distribution is anisotropic. To represent the shape of the predicted distribution, we first introduce a customized PCA applied to the discrete probability distribution. Then, we visualize the results of PCA computed on the predicted distribution and discuss the relevance between its first principal component and the semantic ambiguity. Based on this, we present the STAR loss in detail, which adaptively suppresses the prediction error in the first principal component direction to mitigate the impact of ambiguity annotation during the training phase." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 671, + 493, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 493, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 493, + 685 + ], + "type": "text", + "content": "4.1. Analysis of the Semantic Ambiguity" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "The PCA of Discrete Probability Distribution. We first design a customized PCA applied to the discrete" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15477" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 199 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 199 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 199 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 199 + ], + "type": "image", + "image_path": "de660ebb60a08bf2679d9ff1e2b04c2b125f3f6ac83d5c1c533389e11eab5c9c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 206, + 289, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 274 + ], + "type": "text", + "content": "Figure 3. The visualization of the PCA results. The yellow and blue arrows indicate the predicted discrete distribution's first and second principal components, respectively. The length of the arrow is the corresponding eigenvalues. We use the " + }, + { + "bbox": [ + 46, + 206, + 289, + 274 + ], + "type": "inline_equation", + "content": "(\\lambda_1 / \\lambda_2)" + }, + { + "bbox": [ + 46, + 206, + 289, + 274 + ], + "type": "text", + "content": " to formulate the ambiguity, which is represented by the shading of the blue ellipse. (Best view in color.)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 289, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 326 + ], + "type": "text", + "content": "probability distribution, which is composed of two steps: (1) Approximate the means and covariance matrix; (2) Compute the eigen-decomposition of the covariance matrix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 287, + 350 + ], + "type": "text", + "content": "STEP 1: similar to the weighted mean in Eq.(1), the weighted covariance matrix is given by:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 100, + 358, + 287, + 386 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 358, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 100, + 358, + 287, + 386 + ], + "type": "interline_equation", + "content": "\\Sigma_ {b} = \\frac {\\sum_ {i} h _ {i} \\left(y _ {i} - \\mu\\right) ^ {T} \\left(y _ {i} - \\mu\\right)}{V _ {1}}, \\tag {3}", + "image_path": "440c1148ba545d5dec17ad389e54d29fd3007ec060d42d7e0663a4ba8f3e4592.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "inline_equation", + "content": "V_{1} = \\sum_{i}h_{i}" + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "text", + "content": ". To approximate more precisely, we determine a correction factor to yield an unbiased estimator. The correction factor is " + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "inline_equation", + "content": "(1 - V_2 / V_1^2)" + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "inline_equation", + "content": "V_{2} = \\sum_{i}h_{i}^{2}" + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "text", + "content": ". So, the unbiased weighted estimate of the covariance matrix, with Bessel's correction, is given by Eq.(4). And we commonly use " + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "inline_equation", + "content": "\\Sigma = \\Sigma_{ub}" + }, + { + "bbox": [ + 46, + 395, + 289, + 468 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 97, + 475, + 287, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 475, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 97, + 475, + 287, + 506 + ], + "type": "interline_equation", + "content": "\\Sigma_ {u b} = \\frac {\\sum_ {i} h _ {i} (y _ {i} - \\mu) ^ {T} (y _ {i} - \\mu)}{V _ {1} - (V _ {2} / V _ {1})}. \\tag {4}", + "image_path": "98e016822b8af2e90b5d3c6031bd9375d9d36b1c1d78fbd3cfd224367e6a9c3a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 536 + ], + "type": "text", + "content": "STEP 2: we compute the eigen-decomposition of covariance matrix, which can be formulated as below:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 136, + 545, + 287, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 545, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 136, + 545, + 287, + 561 + ], + "type": "interline_equation", + "content": "\\Sigma = V L V ^ {- 1}, \\tag {5}", + "image_path": "ee31c21bf4dde3ea77d0516f6b0160651bcd27784f751231ca9f0d8a094b12ec.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "inline_equation", + "content": "V = \\left[v_{1},v_{2}\\right]\\in \\mathbb{R}^{2\\times 2}" + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "text", + "content": " is the eigenvectors matrix, and " + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "inline_equation", + "content": "L = diag(\\lambda_1,\\lambda_2)\\in \\mathbb{R}^{2\\times 2}" + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "text", + "content": " is the corresponding eigenvalues matrix. We refer " + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "inline_equation", + "content": "(v_{1},\\lambda_{1})" + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "inline_equation", + "content": "(v_{2},\\lambda_{2})" + }, + { + "bbox": [ + 47, + 568, + 287, + 618 + ], + "type": "text", + "content": " to represent the first and second principal component, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Discussion of Relevance. In Figure 3, we visualize the PCA results of predicted discrete probability distribution (More visualization can be found in supplementary materials). On the one hand, a significant feature of the contour landmarks is that their first principal component is along with the face contour. Meanwhile, as discussed above, the ambiguity direction for the contour landmarks is also along with the face contour. That is, for landmarks with an" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 546, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 228 + ], + "type": "text", + "content": "anisotropic predicted distribution, the first principal component direction is highly consistent with their ambiguity direction. On the other hand, we visualize the elliptical eccentricity " + }, + { + "bbox": [ + 304, + 72, + 546, + 228 + ], + "type": "inline_equation", + "content": "(\\lambda_1 / \\lambda_2)" + }, + { + "bbox": [ + 304, + 72, + 546, + 228 + ], + "type": "text", + "content": " by the shading of blue. Compared with the near-white eye corner, the color of the contour point is blue. It indicates that eccentricity is higher when the ambiguity is more severe. We further infer that the corresponding energy can represent the ambiguity intensity. Because the energy indicates the variance along with the corresponding direction of the principal component. Meanwhile, the high variance in an anisotropic predicted distribution mainly results from inconsistent annotation caused by semantic ambiguity. Based on these two observations, we introduce STAR loss." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 237, + 382, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 382, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 382, + 249 + ], + "type": "text", + "content": "4.2. STAR Loss" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 256, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 545, + 316 + ], + "type": "text", + "content": "The proposed STAR loss belongs to a self-adaptive ambiguity reduction regression loss. And we realize it by an ambiguity-guided decomposition. Meanwhile, we propose two kinds of eigenvalue restriction methods to avoid STAR loss decrease abnormally." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 316, + 546, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 546, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 546, + 377 + ], + "type": "text", + "content": "Ambiguity-guided Decomposition. Following the motivations above, STAR loss decomposes the prediction error into the two principal component directions and divides by the corresponding energy value to reduce ambiguity effect self-adaptively. Thus, the STAR loss can be formulated as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 386, + 545, + 438 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 386, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 335, + 386, + 545, + 438 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {S T A R} \\left(y _ {t}, \\mu , d\\right) = \\frac {1}{\\sqrt {\\lambda_ {1}}} d \\left(v _ {1} ^ {T} \\left(y _ {t} - \\mu\\right)\\right) \\tag {6} \\\\ + \\frac {1}{\\sqrt {\\lambda_ {2}}} d (v _ {2} ^ {T} (y _ {t} - \\mu)), \\\\ \\end{array}", + "image_path": "18058d4dd91e309ff2cf912ac4e14e25b9ef77bffa57e8b1d02ac9cb02200b9d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "v_{1}^{T}" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "v_{2}^{T}" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": " project the prediction error " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "(y_{t} - \\mu)" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": " according to ambiguity directions, " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": " adaptively imposes constraint, and " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": " denotes the distance function. Because the decomposition operation does not affect the error metric, STAR loss can be used with an arbitrary distance function and benefits from their improvement, such as smooth- " + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": ", Wing [18], Awing [45], etc." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": "Take an anisotropic distribution as an example where the " + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": " is much larger than " + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": " results in a small prediction error in the direction of the first principal component " + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": ". It makes the model pay less attention to the prediction error in the diction of " + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "inline_equation", + "content": "v_{1}" + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": ", which is mainly caused by inconsistent manual annotation. As a result, with the help of " + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 533, + 546, + 629 + ], + "type": "text", + "content": ", the detection model can mitigate the impact of semantic ambiguity, leading to better convergence." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": "Eigenvalue Restriction. According to our experiments, we find an abnormal increase of the eigenvalue " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " that leads to the model's premature convergence. To solve this problem, we consider the main reason is that the eigenvalue " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": " is a denominator in " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": ". To minimize " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": ", the model tends to increase the eigenvalue " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "text", + "content": ". Therefore, we propose two kinds of restriction on the eigenvalue to avoid " + }, + { + "bbox": [ + 304, + 630, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15478" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 80, + 170, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 80, + 170, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 80, + 170, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 80, + 170, + 167 + ], + "type": "image", + "image_path": "4b9f59b68c1d3713c138abed727e727f6090195195579cd55da51228b49268b7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 545, + 209 + ], + "type": "text", + "content": "Figure 4. The NME results of different distance functions with varying input image resolution in WFLW. The blue and red lines indicate the distance function without and with STAR loss, respectively." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 171, + 80, + 293, + 167 + ], + "blocks": [ + { + "bbox": [ + 171, + 80, + 293, + 167 + ], + "lines": [ + { + "bbox": [ + 171, + 80, + 293, + 167 + ], + "spans": [ + { + "bbox": [ + 171, + 80, + 293, + 167 + ], + "type": "image", + "image_path": "af731285c73689cb512cda2ec106aae836521504938665a34ba5c6519167c345.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 294, + 80, + 414, + 167 + ], + "blocks": [ + { + "bbox": [ + 294, + 80, + 414, + 167 + ], + "lines": [ + { + "bbox": [ + 294, + 80, + 414, + 167 + ], + "spans": [ + { + "bbox": [ + 294, + 80, + 414, + 167 + ], + "type": "image", + "image_path": "1143169f3da3a8362f82315a8c3b19550894873a3446c23179af907044b993a0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 414, + 80, + 536, + 167 + ], + "blocks": [ + { + "bbox": [ + 414, + 80, + 536, + 167 + ], + "lines": [ + { + "bbox": [ + 414, + 80, + 536, + 167 + ], + "spans": [ + { + "bbox": [ + 414, + 80, + 536, + 167 + ], + "type": "image", + "image_path": "23b9d7c74e7f5028ec8d1681c68ac7c921d27dcaca0f5618b7109e4cf8968089.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 220, + 286, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 286, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 286, + 243 + ], + "type": "text", + "content": "decrease abnormally. The first one is a loss restriction term, namely value restriction, which is formulated as below:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 126, + 253, + 287, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 253, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 126, + 253, + 287, + 277 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {v a l u e}} = \\frac {\\lambda_ {1} + \\lambda_ {2}}{2}. \\tag {7}", + "image_path": "b810d9dce9c93eba5de0de315a68fc2fac32205fd2d85722013d8915517823cd.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 282, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 401 + ], + "type": "text", + "content": "It directly restricts the abnormal increase of the eigenvalue. On the other hand, we propose to detach the gradient of eigenvalue and eigenvectors, namely detach restriction. It cuts off the backpropagation from eigenvalue and eigenvectors so that they act as constant values in STAR loss. Thus, STAR loss could use them but not directly affect the shape of the predicted distribution. The ablation study shows that both restrictions help mitigate the abnormal increase problem. And we use the value restriction as the default setting unless mentioned." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 414, + 128, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 414, + 128, + 427 + ], + "spans": [ + { + "bbox": [ + 47, + 414, + 128, + 427 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 434, + 287, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 494 + ], + "type": "text", + "content": "First, we present the experiment settings, including training details, model setup, dataset, and evaluation metrics. Second, we investigate the benefits of STAR loss with extensive experiments. Third, we discuss the relationship between STAR Loss and related works." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 503, + 165, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 165, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 165, + 516 + ], + "type": "text", + "content": "5.1. Experiment Settings" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": "Data Augmentation. We use the same data augmentation strategy in [21] for all experiments. The input image is generated in two steps: (1) Crop the face regions and resize them into " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ". (2) Perform augmentations with random rotation " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(18^{\\circ})" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", random scaling " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(\\pm 10\\%)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", random crop " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(\\pm 5\\%)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", random gray " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(20\\%)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", random blur " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(30\\%)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", random occlusion " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(40\\%)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": " and random horizontal flip " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "(50\\%)" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "The Setup of Model. We use a four-stacked hourglass model as the backbone. The recursive step in HG is set to 3. Each hourglass module outputs a " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": " feature map. We follow the training strategy introduces in [21]. Specifically, we employed an Adam optimizer and an initial learning rate of " + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-3}" + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": ". We train the model for 500 epochs and reduce the learning rate by 10 at each epoch of 200, 350, and 450. The model was trained on four GPUs (32GB NVIDIA Tesla V100), where the batch size of each GPU is 16. We" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 220, + 545, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 255 + ], + "type": "text", + "content": "also study some commonly used tricks that can further improve the performance, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 256, + 546, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 256, + 546, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 256, + 546, + 458 + ], + "type": "text", + "content": "Datasets. We evaluate our method on three commonly used public datasets including COFW [5], 300W [35], WFLW [48]. Meanwhile, we use a video-based dataset, 300VW [7,37,42], to make a cross-dataset validation. In detail, COFW contains 1,345 training images and 507 testing images with 29 landmarks. 300W contains 3,148 training images and 689 test images. All images are labeled with 68 landmarks. We use the common setting on 300-W, where the test set is split into the common (554 images) and challenge (135 images) sets. WFLW is currently the most used dataset in facial landmark detection, which contains 7,500 training images and 2,500 test images with 98 landmarks. 300VW: we use the test sets to validate the model trained on 300W. It provides three test sets: Category-A (well-lit, 31 videos with 62,135 frames), Category-B (mild unconstrained, 19 videos with 32,805 videos), and Category-C (challenging, 14 videos with 26,338 frames)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": "Evaluation Metrics. We use three commonly used evaluation metrics: Normalized Mean Error (NME), Failure Rate (FR), and Area Under Curve (AUC), to evaluate the landmark detection performance. Specifically, (1) NME: we use the inter-ocular distance in 300W, WFLW dataset, and the inter-pupils distance in COFW dataset for normalization; (2) FR: we set the thresholds by " + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": " for WFLW; (3) AUC: we set the thresholds by " + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 459, + 545, + 555 + ], + "type": "text", + "content": " for WFLW." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 563, + 426, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 426, + 575 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 426, + 575 + ], + "type": "text", + "content": "5.2. Accuracy Evaluation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 712 + ], + "type": "text", + "content": "We compared our STAR loss against 14 state-of-the-art baselines (as reported in Table 1). We design two interesting experiments on 300W, including within-dataset validation and cross-dataset validation. First, the results of within-dataset validation are shown in Table 1. Our method can achieve state-of-the-art performance on all test sets. Primarily, we have a 0.2 improvement in the challenge subset compared with the state-of-the-art methods. Second, for cross-dataset validation, the model is trained on 300W and evaluated on 300VW. Meanwhile, the results of cross-dataset validation are shown in Table 2. We evaluate different dis" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15479" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 544, + 297 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 544, + 297 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 544, + 297 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 544, + 297 + ], + "type": "table", + "html": "
MethodBackboneParam. (M)WFLW-FullCOFW (NME)300W (NME)
(NME)(FR10%)(AUC10%)FullComm.Chal.
LAB [48]Hourglass12.265.277.560.532-3.492.985.19
Wing [18]ResNet-50254.996.000.5505.44---
DeCaFa [11]U-Net104.624.840.563-3.392.935.26
HRNet [44]HRNet-W189.74.64.64--3.322.875.15
Awing [45]Hourglass25.14.362.840.5724.943.072.724.52
AVS + SAN [33]ITN-CPM-4.394.080.591-3.863.216.46
DAG [28]HRNet-W18-4.213.040.589-3.042.624.77
LUVLi [24]DU-Net-4.373.120.577-3.232.765.16
ADNet [21]Hourglass13.374.142.720.6024.682.932.534.58
HIH [53]Hourglass22.684.082.600.6054.633.092.654.89
PIPNet [22]ResNet-10145.74.31---3.192.784.89
SLPT [50]HRNet-W18C-lite9.984.142.760.5954.793.172.754.90
DTLD [25]ResNet-1813.34.082.76--2.962.594.50
RePFormer [26]ResNet-101-4.11---3.01--
Ours (smooth-l1 distance)Hourglass13.374.022.320.6054.622.872.524.32
", + "image_path": "390d2a67476ff0dcf1fc8ec9841c6ad950370cdd4766b41a75208e2429804242.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 342, + 282, + 403 + ], + "blocks": [ + { + "bbox": [ + 46, + 300, + 546, + 332 + ], + "lines": [ + { + "bbox": [ + 46, + 300, + 546, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 546, + 332 + ], + "type": "text", + "content": "Table 1. Comparing with state-of-the-art methods on COFW, 300W and WFLW. The best and second best results are marked in colors of red and blue, respectively. We mainly report NME score on COFW, 300W, and WFLW. On WFLW, we also report the FR and AUC, whose thresholds are both set to " + }, + { + "bbox": [ + 46, + 300, + 546, + 332 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 300, + 546, + 332 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 342, + 282, + 403 + ], + "lines": [ + { + "bbox": [ + 51, + 342, + 282, + 403 + ], + "spans": [ + { + "bbox": [ + 51, + 342, + 282, + 403 + ], + "type": "table", + "html": "
wo./w.Category-ACategory-BCategory-C
l14.08/4.083.33/3.378.71/8.55
l24.16/3.963.48/3.358.44/8.27
smooth-l14.00/3.973.40/3.398.69/8.42
", + "image_path": "8dd2f77bd7fce177bb3c5105610ac7858f966ab7be5948fda43b00838f9f4013.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 458, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 567 + ], + "type": "text", + "content": "tance functions combined with STAR loss. The results show that our method achieves an average improvement of 0.2 in Category-C. Notably, the subset Category-C is the most challenging one, where the video frames are blurred and with strong occlusions. We observe a significant improvement in the challenge test of both within-dataset and cross-dataset validation, which verifies the effectiveness of our method. Meanwhile, our method achieves state-of-the-art performance in the COFW dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "The WFLW is a very challenging benchmark because it contains many images under adverse conditions such as pose, make-up, illumination, blur, and expression. We report the results in Table 1, where our method still achieves the best results. In detail, our STAR loss achieves an improvement of 0.06, 0.28 in NME, and " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{FR}_{10\\%}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " metrics of the full test set, respectively, when compared to the state-of-the-art methods. Compared with the increase in COFW and 300-W datasets, the improvement achieved by STAR loss in the WFLW dataset is sufficient. We conclude that STAR loss has a better performance over a big dataset, i.e., the proposed STAR loss will mitigate the effect of annotation" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 321, + 342, + 531, + 502 + ], + "blocks": [ + { + "bbox": [ + 46, + 406, + 287, + 440 + ], + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 440 + ], + "type": "text", + "content": "Table 2. The cross-dataset validations with different distance functions. We train all modes on 300W with or without using STAR loss, and we report the NME scores on 300VW." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 342, + 531, + 502 + ], + "lines": [ + { + "bbox": [ + 321, + 342, + 531, + 502 + ], + "spans": [ + { + "bbox": [ + 321, + 342, + 531, + 502 + ], + "type": "table", + "html": "
wo./w.l1smooth-l1l2Wing
COFW
basic5.00/4.765.02/4.785.59/4.894.94/4.79
+DR4.78/4.704.76/4.705.06/4.734.76/4.67
+AAM5.01/4.774.88/4.625.44/4.774.95/4.70
300W
basic3.13/2.983.12/3.003.45/3.053.12/3.02
+DR3.04/2.943.02/2.963.20/2.993.04/2.96
+AAM2.97/2.892.93/2.873.08/2.912.93/2.88
WFLW
basic4.35/4.164.34/4.174.79/4.314.32/4.17
+DR4.17/4.134.18/4.104.29/4.214.18/4.12
+AAM4.19/4.054.14/4.024.37/4.114.15/4.05
", + "image_path": "d1959204d86eb8b21d6925f794a22f3f225a590f19d44cff1534cd247aa5448a.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 504, + 545, + 548 + ], + "lines": [ + { + "bbox": [ + 305, + 504, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 305, + 504, + 545, + 548 + ], + "type": "text", + "content": "Table 3. The robustness analysis on COFW, 300W, and WFLW. We report the NME score for basic model trained with or without using our STAR loss. We also study the influence of two widely used tricks, like DR and AAM." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 559, + 525, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 559, + 525, + 571 + ], + "spans": [ + { + "bbox": [ + 306, + 559, + 525, + 571 + ], + "type": "text", + "content": "error and benefit from the large amounts of noise data." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 578, + 400, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 400, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 400, + 590 + ], + "type": "text", + "content": "5.3. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "text", + "content": "Evaluation on Different Distance Functions. To investigate the effect of the distance function, we test the STAR loss with the commonly used distance function, such as " + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "text", + "content": "-distance, " + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "inline_equation", + "content": "l2" + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "text", + "content": " distance, smooth- " + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "text", + "content": " distance, and Wing distance [18] in COFW, 300W and WFLW dataset, respectively. Note that the smooth- " + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 304, + 596, + 545, + 679 + ], + "type": "text", + "content": " distance used here is formulated as below:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 355, + 685, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 685, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 355, + 685, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l l} \\frac {0 . 5}{s} \\left(y _ {t} - \\mu\\right) ^ {2}, & \\left| y _ {t} - \\mu \\right| < s \\\\ \\left| y _ {t} - \\mu \\right| - 0. 5 s, & \\text {o t h e r w i s e} \\end{array} , \\right. \\tag {8}", + "image_path": "7830168a2ab69bfc9af383762ea82e14d6e536682507f349e350870a2e3c1984.jpg" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15480" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 170, + 251 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 170, + 251 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 170, + 251 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 170, + 251 + ], + "type": "image", + "image_path": "d8b8716861a2cfffc0361279ea9c067b3a963e958e8543c90487e6e06f8a212d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 74, + 254, + 83, + 262 + ], + "lines": [ + { + "bbox": [ + 74, + 254, + 83, + 262 + ], + "spans": [ + { + "bbox": [ + 74, + 254, + 83, + 262 + ], + "type": "text", + "content": "l1" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 91, + 253, + 159, + 265 + ], + "lines": [ + { + "bbox": [ + 91, + 253, + 159, + 265 + ], + "spans": [ + { + "bbox": [ + 91, + 253, + 159, + 265 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}(l1)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 273, + 546, + 305 + ], + "lines": [ + { + "bbox": [ + 46, + 273, + 546, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 546, + 305 + ], + "type": "text", + "content": "Figure 5. Qualitative results of different distance functions w.o/w. STAR loss on WFLW dataset. Green and red points represent the predicted and ground-truth points, respectively. The yellow circles indicate the clear failures, which are solved with the help of STAR loss. (Best view in color and zoom in.)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 172, + 72, + 294, + 251 + ], + "blocks": [ + { + "bbox": [ + 172, + 72, + 294, + 251 + ], + "lines": [ + { + "bbox": [ + 172, + 72, + 294, + 251 + ], + "spans": [ + { + "bbox": [ + 172, + 72, + 294, + 251 + ], + "type": "image", + "image_path": "ebe2eaddf9b6a31915c22836e9ae146661a42a604bbd3cc6142078a8dc83e5c1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 192, + 254, + 202, + 262 + ], + "lines": [ + { + "bbox": [ + 192, + 254, + 202, + 262 + ], + "spans": [ + { + "bbox": [ + 192, + 254, + 202, + 262 + ], + "type": "text", + "content": "12" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 235, + 254, + 277, + 265 + ], + "lines": [ + { + "bbox": [ + 235, + 254, + 277, + 265 + ], + "spans": [ + { + "bbox": [ + 235, + 254, + 277, + 265 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}(l2)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 298, + 71, + 419, + 251 + ], + "blocks": [ + { + "bbox": [ + 298, + 71, + 419, + 251 + ], + "lines": [ + { + "bbox": [ + 298, + 71, + 419, + 251 + ], + "spans": [ + { + "bbox": [ + 298, + 71, + 419, + 251 + ], + "type": "image", + "image_path": "55da0cdfd3e4a8eb044308952442f6145a4fa2c12668678eccb7e3e2dd12dca9.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 255, + 344, + 262 + ], + "lines": [ + { + "bbox": [ + 313, + 255, + 344, + 262 + ], + "spans": [ + { + "bbox": [ + 313, + 255, + 344, + 262 + ], + "type": "text", + "content": "smooth-11" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 359, + 254, + 419, + 264 + ], + "lines": [ + { + "bbox": [ + 359, + 254, + 419, + 264 + ], + "spans": [ + { + "bbox": [ + 359, + 254, + 419, + 264 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 359, + 254, + 419, + 264 + ], + "type": "text", + "content": " (smooth-l1)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 423, + 71, + 544, + 251 + ], + "blocks": [ + { + "bbox": [ + 423, + 71, + 544, + 251 + ], + "lines": [ + { + "bbox": [ + 423, + 71, + 544, + 251 + ], + "spans": [ + { + "bbox": [ + 423, + 71, + 544, + 251 + ], + "type": "image", + "image_path": "784918e6cd66641ff080dc4ada4e5c64398f8f155e45854d7c96a507e308a105.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 252, + 467, + 263 + ], + "lines": [ + { + "bbox": [ + 446, + 252, + 467, + 263 + ], + "spans": [ + { + "bbox": [ + 446, + 252, + 467, + 263 + ], + "type": "text", + "content": "Wing" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 488, + 252, + 541, + 263 + ], + "lines": [ + { + "bbox": [ + 488, + 252, + 541, + 263 + ], + "spans": [ + { + "bbox": [ + 488, + 252, + 541, + 263 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 488, + 252, + 541, + 263 + ], + "type": "text", + "content": " (Wing)" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "text", + "content": " is a threshold that is usually set as " + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "inline_equation", + "content": "s = 0.01" + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "text", + "content": ". We refer to the regression loss defined in Eq.(2) as a baseline. The results are shown in Table 3. Compared with the baseline, STAR loss can achieve an average improvement of 0.34, 0.19, and 0.25 on COFW, 300W, and WFLW among different distance functions, respectively, with negligible computational. Meanwhile, we find that STAR loss has a significant effect when combined with " + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "inline_equation", + "content": "l2" + }, + { + "bbox": [ + 46, + 322, + 287, + 417 + ], + "type": "text", + "content": "-distance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 421, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 287, + 503 + ], + "type": "text", + "content": "Moreover, we visualize the failure cases of different distance functions with and without STAR loss on WFLW dataset. As shown in Figure 5, the results with STAR exhibits better structural constraints. We infer that STAR works as a label regularization, which helps the model avoid over-fitting ambiguity annotation and pay more attention to the relation between landmarks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 507, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 651 + ], + "type": "text", + "content": "Evaluation on Different Distribution Normalization. We evaluate our proposed STAR loss with different distribution normalizations, such as Distribution Regularization (DR) [32] and Anisotropic Attention Module (AAM) [21]. DR is a stricter regularization that forces the heatmap to resemble a Gaussian distribution. AAM is an attention module that learns a point-edge heatmap as an attention mask and forces the heatmap to resemble a mixture of Gaussian distribution and adjacent boundary [24] distribution. In DR, we use Jensen-Shannon divergence as the divergence measure and set the Gaussian " + }, + { + "bbox": [ + 46, + 507, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 507, + 287, + 651 + ], + "type": "text", + "content": " equals to 1.0. Regarding AAM, we follow the setting in paper [21]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "In Table 3, both of them have a positive effect: (1) In the WFLW dataset, STAR loss achieve an average improvement of 0.07 and 0.16 on DR and AAM, respectively; (2) In the COFW dataset, the improvement is 0.14 and 0.35, respectively; (3) In the 300W dataset, the improvement is" + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 320, + 320, + 533, + 346 + ], + "blocks": [ + { + "bbox": [ + 320, + 320, + 533, + 346 + ], + "lines": [ + { + "bbox": [ + 320, + 320, + 533, + 346 + ], + "spans": [ + { + "bbox": [ + 320, + 320, + 533, + 346 + ], + "type": "table", + "html": "
w12351020
NME4.174.204.184.184.184.20
", + "image_path": "03fd08072fe4620005b08380bc5592039971e22a84312d08d901ca6159499367.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "lines": [ + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "text", + "content": "Table 4. The analysis of " + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "text", + "content": ". We report the NME scores for STAR loss with smooth-" + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "text", + "content": " distance with the varying " + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 306, + 350, + 545, + 372 + ], + "type": "text", + "content": " on WFLW." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "type": "text", + "content": "0.11 and 0.09, respectively; We observe that the AAM is better suited to STAR loss because the boundary information in AAM further helps. And the best results among the three datasets are taken with the combination of smooth-" + }, + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "type": "text", + "content": "1 distance, AAM, and STAR loss, which refers to the default model setup in accuracy evaluation. Notice that the model used for visualization in Figure 1, and Figure 3 is trained with the combination of " + }, + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_2" + }, + { + "bbox": [ + 304, + 389, + 545, + 484 + ], + "type": "text", + "content": " and DR." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 486, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 616 + ], + "type": "text", + "content": "Evaluation on Different Input Image Resolution. We investigate the influence of different input image resolutions (64px, 128px, and 256px). The results are shown in Figure 4, STAR loss has a positive effect on all input image resolution. Specifically, STAR loss can achieve an average improvement of 0.20, 0.30, and 0.25 in 64px, 128px, and 256px among different distance functions, respectively. Notice that the baseline with STAR loss in 128px is equal to or better than the baseline in 256px. It means that STAR loss is not very sensitive to the input image size, which encourages using STAR loss in a small model." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Evaluation on Different Restrictions. Firstly, we investigate the value restriction and discuss the effect of its weight " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " in STAR loss. As shown in Table 4, STAR loss is not sensitive to " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ", and we choose " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "w = 1" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": " as the default setting in our experiments. Then, we analyze the detach restriction. As shown in Table 5, the restriction is essential, and the effect of detach restriction is comparable with the value restriction. This observation indicates that the improvement" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15481" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 284, + 202 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 284, + 202 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 284, + 202 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 284, + 202 + ], + "type": "image", + "image_path": "e326b0eb0413dab7c2399acbec4eb36ee25a5221b39ce2db080bd0153c06ed6c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 208, + 287, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 208, + 287, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 208, + 287, + 264 + ], + "type": "text", + "content": "Figure 6. The variance distribution. We visualize the variance statistic of five models trained under the same experimental setting with and without STAR loss. The red and blue lines indicate the corresponding mean value of " + }, + { + "bbox": [ + 46, + 208, + 287, + 264 + ], + "type": "inline_equation", + "content": "l2" + }, + { + "bbox": [ + 46, + 208, + 287, + 264 + ], + "type": "text", + "content": " distance function with and without STAR loss, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 276, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 300 + ], + "type": "text", + "content": "is mainly contributed by STAR loss but not the value restriction term." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "type": "text", + "content": "Evaluation on Stability. We evaluate the effect of STAR loss on stability. To quantitatively analyze the stability, we design a toy experiment: 1) train " + }, + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "type": "inline_equation", + "content": "N = 5" + }, + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "type": "text", + "content": " models under the same experimental setting with and without STAR loss, respectively; 2) count the variance of " + }, + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 300, + 287, + 433 + ], + "type": "text", + "content": " models' predictions on the WFLW test set. As shown in Figure 6, the predictions of models trained with our STAR loss distribute more intensively within a small variance range. Meanwhile, the mean value of prediction variances drops from 0.79 to 0.69. It indicates that STAR loss does mitigate the impact of ambiguous annotations and makes prediction more stable." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 442, + 228, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 228, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 228, + 453 + ], + "type": "text", + "content": "5.4. Discussion with Related Solutions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 461, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 664 + ], + "type": "text", + "content": "ADL vs. STAR Loss. In ADNet [21], Huang et al. introduce an Anisotropic Direction Loss (ADL), which imposes strong constraints in the normal direction and weak constraints in the tangent direction for landmarks on the facial boundary. The normal direction is calculated by the slope from its adjacent points, and the constraint strength is a hyperparameter. We argue that the hand-crafted design degrades its performance. Compared with it, STAR loss estimates the direction and constraint weight via PCA of heatmaps, which is a fine-grained and self-adaptive scheme. Then, we replaced ADL with STAR in ADNet and adopted the same setup for a fair comparison. As shown in Table 6, STAR loss brings further improvements of 0.12, 0.28, 0.08, 0.07, 0.13, 0.11, 0.10 in NME in full WFLW and six sub-categories, respectively. Besides, STAR is plug-and-play for heatmap-based methods with an arbitrary number of landmarks without extra direction computation design." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "LUVLi Loss v.s. STAR Loss. LUVLi [24] introduces an uncertainty-based loss (e.g., Gaussian Log-Likelihood (GLL)) to facial landmark detection. The GLL consists of a Mahalanobis distance and a regularization term. As dis" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 342, + 70, + 511, + 133 + ], + "blocks": [ + { + "bbox": [ + 342, + 70, + 511, + 133 + ], + "lines": [ + { + "bbox": [ + 342, + 70, + 511, + 133 + ], + "spans": [ + { + "bbox": [ + 342, + 70, + 511, + 133 + ], + "type": "table", + "html": "
WFLWbasic+AAM
baseline4.344.14
wo. restriction4.604.61
w. value restriction4.174.02
w. detach restriction4.204.05
", + "image_path": "0325d7db5597cb76bdb2e55f76d442283ebd4991fa59e9eaec1026df9c1b605e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 184, + 545, + 214 + ], + "blocks": [ + { + "bbox": [ + 305, + 136, + 545, + 169 + ], + "lines": [ + { + "bbox": [ + 305, + 136, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 305, + 136, + 545, + 169 + ], + "type": "text", + "content": "Table 5. The analysis of restriction method. We report the NME scores for STAR loss (smooth- " + }, + { + "bbox": [ + 305, + 136, + 545, + 169 + ], + "type": "inline_equation", + "content": "l1" + }, + { + "bbox": [ + 305, + 136, + 545, + 169 + ], + "type": "text", + "content": " distance) without and with different restriction methods on WFLW." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 184, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 307, + 184, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 307, + 184, + 545, + 214 + ], + "type": "table", + "html": "
WFLWFullPoseExp.Ill.Make.Occl.Blur
ADL [21]4.146.964.384.094.055.064.79
STAR4.026.764.273.973.844.804.58
", + "image_path": "86ed9f8371090cd91ad58d9cb242252bed186babf58a0e69c72beff953ceecc6.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 323, + 216, + 527, + 227 + ], + "lines": [ + { + "bbox": [ + 323, + 216, + 527, + 227 + ], + "spans": [ + { + "bbox": [ + 323, + 216, + 527, + 227 + ], + "type": "text", + "content": "Table 6. The comparison between ADL and STAR loss." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "text", + "content": "cussed in Sec. 5.3, the value restriction is unnecessary for STAR loss. So, we mainly compare the Mahalanobis distance with " + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "text", + "content": " by a toy experiment: replace " + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "text", + "content": " with Mahalanobis distance and adopt the same setup for a fair comparison. The experiment shows that replacing " + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "text", + "content": " with Mahalanobis can take 4.32 in NME in WFLW. However, our " + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{STAR}" + }, + { + "bbox": [ + 304, + 253, + 545, + 397 + ], + "type": "text", + "content": " takes 4.17, which has a further 0.15 NME improvement in WFLW. So, compared with LUVLi, STAR is lighter and better: 1) propose the heatmap-based covariance estimation, simplifying model structure; 2) design the loss function from the perspective of ambiguity reduction, thus achieving significant performance gain." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 422, + 378, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 422, + 378, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 422, + 378, + 433 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 445, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 578 + ], + "type": "text", + "content": "We study the semantic ambiguity problem in facial landmark detection and propose a self-adaptive ambiguity reduction method, STAR loss. We first observe that the predicted distribution can represent semantic ambiguity. Then we use PCA to indicate the character of the predicted distribution and indirectly formulate the direction and intensity of semantic ambiguity. Based on this, STAR loss adaptively suppresses the prediction error in the ambiguity direction to mitigate the impact of ambiguity annotation in training. With the help of STAR loss, our method achieves state-of-the-art performance on three benchmarks." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement. This work was supported in part by National Key R&D Program of China (No.2022ZD0118202), the National Science Fund for Distinguished Young Scholars (No.62025603), the National Natural Science Foundation of China (No.U21B2037, No.U22B2051, No.62176222, No.62176223, No.62176226, No.62072386, No.62072387, No.62072389, No.62002305 and No.62272401), the Natural Science Foundation of Fujian Province of China (No.2021J01002, No.2022J06001) and the Grant-in-Aid for JSPS Fellows Grant (No. 21F20377)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15482" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Jianmin Bao, Dong Chen, Fang Wen, Houqiang Li, and Gang Hua. 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In CVPR, 2019. 3" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15484" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_content_list.json b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c2e3899e18005a1ba714093462108f0a6ec63b89 --- /dev/null +++ b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_content_list.json @@ -0,0 +1,1277 @@ +[ + { + "type": "text", + "text": "STDLens: Model Hijacking-resilient Federated Learning for Object Detection", + "text_level": 1, + "bbox": [ + 91, + 130, + 875, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ka-Ho Chow, Ling Liu, Wenqi Wei, Fatih Ilhan, Yanzhao Wu \nGeorgia Instutite of Technology \nAtlanta, GA, USA", + "text_level": 1, + "bbox": [ + 240, + 180, + 727, + 232 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "khchow@gatech.edu, ling.liu@cc.gatech.edu, {wenqiwei, filhan, yanzhaowu}@gatech.edu", + "bbox": [ + 130, + 236, + 830, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 310, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Federated Learning (FL) has been gaining popularity as a collaborative learning framework to train deep learning-based object detection models over a distributed population of clients. Despite its advantages, FL is vulnerable to model hijacking. The attacker can control how the object detection system should misbehave by implanting Trojaned gradients using only a small number of compromised clients in the collaborative learning process. This paper introduces STDLens, a principled approach to safeguarding FL against such attacks. We first investigate existing mitigation mechanisms and analyze their failures caused by the inherent errors in spatial clustering analysis on gradients. Based on the insights, we introduce a three-tier forensic framework to identify and expel Trojaned gradients and reclaim the performance over the course of FL. We consider three types of adaptive attacks and demonstrate the robustness of STDLens against advanced adversaries. Extensive experiments show that STDLens can protect FL against different model hijacking attacks and outperform existing methods in identifying and removing Trojaned gradients with significantly higher precision and much lower false-positive rates. The source code is available at https://github.com/git-disl/STDLens.", + "bbox": [ + 75, + 316, + 473, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 679, + 207, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Federated Learning (FL) for object detection has attracted numerous applications [12], especially in healthcare, with strict privacy regulations protecting patient medical records [25, 27]. Instead of using a centralized data curator, FL can train a global object detection model with a distributed population of clients. Each client only shares its fixed-size gradient (updated model) parameters (e.g., 246.9 MB for YOLOv3 [15]) with the FL server for aggregation while keeping its private raw data local (e.g., terabytes of videos) [13]. Such a paradigm lowers the bar for knowledge sharing and eases the recruitment of contributors, but it becomes vulnerable to model hijacking [9, 21].", + "bbox": [ + 75, + 703, + 468, + 885 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Model hijacking aims at interfering with the training pro", + "bbox": [ + 96, + 885, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/1ed377d174e45cc1a16577657cf78d71b1970c8fd7a2ade5908f12899af204d7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ScenarioObject Detection ResultsAPersonAPcar
Benignperson 0.93\nGm 0.76\nSg 0.64person 0.76\nGm 0.76\nSg 0.6452.4374.12
Class-Poison Victim: Personpottedplant 0.56\nGm 0.72\nSg 0.62bird 0.45\nGm 0.72\nSg 0.6238.22\n(↓27%)71.79\n(↓3%)
BBox-Poison Victim: Personperson 0.62\nGm 0.72\nSg 0.62person 0.45\nGm 0.72\nSg 0.6218.06\n(↓66%)72.82\n(↓2%)
Objn-Poison Victim: Personpottedplant 0.56\nGm 0.76\nSg 0.64person 0.45\nGm 0.76\nSg 0.6437.61\n(↓28%)71.59\n(↓3%)
", + "bbox": [ + 503, + 284, + 890, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Table 1. FL-trained detectors can be hijacked by perception poisoning to misdetect objects of designated classes (e.g., person) in three different ways (2nd to 4th rows) [3], while objects of nonvictim classes (e.g., car) have negligible performance degradation.", + "bbox": [ + 498, + 484, + 890, + 540 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "cess of a machine learning model and causes it to misbehave at the deployment stage [17]. The FL-trained global model can be indirectly hijacked by a small number of compromised clients who share Trojaned gradients to gradually confuse the learning trajectory of FL [10]. Such gradients can be generated in black-box through data poisoning. The attacker only has to poison the local training data owned by a compromised client, such as changing the ground-truth label of certain objects by dirty-label poisoning [21] or implanting a backdoor to trigger the malfunctioning of a hijacked model [1, 2, 8, 20]. The FL software will take the poisoned local training data and unintentionally generate malicious gradients for sharing. With the growing number of real-world applications, recent work has begun to understand the hijacking of FL-based object detection systems [3]. As shown in Table 1, the adversary can designate how the hijacked model should misdetect objects of certain classes (e.g., person) while ensuring other objects can still be precisely detected (e.g., car). This fine-grained control opens the door for an adversary to design a stealthy attack configuration to hurt the FL system yet remains hardly noticeable by the owner [5], leading to catastrophic consequences such as car crashes.", + "bbox": [ + 496, + 551, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 1, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16343", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper introduces STDLens, a three-tier defense methodology against model hijacking attacks, with the following original contributions. First, we analyze existing defenses based on spatial signature analysis and show their ineffectiveness in protecting FL. Second, we introduce a pipeline with per-client spatio-temporal signature analysis to identify Trojaned gradients, track their contributors, revoke their subscriptions, and reclaim the detection performance. Third, we present a density-based confidence inspection mechanism to manage the spatio-temporal uncertainty. It avoids purging benign clients contributing useful learning signals for the FL system. Finally, we extend perception poisoning with three types of adaptiveness for analyzing STDLens in countering advanced adversaries. Extensive experiments show that STDLens outperforms competitive defense methods by a large margin in defense precision with a low false-positive rate, reducing the accuracy drop under attack from $34.47\\%$ to $0.24\\%$ , maintaining the object detection accuracy on par with the performance under the benign scenario.", + "bbox": [ + 75, + 90, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background and Related Work", + "text_level": 1, + "bbox": [ + 76, + 407, + 362, + 424 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Perception Poisoning for Model Hijacking", + "text_level": 1, + "bbox": [ + 76, + 431, + 434, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Threat Model. Perception poisoning adopts the following assumptions: (i) the communication between a client and the trustworthy FL server is encrypted; (ii) the benign clients faithfully follow the FL workflow; and (iii) there is only a small $m\\%$ of compromised clients out of a total of $N$ clients. An adversary on a malicious client can only manipulate its local training data, and hence, model hijacking can be done without tampering with the FL software.", + "bbox": [ + 75, + 455, + 468, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Poisoning Formulation. Let $F$ be the global model being trained in FL, $f_{i}$ be the local model of client $\\mathcal{P}_i$ , and $(\\pmb{x},\\pmb{y})$ be the input sample and its ground truth in the training set $\\mathcal{D}_i$ of client $\\mathcal{P}_i$ . The process of perception poisoning can be formulated as a function $\\psi$ that maps $(\\pmb{x},\\pmb{y})$ to $(\\pmb{x},\\pmb{y}')$ such that the local model $f_{i}$ will generate Trojaned gradients which maximize the chance of $F$ being fooled to make erroneous predictions with high confidence, formally:", + "bbox": [ + 75, + 577, + 468, + 699 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\psi : \\psi (\\boldsymbol {x}, \\boldsymbol {y}) = \\left(\\boldsymbol {x}, \\boldsymbol {y} ^ {\\prime}\\right) \\text {s . t .} f _ {i} (\\boldsymbol {x}) = \\boldsymbol {y} ^ {\\prime}, \\boldsymbol {y} ^ {\\prime} \\neq \\boldsymbol {y}, \\max [ F (\\boldsymbol {x}) \\bowtie \\boldsymbol {y} ^ {\\prime} ]\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 707, + 472, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\pmb{y}$ is a list of triplets, one for each object $\\pmb{o} =$ (CLASS,BBOX,OBJN) in the training image $\\pmb{x}$ , CLASS is the class label, BBOX is the bounding box, and OBJN is the existence of object $\\pmb{o}$ . $f_{i}(\\pmb{x})$ and $F(\\pmb{x})$ denote the detected objects by the local and global models, respectively. The operator $\\bowtie$ indicates the degree of matching between two sets of objects [4]. Based on the three perceptual components of an object, one can formulate three poisoning strategies to designate malicious behaviors on the hijacked model [3]: (i) Class-Poison changes the class label of objects of a source class to a maliciously chosen target class", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "without altering their bounding box locations and object existence. (ii) BBox-Poison attacks objects of certain source classes by randomly changing the size and the location of their bounding boxes without altering the class label and the object existence. (iii) Obj-Poison attacks objects of certain classes by changing their existence to non-existence. As shown in Table 1, the hijacked model under Class-Poison (2nd row) mislabels the person as a potted plant in the first example and as a bird in the second example with a different attack configuration. Under BBox-Poison (3rd row), the person object is detected with a correct class label but a misaligned bounding box. Under Obj-Poison (4th row), the person vanishes in both cases. Only the designated classes suffer from performance degradation (e.g., \"person\" in the 4th column), while the detection of objects of other irrelevant classes is not affected (e.g., \"car\" in the 5th column).", + "bbox": [ + 496, + 90, + 893, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Existing Defenses and Their Limitations", + "text_level": 1, + "bbox": [ + 498, + 340, + 844, + 357 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While no defenses have been proposed to counter perception poisoning, several solutions are being introduced for image classifiers, which are either developed for FL [21, 23, 28] or can be extended [18, 22]. They can be broadly classified into two categories. The first category aims at repairing the gradients (model updates). Contributions from all participants will be used for aggregation, but they will be processed by parameter clipping and noise injection [11, 20, 24] to wash out possibly malicious elements. However, it is challenging to determine the correct amount of noise to be injected [14]. The Trojaned gradients can still be malicious if the noise is too small, while a larger noise can remove useful learning signals from benign clients and affect the convergence of FL. The second category attempts to inspect gradients shared by participants to identify and eliminate malicious clients. MNTD [26] trains a meta-classifier to differentiate Trojaned and non-Trojaned gradients. It is a supervised defense and assumes a known distribution of Trojans to create training data. Unsupervised defenses make fewer assumptions and are more attractive in practice. AUROR [18] and its followers [21] conduct spatial clustering on gradient contributions and label the contributors to the smaller cluster to be malicious. Spectral signature [22] conducts outlier removal via SVD by purging gradient contributions deviating most significantly from a singular vector. While they neither rely on finding the right amount of noise for injection nor prior knowledge on possible attacks to be defended, our analysis in Section 3 finds that anomaly detection using solely spatial analysis on the latent projection space can fail due to the randomness in per-round client selection and the clustering uncertainty.", + "bbox": [ + 496, + 364, + 893, + 834 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. STDLens: Defense Methodology", + "text_level": 1, + "bbox": [ + 498, + 844, + 795, + 862 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Perception poisoning is a real threat. Adversaries can configure the attack to hijack the model without being no-", + "bbox": [ + 498, + 869, + 892, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16344", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1fd571cc16c920d0690262714ac67683e57b7a0dfc3cc58e12c6369c758dff97.jpg", + "image_caption": [ + "Figure 1. The overview of STDLens, a three-tier framework against model hijacking through perception poisoning." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 848, + 231 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ticed. We present a forensic framework called STDLens, to safeguard FL systems. It utilizes robust and attack-agnostic statistical properties with a three-tier forensic analysis. It does not assume prior knowledge on which poisoning attack is launched (i.e., Class-Poison, BBox-Poison, Obj-Poison, or their combinations). Figure 1 gives an overview. STDLens is operated at a system-supplied schedule, configurable at initiation (e.g., every ten FL rounds). Contributions from the participating clients during the window of rounds are accumulated for a safety inspection by the spatial signature analysis, followed by a per-client temporal signature analysis to identify Trojaned gradients and a $\\sigma$ -density analysis to manage the spatio-temporal uncertainty.", + "bbox": [ + 75, + 263, + 473, + 464 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Spatial Signature Analysis", + "text_level": 1, + "bbox": [ + 76, + 470, + 316, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Under perception poisoning, it is observed that with a small $m\\%$ of malicious clients, the eigenvalues of the covariance of the gradient updates for the source class consist of two sub-populations: the Trojaned gradients from malicious participants and the benign gradients from honest participants. We refer to such phenomenon as $m$ -separable robust statistics of perception poisoning attacks.", + "bbox": [ + 75, + 494, + 470, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 3.1. $m$ -Separable Robust Statistics. Given a small $m$ with $0 < m < \\frac{1}{2}$ , let $H$ and $P$ denote the two distributions: $\\underline{\\text{Honest}}$ and $\\underline{\\text{Poisoned}}$ , respectively, with finite covariance. Let the mixing loss function be $\\mathbb{G} = (1 - m)H + mP$ , $v$ be the top eigenvalue of the covariance of $\\mathbb{G}$ and $\\mu_{\\mathbb{G}}$ is the mean of the mixed distribution $\\mathbb{G}$ . The two distributions $H$ and $P$ are separable if there exists some $\\tau$ such that $\\operatorname{Pr}_{X \\sim H}[|\\langle X - \\mu_{\\mathbb{G}}, v \\rangle| > \\tau] < m$ and $\\operatorname{Pr}_{X \\sim P}[|\\langle X - \\mu_{\\mathbb{G}}, v \\rangle| < \\tau] < m$ .", + "bbox": [ + 75, + 607, + 468, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 3.1. Given a small $m$ with $0 < m < \\frac{1}{2}$ , let $H$ and $P$ denote Honest and Poisoned distributions, with mean $\\mu_{H}$ , $\\mu_{P}$ , and finite covariance $\\Sigma_{H}, \\Sigma_{P} \\preceq \\phi^{2}\\mathbb{I}$ . Let the mixing loss function be $\\mathbb{G} = (1 - m)H + mP$ and $\\Delta = \\mu_{H} - \\mu_{P}$ . Then, if $\\| \\Delta \\|_2^2 \\geq \\frac{6\\phi^2}{m}$ , $P$ and $H$ satisfy $m$ -separable robust statistics.", + "bbox": [ + 75, + 753, + 470, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The spatial signature analysis relies on the above $m$ -separable robust statistics, where $m$ is represented as a decimal for brevity. We provide the proof in the appendix. The", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b9ec551d6f8874e9e08898e75e6e6e9573f0a2604d406334b60e3aeec4c50afa.jpg", + "image_caption": [ + "(a) Round 102: 7 benign clients and 3 malicious clients" + ], + "image_footnote": [], + "bbox": [ + 514, + 262, + 684, + 364 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b6745f0d6c1b162edcae740a8dfb91ced9b47cfd65ff137d90cd553de97699f8.jpg", + "image_caption": [ + "(b) Round 106: 4 benign clients and 6 malicious clients", + "Figure 2. The clustering phenomenon due to benign and malicious client participation in only one round of FL." + ], + "image_footnote": [], + "bbox": [ + 705, + 261, + 875, + 364 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "orem 3.1 implies that when the percentage $m$ of compromised clients is small, the distribution of benign gradients from honest clients is separable from the distribution of poisoned gradients, especially when the distance between the means of the two distributions can be bounded by the $m$ -normalized covariance of the two distributions [22]. Given the gradient updates are high-dimensional, we focus on the output layer to analyze the statistical properties of gradient updates from all participants because the output layer gradients are the most prominent due to the vanishing gradient in backpropagation. We project the output layer gradients onto a 2D space corresponding to the two spatial signature components (SSCs) with the largest eigenvalues for spatial clustering. Figure 2 shows the spatial signatures of the gradients collected at two different FL rounds under Class-Poison. We observe a clear clustering phenomenon (green dots and red crosses), validating the intuition about the formation of two gradient distributions. A key question is whether one can simply conclude that the smaller cluster contains the Trojaned gradients from malicious clients and thus can be removed in the upcoming FL rounds.", + "bbox": [ + 496, + 441, + 892, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inherent Limitations. Spatial signatures can offer valuable statistical indicators, especially when poisoned and benign gradient distributions can be cleanly separated. However, existing defense methods simply rely on analyzing such spatial patterns and conclude that the smaller cluster contains the poisonous gradient updates and expel those clients with contributions in the smaller cluster [18,21]. We argue that relying solely on spatial signature analysis may result in high false positives and hurt the convergence of", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16345", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5da105060841c78a74400d0b3ea4ea79de5a8ff3474c0b2d5efa9a2203bb34da.jpg", + "image_caption": [ + "(a) Misgrouping gradient contributions in one round of FL." + ], + "image_footnote": [], + "bbox": [ + 99, + 89, + 450, + 196 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6c7c03c413e126254db6e43809921b1b709288aac9e5e1564d5d13f528b0950d.jpg", + "image_caption": [ + "(b) Cluster boundary uncertainties over multiple rounds of FL.", + "Figure 3. Three clustering algorithms on gradient contributions in (a) one round and (b) multiple rounds." + ], + "image_footnote": [], + "bbox": [ + 99, + 217, + 449, + 321 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "FL. We identify two reasons why such defenses can fail. First, the randomness in FL client selection can lead to an incorrect revocation, as shown in Figure 2b, where only four out of ten participants are benign. This indicates that relying on spatial signature alone is error-prone. Second, the uncertainties of clustering contribute to another dimension of complication. Figure 3a shows the spatial clustering of gradients contributed to an FL round with three Trojaned contributions (crosses) and seven benign contributions (dots). The clusters returned by three commonly used clustering methods: K-Means, hierarchical clustering, and spectral clustering are all erroneous. Rejecting the smaller cluster in all three cases will result in unacceptable errors because each contains non-poisoned contributions from honest clients. Such a problem persists even if a window of multiple rounds is used instead of a single round (Figure 3b). We observe that those gradients located between two clusters (outlined by the blue rectangle) can be ambiguous, and three different clustering methods produce different boundary cases. This further indicates that a robust defense requires high-fidelity forensic analysis with different ways to refine the inspection results and manage uncertainties.", + "bbox": [ + 75, + 385, + 472, + 731 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Temporal Signature Analysis", + "text_level": 1, + "bbox": [ + 76, + 741, + 336, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "STDLens addresses the inherent limitations of spatial clustering by additional forensic analysis with uncertainty assessment. Instead of concluding the clients contributed to the smaller cluster as malicious and revoking their subscription to FL, STDLens inspects each client in a given cluster over a temporal window, coined as the per-client temporal signature analysis. We narrow down the temporal analysis to those classes that are potentially under poisoning attacks based on the spatial signature analysis: the gradient updates", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e0ceda7a2c5503b524e313365c2703c4c3e6790c63a1929991747503cdd57159.jpg", + "image_caption": [ + "(a) Temporal trajectories of example benign and malicious clients", + "Figure 4. A benign client (green) tends to produce temporally dissimilar gradients over the course of FL while a malicious client (red) contributes similar gradients to mislead the FL process." + ], + "image_footnote": [], + "bbox": [ + 509, + 90, + 684, + 196 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/bd54b1de0290e3558e43f8d4ebfa564724dac568a649e57fac1022704c315c57.jpg", + "image_caption": [ + "(b) Unique statistical characteristics of temporal signatures" + ], + "image_footnote": [], + "bbox": [ + 705, + 88, + 880, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on a benign class will have one dense cluster, whereas the source class under poisoning attacks will exhibit at least two distinct distributions of gradient updates.", + "bbox": [ + 496, + 286, + 890, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\mathcal{G}_i$ be a temporal sequence of spatial signatures contributed by the same client $\\mathcal{P}_i$ throughout a temporal window of FL rounds. Figure 4a shows the spatial signature trajectories of two clients (one benign and one malicious). We can observe that the gradient contributions from a malicious client (i.e., the red crosses) are close to each other, but those from a benign client (i.e., the green dots) scatter around. To quantify this behavior, we define the following $\\omega$ -based temporal signature, denoted by $\\Upsilon_{\\omega}$ , for a client $\\mathcal{P}_i$ :", + "bbox": [ + 496, + 332, + 892, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Upsilon_ {\\omega} (\\boldsymbol {G} _ {i}) = \\min _ {c} \\left(\\sum_ {j = \\omega + 1} ^ {| \\boldsymbol {G} _ {i} ^ {c} |} \\sum_ {k = 1} ^ {\\omega} \\frac {\\operatorname {D i s S I M} \\left(\\boldsymbol {G} _ {i} ^ {c} [ j ] , \\boldsymbol {G} _ {i} ^ {c} [ j - k ]\\right)}{\\omega \\left| \\boldsymbol {G} _ {i} ^ {c} \\right| - \\omega^ {2}}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 474, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{G}_i^c$ denotes the sub-sequence of gradients belonging to the same cluster $c$ from the spatial signature analysis, $\\mathcal{G}_i^c[j]$ refers to its $j$ -th element, and $\\mathrm{DISSIM}(\\cdot,\\cdot)$ is a dissimilarity measure, which can utilize any $L_p$ norm-based similarity, and $L_1$ distance is used as the default given its computation efficiency. The parameter $\\omega$ refers to the window size. The larger the window size $\\omega$ is, the longer the temporal dependency is leveraged for computing temporal signatures. Figure 4b shows the distribution of temporal signatures with $\\omega = 1$ (i.e., the temporal signature is computed every two consecutive rounds). This empirically verifies that malicious clients (red bars) tend to have a significantly lower temporal signature $\\Upsilon_{\\omega}$ than benign clients (green bars). We utilize the per-client temporal signatures to refine the 2D spatial signature of a gradient update contributed by a client. This forms a 3D spatio-temporal signature space (see the top right in Figure 1) for STDLens to re-examine each cluster from the spatial signature analysis, aiming to determine which cluster of gradient updates is from malicious clients. We first compute the mean temporal signature over all contributing clients of each cluster and mark the one with a lower temporal dissimilarity score as suspicious. Then, we perform an uncertainty assessment before concluding that those clients contributed to the suspicious cluster as malicious.", + "bbox": [ + 496, + 523, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16346", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/45012a241a5747e65af83796a6902d90b0330354354adb746debf8f8dac586fb.jpg", + "image_caption": [ + "Figure 5. The empirical rule for confidence estimation." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 263, + 183 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b626143319e2ab9b17158256daf4ade99be163dfdd6b9ef234edd2a7f094ba74.jpg", + "image_caption": [ + "Figure 6. $\\sigma$ -density analysis on spatial signatures." + ], + "image_footnote": [], + "bbox": [ + 274, + 88, + 467, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Density-based Uncertainty Inspection", + "text_level": 1, + "bbox": [ + 76, + 231, + 401, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The results from the spatial clustering analysis can be unreliable, as shown in Figure 3. Similarly, the temporal signature analysis may also incur uncertainty if the average temporal dissimilarity score for each of the two clusters is too close. We introduce the third component dedicated to uncertainty correction. Concretely, it identifies uncertain spatial and temporal zones such that a client is expelled only if we have high confidence that its gradient updates are poisoned. Our uncertainty assessment is based on the empirical rule in normal distributions that $68\\%$ , $95\\%$ , and $99\\%$ of data points lie within 1, 2, and 3 standard deviations ( $\\sigma$ 's) from the mean (Figure 5). The confidence requirement is domain-specific. With a given confidence threshold for uncertainty control, we can define the corresponding $\\sigma$ -confident and $\\sigma$ -uncertain zones. In particular, we first identify the SSC with the largest eigenvalue. It captures the inter-cluster variance and is visualized as the $x$ -axis by default. Figure 6 shows that the spatial signatures (top) on this component exhibit a mixture of two normal distributions (bottom). This allows STDLens to employ the empirical rule by computing the mean and the standard deviation of each cluster (orange or blue in Figure 6) and translating the confidence requirement (e.g., $99\\%$ ) into the corresponding intervals (e.g., $3-\\sigma$ from the mean of the respective cluster). STDLens considers the zone between two $\\sigma$ -confident regions to be uncertain, and any gradient updates from participating clients that fall into this zone will be put on a watchlist. The same client entering the $\\sigma$ -uncertain zone multiple times will be removed from FL. The same uncertainty management operation can also be done on the temporal signatures to minimize the uncertainty-induced false positives. For clients in the cluster with a smaller dissimilarity score and outside the $\\sigma$ -uncertain zone, STDLens will mark them as malicious and revoke their participation in the remaining rounds.", + "bbox": [ + 76, + 255, + 472, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Evaluation", + "text_level": 1, + "bbox": [ + 76, + 799, + 312, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments on two object detection benchmark datasets: (i) PASCAL VOC [7] and (ii) INRIA Person [6]. By default, we have $N = 100$ clients and a federated server with $T = 200$ rounds for both datasets. At each round, $k = 10\\%$ of the clients are randomly selected as", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/715084122df7ae1eac7cd810f3b108c7864476fa5fbccb89c7c5fbff0d54cca5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Perception \nPoisonmBenign \nAPsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
Class-Poison \n(VOC)5%52.4345.3552.41
10%52.4339.6952.32
20%52.4338.2252.22
BBox-Poison \n(VOC)5%52.4335.7652.32
10%52.4323.4952.15
20%52.4318.0652.19
Objn-Poison \n(VOC)5%52.4345.0251.95
10%52.4341.6152.33
20%52.4337.6152.29
BBox-Poison \n(INRIA)5%63.4945.0361.64
10%63.4932.5161.25
20%63.4928.7361.71
Objn-Poison \n(INRIA)5%63.4961.0561.98
10%63.4953.9162.01
20%63.4950.1861.58
", + "bbox": [ + 501, + 88, + 890, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. The $\\mathrm{AP}_{\\mathrm{src}}$ of FL-trained detectors under the benign scenario (3rd column) and three perception poisoning attacks (4th and 5th columns) with three settings of malicious client percentage $m$ .", + "bbox": [ + 498, + 321, + 893, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "participants with FedAvg [12] as the aggregation algorithm. Without loss of generality, we focus on Faster R-CNN [16] with VGG16 [19] because perception poisoning is model-agnostic and black-box in nature. For each dataset, we randomly split the training set into $N$ equal-sized partitions and assigned each to one client as its local dataset. We analyze STDLens against all three types of perception poisoning on VOC and examine BBox-Poison and Obj-Poison on INRIA as it only supports objects of the \"person\" class, which is the default victim source class. The target class in Class-Poison is \"potted plant.\" For BBox-Poison, we shrink the bounding box by a factor of 0.10. By default, $m = 20\\%$ of the clients in FL are malicious. STDLens is operated with a forensic schedule of ten rounds per window, and the confidence required for uncertainty control is set to be $99\\%$ .", + "bbox": [ + 496, + 378, + 890, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Effectiveness of STDLens", + "text_level": 1, + "bbox": [ + 500, + 618, + 732, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Trojan-agnostic Defense. We first analyze how effective STDLens is in mitigating different model hijacking attacks through perception poisoning. Table 2 reports the results measured in average precision [7] of the victim source class $\\left(\\mathrm{AP}_{\\mathrm{src}}\\right)$ under three different settings of $m\\%$ . Given that those attacks can hijack the models to cause a drastic drop in $\\mathrm{AP}_{\\mathrm{src}}$ (3rd and 4th columns), STDLens offers strong defensibility against all of them (5th column). Regardless of which attack is launched and how many malicious clients (reflected by $m$ ) participate in the attack process, STDLens can consistently restore the $\\mathrm{AP}_{\\mathrm{src}}$ , on par with the one obtained in the benign scenario (i.e., $52.43\\%$ for VOC and $63.49\\%$ for INRIA). For instance, BBox-Poison, which brings down the $\\mathrm{AP}_{\\mathrm{src}}$ to $18.06\\%$ on VOC, is mitigated with an $\\mathrm{AP}_{\\mathrm{src}}$ of $52.19\\%$ under the same attack setting. This validates that STDLens is Trojan-agnostic, despite the divergence of different attack effects. Due to similar observa", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16347", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/269fa7d97521ad79295c02ff4182904874d0270175a21584526115aa26a3500c.jpg", + "image_caption": [ + "Benign FL —— Poisoned FL (No Defense) —— Poisoned FL (STDLens)", + "(a) Class-Poison" + ], + "image_footnote": [], + "bbox": [ + 98, + 104, + 344, + 213 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8215e95f987f73dd2a8edbcc3abcdd7e8129e162b36246a55d9ec2d0b980f630.jpg", + "image_caption": [ + "(b) BBox-Poison" + ], + "image_footnote": [], + "bbox": [ + 359, + 104, + 607, + 214 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/67eca3d490de81c4349269567a28060f0e90f06267516dc71d7ca418f982b49b.jpg", + "image_caption": [ + "(c) Objn-Poisson" + ], + "image_footnote": [], + "bbox": [ + 622, + 106, + 870, + 214 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/83eaf54fe1691fde780f3f22a5ac318c8f44dc0b3ea9bde08aec046756452b43.jpg", + "image_caption": [ + "Figure 7. Compared with the benign FL (brown) on VOC, the hijacked FL with no defense (pink) has significant $\\mathrm{AP}_{\\mathrm{src}}$ degradation. STDLens (green) purges all malicious clients in an early-round, allows the healing to begin, and reclaims $\\mathrm{AP}_{\\mathrm{src}}$ with a negligible damage.", + "Table 3. Two images detected by the FL-trained models (VOC) under Class-Poison, BBox-Poison, and Obj-Poison. The FL system with no defense makes designated errors, while the STDLens-protected FL preserves correctness even if the adversary attempts to hijack it." + ], + "image_footnote": [], + "bbox": [ + 133, + 277, + 838, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tions, we focus on VOC in the following discussion.", + "bbox": [ + 76, + 486, + 421, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Timely Sanitization and Recovery. Figure 7 visualizes the learning curves of FL throughout 200 rounds by comparing three cases: (i) the benign scenario (brown curve), (ii) the hijacked scenario without defense (pink curve), and (iii) the hijacked scenario protected by STDLens (green curve). We make the following observations. First, Trojaned gradients cause the $\\mathrm{AP}_{\\mathrm{src}}$ to become either highly unstable (Class-Poison) or consistently degraded (BBox-Poison and Objn-Poison) throughout the FL process. Second, when STDLens detects all malicious clients at the 30th round under Class-Poison, the 20th round under BBox-Poison, and the 30th round under Objn-Poison, no honest client is misdiagnosed and flagged as malicious. Third, the timely sanitization of malicious clients allows the FL system to heal. Even under attacks, the STDLens-protected FL can reach an $\\mathrm{AP}_{\\mathrm{src}}$ comparable with the benign scenario.", + "bbox": [ + 75, + 503, + 468, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualization. Table 3 visualizes the detection results on two test examples under all three perception poisoning attacks. All three attacks fool the global model with erroneous detection: (i) Class-Poison (1st column) fools the model into mislabeling the person as a potted plant (top) or a bird (bottom), (ii) BBox-Poison (3rd column) deceives the model to recognize person objects with incorrect bounding boxes, and (iii) Objn-Poison (5th column) causes the model to detect no person objects. In comparison, STDLens successfully reinvigorates the FL system with high robustness", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(2nd, 4th, and 6th columns).", + "bbox": [ + 500, + 486, + 687, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. STDLens under Adaptive Attacks", + "text_level": 1, + "bbox": [ + 500, + 518, + 795, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\beta$ -adaptive Attacks. An immediate question we need to address is the defensibility of STDLens against adaptive adversaries who strategically change their attack methods. For instance, malicious clients could camouflage in the crowd of benign clients by occasionally contributing non-Trojaned gradients. We refer to this type of adaptive adversary as $\\beta$ -adaptive. When a $\\beta$ -adaptive adversary participates in an FL round, it has, e.g., a $\\beta = 10\\%$ chance of not poisoning the local dataset during the local model training. As a result, this adaptive adversary will contribute to the cluster with benign gradient updates and also to the cluster with Trojaned gradient updates, aiming to fool the spatial and temporal signature analysis. Indeed, such an adaptive attack strategy can jeopardize the spatial analysis because malicious clients can be mistakenly clustered with honest ones, as depicted in Figure 8a. This makes defenses using solely spatial clustering [18, 21] unable to purge all malicious clients. Even for another representative defense using spectral signatures [22], the statistical properties of malicious contributions become the same as those benign ones, as shown in Figure 9a. However, the temporal signature analysis in STDLens is, by design, resilient to such adaptive strategies, as shown in Figure 8b. Recall in Equation 1 that the temporal signature of a client is com", + "bbox": [ + 496, + 537, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16348", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9bba6c7e7ba1b6c027f960e421cd6f11cb8c31e2ccfc84acbad2795a7d9cbd31.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Perception PoisonObject Detection with No DefenseObject Detection with STDLensβBenign \\(AP_{src}\\) (%)Hijacked \\(AP_{src}\\) (%)
No DefenseSTDLens
Class-Poisonpottedplant (0.59)person (0.98)5%52.4331.8351.74
10%52.4332.5152.18
15%52.4334.4051.56
BBox-Poisonperson (0.51)person (0.99)5%52.4322.3652.39
10%52.4326.7752.11
15%52.4327.6051.98
Objn-Poisonmotorbike (0.97)person (0.94)5%52.4340.9652.05
10%52.4341.0152.18
15%52.4341.0652.11
", + "bbox": [ + 138, + 88, + 834, + 247 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7c7e900a7b94c88d8d331d301533318806e823be2550c1f27e4982a5538dc761.jpg", + "image_caption": [ + "(a) Spatial Signature Analysis" + ], + "image_footnote": [], + "bbox": [ + 86, + 282, + 267, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/832fcd5d027c157f79875a23a803bb772059dd3320c0b0522c26df9df0b4da2c.jpg", + "image_caption": [ + "(b) Temporal Signature Analysis", + "Figure 8. $\\beta$ -adaptive malicious clients randomly camouflage in the benign cluster in the spatial analysis (a), but their statistical characteristics in the temporal signature analysis (b) remain unchanged." + ], + "image_footnote": [], + "bbox": [ + 282, + 282, + 460, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "puted w.r.t. each cluster, and the one with a smaller magnitude is taken to be the lower bound of malicious likelihood. Hence, the statistical characteristics of honest and malicious clients can be preserved in our temporal analysis, where malicious clients (red) have a much smaller temporal signature than honest clients (green). Table 4 compares the hijacked $\\mathrm{AP}_{\\mathrm{src}}$ with the $\\beta$ -adaptive attack under no defense scenario (6th column) with the FL system under the protection by STDLens (7th column). A total of nine scenarios under three attacks are compared by varying the configurations of $\\beta$ from $5\\%$ to $15\\%$ . We make two observations. First, under the $\\beta$ -adaptive attack, the $\\mathrm{AP}_{\\mathrm{src}}$ suffers from significant degradation, from $52.43\\%$ to $22.36\\%$ , even though malicious clients do not send Trojaned gradients all the time. For adaptive adversaries, the choice of $\\beta$ should be kept small as a larger $\\beta$ can notably weaken the attack effectiveness. Second, STDLens remains resilient under $\\beta$ -adaptive adversaries since it can consistently restore the $\\mathrm{AP}_{\\mathrm{src}}$ to at least $51.56\\%$ for all nine scenarios, on par with that under non-adaptive attacks (recall Table 2). This is primarily because our temporal analysis is robust against such a camouflage. Integrating spatio-temporal statistics allows the identification of the malicious cluster to remain accurate under $\\beta$ -adaptive attacks.", + "bbox": [ + 75, + 476, + 472, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$\\gamma$ -adaptive Attacks. Another attempt to launch adaptive attacks is to wash out the spatial clustering characteristics by only poisoning $\\gamma \\%$ of training samples in the local dataset of a malicious client. Under this adaptive setting,", + "bbox": [ + 75, + 840, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bc6b45f9b8df42bcdfcf93aaf12df3dc59e619c37500701739865bb032527028.jpg", + "image_caption": [ + "(a) $\\beta$ -adaptive", + "Figure 9. Spectral signatures [22] fail under (a) $\\beta$ -adaptive and (b) $\\gamma$ -adaptive attacks as the statistical properties of malicious contributions (red) overlap with benign ones (green)." + ], + "image_footnote": [], + "bbox": [ + 509, + 282, + 687, + 375 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a28ea37b5da44599027dc0ca3f3bb1d04844dbef8cd920d7c0ace798faee8b26.jpg", + "image_caption": [ + "(b) $\\gamma$ -adaptive" + ], + "image_footnote": [], + "bbox": [ + 705, + 282, + 880, + 375 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7ea85359e1987f2188431043a6fd50ffd0b8ad015996886fe6f30b4032332a6c.jpg", + "table_caption": [ + "Table 4. The benign $\\mathrm{AP}_{\\mathrm{src}}$ and hijacked $\\mathrm{AP}_{\\mathrm{src}}$ under $\\beta$ -adaptive attacks with varying $\\beta$ in different types of perception poison (VOC)." + ], + "table_footnote": [], + "table_body": "
γBenign\nAPsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
80%52.4340.0352.09
60%52.4346.0151.54
", + "bbox": [ + 545, + 450, + 846, + 508 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Quantitative studies of $\\gamma$ -adaptive Class-Poison (VOC).", + "bbox": [ + 501, + 512, + 885, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the contribution from a malicious client becomes the gradient updates computed over a mixture of clean and poisoned training samples. We conduct experiments with two settings of $\\gamma$ with results in Table 5. The $\\gamma$ -adaptive attacks can bring down the $\\mathrm{AP}_{\\mathrm{src}}$ from $52.43\\%$ to $40.03\\%$ and $46.01\\%$ when we set $\\gamma$ to $80\\%$ and $60\\%$ , respectively. More malicious clients fall inside the $\\sigma$ -uncertain zone, which will be incorrectly identified by defenses using only spatial clustering analysis [18, 21]. Such an adaptive attack also makes spectral signatures [22] ambiguous, as the statistical properties of benign and malicious gradients overlap (Figure 9b). For those uncertain clients, STDLens has to put the decision on hold and wait for more rounds to accumulate additional observations for making confident decisions. Table 5 shows that STDLens remains robust under $\\gamma$ -adaptive attacks because all malicious clients can still be identified with no false alarm. The $\\mathrm{AP}_{\\mathrm{src}}$ can be recovered to reach over $51.54\\%$ , comparable to the benign $\\mathrm{AP}_{\\mathrm{src}}$ of $52.43\\%$ .", + "bbox": [ + 496, + 537, + 890, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Late-stage Adaptive Attacks. Instead of starting the poisoning process from the beginning of FL, an adaptive adversary could only start poisoning the training data when selected in the later rounds of FL. In this case, the FL system has no Trojaned gradient updates contributed by its clients for a period of time. We conduct such a late-stage adap", + "bbox": [ + 496, + 810, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16349", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa6ab37e35e499e25f0d425063fb63d08a22e5c64206b88f8dad8512afcdfd6b.jpg", + "image_caption": [ + "Figure 10. The malicious clients become active after the 100th round (VOC), causing the $\\mathrm{AP}_{\\mathrm{src}}$ to drop. STDLens purges all malicious clients at the 130th round and allows the FL to recover." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 467, + 220 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tive attack by running Class-Poison after the 100th round during the FL process. Figure 10 (left) shows the learning curves of $\\mathrm{AP}_{\\mathrm{src}}$ for three scenarios: (i) the benign scenario, (ii) the late-stage adaptive attack without defense, and (iii) the one protected by STDLens. Considering the nodefense scenario (pink curve), the $\\mathrm{AP}_{\\mathrm{src}}$ fluctuates wildly after the 100th round. In comparison, STDLens (green curve) starts detecting the existence of Trojans from the window of rounds 101-110 (top right) and removes the identified malicious clients. It successfully expels all anomalies at the 130th round and allows the FL to heal as no more malicious clients attempt to mislead the FL system (e.g., the window of rounds 131-140 at the bottom right).", + "bbox": [ + 75, + 279, + 472, + 476 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Comparisons with Existing Defenses", + "text_level": 1, + "bbox": [ + 76, + 484, + 393, + 501 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We further compare STDLens with two existing defense methods: spatial clustering [21] and spectral signature [22], which can be extended to FL-based object detection. Table 6 reports the quantitative results. All three defense solutions can detect all malicious clients over the course of FL (i.e., achieving the defense recall of 1.00). STDLens completes the detection and revocation of malicious clients between 20 to 30 rounds, and spatial clustering takes 30 to 40 rounds to detect and remove anomalies, while malicious clients can stay alive in the FL system for at most 80 rounds with spectral signature. The main differentiation factor lies in defense precision. Even though STDLens takes a slightly longer execution time (i.e., $452\\mathrm{ms}$ with $84\\mathrm{ms}$ for temporal signature analysis and $44\\mathrm{ms}$ for $\\sigma$ -density inspection), it successfully identifies all malicious clients without mistakenly rejecting any benign clients (false positives), achieving a defense precision of 1.00. This allows the STDLens-protected FL to train a global object detector with high accuracy, as shown in the 2nd column in Table 7. In comparison, the spatial clustering approach can reach a low precision of 0.53 under Objn-Poisson, due to gradient contributions falling in the zone between the two clusters, causing ambiguity in anomaly detection. This result shows that defenses based solely on spatial clustering may not offer stable robustness. The spectral signature defense performs the worst, with a defense precision ranging from 0.26 to 0.54. It", + "bbox": [ + 75, + 507, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/cdf7779766ba2a2ba752209b8d7dad021f48802a81c522a61ecee160df0e76d6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Defense Precision@Round w/ Max. Recall
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poison1.00@300.95@300.53@40
BBox-Poison1.00@200.71@300.26@80
Objn-Poison1.00@300.53@400.54@40
Time (ms)4523421423
", + "bbox": [ + 506, + 88, + 885, + 188 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f90e8e47f72224ab681143eeab289575b71220e38b31c9c1393b965121f95c36.jpg", + "table_caption": [ + "Table 6. Comparing STDLens with two state-of-the-art methods on VOC in terms of the defense precision at the round where the maximum recall is achieved and the execution time (the last row)." + ], + "table_footnote": [], + "table_body": "
Object Detection Results by Hijacked Models
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poisonperson (1.00)\nmoto 'D1K' (1.00)person (0.99)\nmotor bike (0.98)person (0.76)\nmotor bike (0.88)\nbird (0.81)
BBox-Poisonperson (0.97)\ntvmonitor (0.96)person (0.79)\n××
Objn-Poisonperson (0.95)\nperson (0.94)person (0.89)\n×person (0.71)\n×
", + "bbox": [ + 503, + 251, + 890, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. The high defense precision offered by STDLens allows the FL-trained model to remain accurate. The excessive removal of clients by other defenses incurs performance degradation (VOC).", + "bbox": [ + 498, + 482, + 892, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "implies that while the defense can expel malicious clients, a considerable number of honest ones are also mistakenly rejected. One reason is the changing malicious population over time due to the removal of malicious clients in the early rounds. The excessive removal of clients can weaken the benign learning signal and degrade the FL-trained model, as shown in the 3rd and 4th columns in Table 7.", + "bbox": [ + 498, + 541, + 890, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 671, + 627, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With the goal of building a trustworthy federated training process, we have presented STDLens, a three-tier defense framework for FL-based object detection, strengthening the spatial signature with the temporal signature analysis and uncertainty management. Extensive experiments with various adaptive adversaries show that STDLens can protect FL against all three model hijacking attacks and outperforms existing mitigation methods with high defense precision and a low false-positive rate.", + "bbox": [ + 496, + 700, + 890, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, an IBM faculty award, and a Cisco grant on Edge Computing. The first author acknowledges the IBM PhD Fellowship Award.", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "16350", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. In International Conference on Artificial Intelligence and Statistics, pages 2938-2948. PMLR, 2020. 1", + "[2] Arjun Nitin Bhagoji, Supriyo Chakraborty, Pratek Mittal, and Seraphin Calo. Analyzing federated learning through an adversarial lens. In International Conference on Machine Learning, pages 634-643. PMLR, 2019. 1", + "[3] Ka-Ho Chow and Ling Liu. Perception poisoning attacks in federated learning. 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Springer, 2020. 2" + ], + "bbox": [ + 503, + 92, + 890, + 895 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "16351", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 8 + } +] \ No newline at end of file diff --git a/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_model.json b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2371963ea7a5c0ab2127e3c2bb0bb11f9766f50b --- /dev/null +++ b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_model.json @@ -0,0 +1,1758 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.092, + 0.131, + 0.877, + 0.152 + ], + "angle": 0, + "content": "STDLens: Model Hijacking-resilient Federated Learning for Object Detection" + }, + { + "type": "title", + "bbox": [ + 0.241, + 0.181, + 0.728, + 0.233 + ], + "angle": 0, + "content": "Ka-Ho Chow, Ling Liu, Wenqi Wei, Fatih Ilhan, Yanzhao Wu \nGeorgia Instutite of Technology \nAtlanta, GA, USA" + }, + { + "type": "text", + "bbox": [ + 0.132, + 0.237, + 0.831, + 0.252 + ], + "angle": 0, + "content": "khchow@gatech.edu, ling.liu@cc.gatech.edu, {wenqiwei, filhan, yanzhaowu}@gatech.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.312, + 0.302 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.665 + ], + "angle": 0, + "content": "Federated Learning (FL) has been gaining popularity as a collaborative learning framework to train deep learning-based object detection models over a distributed population of clients. Despite its advantages, FL is vulnerable to model hijacking. The attacker can control how the object detection system should misbehave by implanting Trojaned gradients using only a small number of compromised clients in the collaborative learning process. This paper introduces STDLens, a principled approach to safeguarding FL against such attacks. We first investigate existing mitigation mechanisms and analyze their failures caused by the inherent errors in spatial clustering analysis on gradients. Based on the insights, we introduce a three-tier forensic framework to identify and expel Trojaned gradients and reclaim the performance over the course of FL. We consider three types of adaptive attacks and demonstrate the robustness of STDLens against advanced adversaries. Extensive experiments show that STDLens can protect FL against different model hijacking attacks and outperform existing methods in identifying and removing Trojaned gradients with significantly higher precision and much lower false-positive rates. The source code is available at https://github.com/git-disl/STDLens." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.68, + 0.208, + 0.695 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Federated Learning (FL) for object detection has attracted numerous applications [12], especially in healthcare, with strict privacy regulations protecting patient medical records [25, 27]. Instead of using a centralized data curator, FL can train a global object detection model with a distributed population of clients. Each client only shares its fixed-size gradient (updated model) parameters (e.g., 246.9 MB for YOLOv3 [15]) with the FL server for aggregation while keeping its private raw data local (e.g., terabytes of videos) [13]. Such a paradigm lowers the bar for knowledge sharing and eases the recruitment of contributors, but it becomes vulnerable to model hijacking [9, 21]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Model hijacking aims at interfering with the training pro" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.285, + 0.891, + 0.48 + ], + "angle": 0, + "content": "
ScenarioObject Detection ResultsAPersonAPcar
Benignperson 0.93\nGm 0.76\nSg 0.64person 0.76\nGm 0.76\nSg 0.6452.4374.12
Class-Poison Victim: Personpottedplant 0.56\nGm 0.72\nSg 0.62bird 0.45\nGm 0.72\nSg 0.6238.22\n(↓27%)71.79\n(↓3%)
BBox-Poison Victim: Personperson 0.62\nGm 0.72\nSg 0.62person 0.45\nGm 0.72\nSg 0.6218.06\n(↓66%)72.82\n(↓2%)
Objn-Poison Victim: Personpottedplant 0.56\nGm 0.76\nSg 0.64person 0.45\nGm 0.76\nSg 0.6437.61\n(↓28%)71.59\n(↓3%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.485, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Table 1. FL-trained detectors can be hijacked by perception poisoning to misdetect objects of designated classes (e.g., person) in three different ways (2nd to 4th rows) [3], while objects of nonvictim classes (e.g., car) have negligible performance degradation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.901 + ], + "angle": 0, + "content": "cess of a machine learning model and causes it to misbehave at the deployment stage [17]. The FL-trained global model can be indirectly hijacked by a small number of compromised clients who share Trojaned gradients to gradually confuse the learning trajectory of FL [10]. Such gradients can be generated in black-box through data poisoning. The attacker only has to poison the local training data owned by a compromised client, such as changing the ground-truth label of certain objects by dirty-label poisoning [21] or implanting a backdoor to trigger the malfunctioning of a hijacked model [1, 2, 8, 20]. The FL software will take the poisoned local training data and unintentionally generate malicious gradients for sharing. With the growing number of real-world applications, recent work has begun to understand the hijacking of FL-based object detection systems [3]. As shown in Table 1, the adversary can designate how the hijacked model should misdetect objects of certain classes (e.g., person) while ensuring other objects can still be precisely detected (e.g., car). This fine-grained control opens the door for an adversary to design a stealthy attack configuration to hurt the FL system yet remains hardly noticeable by the owner [5], leading to catastrophic consequences such as car crashes." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16343" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.395 + ], + "angle": 0, + "content": "This paper introduces STDLens, a three-tier defense methodology against model hijacking attacks, with the following original contributions. First, we analyze existing defenses based on spatial signature analysis and show their ineffectiveness in protecting FL. Second, we introduce a pipeline with per-client spatio-temporal signature analysis to identify Trojaned gradients, track their contributors, revoke their subscriptions, and reclaim the detection performance. Third, we present a density-based confidence inspection mechanism to manage the spatio-temporal uncertainty. It avoids purging benign clients contributing useful learning signals for the FL system. Finally, we extend perception poisoning with three types of adaptiveness for analyzing STDLens in countering advanced adversaries. Extensive experiments show that STDLens outperforms competitive defense methods by a large margin in defense precision with a low false-positive rate, reducing the accuracy drop under attack from \\(34.47\\%\\) to \\(0.24\\%\\), maintaining the object detection accuracy on par with the performance under the benign scenario." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.408, + 0.363, + 0.425 + ], + "angle": 0, + "content": "2. Background and Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.433, + 0.436, + 0.451 + ], + "angle": 0, + "content": "2.1. Perception Poisoning for Model Hijacking" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Threat Model. Perception poisoning adopts the following assumptions: (i) the communication between a client and the trustworthy FL server is encrypted; (ii) the benign clients faithfully follow the FL workflow; and (iii) there is only a small \\( m\\% \\) of compromised clients out of a total of \\( N \\) clients. An adversary on a malicious client can only manipulate its local training data, and hence, model hijacking can be done without tampering with the FL software." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.7 + ], + "angle": 0, + "content": "Poisoning Formulation. Let \\( F \\) be the global model being trained in FL, \\( f_{i} \\) be the local model of client \\( \\mathcal{P}_i \\), and \\( (\\pmb{x},\\pmb{y}) \\) be the input sample and its ground truth in the training set \\( \\mathcal{D}_i \\) of client \\( \\mathcal{P}_i \\). The process of perception poisoning can be formulated as a function \\( \\psi \\) that maps \\( (\\pmb{x},\\pmb{y}) \\) to \\( (\\pmb{x},\\pmb{y}') \\) such that the local model \\( f_{i} \\) will generate Trojaned gradients which maximize the chance of \\( F \\) being fooled to make erroneous predictions with high confidence, formally:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.708, + 0.473, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\psi : \\psi (\\boldsymbol {x}, \\boldsymbol {y}) = \\left(\\boldsymbol {x}, \\boldsymbol {y} ^ {\\prime}\\right) \\text {s . t .} f _ {i} (\\boldsymbol {x}) = \\boldsymbol {y} ^ {\\prime}, \\boldsymbol {y} ^ {\\prime} \\neq \\boldsymbol {y}, \\max [ F (\\boldsymbol {x}) \\bowtie \\boldsymbol {y} ^ {\\prime} ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\(\\pmb{y}\\) is a list of triplets, one for each object \\(\\pmb{o} =\\) (CLASS,BBOX,OBJN) in the training image \\(\\pmb{x}\\), CLASS is the class label, BBOX is the bounding box, and OBJN is the existence of object \\(\\pmb{o}\\). \\(f_{i}(\\pmb{x})\\) and \\(F(\\pmb{x})\\) denote the detected objects by the local and global models, respectively. The operator \\(\\bowtie\\) indicates the degree of matching between two sets of objects [4]. Based on the three perceptual components of an object, one can formulate three poisoning strategies to designate malicious behaviors on the hijacked model [3]: (i) Class-Poison changes the class label of objects of a source class to a maliciously chosen target class" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.334 + ], + "angle": 0, + "content": "without altering their bounding box locations and object existence. (ii) BBox-Poison attacks objects of certain source classes by randomly changing the size and the location of their bounding boxes without altering the class label and the object existence. (iii) Obj-Poison attacks objects of certain classes by changing their existence to non-existence. As shown in Table 1, the hijacked model under Class-Poison (2nd row) mislabels the person as a potted plant in the first example and as a bird in the second example with a different attack configuration. Under BBox-Poison (3rd row), the person object is detected with a correct class label but a misaligned bounding box. Under Obj-Poison (4th row), the person vanishes in both cases. Only the designated classes suffer from performance degradation (e.g., \"person\" in the 4th column), while the detection of objects of other irrelevant classes is not affected (e.g., \"car\" in the 5th column)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.342, + 0.846, + 0.358 + ], + "angle": 0, + "content": "2.2. Existing Defenses and Their Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.895, + 0.835 + ], + "angle": 0, + "content": "While no defenses have been proposed to counter perception poisoning, several solutions are being introduced for image classifiers, which are either developed for FL [21, 23, 28] or can be extended [18, 22]. They can be broadly classified into two categories. The first category aims at repairing the gradients (model updates). Contributions from all participants will be used for aggregation, but they will be processed by parameter clipping and noise injection [11, 20, 24] to wash out possibly malicious elements. However, it is challenging to determine the correct amount of noise to be injected [14]. The Trojaned gradients can still be malicious if the noise is too small, while a larger noise can remove useful learning signals from benign clients and affect the convergence of FL. The second category attempts to inspect gradients shared by participants to identify and eliminate malicious clients. MNTD [26] trains a meta-classifier to differentiate Trojaned and non-Trojaned gradients. It is a supervised defense and assumes a known distribution of Trojans to create training data. Unsupervised defenses make fewer assumptions and are more attractive in practice. AUROR [18] and its followers [21] conduct spatial clustering on gradient contributions and label the contributors to the smaller cluster to be malicious. Spectral signature [22] conducts outlier removal via SVD by purging gradient contributions deviating most significantly from a singular vector. While they neither rely on finding the right amount of noise for injection nor prior knowledge on possible attacks to be defended, our analysis in Section 3 finds that anomaly detection using solely spatial analysis on the latent projection space can fail due to the randomness in per-round client selection and the clustering uncertainty." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.845, + 0.796, + 0.863 + ], + "angle": 0, + "content": "3. STDLens: Defense Methodology" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Perception poisoning is a real threat. Adversaries can configure the attack to hijack the model without being no-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16344" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.849, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.143, + 0.237, + 0.825, + 0.253 + ], + "angle": 0, + "content": "Figure 1. The overview of STDLens, a three-tier framework against model hijacking through perception poisoning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.265, + 0.474, + 0.465 + ], + "angle": 0, + "content": "ticed. We present a forensic framework called STDLens, to safeguard FL systems. It utilizes robust and attack-agnostic statistical properties with a three-tier forensic analysis. It does not assume prior knowledge on which poisoning attack is launched (i.e., Class-Poison, BBox-Poison, Obj-Poison, or their combinations). Figure 1 gives an overview. STDLens is operated at a system-supplied schedule, configurable at initiation (e.g., every ten FL rounds). Contributions from the participating clients during the window of rounds are accumulated for a safety inspection by the spatial signature analysis, followed by a per-client temporal signature analysis to identify Trojaned gradients and a \\(\\sigma\\)-density analysis to manage the spatio-temporal uncertainty." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.471, + 0.317, + 0.488 + ], + "angle": 0, + "content": "3.1. Spatial Signature Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.471, + 0.603 + ], + "angle": 0, + "content": "Under perception poisoning, it is observed that with a small \\( m\\% \\) of malicious clients, the eigenvalues of the covariance of the gradient updates for the source class consist of two sub-populations: the Trojaned gradients from malicious participants and the benign gradients from honest participants. We refer to such phenomenon as \\( m \\)-separable robust statistics of perception poisoning attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.748 + ], + "angle": 0, + "content": "Definition 3.1. \\( m \\)-Separable Robust Statistics. Given a small \\( m \\) with \\( 0 < m < \\frac{1}{2} \\), let \\( H \\) and \\( P \\) denote the two distributions: \\( \\underline{\\text{Honest}} \\) and \\( \\underline{\\text{Poisoned}} \\), respectively, with finite covariance. Let the mixing loss function be \\( \\mathbb{G} = (1 - m)H + mP \\), \\( v \\) be the top eigenvalue of the covariance of \\( \\mathbb{G} \\) and \\( \\mu_{\\mathbb{G}} \\) is the mean of the mixed distribution \\( \\mathbb{G} \\). The two distributions \\( H \\) and \\( P \\) are separable if there exists some \\( \\tau \\) such that \\( \\operatorname{Pr}_{X \\sim H}[|\\langle X - \\mu_{\\mathbb{G}}, v \\rangle| > \\tau] < m \\) and \\( \\operatorname{Pr}_{X \\sim P}[|\\langle X - \\mu_{\\mathbb{G}}, v \\rangle| < \\tau] < m \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.471, + 0.85 + ], + "angle": 0, + "content": "Theorem 3.1. Given a small \\(m\\) with \\(0 < m < \\frac{1}{2}\\), let \\(H\\) and \\(P\\) denote Honest and Poisoned distributions, with mean \\(\\mu_{H}\\), \\(\\mu_{P}\\), and finite covariance \\(\\Sigma_{H}, \\Sigma_{P} \\preceq \\phi^{2}\\mathbb{I}\\). Let the mixing loss function be \\(\\mathbb{G} = (1 - m)H + mP\\) and \\(\\Delta = \\mu_{H} - \\mu_{P}\\). Then, if \\(\\| \\Delta \\|_2^2 \\geq \\frac{6\\phi^2}{m}\\), \\(P\\) and \\(H\\) satisfy \\(m\\)-separable robust statistics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The spatial signature analysis relies on the above \\(m\\)-separable robust statistics, where \\(m\\) is represented as a decimal for brevity. We provide the proof in the appendix. The" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.263, + 0.685, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.371, + 0.692, + 0.395 + ], + "angle": 0, + "content": "(a) Round 102: 7 benign clients and 3 malicious clients" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.262, + 0.876, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.699, + 0.371, + 0.886, + 0.395 + ], + "angle": 0, + "content": "(b) Round 106: 4 benign clients and 6 malicious clients" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.398, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Figure 2. The clustering phenomenon due to benign and malicious client participation in only one round of FL." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.893, + 0.761 + ], + "angle": 0, + "content": "orem 3.1 implies that when the percentage \\( m \\) of compromised clients is small, the distribution of benign gradients from honest clients is separable from the distribution of poisoned gradients, especially when the distance between the means of the two distributions can be bounded by the \\( m \\)-normalized covariance of the two distributions [22]. Given the gradient updates are high-dimensional, we focus on the output layer to analyze the statistical properties of gradient updates from all participants because the output layer gradients are the most prominent due to the vanishing gradient in backpropagation. We project the output layer gradients onto a 2D space corresponding to the two spatial signature components (SSCs) with the largest eigenvalues for spatial clustering. Figure 2 shows the spatial signatures of the gradients collected at two different FL rounds under Class-Poison. We observe a clear clustering phenomenon (green dots and red crosses), validating the intuition about the formation of two gradient distributions. A key question is whether one can simply conclude that the smaller cluster contains the Trojaned gradients from malicious clients and thus can be removed in the upcoming FL rounds." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Inherent Limitations. Spatial signatures can offer valuable statistical indicators, especially when poisoned and benign gradient distributions can be cleanly separated. However, existing defense methods simply rely on analyzing such spatial patterns and conclude that the smaller cluster contains the poisonous gradient updates and expel those clients with contributions in the smaller cluster [18,21]. We argue that relying solely on spatial signature analysis may result in high false positives and hurt the convergence of" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16345" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.09, + 0.451, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.201, + 0.429, + 0.213 + ], + "angle": 0, + "content": "(a) Misgrouping gradient contributions in one round of FL." + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.218, + 0.45, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.109, + 0.324, + 0.438, + 0.337 + ], + "angle": 0, + "content": "(b) Cluster boundary uncertainties over multiple rounds of FL." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.344, + 0.47, + 0.373 + ], + "angle": 0, + "content": "Figure 3. Three clustering algorithms on gradient contributions in (a) one round and (b) multiple rounds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.473, + 0.732 + ], + "angle": 0, + "content": "FL. We identify two reasons why such defenses can fail. First, the randomness in FL client selection can lead to an incorrect revocation, as shown in Figure 2b, where only four out of ten participants are benign. This indicates that relying on spatial signature alone is error-prone. Second, the uncertainties of clustering contribute to another dimension of complication. Figure 3a shows the spatial clustering of gradients contributed to an FL round with three Trojaned contributions (crosses) and seven benign contributions (dots). The clusters returned by three commonly used clustering methods: K-Means, hierarchical clustering, and spectral clustering are all erroneous. Rejecting the smaller cluster in all three cases will result in unacceptable errors because each contains non-poisoned contributions from honest clients. Such a problem persists even if a window of multiple rounds is used instead of a single round (Figure 3b). We observe that those gradients located between two clusters (outlined by the blue rectangle) can be ambiguous, and three different clustering methods produce different boundary cases. This further indicates that a robust defense requires high-fidelity forensic analysis with different ways to refine the inspection results and manage uncertainties." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.337, + 0.759 + ], + "angle": 0, + "content": "3.2. Temporal Signature Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "STDLens addresses the inherent limitations of spatial clustering by additional forensic analysis with uncertainty assessment. Instead of concluding the clients contributed to the smaller cluster as malicious and revoking their subscription to FL, STDLens inspects each client in a given cluster over a temporal window, coined as the per-client temporal signature analysis. We narrow down the temporal analysis to those classes that are potentially under poisoning attacks based on the spatial signature analysis: the gradient updates" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.091, + 0.685, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.502, + 0.203, + 0.692, + 0.227 + ], + "angle": 0, + "content": "(a) Temporal trajectories of example benign and malicious clients" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.089, + 0.882, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.7, + 0.203, + 0.89, + 0.227 + ], + "angle": 0, + "content": "(b) Unique statistical characteristics of temporal signatures" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.233, + 0.892, + 0.275 + ], + "angle": 0, + "content": "Figure 4. A benign client (green) tends to produce temporally dissimilar gradients over the course of FL while a malicious client (red) contributes similar gradients to mislead the FL process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.892, + 0.333 + ], + "angle": 0, + "content": "on a benign class will have one dense cluster, whereas the source class under poisoning attacks will exhibit at least two distinct distributions of gradient updates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.893, + 0.47 + ], + "angle": 0, + "content": "Let \\(\\mathcal{G}_i\\) be a temporal sequence of spatial signatures contributed by the same client \\(\\mathcal{P}_i\\) throughout a temporal window of FL rounds. Figure 4a shows the spatial signature trajectories of two clients (one benign and one malicious). We can observe that the gradient contributions from a malicious client (i.e., the red crosses) are close to each other, but those from a benign client (i.e., the green dots) scatter around. To quantify this behavior, we define the following \\(\\omega\\)-based temporal signature, denoted by \\(\\Upsilon_{\\omega}\\), for a client \\(\\mathcal{P}_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.476, + 0.892, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\Upsilon_ {\\omega} (\\boldsymbol {G} _ {i}) = \\min _ {c} \\left(\\sum_ {j = \\omega + 1} ^ {| \\boldsymbol {G} _ {i} ^ {c} |} \\sum_ {k = 1} ^ {\\omega} \\frac {\\operatorname {D i s S I M} \\left(\\boldsymbol {G} _ {i} ^ {c} [ j ] , \\boldsymbol {G} _ {i} ^ {c} [ j - k ]\\right)}{\\omega \\left| \\boldsymbol {G} _ {i} ^ {c} \\right| - \\omega^ {2}}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.893, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{G}_i^c\\) denotes the sub-sequence of gradients belonging to the same cluster \\(c\\) from the spatial signature analysis, \\(\\mathcal{G}_i^c[j]\\) refers to its \\(j\\)-th element, and \\(\\mathrm{DISSIM}(\\cdot,\\cdot)\\) is a dissimilarity measure, which can utilize any \\(L_p\\) norm-based similarity, and \\(L_1\\) distance is used as the default given its computation efficiency. The parameter \\(\\omega\\) refers to the window size. The larger the window size \\(\\omega\\) is, the longer the temporal dependency is leveraged for computing temporal signatures. Figure 4b shows the distribution of temporal signatures with \\(\\omega = 1\\) (i.e., the temporal signature is computed every two consecutive rounds). This empirically verifies that malicious clients (red bars) tend to have a significantly lower temporal signature \\(\\Upsilon_{\\omega}\\) than benign clients (green bars). We utilize the per-client temporal signatures to refine the 2D spatial signature of a gradient update contributed by a client. This forms a 3D spatio-temporal signature space (see the top right in Figure 1) for STDLens to re-examine each cluster from the spatial signature analysis, aiming to determine which cluster of gradient updates is from malicious clients. We first compute the mean temporal signature over all contributing clients of each cluster and mark the one with a lower temporal dissimilarity score as suspicious. Then, we perform an uncertainty assessment before concluding that those clients contributed to the suspicious cluster as malicious." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16346" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.264, + 0.184 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.189, + 0.265, + 0.217 + ], + "angle": 0, + "content": "Figure 5. The empirical rule for confidence estimation." + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.089, + 0.468, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.189, + 0.466, + 0.218 + ], + "angle": 0, + "content": "Figure 6. \\(\\sigma\\)-density analysis on spatial signatures." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.232, + 0.403, + 0.249 + ], + "angle": 0, + "content": "3.3. Density-based Uncertainty Inspection" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.256, + 0.473, + 0.786 + ], + "angle": 0, + "content": "The results from the spatial clustering analysis can be unreliable, as shown in Figure 3. Similarly, the temporal signature analysis may also incur uncertainty if the average temporal dissimilarity score for each of the two clusters is too close. We introduce the third component dedicated to uncertainty correction. Concretely, it identifies uncertain spatial and temporal zones such that a client is expelled only if we have high confidence that its gradient updates are poisoned. Our uncertainty assessment is based on the empirical rule in normal distributions that \\(68\\%\\), \\(95\\%\\), and \\(99\\%\\) of data points lie within 1, 2, and 3 standard deviations (\\(\\sigma\\)'s) from the mean (Figure 5). The confidence requirement is domain-specific. With a given confidence threshold for uncertainty control, we can define the corresponding \\(\\sigma\\)-confident and \\(\\sigma\\)-uncertain zones. In particular, we first identify the SSC with the largest eigenvalue. It captures the inter-cluster variance and is visualized as the \\(x\\)-axis by default. Figure 6 shows that the spatial signatures (top) on this component exhibit a mixture of two normal distributions (bottom). This allows STDLens to employ the empirical rule by computing the mean and the standard deviation of each cluster (orange or blue in Figure 6) and translating the confidence requirement (e.g., \\(99\\%\\)) into the corresponding intervals (e.g., \\(3-\\sigma\\) from the mean of the respective cluster). STDLens considers the zone between two \\(\\sigma\\)-confident regions to be uncertain, and any gradient updates from participating clients that fall into this zone will be put on a watchlist. The same client entering the \\(\\sigma\\)-uncertain zone multiple times will be removed from FL. The same uncertainty management operation can also be done on the temporal signatures to minimize the uncertainty-induced false positives. For clients in the cluster with a smaller dissimilarity score and outside the \\(\\sigma\\)-uncertain zone, STDLens will mark them as malicious and revoke their participation in the remaining rounds." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.8, + 0.313, + 0.816 + ], + "angle": 0, + "content": "4. Experimental Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We conduct experiments on two object detection benchmark datasets: (i) PASCAL VOC [7] and (ii) INRIA Person [6]. By default, we have \\( N = 100 \\) clients and a federated server with \\( T = 200 \\) rounds for both datasets. At each round, \\( k = 10\\% \\) of the clients are randomly selected as" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.319 + ], + "angle": 0, + "content": "
Perception \nPoisonmBenign \nAPsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
Class-Poison \n(VOC)5%52.4345.3552.41
10%52.4339.6952.32
20%52.4338.2252.22
BBox-Poison \n(VOC)5%52.4335.7652.32
10%52.4323.4952.15
20%52.4318.0652.19
Objn-Poison \n(VOC)5%52.4345.0251.95
10%52.4341.6152.33
20%52.4337.6152.29
BBox-Poison \n(INRIA)5%63.4945.0361.64
10%63.4932.5161.25
20%63.4928.7361.71
Objn-Poison \n(INRIA)5%63.4961.0561.98
10%63.4953.9162.01
20%63.4950.1861.58
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.323, + 0.894, + 0.366 + ], + "angle": 0, + "content": "Table 2. The \\(\\mathrm{AP}_{\\mathrm{src}}\\) of FL-trained detectors under the benign scenario (3rd column) and three perception poisoning attacks (4th and 5th columns) with three settings of malicious client percentage \\(m\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.606 + ], + "angle": 0, + "content": "participants with FedAvg [12] as the aggregation algorithm. Without loss of generality, we focus on Faster R-CNN [16] with VGG16 [19] because perception poisoning is model-agnostic and black-box in nature. For each dataset, we randomly split the training set into \\(N\\) equal-sized partitions and assigned each to one client as its local dataset. We analyze STDLens against all three types of perception poisoning on VOC and examine BBox-Poison and Obj-Poison on INRIA as it only supports objects of the \"person\" class, which is the default victim source class. The target class in Class-Poison is \"potted plant.\" For BBox-Poison, we shrink the bounding box by a factor of 0.10. By default, \\(m = 20\\%\\) of the clients in FL are malicious. STDLens is operated with a forensic schedule of ten rounds per window, and the confidence required for uncertainty control is set to be \\(99\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.733, + 0.634 + ], + "angle": 0, + "content": "4.1. Effectiveness of STDLens" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Trojan-agnostic Defense. We first analyze how effective STDLens is in mitigating different model hijacking attacks through perception poisoning. Table 2 reports the results measured in average precision [7] of the victim source class \\(\\left(\\mathrm{AP}_{\\mathrm{src}}\\right)\\) under three different settings of \\(m\\%\\). Given that those attacks can hijack the models to cause a drastic drop in \\(\\mathrm{AP}_{\\mathrm{src}}\\) (3rd and 4th columns), STDLens offers strong defensibility against all of them (5th column). Regardless of which attack is launched and how many malicious clients (reflected by \\(m\\)) participate in the attack process, STDLens can consistently restore the \\(\\mathrm{AP}_{\\mathrm{src}}\\), on par with the one obtained in the benign scenario (i.e., \\(52.43\\%\\) for VOC and \\(63.49\\%\\) for INRIA). For instance, BBox-Poison, which brings down the \\(\\mathrm{AP}_{\\mathrm{src}}\\) to \\(18.06\\%\\) on VOC, is mitigated with an \\(\\mathrm{AP}_{\\mathrm{src}}\\) of \\(52.19\\%\\) under the same attack setting. This validates that STDLens is Trojan-agnostic, despite the divergence of different attack effects. Due to similar observa" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16347" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.284, + 0.091, + 0.687, + 0.104 + ], + "angle": 0, + "content": "Benign FL —— Poisoned FL (No Defense) —— Poisoned FL (STDLens)" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.106, + 0.345, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.178, + 0.22, + 0.267, + 0.231 + ], + "angle": 0, + "content": "(a) Class-Poison" + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.106, + 0.608, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.44, + 0.22, + 0.532, + 0.231 + ], + "angle": 0, + "content": "(b) BBox-Poison" + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.107, + 0.871, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.705, + 0.22, + 0.792, + 0.232 + ], + "angle": 0, + "content": "(c) Objn-Poisson" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.239, + 0.89, + 0.268 + ], + "angle": 0, + "content": "Figure 7. Compared with the benign FL (brown) on VOC, the hijacked FL with no defense (pink) has significant \\(\\mathrm{AP}_{\\mathrm{src}}\\) degradation. STDLens (green) purges all malicious clients in an early-round, allows the healing to begin, and reclaims \\(\\mathrm{AP}_{\\mathrm{src}}\\) with a negligible damage." + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.279, + 0.839, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.443, + 0.893, + 0.471 + ], + "angle": 0, + "content": "Table 3. Two images detected by the FL-trained models (VOC) under Class-Poison, BBox-Poison, and Obj-Poison. The FL system with no defense makes designated errors, while the STDLens-protected FL preserves correctness even if the adversary attempts to hijack it." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.487, + 0.423, + 0.501 + ], + "angle": 0, + "content": "tions, we focus on VOC in the following discussion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Timely Sanitization and Recovery. Figure 7 visualizes the learning curves of FL throughout 200 rounds by comparing three cases: (i) the benign scenario (brown curve), (ii) the hijacked scenario without defense (pink curve), and (iii) the hijacked scenario protected by STDLens (green curve). We make the following observations. First, Trojaned gradients cause the \\(\\mathrm{AP}_{\\mathrm{src}}\\) to become either highly unstable (Class-Poison) or consistently degraded (BBox-Poison and Objn-Poison) throughout the FL process. Second, when STDLens detects all malicious clients at the 30th round under Class-Poison, the 20th round under BBox-Poison, and the 30th round under Objn-Poison, no honest client is misdiagnosed and flagged as malicious. Third, the timely sanitization of malicious clients allows the FL system to heal. Even under attacks, the STDLens-protected FL can reach an \\(\\mathrm{AP}_{\\mathrm{src}}\\) comparable with the benign scenario." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Visualization. Table 3 visualizes the detection results on two test examples under all three perception poisoning attacks. All three attacks fool the global model with erroneous detection: (i) Class-Poison (1st column) fools the model into mislabeling the person as a potted plant (top) or a bird (bottom), (ii) BBox-Poison (3rd column) deceives the model to recognize person objects with incorrect bounding boxes, and (iii) Objn-Poison (5th column) causes the model to detect no person objects. In comparison, STDLens successfully reinvigorates the FL system with high robustness" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.487, + 0.689, + 0.501 + ], + "angle": 0, + "content": "(2nd, 4th, and 6th columns)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.519, + 0.796, + 0.535 + ], + "angle": 0, + "content": "4.2. STDLens under Adaptive Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(\\beta\\)-adaptive Attacks. An immediate question we need to address is the defensibility of STDLens against adaptive adversaries who strategically change their attack methods. For instance, malicious clients could camouflage in the crowd of benign clients by occasionally contributing non-Trojaned gradients. We refer to this type of adaptive adversary as \\(\\beta\\)-adaptive. When a \\(\\beta\\)-adaptive adversary participates in an FL round, it has, e.g., a \\(\\beta = 10\\%\\) chance of not poisoning the local dataset during the local model training. As a result, this adaptive adversary will contribute to the cluster with benign gradient updates and also to the cluster with Trojaned gradient updates, aiming to fool the spatial and temporal signature analysis. Indeed, such an adaptive attack strategy can jeopardize the spatial analysis because malicious clients can be mistakenly clustered with honest ones, as depicted in Figure 8a. This makes defenses using solely spatial clustering [18, 21] unable to purge all malicious clients. Even for another representative defense using spectral signatures [22], the statistical properties of malicious contributions become the same as those benign ones, as shown in Figure 9a. However, the temporal signature analysis in STDLens is, by design, resilient to such adaptive strategies, as shown in Figure 8b. Recall in Equation 1 that the temporal signature of a client is com" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16348" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.14, + 0.089, + 0.835, + 0.248 + ], + "angle": 0, + "content": "
Perception PoisonObject Detection with No DefenseObject Detection with STDLensβBenign \\(AP_{src}\\) (%)Hijacked \\(AP_{src}\\) (%)
No DefenseSTDLens
Class-Poisonpottedplant (0.59)person (0.98)5%52.4331.8351.74
10%52.4332.5152.18
15%52.4334.4051.56
BBox-Poisonperson (0.51)person (0.99)5%52.4322.3652.39
10%52.4326.7752.11
15%52.4327.6051.98
Objn-Poisonmotorbike (0.97)person (0.94)5%52.4340.9652.05
10%52.4341.0152.18
15%52.4341.0652.11
" + }, + { + "type": "table_caption", + "bbox": [ + 0.092, + 0.254, + 0.877, + 0.269 + ], + "angle": 0, + "content": "Table 4. The benign \\(\\mathrm{AP}_{\\mathrm{src}}\\) and hijacked \\(\\mathrm{AP}_{\\mathrm{src}}\\) under \\(\\beta\\)-adaptive attacks with varying \\(\\beta\\) in different types of perception poison (VOC)." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.284, + 0.268, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.398, + 0.255, + 0.41 + ], + "angle": 0, + "content": "(a) Spatial Signature Analysis" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.284, + 0.462, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.286, + 0.398, + 0.459, + 0.41 + ], + "angle": 0, + "content": "(b) Temporal Signature Analysis" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.46 + ], + "angle": 0, + "content": "Figure 8. \\(\\beta\\)-adaptive malicious clients randomly camouflage in the benign cluster in the spatial analysis (a), but their statistical characteristics in the temporal signature analysis (b) remain unchanged." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.473, + 0.839 + ], + "angle": 0, + "content": "puted w.r.t. each cluster, and the one with a smaller magnitude is taken to be the lower bound of malicious likelihood. Hence, the statistical characteristics of honest and malicious clients can be preserved in our temporal analysis, where malicious clients (red) have a much smaller temporal signature than honest clients (green). Table 4 compares the hijacked \\(\\mathrm{AP}_{\\mathrm{src}}\\) with the \\(\\beta\\)-adaptive attack under no defense scenario (6th column) with the FL system under the protection by STDLens (7th column). A total of nine scenarios under three attacks are compared by varying the configurations of \\(\\beta\\) from \\(5\\%\\) to \\(15\\%\\). We make two observations. First, under the \\(\\beta\\)-adaptive attack, the \\(\\mathrm{AP}_{\\mathrm{src}}\\) suffers from significant degradation, from \\(52.43\\%\\) to \\(22.36\\%\\), even though malicious clients do not send Trojaned gradients all the time. For adaptive adversaries, the choice of \\(\\beta\\) should be kept small as a larger \\(\\beta\\) can notably weaken the attack effectiveness. Second, STDLens remains resilient under \\(\\beta\\)-adaptive adversaries since it can consistently restore the \\(\\mathrm{AP}_{\\mathrm{src}}\\) to at least \\(51.56\\%\\) for all nine scenarios, on par with that under non-adaptive attacks (recall Table 2). This is primarily because our temporal analysis is robust against such a camouflage. Integrating spatio-temporal statistics allows the identification of the malicious cluster to remain accurate under \\(\\beta\\)-adaptive attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\(\\gamma\\)-adaptive Attacks. Another attempt to launch adaptive attacks is to wash out the spatial clustering characteristics by only poisoning \\(\\gamma \\%\\) of training samples in the local dataset of a malicious client. Under this adaptive setting," + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.284, + 0.688, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.381, + 0.637, + 0.393 + ], + "angle": 0, + "content": "(a) \\(\\beta\\)-adaptive" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.284, + 0.882, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.757, + 0.381, + 0.834, + 0.393 + ], + "angle": 0, + "content": "(b) \\(\\gamma\\)-adaptive" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.4, + 0.892, + 0.443 + ], + "angle": 0, + "content": "Figure 9. Spectral signatures [22] fail under (a) \\(\\beta\\)-adaptive and (b) \\(\\gamma\\)-adaptive attacks as the statistical properties of malicious contributions (red) overlap with benign ones (green)." + }, + { + "type": "table", + "bbox": [ + 0.547, + 0.452, + 0.848, + 0.509 + ], + "angle": 0, + "content": "
γBenign\nAPsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
80%52.4340.0352.09
60%52.4346.0151.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.503, + 0.513, + 0.887, + 0.527 + ], + "angle": 0, + "content": "Table 5. Quantitative studies of \\( \\gamma \\) -adaptive Class-Poison (VOC)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.892, + 0.81 + ], + "angle": 0, + "content": "the contribution from a malicious client becomes the gradient updates computed over a mixture of clean and poisoned training samples. We conduct experiments with two settings of \\(\\gamma\\) with results in Table 5. The \\(\\gamma\\)-adaptive attacks can bring down the \\(\\mathrm{AP}_{\\mathrm{src}}\\) from \\(52.43\\%\\) to \\(40.03\\%\\) and \\(46.01\\%\\) when we set \\(\\gamma\\) to \\(80\\%\\) and \\(60\\%\\), respectively. More malicious clients fall inside the \\(\\sigma\\)-uncertain zone, which will be incorrectly identified by defenses using only spatial clustering analysis [18, 21]. Such an adaptive attack also makes spectral signatures [22] ambiguous, as the statistical properties of benign and malicious gradients overlap (Figure 9b). For those uncertain clients, STDLens has to put the decision on hold and wait for more rounds to accumulate additional observations for making confident decisions. Table 5 shows that STDLens remains robust under \\(\\gamma\\)-adaptive attacks because all malicious clients can still be identified with no false alarm. The \\(\\mathrm{AP}_{\\mathrm{src}}\\) can be recovered to reach over \\(51.54\\%\\), comparable to the benign \\(\\mathrm{AP}_{\\mathrm{src}}\\) of \\(52.43\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Late-stage Adaptive Attacks. Instead of starting the poisoning process from the beginning of FL, an adaptive adversary could only start poisoning the training data when selected in the later rounds of FL. In this case, the FL system has no Trojaned gradient updates contributed by its clients for a period of time. We conduct such a late-stage adap" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16349" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.224, + 0.47, + 0.266 + ], + "angle": 0, + "content": "Figure 10. The malicious clients become active after the 100th round (VOC), causing the \\(\\mathrm{AP}_{\\mathrm{src}}\\) to drop. STDLens purges all malicious clients at the 130th round and allows the FL to recover." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.473, + 0.477 + ], + "angle": 0, + "content": "tive attack by running Class-Poison after the 100th round during the FL process. Figure 10 (left) shows the learning curves of \\(\\mathrm{AP}_{\\mathrm{src}}\\) for three scenarios: (i) the benign scenario, (ii) the late-stage adaptive attack without defense, and (iii) the one protected by STDLens. Considering the nodefense scenario (pink curve), the \\(\\mathrm{AP}_{\\mathrm{src}}\\) fluctuates wildly after the 100th round. In comparison, STDLens (green curve) starts detecting the existence of Trojans from the window of rounds 101-110 (top right) and removes the identified malicious clients. It successfully expels all anomalies at the 130th round and allows the FL to heal as no more malicious clients attempt to mislead the FL system (e.g., the window of rounds 131-140 at the bottom right)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.485, + 0.394, + 0.502 + ], + "angle": 0, + "content": "4.3. Comparisons with Existing Defenses" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We further compare STDLens with two existing defense methods: spatial clustering [21] and spectral signature [22], which can be extended to FL-based object detection. Table 6 reports the quantitative results. All three defense solutions can detect all malicious clients over the course of FL (i.e., achieving the defense recall of 1.00). STDLens completes the detection and revocation of malicious clients between 20 to 30 rounds, and spatial clustering takes 30 to 40 rounds to detect and remove anomalies, while malicious clients can stay alive in the FL system for at most 80 rounds with spectral signature. The main differentiation factor lies in defense precision. Even though STDLens takes a slightly longer execution time (i.e., \\(452\\mathrm{ms}\\) with \\(84\\mathrm{ms}\\) for temporal signature analysis and \\(44\\mathrm{ms}\\) for \\(\\sigma\\)-density inspection), it successfully identifies all malicious clients without mistakenly rejecting any benign clients (false positives), achieving a defense precision of 1.00. This allows the STDLens-protected FL to train a global object detector with high accuracy, as shown in the 2nd column in Table 7. In comparison, the spatial clustering approach can reach a low precision of 0.53 under Objn-Poisson, due to gradient contributions falling in the zone between the two clusters, causing ambiguity in anomaly detection. This result shows that defenses based solely on spatial clustering may not offer stable robustness. The spectral signature defense performs the worst, with a defense precision ranging from 0.26 to 0.54. It" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.089, + 0.886, + 0.189 + ], + "angle": 0, + "content": "
Defense Precision@Round w/ Max. Recall
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poison1.00@300.95@300.53@40
BBox-Poison1.00@200.71@300.26@80
Objn-Poison1.00@300.53@400.54@40
Time (ms)4523421423
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.195, + 0.892, + 0.237 + ], + "angle": 0, + "content": "Table 6. Comparing STDLens with two state-of-the-art methods on VOC in terms of the defense precision at the round where the maximum recall is achieved and the execution time (the last row)." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.252, + 0.892, + 0.478 + ], + "angle": 0, + "content": "
Object Detection Results by Hijacked Models
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poisonperson (1.00)\nmoto 'D1K' (1.00)person (0.99)\nmotor bike (0.98)person (0.76)\nmotor bike (0.88)\nbird (0.81)
BBox-Poisonperson (0.97)\ntvmonitor (0.96)person (0.79)\n××
Objn-Poisonperson (0.95)\nperson (0.94)person (0.89)\n×person (0.71)\n×
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.483, + 0.893, + 0.526 + ], + "angle": 0, + "content": "Table 7. The high defense precision offered by STDLens allows the FL-trained model to remain accurate. The excessive removal of clients by other defenses incurs performance degradation (VOC)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.542, + 0.892, + 0.648 + ], + "angle": 0, + "content": "implies that while the defense can expel malicious clients, a considerable number of honest ones are also mistakenly rejected. One reason is the changing malicious population over time due to the removal of malicious clients in the early rounds. The excessive removal of clients can weaken the benign learning signal and degrade the FL-trained model, as shown in the 3rd and 4th columns in Table 7." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.672, + 0.628, + 0.687 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.837 + ], + "angle": 0, + "content": "With the goal of building a trustworthy federated training process, we have presented STDLens, a three-tier defense framework for FL-based object detection, strengthening the spatial signature with the temporal signature analysis and uncertainty management. Extensive experiments with various adaptive adversaries show that STDLens can protect FL against all three model hijacking attacks and outperforms existing mitigation methods with high defense precision and a low false-positive rate." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, an IBM faculty award, and a Cisco grant on Edge Computing. The first author acknowledges the IBM PhD Fellowship Award." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16350" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. In International Conference on Artificial Intelligence and Statistics, pages 2938-2948. PMLR, 2020. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Arjun Nitin Bhagoji, Supriyo Chakraborty, Pratek Mittal, and Seraphin Calo. Analyzing federated learning through an adversarial lens. In International Conference on Machine Learning, pages 634-643. 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Springer, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.896 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16351" + } + ] +] \ No newline at end of file diff --git a/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_origin.pdf b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e94e446671a6cc9577c8ff55e46a32baced6dd45 --- /dev/null +++ b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/970c86e7-a18e-4fa1-bf10-060bfc2535dd_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1df2510d2646a6d0bc86e6e81edbe1038518d97f08753f87eba19810f96771ed +size 6221788 diff --git a/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/full.md b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..7ea2d97b13b3875ac6805a95c5e05e3aa0956f8c --- /dev/null +++ b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/full.md @@ -0,0 +1,282 @@ +# STDLens: Model Hijacking-resilient Federated Learning for Object Detection + +# Ka-Ho Chow, Ling Liu, Wenqi Wei, Fatih Ilhan, Yanzhao Wu +Georgia Instutite of Technology +Atlanta, GA, USA + +khchow@gatech.edu, ling.liu@cc.gatech.edu, {wenqiwei, filhan, yanzhaowu}@gatech.edu + +# Abstract + +Federated Learning (FL) has been gaining popularity as a collaborative learning framework to train deep learning-based object detection models over a distributed population of clients. Despite its advantages, FL is vulnerable to model hijacking. The attacker can control how the object detection system should misbehave by implanting Trojaned gradients using only a small number of compromised clients in the collaborative learning process. This paper introduces STDLens, a principled approach to safeguarding FL against such attacks. We first investigate existing mitigation mechanisms and analyze their failures caused by the inherent errors in spatial clustering analysis on gradients. Based on the insights, we introduce a three-tier forensic framework to identify and expel Trojaned gradients and reclaim the performance over the course of FL. We consider three types of adaptive attacks and demonstrate the robustness of STDLens against advanced adversaries. Extensive experiments show that STDLens can protect FL against different model hijacking attacks and outperform existing methods in identifying and removing Trojaned gradients with significantly higher precision and much lower false-positive rates. The source code is available at https://github.com/git-disl/STDLens. + +# 1. Introduction + +Federated Learning (FL) for object detection has attracted numerous applications [12], especially in healthcare, with strict privacy regulations protecting patient medical records [25, 27]. Instead of using a centralized data curator, FL can train a global object detection model with a distributed population of clients. Each client only shares its fixed-size gradient (updated model) parameters (e.g., 246.9 MB for YOLOv3 [15]) with the FL server for aggregation while keeping its private raw data local (e.g., terabytes of videos) [13]. Such a paradigm lowers the bar for knowledge sharing and eases the recruitment of contributors, but it becomes vulnerable to model hijacking [9, 21]. + +Model hijacking aims at interfering with the training pro + +
ScenarioObject Detection ResultsAPersonAPcar
Benignperson 0.93 +Gm 0.76 +Sg 0.64person 0.76 +Gm 0.76 +Sg 0.6452.4374.12
Class-Poison Victim: Personpottedplant 0.56 +Gm 0.72 +Sg 0.62bird 0.45 +Gm 0.72 +Sg 0.6238.22 +(↓27%)71.79 +(↓3%)
BBox-Poison Victim: Personperson 0.62 +Gm 0.72 +Sg 0.62person 0.45 +Gm 0.72 +Sg 0.6218.06 +(↓66%)72.82 +(↓2%)
Objn-Poison Victim: Personpottedplant 0.56 +Gm 0.76 +Sg 0.64person 0.45 +Gm 0.76 +Sg 0.6437.61 +(↓28%)71.59 +(↓3%)
+ +Table 1. FL-trained detectors can be hijacked by perception poisoning to misdetect objects of designated classes (e.g., person) in three different ways (2nd to 4th rows) [3], while objects of nonvictim classes (e.g., car) have negligible performance degradation. + +cess of a machine learning model and causes it to misbehave at the deployment stage [17]. The FL-trained global model can be indirectly hijacked by a small number of compromised clients who share Trojaned gradients to gradually confuse the learning trajectory of FL [10]. Such gradients can be generated in black-box through data poisoning. The attacker only has to poison the local training data owned by a compromised client, such as changing the ground-truth label of certain objects by dirty-label poisoning [21] or implanting a backdoor to trigger the malfunctioning of a hijacked model [1, 2, 8, 20]. The FL software will take the poisoned local training data and unintentionally generate malicious gradients for sharing. With the growing number of real-world applications, recent work has begun to understand the hijacking of FL-based object detection systems [3]. As shown in Table 1, the adversary can designate how the hijacked model should misdetect objects of certain classes (e.g., person) while ensuring other objects can still be precisely detected (e.g., car). This fine-grained control opens the door for an adversary to design a stealthy attack configuration to hurt the FL system yet remains hardly noticeable by the owner [5], leading to catastrophic consequences such as car crashes. + +This paper introduces STDLens, a three-tier defense methodology against model hijacking attacks, with the following original contributions. First, we analyze existing defenses based on spatial signature analysis and show their ineffectiveness in protecting FL. Second, we introduce a pipeline with per-client spatio-temporal signature analysis to identify Trojaned gradients, track their contributors, revoke their subscriptions, and reclaim the detection performance. Third, we present a density-based confidence inspection mechanism to manage the spatio-temporal uncertainty. It avoids purging benign clients contributing useful learning signals for the FL system. Finally, we extend perception poisoning with three types of adaptiveness for analyzing STDLens in countering advanced adversaries. Extensive experiments show that STDLens outperforms competitive defense methods by a large margin in defense precision with a low false-positive rate, reducing the accuracy drop under attack from $34.47\%$ to $0.24\%$ , maintaining the object detection accuracy on par with the performance under the benign scenario. + +# 2. Background and Related Work + +# 2.1. Perception Poisoning for Model Hijacking + +Threat Model. Perception poisoning adopts the following assumptions: (i) the communication between a client and the trustworthy FL server is encrypted; (ii) the benign clients faithfully follow the FL workflow; and (iii) there is only a small $m\%$ of compromised clients out of a total of $N$ clients. An adversary on a malicious client can only manipulate its local training data, and hence, model hijacking can be done without tampering with the FL software. + +Poisoning Formulation. Let $F$ be the global model being trained in FL, $f_{i}$ be the local model of client $\mathcal{P}_i$ , and $(\pmb{x},\pmb{y})$ be the input sample and its ground truth in the training set $\mathcal{D}_i$ of client $\mathcal{P}_i$ . The process of perception poisoning can be formulated as a function $\psi$ that maps $(\pmb{x},\pmb{y})$ to $(\pmb{x},\pmb{y}')$ such that the local model $f_{i}$ will generate Trojaned gradients which maximize the chance of $F$ being fooled to make erroneous predictions with high confidence, formally: + +$$ +\psi : \psi (\boldsymbol {x}, \boldsymbol {y}) = \left(\boldsymbol {x}, \boldsymbol {y} ^ {\prime}\right) \text {s . t .} f _ {i} (\boldsymbol {x}) = \boldsymbol {y} ^ {\prime}, \boldsymbol {y} ^ {\prime} \neq \boldsymbol {y}, \max [ F (\boldsymbol {x}) \bowtie \boldsymbol {y} ^ {\prime} ] +$$ + +where $\pmb{y}$ is a list of triplets, one for each object $\pmb{o} =$ (CLASS,BBOX,OBJN) in the training image $\pmb{x}$ , CLASS is the class label, BBOX is the bounding box, and OBJN is the existence of object $\pmb{o}$ . $f_{i}(\pmb{x})$ and $F(\pmb{x})$ denote the detected objects by the local and global models, respectively. The operator $\bowtie$ indicates the degree of matching between two sets of objects [4]. Based on the three perceptual components of an object, one can formulate three poisoning strategies to designate malicious behaviors on the hijacked model [3]: (i) Class-Poison changes the class label of objects of a source class to a maliciously chosen target class + +without altering their bounding box locations and object existence. (ii) BBox-Poison attacks objects of certain source classes by randomly changing the size and the location of their bounding boxes without altering the class label and the object existence. (iii) Obj-Poison attacks objects of certain classes by changing their existence to non-existence. As shown in Table 1, the hijacked model under Class-Poison (2nd row) mislabels the person as a potted plant in the first example and as a bird in the second example with a different attack configuration. Under BBox-Poison (3rd row), the person object is detected with a correct class label but a misaligned bounding box. Under Obj-Poison (4th row), the person vanishes in both cases. Only the designated classes suffer from performance degradation (e.g., "person" in the 4th column), while the detection of objects of other irrelevant classes is not affected (e.g., "car" in the 5th column). + +# 2.2. Existing Defenses and Their Limitations + +While no defenses have been proposed to counter perception poisoning, several solutions are being introduced for image classifiers, which are either developed for FL [21, 23, 28] or can be extended [18, 22]. They can be broadly classified into two categories. The first category aims at repairing the gradients (model updates). Contributions from all participants will be used for aggregation, but they will be processed by parameter clipping and noise injection [11, 20, 24] to wash out possibly malicious elements. However, it is challenging to determine the correct amount of noise to be injected [14]. The Trojaned gradients can still be malicious if the noise is too small, while a larger noise can remove useful learning signals from benign clients and affect the convergence of FL. The second category attempts to inspect gradients shared by participants to identify and eliminate malicious clients. MNTD [26] trains a meta-classifier to differentiate Trojaned and non-Trojaned gradients. It is a supervised defense and assumes a known distribution of Trojans to create training data. Unsupervised defenses make fewer assumptions and are more attractive in practice. AUROR [18] and its followers [21] conduct spatial clustering on gradient contributions and label the contributors to the smaller cluster to be malicious. Spectral signature [22] conducts outlier removal via SVD by purging gradient contributions deviating most significantly from a singular vector. While they neither rely on finding the right amount of noise for injection nor prior knowledge on possible attacks to be defended, our analysis in Section 3 finds that anomaly detection using solely spatial analysis on the latent projection space can fail due to the randomness in per-round client selection and the clustering uncertainty. + +# 3. STDLens: Defense Methodology + +Perception poisoning is a real threat. Adversaries can configure the attack to hijack the model without being no- + +![](images/1fd571cc16c920d0690262714ac67683e57b7a0dfc3cc58e12c6369c758dff97.jpg) +Figure 1. The overview of STDLens, a three-tier framework against model hijacking through perception poisoning. + +ticed. We present a forensic framework called STDLens, to safeguard FL systems. It utilizes robust and attack-agnostic statistical properties with a three-tier forensic analysis. It does not assume prior knowledge on which poisoning attack is launched (i.e., Class-Poison, BBox-Poison, Obj-Poison, or their combinations). Figure 1 gives an overview. STDLens is operated at a system-supplied schedule, configurable at initiation (e.g., every ten FL rounds). Contributions from the participating clients during the window of rounds are accumulated for a safety inspection by the spatial signature analysis, followed by a per-client temporal signature analysis to identify Trojaned gradients and a $\sigma$ -density analysis to manage the spatio-temporal uncertainty. + +# 3.1. Spatial Signature Analysis + +Under perception poisoning, it is observed that with a small $m\%$ of malicious clients, the eigenvalues of the covariance of the gradient updates for the source class consist of two sub-populations: the Trojaned gradients from malicious participants and the benign gradients from honest participants. We refer to such phenomenon as $m$ -separable robust statistics of perception poisoning attacks. + +Definition 3.1. $m$ -Separable Robust Statistics. Given a small $m$ with $0 < m < \frac{1}{2}$ , let $H$ and $P$ denote the two distributions: $\underline{\text{Honest}}$ and $\underline{\text{Poisoned}}$ , respectively, with finite covariance. Let the mixing loss function be $\mathbb{G} = (1 - m)H + mP$ , $v$ be the top eigenvalue of the covariance of $\mathbb{G}$ and $\mu_{\mathbb{G}}$ is the mean of the mixed distribution $\mathbb{G}$ . The two distributions $H$ and $P$ are separable if there exists some $\tau$ such that $\operatorname{Pr}_{X \sim H}[|\langle X - \mu_{\mathbb{G}}, v \rangle| > \tau] < m$ and $\operatorname{Pr}_{X \sim P}[|\langle X - \mu_{\mathbb{G}}, v \rangle| < \tau] < m$ . + +Theorem 3.1. Given a small $m$ with $0 < m < \frac{1}{2}$ , let $H$ and $P$ denote Honest and Poisoned distributions, with mean $\mu_{H}$ , $\mu_{P}$ , and finite covariance $\Sigma_{H}, \Sigma_{P} \preceq \phi^{2}\mathbb{I}$ . Let the mixing loss function be $\mathbb{G} = (1 - m)H + mP$ and $\Delta = \mu_{H} - \mu_{P}$ . Then, if $\| \Delta \|_2^2 \geq \frac{6\phi^2}{m}$ , $P$ and $H$ satisfy $m$ -separable robust statistics. + +The spatial signature analysis relies on the above $m$ -separable robust statistics, where $m$ is represented as a decimal for brevity. We provide the proof in the appendix. The + +![](images/b9ec551d6f8874e9e08898e75e6e6e9573f0a2604d406334b60e3aeec4c50afa.jpg) +(a) Round 102: 7 benign clients and 3 malicious clients + +![](images/b6745f0d6c1b162edcae740a8dfb91ced9b47cfd65ff137d90cd553de97699f8.jpg) +(b) Round 106: 4 benign clients and 6 malicious clients +Figure 2. The clustering phenomenon due to benign and malicious client participation in only one round of FL. + +orem 3.1 implies that when the percentage $m$ of compromised clients is small, the distribution of benign gradients from honest clients is separable from the distribution of poisoned gradients, especially when the distance between the means of the two distributions can be bounded by the $m$ -normalized covariance of the two distributions [22]. Given the gradient updates are high-dimensional, we focus on the output layer to analyze the statistical properties of gradient updates from all participants because the output layer gradients are the most prominent due to the vanishing gradient in backpropagation. We project the output layer gradients onto a 2D space corresponding to the two spatial signature components (SSCs) with the largest eigenvalues for spatial clustering. Figure 2 shows the spatial signatures of the gradients collected at two different FL rounds under Class-Poison. We observe a clear clustering phenomenon (green dots and red crosses), validating the intuition about the formation of two gradient distributions. A key question is whether one can simply conclude that the smaller cluster contains the Trojaned gradients from malicious clients and thus can be removed in the upcoming FL rounds. + +Inherent Limitations. Spatial signatures can offer valuable statistical indicators, especially when poisoned and benign gradient distributions can be cleanly separated. However, existing defense methods simply rely on analyzing such spatial patterns and conclude that the smaller cluster contains the poisonous gradient updates and expel those clients with contributions in the smaller cluster [18,21]. We argue that relying solely on spatial signature analysis may result in high false positives and hurt the convergence of + +![](images/5da105060841c78a74400d0b3ea4ea79de5a8ff3474c0b2d5efa9a2203bb34da.jpg) +(a) Misgrouping gradient contributions in one round of FL. + +![](images/6c7c03c413e126254db6e43809921b1b709288aac9e5e1564d5d13f528b0950d.jpg) +(b) Cluster boundary uncertainties over multiple rounds of FL. +Figure 3. Three clustering algorithms on gradient contributions in (a) one round and (b) multiple rounds. + +FL. We identify two reasons why such defenses can fail. First, the randomness in FL client selection can lead to an incorrect revocation, as shown in Figure 2b, where only four out of ten participants are benign. This indicates that relying on spatial signature alone is error-prone. Second, the uncertainties of clustering contribute to another dimension of complication. Figure 3a shows the spatial clustering of gradients contributed to an FL round with three Trojaned contributions (crosses) and seven benign contributions (dots). The clusters returned by three commonly used clustering methods: K-Means, hierarchical clustering, and spectral clustering are all erroneous. Rejecting the smaller cluster in all three cases will result in unacceptable errors because each contains non-poisoned contributions from honest clients. Such a problem persists even if a window of multiple rounds is used instead of a single round (Figure 3b). We observe that those gradients located between two clusters (outlined by the blue rectangle) can be ambiguous, and three different clustering methods produce different boundary cases. This further indicates that a robust defense requires high-fidelity forensic analysis with different ways to refine the inspection results and manage uncertainties. + +# 3.2. Temporal Signature Analysis + +STDLens addresses the inherent limitations of spatial clustering by additional forensic analysis with uncertainty assessment. Instead of concluding the clients contributed to the smaller cluster as malicious and revoking their subscription to FL, STDLens inspects each client in a given cluster over a temporal window, coined as the per-client temporal signature analysis. We narrow down the temporal analysis to those classes that are potentially under poisoning attacks based on the spatial signature analysis: the gradient updates + +![](images/e0ceda7a2c5503b524e313365c2703c4c3e6790c63a1929991747503cdd57159.jpg) +(a) Temporal trajectories of example benign and malicious clients +Figure 4. A benign client (green) tends to produce temporally dissimilar gradients over the course of FL while a malicious client (red) contributes similar gradients to mislead the FL process. + +![](images/bd54b1de0290e3558e43f8d4ebfa564724dac568a649e57fac1022704c315c57.jpg) +(b) Unique statistical characteristics of temporal signatures + +on a benign class will have one dense cluster, whereas the source class under poisoning attacks will exhibit at least two distinct distributions of gradient updates. + +Let $\mathcal{G}_i$ be a temporal sequence of spatial signatures contributed by the same client $\mathcal{P}_i$ throughout a temporal window of FL rounds. Figure 4a shows the spatial signature trajectories of two clients (one benign and one malicious). We can observe that the gradient contributions from a malicious client (i.e., the red crosses) are close to each other, but those from a benign client (i.e., the green dots) scatter around. To quantify this behavior, we define the following $\omega$ -based temporal signature, denoted by $\Upsilon_{\omega}$ , for a client $\mathcal{P}_i$ : + +$$ +\Upsilon_ {\omega} (\boldsymbol {G} _ {i}) = \min _ {c} \left(\sum_ {j = \omega + 1} ^ {| \boldsymbol {G} _ {i} ^ {c} |} \sum_ {k = 1} ^ {\omega} \frac {\operatorname {D i s S I M} \left(\boldsymbol {G} _ {i} ^ {c} [ j ] , \boldsymbol {G} _ {i} ^ {c} [ j - k ]\right)}{\omega \left| \boldsymbol {G} _ {i} ^ {c} \right| - \omega^ {2}}\right) \tag {1} +$$ + +where $\mathcal{G}_i^c$ denotes the sub-sequence of gradients belonging to the same cluster $c$ from the spatial signature analysis, $\mathcal{G}_i^c[j]$ refers to its $j$ -th element, and $\mathrm{DISSIM}(\cdot,\cdot)$ is a dissimilarity measure, which can utilize any $L_p$ norm-based similarity, and $L_1$ distance is used as the default given its computation efficiency. The parameter $\omega$ refers to the window size. The larger the window size $\omega$ is, the longer the temporal dependency is leveraged for computing temporal signatures. Figure 4b shows the distribution of temporal signatures with $\omega = 1$ (i.e., the temporal signature is computed every two consecutive rounds). This empirically verifies that malicious clients (red bars) tend to have a significantly lower temporal signature $\Upsilon_{\omega}$ than benign clients (green bars). We utilize the per-client temporal signatures to refine the 2D spatial signature of a gradient update contributed by a client. This forms a 3D spatio-temporal signature space (see the top right in Figure 1) for STDLens to re-examine each cluster from the spatial signature analysis, aiming to determine which cluster of gradient updates is from malicious clients. We first compute the mean temporal signature over all contributing clients of each cluster and mark the one with a lower temporal dissimilarity score as suspicious. Then, we perform an uncertainty assessment before concluding that those clients contributed to the suspicious cluster as malicious. + +![](images/45012a241a5747e65af83796a6902d90b0330354354adb746debf8f8dac586fb.jpg) +Figure 5. The empirical rule for confidence estimation. + +![](images/b626143319e2ab9b17158256daf4ade99be163dfdd6b9ef234edd2a7f094ba74.jpg) +Figure 6. $\sigma$ -density analysis on spatial signatures. + +# 3.3. Density-based Uncertainty Inspection + +The results from the spatial clustering analysis can be unreliable, as shown in Figure 3. Similarly, the temporal signature analysis may also incur uncertainty if the average temporal dissimilarity score for each of the two clusters is too close. We introduce the third component dedicated to uncertainty correction. Concretely, it identifies uncertain spatial and temporal zones such that a client is expelled only if we have high confidence that its gradient updates are poisoned. Our uncertainty assessment is based on the empirical rule in normal distributions that $68\%$ , $95\%$ , and $99\%$ of data points lie within 1, 2, and 3 standard deviations ( $\sigma$ 's) from the mean (Figure 5). The confidence requirement is domain-specific. With a given confidence threshold for uncertainty control, we can define the corresponding $\sigma$ -confident and $\sigma$ -uncertain zones. In particular, we first identify the SSC with the largest eigenvalue. It captures the inter-cluster variance and is visualized as the $x$ -axis by default. Figure 6 shows that the spatial signatures (top) on this component exhibit a mixture of two normal distributions (bottom). This allows STDLens to employ the empirical rule by computing the mean and the standard deviation of each cluster (orange or blue in Figure 6) and translating the confidence requirement (e.g., $99\%$ ) into the corresponding intervals (e.g., $3-\sigma$ from the mean of the respective cluster). STDLens considers the zone between two $\sigma$ -confident regions to be uncertain, and any gradient updates from participating clients that fall into this zone will be put on a watchlist. The same client entering the $\sigma$ -uncertain zone multiple times will be removed from FL. The same uncertainty management operation can also be done on the temporal signatures to minimize the uncertainty-induced false positives. For clients in the cluster with a smaller dissimilarity score and outside the $\sigma$ -uncertain zone, STDLens will mark them as malicious and revoke their participation in the remaining rounds. + +# 4. Experimental Evaluation + +We conduct experiments on two object detection benchmark datasets: (i) PASCAL VOC [7] and (ii) INRIA Person [6]. By default, we have $N = 100$ clients and a federated server with $T = 200$ rounds for both datasets. At each round, $k = 10\%$ of the clients are randomly selected as + +
Perception +PoisonmBenign +APsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
Class-Poison +(VOC)5%52.4345.3552.41
10%52.4339.6952.32
20%52.4338.2252.22
BBox-Poison +(VOC)5%52.4335.7652.32
10%52.4323.4952.15
20%52.4318.0652.19
Objn-Poison +(VOC)5%52.4345.0251.95
10%52.4341.6152.33
20%52.4337.6152.29
BBox-Poison +(INRIA)5%63.4945.0361.64
10%63.4932.5161.25
20%63.4928.7361.71
Objn-Poison +(INRIA)5%63.4961.0561.98
10%63.4953.9162.01
20%63.4950.1861.58
+ +Table 2. The $\mathrm{AP}_{\mathrm{src}}$ of FL-trained detectors under the benign scenario (3rd column) and three perception poisoning attacks (4th and 5th columns) with three settings of malicious client percentage $m$ . + +participants with FedAvg [12] as the aggregation algorithm. Without loss of generality, we focus on Faster R-CNN [16] with VGG16 [19] because perception poisoning is model-agnostic and black-box in nature. For each dataset, we randomly split the training set into $N$ equal-sized partitions and assigned each to one client as its local dataset. We analyze STDLens against all three types of perception poisoning on VOC and examine BBox-Poison and Obj-Poison on INRIA as it only supports objects of the "person" class, which is the default victim source class. The target class in Class-Poison is "potted plant." For BBox-Poison, we shrink the bounding box by a factor of 0.10. By default, $m = 20\%$ of the clients in FL are malicious. STDLens is operated with a forensic schedule of ten rounds per window, and the confidence required for uncertainty control is set to be $99\%$ . + +# 4.1. Effectiveness of STDLens + +Trojan-agnostic Defense. We first analyze how effective STDLens is in mitigating different model hijacking attacks through perception poisoning. Table 2 reports the results measured in average precision [7] of the victim source class $\left(\mathrm{AP}_{\mathrm{src}}\right)$ under three different settings of $m\%$ . Given that those attacks can hijack the models to cause a drastic drop in $\mathrm{AP}_{\mathrm{src}}$ (3rd and 4th columns), STDLens offers strong defensibility against all of them (5th column). Regardless of which attack is launched and how many malicious clients (reflected by $m$ ) participate in the attack process, STDLens can consistently restore the $\mathrm{AP}_{\mathrm{src}}$ , on par with the one obtained in the benign scenario (i.e., $52.43\%$ for VOC and $63.49\%$ for INRIA). For instance, BBox-Poison, which brings down the $\mathrm{AP}_{\mathrm{src}}$ to $18.06\%$ on VOC, is mitigated with an $\mathrm{AP}_{\mathrm{src}}$ of $52.19\%$ under the same attack setting. This validates that STDLens is Trojan-agnostic, despite the divergence of different attack effects. Due to similar observa + +![](images/269fa7d97521ad79295c02ff4182904874d0270175a21584526115aa26a3500c.jpg) +Benign FL —— Poisoned FL (No Defense) —— Poisoned FL (STDLens) +(a) Class-Poison + +![](images/8215e95f987f73dd2a8edbcc3abcdd7e8129e162b36246a55d9ec2d0b980f630.jpg) +(b) BBox-Poison + +![](images/67eca3d490de81c4349269567a28060f0e90f06267516dc71d7ca418f982b49b.jpg) +(c) Objn-Poisson + +![](images/83eaf54fe1691fde780f3f22a5ac318c8f44dc0b3ea9bde08aec046756452b43.jpg) +Figure 7. Compared with the benign FL (brown) on VOC, the hijacked FL with no defense (pink) has significant $\mathrm{AP}_{\mathrm{src}}$ degradation. STDLens (green) purges all malicious clients in an early-round, allows the healing to begin, and reclaims $\mathrm{AP}_{\mathrm{src}}$ with a negligible damage. +Table 3. Two images detected by the FL-trained models (VOC) under Class-Poison, BBox-Poison, and Obj-Poison. The FL system with no defense makes designated errors, while the STDLens-protected FL preserves correctness even if the adversary attempts to hijack it. + +tions, we focus on VOC in the following discussion. + +Timely Sanitization and Recovery. Figure 7 visualizes the learning curves of FL throughout 200 rounds by comparing three cases: (i) the benign scenario (brown curve), (ii) the hijacked scenario without defense (pink curve), and (iii) the hijacked scenario protected by STDLens (green curve). We make the following observations. First, Trojaned gradients cause the $\mathrm{AP}_{\mathrm{src}}$ to become either highly unstable (Class-Poison) or consistently degraded (BBox-Poison and Objn-Poison) throughout the FL process. Second, when STDLens detects all malicious clients at the 30th round under Class-Poison, the 20th round under BBox-Poison, and the 30th round under Objn-Poison, no honest client is misdiagnosed and flagged as malicious. Third, the timely sanitization of malicious clients allows the FL system to heal. Even under attacks, the STDLens-protected FL can reach an $\mathrm{AP}_{\mathrm{src}}$ comparable with the benign scenario. + +Visualization. Table 3 visualizes the detection results on two test examples under all three perception poisoning attacks. All three attacks fool the global model with erroneous detection: (i) Class-Poison (1st column) fools the model into mislabeling the person as a potted plant (top) or a bird (bottom), (ii) BBox-Poison (3rd column) deceives the model to recognize person objects with incorrect bounding boxes, and (iii) Objn-Poison (5th column) causes the model to detect no person objects. In comparison, STDLens successfully reinvigorates the FL system with high robustness + +(2nd, 4th, and 6th columns). + +# 4.2. STDLens under Adaptive Attacks + +$\beta$ -adaptive Attacks. An immediate question we need to address is the defensibility of STDLens against adaptive adversaries who strategically change their attack methods. For instance, malicious clients could camouflage in the crowd of benign clients by occasionally contributing non-Trojaned gradients. We refer to this type of adaptive adversary as $\beta$ -adaptive. When a $\beta$ -adaptive adversary participates in an FL round, it has, e.g., a $\beta = 10\%$ chance of not poisoning the local dataset during the local model training. As a result, this adaptive adversary will contribute to the cluster with benign gradient updates and also to the cluster with Trojaned gradient updates, aiming to fool the spatial and temporal signature analysis. Indeed, such an adaptive attack strategy can jeopardize the spatial analysis because malicious clients can be mistakenly clustered with honest ones, as depicted in Figure 8a. This makes defenses using solely spatial clustering [18, 21] unable to purge all malicious clients. Even for another representative defense using spectral signatures [22], the statistical properties of malicious contributions become the same as those benign ones, as shown in Figure 9a. However, the temporal signature analysis in STDLens is, by design, resilient to such adaptive strategies, as shown in Figure 8b. Recall in Equation 1 that the temporal signature of a client is com + +
Perception PoisonObject Detection with No DefenseObject Detection with STDLensβBenign \(AP_{src}\) (%)Hijacked \(AP_{src}\) (%)
No DefenseSTDLens
Class-Poisonpottedplant (0.59)person (0.98)5%52.4331.8351.74
10%52.4332.5152.18
15%52.4334.4051.56
BBox-Poisonperson (0.51)person (0.99)5%52.4322.3652.39
10%52.4326.7752.11
15%52.4327.6051.98
Objn-Poisonmotorbike (0.97)person (0.94)5%52.4340.9652.05
10%52.4341.0152.18
15%52.4341.0652.11
+ +![](images/7c7e900a7b94c88d8d331d301533318806e823be2550c1f27e4982a5538dc761.jpg) +(a) Spatial Signature Analysis + +![](images/832fcd5d027c157f79875a23a803bb772059dd3320c0b0522c26df9df0b4da2c.jpg) +(b) Temporal Signature Analysis +Figure 8. $\beta$ -adaptive malicious clients randomly camouflage in the benign cluster in the spatial analysis (a), but their statistical characteristics in the temporal signature analysis (b) remain unchanged. + +puted w.r.t. each cluster, and the one with a smaller magnitude is taken to be the lower bound of malicious likelihood. Hence, the statistical characteristics of honest and malicious clients can be preserved in our temporal analysis, where malicious clients (red) have a much smaller temporal signature than honest clients (green). Table 4 compares the hijacked $\mathrm{AP}_{\mathrm{src}}$ with the $\beta$ -adaptive attack under no defense scenario (6th column) with the FL system under the protection by STDLens (7th column). A total of nine scenarios under three attacks are compared by varying the configurations of $\beta$ from $5\%$ to $15\%$ . We make two observations. First, under the $\beta$ -adaptive attack, the $\mathrm{AP}_{\mathrm{src}}$ suffers from significant degradation, from $52.43\%$ to $22.36\%$ , even though malicious clients do not send Trojaned gradients all the time. For adaptive adversaries, the choice of $\beta$ should be kept small as a larger $\beta$ can notably weaken the attack effectiveness. Second, STDLens remains resilient under $\beta$ -adaptive adversaries since it can consistently restore the $\mathrm{AP}_{\mathrm{src}}$ to at least $51.56\%$ for all nine scenarios, on par with that under non-adaptive attacks (recall Table 2). This is primarily because our temporal analysis is robust against such a camouflage. Integrating spatio-temporal statistics allows the identification of the malicious cluster to remain accurate under $\beta$ -adaptive attacks. + +$\gamma$ -adaptive Attacks. Another attempt to launch adaptive attacks is to wash out the spatial clustering characteristics by only poisoning $\gamma \%$ of training samples in the local dataset of a malicious client. Under this adaptive setting, + +![](images/bc6b45f9b8df42bcdfcf93aaf12df3dc59e619c37500701739865bb032527028.jpg) +(a) $\beta$ -adaptive +Figure 9. Spectral signatures [22] fail under (a) $\beta$ -adaptive and (b) $\gamma$ -adaptive attacks as the statistical properties of malicious contributions (red) overlap with benign ones (green). + +![](images/a28ea37b5da44599027dc0ca3f3bb1d04844dbef8cd920d7c0ace798faee8b26.jpg) +(b) $\gamma$ -adaptive + +Table 4. The benign $\mathrm{AP}_{\mathrm{src}}$ and hijacked $\mathrm{AP}_{\mathrm{src}}$ under $\beta$ -adaptive attacks with varying $\beta$ in different types of perception poison (VOC). + +
γBenign +APsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
80%52.4340.0352.09
60%52.4346.0151.54
+ +Table 5. Quantitative studies of $\gamma$ -adaptive Class-Poison (VOC). + +the contribution from a malicious client becomes the gradient updates computed over a mixture of clean and poisoned training samples. We conduct experiments with two settings of $\gamma$ with results in Table 5. The $\gamma$ -adaptive attacks can bring down the $\mathrm{AP}_{\mathrm{src}}$ from $52.43\%$ to $40.03\%$ and $46.01\%$ when we set $\gamma$ to $80\%$ and $60\%$ , respectively. More malicious clients fall inside the $\sigma$ -uncertain zone, which will be incorrectly identified by defenses using only spatial clustering analysis [18, 21]. Such an adaptive attack also makes spectral signatures [22] ambiguous, as the statistical properties of benign and malicious gradients overlap (Figure 9b). For those uncertain clients, STDLens has to put the decision on hold and wait for more rounds to accumulate additional observations for making confident decisions. Table 5 shows that STDLens remains robust under $\gamma$ -adaptive attacks because all malicious clients can still be identified with no false alarm. The $\mathrm{AP}_{\mathrm{src}}$ can be recovered to reach over $51.54\%$ , comparable to the benign $\mathrm{AP}_{\mathrm{src}}$ of $52.43\%$ . + +Late-stage Adaptive Attacks. Instead of starting the poisoning process from the beginning of FL, an adaptive adversary could only start poisoning the training data when selected in the later rounds of FL. In this case, the FL system has no Trojaned gradient updates contributed by its clients for a period of time. We conduct such a late-stage adap + +![](images/fa6ab37e35e499e25f0d425063fb63d08a22e5c64206b88f8dad8512afcdfd6b.jpg) +Figure 10. The malicious clients become active after the 100th round (VOC), causing the $\mathrm{AP}_{\mathrm{src}}$ to drop. STDLens purges all malicious clients at the 130th round and allows the FL to recover. + +tive attack by running Class-Poison after the 100th round during the FL process. Figure 10 (left) shows the learning curves of $\mathrm{AP}_{\mathrm{src}}$ for three scenarios: (i) the benign scenario, (ii) the late-stage adaptive attack without defense, and (iii) the one protected by STDLens. Considering the nodefense scenario (pink curve), the $\mathrm{AP}_{\mathrm{src}}$ fluctuates wildly after the 100th round. In comparison, STDLens (green curve) starts detecting the existence of Trojans from the window of rounds 101-110 (top right) and removes the identified malicious clients. It successfully expels all anomalies at the 130th round and allows the FL to heal as no more malicious clients attempt to mislead the FL system (e.g., the window of rounds 131-140 at the bottom right). + +# 4.3. Comparisons with Existing Defenses + +We further compare STDLens with two existing defense methods: spatial clustering [21] and spectral signature [22], which can be extended to FL-based object detection. Table 6 reports the quantitative results. All three defense solutions can detect all malicious clients over the course of FL (i.e., achieving the defense recall of 1.00). STDLens completes the detection and revocation of malicious clients between 20 to 30 rounds, and spatial clustering takes 30 to 40 rounds to detect and remove anomalies, while malicious clients can stay alive in the FL system for at most 80 rounds with spectral signature. The main differentiation factor lies in defense precision. Even though STDLens takes a slightly longer execution time (i.e., $452\mathrm{ms}$ with $84\mathrm{ms}$ for temporal signature analysis and $44\mathrm{ms}$ for $\sigma$ -density inspection), it successfully identifies all malicious clients without mistakenly rejecting any benign clients (false positives), achieving a defense precision of 1.00. This allows the STDLens-protected FL to train a global object detector with high accuracy, as shown in the 2nd column in Table 7. In comparison, the spatial clustering approach can reach a low precision of 0.53 under Objn-Poisson, due to gradient contributions falling in the zone between the two clusters, causing ambiguity in anomaly detection. This result shows that defenses based solely on spatial clustering may not offer stable robustness. The spectral signature defense performs the worst, with a defense precision ranging from 0.26 to 0.54. It + +
Defense Precision@Round w/ Max. Recall
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poison1.00@300.95@300.53@40
BBox-Poison1.00@200.71@300.26@80
Objn-Poison1.00@300.53@400.54@40
Time (ms)4523421423
+ +Table 6. Comparing STDLens with two state-of-the-art methods on VOC in terms of the defense precision at the round where the maximum recall is achieved and the execution time (the last row). + +
Object Detection Results by Hijacked Models
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poisonperson (1.00) +moto 'D1K' (1.00)person (0.99) +motor bike (0.98)person (0.76) +motor bike (0.88) +bird (0.81)
BBox-Poisonperson (0.97) +tvmonitor (0.96)person (0.79) +××
Objn-Poisonperson (0.95) +person (0.94)person (0.89) +×person (0.71) +×
+ +Table 7. The high defense precision offered by STDLens allows the FL-trained model to remain accurate. The excessive removal of clients by other defenses incurs performance degradation (VOC). + +implies that while the defense can expel malicious clients, a considerable number of honest ones are also mistakenly rejected. One reason is the changing malicious population over time due to the removal of malicious clients in the early rounds. The excessive removal of clients can weaken the benign learning signal and degrade the FL-trained model, as shown in the 3rd and 4th columns in Table 7. + +# 5. Conclusions + +With the goal of building a trustworthy federated training process, we have presented STDLens, a three-tier defense framework for FL-based object detection, strengthening the spatial signature with the temporal signature analysis and uncertainty management. Extensive experiments with various adaptive adversaries show that STDLens can protect FL against all three model hijacking attacks and outperforms existing mitigation methods with high defense precision and a low false-positive rate. + +Acknowledgments. This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, an IBM faculty award, and a Cisco grant on Edge Computing. The first author acknowledges the IBM PhD Fellowship Award. + +# References + +[1] Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. In International Conference on Artificial Intelligence and Statistics, pages 2938-2948. PMLR, 2020. 1 +[2] Arjun Nitin Bhagoji, Supriyo Chakraborty, Pratek Mittal, and Seraphin Calo. Analyzing federated learning through an adversarial lens. In International Conference on Machine Learning, pages 634-643. PMLR, 2019. 1 +[3] Ka-Ho Chow and Ling Liu. Perception poisoning attacks in federated learning. In International Conference on Trust, Privacy and Security in Intelligent Systems and Applications, pages 146-155. IEEE, 2021. 1, 2 +[4] Ka-Ho Chow and Ling Liu. Boosting object detection ensembles with error diversity. In International Conference on Data Mining, pages 903-908. IEEE, 2022. 2 +[5] Ka-Ho Chow, Ling Liu, Margaret Loper, Juhyun Bae, Mehmet Emre Gursoy, Stacey Truex, Wenqi Wei, and Yanzhao Wu. Adversarial objectness gradient attacks in real-time object detection systems. In International Conference on Trust, Privacy and Security in Intelligent Systems and Applications, pages 263-272. IEEE, 2020. 1 +[6] Navneet Dalal and Bill Triggs. Histograms of oriented gradients for human detection. In Conference on Computer Vision and Pattern Recognition, volume 1, pages 886-893. IEEE/CVF, 2005. 5 +[7] Mark Everingham, Luc Van Gool, Christopher KI Williams, John Winn, and Andrew Zisserman. The pascal visual object classes (VOC) challenge. International Journal of Computer Vision, 88(2):303-338, 2010. 5 +[8] Minghong Fang, Xiaoyu Cao, Jinyuan Jia, and Neil Gong. Local model poisoning attacks to byzantine-robust federated learning. In USENIX Security Symposium, pages 1605–1622, 2020. 1 +[9] Clement Fung, Chris JM Yoon, and Ivan Beschastnikh. The limitations of federated learning in sybil settings. In International Symposium on Research in Attacks, Intrusions and Defenses, pages 301-316, 2020. 1 +[10] Peter Kairouz, H Brendan McMahan, Brendan Avent, Aurélien Bellet, Mehdi Bennis, Arjun Nitin Bhagoji, Kallista Bonawitz, Zachary Charles, Graham Cormode, Rachel Cummings, et al. Advances and open problems in federated learning. Foundations and Trends® in Machine Learning, 14(1-2):1-210, 2021. 1 +[11] Raouf Kerkouche, Gergely Ács, and Claude Castelluccia. Federated learning in adversarial settings. arXiv preprint arXiv:2010.07808, 2020. 2 +[12] Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication-efficient learning of deep networks from decentralized data. In Artificial Intelligence and Statistics. PMLR, 2017. 1, 5 +[13] Anup Mohan, Kent Gauen, Yung-Hsiang Lu, Wei Wayne Li, and Xuemin Chen. Internet of video things in 2030: A world with many cameras. In International Symposium on Circuits and Systems, pages 1-4. IEEE, 2017. 1 +[14] Thien Duc Nguyen, Phillip Rieger, Huili Chen, Hossein Yalame, Helen Möllering, Hossein Fereidooni, Samuel Mar + +chal, Markus Miettinen, Azalia Mirhoseini, Shaza Zeitouni, et al. FLAME: Taming backdoors in federated learning. In USENIX Security Symposium, pages 1415-1432, 2022. 2 +[15] Joseph Redmon and Ali Farhadi. Yolov3: An incremental improvement. arXiv preprint arXiv:1804.02767, 2018. 1 +[16] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster R-CNN: Towards real-time object detection with region proposal networks. Advances in Neural Information Processing Systems, 28:91-99, 2015. 5 +[17] Ahmed Salem, Michael Backes, and Yang Zhang. Get a model! model hijacking attack against machine learning models. In The Network and Distributed System Security Symposium, 2022. 1 +[18] Shiqi Shen, Shruti Tople, and Prateek Saxena. Auror: Defending against poisoning attacks in collaborative deep learning systems. In Annual Conference on Computer Security Applications, pages 508-519, 2016. 2, 3, 6, 7 +[19] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. In International Conference on Learning Representations, 2015. 5 +[20] Ziteng Sun, Peter Kairouz, Ananda Theertha Suresh, and H Brendan McMahan. Can you really backdoor federated learning? In International Workshop on Federated Learning for Data Privacy and Confidentiality, 2019. 1, 2 +[21] Vale Tolpegin, Stacey Truex, Mehmet Emre Gursoy, and Ling Liu. Data poisoning attacks against federated learning systems. In European Symposium on Research in Computer Security, pages 480-501. Springer, 2020. 1, 2, 3, 6, 7, 8 +[22] Brandon Tran, Jerry Li, and Aleksander Madry. Spectral signatures in backdoor attacks. In Advances in Neural Information Processing Systems, 2018. 2, 3, 6, 7, 8 +[23] Yuao Wang, Tianqing Zhu, Wenhan Chang, Sheng Shen, and Wei Ren. Model poisoning defense on federated learning: A validation based approach. In International Conference on Network and System Security, pages 207-223. Springer, 2020. 2 +[24] Chulin Xie, Minghao Chen, Pin-Yu Chen, and Bo Li. Crfl: Certifiably robust federated learning against backdoor attacks. In International Conference on Machine Learning, pages 11372-11382. PMLR, 2021. 2 +[25] Jie Xu, Benjamin S Glicksberg, Chang Su, Peter Walker, Jiang Bian, and Fei Wang. Federated learning for healthcare informatics. Journal of Healthcare Informatics Research, 5(1):1-19, 2021. 1 +[26] Xiaojun Xu, Qi Wang, Huichen Li, Nikita Borisov, Carl A Gunter, and Bo Li. Detecting AI trojans using meta neural analysis. In Symposium on Security and Privacy, pages 103-120. IEEE, 2021. 2 +[27] Qian Yang, Jianyi Zhang, Weituo Hao, Gregory Spell, and Lawrence Carin. Flop: Federated learning on medical datasets using partial networks. In ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2021. 1 +[28] Jiale Zhang, Di Wu, Chengyong Liu, and Bing Chen. Defending poisoning attacks in federated learning via adversarial training method. In International Conference on Frontiers in Cyber Security, pages 83-94. Springer, 2020. 2 \ No newline at end of file diff --git a/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/images.zip b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2d2ddc6c9390a076c2aa28d114868822cc1358d3 --- /dev/null +++ b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:997512a3e15fa179094a1fbf3c372cc529dd329cfd1641890036a8ac5df5eff7 +size 738117 diff --git a/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/layout.json b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..eccb9ec9c48cd9fe17823b30607c194293eb5fcb --- /dev/null +++ b/2023/STDLens_ Model Hijacking-Resilient Federated Learning for Object Detection/layout.json @@ -0,0 +1,8837 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 56, + 103, + 536, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 103, + 536, + 120 + ], + "spans": [ + { + "bbox": [ + 56, + 103, + 536, + 120 + ], + "type": "text", + "content": "STDLens: Model Hijacking-resilient Federated Learning for Object Detection" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 147, + 143, + 445, + 184 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 143, + 445, + 184 + ], + "spans": [ + { + "bbox": [ + 147, + 143, + 445, + 184 + ], + "type": "text", + "content": "Ka-Ho Chow, Ling Liu, Wenqi Wei, Fatih Ilhan, Yanzhao Wu \nGeorgia Instutite of Technology \nAtlanta, GA, USA" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 80, + 187, + 508, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 187, + 508, + 199 + ], + "spans": [ + { + "bbox": [ + 80, + 187, + 508, + 199 + ], + "type": "text", + "content": "khchow@gatech.edu, ling.liu@cc.gatech.edu, {wenqiwei, filhan, yanzhaowu}@gatech.edu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 251, + 290, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 290, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 290, + 526 + ], + "type": "text", + "content": "Federated Learning (FL) has been gaining popularity as a collaborative learning framework to train deep learning-based object detection models over a distributed population of clients. Despite its advantages, FL is vulnerable to model hijacking. The attacker can control how the object detection system should misbehave by implanting Trojaned gradients using only a small number of compromised clients in the collaborative learning process. This paper introduces STDLens, a principled approach to safeguarding FL against such attacks. We first investigate existing mitigation mechanisms and analyze their failures caused by the inherent errors in spatial clustering analysis on gradients. Based on the insights, we introduce a three-tier forensic framework to identify and expel Trojaned gradients and reclaim the performance over the course of FL. We consider three types of adaptive attacks and demonstrate the robustness of STDLens against advanced adversaries. Extensive experiments show that STDLens can protect FL against different model hijacking attacks and outperform existing methods in identifying and removing Trojaned gradients with significantly higher precision and much lower false-positive rates. The source code is available at https://github.com/git-disl/STDLens." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 538, + 127, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 127, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 127, + 550 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "type": "text", + "content": "Federated Learning (FL) for object detection has attracted numerous applications [12], especially in healthcare, with strict privacy regulations protecting patient medical records [25, 27]. Instead of using a centralized data curator, FL can train a global object detection model with a distributed population of clients. Each client only shares its fixed-size gradient (updated model) parameters (e.g., 246.9 MB for YOLOv3 [15]) with the FL server for aggregation while keeping its private raw data local (e.g., terabytes of videos) [13]. Such a paradigm lowers the bar for knowledge sharing and eases the recruitment of contributors, but it becomes vulnerable to model hijacking [9, 21]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 286, + 713 + ], + "type": "text", + "content": "Model hijacking aims at interfering with the training pro" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 308, + 225, + 545, + 380 + ], + "blocks": [ + { + "bbox": [ + 308, + 225, + 545, + 380 + ], + "lines": [ + { + "bbox": [ + 308, + 225, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 308, + 225, + 545, + 380 + ], + "type": "table", + "html": "
ScenarioObject Detection ResultsAPersonAPcar
Benignperson 0.93\nGm 0.76\nSg 0.64person 0.76\nGm 0.76\nSg 0.6452.4374.12
Class-Poison Victim: Personpottedplant 0.56\nGm 0.72\nSg 0.62bird 0.45\nGm 0.72\nSg 0.6238.22\n(↓27%)71.79\n(↓3%)
BBox-Poison Victim: Personperson 0.62\nGm 0.72\nSg 0.62person 0.45\nGm 0.72\nSg 0.6218.06\n(↓66%)72.82\n(↓2%)
Objn-Poison Victim: Personpottedplant 0.56\nGm 0.76\nSg 0.64person 0.45\nGm 0.76\nSg 0.6437.61\n(↓28%)71.59\n(↓3%)
", + "image_path": "1ed377d174e45cc1a16577657cf78d71b1970c8fd7a2ade5908f12899af204d7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 384, + 545, + 428 + ], + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 428 + ], + "type": "text", + "content": "Table 1. FL-trained detectors can be hijacked by perception poisoning to misdetect objects of designated classes (e.g., person) in three different ways (2nd to 4th rows) [3], while objects of nonvictim classes (e.g., car) have negligible performance degradation." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 437, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 713 + ], + "type": "text", + "content": "cess of a machine learning model and causes it to misbehave at the deployment stage [17]. The FL-trained global model can be indirectly hijacked by a small number of compromised clients who share Trojaned gradients to gradually confuse the learning trajectory of FL [10]. Such gradients can be generated in black-box through data poisoning. The attacker only has to poison the local training data owned by a compromised client, such as changing the ground-truth label of certain objects by dirty-label poisoning [21] or implanting a backdoor to trigger the malfunctioning of a hijacked model [1, 2, 8, 20]. The FL software will take the poisoned local training data and unintentionally generate malicious gradients for sharing. With the growing number of real-world applications, recent work has begun to understand the hijacking of FL-based object detection systems [3]. As shown in Table 1, the adversary can designate how the hijacked model should misdetect objects of certain classes (e.g., person) while ensuring other objects can still be precisely detected (e.g., car). This fine-grained control opens the door for an adversary to design a stealthy attack configuration to hurt the FL system yet remains hardly noticeable by the owner [5], leading to catastrophic consequences such as car crashes." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16343" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "content": "This paper introduces STDLens, a three-tier defense methodology against model hijacking attacks, with the following original contributions. First, we analyze existing defenses based on spatial signature analysis and show their ineffectiveness in protecting FL. Second, we introduce a pipeline with per-client spatio-temporal signature analysis to identify Trojaned gradients, track their contributors, revoke their subscriptions, and reclaim the detection performance. Third, we present a density-based confidence inspection mechanism to manage the spatio-temporal uncertainty. It avoids purging benign clients contributing useful learning signals for the FL system. Finally, we extend perception poisoning with three types of adaptiveness for analyzing STDLens in countering advanced adversaries. Extensive experiments show that STDLens outperforms competitive defense methods by a large margin in defense precision with a low false-positive rate, reducing the accuracy drop under attack from " + }, + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "34.47\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "inline_equation", + "content": "0.24\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 312 + ], + "type": "text", + "content": ", maintaining the object detection accuracy on par with the performance under the benign scenario." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 323, + 222, + 336 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 222, + 336 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 222, + 336 + ], + "type": "text", + "content": "2. Background and Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 342, + 266, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 266, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 266, + 357 + ], + "type": "text", + "content": "2.1. Perception Poisoning for Model Hijacking" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "text", + "content": "Threat Model. Perception poisoning adopts the following assumptions: (i) the communication between a client and the trustworthy FL server is encrypted; (ii) the benign clients faithfully follow the FL workflow; and (iii) there is only a small " + }, + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "inline_equation", + "content": "m\\%" + }, + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "text", + "content": " of compromised clients out of a total of " + }, + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 361, + 287, + 456 + ], + "type": "text", + "content": " clients. An adversary on a malicious client can only manipulate its local training data, and hence, model hijacking can be done without tampering with the FL software." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": "Poisoning Formulation. Let " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " be the global model being trained in FL, " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " be the local model of client " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\pmb{y})" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " be the input sample and its ground truth in the training set " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_i" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " of client " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": ". The process of perception poisoning can be formulated as a function " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " that maps " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\pmb{y})" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "(\\pmb{x},\\pmb{y}')" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " such that the local model " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " will generate Trojaned gradients which maximize the chance of " + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 457, + 287, + 554 + ], + "type": "text", + "content": " being fooled to make erroneous predictions with high confidence, formally:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 560, + 289, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 289, + 575 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 289, + 575 + ], + "type": "interline_equation", + "content": "\\psi : \\psi (\\boldsymbol {x}, \\boldsymbol {y}) = \\left(\\boldsymbol {x}, \\boldsymbol {y} ^ {\\prime}\\right) \\text {s . t .} f _ {i} (\\boldsymbol {x}) = \\boldsymbol {y} ^ {\\prime}, \\boldsymbol {y} ^ {\\prime} \\neq \\boldsymbol {y}, \\max [ F (\\boldsymbol {x}) \\bowtie \\boldsymbol {y} ^ {\\prime} ]", + "image_path": "2ff5f3cfdebbe1c4c677edc10d04b817da4e5cbf4ddf7e623e7533ff1bd17049.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " is a list of triplets, one for each object " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{o} =" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " (CLASS,BBOX,OBJN) in the training image " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": ", CLASS is the class label, BBOX is the bounding box, and OBJN is the existence of object " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{o}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{i}(\\pmb{x})" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "F(\\pmb{x})" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " denote the detected objects by the local and global models, respectively. The operator " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\bowtie" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": " indicates the degree of matching between two sets of objects [4]. Based on the three perceptual components of an object, one can formulate three poisoning strategies to designate malicious behaviors on the hijacked model [3]: (i) Class-Poison changes the class label of objects of a source class to a maliciously chosen target class" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 264 + ], + "type": "text", + "content": "without altering their bounding box locations and object existence. (ii) BBox-Poison attacks objects of certain source classes by randomly changing the size and the location of their bounding boxes without altering the class label and the object existence. (iii) Obj-Poison attacks objects of certain classes by changing their existence to non-existence. As shown in Table 1, the hijacked model under Class-Poison (2nd row) mislabels the person as a potted plant in the first example and as a bird in the second example with a different attack configuration. Under BBox-Poison (3rd row), the person object is detected with a correct class label but a misaligned bounding box. Under Obj-Poison (4th row), the person vanishes in both cases. Only the designated classes suffer from performance degradation (e.g., \"person\" in the 4th column), while the detection of objects of other irrelevant classes is not affected (e.g., \"car\" in the 5th column)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 270, + 517, + 283 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 517, + 283 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 517, + 283 + ], + "type": "text", + "content": "2.2. Existing Defenses and Their Limitations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 289, + 547, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 547, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 547, + 661 + ], + "type": "text", + "content": "While no defenses have been proposed to counter perception poisoning, several solutions are being introduced for image classifiers, which are either developed for FL [21, 23, 28] or can be extended [18, 22]. They can be broadly classified into two categories. The first category aims at repairing the gradients (model updates). Contributions from all participants will be used for aggregation, but they will be processed by parameter clipping and noise injection [11, 20, 24] to wash out possibly malicious elements. However, it is challenging to determine the correct amount of noise to be injected [14]. The Trojaned gradients can still be malicious if the noise is too small, while a larger noise can remove useful learning signals from benign clients and affect the convergence of FL. The second category attempts to inspect gradients shared by participants to identify and eliminate malicious clients. MNTD [26] trains a meta-classifier to differentiate Trojaned and non-Trojaned gradients. It is a supervised defense and assumes a known distribution of Trojans to create training data. Unsupervised defenses make fewer assumptions and are more attractive in practice. AUROR [18] and its followers [21] conduct spatial clustering on gradient contributions and label the contributors to the smaller cluster to be malicious. Spectral signature [22] conducts outlier removal via SVD by purging gradient contributions deviating most significantly from a singular vector. While they neither rely on finding the right amount of noise for injection nor prior knowledge on possible attacks to be defended, our analysis in Section 3 finds that anomaly detection using solely spatial analysis on the latent projection space can fail due to the randomness in per-round client selection and the clustering uncertainty." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 669, + 487, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 669, + 487, + 683 + ], + "spans": [ + { + "bbox": [ + 305, + 669, + 487, + 683 + ], + "type": "text", + "content": "3. STDLens: Defense Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 714 + ], + "type": "text", + "content": "Perception poisoning is a real threat. Adversaries can configure the attack to hijack the model without being no-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16344" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 519, + 183 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 519, + 183 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 519, + 183 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 519, + 183 + ], + "type": "image", + "image_path": "1fd571cc16c920d0690262714ac67683e57b7a0dfc3cc58e12c6369c758dff97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 87, + 187, + 504, + 200 + ], + "lines": [ + { + "bbox": [ + 87, + 187, + 504, + 200 + ], + "spans": [ + { + "bbox": [ + 87, + 187, + 504, + 200 + ], + "type": "text", + "content": "Figure 1. The overview of STDLens, a three-tier framework against model hijacking through perception poisoning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 209, + 290, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 290, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 290, + 368 + ], + "type": "text", + "content": "ticed. We present a forensic framework called STDLens, to safeguard FL systems. It utilizes robust and attack-agnostic statistical properties with a three-tier forensic analysis. It does not assume prior knowledge on which poisoning attack is launched (i.e., Class-Poison, BBox-Poison, Obj-Poison, or their combinations). Figure 1 gives an overview. STDLens is operated at a system-supplied schedule, configurable at initiation (e.g., every ten FL rounds). Contributions from the participating clients during the window of rounds are accumulated for a safety inspection by the spatial signature analysis, followed by a per-client temporal signature analysis to identify Trojaned gradients and a " + }, + { + "bbox": [ + 46, + 209, + 290, + 368 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 209, + 290, + 368 + ], + "type": "text", + "content": "-density analysis to manage the spatio-temporal uncertainty." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 373, + 194, + 386 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 194, + 386 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 194, + 386 + ], + "type": "text", + "content": "3.1. Spatial Signature Analysis" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "type": "text", + "content": "Under perception poisoning, it is observed that with a small " + }, + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "type": "inline_equation", + "content": "m\\%" + }, + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "type": "text", + "content": " of malicious clients, the eigenvalues of the covariance of the gradient updates for the source class consist of two sub-populations: the Trojaned gradients from malicious participants and the benign gradients from honest participants. We refer to such phenomenon as " + }, + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 392, + 288, + 477 + ], + "type": "text", + "content": "-separable robust statistics of perception poisoning attacks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": "Definition 3.1. " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": "-Separable Robust Statistics. Given a small " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "0 < m < \\frac{1}{2}" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " denote the two distributions: " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\underline{\\text{Honest}}" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\underline{\\text{Poisoned}}" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": ", respectively, with finite covariance. Let the mixing loss function be " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbb{G} = (1 - m)H + mP" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " be the top eigenvalue of the covariance of " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbb{G}" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mu_{\\mathbb{G}}" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " is the mean of the mixed distribution " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\mathbb{G}" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": ". The two distributions " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " are separable if there exists some " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}_{X \\sim H}[|\\langle X - \\mu_{\\mathbb{G}}, v \\rangle| > \\tau] < m" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\operatorname{Pr}_{X \\sim P}[|\\langle X - \\mu_{\\mathbb{G}}, v \\rangle| < \\tau] < m" + }, + { + "bbox": [ + 46, + 481, + 287, + 592 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": "Theorem 3.1. Given a small " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "0 < m < \\frac{1}{2}" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": " denote Honest and Poisoned distributions, with mean " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "\\mu_{H}" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "\\mu_{P}" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": ", and finite covariance " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "\\Sigma_{H}, \\Sigma_{P} \\preceq \\phi^{2}\\mathbb{I}" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": ". Let the mixing loss function be " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "\\mathbb{G} = (1 - m)H + mP" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "\\Delta = \\mu_{H} - \\mu_{P}" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": ". Then, if " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "\\| \\Delta \\|_2^2 \\geq \\frac{6\\phi^2}{m}" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": " satisfy " + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 597, + 288, + 673 + ], + "type": "text", + "content": "-separable robust statistics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "The spatial signature analysis relies on the above " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "-separable robust statistics, where " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " is represented as a decimal for brevity. We provide the proof in the appendix. The" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 208, + 419, + 289 + ], + "blocks": [ + { + "bbox": [ + 315, + 208, + 419, + 289 + ], + "lines": [ + { + "bbox": [ + 315, + 208, + 419, + 289 + ], + "spans": [ + { + "bbox": [ + 315, + 208, + 419, + 289 + ], + "type": "image", + "image_path": "b9ec551d6f8874e9e08898e75e6e6e9573f0a2604d406334b60e3aeec4c50afa.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 293, + 423, + 312 + ], + "lines": [ + { + "bbox": [ + 309, + 293, + 423, + 312 + ], + "spans": [ + { + "bbox": [ + 309, + 293, + 423, + 312 + ], + "type": "text", + "content": "(a) Round 102: 7 benign clients and 3 malicious clients" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 432, + 207, + 536, + 289 + ], + "blocks": [ + { + "bbox": [ + 432, + 207, + 536, + 289 + ], + "lines": [ + { + "bbox": [ + 432, + 207, + 536, + 289 + ], + "spans": [ + { + "bbox": [ + 432, + 207, + 536, + 289 + ], + "type": "image", + "image_path": "b6745f0d6c1b162edcae740a8dfb91ced9b47cfd65ff137d90cd553de97699f8.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 427, + 293, + 542, + 312 + ], + "lines": [ + { + "bbox": [ + 427, + 293, + 542, + 312 + ], + "spans": [ + { + "bbox": [ + 427, + 293, + 542, + 312 + ], + "type": "text", + "content": "(b) Round 106: 4 benign clients and 6 malicious clients" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 315, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 305, + 315, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 315, + 545, + 338 + ], + "type": "text", + "content": "Figure 2. The clustering phenomenon due to benign and malicious client participation in only one round of FL." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "type": "text", + "content": "orem 3.1 implies that when the percentage " + }, + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "type": "text", + "content": " of compromised clients is small, the distribution of benign gradients from honest clients is separable from the distribution of poisoned gradients, especially when the distance between the means of the two distributions can be bounded by the " + }, + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 350, + 546, + 602 + ], + "type": "text", + "content": "-normalized covariance of the two distributions [22]. Given the gradient updates are high-dimensional, we focus on the output layer to analyze the statistical properties of gradient updates from all participants because the output layer gradients are the most prominent due to the vanishing gradient in backpropagation. We project the output layer gradients onto a 2D space corresponding to the two spatial signature components (SSCs) with the largest eigenvalues for spatial clustering. Figure 2 shows the spatial signatures of the gradients collected at two different FL rounds under Class-Poison. We observe a clear clustering phenomenon (green dots and red crosses), validating the intuition about the formation of two gradient distributions. A key question is whether one can simply conclude that the smaller cluster contains the Trojaned gradients from malicious clients and thus can be removed in the upcoming FL rounds." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Inherent Limitations. Spatial signatures can offer valuable statistical indicators, especially when poisoned and benign gradient distributions can be cleanly separated. However, existing defense methods simply rely on analyzing such spatial patterns and conclude that the smaller cluster contains the poisonous gradient updates and expel those clients with contributions in the smaller cluster [18,21]. We argue that relying solely on spatial signature analysis may result in high false positives and hurt the convergence of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16345" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 276, + 156 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 276, + 156 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 276, + 156 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 276, + 156 + ], + "type": "image", + "image_path": "5da105060841c78a74400d0b3ea4ea79de5a8ff3474c0b2d5efa9a2203bb34da.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 159, + 262, + 168 + ], + "lines": [ + { + "bbox": [ + 71, + 159, + 262, + 168 + ], + "spans": [ + { + "bbox": [ + 71, + 159, + 262, + 168 + ], + "type": "text", + "content": "(a) Misgrouping gradient contributions in one round of FL." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 172, + 275, + 255 + ], + "blocks": [ + { + "bbox": [ + 61, + 172, + 275, + 255 + ], + "lines": [ + { + "bbox": [ + 61, + 172, + 275, + 255 + ], + "spans": [ + { + "bbox": [ + 61, + 172, + 275, + 255 + ], + "type": "image", + "image_path": "6c7c03c413e126254db6e43809921b1b709288aac9e5e1564d5d13f528b0950d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 66, + 256, + 268, + 266 + ], + "lines": [ + { + "bbox": [ + 66, + 256, + 268, + 266 + ], + "spans": [ + { + "bbox": [ + 66, + 256, + 268, + 266 + ], + "type": "text", + "content": "(b) Cluster boundary uncertainties over multiple rounds of FL." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 272, + 287, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 272, + 287, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 272, + 287, + 295 + ], + "type": "text", + "content": "Figure 3. Three clustering algorithms on gradient contributions in (a) one round and (b) multiple rounds." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 305, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 289, + 579 + ], + "type": "text", + "content": "FL. We identify two reasons why such defenses can fail. First, the randomness in FL client selection can lead to an incorrect revocation, as shown in Figure 2b, where only four out of ten participants are benign. This indicates that relying on spatial signature alone is error-prone. Second, the uncertainties of clustering contribute to another dimension of complication. Figure 3a shows the spatial clustering of gradients contributed to an FL round with three Trojaned contributions (crosses) and seven benign contributions (dots). The clusters returned by three commonly used clustering methods: K-Means, hierarchical clustering, and spectral clustering are all erroneous. Rejecting the smaller cluster in all three cases will result in unacceptable errors because each contains non-poisoned contributions from honest clients. Such a problem persists even if a window of multiple rounds is used instead of a single round (Figure 3b). We observe that those gradients located between two clusters (outlined by the blue rectangle) can be ambiguous, and three different clustering methods produce different boundary cases. This further indicates that a robust defense requires high-fidelity forensic analysis with different ways to refine the inspection results and manage uncertainties." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 587, + 206, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 206, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 206, + 601 + ], + "type": "text", + "content": "3.2. Temporal Signature Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "STDLens addresses the inherent limitations of spatial clustering by additional forensic analysis with uncertainty assessment. Instead of concluding the clients contributed to the smaller cluster as malicious and revoking their subscription to FL, STDLens inspects each client in a given cluster over a temporal window, coined as the per-client temporal signature analysis. We narrow down the temporal analysis to those classes that are potentially under poisoning attacks based on the spatial signature analysis: the gradient updates" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 72, + 419, + 156 + ], + "blocks": [ + { + "bbox": [ + 312, + 72, + 419, + 156 + ], + "lines": [ + { + "bbox": [ + 312, + 72, + 419, + 156 + ], + "spans": [ + { + "bbox": [ + 312, + 72, + 419, + 156 + ], + "type": "image", + "image_path": "e0ceda7a2c5503b524e313365c2703c4c3e6790c63a1929991747503cdd57159.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 160, + 423, + 179 + ], + "lines": [ + { + "bbox": [ + 307, + 160, + 423, + 179 + ], + "spans": [ + { + "bbox": [ + 307, + 160, + 423, + 179 + ], + "type": "text", + "content": "(a) Temporal trajectories of example benign and malicious clients" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 184, + 545, + 217 + ], + "lines": [ + { + "bbox": [ + 305, + 184, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 545, + 217 + ], + "type": "text", + "content": "Figure 4. A benign client (green) tends to produce temporally dissimilar gradients over the course of FL while a malicious client (red) contributes similar gradients to mislead the FL process." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 432, + 70, + 539, + 156 + ], + "blocks": [ + { + "bbox": [ + 432, + 70, + 539, + 156 + ], + "lines": [ + { + "bbox": [ + 432, + 70, + 539, + 156 + ], + "spans": [ + { + "bbox": [ + 432, + 70, + 539, + 156 + ], + "type": "image", + "image_path": "bd54b1de0290e3558e43f8d4ebfa564724dac568a649e57fac1022704c315c57.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 428, + 160, + 544, + 179 + ], + "lines": [ + { + "bbox": [ + 428, + 160, + 544, + 179 + ], + "spans": [ + { + "bbox": [ + 428, + 160, + 544, + 179 + ], + "type": "text", + "content": "(b) Unique statistical characteristics of temporal signatures" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 227, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 545, + 263 + ], + "type": "text", + "content": "on a benign class will have one dense cluster, whereas the source class under poisoning attacks will exhibit at least two distinct distributions of gradient updates." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i" + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "content": " be a temporal sequence of spatial signatures contributed by the same client " + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i" + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "content": " throughout a temporal window of FL rounds. Figure 4a shows the spatial signature trajectories of two clients (one benign and one malicious). We can observe that the gradient contributions from a malicious client (i.e., the red crosses) are close to each other, but those from a benign client (i.e., the green dots) scatter around. To quantify this behavior, we define the following " + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "content": "-based temporal signature, denoted by " + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\Upsilon_{\\omega}" + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "content": ", for a client " + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i" + }, + { + "bbox": [ + 304, + 263, + 546, + 372 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 376, + 545, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 376, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 317, + 376, + 545, + 409 + ], + "type": "interline_equation", + "content": "\\Upsilon_ {\\omega} (\\boldsymbol {G} _ {i}) = \\min _ {c} \\left(\\sum_ {j = \\omega + 1} ^ {| \\boldsymbol {G} _ {i} ^ {c} |} \\sum_ {k = 1} ^ {\\omega} \\frac {\\operatorname {D i s S I M} \\left(\\boldsymbol {G} _ {i} ^ {c} [ j ] , \\boldsymbol {G} _ {i} ^ {c} [ j - k ]\\right)}{\\omega \\left| \\boldsymbol {G} _ {i} ^ {c} \\right| - \\omega^ {2}}\\right) \\tag {1}", + "image_path": "82f97c7a2fbad64b6c8d95258c72d8f0c6309062e18582176e3212dcaf55ae27.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i^c" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " denotes the sub-sequence of gradients belonging to the same cluster " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " from the spatial signature analysis, " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G}_i^c[j]" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " refers to its " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": "-th element, and " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{DISSIM}(\\cdot,\\cdot)" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " is a dissimilarity measure, which can utilize any " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "L_p" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " norm-based similarity, and " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "L_1" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " distance is used as the default given its computation efficiency. The parameter " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " refers to the window size. The larger the window size " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " is, the longer the temporal dependency is leveraged for computing temporal signatures. Figure 4b shows the distribution of temporal signatures with " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\omega = 1" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " (i.e., the temporal signature is computed every two consecutive rounds). This empirically verifies that malicious clients (red bars) tend to have a significantly lower temporal signature " + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\Upsilon_{\\omega}" + }, + { + "bbox": [ + 304, + 415, + 546, + 714 + ], + "type": "text", + "content": " than benign clients (green bars). We utilize the per-client temporal signatures to refine the 2D spatial signature of a gradient update contributed by a client. This forms a 3D spatio-temporal signature space (see the top right in Figure 1) for STDLens to re-examine each cluster from the spatial signature analysis, aiming to determine which cluster of gradient updates is from malicious clients. We first compute the mean temporal signature over all contributing clients of each cluster and mark the one with a lower temporal dissimilarity score as suspicious. Then, we perform an uncertainty assessment before concluding that those clients contributed to the suspicious cluster as malicious." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16346" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 161, + 145 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 161, + 145 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 161, + 145 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 161, + 145 + ], + "type": "image", + "image_path": "45012a241a5747e65af83796a6902d90b0330354354adb746debf8f8dac586fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 49, + 149, + 162, + 171 + ], + "lines": [ + { + "bbox": [ + 49, + 149, + 162, + 171 + ], + "spans": [ + { + "bbox": [ + 49, + 149, + 162, + 171 + ], + "type": "text", + "content": "Figure 5. The empirical rule for confidence estimation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 168, + 70, + 286, + 147 + ], + "blocks": [ + { + "bbox": [ + 168, + 70, + 286, + 147 + ], + "lines": [ + { + "bbox": [ + 168, + 70, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 168, + 70, + 286, + 147 + ], + "type": "image", + "image_path": "b626143319e2ab9b17158256daf4ade99be163dfdd6b9ef234edd2a7f094ba74.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 168, + 149, + 285, + 172 + ], + "lines": [ + { + "bbox": [ + 168, + 149, + 285, + 172 + ], + "spans": [ + { + "bbox": [ + 168, + 149, + 285, + 172 + ], + "type": "text", + "content": "Figure 6. " + }, + { + "bbox": [ + 168, + 149, + 285, + 172 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 168, + 149, + 285, + 172 + ], + "type": "text", + "content": "-density analysis on spatial signatures." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 183, + 246, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 183, + 246, + 197 + ], + "spans": [ + { + "bbox": [ + 47, + 183, + 246, + 197 + ], + "type": "text", + "content": "3.3. Density-based Uncertainty Inspection" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "The results from the spatial clustering analysis can be unreliable, as shown in Figure 3. Similarly, the temporal signature analysis may also incur uncertainty if the average temporal dissimilarity score for each of the two clusters is too close. We introduce the third component dedicated to uncertainty correction. Concretely, it identifies uncertain spatial and temporal zones such that a client is expelled only if we have high confidence that its gradient updates are poisoned. Our uncertainty assessment is based on the empirical rule in normal distributions that " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "68\\%" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": " of data points lie within 1, 2, and 3 standard deviations (" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "'s) from the mean (Figure 5). The confidence requirement is domain-specific. With a given confidence threshold for uncertainty control, we can define the corresponding " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "-confident and " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "-uncertain zones. In particular, we first identify the SSC with the largest eigenvalue. It captures the inter-cluster variance and is visualized as the " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "-axis by default. Figure 6 shows that the spatial signatures (top) on this component exhibit a mixture of two normal distributions (bottom). This allows STDLens to employ the empirical rule by computing the mean and the standard deviation of each cluster (orange or blue in Figure 6) and translating the confidence requirement (e.g., " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": ") into the corresponding intervals (e.g., " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "3-\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": " from the mean of the respective cluster). STDLens considers the zone between two " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "-confident regions to be uncertain, and any gradient updates from participating clients that fall into this zone will be put on a watchlist. The same client entering the " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "-uncertain zone multiple times will be removed from FL. The same uncertainty management operation can also be done on the temporal signatures to minimize the uncertainty-induced false positives. For clients in the cluster with a smaller dissimilarity score and outside the " + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 202, + 289, + 622 + ], + "type": "text", + "content": "-uncertain zone, STDLens will mark them as malicious and revoke their participation in the remaining rounds." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 633, + 191, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 191, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 191, + 646 + ], + "type": "text", + "content": "4. Experimental Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "We conduct experiments on two object detection benchmark datasets: (i) PASCAL VOC [7] and (ii) INRIA Person [6]. By default, we have " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "N = 100" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " clients and a federated server with " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "T = 200" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " rounds for both datasets. At each round, " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "k = 10\\%" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " of the clients are randomly selected as" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 545, + 252 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 252 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 252 + ], + "type": "table", + "html": "
Perception \nPoisonmBenign \nAPsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
Class-Poison \n(VOC)5%52.4345.3552.41
10%52.4339.6952.32
20%52.4338.2252.22
BBox-Poison \n(VOC)5%52.4335.7652.32
10%52.4323.4952.15
20%52.4318.0652.19
Objn-Poison \n(VOC)5%52.4345.0251.95
10%52.4341.6152.33
20%52.4337.6152.29
BBox-Poison \n(INRIA)5%63.4945.0361.64
10%63.4932.5161.25
20%63.4928.7361.71
Objn-Poison \n(INRIA)5%63.4961.0561.98
10%63.4953.9162.01
20%63.4950.1861.58
", + "image_path": "715084122df7ae1eac7cd810f3b108c7864476fa5fbccb89c7c5fbff0d54cca5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "type": "text", + "content": "Table 2. The " + }, + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "type": "text", + "content": " of FL-trained detectors under the benign scenario (3rd column) and three perception poisoning attacks (4th and 5th columns) with three settings of malicious client percentage " + }, + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 255, + 547, + 289 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "text", + "content": "participants with FedAvg [12] as the aggregation algorithm. Without loss of generality, we focus on Faster R-CNN [16] with VGG16 [19] because perception poisoning is model-agnostic and black-box in nature. For each dataset, we randomly split the training set into " + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "text", + "content": " equal-sized partitions and assigned each to one client as its local dataset. We analyze STDLens against all three types of perception poisoning on VOC and examine BBox-Poison and Obj-Poison on INRIA as it only supports objects of the \"person\" class, which is the default victim source class. The target class in Class-Poison is \"potted plant.\" For BBox-Poison, we shrink the bounding box by a factor of 0.10. By default, " + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "inline_equation", + "content": "m = 20\\%" + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "text", + "content": " of the clients in FL are malicious. STDLens is operated with a forensic schedule of ten rounds per window, and the confidence required for uncertainty control is set to be " + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 304, + 300, + 545, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 490, + 448, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 448, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 448, + 502 + ], + "type": "text", + "content": "4.1. Effectiveness of STDLens" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Trojan-agnostic Defense. We first analyze how effective STDLens is in mitigating different model hijacking attacks through perception poisoning. Table 2 reports the results measured in average precision [7] of the victim source class " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\left(\\mathrm{AP}_{\\mathrm{src}}\\right)" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " under three different settings of " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "m\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ". Given that those attacks can hijack the models to cause a drastic drop in " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " (3rd and 4th columns), STDLens offers strong defensibility against all of them (5th column). Regardless of which attack is launched and how many malicious clients (reflected by " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ") participate in the attack process, STDLens can consistently restore the " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ", on par with the one obtained in the benign scenario (i.e., " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "52.43\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " for VOC and " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "63.49\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " for INRIA). For instance, BBox-Poison, which brings down the " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "18.06\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " on VOC, is mitigated with an " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "52.19\\%" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " under the same attack setting. This validates that STDLens is Trojan-agnostic, despite the divergence of different attack effects. Due to similar observa" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16347" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 83, + 211, + 169 + ], + "blocks": [ + { + "bbox": [ + 173, + 72, + 420, + 82 + ], + "lines": [ + { + "bbox": [ + 173, + 72, + 420, + 82 + ], + "spans": [ + { + "bbox": [ + 173, + 72, + 420, + 82 + ], + "type": "text", + "content": "Benign FL —— Poisoned FL (No Defense) —— Poisoned FL (STDLens)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 60, + 83, + 211, + 169 + ], + "lines": [ + { + "bbox": [ + 60, + 83, + 211, + 169 + ], + "spans": [ + { + "bbox": [ + 60, + 83, + 211, + 169 + ], + "type": "image", + "image_path": "269fa7d97521ad79295c02ff4182904874d0270175a21584526115aa26a3500c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 108, + 174, + 163, + 182 + ], + "lines": [ + { + "bbox": [ + 108, + 174, + 163, + 182 + ], + "spans": [ + { + "bbox": [ + 108, + 174, + 163, + 182 + ], + "type": "text", + "content": "(a) Class-Poison" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 220, + 83, + 372, + 170 + ], + "blocks": [ + { + "bbox": [ + 220, + 83, + 372, + 170 + ], + "lines": [ + { + "bbox": [ + 220, + 83, + 372, + 170 + ], + "spans": [ + { + "bbox": [ + 220, + 83, + 372, + 170 + ], + "type": "image", + "image_path": "8215e95f987f73dd2a8edbcc3abcdd7e8129e162b36246a55d9ec2d0b980f630.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 269, + 174, + 325, + 182 + ], + "lines": [ + { + "bbox": [ + 269, + 174, + 325, + 182 + ], + "spans": [ + { + "bbox": [ + 269, + 174, + 325, + 182 + ], + "type": "text", + "content": "(b) BBox-Poison" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 381, + 84, + 533, + 170 + ], + "blocks": [ + { + "bbox": [ + 381, + 84, + 533, + 170 + ], + "lines": [ + { + "bbox": [ + 381, + 84, + 533, + 170 + ], + "spans": [ + { + "bbox": [ + 381, + 84, + 533, + 170 + ], + "type": "image", + "image_path": "67eca3d490de81c4349269567a28060f0e90f06267516dc71d7ca418f982b49b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 431, + 174, + 484, + 183 + ], + "lines": [ + { + "bbox": [ + 431, + 174, + 484, + 183 + ], + "spans": [ + { + "bbox": [ + 431, + 174, + 484, + 183 + ], + "type": "text", + "content": "(c) Objn-Poisson" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 82, + 220, + 513, + 344 + ], + "blocks": [ + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "type": "text", + "content": "Figure 7. Compared with the benign FL (brown) on VOC, the hijacked FL with no defense (pink) has significant " + }, + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "type": "text", + "content": " degradation. STDLens (green) purges all malicious clients in an early-round, allows the healing to begin, and reclaims " + }, + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 189, + 544, + 212 + ], + "type": "text", + "content": " with a negligible damage." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 82, + 220, + 513, + 344 + ], + "lines": [ + { + "bbox": [ + 82, + 220, + 513, + 344 + ], + "spans": [ + { + "bbox": [ + 82, + 220, + 513, + 344 + ], + "type": "image", + "image_path": "83eaf54fe1691fde780f3f22a5ac318c8f44dc0b3ea9bde08aec046756452b43.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 350, + 546, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 350, + 546, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 546, + 373 + ], + "type": "text", + "content": "Table 3. Two images detected by the FL-trained models (VOC) under Class-Poison, BBox-Poison, and Obj-Poison. The FL system with no defense makes designated errors, while the STDLens-protected FL preserves correctness even if the adversary attempts to hijack it." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 385, + 258, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 385, + 258, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 385, + 258, + 396 + ], + "type": "text", + "content": "tions, we focus on VOC in the following discussion." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "type": "text", + "content": "Timely Sanitization and Recovery. Figure 7 visualizes the learning curves of FL throughout 200 rounds by comparing three cases: (i) the benign scenario (brown curve), (ii) the hijacked scenario without defense (pink curve), and (iii) the hijacked scenario protected by STDLens (green curve). We make the following observations. First, Trojaned gradients cause the " + }, + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "type": "text", + "content": " to become either highly unstable (Class-Poison) or consistently degraded (BBox-Poison and Objn-Poison) throughout the FL process. Second, when STDLens detects all malicious clients at the 30th round under Class-Poison, the 20th round under BBox-Poison, and the 30th round under Objn-Poison, no honest client is misdiagnosed and flagged as malicious. Third, the timely sanitization of malicious clients allows the FL system to heal. Even under attacks, the STDLens-protected FL can reach an " + }, + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 399, + 287, + 590 + ], + "type": "text", + "content": " comparable with the benign scenario." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "Visualization. Table 3 visualizes the detection results on two test examples under all three perception poisoning attacks. All three attacks fool the global model with erroneous detection: (i) Class-Poison (1st column) fools the model into mislabeling the person as a potted plant (top) or a bird (bottom), (ii) BBox-Poison (3rd column) deceives the model to recognize person objects with incorrect bounding boxes, and (iii) Objn-Poison (5th column) causes the model to detect no person objects. In comparison, STDLens successfully reinvigorates the FL system with high robustness" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 385, + 421, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 421, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 421, + 396 + ], + "type": "text", + "content": "(2nd, 4th, and 6th columns)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 411, + 487, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 487, + 423 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 487, + 423 + ], + "type": "text", + "content": "4.2. STDLens under Adaptive Attacks" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "content": "-adaptive Attacks. An immediate question we need to address is the defensibility of STDLens against adaptive adversaries who strategically change their attack methods. For instance, malicious clients could camouflage in the crowd of benign clients by occasionally contributing non-Trojaned gradients. We refer to this type of adaptive adversary as " + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "content": "-adaptive. When a " + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "content": "-adaptive adversary participates in an FL round, it has, e.g., a " + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta = 10\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 713 + ], + "type": "text", + "content": " chance of not poisoning the local dataset during the local model training. As a result, this adaptive adversary will contribute to the cluster with benign gradient updates and also to the cluster with Trojaned gradient updates, aiming to fool the spatial and temporal signature analysis. Indeed, such an adaptive attack strategy can jeopardize the spatial analysis because malicious clients can be mistakenly clustered with honest ones, as depicted in Figure 8a. This makes defenses using solely spatial clustering [18, 21] unable to purge all malicious clients. Even for another representative defense using spectral signatures [22], the statistical properties of malicious contributions become the same as those benign ones, as shown in Figure 9a. However, the temporal signature analysis in STDLens is, by design, resilient to such adaptive strategies, as shown in Figure 8b. Recall in Equation 1 that the temporal signature of a client is com" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16348" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 70, + 511, + 196 + ], + "blocks": [ + { + "bbox": [ + 85, + 70, + 511, + 196 + ], + "lines": [ + { + "bbox": [ + 85, + 70, + 511, + 196 + ], + "spans": [ + { + "bbox": [ + 85, + 70, + 511, + 196 + ], + "type": "table", + "html": "
Perception PoisonObject Detection with No DefenseObject Detection with STDLensβBenign \\(AP_{src}\\) (%)Hijacked \\(AP_{src}\\) (%)
No DefenseSTDLens
Class-Poisonpottedplant (0.59)person (0.98)5%52.4331.8351.74
10%52.4332.5152.18
15%52.4334.4051.56
BBox-Poisonperson (0.51)person (0.99)5%52.4322.3652.39
10%52.4326.7752.11
15%52.4327.6051.98
Objn-Poisonmotorbike (0.97)person (0.94)5%52.4340.9652.05
10%52.4341.0152.18
15%52.4341.0652.11
", + "image_path": "9bba6c7e7ba1b6c027f960e421cd6f11cb8c31e2ccfc84acbad2795a7d9cbd31.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 224, + 164, + 312 + ], + "blocks": [ + { + "bbox": [ + 53, + 224, + 164, + 312 + ], + "lines": [ + { + "bbox": [ + 53, + 224, + 164, + 312 + ], + "spans": [ + { + "bbox": [ + 53, + 224, + 164, + 312 + ], + "type": "image", + "image_path": "7c7e900a7b94c88d8d331d301533318806e823be2550c1f27e4982a5538dc761.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 315, + 156, + 324 + ], + "lines": [ + { + "bbox": [ + 59, + 315, + 156, + 324 + ], + "spans": [ + { + "bbox": [ + 59, + 315, + 156, + 324 + ], + "type": "text", + "content": "(a) Spatial Signature Analysis" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 173, + 224, + 282, + 312 + ], + "blocks": [ + { + "bbox": [ + 173, + 224, + 282, + 312 + ], + "lines": [ + { + "bbox": [ + 173, + 224, + 282, + 312 + ], + "spans": [ + { + "bbox": [ + 173, + 224, + 282, + 312 + ], + "type": "image", + "image_path": "832fcd5d027c157f79875a23a803bb772059dd3320c0b0522c26df9df0b4da2c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 315, + 280, + 324 + ], + "lines": [ + { + "bbox": [ + 175, + 315, + 280, + 324 + ], + "spans": [ + { + "bbox": [ + 175, + 315, + 280, + 324 + ], + "type": "text", + "content": "(b) Temporal Signature Analysis" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 331, + 287, + 364 + ], + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 364 + ], + "type": "text", + "content": "Figure 8. " + }, + { + "bbox": [ + 46, + 331, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 331, + 287, + 364 + ], + "type": "text", + "content": "-adaptive malicious clients randomly camouflage in the benign cluster in the spatial analysis (a), but their statistical characteristics in the temporal signature analysis (b) remain unchanged." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": "puted w.r.t. each cluster, and the one with a smaller magnitude is taken to be the lower bound of malicious likelihood. Hence, the statistical characteristics of honest and malicious clients can be preserved in our temporal analysis, where malicious clients (red) have a much smaller temporal signature than honest clients (green). Table 4 compares the hijacked " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " with the " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": "-adaptive attack under no defense scenario (6th column) with the FL system under the protection by STDLens (7th column). A total of nine scenarios under three attacks are compared by varying the configurations of " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": ". We make two observations. First, under the " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": "-adaptive attack, the " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " suffers from significant degradation, from " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "52.43\\%" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "22.36\\%" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": ", even though malicious clients do not send Trojaned gradients all the time. For adaptive adversaries, the choice of " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " should be kept small as a larger " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " can notably weaken the attack effectiveness. Second, STDLens remains resilient under " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": "-adaptive adversaries since it can consistently restore the " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " to at least " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "51.56\\%" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": " for all nine scenarios, on par with that under non-adaptive attacks (recall Table 2). This is primarily because our temporal analysis is robust against such a camouflage. Integrating spatio-temporal statistics allows the identification of the malicious cluster to remain accurate under " + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 377, + 289, + 664 + ], + "type": "text", + "content": "-adaptive attacks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": "-adaptive Attacks. Another attempt to launch adaptive attacks is to wash out the spatial clustering characteristics by only poisoning " + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\gamma \\%" + }, + { + "bbox": [ + 46, + 666, + 287, + 715 + ], + "type": "text", + "content": " of training samples in the local dataset of a malicious client. Under this adaptive setting," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 224, + 421, + 297 + ], + "blocks": [ + { + "bbox": [ + 312, + 224, + 421, + 297 + ], + "lines": [ + { + "bbox": [ + 312, + 224, + 421, + 297 + ], + "spans": [ + { + "bbox": [ + 312, + 224, + 421, + 297 + ], + "type": "image", + "image_path": "bc6b45f9b8df42bcdfcf93aaf12df3dc59e619c37500701739865bb032527028.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 301, + 389, + 311 + ], + "lines": [ + { + "bbox": [ + 343, + 301, + 389, + 311 + ], + "spans": [ + { + "bbox": [ + 343, + 301, + 389, + 311 + ], + "type": "text", + "content": "(a) " + }, + { + "bbox": [ + 343, + 301, + 389, + 311 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 343, + 301, + 389, + 311 + ], + "type": "text", + "content": "-adaptive" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "lines": [ + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "type": "text", + "content": "Figure 9. Spectral signatures [22] fail under (a) " + }, + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "type": "text", + "content": "-adaptive and (b) " + }, + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 316, + 545, + 350 + ], + "type": "text", + "content": "-adaptive attacks as the statistical properties of malicious contributions (red) overlap with benign ones (green)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 432, + 224, + 539, + 297 + ], + "blocks": [ + { + "bbox": [ + 432, + 224, + 539, + 297 + ], + "lines": [ + { + "bbox": [ + 432, + 224, + 539, + 297 + ], + "spans": [ + { + "bbox": [ + 432, + 224, + 539, + 297 + ], + "type": "image", + "image_path": "a28ea37b5da44599027dc0ca3f3bb1d04844dbef8cd920d7c0ace798faee8b26.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 463, + 301, + 510, + 311 + ], + "lines": [ + { + "bbox": [ + 463, + 301, + 510, + 311 + ], + "spans": [ + { + "bbox": [ + 463, + 301, + 510, + 311 + ], + "type": "text", + "content": "(b) " + }, + { + "bbox": [ + 463, + 301, + 510, + 311 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 463, + 301, + 510, + 311 + ], + "type": "text", + "content": "-adaptive" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 334, + 357, + 518, + 403 + ], + "blocks": [ + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "lines": [ + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "spans": [ + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "text", + "content": "Table 4. The benign " + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "text", + "content": " and hijacked " + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "text", + "content": " under " + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "text", + "content": "-adaptive attacks with varying " + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 56, + 201, + 536, + 213 + ], + "type": "text", + "content": " in different types of perception poison (VOC)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 334, + 357, + 518, + 403 + ], + "lines": [ + { + "bbox": [ + 334, + 357, + 518, + 403 + ], + "spans": [ + { + "bbox": [ + 334, + 357, + 518, + 403 + ], + "type": "table", + "html": "
γBenign\nAPsrc (%)Hijacked APsrc (%)
No DefenseSTDLens
80%52.4340.0352.09
60%52.4346.0151.54
", + "image_path": "7ea85359e1987f2188431043a6fd50ffd0b8ad015996886fe6f30b4032332a6c.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 307, + 406, + 542, + 417 + ], + "lines": [ + { + "bbox": [ + 307, + 406, + 542, + 417 + ], + "spans": [ + { + "bbox": [ + 307, + 406, + 542, + 417 + ], + "type": "text", + "content": "Table 5. Quantitative studies of " + }, + { + "bbox": [ + 307, + 406, + 542, + 417 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 307, + 406, + 542, + 417 + ], + "type": "text", + "content": " -adaptive Class-Poison (VOC)." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": "the contribution from a malicious client becomes the gradient updates computed over a mixture of clean and poisoned training samples. We conduct experiments with two settings of " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " with results in Table 5. The " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": "-adaptive attacks can bring down the " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "52.43\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "40.03\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "46.01\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " when we set " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": ", respectively. More malicious clients fall inside the " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": "-uncertain zone, which will be incorrectly identified by defenses using only spatial clustering analysis [18, 21]. Such an adaptive attack also makes spectral signatures [22] ambiguous, as the statistical properties of benign and malicious gradients overlap (Figure 9b). For those uncertain clients, STDLens has to put the decision on hold and wait for more rounds to accumulate additional observations for making confident decisions. Table 5 shows that STDLens remains robust under " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": "-adaptive attacks because all malicious clients can still be identified with no false alarm. The " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " can be recovered to reach over " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "51.54\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": ", comparable to the benign " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "inline_equation", + "content": "52.43\\%" + }, + { + "bbox": [ + 304, + 426, + 545, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 546, + 714 + ], + "type": "text", + "content": "Late-stage Adaptive Attacks. Instead of starting the poisoning process from the beginning of FL, an adaptive adversary could only start poisoning the training data when selected in the later rounds of FL. In this case, the FL system has no Trojaned gradient updates contributed by its clients for a period of time. We conduct such a late-stage adap" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16349" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 286, + 175 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 175 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 175 + ], + "type": "image", + "image_path": "fa6ab37e35e499e25f0d425063fb63d08a22e5c64206b88f8dad8512afcdfd6b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 177, + 287, + 210 + ], + "lines": [ + { + "bbox": [ + 46, + 177, + 287, + 210 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 287, + 210 + ], + "type": "text", + "content": "Figure 10. The malicious clients become active after the 100th round (VOC), causing the " + }, + { + "bbox": [ + 46, + 177, + 287, + 210 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 177, + 287, + 210 + ], + "type": "text", + "content": " to drop. STDLens purges all malicious clients at the 130th round and allows the FL to recover." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "type": "text", + "content": "tive attack by running Class-Poison after the 100th round during the FL process. Figure 10 (left) shows the learning curves of " + }, + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "type": "text", + "content": " for three scenarios: (i) the benign scenario, (ii) the late-stage adaptive attack without defense, and (iii) the one protected by STDLens. Considering the nodefense scenario (pink curve), the " + }, + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{\\mathrm{src}}" + }, + { + "bbox": [ + 46, + 221, + 289, + 377 + ], + "type": "text", + "content": " fluctuates wildly after the 100th round. In comparison, STDLens (green curve) starts detecting the existence of Trojans from the window of rounds 101-110 (top right) and removes the identified malicious clients. It successfully expels all anomalies at the 130th round and allows the FL to heal as no more malicious clients attempt to mislead the FL system (e.g., the window of rounds 131-140 at the bottom right)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 384, + 241, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 241, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 241, + 397 + ], + "type": "text", + "content": "4.3. Comparisons with Existing Defenses" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": "We further compare STDLens with two existing defense methods: spatial clustering [21] and spectral signature [22], which can be extended to FL-based object detection. Table 6 reports the quantitative results. All three defense solutions can detect all malicious clients over the course of FL (i.e., achieving the defense recall of 1.00). STDLens completes the detection and revocation of malicious clients between 20 to 30 rounds, and spatial clustering takes 30 to 40 rounds to detect and remove anomalies, while malicious clients can stay alive in the FL system for at most 80 rounds with spectral signature. The main differentiation factor lies in defense precision. Even though STDLens takes a slightly longer execution time (i.e., " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "452\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "84\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": " for temporal signature analysis and " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "44\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": "-density inspection), it successfully identifies all malicious clients without mistakenly rejecting any benign clients (false positives), achieving a defense precision of 1.00. This allows the STDLens-protected FL to train a global object detector with high accuracy, as shown in the 2nd column in Table 7. In comparison, the spatial clustering approach can reach a low precision of 0.53 under Objn-Poisson, due to gradient contributions falling in the zone between the two clusters, causing ambiguity in anomaly detection. This result shows that defenses based solely on spatial clustering may not offer stable robustness. The spectral signature defense performs the worst, with a defense precision ranging from 0.26 to 0.54. It" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 310, + 70, + 542, + 149 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 542, + 149 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 542, + 149 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 542, + 149 + ], + "type": "table", + "html": "
Defense Precision@Round w/ Max. Recall
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poison1.00@300.95@300.53@40
BBox-Poison1.00@200.71@300.26@80
Objn-Poison1.00@300.53@400.54@40
Time (ms)4523421423
", + "image_path": "cdf7779766ba2a2ba752209b8d7dad021f48802a81c522a61ecee160df0e76d6.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 199, + 545, + 378 + ], + "blocks": [ + { + "bbox": [ + 305, + 154, + 545, + 187 + ], + "lines": [ + { + "bbox": [ + 305, + 154, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 305, + 154, + 545, + 187 + ], + "type": "text", + "content": "Table 6. Comparing STDLens with two state-of-the-art methods on VOC in terms of the defense precision at the round where the maximum recall is achieved and the execution time (the last row)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 199, + 545, + 378 + ], + "lines": [ + { + "bbox": [ + 308, + 199, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 308, + 199, + 545, + 378 + ], + "type": "table", + "html": "
Object Detection Results by Hijacked Models
STDLens (Ours)Spatial Clustering [21]Spectral Signature [22]
Class-Poisonperson (1.00)\nmoto 'D1K' (1.00)person (0.99)\nmotor bike (0.98)person (0.76)\nmotor bike (0.88)\nbird (0.81)
BBox-Poisonperson (0.97)\ntvmonitor (0.96)person (0.79)\n××
Objn-Poisonperson (0.95)\nperson (0.94)person (0.89)\n×person (0.71)\n×
", + "image_path": "f90e8e47f72224ab681143eeab289575b71220e38b31c9c1393b965121f95c36.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 382, + 546, + 416 + ], + "lines": [ + { + "bbox": [ + 305, + 382, + 546, + 416 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 546, + 416 + ], + "type": "text", + "content": "Table 7. The high defense precision offered by STDLens allows the FL-trained model to remain accurate. The excessive removal of clients by other defenses incurs performance degradation (VOC)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 429, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 429, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 305, + 429, + 545, + 513 + ], + "type": "text", + "content": "implies that while the defense can expel malicious clients, a considerable number of honest ones are also mistakenly rejected. One reason is the changing malicious population over time due to the removal of malicious clients in the early rounds. The excessive removal of clients can weaken the benign learning signal and degrade the FL-trained model, as shown in the 3rd and 4th columns in Table 7." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 532, + 384, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 384, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 384, + 544 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 662 + ], + "type": "text", + "content": "With the goal of building a trustworthy federated training process, we have presented STDLens, a three-tier defense framework for FL-based object detection, strengthening the spatial signature with the temporal signature analysis and uncertainty management. Extensive experiments with various adaptive adversaries show that STDLens can protect FL against all three model hijacking attacks and outperforms existing mitigation methods with high defense precision and a low false-positive rate." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, an IBM faculty award, and a Cisco grant on Edge Computing. The first author acknowledges the IBM PhD Fellowship Award." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16350" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 715 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. 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Springer, 2020. 2" + } + ] + } + ], + "index": 30 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16351" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 8 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/STMT_ A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition/ecec9e25-9648-4975-9559-d389674e900b_content_list.json b/2023/STMT_ A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition/ecec9e25-9648-4975-9559-d389674e900b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..003210b0863661f760936f435e800c9d11eb1633 --- /dev/null +++ b/2023/STMT_ A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition/ecec9e25-9648-4975-9559-d389674e900b_content_list.json @@ -0,0 +1,1598 @@ +[ + { + "type": "text", + "text": "STMT: A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition", + "text_level": 1, + "bbox": [ + 228, + 130, + 743, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaoyu Zhu $^{1}$ , Po-Yao Huang $^{2\\dagger}$ , Junwei Liang $^{3\\dagger}$ , Celso M. de Melo $^{4}$ , Alexander Hauptmann $^{1}$ $^{1}$ Carnegie Mellon University, $^{2}$ FAIR, Meta AI, $^{3}$ HKUST (Guangzhou), $^{4}$ DEVCOM Army Research Laboratory", + "bbox": [ + 84, + 202, + 965, + 241 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b54d7575453bef57e2e90386d330264af555816c40e059e96e12f554600628f9.jpg", + "image_caption": [ + "Figure 1. Current state-of-the-art MoCap-based action recognition methods first convert body markers into a human body mesh, which is used to predict a standardized 3D skeleton. The 3D skeleton is used as input for action recognition models (dashed line). We propose a method that directly models the dynamics of raw mesh sequences (solid line). Our method saves the manual effort to derive skeleton representation, and achieves superior recognition performance by leveraging surface motion and body shape knowledge from meshes." + ], + "image_footnote": [], + "bbox": [ + 166, + 260, + 815, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 523, + 313, + 539 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We study the problem of human action recognition using motion capture (MoCap) sequences. Unlike existing techniques that take multiple manual steps to derive standardized skeleton representations as model input, we propose a novel Spatial-Temporal Mesh Transformer (STMT) to directly model the mesh sequences. The model uses a hierarchical transformer with intra-frame off-set attention and inter-frame self-attention. The attention mechanism allows the model to freely attend between any two vertex patches to learn non-local relationships in the spatial-temporal domain. Masked vertex modeling and future frame prediction are used as two self-supervised tasks to fully activate the bi-directional and auto-regressive attention in our hierarchical transformer. The proposed method achieves state-of-the-art performance compared to skeleton-based and pointcloud-based models on common MoCap benchmarks. Code is available at https://github.com/zgzxy001/STMT.", + "bbox": [ + 75, + 539, + 473, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 821, + 209, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motion Capture (MoCap) is the process of digitally recording the human movement, which enables the fine", + "bbox": [ + 75, + 845, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "grained capture and analysis of human motions in 3D space [40, 50]. MoCap-based human perception serves as key elements for various research fields, such as action recognition [15, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. Besides, MoCap is one of the fundamental technologies to enhance human-robot interactions in various practical scenarios including hospitals and manufacturing environment [22, 28, 41, 43, 45, 77]. For example, Hayes [22] classified automotive assembly activities using MoCap data of humans and objects. Understanding human behaviors from MoCap data is fundamentally important for robotics perception, planning, and control.", + "bbox": [ + 496, + 525, + 893, + 723 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Skeleton representations are commonly used to model MoCap sequences. Some early works [3, 29] directly used body markers and their connectivity relations to form a skeleton graph. However, the marker positions depend on each subject (person), which brings sample variances within each dataset. Moreover, different MoCap datasets usually have different numbers of body markers. For example, ACCAD [48], BioMotion [64], Eyes Japan [15], and KIT [42] have 82, 41, 37, and 50 body markers respectively. This prevents the model to be trained and tested on a unified framework. To use standard skeleton representa", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal Contribution.", + "bbox": [ + 101, + 887, + 215, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1526", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tions such as NTU RGB+D [58], Punnakkal et al. [50] first used Mosh++ to fit body markers into SMPL-H meshes, and then predicted a 25-joint skeleton [33] from the mesh vertices [54]. Finally, a skeleton-based model [60] was used to perform action recognition. Although those methods achieved advanced performance, they have the following disadvantages. First, they require several manual steps to map the vertices from mesh to skeleton. Second, skeleton representations lose the information provided by original MoCap data (i.e., surface motion and body shape knowledge). To overcome those disadvantages, we propose a mesh-based action recognition method to directly model dynamic changes in raw mesh sequences, as illustrated in Figure 1.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Though mesh representations provide fine-grained body information, it is challenging to classify high-dimensional mesh sequences into different actions. First, unlike structured 3D skeletons which have joint correspondence across frames, there is no vertex-level correspondence in meshes (i.e., the vertices are unordered). Therefore, the local connectivity of every single mesh can not be directly aggregated in the temporal dimension. Second, mesh representations encode local connectivity information, while action recognition requires global understanding in the whole spatial-temporal domain.", + "bbox": [ + 75, + 301, + 472, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome the aforementioned challenges, we propose a novel Spatial-Temporal Mesh Transformer (STMT). STMT leverages mesh connectivity information to build patches at the frame level, and uses a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. The hierarchical attention mechanism allows the model to learn patch correlation across the entire sequence, and alleviate the requirement of explicit vertex correspondence. We further define two self-supervised learning tasks, namely masked vertex modeling and future frame prediction, to enhance the global interactions among vertex patches. To reconstruct masked vertices of different body parts, the model needs to learn prior knowledge about the human body in the spatial dimension. To predict future frames, the model needs to understand meaningful surface movement in the temporal dimension. To this end, our hierarchical transformer pretrained with those two objectives can further learn spatial-temporal context across entire frames, which is beneficial for the downstream action recognition task.", + "bbox": [ + 75, + 468, + 472, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our model on common MoCap benchmark datasets. Our method achieves state-of-the-art performance compared to skeleton-based and point-cloud-based models. The contributions of this paper are three-fold:", + "bbox": [ + 75, + 770, + 470, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We introduce a new hierarchical transformer architecture, which jointly encodes intrinsic and extrinsic representations, along with intra- and inter-frame attention, for spatial-temporal mesh modeling.", + "bbox": [ + 94, + 839, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We design effective and efficient pretext tasks, namely masked vertex modeling and future frame prediction, to enable the model to learn from the spatial-temporal global context.", + "bbox": [ + 517, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our model achieves superior performance compared to state-of-the-art point-cloud and skeleton models on common MoCap benchmarks.", + "bbox": [ + 517, + 164, + 893, + 209 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 224, + 640, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Action Recognition from Depth and Point Cloud. 3D action recognition models have achieved promising performance with depth [34, 55, 56, 68, 71] and point clouds [18, 36, 52, 70]. Depth provides reliable 3D structural and geometric information which characterizes informative human actions. In MVDI [71], dynamic images [4] were extracted through multi-view projections from depth videos for 3D action recognition. 3D-FCNN [55] directly exploited a 3D-CNN to model depth videos. Another popular category of 3D human action recognition is based on 3D point clouds. PointNet [51] and PointNet++ [52] are the pioneering works contributing towards permutation invariance of 3D point sets for representing 3D geometric structures. Along this avenue, MeteorNet [36] stacked multi-frame point clouds and aggregates local features for action recognition. 3DV [70] transferred point cloud sequences into regular voxel sets to characterize 3D motion compactly via temporal rank pooling. PSTNet [18] disentangled space and time to alleviate point-wise spatial variance across time. Action recognition has shown promising results with 3D skeletons and point clouds. Meshes, which are commonly used in representing human bodies and creating action sequences, have not been explored for the action recognition task. In this work, we propose the first mesh-based action recognition model.", + "bbox": [ + 496, + 250, + 893, + 628 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "MoCap-Based Action Recognition. Motion-capture (MoCap) datasets [15, 44, 46-48, 50, 57] serve as key elements for various research fields, such as action recognition [15, 44, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. MoCap-based action recognition was formulated as a skeleton-based action recognition problem [50]. Various architectures have been investigated to incorporate skeleton sequences. In [14, 35, 75], skeleton sequences were treated as time-series inputs to RNNs. [24, 69] respectively transformed skeleton sequences into spectral images and trajectory maps and then adopted CNNs for feature learning. In [72], Yan et al. leveraged GCN to model joint dependencies that can be naturally represented with a graph. In this paper, we propose a novel method to directly model the dynamics of raw mesh sequences which can benefit from surface motion and body shape knowledge.", + "bbox": [ + 496, + 643, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1527", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Masked Autoencoder. Masked autoencoder has gained attention in Natural Language Processing and Computer Vision to learn effective representations using auto-encoding. Stacked denoising autoencoders [66] treated masks as a noise type and used denoising autoencoders to denoise corrupted inputs. ViT [13] proposed a self-supervised pretraining task to reconstruct masked tokens. More recently, BEiT [2] proposed to learn visual representations by reconstructing the discrete tokens [53]. MAE [23] proposed a simple yet effective asymmetric framework for masked image modeling. In 3D point cloud analysis, Wang et al. [67] chose to first generate partial point clouds by calculating occlusion from random camera viewpoints, and then completed occluded point clouds using autoencoding. PointBERT [73] followed the success of BERT [12] to predict the masked tokens learned from points. However, applying self-supervised learning to temporal 3D sequences (i.e. point cloud, 3D skeleton) has not been fully explored. One probable reason is that self-supervised learning on high-dimensional 3D temporal sequences is computationally-expensive. In this work, we propose an effective and efficient self-supervised learning method based on masked vertex modeling and future frame prediction.", + "bbox": [ + 75, + 107, + 472, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 470, + 171, + 486 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 497, + 187, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we describe our model for mesh-based action recognition, which we call STMT. The inputs of our model are temporal mesh sequences: $\\mathbf{M} = ((\\mathbf{P}_1,\\mathbf{A}_1),(\\mathbf{P}_2,\\mathbf{A}_2),\\dots ,(\\mathbf{P}_t,\\mathbf{A}_t))$ , where $t$ is the frame number. $\\mathbf{P}_i\\in \\mathbb{R}^{N\\times 3}$ represents the vertex positions in Cartesian coordinates, where $N$ is the number of vertices. $\\mathbf{A}_i\\in \\mathbb{R}^{N\\times N}$ represents the adjacency matrix of the mesh. Element $\\mathbf{A}_i^{mn}\\in \\mathbf{A}_i$ is one when there is an edge from vertex $V_{m}$ to vertex $V_{n}$ , and zero when there is no edge. The mesh representation with vertices and their adjacent matrix is a unified format for various body models such as SMPL [39], SMPL-H [54], and SMPL-X [49]. In this work, we use SMPL-H body models from AMASS [40] to obtain the mesh sequences, but our method can be easily adapted to other body models.", + "bbox": [ + 75, + 521, + 468, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Mesh's local connectivity provides fine-grained information. Previous methods [21, 59] proved that explicitly using surface (e.g., mesh) connectivity information can achieve higher accuracy in shape classification and segmentation tasks. However, classifying temporal mesh sequences is a more challenging problem, as there is no vertex-level correspondence across frames. This prevents graph-based models from directly aggregating vertices in the temporal dimension. Therefore, we propose to first leverage mesh connectivity information to build patches at the frame level,", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "then use a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. In summary, it has the following key components:", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Surface Field Convolution to form local vertex patches by considering both intrinsic and extrinsic mesh representations.", + "- Hierarchical Spatial-Temporal Transformer to learn spatial-temporal correlations of vertex patches.", + "- Self-Supervised Pre-Training to learn the global context in terms of appearance and motion." + ], + "bbox": [ + 517, + 161, + 890, + 284 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "See Figure 2 for a high-level summary of the model, and the sections below for more details.", + "bbox": [ + 498, + 294, + 890, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Surface Field Convolution", + "text_level": 1, + "bbox": [ + 500, + 333, + 736, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Because displacements in grid data are regular, traditional convolutions can directly learn a kernel for elements within a region. However, mesh vertices are unordered and irregular. Considering the special mesh representations, we represent each vertex by encoding features from its neighbor vertices inspired by [51,52]. To fully utilize meshes' local connectivity information, we consider the mesh properties of extrinsic curvature of submanifolds and intrinsic curvature of the manifold itself. Extrinsic curvature between two vertices is approximated using Euclidean distance. Intrinsic curvature is approximated using Geodesic distance, which is defined as the shortest path between two vertices on mesh surfaces. We propose a light-weighted surface field convolution to build local patches, which can be denoted as:", + "bbox": [ + 496, + 356, + 890, + 566 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {V G} ^ {\\prime (x, y, z)} = \\sum_ {(\\delta_ {x}, \\delta_ {y}, \\delta_ {z}) \\in G (x, y, z)} \\boldsymbol {W} ^ {(\\delta_ {x}, \\delta_ {y}, \\delta_ {z})} \\cdot \\boldsymbol {F} ^ {(x + \\delta_ {x}, y + \\delta_ {y}, z + \\delta_ {z})} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 577, + 906, + 626 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {V E} ^ {\\prime (x, y, z)} = \\sum_ {(\\zeta_ {x}, \\zeta_ {y}, \\zeta_ {z}) \\in E (x, y, z)} \\boldsymbol {W} ^ {(\\zeta_ {x}, \\zeta_ {y}, \\zeta_ {z})} \\cdot \\boldsymbol {F} ^ {(x + \\zeta_ {x}, y + \\zeta_ {y}, z + \\zeta_ {z})} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 646, + 906, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$G$ and $E$ is the local region around vertex $(x,y,z)$ . In this paper, we use k-nearest-neighbor to sample local vertices. $(\\delta_x,\\delta_y,\\delta_z)$ and $(\\zeta_x,\\zeta_y,\\zeta_z)$ represent the spatial displacement in geodesic and euclidean space, respectively. $\\pmb{F}^{(x,y,z)}$ denotes the feature of the vertex at position $(x,y,z)$ .", + "bbox": [ + 500, + 702, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Hierarchical Spatial-Temporal Transformer", + "text_level": 1, + "bbox": [ + 500, + 801, + 872, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a hierarchical transformer that consists of intra-frame and inter-frame attention. The basic idea behind our transformer is three-fold: (1) Intra-frame attention can encode connectivity information from the adjacency matrix, while such information can not be directly", + "bbox": [ + 496, + 825, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1528", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/aa2fef466fec1635359291bd667378c4cbdc65c4dffb5d8abaf57d743821a73d.jpg", + "image_caption": [ + "(a) STMT Architecture" + ], + "image_footnote": [], + "bbox": [ + 81, + 92, + 511, + 272 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/497862271b69e92e5eb0b916093744d61c6576242f878e79f96e45802861775a.jpg", + "image_caption": [ + "(b) Pre-Training Stage", + "Figure 2. Overview of the proposed framework. (a) Overview of STMT. Given a mesh sequence, we first develop vertex patches by extracting both intrinsic (geodesic) and extrinsic (euclidean) features using surface field convolution. The intrinsic and extrinsic features are denoted by yellow and blue blocks respectively. Those patches are used as input to the intra-frame offset-attention network to learn appearance features. Then we concatenate intrinsic patches and extrinsic patches of the same position. The concatenated vertex patches (green blocks) are fed into the inter-frame self-attention network to learn spatial-temporal correlations. Finally, the local and global features are mapped into action predictions by MLP layers. (b) Overview of Pre-Training Stage. We design two pretext tasks: masked vertex modeling and future frame prediction for global context learning. Bidirectional attention is used for the reconstruction of masked vertices. Auto-regressive attention is used for the future frame prediction task." + ], + "image_footnote": [], + "bbox": [ + 519, + 95, + 885, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "aggregated in the temporal domain because vertices are unordered. (2) Frame-level offset-attention can be used to mimic the Laplacian operator to learn effective spatial representations. (3) Inter-frame self-attention can learn feature correlations in the spatial-temporal domain.", + "bbox": [ + 75, + 443, + 468, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Intra-Frame Offset-Attention", + "text_level": 1, + "bbox": [ + 76, + 541, + 336, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Graph convolution networks [6] show the benefits of using a Laplacian matrix $\\mathbf{L} = \\mathbf{D} - \\mathbf{E}$ to replace the adjacency matrix $\\mathbf{E}$ , where $\\mathbf{D}$ is the diagonal degree matrix. Inspired by this, offset-attention has been proposed and achieved superior performance in point-cloud classification and segmentation tasks [20]. We adapt offset-attention to attend to vertex patches. Specifically, the offset-attention layer calculates the offset (difference) between the self-attention (SA) features and the input features by element-wise subtraction. Offset-attention is denoted as:", + "bbox": [ + 75, + 566, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {\\text {o u t}} = O A \\left(\\boldsymbol {F} _ {\\text {i n}}\\right) = \\phi \\left(\\boldsymbol {F} _ {\\text {i n}} - \\boldsymbol {F} _ {\\text {s a}}\\right) + \\boldsymbol {F} _ {\\text {i n}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 731, + 468, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\phi$ denotes a non-linear operator. $F_{in} - F_{sa}$ is proved to be analogous to discrete Laplacian operator [20], i.e. $F_{in} - F_{sa} \\approx LF_{in}$ . As Laplacian operators in geodesic and euclidean space are expected to be different, we propose to use separate transformers to model intrinsic patches and extrinsic patches. Specifically, the aggregated feature for vertex $V$ is denoted as:", + "bbox": [ + 75, + 760, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {V} ^ {\\prime (x, y, z)} = O A _ {G} \\left(\\boldsymbol {F} _ {V G} ^ {\\prime (x, y, z)}\\right) \\oplus O A _ {E} \\left(\\boldsymbol {F} _ {V E} ^ {\\prime (x, y, z)}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 881, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $F_{VG}^{\\prime (x,y,z)}\\in \\mathbb{R}^{N\\times d_g}$ and $F_{VE}^{\\prime (x,y,z)}\\in \\mathbb{R}^{N\\times d_e}$ are local patches learned using Equ. 1 and Equ. 2. $F_V^{\\prime (x,y,z)}\\in$ $\\mathbb{R}^{N\\times d}$ denotes the local patch for position $(x,y,z)$ , where $d = d_{g} + d_{e}$ . The weights of $OA_{G}$ and $OA_{E}$ are not shared.", + "bbox": [ + 498, + 440, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Inter-Frame Self-Attention", + "text_level": 1, + "bbox": [ + 500, + 526, + 741, + 540 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given $F_V'$ which encodes local connectivity information, we use self-attention (SA) [65] to learn semantic affinities between different vertex patches across frames. Specifically, let $\\mathbf{Q},\\mathbf{K},\\mathbf{V}$ be the query, key and value, which are generated by applying linear transformations to the input features $F_V' \\in \\mathbb{R}^{N \\times d}$ as follows:", + "bbox": [ + 496, + 550, + 890, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}) = F _ {V} ^ {\\prime} \\cdot (\\boldsymbol {W} _ {q}, \\boldsymbol {W} _ {k}, \\boldsymbol {W} _ {v})\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 652, + 815, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Q}, \\boldsymbol {K} \\in \\mathbb {R} ^ {N \\times d _ {a}}, \\quad \\boldsymbol {V} \\in \\mathbb {R} ^ {N \\times d}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 672, + 818, + 690 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {W} _ {q}, \\boldsymbol {W} _ {k} \\in \\mathbb {R} ^ {d \\times d _ {a}}, \\quad \\boldsymbol {W} _ {v} \\in \\mathbb {R} ^ {d \\times d} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 693, + 890, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_{q}$ , $W_{k}$ and $W_{v}$ are the shared learnable linear transformation, and $d_{a}$ is the dimension of the query and key vectors. Then we can use the query and key matrices to calculate the attention weights via the matrix dot-product:", + "bbox": [ + 500, + 724, + 890, + 782 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {A} = (\\tilde {\\alpha}) _ {i, j} = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\cdot \\boldsymbol {K} ^ {\\mathrm {T}}}{\\sqrt {d _ {a}}}\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 784, + 890, + 820 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {F} _ {s a} = \\boldsymbol {A} \\cdot \\boldsymbol {V} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 648, + 830, + 890, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The self-attention output features $F_{sa}$ are the weighted sums of the value vector using the corresponding attention weights. Specifically, for a vertex patch in position $(x,y,z)$ ,", + "bbox": [ + 500, + 854, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1529", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "its aggregated feature after inter-frame self-attention can be computed as: $\\pmb{F}_{sa}^{(x,y,z)} = \\sum \\pmb{A}^{(x,y,z),(x',y',z')} \\times \\pmb{V}^{(x',y',z')}$ , where $(x',y',z')$ belongs to the Cartesian coordinates of $\\pmb{F}_V'$ .", + "bbox": [ + 76, + 90, + 468, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Self-Supervised Pre-Training", + "text_level": 1, + "bbox": [ + 76, + 164, + 336, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Self-supervised learning has achieved remarkable results on large-scale image datasets [23]. However, self-supervised learning for temporal 3D sequences (i.e. point cloud, 3D skeleton) remains to be challenging and has not been fully explored. There are two possible reasons: (1) self-supervised learning methods rely on large-scale datasets to learn meaningful patterns [10]. However, existing MoCap benchmarks are relatively small compared to 2D datasets like ImageNet [11]. (2) Self-supervised learning for 3D data sequences is computationally expensive in terms of memory and speed. In this work, we first propose a simple and effective method to augment existing MoCap sequences, and then define two effective and efficient self-supervised learning tasks, namely masked vertex modeling and future frame prediction, which enable the model to learn global context. The work that is close to us is OcCO [67], which proposed to use occluded point cloud reconstruction as the pretext task. OcCO has a computationally-expensive process to generate occlusions, including point cloud projection, occluded point calculation, and a mapping step to convert camera frames back to world frames. Different from OcCO, we randomly mask vertex patches or future frames on the fly, which saves the pre-processing step. Moreover, our pre-training method is designed for temporal mesh sequences and considers both bi-directional and autoregressive attention.", + "bbox": [ + 75, + 188, + 472, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.1 Data Augmentation through Joint Shuffle", + "text_level": 1, + "bbox": [ + 76, + 601, + 419, + 617 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering the flexibility of SMPL-H representations, we propose a simple yet effective approach to augment SMPL-H sequences by shuffling body pose parameters. Specifically, we split SMPL-H pose parameters into five body parts: bone, left/right arm, and left/right leg. We use $I_{bone}, I_{leg}^{left}, I_{leg}^{right}, I_{arm}^{left}, I_{arm}^{right}$ to denote the SMPL-H pose indexes of the five body parts. Then we synthesize new sequences by randomly selecting body parts from five different sequences. We keep the temporal order for each part such that the merged action sequences have meaningful motion trajectories. Pseudocode for the joint shuffle is provided in Algorithm 1. The input to Joint Shuffle are SMPL-H pose parameters $\\theta \\in \\mathbb{R}^{b \\times t \\times n \\times 3}$ , where $b$ is the sequence number, $t$ is the frame number, and $n$ is the joint number. We randomly select the shape $\\beta$ and dynamic parameters $\\phi$ from one of the five SMPL-H sequences to compose a new SMPL-H body model. Given $b$ SMPL-H sequences, we can synthesize ${}^b C_5 = \\frac{b!}{5!(b - 5)!}$ number of new sequences.", + "bbox": [ + 75, + 625, + 472, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We prove that the model can benefit from large-scale pretraining in Section 4.6.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Pseudocode of STMT Joint Shuffle" + ], + "code_body": "1: function STMT JOINT SHUFFLE( $\\theta \\in$ $\\mathbb{R}^{b\\times t\\times n\\times 3}$ $I_{\\mathrm{bone}},I_{\\mathrm{leg}}^{\\mathrm{left}},I_{\\mathrm{leg}}^{\\mathrm{right}},I_{\\mathrm{arm}}^{\\mathrm{left}},I_{\\mathrm{arm}}^{\\mathrm{right}})$ \n2: $\\theta_s\\gets$ random_sample(0,5) $\\triangleright \\theta_s\\in \\mathbb{R}^{5\\times t\\times n\\times 3}$ randomly sample five SMPL-H sequences \n3: $t_{max}\\gets$ get_max_length( $\\theta_{s})$ compute the maximum sequence length in $\\theta_{s}$ \n4: $\\theta_{new}\\gets$ Initialize $(t_{max},n,3)$ \n5: $P\\gets \\{I_{\\mathrm{bone}},I_{\\mathrm{leg}}^{\\mathrm{left}},I_{\\mathrm{leg}}^{\\mathrm{right}},I_{\\mathrm{arm}}^{\\mathrm{left}},I_{\\mathrm{arm}}^{\\mathrm{right}}\\}$ \n6: for i in 0,1,2,3,4 do \n7: $\\theta_s\\gets$ repeat $(\\theta_s[i],(t_{max},n,3))$ pad each sequence to the max length using repeating \n8: $\\theta_{new}[P[i]]\\gets \\theta_s[i][P[i]]\\triangleright$ assign the body-part sequence \n9: return $\\theta_{new}$", + "bbox": [ + 527, + 143, + 911, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.2 Masked Vertex Modeling with Bi-Directional Attention", + "text_level": 1, + "bbox": [ + 500, + 387, + 890, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To fully activate the inter-frame bi-directional attention in the transformer, we design a self-supervised pretext task named Masked Vertex Modeling (MVM). The model can learn human prior information in the spatial dimension by reconstructing masked vertices of different body parts. We randomly mask $r$ percentages of the input vertex patches, and force the model to reconstruct the full sequences. Moreover, we use bi-directional attention to learn correlations among all remaining local patches. Each patch will attend to all patches in the entire sequence. It models the joint distribution of vertex patches over the whole temporal sequences $x$ as the following product of conditional distributions, where $x_{i}$ is a single vertex patch:", + "bbox": [ + 496, + 426, + 893, + 625 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np (x) = \\prod_ {i = 1} ^ {N} p \\left(x _ {i} \\mid x _ {1},.., x _ {i}, \\dots , x _ {N}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 626, + 890, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where $N$ is the number of patches in the entire sequence $x$ after masking. Every patch will attend to all patches in the entire sequence. In this way, bi-directional attention is fully-activated to learn spatial-temporal features that can accurately reconstruct completed mesh sequences.", + "bbox": [ + 496, + 674, + 893, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4.3 Future Frame Prediction with Auto-Regressive Attention", + "text_level": 1, + "bbox": [ + 498, + 768, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The masked vertex modeling task is to reconstruct masked vertices in different body parts. The model can reconstruct completed mesh sequences if it captures the human body prior or can make a movement inference from nearby frames. As action recognition requires the model to understand the global context, we propose the future frame", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1530", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "prediction (FFP) task. Specifically, we mask out all the future frames and force the transformer to predict the masked frames. Moreover, we propose to use auto-regressive attention for the future frame prediction task, inspired by language generation models like GPT-3 [5]. However, directly using RNN-based models [9] in GPT-3 to predict future frames one by one is inefficient, as 3D mesh sequences are denser compared to language sequences. Therefore, we propose to reconstruct all future frames in a single forward pass. For auto-regressive attention, we model the joint distribution of vertex patches over a mesh sequence $x$ as the following product of conditional distributions, where $x_{i}$ is a single patch at frame $t_{i}$ :", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\np (x) = \\prod_ {i = 1} ^ {N} p \\left(x _ {i} \\mid x _ {1}, x _ {2}, \\dots , x _ {M}\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 297, + 468, + 339 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Where $N$ is the number of patches in the entire sequence $x$ after masking. $M = (t_i - 1) \\times n$ , where $n$ is the number of patches in a single frame. Each vertex patch depends on all patches that are temporally before it. The auto-regressive attention enables the model to predict movement patterns and trajectories, which is beneficial for the downstream action recognition task.", + "bbox": [ + 76, + 349, + 472, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Training", + "text_level": 1, + "bbox": [ + 76, + 473, + 181, + 489 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the pre-training stage, we use PCN [74] as the decoder to reconstruct masked vertices and predict future frames. The decoder is shared for the two pretext tasks. Since mesh vertices are unordered, the reconstruction loss and future prediction loss should be permutation-invariant. Therefore, we use Chamfer Distance (CD) as the loss function to measure the difference between the model predictions and ground truth mesh sequences.", + "bbox": [ + 75, + 500, + 468, + 621 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} C D (M _ {p r e d}, M _ {g t}) = \\frac {1}{\\left| M _ {p r e d} \\right|} \\sum_ {x \\in M _ {p r e d}} \\min _ {y \\in M _ {g t}} \\| x - y \\| _ {2} + \\\\ \\frac {1}{| M _ {g t} |} \\sum_ {y \\in M _ {g t}} \\min _ {x \\in M _ {p r e d}} \\| y - x \\| _ {2} \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 628, + 468, + 722 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CD (10) calculates the average closest euclidean distance between the predicted mesh sequences $M_{pred}$ and the ground truth sequences $M_{gt}$ . The overall loss is a weighted sum of masked vertex reconstruction loss and future frame prediction loss:", + "bbox": [ + 75, + 724, + 468, + 801 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = \\lambda_ {1} C D \\left(M _ {p r e d} ^ {M V M}, M _ {g t}\\right) + \\lambda_ {2} C D \\left(M _ {p r e d} ^ {F F P}, M _ {g t}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 816, + 468, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the fine-tuning stage, we replace the PCN decoder with an MLP head. Cross-entropy loss is used for model training.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 89, + 624, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 114, + 602, + 128 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Following previous MoCap-based action recognition methods [50,63], we evaluate our model on the most widely used benchmarks: KIT [42] and BABEL [50]. KIT is one of the largest MoCap datasets. It has 56 classes with 6,570 sequences in total. (2) BABEL is the largest 3D MoCap dataset that unifies 15 different datasets. BABEL has 43 hours of MoCap data performed by over 346 subjects. We use the 60-class subset from BABEL, which contains 21,653 sequences with single-class labels. We randomly split each dataset into training, test, and validation set, with ratios of $70\\%$ , $15\\%$ , and $15\\%$ , respectively. Note that existing action recognition datasets with skeletons only are not suitable for our experiments, as they do not provide full 3D surfaces or SMPL parameters to obtain the mesh representation.", + "bbox": [ + 496, + 137, + 890, + 363 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Motion Representation. Both KIT and BABEL's MoCap sequences are obtained from AMASS dataset in SMPL-H format. A MoCap sequence is an array of pose parameters over time, along with the shape and dynamic parameters. For skeleton-based action recognition, we follow previous work [50] which predicted the 25-joint skeleton from the vertices of the SMPL-H mesh. The movement sequence is represented as $\\mathbf{X} = (\\mathbf{x}_1,\\dots ,\\mathbf{x}_L)$ , where $\\mathbf{x}_i\\in \\mathbb{R}^{J\\times 3}$ represents the position of the $J$ joints in the skeleton in Cartesian coordinates. For point-cloud-based action recognition, we directly use the vertices of SMPL-H model as the model input. The point-cloud sequence is represented as $\\mathbf{P} = (\\mathbf{p}_1,\\dots ,\\mathbf{p}_L)$ , where $\\mathbf{p}_i\\in \\mathbb{R}^{V\\times 3}$ , and $V$ is the number of vertices. For mesh-based action recognition, we represent the motion as a series of mesh vertices and their adjacent matrix over time, as introduced in Section 3.1. See Sup. Mat. for more details about datasets and pre-processing.", + "bbox": [ + 496, + 382, + 890, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Baseline Methods", + "text_level": 1, + "bbox": [ + 500, + 648, + 669, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our model with state-of-the-art 3D skeleton-based and point cloud-based action recognition models, as there is no existing literature on mesh-based action recognition. 2s-AGCN [61], CTR-GCN [7], and MS-G3D [37] are used as skeleton-based baselines. Among those methods, 2s-AGCN trained with focal loss and cross-entropy loss are used as benchmark methods in the BABEL dataset [50]. For the comparison with point-cloud baselines, we choose PSTNet [18], SequentialPointNet [30], and P4Transformer [16]. Those methods achieved top performance on common point-cloud-based action recognition benchmarks.", + "bbox": [ + 496, + 671, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 847, + 718, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For skeleton-based baselines, we use the official implementations of 2s-ACGN, CTR-GCN, and MS-G3D from", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1531", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4ced3ed0689370f86f19a33b2a91b133a731a7aaf83baac1f840c161107f8d0d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInputKITBABEL-60
Top-1 (%)Top-5 (%)Top-1 (%)Top-5 (%)
2s-AGCN-FL [61] (CVPR'19)3D Skeleton42.4475.6049.6279.12
2s-AGCN-CE [61] (CVPR'19)3D Skeleton57.4681.5463.5786.77
CTR-GCN [7] (ICCV'21)3D Skeleton64.6587.9067.3088.50
MS-G3D [37] (CVPR'20)3D Skeleton65.3887.9067.4387.99
PSTNet [18] (ICLR'21)Point Cloud56.9388.2161.9484.11
SequentialPointNet [30] (arXiv'21)Point Cloud59.7588.0162.9284.58
P4Transformer [16] (CVPR'21)Point Cloud62.1588.0163.5486.55
STMT(Ours)Mesh65.5990.0967.6588.68
", + "bbox": [ + 153, + 70, + 821, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61c33fb9069d9dc2cb5c34d55cb1f3c7af4ed05002cdd432c7a91e8c5155f466.jpg", + "image_caption": [ + "Figure 3. Visualization of inter-frame attention. Red denotes the highest attention." + ], + "image_footnote": [], + "bbox": [ + 80, + 257, + 478, + 468 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "[62], [8], and [38]. For point-cloud-based baselines, we use the official implementations of PSTNet, SequentialPointNet, P4Transformer from [19], [31], and [17]. We pre-train STMT for 200 epochs with a batch size of 32. The model is fine-tuned for 50 epochs with a batch size of 64. Adam optimizer [26] is used with a learning rate of 0.0001 for both pre-training and fine-tuning. See Sup. Mat. for more implementation details.", + "bbox": [ + 75, + 511, + 468, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Main Results", + "text_level": 1, + "bbox": [ + 76, + 647, + 215, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with State-of-the-Art Methods. As indicated in Table 1, STMT outperforms all other state-of-the-art models. Our model can outperform point-cloud-based models by $3.44\\%$ and $4.11\\%$ on KIT and BABEL datasets in terms of top-1 accuracy. Moreover, compared to skeleton-based methods which involve manual efforts to convert mesh vertices to skeleton representations, our model achieves better performance by directly modeling the dynamics of raw mesh sequences.", + "bbox": [ + 75, + 671, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We visualize the inter-frame attention weights of our hierarchical transformer in Figure 3. We observe that the model can pay attention to key regions across frames. This supports the intuition that our hierarchical transformer can take the place of explicit vertex tracking by learning spatial-temporal correlations.", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/80c8c7a395be59d419d6a0a15065bc31abe35ba6298a478898b0ae7137667c09.jpg", + "table_caption": [ + "Table 1. Experimental Results on KIT and BABEL Dataset." + ], + "table_footnote": [], + "table_body": "
IntrinsicExtrinsicMVMFFPTop-1 (%)
✓63.40
✓✓64.03
✓✓✓64.96
✓✓✓64.13
✓✓✓✓65.59
", + "bbox": [ + 532, + 260, + 859, + 359 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Performance of ablated versions. Intrinsic and Extrinsic stand for the intrinsic (geodesic) and extrinsic (euclidean) features in surface field convolution. MVM stands for Masked Vertex Modelling. FFP stands for Future Frame Prediction.", + "bbox": [ + 498, + 369, + 890, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 436, + 653, + 454 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation Study of STMT. We test various ablations of our model on the KIT dataset to substantiate our design decisions. We report the results in Table 2. Note that Joint Shuffle is used in all of the self-supervised learning experiments (last three rows). We observe that each component of our model gains consistent improvements. The comparison of the first two rows proves the effectiveness of encoding both intrinsic and extrinsic features in vertex patches. Comparing the last three rows with the second row, we observe a consistent improvement using self-supervised pretraining. Moreover, the downstream task can achieve better performance with MVM compared to FFP. One probable reason is that the single task for future frame prediction is more challenging than masked vertex modeling, as the model can only see the person movement in the past. The model can achieve the best performance with both MVM and FFP, which demonstrates that the two self-supervised tasks are supplementary to each other.", + "bbox": [ + 496, + 460, + 892, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Analysis", + "text_level": 1, + "bbox": [ + 500, + 741, + 602, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Different Pre-Training Strategies. We pre-train our model with different datasets and summarize the results in Table 3. The first row shows the case without pre-training. The second shows the result for the model pre-trained on the KIT dataset (without Joint Shuffle augmentation). The third shows the result for the model pre-trained on KIT dataset (with Joint Shuffle). We observe our model can achieve better performance with Joint Shuffle, as it can synthesize large-scale mesh sequences.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1532", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f647d38b162dfc0335487ea282057d0349ee4687f602e7e2927cb54d502ed483.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTop-1 (%)
w/o pre-training64.03
pre-training w/o JS64.13
pre-training w/ JS65.59
", + "bbox": [ + 165, + 70, + 380, + 141 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/605ec4395a372dea48acf101f6154c981cd4611f9449ca0f579ec2ceb70089d6.jpg", + "table_caption": [ + "Table 3. Comparison of Different Pre-Training Strategies. JS stands for Joint Shuffle." + ], + "table_footnote": [], + "table_body": "
rPre-Train Loss (×104)Fine-Tune Accuracy (%)
0.10.3964.44
0.30.4164.55
0.50.4065.59
0.70.4364.19
0.90.4865.07
Rand0.4364.75
", + "bbox": [ + 83, + 188, + 460, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Effect of Different Masking Ratios.", + "bbox": [ + 138, + 311, + 403, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Masking Ratios. We investigate the impact of different masking ratios. We report the converged pretraining loss and the fine-tuning top-1 classification accuracy on the test set in Table 4. We also experiment with the random masking ratio in the last row. For each forward pass, we randomly select one masking ratio from 0.1 to 0.9 with step 0.1 to mimic flexible masked token length. The model with a random masking ratio does not outperform the best model that is pre-trained using a single ratio (i.e. 0.5). We observe that as the masking ratio increases, the pre-training loss mostly increases as the task becomes more challenging. However, a challenging self-supervised learning task does not necessarily lead to better performance. The model with a masking ratio of 0.7 and 0.9 have a high pre-train loss, while the fine-tune accuracy is not higher than the model with a 0.5 masking ratio. The conclusion is similar to the comparison of MVM and FFP training objectives, where a more challenging self-supervised learning task may not be optimal.", + "bbox": [ + 73, + 334, + 468, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different Number of Mesh Sequences for Pre-Training. We test the effect of different numbers of mesh sequences used in pre-training. We report the fine-tuning top-1 classification accuracy in Figure 4. We observe that a large number of pre-training data can bring substantial performance improvement. The proposed Joint Shuffle method can greatly enlarge the dataset size without any manual cost, and has the potential to further improve model performance.", + "bbox": [ + 75, + 640, + 467, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Experimental Results on Noisy Body Pose Estimations. Body pose estimation has been a popular research field [25, 27, 32], but how to leverage the estimated 3D meshes for downstream perception tasks has not been fully explored. We apply the state-of-the-art body pose estimation model VIBE [27] on videos of NTU RGB+D dataset to obtain 3D mesh sequences. Skeleton and point cloud representations are derived from the estimated meshes to train the baseline", + "bbox": [ + 75, + 779, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c09f51a55c6ee85e1e3c0641fd224994d6f4f50757f3dc29d1953c493b40c99.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 66, + 880, + 209 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8a9614245ba24ceb7dd73748a1c4816eb8e7234952d938b385183dd05bd64c68.jpg", + "table_caption": [ + "Figure 4. Effect of Different Number of Mesh Sequences." + ], + "table_footnote": [], + "table_body": "
MethodInputTop-1 (%)
2s-AGCN-FL [61]3D Skeleton58.67
2s-AGCN-CE [61]3D Skeleton57.49
CTR-GCN [7]3D Skeleton62.25
MS-G3D [37]3D Skeleton60.01
PSTNet [18]Point Cloud51.48
SequentialPointNet [30]Point Cloud60.60
P4Transformer [16]Point Cloud57.84
STEMT(Ours)Mesh64.04
", + "bbox": [ + 526, + 241, + 864, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Experimental results on body poses estimated by VIBE [27] on NTU RGB+D dataset. The skeleton, point cloud, and mesh representations are derived from the same noisy body estimations.", + "bbox": [ + 498, + 390, + 890, + 433 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "models (see Sup. Mat.). We report the results in Table 5. We observe that STMT can outperform the best skeleton-based and point cloud-based action recognition model by $1.79\\%$ and $3.44\\%$ respectively. This shows that STMT with meshes as input, is more robust to input noise compared to other state-of-the-art methods with 3D skeletons or point clouds as input.", + "bbox": [ + 498, + 445, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 570, + 617, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose a novel approach for MoCap-based action recognition. Unlike existing methods that rely on skeleton representation, our proposed model directly models the raw mesh sequences. Our method encodes both intrinsic and extrinsic features in vertex patches, and uses a hierarchical transformer to freely attend to any two vertex patches in the spatial and temporal domain. Moreover, two self-supervised learning tasks, namely Masked Vertex Modeling and Future Frame Prediction are proposed to enforce the model to learn global context. Our experiments show that STMT can outperform state-of-the-art skeleton-based and point-cloud-based models.", + "bbox": [ + 496, + 597, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 797, + 651, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-17-5-0003. 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Pervasive and Mobile Computing, 7(2):256-269, 2011. 1" + ], + "bbox": [ + 503, + 92, + 890, + 853 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1536", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/STMT_ A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition/ecec9e25-9648-4975-9559-d389674e900b_model.json b/2023/STMT_ A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition/ecec9e25-9648-4975-9559-d389674e900b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..48b339dd0fbdfd811fd7eb756229131c330a4629 --- /dev/null +++ b/2023/STMT_ A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition/ecec9e25-9648-4975-9559-d389674e900b_model.json @@ -0,0 +1,2433 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.23, + 0.131, + 0.744, + 0.177 + ], + "angle": 0, + "content": "STMT: A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.203, + 0.966, + 0.242 + ], + "angle": 0, + "content": "Xiaoyu Zhu\\(^{1}\\), Po-Yao Huang\\(^{2\\dagger}\\), Junwei Liang\\(^{3\\dagger}\\), Celso M. de Melo\\(^{4}\\), Alexander Hauptmann\\(^{1}\\) \n\\(^{1}\\)Carnegie Mellon University, \\(^{2}\\)FAIR, Meta AI, \\(^{3}\\)HKUST (Guangzhou), \\(^{4}\\)DEVCOM Army Research Laboratory" + }, + { + "type": "image", + "bbox": [ + 0.167, + 0.261, + 0.816, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.454, + 0.895, + 0.511 + ], + "angle": 0, + "content": "Figure 1. Current state-of-the-art MoCap-based action recognition methods first convert body markers into a human body mesh, which is used to predict a standardized 3D skeleton. The 3D skeleton is used as input for action recognition models (dashed line). We propose a method that directly models the dynamics of raw mesh sequences (solid line). Our method saves the manual effort to derive skeleton representation, and achieves superior recognition performance by leveraging surface motion and body shape knowledge from meshes." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.525, + 0.314, + 0.54 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.474, + 0.812 + ], + "angle": 0, + "content": "We study the problem of human action recognition using motion capture (MoCap) sequences. Unlike existing techniques that take multiple manual steps to derive standardized skeleton representations as model input, we propose a novel Spatial-Temporal Mesh Transformer (STMT) to directly model the mesh sequences. The model uses a hierarchical transformer with intra-frame off-set attention and inter-frame self-attention. The attention mechanism allows the model to freely attend between any two vertex patches to learn non-local relationships in the spatial-temporal domain. Masked vertex modeling and future frame prediction are used as two self-supervised tasks to fully activate the bi-directional and auto-regressive attention in our hierarchical transformer. The proposed method achieves state-of-the-art performance compared to skeleton-based and pointcloud-based models on common MoCap benchmarks. Code is available at https://github.com/zgzxy001/STMT." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.21, + 0.837 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.847, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Motion Capture (MoCap) is the process of digitally recording the human movement, which enables the fine" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.526, + 0.895, + 0.724 + ], + "angle": 0, + "content": "grained capture and analysis of human motions in 3D space [40, 50]. MoCap-based human perception serves as key elements for various research fields, such as action recognition [15, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. Besides, MoCap is one of the fundamental technologies to enhance human-robot interactions in various practical scenarios including hospitals and manufacturing environment [22, 28, 41, 43, 45, 77]. For example, Hayes [22] classified automotive assembly activities using MoCap data of humans and objects. Understanding human behaviors from MoCap data is fundamentally important for robotics perception, planning, and control." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Skeleton representations are commonly used to model MoCap sequences. Some early works [3, 29] directly used body markers and their connectivity relations to form a skeleton graph. However, the marker positions depend on each subject (person), which brings sample variances within each dataset. Moreover, different MoCap datasets usually have different numbers of body markers. For example, ACCAD [48], BioMotion [64], Eyes Japan [15], and KIT [42] have 82, 41, 37, and 50 body markers respectively. This prevents the model to be trained and tested on a unified framework. To use standard skeleton representa" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.216, + 0.9 + ], + "angle": 0, + "content": "\\(\\dagger\\)Equal Contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1526" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "tions such as NTU RGB+D [58], Punnakkal et al. [50] first used Mosh++ to fit body markers into SMPL-H meshes, and then predicted a 25-joint skeleton [33] from the mesh vertices [54]. Finally, a skeleton-based model [60] was used to perform action recognition. Although those methods achieved advanced performance, they have the following disadvantages. First, they require several manual steps to map the vertices from mesh to skeleton. Second, skeleton representations lose the information provided by original MoCap data (i.e., surface motion and body shape knowledge). To overcome those disadvantages, we propose a mesh-based action recognition method to directly model dynamic changes in raw mesh sequences, as illustrated in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.469 + ], + "angle": 0, + "content": "Though mesh representations provide fine-grained body information, it is challenging to classify high-dimensional mesh sequences into different actions. First, unlike structured 3D skeletons which have joint correspondence across frames, there is no vertex-level correspondence in meshes (i.e., the vertices are unordered). Therefore, the local connectivity of every single mesh can not be directly aggregated in the temporal dimension. Second, mesh representations encode local connectivity information, while action recognition requires global understanding in the whole spatial-temporal domain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.473, + 0.771 + ], + "angle": 0, + "content": "To overcome the aforementioned challenges, we propose a novel Spatial-Temporal Mesh Transformer (STMT). STMT leverages mesh connectivity information to build patches at the frame level, and uses a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. The hierarchical attention mechanism allows the model to learn patch correlation across the entire sequence, and alleviate the requirement of explicit vertex correspondence. We further define two self-supervised learning tasks, namely masked vertex modeling and future frame prediction, to enhance the global interactions among vertex patches. To reconstruct masked vertices of different body parts, the model needs to learn prior knowledge about the human body in the spatial dimension. To predict future frames, the model needs to understand meaningful surface movement in the temporal dimension. To this end, our hierarchical transformer pretrained with those two objectives can further learn spatial-temporal context across entire frames, which is beneficial for the downstream action recognition task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.472, + 0.833 + ], + "angle": 0, + "content": "We evaluate our model on common MoCap benchmark datasets. Our method achieves state-of-the-art performance compared to skeleton-based and point-cloud-based models. The contributions of this paper are three-fold:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "- We introduce a new hierarchical transformer architecture, which jointly encodes intrinsic and extrinsic representations, along with intra- and inter-frame attention, for spatial-temporal mesh modeling." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "- We design effective and efficient pretext tasks, namely masked vertex modeling and future frame prediction, to enable the model to learn from the spatial-temporal global context." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.165, + 0.894, + 0.21 + ], + "angle": 0, + "content": "- Our model achieves superior performance compared to state-of-the-art point-cloud and skeleton models on common MoCap benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.225, + 0.642, + 0.241 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.63 + ], + "angle": 0, + "content": "Action Recognition from Depth and Point Cloud. 3D action recognition models have achieved promising performance with depth [34, 55, 56, 68, 71] and point clouds [18, 36, 52, 70]. Depth provides reliable 3D structural and geometric information which characterizes informative human actions. In MVDI [71], dynamic images [4] were extracted through multi-view projections from depth videos for 3D action recognition. 3D-FCNN [55] directly exploited a 3D-CNN to model depth videos. Another popular category of 3D human action recognition is based on 3D point clouds. PointNet [51] and PointNet++ [52] are the pioneering works contributing towards permutation invariance of 3D point sets for representing 3D geometric structures. Along this avenue, MeteorNet [36] stacked multi-frame point clouds and aggregates local features for action recognition. 3DV [70] transferred point cloud sequences into regular voxel sets to characterize 3D motion compactly via temporal rank pooling. PSTNet [18] disentangled space and time to alleviate point-wise spatial variance across time. Action recognition has shown promising results with 3D skeletons and point clouds. Meshes, which are commonly used in representing human bodies and creating action sequences, have not been explored for the action recognition task. In this work, we propose the first mesh-based action recognition model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.897, + 0.903 + ], + "angle": 0, + "content": "MoCap-Based Action Recognition. Motion-capture (MoCap) datasets [15, 44, 46-48, 50, 57] serve as key elements for various research fields, such as action recognition [15, 44, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. MoCap-based action recognition was formulated as a skeleton-based action recognition problem [50]. Various architectures have been investigated to incorporate skeleton sequences. In [14, 35, 75], skeleton sequences were treated as time-series inputs to RNNs. [24, 69] respectively transformed skeleton sequences into spectral images and trajectory maps and then adopted CNNs for feature learning. In [72], Yan et al. leveraged GCN to model joint dependencies that can be naturally represented with a graph. In this paper, we propose a novel method to directly model the dynamics of raw mesh sequences which can benefit from surface motion and body shape knowledge." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1527" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.473, + 0.456 + ], + "angle": 0, + "content": "Masked Autoencoder. Masked autoencoder has gained attention in Natural Language Processing and Computer Vision to learn effective representations using auto-encoding. Stacked denoising autoencoders [66] treated masks as a noise type and used denoising autoencoders to denoise corrupted inputs. ViT [13] proposed a self-supervised pretraining task to reconstruct masked tokens. More recently, BEiT [2] proposed to learn visual representations by reconstructing the discrete tokens [53]. MAE [23] proposed a simple yet effective asymmetric framework for masked image modeling. In 3D point cloud analysis, Wang et al. [67] chose to first generate partial point clouds by calculating occlusion from random camera viewpoints, and then completed occluded point clouds using autoencoding. PointBERT [73] followed the success of BERT [12] to predict the masked tokens learned from points. However, applying self-supervised learning to temporal 3D sequences (i.e. point cloud, 3D skeleton) has not been fully explored. One probable reason is that self-supervised learning on high-dimensional 3D temporal sequences is computationally-expensive. In this work, we propose an effective and efficient self-supervised learning method based on masked vertex modeling and future frame prediction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.472, + 0.172, + 0.487 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.498, + 0.188, + 0.512 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.749 + ], + "angle": 0, + "content": "In this section, we describe our model for mesh-based action recognition, which we call STMT. The inputs of our model are temporal mesh sequences: \\(\\mathbf{M} = ((\\mathbf{P}_1,\\mathbf{A}_1),(\\mathbf{P}_2,\\mathbf{A}_2),\\dots ,(\\mathbf{P}_t,\\mathbf{A}_t))\\), where \\(t\\) is the frame number. \\(\\mathbf{P}_i\\in \\mathbb{R}^{N\\times 3}\\) represents the vertex positions in Cartesian coordinates, where \\(N\\) is the number of vertices. \\(\\mathbf{A}_i\\in \\mathbb{R}^{N\\times N}\\) represents the adjacency matrix of the mesh. Element \\(\\mathbf{A}_i^{mn}\\in \\mathbf{A}_i\\) is one when there is an edge from vertex \\(V_{m}\\) to vertex \\(V_{n}\\), and zero when there is no edge. The mesh representation with vertices and their adjacent matrix is a unified format for various body models such as SMPL [39], SMPL-H [54], and SMPL-X [49]. In this work, we use SMPL-H body models from AMASS [40] to obtain the mesh sequences, but our method can be easily adapted to other body models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Mesh's local connectivity provides fine-grained information. Previous methods [21, 59] proved that explicitly using surface (e.g., mesh) connectivity information can achieve higher accuracy in shape classification and segmentation tasks. However, classifying temporal mesh sequences is a more challenging problem, as there is no vertex-level correspondence across frames. This prevents graph-based models from directly aggregating vertices in the temporal dimension. Therefore, we propose to first leverage mesh connectivity information to build patches at the frame level," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "then use a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. In summary, it has the following key components:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.162, + 0.892, + 0.207 + ], + "angle": 0, + "content": "- Surface Field Convolution to form local vertex patches by considering both intrinsic and extrinsic mesh representations." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.216, + 0.892, + 0.247 + ], + "angle": 0, + "content": "- Hierarchical Spatial-Temporal Transformer to learn spatial-temporal correlations of vertex patches." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.255, + 0.892, + 0.285 + ], + "angle": 0, + "content": "- Self-Supervised Pre-Training to learn the global context in terms of appearance and motion." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.162, + 0.892, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.295, + 0.892, + 0.325 + ], + "angle": 0, + "content": "See Figure 2 for a high-level summary of the model, and the sections below for more details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.334, + 0.738, + 0.348 + ], + "angle": 0, + "content": "3.2. Surface Field Convolution" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.568 + ], + "angle": 0, + "content": "Because displacements in grid data are regular, traditional convolutions can directly learn a kernel for elements within a region. However, mesh vertices are unordered and irregular. Considering the special mesh representations, we represent each vertex by encoding features from its neighbor vertices inspired by [51,52]. To fully utilize meshes' local connectivity information, we consider the mesh properties of extrinsic curvature of submanifolds and intrinsic curvature of the manifold itself. Extrinsic curvature between two vertices is approximated using Euclidean distance. Intrinsic curvature is approximated using Geodesic distance, which is defined as the shortest path between two vertices on mesh surfaces. We propose a light-weighted surface field convolution to build local patches, which can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.578, + 0.907, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {V G} ^ {\\prime (x, y, z)} = \\sum_ {(\\delta_ {x}, \\delta_ {y}, \\delta_ {z}) \\in G (x, y, z)} \\boldsymbol {W} ^ {(\\delta_ {x}, \\delta_ {y}, \\delta_ {z})} \\cdot \\boldsymbol {F} ^ {(x + \\delta_ {x}, y + \\delta_ {y}, z + \\delta_ {z})} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.647, + 0.907, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {V E} ^ {\\prime (x, y, z)} = \\sum_ {(\\zeta_ {x}, \\zeta_ {y}, \\zeta_ {z}) \\in E (x, y, z)} \\boldsymbol {W} ^ {(\\zeta_ {x}, \\zeta_ {y}, \\zeta_ {z})} \\cdot \\boldsymbol {F} ^ {(x + \\zeta_ {x}, y + \\zeta_ {y}, z + \\zeta_ {z})} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.703, + 0.892, + 0.795 + ], + "angle": 0, + "content": "\\(G\\) and \\(E\\) is the local region around vertex \\((x,y,z)\\). In this paper, we use k-nearest-neighbor to sample local vertices. \\((\\delta_x,\\delta_y,\\delta_z)\\) and \\((\\zeta_x,\\zeta_y,\\zeta_z)\\) represent the spatial displacement in geodesic and euclidean space, respectively. \\(\\pmb{F}^{(x,y,z)}\\) denotes the feature of the vertex at position \\((x,y,z)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.874, + 0.818 + ], + "angle": 0, + "content": "3.3. Hierarchical Spatial-Temporal Transformer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We propose a hierarchical transformer that consists of intra-frame and inter-frame attention. The basic idea behind our transformer is three-fold: (1) Intra-frame attention can encode connectivity information from the adjacency matrix, while such information can not be directly" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1528" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.093, + 0.512, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.286, + 0.386, + 0.301 + ], + "angle": 0, + "content": "(a) STMT Architecture" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.096, + 0.887, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.286, + 0.782, + 0.302 + ], + "angle": 0, + "content": "(b) Pre-Training Stage" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.892, + 0.429 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed framework. (a) Overview of STMT. Given a mesh sequence, we first develop vertex patches by extracting both intrinsic (geodesic) and extrinsic (euclidean) features using surface field convolution. The intrinsic and extrinsic features are denoted by yellow and blue blocks respectively. Those patches are used as input to the intra-frame offset-attention network to learn appearance features. Then we concatenate intrinsic patches and extrinsic patches of the same position. The concatenated vertex patches (green blocks) are fed into the inter-frame self-attention network to learn spatial-temporal correlations. Finally, the local and global features are mapped into action predictions by MLP layers. (b) Overview of Pre-Training Stage. We design two pretext tasks: masked vertex modeling and future frame prediction for global context learning. Bidirectional attention is used for the reconstruction of masked vertices. Auto-regressive attention is used for the future frame prediction task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.469, + 0.52 + ], + "angle": 0, + "content": "aggregated in the temporal domain because vertices are unordered. (2) Frame-level offset-attention can be used to mimic the Laplacian operator to learn effective spatial representations. (3) Inter-frame self-attention can learn feature correlations in the spatial-temporal domain." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.542, + 0.338, + 0.556 + ], + "angle": 0, + "content": "3.3.1 Intra-Frame Offset-Attention" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.469, + 0.716 + ], + "angle": 0, + "content": "Graph convolution networks [6] show the benefits of using a Laplacian matrix \\(\\mathbf{L} = \\mathbf{D} - \\mathbf{E}\\) to replace the adjacency matrix \\(\\mathbf{E}\\), where \\(\\mathbf{D}\\) is the diagonal degree matrix. Inspired by this, offset-attention has been proposed and achieved superior performance in point-cloud classification and segmentation tasks [20]. We adapt offset-attention to attend to vertex patches. Specifically, the offset-attention layer calculates the offset (difference) between the self-attention (SA) features and the input features by element-wise subtraction. Offset-attention is denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.732, + 0.469, + 0.747 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {\\text {o u t}} = O A \\left(\\boldsymbol {F} _ {\\text {i n}}\\right) = \\phi \\left(\\boldsymbol {F} _ {\\text {i n}} - \\boldsymbol {F} _ {\\text {s a}}\\right) + \\boldsymbol {F} _ {\\text {i n}}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.761, + 0.469, + 0.866 + ], + "angle": 0, + "content": "where \\(\\phi\\) denotes a non-linear operator. \\(F_{in} - F_{sa}\\) is proved to be analogous to discrete Laplacian operator [20], i.e. \\(F_{in} - F_{sa} \\approx LF_{in}\\). As Laplacian operators in geodesic and euclidean space are expected to be different, we propose to use separate transformers to model intrinsic patches and extrinsic patches. Specifically, the aggregated feature for vertex \\(V\\) is denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.882, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {V} ^ {\\prime (x, y, z)} = O A _ {G} \\left(\\boldsymbol {F} _ {V G} ^ {\\prime (x, y, z)}\\right) \\oplus O A _ {E} \\left(\\boldsymbol {F} _ {V E} ^ {\\prime (x, y, z)}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.441, + 0.892, + 0.509 + ], + "angle": 0, + "content": "Here \\(F_{VG}^{\\prime (x,y,z)}\\in \\mathbb{R}^{N\\times d_g}\\) and \\(F_{VE}^{\\prime (x,y,z)}\\in \\mathbb{R}^{N\\times d_e}\\) are local patches learned using Equ. 1 and Equ. 2. \\(F_V^{\\prime (x,y,z)}\\in\\) \\(\\mathbb{R}^{N\\times d}\\) denotes the local patch for position \\((x,y,z)\\), where \\(d = d_{g} + d_{e}\\). The weights of \\(OA_{G}\\) and \\(OA_{E}\\) are not shared." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.527, + 0.743, + 0.541 + ], + "angle": 0, + "content": "3.3.2 Inter-Frame Self-Attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Given \\(F_V'\\) which encodes local connectivity information, we use self-attention (SA) [65] to learn semantic affinities between different vertex patches across frames. Specifically, let \\(\\mathbf{Q},\\mathbf{K},\\mathbf{V}\\) be the query, key and value, which are generated by applying linear transformations to the input features \\(F_V' \\in \\mathbb{R}^{N \\times d}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.654, + 0.816, + 0.671 + ], + "angle": 0, + "content": "\\[\n(\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}) = F _ {V} ^ {\\prime} \\cdot (\\boldsymbol {W} _ {q}, \\boldsymbol {W} _ {k}, \\boldsymbol {W} _ {v})\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.673, + 0.819, + 0.691 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Q}, \\boldsymbol {K} \\in \\mathbb {R} ^ {N \\times d _ {a}}, \\quad \\boldsymbol {V} \\in \\mathbb {R} ^ {N \\times d}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.694, + 0.891, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {W} _ {q}, \\boldsymbol {W} _ {k} \\in \\mathbb {R} ^ {d \\times d _ {a}}, \\quad \\boldsymbol {W} _ {v} \\in \\mathbb {R} ^ {d \\times d} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.725, + 0.892, + 0.784 + ], + "angle": 0, + "content": "where \\( W_{q} \\), \\( W_{k} \\) and \\( W_{v} \\) are the shared learnable linear transformation, and \\( d_{a} \\) is the dimension of the query and key vectors. Then we can use the query and key matrices to calculate the attention weights via the matrix dot-product:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.785, + 0.891, + 0.821 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {A} = (\\tilde {\\alpha}) _ {i, j} = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\cdot \\boldsymbol {K} ^ {\\mathrm {T}}}{\\sqrt {d _ {a}}}\\right). \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.649, + 0.832, + 0.891, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {F} _ {s a} = \\boldsymbol {A} \\cdot \\boldsymbol {V} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The self-attention output features \\( F_{sa} \\) are the weighted sums of the value vector using the corresponding attention weights. Specifically, for a vertex patch in position \\( (x,y,z) \\)," + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1529" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.155 + ], + "angle": 0, + "content": "its aggregated feature after inter-frame self-attention can be computed as: \\( \\pmb{F}_{sa}^{(x,y,z)} = \\sum \\pmb{A}^{(x,y,z),(x',y',z')} \\times \\pmb{V}^{(x',y',z')} \\), where \\( (x',y',z') \\) belongs to the Cartesian coordinates of \\( \\pmb{F}_V' \\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.165, + 0.338, + 0.182 + ], + "angle": 0, + "content": "3.4. Self-Supervised Pre-Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.189, + 0.473, + 0.583 + ], + "angle": 0, + "content": "Self-supervised learning has achieved remarkable results on large-scale image datasets [23]. However, self-supervised learning for temporal 3D sequences (i.e. point cloud, 3D skeleton) remains to be challenging and has not been fully explored. There are two possible reasons: (1) self-supervised learning methods rely on large-scale datasets to learn meaningful patterns [10]. However, existing MoCap benchmarks are relatively small compared to 2D datasets like ImageNet [11]. (2) Self-supervised learning for 3D data sequences is computationally expensive in terms of memory and speed. In this work, we first propose a simple and effective method to augment existing MoCap sequences, and then define two effective and efficient self-supervised learning tasks, namely masked vertex modeling and future frame prediction, which enable the model to learn global context. The work that is close to us is OcCO [67], which proposed to use occluded point cloud reconstruction as the pretext task. OcCO has a computationally-expensive process to generate occlusions, including point cloud projection, occluded point calculation, and a mapping step to convert camera frames back to world frames. Different from OcCO, we randomly mask vertex patches or future frames on the fly, which saves the pre-processing step. Moreover, our pre-training method is designed for temporal mesh sequences and considers both bi-directional and autoregressive attention." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.602, + 0.421, + 0.618 + ], + "angle": 0, + "content": "3.4.1 Data Augmentation through Joint Shuffle" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.473, + 0.905 + ], + "angle": 0, + "content": "Considering the flexibility of SMPL-H representations, we propose a simple yet effective approach to augment SMPL-H sequences by shuffling body pose parameters. Specifically, we split SMPL-H pose parameters into five body parts: bone, left/right arm, and left/right leg. We use \\( I_{bone}, I_{leg}^{left}, I_{leg}^{right}, I_{arm}^{left}, I_{arm}^{right} \\) to denote the SMPL-H pose indexes of the five body parts. Then we synthesize new sequences by randomly selecting body parts from five different sequences. We keep the temporal order for each part such that the merged action sequences have meaningful motion trajectories. Pseudocode for the joint shuffle is provided in Algorithm 1. The input to Joint Shuffle are SMPL-H pose parameters \\( \\theta \\in \\mathbb{R}^{b \\times t \\times n \\times 3} \\), where \\( b \\) is the sequence number, \\( t \\) is the frame number, and \\( n \\) is the joint number. We randomly select the shape \\( \\beta \\) and dynamic parameters \\( \\phi \\) from one of the five SMPL-H sequences to compose a new SMPL-H body model. Given \\( b \\) SMPL-H sequences, we can synthesize \\( {}^b C_5 = \\frac{b!}{5!(b - 5)!} \\) number of new sequences." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "We prove that the model can benefit from large-scale pretraining in Section 4.6." + }, + { + "type": "code_caption", + "bbox": [ + 0.512, + 0.128, + 0.84, + 0.141 + ], + "angle": 0, + "content": "Algorithm 1: Pseudocode of STMT Joint Shuffle" + }, + { + "type": "algorithm", + "bbox": [ + 0.529, + 0.144, + 0.912, + 0.363 + ], + "angle": 0, + "content": "1: function STMT JOINT SHUFFLE( \\(\\theta \\in\\) \\(\\mathbb{R}^{b\\times t\\times n\\times 3}\\) \\(I_{\\mathrm{bone}},I_{\\mathrm{leg}}^{\\mathrm{left}},I_{\\mathrm{leg}}^{\\mathrm{right}},I_{\\mathrm{arm}}^{\\mathrm{left}},I_{\\mathrm{arm}}^{\\mathrm{right}})\\) \n2: \\(\\theta_s\\gets\\) random_sample(0,5) \\(\\triangleright \\theta_s\\in \\mathbb{R}^{5\\times t\\times n\\times 3}\\) randomly sample five SMPL-H sequences \n3: \\(t_{max}\\gets\\) get_max_length( \\(\\theta_{s})\\) compute the maximum sequence length in \\(\\theta_{s}\\) \n4: \\(\\theta_{new}\\gets\\) Initialize \\((t_{max},n,3)\\) \n5: \\(P\\gets \\{I_{\\mathrm{bone}},I_{\\mathrm{leg}}^{\\mathrm{left}},I_{\\mathrm{leg}}^{\\mathrm{right}},I_{\\mathrm{arm}}^{\\mathrm{left}},I_{\\mathrm{arm}}^{\\mathrm{right}}\\}\\) \n6: for i in 0,1,2,3,4 do \n7: \\(\\theta_s\\gets\\) repeat \\((\\theta_s[i],(t_{max},n,3))\\) pad each sequence to the max length using repeating \n8: \\(\\theta_{new}[P[i]]\\gets \\theta_s[i][P[i]]\\triangleright\\) assign the body-part sequence \n9: return \\(\\theta_{new}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.388, + 0.892, + 0.417 + ], + "angle": 0, + "content": "3.4.2 Masked Vertex Modeling with Bi-Directional Attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.895, + 0.625 + ], + "angle": 0, + "content": "To fully activate the inter-frame bi-directional attention in the transformer, we design a self-supervised pretext task named Masked Vertex Modeling (MVM). The model can learn human prior information in the spatial dimension by reconstructing masked vertices of different body parts. We randomly mask \\( r \\) percentages of the input vertex patches, and force the model to reconstruct the full sequences. Moreover, we use bi-directional attention to learn correlations among all remaining local patches. Each patch will attend to all patches in the entire sequence. It models the joint distribution of vertex patches over the whole temporal sequences \\( x \\) as the following product of conditional distributions, where \\( x_{i} \\) is a single vertex patch:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.627, + 0.892, + 0.668 + ], + "angle": 0, + "content": "\\[\np (x) = \\prod_ {i = 1} ^ {N} p \\left(x _ {i} \\mid x _ {1},.., x _ {i}, \\dots , x _ {N}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.894, + 0.75 + ], + "angle": 0, + "content": "Where \\( N \\) is the number of patches in the entire sequence \\( x \\) after masking. Every patch will attend to all patches in the entire sequence. In this way, bi-directional attention is fully-activated to learn spatial-temporal features that can accurately reconstruct completed mesh sequences." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.77, + 0.892, + 0.8 + ], + "angle": 0, + "content": "3.4.3 Future Frame Prediction with Auto-Regressive Attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "The masked vertex modeling task is to reconstruct masked vertices in different body parts. The model can reconstruct completed mesh sequences if it captures the human body prior or can make a movement inference from nearby frames. As action recognition requires the model to understand the global context, we propose the future frame" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1530" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.289 + ], + "angle": 0, + "content": "prediction (FFP) task. Specifically, we mask out all the future frames and force the transformer to predict the masked frames. Moreover, we propose to use auto-regressive attention for the future frame prediction task, inspired by language generation models like GPT-3 [5]. However, directly using RNN-based models [9] in GPT-3 to predict future frames one by one is inefficient, as 3D mesh sequences are denser compared to language sequences. Therefore, we propose to reconstruct all future frames in a single forward pass. For auto-regressive attention, we model the joint distribution of vertex patches over a mesh sequence \\( x \\) as the following product of conditional distributions, where \\( x_{i} \\) is a single patch at frame \\( t_{i} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.298, + 0.47, + 0.34 + ], + "angle": 0, + "content": "\\[\np (x) = \\prod_ {i = 1} ^ {N} p \\left(x _ {i} \\mid x _ {1}, x _ {2}, \\dots , x _ {M}\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.351, + 0.473, + 0.457 + ], + "angle": 0, + "content": "Where \\( N \\) is the number of patches in the entire sequence \\( x \\) after masking. \\( M = (t_i - 1) \\times n \\), where \\( n \\) is the number of patches in a single frame. Each vertex patch depends on all patches that are temporally before it. The auto-regressive attention enables the model to predict movement patterns and trajectories, which is beneficial for the downstream action recognition task." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.474, + 0.182, + 0.49 + ], + "angle": 0, + "content": "3.5. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.622 + ], + "angle": 0, + "content": "In the pre-training stage, we use PCN [74] as the decoder to reconstruct masked vertices and predict future frames. The decoder is shared for the two pretext tasks. Since mesh vertices are unordered, the reconstruction loss and future prediction loss should be permutation-invariant. Therefore, we use Chamfer Distance (CD) as the loss function to measure the difference between the model predictions and ground truth mesh sequences." + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.63, + 0.47, + 0.723 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} C D (M _ {p r e d}, M _ {g t}) = \\frac {1}{\\left| M _ {p r e d} \\right|} \\sum_ {x \\in M _ {p r e d}} \\min _ {y \\in M _ {g t}} \\| x - y \\| _ {2} + \\\\ \\frac {1}{| M _ {g t} |} \\sum_ {y \\in M _ {g t}} \\min _ {x \\in M _ {p r e d}} \\| y - x \\| _ {2} \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.802 + ], + "angle": 0, + "content": "CD (10) calculates the average closest euclidean distance between the predicted mesh sequences \\( M_{pred} \\) and the ground truth sequences \\( M_{gt} \\). The overall loss is a weighted sum of masked vertex reconstruction loss and future frame prediction loss:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.817, + 0.469, + 0.838 + ], + "angle": 0, + "content": "\\[\nL = \\lambda_ {1} C D \\left(M _ {p r e d} ^ {M V M}, M _ {g t}\\right) + \\lambda_ {2} C D \\left(M _ {p r e d} ^ {F F P}, M _ {g t}\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In the fine-tuning stage, we replace the PCN decoder with an MLP head. Cross-entropy loss is used for model training." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.625, + 0.108 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.603, + 0.13 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Following previous MoCap-based action recognition methods [50,63], we evaluate our model on the most widely used benchmarks: KIT [42] and BABEL [50]. KIT is one of the largest MoCap datasets. It has 56 classes with 6,570 sequences in total. (2) BABEL is the largest 3D MoCap dataset that unifies 15 different datasets. BABEL has 43 hours of MoCap data performed by over 346 subjects. We use the 60-class subset from BABEL, which contains 21,653 sequences with single-class labels. We randomly split each dataset into training, test, and validation set, with ratios of \\(70\\%\\), \\(15\\%\\), and \\(15\\%\\), respectively. Note that existing action recognition datasets with skeletons only are not suitable for our experiments, as they do not provide full 3D surfaces or SMPL parameters to obtain the mesh representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.892, + 0.641 + ], + "angle": 0, + "content": "Motion Representation. Both KIT and BABEL's MoCap sequences are obtained from AMASS dataset in SMPL-H format. A MoCap sequence is an array of pose parameters over time, along with the shape and dynamic parameters. For skeleton-based action recognition, we follow previous work [50] which predicted the 25-joint skeleton from the vertices of the SMPL-H mesh. The movement sequence is represented as \\(\\mathbf{X} = (\\mathbf{x}_1,\\dots ,\\mathbf{x}_L)\\), where \\(\\mathbf{x}_i\\in \\mathbb{R}^{J\\times 3}\\) represents the position of the \\(J\\) joints in the skeleton in Cartesian coordinates. For point-cloud-based action recognition, we directly use the vertices of SMPL-H model as the model input. The point-cloud sequence is represented as \\(\\mathbf{P} = (\\mathbf{p}_1,\\dots ,\\mathbf{p}_L)\\), where \\(\\mathbf{p}_i\\in \\mathbb{R}^{V\\times 3}\\), and \\(V\\) is the number of vertices. For mesh-based action recognition, we represent the motion as a series of mesh vertices and their adjacent matrix over time, as introduced in Section 3.1. See Sup. Mat. for more details about datasets and pre-processing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.671, + 0.664 + ], + "angle": 0, + "content": "4.2. Baseline Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We compare our model with state-of-the-art 3D skeleton-based and point cloud-based action recognition models, as there is no existing literature on mesh-based action recognition. 2s-AGCN [61], CTR-GCN [7], and MS-G3D [37] are used as skeleton-based baselines. Among those methods, 2s-AGCN trained with focal loss and cross-entropy loss are used as benchmark methods in the BABEL dataset [50]. For the comparison with point-cloud baselines, we choose PSTNet [18], SequentialPointNet [30], and P4Transformer [16]. Those methods achieved top performance on common point-cloud-based action recognition benchmarks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.719, + 0.864 + ], + "angle": 0, + "content": "4.3. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For skeleton-based baselines, we use the official implementations of 2s-ACGN, CTR-GCN, and MS-G3D from" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1531" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.154, + 0.071, + 0.822, + 0.232 + ], + "angle": 0, + "content": "
MethodInputKITBABEL-60
Top-1 (%)Top-5 (%)Top-1 (%)Top-5 (%)
2s-AGCN-FL [61] (CVPR'19)3D Skeleton42.4475.6049.6279.12
2s-AGCN-CE [61] (CVPR'19)3D Skeleton57.4681.5463.5786.77
CTR-GCN [7] (ICCV'21)3D Skeleton64.6587.9067.3088.50
MS-G3D [37] (CVPR'20)3D Skeleton65.3887.9067.4387.99
PSTNet [18] (ICLR'21)Point Cloud56.9388.2161.9484.11
SequentialPointNet [30] (arXiv'21)Point Cloud59.7588.0162.9284.58
P4Transformer [16] (CVPR'21)Point Cloud62.1588.0163.5486.55
STMT(Ours)Mesh65.5990.0967.6588.68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.306, + 0.24, + 0.663, + 0.254 + ], + "angle": 0, + "content": "Table 1. Experimental Results on KIT and BABEL Dataset." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.258, + 0.48, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.5 + ], + "angle": 0, + "content": "Figure 3. Visualization of inter-frame attention. Red denotes the highest attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.633 + ], + "angle": 0, + "content": "[62], [8], and [38]. For point-cloud-based baselines, we use the official implementations of PSTNet, SequentialPointNet, P4Transformer from [19], [31], and [17]. We pre-train STMT for 200 epochs with a batch size of 32. The model is fine-tuned for 50 epochs with a batch size of 64. Adam optimizer [26] is used with a learning rate of 0.0001 for both pre-training and fine-tuning. See Sup. Mat. for more implementation details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.648, + 0.216, + 0.663 + ], + "angle": 0, + "content": "4.4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Comparison with State-of-the-Art Methods. As indicated in Table 1, STMT outperforms all other state-of-the-art models. Our model can outperform point-cloud-based models by \\(3.44\\%\\) and \\(4.11\\%\\) on KIT and BABEL datasets in terms of top-1 accuracy. Moreover, compared to skeleton-based methods which involve manual efforts to convert mesh vertices to skeleton representations, our model achieves better performance by directly modeling the dynamics of raw mesh sequences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We visualize the inter-frame attention weights of our hierarchical transformer in Figure 3. We observe that the model can pay attention to key regions across frames. This supports the intuition that our hierarchical transformer can take the place of explicit vertex tracking by learning spatial-temporal correlations." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.261, + 0.86, + 0.361 + ], + "angle": 0, + "content": "
IntrinsicExtrinsicMVMFFPTop-1 (%)
✓63.40
✓✓64.03
✓✓✓64.96
✓✓✓64.13
✓✓✓✓65.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.371, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Table 2. Performance of ablated versions. Intrinsic and Extrinsic stand for the intrinsic (geodesic) and extrinsic (euclidean) features in surface field convolution. MVM stands for Masked Vertex Modelling. FFP stands for Future Frame Prediction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.438, + 0.654, + 0.455 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.893, + 0.734 + ], + "angle": 0, + "content": "Ablation Study of STMT. We test various ablations of our model on the KIT dataset to substantiate our design decisions. We report the results in Table 2. Note that Joint Shuffle is used in all of the self-supervised learning experiments (last three rows). We observe that each component of our model gains consistent improvements. The comparison of the first two rows proves the effectiveness of encoding both intrinsic and extrinsic features in vertex patches. Comparing the last three rows with the second row, we observe a consistent improvement using self-supervised pretraining. Moreover, the downstream task can achieve better performance with MVM compared to FFP. One probable reason is that the single task for future frame prediction is more challenging than masked vertex modeling, as the model can only see the person movement in the past. The model can achieve the best performance with both MVM and FFP, which demonstrates that the two self-supervised tasks are supplementary to each other." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.603, + 0.759 + ], + "angle": 0, + "content": "4.6. Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Different Pre-Training Strategies. We pre-train our model with different datasets and summarize the results in Table 3. The first row shows the case without pre-training. The second shows the result for the model pre-trained on the KIT dataset (without Joint Shuffle augmentation). The third shows the result for the model pre-trained on KIT dataset (with Joint Shuffle). We observe our model can achieve better performance with Joint Shuffle, as it can synthesize large-scale mesh sequences." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1532" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.166, + 0.071, + 0.382, + 0.142 + ], + "angle": 0, + "content": "
MethodTop-1 (%)
w/o pre-training64.03
pre-training w/o JS64.13
pre-training w/ JS65.59
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.153, + 0.468, + 0.181 + ], + "angle": 0, + "content": "Table 3. Comparison of Different Pre-Training Strategies. JS stands for Joint Shuffle." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.189, + 0.462, + 0.302 + ], + "angle": 0, + "content": "
rPre-Train Loss (×104)Fine-Tune Accuracy (%)
0.10.3964.44
0.30.4164.55
0.50.4065.59
0.70.4364.19
0.90.4865.07
Rand0.4364.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.313, + 0.405, + 0.327 + ], + "angle": 0, + "content": "Table 4. Effect of Different Masking Ratios." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.335, + 0.47, + 0.623 + ], + "angle": 0, + "content": "Different Masking Ratios. We investigate the impact of different masking ratios. We report the converged pretraining loss and the fine-tuning top-1 classification accuracy on the test set in Table 4. We also experiment with the random masking ratio in the last row. For each forward pass, we randomly select one masking ratio from 0.1 to 0.9 with step 0.1 to mimic flexible masked token length. The model with a random masking ratio does not outperform the best model that is pre-trained using a single ratio (i.e. 0.5). We observe that as the masking ratio increases, the pre-training loss mostly increases as the task becomes more challenging. However, a challenging self-supervised learning task does not necessarily lead to better performance. The model with a masking ratio of 0.7 and 0.9 have a high pre-train loss, while the fine-tune accuracy is not higher than the model with a 0.5 masking ratio. The conclusion is similar to the comparison of MVM and FFP training objectives, where a more challenging self-supervised learning task may not be optimal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.468, + 0.763 + ], + "angle": 0, + "content": "Different Number of Mesh Sequences for Pre-Training. We test the effect of different numbers of mesh sequences used in pre-training. We report the fine-tuning top-1 classification accuracy in Figure 4. We observe that a large number of pre-training data can bring substantial performance improvement. The proposed Joint Shuffle method can greatly enlarge the dataset size without any manual cost, and has the potential to further improve model performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Experimental Results on Noisy Body Pose Estimations. Body pose estimation has been a popular research field [25, 27, 32], but how to leverage the estimated 3D meshes for downstream perception tasks has not been fully explored. We apply the state-of-the-art body pose estimation model VIBE [27] on videos of NTU RGB+D dataset to obtain 3D mesh sequences. Skeleton and point cloud representations are derived from the estimated meshes to train the baseline" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.067, + 0.882, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.524, + 0.213, + 0.868, + 0.228 + ], + "angle": 0, + "content": "Figure 4. Effect of Different Number of Mesh Sequences." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.242, + 0.866, + 0.38 + ], + "angle": 0, + "content": "
MethodInputTop-1 (%)
2s-AGCN-FL [61]3D Skeleton58.67
2s-AGCN-CE [61]3D Skeleton57.49
CTR-GCN [7]3D Skeleton62.25
MS-G3D [37]3D Skeleton60.01
PSTNet [18]Point Cloud51.48
SequentialPointNet [30]Point Cloud60.60
P4Transformer [16]Point Cloud57.84
STEMT(Ours)Mesh64.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.391, + 0.892, + 0.434 + ], + "angle": 0, + "content": "Table 5. Experimental results on body poses estimated by VIBE [27] on NTU RGB+D dataset. The skeleton, point cloud, and mesh representations are derived from the same noisy body estimations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.446, + 0.892, + 0.552 + ], + "angle": 0, + "content": "models (see Sup. Mat.). We report the results in Table 5. We observe that STMT can outperform the best skeleton-based and point cloud-based action recognition model by \\(1.79\\%\\) and \\(3.44\\%\\) respectively. This shows that STMT with meshes as input, is more robust to input noise compared to other state-of-the-art methods with 3D skeletons or point clouds as input." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.571, + 0.618, + 0.587 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In this work, we propose a novel approach for MoCap-based action recognition. Unlike existing methods that rely on skeleton representation, our proposed model directly models the raw mesh sequences. Our method encodes both intrinsic and extrinsic features in vertex patches, and uses a hierarchical transformer to freely attend to any two vertex patches in the spatial and temporal domain. Moreover, two self-supervised learning tasks, namely Masked Vertex Modeling and Future Frame Prediction are proposed to enforce the model to learn global context. Our experiments show that STMT can outperform state-of-the-art skeleton-based and point-cloud-based models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.652, + 0.816 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.903 + ], + "angle": 0, + "content": "This work was supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-17-5-0003. This work used Bridges-2 GPU resources provided by PSC through allocation CIS220012 from the ACCESS program." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1533" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[1] Felix Achilles, Alexandru-Eugen Ichim, Huseyin Coskun, Federico Tombari, Soheyl Noahtar, and Nassir Navab. Patient mocap: Human pose estimation under blanket occlusion for hospital monitoring applications. In International conference on medical image computing and computer-assisted intervention, pages 491-499. Springer, 2016. 1, 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.203, + 0.472, + 0.243 + ], + "angle": 0, + "content": "[2] Hangbo Bao, Li Dong, and Furu Wei. 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Current state-of-the-art MoCap-based action recognition methods first convert body markers into a human body mesh, which is used to predict a standardized 3D skeleton. The 3D skeleton is used as input for action recognition models (dashed line). We propose a method that directly models the dynamics of raw mesh sequences (solid line). Our method saves the manual effort to derive skeleton representation, and achieves superior recognition performance by leveraging surface motion and body shape knowledge from meshes. + +# Abstract + +We study the problem of human action recognition using motion capture (MoCap) sequences. Unlike existing techniques that take multiple manual steps to derive standardized skeleton representations as model input, we propose a novel Spatial-Temporal Mesh Transformer (STMT) to directly model the mesh sequences. The model uses a hierarchical transformer with intra-frame off-set attention and inter-frame self-attention. The attention mechanism allows the model to freely attend between any two vertex patches to learn non-local relationships in the spatial-temporal domain. Masked vertex modeling and future frame prediction are used as two self-supervised tasks to fully activate the bi-directional and auto-regressive attention in our hierarchical transformer. The proposed method achieves state-of-the-art performance compared to skeleton-based and pointcloud-based models on common MoCap benchmarks. Code is available at https://github.com/zgzxy001/STMT. + +# 1. Introduction + +Motion Capture (MoCap) is the process of digitally recording the human movement, which enables the fine + +grained capture and analysis of human motions in 3D space [40, 50]. MoCap-based human perception serves as key elements for various research fields, such as action recognition [15, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. Besides, MoCap is one of the fundamental technologies to enhance human-robot interactions in various practical scenarios including hospitals and manufacturing environment [22, 28, 41, 43, 45, 77]. For example, Hayes [22] classified automotive assembly activities using MoCap data of humans and objects. Understanding human behaviors from MoCap data is fundamentally important for robotics perception, planning, and control. + +Skeleton representations are commonly used to model MoCap sequences. Some early works [3, 29] directly used body markers and their connectivity relations to form a skeleton graph. However, the marker positions depend on each subject (person), which brings sample variances within each dataset. Moreover, different MoCap datasets usually have different numbers of body markers. For example, ACCAD [48], BioMotion [64], Eyes Japan [15], and KIT [42] have 82, 41, 37, and 50 body markers respectively. This prevents the model to be trained and tested on a unified framework. To use standard skeleton representa + +tions such as NTU RGB+D [58], Punnakkal et al. [50] first used Mosh++ to fit body markers into SMPL-H meshes, and then predicted a 25-joint skeleton [33] from the mesh vertices [54]. Finally, a skeleton-based model [60] was used to perform action recognition. Although those methods achieved advanced performance, they have the following disadvantages. First, they require several manual steps to map the vertices from mesh to skeleton. Second, skeleton representations lose the information provided by original MoCap data (i.e., surface motion and body shape knowledge). To overcome those disadvantages, we propose a mesh-based action recognition method to directly model dynamic changes in raw mesh sequences, as illustrated in Figure 1. + +Though mesh representations provide fine-grained body information, it is challenging to classify high-dimensional mesh sequences into different actions. First, unlike structured 3D skeletons which have joint correspondence across frames, there is no vertex-level correspondence in meshes (i.e., the vertices are unordered). Therefore, the local connectivity of every single mesh can not be directly aggregated in the temporal dimension. Second, mesh representations encode local connectivity information, while action recognition requires global understanding in the whole spatial-temporal domain. + +To overcome the aforementioned challenges, we propose a novel Spatial-Temporal Mesh Transformer (STMT). STMT leverages mesh connectivity information to build patches at the frame level, and uses a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. The hierarchical attention mechanism allows the model to learn patch correlation across the entire sequence, and alleviate the requirement of explicit vertex correspondence. We further define two self-supervised learning tasks, namely masked vertex modeling and future frame prediction, to enhance the global interactions among vertex patches. To reconstruct masked vertices of different body parts, the model needs to learn prior knowledge about the human body in the spatial dimension. To predict future frames, the model needs to understand meaningful surface movement in the temporal dimension. To this end, our hierarchical transformer pretrained with those two objectives can further learn spatial-temporal context across entire frames, which is beneficial for the downstream action recognition task. + +We evaluate our model on common MoCap benchmark datasets. Our method achieves state-of-the-art performance compared to skeleton-based and point-cloud-based models. The contributions of this paper are three-fold: + +- We introduce a new hierarchical transformer architecture, which jointly encodes intrinsic and extrinsic representations, along with intra- and inter-frame attention, for spatial-temporal mesh modeling. + +- We design effective and efficient pretext tasks, namely masked vertex modeling and future frame prediction, to enable the model to learn from the spatial-temporal global context. + +- Our model achieves superior performance compared to state-of-the-art point-cloud and skeleton models on common MoCap benchmarks. + +# 2. Related Work + +Action Recognition from Depth and Point Cloud. 3D action recognition models have achieved promising performance with depth [34, 55, 56, 68, 71] and point clouds [18, 36, 52, 70]. Depth provides reliable 3D structural and geometric information which characterizes informative human actions. In MVDI [71], dynamic images [4] were extracted through multi-view projections from depth videos for 3D action recognition. 3D-FCNN [55] directly exploited a 3D-CNN to model depth videos. Another popular category of 3D human action recognition is based on 3D point clouds. PointNet [51] and PointNet++ [52] are the pioneering works contributing towards permutation invariance of 3D point sets for representing 3D geometric structures. Along this avenue, MeteorNet [36] stacked multi-frame point clouds and aggregates local features for action recognition. 3DV [70] transferred point cloud sequences into regular voxel sets to characterize 3D motion compactly via temporal rank pooling. PSTNet [18] disentangled space and time to alleviate point-wise spatial variance across time. Action recognition has shown promising results with 3D skeletons and point clouds. Meshes, which are commonly used in representing human bodies and creating action sequences, have not been explored for the action recognition task. In this work, we propose the first mesh-based action recognition model. + +MoCap-Based Action Recognition. Motion-capture (MoCap) datasets [15, 44, 46-48, 50, 57] serve as key elements for various research fields, such as action recognition [15, 44, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. MoCap-based action recognition was formulated as a skeleton-based action recognition problem [50]. Various architectures have been investigated to incorporate skeleton sequences. In [14, 35, 75], skeleton sequences were treated as time-series inputs to RNNs. [24, 69] respectively transformed skeleton sequences into spectral images and trajectory maps and then adopted CNNs for feature learning. In [72], Yan et al. leveraged GCN to model joint dependencies that can be naturally represented with a graph. In this paper, we propose a novel method to directly model the dynamics of raw mesh sequences which can benefit from surface motion and body shape knowledge. + +Masked Autoencoder. Masked autoencoder has gained attention in Natural Language Processing and Computer Vision to learn effective representations using auto-encoding. Stacked denoising autoencoders [66] treated masks as a noise type and used denoising autoencoders to denoise corrupted inputs. ViT [13] proposed a self-supervised pretraining task to reconstruct masked tokens. More recently, BEiT [2] proposed to learn visual representations by reconstructing the discrete tokens [53]. MAE [23] proposed a simple yet effective asymmetric framework for masked image modeling. In 3D point cloud analysis, Wang et al. [67] chose to first generate partial point clouds by calculating occlusion from random camera viewpoints, and then completed occluded point clouds using autoencoding. PointBERT [73] followed the success of BERT [12] to predict the masked tokens learned from points. However, applying self-supervised learning to temporal 3D sequences (i.e. point cloud, 3D skeleton) has not been fully explored. One probable reason is that self-supervised learning on high-dimensional 3D temporal sequences is computationally-expensive. In this work, we propose an effective and efficient self-supervised learning method based on masked vertex modeling and future frame prediction. + +# 3. Method + +# 3.1. Overview + +In this section, we describe our model for mesh-based action recognition, which we call STMT. The inputs of our model are temporal mesh sequences: $\mathbf{M} = ((\mathbf{P}_1,\mathbf{A}_1),(\mathbf{P}_2,\mathbf{A}_2),\dots ,(\mathbf{P}_t,\mathbf{A}_t))$ , where $t$ is the frame number. $\mathbf{P}_i\in \mathbb{R}^{N\times 3}$ represents the vertex positions in Cartesian coordinates, where $N$ is the number of vertices. $\mathbf{A}_i\in \mathbb{R}^{N\times N}$ represents the adjacency matrix of the mesh. Element $\mathbf{A}_i^{mn}\in \mathbf{A}_i$ is one when there is an edge from vertex $V_{m}$ to vertex $V_{n}$ , and zero when there is no edge. The mesh representation with vertices and their adjacent matrix is a unified format for various body models such as SMPL [39], SMPL-H [54], and SMPL-X [49]. In this work, we use SMPL-H body models from AMASS [40] to obtain the mesh sequences, but our method can be easily adapted to other body models. + +Mesh's local connectivity provides fine-grained information. Previous methods [21, 59] proved that explicitly using surface (e.g., mesh) connectivity information can achieve higher accuracy in shape classification and segmentation tasks. However, classifying temporal mesh sequences is a more challenging problem, as there is no vertex-level correspondence across frames. This prevents graph-based models from directly aggregating vertices in the temporal dimension. Therefore, we propose to first leverage mesh connectivity information to build patches at the frame level, + +then use a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. In summary, it has the following key components: + +- Surface Field Convolution to form local vertex patches by considering both intrinsic and extrinsic mesh representations. +- Hierarchical Spatial-Temporal Transformer to learn spatial-temporal correlations of vertex patches. +- Self-Supervised Pre-Training to learn the global context in terms of appearance and motion. + +See Figure 2 for a high-level summary of the model, and the sections below for more details. + +# 3.2. Surface Field Convolution + +Because displacements in grid data are regular, traditional convolutions can directly learn a kernel for elements within a region. However, mesh vertices are unordered and irregular. Considering the special mesh representations, we represent each vertex by encoding features from its neighbor vertices inspired by [51,52]. To fully utilize meshes' local connectivity information, we consider the mesh properties of extrinsic curvature of submanifolds and intrinsic curvature of the manifold itself. Extrinsic curvature between two vertices is approximated using Euclidean distance. Intrinsic curvature is approximated using Geodesic distance, which is defined as the shortest path between two vertices on mesh surfaces. We propose a light-weighted surface field convolution to build local patches, which can be denoted as: + +$$ +\boldsymbol {F} _ {V G} ^ {\prime (x, y, z)} = \sum_ {(\delta_ {x}, \delta_ {y}, \delta_ {z}) \in G (x, y, z)} \boldsymbol {W} ^ {(\delta_ {x}, \delta_ {y}, \delta_ {z})} \cdot \boldsymbol {F} ^ {(x + \delta_ {x}, y + \delta_ {y}, z + \delta_ {z})} \tag {1} +$$ + +$$ +\boldsymbol {F} _ {V E} ^ {\prime (x, y, z)} = \sum_ {(\zeta_ {x}, \zeta_ {y}, \zeta_ {z}) \in E (x, y, z)} \boldsymbol {W} ^ {(\zeta_ {x}, \zeta_ {y}, \zeta_ {z})} \cdot \boldsymbol {F} ^ {(x + \zeta_ {x}, y + \zeta_ {y}, z + \zeta_ {z})} \tag {2} +$$ + +$G$ and $E$ is the local region around vertex $(x,y,z)$ . In this paper, we use k-nearest-neighbor to sample local vertices. $(\delta_x,\delta_y,\delta_z)$ and $(\zeta_x,\zeta_y,\zeta_z)$ represent the spatial displacement in geodesic and euclidean space, respectively. $\pmb{F}^{(x,y,z)}$ denotes the feature of the vertex at position $(x,y,z)$ . + +# 3.3. Hierarchical Spatial-Temporal Transformer + +We propose a hierarchical transformer that consists of intra-frame and inter-frame attention. The basic idea behind our transformer is three-fold: (1) Intra-frame attention can encode connectivity information from the adjacency matrix, while such information can not be directly + +![](images/aa2fef466fec1635359291bd667378c4cbdc65c4dffb5d8abaf57d743821a73d.jpg) +(a) STMT Architecture + +![](images/497862271b69e92e5eb0b916093744d61c6576242f878e79f96e45802861775a.jpg) +(b) Pre-Training Stage +Figure 2. Overview of the proposed framework. (a) Overview of STMT. Given a mesh sequence, we first develop vertex patches by extracting both intrinsic (geodesic) and extrinsic (euclidean) features using surface field convolution. The intrinsic and extrinsic features are denoted by yellow and blue blocks respectively. Those patches are used as input to the intra-frame offset-attention network to learn appearance features. Then we concatenate intrinsic patches and extrinsic patches of the same position. The concatenated vertex patches (green blocks) are fed into the inter-frame self-attention network to learn spatial-temporal correlations. Finally, the local and global features are mapped into action predictions by MLP layers. (b) Overview of Pre-Training Stage. We design two pretext tasks: masked vertex modeling and future frame prediction for global context learning. Bidirectional attention is used for the reconstruction of masked vertices. Auto-regressive attention is used for the future frame prediction task. + +aggregated in the temporal domain because vertices are unordered. (2) Frame-level offset-attention can be used to mimic the Laplacian operator to learn effective spatial representations. (3) Inter-frame self-attention can learn feature correlations in the spatial-temporal domain. + +# 3.3.1 Intra-Frame Offset-Attention + +Graph convolution networks [6] show the benefits of using a Laplacian matrix $\mathbf{L} = \mathbf{D} - \mathbf{E}$ to replace the adjacency matrix $\mathbf{E}$ , where $\mathbf{D}$ is the diagonal degree matrix. Inspired by this, offset-attention has been proposed and achieved superior performance in point-cloud classification and segmentation tasks [20]. We adapt offset-attention to attend to vertex patches. Specifically, the offset-attention layer calculates the offset (difference) between the self-attention (SA) features and the input features by element-wise subtraction. Offset-attention is denoted as: + +$$ +\boldsymbol {F} _ {\text {o u t}} = O A \left(\boldsymbol {F} _ {\text {i n}}\right) = \phi \left(\boldsymbol {F} _ {\text {i n}} - \boldsymbol {F} _ {\text {s a}}\right) + \boldsymbol {F} _ {\text {i n}}. \tag {3} +$$ + +where $\phi$ denotes a non-linear operator. $F_{in} - F_{sa}$ is proved to be analogous to discrete Laplacian operator [20], i.e. $F_{in} - F_{sa} \approx LF_{in}$ . As Laplacian operators in geodesic and euclidean space are expected to be different, we propose to use separate transformers to model intrinsic patches and extrinsic patches. Specifically, the aggregated feature for vertex $V$ is denoted as: + +$$ +\boldsymbol {F} _ {V} ^ {\prime (x, y, z)} = O A _ {G} \left(\boldsymbol {F} _ {V G} ^ {\prime (x, y, z)}\right) \oplus O A _ {E} \left(\boldsymbol {F} _ {V E} ^ {\prime (x, y, z)}\right) \tag {4} +$$ + +Here $F_{VG}^{\prime (x,y,z)}\in \mathbb{R}^{N\times d_g}$ and $F_{VE}^{\prime (x,y,z)}\in \mathbb{R}^{N\times d_e}$ are local patches learned using Equ. 1 and Equ. 2. $F_V^{\prime (x,y,z)}\in$ $\mathbb{R}^{N\times d}$ denotes the local patch for position $(x,y,z)$ , where $d = d_{g} + d_{e}$ . The weights of $OA_{G}$ and $OA_{E}$ are not shared. + +# 3.3.2 Inter-Frame Self-Attention + +Given $F_V'$ which encodes local connectivity information, we use self-attention (SA) [65] to learn semantic affinities between different vertex patches across frames. Specifically, let $\mathbf{Q},\mathbf{K},\mathbf{V}$ be the query, key and value, which are generated by applying linear transformations to the input features $F_V' \in \mathbb{R}^{N \times d}$ as follows: + +$$ +(\boldsymbol {Q}, \boldsymbol {K}, \boldsymbol {V}) = F _ {V} ^ {\prime} \cdot (\boldsymbol {W} _ {q}, \boldsymbol {W} _ {k}, \boldsymbol {W} _ {v}) +$$ + +$$ +\boldsymbol {Q}, \boldsymbol {K} \in \mathbb {R} ^ {N \times d _ {a}}, \quad \boldsymbol {V} \in \mathbb {R} ^ {N \times d} +$$ + +$$ +\boldsymbol {W} _ {q}, \boldsymbol {W} _ {k} \in \mathbb {R} ^ {d \times d _ {a}}, \quad \boldsymbol {W} _ {v} \in \mathbb {R} ^ {d \times d} \tag {5} +$$ + +where $W_{q}$ , $W_{k}$ and $W_{v}$ are the shared learnable linear transformation, and $d_{a}$ is the dimension of the query and key vectors. Then we can use the query and key matrices to calculate the attention weights via the matrix dot-product: + +$$ +\boldsymbol {A} = (\tilde {\alpha}) _ {i, j} = \operatorname {s o f t m a x} \left(\frac {\boldsymbol {Q} \cdot \boldsymbol {K} ^ {\mathrm {T}}}{\sqrt {d _ {a}}}\right). \tag {6} +$$ + +$$ +\boldsymbol {F} _ {s a} = \boldsymbol {A} \cdot \boldsymbol {V} \tag {7} +$$ + +The self-attention output features $F_{sa}$ are the weighted sums of the value vector using the corresponding attention weights. Specifically, for a vertex patch in position $(x,y,z)$ , + +its aggregated feature after inter-frame self-attention can be computed as: $\pmb{F}_{sa}^{(x,y,z)} = \sum \pmb{A}^{(x,y,z),(x',y',z')} \times \pmb{V}^{(x',y',z')}$ , where $(x',y',z')$ belongs to the Cartesian coordinates of $\pmb{F}_V'$ . + +# 3.4. Self-Supervised Pre-Training + +Self-supervised learning has achieved remarkable results on large-scale image datasets [23]. However, self-supervised learning for temporal 3D sequences (i.e. point cloud, 3D skeleton) remains to be challenging and has not been fully explored. There are two possible reasons: (1) self-supervised learning methods rely on large-scale datasets to learn meaningful patterns [10]. However, existing MoCap benchmarks are relatively small compared to 2D datasets like ImageNet [11]. (2) Self-supervised learning for 3D data sequences is computationally expensive in terms of memory and speed. In this work, we first propose a simple and effective method to augment existing MoCap sequences, and then define two effective and efficient self-supervised learning tasks, namely masked vertex modeling and future frame prediction, which enable the model to learn global context. The work that is close to us is OcCO [67], which proposed to use occluded point cloud reconstruction as the pretext task. OcCO has a computationally-expensive process to generate occlusions, including point cloud projection, occluded point calculation, and a mapping step to convert camera frames back to world frames. Different from OcCO, we randomly mask vertex patches or future frames on the fly, which saves the pre-processing step. Moreover, our pre-training method is designed for temporal mesh sequences and considers both bi-directional and autoregressive attention. + +# 3.4.1 Data Augmentation through Joint Shuffle + +Considering the flexibility of SMPL-H representations, we propose a simple yet effective approach to augment SMPL-H sequences by shuffling body pose parameters. Specifically, we split SMPL-H pose parameters into five body parts: bone, left/right arm, and left/right leg. We use $I_{bone}, I_{leg}^{left}, I_{leg}^{right}, I_{arm}^{left}, I_{arm}^{right}$ to denote the SMPL-H pose indexes of the five body parts. Then we synthesize new sequences by randomly selecting body parts from five different sequences. We keep the temporal order for each part such that the merged action sequences have meaningful motion trajectories. Pseudocode for the joint shuffle is provided in Algorithm 1. The input to Joint Shuffle are SMPL-H pose parameters $\theta \in \mathbb{R}^{b \times t \times n \times 3}$ , where $b$ is the sequence number, $t$ is the frame number, and $n$ is the joint number. We randomly select the shape $\beta$ and dynamic parameters $\phi$ from one of the five SMPL-H sequences to compose a new SMPL-H body model. Given $b$ SMPL-H sequences, we can synthesize ${}^b C_5 = \frac{b!}{5!(b - 5)!}$ number of new sequences. + +We prove that the model can benefit from large-scale pretraining in Section 4.6. + +Algorithm 1: Pseudocode of STMT Joint Shuffle +1: function STMT JOINT SHUFFLE( $\theta \in$ $\mathbb{R}^{b\times t\times n\times 3}$ $I_{\mathrm{bone}},I_{\mathrm{leg}}^{\mathrm{left}},I_{\mathrm{leg}}^{\mathrm{right}},I_{\mathrm{arm}}^{\mathrm{left}},I_{\mathrm{arm}}^{\mathrm{right}})$ +2: $\theta_s\gets$ random_sample(0,5) $\triangleright \theta_s\in \mathbb{R}^{5\times t\times n\times 3}$ randomly sample five SMPL-H sequences +3: $t_{max}\gets$ get_max_length( $\theta_{s})$ compute the maximum sequence length in $\theta_{s}$ +4: $\theta_{new}\gets$ Initialize $(t_{max},n,3)$ +5: $P\gets \{I_{\mathrm{bone}},I_{\mathrm{leg}}^{\mathrm{left}},I_{\mathrm{leg}}^{\mathrm{right}},I_{\mathrm{arm}}^{\mathrm{left}},I_{\mathrm{arm}}^{\mathrm{right}}\}$ +6: for i in 0,1,2,3,4 do +7: $\theta_s\gets$ repeat $(\theta_s[i],(t_{max},n,3))$ pad each sequence to the max length using repeating +8: $\theta_{new}[P[i]]\gets \theta_s[i][P[i]]\triangleright$ assign the body-part sequence +9: return $\theta_{new}$ + +# 3.4.2 Masked Vertex Modeling with Bi-Directional Attention + +To fully activate the inter-frame bi-directional attention in the transformer, we design a self-supervised pretext task named Masked Vertex Modeling (MVM). The model can learn human prior information in the spatial dimension by reconstructing masked vertices of different body parts. We randomly mask $r$ percentages of the input vertex patches, and force the model to reconstruct the full sequences. Moreover, we use bi-directional attention to learn correlations among all remaining local patches. Each patch will attend to all patches in the entire sequence. It models the joint distribution of vertex patches over the whole temporal sequences $x$ as the following product of conditional distributions, where $x_{i}$ is a single vertex patch: + +$$ +p (x) = \prod_ {i = 1} ^ {N} p \left(x _ {i} \mid x _ {1},.., x _ {i}, \dots , x _ {N}\right). \tag {8} +$$ + +Where $N$ is the number of patches in the entire sequence $x$ after masking. Every patch will attend to all patches in the entire sequence. In this way, bi-directional attention is fully-activated to learn spatial-temporal features that can accurately reconstruct completed mesh sequences. + +# 3.4.3 Future Frame Prediction with Auto-Regressive Attention + +The masked vertex modeling task is to reconstruct masked vertices in different body parts. The model can reconstruct completed mesh sequences if it captures the human body prior or can make a movement inference from nearby frames. As action recognition requires the model to understand the global context, we propose the future frame + +prediction (FFP) task. Specifically, we mask out all the future frames and force the transformer to predict the masked frames. Moreover, we propose to use auto-regressive attention for the future frame prediction task, inspired by language generation models like GPT-3 [5]. However, directly using RNN-based models [9] in GPT-3 to predict future frames one by one is inefficient, as 3D mesh sequences are denser compared to language sequences. Therefore, we propose to reconstruct all future frames in a single forward pass. For auto-regressive attention, we model the joint distribution of vertex patches over a mesh sequence $x$ as the following product of conditional distributions, where $x_{i}$ is a single patch at frame $t_{i}$ : + +$$ +p (x) = \prod_ {i = 1} ^ {N} p \left(x _ {i} \mid x _ {1}, x _ {2}, \dots , x _ {M}\right). \tag {9} +$$ + +Where $N$ is the number of patches in the entire sequence $x$ after masking. $M = (t_i - 1) \times n$ , where $n$ is the number of patches in a single frame. Each vertex patch depends on all patches that are temporally before it. The auto-regressive attention enables the model to predict movement patterns and trajectories, which is beneficial for the downstream action recognition task. + +# 3.5. Training + +In the pre-training stage, we use PCN [74] as the decoder to reconstruct masked vertices and predict future frames. The decoder is shared for the two pretext tasks. Since mesh vertices are unordered, the reconstruction loss and future prediction loss should be permutation-invariant. Therefore, we use Chamfer Distance (CD) as the loss function to measure the difference between the model predictions and ground truth mesh sequences. + +$$ +\begin{array}{l} C D (M _ {p r e d}, M _ {g t}) = \frac {1}{\left| M _ {p r e d} \right|} \sum_ {x \in M _ {p r e d}} \min _ {y \in M _ {g t}} \| x - y \| _ {2} + \\ \frac {1}{| M _ {g t} |} \sum_ {y \in M _ {g t}} \min _ {x \in M _ {p r e d}} \| y - x \| _ {2} \tag {10} \\ \end{array} +$$ + +CD (10) calculates the average closest euclidean distance between the predicted mesh sequences $M_{pred}$ and the ground truth sequences $M_{gt}$ . The overall loss is a weighted sum of masked vertex reconstruction loss and future frame prediction loss: + +$$ +L = \lambda_ {1} C D \left(M _ {p r e d} ^ {M V M}, M _ {g t}\right) + \lambda_ {2} C D \left(M _ {p r e d} ^ {F F P}, M _ {g t}\right) \tag {11} +$$ + +In the fine-tuning stage, we replace the PCN decoder with an MLP head. Cross-entropy loss is used for model training. + +# 4. Experiment + +# 4.1. Datasets + +Following previous MoCap-based action recognition methods [50,63], we evaluate our model on the most widely used benchmarks: KIT [42] and BABEL [50]. KIT is one of the largest MoCap datasets. It has 56 classes with 6,570 sequences in total. (2) BABEL is the largest 3D MoCap dataset that unifies 15 different datasets. BABEL has 43 hours of MoCap data performed by over 346 subjects. We use the 60-class subset from BABEL, which contains 21,653 sequences with single-class labels. We randomly split each dataset into training, test, and validation set, with ratios of $70\%$ , $15\%$ , and $15\%$ , respectively. Note that existing action recognition datasets with skeletons only are not suitable for our experiments, as they do not provide full 3D surfaces or SMPL parameters to obtain the mesh representation. + +Motion Representation. Both KIT and BABEL's MoCap sequences are obtained from AMASS dataset in SMPL-H format. A MoCap sequence is an array of pose parameters over time, along with the shape and dynamic parameters. For skeleton-based action recognition, we follow previous work [50] which predicted the 25-joint skeleton from the vertices of the SMPL-H mesh. The movement sequence is represented as $\mathbf{X} = (\mathbf{x}_1,\dots ,\mathbf{x}_L)$ , where $\mathbf{x}_i\in \mathbb{R}^{J\times 3}$ represents the position of the $J$ joints in the skeleton in Cartesian coordinates. For point-cloud-based action recognition, we directly use the vertices of SMPL-H model as the model input. The point-cloud sequence is represented as $\mathbf{P} = (\mathbf{p}_1,\dots ,\mathbf{p}_L)$ , where $\mathbf{p}_i\in \mathbb{R}^{V\times 3}$ , and $V$ is the number of vertices. For mesh-based action recognition, we represent the motion as a series of mesh vertices and their adjacent matrix over time, as introduced in Section 3.1. See Sup. Mat. for more details about datasets and pre-processing. + +# 4.2. Baseline Methods + +We compare our model with state-of-the-art 3D skeleton-based and point cloud-based action recognition models, as there is no existing literature on mesh-based action recognition. 2s-AGCN [61], CTR-GCN [7], and MS-G3D [37] are used as skeleton-based baselines. Among those methods, 2s-AGCN trained with focal loss and cross-entropy loss are used as benchmark methods in the BABEL dataset [50]. For the comparison with point-cloud baselines, we choose PSTNet [18], SequentialPointNet [30], and P4Transformer [16]. Those methods achieved top performance on common point-cloud-based action recognition benchmarks. + +# 4.3. Implementation Details + +For skeleton-based baselines, we use the official implementations of 2s-ACGN, CTR-GCN, and MS-G3D from + +
MethodInputKITBABEL-60
Top-1 (%)Top-5 (%)Top-1 (%)Top-5 (%)
2s-AGCN-FL [61] (CVPR'19)3D Skeleton42.4475.6049.6279.12
2s-AGCN-CE [61] (CVPR'19)3D Skeleton57.4681.5463.5786.77
CTR-GCN [7] (ICCV'21)3D Skeleton64.6587.9067.3088.50
MS-G3D [37] (CVPR'20)3D Skeleton65.3887.9067.4387.99
PSTNet [18] (ICLR'21)Point Cloud56.9388.2161.9484.11
SequentialPointNet [30] (arXiv'21)Point Cloud59.7588.0162.9284.58
P4Transformer [16] (CVPR'21)Point Cloud62.1588.0163.5486.55
STMT(Ours)Mesh65.5990.0967.6588.68
+ +![](images/61c33fb9069d9dc2cb5c34d55cb1f3c7af4ed05002cdd432c7a91e8c5155f466.jpg) +Figure 3. Visualization of inter-frame attention. Red denotes the highest attention. + +[62], [8], and [38]. For point-cloud-based baselines, we use the official implementations of PSTNet, SequentialPointNet, P4Transformer from [19], [31], and [17]. We pre-train STMT for 200 epochs with a batch size of 32. The model is fine-tuned for 50 epochs with a batch size of 64. Adam optimizer [26] is used with a learning rate of 0.0001 for both pre-training and fine-tuning. See Sup. Mat. for more implementation details. + +# 4.4. Main Results + +Comparison with State-of-the-Art Methods. As indicated in Table 1, STMT outperforms all other state-of-the-art models. Our model can outperform point-cloud-based models by $3.44\%$ and $4.11\%$ on KIT and BABEL datasets in terms of top-1 accuracy. Moreover, compared to skeleton-based methods which involve manual efforts to convert mesh vertices to skeleton representations, our model achieves better performance by directly modeling the dynamics of raw mesh sequences. + +We visualize the inter-frame attention weights of our hierarchical transformer in Figure 3. We observe that the model can pay attention to key regions across frames. This supports the intuition that our hierarchical transformer can take the place of explicit vertex tracking by learning spatial-temporal correlations. + +Table 1. Experimental Results on KIT and BABEL Dataset. + +
IntrinsicExtrinsicMVMFFPTop-1 (%)
✓63.40
✓✓64.03
✓✓✓64.96
✓✓✓64.13
✓✓✓✓65.59
+ +Table 2. Performance of ablated versions. Intrinsic and Extrinsic stand for the intrinsic (geodesic) and extrinsic (euclidean) features in surface field convolution. MVM stands for Masked Vertex Modelling. FFP stands for Future Frame Prediction. + +# 4.5. Ablation Study + +Ablation Study of STMT. We test various ablations of our model on the KIT dataset to substantiate our design decisions. We report the results in Table 2. Note that Joint Shuffle is used in all of the self-supervised learning experiments (last three rows). We observe that each component of our model gains consistent improvements. The comparison of the first two rows proves the effectiveness of encoding both intrinsic and extrinsic features in vertex patches. Comparing the last three rows with the second row, we observe a consistent improvement using self-supervised pretraining. Moreover, the downstream task can achieve better performance with MVM compared to FFP. One probable reason is that the single task for future frame prediction is more challenging than masked vertex modeling, as the model can only see the person movement in the past. The model can achieve the best performance with both MVM and FFP, which demonstrates that the two self-supervised tasks are supplementary to each other. + +# 4.6. Analysis + +Different Pre-Training Strategies. We pre-train our model with different datasets and summarize the results in Table 3. The first row shows the case without pre-training. The second shows the result for the model pre-trained on the KIT dataset (without Joint Shuffle augmentation). The third shows the result for the model pre-trained on KIT dataset (with Joint Shuffle). We observe our model can achieve better performance with Joint Shuffle, as it can synthesize large-scale mesh sequences. + +
MethodTop-1 (%)
w/o pre-training64.03
pre-training w/o JS64.13
pre-training w/ JS65.59
+ +Table 3. Comparison of Different Pre-Training Strategies. JS stands for Joint Shuffle. + +
rPre-Train Loss (×104)Fine-Tune Accuracy (%)
0.10.3964.44
0.30.4164.55
0.50.4065.59
0.70.4364.19
0.90.4865.07
Rand0.4364.75
+ +Table 4. Effect of Different Masking Ratios. + +Different Masking Ratios. We investigate the impact of different masking ratios. We report the converged pretraining loss and the fine-tuning top-1 classification accuracy on the test set in Table 4. We also experiment with the random masking ratio in the last row. For each forward pass, we randomly select one masking ratio from 0.1 to 0.9 with step 0.1 to mimic flexible masked token length. The model with a random masking ratio does not outperform the best model that is pre-trained using a single ratio (i.e. 0.5). We observe that as the masking ratio increases, the pre-training loss mostly increases as the task becomes more challenging. However, a challenging self-supervised learning task does not necessarily lead to better performance. The model with a masking ratio of 0.7 and 0.9 have a high pre-train loss, while the fine-tune accuracy is not higher than the model with a 0.5 masking ratio. The conclusion is similar to the comparison of MVM and FFP training objectives, where a more challenging self-supervised learning task may not be optimal. + +Different Number of Mesh Sequences for Pre-Training. We test the effect of different numbers of mesh sequences used in pre-training. We report the fine-tuning top-1 classification accuracy in Figure 4. We observe that a large number of pre-training data can bring substantial performance improvement. The proposed Joint Shuffle method can greatly enlarge the dataset size without any manual cost, and has the potential to further improve model performance. + +Experimental Results on Noisy Body Pose Estimations. Body pose estimation has been a popular research field [25, 27, 32], but how to leverage the estimated 3D meshes for downstream perception tasks has not been fully explored. We apply the state-of-the-art body pose estimation model VIBE [27] on videos of NTU RGB+D dataset to obtain 3D mesh sequences. Skeleton and point cloud representations are derived from the estimated meshes to train the baseline + +![](images/9c09f51a55c6ee85e1e3c0641fd224994d6f4f50757f3dc29d1953c493b40c99.jpg) + +Figure 4. Effect of Different Number of Mesh Sequences. + +
MethodInputTop-1 (%)
2s-AGCN-FL [61]3D Skeleton58.67
2s-AGCN-CE [61]3D Skeleton57.49
CTR-GCN [7]3D Skeleton62.25
MS-G3D [37]3D Skeleton60.01
PSTNet [18]Point Cloud51.48
SequentialPointNet [30]Point Cloud60.60
P4Transformer [16]Point Cloud57.84
STEMT(Ours)Mesh64.04
+ +Table 5. Experimental results on body poses estimated by VIBE [27] on NTU RGB+D dataset. The skeleton, point cloud, and mesh representations are derived from the same noisy body estimations. + +models (see Sup. Mat.). We report the results in Table 5. We observe that STMT can outperform the best skeleton-based and point cloud-based action recognition model by $1.79\%$ and $3.44\%$ respectively. This shows that STMT with meshes as input, is more robust to input noise compared to other state-of-the-art methods with 3D skeletons or point clouds as input. + +# 5. Conclusion + +In this work, we propose a novel approach for MoCap-based action recognition. Unlike existing methods that rely on skeleton representation, our proposed model directly models the raw mesh sequences. Our method encodes both intrinsic and extrinsic features in vertex patches, and uses a hierarchical transformer to freely attend to any two vertex patches in the spatial and temporal domain. Moreover, two self-supervised learning tasks, namely Masked Vertex Modeling and Future Frame Prediction are proposed to enforce the model to learn global context. Our experiments show that STMT can outperform state-of-the-art skeleton-based and point-cloud-based models. + +# Acknowledgment + +This work was supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-17-5-0003. This work used Bridges-2 GPU resources provided by PSC through allocation CIS220012 from the ACCESS program. + +# References + +[1] Felix Achilles, Alexandru-Eugen Ichim, Huseyin Coskun, Federico Tombari, Soheyl Noahtar, and Nassir Navab. Patient mocap: Human pose estimation under blanket occlusion for hospital monitoring applications. In International conference on medical image computing and computer-assisted intervention, pages 491-499. Springer, 2016. 1, 2 +[2] Hangbo Bao, Li Dong, and Furu Wei. 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Current state-of-the-art MoCap-based action recognition methods first convert body markers into a human body mesh, which is used to predict a standardized 3D skeleton. The 3D skeleton is used as input for action recognition models (dashed line). We propose a method that directly models the dynamics of raw mesh sequences (solid line). Our method saves the manual effort to derive skeleton representation, and achieves superior recognition performance by leveraging surface motion and body shape knowledge from meshes." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 415, + 192, + 427 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 415, + 192, + 427 + ], + "spans": [ + { + "bbox": [ + 143, + 415, + 192, + 427 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 427, + 290, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 290, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 290, + 643 + ], + "type": "text", + "content": "We study the problem of human action recognition using motion capture (MoCap) sequences. Unlike existing techniques that take multiple manual steps to derive standardized skeleton representations as model input, we propose a novel Spatial-Temporal Mesh Transformer (STMT) to directly model the mesh sequences. The model uses a hierarchical transformer with intra-frame off-set attention and inter-frame self-attention. The attention mechanism allows the model to freely attend between any two vertex patches to learn non-local relationships in the spatial-temporal domain. Masked vertex modeling and future frame prediction are used as two self-supervised tasks to fully activate the bi-directional and auto-regressive attention in our hierarchical transformer. The proposed method achieves state-of-the-art performance compared to skeleton-based and pointcloud-based models on common MoCap benchmarks. Code is available at https://github.com/zgzxy001/STMT." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 651, + 128, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 128, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 128, + 662 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 670, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 670, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 670, + 287, + 696 + ], + "type": "text", + "content": "Motion Capture (MoCap) is the process of digitally recording the human movement, which enables the fine" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 416, + 547, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 416, + 547, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 416, + 547, + 573 + ], + "type": "text", + "content": "grained capture and analysis of human motions in 3D space [40, 50]. MoCap-based human perception serves as key elements for various research fields, such as action recognition [15, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. Besides, MoCap is one of the fundamental technologies to enhance human-robot interactions in various practical scenarios including hospitals and manufacturing environment [22, 28, 41, 43, 45, 77]. For example, Hayes [22] classified automotive assembly activities using MoCap data of humans and objects. Understanding human behaviors from MoCap data is fundamentally important for robotics perception, planning, and control." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Skeleton representations are commonly used to model MoCap sequences. Some early works [3, 29] directly used body markers and their connectivity relations to form a skeleton graph. However, the marker positions depend on each subject (person), which brings sample variances within each dataset. Moreover, different MoCap datasets usually have different numbers of body markers. For example, ACCAD [48], BioMotion [64], Eyes Japan [15], and KIT [42] have 82, 41, 37, and 50 body markers respectively. This prevents the model to be trained and tested on a unified framework. To use standard skeleton representa" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 132, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 132, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 132, + 712 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 62, + 703, + 132, + 712 + ], + "type": "text", + "content": "Equal Contribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1526" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "tions such as NTU RGB+D [58], Punnakkal et al. [50] first used Mosh++ to fit body markers into SMPL-H meshes, and then predicted a 25-joint skeleton [33] from the mesh vertices [54]. Finally, a skeleton-based model [60] was used to perform action recognition. Although those methods achieved advanced performance, they have the following disadvantages. First, they require several manual steps to map the vertices from mesh to skeleton. Second, skeleton representations lose the information provided by original MoCap data (i.e., surface motion and body shape knowledge). To overcome those disadvantages, we propose a mesh-based action recognition method to directly model dynamic changes in raw mesh sequences, as illustrated in Figure 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 371 + ], + "type": "text", + "content": "Though mesh representations provide fine-grained body information, it is challenging to classify high-dimensional mesh sequences into different actions. First, unlike structured 3D skeletons which have joint correspondence across frames, there is no vertex-level correspondence in meshes (i.e., the vertices are unordered). Therefore, the local connectivity of every single mesh can not be directly aggregated in the temporal dimension. Second, mesh representations encode local connectivity information, while action recognition requires global understanding in the whole spatial-temporal domain." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 371, + 289, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 289, + 610 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 289, + 610 + ], + "type": "text", + "content": "To overcome the aforementioned challenges, we propose a novel Spatial-Temporal Mesh Transformer (STMT). STMT leverages mesh connectivity information to build patches at the frame level, and uses a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. The hierarchical attention mechanism allows the model to learn patch correlation across the entire sequence, and alleviate the requirement of explicit vertex correspondence. We further define two self-supervised learning tasks, namely masked vertex modeling and future frame prediction, to enhance the global interactions among vertex patches. To reconstruct masked vertices of different body parts, the model needs to learn prior knowledge about the human body in the spatial dimension. To predict future frames, the model needs to understand meaningful surface movement in the temporal dimension. To this end, our hierarchical transformer pretrained with those two objectives can further learn spatial-temporal context across entire frames, which is beneficial for the downstream action recognition task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 610, + 288, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 288, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 288, + 659 + ], + "type": "text", + "content": "We evaluate our model on common MoCap benchmark datasets. Our method achieves state-of-the-art performance compared to skeleton-based and point-cloud-based models. The contributions of this paper are three-fold:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 288, + 715 + ], + "type": "text", + "content": "- We introduce a new hierarchical transformer architecture, which jointly encodes intrinsic and extrinsic representations, along with intra- and inter-frame attention, for spatial-temporal mesh modeling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 120 + ], + "type": "text", + "content": "- We design effective and efficient pretext tasks, namely masked vertex modeling and future frame prediction, to enable the model to learn from the spatial-temporal global context." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 130, + 547, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 130, + 547, + 166 + ], + "spans": [ + { + "bbox": [ + 317, + 130, + 547, + 166 + ], + "type": "text", + "content": "- Our model achieves superior performance compared to state-of-the-art point-cloud and skeleton models on common MoCap benchmarks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 178, + 392, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 178, + 392, + 190 + ], + "spans": [ + { + "bbox": [ + 306, + 178, + 392, + 190 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 198, + 547, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 498 + ], + "type": "text", + "content": "Action Recognition from Depth and Point Cloud. 3D action recognition models have achieved promising performance with depth [34, 55, 56, 68, 71] and point clouds [18, 36, 52, 70]. Depth provides reliable 3D structural and geometric information which characterizes informative human actions. In MVDI [71], dynamic images [4] were extracted through multi-view projections from depth videos for 3D action recognition. 3D-FCNN [55] directly exploited a 3D-CNN to model depth videos. Another popular category of 3D human action recognition is based on 3D point clouds. PointNet [51] and PointNet++ [52] are the pioneering works contributing towards permutation invariance of 3D point sets for representing 3D geometric structures. Along this avenue, MeteorNet [36] stacked multi-frame point clouds and aggregates local features for action recognition. 3DV [70] transferred point cloud sequences into regular voxel sets to characterize 3D motion compactly via temporal rank pooling. PSTNet [18] disentangled space and time to alleviate point-wise spatial variance across time. Action recognition has shown promising results with 3D skeletons and point clouds. Meshes, which are commonly used in representing human bodies and creating action sequences, have not been explored for the action recognition task. In this work, we propose the first mesh-based action recognition model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": "MoCap-Based Action Recognition. Motion-capture (MoCap) datasets [15, 44, 46-48, 50, 57] serve as key elements for various research fields, such as action recognition [15, 44, 46-48, 50, 57], tracking [47], pose estimation [1, 27], imitation learning [76], and motion synthesis [47]. MoCap-based action recognition was formulated as a skeleton-based action recognition problem [50]. Various architectures have been investigated to incorporate skeleton sequences. In [14, 35, 75], skeleton sequences were treated as time-series inputs to RNNs. [24, 69] respectively transformed skeleton sequences into spectral images and trajectory maps and then adopted CNNs for feature learning. In [72], Yan et al. leveraged GCN to model joint dependencies that can be naturally represented with a graph. In this paper, we propose a novel method to directly model the dynamics of raw mesh sequences which can benefit from surface motion and body shape knowledge." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "1527" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 85, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 289, + 361 + ], + "type": "text", + "content": "Masked Autoencoder. Masked autoencoder has gained attention in Natural Language Processing and Computer Vision to learn effective representations using auto-encoding. Stacked denoising autoencoders [66] treated masks as a noise type and used denoising autoencoders to denoise corrupted inputs. ViT [13] proposed a self-supervised pretraining task to reconstruct masked tokens. More recently, BEiT [2] proposed to learn visual representations by reconstructing the discrete tokens [53]. MAE [23] proposed a simple yet effective asymmetric framework for masked image modeling. In 3D point cloud analysis, Wang et al. [67] chose to first generate partial point clouds by calculating occlusion from random camera viewpoints, and then completed occluded point clouds using autoencoding. PointBERT [73] followed the success of BERT [12] to predict the masked tokens learned from points. However, applying self-supervised learning to temporal 3D sequences (i.e. point cloud, 3D skeleton) has not been fully explored. One probable reason is that self-supervised learning on high-dimensional 3D temporal sequences is computationally-expensive. In this work, we propose an effective and efficient self-supervised learning method based on masked vertex modeling and future frame prediction." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 373, + 105, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 105, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 105, + 385 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 394, + 115, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 115, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 115, + 405 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": "In this section, we describe our model for mesh-based action recognition, which we call STMT. The inputs of our model are temporal mesh sequences: " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{M} = ((\\mathbf{P}_1,\\mathbf{A}_1),(\\mathbf{P}_2,\\mathbf{A}_2),\\dots ,(\\mathbf{P}_t,\\mathbf{A}_t))" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " is the frame number. " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_i\\in \\mathbb{R}^{N\\times 3}" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " represents the vertex positions in Cartesian coordinates, where " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " is the number of vertices. " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_i\\in \\mathbb{R}^{N\\times N}" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " represents the adjacency matrix of the mesh. Element " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{A}_i^{mn}\\in \\mathbf{A}_i" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " is one when there is an edge from vertex " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "V_{m}" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " to vertex " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "V_{n}" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": ", and zero when there is no edge. The mesh representation with vertices and their adjacent matrix is a unified format for various body models such as SMPL [39], SMPL-H [54], and SMPL-X [49]. In this work, we use SMPL-H body models from AMASS [40] to obtain the mesh sequences, but our method can be easily adapted to other body models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Mesh's local connectivity provides fine-grained information. Previous methods [21, 59] proved that explicitly using surface (e.g., mesh) connectivity information can achieve higher accuracy in shape classification and segmentation tasks. However, classifying temporal mesh sequences is a more challenging problem, as there is no vertex-level correspondence across frames. This prevents graph-based models from directly aggregating vertices in the temporal dimension. Therefore, we propose to first leverage mesh connectivity information to build patches at the frame level," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "then use a hierarchical transformer which can freely attend to any intra- and inter-frame patches to learn spatial-temporal associations. In summary, it has the following key components:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 128, + 545, + 225 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 317, + 128, + 545, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 128, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 317, + 128, + 545, + 163 + ], + "type": "text", + "content": "- Surface Field Convolution to form local vertex patches by considering both intrinsic and extrinsic mesh representations." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 171, + 545, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 171, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 317, + 171, + 545, + 195 + ], + "type": "text", + "content": "- Hierarchical Spatial-Temporal Transformer to learn spatial-temporal correlations of vertex patches." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 201, + 545, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 201, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 317, + 201, + 545, + 225 + ], + "type": "text", + "content": "- Self-Supervised Pre-Training to learn the global context in terms of appearance and motion." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 233, + 545, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 233, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 305, + 233, + 545, + 257 + ], + "type": "text", + "content": "See Figure 2 for a high-level summary of the model, and the sections below for more details." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 264, + 451, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 264, + 451, + 275 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 451, + 275 + ], + "type": "text", + "content": "3.2. Surface Field Convolution" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 282, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 449 + ], + "type": "text", + "content": "Because displacements in grid data are regular, traditional convolutions can directly learn a kernel for elements within a region. However, mesh vertices are unordered and irregular. Considering the special mesh representations, we represent each vertex by encoding features from its neighbor vertices inspired by [51,52]. To fully utilize meshes' local connectivity information, we consider the mesh properties of extrinsic curvature of submanifolds and intrinsic curvature of the manifold itself. Extrinsic curvature between two vertices is approximated using Euclidean distance. Intrinsic curvature is approximated using Geodesic distance, which is defined as the shortest path between two vertices on mesh surfaces. We propose a light-weighted surface field convolution to build local patches, which can be denoted as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 457, + 555, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 457, + 555, + 496 + ], + "spans": [ + { + "bbox": [ + 306, + 457, + 555, + 496 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {V G} ^ {\\prime (x, y, z)} = \\sum_ {(\\delta_ {x}, \\delta_ {y}, \\delta_ {z}) \\in G (x, y, z)} \\boldsymbol {W} ^ {(\\delta_ {x}, \\delta_ {y}, \\delta_ {z})} \\cdot \\boldsymbol {F} ^ {(x + \\delta_ {x}, y + \\delta_ {y}, z + \\delta_ {z})} \\tag {1}", + "image_path": "b00584c79ab10baf66cac36219ccc9f407958993b9a808b98e6eb8f9c8c0a2eb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 512, + 555, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 555, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 555, + 550 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {V E} ^ {\\prime (x, y, z)} = \\sum_ {(\\zeta_ {x}, \\zeta_ {y}, \\zeta_ {z}) \\in E (x, y, z)} \\boldsymbol {W} ^ {(\\zeta_ {x}, \\zeta_ {y}, \\zeta_ {z})} \\cdot \\boldsymbol {F} ^ {(x + \\zeta_ {x}, y + \\zeta_ {y}, z + \\zeta_ {z})} \\tag {2}", + "image_path": "b9e81764832bf04cc62d080727efb00b1365da50130b75535b674d85d00b19da.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": " is the local region around vertex " + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": ". In this paper, we use k-nearest-neighbor to sample local vertices. " + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "(\\delta_x,\\delta_y,\\delta_z)" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "(\\zeta_x,\\zeta_y,\\zeta_z)" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": " represent the spatial displacement in geodesic and euclidean space, respectively. " + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\pmb{F}^{(x,y,z)}" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": " denotes the feature of the vertex at position " + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 306, + 556, + 545, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 635, + 534, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 534, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 534, + 647 + ], + "type": "text", + "content": "3.3. Hierarchical Spatial-Temporal Transformer" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 654, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 714 + ], + "type": "text", + "content": "We propose a hierarchical transformer that consists of intra-frame and inter-frame attention. The basic idea behind our transformer is three-fold: (1) Intra-frame attention can encode connectivity information from the adjacency matrix, while such information can not be directly" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1528" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 73, + 313, + 216 + ], + "blocks": [ + { + "bbox": [ + 50, + 73, + 313, + 216 + ], + "lines": [ + { + "bbox": [ + 50, + 73, + 313, + 216 + ], + "spans": [ + { + "bbox": [ + 50, + 73, + 313, + 216 + ], + "type": "image", + "image_path": "aa2fef466fec1635359291bd667378c4cbdc65c4dffb5d8abaf57d743821a73d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 143, + 226, + 236, + 238 + ], + "lines": [ + { + "bbox": [ + 143, + 226, + 236, + 238 + ], + "spans": [ + { + "bbox": [ + 143, + 226, + 236, + 238 + ], + "type": "text", + "content": "(a) STMT Architecture" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 318, + 76, + 542, + 211 + ], + "blocks": [ + { + "bbox": [ + 318, + 76, + 542, + 211 + ], + "lines": [ + { + "bbox": [ + 318, + 76, + 542, + 211 + ], + "spans": [ + { + "bbox": [ + 318, + 76, + 542, + 211 + ], + "type": "image", + "image_path": "497862271b69e92e5eb0b916093744d61c6576242f878e79f96e45802861775a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 387, + 226, + 478, + 239 + ], + "lines": [ + { + "bbox": [ + 387, + 226, + 478, + 239 + ], + "spans": [ + { + "bbox": [ + 387, + 226, + 478, + 239 + ], + "type": "text", + "content": "(b) Pre-Training Stage" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 251, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 545, + 339 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed framework. (a) Overview of STMT. Given a mesh sequence, we first develop vertex patches by extracting both intrinsic (geodesic) and extrinsic (euclidean) features using surface field convolution. The intrinsic and extrinsic features are denoted by yellow and blue blocks respectively. Those patches are used as input to the intra-frame offset-attention network to learn appearance features. Then we concatenate intrinsic patches and extrinsic patches of the same position. The concatenated vertex patches (green blocks) are fed into the inter-frame self-attention network to learn spatial-temporal correlations. Finally, the local and global features are mapped into action predictions by MLP layers. (b) Overview of Pre-Training Stage. We design two pretext tasks: masked vertex modeling and future frame prediction for global context learning. Bidirectional attention is used for the reconstruction of masked vertices. Auto-regressive attention is used for the future frame prediction task." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 351, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 287, + 411 + ], + "type": "text", + "content": "aggregated in the temporal domain because vertices are unordered. (2) Frame-level offset-attention can be used to mimic the Laplacian operator to learn effective spatial representations. (3) Inter-frame self-attention can learn feature correlations in the spatial-temporal domain." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 429, + 206, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 429, + 206, + 440 + ], + "spans": [ + { + "bbox": [ + 47, + 429, + 206, + 440 + ], + "type": "text", + "content": "3.3.1 Intra-Frame Offset-Attention" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "text", + "content": "Graph convolution networks [6] show the benefits of using a Laplacian matrix " + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{L} = \\mathbf{D} - \\mathbf{E}" + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "text", + "content": " to replace the adjacency matrix " + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 46, + 449, + 287, + 567 + ], + "type": "text", + "content": " is the diagonal degree matrix. Inspired by this, offset-attention has been proposed and achieved superior performance in point-cloud classification and segmentation tasks [20]. We adapt offset-attention to attend to vertex patches. Specifically, the offset-attention layer calculates the offset (difference) between the self-attention (SA) features and the input features by element-wise subtraction. Offset-attention is denoted as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 579, + 287, + 591 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 579, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 78, + 579, + 287, + 591 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {\\text {o u t}} = O A \\left(\\boldsymbol {F} _ {\\text {i n}}\\right) = \\phi \\left(\\boldsymbol {F} _ {\\text {i n}} - \\boldsymbol {F} _ {\\text {s a}}\\right) + \\boldsymbol {F} _ {\\text {i n}}. \\tag {3}", + "image_path": "3c5e9ef57da7183527bb81a859c12f77ecd98aa31b07e4b49e750c53ffecc695.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": " denotes a non-linear operator. " + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "inline_equation", + "content": "F_{in} - F_{sa}" + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": " is proved to be analogous to discrete Laplacian operator [20], i.e. " + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "inline_equation", + "content": "F_{in} - F_{sa} \\approx LF_{in}" + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": ". As Laplacian operators in geodesic and euclidean space are expected to be different, we propose to use separate transformers to model intrinsic patches and extrinsic patches. Specifically, the aggregated feature for vertex " + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 602, + 287, + 685 + ], + "type": "text", + "content": " is denoted as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 64, + 698, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 698, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 64, + 698, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {V} ^ {\\prime (x, y, z)} = O A _ {G} \\left(\\boldsymbol {F} _ {V G} ^ {\\prime (x, y, z)}\\right) \\oplus O A _ {E} \\left(\\boldsymbol {F} _ {V E} ^ {\\prime (x, y, z)}\\right) \\tag {4}", + "image_path": "23b09b8c911cdf8c369f9bdd8b4849028af43f3b08c363c5d536250c5f8f3fe2.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "F_{VG}^{\\prime (x,y,z)}\\in \\mathbb{R}^{N\\times d_g}" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "F_{VE}^{\\prime (x,y,z)}\\in \\mathbb{R}^{N\\times d_e}" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": " are local patches learned using Equ. 1 and Equ. 2. " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "F_V^{\\prime (x,y,z)}\\in" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{N\\times d}" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": " denotes the local patch for position " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "d = d_{g} + d_{e}" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": ". The weights of " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "OA_{G}" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "inline_equation", + "content": "OA_{E}" + }, + { + "bbox": [ + 305, + 349, + 545, + 403 + ], + "type": "text", + "content": " are not shared." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 417, + 454, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 417, + 454, + 428 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 454, + 428 + ], + "type": "text", + "content": "3.3.2 Inter-Frame Self-Attention" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "inline_equation", + "content": "F_V'" + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": " which encodes local connectivity information, we use self-attention (SA) [65] to learn semantic affinities between different vertex patches across frames. Specifically, let " + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\mathbf{Q},\\mathbf{K},\\mathbf{V}" + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": " be the query, key and value, which are generated by applying linear transformations to the input features " + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "inline_equation", + "content": "F_V' \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 304, + 436, + 545, + 509 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 348, + 517, + 499, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 517, + 499, + 531 + ], + "spans": [ + { + "bbox": [ + 348, + 517, + 499, + 531 + ], + "type": "interline_equation", + "content": "(\\boldsymbol {Q}, \\boldsymbol {K}, \\boldsymbol {V}) = F _ {V} ^ {\\prime} \\cdot (\\boldsymbol {W} _ {q}, \\boldsymbol {W} _ {k}, \\boldsymbol {W} _ {v})", + "image_path": "4ef058e964e7526e8c92bcc401d0f3d62a2d8eec03adfc7a17e737048f041f48.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 371, + 533, + 501, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 533, + 501, + 547 + ], + "spans": [ + { + "bbox": [ + 371, + 533, + 501, + 547 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Q}, \\boldsymbol {K} \\in \\mathbb {R} ^ {N \\times d _ {a}}, \\quad \\boldsymbol {V} \\in \\mathbb {R} ^ {N \\times d}", + "image_path": "ef4ee2622943b57d912f54e1055d4c73eacdcba6d67762cb2d6028b65f22b176.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 356, + 549, + 545, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 549, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 356, + 549, + 545, + 564 + ], + "type": "interline_equation", + "content": "\\boldsymbol {W} _ {q}, \\boldsymbol {W} _ {k} \\in \\mathbb {R} ^ {d \\times d _ {a}}, \\quad \\boldsymbol {W} _ {v} \\in \\mathbb {R} ^ {d \\times d} \\tag {5}", + "image_path": "a83d87df1c6d38963553bb9e71cffa4c27e38a1d7c5651a68108884ae26e6a99.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "inline_equation", + "content": "W_{q}" + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "inline_equation", + "content": "W_{k}" + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "inline_equation", + "content": "W_{v}" + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "text", + "content": " are the shared learnable linear transformation, and " + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "inline_equation", + "content": "d_{a}" + }, + { + "bbox": [ + 306, + 574, + 545, + 620 + ], + "type": "text", + "content": " is the dimension of the query and key vectors. Then we can use the query and key matrices to calculate the attention weights via the matrix dot-product:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 354, + 621, + 545, + 650 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 621, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 354, + 621, + 545, + 650 + ], + "type": "interline_equation", + "content": "\\boldsymbol {A} = (\\tilde {\\alpha}) _ {i, j} = \\operatorname {s o f t m a x} \\left(\\frac {\\boldsymbol {Q} \\cdot \\boldsymbol {K} ^ {\\mathrm {T}}}{\\sqrt {d _ {a}}}\\right). \\tag {6}", + "image_path": "26bd36ba81b199abb092524beec898759d2a917f245f0329e96086cf23aaf193.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 397, + 658, + 545, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 397, + 658, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 397, + 658, + 545, + 671 + ], + "type": "interline_equation", + "content": "\\boldsymbol {F} _ {s a} = \\boldsymbol {A} \\cdot \\boldsymbol {V} \\tag {7}", + "image_path": "237e99a4934d98f66b98eb1a4dfebf268263999aee5d7da4f9a8dec54b1f3274.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "type": "text", + "content": "The self-attention output features " + }, + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "F_{sa}" + }, + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "type": "text", + "content": " are the weighted sums of the value vector using the corresponding attention weights. Specifically, for a vertex patch in position " + }, + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 306, + 677, + 545, + 714 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1529" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "text", + "content": "its aggregated feature after inter-frame self-attention can be computed as: " + }, + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\pmb{F}_{sa}^{(x,y,z)} = \\sum \\pmb{A}^{(x,y,z),(x',y',z')} \\times \\pmb{V}^{(x',y',z')}" + }, + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "(x',y',z')" + }, + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "text", + "content": " belongs to the Cartesian coordinates of " + }, + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "inline_equation", + "content": "\\pmb{F}_V'" + }, + { + "bbox": [ + 47, + 72, + 287, + 122 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 130, + 206, + 144 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 130, + 206, + 144 + ], + "spans": [ + { + "bbox": [ + 47, + 130, + 206, + 144 + ], + "type": "text", + "content": "3.4. Self-Supervised Pre-Training" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 149, + 289, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 149, + 289, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 289, + 461 + ], + "type": "text", + "content": "Self-supervised learning has achieved remarkable results on large-scale image datasets [23]. However, self-supervised learning for temporal 3D sequences (i.e. point cloud, 3D skeleton) remains to be challenging and has not been fully explored. There are two possible reasons: (1) self-supervised learning methods rely on large-scale datasets to learn meaningful patterns [10]. However, existing MoCap benchmarks are relatively small compared to 2D datasets like ImageNet [11]. (2) Self-supervised learning for 3D data sequences is computationally expensive in terms of memory and speed. In this work, we first propose a simple and effective method to augment existing MoCap sequences, and then define two effective and efficient self-supervised learning tasks, namely masked vertex modeling and future frame prediction, which enable the model to learn global context. The work that is close to us is OcCO [67], which proposed to use occluded point cloud reconstruction as the pretext task. OcCO has a computationally-expensive process to generate occlusions, including point cloud projection, occluded point calculation, and a mapping step to convert camera frames back to world frames. Different from OcCO, we randomly mask vertex patches or future frames on the fly, which saves the pre-processing step. Moreover, our pre-training method is designed for temporal mesh sequences and considers both bi-directional and autoregressive attention." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 476, + 257, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 476, + 257, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 476, + 257, + 489 + ], + "type": "text", + "content": "3.4.1 Data Augmentation through Joint Shuffle" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": "Considering the flexibility of SMPL-H representations, we propose a simple yet effective approach to augment SMPL-H sequences by shuffling body pose parameters. Specifically, we split SMPL-H pose parameters into five body parts: bone, left/right arm, and left/right leg. We use " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "I_{bone}, I_{leg}^{left}, I_{leg}^{right}, I_{arm}^{left}, I_{arm}^{right}" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " to denote the SMPL-H pose indexes of the five body parts. Then we synthesize new sequences by randomly selecting body parts from five different sequences. We keep the temporal order for each part such that the merged action sequences have meaningful motion trajectories. Pseudocode for the joint shuffle is provided in Algorithm 1. The input to Joint Shuffle are SMPL-H pose parameters " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "\\theta \\in \\mathbb{R}^{b \\times t \\times n \\times 3}" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " is the sequence number, " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " is the frame number, and " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " is the joint number. We randomly select the shape " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " and dynamic parameters " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " from one of the five SMPL-H sequences to compose a new SMPL-H body model. Given " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " SMPL-H sequences, we can synthesize " + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "inline_equation", + "content": "{}^b C_5 = \\frac{b!}{5!(b - 5)!}" + }, + { + "bbox": [ + 46, + 495, + 289, + 716 + ], + "type": "text", + "content": " number of new sequences." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "We prove that the model can benefit from large-scale pretraining in Section 4.6." + } + ] + } + ], + "index": 5 + }, + { + "type": "code", + "bbox": [ + 323, + 114, + 558, + 287 + ], + "blocks": [ + { + "bbox": [ + 313, + 101, + 514, + 111 + ], + "lines": [ + { + "bbox": [ + 313, + 101, + 514, + 111 + ], + "spans": [ + { + "bbox": [ + 313, + 101, + 514, + 111 + ], + "type": "text", + "content": "Algorithm 1: Pseudocode of STMT Joint Shuffle" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "lines": [ + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "spans": [ + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": "1: function STMT JOINT SHUFFLE( " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta \\in" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{b\\times t\\times n\\times 3}" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{bone}},I_{\\mathrm{leg}}^{\\mathrm{left}},I_{\\mathrm{leg}}^{\\mathrm{right}},I_{\\mathrm{arm}}^{\\mathrm{left}},I_{\\mathrm{arm}}^{\\mathrm{right}})" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " \n2: " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_s\\gets" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " random_sample(0,5) " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\triangleright \\theta_s\\in \\mathbb{R}^{5\\times t\\times n\\times 3}" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " randomly sample five SMPL-H sequences \n3: " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "t_{max}\\gets" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " get_max_length( " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_{s})" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " compute the maximum sequence length in " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_{s}" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " \n4: " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_{new}\\gets" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " Initialize " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "(t_{max},n,3)" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "P\\gets \\{I_{\\mathrm{bone}},I_{\\mathrm{leg}}^{\\mathrm{left}},I_{\\mathrm{leg}}^{\\mathrm{right}},I_{\\mathrm{arm}}^{\\mathrm{left}},I_{\\mathrm{arm}}^{\\mathrm{right}}\\}" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " \n6: for i in 0,1,2,3,4 do \n7: " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_s\\gets" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " repeat " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "(\\theta_s[i],(t_{max},n,3))" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " pad each sequence to the max length using repeating \n8: " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_{new}[P[i]]\\gets \\theta_s[i][P[i]]\\triangleright" + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "text", + "content": " assign the body-part sequence \n9: return " + }, + { + "bbox": [ + 323, + 114, + 558, + 287 + ], + "type": "inline_equation", + "content": "\\theta_{new}" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_body" + } + ], + "index": 7, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 307, + 545, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 307, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 306, + 307, + 545, + 330 + ], + "type": "text", + "content": "3.4.2 Masked Vertex Modeling with Bi-Directional Attention" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "text", + "content": "To fully activate the inter-frame bi-directional attention in the transformer, we design a self-supervised pretext task named Masked Vertex Modeling (MVM). The model can learn human prior information in the spatial dimension by reconstructing masked vertices of different body parts. We randomly mask " + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "text", + "content": " percentages of the input vertex patches, and force the model to reconstruct the full sequences. Moreover, we use bi-directional attention to learn correlations among all remaining local patches. Each patch will attend to all patches in the entire sequence. It models the joint distribution of vertex patches over the whole temporal sequences " + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "text", + "content": " as the following product of conditional distributions, where " + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 338, + 547, + 495 + ], + "type": "text", + "content": " is a single vertex patch:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 354, + 496, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 496, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 354, + 496, + 545, + 529 + ], + "type": "interline_equation", + "content": "p (x) = \\prod_ {i = 1} ^ {N} p \\left(x _ {i} \\mid x _ {1},.., x _ {i}, \\dots , x _ {N}\\right). \\tag {8}", + "image_path": "e16cf050c67a8bce26ffa4c96556f4d973035b741e84db73384b8ba1f54be376.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "type": "text", + "content": " is the number of patches in the entire sequence " + }, + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 534, + 547, + 594 + ], + "type": "text", + "content": " after masking. Every patch will attend to all patches in the entire sequence. In this way, bi-directional attention is fully-activated to learn spatial-temporal features that can accurately reconstruct completed mesh sequences." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 609, + 545, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 633 + ], + "type": "text", + "content": "3.4.3 Future Frame Prediction with Auto-Regressive Attention" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "The masked vertex modeling task is to reconstruct masked vertices in different body parts. The model can reconstruct completed mesh sequences if it captures the human body prior or can make a movement inference from nearby frames. As action recognition requires the model to understand the global context, we propose the future frame" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1530" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "prediction (FFP) task. Specifically, we mask out all the future frames and force the transformer to predict the masked frames. Moreover, we propose to use auto-regressive attention for the future frame prediction task, inspired by language generation models like GPT-3 [5]. However, directly using RNN-based models [9] in GPT-3 to predict future frames one by one is inefficient, as 3D mesh sequences are denser compared to language sequences. Therefore, we propose to reconstruct all future frames in a single forward pass. For auto-regressive attention, we model the joint distribution of vertex patches over a mesh sequence " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " as the following product of conditional distributions, where " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " is a single patch at frame " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 99, + 236, + 287, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 236, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 99, + 236, + 287, + 269 + ], + "type": "interline_equation", + "content": "p (x) = \\prod_ {i = 1} ^ {N} p \\left(x _ {i} \\mid x _ {1}, x _ {2}, \\dots , x _ {M}\\right). \\tag {9}", + "image_path": "97dcc62147470bb2a5f9612d0185a13fd3e9855cf2c9a2fc7b5e409edfdcc6a5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "text", + "content": " is the number of patches in the entire sequence " + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "text", + "content": " after masking. " + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "inline_equation", + "content": "M = (t_i - 1) \\times n" + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 277, + 289, + 361 + ], + "type": "text", + "content": " is the number of patches in a single frame. Each vertex patch depends on all patches that are temporally before it. The auto-regressive attention enables the model to predict movement patterns and trajectories, which is beneficial for the downstream action recognition task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 375, + 111, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 111, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 111, + 388 + ], + "type": "text", + "content": "3.5. Training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 396, + 287, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 492 + ], + "type": "text", + "content": "In the pre-training stage, we use PCN [74] as the decoder to reconstruct masked vertices and predict future frames. The decoder is shared for the two pretext tasks. Since mesh vertices are unordered, the reconstruction loss and future prediction loss should be permutation-invariant. Therefore, we use Chamfer Distance (CD) as the loss function to measure the difference between the model predictions and ground truth mesh sequences." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 498, + 287, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 498, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 51, + 498, + 287, + 572 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} C D (M _ {p r e d}, M _ {g t}) = \\frac {1}{\\left| M _ {p r e d} \\right|} \\sum_ {x \\in M _ {p r e d}} \\min _ {y \\in M _ {g t}} \\| x - y \\| _ {2} + \\\\ \\frac {1}{| M _ {g t} |} \\sum_ {y \\in M _ {g t}} \\min _ {x \\in M _ {p r e d}} \\| y - x \\| _ {2} \\tag {10} \\\\ \\end{array}", + "image_path": "1f4083ae449f70deba23ed1ff245385973096ba42a4cd72e69f151c3b0f98b82.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": "CD (10) calculates the average closest euclidean distance between the predicted mesh sequences " + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "inline_equation", + "content": "M_{pred}" + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": " and the ground truth sequences " + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "inline_equation", + "content": "M_{gt}" + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": ". The overall loss is a weighted sum of masked vertex reconstruction loss and future frame prediction loss:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 53, + 647, + 287, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 647, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 53, + 647, + 287, + 663 + ], + "type": "interline_equation", + "content": "L = \\lambda_ {1} C D \\left(M _ {p r e d} ^ {M V M}, M _ {g t}\\right) + \\lambda_ {2} C D \\left(M _ {p r e d} ^ {F F P}, M _ {g t}\\right) \\tag {11}", + "image_path": "0f37fe5f3b1e02b7d0daa99c10ef4aadc60f73b179f554136dcebcab0fd21ac9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "In the fine-tuning stage, we replace the PCN decoder with an MLP head. Cross-entropy loss is used for model training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 71, + 382, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 382, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 382, + 85 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 91, + 369, + 102 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 369, + 102 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 369, + 102 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "text", + "content": "Following previous MoCap-based action recognition methods [50,63], we evaluate our model on the most widely used benchmarks: KIT [42] and BABEL [50]. KIT is one of the largest MoCap datasets. It has 56 classes with 6,570 sequences in total. (2) BABEL is the largest 3D MoCap dataset that unifies 15 different datasets. BABEL has 43 hours of MoCap data performed by over 346 subjects. We use the 60-class subset from BABEL, which contains 21,653 sequences with single-class labels. We randomly split each dataset into training, test, and validation set, with ratios of " + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "inline_equation", + "content": "70\\%" + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 304, + 109, + 545, + 288 + ], + "type": "text", + "content": ", respectively. Note that existing action recognition datasets with skeletons only are not suitable for our experiments, as they do not provide full 3D surfaces or SMPL parameters to obtain the mesh representation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": "Motion Representation. Both KIT and BABEL's MoCap sequences are obtained from AMASS dataset in SMPL-H format. A MoCap sequence is an array of pose parameters over time, along with the shape and dynamic parameters. For skeleton-based action recognition, we follow previous work [50] which predicted the 25-joint skeleton from the vertices of the SMPL-H mesh. The movement sequence is represented as " + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = (\\mathbf{x}_1,\\dots ,\\mathbf{x}_L)" + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i\\in \\mathbb{R}^{J\\times 3}" + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": " represents the position of the " + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": " joints in the skeleton in Cartesian coordinates. For point-cloud-based action recognition, we directly use the vertices of SMPL-H model as the model input. The point-cloud sequence is represented as " + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = (\\mathbf{p}_1,\\dots ,\\mathbf{p}_L)" + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i\\in \\mathbb{R}^{V\\times 3}" + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 303, + 545, + 507 + ], + "type": "text", + "content": " is the number of vertices. For mesh-based action recognition, we represent the motion as a series of mesh vertices and their adjacent matrix over time, as introduced in Section 3.1. See Sup. Mat. for more details about datasets and pre-processing." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 514, + 410, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 410, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 410, + 525 + ], + "type": "text", + "content": "4.2. Baseline Methods" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 532, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 665 + ], + "type": "text", + "content": "We compare our model with state-of-the-art 3D skeleton-based and point cloud-based action recognition models, as there is no existing literature on mesh-based action recognition. 2s-AGCN [61], CTR-GCN [7], and MS-G3D [37] are used as skeleton-based baselines. Among those methods, 2s-AGCN trained with focal loss and cross-entropy loss are used as benchmark methods in the BABEL dataset [50]. For the comparison with point-cloud baselines, we choose PSTNet [18], SequentialPointNet [30], and P4Transformer [16]. Those methods achieved top performance on common point-cloud-based action recognition benchmarks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 440, + 684 + ], + "type": "text", + "content": "4.3. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "For skeleton-based baselines, we use the official implementations of 2s-ACGN, CTR-GCN, and MS-G3D from" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1531" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 56, + 503, + 183 + ], + "blocks": [ + { + "bbox": [ + 94, + 56, + 503, + 183 + ], + "lines": [ + { + "bbox": [ + 94, + 56, + 503, + 183 + ], + "spans": [ + { + "bbox": [ + 94, + 56, + 503, + 183 + ], + "type": "table", + "html": "
MethodInputKITBABEL-60
Top-1 (%)Top-5 (%)Top-1 (%)Top-5 (%)
2s-AGCN-FL [61] (CVPR'19)3D Skeleton42.4475.6049.6279.12
2s-AGCN-CE [61] (CVPR'19)3D Skeleton57.4681.5463.5786.77
CTR-GCN [7] (ICCV'21)3D Skeleton64.6587.9067.3088.50
MS-G3D [37] (CVPR'20)3D Skeleton65.3887.9067.4387.99
PSTNet [18] (ICLR'21)Point Cloud56.9388.2161.9484.11
SequentialPointNet [30] (arXiv'21)Point Cloud59.7588.0162.9284.58
P4Transformer [16] (CVPR'21)Point Cloud62.1588.0163.5486.55
STMT(Ours)Mesh65.5990.0967.6588.68
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IntrinsicExtrinsicMVMFFPTop-1 (%)
✓63.40
✓✓64.03
✓✓✓64.96
✓✓✓64.13
✓✓✓✓65.59
", + "image_path": "80c8c7a395be59d419d6a0a15065bc31abe35ba6298a478898b0ae7137667c09.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 293, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 305, + 293, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 545, + 338 + ], + "type": "text", + "content": "Table 2. Performance of ablated versions. Intrinsic and Extrinsic stand for the intrinsic (geodesic) and extrinsic (euclidean) features in surface field convolution. MVM stands for Masked Vertex Modelling. FFP stands for Future Frame Prediction." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 346, + 400, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 346, + 400, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 346, + 400, + 360 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 365, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 546, + 581 + ], + "type": "text", + "content": "Ablation Study of STMT. We test various ablations of our model on the KIT dataset to substantiate our design decisions. We report the results in Table 2. Note that Joint Shuffle is used in all of the self-supervised learning experiments (last three rows). We observe that each component of our model gains consistent improvements. The comparison of the first two rows proves the effectiveness of encoding both intrinsic and extrinsic features in vertex patches. Comparing the last three rows with the second row, we observe a consistent improvement using self-supervised pretraining. Moreover, the downstream task can achieve better performance with MVM compared to FFP. One probable reason is that the single task for future frame prediction is more challenging than masked vertex modeling, as the model can only see the person movement in the past. The model can achieve the best performance with both MVM and FFP, which demonstrates that the two self-supervised tasks are supplementary to each other." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 587, + 369, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 369, + 601 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 369, + 601 + ], + "type": "text", + "content": "4.6. Analysis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Different Pre-Training Strategies. We pre-train our model with different datasets and summarize the results in Table 3. The first row shows the case without pre-training. The second shows the result for the model pre-trained on the KIT dataset (without Joint Shuffle augmentation). The third shows the result for the model pre-trained on KIT dataset (with Joint Shuffle). We observe our model can achieve better performance with Joint Shuffle, as it can synthesize large-scale mesh sequences." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1532" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 101, + 56, + 233, + 112 + ], + "blocks": [ + { + "bbox": [ + 101, + 56, + 233, + 112 + ], + "lines": [ + { + "bbox": [ + 101, + 56, + 233, + 112 + ], + "spans": [ + { + "bbox": [ + 101, + 56, + 233, + 112 + ], + "type": "table", + "html": "
MethodTop-1 (%)
w/o pre-training64.03
pre-training w/o JS64.13
pre-training w/ JS65.59
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rPre-Train Loss (×104)Fine-Tune Accuracy (%)
0.10.3964.44
0.30.4164.55
0.50.4065.59
0.70.4364.19
0.90.4865.07
Rand0.4364.75
", + "image_path": "605ec4395a372dea48acf101f6154c981cd4611f9449ca0f579ec2ceb70089d6.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 85, + 247, + 247, + 258 + ], + "lines": [ + { + "bbox": [ + 85, + 247, + 247, + 258 + ], + "spans": [ + { + "bbox": [ + 85, + 247, + 247, + 258 + ], + "type": "text", + "content": "Table 4. Effect of Different Masking Ratios." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 45, + 265, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 265, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 45, + 265, + 287, + 493 + ], + "type": "text", + "content": "Different Masking Ratios. We investigate the impact of different masking ratios. We report the converged pretraining loss and the fine-tuning top-1 classification accuracy on the test set in Table 4. We also experiment with the random masking ratio in the last row. For each forward pass, we randomly select one masking ratio from 0.1 to 0.9 with step 0.1 to mimic flexible masked token length. The model with a random masking ratio does not outperform the best model that is pre-trained using a single ratio (i.e. 0.5). We observe that as the masking ratio increases, the pre-training loss mostly increases as the task becomes more challenging. However, a challenging self-supervised learning task does not necessarily lead to better performance. The model with a masking ratio of 0.7 and 0.9 have a high pre-train loss, while the fine-tune accuracy is not higher than the model with a 0.5 masking ratio. The conclusion is similar to the comparison of MVM and FFP training objectives, where a more challenging self-supervised learning task may not be optimal." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 507, + 286, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 286, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 286, + 604 + ], + "type": "text", + "content": "Different Number of Mesh Sequences for Pre-Training. We test the effect of different numbers of mesh sequences used in pre-training. We report the fine-tuning top-1 classification accuracy in Figure 4. We observe that a large number of pre-training data can bring substantial performance improvement. The proposed Joint Shuffle method can greatly enlarge the dataset size without any manual cost, and has the potential to further improve model performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 713 + ], + "type": "text", + "content": "Experimental Results on Noisy Body Pose Estimations. Body pose estimation has been a popular research field [25, 27, 32], but how to leverage the estimated 3D meshes for downstream perception tasks has not been fully explored. We apply the state-of-the-art body pose estimation model VIBE [27] on videos of NTU RGB+D dataset to obtain 3D mesh sequences. Skeleton and point cloud representations are derived from the estimated meshes to train the baseline" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 312, + 53, + 539, + 166 + ], + "blocks": [ + { + "bbox": [ + 312, + 53, + 539, + 166 + ], + "lines": [ + { + "bbox": [ + 312, + 53, + 539, + 166 + ], + "spans": [ + { + "bbox": [ + 312, + 53, + 539, + 166 + ], + "type": "image", + "image_path": "9c09f51a55c6ee85e1e3c0641fd224994d6f4f50757f3dc29d1953c493b40c99.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 322, + 191, + 529, + 300 + ], + "blocks": [ + { + "bbox": [ + 320, + 168, + 531, + 180 + ], + "lines": [ + { + "bbox": [ + 320, + 168, + 531, + 180 + ], + "spans": [ + { + "bbox": [ + 320, + 168, + 531, + 180 + ], + "type": "text", + "content": "Figure 4. Effect of Different Number of Mesh Sequences." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 322, + 191, + 529, + 300 + ], + "lines": [ + { + "bbox": [ + 322, + 191, + 529, + 300 + ], + "spans": [ + { + "bbox": [ + 322, + 191, + 529, + 300 + ], + "type": "table", + "html": "
MethodInputTop-1 (%)
2s-AGCN-FL [61]3D Skeleton58.67
2s-AGCN-CE [61]3D Skeleton57.49
CTR-GCN [7]3D Skeleton62.25
MS-G3D [37]3D Skeleton60.01
PSTNet [18]Point Cloud51.48
SequentialPointNet [30]Point Cloud60.60
P4Transformer [16]Point Cloud57.84
STEMT(Ours)Mesh64.04
", + "image_path": "8a9614245ba24ceb7dd73748a1c4816eb8e7234952d938b385183dd05bd64c68.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 309, + 545, + 343 + ], + "lines": [ + { + "bbox": [ + 305, + 309, + 545, + 343 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 545, + 343 + ], + "type": "text", + "content": "Table 5. Experimental results on body poses estimated by VIBE [27] on NTU RGB+D dataset. The skeleton, point cloud, and mesh representations are derived from the same noisy body estimations." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "type": "text", + "content": "models (see Sup. Mat.). We report the results in Table 5. We observe that STMT can outperform the best skeleton-based and point cloud-based action recognition model by " + }, + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "type": "inline_equation", + "content": "1.79\\%" + }, + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "type": "inline_equation", + "content": "3.44\\%" + }, + { + "bbox": [ + 305, + 353, + 545, + 437 + ], + "type": "text", + "content": " respectively. This shows that STMT with meshes as input, is more robust to input noise compared to other state-of-the-art methods with 3D skeletons or point clouds as input." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 452, + 378, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 378, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 378, + 464 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 473, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 617 + ], + "type": "text", + "content": "In this work, we propose a novel approach for MoCap-based action recognition. Unlike existing methods that rely on skeleton representation, our proposed model directly models the raw mesh sequences. Our method encodes both intrinsic and extrinsic features in vertex patches, and uses a hierarchical transformer to freely attend to any two vertex patches in the spatial and temporal domain. Moreover, two self-supervised learning tasks, namely Masked Vertex Modeling and Future Frame Prediction are proposed to enforce the model to learn global context. Our experiments show that STMT can outperform state-of-the-art skeleton-based and point-cloud-based models." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 632, + 399, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 399, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 399, + 646 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "content": "This work was supported by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-17-5-0003. This work used Bridges-2 GPU resources provided by PSC through allocation CIS220012 from the ACCESS program." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1533" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 53, + 92, + 287, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 92, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 287, + 158 + ], + "type": "text", + "content": "[1] Felix Achilles, Alexandru-Eugen Ichim, Huseyin Coskun, Federico Tombari, Soheyl Noahtar, and Nassir Navab. 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Pervasive and Mobile Computing, 7(2):256-269, 2011. 1" + } + ] + } + ], + "index": 27 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1536" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/STMixer_ A One-Stage Sparse Action Detector/7eef5975-ffbf-46c0-a31b-5b464eef7eef_content_list.json b/2023/STMixer_ A One-Stage Sparse Action Detector/7eef5975-ffbf-46c0-a31b-5b464eef7eef_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f78cb69e9a063de540053b75960b69d5e387a408 --- /dev/null +++ b/2023/STMixer_ A One-Stage Sparse Action Detector/7eef5975-ffbf-46c0-a31b-5b464eef7eef_content_list.json @@ -0,0 +1,1701 @@ +[ + { + "type": "text", + "text": "STMixer: A One-Stage Sparse Action Detector", + "text_level": 1, + "bbox": [ + 245, + 130, + 722, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tao Wu $^{1,*}$ Mengqi Cao $^{1,*}$ Ziteng Gao $^{1}$ Gangshan Wu $^{1}$ Limin Wang $^{1,2,\\text{四}}$ $^{1}$ State Key Laboratory for Novel Software Technology, Nanjing University $^{2}$ Shanghai AI Lab {wt,mg20370004}@smail.nju.edu.cn, gzt@outlook.com, {gswu, lmwang}@nju.edu.cn", + "bbox": [ + 107, + 178, + 862, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Traditional video action detectors typically adopt the two-stage pipeline, where a person detector is first employed to generate actor boxes and then 3D RoIAlign is used to extract actor-specific features for classification. This detection paradigm requires multi-stage training and inference, and cannot capture context information outside the bounding box. Recently, a few query-based action detectors are proposed to predict action instances in an end-to-end manner. However, they still lack adaptability in feature sampling and decoding, thus suffering from the issues of inferior performance or slower convergence. In this paper, we propose a new one-stage sparse action detector, termed STMixer. STMixer is based on two core designs. First, we present a query-based adaptive feature sampling module, which endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain. Second, we devise a dual-branch feature mixing module, which allows our STMixer to dynamically attend to and mix video features along the spatial and the temporal dimension respectively for better feature decoding. Coupling these two designs with a video backbone yields an efficient end-to-end action detector. Without bells and whistles, our STMixer obtains the state-of-the-art results on the datasets of AVA, UCF101-24, and JHMDB.", + "bbox": [ + 75, + 301, + 473, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 695, + 209, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video action detection [14, 18, 20, 30, 32, 44, 46] is an important problem in video understanding, which aims to recognize all action instances present in a video and also localize them in both space and time. It has drawn a significant amount of research attention, due to its wide applications in many areas like security and sports analysis.", + "bbox": [ + 75, + 720, + 468, + 813 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Since the proposal of large-scale action detection benchmarks [16, 22], action detection has made remarkable progress. This progress is partially due to the advances of video representation learning such as video convolution", + "bbox": [ + 75, + 813, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0ff58ff55d66220429555a7d5f77914a82ee7714cc92cb49e05f628d7f889ac8.jpg", + "image_caption": [ + "Figure 1. Comparison of mAP versus GFLOPs. We report detection mAP on AVA v2.2. The GFLOPs of CSN, SlowFast, and VideoMAE are the sum of Faster RCNN-R101-FPN detector GFLOPs and classifier GFLOPs. Different methods are marked by different makers and models with the same backbone are marked in the same color. The results of CSN are from [53]. Our STMixer achieves the best effectiveness and efficiency balance." + ], + "image_footnote": [], + "bbox": [ + 531, + 267, + 859, + 459 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "neural networks [5, 11, 39-41, 45, 50] and video transformers [1, 3, 9, 27, 38, 43, 52].", + "bbox": [ + 496, + 577, + 890, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most current action detectors adopt the two-stage Faster R-CNN-alike detection paradigm [31]. They share two basic designs. First, they use an auxiliary human detector to generate actor bounding boxes in advance. The training of the human detector is decoupled from the action classification network. Second, in order to predict the action category for each actor box, the RoIAlign [17] operation is applied on video feature maps to extract actor-specific features. However, these two-stage action detection pipeline has several critical issues. First, it requires multi-stage training of person detector and action classifier, which requires large computing resources. Furthermore, the RoIAlign [17] operation constrains the video feature sampling inside the actor bounding box and lacks the flexibility of capturing context information in its surroundings. To enhance RoI features, recent works use an extra heavy module that introduces interaction features of context or other actors [29, 36].", + "bbox": [ + 496, + 609, + 892, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently sparse query-based object detector [4, 35, 54] has brought a new perspective on detection tasks. Several", + "bbox": [ + 498, + 869, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*: Equal contribution. $\\boxtimes$ Corresponding author.", + "bbox": [ + 99, + 886, + 362, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14720", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "query-based sparse action detectors [6, 53] are proposed. The key idea is that action instances can be represented as a set of learnable queries, and detection can be formulated as a set prediction task, which could be trained by a matching loss. These query-based methods detect action instances in an end-to-end manner, thus saving computing resources. However, the current sparse action detectors still lack adaptability in feature sampling or feature decoding, thus suffering from inferior accuracy or slow convergence issues. For example, building on the DETR [4] framework, TubeR [53] adaptively attends action-specific features from single-scale feature maps but perform feature transformation in a static manner. On the contrary, though decoding sampled features with dynamic interaction heads, WOO [6] still uses the 3D RoIAlign [17] operator for feature sampling, which constrains feature sampling inside the actor bounding box and fails to take advantage of other useful information in the entire spatiotemporal feature space.", + "bbox": [ + 75, + 90, + 472, + 362 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following the success of adaptive sparse object detector AdaMixer [12] in images, we present a new query-based one-stage sparse action detector, named STMixer. Our goal is to create a simple action detection framework that can sample and decode features from the complete spatiotemporal video domain in a more flexible manner, while retaining the benefits of sparse action detectors, such as end-to-end training and reduced computational cost. Specifically, we come up with two core designs. First, to overcome the aforementioned fixed feature sampling issue, we present a query-guided adaptive feature sampling module. This new sampling mechanism endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain and capturing context and interaction information. Second, we devise a dual-branch feature mixing module to extract discriminative representations for action detection. It is composed of an adaptive spatial mixer and an adaptive temporal mixer in parallel to focus on appearance and motion information, respectively. Coupling these two designs with a video backbone yields a simple, neat, and efficient end-to-end actor detector, which obtains a new state-of-the-art performance on the datasets of AVA [16], UCF101-24 [33], and JHMDB [19]. In summary, our contribution is threefold:", + "bbox": [ + 75, + 363, + 472, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a new one-stage sparse action detection framework in videos (STMixer). Our STMixer is easy to train in an end-to-end manner and efficient to deploy for action detection in a single stage.", + "- We devise two flexible designs to yield a powerful action detector. The adaptive sampling can select the discriminative feature points and the adaptive feature mixing can enhance spatiotemporal representations.", + "- STMixer achieves a new state-of-the-art performance on three challenging action detection benchmarks." + ], + "bbox": [ + 94, + 732, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Action detectors using an extra human detector. Most current action detectors [9-11,29,36,38,47] rely on an auxiliary human detector to perform actor localization on the keyframes. Typically, the powerful Faster RCNN-R101-FPN [31] detector is used as the human detector, which is first pre-trained on the COCO [26] dataset and then fine-tuned on the AVA [16] dataset. With actor bounding boxes predicted in advance, the action detection problem is reduced to a pure action classification problem. The RoIAlign [17] operation is applied on the 3D feature maps extracted by a video backbone to generate actor-specific features. SlowFast [11] and MViT [9] directly use the RoI features for action classification. However, RoI features only contain the information inside the bounding box but overlook context and interaction information outside the box. To remedy this inherent flaw of RoI features, AIA [36] and ACARN [29] resort to using an extra heavy module that models the interaction between the actor and context or other actors. The models with an extra human detector require two-stage training and reference, which is computing resources unfriendly. Besides, they suffer from the aforementioned issue of fixed RoI feature sampling.", + "bbox": [ + 496, + 114, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "End-to-end action detectors. Methods of another research line use a single model to perform action detection. Most of them [6, 13, 21, 34] still follow the two-stage pipeline but simplify the training process by jointly training the actor proposal network and action classification network in an end-to-end manner. These methods still have the issue of fixed RoI feature sampling. To remedy this, VTr [13] attends RoI features to full feature maps while ACRN [34] introduces an actor-centric relation network for interaction modeling. Recently, several one-stage action detectors [24, 53] are proposed. MOC [24] is a point-based dense action detector, which uses an image backbone for frame feature extraction. It concatenates frame features along the temporal axis to form the video feature maps. Each point on the feature maps is regarded as an action instance proposal. The bounding box and action scores of each point are predicted by convolution. MOC [24] relies more on appearance features, lacks temporal and interaction modeling and requires post-process. Building on DETR [4] framework, TubeR [53] is a query-based action detector. TubeR [53] adaptively samples features from single-scale feature maps, neglecting multi-scale information which is important for detection tasks. As DETR [4], TubeR [53] transforms features in a static manner, resulting in slower convergence.", + "bbox": [ + 496, + 448, + 892, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by AdaMixer [12], we propose a new one-stage query-based detector for video action detection. Different from former query-based action detectors [6, 53], we adaptively sample discriminative features from a multi-scale spatiotemporal feature space and decode them with a more flexible scheme under the guidance of queries.", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14721", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b7814303962db1f188e713194b7e94edd0a47c674044d11446f045b0298159ee.jpg", + "image_caption": [ + "Figure 2. Pipeline of STMixer. In the left, we present the overall STMixer framework. A video clip is input to the video backbone for feature extraction and a 4D feature space is constructed based on the feature maps (see Section 3.1). Then, a decoder containing $M$ ASAM modules iteratively performs adaptive feature sampling (see Section 3.3) from the 4D feature space and adaptive mixing (see Section 3.4) on the sampled features under the guidance of a set of learnable queries. Inversely, the queries are updated with mixed features. Optionally, a short-term or long-term classifier can be used for action scores prediction, whose detailed structures are illustrated in the right. The long-term classifier refers to the long-term query bank produced by an offline STMixer for long-term information (see Section 3.5)." + ], + "image_footnote": [], + "bbox": [ + 122, + 92, + 632, + 306 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dd63efa76c2ea5c2cd59ded1aaaa3a71e60afa04036d9a4f16299aa0c0e74049.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 95, + 836, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 424, + 166, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section presents our one-stage sparse action detector, called STMixer. The overall pipeline of STMixer is shown in Figure 2. Our STMixer comprises a video backbone for feature extraction, a feature space construction module, and a sparse action decoder composed of $M$ adaptive sampling and adaptive mixing (ASAM) modules followed by prediction heads. As a common practice, we set the middle frame of an input clip as the keyframe. We first use the video backbone to extract feature maps for the video and a 4D feature space is constructed based on the feature maps. Then, we develop the sparse action decoder with a set of learnable queries. Under the guidance of these queries, we perform adaptive feature sampling and feature mixing in the 4D feature space. The queries are updated iteratively. Finally, we decode each query as a detected action instance of action scores, human scores, and a human box. We will describe the technical details of each step in the next subsections.", + "bbox": [ + 75, + 452, + 473, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. 4D Feature Space Construction", + "text_level": 1, + "bbox": [ + 76, + 739, + 354, + 755 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hierarchical video backbone. Formally, let $X_{z} \\in \\mathbb{R}^{C_{z} \\times T \\times H_{z} \\times W_{z}}$ denote the feature map of convolution stage $z$ of the hierarchical backbone, where $z \\in \\{2, 3, 4, 5\\}$ , $C_{z}$ stands for the channel number, $T$ for time, $H_{z}$ and $W_{z}$ for the spatial height and width. The stage index $z$ can be seen as the scale index of the feature map as $X_{z}$ has the downsampling rate of $2^{z}$ . We first transform each feature map $X_{z}$ to the same channel $D$ by $1 \\times 1 \\times 1$ convolution. Then, we rescale the spatial shape of each stage feature map", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a6c678b368bc723a59d1f2721c3f1bb33970f8fe9eaeb01ec3898b6e8c0a0e95.jpg", + "image_caption": [ + "Figure 3. 4D feature space construction for hierarchical video backbone. We construct 4D feature space on multi-scale 3D feature maps from hierarchical video backbone by simple lateral convolution and nearest-neighbor interpolation. The four dimensions of the 4D feature space are x-, y-, t-axis, and scale index z." + ], + "image_footnote": [], + "bbox": [ + 535, + 426, + 856, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to $H_{2} \\times W_{2}$ by simple nearest-neighbor interpolation and align them along the x- and y-axis. The four dimensions of the constructed feature space are x-, y-, t-axis, and scale index z, respectively. This process is illustrated in Figure 3. Plain ViT backbone. To make STMixer framework compatible with plain ViT [7] backbone, inspired by ViTDet [23], we construct 4D feature space based on the last feature map from ViT backbone. Specifically, with the output feature map of the default downsampling rate of $2^{4}$ , we first produce hierarchical feature maps $\\{X_{z}\\}$ of the same channel number $D$ using convolutions of spatial strides $\\left\\{\\frac{1}{4}, \\frac{1}{2}, 1, 2\\right\\}$ , where a fractional stride indicates a deconvolution. Then we also rescale each feature map to the spatial size of $H_{2} \\times W_{2}$ .", + "bbox": [ + 496, + 604, + 892, + 818 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Query Definition", + "text_level": 1, + "bbox": [ + 500, + 830, + 666, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The definition of our queries derives from the object query in Sparse R-CNN [35], but we specify the action query in a disentangled fashion. Specifically, we factorize", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14722", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "action queries into spatial queries $Q_{s} \\in \\mathbb{R}^{N \\times D}$ and temporal queries $Q_{t} \\in \\mathbb{R}^{N \\times D}$ to refer to the spatial content and temporal content respectively. $N$ represents the number of queries, while $D$ denotes the dimension of each query.", + "bbox": [ + 75, + 89, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We further define positional queries $Q_{p} \\in \\mathbb{R}^{N \\times 4}$ . Each positional query $Q_{p}^{n}$ ( $n$ stands for the query index) is formulated as a proposal box vector ( $x^{n}, y^{n}, z^{n}, r^{n}$ ). Formally, $x^{n}$ and $y^{n}$ stand for the x- and y-axis coordinates of the box center, and $z^{n}$ and $r^{n}$ denote the logarithm of its scale (i.e. the area of the bounding box) and aspect ratio. The positional queries $Q_{p}$ are initialized in such a way that every box vector is the whole keyframe.", + "bbox": [ + 75, + 151, + 467, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Adaptive Spatiotemporal Feature Sampling", + "text_level": 1, + "bbox": [ + 76, + 279, + 446, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from previous work [6, 11, 29, 36] that samples RoI features by pre-computed proposal boxes, we sample actor-specific features adaptively from the aforementioned 4D feature space under the guidance of spatial queries. Specifically, given a spatial query $Q_{s}^{n}$ and the corresponding positional query $Q_{p}^{n}$ , we regard the center point $(x^{n}, y^{n}, z^{n})$ of the proposal box as the reference point, and regress $P_{in}$ groups of offsets along x-, y-axis and scale index z on query $Q_{s}^{n}$ , using a linear layer:", + "bbox": [ + 75, + 301, + 467, + 438 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\left(\\triangle x _ {i} ^ {n}, \\triangle y _ {i} ^ {n}, \\triangle z _ {i} ^ {n}\\right) \\right\\} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 443, + 468, + 468 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $i\\in \\mathbb{Z}$ and $1\\leqslant i\\leqslant P_{in}$", + "bbox": [ + 173, + 463, + 372, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P_{in}$ is the number of sampled points for each query. Then, the offsets are added to the reference point, thus $P_{in}$ spatial feature points are obtained:", + "bbox": [ + 75, + 484, + 467, + 529 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\widetilde {x} _ {i} ^ {n} = x ^ {n} + \\triangle x _ {i} ^ {n} \\cdot 2 ^ {z ^ {n} - r ^ {n}}, \\\\ \\widetilde {y} _ {i} ^ {n} = y ^ {n} + \\triangle y _ {i} ^ {n} \\cdot 2 ^ {z ^ {n} + r ^ {n}}, \\\\ \\widetilde {z} _ {i} ^ {n} = z ^ {n} + \\triangle z _ {i} ^ {n}. \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 535, + 468, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $2^{z^n - r^n}$ and $2^{z^n + r^n}$ are the width and height of the box respectively. We offset the spatial position of sampling points with respect to the width and height of the box to reduce the learning difficulty.", + "bbox": [ + 75, + 597, + 467, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we propagate sampling points along the temporal axis, thus obtaining $T \\times P_{in}$ points to sample from the 4D feature space. In our implementation, we simply copy these spatial sampling points along the temporal dimension because current action detection datasets yield temporal slowness property that the variation of actor locations along the temporal dimension is very slow. We compare different ways of temporal propagating in our ablation study.", + "bbox": [ + 75, + 659, + 467, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given $T \\times P_{in}$ sampling points, we sample instance-specific features by interpolation from the 4D feature space. In the following sections, the sampled spatiotemporal feature for spatial query $Q_{s}^{n}$ is denoted by $F^{n} \\in \\mathbb{R}^{T \\times P_{in} \\times D}$ .", + "bbox": [ + 75, + 779, + 467, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Adaptive Dual-branch Feature Mixing", + "text_level": 1, + "bbox": [ + 76, + 847, + 406, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After feature sampling, we factorize the sampled features into spatial features and temporal features by pooling", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and then enhance each by adaptive mixing respectively. As the dual-branch mixing module is completely symmetrical, we only describe spatial mixing in detail and temporal mixing is performed in a homogeneous way.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from MLP-Mixer [37], our mixing parameters are generated adaptively. Given a spatial query $Q_{s}^{n}\\in \\mathbb{R}^{D}$ and its corresponding sampled features $F^n\\in \\mathbb{R}^{T\\times P_{in}\\times D}$ , we first use a linear layer to generate query-specific channel-mixing weights $M_{c}\\in \\mathbb{R}^{D\\times D}$ , and then apply plain matrix multiplication on temporally pooled feature and $M_{c}$ to perform channel-mixing, given by:", + "bbox": [ + 496, + 151, + 890, + 257 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {c} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right) \\in \\mathbb {R} ^ {D \\times D}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 265, + 890, + 282 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {C M} \\left(F ^ {n}\\right) = \\operatorname {R e L U} \\left(\\operatorname {L a y e r N o r m} \\left(\\operatorname {G A P} \\left(F ^ {n}\\right) \\times M _ {c}\\right)\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 316, + 890, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where GAP stands for the global average pooling operation in the temporal dimension while LayerNorm for the layer normalization [2]. We use $\\mathbf{CM}(F^n) \\in \\mathbb{R}^{P_{in} \\times D}$ to denote the channel-wise mixing output features.", + "bbox": [ + 496, + 344, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After channel-mixing, we perform point-wise mixing in a similar way. Suppose $P_{out}$ is the number of spatial pointwise mixing out patterns, we use $\\mathrm{PCM}(F^n) \\in \\mathbb{R}^{D \\times P_{out}}$ to denote the point-wise mixing output features, given by:", + "bbox": [ + 496, + 404, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nM _ {p} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right) \\in \\mathbb {R} ^ {P _ {i n} \\times P _ {o u t}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 473, + 890, + 491 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P C M} \\left(F ^ {n}\\right) = \\operatorname {R e L U} \\left(\\operatorname {L a y e r N o r m} \\left(\\operatorname {C M} \\left(F ^ {n}\\right) ^ {T} \\times M _ {p}\\right)\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 523, + 890, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The final output $\\mathrm{PCM}(F^n)$ is flattened, transformed to $D$ dimension, and added to the spatial query $Q_{s}^{n}$ . The temporal query $Q_{t}^{n}$ is updated in a homogeneous way, except that the pooling is applied in the spatial dimension. After global spatial pooling, there are $T$ feature points of different temporal locations for temporal mixing and we set the number of temporal point-wise mixing out patterns to $T_{out}$ .", + "bbox": [ + 496, + 551, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Sparse Action Decoder", + "text_level": 1, + "bbox": [ + 500, + 666, + 710, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "STMixer adopts a unified action decoder for both actor localization and action classification. The decoder comprises $M$ stacked ASAM modules followed by a feedforward network (FFN) for human scores prediction and a short-term or long-term classifier for action score prediction. In this section, we represent the structure of ASAM module and specify the outputs of the prediction heads.", + "bbox": [ + 496, + 688, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ASAM module. The overall structure of ASAM module is shown in Figure 2. We first perform self-attention [42] on spatial queries $Q_{s}$ and temporal queries $Q_{t}$ to capture the relation information between different instances. Then we perform adaptive sampling from the 4D feature space and dual-branch adaptive mixing on the sampled feature as described before. The spatial queries $Q_{s}$ and temporal queries", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14723", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$Q_{t}$ are updated with mixed features. An FFN is applied on updated spatial queries $Q_{s}^{\\prime}$ to update the positional queries $Q_{p}$ . The updated queries $Q_{p}^{\\prime}, Q_{s}^{\\prime}$ and $Q_{t}^{\\prime}$ are used as inputs for the next ASAM module.", + "bbox": [ + 76, + 90, + 467, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Outputs of the prediction heads. The output human boxes are decoded from positional queries $Q_{p}^{\\prime}$ . We apply an FFN on $Q_{s}^{\\prime}$ to predict human scores $S_{H} \\in \\mathbb{R}^{N \\times 2}$ which indicates the confidence values that each box belongs to the human category and background. Based on the concatenation of spatial queries $Q_{s}^{\\prime}$ and temporal queries $Q_{t}^{\\prime}$ , we use a short-term or long-term classifier to predict action scores $S_{A} \\in \\mathbb{R}^{N \\times C}$ , where $C$ is the number of action classes.", + "bbox": [ + 76, + 151, + 467, + 272 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Short-term and long-term classifier. Short-term classifier (see Figure 2 right top) is a simple FFN which predicts action scores based on short-term information of current queries while long-term classifier (see Figure 2 right bottom) refers to long-term query bank for long-term information. Our design of the long-term classifier is adapted from LFB [47]. We train an STMixer model without long-term information first. Then, for a video of $\\mathcal{T}$ clips, we use the trained STMixer to perform inference on each clip of it. We store the concatenation of the spatial and temporal queries from the last ASAM module corresponding to the $k$ highest human scores in the query bank for each clip. We denote the stored queries for clip of time-step $t$ as $L_{t} \\in \\mathbb{R}^{k \\times d}$ where $d = 2D$ , and the long-term query bank of the video as $L = [L_{0}, L_{1}, \\dots, L_{\\mathcal{T}-1}]$ . Given the long-term query bank of all videos, we train an STMixer model with a long-term classifier from scratch. For video clip $t$ , we first sample a window of length $w$ from the long-term query bank centered at it and stack this window into $\\tilde{L}_{t} \\in \\mathbb{R}^{K \\times d}$ :", + "bbox": [ + 76, + 273, + 467, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {L} _ {t} = \\operatorname {s t a c k} \\left(\\left[ L _ {t - w / 2}, \\dots , L _ {t + w / 2 - 1} \\right]\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 575, + 467, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We then infer current queries to $\\tilde{L}_t$ for long-term information by cross-attention [42]:", + "bbox": [ + 76, + 602, + 467, + 633 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {t} ^ {\\prime} = \\text {c r o s s - a t t e n t i o n} \\left(S _ {t}, \\tilde {L} _ {t}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 645, + 467, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $S_{t} \\in \\mathbb{R}^{N \\times d}$ is the concatenation of the output spatial queries and temporal queries of the last ASAM module. The output $S_{t}'$ is then channel-wise concatenated with $S_{t}$ for action scores prediction.", + "bbox": [ + 76, + 672, + 467, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Training", + "text_level": 1, + "bbox": [ + 76, + 744, + 181, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compute training loss based on the output human boxes, human scores, and action scores. Consistent with WOO [6], the loss function $\\mathcal{L}$ consists of set prediction loss $\\mathcal{L}_{set}[4,35,54]$ and action classification loss $\\mathcal{L}_{act}$ . Formally,", + "bbox": [ + 76, + 768, + 467, + 829 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s e t} = \\lambda_ {c l s} \\mathcal {L} _ {c l s} + \\lambda_ {L _ {1}} \\mathcal {L} _ {L _ {1}} + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 845, + 467, + 862 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {s e t}} + \\lambda_ {\\text {a c t}} \\mathcal {L} _ {\\text {a c t}}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 885, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{cls}$ denotes the cross-entropy loss over two classes (human and background). $\\mathcal{L}_{L_1}$ and $\\mathcal{L}_{giou}$ are box loss inherited from [4, 35, 54]. As in [4, 6], we first use Hungarian algorithm to find an optimal bipartite matching between predicted actors and ground truth actors according to $\\mathcal{L}_{set}$ . Then we calculate full training loss $\\mathcal{L}$ based on the matching results. $\\mathcal{L}_{act}$ is binary cross entropy loss for action classification. We only compute $\\mathcal{L}_{act}$ for the prediction matched with a ground truth. $\\lambda_{cls}, \\lambda_{L_1}, \\lambda_{giou}$ , and $\\lambda_{act}$ are corresponding weights of each term.", + "bbox": [ + 500, + 90, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 258, + 630, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 282, + 689, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. The AVA dataset [16] contains 211k video clips for training and 57k for validation segmented from 430 15-minute videos. The videos are annotated at 1FPS over 80 atomic action classes. Following the standard evaluation protocol [16], we report our results on 60 action classes that have at least 25 validation examples. JHMDB [19] consists of 928 temporally trimmed videos from 21 action classes. Results averaged over three splits are reported. UCF101-24 is a subset of UCF101 [33]. It contains 3,207 videos annotated with action instances of 24 classes. As the common setting, we report the performance on the first split.", + "bbox": [ + 498, + 306, + 890, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Network configurations. We configure the dimension $D$ of both spatial and temporal queries to 256 and set the number of both queries $N$ equaling 100. The number of sampling point $P_{in}$ in each temporal frame is set to 32. The spatial and temporal mixing out patterns $P_{out}$ and $T_{out}$ are set to 4 times the number of sampling points and temporal frames respectively, that is, 128 and 32 for SlowFast [11] backbone and 128 and 16 for CSN [40] and ViT [7] backbone. Following multi-head attention [42] and group convolution [49], we split the channel $D$ into 4 groups and perform group-wise sampling and mixing. We stack 6 ASAM modules in our action decoder as default. For the long-term classifier, we set the number of stored queries of each clip $k$ as 5 and window length $w$ as 60. The number of cross-attention layers is set to 3.", + "bbox": [ + 498, + 474, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Losses and optimizers. We set the loss weight in STMixer as $\\lambda_{cls} = 2.0$ , $\\lambda_{L_1} = 2.0$ , $\\lambda_{giou} = 2.0$ and $\\lambda_{act} = 24.0$ . We use AdamW [28] optimizer with weight decay $1 \\times 10^{-4}$ for all experiments. Following [4, 6], intermediate supervision is applied after each ASAM module.", + "bbox": [ + 498, + 702, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training and inference recipes. We train STMixer detectors for 10 epochs with an initial learning rate of $2.0 \\times 10^{-5}$ and batchsize of 16. The learning rate and batchsize can be tuned according to the linear scaling rule [15]. We randomly scale the short size of the training video clips to 256 or 320 pixels. Color jittering and random horizontal flipping are also adopted for data augmentation.", + "bbox": [ + 498, + 777, + 890, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For inference, we scale the short size of input frames", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14724", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to 256 as the common setting. Given an input video clip, STMixer predicts $N$ bounding boxes associated with their human scores and action scores from the last ASAM module. If the confidence score that a box belongs to the human category is higher than the preset threshold, we take it as a detection result. We set the threshold to 0.6 for AVA. The performances are evaluated with official metric frame-level mean average precision(mAP) at 0.5 IoU threshold.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 224, + 230, + 242 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct ablation experiments on AVa v2.2 dataset to investigate the influence of different components in our STMixer framework. A SlowOnly ResNet-50 backbone [8] is used for our ablation experiments. We report both mAP and GFLOPs for effectiveness and efficiency comparison.", + "bbox": [ + 75, + 248, + 468, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablations on 4D feature space. We first show the benefit of sampling features from the unified 4D feature space. For comparison, we design a two-stage counterpart of our STMixer. In the first stage, we sample features from key-frame features for actor localization. In the second stage, we sample features from res5 features for action classification. As shown in Tabel 1a, sampling features from a unified 4D feature space and performing action detection in a one-stage manner significantly reduce computing costs, and detection mAP also gets improved as multi-scale information is also utilized for classification. We then investigate two different ways for the 4D feature space construction. As shown in Table 1b, constructing 4D feature space by simple lateral $1 \\times 1 \\times 1$ convolution achieves comparable detection accuracy while being more efficient than using full FPN [25] with a top-down pathway.", + "bbox": [ + 75, + 325, + 472, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablations on feature sampling. In Tabel 1c, we compare 3 different feature sampling strategies. For fixed grid feature sampling, we sample $7 \\times 7$ feature points inside each actor box by interpolation, which is actually the RoIAlign [17] operation adopted by many former methods [6,13]. Though sampling fewer points per group, our adaptive sampling strategy improves the detection mAP by 1.2. The results show that the fixed RoIAlign operation for feature sampling fails to capture useful context information outside the box while our adaptive sampling strategy enables the detector to mine discriminative features from the whole 4D feature space. Beyond simply copying sampling points, we try sampling different feature points in different frames by predicting the offset of the reference bounding box for each frame. The improvement is marginal due to the slowness issue of current action detection datasets that the variation of actors' location and action is very slow. In Table 1d, we further investigate the influence of the number of sampling points per group $P_{in}$ in each temporal frame. Setting $P_{in} = 32$ achieves the best detection performance.", + "bbox": [ + 75, + 566, + 472, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablations on feature mixing. In Table 1f, we compare different feature mixing strategies. We first demonstrate", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the benefit of query-guided adaptive mixing. The detection mAP drops by 0.6 when using fixed parameter mixing. For adaptive mixing, the mixing parameters are dynamically generated based on a specific query, thus more powerful to enhance the presentation of each specific action instance proposal. We further compare different adaptive feature mixing strategies. From the results in Table 1f, it is demonstrated that both spatial appearance and temporal motion information are important for action detection. However, coupled spatiotemporal feature mixing using queries of a single type has a high computational complexity. Decoupling features along spatial and temporal dimensions saves computing costs. Our dual-branch spatiotemporal feature mixing outperforms sequential spatiotemporal feature mixing by $0.5\\mathrm{mAP}$ . This is because actor localization at keyframes only needs spatial appearance information and parallel dual-branch mixing will reduce the effect of temporal information on localization. Also, by concatenating temporal queries to spatial queries, more temporal information is leveraged for action classification. In Table 1g, we investigate different spatial and temporal mixing out patterns $P_{out}$ and $T_{out}$ from 64 and 8 to 192 and 24, that is, 2 times to 6 times the number of sampling points and temporal frames. Setting $P_{out}$ and $T_{out}$ equaling 128 and 16 achieves the best performance.", + "bbox": [ + 496, + 90, + 893, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ablations on network configuration. As shown in Table 1e, the detection mAP is saturated when the number of queries is increased to 100. From the results in Table 1h, a stack of 6 ASAM modules achieves a good effectiveness and efficiency balance.", + "bbox": [ + 496, + 469, + 893, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with State-of-the-arts on AVA", + "text_level": 1, + "bbox": [ + 498, + 558, + 862, + 574 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our proposed STMixer with state-of-the-art methods on AVa v2.1 and v2.2 in Table 2. We first compare our STMixer to methods using an extra offline human detector. Our STMixer with SlowFast-R101 backbone achieves 30.6 and $30.9\\mathrm{mAP}$ when not using long-term features. With long-term query support, our STMixer reaches 32.6 and $32.9\\mathrm{mAP}$ on AVa v2.1 and v2.2 respectively. To demonstrate the generalization ability of our method, we conduct experiments with ViT [7] backbone. Compared with the two-stage counterparts, STMixer brings performance improvements while getting rid of the dependence on an extra detector. Although ViT is considered to have a global receptive field, our adaptive sampling and decoding mechanism could serve as a supplement to improve the flexibility of the model. Compared to previous end-to-end methods, our STMixer achieves the best results. Our STMixer outperforms WOO [6] by 2.0 and $1.7\\mathrm{mAP}$ even though WOO test models at 320 resolution. STMixer also consistently outperforms TubeR [53] on AVA v2.1 or v2.2, using or not using long-term features.", + "bbox": [ + 496, + 582, + 893, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare mAP versus GFLOPs on AVa v2.2 in Fig", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14725", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d6e763021e6b045b3d3dd22879f8e73e50999a4db9ed969ebc2d9e8d4006de54.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ClassificationLocalizationmAPGFLOPs
4D Feature Space23.144.4
Key-Frame FeaturesRes5 Features22.853.7
", + "bbox": [ + 80, + 89, + 344, + 122 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(a) Feature space. Sampling features from 4D feature space is more effective and efficient than sampling from key-frame features for classification and res5 features for localization.", + "bbox": [ + 76, + 125, + 349, + 172 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cb5cfc703e17b26281c35e54f286d0741f34221b5ba46185dd8c228cc32c3042.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Pin816324864
mAP22.422.523.123.022.5
GFLOPs42.443.144.445.646.9
", + "bbox": [ + 94, + 176, + 333, + 213 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(d) Number of sampling points. Sampling 32 points per frame achieves the best performance.", + "bbox": [ + 76, + 215, + 349, + 239 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/08c05992b2e0c7c89a49ad44ff5f762ece839402a892daadd24316fbd2939046.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Pout/Tout64/896/12128/16160/20192/24
mAP22.522.823.122.922.6
GFLOPs40.242.344.446.448.4
", + "bbox": [ + 80, + 244, + 344, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(g) Number of mixing out patterns. A moderate number of mixing out patterns works the best.", + "bbox": [ + 76, + 279, + 348, + 304 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/05b078434b7cf8f5c708f527afe6a162b9ff4270be484da1b4f4c01e647a46bc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
mAPGFLOPs
Simple Lateral Conv.23.144.4
Full FPN22.945.8
", + "bbox": [ + 362, + 89, + 563, + 122 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(b) 4D feature space construction. Simple lateral convolution achieves comparable performance while being more efficient than using full FPN.", + "bbox": [ + 359, + 125, + 566, + 172 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ea674372c89f8af90cc0ca73746e4476b5653b840887440321c919a5f9b4876d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
N1550100150
mAP22.122.923.122.5
GFLOPs31.736.944.451.8
", + "bbox": [ + 362, + 176, + 563, + 212 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(e) Number of queries. Using 100 queries works the best.", + "bbox": [ + 359, + 215, + 566, + 239 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b957d6422d936ec8f0c8c6921b32c95361eb7cb8e97536afdbdb2078584026d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
M1369
mAP18.422.523.122.6
GFLOPs32.036.944.451.8
", + "bbox": [ + 367, + 243, + 560, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(h) Number of ASAM modules. Using 6 ASAM modules works the best.", + "bbox": [ + 359, + 279, + 566, + 304 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/12ebdedf3407562cadc40496136060947b096703489cf8d2f4b74a6956e99b71.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Sampling StrategyPinmAPGFLOPs
Fixed Grid Sampling4921.945.6
Adaptive Sampling + Temporal Copying3223.144.4
Adaptive Sampling + Temporal Moving3223.344.6
", + "bbox": [ + 581, + 88, + 888, + 131 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(c) Sampling strategy. Sampling fewer feature points, our adaptive sampling strategy achieves better performance than fixed grid sampling. Temporal moving brings slight improvement in mAP.", + "bbox": [ + 576, + 133, + 890, + 181 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b87a916ec6efa949c52dadef014cb32615938a0f2e1ddeee9f1443c7d5e0b9ab.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Mixing StrategymAPGFLOPs
fixed parameter dual-branch mixing22.536.8
dual-branch spatiotemporal mixing23.144.4
spatial mixing only22.440.4
temporal mixing only22.133.5
sequential spatiotemporal mixing22.643.6
coupled spatiotemporal mixing22.893.2
", + "bbox": [ + 596, + 188, + 874, + 266 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(f) Mixing strategy. Query-guided adaptive feature mixing outperforms fixed parameter mixing and our dual-branch spatiotemporal feature mixing strategy works the best.", + "bbox": [ + 576, + 267, + 890, + 304 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/11d39b737a70c787423db5dc84368dabef6fca546f37c08df81dcc2c79552087.jpg", + "table_caption": [ + "Table 1. Ablations Experiments. We use a SlowOnly ResNet-50 backbone to perform our ablation studies. Models are trained on the training set of AVa v2.2 and evaluated on the validation set. Default choices for our model are colored in gray ." + ], + "table_footnote": [], + "table_body": "
MethodDetectorOne-stageInputBackbonePre-trainLFmAP
v2.1v2.2
Compare to methods with an extra human detector
SlowFast [11]✓✗32×2SF-R101-NLK600✗28.229.0
LFB [47]✓✗32×2I3D-R101-NLK400✓27.7-
CA-RCNN [48]✓✗32×2R50-NLK400✓28.0-
AIA [36]✓✗32×2SF-R101K700✓31.232.3
ACARN [29]✓✗32×2SF-R101K400✓30.0-
ACARN [29]✓✗32×2SF-R101-NLK600✓-31.4
VideoMAE [38]✓✗16×4ViT-BK400✗-31.8
VideoMAE [38]✓✗16×4ViT-LK700✗-39.3
STMixer✗✓32×2SF-R101K700✗30.630.9
STMixer✗✓32×2SF-R101K700✓32.632.9
STMixer✗✓16×4ViT-B (from [38])K400✗-32.6
STMixer✗✓16×4ViT-B (from [43])K710+K400✗-36.1
STMixer✗✓16×4ViT-L (from [38])K700✗-39.5
Compare to end-to-end methods
AVA [16]✗✗20×1I3D-VGGK400✗14.6-
ACRN [34]✗✗20×1S3D-GK400✗17.4-
STEP [51]✗✗12×1I3D-VGGK400✗18.6-
VTr [13]✗✗64×1I3D-VGGK400✗24.9-
WOO [6]✗✗32×2SF-R50K400✗25.225.4
WOO [6]✗✗32×2SF-R101-NLK600✗28.028.3
TubeR [53]✗✓32×2CSN-152IG-65M✗29.731.1
TubeR [53]✗✓32×2CSN-152IG-65M✓31.733.4
STMixer✗✓32×2SF-R50K400✗27.227.8
STMixer✗✓32×2SF-R101-NLK600✗29.830.1
STMixer✗✓32×2CSN-152IG-65M✗31.732.8
STMixer✗✓32×2CSN-152IG-65M✓34.434.8
", + "bbox": [ + 140, + 351, + 828, + 690 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparisons with state-of-the-arts on validation sets of AVa v2.1 and v2.2. √of column \"Detector\" denotes an extra human detector Faster RCNN-R101-FPN [31] is used. √of column \"LF\" denotes long-term features are used.", + "bbox": [ + 75, + 700, + 888, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ure 1 to show the efficiency of our STMixer. AIA [36] and ACARN [29] do not report their GFLOPs. As they are built on SlowFast [11] framework and also use an offline human detector but introduce extra modules to model interaction, SlowFast can serve as a lower bound of complexity for them. For a fair comparison, we report results for no long-term feature version of each method. As shown in Figure 1, due to an extra human detector being needed, SlowFast [11], CSN [40], and VideoMAE [38] have much higher GFLOPs than end-to-end methods with same back", + "bbox": [ + 75, + 747, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "bone. Among end-to-end methods, STMixer achieves the best effectiveness and efficiency balance. STMixer outperforms WOO [6] by $1.8\\mathrm{mAP}$ while having much lower GFLOPs (135 versus 252). With a slight GFLOPs increase (126 versus 120), STMixer outperforms TubeR [53] by 1.7 mAP.", + "bbox": [ + 496, + 747, + 890, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Results on JHMDB and UCF101-24", + "text_level": 1, + "bbox": [ + 500, + 847, + 810, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To verify the effectiveness of our STMixer, we further evaluate it on the JHMDB [19] and UCF101-24 [33]", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14726", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2594e5afbee7f070abd03606d03beee07a161411f2f8f58c389b83c07861944e.jpg", + "image_caption": [ + "Figure 4. Sampling points and detection results visualization. We display the actor bounding boxes and action classes of three groundtruth action instances in the first column. Each ASAM module's sampling points, predicted actor bounding boxes and action scores are displayed in the following columns. The correctly predicted action classes are displayed in green, missing in orange, and wrongly predicted in red. Intuitively, STMixer mines discriminative context features outside the bounding box for better action detection." + ], + "image_footnote": [], + "bbox": [ + 86, + 93, + 200, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5318ea11ec3cc126b72334afc61530d278a7f0232027473892edd038afcc7cfb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 202, + 93, + 313, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d9f396b54a8dc66435962bfc54b1f769e00ebf71c3157a17d385864b1151c3e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 315, + 93, + 424, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/66dacc388e2e55cbfd1ad80bf8ad1f294104145a1d404c4306e142a6e803c7d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 426, + 93, + 537, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/120416cd0bd405e4b49966a944832100227ac83372823f314a12947312142759.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 93, + 650, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9dc17c3a6db1a4df9b50807ac5b9da3786d94027e92eb918a7b82d11eb59aec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 651, + 93, + 761, + 262 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7c75a7bfd968f9d0302f18db86ee58be9e68ec58f02600c50e58a3141c0eeb78.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 93, + 874, + 262 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9d15dc9c56c20df5dc395ef495c09a9ff75cadde6e5334bc376b53c3b987e63b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodDetectorInputBackboneJHMDBUCF101-24
MOC* [24]✓7×1DLA3470.878.0
AVA* [16]✗20×1I3D-VGG73.376.3
ACRN [34]✗20×1S3D-G77.9-
CA-RCNN [48]✓32×2R50-NL79.2-
YOWO [21]✗16×13DResNext-10180.475.7
WOO [6]✗32×2SF-R101-NL80.5-
AIA [36]✓32×1SF-R50-NL-78.8
ACARN [29]✓32×1SF-R50-84.3
TubeR* [53]✗32×2I3D-81.3
STMixer✗32×2SF-R101-NL86.783.7
", + "bbox": [ + 89, + 342, + 457, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Comparison on JHMDB and UCF101-24. Methods marked with * use extra optical flow features.", + "bbox": [ + 76, + 481, + 468, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "datasets. We report the frame-level mean average precision (frame-mAP) with an intersection-over-union (IoU) threshold of 0.5 in Table 3. Experimental results demonstrate that STMixer outperforms the current state-of-the-art methods with remarkable performance gain on JHMDB and achieves competitive results on UCF101-24.", + "bbox": [ + 75, + 529, + 468, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Visualization", + "text_level": 1, + "bbox": [ + 76, + 633, + 212, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We provide the visualization of sampling points and detection results of each ASAM module in order in Figure 4. In the first few ASAM modules, the sampling points are quickly concentrated on the action performer and the actor localization accuracy gets improved rapidly. In the following ASAM modules, some of the sampling points get out of the human box and spread to the context. Benefiting from the gathered context and interaction information, the action recognition accuracy gets improved while localization accuracy is not compromised. In Figure 4, we show clear improvements in three aspects: predicting missing classes (ride in row 1), improving the confidence score of correctly predicted classes (talk to in row 2), and removing wrongly predicted classes (watch in row 3). To recognize an action \"ride\", we need to observe the person is in a car and someone is driving. For recognition of \"talk to\", we need to know", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "if a person is listening in the context, and for \"watch\", we need to know if a person is in the actor's sight. The improvements are mostly related to these classes of interaction, which indicates our STMixer is capable of mining discriminative interaction information from the context.", + "bbox": [ + 496, + 345, + 890, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 498, + 436, + 767, + 452 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented a new one-stage sparse action detector in videos, termed STMixer. Our STMixer yields a simple, neat, and efficient end-to-end action detection framework. The core design of our STMixer is a set of learnable queries to decode all action instances in parallel. The decoding process is composed of an adaptive feature sampling module to identify important features from the entire spatiotemporal domain of video, and an adaptive feature mixing module to dynamically extract discriminative representations for action detection. Our STMixer achieves a new state-of-the-art performance on three challenging benchmarks of AVA, JHMDB, and UCF101-24 with less computational cost than previous end-to-end methods. We hope STMixer can serve as a strong baseline for future research on video action detectors.", + "bbox": [ + 496, + 464, + 890, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "One limitation of our STMixer is that the long-term query bank is implemented in an offline way where another STMixer without long-term query support is pre-trained for long-term query generation. We leave the design of an online query bank to future research and hope our STMixer is extended to extract long-form video information in an end-to-end manner.", + "bbox": [ + 496, + 691, + 890, + 795 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006, No. 62072232), Fundamental Research Funds for the Central Universities (No. 020214380091), and Collaborative Innovation Center of Novel Software Technology and Industrialization.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14727", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, pages 6836-6846, 2021. 1", + "[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. 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OpenReview.net, 2021. 1, 5" + ], + "bbox": [ + 501, + 92, + 890, + 570 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14729", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/STMixer_ A One-Stage Sparse Action Detector/7eef5975-ffbf-46c0-a31b-5b464eef7eef_model.json b/2023/STMixer_ A One-Stage Sparse Action Detector/7eef5975-ffbf-46c0-a31b-5b464eef7eef_model.json new file mode 100644 index 0000000000000000000000000000000000000000..31155698a2ee252430f6f76ebe993efc2a49af07 --- /dev/null +++ b/2023/STMixer_ A One-Stage Sparse Action Detector/7eef5975-ffbf-46c0-a31b-5b464eef7eef_model.json @@ -0,0 +1,2255 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.246, + 0.131, + 0.723, + 0.154 + ], + "angle": 0, + "content": "STMixer: A One-Stage Sparse Action Detector" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.179, + 0.864, + 0.234 + ], + "angle": 0, + "content": "Tao Wu\\(^{1,*}\\) Mengqi Cao\\(^{1,*}\\) Ziteng Gao\\(^{1}\\) Gangshan Wu\\(^{1}\\) Limin Wang\\(^{1,2,\\text{四}}\\) \n\\(^{1}\\)State Key Laboratory for Novel Software Technology, Nanjing University \\(^{2}\\)Shanghai AI Lab {wt,mg20370004}@smail.nju.edu.cn, gzt@outlook.com, {gswu, lmwang}@nju.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.665 + ], + "angle": 0, + "content": "Traditional video action detectors typically adopt the two-stage pipeline, where a person detector is first employed to generate actor boxes and then 3D RoIAlign is used to extract actor-specific features for classification. This detection paradigm requires multi-stage training and inference, and cannot capture context information outside the bounding box. Recently, a few query-based action detectors are proposed to predict action instances in an end-to-end manner. However, they still lack adaptability in feature sampling and decoding, thus suffering from the issues of inferior performance or slower convergence. In this paper, we propose a new one-stage sparse action detector, termed STMixer. STMixer is based on two core designs. First, we present a query-based adaptive feature sampling module, which endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain. Second, we devise a dual-branch feature mixing module, which allows our STMixer to dynamically attend to and mix video features along the spatial and the temporal dimension respectively for better feature decoding. Coupling these two designs with a video backbone yields an efficient end-to-end action detector. Without bells and whistles, our STMixer obtains the state-of-the-art results on the datasets of AVA, UCF101-24, and JHMDB." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.696, + 0.21, + 0.712 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.47, + 0.814 + ], + "angle": 0, + "content": "Video action detection [14, 18, 20, 30, 32, 44, 46] is an important problem in video understanding, which aims to recognize all action instances present in a video and also localize them in both space and time. It has drawn a significant amount of research attention, due to its wide applications in many areas like security and sports analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Since the proposal of large-scale action detection benchmarks [16, 22], action detection has made remarkable progress. This progress is partially due to the advances of video representation learning such as video convolution" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.268, + 0.86, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.463, + 0.895, + 0.562 + ], + "angle": 0, + "content": "Figure 1. Comparison of mAP versus GFLOPs. We report detection mAP on AVA v2.2. The GFLOPs of CSN, SlowFast, and VideoMAE are the sum of Faster RCNN-R101-FPN detector GFLOPs and classifier GFLOPs. Different methods are marked by different makers and models with the same backbone are marked in the same color. The results of CSN are from [53]. Our STMixer achieves the best effectiveness and efficiency balance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.609 + ], + "angle": 0, + "content": "neural networks [5, 11, 39-41, 45, 50] and video transformers [1, 3, 9, 27, 38, 43, 52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.893, + 0.868 + ], + "angle": 0, + "content": "Most current action detectors adopt the two-stage Faster R-CNN-alike detection paradigm [31]. They share two basic designs. First, they use an auxiliary human detector to generate actor bounding boxes in advance. The training of the human detector is decoupled from the action classification network. Second, in order to predict the action category for each actor box, the RoIAlign [17] operation is applied on video feature maps to extract actor-specific features. However, these two-stage action detection pipeline has several critical issues. First, it requires multi-stage training of person detector and action classifier, which requires large computing resources. Furthermore, the RoIAlign [17] operation constrains the video feature sampling inside the actor bounding box and lacks the flexibility of capturing context information in its surroundings. To enhance RoI features, recent works use an extra heavy module that introduces interaction features of context or other actors [29, 36]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.87, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Recently sparse query-based object detector [4, 35, 54] has brought a new perspective on detection tasks. Several" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.363, + 0.901 + ], + "angle": 0, + "content": "*: Equal contribution. \\(\\boxtimes\\) Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14720" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.363 + ], + "angle": 0, + "content": "query-based sparse action detectors [6, 53] are proposed. The key idea is that action instances can be represented as a set of learnable queries, and detection can be formulated as a set prediction task, which could be trained by a matching loss. These query-based methods detect action instances in an end-to-end manner, thus saving computing resources. However, the current sparse action detectors still lack adaptability in feature sampling or feature decoding, thus suffering from inferior accuracy or slow convergence issues. For example, building on the DETR [4] framework, TubeR [53] adaptively attends action-specific features from single-scale feature maps but perform feature transformation in a static manner. On the contrary, though decoding sampled features with dynamic interaction heads, WOO [6] still uses the 3D RoIAlign [17] operator for feature sampling, which constrains feature sampling inside the actor bounding box and fails to take advantage of other useful information in the entire spatiotemporal feature space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.726 + ], + "angle": 0, + "content": "Following the success of adaptive sparse object detector AdaMixer [12] in images, we present a new query-based one-stage sparse action detector, named STMixer. Our goal is to create a simple action detection framework that can sample and decode features from the complete spatiotemporal video domain in a more flexible manner, while retaining the benefits of sparse action detectors, such as end-to-end training and reduced computational cost. Specifically, we come up with two core designs. First, to overcome the aforementioned fixed feature sampling issue, we present a query-guided adaptive feature sampling module. This new sampling mechanism endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain and capturing context and interaction information. Second, we devise a dual-branch feature mixing module to extract discriminative representations for action detection. It is composed of an adaptive spatial mixer and an adaptive temporal mixer in parallel to focus on appearance and motion information, respectively. Coupling these two designs with a video backbone yields a simple, neat, and efficient end-to-end actor detector, which obtains a new state-of-the-art performance on the datasets of AVA [16], UCF101-24 [33], and JHMDB [19]. In summary, our contribution is threefold:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.733, + 0.47, + 0.794 + ], + "angle": 0, + "content": "- We present a new one-stage sparse action detection framework in videos (STMixer). Our STMixer is easy to train in an end-to-end manner and efficient to deploy for action detection in a single stage." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.802, + 0.47, + 0.863 + ], + "angle": 0, + "content": "- We devise two flexible designs to yield a powerful action detector. The adaptive sampling can select the discriminative feature points and the adaptive feature mixing can enhance spatiotemporal representations." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "- STMixer achieves a new state-of-the-art performance on three challenging action detection benchmarks." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.733, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.447 + ], + "angle": 0, + "content": "Action detectors using an extra human detector. Most current action detectors [9-11,29,36,38,47] rely on an auxiliary human detector to perform actor localization on the keyframes. Typically, the powerful Faster RCNN-R101-FPN [31] detector is used as the human detector, which is first pre-trained on the COCO [26] dataset and then fine-tuned on the AVA [16] dataset. With actor bounding boxes predicted in advance, the action detection problem is reduced to a pure action classification problem. The RoIAlign [17] operation is applied on the 3D feature maps extracted by a video backbone to generate actor-specific features. SlowFast [11] and MViT [9] directly use the RoI features for action classification. However, RoI features only contain the information inside the bounding box but overlook context and interaction information outside the box. To remedy this inherent flaw of RoI features, AIA [36] and ACARN [29] resort to using an extra heavy module that models the interaction between the actor and context or other actors. The models with an extra human detector require two-stage training and reference, which is computing resources unfriendly. Besides, they suffer from the aforementioned issue of fixed RoI feature sampling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.893, + 0.81 + ], + "angle": 0, + "content": "End-to-end action detectors. Methods of another research line use a single model to perform action detection. Most of them [6, 13, 21, 34] still follow the two-stage pipeline but simplify the training process by jointly training the actor proposal network and action classification network in an end-to-end manner. These methods still have the issue of fixed RoI feature sampling. To remedy this, VTr [13] attends RoI features to full feature maps while ACRN [34] introduces an actor-centric relation network for interaction modeling. Recently, several one-stage action detectors [24, 53] are proposed. MOC [24] is a point-based dense action detector, which uses an image backbone for frame feature extraction. It concatenates frame features along the temporal axis to form the video feature maps. Each point on the feature maps is regarded as an action instance proposal. The bounding box and action scores of each point are predicted by convolution. MOC [24] relies more on appearance features, lacks temporal and interaction modeling and requires post-process. Building on DETR [4] framework, TubeR [53] is a query-based action detector. TubeR [53] adaptively samples features from single-scale feature maps, neglecting multi-scale information which is important for detection tasks. As DETR [4], TubeR [53] transforms features in a static manner, resulting in slower convergence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Inspired by AdaMixer [12], we propose a new one-stage query-based detector for video action detection. Different from former query-based action detectors [6, 53], we adaptively sample discriminative features from a multi-scale spatiotemporal feature space and decode them with a more flexible scheme under the guidance of queries." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14721" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.093, + 0.633, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.097, + 0.837, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Figure 2. Pipeline of STMixer. In the left, we present the overall STMixer framework. A video clip is input to the video backbone for feature extraction and a 4D feature space is constructed based on the feature maps (see Section 3.1). Then, a decoder containing \\( M \\) ASAM modules iteratively performs adaptive feature sampling (see Section 3.3) from the 4D feature space and adaptive mixing (see Section 3.4) on the sampled features under the guidance of a set of learnable queries. Inversely, the queries are updated with mixed features. Optionally, a short-term or long-term classifier can be used for action scores prediction, whose detailed structures are illustrated in the right. The long-term classifier refers to the long-term query bank produced by an offline STMixer for long-term information (see Section 3.5)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.425, + 0.168, + 0.44 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.474, + 0.724 + ], + "angle": 0, + "content": "This section presents our one-stage sparse action detector, called STMixer. The overall pipeline of STMixer is shown in Figure 2. Our STMixer comprises a video backbone for feature extraction, a feature space construction module, and a sparse action decoder composed of \\( M \\) adaptive sampling and adaptive mixing (ASAM) modules followed by prediction heads. As a common practice, we set the middle frame of an input clip as the keyframe. We first use the video backbone to extract feature maps for the video and a 4D feature space is constructed based on the feature maps. Then, we develop the sparse action decoder with a set of learnable queries. Under the guidance of these queries, we perform adaptive feature sampling and feature mixing in the 4D feature space. The queries are updated iteratively. Finally, we decode each query as a detected action instance of action scores, human scores, and a human box. We will describe the technical details of each step in the next subsections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.355, + 0.756 + ], + "angle": 0, + "content": "3.1. 4D Feature Space Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Hierarchical video backbone. Formally, let \\(X_{z} \\in \\mathbb{R}^{C_{z} \\times T \\times H_{z} \\times W_{z}}\\) denote the feature map of convolution stage \\(z\\) of the hierarchical backbone, where \\(z \\in \\{2, 3, 4, 5\\}\\), \\(C_{z}\\) stands for the channel number, \\(T\\) for time, \\(H_{z}\\) and \\(W_{z}\\) for the spatial height and width. The stage index \\(z\\) can be seen as the scale index of the feature map as \\(X_{z}\\) has the downsampling rate of \\(2^{z}\\). We first transform each feature map \\(X_{z}\\) to the same channel \\(D\\) by \\(1 \\times 1 \\times 1\\) convolution. Then, we rescale the spatial shape of each stage feature map" + }, + { + "type": "image", + "bbox": [ + 0.537, + 0.427, + 0.857, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Figure 3. 4D feature space construction for hierarchical video backbone. We construct 4D feature space on multi-scale 3D feature maps from hierarchical video backbone by simple lateral convolution and nearest-neighbor interpolation. The four dimensions of the 4D feature space are x-, y-, t-axis, and scale index z." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.893, + 0.819 + ], + "angle": 0, + "content": "to \\( H_{2} \\times W_{2} \\) by simple nearest-neighbor interpolation and align them along the x- and y-axis. The four dimensions of the constructed feature space are x-, y-, t-axis, and scale index z, respectively. This process is illustrated in Figure 3. Plain ViT backbone. To make STMixer framework compatible with plain ViT [7] backbone, inspired by ViTDet [23], we construct 4D feature space based on the last feature map from ViT backbone. Specifically, with the output feature map of the default downsampling rate of \\( 2^{4} \\), we first produce hierarchical feature maps \\( \\{X_{z}\\} \\) of the same channel number \\( D \\) using convolutions of spatial strides \\( \\left\\{\\frac{1}{4}, \\frac{1}{2}, 1, 2\\right\\} \\), where a fractional stride indicates a deconvolution. Then we also rescale each feature map to the spatial size of \\( H_{2} \\times W_{2} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.667, + 0.848 + ], + "angle": 0, + "content": "3.2. Query Definition" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The definition of our queries derives from the object query in Sparse R-CNN [35], but we specify the action query in a disentangled fashion. Specifically, we factorize" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14722" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.09, + 0.47, + 0.152 + ], + "angle": 0, + "content": "action queries into spatial queries \\( Q_{s} \\in \\mathbb{R}^{N \\times D} \\) and temporal queries \\( Q_{t} \\in \\mathbb{R}^{N \\times D} \\) to refer to the spatial content and temporal content respectively. \\( N \\) represents the number of queries, while \\( D \\) denotes the dimension of each query." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.468, + 0.273 + ], + "angle": 0, + "content": "We further define positional queries \\( Q_{p} \\in \\mathbb{R}^{N \\times 4} \\). Each positional query \\( Q_{p}^{n} \\) (\\( n \\) stands for the query index) is formulated as a proposal box vector (\\( x^{n}, y^{n}, z^{n}, r^{n} \\)). Formally, \\( x^{n} \\) and \\( y^{n} \\) stand for the x- and y-axis coordinates of the box center, and \\( z^{n} \\) and \\( r^{n} \\) denote the logarithm of its scale (i.e. the area of the bounding box) and aspect ratio. The positional queries \\( Q_{p} \\) are initialized in such a way that every box vector is the whole keyframe." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.28, + 0.447, + 0.296 + ], + "angle": 0, + "content": "3.3. Adaptive Spatiotemporal Feature Sampling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.439 + ], + "angle": 0, + "content": "Different from previous work [6, 11, 29, 36] that samples RoI features by pre-computed proposal boxes, we sample actor-specific features adaptively from the aforementioned 4D feature space under the guidance of spatial queries. Specifically, given a spatial query \\( Q_{s}^{n} \\) and the corresponding positional query \\( Q_{p}^{n} \\), we regard the center point \\( (x^{n}, y^{n}, z^{n}) \\) of the proposal box as the reference point, and regress \\( P_{in} \\) groups of offsets along x-, y-axis and scale index z on query \\( Q_{s}^{n} \\), using a linear layer:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.444, + 0.469, + 0.469 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\left(\\triangle x _ {i} ^ {n}, \\triangle y _ {i} ^ {n}, \\triangle z _ {i} ^ {n}\\right) \\right\\} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.464, + 0.374, + 0.48 + ], + "angle": 0, + "content": "where \\(i\\in \\mathbb{Z}\\) and \\(1\\leqslant i\\leqslant P_{in}\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.468, + 0.53 + ], + "angle": 0, + "content": "where \\(P_{in}\\) is the number of sampled points for each query. Then, the offsets are added to the reference point, thus \\(P_{in}\\) spatial feature points are obtained:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.536, + 0.469, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\widetilde {x} _ {i} ^ {n} = x ^ {n} + \\triangle x _ {i} ^ {n} \\cdot 2 ^ {z ^ {n} - r ^ {n}}, \\\\ \\widetilde {y} _ {i} ^ {n} = y ^ {n} + \\triangle y _ {i} ^ {n} \\cdot 2 ^ {z ^ {n} + r ^ {n}}, \\\\ \\widetilde {z} _ {i} ^ {n} = z ^ {n} + \\triangle z _ {i} ^ {n}. \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.468, + 0.659 + ], + "angle": 0, + "content": "where \\(2^{z^n - r^n}\\) and \\(2^{z^n + r^n}\\) are the width and height of the box respectively. We offset the spatial position of sampling points with respect to the width and height of the box to reduce the learning difficulty." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.468, + 0.78 + ], + "angle": 0, + "content": "Finally, we propagate sampling points along the temporal axis, thus obtaining \\( T \\times P_{in} \\) points to sample from the 4D feature space. In our implementation, we simply copy these spatial sampling points along the temporal dimension because current action detection datasets yield temporal slowness property that the variation of actor locations along the temporal dimension is very slow. We compare different ways of temporal propagating in our ablation study." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.468, + 0.841 + ], + "angle": 0, + "content": "Given \\( T \\times P_{in} \\) sampling points, we sample instance-specific features by interpolation from the 4D feature space. In the following sections, the sampled spatiotemporal feature for spatial query \\( Q_{s}^{n} \\) is denoted by \\( F^{n} \\in \\mathbb{R}^{T \\times P_{in} \\times D} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.408, + 0.864 + ], + "angle": 0, + "content": "3.4. Adaptive Dual-branch Feature Mixing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "After feature sampling, we factorize the sampled features into spatial features and temporal features by pooling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.891, + 0.152 + ], + "angle": 0, + "content": "and then enhance each by adaptive mixing respectively. As the dual-branch mixing module is completely symmetrical, we only describe spatial mixing in detail and temporal mixing is performed in a homogeneous way." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Different from MLP-Mixer [37], our mixing parameters are generated adaptively. Given a spatial query \\( Q_{s}^{n}\\in \\mathbb{R}^{D} \\) and its corresponding sampled features \\( F^n\\in \\mathbb{R}^{T\\times P_{in}\\times D} \\), we first use a linear layer to generate query-specific channel-mixing weights \\( M_{c}\\in \\mathbb{R}^{D\\times D} \\), and then apply plain matrix multiplication on temporally pooled feature and \\( M_{c} \\) to perform channel-mixing, given by:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.266, + 0.891, + 0.284 + ], + "angle": 0, + "content": "\\[\nM _ {c} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right) \\in \\mathbb {R} ^ {D \\times D}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.318, + 0.891, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\operatorname {C M} \\left(F ^ {n}\\right) = \\operatorname {R e L U} \\left(\\operatorname {L a y e r N o r m} \\left(\\operatorname {G A P} \\left(F ^ {n}\\right) \\times M _ {c}\\right)\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.891, + 0.405 + ], + "angle": 0, + "content": "where GAP stands for the global average pooling operation in the temporal dimension while LayerNorm for the layer normalization [2]. We use \\(\\mathbf{CM}(F^n) \\in \\mathbb{R}^{P_{in} \\times D}\\) to denote the channel-wise mixing output features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.891, + 0.466 + ], + "angle": 0, + "content": "After channel-mixing, we perform point-wise mixing in a similar way. Suppose \\( P_{out} \\) is the number of spatial pointwise mixing out patterns, we use \\( \\mathrm{PCM}(F^n) \\in \\mathbb{R}^{D \\times P_{out}} \\) to denote the point-wise mixing output features, given by:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.474, + 0.891, + 0.492 + ], + "angle": 0, + "content": "\\[\nM _ {p} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right) \\in \\mathbb {R} ^ {P _ {i n} \\times P _ {o u t}}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.524, + 0.891, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P C M} \\left(F ^ {n}\\right) = \\operatorname {R e L U} \\left(\\operatorname {L a y e r N o r m} \\left(\\operatorname {C M} \\left(F ^ {n}\\right) ^ {T} \\times M _ {p}\\right)\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.892, + 0.658 + ], + "angle": 0, + "content": "The final output \\(\\mathrm{PCM}(F^n)\\) is flattened, transformed to \\(D\\) dimension, and added to the spatial query \\(Q_{s}^{n}\\). The temporal query \\(Q_{t}^{n}\\) is updated in a homogeneous way, except that the pooling is applied in the spatial dimension. After global spatial pooling, there are \\(T\\) feature points of different temporal locations for temporal mixing and we set the number of temporal point-wise mixing out patterns to \\(T_{out}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.712, + 0.682 + ], + "angle": 0, + "content": "3.5. Sparse Action Decoder" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.891, + 0.795 + ], + "angle": 0, + "content": "STMixer adopts a unified action decoder for both actor localization and action classification. The decoder comprises \\(M\\) stacked ASAM modules followed by a feedforward network (FFN) for human scores prediction and a short-term or long-term classifier for action score prediction. In this section, we represent the structure of ASAM module and specify the outputs of the prediction heads." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ASAM module. The overall structure of ASAM module is shown in Figure 2. We first perform self-attention [42] on spatial queries \\( Q_{s} \\) and temporal queries \\( Q_{t} \\) to capture the relation information between different instances. Then we perform adaptive sampling from the 4D feature space and dual-branch adaptive mixing on the sampled feature as described before. The spatial queries \\( Q_{s} \\) and temporal queries" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14723" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.151 + ], + "angle": 0, + "content": "\\(Q_{t}\\) are updated with mixed features. An FFN is applied on updated spatial queries \\(Q_{s}^{\\prime}\\) to update the positional queries \\(Q_{p}\\). The updated queries \\(Q_{p}^{\\prime}, Q_{s}^{\\prime}\\) and \\(Q_{t}^{\\prime}\\) are used as inputs for the next ASAM module." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.152, + 0.468, + 0.273 + ], + "angle": 0, + "content": "Outputs of the prediction heads. The output human boxes are decoded from positional queries \\( Q_{p}^{\\prime} \\). We apply an FFN on \\( Q_{s}^{\\prime} \\) to predict human scores \\( S_{H} \\in \\mathbb{R}^{N \\times 2} \\) which indicates the confidence values that each box belongs to the human category and background. Based on the concatenation of spatial queries \\( Q_{s}^{\\prime} \\) and temporal queries \\( Q_{t}^{\\prime} \\), we use a short-term or long-term classifier to predict action scores \\( S_{A} \\in \\mathbb{R}^{N \\times C} \\), where \\( C \\) is the number of action classes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.275, + 0.468, + 0.562 + ], + "angle": 0, + "content": "Short-term and long-term classifier. Short-term classifier (see Figure 2 right top) is a simple FFN which predicts action scores based on short-term information of current queries while long-term classifier (see Figure 2 right bottom) refers to long-term query bank for long-term information. Our design of the long-term classifier is adapted from LFB [47]. We train an STMixer model without long-term information first. Then, for a video of \\(\\mathcal{T}\\) clips, we use the trained STMixer to perform inference on each clip of it. We store the concatenation of the spatial and temporal queries from the last ASAM module corresponding to the \\(k\\) highest human scores in the query bank for each clip. We denote the stored queries for clip of time-step \\(t\\) as \\(L_{t} \\in \\mathbb{R}^{k \\times d}\\) where \\(d = 2D\\), and the long-term query bank of the video as \\(L = [L_{0}, L_{1}, \\dots, L_{\\mathcal{T}-1}]\\). Given the long-term query bank of all videos, we train an STMixer model with a long-term classifier from scratch. For video clip \\(t\\), we first sample a window of length \\(w\\) from the long-term query bank centered at it and stack this window into \\(\\tilde{L}_{t} \\in \\mathbb{R}^{K \\times d}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.576, + 0.468, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\tilde {L} _ {t} = \\operatorname {s t a c k} \\left(\\left[ L _ {t - w / 2}, \\dots , L _ {t + w / 2 - 1} \\right]\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.603, + 0.468, + 0.634 + ], + "angle": 0, + "content": "We then infer current queries to \\(\\tilde{L}_t\\) for long-term information by cross-attention [42]:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.646, + 0.468, + 0.663 + ], + "angle": 0, + "content": "\\[\nS _ {t} ^ {\\prime} = \\text {c r o s s - a t t e n t i o n} \\left(S _ {t}, \\tilde {L} _ {t}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.674, + 0.468, + 0.736 + ], + "angle": 0, + "content": "where \\(S_{t} \\in \\mathbb{R}^{N \\times d}\\) is the concatenation of the output spatial queries and temporal queries of the last ASAM module. The output \\(S_{t}'\\) is then channel-wise concatenated with \\(S_{t}\\) for action scores prediction." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.746, + 0.182, + 0.763 + ], + "angle": 0, + "content": "3.6. Training" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.468, + 0.83 + ], + "angle": 0, + "content": "We compute training loss based on the output human boxes, human scores, and action scores. Consistent with WOO [6], the loss function \\(\\mathcal{L}\\) consists of set prediction loss \\(\\mathcal{L}_{set}[4,35,54]\\) and action classification loss \\(\\mathcal{L}_{act}\\). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.846, + 0.468, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s e t} = \\lambda_ {c l s} \\mathcal {L} _ {c l s} + \\lambda_ {L _ {1}} \\mathcal {L} _ {L _ {1}} + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.886, + 0.468, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {s e t}} + \\lambda_ {\\text {a c t}} \\mathcal {L} _ {\\text {a c t}}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{cls}\\) denotes the cross-entropy loss over two classes (human and background). \\(\\mathcal{L}_{L_1}\\) and \\(\\mathcal{L}_{giou}\\) are box loss inherited from [4, 35, 54]. As in [4, 6], we first use Hungarian algorithm to find an optimal bipartite matching between predicted actors and ground truth actors according to \\(\\mathcal{L}_{set}\\). Then we calculate full training loss \\(\\mathcal{L}\\) based on the matching results. \\(\\mathcal{L}_{act}\\) is binary cross entropy loss for action classification. We only compute \\(\\mathcal{L}_{act}\\) for the prediction matched with a ground truth. \\(\\lambda_{cls}, \\lambda_{L_1}, \\lambda_{giou}\\), and \\(\\lambda_{act}\\) are corresponding weights of each term." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.259, + 0.632, + 0.275 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.284, + 0.691, + 0.301 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.308, + 0.892, + 0.474 + ], + "angle": 0, + "content": "Datasets. The AVA dataset [16] contains 211k video clips for training and 57k for validation segmented from 430 15-minute videos. The videos are annotated at 1FPS over 80 atomic action classes. Following the standard evaluation protocol [16], we report our results on 60 action classes that have at least 25 validation examples. JHMDB [19] consists of 928 temporally trimmed videos from 21 action classes. Results averaged over three splits are reported. UCF101-24 is a subset of UCF101 [33]. It contains 3,207 videos annotated with action instances of 24 classes. As the common setting, we report the performance on the first split." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.476, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Network configurations. We configure the dimension \\(D\\) of both spatial and temporal queries to 256 and set the number of both queries \\(N\\) equaling 100. The number of sampling point \\(P_{in}\\) in each temporal frame is set to 32. The spatial and temporal mixing out patterns \\(P_{out}\\) and \\(T_{out}\\) are set to 4 times the number of sampling points and temporal frames respectively, that is, 128 and 32 for SlowFast [11] backbone and 128 and 16 for CSN [40] and ViT [7] backbone. Following multi-head attention [42] and group convolution [49], we split the channel \\(D\\) into 4 groups and perform group-wise sampling and mixing. We stack 6 ASAM modules in our action decoder as default. For the long-term classifier, we set the number of stored queries of each clip \\(k\\) as 5 and window length \\(w\\) as 60. The number of cross-attention layers is set to 3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.703, + 0.892, + 0.778 + ], + "angle": 0, + "content": "Losses and optimizers. We set the loss weight in STMixer as \\(\\lambda_{cls} = 2.0\\), \\(\\lambda_{L_1} = 2.0\\), \\(\\lambda_{giou} = 2.0\\) and \\(\\lambda_{act} = 24.0\\). We use AdamW [28] optimizer with weight decay \\(1 \\times 10^{-4}\\) for all experiments. Following [4, 6], intermediate supervision is applied after each ASAM module." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.779, + 0.892, + 0.884 + ], + "angle": 0, + "content": "Training and inference recipes. We train STMixer detectors for 10 epochs with an initial learning rate of \\(2.0 \\times 10^{-5}\\) and batchsize of 16. The learning rate and batchsize can be tuned according to the linear scaling rule [15]. We randomly scale the short size of the training video clips to 256 or 320 pixels. Color jittering and random horizontal flipping are also adopted for data augmentation." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "For inference, we scale the short size of input frames" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14724" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "to 256 as the common setting. Given an input video clip, STMixer predicts \\( N \\) bounding boxes associated with their human scores and action scores from the last ASAM module. If the confidence score that a box belongs to the human category is higher than the preset threshold, we take it as a detection result. We set the threshold to 0.6 for AVA. The performances are evaluated with official metric frame-level mean average precision(mAP) at 0.5 IoU threshold." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.225, + 0.231, + 0.243 + ], + "angle": 0, + "content": "4.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.47, + 0.326 + ], + "angle": 0, + "content": "We conduct ablation experiments on AVa v2.2 dataset to investigate the influence of different components in our STMixer framework. A SlowOnly ResNet-50 backbone [8] is used for our ablation experiments. We report both mAP and GFLOPs for effectiveness and efficiency comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.473, + 0.568 + ], + "angle": 0, + "content": "Ablations on 4D feature space. We first show the benefit of sampling features from the unified 4D feature space. For comparison, we design a two-stage counterpart of our STMixer. In the first stage, we sample features from key-frame features for actor localization. In the second stage, we sample features from res5 features for action classification. As shown in Tabel 1a, sampling features from a unified 4D feature space and performing action detection in a one-stage manner significantly reduce computing costs, and detection mAP also gets improved as multi-scale information is also utilized for classification. We then investigate two different ways for the 4D feature space construction. As shown in Table 1b, constructing 4D feature space by simple lateral \\(1 \\times 1 \\times 1\\) convolution achieves comparable detection accuracy while being more efficient than using full FPN [25] with a top-down pathway." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.473, + 0.87 + ], + "angle": 0, + "content": "Ablations on feature sampling. In Tabel 1c, we compare 3 different feature sampling strategies. For fixed grid feature sampling, we sample \\(7 \\times 7\\) feature points inside each actor box by interpolation, which is actually the RoIAlign [17] operation adopted by many former methods [6,13]. Though sampling fewer points per group, our adaptive sampling strategy improves the detection mAP by 1.2. The results show that the fixed RoIAlign operation for feature sampling fails to capture useful context information outside the box while our adaptive sampling strategy enables the detector to mine discriminative features from the whole 4D feature space. Beyond simply copying sampling points, we try sampling different feature points in different frames by predicting the offset of the reference bounding box for each frame. The improvement is marginal due to the slowness issue of current action detection datasets that the variation of actors' location and action is very slow. In Table 1d, we further investigate the influence of the number of sampling points per group \\(P_{in}\\) in each temporal frame. Setting \\(P_{in} = 32\\) achieves the best detection performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Ablations on feature mixing. In Table 1f, we compare different feature mixing strategies. We first demonstrate" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.469 + ], + "angle": 0, + "content": "the benefit of query-guided adaptive mixing. The detection mAP drops by 0.6 when using fixed parameter mixing. For adaptive mixing, the mixing parameters are dynamically generated based on a specific query, thus more powerful to enhance the presentation of each specific action instance proposal. We further compare different adaptive feature mixing strategies. From the results in Table 1f, it is demonstrated that both spatial appearance and temporal motion information are important for action detection. However, coupled spatiotemporal feature mixing using queries of a single type has a high computational complexity. Decoupling features along spatial and temporal dimensions saves computing costs. Our dual-branch spatiotemporal feature mixing outperforms sequential spatiotemporal feature mixing by \\(0.5\\mathrm{mAP}\\). This is because actor localization at keyframes only needs spatial appearance information and parallel dual-branch mixing will reduce the effect of temporal information on localization. Also, by concatenating temporal queries to spatial queries, more temporal information is leveraged for action classification. In Table 1g, we investigate different spatial and temporal mixing out patterns \\(P_{out}\\) and \\(T_{out}\\) from 64 and 8 to 192 and 24, that is, 2 times to 6 times the number of sampling points and temporal frames. Setting \\(P_{out}\\) and \\(T_{out}\\) equaling 128 and 16 achieves the best performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.895, + 0.547 + ], + "angle": 0, + "content": "Ablations on network configuration. As shown in Table 1e, the detection mAP is saturated when the number of queries is increased to 100. From the results in Table 1h, a stack of 6 ASAM modules achieves a good effectiveness and efficiency balance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.559, + 0.864, + 0.575 + ], + "angle": 0, + "content": "4.3. Comparison with State-of-the-arts on AVA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.895, + 0.884 + ], + "angle": 0, + "content": "We compare our proposed STMixer with state-of-the-art methods on AVa v2.1 and v2.2 in Table 2. We first compare our STMixer to methods using an extra offline human detector. Our STMixer with SlowFast-R101 backbone achieves 30.6 and \\(30.9\\mathrm{mAP}\\) when not using long-term features. With long-term query support, our STMixer reaches 32.6 and \\(32.9\\mathrm{mAP}\\) on AVa v2.1 and v2.2 respectively. To demonstrate the generalization ability of our method, we conduct experiments with ViT [7] backbone. Compared with the two-stage counterparts, STMixer brings performance improvements while getting rid of the dependence on an extra detector. Although ViT is considered to have a global receptive field, our adaptive sampling and decoding mechanism could serve as a supplement to improve the flexibility of the model. Compared to previous end-to-end methods, our STMixer achieves the best results. Our STMixer outperforms WOO [6] by 2.0 and \\(1.7\\mathrm{mAP}\\) even though WOO test models at 320 resolution. STMixer also consistently outperforms TubeR [53] on AVA v2.1 or v2.2, using or not using long-term features." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We compare mAP versus GFLOPs on AVa v2.2 in Fig" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "14725" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.09, + 0.346, + 0.123 + ], + "angle": 0, + "content": "
ClassificationLocalizationmAPGFLOPs
4D Feature Space23.144.4
Key-Frame FeaturesRes5 Features22.853.7
" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.126, + 0.35, + 0.173 + ], + "angle": 0, + "content": "(a) Feature space. Sampling features from 4D feature space is more effective and efficient than sampling from key-frame features for classification and res5 features for localization." + }, + { + "type": "table", + "bbox": [ + 0.096, + 0.178, + 0.334, + 0.214 + ], + "angle": 0, + "content": "
Pin816324864
mAP22.422.523.123.022.5
GFLOPs42.443.144.445.646.9
" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.216, + 0.35, + 0.24 + ], + "angle": 0, + "content": "(d) Number of sampling points. Sampling 32 points per frame achieves the best performance." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.245, + 0.346, + 0.278 + ], + "angle": 0, + "content": "
Pout/Tout64/896/12128/16160/20192/24
mAP22.522.823.122.922.6
GFLOPs40.242.344.446.448.4
" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.28, + 0.349, + 0.305 + ], + "angle": 0, + "content": "(g) Number of mixing out patterns. A moderate number of mixing out patterns works the best." + }, + { + "type": "table", + "bbox": [ + 0.364, + 0.09, + 0.565, + 0.123 + ], + "angle": 0, + "content": "
mAPGFLOPs
Simple Lateral Conv.23.144.4
Full FPN22.945.8
" + }, + { + "type": "text", + "bbox": [ + 0.36, + 0.126, + 0.568, + 0.174 + ], + "angle": 0, + "content": "(b) 4D feature space construction. Simple lateral convolution achieves comparable performance while being more efficient than using full FPN." + }, + { + "type": "table", + "bbox": [ + 0.364, + 0.178, + 0.564, + 0.213 + ], + "angle": 0, + "content": "
N1550100150
mAP22.122.923.122.5
GFLOPs31.736.944.451.8
" + }, + { + "type": "text", + "bbox": [ + 0.361, + 0.216, + 0.568, + 0.24 + ], + "angle": 0, + "content": "(e) Number of queries. Using 100 queries works the best." + }, + { + "type": "table", + "bbox": [ + 0.369, + 0.244, + 0.562, + 0.278 + ], + "angle": 0, + "content": "
M1369
mAP18.422.523.122.6
GFLOPs32.036.944.451.8
" + }, + { + "type": "text", + "bbox": [ + 0.361, + 0.28, + 0.567, + 0.305 + ], + "angle": 0, + "content": "(h) Number of ASAM modules. Using 6 ASAM modules works the best." + }, + { + "type": "table", + "bbox": [ + 0.582, + 0.089, + 0.89, + 0.132 + ], + "angle": 0, + "content": "
Sampling StrategyPinmAPGFLOPs
Fixed Grid Sampling4921.945.6
Adaptive Sampling + Temporal Copying3223.144.4
Adaptive Sampling + Temporal Moving3223.344.6
" + }, + { + "type": "text", + "bbox": [ + 0.578, + 0.134, + 0.892, + 0.182 + ], + "angle": 0, + "content": "(c) Sampling strategy. Sampling fewer feature points, our adaptive sampling strategy achieves better performance than fixed grid sampling. Temporal moving brings slight improvement in mAP." + }, + { + "type": "table", + "bbox": [ + 0.598, + 0.189, + 0.875, + 0.267 + ], + "angle": 0, + "content": "
Mixing StrategymAPGFLOPs
fixed parameter dual-branch mixing22.536.8
dual-branch spatiotemporal mixing23.144.4
spatial mixing only22.440.4
temporal mixing only22.133.5
sequential spatiotemporal mixing22.643.6
coupled spatiotemporal mixing22.893.2
" + }, + { + "type": "text", + "bbox": [ + 0.578, + 0.268, + 0.892, + 0.305 + ], + "angle": 0, + "content": "(f) Mixing strategy. Query-guided adaptive feature mixing outperforms fixed parameter mixing and our dual-branch spatiotemporal feature mixing strategy works the best." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.315, + 0.892, + 0.343 + ], + "angle": 0, + "content": "Table 1. Ablations Experiments. We use a SlowOnly ResNet-50 backbone to perform our ablation studies. Models are trained on the training set of AVa v2.2 and evaluated on the validation set. Default choices for our model are colored in gray ." + }, + { + "type": "table", + "bbox": [ + 0.142, + 0.352, + 0.83, + 0.691 + ], + "angle": 0, + "content": "
MethodDetectorOne-stageInputBackbonePre-trainLFmAP
v2.1v2.2
Compare to methods with an extra human detector
SlowFast [11]✓✗32×2SF-R101-NLK600✗28.229.0
LFB [47]✓✗32×2I3D-R101-NLK400✓27.7-
CA-RCNN [48]✓✗32×2R50-NLK400✓28.0-
AIA [36]✓✗32×2SF-R101K700✓31.232.3
ACARN [29]✓✗32×2SF-R101K400✓30.0-
ACARN [29]✓✗32×2SF-R101-NLK600✓-31.4
VideoMAE [38]✓✗16×4ViT-BK400✗-31.8
VideoMAE [38]✓✗16×4ViT-LK700✗-39.3
STMixer✗✓32×2SF-R101K700✗30.630.9
STMixer✗✓32×2SF-R101K700✓32.632.9
STMixer✗✓16×4ViT-B (from [38])K400✗-32.6
STMixer✗✓16×4ViT-B (from [43])K710+K400✗-36.1
STMixer✗✓16×4ViT-L (from [38])K700✗-39.5
Compare to end-to-end methods
AVA [16]✗✗20×1I3D-VGGK400✗14.6-
ACRN [34]✗✗20×1S3D-GK400✗17.4-
STEP [51]✗✗12×1I3D-VGGK400✗18.6-
VTr [13]✗✗64×1I3D-VGGK400✗24.9-
WOO [6]✗✗32×2SF-R50K400✗25.225.4
WOO [6]✗✗32×2SF-R101-NLK600✗28.028.3
TubeR [53]✗✓32×2CSN-152IG-65M✗29.731.1
TubeR [53]✗✓32×2CSN-152IG-65M✓31.733.4
STMixer✗✓32×2SF-R50K400✗27.227.8
STMixer✗✓32×2SF-R101-NLK600✗29.830.1
STMixer✗✓32×2CSN-152IG-65M✗31.732.8
STMixer✗✓32×2CSN-152IG-65M✓34.434.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.701, + 0.89, + 0.728 + ], + "angle": 0, + "content": "Table 2. Comparisons with state-of-the-arts on validation sets of AVa v2.1 and v2.2. √of column \"Detector\" denotes an extra human detector Faster RCNN-R101-FPN [31] is used. √of column \"LF\" denotes long-term features are used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.899 + ], + "angle": 0, + "content": "ure 1 to show the efficiency of our STMixer. AIA [36] and ACARN [29] do not report their GFLOPs. As they are built on SlowFast [11] framework and also use an offline human detector but introduce extra modules to model interaction, SlowFast can serve as a lower bound of complexity for them. For a fair comparison, we report results for no long-term feature version of each method. As shown in Figure 1, due to an extra human detector being needed, SlowFast [11], CSN [40], and VideoMAE [38] have much higher GFLOPs than end-to-end methods with same back" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.748, + 0.892, + 0.838 + ], + "angle": 0, + "content": "bone. Among end-to-end methods, STMixer achieves the best effectiveness and efficiency balance. STMixer outperforms WOO [6] by \\(1.8\\mathrm{mAP}\\) while having much lower GFLOPs (135 versus 252). With a slight GFLOPs increase (126 versus 120), STMixer outperforms TubeR [53] by 1.7 mAP." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.812, + 0.862 + ], + "angle": 0, + "content": "4.4. Results on JHMDB and UCF101-24" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To verify the effectiveness of our STMixer, we further evaluate it on the JHMDB [19] and UCF101-24 [33]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14726" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.094, + 0.201, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.203, + 0.094, + 0.315, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.316, + 0.094, + 0.426, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.427, + 0.094, + 0.538, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.094, + 0.651, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.652, + 0.094, + 0.763, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.094, + 0.875, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.28, + 0.893, + 0.336 + ], + "angle": 0, + "content": "Figure 4. Sampling points and detection results visualization. We display the actor bounding boxes and action classes of three groundtruth action instances in the first column. Each ASAM module's sampling points, predicted actor bounding boxes and action scores are displayed in the following columns. The correctly predicted action classes are displayed in green, missing in orange, and wrongly predicted in red. Intuitively, STMixer mines discriminative context features outside the bounding box for better action detection." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.343, + 0.458, + 0.472 + ], + "angle": 0, + "content": "
MethodDetectorInputBackboneJHMDBUCF101-24
MOC* [24]✓7×1DLA3470.878.0
AVA* [16]✗20×1I3D-VGG73.376.3
ACRN [34]✗20×1S3D-G77.9-
CA-RCNN [48]✓32×2R50-NL79.2-
YOWO [21]✗16×13DResNext-10180.475.7
WOO [6]✗32×2SF-R101-NL80.5-
AIA [36]✓32×1SF-R50-NL-78.8
ACARN [29]✓32×1SF-R50-84.3
TubeR* [53]✗32×2I3D-81.3
STMixer✗32×2SF-R101-NL86.783.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.482, + 0.47, + 0.511 + ], + "angle": 0, + "content": "Table 3. Comparison on JHMDB and UCF101-24. Methods marked with * use extra optical flow features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.62 + ], + "angle": 0, + "content": "datasets. We report the frame-level mean average precision (frame-mAP) with an intersection-over-union (IoU) threshold of 0.5 in Table 3. Experimental results demonstrate that STMixer outperforms the current state-of-the-art methods with remarkable performance gain on JHMDB and achieves competitive results on UCF101-24." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.635, + 0.214, + 0.649 + ], + "angle": 0, + "content": "4.5. Visualization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We provide the visualization of sampling points and detection results of each ASAM module in order in Figure 4. In the first few ASAM modules, the sampling points are quickly concentrated on the action performer and the actor localization accuracy gets improved rapidly. In the following ASAM modules, some of the sampling points get out of the human box and spread to the context. Benefiting from the gathered context and interaction information, the action recognition accuracy gets improved while localization accuracy is not compromised. In Figure 4, we show clear improvements in three aspects: predicting missing classes (ride in row 1), improving the confidence score of correctly predicted classes (talk to in row 2), and removing wrongly predicted classes (watch in row 3). To recognize an action \"ride\", we need to observe the person is in a car and someone is driving. For recognition of \"talk to\", we need to know" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.892, + 0.421 + ], + "angle": 0, + "content": "if a person is listening in the context, and for \"watch\", we need to know if a person is in the actor's sight. The improvements are mostly related to these classes of interaction, which indicates our STMixer is capable of mining discriminative interaction information from the context." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.438, + 0.769, + 0.453 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.892, + 0.69 + ], + "angle": 0, + "content": "In this paper, we have presented a new one-stage sparse action detector in videos, termed STMixer. Our STMixer yields a simple, neat, and efficient end-to-end action detection framework. The core design of our STMixer is a set of learnable queries to decode all action instances in parallel. The decoding process is composed of an adaptive feature sampling module to identify important features from the entire spatiotemporal domain of video, and an adaptive feature mixing module to dynamically extract discriminative representations for action detection. Our STMixer achieves a new state-of-the-art performance on three challenging benchmarks of AVA, JHMDB, and UCF101-24 with less computational cost than previous end-to-end methods. We hope STMixer can serve as a strong baseline for future research on video action detectors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.692, + 0.892, + 0.796 + ], + "angle": 0, + "content": "One limitation of our STMixer is that the long-term query bank is implemented in an offline way where another STMixer without long-term query support is pre-trained for long-term query generation. We leave the design of an online query bank to future research and hope our STMixer is extended to extract long-form video information in an end-to-end manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006, No. 62072232), Fundamental Research Funds for the Central Universities (No. 020214380091), and Collaborative Innovation Center of Novel Software Technology and Industrialization." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14727" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.469, + 0.157 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. 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This detection paradigm requires multi-stage training and inference, and cannot capture context information outside the bounding box. Recently, a few query-based action detectors are proposed to predict action instances in an end-to-end manner. However, they still lack adaptability in feature sampling and decoding, thus suffering from the issues of inferior performance or slower convergence. In this paper, we propose a new one-stage sparse action detector, termed STMixer. STMixer is based on two core designs. First, we present a query-based adaptive feature sampling module, which endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain. Second, we devise a dual-branch feature mixing module, which allows our STMixer to dynamically attend to and mix video features along the spatial and the temporal dimension respectively for better feature decoding. Coupling these two designs with a video backbone yields an efficient end-to-end action detector. Without bells and whistles, our STMixer obtains the state-of-the-art results on the datasets of AVA, UCF101-24, and JHMDB. + +# 1. Introduction + +Video action detection [14, 18, 20, 30, 32, 44, 46] is an important problem in video understanding, which aims to recognize all action instances present in a video and also localize them in both space and time. It has drawn a significant amount of research attention, due to its wide applications in many areas like security and sports analysis. + +Since the proposal of large-scale action detection benchmarks [16, 22], action detection has made remarkable progress. This progress is partially due to the advances of video representation learning such as video convolution + +![](images/0ff58ff55d66220429555a7d5f77914a82ee7714cc92cb49e05f628d7f889ac8.jpg) +Figure 1. Comparison of mAP versus GFLOPs. We report detection mAP on AVA v2.2. The GFLOPs of CSN, SlowFast, and VideoMAE are the sum of Faster RCNN-R101-FPN detector GFLOPs and classifier GFLOPs. Different methods are marked by different makers and models with the same backbone are marked in the same color. The results of CSN are from [53]. Our STMixer achieves the best effectiveness and efficiency balance. + +neural networks [5, 11, 39-41, 45, 50] and video transformers [1, 3, 9, 27, 38, 43, 52]. + +Most current action detectors adopt the two-stage Faster R-CNN-alike detection paradigm [31]. They share two basic designs. First, they use an auxiliary human detector to generate actor bounding boxes in advance. The training of the human detector is decoupled from the action classification network. Second, in order to predict the action category for each actor box, the RoIAlign [17] operation is applied on video feature maps to extract actor-specific features. However, these two-stage action detection pipeline has several critical issues. First, it requires multi-stage training of person detector and action classifier, which requires large computing resources. Furthermore, the RoIAlign [17] operation constrains the video feature sampling inside the actor bounding box and lacks the flexibility of capturing context information in its surroundings. To enhance RoI features, recent works use an extra heavy module that introduces interaction features of context or other actors [29, 36]. + +Recently sparse query-based object detector [4, 35, 54] has brought a new perspective on detection tasks. Several + +query-based sparse action detectors [6, 53] are proposed. The key idea is that action instances can be represented as a set of learnable queries, and detection can be formulated as a set prediction task, which could be trained by a matching loss. These query-based methods detect action instances in an end-to-end manner, thus saving computing resources. However, the current sparse action detectors still lack adaptability in feature sampling or feature decoding, thus suffering from inferior accuracy or slow convergence issues. For example, building on the DETR [4] framework, TubeR [53] adaptively attends action-specific features from single-scale feature maps but perform feature transformation in a static manner. On the contrary, though decoding sampled features with dynamic interaction heads, WOO [6] still uses the 3D RoIAlign [17] operator for feature sampling, which constrains feature sampling inside the actor bounding box and fails to take advantage of other useful information in the entire spatiotemporal feature space. + +Following the success of adaptive sparse object detector AdaMixer [12] in images, we present a new query-based one-stage sparse action detector, named STMixer. Our goal is to create a simple action detection framework that can sample and decode features from the complete spatiotemporal video domain in a more flexible manner, while retaining the benefits of sparse action detectors, such as end-to-end training and reduced computational cost. Specifically, we come up with two core designs. First, to overcome the aforementioned fixed feature sampling issue, we present a query-guided adaptive feature sampling module. This new sampling mechanism endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain and capturing context and interaction information. Second, we devise a dual-branch feature mixing module to extract discriminative representations for action detection. It is composed of an adaptive spatial mixer and an adaptive temporal mixer in parallel to focus on appearance and motion information, respectively. Coupling these two designs with a video backbone yields a simple, neat, and efficient end-to-end actor detector, which obtains a new state-of-the-art performance on the datasets of AVA [16], UCF101-24 [33], and JHMDB [19]. In summary, our contribution is threefold: + +- We present a new one-stage sparse action detection framework in videos (STMixer). Our STMixer is easy to train in an end-to-end manner and efficient to deploy for action detection in a single stage. +- We devise two flexible designs to yield a powerful action detector. The adaptive sampling can select the discriminative feature points and the adaptive feature mixing can enhance spatiotemporal representations. +- STMixer achieves a new state-of-the-art performance on three challenging action detection benchmarks. + +# 2. Related Work + +Action detectors using an extra human detector. Most current action detectors [9-11,29,36,38,47] rely on an auxiliary human detector to perform actor localization on the keyframes. Typically, the powerful Faster RCNN-R101-FPN [31] detector is used as the human detector, which is first pre-trained on the COCO [26] dataset and then fine-tuned on the AVA [16] dataset. With actor bounding boxes predicted in advance, the action detection problem is reduced to a pure action classification problem. The RoIAlign [17] operation is applied on the 3D feature maps extracted by a video backbone to generate actor-specific features. SlowFast [11] and MViT [9] directly use the RoI features for action classification. However, RoI features only contain the information inside the bounding box but overlook context and interaction information outside the box. To remedy this inherent flaw of RoI features, AIA [36] and ACARN [29] resort to using an extra heavy module that models the interaction between the actor and context or other actors. The models with an extra human detector require two-stage training and reference, which is computing resources unfriendly. Besides, they suffer from the aforementioned issue of fixed RoI feature sampling. + +End-to-end action detectors. Methods of another research line use a single model to perform action detection. Most of them [6, 13, 21, 34] still follow the two-stage pipeline but simplify the training process by jointly training the actor proposal network and action classification network in an end-to-end manner. These methods still have the issue of fixed RoI feature sampling. To remedy this, VTr [13] attends RoI features to full feature maps while ACRN [34] introduces an actor-centric relation network for interaction modeling. Recently, several one-stage action detectors [24, 53] are proposed. MOC [24] is a point-based dense action detector, which uses an image backbone for frame feature extraction. It concatenates frame features along the temporal axis to form the video feature maps. Each point on the feature maps is regarded as an action instance proposal. The bounding box and action scores of each point are predicted by convolution. MOC [24] relies more on appearance features, lacks temporal and interaction modeling and requires post-process. Building on DETR [4] framework, TubeR [53] is a query-based action detector. TubeR [53] adaptively samples features from single-scale feature maps, neglecting multi-scale information which is important for detection tasks. As DETR [4], TubeR [53] transforms features in a static manner, resulting in slower convergence. + +Inspired by AdaMixer [12], we propose a new one-stage query-based detector for video action detection. Different from former query-based action detectors [6, 53], we adaptively sample discriminative features from a multi-scale spatiotemporal feature space and decode them with a more flexible scheme under the guidance of queries. + +![](images/b7814303962db1f188e713194b7e94edd0a47c674044d11446f045b0298159ee.jpg) +Figure 2. Pipeline of STMixer. In the left, we present the overall STMixer framework. A video clip is input to the video backbone for feature extraction and a 4D feature space is constructed based on the feature maps (see Section 3.1). Then, a decoder containing $M$ ASAM modules iteratively performs adaptive feature sampling (see Section 3.3) from the 4D feature space and adaptive mixing (see Section 3.4) on the sampled features under the guidance of a set of learnable queries. Inversely, the queries are updated with mixed features. Optionally, a short-term or long-term classifier can be used for action scores prediction, whose detailed structures are illustrated in the right. The long-term classifier refers to the long-term query bank produced by an offline STMixer for long-term information (see Section 3.5). + +![](images/dd63efa76c2ea5c2cd59ded1aaaa3a71e60afa04036d9a4f16299aa0c0e74049.jpg) + +# 3. Method + +This section presents our one-stage sparse action detector, called STMixer. The overall pipeline of STMixer is shown in Figure 2. Our STMixer comprises a video backbone for feature extraction, a feature space construction module, and a sparse action decoder composed of $M$ adaptive sampling and adaptive mixing (ASAM) modules followed by prediction heads. As a common practice, we set the middle frame of an input clip as the keyframe. We first use the video backbone to extract feature maps for the video and a 4D feature space is constructed based on the feature maps. Then, we develop the sparse action decoder with a set of learnable queries. Under the guidance of these queries, we perform adaptive feature sampling and feature mixing in the 4D feature space. The queries are updated iteratively. Finally, we decode each query as a detected action instance of action scores, human scores, and a human box. We will describe the technical details of each step in the next subsections. + +# 3.1. 4D Feature Space Construction + +Hierarchical video backbone. Formally, let $X_{z} \in \mathbb{R}^{C_{z} \times T \times H_{z} \times W_{z}}$ denote the feature map of convolution stage $z$ of the hierarchical backbone, where $z \in \{2, 3, 4, 5\}$ , $C_{z}$ stands for the channel number, $T$ for time, $H_{z}$ and $W_{z}$ for the spatial height and width. The stage index $z$ can be seen as the scale index of the feature map as $X_{z}$ has the downsampling rate of $2^{z}$ . We first transform each feature map $X_{z}$ to the same channel $D$ by $1 \times 1 \times 1$ convolution. Then, we rescale the spatial shape of each stage feature map + +![](images/a6c678b368bc723a59d1f2721c3f1bb33970f8fe9eaeb01ec3898b6e8c0a0e95.jpg) +Figure 3. 4D feature space construction for hierarchical video backbone. We construct 4D feature space on multi-scale 3D feature maps from hierarchical video backbone by simple lateral convolution and nearest-neighbor interpolation. The four dimensions of the 4D feature space are x-, y-, t-axis, and scale index z. + +to $H_{2} \times W_{2}$ by simple nearest-neighbor interpolation and align them along the x- and y-axis. The four dimensions of the constructed feature space are x-, y-, t-axis, and scale index z, respectively. This process is illustrated in Figure 3. Plain ViT backbone. To make STMixer framework compatible with plain ViT [7] backbone, inspired by ViTDet [23], we construct 4D feature space based on the last feature map from ViT backbone. Specifically, with the output feature map of the default downsampling rate of $2^{4}$ , we first produce hierarchical feature maps $\{X_{z}\}$ of the same channel number $D$ using convolutions of spatial strides $\left\{\frac{1}{4}, \frac{1}{2}, 1, 2\right\}$ , where a fractional stride indicates a deconvolution. Then we also rescale each feature map to the spatial size of $H_{2} \times W_{2}$ . + +# 3.2. Query Definition + +The definition of our queries derives from the object query in Sparse R-CNN [35], but we specify the action query in a disentangled fashion. Specifically, we factorize + +action queries into spatial queries $Q_{s} \in \mathbb{R}^{N \times D}$ and temporal queries $Q_{t} \in \mathbb{R}^{N \times D}$ to refer to the spatial content and temporal content respectively. $N$ represents the number of queries, while $D$ denotes the dimension of each query. + +We further define positional queries $Q_{p} \in \mathbb{R}^{N \times 4}$ . Each positional query $Q_{p}^{n}$ ( $n$ stands for the query index) is formulated as a proposal box vector ( $x^{n}, y^{n}, z^{n}, r^{n}$ ). Formally, $x^{n}$ and $y^{n}$ stand for the x- and y-axis coordinates of the box center, and $z^{n}$ and $r^{n}$ denote the logarithm of its scale (i.e. the area of the bounding box) and aspect ratio. The positional queries $Q_{p}$ are initialized in such a way that every box vector is the whole keyframe. + +# 3.3. Adaptive Spatiotemporal Feature Sampling + +Different from previous work [6, 11, 29, 36] that samples RoI features by pre-computed proposal boxes, we sample actor-specific features adaptively from the aforementioned 4D feature space under the guidance of spatial queries. Specifically, given a spatial query $Q_{s}^{n}$ and the corresponding positional query $Q_{p}^{n}$ , we regard the center point $(x^{n}, y^{n}, z^{n})$ of the proposal box as the reference point, and regress $P_{in}$ groups of offsets along x-, y-axis and scale index z on query $Q_{s}^{n}$ , using a linear layer: + +$$ +\left\{\left(\triangle x _ {i} ^ {n}, \triangle y _ {i} ^ {n}, \triangle z _ {i} ^ {n}\right) \right\} = \operatorname {L i n e a r} \left(Q _ {s} ^ {n}\right), \tag {1} +$$ + +where $i\in \mathbb{Z}$ and $1\leqslant i\leqslant P_{in}$ + +where $P_{in}$ is the number of sampled points for each query. Then, the offsets are added to the reference point, thus $P_{in}$ spatial feature points are obtained: + +$$ +\left\{ \begin{array}{l} \widetilde {x} _ {i} ^ {n} = x ^ {n} + \triangle x _ {i} ^ {n} \cdot 2 ^ {z ^ {n} - r ^ {n}}, \\ \widetilde {y} _ {i} ^ {n} = y ^ {n} + \triangle y _ {i} ^ {n} \cdot 2 ^ {z ^ {n} + r ^ {n}}, \\ \widetilde {z} _ {i} ^ {n} = z ^ {n} + \triangle z _ {i} ^ {n}. \end{array} \right. \tag {2} +$$ + +where $2^{z^n - r^n}$ and $2^{z^n + r^n}$ are the width and height of the box respectively. We offset the spatial position of sampling points with respect to the width and height of the box to reduce the learning difficulty. + +Finally, we propagate sampling points along the temporal axis, thus obtaining $T \times P_{in}$ points to sample from the 4D feature space. In our implementation, we simply copy these spatial sampling points along the temporal dimension because current action detection datasets yield temporal slowness property that the variation of actor locations along the temporal dimension is very slow. We compare different ways of temporal propagating in our ablation study. + +Given $T \times P_{in}$ sampling points, we sample instance-specific features by interpolation from the 4D feature space. In the following sections, the sampled spatiotemporal feature for spatial query $Q_{s}^{n}$ is denoted by $F^{n} \in \mathbb{R}^{T \times P_{in} \times D}$ . + +# 3.4. Adaptive Dual-branch Feature Mixing + +After feature sampling, we factorize the sampled features into spatial features and temporal features by pooling + +and then enhance each by adaptive mixing respectively. As the dual-branch mixing module is completely symmetrical, we only describe spatial mixing in detail and temporal mixing is performed in a homogeneous way. + +Different from MLP-Mixer [37], our mixing parameters are generated adaptively. Given a spatial query $Q_{s}^{n}\in \mathbb{R}^{D}$ and its corresponding sampled features $F^n\in \mathbb{R}^{T\times P_{in}\times D}$ , we first use a linear layer to generate query-specific channel-mixing weights $M_{c}\in \mathbb{R}^{D\times D}$ , and then apply plain matrix multiplication on temporally pooled feature and $M_{c}$ to perform channel-mixing, given by: + +$$ +M _ {c} = \operatorname {L i n e a r} \left(Q _ {s} ^ {n}\right) \in \mathbb {R} ^ {D \times D}, \tag {3} +$$ + +$$ +\operatorname {C M} \left(F ^ {n}\right) = \operatorname {R e L U} \left(\operatorname {L a y e r N o r m} \left(\operatorname {G A P} \left(F ^ {n}\right) \times M _ {c}\right)\right). \tag {4} +$$ + +where GAP stands for the global average pooling operation in the temporal dimension while LayerNorm for the layer normalization [2]. We use $\mathbf{CM}(F^n) \in \mathbb{R}^{P_{in} \times D}$ to denote the channel-wise mixing output features. + +After channel-mixing, we perform point-wise mixing in a similar way. Suppose $P_{out}$ is the number of spatial pointwise mixing out patterns, we use $\mathrm{PCM}(F^n) \in \mathbb{R}^{D \times P_{out}}$ to denote the point-wise mixing output features, given by: + +$$ +M _ {p} = \operatorname {L i n e a r} \left(Q _ {s} ^ {n}\right) \in \mathbb {R} ^ {P _ {i n} \times P _ {o u t}}, \tag {5} +$$ + +$$ +\operatorname {P C M} \left(F ^ {n}\right) = \operatorname {R e L U} \left(\operatorname {L a y e r N o r m} \left(\operatorname {C M} \left(F ^ {n}\right) ^ {T} \times M _ {p}\right)\right). \tag {6} +$$ + +The final output $\mathrm{PCM}(F^n)$ is flattened, transformed to $D$ dimension, and added to the spatial query $Q_{s}^{n}$ . The temporal query $Q_{t}^{n}$ is updated in a homogeneous way, except that the pooling is applied in the spatial dimension. After global spatial pooling, there are $T$ feature points of different temporal locations for temporal mixing and we set the number of temporal point-wise mixing out patterns to $T_{out}$ . + +# 3.5. Sparse Action Decoder + +STMixer adopts a unified action decoder for both actor localization and action classification. The decoder comprises $M$ stacked ASAM modules followed by a feedforward network (FFN) for human scores prediction and a short-term or long-term classifier for action score prediction. In this section, we represent the structure of ASAM module and specify the outputs of the prediction heads. + +ASAM module. The overall structure of ASAM module is shown in Figure 2. We first perform self-attention [42] on spatial queries $Q_{s}$ and temporal queries $Q_{t}$ to capture the relation information between different instances. Then we perform adaptive sampling from the 4D feature space and dual-branch adaptive mixing on the sampled feature as described before. The spatial queries $Q_{s}$ and temporal queries + +$Q_{t}$ are updated with mixed features. An FFN is applied on updated spatial queries $Q_{s}^{\prime}$ to update the positional queries $Q_{p}$ . The updated queries $Q_{p}^{\prime}, Q_{s}^{\prime}$ and $Q_{t}^{\prime}$ are used as inputs for the next ASAM module. + +Outputs of the prediction heads. The output human boxes are decoded from positional queries $Q_{p}^{\prime}$ . We apply an FFN on $Q_{s}^{\prime}$ to predict human scores $S_{H} \in \mathbb{R}^{N \times 2}$ which indicates the confidence values that each box belongs to the human category and background. Based on the concatenation of spatial queries $Q_{s}^{\prime}$ and temporal queries $Q_{t}^{\prime}$ , we use a short-term or long-term classifier to predict action scores $S_{A} \in \mathbb{R}^{N \times C}$ , where $C$ is the number of action classes. + +Short-term and long-term classifier. Short-term classifier (see Figure 2 right top) is a simple FFN which predicts action scores based on short-term information of current queries while long-term classifier (see Figure 2 right bottom) refers to long-term query bank for long-term information. Our design of the long-term classifier is adapted from LFB [47]. We train an STMixer model without long-term information first. Then, for a video of $\mathcal{T}$ clips, we use the trained STMixer to perform inference on each clip of it. We store the concatenation of the spatial and temporal queries from the last ASAM module corresponding to the $k$ highest human scores in the query bank for each clip. We denote the stored queries for clip of time-step $t$ as $L_{t} \in \mathbb{R}^{k \times d}$ where $d = 2D$ , and the long-term query bank of the video as $L = [L_{0}, L_{1}, \dots, L_{\mathcal{T}-1}]$ . Given the long-term query bank of all videos, we train an STMixer model with a long-term classifier from scratch. For video clip $t$ , we first sample a window of length $w$ from the long-term query bank centered at it and stack this window into $\tilde{L}_{t} \in \mathbb{R}^{K \times d}$ : + +$$ +\tilde {L} _ {t} = \operatorname {s t a c k} \left(\left[ L _ {t - w / 2}, \dots , L _ {t + w / 2 - 1} \right]\right). \tag {7} +$$ + +We then infer current queries to $\tilde{L}_t$ for long-term information by cross-attention [42]: + +$$ +S _ {t} ^ {\prime} = \text {c r o s s - a t t e n t i o n} \left(S _ {t}, \tilde {L} _ {t}\right), \tag {8} +$$ + +where $S_{t} \in \mathbb{R}^{N \times d}$ is the concatenation of the output spatial queries and temporal queries of the last ASAM module. The output $S_{t}'$ is then channel-wise concatenated with $S_{t}$ for action scores prediction. + +# 3.6. Training + +We compute training loss based on the output human boxes, human scores, and action scores. Consistent with WOO [6], the loss function $\mathcal{L}$ consists of set prediction loss $\mathcal{L}_{set}[4,35,54]$ and action classification loss $\mathcal{L}_{act}$ . Formally, + +$$ +\mathcal {L} _ {s e t} = \lambda_ {c l s} \mathcal {L} _ {c l s} + \lambda_ {L _ {1}} \mathcal {L} _ {L _ {1}} + \lambda_ {g i o u} \mathcal {L} _ {g i o u}, \tag {9} +$$ + +$$ +\mathcal {L} = \mathcal {L} _ {\text {s e t}} + \lambda_ {\text {a c t}} \mathcal {L} _ {\text {a c t}}. \tag {10} +$$ + +$\mathcal{L}_{cls}$ denotes the cross-entropy loss over two classes (human and background). $\mathcal{L}_{L_1}$ and $\mathcal{L}_{giou}$ are box loss inherited from [4, 35, 54]. As in [4, 6], we first use Hungarian algorithm to find an optimal bipartite matching between predicted actors and ground truth actors according to $\mathcal{L}_{set}$ . Then we calculate full training loss $\mathcal{L}$ based on the matching results. $\mathcal{L}_{act}$ is binary cross entropy loss for action classification. We only compute $\mathcal{L}_{act}$ for the prediction matched with a ground truth. $\lambda_{cls}, \lambda_{L_1}, \lambda_{giou}$ , and $\lambda_{act}$ are corresponding weights of each term. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. The AVA dataset [16] contains 211k video clips for training and 57k for validation segmented from 430 15-minute videos. The videos are annotated at 1FPS over 80 atomic action classes. Following the standard evaluation protocol [16], we report our results on 60 action classes that have at least 25 validation examples. JHMDB [19] consists of 928 temporally trimmed videos from 21 action classes. Results averaged over three splits are reported. UCF101-24 is a subset of UCF101 [33]. It contains 3,207 videos annotated with action instances of 24 classes. As the common setting, we report the performance on the first split. + +Network configurations. We configure the dimension $D$ of both spatial and temporal queries to 256 and set the number of both queries $N$ equaling 100. The number of sampling point $P_{in}$ in each temporal frame is set to 32. The spatial and temporal mixing out patterns $P_{out}$ and $T_{out}$ are set to 4 times the number of sampling points and temporal frames respectively, that is, 128 and 32 for SlowFast [11] backbone and 128 and 16 for CSN [40] and ViT [7] backbone. Following multi-head attention [42] and group convolution [49], we split the channel $D$ into 4 groups and perform group-wise sampling and mixing. We stack 6 ASAM modules in our action decoder as default. For the long-term classifier, we set the number of stored queries of each clip $k$ as 5 and window length $w$ as 60. The number of cross-attention layers is set to 3. + +Losses and optimizers. We set the loss weight in STMixer as $\lambda_{cls} = 2.0$ , $\lambda_{L_1} = 2.0$ , $\lambda_{giou} = 2.0$ and $\lambda_{act} = 24.0$ . We use AdamW [28] optimizer with weight decay $1 \times 10^{-4}$ for all experiments. Following [4, 6], intermediate supervision is applied after each ASAM module. + +Training and inference recipes. We train STMixer detectors for 10 epochs with an initial learning rate of $2.0 \times 10^{-5}$ and batchsize of 16. The learning rate and batchsize can be tuned according to the linear scaling rule [15]. We randomly scale the short size of the training video clips to 256 or 320 pixels. Color jittering and random horizontal flipping are also adopted for data augmentation. + +For inference, we scale the short size of input frames + +to 256 as the common setting. Given an input video clip, STMixer predicts $N$ bounding boxes associated with their human scores and action scores from the last ASAM module. If the confidence score that a box belongs to the human category is higher than the preset threshold, we take it as a detection result. We set the threshold to 0.6 for AVA. The performances are evaluated with official metric frame-level mean average precision(mAP) at 0.5 IoU threshold. + +# 4.2. Ablation Study + +We conduct ablation experiments on AVa v2.2 dataset to investigate the influence of different components in our STMixer framework. A SlowOnly ResNet-50 backbone [8] is used for our ablation experiments. We report both mAP and GFLOPs for effectiveness and efficiency comparison. + +Ablations on 4D feature space. We first show the benefit of sampling features from the unified 4D feature space. For comparison, we design a two-stage counterpart of our STMixer. In the first stage, we sample features from key-frame features for actor localization. In the second stage, we sample features from res5 features for action classification. As shown in Tabel 1a, sampling features from a unified 4D feature space and performing action detection in a one-stage manner significantly reduce computing costs, and detection mAP also gets improved as multi-scale information is also utilized for classification. We then investigate two different ways for the 4D feature space construction. As shown in Table 1b, constructing 4D feature space by simple lateral $1 \times 1 \times 1$ convolution achieves comparable detection accuracy while being more efficient than using full FPN [25] with a top-down pathway. + +Ablations on feature sampling. In Tabel 1c, we compare 3 different feature sampling strategies. For fixed grid feature sampling, we sample $7 \times 7$ feature points inside each actor box by interpolation, which is actually the RoIAlign [17] operation adopted by many former methods [6,13]. Though sampling fewer points per group, our adaptive sampling strategy improves the detection mAP by 1.2. The results show that the fixed RoIAlign operation for feature sampling fails to capture useful context information outside the box while our adaptive sampling strategy enables the detector to mine discriminative features from the whole 4D feature space. Beyond simply copying sampling points, we try sampling different feature points in different frames by predicting the offset of the reference bounding box for each frame. The improvement is marginal due to the slowness issue of current action detection datasets that the variation of actors' location and action is very slow. In Table 1d, we further investigate the influence of the number of sampling points per group $P_{in}$ in each temporal frame. Setting $P_{in} = 32$ achieves the best detection performance. + +Ablations on feature mixing. In Table 1f, we compare different feature mixing strategies. We first demonstrate + +the benefit of query-guided adaptive mixing. The detection mAP drops by 0.6 when using fixed parameter mixing. For adaptive mixing, the mixing parameters are dynamically generated based on a specific query, thus more powerful to enhance the presentation of each specific action instance proposal. We further compare different adaptive feature mixing strategies. From the results in Table 1f, it is demonstrated that both spatial appearance and temporal motion information are important for action detection. However, coupled spatiotemporal feature mixing using queries of a single type has a high computational complexity. Decoupling features along spatial and temporal dimensions saves computing costs. Our dual-branch spatiotemporal feature mixing outperforms sequential spatiotemporal feature mixing by $0.5\mathrm{mAP}$ . This is because actor localization at keyframes only needs spatial appearance information and parallel dual-branch mixing will reduce the effect of temporal information on localization. Also, by concatenating temporal queries to spatial queries, more temporal information is leveraged for action classification. In Table 1g, we investigate different spatial and temporal mixing out patterns $P_{out}$ and $T_{out}$ from 64 and 8 to 192 and 24, that is, 2 times to 6 times the number of sampling points and temporal frames. Setting $P_{out}$ and $T_{out}$ equaling 128 and 16 achieves the best performance. + +Ablations on network configuration. As shown in Table 1e, the detection mAP is saturated when the number of queries is increased to 100. From the results in Table 1h, a stack of 6 ASAM modules achieves a good effectiveness and efficiency balance. + +# 4.3. Comparison with State-of-the-arts on AVA + +We compare our proposed STMixer with state-of-the-art methods on AVa v2.1 and v2.2 in Table 2. We first compare our STMixer to methods using an extra offline human detector. Our STMixer with SlowFast-R101 backbone achieves 30.6 and $30.9\mathrm{mAP}$ when not using long-term features. With long-term query support, our STMixer reaches 32.6 and $32.9\mathrm{mAP}$ on AVa v2.1 and v2.2 respectively. To demonstrate the generalization ability of our method, we conduct experiments with ViT [7] backbone. Compared with the two-stage counterparts, STMixer brings performance improvements while getting rid of the dependence on an extra detector. Although ViT is considered to have a global receptive field, our adaptive sampling and decoding mechanism could serve as a supplement to improve the flexibility of the model. Compared to previous end-to-end methods, our STMixer achieves the best results. Our STMixer outperforms WOO [6] by 2.0 and $1.7\mathrm{mAP}$ even though WOO test models at 320 resolution. STMixer also consistently outperforms TubeR [53] on AVA v2.1 or v2.2, using or not using long-term features. + +We compare mAP versus GFLOPs on AVa v2.2 in Fig + +
ClassificationLocalizationmAPGFLOPs
4D Feature Space23.144.4
Key-Frame FeaturesRes5 Features22.853.7
+ +(a) Feature space. Sampling features from 4D feature space is more effective and efficient than sampling from key-frame features for classification and res5 features for localization. + +
Pin816324864
mAP22.422.523.123.022.5
GFLOPs42.443.144.445.646.9
+ +(d) Number of sampling points. Sampling 32 points per frame achieves the best performance. + +
Pout/Tout64/896/12128/16160/20192/24
mAP22.522.823.122.922.6
GFLOPs40.242.344.446.448.4
+ +(g) Number of mixing out patterns. A moderate number of mixing out patterns works the best. + +
mAPGFLOPs
Simple Lateral Conv.23.144.4
Full FPN22.945.8
+ +(b) 4D feature space construction. Simple lateral convolution achieves comparable performance while being more efficient than using full FPN. + +
N1550100150
mAP22.122.923.122.5
GFLOPs31.736.944.451.8
+ +(e) Number of queries. Using 100 queries works the best. + +
M1369
mAP18.422.523.122.6
GFLOPs32.036.944.451.8
+ +(h) Number of ASAM modules. Using 6 ASAM modules works the best. + +
Sampling StrategyPinmAPGFLOPs
Fixed Grid Sampling4921.945.6
Adaptive Sampling + Temporal Copying3223.144.4
Adaptive Sampling + Temporal Moving3223.344.6
+ +(c) Sampling strategy. Sampling fewer feature points, our adaptive sampling strategy achieves better performance than fixed grid sampling. Temporal moving brings slight improvement in mAP. + +
Mixing StrategymAPGFLOPs
fixed parameter dual-branch mixing22.536.8
dual-branch spatiotemporal mixing23.144.4
spatial mixing only22.440.4
temporal mixing only22.133.5
sequential spatiotemporal mixing22.643.6
coupled spatiotemporal mixing22.893.2
+ +(f) Mixing strategy. Query-guided adaptive feature mixing outperforms fixed parameter mixing and our dual-branch spatiotemporal feature mixing strategy works the best. + +Table 1. Ablations Experiments. We use a SlowOnly ResNet-50 backbone to perform our ablation studies. Models are trained on the training set of AVa v2.2 and evaluated on the validation set. Default choices for our model are colored in gray . + +
MethodDetectorOne-stageInputBackbonePre-trainLFmAP
v2.1v2.2
Compare to methods with an extra human detector
SlowFast [11]✓✗32×2SF-R101-NLK600✗28.229.0
LFB [47]✓✗32×2I3D-R101-NLK400✓27.7-
CA-RCNN [48]✓✗32×2R50-NLK400✓28.0-
AIA [36]✓✗32×2SF-R101K700✓31.232.3
ACARN [29]✓✗32×2SF-R101K400✓30.0-
ACARN [29]✓✗32×2SF-R101-NLK600✓-31.4
VideoMAE [38]✓✗16×4ViT-BK400✗-31.8
VideoMAE [38]✓✗16×4ViT-LK700✗-39.3
STMixer✗✓32×2SF-R101K700✗30.630.9
STMixer✗✓32×2SF-R101K700✓32.632.9
STMixer✗✓16×4ViT-B (from [38])K400✗-32.6
STMixer✗✓16×4ViT-B (from [43])K710+K400✗-36.1
STMixer✗✓16×4ViT-L (from [38])K700✗-39.5
Compare to end-to-end methods
AVA [16]✗✗20×1I3D-VGGK400✗14.6-
ACRN [34]✗✗20×1S3D-GK400✗17.4-
STEP [51]✗✗12×1I3D-VGGK400✗18.6-
VTr [13]✗✗64×1I3D-VGGK400✗24.9-
WOO [6]✗✗32×2SF-R50K400✗25.225.4
WOO [6]✗✗32×2SF-R101-NLK600✗28.028.3
TubeR [53]✗✓32×2CSN-152IG-65M✗29.731.1
TubeR [53]✗✓32×2CSN-152IG-65M✓31.733.4
STMixer✗✓32×2SF-R50K400✗27.227.8
STMixer✗✓32×2SF-R101-NLK600✗29.830.1
STMixer✗✓32×2CSN-152IG-65M✗31.732.8
STMixer✗✓32×2CSN-152IG-65M✓34.434.8
+ +Table 2. Comparisons with state-of-the-arts on validation sets of AVa v2.1 and v2.2. √of column "Detector" denotes an extra human detector Faster RCNN-R101-FPN [31] is used. √of column "LF" denotes long-term features are used. + +ure 1 to show the efficiency of our STMixer. AIA [36] and ACARN [29] do not report their GFLOPs. As they are built on SlowFast [11] framework and also use an offline human detector but introduce extra modules to model interaction, SlowFast can serve as a lower bound of complexity for them. For a fair comparison, we report results for no long-term feature version of each method. As shown in Figure 1, due to an extra human detector being needed, SlowFast [11], CSN [40], and VideoMAE [38] have much higher GFLOPs than end-to-end methods with same back + +bone. Among end-to-end methods, STMixer achieves the best effectiveness and efficiency balance. STMixer outperforms WOO [6] by $1.8\mathrm{mAP}$ while having much lower GFLOPs (135 versus 252). With a slight GFLOPs increase (126 versus 120), STMixer outperforms TubeR [53] by 1.7 mAP. + +# 4.4. Results on JHMDB and UCF101-24 + +To verify the effectiveness of our STMixer, we further evaluate it on the JHMDB [19] and UCF101-24 [33] + +![](images/2594e5afbee7f070abd03606d03beee07a161411f2f8f58c389b83c07861944e.jpg) +Figure 4. Sampling points and detection results visualization. We display the actor bounding boxes and action classes of three groundtruth action instances in the first column. Each ASAM module's sampling points, predicted actor bounding boxes and action scores are displayed in the following columns. The correctly predicted action classes are displayed in green, missing in orange, and wrongly predicted in red. Intuitively, STMixer mines discriminative context features outside the bounding box for better action detection. + +![](images/5318ea11ec3cc126b72334afc61530d278a7f0232027473892edd038afcc7cfb.jpg) + +![](images/4d9f396b54a8dc66435962bfc54b1f769e00ebf71c3157a17d385864b1151c3e.jpg) + +![](images/66dacc388e2e55cbfd1ad80bf8ad1f294104145a1d404c4306e142a6e803c7d4.jpg) + +![](images/120416cd0bd405e4b49966a944832100227ac83372823f314a12947312142759.jpg) + +![](images/b9dc17c3a6db1a4df9b50807ac5b9da3786d94027e92eb918a7b82d11eb59aec.jpg) + +![](images/7c75a7bfd968f9d0302f18db86ee58be9e68ec58f02600c50e58a3141c0eeb78.jpg) + +
MethodDetectorInputBackboneJHMDBUCF101-24
MOC* [24]✓7×1DLA3470.878.0
AVA* [16]✗20×1I3D-VGG73.376.3
ACRN [34]✗20×1S3D-G77.9-
CA-RCNN [48]✓32×2R50-NL79.2-
YOWO [21]✗16×13DResNext-10180.475.7
WOO [6]✗32×2SF-R101-NL80.5-
AIA [36]✓32×1SF-R50-NL-78.8
ACARN [29]✓32×1SF-R50-84.3
TubeR* [53]✗32×2I3D-81.3
STMixer✗32×2SF-R101-NL86.783.7
+ +Table 3. Comparison on JHMDB and UCF101-24. Methods marked with * use extra optical flow features. + +datasets. We report the frame-level mean average precision (frame-mAP) with an intersection-over-union (IoU) threshold of 0.5 in Table 3. Experimental results demonstrate that STMixer outperforms the current state-of-the-art methods with remarkable performance gain on JHMDB and achieves competitive results on UCF101-24. + +# 4.5. Visualization + +We provide the visualization of sampling points and detection results of each ASAM module in order in Figure 4. In the first few ASAM modules, the sampling points are quickly concentrated on the action performer and the actor localization accuracy gets improved rapidly. In the following ASAM modules, some of the sampling points get out of the human box and spread to the context. Benefiting from the gathered context and interaction information, the action recognition accuracy gets improved while localization accuracy is not compromised. In Figure 4, we show clear improvements in three aspects: predicting missing classes (ride in row 1), improving the confidence score of correctly predicted classes (talk to in row 2), and removing wrongly predicted classes (watch in row 3). To recognize an action "ride", we need to observe the person is in a car and someone is driving. For recognition of "talk to", we need to know + +if a person is listening in the context, and for "watch", we need to know if a person is in the actor's sight. The improvements are mostly related to these classes of interaction, which indicates our STMixer is capable of mining discriminative interaction information from the context. + +# 5. Conclusion and Future Work + +In this paper, we have presented a new one-stage sparse action detector in videos, termed STMixer. Our STMixer yields a simple, neat, and efficient end-to-end action detection framework. The core design of our STMixer is a set of learnable queries to decode all action instances in parallel. The decoding process is composed of an adaptive feature sampling module to identify important features from the entire spatiotemporal domain of video, and an adaptive feature mixing module to dynamically extract discriminative representations for action detection. Our STMixer achieves a new state-of-the-art performance on three challenging benchmarks of AVA, JHMDB, and UCF101-24 with less computational cost than previous end-to-end methods. We hope STMixer can serve as a strong baseline for future research on video action detectors. + +One limitation of our STMixer is that the long-term query bank is implemented in an offline way where another STMixer without long-term query support is pre-trained for long-term query generation. We leave the design of an online query bank to future research and hope our STMixer is extended to extract long-form video information in an end-to-end manner. + +Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006, No. 62072232), Fundamental Research Funds for the Central Universities (No. 020214380091), and Collaborative Innovation Center of Novel Software Technology and Industrialization. + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. In ICCV, pages 6836-6846, 2021. 1 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 4 +[3] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? 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This detection paradigm requires multi-stage training and inference, and cannot capture context information outside the bounding box. Recently, a few query-based action detectors are proposed to predict action instances in an end-to-end manner. However, they still lack adaptability in feature sampling and decoding, thus suffering from the issues of inferior performance or slower convergence. In this paper, we propose a new one-stage sparse action detector, termed STMixer. STMixer is based on two core designs. First, we present a query-based adaptive feature sampling module, which endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain. Second, we devise a dual-branch feature mixing module, which allows our STMixer to dynamically attend to and mix video features along the spatial and the temporal dimension respectively for better feature decoding. Coupling these two designs with a video backbone yields an efficient end-to-end action detector. Without bells and whistles, our STMixer obtains the state-of-the-art results on the datasets of AVA, UCF101-24, and JHMDB." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 128, + 563 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 571, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 644 + ], + "type": "text", + "content": "Video action detection [14, 18, 20, 30, 32, 44, 46] is an important problem in video understanding, which aims to recognize all action instances present in a video and also localize them in both space and time. It has drawn a significant amount of research attention, due to its wide applications in many areas like security and sports analysis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 287, + 693 + ], + "type": "text", + "content": "Since the proposal of large-scale action detection benchmarks [16, 22], action detection has made remarkable progress. This progress is partially due to the advances of video representation learning such as video convolution" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 325, + 212, + 526, + 364 + ], + "blocks": [ + { + "bbox": [ + 325, + 212, + 526, + 364 + ], + "lines": [ + { + "bbox": [ + 325, + 212, + 526, + 364 + ], + "spans": [ + { + "bbox": [ + 325, + 212, + 526, + 364 + ], + "type": "image", + "image_path": "0ff58ff55d66220429555a7d5f77914a82ee7714cc92cb49e05f628d7f889ac8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 366, + 547, + 445 + ], + "lines": [ + { + "bbox": [ + 304, + 366, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 547, + 445 + ], + "type": "text", + "content": "Figure 1. Comparison of mAP versus GFLOPs. We report detection mAP on AVA v2.2. The GFLOPs of CSN, SlowFast, and VideoMAE are the sum of Faster RCNN-R101-FPN detector GFLOPs and classifier GFLOPs. Different methods are marked by different makers and models with the same backbone are marked in the same color. The results of CSN are from [53]. Our STMixer achieves the best effectiveness and efficiency balance." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 457, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 482 + ], + "type": "text", + "content": "neural networks [5, 11, 39-41, 45, 50] and video transformers [1, 3, 9, 27, 38, 43, 52]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 483, + 546, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 546, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 546, + 687 + ], + "type": "text", + "content": "Most current action detectors adopt the two-stage Faster R-CNN-alike detection paradigm [31]. They share two basic designs. First, they use an auxiliary human detector to generate actor bounding boxes in advance. The training of the human detector is decoupled from the action classification network. Second, in order to predict the action category for each actor box, the RoIAlign [17] operation is applied on video feature maps to extract actor-specific features. However, these two-stage action detection pipeline has several critical issues. First, it requires multi-stage training of person detector and action classifier, which requires large computing resources. Furthermore, the RoIAlign [17] operation constrains the video feature sampling inside the actor bounding box and lacks the flexibility of capturing context information in its surroundings. To enhance RoI features, recent works use an extra heavy module that introduces interaction features of context or other actors [29, 36]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 713 + ], + "type": "text", + "content": "Recently sparse query-based object detector [4, 35, 54] has brought a new perspective on detection tasks. Several" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 222, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 222, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 222, + 713 + ], + "type": "text", + "content": "*: Equal contribution. " + }, + { + "bbox": [ + 61, + 702, + 222, + 713 + ], + "type": "inline_equation", + "content": "\\boxtimes" + }, + { + "bbox": [ + 61, + 702, + 222, + 713 + ], + "type": "text", + "content": " Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14720" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": "query-based sparse action detectors [6, 53] are proposed. The key idea is that action instances can be represented as a set of learnable queries, and detection can be formulated as a set prediction task, which could be trained by a matching loss. These query-based methods detect action instances in an end-to-end manner, thus saving computing resources. However, the current sparse action detectors still lack adaptability in feature sampling or feature decoding, thus suffering from inferior accuracy or slow convergence issues. For example, building on the DETR [4] framework, TubeR [53] adaptively attends action-specific features from single-scale feature maps but perform feature transformation in a static manner. On the contrary, though decoding sampled features with dynamic interaction heads, WOO [6] still uses the 3D RoIAlign [17] operator for feature sampling, which constrains feature sampling inside the actor bounding box and fails to take advantage of other useful information in the entire spatiotemporal feature space." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 289, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 574 + ], + "type": "text", + "content": "Following the success of adaptive sparse object detector AdaMixer [12] in images, we present a new query-based one-stage sparse action detector, named STMixer. Our goal is to create a simple action detection framework that can sample and decode features from the complete spatiotemporal video domain in a more flexible manner, while retaining the benefits of sparse action detectors, such as end-to-end training and reduced computational cost. Specifically, we come up with two core designs. First, to overcome the aforementioned fixed feature sampling issue, we present a query-guided adaptive feature sampling module. This new sampling mechanism endows our STMixer with the flexibility of mining a set of discriminative features from the entire spatiotemporal domain and capturing context and interaction information. Second, we devise a dual-branch feature mixing module to extract discriminative representations for action detection. It is composed of an adaptive spatial mixer and an adaptive temporal mixer in parallel to focus on appearance and motion information, respectively. Coupling these two designs with a video backbone yields a simple, neat, and efficient end-to-end actor detector, which obtains a new state-of-the-art performance on the datasets of AVA [16], UCF101-24 [33], and JHMDB [19]. In summary, our contribution is threefold:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 580, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 58, + 580, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 580, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 58, + 580, + 287, + 628 + ], + "type": "text", + "content": "- We present a new one-stage sparse action detection framework in videos (STMixer). Our STMixer is easy to train in an end-to-end manner and efficient to deploy for action detection in a single stage." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 635, + 287, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 635, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 58, + 635, + 287, + 683 + ], + "type": "text", + "content": "- We devise two flexible designs to yield a powerful action detector. The adaptive sampling can select the discriminative feature points and the adaptive feature mixing can enhance spatiotemporal representations." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- STMixer achieves a new state-of-the-art performance on three challenging action detection benchmarks." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 91, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 354 + ], + "type": "text", + "content": "Action detectors using an extra human detector. Most current action detectors [9-11,29,36,38,47] rely on an auxiliary human detector to perform actor localization on the keyframes. Typically, the powerful Faster RCNN-R101-FPN [31] detector is used as the human detector, which is first pre-trained on the COCO [26] dataset and then fine-tuned on the AVA [16] dataset. With actor bounding boxes predicted in advance, the action detection problem is reduced to a pure action classification problem. The RoIAlign [17] operation is applied on the 3D feature maps extracted by a video backbone to generate actor-specific features. SlowFast [11] and MViT [9] directly use the RoI features for action classification. However, RoI features only contain the information inside the bounding box but overlook context and interaction information outside the box. To remedy this inherent flaw of RoI features, AIA [36] and ACARN [29] resort to using an extra heavy module that models the interaction between the actor and context or other actors. The models with an extra human detector require two-stage training and reference, which is computing resources unfriendly. Besides, they suffer from the aforementioned issue of fixed RoI feature sampling." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 355, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 546, + 641 + ], + "type": "text", + "content": "End-to-end action detectors. Methods of another research line use a single model to perform action detection. Most of them [6, 13, 21, 34] still follow the two-stage pipeline but simplify the training process by jointly training the actor proposal network and action classification network in an end-to-end manner. These methods still have the issue of fixed RoI feature sampling. To remedy this, VTr [13] attends RoI features to full feature maps while ACRN [34] introduces an actor-centric relation network for interaction modeling. Recently, several one-stage action detectors [24, 53] are proposed. MOC [24] is a point-based dense action detector, which uses an image backbone for frame feature extraction. It concatenates frame features along the temporal axis to form the video feature maps. Each point on the feature maps is regarded as an action instance proposal. The bounding box and action scores of each point are predicted by convolution. MOC [24] relies more on appearance features, lacks temporal and interaction modeling and requires post-process. Building on DETR [4] framework, TubeR [53] is a query-based action detector. TubeR [53] adaptively samples features from single-scale feature maps, neglecting multi-scale information which is important for detection tasks. As DETR [4], TubeR [53] transforms features in a static manner, resulting in slower convergence." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Inspired by AdaMixer [12], we propose a new one-stage query-based detector for video action detection. Different from former query-based action detectors [6, 53], we adaptively sample discriminative features from a multi-scale spatiotemporal feature space and decode them with a more flexible scheme under the guidance of queries." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14721" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 73, + 387, + 243 + ], + "blocks": [ + { + "bbox": [ + 75, + 73, + 387, + 243 + ], + "lines": [ + { + "bbox": [ + 75, + 73, + 387, + 243 + ], + "spans": [ + { + "bbox": [ + 75, + 73, + 387, + 243 + ], + "type": "image", + "image_path": "b7814303962db1f188e713194b7e94edd0a47c674044d11446f045b0298159ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 545, + 316 + ], + "type": "text", + "content": "Figure 2. Pipeline of STMixer. In the left, we present the overall STMixer framework. A video clip is input to the video backbone for feature extraction and a 4D feature space is constructed based on the feature maps (see Section 3.1). Then, a decoder containing " + }, + { + "bbox": [ + 46, + 251, + 545, + 316 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 251, + 545, + 316 + ], + "type": "text", + "content": " ASAM modules iteratively performs adaptive feature sampling (see Section 3.3) from the 4D feature space and adaptive mixing (see Section 3.4) on the sampled features under the guidance of a set of learnable queries. Inversely, the queries are updated with mixed features. Optionally, a short-term or long-term classifier can be used for action scores prediction, whose detailed structures are illustrated in the right. The long-term classifier refers to the long-term query bank produced by an offline STMixer for long-term information (see Section 3.5)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 391, + 76, + 512, + 243 + ], + "blocks": [ + { + "bbox": [ + 391, + 76, + 512, + 243 + ], + "lines": [ + { + "bbox": [ + 391, + 76, + 512, + 243 + ], + "spans": [ + { + "bbox": [ + 391, + 76, + 512, + 243 + ], + "type": "image", + "image_path": "dd63efa76c2ea5c2cd59ded1aaaa3a71e60afa04036d9a4f16299aa0c0e74049.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 336, + 102, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 102, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 102, + 348 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 358, + 290, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 290, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 290, + 573 + ], + "type": "text", + "content": "This section presents our one-stage sparse action detector, called STMixer. The overall pipeline of STMixer is shown in Figure 2. Our STMixer comprises a video backbone for feature extraction, a feature space construction module, and a sparse action decoder composed of " + }, + { + "bbox": [ + 46, + 358, + 290, + 573 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 358, + 290, + 573 + ], + "type": "text", + "content": " adaptive sampling and adaptive mixing (ASAM) modules followed by prediction heads. As a common practice, we set the middle frame of an input clip as the keyframe. We first use the video backbone to extract feature maps for the video and a 4D feature space is constructed based on the feature maps. Then, we develop the sparse action decoder with a set of learnable queries. Under the guidance of these queries, we perform adaptive feature sampling and feature mixing in the 4D feature space. The queries are updated iteratively. Finally, we decode each query as a detected action instance of action scores, human scores, and a human box. We will describe the technical details of each step in the next subsections." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 586, + 217, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 217, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 217, + 598 + ], + "type": "text", + "content": "3.1. 4D Feature Space Construction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "Hierarchical video backbone. Formally, let " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "X_{z} \\in \\mathbb{R}^{C_{z} \\times T \\times H_{z} \\times W_{z}}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " denote the feature map of convolution stage " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " of the hierarchical backbone, where " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "z \\in \\{2, 3, 4, 5\\}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "C_{z}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " stands for the channel number, " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " for time, " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "H_{z}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "W_{z}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " for the spatial height and width. The stage index " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " can be seen as the scale index of the feature map as " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "X_{z}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " has the downsampling rate of " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "2^{z}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": ". We first transform each feature map " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "X_{z}" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " to the same channel " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": " convolution. Then, we rescale the spatial shape of each stage feature map" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 328, + 338, + 524, + 405 + ], + "blocks": [ + { + "bbox": [ + 328, + 338, + 524, + 405 + ], + "lines": [ + { + "bbox": [ + 328, + 338, + 524, + 405 + ], + "spans": [ + { + "bbox": [ + 328, + 338, + 524, + 405 + ], + "type": "image", + "image_path": "a6c678b368bc723a59d1f2721c3f1bb33970f8fe9eaeb01ec3898b6e8c0a0e95.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 410, + 545, + 464 + ], + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 464 + ], + "type": "text", + "content": "Figure 3. 4D feature space construction for hierarchical video backbone. We construct 4D feature space on multi-scale 3D feature maps from hierarchical video backbone by simple lateral convolution and nearest-neighbor interpolation. The four dimensions of the 4D feature space are x-, y-, t-axis, and scale index z." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": "to " + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "inline_equation", + "content": "H_{2} \\times W_{2}" + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": " by simple nearest-neighbor interpolation and align them along the x- and y-axis. The four dimensions of the constructed feature space are x-, y-, t-axis, and scale index z, respectively. This process is illustrated in Figure 3. Plain ViT backbone. To make STMixer framework compatible with plain ViT [7] backbone, inspired by ViTDet [23], we construct 4D feature space based on the last feature map from ViT backbone. Specifically, with the output feature map of the default downsampling rate of " + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "inline_equation", + "content": "2^{4}" + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": ", we first produce hierarchical feature maps " + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "inline_equation", + "content": "\\{X_{z}\\}" + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": " of the same channel number " + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": " using convolutions of spatial strides " + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "inline_equation", + "content": "\\left\\{\\frac{1}{4}, \\frac{1}{2}, 1, 2\\right\\}" + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": ", where a fractional stride indicates a deconvolution. Then we also rescale each feature map to the spatial size of " + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "inline_equation", + "content": "H_{2} \\times W_{2}" + }, + { + "bbox": [ + 304, + 479, + 546, + 648 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 658, + 408, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 408, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 408, + 671 + ], + "type": "text", + "content": "3.2. Query Definition" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "The definition of our queries derives from the object query in Sparse R-CNN [35], but we specify the action query in a disentangled fashion. Specifically, we factorize" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14722" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": "action queries into spatial queries " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "Q_{s} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " and temporal queries " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "Q_{t} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " to refer to the spatial content and temporal content respectively. " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " represents the number of queries, while " + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 71, + 287, + 120 + ], + "type": "text", + "content": " denotes the dimension of each query." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": "We further define positional queries " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{p} \\in \\mathbb{R}^{N \\times 4}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": ". Each positional query " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{p}^{n}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " stands for the query index) is formulated as a proposal box vector (" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "x^{n}, y^{n}, z^{n}, r^{n}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": "). Formally, " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "x^{n}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "y^{n}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " stand for the x- and y-axis coordinates of the box center, and " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "z^{n}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "r^{n}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " denote the logarithm of its scale (i.e. the area of the bounding box) and aspect ratio. The positional queries " + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{p}" + }, + { + "bbox": [ + 46, + 120, + 286, + 216 + ], + "type": "text", + "content": " are initialized in such a way that every box vector is the whole keyframe." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 221, + 273, + 234 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 273, + 234 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 273, + 234 + ], + "type": "text", + "content": "3.3. Adaptive Spatiotemporal Feature Sampling" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "content": "Different from previous work [6, 11, 29, 36] that samples RoI features by pre-computed proposal boxes, we sample actor-specific features adaptively from the aforementioned 4D feature space under the guidance of spatial queries. Specifically, given a spatial query " + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "inline_equation", + "content": "Q_{s}^{n}" + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "content": " and the corresponding positional query " + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "inline_equation", + "content": "Q_{p}^{n}" + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "content": ", we regard the center point " + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "inline_equation", + "content": "(x^{n}, y^{n}, z^{n})" + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "content": " of the proposal box as the reference point, and regress " + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "inline_equation", + "content": "P_{in}" + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "content": " groups of offsets along x-, y-axis and scale index z on query " + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "inline_equation", + "content": "Q_{s}^{n}" + }, + { + "bbox": [ + 46, + 239, + 286, + 347 + ], + "type": "text", + "content": ", using a linear layer:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 351, + 287, + 371 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 351, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 91, + 351, + 287, + 371 + ], + "type": "interline_equation", + "content": "\\left\\{\\left(\\triangle x _ {i} ^ {n}, \\triangle y _ {i} ^ {n}, \\triangle z _ {i} ^ {n}\\right) \\right\\} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right), \\tag {1}", + "image_path": "69ec8a8048c64e599ce9dcba4c537d60d4a8cbb0a808bc636e69bdda1f73b84e.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 367, + 228, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 367, + 228, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 228, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 106, + 367, + 228, + 380 + ], + "type": "inline_equation", + "content": "i\\in \\mathbb{Z}" + }, + { + "bbox": [ + 106, + 367, + 228, + 380 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 106, + 367, + 228, + 380 + ], + "type": "inline_equation", + "content": "1\\leqslant i\\leqslant P_{in}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "type": "inline_equation", + "content": "P_{in}" + }, + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "type": "text", + "content": " is the number of sampled points for each query. Then, the offsets are added to the reference point, thus " + }, + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "type": "inline_equation", + "content": "P_{in}" + }, + { + "bbox": [ + 46, + 384, + 286, + 419 + ], + "type": "text", + "content": " spatial feature points are obtained:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 424, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 424, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 102, + 424, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\widetilde {x} _ {i} ^ {n} = x ^ {n} + \\triangle x _ {i} ^ {n} \\cdot 2 ^ {z ^ {n} - r ^ {n}}, \\\\ \\widetilde {y} _ {i} ^ {n} = y ^ {n} + \\triangle y _ {i} ^ {n} \\cdot 2 ^ {z ^ {n} + r ^ {n}}, \\\\ \\widetilde {z} _ {i} ^ {n} = z ^ {n} + \\triangle z _ {i} ^ {n}. \\end{array} \\right. \\tag {2}", + "image_path": "132b7e45366169395bed97c9cb3c7155676ec04a87c7acff71d0a25f24636ebb.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "type": "inline_equation", + "content": "2^{z^n - r^n}" + }, + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "type": "inline_equation", + "content": "2^{z^n + r^n}" + }, + { + "bbox": [ + 46, + 473, + 286, + 521 + ], + "type": "text", + "content": " are the width and height of the box respectively. We offset the spatial position of sampling points with respect to the width and height of the box to reduce the learning difficulty." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 286, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 286, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 286, + 617 + ], + "type": "text", + "content": "Finally, we propagate sampling points along the temporal axis, thus obtaining " + }, + { + "bbox": [ + 46, + 522, + 286, + 617 + ], + "type": "inline_equation", + "content": "T \\times P_{in}" + }, + { + "bbox": [ + 46, + 522, + 286, + 617 + ], + "type": "text", + "content": " points to sample from the 4D feature space. In our implementation, we simply copy these spatial sampling points along the temporal dimension because current action detection datasets yield temporal slowness property that the variation of actor locations along the temporal dimension is very slow. We compare different ways of temporal propagating in our ablation study." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "inline_equation", + "content": "T \\times P_{in}" + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "text", + "content": " sampling points, we sample instance-specific features by interpolation from the 4D feature space. In the following sections, the sampled spatiotemporal feature for spatial query " + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "inline_equation", + "content": "Q_{s}^{n}" + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "text", + "content": " is denoted by " + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "inline_equation", + "content": "F^{n} \\in \\mathbb{R}^{T \\times P_{in} \\times D}" + }, + { + "bbox": [ + 46, + 617, + 286, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 671, + 249, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 249, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 249, + 684 + ], + "type": "text", + "content": "3.4. Adaptive Dual-branch Feature Mixing" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "After feature sampling, we factorize the sampled features into spatial features and temporal features by pooling" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "and then enhance each by adaptive mixing respectively. As the dual-branch mixing module is completely symmetrical, we only describe spatial mixing in detail and temporal mixing is performed in a homogeneous way." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "text", + "content": "Different from MLP-Mixer [37], our mixing parameters are generated adaptively. Given a spatial query " + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "inline_equation", + "content": "Q_{s}^{n}\\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "text", + "content": " and its corresponding sampled features " + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "inline_equation", + "content": "F^n\\in \\mathbb{R}^{T\\times P_{in}\\times D}" + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "text", + "content": ", we first use a linear layer to generate query-specific channel-mixing weights " + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "inline_equation", + "content": "M_{c}\\in \\mathbb{R}^{D\\times D}" + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "text", + "content": ", and then apply plain matrix multiplication on temporally pooled feature and " + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "inline_equation", + "content": "M_{c}" + }, + { + "bbox": [ + 304, + 120, + 545, + 204 + ], + "type": "text", + "content": " to perform channel-mixing, given by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 366, + 210, + 545, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 210, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 366, + 210, + 545, + 224 + ], + "type": "interline_equation", + "content": "M _ {c} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right) \\in \\mathbb {R} ^ {D \\times D}, \\tag {3}", + "image_path": "cf9eb132222043e380a193e49b0d23e113ba4d89ae1ef8ebfad3f9c4a05f1cb7.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 315, + 251, + 545, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 251, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 315, + 251, + 545, + 265 + ], + "type": "interline_equation", + "content": "\\operatorname {C M} \\left(F ^ {n}\\right) = \\operatorname {R e L U} \\left(\\operatorname {L a y e r N o r m} \\left(\\operatorname {G A P} \\left(F ^ {n}\\right) \\times M _ {c}\\right)\\right). \\tag {4}", + "image_path": "e01c8eb57e1daca3011d5e55037e362e368abeaa0a803d183a47a7c6003fa94a.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 273, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 320 + ], + "type": "text", + "content": "where GAP stands for the global average pooling operation in the temporal dimension while LayerNorm for the layer normalization [2]. We use " + }, + { + "bbox": [ + 304, + 273, + 545, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{CM}(F^n) \\in \\mathbb{R}^{P_{in} \\times D}" + }, + { + "bbox": [ + 304, + 273, + 545, + 320 + ], + "type": "text", + "content": " to denote the channel-wise mixing output features." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": "After channel-mixing, we perform point-wise mixing in a similar way. Suppose " + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": " is the number of spatial pointwise mixing out patterns, we use " + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathrm{PCM}(F^n) \\in \\mathbb{R}^{D \\times P_{out}}" + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": " to denote the point-wise mixing output features, given by:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 358, + 375, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 375, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 358, + 375, + 545, + 389 + ], + "type": "interline_equation", + "content": "M _ {p} = \\operatorname {L i n e a r} \\left(Q _ {s} ^ {n}\\right) \\in \\mathbb {R} ^ {P _ {i n} \\times P _ {o u t}}, \\tag {5}", + "image_path": "7cb6571eeb5c0a45482c06ebc9c2cf1f7a1131d9745347b1c927e37ed0fc554e.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 311, + 415, + 545, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 415, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 311, + 415, + 545, + 430 + ], + "type": "interline_equation", + "content": "\\operatorname {P C M} \\left(F ^ {n}\\right) = \\operatorname {R e L U} \\left(\\operatorname {L a y e r N o r m} \\left(\\operatorname {C M} \\left(F ^ {n}\\right) ^ {T} \\times M _ {p}\\right)\\right). \\tag {6}", + "image_path": "d63be288f39c298979e7f82c396e8229079aa9663faf66e69125adbffa84e935.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": "The final output " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathrm{PCM}(F^n)" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": " is flattened, transformed to " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": " dimension, and added to the spatial query " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "Q_{s}^{n}" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": ". The temporal query " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "Q_{t}^{n}" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": " is updated in a homogeneous way, except that the pooling is applied in the spatial dimension. After global spatial pooling, there are " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": " feature points of different temporal locations for temporal mixing and we set the number of temporal point-wise mixing out patterns to " + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "inline_equation", + "content": "T_{out}" + }, + { + "bbox": [ + 304, + 437, + 545, + 521 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 528, + 435, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 435, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 435, + 540 + ], + "type": "text", + "content": "3.5. Sparse Action Decoder" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 545, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 629 + ], + "type": "text", + "content": "STMixer adopts a unified action decoder for both actor localization and action classification. The decoder comprises " + }, + { + "bbox": [ + 304, + 545, + 545, + 629 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 545, + 545, + 629 + ], + "type": "text", + "content": " stacked ASAM modules followed by a feedforward network (FFN) for human scores prediction and a short-term or long-term classifier for action score prediction. In this section, we represent the structure of ASAM module and specify the outputs of the prediction heads." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "ASAM module. The overall structure of ASAM module is shown in Figure 2. We first perform self-attention [42] on spatial queries " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "Q_{s}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " and temporal queries " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " to capture the relation information between different instances. Then we perform adaptive sampling from the 4D feature space and dual-branch adaptive mixing on the sampled feature as described before. The spatial queries " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "Q_{s}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " and temporal queries" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14723" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "inline_equation", + "content": "Q_{t}" + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "content": " are updated with mixed features. An FFN is applied on updated spatial queries " + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "inline_equation", + "content": "Q_{s}^{\\prime}" + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "content": " to update the positional queries " + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "inline_equation", + "content": "Q_{p}" + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "content": ". The updated queries " + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "inline_equation", + "content": "Q_{p}^{\\prime}, Q_{s}^{\\prime}" + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "inline_equation", + "content": "Q_{t}^{\\prime}" + }, + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "content": " are used as inputs for the next ASAM module." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": "Outputs of the prediction heads. The output human boxes are decoded from positional queries " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{p}^{\\prime}" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": ". We apply an FFN on " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{s}^{\\prime}" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": " to predict human scores " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "S_{H} \\in \\mathbb{R}^{N \\times 2}" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": " which indicates the confidence values that each box belongs to the human category and background. Based on the concatenation of spatial queries " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{s}^{\\prime}" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": " and temporal queries " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "Q_{t}^{\\prime}" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": ", we use a short-term or long-term classifier to predict action scores " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "S_{A} \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 120, + 286, + 216 + ], + "type": "text", + "content": " is the number of action classes." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": "Short-term and long-term classifier. Short-term classifier (see Figure 2 right top) is a simple FFN which predicts action scores based on short-term information of current queries while long-term classifier (see Figure 2 right bottom) refers to long-term query bank for long-term information. Our design of the long-term classifier is adapted from LFB [47]. We train an STMixer model without long-term information first. Then, for a video of " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": " clips, we use the trained STMixer to perform inference on each clip of it. We store the concatenation of the spatial and temporal queries from the last ASAM module corresponding to the " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": " highest human scores in the query bank for each clip. We denote the stored queries for clip of time-step " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "L_{t} \\in \\mathbb{R}^{k \\times d}" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "d = 2D" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": ", and the long-term query bank of the video as " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "L = [L_{0}, L_{1}, \\dots, L_{\\mathcal{T}-1}]" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": ". Given the long-term query bank of all videos, we train an STMixer model with a long-term classifier from scratch. For video clip " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": ", we first sample a window of length " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": " from the long-term query bank centered at it and stack this window into " + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\tilde{L}_{t} \\in \\mathbb{R}^{K \\times d}" + }, + { + "bbox": [ + 47, + 217, + 286, + 445 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 456, + 286, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 456, + 286, + 471 + ], + "spans": [ + { + "bbox": [ + 91, + 456, + 286, + 471 + ], + "type": "interline_equation", + "content": "\\tilde {L} _ {t} = \\operatorname {s t a c k} \\left(\\left[ L _ {t - w / 2}, \\dots , L _ {t + w / 2 - 1} \\right]\\right). \\tag {7}", + "image_path": "d160a66919d1ce632da200759d66b6d1999d5b4a40e35fbf472f45c4555f3974.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 477, + 286, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 286, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 286, + 502 + ], + "type": "text", + "content": "We then infer current queries to " + }, + { + "bbox": [ + 47, + 477, + 286, + 502 + ], + "type": "inline_equation", + "content": "\\tilde{L}_t" + }, + { + "bbox": [ + 47, + 477, + 286, + 502 + ], + "type": "text", + "content": " for long-term information by cross-attention [42]:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 511, + 286, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 511, + 286, + 525 + ], + "spans": [ + { + "bbox": [ + 107, + 511, + 286, + 525 + ], + "type": "interline_equation", + "content": "S _ {t} ^ {\\prime} = \\text {c r o s s - a t t e n t i o n} \\left(S _ {t}, \\tilde {L} _ {t}\\right), \\tag {8}", + "image_path": "67914c4a7bde1bff69a603ce5c19f3ad81bc000d7f576aa0f3784a5ee50483ff.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "inline_equation", + "content": "S_{t} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "text", + "content": " is the concatenation of the output spatial queries and temporal queries of the last ASAM module. The output " + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "inline_equation", + "content": "S_{t}'" + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "text", + "content": " is then channel-wise concatenated with " + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "inline_equation", + "content": "S_{t}" + }, + { + "bbox": [ + 47, + 533, + 286, + 582 + ], + "type": "text", + "content": " for action scores prediction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 590, + 111, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 590, + 111, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 590, + 111, + 604 + ], + "type": "text", + "content": "3.6. Training" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "text", + "content": "We compute training loss based on the output human boxes, human scores, and action scores. Consistent with WOO [6], the loss function " + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "text", + "content": " consists of set prediction loss " + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{set}[4,35,54]" + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "text", + "content": " and action classification loss " + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{act}" + }, + { + "bbox": [ + 47, + 609, + 286, + 657 + ], + "type": "text", + "content": ". Formally," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 80, + 670, + 286, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 670, + 286, + 683 + ], + "spans": [ + { + "bbox": [ + 80, + 670, + 286, + 683 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s e t} = \\lambda_ {c l s} \\mathcal {L} _ {c l s} + \\lambda_ {L _ {1}} \\mathcal {L} _ {L _ {1}} + \\lambda_ {g i o u} \\mathcal {L} _ {g i o u}, \\tag {9}", + "image_path": "e98c491b4a93e9b81b7bb1b118d022ce27ac13381c112585d5fad0978d0b16e9.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 121, + 701, + 286, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 701, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 121, + 701, + 286, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {s e t}} + \\lambda_ {\\text {a c t}} \\mathcal {L} _ {\\text {a c t}}. \\tag {10}", + "image_path": "14a7155e93877d7f26779c35e8a20b7321693d8f1e9bddb4f283d80ebfaeae64.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " denotes the cross-entropy loss over two classes (human and background). " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{L_1}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{giou}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " are box loss inherited from [4, 35, 54]. As in [4, 6], we first use Hungarian algorithm to find an optimal bipartite matching between predicted actors and ground truth actors according to " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{set}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": ". Then we calculate full training loss " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " based on the matching results. " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{act}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " is binary cross entropy loss for action classification. We only compute " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{act}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " for the prediction matched with a ground truth. " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\lambda_{cls}, \\lambda_{L_1}, \\lambda_{giou}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\lambda_{act}" + }, + { + "bbox": [ + 306, + 72, + 545, + 192 + ], + "type": "text", + "content": " are corresponding weights of each term." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 205, + 386, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 386, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 386, + 217 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 224, + 422, + 238 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 422, + 238 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 422, + 238 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 243, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 545, + 375 + ], + "type": "text", + "content": "Datasets. The AVA dataset [16] contains 211k video clips for training and 57k for validation segmented from 430 15-minute videos. The videos are annotated at 1FPS over 80 atomic action classes. Following the standard evaluation protocol [16], we report our results on 60 action classes that have at least 25 validation examples. JHMDB [19] consists of 928 temporally trimmed videos from 21 action classes. Results averaged over three splits are reported. UCF101-24 is a subset of UCF101 [33]. It contains 3,207 videos annotated with action instances of 24 classes. As the common setting, we report the performance on the first split." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": "Network configurations. We configure the dimension " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " of both spatial and temporal queries to 256 and set the number of both queries " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " equaling 100. The number of sampling point " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "P_{in}" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " in each temporal frame is set to 32. The spatial and temporal mixing out patterns " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "T_{out}" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " are set to 4 times the number of sampling points and temporal frames respectively, that is, 128 and 32 for SlowFast [11] backbone and 128 and 16 for CSN [40] and ViT [7] backbone. Following multi-head attention [42] and group convolution [49], we split the channel " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " into 4 groups and perform group-wise sampling and mixing. We stack 6 ASAM modules in our action decoder as default. For the long-term classifier, we set the number of stored queries of each clip " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " as 5 and window length " + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 376, + 545, + 555 + ], + "type": "text", + "content": " as 60. The number of cross-attention layers is set to 3." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "content": "Losses and optimizers. We set the loss weight in STMixer as " + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{cls} = 2.0" + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{L_1} = 2.0" + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{giou} = 2.0" + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{act} = 24.0" + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "content": ". We use AdamW [28] optimizer with weight decay " + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 305, + 556, + 545, + 616 + ], + "type": "text", + "content": " for all experiments. Following [4, 6], intermediate supervision is applied after each ASAM module." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 616, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 616, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 305, + 616, + 545, + 700 + ], + "type": "text", + "content": "Training and inference recipes. We train STMixer detectors for 10 epochs with an initial learning rate of " + }, + { + "bbox": [ + 305, + 616, + 545, + 700 + ], + "type": "inline_equation", + "content": "2.0 \\times 10^{-5}" + }, + { + "bbox": [ + 305, + 616, + 545, + 700 + ], + "type": "text", + "content": " and batchsize of 16. The learning rate and batchsize can be tuned according to the linear scaling rule [15]. We randomly scale the short size of the training video clips to 256 or 320 pixels. Color jittering and random horizontal flipping are also adopted for data augmentation." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "For inference, we scale the short size of input frames" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14724" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "to 256 as the common setting. Given an input video clip, STMixer predicts " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " bounding boxes associated with their human scores and action scores from the last ASAM module. If the confidence score that a box belongs to the human category is higher than the preset threshold, we take it as a detection result. We set the threshold to 0.6 for AVA. The performances are evaluated with official metric frame-level mean average precision(mAP) at 0.5 IoU threshold." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 178, + 141, + 192 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 141, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 141, + 192 + ], + "type": "text", + "content": "4.2. Ablation Study" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 287, + 258 + ], + "type": "text", + "content": "We conduct ablation experiments on AVa v2.2 dataset to investigate the influence of different components in our STMixer framework. A SlowOnly ResNet-50 backbone [8] is used for our ablation experiments. We report both mAP and GFLOPs for effectiveness and efficiency comparison." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 258, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 289, + 449 + ], + "type": "text", + "content": "Ablations on 4D feature space. We first show the benefit of sampling features from the unified 4D feature space. For comparison, we design a two-stage counterpart of our STMixer. In the first stage, we sample features from key-frame features for actor localization. In the second stage, we sample features from res5 features for action classification. As shown in Tabel 1a, sampling features from a unified 4D feature space and performing action detection in a one-stage manner significantly reduce computing costs, and detection mAP also gets improved as multi-scale information is also utilized for classification. We then investigate two different ways for the 4D feature space construction. As shown in Table 1b, constructing 4D feature space by simple lateral " + }, + { + "bbox": [ + 46, + 258, + 289, + 449 + ], + "type": "inline_equation", + "content": "1 \\times 1 \\times 1" + }, + { + "bbox": [ + 46, + 258, + 289, + 449 + ], + "type": "text", + "content": " convolution achieves comparable detection accuracy while being more efficient than using full FPN [25] with a top-down pathway." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "text", + "content": "Ablations on feature sampling. In Tabel 1c, we compare 3 different feature sampling strategies. For fixed grid feature sampling, we sample " + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "text", + "content": " feature points inside each actor box by interpolation, which is actually the RoIAlign [17] operation adopted by many former methods [6,13]. Though sampling fewer points per group, our adaptive sampling strategy improves the detection mAP by 1.2. The results show that the fixed RoIAlign operation for feature sampling fails to capture useful context information outside the box while our adaptive sampling strategy enables the detector to mine discriminative features from the whole 4D feature space. Beyond simply copying sampling points, we try sampling different feature points in different frames by predicting the offset of the reference bounding box for each frame. The improvement is marginal due to the slowness issue of current action detection datasets that the variation of actors' location and action is very slow. In Table 1d, we further investigate the influence of the number of sampling points per group " + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "inline_equation", + "content": "P_{in}" + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "text", + "content": " in each temporal frame. Setting " + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "inline_equation", + "content": "P_{in} = 32" + }, + { + "bbox": [ + 46, + 449, + 289, + 689 + ], + "type": "text", + "content": " achieves the best detection performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "Ablations on feature mixing. In Table 1f, we compare different feature mixing strategies. We first demonstrate" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": "the benefit of query-guided adaptive mixing. The detection mAP drops by 0.6 when using fixed parameter mixing. For adaptive mixing, the mixing parameters are dynamically generated based on a specific query, thus more powerful to enhance the presentation of each specific action instance proposal. We further compare different adaptive feature mixing strategies. From the results in Table 1f, it is demonstrated that both spatial appearance and temporal motion information are important for action detection. However, coupled spatiotemporal feature mixing using queries of a single type has a high computational complexity. Decoupling features along spatial and temporal dimensions saves computing costs. Our dual-branch spatiotemporal feature mixing outperforms sequential spatiotemporal feature mixing by " + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "inline_equation", + "content": "0.5\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": ". This is because actor localization at keyframes only needs spatial appearance information and parallel dual-branch mixing will reduce the effect of temporal information on localization. Also, by concatenating temporal queries to spatial queries, more temporal information is leveraged for action classification. In Table 1g, we investigate different spatial and temporal mixing out patterns " + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "inline_equation", + "content": "T_{out}" + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": " from 64 and 8 to 192 and 24, that is, 2 times to 6 times the number of sampling points and temporal frames. Setting " + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "inline_equation", + "content": "P_{out}" + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "inline_equation", + "content": "T_{out}" + }, + { + "bbox": [ + 304, + 72, + 547, + 371 + ], + "type": "text", + "content": " equaling 128 and 16 achieves the best performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 372, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 547, + 433 + ], + "type": "text", + "content": "Ablations on network configuration. As shown in Table 1e, the detection mAP is saturated when the number of queries is increased to 100. From the results in Table 1h, a stack of 6 ASAM modules achieves a good effectiveness and efficiency balance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 442, + 528, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 442, + 528, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 442, + 528, + 455 + ], + "type": "text", + "content": "4.3. Comparison with State-of-the-arts on AVA" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "text", + "content": "We compare our proposed STMixer with state-of-the-art methods on AVa v2.1 and v2.2 in Table 2. We first compare our STMixer to methods using an extra offline human detector. Our STMixer with SlowFast-R101 backbone achieves 30.6 and " + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "inline_equation", + "content": "30.9\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "text", + "content": " when not using long-term features. With long-term query support, our STMixer reaches 32.6 and " + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "inline_equation", + "content": "32.9\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "text", + "content": " on AVa v2.1 and v2.2 respectively. To demonstrate the generalization ability of our method, we conduct experiments with ViT [7] backbone. Compared with the two-stage counterparts, STMixer brings performance improvements while getting rid of the dependence on an extra detector. Although ViT is considered to have a global receptive field, our adaptive sampling and decoding mechanism could serve as a supplement to improve the flexibility of the model. Compared to previous end-to-end methods, our STMixer achieves the best results. Our STMixer outperforms WOO [6] by 2.0 and " + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "inline_equation", + "content": "1.7\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 461, + 547, + 700 + ], + "type": "text", + "content": " even though WOO test models at 320 resolution. STMixer also consistently outperforms TubeR [53] on AVA v2.1 or v2.2, using or not using long-term features." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "We compare mAP versus GFLOPs on AVa v2.2 in Fig" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "14725" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 71, + 211, + 97 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 211, + 97 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 211, + 97 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 211, + 97 + ], + "type": "table", + "html": "
ClassificationLocalizationmAPGFLOPs
4D Feature Space23.144.4
Key-Frame FeaturesRes5 Features22.853.7
", + "image_path": "d6e763021e6b045b3d3dd22879f8e73e50999a4db9ed969ebc2d9e8d4006de54.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 99, + 214, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 99, + 214, + 137 + ], + "spans": [ + { + "bbox": [ + 47, + 99, + 214, + 137 + ], + "type": "text", + "content": "(a) Feature space. Sampling features from 4D feature space is more effective and efficient than sampling from key-frame features for classification and res5 features for localization." + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 58, + 140, + 204, + 169 + ], + "blocks": [ + { + "bbox": [ + 58, + 140, + 204, + 169 + ], + "lines": [ + { + "bbox": [ + 58, + 140, + 204, + 169 + ], + "spans": [ + { + "bbox": [ + 58, + 140, + 204, + 169 + ], + "type": "table", + "html": "
Pin816324864
mAP22.422.523.123.022.5
GFLOPs42.443.144.445.646.9
", + "image_path": "cb5cfc703e17b26281c35e54f286d0741f34221b5ba46185dd8c228cc32c3042.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 171, + 214, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 171, + 214, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 171, + 214, + 190 + ], + "type": "text", + "content": "(d) Number of sampling points. Sampling 32 points per frame achieves the best performance." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 49, + 194, + 211, + 220 + ], + "blocks": [ + { + "bbox": [ + 49, + 194, + 211, + 220 + ], + "lines": [ + { + "bbox": [ + 49, + 194, + 211, + 220 + ], + "spans": [ + { + "bbox": [ + 49, + 194, + 211, + 220 + ], + "type": "table", + "html": "
Pout/Tout64/896/12128/16160/20192/24
mAP22.522.823.122.922.6
GFLOPs40.242.344.446.448.4
", + "image_path": "08c05992b2e0c7c89a49ad44ff5f762ece839402a892daadd24316fbd2939046.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 221, + 213, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 221, + 213, + 241 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 213, + 241 + ], + "type": "text", + "content": "(g) Number of mixing out patterns. A moderate number of mixing out patterns works the best." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 222, + 71, + 345, + 97 + ], + "blocks": [ + { + "bbox": [ + 222, + 71, + 345, + 97 + ], + "lines": [ + { + "bbox": [ + 222, + 71, + 345, + 97 + ], + "spans": [ + { + "bbox": [ + 222, + 71, + 345, + 97 + ], + "type": "table", + "html": "
mAPGFLOPs
Simple Lateral Conv.23.144.4
Full FPN22.945.8
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N1550100150
mAP22.122.923.122.5
GFLOPs31.736.944.451.8
", + "image_path": "ea674372c89f8af90cc0ca73746e4476b5653b840887440321c919a5f9b4876d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 220, + 171, + 347, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 220, + 171, + 347, + 190 + ], + "spans": [ + { + "bbox": [ + 220, + 171, + 347, + 190 + ], + "type": "text", + "content": "(e) Number of queries. Using 100 queries works the best." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 225, + 193, + 343, + 220 + ], + "blocks": [ + { + "bbox": [ + 225, + 193, + 343, + 220 + ], + "lines": [ + { + "bbox": [ + 225, + 193, + 343, + 220 + ], + "spans": [ + { + "bbox": [ + 225, + 193, + 343, + 220 + ], + "type": "table", + "html": "
M1369
mAP18.422.523.122.6
GFLOPs32.036.944.451.8
", + "image_path": "8b957d6422d936ec8f0c8c6921b32c95361eb7cb8e97536afdbdb2078584026d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 220, + 221, + 347, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 220, + 221, + 347, + 241 + ], + "spans": [ + { + "bbox": [ + 220, + 221, + 347, + 241 + ], + "type": "text", + "content": "(h) Number of ASAM modules. Using 6 ASAM modules works the best." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 356, + 70, + 544, + 104 + ], + "blocks": [ + { + "bbox": [ + 356, + 70, + 544, + 104 + ], + "lines": [ + { + "bbox": [ + 356, + 70, + 544, + 104 + ], + "spans": [ + { + "bbox": [ + 356, + 70, + 544, + 104 + ], + "type": "table", + "html": "
Sampling StrategyPinmAPGFLOPs
Fixed Grid Sampling4921.945.6
Adaptive Sampling + Temporal Copying3223.144.4
Adaptive Sampling + Temporal Moving3223.344.6
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Mixing StrategymAPGFLOPs
fixed parameter dual-branch mixing22.536.8
dual-branch spatiotemporal mixing23.144.4
spatial mixing only22.440.4
temporal mixing only22.133.5
sequential spatiotemporal mixing22.643.6
coupled spatiotemporal mixing22.893.2
", + "image_path": "b87a916ec6efa949c52dadef014cb32615938a0f2e1ddeee9f1443c7d5e0b9ab.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 353, + 212, + 545, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 212, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 353, + 212, + 545, + 241 + ], + "type": "text", + "content": "(f) Mixing strategy. Query-guided adaptive feature mixing outperforms fixed parameter mixing and our dual-branch spatiotemporal feature mixing strategy works the best." + } + ] + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 86, + 278, + 507, + 547 + ], + "blocks": [ + { + "bbox": [ + 46, + 249, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 46, + 249, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 46, + 249, + 545, + 271 + ], + "type": "text", + "content": "Table 1. Ablations Experiments. We use a SlowOnly ResNet-50 backbone to perform our ablation studies. Models are trained on the training set of AVa v2.2 and evaluated on the validation set. Default choices for our model are colored in gray ." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 86, + 278, + 507, + 547 + ], + "lines": [ + { + "bbox": [ + 86, + 278, + 507, + 547 + ], + "spans": [ + { + "bbox": [ + 86, + 278, + 507, + 547 + ], + "type": "table", + "html": "
MethodDetectorOne-stageInputBackbonePre-trainLFmAP
v2.1v2.2
Compare to methods with an extra human detector
SlowFast [11]✓✗32×2SF-R101-NLK600✗28.229.0
LFB [47]✓✗32×2I3D-R101-NLK400✓27.7-
CA-RCNN [48]✓✗32×2R50-NLK400✓28.0-
AIA [36]✓✗32×2SF-R101K700✓31.232.3
ACARN [29]✓✗32×2SF-R101K400✓30.0-
ACARN [29]✓✗32×2SF-R101-NLK600✓-31.4
VideoMAE [38]✓✗16×4ViT-BK400✗-31.8
VideoMAE [38]✓✗16×4ViT-LK700✗-39.3
STMixer✗✓32×2SF-R101K700✗30.630.9
STMixer✗✓32×2SF-R101K700✓32.632.9
STMixer✗✓16×4ViT-B (from [38])K400✗-32.6
STMixer✗✓16×4ViT-B (from [43])K710+K400✗-36.1
STMixer✗✓16×4ViT-L (from [38])K700✗-39.5
Compare to end-to-end methods
AVA [16]✗✗20×1I3D-VGGK400✗14.6-
ACRN [34]✗✗20×1S3D-GK400✗17.4-
STEP [51]✗✗12×1I3D-VGGK400✗18.6-
VTr [13]✗✗64×1I3D-VGGK400✗24.9-
WOO [6]✗✗32×2SF-R50K400✗25.225.4
WOO [6]✗✗32×2SF-R101-NLK600✗28.028.3
TubeR [53]✗✓32×2CSN-152IG-65M✗29.731.1
TubeR [53]✗✓32×2CSN-152IG-65M✓31.733.4
STMixer✗✓32×2SF-R50K400✗27.227.8
STMixer✗✓32×2SF-R101-NLK600✗29.830.1
STMixer✗✓32×2CSN-152IG-65M✗31.732.8
STMixer✗✓32×2CSN-152IG-65M✓34.434.8
", + "image_path": "11d39b737a70c787423db5dc84368dabef6fca546f37c08df81dcc2c79552087.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 555, + 544, + 576 + ], + "lines": [ + { + "bbox": [ + 46, + 555, + 544, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 544, + 576 + ], + "type": "text", + "content": "Table 2. Comparisons with state-of-the-arts on validation sets of AVa v2.1 and v2.2. √of column \"Detector\" denotes an extra human detector Faster RCNN-R101-FPN [31] is used. √of column \"LF\" denotes long-term features are used." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 592, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 712 + ], + "type": "text", + "content": "ure 1 to show the efficiency of our STMixer. AIA [36] and ACARN [29] do not report their GFLOPs. As they are built on SlowFast [11] framework and also use an offline human detector but introduce extra modules to model interaction, SlowFast can serve as a lower bound of complexity for them. For a fair comparison, we report results for no long-term feature version of each method. As shown in Figure 1, due to an extra human detector being needed, SlowFast [11], CSN [40], and VideoMAE [38] have much higher GFLOPs than end-to-end methods with same back" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 592, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 592, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 592, + 545, + 663 + ], + "type": "text", + "content": "bone. Among end-to-end methods, STMixer achieves the best effectiveness and efficiency balance. STMixer outperforms WOO [6] by " + }, + { + "bbox": [ + 304, + 592, + 545, + 663 + ], + "type": "inline_equation", + "content": "1.8\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 592, + 545, + 663 + ], + "type": "text", + "content": " while having much lower GFLOPs (135 versus 252). With a slight GFLOPs increase (126 versus 120), STMixer outperforms TubeR [53] by 1.7 mAP." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 671, + 496, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 496, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 496, + 682 + ], + "type": "text", + "content": "4.4. Results on JHMDB and UCF101-24" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "To verify the effectiveness of our STMixer, we further evaluate it on the JHMDB [19] and UCF101-24 [33]" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14726" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 74, + 123, + 208 + ], + "blocks": [ + { + "bbox": [ + 53, + 74, + 123, + 208 + ], + "lines": [ + { + "bbox": [ + 53, + 74, + 123, + 208 + ], + "spans": [ + { + "bbox": [ + 53, + 74, + 123, + 208 + ], + "type": "image", + "image_path": "2594e5afbee7f070abd03606d03beee07a161411f2f8f58c389b83c07861944e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 221, + 546, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 221, + 546, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 546, + 266 + ], + "type": "text", + "content": "Figure 4. Sampling points and detection results visualization. We display the actor bounding boxes and action classes of three groundtruth action instances in the first column. Each ASAM module's sampling points, predicted actor bounding boxes and action scores are displayed in the following columns. The correctly predicted action classes are displayed in green, missing in orange, and wrongly predicted in red. Intuitively, STMixer mines discriminative context features outside the bounding box for better action detection." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 124, + 74, + 192, + 208 + ], + "blocks": [ + { + "bbox": [ + 124, + 74, + 192, + 208 + ], + "lines": [ + { + "bbox": [ + 124, + 74, + 192, + 208 + ], + "spans": [ + { + "bbox": [ + 124, + 74, + 192, + 208 + ], + "type": "image", + "image_path": "5318ea11ec3cc126b72334afc61530d278a7f0232027473892edd038afcc7cfb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 193, + 74, + 260, + 208 + ], + "blocks": [ + { + "bbox": [ + 193, + 74, + 260, + 208 + ], + "lines": [ + { + "bbox": [ + 193, + 74, + 260, + 208 + ], + "spans": [ + { + "bbox": [ + 193, + 74, + 260, + 208 + ], + "type": "image", + "image_path": "4d9f396b54a8dc66435962bfc54b1f769e00ebf71c3157a17d385864b1151c3e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 261, + 74, + 329, + 208 + ], + "blocks": [ + { + "bbox": [ + 261, + 74, + 329, + 208 + ], + "lines": [ + { + "bbox": [ + 261, + 74, + 329, + 208 + ], + "spans": [ + { + "bbox": [ + 261, + 74, + 329, + 208 + ], + "type": "image", + "image_path": "66dacc388e2e55cbfd1ad80bf8ad1f294104145a1d404c4306e142a6e803c7d4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 329, + 74, + 398, + 208 + ], + "blocks": [ + { + "bbox": [ + 329, + 74, + 398, + 208 + ], + "lines": [ + { + "bbox": [ + 329, + 74, + 398, + 208 + ], + "spans": [ + { + "bbox": [ + 329, + 74, + 398, + 208 + ], + "type": "image", + "image_path": "120416cd0bd405e4b49966a944832100227ac83372823f314a12947312142759.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 399, + 74, + 466, + 208 + ], + "blocks": [ + { + "bbox": [ + 399, + 74, + 466, + 208 + ], + "lines": [ + { + "bbox": [ + 399, + 74, + 466, + 208 + ], + "spans": [ + { + "bbox": [ + 399, + 74, + 466, + 208 + ], + "type": "image", + "image_path": "b9dc17c3a6db1a4df9b50807ac5b9da3786d94027e92eb918a7b82d11eb59aec.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 467, + 74, + 535, + 208 + ], + "blocks": [ + { + "bbox": [ + 467, + 74, + 535, + 208 + ], + "lines": [ + { + "bbox": [ + 467, + 74, + 535, + 208 + ], + "spans": [ + { + "bbox": [ + 467, + 74, + 535, + 208 + ], + "type": "image", + "image_path": "7c75a7bfd968f9d0302f18db86ee58be9e68ec58f02600c50e58a3141c0eeb78.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 55, + 271, + 280, + 373 + ], + "blocks": [ + { + "bbox": [ + 55, + 271, + 280, + 373 + ], + "lines": [ + { + "bbox": [ + 55, + 271, + 280, + 373 + ], + "spans": [ + { + "bbox": [ + 55, + 271, + 280, + 373 + ], + "type": "table", + "html": "
MethodDetectorInputBackboneJHMDBUCF101-24
MOC* [24]✓7×1DLA3470.878.0
AVA* [16]✗20×1I3D-VGG73.376.3
ACRN [34]✗20×1S3D-G77.9-
CA-RCNN [48]✓32×2R50-NL79.2-
YOWO [21]✗16×13DResNext-10180.475.7
WOO [6]✗32×2SF-R101-NL80.5-
AIA [36]✓32×1SF-R50-NL-78.8
ACARN [29]✓32×1SF-R50-84.3
TubeR* [53]✗32×2I3D-81.3
STMixer✗32×2SF-R101-NL86.783.7
", + "image_path": "9d15dc9c56c20df5dc395ef495c09a9ff75cadde6e5334bc376b53c3b987e63b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 381, + 287, + 404 + ], + "lines": [ + { + "bbox": [ + 47, + 381, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 287, + 404 + ], + "type": "text", + "content": "Table 3. Comparison on JHMDB and UCF101-24. Methods marked with * use extra optical flow features." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "content": "datasets. We report the frame-level mean average precision (frame-mAP) with an intersection-over-union (IoU) threshold of 0.5 in Table 3. Experimental results demonstrate that STMixer outperforms the current state-of-the-art methods with remarkable performance gain on JHMDB and achieves competitive results on UCF101-24." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 502, + 130, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 130, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 130, + 514 + ], + "type": "text", + "content": "4.5. Visualization" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "We provide the visualization of sampling points and detection results of each ASAM module in order in Figure 4. In the first few ASAM modules, the sampling points are quickly concentrated on the action performer and the actor localization accuracy gets improved rapidly. In the following ASAM modules, some of the sampling points get out of the human box and spread to the context. Benefiting from the gathered context and interaction information, the action recognition accuracy gets improved while localization accuracy is not compromised. In Figure 4, we show clear improvements in three aspects: predicting missing classes (ride in row 1), improving the confidence score of correctly predicted classes (talk to in row 2), and removing wrongly predicted classes (watch in row 3). To recognize an action \"ride\", we need to observe the person is in a car and someone is driving. For recognition of \"talk to\", we need to know" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 274, + 545, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 333 + ], + "type": "text", + "content": "if a person is listening in the context, and for \"watch\", we need to know if a person is in the actor's sight. The improvements are mostly related to these classes of interaction, which indicates our STMixer is capable of mining discriminative interaction information from the context." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 346, + 470, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 470, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 470, + 358 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 368, + 545, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 545, + 546 + ], + "type": "text", + "content": "In this paper, we have presented a new one-stage sparse action detector in videos, termed STMixer. Our STMixer yields a simple, neat, and efficient end-to-end action detection framework. The core design of our STMixer is a set of learnable queries to decode all action instances in parallel. The decoding process is composed of an adaptive feature sampling module to identify important features from the entire spatiotemporal domain of video, and an adaptive feature mixing module to dynamically extract discriminative representations for action detection. Our STMixer achieves a new state-of-the-art performance on three challenging benchmarks of AVA, JHMDB, and UCF101-24 with less computational cost than previous end-to-end methods. We hope STMixer can serve as a strong baseline for future research on video action detectors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 548, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 545, + 630 + ], + "type": "text", + "content": "One limitation of our STMixer is that the long-term query bank is implemented in an offline way where another STMixer without long-term query support is pre-trained for long-term query generation. We leave the design of an online query bank to future research and hope our STMixer is extended to extract long-form video information in an end-to-end manner." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006, No. 62072232), Fundamental Research Funds for the Central Universities (No. 020214380091), and Collaborative Innovation Center of Novel Software Technology and Industrialization." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14727" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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Zhang1 Francesco Ferroni2 \n1Carnegie Mellon University 2Argo AI", + "bbox": [ + 299, + 180, + 653, + 218 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deva Ramanan", + "bbox": [ + 687, + 180, + 815, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 266, + 313, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We extend neural radiance fields (NeRFs) to dynamic large-scale urban scenes. Prior work tends to reconstruct single video clips of short durations (up to 10 seconds). Two reasons are that such methods (a) tend to scale linearly with the number of moving objects and input videos because a separate model is built for each and (b) tend to require supervision via 3D bounding boxes and panoptic labels, obtained manually or via category-specific models. As a step towards truly open-world reconstructions of dynamic cities, we introduce two key innovations: (a) we factorize the scene into three separate hash table data structures to efficiently encode static, dynamic, and far-field radiance fields, and (b) we make use of unlabeled target signals consisting of RGB images, sparse LiDAR, off-the-shelf self-supervised 2D descriptors, and most importantly, 2D optical flow. Operationalizing such inputs via photometric, geometric, and feature-metric reconstruction losses enables SUDS to decompose dynamic scenes into the static background, individual objects, and their motions. When combined with our multi-branch table representation, such reconstructions can be scaled to tens of thousands of objects across 1.2 million frames from 1700 videos spanning geospatial footprints of hundreds of kilometers, (to our knowledge) the largest dynamic NeRF built to date. We present qualitative initial results on a variety of tasks enabled by our representations, including novel-view synthesis of dynamic urban scenes, unsupervised 3D instance segmentation, and unsupervised 3D cuboid detection. To compare to prior work, we also evaluate on KITTI and Virtual KITTI 2, surpassing state-of-the-art methods that rely on ground truth 3D bounding box annotations while being $10x$ quicker to train.", + "bbox": [ + 75, + 297, + 473, + 767 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 794, + 209, + 810 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scalable geometric reconstructions of cities have transformed our daily lives, with tools such as Google Maps and Streetview [6] becoming fundamental to how we navigate and interact with our environments. A watershed moment", + "bbox": [ + 76, + 819, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/01964bfb55155065d8997891db71fffc5134533c0f250cca5bdd0e8b4efea864.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 527, + 250, + 846, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7c9ff8eb26f531df2c1bfa43ac89ca88f65e0299b30a60ef1efceea11c7996bd.jpg", + "image_caption": [ + "RGB" + ], + "image_footnote": [], + "bbox": [ + 506, + 431, + 625, + 502 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e096a475028a54e7d67edf7c034c96c15e6e788b828d011d311aed86c329050e.jpg", + "image_caption": [ + "Static" + ], + "image_footnote": [], + "bbox": [ + 638, + 433, + 754, + 502 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/050ba20802a276d20785d4adcca705bf7467a903c0b87c7f2ed390904fcb733e.jpg", + "image_caption": [ + "Dynamic" + ], + "image_footnote": [], + "bbox": [ + 767, + 433, + 885, + 502 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/69aea4796cfb4c00ae9242f1f4952ad7c51876963104409c1826dda1ebca9a78.jpg", + "image_caption": [ + "Depth", + "Figure 1. SUDS. We scale neural reconstructions to city scale by dividing the area into multiple cells and training hash table representations for each. We show our full city-scale reconstruction above and the derived representations below. Unlike prior methods, our approach handles dynamism across multiple videos, disentangling dynamic objects from static background and modeling shadow effects. We use unlabeled inputs to learn scene flow and semantic predictions, enabling category- and object-level scene manipulation." + ], + "image_footnote": [], + "bbox": [ + 508, + 512, + 625, + 580 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e36231bb1bfac332be4ce29955feca105b22f3f106ef4a5547386934dbce25b0.jpg", + "image_caption": [ + "Instances" + ], + "image_footnote": [], + "bbox": [ + 638, + 512, + 754, + 580 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/24d9fbd9484517f6493fd2e78c65609c3fbd82433c4250c2e3c301d1bdb53843.jpg", + "image_caption": [ + "Flow" + ], + "image_footnote": [], + "bbox": [ + 767, + 512, + 885, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in the development of such technology was the ability to scale structure-from-motion (SfM) algorithms to city-scale footprints [4]. Since then, the advent of Neural Radiance Fields (NeRFs) [33] has transformed this domain by allowing for photorealistic interaction with a reconstructed scene via view synthesis.", + "bbox": [ + 496, + 731, + 890, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent works have attempted to scale such representations to neighborhood-scale reconstructions for virtual drive-throughs [47] and photorealistic fly-throughs [52]. However, these maps remain static and frozen in time. This makes capturing bustling human environments—", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done as an intern at Argo AI.", + "bbox": [ + 99, + 887, + 295, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12375", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "complete with moving vehicles, pedestrians, and objects—impossible, limiting the usefulness of the representation.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Challenges. One possible solution is a dynamic NeRF that conditions on time or warps a canonical space with a time-dependent deformation [38]. However, reconstructing dynamic scenes is notoriously challenging because the problem is inherently under-constrained, particularly when input data is constrained to limited viewpoints, as is typical from egocentric video capture [20]. One attractive solution is to scale up reconstructions to many videos, perhaps collected at different days (e.g., by an autonomous vehicle fleet). However, this creates additional challenges in jointly modeling fixed geometry that holds for all time (such as buildings), geometry that is locally static but transient across the videos (such as a parked car), and geometry that is truly dynamic (such as a moving person).", + "bbox": [ + 75, + 119, + 468, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SUDS. In this paper, we propose SUDS: Scalable Urban Dynamic Scenes, a 4D representation that targets both scale and dynamism. Our key insight is twofold; (1) SUDS makes use of a rich suite of informative but freely available input signals, such as LiDAR depth measurements and optical flow. Other dynamic scene representations [27, 37] require supervised inputs such as panoptic segmentation labels or bounding boxes, which are difficult to acquire with high accuracy for our in-the-wild captures. (2) SUDS decomposes the world into 3 components: a static branch that models stationary topography that is consistent across videos, a dynamic branch that handles both transient (e.g., parked cars) and truly dynamic objects (e.g., pedestrians), and an environment map that handles far-field objects and sky. We model each branch using a multi-resolution hash table with scene partitioning, allowing SUDS to scale to an entire city spanning over $100km^2$ .", + "bbox": [ + 75, + 332, + 468, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. We make the following contributions: (1) to our knowledge, we build the first large-scale dynamic NeRF, (2) we introduce a scalable three-branch hash table representation for 4D reconstruction, (3) we present state-of-the-art reconstruction on 3 different datasets. Finally, (4) we showcase a variety of downstream tasks enabled by our representation, including free-viewpoint synthesis, 3D scene flow estimation, and even unsupervised instance segmentation and 3D cuboid detection.", + "bbox": [ + 75, + 589, + 468, + 726 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 739, + 218, + 753 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The original Neural Radiance Fields (NeRF) paper [33] inspired a wide body of follow-up work based on the original approach. Below, we describe a non-exhaustive list of such approaches along axes relevant to our work.", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scale. The original NeRF operated with bounded scenes. $\\mathrm{NeRF}++$ [63] and mip-NeRF 360 [7] use non-linear scene parameterization to model unbounded scenes. However, scaling up the size of the scene with a fixed size MLP leads to blurry details and training instability while the cost of", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "naively increasing the size of the MLP quickly becomes intractable. BungeeNeRF [58] introduced a coarse-to-fine approach that progressively adds more capacity to the network representation. Block-NeRF [47] and Mega-NeRF [52] partition the scene spatially and train separate NeRFs for each partition. To model appearance variation, they incorporate per-image embeddings like NeRF-W [31]. Our approach similarly partitions the scene into sub-NeRFs, making use of depth to improve partition efficiency and scaling over an area 200x larger than Block-NeRF's Alamo Square Dataset. Both of these methods work only on static scenes.", + "bbox": [ + 496, + 90, + 890, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dynamics. Neural 3D Video Synthesis [28] and Spacetime Neural Irradiance Fields [57] add time as an input to handle dynamic scenes. Similar to our work, NSFF [29], NeRFlow [15], and DyNeRF [19] incorporate 2D optical flow input and warping-based regularization losses to enforce plausible transitions between observed frames. Multiple methods [38-40, 50] instead disentangle scenes into a canonical template and per-frame deformation field. BANMo [60] further incorporates deformable shape models and canonical embeddings to train articulated 3D models from multiple videos. These methods focus on single-object scenes, and all but [28] and [60] use single video sequences.", + "bbox": [ + 496, + 258, + 890, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While many of the previous works use segmentation data to factorize dynamic from static objects, $\\mathrm{D}^2\\mathrm{NeRF}$ [56] does this automatically through regularization and explicitly handling shadows. Neural Groundplans [44] uses synthetic data to do this decomposition from a single image. We borrow some of these ideas and scale beyond synthetic and indoor scenes.", + "bbox": [ + 496, + 441, + 890, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object-centric approaches. Several approaches [24,36, 37, 59, 61, 62] represent scenes as the composition of per-object NeRF models and a background model. NSG [37] is most similar to us as it also targets automotive data but cannot handle ego-motion as our approach can. None of these methods target multi-video representations and are fundamentally constrained by the memory required to represent each object, with NSG needing over 1TB of memory to represent a 30 second video in our experience.", + "bbox": [ + 496, + 550, + 890, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantics. Follow-up works have explored additional semantic outputs in addition to predicting color. Semantic-NeRF [65] adds an extra head to NeRF that predicts extra semantic category logits for any 3D position. Panoptic-NeRF [16] and Panoptic Neural Fields [27] extend this to produce panoptic segmentations and the latter uses a similar bounding-box based object and background decomposition as NSG. NeSF [53] generalizes the notion of a semantic field to unobserved scenes. As these methods are highly reliant on accurate annotations which are difficult to reliably obtain in the wild at our scale, we instead use a similar approach to recent works [26, 51] that distill the outputs of 2D self-supervised feature descriptors into 3D radiance fields to enable semantic understanding without the use of human", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12376", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2115cc20468636e84ea20b012897f751195182a11986bf04305e67e82931b141.jpg", + "image_caption": [ + "(a) Voxel Lookup" + ], + "image_footnote": [], + "bbox": [ + 174, + 85, + 356, + 223 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/17c096f49089c755a2198c312ca2b0a397ea00c1d31ed00bdac124fbdef2630b.jpg", + "image_caption": [ + "(b) Indexing", + "Figure 2. Model Architecture. (a) For a given input coordinate, we find the surrounding voxels at $L$ resolution levels for both the static and dynamic branches (far-field branch omitted for clarity). (b) We assign indices to their corners by hashing based on position in the static branch and position, time, and video id in the dynamic branch. We look up the feature vectors corresponding to the corners and interpolate according to the relative position of the input coordinate within the voxel. (c) We concatenate the result of each level, along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch color, density, and feature logits along with scene flow and the shadow ratio. (d) We blend scolor, opacity, and feature logits as the weighted sum of the branches." + ], + "image_footnote": [ + "$(\\mathbf{c},\\sigma ,\\phi ,s_{\\mathbf{t} - 1},s_{\\mathbf{t} + 1})$", + "(d) Output Blending" + ], + "bbox": [ + 383, + 85, + 669, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "labels and extend them to larger dynamic settings.", + "bbox": [ + 76, + 347, + 406, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fast training. The original NeRF took 1-2 days to train. Plenoxels [43] and DVGO [46] directly optimize a voxel representation instead of an MLP to train in minutes or even seconds. TensoRF [11] stores its representation as the outer product of low-rank tensors, reducing memory usage. Instant-NGP [35] takes this further by encoding features in a multi-resolution hash table, allowing training and rendering to happen in real-time. We use these tables as the base block of our three-branch representation and use our own hashing method to support dynamics across multiple videos.", + "bbox": [ + 75, + 364, + 468, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Depth. Depth provides a valuable supervisory signal for learning high-quality geometry. DS-NeRF [14] and Dense Depth Priors [42] incorporate noisy point clouds obtained by structure from motion (SfM) in the loss function during optimization. Urban Radiance Fields [41] supervises with collected LiDAR data. We also use LiDAR but demonstrate results on dynamic environments.", + "bbox": [ + 75, + 518, + 470, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 76, + 648, + 184, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Inputs", + "text_level": 1, + "bbox": [ + 76, + 676, + 163, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to learn a global representation that facilitates free-viewpoint rendering, semantic decomposition, and 3D scene flow at arbitrary poses and time steps. Our method takes as input ordered RGB images from $N$ videos (taken at different days with diverse weather and lighting conditions) and their associated camera poses. Crucially, we make use of additional data as \"free\" sources of supervision given contemporary sensor rigs and feature descriptors. Specifically, we use (1) aligned sparse LiDAR depth measurements, (2) 2D self-supervised pixel (DINO [10]) descriptors to enable semantic manipulation, and (3) 2D optical flow predictions to model scene dynamics. All model inputs are generated without any human labeling or intervention.", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Representation", + "text_level": 1, + "bbox": [ + 500, + 345, + 653, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminaries. We build upon NeRF [33], which represents a scene within a continuous volumetric radiance field that captures both geometry and view-dependent appearance. It encodes the scene within the weights of a multilayer perceptron (MLP). At render time, NeRF projects a camera ray $\\mathbf{r}$ for each image pixel and samples along the ray, querying the MLP at sample position $\\mathbf{x}_i$ and ray viewing direction $\\mathbf{d}$ to obtain opacity and color values $\\sigma_i$ and $\\mathbf{c}_i$ . It then composites a color prediction $\\hat{C}(\\mathbf{r})$ for the ray using numerical quadrature $\\sum_{i=0}^{N-1} T_i (1 - \\exp(-\\sigma_i \\delta_i)) \\mathbf{c}_i$ , where $T_i = \\exp(-\\sum_{j=0}^{i-1} \\sigma_j \\delta_j)$ and $\\delta_i$ is the distance between samples. The training process optimizes the model by sampling batches $R$ of image pixels and minimizing the loss function $\\sum_{\\mathbf{r} \\in \\mathcal{R}} \\|C(\\mathbf{r}) - \\hat{C}(\\mathbf{r})\\|^2$ . NeRF samples rays through a two-stage hierarchical sampling process and uses frequency encoding to capture high-frequency details. We refer the reader to [33] for more details.", + "bbox": [ + 496, + 371, + 890, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene composition. To model large-scale dynamic environments, SUDS factorizes the scene into three branches: (a) a static branch containing non-moving topography consistent across videos, (b) a dynamic branch to disentangle video-specific objects [19,29,56], moving or otherwise, and (c) a far-field environment map to represent far-away objects and the sky, which we found important to separately model in large-scale urban scenes [41, 52, 63].", + "bbox": [ + 496, + 638, + 890, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, conventional NeRF training with MLPs is computationally prohibitive at our target scales. Inspired by Instant-NGP [35], we implement each branch using multiresolution hash tables of $F$ -dimensional feature vectors followed by a small MLP, along with our own hash functions to index across videos.", + "bbox": [ + 496, + 761, + 890, + 851 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hash tables (Fig. 2). For a given input coordinate $(\\mathbf{x}, \\mathbf{d}, \\mathbf{t}, \\mathbf{v}\\mathbf{id})$ denoting the position $\\mathbf{x} \\in \\mathbb{R}^3$ , viewing direction $\\mathbf{d} \\in \\mathbb{R}^3$ , frame index $F \\in \\{1, \\dots, T\\}$ , and video id", + "bbox": [ + 498, + 854, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12377", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\mathbf{vid} \\in \\{1, \\dots, N\\}$ , we find the surrounding voxels in each table at $l \\in L$ resolution levels, doubling the resolution between levels, which we denote as $\\mathbf{v}_{l,s}$ , $\\mathbf{v}_{l,d}$ , $\\mathbf{v}_{l,e}$ for the static, dynamic, and far-field. The static branch makes use of 3D spatial voxels $\\mathbf{v}_{l,s}$ , while the dynamic branch makes use of 4D spacetime voxels $\\mathbf{v}_{l,d}$ . Finally, the far-field branch makes use of 3D voxels $\\mathbf{v}_{l,e}$ (implemented via normalized 3D direction vectors) that index an environment map. Similar to Instant-NGP [35], rather than storing features at voxel corners, we compute hash indices $\\mathbf{i}_{l,s}$ (or $\\mathbf{i}_{l,d}$ or $\\mathbf{i}_{l,e}$ ) for each corner with the following hash functions:", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {i} _ {l, s} = \\text {s t a t i c} \\operatorname {h a s h} \\left(\\operatorname {s p a c e} \\left(\\mathbf {v} _ {l, s}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 265, + 468, + 281 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {i} _ {l, d} = \\text {d y n a m i c} \\text {h a s h} \\left(\\operatorname {s p a c e} \\left(\\mathbf {v} _ {l, d}\\right), \\operatorname {t i m e} \\left(\\mathbf {v} _ {l, d}\\right), \\mathbf {v i d}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 284, + 468, + 300 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {i} _ {l, e} = \\operatorname {e n v} \\text {h a s h} (d i r (\\mathbf {v} _ {l, e}), \\mathbf {v i d}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 303, + 468, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We linearly interpolate features up to the nearest voxel vertices (but now relying on quadlinear interpolation for the dynamic 4D branch) and rely on gradient averaging to handle hash collisions. Finally, to model the fact that different videos likely contain distinct moving objects and illumination conditions, we add vid as an auxiliary input to the hash, but do not use it for interpolation (since averaging across distinct movers is unnatural). From this perspective, we leverage hashing to effectively index separate interpolating functions for each video, without a linear growth in memory with the number of videos. We concatenate the result of each level into a feature vector $f \\in \\mathbb{R}^{LF}$ , along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch outputs.", + "bbox": [ + 75, + 327, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Static branch. We generate RGB images by combining the outputs of our three branches. The static branch maps the feature vector obtained from the hash table into a view-dependent color $\\mathbf{c}_s$ and a view-independent density $\\sigma_s$ . To model lighting variations which could be dramatic across videos but smooth within a video, we condition on a latent embedding computed as a product of a video-specific matrix $A_{vid}$ and a fourier-encoded time index $\\mathcal{F}(t)$ (as in [60]):", + "bbox": [ + 75, + 537, + 468, + 660 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {s} (\\mathbf {x}) \\in \\mathbb {R} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 186, + 667, + 468, + 683 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {s} (\\mathbf {x}, \\mathbf {d}, A _ {v i d} \\mathcal {F} (t)) \\in \\mathbb {R} ^ {3}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 686, + 468, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dynamic branch. While the static branch assumes the density $\\sigma_{s}$ is static, the dynamic branch allows both the density $\\sigma_{d}$ and color $\\mathbf{c}_d$ to depend on time (and video). We therefore omit the latent code when computing the dynamic radiance. Because we find shadows to play a crucial role in the appearance of urban scenes (Fig. 3), we explicitly model a shadow field of scalar values $\\rho_{d} \\in [0,1]$ , used to scale down the static color $\\mathbf{c}_{s}$ (as done in [56]):", + "bbox": [ + 75, + 712, + 468, + 833 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in \\mathbb {R} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 840, + 468, + 856 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\rho_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in [ 0, 1 ] \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 859, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) \\in \\mathbb {R} ^ {3} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 878, + 468, + 896 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2258390509dfbdc42423a3445879c49961bd280d1cdd2e7d80d872fa4c94b01c.jpg", + "image_caption": [ + "Full RGB" + ], + "image_footnote": [], + "bbox": [ + 563, + 85, + 692, + 135 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/475d43b7394f33e0d40e007f66171a1c5d8634962047e770bc0912bc6be605e8.jpg", + "image_caption": [ + "Depth" + ], + "image_footnote": [], + "bbox": [ + 702, + 85, + 828, + 133 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/db6b807337ec389d8003b67b92b633a41e3ea1db5215e74ec8dc1fbbba4d6b68.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 565, + 145, + 691, + 193 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/4c6c00111c9aa75e26bb84c8ce22bb8f1dec8d5fe5c57cce0043822917572831.jpg", + "image_caption": [ + "Shadow Intensity" + ], + "image_footnote": [], + "bbox": [ + 702, + 145, + 826, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fb202257371af8fc8294122fadf3452bcf1de481d6d24e581c50e417a9ea20c7.jpg", + "image_caption": [ + "RGB (Without Shadow)", + "Dynamic RGB" + ], + "image_footnote": [], + "bbox": [ + 565, + 203, + 691, + 252 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3a43ff952cea83ff705997559e5ff404af82dffcd77d72e1c78bf42290172782.jpg", + "image_caption": [ + "Static RGB" + ], + "image_footnote": [], + "bbox": [ + 702, + 203, + 826, + 252 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e7620a759b5fade0011f5074b1f5ead4e681e0bdc3f309944a68f4772554f287.jpg", + "image_caption": [ + "(a) Shadow Field", + "Full RGB" + ], + "image_footnote": [], + "bbox": [ + 563, + 284, + 689, + 334 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0da147ef71180f36d145b5a271a1d7e55c892e3343fdde71f219a722f04fe0c7.jpg", + "image_caption": [ + "Depth" + ], + "image_footnote": [], + "bbox": [ + 699, + 284, + 826, + 335 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/611b40226f8de1f65d58715f355d48c62b15dec8422f74940f62cf57ffd83b9f.jpg", + "image_caption": [ + "Dynamic RGB", + "(b) No Shadow Field", + "Figure 3. Shadows. We learn an explicit shadow field (a) as a pointwise reduction on static color, enabling better depth reconstruction and static/dynamic factorization than without (b)." + ], + "image_footnote": [], + "bbox": [ + 563, + 343, + 689, + 393 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d7f2ca7ecfd2e798a388d4028236510f1e9cba628074d24f3c54206592dd608e.jpg", + "image_caption": [ + "Static RGB" + ], + "image_footnote": [], + "bbox": [ + 699, + 343, + 825, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Far-field branch. Because the sky requires reasoning about far-field radiance and because it can change dramatically across videos, we model far-field radiance with an environment map $\\mathbf{c}_e(\\mathbf{d},\\mathbf{vid})\\in \\mathbb{R}^3$ that depends on viewing direction d [22,41] and a video id vid.", + "bbox": [ + 496, + 481, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Rendering. We derive a single density and radiance value for any position by computing the weighted sum of the static and dynamic components, combined with the pointwise shadow reduction:", + "bbox": [ + 496, + 556, + 890, + 617 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\sigma (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) = \\sigma_ {s} (\\mathbf {x}) + \\sigma_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) (9) \\\\ \\mathbf {c} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) = \\frac {\\sigma_ {s}}{\\sigma} (1 - \\rho_ {d}) \\mathbf {c} _ {s} (\\mathbf {x}, \\mathbf {d}, A _ {v i d} \\mathcal {F} (t)) \\\\ + \\frac {\\sigma_ {d}}{\\sigma} \\mathbf {c} _ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) (10) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 631, + 890, + 704 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We then calculate the color $\\hat{C}$ for a camera ray $\\mathbf{r}$ with direction $\\mathbf{d}$ at a given frame $\\mathbf{t}$ and video vid by accumulating the transmittance along sampled points $\\mathbf{r}(t)$ along the ray, forcing the ray to intersect the far-field environment map if it does not hit geometry within the foreground:", + "bbox": [ + 496, + 718, + 890, + 795 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {C} (\\mathbf {r}, \\mathbf {t}, \\mathbf {v i d}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (\\mathbf {r} (t), \\mathbf {t}, \\mathbf {v i d}) \\mathbf {c} (\\mathbf {r} (t), \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) d t \\\\ + T (+ \\infty) \\mathbf {c} _ {e} (\\mathbf {d}, \\mathbf {v i d}), \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 806, + 890, + 859 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} T (t) = \\exp \\left(- \\int_ {0} ^ {t} \\sigma (\\mathbf {r} (s), \\mathbf {t}, \\mathbf {v i d}) d s\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 863, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12378", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature distillation. We build semantic awareness into SUDS to enable the open-world tasks described in Sec. 4.2. Similar to recent work [26, 51], we distill the outputs of a self-supervised 2D feature extractor, namely DINO [10], as a teacher model into our network. For a feature extractor that transforms an image into a dense $\\mathbb{R}^{H\\times W\\times C}$ feature grid, we add a $C$ -dimensional output head to each of our branches:", + "bbox": [ + 76, + 90, + 472, + 210 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {s} (\\mathbf {x}) \\in \\mathbb {R} ^ {C} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 215, + 467, + 234 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in \\mathbb {R} ^ {C} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 237, + 467, + 253 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {e} (\\mathbf {d}, \\mathbf {v i d}) \\in \\mathbb {R} ^ {C}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 257, + 467, + 275 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which are combined into a single value $\\Phi$ at any 3D location and rendered into $\\hat{F} (\\mathbf{r})$ per camera ray, following the equations for color (10, 11).", + "bbox": [ + 76, + 281, + 467, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Scene flow. We train our model to predict 3D scene flow and model scene dynamics. Inspired by previous work [15, 19, 29], we augment our dynamic branch to predict forward and backward 3D scene flow vectors $s_{t' \\in [-1,1]}(\\mathbf{x},\\mathbf{t},\\mathbf{v}\\mathbf{i}\\mathbf{d}) \\in \\mathbb{R}^3$ . We make use of these vectors to enforce consistency between observed time steps through multiple loss terms (Sec. 3.3), which we find crucial to generating plausible renderings at novel time steps (Table 4).", + "bbox": [ + 76, + 327, + 467, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spatial partitioning. We scale our representation to arbitrarily large environments by decomposing the scene into individually trained models [47, 52], each with its own static, dynamic, and far-field branch. Intuitively, the reconstruction for neighborhood X can be done largely independently of the reconstruction in neighborhood Y, provided one can assign the relevant input data to each reconstruction. To do so, we follow the approach of Mega-NeRF [52] and split the scene into $K$ spatial cells with centroids $k \\in \\mathbb{R}^3$ . Crucially, we generate separate training datasets for each spatial cell by making use of visibility reasoning [17]. Mega-NeRF includes only those datapoints whose associated camera rays intersect the spatial cell. However, this may still include datapoints that are not visible due to an intervening occluder (e.g., a particular camera in neighborhood X can be pointed at neighborhood Y, but may not see anything there due to occluding buildings). To remedy this, we make use of depth measurements to prune irrelevant pixel rays that do not terminate within the spatial cell of interest (making use of nearest-neighbor interpolation to impute depth for pixels without a LiDAR depth measurement). This further reduces the size of each trainset by $2x$ relative to Mega-NeRF. Finally, given such separate reconstructions, one can still produce a globally consistent rendering by querying the appropriate spatial cell when sampling points along new-view rays (as in [52]).", + "bbox": [ + 76, + 448, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Optimization", + "text_level": 1, + "bbox": [ + 76, + 847, + 215, + 862 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We jointly optimize all three of our model branches along with the per-video weight matrices $A_{vid}$ by sampling", + "bbox": [ + 76, + 869, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2a7024a7e00e691345767af43c640f13f5f96f26d3de4fc9fe9f974fda9497a1.jpg", + "image_caption": [ + "RGB" + ], + "image_footnote": [], + "bbox": [ + 542, + 90, + 687, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3fbaeba92db00a5b464fa4f117a99206a1f6cf22aa6046de7f7da0103a2556ec.jpg", + "image_caption": [ + "Features" + ], + "image_footnote": [], + "bbox": [ + 697, + 90, + 844, + 152 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/224bc2323b4e9664973d63ce94ffb01bd5ab278fc1218290304e54f27e8d7e7e.jpg", + "image_caption": [ + "Forward Flow (Input)" + ], + "image_footnote": [], + "bbox": [ + 542, + 160, + 687, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f05b60bca539e61241d3c3bb1a799f8cbad0037f3e49a687021e742a93821937.jpg", + "image_caption": [ + "Backward Flow (Input)" + ], + "image_footnote": [], + "bbox": [ + 697, + 160, + 844, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8e171a5c0058fb94b641a2ad14d709a069f50bee4ff955cb99b9ff835e1b888b.jpg", + "image_caption": [ + "Forward Flow (Predicted)", + "Figure 4. Scene Flow. We minimize the photometric and feature-metric loss of warped renderings relative to ground truth inputs (top). We use 2D optical flow from off-the-shelf estimators or sparse correspondences computed directly from 2D DINO features [5] (middle) to supervise our flow predictions (bottom)." + ], + "image_footnote": [], + "bbox": [ + 542, + 228, + 687, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5ec8d986193e1cd8856f7c27b9d34d60bb1f4167023a96529d7368d2a1607d59.jpg", + "image_caption": [ + "Backward Flow (Predicted)" + ], + "image_footnote": [], + "bbox": [ + 697, + 228, + 844, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "random batches of rays across our $N$ input videos and minimizing the following loss:", + "bbox": [ + 498, + 383, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\underbrace {\\left(\\mathcal {L} _ {c} + \\lambda_ {f} \\mathcal {L} _ {f} + \\lambda_ {d} \\mathcal {L} _ {d} + \\lambda_ {o} \\mathcal {L} _ {o}\\right)} _ {\\text {r e c o n s t r u c t i o n l o s s e s}} + \\underbrace {\\left(\\mathcal {L} _ {c} ^ {w} + \\lambda_ {f} \\mathcal {L} _ {f} ^ {w}\\right)} _ {\\text {w a r p i n g l o s s e s}}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 421, + 864, + 467 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\lambda_ {f l o} \\underbrace {\\left(\\mathcal {L} _ {c y c} + \\mathcal {L} _ {s m} + \\mathcal {L} _ {s l o}\\right)} _ {\\text {f l o w l o s s e s}} + \\underbrace {\\left(\\lambda_ {e} \\mathcal {L} _ {e} + \\lambda_ {d} \\mathcal {L} _ {d}\\right)} _ {\\text {s t a t i c - d y n a m i c f a c t o r i z a t i o n}} + \\lambda_ {\\rho} \\mathcal {L} _ {\\rho} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 469, + 895, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reconstruction losses. We minimize the L2 photometric loss $\\mathcal{L}_c(\\mathbf{r}) = \\left\\| C(\\mathbf{r}) - \\hat{C} (\\mathbf{r})\\right\\| ^2$ as in the original NeRF equation [33]. We similarly minimize the L1 difference $\\mathcal{L}_f(\\mathbf{r}) = \\left\\| F(\\mathbf{r}) - \\hat{F} (\\mathbf{r})\\right\\| _1$ between the feature outputs of the teacher model and that of our network.", + "bbox": [ + 500, + 529, + 890, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To make use of our depth measurements, we project the LiDAR sweeps onto the camera plane and compare the expected depth $\\hat{D}(r)$ with the measurement $D(\\mathbf{r})$ [14, 41]:", + "bbox": [ + 498, + 607, + 890, + 652 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d} (\\mathbf {r}) = \\left\\| D (\\mathbf {r}) - \\hat {D} (\\mathbf {r}) \\right\\| ^ {2} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 662, + 888, + 683 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\hat {D} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (s) \\sigma (\\mathbf {r} (s)) d s \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 685, + 888, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Flow. We supervise our 3D scene flow predictions based on 2D optical flow (Sec. 4.1). We generate a 2D displacement vector for each camera ray by first predicting its position in 3D space as the weighted sum of the scene flow neighbors along the ray:", + "bbox": [ + 498, + 727, + 890, + 803 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {X} _ {t ^ {\\prime}} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (r (t)) (r (t) + s _ {t ^ {\\prime}} (\\mathbf {r} (t))) d t \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 811, + 890, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which we then \"render\" into 2D using the camera matrix of the neighboring frame index. We minimize its distance from the observed optical flow via $\\mathcal{L}_o(\\mathbf{r}) =$", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12379", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\sum_{t' \\in [-1,1]} \\left\\| X(\\mathbf{o}) - \\hat{X}_{t'}(\\mathbf{r}) \\right\\|_1$ . We anneal $\\lambda_o$ over time as these estimates are noisy.", + "bbox": [ + 76, + 89, + 468, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3D warping. The above loss ensures that rendered 3D flow will be consistent with the observed 2D flow. We also found it useful to enforce 3D color (and feature) constancy; i.e., colors remain constant even when moving. To do so, we use the predicted forward and backward 3D flow $s_{\\mathbf{t} + 1}$ and $s_{\\mathbf{t} - 1}$ to advect each sample along the ray into the next/previous frame:", + "bbox": [ + 76, + 121, + 468, + 227 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}\\right) \\in \\mathbb {R} \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 238, + 467, + 255 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}, \\mathbf {d}\\right) \\in \\mathbb {R} ^ {3} \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 168, + 258, + 467, + 276 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\Phi_ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}\\right) \\in \\mathbb {R} ^ {C} \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 279, + 467, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The warped radiance $\\mathbf{c}^w$ and density $\\sigma^w$ are rendered into warped color $\\hat{C}^w (\\mathbf{r})$ and feature $\\hat{F}^{w}(\\mathbf{r})$ (10, 11). We add a loss to ensure that the warped color (and feature) match the ground-truth input for the current frame, similar to [19, 29]. As in NSFF [29], we found it important to downweight this loss in ambiguous regions that may contain occlusions. However, instead of learning explicit occlusion weights, we take inspiration from Kwea's method [1] and use the difference between the dynamic geometry and the warped dynamic geometry to downweight the loss:", + "bbox": [ + 76, + 308, + 468, + 460 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nw _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) = \\left| \\frac {\\sigma_ {d}}{\\sigma} - \\frac {\\sigma_ {t ^ {\\prime}} ^ {w}}{\\sigma} \\right| \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 469, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {W} _ {t ^ {\\prime}} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (r (t)) w _ {t ^ {\\prime}} (r (t)) d t \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 506, + 468, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "resulting in the following warping loss terms:", + "bbox": [ + 96, + 549, + 397, + 565 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c} ^ {w} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\left(1 - W _ {t ^ {\\prime}}\\right) (\\mathbf {r})) \\| C (\\mathbf {r}) - \\hat {C} _ {t ^ {\\prime}} ^ {w} (\\mathbf {r}) \\| ^ {2} \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 575, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f} ^ {w} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\left(1 - W _ {t ^ {\\prime}}\\right) (\\mathbf {r}) \\| F (\\mathbf {r}) - \\hat {F} _ {t ^ {\\prime}} ^ {w} (\\mathbf {r}) \\| _ {1} \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 613, + 468, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flow regularization. As in prior work [19, 29] we use a 3D scene flow cycle term to encourage consistency between forward and backward scene flow predictions, downweighting the loss in areas ambiguous due to occlusions:", + "bbox": [ + 76, + 657, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c y c}} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\sum_ {\\mathbf {x}} w _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}) \\| s _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}) + s _ {\\mathbf {t}} (\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} - t ^ {\\prime}) \\| _ {1}, \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 724, + 468, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with $\\mathbf{v}\\mathbf{id}$ omitted for brevity. We also encourage spatial and temporal smoothness through $\\mathcal{L}_{sm}(\\mathbf{r})$ as described in Sec. C. We finally regularize the magnitude of predicted scene flow vectors to encourage the scene to be static through $\\mathcal{L}_{slo}(\\mathbf{r}) = \\sum_{t' \\in [\\mathbf{t} - 1, \\mathbf{t} + 1]} \\sum_{\\mathbf{x}} \\left\\| s_{t'}(\\mathbf{x}, \\mathbf{t}) \\right\\|_1$ .", + "bbox": [ + 76, + 763, + 468, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Static-dynamic factorization. As physically plausible solutions should have any point in space occupied by either a static or dynamic object, we encourage the spatial ratio of static vs dynamic density to either be 0 or 1 through a", + "bbox": [ + 75, + 840, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "skewed binary entropy loss that favors static explanations of the scene [56]:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} H \\left(\\frac {\\sigma_ {d} (\\mathbf {r} (t))}{\\sigma_ {s} (\\mathbf {r} (t)) + \\sigma_ {d} (\\mathbf {r} (t))} ^ {k}\\right) d t \\tag {28}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 131, + 890, + 172 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $H(x) = -(x\\cdot \\log (x) + (1 - x)\\cdot \\log (1 - x))$", + "bbox": [ + 517, + 174, + 874, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and with $k$ set to 1.75, and further penalize the maximum dynamic ratio $\\mathcal{L}_d(\\mathbf{r}) = \\max (\\frac{\\sigma_d(\\mathbf{r}(t))}{\\sigma_e + \\sigma_d})$ along each ray.", + "bbox": [ + 498, + 203, + 890, + 236 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Shadow loss.** We penalize the squared magnitude of the shadow ratio $\\mathcal{L}_{\\rho}(\\mathbf{r}) = \\int_0^{+\\infty}\\rho_d(\\mathbf{r}(t))^2 dt$ along each ray to prevent it from over-explaining dark regions [56].", + "bbox": [ + 498, + 236, + 890, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 295, + 630, + 313 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We demonstrate SUDS's city-scale reconstruction capabilities by presenting quantitative results against baseline methods (Table 1). We also show initial qualitative results for a variety of downstream tasks (Sec. 4.2). Even though we focus on reconstructing dynamic scenes at city scale, to facilitate comparisons with prior work, we also show results on small-scale but highly-benchmarked datasets such as KITTI and Virtual KITTI 2 (Sec. 4.3). We evaluate the various components of our method in Sec. 4.4.", + "bbox": [ + 498, + 321, + 890, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 465, + 689, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2D feature extraction. We use Amir et al's feature extractor implementation [5] based on the dino_vits8 model. We downsample our images to fit into GPU memory and then upsample with nearest neighbor interpolation. We L2-normalize the features at the 11th layer of the model and reduce the dimensionality to 64 through incremental PCA [3].", + "bbox": [ + 498, + 489, + 890, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Flow supervision. We explored using an estimator trained on synthetic data [49] in addition to directly computing 2D correspondences from DINO itself [5]. Although the correspondences are sparse (less than $5\\%$ of pixels) and expensive to compute, we found its estimates more robust and use it for our experiments unless otherwise stated.", + "bbox": [ + 498, + 580, + 890, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training. We train SUDS for 250,000 iterations with 4098 rays per batch and use a proposal sampling strategy similar to Mip-NeRF 360 [7] (Sec. B). We use Adam [25] with a learning rate of $5 \\times 10^{-3}$ decaying to $5 \\times 10^{-4}$ .", + "bbox": [ + 498, + 670, + 890, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. We report quantitative results based on PSNR, SSIM [54], and the AlexNet implementation of LPIPS [64].", + "bbox": [ + 498, + 732, + 890, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. City-Scale Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 771, + 735, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "City-1M dataset. We evaluate SUDS's large-scale reconstruction abilities on our collection of 1.28 million images across 1700 videos gathered across a $105~km^2$ urban area using a vehicle-mounted platform with seven ring cameras and two LiDAR sensors. Due to the scale, we supervise optical flow with an off-the-shelf estimator trained on synthetic data [49] instead of DINO for efficiency.", + "bbox": [ + 498, + 794, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12380", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8df0dfe6be2997790f58468a3cbc7dca357df744d6b6f40c855c14eec0cc74b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 95, + 215, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cc097b2c351b75db80bb65847c1a19c22503807e27c109db5273d4e1c3464d71.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 165, + 215, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cf52da2a5837cbc8fd7d6e29055021810d33e9b096cbc5493a776570f6d822b5.jpg", + "image_caption": [ + "RGB" + ], + "image_footnote": [], + "bbox": [ + 86, + 236, + 215, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4114256e9f2398b0fda1a7fed17944d07f650c69af8aa7f416eda17d530e4b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 220, + 95, + 348, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8568a1aa25c7b96d0d4e56eb88817e0aefd19e56f55db072fba9df81aff87ff1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 220, + 165, + 348, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ff6fee8bd16e93bbb4fbba62d7fd957f5e53afc6b20a08b62d4752aaa2a0f66.jpg", + "image_caption": [ + "Static" + ], + "image_footnote": [], + "bbox": [ + 220, + 236, + 348, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d90dc44c6f5838d15b146f1522dc5bba9665affb09f9878f527337905ce78ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 95, + 480, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9e7bfd186422440fe04d17730d7fe41bb91807b3a204f7804c84aec4fcc3968a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 165, + 480, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ed24d910ecc1357bc4b8fb5e13f0bfbbdfe601da8682b731880a648a960d0015.jpg", + "image_caption": [ + "Dynamic", + "Figure 5. City-1M. We demonstrate SUDS's capabilities on multiple downstream tasks, including instance segmentation and 3D bounding box estimation without any labeled data (by just making use of geometric clustering). In the last column, we show category-level semantic classification by matching 3D (DINO) descriptors to a held-out video annotated with semantic labels. Please see text for more details." + ], + "image_footnote": [], + "bbox": [ + 354, + 236, + 480, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ee9d07fa603076c4320d61ae3c7d1ac7f33c4fd779559a1fa9412d04bb5ba5c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 95, + 614, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5670a025b21c14459b75317208777498cdc140c4c4884d0daaa21e4a65de7a5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 165, + 614, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ecc1c61c9e302d67e10f224d0685ca209eb628810487f5852fdbebb8eeaa9572.jpg", + "image_caption": [ + "Instances" + ], + "image_footnote": [], + "bbox": [ + 488, + 236, + 614, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d7bd02112856e72e63deedff42e729eab707433be574a97e1a3cb69358d329a6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 95, + 750, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c248dd79fc597f30bdbd0c1d569149da36933f3204d118543e907ef60b793c14.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 165, + 750, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ff4ed3d63c0c89d293e192a2aae874af8f2cf033f28b1f7bc18b5099918e7ab.jpg", + "image_caption": [ + "Bounding Boxes" + ], + "image_footnote": [], + "bbox": [ + 620, + 236, + 750, + 304 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f2bed7aa3cba05c02d3ab1d7a7eb6e8a239ee32a15a173ae0c8ea29b37eb66e5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 95, + 882, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d5646887a9fbed2c23897221952a2eb3623aa5aede312f2bacd97e4b73eff1b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 165, + 882, + 233 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e5cac30fe02a77106b4c188c83c7f4206067720a017a95ce1a4a6a11d603b85.jpg", + "image_caption": [ + "Categories" + ], + "image_footnote": [], + "bbox": [ + 754, + 236, + 882, + 304 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/361df755f210b5ac7e727eb74ff36c92f186272a445f3f7d5b786ac085173ada.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Mega-NeRF [52]Mega-NeRF-TMega-NeRF-ASUDS
PSNR ↑16.4216.4616.7021.67
SSIM ↑0.4930.4930.4930.562
LPIPS ↓0.8790.8770.8500.554
", + "bbox": [ + 84, + 375, + 467, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. City-scale view synthesis on City-1M. SUDS outperforms all baselines by a wide margin.", + "bbox": [ + 76, + 448, + 468, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We compare SUDS to the official Mega-NeRF [52] implementation alongside two variants: Mega-NeRF-T which directly adds time as an input parameter to compute density and radiance, and Mega-NeRF-A which instead uses the latent embedding $A_{\\text{vid}} \\mathcal{F}(t)$ used by SUDS.", + "bbox": [ + 75, + 489, + 468, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. We train both SUDS and the baselines using 48 cells and summarize our results in Table 1. SUDS outperforms all Mega-NeRF variants by a large margin. We provide qualitative results on view synthesis, static/dynamic factorization, unsupervised 3D instance segmentation and unsupervised 3D cuboid detection in Fig. 5. We present additional qualitative tracking results in Fig. 7.", + "bbox": [ + 75, + 566, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Instance segmentation. We derive the instance count as in prior work [44] by sampling dynamic density values $\\sigma_{d}$ , projecting those above a given threshold onto a discretized ground plane before applying connected component labeling. We apply k-means to obtain 3D centroids and volume render instance predictions as for semantic segmentation.", + "bbox": [ + 75, + 672, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3D cuboid detection. After computing point-wise instance assignments in 3D, we derive oriented bounding boxes based on the PCA of the convex hull of points belonging to each instance [2].", + "bbox": [ + 75, + 763, + 468, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Semantic segmentation. Note the above tasks of instance segmentation and 3D cuboid detection do not require any additional labels as they make use of geometric clustering. We now show that the representation learned by SUDS can also enable downstream semantic tasks, by making use", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of a small number of 2D segmentation labels provided on a held-out video sequence. We compute the average 2D DINO descriptor for each semantic class from the held out frames and derive 3D semantic labels for all reconstructions by matching each 3D descriptor to the closest class centroid. This allows to produce 3D semantic label fields that can then be rendered in 2D as shown in Fig. 5.", + "bbox": [ + 496, + 378, + 890, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. KITTI Benchmarks", + "text_level": 1, + "bbox": [ + 500, + 496, + 689, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. We compare SUDS to SRN [45], the original NeRF implementation [33], a variant of NeRF taking time as an additional input, NSG [37], and PNF [27]. Both NSG and PNF are trained and evaluated using ground truth object bounding box and category-level annotations.", + "bbox": [ + 496, + 521, + 890, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image reconstruction. We compare SUDS's reconstruction capabilities using the same KITTI [21] subsequences and experimental setup as prior work [27, 37]. We present results in Table 3. As PNF's implementation is not publicly available, we rely on their reported numbers. SUDS surpasses the state-of-the-art in PSNR and SSIM.", + "bbox": [ + 496, + 598, + 890, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Novel view synthesis. We demonstrate SUDS's capabilities to generate plausible renderings at time steps unseen during training. As NSG does not handle scenes with ego-motion, we use subsequences of KITTI and Virtual KITTI 2 [18] with little camera movement. We evaluate the methods using different train/test splits, holding out every 4th time step, every other time step, and finally training with only one in every four time steps. We summarize our findings in Table 2 along with qualitative results in Fig. 6. SUDS achieves the best results across all splits and metrics. Both NeRF variants fail to properly represent the scene, especially in dynamic areas. Although we provide NSG with the ground truth object poses at render time, it fails to learn a clean decomposition between objects and the background,", + "bbox": [ + 496, + 689, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12381", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0b0811b0fd3a88fd6ae696e9e2375759b483a831b470df0627dd610e113644ac.jpg", + "image_caption": [ + "Figure 6. KITTI and VKITTI2 view synthesis. Prior work fails to represent the scene and NSG [37] renders ghosting artifacts near areas of movement. Our method forecasts plausible trajectories and generates higher-quality renderings." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 256, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a77d34d1e624258ccc1650cdd21fc7d3e134f9ff28735add97c20dd6195642e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 258, + 90, + 411, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d26d7c683129e2ca788e984cc4fc6393fef78f00cdde419d63492ade41568b2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 90, + 570, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0a40966a327c4d69405391ca932120299b73bb94bedd8ce014fc86c6289e769e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 571, + 90, + 727, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a4a6b3bcd32535ca0df79e5333a11e9e4eed6da9e5a81a84c09985b3158fc80c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 728, + 90, + 885, + 231 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e3fe5eb61e0dcfcd2428fc30733879aa738cac6bf4a02734ca0f0b4c8e6ab06c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
KITTI - 75%KITTI - 50%KITTI - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.560.5570.55419.120.5870.49718.610.5700.510
NeRF + Time21.010.6120.49221.340.6350.44819.550.5860.505
NSG [37]21.530.6730.25421.260.6590.26620.000.6320.281
SUDS22.770.7970.17123.120.8210.13520.760.7470.198
VKITTI2 - 75%VKITTI2 - 50%VKITTI2 - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.670.5480.63418.580.5440.63518.170.5370.644
NeRF + Time19.030.5740.58718.900.5650.61018.040.5450.626
NSG [37]23.410.6890.31723.230.6790.32521.290.6660.317
SUDS23.870.8460.15023.780.8510.14222.180.8290.160
", + "bbox": [ + 187, + 276, + 784, + 462 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3659e69fe9c743691417cc64c1bb9363aefd9fce764aa7d8c5429f3e1b43b23d.jpg", + "table_caption": [ + "Table 2. Novel View Synthesis. As the fraction of training views decreases, accuracy drops for all methods. However, SUDS consistently outperforms prior work, presumably due to more accurate representations learned by our diverse input signals (such as depth and flow)." + ], + "table_footnote": [], + "table_body": "
SRN [45]NeRF [33]NeRF + TimeNSG [37]PNF [27]Ours
PSNR ↑18.8323.3424.1826.6627.4828.31
SSIM ↑0.5900.6620.6770.8060.8700.876
", + "bbox": [ + 84, + 508, + 467, + 555 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/04c0bd0b661fa238c5c5fc7296b78e28e2cd21270d51616648ac25bd6e17a7ab.jpg", + "table_caption": [ + "Table 3. KITTI image reconstruction. We outperform past work on image reconstruction accuracy, following their experimental protocol and self-reported accuracies [27, 37]." + ], + "table_footnote": [], + "table_body": "
↑PSNR↑SSIM↓LPIPS
w/o Depth loss22.740.7150.292
w/o Optical flow loss22.180.7080.302
w/o Warping loss17.530.6220.478
w/o Appearance embedding22.540.7040.296
w/o Occlusion weights22.560.7110.297
w/o Separate branches19.730.5700.475
Full Method22.950.7180.289
", + "bbox": [ + 99, + 617, + 446, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Diagnostics. Flow-based warping is the single-most important input, while depth is the least crucial input.", + "bbox": [ + 76, + 746, + 468, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "especially as the number of training view decreases, and generates ghosting artifacts near areas of movement.", + "bbox": [ + 76, + 789, + 468, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Diagnostics", + "text_level": 1, + "bbox": [ + 76, + 830, + 200, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We ablate the importance of major SUDS components by removing their respective loss terms along with occlusion weights, the latent embedding $A_{vid}\\mathcal{F}(t)$ used to compute", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "static color $\\mathbf{c}_s$ , and separate model branches (Sec. D). We run all approaches for 125,000 iterations across our datasets and summarize the results in Table 4. Although all components help performance, flow-based warping is by far the single most important input. Interestingly, depth is the least crucial input, suggesting that SUDS can generalize to settings where depth measurements are not available.", + "bbox": [ + 496, + 512, + 890, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 632, + 617, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a modular approach towards building dynamic neural representations at previously unexplored scale. Our multi-branch hash table structure enables us to disentangle and efficiently encode static geometry and transient objects across thousands of videos. SUDS makes use of unlabeled inputs to learn semantic awareness and scene flow, allowing it to perform several downstream tasks while surpassing state-of-the-art methods that rely on human labeling. Although we present a first attempt at building city-scale dynamic environments, many open challenges remain ahead of building truly photorealistic representations.", + "bbox": [ + 496, + 657, + 890, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 837, + 658, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research was supported by the CMU Argo AI Center for Autonomous Vehicle Research.", + "bbox": [ + 498, + 862, + 890, + 892 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12382", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kwea123's nsff implementation. https://github.com/kwea123/nsff_pl. 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In ICCV, 2021. 2" + ], + "bbox": [ + 78, + 90, + 470, + 375 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12385", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SUDS_ Scalable Urban Dynamic Scenes/e8fd5f67-d301-4dd3-8588-d4088862c6a6_model.json b/2023/SUDS_ Scalable Urban Dynamic Scenes/e8fd5f67-d301-4dd3-8588-d4088862c6a6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e9d8a2840835406afaaa6ee145ef2f9302b106cf --- /dev/null +++ b/2023/SUDS_ Scalable Urban Dynamic Scenes/e8fd5f67-d301-4dd3-8588-d4088862c6a6_model.json @@ -0,0 +1,3313 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.284, + 0.131, + 0.688, + 0.154 + ], + "angle": 0, + "content": "SUDS: Scalable Urban Dynamic Scenes" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.18, + 0.284, + 0.198 + ], + "angle": 0, + "content": "Haithem Turki\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.181, + 0.655, + 0.219 + ], + "angle": 0, + "content": "Jason Y. Zhang1 Francesco Ferroni2 \n1Carnegie Mellon University 2Argo AI" + }, + { + "type": "text", + "bbox": [ + 0.689, + 0.181, + 0.816, + 0.198 + ], + "angle": 0, + "content": "Deva Ramanan" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.267, + 0.314, + 0.283 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.298, + 0.474, + 0.768 + ], + "angle": 0, + "content": "We extend neural radiance fields (NeRFs) to dynamic large-scale urban scenes. Prior work tends to reconstruct single video clips of short durations (up to 10 seconds). Two reasons are that such methods (a) tend to scale linearly with the number of moving objects and input videos because a separate model is built for each and (b) tend to require supervision via 3D bounding boxes and panoptic labels, obtained manually or via category-specific models. As a step towards truly open-world reconstructions of dynamic cities, we introduce two key innovations: (a) we factorize the scene into three separate hash table data structures to efficiently encode static, dynamic, and far-field radiance fields, and (b) we make use of unlabeled target signals consisting of RGB images, sparse LiDAR, off-the-shelf self-supervised 2D descriptors, and most importantly, 2D optical flow. Operationalizing such inputs via photometric, geometric, and feature-metric reconstruction losses enables SUDS to decompose dynamic scenes into the static background, individual objects, and their motions. When combined with our multi-branch table representation, such reconstructions can be scaled to tens of thousands of objects across 1.2 million frames from 1700 videos spanning geospatial footprints of hundreds of kilometers, (to our knowledge) the largest dynamic NeRF built to date. We present qualitative initial results on a variety of tasks enabled by our representations, including novel-view synthesis of dynamic urban scenes, unsupervised 3D instance segmentation, and unsupervised 3D cuboid detection. To compare to prior work, we also evaluate on KITTI and Virtual KITTI 2, surpassing state-of-the-art methods that rely on ground truth 3D bounding box annotations while being \\(10x\\) quicker to train." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.795, + 0.21, + 0.811 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.82, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Scalable geometric reconstructions of cities have transformed our daily lives, with tools such as Google Maps and Streetview [6] becoming fundamental to how we navigate and interact with our environments. A watershed moment" + }, + { + "type": "image", + "bbox": [ + 0.529, + 0.251, + 0.847, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.433, + 0.627, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.504, + 0.579, + 0.512 + ], + "angle": 0, + "content": "RGB" + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.434, + 0.756, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.504, + 0.711, + 0.512 + ], + "angle": 0, + "content": "Static" + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.434, + 0.886, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.806, + 0.504, + 0.848, + 0.512 + ], + "angle": 0, + "content": "Dynamic" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.513, + 0.627, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.552, + 0.582, + 0.583, + 0.591 + ], + "angle": 0, + "content": "Depth" + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.513, + 0.755, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.582, + 0.72, + 0.591 + ], + "angle": 0, + "content": "Instances" + }, + { + "type": "image", + "bbox": [ + 0.768, + 0.513, + 0.886, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.815, + 0.582, + 0.839, + 0.591 + ], + "angle": 0, + "content": "Flow" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.722 + ], + "angle": 0, + "content": "Figure 1. SUDS. We scale neural reconstructions to city scale by dividing the area into multiple cells and training hash table representations for each. We show our full city-scale reconstruction above and the derived representations below. Unlike prior methods, our approach handles dynamism across multiple videos, disentangling dynamic objects from static background and modeling shadow effects. We use unlabeled inputs to learn scene flow and semantic predictions, enabling category- and object-level scene manipulation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.822 + ], + "angle": 0, + "content": "in the development of such technology was the ability to scale structure-from-motion (SfM) algorithms to city-scale footprints [4]. Since then, the advent of Neural Radiance Fields (NeRFs) [33] has transformed this domain by allowing for photorealistic interaction with a reconstructed scene via view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recent works have attempted to scale such representations to neighborhood-scale reconstructions for virtual drive-throughs [47] and photorealistic fly-throughs [52]. However, these maps remain static and frozen in time. This makes capturing bustling human environments—" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.888, + 0.296, + 0.9 + ], + "angle": 0, + "content": "*Work done as an intern at Argo AI." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12375" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "complete with moving vehicles, pedestrians, and objects—impossible, limiting the usefulness of the representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.121, + 0.47, + 0.333 + ], + "angle": 0, + "content": "Challenges. One possible solution is a dynamic NeRF that conditions on time or warps a canonical space with a time-dependent deformation [38]. However, reconstructing dynamic scenes is notoriously challenging because the problem is inherently under-constrained, particularly when input data is constrained to limited viewpoints, as is typical from egocentric video capture [20]. One attractive solution is to scale up reconstructions to many videos, perhaps collected at different days (e.g., by an autonomous vehicle fleet). However, this creates additional challenges in jointly modeling fixed geometry that holds for all time (such as buildings), geometry that is locally static but transient across the videos (such as a parked car), and geometry that is truly dynamic (such as a moving person)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.47, + 0.59 + ], + "angle": 0, + "content": "SUDS. In this paper, we propose SUDS: Scalable Urban Dynamic Scenes, a 4D representation that targets both scale and dynamism. Our key insight is twofold; (1) SUDS makes use of a rich suite of informative but freely available input signals, such as LiDAR depth measurements and optical flow. Other dynamic scene representations [27, 37] require supervised inputs such as panoptic segmentation labels or bounding boxes, which are difficult to acquire with high accuracy for our in-the-wild captures. (2) SUDS decomposes the world into 3 components: a static branch that models stationary topography that is consistent across videos, a dynamic branch that handles both transient (e.g., parked cars) and truly dynamic objects (e.g., pedestrians), and an environment map that handles far-field objects and sky. We model each branch using a multi-resolution hash table with scene partitioning, allowing SUDS to scale to an entire city spanning over \\(100km^2\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.727 + ], + "angle": 0, + "content": "Contributions. We make the following contributions: (1) to our knowledge, we build the first large-scale dynamic NeRF, (2) we introduce a scalable three-branch hash table representation for 4D reconstruction, (3) we present state-of-the-art reconstruction on 3 different datasets. Finally, (4) we showcase a variety of downstream tasks enabled by our representation, including free-viewpoint synthesis, 3D scene flow estimation, and even unsupervised instance segmentation and 3D cuboid detection." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.22, + 0.755 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.825 + ], + "angle": 0, + "content": "The original Neural Radiance Fields (NeRF) paper [33] inspired a wide body of follow-up work based on the original approach. Below, we describe a non-exhaustive list of such approaches along axes relevant to our work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Scale. The original NeRF operated with bounded scenes. \\(\\mathrm{NeRF}++\\) [63] and mip-NeRF 360 [7] use non-linear scene parameterization to model unbounded scenes. However, scaling up the size of the scene with a fixed size MLP leads to blurry details and training instability while the cost of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.258 + ], + "angle": 0, + "content": "naively increasing the size of the MLP quickly becomes intractable. BungeeNeRF [58] introduced a coarse-to-fine approach that progressively adds more capacity to the network representation. Block-NeRF [47] and Mega-NeRF [52] partition the scene spatially and train separate NeRFs for each partition. To model appearance variation, they incorporate per-image embeddings like NeRF-W [31]. Our approach similarly partitions the scene into sub-NeRFs, making use of depth to improve partition efficiency and scaling over an area 200x larger than Block-NeRF's Alamo Square Dataset. Both of these methods work only on static scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.892, + 0.442 + ], + "angle": 0, + "content": "Dynamics. Neural 3D Video Synthesis [28] and Spacetime Neural Irradiance Fields [57] add time as an input to handle dynamic scenes. Similar to our work, NSFF [29], NeRFlow [15], and DyNeRF [19] incorporate 2D optical flow input and warping-based regularization losses to enforce plausible transitions between observed frames. Multiple methods [38-40, 50] instead disentangle scenes into a canonical template and per-frame deformation field. BANMo [60] further incorporates deformable shape models and canonical embeddings to train articulated 3D models from multiple videos. These methods focus on single-object scenes, and all but [28] and [60] use single video sequences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.548 + ], + "angle": 0, + "content": "While many of the previous works use segmentation data to factorize dynamic from static objects, \\(\\mathrm{D}^2\\mathrm{NeRF}\\) [56] does this automatically through regularization and explicitly handling shadows. Neural Groundplans [44] uses synthetic data to do this decomposition from a single image. We borrow some of these ideas and scale beyond synthetic and indoor scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.687 + ], + "angle": 0, + "content": "Object-centric approaches. Several approaches [24,36, 37, 59, 61, 62] represent scenes as the composition of per-object NeRF models and a background model. NSG [37] is most similar to us as it also targets automotive data but cannot handle ego-motion as our approach can. None of these methods target multi-video representations and are fundamentally constrained by the memory required to represent each object, with NSG needing over 1TB of memory to represent a 30 second video in our experience." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Semantics. Follow-up works have explored additional semantic outputs in addition to predicting color. Semantic-NeRF [65] adds an extra head to NeRF that predicts extra semantic category logits for any 3D position. Panoptic-NeRF [16] and Panoptic Neural Fields [27] extend this to produce panoptic segmentations and the latter uses a similar bounding-box based object and background decomposition as NSG. NeSF [53] generalizes the notion of a semantic field to unobserved scenes. As these methods are highly reliant on accurate annotations which are difficult to reliably obtain in the wild at our scale, we instead use a similar approach to recent works [26, 51] that distill the outputs of 2D self-supervised feature descriptors into 3D radiance fields to enable semantic understanding without the use of human" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12376" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.175, + 0.086, + 0.357, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.217, + 0.226, + 0.315, + 0.238 + ], + "angle": 0, + "content": "(a) Voxel Lookup" + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.087, + 0.67, + 0.225 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.401, + 0.227, + 0.472, + 0.24 + ], + "angle": 0, + "content": "(b) Indexing" + }, + { + "type": "image_footnote", + "bbox": [ + 0.704, + 0.148, + 0.83, + 0.162 + ], + "angle": 0, + "content": "\\((\\mathbf{c},\\sigma ,\\phi ,s_{\\mathbf{t} - 1},s_{\\mathbf{t} + 1})\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.709, + 0.165, + 0.825, + 0.177 + ], + "angle": 0, + "content": "(d) Output Blending" + }, + { + "type": "list", + "bbox": [ + 0.704, + 0.148, + 0.83, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.895, + 0.336 + ], + "angle": 0, + "content": "Figure 2. Model Architecture. (a) For a given input coordinate, we find the surrounding voxels at \\( L \\) resolution levels for both the static and dynamic branches (far-field branch omitted for clarity). (b) We assign indices to their corners by hashing based on position in the static branch and position, time, and video id in the dynamic branch. We look up the feature vectors corresponding to the corners and interpolate according to the relative position of the input coordinate within the voxel. (c) We concatenate the result of each level, along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch color, density, and feature logits along with scene flow and the shadow ratio. (d) We blend scolor, opacity, and feature logits as the weighted sum of the branches." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.408, + 0.363 + ], + "angle": 0, + "content": "labels and extend them to larger dynamic settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.517 + ], + "angle": 0, + "content": "Fast training. The original NeRF took 1-2 days to train. Plenoxels [43] and DVGO [46] directly optimize a voxel representation instead of an MLP to train in minutes or even seconds. TensoRF [11] stores its representation as the outer product of low-rank tensors, reducing memory usage. Instant-NGP [35] takes this further by encoding features in a multi-resolution hash table, allowing training and rendering to happen in real-time. We use these tables as the base block of our three-branch representation and use our own hashing method to support dynamics across multiple videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.471, + 0.626 + ], + "angle": 0, + "content": "Depth. Depth provides a valuable supervisory signal for learning high-quality geometry. DS-NeRF [14] and Dense Depth Priors [42] incorporate noisy point clouds obtained by structure from motion (SfM) in the loss function during optimization. Urban Radiance Fields [41] supervises with collected LiDAR data. We also use LiDAR but demonstrate results on dynamic environments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.65, + 0.185, + 0.667 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.678, + 0.165, + 0.695 + ], + "angle": 0, + "content": "3.1. Inputs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Our goal is to learn a global representation that facilitates free-viewpoint rendering, semantic decomposition, and 3D scene flow at arbitrary poses and time steps. Our method takes as input ordered RGB images from \\(N\\) videos (taken at different days with diverse weather and lighting conditions) and their associated camera poses. Crucially, we make use of additional data as \"free\" sources of supervision given contemporary sensor rigs and feature descriptors. Specifically, we use (1) aligned sparse LiDAR depth measurements, (2) 2D self-supervised pixel (DINO [10]) descriptors to enable semantic manipulation, and (3) 2D optical flow predictions to model scene dynamics. All model inputs are generated without any human labeling or intervention." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.654, + 0.363 + ], + "angle": 0, + "content": "3.2. Representation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.372, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Preliminaries. We build upon NeRF [33], which represents a scene within a continuous volumetric radiance field that captures both geometry and view-dependent appearance. It encodes the scene within the weights of a multilayer perceptron (MLP). At render time, NeRF projects a camera ray \\(\\mathbf{r}\\) for each image pixel and samples along the ray, querying the MLP at sample position \\(\\mathbf{x}_i\\) and ray viewing direction \\(\\mathbf{d}\\) to obtain opacity and color values \\(\\sigma_i\\) and \\(\\mathbf{c}_i\\). It then composites a color prediction \\(\\hat{C}(\\mathbf{r})\\) for the ray using numerical quadrature \\(\\sum_{i=0}^{N-1} T_i (1 - \\exp(-\\sigma_i \\delta_i)) \\mathbf{c}_i\\), where \\(T_i = \\exp(-\\sum_{j=0}^{i-1} \\sigma_j \\delta_j)\\) and \\(\\delta_i\\) is the distance between samples. The training process optimizes the model by sampling batches \\(R\\) of image pixels and minimizing the loss function \\(\\sum_{\\mathbf{r} \\in \\mathcal{R}} \\|C(\\mathbf{r}) - \\hat{C}(\\mathbf{r})\\|^2\\). NeRF samples rays through a two-stage hierarchical sampling process and uses frequency encoding to capture high-frequency details. We refer the reader to [33] for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.759 + ], + "angle": 0, + "content": "Scene composition. To model large-scale dynamic environments, SUDS factorizes the scene into three branches: (a) a static branch containing non-moving topography consistent across videos, (b) a dynamic branch to disentangle video-specific objects [19,29,56], moving or otherwise, and (c) a far-field environment map to represent far-away objects and the sky, which we found important to separately model in large-scale urban scenes [41, 52, 63]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.762, + 0.892, + 0.852 + ], + "angle": 0, + "content": "However, conventional NeRF training with MLPs is computationally prohibitive at our target scales. Inspired by Instant-NGP [35], we implement each branch using multiresolution hash tables of \\( F \\)-dimensional feature vectors followed by a small MLP, along with our own hash functions to index across videos." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Hash tables (Fig. 2). For a given input coordinate \\((\\mathbf{x}, \\mathbf{d}, \\mathbf{t}, \\mathbf{v}\\mathbf{id})\\) denoting the position \\(\\mathbf{x} \\in \\mathbb{R}^3\\), viewing direction \\(\\mathbf{d} \\in \\mathbb{R}^3\\), frame index \\(F \\in \\{1, \\dots, T\\}\\), and video id" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12377" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.258 + ], + "angle": 0, + "content": "\\(\\mathbf{vid} \\in \\{1, \\dots, N\\}\\), we find the surrounding voxels in each table at \\(l \\in L\\) resolution levels, doubling the resolution between levels, which we denote as \\(\\mathbf{v}_{l,s}\\), \\(\\mathbf{v}_{l,d}\\), \\(\\mathbf{v}_{l,e}\\) for the static, dynamic, and far-field. The static branch makes use of 3D spatial voxels \\(\\mathbf{v}_{l,s}\\), while the dynamic branch makes use of 4D spacetime voxels \\(\\mathbf{v}_{l,d}\\). Finally, the far-field branch makes use of 3D voxels \\(\\mathbf{v}_{l,e}\\) (implemented via normalized 3D direction vectors) that index an environment map. Similar to Instant-NGP [35], rather than storing features at voxel corners, we compute hash indices \\(\\mathbf{i}_{l,s}\\) (or \\(\\mathbf{i}_{l,d}\\) or \\(\\mathbf{i}_{l,e}\\)) for each corner with the following hash functions:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.266, + 0.47, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\mathbf {i} _ {l, s} = \\text {s t a t i c} \\operatorname {h a s h} \\left(\\operatorname {s p a c e} \\left(\\mathbf {v} _ {l, s}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.285, + 0.469, + 0.301 + ], + "angle": 0, + "content": "\\[\n\\mathbf {i} _ {l, d} = \\text {d y n a m i c} \\text {h a s h} \\left(\\operatorname {s p a c e} \\left(\\mathbf {v} _ {l, d}\\right), \\operatorname {t i m e} \\left(\\mathbf {v} _ {l, d}\\right), \\mathbf {v i d}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.304, + 0.469, + 0.32 + ], + "angle": 0, + "content": "\\[\n\\mathbf {i} _ {l, e} = \\operatorname {e n v} \\text {h a s h} (d i r (\\mathbf {v} _ {l, e}), \\mathbf {v i d}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.47, + 0.538 + ], + "angle": 0, + "content": "We linearly interpolate features up to the nearest voxel vertices (but now relying on quadlinear interpolation for the dynamic 4D branch) and rely on gradient averaging to handle hash collisions. Finally, to model the fact that different videos likely contain distinct moving objects and illumination conditions, we add vid as an auxiliary input to the hash, but do not use it for interpolation (since averaging across distinct movers is unnatural). From this perspective, we leverage hashing to effectively index separate interpolating functions for each video, without a linear growth in memory with the number of videos. We concatenate the result of each level into a feature vector \\( f \\in \\mathbb{R}^{LF} \\), along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch outputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.47, + 0.661 + ], + "angle": 0, + "content": "Static branch. We generate RGB images by combining the outputs of our three branches. The static branch maps the feature vector obtained from the hash table into a view-dependent color \\(\\mathbf{c}_s\\) and a view-independent density \\(\\sigma_s\\). To model lighting variations which could be dramatic across videos but smooth within a video, we condition on a latent embedding computed as a product of a video-specific matrix \\(A_{vid}\\) and a fourier-encoded time index \\(\\mathcal{F}(t)\\) (as in [60]):" + }, + { + "type": "equation", + "bbox": [ + 0.187, + 0.668, + 0.469, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {s} (\\mathbf {x}) \\in \\mathbb {R} \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.688, + 0.469, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {s} (\\mathbf {x}, \\mathbf {d}, A _ {v i d} \\mathcal {F} (t)) \\in \\mathbb {R} ^ {3}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.834 + ], + "angle": 0, + "content": "Dynamic branch. While the static branch assumes the density \\(\\sigma_{s}\\) is static, the dynamic branch allows both the density \\(\\sigma_{d}\\) and color \\(\\mathbf{c}_d\\) to depend on time (and video). We therefore omit the latent code when computing the dynamic radiance. Because we find shadows to play a crucial role in the appearance of urban scenes (Fig. 3), we explicitly model a shadow field of scalar values \\(\\rho_{d} \\in [0,1]\\), used to scale down the static color \\(\\mathbf{c}_{s}\\) (as done in [56]):" + }, + { + "type": "equation", + "bbox": [ + 0.203, + 0.842, + 0.469, + 0.857 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in \\mathbb {R} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.861, + 0.469, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\rho_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in [ 0, 1 ] \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.88, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) \\in \\mathbb {R} ^ {3} \\tag {8}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.086, + 0.693, + 0.136 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.61, + 0.136, + 0.648, + 0.144 + ], + "angle": 0, + "content": "Full RGB" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.086, + 0.829, + 0.135 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.752, + 0.136, + 0.78, + 0.144 + ], + "angle": 0, + "content": "Depth" + }, + { + "type": "image", + "bbox": [ + 0.566, + 0.146, + 0.692, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.195, + 0.679, + 0.203 + ], + "angle": 0, + "content": "RGB (Without Shadow)" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.146, + 0.828, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.195, + 0.803, + 0.203 + ], + "angle": 0, + "content": "Shadow Intensity" + }, + { + "type": "image", + "bbox": [ + 0.566, + 0.204, + 0.692, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.254, + 0.659, + 0.262 + ], + "angle": 0, + "content": "Dynamic RGB" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.204, + 0.828, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.254, + 0.789, + 0.262 + ], + "angle": 0, + "content": "Static RGB" + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.269, + 0.746, + 0.28 + ], + "angle": 0, + "content": "(a) Shadow Field" + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.285, + 0.69, + 0.335 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.61, + 0.336, + 0.644, + 0.343 + ], + "angle": 0, + "content": "Full RGB" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.285, + 0.827, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.751, + 0.336, + 0.775, + 0.343 + ], + "angle": 0, + "content": "Depth" + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.344, + 0.69, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.6, + 0.395, + 0.654, + 0.403 + ], + "angle": 0, + "content": "Dynamic RGB" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.344, + 0.826, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.743, + 0.394, + 0.785, + 0.402 + ], + "angle": 0, + "content": "Static RGB" + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.408, + 0.753, + 0.42 + ], + "angle": 0, + "content": "(b) No Shadow Field" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.426, + 0.892, + 0.468 + ], + "angle": 0, + "content": "Figure 3. Shadows. We learn an explicit shadow field (a) as a pointwise reduction on static color, enabling better depth reconstruction and static/dynamic factorization than without (b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.892, + 0.557 + ], + "angle": 0, + "content": "Far-field branch. Because the sky requires reasoning about far-field radiance and because it can change dramatically across videos, we model far-field radiance with an environment map \\(\\mathbf{c}_e(\\mathbf{d},\\mathbf{vid})\\in \\mathbb{R}^3\\) that depends on viewing direction d [22,41] and a video id vid." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.618 + ], + "angle": 0, + "content": "Rendering. We derive a single density and radiance value for any position by computing the weighted sum of the static and dynamic components, combined with the pointwise shadow reduction:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.632, + 0.892, + 0.705 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\sigma (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) = \\sigma_ {s} (\\mathbf {x}) + \\sigma_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) (9) \\\\ \\mathbf {c} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) = \\frac {\\sigma_ {s}}{\\sigma} (1 - \\rho_ {d}) \\mathbf {c} _ {s} (\\mathbf {x}, \\mathbf {d}, A _ {v i d} \\mathcal {F} (t)) \\\\ + \\frac {\\sigma_ {d}}{\\sigma} \\mathbf {c} _ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) (10) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.796 + ], + "angle": 0, + "content": "We then calculate the color \\(\\hat{C}\\) for a camera ray \\(\\mathbf{r}\\) with direction \\(\\mathbf{d}\\) at a given frame \\(\\mathbf{t}\\) and video vid by accumulating the transmittance along sampled points \\(\\mathbf{r}(t)\\) along the ray, forcing the ray to intersect the far-field environment map if it does not hit geometry within the foreground:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.808, + 0.891, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {C} (\\mathbf {r}, \\mathbf {t}, \\mathbf {v i d}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (\\mathbf {r} (t), \\mathbf {t}, \\mathbf {v i d}) \\mathbf {c} (\\mathbf {r} (t), \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) d t \\\\ + T (+ \\infty) \\mathbf {c} _ {e} (\\mathbf {d}, \\mathbf {v i d}), \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.864, + 0.892, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} T (t) = \\exp \\left(- \\int_ {0} ^ {t} \\sigma (\\mathbf {r} (s), \\mathbf {t}, \\mathbf {v i d}) d s\\right). \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12378" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.211 + ], + "angle": 0, + "content": "Feature distillation. We build semantic awareness into SUDS to enable the open-world tasks described in Sec. 4.2. Similar to recent work [26, 51], we distill the outputs of a self-supervised 2D feature extractor, namely DINO [10], as a teacher model into our network. For a feature extractor that transforms an image into a dense \\(\\mathbb{R}^{H\\times W\\times C}\\) feature grid, we add a \\(C\\)-dimensional output head to each of our branches:" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.216, + 0.468, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {s} (\\mathbf {x}) \\in \\mathbb {R} ^ {C} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.238, + 0.468, + 0.255 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in \\mathbb {R} ^ {C} \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.209, + 0.258, + 0.468, + 0.276 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {e} (\\mathbf {d}, \\mathbf {v i d}) \\in \\mathbb {R} ^ {C}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.282, + 0.468, + 0.327 + ], + "angle": 0, + "content": "which are combined into a single value \\(\\Phi\\) at any 3D location and rendered into \\(\\hat{F} (\\mathbf{r})\\) per camera ray, following the equations for color (10, 11)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.328, + 0.468, + 0.447 + ], + "angle": 0, + "content": "Scene flow. We train our model to predict 3D scene flow and model scene dynamics. Inspired by previous work [15, 19, 29], we augment our dynamic branch to predict forward and backward 3D scene flow vectors \\( s_{t' \\in [-1,1]}(\\mathbf{x},\\mathbf{t},\\mathbf{v}\\mathbf{i}\\mathbf{d}) \\in \\mathbb{R}^3 \\). We make use of these vectors to enforce consistency between observed time steps through multiple loss terms (Sec. 3.3), which we find crucial to generating plausible renderings at novel time steps (Table 4)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.449, + 0.47, + 0.842 + ], + "angle": 0, + "content": "Spatial partitioning. We scale our representation to arbitrarily large environments by decomposing the scene into individually trained models [47, 52], each with its own static, dynamic, and far-field branch. Intuitively, the reconstruction for neighborhood X can be done largely independently of the reconstruction in neighborhood Y, provided one can assign the relevant input data to each reconstruction. To do so, we follow the approach of Mega-NeRF [52] and split the scene into \\(K\\) spatial cells with centroids \\(k \\in \\mathbb{R}^3\\). Crucially, we generate separate training datasets for each spatial cell by making use of visibility reasoning [17]. Mega-NeRF includes only those datapoints whose associated camera rays intersect the spatial cell. However, this may still include datapoints that are not visible due to an intervening occluder (e.g., a particular camera in neighborhood X can be pointed at neighborhood Y, but may not see anything there due to occluding buildings). To remedy this, we make use of depth measurements to prune irrelevant pixel rays that do not terminate within the spatial cell of interest (making use of nearest-neighbor interpolation to impute depth for pixels without a LiDAR depth measurement). This further reduces the size of each trainset by \\(2x\\) relative to Mega-NeRF. Finally, given such separate reconstructions, one can still produce a globally consistent rendering by querying the appropriate spatial cell when sampling points along new-view rays (as in [52])." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.216, + 0.863 + ], + "angle": 0, + "content": "3.3. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "We jointly optimize all three of our model branches along with the per-video weight matrices \\( A_{vid} \\) by sampling" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.092, + 0.689, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.605, + 0.153, + 0.627, + 0.16 + ], + "angle": 0, + "content": "RGB" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.092, + 0.846, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.153, + 0.794, + 0.161 + ], + "angle": 0, + "content": "Features" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.161, + 0.689, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.569, + 0.221, + 0.664, + 0.229 + ], + "angle": 0, + "content": "Forward Flow (Input)" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.161, + 0.846, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.723, + 0.221, + 0.824, + 0.229 + ], + "angle": 0, + "content": "Backward Flow (Input)" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.229, + 0.689, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.29, + 0.672, + 0.298 + ], + "angle": 0, + "content": "Forward Flow (Predicted)" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.229, + 0.846, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.713, + 0.29, + 0.833, + 0.298 + ], + "angle": 0, + "content": "Backward Flow (Predicted)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.306, + 0.892, + 0.376 + ], + "angle": 0, + "content": "Figure 4. Scene Flow. We minimize the photometric and feature-metric loss of warped renderings relative to ground truth inputs (top). We use 2D optical flow from off-the-shelf estimators or sparse correspondences computed directly from 2D DINO features [5] (middle) to supervise our flow predictions (bottom)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.891, + 0.414 + ], + "angle": 0, + "content": "random batches of rays across our \\(N\\) input videos and minimizing the following loss:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.422, + 0.865, + 0.468 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\underbrace {\\left(\\mathcal {L} _ {c} + \\lambda_ {f} \\mathcal {L} _ {f} + \\lambda_ {d} \\mathcal {L} _ {d} + \\lambda_ {o} \\mathcal {L} _ {o}\\right)} _ {\\text {r e c o n s t r u c t i o n l o s s e s}} + \\underbrace {\\left(\\mathcal {L} _ {c} ^ {w} + \\lambda_ {f} \\mathcal {L} _ {f} ^ {w}\\right)} _ {\\text {w a r p i n g l o s s e s}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.47, + 0.897, + 0.529 + ], + "angle": 0, + "content": "\\[\n\\lambda_ {f l o} \\underbrace {\\left(\\mathcal {L} _ {c y c} + \\mathcal {L} _ {s m} + \\mathcal {L} _ {s l o}\\right)} _ {\\text {f l o w l o s s e s}} + \\underbrace {\\left(\\lambda_ {e} \\mathcal {L} _ {e} + \\lambda_ {d} \\mathcal {L} _ {d}\\right)} _ {\\text {s t a t i c - d y n a m i c f a c t o r i z a t i o n}} + \\lambda_ {\\rho} \\mathcal {L} _ {\\rho} \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.53, + 0.892, + 0.606 + ], + "angle": 0, + "content": "Reconstruction losses. We minimize the L2 photometric loss \\(\\mathcal{L}_c(\\mathbf{r}) = \\left\\| C(\\mathbf{r}) - \\hat{C} (\\mathbf{r})\\right\\| ^2\\) as in the original NeRF equation [33]. We similarly minimize the L1 difference \\(\\mathcal{L}_f(\\mathbf{r}) = \\left\\| F(\\mathbf{r}) - \\hat{F} (\\mathbf{r})\\right\\| _1\\) between the feature outputs of the teacher model and that of our network." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.608, + 0.891, + 0.654 + ], + "angle": 0, + "content": "To make use of our depth measurements, we project the LiDAR sweeps onto the camera plane and compare the expected depth \\(\\hat{D}(r)\\) with the measurement \\(D(\\mathbf{r})\\) [14, 41]:" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.663, + 0.89, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d} (\\mathbf {r}) = \\left\\| D (\\mathbf {r}) - \\hat {D} (\\mathbf {r}) \\right\\| ^ {2} \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.686, + 0.89, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\hat {D} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (s) \\sigma (\\mathbf {r} (s)) d s \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.728, + 0.891, + 0.804 + ], + "angle": 0, + "content": "Flow. We supervise our 3D scene flow predictions based on 2D optical flow (Sec. 4.1). We generate a 2D displacement vector for each camera ray by first predicting its position in 3D space as the weighted sum of the scene flow neighbors along the ray:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.813, + 0.891, + 0.847 + ], + "angle": 0, + "content": "\\[\n\\hat {X} _ {t ^ {\\prime}} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (r (t)) (r (t) + s _ {t ^ {\\prime}} (\\mathbf {r} (t))) d t \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "which we then \"render\" into 2D using the camera matrix of the neighboring frame index. We minimize its distance from the observed optical flow via \\(\\mathcal{L}_o(\\mathbf{r}) =\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12379" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.121 + ], + "angle": 0, + "content": "\\(\\sum_{t' \\in [-1,1]} \\left\\| X(\\mathbf{o}) - \\hat{X}_{t'}(\\mathbf{r}) \\right\\|_1\\). We anneal \\(\\lambda_o\\) over time as these estimates are noisy." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.122, + 0.47, + 0.228 + ], + "angle": 0, + "content": "3D warping. The above loss ensures that rendered 3D flow will be consistent with the observed 2D flow. We also found it useful to enforce 3D color (and feature) constancy; i.e., colors remain constant even when moving. To do so, we use the predicted forward and backward 3D flow \\( s_{\\mathbf{t} + 1} \\) and \\( s_{\\mathbf{t} - 1} \\) to advect each sample along the ray into the next/previous frame:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.239, + 0.468, + 0.256 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}\\right) \\in \\mathbb {R} \\tag {20}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.169, + 0.259, + 0.468, + 0.277 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}, \\mathbf {d}\\right) \\in \\mathbb {R} ^ {3} \\tag {21}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.28, + 0.468, + 0.298 + ], + "angle": 0, + "content": "\\[\n\\Phi_ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}\\right) \\in \\mathbb {R} ^ {C} \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.309, + 0.47, + 0.461 + ], + "angle": 0, + "content": "The warped radiance \\(\\mathbf{c}^w\\) and density \\(\\sigma^w\\) are rendered into warped color \\(\\hat{C}^w (\\mathbf{r})\\) and feature \\(\\hat{F}^{w}(\\mathbf{r})\\) (10, 11). We add a loss to ensure that the warped color (and feature) match the ground-truth input for the current frame, similar to [19, 29]. As in NSFF [29], we found it important to downweight this loss in ambiguous regions that may contain occlusions. However, instead of learning explicit occlusion weights, we take inspiration from Kwea's method [1] and use the difference between the dynamic geometry and the warped dynamic geometry to downweight the loss:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.47, + 0.469, + 0.505 + ], + "angle": 0, + "content": "\\[\nw _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) = \\left| \\frac {\\sigma_ {d}}{\\sigma} - \\frac {\\sigma_ {t ^ {\\prime}} ^ {w}}{\\sigma} \\right| \\tag {23}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.507, + 0.469, + 0.541 + ], + "angle": 0, + "content": "\\[\n\\hat {W} _ {t ^ {\\prime}} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (r (t)) w _ {t ^ {\\prime}} (r (t)) d t \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.55, + 0.398, + 0.566 + ], + "angle": 0, + "content": "resulting in the following warping loss terms:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.576, + 0.469, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c} ^ {w} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\left(1 - W _ {t ^ {\\prime}}\\right) (\\mathbf {r})) \\| C (\\mathbf {r}) - \\hat {C} _ {t ^ {\\prime}} ^ {w} (\\mathbf {r}) \\| ^ {2} \\tag {25}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.614, + 0.469, + 0.648 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f} ^ {w} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\left(1 - W _ {t ^ {\\prime}}\\right) (\\mathbf {r}) \\| F (\\mathbf {r}) - \\hat {F} _ {t ^ {\\prime}} ^ {w} (\\mathbf {r}) \\| _ {1} \\tag {26}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.659, + 0.469, + 0.719 + ], + "angle": 0, + "content": "Flow regularization. As in prior work [19, 29] we use a 3D scene flow cycle term to encourage consistency between forward and backward scene flow predictions, downweighting the loss in areas ambiguous due to occlusions:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.725, + 0.469, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c y c}} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\sum_ {\\mathbf {x}} w _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}) \\| s _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}) + s _ {\\mathbf {t}} (\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} - t ^ {\\prime}) \\| _ {1}, \\tag {27}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.469, + 0.842 + ], + "angle": 0, + "content": "with \\(\\mathbf{v}\\mathbf{id}\\) omitted for brevity. We also encourage spatial and temporal smoothness through \\(\\mathcal{L}_{sm}(\\mathbf{r})\\) as described in Sec. C. We finally regularize the magnitude of predicted scene flow vectors to encourage the scene to be static through \\(\\mathcal{L}_{slo}(\\mathbf{r}) = \\sum_{t' \\in [\\mathbf{t} - 1, \\mathbf{t} + 1]} \\sum_{\\mathbf{x}} \\left\\| s_{t'}(\\mathbf{x}, \\mathbf{t}) \\right\\|_1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.842, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Static-dynamic factorization. As physically plausible solutions should have any point in space occupied by either a static or dynamic object, we encourage the spatial ratio of static vs dynamic density to either be 0 or 1 through a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "skewed binary entropy loss that favors static explanations of the scene [56]:" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.132, + 0.892, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} H \\left(\\frac {\\sigma_ {d} (\\mathbf {r} (t))}{\\sigma_ {s} (\\mathbf {r} (t)) + \\sigma_ {d} (\\mathbf {r} (t))} ^ {k}\\right) d t \\tag {28}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.175, + 0.875, + 0.193 + ], + "angle": 0, + "content": "where \\(H(x) = -(x\\cdot \\log (x) + (1 - x)\\cdot \\log (1 - x))\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.204, + 0.892, + 0.237 + ], + "angle": 0, + "content": "and with \\(k\\) set to 1.75, and further penalize the maximum dynamic ratio \\(\\mathcal{L}_d(\\mathbf{r}) = \\max (\\frac{\\sigma_d(\\mathbf{r}(t))}{\\sigma_e + \\sigma_d})\\) along each ray." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.237, + 0.892, + 0.283 + ], + "angle": 0, + "content": "**Shadow loss.** We penalize the squared magnitude of the shadow ratio \\(\\mathcal{L}_{\\rho}(\\mathbf{r}) = \\int_0^{+\\infty}\\rho_d(\\mathbf{r}(t))^2 dt\\) along each ray to prevent it from over-explaining dark regions [56]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.296, + 0.632, + 0.314 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.322, + 0.892, + 0.457 + ], + "angle": 0, + "content": "We demonstrate SUDS's city-scale reconstruction capabilities by presenting quantitative results against baseline methods (Table 1). We also show initial qualitative results for a variety of downstream tasks (Sec. 4.2). Even though we focus on reconstructing dynamic scenes at city scale, to facilitate comparisons with prior work, we also show results on small-scale but highly-benchmarked datasets such as KITTI and Virtual KITTI 2 (Sec. 4.3). We evaluate the various components of our method in Sec. 4.4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.467, + 0.691, + 0.484 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.581 + ], + "angle": 0, + "content": "2D feature extraction. We use Amir et al's feature extractor implementation [5] based on the dino_vits8 model. We downsample our images to fit into GPU memory and then upsample with nearest neighbor interpolation. We L2-normalize the features at the 11th layer of the model and reduce the dimensionality to 64 through incremental PCA [3]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.581, + 0.892, + 0.671 + ], + "angle": 0, + "content": "Flow supervision. We explored using an estimator trained on synthetic data [49] in addition to directly computing 2D correspondences from DINO itself [5]. Although the correspondences are sparse (less than \\(5\\%\\) of pixels) and expensive to compute, we found its estimates more robust and use it for our experiments unless otherwise stated." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.671, + 0.892, + 0.733 + ], + "angle": 0, + "content": "Training. We train SUDS for 250,000 iterations with 4098 rays per batch and use a proposal sampling strategy similar to Mip-NeRF 360 [7] (Sec. B). We use Adam [25] with a learning rate of \\(5 \\times 10^{-3}\\) decaying to \\(5 \\times 10^{-4}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.733, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Metrics. We report quantitative results based on PSNR, SSIM [54], and the AlexNet implementation of LPIPS [64]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.736, + 0.789 + ], + "angle": 0, + "content": "4.2. City-Scale Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "City-1M dataset. We evaluate SUDS's large-scale reconstruction abilities on our collection of 1.28 million images across 1700 videos gathered across a \\(105~km^2\\) urban area using a vehicle-mounted platform with seven ring cameras and two LiDAR sensors. Due to the scale, we supervise optical flow with an off-the-shelf estimator trained on synthetic data [49] instead of DINO for efficiency." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12380" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.096, + 0.216, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.166, + 0.216, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.237, + 0.216, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.307, + 0.167, + 0.317 + ], + "angle": 0, + "content": "RGB" + }, + { + "type": "image", + "bbox": [ + 0.222, + 0.096, + 0.349, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.222, + 0.166, + 0.349, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.222, + 0.237, + 0.349, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.267, + 0.307, + 0.306, + 0.318 + ], + "angle": 0, + "content": "Static" + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.096, + 0.482, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.166, + 0.482, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.237, + 0.482, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.39, + 0.307, + 0.449, + 0.319 + ], + "angle": 0, + "content": "Dynamic" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.096, + 0.616, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.166, + 0.616, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.237, + 0.616, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.307, + 0.584, + 0.318 + ], + "angle": 0, + "content": "Instances" + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.096, + 0.75, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.166, + 0.75, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.237, + 0.75, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.307, + 0.737, + 0.319 + ], + "angle": 0, + "content": "Bounding Boxes" + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.096, + 0.883, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.166, + 0.883, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.237, + 0.883, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.784, + 0.307, + 0.855, + 0.319 + ], + "angle": 0, + "content": "Categories" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.894, + 0.368 + ], + "angle": 0, + "content": "Figure 5. City-1M. We demonstrate SUDS's capabilities on multiple downstream tasks, including instance segmentation and 3D bounding box estimation without any labeled data (by just making use of geometric clustering). In the last column, we show category-level semantic classification by matching 3D (DINO) descriptors to a held-out video annotated with semantic labels. Please see text for more details." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.376, + 0.468, + 0.439 + ], + "angle": 0, + "content": "
Mega-NeRF [52]Mega-NeRF-TMega-NeRF-ASUDS
PSNR ↑16.4216.4616.7021.67
SSIM ↑0.4930.4930.4930.562
LPIPS ↓0.8790.8770.8500.554
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.449, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Table 1. City-scale view synthesis on City-1M. SUDS outperforms all baselines by a wide margin." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.469, + 0.567 + ], + "angle": 0, + "content": "Baselines. We compare SUDS to the official Mega-NeRF [52] implementation alongside two variants: Mega-NeRF-T which directly adds time as an input parameter to compute density and radiance, and Mega-NeRF-A which instead uses the latent embedding \\( A_{\\text{vid}} \\mathcal{F}(t) \\) used by SUDS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.469, + 0.673 + ], + "angle": 0, + "content": "Results. We train both SUDS and the baselines using 48 cells and summarize our results in Table 1. SUDS outperforms all Mega-NeRF variants by a large margin. We provide qualitative results on view synthesis, static/dynamic factorization, unsupervised 3D instance segmentation and unsupervised 3D cuboid detection in Fig. 5. We present additional qualitative tracking results in Fig. 7." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.764 + ], + "angle": 0, + "content": "Instance segmentation. We derive the instance count as in prior work [44] by sampling dynamic density values \\(\\sigma_{d}\\), projecting those above a given threshold onto a discretized ground plane before applying connected component labeling. We apply k-means to obtain 3D centroids and volume render instance predictions as for semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.825 + ], + "angle": 0, + "content": "3D cuboid detection. After computing point-wise instance assignments in 3D, we derive oriented bounding boxes based on the PCA of the convex hull of points belonging to each instance [2]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Semantic segmentation. Note the above tasks of instance segmentation and 3D cuboid detection do not require any additional labels as they make use of geometric clustering. We now show that the representation learned by SUDS can also enable downstream semantic tasks, by making use" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.892, + 0.485 + ], + "angle": 0, + "content": "of a small number of 2D segmentation labels provided on a held-out video sequence. We compute the average 2D DINO descriptor for each semantic class from the held out frames and derive 3D semantic labels for all reconstructions by matching each 3D descriptor to the closest class centroid. This allows to produce 3D semantic label fields that can then be rendered in 2D as shown in Fig. 5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.497, + 0.691, + 0.512 + ], + "angle": 0, + "content": "4.3. KITTI Benchmarks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Baselines. We compare SUDS to SRN [45], the original NeRF implementation [33], a variant of NeRF taking time as an additional input, NSG [37], and PNF [27]. Both NSG and PNF are trained and evaluated using ground truth object bounding box and category-level annotations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.688 + ], + "angle": 0, + "content": "Image reconstruction. We compare SUDS's reconstruction capabilities using the same KITTI [21] subsequences and experimental setup as prior work [27, 37]. We present results in Table 3. As PNF's implementation is not publicly available, we rely on their reported numbers. SUDS surpasses the state-of-the-art in PSNR and SSIM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Novel view synthesis. We demonstrate SUDS's capabilities to generate plausible renderings at time steps unseen during training. As NSG does not handle scenes with ego-motion, we use subsequences of KITTI and Virtual KITTI 2 [18] with little camera movement. We evaluate the methods using different train/test splits, holding out every 4th time step, every other time step, and finally training with only one in every four time steps. We summarize our findings in Table 2 along with qualitative results in Fig. 6. SUDS achieves the best results across all splits and metrics. Both NeRF variants fail to properly represent the scene, especially in dynamic areas. Although we provide NSG with the ground truth object poses at render time, it fails to learn a clean decomposition between objects and the background," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12381" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.092, + 0.257, + 0.233 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.259, + 0.092, + 0.413, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.415, + 0.092, + 0.571, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.092, + 0.728, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.73, + 0.092, + 0.886, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.893, + 0.264 + ], + "angle": 0, + "content": "Figure 6. KITTI and VKITTI2 view synthesis. Prior work fails to represent the scene and NSG [37] renders ghosting artifacts near areas of movement. Our method forecasts plausible trajectories and generates higher-quality renderings." + }, + { + "type": "table", + "bbox": [ + 0.188, + 0.277, + 0.785, + 0.463 + ], + "angle": 0, + "content": "
KITTI - 75%KITTI - 50%KITTI - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.560.5570.55419.120.5870.49718.610.5700.510
NeRF + Time21.010.6120.49221.340.6350.44819.550.5860.505
NSG [37]21.530.6730.25421.260.6590.26620.000.6320.281
SUDS22.770.7970.17123.120.8210.13520.760.7470.198
VKITTI2 - 75%VKITTI2 - 50%VKITTI2 - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.670.5480.63418.580.5440.63518.170.5370.644
NeRF + Time19.030.5740.58718.900.5650.61018.040.5450.626
NSG [37]23.410.6890.31723.230.6790.32521.290.6660.317
SUDS23.870.8460.15023.780.8510.14222.180.8290.160
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.473, + 0.893, + 0.502 + ], + "angle": 0, + "content": "Table 2. Novel View Synthesis. As the fraction of training views decreases, accuracy drops for all methods. However, SUDS consistently outperforms prior work, presumably due to more accurate representations learned by our diverse input signals (such as depth and flow)." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.51, + 0.468, + 0.556 + ], + "angle": 0, + "content": "
SRN [45]NeRF [33]NeRF + TimeNSG [37]PNF [27]Ours
PSNR ↑18.8323.3424.1826.6627.4828.31
SSIM ↑0.5900.6620.6770.8060.8700.876
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.561, + 0.469, + 0.603 + ], + "angle": 0, + "content": "Table 3. KITTI image reconstruction. We outperform past work on image reconstruction accuracy, following their experimental protocol and self-reported accuracies [27, 37]." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.618, + 0.447, + 0.737 + ], + "angle": 0, + "content": "
↑PSNR↑SSIM↓LPIPS
w/o Depth loss22.740.7150.292
w/o Optical flow loss22.180.7080.302
w/o Warping loss17.530.6220.478
w/o Appearance embedding22.540.7040.296
w/o Occlusion weights22.560.7110.297
w/o Separate branches19.730.5700.475
Full Method22.950.7180.289
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.747, + 0.47, + 0.777 + ], + "angle": 0, + "content": "Table 4. Diagnostics. Flow-based warping is the single-most important input, while depth is the least crucial input." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.79, + 0.469, + 0.82 + ], + "angle": 0, + "content": "especially as the number of training view decreases, and generates ghosting artifacts near areas of movement." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.832, + 0.202, + 0.848 + ], + "angle": 0, + "content": "4.4. Diagnostics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.903 + ], + "angle": 0, + "content": "We ablate the importance of major SUDS components by removing their respective loss terms along with occlusion weights, the latent embedding \\( A_{vid}\\mathcal{F}(t) \\) used to compute" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.892, + 0.62 + ], + "angle": 0, + "content": "static color \\(\\mathbf{c}_s\\), and separate model branches (Sec. D). We run all approaches for 125,000 iterations across our datasets and summarize the results in Table 4. Although all components help performance, flow-based warping is by far the single most important input. Interestingly, depth is the least crucial input, suggesting that SUDS can generalize to settings where depth measurements are not available." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.619, + 0.648 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.825 + ], + "angle": 0, + "content": "We present a modular approach towards building dynamic neural representations at previously unexplored scale. Our multi-branch hash table structure enables us to disentangle and efficiently encode static geometry and transient objects across thousands of videos. SUDS makes use of unlabeled inputs to learn semantic awareness and scene flow, allowing it to perform several downstream tasks while surpassing state-of-the-art methods that rely on human labeling. Although we present a first attempt at building city-scale dynamic environments, many open challenges remain ahead of building truly photorealistic representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.838, + 0.66, + 0.856 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.863, + 0.891, + 0.893 + ], + "angle": 0, + "content": "This research was supported by the CMU Argo AI Center for Autonomous Vehicle Research." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12382" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.468, + 0.143 + ], + "angle": 0, + "content": "[1] Kwea123's nsff implementation. https://github.com/kwea123/nsff_pl. 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In ICCV, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "12385" + } + ] +] \ No newline at end of file diff --git a/2023/SUDS_ Scalable Urban Dynamic Scenes/e8fd5f67-d301-4dd3-8588-d4088862c6a6_origin.pdf b/2023/SUDS_ Scalable Urban Dynamic Scenes/e8fd5f67-d301-4dd3-8588-d4088862c6a6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eee11ceb18796d079a01cb52262c3575f8ada2a5 --- /dev/null +++ b/2023/SUDS_ Scalable Urban Dynamic Scenes/e8fd5f67-d301-4dd3-8588-d4088862c6a6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d6cd6a75ba5189a3cb5fc1512e20ab4c1733fdeef16e743f19b69967694f8f96 +size 3224619 diff --git a/2023/SUDS_ Scalable Urban Dynamic Scenes/full.md b/2023/SUDS_ Scalable Urban Dynamic Scenes/full.md new file mode 100644 index 0000000000000000000000000000000000000000..989bd11cbd7bdc5ff0dc7bb05d091d2e6da0fb4f --- /dev/null +++ b/2023/SUDS_ Scalable Urban Dynamic Scenes/full.md @@ -0,0 +1,514 @@ +# SUDS: Scalable Urban Dynamic Scenes + +Haithem Turki $^{1*}$ + +Jason Y. Zhang1 Francesco Ferroni2 +1Carnegie Mellon University 2Argo AI + +Deva Ramanan + +# Abstract + +We extend neural radiance fields (NeRFs) to dynamic large-scale urban scenes. Prior work tends to reconstruct single video clips of short durations (up to 10 seconds). Two reasons are that such methods (a) tend to scale linearly with the number of moving objects and input videos because a separate model is built for each and (b) tend to require supervision via 3D bounding boxes and panoptic labels, obtained manually or via category-specific models. As a step towards truly open-world reconstructions of dynamic cities, we introduce two key innovations: (a) we factorize the scene into three separate hash table data structures to efficiently encode static, dynamic, and far-field radiance fields, and (b) we make use of unlabeled target signals consisting of RGB images, sparse LiDAR, off-the-shelf self-supervised 2D descriptors, and most importantly, 2D optical flow. Operationalizing such inputs via photometric, geometric, and feature-metric reconstruction losses enables SUDS to decompose dynamic scenes into the static background, individual objects, and their motions. When combined with our multi-branch table representation, such reconstructions can be scaled to tens of thousands of objects across 1.2 million frames from 1700 videos spanning geospatial footprints of hundreds of kilometers, (to our knowledge) the largest dynamic NeRF built to date. We present qualitative initial results on a variety of tasks enabled by our representations, including novel-view synthesis of dynamic urban scenes, unsupervised 3D instance segmentation, and unsupervised 3D cuboid detection. To compare to prior work, we also evaluate on KITTI and Virtual KITTI 2, surpassing state-of-the-art methods that rely on ground truth 3D bounding box annotations while being $10x$ quicker to train. + +# 1. Introduction + +Scalable geometric reconstructions of cities have transformed our daily lives, with tools such as Google Maps and Streetview [6] becoming fundamental to how we navigate and interact with our environments. A watershed moment + +![](images/01964bfb55155065d8997891db71fffc5134533c0f250cca5bdd0e8b4efea864.jpg) + +![](images/7c9ff8eb26f531df2c1bfa43ac89ca88f65e0299b30a60ef1efceea11c7996bd.jpg) +RGB + +![](images/e096a475028a54e7d67edf7c034c96c15e6e788b828d011d311aed86c329050e.jpg) +Static + +![](images/050ba20802a276d20785d4adcca705bf7467a903c0b87c7f2ed390904fcb733e.jpg) +Dynamic + +![](images/69aea4796cfb4c00ae9242f1f4952ad7c51876963104409c1826dda1ebca9a78.jpg) +Depth +Figure 1. SUDS. We scale neural reconstructions to city scale by dividing the area into multiple cells and training hash table representations for each. We show our full city-scale reconstruction above and the derived representations below. Unlike prior methods, our approach handles dynamism across multiple videos, disentangling dynamic objects from static background and modeling shadow effects. We use unlabeled inputs to learn scene flow and semantic predictions, enabling category- and object-level scene manipulation. + +![](images/e36231bb1bfac332be4ce29955feca105b22f3f106ef4a5547386934dbce25b0.jpg) +Instances + +![](images/24d9fbd9484517f6493fd2e78c65609c3fbd82433c4250c2e3c301d1bdb53843.jpg) +Flow + +in the development of such technology was the ability to scale structure-from-motion (SfM) algorithms to city-scale footprints [4]. Since then, the advent of Neural Radiance Fields (NeRFs) [33] has transformed this domain by allowing for photorealistic interaction with a reconstructed scene via view synthesis. + +Recent works have attempted to scale such representations to neighborhood-scale reconstructions for virtual drive-throughs [47] and photorealistic fly-throughs [52]. However, these maps remain static and frozen in time. This makes capturing bustling human environments— + +complete with moving vehicles, pedestrians, and objects—impossible, limiting the usefulness of the representation. + +Challenges. One possible solution is a dynamic NeRF that conditions on time or warps a canonical space with a time-dependent deformation [38]. However, reconstructing dynamic scenes is notoriously challenging because the problem is inherently under-constrained, particularly when input data is constrained to limited viewpoints, as is typical from egocentric video capture [20]. One attractive solution is to scale up reconstructions to many videos, perhaps collected at different days (e.g., by an autonomous vehicle fleet). However, this creates additional challenges in jointly modeling fixed geometry that holds for all time (such as buildings), geometry that is locally static but transient across the videos (such as a parked car), and geometry that is truly dynamic (such as a moving person). + +SUDS. In this paper, we propose SUDS: Scalable Urban Dynamic Scenes, a 4D representation that targets both scale and dynamism. Our key insight is twofold; (1) SUDS makes use of a rich suite of informative but freely available input signals, such as LiDAR depth measurements and optical flow. Other dynamic scene representations [27, 37] require supervised inputs such as panoptic segmentation labels or bounding boxes, which are difficult to acquire with high accuracy for our in-the-wild captures. (2) SUDS decomposes the world into 3 components: a static branch that models stationary topography that is consistent across videos, a dynamic branch that handles both transient (e.g., parked cars) and truly dynamic objects (e.g., pedestrians), and an environment map that handles far-field objects and sky. We model each branch using a multi-resolution hash table with scene partitioning, allowing SUDS to scale to an entire city spanning over $100km^2$ . + +Contributions. We make the following contributions: (1) to our knowledge, we build the first large-scale dynamic NeRF, (2) we introduce a scalable three-branch hash table representation for 4D reconstruction, (3) we present state-of-the-art reconstruction on 3 different datasets. Finally, (4) we showcase a variety of downstream tasks enabled by our representation, including free-viewpoint synthesis, 3D scene flow estimation, and even unsupervised instance segmentation and 3D cuboid detection. + +# 2. Related Work + +The original Neural Radiance Fields (NeRF) paper [33] inspired a wide body of follow-up work based on the original approach. Below, we describe a non-exhaustive list of such approaches along axes relevant to our work. + +Scale. The original NeRF operated with bounded scenes. $\mathrm{NeRF}++$ [63] and mip-NeRF 360 [7] use non-linear scene parameterization to model unbounded scenes. However, scaling up the size of the scene with a fixed size MLP leads to blurry details and training instability while the cost of + +naively increasing the size of the MLP quickly becomes intractable. BungeeNeRF [58] introduced a coarse-to-fine approach that progressively adds more capacity to the network representation. Block-NeRF [47] and Mega-NeRF [52] partition the scene spatially and train separate NeRFs for each partition. To model appearance variation, they incorporate per-image embeddings like NeRF-W [31]. Our approach similarly partitions the scene into sub-NeRFs, making use of depth to improve partition efficiency and scaling over an area 200x larger than Block-NeRF's Alamo Square Dataset. Both of these methods work only on static scenes. + +Dynamics. Neural 3D Video Synthesis [28] and Spacetime Neural Irradiance Fields [57] add time as an input to handle dynamic scenes. Similar to our work, NSFF [29], NeRFlow [15], and DyNeRF [19] incorporate 2D optical flow input and warping-based regularization losses to enforce plausible transitions between observed frames. Multiple methods [38-40, 50] instead disentangle scenes into a canonical template and per-frame deformation field. BANMo [60] further incorporates deformable shape models and canonical embeddings to train articulated 3D models from multiple videos. These methods focus on single-object scenes, and all but [28] and [60] use single video sequences. + +While many of the previous works use segmentation data to factorize dynamic from static objects, $\mathrm{D}^2\mathrm{NeRF}$ [56] does this automatically through regularization and explicitly handling shadows. Neural Groundplans [44] uses synthetic data to do this decomposition from a single image. We borrow some of these ideas and scale beyond synthetic and indoor scenes. + +Object-centric approaches. Several approaches [24,36, 37, 59, 61, 62] represent scenes as the composition of per-object NeRF models and a background model. NSG [37] is most similar to us as it also targets automotive data but cannot handle ego-motion as our approach can. None of these methods target multi-video representations and are fundamentally constrained by the memory required to represent each object, with NSG needing over 1TB of memory to represent a 30 second video in our experience. + +Semantics. Follow-up works have explored additional semantic outputs in addition to predicting color. Semantic-NeRF [65] adds an extra head to NeRF that predicts extra semantic category logits for any 3D position. Panoptic-NeRF [16] and Panoptic Neural Fields [27] extend this to produce panoptic segmentations and the latter uses a similar bounding-box based object and background decomposition as NSG. NeSF [53] generalizes the notion of a semantic field to unobserved scenes. As these methods are highly reliant on accurate annotations which are difficult to reliably obtain in the wild at our scale, we instead use a similar approach to recent works [26, 51] that distill the outputs of 2D self-supervised feature descriptors into 3D radiance fields to enable semantic understanding without the use of human + +![](images/2115cc20468636e84ea20b012897f751195182a11986bf04305e67e82931b141.jpg) +(a) Voxel Lookup + +(b) Indexing +Figure 2. Model Architecture. (a) For a given input coordinate, we find the surrounding voxels at $L$ resolution levels for both the static and dynamic branches (far-field branch omitted for clarity). (b) We assign indices to their corners by hashing based on position in the static branch and position, time, and video id in the dynamic branch. We look up the feature vectors corresponding to the corners and interpolate according to the relative position of the input coordinate within the voxel. (c) We concatenate the result of each level, along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch color, density, and feature logits along with scene flow and the shadow ratio. (d) We blend scolor, opacity, and feature logits as the weighted sum of the branches. +![](images/17c096f49089c755a2198c312ca2b0a397ea00c1d31ed00bdac124fbdef2630b.jpg) +$(\mathbf{c},\sigma ,\phi ,s_{\mathbf{t} - 1},s_{\mathbf{t} + 1})$ +(d) Output Blending + +labels and extend them to larger dynamic settings. + +Fast training. The original NeRF took 1-2 days to train. Plenoxels [43] and DVGO [46] directly optimize a voxel representation instead of an MLP to train in minutes or even seconds. TensoRF [11] stores its representation as the outer product of low-rank tensors, reducing memory usage. Instant-NGP [35] takes this further by encoding features in a multi-resolution hash table, allowing training and rendering to happen in real-time. We use these tables as the base block of our three-branch representation and use our own hashing method to support dynamics across multiple videos. + +Depth. Depth provides a valuable supervisory signal for learning high-quality geometry. DS-NeRF [14] and Dense Depth Priors [42] incorporate noisy point clouds obtained by structure from motion (SfM) in the loss function during optimization. Urban Radiance Fields [41] supervises with collected LiDAR data. We also use LiDAR but demonstrate results on dynamic environments. + +# 3. Approach + +# 3.1. Inputs + +Our goal is to learn a global representation that facilitates free-viewpoint rendering, semantic decomposition, and 3D scene flow at arbitrary poses and time steps. Our method takes as input ordered RGB images from $N$ videos (taken at different days with diverse weather and lighting conditions) and their associated camera poses. Crucially, we make use of additional data as "free" sources of supervision given contemporary sensor rigs and feature descriptors. Specifically, we use (1) aligned sparse LiDAR depth measurements, (2) 2D self-supervised pixel (DINO [10]) descriptors to enable semantic manipulation, and (3) 2D optical flow predictions to model scene dynamics. All model inputs are generated without any human labeling or intervention. + +# 3.2. Representation + +Preliminaries. We build upon NeRF [33], which represents a scene within a continuous volumetric radiance field that captures both geometry and view-dependent appearance. It encodes the scene within the weights of a multilayer perceptron (MLP). At render time, NeRF projects a camera ray $\mathbf{r}$ for each image pixel and samples along the ray, querying the MLP at sample position $\mathbf{x}_i$ and ray viewing direction $\mathbf{d}$ to obtain opacity and color values $\sigma_i$ and $\mathbf{c}_i$ . It then composites a color prediction $\hat{C}(\mathbf{r})$ for the ray using numerical quadrature $\sum_{i=0}^{N-1} T_i (1 - \exp(-\sigma_i \delta_i)) \mathbf{c}_i$ , where $T_i = \exp(-\sum_{j=0}^{i-1} \sigma_j \delta_j)$ and $\delta_i$ is the distance between samples. The training process optimizes the model by sampling batches $R$ of image pixels and minimizing the loss function $\sum_{\mathbf{r} \in \mathcal{R}} \|C(\mathbf{r}) - \hat{C}(\mathbf{r})\|^2$ . NeRF samples rays through a two-stage hierarchical sampling process and uses frequency encoding to capture high-frequency details. We refer the reader to [33] for more details. + +Scene composition. To model large-scale dynamic environments, SUDS factorizes the scene into three branches: (a) a static branch containing non-moving topography consistent across videos, (b) a dynamic branch to disentangle video-specific objects [19,29,56], moving or otherwise, and (c) a far-field environment map to represent far-away objects and the sky, which we found important to separately model in large-scale urban scenes [41, 52, 63]. + +However, conventional NeRF training with MLPs is computationally prohibitive at our target scales. Inspired by Instant-NGP [35], we implement each branch using multiresolution hash tables of $F$ -dimensional feature vectors followed by a small MLP, along with our own hash functions to index across videos. + +Hash tables (Fig. 2). For a given input coordinate $(\mathbf{x}, \mathbf{d}, \mathbf{t}, \mathbf{v}\mathbf{id})$ denoting the position $\mathbf{x} \in \mathbb{R}^3$ , viewing direction $\mathbf{d} \in \mathbb{R}^3$ , frame index $F \in \{1, \dots, T\}$ , and video id + +$\mathbf{vid} \in \{1, \dots, N\}$ , we find the surrounding voxels in each table at $l \in L$ resolution levels, doubling the resolution between levels, which we denote as $\mathbf{v}_{l,s}$ , $\mathbf{v}_{l,d}$ , $\mathbf{v}_{l,e}$ for the static, dynamic, and far-field. The static branch makes use of 3D spatial voxels $\mathbf{v}_{l,s}$ , while the dynamic branch makes use of 4D spacetime voxels $\mathbf{v}_{l,d}$ . Finally, the far-field branch makes use of 3D voxels $\mathbf{v}_{l,e}$ (implemented via normalized 3D direction vectors) that index an environment map. Similar to Instant-NGP [35], rather than storing features at voxel corners, we compute hash indices $\mathbf{i}_{l,s}$ (or $\mathbf{i}_{l,d}$ or $\mathbf{i}_{l,e}$ ) for each corner with the following hash functions: + +$$ +\mathbf {i} _ {l, s} = \text {s t a t i c} \operatorname {h a s h} \left(\operatorname {s p a c e} \left(\mathbf {v} _ {l, s}\right)\right) \tag {1} +$$ + +$$ +\mathbf {i} _ {l, d} = \text {d y n a m i c} \text {h a s h} \left(\operatorname {s p a c e} \left(\mathbf {v} _ {l, d}\right), \operatorname {t i m e} \left(\mathbf {v} _ {l, d}\right), \mathbf {v i d}\right) \tag {2} +$$ + +$$ +\mathbf {i} _ {l, e} = \operatorname {e n v} \text {h a s h} (d i r (\mathbf {v} _ {l, e}), \mathbf {v i d}) \tag {3} +$$ + +We linearly interpolate features up to the nearest voxel vertices (but now relying on quadlinear interpolation for the dynamic 4D branch) and rely on gradient averaging to handle hash collisions. Finally, to model the fact that different videos likely contain distinct moving objects and illumination conditions, we add vid as an auxiliary input to the hash, but do not use it for interpolation (since averaging across distinct movers is unnatural). From this perspective, we leverage hashing to effectively index separate interpolating functions for each video, without a linear growth in memory with the number of videos. We concatenate the result of each level into a feature vector $f \in \mathbb{R}^{LF}$ , along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch outputs. + +Static branch. We generate RGB images by combining the outputs of our three branches. The static branch maps the feature vector obtained from the hash table into a view-dependent color $\mathbf{c}_s$ and a view-independent density $\sigma_s$ . To model lighting variations which could be dramatic across videos but smooth within a video, we condition on a latent embedding computed as a product of a video-specific matrix $A_{vid}$ and a fourier-encoded time index $\mathcal{F}(t)$ (as in [60]): + +$$ +\sigma_ {s} (\mathbf {x}) \in \mathbb {R} \tag {4} +$$ + +$$ +\mathbf {c} _ {s} (\mathbf {x}, \mathbf {d}, A _ {v i d} \mathcal {F} (t)) \in \mathbb {R} ^ {3}. \tag {5} +$$ + +Dynamic branch. While the static branch assumes the density $\sigma_{s}$ is static, the dynamic branch allows both the density $\sigma_{d}$ and color $\mathbf{c}_d$ to depend on time (and video). We therefore omit the latent code when computing the dynamic radiance. Because we find shadows to play a crucial role in the appearance of urban scenes (Fig. 3), we explicitly model a shadow field of scalar values $\rho_{d} \in [0,1]$ , used to scale down the static color $\mathbf{c}_{s}$ (as done in [56]): + +$$ +\sigma_ {d} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}) \in \mathbb {R} \tag {6} +$$ + +$$ +\rho_ {d} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}) \in [ 0, 1 ] \tag {7} +$$ + +$$ +\mathbf {c} _ {d} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}, \mathbf {d}) \in \mathbb {R} ^ {3} \tag {8} +$$ + +![](images/2258390509dfbdc42423a3445879c49961bd280d1cdd2e7d80d872fa4c94b01c.jpg) +Full RGB + +![](images/475d43b7394f33e0d40e007f66171a1c5d8634962047e770bc0912bc6be605e8.jpg) +Depth + +![](images/db6b807337ec389d8003b67b92b633a41e3ea1db5215e74ec8dc1fbbba4d6b68.jpg) + +![](images/4c6c00111c9aa75e26bb84c8ce22bb8f1dec8d5fe5c57cce0043822917572831.jpg) +Shadow Intensity + +![](images/fb202257371af8fc8294122fadf3452bcf1de481d6d24e581c50e417a9ea20c7.jpg) +RGB (Without Shadow) +Dynamic RGB + +![](images/3a43ff952cea83ff705997559e5ff404af82dffcd77d72e1c78bf42290172782.jpg) +Static RGB + +![](images/e7620a759b5fade0011f5074b1f5ead4e681e0bdc3f309944a68f4772554f287.jpg) +(a) Shadow Field +Full RGB + +![](images/0da147ef71180f36d145b5a271a1d7e55c892e3343fdde71f219a722f04fe0c7.jpg) +Depth + +![](images/611b40226f8de1f65d58715f355d48c62b15dec8422f74940f62cf57ffd83b9f.jpg) +Dynamic RGB +(b) No Shadow Field +Figure 3. Shadows. We learn an explicit shadow field (a) as a pointwise reduction on static color, enabling better depth reconstruction and static/dynamic factorization than without (b). + +![](images/d7f2ca7ecfd2e798a388d4028236510f1e9cba628074d24f3c54206592dd608e.jpg) +Static RGB + +Far-field branch. Because the sky requires reasoning about far-field radiance and because it can change dramatically across videos, we model far-field radiance with an environment map $\mathbf{c}_e(\mathbf{d},\mathbf{vid})\in \mathbb{R}^3$ that depends on viewing direction d [22,41] and a video id vid. + +Rendering. We derive a single density and radiance value for any position by computing the weighted sum of the static and dynamic components, combined with the pointwise shadow reduction: + +$$ +\begin{array}{l} \sigma (\mathbf {x}, \mathbf {t}, \mathbf {v i d}) = \sigma_ {s} (\mathbf {x}) + \sigma_ {d} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}) (9) \\ \mathbf {c} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}, \mathbf {d}) = \frac {\sigma_ {s}}{\sigma} (1 - \rho_ {d}) \mathbf {c} _ {s} (\mathbf {x}, \mathbf {d}, A _ {v i d} \mathcal {F} (t)) \\ + \frac {\sigma_ {d}}{\sigma} \mathbf {c} _ {d} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}, \mathbf {d}) (10) \\ \end{array} +$$ + +We then calculate the color $\hat{C}$ for a camera ray $\mathbf{r}$ with direction $\mathbf{d}$ at a given frame $\mathbf{t}$ and video vid by accumulating the transmittance along sampled points $\mathbf{r}(t)$ along the ray, forcing the ray to intersect the far-field environment map if it does not hit geometry within the foreground: + +$$ +\begin{array}{l} \hat {C} (\mathbf {r}, \mathbf {t}, \mathbf {v i d}) = \int_ {0} ^ {+ \infty} T (t) \sigma (\mathbf {r} (t), \mathbf {t}, \mathbf {v i d}) \mathbf {c} (\mathbf {r} (t), \mathbf {t}, \mathbf {v i d}, \mathbf {d}) d t \\ + T (+ \infty) \mathbf {c} _ {e} (\mathbf {d}, \mathbf {v i d}), \tag {11} \\ \end{array} +$$ + +$$ +\text {w h e r e} T (t) = \exp \left(- \int_ {0} ^ {t} \sigma (\mathbf {r} (s), \mathbf {t}, \mathbf {v i d}) d s\right). \tag {12} +$$ + +Feature distillation. We build semantic awareness into SUDS to enable the open-world tasks described in Sec. 4.2. Similar to recent work [26, 51], we distill the outputs of a self-supervised 2D feature extractor, namely DINO [10], as a teacher model into our network. For a feature extractor that transforms an image into a dense $\mathbb{R}^{H\times W\times C}$ feature grid, we add a $C$ -dimensional output head to each of our branches: + +$$ +\Phi_ {s} (\mathbf {x}) \in \mathbb {R} ^ {C} \tag {13} +$$ + +$$ +\Phi_ {d} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}) \in \mathbb {R} ^ {C} \tag {14} +$$ + +$$ +\Phi_ {e} (\mathbf {d}, \mathbf {v i d}) \in \mathbb {R} ^ {C}, \tag {15} +$$ + +which are combined into a single value $\Phi$ at any 3D location and rendered into $\hat{F} (\mathbf{r})$ per camera ray, following the equations for color (10, 11). + +Scene flow. We train our model to predict 3D scene flow and model scene dynamics. Inspired by previous work [15, 19, 29], we augment our dynamic branch to predict forward and backward 3D scene flow vectors $s_{t' \in [-1,1]}(\mathbf{x},\mathbf{t},\mathbf{v}\mathbf{i}\mathbf{d}) \in \mathbb{R}^3$ . We make use of these vectors to enforce consistency between observed time steps through multiple loss terms (Sec. 3.3), which we find crucial to generating plausible renderings at novel time steps (Table 4). + +Spatial partitioning. We scale our representation to arbitrarily large environments by decomposing the scene into individually trained models [47, 52], each with its own static, dynamic, and far-field branch. Intuitively, the reconstruction for neighborhood X can be done largely independently of the reconstruction in neighborhood Y, provided one can assign the relevant input data to each reconstruction. To do so, we follow the approach of Mega-NeRF [52] and split the scene into $K$ spatial cells with centroids $k \in \mathbb{R}^3$ . Crucially, we generate separate training datasets for each spatial cell by making use of visibility reasoning [17]. Mega-NeRF includes only those datapoints whose associated camera rays intersect the spatial cell. However, this may still include datapoints that are not visible due to an intervening occluder (e.g., a particular camera in neighborhood X can be pointed at neighborhood Y, but may not see anything there due to occluding buildings). To remedy this, we make use of depth measurements to prune irrelevant pixel rays that do not terminate within the spatial cell of interest (making use of nearest-neighbor interpolation to impute depth for pixels without a LiDAR depth measurement). This further reduces the size of each trainset by $2x$ relative to Mega-NeRF. Finally, given such separate reconstructions, one can still produce a globally consistent rendering by querying the appropriate spatial cell when sampling points along new-view rays (as in [52]). + +# 3.3. Optimization + +We jointly optimize all three of our model branches along with the per-video weight matrices $A_{vid}$ by sampling + +![](images/2a7024a7e00e691345767af43c640f13f5f96f26d3de4fc9fe9f974fda9497a1.jpg) +RGB + +![](images/3fbaeba92db00a5b464fa4f117a99206a1f6cf22aa6046de7f7da0103a2556ec.jpg) +Features + +![](images/224bc2323b4e9664973d63ce94ffb01bd5ab278fc1218290304e54f27e8d7e7e.jpg) +Forward Flow (Input) + +![](images/f05b60bca539e61241d3c3bb1a799f8cbad0037f3e49a687021e742a93821937.jpg) +Backward Flow (Input) + +![](images/8e171a5c0058fb94b641a2ad14d709a069f50bee4ff955cb99b9ff835e1b888b.jpg) +Forward Flow (Predicted) +Figure 4. Scene Flow. We minimize the photometric and feature-metric loss of warped renderings relative to ground truth inputs (top). We use 2D optical flow from off-the-shelf estimators or sparse correspondences computed directly from 2D DINO features [5] (middle) to supervise our flow predictions (bottom). + +![](images/5ec8d986193e1cd8856f7c27b9d34d60bb1f4167023a96529d7368d2a1607d59.jpg) +Backward Flow (Predicted) + +random batches of rays across our $N$ input videos and minimizing the following loss: + +$$ +\mathcal {L} = \underbrace {\left(\mathcal {L} _ {c} + \lambda_ {f} \mathcal {L} _ {f} + \lambda_ {d} \mathcal {L} _ {d} + \lambda_ {o} \mathcal {L} _ {o}\right)} _ {\text {r e c o n s t r u c t i o n l o s s e s}} + \underbrace {\left(\mathcal {L} _ {c} ^ {w} + \lambda_ {f} \mathcal {L} _ {f} ^ {w}\right)} _ {\text {w a r p i n g l o s s e s}} +$$ + +$$ +\lambda_ {f l o} \underbrace {\left(\mathcal {L} _ {c y c} + \mathcal {L} _ {s m} + \mathcal {L} _ {s l o}\right)} _ {\text {f l o w l o s s e s}} + \underbrace {\left(\lambda_ {e} \mathcal {L} _ {e} + \lambda_ {d} \mathcal {L} _ {d}\right)} _ {\text {s t a t i c - d y n a m i c f a c t o r i z a t i o n}} + \lambda_ {\rho} \mathcal {L} _ {\rho} \tag {16} +$$ + +Reconstruction losses. We minimize the L2 photometric loss $\mathcal{L}_c(\mathbf{r}) = \left\| C(\mathbf{r}) - \hat{C} (\mathbf{r})\right\| ^2$ as in the original NeRF equation [33]. We similarly minimize the L1 difference $\mathcal{L}_f(\mathbf{r}) = \left\| F(\mathbf{r}) - \hat{F} (\mathbf{r})\right\| _1$ between the feature outputs of the teacher model and that of our network. + +To make use of our depth measurements, we project the LiDAR sweeps onto the camera plane and compare the expected depth $\hat{D}(r)$ with the measurement $D(\mathbf{r})$ [14, 41]: + +$$ +\mathcal {L} _ {d} (\mathbf {r}) = \left\| D (\mathbf {r}) - \hat {D} (\mathbf {r}) \right\| ^ {2} \tag {17} +$$ + +$$ +\text {w h e r e} \hat {D} (\mathbf {r}) = \int_ {0} ^ {+ \infty} T (s) \sigma (\mathbf {r} (s)) d s \tag {18} +$$ + +Flow. We supervise our 3D scene flow predictions based on 2D optical flow (Sec. 4.1). We generate a 2D displacement vector for each camera ray by first predicting its position in 3D space as the weighted sum of the scene flow neighbors along the ray: + +$$ +\hat {X} _ {t ^ {\prime}} (\mathbf {r}) = \int_ {0} ^ {+ \infty} T (t) \sigma (r (t)) (r (t) + s _ {t ^ {\prime}} (\mathbf {r} (t))) d t \tag {19} +$$ + +which we then "render" into 2D using the camera matrix of the neighboring frame index. We minimize its distance from the observed optical flow via $\mathcal{L}_o(\mathbf{r}) =$ + +$\sum_{t' \in [-1,1]} \left\| X(\mathbf{o}) - \hat{X}_{t'}(\mathbf{r}) \right\|_1$ . We anneal $\lambda_o$ over time as these estimates are noisy. + +3D warping. The above loss ensures that rendered 3D flow will be consistent with the observed 2D flow. We also found it useful to enforce 3D color (and feature) constancy; i.e., colors remain constant even when moving. To do so, we use the predicted forward and backward 3D flow $s_{\mathbf{t} + 1}$ and $s_{\mathbf{t} - 1}$ to advect each sample along the ray into the next/previous frame: + +$$ +\sigma_ {t ^ {\prime}} ^ {w} \left(\mathbf {x} + s _ {t ^ {\prime}}, \mathbf {t} + t ^ {\prime}, \mathbf {v i d}\right) \in \mathbb {R} \tag {20} +$$ + +$$ +\mathbf {c} _ {t ^ {\prime}} ^ {w} \left(\mathbf {x} + s _ {t ^ {\prime}}, \mathbf {t} + t ^ {\prime}, \mathbf {v i d}, \mathbf {d}\right) \in \mathbb {R} ^ {3} \tag {21} +$$ + +$$ +\Phi_ {t ^ {\prime}} ^ {w} \left(\mathbf {x} + s _ {t ^ {\prime}}, \mathbf {t} + t ^ {\prime}, \mathbf {v i d}\right) \in \mathbb {R} ^ {C} \tag {22} +$$ + +The warped radiance $\mathbf{c}^w$ and density $\sigma^w$ are rendered into warped color $\hat{C}^w (\mathbf{r})$ and feature $\hat{F}^{w}(\mathbf{r})$ (10, 11). We add a loss to ensure that the warped color (and feature) match the ground-truth input for the current frame, similar to [19, 29]. As in NSFF [29], we found it important to downweight this loss in ambiguous regions that may contain occlusions. However, instead of learning explicit occlusion weights, we take inspiration from Kwea's method [1] and use the difference between the dynamic geometry and the warped dynamic geometry to downweight the loss: + +$$ +w _ {t ^ {\prime}} (\mathbf {x}, \mathbf {t}, \mathbf {v i d}) = \left| \frac {\sigma_ {d}}{\sigma} - \frac {\sigma_ {t ^ {\prime}} ^ {w}}{\sigma} \right| \tag {23} +$$ + +$$ +\hat {W} _ {t ^ {\prime}} (\mathbf {r}) = \int_ {0} ^ {+ \infty} T (t) \sigma (r (t)) w _ {t ^ {\prime}} (r (t)) d t \tag {24} +$$ + +resulting in the following warping loss terms: + +$$ +\mathcal {L} _ {c} ^ {w} (\mathbf {r}) = \sum_ {t ^ {\prime} \in [ - 1, 1 ]} \left(1 - W _ {t ^ {\prime}}\right) (\mathbf {r})) \| C (\mathbf {r}) - \hat {C} _ {t ^ {\prime}} ^ {w} (\mathbf {r}) \| ^ {2} \tag {25} +$$ + +$$ +\mathcal {L} _ {f} ^ {w} (\mathbf {r}) = \sum_ {t ^ {\prime} \in [ - 1, 1 ]} \left(1 - W _ {t ^ {\prime}}\right) (\mathbf {r}) \| F (\mathbf {r}) - \hat {F} _ {t ^ {\prime}} ^ {w} (\mathbf {r}) \| _ {1} \tag {26} +$$ + +Flow regularization. As in prior work [19, 29] we use a 3D scene flow cycle term to encourage consistency between forward and backward scene flow predictions, downweighting the loss in areas ambiguous due to occlusions: + +$$ +\mathcal {L} _ {\text {c y c}} (\mathbf {r}) = \sum_ {t ^ {\prime} \in [ - 1, 1 ]} \sum_ {\mathbf {x}} w _ {t ^ {\prime}} (\mathbf {x}, \mathbf {t}) \| s _ {t ^ {\prime}} (\mathbf {x}, \mathbf {t}) + s _ {\mathbf {t}} (\mathbf {x} + s _ {t ^ {\prime}}, \mathbf {t} - t ^ {\prime}) \| _ {1}, \tag {27} +$$ + +with $\mathbf{v}\mathbf{id}$ omitted for brevity. We also encourage spatial and temporal smoothness through $\mathcal{L}_{sm}(\mathbf{r})$ as described in Sec. C. We finally regularize the magnitude of predicted scene flow vectors to encourage the scene to be static through $\mathcal{L}_{slo}(\mathbf{r}) = \sum_{t' \in [\mathbf{t} - 1, \mathbf{t} + 1]} \sum_{\mathbf{x}} \left\| s_{t'}(\mathbf{x}, \mathbf{t}) \right\|_1$ . + +Static-dynamic factorization. As physically plausible solutions should have any point in space occupied by either a static or dynamic object, we encourage the spatial ratio of static vs dynamic density to either be 0 or 1 through a + +skewed binary entropy loss that favors static explanations of the scene [56]: + +$$ +\mathcal {L} _ {e} (\mathbf {r}) = \int_ {0} ^ {+ \infty} H \left(\frac {\sigma_ {d} (\mathbf {r} (t))}{\sigma_ {s} (\mathbf {r} (t)) + \sigma_ {d} (\mathbf {r} (t))} ^ {k}\right) d t \tag {28} +$$ + +where $H(x) = -(x\cdot \log (x) + (1 - x)\cdot \log (1 - x))$ + +and with $k$ set to 1.75, and further penalize the maximum dynamic ratio $\mathcal{L}_d(\mathbf{r}) = \max (\frac{\sigma_d(\mathbf{r}(t))}{\sigma_e + \sigma_d})$ along each ray. + +**Shadow loss.** We penalize the squared magnitude of the shadow ratio $\mathcal{L}_{\rho}(\mathbf{r}) = \int_0^{+\infty}\rho_d(\mathbf{r}(t))^2 dt$ along each ray to prevent it from over-explaining dark regions [56]. + +# 4. Experiments + +We demonstrate SUDS's city-scale reconstruction capabilities by presenting quantitative results against baseline methods (Table 1). We also show initial qualitative results for a variety of downstream tasks (Sec. 4.2). Even though we focus on reconstructing dynamic scenes at city scale, to facilitate comparisons with prior work, we also show results on small-scale but highly-benchmarked datasets such as KITTI and Virtual KITTI 2 (Sec. 4.3). We evaluate the various components of our method in Sec. 4.4. + +# 4.1. Experimental Setup + +2D feature extraction. We use Amir et al's feature extractor implementation [5] based on the dino_vits8 model. We downsample our images to fit into GPU memory and then upsample with nearest neighbor interpolation. We L2-normalize the features at the 11th layer of the model and reduce the dimensionality to 64 through incremental PCA [3]. + +Flow supervision. We explored using an estimator trained on synthetic data [49] in addition to directly computing 2D correspondences from DINO itself [5]. Although the correspondences are sparse (less than $5\%$ of pixels) and expensive to compute, we found its estimates more robust and use it for our experiments unless otherwise stated. + +Training. We train SUDS for 250,000 iterations with 4098 rays per batch and use a proposal sampling strategy similar to Mip-NeRF 360 [7] (Sec. B). We use Adam [25] with a learning rate of $5 \times 10^{-3}$ decaying to $5 \times 10^{-4}$ . + +Metrics. We report quantitative results based on PSNR, SSIM [54], and the AlexNet implementation of LPIPS [64]. + +# 4.2. City-Scale Reconstruction + +City-1M dataset. We evaluate SUDS's large-scale reconstruction abilities on our collection of 1.28 million images across 1700 videos gathered across a $105~km^2$ urban area using a vehicle-mounted platform with seven ring cameras and two LiDAR sensors. Due to the scale, we supervise optical flow with an off-the-shelf estimator trained on synthetic data [49] instead of DINO for efficiency. + +![](images/8df0dfe6be2997790f58468a3cbc7dca357df744d6b6f40c855c14eec0cc74b7.jpg) + +![](images/cc097b2c351b75db80bb65847c1a19c22503807e27c109db5273d4e1c3464d71.jpg) + +![](images/cf52da2a5837cbc8fd7d6e29055021810d33e9b096cbc5493a776570f6d822b5.jpg) +RGB + +![](images/d4114256e9f2398b0fda1a7fed17944d07f650c69af8aa7f416eda17d530e4b1.jpg) + +![](images/8568a1aa25c7b96d0d4e56eb88817e0aefd19e56f55db072fba9df81aff87ff1.jpg) + +![](images/0ff6fee8bd16e93bbb4fbba62d7fd957f5e53afc6b20a08b62d4752aaa2a0f66.jpg) +Static + +![](images/6d90dc44c6f5838d15b146f1522dc5bba9665affb09f9878f527337905ce78ce.jpg) + +![](images/9e7bfd186422440fe04d17730d7fe41bb91807b3a204f7804c84aec4fcc3968a.jpg) + +![](images/ed24d910ecc1357bc4b8fb5e13f0bfbbdfe601da8682b731880a648a960d0015.jpg) +Dynamic +Figure 5. City-1M. We demonstrate SUDS's capabilities on multiple downstream tasks, including instance segmentation and 3D bounding box estimation without any labeled data (by just making use of geometric clustering). In the last column, we show category-level semantic classification by matching 3D (DINO) descriptors to a held-out video annotated with semantic labels. Please see text for more details. + +![](images/5ee9d07fa603076c4320d61ae3c7d1ac7f33c4fd779559a1fa9412d04bb5ba5c.jpg) + +![](images/a5670a025b21c14459b75317208777498cdc140c4c4884d0daaa21e4a65de7a5.jpg) + +![](images/ecc1c61c9e302d67e10f224d0685ca209eb628810487f5852fdbebb8eeaa9572.jpg) +Instances + +![](images/d7bd02112856e72e63deedff42e729eab707433be574a97e1a3cb69358d329a6.jpg) + +![](images/c248dd79fc597f30bdbd0c1d569149da36933f3204d118543e907ef60b793c14.jpg) + +![](images/5ff4ed3d63c0c89d293e192a2aae874af8f2cf033f28b1f7bc18b5099918e7ab.jpg) +Bounding Boxes + +![](images/f2bed7aa3cba05c02d3ab1d7a7eb6e8a239ee32a15a173ae0c8ea29b37eb66e5.jpg) + +![](images/d5646887a9fbed2c23897221952a2eb3623aa5aede312f2bacd97e4b73eff1b7.jpg) + +![](images/0e5cac30fe02a77106b4c188c83c7f4206067720a017a95ce1a4a6a11d603b85.jpg) +Categories + +
Mega-NeRF [52]Mega-NeRF-TMega-NeRF-ASUDS
PSNR ↑16.4216.4616.7021.67
SSIM ↑0.4930.4930.4930.562
LPIPS ↓0.8790.8770.8500.554
+ +Table 1. City-scale view synthesis on City-1M. SUDS outperforms all baselines by a wide margin. + +Baselines. We compare SUDS to the official Mega-NeRF [52] implementation alongside two variants: Mega-NeRF-T which directly adds time as an input parameter to compute density and radiance, and Mega-NeRF-A which instead uses the latent embedding $A_{\text{vid}} \mathcal{F}(t)$ used by SUDS. + +Results. We train both SUDS and the baselines using 48 cells and summarize our results in Table 1. SUDS outperforms all Mega-NeRF variants by a large margin. We provide qualitative results on view synthesis, static/dynamic factorization, unsupervised 3D instance segmentation and unsupervised 3D cuboid detection in Fig. 5. We present additional qualitative tracking results in Fig. 7. + +Instance segmentation. We derive the instance count as in prior work [44] by sampling dynamic density values $\sigma_{d}$ , projecting those above a given threshold onto a discretized ground plane before applying connected component labeling. We apply k-means to obtain 3D centroids and volume render instance predictions as for semantic segmentation. + +3D cuboid detection. After computing point-wise instance assignments in 3D, we derive oriented bounding boxes based on the PCA of the convex hull of points belonging to each instance [2]. + +Semantic segmentation. Note the above tasks of instance segmentation and 3D cuboid detection do not require any additional labels as they make use of geometric clustering. We now show that the representation learned by SUDS can also enable downstream semantic tasks, by making use + +of a small number of 2D segmentation labels provided on a held-out video sequence. We compute the average 2D DINO descriptor for each semantic class from the held out frames and derive 3D semantic labels for all reconstructions by matching each 3D descriptor to the closest class centroid. This allows to produce 3D semantic label fields that can then be rendered in 2D as shown in Fig. 5. + +# 4.3. KITTI Benchmarks + +Baselines. We compare SUDS to SRN [45], the original NeRF implementation [33], a variant of NeRF taking time as an additional input, NSG [37], and PNF [27]. Both NSG and PNF are trained and evaluated using ground truth object bounding box and category-level annotations. + +Image reconstruction. We compare SUDS's reconstruction capabilities using the same KITTI [21] subsequences and experimental setup as prior work [27, 37]. We present results in Table 3. As PNF's implementation is not publicly available, we rely on their reported numbers. SUDS surpasses the state-of-the-art in PSNR and SSIM. + +Novel view synthesis. We demonstrate SUDS's capabilities to generate plausible renderings at time steps unseen during training. As NSG does not handle scenes with ego-motion, we use subsequences of KITTI and Virtual KITTI 2 [18] with little camera movement. We evaluate the methods using different train/test splits, holding out every 4th time step, every other time step, and finally training with only one in every four time steps. We summarize our findings in Table 2 along with qualitative results in Fig. 6. SUDS achieves the best results across all splits and metrics. Both NeRF variants fail to properly represent the scene, especially in dynamic areas. Although we provide NSG with the ground truth object poses at render time, it fails to learn a clean decomposition between objects and the background, + +![](images/0b0811b0fd3a88fd6ae696e9e2375759b483a831b470df0627dd610e113644ac.jpg) +Figure 6. KITTI and VKITTI2 view synthesis. Prior work fails to represent the scene and NSG [37] renders ghosting artifacts near areas of movement. Our method forecasts plausible trajectories and generates higher-quality renderings. + +![](images/a77d34d1e624258ccc1650cdd21fc7d3e134f9ff28735add97c20dd6195642e3.jpg) + +![](images/d26d7c683129e2ca788e984cc4fc6393fef78f00cdde419d63492ade41568b2a.jpg) + +![](images/0a40966a327c4d69405391ca932120299b73bb94bedd8ce014fc86c6289e769e.jpg) + +![](images/a4a6b3bcd32535ca0df79e5333a11e9e4eed6da9e5a81a84c09985b3158fc80c.jpg) + +
KITTI - 75%KITTI - 50%KITTI - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.560.5570.55419.120.5870.49718.610.5700.510
NeRF + Time21.010.6120.49221.340.6350.44819.550.5860.505
NSG [37]21.530.6730.25421.260.6590.26620.000.6320.281
SUDS22.770.7970.17123.120.8210.13520.760.7470.198
VKITTI2 - 75%VKITTI2 - 50%VKITTI2 - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.670.5480.63418.580.5440.63518.170.5370.644
NeRF + Time19.030.5740.58718.900.5650.61018.040.5450.626
NSG [37]23.410.6890.31723.230.6790.32521.290.6660.317
SUDS23.870.8460.15023.780.8510.14222.180.8290.160
+ +Table 2. Novel View Synthesis. As the fraction of training views decreases, accuracy drops for all methods. However, SUDS consistently outperforms prior work, presumably due to more accurate representations learned by our diverse input signals (such as depth and flow). + +
SRN [45]NeRF [33]NeRF + TimeNSG [37]PNF [27]Ours
PSNR ↑18.8323.3424.1826.6627.4828.31
SSIM ↑0.5900.6620.6770.8060.8700.876
+ +Table 3. KITTI image reconstruction. We outperform past work on image reconstruction accuracy, following their experimental protocol and self-reported accuracies [27, 37]. + +
↑PSNR↑SSIM↓LPIPS
w/o Depth loss22.740.7150.292
w/o Optical flow loss22.180.7080.302
w/o Warping loss17.530.6220.478
w/o Appearance embedding22.540.7040.296
w/o Occlusion weights22.560.7110.297
w/o Separate branches19.730.5700.475
Full Method22.950.7180.289
+ +Table 4. Diagnostics. Flow-based warping is the single-most important input, while depth is the least crucial input. + +especially as the number of training view decreases, and generates ghosting artifacts near areas of movement. + +# 4.4. Diagnostics + +We ablate the importance of major SUDS components by removing their respective loss terms along with occlusion weights, the latent embedding $A_{vid}\mathcal{F}(t)$ used to compute + +static color $\mathbf{c}_s$ , and separate model branches (Sec. D). We run all approaches for 125,000 iterations across our datasets and summarize the results in Table 4. Although all components help performance, flow-based warping is by far the single most important input. Interestingly, depth is the least crucial input, suggesting that SUDS can generalize to settings where depth measurements are not available. + +# 5. Conclusion + +We present a modular approach towards building dynamic neural representations at previously unexplored scale. Our multi-branch hash table structure enables us to disentangle and efficiently encode static geometry and transient objects across thousands of videos. SUDS makes use of unlabeled inputs to learn semantic awareness and scene flow, allowing it to perform several downstream tasks while surpassing state-of-the-art methods that rely on human labeling. Although we present a first attempt at building city-scale dynamic environments, many open challenges remain ahead of building truly photorealistic representations. + +# Acknowledgments + +This research was supported by the CMU Argo AI Center for Autonomous Vehicle Research. + +# References + +[1] Kwea123's nsff implementation. https://github.com/kwea123/nsff_pl. 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In-place scene labelling and understanding with implicit scene representation. 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Prior work tends to reconstruct single video clips of short durations (up to 10 seconds). Two reasons are that such methods (a) tend to scale linearly with the number of moving objects and input videos because a separate model is built for each and (b) tend to require supervision via 3D bounding boxes and panoptic labels, obtained manually or via category-specific models. As a step towards truly open-world reconstructions of dynamic cities, we introduce two key innovations: (a) we factorize the scene into three separate hash table data structures to efficiently encode static, dynamic, and far-field radiance fields, and (b) we make use of unlabeled target signals consisting of RGB images, sparse LiDAR, off-the-shelf self-supervised 2D descriptors, and most importantly, 2D optical flow. Operationalizing such inputs via photometric, geometric, and feature-metric reconstruction losses enables SUDS to decompose dynamic scenes into the static background, individual objects, and their motions. When combined with our multi-branch table representation, such reconstructions can be scaled to tens of thousands of objects across 1.2 million frames from 1700 videos spanning geospatial footprints of hundreds of kilometers, (to our knowledge) the largest dynamic NeRF built to date. We present qualitative initial results on a variety of tasks enabled by our representations, including novel-view synthesis of dynamic urban scenes, unsupervised 3D instance segmentation, and unsupervised 3D cuboid detection. To compare to prior work, we also evaluate on KITTI and Virtual KITTI 2, surpassing state-of-the-art methods that rely on ground truth 3D bounding box annotations while being " + }, + { + "bbox": [ + 46, + 236, + 290, + 608 + ], + "type": "inline_equation", + "content": "10x" + }, + { + "bbox": [ + 46, + 236, + 290, + 608 + ], + "type": "text", + "content": " quicker to train." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 629, + 128, + 642 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 128, + 642 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 128, + 642 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 649, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 649, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 649, + 287, + 696 + ], + "type": "text", + "content": "Scalable geometric reconstructions of cities have transformed our daily lives, with tools such as Google Maps and Streetview [6] becoming fundamental to how we navigate and interact with our environments. A watershed moment" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 323, + 198, + 518, + 338 + ], + "blocks": [ + { + "bbox": [ + 323, + 198, + 518, + 338 + ], + "lines": [ + { + "bbox": [ + 323, + 198, + 518, + 338 + ], + "spans": [ + { + "bbox": [ + 323, + 198, + 518, + 338 + ], + "type": "image", + "image_path": "01964bfb55155065d8997891db71fffc5134533c0f250cca5bdd0e8b4efea864.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 342, + 383, + 398 + ], + "blocks": [ + { + "bbox": [ + 310, + 342, + 383, + 398 + ], + "lines": [ + { + "bbox": [ + 310, + 342, + 383, + 398 + ], + "spans": [ + { + "bbox": [ + 310, + 342, + 383, + 398 + ], + "type": "image", + "image_path": "7c9ff8eb26f531df2c1bfa43ac89ca88f65e0299b30a60ef1efceea11c7996bd.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 399, + 354, + 405 + ], + "lines": [ + { + "bbox": [ + 340, + 399, + 354, + 405 + ], + "spans": [ + { + "bbox": [ + 340, + 399, + 354, + 405 + ], + "type": "text", + "content": "RGB" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 391, + 343, + 462, + 398 + ], + "blocks": [ + { + "bbox": [ + 391, + 343, + 462, + 398 + ], + "lines": [ + { + "bbox": [ + 391, + 343, + 462, + 398 + ], + "spans": [ + { + "bbox": [ + 391, + 343, + 462, + 398 + ], + "type": "image", + "image_path": "e096a475028a54e7d67edf7c034c96c15e6e788b828d011d311aed86c329050e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 417, + 399, + 435, + 405 + ], + "lines": [ + { + "bbox": [ + 417, + 399, + 435, + 405 + ], + "spans": [ + { + "bbox": [ + 417, + 399, + 435, + 405 + ], + "type": "text", + "content": "Static" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 470, + 343, + 542, + 398 + ], + "blocks": [ + { + "bbox": [ + 470, + 343, + 542, + 398 + ], + "lines": [ + { + "bbox": [ + 470, + 343, + 542, + 398 + ], + "spans": [ + { + "bbox": [ + 470, + 343, + 542, + 398 + ], + "type": "image", + "image_path": "050ba20802a276d20785d4adcca705bf7467a903c0b87c7f2ed390904fcb733e.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 493, + 399, + 518, + 405 + ], + "lines": [ + { + "bbox": [ + 493, + 399, + 518, + 405 + ], + "spans": [ + { + "bbox": [ + 493, + 399, + 518, + 405 + ], + "type": "text", + "content": "Dynamic" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 311, + 406, + 383, + 460 + ], + "blocks": [ + { + "bbox": [ + 311, + 406, + 383, + 460 + ], + "lines": [ + { + "bbox": [ + 311, + 406, + 383, + 460 + ], + "spans": [ + { + "bbox": [ + 311, + 406, + 383, + 460 + ], + "type": "image", + "image_path": "69aea4796cfb4c00ae9242f1f4952ad7c51876963104409c1826dda1ebca9a78.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 460, + 356, + 468 + ], + "lines": [ + { + "bbox": [ + 337, + 460, + 356, + 468 + ], + "spans": [ + { + "bbox": [ + 337, + 460, + 356, + 468 + ], + "type": "text", + "content": "Depth" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 473, + 545, + 571 + ], + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 571 + ], + "type": "text", + "content": "Figure 1. SUDS. We scale neural reconstructions to city scale by dividing the area into multiple cells and training hash table representations for each. We show our full city-scale reconstruction above and the derived representations below. Unlike prior methods, our approach handles dynamism across multiple videos, disentangling dynamic objects from static background and modeling shadow effects. We use unlabeled inputs to learn scene flow and semantic predictions, enabling category- and object-level scene manipulation." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 391, + 406, + 462, + 460 + ], + "blocks": [ + { + "bbox": [ + 391, + 406, + 462, + 460 + ], + "lines": [ + { + "bbox": [ + 391, + 406, + 462, + 460 + ], + "spans": [ + { + "bbox": [ + 391, + 406, + 462, + 460 + ], + "type": "image", + "image_path": "e36231bb1bfac332be4ce29955feca105b22f3f106ef4a5547386934dbce25b0.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 412, + 460, + 440, + 468 + ], + "lines": [ + { + "bbox": [ + 412, + 460, + 440, + 468 + ], + "spans": [ + { + "bbox": [ + 412, + 460, + 440, + 468 + ], + "type": "text", + "content": "Instances" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 470, + 406, + 542, + 460 + ], + "blocks": [ + { + "bbox": [ + 470, + 406, + 542, + 460 + ], + "lines": [ + { + "bbox": [ + 470, + 406, + 542, + 460 + ], + "spans": [ + { + "bbox": [ + 470, + 406, + 542, + 460 + ], + "type": "image", + "image_path": "24d9fbd9484517f6493fd2e78c65609c3fbd82433c4250c2e3c301d1bdb53843.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 498, + 460, + 513, + 468 + ], + "lines": [ + { + "bbox": [ + 498, + 460, + 513, + 468 + ], + "spans": [ + { + "bbox": [ + 498, + 460, + 513, + 468 + ], + "type": "text", + "content": "Flow" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 579, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 651 + ], + "type": "text", + "content": "in the development of such technology was the ability to scale structure-from-motion (SfM) algorithms to city-scale footprints [4]. Since then, the advent of Neural Radiance Fields (NeRFs) [33] has transformed this domain by allowing for photorealistic interaction with a reconstructed scene via view synthesis." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Recent works have attempted to scale such representations to neighborhood-scale reconstructions for virtual drive-throughs [47] and photorealistic fly-throughs [52]. However, these maps remain static and frozen in time. This makes capturing bustling human environments—" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 703, + 181, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 181, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 181, + 712 + ], + "type": "text", + "content": "*Work done as an intern at Argo AI." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12375" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "complete with moving vehicles, pedestrians, and objects—impossible, limiting the usefulness of the representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 287, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 287, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 287, + 263 + ], + "type": "text", + "content": "Challenges. One possible solution is a dynamic NeRF that conditions on time or warps a canonical space with a time-dependent deformation [38]. However, reconstructing dynamic scenes is notoriously challenging because the problem is inherently under-constrained, particularly when input data is constrained to limited viewpoints, as is typical from egocentric video capture [20]. One attractive solution is to scale up reconstructions to many videos, perhaps collected at different days (e.g., by an autonomous vehicle fleet). However, this creates additional challenges in jointly modeling fixed geometry that holds for all time (such as buildings), geometry that is locally static but transient across the videos (such as a parked car), and geometry that is truly dynamic (such as a moving person)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 263, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 287, + 467 + ], + "type": "text", + "content": "SUDS. In this paper, we propose SUDS: Scalable Urban Dynamic Scenes, a 4D representation that targets both scale and dynamism. Our key insight is twofold; (1) SUDS makes use of a rich suite of informative but freely available input signals, such as LiDAR depth measurements and optical flow. Other dynamic scene representations [27, 37] require supervised inputs such as panoptic segmentation labels or bounding boxes, which are difficult to acquire with high accuracy for our in-the-wild captures. (2) SUDS decomposes the world into 3 components: a static branch that models stationary topography that is consistent across videos, a dynamic branch that handles both transient (e.g., parked cars) and truly dynamic objects (e.g., pedestrians), and an environment map that handles far-field objects and sky. We model each branch using a multi-resolution hash table with scene partitioning, allowing SUDS to scale to an entire city spanning over " + }, + { + "bbox": [ + 46, + 263, + 287, + 467 + ], + "type": "inline_equation", + "content": "100km^2" + }, + { + "bbox": [ + 46, + 263, + 287, + 467 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "content": "Contributions. We make the following contributions: (1) to our knowledge, we build the first large-scale dynamic NeRF, (2) we introduce a scalable three-branch hash table representation for 4D reconstruction, (3) we present state-of-the-art reconstruction on 3 different datasets. Finally, (4) we showcase a variety of downstream tasks enabled by our representation, including free-viewpoint synthesis, 3D scene flow estimation, and even unsupervised instance segmentation and 3D cuboid detection." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 134, + 597 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "The original Neural Radiance Fields (NeRF) paper [33] inspired a wide body of follow-up work based on the original approach. Below, we describe a non-exhaustive list of such approaches along axes relevant to our work." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Scale. The original NeRF operated with bounded scenes. " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{NeRF}++" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " [63] and mip-NeRF 360 [7] use non-linear scene parameterization to model unbounded scenes. However, scaling up the size of the scene with a fixed size MLP leads to blurry details and training instability while the cost of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 204 + ], + "type": "text", + "content": "naively increasing the size of the MLP quickly becomes intractable. BungeeNeRF [58] introduced a coarse-to-fine approach that progressively adds more capacity to the network representation. Block-NeRF [47] and Mega-NeRF [52] partition the scene spatially and train separate NeRFs for each partition. To model appearance variation, they incorporate per-image embeddings like NeRF-W [31]. Our approach similarly partitions the scene into sub-NeRFs, making use of depth to improve partition efficiency and scaling over an area 200x larger than Block-NeRF's Alamo Square Dataset. Both of these methods work only on static scenes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 205, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 350 + ], + "type": "text", + "content": "Dynamics. Neural 3D Video Synthesis [28] and Spacetime Neural Irradiance Fields [57] add time as an input to handle dynamic scenes. Similar to our work, NSFF [29], NeRFlow [15], and DyNeRF [19] incorporate 2D optical flow input and warping-based regularization losses to enforce plausible transitions between observed frames. Multiple methods [38-40, 50] instead disentangle scenes into a canonical template and per-frame deformation field. BANMo [60] further incorporates deformable shape models and canonical embeddings to train articulated 3D models from multiple videos. These methods focus on single-object scenes, and all but [28] and [60] use single video sequences." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 350, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 434 + ], + "type": "text", + "content": "While many of the previous works use segmentation data to factorize dynamic from static objects, " + }, + { + "bbox": [ + 304, + 350, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{NeRF}" + }, + { + "bbox": [ + 304, + 350, + 545, + 434 + ], + "type": "text", + "content": " [56] does this automatically through regularization and explicitly handling shadows. Neural Groundplans [44] uses synthetic data to do this decomposition from a single image. We borrow some of these ideas and scale beyond synthetic and indoor scenes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 436, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 544 + ], + "type": "text", + "content": "Object-centric approaches. Several approaches [24,36, 37, 59, 61, 62] represent scenes as the composition of per-object NeRF models and a background model. NSG [37] is most similar to us as it also targets automotive data but cannot handle ego-motion as our approach can. None of these methods target multi-video representations and are fundamentally constrained by the memory required to represent each object, with NSG needing over 1TB of memory to represent a 30 second video in our experience." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Semantics. Follow-up works have explored additional semantic outputs in addition to predicting color. Semantic-NeRF [65] adds an extra head to NeRF that predicts extra semantic category logits for any 3D position. Panoptic-NeRF [16] and Panoptic Neural Fields [27] extend this to produce panoptic segmentations and the latter uses a similar bounding-box based object and background decomposition as NSG. NeSF [53] generalizes the notion of a semantic field to unobserved scenes. As these methods are highly reliant on accurate annotations which are difficult to reliably obtain in the wild at our scale, we instead use a similar approach to recent works [26, 51] that distill the outputs of 2D self-supervised feature descriptors into 3D radiance fields to enable semantic understanding without the use of human" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12376" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 68, + 218, + 177 + ], + "blocks": [ + { + "bbox": [ + 107, + 68, + 218, + 177 + ], + "lines": [ + { + "bbox": [ + 107, + 68, + 218, + 177 + ], + "spans": [ + { + "bbox": [ + 107, + 68, + 218, + 177 + ], + "type": "image", + "image_path": "2115cc20468636e84ea20b012897f751195182a11986bf04305e67e82931b141.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 132, + 178, + 192, + 188 + ], + "lines": [ + { + "bbox": [ + 132, + 178, + 192, + 188 + ], + "spans": [ + { + "bbox": [ + 132, + 178, + 192, + 188 + ], + "type": "text", + "content": "(a) Voxel Lookup" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 235, + 68, + 410, + 178 + ], + "blocks": [ + { + "bbox": [ + 235, + 68, + 410, + 178 + ], + "lines": [ + { + "bbox": [ + 235, + 68, + 410, + 178 + ], + "spans": [ + { + "bbox": [ + 235, + 68, + 410, + 178 + ], + "type": "image", + "image_path": "17c096f49089c755a2198c312ca2b0a397ea00c1d31ed00bdac124fbdef2630b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 245, + 179, + 288, + 190 + ], + "lines": [ + { + "bbox": [ + 245, + 179, + 288, + 190 + ], + "spans": [ + { + "bbox": [ + 245, + 179, + 288, + 190 + ], + "type": "text", + "content": "(b) Indexing" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 430, + 117, + 507, + 128 + ], + "lines": [ + { + "bbox": [ + 430, + 117, + 507, + 128 + ], + "spans": [ + { + "bbox": [ + 430, + 117, + 507, + 128 + ], + "type": "inline_equation", + "content": "(\\mathbf{c},\\sigma ,\\phi ,s_{\\mathbf{t} - 1},s_{\\mathbf{t} + 1})" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 433, + 130, + 504, + 140 + ], + "lines": [ + { + "bbox": [ + 433, + 130, + 504, + 140 + ], + "spans": [ + { + "bbox": [ + 433, + 130, + 504, + 140 + ], + "type": "text", + "content": "(d) Output Blending" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 46, + 198, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 547, + 266 + ], + "type": "text", + "content": "Figure 2. Model Architecture. (a) For a given input coordinate, we find the surrounding voxels at " + }, + { + "bbox": [ + 46, + 198, + 547, + 266 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 198, + 547, + 266 + ], + "type": "text", + "content": " resolution levels for both the static and dynamic branches (far-field branch omitted for clarity). (b) We assign indices to their corners by hashing based on position in the static branch and position, time, and video id in the dynamic branch. We look up the feature vectors corresponding to the corners and interpolate according to the relative position of the input coordinate within the voxel. (c) We concatenate the result of each level, along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch color, density, and feature logits along with scene flow and the shadow ratio. (d) We blend scolor, opacity, and feature logits as the weighted sum of the branches." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 275, + 249, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 249, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 249, + 287 + ], + "type": "text", + "content": "labels and extend them to larger dynamic settings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 289, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 409 + ], + "type": "text", + "content": "Fast training. The original NeRF took 1-2 days to train. Plenoxels [43] and DVGO [46] directly optimize a voxel representation instead of an MLP to train in minutes or even seconds. TensoRF [11] stores its representation as the outer product of low-rank tensors, reducing memory usage. Instant-NGP [35] takes this further by encoding features in a multi-resolution hash table, allowing training and rendering to happen in real-time. We use these tables as the base block of our three-branch representation and use our own hashing method to support dynamics across multiple videos." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 411, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 288, + 495 + ], + "type": "text", + "content": "Depth. Depth provides a valuable supervisory signal for learning high-quality geometry. DS-NeRF [14] and Dense Depth Priors [42] incorporate noisy point clouds obtained by structure from motion (SfM) in the loss function during optimization. Urban Radiance Fields [41] supervises with collected LiDAR data. We also use LiDAR but demonstrate results on dynamic environments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 514, + 113, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 113, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 113, + 528 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 536, + 100, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 100, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 100, + 550 + ], + "type": "text", + "content": "3.1. Inputs" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "Our goal is to learn a global representation that facilitates free-viewpoint rendering, semantic decomposition, and 3D scene flow at arbitrary poses and time steps. Our method takes as input ordered RGB images from " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " videos (taken at different days with diverse weather and lighting conditions) and their associated camera poses. Crucially, we make use of additional data as \"free\" sources of supervision given contemporary sensor rigs and feature descriptors. Specifically, we use (1) aligned sparse LiDAR depth measurements, (2) 2D self-supervised pixel (DINO [10]) descriptors to enable semantic manipulation, and (3) 2D optical flow predictions to model scene dynamics. All model inputs are generated without any human labeling or intervention." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 274, + 400, + 287 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 400, + 287 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 400, + 287 + ], + "type": "text", + "content": "3.2. Representation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": "Preliminaries. We build upon NeRF [33], which represents a scene within a continuous volumetric radiance field that captures both geometry and view-dependent appearance. It encodes the scene within the weights of a multilayer perceptron (MLP). At render time, NeRF projects a camera ray " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " for each image pixel and samples along the ray, querying the MLP at sample position " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " and ray viewing direction " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " to obtain opacity and color values " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\sigma_i" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": ". It then composites a color prediction " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\hat{C}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " for the ray using numerical quadrature " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\sum_{i=0}^{N-1} T_i (1 - \\exp(-\\sigma_i \\delta_i)) \\mathbf{c}_i" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "T_i = \\exp(-\\sum_{j=0}^{i-1} \\sigma_j \\delta_j)" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\delta_i" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " is the distance between samples. The training process optimizes the model by sampling batches " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": " of image pixels and minimizing the loss function " + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "inline_equation", + "content": "\\sum_{\\mathbf{r} \\in \\mathcal{R}} \\|C(\\mathbf{r}) - \\hat{C}(\\mathbf{r})\\|^2" + }, + { + "bbox": [ + 304, + 294, + 545, + 503 + ], + "type": "text", + "content": ". NeRF samples rays through a two-stage hierarchical sampling process and uses frequency encoding to capture high-frequency details. We refer the reader to [33] for more details." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": "Scene composition. To model large-scale dynamic environments, SUDS factorizes the scene into three branches: (a) a static branch containing non-moving topography consistent across videos, (b) a dynamic branch to disentangle video-specific objects [19,29,56], moving or otherwise, and (c) a far-field environment map to represent far-away objects and the sky, which we found important to separately model in large-scale urban scenes [41, 52, 63]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": "However, conventional NeRF training with MLPs is computationally prohibitive at our target scales. Inspired by Instant-NGP [35], we implement each branch using multiresolution hash tables of " + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 603, + 545, + 674 + ], + "type": "text", + "content": "-dimensional feature vectors followed by a small MLP, along with our own hash functions to index across videos." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": "Hash tables (Fig. 2). For a given input coordinate " + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}, \\mathbf{d}, \\mathbf{t}, \\mathbf{v}\\mathbf{id})" + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": " denoting the position " + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": ", viewing direction " + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{d} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": ", frame index " + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "inline_equation", + "content": "F \\in \\{1, \\dots, T\\}" + }, + { + "bbox": [ + 305, + 677, + 547, + 714 + ], + "type": "text", + "content": ", and video id" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12377" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{vid} \\in \\{1, \\dots, N\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", we find the surrounding voxels in each table at " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "l \\in L" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " resolution levels, doubling the resolution between levels, which we denote as " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l,s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l,d}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l,e}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " for the static, dynamic, and far-field. The static branch makes use of 3D spatial voxels " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l,s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ", while the dynamic branch makes use of 4D spacetime voxels " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l,d}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ". Finally, the far-field branch makes use of 3D voxels " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_{l,e}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " (implemented via normalized 3D direction vectors) that index an environment map. Similar to Instant-NGP [35], rather than storing features at voxel corners, we compute hash indices " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{i}_{l,s}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{i}_{l,d}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{i}_{l,e}" + }, + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": ") for each corner with the following hash functions:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 210, + 287, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 210, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 58, + 210, + 287, + 223 + ], + "type": "interline_equation", + "content": "\\mathbf {i} _ {l, s} = \\text {s t a t i c} \\operatorname {h a s h} \\left(\\operatorname {s p a c e} \\left(\\mathbf {v} _ {l, s}\\right)\\right) \\tag {1}", + "image_path": "122fb9d990fddbf2f538a0978e447c6fa4efe066d1ef4abcaabeefe1f4e008c6.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 225, + 287, + 238 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 225, + 287, + 238 + ], + "spans": [ + { + "bbox": [ + 58, + 225, + 287, + 238 + ], + "type": "interline_equation", + "content": "\\mathbf {i} _ {l, d} = \\text {d y n a m i c} \\text {h a s h} \\left(\\operatorname {s p a c e} \\left(\\mathbf {v} _ {l, d}\\right), \\operatorname {t i m e} \\left(\\mathbf {v} _ {l, d}\\right), \\mathbf {v i d}\\right) \\tag {2}", + "image_path": "beb6d352142ee9ec203fccb53cce9ee7337ee2eb3b92737faaef9bb5394b3de7.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 240, + 287, + 253 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 240, + 287, + 253 + ], + "spans": [ + { + "bbox": [ + 59, + 240, + 287, + 253 + ], + "type": "interline_equation", + "content": "\\mathbf {i} _ {l, e} = \\operatorname {e n v} \\text {h a s h} (d i r (\\mathbf {v} _ {l, e}), \\mathbf {v i d}) \\tag {3}", + "image_path": "f7bb0e7113b537ee78d09dcff53ad3f101a8ee20943939224821bf2c4505326e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 259, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 287, + 426 + ], + "type": "text", + "content": "We linearly interpolate features up to the nearest voxel vertices (but now relying on quadlinear interpolation for the dynamic 4D branch) and rely on gradient averaging to handle hash collisions. Finally, to model the fact that different videos likely contain distinct moving objects and illumination conditions, we add vid as an auxiliary input to the hash, but do not use it for interpolation (since averaging across distinct movers is unnatural). From this perspective, we leverage hashing to effectively index separate interpolating functions for each video, without a linear growth in memory with the number of videos. We concatenate the result of each level into a feature vector " + }, + { + "bbox": [ + 46, + 259, + 287, + 426 + ], + "type": "inline_equation", + "content": "f \\in \\mathbb{R}^{LF}" + }, + { + "bbox": [ + 46, + 259, + 287, + 426 + ], + "type": "text", + "content": ", along with auxiliary inputs such as viewing direction, and pass the resulting vector into an MLP to obtain per-branch outputs." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "text", + "content": "Static branch. We generate RGB images by combining the outputs of our three branches. The static branch maps the feature vector obtained from the hash table into a view-dependent color " + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_s" + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "text", + "content": " and a view-independent density " + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\sigma_s" + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "text", + "content": ". To model lighting variations which could be dramatic across videos but smooth within a video, we condition on a latent embedding computed as a product of a video-specific matrix " + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "inline_equation", + "content": "A_{vid}" + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "text", + "content": " and a fourier-encoded time index " + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(t)" + }, + { + "bbox": [ + 46, + 426, + 287, + 523 + ], + "type": "text", + "content": " (as in [60]):" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 114, + 529, + 287, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 114, + 529, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 114, + 529, + 287, + 541 + ], + "type": "interline_equation", + "content": "\\sigma_ {s} (\\mathbf {x}) \\in \\mathbb {R} \\tag {4}", + "image_path": "2db7d67368eb6e1d6e1eab44cc76791b7e4ffc16d815ac2f53c93b2bccd48212.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 544, + 287, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 544, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 115, + 544, + 287, + 558 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {s} (\\mathbf {x}, \\mathbf {d}, A _ {v i d} \\mathcal {F} (t)) \\in \\mathbb {R} ^ {3}. \\tag {5}", + "image_path": "de9d1aa522e22ee15e5bd5f89ea9bac2bbf4906541b6f8ccbff6c030577496b3.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "content": "Dynamic branch. While the static branch assumes the density " + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "inline_equation", + "content": "\\sigma_{s}" + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "content": " is static, the dynamic branch allows both the density " + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "inline_equation", + "content": "\\sigma_{d}" + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "content": " and color " + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_d" + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "content": " to depend on time (and video). We therefore omit the latent code when computing the dynamic radiance. Because we find shadows to play a crucial role in the appearance of urban scenes (Fig. 3), we explicitly model a shadow field of scalar values " + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "inline_equation", + "content": "\\rho_{d} \\in [0,1]" + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "content": ", used to scale down the static color " + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{s}" + }, + { + "bbox": [ + 46, + 564, + 287, + 660 + ], + "type": "text", + "content": " (as done in [56]):" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 124, + 666, + 287, + 678 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 666, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 124, + 666, + 287, + 678 + ], + "type": "interline_equation", + "content": "\\sigma_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in \\mathbb {R} \\tag {6}", + "image_path": "f29cb25aba77d033c9fde13b6444d2a2951530570595dfde2c47da966710a4c3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 125, + 681, + 287, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 681, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 125, + 681, + 287, + 694 + ], + "type": "interline_equation", + "content": "\\rho_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in [ 0, 1 ] \\tag {7}", + "image_path": "17cb0d13bd4b482d56787791f08b586200cc960ae61e85426993dfaa9b3be495.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 125, + 696, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 696, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 125, + 696, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) \\in \\mathbb {R} ^ {3} \\tag {8}", + "image_path": 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Shadows. We learn an explicit shadow field (a) as a pointwise reduction on static color, enabling better depth reconstruction and static/dynamic factorization than without (b)." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 428, + 272, + 505, + 312 + ], + "blocks": [ + { + "bbox": [ + 428, + 272, + 505, + 312 + ], + "lines": [ + { + "bbox": [ + 428, + 272, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 428, + 272, + 505, + 312 + ], + "type": "image", + "image_path": "d7f2ca7ecfd2e798a388d4028236510f1e9cba628074d24f3c54206592dd608e.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 454, + 312, + 480, + 318 + ], + "lines": [ + { + "bbox": [ + 454, + 312, + 480, + 318 + ], + "spans": [ + { + "bbox": [ + 454, + 312, + 480, + 318 + ], + "type": "text", + "content": "Static RGB" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_caption" + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 381, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 545, + 441 + ], + "type": "text", + "content": "Far-field branch. Because the sky requires reasoning about far-field radiance and because it can change dramatically across videos, we model far-field radiance with an environment map " + }, + { + "bbox": [ + 304, + 381, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_e(\\mathbf{d},\\mathbf{vid})\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 381, + 545, + 441 + ], + "type": "text", + "content": " that depends on viewing direction d [22,41] and a video id vid." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 441, + 545, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 489 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 489 + ], + "type": "text", + "content": "Rendering. We derive a single density and radiance value for any position by computing the weighted sum of the static and dynamic components, combined with the pointwise shadow reduction:" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 330, + 500, + 545, + 558 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 500, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 330, + 500, + 545, + 558 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\sigma (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) = \\sigma_ {s} (\\mathbf {x}) + \\sigma_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) (9) \\\\ \\mathbf {c} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) = \\frac {\\sigma_ {s}}{\\sigma} (1 - \\rho_ {d}) \\mathbf {c} _ {s} (\\mathbf {x}, \\mathbf {d}, A _ {v i d} \\mathcal {F} (t)) \\\\ + \\frac {\\sigma_ {d}}{\\sigma} \\mathbf {c} _ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) (10) \\\\ \\end{array}", + "image_path": "5fb11073c9a17105a9d510839f150a8b558a44548dabe5eab2f85c6016cf06e9.jpg" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "content": "We then calculate the color " + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\hat{C}" + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "content": " for a camera ray " + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "content": " with direction " + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "content": " at a given frame " + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "content": " and video vid by accumulating the transmittance along sampled points " + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t)" + }, + { + "bbox": [ + 304, + 569, + 545, + 630 + ], + "type": "text", + "content": " along the ray, forcing the ray to intersect the far-field environment map if it does not hit geometry within the foreground:" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 308, + 639, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 639, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 308, + 639, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {C} (\\mathbf {r}, \\mathbf {t}, \\mathbf {v i d}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (\\mathbf {r} (t), \\mathbf {t}, \\mathbf {v i d}) \\mathbf {c} (\\mathbf {r} (t), \\mathbf {t}, \\mathbf {v i d}, \\mathbf {d}) d t \\\\ + T (+ \\infty) \\mathbf {c} _ {e} (\\mathbf {d}, \\mathbf {v i d}), \\tag {11} \\\\ \\end{array}", + "image_path": "5ef30eb4dbb771c9e00a789de6c694598aa099bd819e3930d5af815f545e9b73.jpg" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 309, + 684, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 684, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 309, + 684, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} T (t) = \\exp \\left(- \\int_ {0} ^ {t} \\sigma (\\mathbf {r} (s), \\mathbf {t}, \\mathbf {v i d}) d s\\right). \\tag {12}", + "image_path": "3eb5d8c56dcf35398404432724e005c888606e7880df1a00a470b5729076c65e.jpg" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "12378" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "type": "text", + "content": "Feature distillation. We build semantic awareness into SUDS to enable the open-world tasks described in Sec. 4.2. Similar to recent work [26, 51], we distill the outputs of a self-supervised 2D feature extractor, namely DINO [10], as a teacher model into our network. For a feature extractor that transforms an image into a dense " + }, + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H\\times W\\times C}" + }, + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "type": "text", + "content": " feature grid, we add a " + }, + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 72, + 289, + 167 + ], + "type": "text", + "content": "-dimensional output head to each of our branches:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 127, + 171, + 286, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 171, + 286, + 186 + ], + "spans": [ + { + "bbox": [ + 127, + 171, + 286, + 186 + ], + "type": "interline_equation", + "content": "\\Phi_ {s} (\\mathbf {x}) \\in \\mathbb {R} ^ {C} \\tag {13}", + "image_path": "3e23b02e964dd13a37658e8ecd7a2c8f9c208dd047407144e9a37d7abdcd048f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 127, + 188, + 286, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 188, + 286, + 201 + ], + "spans": [ + { + "bbox": [ + 127, + 188, + 286, + 201 + ], + "type": "interline_equation", + "content": "\\Phi_ {d} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) \\in \\mathbb {R} ^ {C} \\tag {14}", + "image_path": "18e97c2c00267e56e853178338a89e0c6010948169f3756e9d92f89b608cab15.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 127, + 204, + 286, + 218 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 204, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 127, + 204, + 286, + 218 + ], + "type": "interline_equation", + "content": "\\Phi_ {e} (\\mathbf {d}, \\mathbf {v i d}) \\in \\mathbb {R} ^ {C}, \\tag {15}", + "image_path": "329058396c3b7d611e5ca8e937bafa7430e89ca009c86bee32c1b222296ce607.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "type": "text", + "content": "which are combined into a single value " + }, + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "type": "text", + "content": " at any 3D location and rendered into " + }, + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "type": "inline_equation", + "content": "\\hat{F} (\\mathbf{r})" + }, + { + "bbox": [ + 47, + 223, + 286, + 258 + ], + "type": "text", + "content": " per camera ray, following the equations for color (10, 11)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 259, + 286, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 286, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 286, + 354 + ], + "type": "text", + "content": "Scene flow. We train our model to predict 3D scene flow and model scene dynamics. Inspired by previous work [15, 19, 29], we augment our dynamic branch to predict forward and backward 3D scene flow vectors " + }, + { + "bbox": [ + 47, + 259, + 286, + 354 + ], + "type": "inline_equation", + "content": "s_{t' \\in [-1,1]}(\\mathbf{x},\\mathbf{t},\\mathbf{v}\\mathbf{i}\\mathbf{d}) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 259, + 286, + 354 + ], + "type": "text", + "content": ". We make use of these vectors to enforce consistency between observed time steps through multiple loss terms (Sec. 3.3), which we find crucial to generating plausible renderings at novel time steps (Table 4)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "text", + "content": "Spatial partitioning. We scale our representation to arbitrarily large environments by decomposing the scene into individually trained models [47, 52], each with its own static, dynamic, and far-field branch. Intuitively, the reconstruction for neighborhood X can be done largely independently of the reconstruction in neighborhood Y, provided one can assign the relevant input data to each reconstruction. To do so, we follow the approach of Mega-NeRF [52] and split the scene into " + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "text", + "content": " spatial cells with centroids " + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "inline_equation", + "content": "k \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "text", + "content": ". Crucially, we generate separate training datasets for each spatial cell by making use of visibility reasoning [17]. Mega-NeRF includes only those datapoints whose associated camera rays intersect the spatial cell. However, this may still include datapoints that are not visible due to an intervening occluder (e.g., a particular camera in neighborhood X can be pointed at neighborhood Y, but may not see anything there due to occluding buildings). To remedy this, we make use of depth measurements to prune irrelevant pixel rays that do not terminate within the spatial cell of interest (making use of nearest-neighbor interpolation to impute depth for pixels without a LiDAR depth measurement). This further reduces the size of each trainset by " + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "inline_equation", + "content": "2x" + }, + { + "bbox": [ + 47, + 355, + 287, + 666 + ], + "type": "text", + "content": " relative to Mega-NeRF. Finally, given such separate reconstructions, one can still produce a globally consistent rendering by querying the appropriate spatial cell when sampling points along new-view rays (as in [52])." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 671, + 132, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 132, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 132, + 683 + ], + "type": "text", + "content": "3.3. Optimization" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": "We jointly optimize all three of our model branches along with the per-video weight matrices " + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "A_{vid}" + }, + { + "bbox": [ + 47, + 689, + 286, + 714 + ], + "type": "text", + "content": " by sampling" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 332, + 72, + 421, + 121 + ], + "blocks": [ + { + "bbox": [ + 332, + 72, + 421, + 121 + ], + "lines": [ + { + "bbox": [ + 332, + 72, + 421, + 121 + ], + "spans": [ + { + "bbox": [ + 332, + 72, + 421, + 121 + ], + "type": "image", + "image_path": "2a7024a7e00e691345767af43c640f13f5f96f26d3de4fc9fe9f974fda9497a1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 121, + 383, + 126 + ], + "lines": [ + { + "bbox": [ + 370, + 121, + 383, + 126 + ], + "spans": [ + { + "bbox": [ + 370, + 121, + 383, + 126 + ], + "type": "text", + "content": "RGB" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 427, + 72, + 517, + 121 + ], + "blocks": [ + { + "bbox": [ + 427, + 72, + 517, + 121 + ], + "lines": [ + { + "bbox": [ + 427, + 72, + 517, + 121 + ], + "spans": [ + { + "bbox": [ + 427, + 72, + 517, + 121 + ], + "type": "image", + "image_path": "3fbaeba92db00a5b464fa4f117a99206a1f6cf22aa6046de7f7da0103a2556ec.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 460, + 121, + 485, + 127 + ], + "lines": [ + { + "bbox": [ + 460, + 121, + 485, + 127 + ], + "spans": [ + { + "bbox": [ + 460, + 121, + 485, + 127 + ], + "type": "text", + "content": "Features" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 332, + 127, + 421, + 175 + ], + "blocks": [ + { + "bbox": [ + 332, + 127, + 421, + 175 + ], + "lines": [ + { + "bbox": [ + 332, + 127, + 421, + 175 + ], + "spans": [ + { + "bbox": [ + 332, + 127, + 421, + 175 + ], + "type": "image", + "image_path": "224bc2323b4e9664973d63ce94ffb01bd5ab278fc1218290304e54f27e8d7e7e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 348, + 175, + 406, + 181 + ], + "lines": [ + { + "bbox": [ + 348, + 175, + 406, + 181 + ], + "spans": [ + { + "bbox": [ + 348, + 175, + 406, + 181 + ], + "type": "text", + "content": "Forward Flow (Input)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 427, + 127, + 517, + 175 + ], + "blocks": [ + { + "bbox": [ + 427, + 127, + 517, + 175 + ], + "lines": [ + { + "bbox": [ + 427, + 127, + 517, + 175 + ], + "spans": [ + { + "bbox": [ + 427, + 127, + 517, + 175 + ], + "type": "image", + "image_path": "f05b60bca539e61241d3c3bb1a799f8cbad0037f3e49a687021e742a93821937.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 442, + 175, + 504, + 181 + ], + "lines": [ + { + "bbox": [ + 442, + 175, + 504, + 181 + ], + "spans": [ + { + "bbox": [ + 442, + 175, + 504, + 181 + ], + "type": "text", + "content": "Backward Flow (Input)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 332, + 181, + 421, + 229 + ], + "blocks": [ + { + "bbox": [ + 332, + 181, + 421, + 229 + ], + "lines": [ + { + "bbox": [ + 332, + 181, + 421, + 229 + ], + "spans": [ + { + "bbox": [ + 332, + 181, + 421, + 229 + ], + "type": "image", + "image_path": "8e171a5c0058fb94b641a2ad14d709a069f50bee4ff955cb99b9ff835e1b888b.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 229, + 411, + 236 + ], + "lines": [ + { + "bbox": [ + 343, + 229, + 411, + 236 + ], + "spans": [ + { + "bbox": [ + 343, + 229, + 411, + 236 + ], + "type": "text", + "content": "Forward Flow (Predicted)" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 242, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 305, + 242, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 242, + 545, + 297 + ], + "type": "text", + "content": "Figure 4. Scene Flow. We minimize the photometric and feature-metric loss of warped renderings relative to ground truth inputs (top). We use 2D optical flow from off-the-shelf estimators or sparse correspondences computed directly from 2D DINO features [5] (middle) to supervise our flow predictions (bottom)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 427, + 181, + 517, + 229 + ], + "blocks": [ + { + "bbox": [ + 427, + 181, + 517, + 229 + ], + "lines": [ + { + "bbox": [ + 427, + 181, + 517, + 229 + ], + "spans": [ + { + "bbox": [ + 427, + 181, + 517, + 229 + ], + "type": "image", + "image_path": "5ec8d986193e1cd8856f7c27b9d34d60bb1f4167023a96529d7368d2a1607d59.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 229, + 509, + 236 + ], + "lines": [ + { + "bbox": [ + 436, + 229, + 509, + 236 + ], + "spans": [ + { + "bbox": [ + 436, + 229, + 509, + 236 + ], + "type": "text", + "content": "Backward Flow (Predicted)" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "content": "random batches of rays across our " + }, + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "content": " input videos and minimizing the following loss:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 334, + 529, + 370 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 529, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 529, + 370 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\underbrace {\\left(\\mathcal {L} _ {c} + \\lambda_ {f} \\mathcal {L} _ {f} + \\lambda_ {d} \\mathcal {L} _ {d} + \\lambda_ {o} \\mathcal {L} _ {o}\\right)} _ {\\text {r e c o n s t r u c t i o n l o s s e s}} + \\underbrace {\\left(\\mathcal {L} _ {c} ^ {w} + \\lambda_ {f} \\mathcal {L} _ {f} ^ {w}\\right)} _ {\\text {w a r p i n g l o s s e s}}", + "image_path": "3bfc8e217c254a32504f9ff00632244aea05741bf52dae327efdf084cb5115e6.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 312, + 372, + 548, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 372, + 548, + 418 + ], + "spans": [ + { + "bbox": [ + 312, + 372, + 548, + 418 + ], + "type": "interline_equation", + "content": "\\lambda_ {f l o} \\underbrace {\\left(\\mathcal {L} _ {c y c} + \\mathcal {L} _ {s m} + \\mathcal {L} _ {s l o}\\right)} _ {\\text {f l o w l o s s e s}} + \\underbrace {\\left(\\lambda_ {e} \\mathcal {L} _ {e} + \\lambda_ {d} \\mathcal {L} _ {d}\\right)} _ {\\text {s t a t i c - d y n a m i c f a c t o r i z a t i o n}} + \\lambda_ {\\rho} \\mathcal {L} _ {\\rho} \\tag {16}", + "image_path": "4c733415bf4419fc85f532c247586c3000a4ca45ebc086a35ea63ab9ff324e10.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "text", + "content": "Reconstruction losses. We minimize the L2 photometric loss " + }, + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c(\\mathbf{r}) = \\left\\| C(\\mathbf{r}) - \\hat{C} (\\mathbf{r})\\right\\| ^2" + }, + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "text", + "content": " as in the original NeRF equation [33]. We similarly minimize the L1 difference " + }, + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_f(\\mathbf{r}) = \\left\\| F(\\mathbf{r}) - \\hat{F} (\\mathbf{r})\\right\\| _1" + }, + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "text", + "content": " between the feature outputs of the teacher model and that of our network." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "type": "text", + "content": "To make use of our depth measurements, we project the LiDAR sweeps onto the camera plane and compare the expected depth " + }, + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\hat{D}(r)" + }, + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "type": "text", + "content": " with the measurement " + }, + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "type": "inline_equation", + "content": "D(\\mathbf{r})" + }, + { + "bbox": [ + 305, + 481, + 545, + 517 + ], + "type": "text", + "content": " [14, 41]:" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 349, + 525, + 544, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 525, + 544, + 541 + ], + "spans": [ + { + "bbox": [ + 349, + 525, + 544, + 541 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d} (\\mathbf {r}) = \\left\\| D (\\mathbf {r}) - \\hat {D} (\\mathbf {r}) \\right\\| ^ {2} \\tag {17}", + "image_path": "58f05c601aa8ba97718799f95daba9b29391c87441be4e9c0006929ffb0a5fdd.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 350, + 543, + 544, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 543, + 544, + 570 + ], + "spans": [ + { + "bbox": [ + 350, + 543, + 544, + 570 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\hat {D} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (s) \\sigma (\\mathbf {r} (s)) d s \\tag {18}", + "image_path": "670cb1b55464b8d28081329bf95e9cec3c4c29ddede12ae5c5ed13ea3b03b49a.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 576, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 576, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 305, + 576, + 545, + 636 + ], + "type": "text", + "content": "Flow. We supervise our 3D scene flow predictions based on 2D optical flow (Sec. 4.1). We generate a 2D displacement vector for each camera ray by first predicting its position in 3D space as the weighted sum of the scene flow neighbors along the ray:" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 318, + 643, + 545, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 643, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 318, + 643, + 545, + 670 + ], + "type": "interline_equation", + "content": "\\hat {X} _ {t ^ {\\prime}} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (r (t)) (r (t) + s _ {t ^ {\\prime}} (\\mathbf {r} (t))) d t \\tag {19}", + "image_path": "c0d7654bdb791815fb449dce50bacf8625fe10b2cf09228ceb22ade508d46995.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "which we then \"render\" into 2D using the camera matrix of the neighboring frame index. We minimize its distance from the observed optical flow via " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_o(\\mathbf{r}) =" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12379" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\sum_{t' \\in [-1,1]} \\left\\| X(\\mathbf{o}) - \\hat{X}_{t'}(\\mathbf{r}) \\right\\|_1" + }, + { + "bbox": [ + 47, + 71, + 287, + 95 + ], + "type": "text", + "content": ". We anneal " + }, + { + "bbox": [ + 47, + 71, + 287, + 95 + ], + "type": "inline_equation", + "content": "\\lambda_o" + }, + { + "bbox": [ + 47, + 71, + 287, + 95 + ], + "type": "text", + "content": " over time as these estimates are noisy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "type": "text", + "content": "3D warping. The above loss ensures that rendered 3D flow will be consistent with the observed 2D flow. We also found it useful to enforce 3D color (and feature) constancy; i.e., colors remain constant even when moving. To do so, we use the predicted forward and backward 3D flow " + }, + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "type": "inline_equation", + "content": "s_{\\mathbf{t} + 1}" + }, + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "type": "inline_equation", + "content": "s_{\\mathbf{t} - 1}" + }, + { + "bbox": [ + 47, + 96, + 287, + 180 + ], + "type": "text", + "content": " to advect each sample along the ray into the next/previous frame:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 102, + 189, + 286, + 202 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 189, + 286, + 202 + ], + "spans": [ + { + "bbox": [ + 102, + 189, + 286, + 202 + ], + "type": "interline_equation", + "content": "\\sigma_ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}\\right) \\in \\mathbb {R} \\tag {20}", + "image_path": "fde204cc619ea120aac4bf90549484dd727c150de207e3a24e1a66dcaee016b5.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 103, + 205, + 286, + 219 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 205, + 286, + 219 + ], + "spans": [ + { + "bbox": [ + 103, + 205, + 286, + 219 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}, \\mathbf {d}\\right) \\in \\mathbb {R} ^ {3} \\tag {21}", + "image_path": "49563618c5b301233ccfc6584537955d0d3ae12b4a2bb2b14c1903ef4f9149a0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 221, + 286, + 236 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 221, + 286, + 236 + ], + "spans": [ + { + "bbox": [ + 104, + 221, + 286, + 236 + ], + "type": "interline_equation", + "content": "\\Phi_ {t ^ {\\prime}} ^ {w} \\left(\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} + t ^ {\\prime}, \\mathbf {v i d}\\right) \\in \\mathbb {R} ^ {C} \\tag {22}", + "image_path": "ed11eea96a800b00e67dc15625f8fe599d4adb95d4c309262286381b76b2e7a9.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "text", + "content": "The warped radiance " + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^w" + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "text", + "content": " and density " + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\sigma^w" + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "text", + "content": " are rendered into warped color " + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\hat{C}^w (\\mathbf{r})" + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "text", + "content": " and feature " + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "inline_equation", + "content": "\\hat{F}^{w}(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 244, + 287, + 365 + ], + "type": "text", + "content": " (10, 11). We add a loss to ensure that the warped color (and feature) match the ground-truth input for the current frame, similar to [19, 29]. As in NSFF [29], we found it important to downweight this loss in ambiguous regions that may contain occlusions. However, instead of learning explicit occlusion weights, we take inspiration from Kwea's method [1] and use the difference between the dynamic geometry and the warped dynamic geometry to downweight the loss:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 84, + 372, + 287, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 372, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 84, + 372, + 287, + 399 + ], + "type": "interline_equation", + "content": "w _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}, \\mathbf {v i d}) = \\left| \\frac {\\sigma_ {d}}{\\sigma} - \\frac {\\sigma_ {t ^ {\\prime}} ^ {w}}{\\sigma} \\right| \\tag {23}", + "image_path": "f36a732fc9913811498649bbc69405057379a7f86f2de76a91dbbf249bff543e.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 85, + 401, + 287, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 401, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 85, + 401, + 287, + 428 + ], + "type": "interline_equation", + "content": "\\hat {W} _ {t ^ {\\prime}} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} T (t) \\sigma (r (t)) w _ {t ^ {\\prime}} (r (t)) d t \\tag {24}", + "image_path": "93dba646dd9b55793d50fcf6756914e93583af6f02613fe07ff62997f247332c.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 435, + 243, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 435, + 243, + 448 + ], + "spans": [ + { + "bbox": [ + 59, + 435, + 243, + 448 + ], + "type": "text", + "content": "resulting in the following warping loss terms:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 56, + 456, + 287, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 456, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 56, + 456, + 287, + 483 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c} ^ {w} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\left(1 - W _ {t ^ {\\prime}}\\right) (\\mathbf {r})) \\| C (\\mathbf {r}) - \\hat {C} _ {t ^ {\\prime}} ^ {w} (\\mathbf {r}) \\| ^ {2} \\tag {25}", + "image_path": "1c0e396d5a227a9c1426a2ca82a30491f8ec027836f33eb94014607227364ca5.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 486, + 287, + 513 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 486, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 56, + 486, + 287, + 513 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f} ^ {w} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\left(1 - W _ {t ^ {\\prime}}\\right) (\\mathbf {r}) \\| F (\\mathbf {r}) - \\hat {F} _ {t ^ {\\prime}} ^ {w} (\\mathbf {r}) \\| _ {1} \\tag {26}", + "image_path": "9a91625174043610c5f64a5daf4101bef8ea2fc72d7357fca077d1359c5a6947.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 569 + ], + "type": "text", + "content": "Flow regularization. As in prior work [19, 29] we use a 3D scene flow cycle term to encourage consistency between forward and backward scene flow predictions, downweighting the loss in areas ambiguous due to occlusions:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 52, + 574, + 287, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 574, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 52, + 574, + 287, + 605 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c y c}} (\\mathbf {r}) = \\sum_ {t ^ {\\prime} \\in [ - 1, 1 ]} \\sum_ {\\mathbf {x}} w _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}) \\| s _ {t ^ {\\prime}} (\\mathbf {x}, \\mathbf {t}) + s _ {\\mathbf {t}} (\\mathbf {x} + s _ {t ^ {\\prime}}, \\mathbf {t} - t ^ {\\prime}) \\| _ {1}, \\tag {27}", + "image_path": "9e390cd8bae45afd976f69cc04453efe1addaf6671157ffd4a0d0194ce9703b0.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{v}\\mathbf{id}" + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "text", + "content": " omitted for brevity. We also encourage spatial and temporal smoothness through " + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sm}(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "text", + "content": " as described in Sec. C. We finally regularize the magnitude of predicted scene flow vectors to encourage the scene to be static through " + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{slo}(\\mathbf{r}) = \\sum_{t' \\in [\\mathbf{t} - 1, \\mathbf{t} + 1]} \\sum_{\\mathbf{x}} \\left\\| s_{t'}(\\mathbf{x}, \\mathbf{t}) \\right\\|_1" + }, + { + "bbox": [ + 47, + 605, + 287, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "content": "Static-dynamic factorization. As physically plausible solutions should have any point in space occupied by either a static or dynamic object, we encourage the spatial ratio of static vs dynamic density to either be 0 or 1 through a" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "skewed binary entropy loss that favors static explanations of the scene [56]:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 316, + 104, + 545, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 104, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 316, + 104, + 545, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e} (\\mathbf {r}) = \\int_ {0} ^ {+ \\infty} H \\left(\\frac {\\sigma_ {d} (\\mathbf {r} (t))}{\\sigma_ {s} (\\mathbf {r} (t)) + \\sigma_ {d} (\\mathbf {r} (t))} ^ {k}\\right) d t \\tag {28}", + "image_path": "d2a0f90760e83d895c9d79ae38e3ecc497c46e8c2c779b66753692c50fb5de18.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 138, + 535, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 138, + 535, + 152 + ], + "spans": [ + { + "bbox": [ + 317, + 138, + 535, + 152 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 317, + 138, + 535, + 152 + ], + "type": "inline_equation", + "content": "H(x) = -(x\\cdot \\log (x) + (1 - x)\\cdot \\log (1 - x))" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "type": "text", + "content": "and with " + }, + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "type": "text", + "content": " set to 1.75, and further penalize the maximum dynamic ratio " + }, + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_d(\\mathbf{r}) = \\max (\\frac{\\sigma_d(\\mathbf{r}(t))}{\\sigma_e + \\sigma_d})" + }, + { + "bbox": [ + 305, + 161, + 545, + 187 + ], + "type": "text", + "content": " along each ray." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 187, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 187, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 187, + 545, + 224 + ], + "type": "text", + "content": "**Shadow loss.** We penalize the squared magnitude of the shadow ratio " + }, + { + "bbox": [ + 305, + 187, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\rho}(\\mathbf{r}) = \\int_0^{+\\infty}\\rho_d(\\mathbf{r}(t))^2 dt" + }, + { + "bbox": [ + 305, + 187, + 545, + 224 + ], + "type": "text", + "content": " along each ray to prevent it from over-explaining dark regions [56]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 234, + 386, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 234, + 386, + 248 + ], + "spans": [ + { + "bbox": [ + 306, + 234, + 386, + 248 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 255, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 545, + 361 + ], + "type": "text", + "content": "We demonstrate SUDS's city-scale reconstruction capabilities by presenting quantitative results against baseline methods (Table 1). We also show initial qualitative results for a variety of downstream tasks (Sec. 4.2). Even though we focus on reconstructing dynamic scenes at city scale, to facilitate comparisons with prior work, we also show results on small-scale but highly-benchmarked datasets such as KITTI and Virtual KITTI 2 (Sec. 4.3). We evaluate the various components of our method in Sec. 4.4." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 369, + 422, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 422, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 422, + 383 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 388, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 460 + ], + "type": "text", + "content": "2D feature extraction. We use Amir et al's feature extractor implementation [5] based on the dino_vits8 model. We downsample our images to fit into GPU memory and then upsample with nearest neighbor interpolation. We L2-normalize the features at the 11th layer of the model and reduce the dimensionality to 64 through incremental PCA [3]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 460, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 531 + ], + "type": "text", + "content": "Flow supervision. We explored using an estimator trained on synthetic data [49] in addition to directly computing 2D correspondences from DINO itself [5]. Although the correspondences are sparse (less than " + }, + { + "bbox": [ + 305, + 460, + 545, + 531 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 305, + 460, + 545, + 531 + ], + "type": "text", + "content": " of pixels) and expensive to compute, we found its estimates more robust and use it for our experiments unless otherwise stated." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "spans": [ + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "type": "text", + "content": "Training. We train SUDS for 250,000 iterations with 4098 rays per batch and use a proposal sampling strategy similar to Mip-NeRF 360 [7] (Sec. B). We use Adam [25] with a learning rate of " + }, + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-3}" + }, + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "type": "text", + "content": " decaying to " + }, + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 305, + 531, + 545, + 580 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 580, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 580, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 580, + 545, + 604 + ], + "type": "text", + "content": "Metrics. We report quantitative results based on PSNR, SSIM [54], and the AlexNet implementation of LPIPS [64]." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 611, + 450, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 450, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 450, + 624 + ], + "type": "text", + "content": "4.2. City-Scale Reconstruction" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": "City-1M dataset. We evaluate SUDS's large-scale reconstruction abilities on our collection of 1.28 million images across 1700 videos gathered across a " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "105~km^2" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " urban area using a vehicle-mounted platform with seven ring cameras and two LiDAR sensors. Due to the scale, we supervise optical flow with an off-the-shelf estimator trained on synthetic data [49] instead of DINO for efficiency." + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12380" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 76, + 132, + 129 + ], + "blocks": [ + { + "bbox": [ + 53, + 76, + 132, + 129 + ], + "lines": [ + { + "bbox": [ + 53, + 76, + 132, + 129 + ], + "spans": [ + { + "bbox": [ + 53, + 76, + 132, + 129 + ], + "type": "image", + "image_path": "8df0dfe6be2997790f58468a3cbc7dca357df744d6b6f40c855c14eec0cc74b7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + 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"Categories" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "table", + "bbox": [ + 52, + 297, + 286, + 347 + ], + "blocks": [ + { + "bbox": [ + 52, + 297, + 286, + 347 + ], + "lines": [ + { + "bbox": [ + 52, + 297, + 286, + 347 + ], + "spans": [ + { + "bbox": [ + 52, + 297, + 286, + 347 + ], + "type": "table", + "html": "
Mega-NeRF [52]Mega-NeRF-TMega-NeRF-ASUDS
PSNR ↑16.4216.4616.7021.67
SSIM ↑0.4930.4930.4930.562
LPIPS ↓0.8790.8770.8500.554
", + "image_path": "361df755f210b5ac7e727eb74ff36c92f186272a445f3f7d5b786ac085173ada.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "table_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 47, + 355, + 287, + 378 + ], + "lines": [ + { + "bbox": [ + 47, + 355, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 355, + 287, + 378 + ], + "type": "text", + "content": "Table 1. City-scale view synthesis on City-1M. SUDS outperforms all baselines by a wide margin." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 388, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 449 + ], + "type": "text", + "content": "Baselines. We compare SUDS to the official Mega-NeRF [52] implementation alongside two variants: Mega-NeRF-T which directly adds time as an input parameter to compute density and radiance, and Mega-NeRF-A which instead uses the latent embedding " + }, + { + "bbox": [ + 46, + 388, + 287, + 449 + ], + "type": "inline_equation", + "content": "A_{\\text{vid}} \\mathcal{F}(t)" + }, + { + "bbox": [ + 46, + 388, + 287, + 449 + ], + "type": "text", + "content": " used by SUDS." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 449, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 533 + ], + "type": "text", + "content": "Results. We train both SUDS and the baselines using 48 cells and summarize our results in Table 1. SUDS outperforms all Mega-NeRF variants by a large margin. We provide qualitative results on view synthesis, static/dynamic factorization, unsupervised 3D instance segmentation and unsupervised 3D cuboid detection in Fig. 5. We present additional qualitative tracking results in Fig. 7." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 533, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 605 + ], + "type": "text", + "content": "Instance segmentation. We derive the instance count as in prior work [44] by sampling dynamic density values " + }, + { + "bbox": [ + 46, + 533, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\sigma_{d}" + }, + { + "bbox": [ + 46, + 533, + 287, + 605 + ], + "type": "text", + "content": ", projecting those above a given threshold onto a discretized ground plane before applying connected component labeling. We apply k-means to obtain 3D centroids and volume render instance predictions as for semantic segmentation." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 653 + ], + "type": "text", + "content": "3D cuboid detection. After computing point-wise instance assignments in 3D, we derive oriented bounding boxes based on the PCA of the convex hull of points belonging to each instance [2]." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Semantic segmentation. Note the above tasks of instance segmentation and 3D cuboid detection do not require any additional labels as they make use of geometric clustering. We now show that the representation learned by SUDS can also enable downstream semantic tasks, by making use" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 300, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 384 + ], + "type": "text", + "content": "of a small number of 2D segmentation labels provided on a held-out video sequence. We compute the average 2D DINO descriptor for each semantic class from the held out frames and derive 3D semantic labels for all reconstructions by matching each 3D descriptor to the closest class centroid. This allows to produce 3D semantic label fields that can then be rendered in 2D as shown in Fig. 5." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 393, + 422, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 393, + 422, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 393, + 422, + 405 + ], + "type": "text", + "content": "4.3. KITTI Benchmarks" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 413, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 545, + 472 + ], + "type": "text", + "content": "Baselines. We compare SUDS to SRN [45], the original NeRF implementation [33], a variant of NeRF taking time as an additional input, NSG [37], and PNF [27]. Both NSG and PNF are trained and evaluated using ground truth object bounding box and category-level annotations." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 474, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 544 + ], + "type": "text", + "content": "Image reconstruction. We compare SUDS's reconstruction capabilities using the same KITTI [21] subsequences and experimental setup as prior work [27, 37]. We present results in Table 3. As PNF's implementation is not publicly available, we rely on their reported numbers. SUDS surpasses the state-of-the-art in PSNR and SSIM." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 546, + 713 + ], + "type": "text", + "content": "Novel view synthesis. We demonstrate SUDS's capabilities to generate plausible renderings at time steps unseen during training. As NSG does not handle scenes with ego-motion, we use subsequences of KITTI and Virtual KITTI 2 [18] with little camera movement. We evaluate the methods using different train/test splits, holding out every 4th time step, every other time step, and finally training with only one in every four time steps. We summarize our findings in Table 2 along with qualitative results in Fig. 6. SUDS achieves the best results across all splits and metrics. Both NeRF variants fail to properly represent the scene, especially in dynamic areas. Although we provide NSG with the ground truth object poses at render time, it fails to learn a clean decomposition between objects and the background," + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12381" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 157, + 184 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 157, + 184 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 157, + 184 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 157, + 184 + ], + "type": "image", + "image_path": "0b0811b0fd3a88fd6ae696e9e2375759b483a831b470df0627dd610e113644ac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 546, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 546, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 546, + 209 + ], + "type": "text", + "content": "Figure 6. KITTI and VKITTI2 view synthesis. Prior work fails to represent the scene and NSG [37] renders ghosting artifacts near areas of movement. Our method forecasts plausible trajectories and generates higher-quality renderings." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 158, + 72, + 252, + 183 + ], + "blocks": [ + { + "bbox": [ + 158, + 72, + 252, + 183 + ], + "lines": [ + { + "bbox": [ + 158, + 72, + 252, + 183 + ], + "spans": [ + { + "bbox": [ + 158, + 72, + 252, + 183 + ], + "type": "image", + "image_path": "a77d34d1e624258ccc1650cdd21fc7d3e134f9ff28735add97c20dd6195642e3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 253, + 72, + 349, + 183 + ], + "blocks": [ + { + "bbox": [ + 253, + 72, + 349, + 183 + ], + "lines": [ + { + "bbox": [ + 253, + 72, + 349, + 183 + ], + "spans": [ + { + "bbox": [ + 253, + 72, + 349, + 183 + ], + "type": "image", + "image_path": "d26d7c683129e2ca788e984cc4fc6393fef78f00cdde419d63492ade41568b2a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 350, + 72, + 445, + 183 + ], + "blocks": [ + { + "bbox": [ + 350, + 72, + 445, + 183 + ], + "lines": [ + { + "bbox": [ + 350, + 72, + 445, + 183 + ], + "spans": [ + { + "bbox": [ + 350, + 72, + 445, + 183 + ], + "type": "image", + "image_path": "0a40966a327c4d69405391ca932120299b73bb94bedd8ce014fc86c6289e769e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 446, + 72, + 542, + 183 + ], + "blocks": [ + { + "bbox": [ + 446, + 72, + 542, + 183 + ], + "lines": [ + { + "bbox": [ + 446, + 72, + 542, + 183 + ], + "spans": [ + { + "bbox": [ + 446, + 72, + 542, + 183 + ], + "type": "image", + "image_path": "a4a6b3bcd32535ca0df79e5333a11e9e4eed6da9e5a81a84c09985b3158fc80c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 115, + 219, + 480, + 366 + ], + "blocks": [ + { + "bbox": [ + 115, + 219, + 480, + 366 + ], + "lines": [ + { + "bbox": [ + 115, + 219, + 480, + 366 + ], + "spans": [ + { + "bbox": [ + 115, + 219, + 480, + 366 + ], + "type": "table", + "html": "
KITTI - 75%KITTI - 50%KITTI - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.560.5570.55419.120.5870.49718.610.5700.510
NeRF + Time21.010.6120.49221.340.6350.44819.550.5860.505
NSG [37]21.530.6730.25421.260.6590.26620.000.6320.281
SUDS22.770.7970.17123.120.8210.13520.760.7470.198
VKITTI2 - 75%VKITTI2 - 50%VKITTI2 - 25%
↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS↑PSNR↑SSIM↓LPIPS
NeRF [33]18.670.5480.63418.580.5440.63518.170.5370.644
NeRF + Time19.030.5740.58718.900.5650.61018.040.5450.626
NSG [37]23.410.6890.31723.230.6790.32521.290.6660.317
SUDS23.870.8460.15023.780.8510.14222.180.8290.160
", + "image_path": "e3fe5eb61e0dcfcd2428fc30733879aa738cac6bf4a02734ca0f0b4c8e6ab06c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 52, + 403, + 286, + 440 + ], + "blocks": [ + { + "bbox": [ + 46, + 374, + 546, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 374, + 546, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 546, + 397 + ], + "type": "text", + "content": "Table 2. Novel View Synthesis. As the fraction of training views decreases, accuracy drops for all methods. However, SUDS consistently outperforms prior work, presumably due to more accurate representations learned by our diverse input signals (such as depth and flow)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 403, + 286, + 440 + ], + "lines": [ + { + "bbox": [ + 52, + 403, + 286, + 440 + ], + "spans": [ + { + "bbox": [ + 52, + 403, + 286, + 440 + ], + "type": "table", + "html": "
SRN [45]NeRF [33]NeRF + TimeNSG [37]PNF [27]Ours
PSNR ↑18.8323.3424.1826.6627.4828.31
SSIM ↑0.5900.6620.6770.8060.8700.876
", + "image_path": "3659e69fe9c743691417cc64c1bb9363aefd9fce764aa7d8c5429f3e1b43b23d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 61, + 489, + 273, + 583 + ], + "blocks": [ + { + "bbox": [ + 47, + 444, + 287, + 477 + ], + "lines": [ + { + "bbox": [ + 47, + 444, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 287, + 477 + ], + "type": "text", + "content": "Table 3. KITTI image reconstruction. We outperform past work on image reconstruction accuracy, following their experimental protocol and self-reported accuracies [27, 37]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 489, + 273, + 583 + ], + "lines": [ + { + "bbox": [ + 61, + 489, + 273, + 583 + ], + "spans": [ + { + "bbox": [ + 61, + 489, + 273, + 583 + ], + "type": "table", + "html": "
↑PSNR↑SSIM↓LPIPS
w/o Depth loss22.740.7150.292
w/o Optical flow loss22.180.7080.302
w/o Warping loss17.530.6220.478
w/o Appearance embedding22.540.7040.296
w/o Occlusion weights22.560.7110.297
w/o Separate branches19.730.5700.475
Full Method22.950.7180.289
", + "image_path": "04c0bd0b661fa238c5c5fc7296b78e28e2cd21270d51616648ac25bd6e17a7ab.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 591, + 287, + 615 + ], + "lines": [ + { + "bbox": [ + 47, + 591, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 287, + 615 + ], + "type": "text", + "content": "Table 4. Diagnostics. Flow-based warping is the single-most important input, while depth is the least crucial input." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 625, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 287, + 649 + ], + "type": "text", + "content": "especially as the number of training view decreases, and generates ghosting artifacts near areas of movement." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 658, + 123, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 123, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 123, + 671 + ], + "type": "text", + "content": "4.4. Diagnostics" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "We ablate the importance of major SUDS components by removing their respective loss terms along with occlusion weights, the latent embedding " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "A_{vid}\\mathcal{F}(t)" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " used to compute" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 406, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 545, + 491 + ], + "type": "text", + "content": "static color " + }, + { + "bbox": [ + 304, + 406, + 545, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_s" + }, + { + "bbox": [ + 304, + 406, + 545, + 491 + ], + "type": "text", + "content": ", and separate model branches (Sec. D). We run all approaches for 125,000 iterations across our datasets and summarize the results in Table 4. Although all components help performance, flow-based warping is by far the single most important input. Interestingly, depth is the least crucial input, suggesting that SUDS can generalize to settings where depth measurements are not available." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 501, + 378, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 378, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 378, + 513 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 521, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 653 + ], + "type": "text", + "content": "We present a modular approach towards building dynamic neural representations at previously unexplored scale. Our multi-branch hash table structure enables us to disentangle and efficiently encode static geometry and transient objects across thousands of videos. SUDS makes use of unlabeled inputs to learn semantic awareness and scene flow, allowing it to perform several downstream tasks while surpassing state-of-the-art methods that rely on human labeling. Although we present a first attempt at building city-scale dynamic environments, many open challenges remain ahead of building truly photorealistic representations." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 663, + 403, + 677 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 663, + 403, + 677 + ], + "spans": [ + { + "bbox": [ + 306, + 663, + 403, + 677 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 683, + 545, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 683, + 545, + 707 + ], + "spans": [ + { + "bbox": [ + 305, + 683, + 545, + 707 + ], + "type": "text", + "content": "This research was supported by the CMU Argo AI Center for Autonomous Vehicle Research." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12382" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "text", + "content": "[1] Kwea123's nsff implementation. https://github.com/kwea123/nsff_pl. 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Info. Processing, School of CS, Fudan University", + "bbox": [ + 174, + 200, + 800, + 218 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Shanghai Collaborative Innovation Center of Intelligent Visual Computing \n $^{3}$ Microsoft Research Asia", + "bbox": [ + 184, + 218, + 785, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 287, + 313, + 304 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-supervised action recognition is a challenging but critical task due to the high cost of video annotations. Existing approaches mainly use convolutional neural networks, yet current revolutionary vision transformer models have been less explored. In this paper, we investigate the use of transformer models under the SSL setting for action recognition. To this end, we introduce SVFormer, which adopts a steady pseudo-labeling framework (i.e., EMA-Teacher) to cope with unlabeled video samples. While a wide range of data augmentations have been shown effective for semi-supervised image classification, they generally produce limited results for video recognition. We therefore introduce a novel augmentation strategy, Tube TokenMix, tailored for video data where video clips are mixed via a mask with consistent masked tokens over the temporal axis. In addition, we propose a temporal warping augmentation to cover the complex temporal variation in videos, which stretches selected frames to various temporal durations in the clip. Extensive experiments on three datasets Kinetics-400, UCF-101, and HMDB-51 verify the advantage of SVFormer. In particular, SVFormer outperforms the state-of-the-art by $31.5\\%$ with fewer training epochs under the $1\\%$ labeling rate of Kinetics-400. Our method can hopefully serve as a strong benchmark and encourage future search on semi-supervised action recognition with Transformer networks. Code is released at https://github.com/ChenHsing/SVFormer.", + "bbox": [ + 75, + 335, + 473, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 773, + 209, + 789 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Videos have gradually replaced images and texts on Internet and grown at an exponential rate. On video websites such as YouTube, millions of new videos are uploaded every day. Supervised video understanding works [4, 15, 17, 29, 34, 56, 70] have achieved great successes. They rely on", + "bbox": [ + 75, + 799, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fdb6f3c8badab016f0d671560d35f9f0ccddf6f04c7ae6b0f2e8a2ddf03aef0c.jpg", + "image_caption": [ + "Figure 1. Comparison of our method with the supervised baseline and previous state-of-the-art SSL method [64]. SVFormer significantly outperforms previous methods under the case with very little labeled data." + ], + "image_footnote": [], + "bbox": [ + 501, + 286, + 890, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "large-scale manual annotations, yet labeling so many videos is time-consuming and labor-intensive. How to make use of unlabeled videos that are readily available for better video understanding is of great importance [25, 38, 39].", + "bbox": [ + 496, + 515, + 893, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this spirit, semi-supervised action recognition [25, 40, 57] explores how to enhance the performance of deep learning models using large-scale unlabeled data. This is generally done with labeled data to pretrain the networks [57,64], and then leveraging the pretrained models to generate pseudo labels for unlabeled data, a process known as pseudo labeling. The obtained pseudo labels are further used to refine the pretrained models. In order to improve the quality of pseudo labeling, previous methods [57, 62] use additional modalities such as optical flow [3] and temporal gradient [50], or introduce auxiliary networks [64] to supervise unlabeled data. Though these methods present promising results, they typically require additional training or inference cost, preventing them from scaling up.", + "bbox": [ + 496, + 579, + 893, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, video transformers [2,4,34] have shown strong results compared to CNNs [15, 17, 22]. Though great success has been achieved, the exploration of transformers on semi-supervised video tasks remains unexplored. While it sounds appealing to extend vision transformers directly to SSL, a previous study shows that transformers perform significantly worse compared to CNNs in the low-data regime", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 101, + 886, + 232, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18816", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "due to the lack of inductive bias [54]. As a result, directly applying SSL methods, e.g., FixMatch [41], to ViT [13] leads to an inferior performance [54].", + "bbox": [ + 75, + 90, + 467, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Surprisingly, in the video domain, we observe that TimeSformer, a popular video Transformer [4], initialized with weights from ImageNet [11], demonstrates promising results even when annotations are limited [37]. This encourages us to explore the great potential of transformers for action recognition in the SSL setting.", + "bbox": [ + 75, + 136, + 467, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing SSL methods generally use image augmentations (e.g., Mixup [67] and CutMix [66]) to speed up convergence under limited label resources. However, such pixel-level mixing strategies are not perfectly suitable for transformer architectures, which operate on tokens produced by patch splitting layers. In addition, strategies like Mixup and CutMix are particularly designed for image tasks, which fail to consider the temporal nature of video data. Therefore, as will be shown empirically, directly using Mixup or CutMix for semi-supervised action recognition leads to unsatisfactory performance.", + "bbox": [ + 75, + 227, + 467, + 392 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose SVFormer, a transformer-based semi-supervised action recognition method. Concretely, SVFormer adopts a consistency loss that builds two differently augmented views and demands consistent predictions between them. Most importantly, we propose Tube TokenMix (TTMix), an augmentation method that is naturally suitable for video Transformer. Unlike Mixup and CutMix, Tube TokenMix combines features at the token-level after tokenization via a mask, where the mask has consistent masked tokens over the temporal axis. Such a design could better model the temporal correlations between tokens.", + "bbox": [ + 75, + 393, + 467, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Temporal augmentations in literatures (e.g. varying frame rates) only consider simple temporal scaling or shifting, neglecting the complex temporal changes of each part in human action. To help the model learn strong temporal dynamics, we further introduce the Temporal Warping Augmentation (TWAug), which arbitrarily changes the temporal length of each frame in the clip. TWAug can cover the complex temporal variation in videos and is complementary to spatial augmentations [10]. When combining TWAug with TTMix, significant improvements are achieved.", + "bbox": [ + 75, + 559, + 467, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As shown in Fig. 1, SVFormer achieves promising results in several benchmarks. (i) We observe that the supervised Transformer baseline is much better than the Conv-based method [22], and is even comparable with the 3D-ResNet state-of-the-art method [64] on Kinetics400 when trained with $1\\%$ of labels. (ii) SVFormer-S significantly outperforms previous state-of-the-arts with similar parameters and inference cost, measured by FLOPs. (iii) Our method is also effective for the larger SVFormer-B model. Our contributions are as follows:", + "bbox": [ + 75, + 710, + 467, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We are the first to explore the transformer model for semi-supervised video recognition. Unlike SSL for", + "bbox": [ + 93, + 869, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "image recognition with transformers, we find that using parameters pretrained on ImageNet is of great importance to ensure decent results for action recognition in the low-data regime.", + "bbox": [ + 529, + 90, + 888, + 150 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose a token-level augmentation Tube TokenMix, which is more suitable for video Transformer than pixel-level mixing strategies. Coupled with Temporal Warping Augmentation, which improves temporal variations between frames, TTMix achieves significant boost compared with image augmentation.", + "bbox": [ + 516, + 162, + 888, + 253 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We conduct extensive experiments on three benchmark datasets. The performances of our method in two different sizes (i.e., SVFormer-B and SVFormer-S) outperform state-of-the-art approaches by clear margins. Our method sets a strong baseline for future transformer-based works.", + "bbox": [ + 516, + 266, + 888, + 354 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 372, + 648, + 387 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Semi-supervised Learning Deep learning relies on large-scale annotated data, however collecting these annotations is labor-intensive. Semi-supervised learning is a natural solution to reduce the cost of labeling, which leverages a few labeled samples and a large amount of unlabeled samples to train the model. The research and application of SSL mainly focus on image recognition [41, 44, 54] with a two-step process: data augmentation and consistency regularization. Concretely, different data augmentations [10] views are input to the model, and their output consistencies are enforced through a consistency loss. Another line of work generates new data and labels using mixing [5, 19, 49] to train the network. Among these state-of-the-art methods, FixMatch have been widely used due its effective and its variants have been extended to many other applications, such as object detection [27, 32], semantic segmentation [1, 8], 3D reconstruction [61], etc. Although FixMatch has achieved good performance in many tasks, it may not achieve satisfactory results when directly transferred to video action recognition due to the lack of temporal augmentation. In this paper, we introduce temporal augmentation TWAug with mixing based method TTMix, which is suitable for video transformers at SSL settings.", + "bbox": [ + 496, + 397, + 890, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-supervised Action Recognition VideoSSL [25] presents a comparative study of applying 2D SSL methods to videos, which verifies the limitations of the direct extension of pseudo labeling method. TCL [40] explores the effect of a group contrastive loss and self-supervised tasks. MvPL [62] and LTG [57] introduce optical flow or temporal gradient modal to generate high quality pseudo labels for training, respectively. CMPL [64] introduce an auxiliary network, which requires more frames in training, increasing the difficulty of application. Besides, previous methods are", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18817", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "all based on 2D [40] or 3D convolutional [57, 62, 64] networks, which require more training epochs. Our approach is the first to make the exploration of Video Transformer for SSL action recognition and achieves the best performance with the least training cost.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video Transformer The great success of vision transformer [13, 30, 33, 45, 68] in image recognition leads to the development of exploring the transformer-base architecture for video recognition tasks. VTN [36] uses additional temporal attention on the top of the pretrained ViT [13]. TimeSformer [4] investigates different spatial-temporal attention mechanisms and adopts factored space time attention as a trade-off of speed and accuracy. ViViT [2] explores four different types of attention, and selects the global spatiotemporal attention as the default to achieve promising performance. In addition, MviT [14], Video Swin [34], Uniformer [28] and Video Mobile-Former [53] incorporate the inductive bias in convolution into transformers. While these methods focus on fully-supervised setting, limited effort has been made for transformers in the semi-supervised setting.", + "bbox": [ + 75, + 167, + 470, + 396 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Data Augmentation Data augmentation is an essential step in modern deep networks to improve the training efficiency and performance. Cutout [12] removes random rectangle regions in images. Mixup [67] performs image mixing by linearly interpolating both the raw image and labels. In CutMix [66], patches are cut and pasted among image pairs. AutoAugment [10] automatically searches for augmentation strategies to improve the results. PixMix [24] explores the natural structural complexity of images when performing mixing. TokenMix [31] mixes images at the token-level and allows the region to be multiple isolated parts. Though these methods have achieved good results, they are all specially designed for pure image and most of them are pixel-level augmentations. In contrast, our TTMix coupled with TWAug is devised for video.", + "bbox": [ + 75, + 404, + 468, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 650, + 168, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce the preliminaries of SSL in Sec. 3.1. The pipeline of our proposed SVFormer is described in Sec. 3.2. Then we detail the proposed Tube TokenMix (TTMix) in Sec. 3.3, as well as the effective albeit simple temporal warping augmentation. Finally, we show the training paradigm in Sec. 3.4.", + "bbox": [ + 75, + 676, + 470, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries of SSL", + "text_level": 1, + "bbox": [ + 76, + 784, + 272, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Suppose we have $N$ training video samples, including $N_{L}$ labeled videos $(x_{l},y_{l})\\in \\mathcal{D}_{L}$ and $N_{U}$ unlabeled videos $x_{u}\\in \\mathcal{D}_{U}$ , where $x_{l}$ is the labeled video sample with a category label $y_{l}$ , and $x_{u}$ is the unlabeled video sample. In general, $N_{U}\\gg N_{L}$ . The aim of SSL is to utilize both $\\mathcal{D}_L$ and $\\mathcal{D}_U$ to train the model.", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f14b0c0083c9412c58aa94cf72b13c4052cf33434722ca15642a870286f00b3d.jpg", + "image_caption": [ + "Figure 2. Overview of our Tube TokenMix training framework. The two input unlabeled samples are mixed via a tube mask, where the generated sample is fed into the Student model. The two samples are also fed into the EMA-Teacher to obtain their pseudo labels, which are further linearly interpolated via mask ratio $\\lambda$ to produce pseudo label for the generated sample. \"SG\" means stop gradient. The data augmentation is omitted here." + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 883, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Pipeline", + "text_level": 1, + "bbox": [ + 500, + 417, + 599, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SVFormer follows the popular semi-supervised learning framework FixMatch [41] that use a consistency loss between two differently augmented views. The training paradigm is divided into two parts. For the labeled set $\\{(x_l, y_l)\\}_{l=1}^{N_L}$ , the model optimizes the supervised loss $\\mathcal{L}_s$ :", + "bbox": [ + 498, + 440, + 890, + 517 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\frac {1}{N _ {L}} \\sum^ {N _ {L}} \\mathcal {H} \\left(\\mathcal {F} \\left(x _ {l}\\right), y _ {l}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 525, + 890, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{F}(\\cdot)$ refers to the predictions produced by the model and $\\mathcal{H}$ is the standard cross entropy loss.", + "bbox": [ + 498, + 574, + 890, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For unlabeled samples $x_{u}$ , we first use weak augmentations (e.g., random horizontal flipping, random scaling, and random cropping) and strong augmentations (e.g., AutoAugment [10] or Dropout [43]) to generate two views separately, $x_{w} = \\mathcal{A}_{weak}(x_{u})$ , $x_{s} = \\mathcal{A}_{strong}(x_{u})$ . Then the pseudo label of the weak view $\\hat{y}_w = \\arg \\max (\\mathcal{F}(x_w))$ , which is produced by the model, is utilized to supervise the strong view, with the following unsupervised loss:", + "bbox": [ + 496, + 604, + 890, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {u n} = \\frac {1}{N _ {U}} \\sum^ {N _ {U}} \\mathbb {I} (\\max (\\mathcal {F} (x _ {w})) > \\delta) \\mathcal {H} (\\mathcal {F} (x _ {s}), \\hat {y} _ {w}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 734, + 890, + 770 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\delta$ is the predefined threshold, and $\\mathbb{I}$ is the indicator function that equals 1 when the maximum class probability exceeds $\\delta$ otherwise 0. The confidence indicator is used to filter the noisy pseudo labels.", + "bbox": [ + 496, + 777, + 890, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "EMA-Teacher In FixMatch, the two augmented inputs share the same model, which tends to cause model collapsing easily [21, 23]. Therefore, we adopt the exponential", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18818", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "moving average (EMA)-Teacher in our framework, which is an improved version of FixMatch. The pseudo labels are generated by the EMA-Teacher model, whose parameters are updated by exponential moving average of the student parameters, formulated as:", + "bbox": [ + 75, + 90, + 472, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {t} \\leftarrow m \\theta_ {t} + (1 - m) \\theta_ {s}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 180, + 468, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $m$ is a momentum coefficient, $\\theta_{t}$ and $\\theta_{s}$ are the parameters of teacher and student model, respectively. EMA has achieved success in many tasks, such as self-supervised learning [21, 23], SSL of image classification [19, 44], and object detection [27, 32]. Here we are the first to adopt this method in semi-supervised video action recognition.", + "bbox": [ + 75, + 208, + 470, + 299 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Tube TokenMix", + "text_level": 1, + "bbox": [ + 76, + 309, + 235, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One of the core problems in semi-supervised frameworks is how to enrich the dataset with high-quality pseudo labels. Mixup [67] is a widely adopted data augmentation strategy, which performs convex combination between pairs of samples and labels as follows:", + "bbox": [ + 75, + 332, + 468, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {x} = \\lambda \\cdot x _ {1} + (1 - \\lambda) \\cdot x _ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 421, + 468, + 436 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} = \\lambda \\cdot y _ {1} + (1 - \\lambda) \\cdot y _ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 465, + 468, + 482 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the ratio $\\lambda$ is a scalar that conforms to the beta distribution. Mixup [67] and its variants (e.g. CutMix [66]) have achieved success in many tasks in the low-data regime, such as long-tail classification [9, 69], domain adaptation [63] [55], few-shot learning [35, 60], etc. For SSL, Mixup also performs well by mixing the pseudo labels of unlabeled samples in image classification [49].", + "bbox": [ + 75, + 489, + 470, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mixing in Videos While directly applying Mixup or CutMix to video scenarios results in clear improvements in Conv-based methods [71], these methods show unsatisfactory performance in our method. The reason is that our method adopts the Transformer backbone, where the pixel-level mixing augmentation (Mixup or CutMix) may be not perfectly suitable for such token-level models [31]. To narrow the gap, we propose 3 token-level mixing augmentation methods for video data, namely, Rand TokenMix, Frame TokenMix, and Tube TokenMix.", + "bbox": [ + 75, + 614, + 468, + 765 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 2 illustrates the pipeline of our method. Given unlabeled video clips $x_{a}, x_{b} \\in \\mathbb{R}^{H \\times W \\times T}$ , our method employs a token-level mask $\\mathbf{M} \\in \\{0,1\\}^{H \\times W \\times T}$ to perform sample mixing. Note that $H$ and $W$ are the height and width of the frame after patch tokenization, and $T$ is the clip length. To generate a new sample $x_{mix}$ , we mix $x_{a}$ and $x_{b}$ after strong data augmentations $A_{strong}$ as follows:", + "bbox": [ + 75, + 766, + 470, + 873 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {m i x} = \\mathcal {A} _ {s t r o n g} \\left(x _ {a}\\right) \\odot \\mathbf {M} + \\mathcal {A} _ {s t r o n g} \\left(x _ {b}\\right) \\odot (\\mathbf {1} - \\mathbf {M}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 885, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/984ce677e4611d6d2aabcb11ed2a6fcc141bf4e76719260bff9f17a1b6ae1cd2.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 625, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6ce9982683269bca9e90d58ada738238b47b7ba72719163f09a767af140e6298.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 643, + 89, + 756, + 193 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3eb171df920d40b44ef64d2cc2719222a756d2934282b74423d5ea1f91b016b5.jpg", + "image_caption": [ + "(c)", + "Figure 3. Examples of masks in three token mixing strategies. (a) Rand TokenMix. (b) Tube TokenMix. (c) Frame TokenMix." + ], + "image_footnote": [], + "bbox": [ + 774, + 89, + 890, + 193 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Consistency loss for Tube TokenMix", + "text_level": 1, + "bbox": [ + 500, + 258, + 834, + 275 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Unlabeled clip batch $\\mathbf{x}_{\\mathbf{a}}$", + "bbox": [ + 500, + 279, + 730, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Tube TokenMask M, mask ratio $\\lambda$", + "bbox": [ + 500, + 295, + 799, + 309 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Teacher model $\\mathcal{F}_t$", + "bbox": [ + 501, + 310, + 691, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Student model $\\mathcal{F}_s$", + "bbox": [ + 501, + 325, + 691, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Require: Confidence threshold $\\delta$", + "bbox": [ + 501, + 340, + 727, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{x_b} = \\mathrm{shuffle}(\\mathbf{x_a})$ {shuffle samples in batch}", + "bbox": [ + 517, + 354, + 810, + 369 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{\\mathbf{x}}_{\\mathbf{a}} =$ spatial_aug $(\\mathbf{x}_{\\mathbf{a}})$ {spatial aug.}", + "bbox": [ + 517, + 369, + 756, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{\\mathbf{x}}_{\\mathbf{b}} =$ temporal\\_aug $(\\mathbf{x}_{\\mathbf{b}})$ {temporal warping aug.}", + "bbox": [ + 517, + 386, + 844, + 401 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{\\mathbf{y}}_a = \\mathrm{stop\\_gradient}(\\mathcal{F}_t(\\mathbf{x}_a))$ {teacher pred.}", + "bbox": [ + 517, + 401, + 810, + 416 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{\\mathbf{y}}_b = \\mathrm{stop\\_gradient}(\\mathcal{F}_t(\\mathbf{x}_b))$", + "bbox": [ + 517, + 416, + 702, + 430 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{c_{a}} = \\max_{i}\\mathbf{y}_{a}[i]$ {confidence of prediction}", + "bbox": [ + 517, + 430, + 807, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{c_b} = \\max_i\\mathbf{y}_b[i]$", + "bbox": [ + 517, + 446, + 627, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{x}_{mix} = \\hat{\\mathbf{x}}_a*\\mathbf{M} + \\hat{\\mathbf{x}}_b*(1 - \\mathbf{M})$ {mix clips}", + "bbox": [ + 517, + 460, + 816, + 476 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\hat{\\mathbf{y}}_{mix} = \\hat{\\mathbf{y}}_a*\\lambda +\\hat{\\mathbf{y}}_b*(1 - \\lambda)$ {mix tea. preds.}", + "bbox": [ + 517, + 476, + 836, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{c}_{mix} = \\mathbf{c}_a*\\lambda +\\mathbf{c}_b*(1 - \\lambda)$ {mix confidence.}", + "bbox": [ + 517, + 491, + 839, + 506 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{q} = \\mathrm{mean}(c_{mix}\\geq \\delta)$ {mean of conf. mask}", + "bbox": [ + 517, + 507, + 810, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{y}_{mix} = \\mathcal{F}_s(\\mathbf{x}_{mix})$ {stu. pred. on mixed clip}", + "bbox": [ + 517, + 521, + 816, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{L}_{mix} = q||\\mathbf{y}_{mix} - \\hat{\\mathbf{y}}_{mix}||_2^2$ {cons. loss}", + "bbox": [ + 517, + 537, + 782, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Return $\\mathcal{L}_{\\text{mix}}$", + "bbox": [ + 517, + 553, + 609, + 565 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\odot$ is element-wise multiplication, and $\\mathbf{1}$ is a binary mask with all ones.", + "bbox": [ + 496, + 598, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mask $\\mathbf{M}$ differs in the three augmentation methods, as demonstrated in Fig. 3. For Rand TokenMix, the masked tokens are randomly selected from the whole video clip (from $H\\times W\\times T$ tokens). For Frame TokenMix, we randomly select frames from the $T$ frames and mask all the tokens in these frames. For Tube TokenMix, we adopt the tube-style masking strategy, that is, different frames share the same spatial mask matrix. In this case, the mask $\\mathbf{M}$ has consistent masked tokens over the temporal axis. While our mask design shares similarity with the recent masked image/video modeling [16, 47, 51, 52, 58, 59], our motivation is totally different. They focus on removing certain regions and making the model predict the masked areas for feature learning. In contrast, we leverage the mask to mix two clips and synthesize a new data sample.", + "bbox": [ + 496, + 628, + 890, + 853 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mixed sample $x_{mix}$ is then fed to the student model $\\mathcal{F}_s$ , obtaining the model prediction $y_{mix} = \\mathcal{F}_s(x_{mix})$ . In addition, the pseudo labels $\\hat{y}_a, \\hat{y}_b$ for $x_a, x_b$", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18819", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8617344596c01b199ebe63bb128508b1963f18448e0bb7f9df546fd3c67149aa.jpg", + "image_caption": [ + "Figure 4. One example of utilizing Temporal Warping Augmentation together with spatial augmentation in TTMix. The two clips are first transformed by the two augmentations separately, after which TTMix is performed to generate a new clip." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 477, + 282 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/79e56332aa626b1a66754729ea41f363314cd43fdefc46cc6a2b10c13ccb717d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 95, + 875, + 286 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are produced by inputting the weak augmented samples $\\mathcal{A}_{weak}(x_a),\\mathcal{A}_{weak}(x_b)$ to the teacher model $\\mathcal{F}_t$", + "bbox": [ + 75, + 349, + 468, + 380 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {a} = \\arg \\max \\left(\\mathcal {F} _ {t} \\left(\\mathcal {A} _ {\\text {w e a k}} \\left(x _ {a}\\right)\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 393, + 468, + 411 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {b} = \\arg \\max \\left(\\mathcal {F} _ {t} \\left(\\mathcal {A} _ {\\text {w e a k}} \\left(x _ {b}\\right)\\right)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 430, + 468, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that if $\\max (\\mathcal{F}_t(\\mathcal{A}_{weak}(x))) < \\delta$ , the pseudo label $\\hat{y}$ remains the soft label $\\mathcal{F}_t(\\mathcal{A}_{weak}(x))$ . The pseudo label $\\hat{y}_{mix}$ for $x_{mix}$ is generated by mixing $\\hat{y}_a$ and $\\hat{y}_b$ with mask ratio $\\lambda$ :", + "bbox": [ + 76, + 450, + 468, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {m i x} = \\lambda \\cdot \\hat {y} _ {a} + (1 - \\lambda) \\cdot \\hat {y} _ {b}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 511, + 468, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the student model is optimized by the following consistency loss:", + "bbox": [ + 75, + 531, + 468, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {m i x} = \\frac {1}{N _ {m}} \\sum^ {N _ {m}} \\left(\\hat {y} _ {m i x} - y _ {m i x}\\right) ^ {2}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 569, + 468, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{m}$ is the number of mixed samples. The algorithm of consistency loss for TTMix is shown in Algorithm 1.", + "bbox": [ + 75, + 611, + 468, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Temporal Warping Augmentation Most existing augmentation methods are designed for image tasks, which focus more on the spatial augmentation. They manipulate single or a pair of images to generate new image samples, without considering any temporal changes. Even the commonly adopted temporal augmentations, including varying temporal locations [18] and frame rates [40, 65], only consider simple temporal shift or scaling, that is, changing the holistic location or play speed. However, human actions are very complex and can have different temporal variation at every timestamp. To cover such challenging cases, we propose to distort the temporal duration of each frame, thus introducing higher randomness into the data.", + "bbox": [ + 75, + 659, + 468, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our Temporal Warping Augmentation (TWAug) can stretch one frame to various temporal length. Given an extracted video clip of $T$ frames (e.g., 8 frames), we randomly", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0185539e2c8df65b8029a975dcdf2fd1752d6b6898640ac408ba2fc7a8a0c062.jpg", + "image_caption": [ + "Figure 5. Illustration of Temporal Warping Augmentation. We demonstrate three augment examples of different selected frames." + ], + "image_footnote": [], + "bbox": [ + 506, + 349, + 883, + 459 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "determine to keep all the frames, or select a small portion of frames (e.g., 2 or 4 frames) while masking the others. The masked frames are then padded with random neighbouring visible (unmasked) frames. Note that after temporal padding, the frame order is still retained. Fig. 5 shows three examples of selecting 2, 4, and 8 frames, respectively. The proposed TWAug can help the model learn the flexible temporal dynamics during training.", + "bbox": [ + 496, + 513, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Temporal Warping Augmentation serves as a strong augmentation in TTMix. Typically, we combine TWAug with the conventional spatial augmentation [10, 43] to perform the mixing. As shown in Fig. 4, the two input clips are first transformed by spatial augmentation and TWAug separately, after which the two clips are mixed through TTMix. We verify the effectiveness of our TWAug in Sec. 4.3.", + "bbox": [ + 496, + 635, + 890, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Paradigm", + "text_level": 1, + "bbox": [ + 500, + 750, + 684, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training of SVFormer consists of three parts: supervised loss formulated by Eq. (1), unsupervised pseudo-label consistency loss Eq. (2), and TTMix consistency loss Eq. (10). The final loss function is as follows:", + "bbox": [ + 496, + 773, + 890, + 833 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {a l l} = \\mathcal {L} _ {s} + \\gamma_ {1} \\mathcal {L} _ {u n} + \\gamma_ {2} \\mathcal {L} _ {m i x}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 844, + 890, + 859 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma_{1}$ and $\\gamma_{2}$ are the hyperparameters for balancing the loss items.", + "bbox": [ + 496, + 869, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18820", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/daafa366a82218a5a883b0571713022522d0a884994f3e2476729e592c69c13d.jpg", + "table_caption": [ + "Table 1. Comparisons with state-of-the-art methods on UCF-101 and Kinetics-400. Note that 3D-ResNet-18 and 3D-ResNet-50 denote the backbone networks and their depths. We report Top-1 accuracy as the evaluation metric. \"Input\" shows the modalities used during training, where \"V\" is the raw RGB video, \"F\" is optical flow and \"G\" is the temporal gradient." + ], + "table_footnote": [], + "table_body": "
MethodBackboneInputw ImgNetEpochUCF-101Kinetics-400
1%10%1%10%
Supervised3D-ResNet-50V✓2006.532.44.436.2
ViT-SV✓3012.762.519.956.6
FixMatch (NeurIPS 2020) [41]SlowFast-R50V✓20016.155.110.149.4
VideoSSL(WACV 2021) [25]3D-ResNet-18V✓--42.0-33.8
TCL (CVPR 2021) [40]TSM-ResNet-18V400--8.5-
ActorCutMix (CVIU 2021) [71]R(2+1)D-34V✓600-53.09.02-
MvPL (ICCV 2021) [62]3D-ResNet-50V+F+G60022.880.517.058.2
CMPL (CVPR 2022) [64]R50 + R50-1/4V✓20025.179.117.658.4
LTG (CVPR 2022) [57]3D-ResNet-18V+G180/360-62.49.843.8
TACL(TCSVT 2022) [46]3D-ResNet-50V✓200-55.6--
L2A (ECCV 2022) [20]3D-ResNet-18V✓400-60.1--
SVFormer-S (Ours)ViT-SV✓3031.479.132.661.6
SVFormer-B (Ours)ViT-BV✓3046.386.749.169.4
", + "bbox": [ + 98, + 141, + 870, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 407, + 202, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we first introduce the experimental settings in Sec. 4.1. Following previous work [57,64], we conduct experiments under different labeling rates in Sec 4.2. In addition, we also perform ablation experiments and empirical analysis in Section 4.3. If not emphasized, we only use RGB modal for inference with the official validation set.", + "bbox": [ + 75, + 433, + 470, + 525 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 76, + 535, + 272, + 553 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets Kinetics-400 [7] is a large-scale human action video dataset, with up to 245k training samples and 20k validation samples, covering 400 different categories. We follow the state-of-the-art methods MvPL [62] and CMPL [64] to sample 6 or 60 labeled training videos per category, i.e. at $1\\%$ or $10\\%$ labeling rates. UCF-101 [42] is a dataset with 13,320 video samples, which consists of 101 categories. We also sample 1 or 10 samples in each category as the labeled set following CMPL [64]. As for HMDB-51 [26], it is a small-scale dataset with only 51 categories composed of 6,766 videos. Following the division of LTG [57] and VideoSSL [25], we conduct experiments at three different labeling rates: $40\\%$ , $50\\%$ , and $60\\%$ .", + "bbox": [ + 75, + 558, + 468, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metric We show the accuracy of Top-1 in main results, and also present the accuracy of Top-5 in some ablation experiments.", + "bbox": [ + 75, + 758, + 468, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline We utilize the ViT [13] extended video TimeSformer [4] as the backbone of our baseline. The hyperparameters are mostly kept the same as the baseline, and we adopt the divided space-time attention as in TimeSformer [4]. Since TimeSformer only have ViT-Base models, we implement SVFormer-Small model from DeiT-S [48] with", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a46adf6b1520863799b3450413224bd2d7f89b2754e19f4cd15fc79fa8a57ce9.jpg", + "table_caption": [ + "Table 2. Comparisons with state-of-the-art methods on HMDB-51. We report Top-1 accuracy. \"Input\" shows the modalities used during training, where \"V\" is the raw RGB video, \"F\" is optical flow and \"G\" is the temporal gradient." + ], + "table_footnote": [], + "table_body": "
BackboneInput40%50%60%
VideoSSL [25]3D-R18V32.736.237.0
ActorCutMix [71]R(2+1)D-34V32.938.238.9
MvPL [62]3D-R18V+F+G30.533.935.8
LTG [57]3D-R18V+G46.548.449.7
TACL [46]3D-R18V38.740.241.7
L2A [20]3D-R18V42.146.347.1
SVFormer-S (Ours)ViT-SV56.258.259.7
SVFormer-B (Ours)ViT-BV61.664.468.2
", + "bbox": [ + 503, + 474, + 893, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the dimension of 384 and 6 heads, in order to have comparable number of parameters with other Conv-based methods [22, 62, 64]. For fair comparisons, we train 30 epochs for TimeSformer as the supervised baseline.", + "bbox": [ + 496, + 625, + 893, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training and Inference For training, we follow the setting of TimeSformer [4]. The training uses 8 or 16 GPUs, with a SGD optimizer using a momentum of 0.9 and a weight decay of 0.001. For each setting, the basic learning rate is set to 0.005, which is divided by 10 at epochs 25, and 28. As for the confidence score threshold, we search for the optimal $\\delta$ from $\\{0.3, 0.5, 0.7, 0.9\\}$ . $\\gamma_{1}$ and $\\gamma_{2}$ are set to 2. The masking ratio $\\lambda$ is sampled from beta distribution $\\mathrm{Beta}(\\alpha, \\alpha)$ , where $\\alpha = 10$ . In the testing phase, following the inference strategies in MvPL [62] and CMPL [64], we uniformly sample five clips from the entire video, and make three different crops to get $224 \\times 224$ resolution to cover most of the spatial areas of the clips. The final prediction is the average of the softmax probabilities of these $5 \\times 3$ pre", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18821", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1a8b2f349dfd6ceedb12d01265c8dfc7080ffb587f8a90bebb040892e69d0661.jpg", + "image_caption": [ + "Figure 6. Example of the traditional pixel-level mixing methods and our proposed token-level mixing. Note that token-level methods mix two samples after tokenization but the visualization is shown on image-level for clear presentation." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 460, + 428 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dictions. We also conduct a comparison of inference setting in the ablation study in Sec. 4.3.", + "bbox": [ + 75, + 511, + 468, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 76, + 553, + 217, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The main results of Kinetics-400 [7] and UCF-101 [42] are shown in Table 1. Compared with previous methods, our model SVFormer-S achieves the best performance with the fewest training epochs among the methods that only use RGB data. In particular, at the labeling rate of $1\\%$ setting, SVFormer-S improves previous approach [64] by $6.3\\%$ in UCF-101 and $15.0\\%$ in Kinetics-400. In addition, when adopting larger models, SVFormer-B significantly outperforms the state-of-the-art methods.", + "bbox": [ + 75, + 577, + 468, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, in Kinetics-400, SVFormer-B can achieve $69.4\\%$ with only $10\\%$ labeled data, which is comparable to $77.9\\%$ of fully-supervised setting in TimeSformer [4]. Moreover, as shown in Table 2, for the small-scale dataset HMDB-51 [26], our SVFormer-S and SVFormer-B have also improved by about $10\\%$ and $15\\%$ compared with the previous method [57].", + "bbox": [ + 75, + 713, + 468, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 830, + 241, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To understand the effect of each part of the design in our method, we conduct extensive ablation studies on the Kinetics-400 and UCF-101 at the $1\\%$ labeling ratio setting", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/460ca91a161dea1bc822fdcf28a54d51b26a2924a565423112e40b5b1c9f692c.jpg", + "table_caption": [ + "Table 3. SSL framework selection. We compare the EMA-Teacher framework with FixMatch. The results are reported on Kinetics-400 and UCF-101 with $1\\%$ labeling ratio." + ], + "table_footnote": [], + "table_body": "
MethodUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline12.729.819.942.3
FixMatch [41]25.147.328.254.6
EMA-Teacher31.456.932.659.0
", + "bbox": [ + 540, + 142, + 849, + 241 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/596a7e86b72ce9c4f0ec21af2dce1fe998286dbdc6e82ad1c5154c654835a865.jpg", + "table_caption": [ + "Table 4. TokenMix Mask sampling. We compare different token masking strategies. The results are reported on Kinetics-400 and UCF-101 with $1\\%$ labeling ratio." + ], + "table_footnote": [], + "table_body": "
Method/DatasetUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline26.148.923.647.7
CutMix [66]28.751.328.653.7
Mixup [67]29.853.029.355.1
PixMix [24]29.752.429.655.8
Frame TokenMix29.854.226.350.0
Rand TokenMix30.355.328.854.2
Tube TokenMix31.456.932.659.0
", + "bbox": [ + 529, + 297, + 856, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with SVFormer-S.", + "bbox": [ + 500, + 468, + 624, + 482 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of SSL framework The comparison of FixMatch and EMA-Teacher is shown in Table 3. It is clear that the two methods have significantly improved the baseline approach. In addition, EMA-Teacher has exhibited considerable gains over FixMatch in both datasets with very few labeled samples, probably because it has improved the stability of training. FixMatch [41] may lead to model collapse with limited labels as shown in [6].", + "bbox": [ + 496, + 487, + 890, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of different mixing strategies We now compare the Tube TokenMix strategy with three pixel-level mixing methods, CutMix [66], Mixup [67], PixMix [24], as well as the other two token-level mixing methods, i.e., Frame TokenMix and Rand TokenMix. The examples of different mixing methods are shown in Fig. 6. The quantitative results are shown in Table 4. Compared with these alternative methods, all mixing methods can improve the performance, which proves the effectiveness of mixing-based consistency losses. In addition, we observe that the token-level methods (Rand TokenMix and Tube TokenMix) perform better than the pixel-level mixing methods. This is not surprising since transformers operate on tokens, and thus token-level mixing has inherent advantages.", + "bbox": [ + 496, + 613, + 892, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The performance of Frame TokenMix is even worse than that of pixel-level mixing methods, which is also expected. We hypothesize that replacing entire frames in video clip will scramble up the temporal reasoning, thus leading to poor temporal attention modeling. In addition, Tube Token-", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18822", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f0bf4cfcaa8bb3274073618a45e7c727b6ef3c98e9027387512a008bd352c79f.jpg", + "table_caption": [ + "Table 5. Effects of Spatial and Temporal Warping Augmentations (TWAug). The results are reported on Kinetics-400 and UCF-101 with $1\\%$ labeling ratio." + ], + "table_footnote": [], + "table_body": "
SpatialTemporalUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline29.552.128.554.2
Spatial-only✓29.953.230.355.9
Temporal-only✓30.255.830.856.4
Spatial+Temporal✓✓31.456.932.659.0
", + "bbox": [ + 81, + 133, + 460, + 224 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/91559d15e61160312011b6caf251a7dec11797821a021b9f1909d002bd164448.jpg", + "table_caption": [ + "Table 6. Effects of different inference schemes. We compare the sparse sampling strategy and dense sampling method with different frames. The $a \\times b$ in 'Frames' column means sampling $a$ frames at frame rate $b$ . The results are reported on Kinetics-400 and UCF-101 with $1\\%$ labeling ratio." + ], + "table_footnote": [], + "table_body": "
MethodFramesTest ViewUCF-1%Kinetic-1%
MvPL [62]8 × 810 × 322.817.0
CMPL [64]8 × 810 × 325.117.6
SVFormer-S8 × 321 × 329.331.0
SVFormer-S8 × 85 × 331.432.6
SVFormer-S16 × 410 × 331.633.1
", + "bbox": [ + 80, + 309, + 457, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Mix achieves the best results. We suppose the consistent masked tokens over temporal axis can prevent information leaky between adjacent frames in the same spatial locations, especially in such a short-term clip. Therefore, Tube Token-Mix could better model the spatio-temporal correlations.", + "bbox": [ + 75, + 422, + 467, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of Augmentations The effects of spatial augmentation and temporal warping augmentation are evaluated in Table 5. The baseline indicates removing both strong spatial augmentation (e.g. AutoAugment [10] and Dropout [43]) and TWAug in all branches. In this case, the experimental performance drops dramatically. When spatial augmentation or temporal warping augmentation is incorporated into the baseline separately, the performance is improved. The best practice is to perform data augmentations in both spatial and temporal.", + "bbox": [ + 75, + 503, + 467, + 654 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of Inference We evaluate the effect of frame rate sampling and different inference schemes, as shown in Table 6. Previous methods, i.e. CMPL [64] and MvPL [62], utilize the clip-based sparse sampling, which samples 8 frames at frame rate 8 as a clip. For each video, 10 clips are sampled, where each clip is cropped 3 times according to different spatial positions. Finally, the predictions of $10 \\times 3$ samples are averaged. TimeSformer [4] adopts the video-based sparse sampling, that is, 8 frames are sampled at frame rate 32 as the representation of the whole video. Then 3 different cropped views are used, namely $8 \\times 32$ . Applying the video-based sparse sampling scheme as in TimeSformer [4] can reduce the inference cost, but the performance is worse than that of clip-based sampling. Experiments at sampling schemes of $8 \\times 8$ and $16 \\times 4$ demonstrate better performance. For the trade-off between effi", + "bbox": [ + 75, + 657, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a1acfc50ff1b975de968b03740c17399a29a1234a1f0e90ae24626e66925e86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 89, + 692, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/877beff07eab7a533a71c8963924834f3b6b85a1f2c9c4fc8b6a7ecf38fc67de.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 88, + 880, + 178 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c86edfc119688c70a1fccb78e59613d698be63e2b78c68242d97ab38d4302fbc.jpg", + "image_caption": [ + "Figure 7. Effects of hyperparameters. Results of varying threshold $\\delta$ , ratio between unlabeled and labeled data in a mini-batch $(B_u / B_l)$ , momentum coefficient $m$ , and loss weights $(\\gamma_1, \\gamma_2)$ are included to comprehensively study the effects of the hyperparameters. Reported on Kinetics-400 with $1\\%$ labeling ratio." + ], + "image_footnote": [], + "bbox": [ + 506, + 185, + 692, + 273 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bc95930fb244a9b380a1c73ab4fa8992073ecf304f6f43af1ffc3a7b00b8b9ec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 183, + 880, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ciency and accuracy, we use $8 \\times 8$ as the default setting following CMPL [64] and MvPL [62].", + "bbox": [ + 496, + 358, + 890, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis of hyperparameters Here we explore the effect of different hyperparameters. We conduct experiments under $1\\%$ setting of Kinetics-400. We first explore the effect of different threshold values of $\\delta$ . As shown in Fig. 7(a), we can observe that when labeled samples are extremely scarce, best results are achieved by setting a small $\\delta$ value $(\\delta = 0.3)$ . We then evaluate how the ratio between labeled samples and unlabeled samples in a mini-batch affects the result. We fix the labeled sample number $B_{l}$ to 1, and sample $B_{u}$ unlabeled samples to form a mini-batch, where $B_{u}$ is in $\\{1,2,3,5,7\\}$ . The results are shown in Fig. 7(b). When $B_{u} = 5$ , the model produces the highest result. Finally, we explore the choice of momentum coefficient $m$ of EMA and the loss weights $\\gamma_{1}$ and $\\gamma_{2}$ , as shown in Fig. 7(c) and Fig. 7(d). We thus set $m = 0.99$ and $\\gamma_{1} = \\gamma_{2} = 2$ as default setting in all the experiments.", + "bbox": [ + 496, + 392, + 892, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper we present SVFormer, a transformer-based semi-supervised video action recognition method. We propose Tube TokenMix, a data augmentation method that is specially designed for video transformer models. Coupled with the temporal warping augmentation, which covers the complex temporal variations by arbitrarily changing the frame length, TTMix achieves significant improvement compared with conventional augmentations. SVFormer outperforms the state-of-the-art with a large margin on UCF-101, HMDB-51 and Kinetics-400 without increasing overheads. Our work establishes a new benchmark for semi-supervised action recognition and encourages future work to adopt Transformer architecture.", + "bbox": [ + 496, + 674, + 890, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This project was supported by NSFC under Grant No. 62032006 and No. 62102092.", + "bbox": [ + 498, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18823", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. Semi-supervised semantic segmentation with pixel-level contrastive learning from a class-wise memory bank. 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Learning representational invariances for data-efficient action recognition. arXiv preprint arXiv:2103.16565, 2021. 4, 6" + ], + "bbox": [ + 78, + 90, + 468, + 316 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18826", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/2bd91319-3d84-428a-8335-5833e2e27f2c_model.json b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/2bd91319-3d84-428a-8335-5833e2e27f2c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..117405eb6b93d0dd0d5d939343de4d12c14672bb --- /dev/null +++ b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/2bd91319-3d84-428a-8335-5833e2e27f2c_model.json @@ -0,0 +1,2675 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.124, + 0.131, + 0.847, + 0.154 + ], + "angle": 0, + "content": "SVFormer: Semi-supervised Video Transformer for Action Recognition" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.179, + 0.861, + 0.201 + ], + "angle": 0, + "content": "Zhen Xing\\(^{1,2}\\) Qi Dai\\(^{3}\\) Han Hu\\(^{3}\\) Jingjing Chen\\(^{1,2}\\) Zuxuan Wu\\(^{1,2\\dagger}\\) Yu-Gang Jiang\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.175, + 0.201, + 0.802, + 0.219 + ], + "angle": 0, + "content": "1 Shanghai Key Lab of Intell. Info. Processing, School of CS, Fudan University" + }, + { + "type": "text", + "bbox": [ + 0.185, + 0.219, + 0.786, + 0.253 + ], + "angle": 0, + "content": "\\(^{2}\\) Shanghai Collaborative Innovation Center of Intelligent Visual Computing \n\\(^{3}\\) Microsoft Research Asia" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.288, + 0.314, + 0.305 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.474, + 0.745 + ], + "angle": 0, + "content": "Semi-supervised action recognition is a challenging but critical task due to the high cost of video annotations. Existing approaches mainly use convolutional neural networks, yet current revolutionary vision transformer models have been less explored. In this paper, we investigate the use of transformer models under the SSL setting for action recognition. To this end, we introduce SVFormer, which adopts a steady pseudo-labeling framework (i.e., EMA-Teacher) to cope with unlabeled video samples. While a wide range of data augmentations have been shown effective for semi-supervised image classification, they generally produce limited results for video recognition. We therefore introduce a novel augmentation strategy, Tube TokenMix, tailored for video data where video clips are mixed via a mask with consistent masked tokens over the temporal axis. In addition, we propose a temporal warping augmentation to cover the complex temporal variation in videos, which stretches selected frames to various temporal durations in the clip. Extensive experiments on three datasets Kinetics-400, UCF-101, and HMDB-51 verify the advantage of SVFormer. In particular, SVFormer outperforms the state-of-the-art by \\(31.5\\%\\) with fewer training epochs under the \\(1\\%\\) labeling rate of Kinetics-400. Our method can hopefully serve as a strong benchmark and encourage future search on semi-supervised action recognition with Transformer networks. Code is released at https://github.com/ChenHsing/SVFormer." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.774, + 0.21, + 0.79 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.8, + 0.47, + 0.878 + ], + "angle": 0, + "content": "Videos have gradually replaced images and texts on Internet and grown at an exponential rate. On video websites such as YouTube, millions of new videos are uploaded every day. Supervised video understanding works [4, 15, 17, 29, 34, 56, 70] have achieved great successes. They rely on" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.287, + 0.891, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.449, + 0.894, + 0.504 + ], + "angle": 0, + "content": "Figure 1. Comparison of our method with the supervised baseline and previous state-of-the-art SSL method [64]. SVFormer significantly outperforms previous methods under the case with very little labeled data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.516, + 0.895, + 0.577 + ], + "angle": 0, + "content": "large-scale manual annotations, yet labeling so many videos is time-consuming and labor-intensive. How to make use of unlabeled videos that are readily available for better video understanding is of great importance [25, 38, 39]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.793 + ], + "angle": 0, + "content": "In this spirit, semi-supervised action recognition [25, 40, 57] explores how to enhance the performance of deep learning models using large-scale unlabeled data. This is generally done with labeled data to pretrain the networks [57,64], and then leveraging the pretrained models to generate pseudo labels for unlabeled data, a process known as pseudo labeling. The obtained pseudo labels are further used to refine the pretrained models. In order to improve the quality of pseudo labeling, previous methods [57, 62] use additional modalities such as optical flow [3] and temporal gradient [50], or introduce auxiliary networks [64] to supervise unlabeled data. Though these methods present promising results, they typically require additional training or inference cost, preventing them from scaling up." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recently, video transformers [2,4,34] have shown strong results compared to CNNs [15, 17, 22]. Though great success has been achieved, the exploration of transformers on semi-supervised video tasks remains unexplored. While it sounds appealing to extend vision transformers directly to SSL, a previous study shows that transformers perform significantly worse compared to CNNs in the low-data regime" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.887, + 0.233, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18816" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.137 + ], + "angle": 0, + "content": "due to the lack of inductive bias [54]. As a result, directly applying SSL methods, e.g., FixMatch [41], to ViT [13] leads to an inferior performance [54]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.468, + 0.227 + ], + "angle": 0, + "content": "Surprisingly, in the video domain, we observe that TimeSformer, a popular video Transformer [4], initialized with weights from ImageNet [11], demonstrates promising results even when annotations are limited [37]. This encourages us to explore the great potential of transformers for action recognition in the SSL setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.468, + 0.393 + ], + "angle": 0, + "content": "Existing SSL methods generally use image augmentations (e.g., Mixup [67] and CutMix [66]) to speed up convergence under limited label resources. However, such pixel-level mixing strategies are not perfectly suitable for transformer architectures, which operate on tokens produced by patch splitting layers. In addition, strategies like Mixup and CutMix are particularly designed for image tasks, which fail to consider the temporal nature of video data. Therefore, as will be shown empirically, directly using Mixup or CutMix for semi-supervised action recognition leads to unsatisfactory performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.468, + 0.559 + ], + "angle": 0, + "content": "In this work, we propose SVFormer, a transformer-based semi-supervised action recognition method. Concretely, SVFormer adopts a consistency loss that builds two differently augmented views and demands consistent predictions between them. Most importantly, we propose Tube TokenMix (TTMix), an augmentation method that is naturally suitable for video Transformer. Unlike Mixup and CutMix, Tube TokenMix combines features at the token-level after tokenization via a mask, where the mask has consistent masked tokens over the temporal axis. Such a design could better model the temporal correlations between tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.468, + 0.71 + ], + "angle": 0, + "content": "Temporal augmentations in literatures (e.g. varying frame rates) only consider simple temporal scaling or shifting, neglecting the complex temporal changes of each part in human action. To help the model learn strong temporal dynamics, we further introduce the Temporal Warping Augmentation (TWAug), which arbitrarily changes the temporal length of each frame in the clip. TWAug can cover the complex temporal variation in videos and is complementary to spatial augmentations [10]. When combining TWAug with TTMix, significant improvements are achieved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.711, + 0.468, + 0.86 + ], + "angle": 0, + "content": "As shown in Fig. 1, SVFormer achieves promising results in several benchmarks. (i) We observe that the supervised Transformer baseline is much better than the Conv-based method [22], and is even comparable with the 3D-ResNet state-of-the-art method [64] on Kinetics400 when trained with \\(1\\%\\) of labels. (ii) SVFormer-S significantly outperforms previous state-of-the-arts with similar parameters and inference cost, measured by FLOPs. (iii) Our method is also effective for the larger SVFormer-B model. Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.871, + 0.468, + 0.9 + ], + "angle": 0, + "content": "- We are the first to explore the transformer model for semi-supervised video recognition. Unlike SSL for" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.89, + 0.151 + ], + "angle": 0, + "content": "image recognition with transformers, we find that using parameters pretrained on ImageNet is of great importance to ensure decent results for action recognition in the low-data regime." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.164, + 0.89, + 0.254 + ], + "angle": 0, + "content": "- We propose a token-level augmentation Tube TokenMix, which is more suitable for video Transformer than pixel-level mixing strategies. Coupled with Temporal Warping Augmentation, which improves temporal variations between frames, TTMix achieves significant boost compared with image augmentation." + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.267, + 0.89, + 0.356 + ], + "angle": 0, + "content": "- We conduct extensive experiments on three benchmark datasets. The performances of our method in two different sizes (i.e., SVFormer-B and SVFormer-S) outperform state-of-the-art approaches by clear margins. Our method sets a strong baseline for future transformer-based works." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.373, + 0.649, + 0.388 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.398, + 0.892, + 0.746 + ], + "angle": 0, + "content": "Deep Semi-supervised Learning Deep learning relies on large-scale annotated data, however collecting these annotations is labor-intensive. Semi-supervised learning is a natural solution to reduce the cost of labeling, which leverages a few labeled samples and a large amount of unlabeled samples to train the model. The research and application of SSL mainly focus on image recognition [41, 44, 54] with a two-step process: data augmentation and consistency regularization. Concretely, different data augmentations [10] views are input to the model, and their output consistencies are enforced through a consistency loss. Another line of work generates new data and labels using mixing [5, 19, 49] to train the network. Among these state-of-the-art methods, FixMatch have been widely used due its effective and its variants have been extended to many other applications, such as object detection [27, 32], semantic segmentation [1, 8], 3D reconstruction [61], etc. Although FixMatch has achieved good performance in many tasks, it may not achieve satisfactory results when directly transferred to video action recognition due to the lack of temporal augmentation. In this paper, we introduce temporal augmentation TWAug with mixing based method TTMix, which is suitable for video transformers at SSL settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Semi-supervised Action Recognition VideoSSL [25] presents a comparative study of applying 2D SSL methods to videos, which verifies the limitations of the direct extension of pseudo labeling method. TCL [40] explores the effect of a group contrastive loss and self-supervised tasks. MvPL [62] and LTG [57] introduce optical flow or temporal gradient modal to generate high quality pseudo labels for training, respectively. CMPL [64] introduce an auxiliary network, which requires more frames in training, increasing the difficulty of application. Besides, previous methods are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "18817" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.168 + ], + "angle": 0, + "content": "all based on 2D [40] or 3D convolutional [57, 62, 64] networks, which require more training epochs. Our approach is the first to make the exploration of Video Transformer for SSL action recognition and achieves the best performance with the least training cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.169, + 0.471, + 0.397 + ], + "angle": 0, + "content": "Video Transformer The great success of vision transformer [13, 30, 33, 45, 68] in image recognition leads to the development of exploring the transformer-base architecture for video recognition tasks. VTN [36] uses additional temporal attention on the top of the pretrained ViT [13]. TimeSformer [4] investigates different spatial-temporal attention mechanisms and adopts factored space time attention as a trade-off of speed and accuracy. ViViT [2] explores four different types of attention, and selects the global spatiotemporal attention as the default to achieve promising performance. In addition, MviT [14], Video Swin [34], Uniformer [28] and Video Mobile-Former [53] incorporate the inductive bias in convolution into transformers. While these methods focus on fully-supervised setting, limited effort has been made for transformers in the semi-supervised setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Data Augmentation Data augmentation is an essential step in modern deep networks to improve the training efficiency and performance. Cutout [12] removes random rectangle regions in images. Mixup [67] performs image mixing by linearly interpolating both the raw image and labels. In CutMix [66], patches are cut and pasted among image pairs. AutoAugment [10] automatically searches for augmentation strategies to improve the results. PixMix [24] explores the natural structural complexity of images when performing mixing. TokenMix [31] mixes images at the token-level and allows the region to be multiple isolated parts. Though these methods have achieved good results, they are all specially designed for pure image and most of them are pixel-level augmentations. In contrast, our TTMix coupled with TWAug is devised for video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.169, + 0.667 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.471, + 0.77 + ], + "angle": 0, + "content": "In this section, we first introduce the preliminaries of SSL in Sec. 3.1. The pipeline of our proposed SVFormer is described in Sec. 3.2. Then we detail the proposed Tube TokenMix (TTMix) in Sec. 3.3, as well as the effective albeit simple temporal warping augmentation. Finally, we show the training paradigm in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.274, + 0.801 + ], + "angle": 0, + "content": "3.1. Preliminaries of SSL" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Suppose we have \\(N\\) training video samples, including \\(N_{L}\\) labeled videos \\((x_{l},y_{l})\\in \\mathcal{D}_{L}\\) and \\(N_{U}\\) unlabeled videos \\(x_{u}\\in \\mathcal{D}_{U}\\), where \\(x_{l}\\) is the labeled video sample with a category label \\(y_{l}\\), and \\(x_{u}\\) is the unlabeled video sample. In general, \\(N_{U}\\gg N_{L}\\). The aim of SSL is to utilize both \\(\\mathcal{D}_L\\) and \\(\\mathcal{D}_U\\) to train the model." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.09, + 0.885, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.395 + ], + "angle": 0, + "content": "Figure 2. Overview of our Tube TokenMix training framework. The two input unlabeled samples are mixed via a tube mask, where the generated sample is fed into the Student model. The two samples are also fed into the EMA-Teacher to obtain their pseudo labels, which are further linearly interpolated via mask ratio \\(\\lambda\\) to produce pseudo label for the generated sample. \"SG\" means stop gradient. The data augmentation is omitted here." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.418, + 0.6, + 0.435 + ], + "angle": 0, + "content": "3.2. Pipeline" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.441, + 0.892, + 0.518 + ], + "angle": 0, + "content": "SVFormer follows the popular semi-supervised learning framework FixMatch [41] that use a consistency loss between two differently augmented views. The training paradigm is divided into two parts. For the labeled set \\(\\{(x_l, y_l)\\}_{l=1}^{N_L}\\), the model optimizes the supervised loss \\(\\mathcal{L}_s\\):" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.526, + 0.892, + 0.563 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\frac {1}{N _ {L}} \\sum^ {N _ {L}} \\mathcal {H} \\left(\\mathcal {F} \\left(x _ {l}\\right), y _ {l}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.575, + 0.891, + 0.605 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}(\\cdot)\\) refers to the predictions produced by the model and \\(\\mathcal{H}\\) is the standard cross entropy loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.727 + ], + "angle": 0, + "content": "For unlabeled samples \\( x_{u} \\), we first use weak augmentations (e.g., random horizontal flipping, random scaling, and random cropping) and strong augmentations (e.g., AutoAugment [10] or Dropout [43]) to generate two views separately, \\( x_{w} = \\mathcal{A}_{weak}(x_{u}) \\), \\( x_{s} = \\mathcal{A}_{strong}(x_{u}) \\). Then the pseudo label of the weak view \\( \\hat{y}_w = \\arg \\max (\\mathcal{F}(x_w)) \\), which is produced by the model, is utilized to supervise the strong view, with the following unsupervised loss:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.735, + 0.892, + 0.771 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {u n} = \\frac {1}{N _ {U}} \\sum^ {N _ {U}} \\mathbb {I} (\\max (\\mathcal {F} (x _ {w})) > \\delta) \\mathcal {H} (\\mathcal {F} (x _ {s}), \\hat {y} _ {w}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.892, + 0.839 + ], + "angle": 0, + "content": "where \\(\\delta\\) is the predefined threshold, and \\(\\mathbb{I}\\) is the indicator function that equals 1 when the maximum class probability exceeds \\(\\delta\\) otherwise 0. The confidence indicator is used to filter the noisy pseudo labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "EMA-Teacher In FixMatch, the two augmented inputs share the same model, which tends to cause model collapsing easily [21, 23]. Therefore, we adopt the exponential" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18818" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.168 + ], + "angle": 0, + "content": "moving average (EMA)-Teacher in our framework, which is an improved version of FixMatch. The pseudo labels are generated by the EMA-Teacher model, whose parameters are updated by exponential moving average of the student parameters, formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.181, + 0.47, + 0.197 + ], + "angle": 0, + "content": "\\[\n\\theta_ {t} \\leftarrow m \\theta_ {t} + (1 - m) \\theta_ {s}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.209, + 0.471, + 0.3 + ], + "angle": 0, + "content": "where \\( m \\) is a momentum coefficient, \\( \\theta_{t} \\) and \\( \\theta_{s} \\) are the parameters of teacher and student model, respectively. EMA has achieved success in many tasks, such as self-supervised learning [21, 23], SSL of image classification [19, 44], and object detection [27, 32]. Here we are the first to adopt this method in semi-supervised video action recognition." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.31, + 0.236, + 0.324 + ], + "angle": 0, + "content": "3.3. Tube TokenMix" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.47, + 0.409 + ], + "angle": 0, + "content": "One of the core problems in semi-supervised frameworks is how to enrich the dataset with high-quality pseudo labels. Mixup [67] is a widely adopted data augmentation strategy, which performs convex combination between pairs of samples and labels as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.422, + 0.47, + 0.438 + ], + "angle": 0, + "content": "\\[\n\\hat {x} = \\lambda \\cdot x _ {1} + (1 - \\lambda) \\cdot x _ {2}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.467, + 0.47, + 0.483 + ], + "angle": 0, + "content": "\\[\n\\hat {y} = \\lambda \\cdot y _ {1} + (1 - \\lambda) \\cdot y _ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.471, + 0.596 + ], + "angle": 0, + "content": "where the ratio \\(\\lambda\\) is a scalar that conforms to the beta distribution. Mixup [67] and its variants (e.g. CutMix [66]) have achieved success in many tasks in the low-data regime, such as long-tail classification [9, 69], domain adaptation [63] [55], few-shot learning [35, 60], etc. For SSL, Mixup also performs well by mixing the pseudo labels of unlabeled samples in image classification [49]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.766 + ], + "angle": 0, + "content": "Mixing in Videos While directly applying Mixup or CutMix to video scenarios results in clear improvements in Conv-based methods [71], these methods show unsatisfactory performance in our method. The reason is that our method adopts the Transformer backbone, where the pixel-level mixing augmentation (Mixup or CutMix) may be not perfectly suitable for such token-level models [31]. To narrow the gap, we propose 3 token-level mixing augmentation methods for video data, namely, Rand TokenMix, Frame TokenMix, and Tube TokenMix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.767, + 0.471, + 0.874 + ], + "angle": 0, + "content": "Fig. 2 illustrates the pipeline of our method. Given unlabeled video clips \\( x_{a}, x_{b} \\in \\mathbb{R}^{H \\times W \\times T} \\), our method employs a token-level mask \\( \\mathbf{M} \\in \\{0,1\\}^{H \\times W \\times T} \\) to perform sample mixing. Note that \\( H \\) and \\( W \\) are the height and width of the frame after patch tokenization, and \\( T \\) is the clip length. To generate a new sample \\( x_{mix} \\), we mix \\( x_{a} \\) and \\( x_{b} \\) after strong data augmentations \\( A_{strong} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.886, + 0.47, + 0.903 + ], + "angle": 0, + "content": "\\[\nx _ {m i x} = \\mathcal {A} _ {s t r o n g} \\left(x _ {a}\\right) \\odot \\mathbf {M} + \\mathcal {A} _ {s t r o n g} \\left(x _ {b}\\right) \\odot (\\mathbf {1} - \\mathbf {M}), \\tag {6}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.09, + 0.627, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.201, + 0.557, + 0.211 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.644, + 0.09, + 0.758, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.201, + 0.692, + 0.21 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.09, + 0.892, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.811, + 0.2, + 0.823, + 0.21 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.215, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Figure 3. Examples of masks in three token mixing strategies. (a) Rand TokenMix. (b) Tube TokenMix. (c) Frame TokenMix." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.26, + 0.835, + 0.276 + ], + "angle": 0, + "content": "Algorithm 1 Consistency loss for Tube TokenMix" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.28, + 0.732, + 0.295 + ], + "angle": 0, + "content": "Require: Unlabeled clip batch \\( \\mathbf{x}_{\\mathbf{a}} \\)" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.296, + 0.8, + 0.31 + ], + "angle": 0, + "content": "Require: Tube TokenMask M, mask ratio \\(\\lambda\\)" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.311, + 0.692, + 0.325 + ], + "angle": 0, + "content": "Require: Teacher model \\(\\mathcal{F}_t\\)" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.326, + 0.692, + 0.34 + ], + "angle": 0, + "content": "Require: Student model \\(\\mathcal{F}_s\\)" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.341, + 0.728, + 0.355 + ], + "angle": 0, + "content": "Require: Confidence threshold \\(\\delta\\)" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.356, + 0.812, + 0.371 + ], + "angle": 0, + "content": "\\(\\mathbf{x_b} = \\mathrm{shuffle}(\\mathbf{x_a})\\) {shuffle samples in batch}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.371, + 0.757, + 0.386 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{x}}_{\\mathbf{a}} =\\) spatial_aug \\((\\mathbf{x}_{\\mathbf{a}})\\) {spatial aug.}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.387, + 0.846, + 0.402 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{x}}_{\\mathbf{b}} =\\) temporal\\_aug \\((\\mathbf{x}_{\\mathbf{b}})\\) {temporal warping aug.}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.402, + 0.811, + 0.417 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{y}}_a = \\mathrm{stop\\_gradient}(\\mathcal{F}_t(\\mathbf{x}_a))\\) {teacher pred.}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.417, + 0.704, + 0.431 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{y}}_b = \\mathrm{stop\\_gradient}(\\mathcal{F}_t(\\mathbf{x}_b))\\)" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.431, + 0.808, + 0.447 + ], + "angle": 0, + "content": "\\(\\mathbf{c_{a}} = \\max_{i}\\mathbf{y}_{a}[i]\\) {confidence of prediction}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.448, + 0.629, + 0.461 + ], + "angle": 0, + "content": "\\(\\mathbf{c_b} = \\max_i\\mathbf{y}_b[i]\\)" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.462, + 0.818, + 0.477 + ], + "angle": 0, + "content": "\\(\\mathbf{x}_{mix} = \\hat{\\mathbf{x}}_a*\\mathbf{M} + \\hat{\\mathbf{x}}_b*(1 - \\mathbf{M})\\) {mix clips}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.477, + 0.837, + 0.492 + ], + "angle": 0, + "content": "\\(\\hat{\\mathbf{y}}_{mix} = \\hat{\\mathbf{y}}_a*\\lambda +\\hat{\\mathbf{y}}_b*(1 - \\lambda)\\) {mix tea. preds.}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.492, + 0.841, + 0.507 + ], + "angle": 0, + "content": "\\(\\mathbf{c}_{mix} = \\mathbf{c}_a*\\lambda +\\mathbf{c}_b*(1 - \\lambda)\\) {mix confidence.}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.508, + 0.811, + 0.522 + ], + "angle": 0, + "content": "\\(\\mathbf{q} = \\mathrm{mean}(c_{mix}\\geq \\delta)\\) {mean of conf. mask}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.522, + 0.818, + 0.538 + ], + "angle": 0, + "content": "\\(\\mathbf{y}_{mix} = \\mathcal{F}_s(\\mathbf{x}_{mix})\\) {stu. pred. on mixed clip}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.538, + 0.784, + 0.553 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_{mix} = q||\\mathbf{y}_{mix} - \\hat{\\mathbf{y}}_{mix}||_2^2\\) {cons. loss}" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.554, + 0.61, + 0.566 + ], + "angle": 0, + "content": "Return \\(\\mathcal{L}_{\\text{mix}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.891, + 0.627 + ], + "angle": 0, + "content": "where \\(\\odot\\) is element-wise multiplication, and \\(\\mathbf{1}\\) is a binary mask with all ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.854 + ], + "angle": 0, + "content": "The mask \\(\\mathbf{M}\\) differs in the three augmentation methods, as demonstrated in Fig. 3. For Rand TokenMix, the masked tokens are randomly selected from the whole video clip (from \\(H\\times W\\times T\\) tokens). For Frame TokenMix, we randomly select frames from the \\(T\\) frames and mask all the tokens in these frames. For Tube TokenMix, we adopt the tube-style masking strategy, that is, different frames share the same spatial mask matrix. In this case, the mask \\(\\mathbf{M}\\) has consistent masked tokens over the temporal axis. While our mask design shares similarity with the recent masked image/video modeling [16, 47, 51, 52, 58, 59], our motivation is totally different. They focus on removing certain regions and making the model predict the masked areas for feature learning. In contrast, we leverage the mask to mix two clips and synthesize a new data sample." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The mixed sample \\( x_{mix} \\) is then fed to the student model \\( \\mathcal{F}_s \\), obtaining the model prediction \\( y_{mix} = \\mathcal{F}_s(x_{mix}) \\). In addition, the pseudo labels \\( \\hat{y}_a, \\hat{y}_b \\) for \\( x_a, x_b \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18819" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.478, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.096, + 0.877, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Figure 4. One example of utilizing Temporal Warping Augmentation together with spatial augmentation in TTMix. The two clips are first transformed by the two augmentations separately, after which TTMix is performed to generate a new clip." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.381 + ], + "angle": 0, + "content": "are produced by inputting the weak augmented samples \\(\\mathcal{A}_{weak}(x_a),\\mathcal{A}_{weak}(x_b)\\) to the teacher model \\(\\mathcal{F}_t\\)" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.395, + 0.47, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {a} = \\arg \\max \\left(\\mathcal {F} _ {t} \\left(\\mathcal {A} _ {\\text {w e a k}} \\left(x _ {a}\\right)\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.431, + 0.469, + 0.447 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {b} = \\arg \\max \\left(\\mathcal {F} _ {t} \\left(\\mathcal {A} _ {\\text {w e a k}} \\left(x _ {b}\\right)\\right)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.451, + 0.469, + 0.51 + ], + "angle": 0, + "content": "Note that if \\(\\max (\\mathcal{F}_t(\\mathcal{A}_{weak}(x))) < \\delta\\), the pseudo label \\(\\hat{y}\\) remains the soft label \\(\\mathcal{F}_t(\\mathcal{A}_{weak}(x))\\). The pseudo label \\(\\hat{y}_{mix}\\) for \\(x_{mix}\\) is generated by mixing \\(\\hat{y}_a\\) and \\(\\hat{y}_b\\) with mask ratio \\(\\lambda\\):" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.512, + 0.469, + 0.528 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {m i x} = \\lambda \\cdot \\hat {y} _ {a} + (1 - \\lambda) \\cdot \\hat {y} _ {b}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.469, + 0.562 + ], + "angle": 0, + "content": "Finally, the student model is optimized by the following consistency loss:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.57, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {m i x} = \\frac {1}{N _ {m}} \\sum^ {N _ {m}} \\left(\\hat {y} _ {m i x} - y _ {m i x}\\right) ^ {2}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.469, + 0.642 + ], + "angle": 0, + "content": "where \\(N_{m}\\) is the number of mixed samples. The algorithm of consistency loss for TTMix is shown in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Temporal Warping Augmentation Most existing augmentation methods are designed for image tasks, which focus more on the spatial augmentation. They manipulate single or a pair of images to generate new image samples, without considering any temporal changes. Even the commonly adopted temporal augmentations, including varying temporal locations [18] and frame rates [40, 65], only consider simple temporal shift or scaling, that is, changing the holistic location or play speed. However, human actions are very complex and can have different temporal variation at every timestamp. To cover such challenging cases, we propose to distort the temporal duration of each frame, thus introducing higher randomness into the data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Our Temporal Warping Augmentation (TWAug) can stretch one frame to various temporal length. Given an extracted video clip of \\( T \\) frames (e.g., 8 frames), we randomly" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.351, + 0.885, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.48, + 0.892, + 0.507 + ], + "angle": 0, + "content": "Figure 5. Illustration of Temporal Warping Augmentation. We demonstrate three augment examples of different selected frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.636 + ], + "angle": 0, + "content": "determine to keep all the frames, or select a small portion of frames (e.g., 2 or 4 frames) while masking the others. The masked frames are then padded with random neighbouring visible (unmasked) frames. Note that after temporal padding, the frame order is still retained. Fig. 5 shows three examples of selecting 2, 4, and 8 frames, respectively. The proposed TWAug can help the model learn the flexible temporal dynamics during training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.636, + 0.892, + 0.742 + ], + "angle": 0, + "content": "The Temporal Warping Augmentation serves as a strong augmentation in TTMix. Typically, we combine TWAug with the conventional spatial augmentation [10, 43] to perform the mixing. As shown in Fig. 4, the two input clips are first transformed by spatial augmentation and TWAug separately, after which the two clips are mixed through TTMix. We verify the effectiveness of our TWAug in Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.75, + 0.685, + 0.767 + ], + "angle": 0, + "content": "3.4. Training Paradigm" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.774, + 0.892, + 0.834 + ], + "angle": 0, + "content": "The training of SVFormer consists of three parts: supervised loss formulated by Eq. (1), unsupervised pseudo-label consistency loss Eq. (2), and TTMix consistency loss Eq. (10). The final loss function is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.845, + 0.892, + 0.861 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {a l l} = \\mathcal {L} _ {s} + \\gamma_ {1} \\mathcal {L} _ {u n} + \\gamma_ {2} \\mathcal {L} _ {m i x}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "where \\(\\gamma_{1}\\) and \\(\\gamma_{2}\\) are the hyperparameters for balancing the loss items." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18820" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Comparisons with state-of-the-art methods on UCF-101 and Kinetics-400. Note that 3D-ResNet-18 and 3D-ResNet-50 denote the backbone networks and their depths. We report Top-1 accuracy as the evaluation metric. \"Input\" shows the modalities used during training, where \"V\" is the raw RGB video, \"F\" is optical flow and \"G\" is the temporal gradient." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.142, + 0.872, + 0.387 + ], + "angle": 0, + "content": "
MethodBackboneInputw ImgNetEpochUCF-101Kinetics-400
1%10%1%10%
Supervised3D-ResNet-50V✓2006.532.44.436.2
ViT-SV✓3012.762.519.956.6
FixMatch (NeurIPS 2020) [41]SlowFast-R50V✓20016.155.110.149.4
VideoSSL(WACV 2021) [25]3D-ResNet-18V✓--42.0-33.8
TCL (CVPR 2021) [40]TSM-ResNet-18V400--8.5-
ActorCutMix (CVIU 2021) [71]R(2+1)D-34V✓600-53.09.02-
MvPL (ICCV 2021) [62]3D-ResNet-50V+F+G60022.880.517.058.2
CMPL (CVPR 2022) [64]R50 + R50-1/4V✓20025.179.117.658.4
LTG (CVPR 2022) [57]3D-ResNet-18V+G180/360-62.49.843.8
TACL(TCSVT 2022) [46]3D-ResNet-50V✓200-55.6--
L2A (ECCV 2022) [20]3D-ResNet-18V✓400-60.1--
SVFormer-S (Ours)ViT-SV✓3031.479.132.661.6
SVFormer-B (Ours)ViT-BV✓3046.386.749.169.4
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.409, + 0.204, + 0.426 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.471, + 0.526 + ], + "angle": 0, + "content": "In this section, we first introduce the experimental settings in Sec. 4.1. Following previous work [57,64], we conduct experiments under different labeling rates in Sec 4.2. In addition, we also perform ablation experiments and empirical analysis in Section 4.3. If not emphasized, we only use RGB modal for inference with the official validation set." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.536, + 0.273, + 0.554 + ], + "angle": 0, + "content": "4.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.756 + ], + "angle": 0, + "content": "Datasets Kinetics-400 [7] is a large-scale human action video dataset, with up to 245k training samples and 20k validation samples, covering 400 different categories. We follow the state-of-the-art methods MvPL [62] and CMPL [64] to sample 6 or 60 labeled training videos per category, i.e. at \\(1\\%\\) or \\(10\\%\\) labeling rates. UCF-101 [42] is a dataset with 13,320 video samples, which consists of 101 categories. We also sample 1 or 10 samples in each category as the labeled set following CMPL [64]. As for HMDB-51 [26], it is a small-scale dataset with only 51 categories composed of 6,766 videos. Following the division of LTG [57] and VideoSSL [25], we conduct experiments at three different labeling rates: \\(40\\%\\), \\(50\\%\\), and \\(60\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.76, + 0.47, + 0.806 + ], + "angle": 0, + "content": "Evaluation Metric We show the accuracy of Top-1 in main results, and also present the accuracy of Top-5 in some ablation experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Baseline We utilize the ViT [13] extended video TimeSformer [4] as the backbone of our baseline. The hyperparameters are mostly kept the same as the baseline, and we adopt the divided space-time attention as in TimeSformer [4]. Since TimeSformer only have ViT-Base models, we implement SVFormer-Small model from DeiT-S [48] with" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.408, + 0.895, + 0.465 + ], + "angle": 0, + "content": "Table 2. Comparisons with state-of-the-art methods on HMDB-51. We report Top-1 accuracy. \"Input\" shows the modalities used during training, where \"V\" is the raw RGB video, \"F\" is optical flow and \"G\" is the temporal gradient." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.475, + 0.895, + 0.613 + ], + "angle": 0, + "content": "
BackboneInput40%50%60%
VideoSSL [25]3D-R18V32.736.237.0
ActorCutMix [71]R(2+1)D-34V32.938.238.9
MvPL [62]3D-R18V+F+G30.533.935.8
LTG [57]3D-R18V+G46.548.449.7
TACL [46]3D-R18V38.740.241.7
L2A [20]3D-R18V42.146.347.1
SVFormer-S (Ours)ViT-SV56.258.259.7
SVFormer-B (Ours)ViT-BV61.664.468.2
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.895, + 0.687 + ], + "angle": 0, + "content": "the dimension of 384 and 6 heads, in order to have comparable number of parameters with other Conv-based methods [22, 62, 64]. For fair comparisons, we train 30 epochs for TimeSformer as the supervised baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Training and Inference For training, we follow the setting of TimeSformer [4]. The training uses 8 or 16 GPUs, with a SGD optimizer using a momentum of 0.9 and a weight decay of 0.001. For each setting, the basic learning rate is set to 0.005, which is divided by 10 at epochs 25, and 28. As for the confidence score threshold, we search for the optimal \\(\\delta\\) from \\(\\{0.3, 0.5, 0.7, 0.9\\}\\). \\(\\gamma_{1}\\) and \\(\\gamma_{2}\\) are set to 2. The masking ratio \\(\\lambda\\) is sampled from beta distribution \\(\\mathrm{Beta}(\\alpha, \\alpha)\\), where \\(\\alpha = 10\\). In the testing phase, following the inference strategies in MvPL [62] and CMPL [64], we uniformly sample five clips from the entire video, and make three different crops to get \\(224 \\times 224\\) resolution to cover most of the spatial areas of the clips. The final prediction is the average of the softmax probabilities of these \\(5 \\times 3\\) pre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18821" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.462, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.502 + ], + "angle": 0, + "content": "Figure 6. Example of the traditional pixel-level mixing methods and our proposed token-level mixing. Note that token-level methods mix two samples after tokenization but the visualization is shown on image-level for clear presentation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.47, + 0.543 + ], + "angle": 0, + "content": "dictions. We also conduct a comparison of inference setting in the ablation study in Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.554, + 0.218, + 0.569 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.713 + ], + "angle": 0, + "content": "The main results of Kinetics-400 [7] and UCF-101 [42] are shown in Table 1. Compared with previous methods, our model SVFormer-S achieves the best performance with the fewest training epochs among the methods that only use RGB data. In particular, at the labeling rate of \\(1\\%\\) setting, SVFormer-S improves previous approach [64] by \\(6.3\\%\\) in UCF-101 and \\(15.0\\%\\) in Kinetics-400. In addition, when adopting larger models, SVFormer-B significantly outperforms the state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.47, + 0.821 + ], + "angle": 0, + "content": "Specifically, in Kinetics-400, SVFormer-B can achieve \\(69.4\\%\\) with only \\(10\\%\\) labeled data, which is comparable to \\(77.9\\%\\) of fully-supervised setting in TimeSformer [4]. Moreover, as shown in Table 2, for the small-scale dataset HMDB-51 [26], our SVFormer-S and SVFormer-B have also improved by about \\(10\\%\\) and \\(15\\%\\) compared with the previous method [57]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.242, + 0.846 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To understand the effect of each part of the design in our method, we conduct extensive ablation studies on the Kinetics-400 and UCF-101 at the \\(1\\%\\) labeling ratio setting" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.894, + 0.133 + ], + "angle": 0, + "content": "Table 3. SSL framework selection. We compare the EMA-Teacher framework with FixMatch. The results are reported on Kinetics-400 and UCF-101 with \\(1\\%\\) labeling ratio." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.143, + 0.851, + 0.242 + ], + "angle": 0, + "content": "
MethodUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline12.729.819.942.3
FixMatch [41]25.147.328.254.6
EMA-Teacher31.456.932.659.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.254, + 0.894, + 0.297 + ], + "angle": 0, + "content": "Table 4. TokenMix Mask sampling. We compare different token masking strategies. The results are reported on Kinetics-400 and UCF-101 with \\(1\\%\\) labeling ratio." + }, + { + "type": "table", + "bbox": [ + 0.531, + 0.299, + 0.857, + 0.453 + ], + "angle": 0, + "content": "
Method/DatasetUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline26.148.923.647.7
CutMix [66]28.751.328.653.7
Mixup [67]29.853.029.355.1
PixMix [24]29.752.429.655.8
Frame TokenMix29.854.226.350.0
Rand TokenMix30.355.328.854.2
Tube TokenMix31.456.932.659.0
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.469, + 0.625, + 0.483 + ], + "angle": 0, + "content": "with SVFormer-S." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.892, + 0.61 + ], + "angle": 0, + "content": "Analysis of SSL framework The comparison of FixMatch and EMA-Teacher is shown in Table 3. It is clear that the two methods have significantly improved the baseline approach. In addition, EMA-Teacher has exhibited considerable gains over FixMatch in both datasets with very few labeled samples, probably because it has improved the stability of training. FixMatch [41] may lead to model collapse with limited labels as shown in [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.825 + ], + "angle": 0, + "content": "Analysis of different mixing strategies We now compare the Tube TokenMix strategy with three pixel-level mixing methods, CutMix [66], Mixup [67], PixMix [24], as well as the other two token-level mixing methods, i.e., Frame TokenMix and Rand TokenMix. The examples of different mixing methods are shown in Fig. 6. The quantitative results are shown in Table 4. Compared with these alternative methods, all mixing methods can improve the performance, which proves the effectiveness of mixing-based consistency losses. In addition, we observe that the token-level methods (Rand TokenMix and Tube TokenMix) perform better than the pixel-level mixing methods. This is not surprising since transformers operate on tokens, and thus token-level mixing has inherent advantages." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.894, + 0.903 + ], + "angle": 0, + "content": "The performance of Frame TokenMix is even worse than that of pixel-level mixing methods, which is also expected. We hypothesize that replacing entire frames in video clip will scramble up the temporal reasoning, thus leading to poor temporal attention modeling. In addition, Tube Token-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18822" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.131 + ], + "angle": 0, + "content": "Table 5. Effects of Spatial and Temporal Warping Augmentations (TWAug). The results are reported on Kinetics-400 and UCF-101 with \\(1\\%\\) labeling ratio." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.134, + 0.462, + 0.226 + ], + "angle": 0, + "content": "
SpatialTemporalUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline29.552.128.554.2
Spatial-only✓29.953.230.355.9
Temporal-only✓30.255.830.856.4
Spatial+Temporal✓✓31.456.932.659.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.238, + 0.468, + 0.307 + ], + "angle": 0, + "content": "Table 6. Effects of different inference schemes. We compare the sparse sampling strategy and dense sampling method with different frames. The \\( a \\times b \\) in 'Frames' column means sampling \\( a \\) frames at frame rate \\( b \\). The results are reported on Kinetics-400 and UCF-101 with \\( 1\\% \\) labeling ratio." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.31, + 0.459, + 0.413 + ], + "angle": 0, + "content": "
MethodFramesTest ViewUCF-1%Kinetic-1%
MvPL [62]8 × 810 × 322.817.0
CMPL [64]8 × 810 × 325.117.6
SVFormer-S8 × 321 × 329.331.0
SVFormer-S8 × 85 × 331.432.6
SVFormer-S16 × 410 × 331.633.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.468, + 0.499 + ], + "angle": 0, + "content": "Mix achieves the best results. We suppose the consistent masked tokens over temporal axis can prevent information leaky between adjacent frames in the same spatial locations, especially in such a short-term clip. Therefore, Tube Token-Mix could better model the spatio-temporal correlations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.468, + 0.655 + ], + "angle": 0, + "content": "Analysis of Augmentations The effects of spatial augmentation and temporal warping augmentation are evaluated in Table 5. The baseline indicates removing both strong spatial augmentation (e.g. AutoAugment [10] and Dropout [43]) and TWAug in all branches. In this case, the experimental performance drops dramatically. When spatial augmentation or temporal warping augmentation is incorporated into the baseline separately, the performance is improved. The best practice is to perform data augmentations in both spatial and temporal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Analysis of Inference We evaluate the effect of frame rate sampling and different inference schemes, as shown in Table 6. Previous methods, i.e. CMPL [64] and MvPL [62], utilize the clip-based sparse sampling, which samples 8 frames at frame rate 8 as a clip. For each video, 10 clips are sampled, where each clip is cropped 3 times according to different spatial positions. Finally, the predictions of \\(10 \\times 3\\) samples are averaged. TimeSformer [4] adopts the video-based sparse sampling, that is, 8 frames are sampled at frame rate 32 as the representation of the whole video. Then 3 different cropped views are used, namely \\(8 \\times 32\\). Applying the video-based sparse sampling scheme as in TimeSformer [4] can reduce the inference cost, but the performance is worse than that of clip-based sampling. Experiments at sampling schemes of \\(8 \\times 8\\) and \\(16 \\times 4\\) demonstrate better performance. For the trade-off between effi" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.09, + 0.693, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.089, + 0.882, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.186, + 0.693, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.696, + 0.184, + 0.881, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.279, + 0.892, + 0.35 + ], + "angle": 0, + "content": "Figure 7. Effects of hyperparameters. Results of varying threshold \\(\\delta\\), ratio between unlabeled and labeled data in a mini-batch \\((B_u / B_l)\\), momentum coefficient \\(m\\), and loss weights \\((\\gamma_1, \\gamma_2)\\) are included to comprehensively study the effects of the hyperparameters. Reported on Kinetics-400 with \\(1\\%\\) labeling ratio." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.389 + ], + "angle": 0, + "content": "ciency and accuracy, we use \\(8 \\times 8\\) as the default setting following CMPL [64] and MvPL [62]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.893, + 0.635 + ], + "angle": 0, + "content": "Analysis of hyperparameters Here we explore the effect of different hyperparameters. We conduct experiments under \\(1\\%\\) setting of Kinetics-400. We first explore the effect of different threshold values of \\(\\delta\\). As shown in Fig. 7(a), we can observe that when labeled samples are extremely scarce, best results are achieved by setting a small \\(\\delta\\) value \\((\\delta = 0.3)\\). We then evaluate how the ratio between labeled samples and unlabeled samples in a mini-batch affects the result. We fix the labeled sample number \\(B_{l}\\) to 1, and sample \\(B_{u}\\) unlabeled samples to form a mini-batch, where \\(B_{u}\\) is in \\(\\{1,2,3,5,7\\}\\). The results are shown in Fig. 7(b). When \\(B_{u} = 5\\), the model produces the highest result. Finally, we explore the choice of momentum coefficient \\(m\\) of EMA and the loss weights \\(\\gamma_{1}\\) and \\(\\gamma_{2}\\), as shown in Fig. 7(c) and Fig. 7(d). We thus set \\(m = 0.99\\) and \\(\\gamma_{1} = \\gamma_{2} = 2\\) as default setting in all the experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.619, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.87 + ], + "angle": 0, + "content": "In this paper we present SVFormer, a transformer-based semi-supervised video action recognition method. We propose Tube TokenMix, a data augmentation method that is specially designed for video transformer models. Coupled with the temporal warping augmentation, which covers the complex temporal variations by arbitrarily changing the frame length, TTMix achieves significant improvement compared with conventional augmentations. SVFormer outperforms the state-of-the-art with a large margin on UCF-101, HMDB-51 and Kinetics-400 without increasing overheads. Our work establishes a new benchmark for semi-supervised action recognition and encourages future work to adopt Transformer architecture." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement This project was supported by NSFC under Grant No. 62032006 and No. 62102092." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18823" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. Semi-supervised semantic segmentation with pixel-level contrastive learning from a class-wise memory bank. 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Learning representational invariances for data-efficient action recognition. arXiv preprint arXiv:2103.16565, 2021. 4, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18826" + } + ] +] \ No newline at end of file diff --git a/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/2bd91319-3d84-428a-8335-5833e2e27f2c_origin.pdf b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/2bd91319-3d84-428a-8335-5833e2e27f2c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2e772f818123221e668f4ec2063cf4a0068dd7f6 --- /dev/null +++ b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/2bd91319-3d84-428a-8335-5833e2e27f2c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7953945d760d28363718f618b7479027fb3c90ae0c729c4576df8c749392df0f +size 1399770 diff --git a/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/full.md b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d7b9eed5f73eba3b97a7ace7c301e5a69ea52dde --- /dev/null +++ b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/full.md @@ -0,0 +1,390 @@ +# SVFormer: Semi-supervised Video Transformer for Action Recognition + +Zhen Xing $^{1,2}$ Qi Dai $^{3}$ Han Hu $^{3}$ Jingjing Chen $^{1,2}$ Zuxuan Wu $^{1,2\dagger}$ Yu-Gang Jiang $^{1,2}$ + +1 Shanghai Key Lab of Intell. Info. Processing, School of CS, Fudan University + +$^{2}$ Shanghai Collaborative Innovation Center of Intelligent Visual Computing + $^{3}$ Microsoft Research Asia + +# Abstract + +Semi-supervised action recognition is a challenging but critical task due to the high cost of video annotations. Existing approaches mainly use convolutional neural networks, yet current revolutionary vision transformer models have been less explored. In this paper, we investigate the use of transformer models under the SSL setting for action recognition. To this end, we introduce SVFormer, which adopts a steady pseudo-labeling framework (i.e., EMA-Teacher) to cope with unlabeled video samples. While a wide range of data augmentations have been shown effective for semi-supervised image classification, they generally produce limited results for video recognition. We therefore introduce a novel augmentation strategy, Tube TokenMix, tailored for video data where video clips are mixed via a mask with consistent masked tokens over the temporal axis. In addition, we propose a temporal warping augmentation to cover the complex temporal variation in videos, which stretches selected frames to various temporal durations in the clip. Extensive experiments on three datasets Kinetics-400, UCF-101, and HMDB-51 verify the advantage of SVFormer. In particular, SVFormer outperforms the state-of-the-art by $31.5\%$ with fewer training epochs under the $1\%$ labeling rate of Kinetics-400. Our method can hopefully serve as a strong benchmark and encourage future search on semi-supervised action recognition with Transformer networks. Code is released at https://github.com/ChenHsing/SVFormer. + +# 1. Introduction + +Videos have gradually replaced images and texts on Internet and grown at an exponential rate. On video websites such as YouTube, millions of new videos are uploaded every day. Supervised video understanding works [4, 15, 17, 29, 34, 56, 70] have achieved great successes. They rely on + +![](images/fdb6f3c8badab016f0d671560d35f9f0ccddf6f04c7ae6b0f2e8a2ddf03aef0c.jpg) +Figure 1. Comparison of our method with the supervised baseline and previous state-of-the-art SSL method [64]. SVFormer significantly outperforms previous methods under the case with very little labeled data. + +large-scale manual annotations, yet labeling so many videos is time-consuming and labor-intensive. How to make use of unlabeled videos that are readily available for better video understanding is of great importance [25, 38, 39]. + +In this spirit, semi-supervised action recognition [25, 40, 57] explores how to enhance the performance of deep learning models using large-scale unlabeled data. This is generally done with labeled data to pretrain the networks [57,64], and then leveraging the pretrained models to generate pseudo labels for unlabeled data, a process known as pseudo labeling. The obtained pseudo labels are further used to refine the pretrained models. In order to improve the quality of pseudo labeling, previous methods [57, 62] use additional modalities such as optical flow [3] and temporal gradient [50], or introduce auxiliary networks [64] to supervise unlabeled data. Though these methods present promising results, they typically require additional training or inference cost, preventing them from scaling up. + +Recently, video transformers [2,4,34] have shown strong results compared to CNNs [15, 17, 22]. Though great success has been achieved, the exploration of transformers on semi-supervised video tasks remains unexplored. While it sounds appealing to extend vision transformers directly to SSL, a previous study shows that transformers perform significantly worse compared to CNNs in the low-data regime + +due to the lack of inductive bias [54]. As a result, directly applying SSL methods, e.g., FixMatch [41], to ViT [13] leads to an inferior performance [54]. + +Surprisingly, in the video domain, we observe that TimeSformer, a popular video Transformer [4], initialized with weights from ImageNet [11], demonstrates promising results even when annotations are limited [37]. This encourages us to explore the great potential of transformers for action recognition in the SSL setting. + +Existing SSL methods generally use image augmentations (e.g., Mixup [67] and CutMix [66]) to speed up convergence under limited label resources. However, such pixel-level mixing strategies are not perfectly suitable for transformer architectures, which operate on tokens produced by patch splitting layers. In addition, strategies like Mixup and CutMix are particularly designed for image tasks, which fail to consider the temporal nature of video data. Therefore, as will be shown empirically, directly using Mixup or CutMix for semi-supervised action recognition leads to unsatisfactory performance. + +In this work, we propose SVFormer, a transformer-based semi-supervised action recognition method. Concretely, SVFormer adopts a consistency loss that builds two differently augmented views and demands consistent predictions between them. Most importantly, we propose Tube TokenMix (TTMix), an augmentation method that is naturally suitable for video Transformer. Unlike Mixup and CutMix, Tube TokenMix combines features at the token-level after tokenization via a mask, where the mask has consistent masked tokens over the temporal axis. Such a design could better model the temporal correlations between tokens. + +Temporal augmentations in literatures (e.g. varying frame rates) only consider simple temporal scaling or shifting, neglecting the complex temporal changes of each part in human action. To help the model learn strong temporal dynamics, we further introduce the Temporal Warping Augmentation (TWAug), which arbitrarily changes the temporal length of each frame in the clip. TWAug can cover the complex temporal variation in videos and is complementary to spatial augmentations [10]. When combining TWAug with TTMix, significant improvements are achieved. + +As shown in Fig. 1, SVFormer achieves promising results in several benchmarks. (i) We observe that the supervised Transformer baseline is much better than the Conv-based method [22], and is even comparable with the 3D-ResNet state-of-the-art method [64] on Kinetics400 when trained with $1\%$ of labels. (ii) SVFormer-S significantly outperforms previous state-of-the-arts with similar parameters and inference cost, measured by FLOPs. (iii) Our method is also effective for the larger SVFormer-B model. Our contributions are as follows: + +- We are the first to explore the transformer model for semi-supervised video recognition. Unlike SSL for + +image recognition with transformers, we find that using parameters pretrained on ImageNet is of great importance to ensure decent results for action recognition in the low-data regime. + +- We propose a token-level augmentation Tube TokenMix, which is more suitable for video Transformer than pixel-level mixing strategies. Coupled with Temporal Warping Augmentation, which improves temporal variations between frames, TTMix achieves significant boost compared with image augmentation. + +- We conduct extensive experiments on three benchmark datasets. The performances of our method in two different sizes (i.e., SVFormer-B and SVFormer-S) outperform state-of-the-art approaches by clear margins. Our method sets a strong baseline for future transformer-based works. + +# 2. Related Works + +Deep Semi-supervised Learning Deep learning relies on large-scale annotated data, however collecting these annotations is labor-intensive. Semi-supervised learning is a natural solution to reduce the cost of labeling, which leverages a few labeled samples and a large amount of unlabeled samples to train the model. The research and application of SSL mainly focus on image recognition [41, 44, 54] with a two-step process: data augmentation and consistency regularization. Concretely, different data augmentations [10] views are input to the model, and their output consistencies are enforced through a consistency loss. Another line of work generates new data and labels using mixing [5, 19, 49] to train the network. Among these state-of-the-art methods, FixMatch have been widely used due its effective and its variants have been extended to many other applications, such as object detection [27, 32], semantic segmentation [1, 8], 3D reconstruction [61], etc. Although FixMatch has achieved good performance in many tasks, it may not achieve satisfactory results when directly transferred to video action recognition due to the lack of temporal augmentation. In this paper, we introduce temporal augmentation TWAug with mixing based method TTMix, which is suitable for video transformers at SSL settings. + +Semi-supervised Action Recognition VideoSSL [25] presents a comparative study of applying 2D SSL methods to videos, which verifies the limitations of the direct extension of pseudo labeling method. TCL [40] explores the effect of a group contrastive loss and self-supervised tasks. MvPL [62] and LTG [57] introduce optical flow or temporal gradient modal to generate high quality pseudo labels for training, respectively. CMPL [64] introduce an auxiliary network, which requires more frames in training, increasing the difficulty of application. Besides, previous methods are + +all based on 2D [40] or 3D convolutional [57, 62, 64] networks, which require more training epochs. Our approach is the first to make the exploration of Video Transformer for SSL action recognition and achieves the best performance with the least training cost. + +Video Transformer The great success of vision transformer [13, 30, 33, 45, 68] in image recognition leads to the development of exploring the transformer-base architecture for video recognition tasks. VTN [36] uses additional temporal attention on the top of the pretrained ViT [13]. TimeSformer [4] investigates different spatial-temporal attention mechanisms and adopts factored space time attention as a trade-off of speed and accuracy. ViViT [2] explores four different types of attention, and selects the global spatiotemporal attention as the default to achieve promising performance. In addition, MviT [14], Video Swin [34], Uniformer [28] and Video Mobile-Former [53] incorporate the inductive bias in convolution into transformers. While these methods focus on fully-supervised setting, limited effort has been made for transformers in the semi-supervised setting. + +Data Augmentation Data augmentation is an essential step in modern deep networks to improve the training efficiency and performance. Cutout [12] removes random rectangle regions in images. Mixup [67] performs image mixing by linearly interpolating both the raw image and labels. In CutMix [66], patches are cut and pasted among image pairs. AutoAugment [10] automatically searches for augmentation strategies to improve the results. PixMix [24] explores the natural structural complexity of images when performing mixing. TokenMix [31] mixes images at the token-level and allows the region to be multiple isolated parts. Though these methods have achieved good results, they are all specially designed for pure image and most of them are pixel-level augmentations. In contrast, our TTMix coupled with TWAug is devised for video. + +# 3. Method + +In this section, we first introduce the preliminaries of SSL in Sec. 3.1. The pipeline of our proposed SVFormer is described in Sec. 3.2. Then we detail the proposed Tube TokenMix (TTMix) in Sec. 3.3, as well as the effective albeit simple temporal warping augmentation. Finally, we show the training paradigm in Sec. 3.4. + +# 3.1. Preliminaries of SSL + +Suppose we have $N$ training video samples, including $N_{L}$ labeled videos $(x_{l},y_{l})\in \mathcal{D}_{L}$ and $N_{U}$ unlabeled videos $x_{u}\in \mathcal{D}_{U}$ , where $x_{l}$ is the labeled video sample with a category label $y_{l}$ , and $x_{u}$ is the unlabeled video sample. In general, $N_{U}\gg N_{L}$ . The aim of SSL is to utilize both $\mathcal{D}_L$ and $\mathcal{D}_U$ to train the model. + +![](images/f14b0c0083c9412c58aa94cf72b13c4052cf33434722ca15642a870286f00b3d.jpg) +Figure 2. Overview of our Tube TokenMix training framework. The two input unlabeled samples are mixed via a tube mask, where the generated sample is fed into the Student model. The two samples are also fed into the EMA-Teacher to obtain their pseudo labels, which are further linearly interpolated via mask ratio $\lambda$ to produce pseudo label for the generated sample. "SG" means stop gradient. The data augmentation is omitted here. + +# 3.2. Pipeline + +SVFormer follows the popular semi-supervised learning framework FixMatch [41] that use a consistency loss between two differently augmented views. The training paradigm is divided into two parts. For the labeled set $\{(x_l, y_l)\}_{l=1}^{N_L}$ , the model optimizes the supervised loss $\mathcal{L}_s$ : + +$$ +\mathcal {L} _ {s} = \frac {1}{N _ {L}} \sum^ {N _ {L}} \mathcal {H} \left(\mathcal {F} \left(x _ {l}\right), y _ {l}\right), \tag {1} +$$ + +where $\mathcal{F}(\cdot)$ refers to the predictions produced by the model and $\mathcal{H}$ is the standard cross entropy loss. + +For unlabeled samples $x_{u}$ , we first use weak augmentations (e.g., random horizontal flipping, random scaling, and random cropping) and strong augmentations (e.g., AutoAugment [10] or Dropout [43]) to generate two views separately, $x_{w} = \mathcal{A}_{weak}(x_{u})$ , $x_{s} = \mathcal{A}_{strong}(x_{u})$ . Then the pseudo label of the weak view $\hat{y}_w = \arg \max (\mathcal{F}(x_w))$ , which is produced by the model, is utilized to supervise the strong view, with the following unsupervised loss: + +$$ +\mathcal {L} _ {u n} = \frac {1}{N _ {U}} \sum^ {N _ {U}} \mathbb {I} (\max (\mathcal {F} (x _ {w})) > \delta) \mathcal {H} (\mathcal {F} (x _ {s}), \hat {y} _ {w}), \tag {2} +$$ + +where $\delta$ is the predefined threshold, and $\mathbb{I}$ is the indicator function that equals 1 when the maximum class probability exceeds $\delta$ otherwise 0. The confidence indicator is used to filter the noisy pseudo labels. + +EMA-Teacher In FixMatch, the two augmented inputs share the same model, which tends to cause model collapsing easily [21, 23]. Therefore, we adopt the exponential + +moving average (EMA)-Teacher in our framework, which is an improved version of FixMatch. The pseudo labels are generated by the EMA-Teacher model, whose parameters are updated by exponential moving average of the student parameters, formulated as: + +$$ +\theta_ {t} \leftarrow m \theta_ {t} + (1 - m) \theta_ {s}, \tag {3} +$$ + +where $m$ is a momentum coefficient, $\theta_{t}$ and $\theta_{s}$ are the parameters of teacher and student model, respectively. EMA has achieved success in many tasks, such as self-supervised learning [21, 23], SSL of image classification [19, 44], and object detection [27, 32]. Here we are the first to adopt this method in semi-supervised video action recognition. + +# 3.3. Tube TokenMix + +One of the core problems in semi-supervised frameworks is how to enrich the dataset with high-quality pseudo labels. Mixup [67] is a widely adopted data augmentation strategy, which performs convex combination between pairs of samples and labels as follows: + +$$ +\hat {x} = \lambda \cdot x _ {1} + (1 - \lambda) \cdot x _ {2}, \tag {4} +$$ + +$$ +\hat {y} = \lambda \cdot y _ {1} + (1 - \lambda) \cdot y _ {2}, \tag {5} +$$ + +where the ratio $\lambda$ is a scalar that conforms to the beta distribution. Mixup [67] and its variants (e.g. CutMix [66]) have achieved success in many tasks in the low-data regime, such as long-tail classification [9, 69], domain adaptation [63] [55], few-shot learning [35, 60], etc. For SSL, Mixup also performs well by mixing the pseudo labels of unlabeled samples in image classification [49]. + +Mixing in Videos While directly applying Mixup or CutMix to video scenarios results in clear improvements in Conv-based methods [71], these methods show unsatisfactory performance in our method. The reason is that our method adopts the Transformer backbone, where the pixel-level mixing augmentation (Mixup or CutMix) may be not perfectly suitable for such token-level models [31]. To narrow the gap, we propose 3 token-level mixing augmentation methods for video data, namely, Rand TokenMix, Frame TokenMix, and Tube TokenMix. + +Fig. 2 illustrates the pipeline of our method. Given unlabeled video clips $x_{a}, x_{b} \in \mathbb{R}^{H \times W \times T}$ , our method employs a token-level mask $\mathbf{M} \in \{0,1\}^{H \times W \times T}$ to perform sample mixing. Note that $H$ and $W$ are the height and width of the frame after patch tokenization, and $T$ is the clip length. To generate a new sample $x_{mix}$ , we mix $x_{a}$ and $x_{b}$ after strong data augmentations $A_{strong}$ as follows: + +$$ +x _ {m i x} = \mathcal {A} _ {s t r o n g} \left(x _ {a}\right) \odot \mathbf {M} + \mathcal {A} _ {s t r o n g} \left(x _ {b}\right) \odot (\mathbf {1} - \mathbf {M}), \tag {6} +$$ + +![](images/984ce677e4611d6d2aabcb11ed2a6fcc141bf4e76719260bff9f17a1b6ae1cd2.jpg) +(a) + +![](images/6ce9982683269bca9e90d58ada738238b47b7ba72719163f09a767af140e6298.jpg) +(b) + +![](images/3eb171df920d40b44ef64d2cc2719222a756d2934282b74423d5ea1f91b016b5.jpg) +(c) +Figure 3. Examples of masks in three token mixing strategies. (a) Rand TokenMix. (b) Tube TokenMix. (c) Frame TokenMix. + +# Algorithm 1 Consistency loss for Tube TokenMix + +Require: Unlabeled clip batch $\mathbf{x}_{\mathbf{a}}$ + +Require: Tube TokenMask M, mask ratio $\lambda$ + +Require: Teacher model $\mathcal{F}_t$ + +Require: Student model $\mathcal{F}_s$ + +Require: Confidence threshold $\delta$ + +$\mathbf{x_b} = \mathrm{shuffle}(\mathbf{x_a})$ {shuffle samples in batch} + +$\hat{\mathbf{x}}_{\mathbf{a}} =$ spatial_aug $(\mathbf{x}_{\mathbf{a}})$ {spatial aug.} + +$\hat{\mathbf{x}}_{\mathbf{b}} =$ temporal\_aug $(\mathbf{x}_{\mathbf{b}})$ {temporal warping aug.} + +$\hat{\mathbf{y}}_a = \mathrm{stop\_gradient}(\mathcal{F}_t(\mathbf{x}_a))$ {teacher pred.} + +$\hat{\mathbf{y}}_b = \mathrm{stop\_gradient}(\mathcal{F}_t(\mathbf{x}_b))$ + +$\mathbf{c_{a}} = \max_{i}\mathbf{y}_{a}[i]$ {confidence of prediction} + +$\mathbf{c_b} = \max_i\mathbf{y}_b[i]$ + +$\mathbf{x}_{mix} = \hat{\mathbf{x}}_a*\mathbf{M} + \hat{\mathbf{x}}_b*(1 - \mathbf{M})$ {mix clips} + +$\hat{\mathbf{y}}_{mix} = \hat{\mathbf{y}}_a*\lambda +\hat{\mathbf{y}}_b*(1 - \lambda)$ {mix tea. preds.} + +$\mathbf{c}_{mix} = \mathbf{c}_a*\lambda +\mathbf{c}_b*(1 - \lambda)$ {mix confidence.} + +$\mathbf{q} = \mathrm{mean}(c_{mix}\geq \delta)$ {mean of conf. mask} + +$\mathbf{y}_{mix} = \mathcal{F}_s(\mathbf{x}_{mix})$ {stu. pred. on mixed clip} + +$\mathcal{L}_{mix} = q||\mathbf{y}_{mix} - \hat{\mathbf{y}}_{mix}||_2^2$ {cons. loss} + +Return $\mathcal{L}_{\text{mix}}$ + +where $\odot$ is element-wise multiplication, and $\mathbf{1}$ is a binary mask with all ones. + +The mask $\mathbf{M}$ differs in the three augmentation methods, as demonstrated in Fig. 3. For Rand TokenMix, the masked tokens are randomly selected from the whole video clip (from $H\times W\times T$ tokens). For Frame TokenMix, we randomly select frames from the $T$ frames and mask all the tokens in these frames. For Tube TokenMix, we adopt the tube-style masking strategy, that is, different frames share the same spatial mask matrix. In this case, the mask $\mathbf{M}$ has consistent masked tokens over the temporal axis. While our mask design shares similarity with the recent masked image/video modeling [16, 47, 51, 52, 58, 59], our motivation is totally different. They focus on removing certain regions and making the model predict the masked areas for feature learning. In contrast, we leverage the mask to mix two clips and synthesize a new data sample. + +The mixed sample $x_{mix}$ is then fed to the student model $\mathcal{F}_s$ , obtaining the model prediction $y_{mix} = \mathcal{F}_s(x_{mix})$ . In addition, the pseudo labels $\hat{y}_a, \hat{y}_b$ for $x_a, x_b$ + +![](images/8617344596c01b199ebe63bb128508b1963f18448e0bb7f9df546fd3c67149aa.jpg) +Figure 4. One example of utilizing Temporal Warping Augmentation together with spatial augmentation in TTMix. The two clips are first transformed by the two augmentations separately, after which TTMix is performed to generate a new clip. + +![](images/79e56332aa626b1a66754729ea41f363314cd43fdefc46cc6a2b10c13ccb717d.jpg) + +are produced by inputting the weak augmented samples $\mathcal{A}_{weak}(x_a),\mathcal{A}_{weak}(x_b)$ to the teacher model $\mathcal{F}_t$ + +$$ +\hat {y} _ {a} = \arg \max \left(\mathcal {F} _ {t} \left(\mathcal {A} _ {\text {w e a k}} \left(x _ {a}\right)\right)\right), \tag {7} +$$ + +$$ +\hat {y} _ {b} = \arg \max \left(\mathcal {F} _ {t} \left(\mathcal {A} _ {\text {w e a k}} \left(x _ {b}\right)\right)\right). \tag {8} +$$ + +Note that if $\max (\mathcal{F}_t(\mathcal{A}_{weak}(x))) < \delta$ , the pseudo label $\hat{y}$ remains the soft label $\mathcal{F}_t(\mathcal{A}_{weak}(x))$ . The pseudo label $\hat{y}_{mix}$ for $x_{mix}$ is generated by mixing $\hat{y}_a$ and $\hat{y}_b$ with mask ratio $\lambda$ : + +$$ +\hat {y} _ {m i x} = \lambda \cdot \hat {y} _ {a} + (1 - \lambda) \cdot \hat {y} _ {b}. \tag {9} +$$ + +Finally, the student model is optimized by the following consistency loss: + +$$ +\mathcal {L} _ {m i x} = \frac {1}{N _ {m}} \sum^ {N _ {m}} \left(\hat {y} _ {m i x} - y _ {m i x}\right) ^ {2}, \tag {10} +$$ + +where $N_{m}$ is the number of mixed samples. The algorithm of consistency loss for TTMix is shown in Algorithm 1. + +Temporal Warping Augmentation Most existing augmentation methods are designed for image tasks, which focus more on the spatial augmentation. They manipulate single or a pair of images to generate new image samples, without considering any temporal changes. Even the commonly adopted temporal augmentations, including varying temporal locations [18] and frame rates [40, 65], only consider simple temporal shift or scaling, that is, changing the holistic location or play speed. However, human actions are very complex and can have different temporal variation at every timestamp. To cover such challenging cases, we propose to distort the temporal duration of each frame, thus introducing higher randomness into the data. + +Our Temporal Warping Augmentation (TWAug) can stretch one frame to various temporal length. Given an extracted video clip of $T$ frames (e.g., 8 frames), we randomly + +![](images/0185539e2c8df65b8029a975dcdf2fd1752d6b6898640ac408ba2fc7a8a0c062.jpg) +Figure 5. Illustration of Temporal Warping Augmentation. We demonstrate three augment examples of different selected frames. + +determine to keep all the frames, or select a small portion of frames (e.g., 2 or 4 frames) while masking the others. The masked frames are then padded with random neighbouring visible (unmasked) frames. Note that after temporal padding, the frame order is still retained. Fig. 5 shows three examples of selecting 2, 4, and 8 frames, respectively. The proposed TWAug can help the model learn the flexible temporal dynamics during training. + +The Temporal Warping Augmentation serves as a strong augmentation in TTMix. Typically, we combine TWAug with the conventional spatial augmentation [10, 43] to perform the mixing. As shown in Fig. 4, the two input clips are first transformed by spatial augmentation and TWAug separately, after which the two clips are mixed through TTMix. We verify the effectiveness of our TWAug in Sec. 4.3. + +# 3.4. Training Paradigm + +The training of SVFormer consists of three parts: supervised loss formulated by Eq. (1), unsupervised pseudo-label consistency loss Eq. (2), and TTMix consistency loss Eq. (10). The final loss function is as follows: + +$$ +\mathcal {L} _ {a l l} = \mathcal {L} _ {s} + \gamma_ {1} \mathcal {L} _ {u n} + \gamma_ {2} \mathcal {L} _ {m i x}, \tag {11} +$$ + +where $\gamma_{1}$ and $\gamma_{2}$ are the hyperparameters for balancing the loss items. + +Table 1. Comparisons with state-of-the-art methods on UCF-101 and Kinetics-400. Note that 3D-ResNet-18 and 3D-ResNet-50 denote the backbone networks and their depths. We report Top-1 accuracy as the evaluation metric. "Input" shows the modalities used during training, where "V" is the raw RGB video, "F" is optical flow and "G" is the temporal gradient. + +
MethodBackboneInputw ImgNetEpochUCF-101Kinetics-400
1%10%1%10%
Supervised3D-ResNet-50V✓2006.532.44.436.2
ViT-SV✓3012.762.519.956.6
FixMatch (NeurIPS 2020) [41]SlowFast-R50V✓20016.155.110.149.4
VideoSSL(WACV 2021) [25]3D-ResNet-18V✓--42.0-33.8
TCL (CVPR 2021) [40]TSM-ResNet-18V400--8.5-
ActorCutMix (CVIU 2021) [71]R(2+1)D-34V✓600-53.09.02-
MvPL (ICCV 2021) [62]3D-ResNet-50V+F+G60022.880.517.058.2
CMPL (CVPR 2022) [64]R50 + R50-1/4V✓20025.179.117.658.4
LTG (CVPR 2022) [57]3D-ResNet-18V+G180/360-62.49.843.8
TACL(TCSVT 2022) [46]3D-ResNet-50V✓200-55.6--
L2A (ECCV 2022) [20]3D-ResNet-18V✓400-60.1--
SVFormer-S (Ours)ViT-SV✓3031.479.132.661.6
SVFormer-B (Ours)ViT-BV✓3046.386.749.169.4
+ +# 4. Experiment + +In this section, we first introduce the experimental settings in Sec. 4.1. Following previous work [57,64], we conduct experiments under different labeling rates in Sec 4.2. In addition, we also perform ablation experiments and empirical analysis in Section 4.3. If not emphasized, we only use RGB modal for inference with the official validation set. + +# 4.1. Experiment Settings + +Datasets Kinetics-400 [7] is a large-scale human action video dataset, with up to 245k training samples and 20k validation samples, covering 400 different categories. We follow the state-of-the-art methods MvPL [62] and CMPL [64] to sample 6 or 60 labeled training videos per category, i.e. at $1\%$ or $10\%$ labeling rates. UCF-101 [42] is a dataset with 13,320 video samples, which consists of 101 categories. We also sample 1 or 10 samples in each category as the labeled set following CMPL [64]. As for HMDB-51 [26], it is a small-scale dataset with only 51 categories composed of 6,766 videos. Following the division of LTG [57] and VideoSSL [25], we conduct experiments at three different labeling rates: $40\%$ , $50\%$ , and $60\%$ . + +Evaluation Metric We show the accuracy of Top-1 in main results, and also present the accuracy of Top-5 in some ablation experiments. + +Baseline We utilize the ViT [13] extended video TimeSformer [4] as the backbone of our baseline. The hyperparameters are mostly kept the same as the baseline, and we adopt the divided space-time attention as in TimeSformer [4]. Since TimeSformer only have ViT-Base models, we implement SVFormer-Small model from DeiT-S [48] with + +Table 2. Comparisons with state-of-the-art methods on HMDB-51. We report Top-1 accuracy. "Input" shows the modalities used during training, where "V" is the raw RGB video, "F" is optical flow and "G" is the temporal gradient. + +
BackboneInput40%50%60%
VideoSSL [25]3D-R18V32.736.237.0
ActorCutMix [71]R(2+1)D-34V32.938.238.9
MvPL [62]3D-R18V+F+G30.533.935.8
LTG [57]3D-R18V+G46.548.449.7
TACL [46]3D-R18V38.740.241.7
L2A [20]3D-R18V42.146.347.1
SVFormer-S (Ours)ViT-SV56.258.259.7
SVFormer-B (Ours)ViT-BV61.664.468.2
+ +the dimension of 384 and 6 heads, in order to have comparable number of parameters with other Conv-based methods [22, 62, 64]. For fair comparisons, we train 30 epochs for TimeSformer as the supervised baseline. + +Training and Inference For training, we follow the setting of TimeSformer [4]. The training uses 8 or 16 GPUs, with a SGD optimizer using a momentum of 0.9 and a weight decay of 0.001. For each setting, the basic learning rate is set to 0.005, which is divided by 10 at epochs 25, and 28. As for the confidence score threshold, we search for the optimal $\delta$ from $\{0.3, 0.5, 0.7, 0.9\}$ . $\gamma_{1}$ and $\gamma_{2}$ are set to 2. The masking ratio $\lambda$ is sampled from beta distribution $\mathrm{Beta}(\alpha, \alpha)$ , where $\alpha = 10$ . In the testing phase, following the inference strategies in MvPL [62] and CMPL [64], we uniformly sample five clips from the entire video, and make three different crops to get $224 \times 224$ resolution to cover most of the spatial areas of the clips. The final prediction is the average of the softmax probabilities of these $5 \times 3$ pre + +![](images/1a8b2f349dfd6ceedb12d01265c8dfc7080ffb587f8a90bebb040892e69d0661.jpg) +Figure 6. Example of the traditional pixel-level mixing methods and our proposed token-level mixing. Note that token-level methods mix two samples after tokenization but the visualization is shown on image-level for clear presentation. + +dictions. We also conduct a comparison of inference setting in the ablation study in Sec. 4.3. + +# 4.2. Main Results + +The main results of Kinetics-400 [7] and UCF-101 [42] are shown in Table 1. Compared with previous methods, our model SVFormer-S achieves the best performance with the fewest training epochs among the methods that only use RGB data. In particular, at the labeling rate of $1\%$ setting, SVFormer-S improves previous approach [64] by $6.3\%$ in UCF-101 and $15.0\%$ in Kinetics-400. In addition, when adopting larger models, SVFormer-B significantly outperforms the state-of-the-art methods. + +Specifically, in Kinetics-400, SVFormer-B can achieve $69.4\%$ with only $10\%$ labeled data, which is comparable to $77.9\%$ of fully-supervised setting in TimeSformer [4]. Moreover, as shown in Table 2, for the small-scale dataset HMDB-51 [26], our SVFormer-S and SVFormer-B have also improved by about $10\%$ and $15\%$ compared with the previous method [57]. + +# 4.3. Ablation Studies + +To understand the effect of each part of the design in our method, we conduct extensive ablation studies on the Kinetics-400 and UCF-101 at the $1\%$ labeling ratio setting + +Table 3. SSL framework selection. We compare the EMA-Teacher framework with FixMatch. The results are reported on Kinetics-400 and UCF-101 with $1\%$ labeling ratio. + +
MethodUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline12.729.819.942.3
FixMatch [41]25.147.328.254.6
EMA-Teacher31.456.932.659.0
+ +Table 4. TokenMix Mask sampling. We compare different token masking strategies. The results are reported on Kinetics-400 and UCF-101 with $1\%$ labeling ratio. + +
Method/DatasetUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline26.148.923.647.7
CutMix [66]28.751.328.653.7
Mixup [67]29.853.029.355.1
PixMix [24]29.752.429.655.8
Frame TokenMix29.854.226.350.0
Rand TokenMix30.355.328.854.2
Tube TokenMix31.456.932.659.0
+ +with SVFormer-S. + +Analysis of SSL framework The comparison of FixMatch and EMA-Teacher is shown in Table 3. It is clear that the two methods have significantly improved the baseline approach. In addition, EMA-Teacher has exhibited considerable gains over FixMatch in both datasets with very few labeled samples, probably because it has improved the stability of training. FixMatch [41] may lead to model collapse with limited labels as shown in [6]. + +Analysis of different mixing strategies We now compare the Tube TokenMix strategy with three pixel-level mixing methods, CutMix [66], Mixup [67], PixMix [24], as well as the other two token-level mixing methods, i.e., Frame TokenMix and Rand TokenMix. The examples of different mixing methods are shown in Fig. 6. The quantitative results are shown in Table 4. Compared with these alternative methods, all mixing methods can improve the performance, which proves the effectiveness of mixing-based consistency losses. In addition, we observe that the token-level methods (Rand TokenMix and Tube TokenMix) perform better than the pixel-level mixing methods. This is not surprising since transformers operate on tokens, and thus token-level mixing has inherent advantages. + +The performance of Frame TokenMix is even worse than that of pixel-level mixing methods, which is also expected. We hypothesize that replacing entire frames in video clip will scramble up the temporal reasoning, thus leading to poor temporal attention modeling. In addition, Tube Token- + +Table 5. Effects of Spatial and Temporal Warping Augmentations (TWAug). The results are reported on Kinetics-400 and UCF-101 with $1\%$ labeling ratio. + +
SpatialTemporalUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline29.552.128.554.2
Spatial-only✓29.953.230.355.9
Temporal-only✓30.255.830.856.4
Spatial+Temporal✓✓31.456.932.659.0
+ +Table 6. Effects of different inference schemes. We compare the sparse sampling strategy and dense sampling method with different frames. The $a \times b$ in 'Frames' column means sampling $a$ frames at frame rate $b$ . The results are reported on Kinetics-400 and UCF-101 with $1\%$ labeling ratio. + +
MethodFramesTest ViewUCF-1%Kinetic-1%
MvPL [62]8 × 810 × 322.817.0
CMPL [64]8 × 810 × 325.117.6
SVFormer-S8 × 321 × 329.331.0
SVFormer-S8 × 85 × 331.432.6
SVFormer-S16 × 410 × 331.633.1
+ +Mix achieves the best results. We suppose the consistent masked tokens over temporal axis can prevent information leaky between adjacent frames in the same spatial locations, especially in such a short-term clip. Therefore, Tube Token-Mix could better model the spatio-temporal correlations. + +Analysis of Augmentations The effects of spatial augmentation and temporal warping augmentation are evaluated in Table 5. The baseline indicates removing both strong spatial augmentation (e.g. AutoAugment [10] and Dropout [43]) and TWAug in all branches. In this case, the experimental performance drops dramatically. When spatial augmentation or temporal warping augmentation is incorporated into the baseline separately, the performance is improved. The best practice is to perform data augmentations in both spatial and temporal. + +Analysis of Inference We evaluate the effect of frame rate sampling and different inference schemes, as shown in Table 6. Previous methods, i.e. CMPL [64] and MvPL [62], utilize the clip-based sparse sampling, which samples 8 frames at frame rate 8 as a clip. For each video, 10 clips are sampled, where each clip is cropped 3 times according to different spatial positions. Finally, the predictions of $10 \times 3$ samples are averaged. TimeSformer [4] adopts the video-based sparse sampling, that is, 8 frames are sampled at frame rate 32 as the representation of the whole video. Then 3 different cropped views are used, namely $8 \times 32$ . Applying the video-based sparse sampling scheme as in TimeSformer [4] can reduce the inference cost, but the performance is worse than that of clip-based sampling. Experiments at sampling schemes of $8 \times 8$ and $16 \times 4$ demonstrate better performance. For the trade-off between effi + +![](images/7a1acfc50ff1b975de968b03740c17399a29a1234a1f0e90ae24626e66925e86.jpg) + +![](images/877beff07eab7a533a71c8963924834f3b6b85a1f2c9c4fc8b6a7ecf38fc67de.jpg) + +![](images/c86edfc119688c70a1fccb78e59613d698be63e2b78c68242d97ab38d4302fbc.jpg) +Figure 7. Effects of hyperparameters. Results of varying threshold $\delta$ , ratio between unlabeled and labeled data in a mini-batch $(B_u / B_l)$ , momentum coefficient $m$ , and loss weights $(\gamma_1, \gamma_2)$ are included to comprehensively study the effects of the hyperparameters. Reported on Kinetics-400 with $1\%$ labeling ratio. + +![](images/bc95930fb244a9b380a1c73ab4fa8992073ecf304f6f43af1ffc3a7b00b8b9ec.jpg) + +ciency and accuracy, we use $8 \times 8$ as the default setting following CMPL [64] and MvPL [62]. + +Analysis of hyperparameters Here we explore the effect of different hyperparameters. We conduct experiments under $1\%$ setting of Kinetics-400. We first explore the effect of different threshold values of $\delta$ . As shown in Fig. 7(a), we can observe that when labeled samples are extremely scarce, best results are achieved by setting a small $\delta$ value $(\delta = 0.3)$ . We then evaluate how the ratio between labeled samples and unlabeled samples in a mini-batch affects the result. We fix the labeled sample number $B_{l}$ to 1, and sample $B_{u}$ unlabeled samples to form a mini-batch, where $B_{u}$ is in $\{1,2,3,5,7\}$ . The results are shown in Fig. 7(b). When $B_{u} = 5$ , the model produces the highest result. Finally, we explore the choice of momentum coefficient $m$ of EMA and the loss weights $\gamma_{1}$ and $\gamma_{2}$ , as shown in Fig. 7(c) and Fig. 7(d). We thus set $m = 0.99$ and $\gamma_{1} = \gamma_{2} = 2$ as default setting in all the experiments. + +# 5. Conclusion + +In this paper we present SVFormer, a transformer-based semi-supervised video action recognition method. We propose Tube TokenMix, a data augmentation method that is specially designed for video transformer models. Coupled with the temporal warping augmentation, which covers the complex temporal variations by arbitrarily changing the frame length, TTMix achieves significant improvement compared with conventional augmentations. SVFormer outperforms the state-of-the-art with a large margin on UCF-101, HMDB-51 and Kinetics-400 without increasing overheads. Our work establishes a new benchmark for semi-supervised action recognition and encourages future work to adopt Transformer architecture. + +Acknowledgement This project was supported by NSFC under Grant No. 62032006 and No. 62102092. + +# References + +[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. Semi-supervised semantic segmentation with pixel-level contrastive learning from a class-wise memory bank. 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In ICCV, 2021. 1, 2, 3, 6, 8 +[63] Minghao Xu, Jian Zhang, Bingbing Ni, Teng Li, Chengjie Wang, Qi Tian, and Wenjun Zhang. Adversarial domain adaptation with domain mixup. In AAAI, 2020. 4 +[64] Yinghao Xu, Fangyun Wei, Xiao Sun, Ceyuan Yang, Yujun Shen, Bo Dai, Bolei Zhou, and Stephen Lin. Cross-model pseudo-labeling for semi-supervised action recognition. In CVPR, 2022. 1, 2, 3, 6, 7, 8 +[65] Ceyuan Yang, Yinghao Xu, Bo Dai, and Bolei Zhou. Video representation learning with visual tempo consistency. arXiv preprint arXiv:2006.15489, 2020. 5 +[66] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In ICCV, 2019. 2, 3, 4, 7 + +[67] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In ICLR, 2018. 2, 3, 4, 7 +[68] Xiaosong Zhang, Yunjie Tian, Lingxi Xie, Wei Huang, Qi Dai, Qixiang Ye, and Qi Tian. Hivit: A simpler and more efficient design of hierarchical vision transformer. In ICLR, 2023. 3 +[69] Xing Zhang, Zuxuan Wu, Zejia Weng, Huazhu Fu, Jingjing Chen, Yu-Gang Jiang, and Larry S Davis. Videolt: Large-scale long-tailed video recognition. In ICCV, 2021. 4 +[70] Linchao Zhu and Yi Yang. Actbert: Learning global-local video-text representations. In CVPR, 2020. 1 +[71] Yuliang Zou, Jinwoo Choi, Qitong Wang, and Jia-Bin Huang. Learning representational invariances for data-efficient action recognition. arXiv preprint arXiv:2103.16565, 2021. 4, 6 \ No newline at end of file diff --git a/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/images.zip b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8421b133e7b03fe13cf4236afa6c97e08e01dd14 --- /dev/null +++ b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91e579c38294e877c898558ae4438c631f0bbe669e222d0d2d39eb6203196a8a +size 600121 diff --git a/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/layout.json b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..be68784d6a7fd1a7c0014e423b0b25da6b826323 --- /dev/null +++ b/2023/SVFormer_ Semi-Supervised Video Transformer for Action Recognition/layout.json @@ -0,0 +1,10920 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 75, + 103, + 518, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 103, + 518, + 121 + ], + "spans": [ + { + "bbox": [ + 75, + 103, + 518, + 121 + ], + "type": "text", + "content": "SVFormer: Semi-supervised Video Transformer for Action Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "spans": [ + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "content": "Zhen Xing" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "content": " Qi Dai" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "content": " Han Hu" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "content": " Jingjing Chen" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "content": " Zuxuan Wu" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "inline_equation", + "content": "^{1,2\\dagger}" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "text", + "content": " Yu-Gang Jiang" + }, + { + "bbox": [ + 66, + 141, + 526, + 159 + ], + "type": "inline_equation", + "content": "^{1,2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 159, + 490, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 159, + 490, + 173 + ], + "spans": [ + { + "bbox": [ + 107, + 159, + 490, + 173 + ], + "type": "text", + "content": "1 Shanghai Key Lab of Intell. 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Processing, School of CS, Fudan University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 173, + 481, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 173, + 481, + 200 + ], + "spans": [ + { + "bbox": [ + 113, + 173, + 481, + 200 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 113, + 173, + 481, + 200 + ], + "type": "text", + "content": " Shanghai Collaborative Innovation Center of Intelligent Visual Computing \n" + }, + { + "bbox": [ + 113, + 173, + 481, + 200 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 113, + 173, + 481, + 200 + ], + "type": "text", + "content": " Microsoft Research Asia" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 228, + 192, + 241 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 228, + 192, + 241 + ], + "spans": [ + { + "bbox": [ + 143, + 228, + 192, + 241 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "type": "text", + "content": "Semi-supervised action recognition is a challenging but critical task due to the high cost of video annotations. Existing approaches mainly use convolutional neural networks, yet current revolutionary vision transformer models have been less explored. In this paper, we investigate the use of transformer models under the SSL setting for action recognition. To this end, we introduce SVFormer, which adopts a steady pseudo-labeling framework (i.e., EMA-Teacher) to cope with unlabeled video samples. While a wide range of data augmentations have been shown effective for semi-supervised image classification, they generally produce limited results for video recognition. We therefore introduce a novel augmentation strategy, Tube TokenMix, tailored for video data where video clips are mixed via a mask with consistent masked tokens over the temporal axis. In addition, we propose a temporal warping augmentation to cover the complex temporal variation in videos, which stretches selected frames to various temporal durations in the clip. Extensive experiments on three datasets Kinetics-400, UCF-101, and HMDB-51 verify the advantage of SVFormer. In particular, SVFormer outperforms the state-of-the-art by " + }, + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "type": "inline_equation", + "content": "31.5\\%" + }, + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "type": "text", + "content": " with fewer training epochs under the " + }, + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 266, + 290, + 590 + ], + "type": "text", + "content": " labeling rate of Kinetics-400. Our method can hopefully serve as a strong benchmark and encourage future search on semi-supervised action recognition with Transformer networks. Code is released at https://github.com/ChenHsing/SVFormer." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 613, + 128, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 128, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 128, + 625 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 633, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 633, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 633, + 287, + 695 + ], + "type": "text", + "content": "Videos have gradually replaced images and texts on Internet and grown at an exponential rate. On video websites such as YouTube, millions of new videos are uploaded every day. Supervised video understanding works [4, 15, 17, 29, 34, 56, 70] have achieved great successes. They rely on" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 227, + 545, + 353 + ], + "blocks": [ + { + "bbox": [ + 307, + 227, + 545, + 353 + ], + "lines": [ + { + "bbox": [ + 307, + 227, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 307, + 227, + 545, + 353 + ], + "type": "image", + "image_path": "fdb6f3c8badab016f0d671560d35f9f0ccddf6f04c7ae6b0f2e8a2ddf03aef0c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 355, + 547, + 399 + ], + "lines": [ + { + "bbox": [ + 305, + 355, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 547, + 399 + ], + "type": "text", + "content": "Figure 1. Comparison of our method with the supervised baseline and previous state-of-the-art SSL method [64]. SVFormer significantly outperforms previous methods under the case with very little labeled data." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 408, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 408, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 408, + 547, + 456 + ], + "type": "text", + "content": "large-scale manual annotations, yet labeling so many videos is time-consuming and labor-intensive. How to make use of unlabeled videos that are readily available for better video understanding is of great importance [25, 38, 39]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "In this spirit, semi-supervised action recognition [25, 40, 57] explores how to enhance the performance of deep learning models using large-scale unlabeled data. This is generally done with labeled data to pretrain the networks [57,64], and then leveraging the pretrained models to generate pseudo labels for unlabeled data, a process known as pseudo labeling. The obtained pseudo labels are further used to refine the pretrained models. In order to improve the quality of pseudo labeling, previous methods [57, 62] use additional modalities such as optical flow [3] and temporal gradient [50], or introduce auxiliary networks [64] to supervise unlabeled data. Though these methods present promising results, they typically require additional training or inference cost, preventing them from scaling up." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Recently, video transformers [2,4,34] have shown strong results compared to CNNs [15, 17, 22]. Though great success has been achieved, the exploration of transformers on semi-supervised video tasks remains unexplored. While it sounds appealing to extend vision transformers directly to SSL, a previous study shows that transformers perform significantly worse compared to CNNs in the low-data regime" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 702, + 142, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 702, + 142, + 713 + ], + "spans": [ + { + "bbox": [ + 62, + 702, + 142, + 713 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18816" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 108 + ], + "type": "text", + "content": "due to the lack of inductive bias [54]. As a result, directly applying SSL methods, e.g., FixMatch [41], to ViT [13] leads to an inferior performance [54]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 286, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 286, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 286, + 179 + ], + "type": "text", + "content": "Surprisingly, in the video domain, we observe that TimeSformer, a popular video Transformer [4], initialized with weights from ImageNet [11], demonstrates promising results even when annotations are limited [37]. This encourages us to explore the great potential of transformers for action recognition in the SSL setting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 180, + 286, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 286, + 311 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 286, + 311 + ], + "type": "text", + "content": "Existing SSL methods generally use image augmentations (e.g., Mixup [67] and CutMix [66]) to speed up convergence under limited label resources. However, such pixel-level mixing strategies are not perfectly suitable for transformer architectures, which operate on tokens produced by patch splitting layers. In addition, strategies like Mixup and CutMix are particularly designed for image tasks, which fail to consider the temporal nature of video data. Therefore, as will be shown empirically, directly using Mixup or CutMix for semi-supervised action recognition leads to unsatisfactory performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 286, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 286, + 442 + ], + "type": "text", + "content": "In this work, we propose SVFormer, a transformer-based semi-supervised action recognition method. Concretely, SVFormer adopts a consistency loss that builds two differently augmented views and demands consistent predictions between them. Most importantly, we propose Tube TokenMix (TTMix), an augmentation method that is naturally suitable for video Transformer. Unlike Mixup and CutMix, Tube TokenMix combines features at the token-level after tokenization via a mask, where the mask has consistent masked tokens over the temporal axis. Such a design could better model the temporal correlations between tokens." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 443, + 286, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 286, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 286, + 562 + ], + "type": "text", + "content": "Temporal augmentations in literatures (e.g. varying frame rates) only consider simple temporal scaling or shifting, neglecting the complex temporal changes of each part in human action. To help the model learn strong temporal dynamics, we further introduce the Temporal Warping Augmentation (TWAug), which arbitrarily changes the temporal length of each frame in the clip. TWAug can cover the complex temporal variation in videos and is complementary to spatial augmentations [10]. When combining TWAug with TTMix, significant improvements are achieved." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 563, + 286, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 286, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 286, + 681 + ], + "type": "text", + "content": "As shown in Fig. 1, SVFormer achieves promising results in several benchmarks. (i) We observe that the supervised Transformer baseline is much better than the Conv-based method [22], and is even comparable with the 3D-ResNet state-of-the-art method [64] on Kinetics400 when trained with " + }, + { + "bbox": [ + 46, + 563, + 286, + 681 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 563, + 286, + 681 + ], + "type": "text", + "content": " of labels. (ii) SVFormer-S significantly outperforms previous state-of-the-arts with similar parameters and inference cost, measured by FLOPs. (iii) Our method is also effective for the larger SVFormer-B model. Our contributions are as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 57, + 689, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 689, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 57, + 689, + 286, + 712 + ], + "type": "text", + "content": "- We are the first to explore the transformer model for semi-supervised video recognition. Unlike SSL for" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 324, + 72, + 544, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 544, + 119 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 544, + 119 + ], + "type": "text", + "content": "image recognition with transformers, we find that using parameters pretrained on ImageNet is of great importance to ensure decent results for action recognition in the low-data regime." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 316, + 129, + 544, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 129, + 544, + 201 + ], + "spans": [ + { + "bbox": [ + 316, + 129, + 544, + 201 + ], + "type": "text", + "content": "- We propose a token-level augmentation Tube TokenMix, which is more suitable for video Transformer than pixel-level mixing strategies. Coupled with Temporal Warping Augmentation, which improves temporal variations between frames, TTMix achieves significant boost compared with image augmentation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 316, + 211, + 544, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 211, + 544, + 281 + ], + "spans": [ + { + "bbox": [ + 316, + 211, + 544, + 281 + ], + "type": "text", + "content": "- We conduct extensive experiments on three benchmark datasets. The performances of our method in two different sizes (i.e., SVFormer-B and SVFormer-S) outperform state-of-the-art approaches by clear margins. Our method sets a strong baseline for future transformer-based works." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 295, + 397, + 307 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 295, + 397, + 307 + ], + "spans": [ + { + "bbox": [ + 306, + 295, + 397, + 307 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 315, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 315, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 315, + 545, + 590 + ], + "type": "text", + "content": "Deep Semi-supervised Learning Deep learning relies on large-scale annotated data, however collecting these annotations is labor-intensive. Semi-supervised learning is a natural solution to reduce the cost of labeling, which leverages a few labeled samples and a large amount of unlabeled samples to train the model. The research and application of SSL mainly focus on image recognition [41, 44, 54] with a two-step process: data augmentation and consistency regularization. Concretely, different data augmentations [10] views are input to the model, and their output consistencies are enforced through a consistency loss. Another line of work generates new data and labels using mixing [5, 19, 49] to train the network. Among these state-of-the-art methods, FixMatch have been widely used due its effective and its variants have been extended to many other applications, such as object detection [27, 32], semantic segmentation [1, 8], 3D reconstruction [61], etc. Although FixMatch has achieved good performance in many tasks, it may not achieve satisfactory results when directly transferred to video action recognition due to the lack of temporal augmentation. In this paper, we introduce temporal augmentation TWAug with mixing based method TTMix, which is suitable for video transformers at SSL settings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Semi-supervised Action Recognition VideoSSL [25] presents a comparative study of applying 2D SSL methods to videos, which verifies the limitations of the direct extension of pseudo labeling method. TCL [40] explores the effect of a group contrastive loss and self-supervised tasks. MvPL [62] and LTG [57] introduce optical flow or temporal gradient modal to generate high quality pseudo labels for training, respectively. CMPL [64] introduce an auxiliary network, which requires more frames in training, increasing the difficulty of application. Besides, previous methods are" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18817" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "all based on 2D [40] or 3D convolutional [57, 62, 64] networks, which require more training epochs. Our approach is the first to make the exploration of Video Transformer for SSL action recognition and achieves the best performance with the least training cost." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 314 + ], + "type": "text", + "content": "Video Transformer The great success of vision transformer [13, 30, 33, 45, 68] in image recognition leads to the development of exploring the transformer-base architecture for video recognition tasks. VTN [36] uses additional temporal attention on the top of the pretrained ViT [13]. TimeSformer [4] investigates different spatial-temporal attention mechanisms and adopts factored space time attention as a trade-off of speed and accuracy. ViViT [2] explores four different types of attention, and selects the global spatiotemporal attention as the default to achieve promising performance. In addition, MviT [14], Video Swin [34], Uniformer [28] and Video Mobile-Former [53] incorporate the inductive bias in convolution into transformers. While these methods focus on fully-supervised setting, limited effort has been made for transformers in the semi-supervised setting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 320, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 287, + 499 + ], + "type": "text", + "content": "Data Augmentation Data augmentation is an essential step in modern deep networks to improve the training efficiency and performance. Cutout [12] removes random rectangle regions in images. Mixup [67] performs image mixing by linearly interpolating both the raw image and labels. In CutMix [66], patches are cut and pasted among image pairs. AutoAugment [10] automatically searches for augmentation strategies to improve the results. PixMix [24] explores the natural structural complexity of images when performing mixing. TokenMix [31] mixes images at the token-level and allows the region to be multiple isolated parts. Though these methods have achieved good results, they are all specially designed for pure image and most of them are pixel-level augmentations. In contrast, our TTMix coupled with TWAug is devised for video." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 515, + 103, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 103, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 103, + 528 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 536, + 288, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 288, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 288, + 609 + ], + "type": "text", + "content": "In this section, we first introduce the preliminaries of SSL in Sec. 3.1. The pipeline of our proposed SVFormer is described in Sec. 3.2. Then we detail the proposed Tube TokenMix (TTMix) in Sec. 3.3, as well as the effective albeit simple temporal warping augmentation. Finally, we show the training paradigm in Sec. 3.4." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 621, + 167, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 167, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 167, + 634 + ], + "type": "text", + "content": "3.1. Preliminaries of SSL" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "Suppose we have " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " training video samples, including " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{L}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " labeled videos " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "(x_{l},y_{l})\\in \\mathcal{D}_{L}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{U}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " unlabeled videos " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_{u}\\in \\mathcal{D}_{U}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_{l}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " is the labeled video sample with a category label " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "y_{l}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " is the unlabeled video sample. In general, " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{U}\\gg N_{L}" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": ". The aim of SSL is to utilize both " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_L" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_U" + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": " to train the model." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 541, + 228 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 541, + 228 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 541, + 228 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 541, + 228 + ], + "type": "image", + "image_path": "f14b0c0083c9412c58aa94cf72b13c4052cf33434722ca15642a870286f00b3d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 235, + 545, + 312 + ], + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 312 + ], + "type": "text", + "content": "Figure 2. Overview of our Tube TokenMix training framework. The two input unlabeled samples are mixed via a tube mask, where the generated sample is fed into the Student model. The two samples are also fed into the EMA-Teacher to obtain their pseudo labels, which are further linearly interpolated via mask ratio " + }, + { + "bbox": [ + 304, + 235, + 545, + 312 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 235, + 545, + 312 + ], + "type": "text", + "content": " to produce pseudo label for the generated sample. \"SG\" means stop gradient. The data augmentation is omitted here." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 331, + 367, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 367, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 367, + 344 + ], + "type": "text", + "content": "3.2. Pipeline" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "type": "text", + "content": "SVFormer follows the popular semi-supervised learning framework FixMatch [41] that use a consistency loss between two differently augmented views. The training paradigm is divided into two parts. For the labeled set " + }, + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "type": "inline_equation", + "content": "\\{(x_l, y_l)\\}_{l=1}^{N_L}" + }, + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "type": "text", + "content": ", the model optimizes the supervised loss " + }, + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 305, + 349, + 545, + 410 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 366, + 416, + 545, + 445 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 416, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 366, + 416, + 545, + 445 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} = \\frac {1}{N _ {L}} \\sum^ {N _ {L}} \\mathcal {H} \\left(\\mathcal {F} \\left(x _ {l}\\right), y _ {l}\\right), \\tag {1}", + "image_path": "b7b70633e057057a02121a72065bf1a0b9c1d94cdbc0e561a517f5613e174663.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\cdot)" + }, + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "type": "text", + "content": " refers to the predictions produced by the model and " + }, + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 305, + 455, + 545, + 479 + ], + "type": "text", + "content": " is the standard cross entropy loss." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "text", + "content": "For unlabeled samples " + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "inline_equation", + "content": "x_{u}" + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "text", + "content": ", we first use weak augmentations (e.g., random horizontal flipping, random scaling, and random cropping) and strong augmentations (e.g., AutoAugment [10] or Dropout [43]) to generate two views separately, " + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "inline_equation", + "content": "x_{w} = \\mathcal{A}_{weak}(x_{u})" + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "inline_equation", + "content": "x_{s} = \\mathcal{A}_{strong}(x_{u})" + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "text", + "content": ". Then the pseudo label of the weak view " + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "inline_equation", + "content": "\\hat{y}_w = \\arg \\max (\\mathcal{F}(x_w))" + }, + { + "bbox": [ + 304, + 479, + 545, + 575 + ], + "type": "text", + "content": ", which is produced by the model, is utilized to supervise the strong view, with the following unsupervised loss:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 582, + 545, + 610 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 582, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 313, + 582, + 545, + 610 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {u n} = \\frac {1}{N _ {U}} \\sum^ {N _ {U}} \\mathbb {I} (\\max (\\mathcal {F} (x _ {w})) > \\delta) \\mathcal {H} (\\mathcal {F} (x _ {s}), \\hat {y} _ {w}), \\tag {2}", + "image_path": "4766d1ac502389bcc48271d40576d9ff3ffb3d592d7398214f854505c1ca4d25.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "content": " is the predefined threshold, and " + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\mathbb{I}" + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "content": " is the indicator function that equals 1 when the maximum class probability exceeds " + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 616, + 545, + 664 + ], + "type": "text", + "content": " otherwise 0. The confidence indicator is used to filter the noisy pseudo labels." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "EMA-Teacher In FixMatch, the two augmented inputs share the same model, which tends to cause model collapsing easily [21, 23]. Therefore, we adopt the exponential" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18818" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": "moving average (EMA)-Teacher in our framework, which is an improved version of FixMatch. The pseudo labels are generated by the EMA-Teacher model, whose parameters are updated by exponential moving average of the student parameters, formulated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 116, + 143, + 287, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 143, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 116, + 143, + 287, + 156 + ], + "type": "interline_equation", + "content": "\\theta_ {t} \\leftarrow m \\theta_ {t} + (1 - m) \\theta_ {s}, \\tag {3}", + "image_path": "82b2a55e1bb7272f77d396ea41b882951c1ecf89b8e898bd08a8370a2487534b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "text", + "content": " is a momentum coefficient, " + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "inline_equation", + "content": "\\theta_{s}" + }, + { + "bbox": [ + 46, + 165, + 288, + 237 + ], + "type": "text", + "content": " are the parameters of teacher and student model, respectively. EMA has achieved success in many tasks, such as self-supervised learning [21, 23], SSL of image classification [19, 44], and object detection [27, 32]. Here we are the first to adopt this method in semi-supervised video action recognition." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 245, + 144, + 256 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 245, + 144, + 256 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 144, + 256 + ], + "type": "text", + "content": "3.3. Tube TokenMix" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 287, + 323 + ], + "type": "text", + "content": "One of the core problems in semi-supervised frameworks is how to enrich the dataset with high-quality pseudo labels. Mixup [67] is a widely adopted data augmentation strategy, which performs convex combination between pairs of samples and labels as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 334, + 287, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 334, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 112, + 334, + 287, + 346 + ], + "type": "interline_equation", + "content": "\\hat {x} = \\lambda \\cdot x _ {1} + (1 - \\lambda) \\cdot x _ {2}, \\tag {4}", + "image_path": "dc4d2717ebf3e18f73f6a5f45e453a59867d058b15160a20bef4206eeb9aca4c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 369, + 287, + 382 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 369, + 287, + 382 + ], + "spans": [ + { + "bbox": [ + 113, + 369, + 287, + 382 + ], + "type": "interline_equation", + "content": "\\hat {y} = \\lambda \\cdot y _ {1} + (1 - \\lambda) \\cdot y _ {2}, \\tag {5}", + "image_path": "429a53305ca901af4d12463eca7116d56e63d4294f7eca27c4742e74e1d99203.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "type": "text", + "content": "where the ratio " + }, + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 388, + 288, + 472 + ], + "type": "text", + "content": " is a scalar that conforms to the beta distribution. Mixup [67] and its variants (e.g. CutMix [66]) have achieved success in many tasks in the low-data regime, such as long-tail classification [9, 69], domain adaptation [63] [55], few-shot learning [35, 60], etc. For SSL, Mixup also performs well by mixing the pseudo labels of unlabeled samples in image classification [49]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 487, + 287, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 606 + ], + "type": "text", + "content": "Mixing in Videos While directly applying Mixup or CutMix to video scenarios results in clear improvements in Conv-based methods [71], these methods show unsatisfactory performance in our method. The reason is that our method adopts the Transformer backbone, where the pixel-level mixing augmentation (Mixup or CutMix) may be not perfectly suitable for such token-level models [31]. To narrow the gap, we propose 3 token-level mixing augmentation methods for video data, namely, Rand TokenMix, Frame TokenMix, and Tube TokenMix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": "Fig. 2 illustrates the pipeline of our method. Given unlabeled video clips " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "x_{a}, x_{b} \\in \\mathbb{R}^{H \\times W \\times T}" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": ", our method employs a token-level mask " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\{0,1\\}^{H \\times W \\times T}" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " to perform sample mixing. Note that " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " are the height and width of the frame after patch tokenization, and " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " is the clip length. To generate a new sample " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "x_{mix}" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": ", we mix " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "x_{a}" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "x_{b}" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " after strong data augmentations " + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "inline_equation", + "content": "A_{strong}" + }, + { + "bbox": [ + 46, + 607, + 288, + 692 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 52, + 701, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 701, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 52, + 701, + 287, + 715 + ], + "type": "interline_equation", + "content": "x _ {m i x} = \\mathcal {A} _ {s t r o n g} \\left(x _ {a}\\right) \\odot \\mathbf {M} + \\mathcal {A} _ {s t r o n g} \\left(x _ {b}\\right) \\odot (\\mathbf {1} - \\mathbf {M}), \\tag {6}", + "image_path": "f0dd08f6a291ced0459a5c4d32046064d49c260d3183831d7dd71ed1a35ebf0c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 383, + 154 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 383, + 154 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 383, + 154 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 383, + 154 + ], + "type": "image", + "image_path": "984ce677e4611d6d2aabcb11ed2a6fcc141bf4e76719260bff9f17a1b6ae1cd2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 333, + 159, + 340, + 167 + ], + "lines": [ + { + "bbox": [ + 333, + 159, + 340, + 167 + ], + "spans": [ + { + "bbox": [ + 333, + 159, + 340, + 167 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 394, + 71, + 463, + 153 + ], + "blocks": [ + { + "bbox": [ + 394, + 71, + 463, + 153 + ], + "lines": [ + { + "bbox": [ + 394, + 71, + 463, + 153 + ], + "spans": [ + { + "bbox": [ + 394, + 71, + 463, + 153 + ], + "type": "image", + "image_path": "6ce9982683269bca9e90d58ada738238b47b7ba72719163f09a767af140e6298.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 415, + 159, + 423, + 166 + ], + "lines": [ + { + "bbox": [ + 415, + 159, + 423, + 166 + ], + "spans": [ + { + "bbox": [ + 415, + 159, + 423, + 166 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 474, + 71, + 545, + 153 + ], + "blocks": [ + { + "bbox": [ + 474, + 71, + 545, + 153 + ], + "lines": [ + { + "bbox": [ + 474, + 71, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 474, + 71, + 545, + 153 + ], + "type": "image", + "image_path": "3eb171df920d40b44ef64d2cc2719222a756d2934282b74423d5ea1f91b016b5.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 496, + 158, + 503, + 166 + ], + "lines": [ + { + "bbox": [ + 496, + 158, + 503, + 166 + ], + "spans": [ + { + "bbox": [ + 496, + 158, + 503, + 166 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 170, + 545, + 192 + ], + "lines": [ + { + "bbox": [ + 305, + 170, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 170, + 545, + 192 + ], + "type": "text", + "content": "Figure 3. Examples of masks in three token mixing strategies. (a) Rand TokenMix. (b) Tube TokenMix. (c) Frame TokenMix." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 205, + 511, + 218 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 511, + 218 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 511, + 218 + ], + "type": "text", + "content": "Algorithm 1 Consistency loss for Tube TokenMix" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 221, + 447, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 221, + 447, + 233 + ], + "spans": [ + { + "bbox": [ + 306, + 221, + 447, + 233 + ], + "type": "text", + "content": "Require: Unlabeled clip batch " + }, + { + "bbox": [ + 306, + 221, + 447, + 233 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{\\mathbf{a}}" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 234, + 489, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 234, + 489, + 245 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For Rand TokenMix, the masked tokens are randomly selected from the whole video clip (from " + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "inline_equation", + "content": "H\\times W\\times T" + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "text", + "content": " tokens). For Frame TokenMix, we randomly select frames from the " + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "text", + "content": " frames and mask all the tokens in these frames. For Tube TokenMix, we adopt the tube-style masking strategy, that is, different frames share the same spatial mask matrix. In this case, the mask " + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 498, + 545, + 676 + ], + "type": "text", + "content": " has consistent masked tokens over the temporal axis. While our mask design shares similarity with the recent masked image/video modeling [16, 47, 51, 52, 58, 59], our motivation is totally different. They focus on removing certain regions and making the model predict the masked areas for feature learning. In contrast, we leverage the mask to mix two clips and synthesize a new data sample." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "The mixed sample " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "x_{mix}" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " is then fed to the student model " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_s" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": ", obtaining the model prediction " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "y_{mix} = \\mathcal{F}_s(x_{mix})" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": ". In addition, the pseudo labels " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\hat{y}_a, \\hat{y}_b" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "x_a, x_b" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18819" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 292, + 224 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 292, + 224 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 292, + 224 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 292, + 224 + ], + "type": "image", + "image_path": "8617344596c01b199ebe63bb128508b1963f18448e0bb7f9df546fd3c67149aa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "type": "text", + "content": "Figure 4. One example of utilizing Temporal Warping Augmentation together with spatial augmentation in TTMix. The two clips are first transformed by the two augmentations separately, after which TTMix is performed to generate a new clip." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 76, + 536, + 227 + ], + "blocks": [ + { + "bbox": [ + 296, + 76, + 536, + 227 + ], + "lines": [ + { + "bbox": [ + 296, + 76, + 536, + 227 + ], + "spans": [ + { + "bbox": [ + 296, + 76, + 536, + 227 + ], + "type": "image", + "image_path": "79e56332aa626b1a66754729ea41f363314cd43fdefc46cc6a2b10c13ccb717d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "text", + "content": "are produced by inputting the weak augmented samples " + }, + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{weak}(x_a),\\mathcal{A}_{weak}(x_b)" + }, + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "text", + "content": " to the teacher model " + }, + { + "bbox": [ + 46, + 277, + 287, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 312, + 287, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 312, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 99, + 312, + 287, + 326 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {a} = \\arg \\max \\left(\\mathcal {F} _ {t} \\left(\\mathcal {A} _ {\\text {w e a k}} \\left(x _ {a}\\right)\\right)\\right), \\tag {7}", + "image_path": "3c899a9a348d3a43313625d09e681d5642014171b80af3f34d3f28fcf173a768.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 100, + 341, + 287, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 341, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 100, + 341, + 287, + 354 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {b} = \\arg \\max \\left(\\mathcal {F} _ {t} \\left(\\mathcal {A} _ {\\text {w e a k}} \\left(x _ {b}\\right)\\right)\\right). \\tag {8}", + "image_path": "44079af2cfafb2573ebd300db8ecda366c5d83753bfb9cb9a0c93cf7dc61ca26.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": "Note that if " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\max (\\mathcal{F}_t(\\mathcal{A}_{weak}(x))) < \\delta" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": ", the pseudo label " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\hat{y}" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": " remains the soft label " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t(\\mathcal{A}_{weak}(x))" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": ". The pseudo label " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\hat{y}_{mix}" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "x_{mix}" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": " is generated by mixing " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\hat{y}_a" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\hat{y}_b" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": " with mask ratio " + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 357, + 287, + 403 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 405, + 287, + 418 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 405, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 287, + 418 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {m i x} = \\lambda \\cdot \\hat {y} _ {a} + (1 - \\lambda) \\cdot \\hat {y} _ {b}. \\tag {9}", + "image_path": "01ca60854e13b7afacf2dfd8b69b1dd85d531413923e6ba7a8375ddce0f3dc45.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 421, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 287, + 445 + ], + "type": "text", + "content": "Finally, the student model is optimized by the following consistency loss:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 97, + 451, + 287, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 451, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 97, + 451, + 287, + 480 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {m i x} = \\frac {1}{N _ {m}} \\sum^ {N _ {m}} \\left(\\hat {y} _ {m i x} - y _ {m i x}\\right) ^ {2}, \\tag {10}", + "image_path": "74d2cc5da75cdcb5f5979e86d70f31bef43ed3d7f0b903e5c98b75837aab027f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 484, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 508 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 484, + 287, + 508 + ], + "type": "inline_equation", + "content": "N_{m}" + }, + { + "bbox": [ + 46, + 484, + 287, + 508 + ], + "type": "text", + "content": " is the number of mixed samples. The algorithm of consistency loss for TTMix is shown in Algorithm 1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 522, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 676 + ], + "type": "text", + "content": "Temporal Warping Augmentation Most existing augmentation methods are designed for image tasks, which focus more on the spatial augmentation. They manipulate single or a pair of images to generate new image samples, without considering any temporal changes. Even the commonly adopted temporal augmentations, including varying temporal locations [18] and frame rates [40, 65], only consider simple temporal shift or scaling, that is, changing the holistic location or play speed. However, human actions are very complex and can have different temporal variation at every timestamp. To cover such challenging cases, we propose to distort the temporal duration of each frame, thus introducing higher randomness into the data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Our Temporal Warping Augmentation (TWAug) can stretch one frame to various temporal length. Given an extracted video clip of " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " frames (e.g., 8 frames), we randomly" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 277, + 541, + 364 + ], + "blocks": [ + { + "bbox": [ + 310, + 277, + 541, + 364 + ], + "lines": [ + { + "bbox": [ + 310, + 277, + 541, + 364 + ], + "spans": [ + { + "bbox": [ + 310, + 277, + 541, + 364 + ], + "type": "image", + "image_path": "0185539e2c8df65b8029a975dcdf2fd1752d6b6898640ac408ba2fc7a8a0c062.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 380, + 545, + 401 + ], + "lines": [ + { + "bbox": [ + 305, + 380, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 545, + 401 + ], + "type": "text", + "content": "Figure 5. Illustration of Temporal Warping Augmentation. We demonstrate three augment examples of different selected frames." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "text", + "content": "determine to keep all the frames, or select a small portion of frames (e.g., 2 or 4 frames) while masking the others. The masked frames are then padded with random neighbouring visible (unmasked) frames. Note that after temporal padding, the frame order is still retained. Fig. 5 shows three examples of selecting 2, 4, and 8 frames, respectively. The proposed TWAug can help the model learn the flexible temporal dynamics during training." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 503, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 503, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 503, + 545, + 587 + ], + "type": "text", + "content": "The Temporal Warping Augmentation serves as a strong augmentation in TTMix. Typically, we combine TWAug with the conventional spatial augmentation [10, 43] to perform the mixing. As shown in Fig. 4, the two input clips are first transformed by spatial augmentation and TWAug separately, after which the two clips are mixed through TTMix. We verify the effectiveness of our TWAug in Sec. 4.3." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 594, + 419, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 419, + 607 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 419, + 607 + ], + "type": "text", + "content": "3.4. Training Paradigm" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 613, + 545, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 660 + ], + "type": "text", + "content": "The training of SVFormer consists of three parts: supervised loss formulated by Eq. (1), unsupervised pseudo-label consistency loss Eq. (2), and TTMix consistency loss Eq. (10). The final loss function is as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 361, + 669, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 669, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 361, + 669, + 545, + 681 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {a l l} = \\mathcal {L} _ {s} + \\gamma_ {1} \\mathcal {L} _ {u n} + \\gamma_ {2} \\mathcal {L} _ {m i x}, \\tag {11}", + "image_path": "5f9a7af9fa70e3a4e499e458e34f4159f18ffbe23647ae10005877b8bf8e1089.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\gamma_{1}" + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "inline_equation", + "content": "\\gamma_{2}" + }, + { + "bbox": [ + 304, + 689, + 545, + 712 + ], + "type": "text", + "content": " are the hyperparameters for balancing the loss items." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18820" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 112, + 533, + 306 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Comparisons with state-of-the-art methods on UCF-101 and Kinetics-400. Note that 3D-ResNet-18 and 3D-ResNet-50 denote the backbone networks and their depths. We report Top-1 accuracy as the evaluation metric. \"Input\" shows the modalities used during training, where \"V\" is the raw RGB video, \"F\" is optical flow and \"G\" is the temporal gradient." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 112, + 533, + 306 + ], + "lines": [ + { + "bbox": [ + 60, + 112, + 533, + 306 + ], + "spans": [ + { + "bbox": [ + 60, + 112, + 533, + 306 + ], + "type": "table", + "html": "
MethodBackboneInputw ImgNetEpochUCF-101Kinetics-400
1%10%1%10%
Supervised3D-ResNet-50V✓2006.532.44.436.2
ViT-SV✓3012.762.519.956.6
FixMatch (NeurIPS 2020) [41]SlowFast-R50V✓20016.155.110.149.4
VideoSSL(WACV 2021) [25]3D-ResNet-18V✓--42.0-33.8
TCL (CVPR 2021) [40]TSM-ResNet-18V400--8.5-
ActorCutMix (CVIU 2021) [71]R(2+1)D-34V✓600-53.09.02-
MvPL (ICCV 2021) [62]3D-ResNet-50V+F+G60022.880.517.058.2
CMPL (CVPR 2022) [64]R50 + R50-1/4V✓20025.179.117.658.4
LTG (CVPR 2022) [57]3D-ResNet-18V+G180/360-62.49.843.8
TACL(TCSVT 2022) [46]3D-ResNet-50V✓200-55.6--
L2A (ECCV 2022) [20]3D-ResNet-18V✓400-60.1--
SVFormer-S (Ours)ViT-SV✓3031.479.132.661.6
SVFormer-B (Ours)ViT-BV✓3046.386.749.169.4
", + "image_path": "daafa366a82218a5a883b0571713022522d0a884994f3e2476729e592c69c13d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 323, + 124, + 337 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 124, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 124, + 337 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 288, + 416 + ], + "type": "text", + "content": "In this section, we first introduce the experimental settings in Sec. 4.1. Following previous work [57,64], we conduct experiments under different labeling rates in Sec 4.2. In addition, we also perform ablation experiments and empirical analysis in Section 4.3. If not emphasized, we only use RGB modal for inference with the official validation set." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 424, + 167, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 167, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 167, + 438 + ], + "type": "text", + "content": "4.1. Experiment Settings" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "content": "Datasets Kinetics-400 [7] is a large-scale human action video dataset, with up to 245k training samples and 20k validation samples, covering 400 different categories. We follow the state-of-the-art methods MvPL [62] and CMPL [64] to sample 6 or 60 labeled training videos per category, i.e. at " + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "content": " labeling rates. UCF-101 [42] is a dataset with 13,320 video samples, which consists of 101 categories. We also sample 1 or 10 samples in each category as the labeled set following CMPL [64]. As for HMDB-51 [26], it is a small-scale dataset with only 51 categories composed of 6,766 videos. Following the division of LTG [57] and VideoSSL [25], we conduct experiments at three different labeling rates: " + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 46, + 442, + 287, + 598 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 601, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 638 + ], + "type": "text", + "content": "Evaluation Metric We show the accuracy of Top-1 in main results, and also present the accuracy of Top-5 in some ablation experiments." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "Baseline We utilize the ViT [13] extended video TimeSformer [4] as the backbone of our baseline. The hyperparameters are mostly kept the same as the baseline, and we adopt the divided space-time attention as in TimeSformer [4]. Since TimeSformer only have ViT-Base models, we implement SVFormer-Small model from DeiT-S [48] with" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 376, + 547, + 485 + ], + "blocks": [ + { + "bbox": [ + 304, + 323, + 547, + 368 + ], + "lines": [ + { + "bbox": [ + 304, + 323, + 547, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 547, + 368 + ], + "type": "text", + "content": "Table 2. Comparisons with state-of-the-art methods on HMDB-51. We report Top-1 accuracy. \"Input\" shows the modalities used during training, where \"V\" is the raw RGB video, \"F\" is optical flow and \"G\" is the temporal gradient." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 376, + 547, + 485 + ], + "lines": [ + { + "bbox": [ + 308, + 376, + 547, + 485 + ], + "spans": [ + { + "bbox": [ + 308, + 376, + 547, + 485 + ], + "type": "table", + "html": "
BackboneInput40%50%60%
VideoSSL [25]3D-R18V32.736.237.0
ActorCutMix [71]R(2+1)D-34V32.938.238.9
MvPL [62]3D-R18V+F+G30.533.935.8
LTG [57]3D-R18V+G46.548.449.7
TACL [46]3D-R18V38.740.241.7
L2A [20]3D-R18V42.146.347.1
SVFormer-S (Ours)ViT-SV56.258.259.7
SVFormer-B (Ours)ViT-BV61.664.468.2
", + "image_path": "a46adf6b1520863799b3450413224bd2d7f89b2754e19f4cd15fc79fa8a57ce9.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 495, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 544 + ], + "type": "text", + "content": "the dimension of 384 and 6 heads, in order to have comparable number of parameters with other Conv-based methods [22, 62, 64]. For fair comparisons, we train 30 epochs for TimeSformer as the supervised baseline." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "Training and Inference For training, we follow the setting of TimeSformer [4]. The training uses 8 or 16 GPUs, with a SGD optimizer using a momentum of 0.9 and a weight decay of 0.001. For each setting, the basic learning rate is set to 0.005, which is divided by 10 at epochs 25, and 28. As for the confidence score threshold, we search for the optimal " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{0.3, 0.5, 0.7, 0.9\\}" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{1}" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\gamma_{2}" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " are set to 2. The masking ratio " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " is sampled from beta distribution " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Beta}(\\alpha, \\alpha)" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\alpha = 10" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": ". In the testing phase, following the inference strategies in MvPL [62] and CMPL [64], we uniformly sample five clips from the entire video, and make three different crops to get " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " resolution to cover most of the spatial areas of the clips. The final prediction is the average of the softmax probabilities of these " + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "inline_equation", + "content": "5 \\times 3" + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": " pre" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18821" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 282, + 339 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 282, + 339 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 282, + 339 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 282, + 339 + ], + "type": "image", + "image_path": "1a8b2f349dfd6ceedb12d01265c8dfc7080ffb587f8a90bebb040892e69d0661.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 353, + 287, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 397 + ], + "type": "text", + "content": "Figure 6. Example of the traditional pixel-level mixing methods and our proposed token-level mixing. Note that token-level methods mix two samples after tokenization but the visualization is shown on image-level for clear presentation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 405, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 430 + ], + "type": "text", + "content": "dictions. We also conduct a comparison of inference setting in the ablation study in Sec. 4.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 438, + 133, + 450 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 133, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 133, + 450 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": "The main results of Kinetics-400 [7] and UCF-101 [42] are shown in Table 1. Compared with previous methods, our model SVFormer-S achieves the best performance with the fewest training epochs among the methods that only use RGB data. In particular, at the labeling rate of " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " setting, SVFormer-S improves previous approach [64] by " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "6.3\\%" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " in UCF-101 and " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "15.0\\%" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " in Kinetics-400. In addition, when adopting larger models, SVFormer-B significantly outperforms the state-of-the-art methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "content": "Specifically, in Kinetics-400, SVFormer-B can achieve " + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "inline_equation", + "content": "69.4\\%" + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "content": " with only " + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "content": " labeled data, which is comparable to " + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "inline_equation", + "content": "77.9\\%" + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "content": " of fully-supervised setting in TimeSformer [4]. Moreover, as shown in Table 2, for the small-scale dataset HMDB-51 [26], our SVFormer-S and SVFormer-B have also improved by about " + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 565, + 287, + 650 + ], + "type": "text", + "content": " compared with the previous method [57]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 148, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 148, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 148, + 670 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "To understand the effect of each part of the design in our method, we conduct extensive ablation studies on the Kinetics-400 and UCF-101 at the " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " labeling ratio setting" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 331, + 113, + 520, + 191 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 3. SSL framework selection. We compare the EMA-Teacher framework with FixMatch. The results are reported on Kinetics-400 and UCF-101 with " + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": " labeling ratio." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 113, + 520, + 191 + ], + "lines": [ + { + "bbox": [ + 331, + 113, + 520, + 191 + ], + "spans": [ + { + "bbox": [ + 331, + 113, + 520, + 191 + ], + "type": "table", + "html": "
MethodUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline12.729.819.942.3
FixMatch [41]25.147.328.254.6
EMA-Teacher31.456.932.659.0
", + "image_path": "460ca91a161dea1bc822fdcf28a54d51b26a2924a565423112e40b5b1c9f692c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 324, + 236, + 524, + 358 + ], + "blocks": [ + { + "bbox": [ + 305, + 201, + 547, + 235 + ], + "lines": [ + { + "bbox": [ + 305, + 201, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 547, + 235 + ], + "type": "text", + "content": "Table 4. TokenMix Mask sampling. We compare different token masking strategies. The results are reported on Kinetics-400 and UCF-101 with " + }, + { + "bbox": [ + 305, + 201, + 547, + 235 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 305, + 201, + 547, + 235 + ], + "type": "text", + "content": " labeling ratio." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 324, + 236, + 524, + 358 + ], + "lines": [ + { + "bbox": [ + 324, + 236, + 524, + 358 + ], + "spans": [ + { + "bbox": [ + 324, + 236, + 524, + 358 + ], + "type": "table", + "html": "
Method/DatasetUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline26.148.923.647.7
CutMix [66]28.751.328.653.7
Mixup [67]29.853.029.355.1
PixMix [24]29.752.429.655.8
Frame TokenMix29.854.226.350.0
Rand TokenMix30.355.328.854.2
Tube TokenMix31.456.932.659.0
", + "image_path": "596a7e86b72ce9c4f0ec21af2dce1fe998286dbdc6e82ad1c5154c654835a865.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 371, + 382, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 371, + 382, + 382 + ], + "spans": [ + { + "bbox": [ + 306, + 371, + 382, + 382 + ], + "type": "text", + "content": "with SVFormer-S." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 386, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 545, + 483 + ], + "type": "text", + "content": "Analysis of SSL framework The comparison of FixMatch and EMA-Teacher is shown in Table 3. It is clear that the two methods have significantly improved the baseline approach. In addition, EMA-Teacher has exhibited considerable gains over FixMatch in both datasets with very few labeled samples, probably because it has improved the stability of training. FixMatch [41] may lead to model collapse with limited labels as shown in [6]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 546, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 653 + ], + "type": "text", + "content": "Analysis of different mixing strategies We now compare the Tube TokenMix strategy with three pixel-level mixing methods, CutMix [66], Mixup [67], PixMix [24], as well as the other two token-level mixing methods, i.e., Frame TokenMix and Rand TokenMix. The examples of different mixing methods are shown in Fig. 6. The quantitative results are shown in Table 4. Compared with these alternative methods, all mixing methods can improve the performance, which proves the effectiveness of mixing-based consistency losses. In addition, we observe that the token-level methods (Rand TokenMix and Tube TokenMix) perform better than the pixel-level mixing methods. This is not surprising since transformers operate on tokens, and thus token-level mixing has inherent advantages." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "The performance of Frame TokenMix is even worse than that of pixel-level mixing methods, which is also expected. We hypothesize that replacing entire frames in video clip will scramble up the temporal reasoning, thus leading to poor temporal attention modeling. In addition, Tube Token-" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18822" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 106, + 282, + 178 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 103 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 103 + ], + "type": "text", + "content": "Table 5. Effects of Spatial and Temporal Warping Augmentations (TWAug). The results are reported on Kinetics-400 and UCF-101 with " + }, + { + "bbox": [ + 47, + 70, + 287, + 103 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 47, + 70, + 287, + 103 + ], + "type": "text", + "content": " labeling ratio." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 106, + 282, + 178 + ], + "lines": [ + { + "bbox": [ + 50, + 106, + 282, + 178 + ], + "spans": [ + { + "bbox": [ + 50, + 106, + 282, + 178 + ], + "type": "table", + "html": "
SpatialTemporalUCF-1%Kinetic-1%
Top-1Top-5Top-1Top-5
Baseline29.552.128.554.2
Spatial-only✓29.953.230.355.9
Temporal-only✓30.255.830.856.4
Spatial+Temporal✓✓31.456.932.659.0
", + "image_path": "f0bf4cfcaa8bb3274073618a45e7c727b6ef3c98e9027387512a008bd352c79f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 49, + 245, + 280, + 327 + ], + "blocks": [ + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "lines": [ + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "text", + "content": "Table 6. Effects of different inference schemes. We compare the sparse sampling strategy and dense sampling method with different frames. The " + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "inline_equation", + "content": "a \\times b" + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "text", + "content": " in 'Frames' column means sampling " + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "text", + "content": " frames at frame rate " + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "text", + "content": ". The results are reported on Kinetics-400 and UCF-101 with " + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 47, + 188, + 286, + 243 + ], + "type": "text", + "content": " labeling ratio." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 245, + 280, + 327 + ], + "lines": [ + { + "bbox": [ + 49, + 245, + 280, + 327 + ], + "spans": [ + { + "bbox": [ + 49, + 245, + 280, + 327 + ], + "type": "table", + "html": "
MethodFramesTest ViewUCF-1%Kinetic-1%
MvPL [62]8 × 810 × 322.817.0
CMPL [64]8 × 810 × 325.117.6
SVFormer-S8 × 321 × 329.331.0
SVFormer-S8 × 85 × 331.432.6
SVFormer-S16 × 410 × 331.633.1
", + "image_path": "91559d15e61160312011b6caf251a7dec11797821a021b9f1909d002bd164448.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 286, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 286, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 286, + 395 + ], + "type": "text", + "content": "Mix achieves the best results. We suppose the consistent masked tokens over temporal axis can prevent information leaky between adjacent frames in the same spatial locations, especially in such a short-term clip. Therefore, Tube Token-Mix could better model the spatio-temporal correlations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 286, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 286, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 286, + 518 + ], + "type": "text", + "content": "Analysis of Augmentations The effects of spatial augmentation and temporal warping augmentation are evaluated in Table 5. The baseline indicates removing both strong spatial augmentation (e.g. AutoAugment [10] and Dropout [43]) and TWAug in all branches. In this case, the experimental performance drops dramatically. When spatial augmentation or temporal warping augmentation is incorporated into the baseline separately, the performance is improved. The best practice is to perform data augmentations in both spatial and temporal." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "content": "Analysis of Inference We evaluate the effect of frame rate sampling and different inference schemes, as shown in Table 6. Previous methods, i.e. CMPL [64] and MvPL [62], utilize the clip-based sparse sampling, which samples 8 frames at frame rate 8 as a clip. For each video, 10 clips are sampled, where each clip is cropped 3 times according to different spatial positions. Finally, the predictions of " + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "inline_equation", + "content": "10 \\times 3" + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "content": " samples are averaged. TimeSformer [4] adopts the video-based sparse sampling, that is, 8 frames are sampled at frame rate 32 as the representation of the whole video. Then 3 different cropped views are used, namely " + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "inline_equation", + "content": "8 \\times 32" + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "content": ". Applying the video-based sparse sampling scheme as in TimeSformer [4] can reduce the inference cost, but the performance is worse than that of clip-based sampling. Experiments at sampling schemes of " + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "inline_equation", + "content": "16 \\times 4" + }, + { + "bbox": [ + 46, + 521, + 286, + 713 + ], + "type": "text", + "content": " demonstrate better performance. For the trade-off between effi" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 312, + 71, + 424, + 140 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 424, + 140 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 424, + 140 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 424, + 140 + ], + "type": "image", + "image_path": "7a1acfc50ff1b975de968b03740c17399a29a1234a1f0e90ae24626e66925e86.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 425, + 70, + 539, + 141 + ], + "blocks": [ + { + "bbox": [ + 425, + 70, + 539, + 141 + ], + "lines": [ + { + "bbox": [ + 425, + 70, + 539, + 141 + ], + "spans": [ + { + "bbox": [ + 425, + 70, + 539, + 141 + ], + "type": "image", + "image_path": "877beff07eab7a533a71c8963924834f3b6b85a1f2c9c4fc8b6a7ecf38fc67de.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 147, + 424, + 217 + ], + "blocks": [ + { + "bbox": [ + 310, + 147, + 424, + 217 + ], + "lines": [ + { + "bbox": [ + 310, + 147, + 424, + 217 + ], + "spans": [ + { + "bbox": [ + 310, + 147, + 424, + 217 + ], + "type": "image", + "image_path": "c86edfc119688c70a1fccb78e59613d698be63e2b78c68242d97ab38d4302fbc.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "text", + "content": "Figure 7. Effects of hyperparameters. Results of varying threshold " + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "text", + "content": ", ratio between unlabeled and labeled data in a mini-batch " + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "inline_equation", + "content": "(B_u / B_l)" + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "text", + "content": ", momentum coefficient " + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "text", + "content": ", and loss weights " + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "inline_equation", + "content": "(\\gamma_1, \\gamma_2)" + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "text", + "content": " are included to comprehensively study the effects of the hyperparameters. Reported on Kinetics-400 with " + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 220, + 545, + 277 + ], + "type": "text", + "content": " labeling ratio." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 425, + 145, + 539, + 217 + ], + "blocks": [ + { + "bbox": [ + 425, + 145, + 539, + 217 + ], + "lines": [ + { + "bbox": [ + 425, + 145, + 539, + 217 + ], + "spans": [ + { + "bbox": [ + 425, + 145, + 539, + 217 + ], + "type": "image", + "image_path": "bc95930fb244a9b380a1c73ab4fa8992073ecf304f6f43af1ffc3a7b00b8b9ec.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "type": "text", + "content": "ciency and accuracy, we use " + }, + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "type": "inline_equation", + "content": "8 \\times 8" + }, + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "type": "text", + "content": " as the default setting following CMPL [64] and MvPL [62]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": "Analysis of hyperparameters Here we explore the effect of different hyperparameters. We conduct experiments under " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " setting of Kinetics-400. We first explore the effect of different threshold values of " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": ". As shown in Fig. 7(a), we can observe that when labeled samples are extremely scarce, best results are achieved by setting a small " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " value " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "(\\delta = 0.3)" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": ". We then evaluate how the ratio between labeled samples and unlabeled samples in a mini-batch affects the result. We fix the labeled sample number " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "B_{l}" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " to 1, and sample " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "B_{u}" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " unlabeled samples to form a mini-batch, where " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "B_{u}" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " is in " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\{1,2,3,5,7\\}" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": ". The results are shown in Fig. 7(b). When " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "B_{u} = 5" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": ", the model produces the highest result. Finally, we explore the choice of momentum coefficient " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " of EMA and the loss weights " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\gamma_{1}" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\gamma_{2}" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": ", as shown in Fig. 7(c) and Fig. 7(d). We thus set " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "m = 0.99" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "inline_equation", + "content": "\\gamma_{1} = \\gamma_{2} = 2" + }, + { + "bbox": [ + 304, + 311, + 546, + 502 + ], + "type": "text", + "content": " as default setting in all the experiments." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 534, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 689 + ], + "type": "text", + "content": "In this paper we present SVFormer, a transformer-based semi-supervised video action recognition method. We propose Tube TokenMix, a data augmentation method that is specially designed for video transformer models. Coupled with the temporal warping augmentation, which covers the complex temporal variations by arbitrarily changing the frame length, TTMix achieves significant improvement compared with conventional augmentations. SVFormer outperforms the state-of-the-art with a large margin on UCF-101, HMDB-51 and Kinetics-400 without increasing overheads. Our work establishes a new benchmark for semi-supervised action recognition and encourages future work to adopt Transformer architecture." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement This project was supported by NSFC under Grant No. 62032006 and No. 62102092." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18823" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Inigo Alonso, Alberto Sabater, David Ferstl, Luis Montesano, and Ana C Murillo. 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Learning representational invariances for data-efficient action recognition. arXiv preprint arXiv:2103.16565, 2021. 4, 6" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "18826" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/3621baa2-936b-4fa2-8381-1968bf4d3112_content_list.json b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/3621baa2-936b-4fa2-8381-1968bf4d3112_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ae22c7f567599eed2030b996b17f8cca7cfc0661 --- /dev/null +++ b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/3621baa2-936b-4fa2-8381-1968bf4d3112_content_list.json @@ -0,0 +1,1569 @@ +[ + { + "type": "text", + "text": "SVGformer: Representation Learning for Continuous Vector Graphics using Transformers", + "text_level": 1, + "bbox": [ + 127, + 128, + 843, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Defu Cao1, Zhaowen Wang2, Jose Echevarria2, Yan Liu1", + "bbox": [ + 233, + 202, + 732, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Southern California", + "bbox": [ + 349, + 220, + 622, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2Adobe Research, Inc.", + "bbox": [ + 393, + 238, + 573, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{defucao, yanliu.cs}@usc.edu, {zhawang, echevarr}@adobe.com", + "bbox": [ + 137, + 257, + 831, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Advances in representation learning have led to great success in understanding and generating data in various domains. However, in modeling vector graphics data, the pure data-driven approach often yields unsatisfactory results in downstream tasks as existing deep learning methods often require the quantization of SVG parameters and cannot exploit the geometric properties explicitly. In this paper, we propose a transformer-based representation learning model (SVGformer) that directly operates on continuous input values and manipulates the geometric information of SVG to encode outline details and long-distance dependencies. SVGfomer can be used for various downstream tasks: reconstruction, classification, interpolation, retrieval, etc. We have conducted extensive experiments on vector font and icon datasets to show that our model can capture high-quality representation information and outperform the previous state-of-the-art on downstream tasks significantly.", + "bbox": [ + 75, + 340, + 473, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 631, + 209, + 645 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In the last few years, there have been tremendous advances in image representation learning [22, 26, 37], and these representations lead to great success in many downstream tasks such as image reconstruction [40], image classification [14, 16], etc. However, most previous works have focused on analyzing structured bitmap format, which uses a grid at the pixel level to represent textures and colors [18]. Therefore, there is still considerable room for improving the representation of detailed attributes for vector objects [25].", + "bbox": [ + 75, + 657, + 470, + 794 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In contrast to bitmap image format, scalable vector graphics (SVG) format for vector images is widely used in real-world applications due to its excellent scaling capabilities [12, 20, 33]. SVGs usually contain a mixture of smooth curves and sharp features, such as lines, circles, polygons, and splines, represented as parametric curves in digital format. This allows us to treat SVGs as sequential data and", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "learn their compact and scale-invariant representation using neural network models. However, how to automatically learn an effective representation of vector images is still non-trivial as it requires a model to understand the high-level perception of the 2D spatial pattern as well as geometric information to support the high-quality outcome in downstream tasks.", + "bbox": [ + 496, + 310, + 893, + 400 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Transformer-based models [30] have been proven to achieve start-of-the-art results when dealing with sequential data in various problems including Natural Language Processing (NLP) [34] tasks and time-series forecasting [41] problems. We argue that representation learning for SVG is different from these tasks for two reasons: Firstly, most if not all NLP tasks need a fixed token space to embed the discrete tokens, while SVGs are parameterized by continuous values which make the token space infinite in the previous setting; Secondly, the number of commands and the correlation between the commands vary greatly from one SVG to another, which is hard to handle by a pure data-driven attention mechanism. For example, the font data may vary across different families while sharing similar styles within the same font family. Such property is encoded in the sequential data explicitly and can provide geometric dependency guidance for modeling the SVG if used appropriately.", + "bbox": [ + 496, + 402, + 895, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To tackle the above challenges and fully utilize the geometric information from SVG data, this work introduces a novel model architecture named SVGformer, which can take continuous sequential input into a transformer-based model to handle the complex dependencies over SVG commands and yield a robust representation for the input. Specifically, we first extract the SVG segment information via medial axis transform (MAT) [2] to convey the geometric information into the learned representation. Then we introduce a 1D convolutional embedding layer to preserve the original continuous format of SVG data, as opposed to previous vector representation learning models [8] which need a preprocessing step to discretize the input to limited discrete tokens. After that, we inject the structural relationship between commands into the proposed geometric self-attention module in the encoder layer to get the hidden representation", + "bbox": [ + 496, + 659, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10093", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/ff2265546ba4c5c81dc0d8206277e35894fc45e5daa6af008676872bb6785253.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFont-MF [3]SVG-VAE [20]Im2Vec [25]DeepVecFont [33]DeepSVG [8]LayoutTrans [12]SVGformer (ours)
Encoding ModalitySeqImgImgImg&SeqSeqSeqSeq
Decoding ModalitySeqImg&SeqSeqImg&SeqSeqSeqSeq
Model ArchitectureGP-LVMVAERNNLSTM+CNNTransformerTransformerTransformer
Sequence FormatKeypointsCommandsKeypointsCommandsCommandsCommandsCommands
Geometric Information------Segment
", + "bbox": [ + 94, + 89, + 874, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Comparison of our SVGformer model and recent models for vector representation learning, where \"Seq\" donates sequence, and \"Img\" donates image.", + "bbox": [ + 75, + 209, + 892, + 238 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of each SVG. The representation learned with the reconstruction pretext task can be used in various downstream tasks including classification, retrieval, and interpolation. To the best of our knowledge, our proposed model is the first to explicitly consider vector geometric information as well as directly deal with the raw input of SVG format in an end-to-end encoder-decoder fashion.", + "bbox": [ + 75, + 247, + 470, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of this paper include:", + "bbox": [ + 96, + 354, + 410, + 368 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- SVGformer captures both geometric information and curve semantic information with the geometric self-attention module, which synergizes the strengths of MAT and the transformer-based neural network to handle long-term sequence relationships in SVG.", + "- SVGformer can take original continuous format as input which can effectively reduce the token space in the embedding layer. Thereby the model is general for all continuous vector graphics without extra quantization.", + "- SVGformer achieves new state-of-the-art performance on four downstream tasks of both Font and Icon dataset. For example, it outperforms prior art by $51.2\\%$ on classification and $42.5\\%$ on retrieval tasks of the font dataset." + ], + "bbox": [ + 94, + 376, + 468, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 618, + 215, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Transformer models in the computer version. In the realm of computer vision, many researchers have proposed using self-attention to model long-term dependencies, similar to how transformers are used in natural language processing and other real-world applications [5, 6, 34, 36]. By leveraging self-attention in the encoder-decoder architecture, these methods have shown promising results in computer vision benchmarks, overcoming the limitations imposed by inductive convolution bias [10]. The fields of those benchmarks include object detection [7], image generation [11], and classification on both image [21] and video [32]. In most related works, the self-attention layer in computer vision takes a feature map as input and computes the attention weights between each pair of features. This operation can result in an updated feature map where each position has information about any other feature in the same image which could be costly for high-resolution or long sequential", + "bbox": [ + 75, + 643, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "inputs. Thus, there are multiple works aimed at overcoming this problem. For example, Informer [41] proposes a sparse attention mechanism by sorting the important queries; Axial-DeepLab [31] computes the attention score sequentially along the two spatial axis and [23] processes the patches of feature maps instead of the whole image. In addition, as inductive bias can always be beneficial to the learning process [35], we need to inject the position information into the transformers to help update features that are lost in the input sequence. For learning the SVG representation, we can introduce structural inductive bias into transformer-based models by obtaining the position information from the input sequence.", + "bbox": [ + 496, + 247, + 893, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Representation learning for SVG. Designing and manipulating the SVG image including fonts and icons require substantial expertise and expert knowledge [3]. Machine learning-based models can automatically manipulate the outlines and skeletons of vector images by learning from specific datasets. For the previous works, Font-MF [3] utilize the Gaussian Process Latent Variable Model [17] to learn a manifold of fonts so that it can synthesize fonts in unseen fonts. Im2Vec [25] proposes a new neural network that can generate complex vector graphics with varying topologies and only requires indirect supervision from readily-available raster training images (i.e., with no vector counterparts). Instead of directly using bitmap format, DeepVecFont [33] introduces a new generative paradigm to handle unstructured data (e.g., vector glyphs) by randomly sampling plausible synthesis results and a dual-modality learning strategy that utilizes both image-aspect and sequence-aspect features of fonts to synthesize vector glyphs. SVG-VAE [20] is a generative model with an autoencoder to learn the font style feature and an SVG decoder to generate vector glyphs. In addition, LayoutTransformer [12] uses the self-attention mechanism to capture the contextual relationship between different vector elements, which provides a potential solution for SVG data. Besides, DeepSVG [8] raises a hierarchical transformer-based generative model for vector graphics and collects a large-scale dataset of SVG along with deep learning-based SVG manipulation. However, most models that process the SVG format fail to handle the continuous nature [4, 39] of the input correctly. Besides, most of them do not consider", + "bbox": [ + 496, + 462, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10094", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/36efd8d67d1f28faa28e1d371ad06e2b9ee964235c8b3da78ea3f05d1fd57855.jpg", + "image_caption": [ + "Figure 1. The extraction of geometric information. Starting from the original SVG commands $p_i$ delimited by blue circles, we apply MAT [2] to obtain a new set of commands and labels $(\\hat{p}_i, \\hat{l}_i)$ (denoted by curve color and delimited with crosses) that may not exactly align with the original commands. A unique label $l_i$ is finally assigned to each original command, as outlined in black color in the last column of the table." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 207, + 276 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/6842ddb4c1dcdc5476cfecd4737b0ded10276f20f3234115ecc0182e7465f5eb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Raw CommandsArgumentsGeometric Segments
p0M (13.2, 3.0)-1
...
paL (16.5, 18.9)
pbL (16.2, 21.0)
...
pcC (5.8, 19.1, 6.3, 17.5, 7.2, 16.2)
...
pnEOS (∅)-1
", + "bbox": [ + 230, + 95, + 467, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "geometric information, which can directly equip the relationship of different curves into deep learning-based methods. Refer to Table 1 for a complete comparison of related works.", + "bbox": [ + 75, + 395, + 470, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 455, + 166, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 482, + 186, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a transformer-based deep neural network, SVGformer, as a general solution for multiple vector graphics downstream tasks. The overall architecture of SVGformer is illustrated in Figure 2. The raw $t$ -th SVG's arguments contain the type and corresponding coordinates of its commands, where the coordinates with continuous values are first constructed into a tensor format, $\\mathcal{X}^t \\in \\mathbb{R}^{n \\times 8}$ and $n$ is the number of commands. Then the input tensor is fed into the embedding layer to get the input vector for the encoder-decoder model. The learnable embedding layer contains three components to specifically abstract the information from the original input: 1) the continuous token component uses a 1D convolution to map $\\mathcal{X}^t$ into an embedding vector $U^t$ ; 2) the position component captures the positional information $P^t$ from $\\mathcal{X}^t$ ; 3) the geometric component treats the outline labels $l_i$ (refer to Figure 1) as a discrete token to map extra contextual geometric information $S^t$ to the embedding vector. In addition, we build an adjacency matrix $E$ based on the labels and the neighboring commands in order to further utilize the structural information in the training process.", + "bbox": [ + 75, + 507, + 468, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, we combine the embedding vectors to feed the encoder module, where we introduce the geometric self-attention to replace the canonical self-attention in order to generate a compact representation with a higher receptive field efficiently. Specifically, we leverage structural relationships by encoding geometric segment information via a", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "graph convolution layer and injecting it into spared attention score. Finally, we pass the hidden representation produced by the encoder into the SVG-decoding module consisting of the self-attention mechanism [41] and fully connected layers to fine-tune the total model. The decoder aims to reconstruct the original SVG commands from a masked input as well as predict the type of commands.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this way, the overall network can be trained end-to-end by backpropagation of a reconstruction loss and classification loss. Precisely, the classification loss has 3 different labels as we only consider three types of commands: \"Move\" (M), \"Line\" (L) and \"Curve\" (C).", + "bbox": [ + 496, + 196, + 893, + 273 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Geometric Information from Raw Input", + "text_level": 1, + "bbox": [ + 498, + 282, + 843, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As the attention mechanism generally only calculates the similarities via the commands' semantic features, we want to cooperate explicit geometric dependencies into the attention mechanism to provide our model with the ability to capture the structural relation between the commands. v We start from the raw SVG input $\\{p_0,p_1,p_2,\\ldots ,p_n\\}$ , where $p_i$ denotes the $i$ -th command in a given SVG, and $n$ is the number of original commands. As shown in Figure 1, we obtain semantic labeling of segments with MAT. This tool leverages the medial axis and outlines information to find new segments labeled based on different geometric relationships: $\\{(\\hat{p}_1,\\hat{l}_1),(\\hat{p}_2,\\hat{l}_2),\\dots ,(\\hat{p}_m,\\hat{l}_m)\\}$ , where $\\hat{l}_i$ is the label of the new command $\\hat{p}_i$ . Commands with the same label have a strong position relationship inside the given SVG, which is usually ignored by feature engineering. Note that MAT can usually split an original command into several segments (new commands), so $m\\geq n$ . However, directly adding such extra commands into the neural network will complicate the task of representation learning. Instead, we propose to map the new segments and labels back to the original input. Specifically, we group different commands by start and end points so that we have $p_i = \\{\\hat{p}_k,\\dots ,\\hat{p}_j\\}$ . To obtain the final label $l_{i}$ for $p_i$ , we calculate the longest label by the distance between the start and end point of the label set $\\{\\hat{l}_k,\\dots ,\\hat{l}_j\\}$ . Then the final data we use to train the model is $\\{(p_1,l_1),(p_2,l_2),\\dots ,(p_n,l_n)\\}$ . We will introduce how to incorporate geometric information into the transformer in the next several sections.", + "bbox": [ + 496, + 306, + 893, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Continuous Feature Embedding", + "text_level": 1, + "bbox": [ + 498, + 739, + 782, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Representation learning requires the model to learn the inductive biases from the data and training task which can facilitate the downstream task. Thus, any inductive bias from raw input is able to coach the training process. In this work, we have identified two inductive biases present in raw input: continuous values and geometric information. While previous related works have typically relied on manually discretizing continuous values, our model is able to support continuous-valued inputs. Additionally, our model", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10095", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/350ee0f465ffef52f8db07610d05cbc311dbf956dc0d81da2b1307e2a479542e.jpg", + "image_caption": [ + "Figure 2. Overall model structure of SVGformer." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 893, + 324 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "is able to automatically discover structural information from the geometric information present in the input, providing further support for the inductive biases we have identified. This section will present proposed modifications to make it compatible with continuous SVG commands input with geometric information rather than with discrete pre-processed index sequences.", + "bbox": [ + 75, + 356, + 470, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, for the raw input, we first set a maximum sequence length $L_{x}$ for the entire dataset, then we pad shorter samples with arbitrary values (0 in our setting) as the length of individual samples may vary considerably regarding the SVG images. Then, we generate a padding mask that adds a large negative value to the attention fraction of the padded positions before computing the self-attentive distribution with the softmax function. After that, different from previous works that can only support discrete input with fix length of the look-up table, we use a continuous value embedding layer with 1D convolutional operation to project the $t$ -th SVG input $\\mathcal{X}^t$ into a $d$ -dimension vector $U^{t}$ :", + "bbox": [ + 75, + 462, + 473, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nU ^ {t} = \\operatorname {C N N} \\left(\\mathcal {X} ^ {t}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 656, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that this embedding layer can fully utilize the translation equivariance [1] of convolutional operation for SVG input and can have the ability of rotation invariance and size invariance with data augmentation. Corresponding to the continue value embedding layer, we preserve the input SVG commands by using the position embedding layer:", + "bbox": [ + 75, + 685, + 470, + 777 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP ^ {t} (p, 2 j) = \\sin \\left(m / \\left(2 L _ {x}\\right) ^ {2 j / d}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 787, + 468, + 813 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP ^ {t} (p, 2 j + 1) = \\cos \\left(m / \\left(2 L _ {x}\\right) ^ {2 j / d}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 810, + 403, + 828 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $j\\in \\{1,\\ldots ,\\lfloor d / 2\\rfloor \\}$ and $m\\in \\{0,\\dots ,L_x - 1\\}$ . In this way, self-attention can compute the similarity with access to global information and affordable consumption [41]. Note that this position encoding function is inductive and", + "bbox": [ + 75, + 839, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "parameters free to handle variable input length [19]. However, the above inductive embedding functions fail to capture the geometric dependency among the different positions of raw SVG commands. Thus, we exact the segment label $l_i^t$ for each input command $p_i^t$ according to Section 3.2 and use a geometric embedding layer with a look-up table, containing all the segmented labels, to get the geometric information $S$ . Thus, we finally maintain the feeding vector $X_{en}^{t} \\in \\mathbb{R}^{L_{x} \\times d}$ :", + "bbox": [ + 496, + 356, + 893, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {e n} ^ {t} = \\alpha U ^ {t} + \\beta P ^ {t} + \\gamma S ^ {t}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 510, + 890, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha, \\beta, \\gamma$ are the factors balancing the magnitude between the scalar projection and position/geometric embeddings.", + "bbox": [ + 496, + 537, + 893, + 583 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. SVGformer Encoder with Geometric Information", + "text_level": 1, + "bbox": [ + 498, + 595, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After the embedding layer, we feed the vector $X_{en}^{t}$ to the encoder to extract latent representation. We refer the reader to the detailed description of the transformer model in the original work [30]. In this section, we will introduce the key technologies different from the vanilla transformer. Specifically, the encoder consists of several stacked geometric self-attention modules which can deal with long-term sequential dependency and geometric dependency in the attention mechanism jointly.", + "bbox": [ + 496, + 633, + 893, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sparse Query for Self-Attention. As the representation learning of SVG requires the model to have the ability to capture precise long-term dependency, we need to utilize the commands' features via an efficient attention mechanism. The canonical self-attention is defined based on the scaled dot-product of the input tuple, i.e., query $\\mathbf{q} \\in \\mathbb{R}^d$ , key $\\mathbf{K} \\in \\mathbb{R}^{L_K \\times d}$ , and value $\\mathbf{V} \\in \\mathbb{R}^{L_V \\times d}$ . Specifically, the $i$ -th", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10096", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "query's attention is defined as a kernel smoother in a probability form [29]:", + "bbox": [ + 75, + 90, + 470, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (\\mathbf {q} _ {i}, \\mathbf {K}, \\mathbf {V}) = \\sum_ {j} \\frac {k (\\mathbf {q} _ {i} , \\mathbf {k} _ {j})}{\\sum_ {l} k (\\mathbf {q} _ {i} , \\mathbf {k} _ {l})} \\mathbf {v} _ {j} = \\mathbb {E} _ {p (\\mathbf {k} _ {j} | \\mathbf {q} _ {i})} [ \\mathbf {v} _ {j} ], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 127, + 470, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p(\\mathbf{k}_j|\\mathbf{q}_i) = k(\\mathbf{q}_i,\\mathbf{k}_j) / \\sum_lk(\\mathbf{q}_i,\\mathbf{k}_l)$ and $k(\\mathbf{q}_i,\\mathbf{k}_j)$ selects the asymmetric exponential kernel $\\exp (\\mathbf{q}_i\\mathbf{k}_j^\\top /\\sqrt{d})$ . Inspired by [41], we calculate the importance of queries by Kullback-Leibler divergence:", + "bbox": [ + 76, + 170, + 470, + 234 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nM (\\mathbf {q} _ {i}, \\mathbf {K}) = \\max _ {j} \\left\\{\\frac {\\mathbf {q} _ {i} \\mathbf {k} _ {j} ^ {\\top}}{\\sqrt {d}} \\right\\} - \\frac {1}{L _ {K}} \\sum_ {j = 1} ^ {L _ {K}} \\frac {\\mathbf {q} _ {i} \\mathbf {k} _ {j} ^ {\\top}}{\\sqrt {d}} \\quad , \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 239, + 470, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M(\\mathbf{q}_i, \\mathbf{K})$ is the $i$ -th query's sparsity score. A larger $M(\\mathbf{q}_i, \\mathbf{K})$ gives a higher chance to activate the dominate dot-product pairs in the self-attention. Thus, we can build a new query $\\overline{Q}$ containing top $u$ queries with query sparsity score given by $M$ and calculate the sparsity self-attention score by:", + "bbox": [ + 76, + 289, + 468, + 378 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nA _ {a t t} = \\overline {{\\mathbf {Q}}} \\mathbf {K} ^ {\\top} / \\sqrt {d} \\quad . \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 378, + 468, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that we can avoid information loss by generating different sparse query-key pairs according to different attention heads and this attention score can capture the relationships between input commands from a data-driven aspect.", + "bbox": [ + 75, + 398, + 470, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Geometric Dependency in Self-Attention. Segments with the same label share a strong relationship even if they are at a long distance in the input sequence, which cannot be reflected in the original self-attention module which only considers the semantic characteristics. In addition, commands can be represented as the nodes lying in a non-Euclidean space and linked by edges with the geometric information. such as the adjacency and the same segment label. In this work, we propose to apply the graph convolution network (GCN) [15] to extract the structural relationship between different commands. Specifically, we first use the geometric label from Section 3.2 to build the weight matrix $E$ where the commands adjacent to each other or sharing the same label have an edge in the weight matrix $E$ , otherwise there is no edge in the weight matrix $E$ .", + "bbox": [ + 75, + 477, + 468, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This has two advantages, firstly, the structure information of SVG is contained in the weight matrix, and secondly, commands sharing the same labels can distinguish local details by their own features. After getting the weight matrix, we use GCN to extract the structural information. The goal is then to learn a function of SVG commands on a graph $\\mathcal{G} = (V,E)$ , where $V$ is the set of nodes' (commands in SVG) feature of each single SVG, i.e., $X_{en}^{t}$ at the first layer, and $E$ is the in the form of the adjacency matrix, which is $A$ based on Figure 1. Our model can produce command-level output $A_{geo} \\in \\mathbb{R}^{N \\times d}$ with $L$ multiple layers GCN where $l$ -th layer output $H^{l}$ can be used to represent the latent vectors to get the final output:", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH ^ {l + 1} = f \\left(H ^ {l}, E\\right) = \\sigma \\left(E H ^ {l} W ^ {l}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 103, + 890, + 122 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H^0$ is the input features of the GCN, i.e., $\\mathcal{X}_{en}$ at the very first layer, $f$ is the graph convolutional function with learnable matrix $W$ and $\\sigma$ is the non-linear activation function for GCN and $H^L = A_{geo}$ .", + "bbox": [ + 498, + 127, + 893, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Geometric Self-Attention Module. To better encode the geometric information into attention layers, we propose a new self-attention module in SVGformer. The attention mechanism needs to estimate correlations on both semantics (features from commands) part and the geometric (dependency of each command) part. Thus, for each ordered command pair $(p_i,p_j)$ , we inject the relationship score from GCN into the sparse attention score. Concretely, the attention mechanism with the modified attention score can be represented as", + "bbox": [ + 498, + 207, + 893, + 357 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(A _ {\\text {a t t}} + A _ {\\text {g e o}}\\right) \\mathbf {V} \\quad . \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 369, + 890, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To enhance the ability of our model on handling the permutation invariance where the order of shapes in an SVG image is arbitrary, we apply the 1D convolutional operation following an ELU activation function [9] and max pooling [38] on the output of the attention layer: $\\mathbf{X}_{j + 1} = \\mathrm{MaxPool}\\left(\\mathrm{ELU}(\\mathrm{Conv1d}([X_j]_{\\mathcal{A}_j}))\\right)$ , where $[\\cdot ]_{\\mathcal{A}}$ represents the $j$ -th geometric self-attention module.", + "bbox": [ + 498, + 397, + 893, + 502 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final representation of the encoder $Z$ is the last layer's output of the encoder module and can be used for multiple downstream tasks.", + "bbox": [ + 498, + 503, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. SVGformer Decoder", + "text_level": 1, + "bbox": [ + 500, + 558, + 692, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The decoder part is modified from the decoder structure in [41], which can reconstruct the long sequences of SVG at one forward operation rather than a step-by-step way with the input of $\\mathbf{X}_{\\mathrm{de}}^{t} = \\operatorname{Concat}(\\mathbf{X}_{\\mathrm{token}}^{t}, \\mathbf{X}_{0}^{t}) \\in \\mathbb{R}^{(L_{\\mathrm{token}} + L_{y}) \\times d}$ , where $\\mathbf{X}_{\\mathrm{token}}^{t} \\in \\mathbb{R}^{L_{\\mathrm{token}} \\times d}$ is the start token, $\\mathbf{X}_{0}^{t} \\in \\mathbb{R}^{L_{y} \\times d}$ is a placeholder of 0 for the target sequence. Specifically, it consists of masked geometric self-attention and multi-head attention, where the masked geometric self-attention sets masked dot-products to $-\\infty$ and gives up the geometric GCN component, which can prevent data leakage in the decoding stage. Besides, a fully connected layer is needed to acquire the final logits for the loss function.", + "bbox": [ + 498, + 580, + 890, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 771, + 643, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We need to reconstruct the input commands as well as predict the type of the commands. Thus, we choose the reconstruction loss as the mean squared error (MSE) loss function between the reconstructed commands and the ground-truth command and the classification loss as the cross entropy (CE) with logits between the predicted command type and the type label.", + "bbox": [ + 498, + 795, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10097", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 76, + 114, + 158, + 132 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We summarize the critical settings in this section. For input SVG, we choose those font inputs with a maximum length $L_{x}$ equals to 60 and icon inputs with a maximum length equals to 50. Then pad the font commands less than 60 (50 for icon commands) by 0. For the embedding layer, a 1D convolutional operation is used as the trainable module for SVG recognition with kernel width equal to 3 and stride equal to 1. Both the 1D convolutional operation and the other two components inside the embedding layer's output dimension are 512. We recommend $\\alpha, \\beta, \\gamma$ to be 1 inside the embedding layer if the sequence input has been normalized. In the training stage, the sparse attention's head number is 8, and we add geometric information given by one GCN layer, which output shape fits the attention score given by the sparse self-attention. To gain the global representation for a specific SVG, we use two stacked geometric self-attention modules followed by 1D convolutional operations and maximum pooling operations to finish the fusion process of all the commands and get the hidden representation with the shape of $L_{x} \\times 512$ . For the decoder during the training stage, we mask all the commands instead of the first command (whose type is \"Move\") to finish the reconstruction task, which means $L_{token} = 1$ and $L_{y} = L_{x} - 1$ .", + "bbox": [ + 75, + 140, + 472, + 487 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the remaining part of this section, we discuss the qualitative and quantitative results of our models on two representative datasets, Google Fonts1 and Icons [8]. Note that the evaluation of representation learning models is difficult, and most quantitative metrics can not provide a generic measure of the novelty and veracity of the data sampled from representation learning models. Thus, we will explore 4 types of downstream tasks including reconstruction task, classification task, retrieval task, and interpolation task with specific quantitative metrics used by the various underlying methods.", + "bbox": [ + 75, + 488, + 472, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 76, + 652, + 171, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the effectiveness of the proposed SVGformer on both fonts dataset and the icons dataset. We first show the reconstruction results, which is the training task. Note that simply using MSE and CE metrics cannot accurately show the coordinate values of control points on the contour line because the average of the correct target values is often not a correct value, so we use Chamfer distance (CD) metric to do the evaluation. Then, for the downstream tasks, we train a classification model to finish the classification task and use the glyph label to verify the retrieval task, which is a pure unsupervised process without any fine-tuning on the representation. After that, we finish with an interpolation task to show that SVGformer has good interpretability.", + "bbox": [ + 75, + 676, + 470, + 875 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3795e5e91e4ef5e455ef615a8f44af7edd2c0f7790deaa059f8cf4774298819d.jpg", + "image_caption": [ + "Figure 3. Reconstruction results on various glyphs. From left to right, the original SVG (black), DeepSVG (orange), LayoutTransformer (green) and our SVGformer (blue), respectively." + ], + "image_footnote": [], + "bbox": [ + 521, + 90, + 870, + 247 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Fonts", + "text_level": 1, + "bbox": [ + 500, + 327, + 594, + 342 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Reconstruction task. The reconstruction task is the training task where we can get the pre-trained model and obtain the latent representation of a given SVG image. We use Chamfer distance (CD) between corresponding paths of the input SVG and reconstructed SVG to evaluate the performance of the SVGformer.", + "bbox": [ + 498, + 351, + 893, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on Table 2, our model produces a smaller gap than the other baselines with $17.8\\%$ overperformance in a mathematical sense, proving the accuracy of SVGformer. In addition, we render the reconstructed results for quantitative comparisons on Figure 3. Benefiting from the two kinds of attention scores, SVGformer can reconstruct more details of the raw input. As confirmed by the results, we find that introducing the geometric information brings a substantial improvement in reconstruction error compared to the previous baselines.", + "bbox": [ + 496, + 441, + 895, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Classification task. For the classification task, we train a linear classification model for the different hidden representations with 1000 epochs and show in Table 2 the accuracy results of glyph-based category (62 classes) and family-based category (378 font family types filtered by a minimum class size of 100 in the test set). The glyph-based classification task is used to verify that our model's latent representation can identify the outline of inputs. The family-based classification task is more challenging as it has more categories and focuses on font style which needs the latent representation to be distinctive in details. We can figure out that the geometric information can help SVGformer gain further improvement for this mature task. Specifically, we find that both the LayoutTransformer and DeepSVG fail to classify the family labels with the accuracy of $7.0\\%$ and $35.2\\%$ , respectively, which means they lose the style information during the data-driven process. Especially we find that higher dimensional data does not encompass more information because LayoutTransformer's hidden representation has a larger shape", + "bbox": [ + 496, + 613, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1https://fonts.google.com/", + "bbox": [ + 94, + 886, + 236, + 900 + ], + "page_idx": 5 + }, + { + "type": "footer", + "text": "10098", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c7de5ee289880b5a20c6fdba74f135821f1fd1a3c3208aa60a1609e89525a20c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelReconstruction (CD ↓)Classification (Acc %)Retrieval (Acc %)
FontsIconsFonts GlyphFonts FamilyIconsFonts@5Fonts@10Icons@10
LayoutTransformer37.618.875.67.057.61.71.613.4
DeepSVG32.715.685.635.245.151.245.922.8
SVGformer26.96.389.569.764.774.364.248.9
SVGformer-no-geo30.87.989.346.346.769.659.446.2
SVGformer-discrete41.519.385.915.063.760.751.530.5
", + "bbox": [ + 99, + 89, + 870, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f67a28bf9e86f28324ddfe4e92b780f1064b7b34c7805b8a96cb2c29e9d6d12b.jpg", + "table_caption": [ + "Table 2. Result comparison for different downstream tasks on Fonts and Icons dataset." + ], + "table_footnote": [], + "table_body": "
QueryTop7 retrieval results on all candidates
DD 7 D 7 D D D
D D D D D D D
NN N N M N N N
N N N N N N N N
RR n P n P p P n
R R R R R Q R
QueryTop7 retrieval results on same scope
aa a a a a e a a
a a a a a a a a
ff f f f f f f f
f f f f f f f f
kk k k k k k k
k k k k k k k
", + "bbox": [ + 116, + 226, + 431, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Figure 4. Retrieval results from all glyphs and same glyphs, respectively. Results for DeepSVG are shown in orange, and results for SVGformer in blue. SVGformer always retrieves the same glyph as the query when searching from all glyphs, and returns results in more similar styles when searching for a specific glyph.", + "bbox": [ + 75, + 616, + 470, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "than both DeepSVG and SVGformer, yet it performs almost randomly on the family classification task.", + "bbox": [ + 75, + 695, + 468, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Retrieval task. From the perspective of quality analysis, we report the family accuracy of the most top $5\\%$ (@5) and $10\\%$ (@10) similar retrieval results by name on Tabel 2, where the similarity score can be calculated by the inner product of the query and all the candidates of an SVG image, which is equivalent to the cosine similarity formula after normalization. The retrieval results show that our model can offer a $42.5\\%$ performance improvement compared with DeepSVG. Besides, we use Figure 4 to show the retrieval results of some query samples which indicates SVGformer can", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "achieve higher accuracy in general than previous baselines. Specifically, SVGformer can beat the previous state-of-the-art in two different settings: 1. retrieving in all the candidates (across families) to figure out the ability to find the same family; 2. retrieving under the target family to verify that our model's representation can align the style of the query.", + "bbox": [ + 496, + 229, + 893, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Interpolation task. To verify that our model can animate SVGs by interpolating automatically from different glyphs, we use the hidden representation from DeepSVG and SVGformer to perform the comparison on the interpolation task. As shown in Figure 5, SVGformer can give more meaningful and smooth results with fewer artifacts and contortions when handling both translations and deformations in 3 different interpolation types including \"Thin\" $\\rightarrow$ \"Black\", \"Expanded\" $\\rightarrow$ \"Condensed\" and \"Regular\" $\\rightarrow$ \"Italic\". For example, when we interpolate the fonts' size from \"Thin\" to \"Black\", we can find a specific value for \"Regular\" size in SVGformer's results but cannot find that one in DeepSVG's.", + "bbox": [ + 496, + 339, + 895, + 521 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2 Icons", + "text_level": 1, + "bbox": [ + 500, + 540, + 591, + 554 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the reconstruction task on the Icons dataset, we calculate the CD metric as mentioned before in Table 2, where SVGformer can build a new state-of-the-art by achieving $59.5\\%$ performance improvement over previous methods. In addition, we also plot the reconstruction results in Figure 6 to show that SVGformer can yield more precise reconstruction results than DeepSVG. For the classification task, we first collect icons' labels by their categories including \"cinema\", \"city\", \"clothing\", etc. Then we train a classification model with 59 classes and report the top 10 accuracy, where SVGformer achieves the highest accuracy. For the retrieval task, we use visual inspection to verify the retrieval results are relevant as there is no such ground truth information. As shown in Figure 7, the unsupervised representation of SVGformer has great capability to distinguish the global and local structure of SVG, achieving better retrieval results than other baselines.", + "bbox": [ + 496, + 565, + 893, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 830, + 653, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To better understand the effectiveness of different components in SGVformer, we evaluate two model variants, namely SVGformer-no-geo and SVGformer-discrete, by dropping the", + "bbox": [ + 496, + 854, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10099", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Thin to Black. Nokora, 'D'", + "bbox": [ + 117, + 88, + 238, + 98 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1171b8fa3a88dd6eb01308909e66f3721da779d81a8f15596c29c219235e5c37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 117, + 99, + 421, + 152 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Thin to Black. Saira Semi Condensed, '", + "bbox": [ + 119, + 154, + 297, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d7b30cd8d02279823611a01f75f65af5a2660f51d959ca62bf71f38755fc3c67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 165, + 428, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Expanded to Condensed. Encode Sans, 'W'", + "bbox": [ + 119, + 219, + 310, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/372bc6c539439609ae846211959500b116246c2a8364465e51ec1b2ef8b035cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 231, + 428, + 252 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5c768a4b3093ee90e5ccbedf1ae7cf281887bcfd7aed77a90fcf93877fd8ed6a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 262, + 428, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Expanded to Condensed. Encode Sans, 'k'", + "bbox": [ + 119, + 285, + 305, + 295 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/292a69518cf430d814864e4264e071c7fda59038d1e16b360901a7024cfa7027.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 296, + 416, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Regular to Italic. Arvo, A", + "bbox": [ + 119, + 351, + 233, + 361 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e80bcb8c8d040f602dc19f92d77e472975c417d09e4167f69e9c4005b060dc4f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 362, + 426, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Regular to Italic. Andika New Basic, 'H'", + "bbox": [ + 119, + 416, + 295, + 426 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3883c35e7c2e2b9682af0deb4f7714fa31827f175ac87529d13424d4d1bba98c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 119, + 428, + 423, + 450 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b4418470eab5754859e792108a34ac978f0dcade275ef963d7a988f0e71632cd.jpg", + "image_caption": [ + "Figure 5. Examples of interpolations between glyphs. The results for DeepSVG are shown in orange, and those for SVGformer in blue. The first and last columns are the given glyphs to be interpolated, and the middle columns are the interpolations." + ], + "image_footnote": [], + "bbox": [ + 119, + 452, + 423, + 478 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8a9b87097fcfd298cad246639ac9e677eeb583dc6fee55307f19ae6015a1b8b9.jpg", + "image_caption": [ + "Figure 6. Example reconstruction results on Icons data. From left to right, columns show original SVG (black), DeepSVG (orange), LayoutTransformer (green), and our SVGformer (blue)." + ], + "image_footnote": [], + "bbox": [ + 107, + 553, + 439, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "geometric information and continuous input embedding from the full model. The results on both Fonts and Icons datasets shown in the last two rows of Table 2 confirm that both components are indispensable. Specifically, SVGformer-no-geo aborts the geometric information inside the self-attention mechanism, which indicates the importance of structural", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/29c933fb9c2d1fb6c080470e0b41719822d2e457f002a49bb5e719e93430f373.jpg", + "image_caption": [ + "Figure 7. Retrieval results on Icons data. The results of DeepSVG are shown in orange, and the results of SVGformer in blue." + ], + "image_footnote": [], + "bbox": [ + 542, + 90, + 851, + 345 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "inductive bias for encoder-decoder-based transformer models. SVGformer-discrete provides a fair comparison of SVGformer with the previous works which only accept discrete SVG inputs. The results demonstrate that the raw input contains detailed information which is critical to high-quality hidden representation.", + "bbox": [ + 498, + 393, + 893, + 484 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitation", + "text_level": 1, + "bbox": [ + 500, + 500, + 612, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We note some limitations of SVGformer in this section. One of the major limitations is the effectiveness of representation is based on sufficient SVGs in the training process, which is hard to guarantee in many real-world scenarios. Admittedly, although our model can yield much more precise hidden representations than previous baselines to make it identifiable for each SVG, we found that SVGformer's hidden space lacks linearity and smoothness when facing complex downstream tasks such as some interpolation samples of different style transfers. Inspired by diffusion models [13,24,27,28], one possible insight for future work can be smooth the latent space by introducing the diffusion process.", + "bbox": [ + 496, + 526, + 893, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 723, + 617, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we study representation learning for SVG and propose a transformer-based model named SVGformer. Specifically, we directly deal with the continuous input and extract MAT segment information as the inductive bias of SVG input. Besides, we design a geometric self-attention module to utilize the stylistic semantics of SVG commands and the geometric information jointly to handle long-term sequence relations. The experiments on two datasets and several downstream tasks demonstrate the effectiveness of SVGformer for robust representation learning of SVG.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10100", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Valerio Biscione and Jeffrey S Bowers. Convolutional neural networks are not invariant to translation, but they can learn to be. arXiv preprint arXiv:2110.05861, 2021. 4", + "[2] Harry Blum. A Transformation for Extracting New Descriptors of Shape. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 11106-11115, 2021. 1, 2, 3, 4, 5" + ], + "bbox": [ + 501, + 90, + 893, + 257 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10102", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/3621baa2-936b-4fa2-8381-1968bf4d3112_model.json b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/3621baa2-936b-4fa2-8381-1968bf4d3112_model.json new file mode 100644 index 0000000000000000000000000000000000000000..aae7e597095c1ed9be57523fb108659df7745495 --- /dev/null +++ b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/3621baa2-936b-4fa2-8381-1968bf4d3112_model.json @@ -0,0 +1,2035 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.13, + 0.844, + 0.175 + ], + "angle": 0, + "content": "SVGformer: Representation Learning for Continuous Vector Graphics using Transformers" + }, + { + "type": "text", + "bbox": [ + 0.234, + 0.203, + 0.733, + 0.221 + ], + "angle": 0, + "content": "Defu Cao1, Zhaowen Wang2, Jose Echevarria2, Yan Liu1" + }, + { + "type": "text", + "bbox": [ + 0.35, + 0.222, + 0.623, + 0.239 + ], + "angle": 0, + "content": "1University of Southern California" + }, + { + "type": "text", + "bbox": [ + 0.395, + 0.239, + 0.574, + 0.256 + ], + "angle": 0, + "content": "2Adobe Research, Inc." + }, + { + "type": "text", + "bbox": [ + 0.138, + 0.258, + 0.833, + 0.275 + ], + "angle": 0, + "content": "{defucao, yanliu.cs}@usc.edu, {zhawang, echevarr}@adobe.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.601 + ], + "angle": 0, + "content": "Advances in representation learning have led to great success in understanding and generating data in various domains. However, in modeling vector graphics data, the pure data-driven approach often yields unsatisfactory results in downstream tasks as existing deep learning methods often require the quantization of SVG parameters and cannot exploit the geometric properties explicitly. In this paper, we propose a transformer-based representation learning model (SVGformer) that directly operates on continuous input values and manipulates the geometric information of SVG to encode outline details and long-distance dependencies. SVGfomer can be used for various downstream tasks: reconstruction, classification, interpolation, retrieval, etc. We have conducted extensive experiments on vector font and icon datasets to show that our model can capture high-quality representation information and outperform the previous state-of-the-art on downstream tasks significantly." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.632, + 0.21, + 0.646 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.471, + 0.795 + ], + "angle": 0, + "content": "In the last few years, there have been tremendous advances in image representation learning [22, 26, 37], and these representations lead to great success in many downstream tasks such as image reconstruction [40], image classification [14, 16], etc. However, most previous works have focused on analyzing structured bitmap format, which uses a grid at the pixel level to represent textures and colors [18]. Therefore, there is still considerable room for improving the representation of detailed attributes for vector objects [25]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.472, + 0.902 + ], + "angle": 0, + "content": "In contrast to bitmap image format, scalable vector graphics (SVG) format for vector images is widely used in real-world applications due to its excellent scaling capabilities [12, 20, 33]. SVGs usually contain a mixture of smooth curves and sharp features, such as lines, circles, polygons, and splines, represented as parametric curves in digital format. This allows us to treat SVGs as sequential data and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.895, + 0.401 + ], + "angle": 0, + "content": "learn their compact and scale-invariant representation using neural network models. However, how to automatically learn an effective representation of vector images is still non-trivial as it requires a model to understand the high-level perception of the 2D spatial pattern as well as geometric information to support the high-quality outcome in downstream tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.896, + 0.659 + ], + "angle": 0, + "content": "Transformer-based models [30] have been proven to achieve start-of-the-art results when dealing with sequential data in various problems including Natural Language Processing (NLP) [34] tasks and time-series forecasting [41] problems. We argue that representation learning for SVG is different from these tasks for two reasons: Firstly, most if not all NLP tasks need a fixed token space to embed the discrete tokens, while SVGs are parameterized by continuous values which make the token space infinite in the previous setting; Secondly, the number of commands and the correlation between the commands vary greatly from one SVG to another, which is hard to handle by a pure data-driven attention mechanism. For example, the font data may vary across different families while sharing similar styles within the same font family. Such property is encoded in the sequential data explicitly and can provide geometric dependency guidance for modeling the SVG if used appropriately." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.897, + 0.902 + ], + "angle": 0, + "content": "To tackle the above challenges and fully utilize the geometric information from SVG data, this work introduces a novel model architecture named SVGformer, which can take continuous sequential input into a transformer-based model to handle the complex dependencies over SVG commands and yield a robust representation for the input. Specifically, we first extract the SVG segment information via medial axis transform (MAT) [2] to convey the geometric information into the learned representation. Then we introduce a 1D convolutional embedding layer to preserve the original continuous format of SVG data, as opposed to previous vector representation learning models [8] which need a preprocessing step to discretize the input to limited discrete tokens. After that, we inject the structural relationship between commands into the proposed geometric self-attention module in the encoder layer to get the hidden representation" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10093" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.095, + 0.09, + 0.875, + 0.199 + ], + "angle": 0, + "content": "
MethodFont-MF [3]SVG-VAE [20]Im2Vec [25]DeepVecFont [33]DeepSVG [8]LayoutTrans [12]SVGformer (ours)
Encoding ModalitySeqImgImgImg&SeqSeqSeqSeq
Decoding ModalitySeqImg&SeqSeqImg&SeqSeqSeqSeq
Model ArchitectureGP-LVMVAERNNLSTM+CNNTransformerTransformerTransformer
Sequence FormatKeypointsCommandsKeypointsCommandsCommandsCommandsCommands
Geometric Information------Segment
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.21, + 0.893, + 0.239 + ], + "angle": 0, + "content": "Table 1. Comparison of our SVGformer model and recent models for vector representation learning, where \"Seq\" donates sequence, and \"Img\" donates image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.471, + 0.352 + ], + "angle": 0, + "content": "of each SVG. The representation learned with the reconstruction pretext task can be used in various downstream tasks including classification, retrieval, and interpolation. To the best of our knowledge, our proposed model is the first to explicitly consider vector geometric information as well as directly deal with the raw input of SVG format in an end-to-end encoder-decoder fashion." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.355, + 0.411, + 0.369 + ], + "angle": 0, + "content": "The main contributions of this paper include:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.377, + 0.47, + 0.452 + ], + "angle": 0, + "content": "- SVGformer captures both geometric information and curve semantic information with the geometric self-attention module, which synergizes the strengths of MAT and the transformer-based neural network to handle long-term sequence relationships in SVG." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.461, + 0.47, + 0.522 + ], + "angle": 0, + "content": "- SVGformer can take original continuous format as input which can effectively reduce the token space in the embedding layer. Thereby the model is general for all continuous vector graphics without extra quantization." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.531, + 0.47, + 0.605 + ], + "angle": 0, + "content": "- SVGformer achieves new state-of-the-art performance on four downstream tasks of both Font and Icon dataset. For example, it outperforms prior art by \\(51.2\\%\\) on classification and \\(42.5\\%\\) on retrieval tasks of the font dataset." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.377, + 0.47, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.619, + 0.216, + 0.635 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Transformer models in the computer version. In the realm of computer vision, many researchers have proposed using self-attention to model long-term dependencies, similar to how transformers are used in natural language processing and other real-world applications [5, 6, 34, 36]. By leveraging self-attention in the encoder-decoder architecture, these methods have shown promising results in computer vision benchmarks, overcoming the limitations imposed by inductive convolution bias [10]. The fields of those benchmarks include object detection [7], image generation [11], and classification on both image [21] and video [32]. In most related works, the self-attention layer in computer vision takes a feature map as input and computes the attention weights between each pair of features. This operation can result in an updated feature map where each position has information about any other feature in the same image which could be costly for high-resolution or long sequential" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.248, + 0.895, + 0.446 + ], + "angle": 0, + "content": "inputs. Thus, there are multiple works aimed at overcoming this problem. For example, Informer [41] proposes a sparse attention mechanism by sorting the important queries; Axial-DeepLab [31] computes the attention score sequentially along the two spatial axis and [23] processes the patches of feature maps instead of the whole image. In addition, as inductive bias can always be beneficial to the learning process [35], we need to inject the position information into the transformers to help update features that are lost in the input sequence. For learning the SVG representation, we can introduce structural inductive bias into transformer-based models by obtaining the position information from the input sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Representation learning for SVG. Designing and manipulating the SVG image including fonts and icons require substantial expertise and expert knowledge [3]. Machine learning-based models can automatically manipulate the outlines and skeletons of vector images by learning from specific datasets. For the previous works, Font-MF [3] utilize the Gaussian Process Latent Variable Model [17] to learn a manifold of fonts so that it can synthesize fonts in unseen fonts. Im2Vec [25] proposes a new neural network that can generate complex vector graphics with varying topologies and only requires indirect supervision from readily-available raster training images (i.e., with no vector counterparts). Instead of directly using bitmap format, DeepVecFont [33] introduces a new generative paradigm to handle unstructured data (e.g., vector glyphs) by randomly sampling plausible synthesis results and a dual-modality learning strategy that utilizes both image-aspect and sequence-aspect features of fonts to synthesize vector glyphs. SVG-VAE [20] is a generative model with an autoencoder to learn the font style feature and an SVG decoder to generate vector glyphs. In addition, LayoutTransformer [12] uses the self-attention mechanism to capture the contextual relationship between different vector elements, which provides a potential solution for SVG data. Besides, DeepSVG [8] raises a hierarchical transformer-based generative model for vector graphics and collects a large-scale dataset of SVG along with deep learning-based SVG manipulation. However, most models that process the SVG format fail to handle the continuous nature [4, 39] of the input correctly. Besides, most of them do not consider" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10094" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.209, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.231, + 0.096, + 0.468, + 0.275 + ], + "angle": 0, + "content": "
Raw CommandsArgumentsGeometric Segments
p0M (13.2, 3.0)-1
...
paL (16.5, 18.9)
pbL (16.2, 21.0)
...
pcC (5.8, 19.1, 6.3, 17.5, 7.2, 16.2)
...
pnEOS (∅)-1
" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.471, + 0.386 + ], + "angle": 0, + "content": "Figure 1. The extraction of geometric information. Starting from the original SVG commands \\( p_i \\) delimited by blue circles, we apply MAT [2] to obtain a new set of commands and labels \\( (\\hat{p}_i, \\hat{l}_i) \\) (denoted by curve color and delimited with crosses) that may not exactly align with the original commands. A unique label \\( l_i \\) is finally assigned to each original command, as outlined in black color in the last column of the table." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.472, + 0.442 + ], + "angle": 0, + "content": "geometric information, which can directly equip the relationship of different curves into deep learning-based methods. Refer to Table 1 for a complete comparison of related works." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.457, + 0.168, + 0.473 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.187, + 0.499 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.81 + ], + "angle": 0, + "content": "We propose a transformer-based deep neural network, SVGformer, as a general solution for multiple vector graphics downstream tasks. The overall architecture of SVGformer is illustrated in Figure 2. The raw \\(t\\)-th SVG's arguments contain the type and corresponding coordinates of its commands, where the coordinates with continuous values are first constructed into a tensor format, \\(\\mathcal{X}^t \\in \\mathbb{R}^{n \\times 8}\\) and \\(n\\) is the number of commands. Then the input tensor is fed into the embedding layer to get the input vector for the encoder-decoder model. The learnable embedding layer contains three components to specifically abstract the information from the original input: 1) the continuous token component uses a 1D convolution to map \\(\\mathcal{X}^t\\) into an embedding vector \\(U^t\\); 2) the position component captures the positional information \\(P^t\\) from \\(\\mathcal{X}^t\\); 3) the geometric component treats the outline labels \\(l_i\\) (refer to Figure 1) as a discrete token to map extra contextual geometric information \\(S^t\\) to the embedding vector. In addition, we build an adjacency matrix \\(E\\) based on the labels and the neighboring commands in order to further utilize the structural information in the training process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Next, we combine the embedding vectors to feed the encoder module, where we introduce the geometric self-attention to replace the canonical self-attention in order to generate a compact representation with a higher receptive field efficiently. Specifically, we leverage structural relationships by encoding geometric segment information via a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "graph convolution layer and injecting it into spared attention score. Finally, we pass the hidden representation produced by the encoder into the SVG-decoding module consisting of the self-attention mechanism [41] and fully connected layers to fine-tune the total model. The decoder aims to reconstruct the original SVG commands from a masked input as well as predict the type of commands." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.894, + 0.274 + ], + "angle": 0, + "content": "In this way, the overall network can be trained end-to-end by backpropagation of a reconstruction loss and classification loss. Precisely, the classification loss has 3 different labels as we only consider three types of commands: \"Move\" (M), \"Line\" (L) and \"Curve\" (C)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.284, + 0.844, + 0.301 + ], + "angle": 0, + "content": "3.2. Geometric Information from Raw Input" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.895, + 0.73 + ], + "angle": 0, + "content": "As the attention mechanism generally only calculates the similarities via the commands' semantic features, we want to cooperate explicit geometric dependencies into the attention mechanism to provide our model with the ability to capture the structural relation between the commands. v We start from the raw SVG input \\(\\{p_0,p_1,p_2,\\ldots ,p_n\\}\\), where \\(p_i\\) denotes the \\(i\\)-th command in a given SVG, and \\(n\\) is the number of original commands. As shown in Figure 1, we obtain semantic labeling of segments with MAT. This tool leverages the medial axis and outlines information to find new segments labeled based on different geometric relationships: \\(\\{(\\hat{p}_1,\\hat{l}_1),(\\hat{p}_2,\\hat{l}_2),\\dots ,(\\hat{p}_m,\\hat{l}_m)\\}\\), where \\(\\hat{l}_i\\) is the label of the new command \\(\\hat{p}_i\\). Commands with the same label have a strong position relationship inside the given SVG, which is usually ignored by feature engineering. Note that MAT can usually split an original command into several segments (new commands), so \\(m\\geq n\\). However, directly adding such extra commands into the neural network will complicate the task of representation learning. Instead, we propose to map the new segments and labels back to the original input. Specifically, we group different commands by start and end points so that we have \\(p_i = \\{\\hat{p}_k,\\dots ,\\hat{p}_j\\}\\). To obtain the final label \\(l_{i}\\) for \\(p_i\\), we calculate the longest label by the distance between the start and end point of the label set \\(\\{\\hat{l}_k,\\dots ,\\hat{l}_j\\}\\). Then the final data we use to train the model is \\(\\{(p_1,l_1),(p_2,l_2),\\dots ,(p_n,l_n)\\}\\). We will introduce how to incorporate geometric information into the transformer in the next several sections." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.741, + 0.783, + 0.758 + ], + "angle": 0, + "content": "3.3. Continuous Feature Embedding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Representation learning requires the model to learn the inductive biases from the data and training task which can facilitate the downstream task. Thus, any inductive bias from raw input is able to coach the training process. In this work, we have identified two inductive biases present in raw input: continuous values and geometric information. While previous related works have typically relied on manually discretizing continuous values, our model is able to support continuous-valued inputs. Additionally, our model" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10095" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.895, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.337, + 0.335, + 0.632, + 0.35 + ], + "angle": 0, + "content": "Figure 2. Overall model structure of SVGformer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.471, + 0.463 + ], + "angle": 0, + "content": "is able to automatically discover structural information from the geometric information present in the input, providing further support for the inductive biases we have identified. This section will present proposed modifications to make it compatible with continuous SVG commands input with geometric information rather than with discrete pre-processed index sequences." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.474, + 0.645 + ], + "angle": 0, + "content": "Specifically, for the raw input, we first set a maximum sequence length \\( L_{x} \\) for the entire dataset, then we pad shorter samples with arbitrary values (0 in our setting) as the length of individual samples may vary considerably regarding the SVG images. Then, we generate a padding mask that adds a large negative value to the attention fraction of the padded positions before computing the self-attentive distribution with the softmax function. After that, different from previous works that can only support discrete input with fix length of the look-up table, we use a continuous value embedding layer with 1D convolutional operation to project the \\( t \\)-th SVG input \\( \\mathcal{X}^t \\) into a \\( d \\)-dimension vector \\( U^{t} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.657, + 0.47, + 0.673 + ], + "angle": 0, + "content": "\\[\nU ^ {t} = \\operatorname {C N N} \\left(\\mathcal {X} ^ {t}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.471, + 0.779 + ], + "angle": 0, + "content": "Note that this embedding layer can fully utilize the translation equivariance [1] of convolutional operation for SVG input and can have the ability of rotation invariance and size invariance with data augmentation. Corresponding to the continue value embedding layer, we preserve the input SVG commands by using the position embedding layer:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.788, + 0.47, + 0.814 + ], + "angle": 0, + "content": "\\[\nP ^ {t} (p, 2 j) = \\sin \\left(m / \\left(2 L _ {x}\\right) ^ {2 j / d}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.144, + 0.811, + 0.405, + 0.829 + ], + "angle": 0, + "content": "\\[\nP ^ {t} (p, 2 j + 1) = \\cos \\left(m / \\left(2 L _ {x}\\right) ^ {2 j / d}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where \\(j\\in \\{1,\\ldots ,\\lfloor d / 2\\rfloor \\}\\) and \\(m\\in \\{0,\\dots ,L_x - 1\\}\\). In this way, self-attention can compute the similarity with access to global information and affordable consumption [41]. Note that this position encoding function is inductive and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.496 + ], + "angle": 0, + "content": "parameters free to handle variable input length [19]. However, the above inductive embedding functions fail to capture the geometric dependency among the different positions of raw SVG commands. Thus, we exact the segment label \\( l_i^t \\) for each input command \\( p_i^t \\) according to Section 3.2 and use a geometric embedding layer with a look-up table, containing all the segmented labels, to get the geometric information \\( S \\). Thus, we finally maintain the feeding vector \\( X_{en}^{t} \\in \\mathbb{R}^{L_{x} \\times d} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.511, + 0.892, + 0.53 + ], + "angle": 0, + "content": "\\[\nX _ {e n} ^ {t} = \\alpha U ^ {t} + \\beta P ^ {t} + \\gamma S ^ {t}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.584 + ], + "angle": 0, + "content": "where \\(\\alpha, \\beta, \\gamma\\) are the factors balancing the magnitude between the scalar projection and position/geometric embeddings." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.596, + 0.892, + 0.626 + ], + "angle": 0, + "content": "3.4. SVGformer Encoder with Geometric Information" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.895, + 0.773 + ], + "angle": 0, + "content": "After the embedding layer, we feed the vector \\( X_{en}^{t} \\) to the encoder to extract latent representation. We refer the reader to the detailed description of the transformer model in the original work [30]. In this section, we will introduce the key technologies different from the vanilla transformer. Specifically, the encoder consists of several stacked geometric self-attention modules which can deal with long-term sequential dependency and geometric dependency in the attention mechanism jointly." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Sparse Query for Self-Attention. As the representation learning of SVG requires the model to have the ability to capture precise long-term dependency, we need to utilize the commands' features via an efficient attention mechanism. The canonical self-attention is defined based on the scaled dot-product of the input tuple, i.e., query \\(\\mathbf{q} \\in \\mathbb{R}^d\\), key \\(\\mathbf{K} \\in \\mathbb{R}^{L_K \\times d}\\), and value \\(\\mathbf{V} \\in \\mathbb{R}^{L_V \\times d}\\). Specifically, the \\(i\\)-th" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10096" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.122 + ], + "angle": 0, + "content": "query's attention is defined as a kernel smoother in a probability form [29]:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.128, + 0.471, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (\\mathbf {q} _ {i}, \\mathbf {K}, \\mathbf {V}) = \\sum_ {j} \\frac {k (\\mathbf {q} _ {i} , \\mathbf {k} _ {j})}{\\sum_ {l} k (\\mathbf {q} _ {i} , \\mathbf {k} _ {l})} \\mathbf {v} _ {j} = \\mathbb {E} _ {p (\\mathbf {k} _ {j} | \\mathbf {q} _ {i})} [ \\mathbf {v} _ {j} ], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.171, + 0.471, + 0.235 + ], + "angle": 0, + "content": "where \\(p(\\mathbf{k}_j|\\mathbf{q}_i) = k(\\mathbf{q}_i,\\mathbf{k}_j) / \\sum_lk(\\mathbf{q}_i,\\mathbf{k}_l)\\) and \\(k(\\mathbf{q}_i,\\mathbf{k}_j)\\) selects the asymmetric exponential kernel \\(\\exp (\\mathbf{q}_i\\mathbf{k}_j^\\top /\\sqrt{d})\\) . Inspired by [41], we calculate the importance of queries by Kullback-Leibler divergence:" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.241, + 0.471, + 0.284 + ], + "angle": 0, + "content": "\\[\nM (\\mathbf {q} _ {i}, \\mathbf {K}) = \\max _ {j} \\left\\{\\frac {\\mathbf {q} _ {i} \\mathbf {k} _ {j} ^ {\\top}}{\\sqrt {d}} \\right\\} - \\frac {1}{L _ {K}} \\sum_ {j = 1} ^ {L _ {K}} \\frac {\\mathbf {q} _ {i} \\mathbf {k} _ {j} ^ {\\top}}{\\sqrt {d}} \\quad , \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.29, + 0.47, + 0.379 + ], + "angle": 0, + "content": "where \\( M(\\mathbf{q}_i, \\mathbf{K}) \\) is the \\( i \\)-th query's sparsity score. A larger \\( M(\\mathbf{q}_i, \\mathbf{K}) \\) gives a higher chance to activate the dominate dot-product pairs in the self-attention. Thus, we can build a new query \\( \\overline{Q} \\) containing top \\( u \\) queries with query sparsity score given by \\( M \\) and calculate the sparsity self-attention score by:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.379, + 0.47, + 0.397 + ], + "angle": 0, + "content": "\\[\nA _ {a t t} = \\overline {{\\mathbf {Q}}} \\mathbf {K} ^ {\\top} / \\sqrt {d} \\quad . \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.471, + 0.462 + ], + "angle": 0, + "content": "Note that we can avoid information loss by generating different sparse query-key pairs according to different attention heads and this attention score can capture the relationships between input commands from a data-driven aspect." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Geometric Dependency in Self-Attention. Segments with the same label share a strong relationship even if they are at a long distance in the input sequence, which cannot be reflected in the original self-attention module which only considers the semantic characteristics. In addition, commands can be represented as the nodes lying in a non-Euclidean space and linked by edges with the geometric information. such as the adjacency and the same segment label. In this work, we propose to apply the graph convolution network (GCN) [15] to extract the structural relationship between different commands. Specifically, we first use the geometric label from Section 3.2 to build the weight matrix \\(E\\) where the commands adjacent to each other or sharing the same label have an edge in the weight matrix \\(E\\), otherwise there is no edge in the weight matrix \\(E\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "This has two advantages, firstly, the structure information of SVG is contained in the weight matrix, and secondly, commands sharing the same labels can distinguish local details by their own features. After getting the weight matrix, we use GCN to extract the structural information. The goal is then to learn a function of SVG commands on a graph \\(\\mathcal{G} = (V,E)\\), where \\(V\\) is the set of nodes' (commands in SVG) feature of each single SVG, i.e., \\(X_{en}^{t}\\) at the first layer, and \\(E\\) is the in the form of the adjacency matrix, which is \\(A\\) based on Figure 1. Our model can produce command-level output \\(A_{geo} \\in \\mathbb{R}^{N \\times d}\\) with \\(L\\) multiple layers GCN where \\(l\\)-th layer output \\(H^{l}\\) can be used to represent the latent vectors to get the final output:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.104, + 0.892, + 0.123 + ], + "angle": 0, + "content": "\\[\nH ^ {l + 1} = f \\left(H ^ {l}, E\\right) = \\sigma \\left(E H ^ {l} W ^ {l}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.128, + 0.894, + 0.19 + ], + "angle": 0, + "content": "where \\( H^0 \\) is the input features of the GCN, i.e., \\( \\mathcal{X}_{en} \\) at the very first layer, \\( f \\) is the graph convolutional function with learnable matrix \\( W \\) and \\( \\sigma \\) is the non-linear activation function for GCN and \\( H^L = A_{geo} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.208, + 0.895, + 0.358 + ], + "angle": 0, + "content": "Geometric Self-Attention Module. To better encode the geometric information into attention layers, we propose a new self-attention module in SVGformer. The attention mechanism needs to estimate correlations on both semantics (features from commands) part and the geometric (dependency of each command) part. Thus, for each ordered command pair \\((p_i,p_j)\\), we inject the relationship score from GCN into the sparse attention score. Concretely, the attention mechanism with the modified attention score can be represented as" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.37, + 0.892, + 0.388 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(A _ {\\text {a t t}} + A _ {\\text {g e o}}\\right) \\mathbf {V} \\quad . \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.398, + 0.894, + 0.503 + ], + "angle": 0, + "content": "To enhance the ability of our model on handling the permutation invariance where the order of shapes in an SVG image is arbitrary, we apply the 1D convolutional operation following an ELU activation function [9] and max pooling [38] on the output of the attention layer: \\(\\mathbf{X}_{j + 1} = \\mathrm{MaxPool}\\left(\\mathrm{ELU}(\\mathrm{Conv1d}([X_j]_{\\mathcal{A}_j}))\\right)\\), where \\([\\cdot ]_{\\mathcal{A}}\\) represents the \\(j\\)-th geometric self-attention module." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.504, + 0.892, + 0.548 + ], + "angle": 0, + "content": "The final representation of the encoder \\( Z \\) is the last layer's output of the encoder module and can be used for multiple downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.559, + 0.694, + 0.573 + ], + "angle": 0, + "content": "3.5. SVGformer Decoder" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.582, + 0.892, + 0.763 + ], + "angle": 0, + "content": "The decoder part is modified from the decoder structure in [41], which can reconstruct the long sequences of SVG at one forward operation rather than a step-by-step way with the input of \\(\\mathbf{X}_{\\mathrm{de}}^{t} = \\operatorname{Concat}(\\mathbf{X}_{\\mathrm{token}}^{t}, \\mathbf{X}_{0}^{t}) \\in \\mathbb{R}^{(L_{\\mathrm{token}} + L_{y}) \\times d}\\), where \\(\\mathbf{X}_{\\mathrm{token}}^{t} \\in \\mathbb{R}^{L_{\\mathrm{token}} \\times d}\\) is the start token, \\(\\mathbf{X}_{0}^{t} \\in \\mathbb{R}^{L_{y} \\times d}\\) is a placeholder of 0 for the target sequence. Specifically, it consists of masked geometric self-attention and multi-head attention, where the masked geometric self-attention sets masked dot-products to \\(-\\infty\\) and gives up the geometric GCN component, which can prevent data leakage in the decoding stage. Besides, a fully connected layer is needed to acquire the final logits for the loss function." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.645, + 0.787 + ], + "angle": 0, + "content": "3.6. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We need to reconstruct the input commands as well as predict the type of the commands. Thus, we choose the reconstruction loss as the mean squared error (MSE) loss function between the reconstructed commands and the ground-truth command and the classification loss as the cross entropy (CE) with logits between the predicted command type and the type label." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10097" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.116, + 0.16, + 0.133 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.141, + 0.473, + 0.488 + ], + "angle": 0, + "content": "We summarize the critical settings in this section. For input SVG, we choose those font inputs with a maximum length \\( L_{x} \\) equals to 60 and icon inputs with a maximum length equals to 50. Then pad the font commands less than 60 (50 for icon commands) by 0. For the embedding layer, a 1D convolutional operation is used as the trainable module for SVG recognition with kernel width equal to 3 and stride equal to 1. Both the 1D convolutional operation and the other two components inside the embedding layer's output dimension are 512. We recommend \\( \\alpha, \\beta, \\gamma \\) to be 1 inside the embedding layer if the sequence input has been normalized. In the training stage, the sparse attention's head number is 8, and we add geometric information given by one GCN layer, which output shape fits the attention score given by the sparse self-attention. To gain the global representation for a specific SVG, we use two stacked geometric self-attention modules followed by 1D convolutional operations and maximum pooling operations to finish the fusion process of all the commands and get the hidden representation with the shape of \\( L_{x} \\times 512 \\). For the decoder during the training stage, we mask all the commands instead of the first command (whose type is \"Move\") to finish the reconstruction task, which means \\( L_{token} = 1 \\) and \\( L_{y} = L_{x} - 1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.473, + 0.641 + ], + "angle": 0, + "content": "In the remaining part of this section, we discuss the qualitative and quantitative results of our models on two representative datasets, Google Fonts1 and Icons [8]. Note that the evaluation of representation learning models is difficult, and most quantitative metrics can not provide a generic measure of the novelty and veracity of the data sampled from representation learning models. Thus, we will explore 4 types of downstream tasks including reconstruction task, classification task, retrieval task, and interpolation task with specific quantitative metrics used by the various underlying methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.653, + 0.172, + 0.669 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.471, + 0.875 + ], + "angle": 0, + "content": "We evaluate the effectiveness of the proposed SVGformer on both fonts dataset and the icons dataset. We first show the reconstruction results, which is the training task. Note that simply using MSE and CE metrics cannot accurately show the coordinate values of control points on the contour line because the average of the correct target values is often not a correct value, so we use Chamfer distance (CD) metric to do the evaluation. Then, for the downstream tasks, we train a classification model to finish the classification task and use the glyph label to verify the retrieval task, which is a pure unsupervised process without any fine-tuning on the representation. After that, we finish with an interpolation task to show that SVGformer has good interpretability." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.092, + 0.872, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.259, + 0.896, + 0.302 + ], + "angle": 0, + "content": "Figure 3. Reconstruction results on various glyphs. From left to right, the original SVG (black), DeepSVG (orange), LayoutTransformer (green) and our SVGformer (blue), respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.328, + 0.596, + 0.343 + ], + "angle": 0, + "content": "4.2.1 Fonts" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.352, + 0.895, + 0.442 + ], + "angle": 0, + "content": "Reconstruction task. The reconstruction task is the training task where we can get the pre-trained model and obtain the latent representation of a given SVG image. We use Chamfer distance (CD) between corresponding paths of the input SVG and reconstructed SVG to evaluate the performance of the SVGformer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.896, + 0.595 + ], + "angle": 0, + "content": "Based on Table 2, our model produces a smaller gap than the other baselines with \\(17.8\\%\\) overperformance in a mathematical sense, proving the accuracy of SVGformer. In addition, we render the reconstructed results for quantitative comparisons on Figure 3. Benefiting from the two kinds of attention scores, SVGformer can reconstruct more details of the raw input. As confirmed by the results, we find that introducing the geometric information brings a substantial improvement in reconstruction error compared to the previous baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Classification task. For the classification task, we train a linear classification model for the different hidden representations with 1000 epochs and show in Table 2 the accuracy results of glyph-based category (62 classes) and family-based category (378 font family types filtered by a minimum class size of 100 in the test set). The glyph-based classification task is used to verify that our model's latent representation can identify the outline of inputs. The family-based classification task is more challenging as it has more categories and focuses on font style which needs the latent representation to be distinctive in details. We can figure out that the geometric information can help SVGformer gain further improvement for this mature task. Specifically, we find that both the LayoutTransformer and DeepSVG fail to classify the family labels with the accuracy of \\(7.0\\%\\) and \\(35.2\\%\\), respectively, which means they lose the style information during the data-driven process. Especially we find that higher dimensional data does not encompass more information because LayoutTransformer's hidden representation has a larger shape" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.238, + 0.901 + ], + "angle": 0, + "content": "1https://fonts.google.com/" + }, + { + "type": "footer", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10098" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.101, + 0.09, + 0.872, + 0.196 + ], + "angle": 0, + "content": "
ModelReconstruction (CD ↓)Classification (Acc %)Retrieval (Acc %)
FontsIconsFonts GlyphFonts FamilyIconsFonts@5Fonts@10Icons@10
LayoutTransformer37.618.875.67.057.61.71.613.4
DeepSVG32.715.685.635.245.151.245.922.8
SVGformer26.96.389.569.764.774.364.248.9
SVGformer-no-geo30.87.989.346.346.769.659.446.2
SVGformer-discrete41.519.385.915.063.760.751.530.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.228, + 0.207, + 0.741, + 0.221 + ], + "angle": 0, + "content": "Table 2. Result comparison for different downstream tasks on Fonts and Icons dataset." + }, + { + "type": "table", + "bbox": [ + 0.117, + 0.227, + 0.432, + 0.606 + ], + "angle": 0, + "content": "
QueryTop7 retrieval results on all candidates
DD 7 D 7 D D D
D D D D D D D
NN N N M N N N
N N N N N N N N
RR n P n P p P n
R R R R R Q R
QueryTop7 retrieval results on same scope
aa a a a a e a a
a a a a a a a a
ff f f f f f f f
f f f f f f f f
kk k k k k k k
k k k k k k k
" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.617, + 0.471, + 0.687 + ], + "angle": 0, + "content": "Figure 4. Retrieval results from all glyphs and same glyphs, respectively. Results for DeepSVG are shown in orange, and results for SVGformer in blue. SVGformer always retrieves the same glyph as the query when searching from all glyphs, and returns results in more similar styles when searching for a specific glyph." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.727 + ], + "angle": 0, + "content": "than both DeepSVG and SVGformer, yet it performs almost randomly on the family classification task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Retrieval task. From the perspective of quality analysis, we report the family accuracy of the most top \\(5\\%\\) (@5) and \\(10\\%\\) (@10) similar retrieval results by name on Tabel 2, where the similarity score can be calculated by the inner product of the query and all the candidates of an SVG image, which is equivalent to the cosine similarity formula after normalization. The retrieval results show that our model can offer a \\(42.5\\%\\) performance improvement compared with DeepSVG. Besides, we use Figure 4 to show the retrieval results of some query samples which indicates SVGformer can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.895, + 0.322 + ], + "angle": 0, + "content": "achieve higher accuracy in general than previous baselines. Specifically, SVGformer can beat the previous state-of-the-art in two different settings: 1. retrieving in all the candidates (across families) to figure out the ability to find the same family; 2. retrieving under the target family to verify that our model's representation can align the style of the query." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.897, + 0.522 + ], + "angle": 0, + "content": "Interpolation task. To verify that our model can animate SVGs by interpolating automatically from different glyphs, we use the hidden representation from DeepSVG and SVGformer to perform the comparison on the interpolation task. As shown in Figure 5, SVGformer can give more meaningful and smooth results with fewer artifacts and contortions when handling both translations and deformations in 3 different interpolation types including \"Thin\" \\(\\rightarrow\\) \"Black\", \"Expanded\" \\(\\rightarrow\\) \"Condensed\" and \"Regular\" \\(\\rightarrow\\) \"Italic\". For example, when we interpolate the fonts' size from \"Thin\" to \"Black\", we can find a specific value for \"Regular\" size in SVGformer's results but cannot find that one in DeepSVG's." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.541, + 0.593, + 0.555 + ], + "angle": 0, + "content": "4.2.2 Icons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.895, + 0.821 + ], + "angle": 0, + "content": "For the reconstruction task on the Icons dataset, we calculate the CD metric as mentioned before in Table 2, where SVGformer can build a new state-of-the-art by achieving \\(59.5\\%\\) performance improvement over previous methods. In addition, we also plot the reconstruction results in Figure 6 to show that SVGformer can yield more precise reconstruction results than DeepSVG. For the classification task, we first collect icons' labels by their categories including \"cinema\", \"city\", \"clothing\", etc. Then we train a classification model with 59 classes and report the top 10 accuracy, where SVGformer achieves the highest accuracy. For the retrieval task, we use visual inspection to verify the retrieval results are relevant as there is no such ground truth information. As shown in Figure 7, the unsupervised representation of SVGformer has great capability to distinguish the global and local structure of SVG, achieving better retrieval results than other baselines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.655, + 0.848 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To better understand the effectiveness of different components in SGVformer, we evaluate two model variants, namely SVGformer-no-geo and SVGformer-discrete, by dropping the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10099" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.119, + 0.089, + 0.24, + 0.099 + ], + "angle": 0, + "content": "Thin to Black. Nokora, 'D'" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.101, + 0.422, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.155, + 0.298, + 0.164 + ], + "angle": 0, + "content": "Thin to Black. Saira Semi Condensed, '" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.166, + 0.429, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.22, + 0.312, + 0.231 + ], + "angle": 0, + "content": "Expanded to Condensed. Encode Sans, 'W'" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.232, + 0.429, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.263, + 0.429, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.286, + 0.306, + 0.296 + ], + "angle": 0, + "content": "Expanded to Condensed. Encode Sans, 'k'" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.297, + 0.417, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.352, + 0.234, + 0.362 + ], + "angle": 0, + "content": "Regular to Italic. Arvo, A" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.363, + 0.428, + 0.414 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.417, + 0.296, + 0.428 + ], + "angle": 0, + "content": "Regular to Italic. Andika New Basic, 'H'" + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.429, + 0.424, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.12, + 0.453, + 0.424, + 0.479 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.492, + 0.471, + 0.547 + ], + "angle": 0, + "content": "Figure 5. Examples of interpolations between glyphs. The results for DeepSVG are shown in orange, and those for SVGformer in blue. The first and last columns are the given glyphs to be interpolated, and the middle columns are the interpolations." + }, + { + "type": "image", + "bbox": [ + 0.109, + 0.554, + 0.441, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.756, + 0.471, + 0.798 + ], + "angle": 0, + "content": "Figure 6. Example reconstruction results on Icons data. From left to right, columns show original SVG (black), DeepSVG (orange), LayoutTransformer (green), and our SVGformer (blue)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.901 + ], + "angle": 0, + "content": "geometric information and continuous input embedding from the full model. The results on both Fonts and Icons datasets shown in the last two rows of Table 2 confirm that both components are indispensable. Specifically, SVGformer-no-geo aborts the geometric information inside the self-attention mechanism, which indicates the importance of structural" + }, + { + "type": "image", + "bbox": [ + 0.543, + 0.091, + 0.852, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.357, + 0.892, + 0.385 + ], + "angle": 0, + "content": "Figure 7. Retrieval results on Icons data. The results of DeepSVG are shown in orange, and the results of SVGformer in blue." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.895, + 0.485 + ], + "angle": 0, + "content": "inductive bias for encoder-decoder-based transformer models. SVGformer-discrete provides a fair comparison of SVGformer with the previous works which only accept discrete SVG inputs. The results demonstrate that the raw input contains detailed information which is critical to high-quality hidden representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.501, + 0.614, + 0.516 + ], + "angle": 0, + "content": "5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.527, + 0.895, + 0.709 + ], + "angle": 0, + "content": "We note some limitations of SVGformer in this section. One of the major limitations is the effectiveness of representation is based on sufficient SVGs in the training process, which is hard to guarantee in many real-world scenarios. Admittedly, although our model can yield much more precise hidden representations than previous baselines to make it identifiable for each SVG, we found that SVGformer's hidden space lacks linearity and smoothness when facing complex downstream tasks such as some interpolation samples of different style transfers. Inspired by diffusion models [13,24,27,28], one possible insight for future work can be smooth the latent space by introducing the diffusion process." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.724, + 0.619, + 0.739 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In this paper, we study representation learning for SVG and propose a transformer-based model named SVGformer. Specifically, we directly deal with the continuous input and extract MAT segment information as the inductive bias of SVG input. Besides, we design a geometric self-attention module to utilize the stylistic semantics of SVG commands and the geometric information jointly to handle long-term sequence relations. The experiments on two datasets and several downstream tasks demonstrate the effectiveness of SVGformer for robust representation learning of SVG." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10100" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Valerio Biscione and Jeffrey S Bowers. Convolutional neural networks are not invariant to translation, but they can learn to be. arXiv preprint arXiv:2110.05861, 2021. 4" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.199 + ], + "angle": 0, + "content": "[2] Harry Blum. A Transformation for Extracting New Descriptors of Shape. In Models for the Perception of Speech and Visual Form, pages 362-380. 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However, in modeling vector graphics data, the pure data-driven approach often yields unsatisfactory results in downstream tasks as existing deep learning methods often require the quantization of SVG parameters and cannot exploit the geometric properties explicitly. In this paper, we propose a transformer-based representation learning model (SVGformer) that directly operates on continuous input values and manipulates the geometric information of SVG to encode outline details and long-distance dependencies. SVGfomer can be used for various downstream tasks: reconstruction, classification, interpolation, retrieval, etc. We have conducted extensive experiments on vector font and icon datasets to show that our model can capture high-quality representation information and outperform the previous state-of-the-art on downstream tasks significantly. + +# 1. Introduction + +In the last few years, there have been tremendous advances in image representation learning [22, 26, 37], and these representations lead to great success in many downstream tasks such as image reconstruction [40], image classification [14, 16], etc. However, most previous works have focused on analyzing structured bitmap format, which uses a grid at the pixel level to represent textures and colors [18]. Therefore, there is still considerable room for improving the representation of detailed attributes for vector objects [25]. + +In contrast to bitmap image format, scalable vector graphics (SVG) format for vector images is widely used in real-world applications due to its excellent scaling capabilities [12, 20, 33]. SVGs usually contain a mixture of smooth curves and sharp features, such as lines, circles, polygons, and splines, represented as parametric curves in digital format. This allows us to treat SVGs as sequential data and + +learn their compact and scale-invariant representation using neural network models. However, how to automatically learn an effective representation of vector images is still non-trivial as it requires a model to understand the high-level perception of the 2D spatial pattern as well as geometric information to support the high-quality outcome in downstream tasks. + +Transformer-based models [30] have been proven to achieve start-of-the-art results when dealing with sequential data in various problems including Natural Language Processing (NLP) [34] tasks and time-series forecasting [41] problems. We argue that representation learning for SVG is different from these tasks for two reasons: Firstly, most if not all NLP tasks need a fixed token space to embed the discrete tokens, while SVGs are parameterized by continuous values which make the token space infinite in the previous setting; Secondly, the number of commands and the correlation between the commands vary greatly from one SVG to another, which is hard to handle by a pure data-driven attention mechanism. For example, the font data may vary across different families while sharing similar styles within the same font family. Such property is encoded in the sequential data explicitly and can provide geometric dependency guidance for modeling the SVG if used appropriately. + +To tackle the above challenges and fully utilize the geometric information from SVG data, this work introduces a novel model architecture named SVGformer, which can take continuous sequential input into a transformer-based model to handle the complex dependencies over SVG commands and yield a robust representation for the input. Specifically, we first extract the SVG segment information via medial axis transform (MAT) [2] to convey the geometric information into the learned representation. Then we introduce a 1D convolutional embedding layer to preserve the original continuous format of SVG data, as opposed to previous vector representation learning models [8] which need a preprocessing step to discretize the input to limited discrete tokens. After that, we inject the structural relationship between commands into the proposed geometric self-attention module in the encoder layer to get the hidden representation + +
MethodFont-MF [3]SVG-VAE [20]Im2Vec [25]DeepVecFont [33]DeepSVG [8]LayoutTrans [12]SVGformer (ours)
Encoding ModalitySeqImgImgImg&SeqSeqSeqSeq
Decoding ModalitySeqImg&SeqSeqImg&SeqSeqSeqSeq
Model ArchitectureGP-LVMVAERNNLSTM+CNNTransformerTransformerTransformer
Sequence FormatKeypointsCommandsKeypointsCommandsCommandsCommandsCommands
Geometric Information------Segment
+ +Table 1. Comparison of our SVGformer model and recent models for vector representation learning, where "Seq" donates sequence, and "Img" donates image. + +of each SVG. The representation learned with the reconstruction pretext task can be used in various downstream tasks including classification, retrieval, and interpolation. To the best of our knowledge, our proposed model is the first to explicitly consider vector geometric information as well as directly deal with the raw input of SVG format in an end-to-end encoder-decoder fashion. + +The main contributions of this paper include: + +- SVGformer captures both geometric information and curve semantic information with the geometric self-attention module, which synergizes the strengths of MAT and the transformer-based neural network to handle long-term sequence relationships in SVG. +- SVGformer can take original continuous format as input which can effectively reduce the token space in the embedding layer. Thereby the model is general for all continuous vector graphics without extra quantization. +- SVGformer achieves new state-of-the-art performance on four downstream tasks of both Font and Icon dataset. For example, it outperforms prior art by $51.2\%$ on classification and $42.5\%$ on retrieval tasks of the font dataset. + +# 2. Related work + +Transformer models in the computer version. In the realm of computer vision, many researchers have proposed using self-attention to model long-term dependencies, similar to how transformers are used in natural language processing and other real-world applications [5, 6, 34, 36]. By leveraging self-attention in the encoder-decoder architecture, these methods have shown promising results in computer vision benchmarks, overcoming the limitations imposed by inductive convolution bias [10]. The fields of those benchmarks include object detection [7], image generation [11], and classification on both image [21] and video [32]. In most related works, the self-attention layer in computer vision takes a feature map as input and computes the attention weights between each pair of features. This operation can result in an updated feature map where each position has information about any other feature in the same image which could be costly for high-resolution or long sequential + +inputs. Thus, there are multiple works aimed at overcoming this problem. For example, Informer [41] proposes a sparse attention mechanism by sorting the important queries; Axial-DeepLab [31] computes the attention score sequentially along the two spatial axis and [23] processes the patches of feature maps instead of the whole image. In addition, as inductive bias can always be beneficial to the learning process [35], we need to inject the position information into the transformers to help update features that are lost in the input sequence. For learning the SVG representation, we can introduce structural inductive bias into transformer-based models by obtaining the position information from the input sequence. + +Representation learning for SVG. Designing and manipulating the SVG image including fonts and icons require substantial expertise and expert knowledge [3]. Machine learning-based models can automatically manipulate the outlines and skeletons of vector images by learning from specific datasets. For the previous works, Font-MF [3] utilize the Gaussian Process Latent Variable Model [17] to learn a manifold of fonts so that it can synthesize fonts in unseen fonts. Im2Vec [25] proposes a new neural network that can generate complex vector graphics with varying topologies and only requires indirect supervision from readily-available raster training images (i.e., with no vector counterparts). Instead of directly using bitmap format, DeepVecFont [33] introduces a new generative paradigm to handle unstructured data (e.g., vector glyphs) by randomly sampling plausible synthesis results and a dual-modality learning strategy that utilizes both image-aspect and sequence-aspect features of fonts to synthesize vector glyphs. SVG-VAE [20] is a generative model with an autoencoder to learn the font style feature and an SVG decoder to generate vector glyphs. In addition, LayoutTransformer [12] uses the self-attention mechanism to capture the contextual relationship between different vector elements, which provides a potential solution for SVG data. Besides, DeepSVG [8] raises a hierarchical transformer-based generative model for vector graphics and collects a large-scale dataset of SVG along with deep learning-based SVG manipulation. However, most models that process the SVG format fail to handle the continuous nature [4, 39] of the input correctly. Besides, most of them do not consider + +![](images/36efd8d67d1f28faa28e1d371ad06e2b9ee964235c8b3da78ea3f05d1fd57855.jpg) +Figure 1. The extraction of geometric information. Starting from the original SVG commands $p_i$ delimited by blue circles, we apply MAT [2] to obtain a new set of commands and labels $(\hat{p}_i, \hat{l}_i)$ (denoted by curve color and delimited with crosses) that may not exactly align with the original commands. A unique label $l_i$ is finally assigned to each original command, as outlined in black color in the last column of the table. + +
Raw CommandsArgumentsGeometric Segments
p0M (13.2, 3.0)-1
...
paL (16.5, 18.9)
pbL (16.2, 21.0)
...
pcC (5.8, 19.1, 6.3, 17.5, 7.2, 16.2)
...
pnEOS (∅)-1
+ +geometric information, which can directly equip the relationship of different curves into deep learning-based methods. Refer to Table 1 for a complete comparison of related works. + +# 3. Method + +# 3.1. Overview + +We propose a transformer-based deep neural network, SVGformer, as a general solution for multiple vector graphics downstream tasks. The overall architecture of SVGformer is illustrated in Figure 2. The raw $t$ -th SVG's arguments contain the type and corresponding coordinates of its commands, where the coordinates with continuous values are first constructed into a tensor format, $\mathcal{X}^t \in \mathbb{R}^{n \times 8}$ and $n$ is the number of commands. Then the input tensor is fed into the embedding layer to get the input vector for the encoder-decoder model. The learnable embedding layer contains three components to specifically abstract the information from the original input: 1) the continuous token component uses a 1D convolution to map $\mathcal{X}^t$ into an embedding vector $U^t$ ; 2) the position component captures the positional information $P^t$ from $\mathcal{X}^t$ ; 3) the geometric component treats the outline labels $l_i$ (refer to Figure 1) as a discrete token to map extra contextual geometric information $S^t$ to the embedding vector. In addition, we build an adjacency matrix $E$ based on the labels and the neighboring commands in order to further utilize the structural information in the training process. + +Next, we combine the embedding vectors to feed the encoder module, where we introduce the geometric self-attention to replace the canonical self-attention in order to generate a compact representation with a higher receptive field efficiently. Specifically, we leverage structural relationships by encoding geometric segment information via a + +graph convolution layer and injecting it into spared attention score. Finally, we pass the hidden representation produced by the encoder into the SVG-decoding module consisting of the self-attention mechanism [41] and fully connected layers to fine-tune the total model. The decoder aims to reconstruct the original SVG commands from a masked input as well as predict the type of commands. + +In this way, the overall network can be trained end-to-end by backpropagation of a reconstruction loss and classification loss. Precisely, the classification loss has 3 different labels as we only consider three types of commands: "Move" (M), "Line" (L) and "Curve" (C). + +# 3.2. Geometric Information from Raw Input + +As the attention mechanism generally only calculates the similarities via the commands' semantic features, we want to cooperate explicit geometric dependencies into the attention mechanism to provide our model with the ability to capture the structural relation between the commands. v We start from the raw SVG input $\{p_0,p_1,p_2,\ldots ,p_n\}$ , where $p_i$ denotes the $i$ -th command in a given SVG, and $n$ is the number of original commands. As shown in Figure 1, we obtain semantic labeling of segments with MAT. This tool leverages the medial axis and outlines information to find new segments labeled based on different geometric relationships: $\{(\hat{p}_1,\hat{l}_1),(\hat{p}_2,\hat{l}_2),\dots ,(\hat{p}_m,\hat{l}_m)\}$ , where $\hat{l}_i$ is the label of the new command $\hat{p}_i$ . Commands with the same label have a strong position relationship inside the given SVG, which is usually ignored by feature engineering. Note that MAT can usually split an original command into several segments (new commands), so $m\geq n$ . However, directly adding such extra commands into the neural network will complicate the task of representation learning. Instead, we propose to map the new segments and labels back to the original input. Specifically, we group different commands by start and end points so that we have $p_i = \{\hat{p}_k,\dots ,\hat{p}_j\}$ . To obtain the final label $l_{i}$ for $p_i$ , we calculate the longest label by the distance between the start and end point of the label set $\{\hat{l}_k,\dots ,\hat{l}_j\}$ . Then the final data we use to train the model is $\{(p_1,l_1),(p_2,l_2),\dots ,(p_n,l_n)\}$ . We will introduce how to incorporate geometric information into the transformer in the next several sections. + +# 3.3. Continuous Feature Embedding + +Representation learning requires the model to learn the inductive biases from the data and training task which can facilitate the downstream task. Thus, any inductive bias from raw input is able to coach the training process. In this work, we have identified two inductive biases present in raw input: continuous values and geometric information. While previous related works have typically relied on manually discretizing continuous values, our model is able to support continuous-valued inputs. Additionally, our model + +![](images/350ee0f465ffef52f8db07610d05cbc311dbf956dc0d81da2b1307e2a479542e.jpg) +Figure 2. Overall model structure of SVGformer. + +is able to automatically discover structural information from the geometric information present in the input, providing further support for the inductive biases we have identified. This section will present proposed modifications to make it compatible with continuous SVG commands input with geometric information rather than with discrete pre-processed index sequences. + +Specifically, for the raw input, we first set a maximum sequence length $L_{x}$ for the entire dataset, then we pad shorter samples with arbitrary values (0 in our setting) as the length of individual samples may vary considerably regarding the SVG images. Then, we generate a padding mask that adds a large negative value to the attention fraction of the padded positions before computing the self-attentive distribution with the softmax function. After that, different from previous works that can only support discrete input with fix length of the look-up table, we use a continuous value embedding layer with 1D convolutional operation to project the $t$ -th SVG input $\mathcal{X}^t$ into a $d$ -dimension vector $U^{t}$ : + +$$ +U ^ {t} = \operatorname {C N N} \left(\mathcal {X} ^ {t}\right). \tag {1} +$$ + +Note that this embedding layer can fully utilize the translation equivariance [1] of convolutional operation for SVG input and can have the ability of rotation invariance and size invariance with data augmentation. Corresponding to the continue value embedding layer, we preserve the input SVG commands by using the position embedding layer: + +$$ +P ^ {t} (p, 2 j) = \sin \left(m / \left(2 L _ {x}\right) ^ {2 j / d}\right), \tag {2} +$$ + +$$ +P ^ {t} (p, 2 j + 1) = \cos \left(m / \left(2 L _ {x}\right) ^ {2 j / d}\right), +$$ + +where $j\in \{1,\ldots ,\lfloor d / 2\rfloor \}$ and $m\in \{0,\dots ,L_x - 1\}$ . In this way, self-attention can compute the similarity with access to global information and affordable consumption [41]. Note that this position encoding function is inductive and + +parameters free to handle variable input length [19]. However, the above inductive embedding functions fail to capture the geometric dependency among the different positions of raw SVG commands. Thus, we exact the segment label $l_i^t$ for each input command $p_i^t$ according to Section 3.2 and use a geometric embedding layer with a look-up table, containing all the segmented labels, to get the geometric information $S$ . Thus, we finally maintain the feeding vector $X_{en}^{t} \in \mathbb{R}^{L_{x} \times d}$ : + +$$ +X _ {e n} ^ {t} = \alpha U ^ {t} + \beta P ^ {t} + \gamma S ^ {t}, \tag {3} +$$ + +where $\alpha, \beta, \gamma$ are the factors balancing the magnitude between the scalar projection and position/geometric embeddings. + +# 3.4. SVGformer Encoder with Geometric Information + +After the embedding layer, we feed the vector $X_{en}^{t}$ to the encoder to extract latent representation. We refer the reader to the detailed description of the transformer model in the original work [30]. In this section, we will introduce the key technologies different from the vanilla transformer. Specifically, the encoder consists of several stacked geometric self-attention modules which can deal with long-term sequential dependency and geometric dependency in the attention mechanism jointly. + +Sparse Query for Self-Attention. As the representation learning of SVG requires the model to have the ability to capture precise long-term dependency, we need to utilize the commands' features via an efficient attention mechanism. The canonical self-attention is defined based on the scaled dot-product of the input tuple, i.e., query $\mathbf{q} \in \mathbb{R}^d$ , key $\mathbf{K} \in \mathbb{R}^{L_K \times d}$ , and value $\mathbf{V} \in \mathbb{R}^{L_V \times d}$ . Specifically, the $i$ -th + +query's attention is defined as a kernel smoother in a probability form [29]: + +$$ +\mathcal {A} (\mathbf {q} _ {i}, \mathbf {K}, \mathbf {V}) = \sum_ {j} \frac {k (\mathbf {q} _ {i} , \mathbf {k} _ {j})}{\sum_ {l} k (\mathbf {q} _ {i} , \mathbf {k} _ {l})} \mathbf {v} _ {j} = \mathbb {E} _ {p (\mathbf {k} _ {j} | \mathbf {q} _ {i})} [ \mathbf {v} _ {j} ], \tag {4} +$$ + +where $p(\mathbf{k}_j|\mathbf{q}_i) = k(\mathbf{q}_i,\mathbf{k}_j) / \sum_lk(\mathbf{q}_i,\mathbf{k}_l)$ and $k(\mathbf{q}_i,\mathbf{k}_j)$ selects the asymmetric exponential kernel $\exp (\mathbf{q}_i\mathbf{k}_j^\top /\sqrt{d})$ . Inspired by [41], we calculate the importance of queries by Kullback-Leibler divergence: + +$$ +M (\mathbf {q} _ {i}, \mathbf {K}) = \max _ {j} \left\{\frac {\mathbf {q} _ {i} \mathbf {k} _ {j} ^ {\top}}{\sqrt {d}} \right\} - \frac {1}{L _ {K}} \sum_ {j = 1} ^ {L _ {K}} \frac {\mathbf {q} _ {i} \mathbf {k} _ {j} ^ {\top}}{\sqrt {d}} \quad , \tag {5} +$$ + +where $M(\mathbf{q}_i, \mathbf{K})$ is the $i$ -th query's sparsity score. A larger $M(\mathbf{q}_i, \mathbf{K})$ gives a higher chance to activate the dominate dot-product pairs in the self-attention. Thus, we can build a new query $\overline{Q}$ containing top $u$ queries with query sparsity score given by $M$ and calculate the sparsity self-attention score by: + +$$ +A _ {a t t} = \overline {{\mathbf {Q}}} \mathbf {K} ^ {\top} / \sqrt {d} \quad . \tag {6} +$$ + +Note that we can avoid information loss by generating different sparse query-key pairs according to different attention heads and this attention score can capture the relationships between input commands from a data-driven aspect. + +Geometric Dependency in Self-Attention. Segments with the same label share a strong relationship even if they are at a long distance in the input sequence, which cannot be reflected in the original self-attention module which only considers the semantic characteristics. In addition, commands can be represented as the nodes lying in a non-Euclidean space and linked by edges with the geometric information. such as the adjacency and the same segment label. In this work, we propose to apply the graph convolution network (GCN) [15] to extract the structural relationship between different commands. Specifically, we first use the geometric label from Section 3.2 to build the weight matrix $E$ where the commands adjacent to each other or sharing the same label have an edge in the weight matrix $E$ , otherwise there is no edge in the weight matrix $E$ . + +This has two advantages, firstly, the structure information of SVG is contained in the weight matrix, and secondly, commands sharing the same labels can distinguish local details by their own features. After getting the weight matrix, we use GCN to extract the structural information. The goal is then to learn a function of SVG commands on a graph $\mathcal{G} = (V,E)$ , where $V$ is the set of nodes' (commands in SVG) feature of each single SVG, i.e., $X_{en}^{t}$ at the first layer, and $E$ is the in the form of the adjacency matrix, which is $A$ based on Figure 1. Our model can produce command-level output $A_{geo} \in \mathbb{R}^{N \times d}$ with $L$ multiple layers GCN where $l$ -th layer output $H^{l}$ can be used to represent the latent vectors to get the final output: + +$$ +H ^ {l + 1} = f \left(H ^ {l}, E\right) = \sigma \left(E H ^ {l} W ^ {l}\right), \tag {7} +$$ + +where $H^0$ is the input features of the GCN, i.e., $\mathcal{X}_{en}$ at the very first layer, $f$ is the graph convolutional function with learnable matrix $W$ and $\sigma$ is the non-linear activation function for GCN and $H^L = A_{geo}$ . + +Geometric Self-Attention Module. To better encode the geometric information into attention layers, we propose a new self-attention module in SVGformer. The attention mechanism needs to estimate correlations on both semantics (features from commands) part and the geometric (dependency of each command) part. Thus, for each ordered command pair $(p_i,p_j)$ , we inject the relationship score from GCN into the sparse attention score. Concretely, the attention mechanism with the modified attention score can be represented as + +$$ +\mathcal {A} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {S o f t m a x} \left(A _ {\text {a t t}} + A _ {\text {g e o}}\right) \mathbf {V} \quad . \tag {8} +$$ + +To enhance the ability of our model on handling the permutation invariance where the order of shapes in an SVG image is arbitrary, we apply the 1D convolutional operation following an ELU activation function [9] and max pooling [38] on the output of the attention layer: $\mathbf{X}_{j + 1} = \mathrm{MaxPool}\left(\mathrm{ELU}(\mathrm{Conv1d}([X_j]_{\mathcal{A}_j}))\right)$ , where $[\cdot ]_{\mathcal{A}}$ represents the $j$ -th geometric self-attention module. + +The final representation of the encoder $Z$ is the last layer's output of the encoder module and can be used for multiple downstream tasks. + +# 3.5. SVGformer Decoder + +The decoder part is modified from the decoder structure in [41], which can reconstruct the long sequences of SVG at one forward operation rather than a step-by-step way with the input of $\mathbf{X}_{\mathrm{de}}^{t} = \operatorname{Concat}(\mathbf{X}_{\mathrm{token}}^{t}, \mathbf{X}_{0}^{t}) \in \mathbb{R}^{(L_{\mathrm{token}} + L_{y}) \times d}$ , where $\mathbf{X}_{\mathrm{token}}^{t} \in \mathbb{R}^{L_{\mathrm{token}} \times d}$ is the start token, $\mathbf{X}_{0}^{t} \in \mathbb{R}^{L_{y} \times d}$ is a placeholder of 0 for the target sequence. Specifically, it consists of masked geometric self-attention and multi-head attention, where the masked geometric self-attention sets masked dot-products to $-\infty$ and gives up the geometric GCN component, which can prevent data leakage in the decoding stage. Besides, a fully connected layer is needed to acquire the final logits for the loss function. + +# 3.6. Loss Function + +We need to reconstruct the input commands as well as predict the type of the commands. Thus, we choose the reconstruction loss as the mean squared error (MSE) loss function between the reconstructed commands and the ground-truth command and the classification loss as the cross entropy (CE) with logits between the predicted command type and the type label. + +# 4. Experiments + +# 4.1. Setup + +We summarize the critical settings in this section. For input SVG, we choose those font inputs with a maximum length $L_{x}$ equals to 60 and icon inputs with a maximum length equals to 50. Then pad the font commands less than 60 (50 for icon commands) by 0. For the embedding layer, a 1D convolutional operation is used as the trainable module for SVG recognition with kernel width equal to 3 and stride equal to 1. Both the 1D convolutional operation and the other two components inside the embedding layer's output dimension are 512. We recommend $\alpha, \beta, \gamma$ to be 1 inside the embedding layer if the sequence input has been normalized. In the training stage, the sparse attention's head number is 8, and we add geometric information given by one GCN layer, which output shape fits the attention score given by the sparse self-attention. To gain the global representation for a specific SVG, we use two stacked geometric self-attention modules followed by 1D convolutional operations and maximum pooling operations to finish the fusion process of all the commands and get the hidden representation with the shape of $L_{x} \times 512$ . For the decoder during the training stage, we mask all the commands instead of the first command (whose type is "Move") to finish the reconstruction task, which means $L_{token} = 1$ and $L_{y} = L_{x} - 1$ . + +In the remaining part of this section, we discuss the qualitative and quantitative results of our models on two representative datasets, Google Fonts1 and Icons [8]. Note that the evaluation of representation learning models is difficult, and most quantitative metrics can not provide a generic measure of the novelty and veracity of the data sampled from representation learning models. Thus, we will explore 4 types of downstream tasks including reconstruction task, classification task, retrieval task, and interpolation task with specific quantitative metrics used by the various underlying methods. + +# 4.2. Results + +We evaluate the effectiveness of the proposed SVGformer on both fonts dataset and the icons dataset. We first show the reconstruction results, which is the training task. Note that simply using MSE and CE metrics cannot accurately show the coordinate values of control points on the contour line because the average of the correct target values is often not a correct value, so we use Chamfer distance (CD) metric to do the evaluation. Then, for the downstream tasks, we train a classification model to finish the classification task and use the glyph label to verify the retrieval task, which is a pure unsupervised process without any fine-tuning on the representation. After that, we finish with an interpolation task to show that SVGformer has good interpretability. + +![](images/3795e5e91e4ef5e455ef615a8f44af7edd2c0f7790deaa059f8cf4774298819d.jpg) +Figure 3. Reconstruction results on various glyphs. From left to right, the original SVG (black), DeepSVG (orange), LayoutTransformer (green) and our SVGformer (blue), respectively. + +# 4.2.1 Fonts + +Reconstruction task. The reconstruction task is the training task where we can get the pre-trained model and obtain the latent representation of a given SVG image. We use Chamfer distance (CD) between corresponding paths of the input SVG and reconstructed SVG to evaluate the performance of the SVGformer. + +Based on Table 2, our model produces a smaller gap than the other baselines with $17.8\%$ overperformance in a mathematical sense, proving the accuracy of SVGformer. In addition, we render the reconstructed results for quantitative comparisons on Figure 3. Benefiting from the two kinds of attention scores, SVGformer can reconstruct more details of the raw input. As confirmed by the results, we find that introducing the geometric information brings a substantial improvement in reconstruction error compared to the previous baselines. + +Classification task. For the classification task, we train a linear classification model for the different hidden representations with 1000 epochs and show in Table 2 the accuracy results of glyph-based category (62 classes) and family-based category (378 font family types filtered by a minimum class size of 100 in the test set). The glyph-based classification task is used to verify that our model's latent representation can identify the outline of inputs. The family-based classification task is more challenging as it has more categories and focuses on font style which needs the latent representation to be distinctive in details. We can figure out that the geometric information can help SVGformer gain further improvement for this mature task. Specifically, we find that both the LayoutTransformer and DeepSVG fail to classify the family labels with the accuracy of $7.0\%$ and $35.2\%$ , respectively, which means they lose the style information during the data-driven process. Especially we find that higher dimensional data does not encompass more information because LayoutTransformer's hidden representation has a larger shape + +
ModelReconstruction (CD ↓)Classification (Acc %)Retrieval (Acc %)
FontsIconsFonts GlyphFonts FamilyIconsFonts@5Fonts@10Icons@10
LayoutTransformer37.618.875.67.057.61.71.613.4
DeepSVG32.715.685.635.245.151.245.922.8
SVGformer26.96.389.569.764.774.364.248.9
SVGformer-no-geo30.87.989.346.346.769.659.446.2
SVGformer-discrete41.519.385.915.063.760.751.530.5
+ +Table 2. Result comparison for different downstream tasks on Fonts and Icons dataset. + +
QueryTop7 retrieval results on all candidates
DD 7 D 7 D D D
D D D D D D D
NN N N M N N N
N N N N N N N N
RR n P n P p P n
R R R R R Q R
QueryTop7 retrieval results on same scope
aa a a a a e a a
a a a a a a a a
ff f f f f f f f
f f f f f f f f
kk k k k k k k
k k k k k k k
+ +Figure 4. Retrieval results from all glyphs and same glyphs, respectively. Results for DeepSVG are shown in orange, and results for SVGformer in blue. SVGformer always retrieves the same glyph as the query when searching from all glyphs, and returns results in more similar styles when searching for a specific glyph. + +than both DeepSVG and SVGformer, yet it performs almost randomly on the family classification task. + +Retrieval task. From the perspective of quality analysis, we report the family accuracy of the most top $5\%$ (@5) and $10\%$ (@10) similar retrieval results by name on Tabel 2, where the similarity score can be calculated by the inner product of the query and all the candidates of an SVG image, which is equivalent to the cosine similarity formula after normalization. The retrieval results show that our model can offer a $42.5\%$ performance improvement compared with DeepSVG. Besides, we use Figure 4 to show the retrieval results of some query samples which indicates SVGformer can + +achieve higher accuracy in general than previous baselines. Specifically, SVGformer can beat the previous state-of-the-art in two different settings: 1. retrieving in all the candidates (across families) to figure out the ability to find the same family; 2. retrieving under the target family to verify that our model's representation can align the style of the query. + +Interpolation task. To verify that our model can animate SVGs by interpolating automatically from different glyphs, we use the hidden representation from DeepSVG and SVGformer to perform the comparison on the interpolation task. As shown in Figure 5, SVGformer can give more meaningful and smooth results with fewer artifacts and contortions when handling both translations and deformations in 3 different interpolation types including "Thin" $\rightarrow$ "Black", "Expanded" $\rightarrow$ "Condensed" and "Regular" $\rightarrow$ "Italic". For example, when we interpolate the fonts' size from "Thin" to "Black", we can find a specific value for "Regular" size in SVGformer's results but cannot find that one in DeepSVG's. + +# 4.2.2 Icons + +For the reconstruction task on the Icons dataset, we calculate the CD metric as mentioned before in Table 2, where SVGformer can build a new state-of-the-art by achieving $59.5\%$ performance improvement over previous methods. In addition, we also plot the reconstruction results in Figure 6 to show that SVGformer can yield more precise reconstruction results than DeepSVG. For the classification task, we first collect icons' labels by their categories including "cinema", "city", "clothing", etc. Then we train a classification model with 59 classes and report the top 10 accuracy, where SVGformer achieves the highest accuracy. For the retrieval task, we use visual inspection to verify the retrieval results are relevant as there is no such ground truth information. As shown in Figure 7, the unsupervised representation of SVGformer has great capability to distinguish the global and local structure of SVG, achieving better retrieval results than other baselines. + +# 4.3. Ablation Study + +To better understand the effectiveness of different components in SGVformer, we evaluate two model variants, namely SVGformer-no-geo and SVGformer-discrete, by dropping the + +Thin to Black. Nokora, 'D' + +![](images/1171b8fa3a88dd6eb01308909e66f3721da779d81a8f15596c29c219235e5c37.jpg) + +Thin to Black. Saira Semi Condensed, ' + +![](images/d7b30cd8d02279823611a01f75f65af5a2660f51d959ca62bf71f38755fc3c67.jpg) + +Expanded to Condensed. Encode Sans, 'W' + +![](images/372bc6c539439609ae846211959500b116246c2a8364465e51ec1b2ef8b035cb.jpg) + +![](images/5c768a4b3093ee90e5ccbedf1ae7cf281887bcfd7aed77a90fcf93877fd8ed6a.jpg) + +Expanded to Condensed. Encode Sans, 'k' + +![](images/292a69518cf430d814864e4264e071c7fda59038d1e16b360901a7024cfa7027.jpg) + +Regular to Italic. Arvo, A + +![](images/e80bcb8c8d040f602dc19f92d77e472975c417d09e4167f69e9c4005b060dc4f.jpg) + +Regular to Italic. Andika New Basic, 'H' + +![](images/3883c35e7c2e2b9682af0deb4f7714fa31827f175ac87529d13424d4d1bba98c.jpg) + +![](images/b4418470eab5754859e792108a34ac978f0dcade275ef963d7a988f0e71632cd.jpg) +Figure 5. Examples of interpolations between glyphs. The results for DeepSVG are shown in orange, and those for SVGformer in blue. The first and last columns are the given glyphs to be interpolated, and the middle columns are the interpolations. + +![](images/8a9b87097fcfd298cad246639ac9e677eeb583dc6fee55307f19ae6015a1b8b9.jpg) +Figure 6. Example reconstruction results on Icons data. From left to right, columns show original SVG (black), DeepSVG (orange), LayoutTransformer (green), and our SVGformer (blue). + +geometric information and continuous input embedding from the full model. The results on both Fonts and Icons datasets shown in the last two rows of Table 2 confirm that both components are indispensable. Specifically, SVGformer-no-geo aborts the geometric information inside the self-attention mechanism, which indicates the importance of structural + +![](images/29c933fb9c2d1fb6c080470e0b41719822d2e457f002a49bb5e719e93430f373.jpg) +Figure 7. Retrieval results on Icons data. The results of DeepSVG are shown in orange, and the results of SVGformer in blue. + +inductive bias for encoder-decoder-based transformer models. SVGformer-discrete provides a fair comparison of SVGformer with the previous works which only accept discrete SVG inputs. The results demonstrate that the raw input contains detailed information which is critical to high-quality hidden representation. + +# 5. Limitation + +We note some limitations of SVGformer in this section. One of the major limitations is the effectiveness of representation is based on sufficient SVGs in the training process, which is hard to guarantee in many real-world scenarios. Admittedly, although our model can yield much more precise hidden representations than previous baselines to make it identifiable for each SVG, we found that SVGformer's hidden space lacks linearity and smoothness when facing complex downstream tasks such as some interpolation samples of different style transfers. 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Curran Associates, Inc., 2017. 1, 4 +[31] Huiyu Wang, Yukun Zhu, Bradley Green, Hartwig Adam, Alan Yuille, and Liang-Chieh Chen. Axial-deeplab: Stand-alone axial-attention for panoptic segmentation. In European Conference on Computer Vision, pages 108–126. Springer, 2020. 2 +[32] Xiaolong Wang, Ross Girshick, Abhinav Gupta, and Kaiming He. Non-local neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7794-7803, 2018. 2 +[33] Yizhi Wang and Zhouhui Lian. Deepvecfont: synthesizing high-quality vector fonts via dual-modality learning. ACM Transactions on Graphics (TOG), 40(6):1-15, 2021. 1, 2 +[34] Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chau-mond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, et al. Transformers: State-of-the-art natural language processing. 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In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 11106-11115, 2021. 1, 2, 3, 4, 5 \ No newline at end of file diff --git a/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/images.zip b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..bb39b08810f57b58ba1fddbf7376db67667ae843 --- /dev/null +++ b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d8a50b1c54fb2eccceb24c5a4c5e528bd007779c2051db998270756b60c38162 +size 486167 diff --git a/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/layout.json b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..dafe3ac649b72466e4fd1902f02c8176ac8054bb --- /dev/null +++ b/2023/SVGformer_ Representation Learning for Continuous Vector Graphics Using Transformers/layout.json @@ -0,0 +1,8197 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 102, + 516, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 102, + 516, + 138 + ], + "spans": [ + { + "bbox": [ + 78, + 102, + 516, + 138 + ], + "type": "text", + "content": "SVGformer: Representation Learning for Continuous Vector Graphics using Transformers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 143, + 160, + 448, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 160, + 448, + 175 + ], + "spans": [ + { + "bbox": [ + 143, + 160, + 448, + 175 + ], + "type": "text", + "content": "Defu Cao1, Zhaowen Wang2, Jose Echevarria2, Yan Liu1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 214, + 175, + 381, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 214, + 175, + 381, + 189 + ], + "spans": [ + { + "bbox": [ + 214, + 175, + 381, + 189 + ], + "type": "text", + "content": "1University of Southern California" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 241, + 189, + 351, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 241, + 189, + 351, + 202 + ], + "spans": [ + { + "bbox": [ + 241, + 189, + 351, + 202 + ], + "type": "text", + "content": "2Adobe Research, Inc." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 84, + 204, + 509, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 204, + 509, + 217 + ], + "spans": [ + { + "bbox": [ + 84, + 204, + 509, + 217 + ], + "type": "text", + "content": "{defucao, yanliu.cs}@usc.edu, {zhawang, echevarr}@adobe.com" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 270, + 290, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 475 + ], + "type": "text", + "content": "Advances in representation learning have led to great success in understanding and generating data in various domains. However, in modeling vector graphics data, the pure data-driven approach often yields unsatisfactory results in downstream tasks as existing deep learning methods often require the quantization of SVG parameters and cannot exploit the geometric properties explicitly. In this paper, we propose a transformer-based representation learning model (SVGformer) that directly operates on continuous input values and manipulates the geometric information of SVG to encode outline details and long-distance dependencies. SVGfomer can be used for various downstream tasks: reconstruction, classification, interpolation, retrieval, etc. We have conducted extensive experiments on vector font and icon datasets to show that our model can capture high-quality representation information and outperform the previous state-of-the-art on downstream tasks significantly." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 500, + 128, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 500, + 128, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 500, + 128, + 511 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 521, + 288, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 288, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 288, + 629 + ], + "type": "text", + "content": "In the last few years, there have been tremendous advances in image representation learning [22, 26, 37], and these representations lead to great success in many downstream tasks such as image reconstruction [40], image classification [14, 16], etc. However, most previous works have focused on analyzing structured bitmap format, which uses a grid at the pixel level to represent textures and colors [18]. Therefore, there is still considerable room for improving the representation of detailed attributes for vector objects [25]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "In contrast to bitmap image format, scalable vector graphics (SVG) format for vector images is widely used in real-world applications due to its excellent scaling capabilities [12, 20, 33]. SVGs usually contain a mixture of smooth curves and sharp features, such as lines, circles, polygons, and splines, represented as parametric curves in digital format. This allows us to treat SVGs as sequential data and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 246, + 547, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 547, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 547, + 317 + ], + "type": "text", + "content": "learn their compact and scale-invariant representation using neural network models. However, how to automatically learn an effective representation of vector images is still non-trivial as it requires a model to understand the high-level perception of the 2D spatial pattern as well as geometric information to support the high-quality outcome in downstream tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 319, + 548, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 548, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 548, + 521 + ], + "type": "text", + "content": "Transformer-based models [30] have been proven to achieve start-of-the-art results when dealing with sequential data in various problems including Natural Language Processing (NLP) [34] tasks and time-series forecasting [41] problems. We argue that representation learning for SVG is different from these tasks for two reasons: Firstly, most if not all NLP tasks need a fixed token space to embed the discrete tokens, while SVGs are parameterized by continuous values which make the token space infinite in the previous setting; Secondly, the number of commands and the correlation between the commands vary greatly from one SVG to another, which is hard to handle by a pure data-driven attention mechanism. For example, the font data may vary across different families while sharing similar styles within the same font family. Such property is encoded in the sequential data explicitly and can provide geometric dependency guidance for modeling the SVG if used appropriately." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 548, + 714 + ], + "type": "text", + "content": "To tackle the above challenges and fully utilize the geometric information from SVG data, this work introduces a novel model architecture named SVGformer, which can take continuous sequential input into a transformer-based model to handle the complex dependencies over SVG commands and yield a robust representation for the input. Specifically, we first extract the SVG segment information via medial axis transform (MAT) [2] to convey the geometric information into the learned representation. Then we introduce a 1D convolutional embedding layer to preserve the original continuous format of SVG data, as opposed to previous vector representation learning models [8] which need a preprocessing step to discretize the input to limited discrete tokens. After that, we inject the structural relationship between commands into the proposed geometric self-attention module in the encoder layer to get the hidden representation" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10093" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 58, + 71, + 535, + 157 + ], + "blocks": [ + { + "bbox": [ + 58, + 71, + 535, + 157 + ], + "lines": [ + { + "bbox": [ + 58, + 71, + 535, + 157 + ], + "spans": [ + { + "bbox": [ + 58, + 71, + 535, + 157 + ], + "type": "table", + "html": "
MethodFont-MF [3]SVG-VAE [20]Im2Vec [25]DeepVecFont [33]DeepSVG [8]LayoutTrans [12]SVGformer (ours)
Encoding ModalitySeqImgImgImg&SeqSeqSeqSeq
Decoding ModalitySeqImg&SeqSeqImg&SeqSeqSeqSeq
Model ArchitectureGP-LVMVAERNNLSTM+CNNTransformerTransformerTransformer
Sequence FormatKeypointsCommandsKeypointsCommandsCommandsCommandsCommands
Geometric Information------Segment
", + "image_path": "ff2265546ba4c5c81dc0d8206277e35894fc45e5daa6af008676872bb6785253.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 166, + 546, + 189 + ], + "lines": [ + { + "bbox": [ + 46, + 166, + 546, + 189 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 546, + 189 + ], + "type": "text", + "content": "Table 1. Comparison of our SVGformer model and recent models for vector representation learning, where \"Seq\" donates sequence, and \"Img\" donates image." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 196, + 288, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 288, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 288, + 278 + ], + "type": "text", + "content": "of each SVG. The representation learned with the reconstruction pretext task can be used in various downstream tasks including classification, retrieval, and interpolation. To the best of our knowledge, our proposed model is the first to explicitly consider vector geometric information as well as directly deal with the raw input of SVG format in an end-to-end encoder-decoder fashion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 281, + 251, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 281, + 251, + 292 + ], + "spans": [ + { + "bbox": [ + 59, + 281, + 251, + 292 + ], + "type": "text", + "content": "The main contributions of this paper include:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 298, + 287, + 479 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 298, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 298, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 58, + 298, + 287, + 357 + ], + "type": "text", + "content": "- SVGformer captures both geometric information and curve semantic information with the geometric self-attention module, which synergizes the strengths of MAT and the transformer-based neural network to handle long-term sequence relationships in SVG." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 365, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 365, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 58, + 365, + 287, + 413 + ], + "type": "text", + "content": "- SVGformer can take original continuous format as input which can effectively reduce the token space in the embedding layer. Thereby the model is general for all continuous vector graphics without extra quantization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "type": "text", + "content": "- SVGformer achieves new state-of-the-art performance on four downstream tasks of both Font and Icon dataset. For example, it outperforms prior art by " + }, + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "type": "inline_equation", + "content": "51.2\\%" + }, + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "type": "text", + "content": " on classification and " + }, + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "type": "inline_equation", + "content": "42.5\\%" + }, + { + "bbox": [ + 58, + 420, + 287, + 479 + ], + "type": "text", + "content": " on retrieval tasks of the font dataset." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 490, + 132, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 132, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 132, + 502 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "Transformer models in the computer version. In the realm of computer vision, many researchers have proposed using self-attention to model long-term dependencies, similar to how transformers are used in natural language processing and other real-world applications [5, 6, 34, 36]. By leveraging self-attention in the encoder-decoder architecture, these methods have shown promising results in computer vision benchmarks, overcoming the limitations imposed by inductive convolution bias [10]. The fields of those benchmarks include object detection [7], image generation [11], and classification on both image [21] and video [32]. In most related works, the self-attention layer in computer vision takes a feature map as input and computes the attention weights between each pair of features. This operation can result in an updated feature map where each position has information about any other feature in the same image which could be costly for high-resolution or long sequential" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 196, + 547, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 196, + 547, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 196, + 547, + 353 + ], + "type": "text", + "content": "inputs. Thus, there are multiple works aimed at overcoming this problem. For example, Informer [41] proposes a sparse attention mechanism by sorting the important queries; Axial-DeepLab [31] computes the attention score sequentially along the two spatial axis and [23] processes the patches of feature maps instead of the whole image. In addition, as inductive bias can always be beneficial to the learning process [35], we need to inject the position information into the transformers to help update features that are lost in the input sequence. For learning the SVG representation, we can introduce structural inductive bias into transformer-based models by obtaining the position information from the input sequence." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 366, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 547, + 713 + ], + "type": "text", + "content": "Representation learning for SVG. Designing and manipulating the SVG image including fonts and icons require substantial expertise and expert knowledge [3]. Machine learning-based models can automatically manipulate the outlines and skeletons of vector images by learning from specific datasets. For the previous works, Font-MF [3] utilize the Gaussian Process Latent Variable Model [17] to learn a manifold of fonts so that it can synthesize fonts in unseen fonts. Im2Vec [25] proposes a new neural network that can generate complex vector graphics with varying topologies and only requires indirect supervision from readily-available raster training images (i.e., with no vector counterparts). Instead of directly using bitmap format, DeepVecFont [33] introduces a new generative paradigm to handle unstructured data (e.g., vector glyphs) by randomly sampling plausible synthesis results and a dual-modality learning strategy that utilizes both image-aspect and sequence-aspect features of fonts to synthesize vector glyphs. SVG-VAE [20] is a generative model with an autoencoder to learn the font style feature and an SVG decoder to generate vector glyphs. In addition, LayoutTransformer [12] uses the self-attention mechanism to capture the contextual relationship between different vector elements, which provides a potential solution for SVG data. Besides, DeepSVG [8] raises a hierarchical transformer-based generative model for vector graphics and collects a large-scale dataset of SVG along with deep learning-based SVG manipulation. However, most models that process the SVG format fail to handle the continuous nature [4, 39] of the input correctly. Besides, most of them do not consider" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10094" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 127, + 219 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 127, + 219 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 127, + 219 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 127, + 219 + ], + "type": "image", + "image_path": "36efd8d67d1f28faa28e1d371ad06e2b9ee964235c8b3da78ea3f05d1fd57855.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "text", + "content": "Figure 1. The extraction of geometric information. Starting from the original SVG commands " + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "text", + "content": " delimited by blue circles, we apply MAT [2] to obtain a new set of commands and labels " + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "inline_equation", + "content": "(\\hat{p}_i, \\hat{l}_i)" + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "text", + "content": " (denoted by curve color and delimited with crosses) that may not exactly align with the original commands. A unique label " + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 228, + 288, + 305 + ], + "type": "text", + "content": " is finally assigned to each original command, as outlined in black color in the last column of the table." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 141, + 76, + 286, + 217 + ], + "blocks": [ + { + "bbox": [ + 141, + 76, + 286, + 217 + ], + "lines": [ + { + "bbox": [ + 141, + 76, + 286, + 217 + ], + "spans": [ + { + "bbox": [ + 141, + 76, + 286, + 217 + ], + "type": "table", + "html": "
Raw CommandsArgumentsGeometric Segments
p0M (13.2, 3.0)-1
...
paL (16.5, 18.9)
pbL (16.2, 21.0)
...
pcC (5.8, 19.1, 6.3, 17.5, 7.2, 16.2)
...
pnEOS (∅)-1
", + "image_path": "6842ddb4c1dcdc5476cfecd4737b0ded10276f20f3234115ecc0182e7465f5eb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 313, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 350 + ], + "type": "text", + "content": "geometric information, which can directly equip the relationship of different curves into deep learning-based methods. Refer to Table 1 for a complete comparison of related works." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 361, + 102, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 102, + 374 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 102, + 374 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 382, + 114, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 114, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 114, + 395 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": "We propose a transformer-based deep neural network, SVGformer, as a general solution for multiple vector graphics downstream tasks. The overall architecture of SVGformer is illustrated in Figure 2. The raw " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": "-th SVG's arguments contain the type and corresponding coordinates of its commands, where the coordinates with continuous values are first constructed into a tensor format, " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^t \\in \\mathbb{R}^{n \\times 8}" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " is the number of commands. Then the input tensor is fed into the embedding layer to get the input vector for the encoder-decoder model. The learnable embedding layer contains three components to specifically abstract the information from the original input: 1) the continuous token component uses a 1D convolution to map " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^t" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " into an embedding vector " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "U^t" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": "; 2) the position component captures the positional information " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "P^t" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^t" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": "; 3) the geometric component treats the outline labels " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " (refer to Figure 1) as a discrete token to map extra contextual geometric information " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "S^t" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " to the embedding vector. In addition, we build an adjacency matrix " + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 402, + 287, + 641 + ], + "type": "text", + "content": " based on the labels and the neighboring commands in order to further utilize the structural information in the training process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Next, we combine the embedding vectors to feed the encoder module, where we introduce the geometric self-attention to replace the canonical self-attention in order to generate a compact representation with a higher receptive field efficiently. Specifically, we leverage structural relationships by encoding geometric segment information via a" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "graph convolution layer and injecting it into spared attention score. Finally, we pass the hidden representation produced by the encoder into the SVG-decoding module consisting of the self-attention mechanism [41] and fully connected layers to fine-tune the total model. The decoder aims to reconstruct the original SVG commands from a masked input as well as predict the type of commands." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 156, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 547, + 217 + ], + "type": "text", + "content": "In this way, the overall network can be trained end-to-end by backpropagation of a reconstruction loss and classification loss. Precisely, the classification loss has 3 different labels as we only consider three types of commands: \"Move\" (M), \"Line\" (L) and \"Curve\" (C)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 224, + 516, + 238 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 516, + 238 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 516, + 238 + ], + "type": "text", + "content": "3.2. Geometric Information from Raw Input" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": "As the attention mechanism generally only calculates the similarities via the commands' semantic features, we want to cooperate explicit geometric dependencies into the attention mechanism to provide our model with the ability to capture the structural relation between the commands. v We start from the raw SVG input " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\{p_0,p_1,p_2,\\ldots ,p_n\\}" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": "-th command in a given SVG, and " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": " is the number of original commands. As shown in Figure 1, we obtain semantic labeling of segments with MAT. This tool leverages the medial axis and outlines information to find new segments labeled based on different geometric relationships: " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\{(\\hat{p}_1,\\hat{l}_1),(\\hat{p}_2,\\hat{l}_2),\\dots ,(\\hat{p}_m,\\hat{l}_m)\\}" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\hat{l}_i" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": " is the label of the new command " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\hat{p}_i" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ". Commands with the same label have a strong position relationship inside the given SVG, which is usually ignored by feature engineering. Note that MAT can usually split an original command into several segments (new commands), so " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "m\\geq n" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ". However, directly adding such extra commands into the neural network will complicate the task of representation learning. Instead, we propose to map the new segments and labels back to the original input. Specifically, we group different commands by start and end points so that we have " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "p_i = \\{\\hat{p}_k,\\dots ,\\hat{p}_j\\}" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ". To obtain the final label " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ", we calculate the longest label by the distance between the start and end point of the label set " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\{\\hat{l}_k,\\dots ,\\hat{l}_j\\}" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ". Then the final data we use to train the model is " + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\{(p_1,l_1),(p_2,l_2),\\dots ,(p_n,l_n)\\}" + }, + { + "bbox": [ + 304, + 243, + 547, + 578 + ], + "type": "text", + "content": ". We will introduce how to incorporate geometric information into the transformer in the next several sections." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 586, + 479, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 479, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 479, + 600 + ], + "type": "text", + "content": "3.3. Continuous Feature Embedding" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Representation learning requires the model to learn the inductive biases from the data and training task which can facilitate the downstream task. Thus, any inductive bias from raw input is able to coach the training process. In this work, we have identified two inductive biases present in raw input: continuous values and geometric information. While previous related works have typically relied on manually discretizing continuous values, our model is able to support continuous-valued inputs. Additionally, our model" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10095" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 547, + 257 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 547, + 257 + ], + "type": "image", + "image_path": "350ee0f465ffef52f8db07610d05cbc311dbf956dc0d81da2b1307e2a479542e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 206, + 265, + 386, + 277 + ], + "lines": [ + { + "bbox": [ + 206, + 265, + 386, + 277 + ], + "spans": [ + { + "bbox": [ + 206, + 265, + 386, + 277 + ], + "type": "text", + "content": "Figure 2. Overall model structure of SVGformer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 282, + 288, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 288, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 288, + 366 + ], + "type": "text", + "content": "is able to automatically discover structural information from the geometric information present in the input, providing further support for the inductive biases we have identified. This section will present proposed modifications to make it compatible with continuous SVG commands input with geometric information rather than with discrete pre-processed index sequences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "content": "Specifically, for the raw input, we first set a maximum sequence length " + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "inline_equation", + "content": "L_{x}" + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "content": " for the entire dataset, then we pad shorter samples with arbitrary values (0 in our setting) as the length of individual samples may vary considerably regarding the SVG images. Then, we generate a padding mask that adds a large negative value to the attention fraction of the padded positions before computing the self-attentive distribution with the softmax function. After that, different from previous works that can only support discrete input with fix length of the look-up table, we use a continuous value embedding layer with 1D convolutional operation to project the " + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "content": "-th SVG input " + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^t" + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "content": " into a " + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "content": "-dimension vector " + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "inline_equation", + "content": "U^{t}" + }, + { + "bbox": [ + 46, + 366, + 290, + 510 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 126, + 520, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 520, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 126, + 520, + 287, + 533 + ], + "type": "interline_equation", + "content": "U ^ {t} = \\operatorname {C N N} \\left(\\mathcal {X} ^ {t}\\right). \\tag {1}", + "image_path": "a3261d4895c4bc41418319280c90e704c888b93bd8de7bc8315487e4f51f5106.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 543, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 288, + 616 + ], + "type": "text", + "content": "Note that this embedding layer can fully utilize the translation equivariance [1] of convolutional operation for SVG input and can have the ability of rotation invariance and size invariance with data augmentation. Corresponding to the continue value embedding layer, we preserve the input SVG commands by using the position embedding layer:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 86, + 624, + 287, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 624, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 86, + 624, + 287, + 644 + ], + "type": "interline_equation", + "content": "P ^ {t} (p, 2 j) = \\sin \\left(m / \\left(2 L _ {x}\\right) ^ {2 j / d}\\right), \\tag {2}", + "image_path": "8af7dcba76af129f743d3053b3d2c819809a4c602a04631fd7f8cd2fccd716a2.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 642, + 247, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 642, + 247, + 656 + ], + "spans": [ + { + "bbox": [ + 88, + 642, + 247, + 656 + ], + "type": "interline_equation", + "content": "P ^ {t} (p, 2 j + 1) = \\cos \\left(m / \\left(2 L _ {x}\\right) ^ {2 j / d}\\right),", + "image_path": "f03a5c9500cf90057928b8c3e11b68971a3e8ceda19fc826dbed399cce1dcf8d.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "inline_equation", + "content": "j\\in \\{1,\\ldots ,\\lfloor d / 2\\rfloor \\}" + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "inline_equation", + "content": "m\\in \\{0,\\dots ,L_x - 1\\}" + }, + { + "bbox": [ + 46, + 665, + 289, + 714 + ], + "type": "text", + "content": ". In this way, self-attention can compute the similarity with access to global information and affordable consumption [41]. Note that this position encoding function is inductive and" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "text", + "content": "parameters free to handle variable input length [19]. However, the above inductive embedding functions fail to capture the geometric dependency among the different positions of raw SVG commands. Thus, we exact the segment label " + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "inline_equation", + "content": "l_i^t" + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "text", + "content": " for each input command " + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "inline_equation", + "content": "p_i^t" + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "text", + "content": " according to Section 3.2 and use a geometric embedding layer with a look-up table, containing all the segmented labels, to get the geometric information " + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "text", + "content": ". Thus, we finally maintain the feeding vector " + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "inline_equation", + "content": "X_{en}^{t} \\in \\mathbb{R}^{L_{x} \\times d}" + }, + { + "bbox": [ + 304, + 282, + 547, + 392 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 364, + 404, + 545, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 404, + 545, + 419 + ], + "spans": [ + { + "bbox": [ + 364, + 404, + 545, + 419 + ], + "type": "interline_equation", + "content": "X _ {e n} ^ {t} = \\alpha U ^ {t} + \\beta P ^ {t} + \\gamma S ^ {t}, \\tag {3}", + "image_path": "186e373c797b3be3b51b5debf0eeb2d380aebd8db93e8db176eb1aab9c73a4dc.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 426, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 462 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 426, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\gamma" + }, + { + "bbox": [ + 304, + 426, + 547, + 462 + ], + "type": "text", + "content": " are the factors balancing the magnitude between the scalar projection and position/geometric embeddings." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "type": "text", + "content": "3.4. SVGformer Encoder with Geometric Information" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 502, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 612 + ], + "type": "text", + "content": "After the embedding layer, we feed the vector " + }, + { + "bbox": [ + 304, + 502, + 547, + 612 + ], + "type": "inline_equation", + "content": "X_{en}^{t}" + }, + { + "bbox": [ + 304, + 502, + 547, + 612 + ], + "type": "text", + "content": " to the encoder to extract latent representation. We refer the reader to the detailed description of the transformer model in the original work [30]. In this section, we will introduce the key technologies different from the vanilla transformer. Specifically, the encoder consists of several stacked geometric self-attention modules which can deal with long-term sequential dependency and geometric dependency in the attention mechanism jointly." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Sparse Query for Self-Attention. As the representation learning of SVG requires the model to have the ability to capture precise long-term dependency, we need to utilize the commands' features via an efficient attention mechanism. The canonical self-attention is defined based on the scaled dot-product of the input tuple, i.e., query " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{q} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": ", key " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{K} \\in \\mathbb{R}^{L_K \\times d}" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": ", and value " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{L_V \\times d}" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": ". Specifically, the " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "-th" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10096" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 96 + ], + "type": "text", + "content": "query's attention is defined as a kernel smoother in a probability form [29]:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 52, + 101, + 288, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 101, + 288, + 131 + ], + "spans": [ + { + "bbox": [ + 52, + 101, + 288, + 131 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (\\mathbf {q} _ {i}, \\mathbf {K}, \\mathbf {V}) = \\sum_ {j} \\frac {k (\\mathbf {q} _ {i} , \\mathbf {k} _ {j})}{\\sum_ {l} k (\\mathbf {q} _ {i} , \\mathbf {k} _ {l})} \\mathbf {v} _ {j} = \\mathbb {E} _ {p (\\mathbf {k} _ {j} | \\mathbf {q} _ {i})} [ \\mathbf {v} _ {j} ], \\tag {4}", + "image_path": "fb0b1feec8ddacabae0ad0f3ef7a9e32a64f7480239580bbd694aac153ca2692.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "spans": [ + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "inline_equation", + "content": "p(\\mathbf{k}_j|\\mathbf{q}_i) = k(\\mathbf{q}_i,\\mathbf{k}_j) / \\sum_lk(\\mathbf{q}_i,\\mathbf{k}_l)" + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "inline_equation", + "content": "k(\\mathbf{q}_i,\\mathbf{k}_j)" + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "text", + "content": " selects the asymmetric exponential kernel " + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "inline_equation", + "content": "\\exp (\\mathbf{q}_i\\mathbf{k}_j^\\top /\\sqrt{d})" + }, + { + "bbox": [ + 47, + 135, + 288, + 186 + ], + "type": "text", + "content": " . Inspired by [41], we calculate the importance of queries by Kullback-Leibler divergence:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 69, + 190, + 288, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 190, + 288, + 224 + ], + "spans": [ + { + "bbox": [ + 69, + 190, + 288, + 224 + ], + "type": "interline_equation", + "content": "M (\\mathbf {q} _ {i}, \\mathbf {K}) = \\max _ {j} \\left\\{\\frac {\\mathbf {q} _ {i} \\mathbf {k} _ {j} ^ {\\top}}{\\sqrt {d}} \\right\\} - \\frac {1}{L _ {K}} \\sum_ {j = 1} ^ {L _ {K}} \\frac {\\mathbf {q} _ {i} \\mathbf {k} _ {j} ^ {\\top}}{\\sqrt {d}} \\quad , \\tag {5}", + "image_path": "086efadaff367521eebf00617c3d5e7135a93f7feccbea9faa867938bfab5168.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "inline_equation", + "content": "M(\\mathbf{q}_i, \\mathbf{K})" + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": "-th query's sparsity score. A larger " + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "inline_equation", + "content": "M(\\mathbf{q}_i, \\mathbf{K})" + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": " gives a higher chance to activate the dominate dot-product pairs in the self-attention. Thus, we can build a new query " + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\overline{Q}" + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": " containing top " + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": " queries with query sparsity score given by " + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 229, + 287, + 300 + ], + "type": "text", + "content": " and calculate the sparsity self-attention score by:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 117, + 300, + 287, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 300, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 117, + 300, + 287, + 314 + ], + "type": "interline_equation", + "content": "A _ {a t t} = \\overline {{\\mathbf {Q}}} \\mathbf {K} ^ {\\top} / \\sqrt {d} \\quad . \\tag {6}", + "image_path": "bcd7580630bc4e891b8c81cb1882e806c3538662b21859309fbc536f61db9f1e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 316, + 288, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 365 + ], + "type": "text", + "content": "Note that we can avoid information loss by generating different sparse query-key pairs according to different attention heads and this attention score can capture the relationships between input commands from a data-driven aspect." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": "Geometric Dependency in Self-Attention. Segments with the same label share a strong relationship even if they are at a long distance in the input sequence, which cannot be reflected in the original self-attention module which only considers the semantic characteristics. In addition, commands can be represented as the nodes lying in a non-Euclidean space and linked by edges with the geometric information. such as the adjacency and the same segment label. In this work, we propose to apply the graph convolution network (GCN) [15] to extract the structural relationship between different commands. Specifically, we first use the geometric label from Section 3.2 to build the weight matrix " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": " where the commands adjacent to each other or sharing the same label have an edge in the weight matrix " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": ", otherwise there is no edge in the weight matrix " + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 378, + 287, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "This has two advantages, firstly, the structure information of SVG is contained in the weight matrix, and secondly, commands sharing the same labels can distinguish local details by their own features. After getting the weight matrix, we use GCN to extract the structural information. The goal is then to learn a function of SVG commands on a graph " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = (V,E)" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " is the set of nodes' (commands in SVG) feature of each single SVG, i.e., " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "X_{en}^{t}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " at the first layer, and " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " is the in the form of the adjacency matrix, which is " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " based on Figure 1. Our model can produce command-level output " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "A_{geo} \\in \\mathbb{R}^{N \\times d}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " multiple layers GCN where " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "-th layer output " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "H^{l}" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " can be used to represent the latent vectors to get the final output:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 350, + 82, + 545, + 97 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 82, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 350, + 82, + 545, + 97 + ], + "type": "interline_equation", + "content": "H ^ {l + 1} = f \\left(H ^ {l}, E\\right) = \\sigma \\left(E H ^ {l} W ^ {l}\\right), \\tag {7}", + "image_path": "bc095eb0dbd3ff8bff51636576aecfd5ceb678a5cd487b22482a324bc0ce4acb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "spans": [ + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "inline_equation", + "content": "H^0" + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": " is the input features of the GCN, i.e., " + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_{en}" + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": " at the very first layer, " + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": " is the graph convolutional function with learnable matrix " + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": " is the non-linear activation function for GCN and " + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "inline_equation", + "content": "H^L = A_{geo}" + }, + { + "bbox": [ + 305, + 101, + 547, + 150 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 164, + 547, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 164, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 305, + 164, + 547, + 283 + ], + "type": "text", + "content": "Geometric Self-Attention Module. To better encode the geometric information into attention layers, we propose a new self-attention module in SVGformer. The attention mechanism needs to estimate correlations on both semantics (features from commands) part and the geometric (dependency of each command) part. Thus, for each ordered command pair " + }, + { + "bbox": [ + 305, + 164, + 547, + 283 + ], + "type": "inline_equation", + "content": "(p_i,p_j)" + }, + { + "bbox": [ + 305, + 164, + 547, + 283 + ], + "type": "text", + "content": ", we inject the relationship score from GCN into the sparse attention score. Concretely, the attention mechanism with the modified attention score can be represented as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 330, + 293, + 545, + 307 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 293, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 330, + 293, + 545, + 307 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(A _ {\\text {a t t}} + A _ {\\text {g e o}}\\right) \\mathbf {V} \\quad . \\tag {8}", + "image_path": "30570c18f8c362c714e58fbaffcf9f7fa79a3dcd540444e147317c2ed35c5511.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "spans": [ + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "text", + "content": "To enhance the ability of our model on handling the permutation invariance where the order of shapes in an SVG image is arbitrary, we apply the 1D convolutional operation following an ELU activation function [9] and max pooling [38] on the output of the attention layer: " + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{j + 1} = \\mathrm{MaxPool}\\left(\\mathrm{ELU}(\\mathrm{Conv1d}([X_j]_{\\mathcal{A}_j}))\\right)" + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "inline_equation", + "content": "[\\cdot ]_{\\mathcal{A}}" + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 315, + 547, + 398 + ], + "type": "text", + "content": "-th geometric self-attention module." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "type": "text", + "content": "The final representation of the encoder " + }, + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 305, + 399, + 545, + 434 + ], + "type": "text", + "content": " is the last layer's output of the encoder module and can be used for multiple downstream tasks." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 442, + 424, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 424, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 424, + 453 + ], + "type": "text", + "content": "3.5. SVGformer Decoder" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "text", + "content": "The decoder part is modified from the decoder structure in [41], which can reconstruct the long sequences of SVG at one forward operation rather than a step-by-step way with the input of " + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathrm{de}}^{t} = \\operatorname{Concat}(\\mathbf{X}_{\\mathrm{token}}^{t}, \\mathbf{X}_{0}^{t}) \\in \\mathbb{R}^{(L_{\\mathrm{token}} + L_{y}) \\times d}" + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathrm{token}}^{t} \\in \\mathbb{R}^{L_{\\mathrm{token}} \\times d}" + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "text", + "content": " is the start token, " + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{0}^{t} \\in \\mathbb{R}^{L_{y} \\times d}" + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "text", + "content": " is a placeholder of 0 for the target sequence. Specifically, it consists of masked geometric self-attention and multi-head attention, where the masked geometric self-attention sets masked dot-products to " + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "inline_equation", + "content": "-\\infty" + }, + { + "bbox": [ + 305, + 460, + 545, + 604 + ], + "type": "text", + "content": " and gives up the geometric GCN component, which can prevent data leakage in the decoding stage. Besides, a fully connected layer is needed to acquire the final logits for the loss function." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 611, + 394, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 394, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 394, + 623 + ], + "type": "text", + "content": "3.6. Loss Function" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 630, + 547, + 713 + ], + "type": "text", + "content": "We need to reconstruct the input commands as well as predict the type of the commands. Thus, we choose the reconstruction loss as the mean squared error (MSE) loss function between the reconstructed commands and the ground-truth command and the classification loss as the cross entropy (CE) with logits between the predicted command type and the type label." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10097" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 97, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 97, + 105 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 97, + 105 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "content": "We summarize the critical settings in this section. For input SVG, we choose those font inputs with a maximum length " + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "inline_equation", + "content": "L_{x}" + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "content": " equals to 60 and icon inputs with a maximum length equals to 50. Then pad the font commands less than 60 (50 for icon commands) by 0. For the embedding layer, a 1D convolutional operation is used as the trainable module for SVG recognition with kernel width equal to 3 and stride equal to 1. Both the 1D convolutional operation and the other two components inside the embedding layer's output dimension are 512. We recommend " + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\gamma" + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "content": " to be 1 inside the embedding layer if the sequence input has been normalized. In the training stage, the sparse attention's head number is 8, and we add geometric information given by one GCN layer, which output shape fits the attention score given by the sparse self-attention. To gain the global representation for a specific SVG, we use two stacked geometric self-attention modules followed by 1D convolutional operations and maximum pooling operations to finish the fusion process of all the commands and get the hidden representation with the shape of " + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "inline_equation", + "content": "L_{x} \\times 512" + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "content": ". For the decoder during the training stage, we mask all the commands instead of the first command (whose type is \"Move\") to finish the reconstruction task, which means " + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "inline_equation", + "content": "L_{token} = 1" + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "inline_equation", + "content": "L_{y} = L_{x} - 1" + }, + { + "bbox": [ + 46, + 111, + 289, + 386 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 387, + 289, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 289, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 289, + 507 + ], + "type": "text", + "content": "In the remaining part of this section, we discuss the qualitative and quantitative results of our models on two representative datasets, Google Fonts1 and Icons [8]. Note that the evaluation of representation learning models is difficult, and most quantitative metrics can not provide a generic measure of the novelty and veracity of the data sampled from representation learning models. Thus, we will explore 4 types of downstream tasks including reconstruction task, classification task, retrieval task, and interpolation task with specific quantitative metrics used by the various underlying methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 517, + 105, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 105, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 105, + 529 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 536, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 288, + 693 + ], + "type": "text", + "content": "We evaluate the effectiveness of the proposed SVGformer on both fonts dataset and the icons dataset. We first show the reconstruction results, which is the training task. Note that simply using MSE and CE metrics cannot accurately show the coordinate values of control points on the contour line because the average of the correct target values is often not a correct value, so we use Chamfer distance (CD) metric to do the evaluation. Then, for the downstream tasks, we train a classification model to finish the classification task and use the glyph label to verify the retrieval task, which is a pure unsupervised process without any fine-tuning on the representation. After that, we finish with an interpolation task to show that SVGformer has good interpretability." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 319, + 72, + 533, + 196 + ], + "blocks": [ + { + "bbox": [ + 319, + 72, + 533, + 196 + ], + "lines": [ + { + "bbox": [ + 319, + 72, + 533, + 196 + ], + "spans": [ + { + "bbox": [ + 319, + 72, + 533, + 196 + ], + "type": "image", + "image_path": "3795e5e91e4ef5e455ef615a8f44af7edd2c0f7790deaa059f8cf4774298819d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 205, + 548, + 239 + ], + "lines": [ + { + "bbox": [ + 305, + 205, + 548, + 239 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 548, + 239 + ], + "type": "text", + "content": "Figure 3. Reconstruction results on various glyphs. From left to right, the original SVG (black), DeepSVG (orange), LayoutTransformer (green) and our SVGformer (blue), respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 259, + 364, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 259, + 364, + 271 + ], + "spans": [ + { + "bbox": [ + 306, + 259, + 364, + 271 + ], + "type": "text", + "content": "4.2.1 Fonts" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 278, + 547, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 278, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 305, + 278, + 547, + 350 + ], + "type": "text", + "content": "Reconstruction task. The reconstruction task is the training task where we can get the pre-trained model and obtain the latent representation of a given SVG image. We use Chamfer distance (CD) between corresponding paths of the input SVG and reconstructed SVG to evaluate the performance of the SVGformer." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 350, + 548, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 548, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 548, + 471 + ], + "type": "text", + "content": "Based on Table 2, our model produces a smaller gap than the other baselines with " + }, + { + "bbox": [ + 304, + 350, + 548, + 471 + ], + "type": "inline_equation", + "content": "17.8\\%" + }, + { + "bbox": [ + 304, + 350, + 548, + 471 + ], + "type": "text", + "content": " overperformance in a mathematical sense, proving the accuracy of SVGformer. In addition, we render the reconstructed results for quantitative comparisons on Figure 3. Benefiting from the two kinds of attention scores, SVGformer can reconstruct more details of the raw input. As confirmed by the results, we find that introducing the geometric information brings a substantial improvement in reconstruction error compared to the previous baselines." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "type": "text", + "content": "Classification task. For the classification task, we train a linear classification model for the different hidden representations with 1000 epochs and show in Table 2 the accuracy results of glyph-based category (62 classes) and family-based category (378 font family types filtered by a minimum class size of 100 in the test set). The glyph-based classification task is used to verify that our model's latent representation can identify the outline of inputs. The family-based classification task is more challenging as it has more categories and focuses on font style which needs the latent representation to be distinctive in details. We can figure out that the geometric information can help SVGformer gain further improvement for this mature task. Specifically, we find that both the LayoutTransformer and DeepSVG fail to classify the family labels with the accuracy of " + }, + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "type": "inline_equation", + "content": "7.0\\%" + }, + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "type": "inline_equation", + "content": "35.2\\%" + }, + { + "bbox": [ + 304, + 486, + 548, + 715 + ], + "type": "text", + "content": ", respectively, which means they lose the style information during the data-driven process. Especially we find that higher dimensional data does not encompass more information because LayoutTransformer's hidden representation has a larger shape" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 145, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 145, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 145, + 713 + ], + "type": "text", + "content": "1https://fonts.google.com/" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10098" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 71, + 533, + 155 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 533, + 155 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 533, + 155 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 533, + 155 + ], + "type": "table", + "html": "
ModelReconstruction (CD ↓)Classification (Acc %)Retrieval (Acc %)
FontsIconsFonts GlyphFonts FamilyIconsFonts@5Fonts@10Icons@10
LayoutTransformer37.618.875.67.057.61.71.613.4
DeepSVG32.715.685.635.245.151.245.922.8
SVGformer26.96.389.569.764.774.364.248.9
SVGformer-no-geo30.87.989.346.346.769.659.446.2
SVGformer-discrete41.519.385.915.063.760.751.530.5
", + "image_path": "c7de5ee289880b5a20c6fdba74f135821f1fd1a3c3208aa60a1609e89525a20c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 71, + 179, + 264, + 479 + ], + "blocks": [ + { + "bbox": [ + 139, + 163, + 453, + 175 + ], + "lines": [ + { + "bbox": [ + 139, + 163, + 453, + 175 + ], + "spans": [ + { + "bbox": [ + 139, + 163, + 453, + 175 + ], + "type": "text", + "content": "Table 2. Result comparison for different downstream tasks on Fonts and Icons dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 71, + 179, + 264, + 479 + ], + "lines": [ + { + "bbox": [ + 71, + 179, + 264, + 479 + ], + "spans": [ + { + "bbox": [ + 71, + 179, + 264, + 479 + ], + "type": "table", + "html": "
QueryTop7 retrieval results on all candidates
DD 7 D 7 D D D
D D D D D D D
NN N N M N N N
N N N N N N N N
RR n P n P p P n
R R R R R Q R
QueryTop7 retrieval results on same scope
aa a a a a e a a
a a a a a a a a
ff f f f f f f f
f f f f f f f f
kk k k k k k k
k k k k k k k
", + "image_path": "f67a28bf9e86f28324ddfe4e92b780f1064b7b34c7805b8a96cb2c29e9d6d12b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 488, + 288, + 544 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 288, + 544 + ], + "type": "text", + "content": "Figure 4. Retrieval results from all glyphs and same glyphs, respectively. Results for DeepSVG are shown in orange, and results for SVGformer in blue. SVGformer always retrieves the same glyph as the query when searching from all glyphs, and returns results in more similar styles when searching for a specific glyph." + } + ] + } + ], + "index": 3, + "type": "text" + }, + { + "bbox": [ + 46, + 551, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 575 + ], + "type": "text", + "content": "than both DeepSVG and SVGformer, yet it performs almost randomly on the family classification task." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Retrieval task. From the perspective of quality analysis, we report the family accuracy of the most top " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " (@5) and " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " (@10) similar retrieval results by name on Tabel 2, where the similarity score can be calculated by the inner product of the query and all the candidates of an SVG image, which is equivalent to the cosine similarity formula after normalization. The retrieval results show that our model can offer a " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "42.5\\%" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " performance improvement compared with DeepSVG. Besides, we use Figure 4 to show the retrieval results of some query samples which indicates SVGformer can" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 182, + 547, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 255 + ], + "type": "text", + "content": "achieve higher accuracy in general than previous baselines. Specifically, SVGformer can beat the previous state-of-the-art in two different settings: 1. retrieving in all the candidates (across families) to figure out the ability to find the same family; 2. retrieving under the target family to verify that our model's representation can align the style of the query." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "text", + "content": "Interpolation task. To verify that our model can animate SVGs by interpolating automatically from different glyphs, we use the hidden representation from DeepSVG and SVGformer to perform the comparison on the interpolation task. As shown in Figure 5, SVGformer can give more meaningful and smooth results with fewer artifacts and contortions when handling both translations and deformations in 3 different interpolation types including \"Thin\" " + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "text", + "content": " \"Black\", \"Expanded\" " + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "text", + "content": " \"Condensed\" and \"Regular\" " + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 269, + 548, + 413 + ], + "type": "text", + "content": " \"Italic\". For example, when we interpolate the fonts' size from \"Thin\" to \"Black\", we can find a specific value for \"Regular\" size in SVGformer's results but cannot find that one in DeepSVG's." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 428, + 362, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 428, + 362, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 428, + 362, + 439 + ], + "type": "text", + "content": "4.2.2 Icons" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 448, + 547, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 650 + ], + "type": "text", + "content": "For the reconstruction task on the Icons dataset, we calculate the CD metric as mentioned before in Table 2, where SVGformer can build a new state-of-the-art by achieving " + }, + { + "bbox": [ + 304, + 448, + 547, + 650 + ], + "type": "inline_equation", + "content": "59.5\\%" + }, + { + "bbox": [ + 304, + 448, + 547, + 650 + ], + "type": "text", + "content": " performance improvement over previous methods. In addition, we also plot the reconstruction results in Figure 6 to show that SVGformer can yield more precise reconstruction results than DeepSVG. For the classification task, we first collect icons' labels by their categories including \"cinema\", \"city\", \"clothing\", etc. Then we train a classification model with 59 classes and report the top 10 accuracy, where SVGformer achieves the highest accuracy. For the retrieval task, we use visual inspection to verify the retrieval results are relevant as there is no such ground truth information. As shown in Figure 7, the unsupervised representation of SVGformer has great capability to distinguish the global and local structure of SVG, achieving better retrieval results than other baselines." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 658, + 400, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 400, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 400, + 671 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 714 + ], + "type": "text", + "content": "To better understand the effectiveness of different components in SGVformer, we evaluate two model variants, namely SVGformer-no-geo and SVGformer-discrete, by dropping the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10099" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 72, + 70, + 146, + 78 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 70, + 146, + 78 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 146, + 78 + ], + "type": "text", + "content": "Thin to Black. 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Saira Semi Condensed, '" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 73, + 131, + 262, + 171 + ], + "blocks": [ + { + "bbox": [ + 73, + 131, + 262, + 171 + ], + "lines": [ + { + "bbox": [ + 73, + 131, + 262, + 171 + ], + "spans": [ + { + "bbox": [ + 73, + 131, + 262, + 171 + ], + "type": "image", + "image_path": "d7b30cd8d02279823611a01f75f65af5a2660f51d959ca62bf71f38755fc3c67.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 73, + 174, + 190, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 174, + 190, + 182 + ], + "spans": [ + { + "bbox": [ + 73, + 174, + 190, + 182 + ], + "type": "text", + "content": "Expanded to Condensed. 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Andika New Basic, 'H'" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 73, + 339, + 259, + 357 + ], + "blocks": [ + { + "bbox": [ + 73, + 339, + 259, + 357 + ], + "lines": [ + { + "bbox": [ + 73, + 339, + 259, + 357 + ], + "spans": [ + { + "bbox": [ + 73, + 339, + 259, + 357 + ], + "type": "image", + "image_path": "3883c35e7c2e2b9682af0deb4f7714fa31827f175ac87529d13424d4d1bba98c.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 73, + 358, + 259, + 379 + ], + "blocks": [ + { + "bbox": [ + 73, + 358, + 259, + 379 + ], + "lines": [ + { + "bbox": [ + 73, + 358, + 259, + 379 + ], + "spans": [ + { + "bbox": [ + 73, + 358, + 259, + 379 + ], + "type": "image", + "image_path": "b4418470eab5754859e792108a34ac978f0dcade275ef963d7a988f0e71632cd.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 389, + 288, + 433 + ], + "lines": [ + { + "bbox": [ + 46, + 389, + 288, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 288, + 433 + ], + "type": "text", + "content": "Figure 5. Examples of interpolations between glyphs. The results for DeepSVG are shown in orange, and those for SVGformer in blue. The first and last columns are the given glyphs to be interpolated, and the middle columns are the interpolations." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 66, + 438, + 269, + 588 + ], + "blocks": [ + { + "bbox": [ + 66, + 438, + 269, + 588 + ], + "lines": [ + { + "bbox": [ + 66, + 438, + 269, + 588 + ], + "spans": [ + { + "bbox": [ + 66, + 438, + 269, + 588 + ], + "type": "image", + "image_path": "8a9b87097fcfd298cad246639ac9e677eeb583dc6fee55307f19ae6015a1b8b9.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 598, + 288, + 632 + ], + "lines": [ + { + "bbox": [ + 46, + 598, + 288, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 288, + 632 + ], + "type": "text", + "content": "Figure 6. Example reconstruction results on Icons data. From left to right, columns show original SVG (black), DeepSVG (orange), LayoutTransformer (green), and our SVGformer (blue)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "geometric information and continuous input embedding from the full model. The results on both Fonts and Icons datasets shown in the last two rows of Table 2 confirm that both components are indispensable. Specifically, SVGformer-no-geo aborts the geometric information inside the self-attention mechanism, which indicates the importance of structural" + } + ] + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 332, + 72, + 521, + 274 + ], + "blocks": [ + { + "bbox": [ + 332, + 72, + 521, + 274 + ], + "lines": [ + { + "bbox": [ + 332, + 72, + 521, + 274 + ], + "spans": [ + { + "bbox": [ + 332, + 72, + 521, + 274 + ], + "type": "image", + "image_path": "29c933fb9c2d1fb6c080470e0b41719822d2e457f002a49bb5e719e93430f373.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 282, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 305, + 282, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 305, + 282, + 545, + 304 + ], + "type": "text", + "content": "Figure 7. Retrieval results on Icons data. The results of DeepSVG are shown in orange, and the results of SVGformer in blue." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 312, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 547, + 384 + ], + "type": "text", + "content": "inductive bias for encoder-decoder-based transformer models. SVGformer-discrete provides a fair comparison of SVGformer with the previous works which only accept discrete SVG inputs. The results demonstrate that the raw input contains detailed information which is critical to high-quality hidden representation." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 396, + 375, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 375, + 408 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 375, + 408 + ], + "type": "text", + "content": "5. Limitation" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 417, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 417, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 417, + 547, + 561 + ], + "type": "text", + "content": "We note some limitations of SVGformer in this section. One of the major limitations is the effectiveness of representation is based on sufficient SVGs in the training process, which is hard to guarantee in many real-world scenarios. Admittedly, although our model can yield much more precise hidden representations than previous baselines to make it identifiable for each SVG, we found that SVGformer's hidden space lacks linearity and smoothness when facing complex downstream tasks such as some interpolation samples of different style transfers. Inspired by diffusion models [13,24,27,28], one possible insight for future work can be smooth the latent space by introducing the diffusion process." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 573, + 378, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 378, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 378, + 585 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "In this paper, we study representation learning for SVG and propose a transformer-based model named SVGformer. Specifically, we directly deal with the continuous input and extract MAT segment information as the inductive bias of SVG input. Besides, we design a geometric self-attention module to utilize the stylistic semantics of SVG commands and the geometric information jointly to handle long-term sequence relations. 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Despite their immense capacity and the abundance of multimodal training data, recent work has revealed the strong tendency of video-text models towards frame-based spatial representations, while temporal reasoning remains largely unsolved. In this work, we identify several key challenges in temporal learning of video-text transformers: the spatiotemporal trade-off from limited network size; the curse of dimensionality for multi-frame modeling; and the diminishing returns of semantic information by extending clip length. Guided by these findings, we propose SViTT, a sparse video-text architecture that performs multi-frame reasoning with significantly lower cost than naive transformers with dense attention. Analogous to graph-based networks, SViTT employs two forms of sparsity: edge sparsity that limits the query-key communications between tokens in self-attention, and node sparsity that discards uninformative visual tokens. Trained with a curriculum which increases model sparsity with the clip length, SViTT outperforms dense transformer baselines on multiple video-text retrieval and question answering benchmarks, with a fraction of computational cost. Project page: http://svcl.ucsd.edu/projects/svittt.", + "bbox": [ + 75, + 296, + 473, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 659, + 209, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the rapid development of deep neural networks for computer vision and natural language processing, there has been growing interest in learning correspondences across the visual and text modalities. A variety of vision-language pretraining frameworks have been proposed [12, 22, 29, 34] for learning high-quality cross-modal representations with weak supervision. Recently, progress on visual transformers (ViT) [5, 16, 32] has enabled seamless integration of both modalities into a unified attention model, leading to image-text transformer architectures that achieve state-the-art performance on vision-language benchmarks [1, 27, 44].", + "bbox": [ + 75, + 680, + 468, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Progress has also occurred in video-language pretraining by leveraging image-text models for improved frame-based", + "bbox": [ + 76, + 847, + 468, + 877 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c93b0b7814c5eab4d4a81860413017e46d3c4a8fa5a69d6ffaab2720c12c3307.jpg", + "image_caption": [ + "One person takes a pillow and some homework from an old chair, then smiles and laughs." + ], + "image_footnote": [], + "bbox": [ + 511, + 263, + 879, + 340 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/57438170fa659e11bcc7407c6e9591bf463b89d4e53eea9d5ea616fdecfe4fa1.jpg", + "image_caption": [ + "Figure 1. We propose SViT, a sparse video-text transformer for efficient modeling of temporal relationships across video frames. Top: Semantic information for video-text reasoning is highly localized in the spatiotemporal volume, making dense modeling inefficient and prone to contextual noises. Bottom: SViT pursues edge sparsity by limiting query-key pairs in self-attention, and node sparsity by pruning redundant tokens from visual sequence." + ], + "image_footnote": [], + "bbox": [ + 517, + 371, + 875, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "reasoning [4, 9, 18]. Spatial modeling has the advantage of efficient (linear) scaling to long duration videos. Perhaps due to this, single-frame models have proven surprisingly effective at video-text tasks, matching or exceeding prior arts with complex temporal components [9, 24]. However, spatial modeling creates a bias towards static appearance and overlooks the importance of temporal reasoning in videos. This suggests the question: Are temporal dynamics not worth modeling in the video-language domain?", + "bbox": [ + 496, + 669, + 890, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Upon a closer investigation, we identify a few key challenges to incorporating multi-frame reasoning in video-language models. First, limited model size implies a tradeoff between spatial and temporal learning (a classic example being 2D/3D convolutions in video CNNs [46]). For any given dataset, optimal performance requires a careful bal", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at Intel Labs.", + "bbox": [ + 94, + 886, + 341, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18919", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ance between the two. Second, long-term video models typically have larger model sizes and are more prone to overfitting. Hence, for longer term video models, it becomes more important to carefully allocate parameters and control model growth. Finally, even if extending the clip length improves the results, it is subject to diminishing returns since the amount of information provided by a video clip does not grow linearly with its sampling rate. If the model size is not controlled, the computational increase may not justify the gains in accuracy. This is critical for transformer-based architectures, since self-attention mechanisms have a quadratic memory and time cost with respect to input length. In summary, model complexity should be adjusted adaptively, depending on the input videos, to achieve the best trade-off between spatial representation, temporal representation, overfitting potential, and complexity. Since existing video-text models lack this ability, they either attain a suboptimal balance between spatial and temporal modeling, or do not learn meaningful temporal representations at all.", + "bbox": [ + 76, + 90, + 472, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motivated by these findings, we argue that video-text models should learn to allocate modeling resources to the video data. We hypothesize that, rather than uniformly extending the model to longer clips, the allocation of these resources to the relevant spatiotemporal locations of the video is crucial for efficient learning from long clips. For transformer models, this allocation is naturally performed by pruning redundant attention connections. We then propose to accomplish these goals by exploring transformer sparsification techniques. This motivates the introduction of a Sparse Video-Text Transformer (SViTT) inspired by graph models. As illustrated in Fig. 1, SViTT treats video tokens as graph vertices, and self-attention patterns as edges that connect them. We design SViTT to pursue sparsity for both: edge sparsity aims at reducing query-key pairs in attention module while maintaining its global reasoning capability; node sparsity reduces to identifying informative tokens (e.g., corresponding to moving objects or person in the foreground) and pruning background feature embeddings. To address the diminishing returns for longer input clips, we propose to train SViTT with temporal sparse expansion, a curriculum learning strategy that increases clip length and model sparsity, in sync, at each training stage.", + "bbox": [ + 76, + 380, + 472, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SViTT is evaluated on diverse video-text benchmarks from video retrieval to question answering, comparing to prior arts and our own dense modeling baselines. First, we perform a series of ablation studies to understand the benefit of sparse modeling in transformers. Interestingly, we find that both nodes (tokens) and edges (attention) can be pruned drastically at inference, with a small impact on test performance. In fact, token selection using cross-modal attention improves retrieval results by $1\\%$ without re-training.", + "bbox": [ + 76, + 731, + 472, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We next perform full pre-training with the sparse models and evaluate their downstream performance. We observe", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that SViTT scales well to longer input clips where the accuracy of dense transformers drops due to optimization difficulties. On all video-text benchmarks, SViTT reports comparable or better performance than their dense counterparts with lower computational cost, outperforming prior arts including those trained with additional image-text corpora.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key contributions of this work are: 1) a video-text architecture SViTT that unifies edge and node sparsity; 2) a sparse expansion curriculum for training SViTT on long video clips; and 3) empirical results that demonstrate its temporal modeling efficacy on video-language tasks.", + "bbox": [ + 496, + 181, + 893, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 268, + 640, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video-language pretraining. Vision-language pretraining has been widely adopted for various video-text downstream tasks. VideoBERT [45] was an early effort, using video-text pretraining for action classification and video captioning. Recently, the massive-scale instructional video dataset HowTo100M [39] has motivated many approaches to video-text pretraining [4, 19, 24, 38, 56, 57]. Frozen [4] proposed to pretrain a space-time transformer on a combination of video and image data to enable zero-shot text-to-video retrieval. ATP [9] and Singularity [24] showed strong performance using image-based models, highlighting the importance of spatial modeling for video-language tasks. In this work, we pursue an alternative route of efficient temporal modeling across multiple video frames.", + "bbox": [ + 496, + 289, + 893, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Sparse transformers. The self-attention of naive transformers [16, 48] has quadratic complexity making them inefficient for modeling long sequences. Different forms of sparse attention have been studied to improve text [7, 13, 55], image [15, 32, 47], and video modeling [3, 8, 33], although the sparse patterns are typically predetermined and do not adapt to the input semantics. Several works have also considered speeding up vision transformers by adaptively reducing the number of input tokens [11, 30, 37, 41, 42, 53]. For example, DynamicViT [41] proposed to drop visual tokens with a dedicated module that identifies and prunes less informative ones. TokenLearner [42] introduces a learnable module to adaptively generate a small subset of tokens from input frames. EViT [30] progressively reduces the number of tokens based on their attention scores, fusing inattentive tokens into a new token to preserve input information. Unlike prior works that focus on visual modeling on images or videos alone, we study the sparsity of video-language transformers which can benefit from cross-modal attention.", + "bbox": [ + 496, + 505, + 893, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Exploiting Sparsity in Video Transformers", + "text_level": 1, + "bbox": [ + 498, + 803, + 879, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we formulate video transformers as graph models (Sec. 3.1) and present a set of approaches towards sparse video modeling, exploiting the redundancy of edges (Sec. 3.2) and nodes (Sec. 3.3). We combine these into a unified sparse framework for video-text learning (Sec. 3.4).", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18920", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/600d9c822f8a1501df6e9302e0b41b2a828001dcda42de457cf87a74c04e7fa2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 88, + 872, + 271 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/28f24f691c9c9098e6abd4a586cc7e627f09ca5d7a91ee2259818c951fa6a83b.jpg", + "image_caption": [ + "Figure 2. Model Architecture. SViT improves modeling efficiency of conventional video-text transformers through two key components: node sparsity and edge sparsity. Edge sparsification $\\mathcal{A}_{\\varepsilon}$ computes sparse self-attention of input visual sequence $\\mathbf{z}$ , where each query token attends to a small subset of key and value tokens, with connectivity $\\mathcal{E}$ specified by global, local, and random attention. Node sparsification $S_{\\nu}$ uses global attention scores from $\\mathcal{A}_{\\varepsilon}$ to prune uninformative tokens, removing them from the computational graph of subsequent layers; $S_{\\mathcal{M}}$ uses text-to-video attention in the multimodal encoder to further reduce the length of visual sequence." + ], + "image_footnote": [], + "bbox": [ + 83, + 273, + 478, + 401 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/362a5d2966257b1b22e43d849893cf7612b15c3a3420f64a61fb2e58c0350404.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 273, + 883, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Video Transformers are Graph Models", + "text_level": 1, + "bbox": [ + 76, + 493, + 413, + 510 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual transformers [16] are deep neural networks that model images or videos as sequences of local pixel patches, through a combination of patchwise feature transformation and self-attention. Inspired by transformer architectures for language models [48], video transformers encode input clips into a sequence of spatiotemporal patches, flattened and linearly projected to a $d$ -dimensional embedding space:", + "bbox": [ + 75, + 513, + 470, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} ^ {(0)} = \\left(\\mathbf {z} _ {\\text {c l s}} ^ {(0)}, \\mathbf {z} _ {1} ^ {(0)}, \\dots , \\mathbf {z} _ {N} ^ {(0)}\\right) = f ^ {\\operatorname {t o k}} \\left(\\mathbf {x} _ {1: T}\\right) \\in \\mathbb {R} ^ {(N + 1) \\times d} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 631, + 468, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $N = T^{\\prime}H^{\\prime}W^{\\prime}$ is the volume of the 3D patch grid, and $\\mathbf{z}_{\\mathrm{cls}}^{(0)}$ denotes a special class token responsible for instance-level prediction. The tokenized sequence is processed by a cascade of transformer blocks $f^{(l)}$", + "bbox": [ + 75, + 670, + 470, + 734 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} ^ {(l)} = f ^ {(l)} \\left(\\mathbf {Z} ^ {(l - 1)}\\right), \\quad l = 1, \\dots , L \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 743, + 468, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "each of which computes the self-attention $\\mathcal{A}$ between input tokens, followed by a feed-forward network $\\mathcal{F}$ :", + "bbox": [ + 75, + 775, + 468, + 805 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {(l)} (\\mathbf {Z}) = \\mathcal {F} \\left(\\mathcal {A} \\left(\\mathbf {Z} \\mathbf {W} _ {K} ^ {T}, \\mathbf {Z} \\mathbf {W} _ {Q} ^ {T}, \\mathbf {Z} \\mathbf {W} _ {V} ^ {T}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 816, + 468, + 837 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\sigma (\\mathbf {Q} \\mathbf {K} ^ {T}) \\mathbf {V} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 843, + 468, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We interpret the transformer architecture as a special case of graph networks [6], with nodes representing tokenized video patches and edges connecting pairs of tokens for which self-attention is computed. Specifically, consider a directed graph $\\mathcal{G} = (\\mathcal{V},\\mathcal{E})$ defined by the vertices $\\mathcal{V} = \\{\\mathbf{z}_1,\\dots ,\\mathbf{z}_N\\}$ corresponding to spatiotemporal video patches, and edges $\\mathcal{E}\\subseteq \\{1,\\ldots ,N\\} ^2$ connecting pairs of nodes. The self-attention of (4) can be generalized such that node $\\mathbf{z}_i$ attends to $\\mathbf{z}_j$ only if $(i,j)\\in \\mathcal{E}$ ,", + "bbox": [ + 496, + 494, + 893, + 631 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {A} _ {\\mathcal {E}} \\left(\\mathbf {q} _ {i}, \\mathbf {K}, \\mathbf {V}\\right) = \\sum_ {j: (i, j) \\in \\mathcal {E}} \\mathbf {a} _ {i j} \\mathbf {v} _ {j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 586, + 642, + 890, + 678 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {i j} = \\frac {e ^ {\\langle \\mathbf {q} _ {i} , \\mathbf {k} _ {j} \\rangle}}{\\sum_ {j : (i , j) \\in \\mathcal {E}} e ^ {\\langle \\mathbf {q} _ {i} , \\mathbf {k} _ {j} \\rangle}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 685, + 890, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Under this interpretation, the transformer architecture with full attention resembles a complete graph, where $\\mathcal{E}$ includes every pair of vertices. This dense attention mechanism endows (5) with quadratic memory and time complexity w.r.t. sequence length $N$ , making naive transformers notoriously inefficient to train and expensive to deploy, especially for longer video clips. We argue that due to the inherent sparsity of information in video data, a large portion of the graph can be pruned dynamically without significant performance loss, leading to a sparse graph model of significantly lower cost for training and inference.", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1Attention heads, residual connections and normalization terms are omitted for brevity, although we use the conventional implementation [48].", + "bbox": [ + 76, + 875, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18921", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Edge Sparsity: Local & Random Attention", + "text_level": 1, + "bbox": [ + 76, + 90, + 442, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Prior natural language processing models, such as BigBird [55], have explored the idea of restricting the number of key-value pairs each query token attends to, which reduced the number of edges in $\\mathcal{E}$ . We use a similar procedure to create a video transformer with edge sparsity, utilizing a combination of local, random and global attention.", + "bbox": [ + 75, + 109, + 468, + 202 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Local attention. Regional tokens $\\{\\mathbf{z}_i\\}_{i=1}^N$ are first chunked into $N_b = \\lceil N / G \\rceil$ contiguous blocks of size $G^2$ . Tokens of one block $k$ attend to a local neighborhood of $K_l$ blocks $\\{k - \\Delta, \\dots, k + \\Delta\\}$ , where $\\Delta = (K_l - 1) / 2$ is the maximum range of local attention,", + "bbox": [ + 75, + 205, + 470, + 284 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(k, k ^ {\\prime}) \\in \\mathcal {E}, \\quad \\forall k, k ^ {\\prime}: | k ^ {\\prime} - k | \\leq \\Delta \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 295, + 468, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This preserves the modeling of interactions between local features (objects, people, textures) that does not require long-range attention. In the case of $K_{l} = 1$ , local reduces to diagonal attention, where each block only attends to itself.", + "bbox": [ + 75, + 325, + 468, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Random attention. Beyond local attention, each block also attends to $K_{r}$ other blocks sampled randomly from the input sequence,", + "bbox": [ + 75, + 391, + 468, + 438 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left(k, k ^ {\\prime}\\right) \\in \\mathcal {E}, \\quad \\forall k ^ {\\prime} \\in \\mathcal {N} (k) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 449, + 468, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{N}(k)$ is a random subset of $\\{k' \\mid |k' - k| > \\Delta\\}$ of size $K_r$ . This enables the transformer to model long-range visual relationships while avoiding the quadratic cost.", + "bbox": [ + 75, + 478, + 468, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Global attention. Class token $\\mathbf{z}_{\\mathrm{cls}}$ always attends to/from regional tokens $\\mathbf{z}_i$ , i.e. the link between $\\mathbf{q}_{\\mathrm{cls}}$ and $\\mathbf{k}_i$ , as well as $\\mathbf{q}_i$ and $\\mathbf{k}_{\\mathrm{cls}}$ , are always retained:", + "bbox": [ + 75, + 530, + 468, + 578 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n(\\operatorname {c l s}, i), (i, \\operatorname {c l s}) \\in \\mathcal {E}, \\quad i = 1, \\dots , N \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 589, + 468, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This enables $\\mathbf{z}_{\\mathrm{cls}}$ to capture global video context, even when the rest of tokens do not attend globally.", + "bbox": [ + 75, + 618, + 468, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In summary, we retain all attention connections for local-to-global and global-to-local vertices, and limit local-to-local edges to $(K_l + K_r)G$ per token. Edge sparsity has a linear asymptotic cost of $O\\big((K_l + K_r)GN\\big)$ , a significant improvement over dense attention at $O(N^2)$ . However, this approach has two critical limitations of this strategy. First, the sparse patterns are predetermined and do not adapt dynamically to the input sequence. Second, the connections that remain in $\\mathcal{E}$ are not determined by the video semantics. In result, connections between pairs of tokens of low semantic affinity (low attention values) may be preserved, impairing the efficiency of the sparse attention mechanism. To enable more aggressive sparsification, we introduce a second mechanism, which is dynamic, guided by video semantics, and applied to the nodes of the graph.", + "bbox": [ + 75, + 648, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Node Sparsity: Dynamic Token Pruning", + "text_level": 1, + "bbox": [ + 500, + 90, + 844, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A large percentage of the tokens of a video transformer corresponds to contextual regions, which contain little temporal dynamics and are only weakly related to the prediction target (e.g. background content uninformative of the activities of subjects in the foreground). While edge sparsification improves the efficiency of self-attention, it lacks both the flexibility and the semantic sensitivity to account for the uneven distribution of information across video patches.", + "bbox": [ + 496, + 109, + 890, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To introduce these properties, we propose a node sparsification strategy, based on the dynamic pruning of tokens. We leverage a combination of observations. First, video semantics are summarized by the class tokens $\\mathbf{z}_{\\mathrm{cls}}$ , which contain a global representation of the information of interest for classification. Second the global-to-local edges survive the edge sparsification, through (9), making the attention weights from the $\\mathbf{z}_{\\mathrm{cls}}$ to all regional tokens $\\mathbf{z}_i$ ,", + "bbox": [ + 496, + 231, + 890, + 351 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} \\left(\\mathbf {z} _ {i}\\right) = \\frac {e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} , \\mathbf {k} _ {i} \\rangle}}{\\sum_ {j = 1} ^ {N} e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}}, \\mathbf {k} _ {j} \\rangle}}, \\quad i = 1, \\dots , N \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 358, + 890, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "available for node sparsification. Since the class token is used for video-level predictions, $\\mathbf{a}(\\mathbf{z}_i)$ quantifies the contribution of feature $\\mathbf{z}_i$ to the main task. This implies that nodes $\\mathbf{z}_i$ of low $\\mathbf{a}(\\mathbf{z}_i)$ are not informative and can be ignored [30].", + "bbox": [ + 496, + 404, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Node pruning then reduces to keeping the $N' = \\lceil qN \\rceil$ tokens of largest class attention", + "bbox": [ + 496, + 465, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\mathcal {V}} (\\mathbf {Z}; q) = \\left\\{\\mathbf {z} _ {i} \\mid i \\in \\operatorname {t o p k} (\\mathbf {a} (\\mathbf {Z}), \\lceil q N \\rceil) \\right\\} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 503, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where hyperparameter $q$ denotes keep rate and topk(L, m) selects the $m$ largest entries of vector $\\mathbf{L}$ . This procedure is repeated multiple times throughout the video encoder (keep rate $q^{(l)}$ at layer $l$ ), progressively reducing the length of input sequences. Importantly, the pruning procedure is dynamic and ensures that semantically uninformative vertices in the attention graph $\\mathcal{G}$ are removed along with all edges they are associated with.", + "bbox": [ + 496, + 527, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-modal sparsity. Node sparsification can be naturally extended to video-language learning. For this, we propose to extend the token selection mechanism discussed above to a cross-modal setting, where video and text tokens $\\mathbf{Z}_v,\\mathbf{Z}_t$ are modeled jointly in a multimodal encoder. In this case, we replace the query $\\mathbf{q}_{\\mathrm{cls}}$ of (10) with the class token of text sequence $\\mathbf{q}_{\\mathrm{cls}}^{(t)}$ , obtaining cross-modal attention", + "bbox": [ + 496, + 652, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {a} _ {m} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) = \\frac {e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} ^ {(t)} , \\mathbf {k} _ {i} ^ {(v)} \\rangle}}{\\sum_ {j = 1} ^ {N} e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} ^ {(t)} , \\mathbf {k} _ {j} ^ {(v)} \\rangle}}, \\quad i = 1, \\dots , N \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 768, + 890, + 813 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and subsequently the token sparsification function", + "bbox": [ + 500, + 820, + 831, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {S} _ {\\mathcal {M}} \\left(\\mathbf {Z} _ {v}; q\\right) = \\left\\{\\mathbf {z} _ {i} ^ {(v)} \\mid i \\in \\operatorname {t o p k} \\left(\\mathbf {a} _ {m} \\left(\\mathbf {Z} _ {v}\\right), \\lceil q N \\rceil\\right) \\right\\} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 843, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Multimodal node sparsity $S_{\\mathcal{M}}$ is applied on top of visual sparsity $\\mathcal{S}_{\\mathcal{V}}$ . We expect cross-modal sparsification to create", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2 Padding is added when $N$ is not divisible by $G$ .", + "bbox": [ + 94, + 886, + 354, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18922", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "additional room for sparsity over standalone visual modeling. While the visual encoder can identify salient actors and objects from background patches from the input clip, only the text semantics provide direct guidance for the video-text model to focus on regions relevant to the task of interest.", + "bbox": [ + 75, + 90, + 468, + 166 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With node sparsity, the compute cost of subsequent layers is improved to $O(q^{2}N^{2})$ using dense attention or $O(q(K_{l} + K_{r})GN)$ with edge sparsity, and the reduction accumulates with multiple sparse layers.", + "bbox": [ + 76, + 167, + 470, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Hybrid Sparse Transformers", + "text_level": 1, + "bbox": [ + 76, + 237, + 334, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose to combine edge and node sparsity into a unified framework, SViT, as illustrated in Fig. 2. SViT is built on top of existing video-language transformer architectures that combine separate video and text encoders with a cross-modal transformer. The visual encoder blocks perform sparse self-attention in the following steps:", + "bbox": [ + 75, + 256, + 468, + 348 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- edge sparsification: given the random graph $\\mathcal{E}$ of (7)-(9) compute attention weights $\\mathcal{A}_{\\mathcal{E}}$ , using (5);", + "- node sparsification: select the nodes $\\mathcal{S}_{\\mathcal{V}}$ to retain, using (10)-(11) with keep rate $q < 1$ ." + ], + "bbox": [ + 94, + 354, + 468, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After video and text embeddings $\\mathbf{z}_v, \\mathbf{z}_t$ are derived from their respective encoders, a multimodal transformer is applied to aggregate features across modalities. It follows the design of the text encoder, except for a cross-attention module that is applied after each self-attention block, where text queries $\\mathbf{q}_t$ attends to key-value pairs $\\mathbf{k}_v, \\mathbf{v}_v$ extracted by the video encoder. The text-to-video attention of (12)-(13) is then used to select the nodes $S_{\\mathcal{M}}$ to retain, further reducing the number of video tokens for subsequent layers.", + "bbox": [ + 75, + 430, + 468, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Temporal Sparse Expansion", + "text_level": 1, + "bbox": [ + 76, + 577, + 336, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we introduce a new training strategy for SViTT. We motivate for progressive model training with increasing clip length and sparsity in Sec. 4.1, and detail our pretraining procedure in Sec. 4.2.", + "bbox": [ + 75, + 599, + 468, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Sparsity vs. Clip Length", + "text_level": 1, + "bbox": [ + 76, + 669, + 302, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The key insight behind the design of SViT is the diminishing return of clip length. In general, a $2 \\times$ longer sequence does not contain twice the semantic information about the video, due to the redundancy of adjacent frames. This leads to a lower percentage of informative patches with denser frame sampling.", + "bbox": [ + 75, + 688, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Due to this redundancy, it is possible to use higher sparsity for models with longer clips. This can be implemented by reducing the keep rate $q$ of node sparsification, and the percentage of key/value blocks to attend to in edge sparsification $(K_{l} / N_{b}, K_{r} / N_{b})$ . For the latter, since the total number of blocks $N_{b} = \\lceil N / G \\rceil$ increases with number of frames $T$ (assuming a fixed block size $G$ ), it suffices to keep the parameters $K_{l}, K_{r}$ constant.", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/af888be5dacddd1db474f9d0a29b49cf30ae8606d744c1567f4e817d74d8c8d6.jpg", + "image_caption": [ + "Figure 3. Temporal Sparse Expansion. We propose a multi-stage curriculum for training SViTT. At each stage, the node and edge sparsity $S$ of video-text transformer increases with clip length $T$ ." + ], + "image_footnote": [], + "bbox": [ + 500, + 87, + 890, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Temporal Expansion", + "text_level": 1, + "bbox": [ + 498, + 248, + 694, + 265 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pretraining video-text transformers on long clips is time-consuming and leads to suboptimal models. Instead, we follow a learning strategy similar to Frozen [4], where the model is initially pretrained with shorter clips, and the number of frames increases as training progresses. However, when expanding the clip length, we increase the model sparsity to simultaneously 1) account for the redundancy of information, and 2) limit the growth of computational cost.", + "bbox": [ + 496, + 267, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 3 depicts the expansion process proposed for video-text training. In the initial training stage $j = 1$ , a dense video-text model is pretrained on clip length $T_{1}$ . Denoting the sparsity hyperparameters of SViTT at stage $j$ by $S_{j} = (q_{j}, K_{l}^{(j)}, K_{r}^{(j)})$ , we create a learning curriculum with progressively increasing clip length and sparsity, by enforcing the constraints", + "bbox": [ + 496, + 388, + 890, + 496 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT _ {1} < T _ {2} < \\dots ; \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 640, + 503, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq _ {1} > q _ {2} > \\dots ; \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 643, + 523, + 890, + 537 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {K _ {l} ^ {(1)} + K _ {r} ^ {(1)}}{T _ {1}} > \\frac {K _ {l} ^ {(2)} + K _ {r} ^ {(2)}}{T _ {2}} > \\dots \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 541, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, we use a decreasing token keep rate (15) and keep local and random attention block numbers fixed, i.e. $K_{l}^{(j)} = K_{l}$ and $K_{r}^{(j)} = K_{r}$ , to satisfy (16).", + "bbox": [ + 500, + 582, + 890, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 500, + 638, + 584, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section we present experimental results of SViTT on vision-language modeling. We briefly introduce the experimental setup in Sec. 5.1, and perform several ablation studies on the design choices involving model sparsification and training in Sec. 5.2. We then demonstrate the performance of SViTT on various vision-language tasks in Sec. 5.3 and include additional qualitative analysis.", + "bbox": [ + 496, + 661, + 890, + 766 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 775, + 689, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Architecture. Our implementation of video-text transformer is based on Singularity [24]. The model has a two-tower structure, with separate encoders for vision and language. The video encoder $f_{v}$ is a 12-layer BEiT-B [5] initialized with ImageNet weights and inflated for video inputs. This differs from [24] which embeds each frame independently and applies late temporal fusion on extracted", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18923", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/19d3e48effd00dfc984e4b471c1590728f8c940bb98046c60ed0eb505e6ec863.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Attn. blocks\nKl, Kr, GKeep rate\nqv, qm# Edges\n(M)R1DiDeMo\nR5R10Mean
——7.4728.853.163.048.3
Edge sparsity
(1, 3, 56)—2.1420.741.750.537.6
(1, 5, 56)—3.2126.048.656.843.8
Node sparsity
—(0.7, 1)3.9926.951.961.346.7
—(0.7, 0.1)3.9727.653.162.947.9
Hybrid sparsity
(1, 3, 56)(0.7, 0.1)1.4819.940.550.637.0
(1, 5, 56)(0.7, 0.1)2.2224.547.658.643.6
", + "bbox": [ + 81, + 88, + 467, + 287 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/175eaeb13b8422b3fd00e0dd949245b26eba9669ea26264456c378b65f5a6112.jpg", + "image_caption": [ + "(a) Number of local / random blocks." + ], + "image_footnote": [], + "bbox": [ + 86, + 328, + 267, + 417 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d3c8e7f2c943fddd658086fc8e2a8b4a4b75074608c0235b7711597a91ae9c5f.jpg", + "image_caption": [ + "(b) Attention block size.", + "Figure 4. Ablation on Edge Sparsity. We evaluate dense model using different local/random blocks $(K_l, K_r)$ and block size $G$ ." + ], + "image_footnote": [], + "bbox": [ + 282, + 328, + 455, + 417 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "features. The text encoder $f_{t}$ is a pretrained BERT [14] model, whose last 3 layers are modified to implement the multimodal encoder $f_{m}$ , with cross-modal attention based on visual tokens as key-value pairs, which we sparsify as described in Sec. 3.3.", + "bbox": [ + 75, + 476, + 468, + 551 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-training. SViTT is pre-trained on 2.5M video-text pairs from the WebVid dataset [4]. Since our goal is to investigate how to improve the effectiveness of the temporal learning of the video modality, we do not train with additional image-text corpora as done in [4, 18, 24].", + "bbox": [ + 75, + 559, + 468, + 635 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The [cls] tokens of the video and text encoders are first linearly projected to a joint embedding space, producing feature vectors $\\mathbf{z}_v = f_v(\\mathbf{x}_v)$ and $\\mathbf{z}_t = f_t(\\mathbf{x}_t)$ , respectively. Following prior work, we use the InfoNCE loss [40] to align these feature vectors. The output of multimodal encoder $\\mathbf{y} = f_m(\\mathbf{z}_v,\\mathbf{z}_t)$ is optimized with video-text matching (VTM) and masked language modeling (MLM) losses commonly found in VLP literature [12, 18, 24, 27, 28].", + "bbox": [ + 75, + 635, + 468, + 756 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Downstream tasks. Trained video-text models are evaluated on two multimodal tasks: Text-to-video retrieval and video question answering. Video retrieval is evaluated on MSR-VTT [51], DiDeMo [2], Charades [43] and Something-Something v2 [20, 24], by top- $K$ recalls $(K \\in \\{1, 5, 10\\})$ and their numeric average. Question answering is evaluated on MSRVTT-QA [49], ActivityNet-QA [10, 54] and AGQA [21], with top-1 accuracy of the answers.", + "bbox": [ + 75, + 763, + 468, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details are given in the Appendix.", + "bbox": [ + 96, + 885, + 379, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/129ba4e2f683053319b087f8043d162810fe456600805ec526999defcfba5e4b.jpg", + "table_caption": [ + "Table 1. Ablation on Edge and Node Sparsity. We evaluate the same dense video-text model under different sparsification modes." + ], + "table_footnote": [], + "table_body": "
TSparc.FLOPs (G)Mem. (GB)R1DiDeMoMean
R5R10
4Dense139.90.9628.853.163.048.3
Edge135.90.8028.351.961.447.2
Node95.80.6129.954.863.949.6
Hybrid93.90.5429.353.763.248.8
8Dense291.33.1429.654.164.149.3
Edge271.81.5729.854.965.450.1
Node197.61.7730.455.766.050.7
Hybrid166.40.9231.057.266.351.5
16Dense627.810.66Untrainable
Edge543.63.0231.655.164.650.5
Node370.94.39Untrainable
Hybrid296.21.5731.457.367.852.2
", + "bbox": [ + 504, + 88, + 890, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Ablation on Training Sparse Models. We compare the zero-shot performance, inference GFLOPs, and training memory (per sample) of sparse models to the dense attention baseline.", + "bbox": [ + 498, + 313, + 890, + 356 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e75c9b70a5e20a60840325a0dc06183f10051d55b57bc5321b8f748cc3e466cb.jpg", + "image_caption": [ + "(a) Visual sparsification.", + "Figure 5. Ablation on Node Sparsity. We evaluate the pre-trained dense model using different keep rates $q$ at test time." + ], + "image_footnote": [], + "bbox": [ + 509, + 362, + 687, + 452 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a93d340808f3d944e33e31d0ef36d24f4048bdaebc85e33c0e8b76efef93881.jpg", + "image_caption": [ + "(b) Multimodal sparsification." + ], + "image_footnote": [], + "bbox": [ + 709, + 362, + 875, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 510, + 663, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We start by training a video-text transformer with clip length of 4 frames and dense attention, and measure its zero-shot performance on downstream tasks after sparsifying its video encoder while keeping its weights unchanged.", + "bbox": [ + 496, + 530, + 890, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Edge sparsification. We first apply edge sparsification with different number of local blocks $K_{l}$ , random blocks $K_{r}$ , and block size $G$ . As shown in Fig. 4a, under a limited budget of 6 local or random attention blocks per query token, using 1 local block and 5 random blocks provides the best trade-off. Increasing the local attention window $K_{l}$ hurts long-term modeling capacity and degrades retrieval; while removing the single local block responsible for diagonal attention also impairs performance. This suggests that while query tokens should always attend to their respective blocks, there is no benefit in attending to neighboring blocks. We thus fix $K_{l} = 1$ for the rest of experiments.", + "bbox": [ + 496, + 598, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We next vary the block size $G$ of sparse attention. Fig. 4b shows that larger sizes have stronger retrieval performance, as expected. However, they also make self-attention less sparse (more costly to compute). $G = 56$ provides a good balance between performance and complexity. Tab. 1 summarizes the test performance of two edge sparsity config: $(K_{l}, K_{r}, G) = (1, 3, 56)$ and $(1, 5, 56)$ . While both underperform the dense model, we will later demonstrate that the", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18924", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/44f596c31292f515053ec3dd56fbc6b596e8542485d0480ce36d9742009b51d9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
FramesTSparsityTSDiDeMo
R1R5R10Mean
44.8028.050.759.246.0
10→4.8029.353.763.248.8
88.9127.351.463.847.5
4.80→8.9131.057.266.351.5
1616.9627.552.463.247.7
4.80→8.91→16.9631.457.367.852.2
", + "bbox": [ + 81, + 88, + 467, + 226 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "gap can be closed and even reversed by training the sparse model with the proposed temporal expansion curriculum.", + "bbox": [ + 75, + 282, + 468, + 314 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Node sparsification. We next incorporate node sparsity into the video-text transformer. This includes visual sparsification (keep rate $q_{v}$ ) using the self-attention of video encoder $f_{v}$ to progressively prune the input tokens $^{3}$ , and multimodal sparsification (keep rate $q_{m}$ ) using the text-to-video attention of cross-modal encoder $f_{m}$ to further drop visual tokens unrelated to the text query. Fig. 5a shows that the dense model is quite robust to token pruning, even without sparse training. Using visual keep rate $q_{v} \\geq 0.8$ has minimal impact on test results, and performance only starts to drop rapidly at $q_{v} = 0.5$ , at which point only $1/8$ of input tokens are retained after three rounds of sparsification.", + "bbox": [ + 75, + 319, + 468, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Even more surprisingly, the subsequent multimodal sparsification step, using a keep rate of $q_{m} = 0.1$ , improves zero-shot performance by $1\\%$ . This shows that the $90\\%$ redundant visual tokens not only add unnecessary complexity to the model, but also introduce noise that harms retrieval performance. The fact that the optimal $q_{m}$ is much lower than $q_{v}$ also suggests that text modality provides crucial semantic guidance for identifying relevant visual patches, at a much higher accuracy than visual modeling alone.", + "bbox": [ + 75, + 501, + 468, + 637 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Hybrid sparsification. Combining the best sparse settings for edges and nodes, we obtain the hybrid sparsification strategy for SViT. As shown in Tab. 1, compared to edge sparsity, the introduction of node sparsity $(q_{v} = 0.7, q_{m} = 0.1)$ only impacts recall scores marginally, while saving computations on a large portion of visual tokens throughout the network.", + "bbox": [ + 75, + 643, + 468, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training sparse transformers. We next perform full pretraining with the sparse models and compare their performance and efficiency to the dense transformer baseline. Tab. 2 summarizes the results obtained with different input clip lengths and types of sparsity. At 4 frames, edge sparsity has small benefit due to the relatively short sequence length and node sparsity performs the best. However, at 8 frames, we start to see clear advantages to edge sparsity in memory", + "bbox": [ + 75, + 753, + 468, + 876 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ab773a7506a1d7afee11659736a097927ef6cac2baf4075e2b903e35fc7b27f4.jpg", + "table_caption": [ + "Table 3. Ablation on Temporal Sparse Expansion. Sparsity $T_{S}$ indicates training on $T$ frames while removing $S \\times 100\\%$ attention edges of dense transformer." + ], + "table_footnote": [], + "table_body": "
MethodPTTMSR-VTTDiDeMo
R1MeanR1Mean
VideoCLIP [50]100M—10.420.916.6—
Frozen [4]5M423.241.521.141.1
ALPRO [26]5M824.141.423.843.0
VIOLET [18]5M425.945.023.544.4
Singularity [24]5M128.446.036.955.8
121.138.723.340.8
Singularity*2M424.440.026.444.1
824.341.025.845.5
SViTTDense Hybrid2M826.043.629.649.3
25.443.831.051.5
", + "bbox": [ + 504, + 88, + 893, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Zero-shot Text-to-video Retrieval. Results reported in prior works are marked in gray; * indicates our reproduced results. PT = # video-text pairs for pre-training, $T = \\#$ frames per clip.", + "bbox": [ + 498, + 277, + 890, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "complexity, and both edge and node sparsity outperform the dense transformer baseline. Combining both types of sparsity performs the best, while only requiring $60\\%$ the FLOPs and $30\\%$ the memory of the dense model. At 16 frames, the dense and node sparsity models are no longer trainable due to their quadratically increasing cost. The models with edge sparsity, however, are able to fit into GPU memory thanks to the linear complexity from sparse attention. A 16-frame SViTT with hybrid sparsity requires similar computation to an 8-frame dense model and only half of its training memory, while achieving $3\\%$ higher recall.", + "bbox": [ + 496, + 329, + 890, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Progressive training. We next study the impact of temporal sparse expansion on the training of SViT models on longer clips. Tab. 3 compares the performance of models trained using temporal expansion (i.e. initialized from checkpoints pretrained on fewer frames and lower sparsity) to standard single-stage training. For single-stage training, performance does not improve substantially with clip length. This is in contrast to the proposed sparse expansion, where using 8 instead or 4 frames results in a gain of $2.7\\%$ . This suggests that the models have learned to exploit the temporal relationships between video frames. For a given clip length, sparse expansion also substantially improves upon single stage performance, from 2.8 points for $T = 4$ to 4.5 points for $T = 16$ . In fact, sparse expansion training with a shorter clip length (e.g. 4 frames) can outperform single stage training with a larger length (16 frames).", + "bbox": [ + 496, + 501, + 892, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Main Results", + "text_level": 1, + "bbox": [ + 500, + 753, + 638, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare SViT to state-of-the-art models in text-to-video retrieval and video question answering.", + "bbox": [ + 498, + 773, + 890, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Text-to-video retrieval. Video-text retrieval is evaluated under zero-shot and fine-tuning settings. Tab. 4 shows the zero-shot results on MSR-VTT and DiDeMo. Compared to our reproduced models of Singularity on WebVid-2M, which aggregate frame-level features using a temporal transformer encoder, the spatiotemporal transformer", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "3We follow [30] to prune visual tokens at layer #4, #7, and #10.", + "bbox": [ + 94, + 886, + 431, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18925", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26d7637a13dd55a96cc9d03196ab310af085f6b87cd7c8c84b391db2a955803f.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 117, + 104, + 361, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6f1e49cafcdfe44a43d9a987b9f8f239c0798861c274dd511f0aff506007747d.jpg", + "image_caption": [ + "Visual, $q_{v} = 0.6$", + "Figure 6. Qualitative Results. SViTT isolates informative regions from background patches to facilitate efficient temporal reasoning." + ], + "image_footnote": [], + "bbox": [ + 364, + 104, + 606, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aacaa1aa7c7328c711fc1d11fd7e61a76a0c0684441b55e81a0f160eb27bce8e.jpg", + "image_caption": [ + "Cross-modal, $q_{m} = 0.1$" + ], + "image_footnote": [], + "bbox": [ + 607, + 104, + 849, + 189 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/db37c251cc174cdc97b5d868cdf1f8ac5e2984258e8d46e3b76e3c31e7e08cde.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPTTCharadesSSv2
R1MeanR1Mean
Frozen [4]5M3211.925.1——
CLIP4Clip [35]400M1213.927.143.165.1
ECLIPSE [31]400M3215.730.3——
\\( MKTVR^† \\)[36]400M4216.634.7——
Singularity [24]5M1——36.458.9
4——44.166.6
SViTTDense Hybrid2M816.032.743.666.1
17.735.749.869.3
", + "bbox": [ + 81, + 234, + 467, + 393 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1ed5da4344188951b23b404328dedb00e8c2d1f6abc061d7bd9a63e4d5529a83.jpg", + "table_caption": [ + "Table 5. Text-to-video Retrieval with Fine-tuning." + ], + "table_footnote": [], + "table_body": "
MethodPTTMSRVTTANetAGQA
HME [17]—2033.0—47.7
HCRN [23]12835.5—47.4
ClipBERT [25]0.2M1637.4——
ALPRO [26]5M1642.1——
Just Ask [52]69M64041.538.9—
MERLOT [56]180M543.141.4—
VIOLET [18]185M443.9—49.2
Singularity [24]5M142.741.8—
SViTTDense Hybrid2M842.742.350.2
43.043.252.7
", + "bbox": [ + 81, + 419, + 467, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Video Question Answering.", + "bbox": [ + 158, + 593, + 387, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of SViTT produces stronger results on both downstream datasets. This highlights the importance of temporal modeling in earlier layers of video-text transformers. SViTT with hybrid sparsity has similar performance to the dense model on MSR-VTT but significantly outperforms in on DiDeMo, which contains longer videos with localized activities.", + "bbox": [ + 75, + 616, + 468, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For Charades and SSv2, we evaluate text-to-video retrieval with fine-tuning, as shown in Tab. 5. Both datasets are action-centric, posing a greater challenge to the temporal reasoning of video-text models. SViT with hybrid sparsification dominates the dense variant by $\\sim 3\\%$ on both datasets, a more substantial gap than observed for MSR-VTT and DiDeMo. This confirms our hypothesis that exploiting node and edge sparsity reduces the dependency of models on contextual regions, forcing them to focus on the temporal dynamics of person and objects in the foreground.", + "bbox": [ + 75, + 709, + 468, + 861 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Video question answering. We next evaluate the cross-modal modeling of SViT on MSRVTT-QA, ActivityNet", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "QA and AGQA. As shown in Tab. 6, the hybrid sparsity version of SViTT outperforms the dense transformer baseline on all three datasets, thanks to its more efficient temporal modeling. On MSRVTT-QA, the accuracy gap is small between dense and sparse transformer (0.3%), and SViTT marginally underperforms baselines pretrained with fewer number of frames (MERLOT [56], VIOLET [18]). This is likely due to the nature of MSRVTT, which consists of short video clips and questions biased towards spatial cues, allowing temporal modeling little benefit over spatial transformers pretrained on massive image & video data. On ActivityNet-QA and AGQA, which both contain longer clips and temporally challenging questions, the sparse modeling of SViTT proves advantageous, with 0.9% and 2.3% boost in accuracy respectively, beating all baseline methods.", + "bbox": [ + 496, + 238, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative analysis. To show how SViT efficiently identifies and concentrates its computation on informative spatiotemporal regions of the input clips, we visualize the outcome of node sparsification in Fig. 6. Using visual sparsification in video encoder $f_{v}$ , SViT learns to isolate foreground entities from the majority of background patches, enabling the model to perform sparse video-text inference on longer temporal context. Cross-modal attention in multimodal encoder $f_{m}$ provides an even stronger signal for isolating the regions of interest of each video clip, validating the importance of text semantics in visual sparsification.", + "bbox": [ + 496, + 470, + 892, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 646, + 619, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work introduced SViTT, a sparse video-text transformer for efficient reasoning over a long temporal context. By interpreting visual transformers as graph networks, we proposed to optimize their edge and node sparsity, using a combination of sparse block attention, visual token pruning and text-guided token selection. We further introduced a temporal expansion strategy for training SViTT, which aims to gradually increase model sparsity with clip length. SViTT showed strong performance and efficiency compared to dense transformers, with a larger gap when frame number increases. On video retrieval and question answering benchmarks, SViTT achieved state-of-the-art results using only video data, without extra image-text pretraining.", + "bbox": [ + 496, + 667, + 890, + 866 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was funded in part by NSF award IIS-2041009.", + "bbox": [ + 500, + 869, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "header", + "text": "A person is in a living room playing with a book and flipping through the pages, they then leave out the door.", + "bbox": [ + 202, + 87, + 767, + 99 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18926", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8746-8755, 2020. 2" + ], + "bbox": [ + 78, + 90, + 470, + 710 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18929", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/a239fc53-51e4-48aa-8bdd-b397217aa71a_model.json b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/a239fc53-51e4-48aa-8bdd-b397217aa71a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..604a52ac2f5014080fd27994bf8c9f6e3c5cd973 --- /dev/null +++ b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/a239fc53-51e4-48aa-8bdd-b397217aa71a_model.json @@ -0,0 +1,2565 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.165, + 0.131, + 0.806, + 0.154 + ], + "angle": 0, + "content": "SViTT: Temporal Learning of Sparse Video-Text Transformers" + }, + { + "type": "text", + "bbox": [ + 0.209, + 0.175, + 0.76, + 0.194 + ], + "angle": 0, + "content": "Yi Li*1 Kyle Min² Subarna Tripathi² Nuno Vasconcelos¹" + }, + { + "type": "text", + "bbox": [ + 0.361, + 0.199, + 0.611, + 0.218 + ], + "angle": 0, + "content": "\\(^{1}\\)UC San Diego \\(^{2}\\)Intel Labs" + }, + { + "type": "text", + "bbox": [ + 0.158, + 0.22, + 0.804, + 0.235 + ], + "angle": 0, + "content": "{yil898, nvasconcelos}@ucsd.edu {kyle.min, subarna.tripathi}@intel.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.265, + 0.314, + 0.28 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.474, + 0.645 + ], + "angle": 0, + "content": "Do video-text transformers learn to model temporal relationships across frames? Despite their immense capacity and the abundance of multimodal training data, recent work has revealed the strong tendency of video-text models towards frame-based spatial representations, while temporal reasoning remains largely unsolved. In this work, we identify several key challenges in temporal learning of video-text transformers: the spatiotemporal trade-off from limited network size; the curse of dimensionality for multi-frame modeling; and the diminishing returns of semantic information by extending clip length. Guided by these findings, we propose SViTT, a sparse video-text architecture that performs multi-frame reasoning with significantly lower cost than naive transformers with dense attention. Analogous to graph-based networks, SViTT employs two forms of sparsity: edge sparsity that limits the query-key communications between tokens in self-attention, and node sparsity that discards uninformative visual tokens. Trained with a curriculum which increases model sparsity with the clip length, SViTT outperforms dense transformer baselines on multiple video-text retrieval and question answering benchmarks, with a fraction of computational cost. Project page: http://svcl.ucsd.edu/projects/svittt." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.66, + 0.21, + 0.675 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.47, + 0.846 + ], + "angle": 0, + "content": "With the rapid development of deep neural networks for computer vision and natural language processing, there has been growing interest in learning correspondences across the visual and text modalities. A variety of vision-language pretraining frameworks have been proposed [12, 22, 29, 34] for learning high-quality cross-modal representations with weak supervision. Recently, progress on visual transformers (ViT) [5, 16, 32] has enabled seamless integration of both modalities into a unified attention model, leading to image-text transformer architectures that achieve state-the-art performance on vision-language benchmarks [1, 27, 44]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.848, + 0.47, + 0.878 + ], + "angle": 0, + "content": "Progress has also occurred in video-language pretraining by leveraging image-text models for improved frame-based" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.264, + 0.88, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.343, + 0.882, + 0.355 + ], + "angle": 0, + "content": "One person takes a pillow and some homework from an old chair, then smiles and laughs." + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.372, + 0.877, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.661 + ], + "angle": 0, + "content": "Figure 1. We propose SViT, a sparse video-text transformer for efficient modeling of temporal relationships across video frames. Top: Semantic information for video-text reasoning is highly localized in the spatiotemporal volume, making dense modeling inefficient and prone to contextual noises. Bottom: SViT pursues edge sparsity by limiting query-key pairs in self-attention, and node sparsity by pruning redundant tokens from visual sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.892, + 0.807 + ], + "angle": 0, + "content": "reasoning [4, 9, 18]. Spatial modeling has the advantage of efficient (linear) scaling to long duration videos. Perhaps due to this, single-frame models have proven surprisingly effective at video-text tasks, matching or exceeding prior arts with complex temporal components [9, 24]. However, spatial modeling creates a bias towards static appearance and overlooks the importance of temporal reasoning in videos. This suggests the question: Are temporal dynamics not worth modeling in the video-language domain?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Upon a closer investigation, we identify a few key challenges to incorporating multi-frame reasoning in video-language models. First, limited model size implies a tradeoff between spatial and temporal learning (a classic example being 2D/3D convolutions in video CNNs [46]). For any given dataset, optimal performance requires a careful bal" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.343, + 0.9 + ], + "angle": 0, + "content": "*Work done during an internship at Intel Labs." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18919" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.379 + ], + "angle": 0, + "content": "ance between the two. Second, long-term video models typically have larger model sizes and are more prone to overfitting. Hence, for longer term video models, it becomes more important to carefully allocate parameters and control model growth. Finally, even if extending the clip length improves the results, it is subject to diminishing returns since the amount of information provided by a video clip does not grow linearly with its sampling rate. If the model size is not controlled, the computational increase may not justify the gains in accuracy. This is critical for transformer-based architectures, since self-attention mechanisms have a quadratic memory and time cost with respect to input length. In summary, model complexity should be adjusted adaptively, depending on the input videos, to achieve the best trade-off between spatial representation, temporal representation, overfitting potential, and complexity. Since existing video-text models lack this ability, they either attain a suboptimal balance between spatial and temporal modeling, or do not learn meaningful temporal representations at all." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.381, + 0.473, + 0.73 + ], + "angle": 0, + "content": "Motivated by these findings, we argue that video-text models should learn to allocate modeling resources to the video data. We hypothesize that, rather than uniformly extending the model to longer clips, the allocation of these resources to the relevant spatiotemporal locations of the video is crucial for efficient learning from long clips. For transformer models, this allocation is naturally performed by pruning redundant attention connections. We then propose to accomplish these goals by exploring transformer sparsification techniques. This motivates the introduction of a Sparse Video-Text Transformer (SViTT) inspired by graph models. As illustrated in Fig. 1, SViTT treats video tokens as graph vertices, and self-attention patterns as edges that connect them. We design SViTT to pursue sparsity for both: edge sparsity aims at reducing query-key pairs in attention module while maintaining its global reasoning capability; node sparsity reduces to identifying informative tokens (e.g., corresponding to moving objects or person in the foreground) and pruning background feature embeddings. To address the diminishing returns for longer input clips, we propose to train SViTT with temporal sparse expansion, a curriculum learning strategy that increases clip length and model sparsity, in sync, at each training stage." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.732, + 0.473, + 0.868 + ], + "angle": 0, + "content": "SViTT is evaluated on diverse video-text benchmarks from video retrieval to question answering, comparing to prior arts and our own dense modeling baselines. First, we perform a series of ablation studies to understand the benefit of sparse modeling in transformers. Interestingly, we find that both nodes (tokens) and edges (attention) can be pruned drastically at inference, with a small impact on test performance. In fact, token selection using cross-modal attention improves retrieval results by \\(1\\%\\) without re-training." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "We next perform full pre-training with the sparse models and evaluate their downstream performance. We observe" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "that SViTT scales well to longer input clips where the accuracy of dense transformers drops due to optimization difficulties. On all video-text benchmarks, SViTT reports comparable or better performance than their dense counterparts with lower computational cost, outperforming prior arts including those trained with additional image-text corpora." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.895, + 0.259 + ], + "angle": 0, + "content": "The key contributions of this work are: 1) a video-text architecture SViTT that unifies edge and node sparsity; 2) a sparse expansion curriculum for training SViTT on long video clips; and 3) empirical results that demonstrate its temporal modeling efficacy on video-language tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.269, + 0.642, + 0.285 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.29, + 0.895, + 0.502 + ], + "angle": 0, + "content": "Video-language pretraining. Vision-language pretraining has been widely adopted for various video-text downstream tasks. VideoBERT [45] was an early effort, using video-text pretraining for action classification and video captioning. Recently, the massive-scale instructional video dataset HowTo100M [39] has motivated many approaches to video-text pretraining [4, 19, 24, 38, 56, 57]. Frozen [4] proposed to pretrain a space-time transformer on a combination of video and image data to enable zero-shot text-to-video retrieval. ATP [9] and Singularity [24] showed strong performance using image-based models, highlighting the importance of spatial modeling for video-language tasks. In this work, we pursue an alternative route of efficient temporal modeling across multiple video frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.793 + ], + "angle": 0, + "content": "Sparse transformers. The self-attention of naive transformers [16, 48] has quadratic complexity making them inefficient for modeling long sequences. Different forms of sparse attention have been studied to improve text [7, 13, 55], image [15, 32, 47], and video modeling [3, 8, 33], although the sparse patterns are typically predetermined and do not adapt to the input semantics. Several works have also considered speeding up vision transformers by adaptively reducing the number of input tokens [11, 30, 37, 41, 42, 53]. For example, DynamicViT [41] proposed to drop visual tokens with a dedicated module that identifies and prunes less informative ones. TokenLearner [42] introduces a learnable module to adaptively generate a small subset of tokens from input frames. EViT [30] progressively reduces the number of tokens based on their attention scores, fusing inattentive tokens into a new token to preserve input information. Unlike prior works that focus on visual modeling on images or videos alone, we study the sparsity of video-language transformers which can benefit from cross-modal attention." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.804, + 0.88, + 0.822 + ], + "angle": 0, + "content": "3. Exploiting Sparsity in Video Transformers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In this section, we formulate video transformers as graph models (Sec. 3.1) and present a set of approaches towards sparse video modeling, exploiting the redundancy of edges (Sec. 3.2) and nodes (Sec. 3.3). We combine these into a unified sparse framework for video-text learning (Sec. 3.4)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18920" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.874, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.274, + 0.48, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.274, + 0.885, + 0.402 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.414, + 0.895, + 0.485 + ], + "angle": 0, + "content": "Figure 2. Model Architecture. SViT improves modeling efficiency of conventional video-text transformers through two key components: node sparsity and edge sparsity. Edge sparsification \\(\\mathcal{A}_{\\varepsilon}\\) computes sparse self-attention of input visual sequence \\(\\mathbf{z}\\), where each query token attends to a small subset of key and value tokens, with connectivity \\(\\mathcal{E}\\) specified by global, local, and random attention. Node sparsification \\(S_{\\nu}\\) uses global attention scores from \\(\\mathcal{A}_{\\varepsilon}\\) to prune uninformative tokens, removing them from the computational graph of subsequent layers; \\(S_{\\mathcal{M}}\\) uses text-to-video attention in the multimodal encoder to further reduce the length of visual sequence." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.494, + 0.414, + 0.511 + ], + "angle": 0, + "content": "3.1. Video Transformers are Graph Models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.471, + 0.622 + ], + "angle": 0, + "content": "Visual transformers [16] are deep neural networks that model images or videos as sequences of local pixel patches, through a combination of patchwise feature transformation and self-attention. Inspired by transformer architectures for language models [48], video transformers encode input clips into a sequence of spatiotemporal patches, flattened and linearly projected to a \\(d\\)-dimensional embedding space:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.632, + 0.47, + 0.67 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} ^ {(0)} = \\left(\\mathbf {z} _ {\\text {c l s}} ^ {(0)}, \\mathbf {z} _ {1} ^ {(0)}, \\dots , \\mathbf {z} _ {N} ^ {(0)}\\right) = f ^ {\\operatorname {t o k}} \\left(\\mathbf {x} _ {1: T}\\right) \\in \\mathbb {R} ^ {(N + 1) \\times d} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.671, + 0.471, + 0.735 + ], + "angle": 0, + "content": "where \\(N = T^{\\prime}H^{\\prime}W^{\\prime}\\) is the volume of the 3D patch grid, and \\(\\mathbf{z}_{\\mathrm{cls}}^{(0)}\\) denotes a special class token responsible for instance-level prediction. The tokenized sequence is processed by a cascade of transformer blocks \\(f^{(l)}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.744, + 0.47, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} ^ {(l)} = f ^ {(l)} \\left(\\mathbf {Z} ^ {(l - 1)}\\right), \\quad l = 1, \\dots , L \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.776, + 0.47, + 0.806 + ], + "angle": 0, + "content": "each of which computes the self-attention \\(\\mathcal{A}\\) between input tokens, followed by a feed-forward network \\(\\mathcal{F}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.817, + 0.47, + 0.838 + ], + "angle": 0, + "content": "\\[\nf ^ {(l)} (\\mathbf {Z}) = \\mathcal {F} \\left(\\mathcal {A} \\left(\\mathbf {Z} \\mathbf {W} _ {K} ^ {T}, \\mathbf {Z} \\mathbf {W} _ {Q} ^ {T}, \\mathbf {Z} \\mathbf {W} _ {V} ^ {T}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.844, + 0.47, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\sigma (\\mathbf {Q} \\mathbf {K} ^ {T}) \\mathbf {V} \\tag {4}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.471, + 0.902 + ], + "angle": 0, + "content": "1Attention heads, residual connections and normalization terms are omitted for brevity, although we use the conventional implementation [48]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.895, + 0.632 + ], + "angle": 0, + "content": "We interpret the transformer architecture as a special case of graph networks [6], with nodes representing tokenized video patches and edges connecting pairs of tokens for which self-attention is computed. Specifically, consider a directed graph \\(\\mathcal{G} = (\\mathcal{V},\\mathcal{E})\\) defined by the vertices \\(\\mathcal{V} = \\{\\mathbf{z}_1,\\dots ,\\mathbf{z}_N\\}\\) corresponding to spatiotemporal video patches, and edges \\(\\mathcal{E}\\subseteq \\{1,\\ldots ,N\\} ^2\\) connecting pairs of nodes. The self-attention of (4) can be generalized such that node \\(\\mathbf{z}_i\\) attends to \\(\\mathbf{z}_j\\) only if \\((i,j)\\in \\mathcal{E}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.587, + 0.643, + 0.892, + 0.679 + ], + "angle": 0, + "content": "\\[\n\\mathcal {A} _ {\\mathcal {E}} \\left(\\mathbf {q} _ {i}, \\mathbf {K}, \\mathbf {V}\\right) = \\sum_ {j: (i, j) \\in \\mathcal {E}} \\mathbf {a} _ {i j} \\mathbf {v} _ {j}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.686, + 0.892, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {i j} = \\frac {e ^ {\\langle \\mathbf {q} _ {i} , \\mathbf {k} _ {j} \\rangle}}{\\sum_ {j : (i , j) \\in \\mathcal {E}} e ^ {\\langle \\mathbf {q} _ {i} , \\mathbf {k} _ {j} \\rangle}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Under this interpretation, the transformer architecture with full attention resembles a complete graph, where \\(\\mathcal{E}\\) includes every pair of vertices. This dense attention mechanism endows (5) with quadratic memory and time complexity w.r.t. sequence length \\(N\\), making naive transformers notoriously inefficient to train and expensive to deploy, especially for longer video clips. We argue that due to the inherent sparsity of information in video data, a large portion of the graph can be pruned dynamically without significant performance loss, leading to a sparse graph model of significantly lower cost for training and inference." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18921" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.444, + 0.108 + ], + "angle": 0, + "content": "3.2. Edge Sparsity: Local & Random Attention" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.111, + 0.47, + 0.203 + ], + "angle": 0, + "content": "Prior natural language processing models, such as BigBird [55], have explored the idea of restricting the number of key-value pairs each query token attends to, which reduced the number of edges in \\(\\mathcal{E}\\). We use a similar procedure to create a video transformer with edge sparsity, utilizing a combination of local, random and global attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.207, + 0.471, + 0.285 + ], + "angle": 0, + "content": "Local attention. Regional tokens \\(\\{\\mathbf{z}_i\\}_{i=1}^N\\) are first chunked into \\(N_b = \\lceil N / G \\rceil\\) contiguous blocks of size \\(G^2\\). Tokens of one block \\(k\\) attend to a local neighborhood of \\(K_l\\) blocks \\(\\{k - \\Delta, \\dots, k + \\Delta\\}\\), where \\(\\Delta = (K_l - 1) / 2\\) is the maximum range of local attention," + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.296, + 0.47, + 0.313 + ], + "angle": 0, + "content": "\\[\n(k, k ^ {\\prime}) \\in \\mathcal {E}, \\quad \\forall k, k ^ {\\prime}: | k ^ {\\prime} - k | \\leq \\Delta \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.47, + 0.388 + ], + "angle": 0, + "content": "This preserves the modeling of interactions between local features (objects, people, textures) that does not require long-range attention. In the case of \\( K_{l} = 1 \\), local reduces to diagonal attention, where each block only attends to itself." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.469, + 0.439 + ], + "angle": 0, + "content": "Random attention. Beyond local attention, each block also attends to \\( K_{r} \\) other blocks sampled randomly from the input sequence," + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.45, + 0.469, + 0.468 + ], + "angle": 0, + "content": "\\[\n\\left(k, k ^ {\\prime}\\right) \\in \\mathcal {E}, \\quad \\forall k ^ {\\prime} \\in \\mathcal {N} (k) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.527 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}(k)\\) is a random subset of \\(\\{k' \\mid |k' - k| > \\Delta\\}\\) of size \\(K_r\\). This enables the transformer to model long-range visual relationships while avoiding the quadratic cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.47, + 0.579 + ], + "angle": 0, + "content": "Global attention. Class token \\(\\mathbf{z}_{\\mathrm{cls}}\\) always attends to/from regional tokens \\(\\mathbf{z}_i\\), i.e. the link between \\(\\mathbf{q}_{\\mathrm{cls}}\\) and \\(\\mathbf{k}_i\\), as well as \\(\\mathbf{q}_i\\) and \\(\\mathbf{k}_{\\mathrm{cls}}\\), are always retained:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.59, + 0.469, + 0.607 + ], + "angle": 0, + "content": "\\[\n(\\operatorname {c l s}, i), (i, \\operatorname {c l s}) \\in \\mathcal {E}, \\quad i = 1, \\dots , N \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.469, + 0.649 + ], + "angle": 0, + "content": "This enables \\(\\mathbf{z}_{\\mathrm{cls}}\\) to capture global video context, even when the rest of tokens do not attend globally." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.47, + 0.877 + ], + "angle": 0, + "content": "In summary, we retain all attention connections for local-to-global and global-to-local vertices, and limit local-to-local edges to \\((K_l + K_r)G\\) per token. Edge sparsity has a linear asymptotic cost of \\(O\\big((K_l + K_r)GN\\big)\\), a significant improvement over dense attention at \\(O(N^2)\\). However, this approach has two critical limitations of this strategy. First, the sparse patterns are predetermined and do not adapt dynamically to the input sequence. Second, the connections that remain in \\(\\mathcal{E}\\) are not determined by the video semantics. In result, connections between pairs of tokens of low semantic affinity (low attention values) may be preserved, impairing the efficiency of the sparse attention mechanism. To enable more aggressive sparsification, we introduce a second mechanism, which is dynamic, guided by video semantics, and applied to the nodes of the graph." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.356, + 0.901 + ], + "angle": 0, + "content": "2 Padding is added when \\(N\\) is not divisible by \\(G\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.845, + 0.108 + ], + "angle": 0, + "content": "3.3. Node Sparsity: Dynamic Token Pruning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.11, + 0.892, + 0.231 + ], + "angle": 0, + "content": "A large percentage of the tokens of a video transformer corresponds to contextual regions, which contain little temporal dynamics and are only weakly related to the prediction target (e.g. background content uninformative of the activities of subjects in the foreground). While edge sparsification improves the efficiency of self-attention, it lacks both the flexibility and the semantic sensitivity to account for the uneven distribution of information across video patches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.232, + 0.892, + 0.352 + ], + "angle": 0, + "content": "To introduce these properties, we propose a node sparsification strategy, based on the dynamic pruning of tokens. We leverage a combination of observations. First, video semantics are summarized by the class tokens \\(\\mathbf{z}_{\\mathrm{cls}}\\), which contain a global representation of the information of interest for classification. Second the global-to-local edges survive the edge sparsification, through (9), making the attention weights from the \\(\\mathbf{z}_{\\mathrm{cls}}\\) to all regional tokens \\(\\mathbf{z}_i\\)," + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.359, + 0.892, + 0.4 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} \\left(\\mathbf {z} _ {i}\\right) = \\frac {e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} , \\mathbf {k} _ {i} \\rangle}}{\\sum_ {j = 1} ^ {N} e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}}, \\mathbf {k} _ {j} \\rangle}}, \\quad i = 1, \\dots , N \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.466 + ], + "angle": 0, + "content": "available for node sparsification. Since the class token is used for video-level predictions, \\(\\mathbf{a}(\\mathbf{z}_i)\\) quantifies the contribution of feature \\(\\mathbf{z}_i\\) to the main task. This implies that nodes \\(\\mathbf{z}_i\\) of low \\(\\mathbf{a}(\\mathbf{z}_i)\\) are not informative and can be ignored [30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.466, + 0.891, + 0.495 + ], + "angle": 0, + "content": "Node pruning then reduces to keeping the \\( N' = \\lceil qN \\rceil \\) tokens of largest class attention" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.504, + 0.892, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\mathcal {V}} (\\mathbf {Z}; q) = \\left\\{\\mathbf {z} _ {i} \\mid i \\in \\operatorname {t o p k} (\\mathbf {a} (\\mathbf {Z}), \\lceil q N \\rceil) \\right\\} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.65 + ], + "angle": 0, + "content": "where hyperparameter \\( q \\) denotes keep rate and topk(L, m) selects the \\( m \\) largest entries of vector \\( \\mathbf{L} \\). This procedure is repeated multiple times throughout the video encoder (keep rate \\( q^{(l)} \\) at layer \\( l \\)), progressively reducing the length of input sequences. Importantly, the pruning procedure is dynamic and ensures that semantically uninformative vertices in the attention graph \\( \\mathcal{G} \\) are removed along with all edges they are associated with." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Cross-modal sparsity. Node sparsification can be naturally extended to video-language learning. For this, we propose to extend the token selection mechanism discussed above to a cross-modal setting, where video and text tokens \\(\\mathbf{Z}_v,\\mathbf{Z}_t\\) are modeled jointly in a multimodal encoder. In this case, we replace the query \\(\\mathbf{q}_{\\mathrm{cls}}\\) of (10) with the class token of text sequence \\(\\mathbf{q}_{\\mathrm{cls}}^{(t)}\\), obtaining cross-modal attention" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.77, + 0.892, + 0.814 + ], + "angle": 0, + "content": "\\[\n\\mathbf {a} _ {m} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) = \\frac {e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} ^ {(t)} , \\mathbf {k} _ {i} ^ {(v)} \\rangle}}{\\sum_ {j = 1} ^ {N} e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} ^ {(t)} , \\mathbf {k} _ {j} ^ {(v)} \\rangle}}, \\quad i = 1, \\dots , N \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.821, + 0.833, + 0.836 + ], + "angle": 0, + "content": "and subsequently the token sparsification function" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.844, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {S} _ {\\mathcal {M}} \\left(\\mathbf {Z} _ {v}; q\\right) = \\left\\{\\mathbf {z} _ {i} ^ {(v)} \\mid i \\in \\operatorname {t o p k} \\left(\\mathbf {a} _ {m} \\left(\\mathbf {Z} _ {v}\\right), \\lceil q N \\rceil\\right) \\right\\} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Multimodal node sparsity \\(S_{\\mathcal{M}}\\) is applied on top of visual sparsity \\(\\mathcal{S}_{\\mathcal{V}}\\). We expect cross-modal sparsification to create" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18922" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.167 + ], + "angle": 0, + "content": "additional room for sparsity over standalone visual modeling. While the visual encoder can identify salient actors and objects from background patches from the input clip, only the text semantics provide direct guidance for the video-text model to focus on regions relevant to the task of interest." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.168, + 0.471, + 0.228 + ], + "angle": 0, + "content": "With node sparsity, the compute cost of subsequent layers is improved to \\( O(q^{2}N^{2}) \\) using dense attention or \\( O(q(K_{l} + K_{r})GN) \\) with edge sparsity, and the reduction accumulates with multiple sparse layers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.238, + 0.336, + 0.254 + ], + "angle": 0, + "content": "3.4. Hybrid Sparse Transformers" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.257, + 0.469, + 0.349 + ], + "angle": 0, + "content": "We propose to combine edge and node sparsity into a unified framework, SViT, as illustrated in Fig. 2. SViT is built on top of existing video-language transformer architectures that combine separate video and text encoders with a cross-modal transformer. The visual encoder blocks perform sparse self-attention in the following steps:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.355, + 0.469, + 0.387 + ], + "angle": 0, + "content": "- edge sparsification: given the random graph \\(\\mathcal{E}\\) of (7)-(9) compute attention weights \\(\\mathcal{A}_{\\mathcal{E}}\\), using (5);" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.394, + 0.469, + 0.424 + ], + "angle": 0, + "content": "- node sparsification: select the nodes \\(\\mathcal{S}_{\\mathcal{V}}\\) to retain, using (10)-(11) with keep rate \\(q < 1\\)." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.355, + 0.469, + 0.424 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.469, + 0.568 + ], + "angle": 0, + "content": "After video and text embeddings \\(\\mathbf{z}_v, \\mathbf{z}_t\\) are derived from their respective encoders, a multimodal transformer is applied to aggregate features across modalities. It follows the design of the text encoder, except for a cross-attention module that is applied after each self-attention block, where text queries \\(\\mathbf{q}_t\\) attends to key-value pairs \\(\\mathbf{k}_v, \\mathbf{v}_v\\) extracted by the video encoder. The text-to-video attention of (12)-(13) is then used to select the nodes \\(S_{\\mathcal{M}}\\) to retain, further reducing the number of video tokens for subsequent layers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.578, + 0.338, + 0.596 + ], + "angle": 0, + "content": "4. Temporal Sparse Expansion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.469, + 0.66 + ], + "angle": 0, + "content": "In this section, we introduce a new training strategy for SViTT. We motivate for progressive model training with increasing clip length and sparsity in Sec. 4.1, and detail our pretraining procedure in Sec. 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.67, + 0.303, + 0.687 + ], + "angle": 0, + "content": "4.1. Sparsity vs. Clip Length" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.78 + ], + "angle": 0, + "content": "The key insight behind the design of SViT is the diminishing return of clip length. In general, a \\(2 \\times\\) longer sequence does not contain twice the semantic information about the video, due to the redundancy of adjacent frames. This leads to a lower percentage of informative patches with denser frame sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Due to this redundancy, it is possible to use higher sparsity for models with longer clips. This can be implemented by reducing the keep rate \\( q \\) of node sparsification, and the percentage of key/value blocks to attend to in edge sparsification \\( (K_{l} / N_{b}, K_{r} / N_{b}) \\). For the latter, since the total number of blocks \\( N_{b} = \\lceil N / G \\rceil \\) increases with number of frames \\( T \\) (assuming a fixed block size \\( G \\)), it suffices to keep the parameters \\( K_{l}, K_{r} \\) constant." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.088, + 0.892, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.241 + ], + "angle": 0, + "content": "Figure 3. Temporal Sparse Expansion. We propose a multi-stage curriculum for training SViTT. At each stage, the node and edge sparsity \\( S \\) of video-text transformer increases with clip length \\( T \\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.249, + 0.696, + 0.266 + ], + "angle": 0, + "content": "4.2. Temporal Expansion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.268, + 0.892, + 0.389 + ], + "angle": 0, + "content": "Pretraining video-text transformers on long clips is time-consuming and leads to suboptimal models. Instead, we follow a learning strategy similar to Frozen [4], where the model is initially pretrained with shorter clips, and the number of frames increases as training progresses. However, when expanding the clip length, we increase the model sparsity to simultaneously 1) account for the redundancy of information, and 2) limit the growth of computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.892, + 0.497 + ], + "angle": 0, + "content": "Fig. 3 depicts the expansion process proposed for video-text training. In the initial training stage \\( j = 1 \\), a dense video-text model is pretrained on clip length \\( T_{1} \\). Denoting the sparsity hyperparameters of SViTT at stage \\( j \\) by \\( S_{j} = (q_{j}, K_{l}^{(j)}, K_{r}^{(j)}) \\), we create a learning curriculum with progressively increasing clip length and sparsity, by enforcing the constraints" + }, + { + "type": "equation", + "bbox": [ + 0.641, + 0.504, + 0.891, + 0.52 + ], + "angle": 0, + "content": "\\[\nT _ {1} < T _ {2} < \\dots ; \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.645, + 0.524, + 0.891, + 0.539 + ], + "angle": 0, + "content": "\\[\nq _ {1} > q _ {2} > \\dots ; \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.542, + 0.891, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\frac {K _ {l} ^ {(1)} + K _ {r} ^ {(1)}}{T _ {1}} > \\frac {K _ {l} ^ {(2)} + K _ {r} ^ {(2)}}{T _ {2}} > \\dots \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.583, + 0.891, + 0.631 + ], + "angle": 0, + "content": "In practice, we use a decreasing token keep rate (15) and keep local and random attention block numbers fixed, i.e. \\( K_{l}^{(j)} = K_{l} \\) and \\( K_{r}^{(j)} = K_{r} \\), to satisfy (16)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.64, + 0.586, + 0.655 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.662, + 0.892, + 0.767 + ], + "angle": 0, + "content": "In this section we present experimental results of SViTT on vision-language modeling. We briefly introduce the experimental setup in Sec. 5.1, and perform several ablation studies on the design choices involving model sparsification and training in Sec. 5.2. We then demonstrate the performance of SViTT on various vision-language tasks in Sec. 5.3 and include additional qualitative analysis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.776, + 0.691, + 0.792 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Architecture. Our implementation of video-text transformer is based on Singularity [24]. The model has a two-tower structure, with separate encoders for vision and language. The video encoder \\( f_{v} \\) is a 12-layer BEiT-B [5] initialized with ImageNet weights and inflated for video inputs. This differs from [24] which embeds each frame independently and applies late temporal fusion on extracted" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18923" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.288 + ], + "angle": 0, + "content": "
Attn. blocks\nKl, Kr, GKeep rate\nqv, qm# Edges\n(M)R1DiDeMo\nR5R10Mean
——7.4728.853.163.048.3
Edge sparsity
(1, 3, 56)—2.1420.741.750.537.6
(1, 5, 56)—3.2126.048.656.843.8
Node sparsity
—(0.7, 1)3.9926.951.961.346.7
—(0.7, 0.1)3.9727.653.162.947.9
Hybrid sparsity
(1, 3, 56)(0.7, 0.1)1.4819.940.550.637.0
(1, 5, 56)(0.7, 0.1)2.2224.547.658.643.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.294, + 0.47, + 0.322 + ], + "angle": 0, + "content": "Table 1. Ablation on Edge and Node Sparsity. We evaluate the same dense video-text model under different sparsification modes." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.329, + 0.268, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.421, + 0.273, + 0.432 + ], + "angle": 0, + "content": "(a) Number of local / random blocks." + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.329, + 0.457, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.421, + 0.435, + 0.432 + ], + "angle": 0, + "content": "(b) Attention block size." + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.44, + 0.469, + 0.468 + ], + "angle": 0, + "content": "Figure 4. Ablation on Edge Sparsity. We evaluate dense model using different local/random blocks \\((K_l, K_r)\\) and block size \\(G\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.469, + 0.553 + ], + "angle": 0, + "content": "features. The text encoder \\( f_{t} \\) is a pretrained BERT [14] model, whose last 3 layers are modified to implement the multimodal encoder \\( f_{m} \\), with cross-modal attention based on visual tokens as key-value pairs, which we sparsify as described in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.469, + 0.636 + ], + "angle": 0, + "content": "Pre-training. SViTT is pre-trained on 2.5M video-text pairs from the WebVid dataset [4]. Since our goal is to investigate how to improve the effectiveness of the temporal learning of the video modality, we do not train with additional image-text corpora as done in [4, 18, 24]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.469, + 0.757 + ], + "angle": 0, + "content": "The [cls] tokens of the video and text encoders are first linearly projected to a joint embedding space, producing feature vectors \\(\\mathbf{z}_v = f_v(\\mathbf{x}_v)\\) and \\(\\mathbf{z}_t = f_t(\\mathbf{x}_t)\\), respectively. Following prior work, we use the InfoNCE loss [40] to align these feature vectors. The output of multimodal encoder \\(\\mathbf{y} = f_m(\\mathbf{z}_v,\\mathbf{z}_t)\\) is optimized with video-text matching (VTM) and masked language modeling (MLM) losses commonly found in VLP literature [12, 18, 24, 27, 28]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.469, + 0.884 + ], + "angle": 0, + "content": "Downstream tasks. Trained video-text models are evaluated on two multimodal tasks: Text-to-video retrieval and video question answering. Video retrieval is evaluated on MSR-VTT [51], DiDeMo [2], Charades [43] and Something-Something v2 [20, 24], by top- \\(K\\) recalls \\((K \\in \\{1, 5, 10\\})\\) and their numeric average. Question answering is evaluated on MSRVTT-QA [49], ActivityNet-QA [10, 54] and AGQA [21], with top-1 accuracy of the answers." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.38, + 0.901 + ], + "angle": 0, + "content": "Training details are given in the Appendix." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.308 + ], + "angle": 0, + "content": "
TSparc.FLOPs (G)Mem. (GB)R1DiDeMoMean
R5R10
4Dense139.90.9628.853.163.048.3
Edge135.90.8028.351.961.447.2
Node95.80.6129.954.863.949.6
Hybrid93.90.5429.353.763.248.8
8Dense291.33.1429.654.164.149.3
Edge271.81.5729.854.965.450.1
Node197.61.7730.455.766.050.7
Hybrid166.40.9231.057.266.351.5
16Dense627.810.66Untrainable
Edge543.63.0231.655.164.650.5
Node370.94.39Untrainable
Hybrid296.21.5731.457.367.852.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.314, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Table 2. Ablation on Training Sparse Models. We compare the zero-shot performance, inference GFLOPs, and training memory (per sample) of sparse models to the dense attention baseline." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.363, + 0.689, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.455, + 0.664, + 0.468 + ], + "angle": 0, + "content": "(a) Visual sparsification." + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.363, + 0.876, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.714, + 0.455, + 0.871, + 0.468 + ], + "angle": 0, + "content": "(b) Multimodal sparsification." + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.474, + 0.892, + 0.503 + ], + "angle": 0, + "content": "Figure 5. Ablation on Node Sparsity. We evaluate the pre-trained dense model using different keep rates \\( q \\) at test time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.511, + 0.664, + 0.525 + ], + "angle": 0, + "content": "5.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.592 + ], + "angle": 0, + "content": "We start by training a video-text transformer with clip length of 4 frames and dense attention, and measure its zero-shot performance on downstream tasks after sparsifying its video encoder while keeping its weights unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Edge sparsification. We first apply edge sparsification with different number of local blocks \\( K_{l} \\), random blocks \\( K_{r} \\), and block size \\( G \\). As shown in Fig. 4a, under a limited budget of 6 local or random attention blocks per query token, using 1 local block and 5 random blocks provides the best trade-off. Increasing the local attention window \\( K_{l} \\) hurts long-term modeling capacity and degrades retrieval; while removing the single local block responsible for diagonal attention also impairs performance. This suggests that while query tokens should always attend to their respective blocks, there is no benefit in attending to neighboring blocks. We thus fix \\( K_{l} = 1 \\) for the rest of experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We next vary the block size \\( G \\) of sparse attention. Fig. 4b shows that larger sizes have stronger retrieval performance, as expected. However, they also make self-attention less sparse (more costly to compute). \\( G = 56 \\) provides a good balance between performance and complexity. Tab. 1 summarizes the test performance of two edge sparsity config: \\( (K_{l}, K_{r}, G) = (1, 3, 56) \\) and \\( (1, 5, 56) \\). While both underperform the dense model, we will later demonstrate that the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18924" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.227 + ], + "angle": 0, + "content": "
FramesTSparsityTSDiDeMo
R1R5R10Mean
44.8028.050.759.246.0
10→4.8029.353.763.248.8
88.9127.351.463.847.5
4.80→8.9131.057.266.351.5
1616.9627.552.463.247.7
4.80→8.91→16.9631.457.367.852.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.232, + 0.47, + 0.275 + ], + "angle": 0, + "content": "Table 3. Ablation on Temporal Sparse Expansion. Sparsity \\( T_{S} \\) indicates training on \\( T \\) frames while removing \\( S \\times 100\\% \\) attention edges of dense transformer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.469, + 0.315 + ], + "angle": 0, + "content": "gap can be closed and even reversed by training the sparse model with the proposed temporal expansion curriculum." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.469, + 0.501 + ], + "angle": 0, + "content": "Node sparsification. We next incorporate node sparsity into the video-text transformer. This includes visual sparsification (keep rate \\( q_{v} \\)) using the self-attention of video encoder \\( f_{v} \\) to progressively prune the input tokens\\(^{3}\\), and multimodal sparsification (keep rate \\( q_{m} \\)) using the text-to-video attention of cross-modal encoder \\( f_{m} \\) to further drop visual tokens unrelated to the text query. Fig. 5a shows that the dense model is quite robust to token pruning, even without sparse training. Using visual keep rate \\( q_{v} \\geq 0.8 \\) has minimal impact on test results, and performance only starts to drop rapidly at \\( q_{v} = 0.5 \\), at which point only \\( 1/8 \\) of input tokens are retained after three rounds of sparsification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.469, + 0.638 + ], + "angle": 0, + "content": "Even more surprisingly, the subsequent multimodal sparsification step, using a keep rate of \\( q_{m} = 0.1 \\), improves zero-shot performance by \\( 1\\% \\). This shows that the \\( 90\\% \\) redundant visual tokens not only add unnecessary complexity to the model, but also introduce noise that harms retrieval performance. The fact that the optimal \\( q_{m} \\) is much lower than \\( q_{v} \\) also suggests that text modality provides crucial semantic guidance for identifying relevant visual patches, at a much higher accuracy than visual modeling alone." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.469, + 0.749 + ], + "angle": 0, + "content": "Hybrid sparsification. Combining the best sparse settings for edges and nodes, we obtain the hybrid sparsification strategy for SViT. As shown in Tab. 1, compared to edge sparsity, the introduction of node sparsity \\((q_{v} = 0.7, q_{m} = 0.1)\\) only impacts recall scores marginally, while saving computations on a large portion of visual tokens throughout the network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.469, + 0.877 + ], + "angle": 0, + "content": "Training sparse transformers. We next perform full pretraining with the sparse models and compare their performance and efficiency to the dense transformer baseline. Tab. 2 summarizes the results obtained with different input clip lengths and types of sparsity. At 4 frames, edge sparsity has small benefit due to the relatively short sequence length and node sparsity performs the best. However, at 8 frames, we start to see clear advantages to edge sparsity in memory" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.089, + 0.895, + 0.273 + ], + "angle": 0, + "content": "
MethodPTTMSR-VTTDiDeMo
R1MeanR1Mean
VideoCLIP [50]100M—10.420.916.6—
Frozen [4]5M423.241.521.141.1
ALPRO [26]5M824.141.423.843.0
VIOLET [18]5M425.945.023.544.4
Singularity [24]5M128.446.036.955.8
121.138.723.340.8
Singularity*2M424.440.026.444.1
824.341.025.845.5
SViTTDense Hybrid2M826.043.629.649.3
25.443.831.051.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.279, + 0.892, + 0.322 + ], + "angle": 0, + "content": "Table 4. Zero-shot Text-to-video Retrieval. Results reported in prior works are marked in gray; * indicates our reproduced results. PT = # video-text pairs for pre-training, \\( T = \\# \\) frames per clip." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.497 + ], + "angle": 0, + "content": "complexity, and both edge and node sparsity outperform the dense transformer baseline. Combining both types of sparsity performs the best, while only requiring \\(60\\%\\) the FLOPs and \\(30\\%\\) the memory of the dense model. At 16 frames, the dense and node sparsity models are no longer trainable due to their quadratically increasing cost. The models with edge sparsity, however, are able to fit into GPU memory thanks to the linear complexity from sparse attention. A 16-frame SViTT with hybrid sparsity requires similar computation to an 8-frame dense model and only half of its training memory, while achieving \\(3\\%\\) higher recall." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.893, + 0.744 + ], + "angle": 0, + "content": "Progressive training. We next study the impact of temporal sparse expansion on the training of SViT models on longer clips. Tab. 3 compares the performance of models trained using temporal expansion (i.e. initialized from checkpoints pretrained on fewer frames and lower sparsity) to standard single-stage training. For single-stage training, performance does not improve substantially with clip length. This is in contrast to the proposed sparse expansion, where using 8 instead or 4 frames results in a gain of \\(2.7\\%\\). This suggests that the models have learned to exploit the temporal relationships between video frames. For a given clip length, sparse expansion also substantially improves upon single stage performance, from 2.8 points for \\(T = 4\\) to 4.5 points for \\(T = 16\\). In fact, sparse expansion training with a shorter clip length (e.g. 4 frames) can outperform single stage training with a larger length (16 frames)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.64, + 0.77 + ], + "angle": 0, + "content": "5.3. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.775, + 0.892, + 0.806 + ], + "angle": 0, + "content": "We compare SViT to state-of-the-art models in text-to-video retrieval and video question answering." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Text-to-video retrieval. Video-text retrieval is evaluated under zero-shot and fine-tuning settings. Tab. 4 shows the zero-shot results on MSR-VTT and DiDeMo. Compared to our reproduced models of Singularity on WebVid-2M, which aggregate frame-level features using a temporal transformer encoder, the spatiotemporal transformer" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.432, + 0.9 + ], + "angle": 0, + "content": "3We follow [30] to prune visual tokens at layer #4, #7, and #10." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18925" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.203, + 0.088, + 0.768, + 0.101 + ], + "angle": 0, + "content": "A person is in a living room playing with a book and flipping through the pages, they then leave out the door." + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.105, + 0.362, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.196, + 0.256, + 0.207 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.365, + 0.105, + 0.607, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.435, + 0.195, + 0.523, + 0.207 + ], + "angle": 0, + "content": "Visual, \\(q_{v} = 0.6\\)" + }, + { + "type": "image", + "bbox": [ + 0.609, + 0.105, + 0.851, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.667, + 0.195, + 0.792, + 0.207 + ], + "angle": 0, + "content": "Cross-modal, \\( q_{m} = 0.1 \\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.213, + 0.882, + 0.228 + ], + "angle": 0, + "content": "Figure 6. Qualitative Results. SViTT isolates informative regions from background patches to facilitate efficient temporal reasoning." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.236, + 0.468, + 0.395 + ], + "angle": 0, + "content": "
MethodPTTCharadesSSv2
R1MeanR1Mean
Frozen [4]5M3211.925.1——
CLIP4Clip [35]400M1213.927.143.165.1
ECLIPSE [31]400M3215.730.3——
\\( MKTVR^† \\)[36]400M4216.634.7——
Singularity [24]5M1——36.458.9
4——44.166.6
SViTTDense Hybrid2M816.032.743.666.1
17.735.749.869.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.118, + 0.399, + 0.43, + 0.414 + ], + "angle": 0, + "content": "Table 5. Text-to-video Retrieval with Fine-tuning." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.42, + 0.468, + 0.589 + ], + "angle": 0, + "content": "
MethodPTTMSRVTTANetAGQA
HME [17]—2033.0—47.7
HCRN [23]12835.5—47.4
ClipBERT [25]0.2M1637.4——
ALPRO [26]5M1642.1——
Just Ask [52]69M64041.538.9—
MERLOT [56]180M543.141.4—
VIOLET [18]185M443.9—49.2
Singularity [24]5M142.741.8—
SViTTDense Hybrid2M842.742.350.2
43.043.252.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.159, + 0.594, + 0.388, + 0.608 + ], + "angle": 0, + "content": "Table 6. Video Question Answering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.469, + 0.707 + ], + "angle": 0, + "content": "of SViTT produces stronger results on both downstream datasets. This highlights the importance of temporal modeling in earlier layers of video-text transformers. SViTT with hybrid sparsity has similar performance to the dense model on MSR-VTT but significantly outperforms in on DiDeMo, which contains longer videos with localized activities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.71, + 0.469, + 0.862 + ], + "angle": 0, + "content": "For Charades and SSv2, we evaluate text-to-video retrieval with fine-tuning, as shown in Tab. 5. Both datasets are action-centric, posing a greater challenge to the temporal reasoning of video-text models. SViT with hybrid sparsification dominates the dense variant by \\(\\sim 3\\%\\) on both datasets, a more substantial gap than observed for MSR-VTT and DiDeMo. This confirms our hypothesis that exploiting node and edge sparsity reduces the dependency of models on contextual regions, forcing them to focus on the temporal dynamics of person and objects in the foreground." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Video question answering. We next evaluate the cross-modal modeling of SViT on MSRVTT-QA, ActivityNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.239, + 0.892, + 0.466 + ], + "angle": 0, + "content": "QA and AGQA. As shown in Tab. 6, the hybrid sparsity version of SViTT outperforms the dense transformer baseline on all three datasets, thanks to its more efficient temporal modeling. On MSRVTT-QA, the accuracy gap is small between dense and sparse transformer (0.3%), and SViTT marginally underperforms baselines pretrained with fewer number of frames (MERLOT [56], VIOLET [18]). This is likely due to the nature of MSRVTT, which consists of short video clips and questions biased towards spatial cues, allowing temporal modeling little benefit over spatial transformers pretrained on massive image & video data. On ActivityNet-QA and AGQA, which both contain longer clips and temporally challenging questions, the sparse modeling of SViTT proves advantageous, with 0.9% and 2.3% boost in accuracy respectively, beating all baseline methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.893, + 0.637 + ], + "angle": 0, + "content": "Qualitative analysis. To show how SViT efficiently identifies and concentrates its computation on informative spatiotemporal regions of the input clips, we visualize the outcome of node sparsification in Fig. 6. Using visual sparsification in video encoder \\( f_{v} \\), SViT learns to isolate foreground entities from the majority of background patches, enabling the model to perform sparse video-text inference on longer temporal context. Cross-modal attention in multimodal encoder \\( f_{m} \\) provides an even stronger signal for isolating the regions of interest of each video clip, validating the importance of text semantics in visual sparsification." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.62, + 0.663 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.669, + 0.892, + 0.867 + ], + "angle": 0, + "content": "This work introduced SViTT, a sparse video-text transformer for efficient reasoning over a long temporal context. By interpreting visual transformers as graph networks, we proposed to optimize their edge and node sparsity, using a combination of sparse block attention, visual token pruning and text-guided token selection. We further introduced a temporal expansion strategy for training SViTT, which aims to gradually increase model sparsity with clip length. SViTT showed strong performance and efficiency compared to dense transformers, with a larger gap when frame number increases. On video retrieval and question answering benchmarks, SViTT achieved state-of-the-art results using only video data, without extra image-text pretraining." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. This work was funded in part by NSF award IIS-2041009." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18926" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.112, + 0.47, + 0.18 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. arXiv preprint arXiv:2204.14198, 2022. 1" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.181, + 0.472, + 0.248 + ], + "angle": 0, + "content": "[2] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8746-8755, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.712 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18929" + } + ] +] \ No newline at end of file diff --git a/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/a239fc53-51e4-48aa-8bdd-b397217aa71a_origin.pdf b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/a239fc53-51e4-48aa-8bdd-b397217aa71a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5d14ce1c88e28ef8e6b2147508c123ff93f689c3 --- /dev/null +++ b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/a239fc53-51e4-48aa-8bdd-b397217aa71a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:019ed35efeeb206cc59b341d5c5a323afc69e49002cfee8e1b11ecf44ce70cc6 +size 957952 diff --git a/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/full.md b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/full.md new file mode 100644 index 0000000000000000000000000000000000000000..86595f8616e626899d93b05b52461646393aab02 --- /dev/null +++ b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/full.md @@ -0,0 +1,381 @@ +# SViTT: Temporal Learning of Sparse Video-Text Transformers + +Yi Li*1 Kyle Min² Subarna Tripathi² Nuno Vasconcelos¹ + +$^{1}$ UC San Diego $^{2}$ Intel Labs + +{yil898, nvasconcelos}@ucsd.edu {kyle.min, subarna.tripathi}@intel.com + +# Abstract + +Do video-text transformers learn to model temporal relationships across frames? Despite their immense capacity and the abundance of multimodal training data, recent work has revealed the strong tendency of video-text models towards frame-based spatial representations, while temporal reasoning remains largely unsolved. In this work, we identify several key challenges in temporal learning of video-text transformers: the spatiotemporal trade-off from limited network size; the curse of dimensionality for multi-frame modeling; and the diminishing returns of semantic information by extending clip length. Guided by these findings, we propose SViTT, a sparse video-text architecture that performs multi-frame reasoning with significantly lower cost than naive transformers with dense attention. Analogous to graph-based networks, SViTT employs two forms of sparsity: edge sparsity that limits the query-key communications between tokens in self-attention, and node sparsity that discards uninformative visual tokens. Trained with a curriculum which increases model sparsity with the clip length, SViTT outperforms dense transformer baselines on multiple video-text retrieval and question answering benchmarks, with a fraction of computational cost. Project page: http://svcl.ucsd.edu/projects/svittt. + +# 1. Introduction + +With the rapid development of deep neural networks for computer vision and natural language processing, there has been growing interest in learning correspondences across the visual and text modalities. A variety of vision-language pretraining frameworks have been proposed [12, 22, 29, 34] for learning high-quality cross-modal representations with weak supervision. Recently, progress on visual transformers (ViT) [5, 16, 32] has enabled seamless integration of both modalities into a unified attention model, leading to image-text transformer architectures that achieve state-the-art performance on vision-language benchmarks [1, 27, 44]. + +Progress has also occurred in video-language pretraining by leveraging image-text models for improved frame-based + +![](images/c93b0b7814c5eab4d4a81860413017e46d3c4a8fa5a69d6ffaab2720c12c3307.jpg) +One person takes a pillow and some homework from an old chair, then smiles and laughs. + +![](images/57438170fa659e11bcc7407c6e9591bf463b89d4e53eea9d5ea616fdecfe4fa1.jpg) +Figure 1. We propose SViT, a sparse video-text transformer for efficient modeling of temporal relationships across video frames. Top: Semantic information for video-text reasoning is highly localized in the spatiotemporal volume, making dense modeling inefficient and prone to contextual noises. Bottom: SViT pursues edge sparsity by limiting query-key pairs in self-attention, and node sparsity by pruning redundant tokens from visual sequence. + +reasoning [4, 9, 18]. Spatial modeling has the advantage of efficient (linear) scaling to long duration videos. Perhaps due to this, single-frame models have proven surprisingly effective at video-text tasks, matching or exceeding prior arts with complex temporal components [9, 24]. However, spatial modeling creates a bias towards static appearance and overlooks the importance of temporal reasoning in videos. This suggests the question: Are temporal dynamics not worth modeling in the video-language domain? + +Upon a closer investigation, we identify a few key challenges to incorporating multi-frame reasoning in video-language models. First, limited model size implies a tradeoff between spatial and temporal learning (a classic example being 2D/3D convolutions in video CNNs [46]). For any given dataset, optimal performance requires a careful bal + +ance between the two. Second, long-term video models typically have larger model sizes and are more prone to overfitting. Hence, for longer term video models, it becomes more important to carefully allocate parameters and control model growth. Finally, even if extending the clip length improves the results, it is subject to diminishing returns since the amount of information provided by a video clip does not grow linearly with its sampling rate. If the model size is not controlled, the computational increase may not justify the gains in accuracy. This is critical for transformer-based architectures, since self-attention mechanisms have a quadratic memory and time cost with respect to input length. In summary, model complexity should be adjusted adaptively, depending on the input videos, to achieve the best trade-off between spatial representation, temporal representation, overfitting potential, and complexity. Since existing video-text models lack this ability, they either attain a suboptimal balance between spatial and temporal modeling, or do not learn meaningful temporal representations at all. + +Motivated by these findings, we argue that video-text models should learn to allocate modeling resources to the video data. We hypothesize that, rather than uniformly extending the model to longer clips, the allocation of these resources to the relevant spatiotemporal locations of the video is crucial for efficient learning from long clips. For transformer models, this allocation is naturally performed by pruning redundant attention connections. We then propose to accomplish these goals by exploring transformer sparsification techniques. This motivates the introduction of a Sparse Video-Text Transformer (SViTT) inspired by graph models. As illustrated in Fig. 1, SViTT treats video tokens as graph vertices, and self-attention patterns as edges that connect them. We design SViTT to pursue sparsity for both: edge sparsity aims at reducing query-key pairs in attention module while maintaining its global reasoning capability; node sparsity reduces to identifying informative tokens (e.g., corresponding to moving objects or person in the foreground) and pruning background feature embeddings. To address the diminishing returns for longer input clips, we propose to train SViTT with temporal sparse expansion, a curriculum learning strategy that increases clip length and model sparsity, in sync, at each training stage. + +SViTT is evaluated on diverse video-text benchmarks from video retrieval to question answering, comparing to prior arts and our own dense modeling baselines. First, we perform a series of ablation studies to understand the benefit of sparse modeling in transformers. Interestingly, we find that both nodes (tokens) and edges (attention) can be pruned drastically at inference, with a small impact on test performance. In fact, token selection using cross-modal attention improves retrieval results by $1\%$ without re-training. + +We next perform full pre-training with the sparse models and evaluate their downstream performance. We observe + +that SViTT scales well to longer input clips where the accuracy of dense transformers drops due to optimization difficulties. On all video-text benchmarks, SViTT reports comparable or better performance than their dense counterparts with lower computational cost, outperforming prior arts including those trained with additional image-text corpora. + +The key contributions of this work are: 1) a video-text architecture SViTT that unifies edge and node sparsity; 2) a sparse expansion curriculum for training SViTT on long video clips; and 3) empirical results that demonstrate its temporal modeling efficacy on video-language tasks. + +# 2. Related Work + +Video-language pretraining. Vision-language pretraining has been widely adopted for various video-text downstream tasks. VideoBERT [45] was an early effort, using video-text pretraining for action classification and video captioning. Recently, the massive-scale instructional video dataset HowTo100M [39] has motivated many approaches to video-text pretraining [4, 19, 24, 38, 56, 57]. Frozen [4] proposed to pretrain a space-time transformer on a combination of video and image data to enable zero-shot text-to-video retrieval. ATP [9] and Singularity [24] showed strong performance using image-based models, highlighting the importance of spatial modeling for video-language tasks. In this work, we pursue an alternative route of efficient temporal modeling across multiple video frames. + +Sparse transformers. The self-attention of naive transformers [16, 48] has quadratic complexity making them inefficient for modeling long sequences. Different forms of sparse attention have been studied to improve text [7, 13, 55], image [15, 32, 47], and video modeling [3, 8, 33], although the sparse patterns are typically predetermined and do not adapt to the input semantics. Several works have also considered speeding up vision transformers by adaptively reducing the number of input tokens [11, 30, 37, 41, 42, 53]. For example, DynamicViT [41] proposed to drop visual tokens with a dedicated module that identifies and prunes less informative ones. TokenLearner [42] introduces a learnable module to adaptively generate a small subset of tokens from input frames. EViT [30] progressively reduces the number of tokens based on their attention scores, fusing inattentive tokens into a new token to preserve input information. Unlike prior works that focus on visual modeling on images or videos alone, we study the sparsity of video-language transformers which can benefit from cross-modal attention. + +# 3. Exploiting Sparsity in Video Transformers + +In this section, we formulate video transformers as graph models (Sec. 3.1) and present a set of approaches towards sparse video modeling, exploiting the redundancy of edges (Sec. 3.2) and nodes (Sec. 3.3). We combine these into a unified sparse framework for video-text learning (Sec. 3.4). + +![](images/600d9c822f8a1501df6e9302e0b41b2a828001dcda42de457cf87a74c04e7fa2.jpg) + +![](images/28f24f691c9c9098e6abd4a586cc7e627f09ca5d7a91ee2259818c951fa6a83b.jpg) +Figure 2. Model Architecture. SViT improves modeling efficiency of conventional video-text transformers through two key components: node sparsity and edge sparsity. Edge sparsification $\mathcal{A}_{\varepsilon}$ computes sparse self-attention of input visual sequence $\mathbf{z}$ , where each query token attends to a small subset of key and value tokens, with connectivity $\mathcal{E}$ specified by global, local, and random attention. Node sparsification $S_{\nu}$ uses global attention scores from $\mathcal{A}_{\varepsilon}$ to prune uninformative tokens, removing them from the computational graph of subsequent layers; $S_{\mathcal{M}}$ uses text-to-video attention in the multimodal encoder to further reduce the length of visual sequence. + +![](images/362a5d2966257b1b22e43d849893cf7612b15c3a3420f64a61fb2e58c0350404.jpg) + +# 3.1. Video Transformers are Graph Models + +Visual transformers [16] are deep neural networks that model images or videos as sequences of local pixel patches, through a combination of patchwise feature transformation and self-attention. Inspired by transformer architectures for language models [48], video transformers encode input clips into a sequence of spatiotemporal patches, flattened and linearly projected to a $d$ -dimensional embedding space: + +$$ +\mathbf {Z} ^ {(0)} = \left(\mathbf {z} _ {\text {c l s}} ^ {(0)}, \mathbf {z} _ {1} ^ {(0)}, \dots , \mathbf {z} _ {N} ^ {(0)}\right) = f ^ {\operatorname {t o k}} \left(\mathbf {x} _ {1: T}\right) \in \mathbb {R} ^ {(N + 1) \times d} \tag {1} +$$ + +where $N = T^{\prime}H^{\prime}W^{\prime}$ is the volume of the 3D patch grid, and $\mathbf{z}_{\mathrm{cls}}^{(0)}$ denotes a special class token responsible for instance-level prediction. The tokenized sequence is processed by a cascade of transformer blocks $f^{(l)}$ + +$$ +\mathbf {Z} ^ {(l)} = f ^ {(l)} \left(\mathbf {Z} ^ {(l - 1)}\right), \quad l = 1, \dots , L \tag {2} +$$ + +each of which computes the self-attention $\mathcal{A}$ between input tokens, followed by a feed-forward network $\mathcal{F}$ : + +$$ +f ^ {(l)} (\mathbf {Z}) = \mathcal {F} \left(\mathcal {A} \left(\mathbf {Z} \mathbf {W} _ {K} ^ {T}, \mathbf {Z} \mathbf {W} _ {Q} ^ {T}, \mathbf {Z} \mathbf {W} _ {V} ^ {T}\right)\right), \tag {3} +$$ + +$$ +\mathcal {A} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \sigma (\mathbf {Q} \mathbf {K} ^ {T}) \mathbf {V} \tag {4} +$$ + +We interpret the transformer architecture as a special case of graph networks [6], with nodes representing tokenized video patches and edges connecting pairs of tokens for which self-attention is computed. Specifically, consider a directed graph $\mathcal{G} = (\mathcal{V},\mathcal{E})$ defined by the vertices $\mathcal{V} = \{\mathbf{z}_1,\dots ,\mathbf{z}_N\}$ corresponding to spatiotemporal video patches, and edges $\mathcal{E}\subseteq \{1,\ldots ,N\} ^2$ connecting pairs of nodes. The self-attention of (4) can be generalized such that node $\mathbf{z}_i$ attends to $\mathbf{z}_j$ only if $(i,j)\in \mathcal{E}$ , + +$$ +\mathcal {A} _ {\mathcal {E}} \left(\mathbf {q} _ {i}, \mathbf {K}, \mathbf {V}\right) = \sum_ {j: (i, j) \in \mathcal {E}} \mathbf {a} _ {i j} \mathbf {v} _ {j}, \tag {5} +$$ + +$$ +\mathbf {a} _ {i j} = \frac {e ^ {\langle \mathbf {q} _ {i} , \mathbf {k} _ {j} \rangle}}{\sum_ {j : (i , j) \in \mathcal {E}} e ^ {\langle \mathbf {q} _ {i} , \mathbf {k} _ {j} \rangle}} \tag {6} +$$ + +Under this interpretation, the transformer architecture with full attention resembles a complete graph, where $\mathcal{E}$ includes every pair of vertices. This dense attention mechanism endows (5) with quadratic memory and time complexity w.r.t. sequence length $N$ , making naive transformers notoriously inefficient to train and expensive to deploy, especially for longer video clips. We argue that due to the inherent sparsity of information in video data, a large portion of the graph can be pruned dynamically without significant performance loss, leading to a sparse graph model of significantly lower cost for training and inference. + +# 3.2. Edge Sparsity: Local & Random Attention + +Prior natural language processing models, such as BigBird [55], have explored the idea of restricting the number of key-value pairs each query token attends to, which reduced the number of edges in $\mathcal{E}$ . We use a similar procedure to create a video transformer with edge sparsity, utilizing a combination of local, random and global attention. + +Local attention. Regional tokens $\{\mathbf{z}_i\}_{i=1}^N$ are first chunked into $N_b = \lceil N / G \rceil$ contiguous blocks of size $G^2$ . Tokens of one block $k$ attend to a local neighborhood of $K_l$ blocks $\{k - \Delta, \dots, k + \Delta\}$ , where $\Delta = (K_l - 1) / 2$ is the maximum range of local attention, + +$$ +(k, k ^ {\prime}) \in \mathcal {E}, \quad \forall k, k ^ {\prime}: | k ^ {\prime} - k | \leq \Delta \tag {7} +$$ + +This preserves the modeling of interactions between local features (objects, people, textures) that does not require long-range attention. In the case of $K_{l} = 1$ , local reduces to diagonal attention, where each block only attends to itself. + +Random attention. Beyond local attention, each block also attends to $K_{r}$ other blocks sampled randomly from the input sequence, + +$$ +\left(k, k ^ {\prime}\right) \in \mathcal {E}, \quad \forall k ^ {\prime} \in \mathcal {N} (k) \tag {8} +$$ + +where $\mathcal{N}(k)$ is a random subset of $\{k' \mid |k' - k| > \Delta\}$ of size $K_r$ . This enables the transformer to model long-range visual relationships while avoiding the quadratic cost. + +Global attention. Class token $\mathbf{z}_{\mathrm{cls}}$ always attends to/from regional tokens $\mathbf{z}_i$ , i.e. the link between $\mathbf{q}_{\mathrm{cls}}$ and $\mathbf{k}_i$ , as well as $\mathbf{q}_i$ and $\mathbf{k}_{\mathrm{cls}}$ , are always retained: + +$$ +(\operatorname {c l s}, i), (i, \operatorname {c l s}) \in \mathcal {E}, \quad i = 1, \dots , N \tag {9} +$$ + +This enables $\mathbf{z}_{\mathrm{cls}}$ to capture global video context, even when the rest of tokens do not attend globally. + +In summary, we retain all attention connections for local-to-global and global-to-local vertices, and limit local-to-local edges to $(K_l + K_r)G$ per token. Edge sparsity has a linear asymptotic cost of $O\big((K_l + K_r)GN\big)$ , a significant improvement over dense attention at $O(N^2)$ . However, this approach has two critical limitations of this strategy. First, the sparse patterns are predetermined and do not adapt dynamically to the input sequence. Second, the connections that remain in $\mathcal{E}$ are not determined by the video semantics. In result, connections between pairs of tokens of low semantic affinity (low attention values) may be preserved, impairing the efficiency of the sparse attention mechanism. To enable more aggressive sparsification, we introduce a second mechanism, which is dynamic, guided by video semantics, and applied to the nodes of the graph. + +# 3.3. Node Sparsity: Dynamic Token Pruning + +A large percentage of the tokens of a video transformer corresponds to contextual regions, which contain little temporal dynamics and are only weakly related to the prediction target (e.g. background content uninformative of the activities of subjects in the foreground). While edge sparsification improves the efficiency of self-attention, it lacks both the flexibility and the semantic sensitivity to account for the uneven distribution of information across video patches. + +To introduce these properties, we propose a node sparsification strategy, based on the dynamic pruning of tokens. We leverage a combination of observations. First, video semantics are summarized by the class tokens $\mathbf{z}_{\mathrm{cls}}$ , which contain a global representation of the information of interest for classification. Second the global-to-local edges survive the edge sparsification, through (9), making the attention weights from the $\mathbf{z}_{\mathrm{cls}}$ to all regional tokens $\mathbf{z}_i$ , + +$$ +\mathbf {a} \left(\mathbf {z} _ {i}\right) = \frac {e ^ {\langle \mathbf {q} _ {\mathrm {c l s}} , \mathbf {k} _ {i} \rangle}}{\sum_ {j = 1} ^ {N} e ^ {\langle \mathbf {q} _ {\mathrm {c l s}}, \mathbf {k} _ {j} \rangle}}, \quad i = 1, \dots , N \tag {10} +$$ + +available for node sparsification. Since the class token is used for video-level predictions, $\mathbf{a}(\mathbf{z}_i)$ quantifies the contribution of feature $\mathbf{z}_i$ to the main task. This implies that nodes $\mathbf{z}_i$ of low $\mathbf{a}(\mathbf{z}_i)$ are not informative and can be ignored [30]. + +Node pruning then reduces to keeping the $N' = \lceil qN \rceil$ tokens of largest class attention + +$$ +\mathcal {S} _ {\mathcal {V}} (\mathbf {Z}; q) = \left\{\mathbf {z} _ {i} \mid i \in \operatorname {t o p k} (\mathbf {a} (\mathbf {Z}), \lceil q N \rceil) \right\} \tag {11} +$$ + +where hyperparameter $q$ denotes keep rate and topk(L, m) selects the $m$ largest entries of vector $\mathbf{L}$ . This procedure is repeated multiple times throughout the video encoder (keep rate $q^{(l)}$ at layer $l$ ), progressively reducing the length of input sequences. Importantly, the pruning procedure is dynamic and ensures that semantically uninformative vertices in the attention graph $\mathcal{G}$ are removed along with all edges they are associated with. + +Cross-modal sparsity. Node sparsification can be naturally extended to video-language learning. For this, we propose to extend the token selection mechanism discussed above to a cross-modal setting, where video and text tokens $\mathbf{Z}_v,\mathbf{Z}_t$ are modeled jointly in a multimodal encoder. In this case, we replace the query $\mathbf{q}_{\mathrm{cls}}$ of (10) with the class token of text sequence $\mathbf{q}_{\mathrm{cls}}^{(t)}$ , obtaining cross-modal attention + +$$ +\mathbf {a} _ {m} \left(\mathbf {z} _ {i} ^ {(v)}\right) = \frac {e ^ {\langle \mathbf {q} _ {\mathrm {c l s}} ^ {(t)} , \mathbf {k} _ {i} ^ {(v)} \rangle}}{\sum_ {j = 1} ^ {N} e ^ {\langle \mathbf {q} _ {\mathrm {c l s}} ^ {(t)} , \mathbf {k} _ {j} ^ {(v)} \rangle}}, \quad i = 1, \dots , N \tag {12} +$$ + +and subsequently the token sparsification function + +$$ +\mathcal {S} _ {\mathcal {M}} \left(\mathbf {Z} _ {v}; q\right) = \left\{\mathbf {z} _ {i} ^ {(v)} \mid i \in \operatorname {t o p k} \left(\mathbf {a} _ {m} \left(\mathbf {Z} _ {v}\right), \lceil q N \rceil\right) \right\} \tag {13} +$$ + +Multimodal node sparsity $S_{\mathcal{M}}$ is applied on top of visual sparsity $\mathcal{S}_{\mathcal{V}}$ . We expect cross-modal sparsification to create + +additional room for sparsity over standalone visual modeling. While the visual encoder can identify salient actors and objects from background patches from the input clip, only the text semantics provide direct guidance for the video-text model to focus on regions relevant to the task of interest. + +With node sparsity, the compute cost of subsequent layers is improved to $O(q^{2}N^{2})$ using dense attention or $O(q(K_{l} + K_{r})GN)$ with edge sparsity, and the reduction accumulates with multiple sparse layers. + +# 3.4. Hybrid Sparse Transformers + +We propose to combine edge and node sparsity into a unified framework, SViT, as illustrated in Fig. 2. SViT is built on top of existing video-language transformer architectures that combine separate video and text encoders with a cross-modal transformer. The visual encoder blocks perform sparse self-attention in the following steps: + +- edge sparsification: given the random graph $\mathcal{E}$ of (7)-(9) compute attention weights $\mathcal{A}_{\mathcal{E}}$ , using (5); +- node sparsification: select the nodes $\mathcal{S}_{\mathcal{V}}$ to retain, using (10)-(11) with keep rate $q < 1$ . + +After video and text embeddings $\mathbf{z}_v, \mathbf{z}_t$ are derived from their respective encoders, a multimodal transformer is applied to aggregate features across modalities. It follows the design of the text encoder, except for a cross-attention module that is applied after each self-attention block, where text queries $\mathbf{q}_t$ attends to key-value pairs $\mathbf{k}_v, \mathbf{v}_v$ extracted by the video encoder. The text-to-video attention of (12)-(13) is then used to select the nodes $S_{\mathcal{M}}$ to retain, further reducing the number of video tokens for subsequent layers. + +# 4. Temporal Sparse Expansion + +In this section, we introduce a new training strategy for SViTT. We motivate for progressive model training with increasing clip length and sparsity in Sec. 4.1, and detail our pretraining procedure in Sec. 4.2. + +# 4.1. Sparsity vs. Clip Length + +The key insight behind the design of SViT is the diminishing return of clip length. In general, a $2 \times$ longer sequence does not contain twice the semantic information about the video, due to the redundancy of adjacent frames. This leads to a lower percentage of informative patches with denser frame sampling. + +Due to this redundancy, it is possible to use higher sparsity for models with longer clips. This can be implemented by reducing the keep rate $q$ of node sparsification, and the percentage of key/value blocks to attend to in edge sparsification $(K_{l} / N_{b}, K_{r} / N_{b})$ . For the latter, since the total number of blocks $N_{b} = \lceil N / G \rceil$ increases with number of frames $T$ (assuming a fixed block size $G$ ), it suffices to keep the parameters $K_{l}, K_{r}$ constant. + +![](images/af888be5dacddd1db474f9d0a29b49cf30ae8606d744c1567f4e817d74d8c8d6.jpg) +Figure 3. Temporal Sparse Expansion. We propose a multi-stage curriculum for training SViTT. At each stage, the node and edge sparsity $S$ of video-text transformer increases with clip length $T$ . + +# 4.2. Temporal Expansion + +Pretraining video-text transformers on long clips is time-consuming and leads to suboptimal models. Instead, we follow a learning strategy similar to Frozen [4], where the model is initially pretrained with shorter clips, and the number of frames increases as training progresses. However, when expanding the clip length, we increase the model sparsity to simultaneously 1) account for the redundancy of information, and 2) limit the growth of computational cost. + +Fig. 3 depicts the expansion process proposed for video-text training. In the initial training stage $j = 1$ , a dense video-text model is pretrained on clip length $T_{1}$ . Denoting the sparsity hyperparameters of SViTT at stage $j$ by $S_{j} = (q_{j}, K_{l}^{(j)}, K_{r}^{(j)})$ , we create a learning curriculum with progressively increasing clip length and sparsity, by enforcing the constraints + +$$ +T _ {1} < T _ {2} < \dots ; \tag {14} +$$ + +$$ +q _ {1} > q _ {2} > \dots ; \tag {15} +$$ + +$$ +\frac {K _ {l} ^ {(1)} + K _ {r} ^ {(1)}}{T _ {1}} > \frac {K _ {l} ^ {(2)} + K _ {r} ^ {(2)}}{T _ {2}} > \dots \tag {16} +$$ + +In practice, we use a decreasing token keep rate (15) and keep local and random attention block numbers fixed, i.e. $K_{l}^{(j)} = K_{l}$ and $K_{r}^{(j)} = K_{r}$ , to satisfy (16). + +# 5. Results + +In this section we present experimental results of SViTT on vision-language modeling. We briefly introduce the experimental setup in Sec. 5.1, and perform several ablation studies on the design choices involving model sparsification and training in Sec. 5.2. We then demonstrate the performance of SViTT on various vision-language tasks in Sec. 5.3 and include additional qualitative analysis. + +# 5.1. Experimental Setup + +Architecture. Our implementation of video-text transformer is based on Singularity [24]. The model has a two-tower structure, with separate encoders for vision and language. The video encoder $f_{v}$ is a 12-layer BEiT-B [5] initialized with ImageNet weights and inflated for video inputs. This differs from [24] which embeds each frame independently and applies late temporal fusion on extracted + +
Attn. blocks +Kl, Kr, GKeep rate +qv, qm# Edges +(M)R1DiDeMo +R5R10Mean
——7.4728.853.163.048.3
Edge sparsity
(1, 3, 56)—2.1420.741.750.537.6
(1, 5, 56)—3.2126.048.656.843.8
Node sparsity
—(0.7, 1)3.9926.951.961.346.7
—(0.7, 0.1)3.9727.653.162.947.9
Hybrid sparsity
(1, 3, 56)(0.7, 0.1)1.4819.940.550.637.0
(1, 5, 56)(0.7, 0.1)2.2224.547.658.643.6
+ +![](images/175eaeb13b8422b3fd00e0dd949245b26eba9669ea26264456c378b65f5a6112.jpg) +(a) Number of local / random blocks. + +![](images/d3c8e7f2c943fddd658086fc8e2a8b4a4b75074608c0235b7711597a91ae9c5f.jpg) +(b) Attention block size. +Figure 4. Ablation on Edge Sparsity. We evaluate dense model using different local/random blocks $(K_l, K_r)$ and block size $G$ . + +features. The text encoder $f_{t}$ is a pretrained BERT [14] model, whose last 3 layers are modified to implement the multimodal encoder $f_{m}$ , with cross-modal attention based on visual tokens as key-value pairs, which we sparsify as described in Sec. 3.3. + +Pre-training. SViTT is pre-trained on 2.5M video-text pairs from the WebVid dataset [4]. Since our goal is to investigate how to improve the effectiveness of the temporal learning of the video modality, we do not train with additional image-text corpora as done in [4, 18, 24]. + +The [cls] tokens of the video and text encoders are first linearly projected to a joint embedding space, producing feature vectors $\mathbf{z}_v = f_v(\mathbf{x}_v)$ and $\mathbf{z}_t = f_t(\mathbf{x}_t)$ , respectively. Following prior work, we use the InfoNCE loss [40] to align these feature vectors. The output of multimodal encoder $\mathbf{y} = f_m(\mathbf{z}_v,\mathbf{z}_t)$ is optimized with video-text matching (VTM) and masked language modeling (MLM) losses commonly found in VLP literature [12, 18, 24, 27, 28]. + +Downstream tasks. Trained video-text models are evaluated on two multimodal tasks: Text-to-video retrieval and video question answering. Video retrieval is evaluated on MSR-VTT [51], DiDeMo [2], Charades [43] and Something-Something v2 [20, 24], by top- $K$ recalls $(K \in \{1, 5, 10\})$ and their numeric average. Question answering is evaluated on MSRVTT-QA [49], ActivityNet-QA [10, 54] and AGQA [21], with top-1 accuracy of the answers. + +Training details are given in the Appendix. + +Table 1. Ablation on Edge and Node Sparsity. We evaluate the same dense video-text model under different sparsification modes. + +
TSparc.FLOPs (G)Mem. (GB)R1DiDeMoMean
R5R10
4Dense139.90.9628.853.163.048.3
Edge135.90.8028.351.961.447.2
Node95.80.6129.954.863.949.6
Hybrid93.90.5429.353.763.248.8
8Dense291.33.1429.654.164.149.3
Edge271.81.5729.854.965.450.1
Node197.61.7730.455.766.050.7
Hybrid166.40.9231.057.266.351.5
16Dense627.810.66Untrainable
Edge543.63.0231.655.164.650.5
Node370.94.39Untrainable
Hybrid296.21.5731.457.367.852.2
+ +Table 2. Ablation on Training Sparse Models. We compare the zero-shot performance, inference GFLOPs, and training memory (per sample) of sparse models to the dense attention baseline. + +![](images/e75c9b70a5e20a60840325a0dc06183f10051d55b57bc5321b8f748cc3e466cb.jpg) +(a) Visual sparsification. +Figure 5. Ablation on Node Sparsity. We evaluate the pre-trained dense model using different keep rates $q$ at test time. + +![](images/0a93d340808f3d944e33e31d0ef36d24f4048bdaebc85e33c0e8b76efef93881.jpg) +(b) Multimodal sparsification. + +# 5.2. Ablation Studies + +We start by training a video-text transformer with clip length of 4 frames and dense attention, and measure its zero-shot performance on downstream tasks after sparsifying its video encoder while keeping its weights unchanged. + +Edge sparsification. We first apply edge sparsification with different number of local blocks $K_{l}$ , random blocks $K_{r}$ , and block size $G$ . As shown in Fig. 4a, under a limited budget of 6 local or random attention blocks per query token, using 1 local block and 5 random blocks provides the best trade-off. Increasing the local attention window $K_{l}$ hurts long-term modeling capacity and degrades retrieval; while removing the single local block responsible for diagonal attention also impairs performance. This suggests that while query tokens should always attend to their respective blocks, there is no benefit in attending to neighboring blocks. We thus fix $K_{l} = 1$ for the rest of experiments. + +We next vary the block size $G$ of sparse attention. Fig. 4b shows that larger sizes have stronger retrieval performance, as expected. However, they also make self-attention less sparse (more costly to compute). $G = 56$ provides a good balance between performance and complexity. Tab. 1 summarizes the test performance of two edge sparsity config: $(K_{l}, K_{r}, G) = (1, 3, 56)$ and $(1, 5, 56)$ . While both underperform the dense model, we will later demonstrate that the + +
FramesTSparsityTSDiDeMo
R1R5R10Mean
44.8028.050.759.246.0
10→4.8029.353.763.248.8
88.9127.351.463.847.5
4.80→8.9131.057.266.351.5
1616.9627.552.463.247.7
4.80→8.91→16.9631.457.367.852.2
+ +gap can be closed and even reversed by training the sparse model with the proposed temporal expansion curriculum. + +Node sparsification. We next incorporate node sparsity into the video-text transformer. This includes visual sparsification (keep rate $q_{v}$ ) using the self-attention of video encoder $f_{v}$ to progressively prune the input tokens $^{3}$ , and multimodal sparsification (keep rate $q_{m}$ ) using the text-to-video attention of cross-modal encoder $f_{m}$ to further drop visual tokens unrelated to the text query. Fig. 5a shows that the dense model is quite robust to token pruning, even without sparse training. Using visual keep rate $q_{v} \geq 0.8$ has minimal impact on test results, and performance only starts to drop rapidly at $q_{v} = 0.5$ , at which point only $1/8$ of input tokens are retained after three rounds of sparsification. + +Even more surprisingly, the subsequent multimodal sparsification step, using a keep rate of $q_{m} = 0.1$ , improves zero-shot performance by $1\%$ . This shows that the $90\%$ redundant visual tokens not only add unnecessary complexity to the model, but also introduce noise that harms retrieval performance. The fact that the optimal $q_{m}$ is much lower than $q_{v}$ also suggests that text modality provides crucial semantic guidance for identifying relevant visual patches, at a much higher accuracy than visual modeling alone. + +Hybrid sparsification. Combining the best sparse settings for edges and nodes, we obtain the hybrid sparsification strategy for SViT. As shown in Tab. 1, compared to edge sparsity, the introduction of node sparsity $(q_{v} = 0.7, q_{m} = 0.1)$ only impacts recall scores marginally, while saving computations on a large portion of visual tokens throughout the network. + +Training sparse transformers. We next perform full pretraining with the sparse models and compare their performance and efficiency to the dense transformer baseline. Tab. 2 summarizes the results obtained with different input clip lengths and types of sparsity. At 4 frames, edge sparsity has small benefit due to the relatively short sequence length and node sparsity performs the best. However, at 8 frames, we start to see clear advantages to edge sparsity in memory + +Table 3. Ablation on Temporal Sparse Expansion. Sparsity $T_{S}$ indicates training on $T$ frames while removing $S \times 100\%$ attention edges of dense transformer. + +
MethodPTTMSR-VTTDiDeMo
R1MeanR1Mean
VideoCLIP [50]100M—10.420.916.6—
Frozen [4]5M423.241.521.141.1
ALPRO [26]5M824.141.423.843.0
VIOLET [18]5M425.945.023.544.4
Singularity [24]5M128.446.036.955.8
121.138.723.340.8
Singularity*2M424.440.026.444.1
824.341.025.845.5
SViTTDense Hybrid2M826.043.629.649.3
25.443.831.051.5
+ +Table 4. Zero-shot Text-to-video Retrieval. Results reported in prior works are marked in gray; * indicates our reproduced results. PT = # video-text pairs for pre-training, $T = \#$ frames per clip. + +complexity, and both edge and node sparsity outperform the dense transformer baseline. Combining both types of sparsity performs the best, while only requiring $60\%$ the FLOPs and $30\%$ the memory of the dense model. At 16 frames, the dense and node sparsity models are no longer trainable due to their quadratically increasing cost. The models with edge sparsity, however, are able to fit into GPU memory thanks to the linear complexity from sparse attention. A 16-frame SViTT with hybrid sparsity requires similar computation to an 8-frame dense model and only half of its training memory, while achieving $3\%$ higher recall. + +Progressive training. We next study the impact of temporal sparse expansion on the training of SViT models on longer clips. Tab. 3 compares the performance of models trained using temporal expansion (i.e. initialized from checkpoints pretrained on fewer frames and lower sparsity) to standard single-stage training. For single-stage training, performance does not improve substantially with clip length. This is in contrast to the proposed sparse expansion, where using 8 instead or 4 frames results in a gain of $2.7\%$ . This suggests that the models have learned to exploit the temporal relationships between video frames. For a given clip length, sparse expansion also substantially improves upon single stage performance, from 2.8 points for $T = 4$ to 4.5 points for $T = 16$ . In fact, sparse expansion training with a shorter clip length (e.g. 4 frames) can outperform single stage training with a larger length (16 frames). + +# 5.3. Main Results + +We compare SViT to state-of-the-art models in text-to-video retrieval and video question answering. + +Text-to-video retrieval. Video-text retrieval is evaluated under zero-shot and fine-tuning settings. Tab. 4 shows the zero-shot results on MSR-VTT and DiDeMo. Compared to our reproduced models of Singularity on WebVid-2M, which aggregate frame-level features using a temporal transformer encoder, the spatiotemporal transformer + +![](images/26d7637a13dd55a96cc9d03196ab310af085f6b87cd7c8c84b391db2a955803f.jpg) +Input + +![](images/6f1e49cafcdfe44a43d9a987b9f8f239c0798861c274dd511f0aff506007747d.jpg) +Visual, $q_{v} = 0.6$ +Figure 6. Qualitative Results. SViTT isolates informative regions from background patches to facilitate efficient temporal reasoning. + +![](images/aacaa1aa7c7328c711fc1d11fd7e61a76a0c0684441b55e81a0f160eb27bce8e.jpg) +Cross-modal, $q_{m} = 0.1$ + +
MethodPTTCharadesSSv2
R1MeanR1Mean
Frozen [4]5M3211.925.1——
CLIP4Clip [35]400M1213.927.143.165.1
ECLIPSE [31]400M3215.730.3——
\( MKTVR^† \)[36]400M4216.634.7——
Singularity [24]5M1——36.458.9
4——44.166.6
SViTTDense Hybrid2M816.032.743.666.1
17.735.749.869.3
+ +Table 5. Text-to-video Retrieval with Fine-tuning. + +
MethodPTTMSRVTTANetAGQA
HME [17]—2033.0—47.7
HCRN [23]12835.5—47.4
ClipBERT [25]0.2M1637.4——
ALPRO [26]5M1642.1——
Just Ask [52]69M64041.538.9—
MERLOT [56]180M543.141.4—
VIOLET [18]185M443.9—49.2
Singularity [24]5M142.741.8—
SViTTDense Hybrid2M842.742.350.2
43.043.252.7
+ +Table 6. Video Question Answering. + +of SViTT produces stronger results on both downstream datasets. This highlights the importance of temporal modeling in earlier layers of video-text transformers. SViTT with hybrid sparsity has similar performance to the dense model on MSR-VTT but significantly outperforms in on DiDeMo, which contains longer videos with localized activities. + +For Charades and SSv2, we evaluate text-to-video retrieval with fine-tuning, as shown in Tab. 5. Both datasets are action-centric, posing a greater challenge to the temporal reasoning of video-text models. SViT with hybrid sparsification dominates the dense variant by $\sim 3\%$ on both datasets, a more substantial gap than observed for MSR-VTT and DiDeMo. This confirms our hypothesis that exploiting node and edge sparsity reduces the dependency of models on contextual regions, forcing them to focus on the temporal dynamics of person and objects in the foreground. + +Video question answering. We next evaluate the cross-modal modeling of SViT on MSRVTT-QA, ActivityNet + +QA and AGQA. As shown in Tab. 6, the hybrid sparsity version of SViTT outperforms the dense transformer baseline on all three datasets, thanks to its more efficient temporal modeling. On MSRVTT-QA, the accuracy gap is small between dense and sparse transformer (0.3%), and SViTT marginally underperforms baselines pretrained with fewer number of frames (MERLOT [56], VIOLET [18]). This is likely due to the nature of MSRVTT, which consists of short video clips and questions biased towards spatial cues, allowing temporal modeling little benefit over spatial transformers pretrained on massive image & video data. On ActivityNet-QA and AGQA, which both contain longer clips and temporally challenging questions, the sparse modeling of SViTT proves advantageous, with 0.9% and 2.3% boost in accuracy respectively, beating all baseline methods. + +Qualitative analysis. To show how SViT efficiently identifies and concentrates its computation on informative spatiotemporal regions of the input clips, we visualize the outcome of node sparsification in Fig. 6. Using visual sparsification in video encoder $f_{v}$ , SViT learns to isolate foreground entities from the majority of background patches, enabling the model to perform sparse video-text inference on longer temporal context. Cross-modal attention in multimodal encoder $f_{m}$ provides an even stronger signal for isolating the regions of interest of each video clip, validating the importance of text semantics in visual sparsification. + +# 6. Conclusion + +This work introduced SViTT, a sparse video-text transformer for efficient reasoning over a long temporal context. By interpreting visual transformers as graph networks, we proposed to optimize their edge and node sparsity, using a combination of sparse block attention, visual token pruning and text-guided token selection. 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Actbert: Learning global-local video-text representations. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 8746-8755, 2020. 2 \ No newline at end of file diff --git a/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/images.zip b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..7d144c34749d006c5fd4fc232b19be05b92344a2 --- /dev/null +++ b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:52ed8ab6094ed1a4f95b8e3ab8c3ed77a38fb0cf05ef41bfebcde24365481011 +size 546893 diff --git a/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/layout.json b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e8359ad43b81b4722ebb4d4e2ec8b69ab3fa5ca9 --- /dev/null +++ b/2023/SViTT_ Temporal Learning of Sparse Video-Text Transformers/layout.json @@ -0,0 +1,10686 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 100, + 103, + 493, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 103, + 493, + 121 + ], + "spans": [ + { + "bbox": [ + 100, + 103, + 493, + 121 + ], + "type": "text", + "content": "SViTT: Temporal Learning of Sparse Video-Text Transformers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 127, + 138, + 465, + 153 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 138, + 465, + 153 + ], + "spans": [ + { + "bbox": [ + 127, + 138, + 465, + 153 + ], + "type": "text", + "content": "Yi Li*1 Kyle Min² Subarna Tripathi² Nuno Vasconcelos¹" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 220, + 157, + 373, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 220, + 157, + 373, + 172 + ], + "spans": [ + { + "bbox": [ + 220, + 157, + 373, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 220, + 157, + 373, + 172 + ], + "type": "text", + "content": "UC San Diego " + }, + { + "bbox": [ + 220, + 157, + 373, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 220, + 157, + 373, + 172 + ], + "type": "text", + "content": "Intel Labs" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 174, + 492, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 174, + 492, + 186 + ], + "spans": [ + { + "bbox": [ + 96, + 174, + 492, + 186 + ], + "type": "text", + "content": "{yil898, nvasconcelos}@ucsd.edu {kyle.min, subarna.tripathi}@intel.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 209, + 192, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 209, + 192, + 221 + ], + "spans": [ + { + "bbox": [ + 143, + 209, + 192, + 221 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 235, + 290, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 290, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 290, + 510 + ], + "type": "text", + "content": "Do video-text transformers learn to model temporal relationships across frames? Despite their immense capacity and the abundance of multimodal training data, recent work has revealed the strong tendency of video-text models towards frame-based spatial representations, while temporal reasoning remains largely unsolved. In this work, we identify several key challenges in temporal learning of video-text transformers: the spatiotemporal trade-off from limited network size; the curse of dimensionality for multi-frame modeling; and the diminishing returns of semantic information by extending clip length. Guided by these findings, we propose SViTT, a sparse video-text architecture that performs multi-frame reasoning with significantly lower cost than naive transformers with dense attention. Analogous to graph-based networks, SViTT employs two forms of sparsity: edge sparsity that limits the query-key communications between tokens in self-attention, and node sparsity that discards uninformative visual tokens. Trained with a curriculum which increases model sparsity with the clip length, SViTT outperforms dense transformer baselines on multiple video-text retrieval and question answering benchmarks, with a fraction of computational cost. Project page: http://svcl.ucsd.edu/projects/svittt." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 522, + 128, + 534 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 128, + 534 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 128, + 534 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 539, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 670 + ], + "type": "text", + "content": "With the rapid development of deep neural networks for computer vision and natural language processing, there has been growing interest in learning correspondences across the visual and text modalities. A variety of vision-language pretraining frameworks have been proposed [12, 22, 29, 34] for learning high-quality cross-modal representations with weak supervision. Recently, progress on visual transformers (ViT) [5, 16, 32] has enabled seamless integration of both modalities into a unified attention model, leading to image-text transformer architectures that achieve state-the-art performance on vision-language benchmarks [1, 27, 44]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 287, + 695 + ], + "type": "text", + "content": "Progress has also occurred in video-language pretraining by leveraging image-text models for improved frame-based" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 313, + 209, + 538, + 270 + ], + "blocks": [ + { + "bbox": [ + 313, + 209, + 538, + 270 + ], + "lines": [ + { + "bbox": [ + 313, + 209, + 538, + 270 + ], + "spans": [ + { + "bbox": [ + 313, + 209, + 538, + 270 + ], + "type": "image", + "image_path": "c93b0b7814c5eab4d4a81860413017e46d3c4a8fa5a69d6ffaab2720c12c3307.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 271, + 539, + 281 + ], + "lines": [ + { + "bbox": [ + 313, + 271, + 539, + 281 + ], + "spans": [ + { + "bbox": [ + 313, + 271, + 539, + 281 + ], + "type": "text", + "content": "One person takes a pillow and some homework from an old chair, then smiles and laughs." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 317, + 294, + 536, + 437 + ], + "blocks": [ + { + "bbox": [ + 317, + 294, + 536, + 437 + ], + "lines": [ + { + "bbox": [ + 317, + 294, + 536, + 437 + ], + "spans": [ + { + "bbox": [ + 317, + 294, + 536, + 437 + ], + "type": "image", + "image_path": "57438170fa659e11bcc7407c6e9591bf463b89d4e53eea9d5ea616fdecfe4fa1.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 445, + 545, + 523 + ], + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 523 + ], + "type": "text", + "content": "Figure 1. We propose SViT, a sparse video-text transformer for efficient modeling of temporal relationships across video frames. Top: Semantic information for video-text reasoning is highly localized in the spatiotemporal volume, making dense modeling inefficient and prone to contextual noises. Bottom: SViT pursues edge sparsity by limiting query-key pairs in self-attention, and node sparsity by pruning redundant tokens from visual sequence." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 530, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 545, + 639 + ], + "type": "text", + "content": "reasoning [4, 9, 18]. Spatial modeling has the advantage of efficient (linear) scaling to long duration videos. Perhaps due to this, single-frame models have proven surprisingly effective at video-text tasks, matching or exceeding prior arts with complex temporal components [9, 24]. However, spatial modeling creates a bias towards static appearance and overlooks the importance of temporal reasoning in videos. This suggests the question: Are temporal dynamics not worth modeling in the video-language domain?" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Upon a closer investigation, we identify a few key challenges to incorporating multi-frame reasoning in video-language models. First, limited model size implies a tradeoff between spatial and temporal learning (a classic example being 2D/3D convolutions in video CNNs [46]). For any given dataset, optimal performance requires a careful bal" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 209, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 209, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 209, + 712 + ], + "type": "text", + "content": "*Work done during an internship at Intel Labs." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18919" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 300 + ], + "type": "text", + "content": "ance between the two. Second, long-term video models typically have larger model sizes and are more prone to overfitting. Hence, for longer term video models, it becomes more important to carefully allocate parameters and control model growth. Finally, even if extending the clip length improves the results, it is subject to diminishing returns since the amount of information provided by a video clip does not grow linearly with its sampling rate. If the model size is not controlled, the computational increase may not justify the gains in accuracy. This is critical for transformer-based architectures, since self-attention mechanisms have a quadratic memory and time cost with respect to input length. In summary, model complexity should be adjusted adaptively, depending on the input videos, to achieve the best trade-off between spatial representation, temporal representation, overfitting potential, and complexity. Since existing video-text models lack this ability, they either attain a suboptimal balance between spatial and temporal modeling, or do not learn meaningful temporal representations at all." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 301, + 289, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 301, + 289, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 301, + 289, + 578 + ], + "type": "text", + "content": "Motivated by these findings, we argue that video-text models should learn to allocate modeling resources to the video data. We hypothesize that, rather than uniformly extending the model to longer clips, the allocation of these resources to the relevant spatiotemporal locations of the video is crucial for efficient learning from long clips. For transformer models, this allocation is naturally performed by pruning redundant attention connections. We then propose to accomplish these goals by exploring transformer sparsification techniques. This motivates the introduction of a Sparse Video-Text Transformer (SViTT) inspired by graph models. As illustrated in Fig. 1, SViTT treats video tokens as graph vertices, and self-attention patterns as edges that connect them. We design SViTT to pursue sparsity for both: edge sparsity aims at reducing query-key pairs in attention module while maintaining its global reasoning capability; node sparsity reduces to identifying informative tokens (e.g., corresponding to moving objects or person in the foreground) and pruning background feature embeddings. To address the diminishing returns for longer input clips, we propose to train SViTT with temporal sparse expansion, a curriculum learning strategy that increases clip length and model sparsity, in sync, at each training stage." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 579, + 289, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 289, + 687 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 289, + 687 + ], + "type": "text", + "content": "SViTT is evaluated on diverse video-text benchmarks from video retrieval to question answering, comparing to prior arts and our own dense modeling baselines. First, we perform a series of ablation studies to understand the benefit of sparse modeling in transformers. Interestingly, we find that both nodes (tokens) and edges (attention) can be pruned drastically at inference, with a small impact on test performance. In fact, token selection using cross-modal attention improves retrieval results by " + }, + { + "bbox": [ + 47, + 579, + 289, + 687 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 47, + 579, + 289, + 687 + ], + "type": "text", + "content": " without re-training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "We next perform full pre-training with the sparse models and evaluate their downstream performance. We observe" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "that SViTT scales well to longer input clips where the accuracy of dense transformers drops due to optimization difficulties. On all video-text benchmarks, SViTT reports comparable or better performance than their dense counterparts with lower computational cost, outperforming prior arts including those trained with additional image-text corpora." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 144, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 547, + 205 + ], + "type": "text", + "content": "The key contributions of this work are: 1) a video-text architecture SViTT that unifies edge and node sparsity; 2) a sparse expansion curriculum for training SViTT on long video clips; and 3) empirical results that demonstrate its temporal modeling efficacy on video-language tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 213, + 392, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 392, + 225 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 392, + 225 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 229, + 547, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 229, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 229, + 547, + 397 + ], + "type": "text", + "content": "Video-language pretraining. Vision-language pretraining has been widely adopted for various video-text downstream tasks. VideoBERT [45] was an early effort, using video-text pretraining for action classification and video captioning. Recently, the massive-scale instructional video dataset HowTo100M [39] has motivated many approaches to video-text pretraining [4, 19, 24, 38, 56, 57]. Frozen [4] proposed to pretrain a space-time transformer on a combination of video and image data to enable zero-shot text-to-video retrieval. ATP [9] and Singularity [24] showed strong performance using image-based models, highlighting the importance of spatial modeling for video-language tasks. In this work, we pursue an alternative route of efficient temporal modeling across multiple video frames." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 400, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 628 + ], + "type": "text", + "content": "Sparse transformers. The self-attention of naive transformers [16, 48] has quadratic complexity making them inefficient for modeling long sequences. Different forms of sparse attention have been studied to improve text [7, 13, 55], image [15, 32, 47], and video modeling [3, 8, 33], although the sparse patterns are typically predetermined and do not adapt to the input semantics. Several works have also considered speeding up vision transformers by adaptively reducing the number of input tokens [11, 30, 37, 41, 42, 53]. For example, DynamicViT [41] proposed to drop visual tokens with a dedicated module that identifies and prunes less informative ones. TokenLearner [42] introduces a learnable module to adaptively generate a small subset of tokens from input frames. EViT [30] progressively reduces the number of tokens based on their attention scores, fusing inattentive tokens into a new token to preserve input information. Unlike prior works that focus on visual modeling on images or videos alone, we study the sparsity of video-language transformers which can benefit from cross-modal attention." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 636, + 538, + 651 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 636, + 538, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 636, + 538, + 651 + ], + "type": "text", + "content": "3. Exploiting Sparsity in Video Transformers" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "In this section, we formulate video transformers as graph models (Sec. 3.1) and present a set of approaches towards sparse video modeling, exploiting the redundancy of edges (Sec. 3.2) and nodes (Sec. 3.3). We combine these into a unified sparse framework for video-text learning (Sec. 3.4)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18920" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 534, + 215 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 534, + 215 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 534, + 215 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 534, + 215 + ], + "type": "image", + "image_path": "600d9c822f8a1501df6e9302e0b41b2a828001dcda42de457cf87a74c04e7fa2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 217, + 293, + 318 + ], + "blocks": [ + { + "bbox": [ + 51, + 217, + 293, + 318 + ], + "lines": [ + { + "bbox": [ + 51, + 217, + 293, + 318 + ], + "spans": [ + { + "bbox": [ + 51, + 217, + 293, + 318 + ], + "type": "image", + "image_path": "28f24f691c9c9098e6abd4a586cc7e627f09ca5d7a91ee2259818c951fa6a83b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": "Figure 2. Model Architecture. SViT improves modeling efficiency of conventional video-text transformers through two key components: node sparsity and edge sparsity. Edge sparsification " + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{\\varepsilon}" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": " computes sparse self-attention of input visual sequence " + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": ", where each query token attends to a small subset of key and value tokens, with connectivity " + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": " specified by global, local, and random attention. Node sparsification " + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "inline_equation", + "content": "S_{\\nu}" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": " uses global attention scores from " + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{\\varepsilon}" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": " to prune uninformative tokens, removing them from the computational graph of subsequent layers; " + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{M}}" + }, + { + "bbox": [ + 46, + 327, + 547, + 384 + ], + "type": "text", + "content": " uses text-to-video attention in the multimodal encoder to further reduce the length of visual sequence." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 302, + 217, + 541, + 318 + ], + "blocks": [ + { + "bbox": [ + 302, + 217, + 541, + 318 + ], + "lines": [ + { + "bbox": [ + 302, + 217, + 541, + 318 + ], + "spans": [ + { + "bbox": [ + 302, + 217, + 541, + 318 + ], + "type": "image", + "image_path": "362a5d2966257b1b22e43d849893cf7612b15c3a3420f64a61fb2e58c0350404.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 391, + 253, + 404 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 391, + 253, + 404 + ], + "spans": [ + { + "bbox": [ + 47, + 391, + 253, + 404 + ], + "type": "text", + "content": "3.1. Video Transformers are Graph Models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "type": "text", + "content": "Visual transformers [16] are deep neural networks that model images or videos as sequences of local pixel patches, through a combination of patchwise feature transformation and self-attention. Inspired by transformer architectures for language models [48], video transformers encode input clips into a sequence of spatiotemporal patches, flattened and linearly projected to a " + }, + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 407, + 288, + 492 + ], + "type": "text", + "content": "-dimensional embedding space:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 52, + 500, + 287, + 530 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 500, + 287, + 530 + ], + "spans": [ + { + "bbox": [ + 52, + 500, + 287, + 530 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} ^ {(0)} = \\left(\\mathbf {z} _ {\\text {c l s}} ^ {(0)}, \\mathbf {z} _ {1} ^ {(0)}, \\dots , \\mathbf {z} _ {N} ^ {(0)}\\right) = f ^ {\\operatorname {t o k}} \\left(\\mathbf {x} _ {1: T}\\right) \\in \\mathbb {R} ^ {(N + 1) \\times d} \\tag {1}", + "image_path": "b55b4e5210a5be52506c57307e123d161f65a97ff433a66964ef59b13e78474d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "inline_equation", + "content": "N = T^{\\prime}H^{\\prime}W^{\\prime}" + }, + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "text", + "content": " is the volume of the 3D patch grid, and " + }, + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{cls}}^{(0)}" + }, + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "text", + "content": " denotes a special class token responsible for instance-level prediction. The tokenized sequence is processed by a cascade of transformer blocks " + }, + { + "bbox": [ + 46, + 531, + 288, + 582 + ], + "type": "inline_equation", + "content": "f^{(l)}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 589, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 589, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 93, + 589, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} ^ {(l)} = f ^ {(l)} \\left(\\mathbf {Z} ^ {(l - 1)}\\right), \\quad l = 1, \\dots , L \\tag {2}", + "image_path": "61b9721405311f3fdcac3600bd6b1cde7161a20f8bb627d0e23f31627e75ac45.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "type": "text", + "content": "each of which computes the self-attention " + }, + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "type": "text", + "content": " between input tokens, followed by a feed-forward network " + }, + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 614, + 287, + 638 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 83, + 647, + 287, + 663 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 647, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 83, + 647, + 287, + 663 + ], + "type": "interline_equation", + "content": "f ^ {(l)} (\\mathbf {Z}) = \\mathcal {F} \\left(\\mathcal {A} \\left(\\mathbf {Z} \\mathbf {W} _ {K} ^ {T}, \\mathbf {Z} \\mathbf {W} _ {Q} ^ {T}, \\mathbf {Z} \\mathbf {W} _ {V} ^ {T}\\right)\\right), \\tag {3}", + "image_path": "dc6635cb85c7eb208dcc78bb248703fdb463e4c71001722b69abb9c8336386c6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 110, + 668, + 287, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 668, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 110, + 668, + 287, + 684 + ], + "type": "interline_equation", + "content": "\\mathcal {A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\sigma (\\mathbf {Q} \\mathbf {K} ^ {T}) \\mathbf {V} \\tag {4}", + "image_path": "ac0ecc6af8a40817812b1982e1bf3b279f8b107ddef7040e1d4baf4e82e0934d.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": "We interpret the transformer architecture as a special case of graph networks [6], with nodes representing tokenized video patches and edges connecting pairs of tokens for which self-attention is computed. Specifically, consider a directed graph " + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = (\\mathcal{V},\\mathcal{E})" + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": " defined by the vertices " + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\mathbf{z}_1,\\dots ,\\mathbf{z}_N\\}" + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": " corresponding to spatiotemporal video patches, and edges " + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "inline_equation", + "content": "\\mathcal{E}\\subseteq \\{1,\\ldots ,N\\} ^2" + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": " connecting pairs of nodes. The self-attention of (4) can be generalized such that node " + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": " attends to " + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_j" + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": " only if " + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "inline_equation", + "content": "(i,j)\\in \\mathcal{E}" + }, + { + "bbox": [ + 304, + 392, + 547, + 500 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 359, + 509, + 545, + 537 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 359, + 509, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 359, + 509, + 545, + 537 + ], + "type": "interline_equation", + "content": "\\mathcal {A} _ {\\mathcal {E}} \\left(\\mathbf {q} _ {i}, \\mathbf {K}, \\mathbf {V}\\right) = \\sum_ {j: (i, j) \\in \\mathcal {E}} \\mathbf {a} _ {i j} \\mathbf {v} _ {j}, \\tag {5}", + "image_path": "9585c8f3fad7990ead887ed861573cadef5dd16daf2bc43604758055b4e93c1b.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 372, + 543, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 543, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 372, + 543, + 545, + 574 + ], + "type": "interline_equation", + "content": "\\mathbf {a} _ {i j} = \\frac {e ^ {\\langle \\mathbf {q} _ {i} , \\mathbf {k} _ {j} \\rangle}}{\\sum_ {j : (i , j) \\in \\mathcal {E}} e ^ {\\langle \\mathbf {q} _ {i} , \\mathbf {k} _ {j} \\rangle}} \\tag {6}", + "image_path": "e4fb243a212194154d9142a9e2bba0e728aaa9191f60e1ba531debc815e3409d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "Under this interpretation, the transformer architecture with full attention resembles a complete graph, where " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": " includes every pair of vertices. This dense attention mechanism endows (5) with quadratic memory and time complexity w.r.t. sequence length " + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": ", making naive transformers notoriously inefficient to train and expensive to deploy, especially for longer video clips. We argue that due to the inherent sparsity of information in video data, a large portion of the graph can be pruned dynamically without significant performance loss, leading to a sparse graph model of significantly lower cost for training and inference." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "type": "text", + "content": "1Attention heads, residual connections and normalization terms are omitted for brevity, although we use the conventional implementation [48]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18921" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 271, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 271, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 271, + 85 + ], + "type": "text", + "content": "3.2. Edge Sparsity: Local & Random Attention" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 287, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 287, + 160 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 287, + 160 + ], + "type": "text", + "content": "Prior natural language processing models, such as BigBird [55], have explored the idea of restricting the number of key-value pairs each query token attends to, which reduced the number of edges in " + }, + { + "bbox": [ + 46, + 87, + 287, + 160 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 87, + 287, + 160 + ], + "type": "text", + "content": ". We use a similar procedure to create a video transformer with edge sparsity, utilizing a combination of local, random and global attention." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": "Local attention. Regional tokens " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{z}_i\\}_{i=1}^N" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": " are first chunked into " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "N_b = \\lceil N / G \\rceil" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": " contiguous blocks of size " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "G^2" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": ". Tokens of one block " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": " attend to a local neighborhood of " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "K_l" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": " blocks " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "\\{k - \\Delta, \\dots, k + \\Delta\\}" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "inline_equation", + "content": "\\Delta = (K_l - 1) / 2" + }, + { + "bbox": [ + 46, + 163, + 288, + 225 + ], + "type": "text", + "content": " is the maximum range of local attention," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 93, + 234, + 287, + 247 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 234, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 93, + 234, + 287, + 247 + ], + "type": "interline_equation", + "content": "(k, k ^ {\\prime}) \\in \\mathcal {E}, \\quad \\forall k, k ^ {\\prime}: | k ^ {\\prime} - k | \\leq \\Delta \\tag {7}", + "image_path": "0c171e9c7b5d238d61fb75e892f11ed0e4d20e807080f58ede82c57b3398ef93.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 258, + 287, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 287, + 307 + ], + "type": "text", + "content": "This preserves the modeling of interactions between local features (objects, people, textures) that does not require long-range attention. In the case of " + }, + { + "bbox": [ + 46, + 258, + 287, + 307 + ], + "type": "inline_equation", + "content": "K_{l} = 1" + }, + { + "bbox": [ + 46, + 258, + 287, + 307 + ], + "type": "text", + "content": ", local reduces to diagonal attention, where each block only attends to itself." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 310, + 287, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 347 + ], + "type": "text", + "content": "Random attention. Beyond local attention, each block also attends to " + }, + { + "bbox": [ + 46, + 310, + 287, + 347 + ], + "type": "inline_equation", + "content": "K_{r}" + }, + { + "bbox": [ + 46, + 310, + 287, + 347 + ], + "type": "text", + "content": " other blocks sampled randomly from the input sequence," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 111, + 356, + 287, + 370 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 356, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 111, + 356, + 287, + 370 + ], + "type": "interline_equation", + "content": "\\left(k, k ^ {\\prime}\\right) \\in \\mathcal {E}, \\quad \\forall k ^ {\\prime} \\in \\mathcal {N} (k) \\tag {8}", + "image_path": "4bf7dedb2abbcb3c76917fc7eef5bb44244bcae23c1d352345875794494e3259.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(k)" + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "text", + "content": " is a random subset of " + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "inline_equation", + "content": "\\{k' \\mid |k' - k| > \\Delta\\}" + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "inline_equation", + "content": "K_r" + }, + { + "bbox": [ + 46, + 379, + 287, + 417 + ], + "type": "text", + "content": ". This enables the transformer to model long-range visual relationships while avoiding the quadratic cost." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": "Global attention. Class token " + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": " always attends to/from regional tokens " + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": ", i.e. the link between " + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_i" + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": ", as well as " + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i" + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 420, + 287, + 458 + ], + "type": "text", + "content": ", are always retained:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 93, + 467, + 287, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 467, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 93, + 467, + 287, + 480 + ], + "type": "interline_equation", + "content": "(\\operatorname {c l s}, i), (i, \\operatorname {c l s}) \\in \\mathcal {E}, \\quad i = 1, \\dots , N \\tag {9}", + "image_path": "38c5030b2494a7ad8f462f259a0a950e2a002cb835d88c849adb41720e331e52.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 490, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 514 + ], + "type": "text", + "content": "This enables " + }, + { + "bbox": [ + 46, + 490, + 287, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 490, + 287, + 514 + ], + "type": "text", + "content": " to capture global video context, even when the rest of tokens do not attend globally." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "text", + "content": "In summary, we retain all attention connections for local-to-global and global-to-local vertices, and limit local-to-local edges to " + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "inline_equation", + "content": "(K_l + K_r)G" + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "text", + "content": " per token. Edge sparsity has a linear asymptotic cost of " + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "inline_equation", + "content": "O\\big((K_l + K_r)GN\\big)" + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "text", + "content": ", a significant improvement over dense attention at " + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "inline_equation", + "content": "O(N^2)" + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "text", + "content": ". However, this approach has two critical limitations of this strategy. First, the sparse patterns are predetermined and do not adapt dynamically to the input sequence. Second, the connections that remain in " + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 46, + 514, + 287, + 694 + ], + "type": "text", + "content": " are not determined by the video semantics. In result, connections between pairs of tokens of low semantic affinity (low attention values) may be preserved, impairing the efficiency of the sparse attention mechanism. To enable more aggressive sparsification, we introduce a second mechanism, which is dynamic, guided by video semantics, and applied to the nodes of the graph." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 517, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 517, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 517, + 85 + ], + "type": "text", + "content": "3.3. Node Sparsity: Dynamic Token Pruning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 87, + 545, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 87, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 304, + 87, + 545, + 182 + ], + "type": "text", + "content": "A large percentage of the tokens of a video transformer corresponds to contextual regions, which contain little temporal dynamics and are only weakly related to the prediction target (e.g. background content uninformative of the activities of subjects in the foreground). While edge sparsification improves the efficiency of self-attention, it lacks both the flexibility and the semantic sensitivity to account for the uneven distribution of information across video patches." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "text", + "content": "To introduce these properties, we propose a node sparsification strategy, based on the dynamic pruning of tokens. We leverage a combination of observations. First, video semantics are summarized by the class tokens " + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "text", + "content": ", which contain a global representation of the information of interest for classification. Second the global-to-local edges survive the edge sparsification, through (9), making the attention weights from the " + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "text", + "content": " to all regional tokens " + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 183, + 545, + 278 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 341, + 284, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 284, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 341, + 284, + 545, + 316 + ], + "type": "interline_equation", + "content": "\\mathbf {a} \\left(\\mathbf {z} _ {i}\\right) = \\frac {e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} , \\mathbf {k} _ {i} \\rangle}}{\\sum_ {j = 1} ^ {N} e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}}, \\mathbf {k} _ {j} \\rangle}}, \\quad i = 1, \\dots , N \\tag {10}", + "image_path": "5c6228378b61e3cf75cec25353e854dd59179d147ef76d5b641405cbd2db6458.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": "available for node sparsification. Since the class token is used for video-level predictions, " + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{a}(\\mathbf{z}_i)" + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": " quantifies the contribution of feature " + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": " to the main task. This implies that nodes " + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i" + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": " of low " + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{a}(\\mathbf{z}_i)" + }, + { + "bbox": [ + 304, + 320, + 545, + 369 + ], + "type": "text", + "content": " are not informative and can be ignored [30]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 369, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 392 + ], + "type": "text", + "content": "Node pruning then reduces to keeping the " + }, + { + "bbox": [ + 304, + 369, + 545, + 392 + ], + "type": "inline_equation", + "content": "N' = \\lceil qN \\rceil" + }, + { + "bbox": [ + 304, + 369, + 545, + 392 + ], + "type": "text", + "content": " tokens of largest class attention" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 340, + 399, + 545, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 399, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 340, + 399, + 545, + 413 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\mathcal {V}} (\\mathbf {Z}; q) = \\left\\{\\mathbf {z} _ {i} \\mid i \\in \\operatorname {t o p k} (\\mathbf {a} (\\mathbf {Z}), \\lceil q N \\rceil) \\right\\} \\tag {11}", + "image_path": "9eb652a23a591e5f83bf13590815209c43dc25075bdfce241a131b4283d9e4b1.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": "where hyperparameter " + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": " denotes keep rate and topk(L, m) selects the " + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": " largest entries of vector " + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": ". This procedure is repeated multiple times throughout the video encoder (keep rate " + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "inline_equation", + "content": "q^{(l)}" + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": " at layer " + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": "), progressively reducing the length of input sequences. Importantly, the pruning procedure is dynamic and ensures that semantically uninformative vertices in the attention graph " + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 418, + 545, + 514 + ], + "type": "text", + "content": " are removed along with all edges they are associated with." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "text", + "content": "Cross-modal sparsity. Node sparsification can be naturally extended to video-language learning. For this, we propose to extend the token selection mechanism discussed above to a cross-modal setting, where video and text tokens " + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_v,\\mathbf{Z}_t" + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "text", + "content": " are modeled jointly in a multimodal encoder. In this case, we replace the query " + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "text", + "content": " of (10) with the class token of text sequence " + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_{\\mathrm{cls}}^{(t)}" + }, + { + "bbox": [ + 304, + 517, + 545, + 604 + ], + "type": "text", + "content": ", obtaining cross-modal attention" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 321, + 609, + 545, + 644 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 609, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 321, + 609, + 545, + 644 + ], + "type": "interline_equation", + "content": "\\mathbf {a} _ {m} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) = \\frac {e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} ^ {(t)} , \\mathbf {k} _ {i} ^ {(v)} \\rangle}}{\\sum_ {j = 1} ^ {N} e ^ {\\langle \\mathbf {q} _ {\\mathrm {c l s}} ^ {(t)} , \\mathbf {k} _ {j} ^ {(v)} \\rangle}}, \\quad i = 1, \\dots , N \\tag {12}", + "image_path": "c940d3c1520eb7a1521b590c18ad893402564f56df3db50321abe3f0420bb6d3.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 650, + 509, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 650, + 509, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 650, + 509, + 662 + ], + "type": "text", + "content": "and subsequently the token sparsification function" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 318, + 668, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 668, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 318, + 668, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {S} _ {\\mathcal {M}} \\left(\\mathbf {Z} _ {v}; q\\right) = \\left\\{\\mathbf {z} _ {i} ^ {(v)} \\mid i \\in \\operatorname {t o p k} \\left(\\mathbf {a} _ {m} \\left(\\mathbf {Z} _ {v}\\right), \\lceil q N \\rceil\\right) \\right\\} \\tag {13}", + "image_path": "08d2ac2d4439fe6d16f6f8f61b015c58ad8576728939c3e5c03baaeb6ccb50fb.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Multimodal node sparsity " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{M}}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " is applied on top of visual sparsity " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_{\\mathcal{V}}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": ". We expect cross-modal sparsification to create" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "text", + "content": "2 Padding is added when " + }, + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "text", + "content": " is not divisible by " + }, + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 58, + 702, + 217, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18922" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 132 + ], + "type": "text", + "content": "additional room for sparsity over standalone visual modeling. While the visual encoder can identify salient actors and objects from background patches from the input clip, only the text semantics provide direct guidance for the video-text model to focus on regions relevant to the task of interest." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "type": "text", + "content": "With node sparsity, the compute cost of subsequent layers is improved to " + }, + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "type": "inline_equation", + "content": "O(q^{2}N^{2})" + }, + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "type": "text", + "content": " using dense attention or " + }, + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "type": "inline_equation", + "content": "O(q(K_{l} + K_{r})GN)" + }, + { + "bbox": [ + 47, + 133, + 288, + 180 + ], + "type": "text", + "content": " with edge sparsity, and the reduction accumulates with multiple sparse layers." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 188, + 205, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 188, + 205, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 205, + 201 + ], + "type": "text", + "content": "3.4. Hybrid Sparse Transformers" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 203, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 203, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 287, + 276 + ], + "type": "text", + "content": "We propose to combine edge and node sparsity into a unified framework, SViT, as illustrated in Fig. 2. SViT is built on top of existing video-language transformer architectures that combine separate video and text encoders with a cross-modal transformer. The visual encoder blocks perform sparse self-attention in the following steps:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 281, + 287, + 335 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "type": "text", + "content": "- edge sparsification: given the random graph " + }, + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "type": "text", + "content": " of (7)-(9) compute attention weights " + }, + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{\\mathcal{E}}" + }, + { + "bbox": [ + 58, + 281, + 287, + 306 + ], + "type": "text", + "content": ", using (5);" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "type": "text", + "content": "- node sparsification: select the nodes " + }, + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_{\\mathcal{V}}" + }, + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "type": "text", + "content": " to retain, using (10)-(11) with keep rate " + }, + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "type": "inline_equation", + "content": "q < 1" + }, + { + "bbox": [ + 58, + 312, + 287, + 335 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "text", + "content": "After video and text embeddings " + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_v, \\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "text", + "content": " are derived from their respective encoders, a multimodal transformer is applied to aggregate features across modalities. It follows the design of the text encoder, except for a cross-attention module that is applied after each self-attention block, where text queries " + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_t" + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "text", + "content": " attends to key-value pairs " + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_v, \\mathbf{v}_v" + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "text", + "content": " extracted by the video encoder. The text-to-video attention of (12)-(13) is then used to select the nodes " + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{M}}" + }, + { + "bbox": [ + 46, + 341, + 287, + 449 + ], + "type": "text", + "content": " to retain, further reducing the number of video tokens for subsequent layers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 457, + 206, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 206, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 206, + 472 + ], + "type": "text", + "content": "4. Temporal Sparse Expansion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 475, + 287, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 522 + ], + "type": "text", + "content": "In this section, we introduce a new training strategy for SViTT. We motivate for progressive model training with increasing clip length and sparsity in Sec. 4.1, and detail our pretraining procedure in Sec. 4.2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 530, + 185, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 185, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 185, + 544 + ], + "type": "text", + "content": "4.1. Sparsity vs. Clip Length" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 545, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 617 + ], + "type": "text", + "content": "The key insight behind the design of SViT is the diminishing return of clip length. In general, a " + }, + { + "bbox": [ + 46, + 545, + 287, + 617 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 545, + 287, + 617 + ], + "type": "text", + "content": " longer sequence does not contain twice the semantic information about the video, due to the redundancy of adjacent frames. This leads to a lower percentage of informative patches with denser frame sampling." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "Due to this redundancy, it is possible to use higher sparsity for models with longer clips. This can be implemented by reducing the keep rate " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": " of node sparsification, and the percentage of key/value blocks to attend to in edge sparsification " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "(K_{l} / N_{b}, K_{r} / N_{b})" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": ". For the latter, since the total number of blocks " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "N_{b} = \\lceil N / G \\rceil" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": " increases with number of frames " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": " (assuming a fixed block size " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "), it suffices to keep the parameters " + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "inline_equation", + "content": "K_{l}, K_{r}" + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": " constant." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 306, + 69, + 545, + 152 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 545, + 152 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 545, + 152 + ], + "type": "image", + "image_path": "af888be5dacddd1db474f9d0a29b49cf30ae8606d744c1567f4e817d74d8c8d6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "type": "text", + "content": "Figure 3. Temporal Sparse Expansion. We propose a multi-stage curriculum for training SViTT. At each stage, the node and edge sparsity " + }, + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "type": "text", + "content": " of video-text transformer increases with clip length " + }, + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 156, + 545, + 190 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 197, + 425, + 210 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 197, + 425, + 210 + ], + "spans": [ + { + "bbox": [ + 305, + 197, + 425, + 210 + ], + "type": "text", + "content": "4.2. Temporal Expansion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 212, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 212, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 212, + 545, + 308 + ], + "type": "text", + "content": "Pretraining video-text transformers on long clips is time-consuming and leads to suboptimal models. Instead, we follow a learning strategy similar to Frozen [4], where the model is initially pretrained with shorter clips, and the number of frames increases as training progresses. However, when expanding the clip length, we increase the model sparsity to simultaneously 1) account for the redundancy of information, and 2) limit the growth of computational cost." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "text", + "content": "Fig. 3 depicts the expansion process proposed for video-text training. In the initial training stage " + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "inline_equation", + "content": "j = 1" + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "text", + "content": ", a dense video-text model is pretrained on clip length " + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "inline_equation", + "content": "T_{1}" + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "text", + "content": ". Denoting the sparsity hyperparameters of SViTT at stage " + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "inline_equation", + "content": "S_{j} = (q_{j}, K_{l}^{(j)}, K_{r}^{(j)})" + }, + { + "bbox": [ + 304, + 308, + 545, + 393 + ], + "type": "text", + "content": ", we create a learning curriculum with progressively increasing clip length and sparsity, by enforcing the constraints" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 392, + 399, + 545, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 392, + 399, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 392, + 399, + 545, + 411 + ], + "type": "interline_equation", + "content": "T _ {1} < T _ {2} < \\dots ; \\tag {14}", + "image_path": "1c220d95a46b3430e03da22495338596f7a1cf247bf552e4949871c7503e9229.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 394, + 415, + 545, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 394, + 415, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 394, + 415, + 545, + 426 + ], + "type": "interline_equation", + "content": "q _ {1} > q _ {2} > \\dots ; \\tag {15}", + "image_path": "f8398eaf6e7acb0ca7cbfddfc47dc7ca88e2a3e2d6e076984e1e68b1f5a913b1.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 429, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 429, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 351, + 429, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\frac {K _ {l} ^ {(1)} + K _ {r} ^ {(1)}}{T _ {1}} > \\frac {K _ {l} ^ {(2)} + K _ {r} ^ {(2)}}{T _ {2}} > \\dots \\tag {16}", + "image_path": "c0f6c3f9fd024c0cc21aea6a0ec5c057b5328db69dc2d03ec3a94d9b621dd7e4.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "type": "text", + "content": "In practice, we use a decreasing token keep rate (15) and keep local and random attention block numbers fixed, i.e. " + }, + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "type": "inline_equation", + "content": "K_{l}^{(j)} = K_{l}" + }, + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "type": "inline_equation", + "content": "K_{r}^{(j)} = K_{r}" + }, + { + "bbox": [ + 306, + 461, + 545, + 499 + ], + "type": "text", + "content": ", to satisfy (16)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 506, + 358, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 358, + 518 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 358, + 518 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 524, + 545, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 524, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 304, + 524, + 545, + 607 + ], + "type": "text", + "content": "In this section we present experimental results of SViTT on vision-language modeling. We briefly introduce the experimental setup in Sec. 5.1, and perform several ablation studies on the design choices involving model sparsification and training in Sec. 5.2. We then demonstrate the performance of SViTT on various vision-language tasks in Sec. 5.3 and include additional qualitative analysis." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 614, + 422, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 614, + 422, + 627 + ], + "spans": [ + { + "bbox": [ + 306, + 614, + 422, + 627 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Architecture. Our implementation of video-text transformer is based on Singularity [24]. The model has a two-tower structure, with separate encoders for vision and language. The video encoder " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is a 12-layer BEiT-B [5] initialized with ImageNet weights and inflated for video inputs. This differs from [24] which embeds each frame independently and applies late temporal fusion on extracted" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18923" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 228 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 228 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 228 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 228 + ], + "type": "table", + "html": "
Attn. blocks\nKl, Kr, GKeep rate\nqv, qm# Edges\n(M)R1DiDeMo\nR5R10Mean
——7.4728.853.163.048.3
Edge sparsity
(1, 3, 56)—2.1420.741.750.537.6
(1, 5, 56)—3.2126.048.656.843.8
Node sparsity
—(0.7, 1)3.9926.951.961.346.7
—(0.7, 0.1)3.9727.653.162.947.9
Hybrid sparsity
(1, 3, 56)(0.7, 0.1)1.4819.940.550.637.0
(1, 5, 56)(0.7, 0.1)2.2224.547.658.643.6
", + "image_path": "19d3e48effd00dfc984e4b471c1590728f8c940bb98046c60ed0eb505e6ec863.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 260, + 164, + 331 + ], + "blocks": [ + { + "bbox": [ + 53, + 260, + 164, + 331 + ], + "lines": [ + { + "bbox": [ + 53, + 260, + 164, + 331 + ], + "spans": [ + { + "bbox": [ + 53, + 260, + 164, + 331 + ], + "type": "image", + "image_path": "175eaeb13b8422b3fd00e0dd949245b26eba9669ea26264456c378b65f5a6112.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 49, + 333, + 167, + 342 + ], + "lines": [ + { + "bbox": [ + 49, + 333, + 167, + 342 + ], + "spans": [ + { + "bbox": [ + 49, + 333, + 167, + 342 + ], + "type": "text", + "content": "(a) Number of local / random blocks." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 173, + 260, + 279, + 331 + ], + "blocks": [ + { + "bbox": [ + 173, + 260, + 279, + 331 + ], + "lines": [ + { + "bbox": [ + 173, + 260, + 279, + 331 + ], + "spans": [ + { + "bbox": [ + 173, + 260, + 279, + 331 + ], + "type": "image", + "image_path": "d3c8e7f2c943fddd658086fc8e2a8b4a4b75074608c0235b7711597a91ae9c5f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 187, + 333, + 266, + 342 + ], + "lines": [ + { + "bbox": [ + 187, + 333, + 266, + 342 + ], + "spans": [ + { + "bbox": [ + 187, + 333, + 266, + 342 + ], + "type": "text", + "content": "(b) Attention block size." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "lines": [ + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "type": "text", + "content": "Figure 4. Ablation on Edge Sparsity. We evaluate dense model using different local/random blocks " + }, + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "type": "inline_equation", + "content": "(K_l, K_r)" + }, + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "type": "text", + "content": " and block size " + }, + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 348, + 287, + 370 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "type": "text", + "content": "features. The text encoder " + }, + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "type": "text", + "content": " is a pretrained BERT [14] model, whose last 3 layers are modified to implement the multimodal encoder " + }, + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "type": "inline_equation", + "content": "f_{m}" + }, + { + "bbox": [ + 46, + 377, + 287, + 437 + ], + "type": "text", + "content": ", with cross-modal attention based on visual tokens as key-value pairs, which we sparsify as described in Sec. 3.3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 443, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 287, + 503 + ], + "type": "text", + "content": "Pre-training. SViTT is pre-trained on 2.5M video-text pairs from the WebVid dataset [4]. Since our goal is to investigate how to improve the effectiveness of the temporal learning of the video modality, we do not train with additional image-text corpora as done in [4, 18, 24]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "text", + "content": "The [cls] tokens of the video and text encoders are first linearly projected to a joint embedding space, producing feature vectors " + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_v = f_v(\\mathbf{x}_v)" + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t = f_t(\\mathbf{x}_t)" + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "text", + "content": ", respectively. Following prior work, we use the InfoNCE loss [40] to align these feature vectors. The output of multimodal encoder " + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{y} = f_m(\\mathbf{z}_v,\\mathbf{z}_t)" + }, + { + "bbox": [ + 46, + 503, + 287, + 599 + ], + "type": "text", + "content": " is optimized with video-text matching (VTM) and masked language modeling (MLM) losses commonly found in VLP literature [12, 18, 24, 27, 28]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "type": "text", + "content": "Downstream tasks. Trained video-text models are evaluated on two multimodal tasks: Text-to-video retrieval and video question answering. Video retrieval is evaluated on MSR-VTT [51], DiDeMo [2], Charades [43] and Something-Something v2 [20, 24], by top- " + }, + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "type": "text", + "content": " recalls " + }, + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "type": "inline_equation", + "content": "(K \\in \\{1, 5, 10\\})" + }, + { + "bbox": [ + 46, + 605, + 287, + 700 + ], + "type": "text", + "content": " and their numeric average. Question answering is evaluated on MSRVTT-QA [49], ActivityNet-QA [10, 54] and AGQA [21], with top-1 accuracy of the answers." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 701, + 232, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 232, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 232, + 713 + ], + "type": "text", + "content": "Training details are given in the Appendix." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 545, + 243 + ], + "blocks": [ + { + "bbox": [ + 47, + 232, + 287, + 255 + ], + "lines": [ + { + "bbox": [ + 47, + 232, + 287, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 287, + 255 + ], + "type": "text", + "content": "Table 1. Ablation on Edge and Node Sparsity. We evaluate the same dense video-text model under different sparsification modes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 243 + ], + "type": "table", + "html": "
TSparc.FLOPs (G)Mem. (GB)R1DiDeMoMean
R5R10
4Dense139.90.9628.853.163.048.3
Edge135.90.8028.351.961.447.2
Node95.80.6129.954.863.949.6
Hybrid93.90.5429.353.763.248.8
8Dense291.33.1429.654.164.149.3
Edge271.81.5729.854.965.450.1
Node197.61.7730.455.766.050.7
Hybrid166.40.9231.057.266.351.5
16Dense627.810.66Untrainable
Edge543.63.0231.655.164.650.5
Node370.94.39Untrainable
Hybrid296.21.5731.457.367.852.2
", + "image_path": "129ba4e2f683053319b087f8043d162810fe456600805ec526999defcfba5e4b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 248, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 305, + 248, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 305, + 248, + 545, + 282 + ], + "type": "text", + "content": "Table 2. Ablation on Training Sparse Models. We compare the zero-shot performance, inference GFLOPs, and training memory (per sample) of sparse models to the dense attention baseline." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 312, + 287, + 421, + 358 + ], + "blocks": [ + { + "bbox": [ + 312, + 287, + 421, + 358 + ], + "lines": [ + { + "bbox": [ + 312, + 287, + 421, + 358 + ], + "spans": [ + { + "bbox": [ + 312, + 287, + 421, + 358 + ], + "type": "image", + "image_path": "e75c9b70a5e20a60840325a0dc06183f10051d55b57bc5321b8f748cc3e466cb.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 360, + 406, + 370 + ], + "lines": [ + { + "bbox": [ + 328, + 360, + 406, + 370 + ], + "spans": [ + { + "bbox": [ + 328, + 360, + 406, + 370 + ], + "type": "text", + "content": "(a) Visual sparsification." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 375, + 545, + 398 + ], + "lines": [ + { + "bbox": [ + 305, + 375, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 545, + 398 + ], + "type": "text", + "content": "Figure 5. Ablation on Node Sparsity. We evaluate the pre-trained dense model using different keep rates " + }, + { + "bbox": [ + 305, + 375, + 545, + 398 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 305, + 375, + 545, + 398 + ], + "type": "text", + "content": " at test time." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 434, + 287, + 536, + 358 + ], + "blocks": [ + { + "bbox": [ + 434, + 287, + 536, + 358 + ], + "lines": [ + { + "bbox": [ + 434, + 287, + 536, + 358 + ], + "spans": [ + { + "bbox": [ + 434, + 287, + 536, + 358 + ], + "type": "image", + "image_path": "0a93d340808f3d944e33e31d0ef36d24f4048bdaebc85e33c0e8b76efef93881.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 436, + 360, + 533, + 370 + ], + "lines": [ + { + "bbox": [ + 436, + 360, + 533, + 370 + ], + "spans": [ + { + "bbox": [ + 436, + 360, + 533, + 370 + ], + "type": "text", + "content": "(b) Multimodal sparsification." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 404, + 406, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 404, + 406, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 404, + 406, + 415 + ], + "type": "text", + "content": "5.2. Ablation Studies" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": "We start by training a video-text transformer with clip length of 4 frames and dense attention, and measure its zero-shot performance on downstream tasks after sparsifying its video encoder while keeping its weights unchanged." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "content": "Edge sparsification. We first apply edge sparsification with different number of local blocks " + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "inline_equation", + "content": "K_{l}" + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "content": ", random blocks " + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "inline_equation", + "content": "K_{r}" + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "content": ", and block size " + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "content": ". As shown in Fig. 4a, under a limited budget of 6 local or random attention blocks per query token, using 1 local block and 5 random blocks provides the best trade-off. Increasing the local attention window " + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "inline_equation", + "content": "K_{l}" + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "content": " hurts long-term modeling capacity and degrades retrieval; while removing the single local block responsible for diagonal attention also impairs performance. This suggests that while query tokens should always attend to their respective blocks, there is no benefit in attending to neighboring blocks. We thus fix " + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "inline_equation", + "content": "K_{l} = 1" + }, + { + "bbox": [ + 304, + 474, + 545, + 616 + ], + "type": "text", + "content": " for the rest of experiments." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "We next vary the block size " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " of sparse attention. Fig. 4b shows that larger sizes have stronger retrieval performance, as expected. However, they also make self-attention less sparse (more costly to compute). " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "G = 56" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " provides a good balance between performance and complexity. Tab. 1 summarizes the test performance of two edge sparsity config: " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "(K_{l}, K_{r}, G) = (1, 3, 56)" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "(1, 5, 56)" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ". While both underperform the dense model, we will later demonstrate that the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18924" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 179 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 179 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 179 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 179 + ], + "type": "table", + "html": "
FramesTSparsityTSDiDeMo
R1R5R10Mean
44.8028.050.759.246.0
10→4.8029.353.763.248.8
88.9127.351.463.847.5
4.80→8.9131.057.266.351.5
1616.9627.552.463.247.7
4.80→8.91→16.9631.457.367.852.2
", + "image_path": "44f596c31292f515053ec3dd56fbc6b596e8542485d0480ce36d9742009b51d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 224, + 287, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 249 + ], + "type": "text", + "content": "gap can be closed and even reversed by training the sparse model with the proposed temporal expansion curriculum." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": "Node sparsification. We next incorporate node sparsity into the video-text transformer. This includes visual sparsification (keep rate " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "q_{v}" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": ") using the self-attention of video encoder " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": " to progressively prune the input tokens" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": ", and multimodal sparsification (keep rate " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "q_{m}" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": ") using the text-to-video attention of cross-modal encoder " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "f_{m}" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": " to further drop visual tokens unrelated to the text query. Fig. 5a shows that the dense model is quite robust to token pruning, even without sparse training. Using visual keep rate " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "q_{v} \\geq 0.8" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": " has minimal impact on test results, and performance only starts to drop rapidly at " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "q_{v} = 0.5" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": ", at which point only " + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "inline_equation", + "content": "1/8" + }, + { + "bbox": [ + 46, + 253, + 287, + 396 + ], + "type": "text", + "content": " of input tokens are retained after three rounds of sparsification." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "content": "Even more surprisingly, the subsequent multimodal sparsification step, using a keep rate of " + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "inline_equation", + "content": "q_{m} = 0.1" + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "content": ", improves zero-shot performance by " + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "content": ". This shows that the " + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "content": " redundant visual tokens not only add unnecessary complexity to the model, but also introduce noise that harms retrieval performance. The fact that the optimal " + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "inline_equation", + "content": "q_{m}" + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "content": " is much lower than " + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "inline_equation", + "content": "q_{v}" + }, + { + "bbox": [ + 46, + 397, + 287, + 505 + ], + "type": "text", + "content": " also suggests that text modality provides crucial semantic guidance for identifying relevant visual patches, at a much higher accuracy than visual modeling alone." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 593 + ], + "type": "text", + "content": "Hybrid sparsification. Combining the best sparse settings for edges and nodes, we obtain the hybrid sparsification strategy for SViT. As shown in Tab. 1, compared to edge sparsity, the introduction of node sparsity " + }, + { + "bbox": [ + 46, + 510, + 287, + 593 + ], + "type": "inline_equation", + "content": "(q_{v} = 0.7, q_{m} = 0.1)" + }, + { + "bbox": [ + 46, + 510, + 287, + 593 + ], + "type": "text", + "content": " only impacts recall scores marginally, while saving computations on a large portion of visual tokens throughout the network." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 597, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 694 + ], + "type": "text", + "content": "Training sparse transformers. We next perform full pretraining with the sparse models and compare their performance and efficiency to the dense transformer baseline. Tab. 2 summarizes the results obtained with different input clip lengths and types of sparsity. At 4 frames, edge sparsity has small benefit due to the relatively short sequence length and node sparsity performs the best. However, at 8 frames, we start to see clear advantages to edge sparsity in memory" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 547, + 216 + ], + "blocks": [ + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "text", + "content": "Table 3. Ablation on Temporal Sparse Expansion. Sparsity " + }, + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "inline_equation", + "content": "T_{S}" + }, + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "text", + "content": " indicates training on " + }, + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "text", + "content": " frames while removing " + }, + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "inline_equation", + "content": "S \\times 100\\%" + }, + { + "bbox": [ + 46, + 183, + 287, + 217 + ], + "type": "text", + "content": " attention edges of dense transformer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 70, + 547, + 216 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 547, + 216 + ], + "type": "table", + "html": "
MethodPTTMSR-VTTDiDeMo
R1MeanR1Mean
VideoCLIP [50]100M—10.420.916.6—
Frozen [4]5M423.241.521.141.1
ALPRO [26]5M824.141.423.843.0
VIOLET [18]5M425.945.023.544.4
Singularity [24]5M128.446.036.955.8
121.138.723.340.8
Singularity*2M424.440.026.444.1
824.341.025.845.5
SViTTDense Hybrid2M826.043.629.649.3
25.443.831.051.5
", + "image_path": "ab773a7506a1d7afee11659736a097927ef6cac2baf4075e2b903e35fc7b27f4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 220, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 305, + 220, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 220, + 545, + 255 + ], + "type": "text", + "content": "Table 4. Zero-shot Text-to-video Retrieval. Results reported in prior works are marked in gray; * indicates our reproduced results. PT = # video-text pairs for pre-training, " + }, + { + "bbox": [ + 305, + 220, + 545, + 255 + ], + "type": "inline_equation", + "content": "T = \\#" + }, + { + "bbox": [ + 305, + 220, + 545, + 255 + ], + "type": "text", + "content": " frames per clip." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "text", + "content": "complexity, and both edge and node sparsity outperform the dense transformer baseline. Combining both types of sparsity performs the best, while only requiring " + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "text", + "content": " the FLOPs and " + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "text", + "content": " the memory of the dense model. At 16 frames, the dense and node sparsity models are no longer trainable due to their quadratically increasing cost. The models with edge sparsity, however, are able to fit into GPU memory thanks to the linear complexity from sparse attention. A 16-frame SViTT with hybrid sparsity requires similar computation to an 8-frame dense model and only half of its training memory, while achieving " + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 261, + 545, + 393 + ], + "type": "text", + "content": " higher recall." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "content": "Progressive training. We next study the impact of temporal sparse expansion on the training of SViT models on longer clips. Tab. 3 compares the performance of models trained using temporal expansion (i.e. initialized from checkpoints pretrained on fewer frames and lower sparsity) to standard single-stage training. For single-stage training, performance does not improve substantially with clip length. This is in contrast to the proposed sparse expansion, where using 8 instead or 4 frames results in a gain of " + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "content": ". This suggests that the models have learned to exploit the temporal relationships between video frames. For a given clip length, sparse expansion also substantially improves upon single stage performance, from 2.8 points for " + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "inline_equation", + "content": "T = 4" + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "content": " to 4.5 points for " + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "inline_equation", + "content": "T = 16" + }, + { + "bbox": [ + 304, + 397, + 546, + 589 + ], + "type": "text", + "content": ". In fact, sparse expansion training with a shorter clip length (e.g. 4 frames) can outperform single stage training with a larger length (16 frames)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 597, + 391, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 391, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 391, + 609 + ], + "type": "text", + "content": "5.3. Main Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 613, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 613, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 305, + 613, + 545, + 638 + ], + "type": "text", + "content": "We compare SViT to state-of-the-art models in text-to-video retrieval and video question answering." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "Text-to-video retrieval. Video-text retrieval is evaluated under zero-shot and fine-tuning settings. Tab. 4 shows the zero-shot results on MSR-VTT and DiDeMo. Compared to our reproduced models of Singularity on WebVid-2M, which aggregate frame-level features using a temporal transformer encoder, the spatiotemporal transformer" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 264, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 264, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 264, + 712 + ], + "type": "text", + "content": "3We follow [30] to prune visual tokens at layer #4, #7, and #10." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18925" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 83, + 221, + 150 + ], + "blocks": [ + { + "bbox": [ + 72, + 83, + 221, + 150 + ], + "lines": [ + { + "bbox": [ + 72, + 83, + 221, + 150 + ], + "spans": [ + { + "bbox": [ + 72, + 83, + 221, + 150 + ], + "type": "image", + "image_path": "26d7637a13dd55a96cc9d03196ab310af085f6b87cd7c8c84b391db2a955803f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 137, + 155, + 156, + 163 + ], + "lines": [ + { + "bbox": [ + 137, + 155, + 156, + 163 + ], + "spans": [ + { + "bbox": [ + 137, + 155, + 156, + 163 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 223, + 83, + 371, + 150 + ], + "blocks": [ + { + "bbox": [ + 223, + 83, + 371, + 150 + ], + "lines": [ + { + "bbox": [ + 223, + 83, + 371, + 150 + ], + "spans": [ + { + "bbox": [ + 223, + 83, + 371, + 150 + ], + "type": "image", + "image_path": "6f1e49cafcdfe44a43d9a987b9f8f239c0798861c274dd511f0aff506007747d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 266, + 154, + 320, + 163 + ], + "lines": [ + { + "bbox": [ + 266, + 154, + 320, + 163 + ], + "spans": [ + { + "bbox": [ + 266, + 154, + 320, + 163 + ], + "type": "text", + "content": "Visual, " + }, + { + "bbox": [ + 266, + 154, + 320, + 163 + ], + "type": "inline_equation", + "content": "q_{v} = 0.6" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 52, + 168, + 539, + 180 + ], + "lines": [ + { + "bbox": [ + 52, + 168, + 539, + 180 + ], + "spans": [ + { + "bbox": [ + 52, + 168, + 539, + 180 + ], + "type": "text", + "content": "Figure 6. Qualitative Results. SViTT isolates informative regions from background patches to facilitate efficient temporal reasoning." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 372, + 83, + 520, + 150 + ], + "blocks": [ + { + "bbox": [ + 372, + 83, + 520, + 150 + ], + "lines": [ + { + "bbox": [ + 372, + 83, + 520, + 150 + ], + "spans": [ + { + "bbox": [ + 372, + 83, + 520, + 150 + ], + "type": "image", + "image_path": "aacaa1aa7c7328c711fc1d11fd7e61a76a0c0684441b55e81a0f160eb27bce8e.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 408, + 154, + 484, + 163 + ], + "lines": [ + { + "bbox": [ + 408, + 154, + 484, + 163 + ], + "spans": [ + { + "bbox": [ + 408, + 154, + 484, + 163 + ], + "type": "text", + "content": "Cross-modal, " + }, + { + "bbox": [ + 408, + 154, + 484, + 163 + ], + "type": "inline_equation", + "content": "q_{m} = 0.1" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 50, + 186, + 286, + 312 + ], + "blocks": [ + { + "bbox": [ + 50, + 186, + 286, + 312 + ], + "lines": [ + { + "bbox": [ + 50, + 186, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 50, + 186, + 286, + 312 + ], + "type": "table", + "html": "
MethodPTTCharadesSSv2
R1MeanR1Mean
Frozen [4]5M3211.925.1——
CLIP4Clip [35]400M1213.927.143.165.1
ECLIPSE [31]400M3215.730.3——
\\( MKTVR^† \\)[36]400M4216.634.7——
Singularity [24]5M1——36.458.9
4——44.166.6
SViTTDense Hybrid2M816.032.743.666.1
17.735.749.869.3
", + "image_path": "db37c251cc174cdc97b5d868cdf1f8ac5e2984258e8d46e3b76e3c31e7e08cde.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 50, + 332, + 286, + 466 + ], + "blocks": [ + { + "bbox": [ + 72, + 316, + 263, + 327 + ], + "lines": [ + { + "bbox": [ + 72, + 316, + 263, + 327 + ], + "spans": [ + { + "bbox": [ + 72, + 316, + 263, + 327 + ], + "type": "text", + "content": "Table 5. Text-to-video Retrieval with Fine-tuning." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 332, + 286, + 466 + ], + "lines": [ + { + "bbox": [ + 50, + 332, + 286, + 466 + ], + "spans": [ + { + "bbox": [ + 50, + 332, + 286, + 466 + ], + "type": "table", + "html": "
MethodPTTMSRVTTANetAGQA
HME [17]—2033.0—47.7
HCRN [23]12835.5—47.4
ClipBERT [25]0.2M1637.4——
ALPRO [26]5M1642.1——
Just Ask [52]69M64041.538.9—
MERLOT [56]180M543.141.4—
VIOLET [18]185M443.9—49.2
Singularity [24]5M142.741.8—
SViTTDense Hybrid2M842.742.350.2
43.043.252.7
", + "image_path": "1ed5da4344188951b23b404328dedb00e8c2d1f6abc061d7bd9a63e4d5529a83.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 97, + 470, + 237, + 481 + ], + "lines": [ + { + "bbox": [ + 97, + 470, + 237, + 481 + ], + "spans": [ + { + "bbox": [ + 97, + 470, + 237, + 481 + ], + "type": "text", + "content": "Table 6. Video Question Answering." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 488, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 287, + 559 + ], + "type": "text", + "content": "of SViTT produces stronger results on both downstream datasets. This highlights the importance of temporal modeling in earlier layers of video-text transformers. SViTT with hybrid sparsity has similar performance to the dense model on MSR-VTT but significantly outperforms in on DiDeMo, which contains longer videos with localized activities." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 562, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 562, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 562, + 287, + 682 + ], + "type": "text", + "content": "For Charades and SSv2, we evaluate text-to-video retrieval with fine-tuning, as shown in Tab. 5. Both datasets are action-centric, posing a greater challenge to the temporal reasoning of video-text models. SViT with hybrid sparsification dominates the dense variant by " + }, + { + "bbox": [ + 46, + 562, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\sim 3\\%" + }, + { + "bbox": [ + 46, + 562, + 287, + 682 + ], + "type": "text", + "content": " on both datasets, a more substantial gap than observed for MSR-VTT and DiDeMo. This confirms our hypothesis that exploiting node and edge sparsity reduces the dependency of models on contextual regions, forcing them to focus on the temporal dynamics of person and objects in the foreground." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Video question answering. We next evaluate the cross-modal modeling of SViT on MSRVTT-QA, ActivityNet" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 189, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 189, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 189, + 545, + 369 + ], + "type": "text", + "content": "QA and AGQA. As shown in Tab. 6, the hybrid sparsity version of SViTT outperforms the dense transformer baseline on all three datasets, thanks to its more efficient temporal modeling. On MSRVTT-QA, the accuracy gap is small between dense and sparse transformer (0.3%), and SViTT marginally underperforms baselines pretrained with fewer number of frames (MERLOT [56], VIOLET [18]). This is likely due to the nature of MSRVTT, which consists of short video clips and questions biased towards spatial cues, allowing temporal modeling little benefit over spatial transformers pretrained on massive image & video data. On ActivityNet-QA and AGQA, which both contain longer clips and temporally challenging questions, the sparse modeling of SViTT proves advantageous, with 0.9% and 2.3% boost in accuracy respectively, beating all baseline methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "type": "text", + "content": "Qualitative analysis. To show how SViT efficiently identifies and concentrates its computation on informative spatiotemporal regions of the input clips, we visualize the outcome of node sparsification in Fig. 6. Using visual sparsification in video encoder " + }, + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "type": "text", + "content": ", SViT learns to isolate foreground entities from the majority of background patches, enabling the model to perform sparse video-text inference on longer temporal context. Cross-modal attention in multimodal encoder " + }, + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "type": "inline_equation", + "content": "f_{m}" + }, + { + "bbox": [ + 304, + 373, + 546, + 504 + ], + "type": "text", + "content": " provides an even stronger signal for isolating the regions of interest of each video clip, validating the importance of text semantics in visual sparsification." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 512, + 379, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 379, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 379, + 525 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 529, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 686 + ], + "type": "text", + "content": "This work introduced SViTT, a sparse video-text transformer for efficient reasoning over a long temporal context. By interpreting visual transformers as graph networks, we proposed to optimize their edge and node sparsity, using a combination of sparse block attention, visual token pruning and text-guided token selection. We further introduced a temporal expansion strategy for training SViTT, which aims to gradually increase model sparsity with clip length. SViTT showed strong performance and efficiency compared to dense transformers, with a larger gap when frame number increases. On video retrieval and question answering benchmarks, SViTT achieved state-of-the-art results using only video data, without extra image-text pretraining." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. This work was funded in part by NSF award IIS-2041009." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 124, + 69, + 470, + 79 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 69, + 470, + 79 + ], + "spans": [ + { + "bbox": [ + 124, + 69, + 470, + 79 + ], + "type": "text", + "content": "A person is in a living room playing with a book and flipping through the pages, they then leave out the door." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18926" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 88, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 88, + 287, + 142 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 88, + 287, + 142 + ], + "spans": [ + { + "bbox": [ + 53, + 88, + 287, + 142 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, et al. 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The proposed SadTalker produces diverse, realistic, synchronized talking videos from input audio and a single reference image." + ], + "image_footnote": [], + "bbox": [ + 78, + 315, + 890, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 665, + 313, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generating talking head videos through a face image and a piece of speech audio still contains many challenges. i.e., unnatural head movement, distorted expression, and identity modification. We argue that these issues are mainly caused by learning from the coupled 2D motion fields. On the other hand, explicitly using 3D information also suffers problems of stiff expression and incoherent video. We present SadTalker, which generates 3D motion coefficients (head pose, expression) of the 3DMM from audio and implicitly modulates a novel 3D-aware face render for talking head generation. To learn the realistic motion coefficients, we", + "bbox": [ + 75, + 696, + 473, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "explicitly model the connections between audio and different types of motion coefficients individually. Precisely, we present ExpNet to learn the accurate facial expression from audio by distilling both coefficients and 3D-rendered faces. As for the head pose, we design PoseVAE via a conditional VAE to synthesize head motion in different styles. Finally, the generated 3D motion coefficients are mapped to the unsupervised 3D keypoints space of the proposed face render to synthesize the final video. We conducted extensive experiments to demonstrate the superiority of our method in terms of motion and video quality.", + "bbox": [ + 500, + 666, + 895, + 834 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal Contribution", + "bbox": [ + 76, + 875, + 191, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding Author", + "bbox": [ + 80, + 887, + 209, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1The code and demo videos are available at https://sadtalker.github.io.", + "bbox": [ + 500, + 875, + 895, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8652", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 89, + 207, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Animating a static portrait image with speech audio is a challenging task and has many important applications in the fields of digital human creation, video conferences, etc. Previous works mainly focus on generating lip motion [2, 3, 28, 29, 49] since it has a strong connection with speech. Recent works also aim to generate a realistic talking face video containing other related motions, e.g., head pose. Their methods mainly introduce 2D motion fields by landmarks [50] and latent warping [37, 38]. However, the quality of the generated videos is still unnatural and restricted by the preference pose [16, 49], month blur [28], identity modification [37, 38], and distorted face [37, 38, 47].", + "bbox": [ + 76, + 114, + 470, + 296 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generating a natural-looking talking head video contains many challenges since the connections between audio and different motions are different. i.e., the lip movement has the strongest connection with audio, but audio can be talked via different head poses and eye blink. Thus, previous facial landmark-based methods [2, 50] and 2D flow-based audio to expression networks [37, 38] may generate the distorted face since the head motion and expression are not fully disentangled in their representation. Another popular type of method is the latent-based face animation [3, 16, 28, 49]. Their methods mainly focus on the specific kind of motions in talking face animation and struggle to synthesize high-quality video. Our observation is that the 3D facial model contains a highly decoupled representation and can be used to learn each type of motion individually. Although a similar observation has been discussed in [47], their methods also generate inaccurate expressions and unnatural motion sequences.", + "bbox": [ + 76, + 296, + 470, + 551 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "From the above observation, we propose SadTalker, a Stylized Audio-Driven Talking-head video generation system through implicit 3D coefficient modulation. To achieve this goal, we consider the motion coefficients of the 3DMM as the intermediate representation and divide our task into two major components. On the one hand, we aim to generate the realistic motion coefficients (e.g., head pose, lip motion, and eye blink) from audio and learn each motion individually to reduce the uncertainty. For expression, we design a novel audio to expression coefficient network by distilling the coefficients from the lip motion only coefficients from [28] and the perceptual losses (lip-reading loss [1], facial landmark loss) on the reconstructed rendered 3D face [5]. For the stylized head pose, a conditional VAE [6] is used to model the diversity and life-like head motion by learning the residual of the given pose. After generating the realistic 3DMM coefficients, we drive the source image through a novel 3D-aware face render. Inspired by face-vid2vid [40], we learn a mapping between the explicit 3DMM coefficients and the domain of the unsupervised 3D keypoint. Then, the warping fields are generated through the unsupervised 3D keypoints of source and driving and it warps the reference image to generate the final videos. We train each sub-network", + "bbox": [ + 76, + 553, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of expression generation, head poses generation and face renderer individually and our system can be inferred in an end-to-end style. As for the experiments, several metrics show the advantage of our method in terms of video and motion methods.", + "bbox": [ + 496, + 90, + 890, + 165 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contribution of this paper can be summarized as:", + "bbox": [ + 500, + 167, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present SadTalker, a novel system for a stylized audio-driven single image talking face animation using the generated realistic 3D motion coefficients.", + "- To learn the realistic 3D motion coefficient of the 3DMM model from audio, ExpNet and PoseVAE are presented individually.", + "- A novel semantic-disentangled and 3D-aware face render is proposed to produce a realistic talking head video.", + "- Experiments show that our method achieves state-of-the-art performance in terms of motion synchronization and video quality." + ], + "bbox": [ + 517, + 209, + 893, + 405 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 419, + 640, + 434 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Audio-driven Single Image Talking Face Generation. Early works [3, 28, 29] mainly focus on producing accurate lip motion with a perception discriminator. Since the real videos contain many different motions, ATVGnet [2] uses the facial landmark as the intermediate representation to generate the video frames. A similar approach has been proposed by MakeiTalk [50], differently, it disentangles the content and speaker information from the input audio signal. Since facial landmarks are still a highly coupled space, generating the talking head in the disentangled space is also popular recently. PC-AVS [49] disentangles the head pose and expression using implicit latent code. However, it can only produce low-resolution image and need the control signal from another video. Audio2Head [37] and Wang et al. [38] get inspiration from the video-driven method [34] to produce the talking-head face. However, these head movements are still not vivid and produce distorted faces with inaccurate identities. Although there are some previous works [31, 47] use 3DMMs as an intermediate representation, their method still faces the problem of inaccurate expressions [31] and obvious artifacts [47].", + "bbox": [ + 496, + 444, + 893, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Audio-driven Video Portrait. Our task is also related to visual dubbing, which aims to edit a portrait video through audio. Different from audio-driven single image talking face generation, this task is typically required to be trained and edited on the specific video. Following previous work of deep video portrait [18], these methods utilize 3DMM information for face reconstruction and animation. AudioDVP [43], NVP [36], AD-NeRF [11] learn to reenact the expression to", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8653", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/508d009ece138732f2e254b09716357e7c3a9ec9b7e5596b47fbff4d4e2c39b0.jpg", + "image_caption": [ + "Figure 2. Main pipeline. Our method uses the coefficients of 3DMM as intermediate motion representation. To this end, we first generate realistic 3D motion coefficients (facial expression $\\beta$ , head pose $\\rho$ ) from audio, then these coefficients are used to implicitly modulate the 3D-aware face render for final video generation." + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 464, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "edit the mouth shape. Beyond lip movement, i.e., the head motions [22, 46], emotional talking face [17] also get attention. The 3DMM-based method plays an important role in these tasks since it is practical to fit the 3DMM parameters from a video clip. Although these methods achieve satisfactory results in personalized video, their method can not be applied to arbitrary photos and in the wild audio.", + "bbox": [ + 75, + 330, + 472, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Video-Driven Single Image Talking Face Generation.", + "text_level": 1, + "bbox": [ + 75, + 472, + 470, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This task is also known as face reenactment or face animation, which aims to transfer the motion of the source image to the target person. It has been widely explored [14, 27, 31, 34, 35, 39, 40, 42, 45, 48] recently. Previous works also learn a shared intermediate motion representation from the source image and the target, which can be roughly divided into the landmark [39] and the unsupervised landmark-based methods [14, 34, 40, 48], 3DMM based methods [7, 31, 45] and the latent animation [23, 42]. This task is much easier than our task since it contains the motion in the same domain. Our face render is also inspired by the method of unsupervised landmark-based method [40] and 3DMM-based method [31] to use coefficients to generate real videos. However, they are not focused on generating realistic motion coefficients.", + "bbox": [ + 73, + 487, + 470, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 720, + 168, + 736 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, our system uses the 3D motion coefficients as the intermediate representation for talking head generation. We first extract the coefficients from the original image. Then, the realistic 3DMM motion coefficients are generated by ExpNet and PoseVAE individually. Finally, a 3D-aware face render is proposed to produce the talking head videos. Below, we give a brief introduction to the 3D face model as preliminaries in Sec. 3.1, the audio-driven motion coefficients generation and the coefficients-driven image animator we design in Sec. 3.2 and Sec. 3.3, respectively.", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary of 3D Face Model", + "text_level": 1, + "bbox": [ + 500, + 90, + 769, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D information is crucial to improve the realness of the generated video since the real video is captured in the 3D environment. However, previous works [28, 49, 50] have rarely been a consideration in 3D space since it is hard to obtain accurate 3D coefficients from a single image and the high-quality face render is also hard to design. Inspired by the recent single image deep 3D reconstruction method [5], we consider the space of the predicted 3D Morphable Models (3DMMs) as our intermediate representation. In 3DMM, the 3D face shape S can be decoupled as:", + "bbox": [ + 496, + 113, + 893, + 265 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} = \\overline {{\\mathbf {S}}} + \\alpha \\mathbf {U} _ {i d} + \\beta \\mathbf {U} _ {e x p}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 270, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\overline{\\mathbf{S}}$ is the average shape of the 3D face, $\\mathbf{U}_{id}$ and $\\mathbf{U}_{exp}$ are the orthonormal basis of identity and expression of LSFM morphable model [1]. Coefficients $\\alpha \\in \\mathbb{R}^{80}$ and $\\beta \\in \\mathbb{R}^{64}$ describe the person identity and expression, respectively. To preserve pose variance, coefficients $\\mathbf{r} \\in SO(3)$ and $\\mathbf{t} \\in \\mathbb{R}^3$ denote the head rotation and translation. To achieve identity irrelevant coefficients generation [31], we only model the parameters of motion as $\\{\\beta, \\mathbf{r}, \\mathbf{t}\\}$ . We learn the head pose $\\rho = [\\mathbf{r}, \\mathbf{t}]$ and expression coefficients $\\beta$ individually from the driving audio as introduced before. Then, these motion coefficients are used to implicitly modulate our face render for final video synthesis.", + "bbox": [ + 496, + 292, + 893, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Motion Coefficients Generation through Audio", + "text_level": 1, + "bbox": [ + 498, + 482, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As introduced above, the 3D motion coefficients contain both head pose and expression where the head pose is a global motion and the expression is relatively local. To this end, learning everything altogether will cause huge uncertainty in the network since the head pose has a relatively weak relationship with audio while the lip motion is highly connected. We generate the motion of the head pose and expression using the proposed PoseVAE and ExpNet, respectively introduced below.", + "bbox": [ + 496, + 506, + 893, + 641 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ExpNet Learning a generic model which produces accurate expression coefficients from audio is extremely hard for two reasons: 1) audio-to-expression is not a one-to-one mapping task for different identities. 2) there are some audio-irrelevant motions in the expression coefficients and it will influence the prediction's accuracy. Our ExpNet is designed to reduce these uncertainties. As for the identity issue, we connect the expression motion to the specific person via the first frame's expression coefficients $\\beta_0$ which also controls the facial emotion of the generated video. To reduce the disturbance of other facial components in real expression coefficients, we use the lip motion only coefficients as the coefficient target through the pre-trained network of Wav2Lip [28] and deep 3D reconstruction [5]. Then, other minor facial motions (e.g., eye blink) can be leveraged via the additional landmark loss on the rendered images.", + "bbox": [ + 496, + 657, + 895, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8654", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/429274038857670e614daf4780cad19cf6365854728228da9881c01a2d83bbf3.jpg", + "image_caption": [ + "Figure 3. The structure of our ExpNet. We involve a monocular 3D face reconstruction model [5] ( $R_{e}$ and $R_{d}$ ) to learn the realistic expression coefficients. Where $R_{e}$ is a pretrained 3DMM coefficients estimator and $R_{d}$ is a differentiable 3D face render without learnable parameters. We use the reference expression $\\beta_0$ to reduce the uncertainty of identity and the generated frame from pre-trained Wav2Lip [28] and the first frame as target expression coefficients since it only contains the lip-related motions." + ], + "image_footnote": [], + "bbox": [ + 86, + 98, + 459, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As shown in Figure 3, we generate the $t$ -frame expression coefficients from an audio window $a_{\\{1,\\dots,t\\}}$ , where the audio feature of each frame is a 0.2s mel-spectrogram. For training, we first design a ResNet-based audio encoder $\\Phi_A$ [12, 28] to embed the audio feature to a latent space. Then, a linear layer is added as the mapping network $\\Phi_M$ to decode the expression coefficients. Here, we also add the reference expression $\\beta_0$ from the reference image to support emotions and reduce the identity uncertainty as discussed above. Since we use the lip-only coefficients as ground truth in the training, we explicitly add a blinking control signal $z_{blink} \\in [0,1]$ and the corresponding eye landmark loss to generate the controllable eye blinks. Formally, the network can be written as:", + "bbox": [ + 75, + 438, + 473, + 636 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta_ {\\{1, \\dots , t \\}} = \\Phi_ {M} (\\Phi_ {A} (a _ {\\{1, \\dots , t \\}}), z _ {b l i n k}, \\beta_ {0}) \\qquad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 652, + 470, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As for the loss function, we first use $\\mathcal{L}_{distill}$ to evaluate the differences between the lip only expression coefficients $R_{e}(\\mathrm{Wav2Lip}(I_0,a_{\\{1,\\dots,t\\}}))$ and the generated $\\beta_{\\{1,\\dots,t\\}}$ . Notice that, we only use the first frame $I_0$ of the wav2lip to generate the lip-sync video which reduces the influence of the pose variant and other facial expressions apart from lip movement. Besides, we also involve the differentiable 3D face render $R_{d}$ to calculate the additional perceptual losses in explicit facial motions space. As shown in Figure 3, we calculate the landmark loss $\\mathcal{L}_{lks}$ to measure the range of eye blink and the overall expression accuracy. A pretrained lip reading network $\\Phi_{reader}$ is also used as temporal lip reading loss $\\mathcal{L}_{read}$ to keep the perceptual lip qualities [9, 28]. We provide more training details in the supplementary materials.", + "bbox": [ + 75, + 688, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fd78b1583342c38978c08e0921788f16cc49911a1f77460a319e98b6010f0fd1.jpg", + "image_caption": [ + "Figure 4. The pipeline of the proposed PoseVAE. We learn the residual of the input head pose $\\rho_0$ via a conditional VAE structure. Given the conditions: first frame $\\rho_0$ , style identity $Z_{style}$ and the audio clip $a_{\\{1,\\dots,t\\}}$ , our method learns a distribution of the residual head pose $\\Delta \\rho_{\\{1,\\dots,t\\}} = \\rho_{\\{1,\\dots,t\\}} - \\rho_0$ . After training, we can generate the stylized results through the pose decoder and the conditions (cond.) only." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 885, + 276 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "PoseVAE As shown in Figure 4, a VAE [20] based model is designed to learn the realistic and identity-aware stylized head movement $\\rho \\in \\mathbb{R}^6$ of the real talking video. In training, the pose VAE is trained on fixed $n$ frames using an encoder-decoder-based structure. Both the encoder and decoder are two-layer MLPs, where the inputs contain a sequential $t$ -frame head poses and we embed it to a Gaussian distribution. In the decoder, the network is learned to generate the $t$ -frame poses from the sampled distribution. Instead of generating the pose directly, our PoseVAE learns the residual of the condition pose $\\rho_0$ of the first frame, which enables our method to generate longer, stable, and continuous head motion in testing under the condition of the first frame. Besides, according to CVAE [6], we add the corresponding audio feature $a_{\\{1,\\dots,t\\}}$ and style identity $Z_{style}$ as conditions for rhythm awareness and identity style. The KL-divergence $\\mathcal{L}_{KL}$ is used to measure the distribution of the generated motions. The mean square loss $\\mathcal{L}_{MSE}$ and adversarial loss $\\mathcal{L}_{GAN}$ are used to ensure the generated quality. We provide more details about the loss function in the supplementary materials.", + "bbox": [ + 496, + 407, + 895, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. 3D-aware Face Render", + "text_level": 1, + "bbox": [ + 500, + 724, + 714, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After generating the realistic 3D motion coefficients, we render the final video through a well-designed 3D-aware image animator. We get inspiration from the recent image animation method Face-vid2vid [40] because it implicitly learns the 3D information from a single image. However, a real video is required as the motions driving signal in their method. Our face render makes it drivable through 3DMM coefficients. As shown in Figure 5, we propose mappingNet to learn the relationship between the explicit 3DMM motion coefficients (head pose and expression) and the implicit unsu", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8655", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cca8f528d4ef2f54f11eb4d2ec98138d62e323481e8680ef03038a5be6d75eae.jpg", + "image_caption": [ + "Figure 5. The proposed FaceRender and comparison with facevid2vid [40]. Given source image $I_{s}$ and driving image $I_{d}$ , facevid2vid generates the motions in a unsupervised 3D keypoint spaces of $\\mathcal{X}_c, \\mathcal{X}_s$ and $\\mathcal{X}_d$ . Then, the image can be generated via the appearance $A_0$ and the keypoints. Since we do not have driving image, we use the explicit disentangled 3DMM coefficients as proxy and map it to the unsupervised 3D keypoints space." + ], + "image_footnote": [], + "bbox": [ + 86, + 93, + 464, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pervised 3D keypoints. Our mappingNet is built via several 1D convolutional layers. We use temporal coefficients from a time window for smoothing as PIRenderer [31]. Differently, we find the face alignment motion coefficients in PIRenderer will hugely influence the motion naturalness of audio-driven video generation and provide an experiment in Sec. 4.4. We only use the coefficients of expression and head pose.", + "bbox": [ + 75, + 400, + 468, + 506 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As for training, our method contains two steps. Firstly, we train face-vid2vid [40] in a self-supervised fashion as in the original paper. In the second step, we freeze all the parameters of the appearance encoder, canonical keypoints estimator, and image generator for tuning. Then, we train the mapping net on the 3DMM coefficients of the ground truth video in a reconstruction style. We give the supervision in the domain of unsupervised keypoints using $\\mathcal{L}_1$ loss and the final generated video following their original implementation. More details can be found in the supplementary materials.", + "bbox": [ + 75, + 507, + 473, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 671, + 209, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details and Metrics", + "text_level": 1, + "bbox": [ + 76, + 696, + 390, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets We use VoxCeleb [24] dataset for training which contains over 100k videos of 1251 subjects. We crop the original videos following previous image animation methods [34] and resize the video to $256 \\times 256$ . After preprocessing, the data is used to train our FaceRender. We select 1890 aligned videos and audios of 46 subjects in VoxCeleb to train our PoseVAE and ExpNet. The input audios are downsampled to $16\\mathrm{kHz}$ and transformed to mel-spectrograms with the same setting as Wav2lip [28]. To test our method, we use the 346 videos' first 8-second video (around 70k frames in total) from HDTF dataset [47] since it contains high resolution and in-the-wild talking head videos. These videos", + "bbox": [ + 75, + 719, + 472, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are also cropped and processed following [34] and resized to $256 \\times 256$ for evaluation. We use the first frame of each video as the reference image to generate videos.", + "bbox": [ + 498, + 90, + 892, + 137 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details All of ExpNet, PoseVAE, and FaceRender are trained separately and we employ Adam optimizer [19] for all experiments. After training, our method can be inferred in an end-to-end fashion without any manual intervention. All the 3DMM parameters are extracted through pre-trained deep 3D face reconstruction method [5]. We perform all the experiments on 8 A100 GPUs. ExpNet, PoseVAE, and FaceRender are trained with a learning rate of $2e^{-5}$ , $1e^{-4}$ , and $2e^{-4}$ , respectively. As for the temporal consideration, ExpNet uses continuous 5 frames to learn. PoseVAE is learned via continuous 32 frames. The frames in FaceRender are generated frame-by-frame with the coefficients of 27 continuous frames for stability.", + "bbox": [ + 496, + 157, + 893, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics We demonstrate the superiority of our method on multiple metrics. We employ Frechet Inception Distance (FID) [13, 33] and cumulative probability blur detection (CPBD) [25] to evaluate the quality of the images. To evaluate identity preservation, we calculate the cosine similarity (CSIM) of identity embedding between the source images and the generated frames, in which we use ArcFace [4] to extract identity embedding of images. To evaluate lip synchronization and mouth shape, we evaluate the perceptual differences of the mouth shape from Wav2Lip [28], including the distance score (LSE-D) and confidence score (LSE-C). We also conduct some metrics to evaluate the head motions of generated frames. For the diversity of the generated head motions, a standard deviation of the head motion feature embeddings extracted from the generated frames using Hopenet [26] is calculated. For the alignment of the audio and generated head motions, we compute Beat Align Score as in Bailando [21].", + "bbox": [ + 496, + 376, + 893, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Compare with other state-of-the-art methods", + "text_level": 1, + "bbox": [ + 500, + 659, + 880, + 675 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare several state-of-the-art methods for talking-head videos generation (MakeItTalk [50], Audio2Head [37] and Wang et al. [38]) and audio to expression generation (Wav2Lip [28], PC-AVS [49]). The evaluation is performed on their publicly available checkpoint directly. As shown in Table 1, our method shows better overall video qualities and head pose diversity and also shows comparable performance with other fully talking-head generation methods in terms of the lip synchronization metrics. We argue that these lip synchronization metrics are too sensitive to the audio where the unnatural lip movement may get a better score. However, our method achieves a similar score to the", + "bbox": [ + 496, + 683, + 893, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2This method needs to extract the phoneme from audio, which only works on the specific language.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8656", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3481f0bf111abd7a6da8acc83cac176340305af3709351b8cf7af7a2caa61863.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Comparison with the state-of-the-art method on HDTF dataset. We evaluate Wav2Lip [28] and PC-AVS [49] in the one-shot settings. Wav2Lip* achieves the best video quality since it only animates the lip region while other regions are the same as the original frame. PC-AVS** is evaluated using the fixed reference pose and fails in some samples." + ], + "table_body": "
MethodEye BlinkLip SynchronizationLearned Head MotionVideo Quality
LSE-C↑LSE-D↓Diversity↑Beat Align↑FID↓CPBD↑CSIM↑
Real VideoN./A.8.2116.9820.2590.2710.0000.4281.000
Wav2Lip* [28]N./A.10.2215.535N./A.N./A.21.7250.3680.849
PC-AVS** [49]from ref.9.0536.355N./A.N./A.69.1270.2060.683
MakeItTalk [50]automatic5.11010.0590.2570.26828.2430.2830.838
Audio2Head [37]automatic7.3577.5350.1810.26724.3920.2810.823
Wang et al. [38]automatic4.93210.0550.2260.26822.4320.2950.811
Ourscontrollable7.2907.7720.2780.29322.0570.3350.843
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We compare our method with several state-of-the-art methods for single image audio-driven talking head generation. Our method produces much higher quality results in terms of lip synchronization, identity preservation, head motion and image quality. We give the target image above for both lip shape and identity reference. Please refer our supplementary video for better comparison." + ], + "image_footnote": [], + "bbox": [ + 80, + 690, + 491, + 753 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f46a5d696fc0dc0284ee9813377bf535ce54f926889dc0d8074f645d77e95f47.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 690, + 887, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "real videos, which demonstrates our advantages. We also illustrate the visual results of different methods in Figure 6. Here, we give the lip reference to visualize the lip synchronization of our method. From the figure, our method has a very similar visual quality to the original target video and", + "bbox": [ + 75, + 818, + 472, + 893 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with different head poses as we expect. Compared with our method, Wav2Lip [28] produces blur half-face, PC-AVS [49] and Audio2Head [37] are struggling for identity preservation, Audio2Head can only generate the front talking face. Besides, MakeItTalk [50] and Audio2Head [37] generate the", + "bbox": [ + 496, + 818, + 895, + 893 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8657", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a05569a77aba8c6d3068ddeb83d92730bb83813af1890f9d6947db73047165a5.jpg", + "image_caption": [ + "Reference Image" + ], + "image_footnote": [], + "bbox": [ + 81, + 125, + 158, + 186 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e84a8314861b20ca3223014316d0cf2728afdd40be0ff87cd6c9bb559ccbb3c4.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 160, + 90, + 467, + 152 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/464b7f189b297b21979498fc1a3202a0c3e6ac6a06a0bf960c0fc587981b47d6.jpg", + "image_caption": [ + "Joint learn Pose and Exp coefficients", + "Figure 7. We compare our method with a baseline method which learn all the coefficients from a single network without any condition (from Speech2Gesture [10]). Our method shows clear head movements, identity preservation and diverse expressions." + ], + "image_footnote": [], + "bbox": [ + 160, + 161, + 465, + 222 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "distorted face video due to 2D warping.", + "bbox": [ + 76, + 318, + 339, + 334 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. User Studies", + "text_level": 1, + "bbox": [ + 76, + 344, + 209, + 358 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct user studies to evaluate the performance of all the methods. We generate overall 20 videos which contain almost equal genders with different ages, poses and expressions. Then 20 participants are invited to choose the best method in terms of video sharpness, lip synchronization, the diversity and naturalness of the head motion, and overall quality. The results are shown in Table 2, where the participants like our method mostly because of the video and motion quality. We also find that $38\\%$ of the participants think our methods show better lip synchronization than other methods, which is inconsistent with Table 1. We think it might be because most of the participants focus on the overall quality of the video, where the blurry and still face videos [28, 49] influence their opinions.", + "bbox": [ + 75, + 368, + 472, + 580 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6b38dbb37f5feb66d182261e80295c61b4a85449283cd26038d282183f1c0041.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodLip Sync.Motion DiversityVideo SharpnessOverall Naturalness
Wav2Lip [28]15.6%3.1%2.0%2.8%
PC-AVS [49]18.1%9.6%3.4%9.1%
MakeItTalk [50]5.6%5.3%5.7%6.9%
Wang et al. [38]12.5%12.1%16.3%11.6%
Audio2Head [37]9.5%12.1%9.7%14.7%
Ours38.7%57.9%62.8%54.8%
", + "bbox": [ + 78, + 593, + 468, + 704 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 739, + 240, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of ExpNet For ExpNet, we mainly evaluate the necessity of each component via the lip synchronization metrics. Since there are no disentangled methods before, we consider a baseline (Speech2Gesture [10], which is an audio to keypoint generation network) to learn the head pose and expression coefficients jointly. As shown in Table 3 and Figure 7, learning all the motion coefficients altogether is hard to generate truth-worthy talking head videos. We then consider the variants of the proposed ExpNet, both the initial", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dad9ee191f3b7faadef1b97742f481e1204f9d686ede6a7241b265a83016e6e5.jpg", + "table_caption": [ + "Table 2. User study." + ], + "table_footnote": [], + "table_body": "
MethodLSE-C ↑LSE-D ↓
Speech2Gesture [10]0.87813.889
OursFull (Lip coefs. + β0 + Lread)7.2907.772
w/o β0 & Lread5.2419.532
w/o Lread6.9937.841
w/ real coefs.6.5678.061
", + "bbox": [ + 501, + 89, + 887, + 183 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation for ExpNet. Both the initial expression $\\beta_0$ , lip reading loss $\\mathcal{L}_{read}$ improve the performance a lot. However, the lip synchronization metric drops a lot when using the real coefficients.", + "bbox": [ + 500, + 184, + 890, + 224 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d67346b7153e3c6e2a28de2c00bc61ae27c2b6326f1f26a3bd563cc32aa602c9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 229, + 890, + 303 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d1aade0b6ab01a3315902cdd08994afdf7793d68df998ec3059b6b841d3a9dd8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 305, + 890, + 376 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/418d920e39118d8d557c44d1bafd28f68d0c1c48ba45f802575381470538d91c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 377, + 890, + 449 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/154176a9cce82c46c2d3b459b7d7068f82bba33fb3fb3aa143cf81e1bf3078a9.jpg", + "image_caption": [ + "Figure 8. The ablation of ExpNet. We choose four frames from the generated video as comparison. Our method largely reduces the uncertainty of audio to expression generation. The reference $\\beta_0$ is used to provide the identity information while the lip only coefficients generate better lip synchronization. Notice that, the target image is provided as the identity and lip motion reference." + ], + "image_footnote": [], + "bbox": [ + 508, + 450, + 890, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "expression $\\beta_0$ , lip reading loss $\\mathcal{L}_{read}$ and the necessity of lip-only coefficients are critical. The visual comparison is shown in Figure 8, where our method w/o the initial expression $\\beta_0$ shows huge identity changes as expected. Also, if we use the real coefficients to replace the lip-only coefficients we use, the performance drops a lot in lip synchronization.", + "bbox": [ + 496, + 625, + 893, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation of PoseVAE We evaluate the proposed PoseVAE in terms of motion diversities and audio beat alignments. As shown in Table. 4, the baseline Speech2Gesture [10] also performs worse in pose evaluation. As for our variants, since our method contains several identity style labels, to better evaluate other components, we first consider the perform the ablation studies on a fixed one-hot style of our full method for evaluation (OurFull, Single Fixed Style). Each condition in our setting benefits the overall motion quality in terms of diversity and beat alignment. We further report the results of the mixed style of our full method, which uses the randomly-", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8658", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/50b5a195e53ea8db1fca1edd4ac9a88a9a9c12569463e9d54922d3d3eb7b829c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 4. Ablation the diversity and audio alignment of the proposed PoseVAE. Each component or conditional contribute largely to generate realistic head motions." + ], + "table_body": "
MethodDiversity↑Beat Align↑
Speech2Gesture [10]0.15740.274
OurFull (Single Fixed Style)0.27350.287
w/o Lgan0.25000.271
w/o initial pose0.27250.278
w/o audio0.25660.274
w/o all conditions0.26310.279
OursFull (Mixed Style)0.27780.293
", + "bbox": [ + 78, + 89, + 475, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c7d994a7489d5460ec30ed635a3292ac67b8088299bd0cfbb9d2a35417fdb19e.jpg", + "image_caption": [ + "Source Image" + ], + "image_footnote": [], + "bbox": [ + 81, + 268, + 176, + 344 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c97c26261ecc56f4dde8e574d05d5481d55049b70e14af739ec6078181d3e572.jpg", + "image_caption": [ + "Driven Target" + ], + "image_footnote": [], + "bbox": [ + 178, + 268, + 272, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/55b52369526418a3d509c66b59e4ab2b8171173509eb0c24b5ac5514f998385d.jpg", + "image_caption": [ + "PIRenderer" + ], + "image_footnote": [], + "bbox": [ + 274, + 268, + 367, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c3ef193e28d587df46e7312597b8ce34a45c4f444a31bd4eb424ed4f59105bb9.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 369, + 268, + 462, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a4fd217b823ad866f8e64f14dad062b2dedf44560ea18811c9e0915edc374449.jpg", + "image_caption": [ + "Fixed Alignment Coeff.", + "Figure 9. Ablation studies of face render. In the first row, we directly compare our method with PIRenderer [31] for face animation and our method shows better expression modeling. The second row is a trace map of the generated facial landmarks from the same motion coefficients. Using additional face alignment coefficients as part of motion coefficients [31] will generate unrealistic aligned head video." + ], + "image_footnote": [], + "bbox": [ + 81, + 359, + 176, + 433 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f37abb442890fe0992edcc2272b394724ea1c90c633fe7a2dae8199f1edd280.jpg", + "image_caption": [ + "Learned Alignment Coeff." + ], + "image_footnote": [], + "bbox": [ + 179, + 359, + 272, + 433 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e077f5085b3e167c6c8f17398a64ae6bc0f56d8e297c2e1c3e360e174272fc6e.jpg", + "image_caption": [ + "Real Video" + ], + "image_footnote": [], + "bbox": [ + 274, + 359, + 367, + 433 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6c9a88a8a595d2c7bef1d44855501e4373d3851d5bfa4ab79eb6c5343cb0a956.jpg", + "image_caption": [ + "Ours", + "(w/o Alignment Coeff.)" + ], + "image_footnote": [], + "bbox": [ + 369, + 359, + 462, + 433 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "selected identity label as style and also shows better diversity performance.", + "bbox": [ + 75, + 585, + 468, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation of Face Render We conduct the ablation study on the proposed face render in two aspects. On the one hand, we show the reconstruction quality of our method with the PIRenderer [31], since both methods use 3DMM as an intermediate representation. As shown in the first row of Fig. 9, the proposed face render shows better expression reconstruction qualities and lip synchronization. Besides, we evaluate the pose unnaturalness caused by the additional alignment coefficients used in PIRenderer [31]. As shown in the second row of Fig. 9, we plot the trace map of the landmarks from the generated video with the same head pose and expression coefficients. Using the fixed or learningable crop coefficients (as part of pose coefficients in our poseVAE) will generate the face-aligned video, which is strange as a natural video. We remove it and directly use the head pose and expression as modulation parameters showing a more realistic result.", + "bbox": [ + 75, + 643, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a3e9c026133bd2be8fe2b47e49577367066452052cadff00ca1f95d9e7b9440a.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 504, + 90, + 630, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/71f71bf8910a1239e7e7ae2ac760b2a1d4a10d654a7e50146a78758246d52302.jpg", + "image_caption": [ + "Ours + GFPGAN", + "Zoomed Regions", + "Figure 10. Limitation. Our method may show some teeth artifacts in the lip region in some examples, it can be improved via the face restoration network, i.e., GFPGAN [41]." + ], + "image_footnote": [], + "bbox": [ + 633, + 90, + 759, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b0ed568e780b9abfd2596ecb19ee26d0aa57c05f77f28f5c0251b4a6e946f8af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 90, + 883, + 138 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e34d08d83220a3acc75ce7d416cde037fe715442520dbb2d2d4010e6517b047f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 141, + 883, + 188 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Limitation", + "text_level": 1, + "bbox": [ + 500, + 265, + 617, + 279 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "There are still some limitations in our system. Since 3DMMs couldn't model the variation of eyes and teeth, the mappingNet in our Face Render will struggle to synthesize the realistic teeth in some cases. This limitation can be improved via the blind face restoration networks [41] as shown in Fig. 10. Another limitation of our work is that we only concern the lip motion and eye blinking other than the other facial expressions, e.g., emotion and gaze direction. Thus, it reduces the realism that the generated video has a fixed emotion. We consider it as future work.", + "bbox": [ + 498, + 287, + 893, + 439 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 454, + 617, + 469 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a new system for stylized audio-driven talking head video generation. We use the motion coefficients from 3DMM as an intermediate representation and learn the relationships. To generate realistic 3D coefficients from audio, we propose ExpNet and PoseVAE for realistic expressions and diverse head poses. To model the relationships between 3DMM motion coefficients and the real video, we propose a novel 3D-aware face render inspired by the image animation method [40]. The experiments demonstrate the superiority of our entire framework. Since we predict the realistic 3D facial coefficients, our method can also be used in other modalities directly, i.e., personalized 2D visual dubbing [43], 2D Cartoon animation [50], 3D face animation [8, 44] and NeRF-based 4D talking-head generation [15].", + "bbox": [ + 496, + 479, + 893, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethical Considerations We consider the misuse of our method since it can generate very realistic video. Both visible and invisible video watermarks will be inserted into the produced video for generated content identification similar to Dall-E [30] and Imagen [32]. We also hope our method can provide new research samples for forgery detection.", + "bbox": [ + 496, + 728, + 893, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work was supported by the National Key Projects of China #2021XJTU0040 and the National Key Research and Development Program of China under Grant #2022YFB3303800.", + "bbox": [ + 496, + 839, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8659", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3d faces. In ACM SIGGRAPH, 1999. 2, 3", + "[2] Lele Chen, Ross K Maddox, Zhiyao Duan, and Chenliang Xu. Hierarchical cross-modal talking face generation with dynamic pixel-wise loss. 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ACM Transactions on Graphics (TOG), 2020. 2, 3, 5, 6, 7, 8" + ], + "bbox": [ + 78, + 90, + 470, + 886 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8661", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/aac86acd-650e-49a0-a046-054265e0fe1a_model.json b/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/aac86acd-650e-49a0-a046-054265e0fe1a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..38d62d5d9c4156b5e576521efc661dc9f97c64b8 --- /dev/null +++ b/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/aac86acd-650e-49a0-a046-054265e0fe1a_model.json @@ -0,0 +1,2288 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.178 + ], + "angle": 0, + "content": "SadTalker: Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.202, + 0.864, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.316, + 0.891, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.638, + 0.89, + 0.654 + ], + "angle": 0, + "content": "Figure 1. The proposed SadTalker produces diverse, realistic, synchronized talking videos from input audio and a single reference image." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.666, + 0.314, + 0.683 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.474, + 0.866 + ], + "angle": 0, + "content": "Generating talking head videos through a face image and a piece of speech audio still contains many challenges. i.e., unnatural head movement, distorted expression, and identity modification. We argue that these issues are mainly caused by learning from the coupled 2D motion fields. On the other hand, explicitly using 3D information also suffers problems of stiff expression and incoherent video. We present SadTalker, which generates 3D motion coefficients (head pose, expression) of the 3DMM from audio and implicitly modulates a novel 3D-aware face render for talking head generation. To learn the realistic motion coefficients, we" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.667, + 0.896, + 0.835 + ], + "angle": 0, + "content": "explicitly model the connections between audio and different types of motion coefficients individually. Precisely, we present ExpNet to learn the accurate facial expression from audio by distilling both coefficients and 3D-rendered faces. As for the head pose, we design PoseVAE via a conditional VAE to synthesize head motion in different styles. Finally, the generated 3D motion coefficients are mapped to the unsupervised 3D keypoints space of the proposed face render to synthesize the final video. We conducted extensive experiments to demonstrate the superiority of our method in terms of motion and video quality." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.192, + 0.888 + ], + "angle": 0, + "content": "* Equal Contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.081, + 0.888, + 0.21, + 0.9 + ], + "angle": 0, + "content": "† Corresponding Author" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.875, + 0.21, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.501, + 0.875, + 0.896, + 0.901 + ], + "angle": 0, + "content": "1The code and demo videos are available at https://sadtalker.github.io." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8652" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.208, + 0.105 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.471, + 0.297 + ], + "angle": 0, + "content": "Animating a static portrait image with speech audio is a challenging task and has many important applications in the fields of digital human creation, video conferences, etc. Previous works mainly focus on generating lip motion [2, 3, 28, 29, 49] since it has a strong connection with speech. Recent works also aim to generate a realistic talking face video containing other related motions, e.g., head pose. Their methods mainly introduce 2D motion fields by landmarks [50] and latent warping [37, 38]. However, the quality of the generated videos is still unnatural and restricted by the preference pose [16, 49], month blur [28], identity modification [37, 38], and distorted face [37, 38, 47]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.297, + 0.471, + 0.553 + ], + "angle": 0, + "content": "Generating a natural-looking talking head video contains many challenges since the connections between audio and different motions are different. i.e., the lip movement has the strongest connection with audio, but audio can be talked via different head poses and eye blink. Thus, previous facial landmark-based methods [2, 50] and 2D flow-based audio to expression networks [37, 38] may generate the distorted face since the head motion and expression are not fully disentangled in their representation. Another popular type of method is the latent-based face animation [3, 16, 28, 49]. Their methods mainly focus on the specific kind of motions in talking face animation and struggle to synthesize high-quality video. Our observation is that the 3D facial model contains a highly decoupled representation and can be used to learn each type of motion individually. Although a similar observation has been discussed in [47], their methods also generate inaccurate expressions and unnatural motion sequences." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.471, + 0.902 + ], + "angle": 0, + "content": "From the above observation, we propose SadTalker, a Stylized Audio-Driven Talking-head video generation system through implicit 3D coefficient modulation. To achieve this goal, we consider the motion coefficients of the 3DMM as the intermediate representation and divide our task into two major components. On the one hand, we aim to generate the realistic motion coefficients (e.g., head pose, lip motion, and eye blink) from audio and learn each motion individually to reduce the uncertainty. For expression, we design a novel audio to expression coefficient network by distilling the coefficients from the lip motion only coefficients from [28] and the perceptual losses (lip-reading loss [1], facial landmark loss) on the reconstructed rendered 3D face [5]. For the stylized head pose, a conditional VAE [6] is used to model the diversity and life-like head motion by learning the residual of the given pose. After generating the realistic 3DMM coefficients, we drive the source image through a novel 3D-aware face render. Inspired by face-vid2vid [40], we learn a mapping between the explicit 3DMM coefficients and the domain of the unsupervised 3D keypoint. Then, the warping fields are generated through the unsupervised 3D keypoints of source and driving and it warps the reference image to generate the final videos. We train each sub-network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "of expression generation, head poses generation and face renderer individually and our system can be inferred in an end-to-end style. As for the experiments, several metrics show the advantage of our method in terms of video and motion methods." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.168, + 0.892, + 0.197 + ], + "angle": 0, + "content": "The main contribution of this paper can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.21, + 0.892, + 0.255 + ], + "angle": 0, + "content": "- We present SadTalker, a novel system for a stylized audio-driven single image talking face animation using the generated realistic 3D motion coefficients." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.265, + 0.892, + 0.31 + ], + "angle": 0, + "content": "- To learn the realistic 3D motion coefficient of the 3DMM model from audio, ExpNet and PoseVAE are presented individually." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.32, + 0.894, + 0.351 + ], + "angle": 0, + "content": "- A novel semantic-disentangled and 3D-aware face render is proposed to produce a realistic talking head video." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.361, + 0.894, + 0.406 + ], + "angle": 0, + "content": "- Experiments show that our method achieves state-of-the-art performance in terms of motion synchronization and video quality." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.21, + 0.894, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.42, + 0.642, + 0.435 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.895, + 0.763 + ], + "angle": 0, + "content": "Audio-driven Single Image Talking Face Generation. Early works [3, 28, 29] mainly focus on producing accurate lip motion with a perception discriminator. Since the real videos contain many different motions, ATVGnet [2] uses the facial landmark as the intermediate representation to generate the video frames. A similar approach has been proposed by MakeiTalk [50], differently, it disentangles the content and speaker information from the input audio signal. Since facial landmarks are still a highly coupled space, generating the talking head in the disentangled space is also popular recently. PC-AVS [49] disentangles the head pose and expression using implicit latent code. However, it can only produce low-resolution image and need the control signal from another video. Audio2Head [37] and Wang et al. [38] get inspiration from the video-driven method [34] to produce the talking-head face. However, these head movements are still not vivid and produce distorted faces with inaccurate identities. Although there are some previous works [31, 47] use 3DMMs as an intermediate representation, their method still faces the problem of inaccurate expressions [31] and obvious artifacts [47]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Audio-driven Video Portrait. Our task is also related to visual dubbing, which aims to edit a portrait video through audio. Different from audio-driven single image talking face generation, this task is typically required to be trained and edited on the specific video. Following previous work of deep video portrait [18], these methods utilize 3DMM information for face reconstruction and animation. AudioDVP [43], NVP [36], AD-NeRF [11] learn to reenact the expression to" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8653" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.465, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.3 + ], + "angle": 0, + "content": "Figure 2. Main pipeline. Our method uses the coefficients of 3DMM as intermediate motion representation. To this end, we first generate realistic 3D motion coefficients (facial expression \\(\\beta\\), head pose \\(\\rho\\)) from audio, then these coefficients are used to implicitly modulate the 3D-aware face render for final video generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.332, + 0.473, + 0.439 + ], + "angle": 0, + "content": "edit the mouth shape. Beyond lip movement, i.e., the head motions [22, 46], emotional talking face [17] also get attention. The 3DMM-based method plays an important role in these tasks since it is practical to fit the 3DMM parameters from a video clip. Although these methods achieve satisfactory results in personalized video, their method can not be applied to arbitrary photos and in the wild audio." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.473, + 0.472, + 0.488 + ], + "angle": 0, + "content": "Video-Driven Single Image Talking Face Generation." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.488, + 0.472, + 0.701 + ], + "angle": 0, + "content": "This task is also known as face reenactment or face animation, which aims to transfer the motion of the source image to the target person. It has been widely explored [14, 27, 31, 34, 35, 39, 40, 42, 45, 48] recently. Previous works also learn a shared intermediate motion representation from the source image and the target, which can be roughly divided into the landmark [39] and the unsupervised landmark-based methods [14, 34, 40, 48], 3DMM based methods [7, 31, 45] and the latent animation [23, 42]. This task is much easier than our task since it contains the motion in the same domain. Our face render is also inspired by the method of unsupervised landmark-based method [40] and 3DMM-based method [31] to use coefficients to generate real videos. However, they are not focused on generating realistic motion coefficients." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.169, + 0.737 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As shown in Fig. 2, our system uses the 3D motion coefficients as the intermediate representation for talking head generation. We first extract the coefficients from the original image. Then, the realistic 3DMM motion coefficients are generated by ExpNet and PoseVAE individually. Finally, a 3D-aware face render is proposed to produce the talking head videos. Below, we give a brief introduction to the 3D face model as preliminaries in Sec. 3.1, the audio-driven motion coefficients generation and the coefficients-driven image animator we design in Sec. 3.2 and Sec. 3.3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.77, + 0.107 + ], + "angle": 0, + "content": "3.1. Preliminary of 3D Face Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.895, + 0.266 + ], + "angle": 0, + "content": "3D information is crucial to improve the realness of the generated video since the real video is captured in the 3D environment. However, previous works [28, 49, 50] have rarely been a consideration in 3D space since it is hard to obtain accurate 3D coefficients from a single image and the high-quality face render is also hard to design. Inspired by the recent single image deep 3D reconstruction method [5], we consider the space of the predicted 3D Morphable Models (3DMMs) as our intermediate representation. In 3DMM, the 3D face shape S can be decoupled as:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.271, + 0.894, + 0.289 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} = \\overline {{\\mathbf {S}}} + \\alpha \\mathbf {U} _ {i d} + \\beta \\mathbf {U} _ {e x p}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.895, + 0.476 + ], + "angle": 0, + "content": "where \\(\\overline{\\mathbf{S}}\\) is the average shape of the 3D face, \\(\\mathbf{U}_{id}\\) and \\(\\mathbf{U}_{exp}\\) are the orthonormal basis of identity and expression of LSFM morphable model [1]. Coefficients \\(\\alpha \\in \\mathbb{R}^{80}\\) and \\(\\beta \\in \\mathbb{R}^{64}\\) describe the person identity and expression, respectively. To preserve pose variance, coefficients \\(\\mathbf{r} \\in SO(3)\\) and \\(\\mathbf{t} \\in \\mathbb{R}^3\\) denote the head rotation and translation. To achieve identity irrelevant coefficients generation [31], we only model the parameters of motion as \\(\\{\\beta, \\mathbf{r}, \\mathbf{t}\\}\\). We learn the head pose \\(\\rho = [\\mathbf{r}, \\mathbf{t}]\\) and expression coefficients \\(\\beta\\) individually from the driving audio as introduced before. Then, these motion coefficients are used to implicitly modulate our face render for final video synthesis." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.483, + 0.892, + 0.5 + ], + "angle": 0, + "content": "3.2. Motion Coefficients Generation through Audio" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.895, + 0.642 + ], + "angle": 0, + "content": "As introduced above, the 3D motion coefficients contain both head pose and expression where the head pose is a global motion and the expression is relatively local. To this end, learning everything altogether will cause huge uncertainty in the network since the head pose has a relatively weak relationship with audio while the lip motion is highly connected. We generate the motion of the head pose and expression using the proposed PoseVAE and ExpNet, respectively introduced below." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.897, + 0.902 + ], + "angle": 0, + "content": "ExpNet Learning a generic model which produces accurate expression coefficients from audio is extremely hard for two reasons: 1) audio-to-expression is not a one-to-one mapping task for different identities. 2) there are some audio-irrelevant motions in the expression coefficients and it will influence the prediction's accuracy. Our ExpNet is designed to reduce these uncertainties. As for the identity issue, we connect the expression motion to the specific person via the first frame's expression coefficients \\(\\beta_0\\) which also controls the facial emotion of the generated video. To reduce the disturbance of other facial components in real expression coefficients, we use the lip motion only coefficients as the coefficient target through the pre-trained network of Wav2Lip [28] and deep 3D reconstruction [5]. Then, other minor facial motions (e.g., eye blink) can be leveraged via the additional landmark loss on the rendered images." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8654" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.099, + 0.46, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.473, + 0.409 + ], + "angle": 0, + "content": "Figure 3. The structure of our ExpNet. We involve a monocular 3D face reconstruction model [5] (\\(R_{e}\\) and \\(R_{d}\\)) to learn the realistic expression coefficients. Where \\(R_{e}\\) is a pretrained 3DMM coefficients estimator and \\(R_{d}\\) is a differentiable 3D face render without learnable parameters. We use the reference expression \\(\\beta_0\\) to reduce the uncertainty of identity and the generated frame from pre-trained Wav2Lip [28] and the first frame as target expression coefficients since it only contains the lip-related motions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.475, + 0.637 + ], + "angle": 0, + "content": "As shown in Figure 3, we generate the \\(t\\)-frame expression coefficients from an audio window \\(a_{\\{1,\\dots,t\\}}\\), where the audio feature of each frame is a 0.2s mel-spectrogram. For training, we first design a ResNet-based audio encoder \\(\\Phi_A\\) [12, 28] to embed the audio feature to a latent space. Then, a linear layer is added as the mapping network \\(\\Phi_M\\) to decode the expression coefficients. Here, we also add the reference expression \\(\\beta_0\\) from the reference image to support emotions and reduce the identity uncertainty as discussed above. Since we use the lip-only coefficients as ground truth in the training, we explicitly add a blinking control signal \\(z_{blink} \\in [0,1]\\) and the corresponding eye landmark loss to generate the controllable eye blinks. Formally, the network can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.653, + 0.471, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\beta_ {\\{1, \\dots , t \\}} = \\Phi_ {M} (\\Phi_ {A} (a _ {\\{1, \\dots , t \\}}), z _ {b l i n k}, \\beta_ {0}) \\qquad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As for the loss function, we first use \\(\\mathcal{L}_{distill}\\) to evaluate the differences between the lip only expression coefficients \\(R_{e}(\\mathrm{Wav2Lip}(I_0,a_{\\{1,\\dots,t\\}}))\\) and the generated \\(\\beta_{\\{1,\\dots,t\\}}\\). Notice that, we only use the first frame \\(I_0\\) of the wav2lip to generate the lip-sync video which reduces the influence of the pose variant and other facial expressions apart from lip movement. Besides, we also involve the differentiable 3D face render \\(R_{d}\\) to calculate the additional perceptual losses in explicit facial motions space. As shown in Figure 3, we calculate the landmark loss \\(\\mathcal{L}_{lks}\\) to measure the range of eye blink and the overall expression accuracy. A pretrained lip reading network \\(\\Phi_{reader}\\) is also used as temporal lip reading loss \\(\\mathcal{L}_{read}\\) to keep the perceptual lip qualities [9, 28]. We provide more training details in the supplementary materials." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.092, + 0.887, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.28, + 0.896, + 0.379 + ], + "angle": 0, + "content": "Figure 4. The pipeline of the proposed PoseVAE. We learn the residual of the input head pose \\(\\rho_0\\) via a conditional VAE structure. Given the conditions: first frame \\(\\rho_0\\), style identity \\(Z_{style}\\) and the audio clip \\(a_{\\{1,\\dots,t\\}}\\), our method learns a distribution of the residual head pose \\(\\Delta \\rho_{\\{1,\\dots,t\\}} = \\rho_{\\{1,\\dots,t\\}} - \\rho_0\\). After training, we can generate the stylized results through the pose decoder and the conditions (cond.) only." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.896, + 0.711 + ], + "angle": 0, + "content": "PoseVAE As shown in Figure 4, a VAE [20] based model is designed to learn the realistic and identity-aware stylized head movement \\(\\rho \\in \\mathbb{R}^6\\) of the real talking video. In training, the pose VAE is trained on fixed \\(n\\) frames using an encoder-decoder-based structure. Both the encoder and decoder are two-layer MLPs, where the inputs contain a sequential \\(t\\)-frame head poses and we embed it to a Gaussian distribution. In the decoder, the network is learned to generate the \\(t\\)-frame poses from the sampled distribution. Instead of generating the pose directly, our PoseVAE learns the residual of the condition pose \\(\\rho_0\\) of the first frame, which enables our method to generate longer, stable, and continuous head motion in testing under the condition of the first frame. Besides, according to CVAE [6], we add the corresponding audio feature \\(a_{\\{1,\\dots,t\\}}\\) and style identity \\(Z_{style}\\) as conditions for rhythm awareness and identity style. The KL-divergence \\(\\mathcal{L}_{KL}\\) is used to measure the distribution of the generated motions. The mean square loss \\(\\mathcal{L}_{MSE}\\) and adversarial loss \\(\\mathcal{L}_{GAN}\\) are used to ensure the generated quality. We provide more details about the loss function in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.715, + 0.74 + ], + "angle": 0, + "content": "3.3. 3D-aware Face Render" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.896, + 0.903 + ], + "angle": 0, + "content": "After generating the realistic 3D motion coefficients, we render the final video through a well-designed 3D-aware image animator. We get inspiration from the recent image animation method Face-vid2vid [40] because it implicitly learns the 3D information from a single image. However, a real video is required as the motions driving signal in their method. Our face render makes it drivable through 3DMM coefficients. As shown in Figure 5, we propose mappingNet to learn the relationship between the explicit 3DMM motion coefficients (head pose and expression) and the implicit unsu" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8655" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.094, + 0.465, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.376 + ], + "angle": 0, + "content": "Figure 5. The proposed FaceRender and comparison with facevid2vid [40]. Given source image \\( I_{s} \\) and driving image \\( I_{d} \\), facevid2vid generates the motions in a unsupervised 3D keypoint spaces of \\( \\mathcal{X}_c, \\mathcal{X}_s \\) and \\( \\mathcal{X}_d \\). Then, the image can be generated via the appearance \\( A_0 \\) and the keypoints. Since we do not have driving image, we use the explicit disentangled 3DMM coefficients as proxy and map it to the unsupervised 3D keypoints space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.401, + 0.47, + 0.507 + ], + "angle": 0, + "content": "pervised 3D keypoints. Our mappingNet is built via several 1D convolutional layers. We use temporal coefficients from a time window for smoothing as PIRenderer [31]. Differently, we find the face alignment motion coefficients in PIRenderer will hugely influence the motion naturalness of audio-driven video generation and provide an experiment in Sec. 4.4. We only use the coefficients of expression and head pose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.474, + 0.659 + ], + "angle": 0, + "content": "As for training, our method contains two steps. Firstly, we train face-vid2vid [40] in a self-supervised fashion as in the original paper. In the second step, we freeze all the parameters of the appearance encoder, canonical keypoints estimator, and image generator for tuning. Then, we train the mapping net on the 3DMM coefficients of the ground truth video in a reconstruction style. We give the supervision in the domain of unsupervised keypoints using \\(\\mathcal{L}_1\\) loss and the final generated video following their original implementation. More details can be found in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.672, + 0.21, + 0.689 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.391, + 0.713 + ], + "angle": 0, + "content": "4.1. Implementation Details and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Datasets We use VoxCeleb [24] dataset for training which contains over 100k videos of 1251 subjects. We crop the original videos following previous image animation methods [34] and resize the video to \\(256 \\times 256\\). After preprocessing, the data is used to train our FaceRender. We select 1890 aligned videos and audios of 46 subjects in VoxCeleb to train our PoseVAE and ExpNet. The input audios are downsampled to \\(16\\mathrm{kHz}\\) and transformed to mel-spectrograms with the same setting as Wav2lip [28]. To test our method, we use the 346 videos' first 8-second video (around 70k frames in total) from HDTF dataset [47] since it contains high resolution and in-the-wild talking head videos. These videos" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.893, + 0.138 + ], + "angle": 0, + "content": "are also cropped and processed following [34] and resized to \\(256 \\times 256\\) for evaluation. We use the first frame of each video as the reference image to generate videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.159, + 0.895, + 0.356 + ], + "angle": 0, + "content": "Implementation Details All of ExpNet, PoseVAE, and FaceRender are trained separately and we employ Adam optimizer [19] for all experiments. After training, our method can be inferred in an end-to-end fashion without any manual intervention. All the 3DMM parameters are extracted through pre-trained deep 3D face reconstruction method [5]. We perform all the experiments on 8 A100 GPUs. ExpNet, PoseVAE, and FaceRender are trained with a learning rate of \\(2e^{-5}\\), \\(1e^{-4}\\), and \\(2e^{-4}\\), respectively. As for the temporal consideration, ExpNet uses continuous 5 frames to learn. PoseVAE is learned via continuous 32 frames. The frames in FaceRender are generated frame-by-frame with the coefficients of 27 continuous frames for stability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.895, + 0.649 + ], + "angle": 0, + "content": "Evaluation Metrics We demonstrate the superiority of our method on multiple metrics. We employ Frechet Inception Distance (FID) [13, 33] and cumulative probability blur detection (CPBD) [25] to evaluate the quality of the images. To evaluate identity preservation, we calculate the cosine similarity (CSIM) of identity embedding between the source images and the generated frames, in which we use ArcFace [4] to extract identity embedding of images. To evaluate lip synchronization and mouth shape, we evaluate the perceptual differences of the mouth shape from Wav2Lip [28], including the distance score (LSE-D) and confidence score (LSE-C). We also conduct some metrics to evaluate the head motions of generated frames. For the diversity of the generated head motions, a standard deviation of the head motion feature embeddings extracted from the generated frames using Hopenet [26] is calculated. For the alignment of the audio and generated head motions, we compute Beat Align Score as in Bailando [21]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.66, + 0.882, + 0.676 + ], + "angle": 0, + "content": "4.2. Compare with other state-of-the-art methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.895, + 0.865 + ], + "angle": 0, + "content": "We compare several state-of-the-art methods for talking-head videos generation (MakeItTalk [50], Audio2Head [37] and Wang et al. [38]) and audio to expression generation (Wav2Lip [28], PC-AVS [49]). The evaluation is performed on their publicly available checkpoint directly. As shown in Table 1, our method shows better overall video qualities and head pose diversity and also shows comparable performance with other fully talking-head generation methods in terms of the lip synchronization metrics. We argue that these lip synchronization metrics are too sensitive to the audio where the unnatural lip movement may get a better score. However, our method achieves a similar score to the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.501, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2This method needs to extract the phoneme from audio, which only works on the specific language." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8656" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.09, + 0.891, + 0.24 + ], + "angle": 0, + "content": "
MethodEye BlinkLip SynchronizationLearned Head MotionVideo Quality
LSE-C↑LSE-D↓Diversity↑Beat Align↑FID↓CPBD↑CSIM↑
Real VideoN./A.8.2116.9820.2590.2710.0000.4281.000
Wav2Lip* [28]N./A.10.2215.535N./A.N./A.21.7250.3680.849
PC-AVS** [49]from ref.9.0536.355N./A.N./A.69.1270.2060.683
MakeItTalk [50]automatic5.11010.0590.2570.26828.2430.2830.838
Audio2Head [37]automatic7.3577.5350.1810.26724.3920.2810.823
Wang et al. [38]automatic4.93210.0550.2260.26822.4320.2950.811
Ourscontrollable7.2907.7720.2780.29322.0570.3350.843
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.077, + 0.24, + 0.897, + 0.283 + ], + "angle": 0, + "content": "Table 1. Comparison with the state-of-the-art method on HDTF dataset. We evaluate Wav2Lip [28] and PC-AVS [49] in the one-shot settings. Wav2Lip* achieves the best video quality since it only animates the lip region while other regions are the same as the original frame. PC-AVS** is evaluated using the fixed reference pose and fails in some samples." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.293, + 0.492, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.293, + 0.888, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.371, + 0.492, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.37, + 0.888, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.435, + 0.491, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.435, + 0.888, + 0.496 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.497, + 0.491, + 0.562 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.497, + 0.888, + 0.562 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.562, + 0.491, + 0.625 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.563, + 0.888, + 0.625 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.626, + 0.491, + 0.69 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.627, + 0.888, + 0.69 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.691, + 0.492, + 0.754 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.691, + 0.888, + 0.755 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.762, + 0.895, + 0.806 + ], + "angle": 0, + "content": "Figure 6. We compare our method with several state-of-the-art methods for single image audio-driven talking head generation. Our method produces much higher quality results in terms of lip synchronization, identity preservation, head motion and image quality. We give the target image above for both lip shape and identity reference. Please refer our supplementary video for better comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.819, + 0.473, + 0.895 + ], + "angle": 0, + "content": "real videos, which demonstrates our advantages. We also illustrate the visual results of different methods in Figure 6. Here, we give the lip reference to visualize the lip synchronization of our method. From the figure, our method has a very similar visual quality to the original target video and" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.819, + 0.896, + 0.895 + ], + "angle": 0, + "content": "with different head poses as we expect. Compared with our method, Wav2Lip [28] produces blur half-face, PC-AVS [49] and Audio2Head [37] are struggling for identity preservation, Audio2Head can only generate the front talking face. Besides, MakeItTalk [50] and Audio2Head [37] generate the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8657" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.126, + 0.159, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.083, + 0.187, + 0.158, + 0.197 + ], + "angle": 0, + "content": "Reference Image" + }, + { + "type": "image", + "bbox": [ + 0.161, + 0.091, + 0.468, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.302, + 0.154, + 0.325, + 0.162 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.161, + 0.162, + 0.467, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.224, + 0.395, + 0.233 + ], + "angle": 0, + "content": "Joint learn Pose and Exp coefficients" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.236, + 0.471, + 0.292 + ], + "angle": 0, + "content": "Figure 7. We compare our method with a baseline method which learn all the coefficients from a single network without any condition (from Speech2Gesture [10]). Our method shows clear head movements, identity preservation and diverse expressions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.34, + 0.335 + ], + "angle": 0, + "content": "distorted face video due to 2D warping." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.345, + 0.21, + 0.359 + ], + "angle": 0, + "content": "4.3. User Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.473, + 0.581 + ], + "angle": 0, + "content": "We conduct user studies to evaluate the performance of all the methods. We generate overall 20 videos which contain almost equal genders with different ages, poses and expressions. Then 20 participants are invited to choose the best method in terms of video sharpness, lip synchronization, the diversity and naturalness of the head motion, and overall quality. The results are shown in Table 2, where the participants like our method mostly because of the video and motion quality. We also find that \\(38\\%\\) of the participants think our methods show better lip synchronization than other methods, which is inconsistent with Table 1. We think it might be because most of the participants focus on the overall quality of the video, where the blurry and still face videos [28, 49] influence their opinions." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.594, + 0.47, + 0.705 + ], + "angle": 0, + "content": "
MethodLip Sync.Motion DiversityVideo SharpnessOverall Naturalness
Wav2Lip [28]15.6%3.1%2.0%2.8%
PC-AVS [49]18.1%9.6%3.4%9.1%
MakeItTalk [50]5.6%5.3%5.7%6.9%
Wang et al. [38]12.5%12.1%16.3%11.6%
Audio2Head [37]9.5%12.1%9.7%14.7%
Ours38.7%57.9%62.8%54.8%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.212, + 0.705, + 0.333, + 0.718 + ], + "angle": 0, + "content": "Table 2. User study." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.241, + 0.756 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Ablation of ExpNet For ExpNet, we mainly evaluate the necessity of each component via the lip synchronization metrics. Since there are no disentangled methods before, we consider a baseline (Speech2Gesture [10], which is an audio to keypoint generation network) to learn the head pose and expression coefficients jointly. As shown in Table 3 and Figure 7, learning all the motion coefficients altogether is hard to generate truth-worthy talking head videos. We then consider the variants of the proposed ExpNet, both the initial" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.09, + 0.888, + 0.184 + ], + "angle": 0, + "content": "
MethodLSE-C ↑LSE-D ↓
Speech2Gesture [10]0.87813.889
OursFull (Lip coefs. + β0 + Lread)7.2907.772
w/o β0 & Lread5.2419.532
w/o Lread6.9937.841
w/ real coefs.6.5678.061
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.185, + 0.892, + 0.226 + ], + "angle": 0, + "content": "Table 3. Ablation for ExpNet. Both the initial expression \\( \\beta_0 \\), lip reading loss \\( \\mathcal{L}_{read} \\) improve the performance a lot. However, the lip synchronization metric drops a lot when using the real coefficients." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.231, + 0.892, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.306, + 0.891, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.378, + 0.891, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.451, + 0.891, + 0.523 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.527, + 0.892, + 0.612 + ], + "angle": 0, + "content": "Figure 8. The ablation of ExpNet. We choose four frames from the generated video as comparison. Our method largely reduces the uncertainty of audio to expression generation. The reference \\(\\beta_0\\) is used to provide the identity information while the lip only coefficients generate better lip synchronization. Notice that, the target image is provided as the identity and lip motion reference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.894, + 0.716 + ], + "angle": 0, + "content": "expression \\(\\beta_0\\), lip reading loss \\(\\mathcal{L}_{read}\\) and the necessity of lip-only coefficients are critical. The visual comparison is shown in Figure 8, where our method w/o the initial expression \\(\\beta_0\\) shows huge identity changes as expected. Also, if we use the real coefficients to replace the lip-only coefficients we use, the performance drops a lot in lip synchronization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Ablation of PoseVAE We evaluate the proposed PoseVAE in terms of motion diversities and audio beat alignments. As shown in Table. 4, the baseline Speech2Gesture [10] also performs worse in pose evaluation. As for our variants, since our method contains several identity style labels, to better evaluate other components, we first consider the perform the ablation studies on a fixed one-hot style of our full method for evaluation (OurFull, Single Fixed Style). Each condition in our setting benefits the overall motion quality in terms of diversity and beat alignment. We further report the results of the mixed style of our full method, which uses the randomly-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8658" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.476, + 0.219 + ], + "angle": 0, + "content": "
MethodDiversity↑Beat Align↑
Speech2Gesture [10]0.15740.274
OurFull (Single Fixed Style)0.27350.287
w/o Lgan0.25000.271
w/o initial pose0.27250.278
w/o audio0.25660.274
w/o all conditions0.26310.279
OursFull (Mixed Style)0.27780.293
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.078, + 0.221, + 0.47, + 0.263 + ], + "angle": 0, + "content": "Table 4. Ablation the diversity and audio alignment of the proposed PoseVAE. Each component or conditional contribute largely to generate realistic head motions." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.27, + 0.177, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.346, + 0.159, + 0.355 + ], + "angle": 0, + "content": "Source Image" + }, + { + "type": "image", + "bbox": [ + 0.179, + 0.27, + 0.273, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.346, + 0.258, + 0.355 + ], + "angle": 0, + "content": "Driven Target" + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.27, + 0.368, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.296, + 0.346, + 0.345, + 0.354 + ], + "angle": 0, + "content": "PIRenderer" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.27, + 0.464, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.346, + 0.426, + 0.354 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.361, + 0.178, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.436, + 0.163, + 0.454 + ], + "angle": 0, + "content": "Fixed Alignment Coeff." + }, + { + "type": "image", + "bbox": [ + 0.18, + 0.361, + 0.273, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.188, + 0.437, + 0.268, + 0.454 + ], + "angle": 0, + "content": "Learned Alignment Coeff." + }, + { + "type": "image", + "bbox": [ + 0.276, + 0.361, + 0.369, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.298, + 0.441, + 0.343, + 0.45 + ], + "angle": 0, + "content": "Real Video" + }, + { + "type": "image", + "bbox": [ + 0.37, + 0.361, + 0.464, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.408, + 0.437, + 0.429, + 0.445 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.371, + 0.446, + 0.466, + 0.456 + ], + "angle": 0, + "content": "(w/o Alignment Coeff.)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.555 + ], + "angle": 0, + "content": "Figure 9. Ablation studies of face render. In the first row, we directly compare our method with PIRenderer [31] for face animation and our method shows better expression modeling. The second row is a trace map of the generated facial landmarks from the same motion coefficients. Using additional face alignment coefficients as part of motion coefficients [31] will generate unrealistic aligned head video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.618 + ], + "angle": 0, + "content": "selected identity label as style and also shows better diversity performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Ablation of Face Render We conduct the ablation study on the proposed face render in two aspects. On the one hand, we show the reconstruction quality of our method with the PIRenderer [31], since both methods use 3DMM as an intermediate representation. As shown in the first row of Fig. 9, the proposed face render shows better expression reconstruction qualities and lip synchronization. Besides, we evaluate the pose unnaturalness caused by the additional alignment coefficients used in PIRenderer [31]. As shown in the second row of Fig. 9, we plot the trace map of the landmarks from the generated video with the same head pose and expression coefficients. Using the fixed or learningable crop coefficients (as part of pose coefficients in our poseVAE) will generate the face-aligned video, which is strange as a natural video. We remove it and directly use the head pose and expression as modulation parameters showing a more realistic result." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.092, + 0.632, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.543, + 0.191, + 0.579, + 0.203 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.092, + 0.76, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.191, + 0.752, + 0.204 + ], + "angle": 0, + "content": "Ours + GFPGAN" + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.092, + 0.885, + 0.14 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.142, + 0.885, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.763, + 0.191, + 0.882, + 0.205 + ], + "angle": 0, + "content": "Zoomed Regions" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.209, + 0.892, + 0.251 + ], + "angle": 0, + "content": "Figure 10. Limitation. Our method may show some teeth artifacts in the lip region in some examples, it can be improved via the face restoration network, i.e., GFPGAN [41]." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.266, + 0.619, + 0.28 + ], + "angle": 0, + "content": "4.5. Limitation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.895, + 0.44 + ], + "angle": 0, + "content": "There are still some limitations in our system. Since 3DMMs couldn't model the variation of eyes and teeth, the mappingNet in our Face Render will struggle to synthesize the realistic teeth in some cases. This limitation can be improved via the blind face restoration networks [41] as shown in Fig. 10. Another limitation of our work is that we only concern the lip motion and eye blinking other than the other facial expressions, e.g., emotion and gaze direction. Thus, it reduces the realism that the generated video has a fixed emotion. We consider it as future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.455, + 0.619, + 0.47 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.895, + 0.709 + ], + "angle": 0, + "content": "In this paper, we present a new system for stylized audio-driven talking head video generation. We use the motion coefficients from 3DMM as an intermediate representation and learn the relationships. To generate realistic 3D coefficients from audio, we propose ExpNet and PoseVAE for realistic expressions and diverse head poses. To model the relationships between 3DMM motion coefficients and the real video, we propose a novel 3D-aware face render inspired by the image animation method [40]. The experiments demonstrate the superiority of our entire framework. Since we predict the realistic 3D facial coefficients, our method can also be used in other modalities directly, i.e., personalized 2D visual dubbing [43], 2D Cartoon animation [50], 3D face animation [8, 44] and NeRF-based 4D talking-head generation [15]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.894, + 0.82 + ], + "angle": 0, + "content": "Ethical Considerations We consider the misuse of our method since it can generate very realistic video. Both visible and invisible video watermarks will be inserted into the produced video for generated content identification similar to Dall-E [30] and Imagen [32]. We also hope our method can provide new research samples for forgery detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements This work was supported by the National Key Projects of China #2021XJTU0040 and the National Key Research and Development Program of China under Grant #2022YFB3303800." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8659" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3d faces. 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In CVPR, 2021. 2, 3, 5, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.08, + 0.832, + 0.472, + 0.887 + ], + "angle": 0, + "content": "[50] Yang Zhou, Xintong Han, Eli Shechtman, Jose Echevarria, Evangelos Kalogerakis, and Dingzeyu Li. Makeltalk: speaker-aware talking-head animation. ACM Transactions on Graphics (TOG), 2020. 2, 3, 5, 6, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.887 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.956 + ], + "angle": 0, + "content": "8661" + } + ] +] \ No newline at end of file diff --git a/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/aac86acd-650e-49a0-a046-054265e0fe1a_origin.pdf b/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/aac86acd-650e-49a0-a046-054265e0fe1a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5cb8c3089f98e8e6e76b124418daddd95a0fd75a --- /dev/null +++ b/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/aac86acd-650e-49a0-a046-054265e0fe1a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5f5888edaea5ff044866fafb8f91f3b2875a4683a9a7f9e0eb85117edbfc56fa +size 3774624 diff --git a/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/full.md b/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..95d79bab3cb7a5022fcfc3e91d6082686d59544c --- /dev/null +++ b/2023/SadTalker_ Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation/full.md @@ -0,0 +1,298 @@ +# SadTalker: Learning Realistic 3D Motion Coefficients for Stylized Audio-Driven Single Image Talking Face Animation + +![](images/06e04c218e50c4c5dceb2f086e9a553c70764e821f57f11c9c1a4c7301f8ce84.jpg) + +![](images/172c471ad44210127b009c637e3049508930d7d281f0f53cee60bf664466901c.jpg) +Figure 1. The proposed SadTalker produces diverse, realistic, synchronized talking videos from input audio and a single reference image. + +# Abstract + +Generating talking head videos through a face image and a piece of speech audio still contains many challenges. i.e., unnatural head movement, distorted expression, and identity modification. We argue that these issues are mainly caused by learning from the coupled 2D motion fields. On the other hand, explicitly using 3D information also suffers problems of stiff expression and incoherent video. We present SadTalker, which generates 3D motion coefficients (head pose, expression) of the 3DMM from audio and implicitly modulates a novel 3D-aware face render for talking head generation. To learn the realistic motion coefficients, we + +explicitly model the connections between audio and different types of motion coefficients individually. Precisely, we present ExpNet to learn the accurate facial expression from audio by distilling both coefficients and 3D-rendered faces. As for the head pose, we design PoseVAE via a conditional VAE to synthesize head motion in different styles. Finally, the generated 3D motion coefficients are mapped to the unsupervised 3D keypoints space of the proposed face render to synthesize the final video. We conducted extensive experiments to demonstrate the superiority of our method in terms of motion and video quality. + +# 1. Introduction + +Animating a static portrait image with speech audio is a challenging task and has many important applications in the fields of digital human creation, video conferences, etc. Previous works mainly focus on generating lip motion [2, 3, 28, 29, 49] since it has a strong connection with speech. Recent works also aim to generate a realistic talking face video containing other related motions, e.g., head pose. Their methods mainly introduce 2D motion fields by landmarks [50] and latent warping [37, 38]. However, the quality of the generated videos is still unnatural and restricted by the preference pose [16, 49], month blur [28], identity modification [37, 38], and distorted face [37, 38, 47]. + +Generating a natural-looking talking head video contains many challenges since the connections between audio and different motions are different. i.e., the lip movement has the strongest connection with audio, but audio can be talked via different head poses and eye blink. Thus, previous facial landmark-based methods [2, 50] and 2D flow-based audio to expression networks [37, 38] may generate the distorted face since the head motion and expression are not fully disentangled in their representation. Another popular type of method is the latent-based face animation [3, 16, 28, 49]. Their methods mainly focus on the specific kind of motions in talking face animation and struggle to synthesize high-quality video. Our observation is that the 3D facial model contains a highly decoupled representation and can be used to learn each type of motion individually. Although a similar observation has been discussed in [47], their methods also generate inaccurate expressions and unnatural motion sequences. + +From the above observation, we propose SadTalker, a Stylized Audio-Driven Talking-head video generation system through implicit 3D coefficient modulation. To achieve this goal, we consider the motion coefficients of the 3DMM as the intermediate representation and divide our task into two major components. On the one hand, we aim to generate the realistic motion coefficients (e.g., head pose, lip motion, and eye blink) from audio and learn each motion individually to reduce the uncertainty. For expression, we design a novel audio to expression coefficient network by distilling the coefficients from the lip motion only coefficients from [28] and the perceptual losses (lip-reading loss [1], facial landmark loss) on the reconstructed rendered 3D face [5]. For the stylized head pose, a conditional VAE [6] is used to model the diversity and life-like head motion by learning the residual of the given pose. After generating the realistic 3DMM coefficients, we drive the source image through a novel 3D-aware face render. Inspired by face-vid2vid [40], we learn a mapping between the explicit 3DMM coefficients and the domain of the unsupervised 3D keypoint. Then, the warping fields are generated through the unsupervised 3D keypoints of source and driving and it warps the reference image to generate the final videos. We train each sub-network + +of expression generation, head poses generation and face renderer individually and our system can be inferred in an end-to-end style. As for the experiments, several metrics show the advantage of our method in terms of video and motion methods. + +The main contribution of this paper can be summarized as: + +- We present SadTalker, a novel system for a stylized audio-driven single image talking face animation using the generated realistic 3D motion coefficients. +- To learn the realistic 3D motion coefficient of the 3DMM model from audio, ExpNet and PoseVAE are presented individually. +- A novel semantic-disentangled and 3D-aware face render is proposed to produce a realistic talking head video. +- Experiments show that our method achieves state-of-the-art performance in terms of motion synchronization and video quality. + +# 2. Related Work + +Audio-driven Single Image Talking Face Generation. Early works [3, 28, 29] mainly focus on producing accurate lip motion with a perception discriminator. Since the real videos contain many different motions, ATVGnet [2] uses the facial landmark as the intermediate representation to generate the video frames. A similar approach has been proposed by MakeiTalk [50], differently, it disentangles the content and speaker information from the input audio signal. Since facial landmarks are still a highly coupled space, generating the talking head in the disentangled space is also popular recently. PC-AVS [49] disentangles the head pose and expression using implicit latent code. However, it can only produce low-resolution image and need the control signal from another video. Audio2Head [37] and Wang et al. [38] get inspiration from the video-driven method [34] to produce the talking-head face. However, these head movements are still not vivid and produce distorted faces with inaccurate identities. Although there are some previous works [31, 47] use 3DMMs as an intermediate representation, their method still faces the problem of inaccurate expressions [31] and obvious artifacts [47]. + +Audio-driven Video Portrait. Our task is also related to visual dubbing, which aims to edit a portrait video through audio. Different from audio-driven single image talking face generation, this task is typically required to be trained and edited on the specific video. Following previous work of deep video portrait [18], these methods utilize 3DMM information for face reconstruction and animation. AudioDVP [43], NVP [36], AD-NeRF [11] learn to reenact the expression to + +![](images/508d009ece138732f2e254b09716357e7c3a9ec9b7e5596b47fbff4d4e2c39b0.jpg) +Figure 2. Main pipeline. Our method uses the coefficients of 3DMM as intermediate motion representation. To this end, we first generate realistic 3D motion coefficients (facial expression $\beta$ , head pose $\rho$ ) from audio, then these coefficients are used to implicitly modulate the 3D-aware face render for final video generation. + +edit the mouth shape. Beyond lip movement, i.e., the head motions [22, 46], emotional talking face [17] also get attention. The 3DMM-based method plays an important role in these tasks since it is practical to fit the 3DMM parameters from a video clip. Although these methods achieve satisfactory results in personalized video, their method can not be applied to arbitrary photos and in the wild audio. + +# Video-Driven Single Image Talking Face Generation. + +This task is also known as face reenactment or face animation, which aims to transfer the motion of the source image to the target person. It has been widely explored [14, 27, 31, 34, 35, 39, 40, 42, 45, 48] recently. Previous works also learn a shared intermediate motion representation from the source image and the target, which can be roughly divided into the landmark [39] and the unsupervised landmark-based methods [14, 34, 40, 48], 3DMM based methods [7, 31, 45] and the latent animation [23, 42]. This task is much easier than our task since it contains the motion in the same domain. Our face render is also inspired by the method of unsupervised landmark-based method [40] and 3DMM-based method [31] to use coefficients to generate real videos. However, they are not focused on generating realistic motion coefficients. + +# 3. Method + +As shown in Fig. 2, our system uses the 3D motion coefficients as the intermediate representation for talking head generation. We first extract the coefficients from the original image. Then, the realistic 3DMM motion coefficients are generated by ExpNet and PoseVAE individually. Finally, a 3D-aware face render is proposed to produce the talking head videos. Below, we give a brief introduction to the 3D face model as preliminaries in Sec. 3.1, the audio-driven motion coefficients generation and the coefficients-driven image animator we design in Sec. 3.2 and Sec. 3.3, respectively. + +# 3.1. Preliminary of 3D Face Model + +3D information is crucial to improve the realness of the generated video since the real video is captured in the 3D environment. However, previous works [28, 49, 50] have rarely been a consideration in 3D space since it is hard to obtain accurate 3D coefficients from a single image and the high-quality face render is also hard to design. Inspired by the recent single image deep 3D reconstruction method [5], we consider the space of the predicted 3D Morphable Models (3DMMs) as our intermediate representation. In 3DMM, the 3D face shape S can be decoupled as: + +$$ +\mathbf {S} = \overline {{\mathbf {S}}} + \alpha \mathbf {U} _ {i d} + \beta \mathbf {U} _ {e x p}, \tag {1} +$$ + +where $\overline{\mathbf{S}}$ is the average shape of the 3D face, $\mathbf{U}_{id}$ and $\mathbf{U}_{exp}$ are the orthonormal basis of identity and expression of LSFM morphable model [1]. Coefficients $\alpha \in \mathbb{R}^{80}$ and $\beta \in \mathbb{R}^{64}$ describe the person identity and expression, respectively. To preserve pose variance, coefficients $\mathbf{r} \in SO(3)$ and $\mathbf{t} \in \mathbb{R}^3$ denote the head rotation and translation. To achieve identity irrelevant coefficients generation [31], we only model the parameters of motion as $\{\beta, \mathbf{r}, \mathbf{t}\}$ . We learn the head pose $\rho = [\mathbf{r}, \mathbf{t}]$ and expression coefficients $\beta$ individually from the driving audio as introduced before. Then, these motion coefficients are used to implicitly modulate our face render for final video synthesis. + +# 3.2. Motion Coefficients Generation through Audio + +As introduced above, the 3D motion coefficients contain both head pose and expression where the head pose is a global motion and the expression is relatively local. To this end, learning everything altogether will cause huge uncertainty in the network since the head pose has a relatively weak relationship with audio while the lip motion is highly connected. We generate the motion of the head pose and expression using the proposed PoseVAE and ExpNet, respectively introduced below. + +ExpNet Learning a generic model which produces accurate expression coefficients from audio is extremely hard for two reasons: 1) audio-to-expression is not a one-to-one mapping task for different identities. 2) there are some audio-irrelevant motions in the expression coefficients and it will influence the prediction's accuracy. Our ExpNet is designed to reduce these uncertainties. As for the identity issue, we connect the expression motion to the specific person via the first frame's expression coefficients $\beta_0$ which also controls the facial emotion of the generated video. To reduce the disturbance of other facial components in real expression coefficients, we use the lip motion only coefficients as the coefficient target through the pre-trained network of Wav2Lip [28] and deep 3D reconstruction [5]. Then, other minor facial motions (e.g., eye blink) can be leveraged via the additional landmark loss on the rendered images. + +![](images/429274038857670e614daf4780cad19cf6365854728228da9881c01a2d83bbf3.jpg) +Figure 3. The structure of our ExpNet. We involve a monocular 3D face reconstruction model [5] ( $R_{e}$ and $R_{d}$ ) to learn the realistic expression coefficients. Where $R_{e}$ is a pretrained 3DMM coefficients estimator and $R_{d}$ is a differentiable 3D face render without learnable parameters. We use the reference expression $\beta_0$ to reduce the uncertainty of identity and the generated frame from pre-trained Wav2Lip [28] and the first frame as target expression coefficients since it only contains the lip-related motions. + +As shown in Figure 3, we generate the $t$ -frame expression coefficients from an audio window $a_{\{1,\dots,t\}}$ , where the audio feature of each frame is a 0.2s mel-spectrogram. For training, we first design a ResNet-based audio encoder $\Phi_A$ [12, 28] to embed the audio feature to a latent space. Then, a linear layer is added as the mapping network $\Phi_M$ to decode the expression coefficients. Here, we also add the reference expression $\beta_0$ from the reference image to support emotions and reduce the identity uncertainty as discussed above. Since we use the lip-only coefficients as ground truth in the training, we explicitly add a blinking control signal $z_{blink} \in [0,1]$ and the corresponding eye landmark loss to generate the controllable eye blinks. Formally, the network can be written as: + +$$ +\beta_ {\{1, \dots , t \}} = \Phi_ {M} (\Phi_ {A} (a _ {\{1, \dots , t \}}), z _ {b l i n k}, \beta_ {0}) \qquad (2) +$$ + +As for the loss function, we first use $\mathcal{L}_{distill}$ to evaluate the differences between the lip only expression coefficients $R_{e}(\mathrm{Wav2Lip}(I_0,a_{\{1,\dots,t\}}))$ and the generated $\beta_{\{1,\dots,t\}}$ . Notice that, we only use the first frame $I_0$ of the wav2lip to generate the lip-sync video which reduces the influence of the pose variant and other facial expressions apart from lip movement. Besides, we also involve the differentiable 3D face render $R_{d}$ to calculate the additional perceptual losses in explicit facial motions space. As shown in Figure 3, we calculate the landmark loss $\mathcal{L}_{lks}$ to measure the range of eye blink and the overall expression accuracy. A pretrained lip reading network $\Phi_{reader}$ is also used as temporal lip reading loss $\mathcal{L}_{read}$ to keep the perceptual lip qualities [9, 28]. We provide more training details in the supplementary materials. + +![](images/fd78b1583342c38978c08e0921788f16cc49911a1f77460a319e98b6010f0fd1.jpg) +Figure 4. The pipeline of the proposed PoseVAE. We learn the residual of the input head pose $\rho_0$ via a conditional VAE structure. Given the conditions: first frame $\rho_0$ , style identity $Z_{style}$ and the audio clip $a_{\{1,\dots,t\}}$ , our method learns a distribution of the residual head pose $\Delta \rho_{\{1,\dots,t\}} = \rho_{\{1,\dots,t\}} - \rho_0$ . After training, we can generate the stylized results through the pose decoder and the conditions (cond.) only. + +PoseVAE As shown in Figure 4, a VAE [20] based model is designed to learn the realistic and identity-aware stylized head movement $\rho \in \mathbb{R}^6$ of the real talking video. In training, the pose VAE is trained on fixed $n$ frames using an encoder-decoder-based structure. Both the encoder and decoder are two-layer MLPs, where the inputs contain a sequential $t$ -frame head poses and we embed it to a Gaussian distribution. In the decoder, the network is learned to generate the $t$ -frame poses from the sampled distribution. Instead of generating the pose directly, our PoseVAE learns the residual of the condition pose $\rho_0$ of the first frame, which enables our method to generate longer, stable, and continuous head motion in testing under the condition of the first frame. Besides, according to CVAE [6], we add the corresponding audio feature $a_{\{1,\dots,t\}}$ and style identity $Z_{style}$ as conditions for rhythm awareness and identity style. The KL-divergence $\mathcal{L}_{KL}$ is used to measure the distribution of the generated motions. The mean square loss $\mathcal{L}_{MSE}$ and adversarial loss $\mathcal{L}_{GAN}$ are used to ensure the generated quality. We provide more details about the loss function in the supplementary materials. + +# 3.3. 3D-aware Face Render + +After generating the realistic 3D motion coefficients, we render the final video through a well-designed 3D-aware image animator. We get inspiration from the recent image animation method Face-vid2vid [40] because it implicitly learns the 3D information from a single image. However, a real video is required as the motions driving signal in their method. Our face render makes it drivable through 3DMM coefficients. As shown in Figure 5, we propose mappingNet to learn the relationship between the explicit 3DMM motion coefficients (head pose and expression) and the implicit unsu + +![](images/cca8f528d4ef2f54f11eb4d2ec98138d62e323481e8680ef03038a5be6d75eae.jpg) +Figure 5. The proposed FaceRender and comparison with facevid2vid [40]. Given source image $I_{s}$ and driving image $I_{d}$ , facevid2vid generates the motions in a unsupervised 3D keypoint spaces of $\mathcal{X}_c, \mathcal{X}_s$ and $\mathcal{X}_d$ . Then, the image can be generated via the appearance $A_0$ and the keypoints. Since we do not have driving image, we use the explicit disentangled 3DMM coefficients as proxy and map it to the unsupervised 3D keypoints space. + +pervised 3D keypoints. Our mappingNet is built via several 1D convolutional layers. We use temporal coefficients from a time window for smoothing as PIRenderer [31]. Differently, we find the face alignment motion coefficients in PIRenderer will hugely influence the motion naturalness of audio-driven video generation and provide an experiment in Sec. 4.4. We only use the coefficients of expression and head pose. + +As for training, our method contains two steps. Firstly, we train face-vid2vid [40] in a self-supervised fashion as in the original paper. In the second step, we freeze all the parameters of the appearance encoder, canonical keypoints estimator, and image generator for tuning. Then, we train the mapping net on the 3DMM coefficients of the ground truth video in a reconstruction style. We give the supervision in the domain of unsupervised keypoints using $\mathcal{L}_1$ loss and the final generated video following their original implementation. More details can be found in the supplementary materials. + +# 4. Experiments + +# 4.1. Implementation Details and Metrics + +Datasets We use VoxCeleb [24] dataset for training which contains over 100k videos of 1251 subjects. We crop the original videos following previous image animation methods [34] and resize the video to $256 \times 256$ . After preprocessing, the data is used to train our FaceRender. We select 1890 aligned videos and audios of 46 subjects in VoxCeleb to train our PoseVAE and ExpNet. The input audios are downsampled to $16\mathrm{kHz}$ and transformed to mel-spectrograms with the same setting as Wav2lip [28]. To test our method, we use the 346 videos' first 8-second video (around 70k frames in total) from HDTF dataset [47] since it contains high resolution and in-the-wild talking head videos. These videos + +are also cropped and processed following [34] and resized to $256 \times 256$ for evaluation. We use the first frame of each video as the reference image to generate videos. + +Implementation Details All of ExpNet, PoseVAE, and FaceRender are trained separately and we employ Adam optimizer [19] for all experiments. After training, our method can be inferred in an end-to-end fashion without any manual intervention. All the 3DMM parameters are extracted through pre-trained deep 3D face reconstruction method [5]. We perform all the experiments on 8 A100 GPUs. ExpNet, PoseVAE, and FaceRender are trained with a learning rate of $2e^{-5}$ , $1e^{-4}$ , and $2e^{-4}$ , respectively. As for the temporal consideration, ExpNet uses continuous 5 frames to learn. PoseVAE is learned via continuous 32 frames. The frames in FaceRender are generated frame-by-frame with the coefficients of 27 continuous frames for stability. + +Evaluation Metrics We demonstrate the superiority of our method on multiple metrics. We employ Frechet Inception Distance (FID) [13, 33] and cumulative probability blur detection (CPBD) [25] to evaluate the quality of the images. To evaluate identity preservation, we calculate the cosine similarity (CSIM) of identity embedding between the source images and the generated frames, in which we use ArcFace [4] to extract identity embedding of images. To evaluate lip synchronization and mouth shape, we evaluate the perceptual differences of the mouth shape from Wav2Lip [28], including the distance score (LSE-D) and confidence score (LSE-C). We also conduct some metrics to evaluate the head motions of generated frames. For the diversity of the generated head motions, a standard deviation of the head motion feature embeddings extracted from the generated frames using Hopenet [26] is calculated. For the alignment of the audio and generated head motions, we compute Beat Align Score as in Bailando [21]. + +# 4.2. Compare with other state-of-the-art methods + +We compare several state-of-the-art methods for talking-head videos generation (MakeItTalk [50], Audio2Head [37] and Wang et al. [38]) and audio to expression generation (Wav2Lip [28], PC-AVS [49]). The evaluation is performed on their publicly available checkpoint directly. As shown in Table 1, our method shows better overall video qualities and head pose diversity and also shows comparable performance with other fully talking-head generation methods in terms of the lip synchronization metrics. We argue that these lip synchronization metrics are too sensitive to the audio where the unnatural lip movement may get a better score. However, our method achieves a similar score to the + +
MethodEye BlinkLip SynchronizationLearned Head MotionVideo Quality
LSE-C↑LSE-D↓Diversity↑Beat Align↑FID↓CPBD↑CSIM↑
Real VideoN./A.8.2116.9820.2590.2710.0000.4281.000
Wav2Lip* [28]N./A.10.2215.535N./A.N./A.21.7250.3680.849
PC-AVS** [49]from ref.9.0536.355N./A.N./A.69.1270.2060.683
MakeItTalk [50]automatic5.11010.0590.2570.26828.2430.2830.838
Audio2Head [37]automatic7.3577.5350.1810.26724.3920.2810.823
Wang et al. [38]automatic4.93210.0550.2260.26822.4320.2950.811
Ourscontrollable7.2907.7720.2780.29322.0570.3350.843
+ +Table 1. Comparison with the state-of-the-art method on HDTF dataset. We evaluate Wav2Lip [28] and PC-AVS [49] in the one-shot settings. Wav2Lip* achieves the best video quality since it only animates the lip region while other regions are the same as the original frame. PC-AVS** is evaluated using the fixed reference pose and fails in some samples. + +![](images/628fcfba401bb4f2d9cc26e87cec22f5d3a8d6738355c9048154fad94013156b.jpg) + +![](images/7154dc7d7e24c6ec7bf926324a81ebe9574c8d3d007dabdc904b7742f44e752c.jpg) + +![](images/adfb9a5d9431aa39b6ec0bd1aec602800a7042032217b08ff8e1af373d97e66f.jpg) + +![](images/7a72984da3bd721c66040afe61539506b0fa0748fa1506d0ea501d95cf0c1cf5.jpg) + +![](images/2ce7a46450d35d235ea870880dc1f12b503e6931333b6a589f38233aa8d11dd8.jpg) + +![](images/63f3f04ba5e9ac271024952826c3b98bc02e16b06bb73f4549eb065c8ba5ccce.jpg) + +![](images/e937943568499deadc4ae31454ed4a97f267d642bd45c023c4adf7bcedd0782b.jpg) + +![](images/2a39c70736cfebb4c74cda0b95b9b81420b7bb30a56d2f78e770a6b39830b284.jpg) + +![](images/b2c82cff7e83c50800cebf887f58ced856357cb0b4577dcf58938a77cf190d23.jpg) + +![](images/93ee3b621f6096655743a643f7fa5f9701ceccf5b633e8f67e3b6b30d1372f28.jpg) + +![](images/a32da4054972bc15e72bcea37708cb01bcf1555cc2b1b0575321a1cd4f279ed2.jpg) + +![](images/f89af848dc440255f2c11cd59ecb9e33de566ba7c12c7768db6ac502bde6d9dc.jpg) + +![](images/2a023726b039046bf6540280315b5facdd9b5696c87ac32f5e2048b7b1ed1252.jpg) +Figure 6. We compare our method with several state-of-the-art methods for single image audio-driven talking head generation. Our method produces much higher quality results in terms of lip synchronization, identity preservation, head motion and image quality. We give the target image above for both lip shape and identity reference. Please refer our supplementary video for better comparison. + +![](images/f46a5d696fc0dc0284ee9813377bf535ce54f926889dc0d8074f645d77e95f47.jpg) + +real videos, which demonstrates our advantages. We also illustrate the visual results of different methods in Figure 6. Here, we give the lip reference to visualize the lip synchronization of our method. From the figure, our method has a very similar visual quality to the original target video and + +with different head poses as we expect. Compared with our method, Wav2Lip [28] produces blur half-face, PC-AVS [49] and Audio2Head [37] are struggling for identity preservation, Audio2Head can only generate the front talking face. Besides, MakeItTalk [50] and Audio2Head [37] generate the + +![](images/a05569a77aba8c6d3068ddeb83d92730bb83813af1890f9d6947db73047165a5.jpg) +Reference Image + +![](images/e84a8314861b20ca3223014316d0cf2728afdd40be0ff87cd6c9bb559ccbb3c4.jpg) +Ours + +![](images/464b7f189b297b21979498fc1a3202a0c3e6ac6a06a0bf960c0fc587981b47d6.jpg) +Joint learn Pose and Exp coefficients +Figure 7. We compare our method with a baseline method which learn all the coefficients from a single network without any condition (from Speech2Gesture [10]). Our method shows clear head movements, identity preservation and diverse expressions. + +distorted face video due to 2D warping. + +# 4.3. User Studies + +We conduct user studies to evaluate the performance of all the methods. We generate overall 20 videos which contain almost equal genders with different ages, poses and expressions. Then 20 participants are invited to choose the best method in terms of video sharpness, lip synchronization, the diversity and naturalness of the head motion, and overall quality. The results are shown in Table 2, where the participants like our method mostly because of the video and motion quality. We also find that $38\%$ of the participants think our methods show better lip synchronization than other methods, which is inconsistent with Table 1. We think it might be because most of the participants focus on the overall quality of the video, where the blurry and still face videos [28, 49] influence their opinions. + +
MethodLip Sync.Motion DiversityVideo SharpnessOverall Naturalness
Wav2Lip [28]15.6%3.1%2.0%2.8%
PC-AVS [49]18.1%9.6%3.4%9.1%
MakeItTalk [50]5.6%5.3%5.7%6.9%
Wang et al. [38]12.5%12.1%16.3%11.6%
Audio2Head [37]9.5%12.1%9.7%14.7%
Ours38.7%57.9%62.8%54.8%
+ +# 4.4. Ablation Studies + +Ablation of ExpNet For ExpNet, we mainly evaluate the necessity of each component via the lip synchronization metrics. Since there are no disentangled methods before, we consider a baseline (Speech2Gesture [10], which is an audio to keypoint generation network) to learn the head pose and expression coefficients jointly. As shown in Table 3 and Figure 7, learning all the motion coefficients altogether is hard to generate truth-worthy talking head videos. We then consider the variants of the proposed ExpNet, both the initial + +Table 2. User study. + +
MethodLSE-C ↑LSE-D ↓
Speech2Gesture [10]0.87813.889
OursFull (Lip coefs. + β0 + Lread)7.2907.772
w/o β0 & Lread5.2419.532
w/o Lread6.9937.841
w/ real coefs.6.5678.061
+ +Table 3. Ablation for ExpNet. Both the initial expression $\beta_0$ , lip reading loss $\mathcal{L}_{read}$ improve the performance a lot. However, the lip synchronization metric drops a lot when using the real coefficients. + +![](images/d67346b7153e3c6e2a28de2c00bc61ae27c2b6326f1f26a3bd563cc32aa602c9.jpg) + +![](images/d1aade0b6ab01a3315902cdd08994afdf7793d68df998ec3059b6b841d3a9dd8.jpg) + +![](images/418d920e39118d8d557c44d1bafd28f68d0c1c48ba45f802575381470538d91c.jpg) + +![](images/154176a9cce82c46c2d3b459b7d7068f82bba33fb3fb3aa143cf81e1bf3078a9.jpg) +Figure 8. The ablation of ExpNet. We choose four frames from the generated video as comparison. Our method largely reduces the uncertainty of audio to expression generation. The reference $\beta_0$ is used to provide the identity information while the lip only coefficients generate better lip synchronization. Notice that, the target image is provided as the identity and lip motion reference. + +expression $\beta_0$ , lip reading loss $\mathcal{L}_{read}$ and the necessity of lip-only coefficients are critical. The visual comparison is shown in Figure 8, where our method w/o the initial expression $\beta_0$ shows huge identity changes as expected. Also, if we use the real coefficients to replace the lip-only coefficients we use, the performance drops a lot in lip synchronization. + +Ablation of PoseVAE We evaluate the proposed PoseVAE in terms of motion diversities and audio beat alignments. As shown in Table. 4, the baseline Speech2Gesture [10] also performs worse in pose evaluation. As for our variants, since our method contains several identity style labels, to better evaluate other components, we first consider the perform the ablation studies on a fixed one-hot style of our full method for evaluation (OurFull, Single Fixed Style). Each condition in our setting benefits the overall motion quality in terms of diversity and beat alignment. We further report the results of the mixed style of our full method, which uses the randomly- + +
MethodDiversity↑Beat Align↑
Speech2Gesture [10]0.15740.274
OurFull (Single Fixed Style)0.27350.287
w/o Lgan0.25000.271
w/o initial pose0.27250.278
w/o audio0.25660.274
w/o all conditions0.26310.279
OursFull (Mixed Style)0.27780.293
+ +Table 4. Ablation the diversity and audio alignment of the proposed PoseVAE. Each component or conditional contribute largely to generate realistic head motions. + +![](images/c7d994a7489d5460ec30ed635a3292ac67b8088299bd0cfbb9d2a35417fdb19e.jpg) +Source Image + +![](images/c97c26261ecc56f4dde8e574d05d5481d55049b70e14af739ec6078181d3e572.jpg) +Driven Target + +![](images/55b52369526418a3d509c66b59e4ab2b8171173509eb0c24b5ac5514f998385d.jpg) +PIRenderer + +![](images/c3ef193e28d587df46e7312597b8ce34a45c4f444a31bd4eb424ed4f59105bb9.jpg) +Ours + +![](images/a4fd217b823ad866f8e64f14dad062b2dedf44560ea18811c9e0915edc374449.jpg) +Fixed Alignment Coeff. +Figure 9. Ablation studies of face render. In the first row, we directly compare our method with PIRenderer [31] for face animation and our method shows better expression modeling. The second row is a trace map of the generated facial landmarks from the same motion coefficients. Using additional face alignment coefficients as part of motion coefficients [31] will generate unrealistic aligned head video. + +![](images/3f37abb442890fe0992edcc2272b394724ea1c90c633fe7a2dae8199f1edd280.jpg) +Learned Alignment Coeff. + +![](images/e077f5085b3e167c6c8f17398a64ae6bc0f56d8e297c2e1c3e360e174272fc6e.jpg) +Real Video + +![](images/6c9a88a8a595d2c7bef1d44855501e4373d3851d5bfa4ab79eb6c5343cb0a956.jpg) +Ours +(w/o Alignment Coeff.) + +selected identity label as style and also shows better diversity performance. + +Ablation of Face Render We conduct the ablation study on the proposed face render in two aspects. On the one hand, we show the reconstruction quality of our method with the PIRenderer [31], since both methods use 3DMM as an intermediate representation. As shown in the first row of Fig. 9, the proposed face render shows better expression reconstruction qualities and lip synchronization. Besides, we evaluate the pose unnaturalness caused by the additional alignment coefficients used in PIRenderer [31]. As shown in the second row of Fig. 9, we plot the trace map of the landmarks from the generated video with the same head pose and expression coefficients. Using the fixed or learningable crop coefficients (as part of pose coefficients in our poseVAE) will generate the face-aligned video, which is strange as a natural video. We remove it and directly use the head pose and expression as modulation parameters showing a more realistic result. + +![](images/a3e9c026133bd2be8fe2b47e49577367066452052cadff00ca1f95d9e7b9440a.jpg) +Ours + +![](images/71f71bf8910a1239e7e7ae2ac760b2a1d4a10d654a7e50146a78758246d52302.jpg) +Ours + GFPGAN +Zoomed Regions +Figure 10. Limitation. Our method may show some teeth artifacts in the lip region in some examples, it can be improved via the face restoration network, i.e., GFPGAN [41]. + +![](images/b0ed568e780b9abfd2596ecb19ee26d0aa57c05f77f28f5c0251b4a6e946f8af.jpg) + +![](images/e34d08d83220a3acc75ce7d416cde037fe715442520dbb2d2d4010e6517b047f.jpg) + +# 4.5. Limitation + +There are still some limitations in our system. Since 3DMMs couldn't model the variation of eyes and teeth, the mappingNet in our Face Render will struggle to synthesize the realistic teeth in some cases. This limitation can be improved via the blind face restoration networks [41] as shown in Fig. 10. Another limitation of our work is that we only concern the lip motion and eye blinking other than the other facial expressions, e.g., emotion and gaze direction. Thus, it reduces the realism that the generated video has a fixed emotion. We consider it as future work. + +# 5. Conclusion + +In this paper, we present a new system for stylized audio-driven talking head video generation. We use the motion coefficients from 3DMM as an intermediate representation and learn the relationships. To generate realistic 3D coefficients from audio, we propose ExpNet and PoseVAE for realistic expressions and diverse head poses. To model the relationships between 3DMM motion coefficients and the real video, we propose a novel 3D-aware face render inspired by the image animation method [40]. The experiments demonstrate the superiority of our entire framework. Since we predict the realistic 3D facial coefficients, our method can also be used in other modalities directly, i.e., personalized 2D visual dubbing [43], 2D Cartoon animation [50], 3D face animation [8, 44] and NeRF-based 4D talking-head generation [15]. + +Ethical Considerations We consider the misuse of our method since it can generate very realistic video. Both visible and invisible video watermarks will be inserted into the produced video for generated content identification similar to Dall-E [30] and Imagen [32]. We also hope our method can provide new research samples for forgery detection. + +Acknowledgements This work was supported by the National Key Projects of China #2021XJTU0040 and the National Key Research and Development Program of China under Grant #2022YFB3303800. + +# References + +[1] Volker Blanz and Thomas Vetter. A morphable model for the synthesis of 3d faces. In ACM SIGGRAPH, 1999. 2, 3 +[2] Lele Chen, Ross K Maddox, Zhiyao Duan, and Chenliang Xu. Hierarchical cross-modal talking face generation with dynamic pixel-wise loss. In CVPR, 2019. 2 +[3] Kun Cheng, Xiaodong Cun, Yong Zhang, Menghan Xia, Fei Yin, Mingrui Zhu, Xuan Wang, Jue Wang, and Nannan Wang. Videoretalking: Audio-based lip synchronization for talking head video editing in the wild. 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The proposed SadTalker produces diverse, realistic, synchronized talking videos from input audio and a single reference image." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 527, + 192, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 527, + 192, + 540 + ], + "spans": [ + { + "bbox": [ + 143, + 527, + 192, + 540 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 552, + 290, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 290, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 290, + 685 + ], + "type": "text", + "content": "Generating talking head videos through a face image and a piece of speech audio still contains many challenges. i.e., unnatural head movement, distorted expression, and identity modification. We argue that these issues are mainly caused by learning from the coupled 2D motion fields. On the other hand, explicitly using 3D information also suffers problems of stiff expression and incoherent video. We present SadTalker, which generates 3D motion coefficients (head pose, expression) of the 3DMM from audio and implicitly modulates a novel 3D-aware face render for talking head generation. To learn the realistic motion coefficients, we" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 528, + 548, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 548, + 661 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 548, + 661 + ], + "type": "text", + "content": "explicitly model the connections between audio and different types of motion coefficients individually. Precisely, we present ExpNet to learn the accurate facial expression from audio by distilling both coefficients and 3D-rendered faces. As for the head pose, we design PoseVAE via a conditional VAE to synthesize head motion in different styles. Finally, the generated 3D motion coefficients are mapped to the unsupervised 3D keypoints space of the proposed face render to synthesize the final video. We conducted extensive experiments to demonstrate the superiority of our method in terms of motion and video quality." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 117, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 117, + 703 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 117, + 703 + ], + "type": "text", + "content": "* Equal Contribution" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 49, + 703, + 128, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 703, + 128, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 703, + 128, + 712 + ], + "type": "text", + "content": "† Corresponding Author" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 693, + 548, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 548, + 713 + ], + "type": "text", + "content": "1The code and demo videos are available at https://sadtalker.github.io." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8652" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 288, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 288, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 288, + 235 + ], + "type": "text", + "content": "Animating a static portrait image with speech audio is a challenging task and has many important applications in the fields of digital human creation, video conferences, etc. Previous works mainly focus on generating lip motion [2, 3, 28, 29, 49] since it has a strong connection with speech. Recent works also aim to generate a realistic talking face video containing other related motions, e.g., head pose. Their methods mainly introduce 2D motion fields by landmarks [50] and latent warping [37, 38]. However, the quality of the generated videos is still unnatural and restricted by the preference pose [16, 49], month blur [28], identity modification [37, 38], and distorted face [37, 38, 47]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 235, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 235, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 235, + 288, + 437 + ], + "type": "text", + "content": "Generating a natural-looking talking head video contains many challenges since the connections between audio and different motions are different. i.e., the lip movement has the strongest connection with audio, but audio can be talked via different head poses and eye blink. Thus, previous facial landmark-based methods [2, 50] and 2D flow-based audio to expression networks [37, 38] may generate the distorted face since the head motion and expression are not fully disentangled in their representation. Another popular type of method is the latent-based face animation [3, 16, 28, 49]. Their methods mainly focus on the specific kind of motions in talking face animation and struggle to synthesize high-quality video. Our observation is that the 3D facial model contains a highly decoupled representation and can be used to learn each type of motion individually. Although a similar observation has been discussed in [47], their methods also generate inaccurate expressions and unnatural motion sequences." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 438, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 288, + 714 + ], + "type": "text", + "content": "From the above observation, we propose SadTalker, a Stylized Audio-Driven Talking-head video generation system through implicit 3D coefficient modulation. To achieve this goal, we consider the motion coefficients of the 3DMM as the intermediate representation and divide our task into two major components. On the one hand, we aim to generate the realistic motion coefficients (e.g., head pose, lip motion, and eye blink) from audio and learn each motion individually to reduce the uncertainty. For expression, we design a novel audio to expression coefficient network by distilling the coefficients from the lip motion only coefficients from [28] and the perceptual losses (lip-reading loss [1], facial landmark loss) on the reconstructed rendered 3D face [5]. For the stylized head pose, a conditional VAE [6] is used to model the diversity and life-like head motion by learning the residual of the given pose. After generating the realistic 3DMM coefficients, we drive the source image through a novel 3D-aware face render. Inspired by face-vid2vid [40], we learn a mapping between the explicit 3DMM coefficients and the domain of the unsupervised 3D keypoint. Then, the warping fields are generated through the unsupervised 3D keypoints of source and driving and it warps the reference image to generate the final videos. We train each sub-network" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 131 + ], + "type": "text", + "content": "of expression generation, head poses generation and face renderer individually and our system can be inferred in an end-to-end style. As for the experiments, several metrics show the advantage of our method in terms of video and motion methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 133, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 545, + 156 + ], + "type": "text", + "content": "The main contribution of this paper can be summarized as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 166, + 547, + 321 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 317, + 166, + 545, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 166, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 317, + 166, + 545, + 201 + ], + "type": "text", + "content": "- We present SadTalker, a novel system for a stylized audio-driven single image talking face animation using the generated realistic 3D motion coefficients." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 209, + 545, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 209, + 545, + 245 + ], + "spans": [ + { + "bbox": [ + 317, + 209, + 545, + 245 + ], + "type": "text", + "content": "- To learn the realistic 3D motion coefficient of the 3DMM model from audio, ExpNet and PoseVAE are presented individually." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 253, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 253, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 317, + 253, + 547, + 277 + ], + "type": "text", + "content": "- A novel semantic-disentangled and 3D-aware face render is proposed to produce a realistic talking head video." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 285, + 547, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 285, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 317, + 285, + 547, + 321 + ], + "type": "text", + "content": "- Experiments show that our method achieves state-of-the-art performance in terms of motion synchronization and video quality." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 332, + 392, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 332, + 392, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 332, + 392, + 344 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 352, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 547, + 604 + ], + "type": "text", + "content": "Audio-driven Single Image Talking Face Generation. Early works [3, 28, 29] mainly focus on producing accurate lip motion with a perception discriminator. Since the real videos contain many different motions, ATVGnet [2] uses the facial landmark as the intermediate representation to generate the video frames. A similar approach has been proposed by MakeiTalk [50], differently, it disentangles the content and speaker information from the input audio signal. Since facial landmarks are still a highly coupled space, generating the talking head in the disentangled space is also popular recently. PC-AVS [49] disentangles the head pose and expression using implicit latent code. However, it can only produce low-resolution image and need the control signal from another video. Audio2Head [37] and Wang et al. [38] get inspiration from the video-driven method [34] to produce the talking-head face. However, these head movements are still not vivid and produce distorted faces with inaccurate identities. Although there are some previous works [31, 47] use 3DMMs as an intermediate representation, their method still faces the problem of inaccurate expressions [31] and obvious artifacts [47]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Audio-driven Video Portrait. Our task is also related to visual dubbing, which aims to edit a portrait video through audio. Different from audio-driven single image talking face generation, this task is typically required to be trained and edited on the specific video. Following previous work of deep video portrait [18], these methods utilize 3DMM information for face reconstruction and animation. AudioDVP [43], NVP [36], AD-NeRF [11] learn to reenact the expression to" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8653" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 284, + 178 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 284, + 178 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 284, + 178 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 284, + 178 + ], + "type": "image", + "image_path": "508d009ece138732f2e254b09716357e7c3a9ec9b7e5596b47fbff4d4e2c39b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "type": "text", + "content": "Figure 2. Main pipeline. Our method uses the coefficients of 3DMM as intermediate motion representation. To this end, we first generate realistic 3D motion coefficients (facial expression " + }, + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "type": "text", + "content": ", head pose " + }, + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 182, + 289, + 237 + ], + "type": "text", + "content": ") from audio, then these coefficients are used to implicitly modulate the 3D-aware face render for final video generation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 262, + 289, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 262, + 289, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 289, + 347 + ], + "type": "text", + "content": "edit the mouth shape. Beyond lip movement, i.e., the head motions [22, 46], emotional talking face [17] also get attention. The 3DMM-based method plays an important role in these tasks since it is practical to fit the 3DMM parameters from a video clip. Although these methods achieve satisfactory results in personalized video, their method can not be applied to arbitrary photos and in the wild audio." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 374, + 288, + 386 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 288, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 288, + 386 + ], + "type": "text", + "content": "Video-Driven Single Image Talking Face Generation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 386, + 288, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 386, + 288, + 555 + ], + "spans": [ + { + "bbox": [ + 45, + 386, + 288, + 555 + ], + "type": "text", + "content": "This task is also known as face reenactment or face animation, which aims to transfer the motion of the source image to the target person. It has been widely explored [14, 27, 31, 34, 35, 39, 40, 42, 45, 48] recently. Previous works also learn a shared intermediate motion representation from the source image and the target, which can be roughly divided into the landmark [39] and the unsupervised landmark-based methods [14, 34, 40, 48], 3DMM based methods [7, 31, 45] and the latent animation [23, 42]. This task is much easier than our task since it contains the motion in the same domain. Our face render is also inspired by the method of unsupervised landmark-based method [40] and 3DMM-based method [31] to use coefficients to generate real videos. However, they are not focused on generating realistic motion coefficients." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 571, + 103, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 103, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 103, + 583 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "As shown in Fig. 2, our system uses the 3D motion coefficients as the intermediate representation for talking head generation. We first extract the coefficients from the original image. Then, the realistic 3DMM motion coefficients are generated by ExpNet and PoseVAE individually. Finally, a 3D-aware face render is proposed to produce the talking head videos. Below, we give a brief introduction to the 3D face model as preliminaries in Sec. 3.1, the audio-driven motion coefficients generation and the coefficients-driven image animator we design in Sec. 3.2 and Sec. 3.3, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 471, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 471, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 471, + 84 + ], + "type": "text", + "content": "3.1. Preliminary of 3D Face Model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 547, + 210 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 210 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 210 + ], + "type": "text", + "content": "3D information is crucial to improve the realness of the generated video since the real video is captured in the 3D environment. However, previous works [28, 49, 50] have rarely been a consideration in 3D space since it is hard to obtain accurate 3D coefficients from a single image and the high-quality face render is also hard to design. Inspired by the recent single image deep 3D reconstruction method [5], we consider the space of the predicted 3D Morphable Models (3DMMs) as our intermediate representation. In 3DMM, the 3D face shape S can be decoupled as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 372, + 214, + 547, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 214, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 372, + 214, + 547, + 228 + ], + "type": "interline_equation", + "content": "\\mathbf {S} = \\overline {{\\mathbf {S}}} + \\alpha \\mathbf {U} _ {i d} + \\beta \\mathbf {U} _ {e x p}, \\tag {1}", + "image_path": "4f2c94adf617535e125bde435050e0999c97c3fec4735f92550a95141aea5efd.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{S}}" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " is the average shape of the 3D face, " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_{id}" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{U}_{exp}" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " are the orthonormal basis of identity and expression of LSFM morphable model [1]. Coefficients " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\mathbb{R}^{80}" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\beta \\in \\mathbb{R}^{64}" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " describe the person identity and expression, respectively. To preserve pose variance, coefficients " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{r} \\in SO(3)" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\mathbf{t} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " denote the head rotation and translation. To achieve identity irrelevant coefficients generation [31], we only model the parameters of motion as " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\{\\beta, \\mathbf{r}, \\mathbf{t}\\}" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": ". We learn the head pose " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\rho = [\\mathbf{r}, \\mathbf{t}]" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " and expression coefficients " + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 232, + 547, + 376 + ], + "type": "text", + "content": " individually from the driving audio as introduced before. Then, these motion coefficients are used to implicitly modulate our face render for final video synthesis." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 382, + 545, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 382, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 305, + 382, + 545, + 396 + ], + "type": "text", + "content": "3.2. Motion Coefficients Generation through Audio" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 401, + 547, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 547, + 508 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 547, + 508 + ], + "type": "text", + "content": "As introduced above, the 3D motion coefficients contain both head pose and expression where the head pose is a global motion and the expression is relatively local. To this end, learning everything altogether will cause huge uncertainty in the network since the head pose has a relatively weak relationship with audio while the lip motion is highly connected. We generate the motion of the head pose and expression using the proposed PoseVAE and ExpNet, respectively introduced below." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "type": "text", + "content": "ExpNet Learning a generic model which produces accurate expression coefficients from audio is extremely hard for two reasons: 1) audio-to-expression is not a one-to-one mapping task for different identities. 2) there are some audio-irrelevant motions in the expression coefficients and it will influence the prediction's accuracy. Our ExpNet is designed to reduce these uncertainties. As for the identity issue, we connect the expression motion to the specific person via the first frame's expression coefficients " + }, + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 304, + 521, + 548, + 714 + ], + "type": "text", + "content": " which also controls the facial emotion of the generated video. To reduce the disturbance of other facial components in real expression coefficients, we use the lip motion only coefficients as the coefficient target through the pre-trained network of Wav2Lip [28] and deep 3D reconstruction [5]. Then, other minor facial motions (e.g., eye blink) can be leveraged via the additional landmark loss on the rendered images." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8654" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 78, + 281, + 232 + ], + "blocks": [ + { + "bbox": [ + 53, + 78, + 281, + 232 + ], + "lines": [ + { + "bbox": [ + 53, + 78, + 281, + 232 + ], + "spans": [ + { + "bbox": [ + 53, + 78, + 281, + 232 + ], + "type": "image", + "image_path": "429274038857670e614daf4780cad19cf6365854728228da9881c01a2d83bbf3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "text", + "content": "Figure 3. The structure of our ExpNet. We involve a monocular 3D face reconstruction model [5] (" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "inline_equation", + "content": "R_{e}" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "inline_equation", + "content": "R_{d}" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "text", + "content": ") to learn the realistic expression coefficients. Where " + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "inline_equation", + "content": "R_{e}" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "text", + "content": " is a pretrained 3DMM coefficients estimator and " + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "inline_equation", + "content": "R_{d}" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "text", + "content": " is a differentiable 3D face render without learnable parameters. We use the reference expression " + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 46, + 234, + 289, + 323 + ], + "type": "text", + "content": " to reduce the uncertainty of identity and the generated frame from pre-trained Wav2Lip [28] and the first frame as target expression coefficients since it only contains the lip-related motions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": "As shown in Figure 3, we generate the " + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": "-frame expression coefficients from an audio window " + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "inline_equation", + "content": "a_{\\{1,\\dots,t\\}}" + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": ", where the audio feature of each frame is a 0.2s mel-spectrogram. For training, we first design a ResNet-based audio encoder " + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "inline_equation", + "content": "\\Phi_A" + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": " [12, 28] to embed the audio feature to a latent space. Then, a linear layer is added as the mapping network " + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "inline_equation", + "content": "\\Phi_M" + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": " to decode the expression coefficients. Here, we also add the reference expression " + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": " from the reference image to support emotions and reduce the identity uncertainty as discussed above. Since we use the lip-only coefficients as ground truth in the training, we explicitly add a blinking control signal " + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "inline_equation", + "content": "z_{blink} \\in [0,1]" + }, + { + "bbox": [ + 46, + 347, + 290, + 504 + ], + "type": "text", + "content": " and the corresponding eye landmark loss to generate the controllable eye blinks. Formally, the network can be written as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 81, + 517, + 288, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 517, + 288, + 533 + ], + "spans": [ + { + "bbox": [ + 81, + 517, + 288, + 533 + ], + "type": "interline_equation", + "content": "\\beta_ {\\{1, \\dots , t \\}} = \\Phi_ {M} (\\Phi_ {A} (a _ {\\{1, \\dots , t \\}}), z _ {b l i n k}, \\beta_ {0}) \\qquad (2)", + "image_path": "3e812cf4e510b33c32d473fe160ca4051c622a680e42c0f68b32142421343f6d.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "As for the loss function, we first use " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{distill}" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " to evaluate the differences between the lip only expression coefficients " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "R_{e}(\\mathrm{Wav2Lip}(I_0,a_{\\{1,\\dots,t\\}}))" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " and the generated " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\beta_{\\{1,\\dots,t\\}}" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": ". Notice that, we only use the first frame " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " of the wav2lip to generate the lip-sync video which reduces the influence of the pose variant and other facial expressions apart from lip movement. Besides, we also involve the differentiable 3D face render " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "R_{d}" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " to calculate the additional perceptual losses in explicit facial motions space. As shown in Figure 3, we calculate the landmark loss " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{lks}" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " to measure the range of eye blink and the overall expression accuracy. A pretrained lip reading network " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\Phi_{reader}" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " is also used as temporal lip reading loss " + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{read}" + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": " to keep the perceptual lip qualities [9, 28]. We provide more training details in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 542, + 219 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 542, + 219 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 542, + 219 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 542, + 219 + ], + "type": "image", + "image_path": "fd78b1583342c38978c08e0921788f16cc49911a1f77460a319e98b6010f0fd1.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "lines": [ + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "text", + "content": "Figure 4. The pipeline of the proposed PoseVAE. We learn the residual of the input head pose " + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "inline_equation", + "content": "\\rho_0" + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "text", + "content": " via a conditional VAE structure. Given the conditions: first frame " + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "inline_equation", + "content": "\\rho_0" + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "text", + "content": ", style identity " + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "inline_equation", + "content": "Z_{style}" + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "text", + "content": " and the audio clip " + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "inline_equation", + "content": "a_{\\{1,\\dots,t\\}}" + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "text", + "content": ", our method learns a distribution of the residual head pose " + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "inline_equation", + "content": "\\Delta \\rho_{\\{1,\\dots,t\\}} = \\rho_{\\{1,\\dots,t\\}} - \\rho_0" + }, + { + "bbox": [ + 304, + 221, + 548, + 300 + ], + "type": "text", + "content": ". After training, we can generate the stylized results through the pose decoder and the conditions (cond.) only." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": "PoseVAE As shown in Figure 4, a VAE [20] based model is designed to learn the realistic and identity-aware stylized head movement " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "\\rho \\in \\mathbb{R}^6" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " of the real talking video. In training, the pose VAE is trained on fixed " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " frames using an encoder-decoder-based structure. Both the encoder and decoder are two-layer MLPs, where the inputs contain a sequential " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": "-frame head poses and we embed it to a Gaussian distribution. In the decoder, the network is learned to generate the " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": "-frame poses from the sampled distribution. Instead of generating the pose directly, our PoseVAE learns the residual of the condition pose " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "\\rho_0" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " of the first frame, which enables our method to generate longer, stable, and continuous head motion in testing under the condition of the first frame. Besides, according to CVAE [6], we add the corresponding audio feature " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "a_{\\{1,\\dots,t\\}}" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " and style identity " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "Z_{style}" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " as conditions for rhythm awareness and identity style. The KL-divergence " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{KL}" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " is used to measure the distribution of the generated motions. The mean square loss " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{MSE}" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " and adversarial loss " + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{GAN}" + }, + { + "bbox": [ + 304, + 323, + 548, + 563 + ], + "type": "text", + "content": " are used to ensure the generated quality. We provide more details about the loss function in the supplementary materials." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 574, + 437, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 437, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 437, + 586 + ], + "type": "text", + "content": "3.3. 3D-aware Face Render" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "After generating the realistic 3D motion coefficients, we render the final video through a well-designed 3D-aware image animator. We get inspiration from the recent image animation method Face-vid2vid [40] because it implicitly learns the 3D information from a single image. However, a real video is required as the motions driving signal in their method. Our face render makes it drivable through 3DMM coefficients. As shown in Figure 5, we propose mappingNet to learn the relationship between the explicit 3DMM motion coefficients (head pose and expression) and the implicit unsu" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8655" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 74, + 284, + 217 + ], + "blocks": [ + { + "bbox": [ + 53, + 74, + 284, + 217 + ], + "lines": [ + { + "bbox": [ + 53, + 74, + 284, + 217 + ], + "spans": [ + { + "bbox": [ + 53, + 74, + 284, + 217 + ], + "type": "image", + "image_path": "cca8f528d4ef2f54f11eb4d2ec98138d62e323481e8680ef03038a5be6d75eae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "text", + "content": "Figure 5. The proposed FaceRender and comparison with facevid2vid [40]. Given source image " + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "inline_equation", + "content": "I_{s}" + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "text", + "content": " and driving image " + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "inline_equation", + "content": "I_{d}" + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "text", + "content": ", facevid2vid generates the motions in a unsupervised 3D keypoint spaces of " + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_c, \\mathcal{X}_s" + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_d" + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "text", + "content": ". Then, the image can be generated via the appearance " + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "inline_equation", + "content": "A_0" + }, + { + "bbox": [ + 46, + 219, + 289, + 297 + ], + "type": "text", + "content": " and the keypoints. Since we do not have driving image, we use the explicit disentangled 3DMM coefficients as proxy and map it to the unsupervised 3D keypoints space." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 317, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 317, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 287, + 401 + ], + "type": "text", + "content": "pervised 3D keypoints. Our mappingNet is built via several 1D convolutional layers. We use temporal coefficients from a time window for smoothing as PIRenderer [31]. Differently, we find the face alignment motion coefficients in PIRenderer will hugely influence the motion naturalness of audio-driven video generation and provide an experiment in Sec. 4.4. We only use the coefficients of expression and head pose." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 290, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 290, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 290, + 521 + ], + "type": "text", + "content": "As for training, our method contains two steps. Firstly, we train face-vid2vid [40] in a self-supervised fashion as in the original paper. In the second step, we freeze all the parameters of the appearance encoder, canonical keypoints estimator, and image generator for tuning. Then, we train the mapping net on the 3DMM coefficients of the ground truth video in a reconstruction style. We give the supervision in the domain of unsupervised keypoints using " + }, + { + "bbox": [ + 46, + 402, + 290, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 402, + 290, + 521 + ], + "type": "text", + "content": " loss and the final generated video following their original implementation. More details can be found in the supplementary materials." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 532, + 128, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 128, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 128, + 545 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 552, + 239, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 239, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 239, + 564 + ], + "type": "text", + "content": "4.1. Implementation Details and Metrics" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": "Datasets We use VoxCeleb [24] dataset for training which contains over 100k videos of 1251 subjects. We crop the original videos following previous image animation methods [34] and resize the video to " + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": ". After preprocessing, the data is used to train our FaceRender. We select 1890 aligned videos and audios of 46 subjects in VoxCeleb to train our PoseVAE and ExpNet. The input audios are downsampled to " + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "inline_equation", + "content": "16\\mathrm{kHz}" + }, + { + "bbox": [ + 46, + 570, + 289, + 713 + ], + "type": "text", + "content": " and transformed to mel-spectrograms with the same setting as Wav2lip [28]. To test our method, we use the 346 videos' first 8-second video (around 70k frames in total) from HDTF dataset [47] since it contains high resolution and in-the-wild talking head videos. These videos" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 546, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 546, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 546, + 109 + ], + "type": "text", + "content": "are also cropped and processed following [34] and resized to " + }, + { + "bbox": [ + 305, + 72, + 546, + 109 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 305, + 72, + 546, + 109 + ], + "type": "text", + "content": " for evaluation. We use the first frame of each video as the reference image to generate videos." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "text", + "content": "Implementation Details All of ExpNet, PoseVAE, and FaceRender are trained separately and we employ Adam optimizer [19] for all experiments. After training, our method can be inferred in an end-to-end fashion without any manual intervention. All the 3DMM parameters are extracted through pre-trained deep 3D face reconstruction method [5]. We perform all the experiments on 8 A100 GPUs. ExpNet, PoseVAE, and FaceRender are trained with a learning rate of " + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "inline_equation", + "content": "2e^{-5}" + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "inline_equation", + "content": "2e^{-4}" + }, + { + "bbox": [ + 304, + 125, + 547, + 281 + ], + "type": "text", + "content": ", respectively. As for the temporal consideration, ExpNet uses continuous 5 frames to learn. PoseVAE is learned via continuous 32 frames. The frames in FaceRender are generated frame-by-frame with the coefficients of 27 continuous frames for stability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 298, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 547, + 514 + ], + "type": "text", + "content": "Evaluation Metrics We demonstrate the superiority of our method on multiple metrics. We employ Frechet Inception Distance (FID) [13, 33] and cumulative probability blur detection (CPBD) [25] to evaluate the quality of the images. To evaluate identity preservation, we calculate the cosine similarity (CSIM) of identity embedding between the source images and the generated frames, in which we use ArcFace [4] to extract identity embedding of images. To evaluate lip synchronization and mouth shape, we evaluate the perceptual differences of the mouth shape from Wav2Lip [28], including the distance score (LSE-D) and confidence score (LSE-C). We also conduct some metrics to evaluate the head motions of generated frames. For the diversity of the generated head motions, a standard deviation of the head motion feature embeddings extracted from the generated frames using Hopenet [26] is calculated. For the alignment of the audio and generated head motions, we compute Beat Align Score as in Bailando [21]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 522, + 539, + 535 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 522, + 539, + 535 + ], + "spans": [ + { + "bbox": [ + 306, + 522, + 539, + 535 + ], + "type": "text", + "content": "4.2. Compare with other state-of-the-art methods" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 541, + 547, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 547, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 547, + 685 + ], + "type": "text", + "content": "We compare several state-of-the-art methods for talking-head videos generation (MakeItTalk [50], Audio2Head [37] and Wang et al. [38]) and audio to expression generation (Wav2Lip [28], PC-AVS [49]). The evaluation is performed on their publicly available checkpoint directly. As shown in Table 1, our method shows better overall video qualities and head pose diversity and also shows comparable performance with other fully talking-head generation methods in terms of the lip synchronization metrics. We argue that these lip synchronization metrics are too sensitive to the audio where the unnatural lip movement may get a better score. However, our method achieves a similar score to the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "2This method needs to extract the phoneme from audio, which only works on the specific language." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8656" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 545, + 190 + ], + "type": "table", + "html": "
MethodEye BlinkLip SynchronizationLearned Head MotionVideo Quality
LSE-C↑LSE-D↓Diversity↑Beat Align↑FID↓CPBD↑CSIM↑
Real VideoN./A.8.2116.9820.2590.2710.0000.4281.000
Wav2Lip* [28]N./A.10.2215.535N./A.N./A.21.7250.3680.849
PC-AVS** [49]from ref.9.0536.355N./A.N./A.69.1270.2060.683
MakeItTalk [50]automatic5.11010.0590.2570.26828.2430.2830.838
Audio2Head [37]automatic7.3577.5350.1810.26724.3920.2810.823
Wang et al. [38]automatic4.93210.0550.2260.26822.4320.2950.811
Ourscontrollable7.2907.7720.2780.29322.0570.3350.843
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"index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 603, + 547, + 638 + ], + "lines": [ + { + "bbox": [ + 46, + 603, + 547, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 603, + 547, + 638 + ], + "type": "text", + "content": "Figure 6. We compare our method with several state-of-the-art methods for single image audio-driven talking head generation. Our method produces much higher quality results in terms of lip synchronization, identity preservation, head motion and image quality. We give the target image above for both lip shape and identity reference. Please refer our supplementary video for better comparison." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 301, + 547, + 543, + 597 + ], + "blocks": [ + { + "bbox": [ + 301, + 547, + 543, + 597 + ], + "lines": [ + { + "bbox": [ + 301, + 547, + 543, + 597 + ], + "spans": [ + { + "bbox": [ + 301, + 547, + 543, + 597 + ], + "type": "image", + "image_path": "f46a5d696fc0dc0284ee9813377bf535ce54f926889dc0d8074f645d77e95f47.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 648, + 289, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 648, + 289, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 648, + 289, + 708 + ], + "type": "text", + "content": "real videos, which demonstrates our advantages. We also illustrate the visual results of different methods in Figure 6. Here, we give the lip reference to visualize the lip synchronization of our method. From the figure, our method has a very similar visual quality to the original target video and" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 648, + 548, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 648, + 548, + 708 + ], + "spans": [ + { + "bbox": [ + 304, + 648, + 548, + 708 + ], + "type": "text", + "content": "with different head poses as we expect. Compared with our method, Wav2Lip [28] produces blur half-face, PC-AVS [49] and Audio2Head [37] are struggling for identity preservation, Audio2Head can only generate the front talking face. Besides, MakeItTalk [50] and Audio2Head [37] generate the" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8657" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 99, + 97, + 148 + ], + "blocks": [ + { + "bbox": [ + 50, + 99, + 97, + 148 + ], + "lines": [ + { + "bbox": [ + 50, + 99, + 97, + 148 + ], + "spans": [ + { + "bbox": [ + 50, + 99, + 97, + 148 + ], + "type": "image", + "image_path": "a05569a77aba8c6d3068ddeb83d92730bb83813af1890f9d6947db73047165a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 148, + 96, + 156 + ], + "lines": [ + { + "bbox": [ + 50, + 148, + 96, + 156 + ], + "spans": [ + { + "bbox": [ + 50, + 148, + 96, + 156 + ], + "type": "text", + "content": "Reference Image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 98, + 72, + 286, + 121 + ], + "blocks": [ + { + "bbox": [ + 98, + 72, + 286, + 121 + ], + "lines": [ + { + "bbox": [ + 98, + 72, + 286, + 121 + ], + "spans": [ + { + "bbox": [ + 98, + 72, + 286, + 121 + ], + "type": "image", + "image_path": "e84a8314861b20ca3223014316d0cf2728afdd40be0ff87cd6c9bb559ccbb3c4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 184, + 121, + 198, + 128 + ], + "lines": [ + { + "bbox": [ + 184, + 121, + 198, + 128 + ], + "spans": [ + { + "bbox": [ + 184, + 121, + 198, + 128 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 98, + 128, + 285, + 176 + ], + "blocks": [ + { + "bbox": [ + 98, + 128, + 285, + 176 + ], + "lines": [ + { + "bbox": [ + 98, + 128, + 285, + 176 + ], + "spans": [ + { + "bbox": [ + 98, + 128, + 285, + 176 + ], + "type": "image", + "image_path": "464b7f189b297b21979498fc1a3202a0c3e6ac6a06a0bf960c0fc587981b47d6.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 143, + 177, + 241, + 184 + ], + "lines": [ + { + "bbox": [ + 143, + 177, + 241, + 184 + ], + "spans": [ + { + "bbox": [ + 143, + 177, + 241, + 184 + ], + "type": "text", + "content": "Joint learn Pose and Exp coefficients" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 186, + 288, + 231 + ], + "lines": [ + { + "bbox": [ + 47, + 186, + 288, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 288, + 231 + ], + "type": "text", + "content": "Figure 7. We compare our method with a baseline method which learn all the coefficients from a single network without any condition (from Speech2Gesture [10]). Our method shows clear head movements, identity preservation and diverse expressions." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 252, + 208, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 208, + 265 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 208, + 265 + ], + "type": "text", + "content": "distorted face video due to 2D warping." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 273, + 128, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 128, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 128, + 284 + ], + "type": "text", + "content": "4.3. User Studies" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "type": "text", + "content": "We conduct user studies to evaluate the performance of all the methods. We generate overall 20 videos which contain almost equal genders with different ages, poses and expressions. Then 20 participants are invited to choose the best method in terms of video sharpness, lip synchronization, the diversity and naturalness of the head motion, and overall quality. The results are shown in Table 2, where the participants like our method mostly because of the video and motion quality. We also find that " + }, + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "type": "inline_equation", + "content": "38\\%" + }, + { + "bbox": [ + 46, + 292, + 289, + 460 + ], + "type": "text", + "content": " of the participants think our methods show better lip synchronization than other methods, which is inconsistent with Table 1. We think it might be because most of the participants focus on the overall quality of the video, where the blurry and still face videos [28, 49] influence their opinions." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 48, + 470, + 287, + 558 + ], + "blocks": [ + { + "bbox": [ + 48, + 470, + 287, + 558 + ], + "lines": [ + { + "bbox": [ + 48, + 470, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 48, + 470, + 287, + 558 + ], + "type": "table", + "html": "
MethodLip Sync.Motion DiversityVideo SharpnessOverall Naturalness
Wav2Lip [28]15.6%3.1%2.0%2.8%
PC-AVS [49]18.1%9.6%3.4%9.1%
MakeItTalk [50]5.6%5.3%5.7%6.9%
Wang et al. [38]12.5%12.1%16.3%11.6%
Audio2Head [37]9.5%12.1%9.7%14.7%
Ours38.7%57.9%62.8%54.8%
", + "image_path": "6b38dbb37f5feb66d182261e80295c61b4a85449283cd26038d282183f1c0041.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 586, + 147, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 147, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 147, + 598 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Ablation of ExpNet For ExpNet, we mainly evaluate the necessity of each component via the lip synchronization metrics. Since there are no disentangled methods before, we consider a baseline (Speech2Gesture [10], which is an audio to keypoint generation network) to learn the head pose and expression coefficients jointly. As shown in Table 3 and Figure 7, learning all the motion coefficients altogether is hard to generate truth-worthy talking head videos. We then consider the variants of the proposed ExpNet, both the initial" + } + ] + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 543, + 145 + ], + "blocks": [ + { + "bbox": [ + 129, + 558, + 203, + 568 + ], + "lines": [ + { + "bbox": [ + 129, + 558, + 203, + 568 + ], + "spans": [ + { + "bbox": [ + 129, + 558, + 203, + 568 + ], + "type": "text", + "content": "Table 2. User study." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 71, + 543, + 145 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 543, + 145 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 543, + 145 + ], + "type": "table", + "html": "
MethodLSE-C ↑LSE-D ↓
Speech2Gesture [10]0.87813.889
OursFull (Lip coefs. + β0 + Lread)7.2907.772
w/o β0 & Lread5.2419.532
w/o Lread6.9937.841
w/ real coefs.6.5678.061
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The ablation of ExpNet. We choose four frames from the generated video as comparison. Our method largely reduces the uncertainty of audio to expression generation. The reference " + }, + { + "bbox": [ + 305, + 417, + 545, + 484 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 305, + 417, + 545, + 484 + ], + "type": "text", + "content": " is used to provide the identity information while the lip only coefficients generate better lip synchronization. Notice that, the target image is provided as the identity and lip motion reference." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "content": "expression " + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "content": ", lip reading loss " + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{read}" + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "content": " and the necessity of lip-only coefficients are critical. The visual comparison is shown in Figure 8, where our method w/o the initial expression " + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "inline_equation", + "content": "\\beta_0" + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "content": " shows huge identity changes as expected. Also, if we use the real coefficients to replace the lip-only coefficients we use, the performance drops a lot in lip synchronization." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "Ablation of PoseVAE We evaluate the proposed PoseVAE in terms of motion diversities and audio beat alignments. As shown in Table. 4, the baseline Speech2Gesture [10] also performs worse in pose evaluation. As for our variants, since our method contains several identity style labels, to better evaluate other components, we first consider the perform the ablation studies on a fixed one-hot style of our full method for evaluation (OurFull, Single Fixed Style). Each condition in our setting benefits the overall motion quality in terms of diversity and beat alignment. We further report the results of the mixed style of our full method, which uses the randomly-" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8658" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 291, + 173 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 291, + 173 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 291, + 173 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 291, + 173 + ], + "type": "table", + "html": "
MethodDiversity↑Beat Align↑
Speech2Gesture [10]0.15740.274
OurFull (Single Fixed Style)0.27350.287
w/o Lgan0.25000.271
w/o initial pose0.27250.278
w/o audio0.25660.274
w/o all conditions0.26310.279
OursFull (Mixed Style)0.27780.293
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Ablation studies of face render. In the first row, we directly compare our method with PIRenderer [31] for face animation and our method shows better expression modeling. The second row is a trace map of the generated facial landmarks from the same motion coefficients. Using additional face alignment coefficients as part of motion coefficients [31] will generate unrealistic aligned head video." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 110, + 285, + 167, + 343 + ], + "blocks": [ + { + "bbox": [ + 110, + 285, + 167, + 343 + ], + "lines": [ + { + "bbox": [ + 110, + 285, + 167, + 343 + ], + "spans": [ + { + "bbox": [ + 110, + 285, + 167, + 343 + ], + "type": "image", + "image_path": "3f37abb442890fe0992edcc2272b394724ea1c90c633fe7a2dae8199f1edd280.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 115, + 346, + 164, + 359 + ], + "lines": [ + { + "bbox": [ + 115, + 346, + 164, + 359 + ], + "spans": [ + { + "bbox": [ + 115, + 346, + 164, + 359 + ], + "type": "text", + "content": "Learned Alignment Coeff." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 168, + 285, + 225, + 343 + ], + "blocks": [ + { + "bbox": [ + 168, + 285, + 225, + 343 + ], + "lines": [ + { + "bbox": [ + 168, + 285, + 225, + 343 + ], + "spans": [ + { + "bbox": [ + 168, + 285, + 225, + 343 + ], + "type": "image", + "image_path": "e077f5085b3e167c6c8f17398a64ae6bc0f56d8e297c2e1c3e360e174272fc6e.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 182, + 349, + 209, + 356 + ], + "lines": [ + { + "bbox": [ + 182, + 349, + 209, + 356 + ], + "spans": [ + { + "bbox": [ + 182, + 349, + 209, + 356 + ], + "type": "text", + "content": "Real Video" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 226, + 285, + 283, + 343 + ], + "blocks": [ + { + "bbox": [ + 226, + 285, + 283, + 343 + ], + "lines": [ + { + "bbox": [ + 226, + 285, + 283, + 343 + ], + "spans": [ + { + "bbox": [ + 226, + 285, + 283, + 343 + ], + "type": "image", + "image_path": "6c9a88a8a595d2c7bef1d44855501e4373d3851d5bfa4ab79eb6c5343cb0a956.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 249, + 346, + 262, + 352 + ], + "lines": [ + { + "bbox": [ + 249, + 346, + 262, + 352 + ], + "spans": [ + { + "bbox": [ + 249, + 346, + 262, + 352 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 227, + 353, + 285, + 361 + ], + "lines": [ + { + "bbox": [ + 227, + 353, + 285, + 361 + ], + "spans": [ + { + "bbox": [ + 227, + 353, + 285, + 361 + ], + "type": "text", + "content": "(w/o Alignment Coeff.)" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 464, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 489 + ], + "type": "text", + "content": "selected identity label as style and also shows better diversity performance." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 289, + 713 + ], + "type": "text", + "content": "Ablation of Face Render We conduct the ablation study on the proposed face render in two aspects. On the one hand, we show the reconstruction quality of our method with the PIRenderer [31], since both methods use 3DMM as an intermediate representation. As shown in the first row of Fig. 9, the proposed face render shows better expression reconstruction qualities and lip synchronization. Besides, we evaluate the pose unnaturalness caused by the additional alignment coefficients used in PIRenderer [31]. As shown in the second row of Fig. 9, we plot the trace map of the landmarks from the generated video with the same head pose and expression coefficients. Using the fixed or learningable crop coefficients (as part of pose coefficients in our poseVAE) will generate the face-aligned video, which is strange as a natural video. We remove it and directly use the head pose and expression as modulation parameters showing a more realistic result." + } + ] + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 386, + 150 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 386, + 150 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 386, + 150 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 386, + 150 + ], + "type": "image", + "image_path": "a3e9c026133bd2be8fe2b47e49577367066452052cadff00ca1f95d9e7b9440a.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 332, + 151, + 354, + 160 + ], + "lines": [ + { + "bbox": [ + 332, + 151, + 354, + 160 + ], + "spans": [ + { + "bbox": [ + 332, + 151, + 354, + 160 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 388, + 72, + 465, + 150 + ], + "blocks": [ + { + "bbox": [ + 388, + 72, + 465, + 150 + ], + "lines": [ + { + "bbox": [ + 388, + 72, + 465, + 150 + ], + "spans": [ + { + "bbox": [ + 388, + 72, + 465, + 150 + ], + "type": "image", + "image_path": "71f71bf8910a1239e7e7ae2ac760b2a1d4a10d654a7e50146a78758246d52302.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 392, + 151, + 460, + 161 + ], + "lines": [ + { + "bbox": [ + 392, + 151, + 460, + 161 + ], + "spans": [ + { + "bbox": [ + 392, + 151, + 460, + 161 + ], + "type": "text", + "content": "Ours + GFPGAN" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 466, + 151, + 539, + 162 + ], + "lines": [ + { + "bbox": [ + 466, + 151, + 539, + 162 + ], + "spans": [ + { + "bbox": [ + 466, + 151, + 539, + 162 + ], + "type": "text", + "content": "Zoomed Regions" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 165, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 305, + 165, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 305, + 165, + 545, + 198 + ], + "type": "text", + "content": "Figure 10. Limitation. Our method may show some teeth artifacts in the lip region in some examples, it can be improved via the face restoration network, i.e., GFPGAN [41]." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 466, + 72, + 541, + 110 + ], + "blocks": [ + { + "bbox": [ + 466, + 72, + 541, + 110 + ], + "lines": [ + { + "bbox": [ + 466, + 72, + 541, + 110 + ], + "spans": [ + { + "bbox": [ + 466, + 72, + 541, + 110 + ], + "type": "image", + "image_path": "b0ed568e780b9abfd2596ecb19ee26d0aa57c05f77f28f5c0251b4a6e946f8af.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 466, + 112, + 541, + 149 + ], + "blocks": [ + { + "bbox": [ + 466, + 112, + 541, + 149 + ], + "lines": [ + { + "bbox": [ + 466, + 112, + 541, + 149 + ], + "spans": [ + { + "bbox": [ + 466, + 112, + 541, + 149 + ], + "type": "image", + "image_path": "e34d08d83220a3acc75ce7d416cde037fe715442520dbb2d2d4010e6517b047f.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 210, + 378, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 210, + 378, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 210, + 378, + 221 + ], + "type": "text", + "content": "4.5. Limitation" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 228, + 547, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 547, + 348 + ], + "type": "text", + "content": "There are still some limitations in our system. Since 3DMMs couldn't model the variation of eyes and teeth, the mappingNet in our Face Render will struggle to synthesize the realistic teeth in some cases. This limitation can be improved via the blind face restoration networks [41] as shown in Fig. 10. Another limitation of our work is that we only concern the lip motion and eye blinking other than the other facial expressions, e.g., emotion and gaze direction. Thus, it reduces the realism that the generated video has a fixed emotion. We consider it as future work." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 360, + 378, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 378, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 378, + 372 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 380, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 561 + ], + "type": "text", + "content": "In this paper, we present a new system for stylized audio-driven talking head video generation. We use the motion coefficients from 3DMM as an intermediate representation and learn the relationships. To generate realistic 3D coefficients from audio, we propose ExpNet and PoseVAE for realistic expressions and diverse head poses. To model the relationships between 3DMM motion coefficients and the real video, we propose a novel 3D-aware face render inspired by the image animation method [40]. The experiments demonstrate the superiority of our entire framework. Since we predict the realistic 3D facial coefficients, our method can also be used in other modalities directly, i.e., personalized 2D visual dubbing [43], 2D Cartoon animation [50], 3D face animation [8, 44] and NeRF-based 4D talking-head generation [15]." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 577, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 547, + 649 + ], + "type": "text", + "content": "Ethical Considerations We consider the misuse of our method since it can generate very realistic video. Both visible and invisible video watermarks will be inserted into the produced video for generated content identification similar to Dall-E [30] and Imagen [32]. We also hope our method can provide new research samples for forgery detection." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 712 + ], + "type": "text", + "content": "Acknowledgements This work was supported by the National Key Projects of China #2021XJTU0040 and the National Key Research and Development Program of China under Grant #2022YFB3303800." + } + ] + } + ], + "index": 35 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8659" + } + ] + } + ], + "index": 36 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Volker Blanz and Thomas Vetter. 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ACM Transactions on Graphics (TOG), 2020. 2, 3, 5, 6, 7, 8" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 314, + 757 + ], + "type": "text", + "content": "8661" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_content_list.json b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f0a690b81f9d6f9485abde2694d13f3ba24b9d6a --- /dev/null +++ b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_content_list.json @@ -0,0 +1,1550 @@ +[ + { + "type": "text", + "text": "Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models", + "text_level": 1, + "bbox": [ + 184, + 130, + 784, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Patrick Schramowski $^{1,2,3,6*}$ Manuel Brack $^{3*}$ Björn Deiseroth $^{2,3,5}$ Kristian Kersting $^{1,2,3,4}$ $^{1}$ DFKI, $^{2}$ Hessian.AI, $^{3}$ Computer Science Department, TU Darmstadt \n $^{4}$ Centre for Cognitive Science, TU Darmstadt, $^{5}$ Aleph Alpha, $^{6}$ LAION \n{schramowski, brack, deiseroth, kersting}@cs.tu-darmstadt.de", + "bbox": [ + 94, + 200, + 875, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Text-conditioned image generation models have recently achieved astonishing results in image quality and text alignment and are consequently employed in a fast-growing number of applications. Since they are highly data-driven, relying on billion-sized datasets randomly scraped from the internet, they also suffer, as we demonstrate, from degenerated and biased human behavior. In turn, they may even reinforce such biases. To help combat these undesired side effects, we present safe latent diffusion (SLD). Specifically, to measure the inappropriate degeneration due to unfiltered and imbalanced training sets, we establish a novel image generation test bed—inappropriate image prompts (I2P)—containing dedicated, real-world image-to-text prompts covering concepts such as nudity and violence. As our exhaustive empirical evaluation demonstrates, the introduced SLD removes and suppresses inappropriate image parts during the diffusion process, with no additional training required and no adverse effect on overall image quality or text alignment.1", + "bbox": [ + 75, + 340, + 473, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Warning: This paper contains sexually explicit imagery, discussions of pornography, racially-charged terminology, and other content that some readers may find disturbing, distressing, and/or offensive.", + "bbox": [ + 75, + 643, + 468, + 705 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 719, + 209, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The primary reasons for recent breakthroughs in text-conditioned generative diffusion models (DM) are the quality of pre-trained backbones' representations and their multimodal training data. They have even been shown to learn and reflect the underlying syntax and semantics. In turn, they retain general knowledge implicitly present in the data [27]. Unfortunately, while they learn to encode and re", + "bbox": [ + 75, + 744, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/795b77456f845a0398eaf4e14c0db7787b89ee0f7389a18c27ba7f07db17c857.jpg", + "image_caption": [ + "Figure 1. Mitigating inappropriate degeneration in diffusion models. I2P (left) is a new testbed for evaluating neural text-to-image generations and their inappropriateness. Percentages represent the portion of inappropriate images this prompt generates using Stable Diffusion (SD). SD may generate inappropriate content (middle), both for prompts explicitly implying such material as well as prompts not mentioning it all, hence generating inappropriate content unexpectedly. Our safe latent diffusion (SLD, right) is able to suppress inappropriate content. (Best viewed in color)" + ], + "image_footnote": [], + "bbox": [ + 535, + 306, + 859, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "flect general information, systems trained on large-scale unfiltered data may suffer from degenerated and biased behavior. While these profound issues are not completely surprising—since many biases are human-like [6,8]—many concerns are grounded in the data collection process failing to report its own bias [14]. The resulting models, including DMs, end up reflecting them and, in turn, have the potential to replicate undesired behavior [1,3-5, 13, 18]. Birhane et al. [5] pinpoint numerous implications and concerns of datasets scraped from the internet, in particular, LAION-400M [37], a predecessor of LAION-5B [36], and subsequent downstream harms of trained models.", + "bbox": [ + 496, + 613, + 893, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We analyze the open-source latent diffusion model Stable Diffusion (SD), which is trained on subsets of LAION-5B [36] and find a significant amount of inappropriate content generated which, viewed directly, might be offensive, ignominious, insulting, threatening, or might otherwise cause anxiety. To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution \n1Code available at https://huggingface.co/docs/diffusers/api/pipelines/ble_diffusion_safe", + "bbox": [ + 94, + 863, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22522", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "models, we provide a test bed for evaluating inappropriate generations by DMs and stress the need for better safety interventions and data selection processes for pre-training. We release I2P (Sec. 5), a set of 4703 dedicated text-to-image prompts extracted from real-world user prompts for image-to-text models paired with inappropriateness scores from three different detectors (cf. Fig. 1). We show that recently introduced open-source DMs, in this case, Stable Diffusion (SD), produce inappropriate content when conditioned on our prompts, even for those that seem to be non-harmful, cf. Sec. 6. Consequently, we introduce a possible mitigation strategy called safe latent diffusion (SLD) (Sec. 3) and quantify its ability to actively suppress the generation of inappropriate content using I2P (Sec. 6). SLD requires no external classifier, i.e., it relies on the model's already acquired knowledge of inappropriateness and needs no further tuning of the DM.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In general, SLD introduces novel techniques for manipulating a generative diffusion model's latent space and provides further insights into the arithmetic of latent vectors. Importantly, to the best of our knowledge, our work is the first to consider image editing from an ethical perspective to counteract the inappropriate degeneration of DMs.", + "bbox": [ + 75, + 347, + 472, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Risks and Promises of Unfiltered Data", + "text_level": 1, + "bbox": [ + 76, + 452, + 421, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let us start discussing the risks but also promises of noisy, unfiltered and large-scale datasets, including background information on SD and its training data.", + "bbox": [ + 75, + 478, + 468, + 523 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Risks. Unfortunately, while modern large-scale models, such as GPT-3 [7], learn to encode and reflect general information, systems trained on large-scale unfiltered data also suffer from degenerated and biased behavior. Nonetheless, computational systems were promised to have the potential to counter human biases and structural inequalities [19]. However, data-driven AI systems often end up reflecting these biases and, in turn, have the potential to reinforce them instead. The associated risks have been broadly discussed and demonstrated in the context of large-scale models [1, 3-5, 13, 18]. These concerns include, for instance, models producing stereotypical and derogatory content [3] and gender and racial biases [10, 24, 38, 41]. Subsequently, approaches have been developed to, e.g., decrease the level of bias in these models [6, 39].", + "bbox": [ + 75, + 523, + 472, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Promises. Besides the performance gains, large-scale models show surprisingly strong abilities to recall factual knowledge from the training data [27]. For example, Roberts et al. [30] showed that large-scale pre-trained language models' capabilities to store and retrieve knowledge scale with model size. Grounded on those findings, Schick et al. [32] demonstrated that language models can self-debias the text they produce, specifically regarding toxic output. Furthermore, Jenetzsch et al. [21] as well as Schramowski et al. [35] showed that the retained knowl", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "edge of such models carries information about moral norms aligning with the human sense of \"right\" and \"wrong\" expressed in language. Similarly, other research demonstrated how to utilize this knowledge to guide autoregressive language models' text generation to prevent their toxic degeneration [32, 34]. Correspondingly, we demonstrate DMs' capabilities to guide image generation away from inappropriateness, only using representations and concepts learned during pre-training and defined in natural language.", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This makes our approach related to other techniques for text-based image editing on diffusion models such as Text2LIVE [2], Imagic [23] or UniTune [40]. Contrary to these works, our SLD approach requires no fine-tuning of the text-encoder or DM, nor does it introduce new downstream components. Instead, we utilize the learned representations of the model itself, thus substantially improving computational efficiency. Previously, Prompt-to-Prompt [15] proposed a text-controlled editing technique using changes to the text prompt and control of the model's cross-attention layers. In contrast, SLD is based on classifier-free guidance and enables more complex changes to the image.", + "bbox": [ + 496, + 233, + 893, + 415 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "LAION-400M and LAION-5B. Whereas the LAION-400M [37] dataset was released as a proof-of-concept, the creators took the raised concern [5] to heart and annotated potential inappropriate content in its successor dataset of LAION-5B [36]. To further facilitate research on safety, fairness, and biased data, these samples were not excluded from the dataset. Users could decide for themselves, depending on their use case, to include those images. Thus, the creators of LAION-5B \"advise against any applications in deployed systems without carefully investigating behavior and possible biases of models trained on LAION-5B.\"", + "bbox": [ + 496, + 420, + 893, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Training Stable Diffusion. Many DMs have reacted to the concerns raised on large-scale training data by either not releasing the model [31], only deploying it in a controlled environment with dedicated guardrails in place [29] or rigorously filtering the training data of the published model [25]. In contrast, SD decided not to exclude the annotated content contained in LAION-5B and to release the model publicly. Similar to LAION, Stable Diffusion encourages research on the safe deployment of models which have the potential to generate harmful content.", + "bbox": [ + 496, + 592, + 893, + 743 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, SD is trained on a subset of LAION-5B, namely LAION-2B-en [36] containing over 2.32 billion English image-text pairs. Training SD is executed in different steps: First, the model is trained on the complete LAION-2B-en. Then it is fine-tuned on various subsets, namely \"LAION High Resolution\" and \"LAION-Aesthetics v2 $5+$ \". With all training samples taken from LAION-5B or subsets thereof, it is expected that the trained model reflects not only human-like biases such as gender occupation correlations but also reporting biases. Furthermore, SD is de", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22523", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6fcb70d0e469040c4b797aa40c94d6e55756489770acff7627965a256d75b025.jpg", + "image_caption": [ + "Figure 2. Grounded in reporting bias, one can observe ethnic biases in DMs (left). For 50 selected countries, we generated 100 images with the prompt ' $<$ country> body'. The country Japan shows the highest probability of generating nude content. SLD uses the strong hyper parameter set to counteract this bias (right). (Best viewed in color)" + ], + "image_footnote": [], + "bbox": [ + 101, + 90, + 444, + 143 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ployed on several platforms including huggingface $^2$ and recently lexica.art $^3$ making it easy to use for the general public, including users unaware of present issues.", + "bbox": [ + 75, + 270, + 468, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Ethnic Bias. This leads us to our first experiment. Following up the studies by Birhane et al. on unfiltered multimodal datasets [5], we extend these investigations by answering whether the same issues occur in downstream generative models. Specifically, we chose to showcase biased representation of Asian women [42], cf. also Sec. 2.1 and Appendix A in [5] wrt. LAION-400M. This social phenomenon is a well-documented trend in western countries [42] that is also reflected in the English-speaking internet [20] and subsequently the web-crawled LAION-2B-en. Our search for the 100 closest images (in CLIP [28] space) in the dataset to the term 'japanese body' yielded almost exclusively inappropriate material, with $90\\%$ showing explicit nudity. For comparison, the global average for 50 selected countries is more than 4 times lower at $22\\%$ (details can be found in Appendix A.1).", + "bbox": [ + 75, + 316, + 468, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now, to investigate the bias transfer to SD, we prompted the model using $\\langle < \\text{country} > \\text{body} \\rangle$ (e.g. 'japanese body' or 'nigerian body') and compared the percentages of explicit nudes for the same 50 countries. We automatically assessed the generated image using the NudeNet image classifier4 to detect exposed genitalia. We chose this ambiguous prompt template to expose the model's biases. Based on image web search results, one can, for instance, expect images of categories such as average body comparison—displaying lightly dressed people—but also culturally related images such as the country flags. For each country, we generated 100 images, each using the same seed and hyperparameters. The results are depicted in Fig. 2 (left). Indeed, one can observe the above-described images such as average body comparison in the case of u.s. american (cf. Appendix A.2). However, as expected, the close association of some ethnic terms with nudity in Stable Diffusion is apparent. Overall it appears that European, Asian, and Oceanic countries are far more likely to be linked with nudity than", + "bbox": [ + 75, + 560, + 468, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "African or American ones. The most nude images are generated for Japan at over $75\\%$ , whereas the global average is at $35\\%$ . Specifically, the terms 'Asian' and 'Japanese' yielded a significantly higher amount of nudity than any other ethnic or geographic term. We attribute the apparent synonym usage of 'Japanese' and 'Asian' in this context to the aforementioned trends and the overwhelming amount of such content in LAION-5B. Unfortunately, biases in SD generation like these may further reinforce problematic social phenomena.", + "bbox": [ + 500, + 90, + 890, + 241 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SD's post-hoc safety measures. Various methods have been proposed to detect and filter out inappropriate images [4, 11, 25, 33]. Similarly, the SD implementation does contain a \"NSFW\" safety checker; an image classifier applied after generation to detect and withhold inappropriate images. However, there seems to be an interest in deactivating this safety measure. We checked the recently added image generation feature of lexica.art using examples we knew to generate content that the safety checker withstands. We note that the generation of these inappropriate images is possible on lexica.art at time of the present study, apparently without any restrictions, cf. Appendix A.3.", + "bbox": [ + 496, + 242, + 892, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now, we are ready to introduce our two main contributions, first SLD and then the I2P benchmark.", + "bbox": [ + 498, + 453, + 890, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Safe Latent Diffusion (SLD)", + "text_level": 1, + "bbox": [ + 500, + 494, + 759, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce safety guidance for latent diffusion models to reduce the inappropriate degeneration of DMs. Our method extends the generative process by combining text conditioning through classifier-free guidance with inappropriate concepts removed or suppressed in the output image. Consequently, SLD performs image editing at inference without any further fine-tuning required.", + "bbox": [ + 496, + 520, + 890, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Intuitively, image generation starts from random noise $\\epsilon$ , and the model predicts an estimate of this noise $\\tilde{\\epsilon}_{\\theta}$ to be subtracted from the initial values. This results in a high-fidelity image $x$ without any noise. Since this is an extremely hard problem, multiple steps are applied, each subtracting a small amount $(\\epsilon_{t})$ of the predictive noise, approximating $\\epsilon$ . For text-to-image generation, the model's $\\epsilon$ -prediction is conditioned on a text prompt $p$ and results in an image faithful to that prompt. The training objective of a diffusion model $\\hat{x}_{\\theta}$ can be written as", + "bbox": [ + 496, + 627, + 892, + 808 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\mathbf {x}, \\mathbf {c} _ {p}, \\epsilon , t} \\left[ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t} \\mathbf {x} + \\omega_ {t} \\epsilon , \\mathbf {c} _ {p}\\right) - \\mathbf {x} \\| _ {2} ^ {2} \\right] \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 814, + 890, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $(\\mathbf{x},\\mathbf{c}_p)$ is conditioned on text prompt $p$ , $t$ is drawn from a uniform distribution $t\\sim \\mathcal{U}([0,1])$ , $\\epsilon$ sampled from a Gaussian $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$ , and $w_{t},\\omega_{t},\\alpha_{t}$ influence image fidelity depending on $t$ . Consequently, the DM is trained to", + "bbox": [ + 496, + 839, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2https://huggingface.co/spaces", + "bbox": [ + 93, + 859, + 259, + 875 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "3 https://lexica.art", + "bbox": [ + 96, + 875, + 189, + 887 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "4 https://github.com/notAI-tech/NudeNet", + "bbox": [ + 94, + 887, + 310, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22524", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/16f6667ededa833b949a178614500363e413434b3bbf0ccd1ef0240d35c72848.jpg", + "image_caption": [ + "Figure 3. Illustration of text-conditioned diffusion processes. SD using classifier-free guidance (blue arrow), SLD (green arrow) utilizing \"unsafe\" prompts (red arrow) to guide the generation in an opposing direction. For a more detailed comparison see Appendix Fig. 15. (Best viewed in color)" + ], + "image_footnote": [], + "bbox": [ + 125, + 88, + 424, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "denoise $\\mathbf{z}_t\\coloneqq \\mathbf{x} + \\epsilon$ to yield $\\mathbf{x}$ with the squared error as loss. At inference, the DM is sampled using the model's prediction of $\\mathbf{x} = (\\mathbf{z}_t - \\bar{\\epsilon_\\theta})$ , with $\\bar{\\epsilon_{\\theta}}$ as described below.", + "bbox": [ + 75, + 352, + 468, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Classifier-free guidance [17] is a conditioning method using a purely generational diffusion model, eliminating the need for an additional pre-trained classifier. The approach randomly drops the text conditioning $\\mathbf{c}_p$ with a fixed probability during training, resulting in a joint model for unconditional and conditional objectives. During inference the score estimates for the $\\mathbf{x}$ -prediction are adjusted so that:", + "bbox": [ + 75, + 398, + 468, + 503 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) := \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right) + s _ {g} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 511, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with guidance scale $s_g$ which is typically chosen as $s_g \\in (0, 20]$ and $\\epsilon_{\\theta}$ defining the noise estimate with parameters $\\theta$ . Intuitively, the unconditioned $\\epsilon$ -prediction $\\epsilon_{\\theta}(\\mathbf{z}_t)$ is pushed in the direction of the conditioned $\\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p)$ to yield an image faithful to prompt $p$ . Lastly, $s_g$ determines the magnitude of the influence of the text $p$ .", + "bbox": [ + 75, + 535, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To influence the diffusion process, SLD makes use of the same principles as classifier-free guidance, cf. the simplified illustration in Fig. 3. In addition to a text prompt $p$ (blue arrow), we define an inappropriate concept (red arrow) via textual description $S$ . Consequently, we use three $\\epsilon$ -predictions with the goal of moving the unconditioned score estimate $\\epsilon_{\\theta}(\\mathbf{z}_t)$ towards the prompt conditioned estimate $\\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p)$ and simultaneously away from concept conditioned estimate $\\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_S)$ . This results in $\\overline{\\epsilon}_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p, \\mathbf{c}_S) =$", + "bbox": [ + 75, + 626, + 468, + 763 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\theta} (\\mathbf {z} _ {t}) + s _ {g} \\left(\\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}) - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}) - \\gamma (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}, \\mathbf {c} _ {S})\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 784, + 468, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with the safety guidance term $\\gamma$", + "bbox": [ + 76, + 809, + 290, + 824 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}, \\mathbf {c} _ {S}) = \\mu (\\mathbf {c} _ {p}, \\mathbf {c} _ {S}; s _ {S}, \\lambda) (\\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c} _ {S}) - \\epsilon_ {\\theta} (\\mathbf {z} _ {t})), (4)\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 830, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu$ applies a guidance scale $s_S$ element-wise. To this extent, $\\mu$ considers those dimensions of the prompt conditioned estimate that would guide the generation process", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "toward the inappropriate concept. Therefore, $\\mu$ scales the element-wise difference between the prompt conditioned estimate and safety conditioned estimate by $s_S$ for all elements where this difference is below a threshold $\\lambda$ and equals 0 otherwise: $\\mu (\\mathbf{c}_p,\\mathbf{c}_S;s_S,\\lambda) =$", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l l} \\max (1, | \\phi |), & \\text {w h e r e} \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) \\ominus \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right) < \\lambda \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 176, + 890, + 217 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w i t h} \\quad \\phi = s _ {S} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right)\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 220, + 890, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with both larger $\\lambda$ and larger $s_S$ leading to a more substantial shift away from the prompt text and in the opposite direction of the defined concept. Note that we clip the scaling factor of $\\mu$ in order to avoid producing image artifacts. As described in previous research [16, 31], the values of each $\\mathbf{x}$ -prediction should adhere to the training bounds of $[-1, 1]$ to prevent low fidelity images.", + "bbox": [ + 496, + 246, + 890, + 351 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SLD is a balancing act between removing all inappropriate content from the generated image while keeping the changes minimal. In order to facilitate these requirements, we make two adjustments to the methodology presented above. We add a warm-up parameter $\\delta$ that will only apply safety guidance $\\gamma$ after an initial warm-up period in the diffusion process, i.e., $\\gamma (\\mathbf{z}_t,\\mathbf{c}_p,\\mathbf{c}_S)\\coloneqq \\mathbf{0}$ if $t < \\delta$ . Naturally, higher values for $\\delta$ lead to less significant adjustments of the generated image. As we aim to keep the overall composition of the image unchanged, selecting a sufficiently high $\\delta$ ensures that only fine-grained details of the output are altered. Furthermore, we add a momentum term $\\nu_{t}$ to the safety guidance $\\gamma$ in order to accelerate guidance over time steps for dimensions that are continuously guided in the same direction. Hence, $\\gamma_{t}$ is defined as: $\\gamma_{t}(\\mathbf{z}_{t},\\mathbf{c}_{p},\\mathbf{c}_{S}) =$", + "bbox": [ + 496, + 352, + 892, + 579 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu \\left(\\mathbf {c} _ {p}, \\mathbf {c} _ {S}; s _ {S}, \\lambda\\right) \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right) + s _ {m} v _ {t} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 604, + 890, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with momentum scale $s_m \\in [0,1]$ and $\\nu$ being updated as", + "bbox": [ + 500, + 628, + 879, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\nu_ {t + 1} = \\beta_ {m} \\nu_ {t} + (1 - \\beta_ {m}) \\gamma_ {t} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 655, + 890, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\nu_{0} = 0$ and $\\beta_{m}\\in [0,1)$ , with larger $\\beta_{m}$ resulting in less volatile changes of the momentum. Momentum is already built up during the warm-up period, even though $\\gamma_{t}$ is not applied during these steps.", + "bbox": [ + 496, + 681, + 890, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall, the resulting SLD progress is exemplary visualized by means of the various diffusion steps in Fig. 3. While the safety-guidance is already applied in early steps it removes and suppresses the inappropriate parts of the images as soon as these are constructed in the latent space. We attached the corresponding SLD pseudo-code in Appendix H.", + "bbox": [ + 496, + 741, + 890, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Configuring Safe Latent Diffusion", + "text_level": 1, + "bbox": [ + 500, + 844, + 808, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inappropriateness may be subjective depending on individual opinions and contexts. For instance, the require", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22525", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/67a9b21a789fba1a6df5761d1e8974d2d66ab083f4d0d6965c346ad3caf01ce2.jpg", + "image_caption": [ + "Figure 4. Illustration and qualitative comparison of different SLD configurations for removing inappropriate content. All prompts taken from I2P (cf. Sec. 5). The left column shows the original image, the four images in the middle are generated using SLD, and the right column uses the inappropriate concept as a negative prompt without SLD. Images were blurred manually after generation. For prompts see Appendix Fig. 12. (Best viewed in color)" + ], + "image_footnote": [], + "bbox": [ + 127, + 88, + 419, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ments of a professional artist differ from those of a 4-year-old child. Therefore, we suggest four possible configurations of the diffusion process varying in the strength of the safety adaptions. The configurations include the before mentioned hyper-parameters and concepts. We believe the proposed values offer a decent trade-off between the degree of alternation but note that these can be easily adapted.", + "bbox": [ + 75, + 491, + 468, + 597 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(Un)safe Concept. Inspired by existing content policies of deployed text-to-image DMs such as DALL-E, the following text prompt is used to define a general inappropriate safety concept: \"hate, harassment, violence, suffering, humiliation, harm, suicide, sexual, nudity, bodily fluids, blood, obscene gestures, illegal activity, drug use, theft, vandalism, weapons, child abuse, brutality, cruelty\". Through the text-based definition, one could easily add further and remove present concepts (cf. Appendix H).", + "bbox": [ + 75, + 597, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Threshold. The most vital parameter of SLD is the safety threshold $\\lambda$ . It determines the location of the hyperplane dividing the latent space into appropriate and inappropriateness, cf. Eq. (5). Theoretically, $\\lambda$ is restricted by the training bounds of $[-1, 1]$ , and intuitively it should be at least 0. However, since our approach relies on the model's understanding of \"right\" and \"wrong\" we recommend choosing a conservative, i.e. small positive values such that $\\lambda \\in [0.0, 0.03]$ .", + "bbox": [ + 75, + 734, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Safety guidance scale. The safety guidance scale $s_S$ can theoretically be chosen arbitrarily high as the scaling factor", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mu$ is clipped either way. Larger values for $s_S$ would simply increase the number of values in latent representation being set to 1. Therefore, there is no adverse effect of large $s_S$ such as image artifacts that are observed for high guidance scales $s_g$ . We recommend $s_S \\in [100,3000]$ .", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Warm-up. The warm-up period $\\delta$ largely influences at which level of the image composition changes are applied. Large safe-guidance scales applied early in the diffusion process could lead to major initial changes before significant parts of the images were constructed. Hence, we recommend using at least a few warm-up steps, $\\delta \\in [5,20]$ , to construct an initial image and, in the worst case, let SLD revise those parts. In any case, $\\delta$ should be no larger than half the number of total diffusion steps.", + "bbox": [ + 496, + 167, + 892, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Momentum. The guidance momentum is particularly useful to remove inappropriate concepts that make up significant portions of the image and thus require more substantial editing, especially those created during warm-up. Therefore, momentum builds up over the warm-up phase, and such images will be altered more rigorously than those with close editing distances. Higher momentum parameters usually allow for a longer warm-up period. With most diffusion processes using around 50 generation steps, the window for momentum build-up is limited. Therefore, we recommend choosing $s_m \\in [0, 0.5]$ and $\\beta_m \\in [0.3, 0.7]$ .", + "bbox": [ + 496, + 301, + 892, + 469 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Configuration sets. These recommendations result in the following four sets of hyper-parameters gradually increasing their aggressiveness of changes on the resulting image (cf. Fig. 4 and Appendix I). Which setting to use highly depends on the use case and individual preferences:", + "bbox": [ + 496, + 469, + 890, + 544 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ef638e88c08096fb415a8bdf9b498d1835febb189b04d92b52f740327dff5d84.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ConfigδsSλsmβm
Hyp-Weak152000.00.0-
Hyp-Medium1010000.010.30.4
Hyp-Strong720000.0250.50.7
Hyp-Max050001.00.50.7
", + "bbox": [ + 508, + 555, + 816, + 630 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The weak configuration is usually sufficient to remove superficial blood splatters, but stronger parameters are required to suppress more severe injuries. Similarly, the weak set may suppress nude content on clearly pornographic images but may not reduce nudity in artistic imagery such as oil paintings. A fact that an adult artist may find perfectly acceptable, however, is problematic for, e.g., a child using the model. Furthermore, on the example of nudity, we observed the medium hyper-parameter set to yield the generation of, e.g., a bikini. In contrast, the strong and maximum one would produce progressively more cloth like a dress.", + "bbox": [ + 496, + 643, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that we can even drive the generation of inappropriate content to zero by choosing strong enough parameters (Hyp-Max). However, doing so likely diverges from our goal of keeping changes minimal. Nevertheless, this could be a requirement for sensitive applications, e.g., involving children. In these cases, we further recommend the usage", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22526", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of post-hoc interventions such as SD's safety checker.", + "bbox": [ + 76, + 90, + 434, + 104 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Regarding the amount of observed changes, the HypMax configuration often behaves similarly to replacing the unconditioned estimate with a conditioned estimate based on a negative prompt during the classifier-free guidance, cf. Neg. in Fig. 4. I.e., replacing $\\epsilon_{\\theta}(\\mathbf{z}_t)$ with $\\epsilon_{\\theta}(\\mathbf{z}_t,\\mathbf{c}_S)$ , cf. Eq. (2). However, as our experimental evaluation (cf. Tab. 1) shows, negative prompting leads to worse mitigation than SLD. Further, the major disadvantage of this approach is the lack of more fine-grained control over the generation process, always leading to images significantly differing from the original, especially for higher guidance scales $s_S$ . Additionally, negative prompts are a vital tool in text-to-image generation that would no longer be available to users if used for safety guidance.", + "bbox": [ + 75, + 107, + 470, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Inappropriate Image Prompts (I2P)", + "text_level": 1, + "bbox": [ + 76, + 334, + 401, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image models, we introduce a new benchmarking dataset of over $4.5\\mathrm{k}$ real-world text prompts for generative models that are likely to produce inappropriate content: the inappropriate image prompts (I2P) dataset, cf. Fig. 1, covers a wide range of inappropriate content beyond nudity. Our dataset is publicly available for other researchers to use.[5]", + "bbox": [ + 75, + 359, + 468, + 479 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inappropriate content. What is considered inappropriate imagery may differ based on context, setting, cultural and social predisposition, and individual factors and is highly subjective overall. In this work, we base our definition of inappropriate content on the work of Gebru et al.: \"[data that] if viewed directly, might be offensive, insulting, threatening, or might otherwise cause anxiety\" [12], which is for example also reflected by the OpenAI content policy6 that applies to the use of DALL-E [29]. Specifically, we consider those images showcasing content that contains one of the following:", + "bbox": [ + 75, + 482, + 468, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "hate, harassment, violence, self-harm, sexual content, shocking images, illegal activity.", + "bbox": [ + 76, + 648, + 468, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that inappropriateness is not limited to these seven concepts, varies between cultures, and constantly evolves. Here we restricted ourselves to images displaying tangible acts of inappropriate behavior.", + "bbox": [ + 75, + 680, + 468, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Prompt collection. For the seven concepts mentioned above, we used 26 keywords and phrases (cf. Appendix C) describing them in more detail and collected up to 250 real-world text prompts for each. For a given keyword, we crawled the prompts of the top 250 images returned by https://lexica.art. Lexica is a collection of real-world, user-generated prompts for SD sourced from its official discord server. It stores the prompt, seed, guidance scale, and image", + "bbox": [ + 75, + 741, + 470, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dimensions used in the generation to facilitate reproducibility. Image retrieval in lexica is based on the similarity of an image and search query in CLIP [28] embedding space. Therefore, the collected prompts are not guaranteed to generate inappropriate content, but the probability is high, as demonstrated in our evaluation.", + "bbox": [ + 496, + 90, + 890, + 180 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset statistics. The data collection described above yielded duplicate entries, as some retrieved images were found among multiple keywords. After reducing those duplicates, the I2P dataset contains 4703 unique prompts assigned to at least one of the seven categories above. We also include an estimate of the percentage of inappropriate images the prompt is predicted to generate, together with the necessary hyper-parameters to reproduce these results. The benchmark also contains a hard annotation for prompts that generate predominantly inappropriate images.", + "bbox": [ + 496, + 181, + 892, + 333 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On average, the prompts are made up of 20 tokens, and we could not observe an apparent correlation between frequent words and the connection to inappropriate images of these prompts. We present a word cloud of frequently used terms in Appendix C. Furthermore, we include the toxicity of each prompt based on the respective toxicity score of the PERSPECTIVE API.7 We only find a weak correlation8 between the toxicity of a prompt and the inappropriateness of images it generates. In fact, prompts with low toxicity scores still have unforeseen high probabilities of generating inappropriate images. Furthermore, out of 4702 prompts, a mere $1.5\\%$ are toxic. This highlights that simply suppressing \"bad\" words in text prompts is no reliable mitigation strategy against generating problematic content.", + "bbox": [ + 496, + 334, + 893, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experimental Evaluation", + "text_level": 1, + "bbox": [ + 500, + 561, + 735, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We now evaluate SD's inappropriate degeneration and SLD based on the suggested configurations using I2P.", + "bbox": [ + 498, + 588, + 890, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experimental Protocol. To assess the reduction of inappropriate content, we generated ten images each for all prompts of the I2P test bed and compared the probability of generating inappropriate images. We used one general concept $S$ across all categories of I2P as specified in Sec. 4. We automatically evaluated inappropriate image content by combining two classifiers. First, the Q16 classifier [33]—also used to annotate the LAION-5B dataset—to detect a wide range of inappropriate content in images. Second, we applied NudeNet (cf. Sec. 2) to identify sexually explicit content. In this paper, we only classify exposed genitalia as inappropriate while allowing otherwise provocative images. If not specified otherwise, an image is classified as inappropriate if one or both of the classifiers output the respective label. Further details can be found in Appendix D.", + "bbox": [ + 496, + 619, + 892, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inappropriateness in Stable Diffusion. We start our", + "bbox": [ + 519, + 847, + 890, + 861 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "5https://huggingface.co/datasets/AIML-TUDA/i2p", + "bbox": [ + 93, + 873, + 364, + 886 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "6https://labs.openai.com/policies/content-policy", + "bbox": [ + 93, + 887, + 349, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "7https://github.com/conversationai/perspectiveapi", + "bbox": [ + 517, + 875, + 779, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "Spearman $r = 0.22$", + "bbox": [ + 517, + 887, + 633, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22527", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d2e138c8f0f7155285fadfa65159e88dd12ac42f7cf9b2b006ed7fd81b93bb30.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CategoryInappropriate Probability ↓Exp. Max. Inappropriateness ↓
SD 1.4Neg. PromptHyp-WeakHyp-MediumHyp-StrongHyp-MaxSDHyp-StrongHyp-Max
Hate0.400.180.270.200.150.090.970.060.770.190.530.18
Harassment0.340.160.240.170.130.090.940.080.730.180.570.20
Violence0.430.240.360.230.170.140.890.040.790.130.680.28
Self-harm0.400.160.270.160.100.070.970.060.610.200.490.21
Sexual0.350.120.230.140.090.060.910.080.530.160.360.11
Shocking0.520.280.410.300.200.131.000.010.850.140.670.20
Illegal activity0.340.140.230.140.090.060.940.100.620.200.430.19
Overall0.390.180.290.190.130.090.960.070.720.190.600.19
", + "bbox": [ + 84, + 87, + 883, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Safe Latent Diffusion (SLD) can considerably reduce the chance of generating inappropriate content (the lower, the better). Shown are the probabilities of generating an image containing inappropriate content as classified by the combined Q16/NudeNet classifier over the I2P benchmark. We note that the Q16 classifier is rather conservative and tends to classify some unobjectionable images as inappropriate. The false positive rate of the classifier is roughly equal to the probabilities reported for Hyp-Max. The expected maximum inappropriateness (the lower, the better) are bootstrap estimates of a model outputting the displayed percentage of inappropriate images at least once for 25 prompts (for further results see Appendix F). Subscript values indicate the standard deviation.", + "bbox": [ + 75, + 241, + 890, + 324 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "experimental evaluation by demonstrating the inappropriate degeneration of Stable Diffusion without any safety measures. Tab. 1 shows SD's probability of generating inappropriate content for each category under investigation. Recall that only $1.5\\%$ of the text prompts could be identified as toxic. Nevertheless, one can clearly observe that depending on the category, the probability of generating inappropriate content ranges from $34\\%$ to $52\\%$ . Furthermore, Tab. 1 reports the expected maximum inappropriateness over 25 prompts. These results show that a user generating images with I2P for 25 prompts is expected to have at least one batch of output images of which $96\\%$ are inappropriate. The benchmark clearly shows SD's inappropriate degeneration and the risks of training on completely unfiltered datasets.", + "bbox": [ + 75, + 351, + 468, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SLD in Stable Diffusion. Next, we investigate whether we can account for noisy, i.e. biased and unfiltered training data based on the model's acquired knowledge in distinguishing between appropriate and inappropriate content.", + "bbox": [ + 76, + 564, + 468, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To this end, we applied SLD. Similarly to the observations made on the examples in Fig. 4, one can observe in Tab. 1 that the number of inappropriate images gradually decreases with stronger hyper-parameters. The strongest hyper-parameter configuration reduces the probability of generating inappropriate content by over $75\\%$ . Consequently, a mere $9\\%$ of the generated images are still classified as inappropriate. However, it is important to note that the Q16 classifier tends to be rather conservative in some of its decisions classifying images as inappropriate where the respective content has already been reduced significantly. We assume the majority of images flagged as potentially inappropriate for Hyp-Max to be false negatives of the classifier. One can observe a similar reduction in the expected maximum inappropriateness but also note a substantial increase in variance. The latter indicates a substantial amount of outliers when using SLD.", + "bbox": [ + 75, + 626, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Overall the results demonstrate that, indeed, we are able", + "bbox": [ + 96, + 885, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to largely mitigate the inappropriate degeneration of SD based on the underlying model's learned representations. This could also apply to issues caused by reporting biases in the training set, as we will investigate in the following.", + "bbox": [ + 496, + 351, + 890, + 411 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Counteracting Bias in Stable Diffusion. Recall the 'ethnic bias' experiments of Sec. 2. We demonstrated that biases reflected in LAION-5B data are, consequently, also reflected in the trained DM. Similarly to its performance on I2P, SLD strongly reduces the number of nude images generated for all countries as shown in Fig. 2 (right). SLD yields $75\\%$ less explicit content and the percentage of nude images are distributed more evenly between countries. The previous outlier Japan now yields $12.0\\%$ of nude content, close to the global percentage of $9.25\\%$ .", + "bbox": [ + 496, + 411, + 890, + 561 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Nonetheless, at least with keeping changes minor (Hyp-Strong), SLD alone is not sufficient to mitigate this racial bias entirely. There remains a medium but statistically significant correlation between the percentages of nude images generated for a country by SD with and without SLD. Thus, SLD can make a valuable contribution towards debiasing DMs trained on datasets that introduce biases. However, these issues still need to be identified beforehand, and an effort towards reducing—or better eliminating—such biases in the dataset itself is still required.", + "bbox": [ + 496, + 563, + 890, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For further evidence, we ran experiments on Stable Diffusion v2.0 which is essentially a different model with a different text encoder and training set. Specifically, rigorous dataset filtering of sexual and nudity related content was applied before training the diffusion model, however, not on the pre-trained text encoder. While this filtering process reduces biased representations, they are still present and more frequent compared to SLD mitigation on SD in version 1.4, cf. Appendix E. Interestingly, the combination of SLD and dataset filtering achieves an even better mitigation. Hence,", + "bbox": [ + 496, + 713, + 890, + 864 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "${}^{9}$ Spearman $r = {0.52}$ ; Null-hypothesis that both distributions are uncorrelated is rejected at a significance level of $p = {0.01}$ .", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22528", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a combination of filtering and SLD could be beneficial and poses an interesting avenue for future work.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Discussion & Limitations", + "text_level": 1, + "bbox": [ + 76, + 135, + 313, + 150 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Before concluding, let us touch upon ethical implications and future work concerning I2P and the introduced SLD.", + "bbox": [ + 76, + 160, + 468, + 189 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethical implications. We introduced an alternative approach to post-hoc prevention of presenting generated images with potentially inappropriate content. Instead, we identify inappropriate content and suppress it during the diffusion process. This intervention would not be possible if the model did not acquire a certain amount of knowledge on inappropriateness and related concepts during pre-training. Consequently, we do not advise removing potentially inappropriate content entirely from the training data, as we can reasonably assume that efforts towards removing all such samples will hurt the model's capabilities to target related material at inference individually. Therefore, we also see a promising avenue for future research in measuring the impact of training on balanced datasets. However, this is likely to require large amounts of manual labor.", + "bbox": [ + 75, + 190, + 468, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Nonetheless, we also demonstrated that highly imbalanced training data could reinforce problematic social phenomena. It must be ensured that potential risks can be reliably mitigated, and if in doubt, datasets must be further curated, such as in the presented case study. Whereas LAION already made a valiant curating effort by annotating the related inappropriate content, we again advocate for carefully investigating behavior and possible biases of models and consequently deploy mitigation strategies against these issues in any deployed application.", + "bbox": [ + 75, + 417, + 468, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We realize that SLD potentially has further ethical implications. Most notably, we recognize the possibility of similar techniques being used for actively censoring generative models. Additionally, one could construct a model generating mainly inappropriate content by reversing the guidance direction of our approach. Thus, we strongly urge all models using SLD to transparently state which contents are being suppressed. However, it could also be applied to cases beyond inappropriateness, such as fairness [22]. Furthermore, we reiterate that inappropriateness is based on social norms, and people have diverse sentiments. The introduced test bed is limited to specific concepts and consequently does not necessarily reflect differing opinions people might have on inappropriateness. Additionally, the model's acquired representation of inappropriateness may reflect the societal dispositions of the social groups represented in the training data and might lack a more diverse sentiment.", + "bbox": [ + 75, + 568, + 468, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Image Fidelity & Text Alignment. Lastly, we discuss the overall impact of SLD on image fidelity and text-alignment. Ideally, the approach should have no adverse effect on either, especially on already appropriate images. In line with previous research on generative text-to-image", + "bbox": [ + 75, + 825, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6f5047f79bd15a56b00d3a248bc4def43193c8e3cd89edeb03c5ed578058f78c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ConfigImage FidelityText Alignment
FID-30k ↓User (%) ↑CLIP ↓User (%) ↑
SD14.43-0.75-
Weak15.8163.700.7560.88
Medium16.9062.370.7559.45
Strong18.2863.130.7659.62
Max18.7663.600.7660.58
", + "bbox": [ + 501, + 88, + 888, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. SLD's image fidelity and text alignment. User scores indicate the percentage of users judging SLD generated image as better or equal in quality/text alignment as its SD counterpart.", + "bbox": [ + 498, + 198, + 890, + 241 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "models, we report the COCO FID-30k scores and CLIP distance of SD, and our four sets of hyper-parameters for SLD in Tab. 2. The scores slightly increase with stronger hyperparameters. However, they do not necessarily align with actual user preference [26]. Therefore, we conducted an exhaustive user study on the DrawBench [31] benchmark and reported results in Tab. 2 (cf. Appendix G for study details). The results indicate that users even slightly prefer images generated with SLD over those without, indicating safety does no sacrifice image quality and text alignment.", + "bbox": [ + 496, + 265, + 890, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 429, + 617, + 444 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We demonstrated text-to-image models' inappropriate degeneration transfers from unfiltered and imbalanced training datasets. To measure related issues, we introduced an image generation test bed called I2P containing dedicated image-to-text prompts representing inappropriate concepts such as nudity and violence. Furthermore, we presented an approach to mitigate these issues based on classifier-free guidance. The proposed SLD removes and suppresses the corresponding image parts during the diffusion process with no additional training required and no adverse effect on overall image quality. Strong representation biases learned from the dataset are attenuated by our approach but not completely removed. Thus, we advocate for the careful use of unfiltered, clearly imbalanced datasets.", + "bbox": [ + 496, + 454, + 890, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 679, + 658, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We gratefully acknowledge support by the German Center for Artificial Intelligence (DFKI) project \"SAINT\" and the Federal Ministry of Education and Research (BMBF) under Grant No. 01IS22091. This work also benefited from the ICT-48 Network of AI Research Excellence Center \"TAILOR\" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the Hessian Ministry of Higher Education, and the Research and the Arts (HMWK) cluster projects \"The Adaptive Mind\" and \"The Third Wave of AI\", and the HMWK and BMBF ATHENE project \"AVSV\". Further, we thank Felix Friedrich, Dominik Hintersdorf and Lukas Struppek for their valuable feedback.", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22529", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Abubakar Abid, Maheen Farooqi, and James Zou. Persistent anti-muslim bias in large language models. 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Journal of the American Philosophical Association, 2, 2016. 3" + ], + "bbox": [ + 501, + 92, + 890, + 667 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "22531", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_model.json b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..530eabb3b708afd246b42990a8298e0592794fd5 --- /dev/null +++ b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_model.json @@ -0,0 +1,2024 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.185, + 0.131, + 0.785, + 0.177 + ], + "angle": 0, + "content": "Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.095, + 0.202, + 0.877, + 0.276 + ], + "angle": 0, + "content": "Patrick Schramowski\\(^{1,2,3,6*}\\) Manuel Brack\\(^{3*}\\) Björn Deiseroth\\(^{2,3,5}\\) Kristian Kersting\\(^{1,2,3,4}\\) \n\\(^{1}\\)DFKI, \\(^{2}\\)Hessian.AI, \\(^{3}\\)Computer Science Department, TU Darmstadt \n\\(^{4}\\)Centre for Cognitive Science, TU Darmstadt, \\(^{5}\\)Aleph Alpha, \\(^{6}\\)LAION \n{schramowski, brack, deiseroth, kersting}@cs.tu-darmstadt.de" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.63 + ], + "angle": 0, + "content": "Text-conditioned image generation models have recently achieved astonishing results in image quality and text alignment and are consequently employed in a fast-growing number of applications. Since they are highly data-driven, relying on billion-sized datasets randomly scraped from the internet, they also suffer, as we demonstrate, from degenerated and biased human behavior. In turn, they may even reinforce such biases. To help combat these undesired side effects, we present safe latent diffusion (SLD). Specifically, to measure the inappropriate degeneration due to unfiltered and imbalanced training sets, we establish a novel image generation test bed—inappropriate image prompts (I2P)—containing dedicated, real-world image-to-text prompts covering concepts such as nudity and violence. As our exhaustive empirical evaluation demonstrates, the introduced SLD removes and suppresses inappropriate image parts during the diffusion process, with no additional training required and no adverse effect on overall image quality or text alignment.1" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.706 + ], + "angle": 0, + "content": "Warning: This paper contains sexually explicit imagery, discussions of pornography, racially-charged terminology, and other content that some readers may find disturbing, distressing, and/or offensive." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.72, + 0.21, + 0.736 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.47, + 0.854 + ], + "angle": 0, + "content": "The primary reasons for recent breakthroughs in text-conditioned generative diffusion models (DM) are the quality of pre-trained backbones' representations and their multimodal training data. They have even been shown to learn and reflect the underlying syntax and semantics. In turn, they retain general knowledge implicitly present in the data [27]. Unfortunately, while they learn to encode and re" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.308, + 0.861, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.462, + 0.895, + 0.588 + ], + "angle": 0, + "content": "Figure 1. Mitigating inappropriate degeneration in diffusion models. I2P (left) is a new testbed for evaluating neural text-to-image generations and their inappropriateness. Percentages represent the portion of inappropriate images this prompt generates using Stable Diffusion (SD). SD may generate inappropriate content (middle), both for prompts explicitly implying such material as well as prompts not mentioning it all, hence generating inappropriate content unexpectedly. Our safe latent diffusion (SLD, right) is able to suppress inappropriate content. (Best viewed in color)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.794 + ], + "angle": 0, + "content": "flect general information, systems trained on large-scale unfiltered data may suffer from degenerated and biased behavior. While these profound issues are not completely surprising—since many biases are human-like [6,8]—many concerns are grounded in the data collection process failing to report its own bias [14]. The resulting models, including DMs, end up reflecting them and, in turn, have the potential to replicate undesired behavior [1,3-5, 13, 18]. Birhane et al. [5] pinpoint numerous implications and concerns of datasets scraped from the internet, in particular, LAION-400M [37], a predecessor of LAION-5B [36], and subsequent downstream harms of trained models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We analyze the open-source latent diffusion model Stable Diffusion (SD), which is trained on subsets of LAION-5B [36] and find a significant amount of inappropriate content generated which, viewed directly, might be offensive, ignominious, insulting, threatening, or might otherwise cause anxiety. To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.864, + 0.47, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution \n1Code available at https://huggingface.co/docs/diffusers/api/pipelines/ble_diffusion_safe" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22522" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "models, we provide a test bed for evaluating inappropriate generations by DMs and stress the need for better safety interventions and data selection processes for pre-training. We release I2P (Sec. 5), a set of 4703 dedicated text-to-image prompts extracted from real-world user prompts for image-to-text models paired with inappropriateness scores from three different detectors (cf. Fig. 1). We show that recently introduced open-source DMs, in this case, Stable Diffusion (SD), produce inappropriate content when conditioned on our prompts, even for those that seem to be non-harmful, cf. Sec. 6. Consequently, we introduce a possible mitigation strategy called safe latent diffusion (SLD) (Sec. 3) and quantify its ability to actively suppress the generation of inappropriate content using I2P (Sec. 6). SLD requires no external classifier, i.e., it relies on the model's already acquired knowledge of inappropriateness and needs no further tuning of the DM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.44 + ], + "angle": 0, + "content": "In general, SLD introduces novel techniques for manipulating a generative diffusion model's latent space and provides further insights into the arithmetic of latent vectors. Importantly, to the best of our knowledge, our work is the first to consider image editing from an ethical perspective to counteract the inappropriate degeneration of DMs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.453, + 0.422, + 0.469 + ], + "angle": 0, + "content": "2. Risks and Promises of Unfiltered Data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.524 + ], + "angle": 0, + "content": "Let us start discussing the risks but also promises of noisy, unfiltered and large-scale datasets, including background information on SD and its training data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.473, + 0.75 + ], + "angle": 0, + "content": "Risks. Unfortunately, while modern large-scale models, such as GPT-3 [7], learn to encode and reflect general information, systems trained on large-scale unfiltered data also suffer from degenerated and biased behavior. Nonetheless, computational systems were promised to have the potential to counter human biases and structural inequalities [19]. However, data-driven AI systems often end up reflecting these biases and, in turn, have the potential to reinforce them instead. The associated risks have been broadly discussed and demonstrated in the context of large-scale models [1, 3-5, 13, 18]. These concerns include, for instance, models producing stereotypical and derogatory content [3] and gender and racial biases [10, 24, 38, 41]. Subsequently, approaches have been developed to, e.g., decrease the level of bias in these models [6, 39]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Promises. Besides the performance gains, large-scale models show surprisingly strong abilities to recall factual knowledge from the training data [27]. For example, Roberts et al. [30] showed that large-scale pre-trained language models' capabilities to store and retrieve knowledge scale with model size. Grounded on those findings, Schick et al. [32] demonstrated that language models can self-debias the text they produce, specifically regarding toxic output. Furthermore, Jenetzsch et al. [21] as well as Schramowski et al. [35] showed that the retained knowl" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "edge of such models carries information about moral norms aligning with the human sense of \"right\" and \"wrong\" expressed in language. Similarly, other research demonstrated how to utilize this knowledge to guide autoregressive language models' text generation to prevent their toxic degeneration [32, 34]. Correspondingly, we demonstrate DMs' capabilities to guide image generation away from inappropriateness, only using representations and concepts learned during pre-training and defined in natural language." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.234, + 0.895, + 0.416 + ], + "angle": 0, + "content": "This makes our approach related to other techniques for text-based image editing on diffusion models such as Text2LIVE [2], Imagic [23] or UniTune [40]. Contrary to these works, our SLD approach requires no fine-tuning of the text-encoder or DM, nor does it introduce new downstream components. Instead, we utilize the learned representations of the model itself, thus substantially improving computational efficiency. Previously, Prompt-to-Prompt [15] proposed a text-controlled editing technique using changes to the text prompt and control of the model's cross-attention layers. In contrast, SLD is based on classifier-free guidance and enables more complex changes to the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.589 + ], + "angle": 0, + "content": "LAION-400M and LAION-5B. Whereas the LAION-400M [37] dataset was released as a proof-of-concept, the creators took the raised concern [5] to heart and annotated potential inappropriate content in its successor dataset of LAION-5B [36]. To further facilitate research on safety, fairness, and biased data, these samples were not excluded from the dataset. Users could decide for themselves, depending on their use case, to include those images. Thus, the creators of LAION-5B \"advise against any applications in deployed systems without carefully investigating behavior and possible biases of models trained on LAION-5B.\"" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.895, + 0.744 + ], + "angle": 0, + "content": "Training Stable Diffusion. Many DMs have reacted to the concerns raised on large-scale training data by either not releasing the model [31], only deploying it in a controlled environment with dedicated guardrails in place [29] or rigorously filtering the training data of the published model [25]. In contrast, SD decided not to exclude the annotated content contained in LAION-5B and to release the model publicly. Similar to LAION, Stable Diffusion encourages research on the safe deployment of models which have the potential to generate harmful content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Specifically, SD is trained on a subset of LAION-5B, namely LAION-2B-en [36] containing over 2.32 billion English image-text pairs. Training SD is executed in different steps: First, the model is trained on the complete LAION-2B-en. Then it is fine-tuned on various subsets, namely \"LAION High Resolution\" and \"LAION-Aesthetics v2 \\(5+\\)\". With all training samples taken from LAION-5B or subsets thereof, it is expected that the trained model reflects not only human-like biases such as gender occupation correlations but also reporting biases. Furthermore, SD is de" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22523" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.092, + 0.445, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.157, + 0.47, + 0.242 + ], + "angle": 0, + "content": "Figure 2. Grounded in reporting bias, one can observe ethnic biases in DMs (left). For 50 selected countries, we generated 100 images with the prompt ' \\(< \\) country> body'. The country Japan shows the highest probability of generating nude content. SLD uses the strong hyper parameter set to counteract this bias (right). (Best viewed in color)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.271, + 0.469, + 0.317 + ], + "angle": 0, + "content": "ployed on several platforms including huggingface\\(^2\\) and recently lexica.art\\(^3\\) making it easy to use for the general public, including users unaware of present issues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.469, + 0.56 + ], + "angle": 0, + "content": "Ethnic Bias. This leads us to our first experiment. Following up the studies by Birhane et al. on unfiltered multimodal datasets [5], we extend these investigations by answering whether the same issues occur in downstream generative models. Specifically, we chose to showcase biased representation of Asian women [42], cf. also Sec. 2.1 and Appendix A in [5] wrt. LAION-400M. This social phenomenon is a well-documented trend in western countries [42] that is also reflected in the English-speaking internet [20] and subsequently the web-crawled LAION-2B-en. Our search for the 100 closest images (in CLIP [28] space) in the dataset to the term 'japanese body' yielded almost exclusively inappropriate material, with \\(90\\%\\) showing explicit nudity. For comparison, the global average for 50 selected countries is more than 4 times lower at \\(22\\%\\) (details can be found in Appendix A.1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.848 + ], + "angle": 0, + "content": "Now, to investigate the bias transfer to SD, we prompted the model using \\( \\langle < \\text{country} > \\text{body} \\rangle \\) (e.g. 'japanese body' or 'nigerian body') and compared the percentages of explicit nudes for the same 50 countries. We automatically assessed the generated image using the NudeNet image classifier4 to detect exposed genitalia. We chose this ambiguous prompt template to expose the model's biases. Based on image web search results, one can, for instance, expect images of categories such as average body comparison—displaying lightly dressed people—but also culturally related images such as the country flags. For each country, we generated 100 images, each using the same seed and hyperparameters. The results are depicted in Fig. 2 (left). Indeed, one can observe the above-described images such as average body comparison in the case of u.s. american (cf. Appendix A.2). However, as expected, the close association of some ethnic terms with nudity in Stable Diffusion is apparent. Overall it appears that European, Asian, and Oceanic countries are far more likely to be linked with nudity than" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "African or American ones. The most nude images are generated for Japan at over \\(75\\%\\), whereas the global average is at \\(35\\%\\). Specifically, the terms 'Asian' and 'Japanese' yielded a significantly higher amount of nudity than any other ethnic or geographic term. We attribute the apparent synonym usage of 'Japanese' and 'Asian' in this context to the aforementioned trends and the overwhelming amount of such content in LAION-5B. Unfortunately, biases in SD generation like these may further reinforce problematic social phenomena." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.893, + 0.44 + ], + "angle": 0, + "content": "SD's post-hoc safety measures. Various methods have been proposed to detect and filter out inappropriate images [4, 11, 25, 33]. Similarly, the SD implementation does contain a \"NSFW\" safety checker; an image classifier applied after generation to detect and withhold inappropriate images. However, there seems to be an interest in deactivating this safety measure. We checked the recently added image generation feature of lexica.art using examples we knew to generate content that the safety checker withstands. We note that the generation of these inappropriate images is possible on lexica.art at time of the present study, apparently without any restrictions, cf. Appendix A.3." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.454, + 0.892, + 0.484 + ], + "angle": 0, + "content": "Now, we are ready to introduce our two main contributions, first SLD and then the I2P benchmark." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.496, + 0.76, + 0.513 + ], + "angle": 0, + "content": "3. Safe Latent Diffusion (SLD)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.627 + ], + "angle": 0, + "content": "We introduce safety guidance for latent diffusion models to reduce the inappropriate degeneration of DMs. Our method extends the generative process by combining text conditioning through classifier-free guidance with inappropriate concepts removed or suppressed in the output image. Consequently, SLD performs image editing at inference without any further fine-tuning required." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.893, + 0.809 + ], + "angle": 0, + "content": "Diffusion models iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Intuitively, image generation starts from random noise \\(\\epsilon\\), and the model predicts an estimate of this noise \\(\\tilde{\\epsilon}_{\\theta}\\) to be subtracted from the initial values. This results in a high-fidelity image \\(x\\) without any noise. Since this is an extremely hard problem, multiple steps are applied, each subtracting a small amount \\((\\epsilon_{t})\\) of the predictive noise, approximating \\(\\epsilon\\). For text-to-image generation, the model's \\(\\epsilon\\)-prediction is conditioned on a text prompt \\(p\\) and results in an image faithful to that prompt. The training objective of a diffusion model \\(\\hat{x}_{\\theta}\\) can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.815, + 0.892, + 0.836 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\mathbf {x}, \\mathbf {c} _ {p}, \\epsilon , t} \\left[ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t} \\mathbf {x} + \\omega_ {t} \\epsilon , \\mathbf {c} _ {p}\\right) - \\mathbf {x} \\| _ {2} ^ {2} \\right] \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.902 + ], + "angle": 0, + "content": "where \\((\\mathbf{x},\\mathbf{c}_p)\\) is conditioned on text prompt \\(p\\), \\(t\\) is drawn from a uniform distribution \\(t\\sim \\mathcal{U}([0,1])\\), \\(\\epsilon\\) sampled from a Gaussian \\(\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})\\), and \\(w_{t},\\omega_{t},\\alpha_{t}\\) influence image fidelity depending on \\(t\\). Consequently, the DM is trained to" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.861, + 0.26, + 0.876 + ], + "angle": 0, + "content": "2https://huggingface.co/spaces" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.876, + 0.191, + 0.888 + ], + "angle": 0, + "content": "3 https://lexica.art" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.312, + 0.9 + ], + "angle": 0, + "content": "4 https://github.com/notAI-tech/NudeNet" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.861, + 0.312, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22524" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.089, + 0.426, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.473, + 0.331 + ], + "angle": 0, + "content": "Figure 3. Illustration of text-conditioned diffusion processes. SD using classifier-free guidance (blue arrow), SLD (green arrow) utilizing \"unsafe\" prompts (red arrow) to guide the generation in an opposing direction. For a more detailed comparison see Appendix Fig. 15. (Best viewed in color)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.47, + 0.398 + ], + "angle": 0, + "content": "denoise \\(\\mathbf{z}_t\\coloneqq \\mathbf{x} + \\epsilon\\) to yield \\(\\mathbf{x}\\) with the squared error as loss. At inference, the DM is sampled using the model's prediction of \\(\\mathbf{x} = (\\mathbf{z}_t - \\bar{\\epsilon_\\theta})\\), with \\(\\bar{\\epsilon_{\\theta}}\\) as described below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.504 + ], + "angle": 0, + "content": "Classifier-free guidance [17] is a conditioning method using a purely generational diffusion model, eliminating the need for an additional pre-trained classifier. The approach randomly drops the text conditioning \\(\\mathbf{c}_p\\) with a fixed probability during training, resulting in a joint model for unconditional and conditional objectives. During inference the score estimates for the \\(\\mathbf{x}\\)-prediction are adjusted so that:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.512, + 0.47, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) := \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right) + s _ {g} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.47, + 0.627 + ], + "angle": 0, + "content": "with guidance scale \\( s_g \\) which is typically chosen as \\( s_g \\in (0, 20] \\) and \\( \\epsilon_{\\theta} \\) defining the noise estimate with parameters \\( \\theta \\). Intuitively, the unconditioned \\( \\epsilon \\)-prediction \\( \\epsilon_{\\theta}(\\mathbf{z}_t) \\) is pushed in the direction of the conditioned \\( \\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p) \\) to yield an image faithful to prompt \\( p \\). Lastly, \\( s_g \\) determines the magnitude of the influence of the text \\( p \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.47, + 0.764 + ], + "angle": 0, + "content": "To influence the diffusion process, SLD makes use of the same principles as classifier-free guidance, cf. the simplified illustration in Fig. 3. In addition to a text prompt \\( p \\) (blue arrow), we define an inappropriate concept (red arrow) via textual description \\( S \\). Consequently, we use three \\( \\epsilon \\)-predictions with the goal of moving the unconditioned score estimate \\( \\epsilon_{\\theta}(\\mathbf{z}_t) \\) towards the prompt conditioned estimate \\( \\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p) \\) and simultaneously away from concept conditioned estimate \\( \\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_S) \\). This results in \\( \\overline{\\epsilon}_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p, \\mathbf{c}_S) = \\)" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.785, + 0.47, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\theta} (\\mathbf {z} _ {t}) + s _ {g} \\left(\\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}) - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}) - \\gamma (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}, \\mathbf {c} _ {S})\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.81, + 0.291, + 0.825 + ], + "angle": 0, + "content": "with the safety guidance term \\(\\gamma\\)" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.832, + 0.47, + 0.85 + ], + "angle": 0, + "content": "\\[\n\\gamma (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}, \\mathbf {c} _ {S}) = \\mu (\\mathbf {c} _ {p}, \\mathbf {c} _ {S}; s _ {S}, \\lambda) (\\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c} _ {S}) - \\epsilon_ {\\theta} (\\mathbf {z} _ {t})), (4)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mu\\) applies a guidance scale \\(s_S\\) element-wise. To this extent, \\(\\mu\\) considers those dimensions of the prompt conditioned estimate that would guide the generation process" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.169 + ], + "angle": 0, + "content": "toward the inappropriate concept. Therefore, \\(\\mu\\) scales the element-wise difference between the prompt conditioned estimate and safety conditioned estimate by \\(s_S\\) for all elements where this difference is below a threshold \\(\\lambda\\) and equals 0 otherwise: \\(\\mu (\\mathbf{c}_p,\\mathbf{c}_S;s_S,\\lambda) =\\)" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.178, + 0.892, + 0.218 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l l} \\max (1, | \\phi |), & \\text {w h e r e} \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) \\ominus \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right) < \\lambda \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.221, + 0.892, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\text {w i t h} \\quad \\phi = s _ {S} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right)\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.352 + ], + "angle": 0, + "content": "with both larger \\(\\lambda\\) and larger \\(s_S\\) leading to a more substantial shift away from the prompt text and in the opposite direction of the defined concept. Note that we clip the scaling factor of \\(\\mu\\) in order to avoid producing image artifacts. As described in previous research [16, 31], the values of each \\(\\mathbf{x}\\)-prediction should adhere to the training bounds of \\([-1, 1]\\) to prevent low fidelity images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.893, + 0.58 + ], + "angle": 0, + "content": "SLD is a balancing act between removing all inappropriate content from the generated image while keeping the changes minimal. In order to facilitate these requirements, we make two adjustments to the methodology presented above. We add a warm-up parameter \\(\\delta\\) that will only apply safety guidance \\(\\gamma\\) after an initial warm-up period in the diffusion process, i.e., \\(\\gamma (\\mathbf{z}_t,\\mathbf{c}_p,\\mathbf{c}_S)\\coloneqq \\mathbf{0}\\) if \\(t < \\delta\\). Naturally, higher values for \\(\\delta\\) lead to less significant adjustments of the generated image. As we aim to keep the overall composition of the image unchanged, selecting a sufficiently high \\(\\delta\\) ensures that only fine-grained details of the output are altered. Furthermore, we add a momentum term \\(\\nu_{t}\\) to the safety guidance \\(\\gamma\\) in order to accelerate guidance over time steps for dimensions that are continuously guided in the same direction. Hence, \\(\\gamma_{t}\\) is defined as: \\(\\gamma_{t}(\\mathbf{z}_{t},\\mathbf{c}_{p},\\mathbf{c}_{S}) =\\)" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.605, + 0.892, + 0.621 + ], + "angle": 0, + "content": "\\[\n\\mu \\left(\\mathbf {c} _ {p}, \\mathbf {c} _ {S}; s _ {S}, \\lambda\\right) \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right) + s _ {m} v _ {t} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.63, + 0.88, + 0.645 + ], + "angle": 0, + "content": "with momentum scale \\( s_m \\in [0,1] \\) and \\( \\nu \\) being updated as" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.656, + 0.892, + 0.672 + ], + "angle": 0, + "content": "\\[\n\\nu_ {t + 1} = \\beta_ {m} \\nu_ {t} + (1 - \\beta_ {m}) \\gamma_ {t} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.742 + ], + "angle": 0, + "content": "where \\(\\nu_{0} = 0\\) and \\(\\beta_{m}\\in [0,1)\\), with larger \\(\\beta_{m}\\) resulting in less volatile changes of the momentum. Momentum is already built up during the warm-up period, even though \\(\\gamma_{t}\\) is not applied during these steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.742, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Overall, the resulting SLD progress is exemplary visualized by means of the various diffusion steps in Fig. 3. While the safety-guidance is already applied in early steps it removes and suppresses the inappropriate parts of the images as soon as these are constructed in the latent space. We attached the corresponding SLD pseudo-code in Appendix H." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.809, + 0.863 + ], + "angle": 0, + "content": "4. Configuring Safe Latent Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Inappropriateness may be subjective depending on individual opinions and contexts. For instance, the require" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22525" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.129, + 0.089, + 0.42, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.473, + 0.466 + ], + "angle": 0, + "content": "Figure 4. Illustration and qualitative comparison of different SLD configurations for removing inappropriate content. All prompts taken from I2P (cf. Sec. 5). The left column shows the original image, the four images in the middle are generated using SLD, and the right column uses the inappropriate concept as a negative prompt without SLD. Images were blurred manually after generation. For prompts see Appendix Fig. 12. (Best viewed in color)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.598 + ], + "angle": 0, + "content": "ments of a professional artist differ from those of a 4-year-old child. Therefore, we suggest four possible configurations of the diffusion process varying in the strength of the safety adaptions. The configurations include the before mentioned hyper-parameters and concepts. We believe the proposed values offer a decent trade-off between the degree of alternation but note that these can be easily adapted." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.47, + 0.734 + ], + "angle": 0, + "content": "(Un)safe Concept. Inspired by existing content policies of deployed text-to-image DMs such as DALL-E, the following text prompt is used to define a general inappropriate safety concept: \"hate, harassment, violence, suffering, humiliation, harm, suicide, sexual, nudity, bodily fluids, blood, obscene gestures, illegal activity, drug use, theft, vandalism, weapons, child abuse, brutality, cruelty\". Through the text-based definition, one could easily add further and remove present concepts (cf. Appendix H)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Threshold. The most vital parameter of SLD is the safety threshold \\(\\lambda\\). It determines the location of the hyperplane dividing the latent space into appropriate and inappropriateness, cf. Eq. (5). Theoretically, \\(\\lambda\\) is restricted by the training bounds of \\([-1, 1]\\), and intuitively it should be at least 0. However, since our approach relies on the model's understanding of \"right\" and \"wrong\" we recommend choosing a conservative, i.e. small positive values such that \\(\\lambda \\in [0.0, 0.03]\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Safety guidance scale. The safety guidance scale \\( s_S \\) can theoretically be chosen arbitrarily high as the scaling factor" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "\\(\\mu\\) is clipped either way. Larger values for \\(s_S\\) would simply increase the number of values in latent representation being set to 1. Therefore, there is no adverse effect of large \\(s_S\\) such as image artifacts that are observed for high guidance scales \\(s_g\\). We recommend \\(s_S \\in [100,3000]\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.893, + 0.303 + ], + "angle": 0, + "content": "Warm-up. The warm-up period \\(\\delta\\) largely influences at which level of the image composition changes are applied. Large safe-guidance scales applied early in the diffusion process could lead to major initial changes before significant parts of the images were constructed. Hence, we recommend using at least a few warm-up steps, \\(\\delta \\in [5,20]\\), to construct an initial image and, in the worst case, let SLD revise those parts. In any case, \\(\\delta\\) should be no larger than half the number of total diffusion steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.893, + 0.47 + ], + "angle": 0, + "content": "Momentum. The guidance momentum is particularly useful to remove inappropriate concepts that make up significant portions of the image and thus require more substantial editing, especially those created during warm-up. Therefore, momentum builds up over the warm-up phase, and such images will be altered more rigorously than those with close editing distances. Higher momentum parameters usually allow for a longer warm-up period. With most diffusion processes using around 50 generation steps, the window for momentum build-up is limited. Therefore, we recommend choosing \\( s_m \\in [0, 0.5] \\) and \\( \\beta_m \\in [0.3, 0.7] \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.545 + ], + "angle": 0, + "content": "Configuration sets. These recommendations result in the following four sets of hyper-parameters gradually increasing their aggressiveness of changes on the resulting image (cf. Fig. 4 and Appendix I). Which setting to use highly depends on the use case and individual preferences:" + }, + { + "type": "table", + "bbox": [ + 0.509, + 0.556, + 0.818, + 0.631 + ], + "angle": 0, + "content": "
ConfigδsSλsmβm
Hyp-Weak152000.00.0-
Hyp-Medium1010000.010.30.4
Hyp-Strong720000.0250.50.7
Hyp-Max050001.00.50.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.81 + ], + "angle": 0, + "content": "The weak configuration is usually sufficient to remove superficial blood splatters, but stronger parameters are required to suppress more severe injuries. Similarly, the weak set may suppress nude content on clearly pornographic images but may not reduce nudity in artistic imagery such as oil paintings. A fact that an adult artist may find perfectly acceptable, however, is problematic for, e.g., a child using the model. Furthermore, on the example of nudity, we observed the medium hyper-parameter set to yield the generation of, e.g., a bikini. In contrast, the strong and maximum one would produce progressively more cloth like a dress." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Note that we can even drive the generation of inappropriate content to zero by choosing strong enough parameters (Hyp-Max). However, doing so likely diverges from our goal of keeping changes minimal. Nevertheless, this could be a requirement for sensitive applications, e.g., involving children. In these cases, we further recommend the usage" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22526" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.435, + 0.106 + ], + "angle": 0, + "content": "of post-hoc interventions such as SD's safety checker." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.471, + 0.319 + ], + "angle": 0, + "content": "Regarding the amount of observed changes, the HypMax configuration often behaves similarly to replacing the unconditioned estimate with a conditioned estimate based on a negative prompt during the classifier-free guidance, cf. Neg. in Fig. 4. I.e., replacing \\(\\epsilon_{\\theta}(\\mathbf{z}_t)\\) with \\(\\epsilon_{\\theta}(\\mathbf{z}_t,\\mathbf{c}_S)\\), cf. Eq. (2). However, as our experimental evaluation (cf. Tab. 1) shows, negative prompting leads to worse mitigation than SLD. Further, the major disadvantage of this approach is the lack of more fine-grained control over the generation process, always leading to images significantly differing from the original, especially for higher guidance scales \\(s_S\\). Additionally, negative prompts are a vital tool in text-to-image generation that would no longer be available to users if used for safety guidance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.403, + 0.354 + ], + "angle": 0, + "content": "5. Inappropriate Image Prompts (I2P)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.481 + ], + "angle": 0, + "content": "To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image models, we introduce a new benchmarking dataset of over \\(4.5\\mathrm{k}\\) real-world text prompts for generative models that are likely to produce inappropriate content: the inappropriate image prompts (I2P) dataset, cf. Fig. 1, covers a wide range of inappropriate content beyond nudity. Our dataset is publicly available for other researchers to use.[5]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.47, + 0.649 + ], + "angle": 0, + "content": "Inappropriate content. What is considered inappropriate imagery may differ based on context, setting, cultural and social predisposition, and individual factors and is highly subjective overall. In this work, we base our definition of inappropriate content on the work of Gebru et al.: \"[data that] if viewed directly, might be offensive, insulting, threatening, or might otherwise cause anxiety\" [12], which is for example also reflected by the OpenAI content policy6 that applies to the use of DALL-E [29]. Specifically, we consider those images showcasing content that contains one of the following:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.65, + 0.469, + 0.68 + ], + "angle": 0, + "content": "hate, harassment, violence, self-harm, sexual content, shocking images, illegal activity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.47, + 0.741 + ], + "angle": 0, + "content": "Note that inappropriateness is not limited to these seven concepts, varies between cultures, and constantly evolves. Here we restricted ourselves to images displaying tangible acts of inappropriate behavior." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.471, + 0.864 + ], + "angle": 0, + "content": "Prompt collection. For the seven concepts mentioned above, we used 26 keywords and phrases (cf. Appendix C) describing them in more detail and collected up to 250 real-world text prompts for each. For a given keyword, we crawled the prompts of the top 250 images returned by https://lexica.art. Lexica is a collection of real-world, user-generated prompts for SD sourced from its official discord server. It stores the prompt, seed, guidance scale, and image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.181 + ], + "angle": 0, + "content": "dimensions used in the generation to facilitate reproducibility. Image retrieval in lexica is based on the similarity of an image and search query in CLIP [28] embedding space. Therefore, the collected prompts are not guaranteed to generate inappropriate content, but the probability is high, as demonstrated in our evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.893, + 0.334 + ], + "angle": 0, + "content": "Dataset statistics. The data collection described above yielded duplicate entries, as some retrieved images were found among multiple keywords. After reducing those duplicates, the I2P dataset contains 4703 unique prompts assigned to at least one of the seven categories above. We also include an estimate of the percentage of inappropriate images the prompt is predicted to generate, together with the necessary hyper-parameters to reproduce these results. The benchmark also contains a hard annotation for prompts that generate predominantly inappropriate images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.895, + 0.548 + ], + "angle": 0, + "content": "On average, the prompts are made up of 20 tokens, and we could not observe an apparent correlation between frequent words and the connection to inappropriate images of these prompts. We present a word cloud of frequently used terms in Appendix C. Furthermore, we include the toxicity of each prompt based on the respective toxicity score of the PERSPECTIVE API.7 We only find a weak correlation8 between the toxicity of a prompt and the inappropriateness of images it generates. In fact, prompts with low toxicity scores still have unforeseen high probabilities of generating inappropriate images. Furthermore, out of 4702 prompts, a mere \\(1.5\\%\\) are toxic. This highlights that simply suppressing \"bad\" words in text prompts is no reliable mitigation strategy against generating problematic content." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.563, + 0.736, + 0.58 + ], + "angle": 0, + "content": "6. Experimental Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.589, + 0.892, + 0.62 + ], + "angle": 0, + "content": "We now evaluate SD's inappropriate degeneration and SLD based on the suggested configurations using I2P." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.893, + 0.846 + ], + "angle": 0, + "content": "Experimental Protocol. To assess the reduction of inappropriate content, we generated ten images each for all prompts of the I2P test bed and compared the probability of generating inappropriate images. We used one general concept \\( S \\) across all categories of I2P as specified in Sec. 4. We automatically evaluated inappropriate image content by combining two classifiers. First, the Q16 classifier [33]—also used to annotate the LAION-5B dataset—to detect a wide range of inappropriate content in images. Second, we applied NudeNet (cf. Sec. 2) to identify sexually explicit content. In this paper, we only classify exposed genitalia as inappropriate while allowing otherwise provocative images. If not specified otherwise, an image is classified as inappropriate if one or both of the classifiers output the respective label. Further details can be found in Appendix D." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.848, + 0.892, + 0.862 + ], + "angle": 0, + "content": "Inappropriateness in Stable Diffusion. We start our" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.874, + 0.366, + 0.887 + ], + "angle": 0, + "content": "5https://huggingface.co/datasets/AIML-TUDA/i2p" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.888, + 0.35, + 0.901 + ], + "angle": 0, + "content": "6https://labs.openai.com/policies/content-policy" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.874, + 0.366, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.875, + 0.781, + 0.888 + ], + "angle": 0, + "content": "7https://github.com/conversationai/perspectiveapi" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.888, + 0.635, + 0.9 + ], + "angle": 0, + "content": "Spearman \\(r = 0.22\\)" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.875, + 0.781, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22527" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.088, + 0.885, + 0.23 + ], + "angle": 0, + "content": "
CategoryInappropriate Probability ↓Exp. Max. Inappropriateness ↓
SD 1.4Neg. PromptHyp-WeakHyp-MediumHyp-StrongHyp-MaxSDHyp-StrongHyp-Max
Hate0.400.180.270.200.150.090.970.060.770.190.530.18
Harassment0.340.160.240.170.130.090.940.080.730.180.570.20
Violence0.430.240.360.230.170.140.890.040.790.130.680.28
Self-harm0.400.160.270.160.100.070.970.060.610.200.490.21
Sexual0.350.120.230.140.090.060.910.080.530.160.360.11
Shocking0.520.280.410.300.200.131.000.010.850.140.670.20
Illegal activity0.340.140.230.140.090.060.940.100.620.200.430.19
Overall0.390.180.290.190.130.090.960.070.720.190.600.19
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.242, + 0.892, + 0.325 + ], + "angle": 0, + "content": "Table 1. Safe Latent Diffusion (SLD) can considerably reduce the chance of generating inappropriate content (the lower, the better). Shown are the probabilities of generating an image containing inappropriate content as classified by the combined Q16/NudeNet classifier over the I2P benchmark. We note that the Q16 classifier is rather conservative and tends to classify some unobjectionable images as inappropriate. The false positive rate of the classifier is roughly equal to the probabilities reported for Hyp-Max. The expected maximum inappropriateness (the lower, the better) are bootstrap estimates of a model outputting the displayed percentage of inappropriate images at least once for 25 prompts (for further results see Appendix F). Subscript values indicate the standard deviation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.469, + 0.563 + ], + "angle": 0, + "content": "experimental evaluation by demonstrating the inappropriate degeneration of Stable Diffusion without any safety measures. Tab. 1 shows SD's probability of generating inappropriate content for each category under investigation. Recall that only \\(1.5\\%\\) of the text prompts could be identified as toxic. Nevertheless, one can clearly observe that depending on the category, the probability of generating inappropriate content ranges from \\(34\\%\\) to \\(52\\%\\). Furthermore, Tab. 1 reports the expected maximum inappropriateness over 25 prompts. These results show that a user generating images with I2P for 25 prompts is expected to have at least one batch of output images of which \\(96\\%\\) are inappropriate. The benchmark clearly shows SD's inappropriate degeneration and the risks of training on completely unfiltered datasets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.565, + 0.469, + 0.626 + ], + "angle": 0, + "content": "SLD in Stable Diffusion. Next, we investigate whether we can account for noisy, i.e. biased and unfiltered training data based on the model's acquired knowledge in distinguishing between appropriate and inappropriate content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.469, + 0.884 + ], + "angle": 0, + "content": "To this end, we applied SLD. Similarly to the observations made on the examples in Fig. 4, one can observe in Tab. 1 that the number of inappropriate images gradually decreases with stronger hyper-parameters. The strongest hyper-parameter configuration reduces the probability of generating inappropriate content by over \\(75\\%\\). Consequently, a mere \\(9\\%\\) of the generated images are still classified as inappropriate. However, it is important to note that the Q16 classifier tends to be rather conservative in some of its decisions classifying images as inappropriate where the respective content has already been reduced significantly. We assume the majority of images flagged as potentially inappropriate for Hyp-Max to be false negatives of the classifier. One can observe a similar reduction in the expected maximum inappropriateness but also note a substantial increase in variance. The latter indicates a substantial amount of outliers when using SLD." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Overall the results demonstrate that, indeed, we are able" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.412 + ], + "angle": 0, + "content": "to largely mitigate the inappropriate degeneration of SD based on the underlying model's learned representations. This could also apply to issues caused by reporting biases in the training set, as we will investigate in the following." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Counteracting Bias in Stable Diffusion. Recall the 'ethnic bias' experiments of Sec. 2. We demonstrated that biases reflected in LAION-5B data are, consequently, also reflected in the trained DM. Similarly to its performance on I2P, SLD strongly reduces the number of nude images generated for all countries as shown in Fig. 2 (right). SLD yields \\(75\\%\\) less explicit content and the percentage of nude images are distributed more evenly between countries. The previous outlier Japan now yields \\(12.0\\%\\) of nude content, close to the global percentage of \\(9.25\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.564, + 0.892, + 0.713 + ], + "angle": 0, + "content": "Nonetheless, at least with keeping changes minor (Hyp-Strong), SLD alone is not sufficient to mitigate this racial bias entirely. There remains a medium but statistically significant correlation between the percentages of nude images generated for a country by SD with and without SLD. Thus, SLD can make a valuable contribution towards debiasing DMs trained on datasets that introduce biases. However, these issues still need to be identified beforehand, and an effort towards reducing—or better eliminating—such biases in the dataset itself is still required." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.866 + ], + "angle": 0, + "content": "For further evidence, we ran experiments on Stable Diffusion v2.0 which is essentially a different model with a different text encoder and training set. Specifically, rigorous dataset filtering of sexual and nudity related content was applied before training the diffusion model, however, not on the pre-trained text encoder. While this filtering process reduces biased representations, they are still present and more frequent compared to SLD mitigation on SD in version 1.4, cf. Appendix E. Interestingly, the combination of SLD and dataset filtering achieves an even better mitigation. Hence," + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{9} \\) Spearman \\( r = {0.52} \\) ; Null-hypothesis that both distributions are uncorrelated is rejected at a significance level of \\( p = {0.01} \\) ." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22528" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "a combination of filtering and SLD could be beneficial and poses an interesting avenue for future work." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.136, + 0.314, + 0.151 + ], + "angle": 0, + "content": "7. Discussion & Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.161, + 0.469, + 0.19 + ], + "angle": 0, + "content": "Before concluding, let us touch upon ethical implications and future work concerning I2P and the introduced SLD." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.191, + 0.469, + 0.417 + ], + "angle": 0, + "content": "Ethical implications. We introduced an alternative approach to post-hoc prevention of presenting generated images with potentially inappropriate content. Instead, we identify inappropriate content and suppress it during the diffusion process. This intervention would not be possible if the model did not acquire a certain amount of knowledge on inappropriateness and related concepts during pre-training. Consequently, we do not advise removing potentially inappropriate content entirely from the training data, as we can reasonably assume that efforts towards removing all such samples will hurt the model's capabilities to target related material at inference individually. Therefore, we also see a promising avenue for future research in measuring the impact of training on balanced datasets. However, this is likely to require large amounts of manual labor." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.569 + ], + "angle": 0, + "content": "Nonetheless, we also demonstrated that highly imbalanced training data could reinforce problematic social phenomena. It must be ensured that potential risks can be reliably mitigated, and if in doubt, datasets must be further curated, such as in the presented case study. Whereas LAION already made a valiant curating effort by annotating the related inappropriate content, we again advocate for carefully investigating behavior and possible biases of models and consequently deploy mitigation strategies against these issues in any deployed application." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.825 + ], + "angle": 0, + "content": "We realize that SLD potentially has further ethical implications. Most notably, we recognize the possibility of similar techniques being used for actively censoring generative models. Additionally, one could construct a model generating mainly inappropriate content by reversing the guidance direction of our approach. Thus, we strongly urge all models using SLD to transparently state which contents are being suppressed. However, it could also be applied to cases beyond inappropriateness, such as fairness [22]. Furthermore, we reiterate that inappropriateness is based on social norms, and people have diverse sentiments. The introduced test bed is limited to specific concepts and consequently does not necessarily reflect differing opinions people might have on inappropriateness. Additionally, the model's acquired representation of inappropriateness may reflect the societal dispositions of the social groups represented in the training data and might lack a more diverse sentiment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Image Fidelity & Text Alignment. Lastly, we discuss the overall impact of SLD on image fidelity and text-alignment. Ideally, the approach should have no adverse effect on either, especially on already appropriate images. In line with previous research on generative text-to-image" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.89, + 0.188 + ], + "angle": 0, + "content": "
ConfigImage FidelityText Alignment
FID-30k ↓User (%) ↑CLIP ↓User (%) ↑
SD14.43-0.75-
Weak15.8163.700.7560.88
Medium16.9062.370.7559.45
Strong18.2863.130.7659.62
Max18.7663.600.7660.58
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.199, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Table 2. SLD's image fidelity and text alignment. User scores indicate the percentage of users judging SLD generated image as better or equal in quality/text alignment as its SD counterpart." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.266, + 0.892, + 0.418 + ], + "angle": 0, + "content": "models, we report the COCO FID-30k scores and CLIP distance of SD, and our four sets of hyper-parameters for SLD in Tab. 2. The scores slightly increase with stronger hyperparameters. However, they do not necessarily align with actual user preference [26]. Therefore, we conducted an exhaustive user study on the DrawBench [31] benchmark and reported results in Tab. 2 (cf. Appendix G for study details). The results indicate that users even slightly prefer images generated with SLD over those without, indicating safety does no sacrifice image quality and text alignment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.43, + 0.618, + 0.445 + ], + "angle": 0, + "content": "8. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.668 + ], + "angle": 0, + "content": "We demonstrated text-to-image models' inappropriate degeneration transfers from unfiltered and imbalanced training datasets. To measure related issues, we introduced an image generation test bed called I2P containing dedicated image-to-text prompts representing inappropriate concepts such as nudity and violence. Furthermore, we presented an approach to mitigate these issues based on classifier-free guidance. The proposed SLD removes and suppresses the corresponding image parts during the diffusion process with no additional training required and no adverse effect on overall image quality. Strong representation biases learned from the dataset are attenuated by our approach but not completely removed. Thus, we advocate for the careful use of unfiltered, clearly imbalanced datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.66, + 0.696 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We gratefully acknowledge support by the German Center for Artificial Intelligence (DFKI) project \"SAINT\" and the Federal Ministry of Education and Research (BMBF) under Grant No. 01IS22091. This work also benefited from the ICT-48 Network of AI Research Excellence Center \"TAILOR\" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the Hessian Ministry of Higher Education, and the Research and the Arts (HMWK) cluster projects \"The Adaptive Mind\" and \"The Third Wave of AI\", and the HMWK and BMBF ATHENE project \"AVSV\". Further, we thank Felix Friedrich, Dominik Hintersdorf and Lukas Struppek for their valuable feedback." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22529" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Abubakar Abid, Maheen Farooqi, and James Zou. Persistent anti-muslim bias in large language models. 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Journal of the American Philosophical Association, 2, 2016. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22531" + } + ] +] \ No newline at end of file diff --git a/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_origin.pdf b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6fb12dc5aab2af4fabfc1cc456d85bb19a0d0301 --- /dev/null +++ b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/27635077-d485-4fba-8dfd-7e03eb609fe0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8b15e43aad2d366144a1a89801fc3254b143378acf104b8fd19a2b066442ab00 +size 1749355 diff --git a/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/full.md b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b2a04b017fc57e363465519fda54509d873ba854 --- /dev/null +++ b/2023/Safe Latent Diffusion_ Mitigating Inappropriate Degeneration in Diffusion Models/full.md @@ -0,0 +1,282 @@ +# Safe Latent Diffusion: Mitigating Inappropriate Degeneration in Diffusion Models + +Patrick Schramowski $^{1,2,3,6*}$ Manuel Brack $^{3*}$ Björn Deiseroth $^{2,3,5}$ Kristian Kersting $^{1,2,3,4}$ $^{1}$ DFKI, $^{2}$ Hessian.AI, $^{3}$ Computer Science Department, TU Darmstadt + $^{4}$ Centre for Cognitive Science, TU Darmstadt, $^{5}$ Aleph Alpha, $^{6}$ LAION +{schramowski, brack, deiseroth, kersting}@cs.tu-darmstadt.de + +# Abstract + +Text-conditioned image generation models have recently achieved astonishing results in image quality and text alignment and are consequently employed in a fast-growing number of applications. Since they are highly data-driven, relying on billion-sized datasets randomly scraped from the internet, they also suffer, as we demonstrate, from degenerated and biased human behavior. In turn, they may even reinforce such biases. To help combat these undesired side effects, we present safe latent diffusion (SLD). Specifically, to measure the inappropriate degeneration due to unfiltered and imbalanced training sets, we establish a novel image generation test bed—inappropriate image prompts (I2P)—containing dedicated, real-world image-to-text prompts covering concepts such as nudity and violence. As our exhaustive empirical evaluation demonstrates, the introduced SLD removes and suppresses inappropriate image parts during the diffusion process, with no additional training required and no adverse effect on overall image quality or text alignment.1 + +Warning: This paper contains sexually explicit imagery, discussions of pornography, racially-charged terminology, and other content that some readers may find disturbing, distressing, and/or offensive. + +# 1. Introduction + +The primary reasons for recent breakthroughs in text-conditioned generative diffusion models (DM) are the quality of pre-trained backbones' representations and their multimodal training data. They have even been shown to learn and reflect the underlying syntax and semantics. In turn, they retain general knowledge implicitly present in the data [27]. Unfortunately, while they learn to encode and re + +![](images/795b77456f845a0398eaf4e14c0db7787b89ee0f7389a18c27ba7f07db17c857.jpg) +Figure 1. Mitigating inappropriate degeneration in diffusion models. I2P (left) is a new testbed for evaluating neural text-to-image generations and their inappropriateness. Percentages represent the portion of inappropriate images this prompt generates using Stable Diffusion (SD). SD may generate inappropriate content (middle), both for prompts explicitly implying such material as well as prompts not mentioning it all, hence generating inappropriate content unexpectedly. Our safe latent diffusion (SLD, right) is able to suppress inappropriate content. (Best viewed in color) + +flect general information, systems trained on large-scale unfiltered data may suffer from degenerated and biased behavior. While these profound issues are not completely surprising—since many biases are human-like [6,8]—many concerns are grounded in the data collection process failing to report its own bias [14]. The resulting models, including DMs, end up reflecting them and, in turn, have the potential to replicate undesired behavior [1,3-5, 13, 18]. Birhane et al. [5] pinpoint numerous implications and concerns of datasets scraped from the internet, in particular, LAION-400M [37], a predecessor of LAION-5B [36], and subsequent downstream harms of trained models. + +We analyze the open-source latent diffusion model Stable Diffusion (SD), which is trained on subsets of LAION-5B [36] and find a significant amount of inappropriate content generated which, viewed directly, might be offensive, ignominious, insulting, threatening, or might otherwise cause anxiety. To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image + +models, we provide a test bed for evaluating inappropriate generations by DMs and stress the need for better safety interventions and data selection processes for pre-training. We release I2P (Sec. 5), a set of 4703 dedicated text-to-image prompts extracted from real-world user prompts for image-to-text models paired with inappropriateness scores from three different detectors (cf. Fig. 1). We show that recently introduced open-source DMs, in this case, Stable Diffusion (SD), produce inappropriate content when conditioned on our prompts, even for those that seem to be non-harmful, cf. Sec. 6. Consequently, we introduce a possible mitigation strategy called safe latent diffusion (SLD) (Sec. 3) and quantify its ability to actively suppress the generation of inappropriate content using I2P (Sec. 6). SLD requires no external classifier, i.e., it relies on the model's already acquired knowledge of inappropriateness and needs no further tuning of the DM. + +In general, SLD introduces novel techniques for manipulating a generative diffusion model's latent space and provides further insights into the arithmetic of latent vectors. Importantly, to the best of our knowledge, our work is the first to consider image editing from an ethical perspective to counteract the inappropriate degeneration of DMs. + +# 2. Risks and Promises of Unfiltered Data + +Let us start discussing the risks but also promises of noisy, unfiltered and large-scale datasets, including background information on SD and its training data. + +Risks. Unfortunately, while modern large-scale models, such as GPT-3 [7], learn to encode and reflect general information, systems trained on large-scale unfiltered data also suffer from degenerated and biased behavior. Nonetheless, computational systems were promised to have the potential to counter human biases and structural inequalities [19]. However, data-driven AI systems often end up reflecting these biases and, in turn, have the potential to reinforce them instead. The associated risks have been broadly discussed and demonstrated in the context of large-scale models [1, 3-5, 13, 18]. These concerns include, for instance, models producing stereotypical and derogatory content [3] and gender and racial biases [10, 24, 38, 41]. Subsequently, approaches have been developed to, e.g., decrease the level of bias in these models [6, 39]. + +Promises. Besides the performance gains, large-scale models show surprisingly strong abilities to recall factual knowledge from the training data [27]. For example, Roberts et al. [30] showed that large-scale pre-trained language models' capabilities to store and retrieve knowledge scale with model size. Grounded on those findings, Schick et al. [32] demonstrated that language models can self-debias the text they produce, specifically regarding toxic output. Furthermore, Jenetzsch et al. [21] as well as Schramowski et al. [35] showed that the retained knowl + +edge of such models carries information about moral norms aligning with the human sense of "right" and "wrong" expressed in language. Similarly, other research demonstrated how to utilize this knowledge to guide autoregressive language models' text generation to prevent their toxic degeneration [32, 34]. Correspondingly, we demonstrate DMs' capabilities to guide image generation away from inappropriateness, only using representations and concepts learned during pre-training and defined in natural language. + +This makes our approach related to other techniques for text-based image editing on diffusion models such as Text2LIVE [2], Imagic [23] or UniTune [40]. Contrary to these works, our SLD approach requires no fine-tuning of the text-encoder or DM, nor does it introduce new downstream components. Instead, we utilize the learned representations of the model itself, thus substantially improving computational efficiency. Previously, Prompt-to-Prompt [15] proposed a text-controlled editing technique using changes to the text prompt and control of the model's cross-attention layers. In contrast, SLD is based on classifier-free guidance and enables more complex changes to the image. + +LAION-400M and LAION-5B. Whereas the LAION-400M [37] dataset was released as a proof-of-concept, the creators took the raised concern [5] to heart and annotated potential inappropriate content in its successor dataset of LAION-5B [36]. To further facilitate research on safety, fairness, and biased data, these samples were not excluded from the dataset. Users could decide for themselves, depending on their use case, to include those images. Thus, the creators of LAION-5B "advise against any applications in deployed systems without carefully investigating behavior and possible biases of models trained on LAION-5B." + +Training Stable Diffusion. Many DMs have reacted to the concerns raised on large-scale training data by either not releasing the model [31], only deploying it in a controlled environment with dedicated guardrails in place [29] or rigorously filtering the training data of the published model [25]. In contrast, SD decided not to exclude the annotated content contained in LAION-5B and to release the model publicly. Similar to LAION, Stable Diffusion encourages research on the safe deployment of models which have the potential to generate harmful content. + +Specifically, SD is trained on a subset of LAION-5B, namely LAION-2B-en [36] containing over 2.32 billion English image-text pairs. Training SD is executed in different steps: First, the model is trained on the complete LAION-2B-en. Then it is fine-tuned on various subsets, namely "LAION High Resolution" and "LAION-Aesthetics v2 $5+$ ". With all training samples taken from LAION-5B or subsets thereof, it is expected that the trained model reflects not only human-like biases such as gender occupation correlations but also reporting biases. Furthermore, SD is de + +![](images/6fcb70d0e469040c4b797aa40c94d6e55756489770acff7627965a256d75b025.jpg) +Figure 2. Grounded in reporting bias, one can observe ethnic biases in DMs (left). For 50 selected countries, we generated 100 images with the prompt ' $<$ country> body'. The country Japan shows the highest probability of generating nude content. SLD uses the strong hyper parameter set to counteract this bias (right). (Best viewed in color) + +ployed on several platforms including huggingface $^2$ and recently lexica.art $^3$ making it easy to use for the general public, including users unaware of present issues. + +Ethnic Bias. This leads us to our first experiment. Following up the studies by Birhane et al. on unfiltered multimodal datasets [5], we extend these investigations by answering whether the same issues occur in downstream generative models. Specifically, we chose to showcase biased representation of Asian women [42], cf. also Sec. 2.1 and Appendix A in [5] wrt. LAION-400M. This social phenomenon is a well-documented trend in western countries [42] that is also reflected in the English-speaking internet [20] and subsequently the web-crawled LAION-2B-en. Our search for the 100 closest images (in CLIP [28] space) in the dataset to the term 'japanese body' yielded almost exclusively inappropriate material, with $90\%$ showing explicit nudity. For comparison, the global average for 50 selected countries is more than 4 times lower at $22\%$ (details can be found in Appendix A.1). + +Now, to investigate the bias transfer to SD, we prompted the model using $\langle < \text{country} > \text{body} \rangle$ (e.g. 'japanese body' or 'nigerian body') and compared the percentages of explicit nudes for the same 50 countries. We automatically assessed the generated image using the NudeNet image classifier4 to detect exposed genitalia. We chose this ambiguous prompt template to expose the model's biases. Based on image web search results, one can, for instance, expect images of categories such as average body comparison—displaying lightly dressed people—but also culturally related images such as the country flags. For each country, we generated 100 images, each using the same seed and hyperparameters. The results are depicted in Fig. 2 (left). Indeed, one can observe the above-described images such as average body comparison in the case of u.s. american (cf. Appendix A.2). However, as expected, the close association of some ethnic terms with nudity in Stable Diffusion is apparent. Overall it appears that European, Asian, and Oceanic countries are far more likely to be linked with nudity than + +African or American ones. The most nude images are generated for Japan at over $75\%$ , whereas the global average is at $35\%$ . Specifically, the terms 'Asian' and 'Japanese' yielded a significantly higher amount of nudity than any other ethnic or geographic term. We attribute the apparent synonym usage of 'Japanese' and 'Asian' in this context to the aforementioned trends and the overwhelming amount of such content in LAION-5B. Unfortunately, biases in SD generation like these may further reinforce problematic social phenomena. + +SD's post-hoc safety measures. Various methods have been proposed to detect and filter out inappropriate images [4, 11, 25, 33]. Similarly, the SD implementation does contain a "NSFW" safety checker; an image classifier applied after generation to detect and withhold inappropriate images. However, there seems to be an interest in deactivating this safety measure. We checked the recently added image generation feature of lexica.art using examples we knew to generate content that the safety checker withstands. We note that the generation of these inappropriate images is possible on lexica.art at time of the present study, apparently without any restrictions, cf. Appendix A.3. + +Now, we are ready to introduce our two main contributions, first SLD and then the I2P benchmark. + +# 3. Safe Latent Diffusion (SLD) + +We introduce safety guidance for latent diffusion models to reduce the inappropriate degeneration of DMs. Our method extends the generative process by combining text conditioning through classifier-free guidance with inappropriate concepts removed or suppressed in the output image. Consequently, SLD performs image editing at inference without any further fine-tuning required. + +Diffusion models iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Intuitively, image generation starts from random noise $\epsilon$ , and the model predicts an estimate of this noise $\tilde{\epsilon}_{\theta}$ to be subtracted from the initial values. This results in a high-fidelity image $x$ without any noise. Since this is an extremely hard problem, multiple steps are applied, each subtracting a small amount $(\epsilon_{t})$ of the predictive noise, approximating $\epsilon$ . For text-to-image generation, the model's $\epsilon$ -prediction is conditioned on a text prompt $p$ and results in an image faithful to that prompt. The training objective of a diffusion model $\hat{x}_{\theta}$ can be written as + +$$ +\mathbb {E} _ {\mathbf {x}, \mathbf {c} _ {p}, \epsilon , t} \left[ w _ {t} \| \hat {\mathbf {x}} _ {\theta} \left(\alpha_ {t} \mathbf {x} + \omega_ {t} \epsilon , \mathbf {c} _ {p}\right) - \mathbf {x} \| _ {2} ^ {2} \right] \tag {1} +$$ + +where $(\mathbf{x},\mathbf{c}_p)$ is conditioned on text prompt $p$ , $t$ is drawn from a uniform distribution $t\sim \mathcal{U}([0,1])$ , $\epsilon$ sampled from a Gaussian $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ , and $w_{t},\omega_{t},\alpha_{t}$ influence image fidelity depending on $t$ . Consequently, the DM is trained to + +![](images/16f6667ededa833b949a178614500363e413434b3bbf0ccd1ef0240d35c72848.jpg) +Figure 3. Illustration of text-conditioned diffusion processes. SD using classifier-free guidance (blue arrow), SLD (green arrow) utilizing "unsafe" prompts (red arrow) to guide the generation in an opposing direction. For a more detailed comparison see Appendix Fig. 15. (Best viewed in color) + +denoise $\mathbf{z}_t\coloneqq \mathbf{x} + \epsilon$ to yield $\mathbf{x}$ with the squared error as loss. At inference, the DM is sampled using the model's prediction of $\mathbf{x} = (\mathbf{z}_t - \bar{\epsilon_\theta})$ , with $\bar{\epsilon_{\theta}}$ as described below. + +Classifier-free guidance [17] is a conditioning method using a purely generational diffusion model, eliminating the need for an additional pre-trained classifier. The approach randomly drops the text conditioning $\mathbf{c}_p$ with a fixed probability during training, resulting in a joint model for unconditional and conditional objectives. During inference the score estimates for the $\mathbf{x}$ -prediction are adjusted so that: + +$$ +\tilde {\epsilon} _ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {p}\right) := \epsilon_ {\theta} \left(\mathbf {z} _ {t}\right) + s _ {g} \left(\epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {p}\right) - \epsilon_ {\theta} \left(\mathbf {z} _ {t}\right)\right) \tag {2} +$$ + +with guidance scale $s_g$ which is typically chosen as $s_g \in (0, 20]$ and $\epsilon_{\theta}$ defining the noise estimate with parameters $\theta$ . Intuitively, the unconditioned $\epsilon$ -prediction $\epsilon_{\theta}(\mathbf{z}_t)$ is pushed in the direction of the conditioned $\epsilon_{\theta}(\mathbf{z}_t, \mathbf{c}_p)$ to yield an image faithful to prompt $p$ . Lastly, $s_g$ determines the magnitude of the influence of the text $p$ . + +To influence the diffusion process, SLD makes use of the same principles as classifier-free guidance, cf. the simplified illustration in Fig. 3. In addition to a text prompt $p$ (blue arrow), we define an inappropriate concept (red arrow) via textual description $S$ . Consequently, we use three $\epsilon$ -predictions with the goal of moving the unconditioned score estimate $\epsilon_{\theta}(\mathbf{z}_t)$ towards the prompt conditioned estimate $\epsilon_{\theta}(\mathbf{z}_t, \mathbf{c}_p)$ and simultaneously away from concept conditioned estimate $\epsilon_{\theta}(\mathbf{z}_t, \mathbf{c}_S)$ . This results in $\overline{\epsilon}_{\theta}(\mathbf{z}_t, \mathbf{c}_p, \mathbf{c}_S) =$ + +$$ +\epsilon_ {\theta} (\mathbf {z} _ {t}) + s _ {g} \left(\epsilon_ {\theta} (\mathbf {z} _ {t}, \mathbf {c} _ {p}) - \epsilon_ {\theta} (\mathbf {z} _ {t}) - \gamma (\mathbf {z} _ {t}, \mathbf {c} _ {p}, \mathbf {c} _ {S})\right) \tag {3} +$$ + +with the safety guidance term $\gamma$ + +$$ +\gamma (\mathbf {z} _ {t}, \mathbf {c} _ {p}, \mathbf {c} _ {S}) = \mu (\mathbf {c} _ {p}, \mathbf {c} _ {S}; s _ {S}, \lambda) (\epsilon_ {\theta} (\mathbf {z} _ {t}, \mathbf {c} _ {S}) - \epsilon_ {\theta} (\mathbf {z} _ {t})), (4) +$$ + +where $\mu$ applies a guidance scale $s_S$ element-wise. To this extent, $\mu$ considers those dimensions of the prompt conditioned estimate that would guide the generation process + +toward the inappropriate concept. Therefore, $\mu$ scales the element-wise difference between the prompt conditioned estimate and safety conditioned estimate by $s_S$ for all elements where this difference is below a threshold $\lambda$ and equals 0 otherwise: $\mu (\mathbf{c}_p,\mathbf{c}_S;s_S,\lambda) =$ + +$$ +\left\{ \begin{array}{l l} \max (1, | \phi |), & \text {w h e r e} \epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {p}\right) \ominus \epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {S}\right) < \lambda \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {5} +$$ + +$$ +\text {w i t h} \quad \phi = s _ {S} \left(\epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {p}\right) - \epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {S}\right)\right) \tag {6} +$$ + +with both larger $\lambda$ and larger $s_S$ leading to a more substantial shift away from the prompt text and in the opposite direction of the defined concept. Note that we clip the scaling factor of $\mu$ in order to avoid producing image artifacts. As described in previous research [16, 31], the values of each $\mathbf{x}$ -prediction should adhere to the training bounds of $[-1, 1]$ to prevent low fidelity images. + +SLD is a balancing act between removing all inappropriate content from the generated image while keeping the changes minimal. In order to facilitate these requirements, we make two adjustments to the methodology presented above. We add a warm-up parameter $\delta$ that will only apply safety guidance $\gamma$ after an initial warm-up period in the diffusion process, i.e., $\gamma (\mathbf{z}_t,\mathbf{c}_p,\mathbf{c}_S)\coloneqq \mathbf{0}$ if $t < \delta$ . Naturally, higher values for $\delta$ lead to less significant adjustments of the generated image. As we aim to keep the overall composition of the image unchanged, selecting a sufficiently high $\delta$ ensures that only fine-grained details of the output are altered. Furthermore, we add a momentum term $\nu_{t}$ to the safety guidance $\gamma$ in order to accelerate guidance over time steps for dimensions that are continuously guided in the same direction. Hence, $\gamma_{t}$ is defined as: $\gamma_{t}(\mathbf{z}_{t},\mathbf{c}_{p},\mathbf{c}_{S}) =$ + +$$ +\mu \left(\mathbf {c} _ {p}, \mathbf {c} _ {S}; s _ {S}, \lambda\right) \left(\epsilon_ {\theta} \left(\mathbf {z} _ {t}, \mathbf {c} _ {S}\right) - \epsilon_ {\theta} \left(\mathbf {z} _ {t}\right)\right) + s _ {m} v _ {t} \tag {7} +$$ + +with momentum scale $s_m \in [0,1]$ and $\nu$ being updated as + +$$ +\nu_ {t + 1} = \beta_ {m} \nu_ {t} + (1 - \beta_ {m}) \gamma_ {t} \tag {8} +$$ + +where $\nu_{0} = 0$ and $\beta_{m}\in [0,1)$ , with larger $\beta_{m}$ resulting in less volatile changes of the momentum. Momentum is already built up during the warm-up period, even though $\gamma_{t}$ is not applied during these steps. + +Overall, the resulting SLD progress is exemplary visualized by means of the various diffusion steps in Fig. 3. While the safety-guidance is already applied in early steps it removes and suppresses the inappropriate parts of the images as soon as these are constructed in the latent space. We attached the corresponding SLD pseudo-code in Appendix H. + +# 4. Configuring Safe Latent Diffusion + +Inappropriateness may be subjective depending on individual opinions and contexts. For instance, the require + +![](images/67a9b21a789fba1a6df5761d1e8974d2d66ab083f4d0d6965c346ad3caf01ce2.jpg) +Figure 4. Illustration and qualitative comparison of different SLD configurations for removing inappropriate content. All prompts taken from I2P (cf. Sec. 5). The left column shows the original image, the four images in the middle are generated using SLD, and the right column uses the inappropriate concept as a negative prompt without SLD. Images were blurred manually after generation. For prompts see Appendix Fig. 12. (Best viewed in color) + +ments of a professional artist differ from those of a 4-year-old child. Therefore, we suggest four possible configurations of the diffusion process varying in the strength of the safety adaptions. The configurations include the before mentioned hyper-parameters and concepts. We believe the proposed values offer a decent trade-off between the degree of alternation but note that these can be easily adapted. + +(Un)safe Concept. Inspired by existing content policies of deployed text-to-image DMs such as DALL-E, the following text prompt is used to define a general inappropriate safety concept: "hate, harassment, violence, suffering, humiliation, harm, suicide, sexual, nudity, bodily fluids, blood, obscene gestures, illegal activity, drug use, theft, vandalism, weapons, child abuse, brutality, cruelty". Through the text-based definition, one could easily add further and remove present concepts (cf. Appendix H). + +Threshold. The most vital parameter of SLD is the safety threshold $\lambda$ . It determines the location of the hyperplane dividing the latent space into appropriate and inappropriateness, cf. Eq. (5). Theoretically, $\lambda$ is restricted by the training bounds of $[-1, 1]$ , and intuitively it should be at least 0. However, since our approach relies on the model's understanding of "right" and "wrong" we recommend choosing a conservative, i.e. small positive values such that $\lambda \in [0.0, 0.03]$ . + +Safety guidance scale. The safety guidance scale $s_S$ can theoretically be chosen arbitrarily high as the scaling factor + +$\mu$ is clipped either way. Larger values for $s_S$ would simply increase the number of values in latent representation being set to 1. Therefore, there is no adverse effect of large $s_S$ such as image artifacts that are observed for high guidance scales $s_g$ . We recommend $s_S \in [100,3000]$ . + +Warm-up. The warm-up period $\delta$ largely influences at which level of the image composition changes are applied. Large safe-guidance scales applied early in the diffusion process could lead to major initial changes before significant parts of the images were constructed. Hence, we recommend using at least a few warm-up steps, $\delta \in [5,20]$ , to construct an initial image and, in the worst case, let SLD revise those parts. In any case, $\delta$ should be no larger than half the number of total diffusion steps. + +Momentum. The guidance momentum is particularly useful to remove inappropriate concepts that make up significant portions of the image and thus require more substantial editing, especially those created during warm-up. Therefore, momentum builds up over the warm-up phase, and such images will be altered more rigorously than those with close editing distances. Higher momentum parameters usually allow for a longer warm-up period. With most diffusion processes using around 50 generation steps, the window for momentum build-up is limited. Therefore, we recommend choosing $s_m \in [0, 0.5]$ and $\beta_m \in [0.3, 0.7]$ . + +Configuration sets. These recommendations result in the following four sets of hyper-parameters gradually increasing their aggressiveness of changes on the resulting image (cf. Fig. 4 and Appendix I). Which setting to use highly depends on the use case and individual preferences: + +
ConfigδsSλsmβm
Hyp-Weak152000.00.0-
Hyp-Medium1010000.010.30.4
Hyp-Strong720000.0250.50.7
Hyp-Max050001.00.50.7
+ +The weak configuration is usually sufficient to remove superficial blood splatters, but stronger parameters are required to suppress more severe injuries. Similarly, the weak set may suppress nude content on clearly pornographic images but may not reduce nudity in artistic imagery such as oil paintings. A fact that an adult artist may find perfectly acceptable, however, is problematic for, e.g., a child using the model. Furthermore, on the example of nudity, we observed the medium hyper-parameter set to yield the generation of, e.g., a bikini. In contrast, the strong and maximum one would produce progressively more cloth like a dress. + +Note that we can even drive the generation of inappropriate content to zero by choosing strong enough parameters (Hyp-Max). However, doing so likely diverges from our goal of keeping changes minimal. Nevertheless, this could be a requirement for sensitive applications, e.g., involving children. In these cases, we further recommend the usage + +of post-hoc interventions such as SD's safety checker. + +Regarding the amount of observed changes, the HypMax configuration often behaves similarly to replacing the unconditioned estimate with a conditioned estimate based on a negative prompt during the classifier-free guidance, cf. Neg. in Fig. 4. I.e., replacing $\epsilon_{\theta}(\mathbf{z}_t)$ with $\epsilon_{\theta}(\mathbf{z}_t,\mathbf{c}_S)$ , cf. Eq. (2). However, as our experimental evaluation (cf. Tab. 1) shows, negative prompting leads to worse mitigation than SLD. Further, the major disadvantage of this approach is the lack of more fine-grained control over the generation process, always leading to images significantly differing from the original, especially for higher guidance scales $s_S$ . Additionally, negative prompts are a vital tool in text-to-image generation that would no longer be available to users if used for safety guidance. + +# 5. Inappropriate Image Prompts (I2P) + +To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image models, we introduce a new benchmarking dataset of over $4.5\mathrm{k}$ real-world text prompts for generative models that are likely to produce inappropriate content: the inappropriate image prompts (I2P) dataset, cf. Fig. 1, covers a wide range of inappropriate content beyond nudity. Our dataset is publicly available for other researchers to use.[5] + +Inappropriate content. What is considered inappropriate imagery may differ based on context, setting, cultural and social predisposition, and individual factors and is highly subjective overall. In this work, we base our definition of inappropriate content on the work of Gebru et al.: "[data that] if viewed directly, might be offensive, insulting, threatening, or might otherwise cause anxiety" [12], which is for example also reflected by the OpenAI content policy6 that applies to the use of DALL-E [29]. Specifically, we consider those images showcasing content that contains one of the following: + +hate, harassment, violence, self-harm, sexual content, shocking images, illegal activity. + +Note that inappropriateness is not limited to these seven concepts, varies between cultures, and constantly evolves. Here we restricted ourselves to images displaying tangible acts of inappropriate behavior. + +Prompt collection. For the seven concepts mentioned above, we used 26 keywords and phrases (cf. Appendix C) describing them in more detail and collected up to 250 real-world text prompts for each. For a given keyword, we crawled the prompts of the top 250 images returned by https://lexica.art. Lexica is a collection of real-world, user-generated prompts for SD sourced from its official discord server. It stores the prompt, seed, guidance scale, and image + +dimensions used in the generation to facilitate reproducibility. Image retrieval in lexica is based on the similarity of an image and search query in CLIP [28] embedding space. Therefore, the collected prompts are not guaranteed to generate inappropriate content, but the probability is high, as demonstrated in our evaluation. + +Dataset statistics. The data collection described above yielded duplicate entries, as some retrieved images were found among multiple keywords. After reducing those duplicates, the I2P dataset contains 4703 unique prompts assigned to at least one of the seven categories above. We also include an estimate of the percentage of inappropriate images the prompt is predicted to generate, together with the necessary hyper-parameters to reproduce these results. The benchmark also contains a hard annotation for prompts that generate predominantly inappropriate images. + +On average, the prompts are made up of 20 tokens, and we could not observe an apparent correlation between frequent words and the connection to inappropriate images of these prompts. We present a word cloud of frequently used terms in Appendix C. Furthermore, we include the toxicity of each prompt based on the respective toxicity score of the PERSPECTIVE API.7 We only find a weak correlation8 between the toxicity of a prompt and the inappropriateness of images it generates. In fact, prompts with low toxicity scores still have unforeseen high probabilities of generating inappropriate images. Furthermore, out of 4702 prompts, a mere $1.5\%$ are toxic. This highlights that simply suppressing "bad" words in text prompts is no reliable mitigation strategy against generating problematic content. + +# 6. Experimental Evaluation + +We now evaluate SD's inappropriate degeneration and SLD based on the suggested configurations using I2P. + +Experimental Protocol. To assess the reduction of inappropriate content, we generated ten images each for all prompts of the I2P test bed and compared the probability of generating inappropriate images. We used one general concept $S$ across all categories of I2P as specified in Sec. 4. We automatically evaluated inappropriate image content by combining two classifiers. First, the Q16 classifier [33]—also used to annotate the LAION-5B dataset—to detect a wide range of inappropriate content in images. Second, we applied NudeNet (cf. Sec. 2) to identify sexually explicit content. In this paper, we only classify exposed genitalia as inappropriate while allowing otherwise provocative images. If not specified otherwise, an image is classified as inappropriate if one or both of the classifiers output the respective label. Further details can be found in Appendix D. + +Inappropriateness in Stable Diffusion. We start our + +
CategoryInappropriate Probability ↓Exp. Max. Inappropriateness ↓
SD 1.4Neg. PromptHyp-WeakHyp-MediumHyp-StrongHyp-MaxSDHyp-StrongHyp-Max
Hate0.400.180.270.200.150.090.970.060.770.190.530.18
Harassment0.340.160.240.170.130.090.940.080.730.180.570.20
Violence0.430.240.360.230.170.140.890.040.790.130.680.28
Self-harm0.400.160.270.160.100.070.970.060.610.200.490.21
Sexual0.350.120.230.140.090.060.910.080.530.160.360.11
Shocking0.520.280.410.300.200.131.000.010.850.140.670.20
Illegal activity0.340.140.230.140.090.060.940.100.620.200.430.19
Overall0.390.180.290.190.130.090.960.070.720.190.600.19
+ +Table 1. Safe Latent Diffusion (SLD) can considerably reduce the chance of generating inappropriate content (the lower, the better). Shown are the probabilities of generating an image containing inappropriate content as classified by the combined Q16/NudeNet classifier over the I2P benchmark. We note that the Q16 classifier is rather conservative and tends to classify some unobjectionable images as inappropriate. The false positive rate of the classifier is roughly equal to the probabilities reported for Hyp-Max. The expected maximum inappropriateness (the lower, the better) are bootstrap estimates of a model outputting the displayed percentage of inappropriate images at least once for 25 prompts (for further results see Appendix F). Subscript values indicate the standard deviation. + +experimental evaluation by demonstrating the inappropriate degeneration of Stable Diffusion without any safety measures. Tab. 1 shows SD's probability of generating inappropriate content for each category under investigation. Recall that only $1.5\%$ of the text prompts could be identified as toxic. Nevertheless, one can clearly observe that depending on the category, the probability of generating inappropriate content ranges from $34\%$ to $52\%$ . Furthermore, Tab. 1 reports the expected maximum inappropriateness over 25 prompts. These results show that a user generating images with I2P for 25 prompts is expected to have at least one batch of output images of which $96\%$ are inappropriate. The benchmark clearly shows SD's inappropriate degeneration and the risks of training on completely unfiltered datasets. + +SLD in Stable Diffusion. Next, we investigate whether we can account for noisy, i.e. biased and unfiltered training data based on the model's acquired knowledge in distinguishing between appropriate and inappropriate content. + +To this end, we applied SLD. Similarly to the observations made on the examples in Fig. 4, one can observe in Tab. 1 that the number of inappropriate images gradually decreases with stronger hyper-parameters. The strongest hyper-parameter configuration reduces the probability of generating inappropriate content by over $75\%$ . Consequently, a mere $9\%$ of the generated images are still classified as inappropriate. However, it is important to note that the Q16 classifier tends to be rather conservative in some of its decisions classifying images as inappropriate where the respective content has already been reduced significantly. We assume the majority of images flagged as potentially inappropriate for Hyp-Max to be false negatives of the classifier. One can observe a similar reduction in the expected maximum inappropriateness but also note a substantial increase in variance. The latter indicates a substantial amount of outliers when using SLD. + +Overall the results demonstrate that, indeed, we are able + +to largely mitigate the inappropriate degeneration of SD based on the underlying model's learned representations. This could also apply to issues caused by reporting biases in the training set, as we will investigate in the following. + +Counteracting Bias in Stable Diffusion. Recall the 'ethnic bias' experiments of Sec. 2. We demonstrated that biases reflected in LAION-5B data are, consequently, also reflected in the trained DM. Similarly to its performance on I2P, SLD strongly reduces the number of nude images generated for all countries as shown in Fig. 2 (right). SLD yields $75\%$ less explicit content and the percentage of nude images are distributed more evenly between countries. The previous outlier Japan now yields $12.0\%$ of nude content, close to the global percentage of $9.25\%$ . + +Nonetheless, at least with keeping changes minor (Hyp-Strong), SLD alone is not sufficient to mitigate this racial bias entirely. There remains a medium but statistically significant correlation between the percentages of nude images generated for a country by SD with and without SLD. Thus, SLD can make a valuable contribution towards debiasing DMs trained on datasets that introduce biases. However, these issues still need to be identified beforehand, and an effort towards reducing—or better eliminating—such biases in the dataset itself is still required. + +For further evidence, we ran experiments on Stable Diffusion v2.0 which is essentially a different model with a different text encoder and training set. Specifically, rigorous dataset filtering of sexual and nudity related content was applied before training the diffusion model, however, not on the pre-trained text encoder. While this filtering process reduces biased representations, they are still present and more frequent compared to SLD mitigation on SD in version 1.4, cf. Appendix E. Interestingly, the combination of SLD and dataset filtering achieves an even better mitigation. Hence, + +a combination of filtering and SLD could be beneficial and poses an interesting avenue for future work. + +# 7. Discussion & Limitations + +Before concluding, let us touch upon ethical implications and future work concerning I2P and the introduced SLD. + +Ethical implications. We introduced an alternative approach to post-hoc prevention of presenting generated images with potentially inappropriate content. Instead, we identify inappropriate content and suppress it during the diffusion process. This intervention would not be possible if the model did not acquire a certain amount of knowledge on inappropriateness and related concepts during pre-training. Consequently, we do not advise removing potentially inappropriate content entirely from the training data, as we can reasonably assume that efforts towards removing all such samples will hurt the model's capabilities to target related material at inference individually. Therefore, we also see a promising avenue for future research in measuring the impact of training on balanced datasets. However, this is likely to require large amounts of manual labor. + +Nonetheless, we also demonstrated that highly imbalanced training data could reinforce problematic social phenomena. It must be ensured that potential risks can be reliably mitigated, and if in doubt, datasets must be further curated, such as in the presented case study. Whereas LAION already made a valiant curating effort by annotating the related inappropriate content, we again advocate for carefully investigating behavior and possible biases of models and consequently deploy mitigation strategies against these issues in any deployed application. + +We realize that SLD potentially has further ethical implications. Most notably, we recognize the possibility of similar techniques being used for actively censoring generative models. Additionally, one could construct a model generating mainly inappropriate content by reversing the guidance direction of our approach. Thus, we strongly urge all models using SLD to transparently state which contents are being suppressed. However, it could also be applied to cases beyond inappropriateness, such as fairness [22]. Furthermore, we reiterate that inappropriateness is based on social norms, and people have diverse sentiments. The introduced test bed is limited to specific concepts and consequently does not necessarily reflect differing opinions people might have on inappropriateness. Additionally, the model's acquired representation of inappropriateness may reflect the societal dispositions of the social groups represented in the training data and might lack a more diverse sentiment. + +Image Fidelity & Text Alignment. Lastly, we discuss the overall impact of SLD on image fidelity and text-alignment. Ideally, the approach should have no adverse effect on either, especially on already appropriate images. In line with previous research on generative text-to-image + +
ConfigImage FidelityText Alignment
FID-30k ↓User (%) ↑CLIP ↓User (%) ↑
SD14.43-0.75-
Weak15.8163.700.7560.88
Medium16.9062.370.7559.45
Strong18.2863.130.7659.62
Max18.7663.600.7660.58
+ +Table 2. SLD's image fidelity and text alignment. User scores indicate the percentage of users judging SLD generated image as better or equal in quality/text alignment as its SD counterpart. + +models, we report the COCO FID-30k scores and CLIP distance of SD, and our four sets of hyper-parameters for SLD in Tab. 2. The scores slightly increase with stronger hyperparameters. However, they do not necessarily align with actual user preference [26]. Therefore, we conducted an exhaustive user study on the DrawBench [31] benchmark and reported results in Tab. 2 (cf. Appendix G for study details). The results indicate that users even slightly prefer images generated with SLD over those without, indicating safety does no sacrifice image quality and text alignment. + +# 8. Conclusion + +We demonstrated text-to-image models' inappropriate degeneration transfers from unfiltered and imbalanced training datasets. To measure related issues, we introduced an image generation test bed called I2P containing dedicated image-to-text prompts representing inappropriate concepts such as nudity and violence. Furthermore, we presented an approach to mitigate these issues based on classifier-free guidance. The proposed SLD removes and suppresses the corresponding image parts during the diffusion process with no additional training required and no adverse effect on overall image quality. Strong representation biases learned from the dataset are attenuated by our approach but not completely removed. Thus, we advocate for the careful use of unfiltered, clearly imbalanced datasets. + +# Acknowledgments + +We gratefully acknowledge support by the German Center for Artificial Intelligence (DFKI) project "SAINT" and the Federal Ministry of Education and Research (BMBF) under Grant No. 01IS22091. This work also benefited from the ICT-48 Network of AI Research Excellence Center "TAILOR" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the Hessian Ministry of Higher Education, and the Research and the Arts (HMWK) cluster projects "The Adaptive Mind" and "The Third Wave of AI", and the HMWK and BMBF ATHENE project "AVSV". Further, we thank Felix Friedrich, Dominik Hintersdorf and Lukas Struppek for their valuable feedback. + +# References + +[1] Abubakar Abid, Maheen Farooqi, and James Zou. Persistent anti-muslim bias in large language models. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society (AIES), page 298-306. Association for Computing Machinery, 2021. 1, 2 +[2] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. Preprint at https://arxiv.org/abs/2204.02491, 2022. 2 +[3] Emily M. 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Since they are highly data-driven, relying on billion-sized datasets randomly scraped from the internet, they also suffer, as we demonstrate, from degenerated and biased human behavior. In turn, they may even reinforce such biases. To help combat these undesired side effects, we present safe latent diffusion (SLD). Specifically, to measure the inappropriate degeneration due to unfiltered and imbalanced training sets, we establish a novel image generation test bed—inappropriate image prompts (I2P)—containing dedicated, real-world image-to-text prompts covering concepts such as nudity and violence. As our exhaustive empirical evaluation demonstrates, the introduced SLD removes and suppresses inappropriate image parts during the diffusion process, with no additional training required and no adverse effect on overall image quality or text alignment.1" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 559 + ], + "type": "text", + "content": "Warning: This paper contains sexually explicit imagery, discussions of pornography, racially-charged terminology, and other content that some readers may find disturbing, distressing, and/or offensive." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 570, + 128, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 128, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 128, + 582 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 590, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 676 + ], + "type": "text", + "content": "The primary reasons for recent breakthroughs in text-conditioned generative diffusion models (DM) are the quality of pre-trained backbones' representations and their multimodal training data. They have even been shown to learn and reflect the underlying syntax and semantics. In turn, they retain general knowledge implicitly present in the data [27]. Unfortunately, while they learn to encode and re" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 328, + 243, + 526, + 358 + ], + "blocks": [ + { + "bbox": [ + 328, + 243, + 526, + 358 + ], + "lines": [ + { + "bbox": [ + 328, + 243, + 526, + 358 + ], + "spans": [ + { + "bbox": [ + 328, + 243, + 526, + 358 + ], + "type": "image", + "image_path": "795b77456f845a0398eaf4e14c0db7787b89ee0f7389a18c27ba7f07db17c857.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 365, + 547, + 465 + ], + "lines": [ + { + "bbox": [ + 304, + 365, + 547, + 465 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 547, + 465 + ], + "type": "text", + "content": "Figure 1. Mitigating inappropriate degeneration in diffusion models. I2P (left) is a new testbed for evaluating neural text-to-image generations and their inappropriateness. Percentages represent the portion of inappropriate images this prompt generates using Stable Diffusion (SD). SD may generate inappropriate content (middle), both for prompts explicitly implying such material as well as prompts not mentioning it all, hence generating inappropriate content unexpectedly. Our safe latent diffusion (SLD, right) is able to suppress inappropriate content. (Best viewed in color)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 628 + ], + "type": "text", + "content": "flect general information, systems trained on large-scale unfiltered data may suffer from degenerated and biased behavior. While these profound issues are not completely surprising—since many biases are human-like [6,8]—many concerns are grounded in the data collection process failing to report its own bias [14]. The resulting models, including DMs, end up reflecting them and, in turn, have the potential to replicate undesired behavior [1,3-5, 13, 18]. Birhane et al. [5] pinpoint numerous implications and concerns of datasets scraped from the internet, in particular, LAION-400M [37], a predecessor of LAION-5B [36], and subsequent downstream harms of trained models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "We analyze the open-source latent diffusion model Stable Diffusion (SD), which is trained on subsets of LAION-5B [36] and find a significant amount of inappropriate content generated which, viewed directly, might be offensive, ignominious, insulting, threatening, or might otherwise cause anxiety. To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 684, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 684, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 684, + 287, + 712 + ], + "type": "text", + "content": "*Equal contribution \n1Code available at https://huggingface.co/docs/diffusers/api/pipelines/ble_diffusion_safe" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22522" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "models, we provide a test bed for evaluating inappropriate generations by DMs and stress the need for better safety interventions and data selection processes for pre-training. We release I2P (Sec. 5), a set of 4703 dedicated text-to-image prompts extracted from real-world user prompts for image-to-text models paired with inappropriateness scores from three different detectors (cf. Fig. 1). We show that recently introduced open-source DMs, in this case, Stable Diffusion (SD), produce inappropriate content when conditioned on our prompts, even for those that seem to be non-harmful, cf. Sec. 6. Consequently, we introduce a possible mitigation strategy called safe latent diffusion (SLD) (Sec. 3) and quantify its ability to actively suppress the generation of inappropriate content using I2P (Sec. 6). SLD requires no external classifier, i.e., it relies on the model's already acquired knowledge of inappropriateness and needs no further tuning of the DM." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 348 + ], + "type": "text", + "content": "In general, SLD introduces novel techniques for manipulating a generative diffusion model's latent space and provides further insights into the arithmetic of latent vectors. Importantly, to the best of our knowledge, our work is the first to consider image editing from an ethical perspective to counteract the inappropriate degeneration of DMs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 358, + 258, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 258, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 258, + 371 + ], + "type": "text", + "content": "2. Risks and Promises of Unfiltered Data" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 379, + 287, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 415 + ], + "type": "text", + "content": "Let us start discussing the risks but also promises of noisy, unfiltered and large-scale datasets, including background information on SD and its training data." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 415, + 289, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 289, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 289, + 594 + ], + "type": "text", + "content": "Risks. Unfortunately, while modern large-scale models, such as GPT-3 [7], learn to encode and reflect general information, systems trained on large-scale unfiltered data also suffer from degenerated and biased behavior. Nonetheless, computational systems were promised to have the potential to counter human biases and structural inequalities [19]. However, data-driven AI systems often end up reflecting these biases and, in turn, have the potential to reinforce them instead. The associated risks have been broadly discussed and demonstrated in the context of large-scale models [1, 3-5, 13, 18]. These concerns include, for instance, models producing stereotypical and derogatory content [3] and gender and racial biases [10, 24, 38, 41]. Subsequently, approaches have been developed to, e.g., decrease the level of bias in these models [6, 39]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Promises. Besides the performance gains, large-scale models show surprisingly strong abilities to recall factual knowledge from the training data [27]. For example, Roberts et al. [30] showed that large-scale pre-trained language models' capabilities to store and retrieve knowledge scale with model size. Grounded on those findings, Schick et al. [32] demonstrated that language models can self-debias the text they produce, specifically regarding toxic output. Furthermore, Jenetzsch et al. [21] as well as Schramowski et al. [35] showed that the retained knowl" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "edge of such models carries information about moral norms aligning with the human sense of \"right\" and \"wrong\" expressed in language. Similarly, other research demonstrated how to utilize this knowledge to guide autoregressive language models' text generation to prevent their toxic degeneration [32, 34]. Correspondingly, we demonstrate DMs' capabilities to guide image generation away from inappropriateness, only using representations and concepts learned during pre-training and defined in natural language." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 185, + 547, + 329 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 185, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 304, + 185, + 547, + 329 + ], + "type": "text", + "content": "This makes our approach related to other techniques for text-based image editing on diffusion models such as Text2LIVE [2], Imagic [23] or UniTune [40]. Contrary to these works, our SLD approach requires no fine-tuning of the text-encoder or DM, nor does it introduce new downstream components. Instead, we utilize the learned representations of the model itself, thus substantially improving computational efficiency. Previously, Prompt-to-Prompt [15] proposed a text-controlled editing technique using changes to the text prompt and control of the model's cross-attention layers. In contrast, SLD is based on classifier-free guidance and enables more complex changes to the image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 333, + 547, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 466 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 466 + ], + "type": "text", + "content": "LAION-400M and LAION-5B. Whereas the LAION-400M [37] dataset was released as a proof-of-concept, the creators took the raised concern [5] to heart and annotated potential inappropriate content in its successor dataset of LAION-5B [36]. To further facilitate research on safety, fairness, and biased data, these samples were not excluded from the dataset. Users could decide for themselves, depending on their use case, to include those images. Thus, the creators of LAION-5B \"advise against any applications in deployed systems without carefully investigating behavior and possible biases of models trained on LAION-5B.\"" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 469, + 547, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 547, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 547, + 589 + ], + "type": "text", + "content": "Training Stable Diffusion. Many DMs have reacted to the concerns raised on large-scale training data by either not releasing the model [31], only deploying it in a controlled environment with dedicated guardrails in place [29] or rigorously filtering the training data of the published model [25]. In contrast, SD decided not to exclude the annotated content contained in LAION-5B and to release the model publicly. Similar to LAION, Stable Diffusion encourages research on the safe deployment of models which have the potential to generate harmful content." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "Specifically, SD is trained on a subset of LAION-5B, namely LAION-2B-en [36] containing over 2.32 billion English image-text pairs. Training SD is executed in different steps: First, the model is trained on the complete LAION-2B-en. Then it is fine-tuned on various subsets, namely \"LAION High Resolution\" and \"LAION-Aesthetics v2 " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "5+" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "\". With all training samples taken from LAION-5B or subsets thereof, it is expected that the trained model reflects not only human-like biases such as gender occupation correlations but also reporting biases. Furthermore, SD is de" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22523" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 72, + 272, + 114 + ], + "blocks": [ + { + "bbox": [ + 62, + 72, + 272, + 114 + ], + "lines": [ + { + "bbox": [ + 62, + 72, + 272, + 114 + ], + "spans": [ + { + "bbox": [ + 62, + 72, + 272, + 114 + ], + "type": "image", + "image_path": "6fcb70d0e469040c4b797aa40c94d6e55756489770acff7627965a256d75b025.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 124, + 287, + 191 + ], + "lines": [ + { + "bbox": [ + 46, + 124, + 287, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 124, + 287, + 191 + ], + "type": "text", + "content": "Figure 2. Grounded in reporting bias, one can observe ethnic biases in DMs (left). For 50 selected countries, we generated 100 images with the prompt ' " + }, + { + "bbox": [ + 46, + 124, + 287, + 191 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 124, + 287, + 191 + ], + "type": "text", + "content": " country> body'. The country Japan shows the highest probability of generating nude content. SLD uses the strong hyper parameter set to counteract this bias (right). (Best viewed in color)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "type": "text", + "content": "ployed on several platforms including huggingface" + }, + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "type": "text", + "content": " and recently lexica.art" + }, + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "type": "inline_equation", + "content": "^3" + }, + { + "bbox": [ + 46, + 214, + 287, + 251 + ], + "type": "text", + "content": " making it easy to use for the general public, including users unaware of present issues." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "type": "text", + "content": "Ethnic Bias. This leads us to our first experiment. Following up the studies by Birhane et al. on unfiltered multimodal datasets [5], we extend these investigations by answering whether the same issues occur in downstream generative models. Specifically, we chose to showcase biased representation of Asian women [42], cf. also Sec. 2.1 and Appendix A in [5] wrt. LAION-400M. This social phenomenon is a well-documented trend in western countries [42] that is also reflected in the English-speaking internet [20] and subsequently the web-crawled LAION-2B-en. Our search for the 100 closest images (in CLIP [28] space) in the dataset to the term 'japanese body' yielded almost exclusively inappropriate material, with " + }, + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "type": "text", + "content": " showing explicit nudity. For comparison, the global average for 50 selected countries is more than 4 times lower at " + }, + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "type": "inline_equation", + "content": "22\\%" + }, + { + "bbox": [ + 46, + 251, + 287, + 443 + ], + "type": "text", + "content": " (details can be found in Appendix A.1)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 444, + 287, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 671 + ], + "type": "text", + "content": "Now, to investigate the bias transfer to SD, we prompted the model using " + }, + { + "bbox": [ + 46, + 444, + 287, + 671 + ], + "type": "inline_equation", + "content": "\\langle < \\text{country} > \\text{body} \\rangle" + }, + { + "bbox": [ + 46, + 444, + 287, + 671 + ], + "type": "text", + "content": " (e.g. 'japanese body' or 'nigerian body') and compared the percentages of explicit nudes for the same 50 countries. We automatically assessed the generated image using the NudeNet image classifier4 to detect exposed genitalia. We chose this ambiguous prompt template to expose the model's biases. Based on image web search results, one can, for instance, expect images of categories such as average body comparison—displaying lightly dressed people—but also culturally related images such as the country flags. For each country, we generated 100 images, each using the same seed and hyperparameters. The results are depicted in Fig. 2 (left). Indeed, one can observe the above-described images such as average body comparison in the case of u.s. american (cf. Appendix A.2). However, as expected, the close association of some ethnic terms with nudity in Stable Diffusion is apparent. Overall it appears that European, Asian, and Oceanic countries are far more likely to be linked with nudity than" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "text", + "content": "African or American ones. The most nude images are generated for Japan at over " + }, + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "text", + "content": ", whereas the global average is at " + }, + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "text", + "content": ". Specifically, the terms 'Asian' and 'Japanese' yielded a significantly higher amount of nudity than any other ethnic or geographic term. We attribute the apparent synonym usage of 'Japanese' and 'Asian' in this context to the aforementioned trends and the overwhelming amount of such content in LAION-5B. Unfortunately, biases in SD generation like these may further reinforce problematic social phenomena." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 192, + 546, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 546, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 546, + 348 + ], + "type": "text", + "content": "SD's post-hoc safety measures. Various methods have been proposed to detect and filter out inappropriate images [4, 11, 25, 33]. Similarly, the SD implementation does contain a \"NSFW\" safety checker; an image classifier applied after generation to detect and withhold inappropriate images. However, there seems to be an interest in deactivating this safety measure. We checked the recently added image generation feature of lexica.art using examples we knew to generate content that the safety checker withstands. We note that the generation of these inappropriate images is possible on lexica.art at time of the present study, apparently without any restrictions, cf. Appendix A.3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 359, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 359, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 545, + 383 + ], + "type": "text", + "content": "Now, we are ready to introduce our two main contributions, first SLD and then the I2P benchmark." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 392, + 465, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 465, + 406 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 465, + 406 + ], + "type": "text", + "content": "3. Safe Latent Diffusion (SLD)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 412, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 496 + ], + "type": "text", + "content": "We introduce safety guidance for latent diffusion models to reduce the inappropriate degeneration of DMs. Our method extends the generative process by combining text conditioning through classifier-free guidance with inappropriate concepts removed or suppressed in the output image. Consequently, SLD performs image editing at inference without any further fine-tuning required." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": "Diffusion models iteratively denoise a Gaussian distributed variable to produce samples of a learned data distribution. Intuitively, image generation starts from random noise " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": ", and the model predicts an estimate of this noise " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\theta}" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": " to be subtracted from the initial values. This results in a high-fidelity image " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": " without any noise. Since this is an extremely hard problem, multiple steps are applied, each subtracting a small amount " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "(\\epsilon_{t})" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": " of the predictive noise, approximating " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": ". For text-to-image generation, the model's " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": "-prediction is conditioned on a text prompt " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": " and results in an image faithful to that prompt. The training objective of a diffusion model " + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "inline_equation", + "content": "\\hat{x}_{\\theta}" + }, + { + "bbox": [ + 304, + 497, + 546, + 640 + ], + "type": "text", + "content": " can be written as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 342, + 645, + 545, + 662 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 645, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 342, + 645, + 545, + 662 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\mathbf {x}, \\mathbf {c} _ {p}, \\epsilon , t} \\left[ w _ {t} \\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\alpha_ {t} \\mathbf {x} + \\omega_ {t} \\epsilon , \\mathbf {c} _ {p}\\right) - \\mathbf {x} \\| _ {2} ^ {2} \\right] \\tag {1}", + "image_path": "468cf47bc0b2c238d8a789278b1607d33ded03aa741c8f53922f464e9cd3be3a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},\\mathbf{c}_p)" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " is conditioned on text prompt " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " is drawn from a uniform distribution " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "t\\sim \\mathcal{U}([0,1])" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " sampled from a Gaussian " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "w_{t},\\omega_{t},\\alpha_{t}" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": " influence image fidelity depending on " + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 665, + 546, + 714 + ], + "type": "text", + "content": ". 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Illustration of text-conditioned diffusion processes. SD using classifier-free guidance (blue arrow), SLD (green arrow) utilizing \"unsafe\" prompts (red arrow) to guide the generation in an opposing direction. For a more detailed comparison see Appendix Fig. 15. (Best viewed in color)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "text", + "content": "denoise " + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t\\coloneqq \\mathbf{x} + \\epsilon" + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "text", + "content": " to yield " + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "text", + "content": " with the squared error as loss. At inference, the DM is sampled using the model's prediction of " + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = (\\mathbf{z}_t - \\bar{\\epsilon_\\theta})" + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\bar{\\epsilon_{\\theta}}" + }, + { + "bbox": [ + 46, + 279, + 287, + 315 + ], + "type": "text", + "content": " as described below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "content": "Classifier-free guidance [17] is a conditioning method using a purely generational diffusion model, eliminating the need for an additional pre-trained classifier. The approach randomly drops the text conditioning " + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_p" + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "content": " with a fixed probability during training, resulting in a joint model for unconditional and conditional objectives. During inference the score estimates for the " + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 316, + 287, + 399 + ], + "type": "text", + "content": "-prediction are adjusted so that:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 72, + 405, + 287, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 405, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 72, + 405, + 287, + 419 + ], + "type": "interline_equation", + "content": "\\tilde {\\epsilon} _ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) := \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right) + s _ {g} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right) \\tag {2}", + "image_path": "f7b0e93c058c4b5e21e9b5eebd711987fbd107827f5af66ca1047d4555035f33.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": "with guidance scale " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "s_g" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": " which is typically chosen as " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "s_g \\in (0, 20]" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": " defining the noise estimate with parameters " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": ". Intuitively, the unconditioned " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": "-prediction " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t)" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": " is pushed in the direction of the conditioned " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p)" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": " to yield an image faithful to prompt " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": ". Lastly, " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "s_g" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": " determines the magnitude of the influence of the text " + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 424, + 287, + 496 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": "To influence the diffusion process, SLD makes use of the same principles as classifier-free guidance, cf. the simplified illustration in Fig. 3. In addition to a text prompt " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": " (blue arrow), we define an inappropriate concept (red arrow) via textual description " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": ". Consequently, we use three " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": "-predictions with the goal of moving the unconditioned score estimate " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t)" + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": " towards the prompt conditioned estimate " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p)" + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": " and simultaneously away from concept conditioned estimate " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_S)" + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "text", + "content": ". This results in " + }, + { + "bbox": [ + 46, + 496, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\overline{\\epsilon}_{\\theta}(\\mathbf{z}_t, \\mathbf{c}_p, \\mathbf{c}_S) =" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 621, + 287, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 621, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 61, + 621, + 287, + 635 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\theta} (\\mathbf {z} _ {t}) + s _ {g} \\left(\\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}) - \\epsilon_ {\\theta} (\\mathbf {z} _ {t}) - \\gamma (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}, \\mathbf {c} _ {S})\\right) \\tag {3}", + "image_path": "335905373da3960fb256c4d1bbbc2bfb81f76c5bab6248d2e82ab25d7bc95748.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 641, + 178, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 178, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 178, + 653 + ], + "type": "text", + "content": "with the safety guidance term " + }, + { + "bbox": [ + 47, + 641, + 178, + 653 + ], + "type": "inline_equation", + "content": "\\gamma" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 52, + 658, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 658, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 52, + 658, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\gamma (\\mathbf {z} _ {t}, \\mathbf {c} _ {p}, \\mathbf {c} _ {S}) = \\mu (\\mathbf {c} _ {p}, \\mathbf {c} _ {S}; s _ {S}, \\lambda) (\\epsilon_ {\\theta} (\\mathbf {z} _ {t}, \\mathbf {c} _ {S}) - \\epsilon_ {\\theta} (\\mathbf {z} _ {t})), (4)", + "image_path": "2bd7a13a67d70e611ffab61a254951ab322fb77c25a52af88cdcfa445d03b9c4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " applies a guidance scale " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " element-wise. To this extent, " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " considers those dimensions of the prompt conditioned estimate that would guide the generation process" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "toward the inappropriate concept. Therefore, " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " scales the element-wise difference between the prompt conditioned estimate and safety conditioned estimate by " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " for all elements where this difference is below a threshold " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " and equals 0 otherwise: " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mu (\\mathbf{c}_p,\\mathbf{c}_S;s_S,\\lambda) =" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 140, + 545, + 172 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 140, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 317, + 140, + 545, + 172 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l l} \\max (1, | \\phi |), & \\text {w h e r e} \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) \\ominus \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right) < \\lambda \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {5}", + "image_path": "fb5d91949adcd3cf4ac3ef12a5ca4e50968bb365a97027879a2f88f9876da563.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 315, + 175, + 545, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 175, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 315, + 175, + 545, + 188 + ], + "type": "interline_equation", + "content": "\\text {w i t h} \\quad \\phi = s _ {S} \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {p}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right)\\right) \\tag {6}", + "image_path": "5c7497dd16cdf05b5d6c3eb1bb86a58691c1058d1178234d26dff44e02a066f3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "content": "with both larger " + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "content": " and larger " + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "content": " leading to a more substantial shift away from the prompt text and in the opposite direction of the defined concept. Note that we clip the scaling factor of " + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "content": " in order to avoid producing image artifacts. As described in previous research [16, 31], the values of each " + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "content": "-prediction should adhere to the training bounds of " + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 304, + 195, + 545, + 278 + ], + "type": "text", + "content": " to prevent low fidelity images." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": "SLD is a balancing act between removing all inappropriate content from the generated image while keeping the changes minimal. In order to facilitate these requirements, we make two adjustments to the methodology presented above. We add a warm-up parameter " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " that will only apply safety guidance " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " after an initial warm-up period in the diffusion process, i.e., " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\gamma (\\mathbf{z}_t,\\mathbf{c}_p,\\mathbf{c}_S)\\coloneqq \\mathbf{0}" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "t < \\delta" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": ". Naturally, higher values for " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " lead to less significant adjustments of the generated image. As we aim to keep the overall composition of the image unchanged, selecting a sufficiently high " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " ensures that only fine-grained details of the output are altered. Furthermore, we add a momentum term " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\nu_{t}" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " to the safety guidance " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " in order to accelerate guidance over time steps for dimensions that are continuously guided in the same direction. Hence, " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "text", + "content": " is defined as: " + }, + { + "bbox": [ + 304, + 279, + 546, + 459 + ], + "type": "inline_equation", + "content": "\\gamma_{t}(\\mathbf{z}_{t},\\mathbf{c}_{p},\\mathbf{c}_{S}) =" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 333, + 479, + 545, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 479, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 333, + 479, + 545, + 491 + ], + "type": "interline_equation", + "content": "\\mu \\left(\\mathbf {c} _ {p}, \\mathbf {c} _ {S}; s _ {S}, \\lambda\\right) \\left(\\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, \\mathbf {c} _ {S}\\right) - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}\\right)\\right) + s _ {m} v _ {t} \\tag {7}", + "image_path": "b230cb9c008dd7a0f1505424432ec0c328c0cf458d4a4ef8c760648d23ccfe0d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "spans": [ + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "type": "text", + "content": "with momentum scale " + }, + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "type": "inline_equation", + "content": "s_m \\in [0,1]" + }, + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 306, + 498, + 538, + 510 + ], + "type": "text", + "content": " being updated as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 367, + 519, + 545, + 532 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 519, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 367, + 519, + 545, + 532 + ], + "type": "interline_equation", + "content": "\\nu_ {t + 1} = \\beta_ {m} \\nu_ {t} + (1 - \\beta_ {m}) \\gamma_ {t} \\tag {8}", + "image_path": "8c33fe12df34d4141a20588316959111f5453598c95a7024fbe06e1259809c2f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\nu_{0} = 0" + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\beta_{m}\\in [0,1)" + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "text", + "content": ", with larger " + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\beta_{m}" + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "text", + "content": " resulting in less volatile changes of the momentum. Momentum is already built up during the warm-up period, even though " + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "inline_equation", + "content": "\\gamma_{t}" + }, + { + "bbox": [ + 304, + 540, + 545, + 587 + ], + "type": "text", + "content": " is not applied during these steps." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 587, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 587, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 587, + 545, + 659 + ], + "type": "text", + "content": "Overall, the resulting SLD progress is exemplary visualized by means of the various diffusion steps in Fig. 3. While the safety-guidance is already applied in early steps it removes and suppresses the inappropriate parts of the images as soon as these are constructed in the latent space. We attached the corresponding SLD pseudo-code in Appendix H." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 669, + 495, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 495, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 495, + 683 + ], + "type": "text", + "content": "4. Configuring Safe Latent Diffusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Inappropriateness may be subjective depending on individual opinions and contexts. For instance, the require" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22525" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 78, + 70, + 257, + 281 + ], + "blocks": [ + { + "bbox": [ + 78, + 70, + 257, + 281 + ], + "lines": [ + { + "bbox": [ + 78, + 70, + 257, + 281 + ], + "spans": [ + { + "bbox": [ + 78, + 70, + 257, + 281 + ], + "type": "image", + "image_path": "67a9b21a789fba1a6df5761d1e8974d2d66ab083f4d0d6965c346ad3caf01ce2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 289, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 369 + ], + "type": "text", + "content": "Figure 4. Illustration and qualitative comparison of different SLD configurations for removing inappropriate content. All prompts taken from I2P (cf. Sec. 5). The left column shows the original image, the four images in the middle are generated using SLD, and the right column uses the inappropriate concept as a negative prompt without SLD. Images were blurred manually after generation. For prompts see Appendix Fig. 12. (Best viewed in color)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 389, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 473 + ], + "type": "text", + "content": "ments of a professional artist differ from those of a 4-year-old child. Therefore, we suggest four possible configurations of the diffusion process varying in the strength of the safety adaptions. The configurations include the before mentioned hyper-parameters and concepts. We believe the proposed values offer a decent trade-off between the degree of alternation but note that these can be easily adapted." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 287, + 581 + ], + "type": "text", + "content": "(Un)safe Concept. Inspired by existing content policies of deployed text-to-image DMs such as DALL-E, the following text prompt is used to define a general inappropriate safety concept: \"hate, harassment, violence, suffering, humiliation, harm, suicide, sexual, nudity, bodily fluids, blood, obscene gestures, illegal activity, drug use, theft, vandalism, weapons, child abuse, brutality, cruelty\". Through the text-based definition, one could easily add further and remove present concepts (cf. Appendix H)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": "Threshold. The most vital parameter of SLD is the safety threshold " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": ". It determines the location of the hyperplane dividing the latent space into appropriate and inappropriateness, cf. Eq. (5). Theoretically, " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": " is restricted by the training bounds of " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": ", and intuitively it should be at least 0. However, since our approach relies on the model's understanding of \"right\" and \"wrong\" we recommend choosing a conservative, i.e. small positive values such that " + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\lambda \\in [0.0, 0.03]" + }, + { + "bbox": [ + 46, + 582, + 287, + 689 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "Safety guidance scale. The safety guidance scale " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " can theoretically be chosen arbitrarily high as the scaling factor" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " is clipped either way. Larger values for " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " would simply increase the number of values in latent representation being set to 1. Therefore, there is no adverse effect of large " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " such as image artifacts that are observed for high guidance scales " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "s_g" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ". We recommend " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "s_S \\in [100,3000]" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "text", + "content": "Warm-up. The warm-up period " + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "text", + "content": " largely influences at which level of the image composition changes are applied. Large safe-guidance scales applied early in the diffusion process could lead to major initial changes before significant parts of the images were constructed. Hence, we recommend using at least a few warm-up steps, " + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "inline_equation", + "content": "\\delta \\in [5,20]" + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "text", + "content": ", to construct an initial image and, in the worst case, let SLD revise those parts. In any case, " + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 133, + 546, + 239 + ], + "type": "text", + "content": " should be no larger than half the number of total diffusion steps." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "type": "text", + "content": "Momentum. The guidance momentum is particularly useful to remove inappropriate concepts that make up significant portions of the image and thus require more substantial editing, especially those created during warm-up. Therefore, momentum builds up over the warm-up phase, and such images will be altered more rigorously than those with close editing distances. Higher momentum parameters usually allow for a longer warm-up period. With most diffusion processes using around 50 generation steps, the window for momentum build-up is limited. Therefore, we recommend choosing " + }, + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "type": "inline_equation", + "content": "s_m \\in [0, 0.5]" + }, + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "type": "inline_equation", + "content": "\\beta_m \\in [0.3, 0.7]" + }, + { + "bbox": [ + 304, + 239, + 546, + 372 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 431 + ], + "type": "text", + "content": "Configuration sets. These recommendations result in the following four sets of hyper-parameters gradually increasing their aggressiveness of changes on the resulting image (cf. Fig. 4 and Appendix I). Which setting to use highly depends on the use case and individual preferences:" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 311, + 440, + 500, + 499 + ], + "blocks": [ + { + "bbox": [ + 311, + 440, + 500, + 499 + ], + "lines": [ + { + "bbox": [ + 311, + 440, + 500, + 499 + ], + "spans": [ + { + "bbox": [ + 311, + 440, + 500, + 499 + ], + "type": "table", + "html": "
ConfigδsSλsmβm
Hyp-Weak152000.00.0-
Hyp-Medium1010000.010.30.4
Hyp-Strong720000.0250.50.7
Hyp-Max050001.00.50.7
", + "image_path": "ef638e88c08096fb415a8bdf9b498d1835febb189b04d92b52f740327dff5d84.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 641 + ], + "type": "text", + "content": "The weak configuration is usually sufficient to remove superficial blood splatters, but stronger parameters are required to suppress more severe injuries. Similarly, the weak set may suppress nude content on clearly pornographic images but may not reduce nudity in artistic imagery such as oil paintings. A fact that an adult artist may find perfectly acceptable, however, is problematic for, e.g., a child using the model. Furthermore, on the example of nudity, we observed the medium hyper-parameter set to yield the generation of, e.g., a bikini. In contrast, the strong and maximum one would produce progressively more cloth like a dress." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Note that we can even drive the generation of inappropriate content to zero by choosing strong enough parameters (Hyp-Max). However, doing so likely diverges from our goal of keeping changes minimal. Nevertheless, this could be a requirement for sensitive applications, e.g., involving children. In these cases, we further recommend the usage" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22526" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 266, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 266, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 266, + 83 + ], + "type": "text", + "content": "of post-hoc interventions such as SD's safety checker." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "text", + "content": "Regarding the amount of observed changes, the HypMax configuration often behaves similarly to replacing the unconditioned estimate with a conditioned estimate based on a negative prompt during the classifier-free guidance, cf. Neg. in Fig. 4. I.e., replacing " + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t)" + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\mathbf{z}_t,\\mathbf{c}_S)" + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "text", + "content": ", cf. Eq. (2). However, as our experimental evaluation (cf. Tab. 1) shows, negative prompting leads to worse mitigation than SLD. Further, the major disadvantage of this approach is the lack of more fine-grained control over the generation process, always leading to images significantly differing from the original, especially for higher guidance scales " + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "inline_equation", + "content": "s_S" + }, + { + "bbox": [ + 46, + 85, + 288, + 252 + ], + "type": "text", + "content": ". Additionally, negative prompts are a vital tool in text-to-image generation that would no longer be available to users if used for safety guidance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 265, + 246, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 246, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 246, + 280 + ], + "type": "text", + "content": "5. Inappropriate Image Prompts (I2P)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "text", + "content": "To systematically measure the risk of inappropriate degeneration by pre-trained text-to-image models, we introduce a new benchmarking dataset of over " + }, + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "inline_equation", + "content": "4.5\\mathrm{k}" + }, + { + "bbox": [ + 46, + 285, + 287, + 380 + ], + "type": "text", + "content": " real-world text prompts for generative models that are likely to produce inappropriate content: the inappropriate image prompts (I2P) dataset, cf. Fig. 1, covers a wide range of inappropriate content beyond nudity. Our dataset is publicly available for other researchers to use.[5]" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 382, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 287, + 514 + ], + "type": "text", + "content": "Inappropriate content. What is considered inappropriate imagery may differ based on context, setting, cultural and social predisposition, and individual factors and is highly subjective overall. In this work, we base our definition of inappropriate content on the work of Gebru et al.: \"[data that] if viewed directly, might be offensive, insulting, threatening, or might otherwise cause anxiety\" [12], which is for example also reflected by the OpenAI content policy6 that applies to the use of DALL-E [29]. Specifically, we consider those images showcasing content that contains one of the following:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 514, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 287, + 538 + ], + "type": "text", + "content": "hate, harassment, violence, self-harm, sexual content, shocking images, illegal activity." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 539, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 586 + ], + "type": "text", + "content": "Note that inappropriateness is not limited to these seven concepts, varies between cultures, and constantly evolves. Here we restricted ourselves to images displaying tangible acts of inappropriate behavior." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 587, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 288, + 684 + ], + "type": "text", + "content": "Prompt collection. For the seven concepts mentioned above, we used 26 keywords and phrases (cf. Appendix C) describing them in more detail and collected up to 250 real-world text prompts for each. For a given keyword, we crawled the prompts of the top 250 images returned by https://lexica.art. Lexica is a collection of real-world, user-generated prompts for SD sourced from its official discord server. It stores the prompt, seed, guidance scale, and image" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 143 + ], + "type": "text", + "content": "dimensions used in the generation to facilitate reproducibility. Image retrieval in lexica is based on the similarity of an image and search query in CLIP [28] embedding space. Therefore, the collected prompts are not guaranteed to generate inappropriate content, but the probability is high, as demonstrated in our evaluation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 144, + 546, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 264 + ], + "type": "text", + "content": "Dataset statistics. The data collection described above yielded duplicate entries, as some retrieved images were found among multiple keywords. After reducing those duplicates, the I2P dataset contains 4703 unique prompts assigned to at least one of the seven categories above. We also include an estimate of the percentage of inappropriate images the prompt is predicted to generate, together with the necessary hyper-parameters to reproduce these results. The benchmark also contains a hard annotation for prompts that generate predominantly inappropriate images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 265, + 547, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 547, + 434 + ], + "type": "text", + "content": "On average, the prompts are made up of 20 tokens, and we could not observe an apparent correlation between frequent words and the connection to inappropriate images of these prompts. We present a word cloud of frequently used terms in Appendix C. Furthermore, we include the toxicity of each prompt based on the respective toxicity score of the PERSPECTIVE API.7 We only find a weak correlation8 between the toxicity of a prompt and the inappropriateness of images it generates. In fact, prompts with low toxicity scores still have unforeseen high probabilities of generating inappropriate images. Furthermore, out of 4702 prompts, a mere " + }, + { + "bbox": [ + 304, + 265, + 547, + 434 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 265, + 547, + 434 + ], + "type": "text", + "content": " are toxic. This highlights that simply suppressing \"bad\" words in text prompts is no reliable mitigation strategy against generating problematic content." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 445, + 450, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 445, + 450, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 445, + 450, + 459 + ], + "type": "text", + "content": "6. Experimental Evaluation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 305, + 466, + 545, + 491 + ], + "type": "text", + "content": "We now evaluate SD's inappropriate degeneration and SLD based on the suggested configurations using I2P." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 491, + 546, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 546, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 546, + 670 + ], + "type": "text", + "content": "Experimental Protocol. To assess the reduction of inappropriate content, we generated ten images each for all prompts of the I2P test bed and compared the probability of generating inappropriate images. We used one general concept " + }, + { + "bbox": [ + 304, + 491, + 546, + 670 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 491, + 546, + 670 + ], + "type": "text", + "content": " across all categories of I2P as specified in Sec. 4. We automatically evaluated inappropriate image content by combining two classifiers. First, the Q16 classifier [33]—also used to annotate the LAION-5B dataset—to detect a wide range of inappropriate content in images. Second, we applied NudeNet (cf. Sec. 2) to identify sexually explicit content. In this paper, we only classify exposed genitalia as inappropriate while allowing otherwise provocative images. If not specified otherwise, an image is classified as inappropriate if one or both of the classifiers output the respective label. Further details can be found in Appendix D." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 671, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 671, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 318, + 671, + 545, + 682 + ], + "type": "text", + "content": "Inappropriateness in Stable Diffusion. We start our" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 692, + 223, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 692, + 223, + 702 + ], + "spans": [ + { + "bbox": [ + 57, + 692, + 223, + 702 + ], + "type": "text", + "content": "5https://huggingface.co/datasets/AIML-TUDA/i2p" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 57, + 703, + 214, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 703, + 214, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 703, + 214, + 713 + ], + "type": "text", + "content": "6https://labs.openai.com/policies/content-policy" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 693, + 477, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 693, + 477, + 703 + ], + "spans": [ + { + "bbox": [ + 317, + 693, + 477, + 703 + ], + "type": "text", + "content": "7https://github.com/conversationai/perspectiveapi" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 317, + 703, + 388, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 388, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 388, + 712 + ], + "type": "text", + "content": "Spearman " + }, + { + "bbox": [ + 317, + 703, + 388, + 712 + ], + "type": "inline_equation", + "content": "r = 0.22" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22527" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 69, + 541, + 182 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 541, + 182 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 541, + 182 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 541, + 182 + ], + "type": "table", + "html": "
CategoryInappropriate Probability ↓Exp. Max. Inappropriateness ↓
SD 1.4Neg. PromptHyp-WeakHyp-MediumHyp-StrongHyp-MaxSDHyp-StrongHyp-Max
Hate0.400.180.270.200.150.090.970.060.770.190.530.18
Harassment0.340.160.240.170.130.090.940.080.730.180.570.20
Violence0.430.240.360.230.170.140.890.040.790.130.680.28
Self-harm0.400.160.270.160.100.070.970.060.610.200.490.21
Sexual0.350.120.230.140.090.060.910.080.530.160.360.11
Shocking0.520.280.410.300.200.131.000.010.850.140.670.20
Illegal activity0.340.140.230.140.090.060.940.100.620.200.430.19
Overall0.390.180.290.190.130.090.960.070.720.190.600.19
", + "image_path": "d2e138c8f0f7155285fadfa65159e88dd12ac42f7cf9b2b006ed7fd81b93bb30.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 191, + 545, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 191, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 545, + 257 + ], + "type": "text", + "content": "Table 1. Safe Latent Diffusion (SLD) can considerably reduce the chance of generating inappropriate content (the lower, the better). Shown are the probabilities of generating an image containing inappropriate content as classified by the combined Q16/NudeNet classifier over the I2P benchmark. We note that the Q16 classifier is rather conservative and tends to classify some unobjectionable images as inappropriate. The false positive rate of the classifier is roughly equal to the probabilities reported for Hyp-Max. The expected maximum inappropriateness (the lower, the better) are bootstrap estimates of a model outputting the displayed percentage of inappropriate images at least once for 25 prompts (for further results see Appendix F). Subscript values indicate the standard deviation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "text", + "content": "experimental evaluation by demonstrating the inappropriate degeneration of Stable Diffusion without any safety measures. Tab. 1 shows SD's probability of generating inappropriate content for each category under investigation. Recall that only " + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "text", + "content": " of the text prompts could be identified as toxic. Nevertheless, one can clearly observe that depending on the category, the probability of generating inappropriate content ranges from " + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "inline_equation", + "content": "52\\%" + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "text", + "content": ". Furthermore, Tab. 1 reports the expected maximum inappropriateness over 25 prompts. These results show that a user generating images with I2P for 25 prompts is expected to have at least one batch of output images of which " + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "inline_equation", + "content": "96\\%" + }, + { + "bbox": [ + 46, + 278, + 287, + 445 + ], + "type": "text", + "content": " are inappropriate. The benchmark clearly shows SD's inappropriate degeneration and the risks of training on completely unfiltered datasets." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 447, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 287, + 495 + ], + "type": "text", + "content": "SLD in Stable Diffusion. Next, we investigate whether we can account for noisy, i.e. biased and unfiltered training data based on the model's acquired knowledge in distinguishing between appropriate and inappropriate content." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "type": "text", + "content": "To this end, we applied SLD. Similarly to the observations made on the examples in Fig. 4, one can observe in Tab. 1 that the number of inappropriate images gradually decreases with stronger hyper-parameters. The strongest hyper-parameter configuration reduces the probability of generating inappropriate content by over " + }, + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "type": "text", + "content": ". Consequently, a mere " + }, + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "type": "inline_equation", + "content": "9\\%" + }, + { + "bbox": [ + 46, + 496, + 287, + 700 + ], + "type": "text", + "content": " of the generated images are still classified as inappropriate. However, it is important to note that the Q16 classifier tends to be rather conservative in some of its decisions classifying images as inappropriate where the respective content has already been reduced significantly. We assume the majority of images flagged as potentially inappropriate for Hyp-Max to be false negatives of the classifier. One can observe a similar reduction in the expected maximum inappropriateness but also note a substantial increase in variance. The latter indicates a substantial amount of outliers when using SLD." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "content": "Overall the results demonstrate that, indeed, we are able" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 326 + ], + "type": "text", + "content": "to largely mitigate the inappropriate degeneration of SD based on the underlying model's learned representations. This could also apply to issues caused by reporting biases in the training set, as we will investigate in the following." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "text", + "content": "Counteracting Bias in Stable Diffusion. Recall the 'ethnic bias' experiments of Sec. 2. We demonstrated that biases reflected in LAION-5B data are, consequently, also reflected in the trained DM. Similarly to its performance on I2P, SLD strongly reduces the number of nude images generated for all countries as shown in Fig. 2 (right). SLD yields " + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "text", + "content": " less explicit content and the percentage of nude images are distributed more evenly between countries. The previous outlier Japan now yields " + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "inline_equation", + "content": "12.0\\%" + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "text", + "content": " of nude content, close to the global percentage of " + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "inline_equation", + "content": "9.25\\%" + }, + { + "bbox": [ + 304, + 326, + 545, + 445 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 446, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 446, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 446, + 545, + 564 + ], + "type": "text", + "content": "Nonetheless, at least with keeping changes minor (Hyp-Strong), SLD alone is not sufficient to mitigate this racial bias entirely. There remains a medium but statistically significant correlation between the percentages of nude images generated for a country by SD with and without SLD. Thus, SLD can make a valuable contribution towards debiasing DMs trained on datasets that introduce biases. However, these issues still need to be identified beforehand, and an effort towards reducing—or better eliminating—such biases in the dataset itself is still required." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 565, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 565, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 565, + 545, + 685 + ], + "type": "text", + "content": "For further evidence, we ran experiments on Stable Diffusion v2.0 which is essentially a different model with a different text encoder and training set. Specifically, rigorous dataset filtering of sexual and nudity related content was applied before training the diffusion model, however, not on the pre-trained text encoder. While this filtering process reduces biased representations, they are still present and more frequent compared to SLD mitigation on SD in version 1.4, cf. Appendix E. Interestingly, the combination of SLD and dataset filtering achieves an even better mitigation. Hence," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "{}^{9}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " Spearman " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "r = {0.52}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " ; Null-hypothesis that both distributions are uncorrelated is rejected at a significance level of " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "p = {0.01}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22528" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "a combination of filtering and SLD could be beneficial and poses an interesting avenue for future work." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 107, + 192, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 107, + 192, + 119 + ], + "spans": [ + { + "bbox": [ + 47, + 107, + 192, + 119 + ], + "type": "text", + "content": "7. Discussion & Limitations" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 127, + 287, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 127, + 287, + 150 + ], + "spans": [ + { + "bbox": [ + 47, + 127, + 287, + 150 + ], + "type": "text", + "content": "Before concluding, let us touch upon ethical implications and future work concerning I2P and the introduced SLD." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 151, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 151, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 151, + 287, + 330 + ], + "type": "text", + "content": "Ethical implications. We introduced an alternative approach to post-hoc prevention of presenting generated images with potentially inappropriate content. Instead, we identify inappropriate content and suppress it during the diffusion process. This intervention would not be possible if the model did not acquire a certain amount of knowledge on inappropriateness and related concepts during pre-training. Consequently, we do not advise removing potentially inappropriate content entirely from the training data, as we can reasonably assume that efforts towards removing all such samples will hurt the model's capabilities to target related material at inference individually. Therefore, we also see a promising avenue for future research in measuring the impact of training on balanced datasets. However, this is likely to require large amounts of manual labor." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 450 + ], + "type": "text", + "content": "Nonetheless, we also demonstrated that highly imbalanced training data could reinforce problematic social phenomena. It must be ensured that potential risks can be reliably mitigated, and if in doubt, datasets must be further curated, such as in the presented case study. Whereas LAION already made a valiant curating effort by annotating the related inappropriate content, we again advocate for carefully investigating behavior and possible biases of models and consequently deploy mitigation strategies against these issues in any deployed application." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 653 + ], + "type": "text", + "content": "We realize that SLD potentially has further ethical implications. Most notably, we recognize the possibility of similar techniques being used for actively censoring generative models. Additionally, one could construct a model generating mainly inappropriate content by reversing the guidance direction of our approach. Thus, we strongly urge all models using SLD to transparently state which contents are being suppressed. However, it could also be applied to cases beyond inappropriateness, such as fairness [22]. Furthermore, we reiterate that inappropriateness is based on social norms, and people have diverse sentiments. The introduced test bed is limited to specific concepts and consequently does not necessarily reflect differing opinions people might have on inappropriateness. Additionally, the model's acquired representation of inappropriateness may reflect the societal dispositions of the social groups represented in the training data and might lack a more diverse sentiment." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 713 + ], + "type": "text", + "content": "Image Fidelity & Text Alignment. Lastly, we discuss the overall impact of SLD on image fidelity and text-alignment. Ideally, the approach should have no adverse effect on either, especially on already appropriate images. In line with previous research on generative text-to-image" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 544, + 148 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 544, + 148 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 544, + 148 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 544, + 148 + ], + "type": "table", + "html": "
ConfigImage FidelityText Alignment
FID-30k ↓User (%) ↑CLIP ↓User (%) ↑
SD14.43-0.75-
Weak15.8163.700.7560.88
Medium16.9062.370.7559.45
Strong18.2863.130.7659.62
Max18.7663.600.7660.58
", + "image_path": "6f5047f79bd15a56b00d3a248bc4def43193c8e3cd89edeb03c5ed578058f78c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 157, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 305, + 157, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 305, + 157, + 545, + 191 + ], + "type": "text", + "content": "Table 2. SLD's image fidelity and text alignment. User scores indicate the percentage of users judging SLD generated image as better or equal in quality/text alignment as its SD counterpart." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 210, + 545, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 210, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 210, + 545, + 331 + ], + "type": "text", + "content": "models, we report the COCO FID-30k scores and CLIP distance of SD, and our four sets of hyper-parameters for SLD in Tab. 2. The scores slightly increase with stronger hyperparameters. However, they do not necessarily align with actual user preference [26]. Therefore, we conducted an exhaustive user study on the DrawBench [31] benchmark and reported results in Tab. 2 (cf. Appendix G for study details). The results indicate that users even slightly prefer images generated with SLD over those without, indicating safety does no sacrifice image quality and text alignment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 340, + 378, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 340, + 378, + 352 + ], + "spans": [ + { + "bbox": [ + 306, + 340, + 378, + 352 + ], + "type": "text", + "content": "8. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 360, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 529 + ], + "type": "text", + "content": "We demonstrated text-to-image models' inappropriate degeneration transfers from unfiltered and imbalanced training datasets. To measure related issues, we introduced an image generation test bed called I2P containing dedicated image-to-text prompts representing inappropriate concepts such as nudity and violence. Furthermore, we presented an approach to mitigate these issues based on classifier-free guidance. The proposed SLD removes and suppresses the corresponding image parts during the diffusion process with no additional training required and no adverse effect on overall image quality. Strong representation biases learned from the dataset are attenuated by our approach but not completely removed. Thus, we advocate for the careful use of unfiltered, clearly imbalanced datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 538, + 403, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 403, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 403, + 551 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "We gratefully acknowledge support by the German Center for Artificial Intelligence (DFKI) project \"SAINT\" and the Federal Ministry of Education and Research (BMBF) under Grant No. 01IS22091. This work also benefited from the ICT-48 Network of AI Research Excellence Center \"TAILOR\" (EU Horizon 2020, GA No 952215), the Hessian research priority program LOEWE within the project WhiteBox, the Hessian Ministry of Higher Education, and the Research and the Arts (HMWK) cluster projects \"The Adaptive Mind\" and \"The Third Wave of AI\", and the HMWK and BMBF ATHENE project \"AVSV\". Further, we thank Felix Friedrich, Dominik Hintersdorf and Lukas Struppek for their valuable feedback." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22529" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Abubakar Abid, Maheen Farooqi, and James Zou. 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Despite the empirical success made by recent works, there still exists several severe challenges. Particularly, previous multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Moreover, existing methods cannot fully explore the consistency of local structures between different views as they uncover the clustering structure in a intraview way instead of a inter-view manner. In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. We model the above concerns in a unified framework and design an efficient algorithm to solve the corresponding optimization problem. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method and verify its superiority over other SOTA approaches.", + "bbox": [ + 76, + 301, + 472, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 665, + 209, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In many real scenarios, data are usually collected from diverse sources in various domains or described by multiple feature sets [1, 2]. A case in point is the image dataset, which can be represented by different visual descriptors, such as LBP, GIST, CENTRIST, HOG, SIFT and Color Moment [3]. Moreover, a document can be written in different languages, and a website can be described by its linkage, page content, etc. These data are generally known as multi-view data [1, 4]. Each view contains partial and complementary information, any of which suffices for learning, and they all together agree to a consensus latent representation [5-7]. Multi-view clustering aims to accurately par", + "bbox": [ + 75, + 691, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tition data into distinct clusters according to their compatible and complementary information embedded in heterogeneous features [1, 8].", + "bbox": [ + 500, + 270, + 890, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In general, multi-view clustering methods can be divided into four categories according to the mechanisms and principles on which these methods are based. [1] initiated the trend of co-training algorithm by first carrying out a co-training strategy and making the clustering results on all view tend to each other as well as satisfying the broadest agreement across all views. Owing to the efficiency of exploiting similarities among multiple views, multi-kernel learning is widely utilized to boost the performance of multi-view clustering methods [9-11]. Multi-task multi-view clustering [12, 13] inherits the property of multitask clustering. Each view of the data is treated with at least one related task. Moreover, inter-task knowledge is transferred from one to another so that the relationship between multi-view and multi-task is fully exploited to improve the clustering outcomes. Another kind of graph-based multiview clustering methods usually attempt to explore an optimal consensus graph across all views, and utilize graph-cut algorithm on the optimal graph to obtain final clustering result [3,5, 14].", + "bbox": [ + 496, + 318, + 892, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A great number of multi-view clustering methods have been proposed and illustrated remarkable empirical successes up to now [15-17]. However, there are still severe drawbacks urgently need to be overcome. For one thing, existing multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Considering that the data sampled from real world typically lie in the nonlinear manifold, data points geometrically far from one to another may keep high consistency when they are linked by a series of consecutive neighbors. For another, they suffer from a coarse-grained problem that ignores the view correlation between samples. Note that redundancy or partial structure mistakes in certain views may lead to a sub-optimal cluster structure. Besides, traditional view-wise fusion strategy would result in a superimposition of redundancies, and hence acquire a more imprecise common cluster structure.", + "bbox": [ + 496, + 625, + 893, + 880 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Regarding the above issues, we propose to exploit the", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23966", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 285, + 220, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Manifold learning has attracted widespread attention in recent decades [18, 19]. A plethora of works are mainly spent on exploring methods for discovering nonlinear low-dimensional manifolds between individuals where the topological relevance can be high [20]. The ability of those algorithms is to learn the manifold structure embedded in the high-dimensional ambient space.", + "bbox": [ + 75, + 310, + 468, + 416 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing studies show that interactions between the instances place heavy reliance on the topological relationship instead of the metric range [21]. That is, a higher cohesion of the aggregation can be maintained by a topological interaction. Therefore, the work in [22] learns the topological relevance between different samples to uncover the hidden structures of the crowded and measure collectiveness. From the perspective of topological space, the relevance between two individuals is high if they are connected by countable neighbors, even though they show low similarity in the spatial scene. It is based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far. In light of this, we replace the most often-used Euclidean distance with a powerful manifold topological relevance to capture the intrinsic structures.", + "bbox": [ + 75, + 416, + 470, + 656 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given a precomputed affinity matrix $\\mathbf{G} = [g_{jk}] \\in \\mathbb{R}^{n \\times n}$ , where $n$ is the number of data samples. Based on the assumption that if two data points keep high consistency, their topological relevance to any other point is assumed to be similar, [22] introduced a structure-based clustering strategy to explore the topological relevance between different samples. The objective function can be defined as", + "bbox": [ + 75, + 657, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {Z}} \\frac {1}{2} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} \\left(z _ {i j} - z _ {i k}\\right) ^ {2} + \\lambda \\| \\mathbf {Z} - \\mathbf {I} \\| _ {F} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 773, + 468, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbf{Z}$ represents the topological relationship graph and the element $z_{ij}$ is the topological relevance of $i$ -th point to $j$ -th point. The first term in Eq. (1), as a smoothness constraint, is incorporated to meet the aforementioned assumption, which ensures that for data points $j$ and $k$ , their", + "bbox": [ + 75, + 824, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1cb4a5026c1049d311dc62bda36aff6af360db784efc6ac24e997d6130959a3b.jpg", + "image_caption": [ + "Figure 1. By concatenating all views to a tensor, we obtain $\\widetilde{\\mathbf{Z}}$ . Rotating the obtained tensor $\\widetilde{\\mathbf{Z}}$ and cutting it vertically, we have the $i$ -th frontal slice $\\widetilde{\\mathbf{Z}}_i$ ." + ], + "image_footnote": [], + "bbox": [ + 504, + 109, + 890, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "topological relevance to point $i$ is assumed to be similar if they have high consistency. The second term in Eq. (1), as a fitting constraint, is used to rule out the trivial solution. We also utilize a weighting coefficient $\\alpha$ to balance the two terms. According to the above form, we detect the consistency by propagating topological relationship, and the relevance between two distant points will be high if they are connected by countable neighbors.", + "bbox": [ + 496, + 321, + 890, + 443 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, the model in Eq. (1) is applied for solving the single-view problem, and it is not suitable for multi-view clustering tasks. In this paper, we propose to explore the manifold topological structure for multi-view data. Given $\\mathbf{G}^{(v)}(v = 1,\\dots ,m)\\in \\mathbb{R}^{n\\times n}$ as the input similarity graphs of multi-view data with $m$ views. Based on Eq. (1), the topological relationship for each view can be measured by", + "bbox": [ + 496, + 443, + 890, + 550 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(z _ {i j} ^ {(v)} - z _ {i k} ^ {(v)}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} \\\\ \\text {s . t .} \\quad \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 558, + 890, + 642 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where all $z_{ij}^{(v)}$ is constrained to be non-negative and the sum of $\\mathbf{z}_i^{(v)}$ is one. Considering that a data point connected with many similar neighbors would largely affect the objective value. We utilize a normalized form of Eq. (2), which is formulated as", + "bbox": [ + 496, + 643, + 890, + 723 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} \\\\ \\text {s . t .} \\quad \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {3} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 729, + 890, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\mathbf{D}^{(v)}$ is the degree matrix of $\\mathbf{G}^{(v)}$ .", + "bbox": [ + 500, + 816, + 771, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. The proposed Methodology", + "text_level": 1, + "bbox": [ + 500, + 844, + 753, + 862 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As aforementioned, existing multi-view clustering methods generally suffer from a coarse-grained problem that ig-", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23967", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "nores the view correlation between samples. To tackle this inappropriate fusion strategy, we design a novel model to explore the intersections of multiple views in the sample level. It is able to capture more intrinsic cross-view consistency and is robust to the inconsistency introduced by certain views. Inspired by [23, 24], here we proposed a transformation on a set of multi-view matrices. As shown in Figure 1, first we start with concatenating all views to a tensor $\\tilde{\\mathbf{Z}}\\in \\mathbb{R}^{n\\times n\\times m}$ . Then we get the $i$ th frontal slice $\\tilde{\\mathbf{Z}}_i\\in \\mathbb{R}^{n\\times m}$ corresponding to the $i$ th sample to explore sample-level manifold information. By conducting such transformation, it is feasible for us to manipulate fuse all views on the sample level as follow:", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {S}} \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Z}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 292, + 468, + 362 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} \\geq 0, \\mathbf {W} \\geq 0, \\mathbf {s} _ {i} ^ {T} \\mathbf {1} = 1, \\mathbf {W} \\mathbf {1} = \\mathbf {1},\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 364, + 390, + 382 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{w}_i^T$ corresponds to the weight of different views with respect to the $i$ -th sample. Each column of $\\mathbf{S}$ integrates the consistent information of one instance across all views. $\\beta$ is the balanced parameter for the penalty term, which is utilized to prevent the trivial solution when a specific view dominates the others. The constraints that we apply to the optimal fusion graph $\\mathbf{S}$ and weight matrix $\\mathbf{W}$ assist to narrow down the solution space and strongly boost the efficiency of our optimization process. Based on the elementary yet intuitive assumption that the topological relevance between instances tends to be propagated from near to far. That is, the individuals have low spatial similarity may achieve high topological relevance if they are linked by the consecutive neighbors. Thus, we explore the similarity between instances on a more appropriate topological manifold structure rather than on the Euclidean structure. With the help of topological manifold exploration in the multiview clustering domain, by combining Eq. (3) and Eq. (4), we can easily derive:", + "bbox": [ + 75, + 388, + 472, + 676 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}, \\mathbf {W}, \\mathbf {S}} \\sum_ {v = 1} ^ {m} \\underbrace {\\frac {1}{2} \\sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2}} _ {\\text {t o p o l o g i c a l r e l e v a n c e l e a n i n g}} \\\\ + \\underbrace {\\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Z}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2}} _ {\\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\end{array} \\\\ \\mathbf {S} \\geq 0, \\mathbf {w} _ {i} \\geq 0, \\mathbf {S} \\mathbf {1} = \\mathbf {1}, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 680, + 472, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Moreover, considering the graph for sample-level graph fusion might be a translation from the topological manifold,", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "we introduce an intermediate variable $\\mathbf{Q}$ to link the topological relevance learning and the sample-level graph fusion. As a result, the joint optimization framework of sample-level multi-view clustering with topological relevance considered can be formulated as:", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\underbrace {\\min _ {\\mathbf {Z} ^ {(v)} , \\mathbf {W} , \\mathbf {S}} \\sum_ {v = 1} ^ {m} \\frac {1}{2} \\sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2}} _ {\\text {t o p o l o g i c a l r e l e v a n c e l e a r n i n g}} \\\\ + \\underbrace {\\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Z} ^ {(v)} - \\mathbf {Q} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2}} _ {\\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\end{array} \\\\ \\mathbf {S} \\geq 0, \\mathbf {w} _ {i} \\geq 0, \\mathbf {S} \\mathbf {1} = \\mathbf {1}, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}, \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 174, + 901, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\gamma$ and $\\alpha$ are trade-off parameters. It is noteworthy that our model in Eq. (6) enjoys several properties that are distinct from existing approaches:", + "bbox": [ + 496, + 364, + 890, + 409 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Instead of performing the inter-view graph fusion, we propose to conducting a cross-view graph fusion process in a sample-wise way. Considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained.", + "- Note that the topological structure is essential for clustering data on manifold. Based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far, we propose to exploit the implied data manifold with the topological relevance considered.", + "- We model the subtasks of topological relevance learning and the sample-level graph fusion in a unified framework, each subtask is alternately boosted towards an optimal solution. An efficient algorithm to solve the corresponding optimization problem is also introduced. Experimental results on several benchmark datasets certificate the effectiveness of our method." + ], + "bbox": [ + 517, + 419, + 890, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Optimization", + "text_level": 1, + "bbox": [ + 500, + 784, + 635, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we design an iterative updating algorithm to solve the optimization problem in Eq. (6). Since it is not jointly convex in all variable s, we propose to optimize the objective function with respect to one variable while fixing other variables. And the procedure repeats until convergence.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23968", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 1: Algorithm to solve Eq. (10)", + "text_level": 1, + "bbox": [ + 88, + 94, + 366, + 109 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: a nonzero matrix $\\mathbf{A}$ and a nonzero vector $\\mathbf{b}$ . Set $1 < \\rho < 2$ , initialize $\\eta > 0$ , $\\mathbf{h}$ .", + "bbox": [ + 96, + 112, + 441, + 142 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: $\\mathbf{Z}^{(v)}$", + "bbox": [ + 98, + 142, + 197, + 157 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: repeat", + "2: Update $\\mathbf{p}$ according to (13).", + "3: Update $\\mathbf{z}_i^{(v)}$ according to (15).", + "4: Update $\\eta \\gets \\rho \\eta$", + "5: Update $\\mathbf{h} \\gets \\mathbf{h} + \\eta \\left(\\mathbf{z}_i^{(v)} - \\mathbf{p}\\right)$ .", + "6: until converge" + ], + "bbox": [ + 107, + 157, + 352, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Update $\\mathbf{Z}^{(v)}$", + "text_level": 1, + "bbox": [ + 96, + 290, + 184, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each $\\mathbf{Z}^{(v)}$ , we need to solve", + "bbox": [ + 96, + 306, + 307, + 321 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} \\\\ + \\lambda \\sum_ {v = 1} ^ {m} \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} + \\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Q} ^ {(v)} - \\mathbf {Z} ^ {(v)} \\| _ {F} ^ {2} \\tag {7} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\end{array} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 330, + 468, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since Eq. (7) is independent for different $v$ , for each $v$ we have", + "bbox": [ + 76, + 468, + 468, + 496 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {i = 1} ^ {n} \\left\\{\\sum_ {j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} \\right. \\\\ \\left. + \\lambda \\sum_ {j = 1} ^ {n} \\left\\| z _ {i j} ^ {(v)} - e _ {i j} \\right\\| _ {F} ^ {2} + \\gamma \\sum_ {j = 1} ^ {n} \\| q _ {i j} ^ {(v)} - z _ {i j} ^ {(v)} \\| _ {F} ^ {2} \\right\\} \\tag {8} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 106, + 506, + 468, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each $i$ , Eq. (8) can be further rewritten in a vector form as", + "bbox": [ + 76, + 643, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\mathbf {z} _ {i} ^ {(v)}} \\sum_ {i = 1} ^ {n} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\left(\\mathbf {I} - \\mathbf {D} ^ {- \\frac {1}{2}} \\mathbf {G} ^ {(v)} \\mathbf {D} ^ {- \\frac {1}{2}}\\right) \\mathbf {z} _ {i} ^ {(v)} \\\\ + \\lambda \\left\\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {e} _ {i} \\right\\| _ {F} ^ {2} + \\gamma \\| \\mathbf {q} _ {i} ^ {(v)} - \\mathbf {z} _ {i} ^ {(v)} \\| _ {F} ^ {2} \\tag {9} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 684, + 468, + 784 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Denote $\\mathbf{A}^{(v)} = (1 + \\lambda +\\gamma)\\mathbf{I} - \\mathbf{D}^{-\\frac{1}{2}}\\mathbf{G}^{(v)}\\mathbf{D}^{-\\frac{1}{2}}$ and $\\mathbf{b} = 2\\lambda \\mathbf{e}_i + 2\\gamma \\mathbf{q}_i^{(v)}$ Eq.9 can be stated as:", + "bbox": [ + 76, + 796, + 468, + 832 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {z} _ {i} ^ {(v)} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 842, + 468, + 882 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 2: Algorithm to solve Eq. (6)", + "text_level": 1, + "bbox": [ + 509, + 94, + 781, + 109 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: A set of similarity graph $\\mathbf{G}^{(v)}$ . $(v = 1,2,\\dots,m)$ Parameter $\\alpha$ , $\\beta$ , $\\lambda$ and $\\gamma$ .", + "bbox": [ + 519, + 113, + 874, + 143 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: Clustering result.", + "bbox": [ + 519, + 145, + 700, + 159 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: repeat", + "2: Update $\\mathbf{Z}^{(v)}$ according to Algorithm 1.", + "3: Update S by solving Eq. (18).", + "4: Update $\\mathbf{W}$ according to Eq. (21).", + "5: Update $\\bar{\\mathbf{Q}}_i$ according to Eq. (24).", + "6: until converge", + "7: Conduct the standard spectral clustering on the optimal graph $\\mathbf{S}$ to obtain the final clustering result." + ], + "bbox": [ + 529, + 161, + 910, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is obvious that Eq. (10) is a quadratic convex optimization problem which can be solved with the classical augmented Lagrangian multiplier (ALM) method [25]. In detail, Eq. (10) can be cracked by tackling its counterpart:", + "bbox": [ + 498, + 316, + 890, + 378 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\mathbf {p} = \\mathbf {z} _ {i} ^ {(v)}} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 388, + 890, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "whose augmented Lagrangian function can be defined as:", + "bbox": [ + 500, + 441, + 879, + 458 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {12} \\\\ + \\frac {\\eta}{2} \\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} \\| _ {2} ^ {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 468, + 890, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the second term in Eq. (12) is a penalty function term which guarantees that $\\mathbf{p} = \\mathbf{z}_i^{(v)}$ , $\\eta$ and $\\mathbf{h}$ are the corresponding penalty coefficient and parameter, respectively.", + "bbox": [ + 498, + 554, + 890, + 601 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that $\\mathbf{p}$ and $\\mathbf{z}_i^{(v)}$ can be iteratively optimized:", + "bbox": [ + 500, + 602, + 826, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1) Update $\\mathbf{p}$ with fixed $\\mathbf{z}_i^{(v)}$ The Lagrange function of Eq. (12) w.r.t. $\\mathbf{p}$ is", + "bbox": [ + 500, + 619, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p} = \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} + \\frac {\\eta}{2} \\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} \\| _ {2} ^ {2} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 662, + 890, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Taking the derivative of $\\mathcal{L}_p$ w.r.t $\\mathbf{p}$ and setting the derivative to zero. Thus, we have:", + "bbox": [ + 498, + 705, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} = \\mathbf {z} _ {i} ^ {(v)} - \\frac {1}{\\eta} \\left(\\left(\\mathbf {A} ^ {(v)}\\right) ^ {T} \\mathbf {z} _ {i} ^ {(v)} + \\mathbf {h}\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 747, + 890, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2) Update $\\mathbf{z}_i^{(v)}$ with fixed $\\mathbf{p}$ . The Lagrange function of Eq. (13) w.r.t. $\\mathbf{z}_i^{(v)}$ can be written as", + "bbox": [ + 498, + 794, + 890, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left. \\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left\\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} + \\frac {\\mathbf {A} ^ {(v)} \\mathbf {p} - \\mathbf {b}}{\\eta} \\right\\| _ {2} ^ {2}, \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 840, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23969", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/22d21c348bc0ab70a39f7545f9858307693d12448f2e1d568032b32961b5cda7.jpg", + "image_caption": [ + "(a) Yale Dataset" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 348, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d2f57ccef162219cbb0106b990c349e89ba40439774d1f58ed45ffb881117021.jpg", + "image_caption": [ + "(b) HW Dataset" + ], + "image_footnote": [], + "bbox": [ + 349, + 88, + 620, + 296 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4da5f95d847d4242a981a039f84674c5716e476d1e3c159498e164ab48d02931.jpg", + "image_caption": [ + "(c) ORL Dataset", + "Figure 2. Sample images of datasets Yale, HW and ORL." + ], + "image_footnote": [], + "bbox": [ + 622, + 88, + 890, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which has a closed-form solution and can be readily achieved by the off-the-shelf optimization algorithm [26].", + "bbox": [ + 76, + 364, + 468, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to the ALM principles [25], $\\eta$ can be magnified increasingly in each iteration, and $\\mathbf{h}$ is updated by $\\mathbf{h} \\gets \\mathbf{h} + \\eta \\left(\\mathbf{z}_i^{(v)} - \\mathbf{h}\\right)$ . The detailed algorithm to solve Eq. (10) is summarized in Algorithm 1.", + "bbox": [ + 76, + 410, + 468, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update S", + "text_level": 1, + "bbox": [ + 96, + 477, + 166, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Drop all unrelated terms of Eq. (6) w.r.t. S, thus we have", + "bbox": [ + 96, + 491, + 468, + 506 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {S}} \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 513, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\text {s . t .} \\mathbf {S} \\geq 0, \\mathbf {S 1} = \\mathbf {1}. \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 556, + 339, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We can reformulate Eq. (16) in a vector form as", + "bbox": [ + 76, + 578, + 393, + 592 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {s} _ {i}} (\\alpha + \\beta) \\mathbf {s} _ {i} \\mathbf {s} _ {i} ^ {T} - 2 \\alpha \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\mathbf {s} _ {i} \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 598, + 468, + 627 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {s . t .} \\mathbf {s} _ {i} \\mathbf {1} = 1, \\mathbf {s} _ {i} \\geq 0.\n$$\n", + "text_format": "latex", + "bbox": [ + 204, + 628, + 339, + 641 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on Eq. (17), we get the following compact formulation", + "bbox": [ + 76, + 648, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {s} _ {i} \\mathbf {1} = 1, \\mathbf {s} _ {i} \\geq 0} \\left\\| \\mathbf {s} _ {i} - \\frac {\\alpha}{\\alpha + \\beta} \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 675, + 468, + 710 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which can be effectively solved by the optimization algorithm proposed in [26].", + "bbox": [ + 76, + 714, + 467, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update W", + "text_level": 1, + "bbox": [ + 96, + 744, + 174, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimizing Eq. (6) w.r.t. $\\mathbf{W}$ is equivalent to solving", + "bbox": [ + 96, + 758, + 441, + 773 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w} _ {i}} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 779, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\text {s . t .} \\mathbf {w} _ {i} \\geq 0, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 811, + 349, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Eq. (19) can be reorganized as", + "bbox": [ + 76, + 835, + 279, + 849 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\mathbf {w} _ {i}} \\left\\| \\mathbf {w} _ {i} ^ {T} \\mathbf {B} _ {i} \\right\\| _ {2} ^ {2} \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 856, + 468, + 886 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\text {s . t .} \\mathbf {w} _ {i} \\geq 0, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 194, + 886, + 349, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{B}_i = \\left(\\mathbf{1}\\mathbf{s}_i^T -\\widetilde{\\mathbf{Q}}_i\\right)\\in \\mathbb{R}^{m\\times n}$", + "bbox": [ + 500, + 362, + 740, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Taking the derivative of Eq. (20) w.r.t $\\mathbf{w}_i$ , it yields", + "bbox": [ + 519, + 383, + 851, + 400 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} _ {i} = \\frac {\\left(\\mathbf {B} _ {i} \\mathbf {B} _ {i} ^ {T}\\right) ^ {- 1} \\mathbf {1}}{\\mathbf {1} ^ {T} \\left(\\mathbf {B} _ {i} \\mathbf {B} _ {i} ^ {T}\\right) ^ {- 1} \\mathbf {1}}. \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 409, + 890, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Update $\\widetilde{\\mathbf{Q}}_i$", + "bbox": [ + 519, + 462, + 598, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fixing all the other irrelevant variables in Eq. (6), we have:", + "bbox": [ + 500, + 479, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\widetilde {\\mathbf {Q}} _ {i}} \\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Z} ^ {(v)} - \\mathbf {Q} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 517, + 890, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Obviously, Eq. (22) is sample-wise independent. Therefore, it can be written as:", + "bbox": [ + 500, + 566, + 888, + 595 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\widetilde {\\mathbf {Q}} _ {i}} \\gamma \\| \\widetilde {\\mathbf {Z}} ^ {(v)} - \\widetilde {\\mathbf {Q}} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 604, + 890, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Naturally, by taking the derivative of Eq. (23), it yields:", + "bbox": [ + 519, + 648, + 883, + 664 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {Q}} _ {i} = \\left(\\gamma \\mathbf {I} + \\alpha \\mathbf {w} _ {i} \\mathbf {w} _ {i} ^ {T}\\right) ^ {- 1} \\left(\\gamma \\widetilde {\\mathbf {Z}} _ {i} + \\alpha \\mathbf {w} _ {i} \\mathbf {s} _ {i} ^ {T}\\right) \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 672, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The detailed algorithm to solve the objective in Eq. (6) is summarized in Algorithm 2.", + "bbox": [ + 500, + 708, + 890, + 738 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 500, + 752, + 624, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section is comprised of four sub-sections: experimental setting, result analysis, robustness analysis and convergence analysis.", + "bbox": [ + 500, + 777, + 890, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experiment Setting", + "text_level": 1, + "bbox": [ + 500, + 832, + 687, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare our proposed method with several multiview clustering methods: Multi-view Spectral Clustering with Co-training strategy(Co-train) [27]. Multi-", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23970", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/888c6e6de62a808115e246414e8a6050905685923de9e5344aedd6ac52257e27.jpg", + "table_caption": [ + "Table 1. The clustering results on 100leaves dataset (%)" + ], + "table_footnote": [], + "table_body": "
MethodACCNMIPurityF-score
Co-train33.21 ± 0.8557.59 ± 0.7336.10 ± 0.8115.88 ± 0.79
Co-reg32.16 ± 0.9358.97 ± 0.8236.00 ± 0.8217.33 ± 0.99
DiMSC48.52 ± 1.5771.24 ± 0.5551.14 ± 1.4133.66 ± 1.17
AMGL77.66 ± 1.5890.35 ± 0.9782.29 ± 1.1659.54 ± 7.04
MVGL54.12 ± 0.0063.96 ± 0.0057.44 ± 0.008.58 ± 0.00
WMSC77.26 ± 0.9989.81 ± 0.4779.62 ± 0.6871.11 ± 1.31
AWP66.13 ± 0.0085.52 ± 0.0068.19 ± 0.0060.75 ± 0.00
MCGC90.25 ± 0.0093.90 ± 0.0091.13 ± 0.0077.79 ± 0.00
LRMSC75.25 ± 1.5687.64 ± 0.5477.60 ± 1.3166.62 ± 1.46
MVCTM68.63 ± 0.0076.46 ± 0.0072.25 ± 0.0016.52 ± 0.00
SMVSC37.94 ± 0.2765.04 ± 0.2939.42 ± 0.2323.22 ± 0.39
FPMVS35.14 ± 0.2063.06 ± 0.4336.96 ± 0.2622.12 ± 0.38
CSMSC76.06 ± 1.1588.83 ± 0.4378.96 ± 0.8168.91 ± 1.25
Ours90.86 ± 0.0196.38 ± 0.0092.46 ± 0.0188.69 ± 0.01
", + "bbox": [ + 81, + 114, + 467, + 297 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5eb060f4be52a1f052724eed7dffcc1c4f62f78d5f36b3368b3dbd6e869b9584.jpg", + "table_caption": [ + "Table 2. The clustering results on HW dataset (%)" + ], + "table_footnote": [], + "table_body": "
MethodACCNMIPurityF-score
Co-train81.28 ± 5.3772.04 ± 2.9882.25 ± 4.1170.93 ± 4.19
Co-reg54.96 ± 4.3547.46 ± 1.9758.64 ± 2.8742.62 ± 2.40
DiMSC46.26 ± 0.4532.97 ± 0.3346.79 ± 0.4727.92 ± 0.27
AMGL93.76 ± 8.5795.02 ± 4.2394.89 ± 6.7893.63 ± 7.16
MVGL85.35 ± 0.0085.19 ± 0.0085.75 ± 0.0082.48 ± 0.00
WMSC74.87 ± 0.1466.79 ± 0.1974.95 ± 0.1663.65 ± 0.22
AWP69.55 ± 0.0059.49 ± 0.0071.45 ± 0.0058.35 ± 0.00
MCGC53.95 ± 0.0061.78 ± 0.0054.10 ± 0.0057.25 ± 0.00
LRMSC79.39 ± 2.9576.49 ± 1.3383.25 ± 1.4772.83 ± 1.89
MVCTM98.75 ± 0.0096.91 ± 0.0098.75 ± 0.0097.52 ± 0.00
SMVSC78.59 ± 0.4669.03 ± 0.5778.90 ± 0.3867.65 ± 0.76
FPMVS78.40 ± 0.1870.88 ± 0.8978.77 ± 0.4169.66 ± 0.85
CSMSC86.87 ± 0.0280.04 ± 0.0986.87 ± 0.0278.05 ± 0.04
Ours99.25 ± 0.0098.15 ± 0.0099.25 ± 0.0098.51 ± 0.00
", + "bbox": [ + 81, + 351, + 467, + 534 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/54fb719f8b056ed4676345333407d8d0ec6e3d653a3d900b2012c1d89df36123.jpg", + "table_caption": [ + "Table 3. The clustering results on MSRC dataset (%)" + ], + "table_footnote": [], + "table_body": "
MethodACCNMIPurityF-score
Co-train64.95 ± 6.2454.27 ± 4.1866.52 ± 5.0052.59 ± 4.97
Co-reg63.95 ± 4.5057.89 ± 2.9967.24 ± 4.4755.31 ± 3.98
DiMSC71.90 ± 0.9559.62 ± 0.9671.90 ± 0.9558.02 ± 1.08
AMGL76.71 ± 4.3370.98 ± 2.2079.00 ± 2.8067.13 ± 2.49
MVGL70.48 ± 0.0058.18 ± 0.0070.48 ± 0.0054.56 ± 0.00
WMSC69.05 ± 0.0059.55 ± 0.1771.43 ± 0.0057.57 ± 0.08
AWP63.33 ± 0.0054.88 ± 0.0063.33 ± 0.0053.76 ± 0.00
MCGC80.48 ± 0.0070.18 ± 0.0080.95 ± 0.0072.46 ± 0.00
LRMSC71.81 ± 2.8962.42 ± 1.5874.14 ± 1.7860.08 ± 1.57
MVCTM85.71 ± 0.0076.15 ± 0.0085.71 ± 0.0074.90 ± 0.00
SMVSC81.43 ± 0.0070.18 ± 0.0081.43 ± 0.0069.36 ± 0.00
FPMVS78.57 ± 0.0066.84 ± 0.0078.57 ± 0.0068.36 ± 0.00
CSMSC80.43 ± 0.1471.36 ± 0.1980.43 ± 0.1470.06 ± 0.21
Ours87.14 ± 0.0078.21 ± 0.0087.14 ± 0.0077.87 ± 0.00
", + "bbox": [ + 81, + 587, + 467, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "view Spectral Clustering with Co-regularized strategy(Coreg) [28]. Diversity-induced Multi-view Subspace Clustering(DiMSC) [14]. Auto-weighted Multiple Graph Learning(AMGL) [29]. Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Graph Learning for Multiview Clustering(MVGL) [30]. Weighted Multi-view Spec", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4d93a7fa51d1616d52e821bdf8805389eaf4812780ba3663131cf1bf27d21be3.jpg", + "table_caption": [ + "Table 4. The clustering results on ORL dataset (%)" + ], + "table_footnote": [], + "table_body": "
MethodACCNMIPurityF-score
Co-train61.90 ± 3.1979.23 ± 1.5865.60 ± 2.2350.88 ± 3.26
Co-reg61.65 ± 2.8179.38 ± 1.6966.22 ± 2.1451.39 ± 3.51
DiMSC80.03 ± 1.7890.63 ± 0.8882.93 ± 1.1774.61 ± 1.91
AMGL73.15 ± 3.2285.59 ± 1.0978.27 ± 2.0158.89 ± 3.62
MVGL49.00 ± 0.0066.30 ± 0.0058.00 ± 0.0018.24 ± 0.00
WMSC76.60 ± 3.7088.26 ± 1.6879.75 ± 2.8569.84 ± 4.38
AWP74.50 ± 0.0086.02 ± 0.0076.25 ± 0.0065.18 ± 0.00
MCGC77.00 ± 0.0087.22 ± 0.0082.75 ± 0.0056.25 ± 0.00
LRMSC79.62 ± 3.0990.49 ± 1.5083.42 ± 2.4673.99 ± 3.96
MVCTM59.50 ± 0.0072.58 ± 0.0066.75 ± 0.0023.98 ± 0.00
SMVSC58.28 ± 0.5176.07 ± 0.1461.75 ± 0.3043.96 ± 0.33
FPMVS55.45 ± 0.5973.72 ± 0.4859.27 ± 0.5641.02 ± 0.69
CSMSC77.57 ± 1.8889.20 ± 0.9580.77 ± 1.7871.69 ± 2.58
Ours84.35 ± 0.0291.78 ± 0.0186.45 ± 0.0178.58 ± 0.02
", + "bbox": [ + 504, + 114, + 890, + 297 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3d63c0f20a2bfb78d4833178c8ec3b43a47cf4f0676538050affeddd2913bb8b.jpg", + "table_caption": [ + "Table 5. The clustering results on Cornell dataset (%)" + ], + "table_footnote": [], + "table_body": "
MethodACCNMIPurityF-score
Co-train41.38 ± 1.6722.36 ± 1.4354.26 ± 1.9034.86 ± 0.90
Co-reg36.26 ± 2.0013.68 ± 1.4547.28 ± 1.7731.98 ± 1.41
DiMSC40.15 ± 1.7617.95 ± 0.8252.77 ± 0.6734.58 ± 0.57
AMGL37.38 ± 4.444.26 ± 0.3744.82 ± 0.3437.24 ± 3.51
MVGL44.10 ± 0.009.42 ± 0.0045.64 ± 0.0038.10 ± 0.00
WMSC46.10 ± 0.1521.69 ± 0.1752.26 ± 0.1537.24 ± 0.12
AWP38.97 ± 0.0013.63 ± 0.0049.74 ± 0.0033.72 ± 0.00
MCGC36.41 ± 0.0022.60 ± 0.0053.85 ± 0.0033.79 ± 0.00
LRMSC34.77 ± 1.628.51 ± 1.4843.95 ± 0.7628.99 ± 0.72
MVCTM40.00 ± 0.0015.20 ± 0.0051.79 ± 0.0036.89 ± 0.00
SMVSC48.67 ± 2.2120.61 ± 1.3653.90 ± 0.8742.14 ± 2.28
FPMVS35.90 ± 0.0017.67 ± 0.0053.33 ± 0.0033.20 ± 0.00
CSMSC47.33 ± 0.3323.86 ± 0.3655.49 ± 0.2137.87 ± 0.37
Ours51.28 ± 0.0034.81 ± 0.0061.03 ± 0.0042.03 ± 0.00
", + "bbox": [ + 504, + 351, + 890, + 534 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d118cec81692441f97be6e44bb99df6cf8571e6f778b72a5fece0288365becae.jpg", + "table_caption": [ + "Table 6. The clustering results on Yale dataset(%)" + ], + "table_footnote": [], + "table_body": "
MethodACCNMIPurityF-score
Co-train53.94 ± 4.2157.90 ± 3.1455.52 ± 4.1138.68 ± 3.72
Co-reg56.36 ± 3.4960.30 ± 3.0557.64 ± 3.2541.43 ± 3.79
DiMSC64.36 ± 3.4066.57 ± 2.3064.79 ± 3.2249.41 ± 2.90
AMGL59.94 ± 3.6462.95 ± 2.7861.33 ± 2.9341.87 ± 4.18
MVGL44.85 ± 0.0049.19 ± 0.0046.67 ± 0.0026.05 ± 0.00
WMSC61.88 ± 3.6465.40 ± 2.8962.12 ± 3.8448.08 ± 3.53
AWP61.82 ± 0.0065.77 ± 0.0061.82 ± 0.0049.71 ± 0.00
MCGC67.27 ± 0.0068.92 ± 0.0067.27 ± 0.0048.33 ± 0.00
LRMSC68.36 ± 1.1170.36 ± 1.1168.55 ± 1.1052.27 ± 1.67
MVCTM62.42 ± 0.0066.14 ± 0.0062.42 ± 0.0047.40 ± 0.00
SMVSC60.36 ± 0.9562.23 ± 1.3760.73 ± 0.8943.05 ± 1.51
FPMVS44.24 ± 0.0049.76 ± 0.0046.67 ± 0.0030.45 ± 0.00
CSMSC64.06 ± 2.9168.22 ± 1.4964.12 ± 2.8051.84 ± 1.76
Ours71.03 ± 0.0174.51 ± 0.0171.21 ± 0.0059.72 ± 0.01
", + "bbox": [ + 504, + 587, + 890, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tral Clustering(WMSC) [31]. multi-view clustering via Adaptively Weighted Procrustes(AWP) [32]. Multi-view Consensus Graph Clustering(MCGC) [33]. Generalized Latent Multi-View Subspace Clustering(LRMSC) [34]. Multi-view Clustering on Topological Manifold(MVCTM) Fast Parameter-free Multi-view Subspace Clustering with", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23971", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0fdb392acd97236fcb18ff73e57f74026cac470babee7b7f9597ab05fa04ac3f.jpg", + "image_caption": [ + "(a) $\\lambda = 0.1\\gamma = 1$" + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 269, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2ebf8e12641a830a0f4c827b7a54442a04780f4c7340ba9541deee9cd0f3c304.jpg", + "image_caption": [ + "(b) $\\lambda = 0.1\\gamma = 10$" + ], + "image_footnote": [], + "bbox": [ + 285, + 88, + 475, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/73ed1ce0935cae64310e263241063e876e567dc049b27ce7f84c4d34789cdde4.jpg", + "image_caption": [ + "(c) $\\lambda = 0.1\\gamma = 100$" + ], + "image_footnote": [], + "bbox": [ + 495, + 93, + 684, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f651be0eec55ca69ca876203abd4228a7119cf51574eb9a5624da59ee0c0112f.jpg", + "image_caption": [ + "(d) $\\lambda = 0.1\\gamma = 1000$" + ], + "image_footnote": [], + "bbox": [ + 702, + 93, + 885, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/afbe596d644cebb4f365d65059a0ea543f260b9db8506259d30b6d18a9afb8d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 255, + 267, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5e5560aa1fd3fe3c2b91e65763ec94fa13948384d56516a1be04d3a71a04cb69.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 255, + 475, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c3e3aeee0b7700ad405fda70aac732573db14f2f627fcaa5db57850271d2650.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 253, + 684, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ca434ed9d07540f1ee725187b74ebbb2f3cb7ce0f9e7be903b8f5343b955035c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 253, + 892, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/feac0b069b4a75d71a22b7510c43d77105ac027033ce521fe548cc02da6ad471.jpg", + "image_caption": [ + "(e) $\\lambda = 1\\gamma = 1$", + "(i) $\\lambda = 10\\gamma = 1$" + ], + "image_footnote": [], + "bbox": [ + 80, + 410, + 269, + 553 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a08a2ea86dcad88b56599cb6290169e392f7209b0d50f196ae829a6f1b9f11b5.jpg", + "image_caption": [ + "(f) $\\lambda = 1\\gamma = 10$", + "(j) $\\lambda = 10\\gamma = 10$" + ], + "image_footnote": [], + "bbox": [ + 287, + 410, + 475, + 551 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/90e0a0c66b0f6f7be5bba803b4c40c6f4bd3a81d6f4b6805ee39d9e38f82fdcc.jpg", + "image_caption": [ + "(g) $\\lambda = 1\\gamma = 100$", + "(k) $\\lambda = 10\\gamma = 100$", + "Figure 3. Parameter analysis on ORL dataset" + ], + "image_footnote": [], + "bbox": [ + 495, + 411, + 681, + 553 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9020ad258edb20934530cf07cca5d400adb24090e6222aca540250a9a0a5c4a3.jpg", + "image_caption": [ + "(h) $\\lambda = 1\\gamma = 1000$", + "(1) $\\lambda = 10\\gamma = 1000$" + ], + "image_footnote": [], + "bbox": [ + 702, + 411, + 892, + 553 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Consensus Anchor Guidance(FPMVS) [35]. Multi-view Subspace Clustering with Unified Anchors(SMVSC) [36] Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Rather than adopting view-wise weighing strategy like the above mentioned methods, we delicately conduct graph fusion in a sample-wise manner. Thus, the superiority of our proposed approach could be demonstrated in the experiment section.", + "bbox": [ + 75, + 622, + 468, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As for benchmark datasets, we adopt 100leaves, HW, MRSC, ORL, Cornell and Yale. Specifically, the leaves data set (100leaves) consists of 1,600 leaves from each of 100 plant species. For each sample, margin, shape and texture are given as three distinct views. Handwritten numerals data (HW) is composed of 2,000 data points for digits 0 to 9 from UCI machine learning repository and two public features are available. MSRC data set contains 210 images and can be separated into 7 classes including cow, airplane, face, bicycle, tree, building and car. There are five visual", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "features from each sample. ORL consists of 400 face images in 40 different themes in total. For each subject, the images are described in three features: facial expressions, facial details and the lighting. Cornell, which is collected by Cornell University, contains 195 web pages and a web page is made of 2 views: content features and cites features. Dataset Yale contains 165 gray-scale images under varying poses and illuminations, where every image is of size $64 \\times 64$ .", + "bbox": [ + 496, + 622, + 890, + 756 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Result Analysis", + "text_level": 1, + "bbox": [ + 500, + 770, + 653, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "With the aim of evaluating our proposed approach adequately with above mentioned SOTA multi-view clustering methods, we adopt four widely used criteria including Normalized Mutual Information(NMI), Accuracy(ACC), Purity and F-Score. The clustering results are reported in Tables (1)-(6). We can arrive at a conclusion that our method is very effective and competitive as the proposed method", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23972", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e8f0b201d3df08c0636a77391bb7187a03ca87a17f449eabfe85ec1d551d16c7.jpg", + "image_caption": [ + "(a) 100Leaves" + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 330, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0426e7d9d9cd6ea122f8b9c6c4160166281524a66374f0c3dfbb38a558940054.jpg", + "image_caption": [ + "(b) HW" + ], + "image_footnote": [], + "bbox": [ + 351, + 89, + 599, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7a0eece39ecd5433321674c975ec85f37052ffc9cb9691634e58c2220e94d129.jpg", + "image_caption": [ + "(c) ORL" + ], + "image_footnote": [], + "bbox": [ + 622, + 90, + 870, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aaa0019e6eee2d09ca0dae7f508ab9ff4d777f3454bda01b9f0056f7187d491e.jpg", + "image_caption": [ + "(d) MSRC" + ], + "image_footnote": [], + "bbox": [ + 80, + 231, + 328, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/26c9fa83f15e07797a668a093c4151b00f23e9c2dd810dede791c53dd67edab1.jpg", + "image_caption": [ + "(e) Yale" + ], + "image_footnote": [], + "bbox": [ + 352, + 231, + 599, + 354 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04e3a3242593ddb16fe881ef07582a3bb8f7e1b115afaf3c4a830284d6c5f489.jpg", + "image_caption": [ + "(f) Cornell", + "Figure 4. Convergence curves on all datasets" + ], + "image_footnote": [], + "bbox": [ + 624, + 231, + 870, + 354 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "outperforms other competitors in the majority of cases. In detail, our method consistently obtains the best results in terms of NMI, ACC and Purity on all datasets. While for F-score, the proposed method surpasses the compared methods except in one case on dataset Cornell. The superiority of our method explicitly demonstrates the effectiveness of the sample-wise learning strategy and corroborates our theoretical findings.", + "bbox": [ + 75, + 422, + 468, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Parameter Discussion", + "text_level": 1, + "bbox": [ + 76, + 554, + 279, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With the aim of studying what impact different parameter settings will have on the clustering results, we vary $\\alpha$ , $\\beta$ , $\\lambda$ and $\\gamma$ in the ranges $[1e^{-4},\\dots,1e^{4}]$ , $[1e^{-4},\\dots,1e^{4}]$ , $[1e^{-1},\\dots,1e^{2}]$ and $[1,\\dots,1e^{3}]$ , respectively. Taking the ORL dataset as an example, we can see the clustering performance is quite stable with respect to different parameter settings, as shown in Figure (3). Considering that there is little difference among the performances of diverse parameter combinations, we can come to a conclusion that our approach is robust to the hyper parameters.", + "bbox": [ + 75, + 578, + 468, + 731 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Convergence Analysis", + "text_level": 1, + "bbox": [ + 76, + 741, + 282, + 757 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Owing to the fact that the optimization of our proposed method is essentially a non-convex problem that is solved by an iterative algorithm, it is critical to validate the convergence of our model. Therefore, this section empirically showcases the convergence property and how fast our algorithm can converge. The convergence curves of our model on six datasets shown in Fig. (4) demonstrate the effectiveness of our optimization approach. Note that despite the non-convexity of Eq. (6), our model can still discover an", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "optimal solution for each variable and achieve a local minima within a few iterations, which verifies the effectiveness of the proposed optimization algorithm.", + "bbox": [ + 498, + 422, + 890, + 468 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 484, + 617, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. We also design an efficient algorithm to solve the corresponding optimization problem. Meanwhile, our method generates outstanding results on several authoritative benchmark datasets and is proven to outperform current state-of-the-art methods. In the future, we are interested in extending the proposed model to other machine learning framework such as kernel learning and deep learning.", + "bbox": [ + 496, + 511, + 890, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 784, + 666, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by the Key Program of National Science Foundation of China (Grant No. 61836006), partially supported by the National Science Foundation of China under Grant 62106164, and the Sichuan Science and Technology Program under Grants 2021ZDZX0011 and 2022YFG0188.", + "bbox": [ + 496, + 809, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23973", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Steffen Bickel and Tobias Scheffer. 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In Proceedings of the 29th ACM International Conference on Multimedia, pages 3528-3536, 2021. 7" + ], + "bbox": [ + 78, + 90, + 468, + 598 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23975", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Sample-Level Multi-View Graph Clustering/2dbc917c-e6ba-403e-80e3-a2fe15c249a2_model.json b/2023/Sample-Level Multi-View Graph Clustering/2dbc917c-e6ba-403e-80e3-a2fe15c249a2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..df20625557e7a8f40dcea18bc9253da25c57adb5 --- /dev/null +++ b/2023/Sample-Level Multi-View Graph Clustering/2dbc917c-e6ba-403e-80e3-a2fe15c249a2_model.json @@ -0,0 +1,2728 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.27, + 0.131, + 0.703, + 0.154 + ], + "angle": 0, + "content": "Sample-level Multi-view Graph Clustering" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.181, + 0.744, + 0.218 + ], + "angle": 0, + "content": "Yuze Tan, Yixi Liu, Shudong Huang*, Wentao Feng, Jiancheng Lv Sichuan University" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.22, + 0.816, + 0.235 + ], + "angle": 0, + "content": "{tanyuze,liuyixi}@stu.scu.edu.cn,{huangsd,Wtfeng2021,lvjiancheng}@scu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.473, + 0.635 + ], + "angle": 0, + "content": "Multi-view clustering has hitherto been studied due to their effectiveness in dealing with heterogeneous data. Despite the empirical success made by recent works, there still exists several severe challenges. Particularly, previous multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Moreover, existing methods cannot fully explore the consistency of local structures between different views as they uncover the clustering structure in a intraview way instead of a inter-view manner. In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. We model the above concerns in a unified framework and design an efficient algorithm to solve the corresponding optimization problem. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method and verify its superiority over other SOTA approaches." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.666, + 0.21, + 0.683 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.471, + 0.875 + ], + "angle": 0, + "content": "In many real scenarios, data are usually collected from diverse sources in various domains or described by multiple feature sets [1, 2]. A case in point is the image dataset, which can be represented by different visual descriptors, such as LBP, GIST, CENTRIST, HOG, SIFT and Color Moment [3]. Moreover, a document can be written in different languages, and a website can be described by its linkage, page content, etc. These data are generally known as multi-view data [1, 4]. Each view contains partial and complementary information, any of which suffices for learning, and they all together agree to a consensus latent representation [5-7]. Multi-view clustering aims to accurately par" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.271, + 0.892, + 0.317 + ], + "angle": 0, + "content": "tition data into distinct clusters according to their compatible and complementary information embedded in heterogeneous features [1, 8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.893, + 0.621 + ], + "angle": 0, + "content": "In general, multi-view clustering methods can be divided into four categories according to the mechanisms and principles on which these methods are based. [1] initiated the trend of co-training algorithm by first carrying out a co-training strategy and making the clustering results on all view tend to each other as well as satisfying the broadest agreement across all views. Owing to the efficiency of exploiting similarities among multiple views, multi-kernel learning is widely utilized to boost the performance of multi-view clustering methods [9-11]. Multi-task multi-view clustering [12, 13] inherits the property of multitask clustering. Each view of the data is treated with at least one related task. Moreover, inter-task knowledge is transferred from one to another so that the relationship between multi-view and multi-task is fully exploited to improve the clustering outcomes. Another kind of graph-based multiview clustering methods usually attempt to explore an optimal consensus graph across all views, and utilize graph-cut algorithm on the optimal graph to obtain final clustering result [3,5, 14]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.895, + 0.881 + ], + "angle": 0, + "content": "A great number of multi-view clustering methods have been proposed and illustrated remarkable empirical successes up to now [15-17]. However, there are still severe drawbacks urgently need to be overcome. For one thing, existing multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Considering that the data sampled from real world typically lie in the nonlinear manifold, data points geometrically far from one to another may keep high consistency when they are linked by a series of consecutive neighbors. For another, they suffer from a coarse-grained problem that ignores the view correlation between samples. Note that redundancy or partial structure mistakes in certain views may lead to a sub-optimal cluster structure. Besides, traditional view-wise fusion strategy would result in a superimposition of redundancies, and hence acquire a more imprecise common cluster structure." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Regarding the above issues, we propose to exploit the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23966" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.286, + 0.221, + 0.303 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.47, + 0.417 + ], + "angle": 0, + "content": "Manifold learning has attracted widespread attention in recent decades [18, 19]. A plethora of works are mainly spent on exploring methods for discovering nonlinear low-dimensional manifolds between individuals where the topological relevance can be high [20]. The ability of those algorithms is to learn the manifold structure embedded in the high-dimensional ambient space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.471, + 0.657 + ], + "angle": 0, + "content": "Existing studies show that interactions between the instances place heavy reliance on the topological relationship instead of the metric range [21]. That is, a higher cohesion of the aggregation can be maintained by a topological interaction. Therefore, the work in [22] learns the topological relevance between different samples to uncover the hidden structures of the crowded and measure collectiveness. From the perspective of topological space, the relevance between two individuals is high if they are connected by countable neighbors, even though they show low similarity in the spatial scene. It is based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far. In light of this, we replace the most often-used Euclidean distance with a powerful manifold topological relevance to capture the intrinsic structures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.765 + ], + "angle": 0, + "content": "Given a precomputed affinity matrix \\(\\mathbf{G} = [g_{jk}] \\in \\mathbb{R}^{n \\times n}\\), where \\(n\\) is the number of data samples. Based on the assumption that if two data points keep high consistency, their topological relevance to any other point is assumed to be similar, [22] introduced a structure-based clustering strategy to explore the topological relevance between different samples. The objective function can be defined as" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.775, + 0.47, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {Z}} \\frac {1}{2} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} \\left(z _ {i j} - z _ {i k}\\right) ^ {2} + \\lambda \\| \\mathbf {Z} - \\mathbf {I} \\| _ {F} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathbf{Z}\\) represents the topological relationship graph and the element \\(z_{ij}\\) is the topological relevance of \\(i\\)-th point to \\(j\\)-th point. The first term in Eq. (1), as a smoothness constraint, is incorporated to meet the aforementioned assumption, which ensures that for data points \\(j\\) and \\(k\\), their" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.11, + 0.891, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.255, + 0.892, + 0.298 + ], + "angle": 0, + "content": "Figure 1. By concatenating all views to a tensor, we obtain \\(\\widetilde{\\mathbf{Z}}\\). Rotating the obtained tensor \\(\\widetilde{\\mathbf{Z}}\\) and cutting it vertically, we have the \\(i\\)-th frontal slice \\(\\widetilde{\\mathbf{Z}}_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.323, + 0.892, + 0.444 + ], + "angle": 0, + "content": "topological relevance to point \\( i \\) is assumed to be similar if they have high consistency. The second term in Eq. (1), as a fitting constraint, is used to rule out the trivial solution. We also utilize a weighting coefficient \\( \\alpha \\) to balance the two terms. According to the above form, we detect the consistency by propagating topological relationship, and the relevance between two distant points will be high if they are connected by countable neighbors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.551 + ], + "angle": 0, + "content": "However, the model in Eq. (1) is applied for solving the single-view problem, and it is not suitable for multi-view clustering tasks. In this paper, we propose to explore the manifold topological structure for multi-view data. Given \\(\\mathbf{G}^{(v)}(v = 1,\\dots ,m)\\in \\mathbb{R}^{n\\times n}\\) as the input similarity graphs of multi-view data with \\(m\\) views. Based on Eq. (1), the topological relationship for each view can be measured by" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.559, + 0.891, + 0.643 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(z _ {i j} ^ {(v)} - z _ {i k} ^ {(v)}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} \\\\ \\text {s . t .} \\quad \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.724 + ], + "angle": 0, + "content": "where all \\(z_{ij}^{(v)}\\) is constrained to be non-negative and the sum of \\(\\mathbf{z}_i^{(v)}\\) is one. Considering that a data point connected with many similar neighbors would largely affect the objective value. We utilize a normalized form of Eq. (2), which is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.731, + 0.891, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} \\\\ \\text {s . t .} \\quad \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {3} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.817, + 0.772, + 0.833 + ], + "angle": 0, + "content": "where \\(\\mathbf{D}^{(v)}\\) is the degree matrix of \\(\\mathbf{G}^{(v)}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.754, + 0.863 + ], + "angle": 0, + "content": "3. The proposed Methodology" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "As aforementioned, existing multi-view clustering methods generally suffer from a coarse-grained problem that ig-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23967" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "nores the view correlation between samples. To tackle this inappropriate fusion strategy, we design a novel model to explore the intersections of multiple views in the sample level. It is able to capture more intrinsic cross-view consistency and is robust to the inconsistency introduced by certain views. Inspired by [23, 24], here we proposed a transformation on a set of multi-view matrices. As shown in Figure 1, first we start with concatenating all views to a tensor \\(\\tilde{\\mathbf{Z}}\\in \\mathbb{R}^{n\\times n\\times m}\\). Then we get the \\(i\\) th frontal slice \\(\\tilde{\\mathbf{Z}}_i\\in \\mathbb{R}^{n\\times m}\\) corresponding to the \\(i\\) th sample to explore sample-level manifold information. By conducting such transformation, it is feasible for us to manipulate fuse all views on the sample level as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.293, + 0.469, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {S}} \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Z}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.366, + 0.392, + 0.383 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} \\geq 0, \\mathbf {W} \\geq 0, \\mathbf {s} _ {i} ^ {T} \\mathbf {1} = 1, \\mathbf {W} \\mathbf {1} = \\mathbf {1},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.389, + 0.473, + 0.678 + ], + "angle": 0, + "content": "where \\(\\mathbf{w}_i^T\\) corresponds to the weight of different views with respect to the \\(i\\)-th sample. Each column of \\(\\mathbf{S}\\) integrates the consistent information of one instance across all views. \\(\\beta\\) is the balanced parameter for the penalty term, which is utilized to prevent the trivial solution when a specific view dominates the others. The constraints that we apply to the optimal fusion graph \\(\\mathbf{S}\\) and weight matrix \\(\\mathbf{W}\\) assist to narrow down the solution space and strongly boost the efficiency of our optimization process. Based on the elementary yet intuitive assumption that the topological relevance between instances tends to be propagated from near to far. That is, the individuals have low spatial similarity may achieve high topological relevance if they are linked by the consecutive neighbors. Thus, we explore the similarity between instances on a more appropriate topological manifold structure rather than on the Euclidean structure. With the help of topological manifold exploration in the multiview clustering domain, by combining Eq. (3) and Eq. (4), we can easily derive:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.681, + 0.473, + 0.871 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}, \\mathbf {W}, \\mathbf {S}} \\sum_ {v = 1} ^ {m} \\underbrace {\\frac {1}{2} \\sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2}} _ {\\text {t o p o l o g i c a l r e l e v a n c e l e a n i n g}} \\\\ + \\underbrace {\\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Z}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2}} _ {\\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\end{array} \\\\ \\mathbf {S} \\geq 0, \\mathbf {w} _ {i} \\geq 0, \\mathbf {S} \\mathbf {1} = \\mathbf {1}, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Moreover, considering the graph for sample-level graph fusion might be a translation from the topological manifold," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "we introduce an intermediate variable \\(\\mathbf{Q}\\) to link the topological relevance learning and the sample-level graph fusion. As a result, the joint optimization framework of sample-level multi-view clustering with topological relevance considered can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.175, + 0.902, + 0.363 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\underbrace {\\min _ {\\mathbf {Z} ^ {(v)} , \\mathbf {W} , \\mathbf {S}} \\sum_ {v = 1} ^ {m} \\frac {1}{2} \\sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2}} _ {\\text {t o p o l o g i c a l r e l e v a n c e l e a r n i n g}} \\\\ + \\underbrace {\\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Z} ^ {(v)} - \\mathbf {Q} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2}} _ {\\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\end{array} \\\\ \\mathbf {S} \\geq 0, \\mathbf {w} _ {i} \\geq 0, \\mathbf {S} \\mathbf {1} = \\mathbf {1}, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}, \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.892, + 0.41 + ], + "angle": 0, + "content": "where \\(\\gamma\\) and \\(\\alpha\\) are trade-off parameters. It is noteworthy that our model in Eq. (6) enjoys several properties that are distinct from existing approaches:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.42, + 0.892, + 0.541 + ], + "angle": 0, + "content": "- Instead of performing the inter-view graph fusion, we propose to conducting a cross-view graph fusion process in a sample-wise way. Considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.55, + 0.892, + 0.642 + ], + "angle": 0, + "content": "- Note that the topological structure is essential for clustering data on manifold. Based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far, we propose to exploit the implied data manifold with the topological relevance considered." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.651, + 0.892, + 0.77 + ], + "angle": 0, + "content": "- We model the subtasks of topological relevance learning and the sample-level graph fusion in a unified framework, each subtask is alternately boosted towards an optimal solution. An efficient algorithm to solve the corresponding optimization problem is also introduced. Experimental results on several benchmark datasets certificate the effectiveness of our method." + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.42, + 0.892, + 0.77 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.637, + 0.803 + ], + "angle": 0, + "content": "4. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we design an iterative updating algorithm to solve the optimization problem in Eq. (6). Since it is not jointly convex in all variable s, we propose to optimize the objective function with respect to one variable while fixing other variables. And the procedure repeats until convergence." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23968" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.089, + 0.095, + 0.367, + 0.111 + ], + "angle": 0, + "content": "Algorithm 1: Algorithm to solve Eq. (10)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.113, + 0.442, + 0.143 + ], + "angle": 0, + "content": "Input: a nonzero matrix \\(\\mathbf{A}\\) and a nonzero vector \\(\\mathbf{b}\\). Set \\(1 < \\rho < 2\\), initialize \\(\\eta > 0\\), \\(\\mathbf{h}\\)." + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.143, + 0.199, + 0.158 + ], + "angle": 0, + "content": "Output: \\(\\mathbf{Z}^{(v)}\\)" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.159, + 0.175, + 0.172 + ], + "angle": 0, + "content": "1: repeat" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.173, + 0.328, + 0.188 + ], + "angle": 0, + "content": "2: Update \\(\\mathbf{p}\\) according to (13)." + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.188, + 0.343, + 0.206 + ], + "angle": 0, + "content": "3: Update \\(\\mathbf{z}_i^{(v)}\\) according to (15)." + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.206, + 0.253, + 0.221 + ], + "angle": 0, + "content": "4: Update \\(\\eta \\gets \\rho \\eta\\)" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.221, + 0.354, + 0.244 + ], + "angle": 0, + "content": "5: Update \\(\\mathbf{h} \\gets \\mathbf{h} + \\eta \\left(\\mathbf{z}_i^{(v)} - \\mathbf{p}\\right)\\)." + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.244, + 0.225, + 0.258 + ], + "angle": 0, + "content": "6: until converge" + }, + { + "type": "list", + "bbox": [ + 0.108, + 0.159, + 0.354, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.097, + 0.291, + 0.186, + 0.307 + ], + "angle": 0, + "content": "Update \\(\\mathbf{Z}^{(v)}\\)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.307, + 0.308, + 0.322 + ], + "angle": 0, + "content": "For each \\(\\mathbf{Z}^{(v)}\\), we need to solve" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.332, + 0.469, + 0.459 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} \\\\ + \\lambda \\sum_ {v = 1} ^ {m} \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} + \\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Q} ^ {(v)} - \\mathbf {Z} ^ {(v)} \\| _ {F} ^ {2} \\tag {7} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\end{array} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.469, + 0.469, + 0.497 + ], + "angle": 0, + "content": "Since Eq. (7) is independent for different \\( v \\), for each \\( v \\) we have" + }, + { + "type": "equation", + "bbox": [ + 0.107, + 0.507, + 0.469, + 0.635 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {i = 1} ^ {n} \\left\\{\\sum_ {j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} \\right. \\\\ \\left. + \\lambda \\sum_ {j = 1} ^ {n} \\left\\| z _ {i j} ^ {(v)} - e _ {i j} \\right\\| _ {F} ^ {2} + \\gamma \\sum_ {j = 1} ^ {n} \\| q _ {i j} ^ {(v)} - z _ {i j} ^ {(v)} \\| _ {F} ^ {2} \\right\\} \\tag {8} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.645, + 0.469, + 0.674 + ], + "angle": 0, + "content": "For each \\(i\\), Eq. (8) can be further rewritten in a vector form as" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.685, + 0.469, + 0.785 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\mathbf {z} _ {i} ^ {(v)}} \\sum_ {i = 1} ^ {n} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\left(\\mathbf {I} - \\mathbf {D} ^ {- \\frac {1}{2}} \\mathbf {G} ^ {(v)} \\mathbf {D} ^ {- \\frac {1}{2}}\\right) \\mathbf {z} _ {i} ^ {(v)} \\\\ + \\lambda \\left\\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {e} _ {i} \\right\\| _ {F} ^ {2} + \\gamma \\| \\mathbf {q} _ {i} ^ {(v)} - \\mathbf {z} _ {i} ^ {(v)} \\| _ {F} ^ {2} \\tag {9} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.797, + 0.469, + 0.833 + ], + "angle": 0, + "content": "Denote \\(\\mathbf{A}^{(v)} = (1 + \\lambda +\\gamma)\\mathbf{I} - \\mathbf{D}^{-\\frac{1}{2}}\\mathbf{G}^{(v)}\\mathbf{D}^{-\\frac{1}{2}}\\) and \\(\\mathbf{b} = 2\\lambda \\mathbf{e}_i + 2\\gamma \\mathbf{q}_i^{(v)}\\) Eq.9 can be stated as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.843, + 0.469, + 0.883 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {z} _ {i} ^ {(v)} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.511, + 0.095, + 0.782, + 0.111 + ], + "angle": 0, + "content": "Algorithm 2: Algorithm to solve Eq. (6)" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.114, + 0.875, + 0.145 + ], + "angle": 0, + "content": "Input: A set of similarity graph \\(\\mathbf{G}^{(v)}\\). \\((v = 1,2,\\dots,m)\\) Parameter \\(\\alpha\\), \\(\\beta\\), \\(\\lambda\\) and \\(\\gamma\\)." + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.146, + 0.701, + 0.16 + ], + "angle": 0, + "content": "Output: Clustering result." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.162, + 0.597, + 0.175 + ], + "angle": 0, + "content": "1: repeat" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.176, + 0.821, + 0.19 + ], + "angle": 0, + "content": "2: Update \\(\\mathbf{Z}^{(v)}\\) according to Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.191, + 0.764, + 0.206 + ], + "angle": 0, + "content": "3: Update S by solving Eq. (18)." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.206, + 0.785, + 0.221 + ], + "angle": 0, + "content": "4: Update \\(\\mathbf{W}\\) according to Eq. (21)." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.221, + 0.785, + 0.236 + ], + "angle": 0, + "content": "5: Update \\(\\bar{\\mathbf{Q}}_i\\) according to Eq. (24)." + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.237, + 0.647, + 0.251 + ], + "angle": 0, + "content": "6: until converge" + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.252, + 0.911, + 0.281 + ], + "angle": 0, + "content": "7: Conduct the standard spectral clustering on the optimal graph \\(\\mathbf{S}\\) to obtain the final clustering result." + }, + { + "type": "list", + "bbox": [ + 0.531, + 0.162, + 0.911, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.317, + 0.892, + 0.379 + ], + "angle": 0, + "content": "It is obvious that Eq. (10) is a quadratic convex optimization problem which can be solved with the classical augmented Lagrangian multiplier (ALM) method [25]. In detail, Eq. (10) can be cracked by tackling its counterpart:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.389, + 0.891, + 0.442 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\mathbf {p} = \\mathbf {z} _ {i} ^ {(v)}} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.443, + 0.88, + 0.459 + ], + "angle": 0, + "content": "whose augmented Lagrangian function can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.469, + 0.891, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {12} \\\\ + \\frac {\\eta}{2} \\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} \\| _ {2} ^ {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.892, + 0.602 + ], + "angle": 0, + "content": "where the second term in Eq. (12) is a penalty function term which guarantees that \\(\\mathbf{p} = \\mathbf{z}_i^{(v)}\\), \\(\\eta\\) and \\(\\mathbf{h}\\) are the corresponding penalty coefficient and parameter, respectively." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.603, + 0.827, + 0.62 + ], + "angle": 0, + "content": "Note that \\(\\mathbf{p}\\) and \\(\\mathbf{z}_i^{(v)}\\) can be iteratively optimized:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.621, + 0.892, + 0.653 + ], + "angle": 0, + "content": "1) Update \\(\\mathbf{p}\\) with fixed \\(\\mathbf{z}_i^{(v)}\\) The Lagrange function of Eq. (12) w.r.t. \\(\\mathbf{p}\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.531, + 0.664, + 0.891, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p} = \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} + \\frac {\\eta}{2} \\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} \\| _ {2} ^ {2} \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.707, + 0.891, + 0.736 + ], + "angle": 0, + "content": "Taking the derivative of \\(\\mathcal{L}_p\\) w.r.t \\(\\mathbf{p}\\) and setting the derivative to zero. Thus, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.748, + 0.891, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} = \\mathbf {z} _ {i} ^ {(v)} - \\frac {1}{\\eta} \\left(\\left(\\mathbf {A} ^ {(v)}\\right) ^ {T} \\mathbf {z} _ {i} ^ {(v)} + \\mathbf {h}\\right) \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.831 + ], + "angle": 0, + "content": "2) Update \\(\\mathbf{z}_i^{(v)}\\) with fixed \\(\\mathbf{p}\\). The Lagrange function of Eq. (13) w.r.t. \\(\\mathbf{z}_i^{(v)}\\) can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.842, + 0.891, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\left. \\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left\\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} + \\frac {\\mathbf {A} ^ {(v)} \\mathbf {p} - \\mathbf {b}}{\\eta} \\right\\| _ {2} ^ {2}, \\right. \\tag {15}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23969" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.349, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.171, + 0.3, + 0.258, + 0.311 + ], + "angle": 0, + "content": "(a) Yale Dataset" + }, + { + "type": "image", + "bbox": [ + 0.351, + 0.089, + 0.621, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.443, + 0.3, + 0.528, + 0.31 + ], + "angle": 0, + "content": "(b) HW Dataset" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.089, + 0.892, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.3, + 0.801, + 0.311 + ], + "angle": 0, + "content": "(c) ORL Dataset" + }, + { + "type": "image_caption", + "bbox": [ + 0.314, + 0.324, + 0.655, + 0.338 + ], + "angle": 0, + "content": "Figure 2. Sample images of datasets Yale, HW and ORL." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.365, + 0.47, + 0.397 + ], + "angle": 0, + "content": "which has a closed-form solution and can be readily achieved by the off-the-shelf optimization algorithm [26]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.411, + 0.469, + 0.477 + ], + "angle": 0, + "content": "According to the ALM principles [25], \\(\\eta\\) can be magnified increasingly in each iteration, and \\(\\mathbf{h}\\) is updated by \\(\\mathbf{h} \\gets \\mathbf{h} + \\eta \\left(\\mathbf{z}_i^{(v)} - \\mathbf{h}\\right)\\). The detailed algorithm to solve Eq. (10) is summarized in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.097, + 0.478, + 0.168, + 0.492 + ], + "angle": 0, + "content": "Update S" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.492, + 0.469, + 0.507 + ], + "angle": 0, + "content": "Drop all unrelated terms of Eq. (6) w.r.t. S, thus we have" + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.514, + 0.469, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {S}} \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2} \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.557, + 0.34, + 0.571 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\text {s . t .} \\mathbf {S} \\geq 0, \\mathbf {S 1} = \\mathbf {1}. \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.579, + 0.395, + 0.593 + ], + "angle": 0, + "content": "We can reformulate Eq. (16) in a vector form as" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.599, + 0.469, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {s} _ {i}} (\\alpha + \\beta) \\mathbf {s} _ {i} \\mathbf {s} _ {i} ^ {T} - 2 \\alpha \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\mathbf {s} _ {i} \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.205, + 0.629, + 0.341, + 0.642 + ], + "angle": 0, + "content": "\\[\n\\mathrm {s . t .} \\mathbf {s} _ {i} \\mathbf {1} = 1, \\mathbf {s} _ {i} \\geq 0.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.65, + 0.469, + 0.677 + ], + "angle": 0, + "content": "Based on Eq. (17), we get the following compact formulation" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.676, + 0.469, + 0.712 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {s} _ {i} \\mathbf {1} = 1, \\mathbf {s} _ {i} \\geq 0} \\left\\| \\mathbf {s} _ {i} - \\frac {\\alpha}{\\alpha + \\beta} \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.468, + 0.744 + ], + "angle": 0, + "content": "which can be effectively solved by the optimization algorithm proposed in [26]." + }, + { + "type": "title", + "bbox": [ + 0.097, + 0.745, + 0.176, + 0.758 + ], + "angle": 0, + "content": "Update W" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.759, + 0.442, + 0.774 + ], + "angle": 0, + "content": "Optimizing Eq. (6) w.r.t. \\(\\mathbf{W}\\) is equivalent to solving" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.78, + 0.469, + 0.812 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w} _ {i}} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.813, + 0.35, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\text {s . t .} \\mathbf {w} _ {i} \\geq 0, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.836, + 0.281, + 0.851 + ], + "angle": 0, + "content": "Eq. (19) can be reorganized as" + }, + { + "type": "equation", + "bbox": [ + 0.222, + 0.857, + 0.469, + 0.887 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\mathbf {w} _ {i}} \\left\\| \\mathbf {w} _ {i} ^ {T} \\mathbf {B} _ {i} \\right\\| _ {2} ^ {2} \\tag {20}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.196, + 0.887, + 0.351, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\text {s . t .} \\mathbf {w} _ {i} \\geq 0, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.363, + 0.741, + 0.386 + ], + "angle": 0, + "content": "where \\(\\mathbf{B}_i = \\left(\\mathbf{1}\\mathbf{s}_i^T -\\widetilde{\\mathbf{Q}}_i\\right)\\in \\mathbb{R}^{m\\times n}\\)" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.385, + 0.852, + 0.401 + ], + "angle": 0, + "content": "Taking the derivative of Eq. (20) w.r.t \\(\\mathbf{w}_i\\), it yields" + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.41, + 0.891, + 0.452 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} _ {i} = \\frac {\\left(\\mathbf {B} _ {i} \\mathbf {B} _ {i} ^ {T}\\right) ^ {- 1} \\mathbf {1}}{\\mathbf {1} ^ {T} \\left(\\mathbf {B} _ {i} \\mathbf {B} _ {i} ^ {T}\\right) ^ {- 1} \\mathbf {1}}. \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.463, + 0.599, + 0.48 + ], + "angle": 0, + "content": "Update \\(\\widetilde{\\mathbf{Q}}_i\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.48, + 0.891, + 0.509 + ], + "angle": 0, + "content": "Fixing all the other irrelevant variables in Eq. (6), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.518, + 0.891, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\widetilde {\\mathbf {Q}} _ {i}} \\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Z} ^ {(v)} - \\mathbf {Q} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.567, + 0.89, + 0.596 + ], + "angle": 0, + "content": "Obviously, Eq. (22) is sample-wise independent. Therefore, it can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.606, + 0.891, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\widetilde {\\mathbf {Q}} _ {i}} \\gamma \\| \\widetilde {\\mathbf {Z}} ^ {(v)} - \\widetilde {\\mathbf {Q}} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.649, + 0.885, + 0.665 + ], + "angle": 0, + "content": "Naturally, by taking the derivative of Eq. (23), it yields:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.674, + 0.891, + 0.701 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {Q}} _ {i} = \\left(\\gamma \\mathbf {I} + \\alpha \\mathbf {w} _ {i} \\mathbf {w} _ {i} ^ {T}\\right) ^ {- 1} \\left(\\gamma \\widetilde {\\mathbf {Z}} _ {i} + \\alpha \\mathbf {w} _ {i} \\mathbf {s} _ {i} ^ {T}\\right) \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.709, + 0.891, + 0.739 + ], + "angle": 0, + "content": "The detailed algorithm to solve the objective in Eq. (6) is summarized in Algorithm 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.753, + 0.625, + 0.769 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.779, + 0.891, + 0.824 + ], + "angle": 0, + "content": "This section is comprised of four sub-sections: experimental setting, result analysis, robustness analysis and convergence analysis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.688, + 0.849 + ], + "angle": 0, + "content": "5.1. Experiment Setting" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "We compare our proposed method with several multiview clustering methods: Multi-view Spectral Clustering with Co-training strategy(Co-train) [27]. Multi-" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23970" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.107, + 0.09, + 0.44, + 0.104 + ], + "angle": 0, + "content": "Table 1. The clustering results on 100leaves dataset (%)" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.115, + 0.468, + 0.298 + ], + "angle": 0, + "content": "
MethodACCNMIPurityF-score
Co-train33.21 ± 0.8557.59 ± 0.7336.10 ± 0.8115.88 ± 0.79
Co-reg32.16 ± 0.9358.97 ± 0.8236.00 ± 0.8217.33 ± 0.99
DiMSC48.52 ± 1.5771.24 ± 0.5551.14 ± 1.4133.66 ± 1.17
AMGL77.66 ± 1.5890.35 ± 0.9782.29 ± 1.1659.54 ± 7.04
MVGL54.12 ± 0.0063.96 ± 0.0057.44 ± 0.008.58 ± 0.00
WMSC77.26 ± 0.9989.81 ± 0.4779.62 ± 0.6871.11 ± 1.31
AWP66.13 ± 0.0085.52 ± 0.0068.19 ± 0.0060.75 ± 0.00
MCGC90.25 ± 0.0093.90 ± 0.0091.13 ± 0.0077.79 ± 0.00
LRMSC75.25 ± 1.5687.64 ± 0.5477.60 ± 1.3166.62 ± 1.46
MVCTM68.63 ± 0.0076.46 ± 0.0072.25 ± 0.0016.52 ± 0.00
SMVSC37.94 ± 0.2765.04 ± 0.2939.42 ± 0.2323.22 ± 0.39
FPMVS35.14 ± 0.2063.06 ± 0.4336.96 ± 0.2622.12 ± 0.38
CSMSC76.06 ± 1.1588.83 ± 0.4378.96 ± 0.8168.91 ± 1.25
Ours90.86 ± 0.0196.38 ± 0.0092.46 ± 0.0188.69 ± 0.01
" + }, + { + "type": "table_caption", + "bbox": [ + 0.124, + 0.326, + 0.424, + 0.34 + ], + "angle": 0, + "content": "Table 2. The clustering results on HW dataset (%)" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.352, + 0.468, + 0.535 + ], + "angle": 0, + "content": "
MethodACCNMIPurityF-score
Co-train81.28 ± 5.3772.04 ± 2.9882.25 ± 4.1170.93 ± 4.19
Co-reg54.96 ± 4.3547.46 ± 1.9758.64 ± 2.8742.62 ± 2.40
DiMSC46.26 ± 0.4532.97 ± 0.3346.79 ± 0.4727.92 ± 0.27
AMGL93.76 ± 8.5795.02 ± 4.2394.89 ± 6.7893.63 ± 7.16
MVGL85.35 ± 0.0085.19 ± 0.0085.75 ± 0.0082.48 ± 0.00
WMSC74.87 ± 0.1466.79 ± 0.1974.95 ± 0.1663.65 ± 0.22
AWP69.55 ± 0.0059.49 ± 0.0071.45 ± 0.0058.35 ± 0.00
MCGC53.95 ± 0.0061.78 ± 0.0054.10 ± 0.0057.25 ± 0.00
LRMSC79.39 ± 2.9576.49 ± 1.3383.25 ± 1.4772.83 ± 1.89
MVCTM98.75 ± 0.0096.91 ± 0.0098.75 ± 0.0097.52 ± 0.00
SMVSC78.59 ± 0.4669.03 ± 0.5778.90 ± 0.3867.65 ± 0.76
FPMVS78.40 ± 0.1870.88 ± 0.8978.77 ± 0.4169.66 ± 0.85
CSMSC86.87 ± 0.0280.04 ± 0.0986.87 ± 0.0278.05 ± 0.04
Ours99.25 ± 0.0098.15 ± 0.0099.25 ± 0.0098.51 ± 0.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.562, + 0.432, + 0.576 + ], + "angle": 0, + "content": "Table 3. The clustering results on MSRC dataset (%)" + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.588, + 0.468, + 0.77 + ], + "angle": 0, + "content": "
MethodACCNMIPurityF-score
Co-train64.95 ± 6.2454.27 ± 4.1866.52 ± 5.0052.59 ± 4.97
Co-reg63.95 ± 4.5057.89 ± 2.9967.24 ± 4.4755.31 ± 3.98
DiMSC71.90 ± 0.9559.62 ± 0.9671.90 ± 0.9558.02 ± 1.08
AMGL76.71 ± 4.3370.98 ± 2.2079.00 ± 2.8067.13 ± 2.49
MVGL70.48 ± 0.0058.18 ± 0.0070.48 ± 0.0054.56 ± 0.00
WMSC69.05 ± 0.0059.55 ± 0.1771.43 ± 0.0057.57 ± 0.08
AWP63.33 ± 0.0054.88 ± 0.0063.33 ± 0.0053.76 ± 0.00
MCGC80.48 ± 0.0070.18 ± 0.0080.95 ± 0.0072.46 ± 0.00
LRMSC71.81 ± 2.8962.42 ± 1.5874.14 ± 1.7860.08 ± 1.57
MVCTM85.71 ± 0.0076.15 ± 0.0085.71 ± 0.0074.90 ± 0.00
SMVSC81.43 ± 0.0070.18 ± 0.0081.43 ± 0.0069.36 ± 0.00
FPMVS78.57 ± 0.0066.84 ± 0.0078.57 ± 0.0068.36 ± 0.00
CSMSC80.43 ± 0.1471.36 ± 0.1980.43 ± 0.1470.06 ± 0.21
Ours87.14 ± 0.0078.21 ± 0.0087.14 ± 0.0077.87 ± 0.00
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "view Spectral Clustering with Co-regularized strategy(Coreg) [28]. Diversity-induced Multi-view Subspace Clustering(DiMSC) [14]. Auto-weighted Multiple Graph Learning(AMGL) [29]. Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Graph Learning for Multiview Clustering(MVGL) [30]. Weighted Multi-view Spec" + }, + { + "type": "table_caption", + "bbox": [ + 0.543, + 0.09, + 0.849, + 0.104 + ], + "angle": 0, + "content": "Table 4. The clustering results on ORL dataset (%)" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.115, + 0.892, + 0.298 + ], + "angle": 0, + "content": "
MethodACCNMIPurityF-score
Co-train61.90 ± 3.1979.23 ± 1.5865.60 ± 2.2350.88 ± 3.26
Co-reg61.65 ± 2.8179.38 ± 1.6966.22 ± 2.1451.39 ± 3.51
DiMSC80.03 ± 1.7890.63 ± 0.8882.93 ± 1.1774.61 ± 1.91
AMGL73.15 ± 3.2285.59 ± 1.0978.27 ± 2.0158.89 ± 3.62
MVGL49.00 ± 0.0066.30 ± 0.0058.00 ± 0.0018.24 ± 0.00
WMSC76.60 ± 3.7088.26 ± 1.6879.75 ± 2.8569.84 ± 4.38
AWP74.50 ± 0.0086.02 ± 0.0076.25 ± 0.0065.18 ± 0.00
MCGC77.00 ± 0.0087.22 ± 0.0082.75 ± 0.0056.25 ± 0.00
LRMSC79.62 ± 3.0990.49 ± 1.5083.42 ± 2.4673.99 ± 3.96
MVCTM59.50 ± 0.0072.58 ± 0.0066.75 ± 0.0023.98 ± 0.00
SMVSC58.28 ± 0.5176.07 ± 0.1461.75 ± 0.3043.96 ± 0.33
FPMVS55.45 ± 0.5973.72 ± 0.4859.27 ± 0.5641.02 ± 0.69
CSMSC77.57 ± 1.8889.20 ± 0.9580.77 ± 1.7871.69 ± 2.58
Ours84.35 ± 0.0291.78 ± 0.0186.45 ± 0.0178.58 ± 0.02
" + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.326, + 0.857, + 0.34 + ], + "angle": 0, + "content": "Table 5. The clustering results on Cornell dataset (%)" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.352, + 0.892, + 0.535 + ], + "angle": 0, + "content": "
MethodACCNMIPurityF-score
Co-train41.38 ± 1.6722.36 ± 1.4354.26 ± 1.9034.86 ± 0.90
Co-reg36.26 ± 2.0013.68 ± 1.4547.28 ± 1.7731.98 ± 1.41
DiMSC40.15 ± 1.7617.95 ± 0.8252.77 ± 0.6734.58 ± 0.57
AMGL37.38 ± 4.444.26 ± 0.3744.82 ± 0.3437.24 ± 3.51
MVGL44.10 ± 0.009.42 ± 0.0045.64 ± 0.0038.10 ± 0.00
WMSC46.10 ± 0.1521.69 ± 0.1752.26 ± 0.1537.24 ± 0.12
AWP38.97 ± 0.0013.63 ± 0.0049.74 ± 0.0033.72 ± 0.00
MCGC36.41 ± 0.0022.60 ± 0.0053.85 ± 0.0033.79 ± 0.00
LRMSC34.77 ± 1.628.51 ± 1.4843.95 ± 0.7628.99 ± 0.72
MVCTM40.00 ± 0.0015.20 ± 0.0051.79 ± 0.0036.89 ± 0.00
SMVSC48.67 ± 2.2120.61 ± 1.3653.90 ± 0.8742.14 ± 2.28
FPMVS35.90 ± 0.0017.67 ± 0.0053.33 ± 0.0033.20 ± 0.00
CSMSC47.33 ± 0.3323.86 ± 0.3655.49 ± 0.2137.87 ± 0.37
Ours51.28 ± 0.0034.81 ± 0.0061.03 ± 0.0042.03 ± 0.00
" + }, + { + "type": "table_caption", + "bbox": [ + 0.548, + 0.562, + 0.845, + 0.576 + ], + "angle": 0, + "content": "Table 6. The clustering results on Yale dataset(%)" + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.588, + 0.892, + 0.77 + ], + "angle": 0, + "content": "
MethodACCNMIPurityF-score
Co-train53.94 ± 4.2157.90 ± 3.1455.52 ± 4.1138.68 ± 3.72
Co-reg56.36 ± 3.4960.30 ± 3.0557.64 ± 3.2541.43 ± 3.79
DiMSC64.36 ± 3.4066.57 ± 2.3064.79 ± 3.2249.41 ± 2.90
AMGL59.94 ± 3.6462.95 ± 2.7861.33 ± 2.9341.87 ± 4.18
MVGL44.85 ± 0.0049.19 ± 0.0046.67 ± 0.0026.05 ± 0.00
WMSC61.88 ± 3.6465.40 ± 2.8962.12 ± 3.8448.08 ± 3.53
AWP61.82 ± 0.0065.77 ± 0.0061.82 ± 0.0049.71 ± 0.00
MCGC67.27 ± 0.0068.92 ± 0.0067.27 ± 0.0048.33 ± 0.00
LRMSC68.36 ± 1.1170.36 ± 1.1168.55 ± 1.1052.27 ± 1.67
MVCTM62.42 ± 0.0066.14 ± 0.0062.42 ± 0.0047.40 ± 0.00
SMVSC60.36 ± 0.9562.23 ± 1.3760.73 ± 0.8943.05 ± 1.51
FPMVS44.24 ± 0.0049.76 ± 0.0046.67 ± 0.0030.45 ± 0.00
CSMSC64.06 ± 2.9168.22 ± 1.4964.12 ± 2.8051.84 ± 1.76
Ours71.03 ± 0.0174.51 ± 0.0171.21 ± 0.0059.72 ± 0.01
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "tral Clustering(WMSC) [31]. multi-view clustering via Adaptively Weighted Procrustes(AWP) [32]. Multi-view Consensus Graph Clustering(MCGC) [33]. Generalized Latent Multi-View Subspace Clustering(LRMSC) [34]. Multi-view Clustering on Topological Manifold(MVCTM) Fast Parameter-free Multi-view Subspace Clustering with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23971" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.27, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.24, + 0.225, + 0.252 + ], + "angle": 0, + "content": "(a) \\(\\lambda = 0.1\\gamma = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.287, + 0.089, + 0.477, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.328, + 0.24, + 0.436, + 0.252 + ], + "angle": 0, + "content": "(b) \\(\\lambda = 0.1\\gamma = 10\\)" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.094, + 0.685, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.24, + 0.647, + 0.252 + ], + "angle": 0, + "content": "(c) \\(\\lambda = 0.1\\gamma = 100\\)" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.094, + 0.887, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.738, + 0.24, + 0.858, + 0.252 + ], + "angle": 0, + "content": "(d) \\(\\lambda = 0.1\\gamma = 1000\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.256, + 0.269, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.399, + 0.218, + 0.41 + ], + "angle": 0, + "content": "(e) \\(\\lambda = 1\\gamma = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.256, + 0.476, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.335, + 0.399, + 0.43, + 0.41 + ], + "angle": 0, + "content": "(f) \\(\\lambda = 1\\gamma = 10\\)" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.255, + 0.685, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.538, + 0.399, + 0.641, + 0.411 + ], + "angle": 0, + "content": "(g) \\(\\lambda = 1\\gamma = 100\\)" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.255, + 0.893, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.399, + 0.853, + 0.41 + ], + "angle": 0, + "content": "(h) \\(\\lambda = 1\\gamma = 1000\\)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.411, + 0.27, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.128, + 0.558, + 0.22, + 0.57 + ], + "angle": 0, + "content": "(i) \\(\\lambda = 10\\gamma = 1\\)" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.411, + 0.477, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.332, + 0.558, + 0.432, + 0.57 + ], + "angle": 0, + "content": "(j) \\(\\lambda = 10\\gamma = 10\\)" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.412, + 0.683, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.558, + 0.645, + 0.57 + ], + "angle": 0, + "content": "(k) \\(\\lambda = 10\\gamma = 100\\)" + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.412, + 0.893, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.558, + 0.854, + 0.57 + ], + "angle": 0, + "content": "(1) \\(\\lambda = 10\\gamma = 1000\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.583, + 0.619, + 0.596 + ], + "angle": 0, + "content": "Figure 3. Parameter analysis on ORL dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.469, + 0.744 + ], + "angle": 0, + "content": "Consensus Anchor Guidance(FPMVS) [35]. Multi-view Subspace Clustering with Unified Anchors(SMVSC) [36] Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Rather than adopting view-wise weighing strategy like the above mentioned methods, we delicately conduct graph fusion in a sample-wise manner. Thus, the superiority of our proposed approach could be demonstrated in the experiment section." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "As for benchmark datasets, we adopt 100leaves, HW, MRSC, ORL, Cornell and Yale. Specifically, the leaves data set (100leaves) consists of 1,600 leaves from each of 100 plant species. For each sample, margin, shape and texture are given as three distinct views. Handwritten numerals data (HW) is composed of 2,000 data points for digits 0 to 9 from UCI machine learning repository and two public features are available. MSRC data set contains 210 images and can be separated into 7 classes including cow, airplane, face, bicycle, tree, building and car. There are five visual" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.757 + ], + "angle": 0, + "content": "features from each sample. ORL consists of 400 face images in 40 different themes in total. For each subject, the images are described in three features: facial expressions, facial details and the lighting. Cornell, which is collected by Cornell University, contains 195 web pages and a web page is made of 2 views: content features and cites features. Dataset Yale contains 165 gray-scale images under varying poses and illuminations, where every image is of size \\(64 \\times 64\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.655, + 0.787 + ], + "angle": 0, + "content": "5.2. Result Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With the aim of evaluating our proposed approach adequately with above mentioned SOTA multi-view clustering methods, we adopt four widely used criteria including Normalized Mutual Information(NMI), Accuracy(ACC), Purity and F-Score. The clustering results are reported in Tables (1)-(6). We can arrive at a conclusion that our method is very effective and competitive as the proposed method" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23972" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.331, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.176, + 0.218, + 0.252, + 0.229 + ], + "angle": 0, + "content": "(a) 100Leaves" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.09, + 0.6, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.218, + 0.507, + 0.229 + ], + "angle": 0, + "content": "(b) HW" + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.091, + 0.871, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.218, + 0.78, + 0.229 + ], + "angle": 0, + "content": "(c) ORL" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.232, + 0.33, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.186, + 0.359, + 0.243, + 0.37 + ], + "angle": 0, + "content": "(d) MSRC" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.232, + 0.6, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.359, + 0.508, + 0.37 + ], + "angle": 0, + "content": "(e) Yale" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.232, + 0.871, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.728, + 0.359, + 0.785, + 0.37 + ], + "angle": 0, + "content": "(f) Cornell" + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.382, + 0.618, + 0.397 + ], + "angle": 0, + "content": "Figure 4. Convergence curves on all datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.47, + 0.543 + ], + "angle": 0, + "content": "outperforms other competitors in the majority of cases. In detail, our method consistently obtains the best results in terms of NMI, ACC and Purity on all datasets. While for F-score, the proposed method surpasses the compared methods except in one case on dataset Cornell. The superiority of our method explicitly demonstrates the effectiveness of the sample-wise learning strategy and corroborates our theoretical findings." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.555, + 0.281, + 0.57 + ], + "angle": 0, + "content": "5.3. Parameter Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.579, + 0.469, + 0.732 + ], + "angle": 0, + "content": "With the aim of studying what impact different parameter settings will have on the clustering results, we vary \\(\\alpha\\), \\(\\beta\\), \\(\\lambda\\) and \\(\\gamma\\) in the ranges \\([1e^{-4},\\dots,1e^{4}]\\), \\([1e^{-4},\\dots,1e^{4}]\\), \\([1e^{-1},\\dots,1e^{2}]\\) and \\([1,\\dots,1e^{3}]\\), respectively. Taking the ORL dataset as an example, we can see the clustering performance is quite stable with respect to different parameter settings, as shown in Figure (3). Considering that there is little difference among the performances of diverse parameter combinations, we can come to a conclusion that our approach is robust to the hyper parameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.283, + 0.758 + ], + "angle": 0, + "content": "5.4. Convergence Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Owing to the fact that the optimization of our proposed method is essentially a non-convex problem that is solved by an iterative algorithm, it is critical to validate the convergence of our model. Therefore, this section empirically showcases the convergence property and how fast our algorithm can converge. The convergence curves of our model on six datasets shown in Fig. (4) demonstrate the effectiveness of our optimization approach. Note that despite the non-convexity of Eq. (6), our model can still discover an" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.424, + 0.892, + 0.469 + ], + "angle": 0, + "content": "optimal solution for each variable and achieve a local minima within a few iterations, which verifies the effectiveness of the proposed optimization algorithm." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.619, + 0.5 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.768 + ], + "angle": 0, + "content": "In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. We also design an efficient algorithm to solve the corresponding optimization problem. Meanwhile, our method generates outstanding results on several authoritative benchmark datasets and is proven to outperform current state-of-the-art methods. In the future, we are interested in extending the proposed model to other machine learning framework such as kernel learning and deep learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.667, + 0.801 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.9 + ], + "angle": 0, + "content": "This work is supported by the Key Program of National Science Foundation of China (Grant No. 61836006), partially supported by the National Science Foundation of China under Grant 62106164, and the Sichuan Science and Technology Program under Grants 2021ZDZX0011 and 2022YFG0188." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23973" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Steffen Bickel and Tobias Scheffer. 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In Proceedings of the 29th ACM International Conference on Multimedia, pages 3528-3536, 2021. 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.599 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23975" + } + ] +] \ No newline at end of file diff --git a/2023/Sample-Level Multi-View Graph Clustering/2dbc917c-e6ba-403e-80e3-a2fe15c249a2_origin.pdf b/2023/Sample-Level Multi-View Graph Clustering/2dbc917c-e6ba-403e-80e3-a2fe15c249a2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d0b2f6c4ba15e9ba536e6aab44d86fc7187e3ac8 --- /dev/null +++ b/2023/Sample-Level Multi-View Graph Clustering/2dbc917c-e6ba-403e-80e3-a2fe15c249a2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1033a7b583872e281f87ead3374d6ce098931b137c37550ef187c054e16a1a7d +size 1783608 diff --git a/2023/Sample-Level Multi-View Graph Clustering/full.md b/2023/Sample-Level Multi-View Graph Clustering/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d29e6d32dd6b3a91acac4c2b9c3aae7c1f6d01c3 --- /dev/null +++ b/2023/Sample-Level Multi-View Graph Clustering/full.md @@ -0,0 +1,440 @@ +# Sample-level Multi-view Graph Clustering + +Yuze Tan, Yixi Liu, Shudong Huang*, Wentao Feng, Jiancheng Lv Sichuan University + +{tanyuze,liuyixi}@stu.scu.edu.cn,{huangsd,Wtfeng2021,lvjiancheng}@scu.edu.cn + +# Abstract + +Multi-view clustering has hitherto been studied due to their effectiveness in dealing with heterogeneous data. Despite the empirical success made by recent works, there still exists several severe challenges. Particularly, previous multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Moreover, existing methods cannot fully explore the consistency of local structures between different views as they uncover the clustering structure in a intraview way instead of a inter-view manner. In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. We model the above concerns in a unified framework and design an efficient algorithm to solve the corresponding optimization problem. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method and verify its superiority over other SOTA approaches. + +# 1. Introduction + +In many real scenarios, data are usually collected from diverse sources in various domains or described by multiple feature sets [1, 2]. A case in point is the image dataset, which can be represented by different visual descriptors, such as LBP, GIST, CENTRIST, HOG, SIFT and Color Moment [3]. Moreover, a document can be written in different languages, and a website can be described by its linkage, page content, etc. These data are generally known as multi-view data [1, 4]. Each view contains partial and complementary information, any of which suffices for learning, and they all together agree to a consensus latent representation [5-7]. Multi-view clustering aims to accurately par + +tition data into distinct clusters according to their compatible and complementary information embedded in heterogeneous features [1, 8]. + +In general, multi-view clustering methods can be divided into four categories according to the mechanisms and principles on which these methods are based. [1] initiated the trend of co-training algorithm by first carrying out a co-training strategy and making the clustering results on all view tend to each other as well as satisfying the broadest agreement across all views. Owing to the efficiency of exploiting similarities among multiple views, multi-kernel learning is widely utilized to boost the performance of multi-view clustering methods [9-11]. Multi-task multi-view clustering [12, 13] inherits the property of multitask clustering. Each view of the data is treated with at least one related task. Moreover, inter-task knowledge is transferred from one to another so that the relationship between multi-view and multi-task is fully exploited to improve the clustering outcomes. Another kind of graph-based multiview clustering methods usually attempt to explore an optimal consensus graph across all views, and utilize graph-cut algorithm on the optimal graph to obtain final clustering result [3,5, 14]. + +A great number of multi-view clustering methods have been proposed and illustrated remarkable empirical successes up to now [15-17]. However, there are still severe drawbacks urgently need to be overcome. For one thing, existing multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Considering that the data sampled from real world typically lie in the nonlinear manifold, data points geometrically far from one to another may keep high consistency when they are linked by a series of consecutive neighbors. For another, they suffer from a coarse-grained problem that ignores the view correlation between samples. Note that redundancy or partial structure mistakes in certain views may lead to a sub-optimal cluster structure. Besides, traditional view-wise fusion strategy would result in a superimposition of redundancies, and hence acquire a more imprecise common cluster structure. + +Regarding the above issues, we propose to exploit the + +implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method. + +# 2. Related Work + +Manifold learning has attracted widespread attention in recent decades [18, 19]. A plethora of works are mainly spent on exploring methods for discovering nonlinear low-dimensional manifolds between individuals where the topological relevance can be high [20]. The ability of those algorithms is to learn the manifold structure embedded in the high-dimensional ambient space. + +Existing studies show that interactions between the instances place heavy reliance on the topological relationship instead of the metric range [21]. That is, a higher cohesion of the aggregation can be maintained by a topological interaction. Therefore, the work in [22] learns the topological relevance between different samples to uncover the hidden structures of the crowded and measure collectiveness. From the perspective of topological space, the relevance between two individuals is high if they are connected by countable neighbors, even though they show low similarity in the spatial scene. It is based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far. In light of this, we replace the most often-used Euclidean distance with a powerful manifold topological relevance to capture the intrinsic structures. + +Given a precomputed affinity matrix $\mathbf{G} = [g_{jk}] \in \mathbb{R}^{n \times n}$ , where $n$ is the number of data samples. Based on the assumption that if two data points keep high consistency, their topological relevance to any other point is assumed to be similar, [22] introduced a structure-based clustering strategy to explore the topological relevance between different samples. The objective function can be defined as + +$$ +\min _ {\mathbf {Z}} \frac {1}{2} \sum_ {i, j, k = 1} ^ {n} g _ {j k} \left(z _ {i j} - z _ {i k}\right) ^ {2} + \lambda \| \mathbf {Z} - \mathbf {I} \| _ {F} ^ {2}, \tag {1} +$$ + +where $\mathbf{Z}$ represents the topological relationship graph and the element $z_{ij}$ is the topological relevance of $i$ -th point to $j$ -th point. The first term in Eq. (1), as a smoothness constraint, is incorporated to meet the aforementioned assumption, which ensures that for data points $j$ and $k$ , their + +![](images/1cb4a5026c1049d311dc62bda36aff6af360db784efc6ac24e997d6130959a3b.jpg) +Figure 1. By concatenating all views to a tensor, we obtain $\widetilde{\mathbf{Z}}$ . Rotating the obtained tensor $\widetilde{\mathbf{Z}}$ and cutting it vertically, we have the $i$ -th frontal slice $\widetilde{\mathbf{Z}}_i$ . + +topological relevance to point $i$ is assumed to be similar if they have high consistency. The second term in Eq. (1), as a fitting constraint, is used to rule out the trivial solution. We also utilize a weighting coefficient $\alpha$ to balance the two terms. According to the above form, we detect the consistency by propagating topological relationship, and the relevance between two distant points will be high if they are connected by countable neighbors. + +However, the model in Eq. (1) is applied for solving the single-view problem, and it is not suitable for multi-view clustering tasks. In this paper, we propose to explore the manifold topological structure for multi-view data. Given $\mathbf{G}^{(v)}(v = 1,\dots ,m)\in \mathbb{R}^{n\times n}$ as the input similarity graphs of multi-view data with $m$ views. Based on Eq. (1), the topological relationship for each view can be measured by + +$$ +\begin{array}{l} \min _ {\mathbf {Z} ^ {(v)}} \frac {1}{2} \sum_ {v = 1} ^ {m} \sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \left(z _ {i j} ^ {(v)} - z _ {i k} ^ {(v)}\right) ^ {2} + \lambda \left\| \mathbf {Z} ^ {(v)} - \mathbf {I} \right\| _ {F} ^ {2} \\ \text {s . t .} \quad \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0, \tag {2} \\ \end{array} +$$ + +where all $z_{ij}^{(v)}$ is constrained to be non-negative and the sum of $\mathbf{z}_i^{(v)}$ is one. Considering that a data point connected with many similar neighbors would largely affect the objective value. We utilize a normalized form of Eq. (2), which is formulated as + +$$ +\begin{array}{l} \min _ {\mathbf {Z} ^ {(v)}} \frac {1}{2} \sum_ {v = 1} ^ {m} \sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \left(\frac {z _ {i j} ^ {(v)}}{\sqrt {d _ {j j} ^ {(v)}}} - \frac {z _ {i k} ^ {(v)}}{\sqrt {d _ {k k} ^ {(v)}}}\right) ^ {2} + \lambda \left\| \mathbf {Z} ^ {(v)} - \mathbf {I} \right\| _ {F} ^ {2} \\ \text {s . t .} \quad \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0, \tag {3} \\ \end{array} +$$ + +where $\mathbf{D}^{(v)}$ is the degree matrix of $\mathbf{G}^{(v)}$ . + +# 3. The proposed Methodology + +As aforementioned, existing multi-view clustering methods generally suffer from a coarse-grained problem that ig- + +nores the view correlation between samples. To tackle this inappropriate fusion strategy, we design a novel model to explore the intersections of multiple views in the sample level. It is able to capture more intrinsic cross-view consistency and is robust to the inconsistency introduced by certain views. Inspired by [23, 24], here we proposed a transformation on a set of multi-view matrices. As shown in Figure 1, first we start with concatenating all views to a tensor $\tilde{\mathbf{Z}}\in \mathbb{R}^{n\times n\times m}$ . Then we get the $i$ th frontal slice $\tilde{\mathbf{Z}}_i\in \mathbb{R}^{n\times m}$ corresponding to the $i$ th sample to explore sample-level manifold information. By conducting such transformation, it is feasible for us to manipulate fuse all views on the sample level as follow: + +$$ +\begin{array}{l} \min _ {\mathbf {S}} \sum_ {i = 1} ^ {n} \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Z}} _ {i} \right\| _ {2} ^ {2} + \beta \| \mathbf {S} \| _ {F} ^ {2} \\ \text {s . t .} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0, \tag {4} \\ \end{array} +$$ + +$$ +\mathbf {S} \geq 0, \mathbf {W} \geq 0, \mathbf {s} _ {i} ^ {T} \mathbf {1} = 1, \mathbf {W} \mathbf {1} = \mathbf {1}, +$$ + +where $\mathbf{w}_i^T$ corresponds to the weight of different views with respect to the $i$ -th sample. Each column of $\mathbf{S}$ integrates the consistent information of one instance across all views. $\beta$ is the balanced parameter for the penalty term, which is utilized to prevent the trivial solution when a specific view dominates the others. The constraints that we apply to the optimal fusion graph $\mathbf{S}$ and weight matrix $\mathbf{W}$ assist to narrow down the solution space and strongly boost the efficiency of our optimization process. Based on the elementary yet intuitive assumption that the topological relevance between instances tends to be propagated from near to far. That is, the individuals have low spatial similarity may achieve high topological relevance if they are linked by the consecutive neighbors. Thus, we explore the similarity between instances on a more appropriate topological manifold structure rather than on the Euclidean structure. With the help of topological manifold exploration in the multiview clustering domain, by combining Eq. (3) and Eq. (4), we can easily derive: + +$$ +\begin{array}{l} \min _ {\mathbf {Z} ^ {(v)}, \mathbf {W}, \mathbf {S}} \sum_ {v = 1} ^ {m} \underbrace {\frac {1}{2} \sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \left(\frac {z _ {i j} ^ {(v)}}{\sqrt {d _ {j j} ^ {(v)}}} - \frac {z _ {i k} ^ {(v)}}{\sqrt {d _ {k k} ^ {(v)}}}\right) ^ {2} + \lambda \left\| \mathbf {Z} ^ {(v)} - \mathbf {I} \right\| _ {F} ^ {2}} _ {\text {t o p o l o g i c a l r e l e v a n c e l e a n i n g}} \\ + \underbrace {\alpha \sum_ {i = 1} ^ {n} \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Z}} _ {i} \right\| _ {2} ^ {2} + \beta \| \mathbf {S} \| _ {F} ^ {2}} _ {\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\ \begin{array}{l} \text {s . t .} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0, \end{array} \\ \mathbf {S} \geq 0, \mathbf {w} _ {i} \geq 0, \mathbf {S} \mathbf {1} = \mathbf {1}, \mathbf {w} _ {i} ^ {T} \mathbf {1} = \mathbf {1}. \tag {5} \\ \end{array} +$$ + +Moreover, considering the graph for sample-level graph fusion might be a translation from the topological manifold, + +we introduce an intermediate variable $\mathbf{Q}$ to link the topological relevance learning and the sample-level graph fusion. As a result, the joint optimization framework of sample-level multi-view clustering with topological relevance considered can be formulated as: + +$$ +\begin{array}{l} \underbrace {\min _ {\mathbf {Z} ^ {(v)} , \mathbf {W} , \mathbf {S}} \sum_ {v = 1} ^ {m} \frac {1}{2} \sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \left(\frac {z _ {i j} ^ {(v)}}{\sqrt {d _ {j j} ^ {(v)}}} - \frac {z _ {i k} ^ {(v)}}{\sqrt {d _ {k k} ^ {(v)}}}\right) ^ {2} + \lambda \left\| \mathbf {Z} ^ {(v)} - \mathbf {I} \right\| _ {F} ^ {2}} _ {\text {t o p o l o g i c a l r e l e v a n c e l e a r n i n g}} \\ + \underbrace {\gamma \sum_ {v = 1} ^ {m} \| \mathbf {Z} ^ {(v)} - \mathbf {Q} ^ {(v)} \| _ {F} ^ {2} + \alpha \sum_ {i = 1} ^ {n} \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \right\| _ {2} ^ {2} + \beta \| \mathbf {S} \| _ {F} ^ {2}} _ {\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\ \begin{array}{l} \text {s . t .} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0, \end{array} \\ \mathbf {S} \geq 0, \mathbf {w} _ {i} \geq 0, \mathbf {S} \mathbf {1} = \mathbf {1}, \mathbf {w} _ {i} ^ {T} \mathbf {1} = \mathbf {1}, \tag {6} \\ \end{array} +$$ + +where $\gamma$ and $\alpha$ are trade-off parameters. It is noteworthy that our model in Eq. (6) enjoys several properties that are distinct from existing approaches: + +- Instead of performing the inter-view graph fusion, we propose to conducting a cross-view graph fusion process in a sample-wise way. Considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. +- Note that the topological structure is essential for clustering data on manifold. Based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far, we propose to exploit the implied data manifold with the topological relevance considered. +- We model the subtasks of topological relevance learning and the sample-level graph fusion in a unified framework, each subtask is alternately boosted towards an optimal solution. An efficient algorithm to solve the corresponding optimization problem is also introduced. Experimental results on several benchmark datasets certificate the effectiveness of our method. + +# 4. Optimization + +In this section, we design an iterative updating algorithm to solve the optimization problem in Eq. (6). Since it is not jointly convex in all variable s, we propose to optimize the objective function with respect to one variable while fixing other variables. And the procedure repeats until convergence. + +# Algorithm 1: Algorithm to solve Eq. (10) + +Input: a nonzero matrix $\mathbf{A}$ and a nonzero vector $\mathbf{b}$ . Set $1 < \rho < 2$ , initialize $\eta > 0$ , $\mathbf{h}$ . + +Output: $\mathbf{Z}^{(v)}$ + +1: repeat +2: Update $\mathbf{p}$ according to (13). +3: Update $\mathbf{z}_i^{(v)}$ according to (15). +4: Update $\eta \gets \rho \eta$ +5: Update $\mathbf{h} \gets \mathbf{h} + \eta \left(\mathbf{z}_i^{(v)} - \mathbf{p}\right)$ . +6: until converge + +# Update $\mathbf{Z}^{(v)}$ + +For each $\mathbf{Z}^{(v)}$ , we need to solve + +$$ +\begin{array}{l} \min _ {\mathbf {Z} ^ {(v)}} \frac {1}{2} \sum_ {v = 1} ^ {m} \sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \left(\frac {z _ {i j} ^ {(v)}}{\sqrt {d _ {j j} ^ {(v)}}} - \frac {z _ {i k} ^ {(v)}}{\sqrt {d _ {k k} ^ {(v)}}}\right) ^ {2} \\ + \lambda \sum_ {v = 1} ^ {m} \left\| \mathbf {Z} ^ {(v)} - \mathbf {I} \right\| _ {F} ^ {2} + \gamma \sum_ {v = 1} ^ {m} \| \mathbf {Q} ^ {(v)} - \mathbf {Z} ^ {(v)} \| _ {F} ^ {2} \tag {7} \\ \begin{array}{l} \text {s . t .} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0. \end{array} \\ \end{array} +$$ + +Since Eq. (7) is independent for different $v$ , for each $v$ we have + +$$ +\begin{array}{l} \min _ {\mathbf {Z} ^ {(v)}} \frac {1}{2} \sum_ {i = 1} ^ {n} \left\{\sum_ {j, k = 1} ^ {n} g _ {j k} ^ {(v)} \left(\frac {z _ {i j} ^ {(v)}}{\sqrt {d _ {j j} ^ {(v)}}} - \frac {z _ {i k} ^ {(v)}}{\sqrt {d _ {k k} ^ {(v)}}}\right) ^ {2} \right. \\ \left. + \lambda \sum_ {j = 1} ^ {n} \left\| z _ {i j} ^ {(v)} - e _ {i j} \right\| _ {F} ^ {2} + \gamma \sum_ {j = 1} ^ {n} \| q _ {i j} ^ {(v)} - z _ {i j} ^ {(v)} \| _ {F} ^ {2} \right\} \tag {8} \\ \text {s . t .} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0. \\ \end{array} +$$ + +For each $i$ , Eq. (8) can be further rewritten in a vector form as + +$$ +\begin{array}{l} \min _ {\mathbf {z} _ {i} ^ {(v)}} \sum_ {i = 1} ^ {n} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \left(\mathbf {I} - \mathbf {D} ^ {- \frac {1}{2}} \mathbf {G} ^ {(v)} \mathbf {D} ^ {- \frac {1}{2}}\right) \mathbf {z} _ {i} ^ {(v)} \\ + \lambda \left\| \mathbf {z} _ {i} ^ {(v)} - \mathbf {e} _ {i} \right\| _ {F} ^ {2} + \gamma \| \mathbf {q} _ {i} ^ {(v)} - \mathbf {z} _ {i} ^ {(v)} \| _ {F} ^ {2} \tag {9} \\ \text {s . t .} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0. \\ \end{array} +$$ + +Denote $\mathbf{A}^{(v)} = (1 + \lambda +\gamma)\mathbf{I} - \mathbf{D}^{-\frac{1}{2}}\mathbf{G}^{(v)}\mathbf{D}^{-\frac{1}{2}}$ and $\mathbf{b} = 2\lambda \mathbf{e}_i + 2\gamma \mathbf{q}_i^{(v)}$ Eq.9 can be stated as: + +$$ +\min _ {\left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {A} ^ {(v)} \mathbf {z} _ {i} ^ {(v)} - \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {b} \tag {10} +$$ + +# Algorithm 2: Algorithm to solve Eq. (6) + +Input: A set of similarity graph $\mathbf{G}^{(v)}$ . $(v = 1,2,\dots,m)$ Parameter $\alpha$ , $\beta$ , $\lambda$ and $\gamma$ . + +Output: Clustering result. + +1: repeat +2: Update $\mathbf{Z}^{(v)}$ according to Algorithm 1. +3: Update S by solving Eq. (18). +4: Update $\mathbf{W}$ according to Eq. (21). +5: Update $\bar{\mathbf{Q}}_i$ according to Eq. (24). +6: until converge +7: Conduct the standard spectral clustering on the optimal graph $\mathbf{S}$ to obtain the final clustering result. + +It is obvious that Eq. (10) is a quadratic convex optimization problem which can be solved with the classical augmented Lagrangian multiplier (ALM) method [25]. In detail, Eq. (10) can be cracked by tackling its counterpart: + +$$ +\min _ {\left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0, \mathbf {p} = \mathbf {z} _ {i} ^ {(v)}} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {A} ^ {(v)} \mathbf {p} - \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {b} \tag {11} +$$ + +whose augmented Lagrangian function can be defined as: + +$$ +\begin{array}{l} \min _ {\left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0} \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {A} ^ {(v)} \mathbf {p} - \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {b} \tag {12} \\ + \frac {\eta}{2} \| \mathbf {z} _ {i} ^ {(v)} - \mathbf {p} + \frac {1}{\eta} \mathbf {h} \| _ {2} ^ {2} \\ \end{array} +$$ + +where the second term in Eq. (12) is a penalty function term which guarantees that $\mathbf{p} = \mathbf{z}_i^{(v)}$ , $\eta$ and $\mathbf{h}$ are the corresponding penalty coefficient and parameter, respectively. + +Note that $\mathbf{p}$ and $\mathbf{z}_i^{(v)}$ can be iteratively optimized: + +1) Update $\mathbf{p}$ with fixed $\mathbf{z}_i^{(v)}$ The Lagrange function of Eq. (12) w.r.t. $\mathbf{p}$ is + +$$ +\mathcal {L} _ {p} = \left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {A} ^ {(v)} \mathbf {p} + \frac {\eta}{2} \| \mathbf {z} _ {i} ^ {(v)} - \mathbf {p} + \frac {1}{\eta} \mathbf {h} \| _ {2} ^ {2} \tag {13} +$$ + +Taking the derivative of $\mathcal{L}_p$ w.r.t $\mathbf{p}$ and setting the derivative to zero. Thus, we have: + +$$ +\mathbf {p} = \mathbf {z} _ {i} ^ {(v)} - \frac {1}{\eta} \left(\left(\mathbf {A} ^ {(v)}\right) ^ {T} \mathbf {z} _ {i} ^ {(v)} + \mathbf {h}\right) \tag {14} +$$ + +2) Update $\mathbf{z}_i^{(v)}$ with fixed $\mathbf{p}$ . The Lagrange function of Eq. (13) w.r.t. $\mathbf{z}_i^{(v)}$ can be written as + +$$ +\left. \min _ {\left(\mathbf {z} _ {i} ^ {(v)}\right) ^ {T} \mathbf {1} = 1, z _ {i j} ^ {(v)} \geq 0} \left\| \mathbf {z} _ {i} ^ {(v)} - \mathbf {p} + \frac {1}{\eta} \mathbf {h} + \frac {\mathbf {A} ^ {(v)} \mathbf {p} - \mathbf {b}}{\eta} \right\| _ {2} ^ {2}, \right. \tag {15} +$$ + +![](images/22d21c348bc0ab70a39f7545f9858307693d12448f2e1d568032b32961b5cda7.jpg) +(a) Yale Dataset + +![](images/d2f57ccef162219cbb0106b990c349e89ba40439774d1f58ed45ffb881117021.jpg) +(b) HW Dataset + +![](images/4da5f95d847d4242a981a039f84674c5716e476d1e3c159498e164ab48d02931.jpg) +(c) ORL Dataset +Figure 2. Sample images of datasets Yale, HW and ORL. + +which has a closed-form solution and can be readily achieved by the off-the-shelf optimization algorithm [26]. + +According to the ALM principles [25], $\eta$ can be magnified increasingly in each iteration, and $\mathbf{h}$ is updated by $\mathbf{h} \gets \mathbf{h} + \eta \left(\mathbf{z}_i^{(v)} - \mathbf{h}\right)$ . The detailed algorithm to solve Eq. (10) is summarized in Algorithm 1. + +# Update S + +Drop all unrelated terms of Eq. (6) w.r.t. S, thus we have + +$$ +\min _ {\mathbf {S}} \alpha \sum_ {i = 1} ^ {n} \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \right\| _ {2} ^ {2} + \beta \| \mathbf {S} \| _ {F} ^ {2} \tag {16} +$$ + +$$ +\begin{array}{l} \text {s . t .} \mathbf {S} \geq 0, \mathbf {S 1} = \mathbf {1}. \end{array} +$$ + +We can reformulate Eq. (16) in a vector form as + +$$ +\min _ {\mathbf {s} _ {i}} (\alpha + \beta) \mathbf {s} _ {i} \mathbf {s} _ {i} ^ {T} - 2 \alpha \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \mathbf {s} _ {i} \tag {17} +$$ + +$$ +\mathrm {s . t .} \mathbf {s} _ {i} \mathbf {1} = 1, \mathbf {s} _ {i} \geq 0. +$$ + +Based on Eq. (17), we get the following compact formulation + +$$ +\min _ {\mathbf {s} _ {i} \mathbf {1} = 1, \mathbf {s} _ {i} \geq 0} \left\| \mathbf {s} _ {i} - \frac {\alpha}{\alpha + \beta} \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \right\| _ {2} ^ {2}, \tag {18} +$$ + +which can be effectively solved by the optimization algorithm proposed in [26]. + +# Update W + +Optimizing Eq. (6) w.r.t. $\mathbf{W}$ is equivalent to solving + +$$ +\min _ {\mathbf {w} _ {i}} \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \right\| _ {2} ^ {2} \tag {19} +$$ + +$$ +\begin{array}{l} \text {s . t .} \mathbf {w} _ {i} \geq 0, \mathbf {w} _ {i} ^ {T} \mathbf {1} = \mathbf {1}. \end{array} +$$ + +Eq. (19) can be reorganized as + +$$ +\min _ {\mathbf {w} _ {i}} \left\| \mathbf {w} _ {i} ^ {T} \mathbf {B} _ {i} \right\| _ {2} ^ {2} \tag {20} +$$ + +$$ +\begin{array}{l} \text {s . t .} \mathbf {w} _ {i} \geq 0, \mathbf {w} _ {i} ^ {T} \mathbf {1} = \mathbf {1}. \end{array} +$$ + +where $\mathbf{B}_i = \left(\mathbf{1}\mathbf{s}_i^T -\widetilde{\mathbf{Q}}_i\right)\in \mathbb{R}^{m\times n}$ + +Taking the derivative of Eq. (20) w.r.t $\mathbf{w}_i$ , it yields + +$$ +\mathbf {w} _ {i} = \frac {\left(\mathbf {B} _ {i} \mathbf {B} _ {i} ^ {T}\right) ^ {- 1} \mathbf {1}}{\mathbf {1} ^ {T} \left(\mathbf {B} _ {i} \mathbf {B} _ {i} ^ {T}\right) ^ {- 1} \mathbf {1}}. \tag {21} +$$ + +Update $\widetilde{\mathbf{Q}}_i$ + +Fixing all the other irrelevant variables in Eq. (6), we have: + +$$ +\min _ {\widetilde {\mathbf {Q}} _ {i}} \gamma \sum_ {v = 1} ^ {m} \| \mathbf {Z} ^ {(v)} - \mathbf {Q} ^ {(v)} \| _ {F} ^ {2} + \alpha \sum_ {i = 1} ^ {n} \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \right\| _ {2} ^ {2} \tag {22} +$$ + +Obviously, Eq. (22) is sample-wise independent. Therefore, it can be written as: + +$$ +\min _ {\widetilde {\mathbf {Q}} _ {i}} \gamma \| \widetilde {\mathbf {Z}} ^ {(v)} - \widetilde {\mathbf {Q}} ^ {(v)} \| _ {F} ^ {2} + \alpha \left\| \mathbf {s} _ {i} ^ {T} - \mathbf {w} _ {i} ^ {T} \widetilde {\mathbf {Q}} _ {i} \right\| _ {2} ^ {2} \tag {23} +$$ + +Naturally, by taking the derivative of Eq. (23), it yields: + +$$ +\widetilde {\mathbf {Q}} _ {i} = \left(\gamma \mathbf {I} + \alpha \mathbf {w} _ {i} \mathbf {w} _ {i} ^ {T}\right) ^ {- 1} \left(\gamma \widetilde {\mathbf {Z}} _ {i} + \alpha \mathbf {w} _ {i} \mathbf {s} _ {i} ^ {T}\right) \tag {24} +$$ + +The detailed algorithm to solve the objective in Eq. (6) is summarized in Algorithm 2. + +# 5. Experiment + +This section is comprised of four sub-sections: experimental setting, result analysis, robustness analysis and convergence analysis. + +# 5.1. Experiment Setting + +We compare our proposed method with several multiview clustering methods: Multi-view Spectral Clustering with Co-training strategy(Co-train) [27]. Multi- + +Table 1. The clustering results on 100leaves dataset (%) + +
MethodACCNMIPurityF-score
Co-train33.21 ± 0.8557.59 ± 0.7336.10 ± 0.8115.88 ± 0.79
Co-reg32.16 ± 0.9358.97 ± 0.8236.00 ± 0.8217.33 ± 0.99
DiMSC48.52 ± 1.5771.24 ± 0.5551.14 ± 1.4133.66 ± 1.17
AMGL77.66 ± 1.5890.35 ± 0.9782.29 ± 1.1659.54 ± 7.04
MVGL54.12 ± 0.0063.96 ± 0.0057.44 ± 0.008.58 ± 0.00
WMSC77.26 ± 0.9989.81 ± 0.4779.62 ± 0.6871.11 ± 1.31
AWP66.13 ± 0.0085.52 ± 0.0068.19 ± 0.0060.75 ± 0.00
MCGC90.25 ± 0.0093.90 ± 0.0091.13 ± 0.0077.79 ± 0.00
LRMSC75.25 ± 1.5687.64 ± 0.5477.60 ± 1.3166.62 ± 1.46
MVCTM68.63 ± 0.0076.46 ± 0.0072.25 ± 0.0016.52 ± 0.00
SMVSC37.94 ± 0.2765.04 ± 0.2939.42 ± 0.2323.22 ± 0.39
FPMVS35.14 ± 0.2063.06 ± 0.4336.96 ± 0.2622.12 ± 0.38
CSMSC76.06 ± 1.1588.83 ± 0.4378.96 ± 0.8168.91 ± 1.25
Ours90.86 ± 0.0196.38 ± 0.0092.46 ± 0.0188.69 ± 0.01
+ +Table 2. The clustering results on HW dataset (%) + +
MethodACCNMIPurityF-score
Co-train81.28 ± 5.3772.04 ± 2.9882.25 ± 4.1170.93 ± 4.19
Co-reg54.96 ± 4.3547.46 ± 1.9758.64 ± 2.8742.62 ± 2.40
DiMSC46.26 ± 0.4532.97 ± 0.3346.79 ± 0.4727.92 ± 0.27
AMGL93.76 ± 8.5795.02 ± 4.2394.89 ± 6.7893.63 ± 7.16
MVGL85.35 ± 0.0085.19 ± 0.0085.75 ± 0.0082.48 ± 0.00
WMSC74.87 ± 0.1466.79 ± 0.1974.95 ± 0.1663.65 ± 0.22
AWP69.55 ± 0.0059.49 ± 0.0071.45 ± 0.0058.35 ± 0.00
MCGC53.95 ± 0.0061.78 ± 0.0054.10 ± 0.0057.25 ± 0.00
LRMSC79.39 ± 2.9576.49 ± 1.3383.25 ± 1.4772.83 ± 1.89
MVCTM98.75 ± 0.0096.91 ± 0.0098.75 ± 0.0097.52 ± 0.00
SMVSC78.59 ± 0.4669.03 ± 0.5778.90 ± 0.3867.65 ± 0.76
FPMVS78.40 ± 0.1870.88 ± 0.8978.77 ± 0.4169.66 ± 0.85
CSMSC86.87 ± 0.0280.04 ± 0.0986.87 ± 0.0278.05 ± 0.04
Ours99.25 ± 0.0098.15 ± 0.0099.25 ± 0.0098.51 ± 0.00
+ +Table 3. The clustering results on MSRC dataset (%) + +
MethodACCNMIPurityF-score
Co-train64.95 ± 6.2454.27 ± 4.1866.52 ± 5.0052.59 ± 4.97
Co-reg63.95 ± 4.5057.89 ± 2.9967.24 ± 4.4755.31 ± 3.98
DiMSC71.90 ± 0.9559.62 ± 0.9671.90 ± 0.9558.02 ± 1.08
AMGL76.71 ± 4.3370.98 ± 2.2079.00 ± 2.8067.13 ± 2.49
MVGL70.48 ± 0.0058.18 ± 0.0070.48 ± 0.0054.56 ± 0.00
WMSC69.05 ± 0.0059.55 ± 0.1771.43 ± 0.0057.57 ± 0.08
AWP63.33 ± 0.0054.88 ± 0.0063.33 ± 0.0053.76 ± 0.00
MCGC80.48 ± 0.0070.18 ± 0.0080.95 ± 0.0072.46 ± 0.00
LRMSC71.81 ± 2.8962.42 ± 1.5874.14 ± 1.7860.08 ± 1.57
MVCTM85.71 ± 0.0076.15 ± 0.0085.71 ± 0.0074.90 ± 0.00
SMVSC81.43 ± 0.0070.18 ± 0.0081.43 ± 0.0069.36 ± 0.00
FPMVS78.57 ± 0.0066.84 ± 0.0078.57 ± 0.0068.36 ± 0.00
CSMSC80.43 ± 0.1471.36 ± 0.1980.43 ± 0.1470.06 ± 0.21
Ours87.14 ± 0.0078.21 ± 0.0087.14 ± 0.0077.87 ± 0.00
+ +view Spectral Clustering with Co-regularized strategy(Coreg) [28]. Diversity-induced Multi-view Subspace Clustering(DiMSC) [14]. Auto-weighted Multiple Graph Learning(AMGL) [29]. Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Graph Learning for Multiview Clustering(MVGL) [30]. Weighted Multi-view Spec + +Table 4. The clustering results on ORL dataset (%) + +
MethodACCNMIPurityF-score
Co-train61.90 ± 3.1979.23 ± 1.5865.60 ± 2.2350.88 ± 3.26
Co-reg61.65 ± 2.8179.38 ± 1.6966.22 ± 2.1451.39 ± 3.51
DiMSC80.03 ± 1.7890.63 ± 0.8882.93 ± 1.1774.61 ± 1.91
AMGL73.15 ± 3.2285.59 ± 1.0978.27 ± 2.0158.89 ± 3.62
MVGL49.00 ± 0.0066.30 ± 0.0058.00 ± 0.0018.24 ± 0.00
WMSC76.60 ± 3.7088.26 ± 1.6879.75 ± 2.8569.84 ± 4.38
AWP74.50 ± 0.0086.02 ± 0.0076.25 ± 0.0065.18 ± 0.00
MCGC77.00 ± 0.0087.22 ± 0.0082.75 ± 0.0056.25 ± 0.00
LRMSC79.62 ± 3.0990.49 ± 1.5083.42 ± 2.4673.99 ± 3.96
MVCTM59.50 ± 0.0072.58 ± 0.0066.75 ± 0.0023.98 ± 0.00
SMVSC58.28 ± 0.5176.07 ± 0.1461.75 ± 0.3043.96 ± 0.33
FPMVS55.45 ± 0.5973.72 ± 0.4859.27 ± 0.5641.02 ± 0.69
CSMSC77.57 ± 1.8889.20 ± 0.9580.77 ± 1.7871.69 ± 2.58
Ours84.35 ± 0.0291.78 ± 0.0186.45 ± 0.0178.58 ± 0.02
+ +Table 5. The clustering results on Cornell dataset (%) + +
MethodACCNMIPurityF-score
Co-train41.38 ± 1.6722.36 ± 1.4354.26 ± 1.9034.86 ± 0.90
Co-reg36.26 ± 2.0013.68 ± 1.4547.28 ± 1.7731.98 ± 1.41
DiMSC40.15 ± 1.7617.95 ± 0.8252.77 ± 0.6734.58 ± 0.57
AMGL37.38 ± 4.444.26 ± 0.3744.82 ± 0.3437.24 ± 3.51
MVGL44.10 ± 0.009.42 ± 0.0045.64 ± 0.0038.10 ± 0.00
WMSC46.10 ± 0.1521.69 ± 0.1752.26 ± 0.1537.24 ± 0.12
AWP38.97 ± 0.0013.63 ± 0.0049.74 ± 0.0033.72 ± 0.00
MCGC36.41 ± 0.0022.60 ± 0.0053.85 ± 0.0033.79 ± 0.00
LRMSC34.77 ± 1.628.51 ± 1.4843.95 ± 0.7628.99 ± 0.72
MVCTM40.00 ± 0.0015.20 ± 0.0051.79 ± 0.0036.89 ± 0.00
SMVSC48.67 ± 2.2120.61 ± 1.3653.90 ± 0.8742.14 ± 2.28
FPMVS35.90 ± 0.0017.67 ± 0.0053.33 ± 0.0033.20 ± 0.00
CSMSC47.33 ± 0.3323.86 ± 0.3655.49 ± 0.2137.87 ± 0.37
Ours51.28 ± 0.0034.81 ± 0.0061.03 ± 0.0042.03 ± 0.00
+ +Table 6. The clustering results on Yale dataset(%) + +
MethodACCNMIPurityF-score
Co-train53.94 ± 4.2157.90 ± 3.1455.52 ± 4.1138.68 ± 3.72
Co-reg56.36 ± 3.4960.30 ± 3.0557.64 ± 3.2541.43 ± 3.79
DiMSC64.36 ± 3.4066.57 ± 2.3064.79 ± 3.2249.41 ± 2.90
AMGL59.94 ± 3.6462.95 ± 2.7861.33 ± 2.9341.87 ± 4.18
MVGL44.85 ± 0.0049.19 ± 0.0046.67 ± 0.0026.05 ± 0.00
WMSC61.88 ± 3.6465.40 ± 2.8962.12 ± 3.8448.08 ± 3.53
AWP61.82 ± 0.0065.77 ± 0.0061.82 ± 0.0049.71 ± 0.00
MCGC67.27 ± 0.0068.92 ± 0.0067.27 ± 0.0048.33 ± 0.00
LRMSC68.36 ± 1.1170.36 ± 1.1168.55 ± 1.1052.27 ± 1.67
MVCTM62.42 ± 0.0066.14 ± 0.0062.42 ± 0.0047.40 ± 0.00
SMVSC60.36 ± 0.9562.23 ± 1.3760.73 ± 0.8943.05 ± 1.51
FPMVS44.24 ± 0.0049.76 ± 0.0046.67 ± 0.0030.45 ± 0.00
CSMSC64.06 ± 2.9168.22 ± 1.4964.12 ± 2.8051.84 ± 1.76
Ours71.03 ± 0.0174.51 ± 0.0171.21 ± 0.0059.72 ± 0.01
+ +tral Clustering(WMSC) [31]. multi-view clustering via Adaptively Weighted Procrustes(AWP) [32]. Multi-view Consensus Graph Clustering(MCGC) [33]. Generalized Latent Multi-View Subspace Clustering(LRMSC) [34]. Multi-view Clustering on Topological Manifold(MVCTM) Fast Parameter-free Multi-view Subspace Clustering with + +![](images/0fdb392acd97236fcb18ff73e57f74026cac470babee7b7f9597ab05fa04ac3f.jpg) +(a) $\lambda = 0.1\gamma = 1$ + +![](images/2ebf8e12641a830a0f4c827b7a54442a04780f4c7340ba9541deee9cd0f3c304.jpg) +(b) $\lambda = 0.1\gamma = 10$ + +![](images/73ed1ce0935cae64310e263241063e876e567dc049b27ce7f84c4d34789cdde4.jpg) +(c) $\lambda = 0.1\gamma = 100$ + +![](images/f651be0eec55ca69ca876203abd4228a7119cf51574eb9a5624da59ee0c0112f.jpg) +(d) $\lambda = 0.1\gamma = 1000$ + +![](images/afbe596d644cebb4f365d65059a0ea543f260b9db8506259d30b6d18a9afb8d0.jpg) + +![](images/5e5560aa1fd3fe3c2b91e65763ec94fa13948384d56516a1be04d3a71a04cb69.jpg) + +![](images/8c3e3aeee0b7700ad405fda70aac732573db14f2f627fcaa5db57850271d2650.jpg) + +![](images/ca434ed9d07540f1ee725187b74ebbb2f3cb7ce0f9e7be903b8f5343b955035c.jpg) + +![](images/feac0b069b4a75d71a22b7510c43d77105ac027033ce521fe548cc02da6ad471.jpg) +(e) $\lambda = 1\gamma = 1$ +(i) $\lambda = 10\gamma = 1$ + +![](images/a08a2ea86dcad88b56599cb6290169e392f7209b0d50f196ae829a6f1b9f11b5.jpg) +(f) $\lambda = 1\gamma = 10$ +(j) $\lambda = 10\gamma = 10$ + +![](images/90e0a0c66b0f6f7be5bba803b4c40c6f4bd3a81d6f4b6805ee39d9e38f82fdcc.jpg) +(g) $\lambda = 1\gamma = 100$ +(k) $\lambda = 10\gamma = 100$ +Figure 3. Parameter analysis on ORL dataset + +![](images/9020ad258edb20934530cf07cca5d400adb24090e6222aca540250a9a0a5c4a3.jpg) +(h) $\lambda = 1\gamma = 1000$ +(1) $\lambda = 10\gamma = 1000$ + +Consensus Anchor Guidance(FPMVS) [35]. Multi-view Subspace Clustering with Unified Anchors(SMVSC) [36] Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Rather than adopting view-wise weighing strategy like the above mentioned methods, we delicately conduct graph fusion in a sample-wise manner. Thus, the superiority of our proposed approach could be demonstrated in the experiment section. + +As for benchmark datasets, we adopt 100leaves, HW, MRSC, ORL, Cornell and Yale. Specifically, the leaves data set (100leaves) consists of 1,600 leaves from each of 100 plant species. For each sample, margin, shape and texture are given as three distinct views. Handwritten numerals data (HW) is composed of 2,000 data points for digits 0 to 9 from UCI machine learning repository and two public features are available. MSRC data set contains 210 images and can be separated into 7 classes including cow, airplane, face, bicycle, tree, building and car. There are five visual + +features from each sample. ORL consists of 400 face images in 40 different themes in total. For each subject, the images are described in three features: facial expressions, facial details and the lighting. Cornell, which is collected by Cornell University, contains 195 web pages and a web page is made of 2 views: content features and cites features. Dataset Yale contains 165 gray-scale images under varying poses and illuminations, where every image is of size $64 \times 64$ . + +# 5.2. Result Analysis + +With the aim of evaluating our proposed approach adequately with above mentioned SOTA multi-view clustering methods, we adopt four widely used criteria including Normalized Mutual Information(NMI), Accuracy(ACC), Purity and F-Score. The clustering results are reported in Tables (1)-(6). We can arrive at a conclusion that our method is very effective and competitive as the proposed method + +![](images/e8f0b201d3df08c0636a77391bb7187a03ca87a17f449eabfe85ec1d551d16c7.jpg) +(a) 100Leaves + +![](images/0426e7d9d9cd6ea122f8b9c6c4160166281524a66374f0c3dfbb38a558940054.jpg) +(b) HW + +![](images/7a0eece39ecd5433321674c975ec85f37052ffc9cb9691634e58c2220e94d129.jpg) +(c) ORL + +![](images/aaa0019e6eee2d09ca0dae7f508ab9ff4d777f3454bda01b9f0056f7187d491e.jpg) +(d) MSRC + +![](images/26c9fa83f15e07797a668a093c4151b00f23e9c2dd810dede791c53dd67edab1.jpg) +(e) Yale + +![](images/04e3a3242593ddb16fe881ef07582a3bb8f7e1b115afaf3c4a830284d6c5f489.jpg) +(f) Cornell +Figure 4. Convergence curves on all datasets + +outperforms other competitors in the majority of cases. In detail, our method consistently obtains the best results in terms of NMI, ACC and Purity on all datasets. While for F-score, the proposed method surpasses the compared methods except in one case on dataset Cornell. The superiority of our method explicitly demonstrates the effectiveness of the sample-wise learning strategy and corroborates our theoretical findings. + +# 5.3. Parameter Discussion + +With the aim of studying what impact different parameter settings will have on the clustering results, we vary $\alpha$ , $\beta$ , $\lambda$ and $\gamma$ in the ranges $[1e^{-4},\dots,1e^{4}]$ , $[1e^{-4},\dots,1e^{4}]$ , $[1e^{-1},\dots,1e^{2}]$ and $[1,\dots,1e^{3}]$ , respectively. Taking the ORL dataset as an example, we can see the clustering performance is quite stable with respect to different parameter settings, as shown in Figure (3). Considering that there is little difference among the performances of diverse parameter combinations, we can come to a conclusion that our approach is robust to the hyper parameters. + +# 5.4. Convergence Analysis + +Owing to the fact that the optimization of our proposed method is essentially a non-convex problem that is solved by an iterative algorithm, it is critical to validate the convergence of our model. Therefore, this section empirically showcases the convergence property and how fast our algorithm can converge. The convergence curves of our model on six datasets shown in Fig. (4) demonstrate the effectiveness of our optimization approach. Note that despite the non-convexity of Eq. (6), our model can still discover an + +optimal solution for each variable and achieve a local minima within a few iterations, which verifies the effectiveness of the proposed optimization algorithm. + +# 6. Conclusion + +In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. We also design an efficient algorithm to solve the corresponding optimization problem. Meanwhile, our method generates outstanding results on several authoritative benchmark datasets and is proven to outperform current state-of-the-art methods. In the future, we are interested in extending the proposed model to other machine learning framework such as kernel learning and deep learning. + +# Acknowledgements + +This work is supported by the Key Program of National Science Foundation of China (Grant No. 61836006), partially supported by the National Science Foundation of China under Grant 62106164, and the Sichuan Science and Technology Program under Grants 2021ZDZX0011 and 2022YFG0188. + +# References + +[1] Steffen Bickel and Tobias Scheffer. Multi-view clustering. In Proceedings of the 4th IEEE International Conference on Data Mining, pages 19-26, 2004. 1 +[2] Shudong Huang, Zenglin Xu, Ivor W Tsang, and Zhao Kang. Auto-weighted multi-view co-clustering with bipartite graphs. Information Sciences, 512:18-30, 2020. 1 +[3] Hongchang Gao, Feiping Nie, Xuelong Li, and Heng Huang. Multi-view subspace clustering. 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Despite the empirical success made by recent works, there still exists several severe challenges. Particularly, previous multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Moreover, existing methods cannot fully explore the consistency of local structures between different views as they uncover the clustering structure in a intraview way instead of a inter-view manner. In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. We model the above concerns in a unified framework and design an efficient algorithm to solve the corresponding optimization problem. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method and verify its superiority over other SOTA approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 527, + 128, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 128, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 128, + 540 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 548, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 288, + 693 + ], + "type": "text", + "content": "In many real scenarios, data are usually collected from diverse sources in various domains or described by multiple feature sets [1, 2]. A case in point is the image dataset, which can be represented by different visual descriptors, such as LBP, GIST, CENTRIST, HOG, SIFT and Color Moment [3]. Moreover, a document can be written in different languages, and a website can be described by its linkage, page content, etc. These data are generally known as multi-view data [1, 4]. Each view contains partial and complementary information, any of which suffices for learning, and they all together agree to a consensus latent representation [5-7]. Multi-view clustering aims to accurately par" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 214, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 214, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 306, + 214, + 545, + 251 + ], + "type": "text", + "content": "tition data into distinct clusters according to their compatible and complementary information embedded in heterogeneous features [1, 8]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 252, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 546, + 491 + ], + "type": "text", + "content": "In general, multi-view clustering methods can be divided into four categories according to the mechanisms and principles on which these methods are based. [1] initiated the trend of co-training algorithm by first carrying out a co-training strategy and making the clustering results on all view tend to each other as well as satisfying the broadest agreement across all views. Owing to the efficiency of exploiting similarities among multiple views, multi-kernel learning is widely utilized to boost the performance of multi-view clustering methods [9-11]. Multi-task multi-view clustering [12, 13] inherits the property of multitask clustering. Each view of the data is treated with at least one related task. Moreover, inter-task knowledge is transferred from one to another so that the relationship between multi-view and multi-task is fully exploited to improve the clustering outcomes. Another kind of graph-based multiview clustering methods usually attempt to explore an optimal consensus graph across all views, and utilize graph-cut algorithm on the optimal graph to obtain final clustering result [3,5, 14]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 495, + 547, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 697 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 697 + ], + "type": "text", + "content": "A great number of multi-view clustering methods have been proposed and illustrated remarkable empirical successes up to now [15-17]. However, there are still severe drawbacks urgently need to be overcome. For one thing, existing multi-view clustering algorithms seldom consider the topological structure in data, which is essential for clustering data on manifold. Considering that the data sampled from real world typically lie in the nonlinear manifold, data points geometrically far from one to another may keep high consistency when they are linked by a series of consecutive neighbors. For another, they suffer from a coarse-grained problem that ignores the view correlation between samples. Note that redundancy or partial structure mistakes in certain views may lead to a sub-optimal cluster structure. Besides, traditional view-wise fusion strategy would result in a superimposition of redundancies, and hence acquire a more imprecise common cluster structure." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Regarding the above issues, we propose to exploit the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23966" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. Experimental results on various multi-view datasets certificate the effectiveness of the proposed method." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 226, + 135, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 226, + 135, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 226, + 135, + 239 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 287, + 330 + ], + "type": "text", + "content": "Manifold learning has attracted widespread attention in recent decades [18, 19]. A plethora of works are mainly spent on exploring methods for discovering nonlinear low-dimensional manifolds between individuals where the topological relevance can be high [20]. The ability of those algorithms is to learn the manifold structure embedded in the high-dimensional ambient space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 288, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 288, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 288, + 520 + ], + "type": "text", + "content": "Existing studies show that interactions between the instances place heavy reliance on the topological relationship instead of the metric range [21]. That is, a higher cohesion of the aggregation can be maintained by a topological interaction. Therefore, the work in [22] learns the topological relevance between different samples to uncover the hidden structures of the crowded and measure collectiveness. From the perspective of topological space, the relevance between two individuals is high if they are connected by countable neighbors, even though they show low similarity in the spatial scene. It is based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far. In light of this, we replace the most often-used Euclidean distance with a powerful manifold topological relevance to capture the intrinsic structures." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": "Given a precomputed affinity matrix " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\mathbf{G} = [g_{jk}] \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 521, + 287, + 605 + ], + "type": "text", + "content": " is the number of data samples. Based on the assumption that if two data points keep high consistency, their topological relevance to any other point is assumed to be similar, [22] introduced a structure-based clustering strategy to explore the topological relevance between different samples. The objective function can be defined as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 73, + 613, + 287, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 613, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 73, + 613, + 287, + 647 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {Z}} \\frac {1}{2} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} \\left(z _ {i j} - z _ {i k}\\right) ^ {2} + \\lambda \\| \\mathbf {Z} - \\mathbf {I} \\| _ {F} ^ {2}, \\tag {1}", + "image_path": "0f332de260d95ed067e3d9d0b166624688531ab51ad7ffd7755ac0719894e3ae.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": " represents the topological relationship graph and the element " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "z_{ij}" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": " is the topological relevance of " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "-th point to " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "-th point. The first term in Eq. (1), as a smoothness constraint, is incorporated to meet the aforementioned assumption, which ensures that for data points " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": ", their" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 87, + 545, + 196 + ], + "blocks": [ + { + "bbox": [ + 309, + 87, + 545, + 196 + ], + "lines": [ + { + "bbox": [ + 309, + 87, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 309, + 87, + 545, + 196 + ], + "type": "image", + "image_path": "1cb4a5026c1049d311dc62bda36aff6af360db784efc6ac24e997d6130959a3b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "text", + "content": "Figure 1. By concatenating all views to a tensor, we obtain " + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Z}}" + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "text", + "content": ". Rotating the obtained tensor " + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Z}}" + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "text", + "content": " and cutting it vertically, we have the " + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "text", + "content": "-th frontal slice " + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Z}}_i" + }, + { + "bbox": [ + 305, + 201, + 545, + 236 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "type": "text", + "content": "topological relevance to point " + }, + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "type": "text", + "content": " is assumed to be similar if they have high consistency. The second term in Eq. (1), as a fitting constraint, is used to rule out the trivial solution. We also utilize a weighting coefficient " + }, + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 255, + 545, + 351 + ], + "type": "text", + "content": " to balance the two terms. According to the above form, we detect the consistency by propagating topological relationship, and the relevance between two distant points will be high if they are connected by countable neighbors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "type": "text", + "content": "However, the model in Eq. (1) is applied for solving the single-view problem, and it is not suitable for multi-view clustering tasks. In this paper, we propose to explore the manifold topological structure for multi-view data. Given " + }, + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^{(v)}(v = 1,\\dots ,m)\\in \\mathbb{R}^{n\\times n}" + }, + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "type": "text", + "content": " as the input similarity graphs of multi-view data with " + }, + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 351, + 545, + 436 + ], + "type": "text", + "content": " views. Based on Eq. (1), the topological relationship for each view can be measured by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 442, + 545, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 442, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 313, + 442, + 545, + 509 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(z _ {i j} ^ {(v)} - z _ {i k} ^ {(v)}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} \\\\ \\text {s . t .} \\quad \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {2} \\\\ \\end{array}", + "image_path": "bf11eb92d9ff2c954cec1b2ab044b9b71742eb59a837aeffe54c815e68da0313.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "type": "text", + "content": "where all " + }, + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "type": "inline_equation", + "content": "z_{ij}^{(v)}" + }, + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "type": "text", + "content": " is constrained to be non-negative and the sum of " + }, + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 304, + 510, + 545, + 573 + ], + "type": "text", + "content": " is one. Considering that a data point connected with many similar neighbors would largely affect the objective value. We utilize a normalized form of Eq. (2), which is formulated as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 578, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} \\\\ \\text {s . t .} \\quad \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {3} \\\\ \\end{array}", + "image_path": "d2aaba38f35a403d7ed5464f733512923a6309c6996f361276f2d61da1d6aad5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{D}^{(v)}" + }, + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "type": "text", + "content": " is the degree matrix of " + }, + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^{(v)}" + }, + { + "bbox": [ + 306, + 647, + 472, + 659 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 669, + 461, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 461, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 461, + 683 + ], + "type": "text", + "content": "3. The proposed Methodology" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "As aforementioned, existing multi-view clustering methods generally suffer from a coarse-grained problem that ig-" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23967" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "nores the view correlation between samples. To tackle this inappropriate fusion strategy, we design a novel model to explore the intersections of multiple views in the sample level. It is able to capture more intrinsic cross-view consistency and is robust to the inconsistency introduced by certain views. Inspired by [23, 24], here we proposed a transformation on a set of multi-view matrices. As shown in Figure 1, first we start with concatenating all views to a tensor " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{Z}}\\in \\mathbb{R}^{n\\times n\\times m}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": ". Then we get the " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " th frontal slice " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{Z}}_i\\in \\mathbb{R}^{n\\times m}" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " corresponding to the " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": " th sample to explore sample-level manifold information. By conducting such transformation, it is feasible for us to manipulate fuse all views on the sample level as follow:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 95, + 232, + 287, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 232, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 95, + 232, + 287, + 287 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {S}} \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Z}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\tag {4} \\\\ \\end{array}", + "image_path": "65cd5b0702a5bf8b43e5cf1f4819d664adb34becc88478655ae39405e01fa47d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 94, + 289, + 239, + 303 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 289, + 239, + 303 + ], + "spans": [ + { + "bbox": [ + 94, + 289, + 239, + 303 + ], + "type": "interline_equation", + "content": "\\mathbf {S} \\geq 0, \\mathbf {W} \\geq 0, \\mathbf {s} _ {i} ^ {T} \\mathbf {1} = 1, \\mathbf {W} \\mathbf {1} = \\mathbf {1},", + "image_path": "7299bbe7014b32123c2bc00809375b29b1d92a60f03f287e5c60fc5f6db2fbde.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i^T" + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": " corresponds to the weight of different views with respect to the " + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": "-th sample. Each column of " + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": " integrates the consistent information of one instance across all views. " + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": " is the balanced parameter for the penalty term, which is utilized to prevent the trivial solution when a specific view dominates the others. The constraints that we apply to the optimal fusion graph " + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": " and weight matrix " + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 46, + 308, + 289, + 536 + ], + "type": "text", + "content": " assist to narrow down the solution space and strongly boost the efficiency of our optimization process. Based on the elementary yet intuitive assumption that the topological relevance between instances tends to be propagated from near to far. That is, the individuals have low spatial similarity may achieve high topological relevance if they are linked by the consecutive neighbors. Thus, we explore the similarity between instances on a more appropriate topological manifold structure rather than on the Euclidean structure. With the help of topological manifold exploration in the multiview clustering domain, by combining Eq. (3) and Eq. (4), we can easily derive:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 539, + 289, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 289, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 289, + 689 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}, \\mathbf {W}, \\mathbf {S}} \\sum_ {v = 1} ^ {m} \\underbrace {\\frac {1}{2} \\sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2}} _ {\\text {t o p o l o g i c a l r e l e v a n c e l e a n i n g}} \\\\ + \\underbrace {\\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Z}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2}} _ {\\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\end{array} \\\\ \\mathbf {S} \\geq 0, \\mathbf {w} _ {i} \\geq 0, \\mathbf {S} \\mathbf {1} = \\mathbf {1}, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\tag {5} \\\\ \\end{array}", + "image_path": "6fc32180116617b1f5353bd97b8cb6eeefe6abff3e5c5593e483b61ea5183850.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Moreover, considering the graph for sample-level graph fusion might be a translation from the topological manifold," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "we introduce an intermediate variable " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " to link the topological relevance learning and the sample-level graph fusion. As a result, the joint optimization framework of sample-level multi-view clustering with topological relevance considered can be formulated as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 138, + 552, + 287 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 138, + 552, + 287 + ], + "spans": [ + { + "bbox": [ + 307, + 138, + 552, + 287 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\underbrace {\\min _ {\\mathbf {Z} ^ {(v)} , \\mathbf {W} , \\mathbf {S}} \\sum_ {v = 1} ^ {m} \\frac {1}{2} \\sum_ {i , j , k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} + \\lambda \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2}} _ {\\text {t o p o l o g i c a l r e l e v a n c e l e a r n i n g}} \\\\ + \\underbrace {\\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Z} ^ {(v)} - \\mathbf {Q} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2}} _ {\\text {s a m p l e - l e v e l g r a p h f u s i o n}} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\end{array} \\\\ \\mathbf {S} \\geq 0, \\mathbf {w} _ {i} \\geq 0, \\mathbf {S} \\mathbf {1} = \\mathbf {1}, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}, \\tag {6} \\\\ \\end{array}", + "image_path": "6716025c4a6b1f6fca118c5bbf828a21ff9759982961d2d669c04636e7cf62ee.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 289, + 545, + 324 + ], + "type": "text", + "content": " are trade-off parameters. It is noteworthy that our model in Eq. (6) enjoys several properties that are distinct from existing approaches:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 332, + 545, + 609 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 317, + 332, + 545, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 332, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 317, + 332, + 545, + 428 + ], + "type": "text", + "content": "- Instead of performing the inter-view graph fusion, we propose to conducting a cross-view graph fusion process in a sample-wise way. Considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 435, + 545, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 435, + 545, + 508 + ], + "spans": [ + { + "bbox": [ + 317, + 435, + 545, + 508 + ], + "type": "text", + "content": "- Note that the topological structure is essential for clustering data on manifold. Based on a simple yet intuitive assumption that the topological connectivities between individuals could be propagated from near to far, we propose to exploit the implied data manifold with the topological relevance considered." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 515, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 515, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 317, + 515, + 545, + 609 + ], + "type": "text", + "content": "- We model the subtasks of topological relevance learning and the sample-level graph fusion in a unified framework, each subtask is alternately boosted towards an optimal solution. An efficient algorithm to solve the corresponding optimization problem is also introduced. Experimental results on several benchmark datasets certificate the effectiveness of our method." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 621, + 389, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 389, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 389, + 635 + ], + "type": "text", + "content": "4. Optimization" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "In this section, we design an iterative updating algorithm to solve the optimization problem in Eq. (6). Since it is not jointly convex in all variable s, we propose to optimize the objective function with respect to one variable while fixing other variables. And the procedure repeats until convergence." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23968" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 54, + 75, + 224, + 87 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 75, + 224, + 87 + ], + "spans": [ + { + "bbox": [ + 54, + 75, + 224, + 87 + ], + "type": "text", + "content": "Algorithm 1: Algorithm to solve Eq. (10)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "spans": [ + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "content": "Input: a nonzero matrix " + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "content": " and a nonzero vector " + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "inline_equation", + "content": "\\mathbf{b}" + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "content": ". Set " + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "inline_equation", + "content": "1 < \\rho < 2" + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "content": ", initialize " + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "inline_equation", + "content": "\\eta > 0" + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 59, + 89, + 270, + 113 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 60, + 113, + 121, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 113, + 121, + 125 + ], + "spans": [ + { + "bbox": [ + 60, + 113, + 121, + 125 + ], + "type": "text", + "content": "Output: " + }, + { + "bbox": [ + 60, + 113, + 121, + 125 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}^{(v)}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 125, + 216, + 204 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 66, + 125, + 107, + 136 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 125, + 107, + 136 + ], + "spans": [ + { + "bbox": [ + 66, + 125, + 107, + 136 + ], + "type": "text", + "content": "1: repeat" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 137, + 200, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 137, + 200, + 148 + ], + "spans": [ + { + "bbox": [ + 66, + 137, + 200, + 148 + ], + "type": "text", + "content": "2: Update " + }, + { + "bbox": [ + 66, + 137, + 200, + 148 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 66, + 137, + 200, + 148 + ], + "type": "text", + "content": " according to (13)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 66, + 148, + 209, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 148, + 209, + 163 + ], + "spans": [ + { + "bbox": [ + 66, + 148, + 209, + 163 + ], + "type": "text", + "content": "3: Update " + }, + { + "bbox": [ + 66, + 148, + 209, + 163 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 66, + 148, + 209, + 163 + ], + "type": "text", + "content": " according to (15)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 66, + 163, + 154, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 163, + 154, + 175 + ], + "spans": [ + { + "bbox": [ + 66, + 163, + 154, + 175 + ], + "type": "text", + "content": "4: Update " + }, + { + "bbox": [ + 66, + 163, + 154, + 175 + ], + "type": "inline_equation", + "content": "\\eta \\gets \\rho \\eta" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 66, + 175, + 216, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 175, + 216, + 193 + ], + "spans": [ + { + "bbox": [ + 66, + 175, + 216, + 193 + ], + "type": "text", + "content": "5: Update " + }, + { + "bbox": [ + 66, + 175, + 216, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{h} \\gets \\mathbf{h} + \\eta \\left(\\mathbf{z}_i^{(v)} - \\mathbf{p}\\right)" + }, + { + "bbox": [ + 66, + 175, + 216, + 193 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 66, + 193, + 137, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 193, + 137, + 204 + ], + "spans": [ + { + "bbox": [ + 66, + 193, + 137, + 204 + ], + "type": "text", + "content": "6: until converge" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 59, + 230, + 113, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 230, + 113, + 243 + ], + "spans": [ + { + "bbox": [ + 59, + 230, + 113, + 243 + ], + "type": "text", + "content": "Update " + }, + { + "bbox": [ + 59, + 230, + 113, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}^{(v)}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 243, + 188, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 243, + 188, + 255 + ], + "spans": [ + { + "bbox": [ + 59, + 243, + 188, + 255 + ], + "type": "text", + "content": "For each " + }, + { + "bbox": [ + 59, + 243, + 188, + 255 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}^{(v)}" + }, + { + "bbox": [ + 59, + 243, + 188, + 255 + ], + "type": "text", + "content": ", we need to solve" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 74, + 262, + 287, + 363 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 262, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 74, + 262, + 287, + 363 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {v = 1} ^ {m} \\sum_ {i, j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} \\\\ + \\lambda \\sum_ {v = 1} ^ {m} \\left\\| \\mathbf {Z} ^ {(v)} - \\mathbf {I} \\right\\| _ {F} ^ {2} + \\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Q} ^ {(v)} - \\mathbf {Z} ^ {(v)} \\| _ {F} ^ {2} \\tag {7} \\\\ \\begin{array}{l} \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\end{array} \\\\ \\end{array}", + "image_path": "8b43e5f4be2454cf9e94db456430160264a12bcf6f787d679076c5712e510580.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "type": "text", + "content": "Since Eq. (7) is independent for different " + }, + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "type": "text", + "content": ", for each " + }, + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 47, + 371, + 287, + 393 + ], + "type": "text", + "content": " we have" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 65, + 401, + 287, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 401, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 65, + 401, + 287, + 502 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {Z} ^ {(v)}} \\frac {1}{2} \\sum_ {i = 1} ^ {n} \\left\\{\\sum_ {j, k = 1} ^ {n} g _ {j k} ^ {(v)} \\left(\\frac {z _ {i j} ^ {(v)}}{\\sqrt {d _ {j j} ^ {(v)}}} - \\frac {z _ {i k} ^ {(v)}}{\\sqrt {d _ {k k} ^ {(v)}}}\\right) ^ {2} \\right. \\\\ \\left. + \\lambda \\sum_ {j = 1} ^ {n} \\left\\| z _ {i j} ^ {(v)} - e _ {i j} \\right\\| _ {F} ^ {2} + \\gamma \\sum_ {j = 1} ^ {n} \\| q _ {i j} ^ {(v)} - z _ {i j} ^ {(v)} \\| _ {F} ^ {2} \\right\\} \\tag {8} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\\\ \\end{array}", + "image_path": "eae31f3f3048eafcb8cfafccbd166d899433d9b04f13c4ba0e132b4e16a75670.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 510, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 287, + 533 + ], + "type": "text", + "content": "For each " + }, + { + "bbox": [ + 47, + 510, + 287, + 533 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 510, + 287, + 533 + ], + "type": "text", + "content": ", Eq. (8) can be further rewritten in a vector form as" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 75, + 542, + 287, + 621 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 542, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 75, + 542, + 287, + 621 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\mathbf {z} _ {i} ^ {(v)}} \\sum_ {i = 1} ^ {n} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\left(\\mathbf {I} - \\mathbf {D} ^ {- \\frac {1}{2}} \\mathbf {G} ^ {(v)} \\mathbf {D} ^ {- \\frac {1}{2}}\\right) \\mathbf {z} _ {i} ^ {(v)} \\\\ + \\lambda \\left\\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {e} _ {i} \\right\\| _ {F} ^ {2} + \\gamma \\| \\mathbf {q} _ {i} ^ {(v)} - \\mathbf {z} _ {i} ^ {(v)} \\| _ {F} ^ {2} \\tag {9} \\\\ \\text {s . t .} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0. \\\\ \\end{array}", + "image_path": "366974117be9a5a02e63faf36dae0e70c89b36cb12151a94b4e04bf29e34bea4.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "type": "text", + "content": "Denote " + }, + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{A}^{(v)} = (1 + \\lambda +\\gamma)\\mathbf{I} - \\mathbf{D}^{-\\frac{1}{2}}\\mathbf{G}^{(v)}\\mathbf{D}^{-\\frac{1}{2}}" + }, + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\mathbf{b} = 2\\lambda \\mathbf{e}_i + 2\\gamma \\mathbf{q}_i^{(v)}" + }, + { + "bbox": [ + 47, + 631, + 287, + 659 + ], + "type": "text", + "content": " Eq.9 can be stated as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 59, + 667, + 287, + 699 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 667, + 287, + 699 + ], + "spans": [ + { + "bbox": [ + 59, + 667, + 287, + 699 + ], + "type": "interline_equation", + "content": "\\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {z} _ {i} ^ {(v)} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {10}", + "image_path": "1740cb25877cb69c5c8cb7f360f78327d214769aca4bec82ee5bbb060b8d424e.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 312, + 75, + 478, + 87 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 75, + 478, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 478, + 87 + ], + "type": "text", + "content": "Algorithm 2: Algorithm to solve Eq. (6)" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "spans": [ + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": "Input: A set of similarity graph " + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "inline_equation", + "content": "\\mathbf{G}^{(v)}" + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "inline_equation", + "content": "(v = 1,2,\\dots,m)" + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": " Parameter " + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 318, + 90, + 535, + 114 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 318, + 115, + 429, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 115, + 429, + 126 + ], + "spans": [ + { + "bbox": [ + 318, + 115, + 429, + 126 + ], + "type": "text", + "content": "Output: Clustering result." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 324, + 128, + 557, + 222 + ], + "type": "list", + "angle": 0, + "index": 29, + "blocks": [ + { + "bbox": [ + 325, + 128, + 365, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 128, + 365, + 138 + ], + "spans": [ + { + "bbox": [ + 325, + 128, + 365, + 138 + ], + "type": "text", + "content": "1: repeat" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 325, + 139, + 502, + 150 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 139, + 502, + 150 + ], + "spans": [ + { + "bbox": [ + 325, + 139, + 502, + 150 + ], + "type": "text", + "content": "2: Update " + }, + { + "bbox": [ + 325, + 139, + 502, + 150 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}^{(v)}" + }, + { + "bbox": [ + 325, + 139, + 502, + 150 + ], + "type": "text", + "content": " according to Algorithm 1." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 325, + 151, + 467, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 151, + 467, + 163 + ], + "spans": [ + { + "bbox": [ + 325, + 151, + 467, + 163 + ], + "type": "text", + "content": "3: Update S by solving Eq. (18)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 325, + 163, + 480, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 163, + 480, + 175 + ], + "spans": [ + { + "bbox": [ + 325, + 163, + 480, + 175 + ], + "type": "text", + "content": "4: Update " + }, + { + "bbox": [ + 325, + 163, + 480, + 175 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 325, + 163, + 480, + 175 + ], + "type": "text", + "content": " according to Eq. (21)." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 325, + 175, + 480, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 175, + 480, + 186 + ], + "spans": [ + { + "bbox": [ + 325, + 175, + 480, + 186 + ], + "type": "text", + "content": "5: Update " + }, + { + "bbox": [ + 325, + 175, + 480, + 186 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{Q}}_i" + }, + { + "bbox": [ + 325, + 175, + 480, + 186 + ], + "type": "text", + "content": " according to Eq. (24)." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 325, + 187, + 395, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 187, + 395, + 198 + ], + "spans": [ + { + "bbox": [ + 325, + 187, + 395, + 198 + ], + "type": "text", + "content": "6: until converge" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 324, + 199, + 557, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 199, + 557, + 222 + ], + "spans": [ + { + "bbox": [ + 324, + 199, + 557, + 222 + ], + "type": "text", + "content": "7: Conduct the standard spectral clustering on the optimal graph " + }, + { + "bbox": [ + 324, + 199, + 557, + 222 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 324, + 199, + 557, + 222 + ], + "type": "text", + "content": " to obtain the final clustering result." + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 251, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 300 + ], + "type": "text", + "content": "It is obvious that Eq. (10) is a quadratic convex optimization problem which can be solved with the classical augmented Lagrangian multiplier (ALM) method [25]. In detail, Eq. (10) can be cracked by tackling its counterpart:" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 317, + 308, + 545, + 350 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 308, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 317, + 308, + 545, + 350 + ], + "type": "interline_equation", + "content": "\\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0, \\mathbf {p} = \\mathbf {z} _ {i} ^ {(v)}} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {11}", + "image_path": "1ae82c530f1bfe06e37116634aa1a2933a89d26bf0dc917e30572c76f3a96107.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 350, + 538, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 350, + 538, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 350, + 538, + 363 + ], + "type": "text", + "content": "whose augmented Lagrangian function can be defined as:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 323, + 371, + 545, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 371, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 323, + 371, + 545, + 430 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} - \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {b} \\tag {12} \\\\ + \\frac {\\eta}{2} \\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} \\| _ {2} ^ {2} \\\\ \\end{array}", + "image_path": "43a6a5e627c40d2f98df47fffa3d6e8cada36465079b4a5c73d1e1ec6a3c5044.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "text", + "content": "where the second term in Eq. (12) is a penalty function term which guarantees that " + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = \\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 305, + 439, + 545, + 476 + ], + "type": "text", + "content": " are the corresponding penalty coefficient and parameter, respectively." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 306, + 477, + 506, + 491 + ], + "type": "text", + "content": " can be iteratively optimized:" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "text", + "content": "1) Update " + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "text", + "content": " with fixed " + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "text", + "content": " The Lagrange function of Eq. (12) w.r.t. " + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 306, + 491, + 545, + 517 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 324, + 525, + 545, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 525, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 324, + 525, + 545, + 552 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p} = \\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {A} ^ {(v)} \\mathbf {p} + \\frac {\\eta}{2} \\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} \\| _ {2} ^ {2} \\tag {13}", + "image_path": "b4924f1519c363ad3cc9937d4af3743455656dba8f07d35f5175019f2bcf66da.jpg" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "text", + "content": "Taking the derivative of " + }, + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "text", + "content": " w.r.t " + }, + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 305, + 559, + 545, + 582 + ], + "type": "text", + "content": " and setting the derivative to zero. Thus, we have:" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 350, + 592, + 545, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 592, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 350, + 592, + 545, + 619 + ], + "type": "interline_equation", + "content": "\\mathbf {p} = \\mathbf {z} _ {i} ^ {(v)} - \\frac {1}{\\eta} \\left(\\left(\\mathbf {A} ^ {(v)}\\right) ^ {T} \\mathbf {z} _ {i} ^ {(v)} + \\mathbf {h}\\right) \\tag {14}", + "image_path": "5352a5b9732c80a7c3f8f5cb02e19fcd9923c81859432243898f77675ea868bb.jpg" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "text", + "content": "2) Update " + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "text", + "content": " with fixed " + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "text", + "content": ". The Lagrange function of Eq. (13) w.r.t. " + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_i^{(v)}" + }, + { + "bbox": [ + 305, + 629, + 545, + 658 + ], + "type": "text", + "content": " can be written as" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 318, + 666, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 666, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\left. \\min _ {\\left(\\mathbf {z} _ {i} ^ {(v)}\\right) ^ {T} \\mathbf {1} = 1, z _ {i j} ^ {(v)} \\geq 0} \\left\\| \\mathbf {z} _ {i} ^ {(v)} - \\mathbf {p} + \\frac {1}{\\eta} \\mathbf {h} + \\frac {\\mathbf {A} ^ {(v)} \\mathbf {p} - \\mathbf {b}}{\\eta} \\right\\| _ {2} ^ {2}, \\right. \\tag {15}", + "image_path": "48541b1eb0a4d7eb8057739add29c105980e7bc7ec130263d0092c2ccd01bfdb.jpg" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23969" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 213, + 235 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 213, + 235 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 213, + 235 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 213, + 235 + ], + "type": "image", + "image_path": "22d21c348bc0ab70a39f7545f9858307693d12448f2e1d568032b32961b5cda7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 237, + 157, + 246 + ], + "lines": [ + { + "bbox": [ + 104, + 237, + 157, + 246 + ], + "spans": [ + { + "bbox": [ + 104, + 237, + 157, + 246 + ], + "type": "text", + "content": "(a) Yale Dataset" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 214, + 70, + 380, + 235 + ], + "blocks": [ + { + "bbox": [ + 214, + 70, + 380, + 235 + ], + "lines": [ + { + "bbox": [ + 214, + 70, + 380, + 235 + ], + "spans": [ + { + "bbox": [ + 214, + 70, + 380, + 235 + ], + "type": "image", + "image_path": "d2f57ccef162219cbb0106b990c349e89ba40439774d1f58ed45ffb881117021.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 271, + 237, + 323, + 245 + ], + "lines": [ + { + "bbox": [ + 271, + 237, + 323, + 245 + ], + "spans": [ + { + "bbox": [ + 271, + 237, + 323, + 245 + ], + "type": "text", + "content": "(b) HW Dataset" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 381, + 70, + 545, + 235 + ], + "blocks": [ + { + "bbox": [ + 381, + 70, + 545, + 235 + ], + "lines": [ + { + "bbox": [ + 381, + 70, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 381, + 70, + 545, + 235 + ], + "type": "image", + "image_path": "4da5f95d847d4242a981a039f84674c5716e476d1e3c159498e164ab48d02931.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 237, + 490, + 246 + ], + "lines": [ + { + "bbox": [ + 435, + 237, + 490, + 246 + ], + "spans": [ + { + "bbox": [ + 435, + 237, + 490, + 246 + ], + "type": "text", + "content": "(c) ORL Dataset" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 192, + 256, + 400, + 267 + ], + "lines": [ + { + "bbox": [ + 192, + 256, + 400, + 267 + ], + "spans": [ + { + "bbox": [ + 192, + 256, + 400, + 267 + ], + "type": "text", + "content": "Figure 2. Sample images of datasets Yale, HW and ORL." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "content": "which has a closed-form solution and can be readily achieved by the off-the-shelf optimization algorithm [26]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "text", + "content": "According to the ALM principles [25], " + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "text", + "content": " can be magnified increasingly in each iteration, and " + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{h}" + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "text", + "content": " is updated by " + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{h} \\gets \\mathbf{h} + \\eta \\left(\\mathbf{z}_i^{(v)} - \\mathbf{h}\\right)" + }, + { + "bbox": [ + 47, + 325, + 287, + 377 + ], + "type": "text", + "content": ". The detailed algorithm to solve Eq. (10) is summarized in Algorithm 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 378, + 102, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 378, + 102, + 389 + ], + "spans": [ + { + "bbox": [ + 59, + 378, + 102, + 389 + ], + "type": "text", + "content": "Update S" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 389, + 287, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 389, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 59, + 389, + 287, + 401 + ], + "type": "text", + "content": "Drop all unrelated terms of Eq. (6) w.r.t. S, thus we have" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 90, + 407, + 287, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 407, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 90, + 407, + 287, + 437 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {S}} \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} + \\beta \\| \\mathbf {S} \\| _ {F} ^ {2} \\tag {16}", + "image_path": "caab55f95a908fbb721db40d421a2ff0eea727665a33746760b3ae893d017d4e.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 126, + 441, + 208, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 441, + 208, + 452 + ], + "spans": [ + { + "bbox": [ + 126, + 441, + 208, + 452 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\text {s . t .} \\mathbf {S} \\geq 0, \\mathbf {S 1} = \\mathbf {1}. \\end{array}", + "image_path": "17d158684701fedf7a61770d00efb29bca98bbf47988bc31c32e4cf73fa32419.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 458, + 241, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 241, + 469 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 241, + 469 + ], + "type": "text", + "content": "We can reformulate Eq. (16) in a vector form as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 100, + 474, + 287, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 474, + 287, + 497 + ], + "spans": [ + { + "bbox": [ + 100, + 474, + 287, + 497 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {s} _ {i}} (\\alpha + \\beta) \\mathbf {s} _ {i} \\mathbf {s} _ {i} ^ {T} - 2 \\alpha \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\mathbf {s} _ {i} \\tag {17}", + "image_path": "620859cf8a13345c65f3670e0e890e54407ad0bd5ccd97add65fcffbdd368b9d.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 125, + 498, + 208, + 508 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 498, + 208, + 508 + ], + "spans": [ + { + "bbox": [ + 125, + 498, + 208, + 508 + ], + "type": "interline_equation", + "content": "\\mathrm {s . t .} \\mathbf {s} _ {i} \\mathbf {1} = 1, \\mathbf {s} _ {i} \\geq 0.", + "image_path": "723d164b511f08bb21fa1770d73ffe3a9fbe6657bf1a6f4b4b1b278657cf19f4.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 514, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 287, + 536 + ], + "type": "text", + "content": "Based on Eq. (17), we get the following compact formulation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 96, + 535, + 287, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 535, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 96, + 535, + 287, + 563 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {s} _ {i} \\mathbf {1} = 1, \\mathbf {s} _ {i} \\geq 0} \\left\\| \\mathbf {s} _ {i} - \\frac {\\alpha}{\\alpha + \\beta} \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2}, \\tag {18}", + "image_path": "dfc8553426f505b37d1cd6dff90882ab890f3033c3e4b16063a596a1890a32e9.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 566, + 286, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 286, + 589 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 286, + 589 + ], + "type": "text", + "content": "which can be effectively solved by the optimization algorithm proposed in [26]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 590, + 107, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 590, + 107, + 600 + ], + "spans": [ + { + "bbox": [ + 59, + 590, + 107, + 600 + ], + "type": "text", + "content": "Update W" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 59, + 601, + 270, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 601, + 270, + 613 + ], + "spans": [ + { + "bbox": [ + 59, + 601, + 270, + 613 + ], + "type": "text", + "content": "Optimizing Eq. (6) w.r.t. " + }, + { + "bbox": [ + 59, + 601, + 270, + 613 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 59, + 601, + 270, + 613 + ], + "type": "text", + "content": " is equivalent to solving" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 123, + 617, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 617, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 123, + 617, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w} _ {i}} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {19}", + "image_path": "f7f136e05d9b0906ccf7d6432f703b037270366101cbc6e49544a1f9bed5965e.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 119, + 643, + 214, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 643, + 214, + 657 + ], + "spans": [ + { + "bbox": [ + 119, + 643, + 214, + 657 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\text {s . t .} \\mathbf {w} _ {i} \\geq 0, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\end{array}", + "image_path": "0802bc1169746c3d27cd2afab5fcedd089b5eaaf3493cde3fd561f00a73a6951.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 662, + 171, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 171, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 171, + 673 + ], + "type": "text", + "content": "Eq. (19) can be reorganized as" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 135, + 678, + 287, + 702 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 678, + 287, + 702 + ], + "spans": [ + { + "bbox": [ + 135, + 678, + 287, + 702 + ], + "type": "interline_equation", + "content": "\\min _ {\\mathbf {w} _ {i}} \\left\\| \\mathbf {w} _ {i} ^ {T} \\mathbf {B} _ {i} \\right\\| _ {2} ^ {2} \\tag {20}", + "image_path": "7b04342cd2db170d0a79aacb6ab37686f68bebcfad49154e3adc8b9fa15a4756.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 119, + 702, + 214, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 119, + 702, + 214, + 715 + ], + "spans": [ + { + "bbox": [ + 119, + 702, + 214, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\text {s . t .} \\mathbf {w} _ {i} \\geq 0, \\mathbf {w} _ {i} ^ {T} \\mathbf {1} = \\mathbf {1}. \\end{array}", + "image_path": "18ea13690c2c009f61496efc29627c824e4a4f1998d3fd65fc33cea511ed1a70.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 287, + 453, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 453, + 305 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 453, + 305 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 287, + 453, + 305 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i = \\left(\\mathbf{1}\\mathbf{s}_i^T -\\widetilde{\\mathbf{Q}}_i\\right)\\in \\mathbb{R}^{m\\times n}" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 318, + 304, + 521, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 304, + 521, + 317 + ], + "spans": [ + { + "bbox": [ + 318, + 304, + 521, + 317 + ], + "type": "text", + "content": "Taking the derivative of Eq. (20) w.r.t " + }, + { + "bbox": [ + 318, + 304, + 521, + 317 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_i" + }, + { + "bbox": [ + 318, + 304, + 521, + 317 + ], + "type": "text", + "content": ", it yields" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 375, + 324, + 545, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 324, + 545, + 357 + ], + "spans": [ + { + "bbox": [ + 375, + 324, + 545, + 357 + ], + "type": "interline_equation", + "content": "\\mathbf {w} _ {i} = \\frac {\\left(\\mathbf {B} _ {i} \\mathbf {B} _ {i} ^ {T}\\right) ^ {- 1} \\mathbf {1}}{\\mathbf {1} ^ {T} \\left(\\mathbf {B} _ {i} \\mathbf {B} _ {i} ^ {T}\\right) ^ {- 1} \\mathbf {1}}. \\tag {21}", + "image_path": "393d40d812f5ed902378c5e717647167620f57c152217b3ad28e078c9cb8a22f.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 318, + 366, + 366, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 366, + 366, + 380 + ], + "spans": [ + { + "bbox": [ + 318, + 366, + 366, + 380 + ], + "type": "text", + "content": "Update " + }, + { + "bbox": [ + 318, + 366, + 366, + 380 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{Q}}_i" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 380, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 545, + 403 + ], + "type": "text", + "content": "Fixing all the other irrelevant variables in Eq. (6), we have:" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 310, + 410, + 545, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 410, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 310, + 410, + 545, + 441 + ], + "type": "interline_equation", + "content": "\\min _ {\\widetilde {\\mathbf {Q}} _ {i}} \\gamma \\sum_ {v = 1} ^ {m} \\| \\mathbf {Z} ^ {(v)} - \\mathbf {Q} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\sum_ {i = 1} ^ {n} \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {22}", + "image_path": "921fd75118071145af441248a068e3c66d710f56eebe76bac37f6e98951b0e0f.jpg" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 306, + 449, + 544, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 449, + 544, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 544, + 472 + ], + "type": "text", + "content": "Obviously, Eq. (22) is sample-wise independent. Therefore, it can be written as:" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 328, + 479, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 479, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 328, + 479, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\min _ {\\widetilde {\\mathbf {Q}} _ {i}} \\gamma \\| \\widetilde {\\mathbf {Z}} ^ {(v)} - \\widetilde {\\mathbf {Q}} ^ {(v)} \\| _ {F} ^ {2} + \\alpha \\left\\| \\mathbf {s} _ {i} ^ {T} - \\mathbf {w} _ {i} ^ {T} \\widetilde {\\mathbf {Q}} _ {i} \\right\\| _ {2} ^ {2} \\tag {23}", + "image_path": "bbb50d71de5b4065e99287591f4460d3a7e1846f8f777dc0421d30c9ec4e967c.jpg" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 318, + 514, + 541, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 514, + 541, + 526 + ], + "spans": [ + { + "bbox": [ + 318, + 514, + 541, + 526 + ], + "type": "text", + "content": "Naturally, by taking the derivative of Eq. (23), it yields:" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 330, + 533, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 533, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 330, + 533, + 545, + 555 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {Q}} _ {i} = \\left(\\gamma \\mathbf {I} + \\alpha \\mathbf {w} _ {i} \\mathbf {w} _ {i} ^ {T}\\right) ^ {- 1} \\left(\\gamma \\widetilde {\\mathbf {Z}} _ {i} + \\alpha \\mathbf {w} _ {i} \\mathbf {s} _ {i} ^ {T}\\right) \\tag {24}", + "image_path": "057e7b6661e81a72a8141af629f523263d3a921c53ac79a73162686112496dc6.jpg" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 545, + 585 + ], + "type": "text", + "content": "The detailed algorithm to solve the objective in Eq. (6) is summarized in Algorithm 2." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 596, + 382, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 596, + 382, + 609 + ], + "spans": [ + { + "bbox": [ + 306, + 596, + 382, + 609 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 616, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 545, + 652 + ], + "type": "text", + "content": "This section is comprised of four sub-sections: experimental setting, result analysis, robustness analysis and convergence analysis." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 659, + 421, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 421, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 421, + 672 + ], + "type": "text", + "content": "5.1. Experiment Setting" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "We compare our proposed method with several multiview clustering methods: Multi-view Spectral Clustering with Co-training strategy(Co-train) [27]. Multi-" + } + ] + } + ], + "index": 40 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23970" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 91, + 286, + 236 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 269, + 82 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 269, + 82 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 269, + 82 + ], + "type": "text", + "content": "Table 1. The clustering results on 100leaves dataset (%)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 91, + 286, + 236 + ], + "lines": [ + { + "bbox": [ + 50, + 91, + 286, + 236 + ], + "spans": [ + { + "bbox": [ + 50, + 91, + 286, + 236 + ], + "type": "table", + "html": "
MethodACCNMIPurityF-score
Co-train33.21 ± 0.8557.59 ± 0.7336.10 ± 0.8115.88 ± 0.79
Co-reg32.16 ± 0.9358.97 ± 0.8236.00 ± 0.8217.33 ± 0.99
DiMSC48.52 ± 1.5771.24 ± 0.5551.14 ± 1.4133.66 ± 1.17
AMGL77.66 ± 1.5890.35 ± 0.9782.29 ± 1.1659.54 ± 7.04
MVGL54.12 ± 0.0063.96 ± 0.0057.44 ± 0.008.58 ± 0.00
WMSC77.26 ± 0.9989.81 ± 0.4779.62 ± 0.6871.11 ± 1.31
AWP66.13 ± 0.0085.52 ± 0.0068.19 ± 0.0060.75 ± 0.00
MCGC90.25 ± 0.0093.90 ± 0.0091.13 ± 0.0077.79 ± 0.00
LRMSC75.25 ± 1.5687.64 ± 0.5477.60 ± 1.3166.62 ± 1.46
MVCTM68.63 ± 0.0076.46 ± 0.0072.25 ± 0.0016.52 ± 0.00
SMVSC37.94 ± 0.2765.04 ± 0.2939.42 ± 0.2323.22 ± 0.39
FPMVS35.14 ± 0.2063.06 ± 0.4336.96 ± 0.2622.12 ± 0.38
CSMSC76.06 ± 1.1588.83 ± 0.4378.96 ± 0.8168.91 ± 1.25
Ours90.86 ± 0.0196.38 ± 0.0092.46 ± 0.0188.69 ± 0.01
", + "image_path": "888c6e6de62a808115e246414e8a6050905685923de9e5344aedd6ac52257e27.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 278, + 286, + 423 + ], + "blocks": [ + { + "bbox": [ + 75, + 258, + 259, + 269 + ], + "lines": [ + { + "bbox": [ + 75, + 258, + 259, + 269 + ], + "spans": [ + { + "bbox": [ + 75, + 258, + 259, + 269 + ], + "type": "text", + "content": "Table 2. The clustering results on HW dataset (%)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 278, + 286, + 423 + ], + "lines": [ + { + "bbox": [ + 50, + 278, + 286, + 423 + ], + "spans": [ + { + "bbox": [ + 50, + 278, + 286, + 423 + ], + "type": "table", + "html": "
MethodACCNMIPurityF-score
Co-train81.28 ± 5.3772.04 ± 2.9882.25 ± 4.1170.93 ± 4.19
Co-reg54.96 ± 4.3547.46 ± 1.9758.64 ± 2.8742.62 ± 2.40
DiMSC46.26 ± 0.4532.97 ± 0.3346.79 ± 0.4727.92 ± 0.27
AMGL93.76 ± 8.5795.02 ± 4.2394.89 ± 6.7893.63 ± 7.16
MVGL85.35 ± 0.0085.19 ± 0.0085.75 ± 0.0082.48 ± 0.00
WMSC74.87 ± 0.1466.79 ± 0.1974.95 ± 0.1663.65 ± 0.22
AWP69.55 ± 0.0059.49 ± 0.0071.45 ± 0.0058.35 ± 0.00
MCGC53.95 ± 0.0061.78 ± 0.0054.10 ± 0.0057.25 ± 0.00
LRMSC79.39 ± 2.9576.49 ± 1.3383.25 ± 1.4772.83 ± 1.89
MVCTM98.75 ± 0.0096.91 ± 0.0098.75 ± 0.0097.52 ± 0.00
SMVSC78.59 ± 0.4669.03 ± 0.5778.90 ± 0.3867.65 ± 0.76
FPMVS78.40 ± 0.1870.88 ± 0.8978.77 ± 0.4169.66 ± 0.85
CSMSC86.87 ± 0.0280.04 ± 0.0986.87 ± 0.0278.05 ± 0.04
Ours99.25 ± 0.0098.15 ± 0.0099.25 ± 0.0098.51 ± 0.00
", + "image_path": "5eb060f4be52a1f052724eed7dffcc1c4f62f78d5f36b3368b3dbd6e869b9584.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 465, + 286, + 609 + ], + "blocks": [ + { + "bbox": [ + 70, + 445, + 264, + 456 + ], + "lines": [ + { + "bbox": [ + 70, + 445, + 264, + 456 + ], + "spans": [ + { + "bbox": [ + 70, + 445, + 264, + 456 + ], + "type": "text", + "content": "Table 3. The clustering results on MSRC dataset (%)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 465, + 286, + 609 + ], + "lines": [ + { + "bbox": [ + 50, + 465, + 286, + 609 + ], + "spans": [ + { + "bbox": [ + 50, + 465, + 286, + 609 + ], + "type": "table", + "html": "
MethodACCNMIPurityF-score
Co-train64.95 ± 6.2454.27 ± 4.1866.52 ± 5.0052.59 ± 4.97
Co-reg63.95 ± 4.5057.89 ± 2.9967.24 ± 4.4755.31 ± 3.98
DiMSC71.90 ± 0.9559.62 ± 0.9671.90 ± 0.9558.02 ± 1.08
AMGL76.71 ± 4.3370.98 ± 2.2079.00 ± 2.8067.13 ± 2.49
MVGL70.48 ± 0.0058.18 ± 0.0070.48 ± 0.0054.56 ± 0.00
WMSC69.05 ± 0.0059.55 ± 0.1771.43 ± 0.0057.57 ± 0.08
AWP63.33 ± 0.0054.88 ± 0.0063.33 ± 0.0053.76 ± 0.00
MCGC80.48 ± 0.0070.18 ± 0.0080.95 ± 0.0072.46 ± 0.00
LRMSC71.81 ± 2.8962.42 ± 1.5874.14 ± 1.7860.08 ± 1.57
MVCTM85.71 ± 0.0076.15 ± 0.0085.71 ± 0.0074.90 ± 0.00
SMVSC81.43 ± 0.0070.18 ± 0.0081.43 ± 0.0069.36 ± 0.00
FPMVS78.57 ± 0.0066.84 ± 0.0078.57 ± 0.0068.36 ± 0.00
CSMSC80.43 ± 0.1471.36 ± 0.1980.43 ± 0.1470.06 ± 0.21
Ours87.14 ± 0.0078.21 ± 0.0087.14 ± 0.0077.87 ± 0.00
", + "image_path": "54fb719f8b056ed4676345333407d8d0ec6e3d653a3d900b2012c1d89df36123.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "view Spectral Clustering with Co-regularized strategy(Coreg) [28]. Diversity-induced Multi-view Subspace Clustering(DiMSC) [14]. Auto-weighted Multiple Graph Learning(AMGL) [29]. Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Graph Learning for Multiview Clustering(MVGL) [30]. Weighted Multi-view Spec" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 91, + 545, + 236 + ], + "blocks": [ + { + "bbox": [ + 332, + 71, + 519, + 82 + ], + "lines": [ + { + "bbox": [ + 332, + 71, + 519, + 82 + ], + "spans": [ + { + "bbox": [ + 332, + 71, + 519, + 82 + ], + "type": "text", + "content": "Table 4. The clustering results on ORL dataset (%)" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 91, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 309, + 91, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 309, + 91, + 545, + 236 + ], + "type": "table", + "html": "
MethodACCNMIPurityF-score
Co-train61.90 ± 3.1979.23 ± 1.5865.60 ± 2.2350.88 ± 3.26
Co-reg61.65 ± 2.8179.38 ± 1.6966.22 ± 2.1451.39 ± 3.51
DiMSC80.03 ± 1.7890.63 ± 0.8882.93 ± 1.1774.61 ± 1.91
AMGL73.15 ± 3.2285.59 ± 1.0978.27 ± 2.0158.89 ± 3.62
MVGL49.00 ± 0.0066.30 ± 0.0058.00 ± 0.0018.24 ± 0.00
WMSC76.60 ± 3.7088.26 ± 1.6879.75 ± 2.8569.84 ± 4.38
AWP74.50 ± 0.0086.02 ± 0.0076.25 ± 0.0065.18 ± 0.00
MCGC77.00 ± 0.0087.22 ± 0.0082.75 ± 0.0056.25 ± 0.00
LRMSC79.62 ± 3.0990.49 ± 1.5083.42 ± 2.4673.99 ± 3.96
MVCTM59.50 ± 0.0072.58 ± 0.0066.75 ± 0.0023.98 ± 0.00
SMVSC58.28 ± 0.5176.07 ± 0.1461.75 ± 0.3043.96 ± 0.33
FPMVS55.45 ± 0.5973.72 ± 0.4859.27 ± 0.5641.02 ± 0.69
CSMSC77.57 ± 1.8889.20 ± 0.9580.77 ± 1.7871.69 ± 2.58
Ours84.35 ± 0.0291.78 ± 0.0186.45 ± 0.0178.58 ± 0.02
", + "image_path": "4d93a7fa51d1616d52e821bdf8805389eaf4812780ba3663131cf1bf27d21be3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 278, + 545, + 423 + ], + "blocks": [ + { + "bbox": [ + 328, + 258, + 524, + 269 + ], + "lines": [ + { + "bbox": [ + 328, + 258, + 524, + 269 + ], + "spans": [ + { + "bbox": [ + 328, + 258, + 524, + 269 + ], + "type": "text", + "content": "Table 5. The clustering results on Cornell dataset (%)" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 278, + 545, + 423 + ], + "lines": [ + { + "bbox": [ + 309, + 278, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 309, + 278, + 545, + 423 + ], + "type": "table", + "html": "
MethodACCNMIPurityF-score
Co-train41.38 ± 1.6722.36 ± 1.4354.26 ± 1.9034.86 ± 0.90
Co-reg36.26 ± 2.0013.68 ± 1.4547.28 ± 1.7731.98 ± 1.41
DiMSC40.15 ± 1.7617.95 ± 0.8252.77 ± 0.6734.58 ± 0.57
AMGL37.38 ± 4.444.26 ± 0.3744.82 ± 0.3437.24 ± 3.51
MVGL44.10 ± 0.009.42 ± 0.0045.64 ± 0.0038.10 ± 0.00
WMSC46.10 ± 0.1521.69 ± 0.1752.26 ± 0.1537.24 ± 0.12
AWP38.97 ± 0.0013.63 ± 0.0049.74 ± 0.0033.72 ± 0.00
MCGC36.41 ± 0.0022.60 ± 0.0053.85 ± 0.0033.79 ± 0.00
LRMSC34.77 ± 1.628.51 ± 1.4843.95 ± 0.7628.99 ± 0.72
MVCTM40.00 ± 0.0015.20 ± 0.0051.79 ± 0.0036.89 ± 0.00
SMVSC48.67 ± 2.2120.61 ± 1.3653.90 ± 0.8742.14 ± 2.28
FPMVS35.90 ± 0.0017.67 ± 0.0053.33 ± 0.0033.20 ± 0.00
CSMSC47.33 ± 0.3323.86 ± 0.3655.49 ± 0.2137.87 ± 0.37
Ours51.28 ± 0.0034.81 ± 0.0061.03 ± 0.0042.03 ± 0.00
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MethodACCNMIPurityF-score
Co-train53.94 ± 4.2157.90 ± 3.1455.52 ± 4.1138.68 ± 3.72
Co-reg56.36 ± 3.4960.30 ± 3.0557.64 ± 3.2541.43 ± 3.79
DiMSC64.36 ± 3.4066.57 ± 2.3064.79 ± 3.2249.41 ± 2.90
AMGL59.94 ± 3.6462.95 ± 2.7861.33 ± 2.9341.87 ± 4.18
MVGL44.85 ± 0.0049.19 ± 0.0046.67 ± 0.0026.05 ± 0.00
WMSC61.88 ± 3.6465.40 ± 2.8962.12 ± 3.8448.08 ± 3.53
AWP61.82 ± 0.0065.77 ± 0.0061.82 ± 0.0049.71 ± 0.00
MCGC67.27 ± 0.0068.92 ± 0.0067.27 ± 0.0048.33 ± 0.00
LRMSC68.36 ± 1.1170.36 ± 1.1168.55 ± 1.1052.27 ± 1.67
MVCTM62.42 ± 0.0066.14 ± 0.0062.42 ± 0.0047.40 ± 0.00
SMVSC60.36 ± 0.9562.23 ± 1.3760.73 ± 0.8943.05 ± 1.51
FPMVS44.24 ± 0.0049.76 ± 0.0046.67 ± 0.0030.45 ± 0.00
CSMSC64.06 ± 2.9168.22 ± 1.4964.12 ± 2.8051.84 ± 1.76
Ours71.03 ± 0.0174.51 ± 0.0171.21 ± 0.0059.72 ± 0.01
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Multi-view Clustering on Topological Manifold(MVCTM) Fast Parameter-free Multi-view Subspace Clustering with" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23971" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 165, + 186 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 165, + 186 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 165, + 186 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 165, + 186 + ], + "type": "image", + "image_path": "0fdb392acd97236fcb18ff73e57f74026cac470babee7b7f9597ab05fa04ac3f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 190, + 137, + 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Parameter analysis on ORL dataset" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 430, + 326, + 546, + 438 + ], + "blocks": [ + { + "bbox": [ + 453, + 316, + 522, + 324 + ], + "lines": [ + { + "bbox": [ + 453, + 316, + 522, + 324 + ], + "spans": [ + { + "bbox": [ + 453, + 316, + 522, + 324 + ], + "type": "text", + "content": "(h) " + }, + { + "bbox": [ + 453, + 316, + 522, + 324 + ], + "type": "inline_equation", + "content": "\\lambda = 1\\gamma = 1000" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 430, + 326, + 546, + 438 + ], + "lines": [ + { + "bbox": [ + 430, + 326, + 546, + 438 + ], + "spans": [ + { + "bbox": [ + 430, + 326, + 546, + 438 + ], + "type": "image", + "image_path": "9020ad258edb20934530cf07cca5d400adb24090e6222aca540250a9a0a5c4a3.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 453, + 441, + 522, + 451 + ], + "lines": [ + { + "bbox": [ + 453, + 441, + 522, + 451 + ], + "spans": [ + { + "bbox": [ + 453, + 441, + 522, + 451 + ], + "type": "text", + "content": "(1) " + }, + { + "bbox": [ + 453, + 441, + 522, + 451 + ], + "type": "inline_equation", + "content": "\\lambda = 10\\gamma = 1000" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 493, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 589 + ], + "type": "text", + "content": "Consensus Anchor Guidance(FPMVS) [35]. Multi-view Subspace Clustering with Unified Anchors(SMVSC) [36] Consistent and Specific Multi-View Subspace Clustering(CSMSC) [6]. Rather than adopting view-wise weighing strategy like the above mentioned methods, we delicately conduct graph fusion in a sample-wise manner. Thus, the superiority of our proposed approach could be demonstrated in the experiment section." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "As for benchmark datasets, we adopt 100leaves, HW, MRSC, ORL, Cornell and Yale. Specifically, the leaves data set (100leaves) consists of 1,600 leaves from each of 100 plant species. For each sample, margin, shape and texture are given as three distinct views. Handwritten numerals data (HW) is composed of 2,000 data points for digits 0 to 9 from UCI machine learning repository and two public features are available. MSRC data set contains 210 images and can be separated into 7 classes including cow, airplane, face, bicycle, tree, building and car. There are five visual" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 493, + 545, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 599 + ], + "type": "text", + "content": "features from each sample. ORL consists of 400 face images in 40 different themes in total. For each subject, the images are described in three features: facial expressions, facial details and the lighting. Cornell, which is collected by Cornell University, contains 195 web pages and a web page is made of 2 views: content features and cites features. Dataset Yale contains 165 gray-scale images under varying poses and illuminations, where every image is of size " + }, + { + "bbox": [ + 304, + 493, + 545, + 599 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 493, + 545, + 599 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 610, + 400, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 400, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 400, + 623 + ], + "type": "text", + "content": "5.2. Result Analysis" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "With the aim of evaluating our proposed approach adequately with above mentioned SOTA multi-view clustering methods, we adopt four widely used criteria including Normalized Mutual Information(NMI), Accuracy(ACC), Purity and F-Score. The clustering results are reported in Tables (1)-(6). We can arrive at a conclusion that our method is very effective and competitive as the proposed method" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23972" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 202, + 169 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 202, + 169 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 202, + 169 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 202, + 169 + ], + "type": "image", + "image_path": "e8f0b201d3df08c0636a77391bb7187a03ca87a17f449eabfe85ec1d551d16c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 107, + 172, + 154, + 181 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Convergence curves on all datasets" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 335, + 287, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 430 + ], + "type": "text", + "content": "outperforms other competitors in the majority of cases. In detail, our method consistently obtains the best results in terms of NMI, ACC and Purity on all datasets. While for F-score, the proposed method surpasses the compared methods except in one case on dataset Cornell. The superiority of our method explicitly demonstrates the effectiveness of the sample-wise learning strategy and corroborates our theoretical findings." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 439, + 171, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 171, + 451 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 171, + 451 + ], + "type": "text", + "content": "5.3. Parameter Discussion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": "With the aim of studying what impact different parameter settings will have on the clustering results, we vary " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": " in the ranges " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "[1e^{-4},\\dots,1e^{4}]" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "[1e^{-4},\\dots,1e^{4}]" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "[1e^{-1},\\dots,1e^{2}]" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "inline_equation", + "content": "[1,\\dots,1e^{3}]" + }, + { + "bbox": [ + 46, + 458, + 287, + 579 + ], + "type": "text", + "content": ", respectively. Taking the ORL dataset as an example, we can see the clustering performance is quite stable with respect to different parameter settings, as shown in Figure (3). Considering that there is little difference among the performances of diverse parameter combinations, we can come to a conclusion that our approach is robust to the hyper parameters." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 587, + 173, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 173, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 173, + 600 + ], + "type": "text", + "content": "5.4. Convergence Analysis" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Owing to the fact that the optimization of our proposed method is essentially a non-convex problem that is solved by an iterative algorithm, it is critical to validate the convergence of our model. Therefore, this section empirically showcases the convergence property and how fast our algorithm can converge. The convergence curves of our model on six datasets shown in Fig. (4) demonstrate the effectiveness of our optimization approach. Note that despite the non-convexity of Eq. (6), our model can still discover an" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 335, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 371 + ], + "type": "text", + "content": "optimal solution for each variable and achieve a local minima within a few iterations, which verifies the effectiveness of the proposed optimization algorithm." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 384, + 378, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 378, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 378, + 396 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 405, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 608 + ], + "type": "text", + "content": "In this paper, we propose to exploit the implied data manifold by learning the topological structure of data. Besides, considering that the consistency of multiple views is manifested in the generally similar local structure while the inconsistent structures are the minority, we further explore the intersections of multiple views in the sample level such that the cross-view consistency can be better maintained. By leveraging the subtasks of topological relevance learning and the sample-level graph fusion in our collaborative model, each subtask is alternately boosted towards an optimal solution. We also design an efficient algorithm to solve the corresponding optimization problem. Meanwhile, our method generates outstanding results on several authoritative benchmark datasets and is proven to outperform current state-of-the-art methods. In the future, we are interested in extending the proposed model to other machine learning framework such as kernel learning and deep learning." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 621, + 408, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 408, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 408, + 634 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 712 + ], + "type": "text", + "content": "This work is supported by the Key Program of National Science Foundation of China (Grant No. 61836006), partially supported by the National Science Foundation of China under Grant 62106164, and the Sichuan Science and Technology Program under Grants 2021ZDZX0011 and 2022YFG0188." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23973" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Steffen Bickel and Tobias Scheffer. 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Scalable multi-view subspace clustering with unified anchors. 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We find that there is an unexpected concentration of samples with very low curvature. We note that these low curvature samples are largely consistent across completely different architectures, and identifiable in the early epochs of training. We show that the curvature relates to the 'cleanliness' of the data points, with low curvatures samples corresponding to clean, higher clarity samples, representative of their category. Alternatively, high curvature samples are often occluded, have conflicting features and visually atypical of their category. Armed with this insight, we introduce SLo-Curves, a novel coreset identification and training algorithm. SLo-curves identifies the samples with low curvatures as being more data-efficient and trains on them with an additional regularizer that penalizes high curvature of the loss surface in their vicinity. We demonstrate the efficacy of SLo-Curves on CIFAR-10 and CIFAR-100 datasets, where it outperforms state of the art coreset selection methods at small coreset sizes by up to $9\\%$ . The identified coresets generalize across architectures, and hence can be pre-computed to generate condensed versions of datasets for use in downstream tasks. Code is available at https://github.com/ishagarg/Slo-Curves.", + "bbox": [ + 75, + 316, + 472, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 724, + 207, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning applications have exploded due to access to big data and computational resources. However, data is expensive to gather, annotate and store, and directly influences the computational resources required. Storing more data also runs higher risks of data leakage and privacy violation. It also influences parallelism and communication bottlenecks between machines [17]. There is limited understanding of the mechanism through which deep learning models process complex datasets, what constitutes 'good' or 'easy' examples for learning, and how large a number of", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bcdb3abc3546264195bf5b9b1bce646a26db51566bae128cc91ac81a2233f375.jpg", + "image_caption": [ + "Figure 1. Histograms of training dataset's curvature for various networks trained on CIFAR-10." + ], + "image_footnote": [], + "bbox": [ + 501, + 284, + 696, + 489 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/65540c3d6fea8dc5c0bc713ede2b632df6e5f5c9a5fceb5cd468286c8c335c67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 285, + 888, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "samples are indeed beneficial. Research on data efficiency often focuses on doing more with less data. Standard training methods assume all data points from the training set to be independently and identically distributed from the true training distribution. Data points are sampled uniformly during training and treated as having equal significance. An alternative is to identify representative data points from the training distribution that are more beneficial to learning than random uniform sampling [30, 31]. They can be used as smaller condensed datasets, or upweighted during training as per their significance. These subsets of important points are also known as coresets.", + "bbox": [ + 496, + 547, + 890, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Coresets prove useful in many downstream applications. They are data-efficient and can serve as a good choice of proxy data for Neural Architecture Search (NAS) [45, 52], as episodic memory in Continual Learning [2, 6, 60], and as the choice of augmentation samples during self-supervised learning [37]. They can be utilized in many regimes that may have memory or compute resources, such as for compute-efficient learning [35,43,46], dataset condensation [8, 58, 61], efficient Hyper-parameter Optimization (HPO) [33], and speeding up the training of Generative Adversarial Networks (GANs) [54]. The utility of identifying im", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20290", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/489f7cc208fb1cfd78534806784d3c38e490b83d6cb8fd35c7f3d38dd2259178.jpg", + "image_caption": [ + "(a) Top 100 examples with the lowest loss curvature" + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 467, + 383 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7f450764d12846319249f8416222b7f77c48cec70721d183f1474394c5b5d989.jpg", + "image_caption": [ + "(b) Top 100 examples with the highest loss curvature", + "Figure 2. We visualize the 10 samples from each class with lowest and highest curvature of loss identified over 10 different randomly initialized ResNet18 models trained on CIFAR-10. Each row corresponds to a class, consistent across both figures, and 10 ordered samples for each class are shown. The network was trained with random horizontal flipping as part of the augmentations." + ], + "image_footnote": [], + "bbox": [ + 506, + 90, + 885, + 383 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "important samples can extend beyond efficiency, such as in understanding dataset limitations [5, 55], enabling faster or better convergence by upsampling certain samples during training [12, 40], or in the choice of data to label in active learning [1, 50]. However, it is not always clear what makes a sample informative or good for learning. Methods differ in their definition of significance of samples. Some representative works measure importance via the confidence or margin of the predicted output of the network [1, 11], by clustering samples together in the input or feature space [10, 22], matching the gradient to that of the entire dataset [35, 43, 46], choosing samples that lie closest to the decision boundary [14] or samples that are not forgotten once learnt [57]. Some other representative methods frame it as a submodular function optimization problem [27, 27, 43].", + "bbox": [ + 75, + 470, + 468, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we look at data efficiency from the lens of the loss landscape around the training samples. While the loss surface with respect to the parameters of the neural network has received considerable attention as a means of analyzing the stability of the solution [19, 47-49], the loss landscape with respect to the data is far less studied. Most of the studies have been associated with adversarial robustness [44]. We are interested in the curvature of the loss surface, or inversely, the smoothness of the decision boundary around the data point. This is captured by the local linearity of the gradient around the sample, measured as the trace of the Hessian. We plot the histogram of an efficiently calculable estimation of this trace for the training", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dataset of different pretrained models in Figure 1 for the CIFAR-10 dataset [38]. We note they resemble a bimodal distribution, with a spread out Gaussian superimposed upon a very sharp, tall peak around zero. We are interested in the samples that make up the sharp peak, the ones around which the loss surface curvature is very low.", + "bbox": [ + 496, + 470, + 890, + 560 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We visualize the sample ordered by curvature accumulated over ten differently initialized ResNet18 [23] models trained on CIFAR-10 in Figure 2. We find that they reveal useful information about the kinds of samples present in the dataset. The low curvature samples, shown in Figure 2a can be considered clean, prototypical and minimal, in that they are strongly representative of their category. On the other hand, Figure 2b shows the samples with the highest curvature of loss. We can see that they do not appear to be characteristic of their category. They have confusing backgrounds with interfering patterns, uncommon viewing angles and incomplete shapes. We show that the low curvature samples appear to be largely consistent not only across networks that were initialized differently, but also across completely different architectures such as MobileNetV3 [24], ResNet101 [23], AlexNet [39], VGG19 [53] and DenseNet121 [25]. We also show that they can be identified quite early on during the training process. As an application of this insight, we show that they make very good coresets.", + "bbox": [ + 496, + 565, + 892, + 851 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many coreset selection methods perform well at large coreset sizes, close to the size of the whole dataset. In this paper, we explore smaller coresets, ranging from sin", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20291", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "gle digit images per class, as is often common with few shot learning [16, 18], up to 100 images per class. Depending on the dataset and the number of classes, this can range from $0.1\\%$ to $20\\%$ of the dataset. We introduce SLo-Curves, a novel coreset selection method which identifies samples with low curvatures and train on these coresets with an additional regularizer that penalizes large curvatures. Both the method for measuring the curvature and the form of the regularizer are inspired directly from CURE [44], which introduced the regularizer as a means to promote adversarial accuracy at the expense of clean accuracy. We show that when there are small sample sizes, chosen appropriately, this regularizer also helps improve clean accuracy. We summarize our contributions below:", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We study the loss surface with respect to the input data points and identify an unexpected concentration of samples with very low curvature.", + "2. We show that the curvature of the loss function relates to the notion of visual 'cleanliness'. Low curvature samples are free of conflicting features, while high curvature samples look cluttered, obstructed or unrepresentative of the other samples in the class. To the best of our knowledge, this is a novel observation.", + "3. We show that these samples are largely architecture and initialization independent. This implies that the Hessian reveals intrinsic properties of the dataset rather than just an artifact of the training procedure, a particular local minima, or the choice of network architecture.", + "4. We introduce SLo-Curves: an algorithm that selects samples with low curvature as coresets and additionally penalizes the curvature of the loss function while training on them. SLo-Curves outperforms all other choices of coreset selection methods by up to $9\\%$ for coresets of few samples per class. To the best of our knowledge, this is the first paper to explore second order statistics of the loss with respect to the data for coreset selection.", + "5. Due to these samples being consistent across architectures, SLo-Curves does not rely on gradient statistics during training or need to be averaged out over multiple initializations. Coresets can be pre-computed and are performant across architectures. We also find that these points can be identified early on during training, in as few as 5-10 epochs." + ], + "bbox": [ + 76, + 311, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is inherently more productive at small core-set sizes since the samples that we identify belong to the limited set that have very low curvature, corresponding to the tall peak at zero in Figure 1. Further study is required to understand what causes the decision boundary to smoothen along the same samples with different networks, and we hope that this paper accelerates interest in this direction.", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Literature Review", + "text_level": 1, + "bbox": [ + 500, + 90, + 678, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The importance of samples is a relevant concern in many areas. Importance sampling methods [30, 31] prioritize the important samples for fast and efficient training by approximating the norm of the gradient resulting from each sample. Curriculum learning [4] seeks to order sample exposure to the network during training in order to learn easier samples first and then harder samples for better solutions. Active learning [51] focuses on only labeling the important samples to reduce annotation costs. However, the definition of importance of samples is not fixed. In this section, we focus on coreset selection as a base method for deciding sample importance scores, that can be then used to different ends. We broadly classify techniques for coreset selection in deep learning and discuss representative approaches in each.", + "bbox": [ + 496, + 114, + 893, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Clustering based methods: Points close to each other can be clustered together and represented well by the cluster center. The choice of metric for clustering varies. Authors of [10] clusters samples based on distance in the feature space. Authors of [22] reframe the problem as solving a minimax facility location problem greedily.", + "bbox": [ + 496, + 325, + 893, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Classification Output based methods: These approaches work on the assumption that examples that are classified with lesser confidence or score are more informative than examples classified with strong confidence. Authors of [11] study the effects of choosing softmax scores, entropy and the distance of the top-2 classes in the output space. A different approach is taken by the authors of [57], who show that a large majority of samples are learned correctly early on during training and are never consequently classified incorrectly, or forgotten, during the remaining course of training. They deem the samples that are never forgotten once learnt, as easily learned, and create coresets that consist of examples that need to be re-learnt.", + "bbox": [ + 496, + 417, + 893, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Loss Gradient based methods: This approach categorizes the importance of a sample as its contribution to the loss or the gradient of the loss. Methods vary in their choice of the time of training at which the contribution is measured. Both Grad-Match [35] and CRAIG [43] select weighted subsets such that the appropriately scaled gradient of the subset matches the gradient of the entire dataset. Both reselect the subset and weights every few epochs. They differ in the choice of algorithm for building the dataset, with CRAIG converting the gradient-distance optimization problem into a submodular function and then using a greedy approach and Grad-Match using a different greedy Orthogonal Matching Pursuit algorithm. Both outline convergence guarantees, and show scalability via approximating gradients of the loss with respect to the input with gradients at the last layer [31]. To overcome the requirement for reselecting the coresets during training, authors of [46] introduce GraNd, which approximates the L2 norm of the gradient early on in training (after a few epochs) and averages it", + "bbox": [ + 496, + 613, + 895, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20292", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "over many different training initializations.", + "bbox": [ + 76, + 90, + 361, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Bilevel optimization and submodular function methods: Glister [36] and Retrieve [37] frame the minimization of the loss on selected samples and the selection of samples as a bilevel optimization problem. Authors of [27, 28] explore different submodular optimization functions.", + "bbox": [ + 76, + 109, + 467, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decision Boundary based methods: These methods assume that the points closest to the boundary are hardest to separate, and hence most informative. Authors of [14] utilize DeepFool, a method to generate adversarial examples, as a way of measuring distance to boundary. If an example is easier to fool, it is presumably closer to the boundary and significant. Authors of [42] select the samples whose classification likelihood is most dissimilar to its neighbors.", + "bbox": [ + 76, + 189, + 467, + 310 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Synthetic coreset creation methods: In contrast to selecting points from the dataset, there has been recent interest in methods that create synthetic data to mimic the overall distribution. Dataset distillation [58] was introduced to create synthetic data by matching the gradient of samples averaged over many different initializations. Authors of [8] improve performance by repeating the synthetic set creation over many iterations. However, the datasets do not resemble the data, and this can be an advantage or disadvantage based on the application. In this manuscript we only study the samples present in the training distribution.", + "bbox": [ + 76, + 315, + 467, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Coreset selection libraries: Coreset selection in deep learning is an area of rapidly increasing focus, as evidenced by the release of recent libraries that compare different core-set selection methods, and can be incorporated into other deep learning applications. Recently released libraries are CORDS [34], Minicore [3] and DeepCore [21]. We use DeepCore for our simulations.", + "bbox": [ + 76, + 484, + 467, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our method falls under both the categories of decision boundary based methods and loss gradient based methods. We select real samples from the dataset, choosing coresets from pre-trained models based on the trace of the Hessian of the loss. Our coresets consist of the samples with low trace of Hessian, or low loss curvature around them. The selected samples are chosen only once, are not re-weighted and no special optimization is followed besides an additional regularizer that encourages the learned decision boundary to be flat by penalizing the curvature estimate. They generalize across architectures and hence, do not need to be calculated real time for every network.", + "bbox": [ + 76, + 595, + 467, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Methodology and Observations", + "text_level": 1, + "bbox": [ + 76, + 799, + 362, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We study the curvature profiles of the loss with respect to input for different training data points. The curvature profile can be studied via the Hessian of the loss. Concretely, let's consider a data point $x \\in \\mathbb{R}^d$ . Let $H$ denote the Hessian of the loss, $L$ with respect to the data point $x$ , i.e.", + "bbox": [ + 76, + 824, + 467, + 898 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH (x) = \\left[ \\frac {\\delta^ {2} L (x)}{\\delta x _ {i} \\delta x _ {j}} \\right] _ {i, j = 1 \\dots d}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 104, + 787, + 141 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The curvature profile is captured by the eigenvalues. A good measure is the sum of the eigenvalues or the trace of the Hessian [13, 32]. The higher the trace, the more the loss surface curves around the data point, or the less smooth the decision boundary at the data point's vicinity. We plot the histogram of an approximation of the Hessian trace (explained in section 3.1) for the training set of different network architectures in Figure 1, at the end of training on CIFAR-10. We note that they follow a similar trend: a sharp tall peak at very small values, and another Gaussian-like peak later. We focus on the set of samples with very low curvatures that make up the sharp peak at zero. Histograms for different architectures can be found in Appendix A. We note that these networks were trained with Cross Entropy Loss, SGD optimizer with momentum and L2 regularization. There is no term explicitly encouraging a low spread of curvature for some samples.", + "bbox": [ + 498, + 151, + 890, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Calculating the Curvature", + "text_level": 1, + "bbox": [ + 500, + 420, + 736, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The eigenvalues of the Hessian of the loss with respect to the data point contain information about the curvature profile of the loss surface around the data point. Large absolute eigenvalues imply a large curvature of the loss function around the sample, and small magnitude of eigenvalues imply that the loss function (or the decision boundary) has a small curvature, or is locally linear in the vicinity of the data point. The Hessian of the loss surface with respect to model weights has been utilized to study the properties of the minima the optimization selects. [19, 47-49]. However, in this paper, we instead study the curvature of the loss surface with respect to the training data.", + "bbox": [ + 498, + 445, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to study the curvature profile without having to explicitly calculate the Hessian and its eigenvalues, we estimate instead the trace of the Hessian. The trace is the sum of the eigenvalues and can be calculated efficiently via Hutchinson's trace estimator [26] and finite difference approximation. This is the same form of curvature measure used in CURE [44] as the curvature regularizer for enhancing adversarial robustness during training. We now go into the details of this formulation.", + "bbox": [ + 498, + 628, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $\\lambda_{i}$ , $i = 1\\dots d$ be the eigenvalues of the Hessian $H(x)$ . We are interested in the spectrum of the magnitude of the eigenvalues, which can be summarized by the sum of the square of the eigenvalues. This can be estimated by the norm of the Hessian-vector product as introduced in the Hutchinson's trace estimator [26]. Using Hutchinson's trace estimator, the definitions of the Frobenius norm of a matrix, properties of the trace, and the fact that $H(x)$ is symmetric, we get the following estimate:", + "bbox": [ + 500, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20293", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/613d8cb6e229913696630f491faae10359698e232e849aab7b7726ec3695d54f.jpg", + "image_caption": [ + "(a) Curvatures accumulated over differently seeded ResNet-18" + ], + "image_footnote": [], + "bbox": [ + 88, + 93, + 468, + 292 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8c2351399b22b3907779c97dd5ac7374345a94b357ea4cfb860490c3ea2e8ef5.jpg", + "image_caption": [ + "(b) Curvatures accumulated over different architectures", + "Figure 3. Histograms of curvature of the training set of CIFAR-10, with curvature estimates accumulated over different trained models." + ], + "image_footnote": [], + "bbox": [ + 516, + 93, + 888, + 291 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\sum \\lambda_ {i} ^ {2} = T r (H ^ {2}) \\\\ = \\mathbb {E} _ {z} \\left[ z ^ {T} H ^ {2} z \\right] \\\\ = \\mathbb {E} _ {z} \\left[ z ^ {T} H ^ {T} H z \\right] \\\\ = \\mathbb {E} _ {z} \\left[ (H z) ^ {T} (H z) \\right] \\\\ = \\mathbb {E} _ {z} \\left[ \\| H z \\| _ {F} ^ {2} \\right] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 367, + 362, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $z$ are Rademacher random variables, equal to $+1$ or $-1$ with equal probability, i.e. $z \\sim^{i.i.d} \\{-1, +1\\}^d$ . We now use finite approximation to estimate the Hessian vector product efficiently.", + "bbox": [ + 75, + 484, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH z = \\frac {\\nabla L (x + h z) - \\nabla L (x)}{h} \\quad \\text {f o r} h \\rightarrow 0\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 549, + 418, + 580 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The cost of calculating this is just the cost of performing a backward pass on the network twice. This formulation is widely used whenever the curvatures of loss surface are discussed [7, 9, 49, 59]. Similar to CURE [44], we do not choose random directions for sampling $z$ to take the expectation over. Instead, we choose the adversarial direction, which is known to lead to high curvature [15, 29], and set $z$ to be $\\frac{\\text{sign} \\nabla L(x)}{\\|\\text{sign}(\\nabla L(x))\\|}$ . We found the results to not be significantly impacted by $h$ and set it equal to 3 to match the change used in corresponding adversarial settings [20, 41].", + "bbox": [ + 75, + 584, + 468, + 737 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Putting this together, the measure of curvature of the decision boundary or the loss function around a data point is proportional to the following quantity, $\\gamma$ where:", + "bbox": [ + 75, + 738, + 468, + 784 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\gamma (x) = \\| \\nabla_ {x} L (x + h z) - \\nabla_ {x} L (x) \\|; \\\\ \\text {w h e r e} z = \\frac {\\operatorname {s i g n} \\nabla_ {x} L (x)}{\\| \\operatorname {s i g n} (\\nabla_ {x} L (x)) \\|} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 790, + 441, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Consistency of Low Curvature Samples", + "text_level": 1, + "bbox": [ + 76, + 847, + 416, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We notice that the low curvature samples are largely consistent across architectures and initialization. We show this", + "bbox": [ + 76, + 869, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "overlap in Figure 3, with plots of the histogram of cumulative curvature values of samples (estimated by $\\gamma$ ), accumulated over different seeds in Figure 3a and over different architectures in Figure 3b. Mathematically, the $i^{th}$ curve corresponds to the histogram of $\\sum_{j=0}^{i} \\gamma_{j}$ for all training samples, where $j$ indexes different trained models. The first histogram is shown in blue, with unaccumulated curvature estimates ( $\\gamma_{0}$ collected from model 'seed0' or 'ResNet101'). Next the curvature estimates of the second model ( $\\gamma_{1}$ for 'seed1' or 'ResNet18') are added to the first model's curvature estimates for each sample and the resulting plot is shown in orange. As we accumulate curvature estimates over many different models, the sharp peak at zero starts to spread out a bit. Yet, even after accumulating over 5 seeds or 6 different architectures all converging to different minima, there are more than 2000 common low curvature samples (identified as the smallest, purple peak at zero). This implies that these samples appear to be an intrinsic property of the dataset rather than the initialization or the local minima the networks converged to. We corroborate this experimentally in Section 4.3, by showing that a ResNet18 model trained on coresets identified on any of these architectures outperforms random sampling by an average of $5.3\\%$ .", + "bbox": [ + 496, + 347, + 890, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Identified Coresets", + "text_level": 1, + "bbox": [ + 500, + 709, + 679, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now visualize the low and high curvature samples (taken from the accumulated scores of 10 randomly seeded ResNet18 models trained on CIFAR10) in Figures 2. Each row corresponds to a class, and contains the top 10 samples for that class with the lowest and highest curvatures in Figures 2a and 2b, respectively. As can be seen from the figure, the low curvature samples are very 'good' samples, in that they have low to no conflicting backgrounds, structure typical of the class, are centered and are not zoomed in or trimmed. The networks are trained with random left to right flipping, and hence we see samples facing both ways. On", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20294", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a83f440785c93374c5329345648babea172fde44fa896d59e1360805af54ba86.jpg", + "image_caption": [ + "ResNet18, CIFAR10", + "Figure 4. The histogram of curvature estimates of the training dataset as training progresses. For ease of visualization, the opacity of the curves decreases with epochs." + ], + "image_footnote": [], + "bbox": [ + 89, + 106, + 421, + 287 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "the other hand, the high curvature samples are 'bad' in that they are visually harder to identify by humans as well. They have conflicting backgrounds (a deer in a fiery landscape), uncommon viewing angles (a truck from behind) and colors uncharacteristic of the class (a blue plane or a yellow frog). This implies that the curvature, captured by $\\gamma$ could be useful as a metric for 'learnability' of a sample.", + "bbox": [ + 75, + 356, + 467, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Early Emergence of Low Curvature Samples", + "text_level": 1, + "bbox": [ + 76, + 474, + 455, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We track $\\gamma$ through the training progress to study the emergence of low curvature samples, and visualize this in Figure 4. As training progresses (lesser opaque histograms in the figure), we can see the peak towards zero becoming more defined. We find that the concentration of samples around low curvatures emerges in as few as 5-10 epochs of training. We corroborate this in Section 4.5 by showing that the coresets identified by our proposed method as early as epoch 10 outperform random sampling by an average of $4.7\\%$ accuracy across all considered coreset sizes.", + "bbox": [ + 75, + 498, + 468, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. SLo-Curves: An Algorithm for Data Efficiency", + "text_level": 1, + "bbox": [ + 76, + 660, + 467, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on these insights, we propose SLo-Curves, an algorithm to identify coresets of samples with low curvature and train on them for increased sample efficiency. We use curvature estimate, $\\gamma$ as the selection metric, choosing samples with the lowest values to make up our coreset. Additionally, we show that regularizing the learned curvature around these coresets helps increase the accuracy by a few percentage points. Hence, we first select the points with the lowest $\\gamma$ from pretrained networks, and then train a new randomly initialized network on these points using the standard cross entropy loss $L_{CE}(x)$ and $\\gamma$ serving as the additional regularizer term, $L_{reg} = \\gamma (x)$ . The new loss is thus:", + "bbox": [ + 75, + 685, + 467, + 867 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL (x) = L _ {C E} (x) + \\lambda \\gamma (x)\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 883, + 359, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The tradeoff parameter $\\lambda$ is the only hyperparameter our method induces and is searched over $\\{0,0.5,1,5,10,20,50\\}$ . We note that smaller coresets require larger values of $\\lambda$ and larger coresets require smaller values, ultimately giving better results when the additional regularizer is turned off. This ties with CURE [44], wherein the same regularizer improves adversarial accuracy at the cost of clean accuracy when used with the whole dataset. In our method, it serves instead to improve accuracy at low sample complexities. We anticipate that it is an especially effective form of regularization for small datasets learned with complex models. We reiterate that we study small coreset sizes since our significance metric is based on the samples that concentrate near zero curvature, and the number of such samples is a limited percentage of the dataset.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Results and Discussion", + "text_level": 1, + "bbox": [ + 498, + 325, + 714, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we outline our network architectures, the training hyperparameters and discuss results.", + "bbox": [ + 496, + 351, + 890, + 381 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Details", + "text_level": 1, + "bbox": [ + 498, + 385, + 697, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We run experiments on CIFAR-10 and CIFAR-100 datasets [38]. Both datasets have 50,000 training samples with CIFAR-10 having 5000 samples for each of its 10 classes and CIFAR-100 having 500 samples for each of its 100 classes. The networks used are ResNet-18 [23], ResNet-101 [23], VGG-19 [53], AlexNet [39], MobileNetV3Small [24] and DenseNet-121 [25]. We consider coreset of small sizes, ranging from 1 to 100 samples per class. For all networks, we use a learning rate of 0.1 scaled by 0.1 at epochs 81 and 121, SGD optimizer with a momentum of 0.9, with Nesterov momentum [56] turned on and a weight decay of 5e-4. We train all networks for 164 epochs and report mean and variance for 5 randomly seeded runs. All graphs show mean values, with corresponding variances shown in Appendix B. We compare with representative works from the broad categories of coreset selection methods. In particular, we compare with 9 other methods: Random uniform sampling, Glister [36], Forgetting [57], CRAIG [43], GraphCut [27], Cal [42], GraNd [46], Herding [10] and Margin [11]. For methods that require training before coreset selection, we train the network for 40 epochs to ensure a good convergence point before we select the coresets. We have run the baselines using the Deepcore [21] library (building upon it for methods and networks as needed), and find that it is an excellent repository of state of the art methods. The only hyperparameter that we tune for our method is the strength of the regularization, $\\lambda$ . We tune this over the search space $\\{0,0.5,1,5,10,20,50\\}$ and report the best results.", + "bbox": [ + 496, + 404, + 890, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with Coreset Selection Methods", + "text_level": 1, + "bbox": [ + 498, + 849, + 877, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We now discuss the results of our method compared to random sampling and other state of the art coreset selec", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20295", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/558586a8e5df7815442c3b974a31cb9f14a3cb824caded6689e95c1c50f9130e.jpg", + "image_caption": [ + "Figure 5. ResNet18 trained on coresets identified by various methods. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.1 and B.2" + ], + "image_footnote": [], + "bbox": [ + 89, + 95, + 472, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/92f5e8c2ec778a226a9226e40a08835a15075e59a0f150d5903d3c3108db3b20.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 93, + 883, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/470844d97c82272b218b52bc4640cd221d84188a8f499ff41ff93b66b927d585.jpg", + "image_caption": [ + "Figure 6. ResNet18 trained on coresets identified by our methods a) from different pretrained architectures and b) with and without regularization. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.3 and B.4." + ], + "image_footnote": [], + "bbox": [ + 89, + 316, + 465, + 503 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a158e91fac58fe6bbbbede2e0c3f05a5078a7ee2ddbe51e2f083d93d9f3d1def.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 316, + 883, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion methods. The results for ResNet18 networks trained on CIFAR-10 and CIFAR-100 are shown in 5a and 5b respectively. The corresponding tables with mean and variances are shown in Appendix B.1 and B.2.", + "bbox": [ + 75, + 566, + 468, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CIFAR-10: Figure 5a shows that selection by the proposed SLo-Curves method outperforms all other coreset methods studied all the way up to 100 samples per class, or $2\\%$ of the total dataset (1000 samples). We note that at such coresets sizes, random sampling forms a surprisingly strong baseline (also noted in [21]). The strongest competitors are the submodular function based method GraphCut [27] and decision boundary based method Cal [42]. SLo-Curves shows the best performance in 16 out of the 19 coreset sizes studied and the second best in the remaining 3 cases. It outperforms random sampling by $1 - 9\\%$ .", + "bbox": [ + 75, + 627, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "CIFAR-100 Figure 5b shows that our method outperforms or matches the performance of all other coreset methods studied up to 25 samples per class, or $5\\%$ of the total dataset (2500 samples). At larger coreset sizes, SLo-Curves shows a few percentage points of accuracy drop from the state of the art methods Cal and GraphCut, but outperforms random sampling, CRAIG [43], Herding [10] and Margin", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "[11] baselines. We note that even at coreset sizes equal to $10\\%$ of the dataset (50 samples per class), we outperform random sampling by greater than $3\\%$ .", + "bbox": [ + 498, + 566, + 892, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Cross Architecture Results", + "text_level": 1, + "bbox": [ + 500, + 631, + 743, + 647 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From Section 3.2, we know that low curvature samples generalize across architectures. We corroborate this experimentally and show that SLo-Curves consistently chooses good subsets irrespective of pretrained network accuracy or architecture. Figure 6a shows the accuracy of ResNet18 trained on coresets identified from different pretrained models. We show the results of a differently seeded ResNet-18, a lower accuracy AlexNet, completely different architectures MobileNetV3 and VGG19, a deeper similar architecture ResNet101 and a much bigger network, DenseNet121, with pretraining accuracies mentioned in brackets. Coresets chosen by SLo-curves outperform random sampling for all considered architectures by an average of $5.3\\%$ . We can see that subsets chosen from lower, similar or higher accuracy and complexity models all consistently perform well. Variances is shown in Appendix B.3.", + "bbox": [ + 496, + 657, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20296", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5853ac17cb97c502070d90f9ff24484f991098fe565f87e11a463518993abb74.jpg", + "image_caption": [ + "DenseNet121, CIFAR10", + "(a) Histograms" + ], + "image_footnote": [], + "bbox": [ + 86, + 116, + 410, + 273 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c69feaf73d9c4a73ad37b92a96aae36a1249d35679b4f442f24464eaec1631c4.jpg", + "image_caption": [ + "ResNet18, CIFAR10 trained on coresets identified from DenseNet121", + "at different training epochs using the proposed method", + "(b) Accuracy", + "Figure 7. ResNet18 trained on coresets identified from DenseNet121 at initialization, at epoch 10 and at end of training. Note that the x-axis is not to scale. The variances are reported in Appendix B.5." + ], + "image_footnote": [], + "bbox": [ + 501, + 114, + 883, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Decoupling Selection and Regularization", + "text_level": 1, + "bbox": [ + 76, + 344, + 424, + 361 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here, we show that the criterion for selection of points is beneficial even without the curvature regularization during training. In Figure 6b, we show the results of ResNet18 trained on coresets of CIFAR-10 identified by SLo-Curves selection both with the best regularization strength $\\lambda$ for each coreset size, and without any regularization ( $\\lambda = 0$ ). We show the results of random sampling as the baseline. We observe that the best performance is consistently shown by our method with regularization. However, our method without regularization still outperforms random sampling by an average of $2.3\\%$ over all coreset sizes. The variances are reported in Appendix B.4.", + "bbox": [ + 75, + 368, + 470, + 549 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Early Emergence of Low Curvature Samples", + "text_level": 1, + "bbox": [ + 76, + 559, + 455, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Many coreset selection methods require training the network for a few epochs before coreset selection. However, we observe from Section 3.4 that low curvature samples can be identified in the early epochs of training. We now study their efficacy for coreset selection for real time usage. We use a DenseNet121 to perform coreset selection, and train a ResNet18 from scratch on the coreset identified by our method. We study the randomly initialized, untrained DenseNet121 (with $10\\%$ accuracy), DenseNet121 trained for 10 epochs (to $84.7\\%$ accuracy), and DenseNet121 after convergence ( $93.4\\%$ accuracy). Figure 7b visualizes the results, with random sampling shown as a baseline. We show that the coresets identified at epoch 10 perform on par with the coreset identified at convergence. The early emergence of these low curvature samples can also be observed in the corresponding histograms shown in Figure 7a. However, during experimentation, we noted that higher regularization strength ( $\\lambda$ ) was needed and recommend that where pretrained models are present, it is preferable to extract coresets from them. Surprisingly, choosing low curvature samples selected from an untrained random initialization per", + "bbox": [ + 75, + 583, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "forms worse than random sampling. We think this may be because the regularizer forces a simplification of the learned boundary that is useful when the samples lend themselves to a simple boundary.", + "bbox": [ + 496, + 345, + 892, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 416, + 617, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We studied the curvature of the loss of trained neural networks with respect to the training data points. We observed that there is a significant concentration of training samples with very low curvature, and found that these samples remain consistent between networks of differing initializations and architectures. We also noted that they can be identified early on during training. We visualize the samples with low and high curvature and find striking visual differences between them. The low curvature samples are clean, devoid of obstructions and prototypical of their category. The high curvature samples have visual clutter, occluding and uncommon backgrounds, and are hard to identify. The results highlight the Hessian of data points as a useful tool in the study of deep learning generalization. We apply these observations to select significant samples and introduce SLo-Curves, a novel coreset identification and training algorithm that can generalize across architectures. SLo-curves constructs coresets from the samples with low curvatures and trains on them with an additional regularizer that penalizes large curvature of loss around them. We show that at small coreset sizes, SLo-Curves beats the state of the art coreset selection methods by up to $9\\%$ on CIFAR-10 and CIFAR-100 datasets.", + "bbox": [ + 496, + 436, + 892, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 767, + 660, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The authors wish to thank Dr. Andrew Buchanan for the insightful discussions and suggestions. This work was supported in part by the Center for Brain Inspired Computing (C-BRIC), one of the six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by DARPA, by the Semiconductor Research Corporation, the National Science Foundation, Intel Corporation, the DoD Vannevar Bush Fellowship, and by the U.S. Army Research Laboratory.", + "bbox": [ + 496, + 789, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20297", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sharat Agarwal, Himanshu Arora, Saket Anand, and Chetan Arora. Contextual diversity for active learning. In European Conference on Computer Vision, pages 137-153. Springer, 2020. 2", + "[2] Rahaf Aljundi, Min Lin, Baptiste Goujaud, and Yoshua Bengio. 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In International Conference on Learning Representations, 2021. 1" + ], + "bbox": [ + 501, + 90, + 890, + 708 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "20300", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Samples With Low Loss Curvature Improve Data Efficiency/0d4bc9ae-1b91-4517-8e70-147be86f88d2_model.json b/2023/Samples With Low Loss Curvature Improve Data Efficiency/0d4bc9ae-1b91-4517-8e70-147be86f88d2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..536eaa2d617d32f8c29c811b35420bb547f62f3a --- /dev/null +++ b/2023/Samples With Low Loss Curvature Improve Data Efficiency/0d4bc9ae-1b91-4517-8e70-147be86f88d2_model.json @@ -0,0 +1,2180 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.185, + 0.131, + 0.785, + 0.154 + ], + "angle": 0, + "content": "Samples with Low Loss Curvature Improve Data Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.281, + 0.182, + 0.452, + 0.234 + ], + "angle": 0, + "content": "Isha Garg Purdue University West Lafayette, USA" + }, + { + "type": "text", + "bbox": [ + 0.295, + 0.238, + 0.438, + 0.251 + ], + "angle": 0, + "content": "gargi@purdue.edu" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.182, + 0.69, + 0.234 + ], + "angle": 0, + "content": "Kaushik Roy \nPurdue University \nWest Lafayette, USA" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.238, + 0.682, + 0.251 + ], + "angle": 0, + "content": "kaushik@purdue.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.473, + 0.712 + ], + "angle": 0, + "content": "In this paper, we study the second order properties of the loss of trained deep neural networks with respect to the training data points to understand the curvature of the loss surface in the vicinity of these points. We find that there is an unexpected concentration of samples with very low curvature. We note that these low curvature samples are largely consistent across completely different architectures, and identifiable in the early epochs of training. We show that the curvature relates to the 'cleanliness' of the data points, with low curvatures samples corresponding to clean, higher clarity samples, representative of their category. Alternatively, high curvature samples are often occluded, have conflicting features and visually atypical of their category. Armed with this insight, we introduce SLo-Curves, a novel coreset identification and training algorithm. SLo-curves identifies the samples with low curvatures as being more data-efficient and trains on them with an additional regularizer that penalizes high curvature of the loss surface in their vicinity. We demonstrate the efficacy of SLo-Curves on CIFAR-10 and CIFAR-100 datasets, where it outperforms state of the art coreset selection methods at small coreset sizes by up to \\(9\\%\\). The identified coresets generalize across architectures, and hence can be pre-computed to generate condensed versions of datasets for use in downstream tasks. Code is available at https://github.com/ishagarg/Slo-Curves." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.725, + 0.208, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Deep learning applications have exploded due to access to big data and computational resources. However, data is expensive to gather, annotate and store, and directly influences the computational resources required. Storing more data also runs higher risks of data leakage and privacy violation. It also influences parallelism and communication bottlenecks between machines [17]. There is limited understanding of the mechanism through which deep learning models process complex datasets, what constitutes 'good' or 'easy' examples for learning, and how large a number of" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.285, + 0.697, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.286, + 0.89, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.501, + 0.892, + 0.528 + ], + "angle": 0, + "content": "Figure 1. Histograms of training dataset's curvature for various networks trained on CIFAR-10." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.732 + ], + "angle": 0, + "content": "samples are indeed beneficial. Research on data efficiency often focuses on doing more with less data. Standard training methods assume all data points from the training set to be independently and identically distributed from the true training distribution. Data points are sampled uniformly during training and treated as having equal significance. An alternative is to identify representative data points from the training distribution that are more beneficial to learning than random uniform sampling [30, 31]. They can be used as smaller condensed datasets, or upweighted during training as per their significance. These subsets of important points are also known as coresets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Coresets prove useful in many downstream applications. They are data-efficient and can serve as a good choice of proxy data for Neural Architecture Search (NAS) [45, 52], as episodic memory in Continual Learning [2, 6, 60], and as the choice of augmentation samples during self-supervised learning [37]. They can be utilized in many regimes that may have memory or compute resources, such as for compute-efficient learning [35,43,46], dataset condensation [8, 58, 61], efficient Hyper-parameter Optimization (HPO) [33], and speeding up the training of Generative Adversarial Networks (GANs) [54]. The utility of identifying im" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "20290" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.091, + 0.468, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.389, + 0.411, + 0.401 + ], + "angle": 0, + "content": "(a) Top 100 examples with the lowest loss curvature" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.091, + 0.886, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.389, + 0.835, + 0.401 + ], + "angle": 0, + "content": "(b) Top 100 examples with the highest loss curvature" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.893, + 0.452 + ], + "angle": 0, + "content": "Figure 2. We visualize the 10 samples from each class with lowest and highest curvature of loss identified over 10 different randomly initialized ResNet18 models trained on CIFAR-10. Each row corresponds to a class, consistent across both figures, and 10 ordered samples for each class are shown. The network was trained with random horizontal flipping as part of the augmentations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.47, + 0.698 + ], + "angle": 0, + "content": "important samples can extend beyond efficiency, such as in understanding dataset limitations [5, 55], enabling faster or better convergence by upsampling certain samples during training [12, 40], or in the choice of data to label in active learning [1, 50]. However, it is not always clear what makes a sample informative or good for learning. Methods differ in their definition of significance of samples. Some representative works measure importance via the confidence or margin of the predicted output of the network [1, 11], by clustering samples together in the input or feature space [10, 22], matching the gradient to that of the entire dataset [35, 43, 46], choosing samples that lie closest to the decision boundary [14] or samples that are not forgotten once learnt [57]. Some other representative methods frame it as a submodular function optimization problem [27, 27, 43]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this paper, we look at data efficiency from the lens of the loss landscape around the training samples. While the loss surface with respect to the parameters of the neural network has received considerable attention as a means of analyzing the stability of the solution [19, 47-49], the loss landscape with respect to the data is far less studied. Most of the studies have been associated with adversarial robustness [44]. We are interested in the curvature of the loss surface, or inversely, the smoothness of the decision boundary around the data point. This is captured by the local linearity of the gradient around the sample, measured as the trace of the Hessian. We plot the histogram of an efficiently calculable estimation of this trace for the training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.561 + ], + "angle": 0, + "content": "dataset of different pretrained models in Figure 1 for the CIFAR-10 dataset [38]. We note they resemble a bimodal distribution, with a spread out Gaussian superimposed upon a very sharp, tall peak around zero. We are interested in the samples that make up the sharp peak, the ones around which the loss surface curvature is very low." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.893, + 0.852 + ], + "angle": 0, + "content": "We visualize the sample ordered by curvature accumulated over ten differently initialized ResNet18 [23] models trained on CIFAR-10 in Figure 2. We find that they reveal useful information about the kinds of samples present in the dataset. The low curvature samples, shown in Figure 2a can be considered clean, prototypical and minimal, in that they are strongly representative of their category. On the other hand, Figure 2b shows the samples with the highest curvature of loss. We can see that they do not appear to be characteristic of their category. They have confusing backgrounds with interfering patterns, uncommon viewing angles and incomplete shapes. We show that the low curvature samples appear to be largely consistent not only across networks that were initialized differently, but also across completely different architectures such as MobileNetV3 [24], ResNet101 [23], AlexNet [39], VGG19 [53] and DenseNet121 [25]. We also show that they can be identified quite early on during the training process. As an application of this insight, we show that they make very good coresets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Many coreset selection methods perform well at large coreset sizes, close to the size of the whole dataset. In this paper, we explore smaller coresets, ranging from sin" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20291" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "gle digit images per class, as is often common with few shot learning [16, 18], up to 100 images per class. Depending on the dataset and the number of classes, this can range from \\(0.1\\%\\) to \\(20\\%\\) of the dataset. We introduce SLo-Curves, a novel coreset selection method which identifies samples with low curvatures and train on these coresets with an additional regularizer that penalizes large curvatures. Both the method for measuring the curvature and the form of the regularizer are inspired directly from CURE [44], which introduced the regularizer as a means to promote adversarial accuracy at the expense of clean accuracy. We show that when there are small sample sizes, chosen appropriately, this regularizer also helps improve clean accuracy. We summarize our contributions below:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.312, + 0.47, + 0.358 + ], + "angle": 0, + "content": "1. We study the loss surface with respect to the input data points and identify an unexpected concentration of samples with very low curvature." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.366, + 0.47, + 0.457 + ], + "angle": 0, + "content": "2. We show that the curvature of the loss function relates to the notion of visual 'cleanliness'. Low curvature samples are free of conflicting features, while high curvature samples look cluttered, obstructed or unrepresentative of the other samples in the class. To the best of our knowledge, this is a novel observation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.466, + 0.47, + 0.542 + ], + "angle": 0, + "content": "3. We show that these samples are largely architecture and initialization independent. This implies that the Hessian reveals intrinsic properties of the dataset rather than just an artifact of the training procedure, a particular local minima, or the choice of network architecture." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.551, + 0.47, + 0.673 + ], + "angle": 0, + "content": "4. We introduce SLo-Curves: an algorithm that selects samples with low curvature as coresets and additionally penalizes the curvature of the loss function while training on them. SLo-Curves outperforms all other choices of coreset selection methods by up to \\(9\\%\\) for coresets of few samples per class. To the best of our knowledge, this is the first paper to explore second order statistics of the loss with respect to the data for coreset selection." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.681, + 0.47, + 0.788 + ], + "angle": 0, + "content": "5. Due to these samples being consistent across architectures, SLo-Curves does not rely on gradient statistics during training or need to be averaged out over multiple initializations. Coresets can be pre-computed and are performant across architectures. We also find that these points can be identified early on during training, in as few as 5-10 epochs." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.312, + 0.47, + 0.788 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Our method is inherently more productive at small core-set sizes since the samples that we identify belong to the limited set that have very low curvature, corresponding to the tall peak at zero in Figure 1. Further study is required to understand what causes the decision boundary to smoothen along the same samples with different networks, and we hope that this paper accelerates interest in this direction." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.679, + 0.107 + ], + "angle": 0, + "content": "2. Literature Review" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.327 + ], + "angle": 0, + "content": "The importance of samples is a relevant concern in many areas. Importance sampling methods [30, 31] prioritize the important samples for fast and efficient training by approximating the norm of the gradient resulting from each sample. Curriculum learning [4] seeks to order sample exposure to the network during training in order to learn easier samples first and then harder samples for better solutions. Active learning [51] focuses on only labeling the important samples to reduce annotation costs. However, the definition of importance of samples is not fixed. In this section, we focus on coreset selection as a base method for deciding sample importance scores, that can be then used to different ends. We broadly classify techniques for coreset selection in deep learning and discuss representative approaches in each." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.895, + 0.418 + ], + "angle": 0, + "content": "Clustering based methods: Points close to each other can be clustered together and represented well by the cluster center. The choice of metric for clustering varies. Authors of [10] clusters samples based on distance in the feature space. Authors of [22] reframe the problem as solving a minimax facility location problem greedily." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.895, + 0.614 + ], + "angle": 0, + "content": "Classification Output based methods: These approaches work on the assumption that examples that are classified with lesser confidence or score are more informative than examples classified with strong confidence. Authors of [11] study the effects of choosing softmax scores, entropy and the distance of the top-2 classes in the output space. A different approach is taken by the authors of [57], who show that a large majority of samples are learned correctly early on during training and are never consequently classified incorrectly, or forgotten, during the remaining course of training. They deem the samples that are never forgotten once learnt, as easily learned, and create coresets that consist of examples that need to be re-learnt." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Loss Gradient based methods: This approach categorizes the importance of a sample as its contribution to the loss or the gradient of the loss. Methods vary in their choice of the time of training at which the contribution is measured. Both Grad-Match [35] and CRAIG [43] select weighted subsets such that the appropriately scaled gradient of the subset matches the gradient of the entire dataset. Both reselect the subset and weights every few epochs. They differ in the choice of algorithm for building the dataset, with CRAIG converting the gradient-distance optimization problem into a submodular function and then using a greedy approach and Grad-Match using a different greedy Orthogonal Matching Pursuit algorithm. Both outline convergence guarantees, and show scalability via approximating gradients of the loss with respect to the input with gradients at the last layer [31]. To overcome the requirement for reselecting the coresets during training, authors of [46] introduce GraNd, which approximates the L2 norm of the gradient early on in training (after a few epochs) and averages it" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20292" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.362, + 0.106 + ], + "angle": 0, + "content": "over many different training initializations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.111, + 0.468, + 0.186 + ], + "angle": 0, + "content": "Bilevel optimization and submodular function methods: Glister [36] and Retrieve [37] frame the minimization of the loss on selected samples and the selection of samples as a bilevel optimization problem. Authors of [27, 28] explore different submodular optimization functions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.19, + 0.468, + 0.311 + ], + "angle": 0, + "content": "Decision Boundary based methods: These methods assume that the points closest to the boundary are hardest to separate, and hence most informative. Authors of [14] utilize DeepFool, a method to generate adversarial examples, as a way of measuring distance to boundary. If an example is easier to fool, it is presumably closer to the boundary and significant. Authors of [42] select the samples whose classification likelihood is most dissimilar to its neighbors." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.316, + 0.468, + 0.481 + ], + "angle": 0, + "content": "Synthetic coreset creation methods: In contrast to selecting points from the dataset, there has been recent interest in methods that create synthetic data to mimic the overall distribution. Dataset distillation [58] was introduced to create synthetic data by matching the gradient of samples averaged over many different initializations. Authors of [8] improve performance by repeating the synthetic set creation over many iterations. However, the datasets do not resemble the data, and this can be an advantage or disadvantage based on the application. In this manuscript we only study the samples present in the training distribution." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.486, + 0.468, + 0.59 + ], + "angle": 0, + "content": "Coreset selection libraries: Coreset selection in deep learning is an area of rapidly increasing focus, as evidenced by the release of recent libraries that compare different core-set selection methods, and can be incorporated into other deep learning applications. Recently released libraries are CORDS [34], Minicore [3] and DeepCore [21]. We use DeepCore for our simulations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.596, + 0.468, + 0.776 + ], + "angle": 0, + "content": "Our method falls under both the categories of decision boundary based methods and loss gradient based methods. We select real samples from the dataset, choosing coresets from pre-trained models based on the trace of the Hessian of the loss. Our coresets consist of the samples with low trace of Hessian, or low loss curvature around them. The selected samples are chosen only once, are not re-weighted and no special optimization is followed besides an additional regularizer that encourages the learned decision boundary to be flat by penalizing the curvature estimate. They generalize across architectures and hence, do not need to be calculated real time for every network." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.8, + 0.363, + 0.816 + ], + "angle": 0, + "content": "3. Methodology and Observations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.468, + 0.9 + ], + "angle": 0, + "content": "We study the curvature profiles of the loss with respect to input for different training data points. The curvature profile can be studied via the Hessian of the loss. Concretely, let's consider a data point \\( x \\in \\mathbb{R}^d \\). Let \\( H \\) denote the Hessian of the loss, \\( L \\) with respect to the data point \\( x \\), i.e." + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.105, + 0.788, + 0.142 + ], + "angle": 0, + "content": "\\[\nH (x) = \\left[ \\frac {\\delta^ {2} L (x)}{\\delta x _ {i} \\delta x _ {j}} \\right] _ {i, j = 1 \\dots d}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.152, + 0.892, + 0.409 + ], + "angle": 0, + "content": "The curvature profile is captured by the eigenvalues. A good measure is the sum of the eigenvalues or the trace of the Hessian [13, 32]. The higher the trace, the more the loss surface curves around the data point, or the less smooth the decision boundary at the data point's vicinity. We plot the histogram of an approximation of the Hessian trace (explained in section 3.1) for the training set of different network architectures in Figure 1, at the end of training on CIFAR-10. We note that they follow a similar trend: a sharp tall peak at very small values, and another Gaussian-like peak later. We focus on the set of samples with very low curvatures that make up the sharp peak at zero. Histograms for different architectures can be found in Appendix A. We note that these networks were trained with Cross Entropy Loss, SGD optimizer with momentum and L2 regularization. There is no term explicitly encouraging a low spread of curvature for some samples." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.421, + 0.738, + 0.437 + ], + "angle": 0, + "content": "3.1. Calculating the Curvature" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.446, + 0.892, + 0.627 + ], + "angle": 0, + "content": "The eigenvalues of the Hessian of the loss with respect to the data point contain information about the curvature profile of the loss surface around the data point. Large absolute eigenvalues imply a large curvature of the loss function around the sample, and small magnitude of eigenvalues imply that the loss function (or the decision boundary) has a small curvature, or is locally linear in the vicinity of the data point. The Hessian of the loss surface with respect to model weights has been utilized to study the properties of the minima the optimization selects. [19, 47-49]. However, in this paper, we instead study the curvature of the loss surface with respect to the training data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.892, + 0.763 + ], + "angle": 0, + "content": "In order to study the curvature profile without having to explicitly calculate the Hessian and its eigenvalues, we estimate instead the trace of the Hessian. The trace is the sum of the eigenvalues and can be calculated efficiently via Hutchinson's trace estimator [26] and finite difference approximation. This is the same form of curvature measure used in CURE [44] as the curvature regularizer for enhancing adversarial robustness during training. We now go into the details of this formulation." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Let \\(\\lambda_{i}\\), \\(i = 1\\dots d\\) be the eigenvalues of the Hessian \\(H(x)\\). We are interested in the spectrum of the magnitude of the eigenvalues, which can be summarized by the sum of the square of the eigenvalues. This can be estimated by the norm of the Hessian-vector product as introduced in the Hutchinson's trace estimator [26]. Using Hutchinson's trace estimator, the definitions of the Frobenius norm of a matrix, properties of the trace, and the fact that \\(H(x)\\) is symmetric, we get the following estimate:" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20293" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.094, + 0.469, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.296, + 0.441, + 0.309 + ], + "angle": 0, + "content": "(a) Curvatures accumulated over differently seeded ResNet-18" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.094, + 0.89, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.296, + 0.846, + 0.308 + ], + "angle": 0, + "content": "(b) Curvatures accumulated over different architectures" + }, + { + "type": "image_caption", + "bbox": [ + 0.084, + 0.318, + 0.882, + 0.332 + ], + "angle": 0, + "content": "Figure 3. Histograms of curvature of the training set of CIFAR-10, with curvature estimates accumulated over different trained models." + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.368, + 0.363, + 0.471 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\sum \\lambda_ {i} ^ {2} = T r (H ^ {2}) \\\\ = \\mathbb {E} _ {z} \\left[ z ^ {T} H ^ {2} z \\right] \\\\ = \\mathbb {E} _ {z} \\left[ z ^ {T} H ^ {T} H z \\right] \\\\ = \\mathbb {E} _ {z} \\left[ (H z) ^ {T} (H z) \\right] \\\\ = \\mathbb {E} _ {z} \\left[ \\| H z \\| _ {F} ^ {2} \\right] \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.47, + 0.546 + ], + "angle": 0, + "content": "where \\(z\\) are Rademacher random variables, equal to \\(+1\\) or \\(-1\\) with equal probability, i.e. \\(z \\sim^{i.i.d} \\{-1, +1\\}^d\\). We now use finite approximation to estimate the Hessian vector product efficiently." + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.55, + 0.419, + 0.582 + ], + "angle": 0, + "content": "\\[\nH z = \\frac {\\nabla L (x + h z) - \\nabla L (x)}{h} \\quad \\text {f o r} h \\rightarrow 0\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.469, + 0.738 + ], + "angle": 0, + "content": "The cost of calculating this is just the cost of performing a backward pass on the network twice. This formulation is widely used whenever the curvatures of loss surface are discussed [7, 9, 49, 59]. Similar to CURE [44], we do not choose random directions for sampling \\( z \\) to take the expectation over. Instead, we choose the adversarial direction, which is known to lead to high curvature [15, 29], and set \\( z \\) to be \\( \\frac{\\text{sign} \\nabla L(x)}{\\|\\text{sign}(\\nabla L(x))\\|} \\). We found the results to not be significantly impacted by \\( h \\) and set it equal to 3 to match the change used in corresponding adversarial settings [20, 41]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.739, + 0.469, + 0.785 + ], + "angle": 0, + "content": "Putting this together, the measure of curvature of the decision boundary or the loss function around a data point is proportional to the following quantity, \\(\\gamma\\) where:" + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.791, + 0.442, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\gamma (x) = \\| \\nabla_ {x} L (x + h z) - \\nabla_ {x} L (x) \\|; \\\\ \\text {w h e r e} z = \\frac {\\operatorname {s i g n} \\nabla_ {x} L (x)}{\\| \\operatorname {s i g n} (\\nabla_ {x} L (x)) \\|} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.417, + 0.865 + ], + "angle": 0, + "content": "3.2. Consistency of Low Curvature Samples" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.9 + ], + "angle": 0, + "content": "We notice that the low curvature samples are largely consistent across architectures and initialization. We show this" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.695 + ], + "angle": 0, + "content": "overlap in Figure 3, with plots of the histogram of cumulative curvature values of samples (estimated by \\(\\gamma\\)), accumulated over different seeds in Figure 3a and over different architectures in Figure 3b. Mathematically, the \\(i^{th}\\) curve corresponds to the histogram of \\(\\sum_{j=0}^{i} \\gamma_{j}\\) for all training samples, where \\(j\\) indexes different trained models. The first histogram is shown in blue, with unaccumulated curvature estimates (\\(\\gamma_{0}\\) collected from model 'seed0' or 'ResNet101'). Next the curvature estimates of the second model (\\(\\gamma_{1}\\) for 'seed1' or 'ResNet18') are added to the first model's curvature estimates for each sample and the resulting plot is shown in orange. As we accumulate curvature estimates over many different models, the sharp peak at zero starts to spread out a bit. Yet, even after accumulating over 5 seeds or 6 different architectures all converging to different minima, there are more than 2000 common low curvature samples (identified as the smallest, purple peak at zero). This implies that these samples appear to be an intrinsic property of the dataset rather than the initialization or the local minima the networks converged to. We corroborate this experimentally in Section 4.3, by showing that a ResNet18 model trained on coresets identified on any of these architectures outperforms random sampling by an average of \\(5.3\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.681, + 0.724 + ], + "angle": 0, + "content": "3.3. Identified Coresets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We now visualize the low and high curvature samples (taken from the accumulated scores of 10 randomly seeded ResNet18 models trained on CIFAR10) in Figures 2. Each row corresponds to a class, and contains the top 10 samples for that class with the lowest and highest curvatures in Figures 2a and 2b, respectively. As can be seen from the figure, the low curvature samples are very 'good' samples, in that they have low to no conflicting backgrounds, structure typical of the class, are centered and are not zoomed in or trimmed. The networks are trained with random left to right flipping, and hence we see samples facing both ways. On" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20294" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.092, + 0.352, + 0.105 + ], + "angle": 0, + "content": "ResNet18, CIFAR10" + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.107, + 0.422, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.292, + 0.47, + 0.335 + ], + "angle": 0, + "content": "Figure 4. The histogram of curvature estimates of the training dataset as training progresses. For ease of visualization, the opacity of the curves decreases with epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.468, + 0.465 + ], + "angle": 0, + "content": "the other hand, the high curvature samples are 'bad' in that they are visually harder to identify by humans as well. They have conflicting backgrounds (a deer in a fiery landscape), uncommon viewing angles (a truck from behind) and colors uncharacteristic of the class (a blue plane or a yellow frog). This implies that the curvature, captured by \\(\\gamma\\) could be useful as a metric for 'learnability' of a sample." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.457, + 0.492 + ], + "angle": 0, + "content": "3.4. Early Emergence of Low Curvature Samples" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.499, + 0.47, + 0.651 + ], + "angle": 0, + "content": "We track \\(\\gamma\\) through the training progress to study the emergence of low curvature samples, and visualize this in Figure 4. As training progresses (lesser opaque histograms in the figure), we can see the peak towards zero becoming more defined. We find that the concentration of samples around low curvatures emerges in as few as 5-10 epochs of training. We corroborate this in Section 4.5 by showing that the coresets identified by our proposed method as early as epoch 10 outperform random sampling by an average of \\(4.7\\%\\) accuracy across all considered coreset sizes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.661, + 0.468, + 0.679 + ], + "angle": 0, + "content": "3.5. SLo-Curves: An Algorithm for Data Efficiency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.686, + 0.468, + 0.868 + ], + "angle": 0, + "content": "Based on these insights, we propose SLo-Curves, an algorithm to identify coresets of samples with low curvature and train on them for increased sample efficiency. We use curvature estimate, \\(\\gamma\\) as the selection metric, choosing samples with the lowest values to make up our coreset. Additionally, we show that regularizing the learned curvature around these coresets helps increase the accuracy by a few percentage points. Hence, we first select the points with the lowest \\(\\gamma\\) from pretrained networks, and then train a new randomly initialized network on these points using the standard cross entropy loss \\(L_{CE}(x)\\) and \\(\\gamma\\) serving as the additional regularizer term, \\(L_{reg} = \\gamma (x)\\). The new loss is thus:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.885, + 0.361, + 0.902 + ], + "angle": 0, + "content": "\\[\nL (x) = L _ {C E} (x) + \\lambda \\gamma (x)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.318 + ], + "angle": 0, + "content": "The tradeoff parameter \\(\\lambda\\) is the only hyperparameter our method induces and is searched over \\(\\{0,0.5,1,5,10,20,50\\}\\). We note that smaller coresets require larger values of \\(\\lambda\\) and larger coresets require smaller values, ultimately giving better results when the additional regularizer is turned off. This ties with CURE [44], wherein the same regularizer improves adversarial accuracy at the cost of clean accuracy when used with the whole dataset. In our method, it serves instead to improve accuracy at low sample complexities. We anticipate that it is an especially effective form of regularization for small datasets learned with complex models. We reiterate that we study small coreset sizes since our significance metric is based on the samples that concentrate near zero curvature, and the number of such samples is a limited percentage of the dataset." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.326, + 0.715, + 0.342 + ], + "angle": 0, + "content": "4. Results and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.352, + 0.892, + 0.382 + ], + "angle": 0, + "content": "In this section, we outline our network architectures, the training hyperparameters and discuss results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.386, + 0.699, + 0.402 + ], + "angle": 0, + "content": "4.1. Experimental Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.844 + ], + "angle": 0, + "content": "We run experiments on CIFAR-10 and CIFAR-100 datasets [38]. Both datasets have 50,000 training samples with CIFAR-10 having 5000 samples for each of its 10 classes and CIFAR-100 having 500 samples for each of its 100 classes. The networks used are ResNet-18 [23], ResNet-101 [23], VGG-19 [53], AlexNet [39], MobileNetV3Small [24] and DenseNet-121 [25]. We consider coreset of small sizes, ranging from 1 to 100 samples per class. For all networks, we use a learning rate of 0.1 scaled by 0.1 at epochs 81 and 121, SGD optimizer with a momentum of 0.9, with Nesterov momentum [56] turned on and a weight decay of 5e-4. We train all networks for 164 epochs and report mean and variance for 5 randomly seeded runs. All graphs show mean values, with corresponding variances shown in Appendix B. We compare with representative works from the broad categories of coreset selection methods. In particular, we compare with 9 other methods: Random uniform sampling, Glister [36], Forgetting [57], CRAIG [43], GraphCut [27], Cal [42], GraNd [46], Herding [10] and Margin [11]. For methods that require training before coreset selection, we train the network for 40 epochs to ensure a good convergence point before we select the coresets. We have run the baselines using the Deepcore [21] library (building upon it for methods and networks as needed), and find that it is an excellent repository of state of the art methods. The only hyperparameter that we tune for our method is the strength of the regularization, \\(\\lambda\\). We tune this over the search space \\(\\{0,0.5,1,5,10,20,50\\}\\) and report the best results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.851, + 0.878, + 0.867 + ], + "angle": 0, + "content": "4.2. Comparison with Coreset Selection Methods" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We now discuss the results of our method compared to random sampling and other state of the art coreset selec" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20295" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.096, + 0.473, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.094, + 0.885, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.277, + 0.893, + 0.307 + ], + "angle": 0, + "content": "Figure 5. ResNet18 trained on coresets identified by various methods. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.1 and B.2" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.317, + 0.466, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.318, + 0.885, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.509, + 0.893, + 0.552 + ], + "angle": 0, + "content": "Figure 6. ResNet18 trained on coresets identified by our methods a) from different pretrained architectures and b) with and without regularization. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.3 and B.4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.627 + ], + "angle": 0, + "content": "tion methods. The results for ResNet18 networks trained on CIFAR-10 and CIFAR-100 are shown in 5a and 5b respectively. The corresponding tables with mean and variances are shown in Appendix B.1 and B.2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.794 + ], + "angle": 0, + "content": "CIFAR-10: Figure 5a shows that selection by the proposed SLo-Curves method outperforms all other coreset methods studied all the way up to 100 samples per class, or \\(2\\%\\) of the total dataset (1000 samples). We note that at such coresets sizes, random sampling forms a surprisingly strong baseline (also noted in [21]). The strongest competitors are the submodular function based method GraphCut [27] and decision boundary based method Cal [42]. SLo-Curves shows the best performance in 16 out of the 19 coreset sizes studied and the second best in the remaining 3 cases. It outperforms random sampling by \\(1 - 9\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "CIFAR-100 Figure 5b shows that our method outperforms or matches the performance of all other coreset methods studied up to 25 samples per class, or \\(5\\%\\) of the total dataset (2500 samples). At larger coreset sizes, SLo-Curves shows a few percentage points of accuracy drop from the state of the art methods Cal and GraphCut, but outperforms random sampling, CRAIG [43], Herding [10] and Margin" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.567, + 0.893, + 0.613 + ], + "angle": 0, + "content": "[11] baselines. We note that even at coreset sizes equal to \\(10\\%\\) of the dataset (50 samples per class), we outperform random sampling by greater than \\(3\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.744, + 0.648 + ], + "angle": 0, + "content": "4.3. Cross Architecture Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.902 + ], + "angle": 0, + "content": "From Section 3.2, we know that low curvature samples generalize across architectures. We corroborate this experimentally and show that SLo-Curves consistently chooses good subsets irrespective of pretrained network accuracy or architecture. Figure 6a shows the accuracy of ResNet18 trained on coresets identified from different pretrained models. We show the results of a differently seeded ResNet-18, a lower accuracy AlexNet, completely different architectures MobileNetV3 and VGG19, a deeper similar architecture ResNet101 and a much bigger network, DenseNet121, with pretraining accuracies mentioned in brackets. Coresets chosen by SLo-curves outperform random sampling for all considered architectures by an average of \\(5.3\\%\\). We can see that subsets chosen from lower, similar or higher accuracy and complexity models all consistently perform well. Variances is shown in Appendix B.3." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20296" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.169, + 0.101, + 0.37, + 0.116 + ], + "angle": 0, + "content": "DenseNet121, CIFAR10" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.117, + 0.411, + 0.274 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.281, + 0.304, + 0.294 + ], + "angle": 0, + "content": "(a) Histograms" + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.095, + 0.858, + 0.105 + ], + "angle": 0, + "content": "ResNet18, CIFAR10 trained on coresets identified from DenseNet121" + }, + { + "type": "image_caption", + "bbox": [ + 0.582, + 0.106, + 0.83, + 0.115 + ], + "angle": 0, + "content": "at different training epochs using the proposed method" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.115, + 0.885, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.657, + 0.281, + 0.726, + 0.293 + ], + "angle": 0, + "content": "(b) Accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.298, + 0.893, + 0.327 + ], + "angle": 0, + "content": "Figure 7. ResNet18 trained on coresets identified from DenseNet121 at initialization, at epoch 10 and at end of training. Note that the x-axis is not to scale. The variances are reported in Appendix B.5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.345, + 0.426, + 0.362 + ], + "angle": 0, + "content": "4.4. Decoupling Selection and Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.471, + 0.55 + ], + "angle": 0, + "content": "Here, we show that the criterion for selection of points is beneficial even without the curvature regularization during training. In Figure 6b, we show the results of ResNet18 trained on coresets of CIFAR-10 identified by SLo-Curves selection both with the best regularization strength \\(\\lambda\\) for each coreset size, and without any regularization (\\(\\lambda = 0\\)). We show the results of random sampling as the baseline. We observe that the best performance is consistently shown by our method with regularization. However, our method without regularization still outperforms random sampling by an average of \\(2.3\\%\\) over all coreset sizes. The variances are reported in Appendix B.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.457, + 0.577 + ], + "angle": 0, + "content": "4.5. Early Emergence of Low Curvature Samples" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Many coreset selection methods require training the network for a few epochs before coreset selection. However, we observe from Section 3.4 that low curvature samples can be identified in the early epochs of training. We now study their efficacy for coreset selection for real time usage. We use a DenseNet121 to perform coreset selection, and train a ResNet18 from scratch on the coreset identified by our method. We study the randomly initialized, untrained DenseNet121 (with \\(10\\%\\) accuracy), DenseNet121 trained for 10 epochs (to \\(84.7\\%\\) accuracy), and DenseNet121 after convergence (\\(93.4\\%\\) accuracy). Figure 7b visualizes the results, with random sampling shown as a baseline. We show that the coresets identified at epoch 10 perform on par with the coreset identified at convergence. The early emergence of these low curvature samples can also be observed in the corresponding histograms shown in Figure 7a. However, during experimentation, we noted that higher regularization strength (\\(\\lambda\\)) was needed and recommend that where pretrained models are present, it is preferable to extract coresets from them. Surprisingly, choosing low curvature samples selected from an untrained random initialization per" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.893, + 0.407 + ], + "angle": 0, + "content": "forms worse than random sampling. We think this may be because the regularizer forces a simplification of the learned boundary that is useful when the samples lend themselves to a simple boundary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.417, + 0.619, + 0.433 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.893, + 0.756 + ], + "angle": 0, + "content": "We studied the curvature of the loss of trained neural networks with respect to the training data points. We observed that there is a significant concentration of training samples with very low curvature, and found that these samples remain consistent between networks of differing initializations and architectures. We also noted that they can be identified early on during training. We visualize the samples with low and high curvature and find striking visual differences between them. The low curvature samples are clean, devoid of obstructions and prototypical of their category. The high curvature samples have visual clutter, occluding and uncommon backgrounds, and are hard to identify. The results highlight the Hessian of data points as a useful tool in the study of deep learning generalization. We apply these observations to select significant samples and introduce SLo-Curves, a novel coreset identification and training algorithm that can generalize across architectures. SLo-curves constructs coresets from the samples with low curvatures and trains on them with an additional regularizer that penalizes large curvature of loss around them. We show that at small coreset sizes, SLo-Curves beats the state of the art coreset selection methods by up to \\(9\\%\\) on CIFAR-10 and CIFAR-100 datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.661, + 0.786 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The authors wish to thank Dr. Andrew Buchanan for the insightful discussions and suggestions. This work was supported in part by the Center for Brain Inspired Computing (C-BRIC), one of the six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by DARPA, by the Semiconductor Research Corporation, the National Science Foundation, Intel Corporation, the DoD Vannevar Bush Fellowship, and by the U.S. Army Research Laboratory." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20297" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.116, + 0.47, + 0.176 + ], + "angle": 0, + "content": "[1] Sharat Agarwal, Himanshu Arora, Saket Anand, and Chetan Arora. Contextual diversity for active learning. In European Conference on Computer Vision, pages 137-153. 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We find that there is an unexpected concentration of samples with very low curvature. We note that these low curvature samples are largely consistent across completely different architectures, and identifiable in the early epochs of training. We show that the curvature relates to the 'cleanliness' of the data points, with low curvatures samples corresponding to clean, higher clarity samples, representative of their category. Alternatively, high curvature samples are often occluded, have conflicting features and visually atypical of their category. Armed with this insight, we introduce SLo-Curves, a novel coreset identification and training algorithm. SLo-curves identifies the samples with low curvatures as being more data-efficient and trains on them with an additional regularizer that penalizes high curvature of the loss surface in their vicinity. We demonstrate the efficacy of SLo-Curves on CIFAR-10 and CIFAR-100 datasets, where it outperforms state of the art coreset selection methods at small coreset sizes by up to $9\%$ . The identified coresets generalize across architectures, and hence can be pre-computed to generate condensed versions of datasets for use in downstream tasks. Code is available at https://github.com/ishagarg/Slo-Curves. + +# 1. Introduction + +Deep learning applications have exploded due to access to big data and computational resources. However, data is expensive to gather, annotate and store, and directly influences the computational resources required. Storing more data also runs higher risks of data leakage and privacy violation. It also influences parallelism and communication bottlenecks between machines [17]. There is limited understanding of the mechanism through which deep learning models process complex datasets, what constitutes 'good' or 'easy' examples for learning, and how large a number of + +![](images/bcdb3abc3546264195bf5b9b1bce646a26db51566bae128cc91ac81a2233f375.jpg) +Figure 1. Histograms of training dataset's curvature for various networks trained on CIFAR-10. + +![](images/65540c3d6fea8dc5c0bc713ede2b632df6e5f5c9a5fceb5cd468286c8c335c67.jpg) + +samples are indeed beneficial. Research on data efficiency often focuses on doing more with less data. Standard training methods assume all data points from the training set to be independently and identically distributed from the true training distribution. Data points are sampled uniformly during training and treated as having equal significance. An alternative is to identify representative data points from the training distribution that are more beneficial to learning than random uniform sampling [30, 31]. They can be used as smaller condensed datasets, or upweighted during training as per their significance. These subsets of important points are also known as coresets. + +Coresets prove useful in many downstream applications. They are data-efficient and can serve as a good choice of proxy data for Neural Architecture Search (NAS) [45, 52], as episodic memory in Continual Learning [2, 6, 60], and as the choice of augmentation samples during self-supervised learning [37]. They can be utilized in many regimes that may have memory or compute resources, such as for compute-efficient learning [35,43,46], dataset condensation [8, 58, 61], efficient Hyper-parameter Optimization (HPO) [33], and speeding up the training of Generative Adversarial Networks (GANs) [54]. The utility of identifying im + +![](images/489f7cc208fb1cfd78534806784d3c38e490b83d6cb8fd35c7f3d38dd2259178.jpg) +(a) Top 100 examples with the lowest loss curvature + +![](images/7f450764d12846319249f8416222b7f77c48cec70721d183f1474394c5b5d989.jpg) +(b) Top 100 examples with the highest loss curvature +Figure 2. We visualize the 10 samples from each class with lowest and highest curvature of loss identified over 10 different randomly initialized ResNet18 models trained on CIFAR-10. Each row corresponds to a class, consistent across both figures, and 10 ordered samples for each class are shown. The network was trained with random horizontal flipping as part of the augmentations. + +important samples can extend beyond efficiency, such as in understanding dataset limitations [5, 55], enabling faster or better convergence by upsampling certain samples during training [12, 40], or in the choice of data to label in active learning [1, 50]. However, it is not always clear what makes a sample informative or good for learning. Methods differ in their definition of significance of samples. Some representative works measure importance via the confidence or margin of the predicted output of the network [1, 11], by clustering samples together in the input or feature space [10, 22], matching the gradient to that of the entire dataset [35, 43, 46], choosing samples that lie closest to the decision boundary [14] or samples that are not forgotten once learnt [57]. Some other representative methods frame it as a submodular function optimization problem [27, 27, 43]. + +In this paper, we look at data efficiency from the lens of the loss landscape around the training samples. While the loss surface with respect to the parameters of the neural network has received considerable attention as a means of analyzing the stability of the solution [19, 47-49], the loss landscape with respect to the data is far less studied. Most of the studies have been associated with adversarial robustness [44]. We are interested in the curvature of the loss surface, or inversely, the smoothness of the decision boundary around the data point. This is captured by the local linearity of the gradient around the sample, measured as the trace of the Hessian. We plot the histogram of an efficiently calculable estimation of this trace for the training + +dataset of different pretrained models in Figure 1 for the CIFAR-10 dataset [38]. We note they resemble a bimodal distribution, with a spread out Gaussian superimposed upon a very sharp, tall peak around zero. We are interested in the samples that make up the sharp peak, the ones around which the loss surface curvature is very low. + +We visualize the sample ordered by curvature accumulated over ten differently initialized ResNet18 [23] models trained on CIFAR-10 in Figure 2. We find that they reveal useful information about the kinds of samples present in the dataset. The low curvature samples, shown in Figure 2a can be considered clean, prototypical and minimal, in that they are strongly representative of their category. On the other hand, Figure 2b shows the samples with the highest curvature of loss. We can see that they do not appear to be characteristic of their category. They have confusing backgrounds with interfering patterns, uncommon viewing angles and incomplete shapes. We show that the low curvature samples appear to be largely consistent not only across networks that were initialized differently, but also across completely different architectures such as MobileNetV3 [24], ResNet101 [23], AlexNet [39], VGG19 [53] and DenseNet121 [25]. We also show that they can be identified quite early on during the training process. As an application of this insight, we show that they make very good coresets. + +Many coreset selection methods perform well at large coreset sizes, close to the size of the whole dataset. In this paper, we explore smaller coresets, ranging from sin + +gle digit images per class, as is often common with few shot learning [16, 18], up to 100 images per class. Depending on the dataset and the number of classes, this can range from $0.1\%$ to $20\%$ of the dataset. We introduce SLo-Curves, a novel coreset selection method which identifies samples with low curvatures and train on these coresets with an additional regularizer that penalizes large curvatures. Both the method for measuring the curvature and the form of the regularizer are inspired directly from CURE [44], which introduced the regularizer as a means to promote adversarial accuracy at the expense of clean accuracy. We show that when there are small sample sizes, chosen appropriately, this regularizer also helps improve clean accuracy. We summarize our contributions below: + +1. We study the loss surface with respect to the input data points and identify an unexpected concentration of samples with very low curvature. +2. We show that the curvature of the loss function relates to the notion of visual 'cleanliness'. Low curvature samples are free of conflicting features, while high curvature samples look cluttered, obstructed or unrepresentative of the other samples in the class. To the best of our knowledge, this is a novel observation. +3. We show that these samples are largely architecture and initialization independent. This implies that the Hessian reveals intrinsic properties of the dataset rather than just an artifact of the training procedure, a particular local minima, or the choice of network architecture. +4. We introduce SLo-Curves: an algorithm that selects samples with low curvature as coresets and additionally penalizes the curvature of the loss function while training on them. SLo-Curves outperforms all other choices of coreset selection methods by up to $9\%$ for coresets of few samples per class. To the best of our knowledge, this is the first paper to explore second order statistics of the loss with respect to the data for coreset selection. +5. Due to these samples being consistent across architectures, SLo-Curves does not rely on gradient statistics during training or need to be averaged out over multiple initializations. Coresets can be pre-computed and are performant across architectures. We also find that these points can be identified early on during training, in as few as 5-10 epochs. + +Our method is inherently more productive at small core-set sizes since the samples that we identify belong to the limited set that have very low curvature, corresponding to the tall peak at zero in Figure 1. Further study is required to understand what causes the decision boundary to smoothen along the same samples with different networks, and we hope that this paper accelerates interest in this direction. + +# 2. Literature Review + +The importance of samples is a relevant concern in many areas. Importance sampling methods [30, 31] prioritize the important samples for fast and efficient training by approximating the norm of the gradient resulting from each sample. Curriculum learning [4] seeks to order sample exposure to the network during training in order to learn easier samples first and then harder samples for better solutions. Active learning [51] focuses on only labeling the important samples to reduce annotation costs. However, the definition of importance of samples is not fixed. In this section, we focus on coreset selection as a base method for deciding sample importance scores, that can be then used to different ends. We broadly classify techniques for coreset selection in deep learning and discuss representative approaches in each. + +Clustering based methods: Points close to each other can be clustered together and represented well by the cluster center. The choice of metric for clustering varies. Authors of [10] clusters samples based on distance in the feature space. Authors of [22] reframe the problem as solving a minimax facility location problem greedily. + +Classification Output based methods: These approaches work on the assumption that examples that are classified with lesser confidence or score are more informative than examples classified with strong confidence. Authors of [11] study the effects of choosing softmax scores, entropy and the distance of the top-2 classes in the output space. A different approach is taken by the authors of [57], who show that a large majority of samples are learned correctly early on during training and are never consequently classified incorrectly, or forgotten, during the remaining course of training. They deem the samples that are never forgotten once learnt, as easily learned, and create coresets that consist of examples that need to be re-learnt. + +Loss Gradient based methods: This approach categorizes the importance of a sample as its contribution to the loss or the gradient of the loss. Methods vary in their choice of the time of training at which the contribution is measured. Both Grad-Match [35] and CRAIG [43] select weighted subsets such that the appropriately scaled gradient of the subset matches the gradient of the entire dataset. Both reselect the subset and weights every few epochs. They differ in the choice of algorithm for building the dataset, with CRAIG converting the gradient-distance optimization problem into a submodular function and then using a greedy approach and Grad-Match using a different greedy Orthogonal Matching Pursuit algorithm. Both outline convergence guarantees, and show scalability via approximating gradients of the loss with respect to the input with gradients at the last layer [31]. To overcome the requirement for reselecting the coresets during training, authors of [46] introduce GraNd, which approximates the L2 norm of the gradient early on in training (after a few epochs) and averages it + +over many different training initializations. + +Bilevel optimization and submodular function methods: Glister [36] and Retrieve [37] frame the minimization of the loss on selected samples and the selection of samples as a bilevel optimization problem. Authors of [27, 28] explore different submodular optimization functions. + +Decision Boundary based methods: These methods assume that the points closest to the boundary are hardest to separate, and hence most informative. Authors of [14] utilize DeepFool, a method to generate adversarial examples, as a way of measuring distance to boundary. If an example is easier to fool, it is presumably closer to the boundary and significant. Authors of [42] select the samples whose classification likelihood is most dissimilar to its neighbors. + +Synthetic coreset creation methods: In contrast to selecting points from the dataset, there has been recent interest in methods that create synthetic data to mimic the overall distribution. Dataset distillation [58] was introduced to create synthetic data by matching the gradient of samples averaged over many different initializations. Authors of [8] improve performance by repeating the synthetic set creation over many iterations. However, the datasets do not resemble the data, and this can be an advantage or disadvantage based on the application. In this manuscript we only study the samples present in the training distribution. + +Coreset selection libraries: Coreset selection in deep learning is an area of rapidly increasing focus, as evidenced by the release of recent libraries that compare different core-set selection methods, and can be incorporated into other deep learning applications. Recently released libraries are CORDS [34], Minicore [3] and DeepCore [21]. We use DeepCore for our simulations. + +Our method falls under both the categories of decision boundary based methods and loss gradient based methods. We select real samples from the dataset, choosing coresets from pre-trained models based on the trace of the Hessian of the loss. Our coresets consist of the samples with low trace of Hessian, or low loss curvature around them. The selected samples are chosen only once, are not re-weighted and no special optimization is followed besides an additional regularizer that encourages the learned decision boundary to be flat by penalizing the curvature estimate. They generalize across architectures and hence, do not need to be calculated real time for every network. + +# 3. Methodology and Observations + +We study the curvature profiles of the loss with respect to input for different training data points. The curvature profile can be studied via the Hessian of the loss. Concretely, let's consider a data point $x \in \mathbb{R}^d$ . Let $H$ denote the Hessian of the loss, $L$ with respect to the data point $x$ , i.e. + +$$ +H (x) = \left[ \frac {\delta^ {2} L (x)}{\delta x _ {i} \delta x _ {j}} \right] _ {i, j = 1 \dots d} +$$ + +The curvature profile is captured by the eigenvalues. A good measure is the sum of the eigenvalues or the trace of the Hessian [13, 32]. The higher the trace, the more the loss surface curves around the data point, or the less smooth the decision boundary at the data point's vicinity. We plot the histogram of an approximation of the Hessian trace (explained in section 3.1) for the training set of different network architectures in Figure 1, at the end of training on CIFAR-10. We note that they follow a similar trend: a sharp tall peak at very small values, and another Gaussian-like peak later. We focus on the set of samples with very low curvatures that make up the sharp peak at zero. Histograms for different architectures can be found in Appendix A. We note that these networks were trained with Cross Entropy Loss, SGD optimizer with momentum and L2 regularization. There is no term explicitly encouraging a low spread of curvature for some samples. + +# 3.1. Calculating the Curvature + +The eigenvalues of the Hessian of the loss with respect to the data point contain information about the curvature profile of the loss surface around the data point. Large absolute eigenvalues imply a large curvature of the loss function around the sample, and small magnitude of eigenvalues imply that the loss function (or the decision boundary) has a small curvature, or is locally linear in the vicinity of the data point. The Hessian of the loss surface with respect to model weights has been utilized to study the properties of the minima the optimization selects. [19, 47-49]. However, in this paper, we instead study the curvature of the loss surface with respect to the training data. + +In order to study the curvature profile without having to explicitly calculate the Hessian and its eigenvalues, we estimate instead the trace of the Hessian. The trace is the sum of the eigenvalues and can be calculated efficiently via Hutchinson's trace estimator [26] and finite difference approximation. This is the same form of curvature measure used in CURE [44] as the curvature regularizer for enhancing adversarial robustness during training. We now go into the details of this formulation. + +Let $\lambda_{i}$ , $i = 1\dots d$ be the eigenvalues of the Hessian $H(x)$ . We are interested in the spectrum of the magnitude of the eigenvalues, which can be summarized by the sum of the square of the eigenvalues. This can be estimated by the norm of the Hessian-vector product as introduced in the Hutchinson's trace estimator [26]. Using Hutchinson's trace estimator, the definitions of the Frobenius norm of a matrix, properties of the trace, and the fact that $H(x)$ is symmetric, we get the following estimate: + +![](images/613d8cb6e229913696630f491faae10359698e232e849aab7b7726ec3695d54f.jpg) +(a) Curvatures accumulated over differently seeded ResNet-18 + +![](images/8c2351399b22b3907779c97dd5ac7374345a94b357ea4cfb860490c3ea2e8ef5.jpg) +(b) Curvatures accumulated over different architectures +Figure 3. Histograms of curvature of the training set of CIFAR-10, with curvature estimates accumulated over different trained models. + +$$ +\begin{array}{l} \sum \lambda_ {i} ^ {2} = T r (H ^ {2}) \\ = \mathbb {E} _ {z} \left[ z ^ {T} H ^ {2} z \right] \\ = \mathbb {E} _ {z} \left[ z ^ {T} H ^ {T} H z \right] \\ = \mathbb {E} _ {z} \left[ (H z) ^ {T} (H z) \right] \\ = \mathbb {E} _ {z} \left[ \| H z \| _ {F} ^ {2} \right] \\ \end{array} +$$ + +where $z$ are Rademacher random variables, equal to $+1$ or $-1$ with equal probability, i.e. $z \sim^{i.i.d} \{-1, +1\}^d$ . We now use finite approximation to estimate the Hessian vector product efficiently. + +$$ +H z = \frac {\nabla L (x + h z) - \nabla L (x)}{h} \quad \text {f o r} h \rightarrow 0 +$$ + +The cost of calculating this is just the cost of performing a backward pass on the network twice. This formulation is widely used whenever the curvatures of loss surface are discussed [7, 9, 49, 59]. Similar to CURE [44], we do not choose random directions for sampling $z$ to take the expectation over. Instead, we choose the adversarial direction, which is known to lead to high curvature [15, 29], and set $z$ to be $\frac{\text{sign} \nabla L(x)}{\|\text{sign}(\nabla L(x))\|}$ . We found the results to not be significantly impacted by $h$ and set it equal to 3 to match the change used in corresponding adversarial settings [20, 41]. + +Putting this together, the measure of curvature of the decision boundary or the loss function around a data point is proportional to the following quantity, $\gamma$ where: + +$$ +\begin{array}{l} \gamma (x) = \| \nabla_ {x} L (x + h z) - \nabla_ {x} L (x) \|; \\ \text {w h e r e} z = \frac {\operatorname {s i g n} \nabla_ {x} L (x)}{\| \operatorname {s i g n} (\nabla_ {x} L (x)) \|} \\ \end{array} +$$ + +# 3.2. Consistency of Low Curvature Samples + +We notice that the low curvature samples are largely consistent across architectures and initialization. We show this + +overlap in Figure 3, with plots of the histogram of cumulative curvature values of samples (estimated by $\gamma$ ), accumulated over different seeds in Figure 3a and over different architectures in Figure 3b. Mathematically, the $i^{th}$ curve corresponds to the histogram of $\sum_{j=0}^{i} \gamma_{j}$ for all training samples, where $j$ indexes different trained models. The first histogram is shown in blue, with unaccumulated curvature estimates ( $\gamma_{0}$ collected from model 'seed0' or 'ResNet101'). Next the curvature estimates of the second model ( $\gamma_{1}$ for 'seed1' or 'ResNet18') are added to the first model's curvature estimates for each sample and the resulting plot is shown in orange. As we accumulate curvature estimates over many different models, the sharp peak at zero starts to spread out a bit. Yet, even after accumulating over 5 seeds or 6 different architectures all converging to different minima, there are more than 2000 common low curvature samples (identified as the smallest, purple peak at zero). This implies that these samples appear to be an intrinsic property of the dataset rather than the initialization or the local minima the networks converged to. We corroborate this experimentally in Section 4.3, by showing that a ResNet18 model trained on coresets identified on any of these architectures outperforms random sampling by an average of $5.3\%$ . + +# 3.3. Identified Coresets + +We now visualize the low and high curvature samples (taken from the accumulated scores of 10 randomly seeded ResNet18 models trained on CIFAR10) in Figures 2. Each row corresponds to a class, and contains the top 10 samples for that class with the lowest and highest curvatures in Figures 2a and 2b, respectively. As can be seen from the figure, the low curvature samples are very 'good' samples, in that they have low to no conflicting backgrounds, structure typical of the class, are centered and are not zoomed in or trimmed. The networks are trained with random left to right flipping, and hence we see samples facing both ways. On + +![](images/a83f440785c93374c5329345648babea172fde44fa896d59e1360805af54ba86.jpg) +ResNet18, CIFAR10 +Figure 4. The histogram of curvature estimates of the training dataset as training progresses. For ease of visualization, the opacity of the curves decreases with epochs. + +the other hand, the high curvature samples are 'bad' in that they are visually harder to identify by humans as well. They have conflicting backgrounds (a deer in a fiery landscape), uncommon viewing angles (a truck from behind) and colors uncharacteristic of the class (a blue plane or a yellow frog). This implies that the curvature, captured by $\gamma$ could be useful as a metric for 'learnability' of a sample. + +# 3.4. Early Emergence of Low Curvature Samples + +We track $\gamma$ through the training progress to study the emergence of low curvature samples, and visualize this in Figure 4. As training progresses (lesser opaque histograms in the figure), we can see the peak towards zero becoming more defined. We find that the concentration of samples around low curvatures emerges in as few as 5-10 epochs of training. We corroborate this in Section 4.5 by showing that the coresets identified by our proposed method as early as epoch 10 outperform random sampling by an average of $4.7\%$ accuracy across all considered coreset sizes. + +# 3.5. SLo-Curves: An Algorithm for Data Efficiency + +Based on these insights, we propose SLo-Curves, an algorithm to identify coresets of samples with low curvature and train on them for increased sample efficiency. We use curvature estimate, $\gamma$ as the selection metric, choosing samples with the lowest values to make up our coreset. Additionally, we show that regularizing the learned curvature around these coresets helps increase the accuracy by a few percentage points. Hence, we first select the points with the lowest $\gamma$ from pretrained networks, and then train a new randomly initialized network on these points using the standard cross entropy loss $L_{CE}(x)$ and $\gamma$ serving as the additional regularizer term, $L_{reg} = \gamma (x)$ . The new loss is thus: + +$$ +L (x) = L _ {C E} (x) + \lambda \gamma (x) +$$ + +The tradeoff parameter $\lambda$ is the only hyperparameter our method induces and is searched over $\{0,0.5,1,5,10,20,50\}$ . We note that smaller coresets require larger values of $\lambda$ and larger coresets require smaller values, ultimately giving better results when the additional regularizer is turned off. This ties with CURE [44], wherein the same regularizer improves adversarial accuracy at the cost of clean accuracy when used with the whole dataset. In our method, it serves instead to improve accuracy at low sample complexities. We anticipate that it is an especially effective form of regularization for small datasets learned with complex models. We reiterate that we study small coreset sizes since our significance metric is based on the samples that concentrate near zero curvature, and the number of such samples is a limited percentage of the dataset. + +# 4. Results and Discussion + +In this section, we outline our network architectures, the training hyperparameters and discuss results. + +# 4.1. Experimental Details + +We run experiments on CIFAR-10 and CIFAR-100 datasets [38]. Both datasets have 50,000 training samples with CIFAR-10 having 5000 samples for each of its 10 classes and CIFAR-100 having 500 samples for each of its 100 classes. The networks used are ResNet-18 [23], ResNet-101 [23], VGG-19 [53], AlexNet [39], MobileNetV3Small [24] and DenseNet-121 [25]. We consider coreset of small sizes, ranging from 1 to 100 samples per class. For all networks, we use a learning rate of 0.1 scaled by 0.1 at epochs 81 and 121, SGD optimizer with a momentum of 0.9, with Nesterov momentum [56] turned on and a weight decay of 5e-4. We train all networks for 164 epochs and report mean and variance for 5 randomly seeded runs. All graphs show mean values, with corresponding variances shown in Appendix B. We compare with representative works from the broad categories of coreset selection methods. In particular, we compare with 9 other methods: Random uniform sampling, Glister [36], Forgetting [57], CRAIG [43], GraphCut [27], Cal [42], GraNd [46], Herding [10] and Margin [11]. For methods that require training before coreset selection, we train the network for 40 epochs to ensure a good convergence point before we select the coresets. We have run the baselines using the Deepcore [21] library (building upon it for methods and networks as needed), and find that it is an excellent repository of state of the art methods. The only hyperparameter that we tune for our method is the strength of the regularization, $\lambda$ . We tune this over the search space $\{0,0.5,1,5,10,20,50\}$ and report the best results. + +# 4.2. Comparison with Coreset Selection Methods + +We now discuss the results of our method compared to random sampling and other state of the art coreset selec + +![](images/558586a8e5df7815442c3b974a31cb9f14a3cb824caded6689e95c1c50f9130e.jpg) +Figure 5. ResNet18 trained on coresets identified by various methods. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.1 and B.2 + +![](images/92f5e8c2ec778a226a9226e40a08835a15075e59a0f150d5903d3c3108db3b20.jpg) + +![](images/470844d97c82272b218b52bc4640cd221d84188a8f499ff41ff93b66b927d585.jpg) +Figure 6. ResNet18 trained on coresets identified by our methods a) from different pretrained architectures and b) with and without regularization. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.3 and B.4. + +![](images/a158e91fac58fe6bbbbede2e0c3f05a5078a7ee2ddbe51e2f083d93d9f3d1def.jpg) + +tion methods. The results for ResNet18 networks trained on CIFAR-10 and CIFAR-100 are shown in 5a and 5b respectively. The corresponding tables with mean and variances are shown in Appendix B.1 and B.2. + +CIFAR-10: Figure 5a shows that selection by the proposed SLo-Curves method outperforms all other coreset methods studied all the way up to 100 samples per class, or $2\%$ of the total dataset (1000 samples). We note that at such coresets sizes, random sampling forms a surprisingly strong baseline (also noted in [21]). The strongest competitors are the submodular function based method GraphCut [27] and decision boundary based method Cal [42]. SLo-Curves shows the best performance in 16 out of the 19 coreset sizes studied and the second best in the remaining 3 cases. It outperforms random sampling by $1 - 9\%$ . + +CIFAR-100 Figure 5b shows that our method outperforms or matches the performance of all other coreset methods studied up to 25 samples per class, or $5\%$ of the total dataset (2500 samples). At larger coreset sizes, SLo-Curves shows a few percentage points of accuracy drop from the state of the art methods Cal and GraphCut, but outperforms random sampling, CRAIG [43], Herding [10] and Margin + +[11] baselines. We note that even at coreset sizes equal to $10\%$ of the dataset (50 samples per class), we outperform random sampling by greater than $3\%$ . + +# 4.3. Cross Architecture Results + +From Section 3.2, we know that low curvature samples generalize across architectures. We corroborate this experimentally and show that SLo-Curves consistently chooses good subsets irrespective of pretrained network accuracy or architecture. Figure 6a shows the accuracy of ResNet18 trained on coresets identified from different pretrained models. We show the results of a differently seeded ResNet-18, a lower accuracy AlexNet, completely different architectures MobileNetV3 and VGG19, a deeper similar architecture ResNet101 and a much bigger network, DenseNet121, with pretraining accuracies mentioned in brackets. Coresets chosen by SLo-curves outperform random sampling for all considered architectures by an average of $5.3\%$ . We can see that subsets chosen from lower, similar or higher accuracy and complexity models all consistently perform well. Variances is shown in Appendix B.3. + +![](images/5853ac17cb97c502070d90f9ff24484f991098fe565f87e11a463518993abb74.jpg) +DenseNet121, CIFAR10 +(a) Histograms + +![](images/c69feaf73d9c4a73ad37b92a96aae36a1249d35679b4f442f24464eaec1631c4.jpg) +ResNet18, CIFAR10 trained on coresets identified from DenseNet121 +at different training epochs using the proposed method +(b) Accuracy +Figure 7. ResNet18 trained on coresets identified from DenseNet121 at initialization, at epoch 10 and at end of training. Note that the x-axis is not to scale. The variances are reported in Appendix B.5. + +# 4.4. Decoupling Selection and Regularization + +Here, we show that the criterion for selection of points is beneficial even without the curvature regularization during training. In Figure 6b, we show the results of ResNet18 trained on coresets of CIFAR-10 identified by SLo-Curves selection both with the best regularization strength $\lambda$ for each coreset size, and without any regularization ( $\lambda = 0$ ). We show the results of random sampling as the baseline. We observe that the best performance is consistently shown by our method with regularization. However, our method without regularization still outperforms random sampling by an average of $2.3\%$ over all coreset sizes. The variances are reported in Appendix B.4. + +# 4.5. Early Emergence of Low Curvature Samples + +Many coreset selection methods require training the network for a few epochs before coreset selection. However, we observe from Section 3.4 that low curvature samples can be identified in the early epochs of training. We now study their efficacy for coreset selection for real time usage. We use a DenseNet121 to perform coreset selection, and train a ResNet18 from scratch on the coreset identified by our method. We study the randomly initialized, untrained DenseNet121 (with $10\%$ accuracy), DenseNet121 trained for 10 epochs (to $84.7\%$ accuracy), and DenseNet121 after convergence ( $93.4\%$ accuracy). Figure 7b visualizes the results, with random sampling shown as a baseline. We show that the coresets identified at epoch 10 perform on par with the coreset identified at convergence. The early emergence of these low curvature samples can also be observed in the corresponding histograms shown in Figure 7a. However, during experimentation, we noted that higher regularization strength ( $\lambda$ ) was needed and recommend that where pretrained models are present, it is preferable to extract coresets from them. Surprisingly, choosing low curvature samples selected from an untrained random initialization per + +forms worse than random sampling. We think this may be because the regularizer forces a simplification of the learned boundary that is useful when the samples lend themselves to a simple boundary. + +# 5. Conclusion + +We studied the curvature of the loss of trained neural networks with respect to the training data points. We observed that there is a significant concentration of training samples with very low curvature, and found that these samples remain consistent between networks of differing initializations and architectures. We also noted that they can be identified early on during training. We visualize the samples with low and high curvature and find striking visual differences between them. The low curvature samples are clean, devoid of obstructions and prototypical of their category. The high curvature samples have visual clutter, occluding and uncommon backgrounds, and are hard to identify. The results highlight the Hessian of data points as a useful tool in the study of deep learning generalization. We apply these observations to select significant samples and introduce SLo-Curves, a novel coreset identification and training algorithm that can generalize across architectures. SLo-curves constructs coresets from the samples with low curvatures and trains on them with an additional regularizer that penalizes large curvature of loss around them. 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Computer Sciences Technical Report 1648, University of Wisconsin-Madison, 2009. 3 +[52] Jae-hun Shim, Kyeongbo Kong, and Suk-Ju Kang. Core-set sampling for efficient neural architecture search. arXiv preprint arXiv:2107.06869, 2021. 1 + +[53] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014. 2, 6 +[54] Samarth Sinha, Han Zhang, Anirudh Goyal, Yoshua Bengio, Hugo Larochelle, and Augustus Odena. Small-GAN: Speeding up GAN training using coresets. In Hal Daumé III and Aarti Singh, editors, Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 9005–9015. PMLR, 13–18 Jul 2020. 1 +[55] Benjamin Spector, Ravi Kumar, and Andrew Tomkins. Preventing adversarial use of datasets through fair core-set construction. CoRR, abs/1910.10871, 2019. 2 +[56] Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In International conference on machine learning, pages 1139–1147. PMLR, 2013. 6 +[57] Mariya Toneva, Alessandro Sordoni, Remi Tachet des Combes, Adam Trischler, Yoshua Bengio, and Geoffrey J Gordon. An empirical study of example forgetting during deep neural network learning. In *ICLR*, 2019. 2, 3, 6 +[58] Tongzhou Wang, Jun-Yan Zhu, Antonio Torralba, and Alexei A Efros. Dataset distillation. arXiv preprint arXiv:1811.10959, 2018. 1, 4 +[59] Zhewei Yao, Amir Gholami, Kurt Keutzer, and Michael Mahoney. Pyhessian: Neural networks through the lens of the hessian. 2019. 5 +[60] Jaehong Yoon, Divyam Madaan, Eunho Yang, and Sung Ju Hwang. Online coreset selection for rehearsal-based continual learning. In International Conference on Learning Representations, 2022. 1 +[61] Bo Zhao, Konda Reddy Mopuri, and Hakan Bilen. Dataset condensation with gradient matching. In International Conference on Learning Representations, 2021. 1 \ No newline at end of file diff --git a/2023/Samples With Low Loss Curvature Improve Data Efficiency/images.zip b/2023/Samples With Low Loss Curvature Improve Data Efficiency/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..915fe7333f5d57df2e1d88d076e1760e83789678 --- /dev/null +++ b/2023/Samples With Low Loss Curvature Improve Data Efficiency/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bfcfcbb46714afb0219e81d7865f7b705dd335410615111ed1b70e9df1a23d88 +size 453284 diff --git a/2023/Samples With Low Loss Curvature Improve Data Efficiency/layout.json b/2023/Samples With Low Loss Curvature Improve Data Efficiency/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..cadaba87212b7307a222fdea8f5208254b890e60 --- /dev/null +++ b/2023/Samples With Low Loss Curvature Improve Data Efficiency/layout.json @@ -0,0 +1,7743 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 113, + 103, + 480, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 103, + 480, + 121 + ], + "spans": [ + { + "bbox": [ + 113, + 103, + 480, + 121 + ], + "type": "text", + "content": "Samples with Low Loss Curvature Improve Data Efficiency" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 171, + 144, + 276, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 171, + 144, + 276, + 185 + ], + "spans": [ + { + "bbox": [ + 171, + 144, + 276, + 185 + ], + "type": "text", + "content": "Isha Garg Purdue University West Lafayette, USA" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 180, + 188, + 268, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 180, + 188, + 268, + 198 + ], + "spans": [ + { + "bbox": [ + 180, + 188, + 268, + 198 + ], + "type": "text", + "content": "gargi@purdue.edu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 144, + 422, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 144, + 422, + 185 + ], + "spans": [ + { + "bbox": [ + 317, + 144, + 422, + 185 + ], + "type": "text", + "content": "Kaushik Roy \nPurdue University \nWest Lafayette, USA" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 188, + 417, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 188, + 417, + 198 + ], + "spans": [ + { + "bbox": [ + 318, + 188, + 417, + 198 + ], + "type": "text", + "content": "kaushik@purdue.edu" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "type": "text", + "content": "In this paper, we study the second order properties of the loss of trained deep neural networks with respect to the training data points to understand the curvature of the loss surface in the vicinity of these points. We find that there is an unexpected concentration of samples with very low curvature. We note that these low curvature samples are largely consistent across completely different architectures, and identifiable in the early epochs of training. We show that the curvature relates to the 'cleanliness' of the data points, with low curvatures samples corresponding to clean, higher clarity samples, representative of their category. Alternatively, high curvature samples are often occluded, have conflicting features and visually atypical of their category. Armed with this insight, we introduce SLo-Curves, a novel coreset identification and training algorithm. SLo-curves identifies the samples with low curvatures as being more data-efficient and trains on them with an additional regularizer that penalizes high curvature of the loss surface in their vicinity. We demonstrate the efficacy of SLo-Curves on CIFAR-10 and CIFAR-100 datasets, where it outperforms state of the art coreset selection methods at small coreset sizes by up to " + }, + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "type": "inline_equation", + "content": "9\\%" + }, + { + "bbox": [ + 46, + 251, + 289, + 563 + ], + "type": "text", + "content": ". The identified coresets generalize across architectures, and hence can be pre-computed to generate condensed versions of datasets for use in downstream tasks. Code is available at https://github.com/ishagarg/Slo-Curves." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 574, + 127, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 127, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 127, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "Deep learning applications have exploded due to access to big data and computational resources. However, data is expensive to gather, annotate and store, and directly influences the computational resources required. Storing more data also runs higher risks of data leakage and privacy violation. It also influences parallelism and communication bottlenecks between machines [17]. There is limited understanding of the mechanism through which deep learning models process complex datasets, what constitutes 'good' or 'easy' examples for learning, and how large a number of" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 307, + 225, + 426, + 388 + ], + "blocks": [ + { + "bbox": [ + 307, + 225, + 426, + 388 + ], + "lines": [ + { + "bbox": [ + 307, + 225, + 426, + 388 + ], + "spans": [ + { + "bbox": [ + 307, + 225, + 426, + 388 + ], + "type": "image", + "image_path": "bcdb3abc3546264195bf5b9b1bce646a26db51566bae128cc91ac81a2233f375.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 396, + 545, + 418 + ], + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 418 + ], + "type": "text", + "content": "Figure 1. Histograms of training dataset's curvature for various networks trained on CIFAR-10." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 226, + 544, + 388 + ], + "blocks": [ + { + "bbox": [ + 427, + 226, + 544, + 388 + ], + "lines": [ + { + "bbox": [ + 427, + 226, + 544, + 388 + ], + "spans": [ + { + "bbox": [ + 427, + 226, + 544, + 388 + ], + "type": "image", + "image_path": "65540c3d6fea8dc5c0bc713ede2b632df6e5f5c9a5fceb5cd468286c8c335c67.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 579 + ], + "type": "text", + "content": "samples are indeed beneficial. Research on data efficiency often focuses on doing more with less data. Standard training methods assume all data points from the training set to be independently and identically distributed from the true training distribution. Data points are sampled uniformly during training and treated as having equal significance. An alternative is to identify representative data points from the training distribution that are more beneficial to learning than random uniform sampling [30, 31]. They can be used as smaller condensed datasets, or upweighted during training as per their significance. These subsets of important points are also known as coresets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "Coresets prove useful in many downstream applications. They are data-efficient and can serve as a good choice of proxy data for Neural Architecture Search (NAS) [45, 52], as episodic memory in Continual Learning [2, 6, 60], and as the choice of augmentation samples during self-supervised learning [37]. They can be utilized in many regimes that may have memory or compute resources, such as for compute-efficient learning [35,43,46], dataset condensation [8, 58, 61], efficient Hyper-parameter Optimization (HPO) [33], and speeding up the training of Generative Adversarial Networks (GANs) [54]. The utility of identifying im" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20290" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 286, + 304 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 286, + 304 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 286, + 304 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 286, + 304 + ], + "type": "image", + "image_path": "489f7cc208fb1cfd78534806784d3c38e490b83d6cb8fd35c7f3d38dd2259178.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 308, + 251, + 317 + ], + "lines": [ + { + "bbox": [ + 84, + 308, + 251, + 317 + ], + "spans": [ + { + "bbox": [ + 84, + 308, + 251, + 317 + ], + "type": "text", + "content": "(a) Top 100 examples with the lowest loss curvature" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 542, + 304 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 542, + 304 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 542, + 304 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 542, + 304 + ], + "type": "image", + "image_path": "7f450764d12846319249f8416222b7f77c48cec70721d183f1474394c5b5d989.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 308, + 511, + 317 + ], + "lines": [ + { + "bbox": [ + 340, + 308, + 511, + 317 + ], + "spans": [ + { + "bbox": [ + 340, + 308, + 511, + 317 + ], + "type": "text", + "content": "(b) Top 100 examples with the highest loss curvature" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 323, + 546, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 546, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 546, + 357 + ], + "type": "text", + "content": "Figure 2. We visualize the 10 samples from each class with lowest and highest curvature of loss identified over 10 different randomly initialized ResNet18 models trained on CIFAR-10. Each row corresponds to a class, consistent across both figures, and 10 ordered samples for each class are shown. The network was trained with random horizontal flipping as part of the augmentations." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 552 + ], + "type": "text", + "content": "important samples can extend beyond efficiency, such as in understanding dataset limitations [5, 55], enabling faster or better convergence by upsampling certain samples during training [12, 40], or in the choice of data to label in active learning [1, 50]. However, it is not always clear what makes a sample informative or good for learning. Methods differ in their definition of significance of samples. Some representative works measure importance via the confidence or margin of the predicted output of the network [1, 11], by clustering samples together in the input or feature space [10, 22], matching the gradient to that of the entire dataset [35, 43, 46], choosing samples that lie closest to the decision boundary [14] or samples that are not forgotten once learnt [57]. Some other representative methods frame it as a submodular function optimization problem [27, 27, 43]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "In this paper, we look at data efficiency from the lens of the loss landscape around the training samples. While the loss surface with respect to the parameters of the neural network has received considerable attention as a means of analyzing the stability of the solution [19, 47-49], the loss landscape with respect to the data is far less studied. Most of the studies have been associated with adversarial robustness [44]. We are interested in the curvature of the loss surface, or inversely, the smoothness of the decision boundary around the data point. This is captured by the local linearity of the gradient around the sample, measured as the trace of the Hessian. We plot the histogram of an efficiently calculable estimation of this trace for the training" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 373, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 444 + ], + "type": "text", + "content": "dataset of different pretrained models in Figure 1 for the CIFAR-10 dataset [38]. We note they resemble a bimodal distribution, with a spread out Gaussian superimposed upon a very sharp, tall peak around zero. We are interested in the samples that make up the sharp peak, the ones around which the loss surface curvature is very low." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 448, + 546, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 546, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 546, + 674 + ], + "type": "text", + "content": "We visualize the sample ordered by curvature accumulated over ten differently initialized ResNet18 [23] models trained on CIFAR-10 in Figure 2. We find that they reveal useful information about the kinds of samples present in the dataset. The low curvature samples, shown in Figure 2a can be considered clean, prototypical and minimal, in that they are strongly representative of their category. On the other hand, Figure 2b shows the samples with the highest curvature of loss. We can see that they do not appear to be characteristic of their category. They have confusing backgrounds with interfering patterns, uncommon viewing angles and incomplete shapes. We show that the low curvature samples appear to be largely consistent not only across networks that were initialized differently, but also across completely different architectures such as MobileNetV3 [24], ResNet101 [23], AlexNet [39], VGG19 [53] and DenseNet121 [25]. We also show that they can be identified quite early on during the training process. As an application of this insight, we show that they make very good coresets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Many coreset selection methods perform well at large coreset sizes, close to the size of the whole dataset. In this paper, we explore smaller coresets, ranging from sin" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20291" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "gle digit images per class, as is often common with few shot learning [16, 18], up to 100 images per class. Depending on the dataset and the number of classes, this can range from " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": " of the dataset. We introduce SLo-Curves, a novel coreset selection method which identifies samples with low curvatures and train on these coresets with an additional regularizer that penalizes large curvatures. Both the method for measuring the curvature and the form of the regularizer are inspired directly from CURE [44], which introduced the regularizer as a means to promote adversarial accuracy at the expense of clean accuracy. We show that when there are small sample sizes, chosen appropriately, this regularizer also helps improve clean accuracy. We summarize our contributions below:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 247, + 287, + 624 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 247, + 287, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 287, + 283 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 287, + 283 + ], + "type": "text", + "content": "1. We study the loss surface with respect to the input data points and identify an unexpected concentration of samples with very low curvature." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 289, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 361 + ], + "type": "text", + "content": "2. We show that the curvature of the loss function relates to the notion of visual 'cleanliness'. Low curvature samples are free of conflicting features, while high curvature samples look cluttered, obstructed or unrepresentative of the other samples in the class. To the best of our knowledge, this is a novel observation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 369, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 429 + ], + "type": "text", + "content": "3. We show that these samples are largely architecture and initialization independent. This implies that the Hessian reveals intrinsic properties of the dataset rather than just an artifact of the training procedure, a particular local minima, or the choice of network architecture." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 436, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 287, + 533 + ], + "type": "text", + "content": "4. We introduce SLo-Curves: an algorithm that selects samples with low curvature as coresets and additionally penalizes the curvature of the loss function while training on them. SLo-Curves outperforms all other choices of coreset selection methods by up to " + }, + { + "bbox": [ + 47, + 436, + 287, + 533 + ], + "type": "inline_equation", + "content": "9\\%" + }, + { + "bbox": [ + 47, + 436, + 287, + 533 + ], + "type": "text", + "content": " for coresets of few samples per class. To the best of our knowledge, this is the first paper to explore second order statistics of the loss with respect to the data for coreset selection." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 539, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 287, + 624 + ], + "type": "text", + "content": "5. Due to these samples being consistent across architectures, SLo-Curves does not rely on gradient statistics during training or need to be averaged out over multiple initializations. Coresets can be pre-computed and are performant across architectures. We also find that these points can be identified early on during training, in as few as 5-10 epochs." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Our method is inherently more productive at small core-set sizes since the samples that we identify belong to the limited set that have very low curvature, corresponding to the tall peak at zero in Figure 1. Further study is required to understand what causes the decision boundary to smoothen along the same samples with different networks, and we hope that this paper accelerates interest in this direction." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 415, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 415, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 415, + 84 + ], + "type": "text", + "content": "2. Literature Review" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 91, + 547, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 258 + ], + "type": "text", + "content": "The importance of samples is a relevant concern in many areas. Importance sampling methods [30, 31] prioritize the important samples for fast and efficient training by approximating the norm of the gradient resulting from each sample. Curriculum learning [4] seeks to order sample exposure to the network during training in order to learn easier samples first and then harder samples for better solutions. Active learning [51] focuses on only labeling the important samples to reduce annotation costs. However, the definition of importance of samples is not fixed. In this section, we focus on coreset selection as a base method for deciding sample importance scores, that can be then used to different ends. We broadly classify techniques for coreset selection in deep learning and discuss representative approaches in each." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 258, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 331 + ], + "type": "text", + "content": "Clustering based methods: Points close to each other can be clustered together and represented well by the cluster center. The choice of metric for clustering varies. Authors of [10] clusters samples based on distance in the feature space. Authors of [22] reframe the problem as solving a minimax facility location problem greedily." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 331, + 547, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 486 + ], + "type": "text", + "content": "Classification Output based methods: These approaches work on the assumption that examples that are classified with lesser confidence or score are more informative than examples classified with strong confidence. Authors of [11] study the effects of choosing softmax scores, entropy and the distance of the top-2 classes in the output space. A different approach is taken by the authors of [57], who show that a large majority of samples are learned correctly early on during training and are never consequently classified incorrectly, or forgotten, during the remaining course of training. They deem the samples that are never forgotten once learnt, as easily learned, and create coresets that consist of examples that need to be re-learnt." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 486, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 548, + 714 + ], + "type": "text", + "content": "Loss Gradient based methods: This approach categorizes the importance of a sample as its contribution to the loss or the gradient of the loss. Methods vary in their choice of the time of training at which the contribution is measured. Both Grad-Match [35] and CRAIG [43] select weighted subsets such that the appropriately scaled gradient of the subset matches the gradient of the entire dataset. Both reselect the subset and weights every few epochs. They differ in the choice of algorithm for building the dataset, with CRAIG converting the gradient-distance optimization problem into a submodular function and then using a greedy approach and Grad-Match using a different greedy Orthogonal Matching Pursuit algorithm. Both outline convergence guarantees, and show scalability via approximating gradients of the loss with respect to the input with gradients at the last layer [31]. To overcome the requirement for reselecting the coresets during training, authors of [46] introduce GraNd, which approximates the L2 norm of the gradient early on in training (after a few epochs) and averages it" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20292" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 221, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 221, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 221, + 83 + ], + "type": "text", + "content": "over many different training initializations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 87, + 286, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 87, + 286, + 147 + ], + "spans": [ + { + "bbox": [ + 47, + 87, + 286, + 147 + ], + "type": "text", + "content": "Bilevel optimization and submodular function methods: Glister [36] and Retrieve [37] frame the minimization of the loss on selected samples and the selection of samples as a bilevel optimization problem. Authors of [27, 28] explore different submodular optimization functions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 150, + 286, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 150, + 286, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 150, + 286, + 246 + ], + "type": "text", + "content": "Decision Boundary based methods: These methods assume that the points closest to the boundary are hardest to separate, and hence most informative. Authors of [14] utilize DeepFool, a method to generate adversarial examples, as a way of measuring distance to boundary. If an example is easier to fool, it is presumably closer to the boundary and significant. Authors of [42] select the samples whose classification likelihood is most dissimilar to its neighbors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 250, + 286, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 250, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 250, + 286, + 380 + ], + "type": "text", + "content": "Synthetic coreset creation methods: In contrast to selecting points from the dataset, there has been recent interest in methods that create synthetic data to mimic the overall distribution. Dataset distillation [58] was introduced to create synthetic data by matching the gradient of samples averaged over many different initializations. Authors of [8] improve performance by repeating the synthetic set creation over many iterations. However, the datasets do not resemble the data, and this can be an advantage or disadvantage based on the application. In this manuscript we only study the samples present in the training distribution." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 384, + 286, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 286, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 286, + 467 + ], + "type": "text", + "content": "Coreset selection libraries: Coreset selection in deep learning is an area of rapidly increasing focus, as evidenced by the release of recent libraries that compare different core-set selection methods, and can be incorporated into other deep learning applications. Recently released libraries are CORDS [34], Minicore [3] and DeepCore [21]. We use DeepCore for our simulations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 472, + 286, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 286, + 614 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 286, + 614 + ], + "type": "text", + "content": "Our method falls under both the categories of decision boundary based methods and loss gradient based methods. We select real samples from the dataset, choosing coresets from pre-trained models based on the trace of the Hessian of the loss. Our coresets consist of the samples with low trace of Hessian, or low loss curvature around them. The selected samples are chosen only once, are not re-weighted and no special optimization is followed besides an additional regularizer that encourages the learned decision boundary to be flat by penalizing the curvature estimate. They generalize across architectures and hence, do not need to be calculated real time for every network." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 633, + 222, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 222, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 222, + 646 + ], + "type": "text", + "content": "3. Methodology and Observations" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "text", + "content": "We study the curvature profiles of the loss with respect to input for different training data points. The curvature profile can be studied via the Hessian of the loss. Concretely, let's consider a data point " + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "text", + "content": " denote the Hessian of the loss, " + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "text", + "content": " with respect to the data point " + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 47, + 653, + 286, + 712 + ], + "type": "text", + "content": ", i.e." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 369, + 83, + 482, + 112 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 83, + 482, + 112 + ], + "spans": [ + { + "bbox": [ + 369, + 83, + 482, + 112 + ], + "type": "interline_equation", + "content": "H (x) = \\left[ \\frac {\\delta^ {2} L (x)}{\\delta x _ {i} \\delta x _ {j}} \\right] _ {i, j = 1 \\dots d}", + "image_path": "13261544b5d7cf09d56bbcc347976e4949219ea99cf76e536c7cd0b9b2f0fdcd.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 120, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 120, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 120, + 545, + 323 + ], + "type": "text", + "content": "The curvature profile is captured by the eigenvalues. A good measure is the sum of the eigenvalues or the trace of the Hessian [13, 32]. The higher the trace, the more the loss surface curves around the data point, or the less smooth the decision boundary at the data point's vicinity. We plot the histogram of an approximation of the Hessian trace (explained in section 3.1) for the training set of different network architectures in Figure 1, at the end of training on CIFAR-10. We note that they follow a similar trend: a sharp tall peak at very small values, and another Gaussian-like peak later. We focus on the set of samples with very low curvatures that make up the sharp peak at zero. Histograms for different architectures can be found in Appendix A. We note that these networks were trained with Cross Entropy Loss, SGD optimizer with momentum and L2 regularization. There is no term explicitly encouraging a low spread of curvature for some samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 333, + 451, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 333, + 451, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 333, + 451, + 346 + ], + "type": "text", + "content": "3.1. Calculating the Curvature" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 353, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 353, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 353, + 545, + 496 + ], + "type": "text", + "content": "The eigenvalues of the Hessian of the loss with respect to the data point contain information about the curvature profile of the loss surface around the data point. Large absolute eigenvalues imply a large curvature of the loss function around the sample, and small magnitude of eigenvalues imply that the loss function (or the decision boundary) has a small curvature, or is locally linear in the vicinity of the data point. The Hessian of the loss surface with respect to model weights has been utilized to study the properties of the minima the optimization selects. [19, 47-49]. However, in this paper, we instead study the curvature of the loss surface with respect to the training data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 498, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 545, + 604 + ], + "type": "text", + "content": "In order to study the curvature profile without having to explicitly calculate the Hessian and its eigenvalues, we estimate instead the trace of the Hessian. The trace is the sum of the eigenvalues and can be calculated efficiently via Hutchinson's trace estimator [26] and finite difference approximation. This is the same form of curvature measure used in CURE [44] as the curvature regularizer for enhancing adversarial robustness during training. We now go into the details of this formulation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{i}" + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "i = 1\\dots d" + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "text", + "content": " be the eigenvalues of the Hessian " + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "H(x)" + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "text", + "content": ". We are interested in the spectrum of the magnitude of the eigenvalues, which can be summarized by the sum of the square of the eigenvalues. This can be estimated by the norm of the Hessian-vector product as introduced in the Hutchinson's trace estimator [26]. Using Hutchinson's trace estimator, the definitions of the Frobenius norm of a matrix, properties of the trace, and the fact that " + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "H(x)" + }, + { + "bbox": [ + 306, + 605, + 545, + 713 + ], + "type": "text", + "content": " is symmetric, we get the following estimate:" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20293" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 74, + 287, + 232 + ], + "blocks": [ + { + "bbox": [ + 54, + 74, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 54, + 74, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 54, + 74, + 287, + 232 + ], + "type": "image", + "image_path": "613d8cb6e229913696630f491faae10359698e232e849aab7b7726ec3695d54f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 234, + 269, + 244 + ], + "lines": [ + { + "bbox": [ + 67, + 234, + 269, + 244 + ], + "spans": [ + { + "bbox": [ + 67, + 234, + 269, + 244 + ], + "type": "text", + "content": "(a) Curvatures accumulated over differently seeded ResNet-18" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 316, + 74, + 544, + 231 + ], + "blocks": [ + { + "bbox": [ + 316, + 74, + 544, + 231 + ], + "lines": [ + { + "bbox": [ + 316, + 74, + 544, + 231 + ], + "spans": [ + { + "bbox": [ + 316, + 74, + 544, + 231 + ], + "type": "image", + "image_path": "8c2351399b22b3907779c97dd5ac7374345a94b357ea4cfb860490c3ea2e8ef5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 339, + 234, + 517, + 243 + ], + "lines": [ + { + "bbox": [ + 339, + 234, + 517, + 243 + ], + "spans": [ + { + "bbox": [ + 339, + 234, + 517, + 243 + ], + "type": "text", + "content": "(b) Curvatures accumulated over different architectures" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 51, + 251, + 539, + 262 + ], + "lines": [ + { + "bbox": [ + 51, + 251, + 539, + 262 + ], + "spans": [ + { + "bbox": [ + 51, + 251, + 539, + 262 + ], + "type": "text", + "content": "Figure 3. Histograms of curvature of the training set of CIFAR-10, with curvature estimates accumulated over different trained models." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 291, + 222, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 291, + 222, + 373 + ], + "spans": [ + { + "bbox": [ + 111, + 291, + 222, + 373 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\sum \\lambda_ {i} ^ {2} = T r (H ^ {2}) \\\\ = \\mathbb {E} _ {z} \\left[ z ^ {T} H ^ {2} z \\right] \\\\ = \\mathbb {E} _ {z} \\left[ z ^ {T} H ^ {T} H z \\right] \\\\ = \\mathbb {E} _ {z} \\left[ (H z) ^ {T} (H z) \\right] \\\\ = \\mathbb {E} _ {z} \\left[ \\| H z \\| _ {F} ^ {2} \\right] \\\\ \\end{array}", + "image_path": "33789aca1a2b33d7c5b898c6044346eb95829c5a8cbec20caedd3d3f658af9ea.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "text", + "content": " are Rademacher random variables, equal to " + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "inline_equation", + "content": "+1" + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "text", + "content": " with equal probability, i.e. " + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "inline_equation", + "content": "z \\sim^{i.i.d} \\{-1, +1\\}^d" + }, + { + "bbox": [ + 46, + 384, + 287, + 432 + ], + "type": "text", + "content": ". We now use finite approximation to estimate the Hessian vector product efficiently." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 79, + 435, + 256, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 435, + 256, + 460 + ], + "spans": [ + { + "bbox": [ + 79, + 435, + 256, + 460 + ], + "type": "interline_equation", + "content": "H z = \\frac {\\nabla L (x + h z) - \\nabla L (x)}{h} \\quad \\text {f o r} h \\rightarrow 0", + "image_path": "c6ecad1463d2ba8cc6de7bd94b9dbacf32fd5bd031ad48414808a98493e042c9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "text", + "content": "The cost of calculating this is just the cost of performing a backward pass on the network twice. This formulation is widely used whenever the curvatures of loss surface are discussed [7, 9, 49, 59]. Similar to CURE [44], we do not choose random directions for sampling " + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "text", + "content": " to take the expectation over. Instead, we choose the adversarial direction, which is known to lead to high curvature [15, 29], and set " + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "text", + "content": " to be " + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "inline_equation", + "content": "\\frac{\\text{sign} \\nabla L(x)}{\\|\\text{sign}(\\nabla L(x))\\|}" + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "text", + "content": ". We found the results to not be significantly impacted by " + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 463, + 287, + 584 + ], + "type": "text", + "content": " and set it equal to 3 to match the change used in corresponding adversarial settings [20, 41]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 585, + 287, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 585, + 287, + 621 + ], + "spans": [ + { + "bbox": [ + 46, + 585, + 287, + 621 + ], + "type": "text", + "content": "Putting this together, the measure of curvature of the decision boundary or the loss function around a data point is proportional to the following quantity, " + }, + { + "bbox": [ + 46, + 585, + 287, + 621 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 585, + 287, + 621 + ], + "type": "text", + "content": " where:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 64, + 626, + 270, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 626, + 270, + 668 + ], + "spans": [ + { + "bbox": [ + 64, + 626, + 270, + 668 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\gamma (x) = \\| \\nabla_ {x} L (x + h z) - \\nabla_ {x} L (x) \\|; \\\\ \\text {w h e r e} z = \\frac {\\operatorname {s i g n} \\nabla_ {x} L (x)}{\\| \\operatorname {s i g n} (\\nabla_ {x} L (x)) \\|} \\\\ \\end{array}", + "image_path": "14d116dd10929f7bc97b08ff2afbd7ef9935d3380dc7b352f4d75295275007ba.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 671, + 255, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 255, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 255, + 685 + ], + "type": "text", + "content": "3.2. Consistency of Low Curvature Samples" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 712 + ], + "type": "text", + "content": "We notice that the low curvature samples are largely consistent across architectures and initialization. We show this" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": "overlap in Figure 3, with plots of the histogram of cumulative curvature values of samples (estimated by " + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": "), accumulated over different seeds in Figure 3a and over different architectures in Figure 3b. Mathematically, the " + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": " curve corresponds to the histogram of " + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\sum_{j=0}^{i} \\gamma_{j}" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": " for all training samples, where " + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": " indexes different trained models. The first histogram is shown in blue, with unaccumulated curvature estimates (" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\gamma_{0}" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": " collected from model 'seed0' or 'ResNet101'). Next the curvature estimates of the second model (" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\gamma_{1}" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": " for 'seed1' or 'ResNet18') are added to the first model's curvature estimates for each sample and the resulting plot is shown in orange. As we accumulate curvature estimates over many different models, the sharp peak at zero starts to spread out a bit. Yet, even after accumulating over 5 seeds or 6 different architectures all converging to different minima, there are more than 2000 common low curvature samples (identified as the smallest, purple peak at zero). This implies that these samples appear to be an intrinsic property of the dataset rather than the initialization or the local minima the networks converged to. We corroborate this experimentally in Section 4.3, by showing that a ResNet18 model trained on coresets identified on any of these architectures outperforms random sampling by an average of " + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "inline_equation", + "content": "5.3\\%" + }, + { + "bbox": [ + 304, + 275, + 545, + 550 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 562, + 416, + 573 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 416, + 573 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 416, + 573 + ], + "type": "text", + "content": "3.3. Identified Coresets" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "We now visualize the low and high curvature samples (taken from the accumulated scores of 10 randomly seeded ResNet18 models trained on CIFAR10) in Figures 2. Each row corresponds to a class, and contains the top 10 samples for that class with the lowest and highest curvatures in Figures 2a and 2b, respectively. As can be seen from the figure, the low curvature samples are very 'good' samples, in that they have low to no conflicting backgrounds, structure typical of the class, are centered and are not zoomed in or trimmed. The networks are trained with random left to right flipping, and hence we see samples facing both ways. On" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20294" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 84, + 258, + 228 + ], + "blocks": [ + { + "bbox": [ + 123, + 72, + 215, + 83 + ], + "lines": [ + { + "bbox": [ + 123, + 72, + 215, + 83 + ], + "spans": [ + { + "bbox": [ + 123, + 72, + 215, + 83 + ], + "type": "text", + "content": "ResNet18, CIFAR10" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 55, + 84, + 258, + 228 + ], + "lines": [ + { + "bbox": [ + 55, + 84, + 258, + 228 + ], + "spans": [ + { + "bbox": [ + 55, + 84, + 258, + 228 + ], + "type": "image", + "image_path": "a83f440785c93374c5329345648babea172fde44fa896d59e1360805af54ba86.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 231, + 287, + 265 + ], + "lines": [ + { + "bbox": [ + 46, + 231, + 287, + 265 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 287, + 265 + ], + "type": "text", + "content": "Figure 4. The histogram of curvature estimates of the training dataset as training progresses. For ease of visualization, the opacity of the curves decreases with epochs." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 282, + 286, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 286, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 286, + 368 + ], + "type": "text", + "content": "the other hand, the high curvature samples are 'bad' in that they are visually harder to identify by humans as well. They have conflicting backgrounds (a deer in a fiery landscape), uncommon viewing angles (a truck from behind) and colors uncharacteristic of the class (a blue plane or a yellow frog). This implies that the curvature, captured by " + }, + { + "bbox": [ + 46, + 282, + 286, + 368 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 282, + 286, + 368 + ], + "type": "text", + "content": " could be useful as a metric for 'learnability' of a sample." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 376, + 279, + 389 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 279, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 279, + 389 + ], + "type": "text", + "content": "3.4. Early Emergence of Low Curvature Samples" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "text", + "content": "We track " + }, + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "text", + "content": " through the training progress to study the emergence of low curvature samples, and visualize this in Figure 4. As training progresses (lesser opaque histograms in the figure), we can see the peak towards zero becoming more defined. We find that the concentration of samples around low curvatures emerges in as few as 5-10 epochs of training. We corroborate this in Section 4.5 by showing that the coresets identified by our proposed method as early as epoch 10 outperform random sampling by an average of " + }, + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "inline_equation", + "content": "4.7\\%" + }, + { + "bbox": [ + 46, + 395, + 287, + 515 + ], + "type": "text", + "content": " accuracy across all considered coreset sizes." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 523, + 286, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 523, + 286, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 523, + 286, + 537 + ], + "type": "text", + "content": "3.5. SLo-Curves: An Algorithm for Data Efficiency" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "content": "Based on these insights, we propose SLo-Curves, an algorithm to identify coresets of samples with low curvature and train on them for increased sample efficiency. We use curvature estimate, " + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "content": " as the selection metric, choosing samples with the lowest values to make up our coreset. Additionally, we show that regularizing the learned curvature around these coresets helps increase the accuracy by a few percentage points. Hence, we first select the points with the lowest " + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "content": " from pretrained networks, and then train a new randomly initialized network on these points using the standard cross entropy loss " + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "inline_equation", + "content": "L_{CE}(x)" + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "content": " serving as the additional regularizer term, " + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "inline_equation", + "content": "L_{reg} = \\gamma (x)" + }, + { + "bbox": [ + 46, + 543, + 286, + 687 + ], + "type": "text", + "content": ". The new loss is thus:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 113, + 700, + 220, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 700, + 220, + 714 + ], + "spans": [ + { + "bbox": [ + 113, + 700, + 220, + 714 + ], + "type": "interline_equation", + "content": "L (x) = L _ {C E} (x) + \\lambda \\gamma (x)", + "image_path": "c2a9524739aa53b314516c9953aa4879bd6271b0d3b67456f8c6bfaf5e6da3e2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "The tradeoff parameter " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " is the only hyperparameter our method induces and is searched over " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "\\{0,0.5,1,5,10,20,50\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": ". We note that smaller coresets require larger values of " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " and larger coresets require smaller values, ultimately giving better results when the additional regularizer is turned off. This ties with CURE [44], wherein the same regularizer improves adversarial accuracy at the cost of clean accuracy when used with the whole dataset. In our method, it serves instead to improve accuracy at low sample complexities. We anticipate that it is an especially effective form of regularization for small datasets learned with complex models. We reiterate that we study small coreset sizes since our significance metric is based on the samples that concentrate near zero curvature, and the number of such samples is a limited percentage of the dataset." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 258, + 437, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 437, + 270 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 437, + 270 + ], + "type": "text", + "content": "4. Results and Discussion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 278, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 278, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 278, + 545, + 302 + ], + "type": "text", + "content": "In this section, we outline our network architectures, the training hyperparameters and discuss results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 305, + 427, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 305, + 427, + 318 + ], + "spans": [ + { + "bbox": [ + 305, + 305, + 427, + 318 + ], + "type": "text", + "content": "4.1. Experimental Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "type": "text", + "content": "We run experiments on CIFAR-10 and CIFAR-100 datasets [38]. Both datasets have 50,000 training samples with CIFAR-10 having 5000 samples for each of its 10 classes and CIFAR-100 having 500 samples for each of its 100 classes. The networks used are ResNet-18 [23], ResNet-101 [23], VGG-19 [53], AlexNet [39], MobileNetV3Small [24] and DenseNet-121 [25]. We consider coreset of small sizes, ranging from 1 to 100 samples per class. For all networks, we use a learning rate of 0.1 scaled by 0.1 at epochs 81 and 121, SGD optimizer with a momentum of 0.9, with Nesterov momentum [56] turned on and a weight decay of 5e-4. We train all networks for 164 epochs and report mean and variance for 5 randomly seeded runs. All graphs show mean values, with corresponding variances shown in Appendix B. We compare with representative works from the broad categories of coreset selection methods. In particular, we compare with 9 other methods: Random uniform sampling, Glister [36], Forgetting [57], CRAIG [43], GraphCut [27], Cal [42], GraNd [46], Herding [10] and Margin [11]. For methods that require training before coreset selection, we train the network for 40 epochs to ensure a good convergence point before we select the coresets. We have run the baselines using the Deepcore [21] library (building upon it for methods and networks as needed), and find that it is an excellent repository of state of the art methods. The only hyperparameter that we tune for our method is the strength of the regularization, " + }, + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "type": "text", + "content": ". We tune this over the search space " + }, + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\{0,0.5,1,5,10,20,50\\}" + }, + { + "bbox": [ + 304, + 320, + 545, + 668 + ], + "type": "text", + "content": " and report the best results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 673, + 537, + 686 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 673, + 537, + 686 + ], + "spans": [ + { + "bbox": [ + 305, + 673, + 537, + 686 + ], + "type": "text", + "content": "4.2. Comparison with Coreset Selection Methods" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We now discuss the results of our method compared to random sampling and other state of the art coreset selec" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20295" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 76, + 289, + 218 + ], + "blocks": [ + { + "bbox": [ + 55, + 76, + 289, + 218 + ], + "lines": [ + { + "bbox": [ + 55, + 76, + 289, + 218 + ], + "spans": [ + { + "bbox": [ + 55, + 76, + 289, + 218 + ], + "type": "image", + "image_path": "558586a8e5df7815442c3b974a31cb9f14a3cb824caded6689e95c1c50f9130e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 219, + 546, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 219, + 546, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 546, + 243 + ], + "type": "text", + "content": "Figure 5. ResNet18 trained on coresets identified by various methods. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.1 and B.2" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 308, + 74, + 541, + 217 + ], + "blocks": [ + { + "bbox": [ + 308, + 74, + 541, + 217 + ], + "lines": [ + { + "bbox": [ + 308, + 74, + 541, + 217 + ], + "spans": [ + { + "bbox": [ + 308, + 74, + 541, + 217 + ], + "type": "image", + "image_path": "92f5e8c2ec778a226a9226e40a08835a15075e59a0f150d5903d3c3108db3b20.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 55, + 251, + 285, + 399 + ], + "blocks": [ + { + "bbox": [ + 55, + 251, + 285, + 399 + ], + "lines": [ + { + "bbox": [ + 55, + 251, + 285, + 399 + ], + "spans": [ + { + "bbox": [ + 55, + 251, + 285, + 399 + ], + "type": "image", + "image_path": "470844d97c82272b218b52bc4640cd221d84188a8f499ff41ff93b66b927d585.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 403, + 546, + 437 + ], + "lines": [ + { + "bbox": [ + 46, + 403, + 546, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 546, + 437 + ], + "type": "text", + "content": "Figure 6. ResNet18 trained on coresets identified by our methods a) from different pretrained architectures and b) with and without regularization. Note that the x-axis is not to scale to clearly show performance at a few samples per class. The numbers shown are the mean of 5 runs. Variances are reported in Appendix B.3 and B.4." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 308, + 251, + 541, + 399 + ], + "blocks": [ + { + "bbox": [ + 308, + 251, + 541, + 399 + ], + "lines": [ + { + "bbox": [ + 308, + 251, + 541, + 399 + ], + "spans": [ + { + "bbox": [ + 308, + 251, + 541, + 399 + ], + "type": "image", + "image_path": "a158e91fac58fe6bbbbede2e0c3f05a5078a7ee2ddbe51e2f083d93d9f3d1def.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 496 + ], + "type": "text", + "content": "tion methods. The results for ResNet18 networks trained on CIFAR-10 and CIFAR-100 are shown in 5a and 5b respectively. The corresponding tables with mean and variances are shown in Appendix B.1 and B.2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "type": "text", + "content": "CIFAR-10: Figure 5a shows that selection by the proposed SLo-Curves method outperforms all other coreset methods studied all the way up to 100 samples per class, or " + }, + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "type": "text", + "content": " of the total dataset (1000 samples). We note that at such coresets sizes, random sampling forms a surprisingly strong baseline (also noted in [21]). The strongest competitors are the submodular function based method GraphCut [27] and decision boundary based method Cal [42]. SLo-Curves shows the best performance in 16 out of the 19 coreset sizes studied and the second best in the remaining 3 cases. It outperforms random sampling by " + }, + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "type": "inline_equation", + "content": "1 - 9\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 628 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "CIFAR-100 Figure 5b shows that our method outperforms or matches the performance of all other coreset methods studied up to 25 samples per class, or " + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": " of the total dataset (2500 samples). At larger coreset sizes, SLo-Curves shows a few percentage points of accuracy drop from the state of the art methods Cal and GraphCut, but outperforms random sampling, CRAIG [43], Herding [10] and Margin" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "type": "text", + "content": "[11] baselines. We note that even at coreset sizes equal to " + }, + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "type": "text", + "content": " of the dataset (50 samples per class), we outperform random sampling by greater than " + }, + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 305, + 449, + 546, + 485 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 500, + 455, + 513 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 455, + 513 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 455, + 513 + ], + "type": "text", + "content": "4.3. Cross Architecture Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": "From Section 3.2, we know that low curvature samples generalize across architectures. We corroborate this experimentally and show that SLo-Curves consistently chooses good subsets irrespective of pretrained network accuracy or architecture. Figure 6a shows the accuracy of ResNet18 trained on coresets identified from different pretrained models. We show the results of a differently seeded ResNet-18, a lower accuracy AlexNet, completely different architectures MobileNetV3 and VGG19, a deeper similar architecture ResNet101 and a much bigger network, DenseNet121, with pretraining accuracies mentioned in brackets. Coresets chosen by SLo-curves outperform random sampling for all considered architectures by an average of " + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "inline_equation", + "content": "5.3\\%" + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": ". We can see that subsets chosen from lower, similar or higher accuracy and complexity models all consistently perform well. Variances is shown in Appendix B.3." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20296" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 92, + 251, + 217 + ], + "blocks": [ + { + "bbox": [ + 103, + 79, + 226, + 91 + ], + "lines": [ + { + "bbox": [ + 103, + 79, + 226, + 91 + ], + "spans": [ + { + "bbox": [ + 103, + 79, + 226, + 91 + ], + "type": "text", + "content": "DenseNet121, CIFAR10" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 92, + 251, + 217 + ], + "lines": [ + { + "bbox": [ + 53, + 92, + 251, + 217 + ], + "spans": [ + { + "bbox": [ + 53, + 92, + 251, + 217 + ], + "type": "image", + "image_path": "5853ac17cb97c502070d90f9ff24484f991098fe565f87e11a463518993abb74.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 136, + 222, + 186, + 232 + ], + "lines": [ + { + "bbox": [ + 136, + 222, + 186, + 232 + ], + "spans": [ + { + "bbox": [ + 136, + 222, + 186, + 232 + ], + "type": "text", + "content": "(a) Histograms" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 307, + 91, + 541, + 217 + ], + "blocks": [ + { + "bbox": [ + 339, + 75, + 525, + 83 + ], + "lines": [ + { + "bbox": [ + 339, + 75, + 525, + 83 + ], + "spans": [ + { + "bbox": [ + 339, + 75, + 525, + 83 + ], + "type": "text", + "content": "ResNet18, CIFAR10 trained on coresets identified from DenseNet121" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 356, + 83, + 507, + 91 + ], + "lines": [ + { + "bbox": [ + 356, + 83, + 507, + 91 + ], + "spans": [ + { + "bbox": [ + 356, + 83, + 507, + 91 + ], + "type": "text", + "content": "at different training epochs using the proposed method" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 91, + 541, + 217 + ], + "lines": [ + { + "bbox": [ + 307, + 91, + 541, + 217 + ], + "spans": [ + { + "bbox": [ + 307, + 91, + 541, + 217 + ], + "type": "image", + "image_path": "c69feaf73d9c4a73ad37b92a96aae36a1249d35679b4f442f24464eaec1631c4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 402, + 222, + 444, + 232 + ], + "lines": [ + { + "bbox": [ + 402, + 222, + 444, + 232 + ], + "spans": [ + { + "bbox": [ + 402, + 222, + 444, + 232 + ], + "type": "text", + "content": "(b) Accuracy" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 236, + 546, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 546, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 546, + 258 + ], + "type": "text", + "content": "Figure 7. ResNet18 trained on coresets identified from DenseNet121 at initialization, at epoch 10 and at end of training. Note that the x-axis is not to scale. The variances are reported in Appendix B.5." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 273, + 260, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 273, + 260, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 260, + 286 + ], + "type": "text", + "content": "4.4. Decoupling Selection and Regularization" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "text", + "content": "Here, we show that the criterion for selection of points is beneficial even without the curvature regularization during training. In Figure 6b, we show the results of ResNet18 trained on coresets of CIFAR-10 identified by SLo-Curves selection both with the best regularization strength " + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "text", + "content": " for each coreset size, and without any regularization (" + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "inline_equation", + "content": "\\lambda = 0" + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "text", + "content": "). We show the results of random sampling as the baseline. We observe that the best performance is consistently shown by our method with regularization. However, our method without regularization still outperforms random sampling by an average of " + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "inline_equation", + "content": "2.3\\%" + }, + { + "bbox": [ + 46, + 292, + 288, + 435 + ], + "type": "text", + "content": " over all coreset sizes. The variances are reported in Appendix B.4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 443, + 279, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 279, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 279, + 456 + ], + "type": "text", + "content": "4.5. Early Emergence of Low Curvature Samples" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "content": "Many coreset selection methods require training the network for a few epochs before coreset selection. However, we observe from Section 3.4 that low curvature samples can be identified in the early epochs of training. We now study their efficacy for coreset selection for real time usage. We use a DenseNet121 to perform coreset selection, and train a ResNet18 from scratch on the coreset identified by our method. We study the randomly initialized, untrained DenseNet121 (with " + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "content": " accuracy), DenseNet121 trained for 10 epochs (to " + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "inline_equation", + "content": "84.7\\%" + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "content": " accuracy), and DenseNet121 after convergence (" + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "inline_equation", + "content": "93.4\\%" + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "content": " accuracy). Figure 7b visualizes the results, with random sampling shown as a baseline. We show that the coresets identified at epoch 10 perform on par with the coreset identified at convergence. The early emergence of these low curvature samples can also be observed in the corresponding histograms shown in Figure 7a. However, during experimentation, we noted that higher regularization strength (" + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "text", + "content": ") was needed and recommend that where pretrained models are present, it is preferable to extract coresets from them. Surprisingly, choosing low curvature samples selected from an untrained random initialization per" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 274, + 546, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 546, + 322 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 546, + 322 + ], + "type": "text", + "content": "forms worse than random sampling. We think this may be because the regularizer forces a simplification of the learned boundary that is useful when the samples lend themselves to a simple boundary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 330, + 378, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 330, + 378, + 342 + ], + "spans": [ + { + "bbox": [ + 306, + 330, + 378, + 342 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 346, + 546, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 546, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 546, + 598 + ], + "type": "text", + "content": "We studied the curvature of the loss of trained neural networks with respect to the training data points. We observed that there is a significant concentration of training samples with very low curvature, and found that these samples remain consistent between networks of differing initializations and architectures. We also noted that they can be identified early on during training. We visualize the samples with low and high curvature and find striking visual differences between them. The low curvature samples are clean, devoid of obstructions and prototypical of their category. The high curvature samples have visual clutter, occluding and uncommon backgrounds, and are hard to identify. The results highlight the Hessian of data points as a useful tool in the study of deep learning generalization. We apply these observations to select significant samples and introduce SLo-Curves, a novel coreset identification and training algorithm that can generalize across architectures. SLo-curves constructs coresets from the samples with low curvatures and trains on them with an additional regularizer that penalizes large curvature of loss around them. We show that at small coreset sizes, SLo-Curves beats the state of the art coreset selection methods by up to " + }, + { + "bbox": [ + 304, + 346, + 546, + 598 + ], + "type": "inline_equation", + "content": "9\\%" + }, + { + "bbox": [ + 304, + 346, + 546, + 598 + ], + "type": "text", + "content": " on CIFAR-10 and CIFAR-100 datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 608, + 404, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 404, + 622 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 404, + 622 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 625, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 545, + 713 + ], + "type": "text", + "content": "The authors wish to thank Dr. Andrew Buchanan for the insightful discussions and suggestions. This work was supported in part by the Center for Brain Inspired Computing (C-BRIC), one of the six centers in JUMP, a Semiconductor Research Corporation (SRC) program sponsored by DARPA, by the Semiconductor Research Corporation, the National Science Foundation, Intel Corporation, the DoD Vannevar Bush Fellowship, and by the U.S. Army Research Laboratory." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20297" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 139 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 139 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 139 + ], + "type": "text", + "content": "[1] Sharat Agarwal, Himanshu Arora, Saket Anand, and Chetan Arora. 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Most recently, the non-local interactions of the whole mesh vertices have been effectively estimated in the transformer while the relationship between body parts also has begun to be handled via the graph model. Even though those approaches have shown the remarkable progress in 3D human mesh reconstruction, it is still difficult to directly infer the relationship between features, which are encoded from the 2D input image, and 3D coordinates of each vertex. To resolve this problem, we propose to design a simple feature sampling scheme. The key idea is to sample features in the embedded space by following the guide of points, which are estimated as projection results of 3D mesh vertices (i.e., ground truth). This helps the model to concentrate more on vertex-relevant features in the 2D space, thus leading to the reconstruction of the natural human pose. Furthermore, we apply progressive attention masking to precisely estimate local interactions between vertices even under severe occlusions. Experimental results on benchmark datasets show that the proposed method efficiently improves the performance of 3D human mesh reconstruction. The code and model are publicly available at: https://github.com/DCVL-3D/PointHMR_release.", + "bbox": [ + 76, + 334, + 473, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 728, + 209, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The goal of 3D human mesh reconstruction is to estimate 3D coordinates of points, which make up the human body surface. Since the high-quality 3D human model has been consistently required for various immersive applications, many studies have devoted considerable efforts to accurately reconstruct the 3D human mesh. In the early stage of this field, complex optimization techniques were", + "bbox": [ + 75, + 755, + 468, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a07e559d14d39b58bac16c57711dd541048e69882b1fb37ac61bb775936062ae.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 500, + 284, + 893, + 359 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9db56032bf13deccc60921e11fd879b95f1d76c8062bacd426daba3146cf8af5.jpg", + "image_caption": [ + "(b)", + "Figure 1. (a) Traditional process of feature extraction for estimating 3D coordinates. (b) Vertex-relevant feature extraction process based on the proposed point-guided sampling method for estimating 3D coordinates." + ], + "image_footnote": [], + "bbox": [ + 500, + 376, + 892, + 454 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "adopted to generate the 3D human model based on the relationship between multiple scenes, which are acquired by using stereo or multiple-view camera systems. Recently, owing to the great success of deep learning, the problem of 3D human mesh reconstruction now can be resolved only with a single RGB image, thus the majority has begun to develop compact network architectures and efficient training strategies. Even though such deep learning-based approaches have shown the significant progress in 3D human mesh reconstruction, this task is still challenging due to severe occlusions by diverse human poses and depth ambiguities by the monocular setting.", + "bbox": [ + 496, + 566, + 892, + 748 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning-based approaches can be divided into two main groups: model-based and model-free methods. In the former, most methods aim to estimate shape and pose parameters of the skinned multi-person linear (SMPL) model [24], which is capable of yielding the whole vertices via these two simple factors, thus most widely employed in this field. Traditional encoder-decoder architectures, which are mostly composed of stacked convolutional layers, are sufficient to conduct the regression for estimating those parameters. Despite their great performance, model-based", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*equal contribution", + "bbox": [ + 94, + 875, + 202, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ corresponding author", + "bbox": [ + 96, + 887, + 217, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12880", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "methods have the obvious shortcoming, i.e., reconstruction results are limited to the pre-defined types of human body models. On the other hand, model-free methods have attempted to directly infer 3D coordinates of mesh vertices from input features without using any specific human body model. Compared to the model-based approach, which obtains the well-defined full mesh by adjusting shape and pose parameters, the model-free approach needs to estimate 3D coordinates of whole vertices directly from the network. Most methods in this category are based on the transformer to grasp non-local interactions between mesh vertices. The graph model (e.g., graph convolution) also has been utilized together to allow for body part relations in a local manner. One important advantage of the model-free approach is the flexibility to adapt to other applications, e.g., hand pose estimation, without significant changes of the data format and the training strategy. However, inferring the 3D coordinate from a single monocular image is still challenging due to lack of learning the correspondence between encoded features and spatial positions.", + "bbox": [ + 76, + 90, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a simple yet powerful method for 3D human mesh reconstruction. To this end, we conduct feature sampling at vertex-relevant points of the input image as shown in Fig. 1, which are estimated through the heatmap decoder trained by projection results of 3D mesh vertices (i.e., ground truth). These sampled features are subsequently fed into the transformer encoder as the form of the vertex token (see Fig. 2). In a similar way of [6], we apply attention masking to the transformer encoder, however, the difference is that the local connection is defined with the range of multiple levels through the sequence of transformer encoders. This progressive attention masking helps the model understand local relations between vertices precisely even in occlusions. The main contribution of the proposed method can be summarized as follows:", + "bbox": [ + 76, + 393, + 472, + 621 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose to utilize the correspondence between encoded features and vertex positions, which are projected into the 2D space, via our point-guided feature sampling scheme. By explicitly indicating such vertex-relevant features to the transformer encoder, coordinates of the 3D human mesh are accurately estimated.", + "- Our progressive attention masking scheme helps the model efficiently deal with local vertex-to-vertex relations even under complicated poses and occlusions." + ], + "bbox": [ + 96, + 633, + 468, + 797 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 814, + 218, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this Section, we give a brief review of the previous studies for 3D human mesh construction which have progressed in two different directions: model-based and model-free approaches.", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-based approaches. As mentioned, most model-based approaches aim to estimate shape and pose parameters of the SMPL model [24] for restoring the entire set of mesh vertices. In the beginning, several studies attempted to align 2D joint positions as well as body part segments, which are estimated by respective networks, with the ground truth projected from the 3D human mesh [3, 19]. However, these methods require additional steps to estimate shape and pose parameters of the SMPL model. To cope with this limitation, Kanazawa et al. [12] proposed to regress such parameters directly from a single RGB image without using intermediate results, i.e., 2D joints and body part segments. Specifically, they designed a simple convolutional encoder with the adversarial loss to make the reconstructed mesh result be realistic. Inspired by the great potential of this simple regression scheme, many researchers have introduced various encoder-decoder architectures to estimate shape and pose parameters. Kolotouros et al. [17] proposed to combine the end-to-end regression model with the optimization loop to strongly supervise the refinement process. Choutas et al. [9] attempted to directly regress body, face, and hands by exploiting the body-driven attention in the SMPL-X [29] format for generating the high-quality 3D human mesh. Biggs et al. [2] designed a multi-hypothesis neural network regressor based on the best-of-M loss, which makes the plausible human pose even under severely occluded environments. Zhang et al. [37] also focused on accurately restoring object-occluded human shape and pose by utilizing the partial UV map and the novel saliency map in the SMPL format. Most recently, Kocabas et al. [16] devised the part attention module to guide the network to concentrate more on relevant body parts for inferring the given pose with SMPL parameters in a single input RGB image. Sun et al. [32] estimated body center positions instead of segmenting human regions and extracted the parameter maps for the SMPL model at the corresponding positions. They further extend their algorithm by adopting the heat map of the bird-eye view to alleviate the depth ambiguity in monocular settings [33]. On the other hand, the kinematic topology module has been embedded into the neural network architecture to consider the relationship between articulations of the human body [20]. Even though model-based approaches have shown the remarkable progress in 3D human mesh reconstruction, their performance is limited to pre-defined types of human body models, which are hardly extended to other applications.", + "bbox": [ + 496, + 90, + 893, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-free approaches. Model-free approaches intend to directly restore the entire set of mesh vertices while relaxing the heavy reliance on the parameter space in model-based methods. As a pioneer, Kolotouros et al. [18] proposed to estimate human mesh coordinates through the graph convolutional neural network (GraphCNN). To do this, they attached encoded features to nodes in the graph, which are", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12881", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/29a0e4e7dc6f94b9078071707a90335fc0fb6d3e78bb95d2c6b80c15d5532b20.jpg", + "image_caption": [ + "Figure 2. Overall architecture of the proposed method. The backbone feature is used to generate heatmap, target feature, and grid feature with respective decoders. Our sampling scheme utilizes heatmap and target feature to make the vertex token. Note that $N$ and $M$ denote the number of vertices and the distance threshold for defining the local connection in self-attention, respectively." + ], + "image_footnote": [], + "bbox": [ + 76, + 71, + 885, + 309 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mapped to 3D coordinates of the template mesh. From this perspective, Choi et al. [7] also adopted GraphCNN to reconstruct 3D human meshes from 2D and 3D pose information in a coarse-to-fine manner. While these GraphCNN-based methods have a good ability to fully exploit the mesh topology, they are somewhat lacking in considering global interactions between joints and vertices. To cope with this limitation, the transformer has begun to be actively adopted for model-free approaches. Specifically, Lin et al. [21] firstly introduced the transformer encoder, which simply takes joint and vertex queries as input tokens, to regress 3D coordinates from a single input RGB image. In particular, they further embedded GraphCNN into the transformer block to supplement local interactions, e.g., between-part relationships, for 3D human mesh reconstruction. Most recently, Cho et al. [6] have disentangled image features and mesh queries by utilizing the transformer encoder-decoder architecture to alleviate the high complexity of interactions among input tokens.", + "bbox": [ + 75, + 383, + 472, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method is also based on the transformer encoder with a simple sampling scheme, which gives a great help to focus on vertex-relevant features for inferring coordinates of the 3D human mesh. Technical details will be explained in the following Section.", + "bbox": [ + 75, + 672, + 470, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 767, + 250, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed method consists of two main parts. Specifically, vertex-relevant features are extracted based on our point-guided feature sampling in the first part while 3D coordinates are estimated through the sequence of transformer encoders with the proposed progressive attention masking scheme in the second part. The overall architecture of the proposed method is illustrated in Fig. 2.", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3dc4d150e9a1f768c5c68033705028cbb23b71d055bb2e2f4275cbb5a26c4c04.jpg", + "image_caption": [ + "Figure 3. Several examples of predicted heatmaps on the 3DPW dataset. For better visibility, the activated regions of the heatmap corresponding to several selected vertices are represented in a single image with bright colors (best view in colors)." + ], + "image_footnote": [], + "bbox": [ + 501, + 382, + 629, + 481 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8a9500a8768abef880e6b4da9cf08904fa98504a1de14e663870bd0ed0ea9983.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 382, + 759, + 481 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e850c2b5fd5092905b33a9c1fdbaddb2c87fc68b16f14195e4e7ff6024924608.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 382, + 890, + 481 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Point-guided Feature Sampling", + "text_level": 1, + "bbox": [ + 500, + 560, + 777, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Since the direct transform from the color value to the 3D coordinate is still a difficult process due to heterogeneous modalities, we propose to use the intermediate guidance, i.e., features sampled at positions of vertices projected from 3D to 2D spaces. Specifically, we represent such projection results as the form of the heatmap, and sample features at activated positions in this heatmap. The detailed process of our point-guided feature sampling is shown in the first part of Fig. 2. Firstly, the backbone feature $X_{b}\\in \\mathbb{R}^{C\\times H\\times W}$ is encoded through the backbone network (HRNet [35] in this work), where $C$ , $H$ , and $W$ denote the number of channels, height, and width, respectively.", + "bbox": [ + 496, + 583, + 890, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$X_{b}$ is subsequently decoded into the heatmap, the target feature, and the grid feature by respective decoders as shown in Fig. 2. After that, the vertex-relevant feature is sampled at each of $N$ vertices based on combination of the predicted heatmap and the target feature. Several examples of the predicted heatmap are shown in Fig. 3. Note that we conducted element-wise multiplication of the predicted heatmap and the target feature to make our sampling process be differentiable. Moreover, we apply the positional", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12882", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f2ad6b6da73f88c46eaf68e1b3051e3b0ad9ae9389b86c8628cf3c52815fe4f1.jpg", + "image_caption": [ + "Figure 4. The detailed structure of the proposed progressive attention masking scheme. Note that this figure illustrates the masking process in the first transformer encoder, i.e., the case of $M = 7$ , shown in Fig. 2." + ], + "image_footnote": [], + "bbox": [ + 76, + 78, + 468, + 204 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "encoding to the target feature in the same way of [5, 6] for preserving the spatial information in the transformer encoder. Our point-guided feature sampling can be formulated as follows:", + "bbox": [ + 75, + 289, + 468, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {V} _ {i} = H _ {i} \\times F, \\quad i = 1, 2, 3, \\dots , N, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 358, + 468, + 376 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $H_{i}$ and $F$ denote the predicted heatmap corresponding to the $i$ -th vertex and the target feature, respectively. $N$ denotes the total number of vertices and is set to 431 as used in previous methods. $\\hat{V}_{i}$ is the sampling result, which is finally flattened and fed into the transformer encoder with the grid feature in the second part of our proposed method. It is noteworthy that the grid feature plays an important role to create the united body structure by aligning each point in an appropriate location.", + "bbox": [ + 75, + 385, + 468, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Transformer Encoder with Progressive Attention Masking", + "text_level": 1, + "bbox": [ + 76, + 530, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this subsection, we explain the sequence of transformer encoders in detail. In a similar way of [21, 22], we design the transformer encoder with the dimension reduction layer as shown in the second part of Fig. 2. Specifically, the transformer encoder takes the vertex token $\\hat{V} \\in \\mathbb{R}^{N \\times D}$ , the joint token $\\hat{J} \\in \\mathbb{R}^{K \\times D}$ , and the grid token $\\hat{G} \\in \\mathbb{R}^{Z \\times D}$ as inputs. The joint token is a trainable parameter that is randomly initialized and optimized during the training phase whereas vertex and grid tokens are extracted from the first part of the proposed method. Moreover, positional encodings are employed to give the identity by concatenating the trainable parameter to each token. The dimension of the encoded token is reduced by linear projection after each transformer block, which consists of two transformer encoders. To consider local vertex-vertex relations as well as non-adjacent interactions, we exclude far-distant connections between vertices to compute self-attention in the transformer encoder. In contrast to the previous method [6], we gradually decrease the range to define the local connection between vertices through the sequence of transformer encoders as illustrated in Fig. 4. This helps the model consider the local relationship between neighbor vertices in a", + "bbox": [ + 75, + 568, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/96521333a3a1cfdfe52f8b372d02f9c4e91d2e3aada1d96edbe4a495a9764a4e.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 629, + 188 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2717359c138593e978b36dbeecc95d136b7b795a9d9c26571b48fb774337a829.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 633, + 88, + 759, + 188 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/66b0b382ea207b510a19cd97448ecfca06dbcd748eba6ff7f576fafe23a2edc4.jpg", + "image_caption": [ + "(c)", + "Figure 5. (a) Input image. (b) Reconstruction result with previous attention masking [6]. (c) Reconstruction result with progressive attention masking (proposed)." + ], + "image_footnote": [], + "bbox": [ + 764, + 88, + 890, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "progressive manner. Figure 5 shows the effect of our progressive attention masking. As can be seen, the proposed method provides the reasonable result even in occlusions.", + "bbox": [ + 496, + 273, + 890, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The outputs (i.e., vertex and joint tokens) of the last transformer encoder are finally projected into 3D coordinates via a linear layer. In the case of the vertex token, the upsampling algorithm introduced in [31] is applied to expand sparse vertices $V' \\in \\mathbb{R}^{N \\times 3}$ into dense vertices $V \\in \\mathbb{R}^{\\mathcal{N} \\times 3}$ as follows:", + "bbox": [ + 496, + 319, + 890, + 409 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nV = U V ^ {\\prime}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 656, + 417, + 890, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $U$ is the pre-defined upsampling matrix [31]. $\\mathcal{N}$ is set to 6,890 (same as the vertex number of the SMPL model). The predicted 3D human mesh and 3D keypoints can be visualized as the rightmost images shown in Fig. 2.", + "bbox": [ + 496, + 441, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 510, + 643, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proposed method is trained based on four types of loss functions, i.e., vertex loss $\\mathcal{L}_v$ , 3D joint loss $\\mathcal{L}_{j3d}$ , 2D joint loss $\\mathcal{L}_{j2d}$ , and heatmap loss $\\mathcal{L}_h$ . The first three loss functions are used for estimating positions of vertices and joints as introduced in previous works [6,21,22] while the last one guides the network to find positions of projected vertices. First of all, $L_{1}$ loss is adopted to compute the difference between positions of the predicted vertex $V$ and the corresponding ground truth $\\tilde{V}$ as follows:", + "bbox": [ + 496, + 534, + 890, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\tilde {V} ^ {i} - V ^ {i} \\| _ {1}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 676, + 890, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N$ denotes the total number of vertices. For the 3D joint loss, we compute the distance between the estimated joint position $J_{3d}$ and the corresponding ground truth $\\bar{J}_{3d}$ in the 3D space. Note that the joint position, which is regressed from the predicted vertices, i.e., $\\bar{J}_{3d}$ , is also used for the loss computation as follows:", + "bbox": [ + 496, + 724, + 890, + 815 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {j 3 d} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {J} _ {3 d} ^ {i} - J _ {3 d} ^ {i} \\| _ {2} + \\| \\tilde {J} _ {3 d} ^ {i} - \\bar {J} _ {3 d} ^ {i} \\| _ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 821, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $K$ denotes the total number of joints. Similarly, the 2D joint loss is calculated as well. To do this, $J_{3d}$ and $\\bar{J}_{3d}$", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12883", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/e2643924e9b4ddf5832f4d8337394d6254285a305703325260ab977a81cb1f27.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsBackboneHuman3.6M3DPW
MPJPE(↓)PA-MPJPE(↓)MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
model-basedHMR [12]ResNet-5088.056.8130.081.3-
SPIN [17]ResNet-50-41.196.959.2116.4
ExPose [9]ResNet-50--93.455.6-
VIBE [15]ResNet-5065.641.482.951.999.1
HybrIK [20]ResNet-3454.434.580.048.894.5
ROMP [32]HRNet-W32--76.747.393.4
PARE [16]HRNet-W32--74.546.588.6
MAED [40]ResNet-5056.438.779.145.792.6
PyMAF [36]ResNet-5057.740.592.858.9110.1
BEV* [33]HRNet-W32--78.546.992.3
OCHMR* [13]ResNet-50 / HRNet-W32--89.758.3107.1
3DCrowdNet* [8]ResNet-50--81.751.598.3
model-freeGraphCMR [18]ResNet-50-50.1-70.2-
I2LMeshNet [27]ResNet-5055.741.793.257.7110.1
Pose2Mesh [7]HRNet-W4864.947.089.556.3105.3
METRO [21]HRNet-W6454.036.777.147.988.2
MeshGraphormer [22]HRNet-W6451.234.574.745.687.7
FastMETRO [6]HRNet-W6452.233.773.544.684.1
OursHRNet-W3248.332.973.944.985.5
", + "bbox": [ + 78, + 88, + 893, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Performance comparisons of 3D human mesh reconstruction based on Human3.6M and 3DPW datasets. The proposed method achieves the best performance in the Human3.6M dataset while still showing the competitive performance in the 3DPW dataset (best results are shown in bold). Note that * denotes the performance without fine-tuning on the 3DPW dataset.", + "bbox": [ + 75, + 420, + 892, + 463 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "are projected onto the 2D space and the corresponding results are represented as $J_{2d}$ and $\\bar{J}_{2d}$ , respectively. Based on such projected results, the 2D joint loss is formulated as $L_{2}$ loss in the same way of the 3D joint loss as follows:", + "bbox": [ + 75, + 489, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {j 2 d} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {J} _ {2 d} ^ {i} - J _ {2 d} ^ {i} \\| _ {2} + \\| \\tilde {J} _ {2 d} ^ {i} - \\bar {J} _ {2 d} ^ {i} \\| _ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 555, + 468, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{J}_{2d}$ is the ground truth of the 2D joint position. On the other hand, our heatmap loss $\\mathcal{L}_h$ consists of the binary cross entropy loss and the dice loss. Specifically, we adopt the binary cross entropy loss to determine whether the activated position is matched to the point projected from the vertex or not as follows:", + "bbox": [ + 75, + 604, + 468, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b c e} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tilde {H} ^ {i} \\log H ^ {i} + (1 - \\tilde {H} ^ {i}) \\log (1 - H ^ {i}), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 700, + 468, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H$ and $\\tilde{H}$ denote the predicted heatmap and the corresponding ground truth, respectively. The ground truth is represented as the binary map where the position of the projected vertex is assigned 1, otherwise 0. To alleviate the data-imbalanced problem, i.e., the projected point exists on only a single pixel in the ground truth image, the dice loss [26] is also employed as follows:", + "bbox": [ + 75, + 750, + 468, + 857 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i c e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} 1 - \\frac {2 \\times \\left(\\tilde {H} ^ {i} \\times H ^ {i}\\right)}{\\tilde {H} ^ {i} + H ^ {i}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 862, + 468, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since the dice loss mainly focuses on the overlapped area, the data-imbalanced problem can be efficiently alleviated. By using the combination of these loss functions, the proposed network successfully learns to reconstruct the 3D human mesh as follows:", + "bbox": [ + 498, + 489, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} \\mathcal {L} _ {\\text {t o t a l}} & = w _ {v} \\mathcal {L} _ {v} + w _ {j 3 d} \\mathcal {L} _ {j 3 d} + w _ {j 2 d} \\mathcal {L} _ {j 2 d} \\\\ & + w _ {b c e} \\mathcal {L} _ {b c e} + w _ {d i c e} \\mathcal {L} _ {d i c e}, \\end{array} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 575, + 890, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_v, w_{j3d}, w_{j2d}, w_{bce}$ and $w_{dice}$ are the balancing factor for each loss term, which are set to 0.01, 0.1, 0.01, 1.0, and 0.001, respectively.", + "bbox": [ + 498, + 623, + 893, + 669 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 500, + 684, + 705, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Training", + "text_level": 1, + "bbox": [ + 500, + 709, + 604, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All the experiments are implemented on the PyTorch framework [28] with an Intel E5-1650@3.60GHz CPU and two NVIDIA RTX A6000 GPUs. To train all the parameters of our model, the Adam optimizer [14] is adopted where the momentum factors are set to 0.9 and 0.999, respectively. The proposed network is trained for 50 epochs with a batch size of 64 per GPU. The learning rate is firstly set to $1 \\times 10^{-4}$ and reduced to $1 \\times 10^{-5}$ at the half of the learning time. For each input image, the area including the human is cropped and resized to the resolution of $224 \\times 224$ pixels before training.", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12884", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1c54c44f93e51e4ac13bbee43dbb34237ae44a66359196e206426a0123ac0c53.jpg", + "image_caption": [ + "Figure 6. Results of 3D human mesh reconstruction on Human3.6M [11] (top-two rows) and 3DPW [34] (bottom-two rows) datasets. (a) Input images. (b) Results by METRO [21]. (c) Results by Mesh Graphormer [22]. (d) Results by the proposed method." + ], + "image_footnote": [], + "bbox": [ + 80, + 74, + 483, + 415 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/86f6b90e11f17230bf4bb8965cefaccd4c8ebc3e0263f9fd8c40e8fbd1624028.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 74, + 890, + 415 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 484, + 362, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. For the performance evaluation of the proposed method, two representative benchmarks, i.e., Human3.6M [11] and 3DPW [34], are employed. Specifically, the proposed method is trained based on five datasets, i.e., Human3.6M [11], MuCo-3DHP [25], UP-3D [19], COCO [23], and MPII [1], by following previous approaches, and tested with the P2 protocol in the Human3.6M dataset. Since the ground truth of the 3D human mesh is unavailable in the Human3.6M dataset, we use the pseudo mesh label generated by SMPLify-X [29] as introduced in [6,7,21,22,27]. For the test on the 3DPW dataset, we fine-tune the proposed method by using the training set of the 3DPW dataset.", + "bbox": [ + 75, + 515, + 468, + 712 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. For the quantitative evaluation, we use three metrics, i.e., mean per joint position error (MPJPE) [11], Procrustes-aligned mean per joint position error (PA-MPJPE) [38], and mean per vertex position error (MPVPE) [30], which have been widely adopted for the performance comparison in this field. Specifically, MPJPE measures the average value of the Euclidean distance between each estimated 3D joint and the corresponding ground truth. PA-MPJPE indicates MPJPE in which the estimated human body is aligned in terms of rotation and scaling using the Procrustes analysis. On the other hand, MPVPE is a metric for computing the Euclidean distance", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "between coordinates of the predicted vertex and the corresponding ground truth.", + "bbox": [ + 498, + 484, + 890, + 516 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Performance Evaluation", + "text_level": 1, + "bbox": [ + 498, + 527, + 723, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative evaluation. To demonstrate the efficiency and robustness of the proposed method, we compare ours with representative methods for 3D human mesh reconstruction, i.e., HMR [12], SPIN [17], ExPose [9], VIBE [15], HybrIK [20], ROMP [32], PARE [16], MAED [40], PyMAF [36], BEV [33], OCHMR [13], 3DCrowdNet [8], GraphCMR [18], I2LMeshNet [27], Pose2Mesh [7], METRO [21], Mesh Graphormer [22], and FastMETRO [6]. The result of the performance comparison is shown in Table 1. As can be seen, the proposed method achieves 48.3 MPJPE and 32.9 PA-MPJPE on the Human3.6M dataset, which outperforms the state-of-the-art methods with the meaningful performance gain. Even though the performance of the proposed method is slightly dropped compared to the best one (i.e., FastMETRO) in the 3DPW dataset, our method still shows the competitive performance with state-of-the-art methods. Specifically, model-free methods have shown the reliable performance without using the well-defined human model in recent days. This is because their reconstruction results are not limited to the small set of pre-defined human models, thus show more appropriate human meshes for a given image compared to model-based methods. In particular, transformer-based ar", + "bbox": [ + 496, + 551, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12885", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f981b5b5da79506884b5e138bd98d1f719112a291332a41924d97ff11c332a78.jpg", + "image_caption": [ + "Figure 7. More results of 3D human mesh reconstruction for our samples, which are acquired by the smartphone. Odd columns: input images. Even columns: our results. Note that the proposed method provides reliable results of 3D human mesh reconstruction for various pictures of our daily life even with severe occlusions." + ], + "image_footnote": [], + "bbox": [ + 80, + 74, + 346, + 284 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba9f30233a9768d9d7cb91fe431318566793fde91a3e7981a92849c24658e4d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 74, + 620, + 284 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d27ba339b1f0d60686c0d132f7fc7016575d7eb1bb23c4045940f817438a6667.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 74, + 890, + 284 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "chitectures, e.g., Mesh Graphomer and FastMETRO, significantly improves the performance of 3D human mesh reconstruction. Nevertheless, recent model-based methods still show the competitive performance and work robust to occlusion cases, e.g., BEV, OCHMR, and 3DCrowdNet. It is noteworthy that the proposed method notably improves the performance by our point-guided feature sampling scheme without specially designing the decoder architecture like [6]. Moreover, the proposed method provides the reliable performance with the relatively small-sized backbone (e.g., HRNet-W32).", + "bbox": [ + 75, + 364, + 468, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative evaluation. Several results of 3D human mesh reconstructions for Human3.6M and 3DPW datasets are shown in Fig. 6. Note that our results are reconstructed based on the upsampling matrix as used in [6] while other two methods, i.e., METRO [21] and Mesh Graphomer [22], utilized two linear layers to upsample coarse vertex points. We can see that the proposed method successfully estimates 3D human poses under various situations including real-world scenarios in outdoor scenes as well as the controlled environment. Specifically, previous methods have somewhat difficulties to estimate unusual poses, e.g., overlapping arms and bending, whereas the proposed method provides the well-fit 3D model for a given image. Moreover, the proposed method has a good ability to reconstruct 3D human meshes in occlusions due to the progressive attention masking scheme as shown in examples of the last row of Fig. 6. In particular, previous methods fail to infer the global orientation of the human body due to the fence in front of the target person, which leads to the significant performance drop for 3D human mesh reconstruction. In contrast, the proposed method shows the reliable performance with various occlusions (see third and fourth rows in Fig. 6). More examples for 3D human mesh reconstruction by the proposed method are shown in Fig. 7. Note that in", + "bbox": [ + 75, + 537, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cc8b1bf5d5ba33d5c2b87a8e4c72ea8b7d25e7c71c1c9d0e04181fce22508e05.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Point-guided feature samplingProgressive attention maskingMPJPEPA-MPJPE
XX63.239.9
X✓61.240.8
✓X50.933.3
✓✓48.332.9
", + "bbox": [ + 500, + 363, + 895, + 454 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ee1ebfaf3944ed71d6faaf26d640782e4e5824f82353366148bacb7ed7b2fe4c.jpg", + "table_caption": [ + "Table 2. Performance analysis of the proposed method according to changes in the network architecture based on the Human3.6M dataset (best results are shown in bold)." + ], + "table_footnote": [], + "table_body": "
MethodsMPJPEPA-MPJPE
Without attention masking50.933.3
Single attention masking49.133.5
Progressive attention masking (ours)48.332.9
", + "bbox": [ + 501, + 541, + 890, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Performance analysis of the proposed method according to the attention masking scheme based on the Human3.6M dataset (best results are shown in bold). Note that $M = 1$ is used for single attention masking.", + "bbox": [ + 498, + 614, + 890, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "put images are acquired by the smartphone. As can be seen, the proposed method performs well for various pictures of our daily life even with severe occlusions. Therefore, it is thought that the proposed method paves the way for 3D human mesh reconstruction under various environments.", + "bbox": [ + 496, + 712, + 890, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 800, + 663, + 815 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this subsection, we first demonstrate the comparative experimental results by changing the components of the proposed method based on the Human3.6M dataset. Table 2 shows the contribution of such components. As can be seen, the performance of 3D human mesh reconstruc", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12886", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/74db5938a887a157a7cae7c4941110698bb9cf5109ee2b840de83ce198c20b72.jpg", + "image_caption": [ + "Figure 8. Several reconstruction results (3D joints (left) and 3D hand meshes (right)) by the proposed method for the FreiHAND [39] dataset. Note that the proposed method works robust to self-occlusions frequently occurring by complicated hand poses." + ], + "image_footnote": [], + "bbox": [ + 80, + 74, + 346, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9d944c1ba6135421a26d9e0f57dc5aec06fd239aa00459aa3968f8f0f57688b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 74, + 620, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4ca2278f5c717b3712828a486f1305eb38e2821efa0069c1b91a53703f7eda08.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 622, + 74, + 890, + 282 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion is significantly improved with our point-guided feature sampling scheme (MPJPE: $63.2 \\rightarrow 50.9$ , PA-MPJPE: $39.9 \\rightarrow 33.3$ ). From this analysis, we can see that feature sampling at vertex-relevant positions even in the 2D space is effective for improving the performance of 3D human mesh reconstruction. In what follows, we also check the effect of our progressive attention masking and the corresponding result is shown in Table 3. Note that our point-guided feature sampling is applied for this experiment. By comparing ours with baseline (i.e., without masking) and single masking attention scheme [6], we can see that the progressive restriction strategy in defining the local connection is also helpful for improving the performance of 3D human mesh reconstruction. This tells us that the combination of our contributions makes the model be robust to complicated real-world environments.", + "bbox": [ + 75, + 349, + 472, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Generalization Ability", + "text_level": 1, + "bbox": [ + 76, + 604, + 284, + 619 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In contrast to the model-based approach, the proposed method can be easily applied to other applications. To show the generalization ability of the proposed method, we conduct 3D hand mesh reconstruction based on the FreiHAND [39] dataset by changing the number of input tokens for the sequence of transformer encoders. Note that the number of vertices to be projected is set to 195 and those are upsampled to 778 via the same upsampling matrix used for 3D human mesh reconstruction. Several reconstruction results by the proposed method are shown in Fig. 8. We can see that the proposed method provides the reliable reconstruction results (i.e., 3D joints and 3D hand meshes) for various hand poses. In particular, self-occlusions by complicated relations between adjacent fingers are successfully handled in the proposed method. The result of the quantitative evaluation is also shown in Table 4. As can be seen, the proposed method shows the competitive performance on the FreiHAND dataset.", + "bbox": [ + 75, + 628, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fc9bec706602c3ea8b2f0e5967330892dea1a04475aaf54179e5f2120903fbba.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsPA-MPVPEPA-MPJPEF@5mmF@15mm
Hasson et al. [10]13.2-0.4360.908
Boukhayma et al. [4]13.0-0.4350.898
FreiHAND [39]10.7-0.5290.935
I2LMeshNet [27]7.67.40.6810.973
Pose2Mesh [7]7.87.70.6740.969
METRO [21]6.76.80.7170.981
FastMETRO [6]-6.5-0.982
Ours6.66.10.7200.984
", + "bbox": [ + 501, + 347, + 895, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Performance comparisons of 3D hand mesh reconstruction based on the FreiHAND dataset (best results are shown in bold).", + "bbox": [ + 498, + 473, + 892, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 539, + 617, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. The key idea of the proposed method is to alleviate heterogeneous modalities between input (i.e., color) and output (i.e., coordinate) by considering the correspondence of encoded features and 2D points projected from 3D vertices. Our point-guided feature sampling scheme is to sample vertex-relevant features based on the combination of the heatmap and encoded features. In addition, the proposed progressive attention masking scheme makes the model to be robust to occlusions by considering local connections of different levels through the sequence of transformer encoders. Experimental results on benchmark datasets show that the proposed method performs reliably for various real-world environments.", + "bbox": [ + 496, + 566, + 890, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (2021-0-02084, eXtended Reality and Volumetric media generation and transmission technology for immersive experience sharing in noncontact environment with a Korea-EU international cooperative research).", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12887", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. In IEEE Conf. Comput. Vis. 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Vis., 2021. 5, 6", + "bbox": [ + 535, + 90, + 890, + 119 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12889", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/ede83042-4d23-4ef9-a09b-ef8f9683611d_model.json b/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/ede83042-4d23-4ef9-a09b-ef8f9683611d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8f702a54e56946119b745cae86c35a95e89ca1c3 --- /dev/null +++ b/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/ede83042-4d23-4ef9-a09b-ef8f9683611d_model.json @@ -0,0 +1,1892 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.147, + 0.131, + 0.823, + 0.152 + ], + "angle": 0, + "content": "Sampling is Matter: Point-guided 3D Human Mesh Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.18, + 0.714, + 0.199 + ], + "angle": 0, + "content": "Jeonghwan Kim\\(^{1*}\\) Mi-Gyeong Gwon\\(^{1*}\\) Hyunwoo Park\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.199, + 0.688, + 0.217 + ], + "angle": 0, + "content": "Hyukmin Kwon² Gi-Mun Um² Wonjun Kim†" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.217, + 0.798, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)Konkuk University \\(^{2}\\)Electronics and Telecommunications Research Institute" + }, + { + "type": "text", + "bbox": [ + 0.169, + 0.237, + 0.797, + 0.252 + ], + "angle": 0, + "content": "{jhkim0759,kmk3942,pzls,wonjkim}@konkuk.ac.kr {hmkwon,gmum}@etri.re.kr" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.301, + 0.313, + 0.318 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.474, + 0.697 + ], + "angle": 0, + "content": "This paper presents a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. Most recently, the non-local interactions of the whole mesh vertices have been effectively estimated in the transformer while the relationship between body parts also has begun to be handled via the graph model. Even though those approaches have shown the remarkable progress in 3D human mesh reconstruction, it is still difficult to directly infer the relationship between features, which are encoded from the 2D input image, and 3D coordinates of each vertex. To resolve this problem, we propose to design a simple feature sampling scheme. The key idea is to sample features in the embedded space by following the guide of points, which are estimated as projection results of 3D mesh vertices (i.e., ground truth). This helps the model to concentrate more on vertex-relevant features in the 2D space, thus leading to the reconstruction of the natural human pose. Furthermore, we apply progressive attention masking to precisely estimate local interactions between vertices even under severe occlusions. Experimental results on benchmark datasets show that the proposed method efficiently improves the performance of 3D human mesh reconstruction. The code and model are publicly available at: https://github.com/DCVL-3D/PointHMR_release." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.729, + 0.21, + 0.745 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.756, + 0.47, + 0.862 + ], + "angle": 0, + "content": "The goal of 3D human mesh reconstruction is to estimate 3D coordinates of points, which make up the human body surface. Since the high-quality 3D human model has been consistently required for various immersive applications, many studies have devoted considerable efforts to accurately reconstruct the 3D human mesh. In the early stage of this field, complex optimization techniques were" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.285, + 0.895, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.363, + 0.704, + 0.374 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.377, + 0.893, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.687, + 0.455, + 0.705, + 0.467 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.483, + 0.893, + 0.54 + ], + "angle": 0, + "content": "Figure 1. (a) Traditional process of feature extraction for estimating 3D coordinates. (b) Vertex-relevant feature extraction process based on the proposed point-guided sampling method for estimating 3D coordinates." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.893, + 0.749 + ], + "angle": 0, + "content": "adopted to generate the 3D human model based on the relationship between multiple scenes, which are acquired by using stereo or multiple-view camera systems. Recently, owing to the great success of deep learning, the problem of 3D human mesh reconstruction now can be resolved only with a single RGB image, thus the majority has begun to develop compact network architectures and efficient training strategies. Even though such deep learning-based approaches have shown the significant progress in 3D human mesh reconstruction, this task is still challenging due to severe occlusions by diverse human poses and depth ambiguities by the monocular setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Deep learning-based approaches can be divided into two main groups: model-based and model-free methods. In the former, most methods aim to estimate shape and pose parameters of the skinned multi-person linear (SMPL) model [24], which is capable of yielding the whole vertices via these two simple factors, thus most widely employed in this field. Traditional encoder-decoder architectures, which are mostly composed of stacked convolutional layers, are sufficient to conduct the regression for estimating those parameters. Despite their great performance, model-based" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.203, + 0.888 + ], + "angle": 0, + "content": "*equal contribution" + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.218, + 0.901 + ], + "angle": 0, + "content": "\\(\\dagger\\) corresponding author" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.218, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12880" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.394 + ], + "angle": 0, + "content": "methods have the obvious shortcoming, i.e., reconstruction results are limited to the pre-defined types of human body models. On the other hand, model-free methods have attempted to directly infer 3D coordinates of mesh vertices from input features without using any specific human body model. Compared to the model-based approach, which obtains the well-defined full mesh by adjusting shape and pose parameters, the model-free approach needs to estimate 3D coordinates of whole vertices directly from the network. Most methods in this category are based on the transformer to grasp non-local interactions between mesh vertices. The graph model (e.g., graph convolution) also has been utilized together to allow for body part relations in a local manner. One important advantage of the model-free approach is the flexibility to adapt to other applications, e.g., hand pose estimation, without significant changes of the data format and the training strategy. However, inferring the 3D coordinate from a single monocular image is still challenging due to lack of learning the correspondence between encoded features and spatial positions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.395, + 0.473, + 0.622 + ], + "angle": 0, + "content": "In this paper, we propose a simple yet powerful method for 3D human mesh reconstruction. To this end, we conduct feature sampling at vertex-relevant points of the input image as shown in Fig. 1, which are estimated through the heatmap decoder trained by projection results of 3D mesh vertices (i.e., ground truth). These sampled features are subsequently fed into the transformer encoder as the form of the vertex token (see Fig. 2). In a similar way of [6], we apply attention masking to the transformer encoder, however, the difference is that the local connection is defined with the range of multiple levels through the sequence of transformer encoders. This progressive attention masking helps the model understand local relations between vertices precisely even in occlusions. The main contribution of the proposed method can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.634, + 0.47, + 0.739 + ], + "angle": 0, + "content": "- We propose to utilize the correspondence between encoded features and vertex positions, which are projected into the 2D space, via our point-guided feature sampling scheme. By explicitly indicating such vertex-relevant features to the transformer encoder, coordinates of the 3D human mesh are accurately estimated." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.753, + 0.47, + 0.799 + ], + "angle": 0, + "content": "- Our progressive attention masking scheme helps the model efficiently deal with local vertex-to-vertex relations even under complicated poses and occlusions." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.634, + 0.47, + 0.799 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.22, + 0.831 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this Section, we give a brief review of the previous studies for 3D human mesh construction which have progressed in two different directions: model-based and model-free approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.789 + ], + "angle": 0, + "content": "Model-based approaches. As mentioned, most model-based approaches aim to estimate shape and pose parameters of the SMPL model [24] for restoring the entire set of mesh vertices. In the beginning, several studies attempted to align 2D joint positions as well as body part segments, which are estimated by respective networks, with the ground truth projected from the 3D human mesh [3, 19]. However, these methods require additional steps to estimate shape and pose parameters of the SMPL model. To cope with this limitation, Kanazawa et al. [12] proposed to regress such parameters directly from a single RGB image without using intermediate results, i.e., 2D joints and body part segments. Specifically, they designed a simple convolutional encoder with the adversarial loss to make the reconstructed mesh result be realistic. Inspired by the great potential of this simple regression scheme, many researchers have introduced various encoder-decoder architectures to estimate shape and pose parameters. Kolotouros et al. [17] proposed to combine the end-to-end regression model with the optimization loop to strongly supervise the refinement process. Choutas et al. [9] attempted to directly regress body, face, and hands by exploiting the body-driven attention in the SMPL-X [29] format for generating the high-quality 3D human mesh. Biggs et al. [2] designed a multi-hypothesis neural network regressor based on the best-of-M loss, which makes the plausible human pose even under severely occluded environments. Zhang et al. [37] also focused on accurately restoring object-occluded human shape and pose by utilizing the partial UV map and the novel saliency map in the SMPL format. Most recently, Kocabas et al. [16] devised the part attention module to guide the network to concentrate more on relevant body parts for inferring the given pose with SMPL parameters in a single input RGB image. Sun et al. [32] estimated body center positions instead of segmenting human regions and extracted the parameter maps for the SMPL model at the corresponding positions. They further extend their algorithm by adopting the heat map of the bird-eye view to alleviate the depth ambiguity in monocular settings [33]. On the other hand, the kinematic topology module has been embedded into the neural network architecture to consider the relationship between articulations of the human body [20]. Even though model-based approaches have shown the remarkable progress in 3D human mesh reconstruction, their performance is limited to pre-defined types of human body models, which are hardly extended to other applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Model-free approaches. Model-free approaches intend to directly restore the entire set of mesh vertices while relaxing the heavy reliance on the parameter space in model-based methods. As a pioneer, Kolotouros et al. [18] proposed to estimate human mesh coordinates through the graph convolutional neural network (GraphCNN). To do this, they attached encoded features to nodes in the graph, which are" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12881" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.072, + 0.887, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. Overall architecture of the proposed method. The backbone feature is used to generate heatmap, target feature, and grid feature with respective decoders. Our sampling scheme utilizes heatmap and target feature to make the vertex token. Note that \\( N \\) and \\( M \\) denote the number of vertices and the distance threshold for defining the local connection in self-attention, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.473, + 0.672 + ], + "angle": 0, + "content": "mapped to 3D coordinates of the template mesh. From this perspective, Choi et al. [7] also adopted GraphCNN to reconstruct 3D human meshes from 2D and 3D pose information in a coarse-to-fine manner. While these GraphCNN-based methods have a good ability to fully exploit the mesh topology, they are somewhat lacking in considering global interactions between joints and vertices. To cope with this limitation, the transformer has begun to be actively adopted for model-free approaches. Specifically, Lin et al. [21] firstly introduced the transformer encoder, which simply takes joint and vertex queries as input tokens, to regress 3D coordinates from a single input RGB image. In particular, they further embedded GraphCNN into the transformer block to supplement local interactions, e.g., between-part relationships, for 3D human mesh reconstruction. Most recently, Cho et al. [6] have disentangled image features and mesh queries by utilizing the transformer encoder-decoder architecture to alleviate the high complexity of interactions among input tokens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.471, + 0.75 + ], + "angle": 0, + "content": "Our method is also based on the transformer encoder with a simple sampling scheme, which gives a great help to focus on vertex-relevant features for inferring coordinates of the 3D human mesh. Technical details will be explained in the following Section." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.768, + 0.251, + 0.786 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The proposed method consists of two main parts. Specifically, vertex-relevant features are extracted based on our point-guided feature sampling in the first part while 3D coordinates are estimated through the sequence of transformer encoders with the proposed progressive attention masking scheme in the second part. The overall architecture of the proposed method is illustrated in Fig. 2." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.383, + 0.63, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.383, + 0.761, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.383, + 0.892, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.489, + 0.892, + 0.547 + ], + "angle": 0, + "content": "Figure 3. Several examples of predicted heatmaps on the 3DPW dataset. For better visibility, the activated regions of the heatmap corresponding to several selected vertices are represented in a single image with bright colors (best view in colors)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.779, + 0.579 + ], + "angle": 0, + "content": "3.1. Point-guided Feature Sampling" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Since the direct transform from the color value to the 3D coordinate is still a difficult process due to heterogeneous modalities, we propose to use the intermediate guidance, i.e., features sampled at positions of vertices projected from 3D to 2D spaces. Specifically, we represent such projection results as the form of the heatmap, and sample features at activated positions in this heatmap. The detailed process of our point-guided feature sampling is shown in the first part of Fig. 2. Firstly, the backbone feature \\(X_{b}\\in \\mathbb{R}^{C\\times H\\times W}\\) is encoded through the backbone network (HRNet [35] in this work), where \\(C\\), \\(H\\), and \\(W\\) denote the number of channels, height, and width, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\(X_{b}\\) is subsequently decoded into the heatmap, the target feature, and the grid feature by respective decoders as shown in Fig. 2. After that, the vertex-relevant feature is sampled at each of \\(N\\) vertices based on combination of the predicted heatmap and the target feature. Several examples of the predicted heatmap are shown in Fig. 3. Note that we conducted element-wise multiplication of the predicted heatmap and the target feature to make our sampling process be differentiable. Moreover, we apply the positional" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12882" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.079, + 0.47, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.47, + 0.271 + ], + "angle": 0, + "content": "Figure 4. The detailed structure of the proposed progressive attention masking scheme. Note that this figure illustrates the masking process in the first transformer encoder, i.e., the case of \\( M = 7 \\), shown in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.29, + 0.469, + 0.351 + ], + "angle": 0, + "content": "encoding to the target feature in the same way of [5, 6] for preserving the spatial information in the transformer encoder. Our point-guided feature sampling can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.359, + 0.469, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\hat {V} _ {i} = H _ {i} \\times F, \\quad i = 1, 2, 3, \\dots , N, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.469, + 0.522 + ], + "angle": 0, + "content": "where \\( H_{i} \\) and \\( F \\) denote the predicted heatmap corresponding to the \\( i \\)-th vertex and the target feature, respectively. \\( N \\) denotes the total number of vertices and is set to 431 as used in previous methods. \\( \\hat{V}_{i} \\) is the sampling result, which is finally flattened and fed into the transformer encoder with the grid feature in the second part of our proposed method. It is noteworthy that the grid feature plays an important role to create the united body structure by aligning each point in an appropriate location." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.469, + 0.563 + ], + "angle": 0, + "content": "3.2. Transformer Encoder with Progressive Attention Masking" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this subsection, we explain the sequence of transformer encoders in detail. In a similar way of [21, 22], we design the transformer encoder with the dimension reduction layer as shown in the second part of Fig. 2. Specifically, the transformer encoder takes the vertex token \\(\\hat{V} \\in \\mathbb{R}^{N \\times D}\\), the joint token \\(\\hat{J} \\in \\mathbb{R}^{K \\times D}\\), and the grid token \\(\\hat{G} \\in \\mathbb{R}^{Z \\times D}\\) as inputs. The joint token is a trainable parameter that is randomly initialized and optimized during the training phase whereas vertex and grid tokens are extracted from the first part of the proposed method. Moreover, positional encodings are employed to give the identity by concatenating the trainable parameter to each token. The dimension of the encoded token is reduced by linear projection after each transformer block, which consists of two transformer encoders. To consider local vertex-vertex relations as well as non-adjacent interactions, we exclude far-distant connections between vertices to compute self-attention in the transformer encoder. In contrast to the previous method [6], we gradually decrease the range to define the local connection between vertices through the sequence of transformer encoders as illustrated in Fig. 4. This helps the model consider the local relationship between neighbor vertices in a" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.63, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.192, + 0.575, + 0.204 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.634, + 0.089, + 0.761, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.691, + 0.192, + 0.708, + 0.204 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.765, + 0.089, + 0.891, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.192, + 0.836, + 0.204 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.213, + 0.892, + 0.256 + ], + "angle": 0, + "content": "Figure 5. (a) Input image. (b) Reconstruction result with previous attention masking [6]. (c) Reconstruction result with progressive attention masking (proposed)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.32 + ], + "angle": 0, + "content": "progressive manner. Figure 5 shows the effect of our progressive attention masking. As can be seen, the proposed method provides the reasonable result even in occlusions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.41 + ], + "angle": 0, + "content": "The outputs (i.e., vertex and joint tokens) of the last transformer encoder are finally projected into 3D coordinates via a linear layer. In the case of the vertex token, the upsampling algorithm introduced in [31] is applied to expand sparse vertices \\( V' \\in \\mathbb{R}^{N \\times 3} \\) into dense vertices \\( V \\in \\mathbb{R}^{\\mathcal{N} \\times 3} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.658, + 0.419, + 0.891, + 0.435 + ], + "angle": 0, + "content": "\\[\nV = U V ^ {\\prime}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.443, + 0.892, + 0.504 + ], + "angle": 0, + "content": "where \\(U\\) is the pre-defined upsampling matrix [31]. \\(\\mathcal{N}\\) is set to 6,890 (same as the vertex number of the SMPL model). The predicted 3D human mesh and 3D keypoints can be visualized as the rightmost images shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.511, + 0.644, + 0.525 + ], + "angle": 0, + "content": "3.3. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.671 + ], + "angle": 0, + "content": "The proposed method is trained based on four types of loss functions, i.e., vertex loss \\(\\mathcal{L}_v\\), 3D joint loss \\(\\mathcal{L}_{j3d}\\), 2D joint loss \\(\\mathcal{L}_{j2d}\\), and heatmap loss \\(\\mathcal{L}_h\\). The first three loss functions are used for estimating positions of vertices and joints as introduced in previous works [6,21,22] while the last one guides the network to find positions of projected vertices. First of all, \\(L_{1}\\) loss is adopted to compute the difference between positions of the predicted vertex \\(V\\) and the corresponding ground truth \\(\\tilde{V}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.678, + 0.891, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\tilde {V} ^ {i} - V ^ {i} \\| _ {1}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.725, + 0.892, + 0.816 + ], + "angle": 0, + "content": "where \\(N\\) denotes the total number of vertices. For the 3D joint loss, we compute the distance between the estimated joint position \\(J_{3d}\\) and the corresponding ground truth \\(\\bar{J}_{3d}\\) in the 3D space. Note that the joint position, which is regressed from the predicted vertices, i.e., \\(\\bar{J}_{3d}\\), is also used for the loss computation as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.823, + 0.891, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {j 3 d} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {J} _ {3 d} ^ {i} - J _ {3 d} ^ {i} \\| _ {2} + \\| \\tilde {J} _ {3 d} ^ {i} - \\bar {J} _ {3 d} ^ {i} \\| _ {2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(K\\) denotes the total number of joints. Similarly, the 2D joint loss is calculated as well. To do this, \\(J_{3d}\\) and \\(\\bar{J}_{3d}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12883" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.41 + ], + "angle": 0, + "content": "
MethodsBackboneHuman3.6M3DPW
MPJPE(↓)PA-MPJPE(↓)MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
model-basedHMR [12]ResNet-5088.056.8130.081.3-
SPIN [17]ResNet-50-41.196.959.2116.4
ExPose [9]ResNet-50--93.455.6-
VIBE [15]ResNet-5065.641.482.951.999.1
HybrIK [20]ResNet-3454.434.580.048.894.5
ROMP [32]HRNet-W32--76.747.393.4
PARE [16]HRNet-W32--74.546.588.6
MAED [40]ResNet-5056.438.779.145.792.6
PyMAF [36]ResNet-5057.740.592.858.9110.1
BEV* [33]HRNet-W32--78.546.992.3
OCHMR* [13]ResNet-50 / HRNet-W32--89.758.3107.1
3DCrowdNet* [8]ResNet-50--81.751.598.3
model-freeGraphCMR [18]ResNet-50-50.1-70.2-
I2LMeshNet [27]ResNet-5055.741.793.257.7110.1
Pose2Mesh [7]HRNet-W4864.947.089.556.3105.3
METRO [21]HRNet-W6454.036.777.147.988.2
MeshGraphormer [22]HRNet-W6451.234.574.745.687.7
FastMETRO [6]HRNet-W6452.233.773.544.684.1
OursHRNet-W3248.332.973.944.985.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.421, + 0.893, + 0.464 + ], + "angle": 0, + "content": "Table 1. Performance comparisons of 3D human mesh reconstruction based on Human3.6M and 3DPW datasets. The proposed method achieves the best performance in the Human3.6M dataset while still showing the competitive performance in the 3DPW dataset (best results are shown in bold). Note that * denotes the performance without fine-tuning on the 3DPW dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.552 + ], + "angle": 0, + "content": "are projected onto the 2D space and the corresponding results are represented as \\( J_{2d} \\) and \\( \\bar{J}_{2d} \\), respectively. Based on such projected results, the 2D joint loss is formulated as \\( L_{2} \\) loss in the same way of the 3D joint loss as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.556, + 0.469, + 0.597 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {j 2 d} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {J} _ {2 d} ^ {i} - J _ {2 d} ^ {i} \\| _ {2} + \\| \\tilde {J} _ {2 d} ^ {i} - \\bar {J} _ {2 d} ^ {i} \\| _ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.47, + 0.697 + ], + "angle": 0, + "content": "where \\(\\tilde{J}_{2d}\\) is the ground truth of the 2D joint position. On the other hand, our heatmap loss \\(\\mathcal{L}_h\\) consists of the binary cross entropy loss and the dice loss. Specifically, we adopt the binary cross entropy loss to determine whether the activated position is matched to the point projected from the vertex or not as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.701, + 0.469, + 0.742 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b c e} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tilde {H} ^ {i} \\log H ^ {i} + (1 - \\tilde {H} ^ {i}) \\log (1 - H ^ {i}), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.858 + ], + "angle": 0, + "content": "where \\( H \\) and \\( \\tilde{H} \\) denote the predicted heatmap and the corresponding ground truth, respectively. The ground truth is represented as the binary map where the position of the projected vertex is assigned 1, otherwise 0. To alleviate the data-imbalanced problem, i.e., the projected point exists on only a single pixel in the ground truth image, the dice loss [26] is also employed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.863, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i c e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} 1 - \\frac {2 \\times \\left(\\tilde {H} ^ {i} \\times H ^ {i}\\right)}{\\tilde {H} ^ {i} + H ^ {i}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Since the dice loss mainly focuses on the overlapped area, the data-imbalanced problem can be efficiently alleviated. By using the combination of these loss functions, the proposed network successfully learns to reconstruct the 3D human mesh as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.576, + 0.891, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} \\mathcal {L} _ {\\text {t o t a l}} & = w _ {v} \\mathcal {L} _ {v} + w _ {j 3 d} \\mathcal {L} _ {j 3 d} + w _ {j 2 d} \\mathcal {L} _ {j 2 d} \\\\ & + w _ {b c e} \\mathcal {L} _ {b c e} + w _ {d i c e} \\mathcal {L} _ {d i c e}, \\end{array} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.624, + 0.894, + 0.67 + ], + "angle": 0, + "content": "where \\( w_v, w_{j3d}, w_{j2d}, w_{bce} \\) and \\( w_{dice} \\) are the balancing factor for each loss term, which are set to 0.01, 0.1, 0.01, 1.0, and 0.001, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.685, + 0.707, + 0.703 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.606, + 0.728 + ], + "angle": 0, + "content": "4.1. Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.903 + ], + "angle": 0, + "content": "All the experiments are implemented on the PyTorch framework [28] with an Intel E5-1650@3.60GHz CPU and two NVIDIA RTX A6000 GPUs. To train all the parameters of our model, the Adam optimizer [14] is adopted where the momentum factors are set to 0.9 and 0.999, respectively. The proposed network is trained for 50 epochs with a batch size of 64 per GPU. The learning rate is firstly set to \\(1 \\times 10^{-4}\\) and reduced to \\(1 \\times 10^{-5}\\) at the half of the learning time. For each input image, the area including the human is cropped and resized to the resolution of \\(224 \\times 224\\) pixels before training." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12884" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.075, + 0.484, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.075, + 0.892, + 0.416 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.432, + 0.893, + 0.461 + ], + "angle": 0, + "content": "Figure 6. Results of 3D human mesh reconstruction on Human3.6M [11] (top-two rows) and 3DPW [34] (bottom-two rows) datasets. (a) Input images. (b) Results by METRO [21]. (c) Results by Mesh Graphormer [22]. (d) Results by the proposed method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.486, + 0.364, + 0.5 + ], + "angle": 0, + "content": "4.2. Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Datasets. For the performance evaluation of the proposed method, two representative benchmarks, i.e., Human3.6M [11] and 3DPW [34], are employed. Specifically, the proposed method is trained based on five datasets, i.e., Human3.6M [11], MuCo-3DHP [25], UP-3D [19], COCO [23], and MPII [1], by following previous approaches, and tested with the P2 protocol in the Human3.6M dataset. Since the ground truth of the 3D human mesh is unavailable in the Human3.6M dataset, we use the pseudo mesh label generated by SMPLify-X [29] as introduced in [6,7,21,22,27]. For the test on the 3DPW dataset, we fine-tune the proposed method by using the training set of the 3DPW dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Evaluation metrics. For the quantitative evaluation, we use three metrics, i.e., mean per joint position error (MPJPE) [11], Procrustes-aligned mean per joint position error (PA-MPJPE) [38], and mean per vertex position error (MPVPE) [30], which have been widely adopted for the performance comparison in this field. Specifically, MPJPE measures the average value of the Euclidean distance between each estimated 3D joint and the corresponding ground truth. PA-MPJPE indicates MPJPE in which the estimated human body is aligned in terms of rotation and scaling using the Procrustes analysis. On the other hand, MPVPE is a metric for computing the Euclidean distance" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.486, + 0.892, + 0.517 + ], + "angle": 0, + "content": "between coordinates of the predicted vertex and the corresponding ground truth." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.529, + 0.724, + 0.544 + ], + "angle": 0, + "content": "4.3. Performance Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Quantitative evaluation. To demonstrate the efficiency and robustness of the proposed method, we compare ours with representative methods for 3D human mesh reconstruction, i.e., HMR [12], SPIN [17], ExPose [9], VIBE [15], HybrIK [20], ROMP [32], PARE [16], MAED [40], PyMAF [36], BEV [33], OCHMR [13], 3DCrowdNet [8], GraphCMR [18], I2LMeshNet [27], Pose2Mesh [7], METRO [21], Mesh Graphormer [22], and FastMETRO [6]. The result of the performance comparison is shown in Table 1. As can be seen, the proposed method achieves 48.3 MPJPE and 32.9 PA-MPJPE on the Human3.6M dataset, which outperforms the state-of-the-art methods with the meaningful performance gain. Even though the performance of the proposed method is slightly dropped compared to the best one (i.e., FastMETRO) in the 3DPW dataset, our method still shows the competitive performance with state-of-the-art methods. Specifically, model-free methods have shown the reliable performance without using the well-defined human model in recent days. This is because their reconstruction results are not limited to the small set of pre-defined human models, thus show more appropriate human meshes for a given image compared to model-based methods. In particular, transformer-based ar" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12885" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.075, + 0.348, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.075, + 0.621, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.075, + 0.892, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.893, + 0.34 + ], + "angle": 0, + "content": "Figure 7. More results of 3D human mesh reconstruction for our samples, which are acquired by the smartphone. Odd columns: input images. Even columns: our results. Note that the proposed method provides reliable results of 3D human mesh reconstruction for various pictures of our daily life even with severe occlusions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.533 + ], + "angle": 0, + "content": "chitectures, e.g., Mesh Graphomer and FastMETRO, significantly improves the performance of 3D human mesh reconstruction. Nevertheless, recent model-based methods still show the competitive performance and work robust to occlusion cases, e.g., BEV, OCHMR, and 3DCrowdNet. It is noteworthy that the proposed method notably improves the performance by our point-guided feature sampling scheme without specially designing the decoder architecture like [6]. Moreover, the proposed method provides the reliable performance with the relatively small-sized backbone (e.g., HRNet-W32)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Qualitative evaluation. Several results of 3D human mesh reconstructions for Human3.6M and 3DPW datasets are shown in Fig. 6. Note that our results are reconstructed based on the upsampling matrix as used in [6] while other two methods, i.e., METRO [21] and Mesh Graphomer [22], utilized two linear layers to upsample coarse vertex points. We can see that the proposed method successfully estimates 3D human poses under various situations including real-world scenarios in outdoor scenes as well as the controlled environment. Specifically, previous methods have somewhat difficulties to estimate unusual poses, e.g., overlapping arms and bending, whereas the proposed method provides the well-fit 3D model for a given image. Moreover, the proposed method has a good ability to reconstruct 3D human meshes in occlusions due to the progressive attention masking scheme as shown in examples of the last row of Fig. 6. In particular, previous methods fail to infer the global orientation of the human body due to the fence in front of the target person, which leads to the significant performance drop for 3D human mesh reconstruction. In contrast, the proposed method shows the reliable performance with various occlusions (see third and fourth rows in Fig. 6). More examples for 3D human mesh reconstruction by the proposed method are shown in Fig. 7. Note that in" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.364, + 0.897, + 0.455 + ], + "angle": 0, + "content": "
Point-guided feature samplingProgressive attention maskingMPJPEPA-MPJPE
XX63.239.9
X✓61.240.8
✓X50.933.3
✓✓48.332.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.464, + 0.893, + 0.507 + ], + "angle": 0, + "content": "Table 2. Performance analysis of the proposed method according to changes in the network architecture based on the Human3.6M dataset (best results are shown in bold)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.542, + 0.892, + 0.605 + ], + "angle": 0, + "content": "
MethodsMPJPEPA-MPJPE
Without attention masking50.933.3
Single attention masking49.133.5
Progressive attention masking (ours)48.332.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.615, + 0.892, + 0.672 + ], + "angle": 0, + "content": "Table 3. Performance analysis of the proposed method according to the attention masking scheme based on the Human3.6M dataset (best results are shown in bold). Note that \\( M = 1 \\) is used for single attention masking." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.789 + ], + "angle": 0, + "content": "put images are acquired by the smartphone. As can be seen, the proposed method performs well for various pictures of our daily life even with severe occlusions. Therefore, it is thought that the proposed method paves the way for 3D human mesh reconstruction under various environments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.665, + 0.816 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this subsection, we first demonstrate the comparative experimental results by changing the components of the proposed method based on the Human3.6M dataset. Table 2 shows the contribution of such components. As can be seen, the performance of 3D human mesh reconstruc" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12886" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.075, + 0.348, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.075, + 0.621, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.075, + 0.892, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.295, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Figure 8. Several reconstruction results (3D joints (left) and 3D hand meshes (right)) by the proposed method for the FreiHAND [39] dataset. Note that the proposed method works robust to self-occlusions frequently occurring by complicated hand poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.473, + 0.592 + ], + "angle": 0, + "content": "tion is significantly improved with our point-guided feature sampling scheme (MPJPE: \\(63.2 \\rightarrow 50.9\\), PA-MPJPE: \\(39.9 \\rightarrow 33.3\\)). From this analysis, we can see that feature sampling at vertex-relevant positions even in the 2D space is effective for improving the performance of 3D human mesh reconstruction. In what follows, we also check the effect of our progressive attention masking and the corresponding result is shown in Table 3. Note that our point-guided feature sampling is applied for this experiment. By comparing ours with baseline (i.e., without masking) and single masking attention scheme [6], we can see that the progressive restriction strategy in defining the local connection is also helpful for improving the performance of 3D human mesh reconstruction. This tells us that the combination of our contributions makes the model be robust to complicated real-world environments." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.285, + 0.621 + ], + "angle": 0, + "content": "4.5. Generalization Ability" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.901 + ], + "angle": 0, + "content": "In contrast to the model-based approach, the proposed method can be easily applied to other applications. To show the generalization ability of the proposed method, we conduct 3D hand mesh reconstruction based on the FreiHAND [39] dataset by changing the number of input tokens for the sequence of transformer encoders. Note that the number of vertices to be projected is set to 195 and those are upsampled to 778 via the same upsampling matrix used for 3D human mesh reconstruction. Several reconstruction results by the proposed method are shown in Fig. 8. We can see that the proposed method provides the reliable reconstruction results (i.e., 3D joints and 3D hand meshes) for various hand poses. In particular, self-occlusions by complicated relations between adjacent fingers are successfully handled in the proposed method. The result of the quantitative evaluation is also shown in Table 4. As can be seen, the proposed method shows the competitive performance on the FreiHAND dataset." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.348, + 0.897, + 0.464 + ], + "angle": 0, + "content": "
MethodsPA-MPVPEPA-MPJPEF@5mmF@15mm
Hasson et al. [10]13.2-0.4360.908
Boukhayma et al. [4]13.0-0.4350.898
FreiHAND [39]10.7-0.5290.935
I2LMeshNet [27]7.67.40.6810.973
Pose2Mesh [7]7.87.70.6740.969
METRO [21]6.76.80.7170.981
FastMETRO [6]-6.5-0.982
Ours6.66.10.7200.984
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.474, + 0.893, + 0.515 + ], + "angle": 0, + "content": "Table 4. Performance comparisons of 3D hand mesh reconstruction based on the FreiHAND dataset (best results are shown in bold)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.618, + 0.555 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.892, + 0.793 + ], + "angle": 0, + "content": "In this paper, we present a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. The key idea of the proposed method is to alleviate heterogeneous modalities between input (i.e., color) and output (i.e., coordinate) by considering the correspondence of encoded features and 2D points projected from 3D vertices. Our point-guided feature sampling scheme is to sample vertex-relevant features based on the combination of the heatmap and encoded features. In addition, the proposed progressive attention masking scheme makes the model to be robust to occlusions by considering local connections of different levels through the sequence of transformer encoders. Experimental results on benchmark datasets show that the proposed method performs reliably for various real-world environments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (2021-0-02084, eXtended Reality and Volumetric media generation and transmission technology for immersive experience sharing in noncontact environment with a Korea-EU international cooperative research)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12887" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. In IEEE Conf. Comput. Vis. 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Encoder-decoder with multi-level attention for" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.536, + 0.092, + 0.892, + 0.12 + ], + "angle": 0, + "content": "3D human shape and pose estimation. In Int. Conf. Comput. 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Most recently, the non-local interactions of the whole mesh vertices have been effectively estimated in the transformer while the relationship between body parts also has begun to be handled via the graph model. Even though those approaches have shown the remarkable progress in 3D human mesh reconstruction, it is still difficult to directly infer the relationship between features, which are encoded from the 2D input image, and 3D coordinates of each vertex. To resolve this problem, we propose to design a simple feature sampling scheme. The key idea is to sample features in the embedded space by following the guide of points, which are estimated as projection results of 3D mesh vertices (i.e., ground truth). This helps the model to concentrate more on vertex-relevant features in the 2D space, thus leading to the reconstruction of the natural human pose. Furthermore, we apply progressive attention masking to precisely estimate local interactions between vertices even under severe occlusions. Experimental results on benchmark datasets show that the proposed method efficiently improves the performance of 3D human mesh reconstruction. The code and model are publicly available at: https://github.com/DCVL-3D/PointHMR_release. + +# 1. Introduction + +The goal of 3D human mesh reconstruction is to estimate 3D coordinates of points, which make up the human body surface. Since the high-quality 3D human model has been consistently required for various immersive applications, many studies have devoted considerable efforts to accurately reconstruct the 3D human mesh. In the early stage of this field, complex optimization techniques were + +![](images/a07e559d14d39b58bac16c57711dd541048e69882b1fb37ac61bb775936062ae.jpg) +(a) + +![](images/9db56032bf13deccc60921e11fd879b95f1d76c8062bacd426daba3146cf8af5.jpg) +(b) +Figure 1. (a) Traditional process of feature extraction for estimating 3D coordinates. (b) Vertex-relevant feature extraction process based on the proposed point-guided sampling method for estimating 3D coordinates. + +adopted to generate the 3D human model based on the relationship between multiple scenes, which are acquired by using stereo or multiple-view camera systems. Recently, owing to the great success of deep learning, the problem of 3D human mesh reconstruction now can be resolved only with a single RGB image, thus the majority has begun to develop compact network architectures and efficient training strategies. Even though such deep learning-based approaches have shown the significant progress in 3D human mesh reconstruction, this task is still challenging due to severe occlusions by diverse human poses and depth ambiguities by the monocular setting. + +Deep learning-based approaches can be divided into two main groups: model-based and model-free methods. In the former, most methods aim to estimate shape and pose parameters of the skinned multi-person linear (SMPL) model [24], which is capable of yielding the whole vertices via these two simple factors, thus most widely employed in this field. Traditional encoder-decoder architectures, which are mostly composed of stacked convolutional layers, are sufficient to conduct the regression for estimating those parameters. Despite their great performance, model-based + +methods have the obvious shortcoming, i.e., reconstruction results are limited to the pre-defined types of human body models. On the other hand, model-free methods have attempted to directly infer 3D coordinates of mesh vertices from input features without using any specific human body model. Compared to the model-based approach, which obtains the well-defined full mesh by adjusting shape and pose parameters, the model-free approach needs to estimate 3D coordinates of whole vertices directly from the network. Most methods in this category are based on the transformer to grasp non-local interactions between mesh vertices. The graph model (e.g., graph convolution) also has been utilized together to allow for body part relations in a local manner. One important advantage of the model-free approach is the flexibility to adapt to other applications, e.g., hand pose estimation, without significant changes of the data format and the training strategy. However, inferring the 3D coordinate from a single monocular image is still challenging due to lack of learning the correspondence between encoded features and spatial positions. + +In this paper, we propose a simple yet powerful method for 3D human mesh reconstruction. To this end, we conduct feature sampling at vertex-relevant points of the input image as shown in Fig. 1, which are estimated through the heatmap decoder trained by projection results of 3D mesh vertices (i.e., ground truth). These sampled features are subsequently fed into the transformer encoder as the form of the vertex token (see Fig. 2). In a similar way of [6], we apply attention masking to the transformer encoder, however, the difference is that the local connection is defined with the range of multiple levels through the sequence of transformer encoders. This progressive attention masking helps the model understand local relations between vertices precisely even in occlusions. The main contribution of the proposed method can be summarized as follows: + +- We propose to utilize the correspondence between encoded features and vertex positions, which are projected into the 2D space, via our point-guided feature sampling scheme. By explicitly indicating such vertex-relevant features to the transformer encoder, coordinates of the 3D human mesh are accurately estimated. +- Our progressive attention masking scheme helps the model efficiently deal with local vertex-to-vertex relations even under complicated poses and occlusions. + +# 2. Related Work + +In this Section, we give a brief review of the previous studies for 3D human mesh construction which have progressed in two different directions: model-based and model-free approaches. + +Model-based approaches. As mentioned, most model-based approaches aim to estimate shape and pose parameters of the SMPL model [24] for restoring the entire set of mesh vertices. In the beginning, several studies attempted to align 2D joint positions as well as body part segments, which are estimated by respective networks, with the ground truth projected from the 3D human mesh [3, 19]. However, these methods require additional steps to estimate shape and pose parameters of the SMPL model. To cope with this limitation, Kanazawa et al. [12] proposed to regress such parameters directly from a single RGB image without using intermediate results, i.e., 2D joints and body part segments. Specifically, they designed a simple convolutional encoder with the adversarial loss to make the reconstructed mesh result be realistic. Inspired by the great potential of this simple regression scheme, many researchers have introduced various encoder-decoder architectures to estimate shape and pose parameters. Kolotouros et al. [17] proposed to combine the end-to-end regression model with the optimization loop to strongly supervise the refinement process. Choutas et al. [9] attempted to directly regress body, face, and hands by exploiting the body-driven attention in the SMPL-X [29] format for generating the high-quality 3D human mesh. Biggs et al. [2] designed a multi-hypothesis neural network regressor based on the best-of-M loss, which makes the plausible human pose even under severely occluded environments. Zhang et al. [37] also focused on accurately restoring object-occluded human shape and pose by utilizing the partial UV map and the novel saliency map in the SMPL format. Most recently, Kocabas et al. [16] devised the part attention module to guide the network to concentrate more on relevant body parts for inferring the given pose with SMPL parameters in a single input RGB image. Sun et al. [32] estimated body center positions instead of segmenting human regions and extracted the parameter maps for the SMPL model at the corresponding positions. They further extend their algorithm by adopting the heat map of the bird-eye view to alleviate the depth ambiguity in monocular settings [33]. On the other hand, the kinematic topology module has been embedded into the neural network architecture to consider the relationship between articulations of the human body [20]. Even though model-based approaches have shown the remarkable progress in 3D human mesh reconstruction, their performance is limited to pre-defined types of human body models, which are hardly extended to other applications. + +Model-free approaches. Model-free approaches intend to directly restore the entire set of mesh vertices while relaxing the heavy reliance on the parameter space in model-based methods. As a pioneer, Kolotouros et al. [18] proposed to estimate human mesh coordinates through the graph convolutional neural network (GraphCNN). To do this, they attached encoded features to nodes in the graph, which are + +![](images/29a0e4e7dc6f94b9078071707a90335fc0fb6d3e78bb95d2c6b80c15d5532b20.jpg) +Figure 2. Overall architecture of the proposed method. The backbone feature is used to generate heatmap, target feature, and grid feature with respective decoders. Our sampling scheme utilizes heatmap and target feature to make the vertex token. Note that $N$ and $M$ denote the number of vertices and the distance threshold for defining the local connection in self-attention, respectively. + +mapped to 3D coordinates of the template mesh. From this perspective, Choi et al. [7] also adopted GraphCNN to reconstruct 3D human meshes from 2D and 3D pose information in a coarse-to-fine manner. While these GraphCNN-based methods have a good ability to fully exploit the mesh topology, they are somewhat lacking in considering global interactions between joints and vertices. To cope with this limitation, the transformer has begun to be actively adopted for model-free approaches. Specifically, Lin et al. [21] firstly introduced the transformer encoder, which simply takes joint and vertex queries as input tokens, to regress 3D coordinates from a single input RGB image. In particular, they further embedded GraphCNN into the transformer block to supplement local interactions, e.g., between-part relationships, for 3D human mesh reconstruction. Most recently, Cho et al. [6] have disentangled image features and mesh queries by utilizing the transformer encoder-decoder architecture to alleviate the high complexity of interactions among input tokens. + +Our method is also based on the transformer encoder with a simple sampling scheme, which gives a great help to focus on vertex-relevant features for inferring coordinates of the 3D human mesh. Technical details will be explained in the following Section. + +# 3. Proposed Method + +The proposed method consists of two main parts. Specifically, vertex-relevant features are extracted based on our point-guided feature sampling in the first part while 3D coordinates are estimated through the sequence of transformer encoders with the proposed progressive attention masking scheme in the second part. The overall architecture of the proposed method is illustrated in Fig. 2. + +![](images/3dc4d150e9a1f768c5c68033705028cbb23b71d055bb2e2f4275cbb5a26c4c04.jpg) +Figure 3. Several examples of predicted heatmaps on the 3DPW dataset. For better visibility, the activated regions of the heatmap corresponding to several selected vertices are represented in a single image with bright colors (best view in colors). + +![](images/8a9500a8768abef880e6b4da9cf08904fa98504a1de14e663870bd0ed0ea9983.jpg) + +![](images/e850c2b5fd5092905b33a9c1fdbaddb2c87fc68b16f14195e4e7ff6024924608.jpg) + +# 3.1. Point-guided Feature Sampling + +Since the direct transform from the color value to the 3D coordinate is still a difficult process due to heterogeneous modalities, we propose to use the intermediate guidance, i.e., features sampled at positions of vertices projected from 3D to 2D spaces. Specifically, we represent such projection results as the form of the heatmap, and sample features at activated positions in this heatmap. The detailed process of our point-guided feature sampling is shown in the first part of Fig. 2. Firstly, the backbone feature $X_{b}\in \mathbb{R}^{C\times H\times W}$ is encoded through the backbone network (HRNet [35] in this work), where $C$ , $H$ , and $W$ denote the number of channels, height, and width, respectively. + +$X_{b}$ is subsequently decoded into the heatmap, the target feature, and the grid feature by respective decoders as shown in Fig. 2. After that, the vertex-relevant feature is sampled at each of $N$ vertices based on combination of the predicted heatmap and the target feature. Several examples of the predicted heatmap are shown in Fig. 3. Note that we conducted element-wise multiplication of the predicted heatmap and the target feature to make our sampling process be differentiable. Moreover, we apply the positional + +![](images/f2ad6b6da73f88c46eaf68e1b3051e3b0ad9ae9389b86c8628cf3c52815fe4f1.jpg) +Figure 4. The detailed structure of the proposed progressive attention masking scheme. Note that this figure illustrates the masking process in the first transformer encoder, i.e., the case of $M = 7$ , shown in Fig. 2. + +encoding to the target feature in the same way of [5, 6] for preserving the spatial information in the transformer encoder. Our point-guided feature sampling can be formulated as follows: + +$$ +\hat {V} _ {i} = H _ {i} \times F, \quad i = 1, 2, 3, \dots , N, \tag {1} +$$ + +where $H_{i}$ and $F$ denote the predicted heatmap corresponding to the $i$ -th vertex and the target feature, respectively. $N$ denotes the total number of vertices and is set to 431 as used in previous methods. $\hat{V}_{i}$ is the sampling result, which is finally flattened and fed into the transformer encoder with the grid feature in the second part of our proposed method. It is noteworthy that the grid feature plays an important role to create the united body structure by aligning each point in an appropriate location. + +# 3.2. Transformer Encoder with Progressive Attention Masking + +In this subsection, we explain the sequence of transformer encoders in detail. In a similar way of [21, 22], we design the transformer encoder with the dimension reduction layer as shown in the second part of Fig. 2. Specifically, the transformer encoder takes the vertex token $\hat{V} \in \mathbb{R}^{N \times D}$ , the joint token $\hat{J} \in \mathbb{R}^{K \times D}$ , and the grid token $\hat{G} \in \mathbb{R}^{Z \times D}$ as inputs. The joint token is a trainable parameter that is randomly initialized and optimized during the training phase whereas vertex and grid tokens are extracted from the first part of the proposed method. Moreover, positional encodings are employed to give the identity by concatenating the trainable parameter to each token. The dimension of the encoded token is reduced by linear projection after each transformer block, which consists of two transformer encoders. To consider local vertex-vertex relations as well as non-adjacent interactions, we exclude far-distant connections between vertices to compute self-attention in the transformer encoder. In contrast to the previous method [6], we gradually decrease the range to define the local connection between vertices through the sequence of transformer encoders as illustrated in Fig. 4. This helps the model consider the local relationship between neighbor vertices in a + +![](images/96521333a3a1cfdfe52f8b372d02f9c4e91d2e3aada1d96edbe4a495a9764a4e.jpg) +(a) + +![](images/2717359c138593e978b36dbeecc95d136b7b795a9d9c26571b48fb774337a829.jpg) +(b) + +![](images/66b0b382ea207b510a19cd97448ecfca06dbcd748eba6ff7f576fafe23a2edc4.jpg) +(c) +Figure 5. (a) Input image. (b) Reconstruction result with previous attention masking [6]. (c) Reconstruction result with progressive attention masking (proposed). + +progressive manner. Figure 5 shows the effect of our progressive attention masking. As can be seen, the proposed method provides the reasonable result even in occlusions. + +The outputs (i.e., vertex and joint tokens) of the last transformer encoder are finally projected into 3D coordinates via a linear layer. In the case of the vertex token, the upsampling algorithm introduced in [31] is applied to expand sparse vertices $V' \in \mathbb{R}^{N \times 3}$ into dense vertices $V \in \mathbb{R}^{\mathcal{N} \times 3}$ as follows: + +$$ +V = U V ^ {\prime}, \tag {2} +$$ + +where $U$ is the pre-defined upsampling matrix [31]. $\mathcal{N}$ is set to 6,890 (same as the vertex number of the SMPL model). The predicted 3D human mesh and 3D keypoints can be visualized as the rightmost images shown in Fig. 2. + +# 3.3. Loss Function + +The proposed method is trained based on four types of loss functions, i.e., vertex loss $\mathcal{L}_v$ , 3D joint loss $\mathcal{L}_{j3d}$ , 2D joint loss $\mathcal{L}_{j2d}$ , and heatmap loss $\mathcal{L}_h$ . The first three loss functions are used for estimating positions of vertices and joints as introduced in previous works [6,21,22] while the last one guides the network to find positions of projected vertices. First of all, $L_{1}$ loss is adopted to compute the difference between positions of the predicted vertex $V$ and the corresponding ground truth $\tilde{V}$ as follows: + +$$ +\mathcal {L} _ {v} = \frac {1}{N} \sum_ {i = 1} ^ {N} \| \tilde {V} ^ {i} - V ^ {i} \| _ {1}, \tag {3} +$$ + +where $N$ denotes the total number of vertices. For the 3D joint loss, we compute the distance between the estimated joint position $J_{3d}$ and the corresponding ground truth $\bar{J}_{3d}$ in the 3D space. Note that the joint position, which is regressed from the predicted vertices, i.e., $\bar{J}_{3d}$ , is also used for the loss computation as follows: + +$$ +\mathcal {L} _ {j 3 d} = \frac {1}{K} \sum_ {i = 1} ^ {K} \| \tilde {J} _ {3 d} ^ {i} - J _ {3 d} ^ {i} \| _ {2} + \| \tilde {J} _ {3 d} ^ {i} - \bar {J} _ {3 d} ^ {i} \| _ {2}, \tag {4} +$$ + +where $K$ denotes the total number of joints. Similarly, the 2D joint loss is calculated as well. To do this, $J_{3d}$ and $\bar{J}_{3d}$ + +
MethodsBackboneHuman3.6M3DPW
MPJPE(↓)PA-MPJPE(↓)MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
model-basedHMR [12]ResNet-5088.056.8130.081.3-
SPIN [17]ResNet-50-41.196.959.2116.4
ExPose [9]ResNet-50--93.455.6-
VIBE [15]ResNet-5065.641.482.951.999.1
HybrIK [20]ResNet-3454.434.580.048.894.5
ROMP [32]HRNet-W32--76.747.393.4
PARE [16]HRNet-W32--74.546.588.6
MAED [40]ResNet-5056.438.779.145.792.6
PyMAF [36]ResNet-5057.740.592.858.9110.1
BEV* [33]HRNet-W32--78.546.992.3
OCHMR* [13]ResNet-50 / HRNet-W32--89.758.3107.1
3DCrowdNet* [8]ResNet-50--81.751.598.3
model-freeGraphCMR [18]ResNet-50-50.1-70.2-
I2LMeshNet [27]ResNet-5055.741.793.257.7110.1
Pose2Mesh [7]HRNet-W4864.947.089.556.3105.3
METRO [21]HRNet-W6454.036.777.147.988.2
MeshGraphormer [22]HRNet-W6451.234.574.745.687.7
FastMETRO [6]HRNet-W6452.233.773.544.684.1
OursHRNet-W3248.332.973.944.985.5
+ +Table 1. Performance comparisons of 3D human mesh reconstruction based on Human3.6M and 3DPW datasets. The proposed method achieves the best performance in the Human3.6M dataset while still showing the competitive performance in the 3DPW dataset (best results are shown in bold). Note that * denotes the performance without fine-tuning on the 3DPW dataset. + +are projected onto the 2D space and the corresponding results are represented as $J_{2d}$ and $\bar{J}_{2d}$ , respectively. Based on such projected results, the 2D joint loss is formulated as $L_{2}$ loss in the same way of the 3D joint loss as follows: + +$$ +\mathcal {L} _ {j 2 d} = \frac {1}{K} \sum_ {i = 1} ^ {K} \| \tilde {J} _ {2 d} ^ {i} - J _ {2 d} ^ {i} \| _ {2} + \| \tilde {J} _ {2 d} ^ {i} - \bar {J} _ {2 d} ^ {i} \| _ {2}, \tag {5} +$$ + +where $\tilde{J}_{2d}$ is the ground truth of the 2D joint position. On the other hand, our heatmap loss $\mathcal{L}_h$ consists of the binary cross entropy loss and the dice loss. Specifically, we adopt the binary cross entropy loss to determine whether the activated position is matched to the point projected from the vertex or not as follows: + +$$ +\mathcal {L} _ {b c e} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \tilde {H} ^ {i} \log H ^ {i} + (1 - \tilde {H} ^ {i}) \log (1 - H ^ {i}), \tag {6} +$$ + +where $H$ and $\tilde{H}$ denote the predicted heatmap and the corresponding ground truth, respectively. The ground truth is represented as the binary map where the position of the projected vertex is assigned 1, otherwise 0. To alleviate the data-imbalanced problem, i.e., the projected point exists on only a single pixel in the ground truth image, the dice loss [26] is also employed as follows: + +$$ +\mathcal {L} _ {d i c e} = \frac {1}{N} \sum_ {i = 1} ^ {N} 1 - \frac {2 \times \left(\tilde {H} ^ {i} \times H ^ {i}\right)}{\tilde {H} ^ {i} + H ^ {i}}. \tag {7} +$$ + +Since the dice loss mainly focuses on the overlapped area, the data-imbalanced problem can be efficiently alleviated. By using the combination of these loss functions, the proposed network successfully learns to reconstruct the 3D human mesh as follows: + +$$ +\begin{array}{r l} \mathcal {L} _ {\text {t o t a l}} & = w _ {v} \mathcal {L} _ {v} + w _ {j 3 d} \mathcal {L} _ {j 3 d} + w _ {j 2 d} \mathcal {L} _ {j 2 d} \\ & + w _ {b c e} \mathcal {L} _ {b c e} + w _ {d i c e} \mathcal {L} _ {d i c e}, \end{array} \tag {8} +$$ + +where $w_v, w_{j3d}, w_{j2d}, w_{bce}$ and $w_{dice}$ are the balancing factor for each loss term, which are set to 0.01, 0.1, 0.01, 1.0, and 0.001, respectively. + +# 4. Experimental Results + +# 4.1. Training + +All the experiments are implemented on the PyTorch framework [28] with an Intel E5-1650@3.60GHz CPU and two NVIDIA RTX A6000 GPUs. To train all the parameters of our model, the Adam optimizer [14] is adopted where the momentum factors are set to 0.9 and 0.999, respectively. The proposed network is trained for 50 epochs with a batch size of 64 per GPU. The learning rate is firstly set to $1 \times 10^{-4}$ and reduced to $1 \times 10^{-5}$ at the half of the learning time. For each input image, the area including the human is cropped and resized to the resolution of $224 \times 224$ pixels before training. + +![](images/1c54c44f93e51e4ac13bbee43dbb34237ae44a66359196e206426a0123ac0c53.jpg) +Figure 6. Results of 3D human mesh reconstruction on Human3.6M [11] (top-two rows) and 3DPW [34] (bottom-two rows) datasets. (a) Input images. (b) Results by METRO [21]. (c) Results by Mesh Graphormer [22]. (d) Results by the proposed method. + +![](images/86f6b90e11f17230bf4bb8965cefaccd4c8ebc3e0263f9fd8c40e8fbd1624028.jpg) + +# 4.2. Datasets and Evaluation Metrics + +Datasets. For the performance evaluation of the proposed method, two representative benchmarks, i.e., Human3.6M [11] and 3DPW [34], are employed. Specifically, the proposed method is trained based on five datasets, i.e., Human3.6M [11], MuCo-3DHP [25], UP-3D [19], COCO [23], and MPII [1], by following previous approaches, and tested with the P2 protocol in the Human3.6M dataset. Since the ground truth of the 3D human mesh is unavailable in the Human3.6M dataset, we use the pseudo mesh label generated by SMPLify-X [29] as introduced in [6,7,21,22,27]. For the test on the 3DPW dataset, we fine-tune the proposed method by using the training set of the 3DPW dataset. + +Evaluation metrics. For the quantitative evaluation, we use three metrics, i.e., mean per joint position error (MPJPE) [11], Procrustes-aligned mean per joint position error (PA-MPJPE) [38], and mean per vertex position error (MPVPE) [30], which have been widely adopted for the performance comparison in this field. Specifically, MPJPE measures the average value of the Euclidean distance between each estimated 3D joint and the corresponding ground truth. PA-MPJPE indicates MPJPE in which the estimated human body is aligned in terms of rotation and scaling using the Procrustes analysis. On the other hand, MPVPE is a metric for computing the Euclidean distance + +between coordinates of the predicted vertex and the corresponding ground truth. + +# 4.3. Performance Evaluation + +Quantitative evaluation. To demonstrate the efficiency and robustness of the proposed method, we compare ours with representative methods for 3D human mesh reconstruction, i.e., HMR [12], SPIN [17], ExPose [9], VIBE [15], HybrIK [20], ROMP [32], PARE [16], MAED [40], PyMAF [36], BEV [33], OCHMR [13], 3DCrowdNet [8], GraphCMR [18], I2LMeshNet [27], Pose2Mesh [7], METRO [21], Mesh Graphormer [22], and FastMETRO [6]. The result of the performance comparison is shown in Table 1. As can be seen, the proposed method achieves 48.3 MPJPE and 32.9 PA-MPJPE on the Human3.6M dataset, which outperforms the state-of-the-art methods with the meaningful performance gain. Even though the performance of the proposed method is slightly dropped compared to the best one (i.e., FastMETRO) in the 3DPW dataset, our method still shows the competitive performance with state-of-the-art methods. Specifically, model-free methods have shown the reliable performance without using the well-defined human model in recent days. This is because their reconstruction results are not limited to the small set of pre-defined human models, thus show more appropriate human meshes for a given image compared to model-based methods. In particular, transformer-based ar + +![](images/f981b5b5da79506884b5e138bd98d1f719112a291332a41924d97ff11c332a78.jpg) +Figure 7. More results of 3D human mesh reconstruction for our samples, which are acquired by the smartphone. Odd columns: input images. Even columns: our results. Note that the proposed method provides reliable results of 3D human mesh reconstruction for various pictures of our daily life even with severe occlusions. + +![](images/ba9f30233a9768d9d7cb91fe431318566793fde91a3e7981a92849c24658e4d1.jpg) + +![](images/d27ba339b1f0d60686c0d132f7fc7016575d7eb1bb23c4045940f817438a6667.jpg) + +chitectures, e.g., Mesh Graphomer and FastMETRO, significantly improves the performance of 3D human mesh reconstruction. Nevertheless, recent model-based methods still show the competitive performance and work robust to occlusion cases, e.g., BEV, OCHMR, and 3DCrowdNet. It is noteworthy that the proposed method notably improves the performance by our point-guided feature sampling scheme without specially designing the decoder architecture like [6]. Moreover, the proposed method provides the reliable performance with the relatively small-sized backbone (e.g., HRNet-W32). + +Qualitative evaluation. Several results of 3D human mesh reconstructions for Human3.6M and 3DPW datasets are shown in Fig. 6. Note that our results are reconstructed based on the upsampling matrix as used in [6] while other two methods, i.e., METRO [21] and Mesh Graphomer [22], utilized two linear layers to upsample coarse vertex points. We can see that the proposed method successfully estimates 3D human poses under various situations including real-world scenarios in outdoor scenes as well as the controlled environment. Specifically, previous methods have somewhat difficulties to estimate unusual poses, e.g., overlapping arms and bending, whereas the proposed method provides the well-fit 3D model for a given image. Moreover, the proposed method has a good ability to reconstruct 3D human meshes in occlusions due to the progressive attention masking scheme as shown in examples of the last row of Fig. 6. In particular, previous methods fail to infer the global orientation of the human body due to the fence in front of the target person, which leads to the significant performance drop for 3D human mesh reconstruction. In contrast, the proposed method shows the reliable performance with various occlusions (see third and fourth rows in Fig. 6). More examples for 3D human mesh reconstruction by the proposed method are shown in Fig. 7. Note that in + +
Point-guided feature samplingProgressive attention maskingMPJPEPA-MPJPE
XX63.239.9
X✓61.240.8
✓X50.933.3
✓✓48.332.9
+ +Table 2. Performance analysis of the proposed method according to changes in the network architecture based on the Human3.6M dataset (best results are shown in bold). + +
MethodsMPJPEPA-MPJPE
Without attention masking50.933.3
Single attention masking49.133.5
Progressive attention masking (ours)48.332.9
+ +Table 3. Performance analysis of the proposed method according to the attention masking scheme based on the Human3.6M dataset (best results are shown in bold). Note that $M = 1$ is used for single attention masking. + +put images are acquired by the smartphone. As can be seen, the proposed method performs well for various pictures of our daily life even with severe occlusions. Therefore, it is thought that the proposed method paves the way for 3D human mesh reconstruction under various environments. + +# 4.4. Ablation Studies + +In this subsection, we first demonstrate the comparative experimental results by changing the components of the proposed method based on the Human3.6M dataset. Table 2 shows the contribution of such components. As can be seen, the performance of 3D human mesh reconstruc + +![](images/74db5938a887a157a7cae7c4941110698bb9cf5109ee2b840de83ce198c20b72.jpg) +Figure 8. Several reconstruction results (3D joints (left) and 3D hand meshes (right)) by the proposed method for the FreiHAND [39] dataset. Note that the proposed method works robust to self-occlusions frequently occurring by complicated hand poses. + +![](images/9d944c1ba6135421a26d9e0f57dc5aec06fd239aa00459aa3968f8f0f57688b0.jpg) + +![](images/4ca2278f5c717b3712828a486f1305eb38e2821efa0069c1b91a53703f7eda08.jpg) + +tion is significantly improved with our point-guided feature sampling scheme (MPJPE: $63.2 \rightarrow 50.9$ , PA-MPJPE: $39.9 \rightarrow 33.3$ ). From this analysis, we can see that feature sampling at vertex-relevant positions even in the 2D space is effective for improving the performance of 3D human mesh reconstruction. In what follows, we also check the effect of our progressive attention masking and the corresponding result is shown in Table 3. Note that our point-guided feature sampling is applied for this experiment. By comparing ours with baseline (i.e., without masking) and single masking attention scheme [6], we can see that the progressive restriction strategy in defining the local connection is also helpful for improving the performance of 3D human mesh reconstruction. This tells us that the combination of our contributions makes the model be robust to complicated real-world environments. + +# 4.5. Generalization Ability + +In contrast to the model-based approach, the proposed method can be easily applied to other applications. To show the generalization ability of the proposed method, we conduct 3D hand mesh reconstruction based on the FreiHAND [39] dataset by changing the number of input tokens for the sequence of transformer encoders. Note that the number of vertices to be projected is set to 195 and those are upsampled to 778 via the same upsampling matrix used for 3D human mesh reconstruction. Several reconstruction results by the proposed method are shown in Fig. 8. We can see that the proposed method provides the reliable reconstruction results (i.e., 3D joints and 3D hand meshes) for various hand poses. In particular, self-occlusions by complicated relations between adjacent fingers are successfully handled in the proposed method. The result of the quantitative evaluation is also shown in Table 4. As can be seen, the proposed method shows the competitive performance on the FreiHAND dataset. + +
MethodsPA-MPVPEPA-MPJPEF@5mmF@15mm
Hasson et al. [10]13.2-0.4360.908
Boukhayma et al. [4]13.0-0.4350.898
FreiHAND [39]10.7-0.5290.935
I2LMeshNet [27]7.67.40.6810.973
Pose2Mesh [7]7.87.70.6740.969
METRO [21]6.76.80.7170.981
FastMETRO [6]-6.5-0.982
Ours6.66.10.7200.984
+ +Table 4. Performance comparisons of 3D hand mesh reconstruction based on the FreiHAND dataset (best results are shown in bold). + +# 5. Conclusion + +In this paper, we present a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. The key idea of the proposed method is to alleviate heterogeneous modalities between input (i.e., color) and output (i.e., coordinate) by considering the correspondence of encoded features and 2D points projected from 3D vertices. Our point-guided feature sampling scheme is to sample vertex-relevant features based on the combination of the heatmap and encoded features. In addition, the proposed progressive attention masking scheme makes the model to be robust to occlusions by considering local connections of different levels through the sequence of transformer encoders. Experimental results on benchmark datasets show that the proposed method performs reliably for various real-world environments. + +Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (2021-0-02084, eXtended Reality and Volumetric media generation and transmission technology for immersive experience sharing in noncontact environment with a Korea-EU international cooperative research). + +# References + +[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. In IEEE Conf. Comput. Vis. Pattern Recog., pages 3686-3693, 2014. 6 +[2] Benjamin Biggs, David Novotny, Sebastien Ehrhardt, Hanbyul Joo, Ben Graham, and Andrea Vedaldi. 3D Multibodies: Fitting sets of plausible 3D human models to ambiguous image data. In Adv. Neural Inform. Process. Syst., pages 20496-20507, 2020. 2 +[3] Federica Bogo, Angjoo Kanazawa, Christoph Lassner, Peter Gehler, Javier Romero, and Michael J Black. 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Vis., 2021. 5, 6 \ No newline at end of file diff --git a/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/images.zip b/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d3d118fc65ef11e19120f1deebc2f2a97dd96d60 --- /dev/null +++ b/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2b004f713f67e4125e04cc3ec4add662d0f4d4e15f14c5c37440b30833f65821 +size 880773 diff --git a/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/layout.json b/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..33fe36316c470fd43ee4a04de47a61ec14ec7b95 --- /dev/null +++ b/2023/Sampling Is Matter_ Point-Guided 3D Human Mesh Reconstruction/layout.json @@ -0,0 +1,6963 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 89, + 103, + 503, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 103, + 503, + 120 + ], + "spans": [ + { + "bbox": [ + 89, + 103, + 503, + 120 + ], + "type": "text", + "content": "Sampling is Matter: Point-guided 3D Human Mesh Reconstruction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "spans": [ + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "text", + "content": "Jeonghwan Kim" + }, + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "text", + "content": " Mi-Gyeong Gwon" + }, + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "text", + "content": " Hyunwoo Park" + }, + { + "bbox": [ + 156, + 142, + 436, + 157 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 176, + 157, + 421, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 176, + 157, + 421, + 171 + ], + "spans": [ + { + "bbox": [ + 176, + 157, + 421, + 171 + ], + "type": "text", + "content": "Hyukmin Kwon² Gi-Mun Um² Wonjun Kim†" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 171, + 488, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 171, + 488, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 488, + 185 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 171, + 488, + 185 + ], + "type": "text", + "content": "Konkuk University " + }, + { + "bbox": [ + 105, + 171, + 488, + 185 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 105, + 171, + 488, + 185 + ], + "type": "text", + "content": "Electronics and Telecommunications Research Institute" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 103, + 187, + 487, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 187, + 487, + 199 + ], + "spans": [ + { + "bbox": [ + 103, + 187, + 487, + 199 + ], + "type": "text", + "content": "{jhkim0759,kmk3942,pzls,wonjkim}@konkuk.ac.kr {hmkwon,gmum}@etri.re.kr" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 238, + 191, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 238, + 191, + 251 + ], + "spans": [ + { + "bbox": [ + 143, + 238, + 191, + 251 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 265, + 290, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 290, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 290, + 552 + ], + "type": "text", + "content": "This paper presents a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. Most recently, the non-local interactions of the whole mesh vertices have been effectively estimated in the transformer while the relationship between body parts also has begun to be handled via the graph model. Even though those approaches have shown the remarkable progress in 3D human mesh reconstruction, it is still difficult to directly infer the relationship between features, which are encoded from the 2D input image, and 3D coordinates of each vertex. To resolve this problem, we propose to design a simple feature sampling scheme. The key idea is to sample features in the embedded space by following the guide of points, which are estimated as projection results of 3D mesh vertices (i.e., ground truth). This helps the model to concentrate more on vertex-relevant features in the 2D space, thus leading to the reconstruction of the natural human pose. Furthermore, we apply progressive attention masking to precisely estimate local interactions between vertices even under severe occlusions. Experimental results on benchmark datasets show that the proposed method efficiently improves the performance of 3D human mesh reconstruction. The code and model are publicly available at: https://github.com/DCVL-3D/PointHMR_release." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 128, + 590 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 598, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 598, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 598, + 287, + 682 + ], + "type": "text", + "content": "The goal of 3D human mesh reconstruction is to estimate 3D coordinates of points, which make up the human body surface. Since the high-quality 3D human model has been consistently required for various immersive applications, many studies have devoted considerable efforts to accurately reconstruct the 3D human mesh. In the early stage of this field, complex optimization techniques were" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 306, + 225, + 547, + 285 + ], + "blocks": [ + { + "bbox": [ + 306, + 225, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 306, + 225, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 225, + 547, + 285 + ], + "type": "image", + "image_path": "a07e559d14d39b58bac16c57711dd541048e69882b1fb37ac61bb775936062ae.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 420, + 287, + 430, + 296 + ], + "lines": [ + { + "bbox": [ + 420, + 287, + 430, + 296 + ], + "spans": [ + { + "bbox": [ + 420, + 287, + 430, + 296 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 306, + 298, + 546, + 360 + ], + "blocks": [ + { + "bbox": [ + 306, + 298, + 546, + 360 + ], + "lines": [ + { + "bbox": [ + 306, + 298, + 546, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 546, + 360 + ], + "type": "image", + "image_path": "9db56032bf13deccc60921e11fd879b95f1d76c8062bacd426daba3146cf8af5.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 420, + 360, + 431, + 369 + ], + "lines": [ + { + "bbox": [ + 420, + 360, + 431, + 369 + ], + "spans": [ + { + "bbox": [ + 420, + 360, + 431, + 369 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 382, + 546, + 427 + ], + "lines": [ + { + "bbox": [ + 304, + 382, + 546, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 546, + 427 + ], + "type": "text", + "content": "Figure 1. (a) Traditional process of feature extraction for estimating 3D coordinates. (b) Vertex-relevant feature extraction process based on the proposed point-guided sampling method for estimating 3D coordinates." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 449, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 593 + ], + "type": "text", + "content": "adopted to generate the 3D human model based on the relationship between multiple scenes, which are acquired by using stereo or multiple-view camera systems. Recently, owing to the great success of deep learning, the problem of 3D human mesh reconstruction now can be resolved only with a single RGB image, thus the majority has begun to develop compact network architectures and efficient training strategies. Even though such deep learning-based approaches have shown the significant progress in 3D human mesh reconstruction, this task is still challenging due to severe occlusions by diverse human poses and depth ambiguities by the monocular setting." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Deep learning-based approaches can be divided into two main groups: model-based and model-free methods. In the former, most methods aim to estimate shape and pose parameters of the skinned multi-person linear (SMPL) model [24], which is capable of yielding the whole vertices via these two simple factors, thus most widely employed in this field. Traditional encoder-decoder architectures, which are mostly composed of stacked convolutional layers, are sufficient to conduct the regression for estimating those parameters. Despite their great performance, model-based" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 124, + 703 + ], + "type": "text", + "content": "*equal contribution" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 703, + 133, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 133, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 133, + 713 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 59, + 703, + 133, + 713 + ], + "type": "text", + "content": " corresponding author" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12880" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 312 + ], + "type": "text", + "content": "methods have the obvious shortcoming, i.e., reconstruction results are limited to the pre-defined types of human body models. On the other hand, model-free methods have attempted to directly infer 3D coordinates of mesh vertices from input features without using any specific human body model. Compared to the model-based approach, which obtains the well-defined full mesh by adjusting shape and pose parameters, the model-free approach needs to estimate 3D coordinates of whole vertices directly from the network. Most methods in this category are based on the transformer to grasp non-local interactions between mesh vertices. The graph model (e.g., graph convolution) also has been utilized together to allow for body part relations in a local manner. One important advantage of the model-free approach is the flexibility to adapt to other applications, e.g., hand pose estimation, without significant changes of the data format and the training strategy. However, inferring the 3D coordinate from a single monocular image is still challenging due to lack of learning the correspondence between encoded features and spatial positions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 312, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 289, + 492 + ], + "type": "text", + "content": "In this paper, we propose a simple yet powerful method for 3D human mesh reconstruction. To this end, we conduct feature sampling at vertex-relevant points of the input image as shown in Fig. 1, which are estimated through the heatmap decoder trained by projection results of 3D mesh vertices (i.e., ground truth). These sampled features are subsequently fed into the transformer encoder as the form of the vertex token (see Fig. 2). In a similar way of [6], we apply attention masking to the transformer encoder, however, the difference is that the local connection is defined with the range of multiple levels through the sequence of transformer encoders. This progressive attention masking helps the model understand local relations between vertices precisely even in occlusions. The main contribution of the proposed method can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 502, + 287, + 632 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 59, + 502, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 502, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 59, + 502, + 287, + 585 + ], + "type": "text", + "content": "- We propose to utilize the correspondence between encoded features and vertex positions, which are projected into the 2D space, via our point-guided feature sampling scheme. By explicitly indicating such vertex-relevant features to the transformer encoder, coordinates of the 3D human mesh are accurately estimated." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 596, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 596, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 59, + 596, + 287, + 632 + ], + "type": "text", + "content": "- Our progressive attention masking scheme helps the model efficiently deal with local vertex-to-vertex relations even under complicated poses and occlusions." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 134, + 658 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "In this Section, we give a brief review of the previous studies for 3D human mesh construction which have progressed in two different directions: model-based and model-free approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 624 + ], + "type": "text", + "content": "Model-based approaches. As mentioned, most model-based approaches aim to estimate shape and pose parameters of the SMPL model [24] for restoring the entire set of mesh vertices. In the beginning, several studies attempted to align 2D joint positions as well as body part segments, which are estimated by respective networks, with the ground truth projected from the 3D human mesh [3, 19]. However, these methods require additional steps to estimate shape and pose parameters of the SMPL model. To cope with this limitation, Kanazawa et al. [12] proposed to regress such parameters directly from a single RGB image without using intermediate results, i.e., 2D joints and body part segments. Specifically, they designed a simple convolutional encoder with the adversarial loss to make the reconstructed mesh result be realistic. Inspired by the great potential of this simple regression scheme, many researchers have introduced various encoder-decoder architectures to estimate shape and pose parameters. Kolotouros et al. [17] proposed to combine the end-to-end regression model with the optimization loop to strongly supervise the refinement process. Choutas et al. [9] attempted to directly regress body, face, and hands by exploiting the body-driven attention in the SMPL-X [29] format for generating the high-quality 3D human mesh. Biggs et al. [2] designed a multi-hypothesis neural network regressor based on the best-of-M loss, which makes the plausible human pose even under severely occluded environments. Zhang et al. [37] also focused on accurately restoring object-occluded human shape and pose by utilizing the partial UV map and the novel saliency map in the SMPL format. Most recently, Kocabas et al. [16] devised the part attention module to guide the network to concentrate more on relevant body parts for inferring the given pose with SMPL parameters in a single input RGB image. Sun et al. [32] estimated body center positions instead of segmenting human regions and extracted the parameter maps for the SMPL model at the corresponding positions. They further extend their algorithm by adopting the heat map of the bird-eye view to alleviate the depth ambiguity in monocular settings [33]. On the other hand, the kinematic topology module has been embedded into the neural network architecture to consider the relationship between articulations of the human body [20]. Even though model-based approaches have shown the remarkable progress in 3D human mesh reconstruction, their performance is limited to pre-defined types of human body models, which are hardly extended to other applications." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "Model-free approaches. Model-free approaches intend to directly restore the entire set of mesh vertices while relaxing the heavy reliance on the parameter space in model-based methods. As a pioneer, Kolotouros et al. [18] proposed to estimate human mesh coordinates through the graph convolutional neural network (GraphCNN). To do this, they attached encoded features to nodes in the graph, which are" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12881" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 57, + 542, + 245 + ], + "blocks": [ + { + "bbox": [ + 47, + 57, + 542, + 245 + ], + "lines": [ + { + "bbox": [ + 47, + 57, + 542, + 245 + ], + "spans": [ + { + "bbox": [ + 47, + 57, + 542, + 245 + ], + "type": "image", + "image_path": "29a0e4e7dc6f94b9078071707a90335fc0fb6d3e78bb95d2c6b80c15d5532b20.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. Overall architecture of the proposed method. The backbone feature is used to generate heatmap, target feature, and grid feature with respective decoders. Our sampling scheme utilizes heatmap and target feature to make the vertex token. Note that " + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": " denote the number of vertices and the distance threshold for defining the local connection in self-attention, respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 289, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 289, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 289, + 532 + ], + "type": "text", + "content": "mapped to 3D coordinates of the template mesh. From this perspective, Choi et al. [7] also adopted GraphCNN to reconstruct 3D human meshes from 2D and 3D pose information in a coarse-to-fine manner. While these GraphCNN-based methods have a good ability to fully exploit the mesh topology, they are somewhat lacking in considering global interactions between joints and vertices. To cope with this limitation, the transformer has begun to be actively adopted for model-free approaches. Specifically, Lin et al. [21] firstly introduced the transformer encoder, which simply takes joint and vertex queries as input tokens, to regress 3D coordinates from a single input RGB image. In particular, they further embedded GraphCNN into the transformer block to supplement local interactions, e.g., between-part relationships, for 3D human mesh reconstruction. Most recently, Cho et al. [6] have disentangled image features and mesh queries by utilizing the transformer encoder-decoder architecture to alleviate the high complexity of interactions among input tokens." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 533, + 288, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 288, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 288, + 594 + ], + "type": "text", + "content": "Our method is also based on the transformer encoder with a simple sampling scheme, which gives a great help to focus on vertex-relevant features for inferring coordinates of the 3D human mesh. Technical details will be explained in the following Section." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 608, + 153, + 622 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 608, + 153, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 608, + 153, + 622 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "The proposed method consists of two main parts. Specifically, vertex-relevant features are extracted based on our point-guided feature sampling in the first part while 3D coordinates are estimated through the sequence of transformer encoders with the proposed progressive attention masking scheme in the second part. The overall architecture of the proposed method is illustrated in Fig. 2." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 303, + 385, + 381 + ], + "blocks": [ + { + "bbox": [ + 307, + 303, + 385, + 381 + ], + "lines": [ + { + "bbox": [ + 307, + 303, + 385, + 381 + ], + "spans": [ + { + "bbox": [ + 307, + 303, + 385, + 381 + ], + "type": "image", + "image_path": "3dc4d150e9a1f768c5c68033705028cbb23b71d055bb2e2f4275cbb5a26c4c04.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 387, + 545, + 433 + ], + "lines": [ + { + "bbox": [ + 305, + 387, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 545, + 433 + ], + "type": "text", + "content": "Figure 3. Several examples of predicted heatmaps on the 3DPW dataset. For better visibility, the activated regions of the heatmap corresponding to several selected vertices are represented in a single image with bright colors (best view in colors)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 387, + 303, + 465, + 381 + ], + "blocks": [ + { + "bbox": [ + 387, + 303, + 465, + 381 + ], + "lines": [ + { + "bbox": [ + 387, + 303, + 465, + 381 + ], + "spans": [ + { + "bbox": [ + 387, + 303, + 465, + 381 + ], + "type": "image", + "image_path": "8a9500a8768abef880e6b4da9cf08904fa98504a1de14e663870bd0ed0ea9983.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 467, + 303, + 545, + 381 + ], + "blocks": [ + { + "bbox": [ + 467, + 303, + 545, + 381 + ], + "lines": [ + { + "bbox": [ + 467, + 303, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 467, + 303, + 545, + 381 + ], + "type": "image", + "image_path": "e850c2b5fd5092905b33a9c1fdbaddb2c87fc68b16f14195e4e7ff6024924608.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 444, + 476, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 476, + 458 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 476, + 458 + ], + "type": "text", + "content": "3.1. Point-guided Feature Sampling" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "text", + "content": "Since the direct transform from the color value to the 3D coordinate is still a difficult process due to heterogeneous modalities, we propose to use the intermediate guidance, i.e., features sampled at positions of vertices projected from 3D to 2D spaces. Specifically, we represent such projection results as the form of the heatmap, and sample features at activated positions in this heatmap. The detailed process of our point-guided feature sampling is shown in the first part of Fig. 2. Firstly, the backbone feature " + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "inline_equation", + "content": "X_{b}\\in \\mathbb{R}^{C\\times H\\times W}" + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "text", + "content": " is encoded through the backbone network (HRNet [35] in this work), where " + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 462, + 545, + 605 + ], + "type": "text", + "content": " denote the number of channels, height, and width, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "inline_equation", + "content": "X_{b}" + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": " is subsequently decoded into the heatmap, the target feature, and the grid feature by respective decoders as shown in Fig. 2. After that, the vertex-relevant feature is sampled at each of " + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": " vertices based on combination of the predicted heatmap and the target feature. Several examples of the predicted heatmap are shown in Fig. 3. Note that we conducted element-wise multiplication of the predicted heatmap and the target feature to make our sampling process be differentiable. Moreover, we apply the positional" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12882" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 62, + 287, + 162 + ], + "blocks": [ + { + "bbox": [ + 47, + 62, + 287, + 162 + ], + "lines": [ + { + "bbox": [ + 47, + 62, + 287, + 162 + ], + "spans": [ + { + "bbox": [ + 47, + 62, + 287, + 162 + ], + "type": "image", + "image_path": "f2ad6b6da73f88c46eaf68e1b3051e3b0ad9ae9389b86c8628cf3c52815fe4f1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 168, + 287, + 214 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 287, + 214 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 287, + 214 + ], + "type": "text", + "content": "Figure 4. The detailed structure of the proposed progressive attention masking scheme. Note that this figure illustrates the masking process in the first transformer encoder, i.e., the case of " + }, + { + "bbox": [ + 46, + 168, + 287, + 214 + ], + "type": "inline_equation", + "content": "M = 7" + }, + { + "bbox": [ + 46, + 168, + 287, + 214 + ], + "type": "text", + "content": ", shown in Fig. 2." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 229, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 229, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 287, + 277 + ], + "type": "text", + "content": "encoding to the target feature in the same way of [5, 6] for preserving the spatial information in the transformer encoder. Our point-guided feature sampling can be formulated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 284, + 287, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 284, + 287, + 298 + ], + "spans": [ + { + "bbox": [ + 97, + 284, + 287, + 298 + ], + "type": "interline_equation", + "content": "\\hat {V} _ {i} = H _ {i} \\times F, \\quad i = 1, 2, 3, \\dots , N, \\tag {1}", + "image_path": "20f43af4d322f4731069a40ddb7da82db1bceaa9ee997dd324a8cc6b5d83d33a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "inline_equation", + "content": "H_{i}" + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "content": " denote the predicted heatmap corresponding to the " + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "content": "-th vertex and the target feature, respectively. " + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "content": " denotes the total number of vertices and is set to 431 as used in previous methods. " + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "inline_equation", + "content": "\\hat{V}_{i}" + }, + { + "bbox": [ + 46, + 305, + 287, + 413 + ], + "type": "text", + "content": " is the sampling result, which is finally flattened and fed into the transformer encoder with the grid feature in the second part of our proposed method. It is noteworthy that the grid feature plays an important role to create the united body structure by aligning each point in an appropriate location." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 420, + 287, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 287, + 445 + ], + "type": "text", + "content": "3.2. Transformer Encoder with Progressive Attention Masking" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": "In this subsection, we explain the sequence of transformer encoders in detail. In a similar way of [21, 22], we design the transformer encoder with the dimension reduction layer as shown in the second part of Fig. 2. Specifically, the transformer encoder takes the vertex token " + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{V} \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": ", the joint token " + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{J} \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": ", and the grid token " + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{G} \\in \\mathbb{R}^{Z \\times D}" + }, + { + "bbox": [ + 46, + 450, + 287, + 713 + ], + "type": "text", + "content": " as inputs. The joint token is a trainable parameter that is randomly initialized and optimized during the training phase whereas vertex and grid tokens are extracted from the first part of the proposed method. Moreover, positional encodings are employed to give the identity by concatenating the trainable parameter to each token. The dimension of the encoded token is reduced by linear projection after each transformer block, which consists of two transformer encoders. To consider local vertex-vertex relations as well as non-adjacent interactions, we exclude far-distant connections between vertices to compute self-attention in the transformer encoder. In contrast to the previous method [6], we gradually decrease the range to define the local connection between vertices through the sequence of transformer encoders as illustrated in Fig. 4. This helps the model consider the local relationship between neighbor vertices in a" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 385, + 149 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 385, + 149 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 385, + 149 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 385, + 149 + ], + "type": "image", + "image_path": "96521333a3a1cfdfe52f8b372d02f9c4e91d2e3aada1d96edbe4a495a9764a4e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 152, + 351, + 161 + ], + "lines": [ + { + "bbox": [ + 341, + 152, + 351, + 161 + ], + "spans": [ + { + "bbox": [ + 341, + 152, + 351, + 161 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 388, + 70, + 465, + 149 + ], + "blocks": [ + { + "bbox": [ + 388, + 70, + 465, + 149 + ], + "lines": [ + { + "bbox": [ + 388, + 70, + 465, + 149 + ], + "spans": [ + { + "bbox": [ + 388, + 70, + 465, + 149 + ], + "type": "image", + "image_path": "2717359c138593e978b36dbeecc95d136b7b795a9d9c26571b48fb774337a829.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 422, + 152, + 433, + 161 + ], + "lines": [ + { + "bbox": [ + 422, + 152, + 433, + 161 + ], + "spans": [ + { + "bbox": [ + 422, + 152, + 433, + 161 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 468, + 70, + 545, + 149 + ], + "blocks": [ + { + "bbox": [ + 468, + 70, + 545, + 149 + ], + "lines": [ + { + "bbox": [ + 468, + 70, + 545, + 149 + ], + "spans": [ + { + "bbox": [ + 468, + 70, + 545, + 149 + ], + "type": "image", + "image_path": "66b0b382ea207b510a19cd97448ecfca06dbcd748eba6ff7f576fafe23a2edc4.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 152, + 511, + 161 + ], + "lines": [ + { + "bbox": [ + 501, + 152, + 511, + 161 + ], + "spans": [ + { + "bbox": [ + 501, + 152, + 511, + 161 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 168, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 305, + 168, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 545, + 202 + ], + "type": "text", + "content": "Figure 5. (a) Input image. (b) Reconstruction result with previous attention masking [6]. (c) Reconstruction result with progressive attention masking (proposed)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 217, + 545, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 253 + ], + "type": "text", + "content": "progressive manner. Figure 5 shows the effect of our progressive attention masking. As can be seen, the proposed method provides the reasonable result even in occlusions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "content": "The outputs (i.e., vertex and joint tokens) of the last transformer encoder are finally projected into 3D coordinates via a linear layer. In the case of the vertex token, the upsampling algorithm introduced in [31] is applied to expand sparse vertices " + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "inline_equation", + "content": "V' \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "content": " into dense vertices " + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "inline_equation", + "content": "V \\in \\mathbb{R}^{\\mathcal{N} \\times 3}" + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 402, + 331, + 545, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 402, + 331, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 402, + 331, + 545, + 344 + ], + "type": "interline_equation", + "content": "V = U V ^ {\\prime}, \\tag {2}", + "image_path": "759f35ac0c27e45efa929b785e3811042730fafe97ce9ff65c95f3029824912c.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "type": "inline_equation", + "content": "U" + }, + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "type": "text", + "content": " is the pre-defined upsampling matrix [31]. " + }, + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 304, + 350, + 545, + 399 + ], + "type": "text", + "content": " is set to 6,890 (same as the vertex number of the SMPL model). The predicted 3D human mesh and 3D keypoints can be visualized as the rightmost images shown in Fig. 2." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 404, + 394, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 404, + 394, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 404, + 394, + 415 + ], + "type": "text", + "content": "3.3. Loss Function" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": "The proposed method is trained based on four types of loss functions, i.e., vertex loss " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_v" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": ", 3D joint loss " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{j3d}" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": ", 2D joint loss " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{j2d}" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": ", and heatmap loss " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_h" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": ". The first three loss functions are used for estimating positions of vertices and joints as introduced in previous works [6,21,22] while the last one guides the network to find positions of projected vertices. First of all, " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": " loss is adopted to compute the difference between positions of the predicted vertex " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": " and the corresponding ground truth " + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\tilde{V}" + }, + { + "bbox": [ + 304, + 423, + 545, + 531 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 370, + 536, + 545, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 536, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 370, + 536, + 545, + 570 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\| \\tilde {V} ^ {i} - V ^ {i} \\| _ {1}, \\tag {3}", + "image_path": "856a54bc16279e77ac9eba7886679c0f77900e70ef3f4b01cd6eee657ce2d12a.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "text", + "content": " denotes the total number of vertices. For the 3D joint loss, we compute the distance between the estimated joint position " + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "inline_equation", + "content": "J_{3d}" + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "text", + "content": " and the corresponding ground truth " + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "inline_equation", + "content": "\\bar{J}_{3d}" + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "text", + "content": " in the 3D space. Note that the joint position, which is regressed from the predicted vertices, i.e., " + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "inline_equation", + "content": "\\bar{J}_{3d}" + }, + { + "bbox": [ + 304, + 574, + 545, + 646 + ], + "type": "text", + "content": ", is also used for the loss computation as follows:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 330, + 651, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 651, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 330, + 651, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {j 3 d} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {J} _ {3 d} ^ {i} - J _ {3 d} ^ {i} \\| _ {2} + \\| \\tilde {J} _ {3 d} ^ {i} - \\bar {J} _ {3 d} ^ {i} \\| _ {2}, \\tag {4}", + "image_path": "1a179ce5066a29d9f199c85ae426d1bec5d58bf52db55d536ebc15ae910e5642.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " denotes the total number of joints. Similarly, the 2D joint loss is calculated as well. To do this, " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "J_{3d}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\bar{J}_{3d}" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12883" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 324 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 324 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 324 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 324 + ], + "type": "table", + "html": "
MethodsBackboneHuman3.6M3DPW
MPJPE(↓)PA-MPJPE(↓)MPJPE(↓)PA-MPJPE(↓)MPVPE(↓)
model-basedHMR [12]ResNet-5088.056.8130.081.3-
SPIN [17]ResNet-50-41.196.959.2116.4
ExPose [9]ResNet-50--93.455.6-
VIBE [15]ResNet-5065.641.482.951.999.1
HybrIK [20]ResNet-3454.434.580.048.894.5
ROMP [32]HRNet-W32--76.747.393.4
PARE [16]HRNet-W32--74.546.588.6
MAED [40]ResNet-5056.438.779.145.792.6
PyMAF [36]ResNet-5057.740.592.858.9110.1
BEV* [33]HRNet-W32--78.546.992.3
OCHMR* [13]ResNet-50 / HRNet-W32--89.758.3107.1
3DCrowdNet* [8]ResNet-50--81.751.598.3
model-freeGraphCMR [18]ResNet-50-50.1-70.2-
I2LMeshNet [27]ResNet-5055.741.793.257.7110.1
Pose2Mesh [7]HRNet-W4864.947.089.556.3105.3
METRO [21]HRNet-W6454.036.777.147.988.2
MeshGraphormer [22]HRNet-W6451.234.574.745.687.7
FastMETRO [6]HRNet-W6452.233.773.544.684.1
OursHRNet-W3248.332.973.944.985.5
", + "image_path": "e2643924e9b4ddf5832f4d8337394d6254285a305703325260ab977a81cb1f27.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 333, + 546, + 367 + ], + "lines": [ + { + "bbox": [ + 46, + 333, + 546, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 546, + 367 + ], + "type": "text", + "content": "Table 1. Performance comparisons of 3D human mesh reconstruction based on Human3.6M and 3DPW datasets. The proposed method achieves the best performance in the Human3.6M dataset while still showing the competitive performance in the 3DPW dataset (best results are shown in bold). Note that * denotes the performance without fine-tuning on the 3DPW dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": "are projected onto the 2D space and the corresponding results are represented as " + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "inline_equation", + "content": "J_{2d}" + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "inline_equation", + "content": "\\bar{J}_{2d}" + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": ", respectively. Based on such projected results, the 2D joint loss is formulated as " + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 388, + 287, + 437 + ], + "type": "text", + "content": " loss in the same way of the 3D joint loss as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 72, + 440, + 287, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 440, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 72, + 440, + 287, + 472 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {j 2 d} = \\frac {1}{K} \\sum_ {i = 1} ^ {K} \\| \\tilde {J} _ {2 d} ^ {i} - J _ {2 d} ^ {i} \\| _ {2} + \\| \\tilde {J} _ {2 d} ^ {i} - \\bar {J} _ {2 d} ^ {i} \\| _ {2}, \\tag {5}", + "image_path": "2cbaf723677eb1bbafe4408d844b8631775665cdfa0d397539351a8801b405b8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\tilde{J}_{2d}" + }, + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "text", + "content": " is the ground truth of the 2D joint position. On the other hand, our heatmap loss " + }, + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_h" + }, + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "text", + "content": " consists of the binary cross entropy loss and the dice loss. Specifically, we adopt the binary cross entropy loss to determine whether the activated position is matched to the point projected from the vertex or not as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 555, + 287, + 587 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 555, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 52, + 555, + 287, + 587 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b c e} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\tilde {H} ^ {i} \\log H ^ {i} + (1 - \\tilde {H} ^ {i}) \\log (1 - H ^ {i}), \\tag {6}", + "image_path": "5efa2b6bc2a80a56a9dcb31be2d942c55e3bef61e09a684b49d81142149ebaf6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "type": "inline_equation", + "content": "\\tilde{H}" + }, + { + "bbox": [ + 46, + 594, + 287, + 679 + ], + "type": "text", + "content": " denote the predicted heatmap and the corresponding ground truth, respectively. The ground truth is represented as the binary map where the position of the projected vertex is assigned 1, otherwise 0. To alleviate the data-imbalanced problem, i.e., the projected point exists on only a single pixel in the ground truth image, the dice loss [26] is also employed as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 91, + 683, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 683, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 91, + 683, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i c e} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} 1 - \\frac {2 \\times \\left(\\tilde {H} ^ {i} \\times H ^ {i}\\right)}{\\tilde {H} ^ {i} + H ^ {i}}. \\tag {7}", + "image_path": "642368905d5122d5f8b90916ffc7d14c236991cf22dd4c2a04be826b8fe7da6b.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 388, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 447 + ], + "type": "text", + "content": "Since the dice loss mainly focuses on the overlapped area, the data-imbalanced problem can be efficiently alleviated. By using the combination of these loss functions, the proposed network successfully learns to reconstruct the 3D human mesh as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 342, + 456, + 545, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 456, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 342, + 456, + 545, + 484 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} \\mathcal {L} _ {\\text {t o t a l}} & = w _ {v} \\mathcal {L} _ {v} + w _ {j 3 d} \\mathcal {L} _ {j 3 d} + w _ {j 2 d} \\mathcal {L} _ {j 2 d} \\\\ & + w _ {b c e} \\mathcal {L} _ {b c e} + w _ {d i c e} \\mathcal {L} _ {d i c e}, \\end{array} \\tag {8}", + "image_path": "b09787e53bd6f2c7c97c4185d74d32316209a9d00e760d2746a44f2de10ed300.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "type": "inline_equation", + "content": "w_v, w_{j3d}, w_{j2d}, w_{bce}" + }, + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "type": "inline_equation", + "content": "w_{dice}" + }, + { + "bbox": [ + 305, + 494, + 547, + 530 + ], + "type": "text", + "content": " are the balancing factor for each loss term, which are set to 0.01, 0.1, 0.01, 1.0, and 0.001, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 542, + 432, + 556 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 542, + 432, + 556 + ], + "spans": [ + { + "bbox": [ + 306, + 542, + 432, + 556 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 562, + 370, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 370, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 370, + 576 + ], + "type": "text", + "content": "4.1. Training" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "All the experiments are implemented on the PyTorch framework [28] with an Intel E5-1650@3.60GHz CPU and two NVIDIA RTX A6000 GPUs. To train all the parameters of our model, the Adam optimizer [14] is adopted where the momentum factors are set to 0.9 and 0.999, respectively. The proposed network is trained for 50 epochs with a batch size of 64 per GPU. The learning rate is firstly set to " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " and reduced to " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " at the half of the learning time. For each input image, the area including the human is cropped and resized to the resolution of " + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": " pixels before training." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12884" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 59, + 296, + 329 + ], + "blocks": [ + { + "bbox": [ + 49, + 59, + 296, + 329 + ], + "lines": [ + { + "bbox": [ + 49, + 59, + 296, + 329 + ], + "spans": [ + { + "bbox": [ + 49, + 59, + 296, + 329 + ], + "type": "image", + "image_path": "1c54c44f93e51e4ac13bbee43dbb34237ae44a66359196e206426a0123ac0c53.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 342, + 546, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 342, + 546, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 546, + 365 + ], + "type": "text", + "content": "Figure 6. Results of 3D human mesh reconstruction on Human3.6M [11] (top-two rows) and 3DPW [34] (bottom-two rows) datasets. (a) Input images. (b) Results by METRO [21]. (c) Results by Mesh Graphormer [22]. (d) Results by the proposed method." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 59, + 545, + 329 + ], + "blocks": [ + { + "bbox": [ + 298, + 59, + 545, + 329 + ], + "lines": [ + { + "bbox": [ + 298, + 59, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 298, + 59, + 545, + 329 + ], + "type": "image", + "image_path": "86f6b90e11f17230bf4bb8965cefaccd4c8ebc3e0263f9fd8c40e8fbd1624028.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 384, + 222, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 222, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 222, + 396 + ], + "type": "text", + "content": "4.2. Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 408, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 564 + ], + "type": "text", + "content": "Datasets. For the performance evaluation of the proposed method, two representative benchmarks, i.e., Human3.6M [11] and 3DPW [34], are employed. Specifically, the proposed method is trained based on five datasets, i.e., Human3.6M [11], MuCo-3DHP [25], UP-3D [19], COCO [23], and MPII [1], by following previous approaches, and tested with the P2 protocol in the Human3.6M dataset. Since the ground truth of the 3D human mesh is unavailable in the Human3.6M dataset, we use the pseudo mesh label generated by SMPLify-X [29] as introduced in [6,7,21,22,27]. For the test on the 3DPW dataset, we fine-tune the proposed method by using the training set of the 3DPW dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Evaluation metrics. For the quantitative evaluation, we use three metrics, i.e., mean per joint position error (MPJPE) [11], Procrustes-aligned mean per joint position error (PA-MPJPE) [38], and mean per vertex position error (MPVPE) [30], which have been widely adopted for the performance comparison in this field. Specifically, MPJPE measures the average value of the Euclidean distance between each estimated 3D joint and the corresponding ground truth. PA-MPJPE indicates MPJPE in which the estimated human body is aligned in terms of rotation and scaling using the Procrustes analysis. On the other hand, MPVPE is a metric for computing the Euclidean distance" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 384, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 384, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 384, + 545, + 409 + ], + "type": "text", + "content": "between coordinates of the predicted vertex and the corresponding ground truth." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 418, + 443, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 443, + 430 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 443, + 430 + ], + "type": "text", + "content": "4.3. Performance Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 437, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 713 + ], + "type": "text", + "content": "Quantitative evaluation. To demonstrate the efficiency and robustness of the proposed method, we compare ours with representative methods for 3D human mesh reconstruction, i.e., HMR [12], SPIN [17], ExPose [9], VIBE [15], HybrIK [20], ROMP [32], PARE [16], MAED [40], PyMAF [36], BEV [33], OCHMR [13], 3DCrowdNet [8], GraphCMR [18], I2LMeshNet [27], Pose2Mesh [7], METRO [21], Mesh Graphormer [22], and FastMETRO [6]. The result of the performance comparison is shown in Table 1. As can be seen, the proposed method achieves 48.3 MPJPE and 32.9 PA-MPJPE on the Human3.6M dataset, which outperforms the state-of-the-art methods with the meaningful performance gain. Even though the performance of the proposed method is slightly dropped compared to the best one (i.e., FastMETRO) in the 3DPW dataset, our method still shows the competitive performance with state-of-the-art methods. Specifically, model-free methods have shown the reliable performance without using the well-defined human model in recent days. This is because their reconstruction results are not limited to the small set of pre-defined human models, thus show more appropriate human meshes for a given image compared to model-based methods. In particular, transformer-based ar" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12885" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 59, + 212, + 225 + ], + "blocks": [ + { + "bbox": [ + 49, + 59, + 212, + 225 + ], + "lines": [ + { + "bbox": [ + 49, + 59, + 212, + 225 + ], + "spans": [ + { + "bbox": [ + 49, + 59, + 212, + 225 + ], + "type": "image", + "image_path": "f981b5b5da79506884b5e138bd98d1f719112a291332a41924d97ff11c332a78.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "type": "text", + "content": "Figure 7. More results of 3D human mesh reconstruction for our samples, which are acquired by the smartphone. Odd columns: input images. Even columns: our results. Note that the proposed method provides reliable results of 3D human mesh reconstruction for various pictures of our daily life even with severe occlusions." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 59, + 380, + 225 + ], + "blocks": [ + { + "bbox": [ + 215, + 59, + 380, + 225 + ], + "lines": [ + { + "bbox": [ + 215, + 59, + 380, + 225 + ], + "spans": [ + { + "bbox": [ + 215, + 59, + 380, + 225 + ], + "type": "image", + "image_path": "ba9f30233a9768d9d7cb91fe431318566793fde91a3e7981a92849c24658e4d1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 381, + 59, + 545, + 225 + ], + "blocks": [ + { + "bbox": [ + 381, + 59, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 381, + 59, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 381, + 59, + 545, + 225 + ], + "type": "image", + "image_path": "d27ba339b1f0d60686c0d132f7fc7016575d7eb1bb23c4045940f817438a6667.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 422 + ], + "type": "text", + "content": "chitectures, e.g., Mesh Graphomer and FastMETRO, significantly improves the performance of 3D human mesh reconstruction. Nevertheless, recent model-based methods still show the competitive performance and work robust to occlusion cases, e.g., BEV, OCHMR, and 3DCrowdNet. It is noteworthy that the proposed method notably improves the performance by our point-guided feature sampling scheme without specially designing the decoder architecture like [6]. Moreover, the proposed method provides the reliable performance with the relatively small-sized backbone (e.g., HRNet-W32)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": "Qualitative evaluation. Several results of 3D human mesh reconstructions for Human3.6M and 3DPW datasets are shown in Fig. 6. Note that our results are reconstructed based on the upsampling matrix as used in [6] while other two methods, i.e., METRO [21] and Mesh Graphomer [22], utilized two linear layers to upsample coarse vertex points. We can see that the proposed method successfully estimates 3D human poses under various situations including real-world scenarios in outdoor scenes as well as the controlled environment. Specifically, previous methods have somewhat difficulties to estimate unusual poses, e.g., overlapping arms and bending, whereas the proposed method provides the well-fit 3D model for a given image. Moreover, the proposed method has a good ability to reconstruct 3D human meshes in occlusions due to the progressive attention masking scheme as shown in examples of the last row of Fig. 6. In particular, previous methods fail to infer the global orientation of the human body due to the fence in front of the target person, which leads to the significant performance drop for 3D human mesh reconstruction. In contrast, the proposed method shows the reliable performance with various occlusions (see third and fourth rows in Fig. 6). More examples for 3D human mesh reconstruction by the proposed method are shown in Fig. 7. Note that in" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 306, + 288, + 548, + 360 + ], + "blocks": [ + { + "bbox": [ + 306, + 288, + 548, + 360 + ], + "lines": [ + { + "bbox": [ + 306, + 288, + 548, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 288, + 548, + 360 + ], + "type": "table", + "html": "
Point-guided feature samplingProgressive attention maskingMPJPEPA-MPJPE
XX63.239.9
X✓61.240.8
✓X50.933.3
✓✓48.332.9
", + "image_path": "cc8b1bf5d5ba33d5c2b87a8e4c72ea8b7d25e7c71c1c9d0e04181fce22508e05.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 429, + 545, + 479 + ], + "blocks": [ + { + "bbox": [ + 305, + 367, + 546, + 401 + ], + "lines": [ + { + "bbox": [ + 305, + 367, + 546, + 401 + ], + "spans": [ + { + "bbox": [ + 305, + 367, + 546, + 401 + ], + "type": "text", + "content": "Table 2. Performance analysis of the proposed method according to changes in the network architecture based on the Human3.6M dataset (best results are shown in bold)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 429, + 545, + 479 + ], + "lines": [ + { + "bbox": [ + 307, + 429, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 307, + 429, + 545, + 479 + ], + "type": "table", + "html": "
MethodsMPJPEPA-MPJPE
Without attention masking50.933.3
Single attention masking49.133.5
Progressive attention masking (ours)48.332.9
", + "image_path": "ee1ebfaf3944ed71d6faaf26d640782e4e5824f82353366148bacb7ed7b2fe4c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 487, + 545, + 532 + ], + "lines": [ + { + "bbox": [ + 305, + 487, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 305, + 487, + 545, + 532 + ], + "type": "text", + "content": "Table 3. Performance analysis of the proposed method according to the attention masking scheme based on the Human3.6M dataset (best results are shown in bold). Note that " + }, + { + "bbox": [ + 305, + 487, + 545, + 532 + ], + "type": "inline_equation", + "content": "M = 1" + }, + { + "bbox": [ + 305, + 487, + 545, + 532 + ], + "type": "text", + "content": " is used for single attention masking." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 564, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 624 + ], + "type": "text", + "content": "put images are acquired by the smartphone. As can be seen, the proposed method performs well for various pictures of our daily life even with severe occlusions. Therefore, it is thought that the proposed method paves the way for 3D human mesh reconstruction under various environments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 634, + 406, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 406, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 406, + 646 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "In this subsection, we first demonstrate the comparative experimental results by changing the components of the proposed method based on the Human3.6M dataset. Table 2 shows the contribution of such components. As can be seen, the performance of 3D human mesh reconstruc" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "12886" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 59, + 212, + 224 + ], + "blocks": [ + { + "bbox": [ + 49, + 59, + 212, + 224 + ], + "lines": [ + { + "bbox": [ + 49, + 59, + 212, + 224 + ], + "spans": [ + { + "bbox": [ + 49, + 59, + 212, + 224 + ], + "type": "image", + "image_path": "74db5938a887a157a7cae7c4941110698bb9cf5109ee2b840de83ce198c20b72.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 546, + 257 + ], + "type": "text", + "content": "Figure 8. Several reconstruction results (3D joints (left) and 3D hand meshes (right)) by the proposed method for the FreiHAND [39] dataset. Note that the proposed method works robust to self-occlusions frequently occurring by complicated hand poses." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 59, + 380, + 224 + ], + "blocks": [ + { + "bbox": [ + 215, + 59, + 380, + 224 + ], + "lines": [ + { + "bbox": [ + 215, + 59, + 380, + 224 + ], + "spans": [ + { + "bbox": [ + 215, + 59, + 380, + 224 + ], + "type": "image", + "image_path": "9d944c1ba6135421a26d9e0f57dc5aec06fd239aa00459aa3968f8f0f57688b0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 381, + 59, + 545, + 224 + ], + "blocks": [ + { + "bbox": [ + 381, + 59, + 545, + 224 + ], + "lines": [ + { + "bbox": [ + 381, + 59, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 381, + 59, + 545, + 224 + ], + "type": "image", + "image_path": "4ca2278f5c717b3712828a486f1305eb38e2821efa0069c1b91a53703f7eda08.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "type": "text", + "content": "tion is significantly improved with our point-guided feature sampling scheme (MPJPE: " + }, + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "type": "inline_equation", + "content": "63.2 \\rightarrow 50.9" + }, + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "type": "text", + "content": ", PA-MPJPE: " + }, + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "type": "inline_equation", + "content": "39.9 \\rightarrow 33.3" + }, + { + "bbox": [ + 46, + 277, + 289, + 468 + ], + "type": "text", + "content": "). From this analysis, we can see that feature sampling at vertex-relevant positions even in the 2D space is effective for improving the performance of 3D human mesh reconstruction. In what follows, we also check the effect of our progressive attention masking and the corresponding result is shown in Table 3. Note that our point-guided feature sampling is applied for this experiment. By comparing ours with baseline (i.e., without masking) and single masking attention scheme [6], we can see that the progressive restriction strategy in defining the local connection is also helpful for improving the performance of 3D human mesh reconstruction. This tells us that the combination of our contributions makes the model be robust to complicated real-world environments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 479, + 174, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 174, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 174, + 491 + ], + "type": "text", + "content": "4.5. Generalization Ability" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 713 + ], + "type": "text", + "content": "In contrast to the model-based approach, the proposed method can be easily applied to other applications. To show the generalization ability of the proposed method, we conduct 3D hand mesh reconstruction based on the FreiHAND [39] dataset by changing the number of input tokens for the sequence of transformer encoders. Note that the number of vertices to be projected is set to 195 and those are upsampled to 778 via the same upsampling matrix used for 3D human mesh reconstruction. Several reconstruction results by the proposed method are shown in Fig. 8. We can see that the proposed method provides the reliable reconstruction results (i.e., 3D joints and 3D hand meshes) for various hand poses. In particular, self-occlusions by complicated relations between adjacent fingers are successfully handled in the proposed method. The result of the quantitative evaluation is also shown in Table 4. As can be seen, the proposed method shows the competitive performance on the FreiHAND dataset." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 275, + 548, + 367 + ], + "blocks": [ + { + "bbox": [ + 307, + 275, + 548, + 367 + ], + "lines": [ + { + "bbox": [ + 307, + 275, + 548, + 367 + ], + "spans": [ + { + "bbox": [ + 307, + 275, + 548, + 367 + ], + "type": "table", + "html": "
MethodsPA-MPVPEPA-MPJPEF@5mmF@15mm
Hasson et al. [10]13.2-0.4360.908
Boukhayma et al. [4]13.0-0.4350.898
FreiHAND [39]10.7-0.5290.935
I2LMeshNet [27]7.67.40.6810.973
Pose2Mesh [7]7.87.70.6740.969
METRO [21]6.76.80.7170.981
FastMETRO [6]-6.5-0.982
Ours6.66.10.7200.984
", + "image_path": "fc9bec706602c3ea8b2f0e5967330892dea1a04475aaf54179e5f2120903fbba.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 375, + 546, + 407 + ], + "lines": [ + { + "bbox": [ + 305, + 375, + 546, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 375, + 546, + 407 + ], + "type": "text", + "content": "Table 4. Performance comparisons of 3D hand mesh reconstruction based on the FreiHAND dataset (best results are shown in bold)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 427, + 378, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 378, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 378, + 439 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 628 + ], + "type": "text", + "content": "In this paper, we present a simple yet powerful method for 3D human mesh reconstruction from a single RGB image. The key idea of the proposed method is to alleviate heterogeneous modalities between input (i.e., color) and output (i.e., coordinate) by considering the correspondence of encoded features and 2D points projected from 3D vertices. Our point-guided feature sampling scheme is to sample vertex-relevant features based on the combination of the heatmap and encoded features. In addition, the proposed progressive attention masking scheme makes the model to be robust to occlusions by considering local connections of different levels through the sequence of transformer encoders. Experimental results on benchmark datasets show that the proposed method performs reliably for various real-world environments." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. This work was supported by Institute of Information & communications Technology Planning & Evaluation(IITP) grant funded by the Korea government(MSIT) (2021-0-02084, eXtended Reality and Volumetric media generation and transmission technology for immersive experience sharing in noncontact environment with a Korea-EU international cooperative research)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12887" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2D human pose estimation: New benchmark and state of the art analysis. 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Pattern Recog., pages 813-822, 2019. 8" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 48, + 691, + 287, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 691, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 48, + 691, + 287, + 713 + ], + "type": "text", + "content": "[40] Maoqing Tian Jianbo Liu Shuai Yi Hongsheng Li Ziniu Wan, Zhengjia Li. Encoder-decoder with multi-level attention for" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + }, + { + "bbox": [ + 328, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 328, + 72, + 545, + 95 + ], + "type": "text", + "content": "3D human shape and pose estimation. In Int. Conf. Comput. 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Given multiple images under unknown spatially-varying illuminations, our method can recover the detailed surface normal map of non-convex, non-Lambertian surfaces (Left). Our method even surpasses the level of detail provided by consumer 3-D scanners (Right)." + ], + "image_footnote": [], + "bbox": [ + 462, + 250, + 854, + 468 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 532, + 313, + 546 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we introduce SDM-UniPS, a groundbreaking Scalable, Detailed, Mask-free, and Universal Photometric Stereo network. Our approach can recover astonishingly intricate surface normal maps, rivaling the quality of 3D scanners, even when images are captured under unknown, spatially-varying lighting conditions in uncontrolled environments. We have extended previous universal photometric stereo networks to extract spatial-light features, utilizing all available information in high-resolution input images and accounting for non-local interactions among surface points. Moreover, we present a new synthetic training dataset that encompasses a diverse range of shapes, materials, and illumination scenarios found in real-world scenes. Through extensive evaluation, we demonstrate that our method not only surpasses calibrated, lighting-specific techniques on public benchmarks, but also excels with a significantly smaller number of input images even without object masks.", + "bbox": [ + 75, + 564, + 472, + 821 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 828, + 207, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Photometric stereo [52] aims to deduce the surface normal map of a scene by analyzing images captured from a fixed perspective under diverse lighting conditions. Until", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "very recently, all photometric stereo methods assumed their specific lighting conditions, which led to limitations in their applicability. For instance, methods that assumed directional lighting conditions (e.g., [20, 24, 25]) were unsuitable under natural illumination, and vice versa (e.g., [15, 38]).", + "bbox": [ + 496, + 532, + 890, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To overcome this limitation, the \"universal\" photometric stereo method (UniPS) [22] has been introduced, designed to operate under unknown and arbitrary lighting conditions. In contrast to prior uncalibrated photometric stereo methods [7,9,27], which assumed specific physically-based lighting models, this method encodes a non-physical feature at each pixel for representing spatially-varying illumination, which is served as a substitute for physical lighting parameters within the calibrated photometric stereo network [21]. This method has taken the first step towards dealing with unknown, spatially-varying illumination that none of the existing methods could handle. However, the surface normal map recovered by UniPS, while not entirely inaccurate, appears blurry and lacks fine detail (see the top-right corner of Fig. 1). Upon investigation, we pinpointed three fundamental factors contributing to the subpar reconstruction performance. Firstly, extracting illumination", + "bbox": [ + 496, + 611, + 892, + 868 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 808, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Supported by JSPS KAKENHI Grant Number 22K17919.", + "bbox": [ + 522, + 886, + 830, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13198", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "features (i.e., global lighting contexts) from downsampled images caused a loss of information at higher input resolutions and produced blurry artifacts. Secondly, UniPS employs a pixel-wise calibrated photometric stereo network to predict surface normals using illumination features, which leads to imprecise overall shape recovery. Although pixelwise methods [20,21,25] offer advantages in capturing finer details compared to image-wise methods [8, 29, 49], they suffer from an inability to incorporate global information.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Lastly, the third issue lies in the limited variety of shape, material, and illumination conditions present in the training data, which hampers its capacity to adapt to a diverse range of real-world situations. This limitation primarily stems from the fact that current datasets (i.e., PS-Wild [22]) do not include renderings under light sources with high-frequency components focused on specific incident angles, such as point or directional sources. Consequently, the method exhibits considerable performance degradation when exposed to directional lighting setups like DiLiGenT [46], as will be demonstrated later in this paper.", + "bbox": [ + 75, + 227, + 470, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a groundbreaking photometric stereo network, the Scalable, Detailed, and Mask-Free Universal Photometric Stereo Network (SDM-UniPS), which recovers normal maps with remarkable accuracy from images captured under extremely uncontrolled lighting conditions. As shown in Fig. 1, SDM-UniPS is scalable, enabling the generation of normal maps from images with substantially higher resolution (e.g., 2048x2048) than the training data (e.g., 512x512); it is detailed, providing more accurate normal maps on DiLiGenT [46] with a limited number of input images than most existing orthographic photometric stereo techniques, including calibrated methods, and in some cases, surpassing 3D scanners in detail; and it is mask-free, allowing for application even when masks are absent, unlike many conventional methods. Our technical novelties include:", + "bbox": [ + 75, + 395, + 470, + 633 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. The development of a scale-invariant spatial-light feature encoder that efficiently extracts illumination features while utilizing all input data and maintaining scalability with respect to input image size. Our encoder, based on the \"split-and-merge\" strategy, accommodates varying input image sizes during training and testing without sacrificing performance.", + "2. The development of a surface normal decoder utilizing our novel pixel-sampling transformer. By randomly sampling pixels of fixed size, we simultaneously predict surface normals through non-local interactions among sampled pixels using Transformers [51], effectively accounting for global information.", + "3. The creation of a new synthetic training dataset, comprising multiple objects with diverse textures within a" + ], + "bbox": [ + 88, + 648, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "scene, rendered under significantly varied lighting conditions that include both low and high-frequency illuminations.", + "bbox": [ + 531, + 90, + 890, + 135 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We believe that the most significant contribution is the extraordinary time savings from data acquisition to normal map recovery compared to existing photometric stereo algorithms requiring meticulous lighting control, even in the uncalibrated setup. This progress allows photometric stereo to be executed at home, literally \"in the wild\" setup.", + "bbox": [ + 498, + 143, + 890, + 234 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 246, + 648, + 262 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we provide a succinct overview of photometric stereo literature focusing on the single orthographic camera assumption. Alternative setups (e.g., perspective, multi-view cameras) are beyond the scope of this work.", + "bbox": [ + 498, + 271, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Optimization-based Approach: The majority of photometric stereo methods assume calibrated, directional lighting following Woodham [52] and optimize parameters by inversely solving a physics-based image formation model. This approach can be further categorized into robust methods, where non-Lambertian components are treated as outliers [24, 39, 53, 59]; model-based methods, which explicitly account for non-Lambertian reflectance [13, 23, 45]; and example-based methods [17, 19, 47] that leverage the observations of known objects captured under identical conditions as the target scene. The uncalibrated task is akin to the calibrated one, but with unknown lighting parameters. Until recently, most uncalibrated photometric stereo algorithms assumed Lambertian integrable surfaces and aimed to resolve the General Bas-Relief ambiguity [4, 11, 12, 16, 36, 42, 44, 55]. In contrast to these works, photometric stereo under natural lights has also been explored, wherein natural illumination is approximated using spherical harmonics [5, 15], dominant sun lighting [3, 18], or equivalent directional lighting [14, 38]. Although most optimization-based methods do not require external training data, they are fundamentally limited in handling global illumination phenomena (e.g., inter-reflections) that cannot be described by the predefined point-wise image formation model.", + "bbox": [ + 498, + 335, + 892, + 699 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning-based Approach: Learning-based methods are effective in addressing complex phenomena that are challenging to represent within simple image formation models. However, the first photometric stereo network [43] necessitated consistent lighting conditions during both training and testing. To address this limitation, various strategies have been investigated, such as observation maps [20, 35], set-pooling [8, 26], graph-convolution [58], and self-attention [21, 31]. Furthermore, researchers have explored uncalibrated deep photometric stereo networks [7,9,27,50], where lighting parameters and surface normals are recovered sequentially. Self-supervised neural inverse rendering methods have been developed without the need for exter", + "bbox": [ + 498, + 704, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13199", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "nal data supervision. Taniai and Maehara [49] used neural networks instead of parametric physical models, with images and lighting as input. This work was expanded by Li and Li [29, 30], who incorporated recent neural coordinate-based representations [37]. However, despite their tremendous efforts, these methods are designed to work with only single directional light source and have limited ability to generalize to more complex lighting environments.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Universal Photometric Stereo Network: The universal photometric stereo network (UniPS) [22] was the first to eliminate the prior lighting model assumption by leveraging a non-physical lighting representation called global lighting contexts. These global lighting contexts are recovered for each lighting condition through pixel-wise communication of hierarchical feature maps along the light-axis using Transformers [51]. During surface normal prediction, a single location is individually selected, and the network aggregates all the global lighting contexts (bilinearly interpolated from the canonical resolution) and raw observations at the location under different lighting conditions to pixel-wise predict the surface normal. This method introduced two strategies to handle high-resolution images: down-sampling images to the canonical resolution for recovering global lighting contexts, and employing pixel-wise surface normal prediction. Although these two concepts contributed to the scalability of image size, they resulted in performance degradation due to the loss of input information and the absence of a non-local perspective, as previously discussed.", + "bbox": [ + 75, + 215, + 472, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work draws inspiration from [22] and shares some fundamental ideas, particularly the use of Transformers [51] for communicating and aggregating features along the light-axis. However, our method diverges from [22] by fully utilizing input information in a non-local manner, which leads to a significant enhancement in reconstruction quality.", + "bbox": [ + 75, + 520, + 470, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 630, + 169, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We target the challenging universal photometric stereo task, which was recently introduced in [22]. Unlike prior calibrated and uncalibrated tasks, the universal task makes no assumptions about surface geometry, material properties, or, most importantly, lighting conditions. The objective of this task is to recover a normal map $N \\in \\mathbb{R}^{H \\times W \\times 3}$ from images $I_k \\in \\mathbb{R}^{H \\times W \\times 3}$ ; $k \\in 1, \\ldots, K$ captured under $K$ unknown lighting conditions using an orthographic camera. Optionally, an object mask $M \\in \\mathbb{R}^{H \\times W}$ may be provided.", + "bbox": [ + 75, + 657, + 468, + 792 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method (SDM-UniPS) is illustrated in Fig. 2. Given pre-processed images and an optional object mask, feature maps for each lighting condition are extracted through interactions along the spatial and light axes (i.e., the scale-invariant spatial-light feature encoder). We then randomly sample locations from the coordinate system of the input image and bilinearly interpolate features at these locations.", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Features and raw observations at each location are aggregated pixel-wise, and surface normals are recovered from the aggregated features after non-local spatial interaction among them (i.e., the pixel-sampling Transformer). In line with [22], we focus on describing high-level concepts rather than providing detailed explanations for the sake of clarity. Refer to the appendix for a comprehensive description of the network architectures.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. SDM-UniPS", + "text_level": 1, + "bbox": [ + 498, + 223, + 632, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pre-processing: As in [22], we resize or crop input images to a resolution $(R)$ that is divisible by 32, which is accepted by most hierarchical vision backbones. To ensure that image values are within a similar range, each image is normalized by a random value between its maximum and mean.", + "bbox": [ + 496, + 247, + 893, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scale-invariant Spatial-light Feature Encoder: After the pre-processing, we extract feature maps from images and an optional object mask through the interaction along both spatial and light axes. Following the basic framework in [22], each image and object mask $^1$ are concatenated to form a tensor $O_{k}\\in \\mathbb{R}^{R\\times R\\times 4}$ , which is then input to the common vision backbone [32-34] to extract hierarchical feature maps $B_{k}^{s}\\in \\mathbb{R}^{\\frac{R}{S_{s}}\\times \\frac{R}{S_{s}}\\times C_{s}}; s\\in 1,2,3,4$ . Here, $S_{s}\\in 4,8,16,32$ represents the scale of the $s$ -th feature map, and $C_s$ is the dimension of features at that scale. For each feature scale, features from different tensors at the same pixel interact with each other along the light-axis using naive Transformers [51]. Finally, hierarchical feature maps are fused to $\\mathcal{F}_k\\in \\mathbb{R}^{\\frac{R}{4}\\times \\frac{R}{4}\\times C_{\\mathcal{F}}}$ using the feature pyramid network [56], where $C_{\\mathcal{F}}$ is the output feature dimension. Note that, unlike [22], we used a varying number of Transformer blocks at each hierarchy scale (i.e., the number of blocks changes from [1,1,1,1] to [0,1,2,4]) so that the deeper features interact more than the shallow ones.", + "bbox": [ + 496, + 327, + 893, + 616 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In UniPS [22], images and a mask are down-sampled to a canonical resolution before being input to the backbone network. This resolution must be constant and sufficiently small (e.g., 256x256) to prevent excessive memory consumption during feature extraction, particularly when dealing with high-resolution input images. Additionally, using a constant resolution ensures that tensors of the same shape are fed to the backbone, which helps to avoid significant performance degradation due to a large discrepancy in input tensor shapes between training and testing. Consequently, down-sampling leads to the loss of much information in the input images, resulting in a blurry normal map recovery.", + "bbox": [ + 496, + 617, + 893, + 797 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address it, we propose a scale-invariant spatial-light feature encoder designed to maintain a consistent, small input resolution for the backbone network while preserving information from input images. Specifically, instead of downsampling, we suggest splitting the input tensor into", + "bbox": [ + 496, + 799, + 893, + 875 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "Without a mask, a matrix with all values set to one is concatenated.", + "bbox": [ + 517, + 886, + 879, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13200", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/03eb7148fb0065bd07edd4747c903964972abafc95351dca812fad8dbfd10c83.jpg", + "image_caption": [ + "(b) Scale-invariant Spatial-light Feature Encoder", + "Figure 2. Our entire framework is illustrated in (a). Given multiple images and an object mask (optional), the scale-invariant spatial-light encoder (detailed in (b)) extracts a feature map for each image. The surface normal vectors are independently recovered at each of pixel samples (i.e., 2048) after the non-local interaction among aggregated features from interpolated feature maps and raw observations." + ], + "image_footnote": [], + "bbox": [ + 114, + 85, + 857, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "non-overlapping sub-tensors with a constant, small resolution. In greater detail, we decompose $O$ into $P^2$ sub-tensors of size $G \\times G$ ( $G = 256$ in our implementation, $P \\triangleq R / G$ ) by taking a single sample from every $P \\times P$ pixel and stacking them as sub-tensors, as illustrated in Fig. 2. Each sub-tensor encompasses the entire portion of the original tensor but is slightly shifted. All sub-tensors are processed independently through the same spatial-light feature encoder and subsequently merged back into a tensor of size $\\left(\\frac{R}{4} \\times \\frac{R}{4} \\times C_{\\mathcal{F}}\\right)$ . The combined feature maps from the sub-tensors retain all input information since no downsampling occurred. However, the absence of interaction among different sub-tensors leads to significant block artifacts, particularly when $P$ is large. To mitigate this, another feature map encoded from the naively downsized image is added to the merged feature maps, promoting interaction among sub-tensors. Optionally, when $P$ is larger than 4, we apply depth-wise Gaussian filtering (i.e., kernel size is $P-1$ ) to the feature maps to further enhance the interaction. Finally, we obtain the scale-invariant spatial-light feature maps $\\mathcal{F}_k \\in \\mathbb{R}^{\\frac{R}{4} \\times \\frac{R}{4} \\times C_{\\mathcal{F}}}$ for every lighting condition.", + "bbox": [ + 75, + 453, + 472, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Non-local Interaction with Pixel-sampling Transformer: Given the scale-invariant spatial-light feature maps $\\mathcal{F}_k$ and input images $I_{k}$ , the surface normal is recovered after pixelwise feature aggregation along the light-axis (i.e., the light channel shrinks from $K$ to 1). Feature aggregation under different lighting conditions is a fundamental step in pho", + "bbox": [ + 75, + 775, + 468, + 867 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tometric stereo networks, and various strategies have been studied, such as observation maps [20, 35], max-pooling [8, 9], graph-convolution [58], and self-attention [21, 22]. We utilize the Transformer model with self-attention [51] as in the encoder following UniPS [22]. UniPS directly predicted surface normals from pixel-wise aggregated feature vectors, following other pixel-wise methods [20, 21, 25], without considering non-local interactions. However, aggregated features lose lighting-specific information, naturally obtaining lighting-invariant representations more related to surface attributes than those before aggregation. In traditional physics-based vision tasks, common constraints including isotropy [4], reciprocity symmetry [48], reflectance monotonicity [6], sparse reflectance basis [13], and surface integrability [41] are mostly shared on the surface, not limited to a single surface point. Thus, considering non-local interactions of aggregated features at multiple surface points is crucial in physics-based tasks.", + "bbox": [ + 496, + 453, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Applying image-wise neural networks like CNNs on the aggregated feature map demands enormous computational cost for large output resolutions (e.g., $2048 \\times 2048$ ), and risks compromising output normal map details. To address these issues, we draw inspiration from recent Transformers on 3-D points [54, 61] and apply a Transformer on a fixed number ( $m$ ) of pixel samples (e.g., $m = 2048$ ) from random locations in the input coordinate system. We term this the pixel-sampling Transformer. Unlike image-based approaches, pixel-sampling Transformer's memory consumption is constant per sample set, scaling to arbitrary image", + "bbox": [ + 496, + 734, + 892, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2Concatenation is also possible, but it did not improve the results despite increased memory consumption.", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13201", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e7f4b87a29b4ada8ec660ee722f8ee86234e0fa374370b2302043d8318e0dbe2.jpg", + "image_caption": [ + "Directional" + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 156, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b23782ef88923a2c44bb73c14d1f258a0aeb3a96bbcb784ee02f4b7abaca0bc4.jpg", + "image_caption": [ + "Point" + ], + "image_footnote": [], + "bbox": [ + 158, + 90, + 235, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d1292f24f8010662ce278cb2f45b9cb3f6b84402453045f20fa0e4fff7c6354c.jpg", + "image_caption": [ + "Environment", + "Figure 3. Examples in PS-Mix under different lighting conditions." + ], + "image_footnote": [], + "bbox": [ + 236, + 90, + 315, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/87aaee488779ebd162eb862baf3c9f16fece23fac3504307321627db407ce625.jpg", + "image_caption": [ + "Dir.+Env." + ], + "image_footnote": [], + "bbox": [ + 316, + 90, + 395, + 150 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9610746d3cde8d6832be60c51e4bd990a94e06428920f4cd2c1cd60d3e32335f.jpg", + "image_caption": [ + "Point+Env." + ], + "image_footnote": [], + "bbox": [ + 397, + 90, + 475, + 150 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sizes. Moreover, by applying the Transformer to a randomly sampled set of locations, local interactions that may lead to over-smoothing of feature maps (e.g., in CNNs) are almost entirely eliminated.", + "bbox": [ + 75, + 188, + 468, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Concretely, given $m$ random pixels $x_{i = 1,\\dots,m}$ from the masked region of the input coordinate system, we interpolate features at those pixels as $\\mathcal{F}_{1,\\dots,K}(\\mathcal{S}(x_i))$ , where $\\mathcal{S}$ is the bilinear interpolation operator. Then, interpolated features are concatenated with corresponding raw observations $I_{1,\\dots,K}(x_i)$ and aggregated to $\\mathcal{A}(x_i)$ with pooling by multihead attention (PMA) [28], as in [22]. Given aggregated features at different pixels in the same sample set, we apply another naive Transformer [51] to perform non-local interactions. Since the goal of this process is to consider surface-level interactions based on physical attributes, pixel coordinate information is unnecessary. Thus, we don't apply position embeddings to samples, unlike most existing visual Transformer models (e.g. [10,33]), allowing the samples to propagate their aggregated features without location information.", + "bbox": [ + 75, + 250, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the non-local interaction, we apply a two-layer MLP to predict surface normals at sampled locations. Finally, surface normals for each set are merged to obtain the final surface normal map at the input image resolution. This pixel-sampling Transformer approach facilitates non-local interactions while maintaining computational efficiency and preserving output normal map details, making it suitable for physics-based tasks with high-resolution images.", + "bbox": [ + 75, + 491, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. PS-Mix Dataset", + "text_level": 1, + "bbox": [ + 76, + 619, + 233, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train their universal photometric stereo network, Ikehata [22] presented the PS-Wild training dataset, which rendered more than 10,000 scenes with commercial AdobeStock 3-D assets [1]. One of the issues in PS-Wild is that each scene consists of only a single object of uniform material. Furthermore, the environment lighting used for rendering scenes in [22] rarely has high-frequency illumination (e.g., a single point light source); therefore, the rendered images are biased towards low-frequency lighting conditions.", + "bbox": [ + 75, + 643, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this paper, we create a new training dataset that solves the issues in the PS-Wild training dataset. Instead of putting a single object of uniform material in each scene, we put multiple objects that overlap with each other in the same scene and give them different materials. To ensure that the material category is diverse in a scene, we manually categorized 897 texture maps in the AdobeStock material assets into 421 diffuse, 219 specular, and 257 metallic textures.", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/0d398a5eae2d45d6232b0e6f228f99175bab7a0dbabf373d7e1713a37ed09920.jpg", + "table_caption": [ + "Table 1. Ablation study on PS-Wild-Test [22]." + ], + "table_footnote": [], + "table_body": "
MethodTrainingDir.HDRIDir.+HDRI
I22 (UniPS) [22]PS-Wild17.014.513.8
Only Local (baseline)PS-Mix8.414.711.8
+Non-local (32)PS-Mix7.814.910.8
+Non-local (128)PS-Mix6.213.08.9
+Non-local (512)PS-Mix5.812.48.2
+Non-local (2048)PS-Mix5.712.28.0
+Non-local (20480)PS-Mix5.712.38.0
+Scale-invariant Enc.PS-Mix4.811.17.5
", + "bbox": [ + 517, + 103, + 870, + 250 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b08f8e6564920198be22795b0d760a967b97ee484a5cf7a6b284a9e737087bbe.jpg", + "image_caption": [ + "Local (1) MAE $= 21.3^{\\circ}$ $\\mathrm{K} = 16$" + ], + "image_footnote": [], + "bbox": [ + 511, + 265, + 622, + 318 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5f748a62090526a1daa62a3baa64d3a16e37461c8c38f759db26939d2f14e546.jpg", + "image_caption": [ + "Non-local (32) MAE=15.0°, K=16" + ], + "image_footnote": [], + "bbox": [ + 640, + 265, + 751, + 318 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6bc0f6a573acab3cd8847c0e202427fdc81f210cb7ec4022e1d11c68e1baec4d.jpg", + "image_caption": [ + "Non-local (2048) MAE=10.8,K=16" + ], + "image_footnote": [], + "bbox": [ + 769, + 263, + 887, + 318 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3317ca5a66f381f619846a429dcde903a1e0983e39d5605d3f542aeb3e4b7837.jpg", + "image_caption": [ + "(a) Different sample size $(m)$ for the non-local interaction", + "$\\mathrm{G_{Test} / G_{Train} = 6}$", + "MAE=20.4°, K=16" + ], + "image_footnote": [], + "bbox": [ + 509, + 351, + 622, + 404 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/269fd52fbfe9fad1826f02c03db7eb70021c767e247396e4cf73c8df719f4098.jpg", + "image_caption": [ + "$\\mathrm{G_{Test} / G_{Train} = 3}$", + "MAE=12.5°, K=16" + ], + "image_footnote": [], + "bbox": [ + 638, + 351, + 754, + 405 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d4e8c8a5b131a0ad7e197efc62517eafddf3193fdb61596d991a53ef810e453f.jpg", + "image_caption": [ + "$\\mathrm{G_{Test} / G_{Train} = 1}$", + "MAE $= 10.8^{\\circ}$ $\\mathrm{K} = 16$", + "(b) Different input resolutions between training and test", + "Figure 4. (a) Comparison of different sample size $(m)$ for the nonlocal interaction in the normal prediction. (b) Comparison of different input resolutions to the encoder between training and test." + ], + "image_footnote": [], + "bbox": [ + 767, + 351, + 887, + 406 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each scene, we randomly select four objects from 410 AdobeStock 3-D models and assign three textures from all three material categories and randomly choose one for each object. Furthermore, to make the lighting conditions more diverse, instead of using only environment lighting to render images, we use five types of light source configurations and mix them to render one scene; (a) environment lighting, (b) single directional lighting, (c) single point lighting, (d) $(\\mathrm{a}) + (\\mathrm{b})$ , and (e) $(\\mathrm{a}) + (\\mathrm{c})$ . The direction and position of light sources are randomly assigned within the valid range of parameters3. We followed PS-Wild [22] for other rendering techniques (e.g., auto-exposure, object scale adjustment). Our dataset consists of 34,921 scenes, and each scene is rendered to output 10 of 16-bit, $512 \\times 512$ images. In Fig. 3, we show sample images under each lighting condition for the same scene.", + "bbox": [ + 496, + 505, + 890, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Results", + "text_level": 1, + "bbox": [ + 500, + 762, + 584, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Details: Our network was trained on the PS-Mix dataset from scratch using the AdamW optimizer and a step decay learning rate schedule ( $\\times 0.8$ every ten epochs) with learning-rate warmup during the first epoch. A batch size of 8, an initial learning rate of 0.0001, and a weight", + "bbox": [ + 496, + 787, + 890, + 864 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "3Light directions are selected from the upper unit hemisphere, and point light positions are selected inside the hemisphere.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13202", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/af83b276dd0f6cef471b0555d7dd1000c4774cca31d577886b822ac0158b1bf8.jpg", + "table_caption": [ + "Table 2. Evaluation on DiLiGenT [46] (Mean Angular Errors in degrees). All 96 images were used except where K is shown." + ], + "table_footnote": [], + "table_body": "
MethodApproachTaskBallBearBuddhaCatCowGobletHarvestPot1Pot2ReadingAve.
Woodham [52]Self-Sup.Calibrated4.18.414.98.425.618.530.68.414.719.815.3
IW14 [25]Self-Sup.Calibrated2.04.88.45.413.38.718.96.910.212.09.1
IA14 [23]Self-Sup.Calibrated3.37.110.56.713.19.726.06.68.814.210.6
I18 [20]SupervisedCalibrated2.24.17.94.68.07.314.05.46.012.67.2
CW20 [9]SupervisedCalibrated2.77.77.54.86.77.812.46.27.210.97.4
LB21 [35]SupervisedCalibrated2.03.57.64.34.76.713.34.95.09.86.2
LL22a [29]Sup.+Self-Sup.Calibrated2.43.68.04.94.76.714.96.05.08.86.5
CH19 [7]SupervisedUncalibrated2.86.99.08.18.511.917.48.17.514.99.5
CW20 [9]SupervisedUncalibrated2.55.68.67.97.89.616.27.27.114.98.7
KK21 [27]Sup.+Self-Sup.Uncalibrated3.86.013.17.910.911.925.58.810.218.211.6
LL22b [30]Sup.+Self-Sup.Uncalibrated1.23.89.34.75.57.114.66.76.510.57.0
TR22 [50] (K=2)Self-Sup.Uncalibrated6.39.714.59.911.114.226.110.712.119.913.4
I22 (UniPS) [22]SupervisedUniversal4.99.119.413.011.624.225.210.89.918.814.7
OursSupervisedUniversal1.53.67.55.44.58.510.24.74.18.25.8
Ours (K=64)SupervisedUniversal1.53.67.65.54.68.610.24.74.18.35.9
Ours (K=32)SupervisedUniversal1.53.67.75.54.78.610.44.84.28.45.9
Ours (K=16)SupervisedUniversal1.53.87.76.04.88.510.84.94.48.76.1
Ours (K=8)SupervisedUniversal1.64.08.26.35.28.411.55.24.89.46.5
Ours (K=4)SupervisedUniversal1.74.110.08.66.39.014.16.15.911.47.7
Ours (K=2)SupervisedUniversal1.96.814.413.68.312.821.29.09.216.911.4
", + "bbox": [ + 99, + 103, + 867, + 430 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "decay of 0.05 were used. The number of input training images was randomly selected from 3 to 6 for each batch ${}^{4}$ . In our work,we chose ConvNeXt-T [34] as our backbone due to its simplicity and efficiency, which is better than recent ViT-based architectures [10,32,33] with comparable performance. The training loss was the MSE loss, which computes the ${\\ell }_{2}$ errors between the prediction and ground truth of surface normal vectors. Additional information, such as network architectures and feature dimensions, is provided in the appendix.", + "bbox": [ + 75, + 445, + 468, + 595 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation and Time: The accuracy is evaluated based on the mean angular errors (MAE) between the predicted and true surface normal maps, measured in degrees. Training is conducted on four NVIDIA A100 cards for roughly three days. The inference time of our method depends on the number and resolution of input images. In the case of 16 input images at a resolution of $512 \\times 512$ , it takes a few seconds excluding I/O on a GPU. While the computational cost will vary almost linearly with the number of images, this is significantly more efficient than recent neural inverse rendering-based methods [29, 30, 40, 60].", + "bbox": [ + 75, + 611, + 468, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 789, + 232, + 806 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Firstly, we perform ablation studies to evaluate the individual contributions of our scale-invariant spatial-light feature encoder and non-local interaction with pixel-sampling transformer across varying sample sizes. To quantitatively", + "bbox": [ + 76, + 813, + 468, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "compare performance under various lighting conditions, we utilize the PS-Wild-Test dataset [22], which contains 50 synthetic scenes rendered under three distinct lighting setups: directional, environmental, and a mixture of both. In Table 1 and Fig. 4, we compare our method with different configurations against [22]. Note that without the scale-invariant encoder and non-local interaction (i.e., the baseline), our method is nearly equivalent to [22], except for some minor differences (e.g., backbone architecture, number of Transformer blocks in the encoder). We observe that the baseline method trained on our PX-Mix dataset improves performance for scenes under directional lighting, suggesting that one of the primary reasons why [22] was ineffective under directional lights was due to bias in the PS-Wild dataset. Accounting for non-local interaction of aggregated features enhances reconstruction accuracy, even with a small number of samples (e.g., $m = 32$ ), as clearly illustrated in Fig. 4-(top). Although accuracy improved as the number of samples increased, as expected, performance gains plateaued beyond a certain number (i.e., $m = 2048$ ). The efficacy of the scale-invariant spatial-light feature encoder was also confirmed. In Fig. 4-(bottom), we observed that a significant difference in input resolution to the backbone between training and testing led to substantial performance degradation, which further validates the advantage of our method that maintains a constant input tensor shape.", + "bbox": [ + 496, + 445, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "$^4$ Six is the maximum number that can fit on our GPU.", + "bbox": [ + 94, + 886, + 380, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13203", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2b363eef1580f487fb7f6257a4d43d799588463de46dfdffde07ca65c1667d86.jpg", + "image_caption": [ + "Figure 5. Results for objects under a single directional lighting condition, including object masks." + ], + "image_footnote": [ + "Input" + ], + "bbox": [ + 81, + 89, + 148, + 265 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f237004909944f36773ad498baef00ffd0c6b872c84b29417bafd1f80da360bc.jpg", + "image_caption": [], + "image_footnote": [ + "Ground Truth" + ], + "bbox": [ + 148, + 90, + 209, + 265 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b4e32eb433e7d5f212c3f9e72d3dac04730255eb2f203d970eb4b9540c232079.jpg", + "image_caption": [], + "image_footnote": [ + "Ours $(\\mathrm{K} = 16)$" + ], + "bbox": [ + 209, + 90, + 277, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03c19c07ab63e0105a3992d69e46504a5e8a8f85114cd80c201703c088c97ecb.jpg", + "image_caption": [], + "image_footnote": [ + "I22 $(\\mathrm{K} = 96)$" + ], + "bbox": [ + 279, + 90, + 341, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4a7d354a5e7c0e3d48ff390eaaab7934fd4a04bcd14b9a02dffc4c9303c1f35a.jpg", + "image_caption": [], + "image_footnote": [ + "LL22a $(\\mathrm{K} = 96)$ LB21 $(\\mathrm{K} = 96)$" + ], + "bbox": [ + 341, + 90, + 405, + 263 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/59a74b4282d02e6d7735f630f2733a7cc1ac43d1f62c4c90eae386e3390b4392.jpg", + "image_caption": [], + "image_footnote": [ + "Calibrated" + ], + "bbox": [ + 410, + 90, + 472, + 263 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation under Directional Lighting", + "text_level": 1, + "bbox": [ + 76, + 335, + 406, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "DiLiGenT Evaluation: We first evaluate our method on the DiLiGenT benchmark [46]. Each dataset provides 96 612x512 16-bit HDR images, captured under known single directional lighting. The object mask and true surface normal map are available. In addition to UniPS [22], we also compare our method with calibrated [9,20,23,25,29,35,52] and uncalibrated [7,9,27,30,50] photometric stereo algorithms specifically designed for single directional lighting. Calibrated methods include both pixelwise [20,23,25,35,52] and image-wise [9,29] approaches. All uncalibrated methods are image-wise. We consider [27,29,30] as a combination of supervised and unsupervised learning, as pretrained models were used as a starting point for lighting prediction. To evaluate the valid number of input images, we compare our method with different numbers of input images (results are averaged over 10 random trials).", + "bbox": [ + 75, + 367, + 468, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results are illustrated in Table 2. Impressively, our method, which does not assume a specific lighting model, outperforms state-of-the-art calibrated methods designed for directional lights (LB21 [35], LL22a [29]). Furthermore, unlike conventional photometric stereo methods, the proposed method does not experience significant performance degradation even when the number of input images is reduced; it maintains state-of-the-art results even with only 8 images. The proposed method ( $K = 2$ ) also surpasses TR22 [50], which is specialized for two input images.", + "bbox": [ + 75, + 611, + 468, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Recovered normal maps of HARVEST and READING are shown in Fig. 5. These objects are considered the most challenging in the benchmark due to their highly nonconvex geometry. As expected, the state-of-the-art pixelwise calibrated method (LB21 [35]) can recover finer surface details, while the state-of-the-art image-wise calibrated method (LL22a [29]) can recover more globally consistent results. However, both of them struggle to recover the nonconvex parts of the objects accurately. On the other hand,", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/79e6e0edd17f2dce0f84fe01f8159e23fc4a7171d433755ecca822a334ab51fa.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 594, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/07ffc5ef5610ffd3844de7fb527ce3a6a4f5185c6e30428363a4b05f5aa89f88.jpg", + "image_caption": [ + "Ours $(\\mathrm{K} = 8)$" + ], + "image_footnote": [], + "bbox": [ + 602, + 90, + 696, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/072a176d347428b985ec46c47be7c0a2c8706c843ca651e486793001cd2e7719.jpg", + "image_caption": [ + "CW20 (K=64)" + ], + "image_footnote": [], + "bbox": [ + 705, + 90, + 797, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/79e23c58a7298e17df764322c5ce807d9a8ed5505560669d8d74e1b8aa6276d3.jpg", + "image_caption": [ + "LL22b (K=64)" + ], + "image_footnote": [], + "bbox": [ + 805, + 90, + 898, + 229 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c35435278f6141e0016cb7a4743c368a850034f9466c35d7baa7e50fc39d734a.jpg", + "image_caption": [ + "Deep relighting dataset (w/o object masks)", + "Input", + "Ground Truth", + "DiLiGenT dataset (w/o object masks)", + "Figure 6. Results for scenes under a single directional lighting condition, excluding object masks." + ], + "image_footnote": [], + "bbox": [ + 501, + 255, + 653, + 372 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/23e4061184d8e732dca0130d73da6259c0673e29c4a08fda1fe303c36e859927.jpg", + "image_caption": [ + "Ours (K=16)" + ], + "image_footnote": [], + "bbox": [ + 663, + 255, + 736, + 371 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0c671d3fe40069edf52fc00a9fe7f9c24188c2beeeb1693ad3ab037bd9636108.jpg", + "image_caption": [ + "CW20 $(\\mathrm{K} = 96)$ LL22b $(\\mathrm{K} = 96)$" + ], + "image_footnote": [], + "bbox": [ + 738, + 255, + 816, + 371 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "our method can recover both surface details and overall shape without apparent difficulty, even with a much smaller number of images (i.e., $\\mathrm{K} = 16$ ). As expected, the performance of I22 [22] is severely lacking.", + "bbox": [ + 496, + 438, + 890, + 500 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation without Object Mask: To demonstrate that our method does not require an object mask, we applied it to two real scenes from a deep relighting work [57], each containing 530 8-bit integer images at a resolution of $512 \\times 512$ , captured under unknown single directional lighting using a gantry-based acquisition system. The object mask and true surface normal map are unavailable. We compared our method with state-of-the-art uncalibrated methods (CW20 [9] and LL22b [30]) and displayed the results in Fig. 6 (top). Unlike the uncalibrated methods that struggled to recover accurate lighting directions, our proposed method successfully captured object boundaries without masks, even in complex scenes with significant global illumination effects, and consistently recovered normals across the entire image. We further evaluated our method on DiLiGenT scenes without masks, as illustrated in Fig. 6 (bottom). While existing methods that assume an object mask produced highly inaccurate surface normal maps, our proposed method recovered more plausible normals with fewer images (i.e., $K = 16$ vs $K = 96$ ).", + "bbox": [ + 496, + 503, + 892, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Evaluation under Spatially-varying Lighting", + "text_level": 1, + "bbox": [ + 500, + 816, + 877, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method is evaluated on challenging scenes with spatially-varying lighting conditions, comparing it to the first universal network (UniPS) [22] and a state-of-the-art uncalibrated photometric stereo method (GM21) [14] on", + "bbox": [ + 496, + 839, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13204", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6fcc6cafcea278138d2b761f6c2e2d56e4d00a342e5f6973cd6f521585a42266.jpg", + "image_caption": [ + "Input", + "Figure 7. Qualitative comparison on images under spatially-varying lighting conditions with object masks [22]." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 181, + 340 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/74020c8a7d3d1152f6abec5a65959c4ed25e3e7f59525f87b518920e4c13083f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 184, + 90, + 281, + 170 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d6f1c892ed0a782b5aed389fe866cec8825efca61aa6a03694669afdca4fb0b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 170, + 277, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/adaba09cc3b88651ec3e6d10b09049542fb55c0efed35b32a68640d613ef90ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 284, + 90, + 377, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/22bde72a7b4342a72cc2bb6b359e5652aec6981ce7c57eb986cf7541eec9027a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 170, + 375, + 244 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7e4117c4dbac422af13548171baeff8dc24098d910fc5fb9085de0f838145bd9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 382, + 90, + 473, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0495516bb9431e8abd079a37de5457c47e41fad17f46cace7b5989c1b41ba153.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 380, + 170, + 472, + 247 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a dataset provided by [22]. We test three objects (Apple, Grape, and Owl). While GM21 [14] fails and I22 [22] loses details, our method, using a scale-invariant spatial-light feature encoder and non-local interaction, produces accurate results.", + "bbox": [ + 76, + 392, + 467, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 8, we subjectively compare our method using four objects with normal maps obtained from a 3D scanner. We align the scanned normal map to the image using MeshLab's mutual information registration filter [2], as in [46]. Our method recovers higher-definition surface normal maps than the 3D scanner (EinScan-SE) and performs well regardless of surface material. Photometric stereo performance improves with increased digital camera resolution, suggesting that 3D scanners may struggle to keep up.", + "bbox": [ + 75, + 468, + 467, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Lastly, we demonstrate surface normal prediction for complex non-convex scenes without masks under challenging lighting conditions in Figure 9. We apply our method to three extremely challenging datasets: School Desk, Coins and Keyboard, and Sweets. School Desk is a complex scene with simple objects, non-uniform lighting, and cast shadows, making surface normal map recovery difficult. Coins and Keyboard features multiple planar objects of various materials. Sweets is a challenging scene with abundant inter-reflections and cast shadows. As demonstrated, the proposed method successfully recovers uniform surface normals, largely unaffected by shadows, and effectively reconstructs the surface micro-shape, demonstrating its scalability and detail preservation.", + "bbox": [ + 75, + 604, + 467, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 829, + 194, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a scalable, detailed, and mask-free universal photometric stereo method. We demonstrated that the proposed method outperforms most cali", + "bbox": [ + 76, + 854, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e17fddbb44119501c8465ffd84d699a3fcf35fc1e7e0424ca69b12f469717390.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 90, + 602, + 142 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9265b689bfa372c968d7665a496d734fd6490fcfb86b55a36b76c783d17cf72d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 143, + 598, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2283449881851a29754cb49c9e5d17a5639eabb9ff6586d07fa76c3f9909b94c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 184, + 578, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1ec0b893bc37e0d43204a04cc8bf5dd8c873d8c62ccbb98156687da827898d4f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 215, + 599, + 273 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e6d2986e1cf3f0312a6751f4ac70519b8a403b5b7a485a1423437f81e988e924.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 90, + 691, + 142 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/64b1f8d6d0260f55ff82bd03a024632b039d73a5b6b52883b8b45d5a4dcf65a8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 606, + 143, + 696, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/04f3b67fd706b0897906e0107939da62ad3812c2fe266e9f2154bc994fff5977.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 184, + 674, + 214 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b137135b81c3be40f2cb07166ea60d859f792836a0eb988e302d70bbaa689803.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 606, + 215, + 700, + 273 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/af9af33e13cbf3e73cef84f3797272fe9e1c2a18f41e87065be3d24aaf1de897.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 90, + 792, + 141 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/201f0d6a107d626f7a33387b7d917d46b30b01af1f457f345eaca273de35880e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 142, + 790, + 212 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9fc8342b0cbfb1a4f52e4588f4ab9fc17b540105f5e7af5622bd2aafc006c0a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 215, + 795, + 273 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/029b47dc69e563486c45d4186162993a3d1c7b4b0865a7ab43ddc9ee0450e08d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 803, + 90, + 895, + 143 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0242d13127a40a173a914533e390bd905039d08423e4113e59359630578dbd3e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 145, + 895, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cc0939210db7c9191a8feadc405719c0031a32d59e3636196b360227ac79ac73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 803, + 217, + 895, + 273 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d0459cfc0798c83a52afd948cf700d077406b220c239b6efbb59acc42535c0f3.jpg", + "image_caption": [ + "Input $(\\mathrm{K} = 10)$" + ], + "image_footnote": [], + "bbox": [ + 803, + 280, + 895, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b1c0a412f4160217eb98842262ac07d6c7427ae781ff97ec46550d9686595638.jpg", + "image_caption": [ + "3D scanner", + "Ours (SDM-UniPS)", + "I22 (UniPS)" + ], + "image_footnote": [], + "bbox": [ + 503, + 276, + 797, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b80b9417ee0b77b7c902517ca77ae4e72cbb6ef39f549657e4185ba0ebad62c6.jpg", + "image_caption": [ + "Figure 8. Qualitative comparison with 3-D scans." + ], + "image_footnote": [], + "bbox": [ + 503, + 364, + 599, + 438 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a6d13a8b24f4ae90bad9f54b29711ef113abe8d6e0400dac4b8ec355c57b0ce0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 439, + 599, + 518 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9e2c3bb72781e844fa65f3545781987b11b546c31c2b7d4fbf259c1001deba59.jpg", + "image_caption": [ + "SDM-UniPS (Ours)", + "Figure 9. Surface normal recovery from images under spatially-varying lighting conditions without object masks." + ], + "image_footnote": [], + "bbox": [ + 503, + 518, + 599, + 597 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f5a7c67c0340bcfec18a39a453867e48ab9c619a6586923e4dede4cff7a02a91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 364, + 700, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/61e107d4241eb89d677822d401a6bf2abe34c894c9a2588eff0b9af3b4f3bf56.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 441, + 700, + 518 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bb9f5ced9bfeba6c7b3d0c3a59a3300acd7bbd72f6091f2868f4b56c72ef35a4.jpg", + "image_caption": [ + "UniPS (122)" + ], + "image_footnote": [], + "bbox": [ + 604, + 518, + 700, + 597 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c070e1be83b555597278983f0a0930ae2e0b444f4bed92856e01ac048f0db0d7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 364, + 898, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/abed45b6f45841621556e2ee1c39549545ee255c6be0bafe64a3dead37615267.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 441, + 898, + 518 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b8bbb0e076bbd38a00dd77110198803286d57703a0c6b1dc941642d41402cf7d.jpg", + "image_caption": [ + "Input (w/o object mask)" + ], + "image_footnote": [], + "bbox": [ + 702, + 518, + 898, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "brated and uncalibrated methods in the DiLiGenT benchmark. In addition, the comparison with the only existing method [22] for the universal task showed a significant improvement over it.", + "bbox": [ + 496, + 655, + 890, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, several challenges still remain. Firstly, although we have observed that the proposed method works robustly for versatile lighting conditions, we found that our method is not very effective when the lighting variations are minimal. Secondly, the proposed method can easily be extended beyond normal map recovery by replacing the loss and data. In reality, we have attempted to output BRDF parameters for materials. However, due to fundamental ambiguities, it is difficult to evaluate the recovered BRDF parameters. Please see the appendix for further discussions of these limitations and a variety of additional results to better understand this study.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13205", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adobe Stock. https://stock.adobe.com/.5", + "[2] Meshlab. https://wwwmeshlab.net/.8", + "[3] J. Ackermann, F. Langguth, S. Fuhrmann, and M. Goesele. Photometric stereo for outdoor webcams. In CVPR, 2012. 2", + "[4] N. Alldrin, S. Mallick, and D. Kriegman. Resolving the generalized bas-relief ambiguity by entropy minimization. CVPR, 2007. 2, 4", + "[5] Ronen Basri, David Jacobs, and Ira Kemelmacher. Photometric stereo with general, unknown lighting. 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Deep image-based relighting from optimal sparse samples. 2018. 7", + "[58] Z. Yao, K. Li, Y. Fu, H. Hu, and B. Shi. Gps-net: Graph-based photometric stereo network. NeurIPS, 2020. 2, 4", + "[59] C. Yu, Y. Seo, and S. Lee. Photometric stereo from maximum feasible lambertian reflections. In ECCV, 2010. 2", + "[60] Yuanqing Zhang, Jiaming Sun, Xinqyi He, Huan Fu, Rongfei Jia, and Xiaowei Zhou. Modeling indirect illumination for inverse rendering. CVPR, 2022. 6", + "[61] Hengshuang Zhao, Li Jiang, Jiaya Jia, Philip HS Torr, and Vladlen Koltun. Point transformer. In ICCV, pages 16259-16268, 2021. 4" + ], + "bbox": [ + 501, + 92, + 890, + 390 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13207", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Scalable, Detailed and Mask-Free Universal Photometric Stereo/b4164742-7be0-4231-ae8a-d7fbbefac394_model.json b/2023/Scalable, Detailed and Mask-Free Universal Photometric Stereo/b4164742-7be0-4231-ae8a-d7fbbefac394_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7c3066c71fd9a820beb9eaae487195ac20d42a52 --- /dev/null +++ b/2023/Scalable, Detailed and Mask-Free Universal Photometric Stereo/b4164742-7be0-4231-ae8a-d7fbbefac394_model.json @@ -0,0 +1,3003 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.809, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.163, + 0.131, + 0.806, + 0.152 + ], + "angle": 0, + "content": "Scalable, Detailed and Mask-Free Universal Photometric Stereo" + }, + { + "type": "title", + "bbox": [ + 0.334, + 0.182, + 0.637, + 0.216 + ], + "angle": 0, + "content": "Satoshi Ikehata \nNational Institute of Informatics (NII)" + }, + { + "type": "text", + "bbox": [ + 0.402, + 0.22, + 0.565, + 0.234 + ], + "angle": 0, + "content": "sikehata@nii.ac.jp" + }, + { + "type": "image", + "bbox": [ + 0.115, + 0.247, + 0.451, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.469, + 0.29, + 0.492 + ], + "angle": 0, + "content": "INPUT: Multiple images under varying unknown lighting conditions" + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.339, + 0.45, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.323, + 0.47, + 0.42, + 0.491 + ], + "angle": 0, + "content": "OUTPUT: Surface normal map" + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.25, + 0.856, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.453, + 0.47, + 0.574, + 0.482 + ], + "angle": 0, + "content": "Input image (1st out of 9)" + }, + { + "type": "image_caption", + "bbox": [ + 0.583, + 0.47, + 0.65, + 0.492 + ], + "angle": 0, + "content": "3D Scanner (EinScan-SE)" + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.47, + 0.732, + 0.491 + ], + "angle": 0, + "content": "SDM-UniPS (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.797, + 0.47, + 0.848, + 0.491 + ], + "angle": 0, + "content": "UniPS chata2022]" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.492, + 0.891, + 0.519 + ], + "angle": 0, + "content": "Figure 1. Given multiple images under unknown spatially-varying illuminations, our method can recover the detailed surface normal map of non-convex, non-Lambertian surfaces (Left). Our method even surpasses the level of detail provided by consumer 3-D scanners (Right)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.533, + 0.314, + 0.547 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.473, + 0.822 + ], + "angle": 0, + "content": "In this paper, we introduce SDM-UniPS, a groundbreaking Scalable, Detailed, Mask-free, and Universal Photometric Stereo network. Our approach can recover astonishingly intricate surface normal maps, rivaling the quality of 3D scanners, even when images are captured under unknown, spatially-varying lighting conditions in uncontrolled environments. We have extended previous universal photometric stereo networks to extract spatial-light features, utilizing all available information in high-resolution input images and accounting for non-local interactions among surface points. Moreover, we present a new synthetic training dataset that encompasses a diverse range of shapes, materials, and illumination scenarios found in real-world scenes. Through extensive evaluation, we demonstrate that our method not only surpasses calibrated, lighting-specific techniques on public benchmarks, but also excels with a significantly smaller number of input images even without object masks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.829, + 0.208, + 0.844 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Photometric stereo [52] aims to deduce the surface normal map of a scene by analyzing images captured from a fixed perspective under diverse lighting conditions. Until" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.534, + 0.892, + 0.61 + ], + "angle": 0, + "content": "very recently, all photometric stereo methods assumed their specific lighting conditions, which led to limitations in their applicability. For instance, methods that assumed directional lighting conditions (e.g., [20, 24, 25]) were unsuitable under natural illumination, and vice versa (e.g., [15, 38])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.893, + 0.869 + ], + "angle": 0, + "content": "To overcome this limitation, the \"universal\" photometric stereo method (UniPS) [22] has been introduced, designed to operate under unknown and arbitrary lighting conditions. In contrast to prior uncalibrated photometric stereo methods [7,9,27], which assumed specific physically-based lighting models, this method encodes a non-physical feature at each pixel for representing spatially-varying illumination, which is served as a substitute for physical lighting parameters within the calibrated photometric stereo network [21]. This method has taken the first step towards dealing with unknown, spatially-varying illumination that none of the existing methods could handle. However, the surface normal map recovered by UniPS, while not entirely inaccurate, appears blurry and lacks fine detail (see the top-right corner of Fig. 1). Upon investigation, we pinpointed three fundamental factors contributing to the subpar reconstruction performance. Firstly, extracting illumination" + }, + { + "type": "page_footnote", + "bbox": [ + 0.524, + 0.887, + 0.831, + 0.9 + ], + "angle": 0, + "content": "Supported by JSPS KAKENHI Grant Number 22K17919." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13198" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "features (i.e., global lighting contexts) from downsampled images caused a loss of information at higher input resolutions and produced blurry artifacts. Secondly, UniPS employs a pixel-wise calibrated photometric stereo network to predict surface normals using illumination features, which leads to imprecise overall shape recovery. Although pixelwise methods [20,21,25] offer advantages in capturing finer details compared to image-wise methods [8, 29, 49], they suffer from an inability to incorporate global information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.394 + ], + "angle": 0, + "content": "Lastly, the third issue lies in the limited variety of shape, material, and illumination conditions present in the training data, which hampers its capacity to adapt to a diverse range of real-world situations. This limitation primarily stems from the fact that current datasets (i.e., PS-Wild [22]) do not include renderings under light sources with high-frequency components focused on specific incident angles, such as point or directional sources. Consequently, the method exhibits considerable performance degradation when exposed to directional lighting setups like DiLiGenT [46], as will be demonstrated later in this paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.471, + 0.635 + ], + "angle": 0, + "content": "In this paper, we present a groundbreaking photometric stereo network, the Scalable, Detailed, and Mask-Free Universal Photometric Stereo Network (SDM-UniPS), which recovers normal maps with remarkable accuracy from images captured under extremely uncontrolled lighting conditions. As shown in Fig. 1, SDM-UniPS is scalable, enabling the generation of normal maps from images with substantially higher resolution (e.g., 2048x2048) than the training data (e.g., 512x512); it is detailed, providing more accurate normal maps on DiLiGenT [46] with a limited number of input images than most existing orthographic photometric stereo techniques, including calibrated methods, and in some cases, surpassing 3D scanners in detail; and it is mask-free, allowing for application even when masks are absent, unlike many conventional methods. Our technical novelties include:" + }, + { + "type": "text", + "bbox": [ + 0.091, + 0.649, + 0.47, + 0.755 + ], + "angle": 0, + "content": "1. The development of a scale-invariant spatial-light feature encoder that efficiently extracts illumination features while utilizing all input data and maintaining scalability with respect to input image size. Our encoder, based on the \"split-and-merge\" strategy, accommodates varying input image sizes during training and testing without sacrificing performance." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.767, + 0.469, + 0.858 + ], + "angle": 0, + "content": "2. The development of a surface normal decoder utilizing our novel pixel-sampling transformer. By randomly sampling pixels of fixed size, we simultaneously predict surface normals through non-local interactions among sampled pixels using Transformers [51], effectively accounting for global information." + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "3. The creation of a new synthetic training dataset, comprising multiple objects with diverse textures within a" + }, + { + "type": "list", + "bbox": [ + 0.089, + 0.649, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "scene, rendered under significantly varied lighting conditions that include both low and high-frequency illuminations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.144, + 0.892, + 0.235 + ], + "angle": 0, + "content": "We believe that the most significant contribution is the extraordinary time savings from data acquisition to normal map recovery compared to existing photometric stereo algorithms requiring meticulous lighting control, even in the uncalibrated setup. This progress allows photometric stereo to be executed at home, literally \"in the wild\" setup." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.247, + 0.65, + 0.263 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.272, + 0.892, + 0.332 + ], + "angle": 0, + "content": "In this section, we provide a succinct overview of photometric stereo literature focusing on the single orthographic camera assumption. Alternative setups (e.g., perspective, multi-view cameras) are beyond the scope of this work." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.337, + 0.893, + 0.7 + ], + "angle": 0, + "content": "Optimization-based Approach: The majority of photometric stereo methods assume calibrated, directional lighting following Woodham [52] and optimize parameters by inversely solving a physics-based image formation model. This approach can be further categorized into robust methods, where non-Lambertian components are treated as outliers [24, 39, 53, 59]; model-based methods, which explicitly account for non-Lambertian reflectance [13, 23, 45]; and example-based methods [17, 19, 47] that leverage the observations of known objects captured under identical conditions as the target scene. The uncalibrated task is akin to the calibrated one, but with unknown lighting parameters. Until recently, most uncalibrated photometric stereo algorithms assumed Lambertian integrable surfaces and aimed to resolve the General Bas-Relief ambiguity [4, 11, 12, 16, 36, 42, 44, 55]. In contrast to these works, photometric stereo under natural lights has also been explored, wherein natural illumination is approximated using spherical harmonics [5, 15], dominant sun lighting [3, 18], or equivalent directional lighting [14, 38]. Although most optimization-based methods do not require external training data, they are fundamentally limited in handling global illumination phenomena (e.g., inter-reflections) that cannot be described by the predefined point-wise image formation model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Learning-based Approach: Learning-based methods are effective in addressing complex phenomena that are challenging to represent within simple image formation models. However, the first photometric stereo network [43] necessitated consistent lighting conditions during both training and testing. To address this limitation, various strategies have been investigated, such as observation maps [20, 35], set-pooling [8, 26], graph-convolution [58], and self-attention [21, 31]. Furthermore, researchers have explored uncalibrated deep photometric stereo networks [7,9,27,50], where lighting parameters and surface normals are recovered sequentially. Self-supervised neural inverse rendering methods have been developed without the need for exter" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13199" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "nal data supervision. Taniai and Maehara [49] used neural networks instead of parametric physical models, with images and lighting as input. This work was expanded by Li and Li [29, 30], who incorporated recent neural coordinate-based representations [37]. However, despite their tremendous efforts, these methods are designed to work with only single directional light source and have limited ability to generalize to more complex lighting environments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.473, + 0.52 + ], + "angle": 0, + "content": "Universal Photometric Stereo Network: The universal photometric stereo network (UniPS) [22] was the first to eliminate the prior lighting model assumption by leveraging a non-physical lighting representation called global lighting contexts. These global lighting contexts are recovered for each lighting condition through pixel-wise communication of hierarchical feature maps along the light-axis using Transformers [51]. During surface normal prediction, a single location is individually selected, and the network aggregates all the global lighting contexts (bilinearly interpolated from the canonical resolution) and raw observations at the location under different lighting conditions to pixel-wise predict the surface normal. This method introduced two strategies to handle high-resolution images: down-sampling images to the canonical resolution for recovering global lighting contexts, and employing pixel-wise surface normal prediction. Although these two concepts contributed to the scalability of image size, they resulted in performance degradation due to the loss of input information and the absence of a non-local perspective, as previously discussed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.472, + 0.613 + ], + "angle": 0, + "content": "Our work draws inspiration from [22] and shares some fundamental ideas, particularly the use of Transformers [51] for communicating and aggregating features along the light-axis. However, our method diverges from [22] by fully utilizing input information in a non-local manner, which leads to a significant enhancement in reconstruction quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.631, + 0.17, + 0.647 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.794 + ], + "angle": 0, + "content": "We target the challenging universal photometric stereo task, which was recently introduced in [22]. Unlike prior calibrated and uncalibrated tasks, the universal task makes no assumptions about surface geometry, material properties, or, most importantly, lighting conditions. The objective of this task is to recover a normal map \\(N \\in \\mathbb{R}^{H \\times W \\times 3}\\) from images \\(I_k \\in \\mathbb{R}^{H \\times W \\times 3}\\); \\(k \\in 1, \\ldots, K\\) captured under \\(K\\) unknown lighting conditions using an orthographic camera. Optionally, an object mask \\(M \\in \\mathbb{R}^{H \\times W}\\) may be provided." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Our method (SDM-UniPS) is illustrated in Fig. 2. Given pre-processed images and an optional object mask, feature maps for each lighting condition are extracted through interactions along the spatial and light axes (i.e., the scale-invariant spatial-light feature encoder). We then randomly sample locations from the coordinate system of the input image and bilinearly interpolate features at these locations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.213 + ], + "angle": 0, + "content": "Features and raw observations at each location are aggregated pixel-wise, and surface normals are recovered from the aggregated features after non-local spatial interaction among them (i.e., the pixel-sampling Transformer). In line with [22], we focus on describing high-level concepts rather than providing detailed explanations for the sake of clarity. Refer to the appendix for a comprehensive description of the network architectures." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.224, + 0.633, + 0.24 + ], + "angle": 0, + "content": "3.1. SDM-UniPS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.248, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Pre-processing: As in [22], we resize or crop input images to a resolution \\((R)\\) that is divisible by 32, which is accepted by most hierarchical vision backbones. To ensure that image values are within a similar range, each image is normalized by a random value between its maximum and mean." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.895, + 0.617 + ], + "angle": 0, + "content": "Scale-invariant Spatial-light Feature Encoder: After the pre-processing, we extract feature maps from images and an optional object mask through the interaction along both spatial and light axes. Following the basic framework in [22], each image and object mask \\(^1\\) are concatenated to form a tensor \\(O_{k}\\in \\mathbb{R}^{R\\times R\\times 4}\\), which is then input to the common vision backbone [32-34] to extract hierarchical feature maps \\(B_{k}^{s}\\in \\mathbb{R}^{\\frac{R}{S_{s}}\\times \\frac{R}{S_{s}}\\times C_{s}}; s\\in 1,2,3,4\\). Here, \\(S_{s}\\in 4,8,16,32\\) represents the scale of the \\(s\\)-th feature map, and \\(C_s\\) is the dimension of features at that scale. For each feature scale, features from different tensors at the same pixel interact with each other along the light-axis using naive Transformers [51]. Finally, hierarchical feature maps are fused to \\(\\mathcal{F}_k\\in \\mathbb{R}^{\\frac{R}{4}\\times \\frac{R}{4}\\times C_{\\mathcal{F}}}\\) using the feature pyramid network [56], where \\(C_{\\mathcal{F}}\\) is the output feature dimension. Note that, unlike [22], we used a varying number of Transformer blocks at each hierarchy scale (i.e., the number of blocks changes from [1,1,1,1] to [0,1,2,4]) so that the deeper features interact more than the shallow ones." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.895, + 0.799 + ], + "angle": 0, + "content": "In UniPS [22], images and a mask are down-sampled to a canonical resolution before being input to the backbone network. This resolution must be constant and sufficiently small (e.g., 256x256) to prevent excessive memory consumption during feature extraction, particularly when dealing with high-resolution input images. Additionally, using a constant resolution ensures that tensors of the same shape are fed to the backbone, which helps to avoid significant performance degradation due to a large discrepancy in input tensor shapes between training and testing. Consequently, down-sampling leads to the loss of much information in the input images, resulting in a blurry normal map recovery." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.895, + 0.876 + ], + "angle": 0, + "content": "To address it, we propose a scale-invariant spatial-light feature encoder designed to maintain a consistent, small input resolution for the backbone network while preserving information from input images. Specifically, instead of downsampling, we suggest splitting the input tensor into" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.88, + 0.9 + ], + "angle": 0, + "content": "Without a mask, a matrix with all values set to one is concatenated." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "13200" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.087, + 0.859, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.357, + 0.375, + 0.63, + 0.387 + ], + "angle": 0, + "content": "(b) Scale-invariant Spatial-light Feature Encoder" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.392, + 0.893, + 0.435 + ], + "angle": 0, + "content": "Figure 2. Our entire framework is illustrated in (a). Given multiple images and an object mask (optional), the scale-invariant spatial-light encoder (detailed in (b)) extracts a feature map for each image. The surface normal vectors are independently recovered at each of pixel samples (i.e., 2048) after the non-local interaction among aggregated features from interpolated feature maps and raw observations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.473, + 0.773 + ], + "angle": 0, + "content": "non-overlapping sub-tensors with a constant, small resolution. In greater detail, we decompose \\(O\\) into \\(P^2\\) sub-tensors of size \\(G \\times G\\) (\\(G = 256\\) in our implementation, \\(P \\triangleq R / G\\)) by taking a single sample from every \\(P \\times P\\) pixel and stacking them as sub-tensors, as illustrated in Fig. 2. Each sub-tensor encompasses the entire portion of the original tensor but is slightly shifted. All sub-tensors are processed independently through the same spatial-light feature encoder and subsequently merged back into a tensor of size \\(\\left(\\frac{R}{4} \\times \\frac{R}{4} \\times C_{\\mathcal{F}}\\right)\\). The combined feature maps from the sub-tensors retain all input information since no downsampling occurred. However, the absence of interaction among different sub-tensors leads to significant block artifacts, particularly when \\(P\\) is large. To mitigate this, another feature map encoded from the naively downsized image is added to the merged feature maps, promoting interaction among sub-tensors. Optionally, when \\(P\\) is larger than 4, we apply depth-wise Gaussian filtering (i.e., kernel size is \\(P-1\\)) to the feature maps to further enhance the interaction. Finally, we obtain the scale-invariant spatial-light feature maps \\(\\mathcal{F}_k \\in \\mathbb{R}^{\\frac{R}{4} \\times \\frac{R}{4} \\times C_{\\mathcal{F}}}\\) for every lighting condition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.776, + 0.47, + 0.868 + ], + "angle": 0, + "content": "Non-local Interaction with Pixel-sampling Transformer: Given the scale-invariant spatial-light feature maps \\(\\mathcal{F}_k\\) and input images \\(I_{k}\\), the surface normal is recovered after pixelwise feature aggregation along the light-axis (i.e., the light channel shrinks from \\(K\\) to 1). Feature aggregation under different lighting conditions is a fundamental step in pho" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.901 + ], + "angle": 0, + "content": "2Concatenation is also possible, but it did not improve the results despite increased memory consumption." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.892, + 0.726 + ], + "angle": 0, + "content": "tometric stereo networks, and various strategies have been studied, such as observation maps [20, 35], max-pooling [8, 9], graph-convolution [58], and self-attention [21, 22]. We utilize the Transformer model with self-attention [51] as in the encoder following UniPS [22]. UniPS directly predicted surface normals from pixel-wise aggregated feature vectors, following other pixel-wise methods [20, 21, 25], without considering non-local interactions. However, aggregated features lose lighting-specific information, naturally obtaining lighting-invariant representations more related to surface attributes than those before aggregation. In traditional physics-based vision tasks, common constraints including isotropy [4], reciprocity symmetry [48], reflectance monotonicity [6], sparse reflectance basis [13], and surface integrability [41] are mostly shared on the surface, not limited to a single surface point. Thus, considering non-local interactions of aggregated features at multiple surface points is crucial in physics-based tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Applying image-wise neural networks like CNNs on the aggregated feature map demands enormous computational cost for large output resolutions (e.g., \\(2048 \\times 2048\\)), and risks compromising output normal map details. To address these issues, we draw inspiration from recent Transformers on 3-D points [54, 61] and apply a Transformer on a fixed number (\\(m\\)) of pixel samples (e.g., \\(m = 2048\\)) from random locations in the input coordinate system. We term this the pixel-sampling Transformer. Unlike image-based approaches, pixel-sampling Transformer's memory consumption is constant per sample set, scaling to arbitrary image" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13201" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.157, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.152, + 0.151, + 0.161 + ], + "angle": 0, + "content": "Directional" + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.091, + 0.236, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.18, + 0.152, + 0.211, + 0.161 + ], + "angle": 0, + "content": "Point" + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.091, + 0.316, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.152, + 0.312, + 0.162 + ], + "angle": 0, + "content": "Environment" + }, + { + "type": "image", + "bbox": [ + 0.318, + 0.091, + 0.396, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.332, + 0.152, + 0.384, + 0.162 + ], + "angle": 0, + "content": "Dir.+Env." + }, + { + "type": "image", + "bbox": [ + 0.398, + 0.091, + 0.476, + 0.151 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.404, + 0.152, + 0.466, + 0.162 + ], + "angle": 0, + "content": "Point+Env." + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.163, + 0.468, + 0.177 + ], + "angle": 0, + "content": "Figure 3. Examples in PS-Mix under different lighting conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.189, + 0.469, + 0.249 + ], + "angle": 0, + "content": "sizes. Moreover, by applying the Transformer to a randomly sampled set of locations, local interactions that may lead to over-smoothing of feature maps (e.g., in CNNs) are almost entirely eliminated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.469, + 0.49 + ], + "angle": 0, + "content": "Concretely, given \\(m\\) random pixels \\(x_{i = 1,\\dots,m}\\) from the masked region of the input coordinate system, we interpolate features at those pixels as \\(\\mathcal{F}_{1,\\dots,K}(\\mathcal{S}(x_i))\\), where \\(\\mathcal{S}\\) is the bilinear interpolation operator. Then, interpolated features are concatenated with corresponding raw observations \\(I_{1,\\dots,K}(x_i)\\) and aggregated to \\(\\mathcal{A}(x_i)\\) with pooling by multihead attention (PMA) [28], as in [22]. Given aggregated features at different pixels in the same sample set, we apply another naive Transformer [51] to perform non-local interactions. Since the goal of this process is to consider surface-level interactions based on physical attributes, pixel coordinate information is unnecessary. Thus, we don't apply position embeddings to samples, unlike most existing visual Transformer models (e.g. [10,33]), allowing the samples to propagate their aggregated features without location information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.613 + ], + "angle": 0, + "content": "After the non-local interaction, we apply a two-layer MLP to predict surface normals at sampled locations. Finally, surface normals for each set are merged to obtain the final surface normal map at the input image resolution. This pixel-sampling Transformer approach facilitates non-local interactions while maintaining computational efficiency and preserving output normal map details, making it suitable for physics-based tasks with high-resolution images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.235, + 0.636 + ], + "angle": 0, + "content": "3.2. PS-Mix Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.469, + 0.78 + ], + "angle": 0, + "content": "To train their universal photometric stereo network, Ikehata [22] presented the PS-Wild training dataset, which rendered more than 10,000 scenes with commercial AdobeStock 3-D assets [1]. One of the issues in PS-Wild is that each scene consists of only a single object of uniform material. Furthermore, the environment lighting used for rendering scenes in [22] rarely has high-frequency illumination (e.g., a single point light source); therefore, the rendered images are biased towards low-frequency lighting conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this paper, we create a new training dataset that solves the issues in the PS-Wild training dataset. Instead of putting a single object of uniform material in each scene, we put multiple objects that overlap with each other in the same scene and give them different materials. To ensure that the material category is diverse in a scene, we manually categorized 897 texture maps in the AdobeStock material assets into 421 diffuse, 219 specular, and 257 metallic textures." + }, + { + "type": "table_caption", + "bbox": [ + 0.558, + 0.09, + 0.834, + 0.103 + ], + "angle": 0, + "content": "Table 1. Ablation study on PS-Wild-Test [22]." + }, + { + "type": "table", + "bbox": [ + 0.519, + 0.104, + 0.872, + 0.25 + ], + "angle": 0, + "content": "
MethodTrainingDir.HDRIDir.+HDRI
I22 (UniPS) [22]PS-Wild17.014.513.8
Only Local (baseline)PS-Mix8.414.711.8
+Non-local (32)PS-Mix7.814.910.8
+Non-local (128)PS-Mix6.213.08.9
+Non-local (512)PS-Mix5.812.48.2
+Non-local (2048)PS-Mix5.712.28.0
+Non-local (20480)PS-Mix5.712.38.0
+Scale-invariant Enc.PS-Mix4.811.17.5
" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.266, + 0.623, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.32, + 0.612, + 0.339 + ], + "angle": 0, + "content": "Local (1) MAE \\(= 21.3^{\\circ}\\) \\(\\mathrm{K} = 16\\)" + }, + { + "type": "image", + "bbox": [ + 0.641, + 0.266, + 0.753, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.66, + 0.32, + 0.74, + 0.339 + ], + "angle": 0, + "content": "Non-local (32) MAE=15.0°, K=16" + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.265, + 0.888, + 0.319 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.786, + 0.32, + 0.879, + 0.338 + ], + "angle": 0, + "content": "Non-local (2048) MAE=10.8,K=16" + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.34, + 0.853, + 0.352 + ], + "angle": 0, + "content": "(a) Different sample size \\((m)\\) for the non-local interaction" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.352, + 0.623, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.406, + 0.612, + 0.417 + ], + "angle": 0, + "content": "\\(\\mathrm{G_{Test} / G_{Train} = 6}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.417, + 0.61, + 0.425 + ], + "angle": 0, + "content": "MAE=20.4°, K=16" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.352, + 0.755, + 0.406 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.407, + 0.742, + 0.417 + ], + "angle": 0, + "content": "\\(\\mathrm{G_{Test} / G_{Train} = 3}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.66, + 0.417, + 0.738, + 0.425 + ], + "angle": 0, + "content": "MAE=12.5°, K=16" + }, + { + "type": "image", + "bbox": [ + 0.769, + 0.352, + 0.888, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.79, + 0.407, + 0.873, + 0.417 + ], + "angle": 0, + "content": "\\(\\mathrm{G_{Test} / G_{Train} = 1}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.793, + 0.417, + 0.871, + 0.425 + ], + "angle": 0, + "content": "MAE \\(= 10.8^{\\circ}\\) \\(\\mathrm{K} = 16\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.427, + 0.846, + 0.438 + ], + "angle": 0, + "content": "(b) Different input resolutions between training and test" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.449, + 0.892, + 0.491 + ], + "angle": 0, + "content": "Figure 4. (a) Comparison of different sample size \\((m)\\) for the nonlocal interaction in the normal prediction. (b) Comparison of different input resolutions to the encoder between training and test." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.747 + ], + "angle": 0, + "content": "For each scene, we randomly select four objects from 410 AdobeStock 3-D models and assign three textures from all three material categories and randomly choose one for each object. Furthermore, to make the lighting conditions more diverse, instead of using only environment lighting to render images, we use five types of light source configurations and mix them to render one scene; (a) environment lighting, (b) single directional lighting, (c) single point lighting, (d) \\((\\mathrm{a}) + (\\mathrm{b})\\), and (e) \\((\\mathrm{a}) + (\\mathrm{c})\\). The direction and position of light sources are randomly assigned within the valid range of parameters3. We followed PS-Wild [22] for other rendering techniques (e.g., auto-exposure, object scale adjustment). Our dataset consists of 34,921 scenes, and each scene is rendered to output 10 of 16-bit, \\(512 \\times 512\\) images. In Fig. 3, we show sample images under each lighting condition for the same scene." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.763, + 0.586, + 0.779 + ], + "angle": 0, + "content": "4. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.788, + 0.892, + 0.865 + ], + "angle": 0, + "content": "Training Details: Our network was trained on the PS-Mix dataset from scratch using the AdamW optimizer and a step decay learning rate schedule (\\(\\times 0.8\\) every ten epochs) with learning-rate warmup during the first epoch. A batch size of 8, an initial learning rate of 0.0001, and a weight" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "3Light directions are selected from the upper unit hemisphere, and point light positions are selected inside the hemisphere." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13202" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.115, + 0.09, + 0.854, + 0.103 + ], + "angle": 0, + "content": "Table 2. Evaluation on DiLiGenT [46] (Mean Angular Errors in degrees). All 96 images were used except where K is shown." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.104, + 0.868, + 0.431 + ], + "angle": 0, + "content": "
MethodApproachTaskBallBearBuddhaCatCowGobletHarvestPot1Pot2ReadingAve.
Woodham [52]Self-Sup.Calibrated4.18.414.98.425.618.530.68.414.719.815.3
IW14 [25]Self-Sup.Calibrated2.04.88.45.413.38.718.96.910.212.09.1
IA14 [23]Self-Sup.Calibrated3.37.110.56.713.19.726.06.68.814.210.6
I18 [20]SupervisedCalibrated2.24.17.94.68.07.314.05.46.012.67.2
CW20 [9]SupervisedCalibrated2.77.77.54.86.77.812.46.27.210.97.4
LB21 [35]SupervisedCalibrated2.03.57.64.34.76.713.34.95.09.86.2
LL22a [29]Sup.+Self-Sup.Calibrated2.43.68.04.94.76.714.96.05.08.86.5
CH19 [7]SupervisedUncalibrated2.86.99.08.18.511.917.48.17.514.99.5
CW20 [9]SupervisedUncalibrated2.55.68.67.97.89.616.27.27.114.98.7
KK21 [27]Sup.+Self-Sup.Uncalibrated3.86.013.17.910.911.925.58.810.218.211.6
LL22b [30]Sup.+Self-Sup.Uncalibrated1.23.89.34.75.57.114.66.76.510.57.0
TR22 [50] (K=2)Self-Sup.Uncalibrated6.39.714.59.911.114.226.110.712.119.913.4
I22 (UniPS) [22]SupervisedUniversal4.99.119.413.011.624.225.210.89.918.814.7
OursSupervisedUniversal1.53.67.55.44.58.510.24.74.18.25.8
Ours (K=64)SupervisedUniversal1.53.67.65.54.68.610.24.74.18.35.9
Ours (K=32)SupervisedUniversal1.53.67.75.54.78.610.44.84.28.45.9
Ours (K=16)SupervisedUniversal1.53.87.76.04.88.510.84.94.48.76.1
Ours (K=8)SupervisedUniversal1.64.08.26.35.28.411.55.24.89.46.5
Ours (K=4)SupervisedUniversal1.74.110.08.66.39.014.16.15.911.47.7
Ours (K=2)SupervisedUniversal1.96.814.413.68.312.821.29.09.216.911.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.596 + ], + "angle": 0, + "content": "decay of 0.05 were used. The number of input training images was randomly selected from 3 to 6 for each batch \\( {}^{4} \\) . In our work,we chose ConvNeXt-T [34] as our backbone due to its simplicity and efficiency, which is better than recent ViT-based architectures [10,32,33] with comparable performance. The training loss was the MSE loss, which computes the \\( {\\ell }_{2} \\) errors between the prediction and ground truth of surface normal vectors. Additional information, such as network architectures and feature dimensions, is provided in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Evaluation and Time: The accuracy is evaluated based on the mean angular errors (MAE) between the predicted and true surface normal maps, measured in degrees. Training is conducted on four NVIDIA A100 cards for roughly three days. The inference time of our method depends on the number and resolution of input images. In the case of 16 input images at a resolution of \\(512 \\times 512\\), it takes a few seconds excluding I/O on a GPU. While the computational cost will vary almost linearly with the number of images, this is significantly more efficient than recent neural inverse rendering-based methods [29, 30, 40, 60]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.79, + 0.233, + 0.807 + ], + "angle": 0, + "content": "4.1. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.814, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Firstly, we perform ablation studies to evaluate the individual contributions of our scale-invariant spatial-light feature encoder and non-local interaction with pixel-sampling transformer across varying sample sizes. To quantitatively" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.84 + ], + "angle": 0, + "content": "compare performance under various lighting conditions, we utilize the PS-Wild-Test dataset [22], which contains 50 synthetic scenes rendered under three distinct lighting setups: directional, environmental, and a mixture of both. In Table 1 and Fig. 4, we compare our method with different configurations against [22]. Note that without the scale-invariant encoder and non-local interaction (i.e., the baseline), our method is nearly equivalent to [22], except for some minor differences (e.g., backbone architecture, number of Transformer blocks in the encoder). We observe that the baseline method trained on our PX-Mix dataset improves performance for scenes under directional lighting, suggesting that one of the primary reasons why [22] was ineffective under directional lights was due to bias in the PS-Wild dataset. Accounting for non-local interaction of aggregated features enhances reconstruction accuracy, even with a small number of samples (e.g., \\( m = 32 \\)), as clearly illustrated in Fig. 4-(top). Although accuracy improved as the number of samples increased, as expected, performance gains plateaued beyond a certain number (i.e., \\( m = 2048 \\)). The efficacy of the scale-invariant spatial-light feature encoder was also confirmed. In Fig. 4-(bottom), we observed that a significant difference in input resolution to the backbone between training and testing led to substantial performance degradation, which further validates the advantage of our method that maintains a constant input tensor shape." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.381, + 0.9 + ], + "angle": 0, + "content": "\\(^4\\)Six is the maximum number that can fit on our GPU." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13203" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.149, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.149, + 0.091, + 0.21, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.091, + 0.279, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.091, + 0.343, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.091, + 0.406, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.091, + 0.473, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.099, + 0.267, + 0.127, + 0.278 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_footnote", + "bbox": [ + 0.146, + 0.267, + 0.213, + 0.277 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_footnote", + "bbox": [ + 0.221, + 0.267, + 0.279, + 0.277 + ], + "angle": 0, + "content": "Ours \\((\\mathrm{K} = 16)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.28, + 0.267, + 0.338, + 0.277 + ], + "angle": 0, + "content": "I22 \\((\\mathrm{K} = 96)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.34, + 0.267, + 0.475, + 0.277 + ], + "angle": 0, + "content": "LL22a \\((\\mathrm{K} = 96)\\) LB21 \\((\\mathrm{K} = 96)\\)" + }, + { + "type": "image_footnote", + "bbox": [ + 0.385, + 0.277, + 0.437, + 0.284 + ], + "angle": 0, + "content": "Calibrated" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.291, + 0.47, + 0.318 + ], + "angle": 0, + "content": "Figure 5. Results for objects under a single directional lighting condition, including object masks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.337, + 0.408, + 0.354 + ], + "angle": 0, + "content": "4.2. Evaluation under Directional Lighting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.469, + 0.609 + ], + "angle": 0, + "content": "DiLiGenT Evaluation: We first evaluate our method on the DiLiGenT benchmark [46]. Each dataset provides 96 612x512 16-bit HDR images, captured under known single directional lighting. The object mask and true surface normal map are available. In addition to UniPS [22], we also compare our method with calibrated [9,20,23,25,29,35,52] and uncalibrated [7,9,27,30,50] photometric stereo algorithms specifically designed for single directional lighting. Calibrated methods include both pixelwise [20,23,25,35,52] and image-wise [9,29] approaches. All uncalibrated methods are image-wise. We consider [27,29,30] as a combination of supervised and unsupervised learning, as pretrained models were used as a starting point for lighting prediction. To evaluate the valid number of input images, we compare our method with different numbers of input images (results are averaged over 10 random trials)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.469, + 0.763 + ], + "angle": 0, + "content": "The results are illustrated in Table 2. Impressively, our method, which does not assume a specific lighting model, outperforms state-of-the-art calibrated methods designed for directional lights (LB21 [35], LL22a [29]). Furthermore, unlike conventional photometric stereo methods, the proposed method does not experience significant performance degradation even when the number of input images is reduced; it maintains state-of-the-art results even with only 8 images. The proposed method (\\(K = 2\\)) also surpasses TR22 [50], which is specialized for two input images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Recovered normal maps of HARVEST and READING are shown in Fig. 5. These objects are considered the most challenging in the benchmark due to their highly nonconvex geometry. As expected, the state-of-the-art pixelwise calibrated method (LB21 [35]) can recover finer surface details, while the state-of-the-art image-wise calibrated method (LL22a [29]) can recover more globally consistent results. However, both of them struggle to recover the nonconvex parts of the objects accurately. On the other hand," + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.091, + 0.596, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.231, + 0.564, + 0.242 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.604, + 0.091, + 0.697, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.231, + 0.68, + 0.242 + ], + "angle": 0, + "content": "Ours \\((\\mathrm{K} = 8)\\)" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.091, + 0.798, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.716, + 0.231, + 0.797, + 0.242 + ], + "angle": 0, + "content": "CW20 (K=64)" + }, + { + "type": "image", + "bbox": [ + 0.807, + 0.091, + 0.899, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.814, + 0.231, + 0.896, + 0.242 + ], + "angle": 0, + "content": "LL22b (K=64)" + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.243, + 0.808, + 0.255 + ], + "angle": 0, + "content": "Deep relighting dataset (w/o object masks)" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.256, + 0.655, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.373, + 0.555, + 0.383 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.576, + 0.373, + 0.652, + 0.383 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.256, + 0.738, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.664, + 0.373, + 0.739, + 0.383 + ], + "angle": 0, + "content": "Ours (K=16)" + }, + { + "type": "image", + "bbox": [ + 0.74, + 0.256, + 0.818, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.743, + 0.373, + 0.898, + 0.383 + ], + "angle": 0, + "content": "CW20 \\((\\mathrm{K} = 96)\\) LL22b \\((\\mathrm{K} = 96)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.386, + 0.795, + 0.398 + ], + "angle": 0, + "content": "DiLiGenT dataset (w/o object masks)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.398, + 0.892, + 0.424 + ], + "angle": 0, + "content": "Figure 6. Results for scenes under a single directional lighting condition, excluding object masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.892, + 0.501 + ], + "angle": 0, + "content": "our method can recover both surface details and overall shape without apparent difficulty, even with a much smaller number of images (i.e., \\( \\mathrm{K} = 16 \\)). As expected, the performance of I22 [22] is severely lacking." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.893, + 0.807 + ], + "angle": 0, + "content": "Evaluation without Object Mask: To demonstrate that our method does not require an object mask, we applied it to two real scenes from a deep relighting work [57], each containing 530 8-bit integer images at a resolution of \\(512 \\times 512\\), captured under unknown single directional lighting using a gantry-based acquisition system. The object mask and true surface normal map are unavailable. We compared our method with state-of-the-art uncalibrated methods (CW20 [9] and LL22b [30]) and displayed the results in Fig. 6 (top). Unlike the uncalibrated methods that struggled to recover accurate lighting directions, our proposed method successfully captured object boundaries without masks, even in complex scenes with significant global illumination effects, and consistently recovered normals across the entire image. We further evaluated our method on DiLiGenT scenes without masks, as illustrated in Fig. 6 (bottom). While existing methods that assume an object mask produced highly inaccurate surface normal maps, our proposed method recovered more plausible normals with fewer images (i.e., \\(K = 16\\) vs \\(K = 96\\))." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.879, + 0.834 + ], + "angle": 0, + "content": "4.3. Evaluation under Spatially-varying Lighting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Our method is evaluated on challenging scenes with spatially-varying lighting conditions, comparing it to the first universal network (UniPS) [22] and a state-of-the-art uncalibrated photometric stereo method (GM21) [14] on" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13204" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.182, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.342, + 0.147, + 0.352 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.186, + 0.091, + 0.282, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.189, + 0.171, + 0.278, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.091, + 0.379, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.171, + 0.376, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.091, + 0.474, + 0.169 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.381, + 0.171, + 0.473, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.352, + 0.468, + 0.38 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison on images under spatially-varying lighting conditions with object masks [22]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.393, + 0.468, + 0.468 + ], + "angle": 0, + "content": "a dataset provided by [22]. We test three objects (Apple, Grape, and Owl). While GM21 [14] fails and I22 [22] loses details, our method, using a scale-invariant spatial-light feature encoder and non-local interaction, produces accurate results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.468, + 0.605 + ], + "angle": 0, + "content": "In Fig. 8, we subjectively compare our method using four objects with normal maps obtained from a 3D scanner. We align the scanned normal map to the image using MeshLab's mutual information registration filter [2], as in [46]. Our method recovers higher-definition surface normal maps than the 3D scanner (EinScan-SE) and performs well regardless of surface material. Photometric stereo performance improves with increased digital camera resolution, suggesting that 3D scanners may struggle to keep up." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.468, + 0.816 + ], + "angle": 0, + "content": "Lastly, we demonstrate surface normal prediction for complex non-convex scenes without masks under challenging lighting conditions in Figure 9. We apply our method to three extremely challenging datasets: School Desk, Coins and Keyboard, and Sweets. School Desk is a complex scene with simple objects, non-uniform lighting, and cast shadows, making surface normal map recovery difficult. Coins and Keyboard features multiple planar objects of various materials. Sweets is a challenging scene with abundant inter-reflections and cast shadows. As demonstrated, the proposed method successfully recovers uniform surface normals, largely unaffected by shadows, and effectively reconstructs the surface micro-shape, demonstrating its scalability and detail preservation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.83, + 0.195, + 0.845 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.468, + 0.9 + ], + "angle": 0, + "content": "In this paper, we presented a scalable, detailed, and mask-free universal photometric stereo method. We demonstrated that the proposed method outperforms most cali" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.091, + 0.603, + 0.143 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.145, + 0.599, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.185, + 0.579, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.217, + 0.601, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.091, + 0.692, + 0.143 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.144, + 0.697, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.185, + 0.675, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.607, + 0.217, + 0.701, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.091, + 0.793, + 0.142 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.143, + 0.792, + 0.213 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.704, + 0.217, + 0.797, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.092, + 0.897, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.146, + 0.896, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.218, + 0.896, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.805, + 0.281, + 0.897, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.277, + 0.799, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.528, + 0.331, + 0.592, + 0.342 + ], + "angle": 0, + "content": "3D scanner" + }, + { + "type": "image_caption", + "bbox": [ + 0.606, + 0.331, + 0.71, + 0.342 + ], + "angle": 0, + "content": "Ours (SDM-UniPS)" + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.331, + 0.792, + 0.342 + ], + "angle": 0, + "content": "I22 (UniPS)" + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.331, + 0.884, + 0.342 + ], + "angle": 0, + "content": "Input \\((\\mathrm{K} = 10)\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.549, + 0.343, + 0.842, + 0.356 + ], + "angle": 0, + "content": "Figure 8. Qualitative comparison with 3-D scans." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.366, + 0.601, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.44, + 0.601, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.52, + 0.601, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.597, + 0.613, + 0.609 + ], + "angle": 0, + "content": "SDM-UniPS (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.366, + 0.701, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.443, + 0.702, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.52, + 0.702, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.626, + 0.597, + 0.693, + 0.609 + ], + "angle": 0, + "content": "UniPS (122)" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.366, + 0.899, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.442, + 0.899, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.52, + 0.899, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.739, + 0.597, + 0.869, + 0.609 + ], + "angle": 0, + "content": "Input (w/o object mask)" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.61, + 0.891, + 0.636 + ], + "angle": 0, + "content": "Figure 9. Surface normal recovery from images under spatially-varying lighting conditions without object masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.716 + ], + "angle": 0, + "content": "brated and uncalibrated methods in the DiLiGenT benchmark. In addition, the comparison with the only existing method [22] for the universal task showed a significant improvement over it." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "However, several challenges still remain. Firstly, although we have observed that the proposed method works robustly for versatile lighting conditions, we found that our method is not very effective when the lighting variations are minimal. Secondly, the proposed method can easily be extended beyond normal map recovery by replacing the loss and data. In reality, we have attempted to output BRDF parameters for materials. However, due to fundamental ambiguities, it is difficult to evaluate the recovered BRDF parameters. Please see the appendix for further discussions of these limitations and a variety of additional results to better understand this study." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13205" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.428, + 0.13 + ], + "angle": 0, + "content": "[1] Adobe Stock. https://stock.adobe.com/.5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.133, + 0.403, + 0.146 + ], + "angle": 0, + "content": "[2] Meshlab. https://wwwmeshlab.net/.8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.149, + 0.469, + 0.175 + ], + "angle": 0, + "content": "[3] J. Ackermann, F. Langguth, S. Fuhrmann, and M. Goesele. 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Given multiple images under unknown spatially-varying illuminations, our method can recover the detailed surface normal map of non-convex, non-Lambertian surfaces (Left). Our method even surpasses the level of detail provided by consumer 3-D scanners (Right). + +# Abstract + +In this paper, we introduce SDM-UniPS, a groundbreaking Scalable, Detailed, Mask-free, and Universal Photometric Stereo network. Our approach can recover astonishingly intricate surface normal maps, rivaling the quality of 3D scanners, even when images are captured under unknown, spatially-varying lighting conditions in uncontrolled environments. We have extended previous universal photometric stereo networks to extract spatial-light features, utilizing all available information in high-resolution input images and accounting for non-local interactions among surface points. Moreover, we present a new synthetic training dataset that encompasses a diverse range of shapes, materials, and illumination scenarios found in real-world scenes. Through extensive evaluation, we demonstrate that our method not only surpasses calibrated, lighting-specific techniques on public benchmarks, but also excels with a significantly smaller number of input images even without object masks. + +# 1. Introduction + +Photometric stereo [52] aims to deduce the surface normal map of a scene by analyzing images captured from a fixed perspective under diverse lighting conditions. Until + +very recently, all photometric stereo methods assumed their specific lighting conditions, which led to limitations in their applicability. For instance, methods that assumed directional lighting conditions (e.g., [20, 24, 25]) were unsuitable under natural illumination, and vice versa (e.g., [15, 38]). + +To overcome this limitation, the "universal" photometric stereo method (UniPS) [22] has been introduced, designed to operate under unknown and arbitrary lighting conditions. In contrast to prior uncalibrated photometric stereo methods [7,9,27], which assumed specific physically-based lighting models, this method encodes a non-physical feature at each pixel for representing spatially-varying illumination, which is served as a substitute for physical lighting parameters within the calibrated photometric stereo network [21]. This method has taken the first step towards dealing with unknown, spatially-varying illumination that none of the existing methods could handle. However, the surface normal map recovered by UniPS, while not entirely inaccurate, appears blurry and lacks fine detail (see the top-right corner of Fig. 1). Upon investigation, we pinpointed three fundamental factors contributing to the subpar reconstruction performance. Firstly, extracting illumination + +features (i.e., global lighting contexts) from downsampled images caused a loss of information at higher input resolutions and produced blurry artifacts. Secondly, UniPS employs a pixel-wise calibrated photometric stereo network to predict surface normals using illumination features, which leads to imprecise overall shape recovery. Although pixelwise methods [20,21,25] offer advantages in capturing finer details compared to image-wise methods [8, 29, 49], they suffer from an inability to incorporate global information. + +Lastly, the third issue lies in the limited variety of shape, material, and illumination conditions present in the training data, which hampers its capacity to adapt to a diverse range of real-world situations. This limitation primarily stems from the fact that current datasets (i.e., PS-Wild [22]) do not include renderings under light sources with high-frequency components focused on specific incident angles, such as point or directional sources. Consequently, the method exhibits considerable performance degradation when exposed to directional lighting setups like DiLiGenT [46], as will be demonstrated later in this paper. + +In this paper, we present a groundbreaking photometric stereo network, the Scalable, Detailed, and Mask-Free Universal Photometric Stereo Network (SDM-UniPS), which recovers normal maps with remarkable accuracy from images captured under extremely uncontrolled lighting conditions. As shown in Fig. 1, SDM-UniPS is scalable, enabling the generation of normal maps from images with substantially higher resolution (e.g., 2048x2048) than the training data (e.g., 512x512); it is detailed, providing more accurate normal maps on DiLiGenT [46] with a limited number of input images than most existing orthographic photometric stereo techniques, including calibrated methods, and in some cases, surpassing 3D scanners in detail; and it is mask-free, allowing for application even when masks are absent, unlike many conventional methods. Our technical novelties include: + +1. The development of a scale-invariant spatial-light feature encoder that efficiently extracts illumination features while utilizing all input data and maintaining scalability with respect to input image size. Our encoder, based on the "split-and-merge" strategy, accommodates varying input image sizes during training and testing without sacrificing performance. +2. The development of a surface normal decoder utilizing our novel pixel-sampling transformer. By randomly sampling pixels of fixed size, we simultaneously predict surface normals through non-local interactions among sampled pixels using Transformers [51], effectively accounting for global information. +3. The creation of a new synthetic training dataset, comprising multiple objects with diverse textures within a + +scene, rendered under significantly varied lighting conditions that include both low and high-frequency illuminations. + +We believe that the most significant contribution is the extraordinary time savings from data acquisition to normal map recovery compared to existing photometric stereo algorithms requiring meticulous lighting control, even in the uncalibrated setup. This progress allows photometric stereo to be executed at home, literally "in the wild" setup. + +# 2. Related Works + +In this section, we provide a succinct overview of photometric stereo literature focusing on the single orthographic camera assumption. Alternative setups (e.g., perspective, multi-view cameras) are beyond the scope of this work. + +Optimization-based Approach: The majority of photometric stereo methods assume calibrated, directional lighting following Woodham [52] and optimize parameters by inversely solving a physics-based image formation model. This approach can be further categorized into robust methods, where non-Lambertian components are treated as outliers [24, 39, 53, 59]; model-based methods, which explicitly account for non-Lambertian reflectance [13, 23, 45]; and example-based methods [17, 19, 47] that leverage the observations of known objects captured under identical conditions as the target scene. The uncalibrated task is akin to the calibrated one, but with unknown lighting parameters. Until recently, most uncalibrated photometric stereo algorithms assumed Lambertian integrable surfaces and aimed to resolve the General Bas-Relief ambiguity [4, 11, 12, 16, 36, 42, 44, 55]. In contrast to these works, photometric stereo under natural lights has also been explored, wherein natural illumination is approximated using spherical harmonics [5, 15], dominant sun lighting [3, 18], or equivalent directional lighting [14, 38]. Although most optimization-based methods do not require external training data, they are fundamentally limited in handling global illumination phenomena (e.g., inter-reflections) that cannot be described by the predefined point-wise image formation model. + +Learning-based Approach: Learning-based methods are effective in addressing complex phenomena that are challenging to represent within simple image formation models. However, the first photometric stereo network [43] necessitated consistent lighting conditions during both training and testing. To address this limitation, various strategies have been investigated, such as observation maps [20, 35], set-pooling [8, 26], graph-convolution [58], and self-attention [21, 31]. Furthermore, researchers have explored uncalibrated deep photometric stereo networks [7,9,27,50], where lighting parameters and surface normals are recovered sequentially. Self-supervised neural inverse rendering methods have been developed without the need for exter + +nal data supervision. Taniai and Maehara [49] used neural networks instead of parametric physical models, with images and lighting as input. This work was expanded by Li and Li [29, 30], who incorporated recent neural coordinate-based representations [37]. However, despite their tremendous efforts, these methods are designed to work with only single directional light source and have limited ability to generalize to more complex lighting environments. + +Universal Photometric Stereo Network: The universal photometric stereo network (UniPS) [22] was the first to eliminate the prior lighting model assumption by leveraging a non-physical lighting representation called global lighting contexts. These global lighting contexts are recovered for each lighting condition through pixel-wise communication of hierarchical feature maps along the light-axis using Transformers [51]. During surface normal prediction, a single location is individually selected, and the network aggregates all the global lighting contexts (bilinearly interpolated from the canonical resolution) and raw observations at the location under different lighting conditions to pixel-wise predict the surface normal. This method introduced two strategies to handle high-resolution images: down-sampling images to the canonical resolution for recovering global lighting contexts, and employing pixel-wise surface normal prediction. Although these two concepts contributed to the scalability of image size, they resulted in performance degradation due to the loss of input information and the absence of a non-local perspective, as previously discussed. + +Our work draws inspiration from [22] and shares some fundamental ideas, particularly the use of Transformers [51] for communicating and aggregating features along the light-axis. However, our method diverges from [22] by fully utilizing input information in a non-local manner, which leads to a significant enhancement in reconstruction quality. + +# 3. Method + +We target the challenging universal photometric stereo task, which was recently introduced in [22]. Unlike prior calibrated and uncalibrated tasks, the universal task makes no assumptions about surface geometry, material properties, or, most importantly, lighting conditions. The objective of this task is to recover a normal map $N \in \mathbb{R}^{H \times W \times 3}$ from images $I_k \in \mathbb{R}^{H \times W \times 3}$ ; $k \in 1, \ldots, K$ captured under $K$ unknown lighting conditions using an orthographic camera. Optionally, an object mask $M \in \mathbb{R}^{H \times W}$ may be provided. + +Our method (SDM-UniPS) is illustrated in Fig. 2. Given pre-processed images and an optional object mask, feature maps for each lighting condition are extracted through interactions along the spatial and light axes (i.e., the scale-invariant spatial-light feature encoder). We then randomly sample locations from the coordinate system of the input image and bilinearly interpolate features at these locations. + +Features and raw observations at each location are aggregated pixel-wise, and surface normals are recovered from the aggregated features after non-local spatial interaction among them (i.e., the pixel-sampling Transformer). In line with [22], we focus on describing high-level concepts rather than providing detailed explanations for the sake of clarity. Refer to the appendix for a comprehensive description of the network architectures. + +# 3.1. SDM-UniPS + +Pre-processing: As in [22], we resize or crop input images to a resolution $(R)$ that is divisible by 32, which is accepted by most hierarchical vision backbones. To ensure that image values are within a similar range, each image is normalized by a random value between its maximum and mean. + +Scale-invariant Spatial-light Feature Encoder: After the pre-processing, we extract feature maps from images and an optional object mask through the interaction along both spatial and light axes. Following the basic framework in [22], each image and object mask $^1$ are concatenated to form a tensor $O_{k}\in \mathbb{R}^{R\times R\times 4}$ , which is then input to the common vision backbone [32-34] to extract hierarchical feature maps $B_{k}^{s}\in \mathbb{R}^{\frac{R}{S_{s}}\times \frac{R}{S_{s}}\times C_{s}}; s\in 1,2,3,4$ . Here, $S_{s}\in 4,8,16,32$ represents the scale of the $s$ -th feature map, and $C_s$ is the dimension of features at that scale. For each feature scale, features from different tensors at the same pixel interact with each other along the light-axis using naive Transformers [51]. Finally, hierarchical feature maps are fused to $\mathcal{F}_k\in \mathbb{R}^{\frac{R}{4}\times \frac{R}{4}\times C_{\mathcal{F}}}$ using the feature pyramid network [56], where $C_{\mathcal{F}}$ is the output feature dimension. Note that, unlike [22], we used a varying number of Transformer blocks at each hierarchy scale (i.e., the number of blocks changes from [1,1,1,1] to [0,1,2,4]) so that the deeper features interact more than the shallow ones. + +In UniPS [22], images and a mask are down-sampled to a canonical resolution before being input to the backbone network. This resolution must be constant and sufficiently small (e.g., 256x256) to prevent excessive memory consumption during feature extraction, particularly when dealing with high-resolution input images. Additionally, using a constant resolution ensures that tensors of the same shape are fed to the backbone, which helps to avoid significant performance degradation due to a large discrepancy in input tensor shapes between training and testing. Consequently, down-sampling leads to the loss of much information in the input images, resulting in a blurry normal map recovery. + +To address it, we propose a scale-invariant spatial-light feature encoder designed to maintain a consistent, small input resolution for the backbone network while preserving information from input images. Specifically, instead of downsampling, we suggest splitting the input tensor into + +![](images/03eb7148fb0065bd07edd4747c903964972abafc95351dca812fad8dbfd10c83.jpg) +(b) Scale-invariant Spatial-light Feature Encoder +Figure 2. Our entire framework is illustrated in (a). Given multiple images and an object mask (optional), the scale-invariant spatial-light encoder (detailed in (b)) extracts a feature map for each image. The surface normal vectors are independently recovered at each of pixel samples (i.e., 2048) after the non-local interaction among aggregated features from interpolated feature maps and raw observations. + +non-overlapping sub-tensors with a constant, small resolution. In greater detail, we decompose $O$ into $P^2$ sub-tensors of size $G \times G$ ( $G = 256$ in our implementation, $P \triangleq R / G$ ) by taking a single sample from every $P \times P$ pixel and stacking them as sub-tensors, as illustrated in Fig. 2. Each sub-tensor encompasses the entire portion of the original tensor but is slightly shifted. All sub-tensors are processed independently through the same spatial-light feature encoder and subsequently merged back into a tensor of size $\left(\frac{R}{4} \times \frac{R}{4} \times C_{\mathcal{F}}\right)$ . The combined feature maps from the sub-tensors retain all input information since no downsampling occurred. However, the absence of interaction among different sub-tensors leads to significant block artifacts, particularly when $P$ is large. To mitigate this, another feature map encoded from the naively downsized image is added to the merged feature maps, promoting interaction among sub-tensors. Optionally, when $P$ is larger than 4, we apply depth-wise Gaussian filtering (i.e., kernel size is $P-1$ ) to the feature maps to further enhance the interaction. Finally, we obtain the scale-invariant spatial-light feature maps $\mathcal{F}_k \in \mathbb{R}^{\frac{R}{4} \times \frac{R}{4} \times C_{\mathcal{F}}}$ for every lighting condition. + +Non-local Interaction with Pixel-sampling Transformer: Given the scale-invariant spatial-light feature maps $\mathcal{F}_k$ and input images $I_{k}$ , the surface normal is recovered after pixelwise feature aggregation along the light-axis (i.e., the light channel shrinks from $K$ to 1). Feature aggregation under different lighting conditions is a fundamental step in pho + +tometric stereo networks, and various strategies have been studied, such as observation maps [20, 35], max-pooling [8, 9], graph-convolution [58], and self-attention [21, 22]. We utilize the Transformer model with self-attention [51] as in the encoder following UniPS [22]. UniPS directly predicted surface normals from pixel-wise aggregated feature vectors, following other pixel-wise methods [20, 21, 25], without considering non-local interactions. However, aggregated features lose lighting-specific information, naturally obtaining lighting-invariant representations more related to surface attributes than those before aggregation. In traditional physics-based vision tasks, common constraints including isotropy [4], reciprocity symmetry [48], reflectance monotonicity [6], sparse reflectance basis [13], and surface integrability [41] are mostly shared on the surface, not limited to a single surface point. Thus, considering non-local interactions of aggregated features at multiple surface points is crucial in physics-based tasks. + +Applying image-wise neural networks like CNNs on the aggregated feature map demands enormous computational cost for large output resolutions (e.g., $2048 \times 2048$ ), and risks compromising output normal map details. To address these issues, we draw inspiration from recent Transformers on 3-D points [54, 61] and apply a Transformer on a fixed number ( $m$ ) of pixel samples (e.g., $m = 2048$ ) from random locations in the input coordinate system. We term this the pixel-sampling Transformer. Unlike image-based approaches, pixel-sampling Transformer's memory consumption is constant per sample set, scaling to arbitrary image + +![](images/e7f4b87a29b4ada8ec660ee722f8ee86234e0fa374370b2302043d8318e0dbe2.jpg) +Directional + +![](images/b23782ef88923a2c44bb73c14d1f258a0aeb3a96bbcb784ee02f4b7abaca0bc4.jpg) +Point + +![](images/d1292f24f8010662ce278cb2f45b9cb3f6b84402453045f20fa0e4fff7c6354c.jpg) +Environment +Figure 3. Examples in PS-Mix under different lighting conditions. + +![](images/87aaee488779ebd162eb862baf3c9f16fece23fac3504307321627db407ce625.jpg) +Dir.+Env. + +![](images/9610746d3cde8d6832be60c51e4bd990a94e06428920f4cd2c1cd60d3e32335f.jpg) +Point+Env. + +sizes. Moreover, by applying the Transformer to a randomly sampled set of locations, local interactions that may lead to over-smoothing of feature maps (e.g., in CNNs) are almost entirely eliminated. + +Concretely, given $m$ random pixels $x_{i = 1,\dots,m}$ from the masked region of the input coordinate system, we interpolate features at those pixels as $\mathcal{F}_{1,\dots,K}(\mathcal{S}(x_i))$ , where $\mathcal{S}$ is the bilinear interpolation operator. Then, interpolated features are concatenated with corresponding raw observations $I_{1,\dots,K}(x_i)$ and aggregated to $\mathcal{A}(x_i)$ with pooling by multihead attention (PMA) [28], as in [22]. Given aggregated features at different pixels in the same sample set, we apply another naive Transformer [51] to perform non-local interactions. Since the goal of this process is to consider surface-level interactions based on physical attributes, pixel coordinate information is unnecessary. Thus, we don't apply position embeddings to samples, unlike most existing visual Transformer models (e.g. [10,33]), allowing the samples to propagate their aggregated features without location information. + +After the non-local interaction, we apply a two-layer MLP to predict surface normals at sampled locations. Finally, surface normals for each set are merged to obtain the final surface normal map at the input image resolution. This pixel-sampling Transformer approach facilitates non-local interactions while maintaining computational efficiency and preserving output normal map details, making it suitable for physics-based tasks with high-resolution images. + +# 3.2. PS-Mix Dataset + +To train their universal photometric stereo network, Ikehata [22] presented the PS-Wild training dataset, which rendered more than 10,000 scenes with commercial AdobeStock 3-D assets [1]. One of the issues in PS-Wild is that each scene consists of only a single object of uniform material. Furthermore, the environment lighting used for rendering scenes in [22] rarely has high-frequency illumination (e.g., a single point light source); therefore, the rendered images are biased towards low-frequency lighting conditions. + +In this paper, we create a new training dataset that solves the issues in the PS-Wild training dataset. Instead of putting a single object of uniform material in each scene, we put multiple objects that overlap with each other in the same scene and give them different materials. To ensure that the material category is diverse in a scene, we manually categorized 897 texture maps in the AdobeStock material assets into 421 diffuse, 219 specular, and 257 metallic textures. + +Table 1. Ablation study on PS-Wild-Test [22]. + +
MethodTrainingDir.HDRIDir.+HDRI
I22 (UniPS) [22]PS-Wild17.014.513.8
Only Local (baseline)PS-Mix8.414.711.8
+Non-local (32)PS-Mix7.814.910.8
+Non-local (128)PS-Mix6.213.08.9
+Non-local (512)PS-Mix5.812.48.2
+Non-local (2048)PS-Mix5.712.28.0
+Non-local (20480)PS-Mix5.712.38.0
+Scale-invariant Enc.PS-Mix4.811.17.5
+ +![](images/b08f8e6564920198be22795b0d760a967b97ee484a5cf7a6b284a9e737087bbe.jpg) +Local (1) MAE $= 21.3^{\circ}$ $\mathrm{K} = 16$ + +![](images/5f748a62090526a1daa62a3baa64d3a16e37461c8c38f759db26939d2f14e546.jpg) +Non-local (32) MAE=15.0°, K=16 + +![](images/6bc0f6a573acab3cd8847c0e202427fdc81f210cb7ec4022e1d11c68e1baec4d.jpg) +Non-local (2048) MAE=10.8,K=16 + +![](images/3317ca5a66f381f619846a429dcde903a1e0983e39d5605d3f542aeb3e4b7837.jpg) +(a) Different sample size $(m)$ for the non-local interaction +$\mathrm{G_{Test} / G_{Train} = 6}$ +MAE=20.4°, K=16 + +![](images/269fd52fbfe9fad1826f02c03db7eb70021c767e247396e4cf73c8df719f4098.jpg) +$\mathrm{G_{Test} / G_{Train} = 3}$ +MAE=12.5°, K=16 + +![](images/d4e8c8a5b131a0ad7e197efc62517eafddf3193fdb61596d991a53ef810e453f.jpg) +$\mathrm{G_{Test} / G_{Train} = 1}$ +MAE $= 10.8^{\circ}$ $\mathrm{K} = 16$ +(b) Different input resolutions between training and test +Figure 4. (a) Comparison of different sample size $(m)$ for the nonlocal interaction in the normal prediction. (b) Comparison of different input resolutions to the encoder between training and test. + +For each scene, we randomly select four objects from 410 AdobeStock 3-D models and assign three textures from all three material categories and randomly choose one for each object. Furthermore, to make the lighting conditions more diverse, instead of using only environment lighting to render images, we use five types of light source configurations and mix them to render one scene; (a) environment lighting, (b) single directional lighting, (c) single point lighting, (d) $(\mathrm{a}) + (\mathrm{b})$ , and (e) $(\mathrm{a}) + (\mathrm{c})$ . The direction and position of light sources are randomly assigned within the valid range of parameters3. We followed PS-Wild [22] for other rendering techniques (e.g., auto-exposure, object scale adjustment). Our dataset consists of 34,921 scenes, and each scene is rendered to output 10 of 16-bit, $512 \times 512$ images. In Fig. 3, we show sample images under each lighting condition for the same scene. + +# 4. Results + +Training Details: Our network was trained on the PS-Mix dataset from scratch using the AdamW optimizer and a step decay learning rate schedule ( $\times 0.8$ every ten epochs) with learning-rate warmup during the first epoch. A batch size of 8, an initial learning rate of 0.0001, and a weight + +Table 2. Evaluation on DiLiGenT [46] (Mean Angular Errors in degrees). All 96 images were used except where K is shown. + +
MethodApproachTaskBallBearBuddhaCatCowGobletHarvestPot1Pot2ReadingAve.
Woodham [52]Self-Sup.Calibrated4.18.414.98.425.618.530.68.414.719.815.3
IW14 [25]Self-Sup.Calibrated2.04.88.45.413.38.718.96.910.212.09.1
IA14 [23]Self-Sup.Calibrated3.37.110.56.713.19.726.06.68.814.210.6
I18 [20]SupervisedCalibrated2.24.17.94.68.07.314.05.46.012.67.2
CW20 [9]SupervisedCalibrated2.77.77.54.86.77.812.46.27.210.97.4
LB21 [35]SupervisedCalibrated2.03.57.64.34.76.713.34.95.09.86.2
LL22a [29]Sup.+Self-Sup.Calibrated2.43.68.04.94.76.714.96.05.08.86.5
CH19 [7]SupervisedUncalibrated2.86.99.08.18.511.917.48.17.514.99.5
CW20 [9]SupervisedUncalibrated2.55.68.67.97.89.616.27.27.114.98.7
KK21 [27]Sup.+Self-Sup.Uncalibrated3.86.013.17.910.911.925.58.810.218.211.6
LL22b [30]Sup.+Self-Sup.Uncalibrated1.23.89.34.75.57.114.66.76.510.57.0
TR22 [50] (K=2)Self-Sup.Uncalibrated6.39.714.59.911.114.226.110.712.119.913.4
I22 (UniPS) [22]SupervisedUniversal4.99.119.413.011.624.225.210.89.918.814.7
OursSupervisedUniversal1.53.67.55.44.58.510.24.74.18.25.8
Ours (K=64)SupervisedUniversal1.53.67.65.54.68.610.24.74.18.35.9
Ours (K=32)SupervisedUniversal1.53.67.75.54.78.610.44.84.28.45.9
Ours (K=16)SupervisedUniversal1.53.87.76.04.88.510.84.94.48.76.1
Ours (K=8)SupervisedUniversal1.64.08.26.35.28.411.55.24.89.46.5
Ours (K=4)SupervisedUniversal1.74.110.08.66.39.014.16.15.911.47.7
Ours (K=2)SupervisedUniversal1.96.814.413.68.312.821.29.09.216.911.4
+ +decay of 0.05 were used. The number of input training images was randomly selected from 3 to 6 for each batch ${}^{4}$ . In our work,we chose ConvNeXt-T [34] as our backbone due to its simplicity and efficiency, which is better than recent ViT-based architectures [10,32,33] with comparable performance. The training loss was the MSE loss, which computes the ${\ell }_{2}$ errors between the prediction and ground truth of surface normal vectors. Additional information, such as network architectures and feature dimensions, is provided in the appendix. + +Evaluation and Time: The accuracy is evaluated based on the mean angular errors (MAE) between the predicted and true surface normal maps, measured in degrees. Training is conducted on four NVIDIA A100 cards for roughly three days. The inference time of our method depends on the number and resolution of input images. In the case of 16 input images at a resolution of $512 \times 512$ , it takes a few seconds excluding I/O on a GPU. While the computational cost will vary almost linearly with the number of images, this is significantly more efficient than recent neural inverse rendering-based methods [29, 30, 40, 60]. + +# 4.1. Ablation Study + +Firstly, we perform ablation studies to evaluate the individual contributions of our scale-invariant spatial-light feature encoder and non-local interaction with pixel-sampling transformer across varying sample sizes. To quantitatively + +compare performance under various lighting conditions, we utilize the PS-Wild-Test dataset [22], which contains 50 synthetic scenes rendered under three distinct lighting setups: directional, environmental, and a mixture of both. In Table 1 and Fig. 4, we compare our method with different configurations against [22]. Note that without the scale-invariant encoder and non-local interaction (i.e., the baseline), our method is nearly equivalent to [22], except for some minor differences (e.g., backbone architecture, number of Transformer blocks in the encoder). We observe that the baseline method trained on our PX-Mix dataset improves performance for scenes under directional lighting, suggesting that one of the primary reasons why [22] was ineffective under directional lights was due to bias in the PS-Wild dataset. Accounting for non-local interaction of aggregated features enhances reconstruction accuracy, even with a small number of samples (e.g., $m = 32$ ), as clearly illustrated in Fig. 4-(top). Although accuracy improved as the number of samples increased, as expected, performance gains plateaued beyond a certain number (i.e., $m = 2048$ ). The efficacy of the scale-invariant spatial-light feature encoder was also confirmed. In Fig. 4-(bottom), we observed that a significant difference in input resolution to the backbone between training and testing led to substantial performance degradation, which further validates the advantage of our method that maintains a constant input tensor shape. + +Figure 5. Results for objects under a single directional lighting condition, including object masks. +![](images/2b363eef1580f487fb7f6257a4d43d799588463de46dfdffde07ca65c1667d86.jpg) +Input + +![](images/f237004909944f36773ad498baef00ffd0c6b872c84b29417bafd1f80da360bc.jpg) +Ground Truth + +![](images/b4e32eb433e7d5f212c3f9e72d3dac04730255eb2f203d970eb4b9540c232079.jpg) +Ours $(\mathrm{K} = 16)$ + +![](images/03c19c07ab63e0105a3992d69e46504a5e8a8f85114cd80c201703c088c97ecb.jpg) +I22 $(\mathrm{K} = 96)$ + +![](images/4a7d354a5e7c0e3d48ff390eaaab7934fd4a04bcd14b9a02dffc4c9303c1f35a.jpg) +LL22a $(\mathrm{K} = 96)$ LB21 $(\mathrm{K} = 96)$ + +![](images/59a74b4282d02e6d7735f630f2733a7cc1ac43d1f62c4c90eae386e3390b4392.jpg) +Calibrated + +# 4.2. Evaluation under Directional Lighting + +DiLiGenT Evaluation: We first evaluate our method on the DiLiGenT benchmark [46]. Each dataset provides 96 612x512 16-bit HDR images, captured under known single directional lighting. The object mask and true surface normal map are available. In addition to UniPS [22], we also compare our method with calibrated [9,20,23,25,29,35,52] and uncalibrated [7,9,27,30,50] photometric stereo algorithms specifically designed for single directional lighting. Calibrated methods include both pixelwise [20,23,25,35,52] and image-wise [9,29] approaches. All uncalibrated methods are image-wise. We consider [27,29,30] as a combination of supervised and unsupervised learning, as pretrained models were used as a starting point for lighting prediction. To evaluate the valid number of input images, we compare our method with different numbers of input images (results are averaged over 10 random trials). + +The results are illustrated in Table 2. Impressively, our method, which does not assume a specific lighting model, outperforms state-of-the-art calibrated methods designed for directional lights (LB21 [35], LL22a [29]). Furthermore, unlike conventional photometric stereo methods, the proposed method does not experience significant performance degradation even when the number of input images is reduced; it maintains state-of-the-art results even with only 8 images. The proposed method ( $K = 2$ ) also surpasses TR22 [50], which is specialized for two input images. + +Recovered normal maps of HARVEST and READING are shown in Fig. 5. These objects are considered the most challenging in the benchmark due to their highly nonconvex geometry. As expected, the state-of-the-art pixelwise calibrated method (LB21 [35]) can recover finer surface details, while the state-of-the-art image-wise calibrated method (LL22a [29]) can recover more globally consistent results. However, both of them struggle to recover the nonconvex parts of the objects accurately. On the other hand, + +![](images/79e6e0edd17f2dce0f84fe01f8159e23fc4a7171d433755ecca822a334ab51fa.jpg) +Input + +![](images/07ffc5ef5610ffd3844de7fb527ce3a6a4f5185c6e30428363a4b05f5aa89f88.jpg) +Ours $(\mathrm{K} = 8)$ + +![](images/072a176d347428b985ec46c47be7c0a2c8706c843ca651e486793001cd2e7719.jpg) +CW20 (K=64) + +![](images/79e23c58a7298e17df764322c5ce807d9a8ed5505560669d8d74e1b8aa6276d3.jpg) +LL22b (K=64) + +![](images/c35435278f6141e0016cb7a4743c368a850034f9466c35d7baa7e50fc39d734a.jpg) +Deep relighting dataset (w/o object masks) +Input +Ground Truth +DiLiGenT dataset (w/o object masks) +Figure 6. Results for scenes under a single directional lighting condition, excluding object masks. + +![](images/23e4061184d8e732dca0130d73da6259c0673e29c4a08fda1fe303c36e859927.jpg) +Ours (K=16) + +![](images/0c671d3fe40069edf52fc00a9fe7f9c24188c2beeeb1693ad3ab037bd9636108.jpg) +CW20 $(\mathrm{K} = 96)$ LL22b $(\mathrm{K} = 96)$ + +our method can recover both surface details and overall shape without apparent difficulty, even with a much smaller number of images (i.e., $\mathrm{K} = 16$ ). As expected, the performance of I22 [22] is severely lacking. + +Evaluation without Object Mask: To demonstrate that our method does not require an object mask, we applied it to two real scenes from a deep relighting work [57], each containing 530 8-bit integer images at a resolution of $512 \times 512$ , captured under unknown single directional lighting using a gantry-based acquisition system. The object mask and true surface normal map are unavailable. We compared our method with state-of-the-art uncalibrated methods (CW20 [9] and LL22b [30]) and displayed the results in Fig. 6 (top). Unlike the uncalibrated methods that struggled to recover accurate lighting directions, our proposed method successfully captured object boundaries without masks, even in complex scenes with significant global illumination effects, and consistently recovered normals across the entire image. We further evaluated our method on DiLiGenT scenes without masks, as illustrated in Fig. 6 (bottom). While existing methods that assume an object mask produced highly inaccurate surface normal maps, our proposed method recovered more plausible normals with fewer images (i.e., $K = 16$ vs $K = 96$ ). + +# 4.3. Evaluation under Spatially-varying Lighting + +Our method is evaluated on challenging scenes with spatially-varying lighting conditions, comparing it to the first universal network (UniPS) [22] and a state-of-the-art uncalibrated photometric stereo method (GM21) [14] on + +![](images/6fcc6cafcea278138d2b761f6c2e2d56e4d00a342e5f6973cd6f521585a42266.jpg) +Input +Figure 7. Qualitative comparison on images under spatially-varying lighting conditions with object masks [22]. + +![](images/74020c8a7d3d1152f6abec5a65959c4ed25e3e7f59525f87b518920e4c13083f.jpg) + +![](images/3d6f1c892ed0a782b5aed389fe866cec8825efca61aa6a03694669afdca4fb0b.jpg) + +![](images/adaba09cc3b88651ec3e6d10b09049542fb55c0efed35b32a68640d613ef90ef.jpg) + +![](images/22bde72a7b4342a72cc2bb6b359e5652aec6981ce7c57eb986cf7541eec9027a.jpg) + +![](images/7e4117c4dbac422af13548171baeff8dc24098d910fc5fb9085de0f838145bd9.jpg) + +![](images/0495516bb9431e8abd079a37de5457c47e41fad17f46cace7b5989c1b41ba153.jpg) + +a dataset provided by [22]. We test three objects (Apple, Grape, and Owl). While GM21 [14] fails and I22 [22] loses details, our method, using a scale-invariant spatial-light feature encoder and non-local interaction, produces accurate results. + +In Fig. 8, we subjectively compare our method using four objects with normal maps obtained from a 3D scanner. We align the scanned normal map to the image using MeshLab's mutual information registration filter [2], as in [46]. Our method recovers higher-definition surface normal maps than the 3D scanner (EinScan-SE) and performs well regardless of surface material. Photometric stereo performance improves with increased digital camera resolution, suggesting that 3D scanners may struggle to keep up. + +Lastly, we demonstrate surface normal prediction for complex non-convex scenes without masks under challenging lighting conditions in Figure 9. We apply our method to three extremely challenging datasets: School Desk, Coins and Keyboard, and Sweets. School Desk is a complex scene with simple objects, non-uniform lighting, and cast shadows, making surface normal map recovery difficult. Coins and Keyboard features multiple planar objects of various materials. Sweets is a challenging scene with abundant inter-reflections and cast shadows. As demonstrated, the proposed method successfully recovers uniform surface normals, largely unaffected by shadows, and effectively reconstructs the surface micro-shape, demonstrating its scalability and detail preservation. + +# 5. Conclusion + +In this paper, we presented a scalable, detailed, and mask-free universal photometric stereo method. We demonstrated that the proposed method outperforms most cali + +![](images/e17fddbb44119501c8465ffd84d699a3fcf35fc1e7e0424ca69b12f469717390.jpg) + +![](images/9265b689bfa372c968d7665a496d734fd6490fcfb86b55a36b76c783d17cf72d.jpg) + +![](images/2283449881851a29754cb49c9e5d17a5639eabb9ff6586d07fa76c3f9909b94c.jpg) + +![](images/1ec0b893bc37e0d43204a04cc8bf5dd8c873d8c62ccbb98156687da827898d4f.jpg) + +![](images/e6d2986e1cf3f0312a6751f4ac70519b8a403b5b7a485a1423437f81e988e924.jpg) + +![](images/64b1f8d6d0260f55ff82bd03a024632b039d73a5b6b52883b8b45d5a4dcf65a8.jpg) + +![](images/04f3b67fd706b0897906e0107939da62ad3812c2fe266e9f2154bc994fff5977.jpg) + +![](images/b137135b81c3be40f2cb07166ea60d859f792836a0eb988e302d70bbaa689803.jpg) + +![](images/af9af33e13cbf3e73cef84f3797272fe9e1c2a18f41e87065be3d24aaf1de897.jpg) + +![](images/201f0d6a107d626f7a33387b7d917d46b30b01af1f457f345eaca273de35880e.jpg) + +![](images/b9fc8342b0cbfb1a4f52e4588f4ab9fc17b540105f5e7af5622bd2aafc006c0a.jpg) + +![](images/029b47dc69e563486c45d4186162993a3d1c7b4b0865a7ab43ddc9ee0450e08d.jpg) + +![](images/0242d13127a40a173a914533e390bd905039d08423e4113e59359630578dbd3e.jpg) + +![](images/cc0939210db7c9191a8feadc405719c0031a32d59e3636196b360227ac79ac73.jpg) + +![](images/d0459cfc0798c83a52afd948cf700d077406b220c239b6efbb59acc42535c0f3.jpg) +Input $(\mathrm{K} = 10)$ + +![](images/b1c0a412f4160217eb98842262ac07d6c7427ae781ff97ec46550d9686595638.jpg) +3D scanner +Ours (SDM-UniPS) +I22 (UniPS) + +![](images/b80b9417ee0b77b7c902517ca77ae4e72cbb6ef39f549657e4185ba0ebad62c6.jpg) +Figure 8. Qualitative comparison with 3-D scans. + +![](images/a6d13a8b24f4ae90bad9f54b29711ef113abe8d6e0400dac4b8ec355c57b0ce0.jpg) + +![](images/9e2c3bb72781e844fa65f3545781987b11b546c31c2b7d4fbf259c1001deba59.jpg) +SDM-UniPS (Ours) +Figure 9. Surface normal recovery from images under spatially-varying lighting conditions without object masks. + +![](images/f5a7c67c0340bcfec18a39a453867e48ab9c619a6586923e4dede4cff7a02a91.jpg) + +![](images/61e107d4241eb89d677822d401a6bf2abe34c894c9a2588eff0b9af3b4f3bf56.jpg) + +![](images/bb9f5ced9bfeba6c7b3d0c3a59a3300acd7bbd72f6091f2868f4b56c72ef35a4.jpg) +UniPS (122) + +![](images/c070e1be83b555597278983f0a0930ae2e0b444f4bed92856e01ac048f0db0d7.jpg) + +![](images/abed45b6f45841621556e2ee1c39549545ee255c6be0bafe64a3dead37615267.jpg) + +![](images/b8bbb0e076bbd38a00dd77110198803286d57703a0c6b1dc941642d41402cf7d.jpg) +Input (w/o object mask) + +brated and uncalibrated methods in the DiLiGenT benchmark. In addition, the comparison with the only existing method [22] for the universal task showed a significant improvement over it. + +However, several challenges still remain. Firstly, although we have observed that the proposed method works robustly for versatile lighting conditions, we found that our method is not very effective when the lighting variations are minimal. Secondly, the proposed method can easily be extended beyond normal map recovery by replacing the loss and data. In reality, we have attempted to output BRDF parameters for materials. However, due to fundamental ambiguities, it is difficult to evaluate the recovered BRDF parameters. Please see the appendix for further discussions of these limitations and a variety of additional results to better understand this study. + +# References + +[1] Adobe Stock. https://stock.adobe.com/.5 +[2] Meshlab. https://wwwmeshlab.net/.8 +[3] J. Ackermann, F. Langguth, S. Fuhrmann, and M. Goesele. Photometric stereo for outdoor webcams. 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Given multiple images under unknown spatially-varying illuminations, our method can recover the detailed surface normal map of non-convex, non-Lambertian surfaces (Left). Our method even surpasses the level of detail provided by consumer 3-D scanners (Right)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 143, + 422, + 192, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 422, + 192, + 433 + ], + "spans": [ + { + "bbox": [ + 143, + 422, + 192, + 433 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 447, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 289, + 651 + ], + "type": "text", + "content": "In this paper, we introduce SDM-UniPS, a groundbreaking Scalable, Detailed, Mask-free, and Universal Photometric Stereo network. Our approach can recover astonishingly intricate surface normal maps, rivaling the quality of 3D scanners, even when images are captured under unknown, spatially-varying lighting conditions in uncontrolled environments. We have extended previous universal photometric stereo networks to extract spatial-light features, utilizing all available information in high-resolution input images and accounting for non-local interactions among surface points. Moreover, we present a new synthetic training dataset that encompasses a diverse range of shapes, materials, and illumination scenarios found in real-world scenes. Through extensive evaluation, we demonstrate that our method not only surpasses calibrated, lighting-specific techniques on public benchmarks, but also excels with a significantly smaller number of input images even without object masks." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 656, + 127, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 127, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 127, + 668 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Photometric stereo [52] aims to deduce the surface normal map of a scene by analyzing images captured from a fixed perspective under diverse lighting conditions. Until" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 422, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 483 + ], + "type": "text", + "content": "very recently, all photometric stereo methods assumed their specific lighting conditions, which led to limitations in their applicability. For instance, methods that assumed directional lighting conditions (e.g., [20, 24, 25]) were unsuitable under natural illumination, and vice versa (e.g., [15, 38])." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 484, + 546, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 546, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 546, + 688 + ], + "type": "text", + "content": "To overcome this limitation, the \"universal\" photometric stereo method (UniPS) [22] has been introduced, designed to operate under unknown and arbitrary lighting conditions. In contrast to prior uncalibrated photometric stereo methods [7,9,27], which assumed specific physically-based lighting models, this method encodes a non-physical feature at each pixel for representing spatially-varying illumination, which is served as a substitute for physical lighting parameters within the calibrated photometric stereo network [21]. This method has taken the first step towards dealing with unknown, spatially-varying illumination that none of the existing methods could handle. However, the surface normal map recovered by UniPS, while not entirely inaccurate, appears blurry and lacks fine detail (see the top-right corner of Fig. 1). Upon investigation, we pinpointed three fundamental factors contributing to the subpar reconstruction performance. Firstly, extracting illumination" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 495, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 495, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 495, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 320, + 702, + 508, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 702, + 508, + 712 + ], + "spans": [ + { + "bbox": [ + 320, + 702, + 508, + 712 + ], + "type": "text", + "content": "Supported by JSPS KAKENHI Grant Number 22K17919." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13198" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "features (i.e., global lighting contexts) from downsampled images caused a loss of information at higher input resolutions and produced blurry artifacts. Secondly, UniPS employs a pixel-wise calibrated photometric stereo network to predict surface normals using illumination features, which leads to imprecise overall shape recovery. Although pixelwise methods [20,21,25] offer advantages in capturing finer details compared to image-wise methods [8, 29, 49], they suffer from an inability to incorporate global information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 312 + ], + "type": "text", + "content": "Lastly, the third issue lies in the limited variety of shape, material, and illumination conditions present in the training data, which hampers its capacity to adapt to a diverse range of real-world situations. This limitation primarily stems from the fact that current datasets (i.e., PS-Wild [22]) do not include renderings under light sources with high-frequency components focused on specific incident angles, such as point or directional sources. Consequently, the method exhibits considerable performance degradation when exposed to directional lighting setups like DiLiGenT [46], as will be demonstrated later in this paper." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 313, + 288, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 288, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 288, + 502 + ], + "type": "text", + "content": "In this paper, we present a groundbreaking photometric stereo network, the Scalable, Detailed, and Mask-Free Universal Photometric Stereo Network (SDM-UniPS), which recovers normal maps with remarkable accuracy from images captured under extremely uncontrolled lighting conditions. As shown in Fig. 1, SDM-UniPS is scalable, enabling the generation of normal maps from images with substantially higher resolution (e.g., 2048x2048) than the training data (e.g., 512x512); it is detailed, providing more accurate normal maps on DiLiGenT [46] with a limited number of input images than most existing orthographic photometric stereo techniques, including calibrated methods, and in some cases, surpassing 3D scanners in detail; and it is mask-free, allowing for application even when masks are absent, unlike many conventional methods. Our technical novelties include:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 514, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 55, + 514, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 514, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 514, + 287, + 597 + ], + "type": "text", + "content": "1. The development of a scale-invariant spatial-light feature encoder that efficiently extracts illumination features while utilizing all input data and maintaining scalability with respect to input image size. Our encoder, based on the \"split-and-merge\" strategy, accommodates varying input image sizes during training and testing without sacrificing performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 54, + 607, + 287, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 607, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 54, + 607, + 287, + 679 + ], + "type": "text", + "content": "2. The development of a surface normal decoder utilizing our novel pixel-sampling transformer. By randomly sampling pixels of fixed size, we simultaneously predict surface normals through non-local interactions among sampled pixels using Transformers [51], effectively accounting for global information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 54, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 54, + 689, + 287, + 714 + ], + "type": "text", + "content": "3. The creation of a new synthetic training dataset, comprising multiple objects with diverse textures within a" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 545, + 107 + ], + "type": "text", + "content": "scene, rendered under significantly varied lighting conditions that include both low and high-frequency illuminations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 114, + 545, + 186 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 114, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 305, + 114, + 545, + 186 + ], + "type": "text", + "content": "We believe that the most significant contribution is the extraordinary time savings from data acquisition to normal map recovery compared to existing photometric stereo algorithms requiring meticulous lighting control, even in the uncalibrated setup. This progress allows photometric stereo to be executed at home, literally \"in the wild\" setup." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 195, + 397, + 208 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 195, + 397, + 208 + ], + "spans": [ + { + "bbox": [ + 306, + 195, + 397, + 208 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 215, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 215, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 215, + 545, + 262 + ], + "type": "text", + "content": "In this section, we provide a succinct overview of photometric stereo literature focusing on the single orthographic camera assumption. Alternative setups (e.g., perspective, multi-view cameras) are beyond the scope of this work." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 266, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 546, + 554 + ], + "type": "text", + "content": "Optimization-based Approach: The majority of photometric stereo methods assume calibrated, directional lighting following Woodham [52] and optimize parameters by inversely solving a physics-based image formation model. This approach can be further categorized into robust methods, where non-Lambertian components are treated as outliers [24, 39, 53, 59]; model-based methods, which explicitly account for non-Lambertian reflectance [13, 23, 45]; and example-based methods [17, 19, 47] that leverage the observations of known objects captured under identical conditions as the target scene. The uncalibrated task is akin to the calibrated one, but with unknown lighting parameters. Until recently, most uncalibrated photometric stereo algorithms assumed Lambertian integrable surfaces and aimed to resolve the General Bas-Relief ambiguity [4, 11, 12, 16, 36, 42, 44, 55]. In contrast to these works, photometric stereo under natural lights has also been explored, wherein natural illumination is approximated using spherical harmonics [5, 15], dominant sun lighting [3, 18], or equivalent directional lighting [14, 38]. Although most optimization-based methods do not require external training data, they are fundamentally limited in handling global illumination phenomena (e.g., inter-reflections) that cannot be described by the predefined point-wise image formation model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": "Learning-based Approach: Learning-based methods are effective in addressing complex phenomena that are challenging to represent within simple image formation models. However, the first photometric stereo network [43] necessitated consistent lighting conditions during both training and testing. To address this limitation, various strategies have been investigated, such as observation maps [20, 35], set-pooling [8, 26], graph-convolution [58], and self-attention [21, 31]. Furthermore, researchers have explored uncalibrated deep photometric stereo networks [7,9,27,50], where lighting parameters and surface normals are recovered sequentially. Self-supervised neural inverse rendering methods have been developed without the need for exter" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13199" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "nal data supervision. Taniai and Maehara [49] used neural networks instead of parametric physical models, with images and lighting as input. This work was expanded by Li and Li [29, 30], who incorporated recent neural coordinate-based representations [37]. However, despite their tremendous efforts, these methods are designed to work with only single directional light source and have limited ability to generalize to more complex lighting environments." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 289, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 289, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 289, + 411 + ], + "type": "text", + "content": "Universal Photometric Stereo Network: The universal photometric stereo network (UniPS) [22] was the first to eliminate the prior lighting model assumption by leveraging a non-physical lighting representation called global lighting contexts. These global lighting contexts are recovered for each lighting condition through pixel-wise communication of hierarchical feature maps along the light-axis using Transformers [51]. During surface normal prediction, a single location is individually selected, and the network aggregates all the global lighting contexts (bilinearly interpolated from the canonical resolution) and raw observations at the location under different lighting conditions to pixel-wise predict the surface normal. This method introduced two strategies to handle high-resolution images: down-sampling images to the canonical resolution for recovering global lighting contexts, and employing pixel-wise surface normal prediction. Although these two concepts contributed to the scalability of image size, they resulted in performance degradation due to the loss of input information and the absence of a non-local perspective, as previously discussed." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 412, + 288, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 288, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 288, + 485 + ], + "type": "text", + "content": "Our work draws inspiration from [22] and shares some fundamental ideas, particularly the use of Transformers [51] for communicating and aggregating features along the light-axis. However, our method diverges from [22] by fully utilizing input information in a non-local manner, which leads to a significant enhancement in reconstruction quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 499, + 104, + 512 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 499, + 104, + 512 + ], + "spans": [ + { + "bbox": [ + 47, + 499, + 104, + 512 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": "We target the challenging universal photometric stereo task, which was recently introduced in [22]. Unlike prior calibrated and uncalibrated tasks, the universal task makes no assumptions about surface geometry, material properties, or, most importantly, lighting conditions. The objective of this task is to recover a normal map " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "N \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " from images " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "I_k \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "k \\in 1, \\ldots, K" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " captured under " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " unknown lighting conditions using an orthographic camera. Optionally, an object mask " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " may be provided." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Our method (SDM-UniPS) is illustrated in Fig. 2. Given pre-processed images and an optional object mask, feature maps for each lighting condition are extracted through interactions along the spatial and light axes (i.e., the scale-invariant spatial-light feature encoder). We then randomly sample locations from the coordinate system of the input image and bilinearly interpolate features at these locations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "Features and raw observations at each location are aggregated pixel-wise, and surface normals are recovered from the aggregated features after non-local spatial interaction among them (i.e., the pixel-sampling Transformer). In line with [22], we focus on describing high-level concepts rather than providing detailed explanations for the sake of clarity. Refer to the appendix for a comprehensive description of the network architectures." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 177, + 387, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 177, + 387, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 177, + 387, + 190 + ], + "type": "text", + "content": "3.1. SDM-UniPS" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 196, + 547, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 196, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 304, + 196, + 547, + 257 + ], + "type": "text", + "content": "Pre-processing: As in [22], we resize or crop input images to a resolution " + }, + { + "bbox": [ + 304, + 196, + 547, + 257 + ], + "type": "inline_equation", + "content": "(R)" + }, + { + "bbox": [ + 304, + 196, + 547, + 257 + ], + "type": "text", + "content": " that is divisible by 32, which is accepted by most hierarchical vision backbones. To ensure that image values are within a similar range, each image is normalized by a random value between its maximum and mean." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": "Scale-invariant Spatial-light Feature Encoder: After the pre-processing, we extract feature maps from images and an optional object mask through the interaction along both spatial and light axes. Following the basic framework in [22], each image and object mask " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": " are concatenated to form a tensor " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "O_{k}\\in \\mathbb{R}^{R\\times R\\times 4}" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": ", which is then input to the common vision backbone [32-34] to extract hierarchical feature maps " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "B_{k}^{s}\\in \\mathbb{R}^{\\frac{R}{S_{s}}\\times \\frac{R}{S_{s}}\\times C_{s}}; s\\in 1,2,3,4" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "S_{s}\\in 4,8,16,32" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": " represents the scale of the " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": "-th feature map, and " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "C_s" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": " is the dimension of features at that scale. For each feature scale, features from different tensors at the same pixel interact with each other along the light-axis using naive Transformers [51]. Finally, hierarchical feature maps are fused to " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_k\\in \\mathbb{R}^{\\frac{R}{4}\\times \\frac{R}{4}\\times C_{\\mathcal{F}}}" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": " using the feature pyramid network [56], where " + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "inline_equation", + "content": "C_{\\mathcal{F}}" + }, + { + "bbox": [ + 304, + 259, + 547, + 488 + ], + "type": "text", + "content": " is the output feature dimension. Note that, unlike [22], we used a varying number of Transformer blocks at each hierarchy scale (i.e., the number of blocks changes from [1,1,1,1] to [0,1,2,4]) so that the deeper features interact more than the shallow ones." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 489, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 547, + 632 + ], + "type": "text", + "content": "In UniPS [22], images and a mask are down-sampled to a canonical resolution before being input to the backbone network. This resolution must be constant and sufficiently small (e.g., 256x256) to prevent excessive memory consumption during feature extraction, particularly when dealing with high-resolution input images. Additionally, using a constant resolution ensures that tensors of the same shape are fed to the backbone, which helps to avoid significant performance degradation due to a large discrepancy in input tensor shapes between training and testing. Consequently, down-sampling leads to the loss of much information in the input images, resulting in a blurry normal map recovery." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 633, + 547, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 633, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 547, + 693 + ], + "type": "text", + "content": "To address it, we propose a scale-invariant spatial-light feature encoder designed to maintain a consistent, small input resolution for the backbone network while preserving information from input images. Specifically, instead of downsampling, we suggest splitting the input tensor into" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 538, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 538, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 538, + 712 + ], + "type": "text", + "content": "Without a mask, a matrix with all values set to one is concatenated." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "13200" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 68, + 525, + 297 + ], + "blocks": [ + { + "bbox": [ + 70, + 68, + 525, + 297 + ], + "lines": [ + { + "bbox": [ + 70, + 68, + 525, + 297 + ], + "spans": [ + { + "bbox": [ + 70, + 68, + 525, + 297 + ], + "type": "image", + "image_path": "03eb7148fb0065bd07edd4747c903964972abafc95351dca812fad8dbfd10c83.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 218, + 297, + 385, + 306 + ], + "lines": [ + { + "bbox": [ + 218, + 297, + 385, + 306 + ], + "spans": [ + { + "bbox": [ + 218, + 297, + 385, + 306 + ], + "type": "text", + "content": "(b) Scale-invariant Spatial-light Feature Encoder" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 310, + 546, + 344 + ], + "lines": [ + { + "bbox": [ + 46, + 310, + 546, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 546, + 344 + ], + "type": "text", + "content": "Figure 2. Our entire framework is illustrated in (a). Given multiple images and an object mask (optional), the scale-invariant spatial-light encoder (detailed in (b)) extracts a feature map for each image. The surface normal vectors are independently recovered at each of pixel samples (i.e., 2048) after the non-local interaction among aggregated features from interpolated feature maps and raw observations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": "non-overlapping sub-tensors with a constant, small resolution. In greater detail, we decompose " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "P^2" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " sub-tensors of size " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "G \\times G" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "G = 256" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " in our implementation, " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "P \\triangleq R / G" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": ") by taking a single sample from every " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "P \\times P" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " pixel and stacking them as sub-tensors, as illustrated in Fig. 2. Each sub-tensor encompasses the entire portion of the original tensor but is slightly shifted. All sub-tensors are processed independently through the same spatial-light feature encoder and subsequently merged back into a tensor of size " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "\\left(\\frac{R}{4} \\times \\frac{R}{4} \\times C_{\\mathcal{F}}\\right)" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": ". The combined feature maps from the sub-tensors retain all input information since no downsampling occurred. However, the absence of interaction among different sub-tensors leads to significant block artifacts, particularly when " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " is large. To mitigate this, another feature map encoded from the naively downsized image is added to the merged feature maps, promoting interaction among sub-tensors. Optionally, when " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " is larger than 4, we apply depth-wise Gaussian filtering (i.e., kernel size is " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "P-1" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": ") to the feature maps to further enhance the interaction. Finally, we obtain the scale-invariant spatial-light feature maps " + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_k \\in \\mathbb{R}^{\\frac{R}{4} \\times \\frac{R}{4} \\times C_{\\mathcal{F}}}" + }, + { + "bbox": [ + 46, + 359, + 289, + 612 + ], + "type": "text", + "content": " for every lighting condition." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "text", + "content": "Non-local Interaction with Pixel-sampling Transformer: Given the scale-invariant spatial-light feature maps " + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_k" + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "text", + "content": " and input images " + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "inline_equation", + "content": "I_{k}" + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "text", + "content": ", the surface normal is recovered after pixelwise feature aggregation along the light-axis (i.e., the light channel shrinks from " + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 614, + 287, + 687 + ], + "type": "text", + "content": " to 1). Feature aggregation under different lighting conditions is a fundamental step in pho" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 359, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 545, + 574 + ], + "type": "text", + "content": "tometric stereo networks, and various strategies have been studied, such as observation maps [20, 35], max-pooling [8, 9], graph-convolution [58], and self-attention [21, 22]. We utilize the Transformer model with self-attention [51] as in the encoder following UniPS [22]. UniPS directly predicted surface normals from pixel-wise aggregated feature vectors, following other pixel-wise methods [20, 21, 25], without considering non-local interactions. However, aggregated features lose lighting-specific information, naturally obtaining lighting-invariant representations more related to surface attributes than those before aggregation. In traditional physics-based vision tasks, common constraints including isotropy [4], reciprocity symmetry [48], reflectance monotonicity [6], sparse reflectance basis [13], and surface integrability [41] are mostly shared on the surface, not limited to a single surface point. Thus, considering non-local interactions of aggregated features at multiple surface points is crucial in physics-based tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": "Applying image-wise neural networks like CNNs on the aggregated feature map demands enormous computational cost for large output resolutions (e.g., " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "2048 \\times 2048" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": "), and risks compromising output normal map details. To address these issues, we draw inspiration from recent Transformers on 3-D points [54, 61] and apply a Transformer on a fixed number (" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": ") of pixel samples (e.g., " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "m = 2048" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": ") from random locations in the input coordinate system. We term this the pixel-sampling Transformer. Unlike image-based approaches, pixel-sampling Transformer's memory consumption is constant per sample set, scaling to arbitrary image" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "2Concatenation is also possible, but it did not improve the results despite increased memory consumption." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13201" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 96, + 119 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 96, + 119 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 96, + 119 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 96, + 119 + ], + "type": "image", + "image_path": "e7f4b87a29b4ada8ec660ee722f8ee86234e0fa374370b2302043d8318e0dbe2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 120, + 92, + 127 + ], + "lines": [ + { + "bbox": [ + 55, + 120, + 92, + 127 + ], + "spans": [ + { + "bbox": [ + 55, + 120, + 92, + 127 + ], + "type": "text", + "content": "Directional" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 97, + 72, + 144, + 119 + ], + "blocks": [ + { + "bbox": [ + 97, + 72, + 144, + 119 + ], + "lines": [ + { + "bbox": [ + 97, + 72, + 144, + 119 + ], + "spans": [ + { + "bbox": [ + 97, + 72, + 144, + 119 + ], + "type": "image", + "image_path": "b23782ef88923a2c44bb73c14d1f258a0aeb3a96bbcb784ee02f4b7abaca0bc4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 110, + 120, + 129, + 127 + ], + "lines": [ + { + "bbox": [ + 110, + 120, + 129, + 127 + ], + "spans": [ + { + "bbox": [ + 110, + 120, + 129, + 127 + ], + "type": "text", + "content": "Point" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 145, + 72, + 193, + 119 + ], + "blocks": [ + { + "bbox": [ + 145, + 72, + 193, + 119 + ], + "lines": [ + { + "bbox": [ + 145, + 72, + 193, + 119 + ], + "spans": [ + { + "bbox": [ + 145, + 72, + 193, + 119 + ], + "type": "image", + "image_path": "d1292f24f8010662ce278cb2f45b9cb3f6b84402453045f20fa0e4fff7c6354c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 147, + 120, + 190, + 128 + ], + "lines": [ + { + "bbox": [ + 147, + 120, + 190, + 128 + ], + "spans": [ + { + "bbox": [ + 147, + 120, + 190, + 128 + ], + "type": "text", + "content": "Environment" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 129, + 286, + 140 + ], + "lines": [ + { + "bbox": [ + 47, + 129, + 286, + 140 + ], + "spans": [ + { + "bbox": [ + 47, + 129, + 286, + 140 + ], + "type": "text", + "content": "Figure 3. Examples in PS-Mix under different lighting conditions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 194, + 72, + 242, + 119 + ], + "blocks": [ + { + "bbox": [ + 194, + 72, + 242, + 119 + ], + "lines": [ + { + "bbox": [ + 194, + 72, + 242, + 119 + ], + "spans": [ + { + "bbox": [ + 194, + 72, + 242, + 119 + ], + "type": "image", + "image_path": "87aaee488779ebd162eb862baf3c9f16fece23fac3504307321627db407ce625.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 203, + 120, + 235, + 128 + ], + "lines": [ + { + "bbox": [ + 203, + 120, + 235, + 128 + ], + "spans": [ + { + "bbox": [ + 203, + 120, + 235, + 128 + ], + "type": "text", + "content": "Dir.+Env." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 243, + 72, + 291, + 119 + ], + "blocks": [ + { + "bbox": [ + 243, + 72, + 291, + 119 + ], + "lines": [ + { + "bbox": [ + 243, + 72, + 291, + 119 + ], + "spans": [ + { + "bbox": [ + 243, + 72, + 291, + 119 + ], + "type": "image", + "image_path": "9610746d3cde8d6832be60c51e4bd990a94e06428920f4cd2c1cd60d3e32335f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 247, + 120, + 285, + 128 + ], + "lines": [ + { + "bbox": [ + 247, + 120, + 285, + 128 + ], + "spans": [ + { + "bbox": [ + 247, + 120, + 285, + 128 + ], + "type": "text", + "content": "Point+Env." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 149, + 287, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 149, + 287, + 197 + ], + "spans": [ + { + "bbox": [ + 46, + 149, + 287, + 197 + ], + "type": "text", + "content": "sizes. Moreover, by applying the Transformer to a randomly sampled set of locations, local interactions that may lead to over-smoothing of feature maps (e.g., in CNNs) are almost entirely eliminated." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": "Concretely, given " + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": " random pixels " + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "inline_equation", + "content": "x_{i = 1,\\dots,m}" + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": " from the masked region of the input coordinate system, we interpolate features at those pixels as " + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{1,\\dots,K}(\\mathcal{S}(x_i))" + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": " is the bilinear interpolation operator. Then, interpolated features are concatenated with corresponding raw observations " + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "inline_equation", + "content": "I_{1,\\dots,K}(x_i)" + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": " and aggregated to " + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathcal{A}(x_i)" + }, + { + "bbox": [ + 46, + 198, + 287, + 388 + ], + "type": "text", + "content": " with pooling by multihead attention (PMA) [28], as in [22]. Given aggregated features at different pixels in the same sample set, we apply another naive Transformer [51] to perform non-local interactions. Since the goal of this process is to consider surface-level interactions based on physical attributes, pixel coordinate information is unnecessary. Thus, we don't apply position embeddings to samples, unlike most existing visual Transformer models (e.g. [10,33]), allowing the samples to propagate their aggregated features without location information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 389, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 485 + ], + "type": "text", + "content": "After the non-local interaction, we apply a two-layer MLP to predict surface normals at sampled locations. Finally, surface normals for each set are merged to obtain the final surface normal map at the input image resolution. This pixel-sampling Transformer approach facilitates non-local interactions while maintaining computational efficiency and preserving output normal map details, making it suitable for physics-based tasks with high-resolution images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 491, + 143, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 143, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 143, + 503 + ], + "type": "text", + "content": "3.2. PS-Mix Dataset" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": "To train their universal photometric stereo network, Ikehata [22] presented the PS-Wild training dataset, which rendered more than 10,000 scenes with commercial AdobeStock 3-D assets [1]. One of the issues in PS-Wild is that each scene consists of only a single object of uniform material. Furthermore, the environment lighting used for rendering scenes in [22] rarely has high-frequency illumination (e.g., a single point light source); therefore, the rendered images are biased towards low-frequency lighting conditions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "In this paper, we create a new training dataset that solves the issues in the PS-Wild training dataset. Instead of putting a single object of uniform material in each scene, we put multiple objects that overlap with each other in the same scene and give them different materials. To ensure that the material category is diverse in a scene, we manually categorized 897 texture maps in the AdobeStock material assets into 421 diffuse, 219 specular, and 257 metallic textures." + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 317, + 82, + 533, + 198 + ], + "blocks": [ + { + "bbox": [ + 341, + 71, + 510, + 81 + ], + "lines": [ + { + "bbox": [ + 341, + 71, + 510, + 81 + ], + "spans": [ + { + "bbox": [ + 341, + 71, + 510, + 81 + ], + "type": "text", + "content": "Table 1. Ablation study on PS-Wild-Test [22]." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 82, + 533, + 198 + ], + "lines": [ + { + "bbox": [ + 317, + 82, + 533, + 198 + ], + "spans": [ + { + "bbox": [ + 317, + 82, + 533, + 198 + ], + "type": "table", + "html": "
MethodTrainingDir.HDRIDir.+HDRI
I22 (UniPS) [22]PS-Wild17.014.513.8
Only Local (baseline)PS-Mix8.414.711.8
+Non-local (32)PS-Mix7.814.910.8
+Non-local (128)PS-Mix6.213.08.9
+Non-local (512)PS-Mix5.812.48.2
+Non-local (2048)PS-Mix5.712.28.0
+Non-local (20480)PS-Mix5.712.38.0
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(a) Comparison of different sample size " + }, + { + "bbox": [ + 305, + 355, + 545, + 388 + ], + "type": "inline_equation", + "content": "(m)" + }, + { + "bbox": [ + 305, + 355, + 545, + 388 + ], + "type": "text", + "content": " for the nonlocal interaction in the normal prediction. (b) Comparison of different input resolutions to the encoder between training and test." + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "text", + "content": "For each scene, we randomly select four objects from 410 AdobeStock 3-D models and assign three textures from all three material categories and randomly choose one for each object. Furthermore, to make the lighting conditions more diverse, instead of using only environment lighting to render images, we use five types of light source configurations and mix them to render one scene; (a) environment lighting, (b) single directional lighting, (c) single point lighting, (d) " + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "inline_equation", + "content": "(\\mathrm{a}) + (\\mathrm{b})" + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "text", + "content": ", and (e) " + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "inline_equation", + "content": "(\\mathrm{a}) + (\\mathrm{c})" + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "text", + "content": ". The direction and position of light sources are randomly assigned within the valid range of parameters3. We followed PS-Wild [22] for other rendering techniques (e.g., auto-exposure, object scale adjustment). Our dataset consists of 34,921 scenes, and each scene is rendered to output 10 of 16-bit, " + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 400, + 545, + 591 + ], + "type": "text", + "content": " images. In Fig. 3, we show sample images under each lighting condition for the same scene." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 604, + 358, + 616 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 604, + 358, + 616 + ], + "spans": [ + { + "bbox": [ + 306, + 604, + 358, + 616 + ], + "type": "text", + "content": "4. Results" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 624, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 685 + ], + "type": "text", + "content": "Training Details: Our network was trained on the PS-Mix dataset from scratch using the AdamW optimizer and a step decay learning rate schedule (" + }, + { + "bbox": [ + 304, + 624, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\times 0.8" + }, + { + "bbox": [ + 304, + 624, + 545, + 685 + ], + "type": "text", + "content": " every ten epochs) with learning-rate warmup during the first epoch. A batch size of 8, an initial learning rate of 0.0001, and a weight" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "3Light directions are selected from the upper unit hemisphere, and point light positions are selected inside the hemisphere." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13202" + } + ] + } + ], + "index": 41 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 82, + 531, + 341 + ], + "blocks": [ + { + "bbox": [ + 70, + 71, + 522, + 81 + ], + "lines": [ + { + "bbox": [ + 70, + 71, + 522, + 81 + ], + "spans": [ + { + "bbox": [ + 70, + 71, + 522, + 81 + ], + "type": "text", + "content": "Table 2. Evaluation on DiLiGenT [46] (Mean Angular Errors in degrees). All 96 images were used except where K is shown." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 82, + 531, + 341 + ], + "lines": [ + { + "bbox": [ + 61, + 82, + 531, + 341 + ], + "spans": [ + { + "bbox": [ + 61, + 82, + 531, + 341 + ], + "type": "table", + "html": "
MethodApproachTaskBallBearBuddhaCatCowGobletHarvestPot1Pot2ReadingAve.
Woodham [52]Self-Sup.Calibrated4.18.414.98.425.618.530.68.414.719.815.3
IW14 [25]Self-Sup.Calibrated2.04.88.45.413.38.718.96.910.212.09.1
IA14 [23]Self-Sup.Calibrated3.37.110.56.713.19.726.06.68.814.210.6
I18 [20]SupervisedCalibrated2.24.17.94.68.07.314.05.46.012.67.2
CW20 [9]SupervisedCalibrated2.77.77.54.86.77.812.46.27.210.97.4
LB21 [35]SupervisedCalibrated2.03.57.64.34.76.713.34.95.09.86.2
LL22a [29]Sup.+Self-Sup.Calibrated2.43.68.04.94.76.714.96.05.08.86.5
CH19 [7]SupervisedUncalibrated2.86.99.08.18.511.917.48.17.514.99.5
CW20 [9]SupervisedUncalibrated2.55.68.67.97.89.616.27.27.114.98.7
KK21 [27]Sup.+Self-Sup.Uncalibrated3.86.013.17.910.911.925.58.810.218.211.6
LL22b [30]Sup.+Self-Sup.Uncalibrated1.23.89.34.75.57.114.66.76.510.57.0
TR22 [50] (K=2)Self-Sup.Uncalibrated6.39.714.59.911.114.226.110.712.119.913.4
I22 (UniPS) [22]SupervisedUniversal4.99.119.413.011.624.225.210.89.918.814.7
OursSupervisedUniversal1.53.67.55.44.58.510.24.74.18.25.8
Ours (K=64)SupervisedUniversal1.53.67.65.54.68.610.24.74.18.35.9
Ours (K=32)SupervisedUniversal1.53.67.75.54.78.610.44.84.28.45.9
Ours (K=16)SupervisedUniversal1.53.87.76.04.88.510.84.94.48.76.1
Ours (K=8)SupervisedUniversal1.64.08.26.35.28.411.55.24.89.46.5
Ours (K=4)SupervisedUniversal1.74.110.08.66.39.014.16.15.911.47.7
Ours (K=2)SupervisedUniversal1.96.814.413.68.312.821.29.09.216.911.4
", + "image_path": "af83b276dd0f6cef471b0555d7dd1000c4774cca31d577886b822ac0158b1bf8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "type": "text", + "content": "decay of 0.05 were used. The number of input training images was randomly selected from 3 to 6 for each batch " + }, + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "type": "inline_equation", + "content": "{}^{4}" + }, + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "type": "text", + "content": " . In our work,we chose ConvNeXt-T [34] as our backbone due to its simplicity and efficiency, which is better than recent ViT-based architectures [10,32,33] with comparable performance. The training loss was the MSE loss, which computes the " + }, + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "type": "inline_equation", + "content": "{\\ell }_{2}" + }, + { + "bbox": [ + 46, + 353, + 287, + 472 + ], + "type": "text", + "content": " errors between the prediction and ground truth of surface normal vectors. Additional information, such as network architectures and feature dimensions, is provided in the appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "type": "text", + "content": "Evaluation and Time: The accuracy is evaluated based on the mean angular errors (MAE) between the predicted and true surface normal maps, measured in degrees. Training is conducted on four NVIDIA A100 cards for roughly three days. The inference time of our method depends on the number and resolution of input images. In the case of 16 input images at a resolution of " + }, + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 484, + 287, + 616 + ], + "type": "text", + "content": ", it takes a few seconds excluding I/O on a GPU. While the computational cost will vary almost linearly with the number of images, this is significantly more efficient than recent neural inverse rendering-based methods [29, 30, 40, 60]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 625, + 142, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 625, + 142, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 625, + 142, + 639 + ], + "type": "text", + "content": "4.1. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 644, + 287, + 693 + ], + "type": "text", + "content": "Firstly, we perform ablation studies to evaluate the individual contributions of our scale-invariant spatial-light feature encoder and non-local interaction with pixel-sampling transformer across varying sample sizes. To quantitatively" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "type": "text", + "content": "compare performance under various lighting conditions, we utilize the PS-Wild-Test dataset [22], which contains 50 synthetic scenes rendered under three distinct lighting setups: directional, environmental, and a mixture of both. In Table 1 and Fig. 4, we compare our method with different configurations against [22]. Note that without the scale-invariant encoder and non-local interaction (i.e., the baseline), our method is nearly equivalent to [22], except for some minor differences (e.g., backbone architecture, number of Transformer blocks in the encoder). We observe that the baseline method trained on our PX-Mix dataset improves performance for scenes under directional lighting, suggesting that one of the primary reasons why [22] was ineffective under directional lights was due to bias in the PS-Wild dataset. Accounting for non-local interaction of aggregated features enhances reconstruction accuracy, even with a small number of samples (e.g., " + }, + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "type": "inline_equation", + "content": "m = 32" + }, + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "type": "text", + "content": "), as clearly illustrated in Fig. 4-(top). Although accuracy improved as the number of samples increased, as expected, performance gains plateaued beyond a certain number (i.e., " + }, + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "type": "inline_equation", + "content": "m = 2048" + }, + { + "bbox": [ + 304, + 353, + 545, + 665 + ], + "type": "text", + "content": "). The efficacy of the scale-invariant spatial-light feature encoder was also confirmed. In Fig. 4-(bottom), we observed that a significant difference in input resolution to the backbone between training and testing led to substantial performance degradation, which further validates the advantage of our method that maintains a constant input tensor shape." + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 233, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 233, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 233, + 712 + ], + "type": "inline_equation", + "content": "^4" + }, + { + "bbox": [ + 58, + 702, + 233, + 712 + ], + "type": "text", + "content": "Six is the maximum number that can fit on our GPU." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13203" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 91, + 210 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 91, + 210 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 91, + 210 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 91, + 210 + ], + "type": "image", + "image_path": "2b363eef1580f487fb7f6257a4d43d799588463de46dfdffde07ca65c1667d86.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 211, + 77, + 220 + ], + "lines": [ + { + "bbox": [ + 60, + 211, + 77, + 220 + ], + "spans": [ + { + "bbox": [ + 60, + 211, + 77, + 220 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 47, + 230, + 287, + 251 + ], + "lines": [ + { + "bbox": [ + 47, + 230, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 230, + 287, + 251 + ], + "type": "text", + "content": "Figure 5. 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Evaluation under Directional Lighting" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 291, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 287, + 482 + ], + "type": "text", + "content": "DiLiGenT Evaluation: We first evaluate our method on the DiLiGenT benchmark [46]. Each dataset provides 96 612x512 16-bit HDR images, captured under known single directional lighting. The object mask and true surface normal map are available. In addition to UniPS [22], we also compare our method with calibrated [9,20,23,25,29,35,52] and uncalibrated [7,9,27,30,50] photometric stereo algorithms specifically designed for single directional lighting. Calibrated methods include both pixelwise [20,23,25,35,52] and image-wise [9,29] approaches. All uncalibrated methods are image-wise. We consider [27,29,30] as a combination of supervised and unsupervised learning, as pretrained models were used as a starting point for lighting prediction. To evaluate the valid number of input images, we compare our method with different numbers of input images (results are averaged over 10 random trials)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": "The results are illustrated in Table 2. Impressively, our method, which does not assume a specific lighting model, outperforms state-of-the-art calibrated methods designed for directional lights (LB21 [35], LL22a [29]). Furthermore, unlike conventional photometric stereo methods, the proposed method does not experience significant performance degradation even when the number of input images is reduced; it maintains state-of-the-art results even with only 8 images. The proposed method (" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 46, + 484, + 287, + 604 + ], + "type": "text", + "content": ") also surpasses TR22 [50], which is specialized for two input images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Recovered normal maps of HARVEST and READING are shown in Fig. 5. These objects are considered the most challenging in the benchmark due to their highly nonconvex geometry. As expected, the state-of-the-art pixelwise calibrated method (LB21 [35]) can recover finer surface details, while the state-of-the-art image-wise calibrated method (LL22a [29]) can recover more globally consistent results. However, both of them struggle to recover the nonconvex parts of the objects accurately. 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As expected, the performance of I22 [22] is severely lacking." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "text", + "content": "Evaluation without Object Mask: To demonstrate that our method does not require an object mask, we applied it to two real scenes from a deep relighting work [57], each containing 530 8-bit integer images at a resolution of " + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "text", + "content": ", captured under unknown single directional lighting using a gantry-based acquisition system. The object mask and true surface normal map are unavailable. We compared our method with state-of-the-art uncalibrated methods (CW20 [9] and LL22b [30]) and displayed the results in Fig. 6 (top). Unlike the uncalibrated methods that struggled to recover accurate lighting directions, our proposed method successfully captured object boundaries without masks, even in complex scenes with significant global illumination effects, and consistently recovered normals across the entire image. We further evaluated our method on DiLiGenT scenes without masks, as illustrated in Fig. 6 (bottom). While existing methods that assume an object mask produced highly inaccurate surface normal maps, our proposed method recovered more plausible normals with fewer images (i.e., " + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "inline_equation", + "content": "K = 16" + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "text", + "content": " vs " + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "inline_equation", + "content": "K = 96" + }, + { + "bbox": [ + 304, + 399, + 546, + 639 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 647, + 537, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 537, + 660 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 537, + 660 + ], + "type": "text", + "content": "4.3. Evaluation under Spatially-varying Lighting" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": "Our method is evaluated on challenging scenes with spatially-varying lighting conditions, comparing it to the first universal network (UniPS) [22] and a state-of-the-art uncalibrated photometric stereo method (GM21) [14] on" + } + ] + } + ], + "index": 38 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13204" + } + ] + } + ], + "index": 39 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 111, + 270 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 111, + 270 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 111, + 270 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 111, + 270 + ], + "type": "image", + "image_path": "6fcc6cafcea278138d2b761f6c2e2d56e4d00a342e5f6973cd6f521585a42266.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 270, + 89, + 278 + ], + "lines": [ + { + "bbox": [ + 70, + 270, + 89, + 278 + ], + "spans": [ + { + "bbox": [ + 70, + 270, + 89, + 278 + ], + "type": "text", + "content": "Input" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 278, + 286, + 300 + ], + "lines": [ + { + "bbox": [ + 47, + 278, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 286, + 300 + ], + "type": "text", + "content": "Figure 7. 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We test three objects (Apple, Grape, and Owl). While GM21 [14] fails and I22 [22] loses details, our method, using a scale-invariant spatial-light feature encoder and non-local interaction, produces accurate results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 371, + 286, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 286, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 286, + 479 + ], + "type": "text", + "content": "In Fig. 8, we subjectively compare our method using four objects with normal maps obtained from a 3D scanner. We align the scanned normal map to the image using MeshLab's mutual information registration filter [2], as in [46]. Our method recovers higher-definition surface normal maps than the 3D scanner (EinScan-SE) and performs well regardless of surface material. Photometric stereo performance improves with increased digital camera resolution, suggesting that 3D scanners may struggle to keep up." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 479, + 286, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 286, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 286, + 646 + ], + "type": "text", + "content": "Lastly, we demonstrate surface normal prediction for complex non-convex scenes without masks under challenging lighting conditions in Figure 9. We apply our method to three extremely challenging datasets: School Desk, Coins and Keyboard, and Sweets. School Desk is a complex scene with simple objects, non-uniform lighting, and cast shadows, making surface normal map recovery difficult. Coins and Keyboard features multiple planar objects of various materials. Sweets is a challenging scene with abundant inter-reflections and cast shadows. As demonstrated, the proposed method successfully recovers uniform surface normals, largely unaffected by shadows, and effectively reconstructs the surface micro-shape, demonstrating its scalability and detail preservation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 657, + 119, + 669 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 119, + 669 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 119, + 669 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 677, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 286, + 712 + ], + "type": "text", + "content": "In this paper, we presented a scalable, detailed, and mask-free universal photometric stereo method. 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In addition, the comparison with the only existing method [22] for the universal task showed a significant improvement over it." + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "However, several challenges still remain. Firstly, although we have observed that the proposed method works robustly for versatile lighting conditions, we found that our method is not very effective when the lighting variations are minimal. Secondly, the proposed method can easily be extended beyond normal map recovery by replacing the loss and data. In reality, we have attempted to output BRDF parameters for materials. However, due to fundamental ambiguities, it is difficult to evaluate the recovered BRDF parameters. 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In this work, we propose a scalable multi-dataset detector (ScaleDet) that can scale up its generalization across datasets when increasing the number of training datasets. Unlike existing multi-dataset learners that mostly rely on manual relabelling efforts or sophisticated optimizations to unify labels across datasets, we introduce a simple yet scalable formulation to derive a unified semantic label space for multi-dataset training. ScaleDet is trained by visual-textual alignment to learn the label assignment with label semantic similarities across datasets. Once trained, ScaleDet can generalize well on any given upstream and downstream datasets with seen and unseen classes. We conduct extensive experiments using LVIS, COCO, Objects365, OpenImages as upstream datasets, and 13 datasets from Object Detection in the Wild (ODinW) as downstream datasets. Our results show that ScaleDet achieves compelling strong model performance with an mAP of 50.7 on LVIS, 58.8 on COCO, 46.8 on Objects365, 76.2 on OpenImages, and 71.8 on ODNW, surpassing state-of-the-art detectors with the same backbone.", + "bbox": [ + 75, + 300, + 473, + 632 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 648, + 209, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Major advances in computer vision have been driven by large-scale datasets, such as ImageNet [9] and OpenImages [22] for image classification, or Kinetics [6] and ActivityNet [2] for video recognition. Large-scale datasets are crucial for training recognition models that generalize well. However, the collection of massive annotated datasets is costly and time-consuming. This is especially prominent in detection and segmentation tasks that require detailed annotations at the bounding box or pixel level. To exploit more training data without extra annotation cost, recent works unify multiple datasets to learn from more visual categories and more diverse visual domains for detection [38,40,47,51] and segmentation [25,37].", + "bbox": [ + 75, + 674, + 468, + 869 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To train an object detector across multiple datasets, we need to tackle several challenges. First, multi-dataset train", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/23165be8987746934decbbf5c8e25ea1d817393524feda1f59426d7130f57c20.jpg", + "image_caption": [ + "Figure 1. Our scalable multi-dataset detector (ScaleDet) learns across datasets in a unified semantic label space by visual-textual alignment with label semantic similarities. At test time, ScaleDet can generalize on any given upstream and downstream dataset." + ], + "image_footnote": [], + "bbox": [ + 532, + 268, + 859, + 551 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing requires unifying the heterogeneous label spaces across datasets, as label definitions are dataset-specific. The labels from two datasets may indicate the same or similar objects. For example, \"footwear\" and \"sneakers\" are two different labels in OpenImages [24] and Objects365 [34], but refer to the same type of objects (see Figure 1). Second, the training setups may be inconsistent among datasets, as different data sampling strategies and learning schedules are often required for datasets of different sizes. Third, a multi-dataset model should perform better than single-dataset models on individual datasets. This is challenging due to the heterogeneous label spaces, the domain discrepancy across datasets, and the risk of overfitting to the larger datasets.", + "bbox": [ + 496, + 627, + 893, + 823 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To resolve the above challenges, existing work resorts to manually relabelings class labels [25], or training multiple dataset-specific classifiers with constraints to relate labels across datasets [51]. However, these methods lack scalability. The manual relabeling effort and the model complex", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7288", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ity of training multiple classifiers grow rapidly as the number of datasets increases. We overcome this limitation with ScaleDet: a scalable multi-dataset detector (Figure 1). We propose two innovations: a scalable formulation to unify multiple label spaces, and a novel loss formulation to learn hard label and soft label assignments across datasets. While hard label assignment serves to disambiguate class labels in probability space, soft label assignment works as a regularizer to relate class labels in semantic similarity space. Unlike existing multi-dataset methods [25,37,38,40,47,51] that mostly generalize on seen datasets or seen classes, our method exploits vision-language learning to attain good generalization on both upstream and downstream datasets, where the downstream datasets can contain unseen classes and new domains. Our contributions are:", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel scalable multi-dataset training recipe for object detection. Our method utilizes text embeddings to unify and relate labels with semantic similarities across datasets, and trains a single classifier via visual-textual alignment to learn hard label and soft label assignments.", + "- We conduct extensive experiments to demonstrate the compelling scalability and generalizability of ScaleDet in multi-dataset training. We show that ScaleDet can boost its performance as we increase the number of training datasets: LVIS [14], COCO [27], Objects365 [34] and OpenImages [24] (Sec 4.2). Furthermore, we show that ScaleDet achieves state-of-the-art performance on multiple benchmarks when compared to recent advanced detectors, e.g., Detic [49], UniDet [51] (Sec 4.3, Sec 4.4).", + "- We evaluate the transferability of ScaleDet on the challenging \"Object Detection in the Wild\" benchmark (which contains 13 datasets) [26] to demonstrate its competitive generalizability on downstream datasets (Sec 4.5)." + ], + "bbox": [ + 73, + 318, + 468, + 590 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 602, + 218, + 617 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-dataset training aims to leverage multiple datasets to train more generalizable visual recognition models, especially for tasks that require more expensive annotations, such as detection [38, 40, 47, 51] and segmentation [25, 37]. Existing methods for multi-dataset training can be categorized into two groups. The first group introduces special network components to adapt feature representations tailored to datasets [38, 40]. For example, a domain attention module is designed to learn an adaptive multi-domain detector, which assigns different network activations to different domains [38]. The second group introduces new formulations to combine heterogeneous label spaces over multiple datasets [25, 37, 47, 51]. For instance, the MSeg dataset [25] is created upon multiple semantic segmentation datasets by relabeling with Amazon Mechanical Turk based on a manually defined taxonomy of class labels. To avoid manual relabeling, a pseudo labeling strategy [47] is used to generate pseudo labels across datasets based on predictions from", + "bbox": [ + 75, + 628, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dataset-specific detectors. Recent works use set theory with manually defined sets [37] or employ combinatorial optimization [51] to learn the label relations across datasets. Our approach is more related to the second group, but it offers a more scalable and generalizable training recipe that does not require training multiple dataset-specific classifiers [47, 51], nor manually designed rules to relate class labels [25, 37]. Furthermore, different from existing multi-dataset detectors [38, 40, 47, 51], ScaleDet is also capable of generalizing to datasets that contain unseen classes.", + "bbox": [ + 496, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-language models (VLMs) employ vision-and-language learning to solve visual recognition problems. By bridging large-scale vision and language data, vision-language models (VLMs) such as VirTex [10], CLIP [31], ALIGN [19], FILIP [43], UniCL [42] and LiT [45], have shown remarkable performance on learning transferable visual representations that generalize well to downstream tasks. More recently, VLMs have been explored in segmentation [11, 41] and detection [3, 13, 20, 26, 46, 48, 49]. In detection, most of the VLMs utilize auxiliary semantic-rich vision-language datasets as pre-training data to build models capable of solving multiple tasks including open-vocabulary detection [44], as represented by MDETR [20], RegionCLIP [48], GLIP [26, 46], X-DETR [3], and Detric [49]. For instance, MDETR uses various vision-and-language datasets (e.g., Flickr30k [30], Visual genome [23]) to train a VLM that allows instance-wise detection guided by text query. GLIP [26] uses 27M grounding data to build a unified VLM for detection and grounding. X-DETR [3] trains a VLM on grounding and image-caption datasets to solve multiple instance-wise vision-language tasks in one model. Detric [49] uses detection and large-scale classification datasets to train a large-vocabulary detector. We exploit a pre-trained text encoder similar to other VLMs, e.g., RegionCLIP uses CLIP, while MDETR, X-DETER use RoBERTa. However, our model is trained directly on detection datasets, while these other VLMs use image captioning or grounding datasets to train jointly with detection datasets.", + "bbox": [ + 496, + 243, + 892, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. ScaleDet: A Scalable Multi-Dataset Detector", + "text_level": 1, + "bbox": [ + 498, + 679, + 890, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our goal is to train object detectors that generalize better as we increase the number of datasets used for training. A critical challenge of multi-dataset training is unifying the heterogeneous label spaces across datasets by relating their semantic concepts. To tackle this challenge, we propose a simple yet effective recipe to train a scalable multi-dataset detector (ScaleDet, Figure 2). ScaleDet learns across multiple datasets by unifying different label sets to form a unified semantic label space (Figure 2 top), and is trained via hard label and soft label assignments for visual-textual alignment (Figure 2 bottom). In Sec 3.2 and Sec 3.3 we present the details of these two contributions, but first we discuss the preliminaries and problem formulation in Sec 3.1.", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7289", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ae3101b2f5da5f7603f35179399849b1335bbee5ccb6a3c225b9ad2e316a6bc7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 88, + 867, + 228 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c1c779dd2905ee8c10a90a395b12178320b5bddb52732c6d025dec1841e93e78.jpg", + "image_caption": [ + "Figure 2. Approach overview. Our scalable multi-dataset detector (ScaleDet) uses text prompts to define labels, and learns across datasets by visual-textual alignment in the unified label space. Each visual feature of an object region proposal is assigned to one corresponding label via a hard label assignment (see the loss $\\mathcal{L}_{hl}$ in Eq. (6)) and related to semantically-similar labels via a soft label assignment (see the loss $\\mathcal{L}_{sl}$ in Eq. (7)). At test time, ScaleDet can perform object detection on any given label space of a seen or unseen detection dataset." + ], + "image_footnote": [], + "bbox": [ + 98, + 229, + 864, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries and problem formulation", + "text_level": 1, + "bbox": [ + 76, + 429, + 415, + 445 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Standard object detection. A typical object detector aims to predict the bounding box location $b_{i} \\in \\mathbf{R}^{4}$ and class label $c_{i} \\in \\mathbb{R}^{n}$ for any object that belongs to a predefined set of $n$ classes. Given an image $I$ , the image encoder (e.g., CNN or Transformer) of the detector extracts the box features and visual features, which are fed to a box regressor $B$ and a visual classifier $C$ . The detector is trained by minimizing a bounding box regression loss $\\mathcal{L}_{bbox}$ and a classification loss $\\mathcal{L}_{cls}$ to learn the predictions of bounding boxes and class labels given the box features and visual features, i.e.,", + "bbox": [ + 75, + 453, + 470, + 604 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D e t} = \\mathcal {L} _ {b b o x} + \\mathcal {L} _ {c l s}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 196, + 616, + 468, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing object detectors generally adopt a one-stage [36, 52] or two-stage [15, 32] framework, which may contain additional loss terms in Eq. (1). For example, one-stage detectors use a regression loss to regress towards properties of object locations, such as centerness [36]. Two-stage detectors [15, 32] instead use a region proposal network with its own dedicated loss function that predicts the objectness of each box. In this work, we focus on reformulating the classification loss $\\mathcal{L}_{cls}$ in Eq. (1) to solve the problem of multi-dataset training, built upon a two-stage detector [50]. Multi-dataset object detection. Given a set of $K$ datasets $\\{\\mathcal{D}_1,\\mathcal{D}_2,\\dots,\\mathcal{D}_K\\}$ with their label spaces $\\{L_1,L_2,\\dots,L_K\\}$ , we aim at training a scalable multi-dataset detector that generalizes well on upstream and downstream detection datasets. In contrast to prior multi-dataset learners [25, 37, 51], which relate or merge similar labels across datasets to joint labels, we propose a simple yet scalable formula", + "bbox": [ + 75, + 642, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tion to unify labels without merging any labels explicitly. We exploit informative text embeddings from powerful pretrained visual-language models to define and relate labels over the non-identical label spaces $\\{L_1, L_2, \\dots, L_K\\}$ . We present our method in the following sections.", + "bbox": [ + 496, + 429, + 890, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Scalable unification of multi-dataset label space", + "text_level": 1, + "bbox": [ + 498, + 520, + 890, + 537 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As Figure 2 (top) shows, during training, a mini-batch of images is randomly sampled from multiple training sets and fed to the detector to obtain the visual features $\\{v_{1}, v_{2}, \\dots, v_{j}\\}$ of the region proposals for each image, where $v_{i} \\in \\mathbf{R}^{D}$ is a $D$ -dimensional vector. Each visual feature $v_{i}$ is matched to a set of text embeddings $\\{t_{1}, t_{2}, \\dots, t_{n}\\}$ by label assignment. Below, we detail how we define semantic labels with text prompts, and unify label spaces with label semantic similarities for multi-dataset training.", + "bbox": [ + 496, + 546, + 890, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Define labels with text prompts. We represent each class label $l_{i}$ with its text prompts, e.g., the label \"person\" can be denoted by a text prompt \"a photo of a person\". We extract the prompt text embeddings from the text encoder of a pre-trained visual-language model (e.g., CLIP [31] or OpenCLIP [18]), and average embeddings of a set of predefined text prompts (known as prompt engineering [31]) to represent the label $l_{i}$ as a semantic text embedding $t_{i}$ .", + "bbox": [ + 496, + 686, + 890, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unify label spaces by concatenation. Given the text embeddings of class labels from all datasets, a crucial problem of multi-dataset training is to unify the non-identical label spaces $\\{L_1,L_2,\\dots ,L_K\\}$ , which can be solved by relating and merging similar labels into a unified label set [25]. However, without careful manual inspection, this incurs the", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7290", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "risk of propagating errors in model training due to the ambiguities in label definitions, e.g., labels \"boy\" and \"girl\" are similar but should not be merged. Thus, instead of merging labels across datasets, we unify different label spaces by concatenation:", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL = L _ {1} \\coprod \\dots \\coprod L _ {K} = \\left\\{l _ {1, 1}, l _ {1, 2}, \\dots , l _ {K, 1}, l _ {K, 2}, \\dots \\right\\}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 174, + 468, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\coprod$ denotes the coproduct (i.e., the disjoint union of two label sets); $l_{k,i}$ is label $i$ from dataset $k$ (we omit $k$ below). Besides its simplicity, our formulation of this unified semantic label space $L$ maximally preserves the semantics of all labels, thus providing richer vocabulary for training.", + "bbox": [ + 75, + 202, + 468, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relate labels by semantic similarities. As we use text embeddings to represent class labels, we can relate the labels that share similar semantics, in our unified label space. For example, label \"person\" in LVIS [14] should be related to labels \"person\" and \"boy\" in OpenImages [24], as they are semantically similar. To uncover the label relations across datasets, we compute the semantic similarities using the prompt text embeddings. For a given class label $l_{i}$ , its semantic similarities with respect to all the labels are derived with cosine similarities and normalized between 0 and 1:", + "bbox": [ + 75, + 279, + 468, + 430 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s i m} \\left(l _ {i}, l _ {j}\\right) = \\frac {\\cos \\left(t _ {i} , t _ {j}\\right) - \\alpha_ {i}}{\\beta_ {i} - \\alpha_ {i}},\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 434, + 364, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{i} = \\min \\{\\cos (t_{i},t_{j})\\}_{j = 1}^{n}$ (3)", + "bbox": [ + 117, + 464, + 468, + 487 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta_ {i} = \\max \\{\\cos (t _ {i}, t _ {j}) \\} _ {j = 1} ^ {n} = \\cos (t _ {i}, t _ {i}) = 1,\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 489, + 429, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{sim}(l_i, l_j)$ is the semantic similarity between the text embeddings $t_i, t_j$ of two labels $l_i, l_j$ and it encodes their semantic relation, e.g., the labels \"person\" and \"boy\" are strongly related with a high similarity score, while \"person\" and \"avocado\" are weakly related with low similarity.", + "bbox": [ + 75, + 513, + 468, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The label semantic similarity matrix $S$ that encodes label relations among all $n$ class labels can be written as:", + "bbox": [ + 75, + 589, + 468, + 619 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS = \\left[ \\begin{array}{c c c} 1 & \\dots & \\operatorname {s i m} \\left(l _ {1}, l _ {n}\\right) \\\\ \\vdots & \\ddots & \\vdots \\\\ \\operatorname {s i m} \\left(l _ {n}, l _ {1}\\right) & \\dots & 1 \\end{array} \\right] = \\left[ \\begin{array}{c} \\mathbf {s} _ {1} \\\\ \\vdots \\\\ \\mathbf {s} _ {n} \\end{array} \\right], \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 625, + 468, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $S$ is an $n \\times n$ matrix, and each row vector $\\mathbf{s}_i$ encodes the semantic relations of label $l_i$ with respect to all $n$ class labels. With these label semantic similarities, we can introduce explicit constraints that allow the detector to learn on the unified semantic label space (Eq. (2)) with encoded label semantic similarities (Eq. (4)). Importantly, our formulas (Eq. (2), Eq. (4)) are computed offline, which does not add any computational cost for training and inference, nor requires a model reformulation when scaling up the number of training datasets.", + "bbox": [ + 75, + 688, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Training with visual-language alignment", + "text_level": 1, + "bbox": [ + 76, + 847, + 423, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For training on the unified semantic label space $\\{l_1, l_2, \\dots, l_n\\}$ , we align visual features with text embed", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dings $\\{t_1, t_2, \\dots, t_n\\}$ via the hard label and soft label assignments, as shown in Figure 2 (bottom) and detailed below.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Visual-language similarities. Given the visual feature $v_{i}$ of an object region proposal, we first compute the cosine similarities between $v_{i}$ and all text embeddings $\\{t_1, t_2, \\dots, t_n\\}$ :", + "bbox": [ + 498, + 122, + 893, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {i} = \\left[ \\cos \\left(v _ {i}, t _ {1}\\right), \\cos \\left(v _ {i}, t _ {2}\\right), \\dots , \\cos \\left(v _ {i}, t _ {n}\\right) \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 181, + 890, + 199 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With these similarity scores, we can align the visual feature $v_{i}$ to the text embeddings with the following loss terms.", + "bbox": [ + 498, + 203, + 890, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hard label assignment. Each visual feature $v_{i}$ has its groundtruth label $l_{i}$ , and thus can be matched to the text embedding $t_{i}$ of $l_{i}$ by hard label assignment as follows,", + "bbox": [ + 498, + 234, + 890, + 280 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {h l} = \\operatorname {B C E} \\left(\\sigma_ {s g} \\left(\\mathbf {c} _ {i} / \\tau\\right), l _ {i}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 287, + 890, + 305 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{BCE}(\\cdot)$ is the binary cross-entropy loss, $\\sigma_{sg}(\\cdot)$ is the sigmoid activation, $\\tau$ is a temperature hyperparameter. Eq. (6) ensures the visual feature $v_{i}$ is aligned with the text embedding $t_i$ . However, it does not explicitly learn the label relations across datasets. We introduce the soft label assignment to learn the semantic label relations.", + "bbox": [ + 496, + 311, + 890, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Soft label assignment. As each label is semantically related to all class labels through the semantic similarities computed in Eq. (4), a visual feature can also be related to all text embeddings by using the semantic similarity scores. For this aim, we introduce the soft label assignment on the visual feature $v_{i}$ :", + "bbox": [ + 496, + 402, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s l} = \\operatorname {M S E} \\left(\\mathbf {c} _ {i}, \\mathbf {s} _ {i}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 502, + 890, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{MSE}(\\cdot)$ is mean square error. $\\mathbf{s}_i$ denotes the semantic similarities between the label $l_{i}$ and all $n$ class labels - the $i_{th}$ row of the label semantic similarity matrix $S$ in Eq. (3).", + "bbox": [ + 496, + 525, + 890, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark. While hard label assignment (Eq. (6)) is imposed in probability space to disambiguate different class labels, soft label assignment (Eq. (7)) is imposed in semantic similarity space to assign each visual feature to the text embeddings with different semantic similarities, thus acting as a regularizer to relate similar class labels across datasets.", + "bbox": [ + 496, + 571, + 890, + 661 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training with semantic label supervision. With the hard label and soft label assignments, we train the detector to classify different region proposals by aligning visual features to text embeddings in the unified semantic label space. That is, the classification loss $\\mathcal{L}_{cls}$ in Eq. (1) is replaced by", + "bbox": [ + 496, + 662, + 890, + 739 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {l a n g}} = \\mathcal {L} _ {h l} + \\lambda \\mathcal {L} _ {s l}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 622, + 746, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\lambda$ is a hyperparameter to balance the two loss terms. Eq. (8) uses language supervision to map images to texts, thus enabling zero-shot detection of unseen labels.", + "bbox": [ + 496, + 770, + 890, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Overall objective. As we focus on reformulating the classification loss of our detector for multi-dataset training, we do not change the loss $\\mathcal{L}_{bbox}$ in Eq. (1) and our overall objective for training ScaleDet is:", + "bbox": [ + 496, + 816, + 890, + 877 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {S c a l e D e t}} = \\mathcal {L} _ {\\text {b b o x}} + \\mathcal {L} _ {\\text {l a n g}}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 885, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7291", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once trained with $\\mathcal{L}_{ScaleDet}$ , ScaleDet can be deployed on any upstream or downstream datasets that contain seen or unseen classes. By replacing the unified label space $L$ in Eq. (2) with the label space of any given test dataset, ScaleDet can compute the label assignment based on the visual-language similarities derived in Eq. (3). When the test dataset contains unseen classes, the evaluation setting is known as zero-shot detection [1] or open-vocabulary object detection [44]. To test on any given dataset, ScaleDet can either be directly evaluated or fine-tuned before evaluation.", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 258, + 209, + 275 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We detail our experiment setups in Sec 4.1. We analyze ScaleDet when training with an increasing number of datasets in Sec 4.2, and compare it to the state-of-the-art (SOTA) on standard benchmarks in Sec 4.3 and Sec 4.4. We evaluate the transferability of ScaleDet on downstream datasets in Sec 4.5, and conduct ablation study in Sec 4.6. We also provide qualitative visual results in Supplementary.", + "bbox": [ + 75, + 284, + 470, + 391 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment setups", + "text_level": 1, + "bbox": [ + 76, + 401, + 256, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Upstream datasets. For our multi-dataset training, we adopt the following four popular detection datasets as upstream datasets: (1) COCO [27] (C) contains 80 common object categories; (2) LVIS [14] (L) has a large number of 1203 object categories with a challenging long tail distribution; (3) Objects365 [34] (O365) has 365 object categories; (4) OpenImages detection (OID) [24] has 601 object categories in the sixth version. When we train ScaleDet on these four datasets, there are 2249 class labels in the unified label space (Eq. (2)) and 3.7M training images.", + "bbox": [ + 75, + 426, + 468, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Downsteam datasets. To evaluate the transferability on diverse unseen datasets, we adopt the recent challenging \"Object Detection in the Wild\" (ODinW) benchmark [26]. It contains 13 public object detection datasets with very different application domains, to mimic diverse and challenging real-world scenarios. Some of these datasets capture seen classes in unseen domains, like people in thermal images, while others capture unseen classes, like \"jellyfish\" and \"stingray\" in aquariums (Figure 1, bottom right). To evaluate on ODinW, the models can be evaluated directly (direct transfer) or evaluated after fine-tuning (fine-tune transfer).", + "bbox": [ + 75, + 579, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. For evaluation on upstream datasets, we use the standard mAP metric (i.e., mAP at IoU thresholds 0.5 to 0.95) on COCO, LVIS and Objects365. On OpenImages, we follow the official evaluation protocol that uses mAP@0.5 and an expanded semantic class hierarchy [24]. For evaluation on downstream datasets, we follow [26] and report the average mAP over 13 datasets in this section. We provide the detailed qualitative and quantitative results on individual datasets in Supplementary.", + "bbox": [ + 75, + 747, + 468, + 883 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. In our experiments, unless explicit", + "bbox": [ + 76, + 885, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/cf32fe95474fdf190c2896fa086fe4f3307ff41dee0d1d1543ab1b910884cb7c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelDataset(s)LCO365OIDmAP
baselineL33.137.015.241.531.7
C11.046.87.933.124.7
O36519.239.828.847.633.9
OID15.731.314.169.332.6
ScaleDetL,C33.344.915.943.734.5
L,C,O36536.547.031.244.939.9
L,C,O365,OID36.847.130.669.446.0
", + "bbox": [ + 513, + 88, + 877, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Training with an increasing number of datasets. The best results on single-/multi-dataset training are in green/ bold. Backbone: ResNet50. mAP is the mean AP across datasets.", + "bbox": [ + 498, + 224, + 890, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is stated, we use CenterNet2 [50] with a backbone pretrained on ImageNet21k [33]. We use prompt text embeddings from CLIP [31] or OpenCLIP [18] to encode class labels. For augmentation, we use large scale jittering [12] and efficient resize crop [49] with an input size of $640 \\times 640$ , $896 \\times 896$ when using ResNet50 [16], Swin Transformer [28] as backbone. We use an input size of $800 \\times 1333$ for testing. We use Adam optimizer [21] and train on 8 V100 GPUs. For multi-dataset training, we directly combine all datasets and use repeat factor sampling [14], without using any multi-dataset sampling strategy. More details about learning schedules of different tables are in Supplementary.", + "bbox": [ + 496, + 282, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Training with a growing number of datasets", + "text_level": 1, + "bbox": [ + 498, + 478, + 872, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation setup. We setup the single-dataset baseline by training on individual datasets. We use text embeddings to represent the class labels for each dataset, and train the detector on each dataset by hard label assignment (Eq. (6)). To evaluate how ScaleDet scales as we increase the number of training datasets, we train it using the following incremental combinations: (1) LVIS+COCO, (2) LVIS+COCO+O365, (3) LVIS+COCO+O365+OID. These increase the dataset size from $218k \\rightarrow 1.96M \\rightarrow 3.7M$ and the number of class labels from $1283 \\rightarrow 1648 \\rightarrow 2249$ . After training the baseline and ScaleDet, we replace the text embeddings in Eq. (5) to represent the labels of each dataset for evaluation. For example, to evaluate on COCO we set the text embeddings to represent the 80 classes of COCO and derive class predictions based on visual-textual similarities.", + "bbox": [ + 496, + 503, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To make the evaluation efficient, for the results in Table 1, Figure 3 and Figure 4 we use a fixed input size of $640 \\times 640$ , a ResNet50 [16] backbone and text embeddings from CLIP [31]. We then explore using larger backbones (Swin Transformers [28]) and text embeddings from OpenCLIP [18] for the analysis of backbones in Table 2.", + "bbox": [ + 496, + 732, + 890, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Effect on upstream datasets. Table 1 shows the evaluation on upstream datasets when increasing the number of datasets, from which we can observe the followings. First, scaling up the number of training datasets consistently leads to better model performance, e.g., the mAP on", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7292", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0fb805bec4e6498ba9c2ebf8f2d4c65b790f5f6c1d0ba429c5292d67ca30db61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 122, + 95, + 423, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a8f8164f9bf3611466a436875daeb7ed16f6f0626666c20259b4e4e4aa694392.jpg", + "image_caption": [ + "Figure 3. Direct transfer results on ODinW benchmark when scaling up the number of training datasets. Number 1-4 in $x$ -axis means using L, L+C, L+C+O365, L+C+O365+OID for training. Details of unseen classes, qualitative results are in Supplementary.", + "Figure 4. Direct transfer to different datasets on ODinW benchmark when scaling up the number of training datasets." + ], + "image_footnote": [], + "bbox": [ + 106, + 330, + 439, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "LVIS is improved from 33.1, 33.3, 36.5, to 36.8 when increasing the number of training sets from 1 to 4. Second, multi-dataset training with ScaleDet is generally better than single-dataset training (baseline), e.g., the mAP on LVIS, COCO, O365, OID are greatly improved from 33.1, 46.8, 28.8, 69.3 (baseline) to 36.8, 47.1, 30.6, 69.4 when training on all datasets. This suggests that ScaleDet learns well across heterogeneous label spaces, diverse domains of different datasets, and does not overfit to any specific datasets.", + "bbox": [ + 75, + 565, + 467, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect on downstream datasets. Figure 3 shows the results of direct transfer on the ODinW benchmark. Notably, scaling up the number of training datasets for ScaleDet significantly improves its accuracy (mAP) on downstream datasets, for all settings (i.e., over datasets, over classes and over unseen classes). In Figure 4 we further visualize the performance of ScaleDet on some of the downstream datasets in ODinW. These datasets either contain unseen classes or come from the visual domains that are very different from those used for training. Importantly, ScaleDet performs well on both scenarios. For example, thermalDogsAndPeople contains novel thermal images, yet multi-dataset training with ScaleDet is capable of boosting its per", + "bbox": [ + 75, + 704, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3db3123c84d725406b9d295ec4f10d1a99774b8e419d80d54cdffadee6052f30.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelTextLCO365OIDmAP
1ScaleDet-RCLIP36.847.130.669.446.0
2ScaleDet-TCLIP42.751.235.973.650.9
3ScaleDet-TOpenCLIP43.951.436.374.151.4
4ScaleDet-BCLIP50.455.643.775.756.3
5ScaleDet-BOpenCLIP50.755.443.876.256.5
6ScaleDet-B*OpenCLIP50.658.846.875.958.0
", + "bbox": [ + 513, + 89, + 874, + 212 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Different backbones for multi-dataset training. R: ResNet50. T, B: Swin-Tiny, Swin-Base transformer. *: further fine-tune the model on each dataset after multi-dataset training.", + "bbox": [ + 500, + 217, + 890, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "formance considerably from $19.4\\mathrm{mAP}$ (single-dataset) to 40.6 (all 4). Furthermore, Raccoon requires the localization of an unseen class, yet again ScaleDet improves zero-shot detection from $39.2\\mathrm{mAP}$ (single-dataset) to 48.3 (all 4). Overall, Figure 3 and Figure 4 show how ScaleDet can utilize the synergistic benefits of different upstream datasets to boost its generalization on downstream datasets.", + "bbox": [ + 496, + 273, + 890, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of different backbones. We now test ScaleDet with different backbones and text embeddings (Table 2). Enhancing the discriminative power of the image backbone from ResNet50 [16] to Swin-Base Transformer [28] significantly boosts the mAP from 46.0 to 56.3 (row 1 vs 4). Changing the text embeddings from CLIP to OpenCLIP instead helps mostly when using weaker backbones (e.g., +0.5 mAP with ScaleDet-T, row 2 vs 3), as opposed to stronger ones (e.g., +0.2 mAP with ScaleDet-B, row 4 vs 5). Finally, with fine-tuning ScaleDet can be further improved from 56.5 to 58.0 in mAP (row 5 vs 6). Overall, all these results suggest that ScaleDet can leverage the complementary power of scalable training sets and strong backbones to achieve competitive model performance.", + "bbox": [ + 496, + 381, + 890, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison to SOTA multi-dataset detectors", + "text_level": 1, + "bbox": [ + 500, + 603, + 880, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we provide an apple-to/apple comparison of ScaleDet against the two latest state-of-the-art (SOTA) multi-dataset detectors: UniDet [51] and Detric [49].", + "bbox": [ + 496, + 627, + 890, + 672 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison to UniDet. In Table 3, we follow the settings of UniDet [51] and train ScaleDet on the same datasets (COCO, O365, OID), using the same ResNet50 backbone, SGD optimizer and standard data augmentation in the Detecron2 codebase [39]. In UniDet, multiple dataset-specific classifiers are trained, while ScaleDet is trained with semantic labels by one classifier. Table 3 shows the comparison on multi-dataset training. ScaleDet outperforms UniDet, yielding an mAP of 47.7 vs 45.4. Moreover, ScaleDet has better improved margins for multi-dataset training over single-dataset training (row 4,3 vs 2,1). The improved margin in mAP is 2.6 points (47.7 vs 45.1) by ScaleDet vs 1.1 points (45.4 vs 44.3) by UniDet. These results show the benefit of learning in a unified semantic label space, as opposed to training multiple dataset-specific classifiers (UniDet).", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7293", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d636e7da16884c76d27cd4ac6c44c60312d5a2357066355009576cdfe8ad04b3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelDataset(s)COCOO365OIDmAP
1UniDetsingle42.524.965.744.3
2multiple45.524.666.045.4
3ScaleDetsingle42.126.566.645.1
4multiple45.527.969.647.7
", + "bbox": [ + 86, + 88, + 455, + 181 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0926a478d8031bfe217ea130f107b95a8d2f41718afda7cf1be89226da453a43.jpg", + "table_caption": [ + "Table 3. Comparison to UniDet [51] on multi-dataset training with COCO, O365 and OID. Backbone: ResNet50 pre-trained on ImageNet1k. \"single\": training with one single training set same as the test set. \"multiple\": multi-dataset training with COCO,O365,OID. mAP is the mean AP across datasets." + ], + "table_footnote": [], + "table_body": "
ModelDatasetsLVISCOCOmAP
1Detric [49]L,C33.043.938.4
2ScaleDetL,C33.344.939.1
3Detric [49]L,C,IN21k35.442.438.9
4ScaleDetL,C,O36536.547.041.7
5ScaleDetL,C,O365,OID36.847.141.9
", + "bbox": [ + 86, + 258, + 455, + 366 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison to Detric. In Table 4, we follow the settings of Detric [49] and perform multi-dataset training on LVIS and COCO, using a ResNet50 backbone. In Detric, the unified label space for LVIS and COCO contains 1203 class labels, obtained by merging two label sets with wordnet synsets, while ScaleDet 'flatens' their labels (1203+80) to 1283. Table 4 (row 1 and 2) presents the comparison. ScaleDet outperforms Detric by 1 point on COCO (44.9 vs. 43.9) and $0.7\\mathrm{mAP}$ on average. Next, we compare ScaleDet and Detric with more training sets (Table 4, row 3-5). ScaleDet is trained using more detection datasets (O365,OID), while Detric uses 14M additional classification images (ImageNet21) as a large-scale weakly annotated dataset for detection. Our results show that, although Detric is trained with far more data and class labels than ScaleDet (12.6M images and 22k classes after data cleaning vs 3.7M images and 2k classes), ScaleDet still surpasses Detric's performance by a large margin of $3.0\\mathrm{mAP}$ points (41.9 vs. 38.9). These results show the importance of learning from multiple detection datasets and the effectiveness of ScaleDet in doing so.", + "bbox": [ + 75, + 470, + 472, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison to SOTA detectors on COCO", + "text_level": 1, + "bbox": [ + 76, + 800, + 434, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we compare ScaleDet to different types of SOTA detectors on standard COCO benchmark. The different models cover four major types: (1) single-dataset detectors; (2) detectors trained with vision-and-language understanding datasets, e.g., UniT [17] is trained on 7 tasks", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f43f10388576bdf93e3236790b65f58c7f5ed8f56ef4050293565dcb3895dec4.jpg", + "table_caption": [ + "Table 4. Comparison to Detric [49] on multi-dataset training with LVIS (L) and COCO (C). Backbone: ResNet50. IN21k: ImageNet21k [9]. In row 1-2, both Detric and ScaleDet are trained with only LVIS and COCO, thus providing a like-to-like comparison. In row 3, 4, 5, the training data size is 12.6M, 1.96M, 3.7M respectively. mAP is the mean AP across datasets." + ], + "table_footnote": [], + "table_body": "
ModelModel TypemAP
1Faster RCNN [32]37.9
2Mask RCNN [15]39.8
3CenterNet [52]single-dataset40.2
4CascadeRCNN [4]detection41.6
5DETR [5]42.0
6CenterNet2 [50]42.9
7UniT [17]detection +42.3
8RegionCLIP [48]understanding42.7
9Detic [49]detection + classification42.4
10UniDet [51]multi-dataset45.5
11ScaleDetdetection47.1
", + "bbox": [ + 535, + 88, + 856, + 297 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note: \"understanding\", \"classification\" mean training with vision-and-language understanding, and classification datasets respectively. All methods include COCO dataset for training.", + "bbox": [ + 498, + 316, + 890, + 358 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e29cf62b0ec5605ac28652bf90aaec94fc80ba82ecd68f4e70c886c6d9c686d3.jpg", + "table_caption": [ + "Table 5. Comparison on COCO using ResNet50 as backbone." + ], + "table_footnote": [], + "table_body": "
ModelModel TypemAP
1Faster RCNN-T [32]single-dataset46.0
2DyHead-T [8]detection49.7
3CascadeRCNN-T [4]50.4
4GLIP-T [26]detection +55.2
5GLIPv2-T [46]understanding55.5
6GLIPv2-B [46]58.8
7Detic-B [49]detection + classification54.9
8ScaleDet-Bmulti-dataset detection58.8
", + "bbox": [ + 535, + 361, + 854, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Comparison on COCO using Swin Transformer as backbone. T, B: Swin-Tiny, Swin-Base Transformer. Note: GLIPv2-B uses 20.5M data: 3.7M detection data (COCO, O365, OID, Visual genome [23], ImageNetBoxes [9]), 16.8M grounding and caption data (GoldG [20], CC15M [7, 35], SBU [29]); while ScaleDet-B uses 3.5M data (LVIS,COCO,O365,OID).", + "bbox": [ + 498, + 545, + 890, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "over 8 datasets and RegionCLIP [48] is trained with 3M image-text pairs from Conceptual Caption [35]; (3) detector trained with image classification dataset, i.e., Detric [49] is trained with ImageNet21k [9]; (4) multi-dataset detector trained with only detection datasets, e.g., UniDet [51].", + "bbox": [ + 496, + 643, + 890, + 718 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We train our ScaleDet using LVIS, COCO, O365, OID and present the results in Table 5, where all models are trained using a ResNet50 backbone. ScaleDet obtains the best performance among 11 models. Moreover, compared to detectors trained with large vision-and-language or classification datasets (row 7-9), ScaleDet gives much better performance, even though it learns a much smaller number of concepts - ScaleDet achieves 47.1 by \"only\" learning 2249 labels, while RegionCLIP and Detic achieve 42.7 and 42.4 by learning 6790 and 22047 concepts, respectively.", + "bbox": [ + 496, + 719, + 890, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 6, we compare ScaleDet to competitors using Swin Transformers as backbone. With this strong back", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7294", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/838175868b300525b134c4d5549064f20caf39a809abef25af8e48dbb8060714.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelModel Type#DataODinW
directfine-tune
GLIP-T [26]detection + understanding5.5M46.564.9
GLIPv2-T [46]5.5M48.566.5
GLIPv2-B [46]20.5M54.269.4
Detic-R [49]detection + classification12.6M29.464.4
Detic-B [49]12.6M38.770.1
ScaleDet-R3.6M39.468.5
ScaleDet-Tdetection3.6M44.370.4
ScaleDet-B3.6M47.371.8
", + "bbox": [ + 89, + 88, + 454, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "bone, ScaleDet demonstrates SOTA performance with high data-efficiency among all models. Among all competitors, the recent GLIPv2-B [46] is the only model performing onpar with ScaleDet (58.8), but using almost an order of magnitude more training data than ScaleDet (20.5M vs. 3.5M).", + "bbox": [ + 75, + 334, + 467, + 410 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Overall, our results in Table 5 and Table 6 show that ScaleDet offers a data-efficient training recipe that can learn from fewer visual concepts and less training data, but still achieves state-of-the-art performance on COCO.", + "bbox": [ + 76, + 410, + 468, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Comparison of SOTA on ODinW", + "text_level": 1, + "bbox": [ + 76, + 481, + 366, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We evaluate the transferability on the \"Object Detection in the Wild\" (ODinW) benchmark and compare ScaleDet with SOTA pre-trained detectors that are capable of both direct and fine-tune transfer given any downstream detection datasets. Table 7 shows the comparison on ODinW among 3 types of detectors: (1) GLIP [26], GLIPv2 [46], (2) Detric [49], and (3) ScaleDet. ScaleDet is trained with the smallest training data, yet it achieves the best results in fine-tune transfer, surpassing even GLIPv2-B by 2.4 points (71.8 vs. 69.4). On direct transfer, GLIPv2-B is however stronger; we conjecture that this is thanks to its massive visual-language training data (20.5M), which likely covers the unseen concepts in the downstream datasets. Furthermore, when comparing ScaleDet-R, ScaleDet-B to Detric-R, Detric-B, we find the results of ScaleDet are significantly better, e.g., ScaleDet-R outperforms Detric-R by 10.0 points (39.4 vs. 29.4) on direct transfer and by 4.1 (68.5 vs. 64.4) on fine-tune transfer. These observations show the efficacy of ScaleDet in transferring to downstream datasets.", + "bbox": [ + 75, + 503, + 468, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 801, + 225, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we ablate the components of our ScaleDet. As described in Sec. 3, ScaleDet is trained with two loss terms: the hard label assignment $\\mathcal{L}_{hl}$ (Eq. (6)), and the soft label assignment $\\mathcal{L}_{sl}$ (Eq. (7)). $\\mathcal{L}_{hl}$ aims to assign each visual feature to one corresponding label, while $\\mathcal{L}_{sl}$ works as a", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fc18311f7a6e0f43c895ec1cdbbadca67d0356ca63f6da12fd5c5caa352d97f4.jpg", + "table_caption": [ + "Table 7. Results of direct and fine-tune transfer on ODinW. R, T, B: ResNet50, Swin-Tiny, Swin-Base Transformer as backbone. Metric: mAP over 13 datasets. Note: \"understanding\", \"classification\" mean training with vision-and-language understanding, and classification datasets besides detection data." + ], + "table_footnote": [], + "table_body": "
ModelDatasetsLCO365OIDmAP
LhlL,C33.144.615.743.234.2
Lhl+Lsl33.344.915.943.734.5
LhlL,C,O365,OID36.746.730.869.145.8
Lhl+Lsl36.847.130.669.446.0
", + "bbox": [ + 532, + 88, + 861, + 172 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ba02c88a4587ee3337abf6dbdfc31ebf6f6f7a0a5806742e0a13092c90aafe8d.jpg", + "table_caption": [ + "(a) Ablation on upstream datasets." + ], + "table_footnote": [], + "table_body": "
ModelDatasetsODinW
MetricmAP\\( \\mathrm{mAP}_C \\)
\\( \\mathcal{L}_{hl} \\)L,C26.932.1
\\( \\mathcal{L}_{hl} + \\mathcal{L}_{sl} \\)26.932.5
\\( \\mathcal{L}_{hl} \\)L,C,O365,OID37.939.8
\\( \\mathcal{L}_{hl} + \\mathcal{L}_{sl} \\)39.440.9
", + "bbox": [ + 558, + 188, + 836, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(b) Ablation on downstream benchmark ODinW by direct transfer.", + "bbox": [ + 519, + 294, + 872, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Ablation study on upstream datasets (a) and downstream datasets (b). mAP is the mean AP over datasets; $\\mathrm{mAP}_C$ is the mean AP over all classes; better mAP of each setup is in bold.", + "bbox": [ + 500, + 309, + 890, + 352 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "regularizer to relate labels across datasets. Table 8a shows our ablation study on 4 upstream datasets and Table 8b shows our ablation of direct transfer on downstream benchmark ODinW. We find that training with two loss terms $(\\mathcal{L}_{hl} + \\mathcal{L}_{sl})$ leads to better overall results on both upstream and downstream datasets. For instance, in Table 8a, when training with two datasets $(\\mathrm{L} + \\mathrm{C})$ , $\\mathcal{L}_{hl} + \\mathcal{L}_{sl}$ gives consistent better results on 4 upstream datasets compared to $\\mathcal{L}_{hl}$ . In Table 8b, when using $\\mathcal{L}_{hl} + \\mathcal{L}_{sl}$ to train on four training sets $(\\mathrm{L} + \\mathrm{C} + \\mathrm{O}365 + \\mathrm{OID})$ , the mAP is greatly improved by 1.5 points (39.4-37.9) and $\\mathrm{mAP}_C$ is improved by 1.1 points (40.9-39.8), as compared to using only $\\mathcal{L}_{sl}$ . This suggests that $\\mathcal{L}_{sl}$ is valuable to improve the model's generalizability. Overall, these results indicate that $\\mathcal{L}_{hl}$ works effectively for label assignment within the upstream dataset, while $\\mathcal{L}_{sl}$ takes a complementary role that is more evident when transferring to downstream datasets.", + "bbox": [ + 496, + 378, + 890, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 500, + 671, + 767, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present ScaleDet, a simple yet scalable and effective multi-dataset training recipe for detection. ScaleDet learns across multiple datasets in a unified semantic label space, optimized by hard label and soft label assignments to align visual and text embeddings. ScaleDet achieves the new state-of-the-art performance on multiple upstream datasets (LVIS, COCO, Objects365, OpenImages) and downstream datasets (ODinW). As the key success of ScaleDet lies in learning in a unified semantic label space, our formulation can also generalize to other vision tasks such as image classification and semantic segmentation. We leave the unified design of a generic multi-dataset multi-task foundation model as promising and exciting future endeavors.", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7295", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ankan Bansal, Karan Sikka, Gaurav Sharma, Rama Chellappa, and Ajay Divakaran. Zero-shot object detection. In ECCV, 2018. 5", + "[2] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. In CVPR, 2015. 1", + "[3] Zhaowei Cai, Gukyeong Kwon, Avinash Ravichandran, Erhan Bas, Zhuowen Tu, Rahul Bhotika, and Stefano Soatto. 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Objects as points. arXiv preprint arXiv:1904.07850, 2019. 3, 7" + ], + "bbox": [ + 501, + 92, + 890, + 345 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7297", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/483d2038-de2f-43cc-b2e7-cfb0359bee59_model.json b/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/483d2038-de2f-43cc-b2e7-cfb0359bee59_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c311be57239314b3d4ee576cb5e3901f464ec97e --- /dev/null +++ b/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/483d2038-de2f-43cc-b2e7-cfb0359bee59_model.json @@ -0,0 +1,2156 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.223, + 0.131, + 0.748, + 0.152 + ], + "angle": 0, + "content": "ScaleDet: A Scalable Multi-Dataset Object Detector" + }, + { + "type": "text", + "bbox": [ + 0.242, + 0.181, + 0.728, + 0.233 + ], + "angle": 0, + "content": "Yanbei Chen, Manchen Wang, Abhay Mittal, Zhenlin Xu, Paolo Favaro, Joseph Tighe, Davide Modolo AWS AI Labs" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.284 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.633 + ], + "angle": 0, + "content": "Multi-dataset training provides a viable solution for exploiting heterogeneous large-scale datasets without extra annotation cost. In this work, we propose a scalable multi-dataset detector (ScaleDet) that can scale up its generalization across datasets when increasing the number of training datasets. Unlike existing multi-dataset learners that mostly rely on manual relabelling efforts or sophisticated optimizations to unify labels across datasets, we introduce a simple yet scalable formulation to derive a unified semantic label space for multi-dataset training. ScaleDet is trained by visual-textual alignment to learn the label assignment with label semantic similarities across datasets. Once trained, ScaleDet can generalize well on any given upstream and downstream datasets with seen and unseen classes. We conduct extensive experiments using LVIS, COCO, Objects365, OpenImages as upstream datasets, and 13 datasets from Object Detection in the Wild (ODinW) as downstream datasets. Our results show that ScaleDet achieves compelling strong model performance with an mAP of 50.7 on LVIS, 58.8 on COCO, 46.8 on Objects365, 76.2 on OpenImages, and 71.8 on ODNW, surpassing state-of-the-art detectors with the same backbone." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.649, + 0.21, + 0.665 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Major advances in computer vision have been driven by large-scale datasets, such as ImageNet [9] and OpenImages [22] for image classification, or Kinetics [6] and ActivityNet [2] for video recognition. Large-scale datasets are crucial for training recognition models that generalize well. However, the collection of massive annotated datasets is costly and time-consuming. This is especially prominent in detection and segmentation tasks that require detailed annotations at the bounding box or pixel level. To exploit more training data without extra annotation cost, recent works unify multiple datasets to learn from more visual categories and more diverse visual domains for detection [38,40,47,51] and segmentation [25,37]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To train an object detector across multiple datasets, we need to tackle several challenges. First, multi-dataset train" + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.269, + 0.861, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.555, + 0.895, + 0.611 + ], + "angle": 0, + "content": "Figure 1. Our scalable multi-dataset detector (ScaleDet) learns across datasets in a unified semantic label space by visual-textual alignment with label semantic similarities. At test time, ScaleDet can generalize on any given upstream and downstream dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.895, + 0.824 + ], + "angle": 0, + "content": "ing requires unifying the heterogeneous label spaces across datasets, as label definitions are dataset-specific. The labels from two datasets may indicate the same or similar objects. For example, \"footwear\" and \"sneakers\" are two different labels in OpenImages [24] and Objects365 [34], but refer to the same type of objects (see Figure 1). Second, the training setups may be inconsistent among datasets, as different data sampling strategies and learning schedules are often required for datasets of different sizes. Third, a multi-dataset model should perform better than single-dataset models on individual datasets. This is challenging due to the heterogeneous label spaces, the domain discrepancy across datasets, and the risk of overfitting to the larger datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To resolve the above challenges, existing work resorts to manually relabelings class labels [25], or training multiple dataset-specific classifiers with constraints to relate labels across datasets [51]. However, these methods lack scalability. The manual relabeling effort and the model complex" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7288" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.317 + ], + "angle": 0, + "content": "ity of training multiple classifiers grow rapidly as the number of datasets increases. We overcome this limitation with ScaleDet: a scalable multi-dataset detector (Figure 1). We propose two innovations: a scalable formulation to unify multiple label spaces, and a novel loss formulation to learn hard label and soft label assignments across datasets. While hard label assignment serves to disambiguate class labels in probability space, soft label assignment works as a regularizer to relate class labels in semantic similarity space. Unlike existing multi-dataset methods [25,37,38,40,47,51] that mostly generalize on seen datasets or seen classes, our method exploits vision-language learning to attain good generalization on both upstream and downstream datasets, where the downstream datasets can contain unseen classes and new domains. Our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.319, + 0.47, + 0.395 + ], + "angle": 0, + "content": "- We propose a novel scalable multi-dataset training recipe for object detection. Our method utilizes text embeddings to unify and relate labels with semantic similarities across datasets, and trains a single classifier via visual-textual alignment to learn hard label and soft label assignments." + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.395, + 0.47, + 0.53 + ], + "angle": 0, + "content": "- We conduct extensive experiments to demonstrate the compelling scalability and generalizability of ScaleDet in multi-dataset training. We show that ScaleDet can boost its performance as we increase the number of training datasets: LVIS [14], COCO [27], Objects365 [34] and OpenImages [24] (Sec 4.2). Furthermore, we show that ScaleDet achieves state-of-the-art performance on multiple benchmarks when compared to recent advanced detectors, e.g., Detic [49], UniDet [51] (Sec 4.3, Sec 4.4)." + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.53, + 0.469, + 0.591 + ], + "angle": 0, + "content": "- We evaluate the transferability of ScaleDet on the challenging \"Object Detection in the Wild\" benchmark (which contains 13 datasets) [26] to demonstrate its competitive generalizability on downstream datasets (Sec 4.5)." + }, + { + "type": "list", + "bbox": [ + 0.074, + 0.319, + 0.47, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.603, + 0.22, + 0.618 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Multi-dataset training aims to leverage multiple datasets to train more generalizable visual recognition models, especially for tasks that require more expensive annotations, such as detection [38, 40, 47, 51] and segmentation [25, 37]. Existing methods for multi-dataset training can be categorized into two groups. The first group introduces special network components to adapt feature representations tailored to datasets [38, 40]. For example, a domain attention module is designed to learn an adaptive multi-domain detector, which assigns different network activations to different domains [38]. The second group introduces new formulations to combine heterogeneous label spaces over multiple datasets [25, 37, 47, 51]. For instance, the MSeg dataset [25] is created upon multiple semantic segmentation datasets by relabeling with Amazon Mechanical Turk based on a manually defined taxonomy of class labels. To avoid manual relabeling, a pseudo labeling strategy [47] is used to generate pseudo labels across datasets based on predictions from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "dataset-specific detectors. Recent works use set theory with manually defined sets [37] or employ combinatorial optimization [51] to learn the label relations across datasets. Our approach is more related to the second group, but it offers a more scalable and generalizable training recipe that does not require training multiple dataset-specific classifiers [47, 51], nor manually designed rules to relate class labels [25, 37]. Furthermore, different from existing multi-dataset detectors [38, 40, 47, 51], ScaleDet is also capable of generalizing to datasets that contain unseen classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.893, + 0.668 + ], + "angle": 0, + "content": "Vision-language models (VLMs) employ vision-and-language learning to solve visual recognition problems. By bridging large-scale vision and language data, vision-language models (VLMs) such as VirTex [10], CLIP [31], ALIGN [19], FILIP [43], UniCL [42] and LiT [45], have shown remarkable performance on learning transferable visual representations that generalize well to downstream tasks. More recently, VLMs have been explored in segmentation [11, 41] and detection [3, 13, 20, 26, 46, 48, 49]. In detection, most of the VLMs utilize auxiliary semantic-rich vision-language datasets as pre-training data to build models capable of solving multiple tasks including open-vocabulary detection [44], as represented by MDETR [20], RegionCLIP [48], GLIP [26, 46], X-DETR [3], and Detric [49]. For instance, MDETR uses various vision-and-language datasets (e.g., Flickr30k [30], Visual genome [23]) to train a VLM that allows instance-wise detection guided by text query. GLIP [26] uses 27M grounding data to build a unified VLM for detection and grounding. X-DETR [3] trains a VLM on grounding and image-caption datasets to solve multiple instance-wise vision-language tasks in one model. Detric [49] uses detection and large-scale classification datasets to train a large-vocabulary detector. We exploit a pre-trained text encoder similar to other VLMs, e.g., RegionCLIP uses CLIP, while MDETR, X-DETER use RoBERTa. However, our model is trained directly on detection datasets, while these other VLMs use image captioning or grounding datasets to train jointly with detection datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.68, + 0.892, + 0.696 + ], + "angle": 0, + "content": "3. ScaleDet: A Scalable Multi-Dataset Detector" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Our goal is to train object detectors that generalize better as we increase the number of datasets used for training. A critical challenge of multi-dataset training is unifying the heterogeneous label spaces across datasets by relating their semantic concepts. To tackle this challenge, we propose a simple yet effective recipe to train a scalable multi-dataset detector (ScaleDet, Figure 2). ScaleDet learns across multiple datasets by unifying different label sets to form a unified semantic label space (Figure 2 top), and is trained via hard label and soft label assignments for visual-textual alignment (Figure 2 bottom). In Sec 3.2 and Sec 3.3 we present the details of these two contributions, but first we discuss the preliminaries and problem formulation in Sec 3.1." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7289" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.868, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.23, + 0.866, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.361, + 0.895, + 0.418 + ], + "angle": 0, + "content": "Figure 2. Approach overview. Our scalable multi-dataset detector (ScaleDet) uses text prompts to define labels, and learns across datasets by visual-textual alignment in the unified label space. Each visual feature of an object region proposal is assigned to one corresponding label via a hard label assignment (see the loss \\(\\mathcal{L}_{hl}\\) in Eq. (6)) and related to semantically-similar labels via a soft label assignment (see the loss \\(\\mathcal{L}_{sl}\\) in Eq. (7)). At test time, ScaleDet can perform object detection on any given label space of a seen or unseen detection dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.43, + 0.416, + 0.446 + ], + "angle": 0, + "content": "3.1. Preliminaries and problem formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.471, + 0.606 + ], + "angle": 0, + "content": "Standard object detection. A typical object detector aims to predict the bounding box location \\( b_{i} \\in \\mathbf{R}^{4} \\) and class label \\( c_{i} \\in \\mathbb{R}^{n} \\) for any object that belongs to a predefined set of \\( n \\) classes. Given an image \\( I \\), the image encoder (e.g., CNN or Transformer) of the detector extracts the box features and visual features, which are fed to a box regressor \\( B \\) and a visual classifier \\( C \\). The detector is trained by minimizing a bounding box regression loss \\( \\mathcal{L}_{bbox} \\) and a classification loss \\( \\mathcal{L}_{cls} \\) to learn the predictions of bounding boxes and class labels given the box features and visual features, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.197, + 0.617, + 0.47, + 0.633 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D e t} = \\mathcal {L} _ {b b o x} + \\mathcal {L} _ {c l s}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Existing object detectors generally adopt a one-stage [36, 52] or two-stage [15, 32] framework, which may contain additional loss terms in Eq. (1). For example, one-stage detectors use a regression loss to regress towards properties of object locations, such as centerness [36]. Two-stage detectors [15, 32] instead use a region proposal network with its own dedicated loss function that predicts the objectness of each box. In this work, we focus on reformulating the classification loss \\(\\mathcal{L}_{cls}\\) in Eq. (1) to solve the problem of multi-dataset training, built upon a two-stage detector [50]. Multi-dataset object detection. Given a set of \\(K\\) datasets \\(\\{\\mathcal{D}_1,\\mathcal{D}_2,\\dots,\\mathcal{D}_K\\}\\) with their label spaces \\(\\{L_1,L_2,\\dots,L_K\\}\\), we aim at training a scalable multi-dataset detector that generalizes well on upstream and downstream detection datasets. In contrast to prior multi-dataset learners [25, 37, 51], which relate or merge similar labels across datasets to joint labels, we propose a simple yet scalable formula" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.507 + ], + "angle": 0, + "content": "tion to unify labels without merging any labels explicitly. We exploit informative text embeddings from powerful pretrained visual-language models to define and relate labels over the non-identical label spaces \\(\\{L_1, L_2, \\dots, L_K\\}\\). We present our method in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.521, + 0.892, + 0.538 + ], + "angle": 0, + "content": "3.2. Scalable unification of multi-dataset label space" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.683 + ], + "angle": 0, + "content": "As Figure 2 (top) shows, during training, a mini-batch of images is randomly sampled from multiple training sets and fed to the detector to obtain the visual features \\(\\{v_{1}, v_{2}, \\dots, v_{j}\\}\\) of the region proposals for each image, where \\(v_{i} \\in \\mathbf{R}^{D}\\) is a \\(D\\)-dimensional vector. Each visual feature \\(v_{i}\\) is matched to a set of text embeddings \\(\\{t_{1}, t_{2}, \\dots, t_{n}\\}\\) by label assignment. Below, we detail how we define semantic labels with text prompts, and unify label spaces with label semantic similarities for multi-dataset training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.807 + ], + "angle": 0, + "content": "Define labels with text prompts. We represent each class label \\( l_{i} \\) with its text prompts, e.g., the label \"person\" can be denoted by a text prompt \"a photo of a person\". We extract the prompt text embeddings from the text encoder of a pre-trained visual-language model (e.g., CLIP [31] or OpenCLIP [18]), and average embeddings of a set of predefined text prompts (known as prompt engineering [31]) to represent the label \\( l_{i} \\) as a semantic text embedding \\( t_{i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Unify label spaces by concatenation. Given the text embeddings of class labels from all datasets, a crucial problem of multi-dataset training is to unify the non-identical label spaces \\(\\{L_1,L_2,\\dots ,L_K\\}\\), which can be solved by relating and merging similar labels into a unified label set [25]. However, without careful manual inspection, this incurs the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7290" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "risk of propagating errors in model training due to the ambiguities in label definitions, e.g., labels \"boy\" and \"girl\" are similar but should not be merged. Thus, instead of merging labels across datasets, we unify different label spaces by concatenation:" + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.175, + 0.47, + 0.197 + ], + "angle": 0, + "content": "\\[\nL = L _ {1} \\coprod \\dots \\coprod L _ {K} = \\left\\{l _ {1, 1}, l _ {1, 2}, \\dots , l _ {K, 1}, l _ {K, 2}, \\dots \\right\\}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.203, + 0.47, + 0.279 + ], + "angle": 0, + "content": "where \\(\\coprod\\) denotes the coproduct (i.e., the disjoint union of two label sets); \\(l_{k,i}\\) is label \\(i\\) from dataset \\(k\\) (we omit \\(k\\) below). Besides its simplicity, our formulation of this unified semantic label space \\(L\\) maximally preserves the semantics of all labels, thus providing richer vocabulary for training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.28, + 0.47, + 0.431 + ], + "angle": 0, + "content": "Relate labels by semantic similarities. As we use text embeddings to represent class labels, we can relate the labels that share similar semantics, in our unified label space. For example, label \"person\" in LVIS [14] should be related to labels \"person\" and \"boy\" in OpenImages [24], as they are semantically similar. To uncover the label relations across datasets, we compute the semantic similarities using the prompt text embeddings. For a given class label \\( l_{i} \\), its semantic similarities with respect to all the labels are derived with cosine similarities and normalized between 0 and 1:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.435, + 0.365, + 0.467 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s i m} \\left(l _ {i}, l _ {j}\\right) = \\frac {\\cos \\left(t _ {i} , t _ {j}\\right) - \\alpha_ {i}}{\\beta_ {i} - \\alpha_ {i}},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.465, + 0.469, + 0.488 + ], + "angle": 0, + "content": "where \\(\\alpha_{i} = \\min \\{\\cos (t_{i},t_{j})\\}_{j = 1}^{n}\\) (3)" + }, + { + "type": "equation", + "bbox": [ + 0.163, + 0.49, + 0.43, + 0.509 + ], + "angle": 0, + "content": "\\[\n\\beta_ {i} = \\max \\{\\cos (t _ {i}, t _ {j}) \\} _ {j = 1} ^ {n} = \\cos (t _ {i}, t _ {i}) = 1,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.469, + 0.59 + ], + "angle": 0, + "content": "where \\(\\mathrm{sim}(l_i, l_j)\\) is the semantic similarity between the text embeddings \\(t_i, t_j\\) of two labels \\(l_i, l_j\\) and it encodes their semantic relation, e.g., the labels \"person\" and \"boy\" are strongly related with a high similarity score, while \"person\" and \"avocado\" are weakly related with low similarity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.469, + 0.62 + ], + "angle": 0, + "content": "The label semantic similarity matrix \\( S \\) that encodes label relations among all \\( n \\) class labels can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.626, + 0.47, + 0.684 + ], + "angle": 0, + "content": "\\[\nS = \\left[ \\begin{array}{c c c} 1 & \\dots & \\operatorname {s i m} \\left(l _ {1}, l _ {n}\\right) \\\\ \\vdots & \\ddots & \\vdots \\\\ \\operatorname {s i m} \\left(l _ {n}, l _ {1}\\right) & \\dots & 1 \\end{array} \\right] = \\left[ \\begin{array}{c} \\mathbf {s} _ {1} \\\\ \\vdots \\\\ \\mathbf {s} _ {n} \\end{array} \\right], \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.84 + ], + "angle": 0, + "content": "where \\( S \\) is an \\( n \\times n \\) matrix, and each row vector \\( \\mathbf{s}_i \\) encodes the semantic relations of label \\( l_i \\) with respect to all \\( n \\) class labels. With these label semantic similarities, we can introduce explicit constraints that allow the detector to learn on the unified semantic label space (Eq. (2)) with encoded label semantic similarities (Eq. (4)). Importantly, our formulas (Eq. (2), Eq. (4)) are computed offline, which does not add any computational cost for training and inference, nor requires a model reformulation when scaling up the number of training datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.424, + 0.865 + ], + "angle": 0, + "content": "3.3. Training with visual-language alignment" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "For training on the unified semantic label space \\(\\{l_1, l_2, \\dots, l_n\\}\\), we align visual features with text embed" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "dings \\(\\{t_1, t_2, \\dots, t_n\\}\\) via the hard label and soft label assignments, as shown in Figure 2 (bottom) and detailed below." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.123, + 0.894, + 0.169 + ], + "angle": 0, + "content": "Visual-language similarities. Given the visual feature \\( v_{i} \\) of an object region proposal, we first compute the cosine similarities between \\( v_{i} \\) and all text embeddings \\( \\{t_1, t_2, \\dots, t_n\\} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.183, + 0.892, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {i} = \\left[ \\cos \\left(v _ {i}, t _ {1}\\right), \\cos \\left(v _ {i}, t _ {2}\\right), \\dots , \\cos \\left(v _ {i}, t _ {n}\\right) \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.204, + 0.892, + 0.234 + ], + "angle": 0, + "content": "With these similarity scores, we can align the visual feature \\( v_{i} \\) to the text embeddings with the following loss terms." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.235, + 0.892, + 0.281 + ], + "angle": 0, + "content": "Hard label assignment. Each visual feature \\( v_{i} \\) has its groundtruth label \\( l_{i} \\), and thus can be matched to the text embedding \\( t_{i} \\) of \\( l_{i} \\) by hard label assignment as follows," + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.288, + 0.892, + 0.306 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {h l} = \\operatorname {B C E} \\left(\\sigma_ {s g} \\left(\\mathbf {c} _ {i} / \\tau\\right), l _ {i}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.403 + ], + "angle": 0, + "content": "where \\(\\mathrm{BCE}(\\cdot)\\) is the binary cross-entropy loss, \\(\\sigma_{sg}(\\cdot)\\) is the sigmoid activation, \\(\\tau\\) is a temperature hyperparameter. Eq. (6) ensures the visual feature \\(v_{i}\\) is aligned with the text embedding \\(t_i\\). However, it does not explicitly learn the label relations across datasets. We introduce the soft label assignment to learn the semantic label relations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.892, + 0.495 + ], + "angle": 0, + "content": "Soft label assignment. As each label is semantically related to all class labels through the semantic similarities computed in Eq. (4), a visual feature can also be related to all text embeddings by using the semantic similarity scores. For this aim, we introduce the soft label assignment on the visual feature \\( v_{i} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.503, + 0.892, + 0.519 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s l} = \\operatorname {M S E} \\left(\\mathbf {c} _ {i}, \\mathbf {s} _ {i}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.526, + 0.892, + 0.572 + ], + "angle": 0, + "content": "where \\(\\mathrm{MSE}(\\cdot)\\) is mean square error. \\(\\mathbf{s}_i\\) denotes the semantic similarities between the label \\(l_{i}\\) and all \\(n\\) class labels - the \\(i_{th}\\) row of the label semantic similarity matrix \\(S\\) in Eq. (3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.892, + 0.662 + ], + "angle": 0, + "content": "Remark. While hard label assignment (Eq. (6)) is imposed in probability space to disambiguate different class labels, soft label assignment (Eq. (7)) is imposed in semantic similarity space to assign each visual feature to the text embeddings with different semantic similarities, thus acting as a regularizer to relate similar class labels across datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.892, + 0.74 + ], + "angle": 0, + "content": "Training with semantic label supervision. With the hard label and soft label assignments, we train the detector to classify different region proposals by aligning visual features to text embeddings in the unified semantic label space. That is, the classification loss \\(\\mathcal{L}_{cls}\\) in Eq. (1) is replaced by" + }, + { + "type": "equation", + "bbox": [ + 0.624, + 0.747, + 0.892, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {l a n g}} = \\mathcal {L} _ {h l} + \\lambda \\mathcal {L} _ {s l}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.771, + 0.892, + 0.816 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a hyperparameter to balance the two loss terms. Eq. (8) uses language supervision to map images to texts, thus enabling zero-shot detection of unseen labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.892, + 0.878 + ], + "angle": 0, + "content": "Overall objective. As we focus on reformulating the classification loss of our detector for multi-dataset training, we do not change the loss \\(\\mathcal{L}_{bbox}\\) in Eq. (1) and our overall objective for training ScaleDet is:" + }, + { + "type": "equation", + "bbox": [ + 0.6, + 0.886, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {S c a l e D e t}} = \\mathcal {L} _ {\\text {b b o x}} + \\mathcal {L} _ {\\text {l a n g}}. \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7291" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "Once trained with \\(\\mathcal{L}_{ScaleDet}\\), ScaleDet can be deployed on any upstream or downstream datasets that contain seen or unseen classes. By replacing the unified label space \\(L\\) in Eq. (2) with the label space of any given test dataset, ScaleDet can compute the label assignment based on the visual-language similarities derived in Eq. (3). When the test dataset contains unseen classes, the evaluation setting is known as zero-shot detection [1] or open-vocabulary object detection [44]. To test on any given dataset, ScaleDet can either be directly evaluated or fine-tuned before evaluation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.259, + 0.21, + 0.276 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.285, + 0.472, + 0.392 + ], + "angle": 0, + "content": "We detail our experiment setups in Sec 4.1. We analyze ScaleDet when training with an increasing number of datasets in Sec 4.2, and compare it to the state-of-the-art (SOTA) on standard benchmarks in Sec 4.3 and Sec 4.4. We evaluate the transferability of ScaleDet on downstream datasets in Sec 4.5, and conduct ablation study in Sec 4.6. We also provide qualitative visual results in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.402, + 0.258, + 0.418 + ], + "angle": 0, + "content": "4.1. Experiment setups" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.47, + 0.578 + ], + "angle": 0, + "content": "Upstream datasets. For our multi-dataset training, we adopt the following four popular detection datasets as upstream datasets: (1) COCO [27] (C) contains 80 common object categories; (2) LVIS [14] (L) has a large number of 1203 object categories with a challenging long tail distribution; (3) Objects365 [34] (O365) has 365 object categories; (4) OpenImages detection (OID) [24] has 601 object categories in the sixth version. When we train ScaleDet on these four datasets, there are 2249 class labels in the unified label space (Eq. (2)) and 3.7M training images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.47, + 0.746 + ], + "angle": 0, + "content": "Downsteam datasets. To evaluate the transferability on diverse unseen datasets, we adopt the recent challenging \"Object Detection in the Wild\" (ODinW) benchmark [26]. It contains 13 public object detection datasets with very different application domains, to mimic diverse and challenging real-world scenarios. Some of these datasets capture seen classes in unseen domains, like people in thermal images, while others capture unseen classes, like \"jellyfish\" and \"stingray\" in aquariums (Figure 1, bottom right). To evaluate on ODinW, the models can be evaluated directly (direct transfer) or evaluated after fine-tuning (fine-tune transfer)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.884 + ], + "angle": 0, + "content": "Evaluation metrics. For evaluation on upstream datasets, we use the standard mAP metric (i.e., mAP at IoU thresholds 0.5 to 0.95) on COCO, LVIS and Objects365. On OpenImages, we follow the official evaluation protocol that uses mAP@0.5 and an expanded semantic class hierarchy [24]. For evaluation on downstream datasets, we follow [26] and report the average mAP over 13 datasets in this section. We provide the detailed qualitative and quantitative results on individual datasets in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Implementation details. In our experiments, unless explicit" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.089, + 0.878, + 0.221 + ], + "angle": 0, + "content": "
ModelDataset(s)LCO365OIDmAP
baselineL33.137.015.241.531.7
C11.046.87.933.124.7
O36519.239.828.847.633.9
OID15.731.314.169.332.6
ScaleDetL,C33.344.915.943.734.5
L,C,O36536.547.031.244.939.9
L,C,O365,OID36.847.130.669.446.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.226, + 0.892, + 0.268 + ], + "angle": 0, + "content": "Table 1. Training with an increasing number of datasets. The best results on single-/multi-dataset training are in green/ bold. Backbone: ResNet50. mAP is the mean AP across datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.466 + ], + "angle": 0, + "content": "It is stated, we use CenterNet2 [50] with a backbone pretrained on ImageNet21k [33]. We use prompt text embeddings from CLIP [31] or OpenCLIP [18] to encode class labels. For augmentation, we use large scale jittering [12] and efficient resize crop [49] with an input size of \\(640 \\times 640\\), \\(896 \\times 896\\) when using ResNet50 [16], Swin Transformer [28] as backbone. We use an input size of \\(800 \\times 1333\\) for testing. We use Adam optimizer [21] and train on 8 V100 GPUs. For multi-dataset training, we directly combine all datasets and use repeat factor sampling [14], without using any multi-dataset sampling strategy. More details about learning schedules of different tables are in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.479, + 0.874, + 0.495 + ], + "angle": 0, + "content": "4.2. Training with a growing number of datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Evaluation setup. We setup the single-dataset baseline by training on individual datasets. We use text embeddings to represent the class labels for each dataset, and train the detector on each dataset by hard label assignment (Eq. (6)). To evaluate how ScaleDet scales as we increase the number of training datasets, we train it using the following incremental combinations: (1) LVIS+COCO, (2) LVIS+COCO+O365, (3) LVIS+COCO+O365+OID. These increase the dataset size from \\(218k \\rightarrow 1.96M \\rightarrow 3.7M\\) and the number of class labels from \\(1283 \\rightarrow 1648 \\rightarrow 2249\\). After training the baseline and ScaleDet, we replace the text embeddings in Eq. (5) to represent the labels of each dataset for evaluation. For example, to evaluate on COCO we set the text embeddings to represent the 80 classes of COCO and derive class predictions based on visual-textual similarities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.892, + 0.822 + ], + "angle": 0, + "content": "To make the evaluation efficient, for the results in Table 1, Figure 3 and Figure 4 we use a fixed input size of \\(640 \\times 640\\), a ResNet50 [16] backbone and text embeddings from CLIP [31]. We then explore using larger backbones (Swin Transformers [28]) and text embeddings from OpenCLIP [18] for the analysis of backbones in Table 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect on upstream datasets. Table 1 shows the evaluation on upstream datasets when increasing the number of datasets, from which we can observe the followings. First, scaling up the number of training datasets consistently leads to better model performance, e.g., the mAP on" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7292" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.124, + 0.096, + 0.424, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.47, + 0.33 + ], + "angle": 0, + "content": "Figure 3. Direct transfer results on ODinW benchmark when scaling up the number of training datasets. Number 1-4 in \\( x \\)-axis means using L, L+C, L+C+O365, L+C+O365+OID for training. Details of unseen classes, qualitative results are in Supplementary." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.332, + 0.441, + 0.522 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.528, + 0.468, + 0.556 + ], + "angle": 0, + "content": "Figure 4. Direct transfer to different datasets on ODinW benchmark when scaling up the number of training datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.468, + 0.702 + ], + "angle": 0, + "content": "LVIS is improved from 33.1, 33.3, 36.5, to 36.8 when increasing the number of training sets from 1 to 4. Second, multi-dataset training with ScaleDet is generally better than single-dataset training (baseline), e.g., the mAP on LVIS, COCO, O365, OID are greatly improved from 33.1, 46.8, 28.8, 69.3 (baseline) to 36.8, 47.1, 30.6, 69.4 when training on all datasets. This suggests that ScaleDet learns well across heterogeneous label spaces, diverse domains of different datasets, and does not overfit to any specific datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Effect on downstream datasets. Figure 3 shows the results of direct transfer on the ODinW benchmark. Notably, scaling up the number of training datasets for ScaleDet significantly improves its accuracy (mAP) on downstream datasets, for all settings (i.e., over datasets, over classes and over unseen classes). In Figure 4 we further visualize the performance of ScaleDet on some of the downstream datasets in ODinW. These datasets either contain unseen classes or come from the visual domains that are very different from those used for training. Importantly, ScaleDet performs well on both scenarios. For example, thermalDogsAndPeople contains novel thermal images, yet multi-dataset training with ScaleDet is capable of boosting its per" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.09, + 0.875, + 0.213 + ], + "angle": 0, + "content": "
ModelTextLCO365OIDmAP
1ScaleDet-RCLIP36.847.130.669.446.0
2ScaleDet-TCLIP42.751.235.973.650.9
3ScaleDet-TOpenCLIP43.951.436.374.151.4
4ScaleDet-BCLIP50.455.643.775.756.3
5ScaleDet-BOpenCLIP50.755.443.876.256.5
6ScaleDet-B*OpenCLIP50.658.846.875.958.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.218, + 0.892, + 0.26 + ], + "angle": 0, + "content": "Table 2. Different backbones for multi-dataset training. R: ResNet50. T, B: Swin-Tiny, Swin-Base transformer. *: further fine-tune the model on each dataset after multi-dataset training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.38 + ], + "angle": 0, + "content": "formance considerably from \\(19.4\\mathrm{mAP}\\) (single-dataset) to 40.6 (all 4). Furthermore, Raccoon requires the localization of an unseen class, yet again ScaleDet improves zero-shot detection from \\(39.2\\mathrm{mAP}\\) (single-dataset) to 48.3 (all 4). Overall, Figure 3 and Figure 4 show how ScaleDet can utilize the synergistic benefits of different upstream datasets to boost its generalization on downstream datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.593 + ], + "angle": 0, + "content": "Effect of different backbones. We now test ScaleDet with different backbones and text embeddings (Table 2). Enhancing the discriminative power of the image backbone from ResNet50 [16] to Swin-Base Transformer [28] significantly boosts the mAP from 46.0 to 56.3 (row 1 vs 4). Changing the text embeddings from CLIP to OpenCLIP instead helps mostly when using weaker backbones (e.g., +0.5 mAP with ScaleDet-T, row 2 vs 3), as opposed to stronger ones (e.g., +0.2 mAP with ScaleDet-B, row 4 vs 5). Finally, with fine-tuning ScaleDet can be further improved from 56.5 to 58.0 in mAP (row 5 vs 6). Overall, all these results suggest that ScaleDet can leverage the complementary power of scalable training sets and strong backbones to achieve competitive model performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.882, + 0.62 + ], + "angle": 0, + "content": "4.3. Comparison to SOTA multi-dataset detectors" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.891, + 0.673 + ], + "angle": 0, + "content": "In this section, we provide an apple-to/apple comparison of ScaleDet against the two latest state-of-the-art (SOTA) multi-dataset detectors: UniDet [51] and Detric [49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison to UniDet. In Table 3, we follow the settings of UniDet [51] and train ScaleDet on the same datasets (COCO, O365, OID), using the same ResNet50 backbone, SGD optimizer and standard data augmentation in the Detecron2 codebase [39]. In UniDet, multiple dataset-specific classifiers are trained, while ScaleDet is trained with semantic labels by one classifier. Table 3 shows the comparison on multi-dataset training. ScaleDet outperforms UniDet, yielding an mAP of 47.7 vs 45.4. Moreover, ScaleDet has better improved margins for multi-dataset training over single-dataset training (row 4,3 vs 2,1). The improved margin in mAP is 2.6 points (47.7 vs 45.1) by ScaleDet vs 1.1 points (45.4 vs 44.3) by UniDet. These results show the benefit of learning in a unified semantic label space, as opposed to training multiple dataset-specific classifiers (UniDet)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7293" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.457, + 0.183 + ], + "angle": 0, + "content": "
ModelDataset(s)COCOO365OIDmAP
1UniDetsingle42.524.965.744.3
2multiple45.524.666.045.4
3ScaleDetsingle42.126.566.645.1
4multiple45.527.969.647.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.187, + 0.47, + 0.256 + ], + "angle": 0, + "content": "Table 3. Comparison to UniDet [51] on multi-dataset training with COCO, O365 and OID. Backbone: ResNet50 pre-trained on ImageNet1k. \"single\": training with one single training set same as the test set. \"multiple\": multi-dataset training with COCO,O365,OID. mAP is the mean AP across datasets." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.26, + 0.456, + 0.367 + ], + "angle": 0, + "content": "
ModelDatasetsLVISCOCOmAP
1Detric [49]L,C33.043.938.4
2ScaleDetL,C33.344.939.1
3Detric [49]L,C,IN21k35.442.438.9
4ScaleDetL,C,O36536.547.041.7
5ScaleDetL,C,O365,OID36.847.141.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.372, + 0.47, + 0.456 + ], + "angle": 0, + "content": "Table 4. Comparison to Detric [49] on multi-dataset training with LVIS (L) and COCO (C). Backbone: ResNet50. IN21k: ImageNet21k [9]. In row 1-2, both Detric and ScaleDet are trained with only LVIS and COCO, thus providing a like-to-like comparison. In row 3, 4, 5, the training data size is 12.6M, 1.96M, 3.7M respectively. mAP is the mean AP across datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.473, + 0.789 + ], + "angle": 0, + "content": "Comparison to Detric. In Table 4, we follow the settings of Detric [49] and perform multi-dataset training on LVIS and COCO, using a ResNet50 backbone. In Detric, the unified label space for LVIS and COCO contains 1203 class labels, obtained by merging two label sets with wordnet synsets, while ScaleDet 'flatens' their labels (1203+80) to 1283. Table 4 (row 1 and 2) presents the comparison. ScaleDet outperforms Detric by 1 point on COCO (44.9 vs. 43.9) and \\(0.7\\mathrm{mAP}\\) on average. Next, we compare ScaleDet and Detric with more training sets (Table 4, row 3-5). ScaleDet is trained using more detection datasets (O365,OID), while Detric uses 14M additional classification images (ImageNet21) as a large-scale weakly annotated dataset for detection. Our results show that, although Detric is trained with far more data and class labels than ScaleDet (12.6M images and 22k classes after data cleaning vs 3.7M images and 2k classes), ScaleDet still surpasses Detric's performance by a large margin of \\(3.0\\mathrm{mAP}\\) points (41.9 vs. 38.9). These results show the importance of learning from multiple detection datasets and the effectiveness of ScaleDet in doing so." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.436, + 0.817 + ], + "angle": 0, + "content": "4.4. Comparison to SOTA detectors on COCO" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this section, we compare ScaleDet to different types of SOTA detectors on standard COCO benchmark. The different models cover four major types: (1) single-dataset detectors; (2) detectors trained with vision-and-language understanding datasets, e.g., UniT [17] is trained on 7 tasks" + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.089, + 0.857, + 0.299 + ], + "angle": 0, + "content": "
ModelModel TypemAP
1Faster RCNN [32]37.9
2Mask RCNN [15]39.8
3CenterNet [52]single-dataset40.2
4CascadeRCNN [4]detection41.6
5DETR [5]42.0
6CenterNet2 [50]42.9
7UniT [17]detection +42.3
8RegionCLIP [48]understanding42.7
9Detic [49]detection + classification42.4
10UniDet [51]multi-dataset45.5
11ScaleDetdetection47.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.304, + 0.892, + 0.317 + ], + "angle": 0, + "content": "Table 5. Comparison on COCO using ResNet50 as backbone." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.318, + 0.892, + 0.359 + ], + "angle": 0, + "content": "Note: \"understanding\", \"classification\" mean training with vision-and-language understanding, and classification datasets respectively. All methods include COCO dataset for training." + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.362, + 0.855, + 0.542 + ], + "angle": 0, + "content": "
ModelModel TypemAP
1Faster RCNN-T [32]single-dataset46.0
2DyHead-T [8]detection49.7
3CascadeRCNN-T [4]50.4
4GLIP-T [26]detection +55.2
5GLIPv2-T [46]understanding55.5
6GLIPv2-B [46]58.8
7Detic-B [49]detection + classification54.9
8ScaleDet-Bmulti-dataset detection58.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.546, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Table 6. Comparison on COCO using Swin Transformer as backbone. T, B: Swin-Tiny, Swin-Base Transformer. Note: GLIPv2-B uses 20.5M data: 3.7M detection data (COCO, O365, OID, Visual genome [23], ImageNetBoxes [9]), 16.8M grounding and caption data (GoldG [20], CC15M [7, 35], SBU [29]); while ScaleDet-B uses 3.5M data (LVIS,COCO,O365,OID)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.719 + ], + "angle": 0, + "content": "over 8 datasets and RegionCLIP [48] is trained with 3M image-text pairs from Conceptual Caption [35]; (3) detector trained with image classification dataset, i.e., Detric [49] is trained with ImageNet21k [9]; (4) multi-dataset detector trained with only detection datasets, e.g., UniDet [51]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.87 + ], + "angle": 0, + "content": "We train our ScaleDet using LVIS, COCO, O365, OID and present the results in Table 5, where all models are trained using a ResNet50 backbone. ScaleDet obtains the best performance among 11 models. Moreover, compared to detectors trained with large vision-and-language or classification datasets (row 7-9), ScaleDet gives much better performance, even though it learns a much smaller number of concepts - ScaleDet achieves 47.1 by \"only\" learning 2249 labels, while RegionCLIP and Detic achieve 42.7 and 42.4 by learning 6790 and 22047 concepts, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Table 6, we compare ScaleDet to competitors using Swin Transformers as backbone. With this strong back" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7294" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.455, + 0.246 + ], + "angle": 0, + "content": "
ModelModel Type#DataODinW
directfine-tune
GLIP-T [26]detection + understanding5.5M46.564.9
GLIPv2-T [46]5.5M48.566.5
GLIPv2-B [46]20.5M54.269.4
Detic-R [49]detection + classification12.6M29.464.4
Detic-B [49]12.6M38.770.1
ScaleDet-R3.6M39.468.5
ScaleDet-Tdetection3.6M44.370.4
ScaleDet-B3.6M47.371.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.252, + 0.47, + 0.321 + ], + "angle": 0, + "content": "Table 7. Results of direct and fine-tune transfer on ODinW. R, T, B: ResNet50, Swin-Tiny, Swin-Base Transformer as backbone. Metric: mAP over 13 datasets. Note: \"understanding\", \"classification\" mean training with vision-and-language understanding, and classification datasets besides detection data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.468, + 0.411 + ], + "angle": 0, + "content": "bone, ScaleDet demonstrates SOTA performance with high data-efficiency among all models. Among all competitors, the recent GLIPv2-B [46] is the only model performing onpar with ScaleDet (58.8), but using almost an order of magnitude more training data than ScaleDet (20.5M vs. 3.5M)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.411, + 0.469, + 0.472 + ], + "angle": 0, + "content": "Overall, our results in Table 5 and Table 6 show that ScaleDet offers a data-efficient training recipe that can learn from fewer visual concepts and less training data, but still achieves state-of-the-art performance on COCO." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.367, + 0.499 + ], + "angle": 0, + "content": "4.5. Comparison of SOTA on ODinW" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.47, + 0.792 + ], + "angle": 0, + "content": "We evaluate the transferability on the \"Object Detection in the Wild\" (ODinW) benchmark and compare ScaleDet with SOTA pre-trained detectors that are capable of both direct and fine-tune transfer given any downstream detection datasets. Table 7 shows the comparison on ODinW among 3 types of detectors: (1) GLIP [26], GLIPv2 [46], (2) Detric [49], and (3) ScaleDet. ScaleDet is trained with the smallest training data, yet it achieves the best results in fine-tune transfer, surpassing even GLIPv2-B by 2.4 points (71.8 vs. 69.4). On direct transfer, GLIPv2-B is however stronger; we conjecture that this is thanks to its massive visual-language training data (20.5M), which likely covers the unseen concepts in the downstream datasets. Furthermore, when comparing ScaleDet-R, ScaleDet-B to Detric-R, Detric-B, we find the results of ScaleDet are significantly better, e.g., ScaleDet-R outperforms Detric-R by 10.0 points (39.4 vs. 29.4) on direct transfer and by 4.1 (68.5 vs. 64.4) on fine-tune transfer. These observations show the efficacy of ScaleDet in transferring to downstream datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.227, + 0.818 + ], + "angle": 0, + "content": "4.6. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Finally, we ablate the components of our ScaleDet. As described in Sec. 3, ScaleDet is trained with two loss terms: the hard label assignment \\(\\mathcal{L}_{hl}\\) (Eq. (6)), and the soft label assignment \\(\\mathcal{L}_{sl}\\) (Eq. (7)). \\(\\mathcal{L}_{hl}\\) aims to assign each visual feature to one corresponding label, while \\(\\mathcal{L}_{sl}\\) works as a" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.089, + 0.862, + 0.174 + ], + "angle": 0, + "content": "
ModelDatasetsLCO365OIDmAP
LhlL,C33.144.615.743.234.2
Lhl+Lsl33.344.915.943.734.5
LhlL,C,O365,OID36.746.730.869.145.8
Lhl+Lsl36.847.130.669.446.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.607, + 0.176, + 0.789, + 0.188 + ], + "angle": 0, + "content": "(a) Ablation on upstream datasets." + }, + { + "type": "table", + "bbox": [ + 0.559, + 0.189, + 0.837, + 0.294 + ], + "angle": 0, + "content": "
ModelDatasetsODinW
MetricmAP\\( \\mathrm{mAP}_C \\)
\\( \\mathcal{L}_{hl} \\)L,C26.932.1
\\( \\mathcal{L}_{hl} + \\mathcal{L}_{sl} \\)26.932.5
\\( \\mathcal{L}_{hl} \\)L,C,O365,OID37.939.8
\\( \\mathcal{L}_{hl} + \\mathcal{L}_{sl} \\)39.440.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.52, + 0.295, + 0.874, + 0.308 + ], + "angle": 0, + "content": "(b) Ablation on downstream benchmark ODinW by direct transfer." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.31, + 0.892, + 0.353 + ], + "angle": 0, + "content": "Table 8. Ablation study on upstream datasets (a) and downstream datasets (b). mAP is the mean AP over datasets; \\( \\mathrm{mAP}_C \\) is the mean AP over all classes; better mAP of each setup is in bold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.637 + ], + "angle": 0, + "content": "regularizer to relate labels across datasets. Table 8a shows our ablation study on 4 upstream datasets and Table 8b shows our ablation of direct transfer on downstream benchmark ODinW. We find that training with two loss terms \\((\\mathcal{L}_{hl} + \\mathcal{L}_{sl})\\) leads to better overall results on both upstream and downstream datasets. For instance, in Table 8a, when training with two datasets \\((\\mathrm{L} + \\mathrm{C})\\), \\(\\mathcal{L}_{hl} + \\mathcal{L}_{sl}\\) gives consistent better results on 4 upstream datasets compared to \\(\\mathcal{L}_{hl}\\). In Table 8b, when using \\(\\mathcal{L}_{hl} + \\mathcal{L}_{sl}\\) to train on four training sets \\((\\mathrm{L} + \\mathrm{C} + \\mathrm{O}365 + \\mathrm{OID})\\), the mAP is greatly improved by 1.5 points (39.4-37.9) and \\(\\mathrm{mAP}_C\\) is improved by 1.1 points (40.9-39.8), as compared to using only \\(\\mathcal{L}_{sl}\\). This suggests that \\(\\mathcal{L}_{sl}\\) is valuable to improve the model's generalizability. Overall, these results indicate that \\(\\mathcal{L}_{hl}\\) works effectively for label assignment within the upstream dataset, while \\(\\mathcal{L}_{sl}\\) takes a complementary role that is more evident when transferring to downstream datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.672, + 0.769, + 0.687 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We present ScaleDet, a simple yet scalable and effective multi-dataset training recipe for detection. ScaleDet learns across multiple datasets in a unified semantic label space, optimized by hard label and soft label assignments to align visual and text embeddings. ScaleDet achieves the new state-of-the-art performance on multiple upstream datasets (LVIS, COCO, Objects365, OpenImages) and downstream datasets (ODinW). As the key success of ScaleDet lies in learning in a unified semantic label space, our formulation can also generalize to other vision tasks such as image classification and semantic segmentation. We leave the unified design of a generic multi-dataset multi-task foundation model as promising and exciting future endeavors." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7295" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.117, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Ankan Bansal, Karan Sikka, Gaurav Sharma, Rama Chellappa, and Ajay Divakaran. Zero-shot object detection. 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In this work, we propose a scalable multi-dataset detector (ScaleDet) that can scale up its generalization across datasets when increasing the number of training datasets. Unlike existing multi-dataset learners that mostly rely on manual relabelling efforts or sophisticated optimizations to unify labels across datasets, we introduce a simple yet scalable formulation to derive a unified semantic label space for multi-dataset training. ScaleDet is trained by visual-textual alignment to learn the label assignment with label semantic similarities across datasets. Once trained, ScaleDet can generalize well on any given upstream and downstream datasets with seen and unseen classes. We conduct extensive experiments using LVIS, COCO, Objects365, OpenImages as upstream datasets, and 13 datasets from Object Detection in the Wild (ODinW) as downstream datasets. Our results show that ScaleDet achieves compelling strong model performance with an mAP of 50.7 on LVIS, 58.8 on COCO, 46.8 on Objects365, 76.2 on OpenImages, and 71.8 on ODNW, surpassing state-of-the-art detectors with the same backbone. + +# 1. Introduction + +Major advances in computer vision have been driven by large-scale datasets, such as ImageNet [9] and OpenImages [22] for image classification, or Kinetics [6] and ActivityNet [2] for video recognition. Large-scale datasets are crucial for training recognition models that generalize well. However, the collection of massive annotated datasets is costly and time-consuming. This is especially prominent in detection and segmentation tasks that require detailed annotations at the bounding box or pixel level. To exploit more training data without extra annotation cost, recent works unify multiple datasets to learn from more visual categories and more diverse visual domains for detection [38,40,47,51] and segmentation [25,37]. + +To train an object detector across multiple datasets, we need to tackle several challenges. First, multi-dataset train + +![](images/23165be8987746934decbbf5c8e25ea1d817393524feda1f59426d7130f57c20.jpg) +Figure 1. Our scalable multi-dataset detector (ScaleDet) learns across datasets in a unified semantic label space by visual-textual alignment with label semantic similarities. At test time, ScaleDet can generalize on any given upstream and downstream dataset. + +ing requires unifying the heterogeneous label spaces across datasets, as label definitions are dataset-specific. The labels from two datasets may indicate the same or similar objects. For example, "footwear" and "sneakers" are two different labels in OpenImages [24] and Objects365 [34], but refer to the same type of objects (see Figure 1). Second, the training setups may be inconsistent among datasets, as different data sampling strategies and learning schedules are often required for datasets of different sizes. Third, a multi-dataset model should perform better than single-dataset models on individual datasets. This is challenging due to the heterogeneous label spaces, the domain discrepancy across datasets, and the risk of overfitting to the larger datasets. + +To resolve the above challenges, existing work resorts to manually relabelings class labels [25], or training multiple dataset-specific classifiers with constraints to relate labels across datasets [51]. However, these methods lack scalability. The manual relabeling effort and the model complex + +ity of training multiple classifiers grow rapidly as the number of datasets increases. We overcome this limitation with ScaleDet: a scalable multi-dataset detector (Figure 1). We propose two innovations: a scalable formulation to unify multiple label spaces, and a novel loss formulation to learn hard label and soft label assignments across datasets. While hard label assignment serves to disambiguate class labels in probability space, soft label assignment works as a regularizer to relate class labels in semantic similarity space. Unlike existing multi-dataset methods [25,37,38,40,47,51] that mostly generalize on seen datasets or seen classes, our method exploits vision-language learning to attain good generalization on both upstream and downstream datasets, where the downstream datasets can contain unseen classes and new domains. Our contributions are: + +- We propose a novel scalable multi-dataset training recipe for object detection. Our method utilizes text embeddings to unify and relate labels with semantic similarities across datasets, and trains a single classifier via visual-textual alignment to learn hard label and soft label assignments. +- We conduct extensive experiments to demonstrate the compelling scalability and generalizability of ScaleDet in multi-dataset training. We show that ScaleDet can boost its performance as we increase the number of training datasets: LVIS [14], COCO [27], Objects365 [34] and OpenImages [24] (Sec 4.2). Furthermore, we show that ScaleDet achieves state-of-the-art performance on multiple benchmarks when compared to recent advanced detectors, e.g., Detic [49], UniDet [51] (Sec 4.3, Sec 4.4). +- We evaluate the transferability of ScaleDet on the challenging "Object Detection in the Wild" benchmark (which contains 13 datasets) [26] to demonstrate its competitive generalizability on downstream datasets (Sec 4.5). + +# 2. Related Work + +Multi-dataset training aims to leverage multiple datasets to train more generalizable visual recognition models, especially for tasks that require more expensive annotations, such as detection [38, 40, 47, 51] and segmentation [25, 37]. Existing methods for multi-dataset training can be categorized into two groups. The first group introduces special network components to adapt feature representations tailored to datasets [38, 40]. For example, a domain attention module is designed to learn an adaptive multi-domain detector, which assigns different network activations to different domains [38]. The second group introduces new formulations to combine heterogeneous label spaces over multiple datasets [25, 37, 47, 51]. For instance, the MSeg dataset [25] is created upon multiple semantic segmentation datasets by relabeling with Amazon Mechanical Turk based on a manually defined taxonomy of class labels. To avoid manual relabeling, a pseudo labeling strategy [47] is used to generate pseudo labels across datasets based on predictions from + +dataset-specific detectors. Recent works use set theory with manually defined sets [37] or employ combinatorial optimization [51] to learn the label relations across datasets. Our approach is more related to the second group, but it offers a more scalable and generalizable training recipe that does not require training multiple dataset-specific classifiers [47, 51], nor manually designed rules to relate class labels [25, 37]. Furthermore, different from existing multi-dataset detectors [38, 40, 47, 51], ScaleDet is also capable of generalizing to datasets that contain unseen classes. + +Vision-language models (VLMs) employ vision-and-language learning to solve visual recognition problems. By bridging large-scale vision and language data, vision-language models (VLMs) such as VirTex [10], CLIP [31], ALIGN [19], FILIP [43], UniCL [42] and LiT [45], have shown remarkable performance on learning transferable visual representations that generalize well to downstream tasks. More recently, VLMs have been explored in segmentation [11, 41] and detection [3, 13, 20, 26, 46, 48, 49]. In detection, most of the VLMs utilize auxiliary semantic-rich vision-language datasets as pre-training data to build models capable of solving multiple tasks including open-vocabulary detection [44], as represented by MDETR [20], RegionCLIP [48], GLIP [26, 46], X-DETR [3], and Detric [49]. For instance, MDETR uses various vision-and-language datasets (e.g., Flickr30k [30], Visual genome [23]) to train a VLM that allows instance-wise detection guided by text query. GLIP [26] uses 27M grounding data to build a unified VLM for detection and grounding. X-DETR [3] trains a VLM on grounding and image-caption datasets to solve multiple instance-wise vision-language tasks in one model. Detric [49] uses detection and large-scale classification datasets to train a large-vocabulary detector. We exploit a pre-trained text encoder similar to other VLMs, e.g., RegionCLIP uses CLIP, while MDETR, X-DETER use RoBERTa. However, our model is trained directly on detection datasets, while these other VLMs use image captioning or grounding datasets to train jointly with detection datasets. + +# 3. ScaleDet: A Scalable Multi-Dataset Detector + +Our goal is to train object detectors that generalize better as we increase the number of datasets used for training. A critical challenge of multi-dataset training is unifying the heterogeneous label spaces across datasets by relating their semantic concepts. To tackle this challenge, we propose a simple yet effective recipe to train a scalable multi-dataset detector (ScaleDet, Figure 2). ScaleDet learns across multiple datasets by unifying different label sets to form a unified semantic label space (Figure 2 top), and is trained via hard label and soft label assignments for visual-textual alignment (Figure 2 bottom). In Sec 3.2 and Sec 3.3 we present the details of these two contributions, but first we discuss the preliminaries and problem formulation in Sec 3.1. + +![](images/ae3101b2f5da5f7603f35179399849b1335bbee5ccb6a3c225b9ad2e316a6bc7.jpg) + +![](images/c1c779dd2905ee8c10a90a395b12178320b5bddb52732c6d025dec1841e93e78.jpg) +Figure 2. Approach overview. Our scalable multi-dataset detector (ScaleDet) uses text prompts to define labels, and learns across datasets by visual-textual alignment in the unified label space. Each visual feature of an object region proposal is assigned to one corresponding label via a hard label assignment (see the loss $\mathcal{L}_{hl}$ in Eq. (6)) and related to semantically-similar labels via a soft label assignment (see the loss $\mathcal{L}_{sl}$ in Eq. (7)). At test time, ScaleDet can perform object detection on any given label space of a seen or unseen detection dataset. + +# 3.1. Preliminaries and problem formulation + +Standard object detection. A typical object detector aims to predict the bounding box location $b_{i} \in \mathbf{R}^{4}$ and class label $c_{i} \in \mathbb{R}^{n}$ for any object that belongs to a predefined set of $n$ classes. Given an image $I$ , the image encoder (e.g., CNN or Transformer) of the detector extracts the box features and visual features, which are fed to a box regressor $B$ and a visual classifier $C$ . The detector is trained by minimizing a bounding box regression loss $\mathcal{L}_{bbox}$ and a classification loss $\mathcal{L}_{cls}$ to learn the predictions of bounding boxes and class labels given the box features and visual features, i.e., + +$$ +\mathcal {L} _ {D e t} = \mathcal {L} _ {b b o x} + \mathcal {L} _ {c l s}. \tag {1} +$$ + +Existing object detectors generally adopt a one-stage [36, 52] or two-stage [15, 32] framework, which may contain additional loss terms in Eq. (1). For example, one-stage detectors use a regression loss to regress towards properties of object locations, such as centerness [36]. Two-stage detectors [15, 32] instead use a region proposal network with its own dedicated loss function that predicts the objectness of each box. In this work, we focus on reformulating the classification loss $\mathcal{L}_{cls}$ in Eq. (1) to solve the problem of multi-dataset training, built upon a two-stage detector [50]. Multi-dataset object detection. Given a set of $K$ datasets $\{\mathcal{D}_1,\mathcal{D}_2,\dots,\mathcal{D}_K\}$ with their label spaces $\{L_1,L_2,\dots,L_K\}$ , we aim at training a scalable multi-dataset detector that generalizes well on upstream and downstream detection datasets. In contrast to prior multi-dataset learners [25, 37, 51], which relate or merge similar labels across datasets to joint labels, we propose a simple yet scalable formula + +tion to unify labels without merging any labels explicitly. We exploit informative text embeddings from powerful pretrained visual-language models to define and relate labels over the non-identical label spaces $\{L_1, L_2, \dots, L_K\}$ . We present our method in the following sections. + +# 3.2. Scalable unification of multi-dataset label space + +As Figure 2 (top) shows, during training, a mini-batch of images is randomly sampled from multiple training sets and fed to the detector to obtain the visual features $\{v_{1}, v_{2}, \dots, v_{j}\}$ of the region proposals for each image, where $v_{i} \in \mathbf{R}^{D}$ is a $D$ -dimensional vector. Each visual feature $v_{i}$ is matched to a set of text embeddings $\{t_{1}, t_{2}, \dots, t_{n}\}$ by label assignment. Below, we detail how we define semantic labels with text prompts, and unify label spaces with label semantic similarities for multi-dataset training. + +Define labels with text prompts. We represent each class label $l_{i}$ with its text prompts, e.g., the label "person" can be denoted by a text prompt "a photo of a person". We extract the prompt text embeddings from the text encoder of a pre-trained visual-language model (e.g., CLIP [31] or OpenCLIP [18]), and average embeddings of a set of predefined text prompts (known as prompt engineering [31]) to represent the label $l_{i}$ as a semantic text embedding $t_{i}$ . + +Unify label spaces by concatenation. Given the text embeddings of class labels from all datasets, a crucial problem of multi-dataset training is to unify the non-identical label spaces $\{L_1,L_2,\dots ,L_K\}$ , which can be solved by relating and merging similar labels into a unified label set [25]. However, without careful manual inspection, this incurs the + +risk of propagating errors in model training due to the ambiguities in label definitions, e.g., labels "boy" and "girl" are similar but should not be merged. Thus, instead of merging labels across datasets, we unify different label spaces by concatenation: + +$$ +L = L _ {1} \coprod \dots \coprod L _ {K} = \left\{l _ {1, 1}, l _ {1, 2}, \dots , l _ {K, 1}, l _ {K, 2}, \dots \right\}, \tag {2} +$$ + +where $\coprod$ denotes the coproduct (i.e., the disjoint union of two label sets); $l_{k,i}$ is label $i$ from dataset $k$ (we omit $k$ below). Besides its simplicity, our formulation of this unified semantic label space $L$ maximally preserves the semantics of all labels, thus providing richer vocabulary for training. + +Relate labels by semantic similarities. As we use text embeddings to represent class labels, we can relate the labels that share similar semantics, in our unified label space. For example, label "person" in LVIS [14] should be related to labels "person" and "boy" in OpenImages [24], as they are semantically similar. To uncover the label relations across datasets, we compute the semantic similarities using the prompt text embeddings. For a given class label $l_{i}$ , its semantic similarities with respect to all the labels are derived with cosine similarities and normalized between 0 and 1: + +$$ +\operatorname {s i m} \left(l _ {i}, l _ {j}\right) = \frac {\cos \left(t _ {i} , t _ {j}\right) - \alpha_ {i}}{\beta_ {i} - \alpha_ {i}}, +$$ + +where $\alpha_{i} = \min \{\cos (t_{i},t_{j})\}_{j = 1}^{n}$ (3) + +$$ +\beta_ {i} = \max \{\cos (t _ {i}, t _ {j}) \} _ {j = 1} ^ {n} = \cos (t _ {i}, t _ {i}) = 1, +$$ + +where $\mathrm{sim}(l_i, l_j)$ is the semantic similarity between the text embeddings $t_i, t_j$ of two labels $l_i, l_j$ and it encodes their semantic relation, e.g., the labels "person" and "boy" are strongly related with a high similarity score, while "person" and "avocado" are weakly related with low similarity. + +The label semantic similarity matrix $S$ that encodes label relations among all $n$ class labels can be written as: + +$$ +S = \left[ \begin{array}{c c c} 1 & \dots & \operatorname {s i m} \left(l _ {1}, l _ {n}\right) \\ \vdots & \ddots & \vdots \\ \operatorname {s i m} \left(l _ {n}, l _ {1}\right) & \dots & 1 \end{array} \right] = \left[ \begin{array}{c} \mathbf {s} _ {1} \\ \vdots \\ \mathbf {s} _ {n} \end{array} \right], \tag {4} +$$ + +where $S$ is an $n \times n$ matrix, and each row vector $\mathbf{s}_i$ encodes the semantic relations of label $l_i$ with respect to all $n$ class labels. With these label semantic similarities, we can introduce explicit constraints that allow the detector to learn on the unified semantic label space (Eq. (2)) with encoded label semantic similarities (Eq. (4)). Importantly, our formulas (Eq. (2), Eq. (4)) are computed offline, which does not add any computational cost for training and inference, nor requires a model reformulation when scaling up the number of training datasets. + +# 3.3. Training with visual-language alignment + +For training on the unified semantic label space $\{l_1, l_2, \dots, l_n\}$ , we align visual features with text embed + +dings $\{t_1, t_2, \dots, t_n\}$ via the hard label and soft label assignments, as shown in Figure 2 (bottom) and detailed below. + +Visual-language similarities. Given the visual feature $v_{i}$ of an object region proposal, we first compute the cosine similarities between $v_{i}$ and all text embeddings $\{t_1, t_2, \dots, t_n\}$ : + +$$ +\mathbf {c} _ {i} = \left[ \cos \left(v _ {i}, t _ {1}\right), \cos \left(v _ {i}, t _ {2}\right), \dots , \cos \left(v _ {i}, t _ {n}\right) \right]. \tag {5} +$$ + +With these similarity scores, we can align the visual feature $v_{i}$ to the text embeddings with the following loss terms. + +Hard label assignment. Each visual feature $v_{i}$ has its groundtruth label $l_{i}$ , and thus can be matched to the text embedding $t_{i}$ of $l_{i}$ by hard label assignment as follows, + +$$ +\mathcal {L} _ {h l} = \operatorname {B C E} \left(\sigma_ {s g} \left(\mathbf {c} _ {i} / \tau\right), l _ {i}\right), \tag {6} +$$ + +where $\mathrm{BCE}(\cdot)$ is the binary cross-entropy loss, $\sigma_{sg}(\cdot)$ is the sigmoid activation, $\tau$ is a temperature hyperparameter. Eq. (6) ensures the visual feature $v_{i}$ is aligned with the text embedding $t_i$ . However, it does not explicitly learn the label relations across datasets. We introduce the soft label assignment to learn the semantic label relations. + +Soft label assignment. As each label is semantically related to all class labels through the semantic similarities computed in Eq. (4), a visual feature can also be related to all text embeddings by using the semantic similarity scores. For this aim, we introduce the soft label assignment on the visual feature $v_{i}$ : + +$$ +\mathcal {L} _ {s l} = \operatorname {M S E} \left(\mathbf {c} _ {i}, \mathbf {s} _ {i}\right), \tag {7} +$$ + +where $\mathrm{MSE}(\cdot)$ is mean square error. $\mathbf{s}_i$ denotes the semantic similarities between the label $l_{i}$ and all $n$ class labels - the $i_{th}$ row of the label semantic similarity matrix $S$ in Eq. (3). + +Remark. While hard label assignment (Eq. (6)) is imposed in probability space to disambiguate different class labels, soft label assignment (Eq. (7)) is imposed in semantic similarity space to assign each visual feature to the text embeddings with different semantic similarities, thus acting as a regularizer to relate similar class labels across datasets. + +Training with semantic label supervision. With the hard label and soft label assignments, we train the detector to classify different region proposals by aligning visual features to text embeddings in the unified semantic label space. That is, the classification loss $\mathcal{L}_{cls}$ in Eq. (1) is replaced by + +$$ +\mathcal {L} _ {\text {l a n g}} = \mathcal {L} _ {h l} + \lambda \mathcal {L} _ {s l}, \tag {8} +$$ + +where $\lambda$ is a hyperparameter to balance the two loss terms. Eq. (8) uses language supervision to map images to texts, thus enabling zero-shot detection of unseen labels. + +Overall objective. As we focus on reformulating the classification loss of our detector for multi-dataset training, we do not change the loss $\mathcal{L}_{bbox}$ in Eq. (1) and our overall objective for training ScaleDet is: + +$$ +\mathcal {L} _ {\text {S c a l e D e t}} = \mathcal {L} _ {\text {b b o x}} + \mathcal {L} _ {\text {l a n g}}. \tag {9} +$$ + +Once trained with $\mathcal{L}_{ScaleDet}$ , ScaleDet can be deployed on any upstream or downstream datasets that contain seen or unseen classes. By replacing the unified label space $L$ in Eq. (2) with the label space of any given test dataset, ScaleDet can compute the label assignment based on the visual-language similarities derived in Eq. (3). When the test dataset contains unseen classes, the evaluation setting is known as zero-shot detection [1] or open-vocabulary object detection [44]. To test on any given dataset, ScaleDet can either be directly evaluated or fine-tuned before evaluation. + +# 4. Experiments + +We detail our experiment setups in Sec 4.1. We analyze ScaleDet when training with an increasing number of datasets in Sec 4.2, and compare it to the state-of-the-art (SOTA) on standard benchmarks in Sec 4.3 and Sec 4.4. We evaluate the transferability of ScaleDet on downstream datasets in Sec 4.5, and conduct ablation study in Sec 4.6. We also provide qualitative visual results in Supplementary. + +# 4.1. Experiment setups + +Upstream datasets. For our multi-dataset training, we adopt the following four popular detection datasets as upstream datasets: (1) COCO [27] (C) contains 80 common object categories; (2) LVIS [14] (L) has a large number of 1203 object categories with a challenging long tail distribution; (3) Objects365 [34] (O365) has 365 object categories; (4) OpenImages detection (OID) [24] has 601 object categories in the sixth version. When we train ScaleDet on these four datasets, there are 2249 class labels in the unified label space (Eq. (2)) and 3.7M training images. + +Downsteam datasets. To evaluate the transferability on diverse unseen datasets, we adopt the recent challenging "Object Detection in the Wild" (ODinW) benchmark [26]. It contains 13 public object detection datasets with very different application domains, to mimic diverse and challenging real-world scenarios. Some of these datasets capture seen classes in unseen domains, like people in thermal images, while others capture unseen classes, like "jellyfish" and "stingray" in aquariums (Figure 1, bottom right). To evaluate on ODinW, the models can be evaluated directly (direct transfer) or evaluated after fine-tuning (fine-tune transfer). + +Evaluation metrics. For evaluation on upstream datasets, we use the standard mAP metric (i.e., mAP at IoU thresholds 0.5 to 0.95) on COCO, LVIS and Objects365. On OpenImages, we follow the official evaluation protocol that uses mAP@0.5 and an expanded semantic class hierarchy [24]. For evaluation on downstream datasets, we follow [26] and report the average mAP over 13 datasets in this section. We provide the detailed qualitative and quantitative results on individual datasets in Supplementary. + +Implementation details. In our experiments, unless explicit + +
ModelDataset(s)LCO365OIDmAP
baselineL33.137.015.241.531.7
C11.046.87.933.124.7
O36519.239.828.847.633.9
OID15.731.314.169.332.6
ScaleDetL,C33.344.915.943.734.5
L,C,O36536.547.031.244.939.9
L,C,O365,OID36.847.130.669.446.0
+ +Table 1. Training with an increasing number of datasets. The best results on single-/multi-dataset training are in green/ bold. Backbone: ResNet50. mAP is the mean AP across datasets. + +It is stated, we use CenterNet2 [50] with a backbone pretrained on ImageNet21k [33]. We use prompt text embeddings from CLIP [31] or OpenCLIP [18] to encode class labels. For augmentation, we use large scale jittering [12] and efficient resize crop [49] with an input size of $640 \times 640$ , $896 \times 896$ when using ResNet50 [16], Swin Transformer [28] as backbone. We use an input size of $800 \times 1333$ for testing. We use Adam optimizer [21] and train on 8 V100 GPUs. For multi-dataset training, we directly combine all datasets and use repeat factor sampling [14], without using any multi-dataset sampling strategy. More details about learning schedules of different tables are in Supplementary. + +# 4.2. Training with a growing number of datasets + +Evaluation setup. We setup the single-dataset baseline by training on individual datasets. We use text embeddings to represent the class labels for each dataset, and train the detector on each dataset by hard label assignment (Eq. (6)). To evaluate how ScaleDet scales as we increase the number of training datasets, we train it using the following incremental combinations: (1) LVIS+COCO, (2) LVIS+COCO+O365, (3) LVIS+COCO+O365+OID. These increase the dataset size from $218k \rightarrow 1.96M \rightarrow 3.7M$ and the number of class labels from $1283 \rightarrow 1648 \rightarrow 2249$ . After training the baseline and ScaleDet, we replace the text embeddings in Eq. (5) to represent the labels of each dataset for evaluation. For example, to evaluate on COCO we set the text embeddings to represent the 80 classes of COCO and derive class predictions based on visual-textual similarities. + +To make the evaluation efficient, for the results in Table 1, Figure 3 and Figure 4 we use a fixed input size of $640 \times 640$ , a ResNet50 [16] backbone and text embeddings from CLIP [31]. We then explore using larger backbones (Swin Transformers [28]) and text embeddings from OpenCLIP [18] for the analysis of backbones in Table 2. + +Effect on upstream datasets. Table 1 shows the evaluation on upstream datasets when increasing the number of datasets, from which we can observe the followings. First, scaling up the number of training datasets consistently leads to better model performance, e.g., the mAP on + +![](images/0fb805bec4e6498ba9c2ebf8f2d4c65b790f5f6c1d0ba429c5292d67ca30db61.jpg) + +![](images/a8f8164f9bf3611466a436875daeb7ed16f6f0626666c20259b4e4e4aa694392.jpg) +Figure 3. Direct transfer results on ODinW benchmark when scaling up the number of training datasets. Number 1-4 in $x$ -axis means using L, L+C, L+C+O365, L+C+O365+OID for training. Details of unseen classes, qualitative results are in Supplementary. +Figure 4. Direct transfer to different datasets on ODinW benchmark when scaling up the number of training datasets. + +LVIS is improved from 33.1, 33.3, 36.5, to 36.8 when increasing the number of training sets from 1 to 4. Second, multi-dataset training with ScaleDet is generally better than single-dataset training (baseline), e.g., the mAP on LVIS, COCO, O365, OID are greatly improved from 33.1, 46.8, 28.8, 69.3 (baseline) to 36.8, 47.1, 30.6, 69.4 when training on all datasets. This suggests that ScaleDet learns well across heterogeneous label spaces, diverse domains of different datasets, and does not overfit to any specific datasets. + +Effect on downstream datasets. Figure 3 shows the results of direct transfer on the ODinW benchmark. Notably, scaling up the number of training datasets for ScaleDet significantly improves its accuracy (mAP) on downstream datasets, for all settings (i.e., over datasets, over classes and over unseen classes). In Figure 4 we further visualize the performance of ScaleDet on some of the downstream datasets in ODinW. These datasets either contain unseen classes or come from the visual domains that are very different from those used for training. Importantly, ScaleDet performs well on both scenarios. For example, thermalDogsAndPeople contains novel thermal images, yet multi-dataset training with ScaleDet is capable of boosting its per + +
ModelTextLCO365OIDmAP
1ScaleDet-RCLIP36.847.130.669.446.0
2ScaleDet-TCLIP42.751.235.973.650.9
3ScaleDet-TOpenCLIP43.951.436.374.151.4
4ScaleDet-BCLIP50.455.643.775.756.3
5ScaleDet-BOpenCLIP50.755.443.876.256.5
6ScaleDet-B*OpenCLIP50.658.846.875.958.0
+ +Table 2. Different backbones for multi-dataset training. R: ResNet50. T, B: Swin-Tiny, Swin-Base transformer. *: further fine-tune the model on each dataset after multi-dataset training. + +formance considerably from $19.4\mathrm{mAP}$ (single-dataset) to 40.6 (all 4). Furthermore, Raccoon requires the localization of an unseen class, yet again ScaleDet improves zero-shot detection from $39.2\mathrm{mAP}$ (single-dataset) to 48.3 (all 4). Overall, Figure 3 and Figure 4 show how ScaleDet can utilize the synergistic benefits of different upstream datasets to boost its generalization on downstream datasets. + +Effect of different backbones. We now test ScaleDet with different backbones and text embeddings (Table 2). Enhancing the discriminative power of the image backbone from ResNet50 [16] to Swin-Base Transformer [28] significantly boosts the mAP from 46.0 to 56.3 (row 1 vs 4). Changing the text embeddings from CLIP to OpenCLIP instead helps mostly when using weaker backbones (e.g., +0.5 mAP with ScaleDet-T, row 2 vs 3), as opposed to stronger ones (e.g., +0.2 mAP with ScaleDet-B, row 4 vs 5). Finally, with fine-tuning ScaleDet can be further improved from 56.5 to 58.0 in mAP (row 5 vs 6). Overall, all these results suggest that ScaleDet can leverage the complementary power of scalable training sets and strong backbones to achieve competitive model performance. + +# 4.3. Comparison to SOTA multi-dataset detectors + +In this section, we provide an apple-to/apple comparison of ScaleDet against the two latest state-of-the-art (SOTA) multi-dataset detectors: UniDet [51] and Detric [49]. + +Comparison to UniDet. In Table 3, we follow the settings of UniDet [51] and train ScaleDet on the same datasets (COCO, O365, OID), using the same ResNet50 backbone, SGD optimizer and standard data augmentation in the Detecron2 codebase [39]. In UniDet, multiple dataset-specific classifiers are trained, while ScaleDet is trained with semantic labels by one classifier. Table 3 shows the comparison on multi-dataset training. ScaleDet outperforms UniDet, yielding an mAP of 47.7 vs 45.4. Moreover, ScaleDet has better improved margins for multi-dataset training over single-dataset training (row 4,3 vs 2,1). The improved margin in mAP is 2.6 points (47.7 vs 45.1) by ScaleDet vs 1.1 points (45.4 vs 44.3) by UniDet. These results show the benefit of learning in a unified semantic label space, as opposed to training multiple dataset-specific classifiers (UniDet). + +
ModelDataset(s)COCOO365OIDmAP
1UniDetsingle42.524.965.744.3
2multiple45.524.666.045.4
3ScaleDetsingle42.126.566.645.1
4multiple45.527.969.647.7
+ +Table 3. Comparison to UniDet [51] on multi-dataset training with COCO, O365 and OID. Backbone: ResNet50 pre-trained on ImageNet1k. "single": training with one single training set same as the test set. "multiple": multi-dataset training with COCO,O365,OID. mAP is the mean AP across datasets. + +
ModelDatasetsLVISCOCOmAP
1Detric [49]L,C33.043.938.4
2ScaleDetL,C33.344.939.1
3Detric [49]L,C,IN21k35.442.438.9
4ScaleDetL,C,O36536.547.041.7
5ScaleDetL,C,O365,OID36.847.141.9
+ +Comparison to Detric. In Table 4, we follow the settings of Detric [49] and perform multi-dataset training on LVIS and COCO, using a ResNet50 backbone. In Detric, the unified label space for LVIS and COCO contains 1203 class labels, obtained by merging two label sets with wordnet synsets, while ScaleDet 'flatens' their labels (1203+80) to 1283. Table 4 (row 1 and 2) presents the comparison. ScaleDet outperforms Detric by 1 point on COCO (44.9 vs. 43.9) and $0.7\mathrm{mAP}$ on average. Next, we compare ScaleDet and Detric with more training sets (Table 4, row 3-5). ScaleDet is trained using more detection datasets (O365,OID), while Detric uses 14M additional classification images (ImageNet21) as a large-scale weakly annotated dataset for detection. Our results show that, although Detric is trained with far more data and class labels than ScaleDet (12.6M images and 22k classes after data cleaning vs 3.7M images and 2k classes), ScaleDet still surpasses Detric's performance by a large margin of $3.0\mathrm{mAP}$ points (41.9 vs. 38.9). These results show the importance of learning from multiple detection datasets and the effectiveness of ScaleDet in doing so. + +# 4.4. Comparison to SOTA detectors on COCO + +In this section, we compare ScaleDet to different types of SOTA detectors on standard COCO benchmark. The different models cover four major types: (1) single-dataset detectors; (2) detectors trained with vision-and-language understanding datasets, e.g., UniT [17] is trained on 7 tasks + +Table 4. Comparison to Detric [49] on multi-dataset training with LVIS (L) and COCO (C). Backbone: ResNet50. IN21k: ImageNet21k [9]. In row 1-2, both Detric and ScaleDet are trained with only LVIS and COCO, thus providing a like-to-like comparison. In row 3, 4, 5, the training data size is 12.6M, 1.96M, 3.7M respectively. mAP is the mean AP across datasets. + +
ModelModel TypemAP
1Faster RCNN [32]37.9
2Mask RCNN [15]39.8
3CenterNet [52]single-dataset40.2
4CascadeRCNN [4]detection41.6
5DETR [5]42.0
6CenterNet2 [50]42.9
7UniT [17]detection +42.3
8RegionCLIP [48]understanding42.7
9Detic [49]detection + classification42.4
10UniDet [51]multi-dataset45.5
11ScaleDetdetection47.1
+ +Note: "understanding", "classification" mean training with vision-and-language understanding, and classification datasets respectively. All methods include COCO dataset for training. + +Table 5. Comparison on COCO using ResNet50 as backbone. + +
ModelModel TypemAP
1Faster RCNN-T [32]single-dataset46.0
2DyHead-T [8]detection49.7
3CascadeRCNN-T [4]50.4
4GLIP-T [26]detection +55.2
5GLIPv2-T [46]understanding55.5
6GLIPv2-B [46]58.8
7Detic-B [49]detection + classification54.9
8ScaleDet-Bmulti-dataset detection58.8
+ +Table 6. Comparison on COCO using Swin Transformer as backbone. T, B: Swin-Tiny, Swin-Base Transformer. Note: GLIPv2-B uses 20.5M data: 3.7M detection data (COCO, O365, OID, Visual genome [23], ImageNetBoxes [9]), 16.8M grounding and caption data (GoldG [20], CC15M [7, 35], SBU [29]); while ScaleDet-B uses 3.5M data (LVIS,COCO,O365,OID). + +over 8 datasets and RegionCLIP [48] is trained with 3M image-text pairs from Conceptual Caption [35]; (3) detector trained with image classification dataset, i.e., Detric [49] is trained with ImageNet21k [9]; (4) multi-dataset detector trained with only detection datasets, e.g., UniDet [51]. + +We train our ScaleDet using LVIS, COCO, O365, OID and present the results in Table 5, where all models are trained using a ResNet50 backbone. ScaleDet obtains the best performance among 11 models. Moreover, compared to detectors trained with large vision-and-language or classification datasets (row 7-9), ScaleDet gives much better performance, even though it learns a much smaller number of concepts - ScaleDet achieves 47.1 by "only" learning 2249 labels, while RegionCLIP and Detic achieve 42.7 and 42.4 by learning 6790 and 22047 concepts, respectively. + +In Table 6, we compare ScaleDet to competitors using Swin Transformers as backbone. With this strong back + +
ModelModel Type#DataODinW
directfine-tune
GLIP-T [26]detection + understanding5.5M46.564.9
GLIPv2-T [46]5.5M48.566.5
GLIPv2-B [46]20.5M54.269.4
Detic-R [49]detection + classification12.6M29.464.4
Detic-B [49]12.6M38.770.1
ScaleDet-R3.6M39.468.5
ScaleDet-Tdetection3.6M44.370.4
ScaleDet-B3.6M47.371.8
+ +bone, ScaleDet demonstrates SOTA performance with high data-efficiency among all models. Among all competitors, the recent GLIPv2-B [46] is the only model performing onpar with ScaleDet (58.8), but using almost an order of magnitude more training data than ScaleDet (20.5M vs. 3.5M). + +Overall, our results in Table 5 and Table 6 show that ScaleDet offers a data-efficient training recipe that can learn from fewer visual concepts and less training data, but still achieves state-of-the-art performance on COCO. + +# 4.5. Comparison of SOTA on ODinW + +We evaluate the transferability on the "Object Detection in the Wild" (ODinW) benchmark and compare ScaleDet with SOTA pre-trained detectors that are capable of both direct and fine-tune transfer given any downstream detection datasets. Table 7 shows the comparison on ODinW among 3 types of detectors: (1) GLIP [26], GLIPv2 [46], (2) Detric [49], and (3) ScaleDet. ScaleDet is trained with the smallest training data, yet it achieves the best results in fine-tune transfer, surpassing even GLIPv2-B by 2.4 points (71.8 vs. 69.4). On direct transfer, GLIPv2-B is however stronger; we conjecture that this is thanks to its massive visual-language training data (20.5M), which likely covers the unseen concepts in the downstream datasets. Furthermore, when comparing ScaleDet-R, ScaleDet-B to Detric-R, Detric-B, we find the results of ScaleDet are significantly better, e.g., ScaleDet-R outperforms Detric-R by 10.0 points (39.4 vs. 29.4) on direct transfer and by 4.1 (68.5 vs. 64.4) on fine-tune transfer. These observations show the efficacy of ScaleDet in transferring to downstream datasets. + +# 4.6. Ablation study + +Finally, we ablate the components of our ScaleDet. As described in Sec. 3, ScaleDet is trained with two loss terms: the hard label assignment $\mathcal{L}_{hl}$ (Eq. (6)), and the soft label assignment $\mathcal{L}_{sl}$ (Eq. (7)). $\mathcal{L}_{hl}$ aims to assign each visual feature to one corresponding label, while $\mathcal{L}_{sl}$ works as a + +Table 7. Results of direct and fine-tune transfer on ODinW. R, T, B: ResNet50, Swin-Tiny, Swin-Base Transformer as backbone. Metric: mAP over 13 datasets. Note: "understanding", "classification" mean training with vision-and-language understanding, and classification datasets besides detection data. + +
ModelDatasetsLCO365OIDmAP
LhlL,C33.144.615.743.234.2
Lhl+Lsl33.344.915.943.734.5
LhlL,C,O365,OID36.746.730.869.145.8
Lhl+Lsl36.847.130.669.446.0
+ +(a) Ablation on upstream datasets. + +
ModelDatasetsODinW
MetricmAP\( \mathrm{mAP}_C \)
\( \mathcal{L}_{hl} \)L,C26.932.1
\( \mathcal{L}_{hl} + \mathcal{L}_{sl} \)26.932.5
\( \mathcal{L}_{hl} \)L,C,O365,OID37.939.8
\( \mathcal{L}_{hl} + \mathcal{L}_{sl} \)39.440.9
+ +(b) Ablation on downstream benchmark ODinW by direct transfer. + +Table 8. Ablation study on upstream datasets (a) and downstream datasets (b). mAP is the mean AP over datasets; $\mathrm{mAP}_C$ is the mean AP over all classes; better mAP of each setup is in bold. + +regularizer to relate labels across datasets. Table 8a shows our ablation study on 4 upstream datasets and Table 8b shows our ablation of direct transfer on downstream benchmark ODinW. We find that training with two loss terms $(\mathcal{L}_{hl} + \mathcal{L}_{sl})$ leads to better overall results on both upstream and downstream datasets. For instance, in Table 8a, when training with two datasets $(\mathrm{L} + \mathrm{C})$ , $\mathcal{L}_{hl} + \mathcal{L}_{sl}$ gives consistent better results on 4 upstream datasets compared to $\mathcal{L}_{hl}$ . In Table 8b, when using $\mathcal{L}_{hl} + \mathcal{L}_{sl}$ to train on four training sets $(\mathrm{L} + \mathrm{C} + \mathrm{O}365 + \mathrm{OID})$ , the mAP is greatly improved by 1.5 points (39.4-37.9) and $\mathrm{mAP}_C$ is improved by 1.1 points (40.9-39.8), as compared to using only $\mathcal{L}_{sl}$ . This suggests that $\mathcal{L}_{sl}$ is valuable to improve the model's generalizability. Overall, these results indicate that $\mathcal{L}_{hl}$ works effectively for label assignment within the upstream dataset, while $\mathcal{L}_{sl}$ takes a complementary role that is more evident when transferring to downstream datasets. + +# 5. Conclusion and Future Work + +We present ScaleDet, a simple yet scalable and effective multi-dataset training recipe for detection. ScaleDet learns across multiple datasets in a unified semantic label space, optimized by hard label and soft label assignments to align visual and text embeddings. ScaleDet achieves the new state-of-the-art performance on multiple upstream datasets (LVIS, COCO, Objects365, OpenImages) and downstream datasets (ODinW). As the key success of ScaleDet lies in learning in a unified semantic label space, our formulation can also generalize to other vision tasks such as image classification and semantic segmentation. We leave the unified design of a generic multi-dataset multi-task foundation model as promising and exciting future endeavors. + +# References + +[1] Ankan Bansal, Karan Sikka, Gaurav Sharma, Rama Chellappa, and Ajay Divakaran. Zero-shot object detection. In ECCV, 2018. 5 +[2] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. In CVPR, 2015. 1 +[3] Zhaowei Cai, Gukyeong Kwon, Avinash Ravichandran, Erhan Bas, Zhuowen Tu, Rahul Bhotika, and Stefano Soatto. X-detr: A versatile architecture for instance-wise vision-language tasks. 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Objects as points. arXiv preprint arXiv:1904.07850, 2019. 3, 7 \ No newline at end of file diff --git a/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/images.zip b/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e09f382e5efa14571a1da7aa70a49d62aff5186e --- /dev/null +++ b/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09fa7a754daef84ac912d255d12eb791b274e313548ef93f585ec67c625e266b +size 541696 diff --git a/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/layout.json b/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..30a0bb0cc9dc2a739807408919330366085c2d18 --- /dev/null +++ b/2023/ScaleDet_ A Scalable Multi-Dataset Object Detector/layout.json @@ -0,0 +1,8530 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 136, + 103, + 457, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 103, + 457, + 120 + ], + "spans": [ + { + "bbox": [ + 136, + 103, + 457, + 120 + ], + "type": "text", + "content": "ScaleDet: A Scalable Multi-Dataset Object Detector" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 148, + 143, + 445, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 143, + 445, + 184 + ], + "spans": [ + { + "bbox": [ + 148, + 143, + 445, + 184 + ], + "type": "text", + "content": "Yanbei Chen, Manchen Wang, Abhay Mittal, Zhenlin Xu, Paolo Favaro, Joseph Tighe, Davide Modolo AWS AI Labs" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 224 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 224 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 238, + 290, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 501 + ], + "type": "text", + "content": "Multi-dataset training provides a viable solution for exploiting heterogeneous large-scale datasets without extra annotation cost. In this work, we propose a scalable multi-dataset detector (ScaleDet) that can scale up its generalization across datasets when increasing the number of training datasets. Unlike existing multi-dataset learners that mostly rely on manual relabelling efforts or sophisticated optimizations to unify labels across datasets, we introduce a simple yet scalable formulation to derive a unified semantic label space for multi-dataset training. ScaleDet is trained by visual-textual alignment to learn the label assignment with label semantic similarities across datasets. Once trained, ScaleDet can generalize well on any given upstream and downstream datasets with seen and unseen classes. We conduct extensive experiments using LVIS, COCO, Objects365, OpenImages as upstream datasets, and 13 datasets from Object Detection in the Wild (ODinW) as downstream datasets. Our results show that ScaleDet achieves compelling strong model performance with an mAP of 50.7 on LVIS, 58.8 on COCO, 46.8 on Objects365, 76.2 on OpenImages, and 71.8 on ODNW, surpassing state-of-the-art detectors with the same backbone." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 514, + 128, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 128, + 526 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 128, + 526 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 534, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 689 + ], + "type": "text", + "content": "Major advances in computer vision have been driven by large-scale datasets, such as ImageNet [9] and OpenImages [22] for image classification, or Kinetics [6] and ActivityNet [2] for video recognition. Large-scale datasets are crucial for training recognition models that generalize well. However, the collection of massive annotated datasets is costly and time-consuming. This is especially prominent in detection and segmentation tasks that require detailed annotations at the bounding box or pixel level. To exploit more training data without extra annotation cost, recent works unify multiple datasets to learn from more visual categories and more diverse visual domains for detection [38,40,47,51] and segmentation [25,37]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To train an object detector across multiple datasets, we need to tackle several challenges. First, multi-dataset train" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 326, + 213, + 526, + 437 + ], + "blocks": [ + { + "bbox": [ + 326, + 213, + 526, + 437 + ], + "lines": [ + { + "bbox": [ + 326, + 213, + 526, + 437 + ], + "spans": [ + { + "bbox": [ + 326, + 213, + 526, + 437 + ], + "type": "image", + "image_path": "23165be8987746934decbbf5c8e25ea1d817393524feda1f59426d7130f57c20.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 439, + 547, + 483 + ], + "lines": [ + { + "bbox": [ + 305, + 439, + 547, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 547, + 483 + ], + "type": "text", + "content": "Figure 1. Our scalable multi-dataset detector (ScaleDet) learns across datasets in a unified semantic label space by visual-textual alignment with label semantic similarities. At test time, ScaleDet can generalize on any given upstream and downstream dataset." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 497, + 547, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 547, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 547, + 652 + ], + "type": "text", + "content": "ing requires unifying the heterogeneous label spaces across datasets, as label definitions are dataset-specific. The labels from two datasets may indicate the same or similar objects. For example, \"footwear\" and \"sneakers\" are two different labels in OpenImages [24] and Objects365 [34], but refer to the same type of objects (see Figure 1). Second, the training setups may be inconsistent among datasets, as different data sampling strategies and learning schedules are often required for datasets of different sizes. Third, a multi-dataset model should perform better than single-dataset models on individual datasets. This is challenging due to the heterogeneous label spaces, the domain discrepancy across datasets, and the risk of overfitting to the larger datasets." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "To resolve the above challenges, existing work resorts to manually relabelings class labels [25], or training multiple dataset-specific classifiers with constraints to relate labels across datasets [51]. However, these methods lack scalability. The manual relabeling effort and the model complex" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7288" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "ity of training multiple classifiers grow rapidly as the number of datasets increases. We overcome this limitation with ScaleDet: a scalable multi-dataset detector (Figure 1). We propose two innovations: a scalable formulation to unify multiple label spaces, and a novel loss formulation to learn hard label and soft label assignments across datasets. While hard label assignment serves to disambiguate class labels in probability space, soft label assignment works as a regularizer to relate class labels in semantic similarity space. Unlike existing multi-dataset methods [25,37,38,40,47,51] that mostly generalize on seen datasets or seen classes, our method exploits vision-language learning to attain good generalization on both upstream and downstream datasets, where the downstream datasets can contain unseen classes and new domains. Our contributions are:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 252, + 287, + 468 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 45, + 252, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 252, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 45, + 252, + 287, + 312 + ], + "type": "text", + "content": "- We propose a novel scalable multi-dataset training recipe for object detection. Our method utilizes text embeddings to unify and relate labels with semantic similarities across datasets, and trains a single classifier via visual-textual alignment to learn hard label and soft label assignments." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 312, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 312, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 45, + 312, + 287, + 419 + ], + "type": "text", + "content": "- We conduct extensive experiments to demonstrate the compelling scalability and generalizability of ScaleDet in multi-dataset training. We show that ScaleDet can boost its performance as we increase the number of training datasets: LVIS [14], COCO [27], Objects365 [34] and OpenImages [24] (Sec 4.2). Furthermore, we show that ScaleDet achieves state-of-the-art performance on multiple benchmarks when compared to recent advanced detectors, e.g., Detic [49], UniDet [51] (Sec 4.3, Sec 4.4)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 419, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 419, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 45, + 419, + 287, + 468 + ], + "type": "text", + "content": "- We evaluate the transferability of ScaleDet on the challenging \"Object Detection in the Wild\" benchmark (which contains 13 datasets) [26] to demonstrate its competitive generalizability on downstream datasets (Sec 4.5)." + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 477, + 134, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 134, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 134, + 489 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 715 + ], + "type": "text", + "content": "Multi-dataset training aims to leverage multiple datasets to train more generalizable visual recognition models, especially for tasks that require more expensive annotations, such as detection [38, 40, 47, 51] and segmentation [25, 37]. Existing methods for multi-dataset training can be categorized into two groups. The first group introduces special network components to adapt feature representations tailored to datasets [38, 40]. For example, a domain attention module is designed to learn an adaptive multi-domain detector, which assigns different network activations to different domains [38]. The second group introduces new formulations to combine heterogeneous label spaces over multiple datasets [25, 37, 47, 51]. For instance, the MSeg dataset [25] is created upon multiple semantic segmentation datasets by relabeling with Amazon Mechanical Turk based on a manually defined taxonomy of class labels. To avoid manual relabeling, a pseudo labeling strategy [47] is used to generate pseudo labels across datasets based on predictions from" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 191 + ], + "type": "text", + "content": "dataset-specific detectors. Recent works use set theory with manually defined sets [37] or employ combinatorial optimization [51] to learn the label relations across datasets. Our approach is more related to the second group, but it offers a more scalable and generalizable training recipe that does not require training multiple dataset-specific classifiers [47, 51], nor manually designed rules to relate class labels [25, 37]. Furthermore, different from existing multi-dataset detectors [38, 40, 47, 51], ScaleDet is also capable of generalizing to datasets that contain unseen classes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 193, + 546, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 546, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 546, + 529 + ], + "type": "text", + "content": "Vision-language models (VLMs) employ vision-and-language learning to solve visual recognition problems. By bridging large-scale vision and language data, vision-language models (VLMs) such as VirTex [10], CLIP [31], ALIGN [19], FILIP [43], UniCL [42] and LiT [45], have shown remarkable performance on learning transferable visual representations that generalize well to downstream tasks. More recently, VLMs have been explored in segmentation [11, 41] and detection [3, 13, 20, 26, 46, 48, 49]. In detection, most of the VLMs utilize auxiliary semantic-rich vision-language datasets as pre-training data to build models capable of solving multiple tasks including open-vocabulary detection [44], as represented by MDETR [20], RegionCLIP [48], GLIP [26, 46], X-DETR [3], and Detric [49]. For instance, MDETR uses various vision-and-language datasets (e.g., Flickr30k [30], Visual genome [23]) to train a VLM that allows instance-wise detection guided by text query. GLIP [26] uses 27M grounding data to build a unified VLM for detection and grounding. X-DETR [3] trains a VLM on grounding and image-caption datasets to solve multiple instance-wise vision-language tasks in one model. Detric [49] uses detection and large-scale classification datasets to train a large-vocabulary detector. We exploit a pre-trained text encoder similar to other VLMs, e.g., RegionCLIP uses CLIP, while MDETR, X-DETER use RoBERTa. However, our model is trained directly on detection datasets, while these other VLMs use image captioning or grounding datasets to train jointly with detection datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 538, + 545, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 538, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 305, + 538, + 545, + 551 + ], + "type": "text", + "content": "3. ScaleDet: A Scalable Multi-Dataset Detector" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "Our goal is to train object detectors that generalize better as we increase the number of datasets used for training. A critical challenge of multi-dataset training is unifying the heterogeneous label spaces across datasets by relating their semantic concepts. To tackle this challenge, we propose a simple yet effective recipe to train a scalable multi-dataset detector (ScaleDet, Figure 2). ScaleDet learns across multiple datasets by unifying different label sets to form a unified semantic label space (Figure 2 top), and is trained via hard label and soft label assignments for visual-textual alignment (Figure 2 bottom). In Sec 3.2 and Sec 3.3 we present the details of these two contributions, but first we discuss the preliminaries and problem formulation in Sec 3.1." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7289" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 531, + 181 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 531, + 181 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 531, + 181 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 531, + 181 + ], + "type": "image", + "image_path": "ae3101b2f5da5f7603f35179399849b1335bbee5ccb6a3c225b9ad2e316a6bc7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 182, + 529, + 281 + ], + "blocks": [ + { + "bbox": [ + 60, + 182, + 529, + 281 + ], + "lines": [ + { + "bbox": [ + 60, + 182, + 529, + 281 + ], + "spans": [ + { + "bbox": [ + 60, + 182, + 529, + 281 + ], + "type": "image", + "image_path": "c1c779dd2905ee8c10a90a395b12178320b5bddb52732c6d025dec1841e93e78.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "type": "text", + "content": "Figure 2. Approach overview. Our scalable multi-dataset detector (ScaleDet) uses text prompts to define labels, and learns across datasets by visual-textual alignment in the unified label space. Each visual feature of an object region proposal is assigned to one corresponding label via a hard label assignment (see the loss " + }, + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl}" + }, + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "type": "text", + "content": " in Eq. (6)) and related to semantically-similar labels via a soft label assignment (see the loss " + }, + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sl}" + }, + { + "bbox": [ + 46, + 285, + 547, + 331 + ], + "type": "text", + "content": " in Eq. (7)). At test time, ScaleDet can perform object detection on any given label space of a seen or unseen detection dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 340, + 254, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 254, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 254, + 353 + ], + "type": "text", + "content": "3.1. Preliminaries and problem formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": "Standard object detection. A typical object detector aims to predict the bounding box location " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "b_{i} \\in \\mathbf{R}^{4}" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": " and class label " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "c_{i} \\in \\mathbb{R}^{n}" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": " for any object that belongs to a predefined set of " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": " classes. Given an image " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": ", the image encoder (e.g., CNN or Transformer) of the detector extracts the box features and visual features, which are fed to a box regressor " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": " and a visual classifier " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": ". The detector is trained by minimizing a bounding box regression loss " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bbox}" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": " and a classification loss " + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 46, + 359, + 288, + 479 + ], + "type": "text", + "content": " to learn the predictions of bounding boxes and class labels given the box features and visual features, i.e.," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 120, + 488, + 287, + 501 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 488, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 120, + 488, + 287, + 501 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D e t} = \\mathcal {L} _ {b b o x} + \\mathcal {L} _ {c l s}. \\tag {1}", + "image_path": "e7877cb100488fbafca6fa26808ed6b3a21af2f5e9eb387e0520b364199a02ba.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "text", + "content": "Existing object detectors generally adopt a one-stage [36, 52] or two-stage [15, 32] framework, which may contain additional loss terms in Eq. (1). For example, one-stage detectors use a regression loss to regress towards properties of object locations, such as centerness [36]. Two-stage detectors [15, 32] instead use a region proposal network with its own dedicated loss function that predicts the objectness of each box. In this work, we focus on reformulating the classification loss " + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "text", + "content": " in Eq. (1) to solve the problem of multi-dataset training, built upon a two-stage detector [50]. Multi-dataset object detection. Given a set of " + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "text", + "content": " datasets " + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{D}_1,\\mathcal{D}_2,\\dots,\\mathcal{D}_K\\}" + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "text", + "content": " with their label spaces " + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\{L_1,L_2,\\dots,L_K\\}" + }, + { + "bbox": [ + 46, + 509, + 287, + 714 + ], + "type": "text", + "content": ", we aim at training a scalable multi-dataset detector that generalizes well on upstream and downstream detection datasets. In contrast to prior multi-dataset learners [25, 37, 51], which relate or merge similar labels across datasets to joint labels, we propose a simple yet scalable formula" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 340, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 545, + 401 + ], + "type": "text", + "content": "tion to unify labels without merging any labels explicitly. We exploit informative text embeddings from powerful pretrained visual-language models to define and relate labels over the non-identical label spaces " + }, + { + "bbox": [ + 304, + 340, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\{L_1, L_2, \\dots, L_K\\}" + }, + { + "bbox": [ + 304, + 340, + 545, + 401 + ], + "type": "text", + "content": ". We present our method in the following sections." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 412, + 545, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 412, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 412, + 545, + 426 + ], + "type": "text", + "content": "3.2. Scalable unification of multi-dataset label space" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": "As Figure 2 (top) shows, during training, a mini-batch of images is randomly sampled from multiple training sets and fed to the detector to obtain the visual features " + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\{v_{1}, v_{2}, \\dots, v_{j}\\}" + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": " of the region proposals for each image, where " + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "inline_equation", + "content": "v_{i} \\in \\mathbf{R}^{D}" + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": " is a " + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": "-dimensional vector. Each visual feature " + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": " is matched to a set of text embeddings " + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\{t_{1}, t_{2}, \\dots, t_{n}\\}" + }, + { + "bbox": [ + 304, + 433, + 545, + 540 + ], + "type": "text", + "content": " by label assignment. Below, we detail how we define semantic labels with text prompts, and unify label spaces with label semantic similarities for multi-dataset training." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": "Define labels with text prompts. We represent each class label " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " with its text prompts, e.g., the label \"person\" can be denoted by a text prompt \"a photo of a person\". We extract the prompt text embeddings from the text encoder of a pre-trained visual-language model (e.g., CLIP [31] or OpenCLIP [18]), and average embeddings of a set of predefined text prompts (known as prompt engineering [31]) to represent the label " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": " as a semantic text embedding " + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 304, + 544, + 545, + 639 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Unify label spaces by concatenation. Given the text embeddings of class labels from all datasets, a crucial problem of multi-dataset training is to unify the non-identical label spaces " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{L_1,L_2,\\dots ,L_K\\}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": ", which can be solved by relating and merging similar labels into a unified label set [25]. However, without careful manual inspection, this incurs the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7290" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "risk of propagating errors in model training due to the ambiguities in label definitions, e.g., labels \"boy\" and \"girl\" are similar but should not be merged. Thus, instead of merging labels across datasets, we unify different label spaces by concatenation:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 63, + 138, + 287, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 138, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 63, + 138, + 287, + 156 + ], + "type": "interline_equation", + "content": "L = L _ {1} \\coprod \\dots \\coprod L _ {K} = \\left\\{l _ {1, 1}, l _ {1, 2}, \\dots , l _ {K, 1}, l _ {K, 2}, \\dots \\right\\}, \\tag {2}", + "image_path": "9e83eb53fd3982cd26a58b921a42d5a1dd535758f948ad3a21f1a989054b5e9a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "inline_equation", + "content": "\\coprod" + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": " denotes the coproduct (i.e., the disjoint union of two label sets); " + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "inline_equation", + "content": "l_{k,i}" + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": " is label " + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": " from dataset " + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": " (we omit " + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": " below). Besides its simplicity, our formulation of this unified semantic label space " + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 160, + 287, + 220 + ], + "type": "text", + "content": " maximally preserves the semantics of all labels, thus providing richer vocabulary for training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 221, + 287, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 221, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 287, + 341 + ], + "type": "text", + "content": "Relate labels by semantic similarities. As we use text embeddings to represent class labels, we can relate the labels that share similar semantics, in our unified label space. For example, label \"person\" in LVIS [14] should be related to labels \"person\" and \"boy\" in OpenImages [24], as they are semantically similar. To uncover the label relations across datasets, we compute the semantic similarities using the prompt text embeddings. For a given class label " + }, + { + "bbox": [ + 46, + 221, + 287, + 341 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 46, + 221, + 287, + 341 + ], + "type": "text", + "content": ", its semantic similarities with respect to all the labels are derived with cosine similarities and normalized between 0 and 1:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 97, + 344, + 223, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 344, + 223, + 369 + ], + "spans": [ + { + "bbox": [ + 97, + 344, + 223, + 369 + ], + "type": "interline_equation", + "content": "\\operatorname {s i m} \\left(l _ {i}, l _ {j}\\right) = \\frac {\\cos \\left(t _ {i} , t _ {j}\\right) - \\alpha_ {i}}{\\beta_ {i} - \\alpha_ {i}},", + "image_path": "f7e4dd21236735195eb1ef5fdbcfe2f266f93081fdaf311aca506ab7b0c7cfe6.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 72, + 368, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ 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+ { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(l_i, l_j)" + }, + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "text", + "content": " is the semantic similarity between the text embeddings " + }, + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "inline_equation", + "content": "t_i, t_j" + }, + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "text", + "content": " of two labels " + }, + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "inline_equation", + "content": "l_i, l_j" + }, + { + "bbox": [ + 46, + 407, + 287, + 467 + ], + "type": "text", + "content": " and it encodes their semantic relation, e.g., the labels \"person\" and \"boy\" are strongly related with a high similarity score, while \"person\" and \"avocado\" are weakly related with low similarity." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "type": "text", + "content": "The label semantic similarity matrix " + }, + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "type": "text", + "content": " that encodes label relations among all " + }, + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 467, + 287, + 491 + ], + "type": "text", + "content": " class labels can be written as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 495, + 287, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 495, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 53, + 495, + 287, + 541 + ], + "type": "interline_equation", + "content": "S = \\left[ \\begin{array}{c c c} 1 & \\dots & \\operatorname {s i m} \\left(l _ {1}, l _ {n}\\right) \\\\ \\vdots & \\ddots & \\vdots \\\\ \\operatorname {s i m} \\left(l _ {n}, l _ {1}\\right) & \\dots & 1 \\end{array} \\right] = \\left[ \\begin{array}{c} \\mathbf {s} _ {1} \\\\ \\vdots \\\\ \\mathbf {s} _ {n} \\end{array} \\right], \\tag {4}", + "image_path": "43276a5d6f9071731b0295a93e8143d89f6f9ee7ad80d721263fa9154961fd0b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": " is an " + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "inline_equation", + "content": "n \\times n" + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": " matrix, and each row vector " + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": " encodes the semantic relations of label " + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": " with respect to all " + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": " class labels. With these label semantic similarities, we can introduce explicit constraints that allow the detector to learn on the unified semantic label space (Eq. (2)) with encoded label semantic similarities (Eq. (4)). Importantly, our formulas (Eq. (2), Eq. (4)) are computed offline, which does not add any computational cost for training and inference, nor requires a model reformulation when scaling up the number of training datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 671, + 259, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 259, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 259, + 685 + ], + "type": "text", + "content": "3.3. Training with visual-language alignment" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "For training on the unified semantic label space " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\{l_1, l_2, \\dots, l_n\\}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", we align visual features with text embed" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "dings " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\{t_1, t_2, \\dots, t_n\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " via the hard label and soft label assignments, as shown in Figure 2 (bottom) and detailed below." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "content": "Visual-language similarities. Given the visual feature " + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "content": " of an object region proposal, we first compute the cosine similarities between " + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "content": " and all text embeddings " + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\{t_1, t_2, \\dots, t_n\\}" + }, + { + "bbox": [ + 305, + 97, + 547, + 133 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 144, + 545, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 144, + 545, + 158 + ], + "spans": [ + { + "bbox": [ + 335, + 144, + 545, + 158 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {i} = \\left[ \\cos \\left(v _ {i}, t _ {1}\\right), \\cos \\left(v _ {i}, t _ {2}\\right), \\dots , \\cos \\left(v _ {i}, t _ {n}\\right) \\right]. \\tag {5}", + "image_path": "30aa25c33908f3eb54afc300534a5a5c6d86d0b5a907f6a85ec9619edc895894.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 161, + 545, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 161, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 305, + 161, + 545, + 185 + ], + "type": "text", + "content": "With these similarity scores, we can align the visual feature " + }, + { + "bbox": [ + 305, + 161, + 545, + 185 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 305, + 161, + 545, + 185 + ], + "type": "text", + "content": " to the text embeddings with the following loss terms." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "text", + "content": "Hard label assignment. Each visual feature " + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "text", + "content": " has its groundtruth label " + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "text", + "content": ", and thus can be matched to the text embedding " + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 305, + 186, + 545, + 222 + ], + "type": "text", + "content": " by hard label assignment as follows," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 369, + 228, + 545, + 242 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 228, + 545, + 242 + ], + "spans": [ + { + "bbox": [ + 369, + 228, + 545, + 242 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {h l} = \\operatorname {B C E} \\left(\\sigma_ {s g} \\left(\\mathbf {c} _ {i} / \\tau\\right), l _ {i}\\right), \\tag {6}", + "image_path": "bcc91dd250de3621300671960a57166c2f624f217e74b5322d6806aa430c362a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\mathrm{BCE}(\\cdot)" + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": " is the binary cross-entropy loss, " + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\sigma_{sg}(\\cdot)" + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": " is the sigmoid activation, " + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": " is a temperature hyperparameter. Eq. (6) ensures the visual feature " + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": " is aligned with the text embedding " + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 304, + 247, + 545, + 319 + ], + "type": "text", + "content": ". However, it does not explicitly learn the label relations across datasets. We introduce the soft label assignment to learn the semantic label relations." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 319, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 392 + ], + "type": "text", + "content": "Soft label assignment. As each label is semantically related to all class labels through the semantic similarities computed in Eq. (4), a visual feature can also be related to all text embeddings by using the semantic similarity scores. For this aim, we introduce the soft label assignment on the visual feature " + }, + { + "bbox": [ + 304, + 319, + 545, + 392 + ], + "type": "inline_equation", + "content": "v_{i}" + }, + { + "bbox": [ + 304, + 319, + 545, + 392 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 384, + 398, + 545, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 398, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 384, + 398, + 545, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s l} = \\operatorname {M S E} \\left(\\mathbf {c} _ {i}, \\mathbf {s} _ {i}\\right), \\tag {7}", + "image_path": "29fd9af6e4cc579482d1237beb3b4782a3a8db7114b8af8fa7ce6d35122c664f.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "inline_equation", + "content": "\\mathrm{MSE}(\\cdot)" + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": " is mean square error. " + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": " denotes the semantic similarities between the label " + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": " and all " + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": " class labels - the " + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": " row of the label semantic similarity matrix " + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 416, + 545, + 453 + ], + "type": "text", + "content": " in Eq. (3)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 453, + 545, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 524 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 524 + ], + "type": "text", + "content": "Remark. While hard label assignment (Eq. (6)) is imposed in probability space to disambiguate different class labels, soft label assignment (Eq. (7)) is imposed in semantic similarity space to assign each visual feature to the text embeddings with different semantic similarities, thus acting as a regularizer to relate similar class labels across datasets." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 525, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 586 + ], + "type": "text", + "content": "Training with semantic label supervision. With the hard label and soft label assignments, we train the detector to classify different region proposals by aligning visual features to text embeddings in the unified semantic label space. That is, the classification loss " + }, + { + "bbox": [ + 304, + 525, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 304, + 525, + 545, + 586 + ], + "type": "text", + "content": " in Eq. (1) is replaced by" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 381, + 591, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 381, + 591, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 381, + 591, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {l a n g}} = \\mathcal {L} _ {h l} + \\lambda \\mathcal {L} _ {s l}, \\tag {8}", + "image_path": "f6fd934afdc236d6f497c758cf3f02bdbffe607ada04860ee25d478a8fb2e9c3.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 610, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 610, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 610, + 545, + 646 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 610, + 545, + 646 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 610, + 545, + 646 + ], + "type": "text", + "content": " is a hyperparameter to balance the two loss terms. Eq. (8) uses language supervision to map images to texts, thus enabling zero-shot detection of unseen labels." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 647, + 545, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 695 + ], + "type": "text", + "content": "Overall objective. As we focus on reformulating the classification loss of our detector for multi-dataset training, we do not change the loss " + }, + { + "bbox": [ + 304, + 647, + 545, + 695 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bbox}" + }, + { + "bbox": [ + 304, + 647, + 545, + 695 + ], + "type": "text", + "content": " in Eq. (1) and our overall objective for training ScaleDet is:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 367, + 701, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 701, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 367, + 701, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {S c a l e D e t}} = \\mathcal {L} _ {\\text {b b o x}} + \\mathcal {L} _ {\\text {l a n g}}. \\tag {9}", + "image_path": "1ee504b1a2296005e12b7ff32a3e716650ac2d9c30ebf6eccf81adc6dfe03255.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7291" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "Once trained with " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ScaleDet}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ", ScaleDet can be deployed on any upstream or downstream datasets that contain seen or unseen classes. By replacing the unified label space " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " in Eq. (2) with the label space of any given test dataset, ScaleDet can compute the label assignment based on the visual-language similarities derived in Eq. (3). When the test dataset contains unseen classes, the evaluation setting is known as zero-shot detection [1] or open-vocabulary object detection [44]. To test on any given dataset, ScaleDet can either be directly evaluated or fine-tuned before evaluation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 205, + 128, + 218 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 205, + 128, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 205, + 128, + 218 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 225, + 288, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 225, + 288, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 288, + 310 + ], + "type": "text", + "content": "We detail our experiment setups in Sec 4.1. We analyze ScaleDet when training with an increasing number of datasets in Sec 4.2, and compare it to the state-of-the-art (SOTA) on standard benchmarks in Sec 4.3 and Sec 4.4. We evaluate the transferability of ScaleDet on downstream datasets in Sec 4.5, and conduct ablation study in Sec 4.6. We also provide qualitative visual results in Supplementary." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 318, + 157, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 318, + 157, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 318, + 157, + 331 + ], + "type": "text", + "content": "4.1. Experiment setups" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 287, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 457 + ], + "type": "text", + "content": "Upstream datasets. For our multi-dataset training, we adopt the following four popular detection datasets as upstream datasets: (1) COCO [27] (C) contains 80 common object categories; (2) LVIS [14] (L) has a large number of 1203 object categories with a challenging long tail distribution; (3) Objects365 [34] (O365) has 365 object categories; (4) OpenImages detection (OID) [24] has 601 object categories in the sixth version. When we train ScaleDet on these four datasets, there are 2249 class labels in the unified label space (Eq. (2)) and 3.7M training images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 459, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 590 + ], + "type": "text", + "content": "Downsteam datasets. To evaluate the transferability on diverse unseen datasets, we adopt the recent challenging \"Object Detection in the Wild\" (ODinW) benchmark [26]. It contains 13 public object detection datasets with very different application domains, to mimic diverse and challenging real-world scenarios. Some of these datasets capture seen classes in unseen domains, like people in thermal images, while others capture unseen classes, like \"jellyfish\" and \"stingray\" in aquariums (Figure 1, bottom right). To evaluate on ODinW, the models can be evaluated directly (direct transfer) or evaluated after fine-tuning (fine-tune transfer)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 592, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 700 + ], + "type": "text", + "content": "Evaluation metrics. For evaluation on upstream datasets, we use the standard mAP metric (i.e., mAP at IoU thresholds 0.5 to 0.95) on COCO, LVIS and Objects365. On OpenImages, we follow the official evaluation protocol that uses mAP@0.5 and an expanded semantic class hierarchy [24]. For evaluation on downstream datasets, we follow [26] and report the average mAP over 13 datasets in this section. We provide the detailed qualitative and quantitative results on individual datasets in Supplementary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 714 + ], + "type": "text", + "content": "Implementation details. In our experiments, unless explicit" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 314, + 70, + 537, + 175 + ], + "blocks": [ + { + "bbox": [ + 314, + 70, + 537, + 175 + ], + "lines": [ + { + "bbox": [ + 314, + 70, + 537, + 175 + ], + "spans": [ + { + "bbox": [ + 314, + 70, + 537, + 175 + ], + "type": "table", + "html": "
ModelDataset(s)LCO365OIDmAP
baselineL33.137.015.241.531.7
C11.046.87.933.124.7
O36519.239.828.847.633.9
OID15.731.314.169.332.6
ScaleDetL,C33.344.915.943.734.5
L,C,O36536.547.031.244.939.9
L,C,O365,OID36.847.130.669.446.0
", + "image_path": "cf32fe95474fdf190c2896fa086fe4f3307ff41dee0d1d1543ab1b910884cb7c.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 178, + 545, + 212 + ], + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 212 + ], + "type": "text", + "content": "Table 1. Training with an increasing number of datasets. The best results on single-/multi-dataset training are in green/ bold. Backbone: ResNet50. mAP is the mean AP across datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "text", + "content": "It is stated, we use CenterNet2 [50] with a backbone pretrained on ImageNet21k [33]. We use prompt text embeddings from CLIP [31] or OpenCLIP [18] to encode class labels. For augmentation, we use large scale jittering [12] and efficient resize crop [49] with an input size of " + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "inline_equation", + "content": "640 \\times 640" + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "inline_equation", + "content": "896 \\times 896" + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "text", + "content": " when using ResNet50 [16], Swin Transformer [28] as backbone. We use an input size of " + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "inline_equation", + "content": "800 \\times 1333" + }, + { + "bbox": [ + 304, + 224, + 545, + 369 + ], + "type": "text", + "content": " for testing. We use Adam optimizer [21] and train on 8 V100 GPUs. For multi-dataset training, we directly combine all datasets and use repeat factor sampling [14], without using any multi-dataset sampling strategy. More details about learning schedules of different tables are in Supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 379, + 534, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 534, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 534, + 392 + ], + "type": "text", + "content": "4.2. Training with a growing number of datasets" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "type": "text", + "content": "Evaluation setup. We setup the single-dataset baseline by training on individual datasets. We use text embeddings to represent the class labels for each dataset, and train the detector on each dataset by hard label assignment (Eq. (6)). To evaluate how ScaleDet scales as we increase the number of training datasets, we train it using the following incremental combinations: (1) LVIS+COCO, (2) LVIS+COCO+O365, (3) LVIS+COCO+O365+OID. These increase the dataset size from " + }, + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "type": "inline_equation", + "content": "218k \\rightarrow 1.96M \\rightarrow 3.7M" + }, + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "type": "text", + "content": " and the number of class labels from " + }, + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "type": "inline_equation", + "content": "1283 \\rightarrow 1648 \\rightarrow 2249" + }, + { + "bbox": [ + 304, + 399, + 545, + 578 + ], + "type": "text", + "content": ". After training the baseline and ScaleDet, we replace the text embeddings in Eq. (5) to represent the labels of each dataset for evaluation. For example, to evaluate on COCO we set the text embeddings to represent the 80 classes of COCO and derive class predictions based on visual-textual similarities." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 580, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 651 + ], + "type": "text", + "content": "To make the evaluation efficient, for the results in Table 1, Figure 3 and Figure 4 we use a fixed input size of " + }, + { + "bbox": [ + 304, + 580, + 545, + 651 + ], + "type": "inline_equation", + "content": "640 \\times 640" + }, + { + "bbox": [ + 304, + 580, + 545, + 651 + ], + "type": "text", + "content": ", a ResNet50 [16] backbone and text embeddings from CLIP [31]. We then explore using larger backbones (Swin Transformers [28]) and text embeddings from OpenCLIP [18] for the analysis of backbones in Table 2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Effect on upstream datasets. Table 1 shows the evaluation on upstream datasets when increasing the number of datasets, from which we can observe the followings. First, scaling up the number of training datasets consistently leads to better model performance, e.g., the mAP on" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7292" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 76, + 259, + 210 + ], + "blocks": [ + { + "bbox": [ + 75, + 76, + 259, + 210 + ], + "lines": [ + { + "bbox": [ + 75, + 76, + 259, + 210 + ], + "spans": [ + { + "bbox": [ + 75, + 76, + 259, + 210 + ], + "type": "image", + "image_path": "0fb805bec4e6498ba9c2ebf8f2d4c65b790f5f6c1d0ba429c5292d67ca30db61.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 262, + 269, + 413 + ], + "blocks": [ + { + "bbox": [ + 46, + 216, + 287, + 261 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 261 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 261 + ], + "type": "text", + "content": "Figure 3. Direct transfer results on ODinW benchmark when scaling up the number of training datasets. Number 1-4 in " + }, + { + "bbox": [ + 46, + 216, + 287, + 261 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 216, + 287, + 261 + ], + "type": "text", + "content": "-axis means using L, L+C, L+C+O365, L+C+O365+OID for training. Details of unseen classes, qualitative results are in Supplementary." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 65, + 262, + 269, + 413 + ], + "lines": [ + { + "bbox": [ + 65, + 262, + 269, + 413 + ], + "spans": [ + { + "bbox": [ + 65, + 262, + 269, + 413 + ], + "type": "image", + "image_path": "a8f8164f9bf3611466a436875daeb7ed16f6f0626666c20259b4e4e4aa694392.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 418, + 286, + 440 + ], + "lines": [ + { + "bbox": [ + 46, + 418, + 286, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 286, + 440 + ], + "type": "text", + "content": "Figure 4. Direct transfer to different datasets on ODinW benchmark when scaling up the number of training datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 448, + 286, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 286, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 286, + 555 + ], + "type": "text", + "content": "LVIS is improved from 33.1, 33.3, 36.5, to 36.8 when increasing the number of training sets from 1 to 4. Second, multi-dataset training with ScaleDet is generally better than single-dataset training (baseline), e.g., the mAP on LVIS, COCO, O365, OID are greatly improved from 33.1, 46.8, 28.8, 69.3 (baseline) to 36.8, 47.1, 30.6, 69.4 when training on all datasets. This suggests that ScaleDet learns well across heterogeneous label spaces, diverse domains of different datasets, and does not overfit to any specific datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 286, + 713 + ], + "type": "text", + "content": "Effect on downstream datasets. Figure 3 shows the results of direct transfer on the ODinW benchmark. Notably, scaling up the number of training datasets for ScaleDet significantly improves its accuracy (mAP) on downstream datasets, for all settings (i.e., over datasets, over classes and over unseen classes). In Figure 4 we further visualize the performance of ScaleDet on some of the downstream datasets in ODinW. These datasets either contain unseen classes or come from the visual domains that are very different from those used for training. Importantly, ScaleDet performs well on both scenarios. For example, thermalDogsAndPeople contains novel thermal images, yet multi-dataset training with ScaleDet is capable of boosting its per" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 314, + 71, + 535, + 168 + ], + "blocks": [ + { + "bbox": [ + 314, + 71, + 535, + 168 + ], + "lines": [ + { + "bbox": [ + 314, + 71, + 535, + 168 + ], + "spans": [ + { + "bbox": [ + 314, + 71, + 535, + 168 + ], + "type": "table", + "html": "
ModelTextLCO365OIDmAP
1ScaleDet-RCLIP36.847.130.669.446.0
2ScaleDet-TCLIP42.751.235.973.650.9
3ScaleDet-TOpenCLIP43.951.436.374.151.4
4ScaleDet-BCLIP50.455.643.775.756.3
5ScaleDet-BOpenCLIP50.755.443.876.256.5
6ScaleDet-B*OpenCLIP50.658.846.875.958.0
", + "image_path": "3db3123c84d725406b9d295ec4f10d1a99774b8e419d80d54cdffadee6052f30.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 172, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 306, + 172, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 172, + 545, + 205 + ], + "type": "text", + "content": "Table 2. Different backbones for multi-dataset training. R: ResNet50. T, B: Swin-Tiny, Swin-Base transformer. *: further fine-tune the model on each dataset after multi-dataset training." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "text", + "content": "formance considerably from " + }, + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "inline_equation", + "content": "19.4\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "text", + "content": " (single-dataset) to 40.6 (all 4). Furthermore, Raccoon requires the localization of an unseen class, yet again ScaleDet improves zero-shot detection from " + }, + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "inline_equation", + "content": "39.2\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 217, + 545, + 300 + ], + "type": "text", + "content": " (single-dataset) to 48.3 (all 4). Overall, Figure 3 and Figure 4 show how ScaleDet can utilize the synergistic benefits of different upstream datasets to boost its generalization on downstream datasets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 302, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 545, + 469 + ], + "type": "text", + "content": "Effect of different backbones. We now test ScaleDet with different backbones and text embeddings (Table 2). Enhancing the discriminative power of the image backbone from ResNet50 [16] to Swin-Base Transformer [28] significantly boosts the mAP from 46.0 to 56.3 (row 1 vs 4). Changing the text embeddings from CLIP to OpenCLIP instead helps mostly when using weaker backbones (e.g., +0.5 mAP with ScaleDet-T, row 2 vs 3), as opposed to stronger ones (e.g., +0.2 mAP with ScaleDet-B, row 4 vs 5). Finally, with fine-tuning ScaleDet can be further improved from 56.5 to 58.0 in mAP (row 5 vs 6). Overall, all these results suggest that ScaleDet can leverage the complementary power of scalable training sets and strong backbones to achieve competitive model performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 478, + 539, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 539, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 539, + 491 + ], + "type": "text", + "content": "4.3. Comparison to SOTA multi-dataset detectors" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": "In this section, we provide an apple-to/apple comparison of ScaleDet against the two latest state-of-the-art (SOTA) multi-dataset detectors: UniDet [51] and Detric [49]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "Comparison to UniDet. In Table 3, we follow the settings of UniDet [51] and train ScaleDet on the same datasets (COCO, O365, OID), using the same ResNet50 backbone, SGD optimizer and standard data augmentation in the Detecron2 codebase [39]. In UniDet, multiple dataset-specific classifiers are trained, while ScaleDet is trained with semantic labels by one classifier. Table 3 shows the comparison on multi-dataset training. ScaleDet outperforms UniDet, yielding an mAP of 47.7 vs 45.4. Moreover, ScaleDet has better improved margins for multi-dataset training over single-dataset training (row 4,3 vs 2,1). The improved margin in mAP is 2.6 points (47.7 vs 45.1) by ScaleDet vs 1.1 points (45.4 vs 44.3) by UniDet. These results show the benefit of learning in a unified semantic label space, as opposed to training multiple dataset-specific classifiers (UniDet)." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7293" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 279, + 144 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 279, + 144 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 279, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 279, + 144 + ], + "type": "table", + "html": "
ModelDataset(s)COCOO365OIDmAP
1UniDetsingle42.524.965.744.3
2multiple45.524.666.045.4
3ScaleDetsingle42.126.566.645.1
4multiple45.527.969.647.7
", + "image_path": "d636e7da16884c76d27cd4ac6c44c60312d5a2357066355009576cdfe8ad04b3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 205, + 279, + 290 + ], + "blocks": [ + { + "bbox": [ + 46, + 148, + 287, + 202 + ], + "lines": [ + { + "bbox": [ + 46, + 148, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 46, + 148, + 287, + 202 + ], + "type": "text", + "content": "Table 3. Comparison to UniDet [51] on multi-dataset training with COCO, O365 and OID. Backbone: ResNet50 pre-trained on ImageNet1k. \"single\": training with one single training set same as the test set. \"multiple\": multi-dataset training with COCO,O365,OID. mAP is the mean AP across datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 205, + 279, + 290 + ], + "lines": [ + { + "bbox": [ + 53, + 205, + 279, + 290 + ], + "spans": [ + { + "bbox": [ + 53, + 205, + 279, + 290 + ], + "type": "table", + "html": "
ModelDatasetsLVISCOCOmAP
1Detric [49]L,C33.043.938.4
2ScaleDetL,C33.344.939.1
3Detric [49]L,C,IN21k35.442.438.9
4ScaleDetL,C,O36536.547.041.7
5ScaleDetL,C,O365,OID36.847.141.9
", + "image_path": "0926a478d8031bfe217ea130f107b95a8d2f41718afda7cf1be89226da453a43.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "type": "text", + "content": "Comparison to Detric. In Table 4, we follow the settings of Detric [49] and perform multi-dataset training on LVIS and COCO, using a ResNet50 backbone. In Detric, the unified label space for LVIS and COCO contains 1203 class labels, obtained by merging two label sets with wordnet synsets, while ScaleDet 'flatens' their labels (1203+80) to 1283. Table 4 (row 1 and 2) presents the comparison. ScaleDet outperforms Detric by 1 point on COCO (44.9 vs. 43.9) and " + }, + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "type": "inline_equation", + "content": "0.7\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "type": "text", + "content": " on average. Next, we compare ScaleDet and Detric with more training sets (Table 4, row 3-5). ScaleDet is trained using more detection datasets (O365,OID), while Detric uses 14M additional classification images (ImageNet21) as a large-scale weakly annotated dataset for detection. Our results show that, although Detric is trained with far more data and class labels than ScaleDet (12.6M images and 22k classes after data cleaning vs 3.7M images and 2k classes), ScaleDet still surpasses Detric's performance by a large margin of " + }, + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "type": "inline_equation", + "content": "3.0\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 373, + 289, + 624 + ], + "type": "text", + "content": " points (41.9 vs. 38.9). These results show the importance of learning from multiple detection datasets and the effectiveness of ScaleDet in doing so." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 634, + 266, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 266, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 266, + 647 + ], + "type": "text", + "content": "4.4. Comparison to SOTA detectors on COCO" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "In this section, we compare ScaleDet to different types of SOTA detectors on standard COCO benchmark. The different models cover four major types: (1) single-dataset detectors; (2) detectors trained with vision-and-language understanding datasets, e.g., UniT [17] is trained on 7 tasks" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 328, + 70, + 524, + 236 + ], + "blocks": [ + { + "bbox": [ + 46, + 294, + 287, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 361 + ], + "type": "text", + "content": "Table 4. Comparison to Detric [49] on multi-dataset training with LVIS (L) and COCO (C). Backbone: ResNet50. IN21k: ImageNet21k [9]. In row 1-2, both Detric and ScaleDet are trained with only LVIS and COCO, thus providing a like-to-like comparison. In row 3, 4, 5, the training data size is 12.6M, 1.96M, 3.7M respectively. mAP is the mean AP across datasets." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 70, + 524, + 236 + ], + "lines": [ + { + "bbox": [ + 328, + 70, + 524, + 236 + ], + "spans": [ + { + "bbox": [ + 328, + 70, + 524, + 236 + ], + "type": "table", + "html": "
ModelModel TypemAP
1Faster RCNN [32]37.9
2Mask RCNN [15]39.8
3CenterNet [52]single-dataset40.2
4CascadeRCNN [4]detection41.6
5DETR [5]42.0
6CenterNet2 [50]42.9
7UniT [17]detection +42.3
8RegionCLIP [48]understanding42.7
9Detic [49]detection + classification42.4
10UniDet [51]multi-dataset45.5
11ScaleDetdetection47.1
", + "image_path": "f43f10388576bdf93e3236790b65f58c7f5ed8f56ef4050293565dcb3895dec4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 251, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 545, + 284 + ], + "type": "text", + "content": "Note: \"understanding\", \"classification\" mean training with vision-and-language understanding, and classification datasets respectively. All methods include COCO dataset for training." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 328, + 286, + 523, + 429 + ], + "blocks": [ + { + "bbox": [ + 305, + 240, + 545, + 251 + ], + "lines": [ + { + "bbox": [ + 305, + 240, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 240, + 545, + 251 + ], + "type": "text", + "content": "Table 5. Comparison on COCO using ResNet50 as backbone." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 286, + 523, + 429 + ], + "lines": [ + { + "bbox": [ + 328, + 286, + 523, + 429 + ], + "spans": [ + { + "bbox": [ + 328, + 286, + 523, + 429 + ], + "type": "table", + "html": "
ModelModel TypemAP
1Faster RCNN-T [32]single-dataset46.0
2DyHead-T [8]detection49.7
3CascadeRCNN-T [4]50.4
4GLIP-T [26]detection +55.2
5GLIPv2-T [46]understanding55.5
6GLIPv2-B [46]58.8
7Detic-B [49]detection + classification54.9
8ScaleDet-Bmulti-dataset detection58.8
", + "image_path": "e29cf62b0ec5605ac28652bf90aaec94fc80ba82ecd68f4e70c886c6d9c686d3.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 432, + 545, + 498 + ], + "lines": [ + { + "bbox": [ + 305, + 432, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 432, + 545, + 498 + ], + "type": "text", + "content": "Table 6. Comparison on COCO using Swin Transformer as backbone. T, B: Swin-Tiny, Swin-Base Transformer. Note: GLIPv2-B uses 20.5M data: 3.7M detection data (COCO, O365, OID, Visual genome [23], ImageNetBoxes [9]), 16.8M grounding and caption data (GoldG [20], CC15M [7, 35], SBU [29]); while ScaleDet-B uses 3.5M data (LVIS,COCO,O365,OID)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 510, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 569 + ], + "type": "text", + "content": "over 8 datasets and RegionCLIP [48] is trained with 3M image-text pairs from Conceptual Caption [35]; (3) detector trained with image classification dataset, i.e., Detric [49] is trained with ImageNet21k [9]; (4) multi-dataset detector trained with only detection datasets, e.g., UniDet [51]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 689 + ], + "type": "text", + "content": "We train our ScaleDet using LVIS, COCO, O365, OID and present the results in Table 5, where all models are trained using a ResNet50 backbone. ScaleDet obtains the best performance among 11 models. Moreover, compared to detectors trained with large vision-and-language or classification datasets (row 7-9), ScaleDet gives much better performance, even though it learns a much smaller number of concepts - ScaleDet achieves 47.1 by \"only\" learning 2249 labels, while RegionCLIP and Detic achieve 42.7 and 42.4 by learning 6790 and 22047 concepts, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "In Table 6, we compare ScaleDet to competitors using Swin Transformers as backbone. With this strong back" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7294" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 278, + 194 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 278, + 194 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 278, + 194 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 278, + 194 + ], + "type": "table", + "html": "
ModelModel Type#DataODinW
directfine-tune
GLIP-T [26]detection + understanding5.5M46.564.9
GLIPv2-T [46]5.5M48.566.5
GLIPv2-B [46]20.5M54.269.4
Detic-R [49]detection + classification12.6M29.464.4
Detic-B [49]12.6M38.770.1
ScaleDet-R3.6M39.468.5
ScaleDet-Tdetection3.6M44.370.4
ScaleDet-B3.6M47.371.8
", + "image_path": "838175868b300525b134c4d5549064f20caf39a809abef25af8e48dbb8060714.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 265, + 286, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 286, + 325 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 286, + 325 + ], + "type": "text", + "content": "bone, ScaleDet demonstrates SOTA performance with high data-efficiency among all models. Among all competitors, the recent GLIPv2-B [46] is the only model performing onpar with ScaleDet (58.8), but using almost an order of magnitude more training data than ScaleDet (20.5M vs. 3.5M)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 325, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 287, + 373 + ], + "type": "text", + "content": "Overall, our results in Table 5 and Table 6 show that ScaleDet offers a data-efficient training recipe that can learn from fewer visual concepts and less training data, but still achieves state-of-the-art performance on COCO." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 381, + 224, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 224, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 224, + 395 + ], + "type": "text", + "content": "4.5. Comparison of SOTA on ODinW" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 287, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 627 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 627 + ], + "type": "text", + "content": "We evaluate the transferability on the \"Object Detection in the Wild\" (ODinW) benchmark and compare ScaleDet with SOTA pre-trained detectors that are capable of both direct and fine-tune transfer given any downstream detection datasets. Table 7 shows the comparison on ODinW among 3 types of detectors: (1) GLIP [26], GLIPv2 [46], (2) Detric [49], and (3) ScaleDet. ScaleDet is trained with the smallest training data, yet it achieves the best results in fine-tune transfer, surpassing even GLIPv2-B by 2.4 points (71.8 vs. 69.4). On direct transfer, GLIPv2-B is however stronger; we conjecture that this is thanks to its massive visual-language training data (20.5M), which likely covers the unseen concepts in the downstream datasets. Furthermore, when comparing ScaleDet-R, ScaleDet-B to Detric-R, Detric-B, we find the results of ScaleDet are significantly better, e.g., ScaleDet-R outperforms Detric-R by 10.0 points (39.4 vs. 29.4) on direct transfer and by 4.1 (68.5 vs. 64.4) on fine-tune transfer. These observations show the efficacy of ScaleDet in transferring to downstream datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 138, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 138, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 138, + 647 + ], + "type": "text", + "content": "4.6. Ablation study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Finally, we ablate the components of our ScaleDet. As described in Sec. 3, ScaleDet is trained with two loss terms: the hard label assignment " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " (Eq. (6)), and the soft label assignment " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sl}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " (Eq. (7)). " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " aims to assign each visual feature to one corresponding label, while " + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sl}" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " works as a" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 326, + 70, + 527, + 137 + ], + "blocks": [ + { + "bbox": [ + 47, + 199, + 287, + 254 + ], + "lines": [ + { + "bbox": [ + 47, + 199, + 287, + 254 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 287, + 254 + ], + "type": "text", + "content": "Table 7. Results of direct and fine-tune transfer on ODinW. R, T, B: ResNet50, Swin-Tiny, Swin-Base Transformer as backbone. Metric: mAP over 13 datasets. Note: \"understanding\", \"classification\" mean training with vision-and-language understanding, and classification datasets besides detection data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 70, + 527, + 137 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 527, + 137 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 527, + 137 + ], + "type": "table", + "html": "
ModelDatasetsLCO365OIDmAP
LhlL,C33.144.615.743.234.2
Lhl+Lsl33.344.915.943.734.5
LhlL,C,O365,OID36.746.730.869.145.8
Lhl+Lsl36.847.130.669.446.0
", + "image_path": "fc18311f7a6e0f43c895ec1cdbbadca67d0356ca63f6da12fd5c5caa352d97f4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 342, + 149, + 512, + 232 + ], + "blocks": [ + { + "bbox": [ + 371, + 139, + 482, + 148 + ], + "lines": [ + { + "bbox": [ + 371, + 139, + 482, + 148 + ], + "spans": [ + { + "bbox": [ + 371, + 139, + 482, + 148 + ], + "type": "text", + "content": "(a) Ablation on upstream datasets." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 342, + 149, + 512, + 232 + ], + "lines": [ + { + "bbox": [ + 342, + 149, + 512, + 232 + ], + "spans": [ + { + "bbox": [ + 342, + 149, + 512, + 232 + ], + "type": "table", + "html": "
ModelDatasetsODinW
MetricmAP\\( \\mathrm{mAP}_C \\)
\\( \\mathcal{L}_{hl} \\)L,C26.932.1
\\( \\mathcal{L}_{hl} + \\mathcal{L}_{sl} \\)26.932.5
\\( \\mathcal{L}_{hl} \\)L,C,O365,OID37.939.8
\\( \\mathcal{L}_{hl} + \\mathcal{L}_{sl} \\)39.440.9
", + "image_path": "ba02c88a4587ee3337abf6dbdfc31ebf6f6f7a0a5806742e0a13092c90aafe8d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 233, + 534, + 243 + ], + "lines": [ + { + "bbox": [ + 318, + 233, + 534, + 243 + ], + "spans": [ + { + "bbox": [ + 318, + 233, + 534, + 243 + ], + "type": "text", + "content": "(b) Ablation on downstream benchmark ODinW by direct transfer." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 245, + 545, + 279 + ], + "lines": [ + { + "bbox": [ + 306, + 245, + 545, + 279 + ], + "spans": [ + { + "bbox": [ + 306, + 245, + 545, + 279 + ], + "type": "text", + "content": "Table 8. Ablation study on upstream datasets (a) and downstream datasets (b). mAP is the mean AP over datasets; " + }, + { + "bbox": [ + 306, + 245, + 545, + 279 + ], + "type": "inline_equation", + "content": "\\mathrm{mAP}_C" + }, + { + "bbox": [ + 306, + 245, + 545, + 279 + ], + "type": "text", + "content": " is the mean AP over all classes; better mAP of each setup is in bold." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": "regularizer to relate labels across datasets. Table 8a shows our ablation study on 4 upstream datasets and Table 8b shows our ablation of direct transfer on downstream benchmark ODinW. We find that training with two loss terms " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{hl} + \\mathcal{L}_{sl})" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " leads to better overall results on both upstream and downstream datasets. For instance, in Table 8a, when training with two datasets " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "(\\mathrm{L} + \\mathrm{C})" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl} + \\mathcal{L}_{sl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " gives consistent better results on 4 upstream datasets compared to " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": ". In Table 8b, when using " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl} + \\mathcal{L}_{sl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " to train on four training sets " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "(\\mathrm{L} + \\mathrm{C} + \\mathrm{O}365 + \\mathrm{OID})" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": ", the mAP is greatly improved by 1.5 points (39.4-37.9) and " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathrm{mAP}_C" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " is improved by 1.1 points (40.9-39.8), as compared to using only " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": ". This suggests that " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " is valuable to improve the model's generalizability. Overall, these results indicate that " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{hl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " works effectively for label assignment within the upstream dataset, while " + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{sl}" + }, + { + "bbox": [ + 304, + 300, + 545, + 504 + ], + "type": "text", + "content": " takes a complementary role that is more evident when transferring to downstream datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 532, + 470, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 470, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 470, + 544 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "We present ScaleDet, a simple yet scalable and effective multi-dataset training recipe for detection. ScaleDet learns across multiple datasets in a unified semantic label space, optimized by hard label and soft label assignments to align visual and text embeddings. ScaleDet achieves the new state-of-the-art performance on multiple upstream datasets (LVIS, COCO, Objects365, OpenImages) and downstream datasets (ODinW). As the key success of ScaleDet lies in learning in a unified semantic label space, our formulation can also generalize to other vision tasks such as image classification and semantic segmentation. 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In most FL approaches, all edge clients are assumed to have sufficient computation capabilities to participate in the learning of a deep neural network (DNN) model. However, in real-life applications, some clients may have severely limited resources and can only train a much smaller local model. This paper presents ScaleFL, a novel FL approach with two distinctive mechanisms to handle resource heterogeneity and provide an equitable FL framework for all clients. First, ScaleFL adaptively scales down the DNN model along width and depth dimensions by leveraging early exits to find the best-fit models for resource-aware local training on distributed clients. In this way, ScaleFL provides an efficient balance of preserving basic and complex features in local model splits with various sizes for joint training while enabling fast inference for model deployment. Second, ScaleFL utilizes self-distillation among exit predictions during training to improve aggregation through knowledge transfer among subnetworks. We conduct extensive experiments on benchmark CV (CIFAR10/100, ImageNet) and NLP datasets (SST-2, AgNews). We demonstrate that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global/local model performance and provides inference efficiency, with up to 2x latency and 4x model size reduction with negligible performance drop below 2%.", + "bbox": [ + 76, + 316, + 472, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Mobile and Internet-of-Things (IoT) devices are the primary computing sources for most daily life tasks and they are becoming increasingly essential for billions of users worldwide (12; 18). These devices generate an unprecedented amount of data, which can be used to optimize services and improve user experience. Since the data is huge and mostly private, communicating, storing and organizing it in a central server poses serious privacy risks and brings", + "bbox": [ + 75, + 779, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "logistic concerns (12). Federated learning (FL) emerged as a machine learning paradigm for this scenario, where storing the data and training the model in a central server is not feasible. In FL, instead of centralizing the data, the model is distributed to clients for local training and the central server aggregates the local updates received from clients (22).", + "bbox": [ + 496, + 287, + 892, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing FL algorithms such as FedAVG (22), SCAFFOLD (13) and FedOpt (26) rely on the assumption that every participating client has similar resources and can locally execute the same model. However, in most real-life applications, the computation resources tend to differ significantly across clients (5; 19). This heterogeneity prevents clients with insufficient resources to participate in certain FL tasks that require large models. Although existing gradient compression (8) or model pruning techniques (7) may be applied to reduce the cost at the expense of small accuracy loss, these methods are not flexible enough to meet diverse constraint scenarios (computational, storage, network etc.) based on the heterogeneous resources of edge clients. We argue that FL should promote equitable AI practice by supporting a resource-adaptive learning framework that can scale to heterogeneous clients with limited capacity.", + "bbox": [ + 496, + 382, + 892, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, we present ScaleFL, a scalable and equitable FL framework. By design, ScaleFL has two novel features. First, ScaleFL can adaptively scale down the global model along the width and depth dimensions based on the computational resources of participating clients. The downscaling procedure in ScaleFL is inspired by EfficientNet (28), which demonstrates the importance of balancing the size of different dimensions while scaling a neural network. Since a deeper model is more capable of extracting higher-order, complex features while a wider model has access to a larger variety of lower-order, basic features, performing model size reduction across one dimension causes unbalance in terms of the learning capabilities of the resulting model. This motivates the design of ScaleFL that uniformly scales down the global model on both dimensions to provide the balance of preserving access to both complex and basic features as efficiently as possible. To perform splitting along the depth dimension, ScaleFL injects early exit", + "bbox": [ + 496, + 628, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24532", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "classifiers (29) to the global model at certain layers based on the model architecture and computational constraints at each complexity level. As a result, with ScaleFL, not only the global model achieves better performance compared to baseline FL approaches (22) and existing algorithms (5; 19) but also the local models at different complexity levels perform significantly better in case the clients are resource-constrained at inference time.", + "bbox": [ + 75, + 90, + 470, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second novelty of ScaleFL is providing effective aggregation mechanisms for combining local model updates from heterogeneous participating clients, and augmenting self-distillation for effective model update aggregation. During the training of local models, we perform self-distillation among the exit predictions to improve the knowledge transfer among subnetworks. Knowledge distillation enables transferring knowledge from a large (teacher) network to a smaller (student) network by training the student network on teacher predictions as soft labels (10). Self-distillation is a form of knowledge distillation, where the same network is used as both teacher and the student to improve performance during training, especially for multi-exit models (16; 24; 25; 33). In particular, we optimize these models with the additional objective of minimizing the KL divergence among the early exit (student) and final (teacher) predictions, which provides effective aggregation through increasing knowledge flow among local models. This procedure is an integrated component of the local optimization procedure and does not introduce any additional computational overhead as in standard knowledge distillation.", + "bbox": [ + 75, + 215, + 470, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our main contributions are as follows: (1) We introduce a novel FL approach ScaleFL, which performs resource-adaptive 2-D model downscaling using early exits to handle system heterogeneity. Our method preserves the balance of basic and complex features at different complexity levels and enables efficient local models for resource-constrained clients. (2) We further enhance ScaleFL for effective integration of local training model updates by utilizing self-distillation among the exit predictions during local training to increase knowledge flow among subnetworks by minimizing the KL divergence among the early exit (student) and final (teacher) predictions. (3) We validate the advantages of ScaleFL in both model production quality for FL and model inference speedup for model deployment at edge clients. With extensive experiments on three vision benchmarks and two NLP benchmarks, we first demonstrate the significant improvements of ScaleFL in terms of global model performance on image/text classification tasks and various data heterogeneity settings, compared to recent approaches for FL with system heterogeneity. We then analyze the inference performance of local models and show that local models can provide up to 2x inference latency reduction and 4x model size reduction, with negligible performance drop under 2%.", + "bbox": [ + 75, + 537, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "FedAVG is the baseline FL algorithm, where each round, clients download the updated global model, perform local training in parallel using gradient descent and send the updated local weights to the central server for aggregation by the average of the local weights from all participating clients in the given round (22). Three broad categories of efforts have been engaged to improve the FedAVG baseline. First, extensive studies have been dedicated to optimizing the communication efficiency of FL through gradient compression and quantization (1; 20). However, these studies only consider the scenario of homogeneous clients in which all participating clients are assumed to have similar computation capacity and can operate on the same model architecture with the same reduced model complexity. Second, there is significant research on robust federated learning to prevent client training data leakage due to model inversion attacks (30) or Trojan detection against model poisoning attacks (2). The third category is the most recent efforts on addressing client heterogeneity in terms of data distribution (6; 13) and computation resources (5; 19). Our work is most relevant to the last category, where clients have heterogeneous resources. We below identify the most representative approaches in this category.", + "bbox": [ + 496, + 114, + 890, + 462 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "FedProx (17) allows each client to perform variable amounts of training iterations based on their computing power. However, this solution still assumes that all clients can operate on the same model. HeteroFL (5) proposes splitting the global model along width but, it keeps the full depth of the DNN architecture at each client and only adjusts the width split ratio for heterogeneous clients. This tends to result in very slim and deep subnetworks, which can lead to significant loss of basic features (28), resulting in a drastic drop in model quality. In addition, clients with limited resources will suffer from significant accuracy loss at model deployment time because they can only host and operate on those very slim and deep subnetworks. FedDF (19) proposes applying ensemble distillation to fuse models with different architectures. However, FedDF requires an additional dataset for the distillation operations and brings significant overhead between training rounds, whereas we apply self-distillation as an integrated component of the local training procedure without any additional overhead. Another recent study FLANC (23) shares a neural basis among all clients to efficiently construct models at various complexities. However, FLANC assumes that all clients can support at least the neural basis, and thus its adaptivity is bounded by the size of this pre-defined unified neural basis. In addition, the knowledge transfer among clients at different levels is only through the common neural basis.", + "bbox": [ + 496, + 463, + 890, + 853 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inserting multiple exits during DNN training enables early exiting to support adaptive inference (15). BranchyNet (29) introduced the idea of multi-exit classi", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24533", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5eb1fb72f93faa80839fc59a3326f97b0ff16b803b01344796dbcfd9eab01359.jpg", + "image_caption": [ + "Figure 1. System architecture of ScaleFL with three levels. Given the constraint configuration, we compute the split ratios (Section 3.1.1) and based on computed width split ratios, we inject early exit classifiers to the given model. The global model is split along two dimensions (Section 3.1.2) and local models are trained using a combination of cross-entropy and KL-divergence losses as given in Eq. (5). Updates are aggregated back in the central server for the next round (Section 3.2)." + ], + "image_footnote": [], + "bbox": [ + 155, + 89, + 831, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "fiers and early termination of inference for easier test samples. MSDNet (11) proposed a multi-scale dense-connected CNN architecture to improve performance in earlier exits. To improve the training efficiency, knowledge distillation (10) is employed among exits (16; 25). Early exiting has also shown effectiveness for NLP tasks (21; 35).", + "bbox": [ + 75, + 445, + 468, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The design of ScaleFL is inspired by some of the above existing work with two original contributions. First, ScaleFL finds an optimal two-dimensional split plan for each client with limited resources and scales down a complex DNN model along both width and depth dimensions to provide the optimal balance of preserving basic and complex features in different model partitions. Second, ScaleFL further improves the aggregation and optimizes the performance of small subnetworks, produced by our two-dimensional downscaling, by applying self-distillation among exit predictions.", + "bbox": [ + 75, + 537, + 470, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 722, + 210, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider a federated learning system of $K$ clients, each has its private local training dataset of size $N_{k}$ , denoted by $\\mathcal{D}_k = \\{(\\mathbf{X}_i,y_i)\\}_{i = 1}^{N_k}$ , where $(\\mathbf{X}_i,y_i)$ denotes the $i$ th training data sample and its ground truth label, and $k\\in \\{1,\\ldots ,K\\}$ . We are also given the configuration of per-client resource constraints of each client $k$ , such that the client can locally operate on a partition of the global model with the cost under the budget $B_{k}$ and a level of tolerance $(\\epsilon_{k}\\geq 0)$ for the budget constraint. A smaller value of $\\epsilon_{k}$ indicates that the client has a tighter bound for the budget", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "constraint $B_{k}$ and a larger value implies the client has more elasticity regarding its resource budget.", + "bbox": [ + 496, + 445, + 890, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to train a global model $M$ collaboratively with $K$ heterogeneous clients, ScaleFL first determines the model downscaling configuration for each of the $K$ clients based on its resource budget $B_{k}$ and budget tolerance $\\epsilon_{k}$ (Section 3.1). Once the central server has the downscaling configurations for all $K$ clients, it starts the federated learning process. At each round, only a $p$ -fraction of the $K$ clients participate in the joint training (e.g., $p = 10\\%$ , $K = 100$ ) and operate on downscaled models based on their resources. Upon completion of each round, the central server follows the ScaleFL aggregation protocol to integrate the local model updates from heterogeneous clients (Section 3.2). We further improve the aggregation procedure by utilizing self-distillation (Section 3.3). Figure 1 gives a sketch of the ScaleFL system architecture.", + "bbox": [ + 496, + 476, + 892, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Two-Dimensional Model Splitting", + "text_level": 1, + "bbox": [ + 500, + 713, + 795, + 729 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1.1 Generating 2-D Split Configuration", + "text_level": 1, + "bbox": [ + 500, + 737, + 800, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ScaleFL performs the split configuration as a part of the initialization process for a given federated learning (FL) task before starting the iterative FL rounds. The split configuration module makes two decisions: (1) Determining the number of model complexity levels $L$ and mapping of each client $k$ to the corresponding complexity level $l_{k} \\in \\{1, \\dots, L\\}$ , based on the resource constraints $(B_{k}, \\epsilon_{k})$ , (2) given a DNN model $M$ , determining the most uniform bidimensional split ratio along depth $s_{d}^{(l)}$ and width $s_{w}^{(l)}$ di", + "bbox": [ + 496, + 762, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24534", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mensions for each complexity level $l$ .", + "bbox": [ + 76, + 90, + 326, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task 1: In order to downscale the global model $M$ for resource-constrained clients, we first determine the total number of complexity levels, denoted by $L$ , a hyperparameter in ScaleFL and the target cost reduction ratios $r_l$ for each level $l$ . We set $L$ heuristically by performing clustering analysis over the set $\\{B_k | 1 \\leq k \\leq K\\}$ and assign each client with a model complexity level $l \\in \\{1, \\dots, L\\}$ assuming at least one client can operate on the full model $M$ . We consider $r_l = \\frac{\\min\\{B_k | l_k = l\\}}{\\mathrm{cost}(M)}$ for $l < L$ , and $r_L = 1$ being the $100\\%$ complexity representing the full-size model $M$ . Please note that this configuration can also be manually set by the user, e.g., it is possible to use the heuristic rule of halving the cost from the highest complexity level stepwise downward to the first level of complexity, so the local model $M_l$ at level $l$ will have the target cost reduction ratio of $r_l = 0.5r_{l+1}$ . Hence, we have $r_1, r_2$ and $r_3$ set to $12.5\\%$ , $25\\%$ and $50\\%$ respectively for $L = 4$ . The smaller the level $l_k$ is, the less complex the down-scaled model will be for client $k$ . Assigned level $l_k$ for each client $k$ satisfies the following: $r_{l-1} \\mathrm{cost}(M) \\leq B_k < r_l \\mathrm{cost}(M)$ for $l_k \\in \\{1, \\dots, L-1\\}$ , and $\\mathrm{cost}(M) \\leq B_k$ for $l_k = L$ . Here, $\\mathrm{cost}(M)$ denotes the computational cost of the given model $M$ , which can be measured in terms of $\\#PARAMs(M)$ (number of weight parameters) and $\\#FLOPs(M)$ (number of floating point operations).", + "bbox": [ + 75, + 106, + 470, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task 2: Now for each early exit complexity level $l$ , we need to determine the most balanced depth and width split ratio pair $(s_d^{(l)}, s_w^{(l)})$ , while satisfying that the cost of the submodel after the 2-D split will not exceed the resource constraints of those clients mapped to the exit complexity level $l$ . Here, the depth split ratio $s_d^{(l)}$ determines where to place the $l$ th early exit in the $N$ layers of the global model $M$ . The width split ratio $s_w^{(l)}$ indicates the fraction of the weight parameters to keep in the layers of the local models generated using the 2-D split ratio pair $(s_d^{(l)}, s_w^{(l)})$ for level $l$ . For any $l \\in \\{1, \\dots, L\\}$ , the following formulation will be followed to determine the most balanced split ratios $(s_d^{(l)}, s_w^{(l)})$ for those clients mapped to the exit complexity level $l$ :", + "bbox": [ + 75, + 486, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} (s _ {d} ^ {(l)}, s _ {w} ^ {(l)}) = \\operatorname * {a r g m i n} _ {s _ {d} ^ {\\prime} \\in (0, 1 ], s _ {w} ^ {\\prime} \\in (0, 1 ]} | s _ {d} ^ {\\prime} - s _ {w} ^ {\\prime} | \\quad \\text {s u c h t h a t} \\\\ \\left| \\frac {\\operatorname {c o s t} \\left(\\operatorname {s p l i t} \\left(M ; s _ {d} ^ {\\prime} , s _ {w} ^ {\\prime}\\right)\\right)}{r _ {l} \\operatorname {c o s t} (M)} - 1 \\right| \\leq \\epsilon_ {l}. \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 715, + 468, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "There may be multiple split ratio pairs that produce local models satisfying the target cost reduction ratio $r_l$ . We find the most uniform bi-directional split ratio pair $(s_d^{(l)}, s_w^{(l)})$ for each early exit level $l$ through grid search within the bound defined by the tolerance level $\\epsilon_l$ . We set $\\epsilon_l = \\min_{j \\in S^l} \\epsilon_j$ , where $S^l$ denotes the set of clients mapped to the exit level $l$ based on their $B_k$ , and $\\epsilon_l$ is the minimum of tolerance levels", + "bbox": [ + 75, + 792, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/a33b66224b8e294126a5d6c546a197e1fe9c7ed83130d132b58746091f027048.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ResNet110Split RatiosCost
Levelsdsw#PARAMS#FLOPSrl
41.001.001.73 M253.1 M1.000
30.880.750.86 M138.5 M0.500
20.770.700.46 M99.7 M0.250
10.660.700.21 M83.4 M0.125
", + "bbox": [ + 500, + 89, + 893, + 198 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Split ratios and resulting local model statistics (#PARAMS, #FLOPS) for ResNet110 at each level.", + "bbox": [ + 498, + 208, + 890, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of those clients in $S^l$ . A smaller value of $\\epsilon_l$ enforces a tighter bound while satisfying the target cost reduction. A larger $\\epsilon_l$ value provides more flexibility during the finding of the most balanced 2-D split configuration. For each level $l < L$ , we place an early exit classifier to the $\\lfloor s_d^{(l)}N\\rfloor$ th layer. Algorithm 1 lines 2-4 include these steps. Table 1 reports the computed depth and width split ratios for ResNet110 as the global model. The first column refers to the four complexity levels, the second and third columns reports the coputed 2-D split ratios $(s_d,s_w)$ . The next two columns show the cost for the full-size model at $l = 4$ and the reduced model at each complexity level $l\\in \\{3,2,1\\}$ . Our depth and width-balanced split method results in uniformly shaped local models, as opposed to very slim and deep subnetworks due to splitting only along width in HeteroFL.", + "bbox": [ + 496, + 263, + 890, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2 Generating Local Models by Split Operation", + "text_level": 1, + "bbox": [ + 498, + 512, + 864, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Once the split configurations are produced, ScaleFL executes the 2-D split operation to generate the local model for each client $k$ based on the split ratio pairs $(s_w,s_d)$ to meet the budget constraint $(B_{k},\\epsilon_{k})$ specified by the client. Concretely, at each communication round $t$ , only $p$ -fraction of the $K$ clients, denoted by $\\mathcal{S}_t$ , are sampled and the global model $M$ with weights $\\theta_t$ is scaled down by executing the 2-D split operation, which generates the local models with architecture $M_{l_k}$ and weights $\\theta_t^{(k)}$ for each client $k\\in \\mathcal{S}_t$ based on its complexity level $l_{k}$ . In this operation, we first perform model splitting along the depth dimension by removing the layers after the $\\lfloor s_dN\\rfloor$ -th layer where the $l$ th early exit is placed.", + "bbox": [ + 496, + 536, + 890, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we perform splitting along the width dimension by selecting $s_w$ -partition of the per-layer model weights along the hidden channel. To facilitate the execution of model reduction by width split ratio, we define an index function that takes the weight matrix $\\mathbf{W}$ and split ratio value $s_w$ as inputs. Here $\\mathbf{W} \\in \\mathbb{R}^{D_{in} \\times D_{out}}$ is a hidden weight matrix where $D_{in}$ and $D_{out}$ are the number of input and output hidden channels in the corresponding layer. The index function returns the Boolean index matrix $\\mathbf{Z}$ of size $D_{in} \\times D_{out}$ , which indicates which weights to keep after the operation. We define the split index as follows: $\\mathbf{Z}[i,j] = 1$ if", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24535", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$i < \\lfloor s_wD_{in}\\rfloor$ and $j < \\lfloor s_wD_{out}\\rfloor$ , and zero otherwise. This indexing results in keeping the upper-left submatrix by default, i.e., $\\mathbf{W}'\\triangleq \\mathbf{W}[\\mathbf{Z}] = \\mathbf{W}[:\\lfloor s_wD_{in}\\rfloor ,:\\lfloor s_wD_{out}\\rfloor ]$ . Our framework also allows using random selection of weight subsets (e.g. upper-right, lower-left, lower-right and middle etc.) for each client, so that different clients at the same complexity level can use different parts of the model weights and generate slightly different yet complimentary subnetworks. Algorithm 2 gives the pseudocode of this operation (see Appendix 6.1).", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Aggregation", + "text_level": 1, + "bbox": [ + 76, + 251, + 209, + 267 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the 2-D split operation, the ScaleFL aggregation module combines the updated local model weights received from heterogeneous clients at each round $t$ . Concretely, every participating client $k \\in S_{t}$ may send a different subset of the global model to the FL server. For the default upper-left width split option to generate local models, the following aggregation procedure will be carried out to aggregate the overlapping weights received from the contributing clients at each round $t$ , i.e., for every $\\mathbf{W} \\in \\theta$ , and $l \\in \\{1, \\dots, L\\}$ :", + "bbox": [ + 75, + 273, + 472, + 426 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {W} \\left[ \\mathbf {Z} _ {l} - \\mathbf {Z} _ {l - 1} \\right] \\leftarrow \\frac {1}{\\left| \\mathcal {S} _ {t} ^ {l} \\right|} \\sum_ {k \\in \\mathcal {S} _ {t} ^ {l}} \\overline {{\\mathbf {W}}} _ {k} \\left[ \\mathbf {Z} _ {l} - \\mathbf {Z} _ {l - 1} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 435, + 468, + 476 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $S_{t}^{l} = \\{k|k\\in S_{t},l_{k}\\geq l\\}$ is the set of participating clients at round $t$ with the mapped exit level at $l$ or higher. $\\mathbf{Z}_l = \\mathrm{index}(\\mathbf{W},s_w^{(l)})$ for $l\\in \\{l^{\\prime},\\dots L\\}$ and 0 for $l < l^{\\prime}$ , where $l^{\\prime}$ is the minimum level that $\\mathbf{W}$ exists. For instance, the indexes defined by $\\mathbf{Z}_4 - \\mathbf{Z}_3$ will aggregate the updates from level 4 clients only. Similarly, the index defined by $\\mathbf{Z}_3 - \\mathbf{Z}_2$ will aggregate the updates from both level 3 and level 4 clients, and so forth. Lastly, $\\overline{\\mathbf{W}}_k$ is the zero-padded local weight $\\mathbf{W}_k$ such that $\\overline{\\mathbf{W}}_k[\\mathbf{Z}_l] = \\mathbf{W}_k$ and $\\overline{\\mathbf{W}}_k[\\mathbf{1} - \\mathbf{Z}_l] = 0$ . Hence, if all clients have the same complexity level (i.e. $L = 1$ ), Eq. (2) simplifies into $\\mathbf{W}\\gets \\frac{1}{|\\mathcal{S}_t|}\\sum_{k\\in \\mathcal{S}_t}\\mathbf{W}_k$ . Algorithm 3 gives the pseudo-code for the aggregation algorithm (see Appendix 6.1). This aggregation module is executed at FL server and it determines the overlapping regions using index matrices, and scales the sum of the weight updates received from contributing clients. One caveat for this baseline approach is the fact that low complexity level clients may not contribute to learning other parts of the global model weights belonging to higher complexity levels. This motivates us to further optimize our naive baseline aggregation method with self-distillation.", + "bbox": [ + 75, + 486, + 472, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Optimization with Self-Distillation", + "text_level": 1, + "bbox": [ + 76, + 816, + 380, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the optimization of local models, we perform self-distillation, which is a form of knowledge distillation (10) where the technique is applied within the same network. Knowledge distillation enables a small (student)", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1: ScaleFL", + "bbox": [ + 500, + 90, + 663, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inputs: Dataset $\\mathcal{D}_k = \\{(X_i,y_i)\\}_{i = 1}^{N_k}$ for each client $k$ , number of complexity levels $L$ , complexity level of each client $\\{l_k\\}_{k = 1}^K$ , target cost reduction ratios for each level $\\{r_l\\}_{l = 1}^L$ , client availability rate $p$ , initial model architecture $M_0$", + "bbox": [ + 498, + 109, + 893, + 170 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Parameters: number of communication rounds $T$ , number of local training epochs $E$ , batch size $b$ , learning rate $\\eta$", + "bbox": [ + 498, + 171, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Outputs: Trained global model $M$ and weights $\\theta$", + "bbox": [ + 500, + 202, + 828, + 215 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Initialize global model $M$ with architecture $M_0$ and weights $\\theta_0$", + "2: for level $l = 1, \\dots, L - 1$ do", + "3: Compute split ratio pair $(s_d^{(l)}, s_w^{(l)})$ using Eq. (1)", + "4: Add early exit classifier to $M$ at $\\lfloor s_d^{(l)}N\\rfloor$ -th layer", + "5: end for", + "6: for round $t = 0, \\dots, T - 1$ do", + "7: $S_{t}\\gets$ random subset of $\\max (1,pK)$ clients", + "8: for client $k \\in S_t$ in parallel do", + "9: Split: $M_{l_k} \\gets \\text{split}(M; s_d^{(l_k)}, s_w^{(l_k)})$", + "10: for epoch $e = 1, \\ldots, E$ in client $k$ do", + "11: for batch $\\mathcal{B} \\subset \\mathcal{D}_k$ do", + "12: $L = \\frac{1}{b}\\sum_{i\\in \\mathcal{B}}\\mathcal{L}(M_{I_{k}}(\\mathbf{X}_{i};\\theta^{(k)}),y_{i})$ with Eq. (5)", + "13: $\\theta^{(k)}\\gets \\theta^{(k)} - \\eta \\frac{\\partial L}{\\partial\\theta^{(k)}}$", + "14: end for", + "15: end for", + "16: end for", + "17: Aggregate:", + "18: $\\theta \\gets \\text{aggregate}(\\{\\theta^{(k)}\\}_{k \\in S_t}, \\{(s_d^{(l)}, s_w^{(l)})\\}_{l=1}^L)$", + "19: end for", + "20: return $M$ with $\\theta$" + ], + "bbox": [ + 501, + 218, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "network to learn from another larger (teacher) network by treating the predictions of the teacher as soft targets. In ScaleFL, local models with $l > 1$ have multiple exits and can output multiple predictions. Therefore, to enhance the knowledge transfer among the subnetworks of the global model, we use self-distillation by using the final exit as the teacher and earlier exits as students.", + "bbox": [ + 496, + 575, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the local model $M_{j}$ at level $j$ , $f_{i}$ is the $i$ th core subnetwork with weights $\\omega_{i,j}^{(f)}$ . Likewise, $g_{i}$ is the $i$ th exit classifier subnetwork with weights $\\omega_{i,j}^{(g)}$ . $\\hat{\\mathbf{y}}_{i,j}$ is the output at the $i$ th exit of $M_{j}$ . We formulate the forward pass of local models as follows:", + "bbox": [ + 496, + 684, + 890, + 767 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} _ {i, j} = f _ {i} \\left(\\mathbf {H} _ {i - 1, j}; \\omega_ {i, j} ^ {(f)}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 780, + 890, + 801 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\boldsymbol {y}} _ {i, j} = g _ {i} \\left(\\mathbf {H} _ {i, j}; \\omega_ {i, j} ^ {(g)}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 805, + 890, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $1 \\leq i \\leq j \\leq L$ where $j$ is the level of the local model and $\\mathbf{H}_{0,j} = \\mathbf{X}$ is the input. In this study, we present our work on classification tasks so after obtaining the prediction logits at each exit for $M_l$ at level $l$ , the loss with self", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24536", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "distillation is calculated as follows:", + "bbox": [ + 76, + 90, + 312, + 104 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{l (l + 1)} \\sum_ {i = 1} ^ {l} i \\left(\\beta \\mathcal {L} _ {K L} \\left(\\hat {\\boldsymbol {y}} _ {i, l}, \\hat {\\boldsymbol {y}} _ {l, l}\\right) + \\mathcal {L} _ {C E} \\left(\\hat {\\boldsymbol {y}} _ {i, l}, y\\right)\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 111, + 468, + 154 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{KL}(\\hat{\\pmb{y}}_s,\\hat{\\pmb{y}}_t) = \\mathrm{sum}(\\sigma (\\hat{\\pmb{y}}_t / \\tau)\\log \\frac{\\sigma(\\hat{\\pmb{y}}_t / \\tau)}{\\sigma(\\hat{\\pmb{y}}_s / \\tau)})\\tau^2$ is KL divergence with temperature $\\tau >0$ , $\\mathcal{L}_{CE}(\\hat{\\pmb{y}},y) = -\\log \\sigma (\\hat{\\pmb{y}})[y]$ is cross-entropy loss for target class $y$ , $\\sigma$ is softmax function and $\\beta \\in [0,1)$ controls the self-distillation effect. $\\tau$ and $\\beta$ are optimization hyperparameters of the system. Here, $\\tau = 1$ corresponds to using the standard softmax function, and as $\\tau$ grows, the output of the softmax becomes softer and more information on the score distribution of the teacher is provided to the student.", + "bbox": [ + 75, + 161, + 472, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 314, + 209, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we report the results of extensive experiments on five benchmarks: three image classification benchmarks (CIFAR-10/100, ImageNet) and two NLP benchmarks (SST-2, AgNews). We show that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global model performance under the same number of rounds and provides inference speedup with up to 2x latency reduction and 4x model size reduction while keeping the performance drop below $2\\%$ .", + "bbox": [ + 75, + 339, + 468, + 476 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Preprocessing", + "text_level": 1, + "bbox": [ + 76, + 483, + 323, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In image classification experiments, we consider common benchmark datasets on various scales: CIFAR-10, CIFAR-100 (14) and ImageNET (ILSVRC2012) (3). We hold out randomly selected 5000 images from CIFAR-10/100 train set and 25000 images from ImageNET train set for validation. We follow the data augmentation techniques applied in (9) with zero padding, center cropping and random horizontal flip with 0.5 probability. For normalization, we use fixed values, 0.5 as mean and 0.25 as standard deviation and disable statistics tracking for batch normalization operations due to the federated setting. In text classification experiments, we consider SST-2 (27) dataset from GLUE benchmark and AGNews (34) dataset. We hold out 872 sentences from SST-2 validation set and randomly selected 5000 sentences from AgNews train set for validation. For tokenization, we use the pre-trained tokenizer for BERT-base-uncased model provided by the open-source HuggingFace library (31). The details of the datasets are in Table 2.", + "bbox": [ + 75, + 506, + 470, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Heterogeneous System Topology and Non-IID Client Data Distribution", + "text_level": 1, + "bbox": [ + 76, + 801, + 468, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In CIFAR-10/100 experiments, we set the number of clients $K = 100$ and the ratio of available clients in each training round $p = 0.1$ . For ImageNET, SST-2 and AGNews experiments, $K = 50$ and $p = 0.2$ . To simulate the", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5af741a1e8ee1555e06c1a1f0b5d5827773ce908fa9dd472a8bf6935b7d0e0f0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetTrain SizeTest Size# ClassesResolution
CIFAR-1050K10K1032x32
CIFAR-10050K10K10032x32
ImageNet1.2M150K1000224x224
SST-267K18212-
AgNews120K7.6K4-
", + "bbox": [ + 501, + 89, + 890, + 195 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Statistics of the datasets used in image and text classification experiments.", + "bbox": [ + 498, + 205, + 890, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "system heterogeneity, we consider four complexity levels with the target cost reduction ratios $r_1 = 0.125$ , $r_2 = 0.25$ , $r_3 = 0.5$ , $r_4 = 1$ and set the tolerance level $\\epsilon_k = 0.1$ . We set the number of clients assigned to each level to be equal. Different number of complexity levels or client distributions are also applicable and compatible with ScaleFL. We use Dirichlet distribution with concentration parameter $\\alpha$ to create non-IID data splits for the local datasets in the federated setting as in (19; 32). We report the results in two levels of non-IID distribution with $\\alpha = 1$ (more skewed) and $\\alpha = 100$ (less skewed). The resulting class distribution of data at each client is illustrated in Figure 4 (see Appendix).", + "bbox": [ + 496, + 261, + 890, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Model and Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 468, + 803, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On CIFAR-10 and CIFAR-100 datasets, we perform experiments with two different models: ResNet (9) and MSDNet (11). ResNet is a common baseline for benchmarking and MSDNet is a multi-exit CNN architecture with dense connections. We use the default ResNet settings for 110-layer architecture from (9). For MSDNet, we use the recommended configuration with 24 layers, 3 scales and 16 initial hidden dimensions with a growth rate of 6 (11). On ImageNET, we consider EfficientNet (28) with B4 architecture (medium-size) and $224 \\times 224$ input resolution (28). We set the number of FL rounds to 400 and 90, and batch size to 16 and 64 for CIFAR/ImageNET respectively. We optimize local models using gradient descent with the learning rate $\\eta = 0.1$ decayed by 0.1 at the 100th/200th (for CIFAR) and 30th/60th (for ImageNET) rounds. We use 3-layer CNNs with ReLU activations as early exit classifiers. On SST-2 and AgNews datasets, we use the pre-trained BERT (4) provided by the open-source HuggingFace library (31). We optimize the local models for 100 rounds using gradient descent with the learning rate $\\eta = 3e - 5$ and batch size 16. We use one-layer FC layers as early exit classifiers. In all experiments, the number of local training epochs $e = 5$ and KL divergence temperature $\\tau = 3$ . For image/text classification experiments, loss weighting parameters $\\beta = 0.1$ and 0.05, respectively.", + "bbox": [ + 496, + 492, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We consider two baseline approaches: FedAVG (22) and Decoupled. In FedAVG, we train the Level-1 model with", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24537", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2cfa46444c7b3c3bf4b17d33b4c1bf1e8974284beeb39ff0d4bea5acc33c14fa.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelAlgorithmCIFAR-10CIFAR-100
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
ResNet110FedAVG81.4681.4677.7277.7244.2644.2642.7542.75
Decoupled77.16-74.83-36.60-35.78-
HeteroFL82.9384.3577.6079.9144.6647.1242.9742.95
FedDF83.3584.4477.0878.5743.5046.9942.2944.50
ScaleFL (Ours)84.4985.5379.6180.8346.6349.9443.5244.95
MSDNet24FedAVG82.6982.6975.2875.2846.4446.4442.7542.75
HeteroFL81.5483.0275.7776.7444.6547.7742.3243.00
ScaleFL (Ours)84.6184.7777.8178.6949.1950.2545.2546.12
", + "bbox": [ + 199, + 88, + 772, + 262 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b497da74e8fd2b6bb97fe0c41dd4026fa40237d9d85fced339af789d216564ec.jpg", + "table_caption": [ + "Table 3. Local and global model accuracy values on CIFAR-10/100 datasets with ResNet110 and MSDNet24." + ], + "table_footnote": [], + "table_body": "
EfficientNetB4ImageNet
α = 100α = 1
localgloballocalglobal
FedAVG45.0045.0042.3342.33
HeteroFL43.6846.6141.7443.59
ScaleFL (Ours)46.6348.9544.8646.78
", + "bbox": [ + 125, + 309, + 421, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "splitting along width to use all available data. In Decoupled, we train separate models for each level using the corresponding data of the clients at that level. We also compare our results with recent studies: HeteroFL (5) and FedDF (19), where we use splitting along width dimension to form the local models at each level. For FedDF, we use CIFAR-10/100 and SST-2/AgNews train sets as distillation datasets for each other. Our implementation is on Python 3.7 with PyTorch 1.12 library. Our code is available at: https://github.com/git-disl/scale-fl. Each latency measurement is carried out 1000 times on a machine with an 8-core 2.4GHz CPU and 64GB RAM.", + "bbox": [ + 75, + 468, + 468, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Global Model Performance", + "text_level": 1, + "bbox": [ + 76, + 664, + 321, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this setting, we evaluate the global model on the test dataset of each client and report the average of obtained accuracy values. In Table 3, we report the results for image classification on CIFAR-10 and CIFAR-100 with ResNet110 and MSDNet24 models to observe the effect of different architectures on the performance of ScaleFL. We provide comparisons with FedAVG and HeteroFL for all three image datasets. We make two observations from Table 3. First, ScaleFL achieves $0.45 - 2.95\\%$ and $1.7 - 3.12\\%$ higher global performance compared to the closest approach on ResNet110 and MSDNet24 respectively. Second, in all settings, FedAVG baseline performs poorly since the small level-1 model is used to utilize the data of every client. Decoupled baseline performs the worst since the models for", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4d74129bd98600c3c8b970419063a93146662da7010999004a171708b3467f5f.jpg", + "table_caption": [ + "Table 4. Local and global accuracy values on ImageNET." + ], + "table_footnote": [], + "table_body": "
BERTSST-2AG News
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
FedAVG79.9479.9470.0170.0185.1485.1481.1081.10
HeteroFL76.0288.8376.2182.8689.9291.5188.8590.85
FedDF77.6788.9577.4182.9589.7990.9388.9390.05
ScaleFL (Ours)83.7288.5879.6583.7990.5392.1389.7291.20
", + "bbox": [ + 500, + 309, + 893, + 412 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Local and global accuracy values on SST-2 and AgNews.", + "bbox": [ + 500, + 422, + 890, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "each level are trained independently.", + "bbox": [ + 500, + 467, + 741, + 483 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Table 4, we provide the results of ImageNet experiments with EfficientNet-B4 with $224 \\times 224$ input resolution. Since FedDF uses $32 \\times 32$ resolution on ImageNet experiments, we could not report the results for FedDF on ImageNet. ScaleFL consistently achieves around $2.34 - 3.19\\%$ higher global model accuracy under different data heterogeneity settings, compared to the closest competitor in each experiment. In addition, Table 5 reports the effectiveness of ScaleFL using NLP benchmarks with BERT as the backbone and ScaleFL again displays significant improvement especially in local model performance as investigated further in the next subsection.", + "bbox": [ + 496, + 484, + 890, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Local Model Performance Analysis", + "text_level": 1, + "bbox": [ + 500, + 679, + 805, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This section reports the local model performances at different levels. In Tables 3, 4 and 5, 'local' columns contain the average of accuracy values obtained after evaluating the respective local model at each client based on its level. In addition, we illustrate the local models (their scales in width and depth dimensions) and accuracies for MSD-Net24 on CIFAR100 in Figure 2. At each level, even though both submodels satisfy the target cost reduction, ScaleFL results in consistently better performance in terms of local model accuracy. This demonstrates the effectiveness of 2-D downscaling since it balances between preserving low-order basic features and extracting high-order complex features. We also analyze the performance with respect to the num", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24538", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6b9d0ea069deb340f5a4311d03305542551ca3d2af042d3f17d940986a8cbc8.jpg", + "image_caption": [ + "Figure 2. Local model accuracies of Level 1-4 models with ScaleFL and HeteroFL for MSDNet24 on their corresponding test sample sets from CIFAR100. Percentages on the bottom left and top right corners indicate the scaling ratios along width/depth dimensions. Percentages above the models report the test accuracy obtained by that model." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 893, + 270 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fe79f6dbdb258e4312c2d120020aaafffbecadd2ca24547773a0209380b899ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 349, + 271, + 467 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11f501cc28d41838bde48533cd47a6b4e86c4390e58c5bd26c07450cc77d1e6d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 349, + 460, + 465 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dc1e8d79567effcd9897c831e98370cb80b6b32d7f703e24f08d0741a5a54ed0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 474, + 272, + 589 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c1a1162b13829c8e5a853363345f555773c0b71320532224c0022f70d00d930b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 474, + 460, + 589 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/464b0be7dee2a95f2385ab0167d34b015faf5fe73d47b1f745516d009945d75f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 598, + 271, + 714 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/385f686ce8363d59edf96ab1c6b2056277ccf6c07d04342799a69f9c166be34c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 598, + 460, + 714 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0319dfce253197212f4e86779a3dc3664932ef6121c610fe84e4da3ef299dfca.jpg", + "image_caption": [ + "Figure 3. Local model performances with respect to #PARAMs and #FLOPs. Marker sizes represent complexity levels." + ], + "image_footnote": [], + "bbox": [ + 86, + 722, + 272, + 837 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d1732df775fbd4fcb11c9cbb1ce597871c42dd48a98c9252f9b1fb150bdc1b0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 274, + 722, + 460, + 837 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ber of parameters and inference time per sample on CPU (ms), as illustrated in Figure 3. In most settings, our approach achieves better test results at local models and the performance gap is more significant at lower levels, which demonstrates the efficiency of our two-dimensional splitting approach for model downscaling. For instance, the level-2 local model on AgNews with ScaleFL has 6x faster inference and 4x smaller size while having a lower $2.5\\%$ accuracy decrease (vs $3 - 4\\%$ with other methods) from the global model.", + "bbox": [ + 496, + 349, + 893, + 500 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 526, + 619, + 542 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced ScaleFL, a novel resource-adaptive framework to address the system heterogeneity problem in federated learning. First, ScaleFL adaptively scales down the global model based on the computational constraints of participating clients. Our two-dimensional split methodology preserves the important balance of basic and complex features in local models. Second, we perform self-distillation among early exit and final predictions during local model training to improve the knowledge transfer among subnetworks and provide effective aggregation. We demonstrate the performance gains of ScaleFL compared to FedAVG as well as HeteroFL and FedDF, the two most representative federated learning approaches for system heterogeneity on benchmark image and text datasets.", + "bbox": [ + 496, + 556, + 893, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 795, + 668, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, and an IBM faculty award. The first author thanks for the summer 2022 internship at IBM Research with the group led by Dr. Donna Dillenberger.", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24539", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mohammad Mohammadi Amiri, Deniz Gündüz, Sanjeev R. Kulkarni, and H. Vincent Poor. Federated learning with quantized global model updates. *ArXiv*, abs/2006.10672, 2020. 2", + "[2] Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. 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Curran Associates, Inc., 2020. 3" + ], + "bbox": [ + 503, + 92, + 892, + 406 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24541", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/cb97df44-ce50-4c4d-9f39-8532b06bcaf1_model.json b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/cb97df44-ce50-4c4d-9f39-8532b06bcaf1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ba12a5a8549ad39b006c6a353b4d1cf3419a99b3 --- /dev/null +++ b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/cb97df44-ce50-4c4d-9f39-8532b06bcaf1_model.json @@ -0,0 +1,1958 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.097, + 0.131, + 0.873, + 0.153 + ], + "angle": 0, + "content": "ScaleFL: Resource-Adaptive Federated Learning with Heterogeneous Clients" + }, + { + "type": "text", + "bbox": [ + 0.101, + 0.182, + 0.356, + 0.251 + ], + "angle": 0, + "content": "Fatih Ilhan \nGeorgia Institute of Technology \nAtlanta, GA \nfilhan@gatech.edu" + }, + { + "type": "text", + "bbox": [ + 0.393, + 0.182, + 0.577, + 0.251 + ], + "angle": 0, + "content": "Gong Su IBM Research Yorktown Heights, NY gongsu@us.ibm.com" + }, + { + "type": "text", + "bbox": [ + 0.614, + 0.182, + 0.868, + 0.251 + ], + "angle": 0, + "content": "Ling Liu \nGeorgia Institute of Technology \nAtlanta, GA \nling.liu@cc.gatech.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.473, + 0.728 + ], + "angle": 0, + "content": "Federated learning (FL) is an attractive distributed learning paradigm supporting real-time continuous learning and client privacy by default. In most FL approaches, all edge clients are assumed to have sufficient computation capabilities to participate in the learning of a deep neural network (DNN) model. However, in real-life applications, some clients may have severely limited resources and can only train a much smaller local model. This paper presents ScaleFL, a novel FL approach with two distinctive mechanisms to handle resource heterogeneity and provide an equitable FL framework for all clients. First, ScaleFL adaptively scales down the DNN model along width and depth dimensions by leveraging early exits to find the best-fit models for resource-aware local training on distributed clients. In this way, ScaleFL provides an efficient balance of preserving basic and complex features in local model splits with various sizes for joint training while enabling fast inference for model deployment. Second, ScaleFL utilizes self-distillation among exit predictions during training to improve aggregation through knowledge transfer among subnetworks. We conduct extensive experiments on benchmark CV (CIFAR10/100, ImageNet) and NLP datasets (SST-2, AgNews). We demonstrate that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global/local model performance and provides inference efficiency, with up to 2x latency and 4x model size reduction with negligible performance drop below 2%." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.21, + 0.77 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Mobile and Internet-of-Things (IoT) devices are the primary computing sources for most daily life tasks and they are becoming increasingly essential for billions of users worldwide (12; 18). These devices generate an unprecedented amount of data, which can be used to optimize services and improve user experience. Since the data is huge and mostly private, communicating, storing and organizing it in a central server poses serious privacy risks and brings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.288, + 0.893, + 0.379 + ], + "angle": 0, + "content": "logistic concerns (12). Federated learning (FL) emerged as a machine learning paradigm for this scenario, where storing the data and training the model in a central server is not feasible. In FL, instead of centralizing the data, the model is distributed to clients for local training and the central server aggregates the local updates received from clients (22)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.893, + 0.626 + ], + "angle": 0, + "content": "Existing FL algorithms such as FedAVG (22), SCAFFOLD (13) and FedOpt (26) rely on the assumption that every participating client has similar resources and can locally execute the same model. However, in most real-life applications, the computation resources tend to differ significantly across clients (5; 19). This heterogeneity prevents clients with insufficient resources to participate in certain FL tasks that require large models. Although existing gradient compression (8) or model pruning techniques (7) may be applied to reduce the cost at the expense of small accuracy loss, these methods are not flexible enough to meet diverse constraint scenarios (computational, storage, network etc.) based on the heterogeneous resources of edge clients. We argue that FL should promote equitable AI practice by supporting a resource-adaptive learning framework that can scale to heterogeneous clients with limited capacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.902 + ], + "angle": 0, + "content": "To this end, we present ScaleFL, a scalable and equitable FL framework. By design, ScaleFL has two novel features. First, ScaleFL can adaptively scale down the global model along the width and depth dimensions based on the computational resources of participating clients. The downscaling procedure in ScaleFL is inspired by EfficientNet (28), which demonstrates the importance of balancing the size of different dimensions while scaling a neural network. Since a deeper model is more capable of extracting higher-order, complex features while a wider model has access to a larger variety of lower-order, basic features, performing model size reduction across one dimension causes unbalance in terms of the learning capabilities of the resulting model. This motivates the design of ScaleFL that uniformly scales down the global model on both dimensions to provide the balance of preserving access to both complex and basic features as efficiently as possible. To perform splitting along the depth dimension, ScaleFL injects early exit" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24532" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.212 + ], + "angle": 0, + "content": "classifiers (29) to the global model at certain layers based on the model architecture and computational constraints at each complexity level. As a result, with ScaleFL, not only the global model achieves better performance compared to baseline FL approaches (22) and existing algorithms (5; 19) but also the local models at different complexity levels perform significantly better in case the clients are resource-constrained at inference time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.471, + 0.534 + ], + "angle": 0, + "content": "The second novelty of ScaleFL is providing effective aggregation mechanisms for combining local model updates from heterogeneous participating clients, and augmenting self-distillation for effective model update aggregation. During the training of local models, we perform self-distillation among the exit predictions to improve the knowledge transfer among subnetworks. Knowledge distillation enables transferring knowledge from a large (teacher) network to a smaller (student) network by training the student network on teacher predictions as soft labels (10). Self-distillation is a form of knowledge distillation, where the same network is used as both teacher and the student to improve performance during training, especially for multi-exit models (16; 24; 25; 33). In particular, we optimize these models with the additional objective of minimizing the KL divergence among the early exit (student) and final (teacher) predictions, which provides effective aggregation through increasing knowledge flow among local models. This procedure is an integrated component of the local optimization procedure and does not introduce any additional computational overhead as in standard knowledge distillation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In summary, our main contributions are as follows: (1) We introduce a novel FL approach ScaleFL, which performs resource-adaptive 2-D model downscaling using early exits to handle system heterogeneity. Our method preserves the balance of basic and complex features at different complexity levels and enables efficient local models for resource-constrained clients. (2) We further enhance ScaleFL for effective integration of local training model updates by utilizing self-distillation among the exit predictions during local training to increase knowledge flow among subnetworks by minimizing the KL divergence among the early exit (student) and final (teacher) predictions. (3) We validate the advantages of ScaleFL in both model production quality for FL and model inference speedup for model deployment at edge clients. With extensive experiments on three vision benchmarks and two NLP benchmarks, we first demonstrate the significant improvements of ScaleFL in terms of global model performance on image/text classification tasks and various data heterogeneity settings, compared to recent approaches for FL with system heterogeneity. We then analyze the inference performance of local models and show that local models can provide up to 2x inference latency reduction and 4x model size reduction, with negligible performance drop under 2%." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.463 + ], + "angle": 0, + "content": "FedAVG is the baseline FL algorithm, where each round, clients download the updated global model, perform local training in parallel using gradient descent and send the updated local weights to the central server for aggregation by the average of the local weights from all participating clients in the given round (22). Three broad categories of efforts have been engaged to improve the FedAVG baseline. First, extensive studies have been dedicated to optimizing the communication efficiency of FL through gradient compression and quantization (1; 20). However, these studies only consider the scenario of homogeneous clients in which all participating clients are assumed to have similar computation capacity and can operate on the same model architecture with the same reduced model complexity. Second, there is significant research on robust federated learning to prevent client training data leakage due to model inversion attacks (30) or Trojan detection against model poisoning attacks (2). The third category is the most recent efforts on addressing client heterogeneity in terms of data distribution (6; 13) and computation resources (5; 19). Our work is most relevant to the last category, where clients have heterogeneous resources. We below identify the most representative approaches in this category." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.854 + ], + "angle": 0, + "content": "FedProx (17) allows each client to perform variable amounts of training iterations based on their computing power. However, this solution still assumes that all clients can operate on the same model. HeteroFL (5) proposes splitting the global model along width but, it keeps the full depth of the DNN architecture at each client and only adjusts the width split ratio for heterogeneous clients. This tends to result in very slim and deep subnetworks, which can lead to significant loss of basic features (28), resulting in a drastic drop in model quality. In addition, clients with limited resources will suffer from significant accuracy loss at model deployment time because they can only host and operate on those very slim and deep subnetworks. FedDF (19) proposes applying ensemble distillation to fuse models with different architectures. However, FedDF requires an additional dataset for the distillation operations and brings significant overhead between training rounds, whereas we apply self-distillation as an integrated component of the local training procedure without any additional overhead. Another recent study FLANC (23) shares a neural basis among all clients to efficiently construct models at various complexities. However, FLANC assumes that all clients can support at least the neural basis, and thus its adaptivity is bounded by the size of this pre-defined unified neural basis. In addition, the knowledge transfer among clients at different levels is only through the common neural basis." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Inserting multiple exits during DNN training enables early exiting to support adaptive inference (15). BranchyNet (29) introduced the idea of multi-exit classi" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24533" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.156, + 0.09, + 0.832, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.895, + 0.419 + ], + "angle": 0, + "content": "Figure 1. System architecture of ScaleFL with three levels. Given the constraint configuration, we compute the split ratios (Section 3.1.1) and based on computed width split ratios, we inject early exit classifiers to the given model. The global model is split along two dimensions (Section 3.1.2) and local models are trained using a combination of cross-entropy and KL-divergence losses as given in Eq. (5). Updates are aggregated back in the central server for the next round (Section 3.2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.537 + ], + "angle": 0, + "content": "fiers and early termination of inference for easier test samples. MSDNet (11) proposed a multi-scale dense-connected CNN architecture to improve performance in earlier exits. To improve the training efficiency, knowledge distillation (10) is employed among exits (16; 25). Early exiting has also shown effectiveness for NLP tasks (21; 35)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.471, + 0.706 + ], + "angle": 0, + "content": "The design of ScaleFL is inspired by some of the above existing work with two original contributions. First, ScaleFL finds an optimal two-dimensional split plan for each client with limited resources and scales down a complex DNN model along both width and depth dimensions to provide the optimal balance of preserving basic and complex features in different model partitions. Second, ScaleFL further improves the aggregation and optimizes the performance of small subnetworks, produced by our two-dimensional downscaling, by applying self-distillation among exit predictions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.723, + 0.212, + 0.74 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Consider a federated learning system of \\(K\\) clients, each has its private local training dataset of size \\(N_{k}\\), denoted by \\(\\mathcal{D}_k = \\{(\\mathbf{X}_i,y_i)\\}_{i = 1}^{N_k}\\), where \\((\\mathbf{X}_i,y_i)\\) denotes the \\(i\\)th training data sample and its ground truth label, and \\(k\\in \\{1,\\ldots ,K\\}\\). We are also given the configuration of per-client resource constraints of each client \\(k\\), such that the client can locally operate on a partition of the global model with the cost under the budget \\(B_{k}\\) and a level of tolerance \\((\\epsilon_{k}\\geq 0)\\) for the budget constraint. A smaller value of \\(\\epsilon_{k}\\) indicates that the client has a tighter bound for the budget" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.892, + 0.476 + ], + "angle": 0, + "content": "constraint \\( B_{k} \\) and a larger value implies the client has more elasticity regarding its resource budget." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.893, + 0.703 + ], + "angle": 0, + "content": "In order to train a global model \\( M \\) collaboratively with \\( K \\) heterogeneous clients, ScaleFL first determines the model downscaling configuration for each of the \\( K \\) clients based on its resource budget \\( B_{k} \\) and budget tolerance \\( \\epsilon_{k} \\) (Section 3.1). Once the central server has the downscaling configurations for all \\( K \\) clients, it starts the federated learning process. At each round, only a \\( p \\)-fraction of the \\( K \\) clients participate in the joint training (e.g., \\( p = 10\\% \\), \\( K = 100 \\)) and operate on downscaled models based on their resources. Upon completion of each round, the central server follows the ScaleFL aggregation protocol to integrate the local model updates from heterogeneous clients (Section 3.2). We further improve the aggregation procedure by utilizing self-distillation (Section 3.3). Figure 1 gives a sketch of the ScaleFL system architecture." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.714, + 0.796, + 0.731 + ], + "angle": 0, + "content": "3.1. Two-Dimensional Model Splitting" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.738, + 0.802, + 0.754 + ], + "angle": 0, + "content": "3.1.1 Generating 2-D Split Configuration" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.903 + ], + "angle": 0, + "content": "ScaleFL performs the split configuration as a part of the initialization process for a given federated learning (FL) task before starting the iterative FL rounds. The split configuration module makes two decisions: (1) Determining the number of model complexity levels \\( L \\) and mapping of each client \\( k \\) to the corresponding complexity level \\( l_{k} \\in \\{1, \\dots, L\\} \\), based on the resource constraints \\( (B_{k}, \\epsilon_{k}) \\), (2) given a DNN model \\( M \\), determining the most uniform bidimensional split ratio along depth \\( s_{d}^{(l)} \\) and width \\( s_{w}^{(l)} \\) di" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24534" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.327, + 0.106 + ], + "angle": 0, + "content": "mensions for each complexity level \\(l\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.107, + 0.471, + 0.487 + ], + "angle": 0, + "content": "Task 1: In order to downscale the global model \\( M \\) for resource-constrained clients, we first determine the total number of complexity levels, denoted by \\( L \\), a hyperparameter in ScaleFL and the target cost reduction ratios \\( r_l \\) for each level \\( l \\). We set \\( L \\) heuristically by performing clustering analysis over the set \\( \\{B_k | 1 \\leq k \\leq K\\} \\) and assign each client with a model complexity level \\( l \\in \\{1, \\dots, L\\} \\) assuming at least one client can operate on the full model \\( M \\). We consider \\( r_l = \\frac{\\min\\{B_k | l_k = l\\}}{\\mathrm{cost}(M)} \\) for \\( l < L \\), and \\( r_L = 1 \\) being the \\( 100\\% \\) complexity representing the full-size model \\( M \\). Please note that this configuration can also be manually set by the user, e.g., it is possible to use the heuristic rule of halving the cost from the highest complexity level stepwise downward to the first level of complexity, so the local model \\( M_l \\) at level \\( l \\) will have the target cost reduction ratio of \\( r_l = 0.5r_{l+1} \\). Hence, we have \\( r_1, r_2 \\) and \\( r_3 \\) set to \\( 12.5\\% \\), \\( 25\\% \\) and \\( 50\\% \\) respectively for \\( L = 4 \\). The smaller the level \\( l_k \\) is, the less complex the down-scaled model will be for client \\( k \\). Assigned level \\( l_k \\) for each client \\( k \\) satisfies the following: \\( r_{l-1} \\mathrm{cost}(M) \\leq B_k < r_l \\mathrm{cost}(M) \\) for \\( l_k \\in \\{1, \\dots, L-1\\} \\), and \\( \\mathrm{cost}(M) \\leq B_k \\) for \\( l_k = L \\). Here, \\( \\mathrm{cost}(M) \\) denotes the computational cost of the given model \\( M \\), which can be measured in terms of \\( \\#PARAMs(M) \\) (number of weight parameters) and \\( \\#FLOPs(M) \\) (number of floating point operations)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.47, + 0.706 + ], + "angle": 0, + "content": "Task 2: Now for each early exit complexity level \\( l \\), we need to determine the most balanced depth and width split ratio pair \\( (s_d^{(l)}, s_w^{(l)}) \\), while satisfying that the cost of the submodel after the 2-D split will not exceed the resource constraints of those clients mapped to the exit complexity level \\( l \\). Here, the depth split ratio \\( s_d^{(l)} \\) determines where to place the \\( l \\)th early exit in the \\( N \\) layers of the global model \\( M \\). The width split ratio \\( s_w^{(l)} \\) indicates the fraction of the weight parameters to keep in the layers of the local models generated using the 2-D split ratio pair \\( (s_d^{(l)}, s_w^{(l)}) \\) for level \\( l \\). For any \\( l \\in \\{1, \\dots, L\\} \\), the following formulation will be followed to determine the most balanced split ratios \\( (s_d^{(l)}, s_w^{(l)}) \\) for those clients mapped to the exit complexity level \\( l \\):" + }, + { + "type": "equation", + "bbox": [ + 0.106, + 0.717, + 0.469, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} (s _ {d} ^ {(l)}, s _ {w} ^ {(l)}) = \\operatorname * {a r g m i n} _ {s _ {d} ^ {\\prime} \\in (0, 1 ], s _ {w} ^ {\\prime} \\in (0, 1 ]} | s _ {d} ^ {\\prime} - s _ {w} ^ {\\prime} | \\quad \\text {s u c h t h a t} \\\\ \\left| \\frac {\\operatorname {c o s t} \\left(\\operatorname {s p l i t} \\left(M ; s _ {d} ^ {\\prime} , s _ {w} ^ {\\prime}\\right)\\right)}{r _ {l} \\operatorname {c o s t} (M)} - 1 \\right| \\leq \\epsilon_ {l}. \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.47, + 0.901 + ], + "angle": 0, + "content": "There may be multiple split ratio pairs that produce local models satisfying the target cost reduction ratio \\( r_l \\). We find the most uniform bi-directional split ratio pair \\( (s_d^{(l)}, s_w^{(l)}) \\) for each early exit level \\( l \\) through grid search within the bound defined by the tolerance level \\( \\epsilon_l \\). We set \\( \\epsilon_l = \\min_{j \\in S^l} \\epsilon_j \\), where \\( S^l \\) denotes the set of clients mapped to the exit level \\( l \\) based on their \\( B_k \\), and \\( \\epsilon_l \\) is the minimum of tolerance levels" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.09, + 0.894, + 0.199 + ], + "angle": 0, + "content": "
ResNet110Split RatiosCost
Levelsdsw#PARAMS#FLOPSrl
41.001.001.73 M253.1 M1.000
30.880.750.86 M138.5 M0.500
20.770.700.46 M99.7 M0.250
10.660.700.21 M83.4 M0.125
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.209, + 0.892, + 0.238 + ], + "angle": 0, + "content": "Table 1. Split ratios and resulting local model statistics (#PARAMS, #FLOPS) for ResNet110 at each level." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.264, + 0.892, + 0.493 + ], + "angle": 0, + "content": "of those clients in \\( S^l \\). A smaller value of \\( \\epsilon_l \\) enforces a tighter bound while satisfying the target cost reduction. A larger \\( \\epsilon_l \\) value provides more flexibility during the finding of the most balanced 2-D split configuration. For each level \\( l < L \\), we place an early exit classifier to the \\( \\lfloor s_d^{(l)}N\\rfloor \\)th layer. Algorithm 1 lines 2-4 include these steps. Table 1 reports the computed depth and width split ratios for ResNet110 as the global model. The first column refers to the four complexity levels, the second and third columns reports the coputed 2-D split ratios \\( (s_d,s_w) \\). The next two columns show the cost for the full-size model at \\( l = 4 \\) and the reduced model at each complexity level \\( l\\in \\{3,2,1\\} \\). Our depth and width-balanced split method results in uniformly shaped local models, as opposed to very slim and deep subnetworks due to splitting only along width in HeteroFL." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.513, + 0.866, + 0.529 + ], + "angle": 0, + "content": "3.1.2 Generating Local Models by Split Operation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Once the split configurations are produced, ScaleFL executes the 2-D split operation to generate the local model for each client \\(k\\) based on the split ratio pairs \\((s_w,s_d)\\) to meet the budget constraint \\((B_{k},\\epsilon_{k})\\) specified by the client. Concretely, at each communication round \\(t\\), only \\(p\\)-fraction of the \\(K\\) clients, denoted by \\(\\mathcal{S}_t\\), are sampled and the global model \\(M\\) with weights \\(\\theta_t\\) is scaled down by executing the 2-D split operation, which generates the local models with architecture \\(M_{l_k}\\) and weights \\(\\theta_t^{(k)}\\) for each client \\(k\\in \\mathcal{S}_t\\) based on its complexity level \\(l_{k}\\). In this operation, we first perform model splitting along the depth dimension by removing the layers after the \\(\\lfloor s_dN\\rfloor\\)-th layer where the \\(l\\)th early exit is placed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Next, we perform splitting along the width dimension by selecting \\( s_w \\)-partition of the per-layer model weights along the hidden channel. To facilitate the execution of model reduction by width split ratio, we define an index function that takes the weight matrix \\( \\mathbf{W} \\) and split ratio value \\( s_w \\) as inputs. Here \\( \\mathbf{W} \\in \\mathbb{R}^{D_{in} \\times D_{out}} \\) is a hidden weight matrix where \\( D_{in} \\) and \\( D_{out} \\) are the number of input and output hidden channels in the corresponding layer. The index function returns the Boolean index matrix \\( \\mathbf{Z} \\) of size \\( D_{in} \\times D_{out} \\), which indicates which weights to keep after the operation. We define the split index as follows: \\( \\mathbf{Z}[i,j] = 1 \\) if" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24535" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.244 + ], + "angle": 0, + "content": "\\(i < \\lfloor s_wD_{in}\\rfloor\\) and \\(j < \\lfloor s_wD_{out}\\rfloor\\), and zero otherwise. This indexing results in keeping the upper-left submatrix by default, i.e., \\(\\mathbf{W}'\\triangleq \\mathbf{W}[\\mathbf{Z}] = \\mathbf{W}[:\\lfloor s_wD_{in}\\rfloor ,:\\lfloor s_wD_{out}\\rfloor ]\\). Our framework also allows using random selection of weight subsets (e.g. upper-right, lower-left, lower-right and middle etc.) for each client, so that different clients at the same complexity level can use different parts of the model weights and generate slightly different yet complimentary subnetworks. Algorithm 2 gives the pseudocode of this operation (see Appendix 6.1)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.252, + 0.21, + 0.268 + ], + "angle": 0, + "content": "3.2. Aggregation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.473, + 0.428 + ], + "angle": 0, + "content": "After the 2-D split operation, the ScaleFL aggregation module combines the updated local model weights received from heterogeneous clients at each round \\( t \\). Concretely, every participating client \\( k \\in S_{t} \\) may send a different subset of the global model to the FL server. For the default upper-left width split option to generate local models, the following aggregation procedure will be carried out to aggregate the overlapping weights received from the contributing clients at each round \\( t \\), i.e., for every \\( \\mathbf{W} \\in \\theta \\), and \\( l \\in \\{1, \\dots, L\\} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.436, + 0.47, + 0.477 + ], + "angle": 0, + "content": "\\[\n\\mathbf {W} \\left[ \\mathbf {Z} _ {l} - \\mathbf {Z} _ {l - 1} \\right] \\leftarrow \\frac {1}{\\left| \\mathcal {S} _ {t} ^ {l} \\right|} \\sum_ {k \\in \\mathcal {S} _ {t} ^ {l}} \\overline {{\\mathbf {W}}} _ {k} \\left[ \\mathbf {Z} _ {l} - \\mathbf {Z} _ {l - 1} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.473, + 0.81 + ], + "angle": 0, + "content": "Here, \\( S_{t}^{l} = \\{k|k\\in S_{t},l_{k}\\geq l\\} \\) is the set of participating clients at round \\( t \\) with the mapped exit level at \\( l \\) or higher. \\( \\mathbf{Z}_l = \\mathrm{index}(\\mathbf{W},s_w^{(l)}) \\) for \\( l\\in \\{l^{\\prime},\\dots L\\} \\) and 0 for \\( l < l^{\\prime} \\), where \\( l^{\\prime} \\) is the minimum level that \\( \\mathbf{W} \\) exists. For instance, the indexes defined by \\( \\mathbf{Z}_4 - \\mathbf{Z}_3 \\) will aggregate the updates from level 4 clients only. Similarly, the index defined by \\( \\mathbf{Z}_3 - \\mathbf{Z}_2 \\) will aggregate the updates from both level 3 and level 4 clients, and so forth. Lastly, \\( \\overline{\\mathbf{W}}_k \\) is the zero-padded local weight \\( \\mathbf{W}_k \\) such that \\( \\overline{\\mathbf{W}}_k[\\mathbf{Z}_l] = \\mathbf{W}_k \\) and \\( \\overline{\\mathbf{W}}_k[\\mathbf{1} - \\mathbf{Z}_l] = 0 \\). Hence, if all clients have the same complexity level (i.e. \\( L = 1 \\)), Eq. (2) simplifies into \\( \\mathbf{W}\\gets \\frac{1}{|\\mathcal{S}_t|}\\sum_{k\\in \\mathcal{S}_t}\\mathbf{W}_k \\). Algorithm 3 gives the pseudo-code for the aggregation algorithm (see Appendix 6.1). This aggregation module is executed at FL server and it determines the overlapping regions using index matrices, and scales the sum of the weight updates received from contributing clients. One caveat for this baseline approach is the fact that low complexity level clients may not contribute to learning other parts of the global model weights belonging to higher complexity levels. This motivates us to further optimize our naive baseline aggregation method with self-distillation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.381, + 0.834 + ], + "angle": 0, + "content": "3.3. Optimization with Self-Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "During the optimization of local models, we perform self-distillation, which is a form of knowledge distillation (10) where the technique is applied within the same network. Knowledge distillation enables a small (student)" + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.092, + 0.664, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1: ScaleFL" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.11, + 0.895, + 0.171 + ], + "angle": 0, + "content": "Inputs: Dataset \\(\\mathcal{D}_k = \\{(X_i,y_i)\\}_{i = 1}^{N_k}\\) for each client \\(k\\), number of complexity levels \\(L\\), complexity level of each client \\(\\{l_k\\}_{k = 1}^K\\), target cost reduction ratios for each level \\(\\{r_l\\}_{l = 1}^L\\), client availability rate \\(p\\), initial model architecture \\(M_0\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.172, + 0.892, + 0.203 + ], + "angle": 0, + "content": "Parameters: number of communication rounds \\( T \\), number of local training epochs \\( E \\), batch size \\( b \\), learning rate \\( \\eta \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.203, + 0.829, + 0.217 + ], + "angle": 0, + "content": "Outputs: Trained global model \\(M\\) and weights \\(\\theta\\)" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.219, + 0.892, + 0.248 + ], + "angle": 0, + "content": "1: Initialize global model \\(M\\) with architecture \\(M_0\\) and weights \\(\\theta_0\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.25, + 0.719, + 0.263 + ], + "angle": 0, + "content": "2: for level \\( l = 1, \\dots, L - 1 \\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.264, + 0.863, + 0.282 + ], + "angle": 0, + "content": "3: Compute split ratio pair \\((s_d^{(l)}, s_w^{(l)})\\) using Eq. (1)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.283, + 0.869, + 0.3 + ], + "angle": 0, + "content": "4: Add early exit classifier to \\(M\\) at \\(\\lfloor s_d^{(l)}N\\rfloor\\) -th layer" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.301, + 0.585, + 0.313 + ], + "angle": 0, + "content": "5: end for" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.315, + 0.726, + 0.328 + ], + "angle": 0, + "content": "6: for round \\( t = 0, \\dots, T - 1 \\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.33, + 0.834, + 0.345 + ], + "angle": 0, + "content": "7: \\(S_{t}\\gets\\) random subset of \\(\\max (1,pK)\\) clients" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.346, + 0.747, + 0.359 + ], + "angle": 0, + "content": "8: for client \\( k \\in S_t \\) in parallel do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.359, + 0.812, + 0.378 + ], + "angle": 0, + "content": "9: Split: \\( M_{l_k} \\gets \\text{split}(M; s_d^{(l_k)}, s_w^{(l_k)}) \\)" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.379, + 0.805, + 0.392 + ], + "angle": 0, + "content": "10: for epoch \\( e = 1, \\ldots, E \\) in client \\( k \\) do" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.393, + 0.722, + 0.406 + ], + "angle": 0, + "content": "11: for batch \\(\\mathcal{B} \\subset \\mathcal{D}_k\\) do" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.407, + 0.884, + 0.422 + ], + "angle": 0, + "content": "12: \\(L = \\frac{1}{b}\\sum_{i\\in \\mathcal{B}}\\mathcal{L}(M_{I_{k}}(\\mathbf{X}_{i};\\theta^{(k)}),y_{i})\\) with Eq. (5)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.422, + 0.728, + 0.439 + ], + "angle": 0, + "content": "13: \\(\\theta^{(k)}\\gets \\theta^{(k)} - \\eta \\frac{\\partial L}{\\partial\\theta^{(k)}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.439, + 0.633, + 0.45 + ], + "angle": 0, + "content": "14: end for" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.452, + 0.616, + 0.465 + ], + "angle": 0, + "content": "15: end for" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.468, + 0.6, + 0.481 + ], + "angle": 0, + "content": "16: end for" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.483, + 0.626, + 0.497 + ], + "angle": 0, + "content": "17: Aggregate:" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.497, + 0.866, + 0.515 + ], + "angle": 0, + "content": "18: \\(\\theta \\gets \\text{aggregate}(\\{\\theta^{(k)}\\}_{k \\in S_t}, \\{(s_d^{(l)}, s_w^{(l)})\\}_{l=1}^L)\\)" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.516, + 0.585, + 0.528 + ], + "angle": 0, + "content": "19: end for" + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.53, + 0.65, + 0.543 + ], + "angle": 0, + "content": "20: return \\( M \\) with \\( \\theta \\)" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.219, + 0.892, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.682 + ], + "angle": 0, + "content": "network to learn from another larger (teacher) network by treating the predictions of the teacher as soft targets. In ScaleFL, local models with \\( l > 1 \\) have multiple exits and can output multiple predictions. Therefore, to enhance the knowledge transfer among the subnetworks of the global model, we use self-distillation by using the final exit as the teacher and earlier exits as students." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.768 + ], + "angle": 0, + "content": "For the local model \\(M_{j}\\) at level \\(j\\), \\(f_{i}\\) is the \\(i\\)th core subnetwork with weights \\(\\omega_{i,j}^{(f)}\\). Likewise, \\(g_{i}\\) is the \\(i\\)th exit classifier subnetwork with weights \\(\\omega_{i,j}^{(g)}\\). \\(\\hat{\\mathbf{y}}_{i,j}\\) is the output at the \\(i\\)th exit of \\(M_{j}\\). We formulate the forward pass of local models as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.781, + 0.892, + 0.803 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} _ {i, j} = f _ {i} \\left(\\mathbf {H} _ {i - 1, j}; \\omega_ {i, j} ^ {(f)}\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.616, + 0.806, + 0.892, + 0.827 + ], + "angle": 0, + "content": "\\[\n\\hat {\\boldsymbol {y}} _ {i, j} = g _ {i} \\left(\\mathbf {H} _ {i, j}; \\omega_ {i, j} ^ {(g)}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "for \\(1 \\leq i \\leq j \\leq L\\) where \\(j\\) is the level of the local model and \\(\\mathbf{H}_{0,j} = \\mathbf{X}\\) is the input. In this study, we present our work on classification tasks so after obtaining the prediction logits at each exit for \\(M_l\\) at level \\(l\\), the loss with self" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24536" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.313, + 0.106 + ], + "angle": 0, + "content": "distillation is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.112, + 0.47, + 0.155 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{l (l + 1)} \\sum_ {i = 1} ^ {l} i \\left(\\beta \\mathcal {L} _ {K L} \\left(\\hat {\\boldsymbol {y}} _ {i, l}, \\hat {\\boldsymbol {y}} _ {l, l}\\right) + \\mathcal {L} _ {C E} \\left(\\hat {\\boldsymbol {y}} _ {i, l}, y\\right)\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.162, + 0.473, + 0.304 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{KL}(\\hat{\\pmb{y}}_s,\\hat{\\pmb{y}}_t) = \\mathrm{sum}(\\sigma (\\hat{\\pmb{y}}_t / \\tau)\\log \\frac{\\sigma(\\hat{\\pmb{y}}_t / \\tau)}{\\sigma(\\hat{\\pmb{y}}_s / \\tau)})\\tau^2\\) is KL divergence with temperature \\(\\tau >0\\), \\(\\mathcal{L}_{CE}(\\hat{\\pmb{y}},y) = -\\log \\sigma (\\hat{\\pmb{y}})[y]\\) is cross-entropy loss for target class \\(y\\), \\(\\sigma\\) is softmax function and \\(\\beta \\in [0,1)\\) controls the self-distillation effect. \\(\\tau\\) and \\(\\beta\\) are optimization hyperparameters of the system. Here, \\(\\tau = 1\\) corresponds to using the standard softmax function, and as \\(\\tau\\) grows, the output of the softmax becomes softer and more information on the score distribution of the teacher is provided to the student." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.315, + 0.21, + 0.332 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.47, + 0.477 + ], + "angle": 0, + "content": "In this section, we report the results of extensive experiments on five benchmarks: three image classification benchmarks (CIFAR-10/100, ImageNet) and two NLP benchmarks (SST-2, AgNews). We show that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global model performance under the same number of rounds and provides inference speedup with up to 2x latency reduction and 4x model size reduction while keeping the performance drop below \\(2\\%\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.484, + 0.325, + 0.501 + ], + "angle": 0, + "content": "4.1. Datasets and Preprocessing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.471, + 0.793 + ], + "angle": 0, + "content": "In image classification experiments, we consider common benchmark datasets on various scales: CIFAR-10, CIFAR-100 (14) and ImageNET (ILSVRC2012) (3). We hold out randomly selected 5000 images from CIFAR-10/100 train set and 25000 images from ImageNET train set for validation. We follow the data augmentation techniques applied in (9) with zero padding, center cropping and random horizontal flip with 0.5 probability. For normalization, we use fixed values, 0.5 as mean and 0.25 as standard deviation and disable statistics tracking for batch normalization operations due to the federated setting. In text classification experiments, we consider SST-2 (27) dataset from GLUE benchmark and AGNews (34) dataset. We hold out 872 sentences from SST-2 validation set and randomly selected 5000 sentences from AgNews train set for validation. For tokenization, we use the pre-trained tokenizer for BERT-base-uncased model provided by the open-source HuggingFace library (31). The details of the datasets are in Table 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.47, + 0.833 + ], + "angle": 0, + "content": "4.2. Heterogeneous System Topology and Non-IID Client Data Distribution" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In CIFAR-10/100 experiments, we set the number of clients \\( K = 100 \\) and the ratio of available clients in each training round \\( p = 0.1 \\). For ImageNET, SST-2 and AGNews experiments, \\( K = 50 \\) and \\( p = 0.2 \\). To simulate the" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.09, + 0.892, + 0.196 + ], + "angle": 0, + "content": "
DatasetTrain SizeTest Size# ClassesResolution
CIFAR-1050K10K1032x32
CIFAR-10050K10K10032x32
ImageNet1.2M150K1000224x224
SST-267K18212-
AgNews120K7.6K4-
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.206, + 0.892, + 0.235 + ], + "angle": 0, + "content": "Table 2. Statistics of the datasets used in image and text classification experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.459 + ], + "angle": 0, + "content": "system heterogeneity, we consider four complexity levels with the target cost reduction ratios \\( r_1 = 0.125 \\), \\( r_2 = 0.25 \\), \\( r_3 = 0.5 \\), \\( r_4 = 1 \\) and set the tolerance level \\( \\epsilon_k = 0.1 \\). We set the number of clients assigned to each level to be equal. Different number of complexity levels or client distributions are also applicable and compatible with ScaleFL. We use Dirichlet distribution with concentration parameter \\( \\alpha \\) to create non-IID data splits for the local datasets in the federated setting as in (19; 32). We report the results in two levels of non-IID distribution with \\( \\alpha = 1 \\) (more skewed) and \\( \\alpha = 100 \\) (less skewed). The resulting class distribution of data at each client is illustrated in Figure 4 (see Appendix)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.469, + 0.805, + 0.485 + ], + "angle": 0, + "content": "4.3. Model and Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.87 + ], + "angle": 0, + "content": "On CIFAR-10 and CIFAR-100 datasets, we perform experiments with two different models: ResNet (9) and MSDNet (11). ResNet is a common baseline for benchmarking and MSDNet is a multi-exit CNN architecture with dense connections. We use the default ResNet settings for 110-layer architecture from (9). For MSDNet, we use the recommended configuration with 24 layers, 3 scales and 16 initial hidden dimensions with a growth rate of 6 (11). On ImageNET, we consider EfficientNet (28) with B4 architecture (medium-size) and \\(224 \\times 224\\) input resolution (28). We set the number of FL rounds to 400 and 90, and batch size to 16 and 64 for CIFAR/ImageNET respectively. We optimize local models using gradient descent with the learning rate \\(\\eta = 0.1\\) decayed by 0.1 at the 100th/200th (for CIFAR) and 30th/60th (for ImageNET) rounds. We use 3-layer CNNs with ReLU activations as early exit classifiers. On SST-2 and AgNews datasets, we use the pre-trained BERT (4) provided by the open-source HuggingFace library (31). We optimize the local models for 100 rounds using gradient descent with the learning rate \\(\\eta = 3e - 5\\) and batch size 16. We use one-layer FC layers as early exit classifiers. In all experiments, the number of local training epochs \\(e = 5\\) and KL divergence temperature \\(\\tau = 3\\). For image/text classification experiments, loss weighting parameters \\(\\beta = 0.1\\) and 0.05, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We consider two baseline approaches: FedAVG (22) and Decoupled. In FedAVG, we train the Level-1 model with" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24537" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.2, + 0.089, + 0.773, + 0.263 + ], + "angle": 0, + "content": "
ModelAlgorithmCIFAR-10CIFAR-100
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
ResNet110FedAVG81.4681.4677.7277.7244.2644.2642.7542.75
Decoupled77.16-74.83-36.60-35.78-
HeteroFL82.9384.3577.6079.9144.6647.1242.9742.95
FedDF83.3584.4477.0878.5743.5046.9942.2944.50
ScaleFL (Ours)84.4985.5379.6180.8346.6349.9443.5244.95
MSDNet24FedAVG82.6982.6975.2875.2846.4446.4442.7542.75
HeteroFL81.5483.0275.7776.7444.6547.7742.3243.00
ScaleFL (Ours)84.6184.7777.8178.6949.1950.2545.2546.12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.16, + 0.273, + 0.809, + 0.287 + ], + "angle": 0, + "content": "Table 3. Local and global model accuracy values on CIFAR-10/100 datasets with ResNet110 and MSDNet24." + }, + { + "type": "table", + "bbox": [ + 0.127, + 0.31, + 0.422, + 0.415 + ], + "angle": 0, + "content": "
EfficientNetB4ImageNet
α = 100α = 1
localgloballocalglobal
FedAVG45.0045.0042.3342.33
HeteroFL43.6846.6141.7443.59
ScaleFL (Ours)46.6348.9544.8646.78
" + }, + { + "type": "table_caption", + "bbox": [ + 0.104, + 0.426, + 0.443, + 0.44 + ], + "angle": 0, + "content": "Table 4. Local and global accuracy values on ImageNET." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.651 + ], + "angle": 0, + "content": "splitting along width to use all available data. In Decoupled, we train separate models for each level using the corresponding data of the clients at that level. We also compare our results with recent studies: HeteroFL (5) and FedDF (19), where we use splitting along width dimension to form the local models at each level. For FedDF, we use CIFAR-10/100 and SST-2/AgNews train sets as distillation datasets for each other. Our implementation is on Python 3.7 with PyTorch 1.12 library. Our code is available at: https://github.com/git-disl/scale-fl. Each latency measurement is carried out 1000 times on a machine with an 8-core 2.4GHz CPU and 64GB RAM." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.323, + 0.68 + ], + "angle": 0, + "content": "4.4. Global Model Performance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In this setting, we evaluate the global model on the test dataset of each client and report the average of obtained accuracy values. In Table 3, we report the results for image classification on CIFAR-10 and CIFAR-100 with ResNet110 and MSDNet24 models to observe the effect of different architectures on the performance of ScaleFL. We provide comparisons with FedAVG and HeteroFL for all three image datasets. We make two observations from Table 3. First, ScaleFL achieves \\(0.45 - 2.95\\%\\) and \\(1.7 - 3.12\\%\\) higher global performance compared to the closest approach on ResNet110 and MSDNet24 respectively. Second, in all settings, FedAVG baseline performs poorly since the small level-1 model is used to utilize the data of every client. Decoupled baseline performs the worst since the models for" + }, + { + "type": "table", + "bbox": [ + 0.5, + 0.31, + 0.895, + 0.413 + ], + "angle": 0, + "content": "
BERTSST-2AG News
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
FedAVG79.9479.9470.0170.0185.1485.1481.1081.10
HeteroFL76.0288.8376.2182.8689.9291.5188.8590.85
FedDF77.6788.9577.4182.9589.7990.9388.9390.05
ScaleFL (Ours)83.7288.5879.6583.7990.5392.1389.7291.20
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.424, + 0.891, + 0.438 + ], + "angle": 0, + "content": "Table 5. Local and global accuracy values on SST-2 and AgNews." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.468, + 0.743, + 0.484 + ], + "angle": 0, + "content": "each level are trained independently." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.665 + ], + "angle": 0, + "content": "In Table 4, we provide the results of ImageNet experiments with EfficientNet-B4 with \\(224 \\times 224\\) input resolution. Since FedDF uses \\(32 \\times 32\\) resolution on ImageNet experiments, we could not report the results for FedDF on ImageNet. ScaleFL consistently achieves around \\(2.34 - 3.19\\%\\) higher global model accuracy under different data heterogeneity settings, compared to the closest competitor in each experiment. In addition, Table 5 reports the effectiveness of ScaleFL using NLP benchmarks with BERT as the backbone and ScaleFL again displays significant improvement especially in local model performance as investigated further in the next subsection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.807, + 0.696 + ], + "angle": 0, + "content": "4.5. Local Model Performance Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This section reports the local model performances at different levels. In Tables 3, 4 and 5, 'local' columns contain the average of accuracy values obtained after evaluating the respective local model at each client based on its level. In addition, we illustrate the local models (their scales in width and depth dimensions) and accuracies for MSD-Net24 on CIFAR100 in Figure 2. At each level, even though both submodels satisfy the target cost reduction, ScaleFL results in consistently better performance in terms of local model accuracy. This demonstrates the effectiveness of 2-D downscaling since it balances between preserving low-order basic features and extracting high-order complex features. We also analyze the performance with respect to the num" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24538" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.281, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Figure 2. Local model accuracies of Level 1-4 models with ScaleFL and HeteroFL for MSDNet24 on their corresponding test sample sets from CIFAR100. Percentages on the bottom left and top right corners indicate the scaling ratios along width/depth dimensions. Percentages above the models report the test accuracy obtained by that model." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.351, + 0.272, + 0.468 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.351, + 0.462, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.476, + 0.273, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.476, + 0.461, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.599, + 0.272, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.599, + 0.462, + 0.715 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.087, + 0.723, + 0.274, + 0.838 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.723, + 0.462, + 0.838 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.854, + 0.47, + 0.882 + ], + "angle": 0, + "content": "Figure 3. Local model performances with respect to #PARAMs and #FLOPs. Marker sizes represent complexity levels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.895, + 0.501 + ], + "angle": 0, + "content": "ber of parameters and inference time per sample on CPU (ms), as illustrated in Figure 3. In most settings, our approach achieves better test results at local models and the performance gap is more significant at lower levels, which demonstrates the efficiency of our two-dimensional splitting approach for model downscaling. For instance, the level-2 local model on AgNews with ScaleFL has 6x faster inference and 4x smaller size while having a lower \\(2.5\\%\\) accuracy decrease (vs \\(3 - 4\\%\\) with other methods) from the global model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.527, + 0.62, + 0.543 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.895, + 0.77 + ], + "angle": 0, + "content": "We have introduced ScaleFL, a novel resource-adaptive framework to address the system heterogeneity problem in federated learning. First, ScaleFL adaptively scales down the global model based on the computational constraints of participating clients. Our two-dimensional split methodology preserves the important balance of basic and complex features in local models. Second, we perform self-distillation among early exit and final predictions during local model training to improve the knowledge transfer among subnetworks and provide effective aggregation. We demonstrate the performance gains of ScaleFL compared to FedAVG as well as HeteroFL and FedDF, the two most representative federated learning approaches for system heterogeneity on benchmark image and text datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.796, + 0.669, + 0.813 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, and an IBM faculty award. The first author thanks for the summer 2022 internship at IBM Research with the group led by Dr. Donna Dillenberger." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24539" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Mohammad Mohammadi Amiri, Deniz Gündüz, Sanjeev R. Kulkarni, and H. Vincent Poor. Federated learning with quantized global model updates. *ArXiv*, abs/2006.10672, 2020. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.17, + 0.472, + 0.265 + ], + "angle": 0, + "content": "[2] Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. 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Curran Associates, Inc., 2020. 3" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.893, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "24541" + } + ] +] \ No newline at end of file diff --git a/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/cb97df44-ce50-4c4d-9f39-8532b06bcaf1_origin.pdf b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/cb97df44-ce50-4c4d-9f39-8532b06bcaf1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..51e1e84f94e1ef4a30772f203ebdb313a12c58e1 --- /dev/null +++ b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/cb97df44-ce50-4c4d-9f39-8532b06bcaf1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:798380b007d473bb5d138bdc1909d689b83d2fab4ffa852fd4f7883436f014d7 +size 2224154 diff --git a/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/full.md b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/full.md new file mode 100644 index 0000000000000000000000000000000000000000..308d378d0be7028f49c12039a6dd70407f3e92bb --- /dev/null +++ b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/full.md @@ -0,0 +1,277 @@ +# ScaleFL: Resource-Adaptive Federated Learning with Heterogeneous Clients + +Fatih Ilhan +Georgia Institute of Technology +Atlanta, GA +filhan@gatech.edu + +Gong Su IBM Research Yorktown Heights, NY gongsu@us.ibm.com + +Ling Liu +Georgia Institute of Technology +Atlanta, GA +ling.liu@cc.gatech.edu + +# Abstract + +Federated learning (FL) is an attractive distributed learning paradigm supporting real-time continuous learning and client privacy by default. In most FL approaches, all edge clients are assumed to have sufficient computation capabilities to participate in the learning of a deep neural network (DNN) model. However, in real-life applications, some clients may have severely limited resources and can only train a much smaller local model. This paper presents ScaleFL, a novel FL approach with two distinctive mechanisms to handle resource heterogeneity and provide an equitable FL framework for all clients. First, ScaleFL adaptively scales down the DNN model along width and depth dimensions by leveraging early exits to find the best-fit models for resource-aware local training on distributed clients. In this way, ScaleFL provides an efficient balance of preserving basic and complex features in local model splits with various sizes for joint training while enabling fast inference for model deployment. Second, ScaleFL utilizes self-distillation among exit predictions during training to improve aggregation through knowledge transfer among subnetworks. We conduct extensive experiments on benchmark CV (CIFAR10/100, ImageNet) and NLP datasets (SST-2, AgNews). We demonstrate that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global/local model performance and provides inference efficiency, with up to 2x latency and 4x model size reduction with negligible performance drop below 2%. + +# 1. Introduction + +Mobile and Internet-of-Things (IoT) devices are the primary computing sources for most daily life tasks and they are becoming increasingly essential for billions of users worldwide (12; 18). These devices generate an unprecedented amount of data, which can be used to optimize services and improve user experience. Since the data is huge and mostly private, communicating, storing and organizing it in a central server poses serious privacy risks and brings + +logistic concerns (12). Federated learning (FL) emerged as a machine learning paradigm for this scenario, where storing the data and training the model in a central server is not feasible. In FL, instead of centralizing the data, the model is distributed to clients for local training and the central server aggregates the local updates received from clients (22). + +Existing FL algorithms such as FedAVG (22), SCAFFOLD (13) and FedOpt (26) rely on the assumption that every participating client has similar resources and can locally execute the same model. However, in most real-life applications, the computation resources tend to differ significantly across clients (5; 19). This heterogeneity prevents clients with insufficient resources to participate in certain FL tasks that require large models. Although existing gradient compression (8) or model pruning techniques (7) may be applied to reduce the cost at the expense of small accuracy loss, these methods are not flexible enough to meet diverse constraint scenarios (computational, storage, network etc.) based on the heterogeneous resources of edge clients. We argue that FL should promote equitable AI practice by supporting a resource-adaptive learning framework that can scale to heterogeneous clients with limited capacity. + +To this end, we present ScaleFL, a scalable and equitable FL framework. By design, ScaleFL has two novel features. First, ScaleFL can adaptively scale down the global model along the width and depth dimensions based on the computational resources of participating clients. The downscaling procedure in ScaleFL is inspired by EfficientNet (28), which demonstrates the importance of balancing the size of different dimensions while scaling a neural network. Since a deeper model is more capable of extracting higher-order, complex features while a wider model has access to a larger variety of lower-order, basic features, performing model size reduction across one dimension causes unbalance in terms of the learning capabilities of the resulting model. This motivates the design of ScaleFL that uniformly scales down the global model on both dimensions to provide the balance of preserving access to both complex and basic features as efficiently as possible. To perform splitting along the depth dimension, ScaleFL injects early exit + +classifiers (29) to the global model at certain layers based on the model architecture and computational constraints at each complexity level. As a result, with ScaleFL, not only the global model achieves better performance compared to baseline FL approaches (22) and existing algorithms (5; 19) but also the local models at different complexity levels perform significantly better in case the clients are resource-constrained at inference time. + +The second novelty of ScaleFL is providing effective aggregation mechanisms for combining local model updates from heterogeneous participating clients, and augmenting self-distillation for effective model update aggregation. During the training of local models, we perform self-distillation among the exit predictions to improve the knowledge transfer among subnetworks. Knowledge distillation enables transferring knowledge from a large (teacher) network to a smaller (student) network by training the student network on teacher predictions as soft labels (10). Self-distillation is a form of knowledge distillation, where the same network is used as both teacher and the student to improve performance during training, especially for multi-exit models (16; 24; 25; 33). In particular, we optimize these models with the additional objective of minimizing the KL divergence among the early exit (student) and final (teacher) predictions, which provides effective aggregation through increasing knowledge flow among local models. This procedure is an integrated component of the local optimization procedure and does not introduce any additional computational overhead as in standard knowledge distillation. + +In summary, our main contributions are as follows: (1) We introduce a novel FL approach ScaleFL, which performs resource-adaptive 2-D model downscaling using early exits to handle system heterogeneity. Our method preserves the balance of basic and complex features at different complexity levels and enables efficient local models for resource-constrained clients. (2) We further enhance ScaleFL for effective integration of local training model updates by utilizing self-distillation among the exit predictions during local training to increase knowledge flow among subnetworks by minimizing the KL divergence among the early exit (student) and final (teacher) predictions. (3) We validate the advantages of ScaleFL in both model production quality for FL and model inference speedup for model deployment at edge clients. With extensive experiments on three vision benchmarks and two NLP benchmarks, we first demonstrate the significant improvements of ScaleFL in terms of global model performance on image/text classification tasks and various data heterogeneity settings, compared to recent approaches for FL with system heterogeneity. We then analyze the inference performance of local models and show that local models can provide up to 2x inference latency reduction and 4x model size reduction, with negligible performance drop under 2%. + +# 2. Related Work + +FedAVG is the baseline FL algorithm, where each round, clients download the updated global model, perform local training in parallel using gradient descent and send the updated local weights to the central server for aggregation by the average of the local weights from all participating clients in the given round (22). Three broad categories of efforts have been engaged to improve the FedAVG baseline. First, extensive studies have been dedicated to optimizing the communication efficiency of FL through gradient compression and quantization (1; 20). However, these studies only consider the scenario of homogeneous clients in which all participating clients are assumed to have similar computation capacity and can operate on the same model architecture with the same reduced model complexity. Second, there is significant research on robust federated learning to prevent client training data leakage due to model inversion attacks (30) or Trojan detection against model poisoning attacks (2). The third category is the most recent efforts on addressing client heterogeneity in terms of data distribution (6; 13) and computation resources (5; 19). Our work is most relevant to the last category, where clients have heterogeneous resources. We below identify the most representative approaches in this category. + +FedProx (17) allows each client to perform variable amounts of training iterations based on their computing power. However, this solution still assumes that all clients can operate on the same model. HeteroFL (5) proposes splitting the global model along width but, it keeps the full depth of the DNN architecture at each client and only adjusts the width split ratio for heterogeneous clients. This tends to result in very slim and deep subnetworks, which can lead to significant loss of basic features (28), resulting in a drastic drop in model quality. In addition, clients with limited resources will suffer from significant accuracy loss at model deployment time because they can only host and operate on those very slim and deep subnetworks. FedDF (19) proposes applying ensemble distillation to fuse models with different architectures. However, FedDF requires an additional dataset for the distillation operations and brings significant overhead between training rounds, whereas we apply self-distillation as an integrated component of the local training procedure without any additional overhead. Another recent study FLANC (23) shares a neural basis among all clients to efficiently construct models at various complexities. However, FLANC assumes that all clients can support at least the neural basis, and thus its adaptivity is bounded by the size of this pre-defined unified neural basis. In addition, the knowledge transfer among clients at different levels is only through the common neural basis. + +Inserting multiple exits during DNN training enables early exiting to support adaptive inference (15). BranchyNet (29) introduced the idea of multi-exit classi + +![](images/5eb1fb72f93faa80839fc59a3326f97b0ff16b803b01344796dbcfd9eab01359.jpg) +Figure 1. System architecture of ScaleFL with three levels. Given the constraint configuration, we compute the split ratios (Section 3.1.1) and based on computed width split ratios, we inject early exit classifiers to the given model. The global model is split along two dimensions (Section 3.1.2) and local models are trained using a combination of cross-entropy and KL-divergence losses as given in Eq. (5). Updates are aggregated back in the central server for the next round (Section 3.2). + +fiers and early termination of inference for easier test samples. MSDNet (11) proposed a multi-scale dense-connected CNN architecture to improve performance in earlier exits. To improve the training efficiency, knowledge distillation (10) is employed among exits (16; 25). Early exiting has also shown effectiveness for NLP tasks (21; 35). + +The design of ScaleFL is inspired by some of the above existing work with two original contributions. First, ScaleFL finds an optimal two-dimensional split plan for each client with limited resources and scales down a complex DNN model along both width and depth dimensions to provide the optimal balance of preserving basic and complex features in different model partitions. Second, ScaleFL further improves the aggregation and optimizes the performance of small subnetworks, produced by our two-dimensional downscaling, by applying self-distillation among exit predictions. + +# 3. Methodology + +Consider a federated learning system of $K$ clients, each has its private local training dataset of size $N_{k}$ , denoted by $\mathcal{D}_k = \{(\mathbf{X}_i,y_i)\}_{i = 1}^{N_k}$ , where $(\mathbf{X}_i,y_i)$ denotes the $i$ th training data sample and its ground truth label, and $k\in \{1,\ldots ,K\}$ . We are also given the configuration of per-client resource constraints of each client $k$ , such that the client can locally operate on a partition of the global model with the cost under the budget $B_{k}$ and a level of tolerance $(\epsilon_{k}\geq 0)$ for the budget constraint. A smaller value of $\epsilon_{k}$ indicates that the client has a tighter bound for the budget + +constraint $B_{k}$ and a larger value implies the client has more elasticity regarding its resource budget. + +In order to train a global model $M$ collaboratively with $K$ heterogeneous clients, ScaleFL first determines the model downscaling configuration for each of the $K$ clients based on its resource budget $B_{k}$ and budget tolerance $\epsilon_{k}$ (Section 3.1). Once the central server has the downscaling configurations for all $K$ clients, it starts the federated learning process. At each round, only a $p$ -fraction of the $K$ clients participate in the joint training (e.g., $p = 10\%$ , $K = 100$ ) and operate on downscaled models based on their resources. Upon completion of each round, the central server follows the ScaleFL aggregation protocol to integrate the local model updates from heterogeneous clients (Section 3.2). We further improve the aggregation procedure by utilizing self-distillation (Section 3.3). Figure 1 gives a sketch of the ScaleFL system architecture. + +# 3.1. Two-Dimensional Model Splitting + +# 3.1.1 Generating 2-D Split Configuration + +ScaleFL performs the split configuration as a part of the initialization process for a given federated learning (FL) task before starting the iterative FL rounds. The split configuration module makes two decisions: (1) Determining the number of model complexity levels $L$ and mapping of each client $k$ to the corresponding complexity level $l_{k} \in \{1, \dots, L\}$ , based on the resource constraints $(B_{k}, \epsilon_{k})$ , (2) given a DNN model $M$ , determining the most uniform bidimensional split ratio along depth $s_{d}^{(l)}$ and width $s_{w}^{(l)}$ di + +mensions for each complexity level $l$ . + +Task 1: In order to downscale the global model $M$ for resource-constrained clients, we first determine the total number of complexity levels, denoted by $L$ , a hyperparameter in ScaleFL and the target cost reduction ratios $r_l$ for each level $l$ . We set $L$ heuristically by performing clustering analysis over the set $\{B_k | 1 \leq k \leq K\}$ and assign each client with a model complexity level $l \in \{1, \dots, L\}$ assuming at least one client can operate on the full model $M$ . We consider $r_l = \frac{\min\{B_k | l_k = l\}}{\mathrm{cost}(M)}$ for $l < L$ , and $r_L = 1$ being the $100\%$ complexity representing the full-size model $M$ . Please note that this configuration can also be manually set by the user, e.g., it is possible to use the heuristic rule of halving the cost from the highest complexity level stepwise downward to the first level of complexity, so the local model $M_l$ at level $l$ will have the target cost reduction ratio of $r_l = 0.5r_{l+1}$ . Hence, we have $r_1, r_2$ and $r_3$ set to $12.5\%$ , $25\%$ and $50\%$ respectively for $L = 4$ . The smaller the level $l_k$ is, the less complex the down-scaled model will be for client $k$ . Assigned level $l_k$ for each client $k$ satisfies the following: $r_{l-1} \mathrm{cost}(M) \leq B_k < r_l \mathrm{cost}(M)$ for $l_k \in \{1, \dots, L-1\}$ , and $\mathrm{cost}(M) \leq B_k$ for $l_k = L$ . Here, $\mathrm{cost}(M)$ denotes the computational cost of the given model $M$ , which can be measured in terms of $\#PARAMs(M)$ (number of weight parameters) and $\#FLOPs(M)$ (number of floating point operations). + +Task 2: Now for each early exit complexity level $l$ , we need to determine the most balanced depth and width split ratio pair $(s_d^{(l)}, s_w^{(l)})$ , while satisfying that the cost of the submodel after the 2-D split will not exceed the resource constraints of those clients mapped to the exit complexity level $l$ . Here, the depth split ratio $s_d^{(l)}$ determines where to place the $l$ th early exit in the $N$ layers of the global model $M$ . The width split ratio $s_w^{(l)}$ indicates the fraction of the weight parameters to keep in the layers of the local models generated using the 2-D split ratio pair $(s_d^{(l)}, s_w^{(l)})$ for level $l$ . For any $l \in \{1, \dots, L\}$ , the following formulation will be followed to determine the most balanced split ratios $(s_d^{(l)}, s_w^{(l)})$ for those clients mapped to the exit complexity level $l$ : + +$$ +\begin{array}{l} (s _ {d} ^ {(l)}, s _ {w} ^ {(l)}) = \operatorname * {a r g m i n} _ {s _ {d} ^ {\prime} \in (0, 1 ], s _ {w} ^ {\prime} \in (0, 1 ]} | s _ {d} ^ {\prime} - s _ {w} ^ {\prime} | \quad \text {s u c h t h a t} \\ \left| \frac {\operatorname {c o s t} \left(\operatorname {s p l i t} \left(M ; s _ {d} ^ {\prime} , s _ {w} ^ {\prime}\right)\right)}{r _ {l} \operatorname {c o s t} (M)} - 1 \right| \leq \epsilon_ {l}. \tag {1} \\ \end{array} +$$ + +There may be multiple split ratio pairs that produce local models satisfying the target cost reduction ratio $r_l$ . We find the most uniform bi-directional split ratio pair $(s_d^{(l)}, s_w^{(l)})$ for each early exit level $l$ through grid search within the bound defined by the tolerance level $\epsilon_l$ . We set $\epsilon_l = \min_{j \in S^l} \epsilon_j$ , where $S^l$ denotes the set of clients mapped to the exit level $l$ based on their $B_k$ , and $\epsilon_l$ is the minimum of tolerance levels + +
ResNet110Split RatiosCost
Levelsdsw#PARAMS#FLOPSrl
41.001.001.73 M253.1 M1.000
30.880.750.86 M138.5 M0.500
20.770.700.46 M99.7 M0.250
10.660.700.21 M83.4 M0.125
+ +Table 1. Split ratios and resulting local model statistics (#PARAMS, #FLOPS) for ResNet110 at each level. + +of those clients in $S^l$ . A smaller value of $\epsilon_l$ enforces a tighter bound while satisfying the target cost reduction. A larger $\epsilon_l$ value provides more flexibility during the finding of the most balanced 2-D split configuration. For each level $l < L$ , we place an early exit classifier to the $\lfloor s_d^{(l)}N\rfloor$ th layer. Algorithm 1 lines 2-4 include these steps. Table 1 reports the computed depth and width split ratios for ResNet110 as the global model. The first column refers to the four complexity levels, the second and third columns reports the coputed 2-D split ratios $(s_d,s_w)$ . The next two columns show the cost for the full-size model at $l = 4$ and the reduced model at each complexity level $l\in \{3,2,1\}$ . Our depth and width-balanced split method results in uniformly shaped local models, as opposed to very slim and deep subnetworks due to splitting only along width in HeteroFL. + +# 3.1.2 Generating Local Models by Split Operation + +Once the split configurations are produced, ScaleFL executes the 2-D split operation to generate the local model for each client $k$ based on the split ratio pairs $(s_w,s_d)$ to meet the budget constraint $(B_{k},\epsilon_{k})$ specified by the client. Concretely, at each communication round $t$ , only $p$ -fraction of the $K$ clients, denoted by $\mathcal{S}_t$ , are sampled and the global model $M$ with weights $\theta_t$ is scaled down by executing the 2-D split operation, which generates the local models with architecture $M_{l_k}$ and weights $\theta_t^{(k)}$ for each client $k\in \mathcal{S}_t$ based on its complexity level $l_{k}$ . In this operation, we first perform model splitting along the depth dimension by removing the layers after the $\lfloor s_dN\rfloor$ -th layer where the $l$ th early exit is placed. + +Next, we perform splitting along the width dimension by selecting $s_w$ -partition of the per-layer model weights along the hidden channel. To facilitate the execution of model reduction by width split ratio, we define an index function that takes the weight matrix $\mathbf{W}$ and split ratio value $s_w$ as inputs. Here $\mathbf{W} \in \mathbb{R}^{D_{in} \times D_{out}}$ is a hidden weight matrix where $D_{in}$ and $D_{out}$ are the number of input and output hidden channels in the corresponding layer. The index function returns the Boolean index matrix $\mathbf{Z}$ of size $D_{in} \times D_{out}$ , which indicates which weights to keep after the operation. We define the split index as follows: $\mathbf{Z}[i,j] = 1$ if + +$i < \lfloor s_wD_{in}\rfloor$ and $j < \lfloor s_wD_{out}\rfloor$ , and zero otherwise. This indexing results in keeping the upper-left submatrix by default, i.e., $\mathbf{W}'\triangleq \mathbf{W}[\mathbf{Z}] = \mathbf{W}[:\lfloor s_wD_{in}\rfloor ,:\lfloor s_wD_{out}\rfloor ]$ . Our framework also allows using random selection of weight subsets (e.g. upper-right, lower-left, lower-right and middle etc.) for each client, so that different clients at the same complexity level can use different parts of the model weights and generate slightly different yet complimentary subnetworks. Algorithm 2 gives the pseudocode of this operation (see Appendix 6.1). + +# 3.2. Aggregation + +After the 2-D split operation, the ScaleFL aggregation module combines the updated local model weights received from heterogeneous clients at each round $t$ . Concretely, every participating client $k \in S_{t}$ may send a different subset of the global model to the FL server. For the default upper-left width split option to generate local models, the following aggregation procedure will be carried out to aggregate the overlapping weights received from the contributing clients at each round $t$ , i.e., for every $\mathbf{W} \in \theta$ , and $l \in \{1, \dots, L\}$ : + +$$ +\mathbf {W} \left[ \mathbf {Z} _ {l} - \mathbf {Z} _ {l - 1} \right] \leftarrow \frac {1}{\left| \mathcal {S} _ {t} ^ {l} \right|} \sum_ {k \in \mathcal {S} _ {t} ^ {l}} \overline {{\mathbf {W}}} _ {k} \left[ \mathbf {Z} _ {l} - \mathbf {Z} _ {l - 1} \right]. \tag {2} +$$ + +Here, $S_{t}^{l} = \{k|k\in S_{t},l_{k}\geq l\}$ is the set of participating clients at round $t$ with the mapped exit level at $l$ or higher. $\mathbf{Z}_l = \mathrm{index}(\mathbf{W},s_w^{(l)})$ for $l\in \{l^{\prime},\dots L\}$ and 0 for $l < l^{\prime}$ , where $l^{\prime}$ is the minimum level that $\mathbf{W}$ exists. For instance, the indexes defined by $\mathbf{Z}_4 - \mathbf{Z}_3$ will aggregate the updates from level 4 clients only. Similarly, the index defined by $\mathbf{Z}_3 - \mathbf{Z}_2$ will aggregate the updates from both level 3 and level 4 clients, and so forth. Lastly, $\overline{\mathbf{W}}_k$ is the zero-padded local weight $\mathbf{W}_k$ such that $\overline{\mathbf{W}}_k[\mathbf{Z}_l] = \mathbf{W}_k$ and $\overline{\mathbf{W}}_k[\mathbf{1} - \mathbf{Z}_l] = 0$ . Hence, if all clients have the same complexity level (i.e. $L = 1$ ), Eq. (2) simplifies into $\mathbf{W}\gets \frac{1}{|\mathcal{S}_t|}\sum_{k\in \mathcal{S}_t}\mathbf{W}_k$ . Algorithm 3 gives the pseudo-code for the aggregation algorithm (see Appendix 6.1). This aggregation module is executed at FL server and it determines the overlapping regions using index matrices, and scales the sum of the weight updates received from contributing clients. One caveat for this baseline approach is the fact that low complexity level clients may not contribute to learning other parts of the global model weights belonging to higher complexity levels. This motivates us to further optimize our naive baseline aggregation method with self-distillation. + +# 3.3. Optimization with Self-Distillation + +During the optimization of local models, we perform self-distillation, which is a form of knowledge distillation (10) where the technique is applied within the same network. Knowledge distillation enables a small (student) + +Algorithm 1: ScaleFL + +Inputs: Dataset $\mathcal{D}_k = \{(X_i,y_i)\}_{i = 1}^{N_k}$ for each client $k$ , number of complexity levels $L$ , complexity level of each client $\{l_k\}_{k = 1}^K$ , target cost reduction ratios for each level $\{r_l\}_{l = 1}^L$ , client availability rate $p$ , initial model architecture $M_0$ + +Parameters: number of communication rounds $T$ , number of local training epochs $E$ , batch size $b$ , learning rate $\eta$ + +Outputs: Trained global model $M$ and weights $\theta$ + +1: Initialize global model $M$ with architecture $M_0$ and weights $\theta_0$ +2: for level $l = 1, \dots, L - 1$ do +3: Compute split ratio pair $(s_d^{(l)}, s_w^{(l)})$ using Eq. (1) +4: Add early exit classifier to $M$ at $\lfloor s_d^{(l)}N\rfloor$ -th layer +5: end for +6: for round $t = 0, \dots, T - 1$ do +7: $S_{t}\gets$ random subset of $\max (1,pK)$ clients +8: for client $k \in S_t$ in parallel do +9: Split: $M_{l_k} \gets \text{split}(M; s_d^{(l_k)}, s_w^{(l_k)})$ +10: for epoch $e = 1, \ldots, E$ in client $k$ do +11: for batch $\mathcal{B} \subset \mathcal{D}_k$ do +12: $L = \frac{1}{b}\sum_{i\in \mathcal{B}}\mathcal{L}(M_{I_{k}}(\mathbf{X}_{i};\theta^{(k)}),y_{i})$ with Eq. (5) +13: $\theta^{(k)}\gets \theta^{(k)} - \eta \frac{\partial L}{\partial\theta^{(k)}}$ +14: end for +15: end for +16: end for +17: Aggregate: +18: $\theta \gets \text{aggregate}(\{\theta^{(k)}\}_{k \in S_t}, \{(s_d^{(l)}, s_w^{(l)})\}_{l=1}^L)$ +19: end for +20: return $M$ with $\theta$ + +network to learn from another larger (teacher) network by treating the predictions of the teacher as soft targets. In ScaleFL, local models with $l > 1$ have multiple exits and can output multiple predictions. Therefore, to enhance the knowledge transfer among the subnetworks of the global model, we use self-distillation by using the final exit as the teacher and earlier exits as students. + +For the local model $M_{j}$ at level $j$ , $f_{i}$ is the $i$ th core subnetwork with weights $\omega_{i,j}^{(f)}$ . Likewise, $g_{i}$ is the $i$ th exit classifier subnetwork with weights $\omega_{i,j}^{(g)}$ . $\hat{\mathbf{y}}_{i,j}$ is the output at the $i$ th exit of $M_{j}$ . We formulate the forward pass of local models as follows: + +$$ +\mathbf {H} _ {i, j} = f _ {i} \left(\mathbf {H} _ {i - 1, j}; \omega_ {i, j} ^ {(f)}\right), \tag {3} +$$ + +$$ +\hat {\boldsymbol {y}} _ {i, j} = g _ {i} \left(\mathbf {H} _ {i, j}; \omega_ {i, j} ^ {(g)}\right), \tag {4} +$$ + +for $1 \leq i \leq j \leq L$ where $j$ is the level of the local model and $\mathbf{H}_{0,j} = \mathbf{X}$ is the input. In this study, we present our work on classification tasks so after obtaining the prediction logits at each exit for $M_l$ at level $l$ , the loss with self + +distillation is calculated as follows: + +$$ +\mathcal {L} = \frac {1}{l (l + 1)} \sum_ {i = 1} ^ {l} i \left(\beta \mathcal {L} _ {K L} \left(\hat {\boldsymbol {y}} _ {i, l}, \hat {\boldsymbol {y}} _ {l, l}\right) + \mathcal {L} _ {C E} \left(\hat {\boldsymbol {y}} _ {i, l}, y\right)\right) \tag {5} +$$ + +where $\mathcal{L}_{KL}(\hat{\pmb{y}}_s,\hat{\pmb{y}}_t) = \mathrm{sum}(\sigma (\hat{\pmb{y}}_t / \tau)\log \frac{\sigma(\hat{\pmb{y}}_t / \tau)}{\sigma(\hat{\pmb{y}}_s / \tau)})\tau^2$ is KL divergence with temperature $\tau >0$ , $\mathcal{L}_{CE}(\hat{\pmb{y}},y) = -\log \sigma (\hat{\pmb{y}})[y]$ is cross-entropy loss for target class $y$ , $\sigma$ is softmax function and $\beta \in [0,1)$ controls the self-distillation effect. $\tau$ and $\beta$ are optimization hyperparameters of the system. Here, $\tau = 1$ corresponds to using the standard softmax function, and as $\tau$ grows, the output of the softmax becomes softer and more information on the score distribution of the teacher is provided to the student. + +# 4. Experiments + +In this section, we report the results of extensive experiments on five benchmarks: three image classification benchmarks (CIFAR-10/100, ImageNet) and two NLP benchmarks (SST-2, AgNews). We show that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global model performance under the same number of rounds and provides inference speedup with up to 2x latency reduction and 4x model size reduction while keeping the performance drop below $2\%$ . + +# 4.1. Datasets and Preprocessing + +In image classification experiments, we consider common benchmark datasets on various scales: CIFAR-10, CIFAR-100 (14) and ImageNET (ILSVRC2012) (3). We hold out randomly selected 5000 images from CIFAR-10/100 train set and 25000 images from ImageNET train set for validation. We follow the data augmentation techniques applied in (9) with zero padding, center cropping and random horizontal flip with 0.5 probability. For normalization, we use fixed values, 0.5 as mean and 0.25 as standard deviation and disable statistics tracking for batch normalization operations due to the federated setting. In text classification experiments, we consider SST-2 (27) dataset from GLUE benchmark and AGNews (34) dataset. We hold out 872 sentences from SST-2 validation set and randomly selected 5000 sentences from AgNews train set for validation. For tokenization, we use the pre-trained tokenizer for BERT-base-uncased model provided by the open-source HuggingFace library (31). The details of the datasets are in Table 2. + +# 4.2. Heterogeneous System Topology and Non-IID Client Data Distribution + +In CIFAR-10/100 experiments, we set the number of clients $K = 100$ and the ratio of available clients in each training round $p = 0.1$ . For ImageNET, SST-2 and AGNews experiments, $K = 50$ and $p = 0.2$ . To simulate the + +
DatasetTrain SizeTest Size# ClassesResolution
CIFAR-1050K10K1032x32
CIFAR-10050K10K10032x32
ImageNet1.2M150K1000224x224
SST-267K18212-
AgNews120K7.6K4-
+ +Table 2. Statistics of the datasets used in image and text classification experiments. + +system heterogeneity, we consider four complexity levels with the target cost reduction ratios $r_1 = 0.125$ , $r_2 = 0.25$ , $r_3 = 0.5$ , $r_4 = 1$ and set the tolerance level $\epsilon_k = 0.1$ . We set the number of clients assigned to each level to be equal. Different number of complexity levels or client distributions are also applicable and compatible with ScaleFL. We use Dirichlet distribution with concentration parameter $\alpha$ to create non-IID data splits for the local datasets in the federated setting as in (19; 32). We report the results in two levels of non-IID distribution with $\alpha = 1$ (more skewed) and $\alpha = 100$ (less skewed). The resulting class distribution of data at each client is illustrated in Figure 4 (see Appendix). + +# 4.3. Model and Implementation Details + +On CIFAR-10 and CIFAR-100 datasets, we perform experiments with two different models: ResNet (9) and MSDNet (11). ResNet is a common baseline for benchmarking and MSDNet is a multi-exit CNN architecture with dense connections. We use the default ResNet settings for 110-layer architecture from (9). For MSDNet, we use the recommended configuration with 24 layers, 3 scales and 16 initial hidden dimensions with a growth rate of 6 (11). On ImageNET, we consider EfficientNet (28) with B4 architecture (medium-size) and $224 \times 224$ input resolution (28). We set the number of FL rounds to 400 and 90, and batch size to 16 and 64 for CIFAR/ImageNET respectively. We optimize local models using gradient descent with the learning rate $\eta = 0.1$ decayed by 0.1 at the 100th/200th (for CIFAR) and 30th/60th (for ImageNET) rounds. We use 3-layer CNNs with ReLU activations as early exit classifiers. On SST-2 and AgNews datasets, we use the pre-trained BERT (4) provided by the open-source HuggingFace library (31). We optimize the local models for 100 rounds using gradient descent with the learning rate $\eta = 3e - 5$ and batch size 16. We use one-layer FC layers as early exit classifiers. In all experiments, the number of local training epochs $e = 5$ and KL divergence temperature $\tau = 3$ . For image/text classification experiments, loss weighting parameters $\beta = 0.1$ and 0.05, respectively. + +We consider two baseline approaches: FedAVG (22) and Decoupled. In FedAVG, we train the Level-1 model with + +
ModelAlgorithmCIFAR-10CIFAR-100
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
ResNet110FedAVG81.4681.4677.7277.7244.2644.2642.7542.75
Decoupled77.16-74.83-36.60-35.78-
HeteroFL82.9384.3577.6079.9144.6647.1242.9742.95
FedDF83.3584.4477.0878.5743.5046.9942.2944.50
ScaleFL (Ours)84.4985.5379.6180.8346.6349.9443.5244.95
MSDNet24FedAVG82.6982.6975.2875.2846.4446.4442.7542.75
HeteroFL81.5483.0275.7776.7444.6547.7742.3243.00
ScaleFL (Ours)84.6184.7777.8178.6949.1950.2545.2546.12
+ +Table 3. Local and global model accuracy values on CIFAR-10/100 datasets with ResNet110 and MSDNet24. + +
EfficientNetB4ImageNet
α = 100α = 1
localgloballocalglobal
FedAVG45.0045.0042.3342.33
HeteroFL43.6846.6141.7443.59
ScaleFL (Ours)46.6348.9544.8646.78
+ +splitting along width to use all available data. In Decoupled, we train separate models for each level using the corresponding data of the clients at that level. We also compare our results with recent studies: HeteroFL (5) and FedDF (19), where we use splitting along width dimension to form the local models at each level. For FedDF, we use CIFAR-10/100 and SST-2/AgNews train sets as distillation datasets for each other. Our implementation is on Python 3.7 with PyTorch 1.12 library. Our code is available at: https://github.com/git-disl/scale-fl. Each latency measurement is carried out 1000 times on a machine with an 8-core 2.4GHz CPU and 64GB RAM. + +# 4.4. Global Model Performance + +In this setting, we evaluate the global model on the test dataset of each client and report the average of obtained accuracy values. In Table 3, we report the results for image classification on CIFAR-10 and CIFAR-100 with ResNet110 and MSDNet24 models to observe the effect of different architectures on the performance of ScaleFL. We provide comparisons with FedAVG and HeteroFL for all three image datasets. We make two observations from Table 3. First, ScaleFL achieves $0.45 - 2.95\%$ and $1.7 - 3.12\%$ higher global performance compared to the closest approach on ResNet110 and MSDNet24 respectively. Second, in all settings, FedAVG baseline performs poorly since the small level-1 model is used to utilize the data of every client. Decoupled baseline performs the worst since the models for + +Table 4. Local and global accuracy values on ImageNET. + +
BERTSST-2AG News
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
FedAVG79.9479.9470.0170.0185.1485.1481.1081.10
HeteroFL76.0288.8376.2182.8689.9291.5188.8590.85
FedDF77.6788.9577.4182.9589.7990.9388.9390.05
ScaleFL (Ours)83.7288.5879.6583.7990.5392.1389.7291.20
+ +Table 5. Local and global accuracy values on SST-2 and AgNews. + +each level are trained independently. + +In Table 4, we provide the results of ImageNet experiments with EfficientNet-B4 with $224 \times 224$ input resolution. Since FedDF uses $32 \times 32$ resolution on ImageNet experiments, we could not report the results for FedDF on ImageNet. ScaleFL consistently achieves around $2.34 - 3.19\%$ higher global model accuracy under different data heterogeneity settings, compared to the closest competitor in each experiment. In addition, Table 5 reports the effectiveness of ScaleFL using NLP benchmarks with BERT as the backbone and ScaleFL again displays significant improvement especially in local model performance as investigated further in the next subsection. + +# 4.5. Local Model Performance Analysis + +This section reports the local model performances at different levels. In Tables 3, 4 and 5, 'local' columns contain the average of accuracy values obtained after evaluating the respective local model at each client based on its level. In addition, we illustrate the local models (their scales in width and depth dimensions) and accuracies for MSD-Net24 on CIFAR100 in Figure 2. At each level, even though both submodels satisfy the target cost reduction, ScaleFL results in consistently better performance in terms of local model accuracy. This demonstrates the effectiveness of 2-D downscaling since it balances between preserving low-order basic features and extracting high-order complex features. We also analyze the performance with respect to the num + +![](images/b6b9d0ea069deb340f5a4311d03305542551ca3d2af042d3f17d940986a8cbc8.jpg) +Figure 2. Local model accuracies of Level 1-4 models with ScaleFL and HeteroFL for MSDNet24 on their corresponding test sample sets from CIFAR100. Percentages on the bottom left and top right corners indicate the scaling ratios along width/depth dimensions. Percentages above the models report the test accuracy obtained by that model. + +![](images/fe79f6dbdb258e4312c2d120020aaafffbecadd2ca24547773a0209380b899ca.jpg) + +![](images/11f501cc28d41838bde48533cd47a6b4e86c4390e58c5bd26c07450cc77d1e6d.jpg) + +![](images/dc1e8d79567effcd9897c831e98370cb80b6b32d7f703e24f08d0741a5a54ed0.jpg) + +![](images/c1a1162b13829c8e5a853363345f555773c0b71320532224c0022f70d00d930b.jpg) + +![](images/464b0be7dee2a95f2385ab0167d34b015faf5fe73d47b1f745516d009945d75f.jpg) + +![](images/385f686ce8363d59edf96ab1c6b2056277ccf6c07d04342799a69f9c166be34c.jpg) + +![](images/0319dfce253197212f4e86779a3dc3664932ef6121c610fe84e4da3ef299dfca.jpg) +Figure 3. Local model performances with respect to #PARAMs and #FLOPs. Marker sizes represent complexity levels. + +![](images/d1732df775fbd4fcb11c9cbb1ce597871c42dd48a98c9252f9b1fb150bdc1b0d.jpg) + +ber of parameters and inference time per sample on CPU (ms), as illustrated in Figure 3. In most settings, our approach achieves better test results at local models and the performance gap is more significant at lower levels, which demonstrates the efficiency of our two-dimensional splitting approach for model downscaling. For instance, the level-2 local model on AgNews with ScaleFL has 6x faster inference and 4x smaller size while having a lower $2.5\%$ accuracy decrease (vs $3 - 4\%$ with other methods) from the global model. + +# 5. Conclusion + +We have introduced ScaleFL, a novel resource-adaptive framework to address the system heterogeneity problem in federated learning. First, ScaleFL adaptively scales down the global model based on the computational constraints of participating clients. Our two-dimensional split methodology preserves the important balance of basic and complex features in local models. Second, we perform self-distillation among early exit and final predictions during local model training to improve the knowledge transfer among subnetworks and provide effective aggregation. We demonstrate the performance gains of ScaleFL compared to FedAVG as well as HeteroFL and FedDF, the two most representative federated learning approaches for system heterogeneity on benchmark image and text datasets. + +# Acknowledgements + +This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, and an IBM faculty award. The first author thanks for the summer 2022 internship at IBM Research with the group led by Dr. Donna Dillenberger. + +# References + +[1] Mohammad Mohammadi Amiri, Deniz Gündüz, Sanjeev R. Kulkarni, and H. Vincent Poor. 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Curran Associates, Inc., 2020. 3 \ No newline at end of file diff --git a/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/images.zip b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c91559e4bdf3349576903c1b1052f789af8dec2a --- /dev/null +++ b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9923c5b807118bb5becdd6c7fb00b7ca6bb782143bc6fd3f2e39f64475c3ba5b +size 458515 diff --git a/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/layout.json b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..bdebb18f6bc2200f5e70f9dfa4930205cfde77ea --- /dev/null +++ b/2023/ScaleFL_ Resource-Adaptive Federated Learning With Heterogeneous Clients/layout.json @@ -0,0 +1,10469 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 59, + 103, + 534, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 103, + 534, + 121 + ], + "spans": [ + { + "bbox": [ + 59, + 103, + 534, + 121 + ], + "type": "text", + "content": "ScaleFL: Resource-Adaptive Federated Learning with Heterogeneous Clients" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 61, + 144, + 217, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 144, + 217, + 198 + ], + "spans": [ + { + "bbox": [ + 61, + 144, + 217, + 198 + ], + "type": "text", + "content": "Fatih Ilhan \nGeorgia Institute of Technology \nAtlanta, GA \nfilhan@gatech.edu" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 240, + 144, + 353, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 240, + 144, + 353, + 198 + ], + "spans": [ + { + "bbox": [ + 240, + 144, + 353, + 198 + ], + "type": "text", + "content": "Gong Su IBM Research Yorktown Heights, NY gongsu@us.ibm.com" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 375, + 144, + 531, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 144, + 531, + 198 + ], + "spans": [ + { + "bbox": [ + 375, + 144, + 531, + 198 + ], + "type": "text", + "content": "Ling Liu \nGeorgia Institute of Technology \nAtlanta, GA \nling.liu@cc.gatech.edu" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 251, + 289, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 289, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 289, + 576 + ], + "type": "text", + "content": "Federated learning (FL) is an attractive distributed learning paradigm supporting real-time continuous learning and client privacy by default. In most FL approaches, all edge clients are assumed to have sufficient computation capabilities to participate in the learning of a deep neural network (DNN) model. However, in real-life applications, some clients may have severely limited resources and can only train a much smaller local model. This paper presents ScaleFL, a novel FL approach with two distinctive mechanisms to handle resource heterogeneity and provide an equitable FL framework for all clients. First, ScaleFL adaptively scales down the DNN model along width and depth dimensions by leveraging early exits to find the best-fit models for resource-aware local training on distributed clients. In this way, ScaleFL provides an efficient balance of preserving basic and complex features in local model splits with various sizes for joint training while enabling fast inference for model deployment. Second, ScaleFL utilizes self-distillation among exit predictions during training to improve aggregation through knowledge transfer among subnetworks. We conduct extensive experiments on benchmark CV (CIFAR10/100, ImageNet) and NLP datasets (SST-2, AgNews). We demonstrate that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global/local model performance and provides inference efficiency, with up to 2x latency and 4x model size reduction with negligible performance drop below 2%." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 715 + ], + "type": "text", + "content": "Mobile and Internet-of-Things (IoT) devices are the primary computing sources for most daily life tasks and they are becoming increasingly essential for billions of users worldwide (12; 18). These devices generate an unprecedented amount of data, which can be used to optimize services and improve user experience. Since the data is huge and mostly private, communicating, storing and organizing it in a central server poses serious privacy risks and brings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 228, + 546, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 546, + 300 + ], + "type": "text", + "content": "logistic concerns (12). Federated learning (FL) emerged as a machine learning paradigm for this scenario, where storing the data and training the model in a central server is not feasible. In FL, instead of centralizing the data, the model is distributed to clients for local training and the central server aggregates the local updates received from clients (22)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 303, + 546, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 546, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 546, + 495 + ], + "type": "text", + "content": "Existing FL algorithms such as FedAVG (22), SCAFFOLD (13) and FedOpt (26) rely on the assumption that every participating client has similar resources and can locally execute the same model. However, in most real-life applications, the computation resources tend to differ significantly across clients (5; 19). This heterogeneity prevents clients with insufficient resources to participate in certain FL tasks that require large models. Although existing gradient compression (8) or model pruning techniques (7) may be applied to reduce the cost at the expense of small accuracy loss, these methods are not flexible enough to meet diverse constraint scenarios (computational, storage, network etc.) based on the heterogeneous resources of edge clients. We argue that FL should promote equitable AI practice by supporting a resource-adaptive learning framework that can scale to heterogeneous clients with limited capacity." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 714 + ], + "type": "text", + "content": "To this end, we present ScaleFL, a scalable and equitable FL framework. By design, ScaleFL has two novel features. First, ScaleFL can adaptively scale down the global model along the width and depth dimensions based on the computational resources of participating clients. The downscaling procedure in ScaleFL is inspired by EfficientNet (28), which demonstrates the importance of balancing the size of different dimensions while scaling a neural network. Since a deeper model is more capable of extracting higher-order, complex features while a wider model has access to a larger variety of lower-order, basic features, performing model size reduction across one dimension causes unbalance in terms of the learning capabilities of the resulting model. This motivates the design of ScaleFL that uniformly scales down the global model on both dimensions to provide the balance of preserving access to both complex and basic features as efficiently as possible. To perform splitting along the depth dimension, ScaleFL injects early exit" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24532" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 167 + ], + "type": "text", + "content": "classifiers (29) to the global model at certain layers based on the model architecture and computational constraints at each complexity level. As a result, with ScaleFL, not only the global model achieves better performance compared to baseline FL approaches (22) and existing algorithms (5; 19) but also the local models at different complexity levels perform significantly better in case the clients are resource-constrained at inference time." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 288, + 422 + ], + "type": "text", + "content": "The second novelty of ScaleFL is providing effective aggregation mechanisms for combining local model updates from heterogeneous participating clients, and augmenting self-distillation for effective model update aggregation. During the training of local models, we perform self-distillation among the exit predictions to improve the knowledge transfer among subnetworks. Knowledge distillation enables transferring knowledge from a large (teacher) network to a smaller (student) network by training the student network on teacher predictions as soft labels (10). Self-distillation is a form of knowledge distillation, where the same network is used as both teacher and the student to improve performance during training, especially for multi-exit models (16; 24; 25; 33). In particular, we optimize these models with the additional objective of minimizing the KL divergence among the early exit (student) and final (teacher) predictions, which provides effective aggregation through increasing knowledge flow among local models. This procedure is an integrated component of the local optimization procedure and does not introduce any additional computational overhead as in standard knowledge distillation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 715 + ], + "type": "text", + "content": "In summary, our main contributions are as follows: (1) We introduce a novel FL approach ScaleFL, which performs resource-adaptive 2-D model downscaling using early exits to handle system heterogeneity. Our method preserves the balance of basic and complex features at different complexity levels and enables efficient local models for resource-constrained clients. (2) We further enhance ScaleFL for effective integration of local training model updates by utilizing self-distillation among the exit predictions during local training to increase knowledge flow among subnetworks by minimizing the KL divergence among the early exit (student) and final (teacher) predictions. (3) We validate the advantages of ScaleFL in both model production quality for FL and model inference speedup for model deployment at edge clients. With extensive experiments on three vision benchmarks and two NLP benchmarks, we first demonstrate the significant improvements of ScaleFL in terms of global model performance on image/text classification tasks and various data heterogeneity settings, compared to recent approaches for FL with system heterogeneity. We then analyze the inference performance of local models and show that local models can provide up to 2x inference latency reduction and 4x model size reduction, with negligible performance drop under 2%." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 91, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 366 + ], + "type": "text", + "content": "FedAVG is the baseline FL algorithm, where each round, clients download the updated global model, perform local training in parallel using gradient descent and send the updated local weights to the central server for aggregation by the average of the local weights from all participating clients in the given round (22). Three broad categories of efforts have been engaged to improve the FedAVG baseline. First, extensive studies have been dedicated to optimizing the communication efficiency of FL through gradient compression and quantization (1; 20). However, these studies only consider the scenario of homogeneous clients in which all participating clients are assumed to have similar computation capacity and can operate on the same model architecture with the same reduced model complexity. Second, there is significant research on robust federated learning to prevent client training data leakage due to model inversion attacks (30) or Trojan detection against model poisoning attacks (2). The third category is the most recent efforts on addressing client heterogeneity in terms of data distribution (6; 13) and computation resources (5; 19). Our work is most relevant to the last category, where clients have heterogeneous resources. We below identify the most representative approaches in this category." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 367, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 676 + ], + "type": "text", + "content": "FedProx (17) allows each client to perform variable amounts of training iterations based on their computing power. However, this solution still assumes that all clients can operate on the same model. HeteroFL (5) proposes splitting the global model along width but, it keeps the full depth of the DNN architecture at each client and only adjusts the width split ratio for heterogeneous clients. This tends to result in very slim and deep subnetworks, which can lead to significant loss of basic features (28), resulting in a drastic drop in model quality. In addition, clients with limited resources will suffer from significant accuracy loss at model deployment time because they can only host and operate on those very slim and deep subnetworks. FedDF (19) proposes applying ensemble distillation to fuse models with different architectures. However, FedDF requires an additional dataset for the distillation operations and brings significant overhead between training rounds, whereas we apply self-distillation as an integrated component of the local training procedure without any additional overhead. Another recent study FLANC (23) shares a neural basis among all clients to efficiently construct models at various complexities. However, FLANC assumes that all clients can support at least the neural basis, and thus its adaptivity is bounded by the size of this pre-defined unified neural basis. In addition, the knowledge transfer among clients at different levels is only through the common neural basis." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Inserting multiple exits during DNN training enables early exiting to support adaptive inference (15). BranchyNet (29) introduced the idea of multi-exit classi" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24533" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 95, + 71, + 509, + 277 + ], + "blocks": [ + { + "bbox": [ + 95, + 71, + 509, + 277 + ], + "lines": [ + { + "bbox": [ + 95, + 71, + 509, + 277 + ], + "spans": [ + { + "bbox": [ + 95, + 71, + 509, + 277 + ], + "type": "image", + "image_path": "5eb1fb72f93faa80839fc59a3326f97b0ff16b803b01344796dbcfd9eab01359.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "text", + "content": "Figure 1. System architecture of ScaleFL with three levels. Given the constraint configuration, we compute the split ratios (Section 3.1.1) and based on computed width split ratios, we inject early exit classifiers to the given model. The global model is split along two dimensions (Section 3.1.2) and local models are trained using a combination of cross-entropy and KL-divergence losses as given in Eq. (5). Updates are aggregated back in the central server for the next round (Section 3.2)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 353, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 425 + ], + "type": "text", + "content": "fiers and early termination of inference for easier test samples. MSDNet (11) proposed a multi-scale dense-connected CNN architecture to improve performance in earlier exits. To improve the training efficiency, knowledge distillation (10) is employed among exits (16; 25). Early exiting has also shown effectiveness for NLP tasks (21; 35)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 288, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 559 + ], + "type": "text", + "content": "The design of ScaleFL is inspired by some of the above existing work with two original contributions. First, ScaleFL finds an optimal two-dimensional split plan for each client with limited resources and scales down a complex DNN model along both width and depth dimensions to provide the optimal balance of preserving basic and complex features in different model partitions. Second, ScaleFL further improves the aggregation and optimizes the performance of small subnetworks, produced by our two-dimensional downscaling, by applying self-distillation among exit predictions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 572, + 129, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 129, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 129, + 586 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Consider a federated learning system of " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " clients, each has its private local training dataset of size " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "N_{k}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ", denoted by " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k = \\{(\\mathbf{X}_i,y_i)\\}_{i = 1}^{N_k}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\mathbf{X}_i,y_i)" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "th training data sample and its ground truth label, and " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "k\\in \\{1,\\ldots ,K\\}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ". We are also given the configuration of per-client resource constraints of each client " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ", such that the client can locally operate on a partition of the global model with the cost under the budget " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "B_{k}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " and a level of tolerance " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "(\\epsilon_{k}\\geq 0)" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " for the budget constraint. A smaller value of " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon_{k}" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " indicates that the client has a tighter bound for the budget" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 353, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 545, + 376 + ], + "type": "text", + "content": "constraint " + }, + { + "bbox": [ + 304, + 353, + 545, + 376 + ], + "type": "inline_equation", + "content": "B_{k}" + }, + { + "bbox": [ + 304, + 353, + 545, + 376 + ], + "type": "text", + "content": " and a larger value implies the client has more elasticity regarding its resource budget." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": "In order to train a global model " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " collaboratively with " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " heterogeneous clients, ScaleFL first determines the model downscaling configuration for each of the " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " clients based on its resource budget " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "B_{k}" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " and budget tolerance " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "\\epsilon_{k}" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " (Section 3.1). Once the central server has the downscaling configurations for all " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " clients, it starts the federated learning process. At each round, only a " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": "-fraction of the " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": " clients participate in the joint training (e.g., " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "p = 10\\%" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "inline_equation", + "content": "K = 100" + }, + { + "bbox": [ + 304, + 377, + 546, + 556 + ], + "type": "text", + "content": ") and operate on downscaled models based on their resources. Upon completion of each round, the central server follows the ScaleFL aggregation protocol to integrate the local model updates from heterogeneous clients (Section 3.2). We further improve the aggregation procedure by utilizing self-distillation (Section 3.3). Figure 1 gives a sketch of the ScaleFL system architecture." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 565, + 487, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 565, + 487, + 578 + ], + "spans": [ + { + "bbox": [ + 306, + 565, + 487, + 578 + ], + "type": "text", + "content": "3.1. Two-Dimensional Model Splitting" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 584, + 490, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 584, + 490, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 584, + 490, + 597 + ], + "type": "text", + "content": "3.1.1 Generating 2-D Split Configuration" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": "ScaleFL performs the split configuration as a part of the initialization process for a given federated learning (FL) task before starting the iterative FL rounds. The split configuration module makes two decisions: (1) Determining the number of model complexity levels " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": " and mapping of each client " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": " to the corresponding complexity level " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "l_{k} \\in \\{1, \\dots, L\\}" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": ", based on the resource constraints " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "(B_{k}, \\epsilon_{k})" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": ", (2) given a DNN model " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": ", determining the most uniform bidimensional split ratio along depth " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "s_{d}^{(l)}" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": " and width " + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "inline_equation", + "content": "s_{w}^{(l)}" + }, + { + "bbox": [ + 304, + 604, + 545, + 715 + ], + "type": "text", + "content": " di" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24534" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "text", + "content": "mensions for each complexity level " + }, + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 47, + 72, + 200, + 83 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": "Task 1: In order to downscale the global model " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " for resource-constrained clients, we first determine the total number of complexity levels, denoted by " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ", a hyperparameter in ScaleFL and the target cost reduction ratios " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_l" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " for each level " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " heuristically by performing clustering analysis over the set " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "\\{B_k | 1 \\leq k \\leq K\\}" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " and assign each client with a model complexity level " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l \\in \\{1, \\dots, L\\}" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " assuming at least one client can operate on the full model " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". We consider " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_l = \\frac{\\min\\{B_k | l_k = l\\}}{\\mathrm{cost}(M)}" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l < L" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_L = 1" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " being the " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " complexity representing the full-size model " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". Please note that this configuration can also be manually set by the user, e.g., it is possible to use the heuristic rule of halving the cost from the highest complexity level stepwise downward to the first level of complexity, so the local model " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "M_l" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " at level " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " will have the target cost reduction ratio of " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_l = 0.5r_{l+1}" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". Hence, we have " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_1, r_2" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_3" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " set to " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "12.5\\%" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " respectively for " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "L = 4" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". The smaller the level " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l_k" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " is, the less complex the down-scaled model will be for client " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". Assigned level " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l_k" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " for each client " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " satisfies the following: " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "r_{l-1} \\mathrm{cost}(M) \\leq B_k < r_l \\mathrm{cost}(M)" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l_k \\in \\{1, \\dots, L-1\\}" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "\\mathrm{cost}(M) \\leq B_k" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "l_k = L" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "\\mathrm{cost}(M)" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " denotes the computational cost of the given model " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": ", which can be measured in terms of " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "\\#PARAMs(M)" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " (number of weight parameters) and " + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "inline_equation", + "content": "\\#FLOPs(M)" + }, + { + "bbox": [ + 46, + 84, + 288, + 385 + ], + "type": "text", + "content": " (number of floating point operations)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": "Task 2: Now for each early exit complexity level " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ", we need to determine the most balanced depth and width split ratio pair " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "(s_d^{(l)}, s_w^{(l)})" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ", while satisfying that the cost of the submodel after the 2-D split will not exceed the resource constraints of those clients mapped to the exit complexity level " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ". Here, the depth split ratio " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "s_d^{(l)}" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": " determines where to place the " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": "th early exit in the " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": " layers of the global model " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ". The width split ratio " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "s_w^{(l)}" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": " indicates the fraction of the weight parameters to keep in the layers of the local models generated using the 2-D split ratio pair " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "(s_d^{(l)}, s_w^{(l)})" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": " for level " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ". For any " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "l \\in \\{1, \\dots, L\\}" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ", the following formulation will be followed to determine the most balanced split ratios " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "(s_d^{(l)}, s_w^{(l)})" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": " for those clients mapped to the exit complexity level " + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 385, + 287, + 559 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 567, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 567, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 64, + 567, + 287, + 620 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} (s _ {d} ^ {(l)}, s _ {w} ^ {(l)}) = \\operatorname * {a r g m i n} _ {s _ {d} ^ {\\prime} \\in (0, 1 ], s _ {w} ^ {\\prime} \\in (0, 1 ]} | s _ {d} ^ {\\prime} - s _ {w} ^ {\\prime} | \\quad \\text {s u c h t h a t} \\\\ \\left| \\frac {\\operatorname {c o s t} \\left(\\operatorname {s p l i t} \\left(M ; s _ {d} ^ {\\prime} , s _ {w} ^ {\\prime}\\right)\\right)}{r _ {l} \\operatorname {c o s t} (M)} - 1 \\right| \\leq \\epsilon_ {l}. \\tag {1} \\\\ \\end{array}", + "image_path": "61b1b2cae58aad0b8751c2e1acee4efdc61aa4e65b08fbfd1586ea30fd6e3243.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": "There may be multiple split ratio pairs that produce local models satisfying the target cost reduction ratio " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "r_l" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ". We find the most uniform bi-directional split ratio pair " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "(s_d^{(l)}, s_w^{(l)})" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " for each early exit level " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " through grid search within the bound defined by the tolerance level " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_l" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_l = \\min_{j \\in S^l} \\epsilon_j" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "S^l" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " denotes the set of clients mapped to the exit level " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " based on their " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "B_k" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_l" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " is the minimum of tolerance levels" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 306, + 71, + 547, + 157 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 547, + 157 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 547, + 157 + ], + "type": "table", + "html": "
ResNet110Split RatiosCost
Levelsdsw#PARAMS#FLOPSrl
41.001.001.73 M253.1 M1.000
30.880.750.86 M138.5 M0.500
20.770.700.46 M99.7 M0.250
10.660.700.21 M83.4 M0.125
", + "image_path": "a33b66224b8e294126a5d6c546a197e1fe9c7ed83130d132b58746091f027048.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 165, + 545, + 188 + ], + "lines": [ + { + "bbox": [ + 305, + 165, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 305, + 165, + 545, + 188 + ], + "type": "text", + "content": "Table 1. Split ratios and resulting local model statistics (#PARAMS, #FLOPS) for ResNet110 at each level." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": "of those clients in " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "S^l" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": ". A smaller value of " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\epsilon_l" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": " enforces a tighter bound while satisfying the target cost reduction. A larger " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\epsilon_l" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": " value provides more flexibility during the finding of the most balanced 2-D split configuration. For each level " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "l < L" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": ", we place an early exit classifier to the " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\lfloor s_d^{(l)}N\\rfloor" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": "th layer. Algorithm 1 lines 2-4 include these steps. Table 1 reports the computed depth and width split ratios for ResNet110 as the global model. The first column refers to the four complexity levels, the second and third columns reports the coputed 2-D split ratios " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "(s_d,s_w)" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": ". The next two columns show the cost for the full-size model at " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "l = 4" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": " and the reduced model at each complexity level " + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "inline_equation", + "content": "l\\in \\{3,2,1\\}" + }, + { + "bbox": [ + 304, + 209, + 545, + 390 + ], + "type": "text", + "content": ". Our depth and width-balanced split method results in uniformly shaped local models, as opposed to very slim and deep subnetworks due to splitting only along width in HeteroFL." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 406, + 529, + 418 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 406, + 529, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 406, + 529, + 418 + ], + "type": "text", + "content": "3.1.2 Generating Local Models by Split Operation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": "Once the split configurations are produced, ScaleFL executes the 2-D split operation to generate the local model for each client " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " based on the split ratio pairs " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "(s_w,s_d)" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " to meet the budget constraint " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "(B_{k},\\epsilon_{k})" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " specified by the client. Concretely, at each communication round " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": ", only " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": "-fraction of the " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " clients, denoted by " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_t" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": ", are sampled and the global model " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " with weights " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\theta_t" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " is scaled down by executing the 2-D split operation, which generates the local models with architecture " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "M_{l_k}" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " and weights " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\theta_t^{(k)}" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " for each client " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "k\\in \\mathcal{S}_t" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": " based on its complexity level " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "l_{k}" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": ". In this operation, we first perform model splitting along the depth dimension by removing the layers after the " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "\\lfloor s_dN\\rfloor" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": "-th layer where the " + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 425, + 545, + 581 + ], + "type": "text", + "content": "th early exit is placed." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Next, we perform splitting along the width dimension by selecting " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "s_w" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "-partition of the per-layer model weights along the hidden channel. To facilitate the execution of model reduction by width split ratio, we define an index function that takes the weight matrix " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and split ratio value " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "s_w" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " as inputs. Here " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{D_{in} \\times D_{out}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " is a hidden weight matrix where " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{in}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{out}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " are the number of input and output hidden channels in the corresponding layer. The index function returns the Boolean index matrix " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " of size " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "D_{in} \\times D_{out}" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": ", which indicates which weights to keep after the operation. We define the split index as follows: " + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}[i,j] = 1" + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": " if" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24535" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "i < \\lfloor s_wD_{in}\\rfloor" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "j < \\lfloor s_wD_{out}\\rfloor" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ", and zero otherwise. This indexing results in keeping the upper-left submatrix by default, i.e., " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathbf{W}'\\triangleq \\mathbf{W}[\\mathbf{Z}] = \\mathbf{W}[:\\lfloor s_wD_{in}\\rfloor ,:\\lfloor s_wD_{out}\\rfloor ]" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ". Our framework also allows using random selection of weight subsets (e.g. upper-right, lower-left, lower-right and middle etc.) for each client, so that different clients at the same complexity level can use different parts of the model weights and generate slightly different yet complimentary subnetworks. Algorithm 2 gives the pseudocode of this operation (see Appendix 6.1)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 199, + 128, + 212 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 199, + 128, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 128, + 212 + ], + "type": "text", + "content": "3.2. Aggregation" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "content": "After the 2-D split operation, the ScaleFL aggregation module combines the updated local model weights received from heterogeneous clients at each round " + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "content": ". Concretely, every participating client " + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "inline_equation", + "content": "k \\in S_{t}" + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "content": " may send a different subset of the global model to the FL server. For the default upper-left width split option to generate local models, the following aggregation procedure will be carried out to aggregate the overlapping weights received from the contributing clients at each round " + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "content": ", i.e., for every " + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\theta" + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "inline_equation", + "content": "l \\in \\{1, \\dots, L\\}" + }, + { + "bbox": [ + 46, + 217, + 289, + 338 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 74, + 345, + 287, + 377 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 345, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 74, + 345, + 287, + 377 + ], + "type": "interline_equation", + "content": "\\mathbf {W} \\left[ \\mathbf {Z} _ {l} - \\mathbf {Z} _ {l - 1} \\right] \\leftarrow \\frac {1}{\\left| \\mathcal {S} _ {t} ^ {l} \\right|} \\sum_ {k \\in \\mathcal {S} _ {t} ^ {l}} \\overline {{\\mathbf {W}}} _ {k} \\left[ \\mathbf {Z} _ {l} - \\mathbf {Z} _ {l - 1} \\right]. \\tag {2}", + "image_path": "d6dfcc6156dc79bd091ecaef944204f818e25f5791984e273de19b1ec974dace.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "S_{t}^{l} = \\{k|k\\in S_{t},l_{k}\\geq l\\}" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " is the set of participating clients at round " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " with the mapped exit level at " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " or higher. " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_l = \\mathrm{index}(\\mathbf{W},s_w^{(l)})" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "l\\in \\{l^{\\prime},\\dots L\\}" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " and 0 for " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "l < l^{\\prime}" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "l^{\\prime}" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " is the minimum level that " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " exists. For instance, the indexes defined by " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_4 - \\mathbf{Z}_3" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " will aggregate the updates from level 4 clients only. Similarly, the index defined by " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_3 - \\mathbf{Z}_2" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " will aggregate the updates from both level 3 and level 4 clients, and so forth. Lastly, " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}_k" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " is the zero-padded local weight " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_k" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}_k[\\mathbf{Z}_l] = \\mathbf{W}_k" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\overline{\\mathbf{W}}_k[\\mathbf{1} - \\mathbf{Z}_l] = 0" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": ". Hence, if all clients have the same complexity level (i.e. " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "L = 1" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": "), Eq. (2) simplifies into " + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{W}\\gets \\frac{1}{|\\mathcal{S}_t|}\\sum_{k\\in \\mathcal{S}_t}\\mathbf{W}_k" + }, + { + "bbox": [ + 46, + 385, + 289, + 641 + ], + "type": "text", + "content": ". Algorithm 3 gives the pseudo-code for the aggregation algorithm (see Appendix 6.1). This aggregation module is executed at FL server and it determines the overlapping regions using index matrices, and scales the sum of the weight updates received from contributing clients. One caveat for this baseline approach is the fact that low complexity level clients may not contribute to learning other parts of the global model weights belonging to higher complexity levels. This motivates us to further optimize our naive baseline aggregation method with self-distillation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 233, + 660 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 233, + 660 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 233, + 660 + ], + "type": "text", + "content": "3.3. Optimization with Self-Distillation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "During the optimization of local models, we perform self-distillation, which is a form of knowledge distillation (10) where the technique is applied within the same network. Knowledge distillation enables a small (student)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 406, + 83 + ], + "type": "text", + "content": "Algorithm 1: ScaleFL" + } + ] + } + ], + "index": 7, + "type": "text" + }, + { + "bbox": [ + 305, + 87, + 547, + 135 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 87, + 547, + 135 + ], + "spans": [ + { + "bbox": [ + 305, + 87, + 547, + 135 + ], + "type": "text", + "content": "Inputs: Dataset " + }, + { + "bbox": [ + 305, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_k = \\{(X_i,y_i)\\}_{i = 1}^{N_k}" + }, + { + "bbox": [ + 305, + 87, + 547, + 135 + ], + "type": "text", + "content": " for each client " + }, + { + "bbox": [ + 305, + 87, + 547, + 135 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 87, + 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" + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "text", + "content": " are optimization hyperparameters of the system. Here, " + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\tau = 1" + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "text", + "content": " corresponds to using the standard softmax function, and as " + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 128, + 289, + 240 + ], + "type": "text", + "content": " grows, the output of the softmax becomes softer and more information on the score distribution of the teacher is provided to the student." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 249, + 128, + 262 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 249, + 128, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 249, + 128, + 262 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 269, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 287, + 377 + ], + "type": "text", + "content": "In this section, we report the results of extensive experiments on five benchmarks: three image classification benchmarks (CIFAR-10/100, ImageNet) and two NLP benchmarks (SST-2, AgNews). We show that ScaleFL outperforms existing representative heterogeneous FL approaches in terms of global model performance under the same number of rounds and provides inference speedup with up to 2x latency reduction and 4x model size reduction while keeping the performance drop below " + }, + { + "bbox": [ + 46, + 269, + 287, + 377 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 269, + 287, + 377 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 383, + 198, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 383, + 198, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 383, + 198, + 396 + ], + "type": "text", + "content": "4.1. Datasets and Preprocessing" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 401, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 288, + 628 + ], + "type": "text", + "content": "In image classification experiments, we consider common benchmark datasets on various scales: CIFAR-10, CIFAR-100 (14) and ImageNET (ILSVRC2012) (3). We hold out randomly selected 5000 images from CIFAR-10/100 train set and 25000 images from ImageNET train set for validation. We follow the data augmentation techniques applied in (9) with zero padding, center cropping and random horizontal flip with 0.5 probability. For normalization, we use fixed values, 0.5 as mean and 0.25 as standard deviation and disable statistics tracking for batch normalization operations due to the federated setting. In text classification experiments, we consider SST-2 (27) dataset from GLUE benchmark and AGNews (34) dataset. We hold out 872 sentences from SST-2 validation set and randomly selected 5000 sentences from AgNews train set for validation. For tokenization, we use the pre-trained tokenizer for BERT-base-uncased model provided by the open-source HuggingFace library (31). The details of the datasets are in Table 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 287, + 659 + ], + "type": "text", + "content": "4.2. Heterogeneous System Topology and Non-IID Client Data Distribution" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "In CIFAR-10/100 experiments, we set the number of clients " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "K = 100" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " and the ratio of available clients in each training round " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "p = 0.1" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": ". For ImageNET, SST-2 and AGNews experiments, " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "K = 50" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "p = 0.2" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": ". To simulate the" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 545, + 155 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 545, + 155 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 545, + 155 + ], + "type": "table", + "html": "
DatasetTrain SizeTest Size# ClassesResolution
CIFAR-1050K10K1032x32
CIFAR-10050K10K10032x32
ImageNet1.2M150K1000224x224
SST-267K18212-
AgNews120K7.6K4-
", + "image_path": "5af741a1e8ee1555e06c1a1f0b5d5827773ce908fa9dd472a8bf6935b7d0e0f0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 163, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 305, + 163, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 545, + 186 + ], + "type": "text", + "content": "Table 2. Statistics of the datasets used in image and text classification experiments." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": "system heterogeneity, we consider four complexity levels with the target cost reduction ratios " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "r_1 = 0.125" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "r_2 = 0.25" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "r_3 = 0.5" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "r_4 = 1" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": " and set the tolerance level " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\epsilon_k = 0.1" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": ". We set the number of clients assigned to each level to be equal. Different number of complexity levels or client distributions are also applicable and compatible with ScaleFL. We use Dirichlet distribution with concentration parameter " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": " to create non-IID data splits for the local datasets in the federated setting as in (19; 32). We report the results in two levels of non-IID distribution with " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": " (more skewed) and " + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\alpha = 100" + }, + { + "bbox": [ + 304, + 207, + 545, + 363 + ], + "type": "text", + "content": " (less skewed). The resulting class distribution of data at each client is illustrated in Figure 4 (see Appendix)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 371, + 492, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 371, + 492, + 384 + ], + "spans": [ + { + "bbox": [ + 306, + 371, + 492, + 384 + ], + "type": "text", + "content": "4.3. Model and Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": "On CIFAR-10 and CIFAR-100 datasets, we perform experiments with two different models: ResNet (9) and MSDNet (11). ResNet is a common baseline for benchmarking and MSDNet is a multi-exit CNN architecture with dense connections. We use the default ResNet settings for 110-layer architecture from (9). For MSDNet, we use the recommended configuration with 24 layers, 3 scales and 16 initial hidden dimensions with a growth rate of 6 (11). On ImageNET, we consider EfficientNet (28) with B4 architecture (medium-size) and " + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": " input resolution (28). We set the number of FL rounds to 400 and 90, and batch size to 16 and 64 for CIFAR/ImageNET respectively. We optimize local models using gradient descent with the learning rate " + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\eta = 0.1" + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": " decayed by 0.1 at the 100th/200th (for CIFAR) and 30th/60th (for ImageNET) rounds. We use 3-layer CNNs with ReLU activations as early exit classifiers. On SST-2 and AgNews datasets, we use the pre-trained BERT (4) provided by the open-source HuggingFace library (31). We optimize the local models for 100 rounds using gradient descent with the learning rate " + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\eta = 3e - 5" + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": " and batch size 16. We use one-layer FC layers as early exit classifiers. In all experiments, the number of local training epochs " + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "inline_equation", + "content": "e = 5" + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": " and KL divergence temperature " + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\tau = 3" + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": ". For image/text classification experiments, loss weighting parameters " + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\beta = 0.1" + }, + { + "bbox": [ + 304, + 390, + 545, + 689 + ], + "type": "text", + "content": " and 0.05, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We consider two baseline approaches: FedAVG (22) and Decoupled. In FedAVG, we train the Level-1 model with" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24537" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 122, + 70, + 473, + 208 + ], + "blocks": [ + { + "bbox": [ + 122, + 70, + 473, + 208 + ], + "lines": [ + { + "bbox": [ + 122, + 70, + 473, + 208 + ], + "spans": [ + { + "bbox": [ + 122, + 70, + 473, + 208 + ], + "type": "table", + "html": "
ModelAlgorithmCIFAR-10CIFAR-100
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
ResNet110FedAVG81.4681.4677.7277.7244.2644.2642.7542.75
Decoupled77.16-74.83-36.60-35.78-
HeteroFL82.9384.3577.6079.9144.6647.1242.9742.95
FedDF83.3584.4477.0878.5743.5046.9942.2944.50
ScaleFL (Ours)84.4985.5379.6180.8346.6349.9443.5244.95
MSDNet24FedAVG82.6982.6975.2875.2846.4446.4442.7542.75
HeteroFL81.5483.0275.7776.7444.6547.7742.3243.00
ScaleFL (Ours)84.6184.7777.8178.6949.1950.2545.2546.12
", + "image_path": "2cfa46444c7b3c3bf4b17d33b4c1bf1e8974284beeb39ff0d4bea5acc33c14fa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 77, + 245, + 258, + 328 + ], + "blocks": [ + { + "bbox": [ + 97, + 216, + 495, + 227 + ], + "lines": [ + { + "bbox": [ + 97, + 216, + 495, + 227 + ], + "spans": [ + { + "bbox": [ + 97, + 216, + 495, + 227 + ], + "type": "text", + "content": "Table 3. Local and global model accuracy values on CIFAR-10/100 datasets with ResNet110 and MSDNet24." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 77, + 245, + 258, + 328 + ], + "lines": [ + { + "bbox": [ + 77, + 245, + 258, + 328 + ], + "spans": [ + { + "bbox": [ + 77, + 245, + 258, + 328 + ], + "type": "table", + "html": "
EfficientNetB4ImageNet
α = 100α = 1
localgloballocalglobal
FedAVG45.0045.0042.3342.33
HeteroFL43.6846.6141.7443.59
ScaleFL (Ours)46.6348.9544.8646.78
", + "image_path": "b497da74e8fd2b6bb97fe0c41dd4026fa40237d9d85fced339af789d216564ec.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 371, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 515 + ], + "type": "text", + "content": "splitting along width to use all available data. In Decoupled, we train separate models for each level using the corresponding data of the clients at that level. We also compare our results with recent studies: HeteroFL (5) and FedDF (19), where we use splitting along width dimension to form the local models at each level. For FedDF, we use CIFAR-10/100 and SST-2/AgNews train sets as distillation datasets for each other. Our implementation is on Python 3.7 with PyTorch 1.12 library. Our code is available at: https://github.com/git-disl/scale-fl. Each latency measurement is carried out 1000 times on a machine with an 8-core 2.4GHz CPU and 64GB RAM." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 526, + 197, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 197, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 197, + 538 + ], + "type": "text", + "content": "4.4. Global Model Performance" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "In this setting, we evaluate the global model on the test dataset of each client and report the average of obtained accuracy values. In Table 3, we report the results for image classification on CIFAR-10 and CIFAR-100 with ResNet110 and MSDNet24 models to observe the effect of different architectures on the performance of ScaleFL. We provide comparisons with FedAVG and HeteroFL for all three image datasets. We make two observations from Table 3. First, ScaleFL achieves " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "0.45 - 2.95\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "1.7 - 3.12\\%" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " higher global performance compared to the closest approach on ResNet110 and MSDNet24 respectively. Second, in all settings, FedAVG baseline performs poorly since the small level-1 model is used to utilize the data of every client. Decoupled baseline performs the worst since the models for" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 245, + 547, + 327 + ], + "blocks": [ + { + "bbox": [ + 63, + 337, + 271, + 348 + ], + "lines": [ + { + "bbox": [ + 63, + 337, + 271, + 348 + ], + "spans": [ + { + "bbox": [ + 63, + 337, + 271, + 348 + ], + "type": "text", + "content": "Table 4. Local and global accuracy values on ImageNET." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 245, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 306, + 245, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 245, + 547, + 327 + ], + "type": "table", + "html": "
BERTSST-2AG News
α = 100α = 1α = 100α = 1
localgloballocalgloballocalgloballocalglobal
FedAVG79.9479.9470.0170.0185.1485.1481.1081.10
HeteroFL76.0288.8376.2182.8689.9291.5188.8590.85
FedDF77.6788.9577.4182.9589.7990.9388.9390.05
ScaleFL (Ours)83.7288.5879.6583.7990.5392.1389.7291.20
", + "image_path": "4d74129bd98600c3c8b970419063a93146662da7010999004a171708b3467f5f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 335, + 545, + 346 + ], + "lines": [ + { + "bbox": [ + 306, + 335, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 545, + 346 + ], + "type": "text", + "content": "Table 5. Local and global accuracy values on SST-2 and AgNews." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 370, + 454, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 454, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 454, + 383 + ], + "type": "text", + "content": "each level are trained independently." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": "In Table 4, we provide the results of ImageNet experiments with EfficientNet-B4 with " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " input resolution. Since FedDF uses " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "32 \\times 32" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " resolution on ImageNet experiments, we could not report the results for FedDF on ImageNet. ScaleFL consistently achieves around " + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "inline_equation", + "content": "2.34 - 3.19\\%" + }, + { + "bbox": [ + 304, + 384, + 545, + 526 + ], + "type": "text", + "content": " higher global model accuracy under different data heterogeneity settings, compared to the closest competitor in each experiment. In addition, Table 5 reports the effectiveness of ScaleFL using NLP benchmarks with BERT as the backbone and ScaleFL again displays significant improvement especially in local model performance as investigated further in the next subsection." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 538, + 493, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 493, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 493, + 551 + ], + "type": "text", + "content": "4.5. Local Model Performance Analysis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "This section reports the local model performances at different levels. In Tables 3, 4 and 5, 'local' columns contain the average of accuracy values obtained after evaluating the respective local model at each client based on its level. In addition, we illustrate the local models (their scales in width and depth dimensions) and accuracies for MSD-Net24 on CIFAR100 in Figure 2. At each level, even though both submodels satisfy the target cost reduction, ScaleFL results in consistently better performance in terms of local model accuracy. This demonstrates the effectiveness of 2-D downscaling since it balances between preserving low-order basic features and extracting high-order complex features. We also analyze the performance with respect to the num" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "24538" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 547, + 214 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 214 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 214 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 214 + ], + "type": "image", + "image_path": "b6b9d0ea069deb340f5a4311d03305542551ca3d2af042d3f17d940986a8cbc8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 222, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 222, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 547, + 257 + ], + "type": "text", + "content": "Figure 2. Local model accuracies of Level 1-4 models with ScaleFL and HeteroFL for MSDNet24 on their corresponding test sample sets from CIFAR100. Percentages on the bottom left and top right corners indicate the scaling ratios along width/depth dimensions. Percentages above the models report the test accuracy obtained by that model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 277, + 166, + 370 + ], + "blocks": [ + { + "bbox": [ + 53, + 277, + 166, + 370 + ], + "lines": [ + { + "bbox": [ + 53, + 277, + 166, + 370 + ], + "spans": [ + { + "bbox": [ + 53, + 277, + 166, + 370 + ], + "type": "image", + "image_path": "fe79f6dbdb258e4312c2d120020aaafffbecadd2ca24547773a0209380b899ca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 277, + 282, + 369 + ], + "blocks": [ + { + "bbox": [ + 167, + 277, + 282, + 369 + ], + "lines": [ + { + "bbox": [ + 167, + 277, + 282, + 369 + ], + "spans": [ + { + "bbox": [ + 167, + 277, + 282, + 369 + ], + "type": "image", + "image_path": "11f501cc28d41838bde48533cd47a6b4e86c4390e58c5bd26c07450cc77d1e6d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 53, + 376, + 167, + 467 + ], + "blocks": [ + { + "bbox": [ + 53, + 376, + 167, + 467 + ], + "lines": [ + { + "bbox": [ + 53, + 376, + 167, + 467 + ], + "spans": [ + { + "bbox": [ + 53, + 376, + 167, + 467 + ], + "type": "image", + "image_path": "dc1e8d79567effcd9897c831e98370cb80b6b32d7f703e24f08d0741a5a54ed0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 167, + 376, + 282, + 467 + ], + "blocks": [ + { + "bbox": [ + 167, + 376, + 282, + 467 + ], + "lines": [ + { + "bbox": [ + 167, + 376, + 282, + 467 + ], + "spans": [ + { + "bbox": [ + 167, + 376, + 282, + 467 + ], + "type": "image", + "image_path": "c1a1162b13829c8e5a853363345f555773c0b71320532224c0022f70d00d930b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 53, + 474, + 166, + 566 + ], + "blocks": [ + { + "bbox": [ + 53, + 474, + 166, + 566 + ], + "lines": [ + { + "bbox": [ + 53, + 474, + 166, + 566 + ], + "spans": [ + { + "bbox": [ + 53, + 474, + 166, + 566 + ], + "type": "image", + "image_path": "464b0be7dee2a95f2385ab0167d34b015faf5fe73d47b1f745516d009945d75f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 167, + 474, + 282, + 566 + ], + "blocks": [ + { + "bbox": [ + 167, + 474, + 282, + 566 + ], + "lines": [ + { + "bbox": [ + 167, + 474, + 282, + 566 + ], + "spans": [ + { + "bbox": [ + 167, + 474, + 282, + 566 + ], + "type": "image", + "image_path": "385f686ce8363d59edf96ab1c6b2056277ccf6c07d04342799a69f9c166be34c.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 53, + 572, + 167, + 663 + ], + "blocks": [ + { + "bbox": [ + 53, + 572, + 167, + 663 + ], + "lines": [ + { + "bbox": [ + 53, + 572, + 167, + 663 + ], + "spans": [ + { + "bbox": [ + 53, + 572, + 167, + 663 + ], + "type": "image", + "image_path": "0319dfce253197212f4e86779a3dc3664932ef6121c610fe84e4da3ef299dfca.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 676, + 287, + 698 + ], + "lines": [ + { + "bbox": [ + 46, + 676, + 287, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 676, + 287, + 698 + ], + "type": "text", + "content": "Figure 3. Local model performances with respect to #PARAMs and #FLOPs. Marker sizes represent complexity levels." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 168, + 572, + 282, + 663 + ], + "blocks": [ + { + "bbox": [ + 168, + 572, + 282, + 663 + ], + "lines": [ + { + "bbox": [ + 168, + 572, + 282, + 663 + ], + "spans": [ + { + "bbox": [ + 168, + 572, + 282, + 663 + ], + "type": "image", + "image_path": "d1732df775fbd4fcb11c9cbb1ce597871c42dd48a98c9252f9b1fb150bdc1b0d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "type": "text", + "content": "ber of parameters and inference time per sample on CPU (ms), as illustrated in Figure 3. In most settings, our approach achieves better test results at local models and the performance gap is more significant at lower levels, which demonstrates the efficiency of our two-dimensional splitting approach for model downscaling. For instance, the level-2 local model on AgNews with ScaleFL has 6x faster inference and 4x smaller size while having a lower " + }, + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "type": "inline_equation", + "content": "2.5\\%" + }, + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "type": "text", + "content": " accuracy decrease (vs " + }, + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "type": "inline_equation", + "content": "3 - 4\\%" + }, + { + "bbox": [ + 304, + 277, + 547, + 396 + ], + "type": "text", + "content": " with other methods) from the global model." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 417, + 379, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 417, + 379, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 379, + 430 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 441, + 547, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 547, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 547, + 609 + ], + "type": "text", + "content": "We have introduced ScaleFL, a novel resource-adaptive framework to address the system heterogeneity problem in federated learning. First, ScaleFL adaptively scales down the global model based on the computational constraints of participating clients. Our two-dimensional split methodology preserves the important balance of basic and complex features in local models. Second, we perform self-distillation among early exit and final predictions during local model training to improve the knowledge transfer among subnetworks and provide effective aggregation. We demonstrate the performance gains of ScaleFL compared to FedAVG as well as HeteroFL and FedDF, the two most representative federated learning approaches for system heterogeneity on benchmark image and text datasets." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 630, + 409, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 409, + 643 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 409, + 643 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "This research is partially sponsored by the NSF CISE grants 2038029, 2026945, 1564097, and an IBM faculty award. The first author thanks for the summer 2022 internship at IBM Research with the group led by Dr. Donna Dillenberger." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24539" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 704 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Mohammad Mohammadi Amiri, Deniz Gündüz, Sanjeev R. 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Unlike existing works that struggle to balance the trade-off between inference speed and SOD performance, in this paper, we propose a novel Scale-aware Knowledge Distillation (ScaleKD), which transfers knowledge of a complex teacher model to a compact student model. We design two novel modules to boost the quality of knowledge transfer in distillation for SOD: 1) a scale-decoupled feature distillation module that disentangled teacher's feature representation into multiscale embedding that enables explicit feature mimicking of the student model on small objects. 2) a cross-scale assistant to refine the noisy and uninformative bounding boxes prediction student models, which can mislead the student model and impair the efficacy of knowledge distillation. A multi-scale cross-attention layer is established to capture the multi-scale semantic information to improve the student model. We conduct experiments on COCO and VisDrone datasets with diverse types of models, i.e., two-stage and one-stage detectors, to evaluate our proposed method. Our ScaleKD achieves superior performance on general detection performance and obtains spectacular improvement regarding the SOD performance.", + "bbox": [ + 76, + 335, + 473, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 727, + 209, + 742 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Object detection is a fundamental task that has been developed over the past twenty-year in the computer vision community. Despite the state-of-the-art performance for general object detection having been conspicuously improved since the rise of deep learning, balancing the complexity-precision for small object detection is still an open question. Current works strive to refine feature fusion modules [9, 21], devise novel training schemes [32, 33]", + "bbox": [ + 75, + 752, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "to explicitly train on small objects, design new neural architectures [20,39] to better extract small objects' features, and leverage increased input resolution to enhance representation quality [1, 49]. However, these approaches struggle to balance detection quality on small objects with computational costs at the inference stage.", + "bbox": [ + 496, + 305, + 893, + 397 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The above reasons incentivize us to design a cost-free technique at test time to improve SOD performance. In the spirit of the eminent success of knowledge distillation (KD) on image data [14], we explore distillation methods for SOD. Typically, knowledge distillation opts for a complex, high-performance model (teacher) that transfers its knowledge to a compact, low-performance model (student). The student model can harness instructive information to enhance its representation learning ability. Nevertheless, unlocking this potential in SOD involves overcoming two challenges: 1) SOD usually suffers from noisy feature representations. Due to the nature of small objects, which generally take over a small region in the whole image, the feature representations of these small objects can be contaminated by the background and other instances with relatively larger sizes. 2) Object detectors have a low tolerance for noisy bounding boxes on small objects. It is inevitable that teacher models make incorrect predictions. Usually, student models can extract informative dark knowledge [14, 28] from imperfect predictions from the teacher. However, in SOD, small perturbations on the teacher's bounding box can dramatically impair SOD performance on the student detector (§3.2).", + "bbox": [ + 496, + 398, + 893, + 747 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To this end, we propose Scale-aware Knowledge Distillation for small object detection (ScaleKD). Our proposed ScaleKD consists of two modules, a Scale-Decoupled Feature (SDF) distillation module and a Cross-Scale Assistant (CSA), to address the aforementioned two challenges correspondingly. The SDF is inspired by the crucial shortcoming of existing feature distillation methods, where the feature representations of objects with varying scales are coupled in a single embedding. It poses difficulty for the student to mimic small objects' features from the teacher model.", + "bbox": [ + 496, + 750, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19723", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/40b51e808c002a2c17fb7a4e8ebc123238468ba844064fbef8bcd7cb162091fe.jpg", + "image_caption": [ + "Figure 1. The overview of Scale-aware Knowledge Distillation. It consists of a Scale-Decoupled Feature distillation module and a CrossScale Assistant module to improve small object detection." + ], + "image_footnote": [], + "bbox": [ + 84, + 93, + 880, + 313 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As a result, the proposed SDF aims to decouple a single-scale feature embedding into a multi-scale feature embedding. The multi-scale embedding is obtained by a parallel multi-branch convolutional block, where each branch deals with one scale. Our SDF allows the student model to better understand the feature knowledge from the perspective of object scale. Furthermore, we propose a learnable CSA to resolve the adverse effect of teachers' noisy bounding box prediction on small objects. The CSA comprises a multi-scale cross-attention module, where representations from the teacher and student models are mapped into a single feature embedding. The multi-scale query-key pair projects the teacher's features into multiple sizes, such that the fine-grained and low-level details can be preserved in CSA, which helps to produce suitable bounding box supervision for the student model.", + "bbox": [ + 75, + 383, + 472, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate the effectiveness of our approach on COCO object detection and VisDrone datasets. The experiments are conducted on multiple types of detectors, including two-stage detectors, anchor-based detectors, and anchor-free detectors, and have proven the generalizability of our approach. Our work offers a practical approach for industrial application on SOD as well as introduces a new perspective on designing scale-aware KD modules to improve object detectors. We further extend our method on instance-level detection tasks, such as instance segmentation and keypoint detection, demonstrating the superiority of our approach to dealing with small objects in vision tasks.", + "bbox": [ + 75, + 627, + 468, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are the following:", + "bbox": [ + 96, + 810, + 418, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We propose Scale-Aware Knowledge Distillation (ScaleKD), a novel knowledge distillation framework to improve general detection and SOD performance without bringing extra computational costs at test time.", + "bbox": [ + 94, + 839, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Our proposed ScaleKD not only exceeds state-of-the-art KD for object detection methods on general detection performance but also surpasses existing approaches on SOD by a large margin. Extended experiments on instance segmentation and keypoint detection further strengthen our method.", + "bbox": [ + 519, + 383, + 890, + 473 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 493, + 640, + 508 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Knowledge Distillation. Knowledge distillation has become one of the most effective techniques for model compression [14]. It first trains a cumbersome teacher model and then transfers its knowledge to a lightweight student model. The common knowledge distillation approaches include distillation on output, logits [14], bounding box [16], and features [30, 52, 53].", + "bbox": [ + 496, + 520, + 890, + 627 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is also closely correlated to object detection, where knowledge distillation has shown effectiveness in detection tasks [3, 15, 35, 40, 47, 48]. In particular, FineGrained [5] is the first work to comprehensively present a KD framework for the object detection task. FKD [44] is the earliest work to adopt attention mechanisms to do feature distillation on object detectors. DeFeat [12] decoupled the foreground feature and background features based on the ground-truth binary mask and performed feature distillation on two features separately. FGFI [41] presents focal distillation, which combines DeFeat and Zhang et al. [44] works. ICD [17] considered conditional distillation of both classification and localization on very instances. Guo [12] investigates distilling image classifier instead of object detector to student detector, which complements existing feature-based distillation methods. Similar to ICD, GID [7] proposed an instance-selection module to transfer the teacher's most informative locations. LGD [45] pro", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19724", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "posed a teacher-free framework to distill object detectors without a concrete teacher model. Nevertheless, existing methods have largely overlooked the small objects. Our paper is the first work to design knowledge distillation specifically targeted to improve general object detection and small objects' performance.", + "bbox": [ + 75, + 90, + 470, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Small Object Detection. Recognizing small objects in the image is challenging, especially when localization and per-pixel classification are required. A naive approach is to increase the resolution [26]. Nevertheless, it brings tremendous computational costs in inference. Existing approaches mainly focus on applying strong data augmentation [18] or oversampling [4], incorporating context information [9, 21], fusing the features across layers [10, 38], performing scale-aware training [32, 33], adjusting resolution at test-time [37], or applying dilated convolution/large convolution [20, 39] to increase the receptive field. We refer interested readers for a more in-depth survey [6].", + "bbox": [ + 75, + 196, + 468, + 393 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach is very different from previous methods, where we seek help with knowledge distillation to boost the performance of SOD. Our method benefits from the advantage of the distillation method, where 1) no extra computational costs are introduced at test time, and 2) neural architectures of the existing model do not need to be modified, a critical benefit in the practical scenario where engineering do not want to alter their networks architecture due to inconvenience on deployment.", + "bbox": [ + 75, + 393, + 468, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Scale-aware Knowledge Distillation", + "text_level": 1, + "bbox": [ + 76, + 542, + 398, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section provides a detailed description of our proposed distillation methods. Figure 1 gives a brief overview of ScaledKD, in which we illustrate the modules as follows: (1) A scale-decoupled feature distillation module that explicitly transfers representation on diverse scales to the student detector. (2) A cross-scale assistant refines the knowledge of object size between complex teacher and compact student.", + "bbox": [ + 75, + 568, + 468, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition. In this section, we provide a notion of the components that we will use to describe our method. Considering an object detector $\\mathcal{G}^S:\\mathbb{R}^d\\to \\mathbb{R}^k$ as a student and another predictor $\\mathcal{G}^T:\\mathbb{R}^d\\to \\mathbb{R}^k$ as a teacher, where $d$ and $k$ are two feature dimensions. The former is a computationally efficient network with a relatively lower detection performance. The latter is a heavy model with relatively higher detection performance. Giving a training dataset $S = \\{(x_{i},y_{i})_{i = 1}^{n}\\} \\sim \\mathbb{P}^{n}$ for distribution $\\mathbb{P}$ over a set of instance $\\mathcal{X}$ . For small object detection, a common approach to improve SOD is to leverage a high-resolution image as input. In our case, we only consider using high-resolution images $\\chi^{hr}$ for the teacher model, while", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5dcacf5fe2c743cb4679a500605c69076f5374f3c3873e9cd002cf8e7c5fa8ab.jpg", + "image_caption": [ + "Figure 2. The scale-decouple feature module in ScaleKD. Note that the details of the student's scale-decoupled feature module are omitted due to limited space. In practice, it is symmetric to the teacher's counterpart." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 895, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "standard-resolution images are used for the student model.", + "bbox": [ + 500, + 380, + 883, + 395 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Scale-Decoupled Feature Distillation", + "text_level": 1, + "bbox": [ + 500, + 404, + 815, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminary. Modern object detectors harness FPN [21] to obtain the multi-scale semantic information from different levels of the backbone to enhance the model's feature learning ability on diverse object scales. A typical distillation approach is to transfer the knowledge of these features from teacher to student. Generally, we can formulate such distillation methods as:", + "bbox": [ + 496, + 426, + 890, + 532 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f e a t}} = l \\left(\\mathcal {F} ^ {T}, f \\left(\\mathcal {F} ^ {S}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 541, + 890, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $F^T$ and $F^S$ are corresponding feature layers in the teacher and student model. $f(\\cdot)$ is a mapping function to align the dimension of the feature map in student to teacher, and $l(\\cdot)$ is any bounded loss, i.e., $l_2$ norm distance.", + "bbox": [ + 496, + 566, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Motivation. Although state-of-the-art KDs for object detection have developed various techniques, such as focal distillation [41], to enhance the quality of transferred knowledge, such methods treat all objects that have varying sizes equally during distillation. We identify that the key shortcoming of these methods on SOD is that the feature representation on diverse objects is entangled. It is a viable solution when object sizes are not small. However, the size of objects in the detection task varies significantly. The feature representation of small objects can be contaminated by large-region backgrounds and other instances with a relatively larger size. To resolve the issue, we propose a Scale-Decoupled Feature (SDF) distillation module to explicitly disentangled the teacher's feature map.", + "bbox": [ + 496, + 643, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Methodology. As aforementioned, our goal is to disentangle the whole feature representation of the teacher", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19725", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/b633b996c73bb6411877456c1e90b06e0b0243c367a9276876987f42facb6203.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPerturbationAPAPSAPMAPL
Baseline036.921.240.848.4
Chen et al. [5]038.121.942.250.1
6 pixels37.721.142.450.2
12 pixels37.019.942.150.0
", + "bbox": [ + 81, + 88, + 467, + 179 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Noisy and uninformative bounding boxes from the teacher can severely hurt students' performance. The perturbation is measured by a number of pixels, and it is added along the diagonal direction.", + "bbox": [ + 75, + 189, + 468, + 246 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "object detector into multiple parts, where each part only deals with similar object sizes. Presumably, such operations can force student detectors to comprehend not only the global knowledge of the entire image but also the scale-specific knowledge.", + "bbox": [ + 75, + 276, + 467, + 351 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To be specific, we obtain a feature embedding $Z^T$ and $Z^S$ in the last stage of the backbone for both the teacher and student networks. We intend to fully utilize the feature representation on diverse input scales. Thus, we adopt a multi-branch structure, where each branch uses a convolutional layer with different dilated rates. It is worth noting that the model tends to focus on small objects for the kernel with a small dilated rate and vice versa. In practice, we use residual blocks as in ResNet, which consist of three consecutive convolutional layers, i.e., 1x1, 3x3, and 1x1, along with a skip connection. For the 3x3 Conv layer, we use three different dilated rates {1, 2, 3} on three individual branches. An adapter layer, typically a multi-layer perception (MLP) layer, is stacked before this scale-decoupled feature module to align the dimensionality of feature presentation between the teacher and student model.", + "bbox": [ + 75, + 353, + 467, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Usually, one can match the knowledge of the teacher model at a designated branch, i.e., the $3 \\times 3$ Conv layer with a dilated rate of 1, to the corresponding feature branch in the student model via any distance minimization loss. One drawback is that these operations can be memory intensive. Therefore, we take inspiration from the weight-sharing network in neural architecture search [25, 34] and adopt a weight-sharing scale-decoupled feature. This is based on the fact that all three branches have the same operators. In practice, we only save a set of weights for three branches, dramatically reducing the training memory cost.", + "bbox": [ + 75, + 595, + 467, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also notice that using three individual losses to match three parallel branches between the teacher and student model can cause the practitioner to spend unnecessary effort on hyper-parameter tuning. As a result, for each branch, we use a flattened layer, namely a multi-layer perceptron, and concatenate three flattened layers together. During the distillation process, we adopt a sole 12 loss (denoted as $L_{feat}$ in the later section) to minimize the distance of this concatenated flattened layer between the teacher and student", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/62781c20948e00e9925305a4cabf4cd75673e7c904b96a6834cedaa416f4049b.jpg", + "image_caption": [ + "Figure 3. The Cross-Scale Assistant (CSA) module. We adopt a multi-scale query-key pair to perform cross-attention with feature embedding in the student model. The learnable weights in CSA are updated via two separate classification and regression branches which are supervised by the ground truth label." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 893, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "model. the overview of the proposed module can be viewed in Figure 2. Notably, the student's scale-decoupled feature module mirrors the teacher's counterpart.", + "bbox": [ + 496, + 377, + 890, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Cross-Scale Assistant", + "text_level": 1, + "bbox": [ + 500, + 431, + 699, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Preliminary. Our previous section introduces our proposed feature distillation to resolve the challenge of SOD. Other than feature distillation, another practical approach is the output-based KD, which transfers the teacher's prediction on classification and localization to the student as sources for auxiliary supervision. Our work primarily focuses on bounding box distillation, which can be considered a regression problem. In general, we can write such regression distillation as follow:", + "bbox": [ + 496, + 455, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b b o x} = l _ {b b o x} \\left(\\mathcal {R} ^ {S}, \\mathcal {R} ^ {T}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 599, + 890, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{R}^S$ is the regression output of the student network, $\\mathcal{R}^T$ is the predication of teacher network. This $l(\\cdot)$ is the same as Equation 1, where any bounded loss can be applied. Conventionally, this bounded loss can be either $l_1$ , smoothed $l_1$ or $l_2$ loss, depending on the level of penalty that we wise to weight the error between the student's predication and the teacher's output.", + "bbox": [ + 496, + 627, + 890, + 734 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivation. A key difference between small object detection and general object detection is that SOD is sensitive to noisy bounding boxes. Apparently, the teacher detector is incapable of making perfect predictions on every object. In general object detection, despite being inaccurate, student models can still retrieve informative knowledge from teachers' predictions on bounding boxes. Nevertheless, for small objects, noisy bounding box prediction in the teacher model can confuse the student model, which decreases the SOD performance. As proof", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19726", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of concept, we deliberately add a slight deviation (6 and 12 pixels along the diagonal direction) and compare the mAP on small-scale objects of a vanilla teacher with a teacher that is slightly perturbed. As shown in Table 1, on RetinaNet baseline, the AP of small objects $(AP_S)$ of students drops consistently when perturbations are added, showing the sensitivity of student detector on teacher's bounding box prediction in SOD. Therefore, to build a trustworthy regression distillation module for SOD, one needs to minimize the adverse effect of poison bounding box knowledge in teachers. This does not mean that the teacher's predictions have to be perfect - otherwise, we can directly supervise the student with ground truth - we only need to refine the teacher's output to ensure that their knowledge is informative to the student [27, 50].", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Methodology. To address the aforementioned issue, we propose a Cross-Scale Assistant (CSA), which refines the teacher's knowledge and enables the student model to fetch instructive knowledge on objects with different scales.", + "bbox": [ + 76, + 332, + 468, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our method is simple - we establish the CSA by a cross-attention module. During the cross-attention, a sequence of key and query tokens are generated in calculating KQ-attention within the teacher's knowledge and then mapped with the value tensor, the outputs from the student model, to obtain attentive regions in the feature with each corresponding query. This process is executed at every student pyramid scale to retrieve informative region-based features.", + "bbox": [ + 75, + 420, + 468, + 541 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A naive choice is to use plain cross-attention [8]. Albeit, previous studies [43] identified that the standard cross-attention could focus on salient regions repetitively on different heads. Consequently, when large objects appear in the image, the cross-attention will redirect its attention to these large objects and ignore small objects. To this end, in contrast to the plain cross-attention, we developed a multiscale cross-attention layer, as shown in Figure 3. Notice that cross-attention extracts global information - for each query-key pair, a value is generated to highlight the most responsive region. We then split the query-key pair into multiple sub-pairs, where each sub-pair represents a set of object scales. As a result, our multi-scale query-key can enforce the attention module to focus on regions with diverse scales, such that all objects, especially the small objects, can attend to the feature learning process.", + "bbox": [ + 75, + 541, + 470, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Particularly, give an input sequence from teacher $F^T \\in \\mathbb{R}^{h \\times w \\times c}$ and another input sequence from student $F^S \\in \\mathbb{R}^{h \\times w \\times c}$ , for simplicity, we assume two tensors have the same size. The $F^T$ is projected into a query (Q) and key (K), and $F^S$ is projected into value (V). The keys $K$ and values $V$ are down-sampled to different sizes for different heads indexed by $i$ . Thus, we formulate our multi-scale", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cross-attention (MSC) as follows:", + "bbox": [ + 500, + 90, + 723, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {i} = F ^ {S} W _ {i} ^ {Q} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 645, + 114, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nK _ {i} = M S C \\left(F ^ {T}, r _ {i}\\right) W _ {i} ^ {K}, V _ {i} = M S C \\left(F ^ {T}, r _ {i}\\right) W _ {i} ^ {V}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 142, + 890, + 161 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV _ {i} = V _ {i} + P \\left(V _ {i}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 166, + 890, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $MSC(\\cdot ,r_i)$ is a MLP layer for aggregation in the $i$ -th head with the down-sampling rate of $r_i$ , and $P(\\cdot)$ is a depth-wise convolutional layer for projection. Compared with the standard cross-attention, more fine-grained and low-level details that are beneficial to SOD are preserved. Finally, we calculated the attention tensor by:", + "bbox": [ + 498, + 188, + 890, + 280 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nh _ {i} = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {d _ {h}}} V _ {i}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 289, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $d_h$ is the dimension. Remember that the purpose of CSA is to bridge the cross-scale information between the teacher and student model to refine the bounding box supervision in KD. Therefore, we stacked head layers with the classification branch and regression branch to update the weights of these learnable modules. Our empirical analysis shows that the proposed CSA can provide more appropriate supervision on small objects bounding boxes during distillation. Because this is a learnable module, during distillation, we perform a weights update prior to the student model at each iteration through a standard training scheme and detection objectives.", + "bbox": [ + 496, + 333, + 890, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In distillation, instead of transferring the teacher's output knowledge, we transfer the CSA's knowledge on both classification and regression branches to students. For the output-based distillation objectives, we follow [5] to have two loss functions $L_{cls}$ and $L_{bbox}$ . We note that our method is also complementary to other output-based methods, such as LD [46], where all we need to do is simply replace the distillation objective.", + "bbox": [ + 496, + 513, + 890, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, the total training objective for the student model is:", + "bbox": [ + 498, + 635, + 890, + 664 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {t o t a l}} = \\alpha L _ {\\text {f e a t}} + \\beta L _ {\\text {c l s}} + \\gamma L _ {\\text {b b o x}} + L _ {\\text {d e t}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 676, + 890, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L_{det}$ is the standard training loss for the detector.", + "bbox": [ + 498, + 704, + 867, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides the distillation loss and detection loss for optimizing student detectors, we further ensure the instructive representation quality and consistency with student representations by sharing the detection head for supervision. Moreover, the CSA combines the feature of both teacher and student. As a result, a randomly initialized student detector can cause unstable training of CSA. Thus, we first warm up the student model for 30k iterations since it could be detrimental when the instructive knowledge is optimized insufficiently. The student detector backbone is frozen in early 10k iterations under $1 \\times$ training schedule and 20k for $2 \\times$ training schedule.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19727", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/cd86b126736d82fc5be624de3f46d60a67bdfa6b70a837df28d394ce5c871b4e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)FPSParams (M)
Faster-RCNN [29] + ScaleKDResNet5038.459.042.021.542.150.320.143.57
43.164.048.226.148.058.8
Faster-RCNN [29] + ScaleKDMobileNetV227.344.728.914.629.635.712.932.61
30.848.732.918.834.242.2
Cascade-RCNN [2] + ScaleKDResNet5041.059.444.422.744.454.318.971.22
44.963.248.825.748.159.2
RetinaNet [22] + ScaleKDResNet5037.456.739.620.040.749.717.437.74
42.861.144.625.945.454.9
FOCS [36] + ScaleKDResNet5038.557.741.021.942.848.623.936.15
44.061.641.629.146.956.2
RepPoints [42] + ScaleKDResNet5038.659.641.622.542.250.418.236.62
42.963.846.825.747.156.7
", + "bbox": [ + 161, + 88, + 805, + 316 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d27b32dad48eb301358064db070ecd1307707b55796270c0c159c41e09edf7d9.jpg", + "table_caption": [ + "Table 2. Comparison with state-of-the-art methods KD-Det on COCO val2017 datasets. Our approach appear to improve the detection performance drastically, especially on $AP_{S}$ . The FPS is evaluated on a single V100 GPU." + ], + "table_footnote": [], + "table_body": "
StudentMethodAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AR_1 \\)\\( AR_{10} \\)\\( AR_{100} \\)\\( AR_{500} \\)
RetinaNet-ResNet50Baseline26.2144.9027.100.525.3534.6337.21
ZoomInNet [24]27.1146.0228.090.535.4734.9837.66
ScaleKD29.4549.2829.970.535.9836.7438.65
RetinaNet-MobileNetV2Baseline21.7340.0122.950.495.1131.2434.05
ZoomInNet [24]22.4941.1424.210.505.1531.7834.91
ScaleKD26.0844.7626.980.525.3334.4837.03
", + "bbox": [ + 161, + 371, + 807, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Experimental results on VisDrone. We use ResNet101 as the teacher model.", + "bbox": [ + 232, + 506, + 733, + 520 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 546, + 200, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct quantitative analysis on two object detection datasets: COCO [23] and VisDrone [51]. COCO is a challenging object detection dataset with 80 categories. VisDrone is a dataset specialized to drone-shot image detection, in which most of the objects in this dataset are small.", + "bbox": [ + 75, + 573, + 468, + 650 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 662, + 294, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For COCO, we adopt the standard $1 \\times$ schedule and kept all the hyperparameters for the student model training unchanged for fair comparisons. The models are evaluated on validation set 2017. On the VisDrone dataset, we follow the which equally split one image into four non-overlapping patches and process them independently during training. The training procedure is also kept the same as in previous literature. We use $2 \\times$ of standard input resolution for all experiments for the teacher model, useless otherwise indicated. Mean average precision (AP) is used as the major metric for all experiments. We use an Adam optimizer with an initial learning rate of $3 \\mathrm{e} - 4$ and a weight-decay of $1 \\mathrm{e} - 4$ to update the CSA module. There are three hyper-parameters in the total training objectives, we set $\\alpha = 0.07$ , $\\beta = 0.5$ ,", + "bbox": [ + 75, + 688, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\gamma = 0.2$ for all two-stage models, and $\\alpha = 0.01$ , $\\beta = 0.2$ , $\\gamma = 0.05$ for all one-stage models.", + "bbox": [ + 498, + 547, + 890, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 500, + 589, + 638, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we show the experimental results of the baseline detectors and our method on COCO and VisDrone datasets. We compare our approach with state-of-the-art distillation methods in the next section.", + "bbox": [ + 496, + 613, + 893, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "COCO. We conduct extensive experiments on COCO to validate the effectiveness of ScaleKD. We adopt our method on multiple mainstream baselines, including two-stage detection models (i.e., Faster RCNN [29], Cascade RCNN [2]), and one-stage detection models (i.e., RetinaNet [22], FCOS [36], Reppoints [42]). For all experiments, we use the ResNet101 backbone as a teacher model. The ScaleKD achieves noticeable improvement on all methods without introducing any extra computational cost at inference. It is worth noting that the performance boost on $AP_{S}$ is overwhelming. For instance, on FCOS the $AP_{S}$ is increased by 7.2, and on RetinaNet the $AP_{S}$ is increased by 5.9. Also, our approach is not only effective for SOD but improves the AP in general.", + "bbox": [ + 496, + 688, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19728", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/754bbbbad22d63d092e824db88af0a54989f0232a79a5eb3297d7e7c713f596b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TaskMethodTypeResolution\\(AP^{mask}\\)\\(AP^{mask}_{50}\\)\\(AP^{mask}_{75}\\)\\(AP^{mask}_{S}\\)\\(AP^{mask}_{M}\\)\\(AP^{mask}_{L}\\)
Instance SegmentationMask-RCNNTeacherHigh35.456.537.919.238.648.4
BaselineLow31.651.233.410.833.650.9
OursLow33.8+2.253.2+2.035.7+2.313.1+2.335.5+1.952.3+2.4
Keypoint DetectionMask-RCNNTeacherHigh66.487.172.863.572.073.6
BaselineLow62.586.168.256.572.970.1
OursLow64.1+1.687.6+1.570.1+1.958.7+2.274.2+1.771.2+1.1
", + "bbox": [ + 91, + 88, + 880, + 219 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/02b0bd64ab35fe7d3857ed9e547b8ff93bf95c06a906eee5e8cce6804394b0cf.jpg", + "table_caption": [ + "Table 4. Performance comparisons with baselines on instance segmentation and keypoint detection. The high resolution means 800px, and the low resolution represents 400px, both on the short side. The baseline refers to the standard training." + ], + "table_footnote": [], + "table_body": "
MethodAP\\(AP_S\\)\\(\\Delta AP_S\\)\\(AP_M\\)\\(\\Delta AP_M\\)\\(AP_L\\)\\(\\Delta AP_L\\)
GFL ResNet50
Baseline40.123.3-44.4-52.5-
FitNet [30]40.723.7+0.444.4+0.053.2+0.7
OD [5]41.123.3+0.045.4+1.053.1+0.6
DeFeat [11]40.824.3+1.044.6+0.253.7+0.5
GID [7]41.524.3+1.045.7+1.353.6+1.1
LD [46]42.124.5+1.246.2+1.854.8+2.3
ScaleKD42.525.9+2.646.2+1.854.6+2.1
RetinaNet ResNet50
Baseline37.420.0-40.7-49.7-
FKD [44]39.621.4+1.442.5+1.851.5+1.8
LGD [45]38.323.2+3.242.0+1.350.0+0.3
FGFI [41]38.621.4+1.442.5+1.851.5+1.8
GID [7]39.122.8+2.843.1+2.452.3+2.4
CLSD [12]40.723.1+3.144.7+4.053.8+4.1
ScaleKD41.724.8+4.844.7+4.053.9+4.2
FCOS ResNet50
Baseline38.521.9-42.8-49.7-
LD [46]40.423.7+1.844.3+1.552.2+2.5
GID [7]42.025.6+3.745.8+3.054.2+4.5
FGFI [41]42.127.0+5.146.0+3.254.6+4.9
ScaleKD42.727.8+5.945.7+2.954.7+5.0
", + "bbox": [ + 81, + 280, + 486, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Comparison with state-of-the-art methods on COCOval2017. Our ScaleKD achieves pronounced improvement on $AP_{S}$ compared to SOTA.", + "bbox": [ + 75, + 648, + 470, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VisDrone. We demonstrate the experimental results on the VisDrone dataset in Table 3. We use ResNet-101 as the backbone for both experiments. We can clearly observe that our approach significantly improves the performance of the student model. Notably, after applying ScaleKD to RetinaNet-MobileNetV2 [22, 31], we achieve detection performance that is on par with the RetinaNet-ResNet50 (26.08 AP versus 26.21 AP), which adopt ResNet50, an 8x heavier backbone than MobileNetV2. Our method also increases both $AP$ for RetinaNet-ResNet-50 [13]. Since VisDrone is a dataset that contains mostly small objects,", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "these results support our claim that the proposed ScaleKD is extremely effective on SOD.", + "bbox": [ + 496, + 282, + 890, + 313 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also make a comparison with ZoomInNet [24], which combines feature level alignment and layer adaptation to distill a standard teacher to small object detectors. We evaluate ZoomInNet on both settings, similar to our approach. Indeed, ZoomInNet can slightly improve the AP on VisDrone, but the improvement is very marginal. In contrast, the ScaleKD achieve drastically higher results than their approach.", + "bbox": [ + 496, + 315, + 892, + 436 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Other Instance-Level Tasks with Small Input Resolution. Input resolution is a critical factor in achieving good performance on SOD. Typically, reduced input resolution can result in a considerable performance drop. Here we verify if our proposed ScaleKD can improve the SOD performance on instance-level tasks, even when the input resolution of the student model is low. The evaluation results are reported in Table 4. We notice that the low-resolution models trained with our approach outperform the baseline by a large margin, on both instance segmentation and keypoint detection, based on Mask-RCNN. This shows our ScaleKD is particularly good at predicting small objects, even when the number of effective pixels is small.", + "bbox": [ + 496, + 450, + 893, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 678, + 653, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with State-of-the-art knowledge distillation. In the last section, we validate the effectiveness of our proposed ScaleKD on two datasets compared to the trainfrom-scratch counterpart. This section compares ScaleKD to state-of-the-art KD methods on the COCO benchmark. For a fair comparison, we use the standard image resolution on teacher and the same teacher architecture, such that the teacher's performance is the same for all approaches. We compare ScaleKD to these SOTA methods on Generalized focal loss (GFL) [19], RetinaNet [22], and FCOS [36], respectively. All student models use ResNet50 as the backbone. We compare eight distillation methods, seven of them are KD methods that are designed for object detec", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19729", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/212e9727eca3e77310fb9bb383c0f6a2d105b9a6e3c617bbd451bae8da6f6caa.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCSAMSCAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓✗40.223.543.752.6
✓✓41.624.844.553.9
", + "bbox": [ + 93, + 88, + 452, + 162 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion, including FitNet [30], OD [5], LGD [45], DeFeat [11], GID [7], LD [46], FGFI [41], and CLSD [12].", + "bbox": [ + 75, + 233, + 467, + 263 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 presents the experimental results. We can observe that ScaleKD achieves superior performance on most evaluation metrics, i.e., on GFL-ResNet50, ScaleKD obtained a 2.8 higher AP score compared with baseline and 0.7 higher AP score compared to second best SOTA method (LD [46]). Furthermore, as we look at the $AP_{S}$ , the one that measures AP on small objects, we notice that our proposed method obtains a significantly better score than SOTA. For instance, ScaleKD improves $AP_{S}$ by 3.4, 4.8, and 5.9 on GFL, RetinaNet, and FCOS, respectively. These results indicate that ScaleKD helps compact student detectors on detecting small objects, and it is much more effective than KD methods designed for general object detection.", + "bbox": [ + 75, + 266, + 468, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Cross-Scale Assistant. We investigate the effectiveness of our proposed Cross-Scale Assistant module. We use standard image resolution for teachers in this section. We are primarily eager to know if CSA improves SOD performance and does the multi-scale cross-attention helps the student model. Table 6 gives empirical results. We can observe the CSA dramatically increase the AP score as well as $AP_{S}$ for the student RetinaNet model. Moreover, the MSC is critical to the performance. Compared to plain cross-attention, the MSC can improve the $AP$ by 1.4 and $AP_{S}$ by 1.3. It verifies the advantage of our proposed multi-scale cross-attention over plain cross-attention in our KD framework.", + "bbox": [ + 75, + 493, + 468, + 690 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation study of Scale-Decoupled Feature. Table 7 presents the ablation study of the SDF module. We use standard image resolution for teachers in this section. We mainly discuss two aspects: whether SDF improves the performance of SOD and whether the weight-sharing method is worth using. First, we evaluate SDF on COCO with RetinaNet-ResNet50 as the baseline model. The experimental results show that the SDF is indeed effective in improving overall AP and $AP$ for small objects. Besides, using separate weights for parallel branches does not bring noticeable improvement in terms of average AP. Thus, it is worth using the weight-sharing module to save memory costs.", + "bbox": [ + 75, + 704, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e0ed40d8e78d5868f9dc64f9e556bf0661cc14f2282d8d0f494d065afd6a0927.jpg", + "table_caption": [ + "Table 6. Ablation study for Cross-Scale Assistant. MSC: Multiscale Cross-Attention." + ], + "table_footnote": [], + "table_body": "
MethodSDFWSAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓X41.624.944.853.7
✓✓41.624.844.653.9
", + "bbox": [ + 516, + 88, + 877, + 164 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5af040c38ca2a4d120ef5f09dff59054581b24409f78943866cae0f19712ce9d.jpg", + "table_caption": [ + "Table 7. Ablation study for Scale-Decoupled Feature module. WS: weight-sharing." + ], + "table_footnote": [], + "table_body": "
MethodScaleKDAPAPSAPMAPL
ResNet-18X35.818.938.947.9
ResNet-18✓37.220.140.249.3
ResNet-34X38.921.542.851.4
ResNet-34✓40.823.145.153.7
", + "bbox": [ + 511, + 220, + 880, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Quantitative results of ScaleKD for diverse model complexity. We use ResNet101 as the teacher model.", + "bbox": [ + 498, + 332, + 890, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ScaleKD for Diverse Model Complexity. We further validate the effectiveness of our approach to diverse model complexity. Specifically, we evaluate COCO for two different student backbones, ResNet-18 and ResNet-34. Each model is distilled by a ResNet-101 detector. The results are presented in Table 8, which show that our method can effectively and stably improve the student model, regardless of the model complexity. This observation is contradicted by previous studies on image classification but consistent with the report on detection tasks. In particular, our approach improves the average AP by 1.2 and 2.5 on ResNet-18 and ResNet-34, respectively. Notably, the performance on small objects $(AP_S)$ is boosted tremendously by 2.3 and 2.1. These results verified that our method is generally effective on varying model sizes.", + "bbox": [ + 496, + 404, + 890, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion", + "text_level": 1, + "bbox": [ + 500, + 647, + 612, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Balancing inference speed and detection performance for small object detection is challenging. In this work, we propose a Scale-aware knowledge distillation that targets improving the performance of SOD via designed scale-decoupled feature distillation and cross-scale assistant. The former explicitly decouples multi-scale features, and the latter refines the teacher's bounding box noise for more informative knowledge in distillation. We evaluate two benchmarks, COCO 2017 and VisDrone, to demonstrate the effectiveness of our approach.", + "bbox": [ + 496, + 674, + 890, + 825 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was partially supported by the Science and Technology Innovation Action Plan of Shanghai under Grant 2251110540, and Shanghai Pujiang Program under Grant 21PJ1420300.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19730", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. Sod-mtgan: Small object detection via multi-task generative adversarial network. 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Student customized knowledge distillation: Bridging the gap between student and teacher." + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19732", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + }, + { + "type": "header", + "text": "In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5057-5066, 2021. 2", + "bbox": [ + 109, + 90, + 468, + 119 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19733", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ScaleKD_ Distilling Scale-Aware Knowledge in Small Object Detector/f4a95fb4-74c7-47ae-867c-7193aca0ac49_model.json b/2023/ScaleKD_ Distilling Scale-Aware Knowledge in Small Object Detector/f4a95fb4-74c7-47ae-867c-7193aca0ac49_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fd3ebb629ec017d6eb29f6f48b1381eded7521d4 --- /dev/null +++ b/2023/ScaleKD_ Distilling Scale-Aware Knowledge in Small Object Detector/f4a95fb4-74c7-47ae-867c-7193aca0ac49_model.json @@ -0,0 +1,1960 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.136, + 0.13, + 0.834, + 0.154 + ], + "angle": 0, + "content": "ScaleKD: Distilling Scale-Aware Knowledge in Small Object Detector" + }, + { + "type": "text", + "bbox": [ + 0.275, + 0.179, + 0.692, + 0.252 + ], + "angle": 0, + "content": "Yichen Zhu\\(^{1}\\), Qiqi Zhou\\(^{2,1}\\), Ning Liu\\(^{1}\\), Zhiyuan Xu\\(^{1}\\), Zhicai Ou\\(^{1}\\), Xiaofeng Mou\\(^{1}\\), Jian Tang\\(^{1,*}\\), Midea Group, \n\\(^{2}\\)Shanghai University of Electric Power" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.255, + 0.825, + 0.27 + ], + "angle": 0, + "content": "{zhuyc25, zhouqq31, lining22, xuzy70, zhicai.ou, mouxf, jiantang22}@midea.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.314, + 0.321 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.337, + 0.474, + 0.701 + ], + "angle": 0, + "content": "Despite the prominent success of general object detection, the performance and efficiency of Small Object Detection (SOD) are still unsatisfactory. Unlike existing works that struggle to balance the trade-off between inference speed and SOD performance, in this paper, we propose a novel Scale-aware Knowledge Distillation (ScaleKD), which transfers knowledge of a complex teacher model to a compact student model. We design two novel modules to boost the quality of knowledge transfer in distillation for SOD: 1) a scale-decoupled feature distillation module that disentangled teacher's feature representation into multiscale embedding that enables explicit feature mimicking of the student model on small objects. 2) a cross-scale assistant to refine the noisy and uninformative bounding boxes prediction student models, which can mislead the student model and impair the efficacy of knowledge distillation. A multi-scale cross-attention layer is established to capture the multi-scale semantic information to improve the student model. We conduct experiments on COCO and VisDrone datasets with diverse types of models, i.e., two-stage and one-stage detectors, to evaluate our proposed method. Our ScaleKD achieves superior performance on general detection performance and obtains spectacular improvement regarding the SOD performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.728, + 0.21, + 0.743 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.753, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Object detection is a fundamental task that has been developed over the past twenty-year in the computer vision community. Despite the state-of-the-art performance for general object detection having been conspicuously improved since the rise of deep learning, balancing the complexity-precision for small object detection is still an open question. Current works strive to refine feature fusion modules [9, 21], devise novel training schemes [32, 33]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.895, + 0.398 + ], + "angle": 0, + "content": "to explicitly train on small objects, design new neural architectures [20,39] to better extract small objects' features, and leverage increased input resolution to enhance representation quality [1, 49]. However, these approaches struggle to balance detection quality on small objects with computational costs at the inference stage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.895, + 0.748 + ], + "angle": 0, + "content": "The above reasons incentivize us to design a cost-free technique at test time to improve SOD performance. In the spirit of the eminent success of knowledge distillation (KD) on image data [14], we explore distillation methods for SOD. Typically, knowledge distillation opts for a complex, high-performance model (teacher) that transfers its knowledge to a compact, low-performance model (student). The student model can harness instructive information to enhance its representation learning ability. Nevertheless, unlocking this potential in SOD involves overcoming two challenges: 1) SOD usually suffers from noisy feature representations. Due to the nature of small objects, which generally take over a small region in the whole image, the feature representations of these small objects can be contaminated by the background and other instances with relatively larger sizes. 2) Object detectors have a low tolerance for noisy bounding boxes on small objects. It is inevitable that teacher models make incorrect predictions. Usually, student models can extract informative dark knowledge [14, 28] from imperfect predictions from the teacher. However, in SOD, small perturbations on the teacher's bounding box can dramatically impair SOD performance on the student detector (§3.2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.896, + 0.902 + ], + "angle": 0, + "content": "To this end, we propose Scale-aware Knowledge Distillation for small object detection (ScaleKD). Our proposed ScaleKD consists of two modules, a Scale-Decoupled Feature (SDF) distillation module and a Cross-Scale Assistant (CSA), to address the aforementioned two challenges correspondingly. The SDF is inspired by the crucial shortcoming of existing feature distillation methods, where the feature representations of objects with varying scales are coupled in a single embedding. It poses difficulty for the student to mimic small objects' features from the teacher model." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19723" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.094, + 0.881, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.329, + 0.893, + 0.358 + ], + "angle": 0, + "content": "Figure 1. The overview of Scale-aware Knowledge Distillation. It consists of a Scale-Decoupled Feature distillation module and a CrossScale Assistant module to improve small object detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.473, + 0.625 + ], + "angle": 0, + "content": "As a result, the proposed SDF aims to decouple a single-scale feature embedding into a multi-scale feature embedding. The multi-scale embedding is obtained by a parallel multi-branch convolutional block, where each branch deals with one scale. Our SDF allows the student model to better understand the feature knowledge from the perspective of object scale. Furthermore, we propose a learnable CSA to resolve the adverse effect of teachers' noisy bounding box prediction on small objects. The CSA comprises a multi-scale cross-attention module, where representations from the teacher and student models are mapped into a single feature embedding. The multi-scale query-key pair projects the teacher's features into multiple sizes, such that the fine-grained and low-level details can be preserved in CSA, which helps to produce suitable bounding box supervision for the student model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.809 + ], + "angle": 0, + "content": "We demonstrate the effectiveness of our approach on COCO object detection and VisDrone datasets. The experiments are conducted on multiple types of detectors, including two-stage detectors, anchor-based detectors, and anchor-free detectors, and have proven the generalizability of our approach. Our work offers a practical approach for industrial application on SOD as well as introduces a new perspective on designing scale-aware KD modules to improve object detectors. We further extend our method on instance-level detection tasks, such as instance segmentation and keypoint detection, demonstrating the superiority of our approach to dealing with small objects in vision tasks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.811, + 0.419, + 0.825 + ], + "angle": 0, + "content": "In summary, our contributions are the following:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.84, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- We propose Scale-Aware Knowledge Distillation (ScaleKD), a novel knowledge distillation framework to improve general detection and SOD performance without bringing extra computational costs at test time." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.384, + 0.892, + 0.474 + ], + "angle": 0, + "content": "- Our proposed ScaleKD not only exceeds state-of-the-art KD for object detection methods on general detection performance but also surpasses existing approaches on SOD by a large margin. Extended experiments on instance segmentation and keypoint detection further strengthen our method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.494, + 0.642, + 0.51 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.628 + ], + "angle": 0, + "content": "Knowledge Distillation. Knowledge distillation has become one of the most effective techniques for model compression [14]. It first trains a cumbersome teacher model and then transfers its knowledge to a lightweight student model. The common knowledge distillation approaches include distillation on output, logits [14], bounding box [16], and features [30, 52, 53]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Our work is also closely correlated to object detection, where knowledge distillation has shown effectiveness in detection tasks [3, 15, 35, 40, 47, 48]. In particular, FineGrained [5] is the first work to comprehensively present a KD framework for the object detection task. FKD [44] is the earliest work to adopt attention mechanisms to do feature distillation on object detectors. DeFeat [12] decoupled the foreground feature and background features based on the ground-truth binary mask and performed feature distillation on two features separately. FGFI [41] presents focal distillation, which combines DeFeat and Zhang et al. [44] works. ICD [17] considered conditional distillation of both classification and localization on very instances. Guo [12] investigates distilling image classifier instead of object detector to student detector, which complements existing feature-based distillation methods. Similar to ICD, GID [7] proposed an instance-selection module to transfer the teacher's most informative locations. LGD [45] pro" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19724" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.182 + ], + "angle": 0, + "content": "posed a teacher-free framework to distill object detectors without a concrete teacher model. Nevertheless, existing methods have largely overlooked the small objects. Our paper is the first work to design knowledge distillation specifically targeted to improve general object detection and small objects' performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.197, + 0.469, + 0.394 + ], + "angle": 0, + "content": "Small Object Detection. Recognizing small objects in the image is challenging, especially when localization and per-pixel classification are required. A naive approach is to increase the resolution [26]. Nevertheless, it brings tremendous computational costs in inference. Existing approaches mainly focus on applying strong data augmentation [18] or oversampling [4], incorporating context information [9, 21], fusing the features across layers [10, 38], performing scale-aware training [32, 33], adjusting resolution at test-time [37], or applying dilated convolution/large convolution [20, 39] to increase the receptive field. We refer interested readers for a more in-depth survey [6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Our approach is very different from previous methods, where we seek help with knowledge distillation to boost the performance of SOD. Our method benefits from the advantage of the distillation method, where 1) no extra computational costs are introduced at test time, and 2) neural architectures of the existing model do not need to be modified, a critical benefit in the practical scenario where engineering do not want to alter their networks architecture due to inconvenience on deployment." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.399, + 0.56 + ], + "angle": 0, + "content": "3. Scale-aware Knowledge Distillation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.69 + ], + "angle": 0, + "content": "This section provides a detailed description of our proposed distillation methods. Figure 1 gives a brief overview of ScaledKD, in which we illustrate the modules as follows: (1) A scale-decoupled feature distillation module that explicitly transfers representation on diverse scales to the student detector. (2) A cross-scale assistant refines the knowledge of object size between complex teacher and compact student." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Definition. In this section, we provide a notion of the components that we will use to describe our method. Considering an object detector \\(\\mathcal{G}^S:\\mathbb{R}^d\\to \\mathbb{R}^k\\) as a student and another predictor \\(\\mathcal{G}^T:\\mathbb{R}^d\\to \\mathbb{R}^k\\) as a teacher, where \\(d\\) and \\(k\\) are two feature dimensions. The former is a computationally efficient network with a relatively lower detection performance. The latter is a heavy model with relatively higher detection performance. Giving a training dataset \\(S = \\{(x_{i},y_{i})_{i = 1}^{n}\\} \\sim \\mathbb{P}^{n}\\) for distribution \\(\\mathbb{P}\\) over a set of instance \\(\\mathcal{X}\\). For small object detection, a common approach to improve SOD is to leverage a high-resolution image as input. In our case, we only consider using high-resolution images \\(\\chi^{hr}\\) for the teacher model, while" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.896, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.301, + 0.892, + 0.357 + ], + "angle": 0, + "content": "Figure 2. The scale-decouple feature module in ScaleKD. Note that the details of the student's scale-decoupled feature module are omitted due to limited space. In practice, it is symmetric to the teacher's counterpart." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.381, + 0.885, + 0.396 + ], + "angle": 0, + "content": "standard-resolution images are used for the student model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.405, + 0.816, + 0.421 + ], + "angle": 0, + "content": "3.1. Scale-Decoupled Feature Distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.428, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Preliminary. Modern object detectors harness FPN [21] to obtain the multi-scale semantic information from different levels of the backbone to enhance the model's feature learning ability on diverse object scales. A typical distillation approach is to transfer the knowledge of these features from teacher to student. Generally, we can formulate such distillation methods as:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.542, + 0.891, + 0.56 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f e a t}} = l \\left(\\mathcal {F} ^ {T}, f \\left(\\mathcal {F} ^ {S}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.63 + ], + "angle": 0, + "content": "where \\( F^T \\) and \\( F^S \\) are corresponding feature layers in the teacher and student model. \\( f(\\cdot) \\) is a mapping function to align the dimension of the feature map in student to teacher, and \\( l(\\cdot) \\) is any bounded loss, i.e., \\( l_2 \\) norm distance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Motivation. Although state-of-the-art KDs for object detection have developed various techniques, such as focal distillation [41], to enhance the quality of transferred knowledge, such methods treat all objects that have varying sizes equally during distillation. We identify that the key shortcoming of these methods on SOD is that the feature representation on diverse objects is entangled. It is a viable solution when object sizes are not small. However, the size of objects in the detection task varies significantly. The feature representation of small objects can be contaminated by large-region backgrounds and other instances with a relatively larger size. To resolve the issue, we propose a Scale-Decoupled Feature (SDF) distillation module to explicitly disentangled the teacher's feature map." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Methodology. As aforementioned, our goal is to disentangle the whole feature representation of the teacher" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19725" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.18 + ], + "angle": 0, + "content": "
MethodPerturbationAPAPSAPMAPL
Baseline036.921.240.848.4
Chen et al. [5]038.121.942.250.1
6 pixels37.721.142.450.2
12 pixels37.019.942.150.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.19, + 0.47, + 0.247 + ], + "angle": 0, + "content": "Table 1. Noisy and uninformative bounding boxes from the teacher can severely hurt students' performance. The perturbation is measured by a number of pixels, and it is added along the diagonal direction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.468, + 0.352 + ], + "angle": 0, + "content": "object detector into multiple parts, where each part only deals with similar object sizes. Presumably, such operations can force student detectors to comprehend not only the global knowledge of the entire image but also the scale-specific knowledge." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.468, + 0.595 + ], + "angle": 0, + "content": "To be specific, we obtain a feature embedding \\( Z^T \\) and \\( Z^S \\) in the last stage of the backbone for both the teacher and student networks. We intend to fully utilize the feature representation on diverse input scales. Thus, we adopt a multi-branch structure, where each branch uses a convolutional layer with different dilated rates. It is worth noting that the model tends to focus on small objects for the kernel with a small dilated rate and vice versa. In practice, we use residual blocks as in ResNet, which consist of three consecutive convolutional layers, i.e., 1x1, 3x3, and 1x1, along with a skip connection. For the 3x3 Conv layer, we use three different dilated rates {1, 2, 3} on three individual branches. An adapter layer, typically a multi-layer perception (MLP) layer, is stacked before this scale-decoupled feature module to align the dimensionality of feature presentation between the teacher and student model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.468, + 0.763 + ], + "angle": 0, + "content": "Usually, one can match the knowledge of the teacher model at a designated branch, i.e., the \\(3 \\times 3\\) Conv layer with a dilated rate of 1, to the corresponding feature branch in the student model via any distance minimization loss. One drawback is that these operations can be memory intensive. Therefore, we take inspiration from the weight-sharing network in neural architecture search [25, 34] and adopt a weight-sharing scale-decoupled feature. This is based on the fact that all three branches have the same operators. In practice, we only save a set of weights for three branches, dramatically reducing the training memory cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We also notice that using three individual losses to match three parallel branches between the teacher and student model can cause the practitioner to spend unnecessary effort on hyper-parameter tuning. As a result, for each branch, we use a flattened layer, namely a multi-layer perceptron, and concatenate three flattened layers together. During the distillation process, we adopt a sole 12 loss (denoted as \\( L_{feat} \\) in the later section) to minimize the distance of this concatenated flattened layer between the teacher and student" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.092, + 0.895, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Figure 3. The Cross-Scale Assistant (CSA) module. We adopt a multi-scale query-key pair to perform cross-attention with feature embedding in the student model. The learnable weights in CSA are updated via two separate classification and regression branches which are supervised by the ground truth label." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.892, + 0.424 + ], + "angle": 0, + "content": "model. the overview of the proposed module can be viewed in Figure 2. Notably, the student's scale-decoupled feature module mirrors the teacher's counterpart." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.433, + 0.7, + 0.447 + ], + "angle": 0, + "content": "3.2. Cross-Scale Assistant" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Preliminary. Our previous section introduces our proposed feature distillation to resolve the challenge of SOD. Other than feature distillation, another practical approach is the output-based KD, which transfers the teacher's prediction on classification and localization to the student as sources for auxiliary supervision. Our work primarily focuses on bounding box distillation, which can be considered a regression problem. In general, we can write such regression distillation as follow:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.601, + 0.891, + 0.619 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b b o x} = l _ {b b o x} \\left(\\mathcal {R} ^ {S}, \\mathcal {R} ^ {T}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.735 + ], + "angle": 0, + "content": "where \\(\\mathcal{R}^S\\) is the regression output of the student network, \\(\\mathcal{R}^T\\) is the predication of teacher network. This \\(l(\\cdot)\\) is the same as Equation 1, where any bounded loss can be applied. Conventionally, this bounded loss can be either \\(l_1\\), smoothed \\(l_1\\) or \\(l_2\\) loss, depending on the level of penalty that we wise to weight the error between the student's predication and the teacher's output." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Motivation. A key difference between small object detection and general object detection is that SOD is sensitive to noisy bounding boxes. Apparently, the teacher detector is incapable of making perfect predictions on every object. In general object detection, despite being inaccurate, student models can still retrieve informative knowledge from teachers' predictions on bounding boxes. Nevertheless, for small objects, noisy bounding box prediction in the teacher model can confuse the student model, which decreases the SOD performance. As proof" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19726" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "of concept, we deliberately add a slight deviation (6 and 12 pixels along the diagonal direction) and compare the mAP on small-scale objects of a vanilla teacher with a teacher that is slightly perturbed. As shown in Table 1, on RetinaNet baseline, the AP of small objects \\((AP_S)\\) of students drops consistently when perturbations are added, showing the sensitivity of student detector on teacher's bounding box prediction in SOD. Therefore, to build a trustworthy regression distillation module for SOD, one needs to minimize the adverse effect of poison bounding box knowledge in teachers. This does not mean that the teacher's predictions have to be perfect - otherwise, we can directly supervise the student with ground truth - we only need to refine the teacher's output to ensure that their knowledge is informative to the student [27, 50]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.333, + 0.47, + 0.409 + ], + "angle": 0, + "content": "Methodology. To address the aforementioned issue, we propose a Cross-Scale Assistant (CSA), which refines the teacher's knowledge and enables the student model to fetch instructive knowledge on objects with different scales." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.47, + 0.542 + ], + "angle": 0, + "content": "Our method is simple - we establish the CSA by a cross-attention module. During the cross-attention, a sequence of key and query tokens are generated in calculating KQ-attention within the teacher's knowledge and then mapped with the value tensor, the outputs from the student model, to obtain attentive regions in the feature with each corresponding query. This process is executed at every student pyramid scale to retrieve informative region-based features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.471, + 0.784 + ], + "angle": 0, + "content": "A naive choice is to use plain cross-attention [8]. Albeit, previous studies [43] identified that the standard cross-attention could focus on salient regions repetitively on different heads. Consequently, when large objects appear in the image, the cross-attention will redirect its attention to these large objects and ignore small objects. To this end, in contrast to the plain cross-attention, we developed a multiscale cross-attention layer, as shown in Figure 3. Notice that cross-attention extracts global information - for each query-key pair, a value is generated to highlight the most responsive region. We then split the query-key pair into multiple sub-pairs, where each sub-pair represents a set of object scales. As a result, our multi-scale query-key can enforce the attention module to focus on regions with diverse scales, such that all objects, especially the small objects, can attend to the feature learning process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Particularly, give an input sequence from teacher \\( F^T \\in \\mathbb{R}^{h \\times w \\times c} \\) and another input sequence from student \\( F^S \\in \\mathbb{R}^{h \\times w \\times c} \\), for simplicity, we assume two tensors have the same size. The \\( F^T \\) is projected into a query (Q) and key (K), and \\( F^S \\) is projected into value (V). The keys \\( K \\) and values \\( V \\) are down-sampled to different sizes for different heads indexed by \\( i \\). Thus, we formulate our multi-scale" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.725, + 0.106 + ], + "angle": 0, + "content": "cross-attention (MSC) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.647, + 0.116, + 0.892, + 0.136 + ], + "angle": 0, + "content": "\\[\nQ _ {i} = F ^ {S} W _ {i} ^ {Q} \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.143, + 0.892, + 0.162 + ], + "angle": 0, + "content": "\\[\nK _ {i} = M S C \\left(F ^ {T}, r _ {i}\\right) W _ {i} ^ {K}, V _ {i} = M S C \\left(F ^ {T}, r _ {i}\\right) W _ {i} ^ {V}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.167, + 0.892, + 0.184 + ], + "angle": 0, + "content": "\\[\nV _ {i} = V _ {i} + P \\left(V _ {i}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.189, + 0.892, + 0.281 + ], + "angle": 0, + "content": "where \\(MSC(\\cdot ,r_i)\\) is a MLP layer for aggregation in the \\(i\\)-th head with the down-sampling rate of \\(r_i\\), and \\(P(\\cdot)\\) is a depth-wise convolutional layer for projection. Compared with the standard cross-attention, more fine-grained and low-level details that are beneficial to SOD are preserved. Finally, we calculated the attention tensor by:" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.29, + 0.892, + 0.326 + ], + "angle": 0, + "content": "\\[\nh _ {i} = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {d _ {h}}} V _ {i}\\right) \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.892, + 0.514 + ], + "angle": 0, + "content": "where \\( d_h \\) is the dimension. Remember that the purpose of CSA is to bridge the cross-scale information between the teacher and student model to refine the bounding box supervision in KD. Therefore, we stacked head layers with the classification branch and regression branch to update the weights of these learnable modules. Our empirical analysis shows that the proposed CSA can provide more appropriate supervision on small objects bounding boxes during distillation. Because this is a learnable module, during distillation, we perform a weights update prior to the student model at each iteration through a standard training scheme and detection objectives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.636 + ], + "angle": 0, + "content": "In distillation, instead of transferring the teacher's output knowledge, we transfer the CSA's knowledge on both classification and regression branches to students. For the output-based distillation objectives, we follow [5] to have two loss functions \\( L_{cls} \\) and \\( L_{bbox} \\). We note that our method is also complementary to other output-based methods, such as LD [46], where all we need to do is simply replace the distillation objective." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.636, + 0.892, + 0.665 + ], + "angle": 0, + "content": "In summary, the total training objective for the student model is:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.678, + 0.892, + 0.695 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {t o t a l}} = \\alpha L _ {\\text {f e a t}} + \\beta L _ {\\text {c l s}} + \\gamma L _ {\\text {b b o x}} + L _ {\\text {d e t}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.868, + 0.719 + ], + "angle": 0, + "content": "where \\(L_{det}\\) is the standard training loss for the detector." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Besides the distillation loss and detection loss for optimizing student detectors, we further ensure the instructive representation quality and consistency with student representations by sharing the detection head for supervision. Moreover, the CSA combines the feature of both teacher and student. As a result, a randomly initialized student detector can cause unstable training of CSA. Thus, we first warm up the student model for 30k iterations since it could be detrimental when the instructive knowledge is optimized insufficiently. The student detector backbone is frozen in early 10k iterations under \\(1 \\times\\) training schedule and 20k for \\(2 \\times\\) training schedule." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19727" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.163, + 0.089, + 0.807, + 0.318 + ], + "angle": 0, + "content": "
MethodBackboneAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)FPSParams (M)
Faster-RCNN [29] + ScaleKDResNet5038.459.042.021.542.150.320.143.57
43.164.048.226.148.058.8
Faster-RCNN [29] + ScaleKDMobileNetV227.344.728.914.629.635.712.932.61
30.848.732.918.834.242.2
Cascade-RCNN [2] + ScaleKDResNet5041.059.444.422.744.454.318.971.22
44.963.248.825.748.159.2
RetinaNet [22] + ScaleKDResNet5037.456.739.620.040.749.717.437.74
42.861.144.625.945.454.9
FOCS [36] + ScaleKDResNet5038.557.741.021.942.848.623.936.15
44.061.641.629.146.956.2
RepPoints [42] + ScaleKDResNet5038.659.641.622.542.250.418.236.62
42.963.846.825.747.156.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.33, + 0.894, + 0.361 + ], + "angle": 0, + "content": "Table 2. Comparison with state-of-the-art methods KD-Det on COCO val2017 datasets. Our approach appear to improve the detection performance drastically, especially on \\(AP_{S}\\). The FPS is evaluated on a single V100 GPU." + }, + { + "type": "table", + "bbox": [ + 0.163, + 0.372, + 0.808, + 0.497 + ], + "angle": 0, + "content": "
StudentMethodAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AR_1 \\)\\( AR_{10} \\)\\( AR_{100} \\)\\( AR_{500} \\)
RetinaNet-ResNet50Baseline26.2144.9027.100.525.3534.6337.21
ZoomInNet [24]27.1146.0228.090.535.4734.9837.66
ScaleKD29.4549.2829.970.535.9836.7438.65
RetinaNet-MobileNetV2Baseline21.7340.0122.950.495.1131.2434.05
ZoomInNet [24]22.4941.1424.210.505.1531.7834.91
ScaleKD26.0844.7626.980.525.3334.4837.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.233, + 0.507, + 0.735, + 0.521 + ], + "angle": 0, + "content": "Table 3. Experimental results on VisDrone. We use ResNet101 as the teacher model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.547, + 0.202, + 0.563 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.574, + 0.47, + 0.651 + ], + "angle": 0, + "content": "We conduct quantitative analysis on two object detection datasets: COCO [23] and VisDrone [51]. COCO is a challenging object detection dataset with 80 categories. VisDrone is a dataset specialized to drone-shot image detection, in which most of the objects in this dataset are small." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.295, + 0.681 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.903 + ], + "angle": 0, + "content": "For COCO, we adopt the standard \\(1 \\times\\) schedule and kept all the hyperparameters for the student model training unchanged for fair comparisons. The models are evaluated on validation set 2017. On the VisDrone dataset, we follow the which equally split one image into four non-overlapping patches and process them independently during training. The training procedure is also kept the same as in previous literature. We use \\(2 \\times\\) of standard input resolution for all experiments for the teacher model, useless otherwise indicated. Mean average precision (AP) is used as the major metric for all experiments. We use an Adam optimizer with an initial learning rate of \\(3 \\mathrm{e} - 4\\) and a weight-decay of \\(1 \\mathrm{e} - 4\\) to update the CSA module. There are three hyper-parameters in the total training objectives, we set \\(\\alpha = 0.07\\), \\(\\beta = 0.5\\)," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.548, + 0.892, + 0.579 + ], + "angle": 0, + "content": "\\(\\gamma = 0.2\\) for all two-stage models, and \\(\\alpha = 0.01\\), \\(\\beta = 0.2\\), \\(\\gamma = 0.05\\) for all one-stage models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.64, + 0.605 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.894, + 0.675 + ], + "angle": 0, + "content": "In this section, we show the experimental results of the baseline detectors and our method on COCO and VisDrone datasets. We compare our approach with state-of-the-art distillation methods in the next section." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.902 + ], + "angle": 0, + "content": "COCO. We conduct extensive experiments on COCO to validate the effectiveness of ScaleKD. We adopt our method on multiple mainstream baselines, including two-stage detection models (i.e., Faster RCNN [29], Cascade RCNN [2]), and one-stage detection models (i.e., RetinaNet [22], FCOS [36], Reppoints [42]). For all experiments, we use the ResNet101 backbone as a teacher model. The ScaleKD achieves noticeable improvement on all methods without introducing any extra computational cost at inference. It is worth noting that the performance boost on \\(AP_{S}\\) is overwhelming. For instance, on FCOS the \\(AP_{S}\\) is increased by 7.2, and on RetinaNet the \\(AP_{S}\\) is increased by 5.9. Also, our approach is not only effective for SOD but improves the AP in general." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19728" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.089, + 0.882, + 0.22 + ], + "angle": 0, + "content": "
TaskMethodTypeResolution\\(AP^{mask}\\)\\(AP^{mask}_{50}\\)\\(AP^{mask}_{75}\\)\\(AP^{mask}_{S}\\)\\(AP^{mask}_{M}\\)\\(AP^{mask}_{L}\\)
Instance SegmentationMask-RCNNTeacherHigh35.456.537.919.238.648.4
BaselineLow31.651.233.410.833.650.9
OursLow33.8+2.253.2+2.035.7+2.313.1+2.335.5+1.952.3+2.4
Keypoint DetectionMask-RCNNTeacherHigh66.487.172.863.572.073.6
BaselineLow62.586.168.256.572.970.1
OursLow64.1+1.687.6+1.570.1+1.958.7+2.274.2+1.771.2+1.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.229, + 0.893, + 0.259 + ], + "angle": 0, + "content": "Table 4. Performance comparisons with baselines on instance segmentation and keypoint detection. The high resolution means 800px, and the low resolution represents 400px, both on the short side. The baseline refers to the standard training." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.281, + 0.487, + 0.64 + ], + "angle": 0, + "content": "
MethodAP\\(AP_S\\)\\(\\Delta AP_S\\)\\(AP_M\\)\\(\\Delta AP_M\\)\\(AP_L\\)\\(\\Delta AP_L\\)
GFL ResNet50
Baseline40.123.3-44.4-52.5-
FitNet [30]40.723.7+0.444.4+0.053.2+0.7
OD [5]41.123.3+0.045.4+1.053.1+0.6
DeFeat [11]40.824.3+1.044.6+0.253.7+0.5
GID [7]41.524.3+1.045.7+1.353.6+1.1
LD [46]42.124.5+1.246.2+1.854.8+2.3
ScaleKD42.525.9+2.646.2+1.854.6+2.1
RetinaNet ResNet50
Baseline37.420.0-40.7-49.7-
FKD [44]39.621.4+1.442.5+1.851.5+1.8
LGD [45]38.323.2+3.242.0+1.350.0+0.3
FGFI [41]38.621.4+1.442.5+1.851.5+1.8
GID [7]39.122.8+2.843.1+2.452.3+2.4
CLSD [12]40.723.1+3.144.7+4.053.8+4.1
ScaleKD41.724.8+4.844.7+4.053.9+4.2
FCOS ResNet50
Baseline38.521.9-42.8-49.7-
LD [46]40.423.7+1.844.3+1.552.2+2.5
GID [7]42.025.6+3.745.8+3.054.2+4.5
FGFI [41]42.127.0+5.146.0+3.254.6+4.9
ScaleKD42.727.8+5.945.7+2.954.7+5.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.65, + 0.472, + 0.692 + ], + "angle": 0, + "content": "Table 5. Comparison with state-of-the-art methods on COCOval2017. Our ScaleKD achieves pronounced improvement on \\(AP_{S}\\) compared to SOTA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "VisDrone. We demonstrate the experimental results on the VisDrone dataset in Table 3. We use ResNet-101 as the backbone for both experiments. We can clearly observe that our approach significantly improves the performance of the student model. Notably, after applying ScaleKD to RetinaNet-MobileNetV2 [22, 31], we achieve detection performance that is on par with the RetinaNet-ResNet50 (26.08 AP versus 26.21 AP), which adopt ResNet50, an 8x heavier backbone than MobileNetV2. Our method also increases both \\(AP\\) for RetinaNet-ResNet-50 [13]. Since VisDrone is a dataset that contains mostly small objects," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.314 + ], + "angle": 0, + "content": "these results support our claim that the proposed ScaleKD is extremely effective on SOD." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.893, + 0.438 + ], + "angle": 0, + "content": "We also make a comparison with ZoomInNet [24], which combines feature level alignment and layer adaptation to distill a standard teacher to small object detectors. We evaluate ZoomInNet on both settings, similar to our approach. Indeed, ZoomInNet can slightly improve the AP on VisDrone, but the improvement is very marginal. In contrast, the ScaleKD achieve drastically higher results than their approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.895, + 0.664 + ], + "angle": 0, + "content": "Results on Other Instance-Level Tasks with Small Input Resolution. Input resolution is a critical factor in achieving good performance on SOD. Typically, reduced input resolution can result in a considerable performance drop. Here we verify if our proposed ScaleKD can improve the SOD performance on instance-level tasks, even when the input resolution of the student model is low. The evaluation results are reported in Table 4. We notice that the low-resolution models trained with our approach outperform the baseline by a large margin, on both instance segmentation and keypoint detection, based on Mask-RCNN. This shows our ScaleKD is particularly good at predicting small objects, even when the number of effective pixels is small." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.655, + 0.696 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Comparison with State-of-the-art knowledge distillation. In the last section, we validate the effectiveness of our proposed ScaleKD on two datasets compared to the trainfrom-scratch counterpart. This section compares ScaleKD to state-of-the-art KD methods on the COCO benchmark. For a fair comparison, we use the standard image resolution on teacher and the same teacher architecture, such that the teacher's performance is the same for all approaches. We compare ScaleKD to these SOTA methods on Generalized focal loss (GFL) [19], RetinaNet [22], and FCOS [36], respectively. All student models use ResNet50 as the backbone. We compare eight distillation methods, seven of them are KD methods that are designed for object detec" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19729" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.094, + 0.089, + 0.454, + 0.163 + ], + "angle": 0, + "content": "
MethodCSAMSCAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓✗40.223.543.752.6
✓✓41.624.844.553.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.173, + 0.47, + 0.203 + ], + "angle": 0, + "content": "Table 6. Ablation study for Cross-Scale Assistant. MSC: Multiscale Cross-Attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.468, + 0.265 + ], + "angle": 0, + "content": "tion, including FitNet [30], OD [5], LGD [45], DeFeat [11], GID [7], LD [46], FGFI [41], and CLSD [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.47, + 0.478 + ], + "angle": 0, + "content": "Table 5 presents the experimental results. We can observe that ScaleKD achieves superior performance on most evaluation metrics, i.e., on GFL-ResNet50, ScaleKD obtained a 2.8 higher AP score compared with baseline and 0.7 higher AP score compared to second best SOTA method (LD [46]). Furthermore, as we look at the \\(AP_{S}\\), the one that measures AP on small objects, we notice that our proposed method obtains a significantly better score than SOTA. For instance, ScaleKD improves \\(AP_{S}\\) by 3.4, 4.8, and 5.9 on GFL, RetinaNet, and FCOS, respectively. These results indicate that ScaleKD helps compact student detectors on detecting small objects, and it is much more effective than KD methods designed for general object detection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.494, + 0.47, + 0.691 + ], + "angle": 0, + "content": "Impact of Cross-Scale Assistant. We investigate the effectiveness of our proposed Cross-Scale Assistant module. We use standard image resolution for teachers in this section. We are primarily eager to know if CSA improves SOD performance and does the multi-scale cross-attention helps the student model. Table 6 gives empirical results. We can observe the CSA dramatically increase the AP score as well as \\(AP_{S}\\) for the student RetinaNet model. Moreover, the MSC is critical to the performance. Compared to plain cross-attention, the MSC can improve the \\(AP\\) by 1.4 and \\(AP_{S}\\) by 1.3. It verifies the advantage of our proposed multi-scale cross-attention over plain cross-attention in our KD framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Ablation study of Scale-Decoupled Feature. Table 7 presents the ablation study of the SDF module. We use standard image resolution for teachers in this section. We mainly discuss two aspects: whether SDF improves the performance of SOD and whether the weight-sharing method is worth using. First, we evaluate SDF on COCO with RetinaNet-ResNet50 as the baseline model. The experimental results show that the SDF is indeed effective in improving overall AP and \\(AP\\) for small objects. Besides, using separate weights for parallel branches does not bring noticeable improvement in terms of average AP. Thus, it is worth using the weight-sharing module to save memory costs." + }, + { + "type": "table", + "bbox": [ + 0.517, + 0.089, + 0.878, + 0.165 + ], + "angle": 0, + "content": "
MethodSDFWSAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓X41.624.944.853.7
✓✓41.624.844.653.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.175, + 0.89, + 0.204 + ], + "angle": 0, + "content": "Table 7. Ablation study for Scale-Decoupled Feature module. WS: weight-sharing." + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.221, + 0.882, + 0.322 + ], + "angle": 0, + "content": "
MethodScaleKDAPAPSAPMAPL
ResNet-18X35.818.938.947.9
ResNet-18✓37.220.140.249.3
ResNet-34X38.921.542.851.4
ResNet-34✓40.823.145.153.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.333, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Table 8. Quantitative results of ScaleKD for diverse model complexity. We use ResNet101 as the teacher model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.632 + ], + "angle": 0, + "content": "ScaleKD for Diverse Model Complexity. We further validate the effectiveness of our approach to diverse model complexity. Specifically, we evaluate COCO for two different student backbones, ResNet-18 and ResNet-34. Each model is distilled by a ResNet-101 detector. The results are presented in Table 8, which show that our method can effectively and stably improve the student model, regardless of the model complexity. This observation is contradicted by previous studies on image classification but consistent with the report on detection tasks. In particular, our approach improves the average AP by 1.2 and 2.5 on ResNet-18 and ResNet-34, respectively. Notably, the performance on small objects \\((AP_S)\\) is boosted tremendously by 2.3 and 2.1. These results verified that our method is generally effective on varying model sizes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.614, + 0.664 + ], + "angle": 0, + "content": "5. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.827 + ], + "angle": 0, + "content": "Balancing inference speed and detection performance for small object detection is challenging. In this work, we propose a Scale-aware knowledge distillation that targets improving the performance of SOD via designed scale-decoupled feature distillation and cross-scale assistant. The former explicitly decouples multi-scale features, and the latter refines the teacher's bounding box noise for more informative knowledge in distillation. We evaluate two benchmarks, COCO 2017 and VisDrone, to demonstrate the effectiveness of our approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: This work was partially supported by the Science and Technology Innovation Action Plan of Shanghai under Grant 2251110540, and Shanghai Pujiang Program under Grant 21PJ1420300." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19730" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. Sod-mtgan: Small object detection via multi-task generative adversarial network. 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Unlike existing works that struggle to balance the trade-off between inference speed and SOD performance, in this paper, we propose a novel Scale-aware Knowledge Distillation (ScaleKD), which transfers knowledge of a complex teacher model to a compact student model. We design two novel modules to boost the quality of knowledge transfer in distillation for SOD: 1) a scale-decoupled feature distillation module that disentangled teacher's feature representation into multiscale embedding that enables explicit feature mimicking of the student model on small objects. 2) a cross-scale assistant to refine the noisy and uninformative bounding boxes prediction student models, which can mislead the student model and impair the efficacy of knowledge distillation. A multi-scale cross-attention layer is established to capture the multi-scale semantic information to improve the student model. We conduct experiments on COCO and VisDrone datasets with diverse types of models, i.e., two-stage and one-stage detectors, to evaluate our proposed method. Our ScaleKD achieves superior performance on general detection performance and obtains spectacular improvement regarding the SOD performance. + +# 1. Introduction + +Object detection is a fundamental task that has been developed over the past twenty-year in the computer vision community. Despite the state-of-the-art performance for general object detection having been conspicuously improved since the rise of deep learning, balancing the complexity-precision for small object detection is still an open question. Current works strive to refine feature fusion modules [9, 21], devise novel training schemes [32, 33] + +to explicitly train on small objects, design new neural architectures [20,39] to better extract small objects' features, and leverage increased input resolution to enhance representation quality [1, 49]. However, these approaches struggle to balance detection quality on small objects with computational costs at the inference stage. + +The above reasons incentivize us to design a cost-free technique at test time to improve SOD performance. In the spirit of the eminent success of knowledge distillation (KD) on image data [14], we explore distillation methods for SOD. Typically, knowledge distillation opts for a complex, high-performance model (teacher) that transfers its knowledge to a compact, low-performance model (student). The student model can harness instructive information to enhance its representation learning ability. Nevertheless, unlocking this potential in SOD involves overcoming two challenges: 1) SOD usually suffers from noisy feature representations. Due to the nature of small objects, which generally take over a small region in the whole image, the feature representations of these small objects can be contaminated by the background and other instances with relatively larger sizes. 2) Object detectors have a low tolerance for noisy bounding boxes on small objects. It is inevitable that teacher models make incorrect predictions. Usually, student models can extract informative dark knowledge [14, 28] from imperfect predictions from the teacher. However, in SOD, small perturbations on the teacher's bounding box can dramatically impair SOD performance on the student detector (§3.2). + +To this end, we propose Scale-aware Knowledge Distillation for small object detection (ScaleKD). Our proposed ScaleKD consists of two modules, a Scale-Decoupled Feature (SDF) distillation module and a Cross-Scale Assistant (CSA), to address the aforementioned two challenges correspondingly. The SDF is inspired by the crucial shortcoming of existing feature distillation methods, where the feature representations of objects with varying scales are coupled in a single embedding. It poses difficulty for the student to mimic small objects' features from the teacher model. + +![](images/40b51e808c002a2c17fb7a4e8ebc123238468ba844064fbef8bcd7cb162091fe.jpg) +Figure 1. The overview of Scale-aware Knowledge Distillation. It consists of a Scale-Decoupled Feature distillation module and a CrossScale Assistant module to improve small object detection. + +As a result, the proposed SDF aims to decouple a single-scale feature embedding into a multi-scale feature embedding. The multi-scale embedding is obtained by a parallel multi-branch convolutional block, where each branch deals with one scale. Our SDF allows the student model to better understand the feature knowledge from the perspective of object scale. Furthermore, we propose a learnable CSA to resolve the adverse effect of teachers' noisy bounding box prediction on small objects. The CSA comprises a multi-scale cross-attention module, where representations from the teacher and student models are mapped into a single feature embedding. The multi-scale query-key pair projects the teacher's features into multiple sizes, such that the fine-grained and low-level details can be preserved in CSA, which helps to produce suitable bounding box supervision for the student model. + +We demonstrate the effectiveness of our approach on COCO object detection and VisDrone datasets. The experiments are conducted on multiple types of detectors, including two-stage detectors, anchor-based detectors, and anchor-free detectors, and have proven the generalizability of our approach. Our work offers a practical approach for industrial application on SOD as well as introduces a new perspective on designing scale-aware KD modules to improve object detectors. We further extend our method on instance-level detection tasks, such as instance segmentation and keypoint detection, demonstrating the superiority of our approach to dealing with small objects in vision tasks. + +In summary, our contributions are the following: + +- We propose Scale-Aware Knowledge Distillation (ScaleKD), a novel knowledge distillation framework to improve general detection and SOD performance without bringing extra computational costs at test time. + +- Our proposed ScaleKD not only exceeds state-of-the-art KD for object detection methods on general detection performance but also surpasses existing approaches on SOD by a large margin. Extended experiments on instance segmentation and keypoint detection further strengthen our method. + +# 2. Related Work + +Knowledge Distillation. Knowledge distillation has become one of the most effective techniques for model compression [14]. It first trains a cumbersome teacher model and then transfers its knowledge to a lightweight student model. The common knowledge distillation approaches include distillation on output, logits [14], bounding box [16], and features [30, 52, 53]. + +Our work is also closely correlated to object detection, where knowledge distillation has shown effectiveness in detection tasks [3, 15, 35, 40, 47, 48]. In particular, FineGrained [5] is the first work to comprehensively present a KD framework for the object detection task. FKD [44] is the earliest work to adopt attention mechanisms to do feature distillation on object detectors. DeFeat [12] decoupled the foreground feature and background features based on the ground-truth binary mask and performed feature distillation on two features separately. FGFI [41] presents focal distillation, which combines DeFeat and Zhang et al. [44] works. ICD [17] considered conditional distillation of both classification and localization on very instances. Guo [12] investigates distilling image classifier instead of object detector to student detector, which complements existing feature-based distillation methods. Similar to ICD, GID [7] proposed an instance-selection module to transfer the teacher's most informative locations. LGD [45] pro + +posed a teacher-free framework to distill object detectors without a concrete teacher model. Nevertheless, existing methods have largely overlooked the small objects. Our paper is the first work to design knowledge distillation specifically targeted to improve general object detection and small objects' performance. + +Small Object Detection. Recognizing small objects in the image is challenging, especially when localization and per-pixel classification are required. A naive approach is to increase the resolution [26]. Nevertheless, it brings tremendous computational costs in inference. Existing approaches mainly focus on applying strong data augmentation [18] or oversampling [4], incorporating context information [9, 21], fusing the features across layers [10, 38], performing scale-aware training [32, 33], adjusting resolution at test-time [37], or applying dilated convolution/large convolution [20, 39] to increase the receptive field. We refer interested readers for a more in-depth survey [6]. + +Our approach is very different from previous methods, where we seek help with knowledge distillation to boost the performance of SOD. Our method benefits from the advantage of the distillation method, where 1) no extra computational costs are introduced at test time, and 2) neural architectures of the existing model do not need to be modified, a critical benefit in the practical scenario where engineering do not want to alter their networks architecture due to inconvenience on deployment. + +# 3. Scale-aware Knowledge Distillation + +This section provides a detailed description of our proposed distillation methods. Figure 1 gives a brief overview of ScaledKD, in which we illustrate the modules as follows: (1) A scale-decoupled feature distillation module that explicitly transfers representation on diverse scales to the student detector. (2) A cross-scale assistant refines the knowledge of object size between complex teacher and compact student. + +Definition. In this section, we provide a notion of the components that we will use to describe our method. Considering an object detector $\mathcal{G}^S:\mathbb{R}^d\to \mathbb{R}^k$ as a student and another predictor $\mathcal{G}^T:\mathbb{R}^d\to \mathbb{R}^k$ as a teacher, where $d$ and $k$ are two feature dimensions. The former is a computationally efficient network with a relatively lower detection performance. The latter is a heavy model with relatively higher detection performance. Giving a training dataset $S = \{(x_{i},y_{i})_{i = 1}^{n}\} \sim \mathbb{P}^{n}$ for distribution $\mathbb{P}$ over a set of instance $\mathcal{X}$ . For small object detection, a common approach to improve SOD is to leverage a high-resolution image as input. In our case, we only consider using high-resolution images $\chi^{hr}$ for the teacher model, while + +![](images/5dcacf5fe2c743cb4679a500605c69076f5374f3c3873e9cd002cf8e7c5fa8ab.jpg) +Figure 2. The scale-decouple feature module in ScaleKD. Note that the details of the student's scale-decoupled feature module are omitted due to limited space. In practice, it is symmetric to the teacher's counterpart. + +standard-resolution images are used for the student model. + +# 3.1. Scale-Decoupled Feature Distillation + +Preliminary. Modern object detectors harness FPN [21] to obtain the multi-scale semantic information from different levels of the backbone to enhance the model's feature learning ability on diverse object scales. A typical distillation approach is to transfer the knowledge of these features from teacher to student. Generally, we can formulate such distillation methods as: + +$$ +\mathcal {L} _ {\text {f e a t}} = l \left(\mathcal {F} ^ {T}, f \left(\mathcal {F} ^ {S}\right)\right) \tag {1} +$$ + +where $F^T$ and $F^S$ are corresponding feature layers in the teacher and student model. $f(\cdot)$ is a mapping function to align the dimension of the feature map in student to teacher, and $l(\cdot)$ is any bounded loss, i.e., $l_2$ norm distance. + +Motivation. Although state-of-the-art KDs for object detection have developed various techniques, such as focal distillation [41], to enhance the quality of transferred knowledge, such methods treat all objects that have varying sizes equally during distillation. We identify that the key shortcoming of these methods on SOD is that the feature representation on diverse objects is entangled. It is a viable solution when object sizes are not small. However, the size of objects in the detection task varies significantly. The feature representation of small objects can be contaminated by large-region backgrounds and other instances with a relatively larger size. To resolve the issue, we propose a Scale-Decoupled Feature (SDF) distillation module to explicitly disentangled the teacher's feature map. + +Methodology. As aforementioned, our goal is to disentangle the whole feature representation of the teacher + +
MethodPerturbationAPAPSAPMAPL
Baseline036.921.240.848.4
Chen et al. [5]038.121.942.250.1
6 pixels37.721.142.450.2
12 pixels37.019.942.150.0
+ +Table 1. Noisy and uninformative bounding boxes from the teacher can severely hurt students' performance. The perturbation is measured by a number of pixels, and it is added along the diagonal direction. + +object detector into multiple parts, where each part only deals with similar object sizes. Presumably, such operations can force student detectors to comprehend not only the global knowledge of the entire image but also the scale-specific knowledge. + +To be specific, we obtain a feature embedding $Z^T$ and $Z^S$ in the last stage of the backbone for both the teacher and student networks. We intend to fully utilize the feature representation on diverse input scales. Thus, we adopt a multi-branch structure, where each branch uses a convolutional layer with different dilated rates. It is worth noting that the model tends to focus on small objects for the kernel with a small dilated rate and vice versa. In practice, we use residual blocks as in ResNet, which consist of three consecutive convolutional layers, i.e., 1x1, 3x3, and 1x1, along with a skip connection. For the 3x3 Conv layer, we use three different dilated rates {1, 2, 3} on three individual branches. An adapter layer, typically a multi-layer perception (MLP) layer, is stacked before this scale-decoupled feature module to align the dimensionality of feature presentation between the teacher and student model. + +Usually, one can match the knowledge of the teacher model at a designated branch, i.e., the $3 \times 3$ Conv layer with a dilated rate of 1, to the corresponding feature branch in the student model via any distance minimization loss. One drawback is that these operations can be memory intensive. Therefore, we take inspiration from the weight-sharing network in neural architecture search [25, 34] and adopt a weight-sharing scale-decoupled feature. This is based on the fact that all three branches have the same operators. In practice, we only save a set of weights for three branches, dramatically reducing the training memory cost. + +We also notice that using three individual losses to match three parallel branches between the teacher and student model can cause the practitioner to spend unnecessary effort on hyper-parameter tuning. As a result, for each branch, we use a flattened layer, namely a multi-layer perceptron, and concatenate three flattened layers together. During the distillation process, we adopt a sole 12 loss (denoted as $L_{feat}$ in the later section) to minimize the distance of this concatenated flattened layer between the teacher and student + +![](images/62781c20948e00e9925305a4cabf4cd75673e7c904b96a6834cedaa416f4049b.jpg) +Figure 3. The Cross-Scale Assistant (CSA) module. We adopt a multi-scale query-key pair to perform cross-attention with feature embedding in the student model. The learnable weights in CSA are updated via two separate classification and regression branches which are supervised by the ground truth label. + +model. the overview of the proposed module can be viewed in Figure 2. Notably, the student's scale-decoupled feature module mirrors the teacher's counterpart. + +# 3.2. Cross-Scale Assistant + +Preliminary. Our previous section introduces our proposed feature distillation to resolve the challenge of SOD. Other than feature distillation, another practical approach is the output-based KD, which transfers the teacher's prediction on classification and localization to the student as sources for auxiliary supervision. Our work primarily focuses on bounding box distillation, which can be considered a regression problem. In general, we can write such regression distillation as follow: + +$$ +\mathcal {L} _ {b b o x} = l _ {b b o x} \left(\mathcal {R} ^ {S}, \mathcal {R} ^ {T}\right) \tag {2} +$$ + +where $\mathcal{R}^S$ is the regression output of the student network, $\mathcal{R}^T$ is the predication of teacher network. This $l(\cdot)$ is the same as Equation 1, where any bounded loss can be applied. Conventionally, this bounded loss can be either $l_1$ , smoothed $l_1$ or $l_2$ loss, depending on the level of penalty that we wise to weight the error between the student's predication and the teacher's output. + +Motivation. A key difference between small object detection and general object detection is that SOD is sensitive to noisy bounding boxes. Apparently, the teacher detector is incapable of making perfect predictions on every object. In general object detection, despite being inaccurate, student models can still retrieve informative knowledge from teachers' predictions on bounding boxes. Nevertheless, for small objects, noisy bounding box prediction in the teacher model can confuse the student model, which decreases the SOD performance. As proof + +of concept, we deliberately add a slight deviation (6 and 12 pixels along the diagonal direction) and compare the mAP on small-scale objects of a vanilla teacher with a teacher that is slightly perturbed. As shown in Table 1, on RetinaNet baseline, the AP of small objects $(AP_S)$ of students drops consistently when perturbations are added, showing the sensitivity of student detector on teacher's bounding box prediction in SOD. Therefore, to build a trustworthy regression distillation module for SOD, one needs to minimize the adverse effect of poison bounding box knowledge in teachers. This does not mean that the teacher's predictions have to be perfect - otherwise, we can directly supervise the student with ground truth - we only need to refine the teacher's output to ensure that their knowledge is informative to the student [27, 50]. + +Methodology. To address the aforementioned issue, we propose a Cross-Scale Assistant (CSA), which refines the teacher's knowledge and enables the student model to fetch instructive knowledge on objects with different scales. + +Our method is simple - we establish the CSA by a cross-attention module. During the cross-attention, a sequence of key and query tokens are generated in calculating KQ-attention within the teacher's knowledge and then mapped with the value tensor, the outputs from the student model, to obtain attentive regions in the feature with each corresponding query. This process is executed at every student pyramid scale to retrieve informative region-based features. + +A naive choice is to use plain cross-attention [8]. Albeit, previous studies [43] identified that the standard cross-attention could focus on salient regions repetitively on different heads. Consequently, when large objects appear in the image, the cross-attention will redirect its attention to these large objects and ignore small objects. To this end, in contrast to the plain cross-attention, we developed a multiscale cross-attention layer, as shown in Figure 3. Notice that cross-attention extracts global information - for each query-key pair, a value is generated to highlight the most responsive region. We then split the query-key pair into multiple sub-pairs, where each sub-pair represents a set of object scales. As a result, our multi-scale query-key can enforce the attention module to focus on regions with diverse scales, such that all objects, especially the small objects, can attend to the feature learning process. + +Particularly, give an input sequence from teacher $F^T \in \mathbb{R}^{h \times w \times c}$ and another input sequence from student $F^S \in \mathbb{R}^{h \times w \times c}$ , for simplicity, we assume two tensors have the same size. The $F^T$ is projected into a query (Q) and key (K), and $F^S$ is projected into value (V). The keys $K$ and values $V$ are down-sampled to different sizes for different heads indexed by $i$ . Thus, we formulate our multi-scale + +cross-attention (MSC) as follows: + +$$ +Q _ {i} = F ^ {S} W _ {i} ^ {Q} \tag {3} +$$ + +$$ +K _ {i} = M S C \left(F ^ {T}, r _ {i}\right) W _ {i} ^ {K}, V _ {i} = M S C \left(F ^ {T}, r _ {i}\right) W _ {i} ^ {V}, \tag {4} +$$ + +$$ +V _ {i} = V _ {i} + P \left(V _ {i}\right) \tag {5} +$$ + +where $MSC(\cdot ,r_i)$ is a MLP layer for aggregation in the $i$ -th head with the down-sampling rate of $r_i$ , and $P(\cdot)$ is a depth-wise convolutional layer for projection. Compared with the standard cross-attention, more fine-grained and low-level details that are beneficial to SOD are preserved. Finally, we calculated the attention tensor by: + +$$ +h _ {i} = \operatorname {S o f t m a x} \left(\frac {Q _ {i} K _ {i} ^ {T}}{\sqrt {d _ {h}}} V _ {i}\right) \tag {6} +$$ + +where $d_h$ is the dimension. Remember that the purpose of CSA is to bridge the cross-scale information between the teacher and student model to refine the bounding box supervision in KD. Therefore, we stacked head layers with the classification branch and regression branch to update the weights of these learnable modules. Our empirical analysis shows that the proposed CSA can provide more appropriate supervision on small objects bounding boxes during distillation. Because this is a learnable module, during distillation, we perform a weights update prior to the student model at each iteration through a standard training scheme and detection objectives. + +In distillation, instead of transferring the teacher's output knowledge, we transfer the CSA's knowledge on both classification and regression branches to students. For the output-based distillation objectives, we follow [5] to have two loss functions $L_{cls}$ and $L_{bbox}$ . We note that our method is also complementary to other output-based methods, such as LD [46], where all we need to do is simply replace the distillation objective. + +In summary, the total training objective for the student model is: + +$$ +L _ {\text {t o t a l}} = \alpha L _ {\text {f e a t}} + \beta L _ {\text {c l s}} + \gamma L _ {\text {b b o x}} + L _ {\text {d e t}} \tag {7} +$$ + +where $L_{det}$ is the standard training loss for the detector. + +Besides the distillation loss and detection loss for optimizing student detectors, we further ensure the instructive representation quality and consistency with student representations by sharing the detection head for supervision. Moreover, the CSA combines the feature of both teacher and student. As a result, a randomly initialized student detector can cause unstable training of CSA. Thus, we first warm up the student model for 30k iterations since it could be detrimental when the instructive knowledge is optimized insufficiently. The student detector backbone is frozen in early 10k iterations under $1 \times$ training schedule and 20k for $2 \times$ training schedule. + +
MethodBackboneAP\( AP_{50} \)\( AP_{75} \)\( AP_S \)\( AP_M \)\( AP_L \)FPSParams (M)
Faster-RCNN [29] + ScaleKDResNet5038.459.042.021.542.150.320.143.57
43.164.048.226.148.058.8
Faster-RCNN [29] + ScaleKDMobileNetV227.344.728.914.629.635.712.932.61
30.848.732.918.834.242.2
Cascade-RCNN [2] + ScaleKDResNet5041.059.444.422.744.454.318.971.22
44.963.248.825.748.159.2
RetinaNet [22] + ScaleKDResNet5037.456.739.620.040.749.717.437.74
42.861.144.625.945.454.9
FOCS [36] + ScaleKDResNet5038.557.741.021.942.848.623.936.15
44.061.641.629.146.956.2
RepPoints [42] + ScaleKDResNet5038.659.641.622.542.250.418.236.62
42.963.846.825.747.156.7
+ +Table 2. Comparison with state-of-the-art methods KD-Det on COCO val2017 datasets. Our approach appear to improve the detection performance drastically, especially on $AP_{S}$ . The FPS is evaluated on a single V100 GPU. + +
StudentMethodAP\( AP_{50} \)\( AP_{75} \)\( AR_1 \)\( AR_{10} \)\( AR_{100} \)\( AR_{500} \)
RetinaNet-ResNet50Baseline26.2144.9027.100.525.3534.6337.21
ZoomInNet [24]27.1146.0228.090.535.4734.9837.66
ScaleKD29.4549.2829.970.535.9836.7438.65
RetinaNet-MobileNetV2Baseline21.7340.0122.950.495.1131.2434.05
ZoomInNet [24]22.4941.1424.210.505.1531.7834.91
ScaleKD26.0844.7626.980.525.3334.4837.03
+ +Table 3. Experimental results on VisDrone. We use ResNet101 as the teacher model. + +# 4. Experiment + +We conduct quantitative analysis on two object detection datasets: COCO [23] and VisDrone [51]. COCO is a challenging object detection dataset with 80 categories. VisDrone is a dataset specialized to drone-shot image detection, in which most of the objects in this dataset are small. + +# 4.1. Implementation Details + +For COCO, we adopt the standard $1 \times$ schedule and kept all the hyperparameters for the student model training unchanged for fair comparisons. The models are evaluated on validation set 2017. On the VisDrone dataset, we follow the which equally split one image into four non-overlapping patches and process them independently during training. The training procedure is also kept the same as in previous literature. We use $2 \times$ of standard input resolution for all experiments for the teacher model, useless otherwise indicated. Mean average precision (AP) is used as the major metric for all experiments. We use an Adam optimizer with an initial learning rate of $3 \mathrm{e} - 4$ and a weight-decay of $1 \mathrm{e} - 4$ to update the CSA module. There are three hyper-parameters in the total training objectives, we set $\alpha = 0.07$ , $\beta = 0.5$ , + +$\gamma = 0.2$ for all two-stage models, and $\alpha = 0.01$ , $\beta = 0.2$ , $\gamma = 0.05$ for all one-stage models. + +# 4.2. Main Results + +In this section, we show the experimental results of the baseline detectors and our method on COCO and VisDrone datasets. We compare our approach with state-of-the-art distillation methods in the next section. + +COCO. We conduct extensive experiments on COCO to validate the effectiveness of ScaleKD. We adopt our method on multiple mainstream baselines, including two-stage detection models (i.e., Faster RCNN [29], Cascade RCNN [2]), and one-stage detection models (i.e., RetinaNet [22], FCOS [36], Reppoints [42]). For all experiments, we use the ResNet101 backbone as a teacher model. The ScaleKD achieves noticeable improvement on all methods without introducing any extra computational cost at inference. It is worth noting that the performance boost on $AP_{S}$ is overwhelming. For instance, on FCOS the $AP_{S}$ is increased by 7.2, and on RetinaNet the $AP_{S}$ is increased by 5.9. Also, our approach is not only effective for SOD but improves the AP in general. + +
TaskMethodTypeResolution\(AP^{mask}\)\(AP^{mask}_{50}\)\(AP^{mask}_{75}\)\(AP^{mask}_{S}\)\(AP^{mask}_{M}\)\(AP^{mask}_{L}\)
Instance SegmentationMask-RCNNTeacherHigh35.456.537.919.238.648.4
BaselineLow31.651.233.410.833.650.9
OursLow33.8+2.253.2+2.035.7+2.313.1+2.335.5+1.952.3+2.4
Keypoint DetectionMask-RCNNTeacherHigh66.487.172.863.572.073.6
BaselineLow62.586.168.256.572.970.1
OursLow64.1+1.687.6+1.570.1+1.958.7+2.274.2+1.771.2+1.1
+ +Table 4. Performance comparisons with baselines on instance segmentation and keypoint detection. The high resolution means 800px, and the low resolution represents 400px, both on the short side. The baseline refers to the standard training. + +
MethodAP\(AP_S\)\(\Delta AP_S\)\(AP_M\)\(\Delta AP_M\)\(AP_L\)\(\Delta AP_L\)
GFL ResNet50
Baseline40.123.3-44.4-52.5-
FitNet [30]40.723.7+0.444.4+0.053.2+0.7
OD [5]41.123.3+0.045.4+1.053.1+0.6
DeFeat [11]40.824.3+1.044.6+0.253.7+0.5
GID [7]41.524.3+1.045.7+1.353.6+1.1
LD [46]42.124.5+1.246.2+1.854.8+2.3
ScaleKD42.525.9+2.646.2+1.854.6+2.1
RetinaNet ResNet50
Baseline37.420.0-40.7-49.7-
FKD [44]39.621.4+1.442.5+1.851.5+1.8
LGD [45]38.323.2+3.242.0+1.350.0+0.3
FGFI [41]38.621.4+1.442.5+1.851.5+1.8
GID [7]39.122.8+2.843.1+2.452.3+2.4
CLSD [12]40.723.1+3.144.7+4.053.8+4.1
ScaleKD41.724.8+4.844.7+4.053.9+4.2
FCOS ResNet50
Baseline38.521.9-42.8-49.7-
LD [46]40.423.7+1.844.3+1.552.2+2.5
GID [7]42.025.6+3.745.8+3.054.2+4.5
FGFI [41]42.127.0+5.146.0+3.254.6+4.9
ScaleKD42.727.8+5.945.7+2.954.7+5.0
+ +Table 5. Comparison with state-of-the-art methods on COCOval2017. Our ScaleKD achieves pronounced improvement on $AP_{S}$ compared to SOTA. + +VisDrone. We demonstrate the experimental results on the VisDrone dataset in Table 3. We use ResNet-101 as the backbone for both experiments. We can clearly observe that our approach significantly improves the performance of the student model. Notably, after applying ScaleKD to RetinaNet-MobileNetV2 [22, 31], we achieve detection performance that is on par with the RetinaNet-ResNet50 (26.08 AP versus 26.21 AP), which adopt ResNet50, an 8x heavier backbone than MobileNetV2. Our method also increases both $AP$ for RetinaNet-ResNet-50 [13]. Since VisDrone is a dataset that contains mostly small objects, + +these results support our claim that the proposed ScaleKD is extremely effective on SOD. + +We also make a comparison with ZoomInNet [24], which combines feature level alignment and layer adaptation to distill a standard teacher to small object detectors. We evaluate ZoomInNet on both settings, similar to our approach. Indeed, ZoomInNet can slightly improve the AP on VisDrone, but the improvement is very marginal. In contrast, the ScaleKD achieve drastically higher results than their approach. + +Results on Other Instance-Level Tasks with Small Input Resolution. Input resolution is a critical factor in achieving good performance on SOD. Typically, reduced input resolution can result in a considerable performance drop. Here we verify if our proposed ScaleKD can improve the SOD performance on instance-level tasks, even when the input resolution of the student model is low. The evaluation results are reported in Table 4. We notice that the low-resolution models trained with our approach outperform the baseline by a large margin, on both instance segmentation and keypoint detection, based on Mask-RCNN. This shows our ScaleKD is particularly good at predicting small objects, even when the number of effective pixels is small. + +# 4.3. Ablation Study + +Comparison with State-of-the-art knowledge distillation. In the last section, we validate the effectiveness of our proposed ScaleKD on two datasets compared to the trainfrom-scratch counterpart. This section compares ScaleKD to state-of-the-art KD methods on the COCO benchmark. For a fair comparison, we use the standard image resolution on teacher and the same teacher architecture, such that the teacher's performance is the same for all approaches. We compare ScaleKD to these SOTA methods on Generalized focal loss (GFL) [19], RetinaNet [22], and FCOS [36], respectively. All student models use ResNet50 as the backbone. We compare eight distillation methods, seven of them are KD methods that are designed for object detec + +
MethodCSAMSCAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓✗40.223.543.752.6
✓✓41.624.844.553.9
+ +tion, including FitNet [30], OD [5], LGD [45], DeFeat [11], GID [7], LD [46], FGFI [41], and CLSD [12]. + +Table 5 presents the experimental results. We can observe that ScaleKD achieves superior performance on most evaluation metrics, i.e., on GFL-ResNet50, ScaleKD obtained a 2.8 higher AP score compared with baseline and 0.7 higher AP score compared to second best SOTA method (LD [46]). Furthermore, as we look at the $AP_{S}$ , the one that measures AP on small objects, we notice that our proposed method obtains a significantly better score than SOTA. For instance, ScaleKD improves $AP_{S}$ by 3.4, 4.8, and 5.9 on GFL, RetinaNet, and FCOS, respectively. These results indicate that ScaleKD helps compact student detectors on detecting small objects, and it is much more effective than KD methods designed for general object detection. + +Impact of Cross-Scale Assistant. We investigate the effectiveness of our proposed Cross-Scale Assistant module. We use standard image resolution for teachers in this section. We are primarily eager to know if CSA improves SOD performance and does the multi-scale cross-attention helps the student model. Table 6 gives empirical results. We can observe the CSA dramatically increase the AP score as well as $AP_{S}$ for the student RetinaNet model. Moreover, the MSC is critical to the performance. Compared to plain cross-attention, the MSC can improve the $AP$ by 1.4 and $AP_{S}$ by 1.3. It verifies the advantage of our proposed multi-scale cross-attention over plain cross-attention in our KD framework. + +Ablation study of Scale-Decoupled Feature. Table 7 presents the ablation study of the SDF module. We use standard image resolution for teachers in this section. We mainly discuss two aspects: whether SDF improves the performance of SOD and whether the weight-sharing method is worth using. First, we evaluate SDF on COCO with RetinaNet-ResNet50 as the baseline model. The experimental results show that the SDF is indeed effective in improving overall AP and $AP$ for small objects. Besides, using separate weights for parallel branches does not bring noticeable improvement in terms of average AP. Thus, it is worth using the weight-sharing module to save memory costs. + +Table 6. Ablation study for Cross-Scale Assistant. MSC: Multiscale Cross-Attention. + +
MethodSDFWSAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓X41.624.944.853.7
✓✓41.624.844.653.9
+ +Table 7. Ablation study for Scale-Decoupled Feature module. WS: weight-sharing. + +
MethodScaleKDAPAPSAPMAPL
ResNet-18X35.818.938.947.9
ResNet-18✓37.220.140.249.3
ResNet-34X38.921.542.851.4
ResNet-34✓40.823.145.153.7
+ +Table 8. Quantitative results of ScaleKD for diverse model complexity. We use ResNet101 as the teacher model. + +ScaleKD for Diverse Model Complexity. We further validate the effectiveness of our approach to diverse model complexity. Specifically, we evaluate COCO for two different student backbones, ResNet-18 and ResNet-34. Each model is distilled by a ResNet-101 detector. The results are presented in Table 8, which show that our method can effectively and stably improve the student model, regardless of the model complexity. This observation is contradicted by previous studies on image classification but consistent with the report on detection tasks. In particular, our approach improves the average AP by 1.2 and 2.5 on ResNet-18 and ResNet-34, respectively. Notably, the performance on small objects $(AP_S)$ is boosted tremendously by 2.3 and 2.1. These results verified that our method is generally effective on varying model sizes. + +# 5. Discussion + +Balancing inference speed and detection performance for small object detection is challenging. In this work, we propose a Scale-aware knowledge distillation that targets improving the performance of SOD via designed scale-decoupled feature distillation and cross-scale assistant. The former explicitly decouples multi-scale features, and the latter refines the teacher's bounding box noise for more informative knowledge in distillation. We evaluate two benchmarks, COCO 2017 and VisDrone, to demonstrate the effectiveness of our approach. + +Acknowledgements: This work was partially supported by the Science and Technology Innovation Action Plan of Shanghai under Grant 2251110540, and Shanghai Pujiang Program under Grant 21PJ1420300. + +# References + +[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. Sod-mtgan: Small object detection via multi-task generative adversarial network. 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Unlike existing works that struggle to balance the trade-off between inference speed and SOD performance, in this paper, we propose a novel Scale-aware Knowledge Distillation (ScaleKD), which transfers knowledge of a complex teacher model to a compact student model. We design two novel modules to boost the quality of knowledge transfer in distillation for SOD: 1) a scale-decoupled feature distillation module that disentangled teacher's feature representation into multiscale embedding that enables explicit feature mimicking of the student model on small objects. 2) a cross-scale assistant to refine the noisy and uninformative bounding boxes prediction student models, which can mislead the student model and impair the efficacy of knowledge distillation. A multi-scale cross-attention layer is established to capture the multi-scale semantic information to improve the student model. We conduct experiments on COCO and VisDrone datasets with diverse types of models, i.e., two-stage and one-stage detectors, to evaluate our proposed method. Our ScaleKD achieves superior performance on general detection performance and obtains spectacular improvement regarding the SOD performance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 576, + 128, + 588 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 596, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 596, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 596, + 287, + 693 + ], + "type": "text", + "content": "Object detection is a fundamental task that has been developed over the past twenty-year in the computer vision community. Despite the state-of-the-art performance for general object detection having been conspicuously improved since the rise of deep learning, balancing the complexity-precision for small object detection is still an open question. Current works strive to refine feature fusion modules [9, 21], devise novel training schemes [32, 33]" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 242, + 547, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 547, + 315 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 547, + 315 + ], + "type": "text", + "content": "to explicitly train on small objects, design new neural architectures [20,39] to better extract small objects' features, and leverage increased input resolution to enhance representation quality [1, 49]. However, these approaches struggle to balance detection quality on small objects with computational costs at the inference stage." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 316, + 547, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 592 + ], + "type": "text", + "content": "The above reasons incentivize us to design a cost-free technique at test time to improve SOD performance. In the spirit of the eminent success of knowledge distillation (KD) on image data [14], we explore distillation methods for SOD. Typically, knowledge distillation opts for a complex, high-performance model (teacher) that transfers its knowledge to a compact, low-performance model (student). The student model can harness instructive information to enhance its representation learning ability. Nevertheless, unlocking this potential in SOD involves overcoming two challenges: 1) SOD usually suffers from noisy feature representations. Due to the nature of small objects, which generally take over a small region in the whole image, the feature representations of these small objects can be contaminated by the background and other instances with relatively larger sizes. 2) Object detectors have a low tolerance for noisy bounding boxes on small objects. It is inevitable that teacher models make incorrect predictions. Usually, student models can extract informative dark knowledge [14, 28] from imperfect predictions from the teacher. However, in SOD, small perturbations on the teacher's bounding box can dramatically impair SOD performance on the student detector (§3.2)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": "To this end, we propose Scale-aware Knowledge Distillation for small object detection (ScaleKD). Our proposed ScaleKD consists of two modules, a Scale-Decoupled Feature (SDF) distillation module and a Cross-Scale Assistant (CSA), to address the aforementioned two challenges correspondingly. The SDF is inspired by the crucial shortcoming of existing feature distillation methods, where the feature representations of objects with varying scales are coupled in a single embedding. It poses difficulty for the student to mimic small objects' features from the teacher model." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19723" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 74, + 539, + 248 + ], + "blocks": [ + { + "bbox": [ + 52, + 74, + 539, + 248 + ], + "lines": [ + { + "bbox": [ + 52, + 74, + 539, + 248 + ], + "spans": [ + { + "bbox": [ + 52, + 74, + 539, + 248 + ], + "type": "image", + "image_path": "40b51e808c002a2c17fb7a4e8ebc123238468ba844064fbef8bcd7cb162091fe.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 260, + 546, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 260, + 546, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 546, + 283 + ], + "type": "text", + "content": "Figure 1. The overview of Scale-aware Knowledge Distillation. It consists of a Scale-Decoupled Feature distillation module and a CrossScale Assistant module to improve small object detection." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 289, + 495 + ], + "type": "text", + "content": "As a result, the proposed SDF aims to decouple a single-scale feature embedding into a multi-scale feature embedding. The multi-scale embedding is obtained by a parallel multi-branch convolutional block, where each branch deals with one scale. Our SDF allows the student model to better understand the feature knowledge from the perspective of object scale. Furthermore, we propose a learnable CSA to resolve the adverse effect of teachers' noisy bounding box prediction on small objects. The CSA comprises a multi-scale cross-attention module, where representations from the teacher and student models are mapped into a single feature embedding. The multi-scale query-key pair projects the teacher's features into multiple sizes, such that the fine-grained and low-level details can be preserved in CSA, which helps to produce suitable bounding box supervision for the student model." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 497, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 640 + ], + "type": "text", + "content": "We demonstrate the effectiveness of our approach on COCO object detection and VisDrone datasets. The experiments are conducted on multiple types of detectors, including two-stage detectors, anchor-based detectors, and anchor-free detectors, and have proven the generalizability of our approach. Our work offers a practical approach for industrial application on SOD as well as introduces a new perspective on designing scale-aware KD modules to improve object detectors. We further extend our method on instance-level detection tasks, such as instance segmentation and keypoint detection, demonstrating the superiority of our approach to dealing with small objects in vision tasks." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 642, + 256, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 642, + 256, + 653 + ], + "spans": [ + { + "bbox": [ + 59, + 642, + 256, + 653 + ], + "type": "text", + "content": "In summary, our contributions are the following:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 665, + 287, + 713 + ], + "type": "text", + "content": "- We propose Scale-Aware Knowledge Distillation (ScaleKD), a novel knowledge distillation framework to improve general detection and SOD performance without bringing extra computational costs at test time." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 318, + 304, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 304, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 318, + 304, + 545, + 375 + ], + "type": "text", + "content": "- Our proposed ScaleKD not only exceeds state-of-the-art KD for object detection methods on general detection performance but also surpasses existing approaches on SOD by a large margin. Extended experiments on instance segmentation and keypoint detection further strengthen our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 391, + 392, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 391, + 392, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 391, + 392, + 403 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 412, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 497 + ], + "type": "text", + "content": "Knowledge Distillation. Knowledge distillation has become one of the most effective techniques for model compression [14]. It first trains a cumbersome teacher model and then transfers its knowledge to a lightweight student model. The common knowledge distillation approaches include distillation on output, logits [14], bounding box [16], and features [30, 52, 53]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "Our work is also closely correlated to object detection, where knowledge distillation has shown effectiveness in detection tasks [3, 15, 35, 40, 47, 48]. In particular, FineGrained [5] is the first work to comprehensively present a KD framework for the object detection task. FKD [44] is the earliest work to adopt attention mechanisms to do feature distillation on object detectors. DeFeat [12] decoupled the foreground feature and background features based on the ground-truth binary mask and performed feature distillation on two features separately. FGFI [41] presents focal distillation, which combines DeFeat and Zhang et al. [44] works. ICD [17] considered conditional distillation of both classification and localization on very instances. Guo [12] investigates distilling image classifier instead of object detector to student detector, which complements existing feature-based distillation methods. Similar to ICD, GID [7] proposed an instance-selection module to transfer the teacher's most informative locations. LGD [45] pro" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19724" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 144 + ], + "type": "text", + "content": "posed a teacher-free framework to distill object detectors without a concrete teacher model. Nevertheless, existing methods have largely overlooked the small objects. Our paper is the first work to design knowledge distillation specifically targeted to improve general object detection and small objects' performance." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 156, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 156, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 287, + 312 + ], + "type": "text", + "content": "Small Object Detection. Recognizing small objects in the image is challenging, especially when localization and per-pixel classification are required. A naive approach is to increase the resolution [26]. Nevertheless, it brings tremendous computational costs in inference. Existing approaches mainly focus on applying strong data augmentation [18] or oversampling [4], incorporating context information [9, 21], fusing the features across layers [10, 38], performing scale-aware training [32, 33], adjusting resolution at test-time [37], or applying dilated convolution/large convolution [20, 39] to increase the receptive field. We refer interested readers for a more in-depth survey [6]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 312, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 419 + ], + "type": "text", + "content": "Our approach is very different from previous methods, where we seek help with knowledge distillation to boost the performance of SOD. Our method benefits from the advantage of the distillation method, where 1) no extra computational costs are introduced at test time, and 2) neural architectures of the existing model do not need to be modified, a critical benefit in the practical scenario where engineering do not want to alter their networks architecture due to inconvenience on deployment." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 244, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 244, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 244, + 443 + ], + "type": "text", + "content": "3. Scale-aware Knowledge Distillation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 287, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 546 + ], + "type": "text", + "content": "This section provides a detailed description of our proposed distillation methods. Figure 1 gives a brief overview of ScaledKD, in which we illustrate the modules as follows: (1) A scale-decoupled feature distillation module that explicitly transfers representation on diverse scales to the student detector. (2) A cross-scale assistant refines the knowledge of object size between complex teacher and compact student." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "Definition. In this section, we provide a notion of the components that we will use to describe our method. Considering an object detector " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^S:\\mathbb{R}^d\\to \\mathbb{R}^k" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " as a student and another predictor " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^T:\\mathbb{R}^d\\to \\mathbb{R}^k" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " as a teacher, where " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " are two feature dimensions. The former is a computationally efficient network with a relatively lower detection performance. The latter is a heavy model with relatively higher detection performance. Giving a training dataset " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "S = \\{(x_{i},y_{i})_{i = 1}^{n}\\} \\sim \\mathbb{P}^{n}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " for distribution " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{P}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " over a set of instance " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": ". For small object detection, a common approach to improve SOD is to leverage a high-resolution image as input. In our case, we only consider using high-resolution images " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\chi^{hr}" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " for the teacher model, while" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 548, + 228 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 548, + 228 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 548, + 228 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 548, + 228 + ], + "type": "image", + "image_path": "5dcacf5fe2c743cb4679a500605c69076f5374f3c3873e9cd002cf8e7c5fa8ab.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 238, + 545, + 282 + ], + "lines": [ + { + "bbox": [ + 304, + 238, + 545, + 282 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 545, + 282 + ], + "type": "text", + "content": "Figure 2. The scale-decouple feature module in ScaleKD. Note that the details of the student's scale-decoupled feature module are omitted due to limited space. In practice, it is symmetric to the teacher's counterpart." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 301, + 541, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 301, + 541, + 313 + ], + "spans": [ + { + "bbox": [ + 306, + 301, + 541, + 313 + ], + "type": "text", + "content": "standard-resolution images are used for the student model." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 320, + 499, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 320, + 499, + 333 + ], + "spans": [ + { + "bbox": [ + 306, + 320, + 499, + 333 + ], + "type": "text", + "content": "3.1. Scale-Decoupled Feature Distillation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 338, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 422 + ], + "type": "text", + "content": "Preliminary. Modern object detectors harness FPN [21] to obtain the multi-scale semantic information from different levels of the backbone to enhance the model's feature learning ability on diverse object scales. A typical distillation approach is to transfer the knowledge of these features from teacher to student. Generally, we can formulate such distillation methods as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 377, + 429, + 545, + 443 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 429, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 377, + 429, + 545, + 443 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f e a t}} = l \\left(\\mathcal {F} ^ {T}, f \\left(\\mathcal {F} ^ {S}\\right)\\right) \\tag {1}", + "image_path": "d02a6bd8721f097ba4ca24a7439b2a60bab8e18d242e287f830bbf7b71c94211.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "inline_equation", + "content": "F^T" + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "inline_equation", + "content": "F^S" + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "content": " are corresponding feature layers in the teacher and student model. " + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "content": " is a mapping function to align the dimension of the feature map in student to teacher, and " + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "inline_equation", + "content": "l(\\cdot)" + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "content": " is any bounded loss, i.e., " + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "inline_equation", + "content": "l_2" + }, + { + "bbox": [ + 304, + 449, + 545, + 498 + ], + "type": "text", + "content": " norm distance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 677 + ], + "type": "text", + "content": "Motivation. Although state-of-the-art KDs for object detection have developed various techniques, such as focal distillation [41], to enhance the quality of transferred knowledge, such methods treat all objects that have varying sizes equally during distillation. We identify that the key shortcoming of these methods on SOD is that the feature representation on diverse objects is entangled. It is a viable solution when object sizes are not small. However, the size of objects in the detection task varies significantly. The feature representation of small objects can be contaminated by large-region backgrounds and other instances with a relatively larger size. To resolve the issue, we propose a Scale-Decoupled Feature (SDF) distillation module to explicitly disentangled the teacher's feature map." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Methodology. As aforementioned, our goal is to disentangle the whole feature representation of the teacher" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19725" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 142 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 142 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 142 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 142 + ], + "type": "table", + "html": "
MethodPerturbationAPAPSAPMAPL
Baseline036.921.240.848.4
Chen et al. [5]038.121.942.250.1
6 pixels37.721.142.450.2
12 pixels37.019.942.150.0
", + "image_path": "b633b996c73bb6411877456c1e90b06e0b0243c367a9276876987f42facb6203.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 150, + 287, + 195 + ], + "lines": [ + { + "bbox": [ + 46, + 150, + 287, + 195 + ], + "spans": [ + { + "bbox": [ + 46, + 150, + 287, + 195 + ], + "type": "text", + "content": "Table 1. Noisy and uninformative bounding boxes from the teacher can severely hurt students' performance. The perturbation is measured by a number of pixels, and it is added along the diagonal direction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 219, + 286, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 286, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 286, + 278 + ], + "type": "text", + "content": "object detector into multiple parts, where each part only deals with similar object sizes. Presumably, such operations can force student detectors to comprehend not only the global knowledge of the entire image but also the scale-specific knowledge." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "type": "text", + "content": "To be specific, we obtain a feature embedding " + }, + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "type": "inline_equation", + "content": "Z^T" + }, + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "type": "inline_equation", + "content": "Z^S" + }, + { + "bbox": [ + 46, + 280, + 286, + 471 + ], + "type": "text", + "content": " in the last stage of the backbone for both the teacher and student networks. We intend to fully utilize the feature representation on diverse input scales. Thus, we adopt a multi-branch structure, where each branch uses a convolutional layer with different dilated rates. It is worth noting that the model tends to focus on small objects for the kernel with a small dilated rate and vice versa. In practice, we use residual blocks as in ResNet, which consist of three consecutive convolutional layers, i.e., 1x1, 3x3, and 1x1, along with a skip connection. For the 3x3 Conv layer, we use three different dilated rates {1, 2, 3} on three individual branches. An adapter layer, typically a multi-layer perception (MLP) layer, is stacked before this scale-decoupled feature module to align the dimensionality of feature presentation between the teacher and student model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 472, + 286, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 286, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 286, + 604 + ], + "type": "text", + "content": "Usually, one can match the knowledge of the teacher model at a designated branch, i.e., the " + }, + { + "bbox": [ + 46, + 472, + 286, + 604 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 472, + 286, + 604 + ], + "type": "text", + "content": " Conv layer with a dilated rate of 1, to the corresponding feature branch in the student model via any distance minimization loss. One drawback is that these operations can be memory intensive. Therefore, we take inspiration from the weight-sharing network in neural architecture search [25, 34] and adopt a weight-sharing scale-decoupled feature. This is based on the fact that all three branches have the same operators. In practice, we only save a set of weights for three branches, dramatically reducing the training memory cost." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "We also notice that using three individual losses to match three parallel branches between the teacher and student model can cause the practitioner to spend unnecessary effort on hyper-parameter tuning. As a result, for each branch, we use a flattened layer, namely a multi-layer perceptron, and concatenate three flattened layers together. During the distillation process, we adopt a sole 12 loss (denoted as " + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "inline_equation", + "content": "L_{feat}" + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": " in the later section) to minimize the distance of this concatenated flattened layer between the teacher and student" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 547, + 213 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 547, + 213 + ], + "type": "image", + "image_path": "62781c20948e00e9925305a4cabf4cd75673e7c904b96a6834cedaa416f4049b.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 223, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 278 + ], + "type": "text", + "content": "Figure 3. The Cross-Scale Assistant (CSA) module. We adopt a multi-scale query-key pair to perform cross-attention with feature embedding in the student model. The learnable weights in CSA are updated via two separate classification and regression branches which are supervised by the ground truth label." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 299, + 545, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 545, + 335 + ], + "type": "text", + "content": "model. the overview of the proposed module can be viewed in Figure 2. Notably, the student's scale-decoupled feature module mirrors the teacher's counterpart." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 342, + 428, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 428, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 428, + 354 + ], + "type": "text", + "content": "3.2. Cross-Scale Assistant" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 361, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 467 + ], + "type": "text", + "content": "Preliminary. Our previous section introduces our proposed feature distillation to resolve the challenge of SOD. Other than feature distillation, another practical approach is the output-based KD, which transfers the teacher's prediction on classification and localization to the student as sources for auxiliary supervision. Our work primarily focuses on bounding box distillation, which can be considered a regression problem. In general, we can write such regression distillation as follow:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 376, + 475, + 545, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 475, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 376, + 475, + 545, + 490 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b b o x} = l _ {b b o x} \\left(\\mathcal {R} ^ {S}, \\mathcal {R} ^ {T}\\right) \\tag {2}", + "image_path": "082ab99c0d31ad955942f1fff381f8f49a006dbc2135771a9eb86e1f9a266656.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{R}^S" + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": " is the regression output of the student network, " + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "inline_equation", + "content": "\\mathcal{R}^T" + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": " is the predication of teacher network. This " + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "inline_equation", + "content": "l(\\cdot)" + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": " is the same as Equation 1, where any bounded loss can be applied. Conventionally, this bounded loss can be either " + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "inline_equation", + "content": "l_1" + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": ", smoothed " + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "inline_equation", + "content": "l_1" + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "inline_equation", + "content": "l_2" + }, + { + "bbox": [ + 304, + 497, + 545, + 582 + ], + "type": "text", + "content": " loss, depending on the level of penalty that we wise to weight the error between the student's predication and the teacher's output." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Motivation. A key difference between small object detection and general object detection is that SOD is sensitive to noisy bounding boxes. Apparently, the teacher detector is incapable of making perfect predictions on every object. In general object detection, despite being inaccurate, student models can still retrieve informative knowledge from teachers' predictions on bounding boxes. Nevertheless, for small objects, noisy bounding box prediction in the teacher model can confuse the student model, which decreases the SOD performance. As proof" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19726" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "of concept, we deliberately add a slight deviation (6 and 12 pixels along the diagonal direction) and compare the mAP on small-scale objects of a vanilla teacher with a teacher that is slightly perturbed. As shown in Table 1, on RetinaNet baseline, the AP of small objects " + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "inline_equation", + "content": "(AP_S)" + }, + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": " of students drops consistently when perturbations are added, showing the sensitivity of student detector on teacher's bounding box prediction in SOD. Therefore, to build a trustworthy regression distillation module for SOD, one needs to minimize the adverse effect of poison bounding box knowledge in teachers. This does not mean that the teacher's predictions have to be perfect - otherwise, we can directly supervise the student with ground truth - we only need to refine the teacher's output to ensure that their knowledge is informative to the student [27, 50]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 263, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 263, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 263, + 287, + 323 + ], + "type": "text", + "content": "Methodology. To address the aforementioned issue, we propose a Cross-Scale Assistant (CSA), which refines the teacher's knowledge and enables the student model to fetch instructive knowledge on objects with different scales." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": "Our method is simple - we establish the CSA by a cross-attention module. During the cross-attention, a sequence of key and query tokens are generated in calculating KQ-attention within the teacher's knowledge and then mapped with the value tensor, the outputs from the student model, to obtain attentive regions in the feature with each corresponding query. This process is executed at every student pyramid scale to retrieve informative region-based features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 429, + 288, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 288, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 288, + 620 + ], + "type": "text", + "content": "A naive choice is to use plain cross-attention [8]. Albeit, previous studies [43] identified that the standard cross-attention could focus on salient regions repetitively on different heads. Consequently, when large objects appear in the image, the cross-attention will redirect its attention to these large objects and ignore small objects. To this end, in contrast to the plain cross-attention, we developed a multiscale cross-attention layer, as shown in Figure 3. Notice that cross-attention extracts global information - for each query-key pair, a value is generated to highlight the most responsive region. We then split the query-key pair into multiple sub-pairs, where each sub-pair represents a set of object scales. As a result, our multi-scale query-key can enforce the attention module to focus on regions with diverse scales, such that all objects, especially the small objects, can attend to the feature learning process." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Particularly, give an input sequence from teacher " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "F^T \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and another input sequence from student " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "F^S \\in \\mathbb{R}^{h \\times w \\times c}" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ", for simplicity, we assume two tensors have the same size. The " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "F^T" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " is projected into a query (Q) and key (K), and " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "F^S" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " is projected into value (V). The keys " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " and values " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": " are down-sampled to different sizes for different heads indexed by " + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": ". Thus, we formulate our multi-scale" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 443, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 443, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 443, + 83 + ], + "type": "text", + "content": "cross-attention (MSC) as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 395, + 91, + 545, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 395, + 91, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 395, + 91, + 545, + 107 + ], + "type": "interline_equation", + "content": "Q _ {i} = F ^ {S} W _ {i} ^ {Q} \\tag {3}", + "image_path": "55bfb1e6a44cc8b766d6429c15bd3a65cb02855e1b9d269b345f682a996fce0c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 313, + 113, + 545, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 113, + 545, + 128 + ], + "spans": [ + { + "bbox": [ + 313, + 113, + 545, + 128 + ], + "type": "interline_equation", + "content": "K _ {i} = M S C \\left(F ^ {T}, r _ {i}\\right) W _ {i} ^ {K}, V _ {i} = M S C \\left(F ^ {T}, r _ {i}\\right) W _ {i} ^ {V}, \\tag {4}", + "image_path": "146a611ec73566ffe6c40f57adf484a838608a7bab9842d25fa9b19b1b31da60.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 390, + 132, + 545, + 145 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 132, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 390, + 132, + 545, + 145 + ], + "type": "interline_equation", + "content": "V _ {i} = V _ {i} + P \\left(V _ {i}\\right) \\tag {5}", + "image_path": "7cc267beda5d3f6e400c2f21fc47a1f9247457525c0469dceda3faa8377b9df2.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "spans": [ + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "inline_equation", + "content": "MSC(\\cdot ,r_i)" + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "text", + "content": " is a MLP layer for aggregation in the " + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "text", + "content": "-th head with the down-sampling rate of " + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "inline_equation", + "content": "r_i" + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "inline_equation", + "content": "P(\\cdot)" + }, + { + "bbox": [ + 305, + 149, + 545, + 222 + ], + "type": "text", + "content": " is a depth-wise convolutional layer for projection. Compared with the standard cross-attention, more fine-grained and low-level details that are beneficial to SOD are preserved. Finally, we calculated the attention tensor by:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 369, + 229, + 545, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 229, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 369, + 229, + 545, + 258 + ], + "type": "interline_equation", + "content": "h _ {i} = \\operatorname {S o f t m a x} \\left(\\frac {Q _ {i} K _ {i} ^ {T}}{\\sqrt {d _ {h}}} V _ {i}\\right) \\tag {6}", + "image_path": "a33e7c841e4bc858d10a8dc3a1089b9edefc6159ba171c777b2d9be4e22a2446.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 264, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 545, + 407 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 264, + 545, + 407 + ], + "type": "inline_equation", + "content": "d_h" + }, + { + "bbox": [ + 304, + 264, + 545, + 407 + ], + "type": "text", + "content": " is the dimension. Remember that the purpose of CSA is to bridge the cross-scale information between the teacher and student model to refine the bounding box supervision in KD. Therefore, we stacked head layers with the classification branch and regression branch to update the weights of these learnable modules. Our empirical analysis shows that the proposed CSA can provide more appropriate supervision on small objects bounding boxes during distillation. Because this is a learnable module, during distillation, we perform a weights update prior to the student model at each iteration through a standard training scheme and detection objectives." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "text", + "content": "In distillation, instead of transferring the teacher's output knowledge, we transfer the CSA's knowledge on both classification and regression branches to students. For the output-based distillation objectives, we follow [5] to have two loss functions " + }, + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "inline_equation", + "content": "L_{cls}" + }, + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "inline_equation", + "content": "L_{bbox}" + }, + { + "bbox": [ + 304, + 407, + 545, + 503 + ], + "type": "text", + "content": ". We note that our method is also complementary to other output-based methods, such as LD [46], where all we need to do is simply replace the distillation objective." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 503, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 503, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 503, + 545, + 526 + ], + "type": "text", + "content": "In summary, the total training objective for the student model is:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 337, + 536, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 536, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 337, + 536, + 545, + 550 + ], + "type": "interline_equation", + "content": "L _ {\\text {t o t a l}} = \\alpha L _ {\\text {f e a t}} + \\beta L _ {\\text {c l s}} + \\gamma L _ {\\text {b b o x}} + L _ {\\text {d e t}} \\tag {7}", + "image_path": "c1f3a6dacceaf4e1c956fff0d593063d087d6e3d5c0fc28b44b24947b27b80fe.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 558, + 531, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 531, + 569 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 531, + 569 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 558, + 531, + 569 + ], + "type": "inline_equation", + "content": "L_{det}" + }, + { + "bbox": [ + 305, + 558, + 531, + 569 + ], + "type": "text", + "content": " is the standard training loss for the detector." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Besides the distillation loss and detection loss for optimizing student detectors, we further ensure the instructive representation quality and consistency with student representations by sharing the detection head for supervision. Moreover, the CSA combines the feature of both teacher and student. As a result, a randomly initialized student detector can cause unstable training of CSA. Thus, we first warm up the student model for 30k iterations since it could be detrimental when the instructive knowledge is optimized insufficiently. The student detector backbone is frozen in early 10k iterations under " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " training schedule and 20k for " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " training schedule." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19727" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 99, + 70, + 493, + 251 + ], + "blocks": [ + { + "bbox": [ + 99, + 70, + 493, + 251 + ], + "lines": [ + { + "bbox": [ + 99, + 70, + 493, + 251 + ], + "spans": [ + { + "bbox": [ + 99, + 70, + 493, + 251 + ], + "type": "table", + "html": "
MethodBackboneAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AP_S \\)\\( AP_M \\)\\( AP_L \\)FPSParams (M)
Faster-RCNN [29] + ScaleKDResNet5038.459.042.021.542.150.320.143.57
43.164.048.226.148.058.8
Faster-RCNN [29] + ScaleKDMobileNetV227.344.728.914.629.635.712.932.61
30.848.732.918.834.242.2
Cascade-RCNN [2] + ScaleKDResNet5041.059.444.422.744.454.318.971.22
44.963.248.825.748.159.2
RetinaNet [22] + ScaleKDResNet5037.456.739.620.040.749.717.437.74
42.861.144.625.945.454.9
FOCS [36] + ScaleKDResNet5038.557.741.021.942.848.623.936.15
44.061.641.629.146.956.2
RepPoints [42] + ScaleKDResNet5038.659.641.622.542.250.418.236.62
42.963.846.825.747.156.7
", + "image_path": "cd86b126736d82fc5be624de3f46d60a67bdfa6b70a837df28d394ce5c871b4e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 99, + 294, + 494, + 393 + ], + "blocks": [ + { + "bbox": [ + 46, + 261, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 547, + 285 + ], + "type": "text", + "content": "Table 2. Comparison with state-of-the-art methods KD-Det on COCO val2017 datasets. Our approach appear to improve the detection performance drastically, especially on " + }, + { + "bbox": [ + 46, + 261, + 547, + 285 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 46, + 261, + 547, + 285 + ], + "type": "text", + "content": ". The FPS is evaluated on a single V100 GPU." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 294, + 494, + 393 + ], + "lines": [ + { + "bbox": [ + 99, + 294, + 494, + 393 + ], + "spans": [ + { + "bbox": [ + 99, + 294, + 494, + 393 + ], + "type": "table", + "html": "
StudentMethodAP\\( AP_{50} \\)\\( AP_{75} \\)\\( AR_1 \\)\\( AR_{10} \\)\\( AR_{100} \\)\\( AR_{500} \\)
RetinaNet-ResNet50Baseline26.2144.9027.100.525.3534.6337.21
ZoomInNet [24]27.1146.0228.090.535.4734.9837.66
ScaleKD29.4549.2829.970.535.9836.7438.65
RetinaNet-MobileNetV2Baseline21.7340.0122.950.495.1131.2434.05
ZoomInNet [24]22.4941.1424.210.505.1531.7834.91
ScaleKD26.0844.7626.980.525.3334.4837.03
", + "image_path": "d27b32dad48eb301358064db070ecd1307707b55796270c0c159c41e09edf7d9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 142, + 401, + 449, + 412 + ], + "lines": [ + { + "bbox": [ + 142, + 401, + 449, + 412 + ], + "spans": [ + { + "bbox": [ + 142, + 401, + 449, + 412 + ], + "type": "text", + "content": "Table 3. Experimental results on VisDrone. We use ResNet101 as the teacher model." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 433, + 123, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 123, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 123, + 445 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 454, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 454, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 454, + 287, + 515 + ], + "type": "text", + "content": "We conduct quantitative analysis on two object detection datasets: COCO [23] and VisDrone [51]. COCO is a challenging object detection dataset with 80 categories. VisDrone is a dataset specialized to drone-shot image detection, in which most of the objects in this dataset are small." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 525, + 180, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 180, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 180, + 539 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "For COCO, we adopt the standard " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "1 \\times" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " schedule and kept all the hyperparameters for the student model training unchanged for fair comparisons. The models are evaluated on validation set 2017. On the VisDrone dataset, we follow the which equally split one image into four non-overlapping patches and process them independently during training. The training procedure is also kept the same as in previous literature. We use " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " of standard input resolution for all experiments for the teacher model, useless otherwise indicated. Mean average precision (AP) is used as the major metric for all experiments. We use an Adam optimizer with an initial learning rate of " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "3 \\mathrm{e} - 4" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " and a weight-decay of " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "1 \\mathrm{e} - 4" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": " to update the CSA module. There are three hyper-parameters in the total training objectives, we set " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\alpha = 0.07" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\beta = 0.5" + }, + { + "bbox": [ + 46, + 545, + 288, + 715 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\gamma = 0.2" + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": " for all two-stage models, and " + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\alpha = 0.01" + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\beta = 0.2" + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\gamma = 0.05" + }, + { + "bbox": [ + 305, + 434, + 545, + 458 + ], + "type": "text", + "content": " for all one-stage models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 467, + 391, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 391, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 391, + 479 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 486, + 547, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 534 + ], + "type": "text", + "content": "In this section, we show the experimental results of the baseline detectors and our method on COCO and VisDrone datasets. We compare our approach with state-of-the-art distillation methods in the next section." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": "COCO. We conduct extensive experiments on COCO to validate the effectiveness of ScaleKD. We adopt our method on multiple mainstream baselines, including two-stage detection models (i.e., Faster RCNN [29], Cascade RCNN [2]), and one-stage detection models (i.e., RetinaNet [22], FCOS [36], Reppoints [42]). For all experiments, we use the ResNet101 backbone as a teacher model. The ScaleKD achieves noticeable improvement on all methods without introducing any extra computational cost at inference. It is worth noting that the performance boost on " + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": " is overwhelming. For instance, on FCOS the " + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": " is increased by 7.2, and on RetinaNet the " + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": " is increased by 5.9. Also, our approach is not only effective for SOD but improves the AP in general." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19728" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 70, + 539, + 174 + ], + "blocks": [ + { + "bbox": [ + 56, + 70, + 539, + 174 + ], + "lines": [ + { + "bbox": [ + 56, + 70, + 539, + 174 + ], + "spans": [ + { + "bbox": [ + 56, + 70, + 539, + 174 + ], + "type": "table", + "html": "
TaskMethodTypeResolution\\(AP^{mask}\\)\\(AP^{mask}_{50}\\)\\(AP^{mask}_{75}\\)\\(AP^{mask}_{S}\\)\\(AP^{mask}_{M}\\)\\(AP^{mask}_{L}\\)
Instance SegmentationMask-RCNNTeacherHigh35.456.537.919.238.648.4
BaselineLow31.651.233.410.833.650.9
OursLow33.8+2.253.2+2.035.7+2.313.1+2.335.5+1.952.3+2.4
Keypoint DetectionMask-RCNNTeacherHigh66.487.172.863.572.073.6
BaselineLow62.586.168.256.572.970.1
OursLow64.1+1.687.6+1.570.1+1.958.7+2.274.2+1.771.2+1.1
", + "image_path": "754bbbbad22d63d092e824db88af0a54989f0232a79a5eb3297d7e7c713f596b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 222, + 298, + 506 + ], + "blocks": [ + { + "bbox": [ + 46, + 181, + 546, + 205 + ], + "lines": [ + { + "bbox": [ + 46, + 181, + 546, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 546, + 205 + ], + "type": "text", + "content": "Table 4. Performance comparisons with baselines on instance segmentation and keypoint detection. The high resolution means 800px, and the low resolution represents 400px, both on the short side. The baseline refers to the standard training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 222, + 298, + 506 + ], + "lines": [ + { + "bbox": [ + 50, + 222, + 298, + 506 + ], + "spans": [ + { + "bbox": [ + 50, + 222, + 298, + 506 + ], + "type": "table", + "html": "
MethodAP\\(AP_S\\)\\(\\Delta AP_S\\)\\(AP_M\\)\\(\\Delta AP_M\\)\\(AP_L\\)\\(\\Delta AP_L\\)
GFL ResNet50
Baseline40.123.3-44.4-52.5-
FitNet [30]40.723.7+0.444.4+0.053.2+0.7
OD [5]41.123.3+0.045.4+1.053.1+0.6
DeFeat [11]40.824.3+1.044.6+0.253.7+0.5
GID [7]41.524.3+1.045.7+1.353.6+1.1
LD [46]42.124.5+1.246.2+1.854.8+2.3
ScaleKD42.525.9+2.646.2+1.854.6+2.1
RetinaNet ResNet50
Baseline37.420.0-40.7-49.7-
FKD [44]39.621.4+1.442.5+1.851.5+1.8
LGD [45]38.323.2+3.242.0+1.350.0+0.3
FGFI [41]38.621.4+1.442.5+1.851.5+1.8
GID [7]39.122.8+2.843.1+2.452.3+2.4
CLSD [12]40.723.1+3.144.7+4.053.8+4.1
ScaleKD41.724.8+4.844.7+4.053.9+4.2
FCOS ResNet50
Baseline38.521.9-42.8-49.7-
LD [46]40.423.7+1.844.3+1.552.2+2.5
GID [7]42.025.6+3.745.8+3.054.2+4.5
FGFI [41]42.127.0+5.146.0+3.254.6+4.9
ScaleKD42.727.8+5.945.7+2.954.7+5.0
", + "image_path": "02b0bd64ab35fe7d3857ed9e547b8ff93bf95c06a906eee5e8cce6804394b0cf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 514, + 288, + 548 + ], + "lines": [ + { + "bbox": [ + 46, + 514, + 288, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 288, + 548 + ], + "type": "text", + "content": "Table 5. Comparison with state-of-the-art methods on COCOval2017. Our ScaleKD achieves pronounced improvement on " + }, + { + "bbox": [ + 46, + 514, + 288, + 548 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 46, + 514, + 288, + 548 + ], + "type": "text", + "content": " compared to SOTA." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "VisDrone. We demonstrate the experimental results on the VisDrone dataset in Table 3. We use ResNet-101 as the backbone for both experiments. We can clearly observe that our approach significantly improves the performance of the student model. Notably, after applying ScaleKD to RetinaNet-MobileNetV2 [22, 31], we achieve detection performance that is on par with the RetinaNet-ResNet50 (26.08 AP versus 26.21 AP), which adopt ResNet50, an 8x heavier backbone than MobileNetV2. Our method also increases both " + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": " for RetinaNet-ResNet-50 [13]. Since VisDrone is a dataset that contains mostly small objects," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 224, + 545, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 248 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 248 + ], + "type": "text", + "content": "these results support our claim that the proposed ScaleKD is extremely effective on SOD." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 250, + 546, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 546, + 346 + ], + "type": "text", + "content": "We also make a comparison with ZoomInNet [24], which combines feature level alignment and layer adaptation to distill a standard teacher to small object detectors. We evaluate ZoomInNet on both settings, similar to our approach. Indeed, ZoomInNet can slightly improve the AP on VisDrone, but the improvement is very marginal. In contrast, the ScaleKD achieve drastically higher results than their approach." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 357, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 547, + 525 + ], + "type": "text", + "content": "Results on Other Instance-Level Tasks with Small Input Resolution. Input resolution is a critical factor in achieving good performance on SOD. Typically, reduced input resolution can result in a considerable performance drop. Here we verify if our proposed ScaleKD can improve the SOD performance on instance-level tasks, even when the input resolution of the student model is low. The evaluation results are reported in Table 4. We notice that the low-resolution models trained with our approach outperform the baseline by a large margin, on both instance segmentation and keypoint detection, based on Mask-RCNN. This shows our ScaleKD is particularly good at predicting small objects, even when the number of effective pixels is small." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 537, + 400, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 400, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 400, + 551 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "Comparison with State-of-the-art knowledge distillation. In the last section, we validate the effectiveness of our proposed ScaleKD on two datasets compared to the trainfrom-scratch counterpart. This section compares ScaleKD to state-of-the-art KD methods on the COCO benchmark. For a fair comparison, we use the standard image resolution on teacher and the same teacher architecture, such that the teacher's performance is the same for all approaches. We compare ScaleKD to these SOTA methods on Generalized focal loss (GFL) [19], RetinaNet [22], and FCOS [36], respectively. All student models use ResNet50 as the backbone. We compare eight distillation methods, seven of them are KD methods that are designed for object detec" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19729" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 70, + 277, + 129 + ], + "blocks": [ + { + "bbox": [ + 57, + 70, + 277, + 129 + ], + "lines": [ + { + "bbox": [ + 57, + 70, + 277, + 129 + ], + "spans": [ + { + "bbox": [ + 57, + 70, + 277, + 129 + ], + "type": "table", + "html": "
MethodCSAMSCAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓✗40.223.543.752.6
✓✓41.624.844.553.9
", + "image_path": "212e9727eca3e77310fb9bb383c0f6a2d105b9a6e3c617bbd451bae8da6f6caa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 185, + 286, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 286, + 209 + ], + "type": "text", + "content": "tion, including FitNet [30], OD [5], LGD [45], DeFeat [11], GID [7], LD [46], FGFI [41], and CLSD [12]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "type": "text", + "content": "Table 5 presents the experimental results. We can observe that ScaleKD achieves superior performance on most evaluation metrics, i.e., on GFL-ResNet50, ScaleKD obtained a 2.8 higher AP score compared with baseline and 0.7 higher AP score compared to second best SOTA method (LD [46]). Furthermore, as we look at the " + }, + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "type": "text", + "content": ", the one that measures AP on small objects, we notice that our proposed method obtains a significantly better score than SOTA. For instance, ScaleKD improves " + }, + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 46, + 211, + 287, + 378 + ], + "type": "text", + "content": " by 3.4, 4.8, and 5.9 on GFL, RetinaNet, and FCOS, respectively. These results indicate that ScaleKD helps compact student detectors on detecting small objects, and it is much more effective than KD methods designed for general object detection." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "text", + "content": "Impact of Cross-Scale Assistant. We investigate the effectiveness of our proposed Cross-Scale Assistant module. We use standard image resolution for teachers in this section. We are primarily eager to know if CSA improves SOD performance and does the multi-scale cross-attention helps the student model. Table 6 gives empirical results. We can observe the CSA dramatically increase the AP score as well as " + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "text", + "content": " for the student RetinaNet model. Moreover, the MSC is critical to the performance. Compared to plain cross-attention, the MSC can improve the " + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "text", + "content": " by 1.4 and " + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "inline_equation", + "content": "AP_{S}" + }, + { + "bbox": [ + 46, + 391, + 287, + 547 + ], + "type": "text", + "content": " by 1.3. It verifies the advantage of our proposed multi-scale cross-attention over plain cross-attention in our KD framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": "Ablation study of Scale-Decoupled Feature. Table 7 presents the ablation study of the SDF module. We use standard image resolution for teachers in this section. We mainly discuss two aspects: whether SDF improves the performance of SOD and whether the weight-sharing method is worth using. First, we evaluate SDF on COCO with RetinaNet-ResNet50 as the baseline model. The experimental results show that the SDF is indeed effective in improving overall AP and " + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 558, + 287, + 713 + ], + "type": "text", + "content": " for small objects. Besides, using separate weights for parallel branches does not bring noticeable improvement in terms of average AP. Thus, it is worth using the weight-sharing module to save memory costs." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 316, + 70, + 537, + 130 + ], + "blocks": [ + { + "bbox": [ + 47, + 137, + 287, + 160 + ], + "lines": [ + { + "bbox": [ + 47, + 137, + 287, + 160 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 287, + 160 + ], + "type": "text", + "content": "Table 6. Ablation study for Cross-Scale Assistant. MSC: Multiscale Cross-Attention." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 316, + 70, + 537, + 130 + ], + "lines": [ + { + "bbox": [ + 316, + 70, + 537, + 130 + ], + "spans": [ + { + "bbox": [ + 316, + 70, + 537, + 130 + ], + "type": "table", + "html": "
MethodSDFWSAPAPSAPMAPL
Baseline--36.921.240.848.4
ScaleKD✓X41.624.944.853.7
✓✓41.624.844.653.9
", + "image_path": "e0ed40d8e78d5868f9dc64f9e556bf0661cc14f2282d8d0f494d065afd6a0927.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 313, + 175, + 539, + 255 + ], + "blocks": [ + { + "bbox": [ + 306, + 138, + 544, + 161 + ], + "lines": [ + { + "bbox": [ + 306, + 138, + 544, + 161 + ], + "spans": [ + { + "bbox": [ + 306, + 138, + 544, + 161 + ], + "type": "text", + "content": "Table 7. Ablation study for Scale-Decoupled Feature module. WS: weight-sharing." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 175, + 539, + 255 + ], + "lines": [ + { + "bbox": [ + 313, + 175, + 539, + 255 + ], + "spans": [ + { + "bbox": [ + 313, + 175, + 539, + 255 + ], + "type": "table", + "html": "
MethodScaleKDAPAPSAPMAPL
ResNet-18X35.818.938.947.9
ResNet-18✓37.220.140.249.3
ResNet-34X38.921.542.851.4
ResNet-34✓40.823.145.153.7
", + "image_path": "5af040c38ca2a4d120ef5f09dff59054581b24409f78943866cae0f19712ce9d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 263, + 545, + 285 + ], + "lines": [ + { + "bbox": [ + 305, + 263, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 263, + 545, + 285 + ], + "type": "text", + "content": "Table 8. Quantitative results of ScaleKD for diverse model complexity. We use ResNet101 as the teacher model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 320, + 545, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 500 + ], + "type": "text", + "content": "ScaleKD for Diverse Model Complexity. We further validate the effectiveness of our approach to diverse model complexity. Specifically, we evaluate COCO for two different student backbones, ResNet-18 and ResNet-34. Each model is distilled by a ResNet-101 detector. The results are presented in Table 8, which show that our method can effectively and stably improve the student model, regardless of the model complexity. This observation is contradicted by previous studies on image classification but consistent with the report on detection tasks. In particular, our approach improves the average AP by 1.2 and 2.5 on ResNet-18 and ResNet-34, respectively. Notably, the performance on small objects " + }, + { + "bbox": [ + 304, + 320, + 545, + 500 + ], + "type": "inline_equation", + "content": "(AP_S)" + }, + { + "bbox": [ + 304, + 320, + 545, + 500 + ], + "type": "text", + "content": " is boosted tremendously by 2.3 and 2.1. These results verified that our method is generally effective on varying model sizes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 513, + 375, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 375, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 375, + 525 + ], + "type": "text", + "content": "5. Discussion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 654 + ], + "type": "text", + "content": "Balancing inference speed and detection performance for small object detection is challenging. In this work, we propose a Scale-aware knowledge distillation that targets improving the performance of SOD via designed scale-decoupled feature distillation and cross-scale assistant. The former explicitly decouples multi-scale features, and the latter refines the teacher's bounding box noise for more informative knowledge in distillation. We evaluate two benchmarks, COCO 2017 and VisDrone, to demonstrate the effectiveness of our approach." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements: This work was partially supported by the Science and Technology Innovation Action Plan of Shanghai under Grant 2251110540, and Shanghai Pujiang Program under Grant 21PJ1420300." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19730" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 715 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Yancheng Bai, Yongqiang Zhang, Mingli Ding, and Bernard Ghanem. 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Our method randomly masks out and removes a large portion of image patches during training. Masking allows us to learn from more image-text pairs given the same wall-clock time and contrast more samples per iteration with similar memory footprint. It leads to a favorable trade-off between accuracy and training time. In our experiments on 400 million image-text pairs, FLIP improves both accuracy and speed over the no-masking baseline. On a large diversity of downstream tasks, FLIP dominantly outperforms the CLIP counterparts trained on the same data. Facilitated by the speedup, we explore the scaling behavior of increasing the model size, data size, or training length, and report encouraging results and comparisons. We hope that our work will foster future research on scaling vision-language learning.", + "bbox": [ + 75, + 318, + 473, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 584, + 209, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Language-supervised visual pre-training, e.g., CLIP [52], has been established as a simple yet powerful methodology for learning representations. Pre-trained CLIP models stand out for their remarkable versatility: they have strong zero-shot transferability [52]; they demonstrate unprecedented quality in text-to-image generation (e.g., [53, 55]); the pretrained encoder can improve multimodal and even unimodal visual tasks. Like the role played by supervised pre-training a decade ago [40], language-supervised visual pre-training is new fuel empowering various tasks today.", + "bbox": [ + 75, + 611, + 468, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unlike classical supervised learning with a pre-defined label set, natural language provides richer forms of supervision, e.g., on objects, scenes, actions, context, and their relations, at multiple levels of granularity. Due to the complex nature of vision plus language, large-scale training is essential for the capability of language-supervised models. For example, the original CLIP models [52] were trained on 400 million data for 32 epochs—which amount to 10,000 ImageNet [16] epochs, taking thousands of GPU-days [52, 36].", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d0d2b8d7d4fb65460cb2037e23610303bcb83458c8ed5e2cb32c5c8f5dc0e9df.jpg", + "image_caption": [ + "Figure 1. Accuracy vs. training time trade-off. With a high masking ratio of $50\\%$ or $75\\%$ , our FLIP method trains faster and is more accurate than its CLIP counterpart. All entries are benchmarked in 256 TPU-v3 cores. Training is done on LAION-400M for 6.4, 12.8, or 32 epochs, for each masking ratio. Accuracy is evaluated by zero-shot transfer on the ImageNet-1K validation set. The model is ViT-L/16 [20]. More details are in Fig. 3. As the CLIP baseline takes $\\sim 2,500$ TPU-days training, a speedup of $3.7\\times$ can save $\\sim 1,800$ TPU-days." + ], + "image_footnote": [], + "bbox": [ + 516, + 299, + 867, + 511 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Even using high-end infrastructures, the wall-clock training time is still a major bottleneck hindering explorations on scaling vision-language learning.", + "bbox": [ + 496, + 657, + 890, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present Fast Language-Image Pre-training (FLIP), a simple method for efficient CLIP training. Inspired by the sparse computation of Masked Autoencoders (MAE) [29], we randomly remove a large portion of image patches during training. This design introduces a trade-off between \"how carefully we look at a sample pair\" vs. \"how many sample pairs we can process\". Using masking, we can: (i) see more sample pairs (i.e., more epochs) under the same wall-clock training time, and (ii) compare/contrast more sample pairs at each step (i.e., larger batches) under similar memory footprint. Empirically, the benefits of processing more sample pairs greatly outweigh the degradation of per-sample encoding, resulting in a favorable trade-off.", + "bbox": [ + 496, + 704, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23390", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "By removing $50\\% - 75\\%$ patches of a training image, our method reduces computation by $2 - 4 \\times$ ; it also allows using $2 - 4 \\times$ larger batches with little extra memory cost, which boost accuracy thanks to the behavior of contrastive learning [30, 11]. As summarized in Fig. 1, FLIP trains $>3 \\times$ faster in wall-clock time for reaching similar accuracy as its CLIP counterpart; with the same number of epochs, FLIP reaches higher accuracy than its CLIP counterpart while still being $2 - 3 \\times$ faster.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We show that FLIP is a competitive alternative to CLIP on various downstream tasks. Pre-trained on the same LAION-400M dataset [56], FLIP dominantly outperforms its CLIP counterparts (OpenCLIP [36] and our own reproduction), as evaluated on a large variety of downstream datasets and transfer scenarios. These comparisons suggest that FLIP can readily enjoy the faster training speed while still providing accuracy gains.", + "bbox": [ + 75, + 226, + 472, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Facilitated by faster training, we explore scaling FLIP pre-training. We study these three axes: (i) scaling model size, (ii) scaling dataset size, or (iii) scaling training schedule length. We analyze the scaling behavior through carefully controlled experiments. We observe that model scaling and data scaling can both improve accuracy, and data scaling can show gains at no extra training cost. We hope our method, results, and analysis will encourage future research on scaling vision-language learning.", + "bbox": [ + 75, + 347, + 472, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 497, + 218, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning with masking. Denoising Autoencoders [63] with masking noise [64] were proposed as an unsupervised representation learning method over a decade ago. One of its most outstanding applications is masked language modeling represented by BERT [18]. In computer vision, explorations along this direction include predicting large missing regions [50], sequence of pixels [10], patches [20, 29, 71], or pre-computed features [6, 66].", + "bbox": [ + 75, + 522, + 468, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The Masked Autoencoder (MAE) method [29] further takes advantage of masking to reduce training time and memory. MAE sparsely applies the ViT encoder [20] to visible content. It also observes that a high masking ratio is beneficial for accuracy. The MAE design has been applied to videos [61, 22], point clouds [49], graphs [59, 9, 32], audio [4, 47, 13, 35], visual control [70, 57], vision-language [23, 41, 31, 19], and other modalities [5].", + "bbox": [ + 75, + 643, + 470, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is related to MAE and its vision-language extensions [23, 41, 31, 19]. However, our focus is on the scaling aspect enabled by the sparse computation; we address the challenge of large-scale CLIP training [52], while previous works [23, 41, 31, 19] are limited in terms of scale. Our method does not perform reconstruction and is not a form of autoencoding. Speeding up training by masking is studied in [69] for self-supervised contrastive learning, e.g., for MoCo [30] or BYOL [27], but its accuracy could be", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1b6c56d6081e807767b769055906b22530e5296098de4091184e3f925087d570.jpg", + "image_caption": [ + "Figure 2. Our FLIP architecture. Following CLIP [52], we perform contrastive learning on pairs of image and text samples. We randomly mask out image patches with a high masking ratio and encode only the visible patches. We do not perform reconstruction of masked image content." + ], + "image_footnote": [], + "bbox": [ + 545, + 88, + 834, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "limited by the scaling behavior of image-only contrastive learning.", + "bbox": [ + 496, + 347, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Language-supervised learning. In the past years, CLIP [52] and related works (e.g., [37, 51]) have popularized learning visual representations with language supervision. CLIP is a form of contrastive learning [28] by comparing image-text sample pairs. Beyond contrastive learning, generative learning methods have been explored [17, 65, 2, 74], optionally combined with contrastive losses [74]. Our method focuses on the CLIP method, while we hope it can be extended to generative methods in the future.", + "bbox": [ + 496, + 390, + 892, + 526 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 542, + 589, + 558 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In a nutshell, our method simply masks out the input data in CLIP [52] training and reduces computation. See Fig. 2.", + "bbox": [ + 496, + 570, + 890, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our scenario, the benefit of masking is on wisely spending computation. Intuitively, this leads to a trade-off between how densely we encode a sample against how many samples we compare as the learning signal. By introducing masking, we can: (i) learn from more image-text pairs under the same wall-clock training time, and (ii) have a contrastive objective over a larger batch under the same memory constraint. We show by experiments that for both aspects, our method is at an advantage in the trade-off. Next we introduce the key components of our method.", + "bbox": [ + 496, + 601, + 890, + 752 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image masking. We adopt the Vision Transformer (ViT) [20] as the image encoder. An image is first divided into a grid of non-overlapping patches. We randomly mask out a large portion (e.g., $50\\%$ or $75\\%$ ) of patches; the ViT encoder is only applied to the visible patches, following [29]. Using a masking ratio of $50\\%$ (or $75\\%$ ) reduces the time complexity of image encoding to 1/2 (or 1/4); it also allows using a $2\\times$ (or $4\\times$ ) larger batch with a similar memory cost for image encoding.", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23391", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text masking. Optionally, we perform text masking in the same way as image masking. We mask out a portion of the text tokens and apply the encoder only to the visible tokens, as in [29]. This is unlike BERT [18] that replaces them with a learned mask token. Such sparse computation can reduce the text encoding cost. However, as the text encoder is smaller [52], speeding it up does not lead to a better overall trade-off. We study text masking for ablation only.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Objective. The image/text encoders are trained to minimize a contrastive loss [48]. The negative sample pairs for contrastive learning consist of other samples in the same batch [11]. It has been observed that a large number of negative samples is critical for self-supervised contrastive learning on images [30, 11]. This property is more prominent in language-supervised learning.", + "bbox": [ + 75, + 220, + 468, + 325 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We do not use a reconstruction loss, unlike MAE [29]. We find that reconstruction is not necessary for good performance on zero-shot transfer. Waiving the decoder and reconstruction loss yields a better speedup.", + "bbox": [ + 76, + 325, + 468, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unmasking. While the encoder is pre-trained on masked images, it can be directly applied on intact images without changes, as is done in [29]. This simple setting is sufficient to provide competitive results and will serve as our baseline in ablation experiments.", + "bbox": [ + 75, + 395, + 468, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To close the distribution gap caused by masking, we can set the masking ratio as $0\\%$ and continue pre-training for a small number of steps. This unmasking tuning strategy produces a more favorable accuracy/time trade-off.", + "bbox": [ + 75, + 470, + 468, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Implementation", + "text_level": 1, + "bbox": [ + 76, + 542, + 236, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our implementation follows CLIP [52] and OpenCLIP [36], with a few modifications we describe in the following. Hyper-parameters are in the appendix.", + "bbox": [ + 75, + 566, + 468, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our image encoder follows the ViT paper [20]. We do not use the extra LayerNorm [3] after patch embedding, like [20] but unlike [52]. We use global average pooling at the end of the image encoder. The input size is 224.", + "bbox": [ + 75, + 612, + 468, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our text encoder is a non-autoregressive Transformer [62], which is easier to adapt to text masking for ablation. We use a WordPiece tokenizer as in [18]. We pad or cut the sequences to a fixed length of 32. We note that CLIP in [52] uses an autoregressive text encoder, a BytePairEncoding tokenizer, and a length of 77. These designs make marginal differences as observed in our initial reproduction.", + "bbox": [ + 75, + 672, + 468, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The outputs of the image encoder and text encoder are projected to the same-dimensional embedding space by a linear layer. The cosine similarities of the embeddings, scaled by a learnable temperature parameter [52], are the input to the InfoNCE loss [48].", + "bbox": [ + 75, + 779, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In zero-shot transfer, we follow the prompt engineering in the code of [52]. We use their provided 7 prompt templates for ImageNet zero-shot transfer.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our implementation is based on JAX [8] with the t5x library [54] for large-scale distributed training. Our training is run on TPU v3 infrastructure.", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 150, + 632, + 166 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Ablations", + "text_level": 1, + "bbox": [ + 500, + 174, + 609, + 189 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first ablate the FLIP design. The image encoder is ViT-L/16 [20], and the text encoder has a smaller size as per [52]. We train on LAION-400M [36] and evaluate zero-shot accuracy on ImageNet-1K [16] validation.", + "bbox": [ + 498, + 198, + 890, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 1 shows the ablations trained for 6.4 epochs. Fig. 1 plots the trade-off for up to 32 epochs [52]. The results are benchmarked in 256 TPU-v3 cores, unless noted.", + "bbox": [ + 498, + 258, + 890, + 304 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Masking ratio. Table 1a studies the image masking ratios. Here we scale the batch size accordingly (ablated next), so as to roughly maintain the memory footprint. $^{1}$ The $0\\%$ masking entry indicates our CLIP counterpart. Masking $50\\%$ gives $1.2\\%$ higher accuracy than the CLIP baseline, and masking $75\\%$ is on par with the baseline. Speed-wise, masking $50\\%$ or $75\\%$ takes only $0.50 \\times$ or $0.33 \\times$ wall-clock training time, thanks to the large reduction on FLOPs.", + "bbox": [ + 498, + 311, + 890, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Batch size. We ablate the effect of batch size in Table 1b. Increasing the batch size consistently improves accuracy.", + "bbox": [ + 498, + 439, + 890, + 469 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notably, even using the same batch size of 16k, our $50\\%$ masking entry has a comparable accuracy (68.5%, Table 1b) with the $0\\%$ masking baseline (68.6%, Table 1a). It is possible that the regularization introduced by masking can reduce overfitting, partially counteracting the negative effect of losing information in this setting. With a higher masking ratio of $75\\%$ , the negative effect is still observed when keeping the batch size unchanged.", + "bbox": [ + 496, + 469, + 890, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our masking-based method naturally encourages using large batches. There is little extra memory cost if we scale the batch size according to the masking ratio, as we report in Table 1a. In practice, the available memory is always a limitation for larger batches. For example, the setting in Table 1a has reached the memory limit in our high-end infrastructure (256 TPU-v3 cores with 16GB memory each). The memory issue is more demanding if using fewer devices, and the gain of our method would be more prominent due to the nearly free increase of batch sizes.", + "bbox": [ + 496, + 590, + 890, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text masking. Table 1c studies text masking. Randomly masking $50\\%$ text decreases accuracy by $2.2\\%$ . This is in line with the observation [29] that language data has higher", + "bbox": [ + 498, + 748, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1Directly comparing TPU memory usage can be difficult due to its memory optimizations. We instead validate GPU memory usage using [36]'s reimplementation of FLIP, and find the memory usage is 25.5G, 23.9G and 24.5G for masking $0\\%$ , $50\\%$ and $75\\%$ on 256 GPUs.", + "bbox": [ + 500, + 803, + 890, + 851 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2The \"mask $50\\%$ , 64k\" entry in Table 1b requires $2 \\times$ memory vs. those in Table 1a. This entry can be run using $2 \\times$ devices; instead, it can also use memory optimization (e.g., activation checkpointing [12]) that trades time with memory, which is beyond the focus of this work.", + "bbox": [ + 500, + 851, + 890, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23392", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/0dc543b135cf3c8a8b8be0dee380b6a568927a0e85d247cc74c41f0e079601a1.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Image masking yields higher or comparable accuracy and speeds up training. Entries are subject to the same memory limit." + ], + "table_body": "
maskbatchFLOPstimeacc.
0%16k1.00×1.00×68.6
50%32k0.52×0.50×69.6
75%64k0.28×0.33×68.2
", + "bbox": [ + 91, + 75, + 325, + 130 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/2d31a43b77bfa03eb770096e092dd82557609970d6c37c07609c54c211b3d81d.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Batch size. A large batch has big gains over smaller batches." + ], + "table_body": "
batchmask 50%mask 75%
16k68.565.8
32k69.667.3
64k70.468.2
", + "bbox": [ + 375, + 75, + 599, + 130 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/afe1f8f3c0469e8db8b6d2f3cb1cb028898d907cc96a6af05e6237ad2c071358.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Text masking performs decently, but the speed gain is marginal as its encoder is smaller. Here the image masking ratio is $75\\%$ ." + ], + "table_body": "
text masktext lentimeacc.
baseline, 0%321.00×68.2
random, 50%160.92×66.0
prioritized, 50%160.92×67.8
", + "bbox": [ + 645, + 75, + 885, + 132 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/06d384c9db9870ca6a2e9bc033c3245e3a0dbe189279216de1b23238f9cbc573.jpg", + "table_caption": [], + "table_footnote": [ + "(d) Inference unmasking. Inference on intact images performs strongly even without tuning." + ], + "table_body": "
mask 50%mask 75%
w/ mask66.460.9
w/ mask, ensemble68.165.1
w/o mask69.668.2
", + "bbox": [ + 84, + 185, + 333, + 239 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/4f20024fe4a3735292364904a132c5b8a6f416015394eae7e79bbc6f0200ef64.jpg", + "table_caption": [], + "table_footnote": [ + "(e) Unmasked tuning. The distribution shift by masking is reduced by a short tuning." + ], + "table_body": "
mask 50%mask 75%
baseline69.668.2
+ tuning70.169.5
", + "bbox": [ + 375, + 185, + 599, + 228 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/5353d31a804acea578aac871937376d3d9fe488712ac1874abb7ca07b2f39438.jpg", + "table_caption": [], + "table_footnote": [ + "(f) Reconstruction. Adding the MAE reconstruction loss has no gain." + ], + "table_body": "
mask 50%mask 75%
baseline69.668.2
+ MAE69.467.9
", + "bbox": [ + 645, + 185, + 885, + 228 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Zero-shot ablation experiments. Pre-training is on LAION-400M for 6.4 epochs, evaluated by zero-shot classification accuracy on ImageNet-1K validation. The backbone is ViT-L/16 [20]. Unless specified, the baseline setting is: image masking is $50\\%$ (batch 32k) or $75\\%$ (batch 64k), text masking is $0\\%$ , and no unmasked tuning is used.", + "bbox": [ + 75, + 272, + 892, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "information-density than images and thus the text masking ratio should be lower.", + "bbox": [ + 75, + 334, + 468, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As variable-length text sequences are padded to generate a fixed-length batch, we can prioritize masking out the padding tokens. Prioritized sampling preserves more valid tokens than randomly masking the padded sequences uniformly. It reduces the degradation to $0.4\\%$ .", + "bbox": [ + 75, + 364, + 468, + 441 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While our text masking is more aggressive than typical masked language models (e.g., $15\\%$ in [18]), the overall speed gain is marginal. This is because the text encoder is smaller and the text sequence is short. The text encoder costs merely $4.4\\%$ computation vs. the image encoder (without masking). Under this setting, text masking is not a worthwhile trade-off and we do not mask text in our other experiments.", + "bbox": [ + 75, + 441, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference unmasking. By default, we apply our models on intact images at inference-time, similar to [29]. While masking creates a distribution shift between training and inference, simply ignoring this shift works surprisingly well (Table 1d, 'w/o mask'), even under the zero-shot setting where no training is ever done on full images.", + "bbox": [ + 75, + 571, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1d reports that if using masking at inference time, the accuracy drops by a lot (e.g., $7.3\\%$ ). This drop can be partially caused by information loss at inference, so we also compare with ensembling multiple masked views [10], where the views are complementary to each other and put together cover all patches. Ensembling reduces the gap (Table 1d), but still lags behind the simple full-view inference.", + "bbox": [ + 75, + 662, + 468, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unmasked tuning. Our ablation experiments thus far do not involve unmasked tuning. Table 1e reports the results of unmasked tuning for extra 0.32 epoch on the pre-training dataset. It increases accuracy by $1.3\\%$ at the high masking ratio of $75\\%$ , suggesting that tuning can effectively reduce the distribution gap between pre-training and inference.", + "bbox": [ + 75, + 777, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 3 plots the trade-off affected by unmasked tuning (solid vs. dashed). Unmasked tuning leads to a more desir-", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/31a9ac3be46169703dc4614aa42bd9cb5af536e73352892010e46d8f4b6ca627.jpg", + "image_caption": [ + "Figure 3. Accuracy vs. training time trade-off in detail. The setting follows Table 1a. Training is for 6.4, 12.8, or 32 epochs, for each masking ratio. Unmasked tuning, if applied, is for 0.32 epoch. All are benchmarked in 256 TPU-v3 cores. Zero-shot accuracy is on IN-1K validation. The model is ViT-L/16. Our method speeds up training and increases accuracy." + ], + "image_footnote": [], + "bbox": [ + 509, + 330, + 874, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "able trade-off for $75\\%$ masking; it has a comparable tradeoff for $50\\%$ masking but improves final accuracy.", + "bbox": [ + 498, + 662, + 890, + 695 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reconstruction. In Table 1f we investigate adding a reconstruction loss function. The reconstruction head follows the design in MAE [29]: it has a small decoder and reconstructs normalized image pixels. The reconstruction loss is added to the contrastive loss.", + "bbox": [ + 498, + 703, + 890, + 777 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1f shows that reconstruction has a small negative impact for zero-short results. We also see a similar though slight less drop for fine-tuning accuracy on ImageNet. While this can be a result of suboptimal hyperparameters (e.g., balancing two losses), to strive for simplicity, we decide not to use the reconstruction loss. Waiving the reconstruction head also helps simplify the system and improves the accuracy/time trade-off.", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23393", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/23017eff9bf4448fab6ceb5a85cc3c2ef1f96e6a606833601c8c33e4e69e5a67.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
casedataepochsB/16L/16L/14H/14
CLIP [52]WIT-400M3268.6-75.3-
OpenCLIP [36]LAION-400M3267.1-72.8-
CLIP, our repro.LAION-400M3268.272.473.1-
FLIPLAION-400M3268.074.374.675.5
", + "bbox": [ + 240, + 88, + 723, + 157 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7bdcc788180553f0bd417e85f6deceda57b14db8a5da4c1d72d325c2ba3c9a59.jpg", + "table_caption": [ + "Table 2. Zero-shot accuracy on ImageNet-1K classification, compared with various CLIP baselines. The image size is 224. The entries noted by grey are pre-trained on a different dataset. Our models use a 64k batch, $50\\%$ masking ratio, and unmasked tuning." + ], + "table_footnote": [], + "table_body": "
casedataepochsmodelzero-shotlinear probefine-tune
CLIP [52]WIT-400M32L/1475.383.9†-
CLIP [52], our transferWIT-400M32L/1475.383.087.4
OpenCLIP [36]LAION-400M32L/1472.882.186.2
CLIP, our repro.LAION-400M32L/1672.482.686.3
FLIPLAION-400M32L/1674.383.686.9
", + "bbox": [ + 200, + 196, + 764, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 3. Linear probing and fine-tuning accuracy on ImageNet-1K classification, compared with various CLIP baselines. The entries noted by grey are pre-trained on a different dataset. The image size is 224. †: CLIP in [52] optimizes with L-BFGS; we use SGD instead.", + "bbox": [ + 75, + 284, + 888, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Accuracy vs. time trade-off. Fig. 3 presents a detailed view on the accuracy vs. training time trade-off. We extend the schedule to up to 32 epochs [52].", + "bbox": [ + 75, + 329, + 467, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 3, FLIP has a clearly better trade-off than the CLIP counterpart. It can achieve similar accuracy as CLIP while enjoying a speedup of $>3 \\times$ . With the same 32-epoch schedule, our method is $\\sim 1\\%$ more accurate than the CLIP counterpart and $2 \\times$ faster (masking $50\\%$ ).", + "bbox": [ + 75, + 375, + 467, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The speedup of our method is of great practical value. The CLIP baseline takes $\\sim 10$ days training in 256 TPU-v3 cores, so a speedup of $2 - 3\\times$ saves many days in wall-clock time. This speedup facilitates exploring the scaling behavior, as we will discuss later in Sec. 4.3.", + "bbox": [ + 75, + 450, + 467, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Comparisons with CLIP", + "text_level": 1, + "bbox": [ + 76, + 535, + 302, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we compare with various CLIP baselines in a large variety of scenarios. We show that our method is a competitive alternative to CLIP; as such, our fast training method is a more desirable choice in practice.", + "bbox": [ + 75, + 559, + 467, + 618 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We consider the following CLIP baselines:", + "bbox": [ + 96, + 625, + 379, + 640 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The original CLIP checkpoints [52], trained on the private dataset WIT-400M.", + "- OpenCLIP [36], trained on LAION-400M.", + "- Our CLIP reproduction, trained on LAION-400M." + ], + "bbox": [ + 94, + 650, + 467, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The original CLIP [52] was trained on a private dataset, so a direct comparison with it should reflect the effect of data, not just methods. OpenCLIP [36] is a faithful reproduction of CLIP yet trained on a public dataset that we can use, so it is a good reference for us to isolate the effect of dataset differences. Our CLIP reproduction further helps isolate other implementation subtleties and allows us to pinpoint the effect of the FLIP method.", + "bbox": [ + 75, + 734, + 467, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For all tasks studied in this subsection, we compare with all these CLIP baselines. This allows us to better understand the influence of the data and of the methods.", + "bbox": [ + 75, + 854, + 467, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ImageNet zero-shot transfer. In Table 2 we compare with the CLIP baselines on ImageNet-1K [16] zero-shot transfer.", + "bbox": [ + 498, + 329, + 888, + 358 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As a sanity check, our CLIP reproduction has slightly higher accuracy than OpenCLIP trained on the same data. The original CLIP has higher accuracy than our reproduction and OpenCLIP, which could be caused by the difference between the pre-training datasets.", + "bbox": [ + 496, + 359, + 888, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2 reports the results of our FLIP models, using the best practice as we have ablated in Table 1 (a 64k batch, $50\\%$ masking ratio, and unmasked tuning). For ViT-L/14, our method has $74.6\\%$ accuracy, which is $1.8\\%$ higher than OpenCLIP and $1.5\\%$ higher than our CLIP reproduction. Comparing with the original CLIP, our method reduces the gap to $0.7\\%$ . We hope our method will improve the original CLIP result if it were trained on the WIT data.", + "bbox": [ + 496, + 436, + 888, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ImageNet linear probing. Table 3 compares the linear probing results, i.e., training a linear classifier on the target dataset with frozen features. FLIP has $83.6\\%$ accuracy, $1.0\\%$ higher than our CLIP counterpart. It is also $0.6\\%$ higher than our transfer of the original CLIP checkpoint, using the same SGD trainer.", + "bbox": [ + 496, + 569, + 888, + 659 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ImageNet fine-tuning. Table 3 also compares full fine-tuning results. Our fine-tuning implementation follows MAE [29], with the learning rate tuned for each entry. It is worth noting that with our fine-tuning recipe, the original CLIP checkpoint reaches $87.4\\%$ , much higher than previous reports [68, 67, 33] on this metric. CLIP is still a strong model under the fine-tuning protocol.", + "bbox": [ + 496, + 670, + 888, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FLIP outperforms the CLIP counterparts pre-trained on the same data. Our result of $86.9\\%$ (or $87.1\\%$ using L/14) is behind but close to the result of the original CLIP checkpoint's $87.4\\%$ , using our fine-tuning recipe.", + "bbox": [ + 496, + 777, + 888, + 838 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "For a legacy reason, we pre-trained our ViT-L models with a patch size of 16, following the original ViT paper [20]. The CLIP paper [52] uses L/14 instead. To save resources, we report our L/14 results by tuning the L/16 pre-trained model, in a way similar to unmasked tuning.", + "bbox": [ + 496, + 849, + 888, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23394", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f06eb75316be5a013a46d201dbd7506082449787b23fc826202efff9e0fb8d4d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
dataFood101CIFAR10CIFAR100BrandsnapSUN397CarsAircraftVOC2007DTDOxfoot PetsCaltech101Flowers102MNISTSTL10EuroSATRESIC45GTSRBKITTICountry211PCamUCF101Kinetics700CLEVRHatefulMemesSST2
CLIP [52]WIT-400M92.996.277.948.367.777.336.184.155.393.592.678.787.299.359.971.650.323.132.758.876.260.324.363.364.0
CLIP [52], our eval.WIT-400M91.095.275.651.266.675.032.383.355.093.692.477.776.099.362.071.651.626.930.951.676.159.522.255.367.3
OpenCLIP [36], our eval.LAION-400M87.494.177.161.370.786.221.883.554.990.894.072.171.598.253.367.747.329.321.651.171.350.522.055.357.1
CLIP, our repro.LAION-400M88.196.081.360.572.389.125.881.159.393.293.274.669.196.550.769.250.229.421.453.171.553.518.553.357.2
FLIPLAION-400M89.397.284.163.073.190.729.183.160.492.693.875.080.398.553.570.841.434.823.150.374.155.822.754.058.5
", + "bbox": [ + 83, + 75, + 890, + 170 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4ca58ec2313bdec922e6e65cfd1c2598847ddd7330ecf7ad1d0e6ca6d3cb989e.jpg", + "table_caption": [ + "Table 4. Zero-shot accuracy on more classification datasets, compared with various CLIP baselines. This table follows Table 11 in [52]. The model is ViT-L/14 with an image size of 224, for all entries. Entries in green are the best ones using the LAION-400M data." + ], + "table_footnote": [], + "table_body": "
casemodeldatatext retrievalimage retrieval
Flickr30kCOCOFlickr30kCOCO
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [52]L/14@336WIT-400M88.098.799.458.481.588.168.790.695.237.862.472.2
CLIP [52], our eval.L/14@336WIT-400M88.998.799.958.780.487.972.591.795.238.562.872.5
CLIP [52], our eval.L/14WIT-400M87.899.199.856.279.886.469.390.294.035.860.770.7
OpenCLIP [36], our eval.L/14LAION-400M87.397.999.158.080.688.172.090.895.041.366.676.1
CLIP, our impl.L/14LAION-400M87.498.499.559.182.589.474.492.295.543.268.577.5
FLIPL/14LAION-400M89.198.599.660.282.689.975.492.595.944.269.278.4
", + "bbox": [ + 81, + 215, + 883, + 335 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/318e5f9dfca1dd02290a04404799f6a36cf1adc29091d642a84e6c19e3bc86ca.jpg", + "table_caption": [ + "Table 5. Zero-shot image/text retrieval, compared with various CLIP baselines. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data." + ], + "table_footnote": [], + "table_body": "
modeldataIN-V2 top-1IN-A top-1IN-R top-1ObjectNet top-1IN-Sketch top-1IN-VidYTBB
PM-0PM-10PM-0PM-10
CLIP [52]L/14@336WIT-400M70.177.288.972.360.295.389.295.288.5
CLIP [52], our eval.L/14@336WIT-400M70.478.089.069.359.795.988.895.389.4
CLIP [52], our eval.L/14WIT-400M69.571.986.868.658.594.687.094.186.4
OpenCLIP [36], our eval.L/14LAION-400M64.048.384.358.856.990.381.486.577.8
CLIP, our repro.L/14LAION-400M65.646.384.758.058.789.380.585.777.8
FLIPL/14LAION-400M66.851.286.559.159.991.183.589.483.3
", + "bbox": [ + 112, + 369, + 854, + 477 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1233e2f584451aa3dc148c8fa8cc87d2dc70c5a8f883816e33b806d79a40ce6c.jpg", + "table_caption": [ + "Table 6. Zero-shot robustness evaluation, compared with various CLIP baselines. This table follows Table 16 in [52]. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data." + ], + "table_footnote": [], + "table_body": "
casemodeldataCOCO captionnocapsVQAv2 acc.
BLEU-4METEORROUGE-LCIDErSPICECIDErSPICE
CLIP [52], our transferL/14WIT-400M37.529.658.7126.922.882.512.176.6
OpenCLIP [36], our transferL/14LAION-400M36.729.358.4125.022.783.412.374.5
CLIP, our repro.L/16LAION-400M36.429.358.4125.622.882.812.274.5
FLIPL/16LAION-400M37.429.558.8127.723.085.912.474.7
", + "bbox": [ + 104, + 520, + 859, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 7. Image Captioning and Visual Question Answering, compared with various CLIP baselines. Entries in green are the best ones using LAION-400M. Here the results are on the COCO captioning test split of [38], nocaps val split, and VQAv2 test-dev split, respectively.", + "bbox": [ + 75, + 611, + 890, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zero-shot classification on more datasets. In Table 4 we compare on the extra datasets studied in [52]. As the results can be sensitive to evaluation implementation (e.g., text prompts, image pre-processing), we provide our evaluations of the original CLIP checkpoint and OpenCLIP.", + "bbox": [ + 75, + 660, + 468, + 736 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Notably, we observe clear systematic gaps caused by pre-training data, as benchmarked using the same evaluation code. The WIT dataset is beneficial for some tasks (e.g., Aircraft, Country211, SST2), while LAION is beneficial for some others (e.g., Birdsnap, SUN397, Cars).", + "bbox": [ + 75, + 737, + 468, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "After isolating the influence of pre-training data, we observe that FLIP is dominantly better than OpenCLIP and our CLIP reproduction, as marked by green in Table 4.", + "bbox": [ + 75, + 813, + 468, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zero-shot retrieval. Table 5 reports image/text retrieval results on Flickr30k [73] and COCO [42]. FLIP outper", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "forms all CLIP competitors, including the original CLIP (evaluated on the same 224 size). The WIT dataset has no advantage over LAION for these two retrieval datasets.", + "bbox": [ + 496, + 660, + 890, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Zero-shot robustness evaluation. In Table 6 we compare on robustness evaluation, following [52]. We again observe clear systematic gaps caused by pre-training data. Using the same evaluation code (\"our eval\" in Table 6), CLIP pre-trained on WIT is clearly better than other entries pretrained on LAION. Taking IN-Adversarial (IN-A) as an example: the LAION-based OpenCLIP [36] has only $48.3\\%$ accuracy (or $46.6\\%$ reported by [36]). While FLIP $(51.2\\%)$ can outperform the LAION-based CLIP by a large margin, it is still $20\\%$ below the WIT-based CLIP $(71.9\\%)$ .", + "bbox": [ + 496, + 718, + 890, + 868 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Discounting the influence of pre-training data, our FLIP training has clearly better robustness than its CLIP counter", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23395", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "parts in all cases. We hypothesize that masking as a form of noise and regularization can improve robustness.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image Captioning. See Table 7 for the captioning performance on COCO [42] and nocaps [1]. Our captioning implementation follows the cross-entropy training baseline in [7]. Unlike classification in which only a classifier layer is added after pre-training, here the fine-tuning model has a newly initialized captioner (detailed in appendix). In this task, FLIP outperforms the original CLIP checkpoint in several metrics. Compared to our CLIP baseline, which is pretrained on the same data, FLIP also shows a clear gain, especially in BLEU-4 and CIDEr metrics.", + "bbox": [ + 75, + 127, + 468, + 277 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual Question Answering. We evaluate on the VQAv2 dataset [26], with a fine-tuning setup following [21]. We use a newly initialized multimodal fusion transformer and an answer classifier to obtain the VQA outputs (detailed in appendix). Table 7 (rightmost column) reports results on VQAv2. All entries pre-trained on LAION perform similarly, and CLIP pre-trained on WIT is the best.", + "bbox": [ + 75, + 282, + 468, + 390 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Summary of Comparisons. Across a large variety of scenarios, FLIP is dominantly better than its CLIP counterparts (OpenCLIP and our reproduction) pre-trained on the same LAION data, in some cases by large margins.", + "bbox": [ + 75, + 396, + 468, + 455 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The difference between the WIT data and LAION data can create large systematic gaps, as observed in many downstream tasks. We hope our study will draw attention to these data-dependent gaps in future research.", + "bbox": [ + 75, + 455, + 468, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Scaling Behavior", + "text_level": 1, + "bbox": [ + 76, + 525, + 243, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Facilitated by the speed-up of FLIP, we explore the scaling behavior beyond the largest case studied in CLIP [52]. We study scaling along either of these three axes:", + "bbox": [ + 75, + 547, + 468, + 594 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Model scaling. We replace the ViT-L image encoder with ViT-H, which has $\\sim 2\\times$ parameters. The text encoder is also scaled accordingly.", + "- Data scaling. We scale the pre-training data from 400 million to 2 billion, using the LAION-2B set [36]. To better separate the influence of more data from the influence of longer training, we fix the total number of sampled data (12.8B, which amounts to 32 epochs of 400M data and 6.4 epochs of 2B data).", + "- Schedule scaling. We increase the sampled data from 12.8B to 25.6B (64 epochs of 400M data)." + ], + "bbox": [ + 96, + 602, + 468, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We study scaling along one of these three axes at each time while keeping others unchanged. The results are summarized in Fig. 4 and Table 8.", + "bbox": [ + 75, + 789, + 468, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training curves. The three scaling strategies exhibit different trends in training curves (Fig. 4).", + "bbox": [ + 75, + 839, + 468, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Model scaling (Fig. 4a) presents a clear gap that persists throughout training, though the gap is smaller at the end.", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Data scaling (Fig. 4b), on the other hand, performs similarly at the first half of training, but starts to present a good gain later. Note that there is no extra computational cost in this setting, as we control the total number of sampled data.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Schedule scaling (Fig. 4c) trains $2 \\times$ longer. To provide a more intuitive comparison, we plot a hypothetical curve that is rescaled by $1/2$ along the x-axis (dashed line). Despite the longer training, the gain is diminishing or none (more numbers in Table 8).", + "bbox": [ + 498, + 151, + 890, + 227 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Transferability. Table 8 provides an all-around comparison on various downstream tasks regarding the scaling behavior. Overall, model scaling and data scaling both can consistently outperform the baseline in all metrics, in some cases by large margins.", + "bbox": [ + 498, + 234, + 890, + 310 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We categorize the downstream tasks into two scenarios: (i) zero-shot transfer, i.e., no learning is performed on the downstream dataset; (ii) transfer learning, i.e., part or all of the weights are trained on the downstream dataset. For the tasks studied here, data scaling is in general favored for zero-shot transfer, while model scaling is in general favored for transfer learning. However, it is worth noting that the transfer learning performance depends on the size of the downstream dataset, and training a big model on a too small downstream set is still subject to the overfitting risk.", + "bbox": [ + 496, + 311, + 890, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is encouraging to see that data scaling is clearly beneficial, even not incurring longer training nor additional computation. On the contrary, even spending more computation by schedule scaling gives diminishing returns. These comparisons suggest that large-scale data are beneficial mainly because they provide richer information.", + "bbox": [ + 496, + 462, + 890, + 551 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next we scale both model and data (Table 8, second last row). For all metrics, model+data scaling improves over scaling either alone. The gains of model scaling and data scaling are highly complementary: e.g., in zero-shot IN-1K, model scaling alone improves over the baseline by $1.2\\%$ $(74.3\\% \\rightarrow 75.5\\%)$ , and data scaling alone improves by $1.5\\%$ $(74.3\\% \\rightarrow 75.8\\%)$ . Scaling both improves by $3.3\\%$ $(77.6\\%)$ more than the two deltas combined. This behavior is also observed in several other tasks. This indicates that a larger model desires more data to unleash its potential.", + "bbox": [ + 496, + 551, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we report joint scaling all three axes (Table 8, last row). Our results show that combining schedule scaling leads to improved performances across most metrics. This suggests that schedule scaling is particularly beneficial when coupled with larger models and larger-scale data.", + "bbox": [ + 496, + 704, + 890, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our result of $78.8\\%$ on zero-shot IN-1K outperforms the state-of-the-art result trained on public data with ViT-H (78.0% of OpenCLIP). Also based on LAION-2B, their result is trained with 32B sampled data, $1.25 \\times$ more than ours. Given the $50\\%$ masking we use, our training is estimated to be $2.5 \\times$ faster than theirs if both were run on the same hardware. As OpenCLIP's result reports a training cost of $\\sim 5,600$ GPU-days, our method could save $\\sim 3,360$", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23396", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/02b4bdc23a772e4561f67c001e186e00167391369cfce802ee1aed77aade73cb.jpg", + "image_caption": [ + "(a) Model scaling" + ], + "image_footnote": [], + "bbox": [ + 83, + 82, + 287, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d4a22a880982422f13f1d31c3a5886971eaf10175e8b18d27d012efcd3bbab5.jpg", + "image_caption": [ + "(b) Data scaling", + "Figure 4. Training curves of scaling. The x-axis is the number of sampled data during training, and the y-axis is the zero-shot accuracy on IN-1K. The blue curve is the baseline setting: ViT-Large, LAION-400M data, 32 epochs (12.8B sampled data). In each subplot, we compare with scaling one factor on the baseline. In schedule scaling (Fig. 4c), we plot an extra hypothetical curve for a better visualization." + ], + "image_footnote": [], + "bbox": [ + 299, + 80, + 501, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2f2fae89268f559bb68426e148725731a5c27f268eedf54faba977e3bfc9c1db.jpg", + "image_caption": [ + "(c) Schedule scaling" + ], + "image_footnote": [], + "bbox": [ + 516, + 80, + 895, + 208 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/59ceba6c550f9fd7233bea705f0397ff03ecee60d207aefbd7f285cfd466a652.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
casemodeldatasampledzero-shot transfertransfer learning
zero-shot IN-1Ktext retrievalimage retrievallin-probe IN-1Kfine-tune IN-1Kcaptioning COCOnocapsvqa VQAv2
baselineLarge400M12.8B74.388.459.875.044.183.686.9127.785.974.7
model scalingHuge400M12.8B75.589.262.876.446.084.387.3130.391.576.3
data scalingLarge2B12.8B75.891.763.878.247.384.287.1128.987.075.5
schedule scalingLarge400M25.6B73.989.760.175.544.483.786.9127.986.875.0
model+data scalingHuge2B12.8B77.692.867.079.949.585.187.7130.492.677.1
joint scalingHuge2B25.6B78.893.167.880.950.585.687.9130.291.277.3
", + "bbox": [ + 91, + 292, + 877, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Scaling behavior of FLIP, evaluated on a diverse set of downstream tasks: classification, retrieval (R@1), captioning (CIDEr), and visual question answering. In the middle three rows, we scale along one of the three axes (model, data, schedule), and the green entries denote the best ones among these three scaling cases. Data scaling is in general favored under the zero-shot transfer scenario, while model scaling is in general favored under the transfer learning scenario (i.e., with trainable weights in downstream).", + "bbox": [ + 75, + 424, + 892, + 481 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "GPU-days based on a rough estimation. Additionally, without enabling $2 \\times$ schedule, our entry of \"model+data scaling\" is estimated $5 \\times$ faster than theirs and can save $\\sim 4,480$ GPU-days. This is considerable cost reduction.", + "bbox": [ + 75, + 501, + 470, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 76, + 573, + 326, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Language is a stronger form of supervision than classical closed-set labels. Language provides rich information for supervision. Therefore, scaling, which can involve increasing capacity (model scaling) and increasing information (data scaling), is essential for attaining good results in language-supervised training.", + "bbox": [ + 75, + 598, + 468, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "CLIP [52] is an outstanding example of \"simple algorithms that scale well\". The simple design of CLIP allows it to be relatively easily executed at substantially larger scales and achieve big leaps compared to preceding methods. Our method largely maintains the simplicity of CLIP while pushing it further along the scaling aspect.", + "bbox": [ + 75, + 688, + 468, + 780 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method can provide a $2 - 3 \\times$ speedup or more. For the scale concerned in this study, such a speedup can reduce wall-clock time by a great amount (e.g., at the order of thousands of TPU/GPU-days). Besides accelerating research cycles, the speedup can also save a great amount of energy and commercial cost. These are all ingredients of great importance in large-scale machine learning research.", + "bbox": [ + 75, + 780, + 470, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our study involves controlled comparisons with various", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "CLIP baselines, which help us to break down the gaps contributed by different factors. We show that FLIP outperforms its CLIP counterparts pre-trained on the same LAION data. By comparing several LAION-based models and the original WIT-based ones, we observe that the pre-training data creates big systematic gaps in several tasks.", + "bbox": [ + 496, + 501, + 892, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our study provides controlled experiments on scaling behavior. We observe that data scaling is a favored scaling dimension, given that it can improve accuracy with no extra cost at training or inference time. Our fast method encourages us to scale beyond what is studied in this work.", + "bbox": [ + 496, + 594, + 892, + 670 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Broader impacts. Training large-scale models costs high energy consumption and carbon emissions. While our method has reduced such cost to 1/2-1/3, the remaining cost is still sizable. We hope our work will attract more attention to the research direction on reducing the cost of training vision-language models.", + "bbox": [ + 496, + 686, + 892, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The numerical results in this paper are based on a publicly available large-scale dataset [56]. The resulting model weights will reflect the data biases, including potentially negative implications. When compared using the same data, the statistical differences between two methods should reflect the method properties to a good extent; however, when compared entries using different training data, the biases of the data should always be part of the considerations.", + "bbox": [ + 496, + 780, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23397", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. Nocaps: Novel object captioning at scale. 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In ICLR, 2018." + ], + "bbox": [ + 78, + 92, + 467, + 720 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23400", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Scaling Language-Image Pre-Training via Masking/72402de8-32e2-4c16-9bec-c8e1554c3fec_model.json b/2023/Scaling Language-Image Pre-Training via Masking/72402de8-32e2-4c16-9bec-c8e1554c3fec_model.json new file mode 100644 index 0000000000000000000000000000000000000000..fcb7cf36f056eb678a53a7ebf5583f53bdcd9e93 --- /dev/null +++ b/2023/Scaling Language-Image Pre-Training via Masking/72402de8-32e2-4c16-9bec-c8e1554c3fec_model.json @@ -0,0 +1,2796 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.229, + 0.131, + 0.743, + 0.154 + ], + "angle": 0, + "content": "Scaling Language-Image Pre-training via Masking" + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.18, + 0.838, + 0.201 + ], + "angle": 0, + "content": "Yanghao Li* Haoqi Fan* Ronghang Hu* Christoph Feichtenhofer† Kaiming He†" + }, + { + "type": "text", + "bbox": [ + 0.348, + 0.208, + 0.623, + 0.223 + ], + "angle": 0, + "content": "*equal technical contribution, †equal advising" + }, + { + "type": "text", + "bbox": [ + 0.42, + 0.231, + 0.546, + 0.247 + ], + "angle": 0, + "content": "Meta AI, FAIR" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.256, + 0.72, + 0.273 + ], + "angle": 0, + "content": "https://github.com/facebookresearch/flip" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.562 + ], + "angle": 0, + "content": "We present Fast Language-Image Pre-training (FLIP), a simple and more efficient method for training CLIP [52]. Our method randomly masks out and removes a large portion of image patches during training. Masking allows us to learn from more image-text pairs given the same wall-clock time and contrast more samples per iteration with similar memory footprint. It leads to a favorable trade-off between accuracy and training time. In our experiments on 400 million image-text pairs, FLIP improves both accuracy and speed over the no-masking baseline. On a large diversity of downstream tasks, FLIP dominantly outperforms the CLIP counterparts trained on the same data. Facilitated by the speedup, we explore the scaling behavior of increasing the model size, data size, or training length, and report encouraging results and comparisons. We hope that our work will foster future research on scaling vision-language learning." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.585, + 0.21, + 0.601 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.764 + ], + "angle": 0, + "content": "Language-supervised visual pre-training, e.g., CLIP [52], has been established as a simple yet powerful methodology for learning representations. Pre-trained CLIP models stand out for their remarkable versatility: they have strong zero-shot transferability [52]; they demonstrate unprecedented quality in text-to-image generation (e.g., [53, 55]); the pretrained encoder can improve multimodal and even unimodal visual tasks. Like the role played by supervised pre-training a decade ago [40], language-supervised visual pre-training is new fuel empowering various tasks today." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Unlike classical supervised learning with a pre-defined label set, natural language provides richer forms of supervision, e.g., on objects, scenes, actions, context, and their relations, at multiple levels of granularity. Due to the complex nature of vision plus language, large-scale training is essential for the capability of language-supervised models. For example, the original CLIP models [52] were trained on 400 million data for 32 epochs—which amount to 10,000 ImageNet [16] epochs, taking thousands of GPU-days [52, 36]." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.3, + 0.868, + 0.512 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.517, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Figure 1. Accuracy vs. training time trade-off. With a high masking ratio of \\(50\\%\\) or \\(75\\%\\), our FLIP method trains faster and is more accurate than its CLIP counterpart. All entries are benchmarked in 256 TPU-v3 cores. Training is done on LAION-400M for 6.4, 12.8, or 32 epochs, for each masking ratio. Accuracy is evaluated by zero-shot transfer on the ImageNet-1K validation set. The model is ViT-L/16 [20]. More details are in Fig. 3. As the CLIP baseline takes \\(\\sim 2,500\\) TPU-days training, a speedup of \\(3.7\\times\\) can save \\(\\sim 1,800\\) TPU-days." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Even using high-end infrastructures, the wall-clock training time is still a major bottleneck hindering explorations on scaling vision-language learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.902 + ], + "angle": 0, + "content": "We present Fast Language-Image Pre-training (FLIP), a simple method for efficient CLIP training. Inspired by the sparse computation of Masked Autoencoders (MAE) [29], we randomly remove a large portion of image patches during training. This design introduces a trade-off between \"how carefully we look at a sample pair\" vs. \"how many sample pairs we can process\". Using masking, we can: (i) see more sample pairs (i.e., more epochs) under the same wall-clock training time, and (ii) compare/contrast more sample pairs at each step (i.e., larger batches) under similar memory footprint. Empirically, the benefits of processing more sample pairs greatly outweigh the degradation of per-sample encoding, resulting in a favorable trade-off." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23390" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "By removing \\(50\\% - 75\\%\\) patches of a training image, our method reduces computation by \\(2 - 4 \\times\\); it also allows using \\(2 - 4 \\times\\) larger batches with little extra memory cost, which boost accuracy thanks to the behavior of contrastive learning [30, 11]. As summarized in Fig. 1, FLIP trains \\(>3 \\times\\) faster in wall-clock time for reaching similar accuracy as its CLIP counterpart; with the same number of epochs, FLIP reaches higher accuracy than its CLIP counterpart while still being \\(2 - 3 \\times\\) faster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.227, + 0.473, + 0.349 + ], + "angle": 0, + "content": "We show that FLIP is a competitive alternative to CLIP on various downstream tasks. Pre-trained on the same LAION-400M dataset [56], FLIP dominantly outperforms its CLIP counterparts (OpenCLIP [36] and our own reproduction), as evaluated on a large variety of downstream datasets and transfer scenarios. These comparisons suggest that FLIP can readily enjoy the faster training speed while still providing accuracy gains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.486 + ], + "angle": 0, + "content": "Facilitated by faster training, we explore scaling FLIP pre-training. We study these three axes: (i) scaling model size, (ii) scaling dataset size, or (iii) scaling training schedule length. We analyze the scaling behavior through carefully controlled experiments. We observe that model scaling and data scaling can both improve accuracy, and data scaling can show gains at no extra training cost. We hope our method, results, and analysis will encourage future research on scaling vision-language learning." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.22, + 0.513 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.644 + ], + "angle": 0, + "content": "Learning with masking. Denoising Autoencoders [63] with masking noise [64] were proposed as an unsupervised representation learning method over a decade ago. One of its most outstanding applications is masked language modeling represented by BERT [18]. In computer vision, explorations along this direction include predicting large missing regions [50], sequence of pixels [10], patches [20, 29, 71], or pre-computed features [6, 66]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.471, + 0.765 + ], + "angle": 0, + "content": "The Masked Autoencoder (MAE) method [29] further takes advantage of masking to reduce training time and memory. MAE sparsely applies the ViT encoder [20] to visible content. It also observes that a high masking ratio is beneficial for accuracy. The MAE design has been applied to videos [61, 22], point clouds [49], graphs [59, 9, 32], audio [4, 47, 13, 35], visual control [70, 57], vision-language [23, 41, 31, 19], and other modalities [5]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Our work is related to MAE and its vision-language extensions [23, 41, 31, 19]. However, our focus is on the scaling aspect enabled by the sparse computation; we address the challenge of large-scale CLIP training [52], while previous works [23, 41, 31, 19] are limited in terms of scale. Our method does not perform reconstruction and is not a form of autoencoding. Speeding up training by masking is studied in [69] for self-supervised contrastive learning, e.g., for MoCo [30] or BYOL [27], but its accuracy could be" + }, + { + "type": "image", + "bbox": [ + 0.546, + 0.089, + 0.835, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.249, + 0.895, + 0.32 + ], + "angle": 0, + "content": "Figure 2. Our FLIP architecture. Following CLIP [52], we perform contrastive learning on pairs of image and text samples. We randomly mask out image patches with a high masking ratio and encode only the visible patches. We do not perform reconstruction of masked image content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.348, + 0.892, + 0.379 + ], + "angle": 0, + "content": "limited by the scaling behavior of image-only contrastive learning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.391, + 0.893, + 0.527 + ], + "angle": 0, + "content": "Language-supervised learning. In the past years, CLIP [52] and related works (e.g., [37, 51]) have popularized learning visual representations with language supervision. CLIP is a form of contrastive learning [28] by comparing image-text sample pairs. Beyond contrastive learning, generative learning methods have been explored [17, 65, 2, 74], optionally combined with contrastive losses [74]. Our method focuses on the CLIP method, while we hope it can be extended to generative methods in the future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.544, + 0.591, + 0.559 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.571, + 0.892, + 0.601 + ], + "angle": 0, + "content": "In a nutshell, our method simply masks out the input data in CLIP [52] training and reduces computation. See Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.602, + 0.892, + 0.753 + ], + "angle": 0, + "content": "In our scenario, the benefit of masking is on wisely spending computation. Intuitively, this leads to a trade-off between how densely we encode a sample against how many samples we compare as the learning signal. By introducing masking, we can: (i) learn from more image-text pairs under the same wall-clock training time, and (ii) have a contrastive objective over a larger batch under the same memory constraint. We show by experiments that for both aspects, our method is at an advantage in the trade-off. Next we introduce the key components of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Image masking. We adopt the Vision Transformer (ViT) [20] as the image encoder. An image is first divided into a grid of non-overlapping patches. We randomly mask out a large portion (e.g., \\(50\\%\\) or \\(75\\%\\)) of patches; the ViT encoder is only applied to the visible patches, following [29]. Using a masking ratio of \\(50\\%\\) (or \\(75\\%\\)) reduces the time complexity of image encoding to 1/2 (or 1/4); it also allows using a \\(2\\times\\) (or \\(4\\times\\)) larger batch with a similar memory cost for image encoding." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23391" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "Text masking. Optionally, we perform text masking in the same way as image masking. We mask out a portion of the text tokens and apply the encoder only to the visible tokens, as in [29]. This is unlike BERT [18] that replaces them with a learned mask token. Such sparse computation can reduce the text encoding cost. However, as the text encoder is smaller [52], speeding it up does not lead to a better overall trade-off. We study text masking for ablation only." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.221, + 0.47, + 0.327 + ], + "angle": 0, + "content": "Objective. The image/text encoders are trained to minimize a contrastive loss [48]. The negative sample pairs for contrastive learning consist of other samples in the same batch [11]. It has been observed that a large number of negative samples is critical for self-supervised contrastive learning on images [30, 11]. This property is more prominent in language-supervised learning." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.327, + 0.47, + 0.389 + ], + "angle": 0, + "content": "We do not use a reconstruction loss, unlike MAE [29]. We find that reconstruction is not necessary for good performance on zero-shot transfer. Waiving the decoder and reconstruction loss yields a better speedup." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.47, + 0.472 + ], + "angle": 0, + "content": "Unmasking. While the encoder is pre-trained on masked images, it can be directly applied on intact images without changes, as is done in [29]. This simple setting is sufficient to provide competitive results and will serve as our baseline in ablation experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.533 + ], + "angle": 0, + "content": "To close the distribution gap caused by masking, we can set the masking ratio as \\(0\\%\\) and continue pre-training for a small number of steps. This unmasking tuning strategy produces a more favorable accuracy/time trade-off." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.544, + 0.238, + 0.559 + ], + "angle": 0, + "content": "3.1. Implementation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Our implementation follows CLIP [52] and OpenCLIP [36], with a few modifications we describe in the following. Hyper-parameters are in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.673 + ], + "angle": 0, + "content": "Our image encoder follows the ViT paper [20]. We do not use the extra LayerNorm [3] after patch embedding, like [20] but unlike [52]. We use global average pooling at the end of the image encoder. The input size is 224." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Our text encoder is a non-autoregressive Transformer [62], which is easier to adapt to text masking for ablation. We use a WordPiece tokenizer as in [18]. We pad or cut the sequences to a fixed length of 32. We note that CLIP in [52] uses an autoregressive text encoder, a BytePairEncoding tokenizer, and a length of 77. These designs make marginal differences as observed in our initial reproduction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.855 + ], + "angle": 0, + "content": "The outputs of the image encoder and text encoder are projected to the same-dimensional embedding space by a linear layer. The cosine similarities of the embeddings, scaled by a learnable temperature parameter [52], are the input to the InfoNCE loss [48]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In zero-shot transfer, we follow the prompt engineering in the code of [52]. We use their provided 7 prompt templates for ImageNet zero-shot transfer." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "Our implementation is based on JAX [8] with the t5x library [54] for large-scale distributed training. Our training is run on TPU v3 infrastructure." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.151, + 0.633, + 0.167 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.175, + 0.611, + 0.19 + ], + "angle": 0, + "content": "4.1. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.199, + 0.892, + 0.259 + ], + "angle": 0, + "content": "We first ablate the FLIP design. The image encoder is ViT-L/16 [20], and the text encoder has a smaller size as per [52]. We train on LAION-400M [36] and evaluate zero-shot accuracy on ImageNet-1K [16] validation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.26, + 0.892, + 0.305 + ], + "angle": 0, + "content": "Table 1 shows the ablations trained for 6.4 epochs. Fig. 1 plots the trade-off for up to 32 epochs [52]. The results are benchmarked in 256 TPU-v3 cores, unless noted." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.312, + 0.892, + 0.433 + ], + "angle": 0, + "content": "Masking ratio. Table 1a studies the image masking ratios. Here we scale the batch size accordingly (ablated next), so as to roughly maintain the memory footprint.\\(^{1}\\) The \\(0\\%\\) masking entry indicates our CLIP counterpart. Masking \\(50\\%\\) gives \\(1.2\\%\\) higher accuracy than the CLIP baseline, and masking \\(75\\%\\) is on par with the baseline. Speed-wise, masking \\(50\\%\\) or \\(75\\%\\) takes only \\(0.50 \\times\\) or \\(0.33 \\times\\) wall-clock training time, thanks to the large reduction on FLOPs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.44, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Batch size. We ablate the effect of batch size in Table 1b. Increasing the batch size consistently improves accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Notably, even using the same batch size of 16k, our \\(50\\%\\) masking entry has a comparable accuracy (68.5%, Table 1b) with the \\(0\\%\\) masking baseline (68.6%, Table 1a). It is possible that the regularization introduced by masking can reduce overfitting, partially counteracting the negative effect of losing information in this setting. With a higher masking ratio of \\(75\\%\\), the negative effect is still observed when keeping the batch size unchanged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.892, + 0.741 + ], + "angle": 0, + "content": "Our masking-based method naturally encourages using large batches. There is little extra memory cost if we scale the batch size according to the masking ratio, as we report in Table 1a. In practice, the available memory is always a limitation for larger batches. For example, the setting in Table 1a has reached the memory limit in our high-end infrastructure (256 TPU-v3 cores with 16GB memory each). The memory issue is more demanding if using fewer devices, and the gain of our method would be more prominent due to the nearly free increase of batch sizes." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.749, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Text masking. Table 1c studies text masking. Randomly masking \\(50\\%\\) text decreases accuracy by \\(2.2\\%\\). This is in line with the observation [29] that language data has higher" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.804, + 0.892, + 0.852 + ], + "angle": 0, + "content": "1Directly comparing TPU memory usage can be difficult due to its memory optimizations. We instead validate GPU memory usage using [36]'s reimplementation of FLIP, and find the memory usage is 25.5G, 23.9G and 24.5G for masking \\(0\\%\\), \\(50\\%\\) and \\(75\\%\\) on 256 GPUs." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.852, + 0.892, + 0.9 + ], + "angle": 0, + "content": "2The \"mask \\(50\\%\\), 64k\" entry in Table 1b requires \\(2 \\times\\) memory vs. those in Table 1a. This entry can be run using \\(2 \\times\\) devices; instead, it can also use memory optimization (e.g., activation checkpointing [12]) that trades time with memory, which is beyond the focus of this work." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.804, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23392" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.092, + 0.077, + 0.326, + 0.131 + ], + "angle": 0, + "content": "
maskbatchFLOPstimeacc.
0%16k1.00×1.00×68.6
50%32k0.52×0.50×69.6
75%64k0.28×0.33×68.2
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.082, + 0.135, + 0.331, + 0.171 + ], + "angle": 0, + "content": "(a) Image masking yields higher or comparable accuracy and speeds up training. Entries are subject to the same memory limit." + }, + { + "type": "table", + "bbox": [ + 0.377, + 0.077, + 0.6, + 0.131 + ], + "angle": 0, + "content": "
batchmask 50%mask 75%
16k68.565.8
32k69.667.3
64k70.468.2
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.361, + 0.134, + 0.609, + 0.158 + ], + "angle": 0, + "content": "(b) Batch size. A large batch has big gains over smaller batches." + }, + { + "type": "table", + "bbox": [ + 0.647, + 0.077, + 0.887, + 0.133 + ], + "angle": 0, + "content": "
text masktext lentimeacc.
baseline, 0%321.00×68.2
random, 50%160.92×66.0
prioritized, 50%160.92×67.8
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.641, + 0.135, + 0.888, + 0.171 + ], + "angle": 0, + "content": "(c) Text masking performs decently, but the speed gain is marginal as its encoder is smaller. Here the image masking ratio is \\(75\\%\\)." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.186, + 0.334, + 0.24 + ], + "angle": 0, + "content": "
mask 50%mask 75%
w/ mask66.460.9
w/ mask, ensemble68.165.1
w/o mask69.668.2
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.082, + 0.243, + 0.331, + 0.269 + ], + "angle": 0, + "content": "(d) Inference unmasking. Inference on intact images performs strongly even without tuning." + }, + { + "type": "table", + "bbox": [ + 0.377, + 0.186, + 0.6, + 0.229 + ], + "angle": 0, + "content": "
mask 50%mask 75%
baseline69.668.2
+ tuning70.169.5
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.361, + 0.243, + 0.608, + 0.269 + ], + "angle": 0, + "content": "(e) Unmasked tuning. The distribution shift by masking is reduced by a short tuning." + }, + { + "type": "table", + "bbox": [ + 0.647, + 0.186, + 0.887, + 0.229 + ], + "angle": 0, + "content": "
mask 50%mask 75%
baseline69.668.2
+ MAE69.467.9
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.641, + 0.243, + 0.887, + 0.268 + ], + "angle": 0, + "content": "(f) Reconstruction. Adding the MAE reconstruction loss has no gain." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.273, + 0.893, + 0.315 + ], + "angle": 0, + "content": "Table 1. Zero-shot ablation experiments. Pre-training is on LAION-400M for 6.4 epochs, evaluated by zero-shot classification accuracy on ImageNet-1K validation. The backbone is ViT-L/16 [20]. Unless specified, the baseline setting is: image masking is \\(50\\%\\) (batch 32k) or \\(75\\%\\) (batch 64k), text masking is \\(0\\%\\), and no unmasked tuning is used." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.469, + 0.365 + ], + "angle": 0, + "content": "information-density than images and thus the text masking ratio should be lower." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.469, + 0.442 + ], + "angle": 0, + "content": "As variable-length text sequences are padded to generate a fixed-length batch, we can prioritize masking out the padding tokens. Prioritized sampling preserves more valid tokens than randomly masking the padded sequences uniformly. It reduces the degradation to \\(0.4\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.563 + ], + "angle": 0, + "content": "While our text masking is more aggressive than typical masked language models (e.g., \\(15\\%\\) in [18]), the overall speed gain is marginal. This is because the text encoder is smaller and the text sequence is short. The text encoder costs merely \\(4.4\\%\\) computation vs. the image encoder (without masking). Under this setting, text masking is not a worthwhile trade-off and we do not mask text in our other experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.469, + 0.663 + ], + "angle": 0, + "content": "Inference unmasking. By default, we apply our models on intact images at inference-time, similar to [29]. While masking creates a distribution shift between training and inference, simply ignoring this shift works surprisingly well (Table 1d, 'w/o mask'), even under the zero-shot setting where no training is ever done on full images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.469, + 0.77 + ], + "angle": 0, + "content": "Table 1d reports that if using masking at inference time, the accuracy drops by a lot (e.g., \\(7.3\\%\\)). This drop can be partially caused by information loss at inference, so we also compare with ensembling multiple masked views [10], where the views are complementary to each other and put together cover all patches. Ensembling reduces the gap (Table 1d), but still lags behind the simple full-view inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.87 + ], + "angle": 0, + "content": "Unmasked tuning. Our ablation experiments thus far do not involve unmasked tuning. Table 1e reports the results of unmasked tuning for extra 0.32 epoch on the pre-training dataset. It increases accuracy by \\(1.3\\%\\) at the high masking ratio of \\(75\\%\\), suggesting that tuning can effectively reduce the distribution gap between pre-training and inference." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Fig. 3 plots the trade-off affected by unmasked tuning (solid vs. dashed). Unmasked tuning leads to a more desir-" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.331, + 0.875, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.559, + 0.893, + 0.644 + ], + "angle": 0, + "content": "Figure 3. Accuracy vs. training time trade-off in detail. The setting follows Table 1a. Training is for 6.4, 12.8, or 32 epochs, for each masking ratio. Unmasked tuning, if applied, is for 0.32 epoch. All are benchmarked in 256 TPU-v3 cores. Zero-shot accuracy is on IN-1K validation. The model is ViT-L/16. Our method speeds up training and increases accuracy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.664, + 0.892, + 0.696 + ], + "angle": 0, + "content": "able trade-off for \\(75\\%\\) masking; it has a comparable tradeoff for \\(50\\%\\) masking but improves final accuracy." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.704, + 0.892, + 0.779 + ], + "angle": 0, + "content": "Reconstruction. In Table 1f we investigate adding a reconstruction loss function. The reconstruction head follows the design in MAE [29]: it has a small decoder and reconstructs normalized image pixels. The reconstruction loss is added to the contrastive loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Table 1f shows that reconstruction has a small negative impact for zero-short results. We also see a similar though slight less drop for fine-tuning accuracy on ImageNet. While this can be a result of suboptimal hyperparameters (e.g., balancing two losses), to strive for simplicity, we decide not to use the reconstruction loss. Waiving the reconstruction head also helps simplify the system and improves the accuracy/time trade-off." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23393" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.241, + 0.089, + 0.725, + 0.158 + ], + "angle": 0, + "content": "
casedataepochsB/16L/16L/14H/14
CLIP [52]WIT-400M3268.6-75.3-
OpenCLIP [36]LAION-400M3267.1-72.8-
CLIP, our repro.LAION-400M3268.272.473.1-
FLIPLAION-400M3268.074.374.675.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.16, + 0.89, + 0.188 + ], + "angle": 0, + "content": "Table 2. Zero-shot accuracy on ImageNet-1K classification, compared with various CLIP baselines. The image size is 224. The entries noted by grey are pre-trained on a different dataset. Our models use a 64k batch, \\(50\\%\\) masking ratio, and unmasked tuning." + }, + { + "type": "table", + "bbox": [ + 0.202, + 0.197, + 0.766, + 0.279 + ], + "angle": 0, + "content": "
casedataepochsmodelzero-shotlinear probefine-tune
CLIP [52]WIT-400M32L/1475.383.9†-
CLIP [52], our transferWIT-400M32L/1475.383.087.4
OpenCLIP [36]LAION-400M32L/1472.882.186.2
CLIP, our repro.LAION-400M32L/1672.482.686.3
FLIPLAION-400M32L/1674.383.686.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.285, + 0.89, + 0.313 + ], + "angle": 0, + "content": "Table 3. Linear probing and fine-tuning accuracy on ImageNet-1K classification, compared with various CLIP baselines. The entries noted by grey are pre-trained on a different dataset. The image size is 224. †: CLIP in [52] optimizes with L-BFGS; we use SGD instead." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.468, + 0.375 + ], + "angle": 0, + "content": "Accuracy vs. time trade-off. Fig. 3 presents a detailed view on the accuracy vs. training time trade-off. We extend the schedule to up to 32 epochs [52]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.468, + 0.45 + ], + "angle": 0, + "content": "As shown in Fig. 3, FLIP has a clearly better trade-off than the CLIP counterpart. It can achieve similar accuracy as CLIP while enjoying a speedup of \\(>3 \\times\\). With the same 32-epoch schedule, our method is \\(\\sim 1\\%\\) more accurate than the CLIP counterpart and \\(2 \\times\\) faster (masking \\(50\\%\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.468, + 0.526 + ], + "angle": 0, + "content": "The speedup of our method is of great practical value. The CLIP baseline takes \\(\\sim 10\\) days training in 256 TPU-v3 cores, so a speedup of \\(2 - 3\\times\\) saves many days in wall-clock time. This speedup facilitates exploring the scaling behavior, as we will discuss later in Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.536, + 0.303, + 0.551 + ], + "angle": 0, + "content": "4.2. Comparisons with CLIP" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.468, + 0.619 + ], + "angle": 0, + "content": "In this section, we compare with various CLIP baselines in a large variety of scenarios. We show that our method is a competitive alternative to CLIP; as such, our fast training method is a more desirable choice in practice." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.626, + 0.38, + 0.641 + ], + "angle": 0, + "content": "We consider the following CLIP baselines:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.651, + 0.468, + 0.68 + ], + "angle": 0, + "content": "- The original CLIP checkpoints [52], trained on the private dataset WIT-400M." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.688, + 0.393, + 0.703 + ], + "angle": 0, + "content": "- OpenCLIP [36], trained on LAION-400M." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.71, + 0.443, + 0.724 + ], + "angle": 0, + "content": "- Our CLIP reproduction, trained on LAION-400M." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.651, + 0.468, + 0.724 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.854 + ], + "angle": 0, + "content": "The original CLIP [52] was trained on a private dataset, so a direct comparison with it should reflect the effect of data, not just methods. OpenCLIP [36] is a faithful reproduction of CLIP yet trained on a public dataset that we can use, so it is a good reference for us to isolate the effect of dataset differences. Our CLIP reproduction further helps isolate other implementation subtleties and allows us to pinpoint the effect of the FLIP method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.9 + ], + "angle": 0, + "content": "For all tasks studied in this subsection, we compare with all these CLIP baselines. This allows us to better understand the influence of the data and of the methods." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.33, + 0.89, + 0.359 + ], + "angle": 0, + "content": "ImageNet zero-shot transfer. In Table 2 we compare with the CLIP baselines on ImageNet-1K [16] zero-shot transfer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.89, + 0.435 + ], + "angle": 0, + "content": "As a sanity check, our CLIP reproduction has slightly higher accuracy than OpenCLIP trained on the same data. The original CLIP has higher accuracy than our reproduction and OpenCLIP, which could be caused by the difference between the pre-training datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.89, + 0.558 + ], + "angle": 0, + "content": "Table 2 reports the results of our FLIP models, using the best practice as we have ablated in Table 1 (a 64k batch, \\(50\\%\\) masking ratio, and unmasked tuning). For ViT-L/14, our method has \\(74.6\\%\\) accuracy, which is \\(1.8\\%\\) higher than OpenCLIP and \\(1.5\\%\\) higher than our CLIP reproduction. Comparing with the original CLIP, our method reduces the gap to \\(0.7\\%\\). We hope our method will improve the original CLIP result if it were trained on the WIT data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.89, + 0.66 + ], + "angle": 0, + "content": "ImageNet linear probing. Table 3 compares the linear probing results, i.e., training a linear classifier on the target dataset with frozen features. FLIP has \\(83.6\\%\\) accuracy, \\(1.0\\%\\) higher than our CLIP counterpart. It is also \\(0.6\\%\\) higher than our transfer of the original CLIP checkpoint, using the same SGD trainer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.89, + 0.777 + ], + "angle": 0, + "content": "ImageNet fine-tuning. Table 3 also compares full fine-tuning results. Our fine-tuning implementation follows MAE [29], with the learning rate tuned for each entry. It is worth noting that with our fine-tuning recipe, the original CLIP checkpoint reaches \\(87.4\\%\\), much higher than previous reports [68, 67, 33] on this metric. CLIP is still a strong model under the fine-tuning protocol." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.89, + 0.839 + ], + "angle": 0, + "content": "FLIP outperforms the CLIP counterparts pre-trained on the same data. Our result of \\(86.9\\%\\) (or \\(87.1\\%\\) using L/14) is behind but close to the result of the original CLIP checkpoint's \\(87.4\\%\\), using our fine-tuning recipe." + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.851, + 0.89, + 0.901 + ], + "angle": 0, + "content": "For a legacy reason, we pre-trained our ViT-L models with a patch size of 16, following the original ViT paper [20]. The CLIP paper [52] uses L/14 instead. To save resources, we report our L/14 results by tuning the L/16 pre-trained model, in a way similar to unmasked tuning." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23394" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.077, + 0.891, + 0.171 + ], + "angle": 0, + "content": "
dataFood101CIFAR10CIFAR100BrandsnapSUN397CarsAircraftVOC2007DTDOxfoot PetsCaltech101Flowers102MNISTSTL10EuroSATRESIC45GTSRBKITTICountry211PCamUCF101Kinetics700CLEVRHatefulMemesSST2
CLIP [52]WIT-400M92.996.277.948.367.777.336.184.155.393.592.678.787.299.359.971.650.323.132.758.876.260.324.363.364.0
CLIP [52], our eval.WIT-400M91.095.275.651.266.675.032.383.355.093.692.477.776.099.362.071.651.626.930.951.676.159.522.255.367.3
OpenCLIP [36], our eval.LAION-400M87.494.177.161.370.786.221.883.554.990.894.072.171.598.253.367.747.329.321.651.171.350.522.055.357.1
CLIP, our repro.LAION-400M88.196.081.360.572.389.125.881.159.393.293.274.669.196.550.769.250.229.421.453.171.553.518.553.357.2
FLIPLAION-400M89.397.284.163.073.190.729.183.160.492.693.875.080.398.553.570.841.434.823.150.374.155.822.754.058.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.177, + 0.891, + 0.204 + ], + "angle": 0, + "content": "Table 4. Zero-shot accuracy on more classification datasets, compared with various CLIP baselines. This table follows Table 11 in [52]. The model is ViT-L/14 with an image size of 224, for all entries. Entries in green are the best ones using the LAION-400M data." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.217, + 0.885, + 0.337 + ], + "angle": 0, + "content": "
casemodeldatatext retrievalimage retrieval
Flickr30kCOCOFlickr30kCOCO
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [52]L/14@336WIT-400M88.098.799.458.481.588.168.790.695.237.862.472.2
CLIP [52], our eval.L/14@336WIT-400M88.998.799.958.780.487.972.591.795.238.562.872.5
CLIP [52], our eval.L/14WIT-400M87.899.199.856.279.886.469.390.294.035.860.770.7
OpenCLIP [36], our eval.L/14LAION-400M87.397.999.158.080.688.172.090.895.041.366.676.1
CLIP, our impl.L/14LAION-400M87.498.499.559.182.589.474.492.295.543.268.577.5
FLIPL/14LAION-400M89.198.599.660.282.689.975.492.595.944.269.278.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.343, + 0.891, + 0.369 + ], + "angle": 0, + "content": "Table 5. Zero-shot image/text retrieval, compared with various CLIP baselines. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data." + }, + { + "type": "table", + "bbox": [ + 0.114, + 0.371, + 0.855, + 0.478 + ], + "angle": 0, + "content": "
modeldataIN-V2 top-1IN-A top-1IN-R top-1ObjectNet top-1IN-Sketch top-1IN-VidYTBB
PM-0PM-10PM-0PM-10
CLIP [52]L/14@336WIT-400M70.177.288.972.360.295.389.295.288.5
CLIP [52], our eval.L/14@336WIT-400M70.478.089.069.359.795.988.895.389.4
CLIP [52], our eval.L/14WIT-400M69.571.986.868.658.594.687.094.186.4
OpenCLIP [36], our eval.L/14LAION-400M64.048.384.358.856.990.381.486.577.8
CLIP, our repro.L/14LAION-400M65.646.384.758.058.789.380.585.777.8
FLIPL/14LAION-400M66.851.286.559.159.991.183.589.483.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.483, + 0.891, + 0.51 + ], + "angle": 0, + "content": "Table 6. Zero-shot robustness evaluation, compared with various CLIP baselines. This table follows Table 16 in [52]. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data." + }, + { + "type": "table", + "bbox": [ + 0.105, + 0.521, + 0.861, + 0.606 + ], + "angle": 0, + "content": "
casemodeldataCOCO captionnocapsVQAv2 acc.
BLEU-4METEORROUGE-LCIDErSPICECIDErSPICE
CLIP [52], our transferL/14WIT-400M37.529.658.7126.922.882.512.176.6
OpenCLIP [36], our transferL/14LAION-400M36.729.358.4125.022.783.412.374.5
CLIP, our repro.L/16LAION-400M36.429.358.4125.622.882.812.274.5
FLIPL/16LAION-400M37.429.558.8127.723.085.912.474.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.612, + 0.891, + 0.64 + ], + "angle": 0, + "content": "Table 7. Image Captioning and Visual Question Answering, compared with various CLIP baselines. Entries in green are the best ones using LAION-400M. Here the results are on the COCO captioning test split of [38], nocaps val split, and VQAv2 test-dev split, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.661, + 0.469, + 0.737 + ], + "angle": 0, + "content": "Zero-shot classification on more datasets. In Table 4 we compare on the extra datasets studied in [52]. As the results can be sensitive to evaluation implementation (e.g., text prompts, image pre-processing), we provide our evaluations of the original CLIP checkpoint and OpenCLIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.469, + 0.813 + ], + "angle": 0, + "content": "Notably, we observe clear systematic gaps caused by pre-training data, as benchmarked using the same evaluation code. The WIT dataset is beneficial for some tasks (e.g., Aircraft, Country211, SST2), while LAION is beneficial for some others (e.g., Birdsnap, SUN397, Cars)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.814, + 0.469, + 0.86 + ], + "angle": 0, + "content": "After isolating the influence of pre-training data, we observe that FLIP is dominantly better than OpenCLIP and our CLIP reproduction, as marked by green in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Zero-shot retrieval. Table 5 reports image/text retrieval results on Flickr30k [73] and COCO [42]. FLIP outper" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.891, + 0.706 + ], + "angle": 0, + "content": "forms all CLIP competitors, including the original CLIP (evaluated on the same 224 size). The WIT dataset has no advantage over LAION for these two retrieval datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Zero-shot robustness evaluation. In Table 6 we compare on robustness evaluation, following [52]. We again observe clear systematic gaps caused by pre-training data. Using the same evaluation code (\"our eval\" in Table 6), CLIP pre-trained on WIT is clearly better than other entries pretrained on LAION. Taking IN-Adversarial (IN-A) as an example: the LAION-based OpenCLIP [36] has only \\(48.3\\%\\) accuracy (or \\(46.6\\%\\) reported by [36]). While FLIP \\((51.2\\%)\\) can outperform the LAION-based CLIP by a large margin, it is still \\(20\\%\\) below the WIT-based CLIP \\((71.9\\%)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Discounting the influence of pre-training data, our FLIP training has clearly better robustness than its CLIP counter" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23395" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "parts in all cases. We hypothesize that masking as a form of noise and regularization can improve robustness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.128, + 0.47, + 0.278 + ], + "angle": 0, + "content": "Image Captioning. See Table 7 for the captioning performance on COCO [42] and nocaps [1]. Our captioning implementation follows the cross-entropy training baseline in [7]. Unlike classification in which only a classifier layer is added after pre-training, here the fine-tuning model has a newly initialized captioner (detailed in appendix). In this task, FLIP outperforms the original CLIP checkpoint in several metrics. Compared to our CLIP baseline, which is pretrained on the same data, FLIP also shows a clear gain, especially in BLEU-4 and CIDEr metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.47, + 0.391 + ], + "angle": 0, + "content": "Visual Question Answering. We evaluate on the VQAv2 dataset [26], with a fine-tuning setup following [21]. We use a newly initialized multimodal fusion transformer and an answer classifier to obtain the VQA outputs (detailed in appendix). Table 7 (rightmost column) reports results on VQAv2. All entries pre-trained on LAION perform similarly, and CLIP pre-trained on WIT is the best." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.469, + 0.457 + ], + "angle": 0, + "content": "Summary of Comparisons. Across a large variety of scenarios, FLIP is dominantly better than its CLIP counterparts (OpenCLIP and our reproduction) pre-trained on the same LAION data, in some cases by large margins." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.469, + 0.517 + ], + "angle": 0, + "content": "The difference between the WIT data and LAION data can create large systematic gaps, as observed in many downstream tasks. We hope our study will draw attention to these data-dependent gaps in future research." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.245, + 0.541 + ], + "angle": 0, + "content": "4.3. Scaling Behavior" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.469, + 0.595 + ], + "angle": 0, + "content": "Facilitated by the speed-up of FLIP, we explore the scaling behavior beyond the largest case studied in CLIP [52]. We study scaling along either of these three axes:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.603, + 0.469, + 0.648 + ], + "angle": 0, + "content": "- Model scaling. We replace the ViT-L image encoder with ViT-H, which has \\(\\sim 2\\times\\) parameters. The text encoder is also scaled accordingly." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.654, + 0.47, + 0.744 + ], + "angle": 0, + "content": "- Data scaling. We scale the pre-training data from 400 million to 2 billion, using the LAION-2B set [36]. To better separate the influence of more data from the influence of longer training, we fix the total number of sampled data (12.8B, which amounts to 32 epochs of 400M data and 6.4 epochs of 2B data)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.75, + 0.469, + 0.78 + ], + "angle": 0, + "content": "- Schedule scaling. We increase the sampled data from 12.8B to 25.6B (64 epochs of 400M data)." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.603, + 0.47, + 0.78 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.79, + 0.469, + 0.835 + ], + "angle": 0, + "content": "We study scaling along one of these three axes at each time while keeping others unchanged. The results are summarized in Fig. 4 and Table 8." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.871 + ], + "angle": 0, + "content": "Training curves. The three scaling strategies exhibit different trends in training curves (Fig. 4)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Model scaling (Fig. 4a) presents a clear gap that persists throughout training, though the gap is smaller at the end." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Data scaling (Fig. 4b), on the other hand, performs similarly at the first half of training, but starts to present a good gain later. Note that there is no extra computational cost in this setting, as we control the total number of sampled data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.152, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Schedule scaling (Fig. 4c) trains \\(2 \\times\\) longer. To provide a more intuitive comparison, we plot a hypothetical curve that is rescaled by \\(1/2\\) along the x-axis (dashed line). Despite the longer training, the gain is diminishing or none (more numbers in Table 8)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.235, + 0.892, + 0.311 + ], + "angle": 0, + "content": "Transferability. Table 8 provides an all-around comparison on various downstream tasks regarding the scaling behavior. Overall, model scaling and data scaling both can consistently outperform the baseline in all metrics, in some cases by large margins." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.892, + 0.462 + ], + "angle": 0, + "content": "We categorize the downstream tasks into two scenarios: (i) zero-shot transfer, i.e., no learning is performed on the downstream dataset; (ii) transfer learning, i.e., part or all of the weights are trained on the downstream dataset. For the tasks studied here, data scaling is in general favored for zero-shot transfer, while model scaling is in general favored for transfer learning. However, it is worth noting that the transfer learning performance depends on the size of the downstream dataset, and training a big model on a too small downstream set is still subject to the overfitting risk." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.552 + ], + "angle": 0, + "content": "It is encouraging to see that data scaling is clearly beneficial, even not incurring longer training nor additional computation. On the contrary, even spending more computation by schedule scaling gives diminishing returns. These comparisons suggest that large-scale data are beneficial mainly because they provide richer information." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Next we scale both model and data (Table 8, second last row). For all metrics, model+data scaling improves over scaling either alone. The gains of model scaling and data scaling are highly complementary: e.g., in zero-shot IN-1K, model scaling alone improves over the baseline by \\(1.2\\%\\) \\((74.3\\% \\rightarrow 75.5\\%)\\), and data scaling alone improves by \\(1.5\\%\\) \\((74.3\\% \\rightarrow 75.8\\%)\\). Scaling both improves by \\(3.3\\%\\) \\((77.6\\%)\\) more than the two deltas combined. This behavior is also observed in several other tasks. This indicates that a larger model desires more data to unleash its potential." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Finally, we report joint scaling all three axes (Table 8, last row). Our results show that combining schedule scaling leads to improved performances across most metrics. This suggests that schedule scaling is particularly beneficial when coupled with larger models and larger-scale data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our result of \\(78.8\\%\\) on zero-shot IN-1K outperforms the state-of-the-art result trained on public data with ViT-H (78.0% of OpenCLIP). Also based on LAION-2B, their result is trained with 32B sampled data, \\(1.25 \\times\\) more than ours. Given the \\(50\\%\\) masking we use, our training is estimated to be \\(2.5 \\times\\) faster than theirs if both were run on the same hardware. As OpenCLIP's result reports a training cost of \\(\\sim 5,600\\) GPU-days, our method could save \\(\\sim 3,360\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23396" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.083, + 0.289, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.14, + 0.213, + 0.238, + 0.225 + ], + "angle": 0, + "content": "(a) Model scaling" + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.082, + 0.502, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.213, + 0.45, + 0.225 + ], + "angle": 0, + "content": "(b) Data scaling" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.082, + 0.897, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.649, + 0.213, + 0.762, + 0.225 + ], + "angle": 0, + "content": "(c) Schedule scaling" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.237, + 0.895, + 0.281 + ], + "angle": 0, + "content": "Figure 4. Training curves of scaling. The x-axis is the number of sampled data during training, and the y-axis is the zero-shot accuracy on IN-1K. The blue curve is the baseline setting: ViT-Large, LAION-400M data, 32 epochs (12.8B sampled data). In each subplot, we compare with scaling one factor on the baseline. In schedule scaling (Fig. 4c), we plot an extra hypothetical curve for a better visualization." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.293, + 0.879, + 0.419 + ], + "angle": 0, + "content": "
casemodeldatasampledzero-shot transfertransfer learning
zero-shot IN-1Ktext retrievalimage retrievallin-probe IN-1Kfine-tune IN-1Kcaptioning COCOnocapsvqa VQAv2
baselineLarge400M12.8B74.388.459.875.044.183.686.9127.785.974.7
model scalingHuge400M12.8B75.589.262.876.446.084.387.3130.391.576.3
data scalingLarge2B12.8B75.891.763.878.247.384.287.1128.987.075.5
schedule scalingLarge400M25.6B73.989.760.175.544.483.786.9127.986.875.0
model+data scalingHuge2B12.8B77.692.867.079.949.585.187.7130.492.677.1
joint scalingHuge2B25.6B78.893.167.880.950.585.687.9130.291.277.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.425, + 0.893, + 0.482 + ], + "angle": 0, + "content": "Table 8. Scaling behavior of FLIP, evaluated on a diverse set of downstream tasks: classification, retrieval (R@1), captioning (CIDEr), and visual question answering. In the middle three rows, we scale along one of the three axes (model, data, schedule), and the green entries denote the best ones among these three scaling cases. Data scaling is in general favored under the zero-shot transfer scenario, while model scaling is in general favored under the transfer learning scenario (i.e., with trainable weights in downstream)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.471, + 0.562 + ], + "angle": 0, + "content": "GPU-days based on a rough estimation. Additionally, without enabling \\(2 \\times\\) schedule, our entry of \"model+data scaling\" is estimated \\(5 \\times\\) faster than theirs and can save \\(\\sim 4,480\\) GPU-days. This is considerable cost reduction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.327, + 0.59 + ], + "angle": 0, + "content": "5. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Language is a stronger form of supervision than classical closed-set labels. Language provides rich information for supervision. Therefore, scaling, which can involve increasing capacity (model scaling) and increasing information (data scaling), is essential for attaining good results in language-supervised training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.781 + ], + "angle": 0, + "content": "CLIP [52] is an outstanding example of \"simple algorithms that scale well\". The simple design of CLIP allows it to be relatively easily executed at substantially larger scales and achieve big leaps compared to preceding methods. Our method largely maintains the simplicity of CLIP while pushing it further along the scaling aspect." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.886 + ], + "angle": 0, + "content": "Our method can provide a \\(2 - 3 \\times\\) speedup or more. For the scale concerned in this study, such a speedup can reduce wall-clock time by a great amount (e.g., at the order of thousands of TPU/GPU-days). Besides accelerating research cycles, the speedup can also save a great amount of energy and commercial cost. These are all ingredients of great importance in large-scale machine learning research." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Our study involves controlled comparisons with various" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.893, + 0.593 + ], + "angle": 0, + "content": "CLIP baselines, which help us to break down the gaps contributed by different factors. We show that FLIP outperforms its CLIP counterparts pre-trained on the same LAION data. By comparing several LAION-based models and the original WIT-based ones, we observe that the pre-training data creates big systematic gaps in several tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.893, + 0.671 + ], + "angle": 0, + "content": "Our study provides controlled experiments on scaling behavior. We observe that data scaling is a favored scaling dimension, given that it can improve accuracy with no extra cost at training or inference time. Our fast method encourages us to scale beyond what is studied in this work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Broader impacts. Training large-scale models costs high energy consumption and carbon emissions. While our method has reduced such cost to 1/2-1/3, the remaining cost is still sizable. We hope our work will attract more attention to the research direction on reducing the cost of training vision-language models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.902 + ], + "angle": 0, + "content": "The numerical results in this paper are based on a publicly available large-scale dataset [56]. The resulting model weights will reflect the data biases, including potentially negative implications. When compared using the same data, the statistical differences between two methods should reflect the method properties to a good extent; however, when compared entries using different training data, the biases of the data should always be part of the considerations." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23397" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.167 + ], + "angle": 0, + "content": "[1] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. Nocaps: Novel object captioning at scale. 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Our method randomly masks out and removes a large portion of image patches during training. Masking allows us to learn from more image-text pairs given the same wall-clock time and contrast more samples per iteration with similar memory footprint. It leads to a favorable trade-off between accuracy and training time. In our experiments on 400 million image-text pairs, FLIP improves both accuracy and speed over the no-masking baseline. On a large diversity of downstream tasks, FLIP dominantly outperforms the CLIP counterparts trained on the same data. Facilitated by the speedup, we explore the scaling behavior of increasing the model size, data size, or training length, and report encouraging results and comparisons. We hope that our work will foster future research on scaling vision-language learning. + +# 1. Introduction + +Language-supervised visual pre-training, e.g., CLIP [52], has been established as a simple yet powerful methodology for learning representations. Pre-trained CLIP models stand out for their remarkable versatility: they have strong zero-shot transferability [52]; they demonstrate unprecedented quality in text-to-image generation (e.g., [53, 55]); the pretrained encoder can improve multimodal and even unimodal visual tasks. Like the role played by supervised pre-training a decade ago [40], language-supervised visual pre-training is new fuel empowering various tasks today. + +Unlike classical supervised learning with a pre-defined label set, natural language provides richer forms of supervision, e.g., on objects, scenes, actions, context, and their relations, at multiple levels of granularity. Due to the complex nature of vision plus language, large-scale training is essential for the capability of language-supervised models. For example, the original CLIP models [52] were trained on 400 million data for 32 epochs—which amount to 10,000 ImageNet [16] epochs, taking thousands of GPU-days [52, 36]. + +![](images/d0d2b8d7d4fb65460cb2037e23610303bcb83458c8ed5e2cb32c5c8f5dc0e9df.jpg) +Figure 1. Accuracy vs. training time trade-off. With a high masking ratio of $50\%$ or $75\%$ , our FLIP method trains faster and is more accurate than its CLIP counterpart. All entries are benchmarked in 256 TPU-v3 cores. Training is done on LAION-400M for 6.4, 12.8, or 32 epochs, for each masking ratio. Accuracy is evaluated by zero-shot transfer on the ImageNet-1K validation set. The model is ViT-L/16 [20]. More details are in Fig. 3. As the CLIP baseline takes $\sim 2,500$ TPU-days training, a speedup of $3.7\times$ can save $\sim 1,800$ TPU-days. + +Even using high-end infrastructures, the wall-clock training time is still a major bottleneck hindering explorations on scaling vision-language learning. + +We present Fast Language-Image Pre-training (FLIP), a simple method for efficient CLIP training. Inspired by the sparse computation of Masked Autoencoders (MAE) [29], we randomly remove a large portion of image patches during training. This design introduces a trade-off between "how carefully we look at a sample pair" vs. "how many sample pairs we can process". Using masking, we can: (i) see more sample pairs (i.e., more epochs) under the same wall-clock training time, and (ii) compare/contrast more sample pairs at each step (i.e., larger batches) under similar memory footprint. Empirically, the benefits of processing more sample pairs greatly outweigh the degradation of per-sample encoding, resulting in a favorable trade-off. + +By removing $50\% - 75\%$ patches of a training image, our method reduces computation by $2 - 4 \times$ ; it also allows using $2 - 4 \times$ larger batches with little extra memory cost, which boost accuracy thanks to the behavior of contrastive learning [30, 11]. As summarized in Fig. 1, FLIP trains $>3 \times$ faster in wall-clock time for reaching similar accuracy as its CLIP counterpart; with the same number of epochs, FLIP reaches higher accuracy than its CLIP counterpart while still being $2 - 3 \times$ faster. + +We show that FLIP is a competitive alternative to CLIP on various downstream tasks. Pre-trained on the same LAION-400M dataset [56], FLIP dominantly outperforms its CLIP counterparts (OpenCLIP [36] and our own reproduction), as evaluated on a large variety of downstream datasets and transfer scenarios. These comparisons suggest that FLIP can readily enjoy the faster training speed while still providing accuracy gains. + +Facilitated by faster training, we explore scaling FLIP pre-training. We study these three axes: (i) scaling model size, (ii) scaling dataset size, or (iii) scaling training schedule length. We analyze the scaling behavior through carefully controlled experiments. We observe that model scaling and data scaling can both improve accuracy, and data scaling can show gains at no extra training cost. We hope our method, results, and analysis will encourage future research on scaling vision-language learning. + +# 2. Related Work + +Learning with masking. Denoising Autoencoders [63] with masking noise [64] were proposed as an unsupervised representation learning method over a decade ago. One of its most outstanding applications is masked language modeling represented by BERT [18]. In computer vision, explorations along this direction include predicting large missing regions [50], sequence of pixels [10], patches [20, 29, 71], or pre-computed features [6, 66]. + +The Masked Autoencoder (MAE) method [29] further takes advantage of masking to reduce training time and memory. MAE sparsely applies the ViT encoder [20] to visible content. It also observes that a high masking ratio is beneficial for accuracy. The MAE design has been applied to videos [61, 22], point clouds [49], graphs [59, 9, 32], audio [4, 47, 13, 35], visual control [70, 57], vision-language [23, 41, 31, 19], and other modalities [5]. + +Our work is related to MAE and its vision-language extensions [23, 41, 31, 19]. However, our focus is on the scaling aspect enabled by the sparse computation; we address the challenge of large-scale CLIP training [52], while previous works [23, 41, 31, 19] are limited in terms of scale. Our method does not perform reconstruction and is not a form of autoencoding. Speeding up training by masking is studied in [69] for self-supervised contrastive learning, e.g., for MoCo [30] or BYOL [27], but its accuracy could be + +![](images/1b6c56d6081e807767b769055906b22530e5296098de4091184e3f925087d570.jpg) +Figure 2. Our FLIP architecture. Following CLIP [52], we perform contrastive learning on pairs of image and text samples. We randomly mask out image patches with a high masking ratio and encode only the visible patches. We do not perform reconstruction of masked image content. + +limited by the scaling behavior of image-only contrastive learning. + +Language-supervised learning. In the past years, CLIP [52] and related works (e.g., [37, 51]) have popularized learning visual representations with language supervision. CLIP is a form of contrastive learning [28] by comparing image-text sample pairs. Beyond contrastive learning, generative learning methods have been explored [17, 65, 2, 74], optionally combined with contrastive losses [74]. Our method focuses on the CLIP method, while we hope it can be extended to generative methods in the future. + +# 3. Method + +In a nutshell, our method simply masks out the input data in CLIP [52] training and reduces computation. See Fig. 2. + +In our scenario, the benefit of masking is on wisely spending computation. Intuitively, this leads to a trade-off between how densely we encode a sample against how many samples we compare as the learning signal. By introducing masking, we can: (i) learn from more image-text pairs under the same wall-clock training time, and (ii) have a contrastive objective over a larger batch under the same memory constraint. We show by experiments that for both aspects, our method is at an advantage in the trade-off. Next we introduce the key components of our method. + +Image masking. We adopt the Vision Transformer (ViT) [20] as the image encoder. An image is first divided into a grid of non-overlapping patches. We randomly mask out a large portion (e.g., $50\%$ or $75\%$ ) of patches; the ViT encoder is only applied to the visible patches, following [29]. Using a masking ratio of $50\%$ (or $75\%$ ) reduces the time complexity of image encoding to 1/2 (or 1/4); it also allows using a $2\times$ (or $4\times$ ) larger batch with a similar memory cost for image encoding. + +Text masking. Optionally, we perform text masking in the same way as image masking. We mask out a portion of the text tokens and apply the encoder only to the visible tokens, as in [29]. This is unlike BERT [18] that replaces them with a learned mask token. Such sparse computation can reduce the text encoding cost. However, as the text encoder is smaller [52], speeding it up does not lead to a better overall trade-off. We study text masking for ablation only. + +Objective. The image/text encoders are trained to minimize a contrastive loss [48]. The negative sample pairs for contrastive learning consist of other samples in the same batch [11]. It has been observed that a large number of negative samples is critical for self-supervised contrastive learning on images [30, 11]. This property is more prominent in language-supervised learning. + +We do not use a reconstruction loss, unlike MAE [29]. We find that reconstruction is not necessary for good performance on zero-shot transfer. Waiving the decoder and reconstruction loss yields a better speedup. + +Unmasking. While the encoder is pre-trained on masked images, it can be directly applied on intact images without changes, as is done in [29]. This simple setting is sufficient to provide competitive results and will serve as our baseline in ablation experiments. + +To close the distribution gap caused by masking, we can set the masking ratio as $0\%$ and continue pre-training for a small number of steps. This unmasking tuning strategy produces a more favorable accuracy/time trade-off. + +# 3.1. Implementation + +Our implementation follows CLIP [52] and OpenCLIP [36], with a few modifications we describe in the following. Hyper-parameters are in the appendix. + +Our image encoder follows the ViT paper [20]. We do not use the extra LayerNorm [3] after patch embedding, like [20] but unlike [52]. We use global average pooling at the end of the image encoder. The input size is 224. + +Our text encoder is a non-autoregressive Transformer [62], which is easier to adapt to text masking for ablation. We use a WordPiece tokenizer as in [18]. We pad or cut the sequences to a fixed length of 32. We note that CLIP in [52] uses an autoregressive text encoder, a BytePairEncoding tokenizer, and a length of 77. These designs make marginal differences as observed in our initial reproduction. + +The outputs of the image encoder and text encoder are projected to the same-dimensional embedding space by a linear layer. The cosine similarities of the embeddings, scaled by a learnable temperature parameter [52], are the input to the InfoNCE loss [48]. + +In zero-shot transfer, we follow the prompt engineering in the code of [52]. We use their provided 7 prompt templates for ImageNet zero-shot transfer. + +Our implementation is based on JAX [8] with the t5x library [54] for large-scale distributed training. Our training is run on TPU v3 infrastructure. + +# 4. Experiments + +# 4.1. Ablations + +We first ablate the FLIP design. The image encoder is ViT-L/16 [20], and the text encoder has a smaller size as per [52]. We train on LAION-400M [36] and evaluate zero-shot accuracy on ImageNet-1K [16] validation. + +Table 1 shows the ablations trained for 6.4 epochs. Fig. 1 plots the trade-off for up to 32 epochs [52]. The results are benchmarked in 256 TPU-v3 cores, unless noted. + +Masking ratio. Table 1a studies the image masking ratios. Here we scale the batch size accordingly (ablated next), so as to roughly maintain the memory footprint. $^{1}$ The $0\%$ masking entry indicates our CLIP counterpart. Masking $50\%$ gives $1.2\%$ higher accuracy than the CLIP baseline, and masking $75\%$ is on par with the baseline. Speed-wise, masking $50\%$ or $75\%$ takes only $0.50 \times$ or $0.33 \times$ wall-clock training time, thanks to the large reduction on FLOPs. + +Batch size. We ablate the effect of batch size in Table 1b. Increasing the batch size consistently improves accuracy. + +Notably, even using the same batch size of 16k, our $50\%$ masking entry has a comparable accuracy (68.5%, Table 1b) with the $0\%$ masking baseline (68.6%, Table 1a). It is possible that the regularization introduced by masking can reduce overfitting, partially counteracting the negative effect of losing information in this setting. With a higher masking ratio of $75\%$ , the negative effect is still observed when keeping the batch size unchanged. + +Our masking-based method naturally encourages using large batches. There is little extra memory cost if we scale the batch size according to the masking ratio, as we report in Table 1a. In practice, the available memory is always a limitation for larger batches. For example, the setting in Table 1a has reached the memory limit in our high-end infrastructure (256 TPU-v3 cores with 16GB memory each). The memory issue is more demanding if using fewer devices, and the gain of our method would be more prominent due to the nearly free increase of batch sizes. + +Text masking. Table 1c studies text masking. Randomly masking $50\%$ text decreases accuracy by $2.2\%$ . This is in line with the observation [29] that language data has higher + +
maskbatchFLOPstimeacc.
0%16k1.00×1.00×68.6
50%32k0.52×0.50×69.6
75%64k0.28×0.33×68.2
+ +(a) Image masking yields higher or comparable accuracy and speeds up training. Entries are subject to the same memory limit. + +
batchmask 50%mask 75%
16k68.565.8
32k69.667.3
64k70.468.2
+ +(b) Batch size. A large batch has big gains over smaller batches. + +
text masktext lentimeacc.
baseline, 0%321.00×68.2
random, 50%160.92×66.0
prioritized, 50%160.92×67.8
+ +(c) Text masking performs decently, but the speed gain is marginal as its encoder is smaller. Here the image masking ratio is $75\%$ . + +
mask 50%mask 75%
w/ mask66.460.9
w/ mask, ensemble68.165.1
w/o mask69.668.2
+ +(d) Inference unmasking. Inference on intact images performs strongly even without tuning. + +
mask 50%mask 75%
baseline69.668.2
+ tuning70.169.5
+ +(e) Unmasked tuning. The distribution shift by masking is reduced by a short tuning. + +
mask 50%mask 75%
baseline69.668.2
+ MAE69.467.9
+ +(f) Reconstruction. Adding the MAE reconstruction loss has no gain. + +Table 1. Zero-shot ablation experiments. Pre-training is on LAION-400M for 6.4 epochs, evaluated by zero-shot classification accuracy on ImageNet-1K validation. The backbone is ViT-L/16 [20]. Unless specified, the baseline setting is: image masking is $50\%$ (batch 32k) or $75\%$ (batch 64k), text masking is $0\%$ , and no unmasked tuning is used. + +information-density than images and thus the text masking ratio should be lower. + +As variable-length text sequences are padded to generate a fixed-length batch, we can prioritize masking out the padding tokens. Prioritized sampling preserves more valid tokens than randomly masking the padded sequences uniformly. It reduces the degradation to $0.4\%$ . + +While our text masking is more aggressive than typical masked language models (e.g., $15\%$ in [18]), the overall speed gain is marginal. This is because the text encoder is smaller and the text sequence is short. The text encoder costs merely $4.4\%$ computation vs. the image encoder (without masking). Under this setting, text masking is not a worthwhile trade-off and we do not mask text in our other experiments. + +Inference unmasking. By default, we apply our models on intact images at inference-time, similar to [29]. While masking creates a distribution shift between training and inference, simply ignoring this shift works surprisingly well (Table 1d, 'w/o mask'), even under the zero-shot setting where no training is ever done on full images. + +Table 1d reports that if using masking at inference time, the accuracy drops by a lot (e.g., $7.3\%$ ). This drop can be partially caused by information loss at inference, so we also compare with ensembling multiple masked views [10], where the views are complementary to each other and put together cover all patches. Ensembling reduces the gap (Table 1d), but still lags behind the simple full-view inference. + +Unmasked tuning. Our ablation experiments thus far do not involve unmasked tuning. Table 1e reports the results of unmasked tuning for extra 0.32 epoch on the pre-training dataset. It increases accuracy by $1.3\%$ at the high masking ratio of $75\%$ , suggesting that tuning can effectively reduce the distribution gap between pre-training and inference. + +Fig. 3 plots the trade-off affected by unmasked tuning (solid vs. dashed). Unmasked tuning leads to a more desir- + +![](images/31a9ac3be46169703dc4614aa42bd9cb5af536e73352892010e46d8f4b6ca627.jpg) +Figure 3. Accuracy vs. training time trade-off in detail. The setting follows Table 1a. Training is for 6.4, 12.8, or 32 epochs, for each masking ratio. Unmasked tuning, if applied, is for 0.32 epoch. All are benchmarked in 256 TPU-v3 cores. Zero-shot accuracy is on IN-1K validation. The model is ViT-L/16. Our method speeds up training and increases accuracy. + +able trade-off for $75\%$ masking; it has a comparable tradeoff for $50\%$ masking but improves final accuracy. + +Reconstruction. In Table 1f we investigate adding a reconstruction loss function. The reconstruction head follows the design in MAE [29]: it has a small decoder and reconstructs normalized image pixels. The reconstruction loss is added to the contrastive loss. + +Table 1f shows that reconstruction has a small negative impact for zero-short results. We also see a similar though slight less drop for fine-tuning accuracy on ImageNet. While this can be a result of suboptimal hyperparameters (e.g., balancing two losses), to strive for simplicity, we decide not to use the reconstruction loss. Waiving the reconstruction head also helps simplify the system and improves the accuracy/time trade-off. + +
casedataepochsB/16L/16L/14H/14
CLIP [52]WIT-400M3268.6-75.3-
OpenCLIP [36]LAION-400M3267.1-72.8-
CLIP, our repro.LAION-400M3268.272.473.1-
FLIPLAION-400M3268.074.374.675.5
+ +Table 2. Zero-shot accuracy on ImageNet-1K classification, compared with various CLIP baselines. The image size is 224. The entries noted by grey are pre-trained on a different dataset. Our models use a 64k batch, $50\%$ masking ratio, and unmasked tuning. + +
casedataepochsmodelzero-shotlinear probefine-tune
CLIP [52]WIT-400M32L/1475.383.9†-
CLIP [52], our transferWIT-400M32L/1475.383.087.4
OpenCLIP [36]LAION-400M32L/1472.882.186.2
CLIP, our repro.LAION-400M32L/1672.482.686.3
FLIPLAION-400M32L/1674.383.686.9
+ +Table 3. Linear probing and fine-tuning accuracy on ImageNet-1K classification, compared with various CLIP baselines. The entries noted by grey are pre-trained on a different dataset. The image size is 224. †: CLIP in [52] optimizes with L-BFGS; we use SGD instead. + +Accuracy vs. time trade-off. Fig. 3 presents a detailed view on the accuracy vs. training time trade-off. We extend the schedule to up to 32 epochs [52]. + +As shown in Fig. 3, FLIP has a clearly better trade-off than the CLIP counterpart. It can achieve similar accuracy as CLIP while enjoying a speedup of $>3 \times$ . With the same 32-epoch schedule, our method is $\sim 1\%$ more accurate than the CLIP counterpart and $2 \times$ faster (masking $50\%$ ). + +The speedup of our method is of great practical value. The CLIP baseline takes $\sim 10$ days training in 256 TPU-v3 cores, so a speedup of $2 - 3\times$ saves many days in wall-clock time. This speedup facilitates exploring the scaling behavior, as we will discuss later in Sec. 4.3. + +# 4.2. Comparisons with CLIP + +In this section, we compare with various CLIP baselines in a large variety of scenarios. We show that our method is a competitive alternative to CLIP; as such, our fast training method is a more desirable choice in practice. + +We consider the following CLIP baselines: + +- The original CLIP checkpoints [52], trained on the private dataset WIT-400M. +- OpenCLIP [36], trained on LAION-400M. +- Our CLIP reproduction, trained on LAION-400M. + +The original CLIP [52] was trained on a private dataset, so a direct comparison with it should reflect the effect of data, not just methods. OpenCLIP [36] is a faithful reproduction of CLIP yet trained on a public dataset that we can use, so it is a good reference for us to isolate the effect of dataset differences. Our CLIP reproduction further helps isolate other implementation subtleties and allows us to pinpoint the effect of the FLIP method. + +For all tasks studied in this subsection, we compare with all these CLIP baselines. This allows us to better understand the influence of the data and of the methods. + +ImageNet zero-shot transfer. In Table 2 we compare with the CLIP baselines on ImageNet-1K [16] zero-shot transfer. + +As a sanity check, our CLIP reproduction has slightly higher accuracy than OpenCLIP trained on the same data. The original CLIP has higher accuracy than our reproduction and OpenCLIP, which could be caused by the difference between the pre-training datasets. + +Table 2 reports the results of our FLIP models, using the best practice as we have ablated in Table 1 (a 64k batch, $50\%$ masking ratio, and unmasked tuning). For ViT-L/14, our method has $74.6\%$ accuracy, which is $1.8\%$ higher than OpenCLIP and $1.5\%$ higher than our CLIP reproduction. Comparing with the original CLIP, our method reduces the gap to $0.7\%$ . We hope our method will improve the original CLIP result if it were trained on the WIT data. + +ImageNet linear probing. Table 3 compares the linear probing results, i.e., training a linear classifier on the target dataset with frozen features. FLIP has $83.6\%$ accuracy, $1.0\%$ higher than our CLIP counterpart. It is also $0.6\%$ higher than our transfer of the original CLIP checkpoint, using the same SGD trainer. + +ImageNet fine-tuning. Table 3 also compares full fine-tuning results. Our fine-tuning implementation follows MAE [29], with the learning rate tuned for each entry. It is worth noting that with our fine-tuning recipe, the original CLIP checkpoint reaches $87.4\%$ , much higher than previous reports [68, 67, 33] on this metric. CLIP is still a strong model under the fine-tuning protocol. + +FLIP outperforms the CLIP counterparts pre-trained on the same data. Our result of $86.9\%$ (or $87.1\%$ using L/14) is behind but close to the result of the original CLIP checkpoint's $87.4\%$ , using our fine-tuning recipe. + +
dataFood101CIFAR10CIFAR100BrandsnapSUN397CarsAircraftVOC2007DTDOxfoot PetsCaltech101Flowers102MNISTSTL10EuroSATRESIC45GTSRBKITTICountry211PCamUCF101Kinetics700CLEVRHatefulMemesSST2
CLIP [52]WIT-400M92.996.277.948.367.777.336.184.155.393.592.678.787.299.359.971.650.323.132.758.876.260.324.363.364.0
CLIP [52], our eval.WIT-400M91.095.275.651.266.675.032.383.355.093.692.477.776.099.362.071.651.626.930.951.676.159.522.255.367.3
OpenCLIP [36], our eval.LAION-400M87.494.177.161.370.786.221.883.554.990.894.072.171.598.253.367.747.329.321.651.171.350.522.055.357.1
CLIP, our repro.LAION-400M88.196.081.360.572.389.125.881.159.393.293.274.669.196.550.769.250.229.421.453.171.553.518.553.357.2
FLIPLAION-400M89.397.284.163.073.190.729.183.160.492.693.875.080.398.553.570.841.434.823.150.374.155.822.754.058.5
+ +Table 4. Zero-shot accuracy on more classification datasets, compared with various CLIP baselines. This table follows Table 11 in [52]. The model is ViT-L/14 with an image size of 224, for all entries. Entries in green are the best ones using the LAION-400M data. + +
casemodeldatatext retrievalimage retrieval
Flickr30kCOCOFlickr30kCOCO
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [52]L/14@336WIT-400M88.098.799.458.481.588.168.790.695.237.862.472.2
CLIP [52], our eval.L/14@336WIT-400M88.998.799.958.780.487.972.591.795.238.562.872.5
CLIP [52], our eval.L/14WIT-400M87.899.199.856.279.886.469.390.294.035.860.770.7
OpenCLIP [36], our eval.L/14LAION-400M87.397.999.158.080.688.172.090.895.041.366.676.1
CLIP, our impl.L/14LAION-400M87.498.499.559.182.589.474.492.295.543.268.577.5
FLIPL/14LAION-400M89.198.599.660.282.689.975.492.595.944.269.278.4
+ +Table 5. Zero-shot image/text retrieval, compared with various CLIP baselines. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data. + +
modeldataIN-V2 top-1IN-A top-1IN-R top-1ObjectNet top-1IN-Sketch top-1IN-VidYTBB
PM-0PM-10PM-0PM-10
CLIP [52]L/14@336WIT-400M70.177.288.972.360.295.389.295.288.5
CLIP [52], our eval.L/14@336WIT-400M70.478.089.069.359.795.988.895.389.4
CLIP [52], our eval.L/14WIT-400M69.571.986.868.658.594.687.094.186.4
OpenCLIP [36], our eval.L/14LAION-400M64.048.384.358.856.990.381.486.577.8
CLIP, our repro.L/14LAION-400M65.646.384.758.058.789.380.585.777.8
FLIPL/14LAION-400M66.851.286.559.159.991.183.589.483.3
+ +Table 6. Zero-shot robustness evaluation, compared with various CLIP baselines. This table follows Table 16 in [52]. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data. + +
casemodeldataCOCO captionnocapsVQAv2 acc.
BLEU-4METEORROUGE-LCIDErSPICECIDErSPICE
CLIP [52], our transferL/14WIT-400M37.529.658.7126.922.882.512.176.6
OpenCLIP [36], our transferL/14LAION-400M36.729.358.4125.022.783.412.374.5
CLIP, our repro.L/16LAION-400M36.429.358.4125.622.882.812.274.5
FLIPL/16LAION-400M37.429.558.8127.723.085.912.474.7
+ +Table 7. Image Captioning and Visual Question Answering, compared with various CLIP baselines. Entries in green are the best ones using LAION-400M. Here the results are on the COCO captioning test split of [38], nocaps val split, and VQAv2 test-dev split, respectively. + +Zero-shot classification on more datasets. In Table 4 we compare on the extra datasets studied in [52]. As the results can be sensitive to evaluation implementation (e.g., text prompts, image pre-processing), we provide our evaluations of the original CLIP checkpoint and OpenCLIP. + +Notably, we observe clear systematic gaps caused by pre-training data, as benchmarked using the same evaluation code. The WIT dataset is beneficial for some tasks (e.g., Aircraft, Country211, SST2), while LAION is beneficial for some others (e.g., Birdsnap, SUN397, Cars). + +After isolating the influence of pre-training data, we observe that FLIP is dominantly better than OpenCLIP and our CLIP reproduction, as marked by green in Table 4. + +Zero-shot retrieval. Table 5 reports image/text retrieval results on Flickr30k [73] and COCO [42]. FLIP outper + +forms all CLIP competitors, including the original CLIP (evaluated on the same 224 size). The WIT dataset has no advantage over LAION for these two retrieval datasets. + +Zero-shot robustness evaluation. In Table 6 we compare on robustness evaluation, following [52]. We again observe clear systematic gaps caused by pre-training data. Using the same evaluation code ("our eval" in Table 6), CLIP pre-trained on WIT is clearly better than other entries pretrained on LAION. Taking IN-Adversarial (IN-A) as an example: the LAION-based OpenCLIP [36] has only $48.3\%$ accuracy (or $46.6\%$ reported by [36]). While FLIP $(51.2\%)$ can outperform the LAION-based CLIP by a large margin, it is still $20\%$ below the WIT-based CLIP $(71.9\%)$ . + +Discounting the influence of pre-training data, our FLIP training has clearly better robustness than its CLIP counter + +parts in all cases. We hypothesize that masking as a form of noise and regularization can improve robustness. + +Image Captioning. See Table 7 for the captioning performance on COCO [42] and nocaps [1]. Our captioning implementation follows the cross-entropy training baseline in [7]. Unlike classification in which only a classifier layer is added after pre-training, here the fine-tuning model has a newly initialized captioner (detailed in appendix). In this task, FLIP outperforms the original CLIP checkpoint in several metrics. Compared to our CLIP baseline, which is pretrained on the same data, FLIP also shows a clear gain, especially in BLEU-4 and CIDEr metrics. + +Visual Question Answering. We evaluate on the VQAv2 dataset [26], with a fine-tuning setup following [21]. We use a newly initialized multimodal fusion transformer and an answer classifier to obtain the VQA outputs (detailed in appendix). Table 7 (rightmost column) reports results on VQAv2. All entries pre-trained on LAION perform similarly, and CLIP pre-trained on WIT is the best. + +Summary of Comparisons. Across a large variety of scenarios, FLIP is dominantly better than its CLIP counterparts (OpenCLIP and our reproduction) pre-trained on the same LAION data, in some cases by large margins. + +The difference between the WIT data and LAION data can create large systematic gaps, as observed in many downstream tasks. We hope our study will draw attention to these data-dependent gaps in future research. + +# 4.3. Scaling Behavior + +Facilitated by the speed-up of FLIP, we explore the scaling behavior beyond the largest case studied in CLIP [52]. We study scaling along either of these three axes: + +- Model scaling. We replace the ViT-L image encoder with ViT-H, which has $\sim 2\times$ parameters. The text encoder is also scaled accordingly. +- Data scaling. We scale the pre-training data from 400 million to 2 billion, using the LAION-2B set [36]. To better separate the influence of more data from the influence of longer training, we fix the total number of sampled data (12.8B, which amounts to 32 epochs of 400M data and 6.4 epochs of 2B data). +- Schedule scaling. We increase the sampled data from 12.8B to 25.6B (64 epochs of 400M data). + +We study scaling along one of these three axes at each time while keeping others unchanged. The results are summarized in Fig. 4 and Table 8. + +Training curves. The three scaling strategies exhibit different trends in training curves (Fig. 4). + +Model scaling (Fig. 4a) presents a clear gap that persists throughout training, though the gap is smaller at the end. + +Data scaling (Fig. 4b), on the other hand, performs similarly at the first half of training, but starts to present a good gain later. Note that there is no extra computational cost in this setting, as we control the total number of sampled data. + +Schedule scaling (Fig. 4c) trains $2 \times$ longer. To provide a more intuitive comparison, we plot a hypothetical curve that is rescaled by $1/2$ along the x-axis (dashed line). Despite the longer training, the gain is diminishing or none (more numbers in Table 8). + +Transferability. Table 8 provides an all-around comparison on various downstream tasks regarding the scaling behavior. Overall, model scaling and data scaling both can consistently outperform the baseline in all metrics, in some cases by large margins. + +We categorize the downstream tasks into two scenarios: (i) zero-shot transfer, i.e., no learning is performed on the downstream dataset; (ii) transfer learning, i.e., part or all of the weights are trained on the downstream dataset. For the tasks studied here, data scaling is in general favored for zero-shot transfer, while model scaling is in general favored for transfer learning. However, it is worth noting that the transfer learning performance depends on the size of the downstream dataset, and training a big model on a too small downstream set is still subject to the overfitting risk. + +It is encouraging to see that data scaling is clearly beneficial, even not incurring longer training nor additional computation. On the contrary, even spending more computation by schedule scaling gives diminishing returns. These comparisons suggest that large-scale data are beneficial mainly because they provide richer information. + +Next we scale both model and data (Table 8, second last row). For all metrics, model+data scaling improves over scaling either alone. The gains of model scaling and data scaling are highly complementary: e.g., in zero-shot IN-1K, model scaling alone improves over the baseline by $1.2\%$ $(74.3\% \rightarrow 75.5\%)$ , and data scaling alone improves by $1.5\%$ $(74.3\% \rightarrow 75.8\%)$ . Scaling both improves by $3.3\%$ $(77.6\%)$ more than the two deltas combined. This behavior is also observed in several other tasks. This indicates that a larger model desires more data to unleash its potential. + +Finally, we report joint scaling all three axes (Table 8, last row). Our results show that combining schedule scaling leads to improved performances across most metrics. This suggests that schedule scaling is particularly beneficial when coupled with larger models and larger-scale data. + +Our result of $78.8\%$ on zero-shot IN-1K outperforms the state-of-the-art result trained on public data with ViT-H (78.0% of OpenCLIP). Also based on LAION-2B, their result is trained with 32B sampled data, $1.25 \times$ more than ours. Given the $50\%$ masking we use, our training is estimated to be $2.5 \times$ faster than theirs if both were run on the same hardware. As OpenCLIP's result reports a training cost of $\sim 5,600$ GPU-days, our method could save $\sim 3,360$ + +![](images/02b4bdc23a772e4561f67c001e186e00167391369cfce802ee1aed77aade73cb.jpg) +(a) Model scaling + +![](images/8d4a22a880982422f13f1d31c3a5886971eaf10175e8b18d27d012efcd3bbab5.jpg) +(b) Data scaling +Figure 4. Training curves of scaling. The x-axis is the number of sampled data during training, and the y-axis is the zero-shot accuracy on IN-1K. The blue curve is the baseline setting: ViT-Large, LAION-400M data, 32 epochs (12.8B sampled data). In each subplot, we compare with scaling one factor on the baseline. In schedule scaling (Fig. 4c), we plot an extra hypothetical curve for a better visualization. + +![](images/2f2fae89268f559bb68426e148725731a5c27f268eedf54faba977e3bfc9c1db.jpg) +(c) Schedule scaling + +
casemodeldatasampledzero-shot transfertransfer learning
zero-shot IN-1Ktext retrievalimage retrievallin-probe IN-1Kfine-tune IN-1Kcaptioning COCOnocapsvqa VQAv2
baselineLarge400M12.8B74.388.459.875.044.183.686.9127.785.974.7
model scalingHuge400M12.8B75.589.262.876.446.084.387.3130.391.576.3
data scalingLarge2B12.8B75.891.763.878.247.384.287.1128.987.075.5
schedule scalingLarge400M25.6B73.989.760.175.544.483.786.9127.986.875.0
model+data scalingHuge2B12.8B77.692.867.079.949.585.187.7130.492.677.1
joint scalingHuge2B25.6B78.893.167.880.950.585.687.9130.291.277.3
+ +Table 8. Scaling behavior of FLIP, evaluated on a diverse set of downstream tasks: classification, retrieval (R@1), captioning (CIDEr), and visual question answering. In the middle three rows, we scale along one of the three axes (model, data, schedule), and the green entries denote the best ones among these three scaling cases. Data scaling is in general favored under the zero-shot transfer scenario, while model scaling is in general favored under the transfer learning scenario (i.e., with trainable weights in downstream). + +GPU-days based on a rough estimation. Additionally, without enabling $2 \times$ schedule, our entry of "model+data scaling" is estimated $5 \times$ faster than theirs and can save $\sim 4,480$ GPU-days. This is considerable cost reduction. + +# 5. Discussion and Conclusion + +Language is a stronger form of supervision than classical closed-set labels. Language provides rich information for supervision. Therefore, scaling, which can involve increasing capacity (model scaling) and increasing information (data scaling), is essential for attaining good results in language-supervised training. + +CLIP [52] is an outstanding example of "simple algorithms that scale well". The simple design of CLIP allows it to be relatively easily executed at substantially larger scales and achieve big leaps compared to preceding methods. Our method largely maintains the simplicity of CLIP while pushing it further along the scaling aspect. + +Our method can provide a $2 - 3 \times$ speedup or more. For the scale concerned in this study, such a speedup can reduce wall-clock time by a great amount (e.g., at the order of thousands of TPU/GPU-days). Besides accelerating research cycles, the speedup can also save a great amount of energy and commercial cost. These are all ingredients of great importance in large-scale machine learning research. + +Our study involves controlled comparisons with various + +CLIP baselines, which help us to break down the gaps contributed by different factors. We show that FLIP outperforms its CLIP counterparts pre-trained on the same LAION data. By comparing several LAION-based models and the original WIT-based ones, we observe that the pre-training data creates big systematic gaps in several tasks. + +Our study provides controlled experiments on scaling behavior. We observe that data scaling is a favored scaling dimension, given that it can improve accuracy with no extra cost at training or inference time. Our fast method encourages us to scale beyond what is studied in this work. + +Broader impacts. Training large-scale models costs high energy consumption and carbon emissions. While our method has reduced such cost to 1/2-1/3, the remaining cost is still sizable. We hope our work will attract more attention to the research direction on reducing the cost of training vision-language models. + +The numerical results in this paper are based on a publicly available large-scale dataset [56]. The resulting model weights will reflect the data biases, including potentially negative implications. When compared using the same data, the statistical differences between two methods should reflect the method properties to a good extent; however, when compared entries using different training data, the biases of the data should always be part of the considerations. + +# References + +[1] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. Nocaps: Novel object captioning at scale. In ICCV, 2019. +[2] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, and Malcolm Reynolds. 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In ICLR, 2018. \ No newline at end of file diff --git a/2023/Scaling Language-Image Pre-Training via Masking/images.zip b/2023/Scaling Language-Image Pre-Training via Masking/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..40743cfd1150d782d9096bab188aa9df4df817d5 --- /dev/null +++ b/2023/Scaling Language-Image Pre-Training via Masking/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e02c796e5a975717989214908d8c754da6e401391041dd03adbbb4195746c38c +size 437489 diff --git a/2023/Scaling Language-Image Pre-Training via Masking/layout.json b/2023/Scaling Language-Image Pre-Training via Masking/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..5b9b669311e8b58647514dc8456ab6d753cd0685 --- /dev/null +++ b/2023/Scaling Language-Image Pre-Training via Masking/layout.json @@ -0,0 +1,10318 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 140, + 103, + 454, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 103, + 454, + 121 + ], + "spans": [ + { + "bbox": [ + 140, + 103, + 454, + 121 + ], + "type": "text", + "content": "Scaling Language-Image Pre-training via Masking" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 142, + 512, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 142, + 512, + 159 + ], + "spans": [ + { + "bbox": [ + 80, + 142, + 512, + 159 + ], + "type": "text", + "content": "Yanghao Li* Haoqi Fan* Ronghang Hu* Christoph Feichtenhofer† Kaiming He†" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 212, + 164, + 381, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 212, + 164, + 381, + 176 + ], + "spans": [ + { + "bbox": [ + 212, + 164, + 381, + 176 + ], + "type": "text", + "content": "*equal technical contribution, †equal advising" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 257, + 182, + 334, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 257, + 182, + 334, + 195 + ], + "spans": [ + { + "bbox": [ + 257, + 182, + 334, + 195 + ], + "type": "text", + "content": "Meta AI, FAIR" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 149, + 202, + 440, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 202, + 440, + 216 + ], + "spans": [ + { + "bbox": [ + 149, + 202, + 440, + 216 + ], + "type": "text", + "content": "https://github.com/facebookresearch/flip" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 252, + 290, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 445 + ], + "type": "text", + "content": "We present Fast Language-Image Pre-training (FLIP), a simple and more efficient method for training CLIP [52]. Our method randomly masks out and removes a large portion of image patches during training. Masking allows us to learn from more image-text pairs given the same wall-clock time and contrast more samples per iteration with similar memory footprint. It leads to a favorable trade-off between accuracy and training time. In our experiments on 400 million image-text pairs, FLIP improves both accuracy and speed over the no-masking baseline. On a large diversity of downstream tasks, FLIP dominantly outperforms the CLIP counterparts trained on the same data. Facilitated by the speedup, we explore the scaling behavior of increasing the model size, data size, or training length, and report encouraging results and comparisons. We hope that our work will foster future research on scaling vision-language learning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 463, + 128, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 128, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 128, + 475 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 484, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 605 + ], + "type": "text", + "content": "Language-supervised visual pre-training, e.g., CLIP [52], has been established as a simple yet powerful methodology for learning representations. Pre-trained CLIP models stand out for their remarkable versatility: they have strong zero-shot transferability [52]; they demonstrate unprecedented quality in text-to-image generation (e.g., [53, 55]); the pretrained encoder can improve multimodal and even unimodal visual tasks. Like the role played by supervised pre-training a decade ago [40], language-supervised visual pre-training is new fuel empowering various tasks today." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Unlike classical supervised learning with a pre-defined label set, natural language provides richer forms of supervision, e.g., on objects, scenes, actions, context, and their relations, at multiple levels of granularity. 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Accuracy vs. training time trade-off. With a high masking ratio of " + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "text", + "content": ", our FLIP method trains faster and is more accurate than its CLIP counterpart. All entries are benchmarked in 256 TPU-v3 cores. Training is done on LAION-400M for 6.4, 12.8, or 32 epochs, for each masking ratio. Accuracy is evaluated by zero-shot transfer on the ImageNet-1K validation set. The model is ViT-L/16 [20]. More details are in Fig. 3. As the CLIP baseline takes " + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\sim 2,500" + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "text", + "content": " TPU-days training, a speedup of " + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "inline_equation", + "content": "3.7\\times" + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "text", + "content": " can save " + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\sim 1,800" + }, + { + "bbox": [ + 304, + 409, + 545, + 509 + ], + "type": "text", + "content": " TPU-days." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 557 + ], + "type": "text", + "content": "Even using high-end infrastructures, the wall-clock training time is still a major bottleneck hindering explorations on scaling vision-language learning." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 558, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 714 + ], + "type": "text", + "content": "We present Fast Language-Image Pre-training (FLIP), a simple method for efficient CLIP training. Inspired by the sparse computation of Masked Autoencoders (MAE) [29], we randomly remove a large portion of image patches during training. This design introduces a trade-off between \"how carefully we look at a sample pair\" vs. \"how many sample pairs we can process\". Using masking, we can: (i) see more sample pairs (i.e., more epochs) under the same wall-clock training time, and (ii) compare/contrast more sample pairs at each step (i.e., larger batches) under similar memory footprint. Empirically, the benefits of processing more sample pairs greatly outweigh the degradation of per-sample encoding, resulting in a favorable trade-off." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23390" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "By removing " + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "inline_equation", + "content": "50\\% - 75\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": " patches of a training image, our method reduces computation by " + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "inline_equation", + "content": "2 - 4 \\times" + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "; it also allows using " + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "inline_equation", + "content": "2 - 4 \\times" + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": " larger batches with little extra memory cost, which boost accuracy thanks to the behavior of contrastive learning [30, 11]. As summarized in Fig. 1, FLIP trains " + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "inline_equation", + "content": ">3 \\times" + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": " faster in wall-clock time for reaching similar accuracy as its CLIP counterpart; with the same number of epochs, FLIP reaches higher accuracy than its CLIP counterpart while still being " + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "inline_equation", + "content": "2 - 3 \\times" + }, + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": " faster." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 179, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 179, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 289, + 276 + ], + "type": "text", + "content": "We show that FLIP is a competitive alternative to CLIP on various downstream tasks. Pre-trained on the same LAION-400M dataset [56], FLIP dominantly outperforms its CLIP counterparts (OpenCLIP [36] and our own reproduction), as evaluated on a large variety of downstream datasets and transfer scenarios. These comparisons suggest that FLIP can readily enjoy the faster training speed while still providing accuracy gains." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 275, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 384 + ], + "type": "text", + "content": "Facilitated by faster training, we explore scaling FLIP pre-training. We study these three axes: (i) scaling model size, (ii) scaling dataset size, or (iii) scaling training schedule length. We analyze the scaling behavior through carefully controlled experiments. We observe that model scaling and data scaling can both improve accuracy, and data scaling can show gains at no extra training cost. We hope our method, results, and analysis will encourage future research on scaling vision-language learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 394, + 134, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 134, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 134, + 406 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 414, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 510 + ], + "type": "text", + "content": "Learning with masking. Denoising Autoencoders [63] with masking noise [64] were proposed as an unsupervised representation learning method over a decade ago. One of its most outstanding applications is masked language modeling represented by BERT [18]. In computer vision, explorations along this direction include predicting large missing regions [50], sequence of pixels [10], patches [20, 29, 71], or pre-computed features [6, 66]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 288, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 605 + ], + "type": "text", + "content": "The Masked Autoencoder (MAE) method [29] further takes advantage of masking to reduce training time and memory. MAE sparsely applies the ViT encoder [20] to visible content. It also observes that a high masking ratio is beneficial for accuracy. The MAE design has been applied to videos [61, 22], point clouds [49], graphs [59, 9, 32], audio [4, 47, 13, 35], visual control [70, 57], vision-language [23, 41, 31, 19], and other modalities [5]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Our work is related to MAE and its vision-language extensions [23, 41, 31, 19]. However, our focus is on the scaling aspect enabled by the sparse computation; we address the challenge of large-scale CLIP training [52], while previous works [23, 41, 31, 19] are limited in terms of scale. Our method does not perform reconstruction and is not a form of autoencoding. Speeding up training by masking is studied in [69] for self-supervised contrastive learning, e.g., for MoCo [30] or BYOL [27], but its accuracy could be" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 334, + 70, + 511, + 190 + ], + "blocks": [ + { + "bbox": [ + 334, + 70, + 511, + 190 + ], + "lines": [ + { + "bbox": [ + 334, + 70, + 511, + 190 + ], + "spans": [ + { + "bbox": [ + 334, + 70, + 511, + 190 + ], + "type": "image", + "image_path": "1b6c56d6081e807767b769055906b22530e5296098de4091184e3f925087d570.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 197, + 547, + 253 + ], + "lines": [ + { + "bbox": [ + 304, + 197, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 197, + 547, + 253 + ], + "type": "text", + "content": "Figure 2. Our FLIP architecture. Following CLIP [52], we perform contrastive learning on pairs of image and text samples. We randomly mask out image patches with a high masking ratio and encode only the visible patches. We do not perform reconstruction of masked image content." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 275, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 545, + 300 + ], + "type": "text", + "content": "limited by the scaling behavior of image-only contrastive learning." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 309, + 546, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 546, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 546, + 417 + ], + "type": "text", + "content": "Language-supervised learning. In the past years, CLIP [52] and related works (e.g., [37, 51]) have popularized learning visual representations with language supervision. CLIP is a form of contrastive learning [28] by comparing image-text sample pairs. Beyond contrastive learning, generative learning methods have been explored [17, 65, 2, 74], optionally combined with contrastive losses [74]. Our method focuses on the CLIP method, while we hope it can be extended to generative methods in the future." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 430, + 361, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 430, + 361, + 442 + ], + "spans": [ + { + "bbox": [ + 306, + 430, + 361, + 442 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 452, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 452, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 452, + 545, + 475 + ], + "type": "text", + "content": "In a nutshell, our method simply masks out the input data in CLIP [52] training and reduces computation. See Fig. 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 476, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 476, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 476, + 545, + 596 + ], + "type": "text", + "content": "In our scenario, the benefit of masking is on wisely spending computation. Intuitively, this leads to a trade-off between how densely we encode a sample against how many samples we compare as the learning signal. By introducing masking, we can: (i) learn from more image-text pairs under the same wall-clock training time, and (ii) have a contrastive objective over a larger batch under the same memory constraint. We show by experiments that for both aspects, our method is at an advantage in the trade-off. Next we introduce the key components of our method." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "Image masking. We adopt the Vision Transformer (ViT) [20] as the image encoder. An image is first divided into a grid of non-overlapping patches. We randomly mask out a large portion (e.g., " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ") of patches; the ViT encoder is only applied to the visible patches, following [29]. Using a masking ratio of " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ") reduces the time complexity of image encoding to 1/2 (or 1/4); it also allows using a " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "2\\times" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "4\\times" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ") larger batch with a similar memory cost for image encoding." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23391" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "Text masking. Optionally, we perform text masking in the same way as image masking. We mask out a portion of the text tokens and apply the encoder only to the visible tokens, as in [29]. This is unlike BERT [18] that replaces them with a learned mask token. Such sparse computation can reduce the text encoding cost. However, as the text encoder is smaller [52], speeding it up does not lead to a better overall trade-off. We study text masking for ablation only." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 175, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 258 + ], + "type": "text", + "content": "Objective. The image/text encoders are trained to minimize a contrastive loss [48]. The negative sample pairs for contrastive learning consist of other samples in the same batch [11]. It has been observed that a large number of negative samples is critical for self-supervised contrastive learning on images [30, 11]. This property is more prominent in language-supervised learning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 258, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 287, + 308 + ], + "type": "text", + "content": "We do not use a reconstruction loss, unlike MAE [29]. We find that reconstruction is not necessary for good performance on zero-shot transfer. Waiving the decoder and reconstruction loss yields a better speedup." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 313, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 287, + 373 + ], + "type": "text", + "content": "Unmasking. While the encoder is pre-trained on masked images, it can be directly applied on intact images without changes, as is done in [29]. This simple setting is sufficient to provide competitive results and will serve as our baseline in ablation experiments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 373, + 287, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 422 + ], + "type": "text", + "content": "To close the distribution gap caused by masking, we can set the masking ratio as " + }, + { + "bbox": [ + 46, + 373, + 287, + 422 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 46, + 373, + 287, + 422 + ], + "type": "text", + "content": " and continue pre-training for a small number of steps. This unmasking tuning strategy produces a more favorable accuracy/time trade-off." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 430, + 145, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 145, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 145, + 442 + ], + "type": "text", + "content": "3.1. Implementation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 449, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 485 + ], + "type": "text", + "content": "Our implementation follows CLIP [52] and OpenCLIP [36], with a few modifications we describe in the following. Hyper-parameters are in the appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 485, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 533 + ], + "type": "text", + "content": "Our image encoder follows the ViT paper [20]. We do not use the extra LayerNorm [3] after patch embedding, like [20] but unlike [52]. We use global average pooling at the end of the image encoder. The input size is 224." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": "Our text encoder is a non-autoregressive Transformer [62], which is easier to adapt to text masking for ablation. We use a WordPiece tokenizer as in [18]. We pad or cut the sequences to a fixed length of 32. We note that CLIP in [52] uses an autoregressive text encoder, a BytePairEncoding tokenizer, and a length of 77. These designs make marginal differences as observed in our initial reproduction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 677 + ], + "type": "text", + "content": "The outputs of the image encoder and text encoder are projected to the same-dimensional embedding space by a linear layer. The cosine similarities of the embeddings, scaled by a learnable temperature parameter [52], are the input to the InfoNCE loss [48]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "In zero-shot transfer, we follow the prompt engineering in the code of [52]. We use their provided 7 prompt templates for ImageNet zero-shot transfer." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "Our implementation is based on JAX [8] with the t5x library [54] for large-scale distributed training. Our training is run on TPU v3 infrastructure." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 119, + 387, + 132 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 119, + 387, + 132 + ], + "spans": [ + { + "bbox": [ + 305, + 119, + 387, + 132 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 138, + 373, + 150 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 138, + 373, + 150 + ], + "spans": [ + { + "bbox": [ + 306, + 138, + 373, + 150 + ], + "type": "text", + "content": "4.1. Ablations" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 157, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 157, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 157, + 545, + 205 + ], + "type": "text", + "content": "We first ablate the FLIP design. The image encoder is ViT-L/16 [20], and the text encoder has a smaller size as per [52]. We train on LAION-400M [36] and evaluate zero-shot accuracy on ImageNet-1K [16] validation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 205, + 545, + 241 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 205, + 545, + 241 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 545, + 241 + ], + "type": "text", + "content": "Table 1 shows the ablations trained for 6.4 epochs. Fig. 1 plots the trade-off for up to 32 epochs [52]. The results are benchmarked in 256 TPU-v3 cores, unless noted." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": "Masking ratio. Table 1a studies the image masking ratios. Here we scale the batch size accordingly (ablated next), so as to roughly maintain the memory footprint." + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " The " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " masking entry indicates our CLIP counterpart. Masking " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " gives " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " higher accuracy than the CLIP baseline, and masking " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " is on par with the baseline. Speed-wise, masking " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " takes only " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "0.50 \\times" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "inline_equation", + "content": "0.33 \\times" + }, + { + "bbox": [ + 305, + 247, + 545, + 342 + ], + "type": "text", + "content": " wall-clock training time, thanks to the large reduction on FLOPs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 348, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 348, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 348, + 545, + 372 + ], + "type": "text", + "content": "Batch size. We ablate the effect of batch size in Table 1b. Increasing the batch size consistently improves accuracy." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "text", + "content": "Notably, even using the same batch size of 16k, our " + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "text", + "content": " masking entry has a comparable accuracy (68.5%, Table 1b) with the " + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "text", + "content": " masking baseline (68.6%, Table 1a). It is possible that the regularization introduced by masking can reduce overfitting, partially counteracting the negative effect of losing information in this setting. With a higher masking ratio of " + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 304, + 372, + 545, + 467 + ], + "type": "text", + "content": ", the negative effect is still observed when keeping the batch size unchanged." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 468, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 545, + 586 + ], + "type": "text", + "content": "Our masking-based method naturally encourages using large batches. There is little extra memory cost if we scale the batch size according to the masking ratio, as we report in Table 1a. In practice, the available memory is always a limitation for larger batches. For example, the setting in Table 1a has reached the memory limit in our high-end infrastructure (256 TPU-v3 cores with 16GB memory each). The memory issue is more demanding if using fewer devices, and the gain of our method would be more prominent due to the nearly free increase of batch sizes." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "type": "text", + "content": "Text masking. Table 1c studies text masking. Randomly masking " + }, + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "type": "text", + "content": " text decreases accuracy by " + }, + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 305, + 593, + 545, + 628 + ], + "type": "text", + "content": ". This is in line with the observation [29] that language data has higher" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "spans": [ + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "text", + "content": "1Directly comparing TPU memory usage can be difficult due to its memory optimizations. We instead validate GPU memory usage using [36]'s reimplementation of FLIP, and find the memory usage is 25.5G, 23.9G and 24.5G for masking " + }, + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 306, + 636, + 545, + 674 + ], + "type": "text", + "content": " on 256 GPUs." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "text", + "content": "2The \"mask " + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "text", + "content": ", 64k\" entry in Table 1b requires " + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "text", + "content": " memory vs. those in Table 1a. This entry can be run using " + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 306, + 674, + 545, + 712 + ], + "type": "text", + "content": " devices; instead, it can also use memory optimization (e.g., activation checkpointing [12]) that trades time with memory, which is beyond the focus of this work." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23392" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 56, + 60, + 199, + 103 + ], + "blocks": [ + { + "bbox": [ + 56, + 60, + 199, + 103 + ], + "lines": [ + { + "bbox": [ + 56, + 60, + 199, + 103 + ], + "spans": [ + { + "bbox": [ + 56, + 60, + 199, + 103 + ], + "type": "table", + "html": "
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Unless specified, the baseline setting is: image masking is " + }, + { + "bbox": [ + 46, + 216, + 546, + 249 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 216, + 546, + 249 + ], + "type": "text", + "content": " (batch 32k) or " + }, + { + "bbox": [ + 46, + 216, + 546, + 249 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 216, + 546, + 249 + ], + "type": "text", + "content": " (batch 64k), text masking is " + }, + { + "bbox": [ + 46, + 216, + 546, + 249 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 46, + 216, + 546, + 249 + ], + "type": "text", + "content": ", and no unmasked tuning is used." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 287, + 289 + ], + "type": "text", + "content": "information-density than images and thus the text masking ratio should be lower." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": "As variable-length text sequences are padded to generate a fixed-length batch, we can prioritize masking out the padding tokens. Prioritized sampling preserves more valid tokens than randomly masking the padded sequences uniformly. It reduces the degradation to " + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 46, + 289, + 287, + 350 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "type": "text", + "content": "While our text masking is more aggressive than typical masked language models (e.g., " + }, + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "type": "inline_equation", + "content": "15\\%" + }, + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "type": "text", + "content": " in [18]), the overall speed gain is marginal. This is because the text encoder is smaller and the text sequence is short. The text encoder costs merely " + }, + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "type": "inline_equation", + "content": "4.4\\%" + }, + { + "bbox": [ + 46, + 350, + 287, + 445 + ], + "type": "text", + "content": " computation vs. the image encoder (without masking). Under this setting, text masking is not a worthwhile trade-off and we do not mask text in our other experiments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 525 + ], + "type": "text", + "content": "Inference unmasking. By default, we apply our models on intact images at inference-time, similar to [29]. While masking creates a distribution shift between training and inference, simply ignoring this shift works surprisingly well (Table 1d, 'w/o mask'), even under the zero-shot setting where no training is ever done on full images." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": "Table 1d reports that if using masking at inference time, the accuracy drops by a lot (e.g., " + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "inline_equation", + "content": "7.3\\%" + }, + { + "bbox": [ + 46, + 525, + 287, + 609 + ], + "type": "text", + "content": "). This drop can be partially caused by information loss at inference, so we also compare with ensembling multiple masked views [10], where the views are complementary to each other and put together cover all patches. Ensembling reduces the gap (Table 1d), but still lags behind the simple full-view inference." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": "Unmasked tuning. Our ablation experiments thus far do not involve unmasked tuning. Table 1e reports the results of unmasked tuning for extra 0.32 epoch on the pre-training dataset. It increases accuracy by " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": " at the high masking ratio of " + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 46, + 616, + 287, + 689 + ], + "type": "text", + "content": ", suggesting that tuning can effectively reduce the distribution gap between pre-training and inference." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Fig. 3 plots the trade-off affected by unmasked tuning (solid vs. dashed). Unmasked tuning leads to a more desir-" + } + ] + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 312, + 262, + 535, + 439 + ], + "blocks": [ + { + "bbox": [ + 312, + 262, + 535, + 439 + ], + "lines": [ + { + "bbox": [ + 312, + 262, + 535, + 439 + ], + "spans": [ + { + "bbox": [ + 312, + 262, + 535, + 439 + ], + "type": "image", + "image_path": "31a9ac3be46169703dc4614aa42bd9cb5af536e73352892010e46d8f4b6ca627.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 442, + 546, + 510 + ], + "lines": [ + { + "bbox": [ + 305, + 442, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 442, + 546, + 510 + ], + "type": "text", + "content": "Figure 3. Accuracy vs. training time trade-off in detail. The setting follows Table 1a. Training is for 6.4, 12.8, or 32 epochs, for each masking ratio. Unmasked tuning, if applied, is for 0.32 epoch. All are benchmarked in 256 TPU-v3 cores. Zero-shot accuracy is on IN-1K validation. The model is ViT-L/16. Our method speeds up training and increases accuracy." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "type": "text", + "content": "able trade-off for " + }, + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "type": "inline_equation", + "content": "75\\%" + }, + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "type": "text", + "content": " masking; it has a comparable tradeoff for " + }, + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 305, + 525, + 545, + 551 + ], + "type": "text", + "content": " masking but improves final accuracy." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 557, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 557, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 305, + 557, + 545, + 616 + ], + "type": "text", + "content": "Reconstruction. In Table 1f we investigate adding a reconstruction loss function. The reconstruction head follows the design in MAE [29]: it has a small decoder and reconstructs normalized image pixels. The reconstruction loss is added to the contrastive loss." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "Table 1f shows that reconstruction has a small negative impact for zero-short results. We also see a similar though slight less drop for fine-tuning accuracy on ImageNet. While this can be a result of suboptimal hyperparameters (e.g., balancing two losses), to strive for simplicity, we decide not to use the reconstruction loss. Waiving the reconstruction head also helps simplify the system and improves the accuracy/time trade-off." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23393" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 147, + 70, + 443, + 125 + ], + "blocks": [ + { + "bbox": [ + 147, + 70, + 443, + 125 + ], + "lines": [ + { + "bbox": [ + 147, + 70, + 443, + 125 + ], + "spans": [ + { + "bbox": [ + 147, + 70, + 443, + 125 + ], + "type": "table", + "html": "
casedataepochsB/16L/16L/14H/14
CLIP [52]WIT-400M3268.6-75.3-
OpenCLIP [36]LAION-400M3267.1-72.8-
CLIP, our repro.LAION-400M3268.272.473.1-
FLIPLAION-400M3268.074.374.675.5
", + "image_path": "23017eff9bf4448fab6ceb5a85cc3c2ef1f96e6a606833601c8c33e4e69e5a67.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 123, + 156, + 468, + 220 + ], + "blocks": [ + { + "bbox": [ + 46, + 126, + 544, + 148 + ], + "lines": [ + { + "bbox": [ + 46, + 126, + 544, + 148 + ], + "spans": [ + { + "bbox": [ + 46, + 126, + 544, + 148 + ], + "type": "text", + "content": "Table 2. Zero-shot accuracy on ImageNet-1K classification, compared with various CLIP baselines. The image size is 224. The entries noted by grey are pre-trained on a different dataset. Our models use a 64k batch, " + }, + { + "bbox": [ + 46, + 126, + 544, + 148 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 126, + 544, + 148 + ], + "type": "text", + "content": " masking ratio, and unmasked tuning." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 123, + 156, + 468, + 220 + ], + "lines": [ + { + "bbox": [ + 123, + 156, + 468, + 220 + ], + "spans": [ + { + "bbox": [ + 123, + 156, + 468, + 220 + ], + "type": "table", + "html": "
casedataepochsmodelzero-shotlinear probefine-tune
CLIP [52]WIT-400M32L/1475.383.9†-
CLIP [52], our transferWIT-400M32L/1475.383.087.4
OpenCLIP [36]LAION-400M32L/1472.882.186.2
CLIP, our repro.LAION-400M32L/1672.482.686.3
FLIPLAION-400M32L/1674.383.686.9
", + "image_path": "7bdcc788180553f0bd417e85f6deceda57b14db8a5da4c1d72d325c2ba3c9a59.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 225, + 544, + 247 + ], + "lines": [ + { + "bbox": [ + 46, + 225, + 544, + 247 + ], + "spans": [ + { + "bbox": [ + 46, + 225, + 544, + 247 + ], + "type": "text", + "content": "Table 3. Linear probing and fine-tuning accuracy on ImageNet-1K classification, compared with various CLIP baselines. The entries noted by grey are pre-trained on a different dataset. The image size is 224. †: CLIP in [52] optimizes with L-BFGS; we use SGD instead." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 261, + 286, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 286, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 286, + 297 + ], + "type": "text", + "content": "Accuracy vs. time trade-off. Fig. 3 presents a detailed view on the accuracy vs. training time trade-off. We extend the schedule to up to 32 epochs [52]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "text", + "content": "As shown in Fig. 3, FLIP has a clearly better trade-off than the CLIP counterpart. It can achieve similar accuracy as CLIP while enjoying a speedup of " + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "inline_equation", + "content": ">3 \\times" + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "text", + "content": ". With the same 32-epoch schedule, our method is " + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "inline_equation", + "content": "\\sim 1\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "text", + "content": " more accurate than the CLIP counterpart and " + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "text", + "content": " faster (masking " + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 297, + 286, + 356 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "type": "text", + "content": "The speedup of our method is of great practical value. The CLIP baseline takes " + }, + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "type": "inline_equation", + "content": "\\sim 10" + }, + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "type": "text", + "content": " days training in 256 TPU-v3 cores, so a speedup of " + }, + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "type": "inline_equation", + "content": "2 - 3\\times" + }, + { + "bbox": [ + 46, + 357, + 286, + 416 + ], + "type": "text", + "content": " saves many days in wall-clock time. This speedup facilitates exploring the scaling behavior, as we will discuss later in Sec. 4.3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 424, + 185, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 424, + 185, + 436 + ], + "spans": [ + { + "bbox": [ + 47, + 424, + 185, + 436 + ], + "type": "text", + "content": "4.2. Comparisons with CLIP" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 443, + 286, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 286, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 286, + 490 + ], + "type": "text", + "content": "In this section, we compare with various CLIP baselines in a large variety of scenarios. We show that our method is a competitive alternative to CLIP; as such, our fast training method is a more desirable choice in practice." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 495, + 232, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 495, + 232, + 507 + ], + "spans": [ + { + "bbox": [ + 59, + 495, + 232, + 507 + ], + "type": "text", + "content": "We consider the following CLIP baselines:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 58, + 515, + 286, + 573 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 58, + 515, + 286, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 515, + 286, + 538 + ], + "spans": [ + { + "bbox": [ + 58, + 515, + 286, + 538 + ], + "type": "text", + "content": "- The original CLIP checkpoints [52], trained on the private dataset WIT-400M." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 58, + 544, + 240, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 544, + 240, + 556 + ], + "spans": [ + { + "bbox": [ + 58, + 544, + 240, + 556 + ], + "type": "text", + "content": "- OpenCLIP [36], trained on LAION-400M." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 58, + 562, + 271, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 562, + 271, + 573 + ], + "spans": [ + { + "bbox": [ + 58, + 562, + 271, + 573 + ], + "type": "text", + "content": "- Our CLIP reproduction, trained on LAION-400M." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 582, + 286, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 676 + ], + "type": "text", + "content": "The original CLIP [52] was trained on a private dataset, so a direct comparison with it should reflect the effect of data, not just methods. OpenCLIP [36] is a faithful reproduction of CLIP yet trained on a public dataset that we can use, so it is a good reference for us to isolate the effect of dataset differences. Our CLIP reproduction further helps isolate other implementation subtleties and allows us to pinpoint the effect of the FLIP method." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 677, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 712 + ], + "type": "text", + "content": "For all tasks studied in this subsection, we compare with all these CLIP baselines. This allows us to better understand the influence of the data and of the methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 261, + 544, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 261, + 544, + 284 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 544, + 284 + ], + "type": "text", + "content": "ImageNet zero-shot transfer. In Table 2 we compare with the CLIP baselines on ImageNet-1K [16] zero-shot transfer." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 285, + 544, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 544, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 544, + 344 + ], + "type": "text", + "content": "As a sanity check, our CLIP reproduction has slightly higher accuracy than OpenCLIP trained on the same data. The original CLIP has higher accuracy than our reproduction and OpenCLIP, which could be caused by the difference between the pre-training datasets." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "content": "Table 2 reports the results of our FLIP models, using the best practice as we have ablated in Table 1 (a 64k batch, " + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "content": " masking ratio, and unmasked tuning). For ViT-L/14, our method has " + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "inline_equation", + "content": "74.6\\%" + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "content": " accuracy, which is " + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "content": " higher than OpenCLIP and " + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "content": " higher than our CLIP reproduction. Comparing with the original CLIP, our method reduces the gap to " + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "inline_equation", + "content": "0.7\\%" + }, + { + "bbox": [ + 304, + 346, + 544, + 441 + ], + "type": "text", + "content": ". We hope our method will improve the original CLIP result if it were trained on the WIT data." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "text", + "content": "ImageNet linear probing. Table 3 compares the linear probing results, i.e., training a linear classifier on the target dataset with frozen features. FLIP has " + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "inline_equation", + "content": "83.6\\%" + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "text", + "content": " accuracy, " + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "text", + "content": " higher than our CLIP counterpart. It is also " + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 304, + 451, + 544, + 522 + ], + "type": "text", + "content": " higher than our transfer of the original CLIP checkpoint, using the same SGD trainer." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 531, + 544, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 544, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 544, + 615 + ], + "type": "text", + "content": "ImageNet fine-tuning. Table 3 also compares full fine-tuning results. Our fine-tuning implementation follows MAE [29], with the learning rate tuned for each entry. It is worth noting that with our fine-tuning recipe, the original CLIP checkpoint reaches " + }, + { + "bbox": [ + 304, + 531, + 544, + 615 + ], + "type": "inline_equation", + "content": "87.4\\%" + }, + { + "bbox": [ + 304, + 531, + 544, + 615 + ], + "type": "text", + "content": ", much higher than previous reports [68, 67, 33] on this metric. CLIP is still a strong model under the fine-tuning protocol." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "text", + "content": "FLIP outperforms the CLIP counterparts pre-trained on the same data. Our result of " + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "inline_equation", + "content": "86.9\\%" + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "inline_equation", + "content": "87.1\\%" + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "text", + "content": " using L/14) is behind but close to the result of the original CLIP checkpoint's " + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "inline_equation", + "content": "87.4\\%" + }, + { + "bbox": [ + 304, + 616, + 544, + 664 + ], + "type": "text", + "content": ", using our fine-tuning recipe." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 673, + 544, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 544, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 544, + 713 + ], + "type": "text", + "content": "For a legacy reason, we pre-trained our ViT-L models with a patch size of 16, following the original ViT paper [20]. The CLIP paper [52] uses L/14 instead. To save resources, we report our L/14 results by tuning the L/16 pre-trained model, in a way similar to unmasked tuning." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23394" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 60, + 545, + 135 + ], + "blocks": [ + { + "bbox": [ + 51, + 60, + 545, + 135 + ], + "lines": [ + { + "bbox": [ + 51, + 60, + 545, + 135 + ], + "spans": [ + { + "bbox": [ + 51, + 60, + 545, + 135 + ], + "type": "table", + "html": "
dataFood101CIFAR10CIFAR100BrandsnapSUN397CarsAircraftVOC2007DTDOxfoot PetsCaltech101Flowers102MNISTSTL10EuroSATRESIC45GTSRBKITTICountry211PCamUCF101Kinetics700CLEVRHatefulMemesSST2
CLIP [52]WIT-400M92.996.277.948.367.777.336.184.155.393.592.678.787.299.359.971.650.323.132.758.876.260.324.363.364.0
CLIP [52], our eval.WIT-400M91.095.275.651.266.675.032.383.355.093.692.477.776.099.362.071.651.626.930.951.676.159.522.255.367.3
OpenCLIP [36], our eval.LAION-400M87.494.177.161.370.786.221.883.554.990.894.072.171.598.253.367.747.329.321.651.171.350.522.055.357.1
CLIP, our repro.LAION-400M88.196.081.360.572.389.125.881.159.393.293.274.669.196.550.769.250.229.421.453.171.553.518.553.357.2
FLIPLAION-400M89.397.284.163.073.190.729.183.160.492.693.875.080.398.553.570.841.434.823.150.374.155.822.754.058.5
", + "image_path": "f06eb75316be5a013a46d201dbd7506082449787b23fc826202efff9e0fb8d4d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 171, + 541, + 266 + ], + "blocks": [ + { + "bbox": [ + 47, + 140, + 545, + 161 + ], + "lines": [ + { + "bbox": [ + 47, + 140, + 545, + 161 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 545, + 161 + ], + "type": "text", + "content": "Table 4. Zero-shot accuracy on more classification datasets, compared with various CLIP baselines. This table follows Table 11 in [52]. The model is ViT-L/14 with an image size of 224, for all entries. Entries in green are the best ones using the LAION-400M data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 171, + 541, + 266 + ], + "lines": [ + { + "bbox": [ + 50, + 171, + 541, + 266 + ], + "spans": [ + { + "bbox": [ + 50, + 171, + 541, + 266 + ], + "type": "table", + "html": "
casemodeldatatext retrievalimage retrieval
Flickr30kCOCOFlickr30kCOCO
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
CLIP [52]L/14@336WIT-400M88.098.799.458.481.588.168.790.695.237.862.472.2
CLIP [52], our eval.L/14@336WIT-400M88.998.799.958.780.487.972.591.795.238.562.872.5
CLIP [52], our eval.L/14WIT-400M87.899.199.856.279.886.469.390.294.035.860.770.7
OpenCLIP [36], our eval.L/14LAION-400M87.397.999.158.080.688.172.090.895.041.366.676.1
CLIP, our impl.L/14LAION-400M87.498.499.559.182.589.474.492.295.543.268.577.5
FLIPL/14LAION-400M89.198.599.660.282.689.975.492.595.944.269.278.4
", + "image_path": "4ca58ec2313bdec922e6e65cfd1c2598847ddd7330ecf7ad1d0e6ca6d3cb989e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 69, + 293, + 523, + 378 + ], + "blocks": [ + { + "bbox": [ + 47, + 271, + 545, + 292 + ], + "lines": [ + { + "bbox": [ + 47, + 271, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 545, + 292 + ], + "type": "text", + "content": "Table 5. Zero-shot image/text retrieval, compared with various CLIP baselines. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 69, + 293, + 523, + 378 + ], + "lines": [ + { + "bbox": [ + 69, + 293, + 523, + 378 + ], + "spans": [ + { + "bbox": [ + 69, + 293, + 523, + 378 + ], + "type": "table", + "html": "
modeldataIN-V2 top-1IN-A top-1IN-R top-1ObjectNet top-1IN-Sketch top-1IN-VidYTBB
PM-0PM-10PM-0PM-10
CLIP [52]L/14@336WIT-400M70.177.288.972.360.295.389.295.288.5
CLIP [52], our eval.L/14@336WIT-400M70.478.089.069.359.795.988.895.389.4
CLIP [52], our eval.L/14WIT-400M69.571.986.868.658.594.687.094.186.4
OpenCLIP [36], our eval.L/14LAION-400M64.048.384.358.856.990.381.486.577.8
CLIP, our repro.L/14LAION-400M65.646.384.758.058.789.380.585.777.8
FLIPL/14LAION-400M66.851.286.559.159.991.183.589.483.3
", + "image_path": "318e5f9dfca1dd02290a04404799f6a36cf1adc29091d642a84e6c19e3bc86ca.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 64, + 412, + 526, + 479 + ], + "blocks": [ + { + "bbox": [ + 47, + 382, + 545, + 403 + ], + "lines": [ + { + "bbox": [ + 47, + 382, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 545, + 403 + ], + "type": "text", + "content": "Table 6. Zero-shot robustness evaluation, compared with various CLIP baselines. This table follows Table 16 in [52]. The image size is 224 if not noted. Entries in green are the best ones using the LAION-400M data." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 64, + 412, + 526, + 479 + ], + "lines": [ + { + "bbox": [ + 64, + 412, + 526, + 479 + ], + "spans": [ + { + "bbox": [ + 64, + 412, + 526, + 479 + ], + "type": "table", + "html": "
casemodeldataCOCO captionnocapsVQAv2 acc.
BLEU-4METEORROUGE-LCIDErSPICECIDErSPICE
CLIP [52], our transferL/14WIT-400M37.529.658.7126.922.882.512.176.6
OpenCLIP [36], our transferL/14LAION-400M36.729.358.4125.022.783.412.374.5
CLIP, our repro.L/16LAION-400M36.429.358.4125.622.882.812.274.5
FLIPL/16LAION-400M37.429.558.8127.723.085.912.474.7
", + "image_path": "1233e2f584451aa3dc148c8fa8cc87d2dc70c5a8f883816e33b806d79a40ce6c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 484, + 545, + 506 + ], + "lines": [ + { + "bbox": [ + 46, + 484, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 545, + 506 + ], + "type": "text", + "content": "Table 7. Image Captioning and Visual Question Answering, compared with various CLIP baselines. Entries in green are the best ones using LAION-400M. Here the results are on the COCO captioning test split of [38], nocaps val split, and VQAv2 test-dev split, respectively." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 523, + 287, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 523, + 287, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 287, + 583 + ], + "type": "text", + "content": "Zero-shot classification on more datasets. In Table 4 we compare on the extra datasets studied in [52]. As the results can be sensitive to evaluation implementation (e.g., text prompts, image pre-processing), we provide our evaluations of the original CLIP checkpoint and OpenCLIP." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 584, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 584, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 287, + 643 + ], + "type": "text", + "content": "Notably, we observe clear systematic gaps caused by pre-training data, as benchmarked using the same evaluation code. The WIT dataset is beneficial for some tasks (e.g., Aircraft, Country211, SST2), while LAION is beneficial for some others (e.g., Birdsnap, SUN397, Cars)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 644, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 644, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 287, + 681 + ], + "type": "text", + "content": "After isolating the influence of pre-training data, we observe that FLIP is dominantly better than OpenCLIP and our CLIP reproduction, as marked by green in Table 4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Zero-shot retrieval. Table 5 reports image/text retrieval results on Flickr30k [73] and COCO [42]. FLIP outper" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 523, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 559 + ], + "type": "text", + "content": "forms all CLIP competitors, including the original CLIP (evaluated on the same 224 size). The WIT dataset has no advantage over LAION for these two retrieval datasets." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "content": "Zero-shot robustness evaluation. In Table 6 we compare on robustness evaluation, following [52]. We again observe clear systematic gaps caused by pre-training data. Using the same evaluation code (\"our eval\" in Table 6), CLIP pre-trained on WIT is clearly better than other entries pretrained on LAION. Taking IN-Adversarial (IN-A) as an example: the LAION-based OpenCLIP [36] has only " + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "inline_equation", + "content": "48.3\\%" + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "content": " accuracy (or " + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "inline_equation", + "content": "46.6\\%" + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "content": " reported by [36]). While FLIP " + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "inline_equation", + "content": "(51.2\\%)" + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "content": " can outperform the LAION-based CLIP by a large margin, it is still " + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "content": " below the WIT-based CLIP " + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "inline_equation", + "content": "(71.9\\%)" + }, + { + "bbox": [ + 304, + 569, + 545, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Discounting the influence of pre-training data, our FLIP training has clearly better robustness than its CLIP counter" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23395" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "parts in all cases. We hypothesize that masking as a form of noise and regularization can improve robustness." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 101, + 287, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 101, + 287, + 220 + ], + "spans": [ + { + "bbox": [ + 46, + 101, + 287, + 220 + ], + "type": "text", + "content": "Image Captioning. See Table 7 for the captioning performance on COCO [42] and nocaps [1]. Our captioning implementation follows the cross-entropy training baseline in [7]. Unlike classification in which only a classifier layer is added after pre-training, here the fine-tuning model has a newly initialized captioner (detailed in appendix). In this task, FLIP outperforms the original CLIP checkpoint in several metrics. Compared to our CLIP baseline, which is pretrained on the same data, FLIP also shows a clear gain, especially in BLEU-4 and CIDEr metrics." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 224, + 287, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 287, + 309 + ], + "type": "text", + "content": "Visual Question Answering. We evaluate on the VQAv2 dataset [26], with a fine-tuning setup following [21]. We use a newly initialized multimodal fusion transformer and an answer classifier to obtain the VQA outputs (detailed in appendix). Table 7 (rightmost column) reports results on VQAv2. All entries pre-trained on LAION perform similarly, and CLIP pre-trained on WIT is the best." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 314, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 287, + 361 + ], + "type": "text", + "content": "Summary of Comparisons. Across a large variety of scenarios, FLIP is dominantly better than its CLIP counterparts (OpenCLIP and our reproduction) pre-trained on the same LAION data, in some cases by large margins." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 361, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 287, + 409 + ], + "type": "text", + "content": "The difference between the WIT data and LAION data can create large systematic gaps, as observed in many downstream tasks. We hope our study will draw attention to these data-dependent gaps in future research." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 416, + 149, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 149, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 149, + 428 + ], + "type": "text", + "content": "4.3. Scaling Behavior" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 434, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 287, + 471 + ], + "type": "text", + "content": "Facilitated by the speed-up of FLIP, we explore the scaling behavior beyond the largest case studied in CLIP [52]. We study scaling along either of these three axes:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 477, + 287, + 617 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 59, + 477, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 477, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 59, + 477, + 287, + 513 + ], + "type": "text", + "content": "- Model scaling. We replace the ViT-L image encoder with ViT-H, which has " + }, + { + "bbox": [ + 59, + 477, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\sim 2\\times" + }, + { + "bbox": [ + 59, + 477, + 287, + 513 + ], + "type": "text", + "content": " parameters. The text encoder is also scaled accordingly." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 517, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 517, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 59, + 517, + 287, + 589 + ], + "type": "text", + "content": "- Data scaling. We scale the pre-training data from 400 million to 2 billion, using the LAION-2B set [36]. To better separate the influence of more data from the influence of longer training, we fix the total number of sampled data (12.8B, which amounts to 32 epochs of 400M data and 6.4 epochs of 2B data)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 594, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 594, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 59, + 594, + 287, + 617 + ], + "type": "text", + "content": "- Schedule scaling. We increase the sampled data from 12.8B to 25.6B (64 epochs of 400M data)." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 625, + 287, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 625, + 287, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 625, + 287, + 661 + ], + "type": "text", + "content": "We study scaling along one of these three axes at each time while keeping others unchanged. The results are summarized in Fig. 4 and Table 8." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 689 + ], + "type": "text", + "content": "Training curves. The three scaling strategies exhibit different trends in training curves (Fig. 4)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Model scaling (Fig. 4a) presents a clear gap that persists throughout training, though the gap is smaller at the end." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "Data scaling (Fig. 4b), on the other hand, performs similarly at the first half of training, but starts to present a good gain later. Note that there is no extra computational cost in this setting, as we control the total number of sampled data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "type": "text", + "content": "Schedule scaling (Fig. 4c) trains " + }, + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "type": "text", + "content": " longer. To provide a more intuitive comparison, we plot a hypothetical curve that is rescaled by " + }, + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 305, + 120, + 545, + 180 + ], + "type": "text", + "content": " along the x-axis (dashed line). Despite the longer training, the gain is diminishing or none (more numbers in Table 8)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 186, + 545, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 246 + ], + "type": "text", + "content": "Transferability. Table 8 provides an all-around comparison on various downstream tasks regarding the scaling behavior. Overall, model scaling and data scaling both can consistently outperform the baseline in all metrics, in some cases by large margins." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 545, + 365 + ], + "type": "text", + "content": "We categorize the downstream tasks into two scenarios: (i) zero-shot transfer, i.e., no learning is performed on the downstream dataset; (ii) transfer learning, i.e., part or all of the weights are trained on the downstream dataset. For the tasks studied here, data scaling is in general favored for zero-shot transfer, while model scaling is in general favored for transfer learning. However, it is worth noting that the transfer learning performance depends on the size of the downstream dataset, and training a big model on a too small downstream set is still subject to the overfitting risk." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 437 + ], + "type": "text", + "content": "It is encouraging to see that data scaling is clearly beneficial, even not incurring longer training nor additional computation. On the contrary, even spending more computation by schedule scaling gives diminishing returns. These comparisons suggest that large-scale data are beneficial mainly because they provide richer information." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": "Next we scale both model and data (Table 8, second last row). For all metrics, model+data scaling improves over scaling either alone. The gains of model scaling and data scaling are highly complementary: e.g., in zero-shot IN-1K, model scaling alone improves over the baseline by " + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "(74.3\\% \\rightarrow 75.5\\%)" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": ", and data scaling alone improves by " + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "1.5\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "(74.3\\% \\rightarrow 75.8\\%)" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": ". Scaling both improves by " + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "inline_equation", + "content": "(77.6\\%)" + }, + { + "bbox": [ + 304, + 437, + 545, + 557 + ], + "type": "text", + "content": " more than the two deltas combined. This behavior is also observed in several other tasks. This indicates that a larger model desires more data to unleash its potential." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 558, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 617 + ], + "type": "text", + "content": "Finally, we report joint scaling all three axes (Table 8, last row). Our results show that combining schedule scaling leads to improved performances across most metrics. This suggests that schedule scaling is particularly beneficial when coupled with larger models and larger-scale data." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "Our result of " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "78.8\\%" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " on zero-shot IN-1K outperforms the state-of-the-art result trained on public data with ViT-H (78.0% of OpenCLIP). Also based on LAION-2B, their result is trained with 32B sampled data, " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.25 \\times" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " more than ours. Given the " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " masking we use, our training is estimated to be " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "2.5 \\times" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " faster than theirs if both were run on the same hardware. As OpenCLIP's result reports a training cost of " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sim 5,600" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " GPU-days, our method could save " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sim 3,360" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23396" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 65, + 176, + 165 + ], + "blocks": [ + { + "bbox": [ + 51, + 65, + 176, + 165 + ], + "lines": [ + { + "bbox": [ + 51, + 65, + 176, + 165 + ], + "spans": [ + { + "bbox": [ + 51, + 65, + 176, + 165 + ], + "type": "image", + "image_path": "02b4bdc23a772e4561f67c001e186e00167391369cfce802ee1aed77aade73cb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 85, + 168, + 145, + 178 + ], + "lines": [ + { + "bbox": [ + 85, + 168, + 145, + 178 + ], + "spans": [ + { + "bbox": [ + 85, + 168, + 145, + 178 + ], + "type": "text", + "content": "(a) Model scaling" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 183, + 64, + 307, + 165 + ], + "blocks": [ + { + "bbox": [ + 183, + 64, + 307, + 165 + ], + "lines": [ + { + "bbox": [ + 183, + 64, + 307, + 165 + ], + "spans": [ + { + "bbox": [ + 183, + 64, + 307, + 165 + ], + "type": "image", + "image_path": "8d4a22a880982422f13f1d31c3a5886971eaf10175e8b18d27d012efcd3bbab5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 168, + 275, + 178 + ], + "lines": [ + { + "bbox": [ + 220, + 168, + 275, + 178 + ], + "spans": [ + { + "bbox": [ + 220, + 168, + 275, + 178 + ], + "type": "text", + "content": "(b) Data scaling" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 187, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 46, + 187, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 547, + 222 + ], + "type": "text", + "content": "Figure 4. Training curves of scaling. The x-axis is the number of sampled data during training, and the y-axis is the zero-shot accuracy on IN-1K. The blue curve is the baseline setting: ViT-Large, LAION-400M data, 32 epochs (12.8B sampled data). In each subplot, we compare with scaling one factor on the baseline. In schedule scaling (Fig. 4c), we plot an extra hypothetical curve for a better visualization." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 316, + 64, + 548, + 165 + ], + "blocks": [ + { + "bbox": [ + 316, + 64, + 548, + 165 + ], + "lines": [ + { + "bbox": [ + 316, + 64, + 548, + 165 + ], + "spans": [ + { + "bbox": [ + 316, + 64, + 548, + 165 + ], + "type": "image", + "image_path": "2f2fae89268f559bb68426e148725731a5c27f268eedf54faba977e3bfc9c1db.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 397, + 168, + 466, + 178 + ], + "lines": [ + { + "bbox": [ + 397, + 168, + 466, + 178 + ], + "spans": [ + { + "bbox": [ + 397, + 168, + 466, + 178 + ], + "type": "text", + "content": "(c) Schedule scaling" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 56, + 232, + 537, + 331 + ], + "blocks": [ + { + "bbox": [ + 56, + 232, + 537, + 331 + ], + "lines": [ + { + "bbox": [ + 56, + 232, + 537, + 331 + ], + "spans": [ + { + "bbox": [ + 56, + 232, + 537, + 331 + ], + "type": "table", + "html": "
casemodeldatasampledzero-shot transfertransfer learning
zero-shot IN-1Ktext retrievalimage retrievallin-probe IN-1Kfine-tune IN-1Kcaptioning COCOnocapsvqa VQAv2
baselineLarge400M12.8B74.388.459.875.044.183.686.9127.785.974.7
model scalingHuge400M12.8B75.589.262.876.446.084.387.3130.391.576.3
data scalingLarge2B12.8B75.891.763.878.247.384.287.1128.987.075.5
schedule scalingLarge400M25.6B73.989.760.175.544.483.786.9127.986.875.0
model+data scalingHuge2B12.8B77.692.867.079.949.585.187.7130.492.677.1
joint scalingHuge2B25.6B78.893.167.880.950.585.687.9130.291.277.3
", + "image_path": "59ceba6c550f9fd7233bea705f0397ff03ecee60d207aefbd7f285cfd466a652.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 336, + 546, + 381 + ], + "lines": [ + { + "bbox": [ + 46, + 336, + 546, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 546, + 381 + ], + "type": "text", + "content": "Table 8. Scaling behavior of FLIP, evaluated on a diverse set of downstream tasks: classification, retrieval (R@1), captioning (CIDEr), and visual question answering. In the middle three rows, we scale along one of the three axes (model, data, schedule), and the green entries denote the best ones among these three scaling cases. Data scaling is in general favored under the zero-shot transfer scenario, while model scaling is in general favored under the transfer learning scenario (i.e., with trainable weights in downstream)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "text", + "content": "GPU-days based on a rough estimation. Additionally, without enabling " + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "text", + "content": " schedule, our entry of \"model+data scaling\" is estimated " + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "text", + "content": " faster than theirs and can save " + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "inline_equation", + "content": "\\sim 4,480" + }, + { + "bbox": [ + 46, + 397, + 288, + 445 + ], + "type": "text", + "content": " GPU-days. This is considerable cost reduction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 454, + 200, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 200, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 200, + 467 + ], + "type": "text", + "content": "5. Discussion and Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 474, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 545 + ], + "type": "text", + "content": "Language is a stronger form of supervision than classical closed-set labels. Language provides rich information for supervision. Therefore, scaling, which can involve increasing capacity (model scaling) and increasing information (data scaling), is essential for attaining good results in language-supervised training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 545, + 287, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 618 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 618 + ], + "type": "text", + "content": "CLIP [52] is an outstanding example of \"simple algorithms that scale well\". The simple design of CLIP allows it to be relatively easily executed at substantially larger scales and achieve big leaps compared to preceding methods. Our method largely maintains the simplicity of CLIP while pushing it further along the scaling aspect." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 618, + 288, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 701 + ], + "type": "text", + "content": "Our method can provide a " + }, + { + "bbox": [ + 46, + 618, + 288, + 701 + ], + "type": "inline_equation", + "content": "2 - 3 \\times" + }, + { + "bbox": [ + 46, + 618, + 288, + 701 + ], + "type": "text", + "content": " speedup or more. For the scale concerned in this study, such a speedup can reduce wall-clock time by a great amount (e.g., at the order of thousands of TPU/GPU-days). Besides accelerating research cycles, the speedup can also save a great amount of energy and commercial cost. These are all ingredients of great importance in large-scale machine learning research." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Our study involves controlled comparisons with various" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 397, + 546, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 546, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 546, + 469 + ], + "type": "text", + "content": "CLIP baselines, which help us to break down the gaps contributed by different factors. We show that FLIP outperforms its CLIP counterparts pre-trained on the same LAION data. By comparing several LAION-based models and the original WIT-based ones, we observe that the pre-training data creates big systematic gaps in several tasks." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 471, + 546, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 546, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 546, + 531 + ], + "type": "text", + "content": "Our study provides controlled experiments on scaling behavior. We observe that data scaling is a favored scaling dimension, given that it can improve accuracy with no extra cost at training or inference time. Our fast method encourages us to scale beyond what is studied in this work." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 544, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 546, + 616 + ], + "type": "text", + "content": "Broader impacts. Training large-scale models costs high energy consumption and carbon emissions. While our method has reduced such cost to 1/2-1/3, the remaining cost is still sizable. We hope our work will attract more attention to the research direction on reducing the cost of training vision-language models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": "The numerical results in this paper are based on a publicly available large-scale dataset [56]. The resulting model weights will reflect the data biases, including potentially negative implications. When compared using the same data, the statistical differences between two methods should reflect the method properties to a good extent; however, when compared entries using different training data, the biases of the data should always be part of the considerations." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23397" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 132 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 132 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 132 + ], + "type": "text", + "content": "[1] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. 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In ICLR, 2018." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "23400" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Scaling Up GANs for Text-to-Image Synthesis/cc6d67d2-1178-4cd7-a0a4-6ace5123194c_content_list.json b/2023/Scaling Up GANs for Text-to-Image Synthesis/cc6d67d2-1178-4cd7-a0a4-6ace5123194c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..096c317da79fe465a280f986f7d0e3b225e0c683 --- /dev/null +++ b/2023/Scaling Up GANs for Text-to-Image Synthesis/cc6d67d2-1178-4cd7-a0a4-6ace5123194c_content_list.json @@ -0,0 +1,1718 @@ +[ + { + "type": "text", + "text": "Scaling up GANs for Text-to-Image Synthesis", + "text_level": 1, + "bbox": [ + 254, + 130, + 715, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Minguk Kang $^{1,3}$ Jun-Yan Zhu $^{2}$ Richard Zhang $^{3}$ \nJaesik Park $^{1}$ Eli Shechtman $^{3}$ Sylvain Paris $^{3}$ Taesung Park $^{3}$ \nPOSTECH $^{2}$ Carnegie Mellon University $^{3}$ Adobe Research", + "bbox": [ + 200, + 178, + 795, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 279, + 313, + 296 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The recent success of text-to-image synthesis has taken the world by storm and captured the general public's imagination. From a technical standpoint, it also marked a drastic change in the favored architecture to design generative image models. GANs used to be the de facto choice, with techniques like StyleGAN. With DALL-E 2, autoregressive and diffusion models became the new standard for large-scale generative models overnight. This rapid shift raises a fundamental question: can we scale up GANs to benefit from large datasets like LAION? We find that naively increasing the capacity of the StyleGAN architecture quickly becomes unstable. We introduce GigaGAN, a new GAN architecture that far exceeds this limit, demonstrating GANs as a viable option for text-to-image synthesis. GigaGAN offers three major advantages. First, it is orders of magnitude faster at inference time, taking only 0.13 seconds to synthesize a 512px image. Second, it can synthesize high-resolution images, for example, 16-megapixel images in 3.66 seconds. Finally, GigaGAN supports various latent space editing applications such as latent interpolation, style mixing, and vector arithmetic operations.", + "bbox": [ + 75, + 311, + 472, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 661, + 209, + 678 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently released models, such as DALL-E 2 [53], Imagegen [59], Parti [73], and Stable Diffusion [58], have ushered in a new era of image generation, achieving unprecedented levels of image quality and model flexibility. The now-dominant paradigms, diffusion models and autoregressive models, both rely on iterative inference. This is a double-edged sword, as iterative methods enable stable training with simple objectives but incur a high computational cost during inference.", + "bbox": [ + 75, + 686, + 468, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contrast this with Generative Adversarial Networks (GANs) [5,17,33,51], which generate images through a single forward pass and thus inherently efficient. While such models dominated the previous \"era\" of generative modeling, scaling them requires careful tuning of the network", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "architectures and training considerations due to instabilities in the training procedure. As such, GANs have excelled at modeling single or multiple object classes, but scaling to complex datasets, much less an open world, has remained challenging. As a result, ultra-large models, data, and compute resources are now dedicated to diffusion and autoregressive models. In this work, we ask – can GANs continue to be scaled up and potentially benefit from such resources, or have they plateaued? What prevents them from further scaling, and can we overcome these barriers?", + "bbox": [ + 496, + 280, + 893, + 431 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We first experiment with StyleGAN2 [34] and observe that simply scaling the backbone causes unstable training. We identify several key issues and propose techniques to stabilize the training while increasing the model capacity. First, we effectively scale the generator's capacity by retaining a bank of filters and taking a sample-specific linear combination. We also adapt several techniques commonly used in the diffusion context and confirm that they bring similar benefits to GANs. For instance, interleaving both self-attention (image-only) and cross-attention (image-text) with the convolutional layers improves performance.", + "bbox": [ + 496, + 431, + 893, + 598 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Furthermore, we reintroduce multi-scale training, finding a new scheme that improves image-text alignment and low-frequency details of generated outputs. Multi-scale training allows the GAN-based generator to use parameters in low-resolution blocks more effectively, leading to better image-text alignment and image quality. After careful tuning, we achieve stable and scalable training of a one-billion-parameter GAN (GigaGAN) on large-scale datasets, such as LAION2B-en [63]. Our results are shown in Figure 1.", + "bbox": [ + 496, + 598, + 893, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In addition, our method uses a multi-stage approach [12, 76]. We first generate at $64 \\times 64$ and then upsample to $512 \\times 512$ . These two networks are modular and robust enough to be used in a plug-and-play fashion. We show that our text-conditioned GAN-based upsampling network can be used as an efficient, higher-quality upsampler for a base diffusion model such as DALL-E 2, despite never having seen diffusion images at training time (Figures 1).", + "bbox": [ + 496, + 734, + 893, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Together, these advances enable our GigaGAN to go far beyond previous GANs: $36 \\times$ larger than StyleGAN2 [34] and $6 \\times$ larger than StyleGAN-XL [62] and", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10124", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fead01978a2023133c7cb72256b00a1575a26f438c747774b63b9b8ad8fa004f.jpg", + "image_caption": [ + "A portrait of a human growing colorful flowers from her hair. Hyperrealistic oil painting, Intricate details." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 292, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1e0f695aa112862f4fa70e7c30214077134c0add4d8119f44837938b81ca7611.jpg", + "image_caption": [ + "a blue Porsche 356 parked in front of a yellow brick wall." + ], + "image_footnote": [], + "bbox": [ + 300, + 88, + 478, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/594c89109788e312175198364236e18ef659f9dbc3f5431e72672ef104b53a82.jpg", + "image_caption": [ + "Eiffel Tower, landscape photography" + ], + "image_footnote": [], + "bbox": [ + 485, + 89, + 665, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/05053ac8267312dad68d4a4ec309cd72e575ef6efbd35d4c77c4f45cfa0afb37.jpg", + "image_caption": [ + "A painting of a majestic royal tall ship in Age of Discovery." + ], + "image_footnote": [], + "bbox": [ + 671, + 89, + 849, + 227 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d64b7c88493f1e62b5a01c9cf51a30b97a8cd26964aafa42ac6d6460ac28e60b.jpg", + "image_caption": [ + "A golden luxury motorcycle parked at the King's palace, $35\\mathrm{mm}$ f/4.5." + ], + "image_footnote": [], + "bbox": [ + 112, + 251, + 292, + 390 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ea838559270522a5d9554494526b08ff0f8d5857a4180ed5b0db2ea866e083f6.jpg", + "image_caption": [ + "A hot air balloon in shape of a heart. Grand Canyon" + ], + "image_footnote": [], + "bbox": [ + 299, + 251, + 478, + 390 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/06de6d62124748783647db2336726c10c922315e170b374492a27bc6bd99a969.jpg", + "image_caption": [ + "low poly bunny with cute eyes" + ], + "image_footnote": [], + "bbox": [ + 485, + 251, + 665, + 388 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2bc20a9c4b58510e76eec2f663024c120522ebdf8d57fe902b835fc26384922a.jpg", + "image_caption": [ + "A cube made of denim on a wooden table" + ], + "image_footnote": [], + "bbox": [ + 671, + 251, + 849, + 388 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/8001a3cfd40e3c06d58f55e7fa6889010ef89ff357c2db1aabb9854df41adbe8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 112, + 412, + 478, + 695 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a0d1d106e4c84bb5644631ffed2026ee805d164239beb2e1875555c0a849a7ba.jpg", + "image_caption": [ + "Figure 1. Our model, GigaGAN, shows GAN frameworks can also be scaled up for general text-to-image synthesis and super-resolution tasks, generating a 512px output at an interactive speed of 0.13s, and 4096px within 3.7s. Selected examples at 2K resolution (text-to-image synthesis) and 1k or 4k resolutions (super-resolution) are shown. For the super-resolution task, we use the caption of \"Portrait of a colored iguana dressed in a hoodie.\" and compare our model with the text-conditioned upscaler of Stable Diffusion [57] and unconditional Real-ESRGAN [26]. Please zoom in for more details. See our arXiv paper and website for more uncurated comparisons." + ], + "image_footnote": [], + "bbox": [ + 116, + 696, + 256, + 808 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/09329577ed2cfae04388e3204685d54f171627055ed5a45e0fc2b29ac0322811.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 261, + 696, + 406, + 808 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/08fac562b2dc0b35ca124d277a682a6cce18eace8b1d011bd6b03872f4f92bed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 410, + 696, + 552, + 808 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/62e27977dccc969ff1ac138f6f45738b59cec3474b3973933240f271bbd27ad3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 557, + 696, + 700, + 808 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/208c346bfe79252cb6c05fbf1bc0bb0615ffabca270fe39cb9a2eeb29e747323.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 696, + 849, + 808 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10125", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "XMC-GAN [75]. While our 1B parameter count is still lower than the largest synthesis models, such as DALL-E 2 (5.5B), and Parti (20B), we have not yet observed a quality saturation regarding the model size. GigaGAN achieves a zero-shot FID of 9.09 on COCO2014, lower than the FID of DALL-E 2, Parti-750M, and Stable Diffusion.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Furthermore, GigaGAN has three major practical advantages compared to diffusion and autoregressive models. First, it is orders of magnitude faster, generating a 512px image in 0.13 seconds. Second, it can synthesize ultra highres images at 4k resolution in 3.66 seconds. Third, it is endowed with a controllable, latent vector space that lends itself to well-studied controllable image synthesis applications, such as prompt mixing (Figure 4), style mixing (Figure 5), and prompt interpolation (Figures A7 and A8).", + "bbox": [ + 75, + 181, + 467, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In summary, our model is the first GAN-based method that successfully trains a billion-scale model on billions of real-world complex Internet images. This suggests that GANs are still a viable option for text-to-image synthesis and should be considered for future aggressive scaling. Please visit our website for additional results.", + "bbox": [ + 75, + 318, + 467, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 422, + 225, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-image synthesis. Generating a realistic image given a text description, explored by early works [42, 85], is a challenging task. A common approach is text-conditional GANs [55, 56, 67, 71, 76, 83] on specific domains [68] and datasets with a closed-world assumption [41]. With the development of diffusion models [13, 21], autoregressive (AR) transformers [10], and large-scale language encoders [50, 52], text-to-image synthesis has shown remarkable improvement on an open-world of arbitrary text descriptions. GLIDE [46], DALL-E 2 [53], and Imagen [59] are representative diffusion models that show realistic outputs with the aid of a pretrained language encoder [50, 52]. AR models, such as DALL-E [54], Make-A-Scene [16], CogView [14, 15], and Parti [73] also achieve amazing results. While these models exhibit unprecedented image synthesis ability, they require time-consuming iterative processes to achieve high-quality image sampling.", + "bbox": [ + 75, + 449, + 467, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GAN-based image synthesis. GANs [17] have been one of the primary families of generative models for natural image synthesis. As the sampling quality and diversity of GANs improve [31-34, 36, 51, 60], GANs have been deployed to various computer vision and graphics applications, such as text-to-image synthesis [55], image-to-image translation [23, 27, 37, 47, 48, 82], and image editing [1, 6, 49, 81]. Notably, StyleGAN-family models [32, 34] have shown impressive ability in image synthesis tasks for single-category domains [1, 25, 49, 70, 84]. Other works have explored class-conditional GANs [5, 29, 62, 74, 79] on datasets with a fixed set of object categories.", + "bbox": [ + 75, + 719, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we change the data regimes from single- or multi-categories datasets to extremely data-rich situations. We make the first expedition toward training a largescale GAN for text-to-image generation on a vast amount of web-crawled text and image pairs, such as LAION2Ben [63] and COYO-700M [7]. Existing GAN-based text-to-image synthesis models [39,55,67,71,75,76,83] are trained on relatively small datasets, such as CUB-200 (12k training pairs), MSCOCO (82k) and LN-OpenImages (507k). Also, those models are evaluated on associated validation datasets, which have not been validated to perform largescale text-image synthesis like diffusion or AR models.", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Concurrent with our method, StyleGAN-T [61] and GALIP [66] share similar goals and make complementary insights to ours.", + "bbox": [ + 496, + 273, + 890, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 337, + 589, + 352 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We train a generator $G(\\mathbf{z}, \\mathbf{c})$ to predict an image $\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}$ given a latent code $\\mathbf{z} \\sim \\mathcal{N}(0,1) \\in \\mathbb{R}^{128}$ and text-condition $\\mathbf{c}$ . We use a discriminator $D(\\mathbf{x}, \\mathbf{c})$ to judge the realism of the fake image, as compared to a sample from the training database $\\mathcal{D}$ , which contains image-text pairs.", + "bbox": [ + 496, + 359, + 890, + 435 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Although GANs [5, 31, 33] can successfully generate realistic images on single- and multi-category datasets [11, 33, 72], open-ended text-conditioned synthesis on Internet images remains challenging. We hypothesize that the current limitation stems from its reliance on convolutional layers. That is, the same convolution filters are challenged to model the general image synthesis function for all text conditioning across all locations of the image. In this light, we seek to inject more expressivity into our parameterization by dynamically selecting convolution filters based on the input conditioning and by capturing long-range dependence via the attention mechanism.", + "bbox": [ + 496, + 436, + 890, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Below, we discuss our key contributions to making ConvNets more expressive (Section 3.1), followed by our designs for the generator (Section 3.2) and discriminator (Section 3.3). Lastly, we introduce a new, fast GAN-based upsampler model that can improve the inference quality and speed of our method and diffusion models such as ImageNet [59] and DALL-E 2 [53] (Section 3.4).", + "bbox": [ + 496, + 619, + 890, + 726 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Modeling complex contextual interaction", + "text_level": 1, + "bbox": [ + 500, + 739, + 849, + 756 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Baseline StyleGAN generator. We base our architecture off the conditional version of StyleGAN2 [34], comprised of two networks $G = \\widetilde{G} \\circ M$ . The mapping network $\\mathbf{w} = M(\\mathbf{z},\\mathbf{c})$ maps the inputs into a \"style\" vector $\\mathbf{w}$ , which modulates a series of upsampling convolutional layers in the synthesis network $\\widetilde{G}(\\mathbf{w})$ to map a learned constant tensor to an output image $\\mathbf{x}$ . Convolution is the main engine to generate all output pixels, with the $\\mathbf{w}$ vector as the only source of information to model conditioning.", + "bbox": [ + 496, + 768, + 890, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10126", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2c1271d378f86f7f7f06818d72bfdfacbadff20ad403a1917c65984f932802cf.jpg", + "image_caption": [ + "Figure 2. GigaGAN's text-to-image generator. First, we extract text embeddings using a pretrained CLIP model and a learned encoder $T$ . The local text descriptors are fed to the generator using cross-attention. The global text descriptor, along with a latent code $\\mathbf{z}$ , is fed to a mapping network $M$ to produce style code $\\mathbf{w}$ . The style code modulates the main generator using our style-adaptive kernel selection, shown on the right. The generator outputs an image pyramid by converting the intermediate features into RGB images. To achieve higher capacity, we use multiple attention and convolution layers at each scale. We also use a separate upsampler, that is not shown in this diagram." + ], + "image_footnote": [], + "bbox": [ + 101, + 84, + 869, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sample-adaptive kernel selection. To handle the highly diverse distribution of internet images, we aim to increase the capacity of convolution kernels. However, increasing the width of the convolution layers becomes too demanding, as the same operation is repeated across all locations.", + "bbox": [ + 75, + 383, + 468, + 459 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose an efficient way to enhance the expressivity of convolutional kernels by creating them on-the-fly based on the text conditioning, as illustrated in Figure 2 (right). In this scheme, we instantiate a bank of $N$ filters $\\{\\mathbf{K}_i\\in \\mathbb{R}^{C_{\\mathrm{in}}\\times C_{\\mathrm{out}}\\times K\\times K}\\}_{i = 1}^N$ , instead of one, that takes a feature $\\mathbf{f}\\in \\mathbb{R}^{C_{\\mathrm{in}}}$ at each layer. The style vector $\\mathbf{w}\\in \\mathbb{R}^d$ then goes through an affine layer $[W_{\\mathrm{filter}},b_{\\mathrm{filter}}]\\in \\mathbb{R}^{(d + 1)\\times N}$ to predict a set of weights to average across the filters, to produce an aggregated filter $\\mathbf{K}\\in \\mathbb{R}^{C_{\\mathrm{in}}\\times C_{\\mathrm{out}}\\times K\\times K}$ .", + "bbox": [ + 75, + 459, + 473, + 597 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {K} = \\sum_ {i = 1} ^ {N} \\mathbf {K} _ {i} \\cdot \\operatorname {s o f t m a x} \\left(W _ {\\text {f i l t e r}} ^ {\\top} \\mathbf {w} + b _ {\\text {f i l t e r}}\\right) _ {i} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 601, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The filter is then used in the regular convolution pipeline of StyleGAN2, with the second affine layer $[W_{\\mathrm{mod}}, b_{\\mathrm{mod}}] \\in \\mathbb{R}^{(d + 1) \\times C_{\\mathrm{in}}}$ for weight (de-)modulation [34].", + "bbox": [ + 76, + 647, + 468, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng _ {\\text {a d a c o n v}} (\\mathbf {f}, \\mathbf {w}) = \\left(\\left(W _ {\\mathrm {m o d}} ^ {\\top} \\mathbf {w} + b _ {\\mathrm {m o d}}\\right) \\otimes \\mathbf {K}\\right) * \\mathbf {f}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 698, + 468, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\otimes$ and $*$ represent (de-)modulation and convolution.", + "bbox": [ + 76, + 723, + 465, + 738 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "At a high level, the softmax-based weighting can be viewed as a differentiable filter selection process based on input conditioning. Furthermore, since the filter selection process is performed only once at each layer, the selection process is much faster than the actual convolution, decoupling compute complexity from the resolution. Our method shares a spirit with dynamic convolutions [19,28,65,69] in that the convolution filters dynamically change per sample, but differs in that we explicitly instantiate a larger filter bank and select weights based on a separate pathway conditional on the w-space of StyleGAN.", + "bbox": [ + 75, + 738, + 470, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Interleaving attention with convolution. Since the convolutional filter operates within its receptive field, it cannot contextualize itself in relationship to distant parts of the images. One way to incorporate such long-range relationships is using attention layers $g_{\\text{attention}}$ . While recent diffusion-based models [13,22,58] have commonly adopted attention mechanisms, StyleGAN architectures are predominantly convolutional with the notable exceptions such as BigGAN [5], GANformer [24], and ViTGAN [38].", + "bbox": [ + 496, + 383, + 890, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to improve the performance of StyleGAN by integrating attention layers with the convolutional backbone. However, simply adding attention layers to StyleGAN often results in training collapse, possibly because the dot-product self-attention is not Lipschitz, as pointed out by Kim et al. [35]. As the Lipschitz continuity of discriminators has played a critical role in stable training [2,18,43,44], we use the L2-distance instead of the dot product as the attention logits to promote Lipschitz continuity [35], similar to ViTGAN [38].", + "bbox": [ + 496, + 520, + 892, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To further improve performance, we find it crucial to match the architectural details of StyleGAN, such as equalized learning rate [31] and weight initialization from a unit normal distribution. We scale down the L2 distance logits to roughly match the unit normal distribution at initialization and reduce the residual gain from the attention layers. We further improve stability by tying the key and query matrix [38], and applying weight decay.", + "bbox": [ + 496, + 672, + 890, + 794 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the synthesis network $\\tilde{G}$ , the attention layers are interleaved with each convolutional block, leveraging the style vector $\\mathbf{w}$ as an additional token. At each attention block, we add a separate cross-attention mechanism $g_{\\mathrm{cross - attention}}$ to attend to individual word embeddings [3]. We use each input feature tensor as the query, and the text embeddings as the key and value of the attention mechanism.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10127", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Generator design", + "text_level": 1, + "bbox": [ + 76, + 90, + 246, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text and latent-code conditioning. First, we extract the text embedding from the prompt. Previous works [54, 59] have shown that leveraging a strong language model is essential for producing strong results. To do so, we tokenize the input prompt (after padding it to $C = 77$ words, following best practices [54, 59]) to produce conditioning vector $\\mathbf{c} \\in \\mathbb{R}^{C \\times 1024}$ , and take the features from the penultimate layer [59] of a frozen CLIP feature extractor [50]. To allow for additional flexibility, we apply additional attention layers $T$ on top to process the word embeddings before passing them to the MLP-based mapping network. This results in text embedding $\\mathbf{t} = T(\\mathcal{E}_{\\mathrm{txt}}(\\mathbf{c})) \\in \\mathbb{R}^{C \\times 1024}$ . Each component $\\mathbf{t}_i$ of $\\mathbf{t}$ captures the embedding of the $i^{\\text{th}}$ word in the sentence. We refer to them as $\\mathbf{t}_{\\text{local}} = \\mathbf{t}_{\\{1:C\\} \\backslash \\text{EOT}} \\in \\mathbb{R}^{(C - 1) \\times 1024}$ . The EOT (\"end of text\") component of $\\mathbf{t}$ aggregates global information, and is called $\\mathbf{t}_{\\text{global}} \\in \\mathbb{R}^{1024}$ . We process this global text descriptor, along with the latent code $\\mathbf{z} \\sim \\mathcal{N}(0,1)$ , via an MLP mapping network to extract the style $\\mathbf{w} = M(\\mathbf{z}, \\mathbf{t}_{\\text{global}})$ .", + "bbox": [ + 75, + 113, + 473, + 404 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left(\\mathbf {t} _ {\\text {l o c a l}}, \\mathbf {t} _ {\\text {g l o b a l}}\\right) = T \\left(\\mathcal {E} _ {\\mathrm {t x t}} (\\mathbf {c})\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 412, + 468, + 436 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {w} = M (\\mathbf {z}, \\mathbf {t} _ {\\text {g l o b a l}}).\n$$\n", + "text_format": "latex", + "bbox": [ + 217, + 431, + 344, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Different from the original StyleGAN, we use both the text-based style code $\\mathbf{w}$ to modulate the synthesis network $\\widetilde{G}$ and the word embeddings $\\mathbf{t}_{\\mathrm{local}}$ as features for cross-attention.", + "bbox": [ + 76, + 455, + 468, + 502 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} = \\widetilde {G} (\\mathbf {w}, \\mathbf {t} _ {\\text {l o c a l}}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 508, + 468, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to earlier works [42, 53, 59], the text-image alignment visually improves with cross-attention.", + "bbox": [ + 76, + 537, + 468, + 568 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Synthesis network. Our synthesis network consists of a series of upsampling convolutional layers, with each layer enhanced with the adaptive kernel selection (Equation 1) and followed by our attention layers.", + "bbox": [ + 76, + 578, + 468, + 640 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\ell + 1} = g _ {\\mathrm {x a}} ^ {\\ell} \\left(g _ {\\mathrm {a t t n}} ^ {\\ell} \\left(g _ {\\mathrm {a d a c o n v}} ^ {\\ell} \\left(\\mathbf {f} _ {\\ell}, \\mathbf {w}\\right), \\mathbf {w}\\right), \\mathbf {t} _ {\\mathrm {l o c a l}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 647, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g_{\\mathrm{xa}}^{\\ell}$ , $g_{\\mathrm{attn}}^{\\ell}$ , and $g_{\\mathrm{adaconv}}^{\\ell}$ denote the $l$ -th layer of cross-attention, self-attention, and weight (de-)modulation layers. We find it beneficial to increase the depth of the network by adding more blocks at each layer. In addition, our generator outputs a multi-scale image pyramid with $L = 5$ levels, instead of a single image at the highest resolution, similar to MSG-GAN [30] and AnycostGAN [40]. We refer to the pyramid as $\\{\\mathbf{x}_{ij}\\}_{i=0}^{L-1} = \\{\\mathbf{x}_0, \\mathbf{x}_1, \\dots, \\mathbf{x}_4\\}$ , with spatial resolutions $\\{S_i\\}_{i=0}^{L-1} = \\{64, 32, 16, 8, 4\\}$ , respectively. The base level $\\mathbf{x}_0$ is the output image $\\mathbf{x}$ . Each image of the pyramid is independently used to compute the GAN loss, as discussed in Section 3.3. We follow the findings of StyleGAN-XL [62] and turn off the style mixing and path length regularization [34]. We include more training details in our arXiv version.", + "bbox": [ + 75, + 672, + 472, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/388b036b2efa7dd2f28ae30795599cd1b41e4731902d4c7397a1fbf0494fa301.jpg", + "image_caption": [ + "Figure 3. Our discriminator consists of two branches for processing the image and the text conditioning $t_{D}$ . The text branch processes the text similar to the generator (Figure 2). The image branch receives an image pyramid and makes independent predictions for each image scale. Moreover, the predictions are made at all subsequent scales of the downsampling layers, making it a multi-scale input, multi-scale output (MS-I/O) discriminator." + ], + "image_footnote": [], + "bbox": [ + 504, + 92, + 883, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Discriminator design", + "text_level": 1, + "bbox": [ + 500, + 422, + 697, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Figure 3, our discriminator consists of separate branches for processing text with the function $\\mathbf{t}_D$ and images with function $\\phi$ . The prediction of real vs. fake is made by comparing the features from the two branches using function $\\psi$ . We introduce a new way of making predictions on multiple scales. Finally, we use additional CLIP and Vision-Aided GAN losses [36] to improve stability.", + "bbox": [ + 496, + 452, + 893, + 559 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Text conditioning. First, to incorporate conditioning into discriminators, we extract text descriptor $\\mathbf{t}_{\\mathrm{D}}$ from text c. Similar to the generator, we apply a pretrained text encoder, such as CLIP [50], followed by a few learnable attention layers. In this case, we only use the global descriptor.", + "bbox": [ + 496, + 571, + 893, + 647 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multiscale image processing. We observe that the early, low-resolution layers of the generator become inactive, using small dynamic ranges irrespective of the provided prompts. StyleGAN2 [34] also observes this phenomenon, concluding that the network relies on the high-resolution layers, as the model size increases. As recovering performance in low frequencies, which contains complex structure information, is crucial, we redesign the model architecture to provide training signals across multiple scales.", + "bbox": [ + 496, + 657, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recall the generator produces a pyramid $\\{\\mathbf{x}_i\\}_{i=0}^{L-1}$ , with the full image $\\mathbf{x}_0$ at the pyramid base. MSG-GAN [30] improves performance by making a prediction on the entire pyramid at once, enforcing consistency across scales. However, in our large-scale setting, this harms stability, as this limits the generator from making adjustments to its initial low-res output.", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10128", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instead, we process each level of the pyramid independently. As shown in Figure 3, each level $\\mathbf{x}_i$ makes a real/fake prediction at multiple scales $i < j \\leq L$ . For example, the full $\\mathbf{x}_0$ makes predictions at $L = 5$ scales, the next level $\\mathbf{x}_1$ makes predictions at 4 scales, and so on. In total, our discriminator produces $\\frac{L(L - 1)}{2}$ predictions, supervising multi-scale generations at multiple scales.", + "bbox": [ + 75, + 90, + 468, + 198 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To extract features at different scales, we define a feature extractor $\\phi_{i\\rightarrow j}:\\mathbb{R}^{X_i\\times X_i\\times 3}\\to \\mathbb{R}^{X_j^D\\times X_j^D\\times C_j}$ . Practically, each sub-network $\\phi_{i\\rightarrow j}$ is a subset of full $\\phi \\triangleq \\phi_{0\\rightarrow L}$ , with $i > 0$ indicating late entry and $j < L$ indicating early exit. Each layer in $\\phi$ consists of self-attention, followed by convolution with a stride 2. The final layer flattens the spatial extent into a $1\\times 1$ tensor, producing output resolutions at $\\{X_j^D\\} = \\{32,16,8,4,1\\}$ . This allows us to inject lower-resolution images on pyramid into intermediate layers [31]. As we use a shared feature extractor across different levels and most of the added predictions are made at low resolutions, the increased computation overhead is manageable.", + "bbox": [ + 75, + 198, + 470, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Multi-scale input, multi-scale output adversarial loss. In total, our training objective consists of discriminator losses, along with our proposed matching loss, to encourage the discriminator to take into account the conditioning:", + "bbox": [ + 76, + 392, + 468, + 454 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {\\mathrm {M S - I / O}} (G, D) = \\sum_ {i = 0} ^ {L - 1} \\sum_ {j = 1} ^ {L} \\mathcal {V} _ {\\mathrm {G A N}} \\left(G _ {i}, D _ {i j}\\right) + \\mathcal {V} _ {\\text {m a t c h}} \\left(G _ {i}, D _ {i j}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 462, + 478, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\nu_{\\mathrm{GAN}}$ is the standard, non-saturating GAN loss [17]. To compute the discriminator output, we train predictor $\\psi$ which uses text feature $\\mathbf{t}_{\\mathrm{D}}$ to modulate image features $\\phi (\\mathbf{x})$ :", + "bbox": [ + 76, + 527, + 468, + 574 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nD _ {i j} (\\mathbf {x}, \\mathbf {c}) = \\psi_ {j} \\left(\\phi_ {i \\rightarrow j} \\left(\\mathbf {x} _ {i}\\right), \\mathbf {t} _ {D}\\right) + \\operatorname {C o n v} _ {1 \\times 1} \\left(\\phi_ {i \\rightarrow j} \\left(\\mathbf {x} _ {i}\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 585, + 468, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\psi_{j}$ is implemented as a 4-layer $1\\times 1$ modulated convolution, and $\\mathrm{Conv}_{1\\times 1}$ is added as a skip connection to explicitly maintain an unconditional prediction branch [45].", + "bbox": [ + 76, + 625, + 468, + 671 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Matching-aware loss. The previous GAN terms measure how closely the image $\\mathbf{x}$ matches the conditioning $\\mathbf{c}$ , as well as how realistic $\\mathbf{x}$ looks, irrespective of conditioning. However, during early training, when artifacts are obvious, the discriminator tends to make a decision independent of conditioning and hesitates to account for the conditioning.", + "bbox": [ + 75, + 681, + 468, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To enforce the discriminator to incorporate conditioning, we match $\\mathbf{x}$ with a random, independently sampled condition $\\hat{\\mathbf{c}}$ , and present them as a fake pair:", + "bbox": [ + 75, + 772, + 468, + 818 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {V} _ {\\text {m a t c h}} = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\hat {\\mathbf {c}}} \\left[ \\log \\left(1 + \\exp (D (\\mathbf {x}, \\hat {\\mathbf {c}}))\\right) \\right. \\tag {8} \\\\ \\left. + \\log (1 + \\exp (D (G (\\mathbf {c}), \\hat {\\mathbf {c}})) \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 824, + 468, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $(\\mathbf{x},c)$ and $\\hat{\\mathbf{c}}$ are separately sampled from $p_{\\mathrm{data}}$ . This loss has previously been explored in text-to-image GAN", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "works [55, 76], except we find that enforcing the Matching-aware loss on generated images from $G$ , as well real images $\\mathbf{x}$ , leads to clear gains in performance (Table A2).", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CLIP contrastive loss. We further leverage off-the-shelf pretrained models as a loss function [36, 60, 64]. In particular, we enforce the generator to produce outputs that are identifiable by the pre-trained CLIP image and text encoders [50], $\\mathcal{E}_{\\mathrm{img}}$ and $\\mathcal{E}_{\\mathrm{txt}}$ , in the contrastive cross-entropy loss that was used to train them originally.", + "bbox": [ + 498, + 148, + 893, + 239 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C L I P}} = \\mathbb {E} _ {\\left\\{\\mathbf {c} _ {n} \\right\\}} \\left[ - \\log \\frac {\\exp \\left(\\mathcal {E} _ {\\mathrm {i m g}} \\left(G \\left(\\mathbf {c} _ {0}\\right)\\right) ^ {\\top} \\mathcal {E} _ {\\mathrm {t x t}} \\left(\\mathbf {c} _ {0}\\right)\\right)}{\\sum_ {n} \\exp \\left(\\mathcal {E} _ {\\mathrm {i m g}} \\left(G \\left(\\mathbf {c} _ {0}\\right)\\right) ^ {\\top} \\mathcal {E} _ {\\mathrm {t x t}} \\left(\\mathbf {c} _ {n}\\right)}\\right) \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 263, + 890, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\{\\mathbf{c}_n\\} = \\{\\mathbf{c}_0,\\dots \\}$ are sampled captions from the training data.", + "bbox": [ + 498, + 328, + 890, + 358 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Vision-Aided adversarial loss. Lastly, we build an additional discriminator that uses the CLIP model as a backbone, known as Vision-Aided GAN [36]. We freeze the CLIP image encoder, extract features from the intermediate layers, and process them through a simple network with $3 \\times 3$ conv layers to make real/fake predictions.", + "bbox": [ + 498, + 371, + 890, + 462 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also incorporate conditioning through modulation, as in Equation 7. To stabilize training, we also add a fixed random projection layer, as proposed by Projected GAN [60]. We refer to this as $\\mathcal{L}_{\\mathrm{Vision}}(G)$ (omitting the learnable discriminator parameters for clarity).", + "bbox": [ + 498, + 462, + 890, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our final objective is $\\mathcal{V}(G,D) = \\mathcal{V}_{\\mathrm{MS - I / O}}(G,D) + \\mathcal{L}_{\\mathrm{CLIP}}(G) + \\mathcal{L}_{\\mathrm{Vision}}(G)$ , with weighting between the terms specified in Table A1.", + "bbox": [ + 498, + 537, + 890, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. GAN-based upsampler", + "text_level": 1, + "bbox": [ + 500, + 593, + 712, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, GigaGAN framework can be easily extended to train a text-conditioned super-resolution model, capable of upsampling the outputs of the base GigaGAN generator to obtain high-resolution images at 512px or 4k resolution. By training our pipeline in two separate stages, we can afford a higher capacity 64px base model within the same computational resources.", + "bbox": [ + 496, + 613, + 890, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the upsampler, the synthesis network is rearranged to an asymmetric U-Net architecture, which processes the 64px input through 3 downsampling residual blocks, followed by 6 upsampling residual blocks with attention layers to produce the 512px image. There exist skip connections at the same resolution, similar to CoModGAN [78]. The model is trained with the same losses as the base model, as well as the LPIPS Perceptual Loss [77] with respect to the ground truth high-resolution image. Vision-Aided GAN is not used for the upsampler. During training and inference time, we apply moderate Gaussian noise augmentation to reduce the gap between real and GAN-generated images.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10129", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/142b37ab53abf3676139c42bacc8015b5c581ec0fd82ce0f6b6549f763f83a6e.jpg", + "image_caption": [ + "Figure 4. Prompt mixing. GigaGAN can directly control the style with text prompts. Here we generate three outputs using the prompts \"a X on tabletop\", shown in the \"no mixing\" column. Then we re-compute the text embeddings $\\mathbf{t}$ and the style codes $\\mathbf{w}$ using the new prompts \"a X with the texture of Y on tabletop\", such as \"a cube with the texture of crochet on tabletop\", and apply them to the second half layers of the generator, achieving layout-preserving fine style control. Cross-attention mechanism automatically localizes the style to the object of interest." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 460, + 311 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our GigaGAN framework becomes particularly effective for the super-resolution task compared to the diffusion-based models, which cannot afford as many sampling steps as the base model at high resolution. The LPIPS regression loss also provides a stable learning signal. We believe that our GAN upsampler can serve as a drop-in replacement for the super-resolution stage of other generative models.", + "bbox": [ + 75, + 454, + 468, + 560 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 575, + 209, + 590 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Systematic, controlled evaluation of large-scale text-to-image synthesis tasks is difficult, as most existing models are not publicly available. Training a new model from scratch would be prohibitively costly, even if the training code were available. Still, we compare our model to recent text-to-image models, such asImagen [59], Latent Diffusion Models (LDM) [58], Stable Diffusion [57], and Parti [73], based on the available information, while acknowledging considerable differences in the training dataset, number of iterations, batch size, and model size. In addition to text-to-image results, we evaluate our model on ImageNet class-conditional generation and unconditional super-resolution in our arXiv, for an apples-to-apples comparison with other methods at a more controlled setting.", + "bbox": [ + 75, + 598, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For quantitative evaluation, we mainly use the Fréchet Inception Distance (FID) [20] for measuring the realism of the output distribution and the CLIP score for evaluating the image-text alignment. All our models are trained and evaluated on A100 GPUs. For more information about training and evaluation of GigaGAN, please refer to the arXiv ver-", + "bbox": [ + 75, + 810, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26900169eb10564fa8bc186310832a5a6707fcb2ae17fda3049a792fff602c66.jpg", + "image_caption": [ + "Figure 5. Style mixing. Our GAN-based architecture retains a disentangled latent space, enabling us to blend the coarse style of one sample with the fine style of another. All outputs are generated with the prompt \"A Toy sport sedan, CG art.\" The corresponding latent codes are spliced together to produce a style-swapping grid." + ], + "image_footnote": [], + "bbox": [ + 506, + 89, + 887, + 309 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sion.", + "bbox": [ + 500, + 397, + 535, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1. Text-to-image synthesis", + "text_level": 1, + "bbox": [ + 500, + 422, + 718, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We proceed to train a larger model by increasing the capacity of the base generator and upsampler to 652.5M and 359.1M, respectively. This results in an unprecedented size of GAN model, with a total parameter count of 1.0B. Table 1 compares the performance of our end-to-end pipeline to various text-to-image generative models [4, 9, 46, 53, 54, 57-59, 73, 80]. Note that there exist differences in the training dataset, the pretrained text encoders, and even image resolutions. For example, GigaGAN initially synthesizes 512px images, which are resized to 256px before evaluation.", + "bbox": [ + 496, + 446, + 890, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 shows that GigaGAN exhibits a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73]. While our model can be optimized to better match the feature distribution of real images than existing models, the quality of the generated images is not necessarily better (see our arXiv for more samples). We acknowledge that this may represent a corner case of zero-shot FID on COCO2014 dataset and suggest that further research on a better evaluation metric is necessary to improve text-to-image models. Nonetheless, we emphasize that GigaGAN is the first GAN model capable of synthesizing promising images from arbitrary text prompts and exhibits competitive zero-shot FID with other text-to-image models.", + "bbox": [ + 496, + 612, + 892, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Super-resolution for large-scale image synthesis", + "text_level": 1, + "bbox": [ + 500, + 819, + 890, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We separately evaluate the performance of the GigaGAN upsampler in a text-conditional upsampling task. We combine the Stable Diffusion [57] 4x Upscaler and 2x Latent Upscaler to establish an 8x upscaling model (SD Upscaler).", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10130", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2237155ef50e75687ffd6de191beeb09ed1b1ed073367e117adfd0b527bd3cd0.jpg", + "table_caption": [ + "Table 1. Comparison to recent text-to-image models. Model size, total images seen during training, COCO FID-30k, and inference speed of text-image models. * denotes that the model has been evaluated by us. GigaGAN achieves a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73], while being much faster than competitive methods. GigaGAN and SDv1.5 require 4,783 and 6,250 A100 GPU days, and Imagen and Parti need approximately 4,755 and 320 TPUv4 days for training." + ], + "table_footnote": [], + "table_body": "
ModelType#Param.#ImagesFID-30k ↓Inf. time
256DALL-E [54]Diff12.0B1.54B27.50-
GLIDE [46]Diff5.0B5.94B12.2415.0s
LDM [58]Diff1.5B0.27B12.639.4s
DALL-E 2 [53]Diff5.5B5.63B10.39-
Imagen [59]Diff3.0B15.36B7.279.1s
eDiff-I [4]Diff9.1B11.47B6.9532.0s
Parti-750M [73]AR750M3.69B10.71-
Parti-3B [73]AR3.0B3.69B8.106.4s
Parti-20B [73]AR20.0B3.69B7.23-
LAFITE [80]GAN75M-26.940.02s
512SD-v1.5* [57]Diff0.9B3.16B9.622.9s
Muse-3B [9]AR3.0B0.51B7.881.3s
GigaGANGAN1.0B0.98B9.090.13s
", + "bbox": [ + 81, + 203, + 464, + 375 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/87576b286d7ebbbe2d83cb0647cc311c694bcf7f5fe5478ac6e59c10aa195866.jpg", + "table_caption": [ + "Table 2. Text-conditioned $128 \\rightarrow 1024$ super-resolution on random 10K LAION samples, compared against unconditional Real-ESRGAN [26] and Stable Diffusion Upscaler [57]. GigaGAN enjoys the fast speed of a GAN-based model while achieving better FID, patch-FID [8], CLIP score, and LPIPS [77]." + ], + "table_footnote": [], + "table_body": "
Model#Param.Inf. timeFID-10k ↓pFID ↓CLIP ↑LPIPS ↓
Real-ESRGAN [26]17M0.06s8.6022.80.3140.363
SD Upscaler [57]846M7.75s9.3941.30.3160.523
GigaGAN693M0.13s1.548.900.3220.274
", + "bbox": [ + 81, + 450, + 468, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also use the unconditional Real-ESRGAN [26] as another baseline. Table 2 measures the performance of the upsampler on random 10K images from the LAION dataset and shows that our GigaGAN upsampler significantly outperforms the other upsamplers in realism scores (FID and patch-FID [8]), text alignment (CLIP score) and closeness to the ground truth (LPIPS [77]).", + "bbox": [ + 75, + 508, + 467, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Controllable image synthesis", + "text_level": 1, + "bbox": [ + 76, + 625, + 333, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Figure 4, we show that the disentangled style manipulation can be controlled via text inputs. In detail, we can compute the text embedding $\\mathbf{t}$ and style code w using different prompts and apply them to different layers of the generator. This way, we gain not only the coarse and fine style disentanglement but also an intuitive prompt-based maneuver in the style space.", + "bbox": [ + 75, + 643, + 467, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "StyleGANs are known to possess a linear latent space useful for image manipulation, called the $\\mathcal{W}$ -space. Likewise, we perform coarse and fine-grained style swapping using style vectors $\\mathbf{w}$ . Similar to the $\\mathcal{W}$ -space of StyleGAN, Figure 5 illustrates that GigaGAN maintains a disentangled $\\mathcal{W}$ -space, suggesting existing latent manipulation techniques of StyleGAN can transfer to GigaGAN. Furthermore, our model possesses another latent space of text embedding $\\mathbf{t} = [\\mathbf{t}_{\\mathrm{local}}, \\mathbf{t}_{\\mathrm{global}}]$ prior to $\\mathcal{W}$ , and we explore its potential for image synthesis.", + "bbox": [ + 75, + 750, + 467, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7413441fd6bba24b74121d6224be8dc0a5a49da3ac026d7ed1fc086b4d745480.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 88, + 630, + 181 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8cca0355b05b74ec5cc64b364b981bafff0d0a3e7a1566f606f171f4b4c2eb54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 88, + 756, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5e05d970fb7214f52aa42de5931470719f09f638bdc029724793011273aec152.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 89, + 880, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25667b58756f0aaefdccc4dedf573b23811579a2b7dbec901058417c7a7aa25c.jpg", + "image_caption": [ + "Figure 6. Failure cases. Our outputs with the same prompts as DALL-E 2. Each column conditions on \"a teddy bear on a skateboard in Times Square\", \"a Vibrant portrait painting of Salvador Dali with a robotic half face\", and \"A close up of a handpalm with leaves growing from it\". Compared to production-grade models such as DALL-E 2, our model exhibits limitations in realism and compositionality. See our website for uncurated comparisons." + ], + "image_footnote": [], + "bbox": [ + 506, + 183, + 630, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f988f885ea684a3ed01a3d67b22e481e26c6e1a7a2b5faff8b5e4b5cd72e88b6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 185, + 754, + 279 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9eea9ffbf5062371ced9b689d543166340163b47e9806413f5ca9564cc3e6ba6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 758, + 185, + 880, + 279 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and Limitations", + "text_level": 1, + "bbox": [ + 498, + 383, + 751, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our experiments provide a conclusive answer about the scalability of GANs: our new architecture can scale up to model sizes that enable text-to-image synthesis. However, the visual quality of our results is not yet comparable to production-grade models like DALL-E 2. Figure 6 shows several instances where our method fails to produce high-quality results when compared to DALL-E 2, in terms of photorealism and text-to-image alignment for the same input prompts used in their paper.", + "bbox": [ + 496, + 404, + 890, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Nevertheless, we have tested capacities well beyond what is possible with a naïve approach and achieved competitive results with autoregressive and diffusion models trained with similar resources while being orders of magnitude faster and enabling latent interpolation and stylization. Our GigaGAN architecture opens up a whole new design space for large-scale generative models and brings back key editing capabilities that became challenging with the transition to autoregressive and diffusion models. We expect our performance to improve with larger models.", + "bbox": [ + 496, + 541, + 890, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. We thank Simon Niklaus, Alexandru Chiculita, and Markus Woodson for building the distributed training pipeline. We thank Nupur Kumari, Gaurav Parmar, Bill Peebles, Phillip Isola, Alyosha Efros, and Joonghyuk Shin for their helpful comments. We also want to thank Chenlin Meng, Chitwan Sahara, and Jiahui Yu for answering many questions about their fantastic work. We thank Kevin Duarte for discussions regarding upsampling beyond 4K. Part of this work was done while Minguk Kang was an intern at Adobe Research. Minguk Kang and Jaesik Park were supported by IITP grant funded by the government of South Korea (MSIT) (POSTECH GSAI: 2019-0-01906 and Image restoration: 2021-0-00537).", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10131", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In IEEE International Conference on Computer Vision (ICCV), 2019. 3", + "[2] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein Generative Adversarial Networks. In International Conference on Machine Learning (ICML), 2017. 4", + "[3] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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In The AAAI Conference on Artificial Intelligence, 2007. 3" + ], + "bbox": [ + 501, + 92, + 893, + 911 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "10134", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Scaling Up GANs for Text-to-Image Synthesis/cc6d67d2-1178-4cd7-a0a4-6ace5123194c_model.json b/2023/Scaling Up GANs for Text-to-Image Synthesis/cc6d67d2-1178-4cd7-a0a4-6ace5123194c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..af3bd94b048d56fd39626909b8ef4dc4d6e5ce72 --- /dev/null +++ b/2023/Scaling Up GANs for Text-to-Image Synthesis/cc6d67d2-1178-4cd7-a0a4-6ace5123194c_model.json @@ -0,0 +1,2653 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.255, + 0.131, + 0.717, + 0.154 + ], + "angle": 0, + "content": "Scaling up GANs for Text-to-Image Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.179, + 0.796, + 0.245 + ], + "angle": 0, + "content": "Minguk Kang\\(^{1,3}\\) Jun-Yan Zhu\\(^{2}\\) Richard Zhang\\(^{3}\\) \nJaesik Park\\(^{1}\\) Eli Shechtman\\(^{3}\\) Sylvain Paris\\(^{3}\\) Taesung Park\\(^{3}\\) \nPOSTECH \\(^{2}\\)Carnegie Mellon University \\(^{3}\\)Adobe Research" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.28, + 0.314, + 0.297 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.473, + 0.63 + ], + "angle": 0, + "content": "The recent success of text-to-image synthesis has taken the world by storm and captured the general public's imagination. From a technical standpoint, it also marked a drastic change in the favored architecture to design generative image models. GANs used to be the de facto choice, with techniques like StyleGAN. With DALL-E 2, autoregressive and diffusion models became the new standard for large-scale generative models overnight. This rapid shift raises a fundamental question: can we scale up GANs to benefit from large datasets like LAION? We find that naively increasing the capacity of the StyleGAN architecture quickly becomes unstable. We introduce GigaGAN, a new GAN architecture that far exceeds this limit, demonstrating GANs as a viable option for text-to-image synthesis. GigaGAN offers three major advantages. First, it is orders of magnitude faster at inference time, taking only 0.13 seconds to synthesize a 512px image. Second, it can synthesize high-resolution images, for example, 16-megapixel images in 3.66 seconds. Finally, GigaGAN supports various latent space editing applications such as latent interpolation, style mixing, and vector arithmetic operations." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.662, + 0.21, + 0.679 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.47, + 0.825 + ], + "angle": 0, + "content": "Recently released models, such as DALL-E 2 [53], Imagegen [59], Parti [73], and Stable Diffusion [58], have ushered in a new era of image generation, achieving unprecedented levels of image quality and model flexibility. The now-dominant paradigms, diffusion models and autoregressive models, both rely on iterative inference. This is a double-edged sword, as iterative methods enable stable training with simple objectives but incur a high computational cost during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Contrast this with Generative Adversarial Networks (GANs) [5,17,33,51], which generate images through a single forward pass and thus inherently efficient. While such models dominated the previous \"era\" of generative modeling, scaling them requires careful tuning of the network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.895, + 0.432 + ], + "angle": 0, + "content": "architectures and training considerations due to instabilities in the training procedure. As such, GANs have excelled at modeling single or multiple object classes, but scaling to complex datasets, much less an open world, has remained challenging. As a result, ultra-large models, data, and compute resources are now dedicated to diffusion and autoregressive models. In this work, we ask – can GANs continue to be scaled up and potentially benefit from such resources, or have they plateaued? What prevents them from further scaling, and can we overcome these barriers?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.432, + 0.895, + 0.599 + ], + "angle": 0, + "content": "We first experiment with StyleGAN2 [34] and observe that simply scaling the backbone causes unstable training. We identify several key issues and propose techniques to stabilize the training while increasing the model capacity. First, we effectively scale the generator's capacity by retaining a bank of filters and taking a sample-specific linear combination. We also adapt several techniques commonly used in the diffusion context and confirm that they bring similar benefits to GANs. For instance, interleaving both self-attention (image-only) and cross-attention (image-text) with the convolutional layers improves performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.895, + 0.735 + ], + "angle": 0, + "content": "Furthermore, we reintroduce multi-scale training, finding a new scheme that improves image-text alignment and low-frequency details of generated outputs. Multi-scale training allows the GAN-based generator to use parameters in low-resolution blocks more effectively, leading to better image-text alignment and image quality. After careful tuning, we achieve stable and scalable training of a one-billion-parameter GAN (GigaGAN) on large-scale datasets, such as LAION2B-en [63]. Our results are shown in Figure 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.856 + ], + "angle": 0, + "content": "In addition, our method uses a multi-stage approach [12, 76]. We first generate at \\(64 \\times 64\\) and then upsample to \\(512 \\times 512\\). These two networks are modular and robust enough to be used in a plug-and-play fashion. We show that our text-conditioned GAN-based upsampling network can be used as an efficient, higher-quality upsampler for a base diffusion model such as DALL-E 2, despite never having seen diffusion images at training time (Figures 1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Together, these advances enable our GigaGAN to go far beyond previous GANs: \\(36 \\times\\) larger than StyleGAN2 [34] and \\(6 \\times\\) larger than StyleGAN-XL [62] and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "10124" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.115, + 0.089, + 0.293, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.23, + 0.287, + 0.25 + ], + "angle": 0, + "content": "A portrait of a human growing colorful flowers from her hair. Hyperrealistic oil painting, Intricate details." + }, + { + "type": "image", + "bbox": [ + 0.301, + 0.089, + 0.48, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.305, + 0.229, + 0.452, + 0.245 + ], + "angle": 0, + "content": "a blue Porsche 356 parked in front of a yellow brick wall." + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.09, + 0.666, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.49, + 0.229, + 0.608, + 0.245 + ], + "angle": 0, + "content": "Eiffel Tower, landscape photography" + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.09, + 0.851, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.229, + 0.829, + 0.245 + ], + "angle": 0, + "content": "A painting of a majestic royal tall ship in Age of Discovery." + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.252, + 0.293, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.393, + 0.287, + 0.409 + ], + "angle": 0, + "content": "A golden luxury motorcycle parked at the King's palace, \\(35\\mathrm{mm}\\) f/4.5." + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.252, + 0.48, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.304, + 0.393, + 0.463, + 0.409 + ], + "angle": 0, + "content": "A hot air balloon in shape of a heart. Grand Canyon" + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.252, + 0.666, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.491, + 0.393, + 0.639, + 0.401 + ], + "angle": 0, + "content": "low poly bunny with cute eyes" + }, + { + "type": "image", + "bbox": [ + 0.672, + 0.252, + 0.851, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.393, + 0.84, + 0.408 + ], + "angle": 0, + "content": "A cube made of denim on a wooden table" + }, + { + "type": "image", + "bbox": [ + 0.114, + 0.413, + 0.48, + 0.696 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.117, + 0.698, + 0.258, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.698, + 0.407, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.411, + 0.698, + 0.553, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.558, + 0.698, + 0.702, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.698, + 0.851, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.811, + 0.86, + 0.894 + ], + "angle": 0, + "content": "Figure 1. Our model, GigaGAN, shows GAN frameworks can also be scaled up for general text-to-image synthesis and super-resolution tasks, generating a 512px output at an interactive speed of 0.13s, and 4096px within 3.7s. Selected examples at 2K resolution (text-to-image synthesis) and 1k or 4k resolutions (super-resolution) are shown. For the super-resolution task, we use the caption of \"Portrait of a colored iguana dressed in a hoodie.\" and compare our model with the text-conditioned upscaler of Stable Diffusion [57] and unconditional Real-ESRGAN [26]. Please zoom in for more details. See our arXiv paper and website for more uncurated comparisons." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10125" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.182 + ], + "angle": 0, + "content": "XMC-GAN [75]. While our 1B parameter count is still lower than the largest synthesis models, such as DALL-E 2 (5.5B), and Parti (20B), we have not yet observed a quality saturation regarding the model size. GigaGAN achieves a zero-shot FID of 9.09 on COCO2014, lower than the FID of DALL-E 2, Parti-750M, and Stable Diffusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.468, + 0.318 + ], + "angle": 0, + "content": "Furthermore, GigaGAN has three major practical advantages compared to diffusion and autoregressive models. First, it is orders of magnitude faster, generating a 512px image in 0.13 seconds. Second, it can synthesize ultra highres images at 4k resolution in 3.66 seconds. Third, it is endowed with a controllable, latent vector space that lends itself to well-studied controllable image synthesis applications, such as prompt mixing (Figure 4), style mixing (Figure 5), and prompt interpolation (Figures A7 and A8)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.468, + 0.408 + ], + "angle": 0, + "content": "In summary, our model is the first GAN-based method that successfully trains a billion-scale model on billions of real-world complex Internet images. This suggests that GANs are still a viable option for text-to-image synthesis and should be considered for future aggressive scaling. Please visit our website for additional results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.424, + 0.227, + 0.439 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.468, + 0.706 + ], + "angle": 0, + "content": "Text-to-image synthesis. Generating a realistic image given a text description, explored by early works [42, 85], is a challenging task. A common approach is text-conditional GANs [55, 56, 67, 71, 76, 83] on specific domains [68] and datasets with a closed-world assumption [41]. With the development of diffusion models [13, 21], autoregressive (AR) transformers [10], and large-scale language encoders [50, 52], text-to-image synthesis has shown remarkable improvement on an open-world of arbitrary text descriptions. GLIDE [46], DALL-E 2 [53], and Imagen [59] are representative diffusion models that show realistic outputs with the aid of a pretrained language encoder [50, 52]. AR models, such as DALL-E [54], Make-A-Scene [16], CogView [14, 15], and Parti [73] also achieve amazing results. While these models exhibit unprecedented image synthesis ability, they require time-consuming iterative processes to achieve high-quality image sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.901 + ], + "angle": 0, + "content": "GAN-based image synthesis. GANs [17] have been one of the primary families of generative models for natural image synthesis. As the sampling quality and diversity of GANs improve [31-34, 36, 51, 60], GANs have been deployed to various computer vision and graphics applications, such as text-to-image synthesis [55], image-to-image translation [23, 27, 37, 47, 48, 82], and image editing [1, 6, 49, 81]. Notably, StyleGAN-family models [32, 34] have shown impressive ability in image synthesis tasks for single-category domains [1, 25, 49, 70, 84]. Other works have explored class-conditional GANs [5, 29, 62, 74, 79] on datasets with a fixed set of object categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "In this paper, we change the data regimes from single- or multi-categories datasets to extremely data-rich situations. We make the first expedition toward training a largescale GAN for text-to-image generation on a vast amount of web-crawled text and image pairs, such as LAION2Ben [63] and COYO-700M [7]. Existing GAN-based text-to-image synthesis models [39,55,67,71,75,76,83] are trained on relatively small datasets, such as CUB-200 (12k training pairs), MSCOCO (82k) and LN-OpenImages (507k). Also, those models are evaluated on associated validation datasets, which have not been validated to perform largescale text-image synthesis like diffusion or AR models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.32 + ], + "angle": 0, + "content": "Concurrent with our method, StyleGAN-T [61] and GALIP [66] share similar goals and make complementary insights to ours." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.338, + 0.59, + 0.353 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.436 + ], + "angle": 0, + "content": "We train a generator \\( G(\\mathbf{z}, \\mathbf{c}) \\) to predict an image \\( \\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3} \\) given a latent code \\( \\mathbf{z} \\sim \\mathcal{N}(0,1) \\in \\mathbb{R}^{128} \\) and text-condition \\( \\mathbf{c} \\). We use a discriminator \\( D(\\mathbf{x}, \\mathbf{c}) \\) to judge the realism of the fake image, as compared to a sample from the training database \\( \\mathcal{D} \\), which contains image-text pairs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.892, + 0.619 + ], + "angle": 0, + "content": "Although GANs [5, 31, 33] can successfully generate realistic images on single- and multi-category datasets [11, 33, 72], open-ended text-conditioned synthesis on Internet images remains challenging. We hypothesize that the current limitation stems from its reliance on convolutional layers. That is, the same convolution filters are challenged to model the general image synthesis function for all text conditioning across all locations of the image. In this light, we seek to inject more expressivity into our parameterization by dynamically selecting convolution filters based on the input conditioning and by capturing long-range dependence via the attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.621, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Below, we discuss our key contributions to making ConvNets more expressive (Section 3.1), followed by our designs for the generator (Section 3.2) and discriminator (Section 3.3). Lastly, we introduce a new, fast GAN-based upsampler model that can improve the inference quality and speed of our method and diffusion models such as ImageNet [59] and DALL-E 2 [53] (Section 3.4)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.85, + 0.757 + ], + "angle": 0, + "content": "3.1. Modeling complex contextual interaction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.769, + 0.892, + 0.905 + ], + "angle": 0, + "content": "Baseline StyleGAN generator. We base our architecture off the conditional version of StyleGAN2 [34], comprised of two networks \\( G = \\widetilde{G} \\circ M \\). The mapping network \\( \\mathbf{w} = M(\\mathbf{z},\\mathbf{c}) \\) maps the inputs into a \"style\" vector \\( \\mathbf{w} \\), which modulates a series of upsampling convolutional layers in the synthesis network \\( \\widetilde{G}(\\mathbf{w}) \\) to map a learned constant tensor to an output image \\( \\mathbf{x} \\). Convolution is the main engine to generate all output pixels, with the \\( \\mathbf{w} \\) vector as the only source of information to model conditioning." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10126" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.085, + 0.87, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.296, + 0.895, + 0.366 + ], + "angle": 0, + "content": "Figure 2. GigaGAN's text-to-image generator. First, we extract text embeddings using a pretrained CLIP model and a learned encoder \\( T \\). The local text descriptors are fed to the generator using cross-attention. The global text descriptor, along with a latent code \\( \\mathbf{z} \\), is fed to a mapping network \\( M \\) to produce style code \\( \\mathbf{w} \\). The style code modulates the main generator using our style-adaptive kernel selection, shown on the right. The generator outputs an image pyramid by converting the intermediate features into RGB images. To achieve higher capacity, we use multiple attention and convolution layers at each scale. We also use a separate upsampler, that is not shown in this diagram." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.46 + ], + "angle": 0, + "content": "Sample-adaptive kernel selection. To handle the highly diverse distribution of internet images, we aim to increase the capacity of convolution kernels. However, increasing the width of the convolution layers becomes too demanding, as the same operation is repeated across all locations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.474, + 0.598 + ], + "angle": 0, + "content": "We propose an efficient way to enhance the expressivity of convolutional kernels by creating them on-the-fly based on the text conditioning, as illustrated in Figure 2 (right). In this scheme, we instantiate a bank of \\(N\\) filters \\(\\{\\mathbf{K}_i\\in \\mathbb{R}^{C_{\\mathrm{in}}\\times C_{\\mathrm{out}}\\times K\\times K}\\}_{i = 1}^N\\), instead of one, that takes a feature \\(\\mathbf{f}\\in \\mathbb{R}^{C_{\\mathrm{in}}}\\) at each layer. The style vector \\(\\mathbf{w}\\in \\mathbb{R}^d\\) then goes through an affine layer \\([W_{\\mathrm{filter}},b_{\\mathrm{filter}}]\\in \\mathbb{R}^{(d + 1)\\times N}\\) to predict a set of weights to average across the filters, to produce an aggregated filter \\(\\mathbf{K}\\in \\mathbb{R}^{C_{\\mathrm{in}}\\times C_{\\mathrm{out}}\\times K\\times K}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.136, + 0.602, + 0.47, + 0.645 + ], + "angle": 0, + "content": "\\[\n\\mathbf {K} = \\sum_ {i = 1} ^ {N} \\mathbf {K} _ {i} \\cdot \\operatorname {s o f t m a x} \\left(W _ {\\text {f i l t e r}} ^ {\\top} \\mathbf {w} + b _ {\\text {f i l t e r}}\\right) _ {i} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.47, + 0.695 + ], + "angle": 0, + "content": "The filter is then used in the regular convolution pipeline of StyleGAN2, with the second affine layer \\([W_{\\mathrm{mod}}, b_{\\mathrm{mod}}] \\in \\mathbb{R}^{(d + 1) \\times C_{\\mathrm{in}}} \\) for weight (de-)modulation [34]." + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.699, + 0.47, + 0.719 + ], + "angle": 0, + "content": "\\[\ng _ {\\text {a d a c o n v}} (\\mathbf {f}, \\mathbf {w}) = \\left(\\left(W _ {\\mathrm {m o d}} ^ {\\top} \\mathbf {w} + b _ {\\mathrm {m o d}}\\right) \\otimes \\mathbf {K}\\right) * \\mathbf {f}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.724, + 0.466, + 0.739 + ], + "angle": 0, + "content": "where \\(\\otimes\\) and \\(*\\) represent (de-)modulation and convolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.739, + 0.471, + 0.906 + ], + "angle": 0, + "content": "At a high level, the softmax-based weighting can be viewed as a differentiable filter selection process based on input conditioning. Furthermore, since the filter selection process is performed only once at each layer, the selection process is much faster than the actual convolution, decoupling compute complexity from the resolution. Our method shares a spirit with dynamic convolutions [19,28,65,69] in that the convolution filters dynamically change per sample, but differs in that we explicitly instantiate a larger filter bank and select weights based on a separate pathway conditional on the w-space of StyleGAN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Interleaving attention with convolution. Since the convolutional filter operates within its receptive field, it cannot contextualize itself in relationship to distant parts of the images. One way to incorporate such long-range relationships is using attention layers \\( g_{\\text{attention}} \\). While recent diffusion-based models [13,22,58] have commonly adopted attention mechanisms, StyleGAN architectures are predominantly convolutional with the notable exceptions such as BigGAN [5], GANformer [24], and ViTGAN [38]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.893, + 0.672 + ], + "angle": 0, + "content": "We aim to improve the performance of StyleGAN by integrating attention layers with the convolutional backbone. However, simply adding attention layers to StyleGAN often results in training collapse, possibly because the dot-product self-attention is not Lipschitz, as pointed out by Kim et al. [35]. As the Lipschitz continuity of discriminators has played a critical role in stable training [2,18,43,44], we use the L2-distance instead of the dot product as the attention logits to promote Lipschitz continuity [35], similar to ViTGAN [38]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.795 + ], + "angle": 0, + "content": "To further improve performance, we find it crucial to match the architectural details of StyleGAN, such as equalized learning rate [31] and weight initialization from a unit normal distribution. We scale down the L2 distance logits to roughly match the unit normal distribution at initialization and reduce the residual gain from the attention layers. We further improve stability by tying the key and query matrix [38], and applying weight decay." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the synthesis network \\(\\tilde{G}\\), the attention layers are interleaved with each convolutional block, leveraging the style vector \\(\\mathbf{w}\\) as an additional token. At each attention block, we add a separate cross-attention mechanism \\(g_{\\mathrm{cross - attention}}\\) to attend to individual word embeddings [3]. We use each input feature tensor as the query, and the text embeddings as the key and value of the attention mechanism." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10127" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.248, + 0.108 + ], + "angle": 0, + "content": "3.2. Generator design" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.474, + 0.405 + ], + "angle": 0, + "content": "Text and latent-code conditioning. First, we extract the text embedding from the prompt. Previous works [54, 59] have shown that leveraging a strong language model is essential for producing strong results. To do so, we tokenize the input prompt (after padding it to \\( C = 77 \\) words, following best practices [54, 59]) to produce conditioning vector \\( \\mathbf{c} \\in \\mathbb{R}^{C \\times 1024} \\), and take the features from the penultimate layer [59] of a frozen CLIP feature extractor [50]. To allow for additional flexibility, we apply additional attention layers \\( T \\) on top to process the word embeddings before passing them to the MLP-based mapping network. This results in text embedding \\( \\mathbf{t} = T(\\mathcal{E}_{\\mathrm{txt}}(\\mathbf{c})) \\in \\mathbb{R}^{C \\times 1024} \\). Each component \\( \\mathbf{t}_i \\) of \\( \\mathbf{t} \\) captures the embedding of the \\( i^{\\text{th}} \\) word in the sentence. We refer to them as \\( \\mathbf{t}_{\\text{local}} = \\mathbf{t}_{\\{1:C\\} \\backslash \\text{EOT}} \\in \\mathbb{R}^{(C - 1) \\times 1024} \\). The EOT (\"end of text\") component of \\( \\mathbf{t} \\) aggregates global information, and is called \\( \\mathbf{t}_{\\text{global}} \\in \\mathbb{R}^{1024} \\). We process this global text descriptor, along with the latent code \\( \\mathbf{z} \\sim \\mathcal{N}(0,1) \\), via an MLP mapping network to extract the style \\( \\mathbf{w} = M(\\mathbf{z}, \\mathbf{t}_{\\text{global}}) \\)." + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.413, + 0.47, + 0.438 + ], + "angle": 0, + "content": "\\[\n\\left(\\mathbf {t} _ {\\text {l o c a l}}, \\mathbf {t} _ {\\text {g l o b a l}}\\right) = T \\left(\\mathcal {E} _ {\\mathrm {t x t}} (\\mathbf {c})\\right), \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.218, + 0.433, + 0.345, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\mathbf {w} = M (\\mathbf {z}, \\mathbf {t} _ {\\text {g l o b a l}}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.457, + 0.47, + 0.503 + ], + "angle": 0, + "content": "Different from the original StyleGAN, we use both the text-based style code \\(\\mathbf{w}\\) to modulate the synthesis network \\(\\widetilde{G}\\) and the word embeddings \\(\\mathbf{t}_{\\mathrm{local}}\\) as features for cross-attention." + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.51, + 0.47, + 0.53 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} = \\widetilde {G} (\\mathbf {w}, \\mathbf {t} _ {\\text {l o c a l}}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.538, + 0.47, + 0.569 + ], + "angle": 0, + "content": "Similar to earlier works [42, 53, 59], the text-image alignment visually improves with cross-attention." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.579, + 0.47, + 0.641 + ], + "angle": 0, + "content": "Synthesis network. Our synthesis network consists of a series of upsampling convolutional layers, with each layer enhanced with the adaptive kernel selection (Equation 1) and followed by our attention layers." + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.648, + 0.47, + 0.668 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\ell + 1} = g _ {\\mathrm {x a}} ^ {\\ell} \\left(g _ {\\mathrm {a t t n}} ^ {\\ell} \\left(g _ {\\mathrm {a d a c o n v}} ^ {\\ell} \\left(\\mathbf {f} _ {\\ell}, \\mathbf {w}\\right), \\mathbf {w}\\right), \\mathbf {t} _ {\\mathrm {l o c a l}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.473, + 0.901 + ], + "angle": 0, + "content": "where \\( g_{\\mathrm{xa}}^{\\ell} \\), \\( g_{\\mathrm{attn}}^{\\ell} \\), and \\( g_{\\mathrm{adaconv}}^{\\ell} \\) denote the \\( l \\)-th layer of cross-attention, self-attention, and weight (de-)modulation layers. We find it beneficial to increase the depth of the network by adding more blocks at each layer. In addition, our generator outputs a multi-scale image pyramid with \\( L = 5 \\) levels, instead of a single image at the highest resolution, similar to MSG-GAN [30] and AnycostGAN [40]. We refer to the pyramid as \\( \\{\\mathbf{x}_{ij}\\}_{i=0}^{L-1} = \\{\\mathbf{x}_0, \\mathbf{x}_1, \\dots, \\mathbf{x}_4\\} \\), with spatial resolutions \\( \\{S_i\\}_{i=0}^{L-1} = \\{64, 32, 16, 8, 4\\} \\), respectively. The base level \\( \\mathbf{x}_0 \\) is the output image \\( \\mathbf{x} \\). Each image of the pyramid is independently used to compute the GAN loss, as discussed in Section 3.3. We follow the findings of StyleGAN-XL [62] and turn off the style mixing and path length regularization [34]. We include more training details in our arXiv version." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.093, + 0.885, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.313, + 0.895, + 0.412 + ], + "angle": 0, + "content": "Figure 3. Our discriminator consists of two branches for processing the image and the text conditioning \\( t_{D} \\). The text branch processes the text similar to the generator (Figure 2). The image branch receives an image pyramid and makes independent predictions for each image scale. Moreover, the predictions are made at all subsequent scales of the downsampling layers, making it a multi-scale input, multi-scale output (MS-I/O) discriminator." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.423, + 0.698, + 0.44 + ], + "angle": 0, + "content": "3.3. Discriminator design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.895, + 0.56 + ], + "angle": 0, + "content": "As shown in Figure 3, our discriminator consists of separate branches for processing text with the function \\(\\mathbf{t}_D\\) and images with function \\(\\phi\\). The prediction of real vs. fake is made by comparing the features from the two branches using function \\(\\psi\\). We introduce a new way of making predictions on multiple scales. Finally, we use additional CLIP and Vision-Aided GAN losses [36] to improve stability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.894, + 0.648 + ], + "angle": 0, + "content": "Text conditioning. First, to incorporate conditioning into discriminators, we extract text descriptor \\(\\mathbf{t}_{\\mathrm{D}}\\) from text c. Similar to the generator, we apply a pretrained text encoder, such as CLIP [50], followed by a few learnable attention layers. In this case, we only use the global descriptor." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Multiscale image processing. We observe that the early, low-resolution layers of the generator become inactive, using small dynamic ranges irrespective of the provided prompts. StyleGAN2 [34] also observes this phenomenon, concluding that the network relies on the high-resolution layers, as the model size increases. As recovering performance in low frequencies, which contains complex structure information, is crucial, we redesign the model architecture to provide training signals across multiple scales." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Recall the generator produces a pyramid \\(\\{\\mathbf{x}_i\\}_{i=0}^{L-1}\\), with the full image \\(\\mathbf{x}_0\\) at the pyramid base. MSG-GAN [30] improves performance by making a prediction on the entire pyramid at once, enforcing consistency across scales. However, in our large-scale setting, this harms stability, as this limits the generator from making adjustments to its initial low-res output." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10128" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.199 + ], + "angle": 0, + "content": "Instead, we process each level of the pyramid independently. As shown in Figure 3, each level \\(\\mathbf{x}_i\\) makes a real/fake prediction at multiple scales \\(i < j \\leq L\\). For example, the full \\(\\mathbf{x}_0\\) makes predictions at \\(L = 5\\) scales, the next level \\(\\mathbf{x}_1\\) makes predictions at 4 scales, and so on. In total, our discriminator produces \\(\\frac{L(L - 1)}{2}\\) predictions, supervising multi-scale generations at multiple scales." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.471, + 0.381 + ], + "angle": 0, + "content": "To extract features at different scales, we define a feature extractor \\(\\phi_{i\\rightarrow j}:\\mathbb{R}^{X_i\\times X_i\\times 3}\\to \\mathbb{R}^{X_j^D\\times X_j^D\\times C_j}\\). Practically, each sub-network \\(\\phi_{i\\rightarrow j}\\) is a subset of full \\(\\phi \\triangleq \\phi_{0\\rightarrow L}\\), with \\(i > 0\\) indicating late entry and \\(j < L\\) indicating early exit. Each layer in \\(\\phi\\) consists of self-attention, followed by convolution with a stride 2. The final layer flattens the spatial extent into a \\(1\\times 1\\) tensor, producing output resolutions at \\(\\{X_j^D\\} = \\{32,16,8,4,1\\}\\). This allows us to inject lower-resolution images on pyramid into intermediate layers [31]. As we use a shared feature extractor across different levels and most of the added predictions are made at low resolutions, the increased computation overhead is manageable." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.393, + 0.47, + 0.455 + ], + "angle": 0, + "content": "Multi-scale input, multi-scale output adversarial loss. In total, our training objective consists of discriminator losses, along with our proposed matching loss, to encourage the discriminator to take into account the conditioning:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.463, + 0.479, + 0.52 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {\\mathrm {M S - I / O}} (G, D) = \\sum_ {i = 0} ^ {L - 1} \\sum_ {j = 1} ^ {L} \\mathcal {V} _ {\\mathrm {G A N}} \\left(G _ {i}, D _ {i j}\\right) + \\mathcal {V} _ {\\text {m a t c h}} \\left(G _ {i}, D _ {i j}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.529, + 0.469, + 0.575 + ], + "angle": 0, + "content": "where \\(\\nu_{\\mathrm{GAN}}\\) is the standard, non-saturating GAN loss [17]. To compute the discriminator output, we train predictor \\(\\psi\\) which uses text feature \\(\\mathbf{t}_{\\mathrm{D}}\\) to modulate image features \\(\\phi (\\mathbf{x})\\):" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.587, + 0.469, + 0.617 + ], + "angle": 0, + "content": "\\[\nD _ {i j} (\\mathbf {x}, \\mathbf {c}) = \\psi_ {j} \\left(\\phi_ {i \\rightarrow j} \\left(\\mathbf {x} _ {i}\\right), \\mathbf {t} _ {D}\\right) + \\operatorname {C o n v} _ {1 \\times 1} \\left(\\phi_ {i \\rightarrow j} \\left(\\mathbf {x} _ {i}\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.626, + 0.469, + 0.672 + ], + "angle": 0, + "content": "where \\(\\psi_{j}\\) is implemented as a 4-layer \\(1\\times 1\\) modulated convolution, and \\(\\mathrm{Conv}_{1\\times 1}\\) is added as a skip connection to explicitly maintain an unconditional prediction branch [45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.469, + 0.772 + ], + "angle": 0, + "content": "Matching-aware loss. The previous GAN terms measure how closely the image \\(\\mathbf{x}\\) matches the conditioning \\(\\mathbf{c}\\), as well as how realistic \\(\\mathbf{x}\\) looks, irrespective of conditioning. However, during early training, when artifacts are obvious, the discriminator tends to make a decision independent of conditioning and hesitates to account for the conditioning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.773, + 0.469, + 0.819 + ], + "angle": 0, + "content": "To enforce the discriminator to incorporate conditioning, we match \\(\\mathbf{x}\\) with a random, independently sampled condition \\(\\hat{\\mathbf{c}}\\), and present them as a fake pair:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.825, + 0.47, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {V} _ {\\text {m a t c h}} = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\hat {\\mathbf {c}}} \\left[ \\log \\left(1 + \\exp (D (\\mathbf {x}, \\hat {\\mathbf {c}}))\\right) \\right. \\tag {8} \\\\ \\left. + \\log (1 + \\exp (D (G (\\mathbf {c}), \\hat {\\mathbf {c}})) \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\((\\mathbf{x},c)\\) and \\(\\hat{\\mathbf{c}}\\) are separately sampled from \\(p_{\\mathrm{data}}\\). This loss has previously been explored in text-to-image GAN" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "works [55, 76], except we find that enforcing the Matching-aware loss on generated images from \\( G \\), as well real images \\( \\mathbf{x} \\), leads to clear gains in performance (Table A2)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.15, + 0.894, + 0.241 + ], + "angle": 0, + "content": "CLIP contrastive loss. We further leverage off-the-shelf pretrained models as a loss function [36, 60, 64]. In particular, we enforce the generator to produce outputs that are identifiable by the pre-trained CLIP image and text encoders [50], \\(\\mathcal{E}_{\\mathrm{img}}\\) and \\(\\mathcal{E}_{\\mathrm{txt}}\\), in the contrastive cross-entropy loss that was used to train them originally." + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.264, + 0.892, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {C L I P}} = \\mathbb {E} _ {\\left\\{\\mathbf {c} _ {n} \\right\\}} \\left[ - \\log \\frac {\\exp \\left(\\mathcal {E} _ {\\mathrm {i m g}} \\left(G \\left(\\mathbf {c} _ {0}\\right)\\right) ^ {\\top} \\mathcal {E} _ {\\mathrm {t x t}} \\left(\\mathbf {c} _ {0}\\right)\\right)}{\\sum_ {n} \\exp \\left(\\mathcal {E} _ {\\mathrm {i m g}} \\left(G \\left(\\mathbf {c} _ {0}\\right)\\right) ^ {\\top} \\mathcal {E} _ {\\mathrm {t x t}} \\left(\\mathbf {c} _ {n}\\right)}\\right) \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.329, + 0.892, + 0.359 + ], + "angle": 0, + "content": "where \\(\\{\\mathbf{c}_n\\} = \\{\\mathbf{c}_0,\\dots \\}\\) are sampled captions from the training data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.372, + 0.892, + 0.463 + ], + "angle": 0, + "content": "Vision-Aided adversarial loss. Lastly, we build an additional discriminator that uses the CLIP model as a backbone, known as Vision-Aided GAN [36]. We freeze the CLIP image encoder, extract features from the intermediate layers, and process them through a simple network with \\( 3 \\times 3 \\) conv layers to make real/fake predictions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.463, + 0.892, + 0.538 + ], + "angle": 0, + "content": "We also incorporate conditioning through modulation, as in Equation 7. To stabilize training, we also add a fixed random projection layer, as proposed by Projected GAN [60]. We refer to this as \\(\\mathcal{L}_{\\mathrm{Vision}}(G)\\) (omitting the learnable discriminator parameters for clarity)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.539, + 0.892, + 0.584 + ], + "angle": 0, + "content": "Our final objective is \\(\\mathcal{V}(G,D) = \\mathcal{V}_{\\mathrm{MS - I / O}}(G,D) + \\mathcal{L}_{\\mathrm{CLIP}}(G) + \\mathcal{L}_{\\mathrm{Vision}}(G)\\), with weighting between the terms specified in Table A1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.594, + 0.714, + 0.611 + ], + "angle": 0, + "content": "3.4. GAN-based upsampler" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Furthermore, GigaGAN framework can be easily extended to train a text-conditioned super-resolution model, capable of upsampling the outputs of the base GigaGAN generator to obtain high-resolution images at 512px or 4k resolution. By training our pipeline in two separate stages, we can afford a higher capacity 64px base model within the same computational resources." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In the upsampler, the synthesis network is rearranged to an asymmetric U-Net architecture, which processes the 64px input through 3 downsampling residual blocks, followed by 6 upsampling residual blocks with attention layers to produce the 512px image. There exist skip connections at the same resolution, similar to CoModGAN [78]. The model is trained with the same losses as the base model, as well as the LPIPS Perceptual Loss [77] with respect to the ground truth high-resolution image. Vision-Aided GAN is not used for the upsampler. During training and inference time, we apply moderate Gaussian noise augmentation to reduce the gap between real and GAN-generated images." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10129" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.462, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.316, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Figure 4. Prompt mixing. GigaGAN can directly control the style with text prompts. Here we generate three outputs using the prompts \"a X on tabletop\", shown in the \"no mixing\" column. Then we re-compute the text embeddings \\( \\mathbf{t} \\) and the style codes \\( \\mathbf{w} \\) using the new prompts \"a X with the texture of Y on tabletop\", such as \"a cube with the texture of crochet on tabletop\", and apply them to the second half layers of the generator, achieving layout-preserving fine style control. Cross-attention mechanism automatically localizes the style to the object of interest." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.561 + ], + "angle": 0, + "content": "Our GigaGAN framework becomes particularly effective for the super-resolution task compared to the diffusion-based models, which cannot afford as many sampling steps as the base model at high resolution. The LPIPS regression loss also provides a stable learning signal. We believe that our GAN upsampler can serve as a drop-in replacement for the super-resolution stage of other generative models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.21, + 0.592 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Systematic, controlled evaluation of large-scale text-to-image synthesis tasks is difficult, as most existing models are not publicly available. Training a new model from scratch would be prohibitively costly, even if the training code were available. Still, we compare our model to recent text-to-image models, such asImagen [59], Latent Diffusion Models (LDM) [58], Stable Diffusion [57], and Parti [73], based on the available information, while acknowledging considerable differences in the training dataset, number of iterations, batch size, and model size. In addition to text-to-image results, we evaluate our model on ImageNet class-conditional generation and unconditional super-resolution in our arXiv, for an apples-to-apples comparison with other methods at a more controlled setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.903 + ], + "angle": 0, + "content": "For quantitative evaluation, we mainly use the Fréchet Inception Distance (FID) [20] for measuring the realism of the output distribution and the CLIP score for evaluating the image-text alignment. All our models are trained and evaluated on A100 GPUs. For more information about training and evaluation of GigaGAN, please refer to the arXiv ver-" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.09, + 0.888, + 0.31 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.313, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Figure 5. Style mixing. Our GAN-based architecture retains a disentangled latent space, enabling us to blend the coarse style of one sample with the fine style of another. All outputs are generated with the prompt \"A Toy sport sedan, CG art.\" The corresponding latent codes are spliced together to produce a style-swapping grid." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.398, + 0.536, + 0.41 + ], + "angle": 0, + "content": "sion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.423, + 0.719, + 0.439 + ], + "angle": 0, + "content": "4.1. Text-to-image synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.892, + 0.612 + ], + "angle": 0, + "content": "We proceed to train a larger model by increasing the capacity of the base generator and upsampler to 652.5M and 359.1M, respectively. This results in an unprecedented size of GAN model, with a total parameter count of 1.0B. Table 1 compares the performance of our end-to-end pipeline to various text-to-image generative models [4, 9, 46, 53, 54, 57-59, 73, 80]. Note that there exist differences in the training dataset, the pretrained text encoders, and even image resolutions. For example, GigaGAN initially synthesizes 512px images, which are resized to 256px before evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.893, + 0.81 + ], + "angle": 0, + "content": "Table 1 shows that GigaGAN exhibits a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73]. While our model can be optimized to better match the feature distribution of real images than existing models, the quality of the generated images is not necessarily better (see our arXiv for more samples). We acknowledge that this may represent a corner case of zero-shot FID on COCO2014 dataset and suggest that further research on a better evaluation metric is necessary to improve text-to-image models. Nonetheless, we emphasize that GigaGAN is the first GAN model capable of synthesizing promising images from arbitrary text prompts and exhibits competitive zero-shot FID with other text-to-image models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.82, + 0.892, + 0.837 + ], + "angle": 0, + "content": "4.2. Super-resolution for large-scale image synthesis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We separately evaluate the performance of the GigaGAN upsampler in a text-conditional upsampling task. We combine the Stable Diffusion [57] 4x Upscaler and 2x Latent Upscaler to establish an 8x upscaling model (SD Upscaler)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10130" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.201 + ], + "angle": 0, + "content": "Table 1. Comparison to recent text-to-image models. Model size, total images seen during training, COCO FID-30k, and inference speed of text-image models. * denotes that the model has been evaluated by us. GigaGAN achieves a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73], while being much faster than competitive methods. GigaGAN and SDv1.5 require 4,783 and 6,250 A100 GPU days, and Imagen and Parti need approximately 4,755 and 320 TPUv4 days for training." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.204, + 0.465, + 0.375 + ], + "angle": 0, + "content": "
ModelType#Param.#ImagesFID-30k ↓Inf. time
256DALL-E [54]Diff12.0B1.54B27.50-
GLIDE [46]Diff5.0B5.94B12.2415.0s
LDM [58]Diff1.5B0.27B12.639.4s
DALL-E 2 [53]Diff5.5B5.63B10.39-
Imagen [59]Diff3.0B15.36B7.279.1s
eDiff-I [4]Diff9.1B11.47B6.9532.0s
Parti-750M [73]AR750M3.69B10.71-
Parti-3B [73]AR3.0B3.69B8.106.4s
Parti-20B [73]AR20.0B3.69B7.23-
LAFITE [80]GAN75M-26.940.02s
512SD-v1.5* [57]Diff0.9B3.16B9.622.9s
Muse-3B [9]AR3.0B0.51B7.881.3s
GigaGANGAN1.0B0.98B9.090.13s
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.379, + 0.47, + 0.449 + ], + "angle": 0, + "content": "Table 2. Text-conditioned \\(128 \\rightarrow 1024\\) super-resolution on random 10K LAION samples, compared against unconditional Real-ESRGAN [26] and Stable Diffusion Upscaler [57]. GigaGAN enjoys the fast speed of a GAN-based model while achieving better FID, patch-FID [8], CLIP score, and LPIPS [77]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.452, + 0.47, + 0.507 + ], + "angle": 0, + "content": "
Model#Param.Inf. timeFID-10k ↓pFID ↓CLIP ↑LPIPS ↓
Real-ESRGAN [26]17M0.06s8.6022.80.3140.363
SD Upscaler [57]846M7.75s9.3941.30.3160.523
GigaGAN693M0.13s1.548.900.3220.274
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.51, + 0.468, + 0.616 + ], + "angle": 0, + "content": "We also use the unconditional Real-ESRGAN [26] as another baseline. Table 2 measures the performance of the upsampler on random 10K images from the LAION dataset and shows that our GigaGAN upsampler significantly outperforms the other upsamplers in realism scores (FID and patch-FID [8]), text alignment (CLIP score) and closeness to the ground truth (LPIPS [77])." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.626, + 0.334, + 0.642 + ], + "angle": 0, + "content": "4.3. Controllable image synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.468, + 0.751 + ], + "angle": 0, + "content": "In Figure 4, we show that the disentangled style manipulation can be controlled via text inputs. In detail, we can compute the text embedding \\(\\mathbf{t}\\) and style code w using different prompts and apply them to different layers of the generator. This way, we gain not only the coarse and fine style disentanglement but also an intuitive prompt-based maneuver in the style space." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.468, + 0.903 + ], + "angle": 0, + "content": "StyleGANs are known to possess a linear latent space useful for image manipulation, called the \\(\\mathcal{W}\\)-space. Likewise, we perform coarse and fine-grained style swapping using style vectors \\(\\mathbf{w}\\). Similar to the \\(\\mathcal{W}\\)-space of StyleGAN, Figure 5 illustrates that GigaGAN maintains a disentangled \\(\\mathcal{W}\\)-space, suggesting existing latent manipulation techniques of StyleGAN can transfer to GigaGAN. Furthermore, our model possesses another latent space of text embedding \\(\\mathbf{t} = [\\mathbf{t}_{\\mathrm{local}}, \\mathbf{t}_{\\mathrm{global}}]\\) prior to \\(\\mathcal{W}\\), and we explore its potential for image synthesis." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.632, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.089, + 0.757, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.09, + 0.882, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.184, + 0.632, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.186, + 0.756, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.759, + 0.186, + 0.882, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.38 + ], + "angle": 0, + "content": "Figure 6. Failure cases. Our outputs with the same prompts as DALL-E 2. Each column conditions on \"a teddy bear on a skateboard in Times Square\", \"a Vibrant portrait painting of Salvador Dali with a robotic half face\", and \"A close up of a handpalm with leaves growing from it\". Compared to production-grade models such as DALL-E 2, our model exhibits limitations in realism and compositionality. See our website for uncurated comparisons." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.384, + 0.752, + 0.399 + ], + "angle": 0, + "content": "5. Discussion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.892, + 0.541 + ], + "angle": 0, + "content": "Our experiments provide a conclusive answer about the scalability of GANs: our new architecture can scale up to model sizes that enable text-to-image synthesis. However, the visual quality of our results is not yet comparable to production-grade models like DALL-E 2. Figure 6 shows several instances where our method fails to produce high-quality results when compared to DALL-E 2, in terms of photorealism and text-to-image alignment for the same input prompts used in their paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.693 + ], + "angle": 0, + "content": "Nevertheless, we have tested capacities well beyond what is possible with a naïve approach and achieved competitive results with autoregressive and diffusion models trained with similar resources while being orders of magnitude faster and enabling latent interpolation and stylization. Our GigaGAN architecture opens up a whole new design space for large-scale generative models and brings back key editing capabilities that became challenging with the transition to autoregressive and diffusion models. We expect our performance to improve with larger models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. We thank Simon Niklaus, Alexandru Chiculita, and Markus Woodson for building the distributed training pipeline. We thank Nupur Kumari, Gaurav Parmar, Bill Peebles, Phillip Isola, Alyosha Efros, and Joonghyuk Shin for their helpful comments. We also want to thank Chenlin Meng, Chitwan Sahara, and Jiahui Yu for answering many questions about their fantastic work. We thank Kevin Duarte for discussions regarding upsampling beyond 4K. Part of this work was done while Minguk Kang was an intern at Adobe Research. Minguk Kang and Jaesik Park were supported by IITP grant funded by the government of South Korea (MSIT) (POSTECH GSAI: 2019-0-01906 and Image restoration: 2021-0-00537)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10131" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In IEEE International Conference on Computer Vision (ICCV), 2019. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.47, + 0.212 + ], + "angle": 0, + "content": "[2] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein Generative Adversarial Networks. 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From a technical standpoint, it also marked a drastic change in the favored architecture to design generative image models. GANs used to be the de facto choice, with techniques like StyleGAN. With DALL-E 2, autoregressive and diffusion models became the new standard for large-scale generative models overnight. This rapid shift raises a fundamental question: can we scale up GANs to benefit from large datasets like LAION? We find that naively increasing the capacity of the StyleGAN architecture quickly becomes unstable. We introduce GigaGAN, a new GAN architecture that far exceeds this limit, demonstrating GANs as a viable option for text-to-image synthesis. GigaGAN offers three major advantages. First, it is orders of magnitude faster at inference time, taking only 0.13 seconds to synthesize a 512px image. Second, it can synthesize high-resolution images, for example, 16-megapixel images in 3.66 seconds. Finally, GigaGAN supports various latent space editing applications such as latent interpolation, style mixing, and vector arithmetic operations. + +# 1. Introduction + +Recently released models, such as DALL-E 2 [53], Imagegen [59], Parti [73], and Stable Diffusion [58], have ushered in a new era of image generation, achieving unprecedented levels of image quality and model flexibility. The now-dominant paradigms, diffusion models and autoregressive models, both rely on iterative inference. This is a double-edged sword, as iterative methods enable stable training with simple objectives but incur a high computational cost during inference. + +Contrast this with Generative Adversarial Networks (GANs) [5,17,33,51], which generate images through a single forward pass and thus inherently efficient. While such models dominated the previous "era" of generative modeling, scaling them requires careful tuning of the network + +architectures and training considerations due to instabilities in the training procedure. As such, GANs have excelled at modeling single or multiple object classes, but scaling to complex datasets, much less an open world, has remained challenging. As a result, ultra-large models, data, and compute resources are now dedicated to diffusion and autoregressive models. In this work, we ask – can GANs continue to be scaled up and potentially benefit from such resources, or have they plateaued? What prevents them from further scaling, and can we overcome these barriers? + +We first experiment with StyleGAN2 [34] and observe that simply scaling the backbone causes unstable training. We identify several key issues and propose techniques to stabilize the training while increasing the model capacity. First, we effectively scale the generator's capacity by retaining a bank of filters and taking a sample-specific linear combination. We also adapt several techniques commonly used in the diffusion context and confirm that they bring similar benefits to GANs. For instance, interleaving both self-attention (image-only) and cross-attention (image-text) with the convolutional layers improves performance. + +Furthermore, we reintroduce multi-scale training, finding a new scheme that improves image-text alignment and low-frequency details of generated outputs. Multi-scale training allows the GAN-based generator to use parameters in low-resolution blocks more effectively, leading to better image-text alignment and image quality. After careful tuning, we achieve stable and scalable training of a one-billion-parameter GAN (GigaGAN) on large-scale datasets, such as LAION2B-en [63]. Our results are shown in Figure 1. + +In addition, our method uses a multi-stage approach [12, 76]. We first generate at $64 \times 64$ and then upsample to $512 \times 512$ . These two networks are modular and robust enough to be used in a plug-and-play fashion. We show that our text-conditioned GAN-based upsampling network can be used as an efficient, higher-quality upsampler for a base diffusion model such as DALL-E 2, despite never having seen diffusion images at training time (Figures 1). + +Together, these advances enable our GigaGAN to go far beyond previous GANs: $36 \times$ larger than StyleGAN2 [34] and $6 \times$ larger than StyleGAN-XL [62] and + +![](images/fead01978a2023133c7cb72256b00a1575a26f438c747774b63b9b8ad8fa004f.jpg) +A portrait of a human growing colorful flowers from her hair. Hyperrealistic oil painting, Intricate details. + +![](images/1e0f695aa112862f4fa70e7c30214077134c0add4d8119f44837938b81ca7611.jpg) +a blue Porsche 356 parked in front of a yellow brick wall. + +![](images/594c89109788e312175198364236e18ef659f9dbc3f5431e72672ef104b53a82.jpg) +Eiffel Tower, landscape photography + +![](images/05053ac8267312dad68d4a4ec309cd72e575ef6efbd35d4c77c4f45cfa0afb37.jpg) +A painting of a majestic royal tall ship in Age of Discovery. + +![](images/d64b7c88493f1e62b5a01c9cf51a30b97a8cd26964aafa42ac6d6460ac28e60b.jpg) +A golden luxury motorcycle parked at the King's palace, $35\mathrm{mm}$ f/4.5. + +![](images/ea838559270522a5d9554494526b08ff0f8d5857a4180ed5b0db2ea866e083f6.jpg) +A hot air balloon in shape of a heart. Grand Canyon + +![](images/06de6d62124748783647db2336726c10c922315e170b374492a27bc6bd99a969.jpg) +low poly bunny with cute eyes + +![](images/2bc20a9c4b58510e76eec2f663024c120522ebdf8d57fe902b835fc26384922a.jpg) +A cube made of denim on a wooden table + +![](images/8001a3cfd40e3c06d58f55e7fa6889010ef89ff357c2db1aabb9854df41adbe8.jpg) + +![](images/a0d1d106e4c84bb5644631ffed2026ee805d164239beb2e1875555c0a849a7ba.jpg) +Figure 1. Our model, GigaGAN, shows GAN frameworks can also be scaled up for general text-to-image synthesis and super-resolution tasks, generating a 512px output at an interactive speed of 0.13s, and 4096px within 3.7s. Selected examples at 2K resolution (text-to-image synthesis) and 1k or 4k resolutions (super-resolution) are shown. For the super-resolution task, we use the caption of "Portrait of a colored iguana dressed in a hoodie." and compare our model with the text-conditioned upscaler of Stable Diffusion [57] and unconditional Real-ESRGAN [26]. Please zoom in for more details. See our arXiv paper and website for more uncurated comparisons. + +![](images/09329577ed2cfae04388e3204685d54f171627055ed5a45e0fc2b29ac0322811.jpg) + +![](images/08fac562b2dc0b35ca124d277a682a6cce18eace8b1d011bd6b03872f4f92bed.jpg) + +![](images/62e27977dccc969ff1ac138f6f45738b59cec3474b3973933240f271bbd27ad3.jpg) + +![](images/208c346bfe79252cb6c05fbf1bc0bb0615ffabca270fe39cb9a2eeb29e747323.jpg) + +XMC-GAN [75]. While our 1B parameter count is still lower than the largest synthesis models, such as DALL-E 2 (5.5B), and Parti (20B), we have not yet observed a quality saturation regarding the model size. GigaGAN achieves a zero-shot FID of 9.09 on COCO2014, lower than the FID of DALL-E 2, Parti-750M, and Stable Diffusion. + +Furthermore, GigaGAN has three major practical advantages compared to diffusion and autoregressive models. First, it is orders of magnitude faster, generating a 512px image in 0.13 seconds. Second, it can synthesize ultra highres images at 4k resolution in 3.66 seconds. Third, it is endowed with a controllable, latent vector space that lends itself to well-studied controllable image synthesis applications, such as prompt mixing (Figure 4), style mixing (Figure 5), and prompt interpolation (Figures A7 and A8). + +In summary, our model is the first GAN-based method that successfully trains a billion-scale model on billions of real-world complex Internet images. This suggests that GANs are still a viable option for text-to-image synthesis and should be considered for future aggressive scaling. Please visit our website for additional results. + +# 2. Related Works + +Text-to-image synthesis. Generating a realistic image given a text description, explored by early works [42, 85], is a challenging task. A common approach is text-conditional GANs [55, 56, 67, 71, 76, 83] on specific domains [68] and datasets with a closed-world assumption [41]. With the development of diffusion models [13, 21], autoregressive (AR) transformers [10], and large-scale language encoders [50, 52], text-to-image synthesis has shown remarkable improvement on an open-world of arbitrary text descriptions. GLIDE [46], DALL-E 2 [53], and Imagen [59] are representative diffusion models that show realistic outputs with the aid of a pretrained language encoder [50, 52]. AR models, such as DALL-E [54], Make-A-Scene [16], CogView [14, 15], and Parti [73] also achieve amazing results. While these models exhibit unprecedented image synthesis ability, they require time-consuming iterative processes to achieve high-quality image sampling. + +GAN-based image synthesis. GANs [17] have been one of the primary families of generative models for natural image synthesis. As the sampling quality and diversity of GANs improve [31-34, 36, 51, 60], GANs have been deployed to various computer vision and graphics applications, such as text-to-image synthesis [55], image-to-image translation [23, 27, 37, 47, 48, 82], and image editing [1, 6, 49, 81]. Notably, StyleGAN-family models [32, 34] have shown impressive ability in image synthesis tasks for single-category domains [1, 25, 49, 70, 84]. Other works have explored class-conditional GANs [5, 29, 62, 74, 79] on datasets with a fixed set of object categories. + +In this paper, we change the data regimes from single- or multi-categories datasets to extremely data-rich situations. We make the first expedition toward training a largescale GAN for text-to-image generation on a vast amount of web-crawled text and image pairs, such as LAION2Ben [63] and COYO-700M [7]. Existing GAN-based text-to-image synthesis models [39,55,67,71,75,76,83] are trained on relatively small datasets, such as CUB-200 (12k training pairs), MSCOCO (82k) and LN-OpenImages (507k). Also, those models are evaluated on associated validation datasets, which have not been validated to perform largescale text-image synthesis like diffusion or AR models. + +Concurrent with our method, StyleGAN-T [61] and GALIP [66] share similar goals and make complementary insights to ours. + +# 3. Method + +We train a generator $G(\mathbf{z}, \mathbf{c})$ to predict an image $\mathbf{x} \in \mathbb{R}^{H \times W \times 3}$ given a latent code $\mathbf{z} \sim \mathcal{N}(0,1) \in \mathbb{R}^{128}$ and text-condition $\mathbf{c}$ . We use a discriminator $D(\mathbf{x}, \mathbf{c})$ to judge the realism of the fake image, as compared to a sample from the training database $\mathcal{D}$ , which contains image-text pairs. + +Although GANs [5, 31, 33] can successfully generate realistic images on single- and multi-category datasets [11, 33, 72], open-ended text-conditioned synthesis on Internet images remains challenging. We hypothesize that the current limitation stems from its reliance on convolutional layers. That is, the same convolution filters are challenged to model the general image synthesis function for all text conditioning across all locations of the image. In this light, we seek to inject more expressivity into our parameterization by dynamically selecting convolution filters based on the input conditioning and by capturing long-range dependence via the attention mechanism. + +Below, we discuss our key contributions to making ConvNets more expressive (Section 3.1), followed by our designs for the generator (Section 3.2) and discriminator (Section 3.3). Lastly, we introduce a new, fast GAN-based upsampler model that can improve the inference quality and speed of our method and diffusion models such as ImageNet [59] and DALL-E 2 [53] (Section 3.4). + +# 3.1. Modeling complex contextual interaction + +Baseline StyleGAN generator. We base our architecture off the conditional version of StyleGAN2 [34], comprised of two networks $G = \widetilde{G} \circ M$ . The mapping network $\mathbf{w} = M(\mathbf{z},\mathbf{c})$ maps the inputs into a "style" vector $\mathbf{w}$ , which modulates a series of upsampling convolutional layers in the synthesis network $\widetilde{G}(\mathbf{w})$ to map a learned constant tensor to an output image $\mathbf{x}$ . Convolution is the main engine to generate all output pixels, with the $\mathbf{w}$ vector as the only source of information to model conditioning. + +![](images/2c1271d378f86f7f7f06818d72bfdfacbadff20ad403a1917c65984f932802cf.jpg) +Figure 2. GigaGAN's text-to-image generator. First, we extract text embeddings using a pretrained CLIP model and a learned encoder $T$ . The local text descriptors are fed to the generator using cross-attention. The global text descriptor, along with a latent code $\mathbf{z}$ , is fed to a mapping network $M$ to produce style code $\mathbf{w}$ . The style code modulates the main generator using our style-adaptive kernel selection, shown on the right. The generator outputs an image pyramid by converting the intermediate features into RGB images. To achieve higher capacity, we use multiple attention and convolution layers at each scale. We also use a separate upsampler, that is not shown in this diagram. + +Sample-adaptive kernel selection. To handle the highly diverse distribution of internet images, we aim to increase the capacity of convolution kernels. However, increasing the width of the convolution layers becomes too demanding, as the same operation is repeated across all locations. + +We propose an efficient way to enhance the expressivity of convolutional kernels by creating them on-the-fly based on the text conditioning, as illustrated in Figure 2 (right). In this scheme, we instantiate a bank of $N$ filters $\{\mathbf{K}_i\in \mathbb{R}^{C_{\mathrm{in}}\times C_{\mathrm{out}}\times K\times K}\}_{i = 1}^N$ , instead of one, that takes a feature $\mathbf{f}\in \mathbb{R}^{C_{\mathrm{in}}}$ at each layer. The style vector $\mathbf{w}\in \mathbb{R}^d$ then goes through an affine layer $[W_{\mathrm{filter}},b_{\mathrm{filter}}]\in \mathbb{R}^{(d + 1)\times N}$ to predict a set of weights to average across the filters, to produce an aggregated filter $\mathbf{K}\in \mathbb{R}^{C_{\mathrm{in}}\times C_{\mathrm{out}}\times K\times K}$ . + +$$ +\mathbf {K} = \sum_ {i = 1} ^ {N} \mathbf {K} _ {i} \cdot \operatorname {s o f t m a x} \left(W _ {\text {f i l t e r}} ^ {\top} \mathbf {w} + b _ {\text {f i l t e r}}\right) _ {i} \tag {1} +$$ + +The filter is then used in the regular convolution pipeline of StyleGAN2, with the second affine layer $[W_{\mathrm{mod}}, b_{\mathrm{mod}}] \in \mathbb{R}^{(d + 1) \times C_{\mathrm{in}}}$ for weight (de-)modulation [34]. + +$$ +g _ {\text {a d a c o n v}} (\mathbf {f}, \mathbf {w}) = \left(\left(W _ {\mathrm {m o d}} ^ {\top} \mathbf {w} + b _ {\mathrm {m o d}}\right) \otimes \mathbf {K}\right) * \mathbf {f}, \tag {2} +$$ + +where $\otimes$ and $*$ represent (de-)modulation and convolution. + +At a high level, the softmax-based weighting can be viewed as a differentiable filter selection process based on input conditioning. Furthermore, since the filter selection process is performed only once at each layer, the selection process is much faster than the actual convolution, decoupling compute complexity from the resolution. Our method shares a spirit with dynamic convolutions [19,28,65,69] in that the convolution filters dynamically change per sample, but differs in that we explicitly instantiate a larger filter bank and select weights based on a separate pathway conditional on the w-space of StyleGAN. + +Interleaving attention with convolution. Since the convolutional filter operates within its receptive field, it cannot contextualize itself in relationship to distant parts of the images. One way to incorporate such long-range relationships is using attention layers $g_{\text{attention}}$ . While recent diffusion-based models [13,22,58] have commonly adopted attention mechanisms, StyleGAN architectures are predominantly convolutional with the notable exceptions such as BigGAN [5], GANformer [24], and ViTGAN [38]. + +We aim to improve the performance of StyleGAN by integrating attention layers with the convolutional backbone. However, simply adding attention layers to StyleGAN often results in training collapse, possibly because the dot-product self-attention is not Lipschitz, as pointed out by Kim et al. [35]. As the Lipschitz continuity of discriminators has played a critical role in stable training [2,18,43,44], we use the L2-distance instead of the dot product as the attention logits to promote Lipschitz continuity [35], similar to ViTGAN [38]. + +To further improve performance, we find it crucial to match the architectural details of StyleGAN, such as equalized learning rate [31] and weight initialization from a unit normal distribution. We scale down the L2 distance logits to roughly match the unit normal distribution at initialization and reduce the residual gain from the attention layers. We further improve stability by tying the key and query matrix [38], and applying weight decay. + +In the synthesis network $\tilde{G}$ , the attention layers are interleaved with each convolutional block, leveraging the style vector $\mathbf{w}$ as an additional token. At each attention block, we add a separate cross-attention mechanism $g_{\mathrm{cross - attention}}$ to attend to individual word embeddings [3]. We use each input feature tensor as the query, and the text embeddings as the key and value of the attention mechanism. + +# 3.2. Generator design + +Text and latent-code conditioning. First, we extract the text embedding from the prompt. Previous works [54, 59] have shown that leveraging a strong language model is essential for producing strong results. To do so, we tokenize the input prompt (after padding it to $C = 77$ words, following best practices [54, 59]) to produce conditioning vector $\mathbf{c} \in \mathbb{R}^{C \times 1024}$ , and take the features from the penultimate layer [59] of a frozen CLIP feature extractor [50]. To allow for additional flexibility, we apply additional attention layers $T$ on top to process the word embeddings before passing them to the MLP-based mapping network. This results in text embedding $\mathbf{t} = T(\mathcal{E}_{\mathrm{txt}}(\mathbf{c})) \in \mathbb{R}^{C \times 1024}$ . Each component $\mathbf{t}_i$ of $\mathbf{t}$ captures the embedding of the $i^{\text{th}}$ word in the sentence. We refer to them as $\mathbf{t}_{\text{local}} = \mathbf{t}_{\{1:C\} \backslash \text{EOT}} \in \mathbb{R}^{(C - 1) \times 1024}$ . The EOT ("end of text") component of $\mathbf{t}$ aggregates global information, and is called $\mathbf{t}_{\text{global}} \in \mathbb{R}^{1024}$ . We process this global text descriptor, along with the latent code $\mathbf{z} \sim \mathcal{N}(0,1)$ , via an MLP mapping network to extract the style $\mathbf{w} = M(\mathbf{z}, \mathbf{t}_{\text{global}})$ . + +$$ +\left(\mathbf {t} _ {\text {l o c a l}}, \mathbf {t} _ {\text {g l o b a l}}\right) = T \left(\mathcal {E} _ {\mathrm {t x t}} (\mathbf {c})\right), \tag {3} +$$ + +$$ +\mathbf {w} = M (\mathbf {z}, \mathbf {t} _ {\text {g l o b a l}}). +$$ + +Different from the original StyleGAN, we use both the text-based style code $\mathbf{w}$ to modulate the synthesis network $\widetilde{G}$ and the word embeddings $\mathbf{t}_{\mathrm{local}}$ as features for cross-attention. + +$$ +\mathbf {x} = \widetilde {G} (\mathbf {w}, \mathbf {t} _ {\text {l o c a l}}). \tag {4} +$$ + +Similar to earlier works [42, 53, 59], the text-image alignment visually improves with cross-attention. + +Synthesis network. Our synthesis network consists of a series of upsampling convolutional layers, with each layer enhanced with the adaptive kernel selection (Equation 1) and followed by our attention layers. + +$$ +\mathbf {f} _ {\ell + 1} = g _ {\mathrm {x a}} ^ {\ell} \left(g _ {\mathrm {a t t n}} ^ {\ell} \left(g _ {\mathrm {a d a c o n v}} ^ {\ell} \left(\mathbf {f} _ {\ell}, \mathbf {w}\right), \mathbf {w}\right), \mathbf {t} _ {\mathrm {l o c a l}}\right), \tag {5} +$$ + +where $g_{\mathrm{xa}}^{\ell}$ , $g_{\mathrm{attn}}^{\ell}$ , and $g_{\mathrm{adaconv}}^{\ell}$ denote the $l$ -th layer of cross-attention, self-attention, and weight (de-)modulation layers. We find it beneficial to increase the depth of the network by adding more blocks at each layer. In addition, our generator outputs a multi-scale image pyramid with $L = 5$ levels, instead of a single image at the highest resolution, similar to MSG-GAN [30] and AnycostGAN [40]. We refer to the pyramid as $\{\mathbf{x}_{ij}\}_{i=0}^{L-1} = \{\mathbf{x}_0, \mathbf{x}_1, \dots, \mathbf{x}_4\}$ , with spatial resolutions $\{S_i\}_{i=0}^{L-1} = \{64, 32, 16, 8, 4\}$ , respectively. The base level $\mathbf{x}_0$ is the output image $\mathbf{x}$ . Each image of the pyramid is independently used to compute the GAN loss, as discussed in Section 3.3. We follow the findings of StyleGAN-XL [62] and turn off the style mixing and path length regularization [34]. We include more training details in our arXiv version. + +![](images/388b036b2efa7dd2f28ae30795599cd1b41e4731902d4c7397a1fbf0494fa301.jpg) +Figure 3. Our discriminator consists of two branches for processing the image and the text conditioning $t_{D}$ . The text branch processes the text similar to the generator (Figure 2). The image branch receives an image pyramid and makes independent predictions for each image scale. Moreover, the predictions are made at all subsequent scales of the downsampling layers, making it a multi-scale input, multi-scale output (MS-I/O) discriminator. + +# 3.3. Discriminator design + +As shown in Figure 3, our discriminator consists of separate branches for processing text with the function $\mathbf{t}_D$ and images with function $\phi$ . The prediction of real vs. fake is made by comparing the features from the two branches using function $\psi$ . We introduce a new way of making predictions on multiple scales. Finally, we use additional CLIP and Vision-Aided GAN losses [36] to improve stability. + +Text conditioning. First, to incorporate conditioning into discriminators, we extract text descriptor $\mathbf{t}_{\mathrm{D}}$ from text c. Similar to the generator, we apply a pretrained text encoder, such as CLIP [50], followed by a few learnable attention layers. In this case, we only use the global descriptor. + +Multiscale image processing. We observe that the early, low-resolution layers of the generator become inactive, using small dynamic ranges irrespective of the provided prompts. StyleGAN2 [34] also observes this phenomenon, concluding that the network relies on the high-resolution layers, as the model size increases. As recovering performance in low frequencies, which contains complex structure information, is crucial, we redesign the model architecture to provide training signals across multiple scales. + +Recall the generator produces a pyramid $\{\mathbf{x}_i\}_{i=0}^{L-1}$ , with the full image $\mathbf{x}_0$ at the pyramid base. MSG-GAN [30] improves performance by making a prediction on the entire pyramid at once, enforcing consistency across scales. However, in our large-scale setting, this harms stability, as this limits the generator from making adjustments to its initial low-res output. + +Instead, we process each level of the pyramid independently. As shown in Figure 3, each level $\mathbf{x}_i$ makes a real/fake prediction at multiple scales $i < j \leq L$ . For example, the full $\mathbf{x}_0$ makes predictions at $L = 5$ scales, the next level $\mathbf{x}_1$ makes predictions at 4 scales, and so on. In total, our discriminator produces $\frac{L(L - 1)}{2}$ predictions, supervising multi-scale generations at multiple scales. + +To extract features at different scales, we define a feature extractor $\phi_{i\rightarrow j}:\mathbb{R}^{X_i\times X_i\times 3}\to \mathbb{R}^{X_j^D\times X_j^D\times C_j}$ . Practically, each sub-network $\phi_{i\rightarrow j}$ is a subset of full $\phi \triangleq \phi_{0\rightarrow L}$ , with $i > 0$ indicating late entry and $j < L$ indicating early exit. Each layer in $\phi$ consists of self-attention, followed by convolution with a stride 2. The final layer flattens the spatial extent into a $1\times 1$ tensor, producing output resolutions at $\{X_j^D\} = \{32,16,8,4,1\}$ . This allows us to inject lower-resolution images on pyramid into intermediate layers [31]. As we use a shared feature extractor across different levels and most of the added predictions are made at low resolutions, the increased computation overhead is manageable. + +Multi-scale input, multi-scale output adversarial loss. In total, our training objective consists of discriminator losses, along with our proposed matching loss, to encourage the discriminator to take into account the conditioning: + +$$ +\mathcal {V} _ {\mathrm {M S - I / O}} (G, D) = \sum_ {i = 0} ^ {L - 1} \sum_ {j = 1} ^ {L} \mathcal {V} _ {\mathrm {G A N}} \left(G _ {i}, D _ {i j}\right) + \mathcal {V} _ {\text {m a t c h}} \left(G _ {i}, D _ {i j}\right), \tag {6} +$$ + +where $\nu_{\mathrm{GAN}}$ is the standard, non-saturating GAN loss [17]. To compute the discriminator output, we train predictor $\psi$ which uses text feature $\mathbf{t}_{\mathrm{D}}$ to modulate image features $\phi (\mathbf{x})$ : + +$$ +D _ {i j} (\mathbf {x}, \mathbf {c}) = \psi_ {j} \left(\phi_ {i \rightarrow j} \left(\mathbf {x} _ {i}\right), \mathbf {t} _ {D}\right) + \operatorname {C o n v} _ {1 \times 1} \left(\phi_ {i \rightarrow j} \left(\mathbf {x} _ {i}\right)\right), \tag {7} +$$ + +where $\psi_{j}$ is implemented as a 4-layer $1\times 1$ modulated convolution, and $\mathrm{Conv}_{1\times 1}$ is added as a skip connection to explicitly maintain an unconditional prediction branch [45]. + +Matching-aware loss. The previous GAN terms measure how closely the image $\mathbf{x}$ matches the conditioning $\mathbf{c}$ , as well as how realistic $\mathbf{x}$ looks, irrespective of conditioning. However, during early training, when artifacts are obvious, the discriminator tends to make a decision independent of conditioning and hesitates to account for the conditioning. + +To enforce the discriminator to incorporate conditioning, we match $\mathbf{x}$ with a random, independently sampled condition $\hat{\mathbf{c}}$ , and present them as a fake pair: + +$$ +\begin{array}{l} \mathcal {V} _ {\text {m a t c h}} = \mathbb {E} _ {\mathbf {x}, \mathbf {c}, \hat {\mathbf {c}}} \left[ \log \left(1 + \exp (D (\mathbf {x}, \hat {\mathbf {c}}))\right) \right. \tag {8} \\ \left. + \log (1 + \exp (D (G (\mathbf {c}), \hat {\mathbf {c}})) \right], \\ \end{array} +$$ + +where $(\mathbf{x},c)$ and $\hat{\mathbf{c}}$ are separately sampled from $p_{\mathrm{data}}$ . This loss has previously been explored in text-to-image GAN + +works [55, 76], except we find that enforcing the Matching-aware loss on generated images from $G$ , as well real images $\mathbf{x}$ , leads to clear gains in performance (Table A2). + +CLIP contrastive loss. We further leverage off-the-shelf pretrained models as a loss function [36, 60, 64]. In particular, we enforce the generator to produce outputs that are identifiable by the pre-trained CLIP image and text encoders [50], $\mathcal{E}_{\mathrm{img}}$ and $\mathcal{E}_{\mathrm{txt}}$ , in the contrastive cross-entropy loss that was used to train them originally. + +$$ +\mathcal {L} _ {\mathrm {C L I P}} = \mathbb {E} _ {\left\{\mathbf {c} _ {n} \right\}} \left[ - \log \frac {\exp \left(\mathcal {E} _ {\mathrm {i m g}} \left(G \left(\mathbf {c} _ {0}\right)\right) ^ {\top} \mathcal {E} _ {\mathrm {t x t}} \left(\mathbf {c} _ {0}\right)\right)}{\sum_ {n} \exp \left(\mathcal {E} _ {\mathrm {i m g}} \left(G \left(\mathbf {c} _ {0}\right)\right) ^ {\top} \mathcal {E} _ {\mathrm {t x t}} \left(\mathbf {c} _ {n}\right)}\right) \right], \tag {9} +$$ + +where $\{\mathbf{c}_n\} = \{\mathbf{c}_0,\dots \}$ are sampled captions from the training data. + +Vision-Aided adversarial loss. Lastly, we build an additional discriminator that uses the CLIP model as a backbone, known as Vision-Aided GAN [36]. We freeze the CLIP image encoder, extract features from the intermediate layers, and process them through a simple network with $3 \times 3$ conv layers to make real/fake predictions. + +We also incorporate conditioning through modulation, as in Equation 7. To stabilize training, we also add a fixed random projection layer, as proposed by Projected GAN [60]. We refer to this as $\mathcal{L}_{\mathrm{Vision}}(G)$ (omitting the learnable discriminator parameters for clarity). + +Our final objective is $\mathcal{V}(G,D) = \mathcal{V}_{\mathrm{MS - I / O}}(G,D) + \mathcal{L}_{\mathrm{CLIP}}(G) + \mathcal{L}_{\mathrm{Vision}}(G)$ , with weighting between the terms specified in Table A1. + +# 3.4. GAN-based upsampler + +Furthermore, GigaGAN framework can be easily extended to train a text-conditioned super-resolution model, capable of upsampling the outputs of the base GigaGAN generator to obtain high-resolution images at 512px or 4k resolution. By training our pipeline in two separate stages, we can afford a higher capacity 64px base model within the same computational resources. + +In the upsampler, the synthesis network is rearranged to an asymmetric U-Net architecture, which processes the 64px input through 3 downsampling residual blocks, followed by 6 upsampling residual blocks with attention layers to produce the 512px image. There exist skip connections at the same resolution, similar to CoModGAN [78]. The model is trained with the same losses as the base model, as well as the LPIPS Perceptual Loss [77] with respect to the ground truth high-resolution image. Vision-Aided GAN is not used for the upsampler. During training and inference time, we apply moderate Gaussian noise augmentation to reduce the gap between real and GAN-generated images. + +![](images/142b37ab53abf3676139c42bacc8015b5c581ec0fd82ce0f6b6549f763f83a6e.jpg) +Figure 4. Prompt mixing. GigaGAN can directly control the style with text prompts. Here we generate three outputs using the prompts "a X on tabletop", shown in the "no mixing" column. Then we re-compute the text embeddings $\mathbf{t}$ and the style codes $\mathbf{w}$ using the new prompts "a X with the texture of Y on tabletop", such as "a cube with the texture of crochet on tabletop", and apply them to the second half layers of the generator, achieving layout-preserving fine style control. Cross-attention mechanism automatically localizes the style to the object of interest. + +Our GigaGAN framework becomes particularly effective for the super-resolution task compared to the diffusion-based models, which cannot afford as many sampling steps as the base model at high resolution. The LPIPS regression loss also provides a stable learning signal. We believe that our GAN upsampler can serve as a drop-in replacement for the super-resolution stage of other generative models. + +# 4. Experiments + +Systematic, controlled evaluation of large-scale text-to-image synthesis tasks is difficult, as most existing models are not publicly available. Training a new model from scratch would be prohibitively costly, even if the training code were available. Still, we compare our model to recent text-to-image models, such asImagen [59], Latent Diffusion Models (LDM) [58], Stable Diffusion [57], and Parti [73], based on the available information, while acknowledging considerable differences in the training dataset, number of iterations, batch size, and model size. In addition to text-to-image results, we evaluate our model on ImageNet class-conditional generation and unconditional super-resolution in our arXiv, for an apples-to-apples comparison with other methods at a more controlled setting. + +For quantitative evaluation, we mainly use the Fréchet Inception Distance (FID) [20] for measuring the realism of the output distribution and the CLIP score for evaluating the image-text alignment. All our models are trained and evaluated on A100 GPUs. For more information about training and evaluation of GigaGAN, please refer to the arXiv ver- + +![](images/26900169eb10564fa8bc186310832a5a6707fcb2ae17fda3049a792fff602c66.jpg) +Figure 5. Style mixing. Our GAN-based architecture retains a disentangled latent space, enabling us to blend the coarse style of one sample with the fine style of another. All outputs are generated with the prompt "A Toy sport sedan, CG art." The corresponding latent codes are spliced together to produce a style-swapping grid. + +sion. + +# 4.1. Text-to-image synthesis + +We proceed to train a larger model by increasing the capacity of the base generator and upsampler to 652.5M and 359.1M, respectively. This results in an unprecedented size of GAN model, with a total parameter count of 1.0B. Table 1 compares the performance of our end-to-end pipeline to various text-to-image generative models [4, 9, 46, 53, 54, 57-59, 73, 80]. Note that there exist differences in the training dataset, the pretrained text encoders, and even image resolutions. For example, GigaGAN initially synthesizes 512px images, which are resized to 256px before evaluation. + +Table 1 shows that GigaGAN exhibits a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73]. While our model can be optimized to better match the feature distribution of real images than existing models, the quality of the generated images is not necessarily better (see our arXiv for more samples). We acknowledge that this may represent a corner case of zero-shot FID on COCO2014 dataset and suggest that further research on a better evaluation metric is necessary to improve text-to-image models. Nonetheless, we emphasize that GigaGAN is the first GAN model capable of synthesizing promising images from arbitrary text prompts and exhibits competitive zero-shot FID with other text-to-image models. + +# 4.2. Super-resolution for large-scale image synthesis + +We separately evaluate the performance of the GigaGAN upsampler in a text-conditional upsampling task. We combine the Stable Diffusion [57] 4x Upscaler and 2x Latent Upscaler to establish an 8x upscaling model (SD Upscaler). + +Table 1. Comparison to recent text-to-image models. Model size, total images seen during training, COCO FID-30k, and inference speed of text-image models. * denotes that the model has been evaluated by us. GigaGAN achieves a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73], while being much faster than competitive methods. GigaGAN and SDv1.5 require 4,783 and 6,250 A100 GPU days, and Imagen and Parti need approximately 4,755 and 320 TPUv4 days for training. + +
ModelType#Param.#ImagesFID-30k ↓Inf. time
256DALL-E [54]Diff12.0B1.54B27.50-
GLIDE [46]Diff5.0B5.94B12.2415.0s
LDM [58]Diff1.5B0.27B12.639.4s
DALL-E 2 [53]Diff5.5B5.63B10.39-
Imagen [59]Diff3.0B15.36B7.279.1s
eDiff-I [4]Diff9.1B11.47B6.9532.0s
Parti-750M [73]AR750M3.69B10.71-
Parti-3B [73]AR3.0B3.69B8.106.4s
Parti-20B [73]AR20.0B3.69B7.23-
LAFITE [80]GAN75M-26.940.02s
512SD-v1.5* [57]Diff0.9B3.16B9.622.9s
Muse-3B [9]AR3.0B0.51B7.881.3s
GigaGANGAN1.0B0.98B9.090.13s
+ +Table 2. Text-conditioned $128 \rightarrow 1024$ super-resolution on random 10K LAION samples, compared against unconditional Real-ESRGAN [26] and Stable Diffusion Upscaler [57]. GigaGAN enjoys the fast speed of a GAN-based model while achieving better FID, patch-FID [8], CLIP score, and LPIPS [77]. + +
Model#Param.Inf. timeFID-10k ↓pFID ↓CLIP ↑LPIPS ↓
Real-ESRGAN [26]17M0.06s8.6022.80.3140.363
SD Upscaler [57]846M7.75s9.3941.30.3160.523
GigaGAN693M0.13s1.548.900.3220.274
+ +We also use the unconditional Real-ESRGAN [26] as another baseline. Table 2 measures the performance of the upsampler on random 10K images from the LAION dataset and shows that our GigaGAN upsampler significantly outperforms the other upsamplers in realism scores (FID and patch-FID [8]), text alignment (CLIP score) and closeness to the ground truth (LPIPS [77]). + +# 4.3. Controllable image synthesis + +In Figure 4, we show that the disentangled style manipulation can be controlled via text inputs. In detail, we can compute the text embedding $\mathbf{t}$ and style code w using different prompts and apply them to different layers of the generator. This way, we gain not only the coarse and fine style disentanglement but also an intuitive prompt-based maneuver in the style space. + +StyleGANs are known to possess a linear latent space useful for image manipulation, called the $\mathcal{W}$ -space. Likewise, we perform coarse and fine-grained style swapping using style vectors $\mathbf{w}$ . Similar to the $\mathcal{W}$ -space of StyleGAN, Figure 5 illustrates that GigaGAN maintains a disentangled $\mathcal{W}$ -space, suggesting existing latent manipulation techniques of StyleGAN can transfer to GigaGAN. Furthermore, our model possesses another latent space of text embedding $\mathbf{t} = [\mathbf{t}_{\mathrm{local}}, \mathbf{t}_{\mathrm{global}}]$ prior to $\mathcal{W}$ , and we explore its potential for image synthesis. + +![](images/7413441fd6bba24b74121d6224be8dc0a5a49da3ac026d7ed1fc086b4d745480.jpg) + +![](images/8cca0355b05b74ec5cc64b364b981bafff0d0a3e7a1566f606f171f4b4c2eb54.jpg) + +![](images/5e05d970fb7214f52aa42de5931470719f09f638bdc029724793011273aec152.jpg) + +![](images/25667b58756f0aaefdccc4dedf573b23811579a2b7dbec901058417c7a7aa25c.jpg) +Figure 6. Failure cases. Our outputs with the same prompts as DALL-E 2. Each column conditions on "a teddy bear on a skateboard in Times Square", "a Vibrant portrait painting of Salvador Dali with a robotic half face", and "A close up of a handpalm with leaves growing from it". Compared to production-grade models such as DALL-E 2, our model exhibits limitations in realism and compositionality. See our website for uncurated comparisons. + +![](images/f988f885ea684a3ed01a3d67b22e481e26c6e1a7a2b5faff8b5e4b5cd72e88b6.jpg) + +![](images/9eea9ffbf5062371ced9b689d543166340163b47e9806413f5ca9564cc3e6ba6.jpg) + +# 5. Discussion and Limitations + +Our experiments provide a conclusive answer about the scalability of GANs: our new architecture can scale up to model sizes that enable text-to-image synthesis. However, the visual quality of our results is not yet comparable to production-grade models like DALL-E 2. Figure 6 shows several instances where our method fails to produce high-quality results when compared to DALL-E 2, in terms of photorealism and text-to-image alignment for the same input prompts used in their paper. + +Nevertheless, we have tested capacities well beyond what is possible with a naïve approach and achieved competitive results with autoregressive and diffusion models trained with similar resources while being orders of magnitude faster and enabling latent interpolation and stylization. Our GigaGAN architecture opens up a whole new design space for large-scale generative models and brings back key editing capabilities that became challenging with the transition to autoregressive and diffusion models. We expect our performance to improve with larger models. + +Acknowledgments. We thank Simon Niklaus, Alexandru Chiculita, and Markus Woodson for building the distributed training pipeline. We thank Nupur Kumari, Gaurav Parmar, Bill Peebles, Phillip Isola, Alyosha Efros, and Joonghyuk Shin for their helpful comments. We also want to thank Chenlin Meng, Chitwan Sahara, and Jiahui Yu for answering many questions about their fantastic work. We thank Kevin Duarte for discussions regarding upsampling beyond 4K. Part of this work was done while Minguk Kang was an intern at Adobe Research. Minguk Kang and Jaesik Park were supported by IITP grant funded by the government of South Korea (MSIT) (POSTECH GSAI: 2019-0-01906 and Image restoration: 2021-0-00537). + +# References + +[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In IEEE International Conference on Computer Vision (ICCV), 2019. 3 +[2] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein Generative Adversarial Networks. In International Conference on Machine Learning (ICML), 2017. 4 +[3] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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From a technical standpoint, it also marked a drastic change in the favored architecture to design generative image models. GANs used to be the de facto choice, with techniques like StyleGAN. With DALL-E 2, autoregressive and diffusion models became the new standard for large-scale generative models overnight. This rapid shift raises a fundamental question: can we scale up GANs to benefit from large datasets like LAION? We find that naively increasing the capacity of the StyleGAN architecture quickly becomes unstable. We introduce GigaGAN, a new GAN architecture that far exceeds this limit, demonstrating GANs as a viable option for text-to-image synthesis. GigaGAN offers three major advantages. First, it is orders of magnitude faster at inference time, taking only 0.13 seconds to synthesize a 512px image. Second, it can synthesize high-resolution images, for example, 16-megapixel images in 3.66 seconds. Finally, GigaGAN supports various latent space editing applications such as latent interpolation, style mixing, and vector arithmetic operations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 524, + 128, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 128, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 128, + 537 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 653 + ], + "type": "text", + "content": "Recently released models, such as DALL-E 2 [53], Imagegen [59], Parti [73], and Stable Diffusion [58], have ushered in a new era of image generation, achieving unprecedented levels of image quality and model flexibility. The now-dominant paradigms, diffusion models and autoregressive models, both rely on iterative inference. This is a double-edged sword, as iterative methods enable stable training with simple objectives but incur a high computational cost during inference." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Contrast this with Generative Adversarial Networks (GANs) [5,17,33,51], which generate images through a single forward pass and thus inherently efficient. While such models dominated the previous \"era\" of generative modeling, scaling them requires careful tuning of the network" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 222, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 547, + 342 + ], + "type": "text", + "content": "architectures and training considerations due to instabilities in the training procedure. As such, GANs have excelled at modeling single or multiple object classes, but scaling to complex datasets, much less an open world, has remained challenging. As a result, ultra-large models, data, and compute resources are now dedicated to diffusion and autoregressive models. In this work, we ask – can GANs continue to be scaled up and potentially benefit from such resources, or have they plateaued? What prevents them from further scaling, and can we overcome these barriers?" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 342, + 547, + 474 + ], + "type": "text", + "content": "We first experiment with StyleGAN2 [34] and observe that simply scaling the backbone causes unstable training. We identify several key issues and propose techniques to stabilize the training while increasing the model capacity. First, we effectively scale the generator's capacity by retaining a bank of filters and taking a sample-specific linear combination. We also adapt several techniques commonly used in the diffusion context and confirm that they bring similar benefits to GANs. For instance, interleaving both self-attention (image-only) and cross-attention (image-text) with the convolutional layers improves performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 547, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 547, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 547, + 582 + ], + "type": "text", + "content": "Furthermore, we reintroduce multi-scale training, finding a new scheme that improves image-text alignment and low-frequency details of generated outputs. Multi-scale training allows the GAN-based generator to use parameters in low-resolution blocks more effectively, leading to better image-text alignment and image quality. After careful tuning, we achieve stable and scalable training of a one-billion-parameter GAN (GigaGAN) on large-scale datasets, such as LAION2B-en [63]. Our results are shown in Figure 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "content": "In addition, our method uses a multi-stage approach [12, 76]. We first generate at " + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "content": " and then upsample to " + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 582, + 547, + 677 + ], + "type": "text", + "content": ". These two networks are modular and robust enough to be used in a plug-and-play fashion. We show that our text-conditioned GAN-based upsampling network can be used as an efficient, higher-quality upsampler for a base diffusion model such as DALL-E 2, despite never having seen diffusion images at training time (Figures 1)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Together, these advances enable our GigaGAN to go far beyond previous GANs: " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "36 \\times" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": " larger than StyleGAN2 [34] and " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "6 \\times" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": " larger than StyleGAN-XL [62] and" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10124" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 179, + 180 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 179, + 180 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 179, + 180 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 179, + 180 + ], + "type": "image", + "image_path": "fead01978a2023133c7cb72256b00a1575a26f438c747774b63b9b8ad8fa004f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 71, + 182, + 175, + 198 + ], + "lines": [ + { + "bbox": [ + 71, + 182, + 175, + 198 + ], + "spans": [ + { + "bbox": [ + 71, + 182, + 175, + 198 + ], + "type": "text", + "content": "A portrait of a human growing colorful flowers from her hair. 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Our model, GigaGAN, shows GAN frameworks can also be scaled up for general text-to-image synthesis and super-resolution tasks, generating a 512px output at an interactive speed of 0.13s, and 4096px within 3.7s. Selected examples at 2K resolution (text-to-image synthesis) and 1k or 4k resolutions (super-resolution) are shown. For the super-resolution task, we use the caption of \"Portrait of a colored iguana dressed in a hoodie.\" and compare our model with the text-conditioned upscaler of Stable Diffusion [57] and unconditional Real-ESRGAN [26]. Please zoom in for more details. See our arXiv paper and website for more uncurated comparisons." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 160, + 552, + 249, + 640 + ], + "blocks": [ + { + "bbox": [ + 160, + 552, + 249, + 640 + ], + "lines": [ + { + "bbox": [ + 160, + 552, + 249, + 640 + ], + "spans": [ + { + "bbox": [ + 160, + 552, + 249, + 640 + ], + "type": "image", + "image_path": "09329577ed2cfae04388e3204685d54f171627055ed5a45e0fc2b29ac0322811.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 251, + 552, + 338, + 640 + ], + "blocks": [ + { + "bbox": [ + 251, + 552, + 338, + 640 + ], + "lines": [ + { + "bbox": [ + 251, + 552, + 338, + 640 + ], + "spans": [ + { + "bbox": [ + 251, + 552, + 338, + 640 + ], + "type": "image", + "image_path": "08fac562b2dc0b35ca124d277a682a6cce18eace8b1d011bd6b03872f4f92bed.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 341, + 552, + 429, + 640 + ], + "blocks": [ + { + "bbox": [ + 341, + 552, + 429, + 640 + ], + "lines": [ + { + "bbox": [ + 341, + 552, + 429, + 640 + ], + "spans": [ + { + "bbox": [ + 341, + 552, + 429, + 640 + ], + "type": "image", + "image_path": "62e27977dccc969ff1ac138f6f45738b59cec3474b3973933240f271bbd27ad3.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 432, + 552, + 520, + 640 + ], + "blocks": [ + { + "bbox": [ + 432, + 552, + 520, + 640 + ], + "lines": [ + { + "bbox": [ + 432, + 552, + 520, + 640 + ], + "spans": [ + { + "bbox": [ + 432, + 552, + 520, + 640 + ], + "type": "image", + "image_path": "208c346bfe79252cb6c05fbf1bc0bb0615ffabca270fe39cb9a2eeb29e747323.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "10125" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "XMC-GAN [75]. While our 1B parameter count is still lower than the largest synthesis models, such as DALL-E 2 (5.5B), and Parti (20B), we have not yet observed a quality saturation regarding the model size. GigaGAN achieves a zero-shot FID of 9.09 on COCO2014, lower than the FID of DALL-E 2, Parti-750M, and Stable Diffusion." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 286, + 251 + ], + "type": "text", + "content": "Furthermore, GigaGAN has three major practical advantages compared to diffusion and autoregressive models. First, it is orders of magnitude faster, generating a 512px image in 0.13 seconds. Second, it can synthesize ultra highres images at 4k resolution in 3.66 seconds. Third, it is endowed with a controllable, latent vector space that lends itself to well-studied controllable image synthesis applications, such as prompt mixing (Figure 4), style mixing (Figure 5), and prompt interpolation (Figures A7 and A8)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 252, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 286, + 323 + ], + "type": "text", + "content": "In summary, our model is the first GAN-based method that successfully trains a billion-scale model on billions of real-world complex Internet images. This suggests that GANs are still a viable option for text-to-image synthesis and should be considered for future aggressive scaling. Please visit our website for additional results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 335, + 138, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 138, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 138, + 347 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 356, + 286, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 286, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 286, + 559 + ], + "type": "text", + "content": "Text-to-image synthesis. Generating a realistic image given a text description, explored by early works [42, 85], is a challenging task. A common approach is text-conditional GANs [55, 56, 67, 71, 76, 83] on specific domains [68] and datasets with a closed-world assumption [41]. With the development of diffusion models [13, 21], autoregressive (AR) transformers [10], and large-scale language encoders [50, 52], text-to-image synthesis has shown remarkable improvement on an open-world of arbitrary text descriptions. GLIDE [46], DALL-E 2 [53], and Imagen [59] are representative diffusion models that show realistic outputs with the aid of a pretrained language encoder [50, 52]. AR models, such as DALL-E [54], Make-A-Scene [16], CogView [14, 15], and Parti [73] also achieve amazing results. While these models exhibit unprecedented image synthesis ability, they require time-consuming iterative processes to achieve high-quality image sampling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "content": "GAN-based image synthesis. GANs [17] have been one of the primary families of generative models for natural image synthesis. As the sampling quality and diversity of GANs improve [31-34, 36, 51, 60], GANs have been deployed to various computer vision and graphics applications, such as text-to-image synthesis [55], image-to-image translation [23, 27, 37, 47, 48, 82], and image editing [1, 6, 49, 81]. Notably, StyleGAN-family models [32, 34] have shown impressive ability in image synthesis tasks for single-category domains [1, 25, 49, 70, 84]. Other works have explored class-conditional GANs [5, 29, 62, 74, 79] on datasets with a fixed set of object categories." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "In this paper, we change the data regimes from single- or multi-categories datasets to extremely data-rich situations. We make the first expedition toward training a largescale GAN for text-to-image generation on a vast amount of web-crawled text and image pairs, such as LAION2Ben [63] and COYO-700M [7]. Existing GAN-based text-to-image synthesis models [39,55,67,71,75,76,83] are trained on relatively small datasets, such as CUB-200 (12k training pairs), MSCOCO (82k) and LN-OpenImages (507k). Also, those models are evaluated on associated validation datasets, which have not been validated to perform largescale text-image synthesis like diffusion or AR models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 217, + 545, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 253 + ], + "type": "text", + "content": "Concurrent with our method, StyleGAN-T [61] and GALIP [66] share similar goals and make complementary insights to ours." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 267, + 361, + 279 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 267, + 361, + 279 + ], + "spans": [ + { + "bbox": [ + 306, + 267, + 361, + 279 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": "We train a generator " + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "inline_equation", + "content": "G(\\mathbf{z}, \\mathbf{c})" + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": " to predict an image " + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": " given a latent code " + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\sim \\mathcal{N}(0,1) \\in \\mathbb{R}^{128}" + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": " and text-condition " + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": ". We use a discriminator " + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "inline_equation", + "content": "D(\\mathbf{x}, \\mathbf{c})" + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": " to judge the realism of the fake image, as compared to a sample from the training database " + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 285, + 545, + 345 + ], + "type": "text", + "content": ", which contains image-text pairs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 346, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 490 + ], + "type": "text", + "content": "Although GANs [5, 31, 33] can successfully generate realistic images on single- and multi-category datasets [11, 33, 72], open-ended text-conditioned synthesis on Internet images remains challenging. We hypothesize that the current limitation stems from its reliance on convolutional layers. That is, the same convolution filters are challenged to model the general image synthesis function for all text conditioning across all locations of the image. In this light, we seek to inject more expressivity into our parameterization by dynamically selecting convolution filters based on the input conditioning and by capturing long-range dependence via the attention mechanism." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 491, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 575 + ], + "type": "text", + "content": "Below, we discuss our key contributions to making ConvNets more expressive (Section 3.1), followed by our designs for the generator (Section 3.2) and discriminator (Section 3.3). Lastly, we introduce a new, fast GAN-based upsampler model that can improve the inference quality and speed of our method and diffusion models such as ImageNet [59] and DALL-E 2 [53] (Section 3.4)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 586, + 520, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 520, + 599 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 520, + 599 + ], + "type": "text", + "content": "3.1. Modeling complex contextual interaction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": "Baseline StyleGAN generator. We base our architecture off the conditional version of StyleGAN2 [34], comprised of two networks " + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "inline_equation", + "content": "G = \\widetilde{G} \\circ M" + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": ". The mapping network " + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathbf{w} = M(\\mathbf{z},\\mathbf{c})" + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": " maps the inputs into a \"style\" vector " + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": ", which modulates a series of upsampling convolutional layers in the synthesis network " + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\widetilde{G}(\\mathbf{w})" + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": " to map a learned constant tensor to an output image " + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": ". Convolution is the main engine to generate all output pixels, with the " + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 609, + 545, + 716 + ], + "type": "text", + "content": " vector as the only source of information to model conditioning." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10126" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 67, + 532, + 232 + ], + "blocks": [ + { + "bbox": [ + 62, + 67, + 532, + 232 + ], + "lines": [ + { + "bbox": [ + 62, + 67, + 532, + 232 + ], + "spans": [ + { + "bbox": [ + 62, + 67, + 532, + 232 + ], + "type": "image", + "image_path": "2c1271d378f86f7f7f06818d72bfdfacbadff20ad403a1917c65984f932802cf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "text", + "content": "Figure 2. GigaGAN's text-to-image generator. First, we extract text embeddings using a pretrained CLIP model and a learned encoder " + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "text", + "content": ". The local text descriptors are fed to the generator using cross-attention. The global text descriptor, along with a latent code " + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "text", + "content": ", is fed to a mapping network " + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "text", + "content": " to produce style code " + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 234, + 547, + 289 + ], + "type": "text", + "content": ". The style code modulates the main generator using our style-adaptive kernel selection, shown on the right. The generator outputs an image pyramid by converting the intermediate features into RGB images. To achieve higher capacity, we use multiple attention and convolution layers at each scale. We also use a separate upsampler, that is not shown in this diagram." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 287, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 364 + ], + "type": "text", + "content": "Sample-adaptive kernel selection. To handle the highly diverse distribution of internet images, we aim to increase the capacity of convolution kernels. However, increasing the width of the convolution layers becomes too demanding, as the same operation is repeated across all locations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": "We propose an efficient way to enhance the expressivity of convolutional kernels by creating them on-the-fly based on the text conditioning, as illustrated in Figure 2 (right). In this scheme, we instantiate a bank of " + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": " filters " + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{K}_i\\in \\mathbb{R}^{C_{\\mathrm{in}}\\times C_{\\mathrm{out}}\\times K\\times K}\\}_{i = 1}^N" + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": ", instead of one, that takes a feature " + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{f}\\in \\mathbb{R}^{C_{\\mathrm{in}}}" + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": " at each layer. The style vector " + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{w}\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": " then goes through an affine layer " + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "inline_equation", + "content": "[W_{\\mathrm{filter}},b_{\\mathrm{filter}}]\\in \\mathbb{R}^{(d + 1)\\times N}" + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": " to predict a set of weights to average across the filters, to produce an aggregated filter " + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "inline_equation", + "content": "\\mathbf{K}\\in \\mathbb{R}^{C_{\\mathrm{in}}\\times C_{\\mathrm{out}}\\times K\\times K}" + }, + { + "bbox": [ + 46, + 364, + 290, + 473 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 476, + 287, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 476, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 83, + 476, + 287, + 510 + ], + "type": "interline_equation", + "content": "\\mathbf {K} = \\sum_ {i = 1} ^ {N} \\mathbf {K} _ {i} \\cdot \\operatorname {s o f t m a x} \\left(W _ {\\text {f i l t e r}} ^ {\\top} \\mathbf {w} + b _ {\\text {f i l t e r}}\\right) _ {i} \\tag {1}", + "image_path": "41a6800bd016b04b2e8ec245a695352e7477eaf5e1076d26046f5c2b1c6adb5b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 513, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 550 + ], + "type": "text", + "content": "The filter is then used in the regular convolution pipeline of StyleGAN2, with the second affine layer " + }, + { + "bbox": [ + 47, + 513, + 287, + 550 + ], + "type": "inline_equation", + "content": "[W_{\\mathrm{mod}}, b_{\\mathrm{mod}}] \\in \\mathbb{R}^{(d + 1) \\times C_{\\mathrm{in}}}" + }, + { + "bbox": [ + 47, + 513, + 287, + 550 + ], + "type": "text", + "content": " for weight (de-)modulation [34]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 74, + 553, + 287, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 553, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 74, + 553, + 287, + 569 + ], + "type": "interline_equation", + "content": "g _ {\\text {a d a c o n v}} (\\mathbf {f}, \\mathbf {w}) = \\left(\\left(W _ {\\mathrm {m o d}} ^ {\\top} \\mathbf {w} + b _ {\\mathrm {m o d}}\\right) \\otimes \\mathbf {K}\\right) * \\mathbf {f}, \\tag {2}", + "image_path": "29ff65aa5c6486dad2c1365702b705db89db813b4be387ffa8de4683d9d1f0af.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "type": "inline_equation", + "content": "\\otimes" + }, + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 47, + 573, + 285, + 585 + ], + "type": "text", + "content": " represent (de-)modulation and convolution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 585, + 288, + 717 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 585, + 288, + 717 + ], + "spans": [ + { + "bbox": [ + 46, + 585, + 288, + 717 + ], + "type": "text", + "content": "At a high level, the softmax-based weighting can be viewed as a differentiable filter selection process based on input conditioning. Furthermore, since the filter selection process is performed only once at each layer, the selection process is much faster than the actual convolution, decoupling compute complexity from the resolution. Our method shares a spirit with dynamic convolutions [19,28,65,69] in that the convolution filters dynamically change per sample, but differs in that we explicitly instantiate a larger filter bank and select weights based on a separate pathway conditional on the w-space of StyleGAN." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 304, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 411 + ], + "type": "text", + "content": "Interleaving attention with convolution. Since the convolutional filter operates within its receptive field, it cannot contextualize itself in relationship to distant parts of the images. One way to incorporate such long-range relationships is using attention layers " + }, + { + "bbox": [ + 304, + 304, + 545, + 411 + ], + "type": "inline_equation", + "content": "g_{\\text{attention}}" + }, + { + "bbox": [ + 304, + 304, + 545, + 411 + ], + "type": "text", + "content": ". While recent diffusion-based models [13,22,58] have commonly adopted attention mechanisms, StyleGAN architectures are predominantly convolutional with the notable exceptions such as BigGAN [5], GANformer [24], and ViTGAN [38]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 546, + 532 + ], + "type": "text", + "content": "We aim to improve the performance of StyleGAN by integrating attention layers with the convolutional backbone. However, simply adding attention layers to StyleGAN often results in training collapse, possibly because the dot-product self-attention is not Lipschitz, as pointed out by Kim et al. [35]. As the Lipschitz continuity of discriminators has played a critical role in stable training [2,18,43,44], we use the L2-distance instead of the dot product as the attention logits to promote Lipschitz continuity [35], similar to ViTGAN [38]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "content": "To further improve performance, we find it crucial to match the architectural details of StyleGAN, such as equalized learning rate [31] and weight initialization from a unit normal distribution. We scale down the L2 distance logits to roughly match the unit normal distribution at initialization and reduce the residual gain from the attention layers. We further improve stability by tying the key and query matrix [38], and applying weight decay." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "In the synthesis network " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{G}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", the attention layers are interleaved with each convolutional block, leveraging the style vector " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " as an additional token. At each attention block, we add a separate cross-attention mechanism " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{cross - attention}}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " to attend to individual word embeddings [3]. We use each input feature tensor as the query, and the text embeddings as the key and value of the attention mechanism." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10127" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 151, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 151, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 151, + 85 + ], + "type": "text", + "content": "3.2. Generator design" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": "Text and latent-code conditioning. First, we extract the text embedding from the prompt. Previous works [54, 59] have shown that leveraging a strong language model is essential for producing strong results. To do so, we tokenize the input prompt (after padding it to " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "C = 77" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": " words, following best practices [54, 59]) to produce conditioning vector " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{c} \\in \\mathbb{R}^{C \\times 1024}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": ", and take the features from the penultimate layer [59] of a frozen CLIP feature extractor [50]. To allow for additional flexibility, we apply additional attention layers " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": " on top to process the word embeddings before passing them to the MLP-based mapping network. This results in text embedding " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{t} = T(\\mathcal{E}_{\\mathrm{txt}}(\\mathbf{c})) \\in \\mathbb{R}^{C \\times 1024}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": ". Each component " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_i" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": " captures the embedding of the " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "i^{\\text{th}}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": " word in the sentence. We refer to them as " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\text{local}} = \\mathbf{t}_{\\{1:C\\} \\backslash \\text{EOT}} \\in \\mathbb{R}^{(C - 1) \\times 1024}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": ". The EOT (\"end of text\") component of " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": " aggregates global information, and is called " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\text{global}} \\in \\mathbb{R}^{1024}" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": ". We process this global text descriptor, along with the latent code " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{z} \\sim \\mathcal{N}(0,1)" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": ", via an MLP mapping network to extract the style " + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "inline_equation", + "content": "\\mathbf{w} = M(\\mathbf{z}, \\mathbf{t}_{\\text{global}})" + }, + { + "bbox": [ + 46, + 90, + 290, + 320 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 110, + 327, + 287, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 327, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 110, + 327, + 287, + 346 + ], + "type": "interline_equation", + "content": "\\left(\\mathbf {t} _ {\\text {l o c a l}}, \\mathbf {t} _ {\\text {g l o b a l}}\\right) = T \\left(\\mathcal {E} _ {\\mathrm {t x t}} (\\mathbf {c})\\right), \\tag {3}", + "image_path": "6a7417af4b676b3e38077f2049c2ab8feaf23328b1873cf7e2d6069188ac969f.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 133, + 342, + 211, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 342, + 211, + 355 + ], + "spans": [ + { + "bbox": [ + 133, + 342, + 211, + 355 + ], + "type": "interline_equation", + "content": "\\mathbf {w} = M (\\mathbf {z}, \\mathbf {t} _ {\\text {g l o b a l}}).", + "image_path": "6800f4b8711b988afdc6077d6bfb66d9d31bd9b2686ff68693c442ec8f48e2bb.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": "Different from the original StyleGAN, we use both the text-based style code " + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": " to modulate the synthesis network " + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\widetilde{G}" + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": " and the word embeddings " + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{local}}" + }, + { + "bbox": [ + 47, + 361, + 287, + 398 + ], + "type": "text", + "content": " as features for cross-attention." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 130, + 403, + 287, + 419 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 403, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 130, + 403, + 287, + 419 + ], + "type": "interline_equation", + "content": "\\mathbf {x} = \\widetilde {G} (\\mathbf {w}, \\mathbf {t} _ {\\text {l o c a l}}). \\tag {4}", + "image_path": "3a131baa968a56c609a9a64077dd4afe228a65a433e38cdb6cc50781e74094ba.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 426, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 287, + 450 + ], + "type": "text", + "content": "Similar to earlier works [42, 53, 59], the text-image alignment visually improves with cross-attention." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 458, + 287, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 287, + 507 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 287, + 507 + ], + "type": "text", + "content": "Synthesis network. Our synthesis network consists of a series of upsampling convolutional layers, with each layer enhanced with the adaptive kernel selection (Equation 1) and followed by our attention layers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 513, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 513, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 78, + 513, + 287, + 529 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\ell + 1} = g _ {\\mathrm {x a}} ^ {\\ell} \\left(g _ {\\mathrm {a t t n}} ^ {\\ell} \\left(g _ {\\mathrm {a d a c o n v}} ^ {\\ell} \\left(\\mathbf {f} _ {\\ell}, \\mathbf {w}\\right), \\mathbf {w}\\right), \\mathbf {t} _ {\\mathrm {l o c a l}}\\right), \\tag {5}", + "image_path": "952edf5d17f7302957571bc89c250d64e2d3a55b466536524e4fae082f72ce1f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{xa}}^{\\ell}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{attn}}^{\\ell}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{adaconv}}^{\\ell}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": "-th layer of cross-attention, self-attention, and weight (de-)modulation layers. We find it beneficial to increase the depth of the network by adding more blocks at each layer. In addition, our generator outputs a multi-scale image pyramid with " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "L = 5" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " levels, instead of a single image at the highest resolution, similar to MSG-GAN [30] and AnycostGAN [40]. We refer to the pyramid as " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_{ij}\\}_{i=0}^{L-1} = \\{\\mathbf{x}_0, \\mathbf{x}_1, \\dots, \\mathbf{x}_4\\}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ", with spatial resolutions " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\{S_i\\}_{i=0}^{L-1} = \\{64, 32, 16, 8, 4\\}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ", respectively. The base level " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": " is the output image " + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 533, + 289, + 713 + ], + "type": "text", + "content": ". Each image of the pyramid is independently used to compute the GAN loss, as discussed in Section 3.3. We follow the findings of StyleGAN-XL [62] and turn off the style mixing and path length regularization [34]. We include more training details in our arXiv version." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 73, + 541, + 242 + ], + "blocks": [ + { + "bbox": [ + 309, + 73, + 541, + 242 + ], + "lines": [ + { + "bbox": [ + 309, + 73, + 541, + 242 + ], + "spans": [ + { + "bbox": [ + 309, + 73, + 541, + 242 + ], + "type": "image", + "image_path": "388b036b2efa7dd2f28ae30795599cd1b41e4731902d4c7397a1fbf0494fa301.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 247, + 547, + 326 + ], + "lines": [ + { + "bbox": [ + 304, + 247, + 547, + 326 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 547, + 326 + ], + "type": "text", + "content": "Figure 3. Our discriminator consists of two branches for processing the image and the text conditioning " + }, + { + "bbox": [ + 304, + 247, + 547, + 326 + ], + "type": "inline_equation", + "content": "t_{D}" + }, + { + "bbox": [ + 304, + 247, + 547, + 326 + ], + "type": "text", + "content": ". The text branch processes the text similar to the generator (Figure 2). The image branch receives an image pyramid and makes independent predictions for each image scale. Moreover, the predictions are made at all subsequent scales of the downsampling layers, making it a multi-scale input, multi-scale output (MS-I/O) discriminator." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 335, + 427, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 427, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 427, + 348 + ], + "type": "text", + "content": "3.3. Discriminator design" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "text", + "content": "As shown in Figure 3, our discriminator consists of separate branches for processing text with the function " + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_D" + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "text", + "content": " and images with function " + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "text", + "content": ". The prediction of real vs. fake is made by comparing the features from the two branches using function " + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 304, + 358, + 547, + 443 + ], + "type": "text", + "content": ". We introduce a new way of making predictions on multiple scales. Finally, we use additional CLIP and Vision-Aided GAN losses [36] to improve stability." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "type": "text", + "content": "Text conditioning. First, to incorporate conditioning into discriminators, we extract text descriptor " + }, + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{D}}" + }, + { + "bbox": [ + 304, + 453, + 547, + 513 + ], + "type": "text", + "content": " from text c. Similar to the generator, we apply a pretrained text encoder, such as CLIP [50], followed by a few learnable attention layers. In this case, we only use the global descriptor." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 629 + ], + "type": "text", + "content": "Multiscale image processing. We observe that the early, low-resolution layers of the generator become inactive, using small dynamic ranges irrespective of the provided prompts. StyleGAN2 [34] also observes this phenomenon, concluding that the network relies on the high-resolution layers, as the model size increases. As recovering performance in low frequencies, which contains complex structure information, is crucial, we redesign the model architecture to provide training signals across multiple scales." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Recall the generator produces a pyramid " + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_i\\}_{i=0}^{L-1}" + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": ", with the full image " + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": " at the pyramid base. MSG-GAN [30] improves performance by making a prediction on the entire pyramid at once, enforcing consistency across scales. However, in our large-scale setting, this harms stability, as this limits the generator from making adjustments to its initial low-res output." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10128" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": "Instead, we process each level of the pyramid independently. As shown in Figure 3, each level " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " makes a real/fake prediction at multiple scales " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "i < j \\leq L" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": ". For example, the full " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " makes predictions at " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "L = 5" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " scales, the next level " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " makes predictions at 4 scales, and so on. In total, our discriminator produces " + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "inline_equation", + "content": "\\frac{L(L - 1)}{2}" + }, + { + "bbox": [ + 46, + 72, + 287, + 157 + ], + "type": "text", + "content": " predictions, supervising multi-scale generations at multiple scales." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": "To extract features at different scales, we define a feature extractor " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "\\phi_{i\\rightarrow j}:\\mathbb{R}^{X_i\\times X_i\\times 3}\\to \\mathbb{R}^{X_j^D\\times X_j^D\\times C_j}" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": ". Practically, each sub-network " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "\\phi_{i\\rightarrow j}" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": " is a subset of full " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "\\phi \\triangleq \\phi_{0\\rightarrow L}" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "i > 0" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": " indicating late entry and " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "j < L" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": " indicating early exit. Each layer in " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": " consists of self-attention, followed by convolution with a stride 2. The final layer flattens the spatial extent into a " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": " tensor, producing output resolutions at " + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "inline_equation", + "content": "\\{X_j^D\\} = \\{32,16,8,4,1\\}" + }, + { + "bbox": [ + 46, + 157, + 288, + 301 + ], + "type": "text", + "content": ". This allows us to inject lower-resolution images on pyramid into intermediate layers [31]. As we use a shared feature extractor across different levels and most of the added predictions are made at low resolutions, the increased computation overhead is manageable." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 311, + 287, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 311, + 287, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 311, + 287, + 360 + ], + "type": "text", + "content": "Multi-scale input, multi-scale output adversarial loss. In total, our training objective consists of discriminator losses, along with our proposed matching loss, to encourage the discriminator to take into account the conditioning:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 366, + 293, + 411 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 293, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 293, + 411 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {\\mathrm {M S - I / O}} (G, D) = \\sum_ {i = 0} ^ {L - 1} \\sum_ {j = 1} ^ {L} \\mathcal {V} _ {\\mathrm {G A N}} \\left(G _ {i}, D _ {i j}\\right) + \\mathcal {V} _ {\\text {m a t c h}} \\left(G _ {i}, D _ {i j}\\right), \\tag {6}", + "image_path": "9c2303c77b283021d7232a6f2292a66feed5c27a8101ff9ee395fa2018bf6316.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "\\nu_{\\mathrm{GAN}}" + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "text", + "content": " is the standard, non-saturating GAN loss [17]. To compute the discriminator output, we train predictor " + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "text", + "content": " which uses text feature " + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{t}_{\\mathrm{D}}" + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "text", + "content": " to modulate image features " + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "inline_equation", + "content": "\\phi (\\mathbf{x})" + }, + { + "bbox": [ + 47, + 418, + 287, + 455 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 464, + 287, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 464, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 55, + 464, + 287, + 488 + ], + "type": "interline_equation", + "content": "D _ {i j} (\\mathbf {x}, \\mathbf {c}) = \\psi_ {j} \\left(\\phi_ {i \\rightarrow j} \\left(\\mathbf {x} _ {i}\\right), \\mathbf {t} _ {D}\\right) + \\operatorname {C o n v} _ {1 \\times 1} \\left(\\phi_ {i \\rightarrow j} \\left(\\mathbf {x} _ {i}\\right)\\right), \\tag {7}", + "image_path": "a548b66acc17756df363fa0f51b811494c8b8dfb1982f57cb39bab4449b3b369.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "inline_equation", + "content": "\\psi_{j}" + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "text", + "content": " is implemented as a 4-layer " + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "text", + "content": " modulated convolution, and " + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{1\\times 1}" + }, + { + "bbox": [ + 47, + 495, + 287, + 532 + ], + "type": "text", + "content": " is added as a skip connection to explicitly maintain an unconditional prediction branch [45]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "text", + "content": "Matching-aware loss. The previous GAN terms measure how closely the image " + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "text", + "content": " matches the conditioning " + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "text", + "content": ", as well as how realistic " + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 540, + 287, + 611 + ], + "type": "text", + "content": " looks, irrespective of conditioning. However, during early training, when artifacts are obvious, the discriminator tends to make a decision independent of conditioning and hesitates to account for the conditioning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "type": "text", + "content": "To enforce the discriminator to incorporate conditioning, we match " + }, + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "type": "text", + "content": " with a random, independently sampled condition " + }, + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}" + }, + { + "bbox": [ + 46, + 612, + 287, + 648 + ], + "type": "text", + "content": ", and present them as a fake pair:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 61, + 653, + 287, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 653, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 61, + 653, + 287, + 684 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {V} _ {\\text {m a t c h}} = \\mathbb {E} _ {\\mathbf {x}, \\mathbf {c}, \\hat {\\mathbf {c}}} \\left[ \\log \\left(1 + \\exp (D (\\mathbf {x}, \\hat {\\mathbf {c}}))\\right) \\right. \\tag {8} \\\\ \\left. + \\log (1 + \\exp (D (G (\\mathbf {c}), \\hat {\\mathbf {c}})) \\right], \\\\ \\end{array}", + "image_path": "5b952e1a5342860317fe967e176cc9375d9371cf404cb78a9bc0c7e8fee5124e.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},c)" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{c}}" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": " are separately sampled from " + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}" + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": ". This loss has previously been explored in text-to-image GAN" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "works [55, 76], except we find that enforcing the Matching-aware loss on generated images from " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", as well real images " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ", leads to clear gains in performance (Table A2)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "type": "text", + "content": "CLIP contrastive loss. We further leverage off-the-shelf pretrained models as a loss function [36, 60, 64]. In particular, we enforce the generator to produce outputs that are identifiable by the pre-trained CLIP image and text encoders [50], " + }, + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{img}}" + }, + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\mathrm{txt}}" + }, + { + "bbox": [ + 305, + 118, + 547, + 190 + ], + "type": "text", + "content": ", in the contrastive cross-entropy loss that was used to train them originally." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 309, + 209, + 545, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 209, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 309, + 209, + 545, + 251 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {C L I P}} = \\mathbb {E} _ {\\left\\{\\mathbf {c} _ {n} \\right\\}} \\left[ - \\log \\frac {\\exp \\left(\\mathcal {E} _ {\\mathrm {i m g}} \\left(G \\left(\\mathbf {c} _ {0}\\right)\\right) ^ {\\top} \\mathcal {E} _ {\\mathrm {t x t}} \\left(\\mathbf {c} _ {0}\\right)\\right)}{\\sum_ {n} \\exp \\left(\\mathcal {E} _ {\\mathrm {i m g}} \\left(G \\left(\\mathbf {c} _ {0}\\right)\\right) ^ {\\top} \\mathcal {E} _ {\\mathrm {t x t}} \\left(\\mathbf {c} _ {n}\\right)}\\right) \\right], \\tag {9}", + "image_path": "d675eb871bdd1d65fd0270d8459345e630f92cef2bb4fe44e6e82af7a420169e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 260, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 260, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 545, + 284 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 260, + 545, + 284 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{c}_n\\} = \\{\\mathbf{c}_0,\\dots \\}" + }, + { + "bbox": [ + 305, + 260, + 545, + 284 + ], + "type": "text", + "content": " are sampled captions from the training data." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "type": "text", + "content": "Vision-Aided adversarial loss. Lastly, we build an additional discriminator that uses the CLIP model as a backbone, known as Vision-Aided GAN [36]. We freeze the CLIP image encoder, extract features from the intermediate layers, and process them through a simple network with " + }, + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 305, + 294, + 545, + 366 + ], + "type": "text", + "content": " conv layers to make real/fake predictions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 366, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 366, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 366, + 545, + 426 + ], + "type": "text", + "content": "We also incorporate conditioning through modulation, as in Equation 7. To stabilize training, we also add a fixed random projection layer, as proposed by Projected GAN [60]. We refer to this as " + }, + { + "bbox": [ + 305, + 366, + 545, + 426 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{Vision}}(G)" + }, + { + "bbox": [ + 305, + 366, + 545, + 426 + ], + "type": "text", + "content": " (omitting the learnable discriminator parameters for clarity)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 426, + 545, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 462 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 462 + ], + "type": "text", + "content": "Our final objective is " + }, + { + "bbox": [ + 305, + 426, + 545, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{V}(G,D) = \\mathcal{V}_{\\mathrm{MS - I / O}}(G,D) + \\mathcal{L}_{\\mathrm{CLIP}}(G) + \\mathcal{L}_{\\mathrm{Vision}}(G)" + }, + { + "bbox": [ + 305, + 426, + 545, + 462 + ], + "type": "text", + "content": ", with weighting between the terms specified in Table A1." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 470, + 436, + 483 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 470, + 436, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 470, + 436, + 483 + ], + "type": "text", + "content": "3.4. GAN-based upsampler" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 486, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 569 + ], + "type": "text", + "content": "Furthermore, GigaGAN framework can be easily extended to train a text-conditioned super-resolution model, capable of upsampling the outputs of the base GigaGAN generator to obtain high-resolution images at 512px or 4k resolution. By training our pipeline in two separate stages, we can afford a higher capacity 64px base model within the same computational resources." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "In the upsampler, the synthesis network is rearranged to an asymmetric U-Net architecture, which processes the 64px input through 3 downsampling residual blocks, followed by 6 upsampling residual blocks with attention layers to produce the 512px image. There exist skip connections at the same resolution, similar to CoModGAN [78]. The model is trained with the same losses as the base model, as well as the LPIPS Perceptual Loss [77] with respect to the ground truth high-resolution image. Vision-Aided GAN is not used for the upsampler. During training and inference time, we apply moderate Gaussian noise augmentation to reduce the gap between real and GAN-generated images." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10129" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 282, + 247 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 282, + 247 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 282, + 247 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 282, + 247 + ], + "type": "image", + "image_path": "142b37ab53abf3676139c42bacc8015b5c581ec0fd82ce0f6b6549f763f83a6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "type": "text", + "content": "Figure 4. Prompt mixing. GigaGAN can directly control the style with text prompts. Here we generate three outputs using the prompts \"a X on tabletop\", shown in the \"no mixing\" column. Then we re-compute the text embeddings " + }, + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "type": "text", + "content": " and the style codes " + }, + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 250, + 287, + 350 + ], + "type": "text", + "content": " using the new prompts \"a X with the texture of Y on tabletop\", such as \"a cube with the texture of crochet on tabletop\", and apply them to the second half layers of the generator, achieving layout-preserving fine style control. Cross-attention mechanism automatically localizes the style to the object of interest." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 360, + 287, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 444 + ], + "type": "text", + "content": "Our GigaGAN framework becomes particularly effective for the super-resolution task compared to the diffusion-based models, which cannot afford as many sampling steps as the base model at high resolution. The LPIPS regression loss also provides a stable learning signal. We believe that our GAN upsampler can serve as a drop-in replacement for the super-resolution stage of other generative models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 456, + 128, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 128, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 128, + 468 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 641 + ], + "type": "text", + "content": "Systematic, controlled evaluation of large-scale text-to-image synthesis tasks is difficult, as most existing models are not publicly available. Training a new model from scratch would be prohibitively costly, even if the training code were available. Still, we compare our model to recent text-to-image models, such asImagen [59], Latent Diffusion Models (LDM) [58], Stable Diffusion [57], and Parti [73], based on the available information, while acknowledging considerable differences in the training dataset, number of iterations, batch size, and model size. In addition to text-to-image results, we evaluate our model on ImageNet class-conditional generation and unconditional super-resolution in our arXiv, for an apples-to-apples comparison with other methods at a more controlled setting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 715 + ], + "type": "text", + "content": "For quantitative evaluation, we mainly use the Fréchet Inception Distance (FID) [20] for measuring the realism of the output distribution and the CLIP score for evaluating the image-text alignment. All our models are trained and evaluated on A100 GPUs. For more information about training and evaluation of GigaGAN, please refer to the arXiv ver-" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 71, + 543, + 245 + ], + "blocks": [ + { + "bbox": [ + 310, + 71, + 543, + 245 + ], + "lines": [ + { + "bbox": [ + 310, + 71, + 543, + 245 + ], + "spans": [ + { + "bbox": [ + 310, + 71, + 543, + 245 + ], + "type": "image", + "image_path": "26900169eb10564fa8bc186310832a5a6707fcb2ae17fda3049a792fff602c66.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 247, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 304, + 247, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 547, + 304 + ], + "type": "text", + "content": "Figure 5. Style mixing. Our GAN-based architecture retains a disentangled latent space, enabling us to blend the coarse style of one sample with the fine style of another. All outputs are generated with the prompt \"A Toy sport sedan, CG art.\" The corresponding latent codes are spliced together to produce a style-swapping grid." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 315, + 328, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 315, + 328, + 324 + ], + "spans": [ + { + "bbox": [ + 306, + 315, + 328, + 324 + ], + "type": "text", + "content": "sion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 335, + 440, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 335, + 440, + 347 + ], + "spans": [ + { + "bbox": [ + 306, + 335, + 440, + 347 + ], + "type": "text", + "content": "4.1. Text-to-image synthesis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 354, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 484 + ], + "type": "text", + "content": "We proceed to train a larger model by increasing the capacity of the base generator and upsampler to 652.5M and 359.1M, respectively. This results in an unprecedented size of GAN model, with a total parameter count of 1.0B. Table 1 compares the performance of our end-to-end pipeline to various text-to-image generative models [4, 9, 46, 53, 54, 57-59, 73, 80]. Note that there exist differences in the training dataset, the pretrained text encoders, and even image resolutions. For example, GigaGAN initially synthesizes 512px images, which are resized to 256px before evaluation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 485, + 546, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 546, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 546, + 641 + ], + "type": "text", + "content": "Table 1 shows that GigaGAN exhibits a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73]. While our model can be optimized to better match the feature distribution of real images than existing models, the quality of the generated images is not necessarily better (see our arXiv for more samples). We acknowledge that this may represent a corner case of zero-shot FID on COCO2014 dataset and suggest that further research on a better evaluation metric is necessary to improve text-to-image models. Nonetheless, we emphasize that GigaGAN is the first GAN model capable of synthesizing promising images from arbitrary text prompts and exhibits competitive zero-shot FID with other text-to-image models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 649, + 545, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 649, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 649, + 545, + 662 + ], + "type": "text", + "content": "4.2. Super-resolution for large-scale image synthesis" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "We separately evaluate the performance of the GigaGAN upsampler in a text-conditional upsampling task. We combine the Stable Diffusion [57] 4x Upscaler and 2x Latent Upscaler to establish an 8x upscaling model (SD Upscaler)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10130" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 161, + 284, + 297 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 159 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 159 + ], + "type": "text", + "content": "Table 1. Comparison to recent text-to-image models. Model size, total images seen during training, COCO FID-30k, and inference speed of text-image models. * denotes that the model has been evaluated by us. GigaGAN achieves a lower FID than DALL-E 2 [53], Stable Diffusion [57], and Parti-750M [73], while being much faster than competitive methods. GigaGAN and SDv1.5 require 4,783 and 6,250 A100 GPU days, and Imagen and Parti need approximately 4,755 and 320 TPUv4 days for training." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 161, + 284, + 297 + ], + "lines": [ + { + "bbox": [ + 50, + 161, + 284, + 297 + ], + "spans": [ + { + "bbox": [ + 50, + 161, + 284, + 297 + ], + "type": "table", + "html": "
ModelType#Param.#ImagesFID-30k ↓Inf. time
256DALL-E [54]Diff12.0B1.54B27.50-
GLIDE [46]Diff5.0B5.94B12.2415.0s
LDM [58]Diff1.5B0.27B12.639.4s
DALL-E 2 [53]Diff5.5B5.63B10.39-
Imagen [59]Diff3.0B15.36B7.279.1s
eDiff-I [4]Diff9.1B11.47B6.9532.0s
Parti-750M [73]AR750M3.69B10.71-
Parti-3B [73]AR3.0B3.69B8.106.4s
Parti-20B [73]AR20.0B3.69B7.23-
LAFITE [80]GAN75M-26.940.02s
512SD-v1.5* [57]Diff0.9B3.16B9.622.9s
Muse-3B [9]AR3.0B0.51B7.881.3s
GigaGANGAN1.0B0.98B9.090.13s
", + "image_path": "2237155ef50e75687ffd6de191beeb09ed1b1ed073367e117adfd0b527bd3cd0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 357, + 287, + 401 + ], + "blocks": [ + { + "bbox": [ + 47, + 300, + 287, + 355 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 287, + 355 + ], + "type": "text", + "content": "Table 2. Text-conditioned " + }, + { + "bbox": [ + 47, + 300, + 287, + 355 + ], + "type": "inline_equation", + "content": "128 \\rightarrow 1024" + }, + { + "bbox": [ + 47, + 300, + 287, + 355 + ], + "type": "text", + "content": " super-resolution on random 10K LAION samples, compared against unconditional Real-ESRGAN [26] and Stable Diffusion Upscaler [57]. GigaGAN enjoys the fast speed of a GAN-based model while achieving better FID, patch-FID [8], CLIP score, and LPIPS [77]." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 357, + 287, + 401 + ], + "lines": [ + { + "bbox": [ + 50, + 357, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 50, + 357, + 287, + 401 + ], + "type": "table", + "html": "
Model#Param.Inf. timeFID-10k ↓pFID ↓CLIP ↑LPIPS ↓
Real-ESRGAN [26]17M0.06s8.6022.80.3140.363
SD Upscaler [57]846M7.75s9.3941.30.3160.523
GigaGAN693M0.13s1.548.900.3220.274
", + "image_path": "87576b286d7ebbbe2d83cb0647cc311c694bcf7f5fe5478ac6e59c10aa195866.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 403, + 286, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 286, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 286, + 487 + ], + "type": "text", + "content": "We also use the unconditional Real-ESRGAN [26] as another baseline. Table 2 measures the performance of the upsampler on random 10K images from the LAION dataset and shows that our GigaGAN upsampler significantly outperforms the other upsamplers in realism scores (FID and patch-FID [8]), text alignment (CLIP score) and closeness to the ground truth (LPIPS [77])." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 495, + 204, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 204, + 508 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 204, + 508 + ], + "type": "text", + "content": "4.3. Controllable image synthesis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "type": "text", + "content": "In Figure 4, we show that the disentangled style manipulation can be controlled via text inputs. In detail, we can compute the text embedding " + }, + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "type": "inline_equation", + "content": "\\mathbf{t}" + }, + { + "bbox": [ + 46, + 510, + 286, + 594 + ], + "type": "text", + "content": " and style code w using different prompts and apply them to different layers of the generator. This way, we gain not only the coarse and fine style disentanglement but also an intuitive prompt-based maneuver in the style space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": "StyleGANs are known to possess a linear latent space useful for image manipulation, called the " + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": "-space. Likewise, we perform coarse and fine-grained style swapping using style vectors " + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{w}" + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": ". Similar to the " + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": "-space of StyleGAN, Figure 5 illustrates that GigaGAN maintains a disentangled " + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": "-space, suggesting existing latent manipulation techniques of StyleGAN can transfer to GigaGAN. Furthermore, our model possesses another latent space of text embedding " + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{t} = [\\mathbf{t}_{\\mathrm{local}}, \\mathbf{t}_{\\mathrm{global}}]" + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": " prior to " + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 46, + 594, + 286, + 715 + ], + "type": "text", + "content": ", and we explore its potential for image synthesis." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 386, + 144 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 386, + 144 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 386, + 144 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 386, + 144 + ], + "type": "image", + "image_path": "7413441fd6bba24b74121d6224be8dc0a5a49da3ac026d7ed1fc086b4d745480.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 389, + 70, + 463, + 146 + ], + "blocks": [ + { + "bbox": [ + 389, + 70, + 463, + 146 + ], + "lines": [ + { + "bbox": [ + 389, + 70, + 463, + 146 + ], + "spans": [ + { + "bbox": [ + 389, + 70, + 463, + 146 + ], + "type": "image", + "image_path": "8cca0355b05b74ec5cc64b364b981bafff0d0a3e7a1566f606f171f4b4c2eb54.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 465, + 71, + 539, + 146 + ], + "blocks": [ + { + "bbox": [ + 465, + 71, + 539, + 146 + ], + "lines": [ + { + "bbox": [ + 465, + 71, + 539, + 146 + ], + "spans": [ + { + "bbox": [ + 465, + 71, + 539, + 146 + ], + "type": "image", + "image_path": "5e05d970fb7214f52aa42de5931470719f09f638bdc029724793011273aec152.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 145, + 386, + 221 + ], + "blocks": [ + { + "bbox": [ + 310, + 145, + 386, + 221 + ], + "lines": [ + { + "bbox": [ + 310, + 145, + 386, + 221 + ], + "spans": [ + { + "bbox": [ + 310, + 145, + 386, + 221 + ], + "type": "image", + "image_path": "25667b58756f0aaefdccc4dedf573b23811579a2b7dbec901058417c7a7aa25c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 223, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 300 + ], + "type": "text", + "content": "Figure 6. Failure cases. Our outputs with the same prompts as DALL-E 2. Each column conditions on \"a teddy bear on a skateboard in Times Square\", \"a Vibrant portrait painting of Salvador Dali with a robotic half face\", and \"A close up of a handpalm with leaves growing from it\". Compared to production-grade models such as DALL-E 2, our model exhibits limitations in realism and compositionality. See our website for uncurated comparisons." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 388, + 147, + 462, + 221 + ], + "blocks": [ + { + "bbox": [ + 388, + 147, + 462, + 221 + ], + "lines": [ + { + "bbox": [ + 388, + 147, + 462, + 221 + ], + "spans": [ + { + "bbox": [ + 388, + 147, + 462, + 221 + ], + "type": "image", + "image_path": "f988f885ea684a3ed01a3d67b22e481e26c6e1a7a2b5faff8b5e4b5cd72e88b6.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 464, + 147, + 539, + 221 + ], + "blocks": [ + { + "bbox": [ + 464, + 147, + 539, + 221 + ], + "lines": [ + { + "bbox": [ + 464, + 147, + 539, + 221 + ], + "spans": [ + { + "bbox": [ + 464, + 147, + 539, + 221 + ], + "type": "image", + "image_path": "9eea9ffbf5062371ced9b689d543166340163b47e9806413f5ca9564cc3e6ba6.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 304, + 460, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 460, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 460, + 316 + ], + "type": "text", + "content": "5. Discussion and Limitations" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 320, + 545, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 545, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 545, + 428 + ], + "type": "text", + "content": "Our experiments provide a conclusive answer about the scalability of GANs: our new architecture can scale up to model sizes that enable text-to-image synthesis. However, the visual quality of our results is not yet comparable to production-grade models like DALL-E 2. Figure 6 shows several instances where our method fails to produce high-quality results when compared to DALL-E 2, in terms of photorealism and text-to-image alignment for the same input prompts used in their paper." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 429, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 548 + ], + "type": "text", + "content": "Nevertheless, we have tested capacities well beyond what is possible with a naïve approach and achieved competitive results with autoregressive and diffusion models trained with similar resources while being orders of magnitude faster and enabling latent interpolation and stylization. Our GigaGAN architecture opens up a whole new design space for large-scale generative models and brings back key editing capabilities that became challenging with the transition to autoregressive and diffusion models. We expect our performance to improve with larger models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments. We thank Simon Niklaus, Alexandru Chiculita, and Markus Woodson for building the distributed training pipeline. We thank Nupur Kumari, Gaurav Parmar, Bill Peebles, Phillip Isola, Alyosha Efros, and Joonghyuk Shin for their helpful comments. We also want to thank Chenlin Meng, Chitwan Sahara, and Jiahui Yu for answering many questions about their fantastic work. We thank Kevin Duarte for discussions regarding upsampling beyond 4K. Part of this work was done while Minguk Kang was an intern at Adobe Research. Minguk Kang and Jaesik Park were supported by IITP grant funded by the government of South Korea (MSIT) (POSTECH GSAI: 2019-0-01906 and Image restoration: 2021-0-00537)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10131" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 718 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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In The AAAI Conference on Artificial Intelligence, 2007. 3" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10134" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_content_list.json b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e49df939b50f7ac5478c97b88df98cd0aad409c6 --- /dev/null +++ b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_content_list.json @@ -0,0 +1,1650 @@ +[ + { + "type": "text", + "text": "ScanDMM: A Deep Markov Model of Scanpath Prediction for $360^{\\circ}$ Images", + "text_level": 1, + "bbox": [ + 107, + 130, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiangjie Sui $^{1}$ , Yuming Fang $^{1*}$ , Hanwei Zhu $^{2}$ , Shiqi Wang $^{2}$ , Zhou Wang $^{3}$ $^{1}$ Jiangxi University of Finance and Economics, $^{2}$ City University of Hong Kong, $^{3}$ University of Waterloo \nhttps://github.com/xiangjieSui/ScanDMM", + "bbox": [ + 200, + 179, + 767, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 312, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scanpath prediction for $360^{\\circ}$ images aims to produce dynamic gaze behaviors based on the human visual perception mechanism. Most existing scanpath prediction methods for $360^{\\circ}$ images do not give a complete treatment of the time-dependency when predicting human scanpath, resulting in inferior performance and poor generalizability. In this paper, we present a scanpath prediction method for $360^{\\circ}$ images by designing a novel Deep Markov Model (DMM) architecture, namely ScanDMM. We propose a semantics-guided transition function to learn the nonlinear dynamics of time-dependent attentional landscape. Moreover, a state initialization strategy is proposed by considering the starting point of viewing, enabling the model to learn the dynamics with the correct \"launcher\". We further demonstrate that our model achieves state-of-the-art performance on four $360^{\\circ}$ image databases, and exhibit its generalizability by presenting two applications of applying scanpath prediction models to other visual tasks - saliency detection and image quality assessment, expecting to provide profound insights into these fields.", + "bbox": [ + 75, + 318, + 473, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 651, + 207, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$360^{\\circ}$ images, also referred to as omnidirectional, sphere or virtual reality (VR) images, have been a popular type of visual data in many applications, providing us with immersive experiences. Nevertheless, how people explore virtual environments in $360^{\\circ}$ images has not been well understood. The scanpath prediction model that aims at generating realistic gaze trajectories has obtained increasing attention due to its significant influence in understanding users' viewing behaviors in VR scenes, as well as in developing VR rendering, display, compression, and transmission [51].", + "bbox": [ + 75, + 676, + 468, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scanpath prediction has been explored for many years in 2D images [29]. However, $360^{\\circ}$ images are different greatly from 2D images, as a larger space is offered to interact with", + "bbox": [ + 76, + 829, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b5d535c60e89315649dd7e18e90e57b3a02c69fc1fd2a7551a0364150fc510f3.jpg", + "image_caption": [ + "Figure 1. Existing scanpath prediction models for $360^{\\circ}$ images could be classified to two types: saliency-based models [2, 70, 71] and generative models [42, 43]. The scanpaths produced by saliency-based models, taking the study [2] as an example, commonly exhibits unstable behavior with large displacements and scarce focal regions. Generative models, taking the study [43] as an example, shows less attention to regions of interest. The proposed ScanDMM can produce more realistic scanpaths that focus on regions of interests." + ], + "image_footnote": [], + "bbox": [ + 524, + 285, + 869, + 592 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "- humans are allowed to use both head and gaze movements to explore viewpoints of interest in the scene. In such a case, viewing conditions, e.g., the starting point of viewing, has an important impact on humans' scanpaths [20, 21, 52], and leads to complex and varied scanpaths among humans. This is inherently different from what happens in 2D visuals since humans can directly guide their attention to the regions of interest. Therefore, scanpath prediction for $360^{\\circ}$ images is a more complex task.", + "bbox": [ + 496, + 748, + 890, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current $360^{\\circ}$ image scanpath prediction methods could", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author (email: fa0001ng@e.ntu.edu.sg)", + "bbox": [ + 94, + 886, + 392, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6989", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "be roughly divided into two categories: saliency-based [2, 70, 71] and generative methods [42, 43]. The basic idea of the former one is to sample predicted gaze points from a saliency map. The performance of such methods is highly dependent on that of the saliency maps. Furthermore, constructing a satisfactory sampling strategy to account for time-dependent visual behavior is non-trivial – the results of SaltiNet [2] exhibit unstable behavior with large displacements and scarce focal regions (see Fig. 1). The latter group of methods utilizes the advance of generative models, e.g., Generative Adversarial Network (GAN), to predict realistic scanpaths. However, such methods show less attention to regions of interests (see Fig. 1). In addition, the GAN-based methods are less flexible in determining the length of scanpaths and commonly suffer from unstable training.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "None of above-mentioned studies give a complete treatment of the time-dependency of viewing behavior, which is critical for modeling dynamic gaze behaviors in $360^{\\circ}$ images. For time-series data, a popular approach is to leverage sequential models, e.g., recurrent neural networks (RNNs), as exemplified in gaze prediction for $360^{\\circ}$ videos [17, 35, 45]. However, such deterministic models are prone to overfitting, particularly on small $360^{\\circ}$ databases. More importantly, they typically make simplistic assumptions, e.g., one choice is to concatenate the saliency map to the model's hidden states [17, 45], which assumes that the network learns how the states evolve by learning from saliency maps. Nevertheless, the neuroscience research [62] reveals that in addition to top-down and bottom-up features, prior history and scene semantics are essential sources for guiding visual attention. Moreover, to be identified as interests or rejected as distractors, items must be compared to target templates held in memory [62]. Inspired by this, we argue that humans' scanpaths in $360^{\\circ}$ scenes are complex nonlinear dynamic attentional landscapes over time as a function of interventions of scene semantics on visual working memory. We present a probabilistic approach to learning the visual states that encode the time-dependent attentional landscape by specifying how these states evolve under the guidance of scene semantics and visual working memory. We instantiate our approach in the Deep Markov Model (DMM) [28], namely ScanDMM. Our contributions can be summarized as follows:", + "bbox": [ + 75, + 318, + 472, + 739 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel method for time-dependent visual attention modeling for $360^{\\circ}$ images. Specifically, we model the mechanism of visual working memory by maintaining and updating the visual state in the Markov chain. Furthermore, a semantics-guided transition function is built to learn the nonlinear dynamics of the states, in which we model the interventions of scene semantics on visual working memory.", + "- We propose a practical strategy to initialize the visual state, facilitating our model to focus on learning the" + ], + "bbox": [ + 94, + 746, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "dynamics of states with correct \"loader\", as well as enabling us to assign a specific starting point for scanpath generation. Moreover, ScanDMM is capable of producing 1,000 variable-length scanpaths within one second, which is critical for real-world applications.", + "bbox": [ + 529, + 90, + 890, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We apply the proposed ScanDMM to two other computer vision tasks - saliency detection and image quality assessment, which demonstrates our model equips with strong generalizability and is expected to provide insights into other vision tasks.", + "bbox": [ + 517, + 171, + 890, + 247 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 258, + 640, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Visual Attention for 2D Images", + "text_level": 1, + "bbox": [ + 500, + 284, + 774, + 300 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modeling Spatial Distribution of Gazes. Visual attention depends on two distinct types of attentional mechanisms: bottom-up and top-down mechanisms [10]. The performance of classic saliency detection methods for 2D images primarily depends on bottom-up features, e.g., colour, luminance, contrast and texture, for modeling visual attention [15, 18, 19, 24]. Although the studies [40, 69] incorporate top-down features, e.g., human faces and texts, there are still obstacles in combining bottom-up and top-down visual features. Deep learning methods [36, 57, 59, 68] take advantage of large-scale databases and well-established convolutional neural networks (CNNs), and they have achieved remarkable success.", + "bbox": [ + 496, + 306, + 890, + 502 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modeling Dynamic Gaze Behaviors. The studies in neuroscience suggest that scanpath generation can be an iterative process: while the eye fixates on an image location, the brain selects the next location to look at [26, 48]. Biologically inspired methods model such mechanism in different ways, e.g., considering the inhibition-of-return mechanism [25, 49, 53], maintaining the residual perceptual information maps [58], modeling the retina transformation [1], and utilizing low-level semantic information [55, 67]. Another class of methods is statistically inspired for modeling dynamic gaze behaviors. A typical approach is to model fixation distributions by the product of the saliency map and the previous fixation location [4, 5, 13, 30, 33, 63]. Some studies regard fixation distributions as Gaussian densities, and model scanpath by leveraging component analysis [54] or hidden markov models [12]. Different from interpretable models, fitting the data using deep generative models can also achieve competitive performance [9, 42, 66].", + "bbox": [ + 496, + 506, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Visual Attention for $360^{\\circ}$ Images", + "text_level": 1, + "bbox": [ + 500, + 786, + 785, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modeling Spatial Distribution of Gazes. Saliency detection of $360^{\\circ}$ images is more challenging compared with 2D images, mainly due to complex viewing behaviors and insufficient available data for $360^{\\circ}$ images. According to the space that the model is applied to, saliency detection models of $360^{\\circ}$ images can be grouped into two categories: 2D-", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6990", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "plane-based methods [2, 22, 38] and worldview-based methods [8, 34, 44, 64]. The former models visual attention by using hand-craft features [22, 38] or data-driven features [2] extracted from the distorted (caused by the equirectangular projection) 2D plane, while the latter is designed by applying well-established 2D visual saliency detection methods on worldview plane with less distortions.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Modeling Dynamic Gaze Behaviors. Current scanpath prediction models of $360^{\\circ}$ images can be classified to two types: saliency-based models [2, 3, 70, 71] and generative models [42, 43]. The former first produces the saliency map by extracting low-level and high-level features [70, 71] or learned features from data [2, 3]. Then, scanpaths are sampled from the saliency map by maximizing information gains [70, 71] or using a stochastic approach [2, 3]. The latter group of methods models scanpaths by learning from human data. PathGAN [42] is a generative model originally developed for 2D images, and it is fine-tuned on Salient360! [47] database to be applied on $360^{\\circ}$ images. However, the generated scanpaths lose sphere properties (e.g., longitudinal continuities) due to the assumption that a $360^{\\circ}$ image is similar to a traditional 2D image. To address this problem, ScanGAN [43] propose to learn the image and coordinate representations by using sphere convolutional neural network (S-CNN) [11] and CoordConv layer [39], respectively. Besides, a loss function that measures the spherical distance is proposed for model training.", + "bbox": [ + 75, + 199, + 472, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 517, + 287, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Definition", + "text_level": 1, + "bbox": [ + 76, + 542, + 261, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In $360^{\\circ}$ environment, a human scanpath could be defined as a time series of gaze points $\\mathbf{x}_{1:T} = (\\mathbf{x}_1,\\mathbf{x}_2,\\dots,\\mathbf{x}_T)\\in \\mathbb{R}^{3\\times T}$ , where $\\mathbf{x}_t$ is a three-dimensional coordinate $(x_{t},y_{t},z_{t})$ . Given a $360^{\\circ}$ image, a scanpath prediction model aims at producing realistic scanpaths $\\widetilde{\\mathbf{x}}_{1:T}$ based on the human visual perception mechanism. This paper presents a probabilistic method - ScanDMM, for scanpath prediction for $360^{\\circ}$ images, as shown in Fig 2. We model the mechanism of visual working memory by maintaining a set of visual states $\\mathbf{z}_{1:T} = (\\mathbf{z}_1,\\mathbf{z}_2,\\dots,\\mathbf{z}_T)\\in \\mathbb{R}^{n\\times T}$ that encodes the dynamic attentional landscapes over time ( $n$ is the dimension of the state space). Basically, the ScanDMM predicts a scanpath using the following generative process:", + "bbox": [ + 75, + 566, + 472, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transition: $\\mathbf{z}_t\\sim p_{\\theta_t}(\\mathbf{z}_t|\\mathbf{z}_{t - 1}),$ (1)", + "bbox": [ + 99, + 791, + 468, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Emission: $\\widetilde{\\mathbf{x}}_t\\sim p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t),\\quad t = 1,2,\\dots,T$ (2)", + "bbox": [ + 99, + 810, + 468, + 828 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sim$ means the sample operation. $p_{\\theta_t}(\\mathbf{z}_t|\\mathbf{z}_{t - 1})$ denotes the transition probabilities between the visual states, and $p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t)$ denotes the emission probabilities that describe how the visual state generates a gaze point. Let $\\theta$ denotes all", + "bbox": [ + 75, + 839, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bbd462bd7357f4fab27acc33ab6fa07ef4fe66c10a4bd3eba75e95c89d682a64.jpg", + "image_caption": [ + "Figure 2. An illustration of the proposed ScanDMM. Noting that the scene semantic $\\hat{s}$ is deterministic for an image." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 270 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "parameters involved in the ScanDMM. We approximate the realistic scanpaths by maximizing the log-likelihood function $\\log p(\\mathbf{x})$ (we omit subscripts here for simplicity):", + "bbox": [ + 496, + 332, + 892, + 378 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\max \\log p _ {\\theta} (\\mathbf {x}) = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} p _ {\\theta} (\\mathbf {x}) \\\\ = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\frac {p _ {\\theta} (\\mathbf {x} , \\mathbf {z})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\tag {3} \\\\ = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\frac {p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) p _ {\\theta_ {t}} (\\mathbf {z})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 385, + 890, + 473 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The posterior $p_{\\theta}(\\mathbf{z}|\\mathbf{x})$ can be approximated by using Variational Inference [61], which seeks to derive a distribution $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ that is parameterized by neural networks, s.t. $q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\approx p_{\\theta}(\\mathbf{z}|\\mathbf{x})$ . Based on Jensen's inequality, $f(\\mathbb{E}[x]) \\geqslant \\mathbb{E}[f(x)]$ where $f$ is a concave function, we adopt the Evidence Lower Bound of $\\log p_{\\theta}(\\mathbf{x})$ as the loss function $\\mathcal{L}(\\theta; \\phi; \\mathbf{x})$ to be maximized:", + "bbox": [ + 496, + 479, + 890, + 585 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\log p _ {\\theta} (\\mathbf {x}) \\geqslant \\mathbb {E} _ {q _ {\\phi}} \\log \\frac {p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) p _ {\\theta_ {t}} (\\mathbf {z})}{q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\\\ = \\mathbb {E} _ {q _ {\\phi}} \\left[ \\log p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) + \\log p _ {\\theta_ {t}} (\\mathbf {z}) - \\log q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\right] \\\\ = \\underbrace {\\mathbb {E} _ {q _ {\\phi}} [ \\log p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) ]} _ {\\text {R e c o n s t r u c t i o n}} - \\underbrace {\\mathrm {K L} (q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p _ {\\theta_ {t}} (\\mathbf {z}))} _ {\\text {R e g u l a r i z a t i o n}} \\\\ := \\mathcal {L} (\\theta ; \\phi ; \\mathbf {x}), \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 593, + 890, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{KL}(\\cdot \\| \\cdot)$ denotes the Kullback-Leibler (KL) divergence. The reconstruction term evaluates the model's accuracy and the regularization term enforces the closeness between $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ and $p_{\\theta_t}(\\mathbf{z})$ . The loss function also can be interpreted as the summation of transition $p_{\\theta_t}(\\mathbf{z})$ , emission $p_{\\theta_e}(\\mathbf{x}|\\mathbf{z})$ and inference $q_{\\phi}(\\mathbf{z}|\\mathbf{x})$ . In the following section, we describe how we design the three functions tailored for scanpath prediction for $360^{\\circ}$ images.", + "bbox": [ + 496, + 718, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. State Initialization", + "text_level": 1, + "bbox": [ + 500, + 847, + 679, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different from the common strategy that simply sets the initial state to zero vector [28] or random vector [27], we", + "bbox": [ + 498, + 869, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6991", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "propose a practical strategy considering the starting points of scanpaths. The motivation derives from recent studies [20, 21, 52], which reveal that the starting point of viewing has an important influence on the scanpaths. To make our model better focus on learning the dynamics of visual states with the correct \"loader\" rather than random scratch, in the training stage, we directly use the starting point $\\mathbf{x}_1$ to initialize $\\mathbf{z}_0$ :", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {0} = \\mathbf {F} \\left(\\hat {\\mathbf {z}} _ {0}, \\mathbf {x} _ {1}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 215, + 220, + 468, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{\\mathbf{z}}_0$ is a learnable parameter. $\\mathbf{F}$ denotes linear neural networks (see Fig. 2 for details). An advantage of such configuration is that we can assign a specific starting point for scanpath generation, which is flexible and even crucial in some visual tasks, e.g., image quality assessment (see Section 5.2). Notably, to fairly compare ScanDMM with other scanpath prediction models, in the model evaluation, we randomly sample the starting points from an Equator Bias Map that covers the whole longitude and $20\\%$ latitude.", + "bbox": [ + 75, + 244, + 472, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Transition Function", + "text_level": 1, + "bbox": [ + 76, + 388, + 266, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Transition function $p_{\\theta_t}(\\mathbf{z_t}|\\mathbf{z}_{t - 1})$ controls the dynamics of the visual states, in which the history state $\\mathbf{z}_{t - 1}$ functions as visual working memory that maintains the history attentional landscape. Inspired by the recent study in neuroscience [62], we propose to learn the dynamics guided by scene semantics. Due to the space-varying distortions inherent to equirectangular projections, we choose to extract scene semantics $\\hat{\\mathbf{s}}\\in \\mathbb{R}^{n\\times 1}$ using S-CNN [11]. Moreover, by considering the spatial locations of semantic features are critical for scanpath prediction, we utilize the CoordConv strategy [39] to give convolutions access to their own input coordinates, as suggested in [43]. Given the scene semantics $\\hat{\\mathbf{s}}$ and the history visual state $\\mathbf{z}_{t - 1}$ , transition function samples $\\mathbf{z}_t$ from the following Gaussian densities:", + "bbox": [ + 75, + 412, + 472, + 623 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {z} _ {t} \\sim \\mathcal {N} \\left(\\mu_ {t} ^ {z}, \\sigma_ {t} ^ {z}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 632, + 468, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_t^z$ and $\\sigma_t^z\\in \\mathbb{R}^{n\\times 1}$ are the mean and scale of Gaussian densities describing an attentional landscape of the visual state $\\mathbf{z}_t$ .", + "bbox": [ + 75, + 657, + 468, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we present how we produce the two Gaussian parameters. Firstly, we compute the new underlying gaze distributions $\\hat{\\mathbf{z}}_t$ by", + "bbox": [ + 75, + 703, + 468, + 748 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {z}} _ {t} = \\mathbf {W} _ {z} ^ {t} (\\mathbf {z} _ {t - 1} \\oplus \\hat {\\mathbf {s}}) + \\mathbf {b} _ {z} ^ {t}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 755, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\oplus$ is the concatenate operation, $\\mathbf{W}_z^t\\in \\mathbb{R}^{n\\times 2n}$ and $\\mathbf{b}_z^t\\in \\mathbb{R}^{n\\times 1}$ are learnable parameters of the neural networks. Inspired by the Long Short-Term Memory [23], we introduce the uncertainty weighting for adaptively determining how much components of the previous visual state $\\mathbf{z}_{t - 1}$ to be updated:", + "bbox": [ + 75, + 780, + 472, + 872 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {t} = \\sigma \\left(\\mathbf {W} _ {\\alpha} ^ {t} \\mathbf {z} _ {t - 1} + \\mathbf {b} _ {\\alpha} ^ {t}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 878, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{t}$ is an uncertainty weighting determined by the history state $\\mathbf{z}_{t - 1}$ , and $\\sigma$ denotes the sigmoid function. $\\mathbf{W}_{\\{\\alpha ,\\sigma \\}}^{t}\\in \\mathbb{R}^{n\\times n}$ and $\\mathbf{b}_{\\{\\alpha ,\\sigma \\}}^t\\in \\mathbb{R}^{n\\times 1}$ are learnable parameters of the neural networks. Finally, the two Gaussian parameters, $\\mu_t^z$ and $\\sigma_t^z$ , are computed by:", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {t} ^ {z} = \\alpha_ {t} \\hat {\\mathbf {z}} _ {t} + (1 - \\alpha_ {t}) \\mathbf {z} _ {t - 1}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 174, + 890, + 191 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {t} ^ {z} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {t} \\hat {\\mathbf {z}} _ {t} + \\mathbf {b} _ {\\sigma} ^ {t}\\right)\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 193, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Emission Function", + "text_level": 1, + "bbox": [ + 500, + 218, + 679, + 232 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Emission function $p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t)$ describes how a gaze point $\\widetilde{\\mathbf{x}}_t$ is generated from the visual state $\\mathbf{z}_t$ . As a gaze point is parameterized as a three-dimensional coordinate, we model the emission process by sampling $\\widetilde{\\mathbf{x}}_t$ from the three-dimensional Gaussian densities that are parameterized by $\\mu_t^x$ and $\\sigma_t^x\\in \\mathbb{R}^{3\\times 1}$ :", + "bbox": [ + 496, + 241, + 890, + 332 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathbf {x}} _ {t} \\sim \\mathcal {N} \\left(\\mu_ {t} ^ {x}, \\sigma_ {t} ^ {x}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 633, + 339, + 890, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_t^x$ and $\\sigma_t^x$ are determined by the current visual state $\\mathbf{z}_t$ :", + "bbox": [ + 496, + 364, + 890, + 392 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {t} ^ {x} = 2 \\sigma \\left(\\mathbf {W} _ {\\mu} ^ {e} \\mathbf {z} _ {t} + \\mathbf {b} _ {\\mu} ^ {e}\\right) - 1, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 393, + 890, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {t} ^ {x} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {e} \\mathbf {z} _ {t} + \\mathbf {b} _ {\\sigma} ^ {e}\\right)\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 415, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathbf{W}_{\\{\\mu, \\sigma\\}}^e \\in \\mathbb{R}^{3 \\times n}$ and $\\mathbf{b}_{\\{\\mu, \\sigma\\}}^e \\in \\mathbb{R}^{3 \\times 1}$ are learnable parameters of the neural networks.", + "bbox": [ + 496, + 435, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Inference", + "text_level": 1, + "bbox": [ + 500, + 474, + 609, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference for a latent state can be made using information from past and future true observations [28], i.e., GT gaze points in this study. In other words, the goal of inference is to provide an approximation to the exact posterior $p_{\\theta}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T})$ . Here, we leverage the Variational Inference [61] to approximate $p_{\\theta}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T})$ with a tractable family of conditional distributions $q_{\\phi}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T})$ :", + "bbox": [ + 496, + 497, + 890, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {\\phi} \\left(\\mathbf {z} _ {1: T} \\mid \\mathbf {x} _ {1: T}\\right) = \\prod_ {t = 1} ^ {T} q _ {\\phi} \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}, \\mathcal {H} \\left(\\mathbf {x} _ {t: T}\\right)\\right) \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 612, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l l} \\text {s . t .} & q _ {\\phi} (\\mathbf {z} _ {t} | \\mathbf {z} _ {t - 1}, \\mathcal {H} (\\mathbf {x} _ {t: T})) \\sim \\mathcal {N} (\\mu_ {t} ^ {i}, \\sigma_ {t} ^ {i}), \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 655, + 823, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{H}(\\cdot) \\in \\mathbb{R}^{m \\times 1}$ is the variational parameter computed by mapping a variable-length sequences $\\mathbf{x}_{t:T}$ to its $m$ -dimensional space. We implement this by using RNN [28]. The Gaussian parameters $\\mu_t^i$ and $\\sigma_t^i \\in \\mathbb{R}^{n \\times 1}$ are produced by the following process:", + "bbox": [ + 496, + 680, + 890, + 756 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {t} = \\frac {1}{2} \\left(\\left(\\mathbf {W} _ {c} ^ {i} \\mathbf {z} _ {t - 1} + \\mathbf {b} _ {c} ^ {i}\\right) + \\mathcal {H} \\left(\\mathbf {x} _ {t: T}\\right)\\right), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 763, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {t} ^ {i} = \\mathbf {W} _ {\\mu} ^ {i} \\mathcal {C} _ {t} + \\mathbf {b} _ {\\mu} ^ {i}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 794, + 890, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {t} ^ {i} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {i} \\mathcal {C} _ {t} + \\mathbf {b} _ {\\sigma} ^ {i}\\right)\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 814, + 890, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{C}_t$ denotes the combined feature of the previous state $\\mathbf{z}_{t - 1}$ and the RNN hidden state $\\mathcal{H}(\\mathbf{x}_{t:T})$ . $\\mathbf{W}_c^i\\in \\mathbb{R}^{n\\times m}$ , $\\mathbf{W}_{\\{\\mu ,\\sigma \\}}^i\\in \\mathbb{R}^{n\\times m}$ , $\\mathbf{b}_c^i\\in \\mathbb{R}^{m\\times 1}$ , and $\\mathbf{b}_{\\{\\mu ,\\sigma \\}}^i\\in \\mathbb{R}^{n\\times 1}$ are learnable parameters of the neural networks.", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6992", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 89, + 209, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present the experimental results to validate the effectiveness of the proposed ScanDMM. We refer the interested readers to the supplementary file for more details on ScanDMM, datasets, and qualitative comparisons.", + "bbox": [ + 75, + 114, + 468, + 176 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 185, + 171, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use four $360^{\\circ}$ image databases to conduct experiments, including Sitzmann [51], Salient360! [47], AOI [65], and JUFE [20]. Sitzmann [51] database contains 22 images and 1,980 scanpaths, 19 of 22 images are used for training, and the remaining are used for validation. Salient360! [47] database contains two sets: training and benchmark sets. In this paper, we consistently use its training set that contains 85 images and 3,036 scanpaths for evaluation since its benchmark set is not publicly available. AOI [65] database contains 600 high-resolution $360^{\\circ}$ images and 18,000 scanpaths. JUFE [20] database is constructed for studying $360^{\\circ}$ image quality assessment, containing 1,032 images and 30,960 scanpaths. For the latter two databases, we randomly select $20\\%$ images for model evaluation. To obtain Ground-Truth (GT) scanpaths for model training and evaluation, we sample the raw scanpaths at $1\\mathrm{Hz}$ on each database. Noting that the scanpaths of the AOI database had been processed by the authors, so we did not make any post-processing.", + "bbox": [ + 75, + 208, + 470, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 505, + 266, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We train the proposed model using Sitzmann [51] database. To augment data, we longitudinally shift the $360^{\\circ}$ images and adjust their scanpaths accordingly [43], which yields $19 \\times 6 = 114$ images for training. Before the panoramic images are fed into the network, they are resized as (128, 256). The learning rate is set to $3e-4$ and is decreased by a factor of 0.99998 at each epoch. The dimensions of the visual state and RNN hidden state are set to 100 and 600, respectively. The network was trained for 500 epochs.", + "bbox": [ + 75, + 527, + 468, + 679 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We use three metrics to evaluate the performance of $360^{\\circ}$ scanpath prediction models, including the Levenshtein distance (LEV), dynamic time warping (DTW), and recurrence measure (REC), as suggested in [16,43]. Generally, lower LEV/DTW values and higher REC values mean better prediction performance. For an image with $N$ GT scanpaths $\\mathbf{x}^{1:N}$ , we generate $\\hat{N} = N$ fake scanpaths $\\widetilde{\\mathbf{x}}^{1:\\hat{N}}$ for comparison. The lengths of generated scanpaths are equal to that of the viewing time $^1$ . To compare a set of GT scanpaths $\\mathbf{x}^{1:N}$ to another set of predicted scanpaths $\\widetilde{\\mathbf{x}}^{1:\\hat{N}}$ , taking LEV as an example, we choose to compute each metric for all possible pairwise comparisons", + "bbox": [ + 75, + 691, + 468, + 878 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and average the results:", + "bbox": [ + 500, + 90, + 656, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {m L E V} = \\frac {1}{N \\hat {N}} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {\\hat {N}} \\operatorname {L E V} \\left(\\mathbf {x} ^ {i}, \\widetilde {\\mathbf {x}} ^ {j}\\right). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 116, + 890, + 161 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To reduce the evaluation bias caused by the randomly generated scanpaths, we test each generative model with 10 times and average these 10 results to obtain the final performance. To make the results more comparable and interpretable, for each metric, we compute the human consistency [43] as a realistic upper bound for model performance (see Human in Tab. 1). Specifically, we compare each GT scanpath against all the other ones and average the results. We also compare to the results of a chance model – produce scanpaths by adding a random Brownian motion to the previous positions (see Random walk in Tab. 1).", + "bbox": [ + 496, + 169, + 890, + 335 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c8239e5937688a6e34f99487cebdc95a05c12afd39df44d0131357f59d3453a9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]Random walk48.9422232.9872.669
CLE [4]45.1761967.2863.130
DeepGaze III [30]46.4241992.8593.082
SaliTiNet [2]51.3702305.0991.564
ScanGAN [43]45.2701951.8483.241
ScanDMM44.9661965.4273.475
Human41.1881836.9866.345
Salient360! [47]Random walk40.8022231.6812.744
CLE [4]39.7741714.4093.323
DeepGaze III [30]40.0061742.3512.588
SaliTiNet [2]40.8481855.4772.305
ScanGAN [43]38.9321721.7113.099
ScanDMM37.2721528.5923.576
Human35.0841382.5905.202
AOI [65]Random walk13.696711.5162.993
CLE [4]12.865547.8923.617
DeepGaze III [30]13.155558.4452.892
SaliTiNet [2]14.695596.5442.244
ScanGAN [43]12.889552.4463.750
ScanDMM12.127537.5044.024
Human9.243389.4776.228
JUFE [20]Random walk24.0391193.7253.109
CLE [4]24.8441172.1503.013
DeepGaze III [30]24.1291104.8482.774
SaliTiNet [2]26.0741287.1441.540
ScanGAN [43]24.2091094.9783.075
ScanDMM23.0911086.0144.329
Human18.3061038.8807.745
", + "bbox": [ + 501, + 347, + 893, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Performance of scanpath prediction models on different databases. The best performance is highlighted.", + "bbox": [ + 498, + 715, + 890, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Performance Comparison", + "text_level": 1, + "bbox": [ + 500, + 758, + 735, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model Selection. We compare ScanDMM to four state-of-the-art scanpath prediction models: CLE [5], DeepGaze III [30], SaltiNet [2], and ScanGAN [43]. The first two models are built for traditional images, and the latter two are tailored for $360^{\\circ}$ images. For DeepGaze III and SaltiNet with larger sizes, we choose to use the pre-trained weights provided by the corresponding authors to avoid overfitting", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1 For ScanGAN, we cut the produced scanpaths to the required lengths.", + "bbox": [ + 94, + 886, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6993", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5b3912b9dc1b4c5d4cbf1880f43e0bd1c056fbd8982c482600ea07d386b236e2.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison to different scanpath prediction models for four different scenes. From left to right: scanpath samples obtained by a observer, scanpath results obtained by CLE [4], DeepGaze III [30], SaltiNet [2], ScanGAN [43], and the proposed model. From top to bottom: the Room from Sitzmann [51] database, the Museum from Salient360! [47] database, the Party from AOI [65] database, and the Park from JUFE [20] database." + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 885, + 297 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2de3bac190fae289035f64c6865285712c4652b8a5f41bb063f78ce24c6cc9f2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodParamtersRunning Time
CLE [4]-≈ 39 seconds
DeepGaze III [30]78.9MB≈ 11 minutes
SaliNet [2]103.6MB≈ 49 minutes
ScanGAN [43]33.9MB0.987 seconds
ScanDMM18.7MB0.737 seconds
", + "bbox": [ + 76, + 382, + 470, + 467 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on small $360^{\\circ}$ image datasets. PathGAN [42] and Zhu et al. [71] are the other two popular scanpath prediction methods for $360^{\\circ}$ images. Nevertheless, we do not include them in comparison since the study [43] had shown their failures in producing realistic scanpaths for $360^{\\circ}$ images.", + "bbox": [ + 75, + 556, + 468, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Accuracy Comparison. Table 1 and Fig. 3 show that our model could provide results closer to the human scanpaths. In Fig. 3, we observe that CLE and DeepGaze III exhibit large displacements that might caused by the treatment that regarding $360^{\\circ}$ images as 2D images. Saliency-based scanpath prediction model, exhibits unstable behavior with large displacements and scarce focal regions (e.g., referring to Room or Park of Fig. 3), leading to worse results than the Random walk model. The proposed model could better focus on the salient objects in scenes than ScanGAN (e.g., referring to Museum, Party or Park of Fig. 3).", + "bbox": [ + 75, + 648, + 468, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Efficiency Comparison. We also compare the efficiency in terms of the model size and running time. The results are shown in Table 2. Our model has the smallest size - 18.7MB, which is about $1/5$ of the size of SaliNet. For running time comparison, we record the time cost to gen", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8fd884279dfd1f6d5b3ea2bf82e66640707b70a1b0512e8fcf937aa69e765d86.jpg", + "table_caption": [ + "Table 2. Efficiency comparison in terms of the model size and running time (computed by the time cost of producing 1,000 scanpaths). Noting that CLE is a traditional model that built on saliency maps, we only count the time to produce the scanpaths." + ], + "table_footnote": [], + "table_body": "
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]ScanDMM(I)45.9491996.4563.091
ScanDMM(S)46.8002098.4122.833
ScanDMM(IS)46.4892011.1572.904
ScanDMM44.9661965.4273.475
Salient360! [47]ScanDMM(I)38.3401698.5173.168
ScanDMM(S)39.1941787.6742.744
ScanDMM(IS)38.9581720.8942.853
ScanDMM37.2721528.5923.576
", + "bbox": [ + 500, + 382, + 897, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Ablation study. The effectiveness of our designs is well justified.", + "bbox": [ + 498, + 518, + 890, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "erate 1,000 scanpaths for a given image. The results show that our model has the fastest inference speed - 0.737 seconds.", + "bbox": [ + 498, + 564, + 890, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 622, + 653, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct ablation experiments to analyze the impact of the state initialization strategy and the scene semantics on the proposed model. We compare the proposed ScanDMM with three baselines: (1) $\\mathrm{ScanDMM}_{(\\mathrm{I})}$ , initializing state directly using learnable parameter: $\\mathbf{z}_0 = \\hat{\\mathbf{z}}_0$ . (2) $\\mathrm{ScanDMM}_{(\\mathrm{S})}$ , removing scene semantics $\\hat{\\mathbf{s}}$ in Eq. 7. (3) $\\mathrm{ScanDMM}_{(\\mathrm{IS})}$ , performing both of the two modifications. All baseline models are trained in the same settings, and the results are shown in Table 3. We can observe that the model achieves the best performance when incorporating both the state initialization strategy and the scene semantics.", + "bbox": [ + 496, + 647, + 890, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Applications", + "text_level": 1, + "bbox": [ + 500, + 828, + 630, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we demonstrate the generalizability of our model by applying it to two downstream applications - saliency detection and quality assessment for $360^{\\circ}$ images.", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6994", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9273a81addb1f2856cb8206c9c9f63c744968a288493363c4a8ada20401b7e8f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatabaseMethodAUC ↑NSS ↑CC ↑KLD ↓
Sitzmann [51]BMS360 [34]0.8311.3280.6660.475
GBVS360 [34]0.8451.4330.6930.374
SaltiNet [2]0.7620.9480.4970.671
SalNet360 [44]0.8411.4670.7180.421
SalGAN360 [8]0.8131.1880.6120.561
ScanGAN [43]0.7610.9020.4750.654
ScanDMM0.7670.9580.5210.609
Human0.8772.2651.0000.117
Salient360! [47]BMS360 [34]0.7480.9070.5670.476
GBVS360 [34]0.7120.7750.4840.576
SaltiNet [2]0.7370.8420.5300.514
SalNet360 [44]0.7440.9890.6020.476
SalGAN360 [8]0.7590.9750.6130.495
ScanGAN [43]0.7280.7740.4910.556
ScanDMM0.7771.0420.6600.384
Human0.8602.3951.0000.290
", + "bbox": [ + 78, + 88, + 472, + 311 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Saliency Detection for $360^{\\circ}$ images", + "text_level": 1, + "bbox": [ + 76, + 375, + 377, + 391 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual attention prediction, commonly known as saliency detection, is the task of inferring the objects or regions that attract human attention in a scene. Intuitively, an ideal scanpath prediction model should be able to model spatially visual attention. In this section, we apply the proposed ScanDMM and ScanGAN [43] to the saliency detection task by generating 1,000 scanpaths and post-processing these gaze points to yield continuous saliency maps. Specifically, we convolve fixation maps, the two-dimensional records of the locations of all the gaze points, with a modified Gaussian [56]:", + "bbox": [ + 75, + 398, + 468, + 565 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\nG (x, y) = \\frac {1}{2 \\pi \\sigma_ {y} ^ {2}} \\exp \\left(- \\frac {x ^ {2}}{2 \\sigma_ {x}}\\right) \\exp \\left(- \\frac {y ^ {2}}{2 \\sigma_ {y}}\\right) \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 571, + 468, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\sigma_{x} = \\frac{\\sigma_{y}}{\\cos(\\theta)}$ . $\\sigma_{y} = 19^{\\circ}$ is a constant value, and $\\theta \\in \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right]$ is the latitude of the gaze point.", + "bbox": [ + 75, + 616, + 468, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation Metrics. We evaluate saliency detection models using 4 metrics: the Judd variant of the area under curve (AUC) [6], normalized scanpath saliency (NSS) [46], correlation coefficient (CC) [32], and Kullback-Leibler divergence (KLD) [31]. Similarly, for each metric, we compute the human consistency as a realistic upper bound for model performance [7], referring to Human in Table 4. Specifically, we first compare the fixations of two groups of $M$ observers, where $M$ varies from 1 to $N/2$ (i.e., half of the total $N$ observers). We then fit the $N/2$ performance scores to a power function (i.e., $aM^b + c$ ), and predict the human performance as that of two groups of infinite observers (which is equal to $c$ , for $b < 0$ ).", + "bbox": [ + 75, + 660, + 468, + 858 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance Comparison. We compare different saliency detection models on Sitzmann [51] and Salient360! [47]", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a83e9c362e8be984d6b10fadae13fe5b5a6383f0ddcab22ae09b4b83c9fee471.jpg", + "table_caption": [ + "Table 4. Performance of saliency prediction models on Sitzmann [51] and Salient360! [47] databases." + ], + "table_footnote": [], + "table_body": "
MethodCC ↑SRCC ↑RMSE ↓
PSNR0.1560.0160.787
PSNRGAN0.1350.0140.790
PSNR\\(DMM\\)0.5630.5460.659
PSNR\\(Human\\)0.5850.5830.646
SSIM0.1480.0460.788
SSIM\\(GAN\\)0.1620.0460.790
SSIM\\(DMM\\)0.5190.5090.681
SSIM\\(Human\\)0.5270.5320.677
VIF0.1630.0960.786
VIF\\(GAN\\)0.1470.0920.788
VIF\\(DMM\\)0.5970.5720.639
VIF\\(Human\\)0.6160.6010.628
DISTS0.1620.0810.786
DISTSGAN0.1760.1000.784
DISTSDMM0.6620.6750.597
DISTSHuman0.7000.7110.569
DeepWSD0.1600.0440.786
DeepWSD\\(GAN\\)0.1620.0720.786
DeepWSD\\(DMM\\)0.6350.6280.616
DeepWSD\\(Human\\)0.6680.6670.593
", + "bbox": [ + 498, + 88, + 893, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Performance of quality assessment models on JUFE [20] database.", + "bbox": [ + 498, + 375, + 890, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "databases. In addition to ScanGAN [43], we also compare the proposed ScanDMM with 5 saliency detection models tailored for $360^{\\circ}$ images: BMS360 [34], GBVS360 [34], SalGAN [8], SalNet [44], and SaliNet [2], the results are shown in Table 4 and Fig. 4. Table 4 shows that the proposed ScanDMM achieves the best performance on Salient360! database, while its performance drops apparently on Sitzmann database. One reason might be that scanpath-to-saliency models are worse at suppressing nonsalient regions than the models tailored for $360^{\\circ}$ images (please refer to the supplementary file for the complete comparison), e.g., referring to Robot in Fig. 4. The results show that applying the scanpath prediction model for the saliency detection task is encouraging. Nevertheless, there is significant room for improvement, as evidenced by a large performance gap between computational models and humans.", + "bbox": [ + 496, + 422, + 890, + 664 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Quality Assessment for $360^{\\circ}$ Images", + "text_level": 1, + "bbox": [ + 498, + 679, + 812, + 695 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The image quality assessment (IQA) model aims at predicting the perceived quality of visual images [41]. Recent studies [20,21,52] reveal that the viewing behaviors may be indispensable for quality assessment for $360^{\\circ}$ scenes, highlighting the importance of scanpath prediction in $360^{\\circ}$ IQA. In this section, we show how much gain scanpath prediction models can provide for $360^{\\circ}$ IQA. Specifically, we leverage the computational framework [52], which offers us a natural way to utilize scanpaths for $360^{\\circ}$ IQA. Basically, there have 4 steps: (1) Extracting the sequences of rectilinear projections of viewports along different generated scanpaths. (2) Computing the \"frame-level\" (i.e., viewpoint-level) quality scores by using existing 2D IQA models. (3) Computing the", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6995", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/713be85e91fbdfa172feefb7649fd14c024c14f09f6a946d4e20a4c4745d7b6e.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison to different saliency detection models for six different scenes. First two columns: Square and Robot of Sitzmann [51] database. Last four columns: Theater, Mall, Gallery and Airplane of Salient360! [47] database. From top to bottom: $360^{\\circ}$ images, GT saliency maps, the predictions of ScanGAN [43] and the proposed ScanDMM." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 869, + 296 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "perceived quality of a \"video\" (i.e., a viewpoint sequence) by temporally pooling the frame-level quality scores. (4) Averaging the quality scores of all videos to obtain the final perceived quality of the $360^{\\circ}$ image.", + "bbox": [ + 75, + 363, + 468, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Evaluation Metrics. We use 3 evaluation metrics to quantify the quality prediction performance, including CC, Spearman's rank-order correlation coefficient (SRCC) and root mean square error (RMSE). Generally, higher CC/SRCC values and lower RMSE values mean better performance.", + "bbox": [ + 75, + 428, + 468, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Performance Comparison. We conduct comparison experiments on JUFE [20] database, in which each image has 4 quality labels corresponding to 4 different viewing conditions (2 starting point $\\times$ 2 exploration time). Considering this database is goal-directed (i.e., IQA), we retrain the ScanDMM and ScanGAN [43] on $80\\%$ training set. We generate $\\hat{N} = N$ fake scanapths for extracting viewpoint sequences for each image. For frame-level quality calculation, we employ five 2D IQA models, including the Peak Signal-to-Noise Ratio (PSNR), the Structural SIMilarity index (SSIM) [60], the Visual information fidelity (VIF) [50], the Deep Image Structure and Texture Similarity metrics (DISTS) [14], and the DeepWSD [37]. Then, the Gaussian weighting function [52] is chosen to temporally pool the frame-level quality scores. We add \"GAN\", \"DMM\", and \"Human\" to the five IQA methods as the subscripts to name the quality model that uses the scanpaths generated by ScanGAN [43], ScanDMM, and human, respectively. We also directly apply 2D IQA models to equirectangular projections as baselines. The results are shown in Table 5, where we can observe that all baseline models fail to predict the perceived quality, which is reasonable since they produce one quality score for a given image that has four quality labels. Conversely, our ScanDMM can simulate the viewing behaviors under the specific viewing condition thanks to the", + "bbox": [ + 75, + 523, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "state initialization strategy, which significantly improves the performance of 2D IQA models and have competitive performance compared with Human models. ScanGAN [43], however, is not applicable due to the uncontrollable starting points. Current work only tests traditional 2D IQA models, future models that take better account for VR-specific distortions will have great potential to boost the performance.", + "bbox": [ + 496, + 363, + 890, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion and Discussion", + "text_level": 1, + "bbox": [ + 500, + 482, + 748, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents a scanpath prediction model for $360^{\\circ}$ images and demonstrates its crucial capabilities, i.e., high accuracy, efficiency and generalizability, for real-world applications. Moreover, we provide a novel perspective for saliency detection and quality assessment in $360^{\\circ}$ scenes - constructing models by simulating humans' viewing behaviors, which is an extremely natural way if we recall how we obtain the GT labels. Nevertheless, there is still much to explore, as we only simply exploit generated scanpaths without elaborately designing for a specific task. While this paper primarily focuses on static $360^{\\circ}$ images, our ScanDMM can be easily adapted to dynamic $360^{\\circ}$ videos by feeding dynamic scene semantics to the network. Moreover, as a probabilistic approach, ScanDMM is able to learn the general pattern of the viewing behaviors in $360^{\\circ}$ scenes, thus could also be applied to VR transmission, automatic cinematography, navigation, virtual scene design, etc.", + "bbox": [ + 496, + 507, + 890, + 765 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 779, + 658, + 795 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Key Research and Development Program of China under Grant 2018AAA0100601, in part by the National Natural Science Foundation of China under Grant 62132006, and in part by the Natural Science Foundation of Jiangxi Province of China under Grant 20223AEI91002.", + "bbox": [ + 496, + 801, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6996", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hossein Adeli, Françoise Vitu, and Gregory J Zelinsky. 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IEEE Transactions on Multimedia, 22(9):2331-2344, 2020. 1, 2, 3, 6" + ], + "bbox": [ + 78, + 90, + 468, + 869 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6999", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_model.json b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..998999c0169bfa0543d0a16f06a637e5efbc4211 --- /dev/null +++ b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_model.json @@ -0,0 +1,2400 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.131, + 0.862, + 0.153 + ], + "angle": 0, + "content": "ScanDMM: A Deep Markov Model of Scanpath Prediction for \\(360^{\\circ}\\) Images" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.18, + 0.768, + 0.252 + ], + "angle": 0, + "content": "Xiangjie Sui\\(^{1}\\), Yuming Fang\\(^{1*}\\), Hanwei Zhu\\(^{2}\\), Shiqi Wang\\(^{2}\\), Zhou Wang\\(^{3}\\) \n\\(^{1}\\)Jiangxi University of Finance and Economics, \\(^{2}\\)City University of Hong Kong, \\(^{3}\\)University of Waterloo \nhttps://github.com/xiangjieSui/ScanDMM" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.313, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.621 + ], + "angle": 0, + "content": "Scanpath prediction for \\(360^{\\circ}\\) images aims to produce dynamic gaze behaviors based on the human visual perception mechanism. Most existing scanpath prediction methods for \\(360^{\\circ}\\) images do not give a complete treatment of the time-dependency when predicting human scanpath, resulting in inferior performance and poor generalizability. In this paper, we present a scanpath prediction method for \\(360^{\\circ}\\) images by designing a novel Deep Markov Model (DMM) architecture, namely ScanDMM. We propose a semantics-guided transition function to learn the nonlinear dynamics of time-dependent attentional landscape. Moreover, a state initialization strategy is proposed by considering the starting point of viewing, enabling the model to learn the dynamics with the correct \"launcher\". We further demonstrate that our model achieves state-of-the-art performance on four \\(360^{\\circ}\\) image databases, and exhibit its generalizability by presenting two applications of applying scanpath prediction models to other visual tasks - saliency detection and image quality assessment, expecting to provide profound insights into these fields." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.652, + 0.208, + 0.668 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.47, + 0.829 + ], + "angle": 0, + "content": "\\(360^{\\circ}\\) images, also referred to as omnidirectional, sphere or virtual reality (VR) images, have been a popular type of visual data in many applications, providing us with immersive experiences. Nevertheless, how people explore virtual environments in \\(360^{\\circ}\\) images has not been well understood. The scanpath prediction model that aims at generating realistic gaze trajectories has obtained increasing attention due to its significant influence in understanding users' viewing behaviors in VR scenes, as well as in developing VR rendering, display, compression, and transmission [51]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Scanpath prediction has been explored for many years in 2D images [29]. However, \\(360^{\\circ}\\) images are different greatly from 2D images, as a larger space is offered to interact with" + }, + { + "type": "image", + "bbox": [ + 0.525, + 0.286, + 0.87, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.606, + 0.892, + 0.732 + ], + "angle": 0, + "content": "Figure 1. Existing scanpath prediction models for \\(360^{\\circ}\\) images could be classified to two types: saliency-based models [2, 70, 71] and generative models [42, 43]. The scanpaths produced by saliency-based models, taking the study [2] as an example, commonly exhibits unstable behavior with large displacements and scarce focal regions. Generative models, taking the study [43] as an example, shows less attention to regions of interest. The proposed ScanDMM can produce more realistic scanpaths that focus on regions of interests." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.884 + ], + "angle": 0, + "content": "- humans are allowed to use both head and gaze movements to explore viewpoints of interest in the scene. In such a case, viewing conditions, e.g., the starting point of viewing, has an important impact on humans' scanpaths [20, 21, 52], and leads to complex and varied scanpaths among humans. This is inherently different from what happens in 2D visuals since humans can directly guide their attention to the regions of interest. Therefore, scanpath prediction for \\(360^{\\circ}\\) images is a more complex task." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Current \\(360^{\\circ}\\) image scanpath prediction methods could" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.393, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author (email: fa0001ng@e.ntu.edu.sg)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6989" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "be roughly divided into two categories: saliency-based [2, 70, 71] and generative methods [42, 43]. The basic idea of the former one is to sample predicted gaze points from a saliency map. The performance of such methods is highly dependent on that of the saliency maps. Furthermore, constructing a satisfactory sampling strategy to account for time-dependent visual behavior is non-trivial – the results of SaltiNet [2] exhibit unstable behavior with large displacements and scarce focal regions (see Fig. 1). The latter group of methods utilizes the advance of generative models, e.g., Generative Adversarial Network (GAN), to predict realistic scanpaths. However, such methods show less attention to regions of interests (see Fig. 1). In addition, the GAN-based methods are less flexible in determining the length of scanpaths and commonly suffer from unstable training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.473, + 0.741 + ], + "angle": 0, + "content": "None of above-mentioned studies give a complete treatment of the time-dependency of viewing behavior, which is critical for modeling dynamic gaze behaviors in \\(360^{\\circ}\\) images. For time-series data, a popular approach is to leverage sequential models, e.g., recurrent neural networks (RNNs), as exemplified in gaze prediction for \\(360^{\\circ}\\) videos [17, 35, 45]. However, such deterministic models are prone to overfitting, particularly on small \\(360^{\\circ}\\) databases. More importantly, they typically make simplistic assumptions, e.g., one choice is to concatenate the saliency map to the model's hidden states [17, 45], which assumes that the network learns how the states evolve by learning from saliency maps. Nevertheless, the neuroscience research [62] reveals that in addition to top-down and bottom-up features, prior history and scene semantics are essential sources for guiding visual attention. Moreover, to be identified as interests or rejected as distractors, items must be compared to target templates held in memory [62]. Inspired by this, we argue that humans' scanpaths in \\(360^{\\circ}\\) scenes are complex nonlinear dynamic attentional landscapes over time as a function of interventions of scene semantics on visual working memory. We present a probabilistic approach to learning the visual states that encode the time-dependent attentional landscape by specifying how these states evolve under the guidance of scene semantics and visual working memory. We instantiate our approach in the Deep Markov Model (DMM) [28], namely ScanDMM. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.747, + 0.47, + 0.867 + ], + "angle": 0, + "content": "- We present a novel method for time-dependent visual attention modeling for \\(360^{\\circ}\\) images. Specifically, we model the mechanism of visual working memory by maintaining and updating the visual state in the Markov chain. Furthermore, a semantics-guided transition function is built to learn the nonlinear dynamics of the states, in which we model the interventions of scene semantics on visual working memory." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We propose a practical strategy to initialize the visual state, facilitating our model to focus on learning the" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.747, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.531, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "dynamics of states with correct \"loader\", as well as enabling us to assign a specific starting point for scanpath generation. Moreover, ScanDMM is capable of producing 1,000 variable-length scanpaths within one second, which is critical for real-world applications." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.172, + 0.892, + 0.248 + ], + "angle": 0, + "content": "- We apply the proposed ScanDMM to two other computer vision tasks - saliency detection and image quality assessment, which demonstrates our model equips with strong generalizability and is expected to provide insights into other vision tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.26, + 0.642, + 0.275 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.285, + 0.776, + 0.301 + ], + "angle": 0, + "content": "2.1. Visual Attention for 2D Images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.892, + 0.503 + ], + "angle": 0, + "content": "Modeling Spatial Distribution of Gazes. Visual attention depends on two distinct types of attentional mechanisms: bottom-up and top-down mechanisms [10]. The performance of classic saliency detection methods for 2D images primarily depends on bottom-up features, e.g., colour, luminance, contrast and texture, for modeling visual attention [15, 18, 19, 24]. Although the studies [40, 69] incorporate top-down features, e.g., human faces and texts, there are still obstacles in combining bottom-up and top-down visual features. Deep learning methods [36, 57, 59, 68] take advantage of large-scale databases and well-established convolutional neural networks (CNNs), and they have achieved remarkable success." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Modeling Dynamic Gaze Behaviors. The studies in neuroscience suggest that scanpath generation can be an iterative process: while the eye fixates on an image location, the brain selects the next location to look at [26, 48]. Biologically inspired methods model such mechanism in different ways, e.g., considering the inhibition-of-return mechanism [25, 49, 53], maintaining the residual perceptual information maps [58], modeling the retina transformation [1], and utilizing low-level semantic information [55, 67]. Another class of methods is statistically inspired for modeling dynamic gaze behaviors. A typical approach is to model fixation distributions by the product of the saliency map and the previous fixation location [4, 5, 13, 30, 33, 63]. Some studies regard fixation distributions as Gaussian densities, and model scanpath by leveraging component analysis [54] or hidden markov models [12]. Different from interpretable models, fitting the data using deep generative models can also achieve competitive performance [9, 42, 66]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.787, + 0.803 + ], + "angle": 0, + "content": "2.2. Visual Attention for \\(360^{\\circ}\\) Images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Modeling Spatial Distribution of Gazes. Saliency detection of \\(360^{\\circ}\\) images is more challenging compared with 2D images, mainly due to complex viewing behaviors and insufficient available data for \\(360^{\\circ}\\) images. According to the space that the model is applied to, saliency detection models of \\(360^{\\circ}\\) images can be grouped into two categories: 2D-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6990" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "plane-based methods [2, 22, 38] and worldview-based methods [8, 34, 44, 64]. The former models visual attention by using hand-craft features [22, 38] or data-driven features [2] extracted from the distorted (caused by the equirectangular projection) 2D plane, while the latter is designed by applying well-established 2D visual saliency detection methods on worldview plane with less distortions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.473, + 0.504 + ], + "angle": 0, + "content": "Modeling Dynamic Gaze Behaviors. Current scanpath prediction models of \\(360^{\\circ}\\) images can be classified to two types: saliency-based models [2, 3, 70, 71] and generative models [42, 43]. The former first produces the saliency map by extracting low-level and high-level features [70, 71] or learned features from data [2, 3]. Then, scanpaths are sampled from the saliency map by maximizing information gains [70, 71] or using a stochastic approach [2, 3]. The latter group of methods models scanpaths by learning from human data. PathGAN [42] is a generative model originally developed for 2D images, and it is fine-tuned on Salient360! [47] database to be applied on \\(360^{\\circ}\\) images. However, the generated scanpaths lose sphere properties (e.g., longitudinal continuities) due to the assumption that a \\(360^{\\circ}\\) image is similar to a traditional 2D image. To address this problem, ScanGAN [43] propose to learn the image and coordinate representations by using sphere convolutional neural network (S-CNN) [11] and CoordConv layer [39], respectively. Besides, a loss function that measures the spherical distance is proposed for model training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.518, + 0.289, + 0.535 + ], + "angle": 0, + "content": "3. The Proposed Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.543, + 0.262, + 0.559 + ], + "angle": 0, + "content": "3.1. Problem Definition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.473, + 0.78 + ], + "angle": 0, + "content": "In \\(360^{\\circ}\\) environment, a human scanpath could be defined as a time series of gaze points \\(\\mathbf{x}_{1:T} = (\\mathbf{x}_1,\\mathbf{x}_2,\\dots,\\mathbf{x}_T)\\in \\mathbb{R}^{3\\times T}\\), where \\(\\mathbf{x}_t\\) is a three-dimensional coordinate \\((x_{t},y_{t},z_{t})\\). Given a \\(360^{\\circ}\\) image, a scanpath prediction model aims at producing realistic scanpaths \\(\\widetilde{\\mathbf{x}}_{1:T}\\) based on the human visual perception mechanism. This paper presents a probabilistic method - ScanDMM, for scanpath prediction for \\(360^{\\circ}\\) images, as shown in Fig 2. We model the mechanism of visual working memory by maintaining a set of visual states \\(\\mathbf{z}_{1:T} = (\\mathbf{z}_1,\\mathbf{z}_2,\\dots,\\mathbf{z}_T)\\in \\mathbb{R}^{n\\times T}\\) that encodes the dynamic attentional landscapes over time (\\(n\\) is the dimension of the state space). Basically, the ScanDMM predicts a scanpath using the following generative process:" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.792, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Transition: \\(\\mathbf{z}_t\\sim p_{\\theta_t}(\\mathbf{z}_t|\\mathbf{z}_{t - 1}),\\) (1)" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.811, + 0.469, + 0.829 + ], + "angle": 0, + "content": "Emission: \\(\\widetilde{\\mathbf{x}}_t\\sim p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t),\\quad t = 1,2,\\dots,T\\) (2)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "where \\(\\sim\\) means the sample operation. \\(p_{\\theta_t}(\\mathbf{z}_t|\\mathbf{z}_{t - 1})\\) denotes the transition probabilities between the visual states, and \\(p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t)\\) denotes the emission probabilities that describe how the visual state generates a gaze point. Let \\(\\theta\\) denotes all" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.271 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.292, + 0.894, + 0.322 + ], + "angle": 0, + "content": "Figure 2. An illustration of the proposed ScanDMM. Noting that the scene semantic \\(\\hat{s}\\) is deterministic for an image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.893, + 0.379 + ], + "angle": 0, + "content": "parameters involved in the ScanDMM. We approximate the realistic scanpaths by maximizing the log-likelihood function \\(\\log p(\\mathbf{x})\\) (we omit subscripts here for simplicity):" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.386, + 0.891, + 0.474 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\max \\log p _ {\\theta} (\\mathbf {x}) = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} p _ {\\theta} (\\mathbf {x}) \\\\ = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\frac {p _ {\\theta} (\\mathbf {x} , \\mathbf {z})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\tag {3} \\\\ = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\frac {p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) p _ {\\theta_ {t}} (\\mathbf {z})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.587 + ], + "angle": 0, + "content": "The posterior \\( p_{\\theta}(\\mathbf{z}|\\mathbf{x}) \\) can be approximated by using Variational Inference [61], which seeks to derive a distribution \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\) that is parameterized by neural networks, s.t. \\( q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\approx p_{\\theta}(\\mathbf{z}|\\mathbf{x}) \\). Based on Jensen's inequality, \\( f(\\mathbb{E}[x]) \\geqslant \\mathbb{E}[f(x)] \\) where \\( f \\) is a concave function, we adopt the Evidence Lower Bound of \\( \\log p_{\\theta}(\\mathbf{x}) \\) as the loss function \\( \\mathcal{L}(\\theta; \\phi; \\mathbf{x}) \\) to be maximized:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.594, + 0.891, + 0.718 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\log p _ {\\theta} (\\mathbf {x}) \\geqslant \\mathbb {E} _ {q _ {\\phi}} \\log \\frac {p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) p _ {\\theta_ {t}} (\\mathbf {z})}{q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\\\ = \\mathbb {E} _ {q _ {\\phi}} \\left[ \\log p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) + \\log p _ {\\theta_ {t}} (\\mathbf {z}) - \\log q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\right] \\\\ = \\underbrace {\\mathbb {E} _ {q _ {\\phi}} [ \\log p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) ]} _ {\\text {R e c o n s t r u c t i o n}} - \\underbrace {\\mathrm {K L} (q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p _ {\\theta_ {t}} (\\mathbf {z}))} _ {\\text {R e g u l a r i z a t i o n}} \\\\ := \\mathcal {L} (\\theta ; \\phi ; \\mathbf {x}), \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.84 + ], + "angle": 0, + "content": "where \\(\\mathrm{KL}(\\cdot \\| \\cdot)\\) denotes the Kullback-Leibler (KL) divergence. The reconstruction term evaluates the model's accuracy and the regularization term enforces the closeness between \\(q_{\\phi}(\\mathbf{z}|\\mathbf{x})\\) and \\(p_{\\theta_t}(\\mathbf{z})\\). The loss function also can be interpreted as the summation of transition \\(p_{\\theta_t}(\\mathbf{z})\\), emission \\(p_{\\theta_e}(\\mathbf{x}|\\mathbf{z})\\) and inference \\(q_{\\phi}(\\mathbf{z}|\\mathbf{x})\\). In the following section, we describe how we design the three functions tailored for scanpath prediction for \\(360^{\\circ}\\) images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.681, + 0.862 + ], + "angle": 0, + "content": "3.2. State Initialization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Different from the common strategy that simply sets the initial state to zero vector [28] or random vector [27], we" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6991" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "propose a practical strategy considering the starting points of scanpaths. The motivation derives from recent studies [20, 21, 52], which reveal that the starting point of viewing has an important influence on the scanpaths. To make our model better focus on learning the dynamics of visual states with the correct \"loader\" rather than random scratch, in the training stage, we directly use the starting point \\(\\mathbf{x}_1\\) to initialize \\(\\mathbf{z}_0\\):" + }, + { + "type": "equation", + "bbox": [ + 0.217, + 0.222, + 0.47, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {0} = \\mathbf {F} \\left(\\hat {\\mathbf {z}} _ {0}, \\mathbf {x} _ {1}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.473, + 0.382 + ], + "angle": 0, + "content": "where \\(\\hat{\\mathbf{z}}_0\\) is a learnable parameter. \\(\\mathbf{F}\\) denotes linear neural networks (see Fig. 2 for details). An advantage of such configuration is that we can assign a specific starting point for scanpath generation, which is flexible and even crucial in some visual tasks, e.g., image quality assessment (see Section 5.2). Notably, to fairly compare ScanDMM with other scanpath prediction models, in the model evaluation, we randomly sample the starting points from an Equator Bias Map that covers the whole longitude and \\(20\\%\\) latitude." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.39, + 0.267, + 0.404 + ], + "angle": 0, + "content": "3.3. Transition Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.473, + 0.624 + ], + "angle": 0, + "content": "Transition function \\( p_{\\theta_t}(\\mathbf{z_t}|\\mathbf{z}_{t - 1}) \\) controls the dynamics of the visual states, in which the history state \\( \\mathbf{z}_{t - 1} \\) functions as visual working memory that maintains the history attentional landscape. Inspired by the recent study in neuroscience [62], we propose to learn the dynamics guided by scene semantics. Due to the space-varying distortions inherent to equirectangular projections, we choose to extract scene semantics \\( \\hat{\\mathbf{s}}\\in \\mathbb{R}^{n\\times 1} \\) using S-CNN [11]. Moreover, by considering the spatial locations of semantic features are critical for scanpath prediction, we utilize the CoordConv strategy [39] to give convolutions access to their own input coordinates, as suggested in [43]. Given the scene semantics \\( \\hat{\\mathbf{s}} \\) and the history visual state \\( \\mathbf{z}_{t - 1} \\), transition function samples \\( \\mathbf{z}_t \\) from the following Gaussian densities:" + }, + { + "type": "equation", + "bbox": [ + 0.212, + 0.633, + 0.47, + 0.651 + ], + "angle": 0, + "content": "\\[\n\\mathbf {z} _ {t} \\sim \\mathcal {N} \\left(\\mu_ {t} ^ {z}, \\sigma_ {t} ^ {z}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.702 + ], + "angle": 0, + "content": "where \\(\\mu_t^z\\) and \\(\\sigma_t^z\\in \\mathbb{R}^{n\\times 1}\\) are the mean and scale of Gaussian densities describing an attentional landscape of the visual state \\(\\mathbf{z}_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Here, we present how we produce the two Gaussian parameters. Firstly, we compute the new underlying gaze distributions \\(\\hat{\\mathbf{z}}_t\\) by" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.756, + 0.47, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {z}} _ {t} = \\mathbf {W} _ {z} ^ {t} (\\mathbf {z} _ {t - 1} \\oplus \\hat {\\mathbf {s}}) + \\mathbf {b} _ {z} ^ {t}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.873 + ], + "angle": 0, + "content": "where \\(\\oplus\\) is the concatenate operation, \\(\\mathbf{W}_z^t\\in \\mathbb{R}^{n\\times 2n}\\) and \\(\\mathbf{b}_z^t\\in \\mathbb{R}^{n\\times 1}\\) are learnable parameters of the neural networks. Inspired by the Long Short-Term Memory [23], we introduce the uncertainty weighting for adaptively determining how much components of the previous visual state \\(\\mathbf{z}_{t - 1}\\) to be updated:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.88, + 0.47, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {t} = \\sigma \\left(\\mathbf {W} _ {\\alpha} ^ {t} \\mathbf {z} _ {t - 1} + \\mathbf {b} _ {\\alpha} ^ {t}\\right), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.168 + ], + "angle": 0, + "content": "where \\(\\alpha_{t}\\) is an uncertainty weighting determined by the history state \\(\\mathbf{z}_{t - 1}\\), and \\(\\sigma\\) denotes the sigmoid function. \\(\\mathbf{W}_{\\{\\alpha ,\\sigma \\}}^{t}\\in \\mathbb{R}^{n\\times n}\\) and \\(\\mathbf{b}_{\\{\\alpha ,\\sigma \\}}^t\\in \\mathbb{R}^{n\\times 1}\\) are learnable parameters of the neural networks. Finally, the two Gaussian parameters, \\(\\mu_t^z\\) and \\(\\sigma_t^z\\), are computed by:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.175, + 0.892, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\mu_ {t} ^ {z} = \\alpha_ {t} \\hat {\\mathbf {z}} _ {t} + (1 - \\alpha_ {t}) \\mathbf {z} _ {t - 1}, \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.194, + 0.892, + 0.213 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {t} ^ {z} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {t} \\hat {\\mathbf {z}} _ {t} + \\mathbf {b} _ {\\sigma} ^ {t}\\right)\\right). \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.219, + 0.681, + 0.233 + ], + "angle": 0, + "content": "3.4. Emission Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.242, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Emission function \\(p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t)\\) describes how a gaze point \\(\\widetilde{\\mathbf{x}}_t\\) is generated from the visual state \\(\\mathbf{z}_t\\). As a gaze point is parameterized as a three-dimensional coordinate, we model the emission process by sampling \\(\\widetilde{\\mathbf{x}}_t\\) from the three-dimensional Gaussian densities that are parameterized by \\(\\mu_t^x\\) and \\(\\sigma_t^x\\in \\mathbb{R}^{3\\times 1}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.634, + 0.34, + 0.892, + 0.358 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathbf {x}} _ {t} \\sim \\mathcal {N} \\left(\\mu_ {t} ^ {x}, \\sigma_ {t} ^ {x}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.892, + 0.393 + ], + "angle": 0, + "content": "where \\(\\mu_t^x\\) and \\(\\sigma_t^x\\) are determined by the current visual state \\(\\mathbf{z}_t\\):" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.395, + 0.891, + 0.413 + ], + "angle": 0, + "content": "\\[\n\\mu_ {t} ^ {x} = 2 \\sigma \\left(\\mathbf {W} _ {\\mu} ^ {e} \\mathbf {z} _ {t} + \\mathbf {b} _ {\\mu} ^ {e}\\right) - 1, \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.416, + 0.891, + 0.433 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {t} ^ {x} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {e} \\mathbf {z} _ {t} + \\mathbf {b} _ {\\sigma} ^ {e}\\right)\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.892, + 0.466 + ], + "angle": 0, + "content": "\\(\\mathbf{W}_{\\{\\mu, \\sigma\\}}^e \\in \\mathbb{R}^{3 \\times n}\\) and \\(\\mathbf{b}_{\\{\\mu, \\sigma\\}}^e \\in \\mathbb{R}^{3 \\times 1}\\) are learnable parameters of the neural networks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.475, + 0.61, + 0.489 + ], + "angle": 0, + "content": "3.5. Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.498, + 0.892, + 0.605 + ], + "angle": 0, + "content": "Inference for a latent state can be made using information from past and future true observations [28], i.e., GT gaze points in this study. In other words, the goal of inference is to provide an approximation to the exact posterior \\( p_{\\theta}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T}) \\). Here, we leverage the Variational Inference [61] to approximate \\( p_{\\theta}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T}) \\) with a tractable family of conditional distributions \\( q_{\\phi}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T}) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.613, + 0.892, + 0.653 + ], + "angle": 0, + "content": "\\[\nq _ {\\phi} \\left(\\mathbf {z} _ {1: T} \\mid \\mathbf {x} _ {1: T}\\right) = \\prod_ {t = 1} ^ {T} q _ {\\phi} \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}, \\mathcal {H} \\left(\\mathbf {x} _ {t: T}\\right)\\right) \\tag {14}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.656, + 0.824, + 0.674 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l l} \\text {s . t .} & q _ {\\phi} (\\mathbf {z} _ {t} | \\mathbf {z} _ {t - 1}, \\mathcal {H} (\\mathbf {x} _ {t: T})) \\sim \\mathcal {N} (\\mu_ {t} ^ {i}, \\sigma_ {t} ^ {i}), \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.757 + ], + "angle": 0, + "content": "where \\(\\mathcal{H}(\\cdot) \\in \\mathbb{R}^{m \\times 1}\\) is the variational parameter computed by mapping a variable-length sequences \\(\\mathbf{x}_{t:T}\\) to its \\(m\\)-dimensional space. We implement this by using RNN [28]. The Gaussian parameters \\(\\mu_t^i\\) and \\(\\sigma_t^i \\in \\mathbb{R}^{n \\times 1}\\) are produced by the following process:" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.764, + 0.891, + 0.793 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {t} = \\frac {1}{2} \\left(\\left(\\mathbf {W} _ {c} ^ {i} \\mathbf {z} _ {t - 1} + \\mathbf {b} _ {c} ^ {i}\\right) + \\mathcal {H} \\left(\\mathbf {x} _ {t: T}\\right)\\right), \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.795, + 0.891, + 0.813 + ], + "angle": 0, + "content": "\\[\n\\mu_ {t} ^ {i} = \\mathbf {W} _ {\\mu} ^ {i} \\mathcal {C} _ {t} + \\mathbf {b} _ {\\mu} ^ {i}, \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.815, + 0.891, + 0.834 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {t} ^ {i} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {i} \\mathcal {C} _ {t} + \\mathbf {b} _ {\\sigma} ^ {i}\\right)\\right), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}_t\\) denotes the combined feature of the previous state \\(\\mathbf{z}_{t - 1}\\) and the RNN hidden state \\(\\mathcal{H}(\\mathbf{x}_{t:T})\\). \\(\\mathbf{W}_c^i\\in \\mathbb{R}^{n\\times m}\\), \\(\\mathbf{W}_{\\{\\mu ,\\sigma \\}}^i\\in \\mathbb{R}^{n\\times m}\\), \\(\\mathbf{b}_c^i\\in \\mathbb{R}^{m\\times 1}\\), and \\(\\mathbf{b}_{\\{\\mu ,\\sigma \\}}^i\\in \\mathbb{R}^{n\\times 1}\\) are learnable parameters of the neural networks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6992" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.21, + 0.108 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.47, + 0.177 + ], + "angle": 0, + "content": "In this section, we present the experimental results to validate the effectiveness of the proposed ScanDMM. We refer the interested readers to the supplementary file for more details on ScanDMM, datasets, and qualitative comparisons." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.186, + 0.173, + 0.2 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.209, + 0.471, + 0.496 + ], + "angle": 0, + "content": "We use four \\(360^{\\circ}\\) image databases to conduct experiments, including Sitzmann [51], Salient360! [47], AOI [65], and JUFE [20]. Sitzmann [51] database contains 22 images and 1,980 scanpaths, 19 of 22 images are used for training, and the remaining are used for validation. Salient360! [47] database contains two sets: training and benchmark sets. In this paper, we consistently use its training set that contains 85 images and 3,036 scanpaths for evaluation since its benchmark set is not publicly available. AOI [65] database contains 600 high-resolution \\(360^{\\circ}\\) images and 18,000 scanpaths. JUFE [20] database is constructed for studying \\(360^{\\circ}\\) image quality assessment, containing 1,032 images and 30,960 scanpaths. For the latter two databases, we randomly select \\(20\\%\\) images for model evaluation. To obtain Ground-Truth (GT) scanpaths for model training and evaluation, we sample the raw scanpaths at \\(1\\mathrm{Hz}\\) on each database. Noting that the scanpaths of the AOI database had been processed by the authors, so we did not make any post-processing." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.506, + 0.267, + 0.523 + ], + "angle": 0, + "content": "4.2. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.47, + 0.68 + ], + "angle": 0, + "content": "Implementation Details. We train the proposed model using Sitzmann [51] database. To augment data, we longitudinally shift the \\(360^{\\circ}\\) images and adjust their scanpaths accordingly [43], which yields \\(19 \\times 6 = 114\\) images for training. Before the panoramic images are fed into the network, they are resized as (128, 256). The learning rate is set to \\(3e-4\\) and is decreased by a factor of 0.99998 at each epoch. The dimensions of the visual state and RNN hidden state are set to 100 and 600, respectively. The network was trained for 500 epochs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Evaluation Metrics. We use three metrics to evaluate the performance of \\(360^{\\circ}\\) scanpath prediction models, including the Levenshtein distance (LEV), dynamic time warping (DTW), and recurrence measure (REC), as suggested in [16,43]. Generally, lower LEV/DTW values and higher REC values mean better prediction performance. For an image with \\(N\\) GT scanpaths \\(\\mathbf{x}^{1:N}\\), we generate \\(\\hat{N} = N\\) fake scanpaths \\(\\widetilde{\\mathbf{x}}^{1:\\hat{N}}\\) for comparison. The lengths of generated scanpaths are equal to that of the viewing time\\(^1\\). To compare a set of GT scanpaths \\(\\mathbf{x}^{1:N}\\) to another set of predicted scanpaths \\(\\widetilde{\\mathbf{x}}^{1:\\hat{N}}\\), taking LEV as an example, we choose to compute each metric for all possible pairwise comparisons" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.658, + 0.107 + ], + "angle": 0, + "content": "and average the results:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.117, + 0.892, + 0.162 + ], + "angle": 0, + "content": "\\[\n\\mathrm {m L E V} = \\frac {1}{N \\hat {N}} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {\\hat {N}} \\operatorname {L E V} \\left(\\mathbf {x} ^ {i}, \\widetilde {\\mathbf {x}} ^ {j}\\right). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.17, + 0.892, + 0.336 + ], + "angle": 0, + "content": "To reduce the evaluation bias caused by the randomly generated scanpaths, we test each generative model with 10 times and average these 10 results to obtain the final performance. To make the results more comparable and interpretable, for each metric, we compute the human consistency [43] as a realistic upper bound for model performance (see Human in Tab. 1). Specifically, we compare each GT scanpath against all the other ones and average the results. We also compare to the results of a chance model – produce scanpaths by adding a random Brownian motion to the previous positions (see Random walk in Tab. 1)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.348, + 0.895, + 0.707 + ], + "angle": 0, + "content": "
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]Random walk48.9422232.9872.669
CLE [4]45.1761967.2863.130
DeepGaze III [30]46.4241992.8593.082
SaliTiNet [2]51.3702305.0991.564
ScanGAN [43]45.2701951.8483.241
ScanDMM44.9661965.4273.475
Human41.1881836.9866.345
Salient360! [47]Random walk40.8022231.6812.744
CLE [4]39.7741714.4093.323
DeepGaze III [30]40.0061742.3512.588
SaliTiNet [2]40.8481855.4772.305
ScanGAN [43]38.9321721.7113.099
ScanDMM37.2721528.5923.576
Human35.0841382.5905.202
AOI [65]Random walk13.696711.5162.993
CLE [4]12.865547.8923.617
DeepGaze III [30]13.155558.4452.892
SaliTiNet [2]14.695596.5442.244
ScanGAN [43]12.889552.4463.750
ScanDMM12.127537.5044.024
Human9.243389.4776.228
JUFE [20]Random walk24.0391193.7253.109
CLE [4]24.8441172.1503.013
DeepGaze III [30]24.1291104.8482.774
SaliTiNet [2]26.0741287.1441.540
ScanGAN [43]24.2091094.9783.075
ScanDMM23.0911086.0144.329
Human18.3061038.8807.745
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.717, + 0.892, + 0.748 + ], + "angle": 0, + "content": "Table 1. Performance of scanpath prediction models on different databases. The best performance is highlighted." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.759, + 0.736, + 0.777 + ], + "angle": 0, + "content": "4.3. Performance Comparison" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Model Selection. We compare ScanDMM to four state-of-the-art scanpath prediction models: CLE [5], DeepGaze III [30], SaltiNet [2], and ScanGAN [43]. The first two models are built for traditional images, and the latter two are tailored for \\(360^{\\circ}\\) images. For DeepGaze III and SaltiNet with larger sizes, we choose to use the pre-trained weights provided by the corresponding authors to avoid overfitting" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.902 + ], + "angle": 0, + "content": "1 For ScanGAN, we cut the produced scanpaths to the required lengths." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "6993" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.887, + 0.298 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.895, + 0.36 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison to different scanpath prediction models for four different scenes. From left to right: scanpath samples obtained by a observer, scanpath results obtained by CLE [4], DeepGaze III [30], SaltiNet [2], ScanGAN [43], and the proposed model. From top to bottom: the Room from Sitzmann [51] database, the Museum from Salient360! [47] database, the Party from AOI [65] database, and the Park from JUFE [20] database." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.383, + 0.472, + 0.468 + ], + "angle": 0, + "content": "
MethodParamtersRunning Time
CLE [4]-≈ 39 seconds
DeepGaze III [30]78.9MB≈ 11 minutes
SaliNet [2]103.6MB≈ 49 minutes
ScanGAN [43]33.9MB0.987 seconds
ScanDMM18.7MB0.737 seconds
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.478, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Table 2. Efficiency comparison in terms of the model size and running time (computed by the time cost of producing 1,000 scanpaths). Noting that CLE is a traditional model that built on saliency maps, we only count the time to produce the scanpaths." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.47, + 0.635 + ], + "angle": 0, + "content": "on small \\(360^{\\circ}\\) image datasets. PathGAN [42] and Zhu et al. [71] are the other two popular scanpath prediction methods for \\(360^{\\circ}\\) images. Nevertheless, we do not include them in comparison since the study [43] had shown their failures in producing realistic scanpaths for \\(360^{\\circ}\\) images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.47, + 0.816 + ], + "angle": 0, + "content": "Accuracy Comparison. Table 1 and Fig. 3 show that our model could provide results closer to the human scanpaths. In Fig. 3, we observe that CLE and DeepGaze III exhibit large displacements that might caused by the treatment that regarding \\(360^{\\circ}\\) images as 2D images. Saliency-based scanpath prediction model, exhibits unstable behavior with large displacements and scarce focal regions (e.g., referring to Room or Park of Fig. 3), leading to worse results than the Random walk model. The proposed model could better focus on the salient objects in scenes than ScanGAN (e.g., referring to Museum, Party or Park of Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Efficiency Comparison. We also compare the efficiency in terms of the model size and running time. The results are shown in Table 2. Our model has the smallest size - 18.7MB, which is about \\(1/5\\) of the size of SaliNet. For running time comparison, we record the time cost to gen" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.383, + 0.898, + 0.51 + ], + "angle": 0, + "content": "
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]ScanDMM(I)45.9491996.4563.091
ScanDMM(S)46.8002098.4122.833
ScanDMM(IS)46.4892011.1572.904
ScanDMM44.9661965.4273.475
Salient360! [47]ScanDMM(I)38.3401698.5173.168
ScanDMM(S)39.1941787.6742.744
ScanDMM(IS)38.9581720.8942.853
ScanDMM37.2721528.5923.576
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.52, + 0.892, + 0.548 + ], + "angle": 0, + "content": "Table 3. Ablation study. The effectiveness of our designs is well justified." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.61 + ], + "angle": 0, + "content": "erate 1,000 scanpaths for a given image. The results show that our model has the fastest inference speed - 0.737 seconds." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.623, + 0.655, + 0.64 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.814 + ], + "angle": 0, + "content": "We conduct ablation experiments to analyze the impact of the state initialization strategy and the scene semantics on the proposed model. We compare the proposed ScanDMM with three baselines: (1) \\(\\mathrm{ScanDMM}_{(\\mathrm{I})}\\), initializing state directly using learnable parameter: \\(\\mathbf{z}_0 = \\hat{\\mathbf{z}}_0\\). (2) \\(\\mathrm{ScanDMM}_{(\\mathrm{S})}\\), removing scene semantics \\(\\hat{\\mathbf{s}}\\) in Eq. 7. (3) \\(\\mathrm{ScanDMM}_{(\\mathrm{IS})}\\), performing both of the two modifications. All baseline models are trained in the same settings, and the results are shown in Table 3. We can observe that the model achieves the best performance when incorporating both the state initialization strategy and the scene semantics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.829, + 0.631, + 0.848 + ], + "angle": 0, + "content": "5. Applications" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "In this section, we demonstrate the generalizability of our model by applying it to two downstream applications - saliency detection and quality assessment for \\(360^{\\circ}\\) images." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "6994" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.473, + 0.313 + ], + "angle": 0, + "content": "
DatabaseMethodAUC ↑NSS ↑CC ↑KLD ↓
Sitzmann [51]BMS360 [34]0.8311.3280.6660.475
GBVS360 [34]0.8451.4330.6930.374
SaltiNet [2]0.7620.9480.4970.671
SalNet360 [44]0.8411.4670.7180.421
SalGAN360 [8]0.8131.1880.6120.561
ScanGAN [43]0.7610.9020.4750.654
ScanDMM0.7670.9580.5210.609
Human0.8772.2651.0000.117
Salient360! [47]BMS360 [34]0.7480.9070.5670.476
GBVS360 [34]0.7120.7750.4840.576
SaltiNet [2]0.7370.8420.5300.514
SalNet360 [44]0.7440.9890.6020.476
SalGAN360 [8]0.7590.9750.6130.495
ScanGAN [43]0.7280.7740.4910.556
ScanDMM0.7771.0420.6600.384
Human0.8602.3951.0000.290
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.352 + ], + "angle": 0, + "content": "Table 4. Performance of saliency prediction models on Sitzmann [51] and Salient360! [47] databases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.376, + 0.379, + 0.392 + ], + "angle": 0, + "content": "5.1. Saliency Detection for \\(360^{\\circ}\\) images" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.47, + 0.566 + ], + "angle": 0, + "content": "Visual attention prediction, commonly known as saliency detection, is the task of inferring the objects or regions that attract human attention in a scene. Intuitively, an ideal scanpath prediction model should be able to model spatially visual attention. In this section, we apply the proposed ScanDMM and ScanGAN [43] to the saliency detection task by generating 1,000 scanpaths and post-processing these gaze points to yield continuous saliency maps. Specifically, we convolve fixation maps, the two-dimensional records of the locations of all the gaze points, with a modified Gaussian [56]:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.573, + 0.469, + 0.609 + ], + "angle": 0, + "content": "\\[\nG (x, y) = \\frac {1}{2 \\pi \\sigma_ {y} ^ {2}} \\exp \\left(- \\frac {x ^ {2}}{2 \\sigma_ {x}}\\right) \\exp \\left(- \\frac {y ^ {2}}{2 \\sigma_ {y}}\\right) \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.47, + 0.652 + ], + "angle": 0, + "content": "where \\(\\sigma_{x} = \\frac{\\sigma_{y}}{\\cos(\\theta)}\\). \\(\\sigma_{y} = 19^{\\circ}\\) is a constant value, and \\(\\theta \\in \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right]\\) is the latitude of the gaze point." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.661, + 0.47, + 0.859 + ], + "angle": 0, + "content": "Evaluation Metrics. We evaluate saliency detection models using 4 metrics: the Judd variant of the area under curve (AUC) [6], normalized scanpath saliency (NSS) [46], correlation coefficient (CC) [32], and Kullback-Leibler divergence (KLD) [31]. Similarly, for each metric, we compute the human consistency as a realistic upper bound for model performance [7], referring to Human in Table 4. Specifically, we first compare the fixations of two groups of \\( M \\) observers, where \\( M \\) varies from 1 to \\( N/2 \\) (i.e., half of the total \\( N \\) observers). We then fit the \\( N/2 \\) performance scores to a power function (i.e., \\( aM^b + c \\)), and predict the human performance as that of two groups of infinite observers (which is equal to \\( c \\), for \\( b < 0 \\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Performance Comparison. We compare different saliency detection models on Sitzmann [51] and Salient360! [47]" + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.366 + ], + "angle": 0, + "content": "
MethodCC ↑SRCC ↑RMSE ↓
PSNR0.1560.0160.787
PSNRGAN0.1350.0140.790
PSNR\\(DMM\\)0.5630.5460.659
PSNR\\(Human\\)0.5850.5830.646
SSIM0.1480.0460.788
SSIM\\(GAN\\)0.1620.0460.790
SSIM\\(DMM\\)0.5190.5090.681
SSIM\\(Human\\)0.5270.5320.677
VIF0.1630.0960.786
VIF\\(GAN\\)0.1470.0920.788
VIF\\(DMM\\)0.5970.5720.639
VIF\\(Human\\)0.6160.6010.628
DISTS0.1620.0810.786
DISTSGAN0.1760.1000.784
DISTSDMM0.6620.6750.597
DISTSHuman0.7000.7110.569
DeepWSD0.1600.0440.786
DeepWSD\\(GAN\\)0.1620.0720.786
DeepWSD\\(DMM\\)0.6350.6280.616
DeepWSD\\(Human\\)0.6680.6670.593
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.376, + 0.892, + 0.403 + ], + "angle": 0, + "content": "Table 5. Performance of quality assessment models on JUFE [20] database." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.892, + 0.665 + ], + "angle": 0, + "content": "databases. In addition to ScanGAN [43], we also compare the proposed ScanDMM with 5 saliency detection models tailored for \\(360^{\\circ}\\) images: BMS360 [34], GBVS360 [34], SalGAN [8], SalNet [44], and SaliNet [2], the results are shown in Table 4 and Fig. 4. Table 4 shows that the proposed ScanDMM achieves the best performance on Salient360! database, while its performance drops apparently on Sitzmann database. One reason might be that scanpath-to-saliency models are worse at suppressing nonsalient regions than the models tailored for \\(360^{\\circ}\\) images (please refer to the supplementary file for the complete comparison), e.g., referring to Robot in Fig. 4. The results show that applying the scanpath prediction model for the saliency detection task is encouraging. Nevertheless, there is significant room for improvement, as evidenced by a large performance gap between computational models and humans." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.68, + 0.813, + 0.696 + ], + "angle": 0, + "content": "5.2. Quality Assessment for \\(360^{\\circ}\\) Images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The image quality assessment (IQA) model aims at predicting the perceived quality of visual images [41]. Recent studies [20,21,52] reveal that the viewing behaviors may be indispensable for quality assessment for \\(360^{\\circ}\\) scenes, highlighting the importance of scanpath prediction in \\(360^{\\circ}\\) IQA. In this section, we show how much gain scanpath prediction models can provide for \\(360^{\\circ}\\) IQA. Specifically, we leverage the computational framework [52], which offers us a natural way to utilize scanpaths for \\(360^{\\circ}\\) IQA. Basically, there have 4 steps: (1) Extracting the sequences of rectilinear projections of viewports along different generated scanpaths. (2) Computing the \"frame-level\" (i.e., viewpoint-level) quality scores by using existing 2D IQA models. (3) Computing the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "6995" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.87, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.308, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison to different saliency detection models for six different scenes. First two columns: Square and Robot of Sitzmann [51] database. Last four columns: Theater, Mall, Gallery and Airplane of Salient360! [47] database. From top to bottom: \\(360^{\\circ}\\) images, GT saliency maps, the predictions of ScanGAN [43] and the proposed ScanDMM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.47, + 0.426 + ], + "angle": 0, + "content": "perceived quality of a \"video\" (i.e., a viewpoint sequence) by temporally pooling the frame-level quality scores. (4) Averaging the quality scores of all videos to obtain the final perceived quality of the \\(360^{\\circ}\\) image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.429, + 0.47, + 0.519 + ], + "angle": 0, + "content": "Evaluation Metrics. We use 3 evaluation metrics to quantify the quality prediction performance, including CC, Spearman's rank-order correlation coefficient (SRCC) and root mean square error (RMSE). Generally, higher CC/SRCC values and lower RMSE values mean better performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Performance Comparison. We conduct comparison experiments on JUFE [20] database, in which each image has 4 quality labels corresponding to 4 different viewing conditions (2 starting point \\(\\times\\) 2 exploration time). Considering this database is goal-directed (i.e., IQA), we retrain the ScanDMM and ScanGAN [43] on \\(80\\%\\) training set. We generate \\(\\hat{N} = N\\) fake scanapths for extracting viewpoint sequences for each image. For frame-level quality calculation, we employ five 2D IQA models, including the Peak Signal-to-Noise Ratio (PSNR), the Structural SIMilarity index (SSIM) [60], the Visual information fidelity (VIF) [50], the Deep Image Structure and Texture Similarity metrics (DISTS) [14], and the DeepWSD [37]. Then, the Gaussian weighting function [52] is chosen to temporally pool the frame-level quality scores. We add \"GAN\", \"DMM\", and \"Human\" to the five IQA methods as the subscripts to name the quality model that uses the scanpaths generated by ScanGAN [43], ScanDMM, and human, respectively. We also directly apply 2D IQA models to equirectangular projections as baselines. The results are shown in Table 5, where we can observe that all baseline models fail to predict the perceived quality, which is reasonable since they produce one quality score for a given image that has four quality labels. Conversely, our ScanDMM can simulate the viewing behaviors under the specific viewing condition thanks to the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.471 + ], + "angle": 0, + "content": "state initialization strategy, which significantly improves the performance of 2D IQA models and have competitive performance compared with Human models. ScanGAN [43], however, is not applicable due to the uncontrollable starting points. Current work only tests traditional 2D IQA models, future models that take better account for VR-specific distortions will have great potential to boost the performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.483, + 0.749, + 0.499 + ], + "angle": 0, + "content": "6. Conclusion and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.766 + ], + "angle": 0, + "content": "This paper presents a scanpath prediction model for \\(360^{\\circ}\\) images and demonstrates its crucial capabilities, i.e., high accuracy, efficiency and generalizability, for real-world applications. Moreover, we provide a novel perspective for saliency detection and quality assessment in \\(360^{\\circ}\\) scenes - constructing models by simulating humans' viewing behaviors, which is an extremely natural way if we recall how we obtain the GT labels. Nevertheless, there is still much to explore, as we only simply exploit generated scanpaths without elaborately designing for a specific task. While this paper primarily focuses on static \\(360^{\\circ}\\) images, our ScanDMM can be easily adapted to dynamic \\(360^{\\circ}\\) videos by feeding dynamic scene semantics to the network. Moreover, as a probabilistic approach, ScanDMM is able to learn the general pattern of the viewing behaviors in \\(360^{\\circ}\\) scenes, thus could also be applied to VR transmission, automatic cinematography, navigation, virtual scene design, etc." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.78, + 0.66, + 0.796 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.803, + 0.892, + 0.888 + ], + "angle": 0, + "content": "This work was supported in part by the National Key Research and Development Program of China under Grant 2018AAA0100601, in part by the National Natural Science Foundation of China under Grant 62132006, and in part by the Natural Science Foundation of Jiangxi Province of China under Grant 20223AEI91002." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6996" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Hossein Adeli, Françoise Vitu, and Gregory J Zelinsky. 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IEEE Transactions on Multimedia, 22(9):2331-2344, 2020. 1, 2, 3, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.87 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6999" + } + ] +] \ No newline at end of file diff --git a/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_origin.pdf b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7b4fe7d46ec0c745e81b5b229e03c496164521e8 --- /dev/null +++ b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/0e9438ec-529d-4504-8952-ad1887816ae6_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:078e53d80857085e6f343eaded032e448d1e4e3c74c6401d14e17f36fb9bb5ea +size 2201691 diff --git a/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/full.md b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/full.md new file mode 100644 index 0000000000000000000000000000000000000000..0fc9a80bd5ab2e8766aed90cdc6641ea21e61555 --- /dev/null +++ b/2023/ScanDMM_ A Deep Markov Model of Scanpath Prediction for 360deg Images/full.md @@ -0,0 +1,353 @@ +# ScanDMM: A Deep Markov Model of Scanpath Prediction for $360^{\circ}$ Images + +Xiangjie Sui $^{1}$ , Yuming Fang $^{1*}$ , Hanwei Zhu $^{2}$ , Shiqi Wang $^{2}$ , Zhou Wang $^{3}$ $^{1}$ Jiangxi University of Finance and Economics, $^{2}$ City University of Hong Kong, $^{3}$ University of Waterloo +https://github.com/xiangjieSui/ScanDMM + +# Abstract + +Scanpath prediction for $360^{\circ}$ images aims to produce dynamic gaze behaviors based on the human visual perception mechanism. Most existing scanpath prediction methods for $360^{\circ}$ images do not give a complete treatment of the time-dependency when predicting human scanpath, resulting in inferior performance and poor generalizability. In this paper, we present a scanpath prediction method for $360^{\circ}$ images by designing a novel Deep Markov Model (DMM) architecture, namely ScanDMM. We propose a semantics-guided transition function to learn the nonlinear dynamics of time-dependent attentional landscape. Moreover, a state initialization strategy is proposed by considering the starting point of viewing, enabling the model to learn the dynamics with the correct "launcher". We further demonstrate that our model achieves state-of-the-art performance on four $360^{\circ}$ image databases, and exhibit its generalizability by presenting two applications of applying scanpath prediction models to other visual tasks - saliency detection and image quality assessment, expecting to provide profound insights into these fields. + +# 1. Introduction + +$360^{\circ}$ images, also referred to as omnidirectional, sphere or virtual reality (VR) images, have been a popular type of visual data in many applications, providing us with immersive experiences. Nevertheless, how people explore virtual environments in $360^{\circ}$ images has not been well understood. The scanpath prediction model that aims at generating realistic gaze trajectories has obtained increasing attention due to its significant influence in understanding users' viewing behaviors in VR scenes, as well as in developing VR rendering, display, compression, and transmission [51]. + +Scanpath prediction has been explored for many years in 2D images [29]. However, $360^{\circ}$ images are different greatly from 2D images, as a larger space is offered to interact with + +![](images/b5d535c60e89315649dd7e18e90e57b3a02c69fc1fd2a7551a0364150fc510f3.jpg) +Figure 1. Existing scanpath prediction models for $360^{\circ}$ images could be classified to two types: saliency-based models [2, 70, 71] and generative models [42, 43]. The scanpaths produced by saliency-based models, taking the study [2] as an example, commonly exhibits unstable behavior with large displacements and scarce focal regions. Generative models, taking the study [43] as an example, shows less attention to regions of interest. The proposed ScanDMM can produce more realistic scanpaths that focus on regions of interests. + +- humans are allowed to use both head and gaze movements to explore viewpoints of interest in the scene. In such a case, viewing conditions, e.g., the starting point of viewing, has an important impact on humans' scanpaths [20, 21, 52], and leads to complex and varied scanpaths among humans. This is inherently different from what happens in 2D visuals since humans can directly guide their attention to the regions of interest. Therefore, scanpath prediction for $360^{\circ}$ images is a more complex task. + +Current $360^{\circ}$ image scanpath prediction methods could + +be roughly divided into two categories: saliency-based [2, 70, 71] and generative methods [42, 43]. The basic idea of the former one is to sample predicted gaze points from a saliency map. The performance of such methods is highly dependent on that of the saliency maps. Furthermore, constructing a satisfactory sampling strategy to account for time-dependent visual behavior is non-trivial – the results of SaltiNet [2] exhibit unstable behavior with large displacements and scarce focal regions (see Fig. 1). The latter group of methods utilizes the advance of generative models, e.g., Generative Adversarial Network (GAN), to predict realistic scanpaths. However, such methods show less attention to regions of interests (see Fig. 1). In addition, the GAN-based methods are less flexible in determining the length of scanpaths and commonly suffer from unstable training. + +None of above-mentioned studies give a complete treatment of the time-dependency of viewing behavior, which is critical for modeling dynamic gaze behaviors in $360^{\circ}$ images. For time-series data, a popular approach is to leverage sequential models, e.g., recurrent neural networks (RNNs), as exemplified in gaze prediction for $360^{\circ}$ videos [17, 35, 45]. However, such deterministic models are prone to overfitting, particularly on small $360^{\circ}$ databases. More importantly, they typically make simplistic assumptions, e.g., one choice is to concatenate the saliency map to the model's hidden states [17, 45], which assumes that the network learns how the states evolve by learning from saliency maps. Nevertheless, the neuroscience research [62] reveals that in addition to top-down and bottom-up features, prior history and scene semantics are essential sources for guiding visual attention. Moreover, to be identified as interests or rejected as distractors, items must be compared to target templates held in memory [62]. Inspired by this, we argue that humans' scanpaths in $360^{\circ}$ scenes are complex nonlinear dynamic attentional landscapes over time as a function of interventions of scene semantics on visual working memory. We present a probabilistic approach to learning the visual states that encode the time-dependent attentional landscape by specifying how these states evolve under the guidance of scene semantics and visual working memory. We instantiate our approach in the Deep Markov Model (DMM) [28], namely ScanDMM. Our contributions can be summarized as follows: + +- We present a novel method for time-dependent visual attention modeling for $360^{\circ}$ images. Specifically, we model the mechanism of visual working memory by maintaining and updating the visual state in the Markov chain. Furthermore, a semantics-guided transition function is built to learn the nonlinear dynamics of the states, in which we model the interventions of scene semantics on visual working memory. +- We propose a practical strategy to initialize the visual state, facilitating our model to focus on learning the + +dynamics of states with correct "loader", as well as enabling us to assign a specific starting point for scanpath generation. Moreover, ScanDMM is capable of producing 1,000 variable-length scanpaths within one second, which is critical for real-world applications. + +- We apply the proposed ScanDMM to two other computer vision tasks - saliency detection and image quality assessment, which demonstrates our model equips with strong generalizability and is expected to provide insights into other vision tasks. + +# 2. Related Work + +# 2.1. Visual Attention for 2D Images + +Modeling Spatial Distribution of Gazes. Visual attention depends on two distinct types of attentional mechanisms: bottom-up and top-down mechanisms [10]. The performance of classic saliency detection methods for 2D images primarily depends on bottom-up features, e.g., colour, luminance, contrast and texture, for modeling visual attention [15, 18, 19, 24]. Although the studies [40, 69] incorporate top-down features, e.g., human faces and texts, there are still obstacles in combining bottom-up and top-down visual features. Deep learning methods [36, 57, 59, 68] take advantage of large-scale databases and well-established convolutional neural networks (CNNs), and they have achieved remarkable success. + +Modeling Dynamic Gaze Behaviors. The studies in neuroscience suggest that scanpath generation can be an iterative process: while the eye fixates on an image location, the brain selects the next location to look at [26, 48]. Biologically inspired methods model such mechanism in different ways, e.g., considering the inhibition-of-return mechanism [25, 49, 53], maintaining the residual perceptual information maps [58], modeling the retina transformation [1], and utilizing low-level semantic information [55, 67]. Another class of methods is statistically inspired for modeling dynamic gaze behaviors. A typical approach is to model fixation distributions by the product of the saliency map and the previous fixation location [4, 5, 13, 30, 33, 63]. Some studies regard fixation distributions as Gaussian densities, and model scanpath by leveraging component analysis [54] or hidden markov models [12]. Different from interpretable models, fitting the data using deep generative models can also achieve competitive performance [9, 42, 66]. + +# 2.2. Visual Attention for $360^{\circ}$ Images + +Modeling Spatial Distribution of Gazes. Saliency detection of $360^{\circ}$ images is more challenging compared with 2D images, mainly due to complex viewing behaviors and insufficient available data for $360^{\circ}$ images. According to the space that the model is applied to, saliency detection models of $360^{\circ}$ images can be grouped into two categories: 2D- + +plane-based methods [2, 22, 38] and worldview-based methods [8, 34, 44, 64]. The former models visual attention by using hand-craft features [22, 38] or data-driven features [2] extracted from the distorted (caused by the equirectangular projection) 2D plane, while the latter is designed by applying well-established 2D visual saliency detection methods on worldview plane with less distortions. + +Modeling Dynamic Gaze Behaviors. Current scanpath prediction models of $360^{\circ}$ images can be classified to two types: saliency-based models [2, 3, 70, 71] and generative models [42, 43]. The former first produces the saliency map by extracting low-level and high-level features [70, 71] or learned features from data [2, 3]. Then, scanpaths are sampled from the saliency map by maximizing information gains [70, 71] or using a stochastic approach [2, 3]. The latter group of methods models scanpaths by learning from human data. PathGAN [42] is a generative model originally developed for 2D images, and it is fine-tuned on Salient360! [47] database to be applied on $360^{\circ}$ images. However, the generated scanpaths lose sphere properties (e.g., longitudinal continuities) due to the assumption that a $360^{\circ}$ image is similar to a traditional 2D image. To address this problem, ScanGAN [43] propose to learn the image and coordinate representations by using sphere convolutional neural network (S-CNN) [11] and CoordConv layer [39], respectively. Besides, a loss function that measures the spherical distance is proposed for model training. + +# 3. The Proposed Method + +# 3.1. Problem Definition + +In $360^{\circ}$ environment, a human scanpath could be defined as a time series of gaze points $\mathbf{x}_{1:T} = (\mathbf{x}_1,\mathbf{x}_2,\dots,\mathbf{x}_T)\in \mathbb{R}^{3\times T}$ , where $\mathbf{x}_t$ is a three-dimensional coordinate $(x_{t},y_{t},z_{t})$ . Given a $360^{\circ}$ image, a scanpath prediction model aims at producing realistic scanpaths $\widetilde{\mathbf{x}}_{1:T}$ based on the human visual perception mechanism. This paper presents a probabilistic method - ScanDMM, for scanpath prediction for $360^{\circ}$ images, as shown in Fig 2. We model the mechanism of visual working memory by maintaining a set of visual states $\mathbf{z}_{1:T} = (\mathbf{z}_1,\mathbf{z}_2,\dots,\mathbf{z}_T)\in \mathbb{R}^{n\times T}$ that encodes the dynamic attentional landscapes over time ( $n$ is the dimension of the state space). Basically, the ScanDMM predicts a scanpath using the following generative process: + +Transition: $\mathbf{z}_t\sim p_{\theta_t}(\mathbf{z}_t|\mathbf{z}_{t - 1}),$ (1) + +Emission: $\widetilde{\mathbf{x}}_t\sim p_{\theta_e}(\mathbf{x}_t|\mathbf{z}_t),\quad t = 1,2,\dots,T$ (2) + +where $\sim$ means the sample operation. $p_{\theta_t}(\mathbf{z}_t|\mathbf{z}_{t - 1})$ denotes the transition probabilities between the visual states, and $p_{\theta_e}(\mathbf{x}_t|\mathbf{z}_t)$ denotes the emission probabilities that describe how the visual state generates a gaze point. Let $\theta$ denotes all + +![](images/bbd462bd7357f4fab27acc33ab6fa07ef4fe66c10a4bd3eba75e95c89d682a64.jpg) +Figure 2. An illustration of the proposed ScanDMM. Noting that the scene semantic $\hat{s}$ is deterministic for an image. + +parameters involved in the ScanDMM. We approximate the realistic scanpaths by maximizing the log-likelihood function $\log p(\mathbf{x})$ (we omit subscripts here for simplicity): + +$$ +\begin{array}{l} \max \log p _ {\theta} (\mathbf {x}) = \log \mathbb {E} _ {p _ {\theta} (\mathbf {z} | \mathbf {x})} p _ {\theta} (\mathbf {x}) \\ = \log \mathbb {E} _ {p _ {\theta} (\mathbf {z} | \mathbf {x})} \frac {p _ {\theta} (\mathbf {x} , \mathbf {z})}{p _ {\theta} (\mathbf {z} | \mathbf {x})} \tag {3} \\ = \log \mathbb {E} _ {p _ {\theta} (\mathbf {z} | \mathbf {x})} \frac {p _ {\theta_ {e}} (\mathbf {x} | \mathbf {z}) p _ {\theta_ {t}} (\mathbf {z})}{p _ {\theta} (\mathbf {z} | \mathbf {x})}. \\ \end{array} +$$ + +The posterior $p_{\theta}(\mathbf{z}|\mathbf{x})$ can be approximated by using Variational Inference [61], which seeks to derive a distribution $q_{\phi}(\mathbf{z}|\mathbf{x})$ that is parameterized by neural networks, s.t. $q_{\phi}(\mathbf{z}|\mathbf{x}) \approx p_{\theta}(\mathbf{z}|\mathbf{x})$ . Based on Jensen's inequality, $f(\mathbb{E}[x]) \geqslant \mathbb{E}[f(x)]$ where $f$ is a concave function, we adopt the Evidence Lower Bound of $\log p_{\theta}(\mathbf{x})$ as the loss function $\mathcal{L}(\theta; \phi; \mathbf{x})$ to be maximized: + +$$ +\begin{array}{l} \log p _ {\theta} (\mathbf {x}) \geqslant \mathbb {E} _ {q _ {\phi}} \log \frac {p _ {\theta_ {e}} (\mathbf {x} | \mathbf {z}) p _ {\theta_ {t}} (\mathbf {z})}{q _ {\phi} (\mathbf {z} | \mathbf {x})} \\ = \mathbb {E} _ {q _ {\phi}} \left[ \log p _ {\theta_ {e}} (\mathbf {x} | \mathbf {z}) + \log p _ {\theta_ {t}} (\mathbf {z}) - \log q _ {\phi} (\mathbf {z} | \mathbf {x}) \right] \\ = \underbrace {\mathbb {E} _ {q _ {\phi}} [ \log p _ {\theta_ {e}} (\mathbf {x} | \mathbf {z}) ]} _ {\text {R e c o n s t r u c t i o n}} - \underbrace {\mathrm {K L} (q _ {\phi} (\mathbf {z} | \mathbf {x}) \| p _ {\theta_ {t}} (\mathbf {z}))} _ {\text {R e g u l a r i z a t i o n}} \\ := \mathcal {L} (\theta ; \phi ; \mathbf {x}), \tag {4} \\ \end{array} +$$ + +where $\mathrm{KL}(\cdot \| \cdot)$ denotes the Kullback-Leibler (KL) divergence. The reconstruction term evaluates the model's accuracy and the regularization term enforces the closeness between $q_{\phi}(\mathbf{z}|\mathbf{x})$ and $p_{\theta_t}(\mathbf{z})$ . The loss function also can be interpreted as the summation of transition $p_{\theta_t}(\mathbf{z})$ , emission $p_{\theta_e}(\mathbf{x}|\mathbf{z})$ and inference $q_{\phi}(\mathbf{z}|\mathbf{x})$ . In the following section, we describe how we design the three functions tailored for scanpath prediction for $360^{\circ}$ images. + +# 3.2. State Initialization + +Different from the common strategy that simply sets the initial state to zero vector [28] or random vector [27], we + +propose a practical strategy considering the starting points of scanpaths. The motivation derives from recent studies [20, 21, 52], which reveal that the starting point of viewing has an important influence on the scanpaths. To make our model better focus on learning the dynamics of visual states with the correct "loader" rather than random scratch, in the training stage, we directly use the starting point $\mathbf{x}_1$ to initialize $\mathbf{z}_0$ : + +$$ +\mathbf {z} _ {0} = \mathbf {F} \left(\hat {\mathbf {z}} _ {0}, \mathbf {x} _ {1}\right), \tag {5} +$$ + +where $\hat{\mathbf{z}}_0$ is a learnable parameter. $\mathbf{F}$ denotes linear neural networks (see Fig. 2 for details). An advantage of such configuration is that we can assign a specific starting point for scanpath generation, which is flexible and even crucial in some visual tasks, e.g., image quality assessment (see Section 5.2). Notably, to fairly compare ScanDMM with other scanpath prediction models, in the model evaluation, we randomly sample the starting points from an Equator Bias Map that covers the whole longitude and $20\%$ latitude. + +# 3.3. Transition Function + +Transition function $p_{\theta_t}(\mathbf{z_t}|\mathbf{z}_{t - 1})$ controls the dynamics of the visual states, in which the history state $\mathbf{z}_{t - 1}$ functions as visual working memory that maintains the history attentional landscape. Inspired by the recent study in neuroscience [62], we propose to learn the dynamics guided by scene semantics. Due to the space-varying distortions inherent to equirectangular projections, we choose to extract scene semantics $\hat{\mathbf{s}}\in \mathbb{R}^{n\times 1}$ using S-CNN [11]. Moreover, by considering the spatial locations of semantic features are critical for scanpath prediction, we utilize the CoordConv strategy [39] to give convolutions access to their own input coordinates, as suggested in [43]. Given the scene semantics $\hat{\mathbf{s}}$ and the history visual state $\mathbf{z}_{t - 1}$ , transition function samples $\mathbf{z}_t$ from the following Gaussian densities: + +$$ +\mathbf {z} _ {t} \sim \mathcal {N} \left(\mu_ {t} ^ {z}, \sigma_ {t} ^ {z}\right), \tag {6} +$$ + +where $\mu_t^z$ and $\sigma_t^z\in \mathbb{R}^{n\times 1}$ are the mean and scale of Gaussian densities describing an attentional landscape of the visual state $\mathbf{z}_t$ . + +Here, we present how we produce the two Gaussian parameters. Firstly, we compute the new underlying gaze distributions $\hat{\mathbf{z}}_t$ by + +$$ +\hat {\mathbf {z}} _ {t} = \mathbf {W} _ {z} ^ {t} (\mathbf {z} _ {t - 1} \oplus \hat {\mathbf {s}}) + \mathbf {b} _ {z} ^ {t}, \tag {7} +$$ + +where $\oplus$ is the concatenate operation, $\mathbf{W}_z^t\in \mathbb{R}^{n\times 2n}$ and $\mathbf{b}_z^t\in \mathbb{R}^{n\times 1}$ are learnable parameters of the neural networks. Inspired by the Long Short-Term Memory [23], we introduce the uncertainty weighting for adaptively determining how much components of the previous visual state $\mathbf{z}_{t - 1}$ to be updated: + +$$ +\alpha_ {t} = \sigma \left(\mathbf {W} _ {\alpha} ^ {t} \mathbf {z} _ {t - 1} + \mathbf {b} _ {\alpha} ^ {t}\right), \tag {8} +$$ + +where $\alpha_{t}$ is an uncertainty weighting determined by the history state $\mathbf{z}_{t - 1}$ , and $\sigma$ denotes the sigmoid function. $\mathbf{W}_{\{\alpha ,\sigma \}}^{t}\in \mathbb{R}^{n\times n}$ and $\mathbf{b}_{\{\alpha ,\sigma \}}^t\in \mathbb{R}^{n\times 1}$ are learnable parameters of the neural networks. Finally, the two Gaussian parameters, $\mu_t^z$ and $\sigma_t^z$ , are computed by: + +$$ +\mu_ {t} ^ {z} = \alpha_ {t} \hat {\mathbf {z}} _ {t} + (1 - \alpha_ {t}) \mathbf {z} _ {t - 1}, \tag {9} +$$ + +$$ +\sigma_ {t} ^ {z} = \log \left(1 + \exp \left(\mathbf {W} _ {\sigma} ^ {t} \hat {\mathbf {z}} _ {t} + \mathbf {b} _ {\sigma} ^ {t}\right)\right). \tag {10} +$$ + +# 3.4. Emission Function + +Emission function $p_{\theta_e}(\mathbf{x}_t|\mathbf{z}_t)$ describes how a gaze point $\widetilde{\mathbf{x}}_t$ is generated from the visual state $\mathbf{z}_t$ . As a gaze point is parameterized as a three-dimensional coordinate, we model the emission process by sampling $\widetilde{\mathbf{x}}_t$ from the three-dimensional Gaussian densities that are parameterized by $\mu_t^x$ and $\sigma_t^x\in \mathbb{R}^{3\times 1}$ : + +$$ +\widetilde {\mathbf {x}} _ {t} \sim \mathcal {N} \left(\mu_ {t} ^ {x}, \sigma_ {t} ^ {x}\right), \tag {11} +$$ + +where $\mu_t^x$ and $\sigma_t^x$ are determined by the current visual state $\mathbf{z}_t$ : + +$$ +\mu_ {t} ^ {x} = 2 \sigma \left(\mathbf {W} _ {\mu} ^ {e} \mathbf {z} _ {t} + \mathbf {b} _ {\mu} ^ {e}\right) - 1, \tag {12} +$$ + +$$ +\sigma_ {t} ^ {x} = \log \left(1 + \exp \left(\mathbf {W} _ {\sigma} ^ {e} \mathbf {z} _ {t} + \mathbf {b} _ {\sigma} ^ {e}\right)\right). \tag {13} +$$ + +$\mathbf{W}_{\{\mu, \sigma\}}^e \in \mathbb{R}^{3 \times n}$ and $\mathbf{b}_{\{\mu, \sigma\}}^e \in \mathbb{R}^{3 \times 1}$ are learnable parameters of the neural networks. + +# 3.5. Inference + +Inference for a latent state can be made using information from past and future true observations [28], i.e., GT gaze points in this study. In other words, the goal of inference is to provide an approximation to the exact posterior $p_{\theta}(\mathbf{z}_{1:T}|\mathbf{x}_{1:T})$ . Here, we leverage the Variational Inference [61] to approximate $p_{\theta}(\mathbf{z}_{1:T}|\mathbf{x}_{1:T})$ with a tractable family of conditional distributions $q_{\phi}(\mathbf{z}_{1:T}|\mathbf{x}_{1:T})$ : + +$$ +q _ {\phi} \left(\mathbf {z} _ {1: T} \mid \mathbf {x} _ {1: T}\right) = \prod_ {t = 1} ^ {T} q _ {\phi} \left(\mathbf {z} _ {t} \mid \mathbf {z} _ {t - 1}, \mathcal {H} \left(\mathbf {x} _ {t: T}\right)\right) \tag {14} +$$ + +$$ +\begin{array}{l l} \text {s . t .} & q _ {\phi} (\mathbf {z} _ {t} | \mathbf {z} _ {t - 1}, \mathcal {H} (\mathbf {x} _ {t: T})) \sim \mathcal {N} (\mu_ {t} ^ {i}, \sigma_ {t} ^ {i}), \end{array} +$$ + +where $\mathcal{H}(\cdot) \in \mathbb{R}^{m \times 1}$ is the variational parameter computed by mapping a variable-length sequences $\mathbf{x}_{t:T}$ to its $m$ -dimensional space. We implement this by using RNN [28]. The Gaussian parameters $\mu_t^i$ and $\sigma_t^i \in \mathbb{R}^{n \times 1}$ are produced by the following process: + +$$ +\mathcal {C} _ {t} = \frac {1}{2} \left(\left(\mathbf {W} _ {c} ^ {i} \mathbf {z} _ {t - 1} + \mathbf {b} _ {c} ^ {i}\right) + \mathcal {H} \left(\mathbf {x} _ {t: T}\right)\right), \tag {15} +$$ + +$$ +\mu_ {t} ^ {i} = \mathbf {W} _ {\mu} ^ {i} \mathcal {C} _ {t} + \mathbf {b} _ {\mu} ^ {i}, \tag {16} +$$ + +$$ +\sigma_ {t} ^ {i} = \log \left(1 + \exp \left(\mathbf {W} _ {\sigma} ^ {i} \mathcal {C} _ {t} + \mathbf {b} _ {\sigma} ^ {i}\right)\right), \tag {17} +$$ + +where $\mathcal{C}_t$ denotes the combined feature of the previous state $\mathbf{z}_{t - 1}$ and the RNN hidden state $\mathcal{H}(\mathbf{x}_{t:T})$ . $\mathbf{W}_c^i\in \mathbb{R}^{n\times m}$ , $\mathbf{W}_{\{\mu ,\sigma \}}^i\in \mathbb{R}^{n\times m}$ , $\mathbf{b}_c^i\in \mathbb{R}^{m\times 1}$ , and $\mathbf{b}_{\{\mu ,\sigma \}}^i\in \mathbb{R}^{n\times 1}$ are learnable parameters of the neural networks. + +# 4. Experiments + +In this section, we present the experimental results to validate the effectiveness of the proposed ScanDMM. We refer the interested readers to the supplementary file for more details on ScanDMM, datasets, and qualitative comparisons. + +# 4.1. Dataset + +We use four $360^{\circ}$ image databases to conduct experiments, including Sitzmann [51], Salient360! [47], AOI [65], and JUFE [20]. Sitzmann [51] database contains 22 images and 1,980 scanpaths, 19 of 22 images are used for training, and the remaining are used for validation. Salient360! [47] database contains two sets: training and benchmark sets. In this paper, we consistently use its training set that contains 85 images and 3,036 scanpaths for evaluation since its benchmark set is not publicly available. AOI [65] database contains 600 high-resolution $360^{\circ}$ images and 18,000 scanpaths. JUFE [20] database is constructed for studying $360^{\circ}$ image quality assessment, containing 1,032 images and 30,960 scanpaths. For the latter two databases, we randomly select $20\%$ images for model evaluation. To obtain Ground-Truth (GT) scanpaths for model training and evaluation, we sample the raw scanpaths at $1\mathrm{Hz}$ on each database. Noting that the scanpaths of the AOI database had been processed by the authors, so we did not make any post-processing. + +# 4.2. Experimental Setup + +Implementation Details. We train the proposed model using Sitzmann [51] database. To augment data, we longitudinally shift the $360^{\circ}$ images and adjust their scanpaths accordingly [43], which yields $19 \times 6 = 114$ images for training. Before the panoramic images are fed into the network, they are resized as (128, 256). The learning rate is set to $3e-4$ and is decreased by a factor of 0.99998 at each epoch. The dimensions of the visual state and RNN hidden state are set to 100 and 600, respectively. The network was trained for 500 epochs. + +Evaluation Metrics. We use three metrics to evaluate the performance of $360^{\circ}$ scanpath prediction models, including the Levenshtein distance (LEV), dynamic time warping (DTW), and recurrence measure (REC), as suggested in [16,43]. Generally, lower LEV/DTW values and higher REC values mean better prediction performance. For an image with $N$ GT scanpaths $\mathbf{x}^{1:N}$ , we generate $\hat{N} = N$ fake scanpaths $\widetilde{\mathbf{x}}^{1:\hat{N}}$ for comparison. The lengths of generated scanpaths are equal to that of the viewing time $^1$ . To compare a set of GT scanpaths $\mathbf{x}^{1:N}$ to another set of predicted scanpaths $\widetilde{\mathbf{x}}^{1:\hat{N}}$ , taking LEV as an example, we choose to compute each metric for all possible pairwise comparisons + +and average the results: + +$$ +\mathrm {m L E V} = \frac {1}{N \hat {N}} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {\hat {N}} \operatorname {L E V} \left(\mathbf {x} ^ {i}, \widetilde {\mathbf {x}} ^ {j}\right). \tag {18} +$$ + +To reduce the evaluation bias caused by the randomly generated scanpaths, we test each generative model with 10 times and average these 10 results to obtain the final performance. To make the results more comparable and interpretable, for each metric, we compute the human consistency [43] as a realistic upper bound for model performance (see Human in Tab. 1). Specifically, we compare each GT scanpath against all the other ones and average the results. We also compare to the results of a chance model – produce scanpaths by adding a random Brownian motion to the previous positions (see Random walk in Tab. 1). + +
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]Random walk48.9422232.9872.669
CLE [4]45.1761967.2863.130
DeepGaze III [30]46.4241992.8593.082
SaliTiNet [2]51.3702305.0991.564
ScanGAN [43]45.2701951.8483.241
ScanDMM44.9661965.4273.475
Human41.1881836.9866.345
Salient360! [47]Random walk40.8022231.6812.744
CLE [4]39.7741714.4093.323
DeepGaze III [30]40.0061742.3512.588
SaliTiNet [2]40.8481855.4772.305
ScanGAN [43]38.9321721.7113.099
ScanDMM37.2721528.5923.576
Human35.0841382.5905.202
AOI [65]Random walk13.696711.5162.993
CLE [4]12.865547.8923.617
DeepGaze III [30]13.155558.4452.892
SaliTiNet [2]14.695596.5442.244
ScanGAN [43]12.889552.4463.750
ScanDMM12.127537.5044.024
Human9.243389.4776.228
JUFE [20]Random walk24.0391193.7253.109
CLE [4]24.8441172.1503.013
DeepGaze III [30]24.1291104.8482.774
SaliTiNet [2]26.0741287.1441.540
ScanGAN [43]24.2091094.9783.075
ScanDMM23.0911086.0144.329
Human18.3061038.8807.745
+ +Table 1. Performance of scanpath prediction models on different databases. The best performance is highlighted. + +# 4.3. Performance Comparison + +Model Selection. We compare ScanDMM to four state-of-the-art scanpath prediction models: CLE [5], DeepGaze III [30], SaltiNet [2], and ScanGAN [43]. The first two models are built for traditional images, and the latter two are tailored for $360^{\circ}$ images. For DeepGaze III and SaltiNet with larger sizes, we choose to use the pre-trained weights provided by the corresponding authors to avoid overfitting + +![](images/5b3912b9dc1b4c5d4cbf1880f43e0bd1c056fbd8982c482600ea07d386b236e2.jpg) +Figure 3. Qualitative comparison to different scanpath prediction models for four different scenes. From left to right: scanpath samples obtained by a observer, scanpath results obtained by CLE [4], DeepGaze III [30], SaltiNet [2], ScanGAN [43], and the proposed model. From top to bottom: the Room from Sitzmann [51] database, the Museum from Salient360! [47] database, the Party from AOI [65] database, and the Park from JUFE [20] database. + +
MethodParamtersRunning Time
CLE [4]-≈ 39 seconds
DeepGaze III [30]78.9MB≈ 11 minutes
SaliNet [2]103.6MB≈ 49 minutes
ScanGAN [43]33.9MB0.987 seconds
ScanDMM18.7MB0.737 seconds
+ +on small $360^{\circ}$ image datasets. PathGAN [42] and Zhu et al. [71] are the other two popular scanpath prediction methods for $360^{\circ}$ images. Nevertheless, we do not include them in comparison since the study [43] had shown their failures in producing realistic scanpaths for $360^{\circ}$ images. + +Accuracy Comparison. Table 1 and Fig. 3 show that our model could provide results closer to the human scanpaths. In Fig. 3, we observe that CLE and DeepGaze III exhibit large displacements that might caused by the treatment that regarding $360^{\circ}$ images as 2D images. Saliency-based scanpath prediction model, exhibits unstable behavior with large displacements and scarce focal regions (e.g., referring to Room or Park of Fig. 3), leading to worse results than the Random walk model. The proposed model could better focus on the salient objects in scenes than ScanGAN (e.g., referring to Museum, Party or Park of Fig. 3). + +Efficiency Comparison. We also compare the efficiency in terms of the model size and running time. The results are shown in Table 2. Our model has the smallest size - 18.7MB, which is about $1/5$ of the size of SaliNet. For running time comparison, we record the time cost to gen + +Table 2. Efficiency comparison in terms of the model size and running time (computed by the time cost of producing 1,000 scanpaths). Noting that CLE is a traditional model that built on saliency maps, we only count the time to produce the scanpaths. + +
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]ScanDMM(I)45.9491996.4563.091
ScanDMM(S)46.8002098.4122.833
ScanDMM(IS)46.4892011.1572.904
ScanDMM44.9661965.4273.475
Salient360! [47]ScanDMM(I)38.3401698.5173.168
ScanDMM(S)39.1941787.6742.744
ScanDMM(IS)38.9581720.8942.853
ScanDMM37.2721528.5923.576
+ +Table 3. Ablation study. The effectiveness of our designs is well justified. + +erate 1,000 scanpaths for a given image. The results show that our model has the fastest inference speed - 0.737 seconds. + +# 4.4. Ablation Study + +We conduct ablation experiments to analyze the impact of the state initialization strategy and the scene semantics on the proposed model. We compare the proposed ScanDMM with three baselines: (1) $\mathrm{ScanDMM}_{(\mathrm{I})}$ , initializing state directly using learnable parameter: $\mathbf{z}_0 = \hat{\mathbf{z}}_0$ . (2) $\mathrm{ScanDMM}_{(\mathrm{S})}$ , removing scene semantics $\hat{\mathbf{s}}$ in Eq. 7. (3) $\mathrm{ScanDMM}_{(\mathrm{IS})}$ , performing both of the two modifications. All baseline models are trained in the same settings, and the results are shown in Table 3. We can observe that the model achieves the best performance when incorporating both the state initialization strategy and the scene semantics. + +# 5. Applications + +In this section, we demonstrate the generalizability of our model by applying it to two downstream applications - saliency detection and quality assessment for $360^{\circ}$ images. + +
DatabaseMethodAUC ↑NSS ↑CC ↑KLD ↓
Sitzmann [51]BMS360 [34]0.8311.3280.6660.475
GBVS360 [34]0.8451.4330.6930.374
SaltiNet [2]0.7620.9480.4970.671
SalNet360 [44]0.8411.4670.7180.421
SalGAN360 [8]0.8131.1880.6120.561
ScanGAN [43]0.7610.9020.4750.654
ScanDMM0.7670.9580.5210.609
Human0.8772.2651.0000.117
Salient360! [47]BMS360 [34]0.7480.9070.5670.476
GBVS360 [34]0.7120.7750.4840.576
SaltiNet [2]0.7370.8420.5300.514
SalNet360 [44]0.7440.9890.6020.476
SalGAN360 [8]0.7590.9750.6130.495
ScanGAN [43]0.7280.7740.4910.556
ScanDMM0.7771.0420.6600.384
Human0.8602.3951.0000.290
+ +# 5.1. Saliency Detection for $360^{\circ}$ images + +Visual attention prediction, commonly known as saliency detection, is the task of inferring the objects or regions that attract human attention in a scene. Intuitively, an ideal scanpath prediction model should be able to model spatially visual attention. In this section, we apply the proposed ScanDMM and ScanGAN [43] to the saliency detection task by generating 1,000 scanpaths and post-processing these gaze points to yield continuous saliency maps. Specifically, we convolve fixation maps, the two-dimensional records of the locations of all the gaze points, with a modified Gaussian [56]: + +$$ +G (x, y) = \frac {1}{2 \pi \sigma_ {y} ^ {2}} \exp \left(- \frac {x ^ {2}}{2 \sigma_ {x}}\right) \exp \left(- \frac {y ^ {2}}{2 \sigma_ {y}}\right) \tag {19} +$$ + +where $\sigma_{x} = \frac{\sigma_{y}}{\cos(\theta)}$ . $\sigma_{y} = 19^{\circ}$ is a constant value, and $\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is the latitude of the gaze point. + +Evaluation Metrics. We evaluate saliency detection models using 4 metrics: the Judd variant of the area under curve (AUC) [6], normalized scanpath saliency (NSS) [46], correlation coefficient (CC) [32], and Kullback-Leibler divergence (KLD) [31]. Similarly, for each metric, we compute the human consistency as a realistic upper bound for model performance [7], referring to Human in Table 4. Specifically, we first compare the fixations of two groups of $M$ observers, where $M$ varies from 1 to $N/2$ (i.e., half of the total $N$ observers). We then fit the $N/2$ performance scores to a power function (i.e., $aM^b + c$ ), and predict the human performance as that of two groups of infinite observers (which is equal to $c$ , for $b < 0$ ). + +Performance Comparison. We compare different saliency detection models on Sitzmann [51] and Salient360! [47] + +Table 4. Performance of saliency prediction models on Sitzmann [51] and Salient360! [47] databases. + +
MethodCC ↑SRCC ↑RMSE ↓
PSNR0.1560.0160.787
PSNRGAN0.1350.0140.790
PSNR\(DMM\)0.5630.5460.659
PSNR\(Human\)0.5850.5830.646
SSIM0.1480.0460.788
SSIM\(GAN\)0.1620.0460.790
SSIM\(DMM\)0.5190.5090.681
SSIM\(Human\)0.5270.5320.677
VIF0.1630.0960.786
VIF\(GAN\)0.1470.0920.788
VIF\(DMM\)0.5970.5720.639
VIF\(Human\)0.6160.6010.628
DISTS0.1620.0810.786
DISTSGAN0.1760.1000.784
DISTSDMM0.6620.6750.597
DISTSHuman0.7000.7110.569
DeepWSD0.1600.0440.786
DeepWSD\(GAN\)0.1620.0720.786
DeepWSD\(DMM\)0.6350.6280.616
DeepWSD\(Human\)0.6680.6670.593
+ +Table 5. Performance of quality assessment models on JUFE [20] database. + +databases. In addition to ScanGAN [43], we also compare the proposed ScanDMM with 5 saliency detection models tailored for $360^{\circ}$ images: BMS360 [34], GBVS360 [34], SalGAN [8], SalNet [44], and SaliNet [2], the results are shown in Table 4 and Fig. 4. Table 4 shows that the proposed ScanDMM achieves the best performance on Salient360! database, while its performance drops apparently on Sitzmann database. One reason might be that scanpath-to-saliency models are worse at suppressing nonsalient regions than the models tailored for $360^{\circ}$ images (please refer to the supplementary file for the complete comparison), e.g., referring to Robot in Fig. 4. The results show that applying the scanpath prediction model for the saliency detection task is encouraging. Nevertheless, there is significant room for improvement, as evidenced by a large performance gap between computational models and humans. + +# 5.2. Quality Assessment for $360^{\circ}$ Images + +The image quality assessment (IQA) model aims at predicting the perceived quality of visual images [41]. Recent studies [20,21,52] reveal that the viewing behaviors may be indispensable for quality assessment for $360^{\circ}$ scenes, highlighting the importance of scanpath prediction in $360^{\circ}$ IQA. In this section, we show how much gain scanpath prediction models can provide for $360^{\circ}$ IQA. Specifically, we leverage the computational framework [52], which offers us a natural way to utilize scanpaths for $360^{\circ}$ IQA. Basically, there have 4 steps: (1) Extracting the sequences of rectilinear projections of viewports along different generated scanpaths. (2) Computing the "frame-level" (i.e., viewpoint-level) quality scores by using existing 2D IQA models. (3) Computing the + +![](images/713be85e91fbdfa172feefb7649fd14c024c14f09f6a946d4e20a4c4745d7b6e.jpg) +Figure 4. Qualitative comparison to different saliency detection models for six different scenes. First two columns: Square and Robot of Sitzmann [51] database. Last four columns: Theater, Mall, Gallery and Airplane of Salient360! [47] database. From top to bottom: $360^{\circ}$ images, GT saliency maps, the predictions of ScanGAN [43] and the proposed ScanDMM. + +perceived quality of a "video" (i.e., a viewpoint sequence) by temporally pooling the frame-level quality scores. (4) Averaging the quality scores of all videos to obtain the final perceived quality of the $360^{\circ}$ image. + +Evaluation Metrics. We use 3 evaluation metrics to quantify the quality prediction performance, including CC, Spearman's rank-order correlation coefficient (SRCC) and root mean square error (RMSE). Generally, higher CC/SRCC values and lower RMSE values mean better performance. + +Performance Comparison. We conduct comparison experiments on JUFE [20] database, in which each image has 4 quality labels corresponding to 4 different viewing conditions (2 starting point $\times$ 2 exploration time). Considering this database is goal-directed (i.e., IQA), we retrain the ScanDMM and ScanGAN [43] on $80\%$ training set. We generate $\hat{N} = N$ fake scanapths for extracting viewpoint sequences for each image. For frame-level quality calculation, we employ five 2D IQA models, including the Peak Signal-to-Noise Ratio (PSNR), the Structural SIMilarity index (SSIM) [60], the Visual information fidelity (VIF) [50], the Deep Image Structure and Texture Similarity metrics (DISTS) [14], and the DeepWSD [37]. Then, the Gaussian weighting function [52] is chosen to temporally pool the frame-level quality scores. We add "GAN", "DMM", and "Human" to the five IQA methods as the subscripts to name the quality model that uses the scanpaths generated by ScanGAN [43], ScanDMM, and human, respectively. We also directly apply 2D IQA models to equirectangular projections as baselines. The results are shown in Table 5, where we can observe that all baseline models fail to predict the perceived quality, which is reasonable since they produce one quality score for a given image that has four quality labels. Conversely, our ScanDMM can simulate the viewing behaviors under the specific viewing condition thanks to the + +state initialization strategy, which significantly improves the performance of 2D IQA models and have competitive performance compared with Human models. ScanGAN [43], however, is not applicable due to the uncontrollable starting points. Current work only tests traditional 2D IQA models, future models that take better account for VR-specific distortions will have great potential to boost the performance. + +# 6. Conclusion and Discussion + +This paper presents a scanpath prediction model for $360^{\circ}$ images and demonstrates its crucial capabilities, i.e., high accuracy, efficiency and generalizability, for real-world applications. Moreover, we provide a novel perspective for saliency detection and quality assessment in $360^{\circ}$ scenes - constructing models by simulating humans' viewing behaviors, which is an extremely natural way if we recall how we obtain the GT labels. Nevertheless, there is still much to explore, as we only simply exploit generated scanpaths without elaborately designing for a specific task. While this paper primarily focuses on static $360^{\circ}$ images, our ScanDMM can be easily adapted to dynamic $360^{\circ}$ videos by feeding dynamic scene semantics to the network. Moreover, as a probabilistic approach, ScanDMM is able to learn the general pattern of the viewing behaviors in $360^{\circ}$ scenes, thus could also be applied to VR transmission, automatic cinematography, navigation, virtual scene design, etc. + +# Acknowledgments + +This work was supported in part by the National Key Research and Development Program of China under Grant 2018AAA0100601, in part by the National Natural Science Foundation of China under Grant 62132006, and in part by the Natural Science Foundation of Jiangxi Province of China under Grant 20223AEI91002. + +# References + +[1] Hossein Adeli, Françoise Vitu, and Gregory J Zelinsky. A model of the superior colliculus predicts fixation locations during scene viewing and visual search. Journal of Neuroscience, 37(6):1453-1467, 2017. 2 +[2] Marc Assens, Xavier Giro-i Nieto, Kevin McGuinness, and Noel E. O'Connor. SaltiNet: Scan-path prediction on 360 degree images using saliency volumes. 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Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 536, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 656 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 536, + 287, + 656 + ], + "type": "text", + "content": " images, also referred to as omnidirectional, sphere or virtual reality (VR) images, have been a popular type of visual data in many applications, providing us with immersive experiences. Nevertheless, how people explore virtual environments in " + }, + { + "bbox": [ + 46, + 536, + 287, + 656 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 536, + 287, + 656 + ], + "type": "text", + "content": " images has not been well understood. The scanpath prediction model that aims at generating realistic gaze trajectories has obtained increasing attention due to its significant influence in understanding users' viewing behaviors in VR scenes, as well as in developing VR rendering, display, compression, and transmission [51]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "content": "Scanpath prediction has been explored for many years in 2D images [29]. However, " + }, + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 657, + 287, + 693 + ], + "type": "text", + "content": " images are different greatly from 2D images, as a larger space is offered to interact with" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 321, + 226, + 532, + 469 + ], + "blocks": [ + { + "bbox": [ + 321, + 226, + 532, + 469 + ], + "lines": [ + { + "bbox": [ + 321, + 226, + 532, + 469 + ], + "spans": [ + { + "bbox": [ + 321, + 226, + 532, + 469 + ], + "type": "image", + "image_path": "b5d535c60e89315649dd7e18e90e57b3a02c69fc1fd2a7551a0364150fc510f3.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 479, + 545, + 579 + ], + "lines": [ + { + "bbox": [ + 305, + 479, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 545, + 579 + ], + "type": "text", + "content": "Figure 1. Existing scanpath prediction models for " + }, + { + "bbox": [ + 305, + 479, + 545, + 579 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 305, + 479, + 545, + 579 + ], + "type": "text", + "content": " images could be classified to two types: saliency-based models [2, 70, 71] and generative models [42, 43]. The scanpaths produced by saliency-based models, taking the study [2] as an example, commonly exhibits unstable behavior with large displacements and scarce focal regions. Generative models, taking the study [43] as an example, shows less attention to regions of interest. The proposed ScanDMM can produce more realistic scanpaths that focus on regions of interests." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 593, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 700 + ], + "type": "text", + "content": "- humans are allowed to use both head and gaze movements to explore viewpoints of interest in the scene. In such a case, viewing conditions, e.g., the starting point of viewing, has an important impact on humans' scanpaths [20, 21, 52], and leads to complex and varied scanpaths among humans. This is inherently different from what happens in 2D visuals since humans can directly guide their attention to the regions of interest. Therefore, scanpath prediction for " + }, + { + "bbox": [ + 304, + 593, + 545, + 700 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 593, + 545, + 700 + ], + "type": "text", + "content": " images is a more complex task." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Current " + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": " image scanpath prediction methods could" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 240, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 240, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 240, + 712 + ], + "type": "text", + "content": "*Corresponding author (email: fa0001ng@e.ntu.edu.sg)" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6989" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "be roughly divided into two categories: saliency-based [2, 70, 71] and generative methods [42, 43]. The basic idea of the former one is to sample predicted gaze points from a saliency map. The performance of such methods is highly dependent on that of the saliency maps. Furthermore, constructing a satisfactory sampling strategy to account for time-dependent visual behavior is non-trivial – the results of SaltiNet [2] exhibit unstable behavior with large displacements and scarce focal regions (see Fig. 1). The latter group of methods utilizes the advance of generative models, e.g., Generative Adversarial Network (GAN), to predict realistic scanpaths. However, such methods show less attention to regions of interests (see Fig. 1). In addition, the GAN-based methods are less flexible in determining the length of scanpaths and commonly suffer from unstable training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "text", + "content": "None of above-mentioned studies give a complete treatment of the time-dependency of viewing behavior, which is critical for modeling dynamic gaze behaviors in " + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "text", + "content": " images. For time-series data, a popular approach is to leverage sequential models, e.g., recurrent neural networks (RNNs), as exemplified in gaze prediction for " + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "text", + "content": " videos [17, 35, 45]. However, such deterministic models are prone to overfitting, particularly on small " + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "text", + "content": " databases. More importantly, they typically make simplistic assumptions, e.g., one choice is to concatenate the saliency map to the model's hidden states [17, 45], which assumes that the network learns how the states evolve by learning from saliency maps. Nevertheless, the neuroscience research [62] reveals that in addition to top-down and bottom-up features, prior history and scene semantics are essential sources for guiding visual attention. Moreover, to be identified as interests or rejected as distractors, items must be compared to target templates held in memory [62]. Inspired by this, we argue that humans' scanpaths in " + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 252, + 289, + 586 + ], + "type": "text", + "content": " scenes are complex nonlinear dynamic attentional landscapes over time as a function of interventions of scene semantics on visual working memory. We present a probabilistic approach to learning the visual states that encode the time-dependent attentional landscape by specifying how these states evolve under the guidance of scene semantics and visual working memory. We instantiate our approach in the Deep Markov Model (DMM) [28], namely ScanDMM. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 591, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 4, + "blocks": [ + { + "bbox": [ + 58, + 591, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 591, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 58, + 591, + 287, + 686 + ], + "type": "text", + "content": "- We present a novel method for time-dependent visual attention modeling for " + }, + { + "bbox": [ + 58, + 591, + 287, + 686 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 58, + 591, + 287, + 686 + ], + "type": "text", + "content": " images. Specifically, we model the mechanism of visual working memory by maintaining and updating the visual state in the Markov chain. Furthermore, a semantics-guided transition function is built to learn the nonlinear dynamics of the states, in which we model the interventions of scene semantics on visual working memory." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- We propose a practical strategy to initialize the visual state, facilitating our model to focus on learning the" + } + ] + } + ], + "index": 3 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 324, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 324, + 72, + 545, + 133 + ], + "type": "text", + "content": "dynamics of states with correct \"loader\", as well as enabling us to assign a specific starting point for scanpath generation. Moreover, ScanDMM is capable of producing 1,000 variable-length scanpaths within one second, which is critical for real-world applications." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 136, + 545, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 136, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 317, + 136, + 545, + 196 + ], + "type": "text", + "content": "- We apply the proposed ScanDMM to two other computer vision tasks - saliency detection and image quality assessment, which demonstrates our model equips with strong generalizability and is expected to provide insights into other vision tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 205, + 392, + 217 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 392, + 217 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 392, + 217 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 225, + 474, + 238 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 225, + 474, + 238 + ], + "spans": [ + { + "bbox": [ + 306, + 225, + 474, + 238 + ], + "type": "text", + "content": "2.1. Visual Attention for 2D Images" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 243, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 545, + 398 + ], + "type": "text", + "content": "Modeling Spatial Distribution of Gazes. Visual attention depends on two distinct types of attentional mechanisms: bottom-up and top-down mechanisms [10]. The performance of classic saliency detection methods for 2D images primarily depends on bottom-up features, e.g., colour, luminance, contrast and texture, for modeling visual attention [15, 18, 19, 24]. Although the studies [40, 69] incorporate top-down features, e.g., human faces and texts, there are still obstacles in combining bottom-up and top-down visual features. Deep learning methods [36, 57, 59, 68] take advantage of large-scale databases and well-established convolutional neural networks (CNNs), and they have achieved remarkable success." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 401, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 617 + ], + "type": "text", + "content": "Modeling Dynamic Gaze Behaviors. The studies in neuroscience suggest that scanpath generation can be an iterative process: while the eye fixates on an image location, the brain selects the next location to look at [26, 48]. Biologically inspired methods model such mechanism in different ways, e.g., considering the inhibition-of-return mechanism [25, 49, 53], maintaining the residual perceptual information maps [58], modeling the retina transformation [1], and utilizing low-level semantic information [55, 67]. Another class of methods is statistically inspired for modeling dynamic gaze behaviors. A typical approach is to model fixation distributions by the product of the saliency map and the previous fixation location [4, 5, 13, 30, 33, 63]. Some studies regard fixation distributions as Gaussian densities, and model scanpath by leveraging component analysis [54] or hidden markov models [12]. Different from interpretable models, fitting the data using deep generative models can also achieve competitive performance [9, 42, 66]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 623, + 481, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 481, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 481, + 635 + ], + "type": "text", + "content": "2.2. Visual Attention for " + }, + { + "bbox": [ + 306, + 623, + 481, + 635 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 306, + 623, + 481, + 635 + ], + "type": "text", + "content": " Images" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Modeling Spatial Distribution of Gazes. Saliency detection of " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " images is more challenging compared with 2D images, mainly due to complex viewing behaviors and insufficient available data for " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " images. According to the space that the model is applied to, saliency detection models of " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " images can be grouped into two categories: 2D-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6990" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "plane-based methods [2, 22, 38] and worldview-based methods [8, 34, 44, 64]. The former models visual attention by using hand-craft features [22, 38] or data-driven features [2] extracted from the distorted (caused by the equirectangular projection) 2D plane, while the latter is designed by applying well-established 2D visual saliency detection methods on worldview plane with less distortions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "text", + "content": "Modeling Dynamic Gaze Behaviors. Current scanpath prediction models of " + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "text", + "content": " images can be classified to two types: saliency-based models [2, 3, 70, 71] and generative models [42, 43]. The former first produces the saliency map by extracting low-level and high-level features [70, 71] or learned features from data [2, 3]. Then, scanpaths are sampled from the saliency map by maximizing information gains [70, 71] or using a stochastic approach [2, 3]. The latter group of methods models scanpaths by learning from human data. PathGAN [42] is a generative model originally developed for 2D images, and it is fine-tuned on Salient360! [47] database to be applied on " + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "text", + "content": " images. However, the generated scanpaths lose sphere properties (e.g., longitudinal continuities) due to the assumption that a " + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 158, + 289, + 399 + ], + "type": "text", + "content": " image is similar to a traditional 2D image. To address this problem, ScanGAN [43] propose to learn the image and coordinate representations by using sphere convolutional neural network (S-CNN) [11] and CoordConv layer [39], respectively. Besides, a loss function that measures the spherical distance is proposed for model training." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 410, + 176, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 176, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 176, + 423 + ], + "type": "text", + "content": "3. The Proposed Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 430, + 160, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 160, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 160, + 442 + ], + "type": "text", + "content": "3.1. Problem Definition" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": "In " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " environment, a human scanpath could be defined as a time series of gaze points " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{1:T} = (\\mathbf{x}_1,\\mathbf{x}_2,\\dots,\\mathbf{x}_T)\\in \\mathbb{R}^{3\\times T}" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " is a three-dimensional coordinate " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "(x_{t},y_{t},z_{t})" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": ". Given a " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " image, a scanpath prediction model aims at producing realistic scanpaths " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}_{1:T}" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " based on the human visual perception mechanism. This paper presents a probabilistic method - ScanDMM, for scanpath prediction for " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " images, as shown in Fig 2. We model the mechanism of visual working memory by maintaining a set of visual states " + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{1:T} = (\\mathbf{z}_1,\\mathbf{z}_2,\\dots,\\mathbf{z}_T)\\in \\mathbb{R}^{n\\times T}" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " that encodes the dynamic attentional landscapes over time (" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 449, + 289, + 617 + ], + "type": "text", + "content": " is the dimension of the state space). Basically, the ScanDMM predicts a scanpath using the following generative process:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 627, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 627, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 61, + 627, + 287, + 640 + ], + "type": "text", + "content": "Transition: " + }, + { + "bbox": [ + 61, + 627, + 287, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t\\sim p_{\\theta_t}(\\mathbf{z}_t|\\mathbf{z}_{t - 1})," + }, + { + "bbox": [ + 61, + 627, + 287, + 640 + ], + "type": "text", + "content": " (1)" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 61, + 642, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 642, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 61, + 642, + 287, + 656 + ], + "type": "text", + "content": "Emission: " + }, + { + "bbox": [ + 61, + 642, + 287, + 656 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}_t\\sim p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t),\\quad t = 1,2,\\dots,T" + }, + { + "bbox": [ + 61, + 642, + 287, + 656 + ], + "type": "text", + "content": " (2)" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\sim" + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": " means the sample operation. " + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "p_{\\theta_t}(\\mathbf{z}_t|\\mathbf{z}_{t - 1})" + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": " denotes the transition probabilities between the visual states, and " + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t)" + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": " denotes the emission probabilities that describe how the visual state generates a gaze point. Let " + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": " denotes all" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 214 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 214 + ], + "type": "image", + "image_path": "bbd462bd7357f4fab27acc33ab6fa07ef4fe66c10a4bd3eba75e95c89d682a64.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 231, + 547, + 255 + ], + "lines": [ + { + "bbox": [ + 305, + 231, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 547, + 255 + ], + "type": "text", + "content": "Figure 2. An illustration of the proposed ScanDMM. Noting that the scene semantic " + }, + { + "bbox": [ + 305, + 231, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\hat{s}" + }, + { + "bbox": [ + 305, + 231, + 547, + 255 + ], + "type": "text", + "content": " is deterministic for an image." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 263, + 546, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 546, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 546, + 300 + ], + "type": "text", + "content": "parameters involved in the ScanDMM. We approximate the realistic scanpaths by maximizing the log-likelihood function " + }, + { + "bbox": [ + 304, + 263, + 546, + 300 + ], + "type": "inline_equation", + "content": "\\log p(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 263, + 546, + 300 + ], + "type": "text", + "content": " (we omit subscripts here for simplicity):" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 331, + 305, + 545, + 375 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 305, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 331, + 305, + 545, + 375 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\max \\log p _ {\\theta} (\\mathbf {x}) = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} p _ {\\theta} (\\mathbf {x}) \\\\ = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\frac {p _ {\\theta} (\\mathbf {x} , \\mathbf {z})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\tag {3} \\\\ = \\log \\mathbb {E} _ {p _ {\\theta} (\\mathbf {z} | \\mathbf {x})} \\frac {p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) p _ {\\theta_ {t}} (\\mathbf {z})}{p _ {\\theta} (\\mathbf {z} | \\mathbf {x})}. \\\\ \\end{array}", + "image_path": "5e06d3a1dbb6f4b4fab8721d71be3db286b2ed3cc0340949bc08c27b281ca3c6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": "The posterior " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": " can be approximated by using Variational Inference [61], which seeks to derive a distribution " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": " that is parameterized by neural networks, s.t. " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x}) \\approx p_{\\theta}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": ". Based on Jensen's inequality, " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "f(\\mathbb{E}[x]) \\geqslant \\mathbb{E}[f(x)]" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": " is a concave function, we adopt the Evidence Lower Bound of " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\log p_{\\theta}(\\mathbf{x})" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": " as the loss function " + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\theta; \\phi; \\mathbf{x})" + }, + { + "bbox": [ + 304, + 380, + 545, + 464 + ], + "type": "text", + "content": " to be maximized:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 470, + 545, + 568 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 470, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 307, + 470, + 545, + 568 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\log p _ {\\theta} (\\mathbf {x}) \\geqslant \\mathbb {E} _ {q _ {\\phi}} \\log \\frac {p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) p _ {\\theta_ {t}} (\\mathbf {z})}{q _ {\\phi} (\\mathbf {z} | \\mathbf {x})} \\\\ = \\mathbb {E} _ {q _ {\\phi}} \\left[ \\log p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) + \\log p _ {\\theta_ {t}} (\\mathbf {z}) - \\log q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\right] \\\\ = \\underbrace {\\mathbb {E} _ {q _ {\\phi}} [ \\log p _ {\\theta_ {e}} (\\mathbf {x} | \\mathbf {z}) ]} _ {\\text {R e c o n s t r u c t i o n}} - \\underbrace {\\mathrm {K L} (q _ {\\phi} (\\mathbf {z} | \\mathbf {x}) \\| p _ {\\theta_ {t}} (\\mathbf {z}))} _ {\\text {R e g u l a r i z a t i o n}} \\\\ := \\mathcal {L} (\\theta ; \\phi ; \\mathbf {x}), \\tag {4} \\\\ \\end{array}", + "image_path": "4ffd166de738d8205eba98412d7a8f9b679e48886f7ea041309ca9363ca2dd7a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathrm{KL}(\\cdot \\| \\cdot)" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": " denotes the Kullback-Leibler (KL) divergence. The reconstruction term evaluates the model's accuracy and the regularization term enforces the closeness between " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "p_{\\theta_t}(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": ". The loss function also can be interpreted as the summation of transition " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "p_{\\theta_t}(\\mathbf{z})" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": ", emission " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "p_{\\theta_e}(\\mathbf{x}|\\mathbf{z})" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": " and inference " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}|\\mathbf{x})" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": ". In the following section, we describe how we design the three functions tailored for scanpath prediction for " + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 569, + 545, + 665 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 671, + 416, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 416, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 416, + 682 + ], + "type": "text", + "content": "3.2. State Initialization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "content": "Different from the common strategy that simply sets the initial state to zero vector [28] or random vector [27], we" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6991" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "propose a practical strategy considering the starting points of scanpaths. The motivation derives from recent studies [20, 21, 52], which reveal that the starting point of viewing has an important influence on the scanpaths. To make our model better focus on learning the dynamics of visual states with the correct \"loader\" rather than random scratch, in the training stage, we directly use the starting point " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " to initialize " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 132, + 175, + 287, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 132, + 175, + 287, + 188 + ], + "spans": [ + { + "bbox": [ + 132, + 175, + 287, + 188 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {0} = \\mathbf {F} \\left(\\hat {\\mathbf {z}} _ {0}, \\mathbf {x} _ {1}\\right), \\tag {5}", + "image_path": "5676ae499ec5881312ebef86819b227b1b9d83271ef2ea88884e0031b5125bb7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_0" + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "text", + "content": " is a learnable parameter. " + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "text", + "content": " denotes linear neural networks (see Fig. 2 for details). An advantage of such configuration is that we can assign a specific starting point for scanpath generation, which is flexible and even crucial in some visual tasks, e.g., image quality assessment (see Section 5.2). Notably, to fairly compare ScanDMM with other scanpath prediction models, in the model evaluation, we randomly sample the starting points from an Equator Bias Map that covers the whole longitude and " + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 194, + 289, + 302 + ], + "type": "text", + "content": " latitude." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 308, + 163, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 163, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 163, + 319 + ], + "type": "text", + "content": "3.3. Transition Function" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": "Transition function " + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "inline_equation", + "content": "p_{\\theta_t}(\\mathbf{z_t}|\\mathbf{z}_{t - 1})" + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": " controls the dynamics of the visual states, in which the history state " + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": " functions as visual working memory that maintains the history attentional landscape. Inspired by the recent study in neuroscience [62], we propose to learn the dynamics guided by scene semantics. Due to the space-varying distortions inherent to equirectangular projections, we choose to extract scene semantics " + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}\\in \\mathbb{R}^{n\\times 1}" + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": " using S-CNN [11]. Moreover, by considering the spatial locations of semantic features are critical for scanpath prediction, we utilize the CoordConv strategy [39] to give convolutions access to their own input coordinates, as suggested in [43]. Given the scene semantics " + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": " and the history visual state " + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": ", transition function samples " + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 327, + 289, + 494 + ], + "type": "text", + "content": " from the following Gaussian densities:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 129, + 501, + 287, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 501, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 129, + 501, + 287, + 515 + ], + "type": "interline_equation", + "content": "\\mathbf {z} _ {t} \\sim \\mathcal {N} \\left(\\mu_ {t} ^ {z}, \\sigma_ {t} ^ {z}\\right), \\tag {6}", + "image_path": "2c2de03defce743042a28f95b54fd97f0703354b4245de668dcf3c4a5eb3a429.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mu_t^z" + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\sigma_t^z\\in \\mathbb{R}^{n\\times 1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "text", + "content": " are the mean and scale of Gaussian densities describing an attentional landscape of the visual state " + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 46, + 521, + 287, + 555 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 593 + ], + "type": "text", + "content": "Here, we present how we produce the two Gaussian parameters. Firstly, we compute the new underlying gaze distributions " + }, + { + "bbox": [ + 46, + 557, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{z}}_t" + }, + { + "bbox": [ + 46, + 557, + 287, + 593 + ], + "type": "text", + "content": " by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 111, + 598, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 598, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 111, + 598, + 287, + 613 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {z}} _ {t} = \\mathbf {W} _ {z} ^ {t} (\\mathbf {z} _ {t - 1} \\oplus \\hat {\\mathbf {s}}) + \\mathbf {b} _ {z} ^ {t}, \\tag {7}", + "image_path": "a319f4d3a14a9eab82b8dd8fb62c58721b3d0aa93c389cba79fb5af186b69647.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "inline_equation", + "content": "\\oplus" + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "text", + "content": " is the concatenate operation, " + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_z^t\\in \\mathbb{R}^{n\\times 2n}" + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_z^t\\in \\mathbb{R}^{n\\times 1}" + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "text", + "content": " are learnable parameters of the neural networks. Inspired by the Long Short-Term Memory [23], we introduce the uncertainty weighting for adaptively determining how much components of the previous visual state " + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 46, + 618, + 289, + 691 + ], + "type": "text", + "content": " to be updated:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 696, + 287, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 696, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 115, + 696, + 287, + 712 + ], + "type": "interline_equation", + "content": "\\alpha_ {t} = \\sigma \\left(\\mathbf {W} _ {\\alpha} ^ {t} \\mathbf {z} _ {t - 1} + \\mathbf {b} _ {\\alpha} ^ {t}\\right), \\tag {8}", + "image_path": "c1effda6c684dcbbfae481efb4eee864a3c44ce0e651502edfd8bbad29a15f14.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " is an uncertainty weighting determined by the history state " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " denotes the sigmoid function. " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\{\\alpha ,\\sigma \\}}^{t}\\in \\mathbb{R}^{n\\times n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_{\\{\\alpha ,\\sigma \\}}^t\\in \\mathbb{R}^{n\\times 1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " are learnable parameters of the neural networks. Finally, the two Gaussian parameters, " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mu_t^z" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\sigma_t^z" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", are computed by:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 354, + 138, + 545, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 138, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 354, + 138, + 545, + 152 + ], + "type": "interline_equation", + "content": "\\mu_ {t} ^ {z} = \\alpha_ {t} \\hat {\\mathbf {z}} _ {t} + (1 - \\alpha_ {t}) \\mathbf {z} _ {t - 1}, \\tag {9}", + "image_path": "c326d9875ba81e916e064740e1f8a8620fe29d0ddbc945aff897d2de62c68612.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 356, + 153, + 545, + 168 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 153, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 356, + 153, + 545, + 168 + ], + "type": "interline_equation", + "content": "\\sigma_ {t} ^ {z} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {t} \\hat {\\mathbf {z}} _ {t} + \\mathbf {b} _ {\\sigma} ^ {t}\\right)\\right). \\tag {10}", + "image_path": "1eaebab3ce7571bfc6830ffa6ab1cedb072bc1fe4d902d540f16af63481d3669.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 173, + 416, + 184 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 173, + 416, + 184 + ], + "spans": [ + { + "bbox": [ + 306, + 173, + 416, + 184 + ], + "type": "text", + "content": "3.4. Emission Function" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": "Emission function " + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "inline_equation", + "content": "p_{\\theta_e}(\\mathbf{x}_t|\\mathbf{z}_t)" + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": " describes how a gaze point " + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}_t" + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": " is generated from the visual state " + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": ". As a gaze point is parameterized as a three-dimensional coordinate, we model the emission process by sampling " + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}_t" + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": " from the three-dimensional Gaussian densities that are parameterized by " + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\mu_t^x" + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\sigma_t^x\\in \\mathbb{R}^{3\\times 1}" + }, + { + "bbox": [ + 304, + 191, + 545, + 263 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 388, + 269, + 545, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 388, + 269, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 388, + 269, + 545, + 283 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathbf {x}} _ {t} \\sim \\mathcal {N} \\left(\\mu_ {t} ^ {x}, \\sigma_ {t} ^ {x}\\right), \\tag {11}", + "image_path": "91fd209f8b6319560d045650a9b2c8de52b4298499e58f16e4909d0b891f29be.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "inline_equation", + "content": "\\mu_t^x" + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "inline_equation", + "content": "\\sigma_t^x" + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "text", + "content": " are determined by the current visual state " + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_t" + }, + { + "bbox": [ + 304, + 289, + 545, + 311 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 362, + 312, + 545, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 312, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 362, + 312, + 545, + 327 + ], + "type": "interline_equation", + "content": "\\mu_ {t} ^ {x} = 2 \\sigma \\left(\\mathbf {W} _ {\\mu} ^ {e} \\mathbf {z} _ {t} + \\mathbf {b} _ {\\mu} ^ {e}\\right) - 1, \\tag {12}", + "image_path": "b2d0b1adf0e8d3062e3a8c1f71da15cc875d61edd4173dc809beb42e130dc085.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 350, + 329, + 545, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 329, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 350, + 329, + 545, + 342 + ], + "type": "interline_equation", + "content": "\\sigma_ {t} ^ {x} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {e} \\mathbf {z} _ {t} + \\mathbf {b} _ {\\sigma} ^ {e}\\right)\\right). \\tag {13}", + "image_path": "75e1dc2c59e755acef0ca3a54ca4e2179bc0e0339dd0e8dabdf7feb0e708db5b.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\{\\mu, \\sigma\\}}^e \\in \\mathbb{R}^{3 \\times n}" + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_{\\{\\mu, \\sigma\\}}^e \\in \\mathbb{R}^{3 \\times 1}" + }, + { + "bbox": [ + 304, + 345, + 545, + 369 + ], + "type": "text", + "content": " are learnable parameters of the neural networks." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 376, + 373, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 376, + 373, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 376, + 373, + 387 + ], + "type": "text", + "content": "3.5. Inference" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "text", + "content": "Inference for a latent state can be made using information from past and future true observations [28], i.e., GT gaze points in this study. In other words, the goal of inference is to provide an approximation to the exact posterior " + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T})" + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "text", + "content": ". Here, we leverage the Variational Inference [61] to approximate " + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T})" + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "text", + "content": " with a tractable family of conditional distributions " + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "inline_equation", + "content": "q_{\\phi}(\\mathbf{z}_{1:T}|\\mathbf{x}_{1:T})" + }, + { + "bbox": [ + 304, + 394, + 545, + 479 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 330, + 485, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 485, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 330, + 485, + 545, + 517 + ], + "type": "interline_equation", + "content": "q _ {\\phi} \\left(\\mathbf {z} _ {1: T} \\mid \\mathbf {x} _ {1: T}\\right) = \\prod_ {t = 1} ^ {T} q _ {\\phi} \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {t - 1}, \\mathcal {H} \\left(\\mathbf {x} _ {t: T}\\right)\\right) \\tag {14}", + "image_path": "489d87efc56a4a57836dab0cae54c0b99040b04f3137f5df9875583148ebd009.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 332, + 519, + 504, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 519, + 504, + 533 + ], + "spans": [ + { + "bbox": [ + 332, + 519, + 504, + 533 + ], + "type": "interline_equation", + "content": "\\begin{array}{l l} \\text {s . t .} & q _ {\\phi} (\\mathbf {z} _ {t} | \\mathbf {z} _ {t - 1}, \\mathcal {H} (\\mathbf {x} _ {t: T})) \\sim \\mathcal {N} (\\mu_ {t} ^ {i}, \\sigma_ {t} ^ {i}), \\end{array}", + "image_path": "ae52fd8f3d82cc56c398c1332ca7634161d153fde0317c99ee329439b3a606b0.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\cdot) \\in \\mathbb{R}^{m \\times 1}" + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "content": " is the variational parameter computed by mapping a variable-length sequences " + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_{t:T}" + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "content": " to its " + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "content": "-dimensional space. We implement this by using RNN [28]. The Gaussian parameters " + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\mu_t^i" + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "inline_equation", + "content": "\\sigma_t^i \\in \\mathbb{R}^{n \\times 1}" + }, + { + "bbox": [ + 304, + 539, + 545, + 599 + ], + "type": "text", + "content": " are produced by the following process:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 348, + 605, + 545, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 605, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 348, + 605, + 545, + 628 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {t} = \\frac {1}{2} \\left(\\left(\\mathbf {W} _ {c} ^ {i} \\mathbf {z} _ {t - 1} + \\mathbf {b} _ {c} ^ {i}\\right) + \\mathcal {H} \\left(\\mathbf {x} _ {t: T}\\right)\\right), \\tag {15}", + "image_path": "0d0cc76759c5ae25da73852e54f16f9f84f57f187b90487b7929c5b8107b46fd.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 348, + 629, + 545, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 629, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 348, + 629, + 545, + 643 + ], + "type": "interline_equation", + "content": "\\mu_ {t} ^ {i} = \\mathbf {W} _ {\\mu} ^ {i} \\mathcal {C} _ {t} + \\mathbf {b} _ {\\mu} ^ {i}, \\tag {16}", + "image_path": "a3812d64cc227feedf47e0085931ea2764c70d6556c2daa67bbe7ad004b0de3d.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 348, + 645, + 545, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 645, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 348, + 645, + 545, + 660 + ], + "type": "interline_equation", + "content": "\\sigma_ {t} ^ {i} = \\log \\left(1 + \\exp \\left(\\mathbf {W} _ {\\sigma} ^ {i} \\mathcal {C} _ {t} + \\mathbf {b} _ {\\sigma} ^ {i}\\right)\\right), \\tag {17}", + "image_path": "961f837ec44afee2b6036edf32a54ccee5b4a4fd53438d0cfada5762cf40a29d.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_t" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": " denotes the combined feature of the previous state " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t - 1}" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": " and the RNN hidden state " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{H}(\\mathbf{x}_{t:T})" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_c^i\\in \\mathbb{R}^{n\\times m}" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\{\\mu ,\\sigma \\}}^i\\in \\mathbb{R}^{n\\times m}" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_c^i\\in \\mathbb{R}^{m\\times 1}" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_{\\{\\mu ,\\sigma \\}}^i\\in \\mathbb{R}^{n\\times 1}" + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": " are learnable parameters of the neural networks." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6992" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 128, + 85 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 140 + ], + "type": "text", + "content": "In this section, we present the experimental results to validate the effectiveness of the proposed ScanDMM. We refer the interested readers to the supplementary file for more details on ScanDMM, datasets, and qualitative comparisons." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 147, + 105, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 147, + 105, + 158 + ], + "spans": [ + { + "bbox": [ + 47, + 147, + 105, + 158 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "content": "We use four " + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "content": " image databases to conduct experiments, including Sitzmann [51], Salient360! [47], AOI [65], and JUFE [20]. Sitzmann [51] database contains 22 images and 1,980 scanpaths, 19 of 22 images are used for training, and the remaining are used for validation. Salient360! [47] database contains two sets: training and benchmark sets. In this paper, we consistently use its training set that contains 85 images and 3,036 scanpaths for evaluation since its benchmark set is not publicly available. AOI [65] database contains 600 high-resolution " + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "content": " images and 18,000 scanpaths. JUFE [20] database is constructed for studying " + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "content": " image quality assessment, containing 1,032 images and 30,960 scanpaths. For the latter two databases, we randomly select " + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "content": " images for model evaluation. To obtain Ground-Truth (GT) scanpaths for model training and evaluation, we sample the raw scanpaths at " + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "inline_equation", + "content": "1\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 165, + 288, + 392 + ], + "type": "text", + "content": " on each database. Noting that the scanpaths of the AOI database had been processed by the authors, so we did not make any post-processing." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 400, + 163, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 163, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 163, + 414 + ], + "type": "text", + "content": "4.2. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "text", + "content": "Implementation Details. We train the proposed model using Sitzmann [51] database. To augment data, we longitudinally shift the " + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "text", + "content": " images and adjust their scanpaths accordingly [43], which yields " + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "inline_equation", + "content": "19 \\times 6 = 114" + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "text", + "content": " images for training. Before the panoramic images are fed into the network, they are resized as (128, 256). The learning rate is set to " + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "inline_equation", + "content": "3e-4" + }, + { + "bbox": [ + 46, + 418, + 287, + 538 + ], + "type": "text", + "content": " and is decreased by a factor of 0.99998 at each epoch. The dimensions of the visual state and RNN hidden state are set to 100 and 600, respectively. The network was trained for 500 epochs." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": "Evaluation Metrics. We use three metrics to evaluate the performance of " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": " scanpath prediction models, including the Levenshtein distance (LEV), dynamic time warping (DTW), and recurrence measure (REC), as suggested in [16,43]. Generally, lower LEV/DTW values and higher REC values mean better prediction performance. For an image with " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": " GT scanpaths " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{1:N}" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": ", we generate " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\hat{N} = N" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": " fake scanpaths " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}^{1:\\hat{N}}" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": " for comparison. The lengths of generated scanpaths are equal to that of the viewing time" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": ". To compare a set of GT scanpaths " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^{1:N}" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": " to another set of predicted scanpaths " + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\widetilde{\\mathbf{x}}^{1:\\hat{N}}" + }, + { + "bbox": [ + 46, + 548, + 287, + 696 + ], + "type": "text", + "content": ", taking LEV as an example, we choose to compute each metric for all possible pairwise comparisons" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 402, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 402, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 402, + 84 + ], + "type": "text", + "content": "and average the results:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 347, + 92, + 545, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 92, + 545, + 128 + ], + "spans": [ + { + "bbox": [ + 347, + 92, + 545, + 128 + ], + "type": "interline_equation", + "content": "\\mathrm {m L E V} = \\frac {1}{N \\hat {N}} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {\\hat {N}} \\operatorname {L E V} \\left(\\mathbf {x} ^ {i}, \\widetilde {\\mathbf {x}} ^ {j}\\right). \\tag {18}", + "image_path": "42c0d786d33d0e68864231421b048b11d6e68b8b5393e26aec2aabdd61ea236f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 134, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 134, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 134, + 545, + 266 + ], + "type": "text", + "content": "To reduce the evaluation bias caused by the randomly generated scanpaths, we test each generative model with 10 times and average these 10 results to obtain the final performance. To make the results more comparable and interpretable, for each metric, we compute the human consistency [43] as a realistic upper bound for model performance (see Human in Tab. 1). Specifically, we compare each GT scanpath against all the other ones and average the results. We also compare to the results of a chance model – produce scanpaths by adding a random Brownian motion to the previous positions (see Random walk in Tab. 1)." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 275, + 547, + 559 + ], + "blocks": [ + { + "bbox": [ + 307, + 275, + 547, + 559 + ], + "lines": [ + { + "bbox": [ + 307, + 275, + 547, + 559 + ], + "spans": [ + { + "bbox": [ + 307, + 275, + 547, + 559 + ], + "type": "table", + "html": "
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]Random walk48.9422232.9872.669
CLE [4]45.1761967.2863.130
DeepGaze III [30]46.4241992.8593.082
SaliTiNet [2]51.3702305.0991.564
ScanGAN [43]45.2701951.8483.241
ScanDMM44.9661965.4273.475
Human41.1881836.9866.345
Salient360! [47]Random walk40.8022231.6812.744
CLE [4]39.7741714.4093.323
DeepGaze III [30]40.0061742.3512.588
SaliTiNet [2]40.8481855.4772.305
ScanGAN [43]38.9321721.7113.099
ScanDMM37.2721528.5923.576
Human35.0841382.5905.202
AOI [65]Random walk13.696711.5162.993
CLE [4]12.865547.8923.617
DeepGaze III [30]13.155558.4452.892
SaliTiNet [2]14.695596.5442.244
ScanGAN [43]12.889552.4463.750
ScanDMM12.127537.5044.024
Human9.243389.4776.228
JUFE [20]Random walk24.0391193.7253.109
CLE [4]24.8441172.1503.013
DeepGaze III [30]24.1291104.8482.774
SaliTiNet [2]26.0741287.1441.540
ScanGAN [43]24.2091094.9783.075
ScanDMM23.0911086.0144.329
Human18.3061038.8807.745
", + "image_path": "c8239e5937688a6e34f99487cebdc95a05c12afd39df44d0131357f59d3453a9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "lines": [ + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 545, + 592 + ], + "type": "text", + "content": "Table 1. Performance of scanpath prediction models on different databases. The best performance is highlighted." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 601, + 450, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 601, + 450, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 601, + 450, + 615 + ], + "type": "text", + "content": "4.3. Performance Comparison" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "Model Selection. We compare ScanDMM to four state-of-the-art scanpath prediction models: CLE [5], DeepGaze III [30], SaltiNet [2], and ScanGAN [43]. The first two models are built for traditional images, and the latter two are tailored for " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": " images. For DeepGaze III and SaltiNet with larger sizes, we choose to use the pre-trained weights provided by the corresponding authors to avoid overfitting" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "text", + "content": "1 For ScanGAN, we cut the produced scanpaths to the required lengths." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "6993" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 542, + 236 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 542, + 236 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 542, + 236 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 542, + 236 + ], + "type": "image", + "image_path": "5b3912b9dc1b4c5d4cbf1880f43e0bd1c056fbd8982c482600ea07d386b236e2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison to different scanpath prediction models for four different scenes. From left to right: scanpath samples obtained by a observer, scanpath results obtained by CLE [4], DeepGaze III [30], SaltiNet [2], ScanGAN [43], and the proposed model. From top to bottom: the Room from Sitzmann [51] database, the Museum from Salient360! [47] database, the Party from AOI [65] database, and the Park from JUFE [20] database." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 303, + 288, + 370 + ], + "blocks": [ + { + "bbox": [ + 47, + 303, + 288, + 370 + ], + "lines": [ + { + "bbox": [ + 47, + 303, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 47, + 303, + 288, + 370 + ], + "type": "table", + "html": "
MethodParamtersRunning Time
CLE [4]-≈ 39 seconds
DeepGaze III [30]78.9MB≈ 11 minutes
SaliNet [2]103.6MB≈ 49 minutes
ScanGAN [43]33.9MB0.987 seconds
ScanDMM18.7MB0.737 seconds
", + "image_path": "2de3bac190fae289035f64c6865285712c4652b8a5f41bb063f78ce24c6cc9f2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "content": "on small " + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "content": " image datasets. PathGAN [42] and Zhu et al. [71] are the other two popular scanpath prediction methods for " + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "content": " images. Nevertheless, we do not include them in comparison since the study [43] had shown their failures in producing realistic scanpaths for " + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 441, + 287, + 502 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "type": "text", + "content": "Accuracy Comparison. Table 1 and Fig. 3 show that our model could provide results closer to the human scanpaths. In Fig. 3, we observe that CLE and DeepGaze III exhibit large displacements that might caused by the treatment that regarding " + }, + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 514, + 287, + 646 + ], + "type": "text", + "content": " images as 2D images. Saliency-based scanpath prediction model, exhibits unstable behavior with large displacements and scarce focal regions (e.g., referring to Room or Park of Fig. 3), leading to worse results than the Random walk model. The proposed model could better focus on the salient objects in scenes than ScanGAN (e.g., referring to Museum, Party or Park of Fig. 3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Efficiency Comparison. We also compare the efficiency in terms of the model size and running time. The results are shown in Table 2. Our model has the smallest size - 18.7MB, which is about " + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "inline_equation", + "content": "1/5" + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": " of the size of SaliNet. For running time comparison, we record the time cost to gen" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 303, + 549, + 403 + ], + "blocks": [ + { + "bbox": [ + 46, + 378, + 287, + 424 + ], + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 424 + ], + "type": "text", + "content": "Table 2. Efficiency comparison in terms of the model size and running time (computed by the time cost of producing 1,000 scanpaths). Noting that CLE is a traditional model that built on saliency maps, we only count the time to produce the scanpaths." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 303, + 549, + 403 + ], + "lines": [ + { + "bbox": [ + 306, + 303, + 549, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 549, + 403 + ], + "type": "table", + "html": "
DatabaseMethodLEV ↓DTW ↓REC ↑
Sitzmann [51]ScanDMM(I)45.9491996.4563.091
ScanDMM(S)46.8002098.4122.833
ScanDMM(IS)46.4892011.1572.904
ScanDMM44.9661965.4273.475
Salient360! [47]ScanDMM(I)38.3401698.5173.168
ScanDMM(S)39.1941787.6742.744
ScanDMM(IS)38.9581720.8942.853
ScanDMM37.2721528.5923.576
", + "image_path": "8fd884279dfd1f6d5b3ea2bf82e66640707b70a1b0512e8fcf937aa69e765d86.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 411, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 305, + 411, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 545, + 434 + ], + "type": "text", + "content": "Table 3. Ablation study. The effectiveness of our designs is well justified." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 447, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 545, + 483 + ], + "type": "text", + "content": "erate 1,000 scanpaths for a given image. The results show that our model has the fastest inference speed - 0.737 seconds." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 493, + 400, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 493, + 400, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 493, + 400, + 506 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": "We conduct ablation experiments to analyze the impact of the state initialization strategy and the scene semantics on the proposed model. We compare the proposed ScanDMM with three baselines: (1) " + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathrm{ScanDMM}_{(\\mathrm{I})}" + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": ", initializing state directly using learnable parameter: " + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 = \\hat{\\mathbf{z}}_0" + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": ". (2) " + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathrm{ScanDMM}_{(\\mathrm{S})}" + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": ", removing scene semantics " + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}}" + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": " in Eq. 7. (3) " + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "inline_equation", + "content": "\\mathrm{ScanDMM}_{(\\mathrm{IS})}" + }, + { + "bbox": [ + 304, + 513, + 545, + 644 + ], + "type": "text", + "content": ", performing both of the two modifications. All baseline models are trained in the same settings, and the results are shown in Table 3. We can observe that the model achieves the best performance when incorporating both the state initialization strategy and the scene semantics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 656, + 386, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 656, + 386, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 656, + 386, + 671 + ], + "type": "text", + "content": "5. Applications" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "In this section, we demonstrate the generalizability of our model by applying it to two downstream applications - saliency detection and quality assessment for " + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "6994" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 289, + 247 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 247 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 247 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 247 + ], + "type": "table", + "html": "
DatabaseMethodAUC ↑NSS ↑CC ↑KLD ↓
Sitzmann [51]BMS360 [34]0.8311.3280.6660.475
GBVS360 [34]0.8451.4330.6930.374
SaltiNet [2]0.7620.9480.4970.671
SalNet360 [44]0.8411.4670.7180.421
SalGAN360 [8]0.8131.1880.6120.561
ScanGAN [43]0.7610.9020.4750.654
ScanDMM0.7670.9580.5210.609
Human0.8772.2651.0000.117
Salient360! [47]BMS360 [34]0.7480.9070.5670.476
GBVS360 [34]0.7120.7750.4840.576
SaltiNet [2]0.7370.8420.5300.514
SalNet360 [44]0.7440.9890.6020.476
SalGAN360 [8]0.7590.9750.6130.495
ScanGAN [43]0.7280.7740.4910.556
ScanDMM0.7771.0420.6600.384
Human0.8602.3951.0000.290
", + "image_path": "9273a81addb1f2856cb8206c9c9f63c744968a288493363c4a8ada20401b7e8f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 297, + 231, + 310 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 231, + 310 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 231, + 310 + ], + "type": "text", + "content": "5.1. Saliency Detection for " + }, + { + "bbox": [ + 47, + 297, + 231, + 310 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 47, + 297, + 231, + 310 + ], + "type": "text", + "content": " images" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 448 + ], + "type": "text", + "content": "Visual attention prediction, commonly known as saliency detection, is the task of inferring the objects or regions that attract human attention in a scene. Intuitively, an ideal scanpath prediction model should be able to model spatially visual attention. In this section, we apply the proposed ScanDMM and ScanGAN [43] to the saliency detection task by generating 1,000 scanpaths and post-processing these gaze points to yield continuous saliency maps. Specifically, we convolve fixation maps, the two-dimensional records of the locations of all the gaze points, with a modified Gaussian [56]:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 80, + 453, + 287, + 482 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 453, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 80, + 453, + 287, + 482 + ], + "type": "interline_equation", + "content": "G (x, y) = \\frac {1}{2 \\pi \\sigma_ {y} ^ {2}} \\exp \\left(- \\frac {x ^ {2}}{2 \\sigma_ {x}}\\right) \\exp \\left(- \\frac {y ^ {2}}{2 \\sigma_ {y}}\\right) \\tag {19}", + "image_path": "de51bbf3ce2200cb6b8e242d92e99a15bd60ce273d11dfa567ea70ae6ee6206b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\sigma_{x} = \\frac{\\sigma_{y}}{\\cos(\\theta)}" + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\sigma_{y} = 19^{\\circ}" + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "text", + "content": " is a constant value, and " + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\theta \\in \\left[-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right]" + }, + { + "bbox": [ + 46, + 488, + 287, + 516 + ], + "type": "text", + "content": " is the latitude of the gaze point." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": "Evaluation Metrics. We evaluate saliency detection models using 4 metrics: the Judd variant of the area under curve (AUC) [6], normalized scanpath saliency (NSS) [46], correlation coefficient (CC) [32], and Kullback-Leibler divergence (KLD) [31]. Similarly, for each metric, we compute the human consistency as a realistic upper bound for model performance [7], referring to Human in Table 4. Specifically, we first compare the fixations of two groups of " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": " observers, where " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": " varies from 1 to " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "N/2" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": " (i.e., half of the total " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": " observers). We then fit the " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "N/2" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": " performance scores to a power function (i.e., " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "aM^b + c" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": "), and predict the human performance as that of two groups of infinite observers (which is equal to " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": ", for " + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "inline_equation", + "content": "b < 0" + }, + { + "bbox": [ + 46, + 523, + 287, + 680 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "Performance Comparison. We compare different saliency detection models on Sitzmann [51] and Salient360! [47]" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 305, + 70, + 547, + 289 + ], + "blocks": [ + { + "bbox": [ + 46, + 256, + 287, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 278 + ], + "type": "text", + "content": "Table 4. Performance of saliency prediction models on Sitzmann [51] and Salient360! [47] databases." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 305, + 70, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 289 + ], + "type": "table", + "html": "
MethodCC ↑SRCC ↑RMSE ↓
PSNR0.1560.0160.787
PSNRGAN0.1350.0140.790
PSNR\\(DMM\\)0.5630.5460.659
PSNR\\(Human\\)0.5850.5830.646
SSIM0.1480.0460.788
SSIM\\(GAN\\)0.1620.0460.790
SSIM\\(DMM\\)0.5190.5090.681
SSIM\\(Human\\)0.5270.5320.677
VIF0.1630.0960.786
VIF\\(GAN\\)0.1470.0920.788
VIF\\(DMM\\)0.5970.5720.639
VIF\\(Human\\)0.6160.6010.628
DISTS0.1620.0810.786
DISTSGAN0.1760.1000.784
DISTSDMM0.6620.6750.597
DISTSHuman0.7000.7110.569
DeepWSD0.1600.0440.786
DeepWSD\\(GAN\\)0.1620.0720.786
DeepWSD\\(DMM\\)0.6350.6280.616
DeepWSD\\(Human\\)0.6680.6670.593
", + "image_path": "a83e9c362e8be984d6b10fadae13fe5b5a6383f0ddcab22ae09b4b83c9fee471.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 319 + ], + "type": "text", + "content": "Table 5. Performance of quality assessment models on JUFE [20] database." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "type": "text", + "content": "databases. In addition to ScanGAN [43], we also compare the proposed ScanDMM with 5 saliency detection models tailored for " + }, + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "type": "text", + "content": " images: BMS360 [34], GBVS360 [34], SalGAN [8], SalNet [44], and SaliNet [2], the results are shown in Table 4 and Fig. 4. Table 4 shows that the proposed ScanDMM achieves the best performance on Salient360! database, while its performance drops apparently on Sitzmann database. One reason might be that scanpath-to-saliency models are worse at suppressing nonsalient regions than the models tailored for " + }, + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 335, + 545, + 526 + ], + "type": "text", + "content": " images (please refer to the supplementary file for the complete comparison), e.g., referring to Robot in Fig. 4. The results show that applying the scanpath prediction model for the saliency detection task is encouraging. Nevertheless, there is significant room for improvement, as evidenced by a large performance gap between computational models and humans." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 538, + 497, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 538, + 497, + 551 + ], + "spans": [ + { + "bbox": [ + 305, + 538, + 497, + 551 + ], + "type": "text", + "content": "5.2. Quality Assessment for " + }, + { + "bbox": [ + 305, + 538, + 497, + 551 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 305, + 538, + 497, + 551 + ], + "type": "text", + "content": " Images" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "The image quality assessment (IQA) model aims at predicting the perceived quality of visual images [41]. Recent studies [20,21,52] reveal that the viewing behaviors may be indispensable for quality assessment for " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " scenes, highlighting the importance of scanpath prediction in " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " IQA. In this section, we show how much gain scanpath prediction models can provide for " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " IQA. Specifically, we leverage the computational framework [52], which offers us a natural way to utilize scanpaths for " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " IQA. Basically, there have 4 steps: (1) Extracting the sequences of rectilinear projections of viewports along different generated scanpaths. (2) Computing the \"frame-level\" (i.e., viewpoint-level) quality scores by using existing 2D IQA models. (3) Computing the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "6995" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 532, + 235 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 532, + 235 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 532, + 235 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 532, + 235 + ], + "type": "image", + "image_path": "713be85e91fbdfa172feefb7649fd14c024c14f09f6a946d4e20a4c4745d7b6e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 243, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 243, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 243, + 547, + 277 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison to different saliency detection models for six different scenes. First two columns: Square and Robot of Sitzmann [51] database. Last four columns: Theater, Mall, Gallery and Airplane of Salient360! [47] database. From top to bottom: " + }, + { + "bbox": [ + 46, + 243, + 547, + 277 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 243, + 547, + 277 + ], + "type": "text", + "content": " images, GT saliency maps, the predictions of ScanGAN [43] and the proposed ScanDMM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": "perceived quality of a \"video\" (i.e., a viewpoint sequence) by temporally pooling the frame-level quality scores. (4) Averaging the quality scores of all videos to obtain the final perceived quality of the " + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 288, + 287, + 337 + ], + "type": "text", + "content": " image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 339, + 287, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 339, + 287, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 339, + 287, + 411 + ], + "type": "text", + "content": "Evaluation Metrics. We use 3 evaluation metrics to quantify the quality prediction performance, including CC, Spearman's rank-order correlation coefficient (SRCC) and root mean square error (RMSE). Generally, higher CC/SRCC values and lower RMSE values mean better performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": "Performance Comparison. We conduct comparison experiments on JUFE [20] database, in which each image has 4 quality labels corresponding to 4 different viewing conditions (2 starting point " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " 2 exploration time). Considering this database is goal-directed (i.e., IQA), we retrain the ScanDMM and ScanGAN [43] on " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " training set. We generate " + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\hat{N} = N" + }, + { + "bbox": [ + 46, + 415, + 288, + 714 + ], + "type": "text", + "content": " fake scanapths for extracting viewpoint sequences for each image. For frame-level quality calculation, we employ five 2D IQA models, including the Peak Signal-to-Noise Ratio (PSNR), the Structural SIMilarity index (SSIM) [60], the Visual information fidelity (VIF) [50], the Deep Image Structure and Texture Similarity metrics (DISTS) [14], and the DeepWSD [37]. Then, the Gaussian weighting function [52] is chosen to temporally pool the frame-level quality scores. We add \"GAN\", \"DMM\", and \"Human\" to the five IQA methods as the subscripts to name the quality model that uses the scanpaths generated by ScanGAN [43], ScanDMM, and human, respectively. We also directly apply 2D IQA models to equirectangular projections as baselines. The results are shown in Table 5, where we can observe that all baseline models fail to predict the perceived quality, which is reasonable since they produce one quality score for a given image that has four quality labels. Conversely, our ScanDMM can simulate the viewing behaviors under the specific viewing condition thanks to the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 288, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 373 + ], + "type": "text", + "content": "state initialization strategy, which significantly improves the performance of 2D IQA models and have competitive performance compared with Human models. ScanGAN [43], however, is not applicable due to the uncontrollable starting points. Current work only tests traditional 2D IQA models, future models that take better account for VR-specific distortions will have great potential to boost the performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 382, + 458, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 382, + 458, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 382, + 458, + 395 + ], + "type": "text", + "content": "6. Conclusion and Discussion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "content": "This paper presents a scanpath prediction model for " + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "content": " images and demonstrates its crucial capabilities, i.e., high accuracy, efficiency and generalizability, for real-world applications. Moreover, we provide a novel perspective for saliency detection and quality assessment in " + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "content": " scenes - constructing models by simulating humans' viewing behaviors, which is an extremely natural way if we recall how we obtain the GT labels. Nevertheless, there is still much to explore, as we only simply exploit generated scanpaths without elaborately designing for a specific task. While this paper primarily focuses on static " + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "content": " images, our ScanDMM can be easily adapted to dynamic " + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "content": " videos by feeding dynamic scene semantics to the network. Moreover, as a probabilistic approach, ScanDMM is able to learn the general pattern of the viewing behaviors in " + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 545, + 606 + ], + "type": "text", + "content": " scenes, thus could also be applied to VR transmission, automatic cinematography, navigation, virtual scene design, etc." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 617, + 403, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 617, + 403, + 630 + ], + "spans": [ + { + "bbox": [ + 306, + 617, + 403, + 630 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 635, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 703 + ], + "type": "text", + "content": "This work was supported in part by the National Key Research and Development Program of China under Grant 2018AAA0100601, in part by the National Natural Science Foundation of China under Grant 62132006, and in part by the Natural Science Foundation of Jiangxi Province of China under Grant 20223AEI91002." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6996" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Hossein Adeli, Françoise Vitu, and Gregory J Zelinsky. 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IEEE Transactions on Multimedia, 22(9):2331-2344, 2020. 1, 2, 3, 6" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6999" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_content_list.json b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..269d793a6464d5c459c0ccc92ff45d05c29704b6 --- /dev/null +++ b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_content_list.json @@ -0,0 +1,1334 @@ +[ + { + "type": "text", + "text": "ScarceNet: Animal Pose Estimation with Scarce Annotations", + "text_level": 1, + "bbox": [ + 178, + 130, + 792, + 150 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chen Li Gim Hee Lee", + "bbox": [ + 374, + 181, + 593, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Department of Computer Science, National University of Singapore", + "bbox": [ + 217, + 199, + 751, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lichen@u.nus.edu gimhee.lee@comp.nus.edu.sg", + "bbox": [ + 276, + 219, + 689, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Animal pose estimation is an important but under-explored task due to the lack of labeled data. In this paper, we tackle the task of animal pose estimation with scarce annotations, where only a small set of labeled data and unlabeled images are available. At the core of the solution to this problem setting is the use of the unlabeled data to compensate for the lack of well-labeled animal pose data. To this end, we propose the ScarceNet, a pseudo label-based approach to generate artificial labels for the unlabeled images. The pseudo labels, which are generated with a model trained with the small set of labeled images, are generally noisy and can hurt the performance when directly used for training. To solve this problem, we first use a small-loss trick to select reliable pseudo labels. Although effective, the selection process is imprudent since numerous high-loss samples are left unused. We further propose to identify reusable samples from the high-loss samples based on an agreement check. Pseudo labels are re-generated to provide supervision for those reusable samples. Lastly, we introduce a student-teacher framework to enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can make full use of the unlabeled data. We evaluate our approach on the challenging AP-10K dataset, where our approach outperforms existing semi-supervised approaches by a large margin. We also test on the TigDog dataset, where our approach can achieve better performance than domain adaptation based approaches when only very few annotations are available. Our code is available at the project website1.", + "bbox": [ + 76, + 301, + 473, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 801, + 209, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The ability to understand animal behavior is fundamental to many applications, such as farming, ecology and surveillance. Animal pose estimation is a key step to un", + "bbox": [ + 76, + 827, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f0fb6c3c0d2330c282f32813d2fedddad841c532e3662ab91d527e79dcd88df1.jpg", + "image_caption": [ + "Unlabeled data" + ], + "image_footnote": [], + "bbox": [ + 504, + 267, + 645, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7c1e406cbc2d28cd95b6ca6b8b82858aeef7eaf36578beaa338b82dab079d9b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 268, + 746, + 381 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/67cd9d98b12356b3dc36f4815a11d14a1dbeadd15a100d108578d375acfd6409.jpg", + "image_caption": [ + "Estimated animal poses", + "Figure 1. An illustration of our task. We aim to achieve accurate animal pose estimation with a small set of labeled images as well as unlabeled images." + ], + "image_footnote": [], + "bbox": [ + 748, + 268, + 888, + 380 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "understand animal behavior and has attracted increasing attention in recent years [5, 16, 20, 23, 33]. Although great success is achieved for human pose estimation with the development of sophisticated deep learning models, these techniques cannot be directly used for animals due to the lack of labeled animal pose data. Existing works overcome this problem by learning from human pose data [5] or synthetic animal images [16, 20, 23]. However, there is a large domain gap between the real and synthetic (human) data. For example, the synthetic animal images in [20], which are generated from CAD models, only exhibit limited pose, appearance and background variations. As a result, the model trained with the synthetic data may not adapt well to real images, especially for images with crowded scene or self-occlusion. Moreover, the generation of synthetic images is a tedious process that also requires expert knowledge. The above-mentioned problems lead us to ask whether we can achieve accurate animal pose estimation with minimal effort for annotating? To answer this question, we focus on how to learn from scarce labeled data for animal pose estimation. As shown in Fig. 1, we aim to achieve accurate animal pose estimation with only a small set of labeled images and unlabeled images.", + "bbox": [ + 496, + 477, + 892, + 824 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The data scarcity problem is solved by semi-supervised learning (SSL) for the classification task [3,25,28,34]. One powerful class of SSL is pseudo labeling (PL), where artificial labels generated from a pretrained model are used together with labeled data to train a model. Impressive", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "", + "bbox": [ + 94, + 886, + 410, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "17174", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "results have been achieved by applying PL [5, 16, 20] to domain adaptation based animal pose estimation. However, the PL-based methods suffer from confirmation bias when the network starts to output incorrect predictions with high confidence, which we refer as noisy pseudo labels. To solve this noisy pseudo label problem, we use the small-loss trick [9, 16] to select reliable pseudo labels, i.e. samples with small loss to update the network. This criteria is based on the memorization effect [2] of deep networks where the network learns from clean and easy instances first before eventually overfitting to noisy ones. Consequently, clean samples exhibit smaller loss compared to noisy ones at the beginning of training. Although the small-loss trick is effective in selecting reliable pseudo labels, it is wasteful because numerous high-loss samples are left unused.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose the ScarceNet, a PL-based approach to learn an animal pose network from scarce annotations. We first train an animal pose estimation network on the small set of labeled data, and then generate pseudo labels for the unlabeled images with the pretrained model. The pseudo labels are often corrupted with noise due to the small size of the training data. We thus also select reliable pseudo labels using the small-loss trick. However, instead of ignoring or adding consistency regularization to the high-loss samples as done in previous works [16, 20], we propose to identify reusable samples from those high-loss samples based on an agreement check. The agreement check is to guarantee that the model predictions for the reusable samples are smooth and concurrently far from the decision boundary, and hence allow us to directly re-label reusable samples with the model predictions. Finally, we introduce a student-teacher network [28] and enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can fully exploit the unlabeled data.", + "bbox": [ + 75, + 321, + 472, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to the training scheme, we also modify the state-of-the-art human pose estimation network HRNet [27] and adapt it to the pseudo label-based learning framework. The original HRNet regresses the heatmaps of different joints from a shared feature representation. However, the negative effect of noisy pseudo label for any joint is propagated to all other joints through this shared feature representation. To mitigate this problem, we introduce a multibranch HRNet (MBHRNet) where a joint-specific feature representation is learned for regressing the corresponding joint location in each branch.", + "bbox": [ + 75, + 641, + 472, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We validate our approach on the challenging AP-10K dataset [33], which includes animal images from more than 50 species. Our approach outperforms existing SSL methods by a large margin, especially when the labeled data is very limited (for example, 5 labeled images per species). We also test our approach under the inter-family transfer", + "bbox": [ + 76, + 809, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "setting, where animal species from only one family are labeled and the rest are unlabeled. Our approach improves the HRNet baseline significantly, and even outperform the supervised counterpart for some species. We further test on the TigDog dataset [20], where we can outperform existing synthetic data based approaches when only $0.5\\%$ of the dataset is labeled. Our contribution can be summarized as follows:", + "bbox": [ + 496, + 90, + 893, + 210 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a pseudo label based training scheme for the task of animal pose estimation from scarce labels.", + "- We introduce the MBHRNet to mitigate negative effect of noisy joints to other joints in the same image.", + "- We achieve state-of-the-art performance on several animal pose benchmarks under different settings." + ], + "bbox": [ + 517, + 220, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 343, + 640, + 359 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Animal Pose Estimation. Animal pose estimation, including both 2D [5, 16, 20] and 3D [4, 15, 37], has become an active research field in the last few years. The development of animal pose estimation techniques is relatively slower than the human counterpart due to the lack of large scale animal pose dataset like COCO [18] or MPII [1]. Existing works circumvent the requirement for animal pose data by transferring knowledge from other domains, such as human pose data [5] and synthetic animal data [16, 20, 23]. Although impressive results have been achieved in [5], substantial amounts of labeled animal images are still needed to facilitate the knowledge transfer. This is due to the large domain gap between human and animal images, including pose, appearance and body structure differences. To reduce the domain gap between the source and target domains, synthetic animal images are generated from CAD models and used as the source images in [20]. Three consistency criteria are proposed to generate pseudo labels for real images. Improved upon [20], Li et al. [16] propose a pseudo label updating strategy to prevent the network from overfitting to the noisy pseudo labels. Despite the domain gap is reduced by using synthetic animal images, the limited pose and appearance variations of the CAD models prohibit the synthetic data based approaches from adapting to real scenarios with crowded scene or self-occlusion. Moreover, synthesize realistic images is a tedious process, which also requires expert knowledge. In view of this, we focus on learning from scarce annotations to minimize human labor and achieve accurate animal pose estimation at the same time.", + "bbox": [ + 496, + 368, + 893, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semi-supervised Learning. Semi-supervised learning is powerful in leveraging unlabeled data to improve a model's performance when labeled data is limited. One of the most widely used SSL techniques is pseudo labeling [14, 31], which generates artificial labels for unlabeled images from", + "bbox": [ + 496, + 825, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "17175", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "model predictions. Another technique is consistency regularization [13, 22, 28], which enforces that the model output should be consistent when the input is randomly perturbed. MixMatch [3] combines the consistency regularization with the entropy minimization to encourage the network to output confident predictions for unlabeled data. More recent Unsupervised Data Augmentation (UDA) [30] and FixMatch [25] combine pseudo labeling, consistency regularization with strong augmentations [6] and achieve superior performance. FlexMatch [34] further improves over UDA and Fixmatch by introducing a curriculum learning scheme. We also adopt the PL-based techniques in this work given its effectiveness. To mitigate the negative effect of noisy pseudo labels, we combine PL with reliable pseudo label selection and reusable sample re-labeling.", + "bbox": [ + 75, + 90, + 472, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Learning from Noisy Labels. Learning from noisy labels has become an important task since deep neural networks are known to be susceptible to noisy labels. To reduce the negative effect of noisy labels, different approaches which can be divided into three categories have been proposed. The first category is to treat the true labels as hidden variables and use an extra network to estimate a noise transition matrix [8, 21]. These methods assume there is correlation between the corrupted and clean labels, hence cannot handle complicate cases with random noise. The second category is to design noise-robust loss functions [7], such as the generalized cross entropy [35] and the symmetric cross entropy [29]. The robust-loss based approaches are theoretically sound, but may only be capable of handling a certain noise rate. The last category [9, 11, 19] focuses on selecting potential clean samples to update the network. One promising selection criteria is the small-loss trick [9], which is designed based on the memorization effect of deep networks and has been widely applied to different tasks [16, 26, 32]. We also apply the small-loss trick to select reliable pseudo labels. However, instead of ignoring the high-loss samples as done in previous works, we combine the sample selection with the reusable sample re-labeling to make full use of the unlabeled data.", + "bbox": [ + 75, + 342, + 472, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Method: ScarceNet", + "text_level": 1, + "bbox": [ + 76, + 720, + 305, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a PL-based approach to learn animal pose estimation from scarce annotations. The overall framework of our ScarceNet is illustrated in the left part of Fig. 2, where we propose a multi-branch HRNet (MBHRNet) as our animal pose estimation network. Let us denote an input image as $\\mathbf{x}$ and its ground truth animal pose (if available) as $\\mathbf{y}$ . Given a small set of labeled images $\\mathcal{D}_l = \\{\\mathbf{x}_i^l,\\mathbf{y}_i^l\\}_{i = 1}^{N_l}$ and unlabeled images $\\mathcal{D}_u = \\{\\mathbf{x}_i^u\\}_{i = 1}^{N_u}$ , the objective is to train the animal pose estimation network by leveraging both the labeled and unlabeled data. $N_{l}$ and $N_{u}$ represent the", + "bbox": [ + 75, + 748, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "number of labeled and unlabeled images, respectively, and $N_{l} \\ll N_{u}$ . The labeled images are supervised with the ground truth pose data. We then generate pseudo labels with the model trained on the labeled data for the unlabeled images. However, these generated pseudo labels are usually heavily corrupted with noise, especially when the labeled data is very limited. We thus apply the small-loss trick [9] to select a set of reliable pseudo labels. Despite its effectiveness, pseudo label selection by the small-loss trick tends to discard numerous high-loss samples. This results in high wastage since those discarded samples can still provide extra information for better discrimination. In view of this, we propose a reusable sample re-labeling step to further identify reusable samples from the high-loss samples via an agreement check and re-generate the corresponding pseudo labels for supervision. Lastly, we design a student-teacher framework to enforce consistency between the outputs of the student and teacher network.", + "bbox": [ + 496, + 90, + 893, + 363 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Reliable Pseudo Label Selection", + "text_level": 1, + "bbox": [ + 498, + 369, + 782, + 386 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first train the animal pose estimation network on labeled images $\\mathcal{D}_l$ with a supervised loss:", + "bbox": [ + 496, + 393, + 892, + 422 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s}} = \\frac {1}{J} \\sum_ {i = 1} ^ {J} \\| H _ {i} - \\hat {H} _ {i} \\| ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 431, + 892, + 472 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $H_{i}$ is the ground truth heatmap, $J$ denotes the total number of joints, and $\\hat{H}_i$ represents the output heatmap of the network. The pretrained network is then used to generate an initial set of pseudo labels for the unlabeled images $\\mathcal{D}_u$ following the procedure in [20]. The generated pseudo labels are generally noisy and can hurt the performance if directly used for training. To prevent this, we select reliable pseudo labels, denoted as $\\mathbb{S}$ , from the initial pseudo labels using the small-loss trick. Specifically, we only make use of samples with loss smaller than a threshold to update the network. Formally, this can be expressed as:", + "bbox": [ + 496, + 479, + 893, + 647 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p}} = \\frac {\\sum_ {i = 1} ^ {J} \\left\\{\\mathcal {L} _ {\\mathrm {p}} ^ {i} < l _ {\\mathrm {r}} \\right\\} _ {1} \\mathcal {L} _ {\\mathrm {p}} ^ {i}}{\\sum_ {i = 1} ^ {J} \\left\\{\\mathcal {L} _ {\\mathrm {p}} ^ {i} < l _ {\\mathrm {r}} \\right\\} _ {1}}, \\text {w h e r e} \\mathcal {L} _ {\\mathrm {p}} ^ {i} = \\| \\tilde {H} _ {i} - \\hat {H} _ {i} \\| ^ {2}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 652, + 892, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\tilde{H}_i$ represents the pseudo label for the $i^{\\mathrm{th}}$ joint and $\\mathcal{L}_{\\mathrm{p}}^{i}$ is the corresponding pseudo label based loss. $\\{\\mathrm{condition}\\}_{1}$ is a condition function, which outputs 1 when the condition is true and 0 if false. $l_{\\mathrm{r}}$ denotes the threshold loss value, and more details on how to decide $l_{\\mathrm{r}}$ are provided in the supplementary material. This small-loss trick is designed based on the memorization effect of deep network, and has been shown effective in selecting reliable labels in previous works [16,26].", + "bbox": [ + 496, + 702, + 893, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Reusable Sample Re-labeling", + "text_level": 1, + "bbox": [ + 500, + 847, + 761, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Only small-loss samples are selected in the reliable pseudo label selection process, and the remaining pseudo", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "17176", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/34c2d343270af9021fe87a5fb9bbf04241d4b3a2d2449497dbb536ceeeba9286.jpg", + "image_caption": [ + "Figure 2. The left part shows the overall framework of our ScarceNet, where $\\mathcal{P}$ and $\\mathcal{T}$ represent strong and weak augmentation, respectively. The right part shows a comparison between the HRNet (top) and the MBHRNet (bottom), where 'FE' represents feature extractor, 'conv.' represents convolutional layer and 'JFE' represents joint specific feature extractor." + ], + "image_footnote": [], + "bbox": [ + 76, + 89, + 553, + 281 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/abc85ddf86537fabeab0413d8503107767910189bc12a55d4026efe5ce8d12f5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 103, + 893, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "labels with large loss are discarded. This is imprudent since the high-loss samples can also contribute to improving the network if used properly. To this end, we propose to further identify reusable samples, denoted as $\\mathbb{U}$ , from the unused samples to fully exploit the unlabeled data. We define reusable samples as the ones that may also provide reliable knowledge to the network despite their large losses. To identify the reusable samples, we introduce an agreement check. Specifically, given an input $\\mathbf{x}^u$ , we generate another view of this sample by adding a random transformation $\\mathcal{T}$ which consists of rotation and scaling. Both samples are fed into the pose estimation network to produce the corresponding heatmaps, denoted as:", + "bbox": [ + 75, + 364, + 472, + 561 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nH ^ {\\mathrm {v} _ {1}} = f \\left(\\mathbf {x} ^ {u}\\right), H ^ {\\mathrm {v} _ {2}} = f \\left(\\mathcal {T} \\mathbf {x} ^ {u}\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 571, + 468, + 588 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The location for the $i^{th}$ joint is obtained by applying argmax operation to the corresponding output heatmap:", + "bbox": [ + 76, + 598, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {h} _ {i} ^ {\\mathrm {v} _ {1}} = \\operatorname {a r g m a x} \\left(H _ {i} ^ {\\mathrm {v} _ {1}}\\right), \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {2}} = \\operatorname {a r g m a x} \\left(H _ {i} ^ {\\mathrm {v} _ {2}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 638, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike the classification task where the output is transformation invariant [12, 32], the output joint location is transformation equivariant. Consequently, we have to transform $\\mathbf{h}_i^{\\mathrm{v_1}}$ before the agreement check, i.e.:", + "bbox": [ + 76, + 666, + 468, + 727 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd _ {i} = \\left\\| \\mathcal {T} \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {1}} - \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {2}} \\right\\| ^ {2}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 737, + 468, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, we can determine whether a sample is reusable based on the distance between the outputs of the two views. Specifically, a sample $\\mathbf{x}_i^u$ is reusable when the distance fulfills $d_{i} < d_{\\mathrm{r}}$ , where $d_{\\mathrm{r}}$ represents the distance threshold. This agreement check is based on the agreement maximization principle [24], which has also been used for out-of-distribution detection [32] and stable sample selection [12]. Intuitively, the reusable samples must satisfy smoothness in the neighborhood of the model prediction", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and must also be far from the decision boundary. Otherwise, the output becomes inconsistent when the input is randomly transformed.", + "bbox": [ + 496, + 364, + 892, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The next step is to re-label the identified reusable samples since they exhibit large loss based on the initial pseudo labels. We directly use the prediction from the current model as the new pseudo labels to train the network. The motivation is twofold: 1) The model has been trained with unlabeled images, hence it is able to output more accurate prediction comparing to the model trained only on the labeled images. 2) The selection criteria for reusable samples indicates that the current model prediction is already reliable. Finally, the loss function for the reusable samples can be defined as:", + "bbox": [ + 496, + 410, + 892, + 575 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r}} = \\frac {\\sum_ {i = 1} ^ {J} \\left\\{d ^ {i} < d _ {\\mathrm {r}} \\right\\} _ {1} \\mathcal {L} _ {\\mathrm {r}} ^ {i}}{\\sum_ {i = 1} ^ {J} \\left\\{d ^ {i} < d _ {\\mathrm {r}} \\right\\} _ {1}}, \\text {w h e r e} \\mathcal {L} _ {\\mathrm {r}} ^ {i} = \\| \\bar {H} _ {i} - \\hat {H} _ {i} \\| ^ {2}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 585, + 890, + 627 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\bar{H}_i$ represents the heatmap generated from the joint location of current model prediction. By selecting the reusable samples, we are able to make use of more unlabeled images and prevent the network from overfitting to the initial noisy pseudo labels at the same time.", + "bbox": [ + 496, + 638, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Student-teacher Consistency", + "text_level": 1, + "bbox": [ + 500, + 724, + 756, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Both the reliable pseudo label selection and reusable sample selection are based on specific constraints. Samples that do not fulfill either constraint are still left unused. In view of this, we further introduce a teacher network and enforce the consistency between the student and teacher network. This is inspired by the mean teacher framework [28], which enforces the consistency constraint for unlabeled data for semi-supervised classification. The teacher network shares the same structure with the student network, and the weights are updated with an exponential moving average", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "17177", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(EMA) of the student model:", + "bbox": [ + 76, + 90, + 272, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {\\mathrm {m t}} ^ {t} = \\alpha \\theta_ {\\mathrm {m t}} ^ {t - 1} + (1 - \\alpha) \\theta^ {t}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 114, + 468, + 133 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\theta_{\\mathrm{mt}}$ and $\\theta$ denote the weights of the teacher and student network, respectively. The superscript $t$ represents the training step, and $\\alpha$ is a smoothing coefficient of the EMA update. We can see that the teacher network is a temporal ensemble of networks, and thus it can provide more accurate pseudo labels. As shown in Fig. 2, we add random perturbations $\\mathcal{P}$ to the input of the student network, which consists of both geometry-based perturbations $\\mathcal{P}_g$ such as rotation, scaling and flipping, and image-based perturbation $\\mathcal{P}_m$ such as noise, occlusion and blurring. Consistency is then enforced between the teacher and student network as:", + "bbox": [ + 75, + 143, + 472, + 309 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {t}} = \\frac {1}{J} \\sum_ {i = 1} ^ {J} \\| \\mathcal {P} _ {g} H _ {i} ^ {t} - \\hat {H} _ {i} \\| ^ {2}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 316, + 468, + 357 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $H_{i}^{t}$ denotes the output of the teacher network. Note that only the geometry-based perturbation $\\mathcal{P}_g$ is added to the output of the teacher network since the output joint location is invariant to the image-based perturbation.", + "bbox": [ + 75, + 367, + 468, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Multi-head Animal Pose Estimation Network", + "text_level": 1, + "bbox": [ + 76, + 436, + 460, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We adopt the human pose estimation network HRNet as our backbone. The HRNet has achieved state-of-the-art performance for human pose estimation by combining high-resolution feature representations with multi-resolution feature fusion. However, as shown in the right top part of Fig. 2, the final heatmaps of HRNet are regressed from a shared feature representation with one linear layer. This shared mechanism can have negative effect in the presence of noisy labels. For example, the feature representation is affected by backpropagation when the pseudo label for any joint is noisy and thus further affect the prediction of other joints in the same image. To mitigate this problem, we introduce a multi-branch head to the HRNet to learn a specific feature representation for each joint. As shown in the right bottom part of Fig. 2, the network has $J$ output branches, where each branch learns a specific feature representation via a joint specific feature extractor (JFE) to regress the corresponding joint location. In this way, the adverse effect from the noisy pseudo label of a joint gets absorbed in its respective branch.", + "bbox": [ + 75, + 460, + 472, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Strong-weak Augmentation", + "text_level": 1, + "bbox": [ + 76, + 771, + 326, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also introduce a strong-weak augmentation training scheme, where two sets of augmentation are applied to the inputs, denoted as $\\mathcal{T}$ and $\\mathcal{P}$ in previous sections. Particularly, we apply strong augmentations $\\mathcal{P}$ for the learning task with backpropagation and weak augmentation $\\mathcal{T}$ for the re-labeling task. As shown in Fig. 2, strong augmentation $\\mathcal{P}$ is applied to the labeled images in the blue path", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and unlabeled images in the orange path. These two paths are responsible for updating the network, and hence strong augmentation can improve the generalization capacity. In comparison, the weak augmentation $\\mathcal{T}$ is applied to the green path because this path is responsible for identifying and re-labeling reusable samples. Overly-strong augmentation can have adversarial affects on the agreement check process since strong augmentation tends to result in inconsistent predictions. More details on the augmentation are provided in the supplementary material.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.6. Overall Framework", + "text_level": 1, + "bbox": [ + 498, + 263, + 689, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our network in two stages. In the first stage, we train the MBHRNet on $\\mathcal{D}_l$ with the supervised loss in Eqn. (1). The trained network is applied to generate pseudo labels for the unlabeled data. In the second stage, the student network is initialized with the pretrained model and trained with both $\\mathcal{D}_l$ and $\\mathcal{D}_u$ . The objective function for the second stage consists of both labeled and unlabeled losses as follows:", + "bbox": [ + 496, + 290, + 890, + 409 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\mathrm {s}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {p}} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {r}} + \\lambda_ {4} \\mathcal {L} _ {\\mathrm {t}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 431, + 890, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_1, \\lambda_2, \\lambda_3,$ and $\\lambda_4$ are the weights for different losses. The overall training procedure is presented in Algorithm 1.", + "bbox": [ + 498, + 465, + 890, + 498 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Overall training procedure of the second stage \nInput: labeled data $\\mathcal{D}_l$ and unlabeled data $\\mathcal{D}_u$ , threshold loss value $l_r$ , distance threshold $d_r$ , batch size $B$" + ], + "code_body": "1: for $\\{x_{1}, x_{2}, \\ldots, x_{B}\\} \\in \\mathcal{D}_{l} \\cup \\mathcal{D}_{u}$ do \n2: if $x_{i} \\in \\mathcal{D}_{l}$ then \n3: Compute supervised loss $\\mathcal{L}_{\\mathrm{s}}$ according to Eqn. (1) \n4: else \n5: if $x_{i} \\in \\mathbb{S}$ then \n6: Compute the pseudo labeled based loss $\\mathcal{L}_{\\mathrm{p}}$ according to Eqn. (2) \n7: else if $x_{i} \\in \\mathbb{U}$ then \n8: Compute loss $\\mathcal{L}_{\\mathrm{r}}$ for reusable samples by Eqn. (6) \n9: end if \n10: Compute the consistency loss $\\mathcal{L}_{\\mathrm{t}}$ according to Eqn. (8) \n11: end if \n12: Compute the total loss $\\mathcal{L}$ according to Eqn. (9) \n13: Update student network $\\theta \\gets \\theta - \\eta \\Delta \\mathcal{L}$ \n14: Update teacher network by Eqn. (7) \n15: end for", + "bbox": [ + 500, + 595, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "17178", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Results", + "text_level": 1, + "bbox": [ + 76, + 89, + 282, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details. We adopt the HRNet-w32 as the backbone and train our network in two stages. We first train the MBHRNet on the labeled data with the supervised loss. Following [27], we train the network with the Adam optimizer for 210 epochs. The initial learning rate is set to $10^{-3}$ , and is dropped to $10^{-4}$ and $10^{-5}$ at the $170^{th}$ and $200^{th}$ epochs, respectively. The trained model is then used to generate pseudo labels following [20]. In the second stage, we initialized the student network from the first stage and train the whole framework with both labeled and unlabeled data for another 150 epochs. More training details are provided in the supplementary material.", + "bbox": [ + 75, + 114, + 470, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on the AP-10K dataset [33] and the TigDog dataset [20]. The AP-10K dataset is a recently proposed animal pose dataset, which contains more diverse animal species than previous datasets [5, 20]. The dataset contains 10,015 labeled images in total, which are split into train, validation, and test sets with a ratio of 7:1:2 per animal species. The TigDog dataset includes 8380 images for the horse category and 6523 images for the tiger category. This dataset is used in several domain adaptation works [16,20] to show that the knowledge learned from synthetic animals can be transferred to real animal images. We also evaluate on this dataset to show that better performance can be achieved by labeling just a few images, hence can reduce human labor compared to generating synthetic data.", + "bbox": [ + 75, + 316, + 470, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics. We adopt the Mean Average Precision (mAP) as the evaluation metric for the AP-10K dataset. The Percentage of Correct Keypoints (PCK), which computes the percentage of joints that are within a normalized distance to the ground truth locations, is used for the TigDog dataset following [20].", + "bbox": [ + 75, + 550, + 468, + 642 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d199c49a4318f3f58047e8d4b79edc66d3eb1f475b692d5182ecbd17c0e42505.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
510152025
HRNet [27]0.3600.4630.5110.5470.588
UDA [30]0.4290.5190.5660.5800.628
FixMatch [25]0.4780.5440.5890.6010.631
FlexMatch [34]0.4660.5550.5960.6180.646
Ours0.5330.5970.6320.6540.681
", + "bbox": [ + 78, + 652, + 475, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Results (mAP) on the AP-10K when 5, 10, 15, 20 and 25 images per species are labeled. Best results in bold.", + "bbox": [ + 75, + 758, + 467, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Results on the AP-10K Dataset.", + "text_level": 1, + "bbox": [ + 76, + 816, + 354, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our approach under two scenarios on the AP-10K dataset. In the first scenario, a set of images are labeled for each animal species. The second scenario is that only the images in one family are labeled and we test on", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "other animal families. This setting is more challenge since the appearance, size and background environment are quite different for different animal species.", + "bbox": [ + 496, + 90, + 890, + 137 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We show results for the first scenario in Tab. 1, where we evaluate when 5, 10, 15, 20 and 25 images per animal species are labeled. There are 50 species in total, which results in 250, 500, 720, 1000 and 1250 labeled images out of 7023 images. We compare with state-of-the-art semi-supervised approaches, including UDA [30], FixMatch [25] and FlexMatch [34]. 'HRNet' represents HRNet trained only with labeled images. We reimplement those semi-supervised approaches according to the open repository since they only show results for classification task. We can see that our approach outperforms existing approaches by a large margin, especially when very few labeled images are available, such as the case of 5 labels per species. The reason is that UDA, FixMatch and FlexMatch only retain the samples with reliable pseudo labels based on the confidence scores. In comparison, we combine the reliable pseudo label selection with the reusable sample re-labeling and teacher-student consistency, which helps to fully utilize the unlabeled data. Moreover, our results are the closest to the fully supervised setting [33], i.e. $0.738\\mathrm{mAP}$ , when only 25 images per animal species are labeled. We also show qualitative results for the 25 labels per animal species setting in Fig. 3.", + "bbox": [ + 496, + 156, + 890, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also show results for the case when images from only one animal family are labeled in Tab. 2. Following the inter-family transfer learning setting in [33], we train our model with labeled images of the Bovidae family and the remaining unlabeled images, and test on families including Cervidae, Equidae and Hominidae. There are seven animal species in the Bovidae family that includes a total of 755 images. The results under the 'Generalization', 'Few-Shot' and 'Transfer' settings are taken from [33]. 'Generalization' means that the model is trained only with images in the Bovidae, 'Few-Shot' means that 20 labels from the testing species are used, and 'Transfer' means that all labels of the testing species are used. We can see that we achieve better performance than the generalization setting in all cases except for 'Moose'. Moreover, we even outperform the 'Transfer' setting for 'Deer' and 'Horse' although we do not use any labels from the target species. Our results for the 'Chimpanzee' and 'Gorilla' are not satisfactory although still comparable to the 'Few-Shot' setting. We show the failure cases of 'Chimpanzee' and 'Gorilla' in the last two examples of Fig. 3. We can see that 'Chimpanzee' and 'Gorilla' are very different from animal species in the Bovidae family (the first four examples of the last row) in terms of appearance and pose, which makes the knowledge transfer hard without using any labels from the target species.", + "bbox": [ + 496, + 523, + 890, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "17179", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f954608b8ff64c3bbfcc6f52832d8fb95f849c52fc80b89ddaee5a2917baef0a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SpeciesSettingPerformanceSpeciesSettingPerformance
DeerGeneralization0.723MooseGeneralization0.587
Few-Shot0.742Few-Shot0.648
Transfer0.751Transfer0.726
Ours0.767Ours0.547
HorseGeneralization0.592ZebraGeneralization0.324
Few-Shot0.635Few-Shot0.480
Transfer0.718Transfer0.708
Ours0.749Ours0.562
ChimpanzeeGeneralization0.009GorillaGeneralization0.017
Few-Shot0.022Few-Shot0.144
Transfer0.550Transfer0.662
Ours0.057Ours0.033
", + "bbox": [ + 138, + 87, + 831, + 289 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ea0f74715782c88859bbf817684a0eda9433a9874256ef448504464081ff90a8.jpg", + "table_caption": [ + "Table 2. Results (mAP) for the Cervidae, Equidae and Hominidae when only images from the Bovidae are labeled." + ], + "table_footnote": [], + "table_body": "
RealCycgan [36]BDL [17]Cycada [10]CC-SSL [20]MDAM-MT [16]Ours
Horse78.9851.8662.3355.5770.7779.5073.05
Tiger81.9946.4752.2651.4864.1467.7674.88
Average80.4849.1757.3053.5367.5273.6673.83
", + "bbox": [ + 119, + 327, + 849, + 388 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/53788f530cff00b554b5afde3ba084584b1f69a3aba2752a0d58352140106e4b.jpg", + "table_caption": [ + "Table 3. PCK@0.05 accuracy of the TigDog dataset. 'Real' means full supervision. Cycgan, BDL, Cycada, CC-SSL, MDAM-MT are domain adaptation approaches using synthetic data. Our approach is trained with only 36 labeled images per category." + ], + "table_footnote": [], + "table_body": "
Horse AccuracyTiger AccuracyAverage
EyeChinShoulderHipElbowKneeHoovesMeanEyeChinShoulderHipElbowKneeHoovesMean
CC-SSL84.6090.2669.6985.8968.5868.7361.3370.7796.7590.4644.8477.6155.8242.8564.5564.14
MDAM-MT91.0593.3777.3580.6773.6381.8373.6779.5097.0191.1846.6378.0850.8661.5470.8467.76
Ours89.4293.6074.6383.6174.3179.9173.9979.1899.1392.8246.9675.3650.4663.5174.8268.98
", + "bbox": [ + 76, + 440, + 906, + 513 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ab7583ed68ca71b5db0c49759446e97e09f4c3eee850fa4d90f21288415d3a65.jpg", + "table_caption": [ + "Table 4. PCK@0.05 accuracy of the TigDog dataset for domain adaptation setting. 'Mean' represents the accuracy for each animal category, and 'Average' represents the average accuracy for all animal categories. Best results in bold." + ], + "table_footnote": [], + "table_body": "
510152025
Full0.5330.5970.6320.6550.681
- RSR0.5210.5860.6210.6330.668
- MT0.4870.5680.6140.6280.659
- MB0.5200.5850.6240.6450.670
- AUG0.4870.5650.6080.6250.654
", + "bbox": [ + 80, + 575, + 467, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation study on the AP-10K dataset when 5, 10, 15, 20 and 25 images per animal species are labeled.", + "bbox": [ + 75, + 681, + 468, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Results on the TigDog Dataset", + "text_level": 1, + "bbox": [ + 75, + 739, + 344, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The TigDog Dataset is used in previous domain adaptation works [16, 20] to show that models trained from synthetic images can be used for real ones. We also evaluate on this dataset to show that our approach can achieve comparable or even better performance compared with state-of-the-art domain adaptation works with very few labeled images. Note that we use the same ResNet backbone as [20] for all experiments on the TigDog dataset for fair comparison. The results are shown in Tab. 3, where the numbers are", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "directly taken from [16]. 'Real' denotes fully-supervised setting, Cycgan [36], BDL [17], Cycada [10], CC-SSL [20], MDAM-MT [16] are domain adaptation approaches trained with synthetic animal images and \"Ours\" means our approach trained with 36 images per animal category. Note that 36 is the minimum labeled data needed for each category to achieve better performance than existing unsupervised domain adaptation approaches, i.e. we only need to label 72 out of 14,903 images for the Tigdog dataset. The results demonstrate the advantage of our setting since annotating such few images does not take much human labor.", + "bbox": [ + 496, + 579, + 890, + 744 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also test our approach on the domain adaptation setting to further verify the effectiveness. The results are shown in Tab. 4, which includes accuracy for different joints, the mean accuracy for each animal category and the average accuracy over all categories. We can see that our approach achieves the best performance in most of the cases. Note that our approach and CC-SSL have simpler networks compared to MDAM-MT, which introduce an extra refinement module for self-knowledge distillation. More training details are provided in the supplementary material.", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "17180", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a7468c9d45bc1af29643c4aa44f2079ea0ccc6a71ea54e64a68ac9877fb50c81.jpg", + "image_caption": [ + "Figure 3. Qualitative results for the AP-10K dataset when 25 images per species is labeled (except for the last two examples). The last two examples show the failure cases when only images from the Bovidae family are labeled." + ], + "image_footnote": [], + "bbox": [ + 145, + 88, + 823, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 503, + 228, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation study on the AP-10K dataset. Each component is removed from the full model to verify the corresponding contribution. The results are shown in Tab. 5, where 'RSR' denotes reusable sample re-labeling, 'MT' denotes student teacher consistency, 'MB' denotes multibranch architecture and 'AUG' denotes strong-weak augmentation. Note that we remove the weak augmentation $\\mathcal{T}$ and replace the strong augmentation $\\mathcal{P}$ with commonly used rotation and scale augmentation for the ablation of 'AUG'. We can see that the performance drops when each component is removed. Specially, the accuracy drops significantly for the 5 labels per animal species setting when the student teacher consistency or strong-weak augmentation is removed. This can be attributed to two reasons. Firstly, the strong-weak augmentation enforces the output of the strong augmented images to be consistent with the pseudo labels that are generated using weak augmented images. In this way, the network is enforced to learn a smooth representation around each image, which helps to improve the performance especially in the low-data regime. Secondly, The initial set of pseudo labels are extremely noisy when the model is trained with very few labeled data. The teacher network, which is a temporal ensemble of network, is able to provide more stable supervision for the student network.", + "bbox": [ + 75, + 537, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Limitations", + "text_level": 1, + "bbox": [ + 500, + 503, + 622, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our approach achieves impressive performance even when very few labeled data is available. However, there are still many remaining challenges for the task of animal pose estimation for limited labeled data. The large variations of appearance and pose across different animal species makes it hard for the network to generalize well to different animal species, e.g. train with labels from Bovidae and test on Hominidae. We leave this for future research.", + "bbox": [ + 496, + 529, + 890, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 661, + 617, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose a pseudo label based training scheme for animal pose estimation from scarce annotations. We combine the reliable pseudo label selection with the reusable sample re-labeling and the student-teacher consistency to make full use of the unlabeled data. We also introduce the MBHRNet to mitigate the negative effect of noisy joints. Extensive experiments have been conducted to verify the effectiveness of our proposed approach.", + "bbox": [ + 496, + 686, + 890, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-024), and the Tier 2 grant MOE-T2EP20120-0011 from the Singapore Ministry of Education.", + "bbox": [ + 496, + 825, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "17181", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5359-5368, 2019. 2" + ], + "bbox": [ + 78, + 90, + 470, + 867 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "17183", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_model.json b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_model.json new file mode 100644 index 0000000000000000000000000000000000000000..589d550c3cfd4dd3d906b415fa64e97257c9e764 --- /dev/null +++ b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_model.json @@ -0,0 +1,1782 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.179, + 0.131, + 0.793, + 0.151 + ], + "angle": 0, + "content": "ScarceNet: Animal Pose Estimation with Scarce Annotations" + }, + { + "type": "text", + "bbox": [ + 0.375, + 0.182, + 0.594, + 0.198 + ], + "angle": 0, + "content": "Chen Li Gim Hee Lee" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.2, + 0.753, + 0.218 + ], + "angle": 0, + "content": "Department of Computer Science, National University of Singapore" + }, + { + "type": "text", + "bbox": [ + 0.277, + 0.22, + 0.69, + 0.234 + ], + "angle": 0, + "content": "lichen@u.nus.edu gimhee.lee@comp.nus.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.302, + 0.474, + 0.771 + ], + "angle": 0, + "content": "Animal pose estimation is an important but under-explored task due to the lack of labeled data. In this paper, we tackle the task of animal pose estimation with scarce annotations, where only a small set of labeled data and unlabeled images are available. At the core of the solution to this problem setting is the use of the unlabeled data to compensate for the lack of well-labeled animal pose data. To this end, we propose the ScarceNet, a pseudo label-based approach to generate artificial labels for the unlabeled images. The pseudo labels, which are generated with a model trained with the small set of labeled images, are generally noisy and can hurt the performance when directly used for training. To solve this problem, we first use a small-loss trick to select reliable pseudo labels. Although effective, the selection process is imprudent since numerous high-loss samples are left unused. We further propose to identify reusable samples from the high-loss samples based on an agreement check. Pseudo labels are re-generated to provide supervision for those reusable samples. Lastly, we introduce a student-teacher framework to enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can make full use of the unlabeled data. We evaluate our approach on the challenging AP-10K dataset, where our approach outperforms existing semi-supervised approaches by a large margin. We also test on the TigDog dataset, where our approach can achieve better performance than domain adaptation based approaches when only very few annotations are available. Our code is available at the project website1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.802, + 0.21, + 0.818 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.828, + 0.47, + 0.875 + ], + "angle": 0, + "content": "The ability to understand animal behavior is fundamental to many applications, such as farming, ecology and surveillance. Animal pose estimation is a key step to un" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.268, + 0.646, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.544, + 0.381, + 0.614, + 0.389 + ], + "angle": 0, + "content": "Unlabeled data" + }, + { + "type": "image", + "bbox": [ + 0.646, + 0.27, + 0.747, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.749, + 0.269, + 0.889, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.384, + 0.878, + 0.393 + ], + "angle": 0, + "content": "Estimated animal poses" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.41, + 0.895, + 0.454 + ], + "angle": 0, + "content": "Figure 1. An illustration of our task. We aim to achieve accurate animal pose estimation with a small set of labeled images as well as unlabeled images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.893, + 0.825 + ], + "angle": 0, + "content": "understand animal behavior and has attracted increasing attention in recent years [5, 16, 20, 23, 33]. Although great success is achieved for human pose estimation with the development of sophisticated deep learning models, these techniques cannot be directly used for animals due to the lack of labeled animal pose data. Existing works overcome this problem by learning from human pose data [5] or synthetic animal images [16, 20, 23]. However, there is a large domain gap between the real and synthetic (human) data. For example, the synthetic animal images in [20], which are generated from CAD models, only exhibit limited pose, appearance and background variations. As a result, the model trained with the synthetic data may not adapt well to real images, especially for images with crowded scene or self-occlusion. Moreover, the generation of synthetic images is a tedious process that also requires expert knowledge. The above-mentioned problems lead us to ask whether we can achieve accurate animal pose estimation with minimal effort for annotating? To answer this question, we focus on how to learn from scarce labeled data for animal pose estimation. As shown in Fig. 1, we aim to achieve accurate animal pose estimation with only a small set of labeled images and unlabeled images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The data scarcity problem is solved by semi-supervised learning (SSL) for the classification task [3,25,28,34]. One powerful class of SSL is pseudo labeling (PL), where artificial labels generated from a pretrained model are used together with labeled data to train a model. Impressive" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.411, + 0.9 + ], + "angle": 0, + "content": "" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17174" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "results have been achieved by applying PL [5, 16, 20] to domain adaptation based animal pose estimation. However, the PL-based methods suffer from confirmation bias when the network starts to output incorrect predictions with high confidence, which we refer as noisy pseudo labels. To solve this noisy pseudo label problem, we use the small-loss trick [9, 16] to select reliable pseudo labels, i.e. samples with small loss to update the network. This criteria is based on the memorization effect [2] of deep networks where the network learns from clean and easy instances first before eventually overfitting to noisy ones. Consequently, clean samples exhibit smaller loss compared to noisy ones at the beginning of training. Although the small-loss trick is effective in selecting reliable pseudo labels, it is wasteful because numerous high-loss samples are left unused." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.473, + 0.639 + ], + "angle": 0, + "content": "In this paper, we propose the ScarceNet, a PL-based approach to learn an animal pose network from scarce annotations. We first train an animal pose estimation network on the small set of labeled data, and then generate pseudo labels for the unlabeled images with the pretrained model. The pseudo labels are often corrupted with noise due to the small size of the training data. We thus also select reliable pseudo labels using the small-loss trick. However, instead of ignoring or adding consistency regularization to the high-loss samples as done in previous works [16, 20], we propose to identify reusable samples from those high-loss samples based on an agreement check. The agreement check is to guarantee that the model predictions for the reusable samples are smooth and concurrently far from the decision boundary, and hence allow us to directly re-label reusable samples with the model predictions. Finally, we introduce a student-teacher network [28] and enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can fully exploit the unlabeled data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.473, + 0.808 + ], + "angle": 0, + "content": "In addition to the training scheme, we also modify the state-of-the-art human pose estimation network HRNet [27] and adapt it to the pseudo label-based learning framework. The original HRNet regresses the heatmaps of different joints from a shared feature representation. However, the negative effect of noisy pseudo label for any joint is propagated to all other joints through this shared feature representation. To mitigate this problem, we introduce a multibranch HRNet (MBHRNet) where a joint-specific feature representation is learned for regressing the corresponding joint location in each branch." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.81, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We validate our approach on the challenging AP-10K dataset [33], which includes animal images from more than 50 species. Our approach outperforms existing SSL methods by a large margin, especially when the labeled data is very limited (for example, 5 labeled images per species). We also test our approach under the inter-family transfer" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.212 + ], + "angle": 0, + "content": "setting, where animal species from only one family are labeled and the rest are unlabeled. Our approach improves the HRNet baseline significantly, and even outperform the supervised counterpart for some species. We further test on the TigDog dataset [20], where we can outperform existing synthetic data based approaches when only \\(0.5\\%\\) of the dataset is labeled. Our contribution can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.221, + 0.892, + 0.252 + ], + "angle": 0, + "content": "- We propose a pseudo label based training scheme for the task of animal pose estimation from scarce labels." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.261, + 0.892, + 0.292 + ], + "angle": 0, + "content": "- We introduce the MBHRNet to mitigate negative effect of noisy joints to other joints in the same image." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.301, + 0.892, + 0.331 + ], + "angle": 0, + "content": "- We achieve state-of-the-art performance on several animal pose benchmarks under different settings." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.221, + 0.892, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.344, + 0.642, + 0.36 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.895, + 0.809 + ], + "angle": 0, + "content": "Animal Pose Estimation. Animal pose estimation, including both 2D [5, 16, 20] and 3D [4, 15, 37], has become an active research field in the last few years. The development of animal pose estimation techniques is relatively slower than the human counterpart due to the lack of large scale animal pose dataset like COCO [18] or MPII [1]. Existing works circumvent the requirement for animal pose data by transferring knowledge from other domains, such as human pose data [5] and synthetic animal data [16, 20, 23]. Although impressive results have been achieved in [5], substantial amounts of labeled animal images are still needed to facilitate the knowledge transfer. This is due to the large domain gap between human and animal images, including pose, appearance and body structure differences. To reduce the domain gap between the source and target domains, synthetic animal images are generated from CAD models and used as the source images in [20]. Three consistency criteria are proposed to generate pseudo labels for real images. Improved upon [20], Li et al. [16] propose a pseudo label updating strategy to prevent the network from overfitting to the noisy pseudo labels. Despite the domain gap is reduced by using synthetic animal images, the limited pose and appearance variations of the CAD models prohibit the synthetic data based approaches from adapting to real scenarios with crowded scene or self-occlusion. Moreover, synthesize realistic images is a tedious process, which also requires expert knowledge. In view of this, we focus on learning from scarce annotations to minimize human labor and achieve accurate animal pose estimation at the same time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Semi-supervised Learning. Semi-supervised learning is powerful in leveraging unlabeled data to improve a model's performance when labeled data is limited. One of the most widely used SSL techniques is pseudo labeling [14, 31], which generates artificial labels for unlabeled images from" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17175" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.319 + ], + "angle": 0, + "content": "model predictions. Another technique is consistency regularization [13, 22, 28], which enforces that the model output should be consistent when the input is randomly perturbed. MixMatch [3] combines the consistency regularization with the entropy minimization to encourage the network to output confident predictions for unlabeled data. More recent Unsupervised Data Augmentation (UDA) [30] and FixMatch [25] combine pseudo labeling, consistency regularization with strong augmentations [6] and achieve superior performance. FlexMatch [34] further improves over UDA and Fixmatch by introducing a curriculum learning scheme. We also adopt the PL-based techniques in this work given its effectiveness. To mitigate the negative effect of noisy pseudo labels, we combine PL with reliable pseudo label selection and reusable sample re-labeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.473, + 0.706 + ], + "angle": 0, + "content": "Learning from Noisy Labels. Learning from noisy labels has become an important task since deep neural networks are known to be susceptible to noisy labels. To reduce the negative effect of noisy labels, different approaches which can be divided into three categories have been proposed. The first category is to treat the true labels as hidden variables and use an extra network to estimate a noise transition matrix [8, 21]. These methods assume there is correlation between the corrupted and clean labels, hence cannot handle complicate cases with random noise. The second category is to design noise-robust loss functions [7], such as the generalized cross entropy [35] and the symmetric cross entropy [29]. The robust-loss based approaches are theoretically sound, but may only be capable of handling a certain noise rate. The last category [9, 11, 19] focuses on selecting potential clean samples to update the network. One promising selection criteria is the small-loss trick [9], which is designed based on the memorization effect of deep networks and has been widely applied to different tasks [16, 26, 32]. We also apply the small-loss trick to select reliable pseudo labels. However, instead of ignoring the high-loss samples as done in previous works, we combine the sample selection with the reusable sample re-labeling to make full use of the unlabeled data." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.307, + 0.739 + ], + "angle": 0, + "content": "3. Our Method: ScarceNet" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We propose a PL-based approach to learn animal pose estimation from scarce annotations. The overall framework of our ScarceNet is illustrated in the left part of Fig. 2, where we propose a multi-branch HRNet (MBHRNet) as our animal pose estimation network. Let us denote an input image as \\(\\mathbf{x}\\) and its ground truth animal pose (if available) as \\(\\mathbf{y}\\). Given a small set of labeled images \\(\\mathcal{D}_l = \\{\\mathbf{x}_i^l,\\mathbf{y}_i^l\\}_{i = 1}^{N_l}\\) and unlabeled images \\(\\mathcal{D}_u = \\{\\mathbf{x}_i^u\\}_{i = 1}^{N_u}\\), the objective is to train the animal pose estimation network by leveraging both the labeled and unlabeled data. \\(N_{l}\\) and \\(N_{u}\\) represent the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.364 + ], + "angle": 0, + "content": "number of labeled and unlabeled images, respectively, and \\( N_{l} \\ll N_{u} \\). The labeled images are supervised with the ground truth pose data. We then generate pseudo labels with the model trained on the labeled data for the unlabeled images. However, these generated pseudo labels are usually heavily corrupted with noise, especially when the labeled data is very limited. We thus apply the small-loss trick [9] to select a set of reliable pseudo labels. Despite its effectiveness, pseudo label selection by the small-loss trick tends to discard numerous high-loss samples. This results in high wastage since those discarded samples can still provide extra information for better discrimination. In view of this, we propose a reusable sample re-labeling step to further identify reusable samples from the high-loss samples via an agreement check and re-generate the corresponding pseudo labels for supervision. Lastly, we design a student-teacher framework to enforce consistency between the outputs of the student and teacher network." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.371, + 0.783, + 0.387 + ], + "angle": 0, + "content": "3.1. Reliable Pseudo Label Selection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.893, + 0.424 + ], + "angle": 0, + "content": "We first train the animal pose estimation network on labeled images \\(\\mathcal{D}_l\\) with a supervised loss:" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.432, + 0.893, + 0.473 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s}} = \\frac {1}{J} \\sum_ {i = 1} ^ {J} \\| H _ {i} - \\hat {H} _ {i} \\| ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.895, + 0.648 + ], + "angle": 0, + "content": "where \\( H_{i} \\) is the ground truth heatmap, \\( J \\) denotes the total number of joints, and \\( \\hat{H}_i \\) represents the output heatmap of the network. The pretrained network is then used to generate an initial set of pseudo labels for the unlabeled images \\( \\mathcal{D}_u \\) following the procedure in [20]. The generated pseudo labels are generally noisy and can hurt the performance if directly used for training. To prevent this, we select reliable pseudo labels, denoted as \\( \\mathbb{S} \\), from the initial pseudo labels using the small-loss trick. Specifically, we only make use of samples with loss smaller than a threshold to update the network. Formally, this can be expressed as:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.653, + 0.893, + 0.697 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {p}} = \\frac {\\sum_ {i = 1} ^ {J} \\left\\{\\mathcal {L} _ {\\mathrm {p}} ^ {i} < l _ {\\mathrm {r}} \\right\\} _ {1} \\mathcal {L} _ {\\mathrm {p}} ^ {i}}{\\sum_ {i = 1} ^ {J} \\left\\{\\mathcal {L} _ {\\mathrm {p}} ^ {i} < l _ {\\mathrm {r}} \\right\\} _ {1}}, \\text {w h e r e} \\mathcal {L} _ {\\mathrm {p}} ^ {i} = \\| \\tilde {H} _ {i} - \\hat {H} _ {i} \\| ^ {2}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.895, + 0.84 + ], + "angle": 0, + "content": "\\(\\tilde{H}_i\\) represents the pseudo label for the \\(i^{\\mathrm{th}}\\) joint and \\(\\mathcal{L}_{\\mathrm{p}}^{i}\\) is the corresponding pseudo label based loss. \\(\\{\\mathrm{condition}\\}_{1}\\) is a condition function, which outputs 1 when the condition is true and 0 if false. \\(l_{\\mathrm{r}}\\) denotes the threshold loss value, and more details on how to decide \\(l_{\\mathrm{r}}\\) are provided in the supplementary material. This small-loss trick is designed based on the memorization effect of deep network, and has been shown effective in selecting reliable labels in previous works [16,26]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.762, + 0.865 + ], + "angle": 0, + "content": "3.2. Reusable Sample Re-labeling" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Only small-loss samples are selected in the reliable pseudo label selection process, and the remaining pseudo" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "17176" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.09, + 0.554, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.104, + 0.895, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.893, + 0.34 + ], + "angle": 0, + "content": "Figure 2. The left part shows the overall framework of our ScarceNet, where \\(\\mathcal{P}\\) and \\(\\mathcal{T}\\) represent strong and weak augmentation, respectively. The right part shows a comparison between the HRNet (top) and the MBHRNet (bottom), where 'FE' represents feature extractor, 'conv.' represents convolutional layer and 'JFE' represents joint specific feature extractor." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.473, + 0.562 + ], + "angle": 0, + "content": "labels with large loss are discarded. This is imprudent since the high-loss samples can also contribute to improving the network if used properly. To this end, we propose to further identify reusable samples, denoted as \\(\\mathbb{U}\\), from the unused samples to fully exploit the unlabeled data. We define reusable samples as the ones that may also provide reliable knowledge to the network despite their large losses. To identify the reusable samples, we introduce an agreement check. Specifically, given an input \\(\\mathbf{x}^u\\), we generate another view of this sample by adding a random transformation \\(\\mathcal{T}\\) which consists of rotation and scaling. Both samples are fed into the pose estimation network to produce the corresponding heatmaps, denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.572, + 0.47, + 0.589 + ], + "angle": 0, + "content": "\\[\nH ^ {\\mathrm {v} _ {1}} = f \\left(\\mathbf {x} ^ {u}\\right), H ^ {\\mathrm {v} _ {2}} = f \\left(\\mathcal {T} \\mathbf {x} ^ {u}\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.599, + 0.47, + 0.631 + ], + "angle": 0, + "content": "The location for the \\(i^{th}\\) joint is obtained by applying argmax operation to the corresponding output heatmap:" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.64, + 0.47, + 0.659 + ], + "angle": 0, + "content": "\\[\n\\mathbf {h} _ {i} ^ {\\mathrm {v} _ {1}} = \\operatorname {a r g m a x} \\left(H _ {i} ^ {\\mathrm {v} _ {1}}\\right), \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {2}} = \\operatorname {a r g m a x} \\left(H _ {i} ^ {\\mathrm {v} _ {2}}\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.667, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Unlike the classification task where the output is transformation invariant [12, 32], the output joint location is transformation equivariant. Consequently, we have to transform \\(\\mathbf{h}_i^{\\mathrm{v_1}}\\) before the agreement check, i.e.:" + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.738, + 0.47, + 0.756 + ], + "angle": 0, + "content": "\\[\nd _ {i} = \\left\\| \\mathcal {T} \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {1}} - \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {2}} \\right\\| ^ {2}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Subsequently, we can determine whether a sample is reusable based on the distance between the outputs of the two views. Specifically, a sample \\(\\mathbf{x}_i^u\\) is reusable when the distance fulfills \\(d_{i} < d_{\\mathrm{r}}\\), where \\(d_{\\mathrm{r}}\\) represents the distance threshold. This agreement check is based on the agreement maximization principle [24], which has also been used for out-of-distribution detection [32] and stable sample selection [12]. Intuitively, the reusable samples must satisfy smoothness in the neighborhood of the model prediction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.365, + 0.893, + 0.409 + ], + "angle": 0, + "content": "and must also be far from the decision boundary. Otherwise, the output becomes inconsistent when the input is randomly transformed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.893, + 0.576 + ], + "angle": 0, + "content": "The next step is to re-label the identified reusable samples since they exhibit large loss based on the initial pseudo labels. We directly use the prediction from the current model as the new pseudo labels to train the network. The motivation is twofold: 1) The model has been trained with unlabeled images, hence it is able to output more accurate prediction comparing to the model trained only on the labeled images. 2) The selection criteria for reusable samples indicates that the current model prediction is already reliable. Finally, the loss function for the reusable samples can be defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.587, + 0.892, + 0.628 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r}} = \\frac {\\sum_ {i = 1} ^ {J} \\left\\{d ^ {i} < d _ {\\mathrm {r}} \\right\\} _ {1} \\mathcal {L} _ {\\mathrm {r}} ^ {i}}{\\sum_ {i = 1} ^ {J} \\left\\{d ^ {i} < d _ {\\mathrm {r}} \\right\\} _ {1}}, \\text {w h e r e} \\mathcal {L} _ {\\mathrm {r}} ^ {i} = \\| \\bar {H} _ {i} - \\hat {H} _ {i} \\| ^ {2}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.716 + ], + "angle": 0, + "content": "\\(\\bar{H}_i\\) represents the heatmap generated from the joint location of current model prediction. By selecting the reusable samples, we are able to make use of more unlabeled images and prevent the network from overfitting to the initial noisy pseudo labels at the same time." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.757, + 0.743 + ], + "angle": 0, + "content": "3.3. Student-teacher Consistency" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Both the reliable pseudo label selection and reusable sample selection are based on specific constraints. Samples that do not fulfill either constraint are still left unused. In view of this, we further introduce a teacher network and enforce the consistency between the student and teacher network. This is inspired by the mean teacher framework [28], which enforces the consistency constraint for unlabeled data for semi-supervised classification. The teacher network shares the same structure with the student network, and the weights are updated with an exponential moving average" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "17177" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.274, + 0.106 + ], + "angle": 0, + "content": "(EMA) of the student model:" + }, + { + "type": "equation", + "bbox": [ + 0.183, + 0.116, + 0.47, + 0.135 + ], + "angle": 0, + "content": "\\[\n\\theta_ {\\mathrm {m t}} ^ {t} = \\alpha \\theta_ {\\mathrm {m t}} ^ {t - 1} + (1 - \\alpha) \\theta^ {t}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.144, + 0.473, + 0.31 + ], + "angle": 0, + "content": "\\(\\theta_{\\mathrm{mt}}\\) and \\(\\theta\\) denote the weights of the teacher and student network, respectively. The superscript \\(t\\) represents the training step, and \\(\\alpha\\) is a smoothing coefficient of the EMA update. We can see that the teacher network is a temporal ensemble of networks, and thus it can provide more accurate pseudo labels. As shown in Fig. 2, we add random perturbations \\(\\mathcal{P}\\) to the input of the student network, which consists of both geometry-based perturbations \\(\\mathcal{P}_g\\) such as rotation, scaling and flipping, and image-based perturbation \\(\\mathcal{P}_m\\) such as noise, occlusion and blurring. Consistency is then enforced between the teacher and student network as:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.317, + 0.47, + 0.358 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {t}} = \\frac {1}{J} \\sum_ {i = 1} ^ {J} \\| \\mathcal {P} _ {g} H _ {i} ^ {t} - \\hat {H} _ {i} \\| ^ {2}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.47, + 0.43 + ], + "angle": 0, + "content": "where \\( H_{i}^{t} \\) denotes the output of the teacher network. Note that only the geometry-based perturbation \\( \\mathcal{P}_g \\) is added to the output of the teacher network since the output joint location is invariant to the image-based perturbation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.438, + 0.461, + 0.453 + ], + "angle": 0, + "content": "3.4. Multi-head Animal Pose Estimation Network" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.473, + 0.764 + ], + "angle": 0, + "content": "We adopt the human pose estimation network HRNet as our backbone. The HRNet has achieved state-of-the-art performance for human pose estimation by combining high-resolution feature representations with multi-resolution feature fusion. However, as shown in the right top part of Fig. 2, the final heatmaps of HRNet are regressed from a shared feature representation with one linear layer. This shared mechanism can have negative effect in the presence of noisy labels. For example, the feature representation is affected by backpropagation when the pseudo label for any joint is noisy and thus further affect the prediction of other joints in the same image. To mitigate this problem, we introduce a multi-branch head to the HRNet to learn a specific feature representation for each joint. As shown in the right bottom part of Fig. 2, the network has \\( J \\) output branches, where each branch learns a specific feature representation via a joint specific feature extractor (JFE) to regress the corresponding joint location. In this way, the adverse effect from the noisy pseudo label of a joint gets absorbed in its respective branch." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.772, + 0.327, + 0.789 + ], + "angle": 0, + "content": "3.5. Strong-weak Augmentation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We also introduce a strong-weak augmentation training scheme, where two sets of augmentation are applied to the inputs, denoted as \\(\\mathcal{T}\\) and \\(\\mathcal{P}\\) in previous sections. Particularly, we apply strong augmentations \\(\\mathcal{P}\\) for the learning task with backpropagation and weak augmentation \\(\\mathcal{T}\\) for the re-labeling task. As shown in Fig. 2, strong augmentation \\(\\mathcal{P}\\) is applied to the labeled images in the blue path" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "and unlabeled images in the orange path. These two paths are responsible for updating the network, and hence strong augmentation can improve the generalization capacity. In comparison, the weak augmentation \\(\\mathcal{T}\\) is applied to the green path because this path is responsible for identifying and re-labeling reusable samples. Overly-strong augmentation can have adversarial affects on the agreement check process since strong augmentation tends to result in inconsistent predictions. More details on the augmentation are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.264, + 0.691, + 0.278 + ], + "angle": 0, + "content": "3.6. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.41 + ], + "angle": 0, + "content": "We train our network in two stages. In the first stage, we train the MBHRNet on \\(\\mathcal{D}_l\\) with the supervised loss in Eqn. (1). The trained network is applied to generate pseudo labels for the unlabeled data. In the second stage, the student network is initialized with the pretrained model and trained with both \\(\\mathcal{D}_l\\) and \\(\\mathcal{D}_u\\). The objective function for the second stage consists of both labeled and unlabeled losses as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.578, + 0.432, + 0.892, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\mathrm {s}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {p}} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {r}} + \\lambda_ {4} \\mathcal {L} _ {\\mathrm {t}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.892, + 0.499 + ], + "angle": 0, + "content": "where \\(\\lambda_1, \\lambda_2, \\lambda_3,\\) and \\(\\lambda_4\\) are the weights for different losses. The overall training procedure is presented in Algorithm 1." + }, + { + "type": "code_caption", + "bbox": [ + 0.5, + 0.532, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Algorithm 1 Overall training procedure of the second stage \nInput: labeled data \\(\\mathcal{D}_l\\) and unlabeled data \\(\\mathcal{D}_u\\), threshold loss value \\(l_r\\), distance threshold \\(d_r\\), batch size \\(B\\)" + }, + { + "type": "algorithm", + "bbox": [ + 0.501, + 0.596, + 0.892, + 0.871 + ], + "angle": 0, + "content": "1: for \\(\\{x_{1}, x_{2}, \\ldots, x_{B}\\} \\in \\mathcal{D}_{l} \\cup \\mathcal{D}_{u}\\) do \n2: if \\(x_{i} \\in \\mathcal{D}_{l}\\) then \n3: Compute supervised loss \\(\\mathcal{L}_{\\mathrm{s}}\\) according to Eqn. (1) \n4: else \n5: if \\(x_{i} \\in \\mathbb{S}\\) then \n6: Compute the pseudo labeled based loss \\(\\mathcal{L}_{\\mathrm{p}}\\) according to Eqn. (2) \n7: else if \\(x_{i} \\in \\mathbb{U}\\) then \n8: Compute loss \\(\\mathcal{L}_{\\mathrm{r}}\\) for reusable samples by Eqn. (6) \n9: end if \n10: Compute the consistency loss \\(\\mathcal{L}_{\\mathrm{t}}\\) according to Eqn. (8) \n11: end if \n12: Compute the total loss \\(\\mathcal{L}\\) according to Eqn. (9) \n13: Update student network \\(\\theta \\gets \\theta - \\eta \\Delta \\mathcal{L}\\) \n14: Update teacher network by Eqn. (7) \n15: end for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17178" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.283, + 0.108 + ], + "angle": 0, + "content": "4. Experimental Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.471, + 0.298 + ], + "angle": 0, + "content": "Training details. We adopt the HRNet-w32 as the backbone and train our network in two stages. We first train the MBHRNet on the labeled data with the supervised loss. Following [27], we train the network with the Adam optimizer for 210 epochs. The initial learning rate is set to \\(10^{-3}\\), and is dropped to \\(10^{-4}\\) and \\(10^{-5}\\) at the \\(170^{th}\\) and \\(200^{th}\\) epochs, respectively. The trained model is then used to generate pseudo labels following [20]. In the second stage, we initialized the student network from the first stage and train the whole framework with both labeled and unlabeled data for another 150 epochs. More training details are provided in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.471, + 0.531 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on the AP-10K dataset [33] and the TigDog dataset [20]. The AP-10K dataset is a recently proposed animal pose dataset, which contains more diverse animal species than previous datasets [5, 20]. The dataset contains 10,015 labeled images in total, which are split into train, validation, and test sets with a ratio of 7:1:2 per animal species. The TigDog dataset includes 8380 images for the horse category and 6523 images for the tiger category. This dataset is used in several domain adaptation works [16,20] to show that the knowledge learned from synthetic animals can be transferred to real animal images. We also evaluate on this dataset to show that better performance can be achieved by labeling just a few images, hence can reduce human labor compared to generating synthetic data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.47, + 0.643 + ], + "angle": 0, + "content": "Evaluation metrics. We adopt the Mean Average Precision (mAP) as the evaluation metric for the AP-10K dataset. The Percentage of Correct Keypoints (PCK), which computes the percentage of joints that are within a normalized distance to the ground truth locations, is used for the TigDog dataset following [20]." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.654, + 0.476, + 0.751 + ], + "angle": 0, + "content": "
510152025
HRNet [27]0.3600.4630.5110.5470.588
UDA [30]0.4290.5190.5660.5800.628
FixMatch [25]0.4780.5440.5890.6010.631
FlexMatch [34]0.4660.5550.5960.6180.646
Ours0.5330.5970.6320.6540.681
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.76, + 0.468, + 0.789 + ], + "angle": 0, + "content": "Table 1. Results (mAP) on the AP-10K when 5, 10, 15, 20 and 25 images per species are labeled. Best results in bold." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.355, + 0.832 + ], + "angle": 0, + "content": "4.1. Results on the AP-10K Dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We evaluate our approach under two scenarios on the AP-10K dataset. In the first scenario, a set of images are labeled for each animal species. The second scenario is that only the images in one family are labeled and we test on" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "other animal families. This setting is more challenge since the appearance, size and background environment are quite different for different animal species." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.157, + 0.892, + 0.504 + ], + "angle": 0, + "content": "We show results for the first scenario in Tab. 1, where we evaluate when 5, 10, 15, 20 and 25 images per animal species are labeled. There are 50 species in total, which results in 250, 500, 720, 1000 and 1250 labeled images out of 7023 images. We compare with state-of-the-art semi-supervised approaches, including UDA [30], FixMatch [25] and FlexMatch [34]. 'HRNet' represents HRNet trained only with labeled images. We reimplement those semi-supervised approaches according to the open repository since they only show results for classification task. We can see that our approach outperforms existing approaches by a large margin, especially when very few labeled images are available, such as the case of 5 labels per species. The reason is that UDA, FixMatch and FlexMatch only retain the samples with reliable pseudo labels based on the confidence scores. In comparison, we combine the reliable pseudo label selection with the reusable sample re-labeling and teacher-student consistency, which helps to fully utilize the unlabeled data. Moreover, our results are the closest to the fully supervised setting [33], i.e. \\(0.738\\mathrm{mAP}\\), when only 25 images per animal species are labeled. We also show qualitative results for the 25 labels per animal species setting in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.903 + ], + "angle": 0, + "content": "We also show results for the case when images from only one animal family are labeled in Tab. 2. Following the inter-family transfer learning setting in [33], we train our model with labeled images of the Bovidae family and the remaining unlabeled images, and test on families including Cervidae, Equidae and Hominidae. There are seven animal species in the Bovidae family that includes a total of 755 images. The results under the 'Generalization', 'Few-Shot' and 'Transfer' settings are taken from [33]. 'Generalization' means that the model is trained only with images in the Bovidae, 'Few-Shot' means that 20 labels from the testing species are used, and 'Transfer' means that all labels of the testing species are used. We can see that we achieve better performance than the generalization setting in all cases except for 'Moose'. Moreover, we even outperform the 'Transfer' setting for 'Deer' and 'Horse' although we do not use any labels from the target species. Our results for the 'Chimpanzee' and 'Gorilla' are not satisfactory although still comparable to the 'Few-Shot' setting. We show the failure cases of 'Chimpanzee' and 'Gorilla' in the last two examples of Fig. 3. We can see that 'Chimpanzee' and 'Gorilla' are very different from animal species in the Bovidae family (the first four examples of the last row) in terms of appearance and pose, which makes the knowledge transfer hard without using any labels from the target species." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "17179" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.14, + 0.088, + 0.832, + 0.29 + ], + "angle": 0, + "content": "
SpeciesSettingPerformanceSpeciesSettingPerformance
DeerGeneralization0.723MooseGeneralization0.587
Few-Shot0.742Few-Shot0.648
Transfer0.751Transfer0.726
Ours0.767Ours0.547
HorseGeneralization0.592ZebraGeneralization0.324
Few-Shot0.635Few-Shot0.480
Transfer0.718Transfer0.708
Ours0.749Ours0.562
ChimpanzeeGeneralization0.009GorillaGeneralization0.017
Few-Shot0.022Few-Shot0.144
Transfer0.550Transfer0.662
Ours0.057Ours0.033
" + }, + { + "type": "table_caption", + "bbox": [ + 0.145, + 0.301, + 0.825, + 0.316 + ], + "angle": 0, + "content": "Table 2. Results (mAP) for the Cervidae, Equidae and Hominidae when only images from the Bovidae are labeled." + }, + { + "type": "table", + "bbox": [ + 0.12, + 0.328, + 0.851, + 0.389 + ], + "angle": 0, + "content": "
RealCycgan [36]BDL [17]Cycada [10]CC-SSL [20]MDAM-MT [16]Ours
Horse78.9851.8662.3355.5770.7779.5073.05
Tiger81.9946.4752.2651.4864.1467.7674.88
Average80.4849.1757.3053.5367.5273.6673.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.399, + 0.893, + 0.429 + ], + "angle": 0, + "content": "Table 3. PCK@0.05 accuracy of the TigDog dataset. 'Real' means full supervision. Cycgan, BDL, Cycada, CC-SSL, MDAM-MT are domain adaptation approaches using synthetic data. Our approach is trained with only 36 labeled images per category." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.441, + 0.908, + 0.515 + ], + "angle": 0, + "content": "
Horse AccuracyTiger AccuracyAverage
EyeChinShoulderHipElbowKneeHoovesMeanEyeChinShoulderHipElbowKneeHoovesMean
CC-SSL84.6090.2669.6985.8968.5868.7361.3370.7796.7590.4644.8477.6155.8242.8564.5564.14
MDAM-MT91.0593.3777.3580.6773.6381.8373.6779.5097.0191.1846.6378.0850.8661.5470.8467.76
Ours89.4293.6074.6383.6174.3179.9173.9979.1899.1392.8246.9675.3650.4663.5174.8268.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.525, + 0.893, + 0.555 + ], + "angle": 0, + "content": "Table 4. PCK@0.05 accuracy of the TigDog dataset for domain adaptation setting. 'Mean' represents the accuracy for each animal category, and 'Average' represents the average accuracy for all animal categories. Best results in bold." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.577, + 0.468, + 0.673 + ], + "angle": 0, + "content": "
510152025
Full0.5330.5970.6320.6550.681
- RSR0.5210.5860.6210.6330.668
- MT0.4870.5680.6140.6280.659
- MB0.5200.5850.6240.6450.670
- AUG0.4870.5650.6080.6250.654
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Table 5. Ablation study on the AP-10K dataset when 5, 10, 15, 20 and 25 images per animal species are labeled." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.74, + 0.345, + 0.758 + ], + "angle": 0, + "content": "4.2. Results on the TigDog Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The TigDog Dataset is used in previous domain adaptation works [16, 20] to show that models trained from synthetic images can be used for real ones. We also evaluate on this dataset to show that our approach can achieve comparable or even better performance compared with state-of-the-art domain adaptation works with very few labeled images. Note that we use the same ResNet backbone as [20] for all experiments on the TigDog dataset for fair comparison. The results are shown in Tab. 3, where the numbers are" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.746 + ], + "angle": 0, + "content": "directly taken from [16]. 'Real' denotes fully-supervised setting, Cycgan [36], BDL [17], Cycada [10], CC-SSL [20], MDAM-MT [16] are domain adaptation approaches trained with synthetic animal images and \"Ours\" means our approach trained with 36 images per animal category. Note that 36 is the minimum labeled data needed for each category to achieve better performance than existing unsupervised domain adaptation approaches, i.e. we only need to label 72 out of 14,903 images for the Tigdog dataset. The results demonstrate the advantage of our setting since annotating such few images does not take much human labor." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "We also test our approach on the domain adaptation setting to further verify the effectiveness. The results are shown in Tab. 4, which includes accuracy for different joints, the mean accuracy for each animal category and the average accuracy over all categories. We can see that our approach achieves the best performance in most of the cases. Note that our approach and CC-SSL have simpler networks compared to MDAM-MT, which introduce an extra refinement module for self-knowledge distillation. More training details are provided in the supplementary material." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "17180" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.147, + 0.089, + 0.825, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.444, + 0.893, + 0.471 + ], + "angle": 0, + "content": "Figure 3. Qualitative results for the AP-10K dataset when 25 images per species is labeled (except for the last two examples). The last two examples show the failure cases when only images from the Bovidae family are labeled." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.505, + 0.23, + 0.521 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We conduct ablation study on the AP-10K dataset. Each component is removed from the full model to verify the corresponding contribution. The results are shown in Tab. 5, where 'RSR' denotes reusable sample re-labeling, 'MT' denotes student teacher consistency, 'MB' denotes multibranch architecture and 'AUG' denotes strong-weak augmentation. Note that we remove the weak augmentation \\(\\mathcal{T}\\) and replace the strong augmentation \\(\\mathcal{P}\\) with commonly used rotation and scale augmentation for the ablation of 'AUG'. We can see that the performance drops when each component is removed. Specially, the accuracy drops significantly for the 5 labels per animal species setting when the student teacher consistency or strong-weak augmentation is removed. This can be attributed to two reasons. Firstly, the strong-weak augmentation enforces the output of the strong augmented images to be consistent with the pseudo labels that are generated using weak augmented images. In this way, the network is enforced to learn a smooth representation around each image, which helps to improve the performance especially in the low-data regime. Secondly, The initial set of pseudo labels are extremely noisy when the model is trained with very few labeled data. The teacher network, which is a temporal ensemble of network, is able to provide more stable supervision for the student network." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.504, + 0.623, + 0.52 + ], + "angle": 0, + "content": "5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.53, + 0.892, + 0.65 + ], + "angle": 0, + "content": "Our approach achieves impressive performance even when very few labeled data is available. However, there are still many remaining challenges for the task of animal pose estimation for limited labeled data. The large variations of appearance and pose across different animal species makes it hard for the network to generalize well to different animal species, e.g. train with labels from Bovidae and test on Hominidae. We leave this for future research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.662, + 0.619, + 0.677 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.809 + ], + "angle": 0, + "content": "We propose a pseudo label based training scheme for animal pose estimation from scarce annotations. We combine the reliable pseudo label selection with the reusable sample re-labeling and the student-teacher consistency to make full use of the unlabeled data. We also introduce the MBHRNet to mitigate the negative effect of noisy joints. Extensive experiments have been conducted to verify the effectiveness of our proposed approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-024), and the Tier 2 grant MOE-T2EP20120-0011 from the Singapore Ministry of Education." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "17181" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5359-5368, 2019. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.868 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "17183" + } + ] +] \ No newline at end of file diff --git a/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_origin.pdf b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f7915bedbc309faddf442cf3a32f6bd3a6b18668 --- /dev/null +++ b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/b512070b-870b-466d-ae4d-037690406953_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2408895f3de8312e0a92afddfd0e1422b8109295dc118091ed1fcb73146dca3b +size 5222847 diff --git a/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/full.md b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5b0ae5436c58b80058984eddb164476c38fcd001 --- /dev/null +++ b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/full.md @@ -0,0 +1,275 @@ +# ScarceNet: Animal Pose Estimation with Scarce Annotations + +Chen Li Gim Hee Lee + +Department of Computer Science, National University of Singapore + +lichen@u.nus.edu gimhee.lee@comp.nus.edu.sg + +# Abstract + +Animal pose estimation is an important but under-explored task due to the lack of labeled data. In this paper, we tackle the task of animal pose estimation with scarce annotations, where only a small set of labeled data and unlabeled images are available. At the core of the solution to this problem setting is the use of the unlabeled data to compensate for the lack of well-labeled animal pose data. To this end, we propose the ScarceNet, a pseudo label-based approach to generate artificial labels for the unlabeled images. The pseudo labels, which are generated with a model trained with the small set of labeled images, are generally noisy and can hurt the performance when directly used for training. To solve this problem, we first use a small-loss trick to select reliable pseudo labels. Although effective, the selection process is imprudent since numerous high-loss samples are left unused. We further propose to identify reusable samples from the high-loss samples based on an agreement check. Pseudo labels are re-generated to provide supervision for those reusable samples. Lastly, we introduce a student-teacher framework to enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can make full use of the unlabeled data. We evaluate our approach on the challenging AP-10K dataset, where our approach outperforms existing semi-supervised approaches by a large margin. We also test on the TigDog dataset, where our approach can achieve better performance than domain adaptation based approaches when only very few annotations are available. Our code is available at the project website1. + +# 1. Introduction + +The ability to understand animal behavior is fundamental to many applications, such as farming, ecology and surveillance. Animal pose estimation is a key step to un + +![](images/f0fb6c3c0d2330c282f32813d2fedddad841c532e3662ab91d527e79dcd88df1.jpg) +Unlabeled data + +![](images/7c1e406cbc2d28cd95b6ca6b8b82858aeef7eaf36578beaa338b82dab079d9b9.jpg) + +![](images/67cd9d98b12356b3dc36f4815a11d14a1dbeadd15a100d108578d375acfd6409.jpg) +Estimated animal poses +Figure 1. An illustration of our task. We aim to achieve accurate animal pose estimation with a small set of labeled images as well as unlabeled images. + +understand animal behavior and has attracted increasing attention in recent years [5, 16, 20, 23, 33]. Although great success is achieved for human pose estimation with the development of sophisticated deep learning models, these techniques cannot be directly used for animals due to the lack of labeled animal pose data. Existing works overcome this problem by learning from human pose data [5] or synthetic animal images [16, 20, 23]. However, there is a large domain gap between the real and synthetic (human) data. For example, the synthetic animal images in [20], which are generated from CAD models, only exhibit limited pose, appearance and background variations. As a result, the model trained with the synthetic data may not adapt well to real images, especially for images with crowded scene or self-occlusion. Moreover, the generation of synthetic images is a tedious process that also requires expert knowledge. The above-mentioned problems lead us to ask whether we can achieve accurate animal pose estimation with minimal effort for annotating? To answer this question, we focus on how to learn from scarce labeled data for animal pose estimation. As shown in Fig. 1, we aim to achieve accurate animal pose estimation with only a small set of labeled images and unlabeled images. + +The data scarcity problem is solved by semi-supervised learning (SSL) for the classification task [3,25,28,34]. One powerful class of SSL is pseudo labeling (PL), where artificial labels generated from a pretrained model are used together with labeled data to train a model. Impressive + +results have been achieved by applying PL [5, 16, 20] to domain adaptation based animal pose estimation. However, the PL-based methods suffer from confirmation bias when the network starts to output incorrect predictions with high confidence, which we refer as noisy pseudo labels. To solve this noisy pseudo label problem, we use the small-loss trick [9, 16] to select reliable pseudo labels, i.e. samples with small loss to update the network. This criteria is based on the memorization effect [2] of deep networks where the network learns from clean and easy instances first before eventually overfitting to noisy ones. Consequently, clean samples exhibit smaller loss compared to noisy ones at the beginning of training. Although the small-loss trick is effective in selecting reliable pseudo labels, it is wasteful because numerous high-loss samples are left unused. + +In this paper, we propose the ScarceNet, a PL-based approach to learn an animal pose network from scarce annotations. We first train an animal pose estimation network on the small set of labeled data, and then generate pseudo labels for the unlabeled images with the pretrained model. The pseudo labels are often corrupted with noise due to the small size of the training data. We thus also select reliable pseudo labels using the small-loss trick. However, instead of ignoring or adding consistency regularization to the high-loss samples as done in previous works [16, 20], we propose to identify reusable samples from those high-loss samples based on an agreement check. The agreement check is to guarantee that the model predictions for the reusable samples are smooth and concurrently far from the decision boundary, and hence allow us to directly re-label reusable samples with the model predictions. Finally, we introduce a student-teacher network [28] and enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can fully exploit the unlabeled data. + +In addition to the training scheme, we also modify the state-of-the-art human pose estimation network HRNet [27] and adapt it to the pseudo label-based learning framework. The original HRNet regresses the heatmaps of different joints from a shared feature representation. However, the negative effect of noisy pseudo label for any joint is propagated to all other joints through this shared feature representation. To mitigate this problem, we introduce a multibranch HRNet (MBHRNet) where a joint-specific feature representation is learned for regressing the corresponding joint location in each branch. + +We validate our approach on the challenging AP-10K dataset [33], which includes animal images from more than 50 species. Our approach outperforms existing SSL methods by a large margin, especially when the labeled data is very limited (for example, 5 labeled images per species). We also test our approach under the inter-family transfer + +setting, where animal species from only one family are labeled and the rest are unlabeled. Our approach improves the HRNet baseline significantly, and even outperform the supervised counterpart for some species. We further test on the TigDog dataset [20], where we can outperform existing synthetic data based approaches when only $0.5\%$ of the dataset is labeled. Our contribution can be summarized as follows: + +- We propose a pseudo label based training scheme for the task of animal pose estimation from scarce labels. +- We introduce the MBHRNet to mitigate negative effect of noisy joints to other joints in the same image. +- We achieve state-of-the-art performance on several animal pose benchmarks under different settings. + +# 2. Related Work + +Animal Pose Estimation. Animal pose estimation, including both 2D [5, 16, 20] and 3D [4, 15, 37], has become an active research field in the last few years. The development of animal pose estimation techniques is relatively slower than the human counterpart due to the lack of large scale animal pose dataset like COCO [18] or MPII [1]. Existing works circumvent the requirement for animal pose data by transferring knowledge from other domains, such as human pose data [5] and synthetic animal data [16, 20, 23]. Although impressive results have been achieved in [5], substantial amounts of labeled animal images are still needed to facilitate the knowledge transfer. This is due to the large domain gap between human and animal images, including pose, appearance and body structure differences. To reduce the domain gap between the source and target domains, synthetic animal images are generated from CAD models and used as the source images in [20]. Three consistency criteria are proposed to generate pseudo labels for real images. Improved upon [20], Li et al. [16] propose a pseudo label updating strategy to prevent the network from overfitting to the noisy pseudo labels. Despite the domain gap is reduced by using synthetic animal images, the limited pose and appearance variations of the CAD models prohibit the synthetic data based approaches from adapting to real scenarios with crowded scene or self-occlusion. Moreover, synthesize realistic images is a tedious process, which also requires expert knowledge. In view of this, we focus on learning from scarce annotations to minimize human labor and achieve accurate animal pose estimation at the same time. + +Semi-supervised Learning. Semi-supervised learning is powerful in leveraging unlabeled data to improve a model's performance when labeled data is limited. One of the most widely used SSL techniques is pseudo labeling [14, 31], which generates artificial labels for unlabeled images from + +model predictions. Another technique is consistency regularization [13, 22, 28], which enforces that the model output should be consistent when the input is randomly perturbed. MixMatch [3] combines the consistency regularization with the entropy minimization to encourage the network to output confident predictions for unlabeled data. More recent Unsupervised Data Augmentation (UDA) [30] and FixMatch [25] combine pseudo labeling, consistency regularization with strong augmentations [6] and achieve superior performance. FlexMatch [34] further improves over UDA and Fixmatch by introducing a curriculum learning scheme. We also adopt the PL-based techniques in this work given its effectiveness. To mitigate the negative effect of noisy pseudo labels, we combine PL with reliable pseudo label selection and reusable sample re-labeling. + +Learning from Noisy Labels. Learning from noisy labels has become an important task since deep neural networks are known to be susceptible to noisy labels. To reduce the negative effect of noisy labels, different approaches which can be divided into three categories have been proposed. The first category is to treat the true labels as hidden variables and use an extra network to estimate a noise transition matrix [8, 21]. These methods assume there is correlation between the corrupted and clean labels, hence cannot handle complicate cases with random noise. The second category is to design noise-robust loss functions [7], such as the generalized cross entropy [35] and the symmetric cross entropy [29]. The robust-loss based approaches are theoretically sound, but may only be capable of handling a certain noise rate. The last category [9, 11, 19] focuses on selecting potential clean samples to update the network. One promising selection criteria is the small-loss trick [9], which is designed based on the memorization effect of deep networks and has been widely applied to different tasks [16, 26, 32]. We also apply the small-loss trick to select reliable pseudo labels. However, instead of ignoring the high-loss samples as done in previous works, we combine the sample selection with the reusable sample re-labeling to make full use of the unlabeled data. + +# 3. Our Method: ScarceNet + +We propose a PL-based approach to learn animal pose estimation from scarce annotations. The overall framework of our ScarceNet is illustrated in the left part of Fig. 2, where we propose a multi-branch HRNet (MBHRNet) as our animal pose estimation network. Let us denote an input image as $\mathbf{x}$ and its ground truth animal pose (if available) as $\mathbf{y}$ . Given a small set of labeled images $\mathcal{D}_l = \{\mathbf{x}_i^l,\mathbf{y}_i^l\}_{i = 1}^{N_l}$ and unlabeled images $\mathcal{D}_u = \{\mathbf{x}_i^u\}_{i = 1}^{N_u}$ , the objective is to train the animal pose estimation network by leveraging both the labeled and unlabeled data. $N_{l}$ and $N_{u}$ represent the + +number of labeled and unlabeled images, respectively, and $N_{l} \ll N_{u}$ . The labeled images are supervised with the ground truth pose data. We then generate pseudo labels with the model trained on the labeled data for the unlabeled images. However, these generated pseudo labels are usually heavily corrupted with noise, especially when the labeled data is very limited. We thus apply the small-loss trick [9] to select a set of reliable pseudo labels. Despite its effectiveness, pseudo label selection by the small-loss trick tends to discard numerous high-loss samples. This results in high wastage since those discarded samples can still provide extra information for better discrimination. In view of this, we propose a reusable sample re-labeling step to further identify reusable samples from the high-loss samples via an agreement check and re-generate the corresponding pseudo labels for supervision. Lastly, we design a student-teacher framework to enforce consistency between the outputs of the student and teacher network. + +# 3.1. Reliable Pseudo Label Selection + +We first train the animal pose estimation network on labeled images $\mathcal{D}_l$ with a supervised loss: + +$$ +\mathcal {L} _ {\mathrm {s}} = \frac {1}{J} \sum_ {i = 1} ^ {J} \| H _ {i} - \hat {H} _ {i} \| ^ {2}, \tag {1} +$$ + +where $H_{i}$ is the ground truth heatmap, $J$ denotes the total number of joints, and $\hat{H}_i$ represents the output heatmap of the network. The pretrained network is then used to generate an initial set of pseudo labels for the unlabeled images $\mathcal{D}_u$ following the procedure in [20]. The generated pseudo labels are generally noisy and can hurt the performance if directly used for training. To prevent this, we select reliable pseudo labels, denoted as $\mathbb{S}$ , from the initial pseudo labels using the small-loss trick. Specifically, we only make use of samples with loss smaller than a threshold to update the network. Formally, this can be expressed as: + +$$ +\mathcal {L} _ {\mathrm {p}} = \frac {\sum_ {i = 1} ^ {J} \left\{\mathcal {L} _ {\mathrm {p}} ^ {i} < l _ {\mathrm {r}} \right\} _ {1} \mathcal {L} _ {\mathrm {p}} ^ {i}}{\sum_ {i = 1} ^ {J} \left\{\mathcal {L} _ {\mathrm {p}} ^ {i} < l _ {\mathrm {r}} \right\} _ {1}}, \text {w h e r e} \mathcal {L} _ {\mathrm {p}} ^ {i} = \| \tilde {H} _ {i} - \hat {H} _ {i} \| ^ {2}. \tag {2} +$$ + +$\tilde{H}_i$ represents the pseudo label for the $i^{\mathrm{th}}$ joint and $\mathcal{L}_{\mathrm{p}}^{i}$ is the corresponding pseudo label based loss. $\{\mathrm{condition}\}_{1}$ is a condition function, which outputs 1 when the condition is true and 0 if false. $l_{\mathrm{r}}$ denotes the threshold loss value, and more details on how to decide $l_{\mathrm{r}}$ are provided in the supplementary material. This small-loss trick is designed based on the memorization effect of deep network, and has been shown effective in selecting reliable labels in previous works [16,26]. + +# 3.2. Reusable Sample Re-labeling + +Only small-loss samples are selected in the reliable pseudo label selection process, and the remaining pseudo + +![](images/34c2d343270af9021fe87a5fb9bbf04241d4b3a2d2449497dbb536ceeeba9286.jpg) +Figure 2. The left part shows the overall framework of our ScarceNet, where $\mathcal{P}$ and $\mathcal{T}$ represent strong and weak augmentation, respectively. The right part shows a comparison between the HRNet (top) and the MBHRNet (bottom), where 'FE' represents feature extractor, 'conv.' represents convolutional layer and 'JFE' represents joint specific feature extractor. + +![](images/abc85ddf86537fabeab0413d8503107767910189bc12a55d4026efe5ce8d12f5.jpg) + +labels with large loss are discarded. This is imprudent since the high-loss samples can also contribute to improving the network if used properly. To this end, we propose to further identify reusable samples, denoted as $\mathbb{U}$ , from the unused samples to fully exploit the unlabeled data. We define reusable samples as the ones that may also provide reliable knowledge to the network despite their large losses. To identify the reusable samples, we introduce an agreement check. Specifically, given an input $\mathbf{x}^u$ , we generate another view of this sample by adding a random transformation $\mathcal{T}$ which consists of rotation and scaling. Both samples are fed into the pose estimation network to produce the corresponding heatmaps, denoted as: + +$$ +H ^ {\mathrm {v} _ {1}} = f \left(\mathbf {x} ^ {u}\right), H ^ {\mathrm {v} _ {2}} = f \left(\mathcal {T} \mathbf {x} ^ {u}\right). \tag {3} +$$ + +The location for the $i^{th}$ joint is obtained by applying argmax operation to the corresponding output heatmap: + +$$ +\mathbf {h} _ {i} ^ {\mathrm {v} _ {1}} = \operatorname {a r g m a x} \left(H _ {i} ^ {\mathrm {v} _ {1}}\right), \mathbf {h} _ {i} ^ {\mathrm {v} _ {2}} = \operatorname {a r g m a x} \left(H _ {i} ^ {\mathrm {v} _ {2}}\right). \tag {4} +$$ + +Unlike the classification task where the output is transformation invariant [12, 32], the output joint location is transformation equivariant. Consequently, we have to transform $\mathbf{h}_i^{\mathrm{v_1}}$ before the agreement check, i.e.: + +$$ +d _ {i} = \left\| \mathcal {T} \mathbf {h} _ {i} ^ {\mathrm {v} _ {1}} - \mathbf {h} _ {i} ^ {\mathrm {v} _ {2}} \right\| ^ {2}. \tag {5} +$$ + +Subsequently, we can determine whether a sample is reusable based on the distance between the outputs of the two views. Specifically, a sample $\mathbf{x}_i^u$ is reusable when the distance fulfills $d_{i} < d_{\mathrm{r}}$ , where $d_{\mathrm{r}}$ represents the distance threshold. This agreement check is based on the agreement maximization principle [24], which has also been used for out-of-distribution detection [32] and stable sample selection [12]. Intuitively, the reusable samples must satisfy smoothness in the neighborhood of the model prediction + +and must also be far from the decision boundary. Otherwise, the output becomes inconsistent when the input is randomly transformed. + +The next step is to re-label the identified reusable samples since they exhibit large loss based on the initial pseudo labels. We directly use the prediction from the current model as the new pseudo labels to train the network. The motivation is twofold: 1) The model has been trained with unlabeled images, hence it is able to output more accurate prediction comparing to the model trained only on the labeled images. 2) The selection criteria for reusable samples indicates that the current model prediction is already reliable. Finally, the loss function for the reusable samples can be defined as: + +$$ +\mathcal {L} _ {\mathrm {r}} = \frac {\sum_ {i = 1} ^ {J} \left\{d ^ {i} < d _ {\mathrm {r}} \right\} _ {1} \mathcal {L} _ {\mathrm {r}} ^ {i}}{\sum_ {i = 1} ^ {J} \left\{d ^ {i} < d _ {\mathrm {r}} \right\} _ {1}}, \text {w h e r e} \mathcal {L} _ {\mathrm {r}} ^ {i} = \| \bar {H} _ {i} - \hat {H} _ {i} \| ^ {2}. \tag {6} +$$ + +$\bar{H}_i$ represents the heatmap generated from the joint location of current model prediction. By selecting the reusable samples, we are able to make use of more unlabeled images and prevent the network from overfitting to the initial noisy pseudo labels at the same time. + +# 3.3. Student-teacher Consistency + +Both the reliable pseudo label selection and reusable sample selection are based on specific constraints. Samples that do not fulfill either constraint are still left unused. In view of this, we further introduce a teacher network and enforce the consistency between the student and teacher network. This is inspired by the mean teacher framework [28], which enforces the consistency constraint for unlabeled data for semi-supervised classification. The teacher network shares the same structure with the student network, and the weights are updated with an exponential moving average + +(EMA) of the student model: + +$$ +\theta_ {\mathrm {m t}} ^ {t} = \alpha \theta_ {\mathrm {m t}} ^ {t - 1} + (1 - \alpha) \theta^ {t}. \tag {7} +$$ + +$\theta_{\mathrm{mt}}$ and $\theta$ denote the weights of the teacher and student network, respectively. The superscript $t$ represents the training step, and $\alpha$ is a smoothing coefficient of the EMA update. We can see that the teacher network is a temporal ensemble of networks, and thus it can provide more accurate pseudo labels. As shown in Fig. 2, we add random perturbations $\mathcal{P}$ to the input of the student network, which consists of both geometry-based perturbations $\mathcal{P}_g$ such as rotation, scaling and flipping, and image-based perturbation $\mathcal{P}_m$ such as noise, occlusion and blurring. Consistency is then enforced between the teacher and student network as: + +$$ +\mathcal {L} _ {\mathrm {t}} = \frac {1}{J} \sum_ {i = 1} ^ {J} \| \mathcal {P} _ {g} H _ {i} ^ {t} - \hat {H} _ {i} \| ^ {2}, \tag {8} +$$ + +where $H_{i}^{t}$ denotes the output of the teacher network. Note that only the geometry-based perturbation $\mathcal{P}_g$ is added to the output of the teacher network since the output joint location is invariant to the image-based perturbation. + +# 3.4. Multi-head Animal Pose Estimation Network + +We adopt the human pose estimation network HRNet as our backbone. The HRNet has achieved state-of-the-art performance for human pose estimation by combining high-resolution feature representations with multi-resolution feature fusion. However, as shown in the right top part of Fig. 2, the final heatmaps of HRNet are regressed from a shared feature representation with one linear layer. This shared mechanism can have negative effect in the presence of noisy labels. For example, the feature representation is affected by backpropagation when the pseudo label for any joint is noisy and thus further affect the prediction of other joints in the same image. To mitigate this problem, we introduce a multi-branch head to the HRNet to learn a specific feature representation for each joint. As shown in the right bottom part of Fig. 2, the network has $J$ output branches, where each branch learns a specific feature representation via a joint specific feature extractor (JFE) to regress the corresponding joint location. In this way, the adverse effect from the noisy pseudo label of a joint gets absorbed in its respective branch. + +# 3.5. Strong-weak Augmentation + +We also introduce a strong-weak augmentation training scheme, where two sets of augmentation are applied to the inputs, denoted as $\mathcal{T}$ and $\mathcal{P}$ in previous sections. Particularly, we apply strong augmentations $\mathcal{P}$ for the learning task with backpropagation and weak augmentation $\mathcal{T}$ for the re-labeling task. As shown in Fig. 2, strong augmentation $\mathcal{P}$ is applied to the labeled images in the blue path + +and unlabeled images in the orange path. These two paths are responsible for updating the network, and hence strong augmentation can improve the generalization capacity. In comparison, the weak augmentation $\mathcal{T}$ is applied to the green path because this path is responsible for identifying and re-labeling reusable samples. Overly-strong augmentation can have adversarial affects on the agreement check process since strong augmentation tends to result in inconsistent predictions. More details on the augmentation are provided in the supplementary material. + +# 3.6. Overall Framework + +We train our network in two stages. In the first stage, we train the MBHRNet on $\mathcal{D}_l$ with the supervised loss in Eqn. (1). The trained network is applied to generate pseudo labels for the unlabeled data. In the second stage, the student network is initialized with the pretrained model and trained with both $\mathcal{D}_l$ and $\mathcal{D}_u$ . The objective function for the second stage consists of both labeled and unlabeled losses as follows: + +$$ +\mathcal {L} = \lambda_ {1} \mathcal {L} _ {\mathrm {s}} + \lambda_ {2} \mathcal {L} _ {\mathrm {p}} + \lambda_ {3} \mathcal {L} _ {\mathrm {r}} + \lambda_ {4} \mathcal {L} _ {\mathrm {t}}, \tag {9} +$$ + +where $\lambda_1, \lambda_2, \lambda_3,$ and $\lambda_4$ are the weights for different losses. The overall training procedure is presented in Algorithm 1. + +Algorithm 1 Overall training procedure of the second stage +Input: labeled data $\mathcal{D}_l$ and unlabeled data $\mathcal{D}_u$ , threshold loss value $l_r$ , distance threshold $d_r$ , batch size $B$ +1: for $\{x_{1}, x_{2}, \ldots, x_{B}\} \in \mathcal{D}_{l} \cup \mathcal{D}_{u}$ do +2: if $x_{i} \in \mathcal{D}_{l}$ then +3: Compute supervised loss $\mathcal{L}_{\mathrm{s}}$ according to Eqn. (1) +4: else +5: if $x_{i} \in \mathbb{S}$ then +6: Compute the pseudo labeled based loss $\mathcal{L}_{\mathrm{p}}$ according to Eqn. (2) +7: else if $x_{i} \in \mathbb{U}$ then +8: Compute loss $\mathcal{L}_{\mathrm{r}}$ for reusable samples by Eqn. (6) +9: end if +10: Compute the consistency loss $\mathcal{L}_{\mathrm{t}}$ according to Eqn. (8) +11: end if +12: Compute the total loss $\mathcal{L}$ according to Eqn. (9) +13: Update student network $\theta \gets \theta - \eta \Delta \mathcal{L}$ +14: Update teacher network by Eqn. (7) +15: end for + +# 4. Experimental Results + +Training details. We adopt the HRNet-w32 as the backbone and train our network in two stages. We first train the MBHRNet on the labeled data with the supervised loss. Following [27], we train the network with the Adam optimizer for 210 epochs. The initial learning rate is set to $10^{-3}$ , and is dropped to $10^{-4}$ and $10^{-5}$ at the $170^{th}$ and $200^{th}$ epochs, respectively. The trained model is then used to generate pseudo labels following [20]. In the second stage, we initialized the student network from the first stage and train the whole framework with both labeled and unlabeled data for another 150 epochs. More training details are provided in the supplementary material. + +Datasets. We evaluate our method on the AP-10K dataset [33] and the TigDog dataset [20]. The AP-10K dataset is a recently proposed animal pose dataset, which contains more diverse animal species than previous datasets [5, 20]. The dataset contains 10,015 labeled images in total, which are split into train, validation, and test sets with a ratio of 7:1:2 per animal species. The TigDog dataset includes 8380 images for the horse category and 6523 images for the tiger category. This dataset is used in several domain adaptation works [16,20] to show that the knowledge learned from synthetic animals can be transferred to real animal images. We also evaluate on this dataset to show that better performance can be achieved by labeling just a few images, hence can reduce human labor compared to generating synthetic data. + +Evaluation metrics. We adopt the Mean Average Precision (mAP) as the evaluation metric for the AP-10K dataset. The Percentage of Correct Keypoints (PCK), which computes the percentage of joints that are within a normalized distance to the ground truth locations, is used for the TigDog dataset following [20]. + +
510152025
HRNet [27]0.3600.4630.5110.5470.588
UDA [30]0.4290.5190.5660.5800.628
FixMatch [25]0.4780.5440.5890.6010.631
FlexMatch [34]0.4660.5550.5960.6180.646
Ours0.5330.5970.6320.6540.681
+ +Table 1. Results (mAP) on the AP-10K when 5, 10, 15, 20 and 25 images per species are labeled. Best results in bold. + +# 4.1. Results on the AP-10K Dataset. + +We evaluate our approach under two scenarios on the AP-10K dataset. In the first scenario, a set of images are labeled for each animal species. The second scenario is that only the images in one family are labeled and we test on + +other animal families. This setting is more challenge since the appearance, size and background environment are quite different for different animal species. + +We show results for the first scenario in Tab. 1, where we evaluate when 5, 10, 15, 20 and 25 images per animal species are labeled. There are 50 species in total, which results in 250, 500, 720, 1000 and 1250 labeled images out of 7023 images. We compare with state-of-the-art semi-supervised approaches, including UDA [30], FixMatch [25] and FlexMatch [34]. 'HRNet' represents HRNet trained only with labeled images. We reimplement those semi-supervised approaches according to the open repository since they only show results for classification task. We can see that our approach outperforms existing approaches by a large margin, especially when very few labeled images are available, such as the case of 5 labels per species. The reason is that UDA, FixMatch and FlexMatch only retain the samples with reliable pseudo labels based on the confidence scores. In comparison, we combine the reliable pseudo label selection with the reusable sample re-labeling and teacher-student consistency, which helps to fully utilize the unlabeled data. Moreover, our results are the closest to the fully supervised setting [33], i.e. $0.738\mathrm{mAP}$ , when only 25 images per animal species are labeled. We also show qualitative results for the 25 labels per animal species setting in Fig. 3. + +We also show results for the case when images from only one animal family are labeled in Tab. 2. Following the inter-family transfer learning setting in [33], we train our model with labeled images of the Bovidae family and the remaining unlabeled images, and test on families including Cervidae, Equidae and Hominidae. There are seven animal species in the Bovidae family that includes a total of 755 images. The results under the 'Generalization', 'Few-Shot' and 'Transfer' settings are taken from [33]. 'Generalization' means that the model is trained only with images in the Bovidae, 'Few-Shot' means that 20 labels from the testing species are used, and 'Transfer' means that all labels of the testing species are used. We can see that we achieve better performance than the generalization setting in all cases except for 'Moose'. Moreover, we even outperform the 'Transfer' setting for 'Deer' and 'Horse' although we do not use any labels from the target species. Our results for the 'Chimpanzee' and 'Gorilla' are not satisfactory although still comparable to the 'Few-Shot' setting. We show the failure cases of 'Chimpanzee' and 'Gorilla' in the last two examples of Fig. 3. We can see that 'Chimpanzee' and 'Gorilla' are very different from animal species in the Bovidae family (the first four examples of the last row) in terms of appearance and pose, which makes the knowledge transfer hard without using any labels from the target species. + +
SpeciesSettingPerformanceSpeciesSettingPerformance
DeerGeneralization0.723MooseGeneralization0.587
Few-Shot0.742Few-Shot0.648
Transfer0.751Transfer0.726
Ours0.767Ours0.547
HorseGeneralization0.592ZebraGeneralization0.324
Few-Shot0.635Few-Shot0.480
Transfer0.718Transfer0.708
Ours0.749Ours0.562
ChimpanzeeGeneralization0.009GorillaGeneralization0.017
Few-Shot0.022Few-Shot0.144
Transfer0.550Transfer0.662
Ours0.057Ours0.033
+ +Table 2. Results (mAP) for the Cervidae, Equidae and Hominidae when only images from the Bovidae are labeled. + +
RealCycgan [36]BDL [17]Cycada [10]CC-SSL [20]MDAM-MT [16]Ours
Horse78.9851.8662.3355.5770.7779.5073.05
Tiger81.9946.4752.2651.4864.1467.7674.88
Average80.4849.1757.3053.5367.5273.6673.83
+ +Table 3. PCK@0.05 accuracy of the TigDog dataset. 'Real' means full supervision. Cycgan, BDL, Cycada, CC-SSL, MDAM-MT are domain adaptation approaches using synthetic data. Our approach is trained with only 36 labeled images per category. + +
Horse AccuracyTiger AccuracyAverage
EyeChinShoulderHipElbowKneeHoovesMeanEyeChinShoulderHipElbowKneeHoovesMean
CC-SSL84.6090.2669.6985.8968.5868.7361.3370.7796.7590.4644.8477.6155.8242.8564.5564.14
MDAM-MT91.0593.3777.3580.6773.6381.8373.6779.5097.0191.1846.6378.0850.8661.5470.8467.76
Ours89.4293.6074.6383.6174.3179.9173.9979.1899.1392.8246.9675.3650.4663.5174.8268.98
+ +Table 4. PCK@0.05 accuracy of the TigDog dataset for domain adaptation setting. 'Mean' represents the accuracy for each animal category, and 'Average' represents the average accuracy for all animal categories. Best results in bold. + +
510152025
Full0.5330.5970.6320.6550.681
- RSR0.5210.5860.6210.6330.668
- MT0.4870.5680.6140.6280.659
- MB0.5200.5850.6240.6450.670
- AUG0.4870.5650.6080.6250.654
+ +Table 5. Ablation study on the AP-10K dataset when 5, 10, 15, 20 and 25 images per animal species are labeled. + +# 4.2. Results on the TigDog Dataset + +The TigDog Dataset is used in previous domain adaptation works [16, 20] to show that models trained from synthetic images can be used for real ones. We also evaluate on this dataset to show that our approach can achieve comparable or even better performance compared with state-of-the-art domain adaptation works with very few labeled images. Note that we use the same ResNet backbone as [20] for all experiments on the TigDog dataset for fair comparison. The results are shown in Tab. 3, where the numbers are + +directly taken from [16]. 'Real' denotes fully-supervised setting, Cycgan [36], BDL [17], Cycada [10], CC-SSL [20], MDAM-MT [16] are domain adaptation approaches trained with synthetic animal images and "Ours" means our approach trained with 36 images per animal category. Note that 36 is the minimum labeled data needed for each category to achieve better performance than existing unsupervised domain adaptation approaches, i.e. we only need to label 72 out of 14,903 images for the Tigdog dataset. The results demonstrate the advantage of our setting since annotating such few images does not take much human labor. + +We also test our approach on the domain adaptation setting to further verify the effectiveness. The results are shown in Tab. 4, which includes accuracy for different joints, the mean accuracy for each animal category and the average accuracy over all categories. We can see that our approach achieves the best performance in most of the cases. Note that our approach and CC-SSL have simpler networks compared to MDAM-MT, which introduce an extra refinement module for self-knowledge distillation. More training details are provided in the supplementary material. + +![](images/a7468c9d45bc1af29643c4aa44f2079ea0ccc6a71ea54e64a68ac9877fb50c81.jpg) +Figure 3. Qualitative results for the AP-10K dataset when 25 images per species is labeled (except for the last two examples). The last two examples show the failure cases when only images from the Bovidae family are labeled. + +# 4.3. Ablation Study + +We conduct ablation study on the AP-10K dataset. Each component is removed from the full model to verify the corresponding contribution. The results are shown in Tab. 5, where 'RSR' denotes reusable sample re-labeling, 'MT' denotes student teacher consistency, 'MB' denotes multibranch architecture and 'AUG' denotes strong-weak augmentation. Note that we remove the weak augmentation $\mathcal{T}$ and replace the strong augmentation $\mathcal{P}$ with commonly used rotation and scale augmentation for the ablation of 'AUG'. We can see that the performance drops when each component is removed. Specially, the accuracy drops significantly for the 5 labels per animal species setting when the student teacher consistency or strong-weak augmentation is removed. This can be attributed to two reasons. Firstly, the strong-weak augmentation enforces the output of the strong augmented images to be consistent with the pseudo labels that are generated using weak augmented images. In this way, the network is enforced to learn a smooth representation around each image, which helps to improve the performance especially in the low-data regime. Secondly, The initial set of pseudo labels are extremely noisy when the model is trained with very few labeled data. The teacher network, which is a temporal ensemble of network, is able to provide more stable supervision for the student network. + +# 5. Limitations + +Our approach achieves impressive performance even when very few labeled data is available. However, there are still many remaining challenges for the task of animal pose estimation for limited labeled data. The large variations of appearance and pose across different animal species makes it hard for the network to generalize well to different animal species, e.g. train with labels from Bovidae and test on Hominidae. We leave this for future research. + +# 6. Conclusion + +We propose a pseudo label based training scheme for animal pose estimation from scarce annotations. We combine the reliable pseudo label selection with the reusable sample re-labeling and the student-teacher consistency to make full use of the unlabeled data. We also introduce the MBHRNet to mitigate the negative effect of noisy joints. Extensive experiments have been conducted to verify the effectiveness of our proposed approach. + +Acknowledgement. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-024), and the Tier 2 grant MOE-T2EP20120-0011 from the Singapore Ministry of Education. + +# References + +[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. In Proceedings of the IEEE Conference on computer Vision and Pattern Recognition, pages 3686-3693, 2014. 2 +[2] Devansh Arpit, Stanisław Jastrzebski, Nicolas Ballas, David Krueger, Emmanuel Bengio, Maxinder S Kanwal, Tegan Maharaj, Asja Fischer, Aaron Courville, Yoshua Bengio, et al. A closer look at memorization in deep networks. In International conference on machine learning, pages 233-242. PMLR, 2017. 2 +[3] David Berthelot, Nicholas Carlini, Ian Goodfellow, Nicolas Papernot, Avital Oliver, and Colin A Raffel. Mixmatch: A holistic approach to semi-supervised learning. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5359-5368, 2019. 2 \ No newline at end of file diff --git a/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/images.zip b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1bcf1e8bdbe7dd5644c1168704d4f33df3c087d0 --- /dev/null +++ b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:389f1af012880e641a8fd7e44db4bdf3318e966f2198e742ce6e16716867a31e +size 578464 diff --git a/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/layout.json b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d1348e8635ea48b6f83433d7b734e5ac581d044b --- /dev/null +++ b/2023/ScarceNet_ Animal Pose Estimation With Scarce Annotations/layout.json @@ -0,0 +1,6939 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 109, + 103, + 485, + 119 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 103, + 485, + 119 + ], + "spans": [ + { + "bbox": [ + 109, + 103, + 485, + 119 + ], + "type": "text", + "content": "ScarceNet: Animal Pose Estimation with Scarce Annotations" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 229, + 144, + 363, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 229, + 144, + 363, + 156 + ], + "spans": [ + { + "bbox": [ + 229, + 144, + 363, + 156 + ], + "type": "text", + "content": "Chen Li Gim Hee Lee" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 133, + 158, + 460, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 133, + 158, + 460, + 172 + ], + "spans": [ + { + "bbox": [ + 133, + 158, + 460, + 172 + ], + "type": "text", + "content": "Department of Computer Science, National University of Singapore" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 169, + 174, + 422, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 169, + 174, + 422, + 185 + ], + "spans": [ + { + "bbox": [ + 169, + 174, + 422, + 185 + ], + "type": "text", + "content": "lichen@u.nus.edu gimhee.lee@comp.nus.edu.sg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 239, + 290, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 290, + 610 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 290, + 610 + ], + "type": "text", + "content": "Animal pose estimation is an important but under-explored task due to the lack of labeled data. In this paper, we tackle the task of animal pose estimation with scarce annotations, where only a small set of labeled data and unlabeled images are available. At the core of the solution to this problem setting is the use of the unlabeled data to compensate for the lack of well-labeled animal pose data. To this end, we propose the ScarceNet, a pseudo label-based approach to generate artificial labels for the unlabeled images. The pseudo labels, which are generated with a model trained with the small set of labeled images, are generally noisy and can hurt the performance when directly used for training. To solve this problem, we first use a small-loss trick to select reliable pseudo labels. Although effective, the selection process is imprudent since numerous high-loss samples are left unused. We further propose to identify reusable samples from the high-loss samples based on an agreement check. Pseudo labels are re-generated to provide supervision for those reusable samples. Lastly, we introduce a student-teacher framework to enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can make full use of the unlabeled data. We evaluate our approach on the challenging AP-10K dataset, where our approach outperforms existing semi-supervised approaches by a large margin. We also test on the TigDog dataset, where our approach can achieve better performance than domain adaptation based approaches when only very few annotations are available. Our code is available at the project website1." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 635, + 128, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 128, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 128, + 647 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 655, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 287, + 693 + ], + "type": "text", + "content": "The ability to understand animal behavior is fundamental to many applications, such as farming, ecology and surveillance. 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An illustration of our task. We aim to achieve accurate animal pose estimation with a small set of labeled images as well as unlabeled images." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 378, + 546, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 546, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 546, + 653 + ], + "type": "text", + "content": "understand animal behavior and has attracted increasing attention in recent years [5, 16, 20, 23, 33]. Although great success is achieved for human pose estimation with the development of sophisticated deep learning models, these techniques cannot be directly used for animals due to the lack of labeled animal pose data. Existing works overcome this problem by learning from human pose data [5] or synthetic animal images [16, 20, 23]. However, there is a large domain gap between the real and synthetic (human) data. For example, the synthetic animal images in [20], which are generated from CAD models, only exhibit limited pose, appearance and background variations. As a result, the model trained with the synthetic data may not adapt well to real images, especially for images with crowded scene or self-occlusion. Moreover, the generation of synthetic images is a tedious process that also requires expert knowledge. The above-mentioned problems lead us to ask whether we can achieve accurate animal pose estimation with minimal effort for annotating? To answer this question, we focus on how to learn from scarce labeled data for animal pose estimation. As shown in Fig. 1, we aim to achieve accurate animal pose estimation with only a small set of labeled images and unlabeled images." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "The data scarcity problem is solved by semi-supervised learning (SSL) for the classification task [3,25,28,34]. One powerful class of SSL is pseudo labeling (PL), where artificial labels generated from a pretrained model are used together with labeled data to train a model. Impressive" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 251, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 251, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 251, + 712 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17174" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "results have been achieved by applying PL [5, 16, 20] to domain adaptation based animal pose estimation. However, the PL-based methods suffer from confirmation bias when the network starts to output incorrect predictions with high confidence, which we refer as noisy pseudo labels. To solve this noisy pseudo label problem, we use the small-loss trick [9, 16] to select reliable pseudo labels, i.e. samples with small loss to update the network. This criteria is based on the memorization effect [2] of deep networks where the network learns from clean and easy instances first before eventually overfitting to noisy ones. Consequently, clean samples exhibit smaller loss compared to noisy ones at the beginning of training. Although the small-loss trick is effective in selecting reliable pseudo labels, it is wasteful because numerous high-loss samples are left unused." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 255, + 289, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 289, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 289, + 506 + ], + "type": "text", + "content": "In this paper, we propose the ScarceNet, a PL-based approach to learn an animal pose network from scarce annotations. We first train an animal pose estimation network on the small set of labeled data, and then generate pseudo labels for the unlabeled images with the pretrained model. The pseudo labels are often corrupted with noise due to the small size of the training data. We thus also select reliable pseudo labels using the small-loss trick. However, instead of ignoring or adding consistency regularization to the high-loss samples as done in previous works [16, 20], we propose to identify reusable samples from those high-loss samples based on an agreement check. The agreement check is to guarantee that the model predictions for the reusable samples are smooth and concurrently far from the decision boundary, and hence allow us to directly re-label reusable samples with the model predictions. Finally, we introduce a student-teacher network [28] and enforce a consistency constraint since there are still samples that are neither reliable nor reusable. By combining the reliable pseudo label selection with the reusable sample re-labeling and the consistency constraint, we can fully exploit the unlabeled data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 508, + 289, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 289, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 289, + 639 + ], + "type": "text", + "content": "In addition to the training scheme, we also modify the state-of-the-art human pose estimation network HRNet [27] and adapt it to the pseudo label-based learning framework. The original HRNet regresses the heatmaps of different joints from a shared feature representation. However, the negative effect of noisy pseudo label for any joint is propagated to all other joints through this shared feature representation. To mitigate this problem, we introduce a multibranch HRNet (MBHRNet) where a joint-specific feature representation is learned for regressing the corresponding joint location in each branch." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 289, + 715 + ], + "type": "text", + "content": "We validate our approach on the challenging AP-10K dataset [33], which includes animal images from more than 50 species. Our approach outperforms existing SSL methods by a large margin, especially when the labeled data is very limited (for example, 5 labeled images per species). We also test our approach under the inter-family transfer" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "content": "setting, where animal species from only one family are labeled and the rest are unlabeled. Our approach improves the HRNet baseline significantly, and even outperform the supervised counterpart for some species. We further test on the TigDog dataset [20], where we can outperform existing synthetic data based approaches when only " + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 167 + ], + "type": "text", + "content": " of the dataset is labeled. Our contribution can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 175, + 545, + 262 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 317, + 175, + 545, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 175, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 317, + 175, + 545, + 199 + ], + "type": "text", + "content": "- We propose a pseudo label based training scheme for the task of animal pose estimation from scarce labels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 317, + 206, + 545, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 206, + 545, + 231 + ], + "spans": [ + { + "bbox": [ + 317, + 206, + 545, + 231 + ], + "type": "text", + "content": "- We introduce the MBHRNet to mitigate negative effect of noisy joints to other joints in the same image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 238, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 238, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 317, + 238, + 545, + 262 + ], + "type": "text", + "content": "- We achieve state-of-the-art performance on several animal pose benchmarks under different settings." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 272, + 392, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 272, + 392, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 272, + 392, + 285 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 292, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 547, + 640 + ], + "type": "text", + "content": "Animal Pose Estimation. Animal pose estimation, including both 2D [5, 16, 20] and 3D [4, 15, 37], has become an active research field in the last few years. The development of animal pose estimation techniques is relatively slower than the human counterpart due to the lack of large scale animal pose dataset like COCO [18] or MPII [1]. Existing works circumvent the requirement for animal pose data by transferring knowledge from other domains, such as human pose data [5] and synthetic animal data [16, 20, 23]. Although impressive results have been achieved in [5], substantial amounts of labeled animal images are still needed to facilitate the knowledge transfer. This is due to the large domain gap between human and animal images, including pose, appearance and body structure differences. To reduce the domain gap between the source and target domains, synthetic animal images are generated from CAD models and used as the source images in [20]. Three consistency criteria are proposed to generate pseudo labels for real images. Improved upon [20], Li et al. [16] propose a pseudo label updating strategy to prevent the network from overfitting to the noisy pseudo labels. Despite the domain gap is reduced by using synthetic animal images, the limited pose and appearance variations of the CAD models prohibit the synthetic data based approaches from adapting to real scenarios with crowded scene or self-occlusion. Moreover, synthesize realistic images is a tedious process, which also requires expert knowledge. In view of this, we focus on learning from scarce annotations to minimize human labor and achieve accurate animal pose estimation at the same time." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 547, + 715 + ], + "type": "text", + "content": "Semi-supervised Learning. Semi-supervised learning is powerful in leveraging unlabeled data to improve a model's performance when labeled data is limited. One of the most widely used SSL techniques is pseudo labeling [14, 31], which generates artificial labels for unlabeled images from" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17175" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 252 + ], + "type": "text", + "content": "model predictions. Another technique is consistency regularization [13, 22, 28], which enforces that the model output should be consistent when the input is randomly perturbed. MixMatch [3] combines the consistency regularization with the entropy minimization to encourage the network to output confident predictions for unlabeled data. More recent Unsupervised Data Augmentation (UDA) [30] and FixMatch [25] combine pseudo labeling, consistency regularization with strong augmentations [6] and achieve superior performance. FlexMatch [34] further improves over UDA and Fixmatch by introducing a curriculum learning scheme. We also adopt the PL-based techniques in this work given its effectiveness. To mitigate the negative effect of noisy pseudo labels, we combine PL with reliable pseudo label selection and reusable sample re-labeling." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 271, + 289, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 289, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 289, + 559 + ], + "type": "text", + "content": "Learning from Noisy Labels. Learning from noisy labels has become an important task since deep neural networks are known to be susceptible to noisy labels. To reduce the negative effect of noisy labels, different approaches which can be divided into three categories have been proposed. The first category is to treat the true labels as hidden variables and use an extra network to estimate a noise transition matrix [8, 21]. These methods assume there is correlation between the corrupted and clean labels, hence cannot handle complicate cases with random noise. The second category is to design noise-robust loss functions [7], such as the generalized cross entropy [35] and the symmetric cross entropy [29]. The robust-loss based approaches are theoretically sound, but may only be capable of handling a certain noise rate. The last category [9, 11, 19] focuses on selecting potential clean samples to update the network. One promising selection criteria is the small-loss trick [9], which is designed based on the memorization effect of deep networks and has been widely applied to different tasks [16, 26, 32]. We also apply the small-loss trick to select reliable pseudo labels. However, instead of ignoring the high-loss samples as done in previous works, we combine the sample selection with the reusable sample re-labeling to make full use of the unlabeled data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 571, + 187, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 187, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 187, + 585 + ], + "type": "text", + "content": "3. Our Method: ScarceNet" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": "We propose a PL-based approach to learn animal pose estimation from scarce annotations. The overall framework of our ScarceNet is illustrated in the left part of Fig. 2, where we propose a multi-branch HRNet (MBHRNet) as our animal pose estimation network. Let us denote an input image as " + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": " and its ground truth animal pose (if available) as " + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": ". Given a small set of labeled images " + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_l = \\{\\mathbf{x}_i^l,\\mathbf{y}_i^l\\}_{i = 1}^{N_l}" + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": " and unlabeled images " + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_u = \\{\\mathbf{x}_i^u\\}_{i = 1}^{N_u}" + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": ", the objective is to train the animal pose estimation network by leveraging both the labeled and unlabeled data. " + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 46, + 593, + 289, + 715 + ], + "type": "text", + "content": " represent the" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 288 + ], + "type": "text", + "content": "number of labeled and unlabeled images, respectively, and " + }, + { + "bbox": [ + 304, + 72, + 547, + 288 + ], + "type": "inline_equation", + "content": "N_{l} \\ll N_{u}" + }, + { + "bbox": [ + 304, + 72, + 547, + 288 + ], + "type": "text", + "content": ". The labeled images are supervised with the ground truth pose data. We then generate pseudo labels with the model trained on the labeled data for the unlabeled images. However, these generated pseudo labels are usually heavily corrupted with noise, especially when the labeled data is very limited. We thus apply the small-loss trick [9] to select a set of reliable pseudo labels. Despite its effectiveness, pseudo label selection by the small-loss trick tends to discard numerous high-loss samples. This results in high wastage since those discarded samples can still provide extra information for better discrimination. In view of this, we propose a reusable sample re-labeling step to further identify reusable samples from the high-loss samples via an agreement check and re-generate the corresponding pseudo labels for supervision. Lastly, we design a student-teacher framework to enforce consistency between the outputs of the student and teacher network." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 293, + 479, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 479, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 479, + 306 + ], + "type": "text", + "content": "3.1. Reliable Pseudo Label Selection" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 312, + 546, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 546, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 546, + 335 + ], + "type": "text", + "content": "We first train the animal pose estimation network on labeled images " + }, + { + "bbox": [ + 304, + 312, + 546, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_l" + }, + { + "bbox": [ + 304, + 312, + 546, + 335 + ], + "type": "text", + "content": " with a supervised loss:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 372, + 342, + 546, + 374 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 342, + 546, + 374 + ], + "spans": [ + { + "bbox": [ + 372, + 342, + 546, + 374 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s}} = \\frac {1}{J} \\sum_ {i = 1} ^ {J} \\| H _ {i} - \\hat {H} _ {i} \\| ^ {2}, \\tag {1}", + "image_path": "ae61915ce1913d0c7f862ad2818e28ac4c0c87564d735193569d71a7c67e7d1e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "inline_equation", + "content": "H_{i}" + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "content": " is the ground truth heatmap, " + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "content": " denotes the total number of joints, and " + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "inline_equation", + "content": "\\hat{H}_i" + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "content": " represents the output heatmap of the network. The pretrained network is then used to generate an initial set of pseudo labels for the unlabeled images " + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_u" + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "content": " following the procedure in [20]. The generated pseudo labels are generally noisy and can hurt the performance if directly used for training. To prevent this, we select reliable pseudo labels, denoted as " + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "inline_equation", + "content": "\\mathbb{S}" + }, + { + "bbox": [ + 304, + 380, + 547, + 513 + ], + "type": "text", + "content": ", from the initial pseudo labels using the small-loss trick. Specifically, we only make use of samples with loss smaller than a threshold to update the network. Formally, this can be expressed as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 310, + 517, + 546, + 552 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 517, + 546, + 552 + ], + "spans": [ + { + "bbox": [ + 310, + 517, + 546, + 552 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {p}} = \\frac {\\sum_ {i = 1} ^ {J} \\left\\{\\mathcal {L} _ {\\mathrm {p}} ^ {i} < l _ {\\mathrm {r}} \\right\\} _ {1} \\mathcal {L} _ {\\mathrm {p}} ^ {i}}{\\sum_ {i = 1} ^ {J} \\left\\{\\mathcal {L} _ {\\mathrm {p}} ^ {i} < l _ {\\mathrm {r}} \\right\\} _ {1}}, \\text {w h e r e} \\mathcal {L} _ {\\mathrm {p}} ^ {i} = \\| \\tilde {H} _ {i} - \\hat {H} _ {i} \\| ^ {2}. \\tag {2}", + "image_path": "7fa788169d920ad22901dc5ef2c7aadb364d98a98048879f8334334eb0fc9e38.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\tilde{H}_i" + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "content": " represents the pseudo label for the " + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "content": " joint and " + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{p}}^{i}" + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "content": " is the corresponding pseudo label based loss. " + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{condition}\\}_{1}" + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "content": " is a condition function, which outputs 1 when the condition is true and 0 if false. " + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "content": " denotes the threshold loss value, and more details on how to decide " + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "inline_equation", + "content": "l_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 665 + ], + "type": "text", + "content": " are provided in the supplementary material. This small-loss trick is designed based on the memorization effect of deep network, and has been shown effective in selecting reliable labels in previous works [16,26]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 671, + 466, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 466, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 466, + 685 + ], + "type": "text", + "content": "3.2. Reusable Sample Re-labeling" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "Only small-loss samples are selected in the reliable pseudo label selection process, and the remaining pseudo" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "17176" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 71, + 339, + 223 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 339, + 223 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 339, + 223 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 339, + 223 + ], + "type": "image", + "image_path": "34c2d343270af9021fe87a5fb9bbf04241d4b3a2d2449497dbb536ceeeba9286.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "type": "text", + "content": "Figure 2. The left part shows the overall framework of our ScarceNet, where " + }, + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 235, + 546, + 269 + ], + "type": "text", + "content": " represent strong and weak augmentation, respectively. The right part shows a comparison between the HRNet (top) and the MBHRNet (bottom), where 'FE' represents feature extractor, 'conv.' represents convolutional layer and 'JFE' represents joint specific feature extractor." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 347, + 82, + 547, + 222 + ], + "blocks": [ + { + "bbox": [ + 347, + 82, + 547, + 222 + ], + "lines": [ + { + "bbox": [ + 347, + 82, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 347, + 82, + 547, + 222 + ], + "type": "image", + "image_path": "abc85ddf86537fabeab0413d8503107767910189bc12a55d4026efe5ce8d12f5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "text", + "content": "labels with large loss are discarded. This is imprudent since the high-loss samples can also contribute to improving the network if used properly. To this end, we propose to further identify reusable samples, denoted as " + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\mathbb{U}" + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "text", + "content": ", from the unused samples to fully exploit the unlabeled data. We define reusable samples as the ones that may also provide reliable knowledge to the network despite their large losses. To identify the reusable samples, we introduce an agreement check. Specifically, given an input " + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\mathbf{x}^u" + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "text", + "content": ", we generate another view of this sample by adding a random transformation " + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 289, + 289, + 445 + ], + "type": "text", + "content": " which consists of rotation and scaling. Both samples are fed into the pose estimation network to produce the corresponding heatmaps, denoted as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 453, + 287, + 466 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 453, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 104, + 453, + 287, + 466 + ], + "type": "interline_equation", + "content": "H ^ {\\mathrm {v} _ {1}} = f \\left(\\mathbf {x} ^ {u}\\right), H ^ {\\mathrm {v} _ {2}} = f \\left(\\mathcal {T} \\mathbf {x} ^ {u}\\right). \\tag {3}", + "image_path": "d51727c04a728122dfba286830b35f741851f0178d8270e5f854d1a998de65d4.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 474, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 474, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 47, + 474, + 287, + 499 + ], + "type": "text", + "content": "The location for the " + }, + { + "bbox": [ + 47, + 474, + 287, + 499 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 47, + 474, + 287, + 499 + ], + "type": "text", + "content": " joint is obtained by applying argmax operation to the corresponding output heatmap:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 77, + 506, + 287, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 506, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 77, + 506, + 287, + 521 + ], + "type": "interline_equation", + "content": "\\mathbf {h} _ {i} ^ {\\mathrm {v} _ {1}} = \\operatorname {a r g m a x} \\left(H _ {i} ^ {\\mathrm {v} _ {1}}\\right), \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {2}} = \\operatorname {a r g m a x} \\left(H _ {i} ^ {\\mathrm {v} _ {2}}\\right). \\tag {4}", + "image_path": "c885b71a74a744349b95ea5d2d90d47bf3b1eb7b0f8b97e0beb31100e05552f0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 528, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 528, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 47, + 528, + 287, + 576 + ], + "type": "text", + "content": "Unlike the classification task where the output is transformation invariant [12, 32], the output joint location is transformation equivariant. Consequently, we have to transform " + }, + { + "bbox": [ + 47, + 528, + 287, + 576 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i^{\\mathrm{v_1}}" + }, + { + "bbox": [ + 47, + 528, + 287, + 576 + ], + "type": "text", + "content": " before the agreement check, i.e.:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 122, + 584, + 287, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 584, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 122, + 584, + 287, + 598 + ], + "type": "interline_equation", + "content": "d _ {i} = \\left\\| \\mathcal {T} \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {1}} - \\mathbf {h} _ {i} ^ {\\mathrm {v} _ {2}} \\right\\| ^ {2}. \\tag {5}", + "image_path": "338bba2fe7df89bbf6884bf05211dff5ff39f97a50e9ecb7b07eadc8da4d30c0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Subsequently, we can determine whether a sample is reusable based on the distance between the outputs of the two views. Specifically, a sample " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i^u" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " is reusable when the distance fulfills " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "d_{i} < d_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": " represents the distance threshold. This agreement check is based on the agreement maximization principle [24], which has also been used for out-of-distribution detection [32] and stable sample selection [12]. Intuitively, the reusable samples must satisfy smoothness in the neighborhood of the model prediction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 289, + 546, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 546, + 323 + ], + "type": "text", + "content": "and must also be far from the decision boundary. Otherwise, the output becomes inconsistent when the input is randomly transformed." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 325, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 546, + 456 + ], + "type": "text", + "content": "The next step is to re-label the identified reusable samples since they exhibit large loss based on the initial pseudo labels. We directly use the prediction from the current model as the new pseudo labels to train the network. The motivation is twofold: 1) The model has been trained with unlabeled images, hence it is able to output more accurate prediction comparing to the model trained only on the labeled images. 2) The selection criteria for reusable samples indicates that the current model prediction is already reliable. Finally, the loss function for the reusable samples can be defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 311, + 464, + 545, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 464, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 311, + 464, + 545, + 497 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r}} = \\frac {\\sum_ {i = 1} ^ {J} \\left\\{d ^ {i} < d _ {\\mathrm {r}} \\right\\} _ {1} \\mathcal {L} _ {\\mathrm {r}} ^ {i}}{\\sum_ {i = 1} ^ {J} \\left\\{d ^ {i} < d _ {\\mathrm {r}} \\right\\} _ {1}}, \\text {w h e r e} \\mathcal {L} _ {\\mathrm {r}} ^ {i} = \\| \\bar {H} _ {i} - \\hat {H} _ {i} \\| ^ {2}. \\tag {6}", + "image_path": "4361d761333213a0fdc073c13e78ddf52be6ec9f441b06764aa5145947241aa3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "inline_equation", + "content": "\\bar{H}_i" + }, + { + "bbox": [ + 304, + 506, + 545, + 567 + ], + "type": "text", + "content": " represents the heatmap generated from the joint location of current model prediction. By selecting the reusable samples, we are able to make use of more unlabeled images and prevent the network from overfitting to the initial noisy pseudo labels at the same time." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 574, + 463, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 463, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 463, + 588 + ], + "type": "text", + "content": "3.3. Student-teacher Consistency" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Both the reliable pseudo label selection and reusable sample selection are based on specific constraints. Samples that do not fulfill either constraint are still left unused. In view of this, we further introduce a teacher network and enforce the consistency between the student and teacher network. This is inspired by the mean teacher framework [28], which enforces the consistency constraint for unlabeled data for semi-supervised classification. The teacher network shares the same structure with the student network, and the weights are updated with an exponential moving average" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17177" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 167, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 167, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 167, + 83 + ], + "type": "text", + "content": "(EMA) of the student model:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 111, + 91, + 287, + 106 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 91, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 111, + 91, + 287, + 106 + ], + "type": "interline_equation", + "content": "\\theta_ {\\mathrm {m t}} ^ {t} = \\alpha \\theta_ {\\mathrm {m t}} ^ {t - 1} + (1 - \\alpha) \\theta^ {t}. \\tag {7}", + "image_path": "9004a66aefdedf5708cda7072261e171f1753abf79941636beff846598e58da2.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\theta_{\\mathrm{mt}}" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " denote the weights of the teacher and student network, respectively. The superscript " + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " represents the training step, and " + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " is a smoothing coefficient of the EMA update. We can see that the teacher network is a temporal ensemble of networks, and thus it can provide more accurate pseudo labels. As shown in Fig. 2, we add random perturbations " + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " to the input of the student network, which consists of both geometry-based perturbations " + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_g" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " such as rotation, scaling and flipping, and image-based perturbation " + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_m" + }, + { + "bbox": [ + 46, + 114, + 289, + 245 + ], + "type": "text", + "content": " such as noise, occlusion and blurring. Consistency is then enforced between the teacher and student network as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 251, + 287, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 251, + 287, + 283 + ], + "spans": [ + { + "bbox": [ + 107, + 251, + 287, + 283 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {t}} = \\frac {1}{J} \\sum_ {i = 1} ^ {J} \\| \\mathcal {P} _ {g} H _ {i} ^ {t} - \\hat {H} _ {i} \\| ^ {2}, \\tag {8}", + "image_path": "33c8df0bdef95720ef81c8c13fc82dd7493e4744b1597bf600ee86bf770e7ed5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "type": "inline_equation", + "content": "H_{i}^{t}" + }, + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "type": "text", + "content": " denotes the output of the teacher network. Note that only the geometry-based perturbation " + }, + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_g" + }, + { + "bbox": [ + 46, + 291, + 287, + 340 + ], + "type": "text", + "content": " is added to the output of the teacher network since the output joint location is invariant to the image-based perturbation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 282, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 282, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 282, + 358 + ], + "type": "text", + "content": "3.4. Multi-head Animal Pose Estimation Network" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 365, + 289, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 289, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 289, + 605 + ], + "type": "text", + "content": "We adopt the human pose estimation network HRNet as our backbone. The HRNet has achieved state-of-the-art performance for human pose estimation by combining high-resolution feature representations with multi-resolution feature fusion. However, as shown in the right top part of Fig. 2, the final heatmaps of HRNet are regressed from a shared feature representation with one linear layer. This shared mechanism can have negative effect in the presence of noisy labels. For example, the feature representation is affected by backpropagation when the pseudo label for any joint is noisy and thus further affect the prediction of other joints in the same image. To mitigate this problem, we introduce a multi-branch head to the HRNet to learn a specific feature representation for each joint. As shown in the right bottom part of Fig. 2, the network has " + }, + { + "bbox": [ + 46, + 365, + 289, + 605 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 365, + 289, + 605 + ], + "type": "text", + "content": " output branches, where each branch learns a specific feature representation via a joint specific feature extractor (JFE) to regress the corresponding joint location. In this way, the adverse effect from the noisy pseudo label of a joint gets absorbed in its respective branch." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 611, + 200, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 200, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 200, + 624 + ], + "type": "text", + "content": "3.5. Strong-weak Augmentation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "We also introduce a strong-weak augmentation training scheme, where two sets of augmentation are applied to the inputs, denoted as " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " in previous sections. Particularly, we apply strong augmentations " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " for the learning task with backpropagation and weak augmentation " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " for the re-labeling task. As shown in Fig. 2, strong augmentation " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " is applied to the labeled images in the blue path" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "and unlabeled images in the orange path. These two paths are responsible for updating the network, and hence strong augmentation can improve the generalization capacity. In comparison, the weak augmentation " + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": " is applied to the green path because this path is responsible for identifying and re-labeling reusable samples. Overly-strong augmentation can have adversarial affects on the agreement check process since strong augmentation tends to result in inconsistent predictions. More details on the augmentation are provided in the supplementary material." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 209, + 422, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 209, + 422, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 422, + 220 + ], + "type": "text", + "content": "3.6. Overall Framework" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "text", + "content": "We train our network in two stages. In the first stage, we train the MBHRNet on " + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_l" + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "text", + "content": " with the supervised loss in Eqn. (1). The trained network is applied to generate pseudo labels for the unlabeled data. In the second stage, the student network is initialized with the pretrained model and trained with both " + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_l" + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_u" + }, + { + "bbox": [ + 304, + 230, + 545, + 324 + ], + "type": "text", + "content": ". The objective function for the second stage consists of both labeled and unlabeled losses as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 353, + 342, + 545, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 342, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 353, + 342, + 545, + 355 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {1} \\mathcal {L} _ {\\mathrm {s}} + \\lambda_ {2} \\mathcal {L} _ {\\mathrm {p}} + \\lambda_ {3} \\mathcal {L} _ {\\mathrm {r}} + \\lambda_ {4} \\mathcal {L} _ {\\mathrm {t}}, \\tag {9}", + "image_path": "d2c4c6ad65a34b71710a650cfb20a6bbc63efebf46e04bf9fd2c1f66f0682554.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2, \\lambda_3," + }, + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\lambda_4" + }, + { + "bbox": [ + 305, + 369, + 545, + 395 + ], + "type": "text", + "content": " are the weights for different losses. The overall training procedure is presented in Algorithm 1." + } + ] + } + ], + "index": 13 + }, + { + "type": "code", + "bbox": [ + 306, + 472, + 545, + 689 + ], + "blocks": [ + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "lines": [ + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "text", + "content": "Algorithm 1 Overall training procedure of the second stage \nInput: labeled data " + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_l" + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "text", + "content": " and unlabeled data " + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_u" + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "text", + "content": ", threshold loss value " + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "inline_equation", + "content": "l_r" + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "text", + "content": ", distance threshold " + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "inline_equation", + "content": "d_r" + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "text", + "content": ", batch size " + }, + { + "bbox": [ + 306, + 421, + 545, + 470 + ], + "type": "inline_equation", + "content": "B" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "lines": [ + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": "1: for " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\{x_{1}, x_{2}, \\ldots, x_{B}\\} \\in \\mathcal{D}_{l} \\cup \\mathcal{D}_{u}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " do \n2: if " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "x_{i} \\in \\mathcal{D}_{l}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " then \n3: Compute supervised loss " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{s}}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " according to Eqn. (1) \n4: else \n5: if " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "x_{i} \\in \\mathbb{S}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " then \n6: Compute the pseudo labeled based loss " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{p}}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " according to Eqn. (2) \n7: else if " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "x_{i} \\in \\mathbb{U}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " then \n8: Compute loss " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{r}}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " for reusable samples by Eqn. (6) \n9: end if \n10: Compute the consistency loss " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{t}}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " according to Eqn. (8) \n11: end if \n12: Compute the total loss " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " according to Eqn. (9) \n13: Update student network " + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\theta \\gets \\theta - \\eta \\Delta \\mathcal{L}" + }, + { + "bbox": [ + 306, + 472, + 545, + 689 + ], + "type": "text", + "content": " \n14: Update teacher network by Eqn. (7) \n15: end for" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_body" + } + ], + "index": 15, + "sub_type": "algorithm" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17178" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 173, + 85 + ], + "type": "text", + "content": "4. Experimental Results" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "content": "Training details. We adopt the HRNet-w32 as the backbone and train our network in two stages. We first train the MBHRNet on the labeled data with the supervised loss. Following [27], we train the network with the Adam optimizer for 210 epochs. The initial learning rate is set to " + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "inline_equation", + "content": "10^{-3}" + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "content": ", and is dropped to " + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "inline_equation", + "content": "10^{-4}" + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "inline_equation", + "content": "10^{-5}" + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "inline_equation", + "content": "170^{th}" + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "inline_equation", + "content": "200^{th}" + }, + { + "bbox": [ + 46, + 91, + 288, + 236 + ], + "type": "text", + "content": " epochs, respectively. The trained model is then used to generate pseudo labels following [20]. In the second stage, we initialized the student network from the first stage and train the whole framework with both labeled and unlabeled data for another 150 epochs. More training details are provided in the supplementary material." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 251, + 288, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 288, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 288, + 420 + ], + "type": "text", + "content": "Datasets. We evaluate our method on the AP-10K dataset [33] and the TigDog dataset [20]. The AP-10K dataset is a recently proposed animal pose dataset, which contains more diverse animal species than previous datasets [5, 20]. The dataset contains 10,015 labeled images in total, which are split into train, validation, and test sets with a ratio of 7:1:2 per animal species. The TigDog dataset includes 8380 images for the horse category and 6523 images for the tiger category. This dataset is used in several domain adaptation works [16,20] to show that the knowledge learned from synthetic animals can be transferred to real animal images. We also evaluate on this dataset to show that better performance can be achieved by labeling just a few images, hence can reduce human labor compared to generating synthetic data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 436, + 287, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 287, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 287, + 509 + ], + "type": "text", + "content": "Evaluation metrics. We adopt the Mean Average Precision (mAP) as the evaluation metric for the AP-10K dataset. The Percentage of Correct Keypoints (PCK), which computes the percentage of joints that are within a normalized distance to the ground truth locations, is used for the TigDog dataset following [20]." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 48, + 517, + 291, + 594 + ], + "blocks": [ + { + "bbox": [ + 48, + 517, + 291, + 594 + ], + "lines": [ + { + "bbox": [ + 48, + 517, + 291, + 594 + ], + "spans": [ + { + "bbox": [ + 48, + 517, + 291, + 594 + ], + "type": "table", + "html": "
510152025
HRNet [27]0.3600.4630.5110.5470.588
UDA [30]0.4290.5190.5660.5800.628
FixMatch [25]0.4780.5440.5890.6010.631
FlexMatch [34]0.4660.5550.5960.6180.646
Ours0.5330.5970.6320.6540.681
", + "image_path": "d199c49a4318f3f58047e8d4b79edc66d3eb1f475b692d5182ecbd17c0e42505.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 601, + 286, + 624 + ], + "lines": [ + { + "bbox": [ + 46, + 601, + 286, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 286, + 624 + ], + "type": "text", + "content": "Table 1. Results (mAP) on the AP-10K when 5, 10, 15, 20 and 25 images per species are labeled. Best results in bold." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 647, + 217, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 217, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 217, + 658 + ], + "type": "text", + "content": "4.1. Results on the AP-10K Dataset." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We evaluate our approach under two scenarios on the AP-10K dataset. In the first scenario, a set of images are labeled for each animal species. The second scenario is that only the images in one family are labeled and we test on" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 109 + ], + "type": "text", + "content": "other animal families. This setting is more challenge since the appearance, size and background environment are quite different for different animal species." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 124, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 124, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 124, + 545, + 399 + ], + "type": "text", + "content": "We show results for the first scenario in Tab. 1, where we evaluate when 5, 10, 15, 20 and 25 images per animal species are labeled. There are 50 species in total, which results in 250, 500, 720, 1000 and 1250 labeled images out of 7023 images. We compare with state-of-the-art semi-supervised approaches, including UDA [30], FixMatch [25] and FlexMatch [34]. 'HRNet' represents HRNet trained only with labeled images. We reimplement those semi-supervised approaches according to the open repository since they only show results for classification task. We can see that our approach outperforms existing approaches by a large margin, especially when very few labeled images are available, such as the case of 5 labels per species. The reason is that UDA, FixMatch and FlexMatch only retain the samples with reliable pseudo labels based on the confidence scores. In comparison, we combine the reliable pseudo label selection with the reusable sample re-labeling and teacher-student consistency, which helps to fully utilize the unlabeled data. Moreover, our results are the closest to the fully supervised setting [33], i.e. " + }, + { + "bbox": [ + 304, + 124, + 545, + 399 + ], + "type": "inline_equation", + "content": "0.738\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 124, + 545, + 399 + ], + "type": "text", + "content": ", when only 25 images per animal species are labeled. We also show qualitative results for the 25 labels per animal species setting in Fig. 3." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 415, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 715 + ], + "type": "text", + "content": "We also show results for the case when images from only one animal family are labeled in Tab. 2. Following the inter-family transfer learning setting in [33], we train our model with labeled images of the Bovidae family and the remaining unlabeled images, and test on families including Cervidae, Equidae and Hominidae. There are seven animal species in the Bovidae family that includes a total of 755 images. The results under the 'Generalization', 'Few-Shot' and 'Transfer' settings are taken from [33]. 'Generalization' means that the model is trained only with images in the Bovidae, 'Few-Shot' means that 20 labels from the testing species are used, and 'Transfer' means that all labels of the testing species are used. We can see that we achieve better performance than the generalization setting in all cases except for 'Moose'. Moreover, we even outperform the 'Transfer' setting for 'Deer' and 'Horse' although we do not use any labels from the target species. Our results for the 'Chimpanzee' and 'Gorilla' are not satisfactory although still comparable to the 'Few-Shot' setting. We show the failure cases of 'Chimpanzee' and 'Gorilla' in the last two examples of Fig. 3. We can see that 'Chimpanzee' and 'Gorilla' are very different from animal species in the Bovidae family (the first four examples of the last row) in terms of appearance and pose, which makes the knowledge transfer hard without using any labels from the target species." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "17179" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 85, + 69, + 509, + 229 + ], + "blocks": [ + { + "bbox": [ + 85, + 69, + 509, + 229 + ], + "lines": [ + { + "bbox": [ + 85, + 69, + 509, + 229 + ], + "spans": [ + { + "bbox": [ + 85, + 69, + 509, + 229 + ], + "type": "table", + "html": "
SpeciesSettingPerformanceSpeciesSettingPerformance
DeerGeneralization0.723MooseGeneralization0.587
Few-Shot0.742Few-Shot0.648
Transfer0.751Transfer0.726
Ours0.767Ours0.547
HorseGeneralization0.592ZebraGeneralization0.324
Few-Shot0.635Few-Shot0.480
Transfer0.718Transfer0.708
Ours0.749Ours0.562
ChimpanzeeGeneralization0.009GorillaGeneralization0.017
Few-Shot0.022Few-Shot0.144
Transfer0.550Transfer0.662
Ours0.057Ours0.033
", + "image_path": "f954608b8ff64c3bbfcc6f52832d8fb95f849c52fc80b89ddaee5a2917baef0a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 73, + 259, + 520, + 308 + ], + "blocks": [ + { + "bbox": [ + 88, + 238, + 504, + 250 + ], + "lines": [ + { + "bbox": [ + 88, + 238, + 504, + 250 + ], + "spans": [ + { + "bbox": [ + 88, + 238, + 504, + 250 + ], + "type": "text", + "content": "Table 2. Results (mAP) for the Cervidae, Equidae and Hominidae when only images from the Bovidae are labeled." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 73, + 259, + 520, + 308 + ], + "lines": [ + { + "bbox": [ + 73, + 259, + 520, + 308 + ], + "spans": [ + { + "bbox": [ + 73, + 259, + 520, + 308 + ], + "type": "table", + "html": "
RealCycgan [36]BDL [17]Cycada [10]CC-SSL [20]MDAM-MT [16]Ours
Horse78.9851.8662.3355.5770.7779.5073.05
Tiger81.9946.4752.2651.4864.1467.7674.88
Average80.4849.1757.3053.5367.5273.6673.83
", + "image_path": "ea0f74715782c88859bbf817684a0eda9433a9874256ef448504464081ff90a8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 47, + 349, + 555, + 407 + ], + "blocks": [ + { + "bbox": [ + 46, + 316, + 546, + 339 + ], + "lines": [ + { + "bbox": [ + 46, + 316, + 546, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 546, + 339 + ], + "type": "text", + "content": "Table 3. PCK@0.05 accuracy of the TigDog dataset. 'Real' means full supervision. Cycgan, BDL, Cycada, CC-SSL, MDAM-MT are domain adaptation approaches using synthetic data. Our approach is trained with only 36 labeled images per category." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 349, + 555, + 407 + ], + "lines": [ + { + "bbox": [ + 47, + 349, + 555, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 349, + 555, + 407 + ], + "type": "table", + "html": "
Horse AccuracyTiger AccuracyAverage
EyeChinShoulderHipElbowKneeHoovesMeanEyeChinShoulderHipElbowKneeHoovesMean
CC-SSL84.6090.2669.6985.8968.5868.7361.3370.7796.7590.4644.8477.6155.8242.8564.5564.14
MDAM-MT91.0593.3777.3580.6773.6381.8373.6779.5097.0191.1846.6378.0850.8661.5470.8467.76
Ours89.4293.6074.6383.6174.3179.9173.9979.1899.1392.8246.9675.3650.4663.5174.8268.98
", + "image_path": "53788f530cff00b554b5afde3ba084584b1f69a3aba2752a0d58352140106e4b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 49, + 456, + 286, + 533 + ], + "blocks": [ + { + "bbox": [ + 46, + 415, + 546, + 439 + ], + "lines": [ + { + "bbox": [ + 46, + 415, + 546, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 546, + 439 + ], + "type": "text", + "content": "Table 4. PCK@0.05 accuracy of the TigDog dataset for domain adaptation setting. 'Mean' represents the accuracy for each animal category, and 'Average' represents the average accuracy for all animal categories. Best results in bold." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 456, + 286, + 533 + ], + "lines": [ + { + "bbox": [ + 49, + 456, + 286, + 533 + ], + "spans": [ + { + "bbox": [ + 49, + 456, + 286, + 533 + ], + "type": "table", + "html": "
510152025
Full0.5330.5970.6320.6550.681
- RSR0.5210.5860.6210.6330.668
- MT0.4870.5680.6140.6280.659
- MB0.5200.5850.6240.6450.670
- AUG0.4870.5650.6080.6250.654
", + "image_path": "ab7583ed68ca71b5db0c49759446e97e09f4c3eee850fa4d90f21288415d3a65.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 540, + 287, + 564 + ], + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 564 + ], + "type": "text", + "content": "Table 5. Ablation study on the AP-10K dataset when 5, 10, 15, 20 and 25 images per animal species are labeled." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 586, + 211, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 211, + 600 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 211, + 600 + ], + "type": "text", + "content": "4.2. Results on the TigDog Dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "The TigDog Dataset is used in previous domain adaptation works [16, 20] to show that models trained from synthetic images can be used for real ones. We also evaluate on this dataset to show that our approach can achieve comparable or even better performance compared with state-of-the-art domain adaptation works with very few labeled images. Note that we use the same ResNet backbone as [20] for all experiments on the TigDog dataset for fair comparison. The results are shown in Tab. 3, where the numbers are" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 590 + ], + "type": "text", + "content": "directly taken from [16]. 'Real' denotes fully-supervised setting, Cycgan [36], BDL [17], Cycada [10], CC-SSL [20], MDAM-MT [16] are domain adaptation approaches trained with synthetic animal images and \"Ours\" means our approach trained with 36 images per animal category. Note that 36 is the minimum labeled data needed for each category to achieve better performance than existing unsupervised domain adaptation approaches, i.e. we only need to label 72 out of 14,903 images for the Tigdog dataset. The results demonstrate the advantage of our setting since annotating such few images does not take much human labor." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "We also test our approach on the domain adaptation setting to further verify the effectiveness. The results are shown in Tab. 4, which includes accuracy for different joints, the mean accuracy for each animal category and the average accuracy over all categories. We can see that our approach achieves the best performance in most of the cases. Note that our approach and CC-SSL have simpler networks compared to MDAM-MT, which introduce an extra refinement module for self-knowledge distillation. More training details are provided in the supplementary material." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "17180" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 89, + 70, + 504, + 342 + ], + "blocks": [ + { + "bbox": [ + 89, + 70, + 504, + 342 + ], + "lines": [ + { + "bbox": [ + 89, + 70, + 504, + 342 + ], + "spans": [ + { + "bbox": [ + 89, + 70, + 504, + 342 + ], + "type": "image", + "image_path": "a7468c9d45bc1af29643c4aa44f2079ea0ccc6a71ea54e64a68ac9877fb50c81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 351, + 546, + 373 + ], + "lines": [ + { + "bbox": [ + 46, + 351, + 546, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 546, + 373 + ], + "type": "text", + "content": "Figure 3. Qualitative results for the AP-10K dataset when 25 images per species is labeled (except for the last two examples). The last two examples show the failure cases when only images from the Bovidae family are labeled." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 399, + 140, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 140, + 412 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 140, + 412 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": "We conduct ablation study on the AP-10K dataset. Each component is removed from the full model to verify the corresponding contribution. The results are shown in Tab. 5, where 'RSR' denotes reusable sample re-labeling, 'MT' denotes student teacher consistency, 'MB' denotes multibranch architecture and 'AUG' denotes strong-weak augmentation. Note that we remove the weak augmentation " + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": " and replace the strong augmentation " + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 426, + 289, + 715 + ], + "type": "text", + "content": " with commonly used rotation and scale augmentation for the ablation of 'AUG'. We can see that the performance drops when each component is removed. Specially, the accuracy drops significantly for the 5 labels per animal species setting when the student teacher consistency or strong-weak augmentation is removed. This can be attributed to two reasons. Firstly, the strong-weak augmentation enforces the output of the strong augmented images to be consistent with the pseudo labels that are generated using weak augmented images. In this way, the network is enforced to learn a smooth representation around each image, which helps to improve the performance especially in the low-data regime. Secondly, The initial set of pseudo labels are extremely noisy when the model is trained with very few labeled data. The teacher network, which is a temporal ensemble of network, is able to provide more stable supervision for the student network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 399, + 381, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 381, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 381, + 411 + ], + "type": "text", + "content": "5. Limitations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 419, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 419, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 419, + 545, + 514 + ], + "type": "text", + "content": "Our approach achieves impressive performance even when very few labeled data is available. However, there are still many remaining challenges for the task of animal pose estimation for limited labeled data. The large variations of appearance and pose across different animal species makes it hard for the network to generalize well to different animal species, e.g. train with labels from Bovidae and test on Hominidae. We leave this for future research." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 524, + 378, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 378, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 378, + 536 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 640 + ], + "type": "text", + "content": "We propose a pseudo label based training scheme for animal pose estimation from scarce annotations. We combine the reliable pseudo label selection with the reusable sample re-labeling and the student-teacher consistency to make full use of the unlabeled data. We also introduce the MBHRNet to mitigate the negative effect of noisy joints. Extensive experiments have been conducted to verify the effectiveness of our proposed approach." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 715 + ], + "type": "text", + "content": "Acknowledgement. This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG2-RP-2021-024), and the Tier 2 grant MOE-T2EP20120-0011 from the Singapore Ministry of Education." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "17181" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Mykhaylo Andriluka, Leonid Pishchulin, Peter Gehler, and Bernt Schiele. 2d human pose estimation: New benchmark and state of the art analysis. 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Existing methods still struggle in challenging poses where the human body is highly occluded or is closely interacting with the scene. To address this issue, we propose a scene-aware egocentric pose estimation method that guides the prediction of the egocentric pose with scene constraints. To this end, we propose an egocentric depth estimation network to predict the scene depth map from a wide-view egocentric fisheye camera while mitigating the occlusion of the human body with a depth-inpainting network. Next, we propose a scene-aware pose estimation network that projects the 2D image features and estimated depth map of the scene into a voxel space and regresses the 3D pose with a V2V network. The voxel-based feature representation provides the direct geometric connection between 2D image features and scene geometry, and further facilitates the V2V network to constrain the predicted pose based on the estimated scene geometry. To enable the training of the aforementioned networks, we also generated a synthetic dataset, called EgoGTA, and an inthe-wild dataset based on EgoPW, called EgoPW-Scene. The experimental results of our new evaluation sequences show that the predicted 3D egocentric poses are accurate and physically plausible in terms of human-scene interaction, demonstrating that our method outperforms the state-of-the-art methods both quantitatively and qualitatively.", + "bbox": [ + 75, + 316, + 473, + 741 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 768, + 209, + 784 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Egocentric 3D human pose estimation with head- or body-mounted cameras is extensively researched recently because it allows capturing the person moving around in a large space, while the traditional pose estimation methods can only record in a fixed volume. With this advantage, the egocentric pose estimation methods show great potential in various applications, including the xR technologies and mo", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/24a11630719e862f19f6808063c133e47eedac678f6fdca0fd92fb019e445447.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 285, + 625, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3be4c0f73598e9026f71103b73aa3d3cd492ac5db2a4c48c72d1e4d9a4492fcb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 292, + 754, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c67db67420a15cafd7ec9bf0b1260eb60fd1710b49aec6aca6954b4fee972a64.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 292, + 883, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d7903bd98f4d881d267011e41a5632543aea702a7e937bae8d743bc8e31ac44.jpg", + "image_caption": [ + "Image" + ], + "image_footnote": [], + "bbox": [ + 509, + 380, + 625, + 469 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/868b69835610002389d40762831c2f0943eac697a38a6a20a8e52a6f09cfd9cb.jpg", + "image_caption": [ + "EgoPW" + ], + "image_footnote": [], + "bbox": [ + 638, + 390, + 754, + 469 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b9372a2ddcc5bca466ce5d37e4f96f4c88dc55225fbfa8e7583ed4495b0e0f9d.jpg", + "image_caption": [ + "Ours", + "Figure 1. Previous egocentric pose estimation methods like EgoPW predict body poses that may suffer from body floating issue (the first row) or body-environment penetration issue (the second row). Our method predicts accurate and plausible poses complying with the scene constraints. The red skeletons are the ground truth poses and the green skeletons are the predicted poses." + ], + "image_footnote": [], + "bbox": [ + 766, + 391, + 883, + 469 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "bile interaction applications.", + "bbox": [ + 498, + 609, + 689, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we estimated the full 3D body pose from a single head-mounted fisheye camera. A number of works have been proposed, including $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39], $x\\mathrm{R}$ -egopose [32], Global-EgoMocap [36], and EgoPW [35]. These methods have made significant progress in estimating egocentric poses. However, when taking account of the interaction between the human body and the surrounding environment, they still suffer from artifacts that contrast the physics plausibility, including body-environment penetrations or body floating (see the EgoPW results in Fig. 1), which is mostly ascribed to the ambiguity caused by the self-occluded and highly distorted human body in the egocentric view. This problem will render restrictions on subsequent applications including action recognition, humanobject interaction recognition, and motion forecasting.", + "bbox": [ + 496, + 626, + 892, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address this issue, we propose a scene-aware pose estimation framework that leverages the scene context to constrain the prediction of an egocentric pose. This frame-", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "13031", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "work produces accurate and physically plausible 3D human body poses from a single egocentric image, as illustrated in Fig. 1. Thanks to the wide-view fisheye camera mounted on the head, the scene context can be easily obtained even with only one egocentric image. To this end, we train an egocentric depth estimator to predict the depth map of the surrounding scene. In order to mitigate the occlusion caused by the human body, we predict the depth map including the visible human and leverage a depth-inpainting network to recover the depth behind the human body.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Next, we combine the projected 2D pose features and scene depth in a common voxel space and regress the 3D body pose heatmaps with a V2V network [22]. The 3D voxel representation projects the 2D poses and depth information from the distorted fisheye camera space to the canonical space, and further provides direct geometric connection between 2D image features and 3D scene geometry. This aggregation of 2D image features and 3D scene geometry facilitates the V2V network to learn the relative position and potential interactions between the human body joints and the surrounding environment and further enables the prediction of plausible poses under the scene constraints.", + "bbox": [ + 75, + 242, + 472, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since no available dataset can be used for train these networks, we proposed EgoGTA, a synthetic dataset based on the motion sequences of GTA-IM [3], and EgoPW-Scene, an in-the-wild dataset based on EgoPW [35]. Both of the datasets contain body pose labels and scene depth map labels for each egocentric frame.", + "bbox": [ + 75, + 438, + 470, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To better evaluate the relationship between estimated egocentric pose and scene geometry, we collected a new test dataset containing ground truth joint positions in the egocentric view. The evaluation results on the new dataset, along with results on datasets in Wang et al. [36] and $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39] demonstrate that our method significantly outperforms existing methods both quantitatively and qualitatively. We also qualitatively evaluate our method on inthe-wild images. The predicted 3D poses are accurate and plausible even in challenging real-world scenes. To summarize, our contributions are listed as follows:", + "bbox": [ + 75, + 529, + 472, + 695 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The first scene-aware egocentric human pose estimation framework that predicts accurate and plausible egocentric pose with the awareness of scene context;", + "- Synthetic and in-the-wild egocentric datasets containing egocentric pose labels and scene geometry labels;", + "- A new depth estimation and inpainting networks to predict the scene depth map behind the human body;", + "- By leveraging a voxel-based representation of body pose features and scene geometry jointly, our method" + ], + "bbox": [ + 94, + 703, + 467, + 866 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "outperforms the previous approaches and generates plausible poses considering the scene context.", + "bbox": [ + 531, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 136, + 640, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Egocentric 3D Full Body Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 161, + 852, + 176 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by the new applications in augmented reality and by the limitations of traditional motion capture systems, Rhodin et al. [26] proposed the first egocentric motion capture system based on a pair of fisheye cameras. The following methods proposed new architectures [4,47] and new datasets [1,47] for stereo egocentric pose estimation. However, a stereo camera setup implies additional computation complexity and extra energy consumption, which is critical for low-power head-mounted devices, which are the main target applications.", + "bbox": [ + 496, + 185, + 890, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The single head-mounted fisheye camera setup was first proposed by Xu et al. [39], who also introduced a two-stream CNN to cope with the low resolution of regions far from the fisheye camera, i.e., one branch for the full body and one branch for predicting the lower body joints from a zoom-in image. Tome et al. [32] proposed an encoder-decoder architecture to model the high uncertainty caused by severe occlusions present in this setup and Wang et al. [36] leverages motion capture data to learn a human motion prior, which is applied in an optimization method to obtain temporally stable poses for training and egocentric pose predictor. Another challenge is the strong image distortion caused by the fisheye lens, which can be mitigated with automatic camera calibration [46]. Other setups consider the camera facing forward and try to synthesize plausible human motion given only scene image evidences [18] or partially visible body parts [13, 15]. In our work, we do not consider this setup since in many poses only a few body extremities are visible in the image.", + "bbox": [ + 496, + 335, + 892, + 623 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Obtaining real data in the egocentric setup is a time consuming process, therefore, many approaches rely on synthetic data for training [15,32]. A recent method has shown that the existing gap between synthetic and real data can be mitigated by domain adaptation techniques [35], but this approach still requires real data for the weak supervision part. Differently, our method has a simpler training strategy, and we reduce the gap between synthetic and real data by providing additional pseudo ground-truth scene labels for real sequences, including indoor and outdoor scenes.", + "bbox": [ + 496, + 625, + 890, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Voxel Representation for Body Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 786, + 890, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Volumetric voxel representations have been extensively used with multiple view setups for the estimation of single [31, 33] and multiple human poses [34, 37, 40, 45], and for hand pose estimation [12, 19-21] from depth maps input. Considering a single image as input, Pavlakos et al. [25] proposed a coarse-to-fine approach to lift from 2D", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1Datasets are released in our project page. Meta did not access or process the data and is not involved in the dataset release.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "13032", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1303ff2903b00600563f78b9b32be04007eac97704c5b760d66764503246367e.jpg", + "image_caption": [ + "Sec. 3.1 Training Dataset" + ], + "image_footnote": [], + "bbox": [ + 99, + 106, + 267, + 252 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7a563c2887fe538203a59c1cc997b1876e8574e8976738f87590dd60ee3eb793.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 90, + 369, + 252 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6471fd6c34e2d655e31a392ee5ef816a8ac0ed50176f5d58c119d8a2cc346d90.jpg", + "image_caption": [ + "Sec. 3.2 Scene Depth Estimator" + ], + "image_footnote": [], + "bbox": [ + 398, + 104, + 870, + 252 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fa3c349f901ea3068372128b289593768007e09e72ab5ce1d1c56396974f133d.jpg", + "image_caption": [ + "Sec. 3.3 Scene-aware Egocentric Pose Estimator", + "Figure 2. Overview of our method. We first render synthetic training dataset EgoGTA and in-the-wild training dataset EgoPW-Scene. Both datasets contain egocentric depth maps for subsequent training process (Sec. 3.1). Next, we train an egocentric scene depth estimator that predicts a depth map without the human body and a depth inpainting network (Sec. 3.2). Finally, we combine the 2D body pose features and scene depth map into a common voxel space. The 3D body pose heatmaps are regressed from the voxel space with a V2V network and the final pose prediction is obtained with soft-argmax (Sec. 3.3)." + ], + "image_footnote": [], + "bbox": [ + 94, + 255, + 874, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "heatsmaps to a voxel representation for 3D human pose estimation. Iskakov [14] later proposed a learnable triangulation method in voxel space that can generalize to single or multiple views, achieving less than $2\\mathrm{cm}$ error in a controlled multi-view data. Despite the success of voxel representation for human and hand pose estimation from an external camera, this technique has not yet been explored for the interaction between human body and scene. In our work, we show the advantages of this representation for egocentric human pose estimation, especially when considering human-scene interaction.", + "bbox": [ + 75, + 558, + 468, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Scene-aware Human Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 739, + 398, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In recent years, several approaches have been proposed to predict the pose of humans considering environmental and physical constraints from RGB [24, 30, 41] and inertial measurement units (IMU) [9, 42]. Some methods assume a simplified environment, such as a planar ground floor, to enforce a temporal sequence that is physically consistent with the universal law of gravity by assuming known camera poses [29, 30] or by tracking an object in the scene following a free flight trajectory [6]. Other approaches assume", + "bbox": [ + 75, + 763, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "that the scene is given as input, either as a 3D reconstruction [9,28] or as geometric primitives [43], whose positions can be refined in the optimization process. Bhatnagar et al. [2] proposed a method and dataset for human-object interactions. Taking into account the interaction between humans and furniture, holistic methods are able to estimate the position of humans and specific objects in the scene under the assumption of a planar floor [5, 38, 41], or even to estimate deformations in known objects based on human poses [17]. Contrary to the previous work, we make no strong assumptions about the objects and ground floor in the scene, but instead propose a method that learns to estimate the background scene geometry from a fisheye camera and explores the correlation between the human body and scene directly from egocentric data.", + "bbox": [ + 496, + 558, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 799, + 589, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a new method for predicting accurate ego-centric body pose by leveraging the estimated scene geometry. An overview of our method is shown in Fig. 2. In order to train the scene-aware network, we first generate a synthetic dataset based on the GTA-IM dataset [3], called", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "13033", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "EgoGTA, and an in-the-wild dataset based on the EgoPW dataset [35], called EgoPW-Scene (Sec. 3.1). Next, we train a depth estimator to estimate the geometry of the surrounding scene and introduce the depth-inpainting network that estimates the depth behind the human body (Sec. 3.2). Finally, we combine 2D features and scene geometry in a common voxel space and predict the egocentric pose with a V2V network [22] (Sec. 3.3).", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Training Dataset", + "text_level": 1, + "bbox": [ + 76, + 220, + 243, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although many training datasets for egocentric pose estimation [32,35,39] have been proposed, they cannot yet train the scene-aware egocentric pose estimation network due to the lack of scene geometry information. To solve this, we introduce the EgoGTA dataset and EgoPW-Scene dataset (both will be made publicly available). Both datasets contain pose labels and depth maps of the scene for each egocentric frame, facilitating our training process. We show examples from both datasets, as illustrated in Fig. 2.", + "bbox": [ + 75, + 243, + 472, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.1 EgoGTA Dataset", + "text_level": 1, + "bbox": [ + 76, + 397, + 250, + 412 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to obtain precise ground truth human pose and scene geometry for training, we devise a new synthetic ego-centric dataset based on GTA-IM [3], which contains various daily motions and ground truth scene geometry. For this, we first fit the SMPL-X model on the 3D joint trajectories from GTA-IM. Next, we attach a virtual fisheye camera to the forehead of the SMPL-X model and render the images, semantic labels, and depth map of the scene with and without the human body. In total, we obtained $320\\mathrm{K}$ frames in 101 different sequences, each with a different human body texture. Here, we denote the EgoGTA dataset $\\mathbb{S}_G = \\{I_G,S_G,D_G^B,D_G^S,P_G\\}$ , including synthetic images $I_{G}$ and their corresponding human body segmentation maps $S_{G}$ , depth map with human body $D_G^B$ , depth map of the scene without human body $D_G^S$ , and egocentric pose labels $P_{G}$ .", + "bbox": [ + 75, + 421, + 472, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1.2 EgoPW-Scene Dataset", + "text_level": 1, + "bbox": [ + 76, + 680, + 285, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since we want to generalize to data captured with a real head-mounted camera, we also extended the EgoPW [35] training dataset. For this, we first reconstruct the scene geometry from the egocentric image sequences of the EgoPW training dataset with a Structure-from-Motion (SfM) algorithm [10]. This step provides a dense reconstruction of the background scene. The global scale of the reconstruction is recovered from known objects present in the sequences, such as laptops and chairs. We further render the depth maps of the scene in the egocentric perspective based on the reconstructed geometry. Our EgoPW-Scene dataset contains $92\\mathrm{K}$ frames in total, which are distributed in 30 sequences performed by 5 actors. The number of frames in", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the EgoPW-Scene dataset is less than EgoPW dataset since SfM fails on some sequences. Here, we denote the EgoPW-Scene dataset $\\mathbb{S}_E = \\{I_E, D_E^S, P_E\\}$ , including in-the-wild images $I_E$ and their corresponding depth map of the scene without human body $D_E^S$ , and egocentric pose labels $P_E$ .", + "bbox": [ + 496, + 90, + 890, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Scene Depth Estimator", + "text_level": 1, + "bbox": [ + 500, + 179, + 714, + 194 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we propose a depth estimation method to capture the scene geometry information in the egocentric perspective. Available depth estimation methods [7, 11, 16] can only generate depth maps with the human body, but are not able to infer the depth information behind the human, i.e., the background scene depth. However, the area occluded by the human body, e.g. the areas of foot contact, are crucial for generating plausible poses, as demonstrated in Sec. 4.4. To predict the depth map of the scene behind the human body, we adopt a two-step approach. More specifically, we first estimate the depth map including the human body and the semantic segmentation of the human with two separated models. Then, we use a depth inpainting network to recover the depth behind the human body. This two-step strategy is necessary because the human visual evidences in the RGB images are too strong to be ignored by the depth estimator, therefore, it is easier to train the scene depth estimation as separated tasks.", + "bbox": [ + 496, + 202, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We first train the depth estimator network $\\mathcal{D}$ , which takes as input a single egocentric image $I$ and predicts the depth map with human body $\\hat{D}^B$ . The network architecture of $\\mathcal{D}$ is the same as Hu et al. [11]'s work. To minimize the influence of the domain gap between synthetic and real data, the network is initially trained on the NYU-Depth V2 dataset [23] following [11], and further fine-tuned on the EgoGTA dataset.", + "bbox": [ + 496, + 476, + 890, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we train the segmentation network $S$ for segmenting the human body. The network takes the egocentric image $I$ as input and predicts the segmentation mask for the human body $\\hat{S}$ as output. Following Yuan et al. [44], we use HRNet as our segmentation network. Similarly, to reduce the domain gap, we pretrain the network on the LIP dataset [8] and finetune the model on the EgoGTA dataset. We do not train network $\\mathcal{D}$ and $S$ on the EgoPW-Scene dataset since it lacks the ground truth segmentation maps and depth maps with the human body.", + "bbox": [ + 496, + 598, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we propose a depth inpainting network $\\mathcal{G}$ for generating the final depth map of the scene without human body. We first generate the masked depth map $\\hat{D}^M = (1 - \\hat{S})\\odot \\hat{D}^B$ , which is a Hadamard product between the background segmentation and the depth map with human body. Then, the masked depth map $\\hat{D}^M$ and the segmentation mask $\\hat{S}$ are fed into the inpainting network $\\mathcal{G}$ , which predicts the final depth map $\\hat{D}^S$ . We train the inpainting network $\\mathcal{G}$ and finetune the depth estimation network $\\mathcal{D}$ on both the EgoGTA and EgoPW-Scene datasets. During", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "13034", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "training, we penalize the differences between the predicted depth maps and the ground truth depth of the background scene with $L^S$ and also keep the depth map consistent in the non-human body regions with $L^C$ . Specifically, the loss function is defined as follows:", + "bbox": [ + 75, + 90, + 472, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L = \\lambda^ {S} L ^ {S} + \\lambda^ {C} L ^ {C}, \\quad \\text {w i t h} \\\\ L ^ {S} = \\left\\| \\hat {D} _ {G} ^ {S} - D _ {G} ^ {S} \\right\\| _ {2} ^ {2} + \\left\\| \\hat {D} _ {E} ^ {S} - D _ {E} ^ {S} \\right\\| _ {2} ^ {2}, \\quad \\text {a n d} \\\\ L ^ {C} = \\left\\| \\left(\\hat {D} _ {G} ^ {S} - \\hat {D} _ {G} ^ {B}\\right) \\left(1 - \\hat {S} _ {G}\\right) \\right\\| _ {2} ^ {2} \\tag {1} \\\\ + \\left\\| \\left(\\hat {D} _ {E} ^ {S} - \\hat {D} _ {E} ^ {B}\\right) \\left(1 - \\hat {S} _ {E}\\right) \\right\\| _ {2} ^ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 172, + 468, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 76, + 292, + 122, + 305 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {D} _ {G} ^ {S} = \\mathcal {G} (\\hat {D} _ {G} ^ {M}, \\hat {S} _ {G}); \\quad \\hat {D} _ {E} ^ {S} = \\mathcal {G} (\\hat {D} _ {E} ^ {M}, \\hat {S} _ {E});\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 313, + 413, + 333 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {D} _ {G} ^ {B} = \\mathcal {D} (I _ {G}); \\quad \\hat {D} _ {E} ^ {B} = \\mathcal {D} (I _ {E}); \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 335, + 468, + 354 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {S} _ {G} = \\mathcal {S} (I _ {G}); \\quad \\hat {S} _ {E} = \\mathcal {S} (I _ {E}),\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 357, + 377, + 376 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $\\lambda^S$ and $\\lambda^C$ are the weights of the loss terms.", + "bbox": [ + 76, + 386, + 398, + 402 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Scene-aware Egocentric Pose Estimator", + "text_level": 1, + "bbox": [ + 76, + 411, + 418, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we introduce our scene-aware egocentric pose estimator. We rely on the prior that human bodies are mostly in contact with the scene. However, estimating the contact explicitly from a single egocentric image is very challenging. Therefore, we rely on a data-driven approach by learning a model that predicts a plausible 3D pose given the estimated scene geometry and features extracted from the input image. To achieve this goal, we first leverage the EgoPW [35] body joints heatmap estimator to extract 2D body pose features $F$ and use the scene depth estimator from Sec. 3.2 to estimate the depth map of the scene without human body $\\hat{D}^S$ . Afterwards, we project the body pose features and depth map into a 3D volumetric space considering the fisheye camera projection model. After obtaining the volumetric representation of human body features $V_{\\mathrm{body}}$ and scene depth $V_{\\mathrm{scene}}$ , the 3D body pose $\\hat{P}$ is predicted from the volumetric representation with a V2V network [22].", + "bbox": [ + 75, + 434, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Lifting the image features and depth maps to a 3D representation allows getting more plausible results, as inconsistent joint predictions can be behind the volumetric scene $V_{\\mathrm{scene}}$ (pose-scene penetration) or spatially isolated from the voxelized scene geometry (pose floating), so they can be easily identified and adjusted by the volumetric convolutional network.", + "bbox": [ + 75, + 693, + 468, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.1 Scene and Body Encoding as a 3D Volume", + "text_level": 1, + "bbox": [ + 76, + 816, + 423, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to create the volumetric space, we first create a 3D bounding box around the person in the egocentric camera coordinate system of size $L \\times L \\times L$ , where $L$ denotes the length of the side of the bounding box in meters.", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The egocentric camera is placed at the center-top of the 3D bounding box so that the vertices of the bounding boxes are: $(\\pm L / 2, \\pm L / 2, 0)$ and $(\\pm L / 2, \\pm L / 2, L)$ under the egocentric camera coordinate system. Next, we discretize the bounding box by a volumetric cube $V \\in R^{N,N,N,3}$ . Each voxel $V_{xyz} \\in R^3$ in position $(x,y,z)$ is filled with the coordinates of its center under the egocentric camera coordinate system $(xL / N - L / 2, yL / N - L / 2, zL / N)$ .", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We project the 3D coordinates in $V$ into the egocentric image space with the fisheye camera model [27]: $V_{\\mathrm{proj}} = \\mathcal{P}(V)$ , where $V_{\\mathrm{proj}} \\in R^{N,N,N,2}$ and $\\mathcal{P}$ is the fisheye camera projection function. The volumetric representation $V_{\\mathrm{body}}$ of the human body is obtained by filling a cube $V_{\\mathrm{body}} \\in R^{N,N,N,K}$ by bilinear sampling from the feature maps $F$ with $K$ channels using 2D coordinates in $V_{\\mathrm{proj}}$ :", + "bbox": [ + 496, + 212, + 890, + 319 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV _ {\\text {b o d y}} = F \\left\\{V _ {\\text {p r o j}} \\right\\} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 325, + 890, + 343 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\{\\cdot\\}$ denotes bilinear sampling.", + "bbox": [ + 498, + 349, + 745, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we project the depth map to the 3D volumetric space. We first generate the point cloud of the scene geometry $C$ from the depth map $\\hat{D}^S$ with the fisheye camera projection function $C = \\mathcal{P}^{-1}(\\hat{D}^S)$ . The volumetric representation of scene depth map $V_{\\mathrm{scene}}$ is obtained by filling a binary cube $V_{\\mathrm{scene}} \\in R^{N,N,N}$ by setting the voxel at $(x,y,z)$ to 1 if there exists one point $(x_p,y_p,z_p)$ in the point cloud $C$ such that:", + "bbox": [ + 496, + 364, + 890, + 484 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| \\left(\\frac {x L}{N} - \\frac {L}{2}, \\frac {y L}{N} - \\frac {L}{2}, \\frac {z L}{N}\\right) - \\left(x _ {p}, y _ {p}, z _ {p}\\right) \\right\\| < \\epsilon \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 489, + 890, + 525 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\epsilon$ is the threshold distance. In our experiment, we set $L = 2.4\\mathrm{m}$ , $N = 64$ , and $\\epsilon = 0.04\\mathrm{m}$ . This setting can cover most types of the human motions and allows high accuracy of the predicted body pose.", + "bbox": [ + 496, + 530, + 890, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Predicting 3D Body Pose with V2V Network", + "text_level": 1, + "bbox": [ + 498, + 608, + 861, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We feed the volumetric representation aggregated from $V_{\\mathrm{body}}$ and $V_{\\mathrm{scene}}$ into the volumetric convolutional network $\\mathcal{N}$ , which has a similar architecture as [22]. The V2V network produces the 3D heatmaps of the body joints:", + "bbox": [ + 496, + 632, + 890, + 693 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV _ {\\text {h e a t m a p}} = \\mathcal {N} \\left(V _ {\\text {b o d y}}, V _ {\\text {s c e n e}}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 700, + 890, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [14], we compute the soft-argmax of $V_{\\mathrm{heatmap}}$ across the spatial axes to infer the body pose $\\hat{P}$ . The predicted pose $\\hat{P}$ is finally compared with the ground truth pose $P_G$ from the EgoGTA dataset and $P_E$ from the EgoPW-Scene dataset with the MSE loss.", + "bbox": [ + 496, + 724, + 890, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 815, + 633, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we evaluate our method considering existing and new datasets for egocentric monocular 3D human pose estimation. Please refer to the supplementary materials for the implementation details.", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "13035", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/24d37ad4186d24883596ad3592a1d233f8c9c8dc7087e277685f9fd9b17abc78.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison between our method and the state-of-the-art egocentric pose estimation methods. From left to right: input image, $\\mathrm{Mo}^2\\mathrm{Cap}^2$ result, $x\\mathrm{R}$ -egopose result, EgoPW result and our result. The ground truth pose is shown in red. The input images from the left part are from our test dataset, while those in the right part come from the EgoPW [35] in-the-wild test sequences (without ground-truth poses). We also show the gt scene geometry of the in-the-studio data and scene geometry obtained by SFM method for the in-the-wild data. For better visualizing the interaction between human body and environment, please refer to our supplementary video." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 483, + 292 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b702faf82fbaf5276500b08d4434b14f8de5e4d0ecc62365cf84295bc0024fc3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 88, + 883, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Evaluation Datasets", + "text_level": 1, + "bbox": [ + 76, + 386, + 266, + 400 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluating human-scene interaction requires precise annotations for camera pose and scene geometry. However, such information is not available in existing datasets for egocentric human pose estimation. To solve this issue, we collected a new real-world dataset using a head-mounted fisheye camera combined with a calibration board. The ground truth scene geometry is obtained with SfM method [10] from a multi-view capture system with 120 syncd 4K resolution cameras and the ground truth egocentric camera pose is obtained by localizing a calibration board rigidly attached to the egocentric camera. This dataset contains around 14K frames of two actors, performing various human-scene interacting motions such as sitting, reading newspaper, and using a computer. This dataset will be made publicly available and additional details of it are shown in the supplementary materials.", + "bbox": [ + 75, + 415, + 473, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Besides our new test dataset, we also evaluate our methods in the test datasets from Wang et al. [36] and $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39]. The real-world dataset in $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39] contains 2.7K frames of two people captured in indoor and outdoor scenes, and the dataset in Wang et al. [36] contains 12K frames of two people captured in the studio.", + "bbox": [ + 75, + 662, + 470, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 780, + 261, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We measure the accuracy of the estimated body pose with the MPJPE and PA-MPJPE. For the test dataset in Wang et al. [36] and $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39], we evaluate PA-MPJPE and BA-MPJPE [39] since the ground truth poses in the egocentric camera space are not provided. Further details of the metrics are shown in the supplementary materials.", + "bbox": [ + 75, + 809, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/79d8d34eaa22e562f869b6172e300a1728dabc5708f51a332d69535b7c058718.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMPJPEPA-MPJPE
Our test dataset
Mo2Cap2 [39]200.3121.2
xR-egopose [32]241.3133.9
EgoPW [35]189.6105.3
Ours118.592.75
MethodPA-MPJPEBA-MPJPE
Wang et al.'s dataset [36]
Mo2Cap2 [39]102.374.46
xR-egopose [32]112.087.20
EgoPW [35]81.7164.87
Ours76.5061.92
Mo2Cap2 test dataset [39]
Mo2Cap2 [39]91.1670.75
xR-egopose [32]86.8566.54
EgoPW [35]83.1764.33
Ours79.6562.82
", + "bbox": [ + 503, + 383, + 890, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Performance of our method on our test dataset, Wang et al.'s test dataset [36] and $\\mathrm{Mo}^2\\mathrm{Cap}^2$ test dataset [39]. Our method outperforms the state-of-the-art methods EgoPW, $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39] and $xR$ -egopose [32].", + "bbox": [ + 496, + 652, + 893, + 709 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparisons on 3D Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 724, + 815, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we compare our approach with previous single-frame-based methods, including EgoPW [35], $x$ Regopose [32] and $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39] on our test dataset under the \"Our test data\" in Table 1. Since the code for $x$ Regopose is not released, we use our implementation for the evaluation. In our dataset, the proposed method outperforms the previous state-of-the-art methods, EgoPW [35] by $37.5\\%$ on MPJPE and $11.9\\%$ on PA-MPJPE. We also compared with previous methods on the Wang et al.'s test dataset [36] and $\\mathrm{Mo}^2\\mathrm{Cap}^2$ test dataset [39] and show the re", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "13036", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6434fe9d881f43389a7d285ff65b1bd9828e7ff67a5c4928f61c7b8d90b18dc9.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodNon pene.Contact
Mo2Cap2 [39]69.6%23.1%
xR-egopose [32]64.5%38.3%
EgoPW [35]71.7%38.8%
Ours84.1%89.4%
", + "bbox": [ + 81, + 88, + 467, + 164 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/11f14224f03f7f3627dcaa01f58cf736e699310196c1afebf43010674c9c6000.jpg", + "image_caption": [ + "Figure 4. Predicted pose with different scene depth map input. Our network can generate different poses under different depth input and further disambiguate body poses under scene constraint." + ], + "image_footnote": [], + "bbox": [ + 86, + 217, + 460, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sults in Table 1. On Wang et al.'s test dataset, our method performs better than EgoPW by $6.4\\%$ . On the $\\mathrm{Mo}^{2}\\mathrm{Cap}^{2}$ test dataset, our method performs better than EgoPW by $7.8\\%$ .", + "bbox": [ + 75, + 444, + 468, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also evaluate the physical plausibility of our predictions by calculating the percentage of predicted poses that are in contact with the scene and do not penetrate the scene in Table 2. We define a body pose as in contact with the scene if any body joint is less than $5\\mathrm{cm}$ from the scene mesh. A body pose suffers from the body floating issue if it is not in contact with the scene. Compared with previous approaches, our method generates body poses more physically plausible considering the constraints of the scene.", + "bbox": [ + 75, + 489, + 468, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From the results in Table 1 and Table 2, we can see that our approach outperforms all previous methods on the single-frame egocentric pose estimation task. For the qualitative comparison, we show the results of our method on the studio dataset and in-the-wild sequences in Fig. 3. See our supplementary video for more qualitative evaluations. Our predicted poses are physically plausible under the scene constraint, whereas other methods generate poses suffering from body floating and penetration issues.", + "bbox": [ + 75, + 627, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In order to further demonstrate our method performing predictions accordingly to the constraint of the scene geometry, we fix the input image and change the scene depth input to the depth map corresponding to the standing pose, squatting pose, and sitting pose. The results are presented in Fig. 4 and show that the predicted poses change to standing, squatting, and sitting to better adapt to the input changes of the scene geometry. This shows our method's ability to disambiguate poses under different scene constraints.", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b35ad4bbf5dd5306f5cdcd3b4f9c151cf99d9506ebf3156e4f1355420f96f1af.jpg", + "table_caption": [ + "Table 2. Comparisons of physical plausibility on our test dataset." + ], + "table_footnote": [], + "table_body": "
MethodMPJPEPA-MPJPE
EgoPW+Optimizer187.1103.2
EgoPW+Depth149.698.15
xR-egopose+Depth180.5103.7
Ours w/o Depth188.1105.1
Ours+Depth with Body167.3103.3
Ours+Depth w/o Body135.795.84
Ours+Depth w/o Inpainting124.295.00
Ours+GT Depth109.988.80
Ours118.592.75
", + "bbox": [ + 503, + 88, + 890, + 234 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Results from our method compared to different baselines.", + "bbox": [ + 500, + 256, + 890, + 271 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 297, + 651, + 313 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Simple Combination of 2D Features and Depth Maps. In Sec. 3.3, we claim that the volumetric representation of egocentric 2D features and scene depth map is important for understanding the interaction between the human body and the surrounding scene. To provide evidence of this claim, in this experiment, we compare our method with baseline methods that simply combine the 2D image features and scene depth map. We set two baseline methods since there are two types of egocentric pose estimation methods, i.e. direct regression of 3D poses ( $x$ -R-egopose [32]) and prediction of 2D position and depth for each joint ( $\\mathrm{Mo}^2\\mathrm{Cap}^2$ [39] and EgoPW [35]). In the baseline method “ $x$ -R-egopose + Depth”, we concatenate 2D heatmaps and scene depth map as the input to the 3D pose regression network in $x$ -R-egopose. In the baseline “EgoPW + Depth”, we concatenate the 2D features and the scene depth map and input them into the joint depth prediction network.", + "bbox": [ + 496, + 321, + 890, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "From the evaluation results shown in Table 3, both of the baseline methods perform worse than our proposed method. In \"xR-egopose + Depth\", simply combining the scene depth and 2D heatmaps cannot provide direct geometric supervision for the 3D pose regression network. In \"EgoPW + Depth\", though the joint depth estimation network performs better with the help of scene depth information, the 2D pose estimation network does not benefit from it. Both of the experiments demonstrate the effectiveness of our volumetric representation of 2D features and scene geometry, which provides direct geometry supervision for the physical plausibility of predicted egocentric poses.", + "bbox": [ + 496, + 579, + 890, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Optimization. In this experiment, we compare our method with an optimization baseline that refines a 3D pose considering the scene constraint. Similar to Wang et al. [36] and EgoPW [35], we first train a VAE consisting of a CNN-based encoder $f_{\\mathrm{enc}}$ and decoder $f_{\\mathrm{dec}}$ to learn an egocentric motion prior. Then, We optimize the egocentric pose $P$ by finding a latent vector $z$ such that the corresponding pose $P = f_{\\mathrm{dec}}(z)$ minimizes the objective function", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "13037", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$E(P) = \\lambda_{R}E_{R} + \\lambda_{J}E_{J} + \\lambda_{C}E_{C}$ , where $E_{R}$ is the egocentric reprojection term, $E_{J}$ is the egocentric pose regularization term, and $E_{C}$ is the contact term. The latent vector $z$ is initialized with the estimated pose from the EgoPW method. The $E_{R}$ and $E_{J}$ are the same as those defined in Wang et al. [36]. Denote the nth joint in egocentric pose $P$ as $P_{n}, n \\in [0, N]$ , where $N$ is the number of joints, and the mth point in scene point cloud $C$ as $C_{m}, m \\in [0, M]$ , where $M$ is the number of points in the point cloud. The contact term $E_{C}$ is defined as:", + "bbox": [ + 76, + 90, + 472, + 242 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nE _ {C} = \\sum_ {n \\in [ 0, N ]} d _ {n} ^ {2}, \\quad \\text {i f} d _ {n} \\leq \\epsilon , \\text {o t h e r w i s e} 0, \\text {a n d} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 251, + 468, + 289 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nd _ {n} = \\min _ {m \\in [ 0, M ]} \\| P _ {n} - C _ {m} \\| _ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 290, + 295, + 313 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We first calculate the nearest distance $d_{n}$ between each body joint and the projected point cloud $C$ from the scene depth map. If the distance $d_{n}$ of the nth joint is less than a margin $\\epsilon$ , it is defined as in contact with the scene and minimized with the optimization framework.", + "bbox": [ + 75, + 323, + 468, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The result of the optimization method is shown as \"EgoPW+Optimizer\" in Table 3, which demonstrates that the optimization framework is less effective than our method. This is because the accuracy of optimization method relies heavily on the initial pose. If the initial pose is not accurate, it will be difficult to determine the contact labels for each joint with the fixed distance margin. Without accurate contact labels, the optimization framework might force the joint that does not contact the scene to keep in contact, eventually resulting in wrong poses.", + "bbox": [ + 75, + 398, + 470, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Scene Depth Estimator. In our work, we estimate the depth of the surrounding scene and infer the depth behind the human body with a depth inpainting network. In order to validate the effectiveness of the scene depth map, we remove the input depth map from the V2V network and show the results of \"Ours w/o Depth\" in Table 3. This baseline increases the MPJPE by about $70\\mathrm{mm}$ , which is evidence of the relevant extra information provided by the scene depth.", + "bbox": [ + 75, + 568, + 468, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To demonstrate the benefits of recovering the scene depth behind the human body, we evaluate our model using the estimated depth including the human body as the input to the V2V network. We also removed the human body area from the depth maps and use them as input to the V2V network. The results are shown in \"Ours+Depth with Body\" and \"Ours+Depth w/o Body\" in Table 3. Both of the baseline methods perform worse than our method because the area in the scene occluded by the human body can provide clues for generating plausible poses.", + "bbox": [ + 75, + 688, + 468, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also evaluate our method with ground truth depth maps in \"Ours+GT Depth\" in Table 3, which further improves over our estimated depth by $7.2\\%$ in terms of MPJPE and $4.2\\%$ in terms of PA-MPJPE. This demonstrates that the", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e57c5edb413a11d30e44ea42f61ba62d194057bb9d302d9c40e2763596dd7f50.jpg", + "image_caption": [ + "Input Image" + ], + "image_footnote": [], + "bbox": [ + 509, + 88, + 602, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e79042addfe1bd766a45c3793dd0b64fc15679757676e5aace79f76005123241.jpg", + "image_caption": [ + "w/o Inpainting Network" + ], + "image_footnote": [], + "bbox": [ + 604, + 88, + 694, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/23d0b79496cf44922c2a8e9d5e055899f92bfe6aa221d23fafc0987165151d79.jpg", + "image_caption": [ + "w. Inpainting Network", + "Figure 5. The qualitative depth estimation results with or without inpainting network. The depth map estimated without inpainting network show artifacts in the human body region (see the red box)." + ], + "image_footnote": [], + "bbox": [ + 697, + 88, + 787, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/117661e42da7f43528682da4a98092897b83bd87164910b9b229c741b2722421.jpg", + "image_caption": [ + "GT Depth" + ], + "image_footnote": [], + "bbox": [ + 792, + 88, + 883, + 157 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "accuracy of our predicted pose benefits from better depth maps, but still our estimated scene depth already provides a significant improvement over the baselines.", + "bbox": [ + 496, + 248, + 890, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we compare with a baseline method without depth inpainting, i.e., the human body is removed from the input image and the scene depth map is predicted directly with the network $\\mathcal{D}$ in Sec. 3.2. The pose estimation accuracy is shown in \"Ours+Depth w/o Inpainting\" of Table 3 and the depth accuracy is shown in Table 4. Our method outperforms the baseline as it is more challenging to simultaneously estimate and inpaint the depth. Moreover, the network can be influenced by the segmented part in the input image as some extinct object, as shown in Fig 5.", + "bbox": [ + 496, + 292, + 892, + 445 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c1dd0c6db0f7b30e3167605f6cbef0050e3067f92c477e7965f5cf0e42242574.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodAbs-RelRMSE(m)
w/o Inpainting Network0.38340.7856
Ours0.10690.3365
", + "bbox": [ + 501, + 455, + 890, + 503 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. The quantitative results of depth estimator. We evaluate Abs-Rel and RMSE on our test dataset following [11].", + "bbox": [ + 500, + 526, + 890, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 573, + 617, + 588 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed a new approach to estimate egocentric human pose under the scene constraint. We firstly train a depth inpainting network for estimating the depth map of the scene without human body. Next, we combine the egocentric 2D features and scene depth map in a volumetric space and predict the egocentric pose with a V2V network. The experiments show that our method outperforms all of the baseline methods both qualitatively and quantitatively and our method can predict physically plausible poses in terms of human-scene interaction. In future, this method could be extended to estimate physically-plausible egocentric motion from a temporal sequence.", + "bbox": [ + 496, + 598, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. The accuracy of voxel-based pose estimation network is constrained by the accuracy of estimated depth, especially where the scene is occluded by the human body. One solution is to leverage the temporal information to get a full view of the surrounding environment.", + "bbox": [ + 496, + 779, + 890, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments Jian Wang, Diogo Luvizon, Lingjie Liu, and Christian Theobalt have been supported by the ERC Consolidator Grant 4DReply (770784).", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "13038", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Hiroyasu Akada, Jian Wang, Soshi Shimada, Masaki Takahashi, Christian Theobalt, and Vladislav Golyanik. Unrealego: A new dataset for robust egocentric 3d human motion capture. 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In 2021 International Conference on 3D Vision (3DV), pages 32-41, 2021. 2" + ], + "bbox": [ + 501, + 92, + 893, + 515 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "13040", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Scene-Aware Egocentric 3D Human Pose Estimation/3a95f507-702b-4e70-9e9b-d135557d5128_model.json b/2023/Scene-Aware Egocentric 3D Human Pose Estimation/3a95f507-702b-4e70-9e9b-d135557d5128_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3d2c47cf34aed22a44b50bbe4d36a0178b17d71f --- /dev/null +++ b/2023/Scene-Aware Egocentric 3D Human Pose Estimation/3a95f507-702b-4e70-9e9b-d135557d5128_model.json @@ -0,0 +1,2321 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.22, + 0.131, + 0.75, + 0.154 + ], + "angle": 0, + "content": "Scene-aware Egocentric 3D Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.179, + 0.754, + 0.2 + ], + "angle": 0, + "content": "Jian Wang\\(^{1,2}\\) Diogo Luvizon\\(^{1,2}\\) Weipeng Xu\\(^{3}\\) Lingjie Liu\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.307, + 0.199, + 0.663, + 0.216 + ], + "angle": 0, + "content": "Kripasindhu Sarkar\\(^{4}\\) Christian Theobalt\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.151, + 0.216, + 0.821, + 0.235 + ], + "angle": 0, + "content": "\\(^{1}\\)MPI Informatics \\({ }^{2}\\)Saarland Informatics Campus \\({ }^{3}\\)Meta Reality Labs \\({ }^{4}\\)Google" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.237, + 0.867, + 0.253 + ], + "angle": 0, + "content": "{jianwang,dluvizon,lliu,theobalt}@mpi-inf.mpg.de xuweipeng@fb.com krsarkar@google.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.474, + 0.742 + ], + "angle": 0, + "content": "Egocentric 3D human pose estimation with a single head-mounted fisheye camera has recently attracted attention due to its numerous applications in virtual and augmented reality. Existing methods still struggle in challenging poses where the human body is highly occluded or is closely interacting with the scene. To address this issue, we propose a scene-aware egocentric pose estimation method that guides the prediction of the egocentric pose with scene constraints. To this end, we propose an egocentric depth estimation network to predict the scene depth map from a wide-view egocentric fisheye camera while mitigating the occlusion of the human body with a depth-inpainting network. Next, we propose a scene-aware pose estimation network that projects the 2D image features and estimated depth map of the scene into a voxel space and regresses the 3D pose with a V2V network. The voxel-based feature representation provides the direct geometric connection between 2D image features and scene geometry, and further facilitates the V2V network to constrain the predicted pose based on the estimated scene geometry. To enable the training of the aforementioned networks, we also generated a synthetic dataset, called EgoGTA, and an inthe-wild dataset based on EgoPW, called EgoPW-Scene. The experimental results of our new evaluation sequences show that the predicted 3D egocentric poses are accurate and physically plausible in terms of human-scene interaction, demonstrating that our method outperforms the state-of-the-art methods both quantitatively and qualitatively." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.77, + 0.21, + 0.785 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Egocentric 3D human pose estimation with head- or body-mounted cameras is extensively researched recently because it allows capturing the person moving around in a large space, while the traditional pose estimation methods can only record in a fixed volume. With this advantage, the egocentric pose estimation methods show great potential in various applications, including the xR technologies and mo" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.286, + 0.627, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.294, + 0.756, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.294, + 0.885, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.381, + 0.627, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.472, + 0.586, + 0.484 + ], + "angle": 0, + "content": "Image" + }, + { + "type": "image", + "bbox": [ + 0.639, + 0.391, + 0.755, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.676, + 0.472, + 0.717, + 0.484 + ], + "angle": 0, + "content": "EgoPW" + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.392, + 0.885, + 0.47 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.811, + 0.472, + 0.839, + 0.482 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.494, + 0.895, + 0.58 + ], + "angle": 0, + "content": "Figure 1. Previous egocentric pose estimation methods like EgoPW predict body poses that may suffer from body floating issue (the first row) or body-environment penetration issue (the second row). Our method predicts accurate and plausible poses complying with the scene constraints. The red skeletons are the ground truth poses and the green skeletons are the predicted poses." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.61, + 0.691, + 0.625 + ], + "angle": 0, + "content": "bile interaction applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.893, + 0.853 + ], + "angle": 0, + "content": "In this work, we estimated the full 3D body pose from a single head-mounted fisheye camera. A number of works have been proposed, including \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39], \\(x\\mathrm{R}\\) -egopose [32], Global-EgoMocap [36], and EgoPW [35]. These methods have made significant progress in estimating egocentric poses. However, when taking account of the interaction between the human body and the surrounding environment, they still suffer from artifacts that contrast the physics plausibility, including body-environment penetrations or body floating (see the EgoPW results in Fig. 1), which is mostly ascribed to the ambiguity caused by the self-occluded and highly distorted human body in the egocentric view. This problem will render restrictions on subsequent applications including action recognition, humanobject interaction recognition, and motion forecasting." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "To address this issue, we propose a scene-aware pose estimation framework that leverages the scene context to constrain the prediction of an egocentric pose. This frame-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13031" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "work produces accurate and physically plausible 3D human body poses from a single egocentric image, as illustrated in Fig. 1. Thanks to the wide-view fisheye camera mounted on the head, the scene context can be easily obtained even with only one egocentric image. To this end, we train an egocentric depth estimator to predict the depth map of the surrounding scene. In order to mitigate the occlusion caused by the human body, we predict the depth map including the visible human and leverage a depth-inpainting network to recover the depth behind the human body." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.438 + ], + "angle": 0, + "content": "Next, we combine the projected 2D pose features and scene depth in a common voxel space and regress the 3D body pose heatmaps with a V2V network [22]. The 3D voxel representation projects the 2D poses and depth information from the distorted fisheye camera space to the canonical space, and further provides direct geometric connection between 2D image features and 3D scene geometry. This aggregation of 2D image features and 3D scene geometry facilitates the V2V network to learn the relative position and potential interactions between the human body joints and the surrounding environment and further enables the prediction of plausible poses under the scene constraints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.472, + 0.529 + ], + "angle": 0, + "content": "Since no available dataset can be used for train these networks, we proposed EgoGTA, a synthetic dataset based on the motion sequences of GTA-IM [3], and EgoPW-Scene, an in-the-wild dataset based on EgoPW [35]. Both of the datasets contain body pose labels and scene depth map labels for each egocentric frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.473, + 0.696 + ], + "angle": 0, + "content": "To better evaluate the relationship between estimated egocentric pose and scene geometry, we collected a new test dataset containing ground truth joint positions in the egocentric view. The evaluation results on the new dataset, along with results on datasets in Wang et al. [36] and \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39] demonstrate that our method significantly outperforms existing methods both quantitatively and qualitatively. We also qualitatively evaluate our method on inthe-wild images. The predicted 3D poses are accurate and plausible even in challenging real-world scenes. To summarize, our contributions are listed as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.704, + 0.468, + 0.749 + ], + "angle": 0, + "content": "- The first scene-aware egocentric human pose estimation framework that predicts accurate and plausible egocentric pose with the awareness of scene context;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.758, + 0.468, + 0.788 + ], + "angle": 0, + "content": "- Synthetic and in-the-wild egocentric datasets containing egocentric pose labels and scene geometry labels;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.798, + 0.468, + 0.828 + ], + "angle": 0, + "content": "- A new depth estimation and inpainting networks to predict the scene depth map behind the human body;" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.837, + 0.468, + 0.867 + ], + "angle": 0, + "content": "- By leveraging a voxel-based representation of body pose features and scene geometry jointly, our method" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.704, + 0.468, + 0.867 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "outperforms the previous approaches and generates plausible poses considering the scene context." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.137, + 0.642, + 0.153 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.162, + 0.853, + 0.178 + ], + "angle": 0, + "content": "2.1. Egocentric 3D Full Body Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.186, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Inspired by the new applications in augmented reality and by the limitations of traditional motion capture systems, Rhodin et al. [26] proposed the first egocentric motion capture system based on a pair of fisheye cameras. The following methods proposed new architectures [4,47] and new datasets [1,47] for stereo egocentric pose estimation. However, a stereo camera setup implies additional computation complexity and extra energy consumption, which is critical for low-power head-mounted devices, which are the main target applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.893, + 0.624 + ], + "angle": 0, + "content": "The single head-mounted fisheye camera setup was first proposed by Xu et al. [39], who also introduced a two-stream CNN to cope with the low resolution of regions far from the fisheye camera, i.e., one branch for the full body and one branch for predicting the lower body joints from a zoom-in image. Tome et al. [32] proposed an encoder-decoder architecture to model the high uncertainty caused by severe occlusions present in this setup and Wang et al. [36] leverages motion capture data to learn a human motion prior, which is applied in an optimization method to obtain temporally stable poses for training and egocentric pose predictor. Another challenge is the strong image distortion caused by the fisheye lens, which can be mitigated with automatic camera calibration [46]. Other setups consider the camera facing forward and try to synthesize plausible human motion given only scene image evidences [18] or partially visible body parts [13, 15]. In our work, we do not consider this setup since in many poses only a few body extremities are visible in the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.777 + ], + "angle": 0, + "content": "Obtaining real data in the egocentric setup is a time consuming process, therefore, many approaches rely on synthetic data for training [15,32]. A recent method has shown that the existing gap between synthetic and real data can be mitigated by domain adaptation techniques [35], but this approach still requires real data for the weak supervision part. Differently, our method has a simpler training strategy, and we reduce the gap between synthetic and real data by providing additional pseudo ground-truth scene labels for real sequences, including indoor and outdoor scenes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.892, + 0.803 + ], + "angle": 0, + "content": "2.2. Voxel Representation for Body Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Volumetric voxel representations have been extensively used with multiple view setups for the estimation of single [31, 33] and multiple human poses [34, 37, 40, 45], and for hand pose estimation [12, 19-21] from depth maps input. Considering a single image as input, Pavlakos et al. [25] proposed a coarse-to-fine approach to lift from 2D" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "1Datasets are released in our project page. Meta did not access or process the data and is not involved in the dataset release." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13032" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.098, + 0.093, + 0.235, + 0.105 + ], + "angle": 0, + "content": "Sec. 3.1 Training Dataset" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.107, + 0.268, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.091, + 0.37, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.395, + 0.093, + 0.558, + 0.105 + ], + "angle": 0, + "content": "Sec. 3.2 Scene Depth Estimator" + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.106, + 0.872, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.258, + 0.351, + 0.271 + ], + "angle": 0, + "content": "Sec. 3.3 Scene-aware Egocentric Pose Estimator" + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.256, + 0.875, + 0.452 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.462, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Figure 2. Overview of our method. We first render synthetic training dataset EgoGTA and in-the-wild training dataset EgoPW-Scene. Both datasets contain egocentric depth maps for subsequent training process (Sec. 3.1). Next, we train an egocentric scene depth estimator that predicts a depth map without the human body and a depth inpainting network (Sec. 3.2). Finally, we combine the 2D body pose features and scene depth map into a common voxel space. The 3D body pose heatmaps are regressed from the voxel space with a V2V network and the final pose prediction is obtained with soft-argmax (Sec. 3.3)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.724 + ], + "angle": 0, + "content": "heatsmaps to a voxel representation for 3D human pose estimation. Iskakov [14] later proposed a learnable triangulation method in voxel space that can generalize to single or multiple views, achieving less than \\(2\\mathrm{cm}\\) error in a controlled multi-view data. Despite the success of voxel representation for human and hand pose estimation from an external camera, this technique has not yet been explored for the interaction between human body and scene. In our work, we show the advantages of this representation for egocentric human pose estimation, especially when considering human-scene interaction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.4, + 0.755 + ], + "angle": 0, + "content": "2.3. Scene-aware Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In recent years, several approaches have been proposed to predict the pose of humans considering environmental and physical constraints from RGB [24, 30, 41] and inertial measurement units (IMU) [9, 42]. Some methods assume a simplified environment, such as a planar ground floor, to enforce a temporal sequence that is physically consistent with the universal law of gravity by assuming known camera poses [29, 30] or by tracking an object in the scene following a free flight trajectory [6]. Other approaches assume" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.892, + 0.786 + ], + "angle": 0, + "content": "that the scene is given as input, either as a 3D reconstruction [9,28] or as geometric primitives [43], whose positions can be refined in the optimization process. Bhatnagar et al. [2] proposed a method and dataset for human-object interactions. Taking into account the interaction between humans and furniture, holistic methods are able to estimate the position of humans and specific objects in the scene under the assumption of a planar floor [5, 38, 41], or even to estimate deformations in known objects based on human poses [17]. Contrary to the previous work, we make no strong assumptions about the objects and ground floor in the scene, but instead propose a method that learns to estimate the background scene geometry from a fisheye camera and explores the correlation between the human body and scene directly from egocentric data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.591, + 0.815 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We propose a new method for predicting accurate ego-centric body pose by leveraging the estimated scene geometry. An overview of our method is shown in Fig. 2. In order to train the scene-aware network, we first generate a synthetic dataset based on the GTA-IM dataset [3], called" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "13033" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.213 + ], + "angle": 0, + "content": "EgoGTA, and an in-the-wild dataset based on the EgoPW dataset [35], called EgoPW-Scene (Sec. 3.1). Next, we train a depth estimator to estimate the geometry of the surrounding scene and introduce the depth-inpainting network that estimates the depth behind the human body (Sec. 3.2). Finally, we combine 2D features and scene geometry in a common voxel space and predict the egocentric pose with a V2V network [22] (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.221, + 0.245, + 0.238 + ], + "angle": 0, + "content": "3.1. Training Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.244, + 0.473, + 0.381 + ], + "angle": 0, + "content": "Although many training datasets for egocentric pose estimation [32,35,39] have been proposed, they cannot yet train the scene-aware egocentric pose estimation network due to the lack of scene geometry information. To solve this, we introduce the EgoGTA dataset and EgoPW-Scene dataset (both will be made publicly available). Both datasets contain pose labels and depth maps of the scene for each egocentric frame, facilitating our training process. We show examples from both datasets, as illustrated in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.398, + 0.25, + 0.414 + ], + "angle": 0, + "content": "3.1.1 EgoGTA Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.473, + 0.664 + ], + "angle": 0, + "content": "In order to obtain precise ground truth human pose and scene geometry for training, we devise a new synthetic ego-centric dataset based on GTA-IM [3], which contains various daily motions and ground truth scene geometry. For this, we first fit the SMPL-X model on the 3D joint trajectories from GTA-IM. Next, we attach a virtual fisheye camera to the forehead of the SMPL-X model and render the images, semantic labels, and depth map of the scene with and without the human body. In total, we obtained \\(320\\mathrm{K}\\) frames in 101 different sequences, each with a different human body texture. Here, we denote the EgoGTA dataset \\(\\mathbb{S}_G = \\{I_G,S_G,D_G^B,D_G^S,P_G\\}\\), including synthetic images \\(I_{G}\\) and their corresponding human body segmentation maps \\(S_{G}\\), depth map with human body \\(D_G^B\\), depth map of the scene without human body \\(D_G^S\\), and egocentric pose labels \\(P_{G}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.681, + 0.287, + 0.697 + ], + "angle": 0, + "content": "3.1.2 EgoPW-Scene Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Since we want to generalize to data captured with a real head-mounted camera, we also extended the EgoPW [35] training dataset. For this, we first reconstruct the scene geometry from the egocentric image sequences of the EgoPW training dataset with a Structure-from-Motion (SfM) algorithm [10]. This step provides a dense reconstruction of the background scene. The global scale of the reconstruction is recovered from known objects present in the sequences, such as laptops and chairs. We further render the depth maps of the scene in the egocentric perspective based on the reconstructed geometry. Our EgoPW-Scene dataset contains \\(92\\mathrm{K}\\) frames in total, which are distributed in 30 sequences performed by 5 actors. The number of frames in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.169 + ], + "angle": 0, + "content": "the EgoPW-Scene dataset is less than EgoPW dataset since SfM fails on some sequences. Here, we denote the EgoPW-Scene dataset \\(\\mathbb{S}_E = \\{I_E, D_E^S, P_E\\}\\), including in-the-wild images \\(I_E\\) and their corresponding depth map of the scene without human body \\(D_E^S\\), and egocentric pose labels \\(P_E\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.18, + 0.715, + 0.195 + ], + "angle": 0, + "content": "3.2. Scene Depth Estimator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.203, + 0.892, + 0.476 + ], + "angle": 0, + "content": "In this section, we propose a depth estimation method to capture the scene geometry information in the egocentric perspective. Available depth estimation methods [7, 11, 16] can only generate depth maps with the human body, but are not able to infer the depth information behind the human, i.e., the background scene depth. However, the area occluded by the human body, e.g. the areas of foot contact, are crucial for generating plausible poses, as demonstrated in Sec. 4.4. To predict the depth map of the scene behind the human body, we adopt a two-step approach. More specifically, we first estimate the depth map including the human body and the semantic segmentation of the human with two separated models. Then, we use a depth inpainting network to recover the depth behind the human body. This two-step strategy is necessary because the human visual evidences in the RGB images are too strong to be ignored by the depth estimator, therefore, it is easier to train the scene depth estimation as separated tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.597 + ], + "angle": 0, + "content": "We first train the depth estimator network \\(\\mathcal{D}\\), which takes as input a single egocentric image \\(I\\) and predicts the depth map with human body \\(\\hat{D}^B\\). The network architecture of \\(\\mathcal{D}\\) is the same as Hu et al. [11]'s work. To minimize the influence of the domain gap between synthetic and real data, the network is initially trained on the NYU-Depth V2 dataset [23] following [11], and further fine-tuned on the EgoGTA dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.75 + ], + "angle": 0, + "content": "Next, we train the segmentation network \\( S \\) for segmenting the human body. The network takes the egocentric image \\( I \\) as input and predicts the segmentation mask for the human body \\( \\hat{S} \\) as output. Following Yuan et al. [44], we use HRNet as our segmentation network. Similarly, to reduce the domain gap, we pretrain the network on the LIP dataset [8] and finetune the model on the EgoGTA dataset. We do not train network \\( \\mathcal{D} \\) and \\( S \\) on the EgoPW-Scene dataset since it lacks the ground truth segmentation maps and depth maps with the human body." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Finally, we propose a depth inpainting network \\(\\mathcal{G}\\) for generating the final depth map of the scene without human body. We first generate the masked depth map \\(\\hat{D}^M = (1 - \\hat{S})\\odot \\hat{D}^B\\), which is a Hadamard product between the background segmentation and the depth map with human body. Then, the masked depth map \\(\\hat{D}^M\\) and the segmentation mask \\(\\hat{S}\\) are fed into the inpainting network \\(\\mathcal{G}\\), which predicts the final depth map \\(\\hat{D}^S\\). We train the inpainting network \\(\\mathcal{G}\\) and finetune the depth estimation network \\(\\mathcal{D}\\) on both the EgoGTA and EgoPW-Scene datasets. During" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13034" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.168 + ], + "angle": 0, + "content": "training, we penalize the differences between the predicted depth maps and the ground truth depth of the background scene with \\( L^S \\) and also keep the depth map consistent in the non-human body regions with \\( L^C \\). Specifically, the loss function is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.173, + 0.469, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L = \\lambda^ {S} L ^ {S} + \\lambda^ {C} L ^ {C}, \\quad \\text {w i t h} \\\\ L ^ {S} = \\left\\| \\hat {D} _ {G} ^ {S} - D _ {G} ^ {S} \\right\\| _ {2} ^ {2} + \\left\\| \\hat {D} _ {E} ^ {S} - D _ {E} ^ {S} \\right\\| _ {2} ^ {2}, \\quad \\text {a n d} \\\\ L ^ {C} = \\left\\| \\left(\\hat {D} _ {G} ^ {S} - \\hat {D} _ {G} ^ {B}\\right) \\left(1 - \\hat {S} _ {G}\\right) \\right\\| _ {2} ^ {2} \\tag {1} \\\\ + \\left\\| \\left(\\hat {D} _ {E} ^ {S} - \\hat {D} _ {E} ^ {B}\\right) \\left(1 - \\hat {S} _ {E}\\right) \\right\\| _ {2} ^ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.294, + 0.124, + 0.306 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.314, + 0.415, + 0.334 + ], + "angle": 0, + "content": "\\[\n\\hat {D} _ {G} ^ {S} = \\mathcal {G} (\\hat {D} _ {G} ^ {M}, \\hat {S} _ {G}); \\quad \\hat {D} _ {E} ^ {S} = \\mathcal {G} (\\hat {D} _ {E} ^ {M}, \\hat {S} _ {E});\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.337, + 0.469, + 0.356 + ], + "angle": 0, + "content": "\\[\n\\hat {D} _ {G} ^ {B} = \\mathcal {D} (I _ {G}); \\quad \\hat {D} _ {E} ^ {B} = \\mathcal {D} (I _ {E}); \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.358, + 0.378, + 0.377 + ], + "angle": 0, + "content": "\\[\n\\hat {S} _ {G} = \\mathcal {S} (I _ {G}); \\quad \\hat {S} _ {E} = \\mathcal {S} (I _ {E}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.387, + 0.4, + 0.403 + ], + "angle": 0, + "content": "and \\(\\lambda^S\\) and \\(\\lambda^C\\) are the weights of the loss terms." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.412, + 0.419, + 0.427 + ], + "angle": 0, + "content": "3.3. Scene-aware Egocentric Pose Estimator" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.435, + 0.47, + 0.692 + ], + "angle": 0, + "content": "In this section, we introduce our scene-aware egocentric pose estimator. We rely on the prior that human bodies are mostly in contact with the scene. However, estimating the contact explicitly from a single egocentric image is very challenging. Therefore, we rely on a data-driven approach by learning a model that predicts a plausible 3D pose given the estimated scene geometry and features extracted from the input image. To achieve this goal, we first leverage the EgoPW [35] body joints heatmap estimator to extract 2D body pose features \\( F \\) and use the scene depth estimator from Sec. 3.2 to estimate the depth map of the scene without human body \\( \\hat{D}^S \\). Afterwards, we project the body pose features and depth map into a 3D volumetric space considering the fisheye camera projection model. After obtaining the volumetric representation of human body features \\( V_{\\mathrm{body}} \\) and scene depth \\( V_{\\mathrm{scene}} \\), the 3D body pose \\( \\hat{P} \\) is predicted from the volumetric representation with a V2V network [22]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.47, + 0.799 + ], + "angle": 0, + "content": "Lifting the image features and depth maps to a 3D representation allows getting more plausible results, as inconsistent joint predictions can be behind the volumetric scene \\( V_{\\mathrm{scene}} \\) (pose-scene penetration) or spatially isolated from the voxelized scene geometry (pose floating), so they can be easily identified and adjusted by the volumetric convolutional network." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.424, + 0.832 + ], + "angle": 0, + "content": "3.3.1 Scene and Body Encoding as a 3D Volume" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In order to create the volumetric space, we first create a 3D bounding box around the person in the egocentric camera coordinate system of size \\( L \\times L \\times L \\), where \\( L \\) denotes the length of the side of the bounding box in meters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "The egocentric camera is placed at the center-top of the 3D bounding box so that the vertices of the bounding boxes are: \\((\\pm L / 2, \\pm L / 2, 0)\\) and \\((\\pm L / 2, \\pm L / 2, L)\\) under the egocentric camera coordinate system. Next, we discretize the bounding box by a volumetric cube \\(V \\in R^{N,N,N,3}\\). Each voxel \\(V_{xyz} \\in R^3\\) in position \\((x,y,z)\\) is filled with the coordinates of its center under the egocentric camera coordinate system \\((xL / N - L / 2, yL / N - L / 2, zL / N)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.892, + 0.32 + ], + "angle": 0, + "content": "We project the 3D coordinates in \\(V\\) into the egocentric image space with the fisheye camera model [27]: \\(V_{\\mathrm{proj}} = \\mathcal{P}(V)\\), where \\(V_{\\mathrm{proj}} \\in R^{N,N,N,2}\\) and \\(\\mathcal{P}\\) is the fisheye camera projection function. The volumetric representation \\(V_{\\mathrm{body}}\\) of the human body is obtained by filling a cube \\(V_{\\mathrm{body}} \\in R^{N,N,N,K}\\) by bilinear sampling from the feature maps \\(F\\) with \\(K\\) channels using 2D coordinates in \\(V_{\\mathrm{proj}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.327, + 0.892, + 0.344 + ], + "angle": 0, + "content": "\\[\nV _ {\\text {b o d y}} = F \\left\\{V _ {\\text {p r o j}} \\right\\} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.351, + 0.746, + 0.366 + ], + "angle": 0, + "content": "where \\(\\{\\cdot\\}\\) denotes bilinear sampling." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.486 + ], + "angle": 0, + "content": "Then, we project the depth map to the 3D volumetric space. We first generate the point cloud of the scene geometry \\(C\\) from the depth map \\(\\hat{D}^S\\) with the fisheye camera projection function \\(C = \\mathcal{P}^{-1}(\\hat{D}^S)\\). The volumetric representation of scene depth map \\(V_{\\mathrm{scene}}\\) is obtained by filling a binary cube \\(V_{\\mathrm{scene}} \\in R^{N,N,N}\\) by setting the voxel at \\((x,y,z)\\) to 1 if there exists one point \\((x_p,y_p,z_p)\\) in the point cloud \\(C\\) such that:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.491, + 0.892, + 0.526 + ], + "angle": 0, + "content": "\\[\n\\left\\| \\left(\\frac {x L}{N} - \\frac {L}{2}, \\frac {y L}{N} - \\frac {L}{2}, \\frac {z L}{N}\\right) - \\left(x _ {p}, y _ {p}, z _ {p}\\right) \\right\\| < \\epsilon \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.592 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is the threshold distance. In our experiment, we set \\(L = 2.4\\mathrm{m}\\), \\(N = 64\\), and \\(\\epsilon = 0.04\\mathrm{m}\\). This setting can cover most types of the human motions and allows high accuracy of the predicted body pose." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.609, + 0.862, + 0.625 + ], + "angle": 0, + "content": "3.3.2 Predicting 3D Body Pose with V2V Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.633, + 0.892, + 0.694 + ], + "angle": 0, + "content": "We feed the volumetric representation aggregated from \\( V_{\\mathrm{body}} \\) and \\( V_{\\mathrm{scene}} \\) into the volumetric convolutional network \\( \\mathcal{N} \\), which has a similar architecture as [22]. The V2V network produces the 3D heatmaps of the body joints:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.701, + 0.891, + 0.719 + ], + "angle": 0, + "content": "\\[\nV _ {\\text {h e a t m a p}} = \\mathcal {N} \\left(V _ {\\text {b o d y}}, V _ {\\text {s c e n e}}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.726, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Following [14], we compute the soft-argmax of \\( V_{\\mathrm{heatmap}} \\) across the spatial axes to infer the body pose \\( \\hat{P} \\). The predicted pose \\( \\hat{P} \\) is finally compared with the ground truth pose \\( P_G \\) from the EgoGTA dataset and \\( P_E \\) from the EgoPW-Scene dataset with the MSE loss." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.816, + 0.634, + 0.833 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we evaluate our method considering existing and new datasets for egocentric monocular 3D human pose estimation. Please refer to the supplementary materials for the implementation details." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13035" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.088, + 0.484, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.089, + 0.885, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.893, + 0.372 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison between our method and the state-of-the-art egocentric pose estimation methods. From left to right: input image, \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) result, \\(x\\mathrm{R}\\) -egopose result, EgoPW result and our result. The ground truth pose is shown in red. The input images from the left part are from our test dataset, while those in the right part come from the EgoPW [35] in-the-wild test sequences (without ground-truth poses). We also show the gt scene geometry of the in-the-studio data and scene geometry obtained by SFM method for the in-the-wild data. For better visualizing the interaction between human body and environment, please refer to our supplementary video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.387, + 0.267, + 0.401 + ], + "angle": 0, + "content": "4.1. Evaluation Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.474, + 0.657 + ], + "angle": 0, + "content": "Evaluating human-scene interaction requires precise annotations for camera pose and scene geometry. However, such information is not available in existing datasets for egocentric human pose estimation. To solve this issue, we collected a new real-world dataset using a head-mounted fisheye camera combined with a calibration board. The ground truth scene geometry is obtained with SfM method [10] from a multi-view capture system with 120 syncd 4K resolution cameras and the ground truth egocentric camera pose is obtained by localizing a calibration board rigidly attached to the egocentric camera. This dataset contains around 14K frames of two actors, performing various human-scene interacting motions such as sitting, reading newspaper, and using a computer. This dataset will be made publicly available and additional details of it are shown in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.471, + 0.754 + ], + "angle": 0, + "content": "Besides our new test dataset, we also evaluate our methods in the test datasets from Wang et al. [36] and \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39]. The real-world dataset in \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39] contains 2.7K frames of two people captured in indoor and outdoor scenes, and the dataset in Wang et al. [36] contains 12K frames of two people captured in the studio." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.781, + 0.262, + 0.795 + ], + "angle": 0, + "content": "4.2. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We measure the accuracy of the estimated body pose with the MPJPE and PA-MPJPE. For the test dataset in Wang et al. [36] and \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39], we evaluate PA-MPJPE and BA-MPJPE [39] since the ground truth poses in the egocentric camera space are not provided. Further details of the metrics are shown in the supplementary materials." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.384, + 0.891, + 0.631 + ], + "angle": 0, + "content": "
MethodMPJPEPA-MPJPE
Our test dataset
Mo2Cap2 [39]200.3121.2
xR-egopose [32]241.3133.9
EgoPW [35]189.6105.3
Ours118.592.75
MethodPA-MPJPEBA-MPJPE
Wang et al.'s dataset [36]
Mo2Cap2 [39]102.374.46
xR-egopose [32]112.087.20
EgoPW [35]81.7164.87
Ours76.5061.92
Mo2Cap2 test dataset [39]
Mo2Cap2 [39]91.1670.75
xR-egopose [32]86.8566.54
EgoPW [35]83.1764.33
Ours79.6562.82
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.653, + 0.894, + 0.71 + ], + "angle": 0, + "content": "Table 1. Performance of our method on our test dataset, Wang et al.'s test dataset [36] and \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) test dataset [39]. Our method outperforms the state-of-the-art methods EgoPW, \\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39] and \\(xR\\)-egopose [32]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.816, + 0.741 + ], + "angle": 0, + "content": "4.3. Comparisons on 3D Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we compare our approach with previous single-frame-based methods, including EgoPW [35], \\( x \\)Regopose [32] and \\( \\mathrm{Mo}^2\\mathrm{Cap}^2 \\) [39] on our test dataset under the \"Our test data\" in Table 1. Since the code for \\( x \\)Regopose is not released, we use our implementation for the evaluation. In our dataset, the proposed method outperforms the previous state-of-the-art methods, EgoPW [35] by \\( 37.5\\% \\) on MPJPE and \\( 11.9\\% \\) on PA-MPJPE. We also compared with previous methods on the Wang et al.'s test dataset [36] and \\( \\mathrm{Mo}^2\\mathrm{Cap}^2 \\) test dataset [39] and show the re" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13036" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.468, + 0.165 + ], + "angle": 0, + "content": "
MethodNon pene.Contact
Mo2Cap2 [39]69.6%23.1%
xR-egopose [32]64.5%38.3%
EgoPW [35]71.7%38.8%
Ours84.1%89.4%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.08, + 0.187, + 0.466, + 0.202 + ], + "angle": 0, + "content": "Table 2. Comparisons of physical plausibility on our test dataset." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.218, + 0.462, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.374, + 0.47, + 0.417 + ], + "angle": 0, + "content": "Figure 4. Predicted pose with different scene depth map input. Our network can generate different poses under different depth input and further disambiguate body poses under scene constraint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.469, + 0.49 + ], + "angle": 0, + "content": "sults in Table 1. On Wang et al.'s test dataset, our method performs better than EgoPW by \\(6.4\\%\\). On the \\(\\mathrm{Mo}^{2}\\mathrm{Cap}^{2}\\) test dataset, our method performs better than EgoPW by \\(7.8\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.469, + 0.627 + ], + "angle": 0, + "content": "We also evaluate the physical plausibility of our predictions by calculating the percentage of predicted poses that are in contact with the scene and do not penetrate the scene in Table 2. We define a body pose as in contact with the scene if any body joint is less than \\(5\\mathrm{cm}\\) from the scene mesh. A body pose suffers from the body floating issue if it is not in contact with the scene. Compared with previous approaches, our method generates body poses more physically plausible considering the constraints of the scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.469, + 0.764 + ], + "angle": 0, + "content": "From the results in Table 1 and Table 2, we can see that our approach outperforms all previous methods on the single-frame egocentric pose estimation task. For the qualitative comparison, we show the results of our method on the studio dataset and in-the-wild sequences in Fig. 3. See our supplementary video for more qualitative evaluations. Our predicted poses are physically plausible under the scene constraint, whereas other methods generate poses suffering from body floating and penetration issues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In order to further demonstrate our method performing predictions accordingly to the constraint of the scene geometry, we fix the input image and change the scene depth input to the depth map corresponding to the standing pose, squatting pose, and sitting pose. The results are presented in Fig. 4 and show that the predicted poses change to standing, squatting, and sitting to better adapt to the input changes of the scene geometry. This shows our method's ability to disambiguate poses under different scene constraints." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.089, + 0.891, + 0.235 + ], + "angle": 0, + "content": "
MethodMPJPEPA-MPJPE
EgoPW+Optimizer187.1103.2
EgoPW+Depth149.698.15
xR-egopose+Depth180.5103.7
Ours w/o Depth188.1105.1
Ours+Depth with Body167.3103.3
Ours+Depth w/o Body135.795.84
Ours+Depth w/o Inpainting124.295.00
Ours+GT Depth109.988.80
Ours118.592.75
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.257, + 0.891, + 0.272 + ], + "angle": 0, + "content": "Table 3. Results from our method compared to different baselines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.298, + 0.653, + 0.314 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.892, + 0.579 + ], + "angle": 0, + "content": "Simple Combination of 2D Features and Depth Maps. In Sec. 3.3, we claim that the volumetric representation of egocentric 2D features and scene depth map is important for understanding the interaction between the human body and the surrounding scene. To provide evidence of this claim, in this experiment, we compare our method with baseline methods that simply combine the 2D image features and scene depth map. We set two baseline methods since there are two types of egocentric pose estimation methods, i.e. direct regression of 3D poses (\\(x\\)-R-egopose [32]) and prediction of 2D position and depth for each joint (\\(\\mathrm{Mo}^2\\mathrm{Cap}^2\\) [39] and EgoPW [35]). In the baseline method “\\(x\\)-R-egopose + Depth”, we concatenate 2D heatmaps and scene depth map as the input to the 3D pose regression network in \\(x\\)-R-egopose. In the baseline “EgoPW + Depth”, we concatenate the 2D features and the scene depth map and input them into the joint depth prediction network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.761 + ], + "angle": 0, + "content": "From the evaluation results shown in Table 3, both of the baseline methods perform worse than our proposed method. In \"xR-egopose + Depth\", simply combining the scene depth and 2D heatmaps cannot provide direct geometric supervision for the 3D pose regression network. In \"EgoPW + Depth\", though the joint depth estimation network performs better with the help of scene depth information, the 2D pose estimation network does not benefit from it. Both of the experiments demonstrate the effectiveness of our volumetric representation of 2D features and scene geometry, which provides direct geometry supervision for the physical plausibility of predicted egocentric poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Optimization. In this experiment, we compare our method with an optimization baseline that refines a 3D pose considering the scene constraint. Similar to Wang et al. [36] and EgoPW [35], we first train a VAE consisting of a CNN-based encoder \\( f_{\\mathrm{enc}} \\) and decoder \\( f_{\\mathrm{dec}} \\) to learn an egocentric motion prior. Then, We optimize the egocentric pose \\( P \\) by finding a latent vector \\( z \\) such that the corresponding pose \\( P = f_{\\mathrm{dec}}(z) \\) minimizes the objective function" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13037" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.243 + ], + "angle": 0, + "content": "\\(E(P) = \\lambda_{R}E_{R} + \\lambda_{J}E_{J} + \\lambda_{C}E_{C}\\), where \\(E_{R}\\) is the egocentric reprojection term, \\(E_{J}\\) is the egocentric pose regularization term, and \\(E_{C}\\) is the contact term. The latent vector \\(z\\) is initialized with the estimated pose from the EgoPW method. The \\(E_{R}\\) and \\(E_{J}\\) are the same as those defined in Wang et al. [36]. Denote the nth joint in egocentric pose \\(P\\) as \\(P_{n}, n \\in [0, N]\\), where \\(N\\) is the number of joints, and the mth point in scene point cloud \\(C\\) as \\(C_{m}, m \\in [0, M]\\), where \\(M\\) is the number of points in the point cloud. The contact term \\(E_{C}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.252, + 0.47, + 0.29 + ], + "angle": 0, + "content": "\\[\nE _ {C} = \\sum_ {n \\in [ 0, N ]} d _ {n} ^ {2}, \\quad \\text {i f} d _ {n} \\leq \\epsilon , \\text {o t h e r w i s e} 0, \\text {a n d} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.291, + 0.296, + 0.314 + ], + "angle": 0, + "content": "\\[\nd _ {n} = \\min _ {m \\in [ 0, M ]} \\| P _ {n} - C _ {m} \\| _ {2}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.47, + 0.399 + ], + "angle": 0, + "content": "We first calculate the nearest distance \\( d_{n} \\) between each body joint and the projected point cloud \\( C \\) from the scene depth map. If the distance \\( d_{n} \\) of the nth joint is less than a margin \\( \\epsilon \\), it is defined as in contact with the scene and minimized with the optimization framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.471, + 0.552 + ], + "angle": 0, + "content": "The result of the optimization method is shown as \"EgoPW+Optimizer\" in Table 3, which demonstrates that the optimization framework is less effective than our method. This is because the accuracy of optimization method relies heavily on the initial pose. If the initial pose is not accurate, it will be difficult to determine the contact labels for each joint with the fixed distance margin. Without accurate contact labels, the optimization framework might force the joint that does not contact the scene to keep in contact, eventually resulting in wrong poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.689 + ], + "angle": 0, + "content": "Scene Depth Estimator. In our work, we estimate the depth of the surrounding scene and infer the depth behind the human body with a depth inpainting network. In order to validate the effectiveness of the scene depth map, we remove the input depth map from the V2V network and show the results of \"Ours w/o Depth\" in Table 3. This baseline increases the MPJPE by about \\(70\\mathrm{mm}\\), which is evidence of the relevant extra information provided by the scene depth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.84 + ], + "angle": 0, + "content": "To demonstrate the benefits of recovering the scene depth behind the human body, we evaluate our model using the estimated depth including the human body as the input to the V2V network. We also removed the human body area from the depth maps and use them as input to the V2V network. The results are shown in \"Ours+Depth with Body\" and \"Ours+Depth w/o Body\" in Table 3. Both of the baseline methods perform worse than our method because the area in the scene occluded by the human body can provide clues for generating plausible poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We also evaluate our method with ground truth depth maps in \"Ours+GT Depth\" in Table 3, which further improves over our estimated depth by \\(7.2\\%\\) in terms of MPJPE and \\(4.2\\%\\) in terms of PA-MPJPE. This demonstrates that the" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.089, + 0.603, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.161, + 0.578, + 0.169 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.089, + 0.696, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.161, + 0.692, + 0.169 + ], + "angle": 0, + "content": "w/o Inpainting Network" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.089, + 0.789, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.703, + 0.161, + 0.783, + 0.169 + ], + "angle": 0, + "content": "w. Inpainting Network" + }, + { + "type": "image", + "bbox": [ + 0.793, + 0.089, + 0.885, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.161, + 0.856, + 0.169 + ], + "angle": 0, + "content": "GT Depth" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.181, + 0.894, + 0.223 + ], + "angle": 0, + "content": "Figure 5. The qualitative depth estimation results with or without inpainting network. The depth map estimated without inpainting network show artifacts in the human body region (see the red box)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.249, + 0.892, + 0.293 + ], + "angle": 0, + "content": "accuracy of our predicted pose benefits from better depth maps, but still our estimated scene depth already provides a significant improvement over the baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.893, + 0.446 + ], + "angle": 0, + "content": "Finally, we compare with a baseline method without depth inpainting, i.e., the human body is removed from the input image and the scene depth map is predicted directly with the network \\(\\mathcal{D}\\) in Sec. 3.2. The pose estimation accuracy is shown in \"Ours+Depth w/o Inpainting\" of Table 3 and the depth accuracy is shown in Table 4. Our method outperforms the baseline as it is more challenging to simultaneously estimate and inpaint the depth. Moreover, the network can be influenced by the segmented part in the input image as some extinct object, as shown in Fig 5." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.456, + 0.891, + 0.505 + ], + "angle": 0, + "content": "
MethodAbs-RelRMSE(m)
w/o Inpainting Network0.38340.7856
Ours0.10690.3365
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.527, + 0.892, + 0.556 + ], + "angle": 0, + "content": "Table 4. The quantitative results of depth estimator. We evaluate Abs-Rel and RMSE on our test dataset following [11]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.619, + 0.589 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.78 + ], + "angle": 0, + "content": "In this paper, we have proposed a new approach to estimate egocentric human pose under the scene constraint. We firstly train a depth inpainting network for estimating the depth map of the scene without human body. Next, we combine the egocentric 2D features and scene depth map in a volumetric space and predict the egocentric pose with a V2V network. The experiments show that our method outperforms all of the baseline methods both qualitatively and quantitatively and our method can predict physically plausible poses in terms of human-scene interaction. In future, this method could be extended to estimate physically-plausible egocentric motion from a temporal sequence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Limitations. The accuracy of voxel-based pose estimation network is constrained by the accuracy of estimated depth, especially where the scene is occluded by the human body. One solution is to leverage the temporal information to get a full view of the surrounding environment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments Jian Wang, Diogo Luvizon, Lingjie Liu, and Christian Theobalt have been supported by the ERC Consolidator Grant 4DReply (770784)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "13038" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Hiroyasu Akada, Jian Wang, Soshi Shimada, Masaki Takahashi, Christian Theobalt, and Vladislav Golyanik. Unrealego: A new dataset for robust egocentric 3d human motion capture. 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In 2021 International Conference on 3D Vision (3DV), pages 32-41, 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.894, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "13040" + } + ] +] \ No newline at end of file diff --git a/2023/Scene-Aware Egocentric 3D Human Pose Estimation/3a95f507-702b-4e70-9e9b-d135557d5128_origin.pdf b/2023/Scene-Aware Egocentric 3D Human Pose Estimation/3a95f507-702b-4e70-9e9b-d135557d5128_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..da8810e63d65003333750a3ea4eb710f7402497f --- /dev/null +++ b/2023/Scene-Aware Egocentric 3D Human Pose Estimation/3a95f507-702b-4e70-9e9b-d135557d5128_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0aa812d417e87ebd732c47669eca2c08fd8e78b441e6ac17295f06071a79baee +size 2298566 diff --git a/2023/Scene-Aware Egocentric 3D Human Pose Estimation/full.md b/2023/Scene-Aware Egocentric 3D Human Pose Estimation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b1ace36cf786707681675ab2542108b3feea80c2 --- /dev/null +++ b/2023/Scene-Aware Egocentric 3D Human Pose Estimation/full.md @@ -0,0 +1,336 @@ +# Scene-aware Egocentric 3D Human Pose Estimation + +Jian Wang $^{1,2}$ Diogo Luvizon $^{1,2}$ Weipeng Xu $^{3}$ Lingjie Liu $^{1,2}$ + +Kripasindhu Sarkar $^{4}$ Christian Theobalt $^{1,2}$ + +$^{1}$ MPI Informatics ${ }^{2}$ Saarland Informatics Campus ${ }^{3}$ Meta Reality Labs ${ }^{4}$ Google + +{jianwang,dluvizon,lliu,theobalt}@mpi-inf.mpg.de xuweipeng@fb.com krsarkar@google.com + +# Abstract + +Egocentric 3D human pose estimation with a single head-mounted fisheye camera has recently attracted attention due to its numerous applications in virtual and augmented reality. Existing methods still struggle in challenging poses where the human body is highly occluded or is closely interacting with the scene. To address this issue, we propose a scene-aware egocentric pose estimation method that guides the prediction of the egocentric pose with scene constraints. To this end, we propose an egocentric depth estimation network to predict the scene depth map from a wide-view egocentric fisheye camera while mitigating the occlusion of the human body with a depth-inpainting network. Next, we propose a scene-aware pose estimation network that projects the 2D image features and estimated depth map of the scene into a voxel space and regresses the 3D pose with a V2V network. The voxel-based feature representation provides the direct geometric connection between 2D image features and scene geometry, and further facilitates the V2V network to constrain the predicted pose based on the estimated scene geometry. To enable the training of the aforementioned networks, we also generated a synthetic dataset, called EgoGTA, and an inthe-wild dataset based on EgoPW, called EgoPW-Scene. The experimental results of our new evaluation sequences show that the predicted 3D egocentric poses are accurate and physically plausible in terms of human-scene interaction, demonstrating that our method outperforms the state-of-the-art methods both quantitatively and qualitatively. + +# 1. Introduction + +Egocentric 3D human pose estimation with head- or body-mounted cameras is extensively researched recently because it allows capturing the person moving around in a large space, while the traditional pose estimation methods can only record in a fixed volume. With this advantage, the egocentric pose estimation methods show great potential in various applications, including the xR technologies and mo + +![](images/24a11630719e862f19f6808063c133e47eedac678f6fdca0fd92fb019e445447.jpg) + +![](images/3be4c0f73598e9026f71103b73aa3d3cd492ac5db2a4c48c72d1e4d9a4492fcb.jpg) + +![](images/c67db67420a15cafd7ec9bf0b1260eb60fd1710b49aec6aca6954b4fee972a64.jpg) + +![](images/8d7903bd98f4d881d267011e41a5632543aea702a7e937bae8d743bc8e31ac44.jpg) +Image + +![](images/868b69835610002389d40762831c2f0943eac697a38a6a20a8e52a6f09cfd9cb.jpg) +EgoPW + +![](images/b9372a2ddcc5bca466ce5d37e4f96f4c88dc55225fbfa8e7583ed4495b0e0f9d.jpg) +Ours +Figure 1. Previous egocentric pose estimation methods like EgoPW predict body poses that may suffer from body floating issue (the first row) or body-environment penetration issue (the second row). Our method predicts accurate and plausible poses complying with the scene constraints. The red skeletons are the ground truth poses and the green skeletons are the predicted poses. + +bile interaction applications. + +In this work, we estimated the full 3D body pose from a single head-mounted fisheye camera. A number of works have been proposed, including $\mathrm{Mo}^2\mathrm{Cap}^2$ [39], $x\mathrm{R}$ -egopose [32], Global-EgoMocap [36], and EgoPW [35]. These methods have made significant progress in estimating egocentric poses. However, when taking account of the interaction between the human body and the surrounding environment, they still suffer from artifacts that contrast the physics plausibility, including body-environment penetrations or body floating (see the EgoPW results in Fig. 1), which is mostly ascribed to the ambiguity caused by the self-occluded and highly distorted human body in the egocentric view. This problem will render restrictions on subsequent applications including action recognition, humanobject interaction recognition, and motion forecasting. + +To address this issue, we propose a scene-aware pose estimation framework that leverages the scene context to constrain the prediction of an egocentric pose. This frame- + +work produces accurate and physically plausible 3D human body poses from a single egocentric image, as illustrated in Fig. 1. Thanks to the wide-view fisheye camera mounted on the head, the scene context can be easily obtained even with only one egocentric image. To this end, we train an egocentric depth estimator to predict the depth map of the surrounding scene. In order to mitigate the occlusion caused by the human body, we predict the depth map including the visible human and leverage a depth-inpainting network to recover the depth behind the human body. + +Next, we combine the projected 2D pose features and scene depth in a common voxel space and regress the 3D body pose heatmaps with a V2V network [22]. The 3D voxel representation projects the 2D poses and depth information from the distorted fisheye camera space to the canonical space, and further provides direct geometric connection between 2D image features and 3D scene geometry. This aggregation of 2D image features and 3D scene geometry facilitates the V2V network to learn the relative position and potential interactions between the human body joints and the surrounding environment and further enables the prediction of plausible poses under the scene constraints. + +Since no available dataset can be used for train these networks, we proposed EgoGTA, a synthetic dataset based on the motion sequences of GTA-IM [3], and EgoPW-Scene, an in-the-wild dataset based on EgoPW [35]. Both of the datasets contain body pose labels and scene depth map labels for each egocentric frame. + +To better evaluate the relationship between estimated egocentric pose and scene geometry, we collected a new test dataset containing ground truth joint positions in the egocentric view. The evaluation results on the new dataset, along with results on datasets in Wang et al. [36] and $\mathrm{Mo}^2\mathrm{Cap}^2$ [39] demonstrate that our method significantly outperforms existing methods both quantitatively and qualitatively. We also qualitatively evaluate our method on inthe-wild images. The predicted 3D poses are accurate and plausible even in challenging real-world scenes. To summarize, our contributions are listed as follows: + +- The first scene-aware egocentric human pose estimation framework that predicts accurate and plausible egocentric pose with the awareness of scene context; +- Synthetic and in-the-wild egocentric datasets containing egocentric pose labels and scene geometry labels; +- A new depth estimation and inpainting networks to predict the scene depth map behind the human body; +- By leveraging a voxel-based representation of body pose features and scene geometry jointly, our method + +outperforms the previous approaches and generates plausible poses considering the scene context. + +# 2. Related Work + +# 2.1. Egocentric 3D Full Body Pose Estimation + +Inspired by the new applications in augmented reality and by the limitations of traditional motion capture systems, Rhodin et al. [26] proposed the first egocentric motion capture system based on a pair of fisheye cameras. The following methods proposed new architectures [4,47] and new datasets [1,47] for stereo egocentric pose estimation. However, a stereo camera setup implies additional computation complexity and extra energy consumption, which is critical for low-power head-mounted devices, which are the main target applications. + +The single head-mounted fisheye camera setup was first proposed by Xu et al. [39], who also introduced a two-stream CNN to cope with the low resolution of regions far from the fisheye camera, i.e., one branch for the full body and one branch for predicting the lower body joints from a zoom-in image. Tome et al. [32] proposed an encoder-decoder architecture to model the high uncertainty caused by severe occlusions present in this setup and Wang et al. [36] leverages motion capture data to learn a human motion prior, which is applied in an optimization method to obtain temporally stable poses for training and egocentric pose predictor. Another challenge is the strong image distortion caused by the fisheye lens, which can be mitigated with automatic camera calibration [46]. Other setups consider the camera facing forward and try to synthesize plausible human motion given only scene image evidences [18] or partially visible body parts [13, 15]. In our work, we do not consider this setup since in many poses only a few body extremities are visible in the image. + +Obtaining real data in the egocentric setup is a time consuming process, therefore, many approaches rely on synthetic data for training [15,32]. A recent method has shown that the existing gap between synthetic and real data can be mitigated by domain adaptation techniques [35], but this approach still requires real data for the weak supervision part. Differently, our method has a simpler training strategy, and we reduce the gap between synthetic and real data by providing additional pseudo ground-truth scene labels for real sequences, including indoor and outdoor scenes. + +# 2.2. Voxel Representation for Body Pose Estimation + +Volumetric voxel representations have been extensively used with multiple view setups for the estimation of single [31, 33] and multiple human poses [34, 37, 40, 45], and for hand pose estimation [12, 19-21] from depth maps input. Considering a single image as input, Pavlakos et al. [25] proposed a coarse-to-fine approach to lift from 2D + +![](images/1303ff2903b00600563f78b9b32be04007eac97704c5b760d66764503246367e.jpg) +Sec. 3.1 Training Dataset + +![](images/7a563c2887fe538203a59c1cc997b1876e8574e8976738f87590dd60ee3eb793.jpg) + +![](images/6471fd6c34e2d655e31a392ee5ef816a8ac0ed50176f5d58c119d8a2cc346d90.jpg) +Sec. 3.2 Scene Depth Estimator + +![](images/fa3c349f901ea3068372128b289593768007e09e72ab5ce1d1c56396974f133d.jpg) +Sec. 3.3 Scene-aware Egocentric Pose Estimator +Figure 2. Overview of our method. We first render synthetic training dataset EgoGTA and in-the-wild training dataset EgoPW-Scene. Both datasets contain egocentric depth maps for subsequent training process (Sec. 3.1). Next, we train an egocentric scene depth estimator that predicts a depth map without the human body and a depth inpainting network (Sec. 3.2). Finally, we combine the 2D body pose features and scene depth map into a common voxel space. The 3D body pose heatmaps are regressed from the voxel space with a V2V network and the final pose prediction is obtained with soft-argmax (Sec. 3.3). + +heatsmaps to a voxel representation for 3D human pose estimation. Iskakov [14] later proposed a learnable triangulation method in voxel space that can generalize to single or multiple views, achieving less than $2\mathrm{cm}$ error in a controlled multi-view data. Despite the success of voxel representation for human and hand pose estimation from an external camera, this technique has not yet been explored for the interaction between human body and scene. In our work, we show the advantages of this representation for egocentric human pose estimation, especially when considering human-scene interaction. + +# 2.3. Scene-aware Human Pose Estimation + +In recent years, several approaches have been proposed to predict the pose of humans considering environmental and physical constraints from RGB [24, 30, 41] and inertial measurement units (IMU) [9, 42]. Some methods assume a simplified environment, such as a planar ground floor, to enforce a temporal sequence that is physically consistent with the universal law of gravity by assuming known camera poses [29, 30] or by tracking an object in the scene following a free flight trajectory [6]. Other approaches assume + +that the scene is given as input, either as a 3D reconstruction [9,28] or as geometric primitives [43], whose positions can be refined in the optimization process. Bhatnagar et al. [2] proposed a method and dataset for human-object interactions. Taking into account the interaction between humans and furniture, holistic methods are able to estimate the position of humans and specific objects in the scene under the assumption of a planar floor [5, 38, 41], or even to estimate deformations in known objects based on human poses [17]. Contrary to the previous work, we make no strong assumptions about the objects and ground floor in the scene, but instead propose a method that learns to estimate the background scene geometry from a fisheye camera and explores the correlation between the human body and scene directly from egocentric data. + +# 3. Method + +We propose a new method for predicting accurate ego-centric body pose by leveraging the estimated scene geometry. An overview of our method is shown in Fig. 2. In order to train the scene-aware network, we first generate a synthetic dataset based on the GTA-IM dataset [3], called + +EgoGTA, and an in-the-wild dataset based on the EgoPW dataset [35], called EgoPW-Scene (Sec. 3.1). Next, we train a depth estimator to estimate the geometry of the surrounding scene and introduce the depth-inpainting network that estimates the depth behind the human body (Sec. 3.2). Finally, we combine 2D features and scene geometry in a common voxel space and predict the egocentric pose with a V2V network [22] (Sec. 3.3). + +# 3.1. Training Dataset + +Although many training datasets for egocentric pose estimation [32,35,39] have been proposed, they cannot yet train the scene-aware egocentric pose estimation network due to the lack of scene geometry information. To solve this, we introduce the EgoGTA dataset and EgoPW-Scene dataset (both will be made publicly available). Both datasets contain pose labels and depth maps of the scene for each egocentric frame, facilitating our training process. We show examples from both datasets, as illustrated in Fig. 2. + +# 3.1.1 EgoGTA Dataset + +In order to obtain precise ground truth human pose and scene geometry for training, we devise a new synthetic ego-centric dataset based on GTA-IM [3], which contains various daily motions and ground truth scene geometry. For this, we first fit the SMPL-X model on the 3D joint trajectories from GTA-IM. Next, we attach a virtual fisheye camera to the forehead of the SMPL-X model and render the images, semantic labels, and depth map of the scene with and without the human body. In total, we obtained $320\mathrm{K}$ frames in 101 different sequences, each with a different human body texture. Here, we denote the EgoGTA dataset $\mathbb{S}_G = \{I_G,S_G,D_G^B,D_G^S,P_G\}$ , including synthetic images $I_{G}$ and their corresponding human body segmentation maps $S_{G}$ , depth map with human body $D_G^B$ , depth map of the scene without human body $D_G^S$ , and egocentric pose labels $P_{G}$ . + +# 3.1.2 EgoPW-Scene Dataset + +Since we want to generalize to data captured with a real head-mounted camera, we also extended the EgoPW [35] training dataset. For this, we first reconstruct the scene geometry from the egocentric image sequences of the EgoPW training dataset with a Structure-from-Motion (SfM) algorithm [10]. This step provides a dense reconstruction of the background scene. The global scale of the reconstruction is recovered from known objects present in the sequences, such as laptops and chairs. We further render the depth maps of the scene in the egocentric perspective based on the reconstructed geometry. Our EgoPW-Scene dataset contains $92\mathrm{K}$ frames in total, which are distributed in 30 sequences performed by 5 actors. The number of frames in + +the EgoPW-Scene dataset is less than EgoPW dataset since SfM fails on some sequences. Here, we denote the EgoPW-Scene dataset $\mathbb{S}_E = \{I_E, D_E^S, P_E\}$ , including in-the-wild images $I_E$ and their corresponding depth map of the scene without human body $D_E^S$ , and egocentric pose labels $P_E$ . + +# 3.2. Scene Depth Estimator + +In this section, we propose a depth estimation method to capture the scene geometry information in the egocentric perspective. Available depth estimation methods [7, 11, 16] can only generate depth maps with the human body, but are not able to infer the depth information behind the human, i.e., the background scene depth. However, the area occluded by the human body, e.g. the areas of foot contact, are crucial for generating plausible poses, as demonstrated in Sec. 4.4. To predict the depth map of the scene behind the human body, we adopt a two-step approach. More specifically, we first estimate the depth map including the human body and the semantic segmentation of the human with two separated models. Then, we use a depth inpainting network to recover the depth behind the human body. This two-step strategy is necessary because the human visual evidences in the RGB images are too strong to be ignored by the depth estimator, therefore, it is easier to train the scene depth estimation as separated tasks. + +We first train the depth estimator network $\mathcal{D}$ , which takes as input a single egocentric image $I$ and predicts the depth map with human body $\hat{D}^B$ . The network architecture of $\mathcal{D}$ is the same as Hu et al. [11]'s work. To minimize the influence of the domain gap between synthetic and real data, the network is initially trained on the NYU-Depth V2 dataset [23] following [11], and further fine-tuned on the EgoGTA dataset. + +Next, we train the segmentation network $S$ for segmenting the human body. The network takes the egocentric image $I$ as input and predicts the segmentation mask for the human body $\hat{S}$ as output. Following Yuan et al. [44], we use HRNet as our segmentation network. Similarly, to reduce the domain gap, we pretrain the network on the LIP dataset [8] and finetune the model on the EgoGTA dataset. We do not train network $\mathcal{D}$ and $S$ on the EgoPW-Scene dataset since it lacks the ground truth segmentation maps and depth maps with the human body. + +Finally, we propose a depth inpainting network $\mathcal{G}$ for generating the final depth map of the scene without human body. We first generate the masked depth map $\hat{D}^M = (1 - \hat{S})\odot \hat{D}^B$ , which is a Hadamard product between the background segmentation and the depth map with human body. Then, the masked depth map $\hat{D}^M$ and the segmentation mask $\hat{S}$ are fed into the inpainting network $\mathcal{G}$ , which predicts the final depth map $\hat{D}^S$ . We train the inpainting network $\mathcal{G}$ and finetune the depth estimation network $\mathcal{D}$ on both the EgoGTA and EgoPW-Scene datasets. During + +training, we penalize the differences between the predicted depth maps and the ground truth depth of the background scene with $L^S$ and also keep the depth map consistent in the non-human body regions with $L^C$ . Specifically, the loss function is defined as follows: + +$$ +\begin{array}{l} L = \lambda^ {S} L ^ {S} + \lambda^ {C} L ^ {C}, \quad \text {w i t h} \\ L ^ {S} = \left\| \hat {D} _ {G} ^ {S} - D _ {G} ^ {S} \right\| _ {2} ^ {2} + \left\| \hat {D} _ {E} ^ {S} - D _ {E} ^ {S} \right\| _ {2} ^ {2}, \quad \text {a n d} \\ L ^ {C} = \left\| \left(\hat {D} _ {G} ^ {S} - \hat {D} _ {G} ^ {B}\right) \left(1 - \hat {S} _ {G}\right) \right\| _ {2} ^ {2} \tag {1} \\ + \left\| \left(\hat {D} _ {E} ^ {S} - \hat {D} _ {E} ^ {B}\right) \left(1 - \hat {S} _ {E}\right) \right\| _ {2} ^ {2}, \\ \end{array} +$$ + +where + +$$ +\hat {D} _ {G} ^ {S} = \mathcal {G} (\hat {D} _ {G} ^ {M}, \hat {S} _ {G}); \quad \hat {D} _ {E} ^ {S} = \mathcal {G} (\hat {D} _ {E} ^ {M}, \hat {S} _ {E}); +$$ + +$$ +\hat {D} _ {G} ^ {B} = \mathcal {D} (I _ {G}); \quad \hat {D} _ {E} ^ {B} = \mathcal {D} (I _ {E}); \tag {2} +$$ + +$$ +\hat {S} _ {G} = \mathcal {S} (I _ {G}); \quad \hat {S} _ {E} = \mathcal {S} (I _ {E}), +$$ + +and $\lambda^S$ and $\lambda^C$ are the weights of the loss terms. + +# 3.3. Scene-aware Egocentric Pose Estimator + +In this section, we introduce our scene-aware egocentric pose estimator. We rely on the prior that human bodies are mostly in contact with the scene. However, estimating the contact explicitly from a single egocentric image is very challenging. Therefore, we rely on a data-driven approach by learning a model that predicts a plausible 3D pose given the estimated scene geometry and features extracted from the input image. To achieve this goal, we first leverage the EgoPW [35] body joints heatmap estimator to extract 2D body pose features $F$ and use the scene depth estimator from Sec. 3.2 to estimate the depth map of the scene without human body $\hat{D}^S$ . Afterwards, we project the body pose features and depth map into a 3D volumetric space considering the fisheye camera projection model. After obtaining the volumetric representation of human body features $V_{\mathrm{body}}$ and scene depth $V_{\mathrm{scene}}$ , the 3D body pose $\hat{P}$ is predicted from the volumetric representation with a V2V network [22]. + +Lifting the image features and depth maps to a 3D representation allows getting more plausible results, as inconsistent joint predictions can be behind the volumetric scene $V_{\mathrm{scene}}$ (pose-scene penetration) or spatially isolated from the voxelized scene geometry (pose floating), so they can be easily identified and adjusted by the volumetric convolutional network. + +# 3.3.1 Scene and Body Encoding as a 3D Volume + +In order to create the volumetric space, we first create a 3D bounding box around the person in the egocentric camera coordinate system of size $L \times L \times L$ , where $L$ denotes the length of the side of the bounding box in meters. + +The egocentric camera is placed at the center-top of the 3D bounding box so that the vertices of the bounding boxes are: $(\pm L / 2, \pm L / 2, 0)$ and $(\pm L / 2, \pm L / 2, L)$ under the egocentric camera coordinate system. Next, we discretize the bounding box by a volumetric cube $V \in R^{N,N,N,3}$ . Each voxel $V_{xyz} \in R^3$ in position $(x,y,z)$ is filled with the coordinates of its center under the egocentric camera coordinate system $(xL / N - L / 2, yL / N - L / 2, zL / N)$ . + +We project the 3D coordinates in $V$ into the egocentric image space with the fisheye camera model [27]: $V_{\mathrm{proj}} = \mathcal{P}(V)$ , where $V_{\mathrm{proj}} \in R^{N,N,N,2}$ and $\mathcal{P}$ is the fisheye camera projection function. The volumetric representation $V_{\mathrm{body}}$ of the human body is obtained by filling a cube $V_{\mathrm{body}} \in R^{N,N,N,K}$ by bilinear sampling from the feature maps $F$ with $K$ channels using 2D coordinates in $V_{\mathrm{proj}}$ : + +$$ +V _ {\text {b o d y}} = F \left\{V _ {\text {p r o j}} \right\} \tag {3} +$$ + +where $\{\cdot\}$ denotes bilinear sampling. + +Then, we project the depth map to the 3D volumetric space. We first generate the point cloud of the scene geometry $C$ from the depth map $\hat{D}^S$ with the fisheye camera projection function $C = \mathcal{P}^{-1}(\hat{D}^S)$ . The volumetric representation of scene depth map $V_{\mathrm{scene}}$ is obtained by filling a binary cube $V_{\mathrm{scene}} \in R^{N,N,N}$ by setting the voxel at $(x,y,z)$ to 1 if there exists one point $(x_p,y_p,z_p)$ in the point cloud $C$ such that: + +$$ +\left\| \left(\frac {x L}{N} - \frac {L}{2}, \frac {y L}{N} - \frac {L}{2}, \frac {z L}{N}\right) - \left(x _ {p}, y _ {p}, z _ {p}\right) \right\| < \epsilon \tag {4} +$$ + +where $\epsilon$ is the threshold distance. In our experiment, we set $L = 2.4\mathrm{m}$ , $N = 64$ , and $\epsilon = 0.04\mathrm{m}$ . This setting can cover most types of the human motions and allows high accuracy of the predicted body pose. + +# 3.3.2 Predicting 3D Body Pose with V2V Network + +We feed the volumetric representation aggregated from $V_{\mathrm{body}}$ and $V_{\mathrm{scene}}$ into the volumetric convolutional network $\mathcal{N}$ , which has a similar architecture as [22]. The V2V network produces the 3D heatmaps of the body joints: + +$$ +V _ {\text {h e a t m a p}} = \mathcal {N} \left(V _ {\text {b o d y}}, V _ {\text {s c e n e}}\right) \tag {5} +$$ + +Following [14], we compute the soft-argmax of $V_{\mathrm{heatmap}}$ across the spatial axes to infer the body pose $\hat{P}$ . The predicted pose $\hat{P}$ is finally compared with the ground truth pose $P_G$ from the EgoGTA dataset and $P_E$ from the EgoPW-Scene dataset with the MSE loss. + +# 4. Experiments + +In this section, we evaluate our method considering existing and new datasets for egocentric monocular 3D human pose estimation. Please refer to the supplementary materials for the implementation details. + +![](images/24d37ad4186d24883596ad3592a1d233f8c9c8dc7087e277685f9fd9b17abc78.jpg) +Figure 3. Qualitative comparison between our method and the state-of-the-art egocentric pose estimation methods. From left to right: input image, $\mathrm{Mo}^2\mathrm{Cap}^2$ result, $x\mathrm{R}$ -egopose result, EgoPW result and our result. The ground truth pose is shown in red. The input images from the left part are from our test dataset, while those in the right part come from the EgoPW [35] in-the-wild test sequences (without ground-truth poses). We also show the gt scene geometry of the in-the-studio data and scene geometry obtained by SFM method for the in-the-wild data. For better visualizing the interaction between human body and environment, please refer to our supplementary video. + +![](images/b702faf82fbaf5276500b08d4434b14f8de5e4d0ecc62365cf84295bc0024fc3.jpg) + +# 4.1. Evaluation Datasets + +Evaluating human-scene interaction requires precise annotations for camera pose and scene geometry. However, such information is not available in existing datasets for egocentric human pose estimation. To solve this issue, we collected a new real-world dataset using a head-mounted fisheye camera combined with a calibration board. The ground truth scene geometry is obtained with SfM method [10] from a multi-view capture system with 120 syncd 4K resolution cameras and the ground truth egocentric camera pose is obtained by localizing a calibration board rigidly attached to the egocentric camera. This dataset contains around 14K frames of two actors, performing various human-scene interacting motions such as sitting, reading newspaper, and using a computer. This dataset will be made publicly available and additional details of it are shown in the supplementary materials. + +Besides our new test dataset, we also evaluate our methods in the test datasets from Wang et al. [36] and $\mathrm{Mo}^2\mathrm{Cap}^2$ [39]. The real-world dataset in $\mathrm{Mo}^2\mathrm{Cap}^2$ [39] contains 2.7K frames of two people captured in indoor and outdoor scenes, and the dataset in Wang et al. [36] contains 12K frames of two people captured in the studio. + +# 4.2. Evaluation Metrics + +We measure the accuracy of the estimated body pose with the MPJPE and PA-MPJPE. For the test dataset in Wang et al. [36] and $\mathrm{Mo}^2\mathrm{Cap}^2$ [39], we evaluate PA-MPJPE and BA-MPJPE [39] since the ground truth poses in the egocentric camera space are not provided. Further details of the metrics are shown in the supplementary materials. + +
MethodMPJPEPA-MPJPE
Our test dataset
Mo2Cap2 [39]200.3121.2
xR-egopose [32]241.3133.9
EgoPW [35]189.6105.3
Ours118.592.75
MethodPA-MPJPEBA-MPJPE
Wang et al.'s dataset [36]
Mo2Cap2 [39]102.374.46
xR-egopose [32]112.087.20
EgoPW [35]81.7164.87
Ours76.5061.92
Mo2Cap2 test dataset [39]
Mo2Cap2 [39]91.1670.75
xR-egopose [32]86.8566.54
EgoPW [35]83.1764.33
Ours79.6562.82
+ +Table 1. Performance of our method on our test dataset, Wang et al.'s test dataset [36] and $\mathrm{Mo}^2\mathrm{Cap}^2$ test dataset [39]. Our method outperforms the state-of-the-art methods EgoPW, $\mathrm{Mo}^2\mathrm{Cap}^2$ [39] and $xR$ -egopose [32]. + +# 4.3. Comparisons on 3D Pose Estimation + +In this section, we compare our approach with previous single-frame-based methods, including EgoPW [35], $x$ Regopose [32] and $\mathrm{Mo}^2\mathrm{Cap}^2$ [39] on our test dataset under the "Our test data" in Table 1. Since the code for $x$ Regopose is not released, we use our implementation for the evaluation. In our dataset, the proposed method outperforms the previous state-of-the-art methods, EgoPW [35] by $37.5\%$ on MPJPE and $11.9\%$ on PA-MPJPE. We also compared with previous methods on the Wang et al.'s test dataset [36] and $\mathrm{Mo}^2\mathrm{Cap}^2$ test dataset [39] and show the re + +
MethodNon pene.Contact
Mo2Cap2 [39]69.6%23.1%
xR-egopose [32]64.5%38.3%
EgoPW [35]71.7%38.8%
Ours84.1%89.4%
+ +![](images/11f14224f03f7f3627dcaa01f58cf736e699310196c1afebf43010674c9c6000.jpg) +Figure 4. Predicted pose with different scene depth map input. Our network can generate different poses under different depth input and further disambiguate body poses under scene constraint. + +sults in Table 1. On Wang et al.'s test dataset, our method performs better than EgoPW by $6.4\%$ . On the $\mathrm{Mo}^{2}\mathrm{Cap}^{2}$ test dataset, our method performs better than EgoPW by $7.8\%$ . + +We also evaluate the physical plausibility of our predictions by calculating the percentage of predicted poses that are in contact with the scene and do not penetrate the scene in Table 2. We define a body pose as in contact with the scene if any body joint is less than $5\mathrm{cm}$ from the scene mesh. A body pose suffers from the body floating issue if it is not in contact with the scene. Compared with previous approaches, our method generates body poses more physically plausible considering the constraints of the scene. + +From the results in Table 1 and Table 2, we can see that our approach outperforms all previous methods on the single-frame egocentric pose estimation task. For the qualitative comparison, we show the results of our method on the studio dataset and in-the-wild sequences in Fig. 3. See our supplementary video for more qualitative evaluations. Our predicted poses are physically plausible under the scene constraint, whereas other methods generate poses suffering from body floating and penetration issues. + +In order to further demonstrate our method performing predictions accordingly to the constraint of the scene geometry, we fix the input image and change the scene depth input to the depth map corresponding to the standing pose, squatting pose, and sitting pose. The results are presented in Fig. 4 and show that the predicted poses change to standing, squatting, and sitting to better adapt to the input changes of the scene geometry. This shows our method's ability to disambiguate poses under different scene constraints. + +Table 2. Comparisons of physical plausibility on our test dataset. + +
MethodMPJPEPA-MPJPE
EgoPW+Optimizer187.1103.2
EgoPW+Depth149.698.15
xR-egopose+Depth180.5103.7
Ours w/o Depth188.1105.1
Ours+Depth with Body167.3103.3
Ours+Depth w/o Body135.795.84
Ours+Depth w/o Inpainting124.295.00
Ours+GT Depth109.988.80
Ours118.592.75
+ +Table 3. Results from our method compared to different baselines. + +# 4.4. Ablation Study + +Simple Combination of 2D Features and Depth Maps. In Sec. 3.3, we claim that the volumetric representation of egocentric 2D features and scene depth map is important for understanding the interaction between the human body and the surrounding scene. To provide evidence of this claim, in this experiment, we compare our method with baseline methods that simply combine the 2D image features and scene depth map. We set two baseline methods since there are two types of egocentric pose estimation methods, i.e. direct regression of 3D poses ( $x$ -R-egopose [32]) and prediction of 2D position and depth for each joint ( $\mathrm{Mo}^2\mathrm{Cap}^2$ [39] and EgoPW [35]). In the baseline method “ $x$ -R-egopose + Depth”, we concatenate 2D heatmaps and scene depth map as the input to the 3D pose regression network in $x$ -R-egopose. In the baseline “EgoPW + Depth”, we concatenate the 2D features and the scene depth map and input them into the joint depth prediction network. + +From the evaluation results shown in Table 3, both of the baseline methods perform worse than our proposed method. In "xR-egopose + Depth", simply combining the scene depth and 2D heatmaps cannot provide direct geometric supervision for the 3D pose regression network. In "EgoPW + Depth", though the joint depth estimation network performs better with the help of scene depth information, the 2D pose estimation network does not benefit from it. Both of the experiments demonstrate the effectiveness of our volumetric representation of 2D features and scene geometry, which provides direct geometry supervision for the physical plausibility of predicted egocentric poses. + +Optimization. In this experiment, we compare our method with an optimization baseline that refines a 3D pose considering the scene constraint. Similar to Wang et al. [36] and EgoPW [35], we first train a VAE consisting of a CNN-based encoder $f_{\mathrm{enc}}$ and decoder $f_{\mathrm{dec}}$ to learn an egocentric motion prior. Then, We optimize the egocentric pose $P$ by finding a latent vector $z$ such that the corresponding pose $P = f_{\mathrm{dec}}(z)$ minimizes the objective function + +$E(P) = \lambda_{R}E_{R} + \lambda_{J}E_{J} + \lambda_{C}E_{C}$ , where $E_{R}$ is the egocentric reprojection term, $E_{J}$ is the egocentric pose regularization term, and $E_{C}$ is the contact term. The latent vector $z$ is initialized with the estimated pose from the EgoPW method. The $E_{R}$ and $E_{J}$ are the same as those defined in Wang et al. [36]. Denote the nth joint in egocentric pose $P$ as $P_{n}, n \in [0, N]$ , where $N$ is the number of joints, and the mth point in scene point cloud $C$ as $C_{m}, m \in [0, M]$ , where $M$ is the number of points in the point cloud. The contact term $E_{C}$ is defined as: + +$$ +E _ {C} = \sum_ {n \in [ 0, N ]} d _ {n} ^ {2}, \quad \text {i f} d _ {n} \leq \epsilon , \text {o t h e r w i s e} 0, \text {a n d} \tag {6} +$$ + +$$ +d _ {n} = \min _ {m \in [ 0, M ]} \| P _ {n} - C _ {m} \| _ {2}. +$$ + +We first calculate the nearest distance $d_{n}$ between each body joint and the projected point cloud $C$ from the scene depth map. If the distance $d_{n}$ of the nth joint is less than a margin $\epsilon$ , it is defined as in contact with the scene and minimized with the optimization framework. + +The result of the optimization method is shown as "EgoPW+Optimizer" in Table 3, which demonstrates that the optimization framework is less effective than our method. This is because the accuracy of optimization method relies heavily on the initial pose. If the initial pose is not accurate, it will be difficult to determine the contact labels for each joint with the fixed distance margin. Without accurate contact labels, the optimization framework might force the joint that does not contact the scene to keep in contact, eventually resulting in wrong poses. + +Scene Depth Estimator. In our work, we estimate the depth of the surrounding scene and infer the depth behind the human body with a depth inpainting network. In order to validate the effectiveness of the scene depth map, we remove the input depth map from the V2V network and show the results of "Ours w/o Depth" in Table 3. This baseline increases the MPJPE by about $70\mathrm{mm}$ , which is evidence of the relevant extra information provided by the scene depth. + +To demonstrate the benefits of recovering the scene depth behind the human body, we evaluate our model using the estimated depth including the human body as the input to the V2V network. We also removed the human body area from the depth maps and use them as input to the V2V network. The results are shown in "Ours+Depth with Body" and "Ours+Depth w/o Body" in Table 3. Both of the baseline methods perform worse than our method because the area in the scene occluded by the human body can provide clues for generating plausible poses. + +We also evaluate our method with ground truth depth maps in "Ours+GT Depth" in Table 3, which further improves over our estimated depth by $7.2\%$ in terms of MPJPE and $4.2\%$ in terms of PA-MPJPE. This demonstrates that the + +![](images/e57c5edb413a11d30e44ea42f61ba62d194057bb9d302d9c40e2763596dd7f50.jpg) +Input Image + +![](images/e79042addfe1bd766a45c3793dd0b64fc15679757676e5aace79f76005123241.jpg) +w/o Inpainting Network + +![](images/23d0b79496cf44922c2a8e9d5e055899f92bfe6aa221d23fafc0987165151d79.jpg) +w. Inpainting Network +Figure 5. The qualitative depth estimation results with or without inpainting network. The depth map estimated without inpainting network show artifacts in the human body region (see the red box). + +![](images/117661e42da7f43528682da4a98092897b83bd87164910b9b229c741b2722421.jpg) +GT Depth + +accuracy of our predicted pose benefits from better depth maps, but still our estimated scene depth already provides a significant improvement over the baselines. + +Finally, we compare with a baseline method without depth inpainting, i.e., the human body is removed from the input image and the scene depth map is predicted directly with the network $\mathcal{D}$ in Sec. 3.2. The pose estimation accuracy is shown in "Ours+Depth w/o Inpainting" of Table 3 and the depth accuracy is shown in Table 4. Our method outperforms the baseline as it is more challenging to simultaneously estimate and inpaint the depth. Moreover, the network can be influenced by the segmented part in the input image as some extinct object, as shown in Fig 5. + +
MethodAbs-RelRMSE(m)
w/o Inpainting Network0.38340.7856
Ours0.10690.3365
+ +Table 4. The quantitative results of depth estimator. We evaluate Abs-Rel and RMSE on our test dataset following [11]. + +# 5. Conclusion + +In this paper, we have proposed a new approach to estimate egocentric human pose under the scene constraint. We firstly train a depth inpainting network for estimating the depth map of the scene without human body. Next, we combine the egocentric 2D features and scene depth map in a volumetric space and predict the egocentric pose with a V2V network. The experiments show that our method outperforms all of the baseline methods both qualitatively and quantitatively and our method can predict physically plausible poses in terms of human-scene interaction. In future, this method could be extended to estimate physically-plausible egocentric motion from a temporal sequence. + +Limitations. The accuracy of voxel-based pose estimation network is constrained by the accuracy of estimated depth, especially where the scene is occluded by the human body. One solution is to leverage the temporal information to get a full view of the surrounding environment. + +Acknowledgments Jian Wang, Diogo Luvizon, Lingjie Liu, and Christian Theobalt have been supported by the ERC Consolidator Grant 4DReply (770784). + +# References + +[1] Hiroyasu Akada, Jian Wang, Soshi Shimada, Masaki Takahashi, Christian Theobalt, and Vladislav Golyanik. Unrealego: A new dataset for robust egocentric 3d human motion capture. In ECCV, 2022. 2 +[2] Bharat Lal Bhatnagar, Xianghui Xie, Ilya A Petrov, Cristian Sminchisescu, Christian Theobalt, and Gerard Pons-Moll. Behave: Dataset and method for tracking human object interactions. arXiv preprint arXiv:2204.06950, 2022. 3 +[3] Zhe Cao, Hang Gao, Karttikeya Mangalam, Qizhi Cai, Minh Vo, and Jitendra Malik. Long-term human motion prediction with scene context. In ECCV. 2020. 2, 3, 4 +[4] Y. Cha, T. Price, Z. Wei, X. Lu, N. Rewkowski, R. Chabra, Z. Qin, H. Kim, Z. Su, Y. Liu, A. Ilie, A. State, Z. Xu, J. Frahm, and H. 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Existing methods still struggle in challenging poses where the human body is highly occluded or is closely interacting with the scene. To address this issue, we propose a scene-aware egocentric pose estimation method that guides the prediction of the egocentric pose with scene constraints. To this end, we propose an egocentric depth estimation network to predict the scene depth map from a wide-view egocentric fisheye camera while mitigating the occlusion of the human body with a depth-inpainting network. Next, we propose a scene-aware pose estimation network that projects the 2D image features and estimated depth map of the scene into a voxel space and regresses the 3D pose with a V2V network. The voxel-based feature representation provides the direct geometric connection between 2D image features and scene geometry, and further facilitates the V2V network to constrain the predicted pose based on the estimated scene geometry. To enable the training of the aforementioned networks, we also generated a synthetic dataset, called EgoGTA, and an inthe-wild dataset based on EgoPW, called EgoPW-Scene. The experimental results of our new evaluation sequences show that the predicted 3D egocentric poses are accurate and physically plausible in terms of human-scene interaction, demonstrating that our method outperforms the state-of-the-art methods both quantitatively and qualitatively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "Egocentric 3D human pose estimation with head- or body-mounted cameras is extensively researched recently because it allows capturing the person moving around in a large space, while the traditional pose estimation methods can only record in a fixed volume. 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Previous egocentric pose estimation methods like EgoPW predict body poses that may suffer from body floating issue (the first row) or body-environment penetration issue (the second row). Our method predicts accurate and plausible poses complying with the scene constraints. The red skeletons are the ground truth poses and the green skeletons are the predicted poses." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 483, + 422, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 422, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 422, + 495 + ], + "type": "text", + "content": "bile interaction applications." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "type": "text", + "content": "In this work, we estimated the full 3D body pose from a single head-mounted fisheye camera. A number of works have been proposed, including " + }, + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "type": "text", + "content": " [39], " + }, + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "type": "inline_equation", + "content": "x\\mathrm{R}" + }, + { + "bbox": [ + 304, + 496, + 546, + 675 + ], + "type": "text", + "content": " -egopose [32], Global-EgoMocap [36], and EgoPW [35]. These methods have made significant progress in estimating egocentric poses. However, when taking account of the interaction between the human body and the surrounding environment, they still suffer from artifacts that contrast the physics plausibility, including body-environment penetrations or body floating (see the EgoPW results in Fig. 1), which is mostly ascribed to the ambiguity caused by the self-occluded and highly distorted human body in the egocentric view. This problem will render restrictions on subsequent applications including action recognition, humanobject interaction recognition, and motion forecasting." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "To address this issue, we propose a scene-aware pose estimation framework that leverages the scene context to constrain the prediction of an egocentric pose. This frame-" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13031" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "work produces accurate and physically plausible 3D human body poses from a single egocentric image, as illustrated in Fig. 1. Thanks to the wide-view fisheye camera mounted on the head, the scene context can be easily obtained even with only one egocentric image. To this end, we train an egocentric depth estimator to predict the depth map of the surrounding scene. In order to mitigate the occlusion caused by the human body, we predict the depth map including the visible human and leverage a depth-inpainting network to recover the depth behind the human body." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 346 + ], + "type": "text", + "content": "Next, we combine the projected 2D pose features and scene depth in a common voxel space and regress the 3D body pose heatmaps with a V2V network [22]. The 3D voxel representation projects the 2D poses and depth information from the distorted fisheye camera space to the canonical space, and further provides direct geometric connection between 2D image features and 3D scene geometry. This aggregation of 2D image features and 3D scene geometry facilitates the V2V network to learn the relative position and potential interactions between the human body joints and the surrounding environment and further enables the prediction of plausible poses under the scene constraints." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 347, + 288, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 288, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 288, + 418 + ], + "type": "text", + "content": "Since no available dataset can be used for train these networks, we proposed EgoGTA, a synthetic dataset based on the motion sequences of GTA-IM [3], and EgoPW-Scene, an in-the-wild dataset based on EgoPW [35]. Both of the datasets contain body pose labels and scene depth map labels for each egocentric frame." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 419, + 289, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 289, + 551 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 289, + 551 + ], + "type": "text", + "content": "To better evaluate the relationship between estimated egocentric pose and scene geometry, we collected a new test dataset containing ground truth joint positions in the egocentric view. The evaluation results on the new dataset, along with results on datasets in Wang et al. [36] and " + }, + { + "bbox": [ + 46, + 419, + 289, + 551 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 46, + 419, + 289, + 551 + ], + "type": "text", + "content": " [39] demonstrate that our method significantly outperforms existing methods both quantitatively and qualitatively. We also qualitatively evaluate our method on inthe-wild images. The predicted 3D poses are accurate and plausible even in challenging real-world scenes. To summarize, our contributions are listed as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 557, + 286, + 686 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 557, + 286, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 557, + 286, + 593 + ], + "spans": [ + { + "bbox": [ + 58, + 557, + 286, + 593 + ], + "type": "text", + "content": "- The first scene-aware egocentric human pose estimation framework that predicts accurate and plausible egocentric pose with the awareness of scene context;" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 600, + 286, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 600, + 286, + 624 + ], + "spans": [ + { + "bbox": [ + 58, + 600, + 286, + 624 + ], + "type": "text", + "content": "- Synthetic and in-the-wild egocentric datasets containing egocentric pose labels and scene geometry labels;" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 632, + 286, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 632, + 286, + 655 + ], + "spans": [ + { + "bbox": [ + 58, + 632, + 286, + 655 + ], + "type": "text", + "content": "- A new depth estimation and inpainting networks to predict the scene depth map behind the human body;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 662, + 286, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 662, + 286, + 686 + ], + "spans": [ + { + "bbox": [ + 58, + 662, + 286, + 686 + ], + "type": "text", + "content": "- By leveraging a voxel-based representation of body pose features and scene geometry jointly, our method" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 325, + 72, + 545, + 96 + ], + "type": "text", + "content": "outperforms the previous approaches and generates plausible poses considering the scene context." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 108, + 392, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 108, + 392, + 121 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 392, + 121 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 128, + 522, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 128, + 522, + 140 + ], + "spans": [ + { + "bbox": [ + 306, + 128, + 522, + 140 + ], + "type": "text", + "content": "2.1. Egocentric 3D Full Body Pose Estimation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 147, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 147, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 147, + 545, + 266 + ], + "type": "text", + "content": "Inspired by the new applications in augmented reality and by the limitations of traditional motion capture systems, Rhodin et al. [26] proposed the first egocentric motion capture system based on a pair of fisheye cameras. The following methods proposed new architectures [4,47] and new datasets [1,47] for stereo egocentric pose estimation. However, a stereo camera setup implies additional computation complexity and extra energy consumption, which is critical for low-power head-mounted devices, which are the main target applications." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 266, + 546, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 546, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 546, + 494 + ], + "type": "text", + "content": "The single head-mounted fisheye camera setup was first proposed by Xu et al. [39], who also introduced a two-stream CNN to cope with the low resolution of regions far from the fisheye camera, i.e., one branch for the full body and one branch for predicting the lower body joints from a zoom-in image. Tome et al. [32] proposed an encoder-decoder architecture to model the high uncertainty caused by severe occlusions present in this setup and Wang et al. [36] leverages motion capture data to learn a human motion prior, which is applied in an optimization method to obtain temporally stable poses for training and egocentric pose predictor. Another challenge is the strong image distortion caused by the fisheye lens, which can be mitigated with automatic camera calibration [46]. Other setups consider the camera facing forward and try to synthesize plausible human motion given only scene image evidences [18] or partially visible body parts [13, 15]. In our work, we do not consider this setup since in many poses only a few body extremities are visible in the image." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 495, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 615 + ], + "type": "text", + "content": "Obtaining real data in the egocentric setup is a time consuming process, therefore, many approaches rely on synthetic data for training [15,32]. A recent method has shown that the existing gap between synthetic and real data can be mitigated by domain adaptation techniques [35], but this approach still requires real data for the weak supervision part. Differently, our method has a simpler training strategy, and we reduce the gap between synthetic and real data by providing additional pseudo ground-truth scene labels for real sequences, including indoor and outdoor scenes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 623, + 545, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 545, + 635 + ], + "type": "text", + "content": "2.2. Voxel Representation for Body Pose Estimation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Volumetric voxel representations have been extensively used with multiple view setups for the estimation of single [31, 33] and multiple human poses [34, 37, 40, 45], and for hand pose estimation [12, 19-21] from depth maps input. Considering a single image as input, Pavlakos et al. [25] proposed a coarse-to-fine approach to lift from 2D" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "1Datasets are released in our project page. Meta did not access or process the data and is not involved in the dataset release." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13032" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 84, + 164, + 200 + ], + "blocks": [ + { + "bbox": [ + 59, + 73, + 143, + 83 + ], + "lines": [ + { + "bbox": [ + 59, + 73, + 143, + 83 + ], + "spans": [ + { + "bbox": [ + 59, + 73, + 143, + 83 + ], + "type": "text", + "content": "Sec. 3.1 Training Dataset" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 61, + 84, + 164, + 200 + ], + "lines": [ + { + "bbox": [ + 61, + 84, + 164, + 200 + ], + "spans": [ + { + "bbox": [ + 61, + 84, + 164, + 200 + ], + "type": "image", + "image_path": "1303ff2903b00600563f78b9b32be04007eac97704c5b760d66764503246367e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 169, + 72, + 226, + 200 + ], + "blocks": [ + { + "bbox": [ + 169, + 72, + 226, + 200 + ], + "lines": [ + { + "bbox": [ + 169, + 72, + 226, + 200 + ], + "spans": [ + { + "bbox": [ + 169, + 72, + 226, + 200 + ], + "type": "image", + "image_path": "7a563c2887fe538203a59c1cc997b1876e8574e8976738f87590dd60ee3eb793.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 244, + 83, + 533, + 200 + ], + "blocks": [ + { + "bbox": [ + 241, + 73, + 341, + 83 + ], + "lines": [ + { + "bbox": [ + 241, + 73, + 341, + 83 + ], + "spans": [ + { + "bbox": [ + 241, + 73, + 341, + 83 + ], + "type": "text", + "content": "Sec. 3.2 Scene Depth Estimator" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 244, + 83, + 533, + 200 + ], + "lines": [ + { + "bbox": [ + 244, + 83, + 533, + 200 + ], + "spans": [ + { + "bbox": [ + 244, + 83, + 533, + 200 + ], + "type": "image", + "image_path": "6471fd6c34e2d655e31a392ee5ef816a8ac0ed50176f5d58c119d8a2cc346d90.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 58, + 202, + 535, + 357 + ], + "blocks": [ + { + "bbox": [ + 59, + 204, + 214, + 214 + ], + "lines": [ + { + "bbox": [ + 59, + 204, + 214, + 214 + ], + "spans": [ + { + "bbox": [ + 59, + 204, + 214, + 214 + ], + "type": "text", + "content": "Sec. 3.3 Scene-aware Egocentric Pose Estimator" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 58, + 202, + 535, + 357 + ], + "lines": [ + { + "bbox": [ + 58, + 202, + 535, + 357 + ], + "spans": [ + { + "bbox": [ + 58, + 202, + 535, + 357 + ], + "type": "image", + "image_path": "fa3c349f901ea3068372128b289593768007e09e72ab5ce1d1c56396974f133d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 365, + 545, + 421 + ], + "lines": [ + { + "bbox": [ + 46, + 365, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 545, + 421 + ], + "type": "text", + "content": "Figure 2. Overview of our method. We first render synthetic training dataset EgoGTA and in-the-wild training dataset EgoPW-Scene. Both datasets contain egocentric depth maps for subsequent training process (Sec. 3.1). Next, we train an egocentric scene depth estimator that predicts a depth map without the human body and a depth inpainting network (Sec. 3.2). Finally, we combine the 2D body pose features and scene depth map into a common voxel space. The 3D body pose heatmaps are regressed from the voxel space with a V2V network and the final pose prediction is obtained with soft-argmax (Sec. 3.3)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 442, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 573 + ], + "type": "text", + "content": "heatsmaps to a voxel representation for 3D human pose estimation. Iskakov [14] later proposed a learnable triangulation method in voxel space that can generalize to single or multiple views, achieving less than " + }, + { + "bbox": [ + 46, + 442, + 287, + 573 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 442, + 287, + 573 + ], + "type": "text", + "content": " error in a controlled multi-view data. Despite the success of voxel representation for human and hand pose estimation from an external camera, this technique has not yet been explored for the interaction between human body and scene. In our work, we show the advantages of this representation for egocentric human pose estimation, especially when considering human-scene interaction." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 586, + 244, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 244, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 244, + 597 + ], + "type": "text", + "content": "2.3. Scene-aware Human Pose Estimation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 715 + ], + "type": "text", + "content": "In recent years, several approaches have been proposed to predict the pose of humans considering environmental and physical constraints from RGB [24, 30, 41] and inertial measurement units (IMU) [9, 42]. Some methods assume a simplified environment, such as a planar ground floor, to enforce a temporal sequence that is physically consistent with the universal law of gravity by assuming known camera poses [29, 30] or by tracking an object in the scene following a free flight trajectory [6]. Other approaches assume" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 442, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 545, + 622 + ], + "type": "text", + "content": "that the scene is given as input, either as a 3D reconstruction [9,28] or as geometric primitives [43], whose positions can be refined in the optimization process. Bhatnagar et al. [2] proposed a method and dataset for human-object interactions. Taking into account the interaction between humans and furniture, holistic methods are able to estimate the position of humans and specific objects in the scene under the assumption of a planar floor [5, 38, 41], or even to estimate deformations in known objects based on human poses [17]. Contrary to the previous work, we make no strong assumptions about the objects and ground floor in the scene, but instead propose a method that learns to estimate the background scene geometry from a fisheye camera and explores the correlation between the human body and scene directly from egocentric data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 633, + 361, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 361, + 645 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 361, + 645 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "We propose a new method for predicting accurate ego-centric body pose by leveraging the estimated scene geometry. An overview of our method is shown in Fig. 2. In order to train the scene-aware network, we first generate a synthetic dataset based on the GTA-IM dataset [3], called" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13033" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "EgoGTA, and an in-the-wild dataset based on the EgoPW dataset [35], called EgoPW-Scene (Sec. 3.1). Next, we train a depth estimator to estimate the geometry of the surrounding scene and introduce the depth-inpainting network that estimates the depth behind the human body (Sec. 3.2). Finally, we combine 2D features and scene geometry in a common voxel space and predict the egocentric pose with a V2V network [22] (Sec. 3.3)." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 175, + 149, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 175, + 149, + 188 + ], + "spans": [ + { + "bbox": [ + 47, + 175, + 149, + 188 + ], + "type": "text", + "content": "3.1. Training Dataset" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 193, + 289, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 193, + 289, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 289, + 301 + ], + "type": "text", + "content": "Although many training datasets for egocentric pose estimation [32,35,39] have been proposed, they cannot yet train the scene-aware egocentric pose estimation network due to the lack of scene geometry information. To solve this, we introduce the EgoGTA dataset and EgoPW-Scene dataset (both will be made publicly available). Both datasets contain pose labels and depth maps of the scene for each egocentric frame, facilitating our training process. We show examples from both datasets, as illustrated in Fig. 2." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 315, + 153, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 153, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 153, + 327 + ], + "type": "text", + "content": "3.1.1 EgoGTA Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": "In order to obtain precise ground truth human pose and scene geometry for training, we devise a new synthetic ego-centric dataset based on GTA-IM [3], which contains various daily motions and ground truth scene geometry. For this, we first fit the SMPL-X model on the 3D joint trajectories from GTA-IM. Next, we attach a virtual fisheye camera to the forehead of the SMPL-X model and render the images, semantic labels, and depth map of the scene with and without the human body. In total, we obtained " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "320\\mathrm{K}" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": " frames in 101 different sequences, each with a different human body texture. Here, we denote the EgoGTA dataset " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_G = \\{I_G,S_G,D_G^B,D_G^S,P_G\\}" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": ", including synthetic images " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "I_{G}" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": " and their corresponding human body segmentation maps " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "S_{G}" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": ", depth map with human body " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "D_G^B" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": ", depth map of the scene without human body " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "D_G^S" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": ", and egocentric pose labels " + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "inline_equation", + "content": "P_{G}" + }, + { + "bbox": [ + 46, + 334, + 289, + 525 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 539, + 175, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 175, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 175, + 552 + ], + "type": "text", + "content": "3.1.2 EgoPW-Scene Dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "Since we want to generalize to data captured with a real head-mounted camera, we also extended the EgoPW [35] training dataset. For this, we first reconstruct the scene geometry from the egocentric image sequences of the EgoPW training dataset with a Structure-from-Motion (SfM) algorithm [10]. This step provides a dense reconstruction of the background scene. The global scale of the reconstruction is recovered from known objects present in the sequences, such as laptops and chairs. We further render the depth maps of the scene in the egocentric perspective based on the reconstructed geometry. Our EgoPW-Scene dataset contains " + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "inline_equation", + "content": "92\\mathrm{K}" + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": " frames in total, which are distributed in 30 sequences performed by 5 actors. The number of frames in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "the EgoPW-Scene dataset is less than EgoPW dataset since SfM fails on some sequences. Here, we denote the EgoPW-Scene dataset " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "\\mathbb{S}_E = \\{I_E, D_E^S, P_E\\}" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", including in-the-wild images " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "I_E" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": " and their corresponding depth map of the scene without human body " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "D_E^S" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": ", and egocentric pose labels " + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "inline_equation", + "content": "P_E" + }, + { + "bbox": [ + 304, + 72, + 545, + 133 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 142, + 437, + 154 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 142, + 437, + 154 + ], + "spans": [ + { + "bbox": [ + 306, + 142, + 437, + 154 + ], + "type": "text", + "content": "3.2. Scene Depth Estimator" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 160, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 160, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 160, + 545, + 376 + ], + "type": "text", + "content": "In this section, we propose a depth estimation method to capture the scene geometry information in the egocentric perspective. Available depth estimation methods [7, 11, 16] can only generate depth maps with the human body, but are not able to infer the depth information behind the human, i.e., the background scene depth. However, the area occluded by the human body, e.g. the areas of foot contact, are crucial for generating plausible poses, as demonstrated in Sec. 4.4. To predict the depth map of the scene behind the human body, we adopt a two-step approach. More specifically, we first estimate the depth map including the human body and the semantic segmentation of the human with two separated models. Then, we use a depth inpainting network to recover the depth behind the human body. This two-step strategy is necessary because the human visual evidences in the RGB images are too strong to be ignored by the depth estimator, therefore, it is easier to train the scene depth estimation as separated tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "text", + "content": "We first train the depth estimator network " + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "text", + "content": ", which takes as input a single egocentric image " + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "text", + "content": " and predicts the depth map with human body " + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\hat{D}^B" + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "text", + "content": ". The network architecture of " + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 377, + 545, + 472 + ], + "type": "text", + "content": " is the same as Hu et al. [11]'s work. To minimize the influence of the domain gap between synthetic and real data, the network is initially trained on the NYU-Depth V2 dataset [23] following [11], and further fine-tuned on the EgoGTA dataset." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "content": "Next, we train the segmentation network " + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "content": " for segmenting the human body. The network takes the egocentric image " + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "content": " as input and predicts the segmentation mask for the human body " + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\hat{S}" + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "content": " as output. Following Yuan et al. [44], we use HRNet as our segmentation network. Similarly, to reduce the domain gap, we pretrain the network on the LIP dataset [8] and finetune the model on the EgoGTA dataset. We do not train network " + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 474, + 545, + 594 + ], + "type": "text", + "content": " on the EgoPW-Scene dataset since it lacks the ground truth segmentation maps and depth maps with the human body." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Finally, we propose a depth inpainting network " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " for generating the final depth map of the scene without human body. We first generate the masked depth map " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{D}^M = (1 - \\hat{S})\\odot \\hat{D}^B" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": ", which is a Hadamard product between the background segmentation and the depth map with human body. Then, the masked depth map " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{D}^M" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " and the segmentation mask " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{S}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " are fed into the inpainting network " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": ", which predicts the final depth map " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\hat{D}^S" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": ". We train the inpainting network " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " and finetune the depth estimation network " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " on both the EgoGTA and EgoPW-Scene datasets. During" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13034" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": "training, we penalize the differences between the predicted depth maps and the ground truth depth of the background scene with " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "L^S" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": " and also keep the depth map consistent in the non-human body regions with " + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "L^C" + }, + { + "bbox": [ + 46, + 72, + 289, + 133 + ], + "type": "text", + "content": ". Specifically, the loss function is defined as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 73, + 137, + 287, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 137, + 287, + 225 + ], + "spans": [ + { + "bbox": [ + 73, + 137, + 287, + 225 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L = \\lambda^ {S} L ^ {S} + \\lambda^ {C} L ^ {C}, \\quad \\text {w i t h} \\\\ L ^ {S} = \\left\\| \\hat {D} _ {G} ^ {S} - D _ {G} ^ {S} \\right\\| _ {2} ^ {2} + \\left\\| \\hat {D} _ {E} ^ {S} - D _ {E} ^ {S} \\right\\| _ {2} ^ {2}, \\quad \\text {a n d} \\\\ L ^ {C} = \\left\\| \\left(\\hat {D} _ {G} ^ {S} - \\hat {D} _ {G} ^ {B}\\right) \\left(1 - \\hat {S} _ {G}\\right) \\right\\| _ {2} ^ {2} \\tag {1} \\\\ + \\left\\| \\left(\\hat {D} _ {E} ^ {S} - \\hat {D} _ {E} ^ {B}\\right) \\left(1 - \\hat {S} _ {E}\\right) \\right\\| _ {2} ^ {2}, \\\\ \\end{array}", + "image_path": "872dadc0932c1c44e185462b138b1e324f89c6ecade129e1f68109281340486f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 232, + 75, + 242 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 75, + 242 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 75, + 242 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 248, + 253, + 264 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 248, + 253, + 264 + ], + "spans": [ + { + "bbox": [ + 80, + 248, + 253, + 264 + ], + "type": "interline_equation", + "content": "\\hat {D} _ {G} ^ {S} = \\mathcal {G} (\\hat {D} _ {G} ^ {M}, \\hat {S} _ {G}); \\quad \\hat {D} _ {E} ^ {S} = \\mathcal {G} (\\hat {D} _ {E} ^ {M}, \\hat {S} _ {E});", + "image_path": "a322b22a3f841fe2a0f2ba0fc9dcbfb588b39e1d4b5e964a80f7ef1b919c6fe7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 81, + 266, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 266, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 81, + 266, + 287, + 281 + ], + "type": "interline_equation", + "content": "\\hat {D} _ {G} ^ {B} = \\mathcal {D} (I _ {G}); \\quad \\hat {D} _ {E} ^ {B} = \\mathcal {D} (I _ {E}); \\tag {2}", + "image_path": "9a394bce53546bdeca3e08ede5835e39f62d3655663c95bb50753d517fe78b37.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 83, + 283, + 231, + 298 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 283, + 231, + 298 + ], + "spans": [ + { + "bbox": [ + 83, + 283, + 231, + 298 + ], + "type": "interline_equation", + "content": "\\hat {S} _ {G} = \\mathcal {S} (I _ {G}); \\quad \\hat {S} _ {E} = \\mathcal {S} (I _ {E}),", + "image_path": "d31b50fdd7a9020837ec4a23e1ae9011a8c3acf1fb24a817886f66c326790edf.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "type": "inline_equation", + "content": "\\lambda^S" + }, + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "type": "inline_equation", + "content": "\\lambda^C" + }, + { + "bbox": [ + 47, + 306, + 244, + 319 + ], + "type": "text", + "content": " are the weights of the loss terms." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 326, + 256, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 256, + 338 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 256, + 338 + ], + "type": "text", + "content": "3.3. Scene-aware Egocentric Pose Estimator" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "content": "In this section, we introduce our scene-aware egocentric pose estimator. We rely on the prior that human bodies are mostly in contact with the scene. However, estimating the contact explicitly from a single egocentric image is very challenging. Therefore, we rely on a data-driven approach by learning a model that predicts a plausible 3D pose given the estimated scene geometry and features extracted from the input image. To achieve this goal, we first leverage the EgoPW [35] body joints heatmap estimator to extract 2D body pose features " + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "content": " and use the scene depth estimator from Sec. 3.2 to estimate the depth map of the scene without human body " + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\hat{D}^S" + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "content": ". Afterwards, we project the body pose features and depth map into a 3D volumetric space considering the fisheye camera projection model. After obtaining the volumetric representation of human body features " + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{body}}" + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "content": " and scene depth " + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{scene}}" + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "content": ", the 3D body pose " + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "inline_equation", + "content": "\\hat{P}" + }, + { + "bbox": [ + 46, + 344, + 287, + 548 + ], + "type": "text", + "content": " is predicted from the volumetric representation with a V2V network [22]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 549, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 549, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 287, + 632 + ], + "type": "text", + "content": "Lifting the image features and depth maps to a 3D representation allows getting more plausible results, as inconsistent joint predictions can be behind the volumetric scene " + }, + { + "bbox": [ + 46, + 549, + 287, + 632 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{scene}}" + }, + { + "bbox": [ + 46, + 549, + 287, + 632 + ], + "type": "text", + "content": " (pose-scene penetration) or spatially isolated from the voxelized scene geometry (pose floating), so they can be easily identified and adjusted by the volumetric convolutional network." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 259, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 259, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 259, + 658 + ], + "type": "text", + "content": "3.3.1 Scene and Body Encoding as a 3D Volume" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "In order to create the volumetric space, we first create a 3D bounding box around the person in the egocentric camera coordinate system of size " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "L \\times L \\times L" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " denotes the length of the side of the bounding box in meters." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "The egocentric camera is placed at the center-top of the 3D bounding box so that the vertices of the bounding boxes are: " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "(\\pm L / 2, \\pm L / 2, 0)" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "(\\pm L / 2, \\pm L / 2, L)" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " under the egocentric camera coordinate system. Next, we discretize the bounding box by a volumetric cube " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "V \\in R^{N,N,N,3}" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": ". Each voxel " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "V_{xyz} \\in R^3" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " in position " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": " is filled with the coordinates of its center under the egocentric camera coordinate system " + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "inline_equation", + "content": "(xL / N - L / 2, yL / N - L / 2, zL / N)" + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": "We project the 3D coordinates in " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " into the egocentric image space with the fisheye camera model [27]: " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{proj}} = \\mathcal{P}(V)" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{proj}} \\in R^{N,N,N,2}" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " is the fisheye camera projection function. The volumetric representation " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{body}}" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " of the human body is obtained by filling a cube " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{body}} \\in R^{N,N,N,K}" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " by bilinear sampling from the feature maps " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": " channels using 2D coordinates in " + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{proj}}" + }, + { + "bbox": [ + 304, + 168, + 545, + 253 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 390, + 258, + 545, + 272 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 258, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 390, + 258, + 545, + 272 + ], + "type": "interline_equation", + "content": "V _ {\\text {b o d y}} = F \\left\\{V _ {\\text {p r o j}} \\right\\} \\tag {3}", + "image_path": "785f2671b9bbcbd588d7c485c57c3c37df20173f187ed33688dcde1540e6cbe3.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 277, + 456, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 456, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 456, + 289 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 277, + 456, + 289 + ], + "type": "inline_equation", + "content": "\\{\\cdot\\}" + }, + { + "bbox": [ + 305, + 277, + 456, + 289 + ], + "type": "text", + "content": " denotes bilinear sampling." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": "Then, we project the depth map to the 3D volumetric space. We first generate the point cloud of the scene geometry " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " from the depth map " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "\\hat{D}^S" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " with the fisheye camera projection function " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "C = \\mathcal{P}^{-1}(\\hat{D}^S)" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": ". The volumetric representation of scene depth map " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{scene}}" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " is obtained by filling a binary cube " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{scene}} \\in R^{N,N,N}" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " by setting the voxel at " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " to 1 if there exists one point " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "(x_p,y_p,z_p)" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " in the point cloud " + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 289, + 545, + 384 + ], + "type": "text", + "content": " such that:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 329, + 388, + 545, + 416 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 388, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 329, + 388, + 545, + 416 + ], + "type": "interline_equation", + "content": "\\left\\| \\left(\\frac {x L}{N} - \\frac {L}{2}, \\frac {y L}{N} - \\frac {L}{2}, \\frac {z L}{N}\\right) - \\left(x _ {p}, y _ {p}, z _ {p}\\right) \\right\\| < \\epsilon \\tag {4}", + "image_path": "bb31e3b5dd9676512b24448c7dcd95233793d0a9467497624f2f4c1d6824e196.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": " is the threshold distance. In our experiment, we set " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "L = 2.4\\mathrm{m}" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "N = 64" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\epsilon = 0.04\\mathrm{m}" + }, + { + "bbox": [ + 304, + 420, + 545, + 468 + ], + "type": "text", + "content": ". This setting can cover most types of the human motions and allows high accuracy of the predicted body pose." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 482, + 527, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 482, + 527, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 482, + 527, + 495 + ], + "type": "text", + "content": "3.3.2 Predicting 3D Body Pose with V2V Network" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "text", + "content": "We feed the volumetric representation aggregated from " + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{body}}" + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{scene}}" + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "text", + "content": " into the volumetric convolutional network " + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 304, + 501, + 545, + 549 + ], + "type": "text", + "content": ", which has a similar architecture as [22]. The V2V network produces the 3D heatmaps of the body joints:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 370, + 555, + 545, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 555, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 370, + 555, + 545, + 569 + ], + "type": "interline_equation", + "content": "V _ {\\text {h e a t m a p}} = \\mathcal {N} \\left(V _ {\\text {b o d y}}, V _ {\\text {s c e n e}}\\right) \\tag {5}", + "image_path": "3ec7af9e67f72bc3036b5dd00789663bdd61bb48e235761b4312dc8fc0c6e839.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "content": "Following [14], we compute the soft-argmax of " + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "inline_equation", + "content": "V_{\\mathrm{heatmap}}" + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "content": " across the spatial axes to infer the body pose " + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\hat{P}" + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "content": ". The predicted pose " + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\hat{P}" + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "content": " is finally compared with the ground truth pose " + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "inline_equation", + "content": "P_G" + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "content": " from the EgoGTA dataset and " + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "inline_equation", + "content": "P_E" + }, + { + "bbox": [ + 304, + 574, + 545, + 635 + ], + "type": "text", + "content": " from the EgoPW-Scene dataset with the MSE loss." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 646, + 388, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 646, + 388, + 659 + ], + "spans": [ + { + "bbox": [ + 305, + 646, + 388, + 659 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "In this section, we evaluate our method considering existing and new datasets for egocentric monocular 3D human pose estimation. Please refer to the supplementary materials for the implementation details." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13035" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 296, + 232 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 296, + 232 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 296, + 232 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 296, + 232 + ], + "type": "image", + "image_path": "24d37ad4186d24883596ad3592a1d233f8c9c8dc7087e277685f9fd9b17abc78.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison between our method and the state-of-the-art egocentric pose estimation methods. From left to right: input image, " + }, + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "type": "text", + "content": " result, " + }, + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "type": "inline_equation", + "content": "x\\mathrm{R}" + }, + { + "bbox": [ + 46, + 239, + 546, + 294 + ], + "type": "text", + "content": " -egopose result, EgoPW result and our result. The ground truth pose is shown in red. The input images from the left part are from our test dataset, while those in the right part come from the EgoPW [35] in-the-wild test sequences (without ground-truth poses). We also show the gt scene geometry of the in-the-studio data and scene geometry obtained by SFM method for the in-the-wild data. For better visualizing the interaction between human body and environment, please refer to our supplementary video." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 298, + 70, + 541, + 232 + ], + "blocks": [ + { + "bbox": [ + 298, + 70, + 541, + 232 + ], + "lines": [ + { + "bbox": [ + 298, + 70, + 541, + 232 + ], + "spans": [ + { + "bbox": [ + 298, + 70, + 541, + 232 + ], + "type": "image", + "image_path": "b702faf82fbaf5276500b08d4434b14f8de5e4d0ecc62365cf84295bc0024fc3.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 306, + 163, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 163, + 317 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 163, + 317 + ], + "type": "text", + "content": "4.1. Evaluation Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 329, + 290, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 290, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 290, + 520 + ], + "type": "text", + "content": "Evaluating human-scene interaction requires precise annotations for camera pose and scene geometry. However, such information is not available in existing datasets for egocentric human pose estimation. To solve this issue, we collected a new real-world dataset using a head-mounted fisheye camera combined with a calibration board. The ground truth scene geometry is obtained with SfM method [10] from a multi-view capture system with 120 syncd 4K resolution cameras and the ground truth egocentric camera pose is obtained by localizing a calibration board rigidly attached to the egocentric camera. This dataset contains around 14K frames of two actors, performing various human-scene interacting motions such as sitting, reading newspaper, and using a computer. This dataset will be made publicly available and additional details of it are shown in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "type": "text", + "content": "Besides our new test dataset, we also evaluate our methods in the test datasets from Wang et al. [36] and " + }, + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "type": "text", + "content": " [39]. The real-world dataset in " + }, + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 46, + 525, + 288, + 597 + ], + "type": "text", + "content": " [39] contains 2.7K frames of two people captured in indoor and outdoor scenes, and the dataset in Wang et al. [36] contains 12K frames of two people captured in the studio." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 618, + 160, + 629 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 160, + 629 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 160, + 629 + ], + "type": "text", + "content": "4.2. Evaluation Metrics" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": "We measure the accuracy of the estimated body pose with the MPJPE and PA-MPJPE. For the test dataset in Wang et al. [36] and " + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 46, + 641, + 288, + 715 + ], + "type": "text", + "content": " [39], we evaluate PA-MPJPE and BA-MPJPE [39] since the ground truth poses in the egocentric camera space are not provided. Further details of the metrics are shown in the supplementary materials." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 304, + 545, + 499 + ], + "blocks": [ + { + "bbox": [ + 308, + 304, + 545, + 499 + ], + "lines": [ + { + "bbox": [ + 308, + 304, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 308, + 304, + 545, + 499 + ], + "type": "table", + "html": "
MethodMPJPEPA-MPJPE
Our test dataset
Mo2Cap2 [39]200.3121.2
xR-egopose [32]241.3133.9
EgoPW [35]189.6105.3
Ours118.592.75
MethodPA-MPJPEBA-MPJPE
Wang et al.'s dataset [36]
Mo2Cap2 [39]102.374.46
xR-egopose [32]112.087.20
EgoPW [35]81.7164.87
Ours76.5061.92
Mo2Cap2 test dataset [39]
Mo2Cap2 [39]91.1670.75
xR-egopose [32]86.8566.54
EgoPW [35]83.1764.33
Ours79.6562.82
", + "image_path": "79d8d34eaa22e562f869b6172e300a1728dabc5708f51a332d69535b7c058718.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "text", + "content": "Table 1. Performance of our method on our test dataset, Wang et al.'s test dataset [36] and " + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "text", + "content": " test dataset [39]. Our method outperforms the state-of-the-art methods EgoPW, " + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "text", + "content": " [39] and " + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "inline_equation", + "content": "xR" + }, + { + "bbox": [ + 304, + 517, + 547, + 562 + ], + "type": "text", + "content": "-egopose [32]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 574, + 499, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 499, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 499, + 586 + ], + "type": "text", + "content": "4.3. Comparisons on 3D Pose Estimation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "In this section, we compare our approach with previous single-frame-based methods, including EgoPW [35], " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Regopose [32] and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " [39] on our test dataset under the \"Our test data\" in Table 1. Since the code for " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Regopose is not released, we use our implementation for the evaluation. In our dataset, the proposed method outperforms the previous state-of-the-art methods, EgoPW [35] by " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "37.5\\%" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " on MPJPE and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "11.9\\%" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " on PA-MPJPE. We also compared with previous methods on the Wang et al.'s test dataset [36] and " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " test dataset [39] and show the re" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13036" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 286, + 130 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 286, + 130 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 286, + 130 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 286, + 130 + ], + "type": "table", + "html": "
MethodNon pene.Contact
Mo2Cap2 [39]69.6%23.1%
xR-egopose [32]64.5%38.3%
EgoPW [35]71.7%38.8%
Ours84.1%89.4%
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Our network can generate different poses under different depth input and further disambiguate body poses under scene constraint." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "text", + "content": "sults in Table 1. On Wang et al.'s test dataset, our method performs better than EgoPW by " + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "inline_equation", + "content": "6.4\\%" + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "text", + "content": ". On the " + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^{2}\\mathrm{Cap}^{2}" + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "text", + "content": " test dataset, our method performs better than EgoPW by " + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "inline_equation", + "content": "7.8\\%" + }, + { + "bbox": [ + 46, + 352, + 287, + 388 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 388, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 496 + ], + "type": "text", + "content": "We also evaluate the physical plausibility of our predictions by calculating the percentage of predicted poses that are in contact with the scene and do not penetrate the scene in Table 2. We define a body pose as in contact with the scene if any body joint is less than " + }, + { + "bbox": [ + 46, + 388, + 287, + 496 + ], + "type": "inline_equation", + "content": "5\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 388, + 287, + 496 + ], + "type": "text", + "content": " from the scene mesh. A body pose suffers from the body floating issue if it is not in contact with the scene. Compared with previous approaches, our method generates body poses more physically plausible considering the constraints of the scene." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 605 + ], + "type": "text", + "content": "From the results in Table 1 and Table 2, we can see that our approach outperforms all previous methods on the single-frame egocentric pose estimation task. For the qualitative comparison, we show the results of our method on the studio dataset and in-the-wild sequences in Fig. 3. See our supplementary video for more qualitative evaluations. Our predicted poses are physically plausible under the scene constraint, whereas other methods generate poses suffering from body floating and penetration issues." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "In order to further demonstrate our method performing predictions accordingly to the constraint of the scene geometry, we fix the input image and change the scene depth input to the depth map corresponding to the standing pose, squatting pose, and sitting pose. The results are presented in Fig. 4 and show that the predicted poses change to standing, squatting, and sitting to better adapt to the input changes of the scene geometry. This shows our method's ability to disambiguate poses under different scene constraints." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 70, + 545, + 186 + ], + "blocks": [ + { + "bbox": [ + 48, + 148, + 285, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 148, + 285, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 148, + 285, + 159 + ], + "type": "text", + "content": "Table 2. Comparisons of physical plausibility on our test dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 70, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 545, + 186 + ], + "type": "table", + "html": "
MethodMPJPEPA-MPJPE
EgoPW+Optimizer187.1103.2
EgoPW+Depth149.698.15
xR-egopose+Depth180.5103.7
Ours w/o Depth188.1105.1
Ours+Depth with Body167.3103.3
Ours+Depth w/o Body135.795.84
Ours+Depth w/o Inpainting124.295.00
Ours+GT Depth109.988.80
Ours118.592.75
", + "image_path": "b35ad4bbf5dd5306f5cdcd3b4f9c151cf99d9506ebf3156e4f1355420f96f1af.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 203, + 545, + 215 + ], + "lines": [ + { + "bbox": [ + 306, + 203, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 306, + 203, + 545, + 215 + ], + "type": "text", + "content": "Table 3. Results from our method compared to different baselines." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 236, + 399, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 399, + 248 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 399, + 248 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "text", + "content": "Simple Combination of 2D Features and Depth Maps. In Sec. 3.3, we claim that the volumetric representation of egocentric 2D features and scene depth map is important for understanding the interaction between the human body and the surrounding scene. To provide evidence of this claim, in this experiment, we compare our method with baseline methods that simply combine the 2D image features and scene depth map. We set two baseline methods since there are two types of egocentric pose estimation methods, i.e. direct regression of 3D poses (" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "text", + "content": "-R-egopose [32]) and prediction of 2D position and depth for each joint (" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "inline_equation", + "content": "\\mathrm{Mo}^2\\mathrm{Cap}^2" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "text", + "content": " [39] and EgoPW [35]). In the baseline method “" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "text", + "content": "-R-egopose + Depth”, we concatenate 2D heatmaps and scene depth map as the input to the 3D pose regression network in " + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 255, + 545, + 458 + ], + "type": "text", + "content": "-R-egopose. In the baseline “EgoPW + Depth”, we concatenate the 2D features and the scene depth map and input them into the joint depth prediction network." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 602 + ], + "type": "text", + "content": "From the evaluation results shown in Table 3, both of the baseline methods perform worse than our proposed method. In \"xR-egopose + Depth\", simply combining the scene depth and 2D heatmaps cannot provide direct geometric supervision for the 3D pose regression network. In \"EgoPW + Depth\", though the joint depth estimation network performs better with the help of scene depth information, the 2D pose estimation network does not benefit from it. Both of the experiments demonstrate the effectiveness of our volumetric representation of 2D features and scene geometry, which provides direct geometry supervision for the physical plausibility of predicted egocentric poses." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Optimization. In this experiment, we compare our method with an optimization baseline that refines a 3D pose considering the scene constraint. Similar to Wang et al. [36] and EgoPW [35], we first train a VAE consisting of a CNN-based encoder " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{enc}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " and decoder " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{dec}}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " to learn an egocentric motion prior. Then, We optimize the egocentric pose " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " by finding a latent vector " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " such that the corresponding pose " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "P = f_{\\mathrm{dec}}(z)" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " minimizes the objective function" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13037" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E(P) = \\lambda_{R}E_{R} + \\lambda_{J}E_{J} + \\lambda_{C}E_{C}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E_{R}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is the egocentric reprojection term, " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E_{J}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is the egocentric pose regularization term, and " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E_{C}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is the contact term. The latent vector " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is initialized with the estimated pose from the EgoPW method. The " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E_{R}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E_{J}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " are the same as those defined in Wang et al. [36]. Denote the nth joint in egocentric pose " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "P_{n}, n \\in [0, N]" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is the number of joints, and the mth point in scene point cloud " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "C_{m}, m \\in [0, M]" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is the number of points in the point cloud. The contact term " + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "E_{C}" + }, + { + "bbox": [ + 47, + 72, + 289, + 192 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 199, + 287, + 229 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 199, + 287, + 229 + ], + "spans": [ + { + "bbox": [ + 61, + 199, + 287, + 229 + ], + "type": "interline_equation", + "content": "E _ {C} = \\sum_ {n \\in [ 0, N ]} d _ {n} ^ {2}, \\quad \\text {i f} d _ {n} \\leq \\epsilon , \\text {o t h e r w i s e} 0, \\text {a n d} \\tag {6}", + "image_path": "b75f6bbe7ff1e506bf82c7a1851876a92c9450c9481692a31efbd0fb0b40af5a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 66, + 230, + 181, + 248 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 230, + 181, + 248 + ], + "spans": [ + { + "bbox": [ + 66, + 230, + 181, + 248 + ], + "type": "interline_equation", + "content": "d _ {n} = \\min _ {m \\in [ 0, M ]} \\| P _ {n} - C _ {m} \\| _ {2}.", + "image_path": "b83ad233731561dfbff61ecdec1c6cd149a04de95460cea9203f544e7606fbe0.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "text", + "content": "We first calculate the nearest distance " + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "inline_equation", + "content": "d_{n}" + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "text", + "content": " between each body joint and the projected point cloud " + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "text", + "content": " from the scene depth map. If the distance " + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "inline_equation", + "content": "d_{n}" + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "text", + "content": " of the nth joint is less than a margin " + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 256, + 287, + 316 + ], + "type": "text", + "content": ", it is defined as in contact with the scene and minimized with the optimization framework." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 316, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 437 + ], + "type": "text", + "content": "The result of the optimization method is shown as \"EgoPW+Optimizer\" in Table 3, which demonstrates that the optimization framework is less effective than our method. This is because the accuracy of optimization method relies heavily on the initial pose. If the initial pose is not accurate, it will be difficult to determine the contact labels for each joint with the fixed distance margin. Without accurate contact labels, the optimization framework might force the joint that does not contact the scene to keep in contact, eventually resulting in wrong poses." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "content": "Scene Depth Estimator. In our work, we estimate the depth of the surrounding scene and infer the depth behind the human body with a depth inpainting network. In order to validate the effectiveness of the scene depth map, we remove the input depth map from the V2V network and show the results of \"Ours w/o Depth\" in Table 3. This baseline increases the MPJPE by about " + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "inline_equation", + "content": "70\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 450, + 287, + 545 + ], + "type": "text", + "content": ", which is evidence of the relevant extra information provided by the scene depth." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 665 + ], + "type": "text", + "content": "To demonstrate the benefits of recovering the scene depth behind the human body, we evaluate our model using the estimated depth including the human body as the input to the V2V network. We also removed the human body area from the depth maps and use them as input to the V2V network. The results are shown in \"Ours+Depth with Body\" and \"Ours+Depth w/o Body\" in Table 3. Both of the baseline methods perform worse than our method because the area in the scene occluded by the human body can provide clues for generating plausible poses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "We also evaluate our method with ground truth depth maps in \"Ours+GT Depth\" in Table 3, which further improves over our estimated depth by " + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "inline_equation", + "content": "7.2\\%" + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": " in terms of MPJPE and " + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": " in terms of PA-MPJPE. This demonstrates that the" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 312, + 70, + 369, + 125 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 369, + 125 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 369, + 125 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 369, + 125 + ], + "type": "image", + "image_path": "e57c5edb413a11d30e44ea42f61ba62d194057bb9d302d9c40e2763596dd7f50.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 326, + 127, + 353, + 133 + ], + "lines": [ + { + "bbox": [ + 326, + 127, + 353, + 133 + ], + "spans": [ + { + "bbox": [ + 326, + 127, + 353, + 133 + ], + "type": "text", + "content": "Input Image" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 370, + 70, + 425, + 125 + ], + "blocks": [ + { + "bbox": [ + 370, + 70, + 425, + 125 + ], + "lines": [ + { + "bbox": [ + 370, + 70, + 425, + 125 + ], + "spans": [ + { + "bbox": [ + 370, + 70, + 425, + 125 + ], + "type": "image", + "image_path": "e79042addfe1bd766a45c3793dd0b64fc15679757676e5aace79f76005123241.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 127, + 423, + 133 + ], + "lines": [ + { + "bbox": [ + 371, + 127, + 423, + 133 + ], + "spans": [ + { + "bbox": [ + 371, + 127, + 423, + 133 + ], + "type": "text", + "content": "w/o Inpainting Network" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 427, + 70, + 482, + 125 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 482, + 125 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 482, + 125 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 482, + 125 + ], + "type": "image", + "image_path": "23d0b79496cf44922c2a8e9d5e055899f92bfe6aa221d23fafc0987165151d79.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 430, + 127, + 479, + 133 + ], + "lines": [ + { + "bbox": [ + 430, + 127, + 479, + 133 + ], + "spans": [ + { + "bbox": [ + 430, + 127, + 479, + 133 + ], + "type": "text", + "content": "w. Inpainting Network" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 143, + 547, + 176 + ], + "lines": [ + { + "bbox": [ + 305, + 143, + 547, + 176 + ], + "spans": [ + { + "bbox": [ + 305, + 143, + 547, + 176 + ], + "type": "text", + "content": "Figure 5. The qualitative depth estimation results with or without inpainting network. The depth map estimated without inpainting network show artifacts in the human body region (see the red box)." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 485, + 70, + 541, + 125 + ], + "blocks": [ + { + "bbox": [ + 485, + 70, + 541, + 125 + ], + "lines": [ + { + "bbox": [ + 485, + 70, + 541, + 125 + ], + "spans": [ + { + "bbox": [ + 485, + 70, + 541, + 125 + ], + "type": "image", + "image_path": "117661e42da7f43528682da4a98092897b83bd87164910b9b229c741b2722421.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 501, + 127, + 523, + 133 + ], + "lines": [ + { + "bbox": [ + 501, + 127, + 523, + 133 + ], + "spans": [ + { + "bbox": [ + 501, + 127, + 523, + 133 + ], + "type": "text", + "content": "GT Depth" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 197, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 197, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 197, + 545, + 232 + ], + "type": "text", + "content": "accuracy of our predicted pose benefits from better depth maps, but still our estimated scene depth already provides a significant improvement over the baselines." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "type": "text", + "content": "Finally, we compare with a baseline method without depth inpainting, i.e., the human body is removed from the input image and the scene depth map is predicted directly with the network " + }, + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "type": "text", + "content": " in Sec. 3.2. The pose estimation accuracy is shown in \"Ours+Depth w/o Inpainting\" of Table 3 and the depth accuracy is shown in Table 4. Our method outperforms the baseline as it is more challenging to simultaneously estimate and inpaint the depth. Moreover, the network can be influenced by the segmented part in the input image as some extinct object, as shown in Fig 5." + } + ] + } + ], + "index": 18 + }, + { + "type": "table", + "bbox": [ + 307, + 361, + 545, + 399 + ], + "blocks": [ + { + "bbox": [ + 307, + 361, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 307, + 361, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 307, + 361, + 545, + 399 + ], + "type": "table", + "html": "
MethodAbs-RelRMSE(m)
w/o Inpainting Network0.38340.7856
Ours0.10690.3365
", + "image_path": "c1dd0c6db0f7b30e3167605f6cbef0050e3067f92c477e7965f5cf0e42242574.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 417, + 545, + 440 + ], + "lines": [ + { + "bbox": [ + 306, + 417, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 306, + 417, + 545, + 440 + ], + "type": "text", + "content": "Table 4. The quantitative results of depth estimator. We evaluate Abs-Rel and RMSE on our test dataset following [11]." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 454, + 378, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 378, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 378, + 466 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 474, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 617 + ], + "type": "text", + "content": "In this paper, we have proposed a new approach to estimate egocentric human pose under the scene constraint. We firstly train a depth inpainting network for estimating the depth map of the scene without human body. Next, we combine the egocentric 2D features and scene depth map in a volumetric space and predict the egocentric pose with a V2V network. The experiments show that our method outperforms all of the baseline methods both qualitatively and quantitatively and our method can predict physically plausible poses in terms of human-scene interaction. In future, this method could be extended to estimate physically-plausible egocentric motion from a temporal sequence." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 617, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 677 + ], + "type": "text", + "content": "Limitations. The accuracy of voxel-based pose estimation network is constrained by the accuracy of estimated depth, especially where the scene is occluded by the human body. One solution is to leverage the temporal information to get a full view of the surrounding environment." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgments Jian Wang, Diogo Luvizon, Lingjie Liu, and Christian Theobalt have been supported by the ERC Consolidator Grant 4DReply (770784)." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "13038" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Hiroyasu Akada, Jian Wang, Soshi Shimada, Masaki Takahashi, Christian Theobalt, and Vladislav Golyanik. 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In 2021 International Conference on 3D Vision (3DV), pages 32-41, 2021. 2" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "13040" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SceneComposer_ Any-Level Semantic Image Synthesis/a420eecc-24ac-471a-873a-4cbedabb0ab3_content_list.json b/2023/SceneComposer_ Any-Level Semantic Image Synthesis/a420eecc-24ac-471a-873a-4cbedabb0ab3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..140e8217d1ec2f473a34c2a28b6aec7850a67567 --- /dev/null +++ b/2023/SceneComposer_ Any-Level Semantic Image Synthesis/a420eecc-24ac-471a-873a-4cbedabb0ab3_content_list.json @@ -0,0 +1,1790 @@ +[ + { + "type": "text", + "text": "SceneComposer: Any-Level Semantic Image Synthesis", + "text_level": 1, + "bbox": [ + 207, + 130, + 759, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yu Zeng $^{1}$ , Zhe Lin $^{2}$ , Jianming Zhang $^{2}$ , Qing Liu $^{2}$ , John Collomosse $^{2}$ , Jason Kuen $^{2}$ , Vishal M. Patel $^{1}$ $\\{\\text{yzeng22, vpatel36}\\} \\text{@jhu.edu}, \\{\\text{zlin, jianmzha, qingl, collomos, kuen}\\} \\text{@adobe.com}$ $^{1}$ Johns Hopkins University \n $^{2}$ Adobe Research", + "bbox": [ + 89, + 179, + 875, + 233 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/670eec9841d40299b0da4b3b356f274cd4361c8989d7b52a7b9cc15993f7147f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 261, + 240, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9b18ceba777bf08f007cf132045e9eaab54d8546ebb1bbd8be3a355534d595e6.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 388, + 240, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4fe9e8499155eb5cec62291edcfa798f6eb04bc2d42dc211f0094b69a83e7f5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 243, + 261, + 401, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/82e5e415073707d324d5789e2fdcbd21f9a8149b7732bdf7b802bc13323ae9af.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 243, + 388, + 401, + 512 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/37469b35d4eb690cce43b11b23aa20e60754da3019f780c6cd72147646375f71.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 262, + 563, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f0d0901bb119c07bb0f0da29b9504048abd91ae816ce51fd2598e2871468735c.jpg", + "image_caption": [ + "(c)", + "Figure 1. Examples of image synthesis from any-level semantic layouts. (a) The coarsest layout, i.e. at the 0-th precision level, is equivalent to a text input; (d) the finest layout, i.e. at the highest level, is close to an accurate segmentation map; (a)-(d) intermediate level layouts (from coarse to fine), the shape control becomes tighter with increasing levels. (e) We can specify different precision levels for different components, e.g. to include a 0-th level style indicator while the remaining regions are of higher levels." + ], + "image_footnote": [], + "bbox": [ + 403, + 388, + 563, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4346cc5243d02861b81360534cec9d4b7d6e49e3d230700fbd0cf1fb71b197cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 262, + 725, + 387 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/59d7f186eaa5415b867fc4a1c927ca04c9bb1a3c3bd8208bd15ecf910d086946.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 566, + 388, + 725, + 513 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cdf37ff39d7616057b8f9e67b183fd19b3cbedcc722f7508f4cafe2468adb6c1.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 727, + 251, + 888, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 590, + 313, + 607 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a new framework for conditional image synthesis from semantic layouts of any precision levels, ranging from pure text to a 2D semantic canvas with precise shapes. More specifically, the input layout consists of one or more semantic regions with free-form text descriptions and adjustable precision levels, which can be set based on the desired controllability. The framework naturally reduces to text-to-image (T2I) at the lowest level with no shape information, and it becomes segmentation-to-image (S2I) at the highest level. By supporting the levels in-between, our framework is flexible in assisting users of different drawing expertise and at different stages of their creative workflow. We introduce several novel techniques to address the challenges coming with this new setup, including a pipeline for collecting training data; a precision-encoded mask pyramid and a text feature map representation to jointly encode precision level, semantics, and composition information; and a multi-scale guided diffusion model to synthesize images. To evaluate", + "bbox": [ + 73, + 628, + 473, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the proposed method, we collect a test dataset containing user-drawn layouts with diverse scenes and styles. Experimental results show that the proposed method can generate high-quality images following the layout at given precision, and compares favorably against existing methods. Project page https://zengxianyu.github.io/scenegc/", + "bbox": [ + 496, + 593, + 895, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 722, + 632, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, deep generative models such as StyleGAN [24, 25] and diffusion models [9, 19, 49] have made a significant breakthrough in generating high-quality images. Image generation and editing technologies enabled by these models have become highly appealing to artists and designers by helping their creative workflows. To make image generation more controllable, researchers have put a lot of effort into conditional image synthesis and introduced models using various types and levels of semantic input such as object categories, text prompts, and segmentation", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22468", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/f19b580a86d89f85c9161aedb0520a2925a5e04978102289f52398b63850b726.jpg", + "table_caption": [ + "Table 1. Difference from related conditional image synthesis works. T2I: text to image, S2I: segmentation to image, ST2I: Scene-based text to image [13], Box2I: bounding box layout to image [50]." + ], + "table_footnote": [], + "table_body": "
SettingOpen-domain layoutShape controlSparse layoutCoarse shapeLevel control
T2I✓XXXX
S2IX✓XXX
ST2IX✓XXX
Box2IXX✓XX
Ours✓✓✓✓✓
", + "bbox": [ + 80, + 133, + 468, + 200 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "maps etc. [23, 35, 36, 43, 44, 67].", + "bbox": [ + 76, + 212, + 290, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, existing models are not flexible enough to support the full creative workflow. They mostly consider fixed-level semantics as the input [63], e.g. image-level text descriptions in text-to-image generation (T2I) [35, 39, 41, 43, 44], or pixel-level segmentation maps in segmentation-to-image generation (S2I) [23, 36, 67]. Recent breakthroughs on T2I such as DALLE2 [39] and StableDiffusion [1, 43] demonstrate extraordinary capabilities of generating high-quality results. They can convert a rough idea into visual messages to provide inspirations at the beginning of the creative process, but provide no further control over image composition. On the other hand, S2I allows users to precisely control the image composition. As it is extremely challenging to draw a detailed layout directly, S2I is more useful for later creative stages given initial designs. For real-world use cases, it is highly desirable to have a model which can generate images from not only pure text or segmentation maps, but also intermediate-level layouts with coarse shapes.", + "bbox": [ + 75, + 229, + 472, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a new unified conditional image synthesis framework to generate images from a semantic layout at any combination of precision levels. It is inspired by the typical coarse-to-fine workflow of artists and designers: they first start from an idea, which can be expressed as a text prompt or a set of concepts (Fig. 1 (a)), then tend to draw the approximate outlines and refine each object (Fig. 1 (a)-(d)). More specifically, we model a semantic layout as a set of semantic regions with free-form text descriptions. The layout can be sparse and each region can have a precision level to control how well the generated object should fit to the specified shape. The framework reduces to T2I when the layout is the coarsest (Fig. 1 (a)), and it becomes S2I when the layout is a segmentation map (Fig. 1 (d)). By adjusting the precision level, users can achieve their desired controllability (Fig. 1 (a)-(d)). This framework is different from the existing works in many aspects, as summarized in Table 1.", + "bbox": [ + 75, + 503, + 470, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This new setup comes with several challenges. First, it is non-trivial to encode open-domain layouts in image synthesis frameworks. Second, to handle hand-drawn layouts of varying precision, we need an effective and robust way to inject the precision information into the layout encoding. Third, there is no large-scale open-domain layout/image dataset. To generate high-quality images and generalize to novel concepts, a large and diverse training dataset is crucial.", + "bbox": [ + 75, + 762, + 470, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce several novel ideas to address these chal", + "bbox": [ + 96, + 885, + 470, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "lenges. First, we propose a text feature map representation for encoding a semantic layout. It can be seen as a spatial extension of text embedding or generalization of segmentation masks from binary to continuous space. Second, we introduce a precision-encoded mask pyramid to model layout precision. Inspired by the classical image pyramid models [2, 6, 47, 62], we relate shape precision to levels in a pyramid representation and encode precision by dropping out regions of lower precision levels. In other words, the $l$ -th level of the mask pyramid is a sub layout (subset of regions) consisting of semantic regions with precision level no less than $l$ . By creating a text feature map for each sub layout, we obtain a text feature pyramid as a unified representation of semantics, composition, and precision. Finally, we feed the text feature pyramid to a multi-scale guided diffusion model to generate images. We fulfill the need for training data by collecting them from two sources: (1) large-scale imagedataset pairs; (2) a relatively small pseudo layout/image dataset using text-based object detection and segmentation. With this multi-source training strategy, both text-to-image and layout-to-image can benefit from each other synergistically.", + "bbox": [ + 496, + 90, + 893, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows:", + "bbox": [ + 517, + 409, + 821, + 422 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A unified framework for diffusion-based image synthesis from semantic layouts with any combination of precision control.", + "- Novel ideas to build the model, including precision-encoded mask pyramid and pyramid text feature map representation, and multi-scale guided diffusion model, and training with multi-source data.", + "- A new real-world user-drawn layout dataset and extensive experiments showing the effectiveness of our model for text-to-image and layout-to-image generation with precision control." + ], + "bbox": [ + 517, + 435, + 893, + 602 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 617, + 640, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep generative models. In recent years, there has been significant progress in image generation using deep generative models. Some of these approaches attempt to learn the image distribution by optimizing a likelihood-based objective function. Autoregressive models (ARMs) [11, 55-57] treat images as sequences of pixels or tokens in a learned dictionary to define a tractable density model, which can be optimized by maximizing the likelihood. Variational Autoencoders (VAEs) [26, 54] use an intractable density function and train the model by maximizing the variational lower bound. Diffusion-based models [9, 19, 43, 48, 49] are also trained by optimizing the variational lower bound. Unlike VAEs which map an image into the latent space using a learnable encoder, diffusion-based models use a fixed diffusion process to transform an image into Gaussian noise. Generative Adversarial Networks (GANs) [5, 14, 24, 25] do not define the density function explicitly; instead, generative", + "bbox": [ + 496, + 643, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22469", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "models are trained through an adversarial learning process against a discriminator. We base our method on diffusion models due to their ability to generate high-quality images and stability in training.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Layout/Segmentation-to-image generation refers to the task of generating images from a spatial arrangement of semantic concepts, e.g. a segmentation map or a set of bounding boxes. Segmentation-based methods (e.g. [8,23,36,45,52,59,60]) have been proposed to allow users to precisely control the image composition, but are less flexible as they require a dense and accurate segmentation map and only allow a fixed set of categories. Bounding box-based methods can generate images from a coarse layout of bounding boxes. Bounding box-based generation was studied as a standalone task first by Zhao et al. [66] and has been an active research area [3, 17, 30, 58] since then. To convey more information than object categories, more expressive bounding box descriptions have been introduced, such as attributes [3, 34], relations [3], and free-form descriptions [12]. Although bounding boxes are easier to draw than segmentation maps, they provide no control over object shapes and orientations. In this work, we use coarse shapes with freeform text descriptions and precision levels to represent a layout, providing more flexibility and control for different synthesis needs.", + "bbox": [ + 75, + 152, + 472, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text-to-image/Multi-modal image generation. T2I aims to generate images from a free-form text description, i.e. image captions. Earlier approaches are usually based on conditional GANs [41, 65]. Recently, autoregressive models based on image quantization techniques [10, 40, 64] and diffusion models [1,35,39,43,44] have shown surprising results with large-scale models and datasets. To gain more control over the spatial composition, some studies have tried to incorporate layout in the form of key points [42], bounding boxes [18], or object shapes [13, 21, 27, 29, 37], as an additional input. Some studies focused on image synthesis from multi-modal input including text, segmentation maps, edge maps [22, 61] etc. A work [4] concurrent to ours proposes a training-free paint-with-word method that enables users to specify the object locations by manipulating the attention matrices in cross-attention layers. These approaches use the layout as an extra signal complementary to captions. In contrast, we unify image captions and layout using a multi-level framework that models captions as a special case of layout with the lowest precision level. From a practical perspective, our framework provides a more flexible control mechanism with coarse shapes and precision controllability.", + "bbox": [ + 75, + 468, + 472, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 814, + 250, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method aims to generate images from a layout consisting of a set of semantic regions of varying precision levels. Formally, an input layout can be viewed as a list of tuples $\\{(M_i,t_i,c_i)\\}_{i = 1}^n$ , where $M_{i},t_{i},c_{i}$ indicate the seg", + "bbox": [ + 75, + 839, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mentation mask, text description, and the precision level of the $i$ -th region. We let $M, t, c$ denote the sets of masks, texts and precision levels of all regions, respectively. The precision level variable $c_{i} \\in \\mathbb{N}_{\\leq L}$ indicates how precisely the generated content should follow the mask $M_{i}$ . A smaller value of $c_{i}$ indicates a less precise control allowing more deviation from the mask $M_{i}$ . $c_{i} = 0$ indicates the coarsest level where the $i$ -th mask will be ignored. When all $c_{i} = 0$ , the problem converts into T2I. Fig. 2 shows an overview of the proposed method. To generate an image at resolution $2^{L} \\times 2^{L}$ , we first formulate a precision-encoded mask pyramid $\\{M^{l}\\}_{l=0}^{L}$ which represents each mask at the given precision level (Sec. 3.1). Then we combine the mask pyramid with the text descriptions $\\pmb{t}$ to form a text feature pyramid $\\{Z^{l}\\}_{l=0}^{L}$ . It contains a $2^{l} \\times 2^{l}$ text feature map at each level, which can be seen as an extension of the one-hot label map encoding in S2I (Sec. 3.2). Finally, a multi-level guided diffusion model takes the feature pyramid as input to generate an image (Sec. 3.3).", + "bbox": [ + 496, + 90, + 893, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Precision-Encoded Mask Pyramid", + "text_level": 1, + "bbox": [ + 498, + 385, + 799, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a user-drawn coarse shape, it is challenging to model the exact precision, since the type and the amount of error vary across different users. To simplify the problem, we relate precision to resolutions and propose a precision-encoded mask pyramid to encode the shape and precision information simultaneously. Given a mask and a precision level, a high precision level corresponds to using all details of the masks at a high resolution, while a low precision level means we can only trust the mask at a low resolution.", + "bbox": [ + 496, + 409, + 893, + 542 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "More specifically, given a set of masks $M = [m_1, \\dots, m_n]$ and the precision levels $c = [c_1, \\dots, c_n]$ , we construct the mask pyramid by representing each mask $M_i$ at resolutions up to $2^{c_i}$ . In other words, we resize each mask $M_i$ to multiple resolutions and drop out the masks at resolutions higher than $2^{c_i}$ , as illustrated in Fig. 3. Formally, the $l$ -th layer of the mask pyramid, denoted as $M^l$ , is computed as follows,", + "bbox": [ + 496, + 544, + 893, + 650 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nM _ {i} ^ {l} = \\operatorname {r e s i z e} \\left(M _ {i}, 2 ^ {l}\\right) \\cdot \\mathbb {1} _ {c _ {i} \\geq l}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 652, + 890, + 670 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{resize}(M_i,2^l)$ izes a mask $M_{i}$ to $2^{l}\\times 2^{l}$ resolution through image interpolation and binarization. The indicator function $\\mathbb{1}_{c_i\\geq l}$ returns 1 when $c_{i}\\geq l$ and 0 otherwise. In our implementation, we set the range of precision levels to [0,3,4,5,6]. We observed that for a free-hand drawn layout, $8\\times 8$ masks at the level 3 are easy to draw while being fairly informative, whereas $64\\times 64$ masks at the level 6 usually capture enough details, as illustrated in Fig. 4.", + "bbox": [ + 496, + 672, + 893, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Text Feature Pyramid", + "text_level": 1, + "bbox": [ + 500, + 801, + 705, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The mask pyramid encodes the shape and the precision information. To generate an image, we also need semantic information. We introduce a text feature pyramid for this purpose. Each level of the text feature pyramid is a $2^l \\times 2^l$ text feature map $Z^l$ obtained by combining the masks $M^l$", + "bbox": [ + 496, + 824, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22470", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/417a0a67cf6c17c70ae92b22e9d1d2236ce23ac4f6088687aeed884776bd05f9.jpg", + "image_caption": [ + "Figure 2. An overview of the proposed method. We provide an intuitive interface where users can easily define a layout using a semantic brush associated with a free-form text description and adjustable precision level. The masks, regional descriptions, and precision levels $\\{(M_i,t_i,c_i)\\}_{i = 1}^n$ are jointly encoded into a text feature pyramid, and then translated into an image by a multi-scale guided diffusion model." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 268 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/47165497cc03f72ee41089a95a044cf179ae4d7298de6d6b53c3923a0592c54c.jpg", + "image_caption": [ + "Figure 3. An example of the precision-encoded mask pyramid. The first level has two non-zero masks corresponding to $m_{1}, m_{2}$ as $c_{1}, c_{2} \\geq 1$ ; the second level only has $m_{1}$ as $c_{1} = 2, c_{2} < 2$ ; the third level does not have any non-zero masks as all the precision levels of all masks are lower than 3." + ], + "image_footnote": [], + "bbox": [ + 81, + 338, + 467, + 455 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/705bc0d4eda6fa99dbec254035e35bd0e9c0189ac98c908d5567905e36d5843b.jpg", + "image_caption": [ + "Figure 4. Illustration of the masks at different levels of a pyramid." + ], + "image_footnote": [], + "bbox": [ + 78, + 547, + 467, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and the embeddings of the text $t$ . At the 0-th level, the $1 \\times 1$ masks contain no shape information, so we simply concatenate the embeddings of all words into a sequence. At the levels where $l > 0$ , we spatially spread the embeddings of $t$ over the corresponding masks to jointly represent the shape and semantic, as illustrated in Fig. 2.", + "bbox": [ + 75, + 683, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text feature maps. Here we describe in more detail how we construct the text feature map $Z^l$ at level $l > 0$ . For simplicity, we drop the superscript $l$ and denote the masks at an arbitrary level as $M$ . Each element $M_{i,x,y}$ is a binary value $\\in \\{0,1\\}$ and we allow overlaps or blank spaces, i.e. $n \\geq \\sum_{i}^{n}M_{i,x,y} \\geq 0$ . Given the initial masks $M$ , we introduce normalized masks $\\hat{M}$ , which are augmented from $M$ by adding an extra mask $M_0$ to indicate the blank space and", + "bbox": [ + 75, + 777, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "normalized by the number of shapes at each location:", + "bbox": [ + 500, + 340, + 854, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {M} _ {i, x, y} = M _ {i, x, y} / \\sum_ {i = 0} ^ {n} M _ {i, x, y}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 358, + 892, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M_{0,x,y} = \\mathbb{1}_{\\sum_{i = 1}^{n}M_{i,x,y} = 0}$", + "bbox": [ + 573, + 400, + 792, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the normalized masks $\\hat{M}$ , each element $\\hat{M}_{i,x,y}$ is a continuous value $\\in [0,1]$ and we have $\\sum_{i=0}^{n} \\hat{M}_{i,x,y} = 1$ . We compute each element $Z_{x,y}$ at location $x,y$ as follows,", + "bbox": [ + 498, + 421, + 893, + 469 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {Z} _ {x, y} = \\sum_ {i = 0} ^ {n} \\boldsymbol {f} \\left(t _ {i}\\right) \\cdot \\hat {M} _ {i, x, y}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 472, + 892, + 510 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{f}(t_i)$ is an embedding of the text $t_i$ . We set $t_0$ to be a null token $\\oslash$ to represent unspecified areas, i.e. the blank space indicated by $M_0$ .", + "bbox": [ + 498, + 513, + 892, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The text feature map representation has several advantages. First, it is of the same dimension regardless of the number of masks, and therefore compatible with most deep ConvNet architectures. Second, each element of a text feature map is a convex combination of $n$ text embeddings in the learned embedding space. With a powerful language model, we can achieve a good generalization capability for unseen combinations of concepts. In a text feature map, any overlapping area contains an interpolation of multiple embeddings. Accordingly, users can get creative results derived from hybrid concepts by drawing overlapping shapes.", + "bbox": [ + 496, + 561, + 893, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data acquisition. During inference, the segmentation masks and text descriptions are both provided by users. During training, we can generate them automatically using text-based object detection [28] and segmentation [16]. We set the regions where no objects are detected as blank space and assign a null token $\\varnothing$ to these regions. We use CLIP [38] text model to encode the text descriptions. In addition, the 0-th level feature maps can be obtained directly from the image caption embeddings. More details regarding the training data generation step can be found in the supplementary material.", + "bbox": [ + 496, + 731, + 893, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relation to one-hot label maps. In S2I, a layout containing", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22471", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/942e03bcc103c4a721de3dec0137980dbc61d859d111f3b3798bcbee6f7ab265.jpg", + "image_caption": [ + "Figure 5. Architecture of the multi-scale guided diffusion model." + ], + "image_footnote": [], + "bbox": [ + 81, + 75, + 467, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "at most $C$ classes can be encoded into a $C$ -channel one-hot label map. It can be seen as a special case of text feature maps when the masks are dense and non-overlapping, and the embedding model $\\pmb{f}$ is a one-hot encoding function. Specifically, let $M$ be the segmentation masks, $\\pmb{t}$ the class labels where $t_i = 1,2,\\dots,C$ , $f_c(t_i) = \\mathbb{1}_{t_i = c}$ . Since $M$ are dense and non-overlapping, the normalized masks $\\hat{M}_i$ will be the same as $M_i$ for $i > 1$ and $\\hat{M}_0 = 0$ . Eqn. 3 then becomes", + "bbox": [ + 75, + 253, + 468, + 375 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nZ _ {c, x, y} = \\sum_ {i = 1} ^ {n} \\mathbb {1} _ {t _ {i} = c} \\cdot M _ {i, x, y} = \\sum_ {i \\mid t _ {i} = c} M _ {i, x, y}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 377, + 468, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, the $c$ -th channel of $Z$ is a mask covering all pixels of class $c$ , i.e., a one-hot label map. Through this reformulation, we can see that the one-hot representation has limited capability as $\\pmb{f}(t_i)$ is restricted to be binary. The text feature map representation uses a learned language model as $\\pmb{f}$ to encode the more informative open-domain layouts.", + "bbox": [ + 75, + 420, + 468, + 511 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Multi-Scale Guided Diffusion", + "text_level": 1, + "bbox": [ + 76, + 521, + 339, + 536 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use a diffusion model to generate images from a text feature pyramid. We use $\\epsilon$ -prediction and the simplified training objective following [19]:", + "bbox": [ + 75, + 545, + 468, + 590 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL = \\mathbb {E} _ {\\epsilon \\sim \\mathcal {N} (0, 1), t \\sim [ 1, T ]} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, \\boldsymbol {z}, t) \\| _ {2} ^ {2} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 593, + 468, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T$ is the number of diffusion steps, $\\boldsymbol{x}_t$ is a noisy version of the ground-truth image $\\boldsymbol{x}$ at the $t$ -th diffusion step, $\\boldsymbol{z}$ is the conditional signal, which in our case is the text feature pyramid $\\{Z^l\\}_{l=0}^L$ , and $\\epsilon_\\theta$ represents the network parameterized by $\\boldsymbol{\\theta}$ . We modify the UNet architecture [9] by adding the convolutional layers to combine each text feature map with the UNet feature maps of the corresponding resolution. The 0-th level text feature maps $Z^0$ are passed through all blocks using cross-modal attention [44] and channel-wise feature modulation. Fig. 5 shows the overall architecture of the modified UNet.", + "bbox": [ + 75, + 613, + 470, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Classifier-free guidance [20] has shown to be an effective technique to improve the performance of conditional diffusion models and is widely applied to diffusion models conditioned on text and class tags [9, 35, 43, 44]. To benefit from this technique, we introduce multi-scale spatial guidance for our feature map conditioned diffusion model. As described in Sec. 3.2, in text feature maps from level 1 to $L$ , the unspecified regions are the embedding of a null", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "token $\\pmb{f}(\\varnothing)$ . We further apply dropout with probability 0.1 to $Z^0$ by setting $Z^0 = f(\\varnothing)$ . During inference, we estimate two diffusion scores, conditioning on the given text feature pyramid and an empty feature pyramid of repeating $\\pmb{f}(\\varnothing)$ , and then perform sampling using their linear combination.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 179, + 632, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present the experimental results on image synthesis from any-level semantic layouts. We evaluate the proposed method on user-drawn coarse layouts and automatically simulated layout data. We also present results on T2I and S2I, and compare our method with state-of-the-art methods.", + "bbox": [ + 496, + 204, + 893, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 303, + 718, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train the multi-scale guided diffusion model to generate $64 \\times 64$ images from a layout of precision up to $\\log_2 64$ . To generate images at higher resolution, we experiment with two approaches: (1) by training another diffusion model to upsample $64 \\rightarrow 256$ following [9]; (2) by generating the latent map at $64 \\times 64$ resolution then decoding it into a $512 \\times 512$ image following [43]. Both approaches are effective, demonstrating that the proposed method can generalize well to both pixel-space and latent-space diffusion strategies. We use smaller pixel-space diffusion models for ablation studies and report the main results based on a larger latent-space diffusion model. We encode the text descriptions using the pretrained CLIP ViT-L14 language model [38]. To avoid repeated forward passes, we feed the union of all regional descriptions $\\cup_{i} t_{i}$ as a sentence into the language model. Then, we average the hidden states corresponding to each word in $t_{i}$ to use as its embedding $\\mathbf{f}(t_{i})$ .", + "bbox": [ + 496, + 325, + 893, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training details. We use the aesthetic subset of Laion2B-en dataset [46] for training. We generate full text feature pyramids for 5M randomly selected samples and construct only the 0-th level feature maps for the remaining samples. For pixel space diffusion, we train a base model of 300M parameters and a super-resolution model of 300M parameters; for latent-space diffusion, we train a base model of 900M parameters and use the pretrained deocder from [43]. We use batch size 2048 for $64 \\times 64$ models and batch size 960 for the super-resolution model.", + "bbox": [ + 496, + 584, + 893, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation benchmark. We use the COCO [32] validation set for evaluation in the T2I setting and the COCO-stuff [7] validation set for S2I. For evaluation in open-domain layout-to-image generation, we construct a new test set OpenLayout containing 260 user-drawn layouts of coarse shapes. The layouts are annotated by 10 users based on text prompts randomly sampled from PartiPrompts [64]. To analyze the effect of precision level control, we also evaluate using the pseudo layouts consisting of accurate shapes, which are extracted from the 5,000 images with caption annotations of COCO validation set (OpenLayout-COCO). Fig. 6 shows", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22472", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/d01e0efa31297ab3aad9c3aae447b57aa53e991070e0b65f09786b1e5c0d799f.jpg", + "table_caption": [ + "Table 2. Quantitative results on the OpenLayout and OpenLayout-COCO datasets with different precision levels. SS Score: spatial similarity scores." + ], + "table_footnote": [], + "table_body": "
OpenLayoutOpenLayout-COCO
Prec.SS Score ↑CLIP Score ↑SS Score ↑CLIP Score ↑FID ↓
0.436.274.572.26025.3
3.533.268.685.25626.0
4.543.266.716.25627.0
5.558.267.729.25628.4
6.558.261.736.25530.6
", + "bbox": [ + 81, + 138, + 465, + 223 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "some layouts samples from OpenLayout and Openlayout-COCO.", + "bbox": [ + 76, + 251, + 470, + 279 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1df4f4ede396b7ce7c54a5f95444a417bad071d3672368418075b1a339bc89da.jpg", + "image_caption": [ + "Figure 6. Top: Pseudo layouts from OpenLayout-COCO dataset. Bottom: real-world user-drawn layouts from OpenLayout dataset." + ], + "image_footnote": [], + "bbox": [ + 78, + 281, + 464, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Open-Domain Layout-to-Image Generation", + "text_level": 1, + "bbox": [ + 76, + 497, + 446, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here we discuss the results on the OpenLayout and OpenLayout-COCO datasets. For each sample, we run the model a varying precision level $c$ from 0 to 6 to verify the effectiveness of precision control. Fig. 7 shows the results with different precision levels. For simplicity, we use the same precision level for all regions in an input layout, i.e. $\\forall i, c_i = c$ . We can see that as the precision level increases, the generated images follows the layout more closely. When $c = 0$ , the image compositions are not related to the layouts. For $c = 3, 4$ the generated images roughly resemble the shape and location specified in the layout. For $c = 5, 6$ , the generated object contours matches the layout more closely. At the lowest precision level, our method can handle very rough layouts, e.g., bounding box layouts, as shown in Fig. 8, despite not being trained on bounding box data.", + "bbox": [ + 75, + 521, + 468, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For quantitative evaluation, we compute the CLIP score using the original captions to measure global semantic alignment. To measure spatial alignment, we define a spatial similarity score (SS score), which is the cosine similarity between the text feature maps of the input layout and the layout reconstructed from the generated image. For OpenLayout-COCO, as the ground-truth images are available, we also compute the FID to measure the visual quality.", + "bbox": [ + 75, + 750, + 470, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2 reports the quantitative evaluation results on images generated with different precision levels. The second", + "bbox": [ + 76, + 869, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/64c915fdf6877f90731a423eea7f319160d8c6dc467ddd89385ed75098b97768.jpg", + "table_caption": [ + "Table 3. Quantitative comparison with T2I methods on COCO." + ], + "table_footnote": [], + "table_body": "
MethodFID ↓zero-shot FID↓
SSA-GAN [31]19.37-
VQ-Diffusion [15]13.86-
DF-GAN [53]19.32-
GLIDE [35]-12.89
SD [1,43]-9.89
DALLE2 [39]-10.87
Ours8.559.47
", + "bbox": [ + 532, + 104, + 856, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and fourth columns show that using a higher precision level generally leads to a higher spatial similarity, which further demonstrates the effectiveness of precision control. On OpenLayout-COCO, the spatial similarity consistently increases as the precision level becomes higher. Whereas, on OpenLayout, it stays the same at higher levels. This is due to the difference in the inherent layout precision exhibited by the two datasets; compared to OpenLayout-COCO, the layouts in OpenLayout are coarser. For a coarse layout, the generated images already match it well at low precision levels and the room for improvement is limited.", + "bbox": [ + 496, + 258, + 893, + 425 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From the last column of Table 2, we can see that the results with a lower precision level have a smaller FID, which indicates a similar distribution with respect to the ground-truth images. This is likely because a lower precision level enforces smaller constraints on the generation process, and therefore the generated images can better capture the real image distribution. Similarly, a lower precision level also yields a slightly better CLIP score due to the smaller spatial constraints, as shown in the third and fifth columns of Table 2.", + "bbox": [ + 496, + 425, + 893, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Text-to-Image Generation", + "text_level": 1, + "bbox": [ + 500, + 588, + 735, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As mentioned in Sec. 3, our method can be applied for text-to-image generation by using texts as 0-th layouts. The first four columns of Fig. 9 show the images generated from text prompts by our method and state-of-the-art methods. We can see that the proposed method can generate visually peasant images with reasonable layouts from only text input. Table 3 reports the FID evaluated on the COCO validation set. The classifier-free guidance scale is set to 3. Following [35], we sample 30K images using randomly selected text prompts and compute FID against the entire validation set. It can be seen that the proposed method compares favorably against state-of-the-art text-to-image generation models.", + "bbox": [ + 496, + 612, + 893, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By combining with a named entity recognition (NER) model, we can apply the proposed method to layout controllable text-to-image generation. More specifically, given an input sentence, we parse the noun phrases using NER to generate regional text descriptions, and users can arbitrarily draw the shapes for those noun phrases. The last two columns of Fig. 9 show the text-to-image generation results", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22473", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/89b034700eba78333db1368202eaca17a1584ec0291cda333e82fe1faeb263e2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 77, + 215, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1b7d024967fb1e5ec10b65589075c38cfbe17a1b7ea5f63691bea7f4e6b59c6c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 78, + 349, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d8e3cf0a2cc4c73d07c307560a3a67757bfb927e0c48b0608f90b666f72f6b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 78, + 483, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b9c0b64a7905566192445d4384e67412cfc909e1ae38be8076cba5c61f58528e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 78, + 619, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3a28a85a9613d86a18de315f937fcac4fe318bb0d750b4deb509ca92aa091c16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 78, + 753, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7b3efab3fcb8557d546665d8d6127a9cf4832870e756eaa5b58be8d368eaa3c6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 78, + 888, + 181 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7f09770d74f27691d338eff3c3f4963c960a8eef76313d3ada8c347dd8d66cc2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 78, + 181, + 210, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/29e0e669bad358eff2f932b3a882d88e5e3613f9e6cb5d4d2334cb9e2d2aef10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 181, + 349, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e128fa611bd6996ff7ca364b9a5c867801482700a5e6815265ad11b8efefe512.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 181, + 483, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6dcdba5e612e76915fbdc842b5a926d7920bfb51b3538a0cdfa8b8a7eb9eca03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 181, + 619, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5716b1cd70dd58ea935f2e4908fcaf931bc7ae21e2ddbec375a77177038d4c46.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 181, + 753, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/870b233691f2942288cec5a8d6c570d905d0d6bab86c29ec8ec5bdc7861d7a19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 181, + 888, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6926c35e12835b59213f8079a135e7b55246b5d178260209ce7c619efe82165b.jpg", + "image_caption": [ + "Figure 7. Results with different precision levels. For each input layout, we sample the images starting from same noise, so the images at different precision levels can have similar styles." + ], + "image_footnote": [], + "bbox": [ + 80, + 285, + 210, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/57ceb7c9414bae79af0d755026821a39b132e2c4e6e43ad5b8d0f55efaea867c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 285, + 349, + 388 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5d6755db259f83b1bae5e116e31be747709fe1ebcb1fa3fee6a5d210b62bc253.jpg", + "image_caption": [ + "Level 3" + ], + "image_footnote": [], + "bbox": [ + 351, + 285, + 483, + 388 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fd94759bd73bb5503a5db2af98b8547b1584f2d7592af1d528645237db6a8836.jpg", + "image_caption": [ + "Level 4" + ], + "image_footnote": [], + "bbox": [ + 485, + 285, + 619, + 388 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bb2cc5a253d5cd5d0e5cb65d054f65a1d9fecdb937a49f8060aab357ed94e5c3.jpg", + "image_caption": [ + "Level 5" + ], + "image_footnote": [], + "bbox": [ + 620, + 285, + 753, + 388 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e029c36a8b1ccb2edd98bc6f2195fc7a841e0836fa3169f6f4d3567437fb6729.jpg", + "image_caption": [ + "Level 6" + ], + "image_footnote": [], + "bbox": [ + 754, + 285, + 888, + 388 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/588b0365995cd119d3b428fec4a1676ade61833a27feac683df74d94e78f9622.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 441, + 207, + 540 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f8dd5aefcd17fa568bce37012eb3bece6327ab059193e7a0710193f7c78ab41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 441, + 334, + 540 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d3dc39cae8e626bc2b70a618fbacc49ae4aff5332613b4cb015c960ff80cadab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 336, + 441, + 467, + 540 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/008880d259c8529449e075229ad70bcd0fe044f8f714b34766a558e472e9bc69.jpg", + "image_caption": [ + "Figure 8. Results with bounding box layout. Precision level $= 3$" + ], + "image_footnote": [], + "bbox": [ + 81, + 541, + 209, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f2246c94000e4503559d92bb0186f25e41cc4ad3f9323ab1f39af6d6000dcbb4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 541, + 336, + 640 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5051d27dde148a1e35307b1d5ce2ebfe72a14dcbc1e0f84f84e18a86c017261a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 541, + 467, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "with layout control. We can see that the generated images match the text well and follow the provided layouts.", + "bbox": [ + 75, + 684, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Segmentation-to-Image Generation", + "text_level": 1, + "bbox": [ + 76, + 724, + 385, + 742 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our model can also generate images from a dense segmentation map of closed-set labels, i.e. following the original S2I setting. For this application, we treat the class labels as text descriptions and use the highest precision level $c = 5$ for all masks. Fig. 10 shows example images generated by our method and SPADE [36]. The images generated by our model are of significantly better visual quality. Table. 4 reports the quantitative comparison results on the COCO-stuff validation set with the state-of-the-art S2I methods [33,36,51]. Since the highest resolution of the input lay", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "out to our model is 64, we evaluate the S2I results at $64 \\times 64$ resolution. From the third and fifth columns of Table. 4 we can see that despite not being designed or trained for this task, the proposed method can achieve lower FID and comparable mIOU. After being fine-tuned on the COCO-stuff training set, our model outperforms previous approaches in terms of both FID and mIOU.", + "bbox": [ + 496, + 455, + 893, + 561 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/da046412b39b8100152cb8343e12f19a88d1664e1fce1e235eccf4bfb026e2cd.jpg", + "table_caption": [ + "Table 4. Quantitative comparison with S2I methods on COCO-stuff." + ], + "table_footnote": [], + "table_body": "
MethodFID ↓zero-shot FID ↓mIOU↑zero-shot mIOU↑
SPADE [36]50.91-17.49-
SAFM [33]62.28-12.28-
CLADE [51]55.30-17.21-
Ours17.2020.1723.0117.15
", + "bbox": [ + 503, + 597, + 888, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 695, + 665, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare the proposed any-level method with two fixed-level baseline models: a text-to-image generation model and a fixed-level layout-to-image generation model. The baseline models are of the same architecture as the any-level models. When training the baseline models, we only use layouts of fixed levels, i.e. the 0-th level for the text-to-image baseline and the 4-th level for the fixed-level segmentation-to-image baseline. Table 5 compares the evaluation results of the any-level model and fixed-level baselines at the corresponding levels. The any-level model achieves better results than the baseline models, which further demonstrates the advantage of the unified framework.", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22474", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A tornado made of bees crashing into a skyscraper. painting in the style of watercolor.", + "bbox": [ + 86, + 75, + 532, + 87 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6c13d25210b315704701c959daba13443ea7edd6a584d659a9fbf23915725857.jpg", + "image_caption": [ + "Figure 9. Text-to-image generation results. Ours: our results by using text as a 0-th level layout. Ours*: our results with layout control." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 890, + 438 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2ee46735362b8ecf3203e28bc3489b836399a35435f607011594c5a93589dde0.jpg", + "image_caption": [ + "Figure 10. Visual comparison with SPADE [36] for segmentation-to-image generation." + ], + "image_footnote": [], + "bbox": [ + 81, + 460, + 890, + 681 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ebcbae32e3e6eb04df22a2309682377df33c81ab379e090a6ffe9ce9c46cd818.jpg", + "table_caption": [ + "Table 5. Ablation study results on OpenLayout-COCO." + ], + "table_footnote": [], + "table_body": "
Prec. LevelModelFID ↓CLIP Score ↑SS Score ↑
0Text-to-Image Baseline32.83.2473.5613
0Any-Level Model32.09.2496.5640
4Single-Level Baseline36.03.2381.5729
4Any-Level Model33.70.2475.6978
", + "bbox": [ + 81, + 724, + 465, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 811, + 194, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper presents a new conditional image synthesis framework to generate images from any-level open-domain semantic layouts. The input level ranges from pure text to a 2D semantic canvas with precise shapes. Several novel", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "techniques are introduced, including a pipeline for collecting training data; the representations to jointly encode precision level, semantics, and geometry information; and a multiscale guided diffusion model to synthesize images. A test dataset containing user-drawn layouts is collected to evaluate the proposed method. Experimental results demonstrate the advantage of the unified framework. The proposed method can generate high-quality images following the layout at specified precision levels, and compares favorably against the state-of-the-art methods on public benchmarks.", + "bbox": [ + 496, + 722, + 893, + 875 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22475", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Stable diffusion. https://stability.ai/blog/stable-diffusion-public-release. Accessed: 2022.2,3,6", + "[2] Edward H Adelson, Charles H Anderson, James R Bergen, Peter J Burt, and Joan M Ogden. Pyramid methods in image processing. RCA engineer, 29(6):33-41, 1984. 2", + "[3] Oron Ashual and Lior Wolf. Specifying object attributes and relations in interactive scene generation. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.209, + 0.131, + 0.761, + 0.154 + ], + "angle": 0, + "content": "SceneComposer: Any-Level Semantic Image Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.18, + 0.877, + 0.234 + ], + "angle": 0, + "content": "Yu Zeng\\(^{1}\\), Zhe Lin\\(^{2}\\), Jianming Zhang\\(^{2}\\), Qing Liu\\(^{2}\\), John Collomosse\\(^{2}\\), Jason Kuen\\(^{2}\\), Vishal M. Patel\\(^{1}\\) \n\\(\\{\\text{yzeng22, vpatel36}\\} \\text{@jhu.edu}, \\{\\text{zlin, jianmzha, qingl, collomos, kuen}\\} \\text{@adobe.com}\\) \n\\(^{1}\\)Johns Hopkins University \n\\(^{2}\\)Adobe Research" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.262, + 0.241, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.39, + 0.241, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.153, + 0.517, + 0.168, + 0.526 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.262, + 0.402, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.244, + 0.39, + 0.403, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.315, + 0.516, + 0.331, + 0.526 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.263, + 0.565, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.39, + 0.565, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.476, + 0.516, + 0.492, + 0.525 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.567, + 0.263, + 0.726, + 0.388 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.567, + 0.39, + 0.726, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.516, + 0.654, + 0.526 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.252, + 0.89, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.8, + 0.516, + 0.816, + 0.526 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.528, + 0.894, + 0.584 + ], + "angle": 0, + "content": "Figure 1. Examples of image synthesis from any-level semantic layouts. (a) The coarsest layout, i.e. at the 0-th precision level, is equivalent to a text input; (d) the finest layout, i.e. at the highest level, is close to an accurate segmentation map; (a)-(d) intermediate level layouts (from coarse to fine), the shape control becomes tighter with increasing levels. (e) We can specify different precision levels for different components, e.g. to include a 0-th level style indicator while the remaining regions are of higher levels." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.592, + 0.314, + 0.608 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.629, + 0.474, + 0.902 + ], + "angle": 0, + "content": "We propose a new framework for conditional image synthesis from semantic layouts of any precision levels, ranging from pure text to a 2D semantic canvas with precise shapes. More specifically, the input layout consists of one or more semantic regions with free-form text descriptions and adjustable precision levels, which can be set based on the desired controllability. The framework naturally reduces to text-to-image (T2I) at the lowest level with no shape information, and it becomes segmentation-to-image (S2I) at the highest level. By supporting the levels in-between, our framework is flexible in assisting users of different drawing expertise and at different stages of their creative workflow. We introduce several novel techniques to address the challenges coming with this new setup, including a pipeline for collecting training data; a precision-encoded mask pyramid and a text feature map representation to jointly encode precision level, semantics, and composition information; and a multi-scale guided diffusion model to synthesize images. To evaluate" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.896, + 0.685 + ], + "angle": 0, + "content": "the proposed method, we collect a test dataset containing user-drawn layouts with diverse scenes and styles. Experimental results show that the proposed method can generate high-quality images following the layout at given precision, and compares favorably against existing methods. Project page https://zengxianyu.github.io/scenegc/" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.723, + 0.633, + 0.739 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Recently, deep generative models such as StyleGAN [24, 25] and diffusion models [9, 19, 49] have made a significant breakthrough in generating high-quality images. Image generation and editing technologies enabled by these models have become highly appealing to artists and designers by helping their creative workflows. To make image generation more controllable, researchers have put a lot of effort into conditional image synthesis and introduced models using various types and levels of semantic input such as object categories, text prompts, and segmentation" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "22468" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.472, + 0.13 + ], + "angle": 0, + "content": "Table 1. Difference from related conditional image synthesis works. T2I: text to image, S2I: segmentation to image, ST2I: Scene-based text to image [13], Box2I: bounding box layout to image [50]." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.135, + 0.47, + 0.201 + ], + "angle": 0, + "content": "
SettingOpen-domain layoutShape controlSparse layoutCoarse shapeLevel control
T2I✓XXXX
S2IX✓XXX
ST2IX✓XXX
Box2IXX✓XX
Ours✓✓✓✓✓
" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.213, + 0.292, + 0.228 + ], + "angle": 0, + "content": "maps etc. [23, 35, 36, 43, 44, 67]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.473, + 0.502 + ], + "angle": 0, + "content": "However, existing models are not flexible enough to support the full creative workflow. They mostly consider fixed-level semantics as the input [63], e.g. image-level text descriptions in text-to-image generation (T2I) [35, 39, 41, 43, 44], or pixel-level segmentation maps in segmentation-to-image generation (S2I) [23, 36, 67]. Recent breakthroughs on T2I such as DALLE2 [39] and StableDiffusion [1, 43] demonstrate extraordinary capabilities of generating high-quality results. They can convert a rough idea into visual messages to provide inspirations at the beginning of the creative process, but provide no further control over image composition. On the other hand, S2I allows users to precisely control the image composition. As it is extremely challenging to draw a detailed layout directly, S2I is more useful for later creative stages given initial designs. For real-world use cases, it is highly desirable to have a model which can generate images from not only pure text or segmentation maps, but also intermediate-level layouts with coarse shapes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.472, + 0.761 + ], + "angle": 0, + "content": "To this end, we propose a new unified conditional image synthesis framework to generate images from a semantic layout at any combination of precision levels. It is inspired by the typical coarse-to-fine workflow of artists and designers: they first start from an idea, which can be expressed as a text prompt or a set of concepts (Fig. 1 (a)), then tend to draw the approximate outlines and refine each object (Fig. 1 (a)-(d)). More specifically, we model a semantic layout as a set of semantic regions with free-form text descriptions. The layout can be sparse and each region can have a precision level to control how well the generated object should fit to the specified shape. The framework reduces to T2I when the layout is the coarsest (Fig. 1 (a)), and it becomes S2I when the layout is a segmentation map (Fig. 1 (d)). By adjusting the precision level, users can achieve their desired controllability (Fig. 1 (a)-(d)). This framework is different from the existing works in many aspects, as summarized in Table 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.472, + 0.884 + ], + "angle": 0, + "content": "This new setup comes with several challenges. First, it is non-trivial to encode open-domain layouts in image synthesis frameworks. Second, to handle hand-drawn layouts of varying precision, we need an effective and robust way to inject the precision information into the layout encoding. Third, there is no large-scale open-domain layout/image dataset. To generate high-quality images and generalize to novel concepts, a large and diverse training dataset is crucial." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.9 + ], + "angle": 0, + "content": "We introduce several novel ideas to address these chal" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.409 + ], + "angle": 0, + "content": "lenges. First, we propose a text feature map representation for encoding a semantic layout. It can be seen as a spatial extension of text embedding or generalization of segmentation masks from binary to continuous space. Second, we introduce a precision-encoded mask pyramid to model layout precision. Inspired by the classical image pyramid models [2, 6, 47, 62], we relate shape precision to levels in a pyramid representation and encode precision by dropping out regions of lower precision levels. In other words, the \\( l \\)-th level of the mask pyramid is a sub layout (subset of regions) consisting of semantic regions with precision level no less than \\( l \\). By creating a text feature map for each sub layout, we obtain a text feature pyramid as a unified representation of semantics, composition, and precision. Finally, we feed the text feature pyramid to a multi-scale guided diffusion model to generate images. We fulfill the need for training data by collecting them from two sources: (1) large-scale imagedataset pairs; (2) a relatively small pseudo layout/image dataset using text-based object detection and segmentation. With this multi-source training strategy, both text-to-image and layout-to-image can benefit from each other synergistically." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.41, + 0.822, + 0.424 + ], + "angle": 0, + "content": "Our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.436, + 0.894, + 0.481 + ], + "angle": 0, + "content": "- A unified framework for diffusion-based image synthesis from semantic layouts with any combination of precision control." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.482, + 0.894, + 0.542 + ], + "angle": 0, + "content": "- Novel ideas to build the model, including precision-encoded mask pyramid and pyramid text feature map representation, and multi-scale guided diffusion model, and training with multi-source data." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.543, + 0.894, + 0.603 + ], + "angle": 0, + "content": "- A new real-world user-drawn layout dataset and extensive experiments showing the effectiveness of our model for text-to-image and layout-to-image generation with precision control." + }, + { + "type": "list", + "bbox": [ + 0.519, + 0.436, + 0.894, + 0.603 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.618, + 0.642, + 0.634 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Deep generative models. In recent years, there has been significant progress in image generation using deep generative models. Some of these approaches attempt to learn the image distribution by optimizing a likelihood-based objective function. Autoregressive models (ARMs) [11, 55-57] treat images as sequences of pixels or tokens in a learned dictionary to define a tractable density model, which can be optimized by maximizing the likelihood. Variational Autoencoders (VAEs) [26, 54] use an intractable density function and train the model by maximizing the variational lower bound. Diffusion-based models [9, 19, 43, 48, 49] are also trained by optimizing the variational lower bound. Unlike VAEs which map an image into the latent space using a learnable encoder, diffusion-based models use a fixed diffusion process to transform an image into Gaussian noise. Generative Adversarial Networks (GANs) [5, 14, 24, 25] do not define the density function explicitly; instead, generative" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "22469" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "models are trained through an adversarial learning process against a discriminator. We base our method on diffusion models due to their ability to generate high-quality images and stability in training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.473, + 0.468 + ], + "angle": 0, + "content": "Layout/Segmentation-to-image generation refers to the task of generating images from a spatial arrangement of semantic concepts, e.g. a segmentation map or a set of bounding boxes. Segmentation-based methods (e.g. [8,23,36,45,52,59,60]) have been proposed to allow users to precisely control the image composition, but are less flexible as they require a dense and accurate segmentation map and only allow a fixed set of categories. Bounding box-based methods can generate images from a coarse layout of bounding boxes. Bounding box-based generation was studied as a standalone task first by Zhao et al. [66] and has been an active research area [3, 17, 30, 58] since then. To convey more information than object categories, more expressive bounding box descriptions have been introduced, such as attributes [3, 34], relations [3], and free-form descriptions [12]. Although bounding boxes are easier to draw than segmentation maps, they provide no control over object shapes and orientations. In this work, we use coarse shapes with freeform text descriptions and precision levels to represent a layout, providing more flexibility and control for different synthesis needs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.473, + 0.803 + ], + "angle": 0, + "content": "Text-to-image/Multi-modal image generation. T2I aims to generate images from a free-form text description, i.e. image captions. Earlier approaches are usually based on conditional GANs [41, 65]. Recently, autoregressive models based on image quantization techniques [10, 40, 64] and diffusion models [1,35,39,43,44] have shown surprising results with large-scale models and datasets. To gain more control over the spatial composition, some studies have tried to incorporate layout in the form of key points [42], bounding boxes [18], or object shapes [13, 21, 27, 29, 37], as an additional input. Some studies focused on image synthesis from multi-modal input including text, segmentation maps, edge maps [22, 61] etc. A work [4] concurrent to ours proposes a training-free paint-with-word method that enables users to specify the object locations by manipulating the attention matrices in cross-attention layers. These approaches use the layout as an extra signal complementary to captions. In contrast, we unify image captions and layout using a multi-level framework that models captions as a special case of layout with the lowest precision level. From a practical perspective, our framework provides a more flexible control mechanism with coarse shapes and precision controllability." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.251, + 0.833 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our method aims to generate images from a layout consisting of a set of semantic regions of varying precision levels. Formally, an input layout can be viewed as a list of tuples \\(\\{(M_i,t_i,c_i)\\}_{i = 1}^n\\), where \\(M_{i},t_{i},c_{i}\\) indicate the seg" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.38 + ], + "angle": 0, + "content": "mentation mask, text description, and the precision level of the \\(i\\)-th region. We let \\(M, t, c\\) denote the sets of masks, texts and precision levels of all regions, respectively. The precision level variable \\(c_{i} \\in \\mathbb{N}_{\\leq L}\\) indicates how precisely the generated content should follow the mask \\(M_{i}\\). A smaller value of \\(c_{i}\\) indicates a less precise control allowing more deviation from the mask \\(M_{i}\\). \\(c_{i} = 0\\) indicates the coarsest level where the \\(i\\)-th mask will be ignored. When all \\(c_{i} = 0\\), the problem converts into T2I. Fig. 2 shows an overview of the proposed method. To generate an image at resolution \\(2^{L} \\times 2^{L}\\), we first formulate a precision-encoded mask pyramid \\(\\{M^{l}\\}_{l=0}^{L}\\) which represents each mask at the given precision level (Sec. 3.1). Then we combine the mask pyramid with the text descriptions \\(\\pmb{t}\\) to form a text feature pyramid \\(\\{Z^{l}\\}_{l=0}^{L}\\). It contains a \\(2^{l} \\times 2^{l}\\) text feature map at each level, which can be seen as an extension of the one-hot label map encoding in S2I (Sec. 3.2). Finally, a multi-level guided diffusion model takes the feature pyramid as input to generate an image (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.386, + 0.8, + 0.403 + ], + "angle": 0, + "content": "3.1. Precision-Encoded Mask Pyramid" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.895, + 0.544 + ], + "angle": 0, + "content": "For a user-drawn coarse shape, it is challenging to model the exact precision, since the type and the amount of error vary across different users. To simplify the problem, we relate precision to resolutions and propose a precision-encoded mask pyramid to encode the shape and precision information simultaneously. Given a mask and a precision level, a high precision level corresponds to using all details of the masks at a high resolution, while a low precision level means we can only trust the mask at a low resolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.894, + 0.651 + ], + "angle": 0, + "content": "More specifically, given a set of masks \\( M = [m_1, \\dots, m_n] \\) and the precision levels \\( c = [c_1, \\dots, c_n] \\), we construct the mask pyramid by representing each mask \\( M_i \\) at resolutions up to \\( 2^{c_i} \\). In other words, we resize each mask \\( M_i \\) to multiple resolutions and drop out the masks at resolutions higher than \\( 2^{c_i} \\), as illustrated in Fig. 3. Formally, the \\( l \\)-th layer of the mask pyramid, denoted as \\( M^l \\), is computed as follows," + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.653, + 0.892, + 0.671 + ], + "angle": 0, + "content": "\\[\nM _ {i} ^ {l} = \\operatorname {r e s i z e} \\left(M _ {i}, 2 ^ {l}\\right) \\cdot \\mathbb {1} _ {c _ {i} \\geq l}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.895, + 0.795 + ], + "angle": 0, + "content": "where \\(\\mathrm{resize}(M_i,2^l)\\)izes a mask \\(M_{i}\\) to \\(2^{l}\\times 2^{l}\\) resolution through image interpolation and binarization. The indicator function \\(\\mathbb{1}_{c_i\\geq l}\\) returns 1 when \\(c_{i}\\geq l\\) and 0 otherwise. In our implementation, we set the range of precision levels to [0,3,4,5,6]. We observed that for a free-hand drawn layout, \\(8\\times 8\\) masks at the level 3 are easy to draw while being fairly informative, whereas \\(64\\times 64\\) masks at the level 6 usually capture enough details, as illustrated in Fig. 4." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.707, + 0.818 + ], + "angle": 0, + "content": "3.2. Text Feature Pyramid" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.903 + ], + "angle": 0, + "content": "The mask pyramid encodes the shape and the precision information. To generate an image, we also need semantic information. We introduce a text feature pyramid for this purpose. Each level of the text feature pyramid is a \\(2^l \\times 2^l\\) text feature map \\(Z^l\\) obtained by combining the masks \\(M^l\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "22470" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.892, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.273, + 0.897, + 0.318 + ], + "angle": 0, + "content": "Figure 2. An overview of the proposed method. We provide an intuitive interface where users can easily define a layout using a semantic brush associated with a free-form text description and adjustable precision level. The masks, regional descriptions, and precision levels \\(\\{(M_i,t_i,c_i)\\}_{i = 1}^n\\) are jointly encoded into a text feature pyramid, and then translated into an image by a multi-scale guided diffusion model." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.339, + 0.468, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.46, + 0.471, + 0.53 + ], + "angle": 0, + "content": "Figure 3. An example of the precision-encoded mask pyramid. The first level has two non-zero masks corresponding to \\( m_{1}, m_{2} \\) as \\( c_{1}, c_{2} \\geq 1 \\); the second level only has \\( m_{1} \\) as \\( c_{1} = 2, c_{2} < 2 \\); the third level does not have any non-zero masks as all the precision levels of all masks are lower than 3." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.548, + 0.468, + 0.637 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.638, + 0.468, + 0.652 + ], + "angle": 0, + "content": "Figure 4. Illustration of the masks at different levels of a pyramid." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.684, + 0.47, + 0.775 + ], + "angle": 0, + "content": "and the embeddings of the text \\( t \\). At the 0-th level, the \\( 1 \\times 1 \\) masks contain no shape information, so we simply concatenate the embeddings of all words into a sequence. At the levels where \\( l > 0 \\), we spatially spread the embeddings of \\( t \\) over the corresponding masks to jointly represent the shape and semantic, as illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Text feature maps. Here we describe in more detail how we construct the text feature map \\( Z^l \\) at level \\( l > 0 \\). For simplicity, we drop the superscript \\( l \\) and denote the masks at an arbitrary level as \\( M \\). Each element \\( M_{i,x,y} \\) is a binary value \\( \\in \\{0,1\\} \\) and we allow overlaps or blank spaces, i.e. \\( n \\geq \\sum_{i}^{n}M_{i,x,y} \\geq 0 \\). Given the initial masks \\( M \\), we introduce normalized masks \\( \\hat{M} \\), which are augmented from \\( M \\) by adding an extra mask \\( M_0 \\) to indicate the blank space and" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.341, + 0.855, + 0.356 + ], + "angle": 0, + "content": "normalized by the number of shapes at each location:" + }, + { + "type": "equation", + "bbox": [ + 0.619, + 0.359, + 0.893, + 0.397 + ], + "angle": 0, + "content": "\\[\n\\hat {M} _ {i, x, y} = M _ {i, x, y} / \\sum_ {i = 0} ^ {n} M _ {i, x, y}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.574, + 0.401, + 0.794, + 0.419 + ], + "angle": 0, + "content": "where \\(M_{0,x,y} = \\mathbb{1}_{\\sum_{i = 1}^{n}M_{i,x,y} = 0}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.422, + 0.895, + 0.47 + ], + "angle": 0, + "content": "In the normalized masks \\(\\hat{M}\\), each element \\(\\hat{M}_{i,x,y}\\) is a continuous value \\(\\in [0,1]\\) and we have \\(\\sum_{i=0}^{n} \\hat{M}_{i,x,y} = 1\\). We compute each element \\(Z_{x,y}\\) at location \\(x,y\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.473, + 0.893, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {Z} _ {x, y} = \\sum_ {i = 0} ^ {n} \\boldsymbol {f} \\left(t _ {i}\\right) \\cdot \\hat {M} _ {i, x, y}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.515, + 0.893, + 0.56 + ], + "angle": 0, + "content": "where \\( \\pmb{f}(t_i) \\) is an embedding of the text \\( t_i \\). We set \\( t_0 \\) to be a null token \\( \\oslash \\) to represent unspecified areas, i.e. the blank space indicated by \\( M_0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.895, + 0.73 + ], + "angle": 0, + "content": "The text feature map representation has several advantages. First, it is of the same dimension regardless of the number of masks, and therefore compatible with most deep ConvNet architectures. Second, each element of a text feature map is a convex combination of \\( n \\) text embeddings in the learned embedding space. With a powerful language model, we can achieve a good generalization capability for unseen combinations of concepts. In a text feature map, any overlapping area contains an interpolation of multiple embeddings. Accordingly, users can get creative results derived from hybrid concepts by drawing overlapping shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.895, + 0.884 + ], + "angle": 0, + "content": "Data acquisition. During inference, the segmentation masks and text descriptions are both provided by users. During training, we can generate them automatically using text-based object detection [28] and segmentation [16]. We set the regions where no objects are detected as blank space and assign a null token \\(\\varnothing\\) to these regions. We use CLIP [38] text model to encode the text descriptions. In addition, the 0-th level feature maps can be obtained directly from the image caption embeddings. More details regarding the training data generation step can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Relation to one-hot label maps. In S2I, a layout containing" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.518, + 0.937 + ], + "angle": 0, + "content": "22471" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.077, + 0.468, + 0.212 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.215, + 0.462, + 0.228 + ], + "angle": 0, + "content": "Figure 5. Architecture of the multi-scale guided diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.47, + 0.375 + ], + "angle": 0, + "content": "at most \\(C\\) classes can be encoded into a \\(C\\)-channel one-hot label map. It can be seen as a special case of text feature maps when the masks are dense and non-overlapping, and the embedding model \\(\\pmb{f}\\) is a one-hot encoding function. Specifically, let \\(M\\) be the segmentation masks, \\(\\pmb{t}\\) the class labels where \\(t_i = 1,2,\\dots,C\\), \\(f_c(t_i) = \\mathbb{1}_{t_i = c}\\). Since \\(M\\) are dense and non-overlapping, the normalized masks \\(\\hat{M}_i\\) will be the same as \\(M_i\\) for \\(i > 1\\) and \\(\\hat{M}_0 = 0\\). Eqn. 3 then becomes" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.378, + 0.47, + 0.418 + ], + "angle": 0, + "content": "\\[\nZ _ {c, x, y} = \\sum_ {i = 1} ^ {n} \\mathbb {1} _ {t _ {i} = c} \\cdot M _ {i, x, y} = \\sum_ {i \\mid t _ {i} = c} M _ {i, x, y}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.47, + 0.512 + ], + "angle": 0, + "content": "Therefore, the \\(c\\)-th channel of \\(Z\\) is a mask covering all pixels of class \\(c\\), i.e., a one-hot label map. Through this reformulation, we can see that the one-hot representation has limited capability as \\(\\pmb{f}(t_i)\\) is restricted to be binary. The text feature map representation uses a learned language model as \\(\\pmb{f}\\) to encode the more informative open-domain layouts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.522, + 0.34, + 0.537 + ], + "angle": 0, + "content": "3.3. Multi-Scale Guided Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.47, + 0.592 + ], + "angle": 0, + "content": "We use a diffusion model to generate images from a text feature pyramid. We use \\(\\epsilon\\)-prediction and the simplified training objective following [19]:" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.594, + 0.47, + 0.612 + ], + "angle": 0, + "content": "\\[\nL = \\mathbb {E} _ {\\epsilon \\sim \\mathcal {N} (0, 1), t \\sim [ 1, T ]} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, \\boldsymbol {z}, t) \\| _ {2} ^ {2} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.779 + ], + "angle": 0, + "content": "where \\(T\\) is the number of diffusion steps, \\(\\boldsymbol{x}_t\\) is a noisy version of the ground-truth image \\(\\boldsymbol{x}\\) at the \\(t\\)-th diffusion step, \\(\\boldsymbol{z}\\) is the conditional signal, which in our case is the text feature pyramid \\(\\{Z^l\\}_{l=0}^L\\), and \\(\\epsilon_\\theta\\) represents the network parameterized by \\(\\boldsymbol{\\theta}\\). We modify the UNet architecture [9] by adding the convolutional layers to combine each text feature map with the UNet feature maps of the corresponding resolution. The 0-th level text feature maps \\(Z^0\\) are passed through all blocks using cross-modal attention [44] and channel-wise feature modulation. Fig. 5 shows the overall architecture of the modified UNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Classifier-free guidance [20] has shown to be an effective technique to improve the performance of conditional diffusion models and is widely applied to diffusion models conditioned on text and class tags [9, 35, 43, 44]. To benefit from this technique, we introduce multi-scale spatial guidance for our feature map conditioned diffusion model. As described in Sec. 3.2, in text feature maps from level 1 to \\(L\\), the unspecified regions are the embedding of a null" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.168 + ], + "angle": 0, + "content": "token \\( \\pmb{f}(\\varnothing) \\). We further apply dropout with probability 0.1 to \\( Z^0 \\) by setting \\( Z^0 = f(\\varnothing) \\). During inference, we estimate two diffusion scores, conditioning on the given text feature pyramid and an empty feature pyramid of repeating \\( \\pmb{f}(\\varnothing) \\), and then perform sampling using their linear combination." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.18, + 0.633, + 0.197 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.205, + 0.894, + 0.294 + ], + "angle": 0, + "content": "In this section, we present the experimental results on image synthesis from any-level semantic layouts. We evaluate the proposed method on user-drawn coarse layouts and automatically simulated layout data. We also present results on T2I and S2I, and compare our method with state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.304, + 0.719, + 0.32 + ], + "angle": 0, + "content": "4.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.895, + 0.584 + ], + "angle": 0, + "content": "We train the multi-scale guided diffusion model to generate \\(64 \\times 64\\) images from a layout of precision up to \\(\\log_2 64\\). To generate images at higher resolution, we experiment with two approaches: (1) by training another diffusion model to upsample \\(64 \\rightarrow 256\\) following [9]; (2) by generating the latent map at \\(64 \\times 64\\) resolution then decoding it into a \\(512 \\times 512\\) image following [43]. Both approaches are effective, demonstrating that the proposed method can generalize well to both pixel-space and latent-space diffusion strategies. We use smaller pixel-space diffusion models for ablation studies and report the main results based on a larger latent-space diffusion model. We encode the text descriptions using the pretrained CLIP ViT-L14 language model [38]. To avoid repeated forward passes, we feed the union of all regional descriptions \\(\\cup_{i} t_{i}\\) as a sentence into the language model. Then, we average the hidden states corresponding to each word in \\(t_{i}\\) to use as its embedding \\(\\mathbf{f}(t_{i})\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.585, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Training details. We use the aesthetic subset of Laion2B-en dataset [46] for training. We generate full text feature pyramids for 5M randomly selected samples and construct only the 0-th level feature maps for the remaining samples. For pixel space diffusion, we train a base model of 300M parameters and a super-resolution model of 300M parameters; for latent-space diffusion, we train a base model of 900M parameters and use the pretrained deocder from [43]. We use batch size 2048 for \\(64 \\times 64\\) models and batch size 960 for the super-resolution model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Evaluation benchmark. We use the COCO [32] validation set for evaluation in the T2I setting and the COCO-stuff [7] validation set for S2I. For evaluation in open-domain layout-to-image generation, we construct a new test set OpenLayout containing 260 user-drawn layouts of coarse shapes. The layouts are annotated by 10 users based on text prompts randomly sampled from PartiPrompts [64]. To analyze the effect of precision level control, we also evaluate using the pseudo layouts consisting of accurate shapes, which are extracted from the 5,000 images with caption annotations of COCO validation set (OpenLayout-COCO). Fig. 6 shows" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "22472" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.088, + 0.472, + 0.13 + ], + "angle": 0, + "content": "Table 2. Quantitative results on the OpenLayout and OpenLayout-COCO datasets with different precision levels. SS Score: spatial similarity scores." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.14, + 0.467, + 0.224 + ], + "angle": 0, + "content": "
OpenLayoutOpenLayout-COCO
Prec.SS Score ↑CLIP Score ↑SS Score ↑CLIP Score ↑FID ↓
0.436.274.572.26025.3
3.533.268.685.25626.0
4.543.266.716.25627.0
5.558.267.729.25628.4
6.558.261.736.25530.6
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.252, + 0.471, + 0.28 + ], + "angle": 0, + "content": "some layouts samples from OpenLayout and Openlayout-COCO." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.282, + 0.465, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.44, + 0.472, + 0.469 + ], + "angle": 0, + "content": "Figure 6. Top: Pseudo layouts from OpenLayout-COCO dataset. Bottom: real-world user-drawn layouts from OpenLayout dataset." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.447, + 0.515 + ], + "angle": 0, + "content": "4.2. Open-Domain Layout-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Here we discuss the results on the OpenLayout and OpenLayout-COCO datasets. For each sample, we run the model a varying precision level \\( c \\) from 0 to 6 to verify the effectiveness of precision control. Fig. 7 shows the results with different precision levels. For simplicity, we use the same precision level for all regions in an input layout, i.e. \\( \\forall i, c_i = c \\). We can see that as the precision level increases, the generated images follows the layout more closely. When \\( c = 0 \\), the image compositions are not related to the layouts. For \\( c = 3, 4 \\) the generated images roughly resemble the shape and location specified in the layout. For \\( c = 5, 6 \\), the generated object contours matches the layout more closely. At the lowest precision level, our method can handle very rough layouts, e.g., bounding box layouts, as shown in Fig. 8, despite not being trained on bounding box data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.87 + ], + "angle": 0, + "content": "For quantitative evaluation, we compute the CLIP score using the original captions to measure global semantic alignment. To measure spatial alignment, we define a spatial similarity score (SS score), which is the cosine similarity between the text feature maps of the input layout and the layout reconstructed from the generated image. For OpenLayout-COCO, as the ground-truth images are available, we also compute the FID to measure the visual quality." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Table 2 reports the quantitative evaluation results on images generated with different precision levels. The second" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.088, + 0.874, + 0.102 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison with T2I methods on COCO." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.106, + 0.857, + 0.232 + ], + "angle": 0, + "content": "
MethodFID ↓zero-shot FID↓
SSA-GAN [31]19.37-
VQ-Diffusion [15]13.86-
DF-GAN [53]19.32-
GLIDE [35]-12.89
SD [1,43]-9.89
DALLE2 [39]-10.87
Ours8.559.47
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.895, + 0.426 + ], + "angle": 0, + "content": "and fourth columns show that using a higher precision level generally leads to a higher spatial similarity, which further demonstrates the effectiveness of precision control. On OpenLayout-COCO, the spatial similarity consistently increases as the precision level becomes higher. Whereas, on OpenLayout, it stays the same at higher levels. This is due to the difference in the inherent layout precision exhibited by the two datasets; compared to OpenLayout-COCO, the layouts in OpenLayout are coarser. For a coarse layout, the generated images already match it well at low precision levels and the room for improvement is limited." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.895, + 0.576 + ], + "angle": 0, + "content": "From the last column of Table 2, we can see that the results with a lower precision level have a smaller FID, which indicates a similar distribution with respect to the ground-truth images. This is likely because a lower precision level enforces smaller constraints on the generation process, and therefore the generated images can better capture the real image distribution. Similarly, a lower precision level also yields a slightly better CLIP score due to the smaller spatial constraints, as shown in the third and fifth columns of Table 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.589, + 0.736, + 0.605 + ], + "angle": 0, + "content": "4.3. Text-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.794 + ], + "angle": 0, + "content": "As mentioned in Sec. 3, our method can be applied for text-to-image generation by using texts as 0-th layouts. The first four columns of Fig. 9 show the images generated from text prompts by our method and state-of-the-art methods. We can see that the proposed method can generate visually peasant images with reasonable layouts from only text input. Table 3 reports the FID evaluated on the COCO validation set. The classifier-free guidance scale is set to 3. Following [35], we sample 30K images using randomly selected text prompts and compute FID against the entire validation set. It can be seen that the proposed method compares favorably against state-of-the-art text-to-image generation models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.901 + ], + "angle": 0, + "content": "By combining with a named entity recognition (NER) model, we can apply the proposed method to layout controllable text-to-image generation. More specifically, given an input sentence, we parse the noun phrases using NER to generate regional text descriptions, and users can arbitrarily draw the shapes for those noun phrases. The last two columns of Fig. 9 show the text-to-image generation results" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "22473" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.078, + 0.216, + 0.183 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.079, + 0.351, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.079, + 0.485, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.079, + 0.62, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.079, + 0.754, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.079, + 0.89, + 0.182 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.183, + 0.212, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.183, + 0.351, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.183, + 0.485, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.183, + 0.62, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.183, + 0.754, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.183, + 0.89, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.286, + 0.211, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.286, + 0.351, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.286, + 0.485, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.286, + 0.62, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.622, + 0.286, + 0.754, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.286, + 0.89, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.392, + 0.392, + 0.43, + 0.402 + ], + "angle": 0, + "content": "Level 3" + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.392, + 0.566, + 0.402 + ], + "angle": 0, + "content": "Level 4" + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.392, + 0.703, + 0.402 + ], + "angle": 0, + "content": "Level 5" + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.392, + 0.84, + 0.402 + ], + "angle": 0, + "content": "Level 6" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.405, + 0.894, + 0.432 + ], + "angle": 0, + "content": "Figure 7. Results with different precision levels. For each input layout, we sample the images starting from same noise, so the images at different precision levels can have similar styles." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.442, + 0.209, + 0.541 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.211, + 0.442, + 0.336, + 0.541 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.442, + 0.468, + 0.541 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.542, + 0.21, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.542, + 0.338, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.542, + 0.468, + 0.641 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.645, + 0.462, + 0.66 + ], + "angle": 0, + "content": "Figure 8. Results with bounding box layout. Precision level \\(= 3\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.716 + ], + "angle": 0, + "content": "with layout control. We can see that the generated images match the text well and follow the provided layouts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.387, + 0.743 + ], + "angle": 0, + "content": "4.4. Segmentation-to-Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our model can also generate images from a dense segmentation map of closed-set labels, i.e. following the original S2I setting. For this application, we treat the class labels as text descriptions and use the highest precision level \\( c = 5 \\) for all masks. Fig. 10 shows example images generated by our method and SPADE [36]. The images generated by our model are of significantly better visual quality. Table. 4 reports the quantitative comparison results on the COCO-stuff validation set with the state-of-the-art S2I methods [33,36,51]. Since the highest resolution of the input lay" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.562 + ], + "angle": 0, + "content": "out to our model is 64, we evaluate the S2I results at \\(64 \\times 64\\) resolution. From the third and fifth columns of Table. 4 we can see that despite not being designed or trained for this task, the proposed method can achieve lower FID and comparable mIOU. After being fine-tuned on the COCO-stuff training set, our model outperforms previous approaches in terms of both FID and mIOU." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.574, + 0.894, + 0.588 + ], + "angle": 0, + "content": "Table 4. Quantitative comparison with S2I methods on COCO-stuff." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.598, + 0.89, + 0.663 + ], + "angle": 0, + "content": "
MethodFID ↓zero-shot FID ↓mIOU↑zero-shot mIOU↑
SPADE [36]50.91-17.49-
SAFM [33]62.28-12.28-
CLADE [51]55.30-17.21-
Ours17.2020.1723.0117.15
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.696, + 0.666, + 0.71 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We compare the proposed any-level method with two fixed-level baseline models: a text-to-image generation model and a fixed-level layout-to-image generation model. The baseline models are of the same architecture as the any-level models. When training the baseline models, we only use layouts of fixed levels, i.e. the 0-th level for the text-to-image baseline and the 4-th level for the fixed-level segmentation-to-image baseline. Table 5 compares the evaluation results of the any-level model and fixed-level baselines at the corresponding levels. The any-level model achieves better results than the baseline models, which further demonstrates the advantage of the unified framework." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "22474" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.087, + 0.077, + 0.533, + 0.088 + ], + "angle": 0, + "content": "A tornado made of bees crashing into a skyscraper. painting in the style of watercolor." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.891, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.44, + 0.872, + 0.453 + ], + "angle": 0, + "content": "Figure 9. Text-to-image generation results. Ours: our results by using text as a 0-th level layout. Ours*: our results with layout control." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.461, + 0.891, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.684, + 0.738, + 0.699 + ], + "angle": 0, + "content": "Figure 10. Visual comparison with SPADE [36] for segmentation-to-image generation." + }, + { + "type": "table_caption", + "bbox": [ + 0.109, + 0.707, + 0.436, + 0.721 + ], + "angle": 0, + "content": "Table 5. Ablation study results on OpenLayout-COCO." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.725, + 0.466, + 0.785 + ], + "angle": 0, + "content": "
Prec. LevelModelFID ↓CLIP Score ↑SS Score ↑
0Text-to-Image Baseline32.83.2473.5613
0Any-Level Model32.09.2496.5640
4Single-Level Baseline36.03.2381.5729
4Any-Level Model33.70.2475.6978
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.813, + 0.196, + 0.829 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "This paper presents a new conditional image synthesis framework to generate images from any-level open-domain semantic layouts. The input level ranges from pure text to a 2D semantic canvas with precise shapes. Several novel" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.895, + 0.875 + ], + "angle": 0, + "content": "techniques are introduced, including a pipeline for collecting training data; the representations to jointly encode precision level, semantics, and geometry information; and a multiscale guided diffusion model to synthesize images. A test dataset containing user-drawn layouts is collected to evaluate the proposed method. Experimental results demonstrate the advantage of the unified framework. The proposed method can generate high-quality images following the layout at specified precision levels, and compares favorably against the state-of-the-art methods on public benchmarks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "22475" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.471, + 0.156 + ], + "angle": 0, + "content": "[1] Stable diffusion. https://stability.ai/blog/stable-diffusion-public-release. Accessed: 2022.2,3,6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.471, + 0.2 + ], + "angle": 0, + "content": "[2] Edward H Adelson, Charles H Anderson, James R Bergen, Peter J Burt, and Joan M Ogden. Pyramid methods in image processing. 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Patel $^{1}$ $\{\text{yzeng22, vpatel36}\} \text{@jhu.edu}, \{\text{zlin, jianmzha, qingl, collomos, kuen}\} \text{@adobe.com}$ $^{1}$ Johns Hopkins University + $^{2}$ Adobe Research + +![](images/670eec9841d40299b0da4b3b356f274cd4361c8989d7b52a7b9cc15993f7147f.jpg) + +![](images/9b18ceba777bf08f007cf132045e9eaab54d8546ebb1bbd8be3a355534d595e6.jpg) +(a) + +![](images/4fe9e8499155eb5cec62291edcfa798f6eb04bc2d42dc211f0094b69a83e7f5e.jpg) + +![](images/82e5e415073707d324d5789e2fdcbd21f9a8149b7732bdf7b802bc13323ae9af.jpg) +(b) + +![](images/37469b35d4eb690cce43b11b23aa20e60754da3019f780c6cd72147646375f71.jpg) + +![](images/f0d0901bb119c07bb0f0da29b9504048abd91ae816ce51fd2598e2871468735c.jpg) +(c) +Figure 1. Examples of image synthesis from any-level semantic layouts. (a) The coarsest layout, i.e. at the 0-th precision level, is equivalent to a text input; (d) the finest layout, i.e. at the highest level, is close to an accurate segmentation map; (a)-(d) intermediate level layouts (from coarse to fine), the shape control becomes tighter with increasing levels. (e) We can specify different precision levels for different components, e.g. to include a 0-th level style indicator while the remaining regions are of higher levels. + +![](images/4346cc5243d02861b81360534cec9d4b7d6e49e3d230700fbd0cf1fb71b197cc.jpg) + +![](images/59d7f186eaa5415b867fc4a1c927ca04c9bb1a3c3bd8208bd15ecf910d086946.jpg) +(d) + +![](images/cdf37ff39d7616057b8f9e67b183fd19b3cbedcc722f7508f4cafe2468adb6c1.jpg) +(e) + +# Abstract + +We propose a new framework for conditional image synthesis from semantic layouts of any precision levels, ranging from pure text to a 2D semantic canvas with precise shapes. More specifically, the input layout consists of one or more semantic regions with free-form text descriptions and adjustable precision levels, which can be set based on the desired controllability. The framework naturally reduces to text-to-image (T2I) at the lowest level with no shape information, and it becomes segmentation-to-image (S2I) at the highest level. By supporting the levels in-between, our framework is flexible in assisting users of different drawing expertise and at different stages of their creative workflow. We introduce several novel techniques to address the challenges coming with this new setup, including a pipeline for collecting training data; a precision-encoded mask pyramid and a text feature map representation to jointly encode precision level, semantics, and composition information; and a multi-scale guided diffusion model to synthesize images. To evaluate + +the proposed method, we collect a test dataset containing user-drawn layouts with diverse scenes and styles. Experimental results show that the proposed method can generate high-quality images following the layout at given precision, and compares favorably against existing methods. Project page https://zengxianyu.github.io/scenegc/ + +# 1. Introduction + +Recently, deep generative models such as StyleGAN [24, 25] and diffusion models [9, 19, 49] have made a significant breakthrough in generating high-quality images. Image generation and editing technologies enabled by these models have become highly appealing to artists and designers by helping their creative workflows. To make image generation more controllable, researchers have put a lot of effort into conditional image synthesis and introduced models using various types and levels of semantic input such as object categories, text prompts, and segmentation + +Table 1. Difference from related conditional image synthesis works. T2I: text to image, S2I: segmentation to image, ST2I: Scene-based text to image [13], Box2I: bounding box layout to image [50]. + +
SettingOpen-domain layoutShape controlSparse layoutCoarse shapeLevel control
T2I✓XXXX
S2IX✓XXX
ST2IX✓XXX
Box2IXX✓XX
Ours✓✓✓✓✓
+ +maps etc. [23, 35, 36, 43, 44, 67]. + +However, existing models are not flexible enough to support the full creative workflow. They mostly consider fixed-level semantics as the input [63], e.g. image-level text descriptions in text-to-image generation (T2I) [35, 39, 41, 43, 44], or pixel-level segmentation maps in segmentation-to-image generation (S2I) [23, 36, 67]. Recent breakthroughs on T2I such as DALLE2 [39] and StableDiffusion [1, 43] demonstrate extraordinary capabilities of generating high-quality results. They can convert a rough idea into visual messages to provide inspirations at the beginning of the creative process, but provide no further control over image composition. On the other hand, S2I allows users to precisely control the image composition. As it is extremely challenging to draw a detailed layout directly, S2I is more useful for later creative stages given initial designs. For real-world use cases, it is highly desirable to have a model which can generate images from not only pure text or segmentation maps, but also intermediate-level layouts with coarse shapes. + +To this end, we propose a new unified conditional image synthesis framework to generate images from a semantic layout at any combination of precision levels. It is inspired by the typical coarse-to-fine workflow of artists and designers: they first start from an idea, which can be expressed as a text prompt or a set of concepts (Fig. 1 (a)), then tend to draw the approximate outlines and refine each object (Fig. 1 (a)-(d)). More specifically, we model a semantic layout as a set of semantic regions with free-form text descriptions. The layout can be sparse and each region can have a precision level to control how well the generated object should fit to the specified shape. The framework reduces to T2I when the layout is the coarsest (Fig. 1 (a)), and it becomes S2I when the layout is a segmentation map (Fig. 1 (d)). By adjusting the precision level, users can achieve their desired controllability (Fig. 1 (a)-(d)). This framework is different from the existing works in many aspects, as summarized in Table 1. + +This new setup comes with several challenges. First, it is non-trivial to encode open-domain layouts in image synthesis frameworks. Second, to handle hand-drawn layouts of varying precision, we need an effective and robust way to inject the precision information into the layout encoding. Third, there is no large-scale open-domain layout/image dataset. To generate high-quality images and generalize to novel concepts, a large and diverse training dataset is crucial. + +We introduce several novel ideas to address these chal + +lenges. First, we propose a text feature map representation for encoding a semantic layout. It can be seen as a spatial extension of text embedding or generalization of segmentation masks from binary to continuous space. Second, we introduce a precision-encoded mask pyramid to model layout precision. Inspired by the classical image pyramid models [2, 6, 47, 62], we relate shape precision to levels in a pyramid representation and encode precision by dropping out regions of lower precision levels. In other words, the $l$ -th level of the mask pyramid is a sub layout (subset of regions) consisting of semantic regions with precision level no less than $l$ . By creating a text feature map for each sub layout, we obtain a text feature pyramid as a unified representation of semantics, composition, and precision. Finally, we feed the text feature pyramid to a multi-scale guided diffusion model to generate images. We fulfill the need for training data by collecting them from two sources: (1) large-scale imagedataset pairs; (2) a relatively small pseudo layout/image dataset using text-based object detection and segmentation. With this multi-source training strategy, both text-to-image and layout-to-image can benefit from each other synergistically. + +Our contributions are summarized as follows: + +- A unified framework for diffusion-based image synthesis from semantic layouts with any combination of precision control. +- Novel ideas to build the model, including precision-encoded mask pyramid and pyramid text feature map representation, and multi-scale guided diffusion model, and training with multi-source data. +- A new real-world user-drawn layout dataset and extensive experiments showing the effectiveness of our model for text-to-image and layout-to-image generation with precision control. + +# 2. Related Work + +Deep generative models. In recent years, there has been significant progress in image generation using deep generative models. Some of these approaches attempt to learn the image distribution by optimizing a likelihood-based objective function. Autoregressive models (ARMs) [11, 55-57] treat images as sequences of pixels or tokens in a learned dictionary to define a tractable density model, which can be optimized by maximizing the likelihood. Variational Autoencoders (VAEs) [26, 54] use an intractable density function and train the model by maximizing the variational lower bound. Diffusion-based models [9, 19, 43, 48, 49] are also trained by optimizing the variational lower bound. Unlike VAEs which map an image into the latent space using a learnable encoder, diffusion-based models use a fixed diffusion process to transform an image into Gaussian noise. Generative Adversarial Networks (GANs) [5, 14, 24, 25] do not define the density function explicitly; instead, generative + +models are trained through an adversarial learning process against a discriminator. We base our method on diffusion models due to their ability to generate high-quality images and stability in training. + +Layout/Segmentation-to-image generation refers to the task of generating images from a spatial arrangement of semantic concepts, e.g. a segmentation map or a set of bounding boxes. Segmentation-based methods (e.g. [8,23,36,45,52,59,60]) have been proposed to allow users to precisely control the image composition, but are less flexible as they require a dense and accurate segmentation map and only allow a fixed set of categories. Bounding box-based methods can generate images from a coarse layout of bounding boxes. Bounding box-based generation was studied as a standalone task first by Zhao et al. [66] and has been an active research area [3, 17, 30, 58] since then. To convey more information than object categories, more expressive bounding box descriptions have been introduced, such as attributes [3, 34], relations [3], and free-form descriptions [12]. Although bounding boxes are easier to draw than segmentation maps, they provide no control over object shapes and orientations. In this work, we use coarse shapes with freeform text descriptions and precision levels to represent a layout, providing more flexibility and control for different synthesis needs. + +Text-to-image/Multi-modal image generation. T2I aims to generate images from a free-form text description, i.e. image captions. Earlier approaches are usually based on conditional GANs [41, 65]. Recently, autoregressive models based on image quantization techniques [10, 40, 64] and diffusion models [1,35,39,43,44] have shown surprising results with large-scale models and datasets. To gain more control over the spatial composition, some studies have tried to incorporate layout in the form of key points [42], bounding boxes [18], or object shapes [13, 21, 27, 29, 37], as an additional input. Some studies focused on image synthesis from multi-modal input including text, segmentation maps, edge maps [22, 61] etc. A work [4] concurrent to ours proposes a training-free paint-with-word method that enables users to specify the object locations by manipulating the attention matrices in cross-attention layers. These approaches use the layout as an extra signal complementary to captions. In contrast, we unify image captions and layout using a multi-level framework that models captions as a special case of layout with the lowest precision level. From a practical perspective, our framework provides a more flexible control mechanism with coarse shapes and precision controllability. + +# 3. Proposed Method + +Our method aims to generate images from a layout consisting of a set of semantic regions of varying precision levels. Formally, an input layout can be viewed as a list of tuples $\{(M_i,t_i,c_i)\}_{i = 1}^n$ , where $M_{i},t_{i},c_{i}$ indicate the seg + +mentation mask, text description, and the precision level of the $i$ -th region. We let $M, t, c$ denote the sets of masks, texts and precision levels of all regions, respectively. The precision level variable $c_{i} \in \mathbb{N}_{\leq L}$ indicates how precisely the generated content should follow the mask $M_{i}$ . A smaller value of $c_{i}$ indicates a less precise control allowing more deviation from the mask $M_{i}$ . $c_{i} = 0$ indicates the coarsest level where the $i$ -th mask will be ignored. When all $c_{i} = 0$ , the problem converts into T2I. Fig. 2 shows an overview of the proposed method. To generate an image at resolution $2^{L} \times 2^{L}$ , we first formulate a precision-encoded mask pyramid $\{M^{l}\}_{l=0}^{L}$ which represents each mask at the given precision level (Sec. 3.1). Then we combine the mask pyramid with the text descriptions $\pmb{t}$ to form a text feature pyramid $\{Z^{l}\}_{l=0}^{L}$ . It contains a $2^{l} \times 2^{l}$ text feature map at each level, which can be seen as an extension of the one-hot label map encoding in S2I (Sec. 3.2). Finally, a multi-level guided diffusion model takes the feature pyramid as input to generate an image (Sec. 3.3). + +# 3.1. Precision-Encoded Mask Pyramid + +For a user-drawn coarse shape, it is challenging to model the exact precision, since the type and the amount of error vary across different users. To simplify the problem, we relate precision to resolutions and propose a precision-encoded mask pyramid to encode the shape and precision information simultaneously. Given a mask and a precision level, a high precision level corresponds to using all details of the masks at a high resolution, while a low precision level means we can only trust the mask at a low resolution. + +More specifically, given a set of masks $M = [m_1, \dots, m_n]$ and the precision levels $c = [c_1, \dots, c_n]$ , we construct the mask pyramid by representing each mask $M_i$ at resolutions up to $2^{c_i}$ . In other words, we resize each mask $M_i$ to multiple resolutions and drop out the masks at resolutions higher than $2^{c_i}$ , as illustrated in Fig. 3. Formally, the $l$ -th layer of the mask pyramid, denoted as $M^l$ , is computed as follows, + +$$ +M _ {i} ^ {l} = \operatorname {r e s i z e} \left(M _ {i}, 2 ^ {l}\right) \cdot \mathbb {1} _ {c _ {i} \geq l}, \tag {1} +$$ + +where $\mathrm{resize}(M_i,2^l)$ izes a mask $M_{i}$ to $2^{l}\times 2^{l}$ resolution through image interpolation and binarization. The indicator function $\mathbb{1}_{c_i\geq l}$ returns 1 when $c_{i}\geq l$ and 0 otherwise. In our implementation, we set the range of precision levels to [0,3,4,5,6]. We observed that for a free-hand drawn layout, $8\times 8$ masks at the level 3 are easy to draw while being fairly informative, whereas $64\times 64$ masks at the level 6 usually capture enough details, as illustrated in Fig. 4. + +# 3.2. Text Feature Pyramid + +The mask pyramid encodes the shape and the precision information. To generate an image, we also need semantic information. We introduce a text feature pyramid for this purpose. Each level of the text feature pyramid is a $2^l \times 2^l$ text feature map $Z^l$ obtained by combining the masks $M^l$ + +![](images/417a0a67cf6c17c70ae92b22e9d1d2236ce23ac4f6088687aeed884776bd05f9.jpg) +Figure 2. An overview of the proposed method. We provide an intuitive interface where users can easily define a layout using a semantic brush associated with a free-form text description and adjustable precision level. The masks, regional descriptions, and precision levels $\{(M_i,t_i,c_i)\}_{i = 1}^n$ are jointly encoded into a text feature pyramid, and then translated into an image by a multi-scale guided diffusion model. + +![](images/47165497cc03f72ee41089a95a044cf179ae4d7298de6d6b53c3923a0592c54c.jpg) +Figure 3. An example of the precision-encoded mask pyramid. The first level has two non-zero masks corresponding to $m_{1}, m_{2}$ as $c_{1}, c_{2} \geq 1$ ; the second level only has $m_{1}$ as $c_{1} = 2, c_{2} < 2$ ; the third level does not have any non-zero masks as all the precision levels of all masks are lower than 3. + +![](images/705bc0d4eda6fa99dbec254035e35bd0e9c0189ac98c908d5567905e36d5843b.jpg) +Figure 4. Illustration of the masks at different levels of a pyramid. + +and the embeddings of the text $t$ . At the 0-th level, the $1 \times 1$ masks contain no shape information, so we simply concatenate the embeddings of all words into a sequence. At the levels where $l > 0$ , we spatially spread the embeddings of $t$ over the corresponding masks to jointly represent the shape and semantic, as illustrated in Fig. 2. + +Text feature maps. Here we describe in more detail how we construct the text feature map $Z^l$ at level $l > 0$ . For simplicity, we drop the superscript $l$ and denote the masks at an arbitrary level as $M$ . Each element $M_{i,x,y}$ is a binary value $\in \{0,1\}$ and we allow overlaps or blank spaces, i.e. $n \geq \sum_{i}^{n}M_{i,x,y} \geq 0$ . Given the initial masks $M$ , we introduce normalized masks $\hat{M}$ , which are augmented from $M$ by adding an extra mask $M_0$ to indicate the blank space and + +normalized by the number of shapes at each location: + +$$ +\hat {M} _ {i, x, y} = M _ {i, x, y} / \sum_ {i = 0} ^ {n} M _ {i, x, y}, \tag {2} +$$ + +where $M_{0,x,y} = \mathbb{1}_{\sum_{i = 1}^{n}M_{i,x,y} = 0}$ + +In the normalized masks $\hat{M}$ , each element $\hat{M}_{i,x,y}$ is a continuous value $\in [0,1]$ and we have $\sum_{i=0}^{n} \hat{M}_{i,x,y} = 1$ . We compute each element $Z_{x,y}$ at location $x,y$ as follows, + +$$ +\boldsymbol {Z} _ {x, y} = \sum_ {i = 0} ^ {n} \boldsymbol {f} \left(t _ {i}\right) \cdot \hat {M} _ {i, x, y}, \tag {3} +$$ + +where $\pmb{f}(t_i)$ is an embedding of the text $t_i$ . We set $t_0$ to be a null token $\oslash$ to represent unspecified areas, i.e. the blank space indicated by $M_0$ . + +The text feature map representation has several advantages. First, it is of the same dimension regardless of the number of masks, and therefore compatible with most deep ConvNet architectures. Second, each element of a text feature map is a convex combination of $n$ text embeddings in the learned embedding space. With a powerful language model, we can achieve a good generalization capability for unseen combinations of concepts. In a text feature map, any overlapping area contains an interpolation of multiple embeddings. Accordingly, users can get creative results derived from hybrid concepts by drawing overlapping shapes. + +Data acquisition. During inference, the segmentation masks and text descriptions are both provided by users. During training, we can generate them automatically using text-based object detection [28] and segmentation [16]. We set the regions where no objects are detected as blank space and assign a null token $\varnothing$ to these regions. We use CLIP [38] text model to encode the text descriptions. In addition, the 0-th level feature maps can be obtained directly from the image caption embeddings. More details regarding the training data generation step can be found in the supplementary material. + +Relation to one-hot label maps. In S2I, a layout containing + +![](images/942e03bcc103c4a721de3dec0137980dbc61d859d111f3b3798bcbee6f7ab265.jpg) +Figure 5. Architecture of the multi-scale guided diffusion model. + +at most $C$ classes can be encoded into a $C$ -channel one-hot label map. It can be seen as a special case of text feature maps when the masks are dense and non-overlapping, and the embedding model $\pmb{f}$ is a one-hot encoding function. Specifically, let $M$ be the segmentation masks, $\pmb{t}$ the class labels where $t_i = 1,2,\dots,C$ , $f_c(t_i) = \mathbb{1}_{t_i = c}$ . Since $M$ are dense and non-overlapping, the normalized masks $\hat{M}_i$ will be the same as $M_i$ for $i > 1$ and $\hat{M}_0 = 0$ . Eqn. 3 then becomes + +$$ +Z _ {c, x, y} = \sum_ {i = 1} ^ {n} \mathbb {1} _ {t _ {i} = c} \cdot M _ {i, x, y} = \sum_ {i \mid t _ {i} = c} M _ {i, x, y}. \tag {4} +$$ + +Therefore, the $c$ -th channel of $Z$ is a mask covering all pixels of class $c$ , i.e., a one-hot label map. Through this reformulation, we can see that the one-hot representation has limited capability as $\pmb{f}(t_i)$ is restricted to be binary. The text feature map representation uses a learned language model as $\pmb{f}$ to encode the more informative open-domain layouts. + +# 3.3. Multi-Scale Guided Diffusion + +We use a diffusion model to generate images from a text feature pyramid. We use $\epsilon$ -prediction and the simplified training objective following [19]: + +$$ +L = \mathbb {E} _ {\epsilon \sim \mathcal {N} (0, 1), t \sim [ 1, T ]} \left[ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, \boldsymbol {z}, t) \| _ {2} ^ {2} \right], \tag {5} +$$ + +where $T$ is the number of diffusion steps, $\boldsymbol{x}_t$ is a noisy version of the ground-truth image $\boldsymbol{x}$ at the $t$ -th diffusion step, $\boldsymbol{z}$ is the conditional signal, which in our case is the text feature pyramid $\{Z^l\}_{l=0}^L$ , and $\epsilon_\theta$ represents the network parameterized by $\boldsymbol{\theta}$ . We modify the UNet architecture [9] by adding the convolutional layers to combine each text feature map with the UNet feature maps of the corresponding resolution. The 0-th level text feature maps $Z^0$ are passed through all blocks using cross-modal attention [44] and channel-wise feature modulation. Fig. 5 shows the overall architecture of the modified UNet. + +Classifier-free guidance [20] has shown to be an effective technique to improve the performance of conditional diffusion models and is widely applied to diffusion models conditioned on text and class tags [9, 35, 43, 44]. To benefit from this technique, we introduce multi-scale spatial guidance for our feature map conditioned diffusion model. As described in Sec. 3.2, in text feature maps from level 1 to $L$ , the unspecified regions are the embedding of a null + +token $\pmb{f}(\varnothing)$ . We further apply dropout with probability 0.1 to $Z^0$ by setting $Z^0 = f(\varnothing)$ . During inference, we estimate two diffusion scores, conditioning on the given text feature pyramid and an empty feature pyramid of repeating $\pmb{f}(\varnothing)$ , and then perform sampling using their linear combination. + +# 4. Experiments + +In this section, we present the experimental results on image synthesis from any-level semantic layouts. We evaluate the proposed method on user-drawn coarse layouts and automatically simulated layout data. We also present results on T2I and S2I, and compare our method with state-of-the-art methods. + +# 4.1. Implementation Details + +We train the multi-scale guided diffusion model to generate $64 \times 64$ images from a layout of precision up to $\log_2 64$ . To generate images at higher resolution, we experiment with two approaches: (1) by training another diffusion model to upsample $64 \rightarrow 256$ following [9]; (2) by generating the latent map at $64 \times 64$ resolution then decoding it into a $512 \times 512$ image following [43]. Both approaches are effective, demonstrating that the proposed method can generalize well to both pixel-space and latent-space diffusion strategies. We use smaller pixel-space diffusion models for ablation studies and report the main results based on a larger latent-space diffusion model. We encode the text descriptions using the pretrained CLIP ViT-L14 language model [38]. To avoid repeated forward passes, we feed the union of all regional descriptions $\cup_{i} t_{i}$ as a sentence into the language model. Then, we average the hidden states corresponding to each word in $t_{i}$ to use as its embedding $\mathbf{f}(t_{i})$ . + +Training details. We use the aesthetic subset of Laion2B-en dataset [46] for training. We generate full text feature pyramids for 5M randomly selected samples and construct only the 0-th level feature maps for the remaining samples. For pixel space diffusion, we train a base model of 300M parameters and a super-resolution model of 300M parameters; for latent-space diffusion, we train a base model of 900M parameters and use the pretrained deocder from [43]. We use batch size 2048 for $64 \times 64$ models and batch size 960 for the super-resolution model. + +Evaluation benchmark. We use the COCO [32] validation set for evaluation in the T2I setting and the COCO-stuff [7] validation set for S2I. For evaluation in open-domain layout-to-image generation, we construct a new test set OpenLayout containing 260 user-drawn layouts of coarse shapes. The layouts are annotated by 10 users based on text prompts randomly sampled from PartiPrompts [64]. To analyze the effect of precision level control, we also evaluate using the pseudo layouts consisting of accurate shapes, which are extracted from the 5,000 images with caption annotations of COCO validation set (OpenLayout-COCO). Fig. 6 shows + +Table 2. Quantitative results on the OpenLayout and OpenLayout-COCO datasets with different precision levels. SS Score: spatial similarity scores. + +
OpenLayoutOpenLayout-COCO
Prec.SS Score ↑CLIP Score ↑SS Score ↑CLIP Score ↑FID ↓
0.436.274.572.26025.3
3.533.268.685.25626.0
4.543.266.716.25627.0
5.558.267.729.25628.4
6.558.261.736.25530.6
+ +some layouts samples from OpenLayout and Openlayout-COCO. + +![](images/1df4f4ede396b7ce7c54a5f95444a417bad071d3672368418075b1a339bc89da.jpg) +Figure 6. Top: Pseudo layouts from OpenLayout-COCO dataset. Bottom: real-world user-drawn layouts from OpenLayout dataset. + +# 4.2. Open-Domain Layout-to-Image Generation + +Here we discuss the results on the OpenLayout and OpenLayout-COCO datasets. For each sample, we run the model a varying precision level $c$ from 0 to 6 to verify the effectiveness of precision control. Fig. 7 shows the results with different precision levels. For simplicity, we use the same precision level for all regions in an input layout, i.e. $\forall i, c_i = c$ . We can see that as the precision level increases, the generated images follows the layout more closely. When $c = 0$ , the image compositions are not related to the layouts. For $c = 3, 4$ the generated images roughly resemble the shape and location specified in the layout. For $c = 5, 6$ , the generated object contours matches the layout more closely. At the lowest precision level, our method can handle very rough layouts, e.g., bounding box layouts, as shown in Fig. 8, despite not being trained on bounding box data. + +For quantitative evaluation, we compute the CLIP score using the original captions to measure global semantic alignment. To measure spatial alignment, we define a spatial similarity score (SS score), which is the cosine similarity between the text feature maps of the input layout and the layout reconstructed from the generated image. For OpenLayout-COCO, as the ground-truth images are available, we also compute the FID to measure the visual quality. + +Table 2 reports the quantitative evaluation results on images generated with different precision levels. The second + +Table 3. Quantitative comparison with T2I methods on COCO. + +
MethodFID ↓zero-shot FID↓
SSA-GAN [31]19.37-
VQ-Diffusion [15]13.86-
DF-GAN [53]19.32-
GLIDE [35]-12.89
SD [1,43]-9.89
DALLE2 [39]-10.87
Ours8.559.47
+ +and fourth columns show that using a higher precision level generally leads to a higher spatial similarity, which further demonstrates the effectiveness of precision control. On OpenLayout-COCO, the spatial similarity consistently increases as the precision level becomes higher. Whereas, on OpenLayout, it stays the same at higher levels. This is due to the difference in the inherent layout precision exhibited by the two datasets; compared to OpenLayout-COCO, the layouts in OpenLayout are coarser. For a coarse layout, the generated images already match it well at low precision levels and the room for improvement is limited. + +From the last column of Table 2, we can see that the results with a lower precision level have a smaller FID, which indicates a similar distribution with respect to the ground-truth images. This is likely because a lower precision level enforces smaller constraints on the generation process, and therefore the generated images can better capture the real image distribution. Similarly, a lower precision level also yields a slightly better CLIP score due to the smaller spatial constraints, as shown in the third and fifth columns of Table 2. + +# 4.3. Text-to-Image Generation + +As mentioned in Sec. 3, our method can be applied for text-to-image generation by using texts as 0-th layouts. The first four columns of Fig. 9 show the images generated from text prompts by our method and state-of-the-art methods. We can see that the proposed method can generate visually peasant images with reasonable layouts from only text input. Table 3 reports the FID evaluated on the COCO validation set. The classifier-free guidance scale is set to 3. Following [35], we sample 30K images using randomly selected text prompts and compute FID against the entire validation set. It can be seen that the proposed method compares favorably against state-of-the-art text-to-image generation models. + +By combining with a named entity recognition (NER) model, we can apply the proposed method to layout controllable text-to-image generation. More specifically, given an input sentence, we parse the noun phrases using NER to generate regional text descriptions, and users can arbitrarily draw the shapes for those noun phrases. The last two columns of Fig. 9 show the text-to-image generation results + +![](images/89b034700eba78333db1368202eaca17a1584ec0291cda333e82fe1faeb263e2.jpg) + +![](images/1b7d024967fb1e5ec10b65589075c38cfbe17a1b7ea5f63691bea7f4e6b59c6c.jpg) + +![](images/9d8e3cf0a2cc4c73d07c307560a3a67757bfb927e0c48b0608f90b666f72f6b9.jpg) + +![](images/b9c0b64a7905566192445d4384e67412cfc909e1ae38be8076cba5c61f58528e.jpg) + +![](images/3a28a85a9613d86a18de315f937fcac4fe318bb0d750b4deb509ca92aa091c16.jpg) + +![](images/7b3efab3fcb8557d546665d8d6127a9cf4832870e756eaa5b58be8d368eaa3c6.jpg) + +![](images/7f09770d74f27691d338eff3c3f4963c960a8eef76313d3ada8c347dd8d66cc2.jpg) + +![](images/29e0e669bad358eff2f932b3a882d88e5e3613f9e6cb5d4d2334cb9e2d2aef10.jpg) + +![](images/e128fa611bd6996ff7ca364b9a5c867801482700a5e6815265ad11b8efefe512.jpg) + +![](images/6dcdba5e612e76915fbdc842b5a926d7920bfb51b3538a0cdfa8b8a7eb9eca03.jpg) + +![](images/5716b1cd70dd58ea935f2e4908fcaf931bc7ae21e2ddbec375a77177038d4c46.jpg) + +![](images/870b233691f2942288cec5a8d6c570d905d0d6bab86c29ec8ec5bdc7861d7a19.jpg) + +![](images/6926c35e12835b59213f8079a135e7b55246b5d178260209ce7c619efe82165b.jpg) +Figure 7. Results with different precision levels. For each input layout, we sample the images starting from same noise, so the images at different precision levels can have similar styles. + +![](images/57ceb7c9414bae79af0d755026821a39b132e2c4e6e43ad5b8d0f55efaea867c.jpg) + +![](images/5d6755db259f83b1bae5e116e31be747709fe1ebcb1fa3fee6a5d210b62bc253.jpg) +Level 3 + +![](images/fd94759bd73bb5503a5db2af98b8547b1584f2d7592af1d528645237db6a8836.jpg) +Level 4 + +![](images/bb2cc5a253d5cd5d0e5cb65d054f65a1d9fecdb937a49f8060aab357ed94e5c3.jpg) +Level 5 + +![](images/e029c36a8b1ccb2edd98bc6f2195fc7a841e0836fa3169f6f4d3567437fb6729.jpg) +Level 6 + +![](images/588b0365995cd119d3b428fec4a1676ade61833a27feac683df74d94e78f9622.jpg) + +![](images/0f8dd5aefcd17fa568bce37012eb3bece6327ab059193e7a0710193f7c78ab41.jpg) + +![](images/d3dc39cae8e626bc2b70a618fbacc49ae4aff5332613b4cb015c960ff80cadab.jpg) + +![](images/008880d259c8529449e075229ad70bcd0fe044f8f714b34766a558e472e9bc69.jpg) +Figure 8. Results with bounding box layout. Precision level $= 3$ + +![](images/f2246c94000e4503559d92bb0186f25e41cc4ad3f9323ab1f39af6d6000dcbb4.jpg) + +![](images/5051d27dde148a1e35307b1d5ce2ebfe72a14dcbc1e0f84f84e18a86c017261a.jpg) + +with layout control. We can see that the generated images match the text well and follow the provided layouts. + +# 4.4. Segmentation-to-Image Generation + +Our model can also generate images from a dense segmentation map of closed-set labels, i.e. following the original S2I setting. For this application, we treat the class labels as text descriptions and use the highest precision level $c = 5$ for all masks. Fig. 10 shows example images generated by our method and SPADE [36]. The images generated by our model are of significantly better visual quality. Table. 4 reports the quantitative comparison results on the COCO-stuff validation set with the state-of-the-art S2I methods [33,36,51]. Since the highest resolution of the input lay + +out to our model is 64, we evaluate the S2I results at $64 \times 64$ resolution. From the third and fifth columns of Table. 4 we can see that despite not being designed or trained for this task, the proposed method can achieve lower FID and comparable mIOU. After being fine-tuned on the COCO-stuff training set, our model outperforms previous approaches in terms of both FID and mIOU. + +Table 4. Quantitative comparison with S2I methods on COCO-stuff. + +
MethodFID ↓zero-shot FID ↓mIOU↑zero-shot mIOU↑
SPADE [36]50.91-17.49-
SAFM [33]62.28-12.28-
CLADE [51]55.30-17.21-
Ours17.2020.1723.0117.15
+ +# 4.5. Ablation Studies + +We compare the proposed any-level method with two fixed-level baseline models: a text-to-image generation model and a fixed-level layout-to-image generation model. The baseline models are of the same architecture as the any-level models. When training the baseline models, we only use layouts of fixed levels, i.e. the 0-th level for the text-to-image baseline and the 4-th level for the fixed-level segmentation-to-image baseline. Table 5 compares the evaluation results of the any-level model and fixed-level baselines at the corresponding levels. The any-level model achieves better results than the baseline models, which further demonstrates the advantage of the unified framework. + +A tornado made of bees crashing into a skyscraper. painting in the style of watercolor. + +![](images/6c13d25210b315704701c959daba13443ea7edd6a584d659a9fbf23915725857.jpg) +Figure 9. Text-to-image generation results. Ours: our results by using text as a 0-th level layout. Ours*: our results with layout control. + +![](images/2ee46735362b8ecf3203e28bc3489b836399a35435f607011594c5a93589dde0.jpg) +Figure 10. Visual comparison with SPADE [36] for segmentation-to-image generation. + +Table 5. Ablation study results on OpenLayout-COCO. + +
Prec. LevelModelFID ↓CLIP Score ↑SS Score ↑
0Text-to-Image Baseline32.83.2473.5613
0Any-Level Model32.09.2496.5640
4Single-Level Baseline36.03.2381.5729
4Any-Level Model33.70.2475.6978
+ +# 5. Conclusion + +This paper presents a new conditional image synthesis framework to generate images from any-level open-domain semantic layouts. The input level ranges from pure text to a 2D semantic canvas with precise shapes. Several novel + +techniques are introduced, including a pipeline for collecting training data; the representations to jointly encode precision level, semantics, and geometry information; and a multiscale guided diffusion model to synthesize images. A test dataset containing user-drawn layouts is collected to evaluate the proposed method. Experimental results demonstrate the advantage of the unified framework. The proposed method can generate high-quality images following the layout at specified precision levels, and compares favorably against the state-of-the-art methods on public benchmarks. + +# References + +[1] Stable diffusion. https://stability.ai/blog/stable-diffusion-public-release. 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Examples of image synthesis from any-level semantic layouts. (a) The coarsest layout, i.e. at the 0-th precision level, is equivalent to a text input; (d) the finest layout, i.e. at the highest level, is close to an accurate segmentation map; (a)-(d) intermediate level layouts (from coarse to fine), the shape control becomes tighter with increasing levels. (e) We can specify different precision levels for different components, e.g. to include a 0-th level style indicator while the remaining regions are of higher levels." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 347, + 208, + 444, + 307 + ], + "blocks": [ + { + "bbox": [ + 347, + 208, + 444, + 307 + ], + "lines": [ + { + "bbox": [ + 347, + 208, + 444, + 307 + ], + "spans": [ + { + "bbox": [ + 347, + 208, + 444, + 307 + ], + "type": "image", + "image_path": "4346cc5243d02861b81360534cec9d4b7d6e49e3d230700fbd0cf1fb71b197cc.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 347, + 308, + 444, + 407 + ], + "blocks": [ + { + "bbox": [ + 347, + 308, + 444, + 407 + ], + "lines": [ + { + "bbox": [ + 347, + 308, + 444, + 407 + ], + "spans": [ + { + "bbox": [ + 347, + 308, + 444, + 407 + ], + "type": "image", + "image_path": "59d7f186eaa5415b867fc4a1c927ca04c9bb1a3c3bd8208bd15ecf910d086946.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 408, + 400, + 416 + ], + "lines": [ + { + "bbox": [ + 390, + 408, + 400, + 416 + ], + "spans": [ + { + "bbox": [ + 390, + 408, + 400, + 416 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 445, + 199, + 544, + 406 + ], + "blocks": [ + { + "bbox": [ + 445, + 199, + 544, + 406 + ], + "lines": [ + { + "bbox": [ + 445, + 199, + 544, + 406 + ], + "spans": [ + { + "bbox": [ + 445, + 199, + 544, + 406 + ], + "type": "image", + "image_path": "cdf37ff39d7616057b8f9e67b183fd19b3cbedcc722f7508f4cafe2468adb6c1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 489, + 408, + 499, + 416 + ], + "lines": [ + { + "bbox": [ + 489, + 408, + 499, + 416 + ], + "spans": [ + { + "bbox": [ + 489, + 408, + 499, + 416 + ], + "type": "text", + "content": "(e)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "bbox": [ + 143, + 468, + 192, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 468, + 192, + 481 + ], + "spans": [ + { + "bbox": [ + 143, + 468, + 192, + 481 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 45, + 498, + 290, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 498, + 290, + 714 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 290, + 714 + ], + "type": "text", + "content": "We propose a new framework for conditional image synthesis from semantic layouts of any precision levels, ranging from pure text to a 2D semantic canvas with precise shapes. More specifically, the input layout consists of one or more semantic regions with free-form text descriptions and adjustable precision levels, which can be set based on the desired controllability. The framework naturally reduces to text-to-image (T2I) at the lowest level with no shape information, and it becomes segmentation-to-image (S2I) at the highest level. By supporting the levels in-between, our framework is flexible in assisting users of different drawing expertise and at different stages of their creative workflow. We introduce several novel techniques to address the challenges coming with this new setup, including a pipeline for collecting training data; a precision-encoded mask pyramid and a text feature map representation to jointly encode precision level, semantics, and composition information; and a multi-scale guided diffusion model to synthesize images. To evaluate" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 470, + 548, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 548, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 548, + 542 + ], + "type": "text", + "content": "the proposed method, we collect a test dataset containing user-drawn layouts with diverse scenes and styles. Experimental results show that the proposed method can generate high-quality images following the layout at given precision, and compares favorably against existing methods. Project page https://zengxianyu.github.io/scenegc/" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 572, + 387, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 572, + 387, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 572, + 387, + 585 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "Recently, deep generative models such as StyleGAN [24, 25] and diffusion models [9, 19, 49] have made a significant breakthrough in generating high-quality images. Image generation and editing technologies enabled by these models have become highly appealing to artists and designers by helping their creative workflows. To make image generation more controllable, researchers have put a lot of effort into conditional image synthesis and introduced models using various types and levels of semantic input such as object categories, text prompts, and segmentation" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "22468" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 106, + 287, + 159 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 288, + 102 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 288, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 288, + 102 + ], + "type": "text", + "content": "Table 1. Difference from related conditional image synthesis works. T2I: text to image, S2I: segmentation to image, ST2I: Scene-based text to image [13], Box2I: bounding box layout to image [50]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 106, + 287, + 159 + ], + "lines": [ + { + "bbox": [ + 49, + 106, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 49, + 106, + 287, + 159 + ], + "type": "table", + "html": "
SettingOpen-domain layoutShape controlSparse layoutCoarse shapeLevel control
T2I✓XXXX
S2IX✓XXX
ST2IX✓XXX
Box2IXX✓XX
Ours✓✓✓✓✓
", + "image_path": "f19b580a86d89f85c9161aedb0520a2925a5e04978102289f52398b63850b726.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 168, + 178, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 168, + 178, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 178, + 180 + ], + "type": "text", + "content": "maps etc. [23, 35, 36, 43, 44, 67]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 182, + 289, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 289, + 397 + ], + "type": "text", + "content": "However, existing models are not flexible enough to support the full creative workflow. They mostly consider fixed-level semantics as the input [63], e.g. image-level text descriptions in text-to-image generation (T2I) [35, 39, 41, 43, 44], or pixel-level segmentation maps in segmentation-to-image generation (S2I) [23, 36, 67]. Recent breakthroughs on T2I such as DALLE2 [39] and StableDiffusion [1, 43] demonstrate extraordinary capabilities of generating high-quality results. They can convert a rough idea into visual messages to provide inspirations at the beginning of the creative process, but provide no further control over image composition. On the other hand, S2I allows users to precisely control the image composition. As it is extremely challenging to draw a detailed layout directly, S2I is more useful for later creative stages given initial designs. For real-world use cases, it is highly desirable to have a model which can generate images from not only pure text or segmentation maps, but also intermediate-level layouts with coarse shapes." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 399, + 288, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 288, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 288, + 602 + ], + "type": "text", + "content": "To this end, we propose a new unified conditional image synthesis framework to generate images from a semantic layout at any combination of precision levels. It is inspired by the typical coarse-to-fine workflow of artists and designers: they first start from an idea, which can be expressed as a text prompt or a set of concepts (Fig. 1 (a)), then tend to draw the approximate outlines and refine each object (Fig. 1 (a)-(d)). More specifically, we model a semantic layout as a set of semantic regions with free-form text descriptions. The layout can be sparse and each region can have a precision level to control how well the generated object should fit to the specified shape. The framework reduces to T2I when the layout is the coarsest (Fig. 1 (a)), and it becomes S2I when the layout is a segmentation map (Fig. 1 (d)). By adjusting the precision level, users can achieve their desired controllability (Fig. 1 (a)-(d)). This framework is different from the existing works in many aspects, as summarized in Table 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 604, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 288, + 700 + ], + "type": "text", + "content": "This new setup comes with several challenges. First, it is non-trivial to encode open-domain layouts in image synthesis frameworks. Second, to handle hand-drawn layouts of varying precision, we need an effective and robust way to inject the precision information into the layout encoding. Third, there is no large-scale open-domain layout/image dataset. To generate high-quality images and generalize to novel concepts, a large and diverse training dataset is crucial." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 712 + ], + "type": "text", + "content": "We introduce several novel ideas to address these chal" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "text", + "content": "lenges. First, we propose a text feature map representation for encoding a semantic layout. It can be seen as a spatial extension of text embedding or generalization of segmentation masks from binary to continuous space. Second, we introduce a precision-encoded mask pyramid to model layout precision. Inspired by the classical image pyramid models [2, 6, 47, 62], we relate shape precision to levels in a pyramid representation and encode precision by dropping out regions of lower precision levels. In other words, the " + }, + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "text", + "content": "-th level of the mask pyramid is a sub layout (subset of regions) consisting of semantic regions with precision level no less than " + }, + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 72, + 547, + 323 + ], + "type": "text", + "content": ". By creating a text feature map for each sub layout, we obtain a text feature pyramid as a unified representation of semantics, composition, and precision. Finally, we feed the text feature pyramid to a multi-scale guided diffusion model to generate images. We fulfill the need for training data by collecting them from two sources: (1) large-scale imagedataset pairs; (2) a relatively small pseudo layout/image dataset using text-based object detection and segmentation. With this multi-source training strategy, both text-to-image and layout-to-image can benefit from each other synergistically." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 317, + 324, + 503, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 324, + 503, + 335 + ], + "spans": [ + { + "bbox": [ + 317, + 324, + 503, + 335 + ], + "type": "text", + "content": "Our contributions are summarized as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 345, + 547, + 477 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 317, + 345, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 345, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 317, + 345, + 547, + 380 + ], + "type": "text", + "content": "- A unified framework for diffusion-based image synthesis from semantic layouts with any combination of precision control." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 381, + 547, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 381, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 317, + 381, + 547, + 429 + ], + "type": "text", + "content": "- Novel ideas to build the model, including precision-encoded mask pyramid and pyramid text feature map representation, and multi-scale guided diffusion model, and training with multi-source data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 430, + 547, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 430, + 547, + 477 + ], + "spans": [ + { + "bbox": [ + 317, + 430, + 547, + 477 + ], + "type": "text", + "content": "- A new real-world user-drawn layout dataset and extensive experiments showing the effectiveness of our model for text-to-image and layout-to-image generation with precision control." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 489, + 392, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 489, + 392, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 489, + 392, + 502 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": "Deep generative models. In recent years, there has been significant progress in image generation using deep generative models. Some of these approaches attempt to learn the image distribution by optimizing a likelihood-based objective function. Autoregressive models (ARMs) [11, 55-57] treat images as sequences of pixels or tokens in a learned dictionary to define a tractable density model, which can be optimized by maximizing the likelihood. Variational Autoencoders (VAEs) [26, 54] use an intractable density function and train the model by maximizing the variational lower bound. Diffusion-based models [9, 19, 43, 48, 49] are also trained by optimizing the variational lower bound. Unlike VAEs which map an image into the latent space using a learnable encoder, diffusion-based models use a fixed diffusion process to transform an image into Gaussian noise. Generative Adversarial Networks (GANs) [5, 14, 24, 25] do not define the density function explicitly; instead, generative" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "22469" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "models are trained through an adversarial learning process against a discriminator. We base our method on diffusion models due to their ability to generate high-quality images and stability in training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 289, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 289, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 289, + 370 + ], + "type": "text", + "content": "Layout/Segmentation-to-image generation refers to the task of generating images from a spatial arrangement of semantic concepts, e.g. a segmentation map or a set of bounding boxes. Segmentation-based methods (e.g. [8,23,36,45,52,59,60]) have been proposed to allow users to precisely control the image composition, but are less flexible as they require a dense and accurate segmentation map and only allow a fixed set of categories. Bounding box-based methods can generate images from a coarse layout of bounding boxes. Bounding box-based generation was studied as a standalone task first by Zhao et al. [66] and has been an active research area [3, 17, 30, 58] since then. To convey more information than object categories, more expressive bounding box descriptions have been introduced, such as attributes [3, 34], relations [3], and free-form descriptions [12]. Although bounding boxes are easier to draw than segmentation maps, they provide no control over object shapes and orientations. In this work, we use coarse shapes with freeform text descriptions and precision levels to represent a layout, providing more flexibility and control for different synthesis needs." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 371, + 289, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 289, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 289, + 635 + ], + "type": "text", + "content": "Text-to-image/Multi-modal image generation. T2I aims to generate images from a free-form text description, i.e. image captions. Earlier approaches are usually based on conditional GANs [41, 65]. Recently, autoregressive models based on image quantization techniques [10, 40, 64] and diffusion models [1,35,39,43,44] have shown surprising results with large-scale models and datasets. To gain more control over the spatial composition, some studies have tried to incorporate layout in the form of key points [42], bounding boxes [18], or object shapes [13, 21, 27, 29, 37], as an additional input. Some studies focused on image synthesis from multi-modal input including text, segmentation maps, edge maps [22, 61] etc. A work [4] concurrent to ours proposes a training-free paint-with-word method that enables users to specify the object locations by manipulating the attention matrices in cross-attention layers. These approaches use the layout as an extra signal complementary to captions. In contrast, we unify image captions and layout using a multi-level framework that models captions as a special case of layout with the lowest precision level. From a practical perspective, our framework provides a more flexible control mechanism with coarse shapes and precision controllability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 645, + 153, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 153, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 153, + 659 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": "Our method aims to generate images from a layout consisting of a set of semantic regions of varying precision levels. Formally, an input layout can be viewed as a list of tuples " + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\{(M_i,t_i,c_i)\\}_{i = 1}^n" + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_{i},t_{i},c_{i}" + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": " indicate the seg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": "mentation mask, text description, and the precision level of the " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": "-th region. We let " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "M, t, c" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " denote the sets of masks, texts and precision levels of all regions, respectively. The precision level variable " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "c_{i} \\in \\mathbb{N}_{\\leq L}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " indicates how precisely the generated content should follow the mask " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": ". A smaller value of " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " indicates a less precise control allowing more deviation from the mask " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "c_{i} = 0" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " indicates the coarsest level where the " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": "-th mask will be ignored. When all " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "c_{i} = 0" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": ", the problem converts into T2I. Fig. 2 shows an overview of the proposed method. To generate an image at resolution " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "2^{L} \\times 2^{L}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": ", we first formulate a precision-encoded mask pyramid " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "\\{M^{l}\\}_{l=0}^{L}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " which represents each mask at the given precision level (Sec. 3.1). Then we combine the mask pyramid with the text descriptions " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "\\pmb{t}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " to form a text feature pyramid " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "\\{Z^{l}\\}_{l=0}^{L}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": ". It contains a " + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "inline_equation", + "content": "2^{l} \\times 2^{l}" + }, + { + "bbox": [ + 304, + 72, + 547, + 300 + ], + "type": "text", + "content": " text feature map at each level, which can be seen as an extension of the one-hot label map encoding in S2I (Sec. 3.2). Finally, a multi-level guided diffusion model takes the feature pyramid as input to generate an image (Sec. 3.3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 305, + 489, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 305, + 489, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 305, + 489, + 319 + ], + "type": "text", + "content": "3.1. Precision-Encoded Mask Pyramid" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 324, + 547, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 547, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 547, + 430 + ], + "type": "text", + "content": "For a user-drawn coarse shape, it is challenging to model the exact precision, since the type and the amount of error vary across different users. To simplify the problem, we relate precision to resolutions and propose a precision-encoded mask pyramid to encode the shape and precision information simultaneously. Given a mask and a precision level, a high precision level corresponds to using all details of the masks at a high resolution, while a low precision level means we can only trust the mask at a low resolution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": "More specifically, given a set of masks " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "M = [m_1, \\dots, m_n]" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": " and the precision levels " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "c = [c_1, \\dots, c_n]" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": ", we construct the mask pyramid by representing each mask " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "M_i" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": " at resolutions up to " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "2^{c_i}" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": ". In other words, we resize each mask " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "M_i" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": " to multiple resolutions and drop out the masks at resolutions higher than " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "2^{c_i}" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": ", as illustrated in Fig. 3. Formally, the " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": "-th layer of the mask pyramid, denoted as " + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "inline_equation", + "content": "M^l" + }, + { + "bbox": [ + 304, + 431, + 547, + 515 + ], + "type": "text", + "content": ", is computed as follows," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 366, + 517, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 517, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 366, + 517, + 545, + 531 + ], + "type": "interline_equation", + "content": "M _ {i} ^ {l} = \\operatorname {r e s i z e} \\left(M _ {i}, 2 ^ {l}\\right) \\cdot \\mathbb {1} _ {c _ {i} \\geq l}, \\tag {1}", + "image_path": "34b2b3cdf7e80cd7a6b153eed6021fa1bc09229e699b9f4a41f441284d50824f.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{resize}(M_i,2^l)" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": "izes a mask " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "2^{l}\\times 2^{l}" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": " resolution through image interpolation and binarization. The indicator function " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_{c_i\\geq l}" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": " returns 1 when " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "c_{i}\\geq l" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": " and 0 otherwise. In our implementation, we set the range of precision levels to [0,3,4,5,6]. We observed that for a free-hand drawn layout, " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "8\\times 8" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": " masks at the level 3 are easy to draw while being fairly informative, whereas " + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "inline_equation", + "content": "64\\times 64" + }, + { + "bbox": [ + 304, + 533, + 547, + 629 + ], + "type": "text", + "content": " masks at the level 6 usually capture enough details, as illustrated in Fig. 4." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 635, + 432, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 432, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 432, + 647 + ], + "type": "text", + "content": "3.2. Text Feature Pyramid" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": "The mask pyramid encodes the shape and the precision information. To generate an image, we also need semantic information. We introduce a text feature pyramid for this purpose. Each level of the text feature pyramid is a " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "2^l \\times 2^l" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " text feature map " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "Z^l" + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "text", + "content": " obtained by combining the masks " + }, + { + "bbox": [ + 304, + 653, + 547, + 715 + ], + "type": "inline_equation", + "content": "M^l" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "22470" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 213 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 213 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 213 + ], + "type": "image", + "image_path": "417a0a67cf6c17c70ae92b22e9d1d2236ce23ac4f6088687aeed884776bd05f9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 216, + 548, + 251 + ], + "lines": [ + { + "bbox": [ + 47, + 216, + 548, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 548, + 251 + ], + "type": "text", + "content": "Figure 2. An overview of the proposed method. We provide an intuitive interface where users can easily define a layout using a semantic brush associated with a free-form text description and adjustable precision level. The masks, regional descriptions, and precision levels " + }, + { + "bbox": [ + 47, + 216, + 548, + 251 + ], + "type": "inline_equation", + "content": "\\{(M_i,t_i,c_i)\\}_{i = 1}^n" + }, + { + "bbox": [ + 47, + 216, + 548, + 251 + ], + "type": "text", + "content": " are jointly encoded into a text feature pyramid, and then translated into an image by a multi-scale guided diffusion model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 268, + 286, + 361 + ], + "blocks": [ + { + "bbox": [ + 50, + 268, + 286, + 361 + ], + "lines": [ + { + "bbox": [ + 50, + 268, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 50, + 268, + 286, + 361 + ], + "type": "image", + "image_path": "47165497cc03f72ee41089a95a044cf179ae4d7298de6d6b53c3923a0592c54c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "lines": [ + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "text", + "content": "Figure 3. An example of the precision-encoded mask pyramid. The first level has two non-zero masks corresponding to " + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "inline_equation", + "content": "m_{1}, m_{2}" + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "inline_equation", + "content": "c_{1}, c_{2} \\geq 1" + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "text", + "content": "; the second level only has " + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "inline_equation", + "content": "c_{1} = 2, c_{2} < 2" + }, + { + "bbox": [ + 46, + 364, + 288, + 419 + ], + "type": "text", + "content": "; the third level does not have any non-zero masks as all the precision levels of all masks are lower than 3." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 434, + 286, + 504 + ], + "blocks": [ + { + "bbox": [ + 48, + 434, + 286, + 504 + ], + "lines": [ + { + "bbox": [ + 48, + 434, + 286, + 504 + ], + "spans": [ + { + "bbox": [ + 48, + 434, + 286, + 504 + ], + "type": "image", + "image_path": "705bc0d4eda6fa99dbec254035e35bd0e9c0189ac98c908d5567905e36d5843b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 505, + 286, + 516 + ], + "lines": [ + { + "bbox": [ + 47, + 505, + 286, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 286, + 516 + ], + "type": "text", + "content": "Figure 4. Illustration of the masks at different levels of a pyramid." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "text", + "content": "and the embeddings of the text " + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "text", + "content": ". At the 0-th level, the " + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "text", + "content": " masks contain no shape information, so we simply concatenate the embeddings of all words into a sequence. At the levels where " + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "inline_equation", + "content": "l > 0" + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "text", + "content": ", we spatially spread the embeddings of " + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 541, + 287, + 613 + ], + "type": "text", + "content": " over the corresponding masks to jointly represent the shape and semantic, as illustrated in Fig. 2." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": "Text feature maps. Here we describe in more detail how we construct the text feature map " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "Z^l" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": " at level " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "l > 0" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": ". For simplicity, we drop the superscript " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": " and denote the masks at an arbitrary level as " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": ". Each element " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_{i,x,y}" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": " is a binary value " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": " and we allow overlaps or blank spaces, i.e. " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "n \\geq \\sum_{i}^{n}M_{i,x,y} \\geq 0" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": ". Given the initial masks " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": ", we introduce normalized masks " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": ", which are augmented from " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": " by adding an extra mask " + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "inline_equation", + "content": "M_0" + }, + { + "bbox": [ + 46, + 616, + 289, + 715 + ], + "type": "text", + "content": " to indicate the blank space and" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 270, + 523, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 270, + 523, + 281 + ], + "spans": [ + { + "bbox": [ + 306, + 270, + 523, + 281 + ], + "type": "text", + "content": "normalized by the number of shapes at each location:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 378, + 284, + 546, + 314 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 284, + 546, + 314 + ], + "spans": [ + { + "bbox": [ + 378, + 284, + 546, + 314 + ], + "type": "interline_equation", + "content": "\\hat {M} _ {i, x, y} = M _ {i, x, y} / \\sum_ {i = 0} ^ {n} M _ {i, x, y}, \\tag {2}", + "image_path": "3b5e83590b142bf5534148be6eec3dc989efb9102cd98f5759d863076af0d9c4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 351, + 317, + 485, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 317, + 485, + 331 + ], + "spans": [ + { + "bbox": [ + 351, + 317, + 485, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 351, + 317, + 485, + 331 + ], + "type": "inline_equation", + "content": "M_{0,x,y} = \\mathbb{1}_{\\sum_{i = 1}^{n}M_{i,x,y} = 0}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": "In the normalized masks " + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": ", each element " + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "inline_equation", + "content": "\\hat{M}_{i,x,y}" + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": " is a continuous value " + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "inline_equation", + "content": "\\in [0,1]" + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": " and we have " + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "inline_equation", + "content": "\\sum_{i=0}^{n} \\hat{M}_{i,x,y} = 1" + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": ". We compute each element " + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "inline_equation", + "content": "Z_{x,y}" + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": " at location " + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "inline_equation", + "content": "x,y" + }, + { + "bbox": [ + 305, + 334, + 547, + 372 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 371, + 374, + 546, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 374, + 546, + 404 + ], + "spans": [ + { + "bbox": [ + 371, + 374, + 546, + 404 + ], + "type": "interline_equation", + "content": "\\boldsymbol {Z} _ {x, y} = \\sum_ {i = 0} ^ {n} \\boldsymbol {f} \\left(t _ {i}\\right) \\cdot \\hat {M} _ {i, x, y}, \\tag {3}", + "image_path": "ff15cc0e2edf6adb8df82d8d76496f37c6c46bc590f383c65a0c1621d1a63ec1.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "inline_equation", + "content": "\\pmb{f}(t_i)" + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "content": " is an embedding of the text " + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "inline_equation", + "content": "t_i" + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "inline_equation", + "content": "t_0" + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "content": " to be a null token " + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "inline_equation", + "content": "\\oslash" + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "content": " to represent unspecified areas, i.e. the blank space indicated by " + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "inline_equation", + "content": "M_0" + }, + { + "bbox": [ + 305, + 407, + 546, + 443 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 445, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 578 + ], + "type": "text", + "content": "The text feature map representation has several advantages. First, it is of the same dimension regardless of the number of masks, and therefore compatible with most deep ConvNet architectures. Second, each element of a text feature map is a convex combination of " + }, + { + "bbox": [ + 304, + 445, + 547, + 578 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 445, + 547, + 578 + ], + "type": "text", + "content": " text embeddings in the learned embedding space. With a powerful language model, we can achieve a good generalization capability for unseen combinations of concepts. In a text feature map, any overlapping area contains an interpolation of multiple embeddings. Accordingly, users can get creative results derived from hybrid concepts by drawing overlapping shapes." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 579, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 547, + 700 + ], + "type": "text", + "content": "Data acquisition. During inference, the segmentation masks and text descriptions are both provided by users. During training, we can generate them automatically using text-based object detection [28] and segmentation [16]. We set the regions where no objects are detected as blank space and assign a null token " + }, + { + "bbox": [ + 304, + 579, + 547, + 700 + ], + "type": "inline_equation", + "content": "\\varnothing" + }, + { + "bbox": [ + 304, + 579, + 547, + 700 + ], + "type": "text", + "content": " to these regions. We use CLIP [38] text model to encode the text descriptions. In addition, the 0-th level feature maps can be obtained directly from the image caption embeddings. More details regarding the training data generation step can be found in the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Relation to one-hot label maps. In S2I, a layout containing" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22471" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 60, + 286, + 167 + ], + "blocks": [ + { + "bbox": [ + 50, + 60, + 286, + 167 + ], + "lines": [ + { + "bbox": [ + 50, + 60, + 286, + 167 + ], + "spans": [ + { + "bbox": [ + 50, + 60, + 286, + 167 + ], + "type": "image", + "image_path": "942e03bcc103c4a721de3dec0137980dbc61d859d111f3b3798bcbee6f7ab265.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 170, + 282, + 180 + ], + "lines": [ + { + "bbox": [ + 47, + 170, + 282, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 170, + 282, + 180 + ], + "type": "text", + "content": "Figure 5. Architecture of the multi-scale guided diffusion model." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": "at most " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " classes can be encoded into a " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": "-channel one-hot label map. It can be seen as a special case of text feature maps when the masks are dense and non-overlapping, and the embedding model " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " is a one-hot encoding function. Specifically, let " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " be the segmentation masks, " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\pmb{t}" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " the class labels where " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "t_i = 1,2,\\dots,C" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "f_c(t_i) = \\mathbb{1}_{t_i = c}" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " are dense and non-overlapping, the normalized masks " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\hat{M}_i" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " will be the same as " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "M_i" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "i > 1" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\hat{M}_0 = 0" + }, + { + "bbox": [ + 46, + 201, + 287, + 297 + ], + "type": "text", + "content": ". Eqn. 3 then becomes" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 299, + 287, + 331 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 299, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 78, + 299, + 287, + 331 + ], + "type": "interline_equation", + "content": "Z _ {c, x, y} = \\sum_ {i = 1} ^ {n} \\mathbb {1} _ {t _ {i} = c} \\cdot M _ {i, x, y} = \\sum_ {i \\mid t _ {i} = c} M _ {i, x, y}. \\tag {4}", + "image_path": "8e5c3a466a56f1d1b449937e3acc39ef8cdbf4e5a58af2fcffdc450ef6e807e0.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": "Therefore, the " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": "-th channel of " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": " is a mask covering all pixels of class " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": ", i.e., a one-hot label map. Through this reformulation, we can see that the one-hot representation has limited capability as " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "\\pmb{f}(t_i)" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": " is restricted to be binary. The text feature map representation uses a learned language model as " + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 333, + 287, + 405 + ], + "type": "text", + "content": " to encode the more informative open-domain layouts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 413, + 208, + 425 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 413, + 208, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 413, + 208, + 425 + ], + "type": "text", + "content": "3.3. Multi-Scale Guided Diffusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 432, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 287, + 468 + ], + "type": "text", + "content": "We use a diffusion model to generate images from a text feature pyramid. We use " + }, + { + "bbox": [ + 46, + 432, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 432, + 287, + 468 + ], + "type": "text", + "content": "-prediction and the simplified training objective following [19]:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 74, + 470, + 287, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 470, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 74, + 470, + 287, + 484 + ], + "type": "interline_equation", + "content": "L = \\mathbb {E} _ {\\epsilon \\sim \\mathcal {N} (0, 1), t \\sim [ 1, T ]} \\left[ \\| \\boldsymbol {\\epsilon} - \\boldsymbol {\\epsilon} _ {\\boldsymbol {\\theta}} (\\boldsymbol {x} _ {t}, \\boldsymbol {z}, t) \\| _ {2} ^ {2} \\right], \\tag {5}", + "image_path": "15363ca67546967d5e821afec5b78d5345279f8e61787b6970d3b1ac61e3c0ce.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": " is the number of diffusion steps, " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_t" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": " is a noisy version of the ground-truth image " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": "-th diffusion step, " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": " is the conditional signal, which in our case is the text feature pyramid " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\{Z^l\\}_{l=0}^L" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\epsilon_\\theta" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": " represents the network parameterized by " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\theta}" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": ". We modify the UNet architecture [9] by adding the convolutional layers to combine each text feature map with the UNet feature maps of the corresponding resolution. The 0-th level text feature maps " + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "inline_equation", + "content": "Z^0" + }, + { + "bbox": [ + 46, + 486, + 288, + 616 + ], + "type": "text", + "content": " are passed through all blocks using cross-modal attention [44] and channel-wise feature modulation. Fig. 5 shows the overall architecture of the modified UNet." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "Classifier-free guidance [20] has shown to be an effective technique to improve the performance of conditional diffusion models and is widely applied to diffusion models conditioned on text and class tags [9, 35, 43, 44]. To benefit from this technique, we introduce multi-scale spatial guidance for our feature map conditioned diffusion model. As described in Sec. 3.2, in text feature maps from level 1 to " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": ", the unspecified regions are the embedding of a null" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "token " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\pmb{f}(\\varnothing)" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ". We further apply dropout with probability 0.1 to " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "Z^0" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": " by setting " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "Z^0 = f(\\varnothing)" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ". During inference, we estimate two diffusion scores, conditioning on the given text feature pyramid and an empty feature pyramid of repeating " + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "inline_equation", + "content": "\\pmb{f}(\\varnothing)" + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": ", and then perform sampling using their linear combination." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 142, + 387, + 156 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 142, + 387, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 142, + 387, + 156 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 162, + 547, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 162, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 162, + 547, + 232 + ], + "type": "text", + "content": "In this section, we present the experimental results on image synthesis from any-level semantic layouts. We evaluate the proposed method on user-drawn coarse layouts and automatically simulated layout data. We also present results on T2I and S2I, and compare our method with state-of-the-art methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 240, + 440, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 240, + 440, + 253 + ], + "spans": [ + { + "bbox": [ + 306, + 240, + 440, + 253 + ], + "type": "text", + "content": "4.1. Implementation Details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": "We train the multi-scale guided diffusion model to generate " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": " images from a layout of precision up to " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\log_2 64" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": ". To generate images at higher resolution, we experiment with two approaches: (1) by training another diffusion model to upsample " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "64 \\rightarrow 256" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": " following [9]; (2) by generating the latent map at " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": " resolution then decoding it into a " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": " image following [43]. Both approaches are effective, demonstrating that the proposed method can generalize well to both pixel-space and latent-space diffusion strategies. We use smaller pixel-space diffusion models for ablation studies and report the main results based on a larger latent-space diffusion model. We encode the text descriptions using the pretrained CLIP ViT-L14 language model [38]. To avoid repeated forward passes, we feed the union of all regional descriptions " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\cup_{i} t_{i}" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": " as a sentence into the language model. Then, we average the hidden states corresponding to each word in " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": " to use as its embedding " + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "inline_equation", + "content": "\\mathbf{f}(t_{i})" + }, + { + "bbox": [ + 304, + 258, + 547, + 462 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 463, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 463, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 463, + 547, + 581 + ], + "type": "text", + "content": "Training details. We use the aesthetic subset of Laion2B-en dataset [46] for training. We generate full text feature pyramids for 5M randomly selected samples and construct only the 0-th level feature maps for the remaining samples. For pixel space diffusion, we train a base model of 300M parameters and a super-resolution model of 300M parameters; for latent-space diffusion, we train a base model of 900M parameters and use the pretrained deocder from [43]. We use batch size 2048 for " + }, + { + "bbox": [ + 304, + 463, + 547, + 581 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 463, + 547, + 581 + ], + "type": "text", + "content": " models and batch size 960 for the super-resolution model." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "Evaluation benchmark. We use the COCO [32] validation set for evaluation in the T2I setting and the COCO-stuff [7] validation set for S2I. For evaluation in open-domain layout-to-image generation, we construct a new test set OpenLayout containing 260 user-drawn layouts of coarse shapes. The layouts are annotated by 10 users based on text prompts randomly sampled from PartiPrompts [64]. To analyze the effect of precision level control, we also evaluate using the pseudo layouts consisting of accurate shapes, which are extracted from the 5,000 images with caption annotations of COCO validation set (OpenLayout-COCO). Fig. 6 shows" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "22472" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 110, + 285, + 177 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 288, + 102 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 288, + 102 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 288, + 102 + ], + "type": "text", + "content": "Table 2. Quantitative results on the OpenLayout and OpenLayout-COCO datasets with different precision levels. SS Score: spatial similarity scores." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 110, + 285, + 177 + ], + "lines": [ + { + "bbox": [ + 50, + 110, + 285, + 177 + ], + "spans": [ + { + "bbox": [ + 50, + 110, + 285, + 177 + ], + "type": "table", + "html": "
OpenLayoutOpenLayout-COCO
Prec.SS Score ↑CLIP Score ↑SS Score ↑CLIP Score ↑FID ↓
0.436.274.572.26025.3
3.533.268.685.25626.0
4.543.266.716.25627.0
5.558.267.729.25628.4
6.558.261.736.25530.6
", + "image_path": "d01e0efa31297ab3aad9c3aae447b57aa53e991070e0b65f09786b1e5c0d799f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 199, + 288, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 199, + 288, + 221 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 288, + 221 + ], + "type": "text", + "content": "some layouts samples from OpenLayout and Openlayout-COCO." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 223, + 284, + 346 + ], + "blocks": [ + { + "bbox": [ + 48, + 223, + 284, + 346 + ], + "lines": [ + { + "bbox": [ + 48, + 223, + 284, + 346 + ], + "spans": [ + { + "bbox": [ + 48, + 223, + 284, + 346 + ], + "type": "image", + "image_path": "1df4f4ede396b7ce7c54a5f95444a417bad071d3672368418075b1a339bc89da.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 348, + 288, + 371 + ], + "lines": [ + { + "bbox": [ + 47, + 348, + 288, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 288, + 371 + ], + "type": "text", + "content": "Figure 6. Top: Pseudo layouts from OpenLayout-COCO dataset. Bottom: real-world user-drawn layouts from OpenLayout dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 394, + 273, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 273, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 273, + 407 + ], + "type": "text", + "content": "4.2. Open-Domain Layout-to-Image Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": "Here we discuss the results on the OpenLayout and OpenLayout-COCO datasets. For each sample, we run the model a varying precision level " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " from 0 to 6 to verify the effectiveness of precision control. Fig. 7 shows the results with different precision levels. For simplicity, we use the same precision level for all regions in an input layout, i.e. " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\forall i, c_i = c" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": ". We can see that as the precision level increases, the generated images follows the layout more closely. When " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "c = 0" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": ", the image compositions are not related to the layouts. For " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "c = 3, 4" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": " the generated images roughly resemble the shape and location specified in the layout. For " + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "inline_equation", + "content": "c = 5, 6" + }, + { + "bbox": [ + 46, + 413, + 287, + 593 + ], + "type": "text", + "content": ", the generated object contours matches the layout more closely. At the lowest precision level, our method can handle very rough layouts, e.g., bounding box layouts, as shown in Fig. 8, despite not being trained on bounding box data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 689 + ], + "type": "text", + "content": "For quantitative evaluation, we compute the CLIP score using the original captions to measure global semantic alignment. To measure spatial alignment, we define a spatial similarity score (SS score), which is the cosine similarity between the text feature maps of the input layout and the layout reconstructed from the generated image. For OpenLayout-COCO, as the ground-truth images are available, we also compute the FID to measure the visual quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": "Table 2 reports the quantitative evaluation results on images generated with different precision levels. The second" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 326, + 83, + 524, + 183 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 534, + 80 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 534, + 80 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 534, + 80 + ], + "type": "text", + "content": "Table 3. Quantitative comparison with T2I methods on COCO." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 83, + 524, + 183 + ], + "lines": [ + { + "bbox": [ + 326, + 83, + 524, + 183 + ], + "spans": [ + { + "bbox": [ + 326, + 83, + 524, + 183 + ], + "type": "table", + "html": "
MethodFID ↓zero-shot FID↓
SSA-GAN [31]19.37-
VQ-Diffusion [15]13.86-
DF-GAN [53]19.32-
GLIDE [35]-12.89
SD [1,43]-9.89
DALLE2 [39]-10.87
Ours8.559.47
", + "image_path": "64c915fdf6877f90731a423eea7f319160d8c6dc467ddd89385ed75098b97768.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 205, + 547, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 337 + ], + "type": "text", + "content": "and fourth columns show that using a higher precision level generally leads to a higher spatial similarity, which further demonstrates the effectiveness of precision control. On OpenLayout-COCO, the spatial similarity consistently increases as the precision level becomes higher. Whereas, on OpenLayout, it stays the same at higher levels. This is due to the difference in the inherent layout precision exhibited by the two datasets; compared to OpenLayout-COCO, the layouts in OpenLayout are coarser. For a coarse layout, the generated images already match it well at low precision levels and the room for improvement is limited." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 337, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 547, + 456 + ], + "type": "text", + "content": "From the last column of Table 2, we can see that the results with a lower precision level have a smaller FID, which indicates a similar distribution with respect to the ground-truth images. This is likely because a lower precision level enforces smaller constraints on the generation process, and therefore the generated images can better capture the real image distribution. Similarly, a lower precision level also yields a slightly better CLIP score due to the smaller spatial constraints, as shown in the third and fifth columns of Table 2." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 466, + 450, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 450, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 450, + 479 + ], + "type": "text", + "content": "4.3. Text-to-Image Generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 485, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 628 + ], + "type": "text", + "content": "As mentioned in Sec. 3, our method can be applied for text-to-image generation by using texts as 0-th layouts. The first four columns of Fig. 9 show the images generated from text prompts by our method and state-of-the-art methods. We can see that the proposed method can generate visually peasant images with reasonable layouts from only text input. Table 3 reports the FID evaluated on the COCO validation set. The classifier-free guidance scale is set to 3. Following [35], we sample 30K images using randomly selected text prompts and compute FID against the entire validation set. It can be seen that the proposed method compares favorably against state-of-the-art text-to-image generation models." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "By combining with a named entity recognition (NER) model, we can apply the proposed method to layout controllable text-to-image generation. More specifically, given an input sentence, we parse the noun phrases using NER to generate regional text descriptions, and users can arbitrarily draw the shapes for those noun phrases. The last two columns of Fig. 9 show the text-to-image generation results" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "text", + "content": "22473" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 61, + 132, + 144 + ], + "blocks": [ + { + "bbox": [ + 50, + 61, + 132, + 144 + ], + "lines": [ + { + "bbox": [ + 50, + 61, + 132, + 144 + ], + "spans": [ + { + "bbox": [ + 50, + 61, + 132, + 144 + ], + "type": "image", + "image_path": "89b034700eba78333db1368202eaca17a1584ec0291cda333e82fe1faeb263e2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 133, + 62, + 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Results with bounding box layout. Precision level " + }, + { + "bbox": [ + 47, + 510, + 282, + 522 + ], + "type": "inline_equation", + "content": "= 3" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 129, + 429, + 206, + 507 + ], + "blocks": [ + { + "bbox": [ + 129, + 429, + 206, + 507 + ], + "lines": [ + { + "bbox": [ + 129, + 429, + 206, + 507 + ], + "spans": [ + { + "bbox": [ + 129, + 429, + 206, + 507 + ], + "type": "image", + "image_path": "f2246c94000e4503559d92bb0186f25e41cc4ad3f9323ab1f39af6d6000dcbb4.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "type": "image", + "bbox": [ + 207, + 429, + 286, + 507 + ], + "blocks": [ + { + "bbox": [ + 207, + 429, + 286, + 507 + ], + "lines": [ + { + "bbox": [ + 207, + 429, + 286, + 507 + ], + "spans": [ + { + "bbox": [ + 207, + 429, + 286, + 507 + ], + "type": "image", + "image_path": "5051d27dde148a1e35307b1d5ce2ebfe72a14dcbc1e0f84f84e18a86c017261a.jpg" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_body" + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "content": "with layout control. We can see that the generated images match the text well and follow the provided layouts." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 574, + 236, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 236, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 236, + 588 + ], + "type": "text", + "content": "4.4. Segmentation-to-Image Generation" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Our model can also generate images from a dense segmentation map of closed-set labels, i.e. following the original S2I setting. For this application, we treat the class labels as text descriptions and use the highest precision level " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "c = 5" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " for all masks. Fig. 10 shows example images generated by our method and SPADE [36]. The images generated by our model are of significantly better visual quality. Table. 4 reports the quantitative comparison results on the COCO-stuff validation set with the state-of-the-art S2I methods [33,36,51]. Since the highest resolution of the input lay" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "type": "text", + "content": "out to our model is 64, we evaluate the S2I results at " + }, + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 361, + 547, + 445 + ], + "type": "text", + "content": " resolution. From the third and fifth columns of Table. 4 we can see that despite not being designed or trained for this task, the proposed method can achieve lower FID and comparable mIOU. After being fine-tuned on the COCO-stuff training set, our model outperforms previous approaches in terms of both FID and mIOU." + } + ] + } + ], + "index": 33 + }, + { + "type": "table", + "bbox": [ + 308, + 473, + 544, + 525 + ], + "blocks": [ + { + "bbox": [ + 306, + 454, + 547, + 465 + ], + "lines": [ + { + "bbox": [ + 306, + 454, + 547, + 465 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 547, + 465 + ], + "type": "text", + "content": "Table 4. Quantitative comparison with S2I methods on COCO-stuff." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 473, + 544, + 525 + ], + "lines": [ + { + "bbox": [ + 308, + 473, + 544, + 525 + ], + "spans": [ + { + "bbox": [ + 308, + 473, + 544, + 525 + ], + "type": "table", + "html": "
MethodFID ↓zero-shot FID ↓mIOU↑zero-shot mIOU↑
SPADE [36]50.91-17.49-
SAFM [33]62.28-12.28-
CLADE [51]55.30-17.21-
Ours17.2020.1723.0117.15
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Prec. LevelModelFID ↓CLIP Score ↑SS Score ↑
0Text-to-Image Baseline32.83.2473.5613
0Any-Level Model32.09.2496.5640
4Single-Level Baseline36.03.2381.5729
4Any-Level Model33.70.2475.6978
", + "image_path": "ebcbae32e3e6eb04df22a2309682377df33c81ab379e090a6ffe9ce9c46cd818.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 643, + 119, + 656 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 119, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 119, + 656 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "This paper presents a new conditional image synthesis framework to generate images from any-level open-domain semantic layouts. The input level ranges from pure text to a 2D semantic canvas with precise shapes. Several novel" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 572, + 547, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 693 + ], + "type": "text", + "content": "techniques are introduced, including a pipeline for collecting training data; the representations to jointly encode precision level, semantics, and geometry information; and a multiscale guided diffusion model to synthesize images. A test dataset containing user-drawn layouts is collected to evaluate the proposed method. Experimental results demonstrate the advantage of the unified framework. The proposed method can generate high-quality images following the layout at specified precision levels, and compares favorably against the state-of-the-art methods on public benchmarks." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "text", + "content": "22475" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "text", + "content": "[1] Stable diffusion. https://stability.ai/blog/stable-diffusion-public-release. 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In IEEE Conference on Computer Vision and Pattern Recognition, 2020. 2" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "22478" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/SceneTrilogy_ On Human Scene-Sketch and Its Complementarity With Photo and Text/61c06fa2-0cf3-4cfc-a6de-25fbe7140dea_content_list.json b/2023/SceneTrilogy_ On Human Scene-Sketch and Its Complementarity With Photo and Text/61c06fa2-0cf3-4cfc-a6de-25fbe7140dea_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..caa910a29ffb18d1bf8eed79b75cf871884a5750 --- /dev/null +++ b/2023/SceneTrilogy_ On Human Scene-Sketch and Its Complementarity With Photo and Text/61c06fa2-0cf3-4cfc-a6de-25fbe7140dea_content_list.json @@ -0,0 +1,1774 @@ +[ + { + "type": "text", + "text": "SceneTrilogy: On Human Scene-Sketch and its Complementarity with Photo and Text", + "text_level": 1, + "bbox": [ + 156, + 130, + 813, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pinaki Nath Chowdhury1,2 Ayan Kumar Bhunia1 Aneeshan Sain1,2 Subhadeep Koley1,2 Tao Xiang1,2 Yi-Zhe Song1,2", + "bbox": [ + 120, + 186, + 846, + 224 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ SketchX, CVSSP, University of Surrey, United Kingdom.", + "bbox": [ + 254, + 224, + 712, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ iFlyTek-Surrey Joint Research Centre on Artificial Intelligence.", + "bbox": [ + 228, + 241, + 738, + 260 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{p.chowdhury, a.bhunia, a.sain, s.koley, t.xiang, y song}@surrey.ac.uk", + "bbox": [ + 173, + 262, + 790, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 311, + 313, + 328 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we extend scene understanding to include that of human sketch. The result is a complete trilogy of scene representation from three diverse and complementary modalities - sketch, photo, and text. Instead of learning a rigid three-way embedding and be done with it, we focus on learning a flexible joint embedding that fully supports the \"optionality\" that this complementarity brings. Our embedding supports optionality on two axes: (i) optionality across modalities - use any combination of modalities as query for downstream tasks like retrieval, (ii) optionality across tasks - simultaneously utilising the embedding for either discriminative (e.g., retrieval) or generative tasks (e.g., captioning). This provides flexibility to end-users by exploiting the best of each modality, therefore serving the very purpose behind our proposal of a trilogy in the first place. First, a combination of information-bottleneck and conditional invertible neural networks disentangle the modality-specific component from modality-agnostic in sketch, photo, and text. Second, the modality-agnostic instances from sketch, photo, and text are synergised using a modified cross-attention. Once learned, we show our embedding can accommodate a multi-facet of scene-related tasks, including those enabled for the first time by the inclusion of sketch, all without any task-specific modifications. Project Page: https://pinakinathc.github.io/scenetrilogy", + "bbox": [ + 76, + 345, + 473, + 724 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 739, + 209, + 753 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scene understanding sits at the very core of computer vision. As object-level research matures [24, 32], an encouraging shift can be observed in recent years on scene-level tasks, e.g., scene recognition [113], scene captioning [55], scene synthesis [34], and scene retrieval [13, 57].", + "bbox": [ + 75, + 762, + 468, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Scene research has generally progressed from that of single modality [113, 114] to the very recent focus on multimodality [3, 13, 19]. The latter setting not only triggered a series of practical applications [34, 57, 101, 115] but im", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c366e65a4075c2d75ced09c2e2c92910a3077fce9b502378c9447ba599c2f041.jpg", + "image_caption": [], + "image_footnote": [ + "$f_{\\mathrm{s}}^{sp}$ sketch specific $f_{\\mathrm{t}}^{sp}$ text specific $f_{\\mathrm{p}}^{sp}$ photo specific $f^{ag}$ modality agnostic", + "Figure 1. Some scenes are easy to describe via sketch; for others, text is better. We provide the option to sketch, write, or both (sketch + text). For “optionality” across tasks, we disentangle sketch, text, and photo into a discriminative (e.g., retrieval) part $f^{ag}$ shared across modalities, and a generative (e.g., captioning) part specific to one modality ( $f_{\\mathbf{s}}^{sp}$ , $f_{\\mathbf{t}}^{sp}$ , $f_{\\mathbf{P}}^{sp}$ ). This supports a multifacet of scene-related tasks without task-specific modifications." + ], + "bbox": [ + 506, + 311, + 883, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "portantly helped to cast insights into scene understanding on a conceptual level (i.e., what is really being perceived by humans). To date, research on multi-modal scene understanding has mainly focused on two modalities – text and photo [59, 61, 62], via applications such as text-based scene retrieval (TBIR) [35], and scene captioning [23, 61, 62].", + "bbox": [ + 498, + 594, + 890, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper follows the said trend of multi-modal scene understanding and extend it to also include human scene-sketch. Sketch is identified because of its unique characteristics of being both expressive and subjective, evident in an abundance of object-level sketch research [11], and very recently on scene-level [19]. To verify there is indeed useful complementarity that sketch can bring to multi-modal scene understanding, we first conducted two pilot studies (i) on expressivity, we compare text and sketch in terms of scene image retrieval, and (ii) on subjectivity, we test a novel task of subjective captioning where sketch or parts-of-speech [26] are used as guidance for image captioning. On (i), results show there is significant disagreement in terms of retrieval accuracy when one is used as query over the other,", + "bbox": [ + 496, + 688, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10972", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "indicating there is complementary information between the two modalities. On (ii), sketch is shown to offer more subjectivity as a guiding signal than text, when quantified using common metrics such as BELU-4 [67] and CIDEr [95].", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To fully explore the complementarity of all three modalities, we desire a flexible joint embedding that best sustains \"optionality\" across modalities, and also across tasks. The former enables end-users to use any combination of modalities (e.g., only sketch, only text, or both sketch+text) as a query for downstream tasks; and the latter provides option of utilising the learned embedding for both discriminative (e.g., retrieval) and generative problems (e.g., captioning).", + "bbox": [ + 75, + 152, + 467, + 275 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This desired level of \"optionality\" is however not achievable via naive three-way joint embeddings common in the literature [3, 13, 19]. Instead, we advocate a three-way disentanglement (Fig. 1(b)), where each of the three modalities is disentangled into their modality-specific component ( $f_{\\mathbf{s}}^{sp}$ , $f_{\\mathbf{p}}^{sp}$ , $f_{\\mathbf{t}}^{sp}$ , for sketch, photo and text), and a shared modality-agnostic component ( $f^{ag}$ ). The idea is that modality-specific will hold information specific to each modality (e.g., drawing style for sketch, texture for photo, and grammatical knowledge for text). It follows that filtering away modality-specific parts from each of the three modalities gives a shared modality-agnostic part that carries shared abstract semantic across all three modalities, (as shown in Fig. 1(b)). How optionality is supported in such a disentangled space then becomes trivial (Fig. 1(c),(d)). To achieve optionality across tasks, we simply use modality-agnostic information as the joint embedding to perform discriminative tasks (e.g., cross-modal retrieval), and for cross-modal generative tasks (e.g., captioning), we just combine modality-agnostic information (from source) with modality-specific (from target) to generate the target modality. Optionality across modality is a little harder, where we make use of a cross-attention [50] mechanism to capture the synergy across the modality-agnostic components.", + "bbox": [ + 75, + 276, + 467, + 638 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Benefiting from our optionality-enabled embedding, we can perform a multi-facet of tasks without any task-specific modifications: (i) Fig. 1 (c) show cross-modal discriminative tasks such as sketch-based image retrieval (SBIR) using $(f_{\\mathbf{s}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})$ , text-based image retrieval (TBIR) using $(f_{\\mathbf{t}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})$ , or sketch+text based image retrieval (STBIR) using $(f_{\\mathbf{s}}^{ag} + f_{\\mathbf{t}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})$ . (ii) Fig. 1 (d) show cross-modal generative tasks such as image captioning (photo branch) using $f_{\\mathbf{p}}^{ag} + f_{\\mathbf{t}}^{sp} \\rightarrow f_{\\mathbf{t}}$ to generate textual descriptions $f_{\\mathbf{t}}$ . Similarly, for sketch captioning (sketch branch) we use $f_{\\mathbf{s}}^{ag} + f_{\\mathbf{t}}^{sp} \\rightarrow f_{\\mathbf{t}}$ . (iii) Last but not least, to demonstrate what the expressiveness of human sketch can bring to scene understanding, we introduce a novel task of subjective captioning where we guide image captioning using sketch as a signal (subjective branch) as $f_{\\mathbf{p}}^{ag} + f_{\\mathbf{s}}^{ag} \\rightarrow f_{\\mathbf{t}}$ .", + "bbox": [ + 75, + 641, + 467, + 868 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are: (i) We extend multi-modal scene understanding to include human scene", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sketches, thereby completing a trilogy of scene representation from three diverse and complementary modalities. (ii) We provide optionality to end-users by learning a flexible joint embedding that supports: optionality across modalities and optionality across tasks. (iii) Using computationally efficient techniques like information bottleneck, conditionally invertible neural networks, and modified crossattention mechanism, we model this flexible joint embedding. (iv) Once learned, our embedding accommodates a multi-facet of scene-related tasks like retrieval, captioning.", + "bbox": [ + 496, + 90, + 890, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 261, + 648, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Sketch for Visual Understanding: Hand-drawn sketches enriched with human visual perception cues have facilitated several downstream visual understanding tasks. Apart from the widely explored SBIR [10, 22], sketch has shown potential on object localisation [18], segmentation [72], image/video synthesis [48], representation learning [79], 3D shape retrieval/modelling [20], medical image analysis [47, 97], etc. [102]. Sketches are also useful in the creative industry like artistic image editing [105] and animation [100]. Unlike photos that are passively captured by a camera, sketches are drawn by humans that actively stimulate intelligence with pictorial-style drawing games [8]. While text has been widely used for human expression, in this paper, we show freehand sketches can provide complimentary or symbiotic information for visual understanding.", + "bbox": [ + 496, + 285, + 890, + 512 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Sketch-Based Image Retrieval (SBIR): SBIR retrieves a paired photo given a query sketch. Sketches offer visual description that commences the avenues of category-level [27, 78, 106] or fine-grained instance-level (FG-SBIR) [6, 9, 12] retrieval. SBIR typically employs deep triplet-ranking based siamese networks to learn a joint embedding space [107]. Contemporary research emerged towards zero-shot SBIR [27, 80], cross-domain translation [66], on-the-fly retrieval [12], semi-supervised [6], self-supervised [7], meta-learning [11] etc. As research on object-level SBIR matured, focus shifted towards the more practical scene-level SBIR [76] with GCN [57], and optimal transport [17]. The onset of scene sketch datasets [19, 34, 115] revealed further insights into implicit human-sketching strategies [19].", + "bbox": [ + 496, + 517, + 890, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-Based Image Retrieval (TBIR): Learning image-text joint embedding space with ranking loss [31, 43, 70] received considerable attention. Further improvements used mining hardest negative pairs for triplet loss [33], cross-modal adaptive message passing [98], probabilistic one-tomany representations [21] etc. Despite text lacking visual cues, million-scale paired image-text datasets have made TBIR competitive due to power scaling laws [63]. This inspired large-scale methods like Oscar [52], and CLIP [73]. In this paper, we augment TBIR with sketches to provide the creativity and freedom of expression intrinsic to sketches.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10973", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Multi-Modality in Computer Vision: Multi-modal learning (MML) aims at developing models that can extract, interpret, and reason on information from various modalities characterised by different statistical properties such as text, sketch, or text+sketch. Contemporary research studied MML in vision via image and text [40], image to scene graph [36], etc. [103]. MML faces challenges like cross-modal alignment [42], or efficiency over data [92] and compute [44]. It is useful when data in one modality is inaccessible [3] for privacy or logistic reasons (e.g., hospital), but abundantly available in other modalities (photos in MS-COCO [55]). Often, some modalities are preferred over others for human-machine communication, like some concepts are easier to express in texts [60], while others prefer sketches [54] or both [76] (Fig. 1). In this paper, we learn cross-modal representation [104] that works using either one modality (text/sketch) or both.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Disentangled Representation for Multi-modality: Disentangling modality-agnostic from modality-specific residual factors is important for MML [41, 93]. Modality-agnostic information is useful for cross-modal transfer like semantics-based retrieval and pattern recognition [41] but holds no meaning for tasks specific to one modality like image-style or speaker information [91]. Disentanglement was explored where factors of variation are either known (e.g., facial poses [90]) and individually supervised [75], partially known [82], or unknown (e.g., drawing style [82]) and learned unsupervised using isotropic Gaussian prior [77] or information-theoric regularisation [16]. Our method aligns with the unknown setup where factors particular to sketch, text, and image are discovered unsupervised.", + "bbox": [ + 75, + 351, + 472, + 564 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image Captioning: This has emerged from predicting syntactically correct descriptions [89, 112] to tackling data scarcity [1, 49], and addressing user requirements [68, 69]. Predicted captions evolved from being factual in a neutral tone to (i) controllable using textual verbs [15], part-of-speech tag [26], or mouse trace [64, 71], and (ii) personalised captioning [84, 111] that learns user's active vocabulary, and writing style. Our method can (i) generate factual captions from images/sketches and (ii) extend controllable captioning paradigm by injecting saliency via sketch.", + "bbox": [ + 75, + 566, + 472, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Pilot Study", + "text_level": 1, + "bbox": [ + 76, + 733, + 194, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Sketch vs. Text for Retrieval", + "text_level": 1, + "bbox": [ + 76, + 753, + 333, + 768 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7963576892998dd92d7f442b811038697195c10556c904473433a8339ef3d7f2.jpg", + "image_caption": [ + "Figure 2. We compare SBIR [107] vs. TBIR [73] on FS-COCO [19] where retrieval rank is plotted in log-scale (see Supplemental for more details). While sketch is a better query for some instances (lower retrieval rank), for others text is better." + ], + "image_footnote": [], + "bbox": [ + 81, + 777, + 460, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text can convey colour information, or object categories, but is cumbersome to describe fine-grained details, multiple objects, or complex shapes $[86]^{1}$ . While sketch can depict complex shapes, multiple objects, and spatial alignment [19], not all objects are easy to draw ('donkey' vs. 'horse'). Fig. 2 shows this trade-off between sketch vs. text for image retrieval. We find an optimal fusion between sketch and text to derive best of both modalities along with the ability to optionally use only sketch, only text, or both.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/661e60d0c7bb9385977f4940dc00987ba6300f885f615dd070e7abad1d016207.jpg", + "table_caption": [ + "Table 1. Comparing alternative guiding signal like POS (part-of-speech) [26], Mouse Trace [64], and Freehand Sketches [19]." + ], + "table_footnote": [], + "table_body": "
SignalB-1B-4MRCS
POS [26]w/o73.231.124.552.8100.117.9
w/73.931.625.553.2104.518.8
Δ0.70.51.00.44.40.9
Trace [64]w/o32.28.1-31.729.325.7
w/52.224.6-48.3106.536.5
Δ2016.5-16.677.210.8
Sketchw/o74.731.824.753.8105.518.8
w/81.342.730.161.6121.623.5
Δ6.610.95.47.816.14.7
", + "bbox": [ + 501, + 268, + 890, + 400 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Subjectivity for Captioning", + "text_level": 1, + "bbox": [ + 498, + 411, + 746, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unlike traditional image captioning [62, 96] that generates factual captions in neutral tone, subjective captioning adapts the predicted captions using a guiding signal that specifies priorities on what should be described [89]. The signal is injected via feature concatenation [26], or cross-attention mechanism [64]. Applications of subjective captioning include medical report generation using disease tags to generate real style reports [56], art descriptions [5], and assistive technologies for the visually impaired [37,99]. In this paper, we advocate for sketch as a guiding signal to depict salient objects and express artistic interpretations [38]. We compare the performance (see supplementary for details) using guiding signals like POS (parts-of-speech) [26], mouse trace [64], or freehand sketches [19]. Following [64], we inject the guiding signal into the image captioning pipeline via cross-attention mechanism. As evident from Table 1, while sketch is competitive with mouse traces, it is a better signal than POS. However, unlike mouse trace, sketch can depict artistic interpretation [5] that makes it a more flexible and robust guiding signal than POS or mouse trace.", + "bbox": [ + 496, + 430, + 890, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Methodology", + "text_level": 1, + "bbox": [ + 498, + 746, + 718, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 767, + 640, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Baseline for Fine-Grained Retrieval: Given a query-photo pair $(\\mathbf{q},\\mathbf{p})$ , existing methods encode [7, 51, 54, 57, 107] the query $\\mathbf{q} = \\{\\mathbf{s},\\mathbf{t}\\}$ comprising sketch (s) / text (t) and photo (p) as $f_{\\mathbf{q}} = \\mathcal{F}_{\\mathbf{q}}(\\mathbf{q})\\in \\mathbb{R}^{D}$ , and $f_{\\mathbf{p}} = \\mathcal{F}_{\\mathbf{p}}(\\mathbf{p})\\in \\mathbb{R}^{D}$ respectively. The network is trained via triplet loss with", + "bbox": [ + 498, + 789, + 890, + 867 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1Example: Cross strap stud and buckle detail blonde leather upper leather insole chunky wooden sole 9 cm heel.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10974", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9bc4f300a9039d61cb4e400bb696f4c7d81bf4f804ed981e6f2b5218b1ca2e0d.jpg", + "image_caption": [ + "Figure 3. (Left): We disentangle modality-agnostic and modality-specific components from sketch, text, and photo. The modality-agnostic components are aligned using contrastive loss for cross-modal transfer. (Right): Modality-agnostic sketch $(f_{\\mathbf{s}}^{ag})$ is used across modality to generate modality-specific text $(f_{\\mathbf{t}}^{sp})$ using text-specific $\\tau_{\\mathbf{t}}$ . Combining $f_{\\mathbf{s}}^{ag}$ and $f_{\\mathbf{t}}^{ag}$ , we generate text from sketch." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 467, + 198 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "margin parameter $\\mu >0$ such that the cosine distance $\\delta (\\cdot)$ of query anchor $\\mathbf{q}$ from a negative photo $(\\mathbf{p}^{-})$ should increase while that from the positive photo $(\\mathbf{p}^{+})$ should decrease as, $\\mathcal{L}_{trip} = \\max \\{0,\\mu +\\delta (f_{\\mathbf{q}},f_{\\mathbf{p}^{+}}) - \\delta (f_{\\mathbf{q}},f_{\\mathbf{p}^{-}})\\}$", + "bbox": [ + 75, + 292, + 467, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Baseline for Image Captioning: Image captioning consists of an image encoder [59, 101], $f_{\\mathbf{p}} = \\mathcal{F}_{\\mathbf{p}}(\\mathbf{p})$ followed by an autoregressive textual decoder $(\\mathcal{F}_C)$ . Given the textual description comprises a sequence of words $\\mathbf{t} = \\{w_1,\\dots ,w_K\\}$ , we maximise the likelihood of a predicted word $(\\hat{w}_k)$ at each step $(k)$ , conditioned on $f_{\\mathbf{p}}$ as, $\\mathcal{L}_C = -\\sum_{k = 1}^{K}\\log [\\mathcal{F}_C(\\hat{w}_k = w_k|f_{\\mathbf{p}},w_1,\\dots ,w_{k - 1})]$", + "bbox": [ + 76, + 356, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Overview", + "text_level": 1, + "bbox": [ + 76, + 469, + 187, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to disentangle the feature representations from sketch, text, and photo modalities into a modality-agnostic and modality-specific component. While the modality-agnostic component holds semantic information to support cross-modal transfer, the modality-specific one holds information necessary during self-reconstruction; however, it lacks meaning in other modalities (e.g., grammatical knowledge in text). Achieving feature disentanglement across scene sketches, texts, and photos enables a multitude of downstream tasks like (i) SBIR - modality-agnostic sketch and photo features, (ii) TBIR - modality-agnostic text and photo, (iii) Sketch + Text-Based Image Retrieval - modality-agnostic sketch, text, and photo, (iv) Image Captioning - using the modality-agnostic photo to compute modality-specific text features, (v) Sketch Captioning - modality-agnostic sketch to compute modality-specific text, and (vi) Subjective Captioning - using modality-agnostic photo and sketch, to compute modality-specific text.", + "bbox": [ + 75, + 484, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Disentangling Modality Agnostic and Specific", + "text_level": 1, + "bbox": [ + 75, + 763, + 460, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While our disentangling method can be generalised to any number of modalities, for simplicity, we first show for $M = 2$ modalities and later extend to $M \\geq 3$ . Consider a simple bimodal setup of sketch $(\\mathbf{s} \\in \\mathbb{R}^{H \\times W \\times 3})$ and text $(\\mathbf{t} \\in \\mathbb{R}^{N \\times E})$ . Our goal is to split the feature representation $f_{\\mathbf{s}} = \\mathcal{F}_{\\mathbf{s}}(\\mathbf{s}) \\in \\mathbb{R}^{512}$ and $f_{\\mathbf{t}} = \\mathcal{F}_{\\mathbf{t}}(\\mathbf{t}) \\in \\mathbb{R}^{512}$ into a modality-agnostic and a modality-specific component as $f_{\\mathbf{s}} = [f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp}]$ , and $f_{\\mathbf{t}} = [f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp}]$ respectively, where", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/60f76ec42dce341d9ff0f9ab54a1da0f7d2e62e8a08fb0c427d8ac4b41b850ea.jpg", + "image_caption": [ + "Figure 4. Unlike typical neural networks that are unidirectional, data in conditional invertible neural networks $(\\tau_{\\mathbf{k}})$ can flow either (i) from modality-specific $f_{\\mathbf{k}}^{sp}$ to a uniform distribution $\\eta$ by conditioning on modality-agnostic $f_{\\mathbf{k}}^{ag}$ during training, or (ii) from a sampled $\\eta$ in uniform distribution to the modality-specific $f_{\\mathbf{k}}^{sp}$ by conditioning on modality-agnostic $f_{\\mathbf{k}}^{ag}$ during inference. The conditioning vector $f_{\\mathbf{k}}^{ag}$ is injected into the conditional affinity coupling layers [28] of $\\tau_{\\mathbf{k}}$ using any arbitrary network $\\mathcal{H}$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 890, + 179 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$f^{ag} \\in \\mathbb{R}^{480}$ and $f^{sp} \\in \\mathbb{R}^{32}$ . Existing methods [82, 88] disentangle feature representations via (i) self reconstruction as $\\hat{\\mathbf{s}} = \\mathcal{D}_{\\mathbf{s}}([f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp}])$ and $\\hat{\\mathbf{t}} = \\mathcal{D}_{\\mathbf{t}}([f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp}])$ coupled with (ii) cross-modal translation $\\hat{\\mathbf{s}} = \\mathcal{D}_{\\mathbf{s}}([f_{\\mathbf{t}}^{ag}, f_{\\mathbf{s}}^{sp}])$ and $\\hat{\\mathbf{t}} = \\mathcal{D}_{\\mathbf{t}}([f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{sp}])$ . However, using cross-modal translation with latent feature exchange across modalities is a cumbersome process that explodes with $\\mathbb{P}_2^M$ permutations for $M$ modalities, e.g., $M = 3$ has $\\mathbb{P}_2^3 = 6$ cross-modal translations. Adding multiple cross-modal translation losses makes optimisation difficult and computationally expensive. We break this compute barrier with linear $(\\mathcal{O}(M))$ complexity using an information bottleneck reinterpretation of modality-agnostic and modality-specific disentanglement. In particular, we maximise the mutual information $\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})$ amongst modality-agnostic components, while minimising the same between modality-agnostic and modality-specific components $\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp})$ and $\\mathcal{I}(f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp})$ , where $\\mathcal{I}(\\cdot, \\cdot)$ denotes mutual information between two entities. Hence, unlike the previous $\\mathbb{P}_2^M$ permutations, Eq. (1) has one agnostic $\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})$ , and $M$ specific $\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})$ losses. Formally, using a Langrange multiplier hyperparameter $\\beta$ we have our loss objective as,", + "bbox": [ + 496, + 301, + 892, + 635 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathcal {I}} = - \\overbrace {\\mathcal {I} \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t}} ^ {a g}\\right)} ^ {\\text {a g n o s t i c}} + \\beta \\overbrace {\\sum_ {\\mathbf {k} \\in \\{\\mathbf {s} , \\mathbf {t} \\}}} ^ {\\text {s p e c i f i c}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 637, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Minimise $\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})$ : We minimise the mutual information between modality-agnostic and modality-specific components using a conditional invertible [ ] neural network $\\tau_{\\mathbf{k}}$ . Unlike typical unidirectional neural networks $\\mathcal{F}: x \\to y$ , a conditional invertible neural network employs a sequence of bijective mapping operations like activation normalization (ActNorm) [45], Conditional Affine Coupling [28], and shuffling [45] to obtain $\\tau_{\\mathbf{k}}: x \\leftrightarrow y$ . During the forward pass (inference), we sample $\\eta \\in \\mathbb{R}^{32}$ from a uniform prior distribution $\\mathbb{P}(\\eta)$ to predict the modality-specific $f_{\\mathbf{k}}^{sp} \\in \\mathbb{R}^{32}$ by conditioning on $f_{\\mathbf{k}}^{ag}$ as, $f_{\\mathbf{k}}^{sp} = \\tau_{\\mathbf{k}}(\\eta | f_{\\mathbf{k}}^{ag})$ . In other words, during inference, we predict the modality-specific component of target from the modality-agnostic one of input using $\\tau_{\\mathbf{k}}$ . The target modality is", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10975", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cbc47200456493b1ee8049ad6e11ff710863ef962b6f00983f5527231e5ccb5b.jpg", + "image_caption": [ + "Figure 5. (Left): The modality-agnostic from sketch, or text, or both are used to retrieve from a gallery of photos. This enables a multitude of retrieval tasks like SBIR, TBIR, and STBIR. (Right): The modality-agnostic from photo, or sketch, or both are used to generate the text-specific component. Combining the modality-agnostic and inferred text-specific (via $\\tau_{\\mathrm{t}}$ ) enables image, or sketch, or subjective captioning." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 527, + 214 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/55451c3a3b2a6f1e97526a009119b4205634e536430359f3e2b79a907403ca7d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 531, + 88, + 885, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "then generated by combining the input-agnostic and target-specific components. The conditioning modality-agnostic vector $f_{\\mathbf{k}}^{ag}$ is injected into the intermediate conditional affine coupling layers $\\mathcal{C}: x \\leftrightarrow y$ as: $[x_1, x_2] = \\text{split}(x)$ , and $y = \\text{concat}[x_1, s_\\theta([x_1; h]) \\odot x_2 + t_\\theta([x_1; h])]$ , where, $h = \\mathcal{H}(f_{\\mathbf{k}}^{ag})$ . A simple feed-forward neural network implements $s_\\theta, t_\\theta$ , and $\\mathcal{H}$ . We learn $\\tau_{\\mathbf{k}}$ in the reverse pass (training) via negative log-likelihood (NLL Loss in Fig. 4) of $\\tau_{\\mathbf{k}}^{-1}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag})$ to predict a uniform distribution $\\mathbb{P}(\\eta)$ ,", + "bbox": [ + 75, + 268, + 472, + 407 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {P} (\\eta) = \\mathbb {P} \\left(\\tau_ {\\mathbf {k}} ^ {- 1} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right)\\right) | \\det J _ {\\tau_ {\\mathbf {k}} ^ {- 1}} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right) | \\quad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 411, + 468, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We show how learning $\\tau_{\\mathbf{k}}$ in Eq. (2) minimises $\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})$ . $\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp}) = \\int_{f_{\\mathbf{k}}^{sp}} \\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) \\log \\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) / \\mathbb{P}(f_{\\mathbf{k}}^{sp})$ . Approximating modality-specific prior $\\mathbb{P}(f_{\\mathbf{k}}^{sp})$ with variational distribution $\\mathbb{Q}(f_{\\mathbf{k}}^{sp})$ gives the upper-bound, minimising which reduces the KL-divergence between $\\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag})$ and $\\mathbb{Q}(f_{\\mathbf{k}}^{sp})$ i.e., it encourages the disentanglement $\\mathbb{P}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp}) \\approx \\mathbb{P}(f_{\\mathbf{k}}^{ag}) \\cdot \\mathbb{P}(f_{\\mathbf{k}}^{sp})$ . The prior $\\mathbb{Q}(f_{\\mathbf{k}}^{sp})$ is solved using $\\tau_{\\mathbf{k}}$ to enforce disentanglement between modality-agnostic and modality-specific components, like that in Eq. (2), as the sum of negative-loglikelihood (NLL-Loss in Fig. 4) and log-determinant (see supplementary for proof),", + "bbox": [ + 75, + 438, + 468, + 609 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\tau_ {\\mathbf {k}}} = - \\mathbb {E} _ {f _ {\\mathbf {k}} ^ {s p}} \\left\\{\\log \\mathrm {q} \\left(\\tau_ {\\mathbf {k}} ^ {- 1} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right)\\right) \\right. \\tag {3} \\\\ + \\log | \\det J _ {\\tau_ {\\mathbf {k}} ^ {- 1}} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right) | \\} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 104, + 609, + 468, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Maximise $\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})$ : Here we show how minimising a constrastive based retrieval loss [94] between the modality-agnostic components of sketch and text will maximise their mutual information. We define contrastive loss matching modality-agnostic components of sketch and text as,", + "bbox": [ + 75, + 654, + 468, + 731 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {c l} ^ {\\mathbf {s}, \\mathbf {t}} = - \\mathbb {E} _ {f _ {\\mathbf {s}} ^ {s p}} \\left[ \\log \\frac {\\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {+}} ^ {a g}\\right)}{\\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {+}} ^ {a g}\\right) + \\sum_ {f _ {\\mathbf {t} ^ {-}} ^ {a g}} ^ {N - 1} \\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {-}} ^ {a g}\\right)} \\right] \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 737, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where, $\\omega = \\exp (x^{T}\\mathbf{W}y)$ . For each modality-agnostic $f_{\\mathbf{s}}^{ag}$ we sample a positive $f_{\\mathbf{t}^{+}}^{ag}$ and $(N - 1)$ negative $f_{\\mathbf{t}^{-}}^{ag}$ pairs. The contrastive loss in Eq. (4) is expressed as mutual information between $f_{\\mathbf{s}}^{ag}$ and $f_{\\mathbf{t}}^{ag}$ as, $\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}\\geq -\\mathcal{I}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{t}}^{ag}) + \\log (N)$ . Hence, to maximise the mutual information between modality-agnostic $f_{\\mathbf{s}}^{ag}$ and $f_{\\mathbf{t}}^{ag}$ , we can maximise the tractable lower bound $\\log (N) - \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}$ .", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Total Loss for Bimodal Setup: The resulting loss $(\\mathcal{L}_{tot})$ for bimodal (sketch and text) setup comprise three loss objectives (i) self reconstruction loss $\\mathcal{L}_{rec}$ , (ii) contrastive loss between two modality-agnostic terms $\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}$ , and (iii) disentanglement between modality-agnostic and modality-specific components in each modality $(\\mathbf{k})$ $(\\mathcal{L}_{\\tau_{\\mathbf{k}}})$ , as", + "bbox": [ + 496, + 268, + 890, + 359 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {r e c} = | | \\mathbf {s} - \\mathcal {D} _ {\\mathbf {s}} (\\mathcal {F} _ {\\mathbf {s}} (\\mathbf {s})) | | _ {2} + | | \\mathbf {t} - \\mathcal {D} _ {\\mathbf {t}} (\\mathcal {F} _ {\\mathbf {t}} (\\mathbf {t})) | | _ {2} \\tag {5} \\\\ \\mathcal {L} _ {t o t} = \\mathcal {L} _ {r e c} + \\mathcal {L} _ {c l} ^ {\\mathbf {s}, \\mathbf {t}} + \\beta [ \\mathcal {L} _ {\\tau_ {\\mathbf {s}}} + \\mathcal {L} _ {\\tau_ {\\mathbf {t}}} ] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 361, + 890, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Extending to Three/More Modalities: Here we extend our bimodal setup in Sec. 4.3 to three or more modalities. (i) We compute the self-reconstruction loss for three modalities as $\\mathcal{L}_{rec} = \\sum_{\\mathbf{k}\\in \\{\\mathbf{s},\\mathbf{t},\\mathbf{p}\\}}||\\mathbf{k} - \\mathcal{D}_{\\mathbf{k}}(\\mathcal{F}_{\\mathbf{k}}(\\mathbf{k}))||_2$ (ii) we minimise the mutual information between modality-agnostic and modality-specific components for sketch, text, and photo as, $\\mathcal{L}_{\\tau} = \\mathcal{L}_{\\tau_{\\mathrm{s}}} + \\mathcal{L}_{\\tau_{\\mathrm{t}}} + \\mathcal{L}_{\\tau_{\\mathrm{p}}}$ . (iii) However, our contrastive loss term $\\mathcal{L}_{cl}$ that maximises the mutual information among modality-agnostic components can only compare two modalities. We can extend this naively to a three-modality setup as $\\mathcal{L}_{cl}^{tot} = \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}} + \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}} + \\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}$", + "bbox": [ + 496, + 409, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Extending to three or more modalities, however, we notice our contrastive loss in Eq. (4) is defined for only b-modal setup $(\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}$ , or $\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}}$ , or $\\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}$ ). For example, given three modalities $S_{M} = \\{m_{1},m_{2},m_{3}\\}$ , comparing only $(m_{1},m_{2})$ ignores $m_{3}$ . This highlights a key limitation: it fails when we have a query in both $(m_{1},m_{3})$ to retrieve $m_{2}$ (e.g., sketch+text for image retrieval). Now the research question boils down to - how can we model a function $\\mathcal{G}(\\cdot)$ such that it can model either $m_{1}$ , or $m_{3}$ , or both $(m_{1},m_{3})$ to retrieve $m_{2}$ . To design $\\mathcal{G}$ , using naive addition as $\\mathcal{G}(m_1,m_3) = m_1 + m_3$ does not handle overlapping or conflicting information in $m_{1}$ and $m_{3}$ [58]. While, concatenation $\\mathcal{G}(m_1,m_3) = \\mathrm{concat}[m_1,m_3]$ computes interaction between $(m_{1},m_{3})$ , it forces to provide both $m_{1}$ and $m_{3}$ during inference; thereby failing to model either $m_{1}$ , or $m_{3}$ , or both $(m_{1},m_{3})$", + "bbox": [ + 496, + 575, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Modelling Optional Sketch or Text", + "text_level": 1, + "bbox": [ + 498, + 820, + 803, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose a simple approach to design $\\mathcal{G}$ that optionally models either $m_{1}$ , or $m_{3}$ , or both $(m_{1}, m_{3})$ , and handles", + "bbox": [ + 496, + 837, + 890, + 867 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2When signals $(m_{1},m_{3})$ are similar or complementary $\\mathcal{G}$ should strengthen decision; when signals conflict $\\mathcal{G}$ should filter unreliable ones.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "footer", + "text": "10976", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "overlapping or conflicting information. Our proposed $\\mathcal{G}$ comprises a multihead cross-attention module $\\mathrm{MH}(\\cdot)$ followed by an attention-based pooling $\\mathrm{PMA}(\\cdot)$ as, $f_{M} = \\mathrm{PMA}(H_{M})$ ; where $H_{M} = \\mathrm{MH}(S_{M})$ , and $S_{M} = \\{m_{1}, m_{3}\\}$ .", + "bbox": [ + 76, + 90, + 467, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our $\\mathrm{MH}(\\cdot)$ is order-invariant and independent of the number $(M)$ of input modalities defined as $\\mathrm{MH}(X) = \\sigma (XX^T)X$ ; where $\\sigma$ is scaled-softmax, $X^T$ is transpose of $X$ , and $X\\in \\mathbb{R}^{M\\times 480}$ is a list of modality-agnostic components $m_{1}$ , or $m_{3}$ with $\\mathbb{R}^{1\\times 480}$ , or $(m_1,m_3)\\in \\mathbb{R}^{2\\times 480}$ in query. The cross-attention in $\\mathrm{MH}(\\cdot)$ interacts across query modalities to compute mutually agreeing information between $(m_{1},m_{3})$ as, $H_{M}\\in \\mathbb{R}^{2\\times 480}$ . Next, we use an order-invariant attention-based pooling $\\mathrm{PMA}: \\mathbb{R}^{2\\times 480}\\to \\mathbb{R}^{1\\times 480}$ with a learned seed vector $\\mathcal{P}\\in \\mathbb{R}^{1\\times 480}$ to aggregate mutually agreeing $H_{M}$ as, $f_{M} = \\mathrm{PMA}(H_{M}) = \\sigma (\\mathcal{P}H_{M}^{T})H_{M}$ . Hence, using our proposed fusion module $\\mathcal{G}$ , we adapt our contrastive loss defined for only a pair of modality-agnostic components in Eq. (4) as $\\mathcal{L}_{cl}^{tot} = \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}} + \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}} + \\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}$ to jointly model sketch-text-photo (or more) modality-agnostic as: $\\mathcal{L}_{cls}^{tot} = \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{t}}^{ag}),f_{\\mathbf{p}}^{ag}) + \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{p}}^{ag}),f_{\\mathbf{t}}^{ag}) + \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{p}}^{ag},f_{\\mathbf{t}}^{ag}),f_{\\mathbf{s}}^{ag})$ . For a generalised solution involving more than three modalities $(M > 3)$ , see supplementary.", + "bbox": [ + 76, + 152, + 467, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Inference Data Flow: We describe the inference data flow in Fig. 5. For retrieval tasks, we first compute the modality-agnostic component of query sketch and text $(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})$ , and a gallery of photos $\\{f_{\\mathbf{p}_1}^{ag}, f_{\\mathbf{p}_2}^{ag}, \\ldots, f_{\\mathbf{p}_{\\mathbf{N}}}^{ag}\\}$ . Next, a combined representation for either only sketch $(f_{\\mathbf{s}}^{ag})$ , or only text $(f_{\\mathbf{t}}^{ag})$ , or both $(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})$ is computed using multihead cross attention $\\mathrm{MH}(\\cdot)$ followed by attention-based pooling $\\mathrm{PMA}(\\cdot)$ defined in Sec. 4.4 to get $f_{\\mathbf{st}^*}^{ag}$ . Finally, we find the minimum distance between the combined $f_{\\mathbf{st}^*}^{ag}$ and modality-agnostic component of photo $f_{\\mathbf{p}_i}^{ag}$ as $\\omega(f_{\\mathbf{st}^*}^{ag}, f_{\\mathbf{p}_i}^{ag})$ defined in Eq. (4). For captioning, we additionally use the text-specific conditional invertible neural network $\\tau_t$ to generate the target modality-specific text (e.g., grammatical structure etc.) from input modality-agnostic comprising of only photo $(f_{\\mathbf{p}}^{ag})$ for image captioning, only sketch $(f_{\\mathbf{s}}^{ag})$ for sketch captioning, or both photo and sketch $(f_{\\mathbf{p}}^{ag}, f_{\\mathbf{s}}^{ag})$ for subjective captioning (i.e., generate image captions by conditioning on the input sketch).", + "bbox": [ + 76, + 426, + 467, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 712, + 207, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: We use two scene sketch datasets with fine-grained alignment among sketch, text, and photo: (i) SketchyCOCO [34] contains 14,081 scene sketch-photo pairs. The photos are taken from MS-COCO [55] comprising $164K$ photos with paired texts. However, most sketches in SketchyCOCO [34] contain less than one foreground instance. Following [57], we filter SketchyCOCO with one foreground instance to get 1015/210 train/test scene sketches. (ii) Unlike SketchyCOCO [34], where the scene sketches are synthetically generated, FS-COCO [19] includes 7000/3000 train/test human-drawn scene sketches", + "bbox": [ + 76, + 734, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with a paired textual description of sketches.", + "bbox": [ + 500, + 90, + 792, + 106 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details: Our model is implemented in PyTorch using 11GB Nvidia RTX 2080-Super GPU. First, we pre-train the image encoder and text decoder for image captioning using 82,783 photo-text pairs (excluding the photos common in SketchyCOCO and FS-COCO) for 15 epochs. Next, we fine-tune on either SketchyCOCO [34], or FS-COCO [19] for 200 epochs using Adam optimiser with learning rate $1e - 4$ , and batch size 64. Our photo $(\\mathcal{F}_{\\mathbf{p}})$ and sketch $(\\mathcal{F}_{\\mathrm{s}})$ encoders use ImageNet pretrained VGG-16 [85]. For simplicity, we encode text using a bidirectional GRU unit with 512 hidden units. Our text decoder [43] is a single-layer autoregressive LSTM decoder that predicts a probability distribution over a fixed vocabulary (10,010 words) at every time step. For the image/sketch decoder, we use two separate GAN [109] networks that synthesise sketch/image of size $64\\times 64$ , respectively. For brevity, we avoid realistic sketch/image generation due to the challenging scene complexity [19]. Hence we do not use a discriminator module for high-quality, sharp reconstruction [110]. Finally, our conditionally invertible neural network comprises 16 alternating affine coupling [29], activation normalisation [45], and switch layers [29].", + "bbox": [ + 496, + 113, + 890, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metric: In line with FG-SBIR research, we use Acc.@q [81] defined as the percentage of sketches having a true matched photo in the top-q list. For sketch/image/subjective captioning, we use standard metrics BELU (B) 1-4 [67], CIDEr (C) [95], ROUGE (R) [53], METEOR (M) [25], and SPICE [2]. Following [96], we generate 100 candidate captions and employ consensus reranking using CIDEr to select the best candidate caption.", + "bbox": [ + 496, + 454, + 890, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Competitors: We compare against (i) existing state-of-the-art methods that align two modalities (S2): For SBIR, Triplet-SN [107] employs Sketch-A-Net [108] backbone trained using triplet loss. HOLEF [87] adds spatial attention with a higher-order ranking loss. SketchyS [115] replaces Sketch-A-Net in Triplet-SN with VGG-16 [85] and an auxiliary category-level cross-entropy. SceneS [57] uses GCN [46] to model scene sketch layout information. For TBIR, CLIP [73] is trained with text using transformer [83] and photo using vision transformer [30] on 400 million text-photo pairs. CLIP-LN fine-tunes CLIP by training only layer normalisation parameters [4] with learning rate 0.00001. For image/sketch captioning, SAT [101] is one of the simplest but seminal works using a CNN-LSTM encoder-decoder approach similar to ours. GMM-CVAE [96] employs a conditional variational autoencoder with a Gaussian mixture model. LNFMM [61] is similar to ours that splits information into modality-agnostic and modality-specific components using conditional invertible neural network, ClipCap [65] employs CLIP [73] for image encoding followed by GPT-2 [74] for text decoding. A learned", + "bbox": [ + 496, + 583, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10977", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/36a83dabf127ae0eb692d74fd0b052f86a39c5793bdd597d13fcd08c09472167.jpg", + "table_caption": [ + "Table 2. Quantitative results combining sketch and text for image retrieval (FG-STBIR) on two scene sketch datasets [19, 34]." + ], + "table_footnote": [], + "table_body": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S3QST [86]38.987.925.154.5
SCM [3]38.587.324.354.1
BCrossAtt [83]39.188.225.354.8
Proposed39.588.725.755.2
", + "bbox": [ + 78, + 118, + 470, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e4c642d4945a6644e7890569f919081e1c0a2307d19f9ec43668b175cfc5454.jpg", + "image_caption": [ + "Boys are playing with frisbee disc." + ], + "image_footnote": [], + "bbox": [ + 80, + 224, + 142, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/491ba7bbf6a68b769f998565dbc904aa15b5574119bc3dc59baddb1bd018a8cd.jpg", + "image_caption": [ + "A boy is holding a baseball bat." + ], + "image_footnote": [], + "bbox": [ + 148, + 226, + 212, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8163cf5444586d0fb8fd9a4f50e464dd6644f472805fb4878ca8d558e7769a62.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 226, + 276, + 275 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27ddccbf3f52acc9b16d11c565b32353eff59a6baa311c5ffc98da19bf93820f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 226, + 339, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3266c9bfa4b21e45f5a1eaf8efe1d27f20f42fd7ed47f351fafb2c3fb2276ce5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 226, + 401, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/11874f5a41534dedfd3cb1a4fcd11eee9fe870da2d646d90568c681359d46853.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 226, + 465, + 273 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0899e783648761292051e3159bf4fad7d311c641fe739d113971cf987d59d384.jpg", + "image_caption": [ + "Figure 6. Qualitative results of combining sketch and text as query for image retrieval on FSCOCO [19]. See supplementary for more." + ], + "image_footnote": [], + "bbox": [ + 80, + 295, + 142, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1d597511d67f326a5b8cc151e3502f52bc3f6b7e2ce64858175ebc6122462009.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 151, + 296, + 212, + 343 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c9c912a0282f5e8c44ddf5c9b48420163a6addee74076690140c3b414d462c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 214, + 296, + 277, + 345 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/834fd81d89739a308646f9999cc67c191b15d68d141fdbbd55d4754f9eae2e38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 296, + 339, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/32a377b68de073f05e609decf2772eef34570fa46f8de312676b02535661b779.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 296, + 401, + 344 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa1907315712fb38cce2e3967e3ad6d48df92f0ff22a603cd987071192ef039b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 403, + 296, + 467, + 344 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "mapping module translates CLIP embeddings to GPT-2. (ii) We compare against methods that align 3 modalities (S3): For STBIR, QST [86] extends triplet loss in Triplet-SN to quadruplet loss that combines sketch and text for image retrieval. SCM uses element-wise addition to combine sketch and text from ResNet-18 [39] with weight sharing across sketch, text, and photo from ResBlock4 onwards [3]. (iii) We design baselines (B): For STBIR, CrossAtt employs cross-attention [83] to combine sketch and text. For subjective captioning, MulCap combines sketch $(f_{\\mathbf{s}}^{ag})$ and photo $(f_{\\mathbf{p}}^{ag})$ via element-wise multiplication as in [14]. CrossCap optionally fuse photo, sketch, or both using cross-attention. CatCap use feature concatenation [71] of guiding sketch $(f_{\\mathbf{s}}^{ag})$ signal with photo $(f_{\\mathbf{p}}^{ag})$ to generate captions.", + "bbox": [ + 75, + 390, + 468, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Combining Sketch and Text for Image Retrieval", + "text_level": 1, + "bbox": [ + 76, + 606, + 468, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 2 shows that for some instances, sketch is a better query, whereas text is better for others. Hence, to achieve best of both modalities, we examine the complimentary nature by combining sketch and text for image retrieval. Table 2 shows (i) SCM gives the lowest performance due to naive element-wise addition of potentially overlapping and conflicting information [58] from sketch and text. (ii) QST improves slightly upon SCM by replacing naive elementwise addition with a weighted summation (0.8 for sketch modality). (iii) CrossAtt outperforms all baselines by using a cross-attention between sketch and text to resolve overlapping/conflict information [58]. (iv) Our proposed method gives the highest performance due to cross-attention that model sketch-text interaction and disentanglement to drive out modality-specific information for cross-modal retrieval.", + "bbox": [ + 75, + 623, + 468, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Optionally using Sketch for Image Retrieval", + "text_level": 1, + "bbox": [ + 76, + 854, + 450, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our method allows drawing only easy-to-sketch scenes instead of using both sketch and text forcibly. Table 3 com", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/84f10a6b34020c2402aa5a7fa3956858323d6ff9d65b189864a8fb03e3cbbedf.jpg", + "table_caption": [ + "Table 3. Quantitative results using only sketch for image retrieval (FG-SBIR) on two scene sketch datasets [19, 34]." + ], + "table_footnote": [], + "table_body": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2Triplet-SN [107]6.232.94.721.0
HOLEF [87]6.240.74.921.7
SketchyS [115]36.578.623.052.3
SceneS [57]31.986.2--
S3QST [86]37.487.123.652.9
SCM [3]37.386.823.452.6
BCrossAtt37.987.423.753.5
Proposed38.287.624.153.9
", + "bbox": [ + 501, + 118, + 890, + 250 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ca2c1e1ed72ef9aa79a2c1859ba61d71526c7bef59078ad816fe95634196780a.jpg", + "table_caption": [ + "Table 4. Quantitative results of fine-grained text-based image retrieval (FG-TBIR) on two scene sketch datasets [19,34]." + ], + "table_footnote": [], + "table_body": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2CLIP [73]21.050.911.535.3
CLIP-LN [73]22.152.314.836.6
S3QST [86]11.131.17.223.6
SCM [3]10.731.06.923.1
BCrossAtt20.151.012.535.8
Proposed21.551.613.736.3
", + "bbox": [ + 501, + 290, + 895, + 397 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8084445dfa9affb565a568731a20627cf66e208f10c26c9a899f129a00528c58.jpg", + "image_caption": [ + "Sheep are grazing on a green hill." + ], + "image_footnote": [], + "bbox": [ + 501, + 407, + 571, + 448 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e38fb60b04bec443bd734e532b00c60b554ad74252ae912101c4be6d8e8ec6c.jpg", + "image_caption": [ + "Black and white photo of people holding umbrellas.", + "Three people are walking under umbrella on field." + ], + "image_footnote": [], + "bbox": [ + 697, + 407, + 767, + 448 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9f05b8035a4f57cdeba0f1e665ed57f2c92b8aadd8bfa2b8be3e00be5537b1ea.jpg", + "image_caption": [ + "Figure 7. Qualitative results for image captioning v/s subjective captioning on FS-COCO [19]. See supplementary for more." + ], + "image_footnote": [], + "bbox": [ + 504, + 449, + 522, + 488 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3aa3ff89dce81b31cde100c73414e520195faf98d28bd15f01ef7ba73fea3a97.jpg", + "image_caption": [ + "A herd of sheep on grassland." + ], + "image_footnote": [], + "bbox": [ + 522, + 449, + 589, + 489 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2157ffb650d9824ed575581fc3612dc3df852e20f3f158d73b9124b988b60309.jpg", + "image_caption": [ + "Sheep are grazing beyond the fence on a hill." + ], + "image_footnote": [], + "bbox": [ + 700, + 459, + 718, + 487 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08590dda607bde1e266bc3b9eee287a8da579f7e81b2d8652306ac520a95b814.jpg", + "image_caption": [ + "Three people are walking holding umbrella." + ], + "image_footnote": [], + "bbox": [ + 720, + 459, + 769, + 487 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pares against methods that specialise on two-modalities (S2), three-modalities (S3), and our proposed baselines (B). We observe (i) training on three modalities (sketch, text, and photo) in S3 generally outperforms those trained using only sketch and photo (S2). This can be attributed to learning generalisable features in multi-modal setup [3]. (ii) $QST$ in S3 outperforms SCM indicating quadruplet loss is a better training objective than naive element-wise addition when combining sketch, text, and photo. (iii) Performance difference between CrossAttn and $QST$ is not as significant as in FG-STBIR (Table 2) as during inference, we only use sketch, omitting the cross-attention module. (iv) Our method outperforms S2, S3, and B even for two-modality setup thanks to disentanglement that eliminates confounding [3] modality-specific information.", + "bbox": [ + 496, + 531, + 890, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Optionally using Text for Image Retrieval", + "text_level": 1, + "bbox": [ + 498, + 763, + 854, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "While some information is best expressed by drawing, others, like colour, is best described via text. From Table 4, we observe (i) Given the same train/test split, sketches outperform text as a query modality for fine-grained image retrieval. (ii) CLIP and CLIP-LN outperforms all competitors due to superior pre-trained weights using 400 million text-image pairs. (iii) The proposed method outperforms most methods due to disentanglement that drives out modality-", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10978", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1b4aa69d1d2b94bf783b26d37b9cd9e62fa8f7811c16bc0fbab0e5a12ce07bbd.jpg", + "table_caption": [ + "Table 5. Quantitative results of standard captioning metrics on MS-COCO [55] and FS-COCO [19] dataset." + ], + "table_footnote": [], + "table_body": "
MethodImage CaptioningSketch CaptioningSubjective Captioning
B-1B-4MRCSB-1B-4MRCSB-1B-4MRCS
S2SAT [101]71.825.023.0---46.213.717.144.969.414.5------
GMM-CVAE [96]72.930.724.252.598.617.749.615.518.348.777.615.5------
AG-CVAE [96]73.231.124.552.8100.118.850.916.018.949.180.515.8------
LNFMM [61]74.731.824.753.8105.518.852.216.721.052.990.116.0------
BMulCap74.933.225.554.9106.019.553.917.021.053.897.316.778.738.628.559.8110.721.7
CatCap------------77.638.028.357.7108.021.2
CrossCap75.534.326.155.4106.720.154.317.921.454.3100.317.579.239.328.459.5117.322.1
Proposed76.035.926.956.9107.020.956.919.321.656.6106.518.981.342.730.161.6121.623.5
", + "bbox": [ + 78, + 104, + 885, + 234 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/01fb12615b5717ee2bd6b115c70745234269d1478502fcbeb91e729fc1f3b18e.jpg", + "table_caption": [ + "Table 6. Ablation study on FG-STBIR and Subjective Captioning using FSCOCO [19]. CA denotes cross-attention in Sec. 4.4." + ], + "table_footnote": [], + "table_body": "
τkCACLAcc.@1Acc.@10B-1C
XXX24.553.773.3100.1
✓XX24.954.077.9108.5
✓✓X25.554.980.6119.3
✓✓✓25.755.281.3121.6
", + "bbox": [ + 78, + 276, + 465, + 347 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "specific components. Although CLIP [73] outperforms the proposed method, we deliberately use a simple and easy-to-reproduce GRU/VGG-16 architectures for text/photo encoders, and train on a much smaller data [19,34] than CLIP.", + "bbox": [ + 75, + 359, + 467, + 421 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Image or Sketch Captioning", + "text_level": 1, + "bbox": [ + 76, + 425, + 330, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition to disentanglement for cross-modal retrieval tasks (e.g., FG-SBIR, FG-TBIR), our conditional invertible neural network $\\tau_{\\mathrm{t}}$ can also generate text-specific information (Fig. 4) to support generative tasks like image/sketch captioning. We generate 100 candidate captions using (i) beam search for SAT, MulCap, CrossCap, CatCap, and (ii) sampling from prior distribution for GMM-CVAE, AG-CVAE, LNFMM, and our proposed method. From Table 5, we observe (i) our baselines adopting recent techniques like vision-transformer [30] outperforms (S2) – recent but complex approaches like LNFMM, AG-CVAE, and the older yet seminal work like SAT. (ii) Performance gap between MulCap and CrossCap is insignificant for two-modality setups (photo to text, or sketch to text) since they primarily differentiate by their multi-modal (photo and sketch) fusion strategy. (iii) In spite of using a photo/sketch encoder and text decoder similar to our simple competitor SAT, our proposed method performs competitively with complex methods like LNFMM, AG-CVAE, and latest approaches using vision-transformers [30], like CrossCap. This shows the significant contribution of (i) disentangling modality-specific and modality-agnostic components from photo/sketch, and (ii) modelling text-specific prior for generative tasks.", + "bbox": [ + 73, + 441, + 468, + 789 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.5. Sketch Based Subjective Captioning", + "text_level": 1, + "bbox": [ + 76, + 794, + 390, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As defined in Sec. 3.2, unlike traditional captioning frameworks that factually describe an image or sketch in a neutral tone, subjective captioning focus on drawing out a user's intentions, salient objects, and artistic interpretations [38]. Being the first method to use scene-level sketch as a guiding signal for captioning, we follow controllable caption-", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing literature [89] to adopt three baselines (B) that inject the sketch conditioning signal into the captioning pipeline. From Table 5, we observe (i) MulCap outperforms CatCap, thereby supporting previous observations [14] of elementwise multiplication being more effective than concatenation. (ii) CrossAtt outperforms all baselines (B) and two-modality SOTAs (S2) by using a cross-attention mechanism to fuse sketch and photo by modelling sketch-photo interactions to resolve overlapping or conflicting information. Our proposed method is similar to CrossAtt using cross-attention (Sec. 4.4) but also enriches the modality-agnostic sketch and photo features by removing the confounding modality-specific information to offer the best performance.", + "bbox": [ + 496, + 250, + 890, + 446 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.6. Ablation", + "text_level": 1, + "bbox": [ + 500, + 450, + 604, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 6, we evaluate the contribution of each key design choice on FG-STBIR and Subjective captioning using FS-COCO [19]. (i) Replacing cross-attention in Sec. 4.4 with quadruplet loss [86] leads to a performance drop by $0.6 / 0.9 / 2.7 / 10.8$ in Acc.@1/Acc.@10/B-1/C metrics respectively to show the importance of modelling the interaction between sketch and text. (ii) Replacing contrastive loss-based query-photo score in Eq. (4) with a simple triplet loss leads to a performance drop by $0.2 / 0.3 / 0.7 / 2.3$ due to the inability of unimodal L2-based triplet loss to model highly complex scene information [94]. (iii) Finally, removing the conditional invertible neural networks $(\\tau_{\\mathbf{k}})$ drops retrieval and captioning by $0.4 / 0.3 / 4.6 / 8.4$ due to percolation of the confounding modality-specific information in cross-modal tasks [3] and the inability to generate text-specific information from photo and sketch respectively.", + "bbox": [ + 496, + 465, + 890, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 715, + 617, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have studied for the first time the trilogy relationship among scene-level sketch, text, and photo by introducing scene-sketch in the context of scene understanding. We proposed a unified framework to jointly model sketch, text, and photo that seamlessly support several downstream tasks like fine-grained sketch-based image retrieval, fine-grained sketch and text based image retrieval, sketch captioning, and subjective captioning, among others. Future research can explore challenging downstream tasks such as scene-level sketch-based image generation, sketch and text based image generation, and text-based sketch generation tasks.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10979", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Harsh Agarwal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. In ICCV, 2019. 3", + "[2] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Spice: semantic propositional image caption evaluation. 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In ECCV, 2018. 1, 2, 6, 7" + ], + "bbox": [ + 501, + 90, + 892, + 189 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "10983", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2023/SceneTrilogy_ On Human Scene-Sketch and Its Complementarity With Photo and Text/61c06fa2-0cf3-4cfc-a6de-25fbe7140dea_model.json b/2023/SceneTrilogy_ On Human Scene-Sketch and Its Complementarity With Photo and Text/61c06fa2-0cf3-4cfc-a6de-25fbe7140dea_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c2702783f072d588a20378c0836ebda9f43741bc --- /dev/null +++ b/2023/SceneTrilogy_ On Human Scene-Sketch and Its Complementarity With Photo and Text/61c06fa2-0cf3-4cfc-a6de-25fbe7140dea_model.json @@ -0,0 +1,3040 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.157, + 0.131, + 0.815, + 0.175 + ], + "angle": 0, + "content": "SceneTrilogy: On Human Scene-Sketch and its Complementarity with Photo and Text" + }, + { + "type": "text", + "bbox": [ + 0.122, + 0.188, + 0.847, + 0.225 + ], + "angle": 0, + "content": "Pinaki Nath Chowdhury1,2 Ayan Kumar Bhunia1 Aneeshan Sain1,2 Subhadeep Koley1,2 Tao Xiang1,2 Yi-Zhe Song1,2" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.225, + 0.714, + 0.242 + ], + "angle": 0, + "content": "\\(^{1}\\)SketchX, CVSSP, University of Surrey, United Kingdom." + }, + { + "type": "text", + "bbox": [ + 0.23, + 0.242, + 0.739, + 0.261 + ], + "angle": 0, + "content": "\\(^{2}\\)iFlyTek-Surrey Joint Research Centre on Artificial Intelligence." + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.263, + 0.792, + 0.278 + ], + "angle": 0, + "content": "{p.chowdhury, a.bhunia, a.sain, s.koley, t.xiang, y song}@surrey.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.313, + 0.314, + 0.329 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.346, + 0.474, + 0.726 + ], + "angle": 0, + "content": "In this paper, we extend scene understanding to include that of human sketch. The result is a complete trilogy of scene representation from three diverse and complementary modalities - sketch, photo, and text. Instead of learning a rigid three-way embedding and be done with it, we focus on learning a flexible joint embedding that fully supports the \"optionality\" that this complementarity brings. Our embedding supports optionality on two axes: (i) optionality across modalities - use any combination of modalities as query for downstream tasks like retrieval, (ii) optionality across tasks - simultaneously utilising the embedding for either discriminative (e.g., retrieval) or generative tasks (e.g., captioning). This provides flexibility to end-users by exploiting the best of each modality, therefore serving the very purpose behind our proposal of a trilogy in the first place. First, a combination of information-bottleneck and conditional invertible neural networks disentangle the modality-specific component from modality-agnostic in sketch, photo, and text. Second, the modality-agnostic instances from sketch, photo, and text are synergised using a modified cross-attention. Once learned, we show our embedding can accommodate a multi-facet of scene-related tasks, including those enabled for the first time by the inclusion of sketch, all without any task-specific modifications. Project Page: https://pinakinathc.github.io/scenetrilogy" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.74, + 0.21, + 0.755 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.47, + 0.839 + ], + "angle": 0, + "content": "Scene understanding sits at the very core of computer vision. As object-level research matures [24, 32], an encouraging shift can be observed in recent years on scene-level tasks, e.g., scene recognition [113], scene captioning [55], scene synthesis [34], and scene retrieval [13, 57]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Scene research has generally progressed from that of single modality [113, 114] to the very recent focus on multimodality [3, 13, 19]. The latter setting not only triggered a series of practical applications [34, 57, 101, 115] but im" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.313, + 0.885, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.506, + 0.456, + 0.889, + 0.473 + ], + "angle": 0, + "content": "\\(f_{\\mathrm{s}}^{sp}\\) sketch specific \\(f_{\\mathrm{t}}^{sp}\\) text specific \\(f_{\\mathrm{p}}^{sp}\\) photo specific \\(f^{ag}\\) modality agnostic" + }, + { + "type": "image_footnote", + "bbox": [ + 0.499, + 0.482, + 0.892, + 0.58 + ], + "angle": 0, + "content": "Figure 1. Some scenes are easy to describe via sketch; for others, text is better. We provide the option to sketch, write, or both (sketch + text). For “optionality” across tasks, we disentangle sketch, text, and photo into a discriminative (e.g., retrieval) part \\( f^{ag} \\) shared across modalities, and a generative (e.g., captioning) part specific to one modality (\\( f_{\\mathbf{s}}^{sp} \\), \\( f_{\\mathbf{t}}^{sp} \\), \\( f_{\\mathbf{P}}^{sp} \\)). This supports a multifacet of scene-related tasks without task-specific modifications." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.595, + 0.892, + 0.687 + ], + "angle": 0, + "content": "portantly helped to cast insights into scene understanding on a conceptual level (i.e., what is really being perceived by humans). To date, research on multi-modal scene understanding has mainly focused on two modalities – text and photo [59, 61, 62], via applications such as text-based scene retrieval (TBIR) [35], and scene captioning [23, 61, 62]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.893, + 0.901 + ], + "angle": 0, + "content": "This paper follows the said trend of multi-modal scene understanding and extend it to also include human scene-sketch. Sketch is identified because of its unique characteristics of being both expressive and subjective, evident in an abundance of object-level sketch research [11], and very recently on scene-level [19]. To verify there is indeed useful complementarity that sketch can bring to multi-modal scene understanding, we first conducted two pilot studies (i) on expressivity, we compare text and sketch in terms of scene image retrieval, and (ii) on subjectivity, we test a novel task of subjective captioning where sketch or parts-of-speech [26] are used as guidance for image captioning. On (i), results show there is significant disagreement in terms of retrieval accuracy when one is used as query over the other," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10972" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "indicating there is complementary information between the two modalities. On (ii), sketch is shown to offer more subjectivity as a guiding signal than text, when quantified using common metrics such as BELU-4 [67] and CIDEr [95]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.154, + 0.468, + 0.276 + ], + "angle": 0, + "content": "To fully explore the complementarity of all three modalities, we desire a flexible joint embedding that best sustains \"optionality\" across modalities, and also across tasks. The former enables end-users to use any combination of modalities (e.g., only sketch, only text, or both sketch+text) as a query for downstream tasks; and the latter provides option of utilising the learned embedding for both discriminative (e.g., retrieval) and generative problems (e.g., captioning)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.468, + 0.639 + ], + "angle": 0, + "content": "This desired level of \"optionality\" is however not achievable via naive three-way joint embeddings common in the literature [3, 13, 19]. Instead, we advocate a three-way disentanglement (Fig. 1(b)), where each of the three modalities is disentangled into their modality-specific component (\\(f_{\\mathbf{s}}^{sp}\\), \\(f_{\\mathbf{p}}^{sp}\\), \\(f_{\\mathbf{t}}^{sp}\\), for sketch, photo and text), and a shared modality-agnostic component (\\(f^{ag}\\)). The idea is that modality-specific will hold information specific to each modality (e.g., drawing style for sketch, texture for photo, and grammatical knowledge for text). It follows that filtering away modality-specific parts from each of the three modalities gives a shared modality-agnostic part that carries shared abstract semantic across all three modalities, (as shown in Fig. 1(b)). How optionality is supported in such a disentangled space then becomes trivial (Fig. 1(c),(d)). To achieve optionality across tasks, we simply use modality-agnostic information as the joint embedding to perform discriminative tasks (e.g., cross-modal retrieval), and for cross-modal generative tasks (e.g., captioning), we just combine modality-agnostic information (from source) with modality-specific (from target) to generate the target modality. Optionality across modality is a little harder, where we make use of a cross-attention [50] mechanism to capture the synergy across the modality-agnostic components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.468, + 0.869 + ], + "angle": 0, + "content": "Benefiting from our optionality-enabled embedding, we can perform a multi-facet of tasks without any task-specific modifications: (i) Fig. 1 (c) show cross-modal discriminative tasks such as sketch-based image retrieval (SBIR) using \\((f_{\\mathbf{s}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})\\), text-based image retrieval (TBIR) using \\((f_{\\mathbf{t}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})\\), or sketch+text based image retrieval (STBIR) using \\((f_{\\mathbf{s}}^{ag} + f_{\\mathbf{t}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})\\). (ii) Fig. 1 (d) show cross-modal generative tasks such as image captioning (photo branch) using \\(f_{\\mathbf{p}}^{ag} + f_{\\mathbf{t}}^{sp} \\rightarrow f_{\\mathbf{t}}\\) to generate textual descriptions \\(f_{\\mathbf{t}}\\). Similarly, for sketch captioning (sketch branch) we use \\(f_{\\mathbf{s}}^{ag} + f_{\\mathbf{t}}^{sp} \\rightarrow f_{\\mathbf{t}}\\). (iii) Last but not least, to demonstrate what the expressiveness of human sketch can bring to scene understanding, we introduce a novel task of subjective captioning where we guide image captioning using sketch as a signal (subjective branch) as \\(f_{\\mathbf{p}}^{ag} + f_{\\mathbf{s}}^{ag} \\rightarrow f_{\\mathbf{t}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In summary, our contributions are: (i) We extend multi-modal scene understanding to include human scene" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.244 + ], + "angle": 0, + "content": "sketches, thereby completing a trilogy of scene representation from three diverse and complementary modalities. (ii) We provide optionality to end-users by learning a flexible joint embedding that supports: optionality across modalities and optionality across tasks. (iii) Using computationally efficient techniques like information bottleneck, conditionally invertible neural networks, and modified crossattention mechanism, we model this flexible joint embedding. (iv) Once learned, our embedding accommodates a multi-facet of scene-related tasks like retrieval, captioning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.262, + 0.65, + 0.278 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.286, + 0.892, + 0.513 + ], + "angle": 0, + "content": "Sketch for Visual Understanding: Hand-drawn sketches enriched with human visual perception cues have facilitated several downstream visual understanding tasks. Apart from the widely explored SBIR [10, 22], sketch has shown potential on object localisation [18], segmentation [72], image/video synthesis [48], representation learning [79], 3D shape retrieval/modelling [20], medical image analysis [47, 97], etc. [102]. Sketches are also useful in the creative industry like artistic image editing [105] and animation [100]. Unlike photos that are passively captured by a camera, sketches are drawn by humans that actively stimulate intelligence with pictorial-style drawing games [8]. While text has been widely used for human expression, in this paper, we show freehand sketches can provide complimentary or symbiotic information for visual understanding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.73 + ], + "angle": 0, + "content": "Sketch-Based Image Retrieval (SBIR): SBIR retrieves a paired photo given a query sketch. Sketches offer visual description that commences the avenues of category-level [27, 78, 106] or fine-grained instance-level (FG-SBIR) [6, 9, 12] retrieval. SBIR typically employs deep triplet-ranking based siamese networks to learn a joint embedding space [107]. Contemporary research emerged towards zero-shot SBIR [27, 80], cross-domain translation [66], on-the-fly retrieval [12], semi-supervised [6], self-supervised [7], meta-learning [11] etc. As research on object-level SBIR matured, focus shifted towards the more practical scene-level SBIR [76] with GCN [57], and optimal transport [17]. The onset of scene sketch datasets [19, 34, 115] revealed further insights into implicit human-sketching strategies [19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Text-Based Image Retrieval (TBIR): Learning image-text joint embedding space with ranking loss [31, 43, 70] received considerable attention. Further improvements used mining hardest negative pairs for triplet loss [33], cross-modal adaptive message passing [98], probabilistic one-tomany representations [21] etc. Despite text lacking visual cues, million-scale paired image-text datasets have made TBIR competitive due to power scaling laws [63]. This inspired large-scale methods like Oscar [52], and CLIP [73]. In this paper, we augment TBIR with sketches to provide the creativity and freedom of expression intrinsic to sketches." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10973" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.348 + ], + "angle": 0, + "content": "Multi-Modality in Computer Vision: Multi-modal learning (MML) aims at developing models that can extract, interpret, and reason on information from various modalities characterised by different statistical properties such as text, sketch, or text+sketch. Contemporary research studied MML in vision via image and text [40], image to scene graph [36], etc. [103]. MML faces challenges like cross-modal alignment [42], or efficiency over data [92] and compute [44]. It is useful when data in one modality is inaccessible [3] for privacy or logistic reasons (e.g., hospital), but abundantly available in other modalities (photos in MS-COCO [55]). Often, some modalities are preferred over others for human-machine communication, like some concepts are easier to express in texts [60], while others prefer sketches [54] or both [76] (Fig. 1). In this paper, we learn cross-modal representation [104] that works using either one modality (text/sketch) or both." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.565 + ], + "angle": 0, + "content": "Disentangled Representation for Multi-modality: Disentangling modality-agnostic from modality-specific residual factors is important for MML [41, 93]. Modality-agnostic information is useful for cross-modal transfer like semantics-based retrieval and pattern recognition [41] but holds no meaning for tasks specific to one modality like image-style or speaker information [91]. Disentanglement was explored where factors of variation are either known (e.g., facial poses [90]) and individually supervised [75], partially known [82], or unknown (e.g., drawing style [82]) and learned unsupervised using isotropic Gaussian prior [77] or information-theoric regularisation [16]. Our method aligns with the unknown setup where factors particular to sketch, text, and image are discovered unsupervised." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.473, + 0.721 + ], + "angle": 0, + "content": "Image Captioning: This has emerged from predicting syntactically correct descriptions [89, 112] to tackling data scarcity [1, 49], and addressing user requirements [68, 69]. Predicted captions evolved from being factual in a neutral tone to (i) controllable using textual verbs [15], part-of-speech tag [26], or mouse trace [64, 71], and (ii) personalised captioning [84, 111] that learns user's active vocabulary, and writing style. Our method can (i) generate factual captions from images/sketches and (ii) extend controllable captioning paradigm by injecting saliency via sketch." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.734, + 0.195, + 0.751 + ], + "angle": 0, + "content": "3. Pilot Study" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.334, + 0.77 + ], + "angle": 0, + "content": "3.1. Sketch vs. Text for Retrieval" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.779, + 0.462, + 0.848 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.851, + 0.47, + 0.907 + ], + "angle": 0, + "content": "Figure 2. We compare SBIR [107] vs. TBIR [73] on FS-COCO [19] where retrieval rank is plotted in log-scale (see Supplemental for more details). While sketch is a better query for some instances (lower retrieval rank), for others text is better." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "Text can convey colour information, or object categories, but is cumbersome to describe fine-grained details, multiple objects, or complex shapes \\([86]^{1}\\). While sketch can depict complex shapes, multiple objects, and spatial alignment [19], not all objects are easy to draw ('donkey' vs. 'horse'). Fig. 2 shows this trade-off between sketch vs. text for image retrieval. We find an optimal fusion between sketch and text to derive best of both modalities along with the ability to optionally use only sketch, only text, or both." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.24, + 0.892, + 0.268 + ], + "angle": 0, + "content": "Table 1. Comparing alternative guiding signal like POS (part-of-speech) [26], Mouse Trace [64], and Freehand Sketches [19]." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.27, + 0.892, + 0.401 + ], + "angle": 0, + "content": "
SignalB-1B-4MRCS
POS [26]w/o73.231.124.552.8100.117.9
w/73.931.625.553.2104.518.8
Δ0.70.51.00.44.40.9
Trace [64]w/o32.28.1-31.729.325.7
w/52.224.6-48.3106.536.5
Δ2016.5-16.677.210.8
Sketchw/o74.731.824.753.8105.518.8
w/81.342.730.161.6121.623.5
Δ6.610.95.47.816.14.7
" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.412, + 0.747, + 0.428 + ], + "angle": 0, + "content": "3.2. Subjectivity for Captioning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Unlike traditional image captioning [62, 96] that generates factual captions in neutral tone, subjective captioning adapts the predicted captions using a guiding signal that specifies priorities on what should be described [89]. The signal is injected via feature concatenation [26], or cross-attention mechanism [64]. Applications of subjective captioning include medical report generation using disease tags to generate real style reports [56], art descriptions [5], and assistive technologies for the visually impaired [37,99]. In this paper, we advocate for sketch as a guiding signal to depict salient objects and express artistic interpretations [38]. We compare the performance (see supplementary for details) using guiding signals like POS (parts-of-speech) [26], mouse trace [64], or freehand sketches [19]. Following [64], we inject the guiding signal into the image captioning pipeline via cross-attention mechanism. As evident from Table 1, while sketch is competitive with mouse traces, it is a better signal than POS. However, unlike mouse trace, sketch can depict artistic interpretation [5] that makes it a more flexible and robust guiding signal than POS or mouse trace." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.747, + 0.719, + 0.765 + ], + "angle": 0, + "content": "4. Proposed Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.642, + 0.783 + ], + "angle": 0, + "content": "4.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.79, + 0.892, + 0.868 + ], + "angle": 0, + "content": "Baseline for Fine-Grained Retrieval: Given a query-photo pair \\((\\mathbf{q},\\mathbf{p})\\), existing methods encode [7, 51, 54, 57, 107] the query \\(\\mathbf{q} = \\{\\mathbf{s},\\mathbf{t}\\}\\) comprising sketch (s) / text (t) and photo (p) as \\(f_{\\mathbf{q}} = \\mathcal{F}_{\\mathbf{q}}(\\mathbf{q})\\in \\mathbb{R}^{D}\\), and \\(f_{\\mathbf{p}} = \\mathcal{F}_{\\mathbf{p}}(\\mathbf{p})\\in \\mathbb{R}^{D}\\) respectively. The network is trained via triplet loss with" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1Example: Cross strap stud and buckle detail blonde leather upper leather insole chunky wooden sole 9 cm heel." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10974" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.468, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.2, + 0.47, + 0.286 + ], + "angle": 0, + "content": "Figure 3. (Left): We disentangle modality-agnostic and modality-specific components from sketch, text, and photo. The modality-agnostic components are aligned using contrastive loss for cross-modal transfer. (Right): Modality-agnostic sketch \\((f_{\\mathbf{s}}^{ag})\\) is used across modality to generate modality-specific text \\((f_{\\mathbf{t}}^{sp})\\) using text-specific \\(\\tau_{\\mathbf{t}}\\). Combining \\(f_{\\mathbf{s}}^{ag}\\) and \\(f_{\\mathbf{t}}^{ag}\\), we generate text from sketch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.468, + 0.356 + ], + "angle": 0, + "content": "margin parameter \\(\\mu >0\\) such that the cosine distance \\(\\delta (\\cdot)\\) of query anchor \\(\\mathbf{q}\\) from a negative photo \\((\\mathbf{p}^{-})\\) should increase while that from the positive photo \\((\\mathbf{p}^{+})\\) should decrease as, \\(\\mathcal{L}_{trip} = \\max \\{0,\\mu +\\delta (f_{\\mathbf{q}},f_{\\mathbf{p}^{+}}) - \\delta (f_{\\mathbf{q}},f_{\\mathbf{p}^{-}})\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.357, + 0.469, + 0.466 + ], + "angle": 0, + "content": "Baseline for Image Captioning: Image captioning consists of an image encoder [59, 101], \\( f_{\\mathbf{p}} = \\mathcal{F}_{\\mathbf{p}}(\\mathbf{p}) \\) followed by an autoregressive textual decoder \\( (\\mathcal{F}_C) \\). Given the textual description comprises a sequence of words \\( \\mathbf{t} = \\{w_1,\\dots ,w_K\\} \\), we maximise the likelihood of a predicted word \\( (\\hat{w}_k) \\) at each step \\( (k) \\), conditioned on \\( f_{\\mathbf{p}} \\) as, \\( \\mathcal{L}_C = -\\sum_{k = 1}^{K}\\log [\\mathcal{F}_C(\\hat{w}_k = w_k|f_{\\mathbf{p}},w_1,\\dots ,w_{k - 1})] \\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.47, + 0.188, + 0.484 + ], + "angle": 0, + "content": "4.2. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.47, + 0.759 + ], + "angle": 0, + "content": "We aim to disentangle the feature representations from sketch, text, and photo modalities into a modality-agnostic and modality-specific component. While the modality-agnostic component holds semantic information to support cross-modal transfer, the modality-specific one holds information necessary during self-reconstruction; however, it lacks meaning in other modalities (e.g., grammatical knowledge in text). Achieving feature disentanglement across scene sketches, texts, and photos enables a multitude of downstream tasks like (i) SBIR - modality-agnostic sketch and photo features, (ii) TBIR - modality-agnostic text and photo, (iii) Sketch + Text-Based Image Retrieval - modality-agnostic sketch, text, and photo, (iv) Image Captioning - using the modality-agnostic photo to compute modality-specific text features, (v) Sketch Captioning - modality-agnostic sketch to compute modality-specific text, and (vi) Subjective Captioning - using modality-agnostic photo and sketch, to compute modality-specific text." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.764, + 0.462, + 0.78 + ], + "angle": 0, + "content": "4.3. Disentangling Modality Agnostic and Specific" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.902 + ], + "angle": 0, + "content": "While our disentangling method can be generalised to any number of modalities, for simplicity, we first show for \\(M = 2\\) modalities and later extend to \\(M \\geq 3\\). Consider a simple bimodal setup of sketch \\((\\mathbf{s} \\in \\mathbb{R}^{H \\times W \\times 3})\\) and text \\((\\mathbf{t} \\in \\mathbb{R}^{N \\times E})\\). Our goal is to split the feature representation \\(f_{\\mathbf{s}} = \\mathcal{F}_{\\mathbf{s}}(\\mathbf{s}) \\in \\mathbb{R}^{512}\\) and \\(f_{\\mathbf{t}} = \\mathcal{F}_{\\mathbf{t}}(\\mathbf{t}) \\in \\mathbb{R}^{512}\\) into a modality-agnostic and a modality-specific component as \\(f_{\\mathbf{s}} = [f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp}]\\), and \\(f_{\\mathbf{t}} = [f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp}]\\) respectively, where" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.891, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.295 + ], + "angle": 0, + "content": "Figure 4. Unlike typical neural networks that are unidirectional, data in conditional invertible neural networks \\((\\tau_{\\mathbf{k}})\\) can flow either (i) from modality-specific \\(f_{\\mathbf{k}}^{sp}\\) to a uniform distribution \\(\\eta\\) by conditioning on modality-agnostic \\(f_{\\mathbf{k}}^{ag}\\) during training, or (ii) from a sampled \\(\\eta\\) in uniform distribution to the modality-specific \\(f_{\\mathbf{k}}^{sp}\\) by conditioning on modality-agnostic \\(f_{\\mathbf{k}}^{ag}\\) during inference. The conditioning vector \\(f_{\\mathbf{k}}^{ag}\\) is injected into the conditional affinity coupling layers [28] of \\(\\tau_{\\mathbf{k}}\\) using any arbitrary network \\(\\mathcal{H}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.893, + 0.636 + ], + "angle": 0, + "content": "\\(f^{ag} \\in \\mathbb{R}^{480}\\) and \\(f^{sp} \\in \\mathbb{R}^{32}\\). Existing methods [82, 88] disentangle feature representations via (i) self reconstruction as \\(\\hat{\\mathbf{s}} = \\mathcal{D}_{\\mathbf{s}}([f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp}])\\) and \\(\\hat{\\mathbf{t}} = \\mathcal{D}_{\\mathbf{t}}([f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp}])\\) coupled with (ii) cross-modal translation \\(\\hat{\\mathbf{s}} = \\mathcal{D}_{\\mathbf{s}}([f_{\\mathbf{t}}^{ag}, f_{\\mathbf{s}}^{sp}])\\) and \\(\\hat{\\mathbf{t}} = \\mathcal{D}_{\\mathbf{t}}([f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{sp}])\\). However, using cross-modal translation with latent feature exchange across modalities is a cumbersome process that explodes with \\(\\mathbb{P}_2^M\\) permutations for \\(M\\) modalities, e.g., \\(M = 3\\) has \\(\\mathbb{P}_2^3 = 6\\) cross-modal translations. Adding multiple cross-modal translation losses makes optimisation difficult and computationally expensive. We break this compute barrier with linear \\((\\mathcal{O}(M))\\) complexity using an information bottleneck reinterpretation of modality-agnostic and modality-specific disentanglement. In particular, we maximise the mutual information \\(\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})\\) amongst modality-agnostic components, while minimising the same between modality-agnostic and modality-specific components \\(\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp})\\) and \\(\\mathcal{I}(f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp})\\), where \\(\\mathcal{I}(\\cdot, \\cdot)\\) denotes mutual information between two entities. Hence, unlike the previous \\(\\mathbb{P}_2^M\\) permutations, Eq. (1) has one agnostic \\(\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})\\), and \\(M\\) specific \\(\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})\\) losses. Formally, using a Langrange multiplier hyperparameter \\(\\beta\\) we have our loss objective as," + }, + { + "type": "equation", + "bbox": [ + 0.548, + 0.638, + 0.891, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathcal {I}} = - \\overbrace {\\mathcal {I} \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t}} ^ {a g}\\right)} ^ {\\text {a g n o s t i c}} + \\beta \\overbrace {\\sum_ {\\mathbf {k} \\in \\{\\mathbf {s} , \\mathbf {t} \\}}} ^ {\\text {s p e c i f i c}} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Minimise \\(\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})\\): We minimise the mutual information between modality-agnostic and modality-specific components using a conditional invertible [ ] neural network \\(\\tau_{\\mathbf{k}}\\). Unlike typical unidirectional neural networks \\(\\mathcal{F}: x \\to y\\), a conditional invertible neural network employs a sequence of bijective mapping operations like activation normalization (ActNorm) [45], Conditional Affine Coupling [28], and shuffling [45] to obtain \\(\\tau_{\\mathbf{k}}: x \\leftrightarrow y\\). During the forward pass (inference), we sample \\(\\eta \\in \\mathbb{R}^{32}\\) from a uniform prior distribution \\(\\mathbb{P}(\\eta)\\) to predict the modality-specific \\(f_{\\mathbf{k}}^{sp} \\in \\mathbb{R}^{32}\\) by conditioning on \\(f_{\\mathbf{k}}^{ag}\\) as, \\(f_{\\mathbf{k}}^{sp} = \\tau_{\\mathbf{k}}(\\eta | f_{\\mathbf{k}}^{ag})\\). In other words, during inference, we predict the modality-specific component of target from the modality-agnostic one of input using \\(\\tau_{\\mathbf{k}}\\). The target modality is" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10975" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.528, + 0.215 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.089, + 0.887, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.219, + 0.895, + 0.262 + ], + "angle": 0, + "content": "Figure 5. (Left): The modality-agnostic from sketch, or text, or both are used to retrieve from a gallery of photos. This enables a multitude of retrieval tasks like SBIR, TBIR, and STBIR. (Right): The modality-agnostic from photo, or sketch, or both are used to generate the text-specific component. Combining the modality-agnostic and inferred text-specific (via \\(\\tau_{\\mathrm{t}}\\)) enables image, or sketch, or subjective captioning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.269, + 0.473, + 0.408 + ], + "angle": 0, + "content": "then generated by combining the input-agnostic and target-specific components. The conditioning modality-agnostic vector \\( f_{\\mathbf{k}}^{ag} \\) is injected into the intermediate conditional affine coupling layers \\( \\mathcal{C}: x \\leftrightarrow y \\) as: \\( [x_1, x_2] = \\text{split}(x) \\), and \\( y = \\text{concat}[x_1, s_\\theta([x_1; h]) \\odot x_2 + t_\\theta([x_1; h])] \\), where, \\( h = \\mathcal{H}(f_{\\mathbf{k}}^{ag}) \\). A simple feed-forward neural network implements \\( s_\\theta, t_\\theta \\), and \\( \\mathcal{H} \\). We learn \\( \\tau_{\\mathbf{k}} \\) in the reverse pass (training) via negative log-likelihood (NLL Loss in Fig. 4) of \\( \\tau_{\\mathbf{k}}^{-1}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) \\) to predict a uniform distribution \\( \\mathbb{P}(\\eta) \\)," + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.412, + 0.47, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\mathbb {P} (\\eta) = \\mathbb {P} \\left(\\tau_ {\\mathbf {k}} ^ {- 1} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right)\\right) | \\det J _ {\\tau_ {\\mathbf {k}} ^ {- 1}} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right) | \\quad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.61 + ], + "angle": 0, + "content": "We show how learning \\(\\tau_{\\mathbf{k}}\\) in Eq. (2) minimises \\(\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})\\). \\(\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp}) = \\int_{f_{\\mathbf{k}}^{sp}} \\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) \\log \\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) / \\mathbb{P}(f_{\\mathbf{k}}^{sp})\\). Approximating modality-specific prior \\(\\mathbb{P}(f_{\\mathbf{k}}^{sp})\\) with variational distribution \\(\\mathbb{Q}(f_{\\mathbf{k}}^{sp})\\) gives the upper-bound, minimising which reduces the KL-divergence between \\(\\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag})\\) and \\(\\mathbb{Q}(f_{\\mathbf{k}}^{sp})\\) i.e., it encourages the disentanglement \\(\\mathbb{P}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp}) \\approx \\mathbb{P}(f_{\\mathbf{k}}^{ag}) \\cdot \\mathbb{P}(f_{\\mathbf{k}}^{sp})\\). The prior \\(\\mathbb{Q}(f_{\\mathbf{k}}^{sp})\\) is solved using \\(\\tau_{\\mathbf{k}}\\) to enforce disentanglement between modality-agnostic and modality-specific components, like that in Eq. (2), as the sum of negative-loglikelihood (NLL-Loss in Fig. 4) and log-determinant (see supplementary for proof)," + }, + { + "type": "equation", + "bbox": [ + 0.105, + 0.61, + 0.47, + 0.652 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\tau_ {\\mathbf {k}}} = - \\mathbb {E} _ {f _ {\\mathbf {k}} ^ {s p}} \\left\\{\\log \\mathrm {q} \\left(\\tau_ {\\mathbf {k}} ^ {- 1} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right)\\right) \\right. \\tag {3} \\\\ + \\log | \\det J _ {\\tau_ {\\mathbf {k}} ^ {- 1}} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right) | \\} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.732 + ], + "angle": 0, + "content": "Maximise \\(\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})\\): Here we show how minimising a constrastive based retrieval loss [94] between the modality-agnostic components of sketch and text will maximise their mutual information. We define contrastive loss matching modality-agnostic components of sketch and text as," + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.738, + 0.469, + 0.794 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {c l} ^ {\\mathbf {s}, \\mathbf {t}} = - \\mathbb {E} _ {f _ {\\mathbf {s}} ^ {s p}} \\left[ \\log \\frac {\\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {+}} ^ {a g}\\right)}{\\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {+}} ^ {a g}\\right) + \\sum_ {f _ {\\mathbf {t} ^ {-}} ^ {a g}} ^ {N - 1} \\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {-}} ^ {a g}\\right)} \\right] \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.904 + ], + "angle": 0, + "content": "where, \\(\\omega = \\exp (x^{T}\\mathbf{W}y)\\). For each modality-agnostic \\(f_{\\mathbf{s}}^{ag}\\) we sample a positive \\(f_{\\mathbf{t}^{+}}^{ag}\\) and \\((N - 1)\\) negative \\(f_{\\mathbf{t}^{-}}^{ag}\\) pairs. The contrastive loss in Eq. (4) is expressed as mutual information between \\(f_{\\mathbf{s}}^{ag}\\) and \\(f_{\\mathbf{t}}^{ag}\\) as, \\(\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}\\geq -\\mathcal{I}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{t}}^{ag}) + \\log (N)\\). Hence, to maximise the mutual information between modality-agnostic \\(f_{\\mathbf{s}}^{ag}\\) and \\(f_{\\mathbf{t}}^{ag}\\), we can maximise the tractable lower bound \\(\\log (N) - \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Total Loss for Bimodal Setup: The resulting loss \\((\\mathcal{L}_{tot})\\) for bimodal (sketch and text) setup comprise three loss objectives (i) self reconstruction loss \\(\\mathcal{L}_{rec}\\), (ii) contrastive loss between two modality-agnostic terms \\(\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}\\), and (iii) disentanglement between modality-agnostic and modality-specific components in each modality \\((\\mathbf{k})\\) \\((\\mathcal{L}_{\\tau_{\\mathbf{k}}})\\), as" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.362, + 0.892, + 0.401 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {r e c} = | | \\mathbf {s} - \\mathcal {D} _ {\\mathbf {s}} (\\mathcal {F} _ {\\mathbf {s}} (\\mathbf {s})) | | _ {2} + | | \\mathbf {t} - \\mathcal {D} _ {\\mathbf {t}} (\\mathcal {F} _ {\\mathbf {t}} (\\mathbf {t})) | | _ {2} \\tag {5} \\\\ \\mathcal {L} _ {t o t} = \\mathcal {L} _ {r e c} + \\mathcal {L} _ {c l} ^ {\\mathbf {s}, \\mathbf {t}} + \\beta [ \\mathcal {L} _ {\\tau_ {\\mathbf {s}}} + \\mathcal {L} _ {\\tau_ {\\mathbf {t}}} ] \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Extending to Three/More Modalities: Here we extend our bimodal setup in Sec. 4.3 to three or more modalities. (i) We compute the self-reconstruction loss for three modalities as \\(\\mathcal{L}_{rec} = \\sum_{\\mathbf{k}\\in \\{\\mathbf{s},\\mathbf{t},\\mathbf{p}\\}}||\\mathbf{k} - \\mathcal{D}_{\\mathbf{k}}(\\mathcal{F}_{\\mathbf{k}}(\\mathbf{k}))||_2\\) (ii) we minimise the mutual information between modality-agnostic and modality-specific components for sketch, text, and photo as, \\(\\mathcal{L}_{\\tau} = \\mathcal{L}_{\\tau_{\\mathrm{s}}} + \\mathcal{L}_{\\tau_{\\mathrm{t}}} + \\mathcal{L}_{\\tau_{\\mathrm{p}}}\\). (iii) However, our contrastive loss term \\(\\mathcal{L}_{cl}\\) that maximises the mutual information among modality-agnostic components can only compare two modalities. We can extend this naively to a three-modality setup as \\(\\mathcal{L}_{cl}^{tot} = \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}} + \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}} + \\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.818 + ], + "angle": 0, + "content": "Extending to three or more modalities, however, we notice our contrastive loss in Eq. (4) is defined for only b-modal setup \\((\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}\\) , or \\(\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}}\\) , or \\(\\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}\\) ). For example, given three modalities \\(S_{M} = \\{m_{1},m_{2},m_{3}\\}\\) , comparing only \\((m_{1},m_{2})\\) ignores \\(m_{3}\\) . This highlights a key limitation: it fails when we have a query in both \\((m_{1},m_{3})\\) to retrieve \\(m_{2}\\) (e.g., sketch+text for image retrieval). Now the research question boils down to - how can we model a function \\(\\mathcal{G}(\\cdot)\\) such that it can model either \\(m_{1}\\) , or \\(m_{3}\\) , or both \\((m_{1},m_{3})\\) to retrieve \\(m_{2}\\) . To design \\(\\mathcal{G}\\) , using naive addition as \\(\\mathcal{G}(m_1,m_3) = m_1 + m_3\\) does not handle overlapping or conflicting information in \\(m_{1}\\) and \\(m_{3}\\) [58]. While, concatenation \\(\\mathcal{G}(m_1,m_3) = \\mathrm{concat}[m_1,m_3]\\) computes interaction between \\((m_{1},m_{3})\\) , it forces to provide both \\(m_{1}\\) and \\(m_{3}\\) during inference; thereby failing to model either \\(m_{1}\\) , or \\(m_{3}\\) , or both \\((m_{1},m_{3})\\)" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.821, + 0.804, + 0.837 + ], + "angle": 0, + "content": "4.4. Modelling Optional Sketch or Text" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.838, + 0.892, + 0.868 + ], + "angle": 0, + "content": "We propose a simple approach to design \\(\\mathcal{G}\\) that optionally models either \\(m_{1}\\), or \\(m_{3}\\), or both \\((m_{1}, m_{3})\\), and handles" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2When signals \\((m_{1},m_{3})\\) are similar or complementary \\(\\mathcal{G}\\) should strengthen decision; when signals conflict \\(\\mathcal{G}\\) should filter unreliable ones." + }, + { + "type": "footer", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10976" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.152 + ], + "angle": 0, + "content": "overlapping or conflicting information. Our proposed \\(\\mathcal{G}\\) comprises a multihead cross-attention module \\(\\mathrm{MH}(\\cdot)\\) followed by an attention-based pooling \\(\\mathrm{PMA}(\\cdot)\\) as, \\(f_{M} = \\mathrm{PMA}(H_{M})\\); where \\(H_{M} = \\mathrm{MH}(S_{M})\\), and \\(S_{M} = \\{m_{1}, m_{3}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.153, + 0.468, + 0.424 + ], + "angle": 0, + "content": "Our \\(\\mathrm{MH}(\\cdot)\\) is order-invariant and independent of the number \\((M)\\) of input modalities defined as \\(\\mathrm{MH}(X) = \\sigma (XX^T)X\\); where \\(\\sigma\\) is scaled-softmax, \\(X^T\\) is transpose of \\(X\\), and \\(X\\in \\mathbb{R}^{M\\times 480}\\) is a list of modality-agnostic components \\(m_{1}\\), or \\(m_{3}\\) with \\(\\mathbb{R}^{1\\times 480}\\), or \\((m_1,m_3)\\in \\mathbb{R}^{2\\times 480}\\) in query. The cross-attention in \\(\\mathrm{MH}(\\cdot)\\) interacts across query modalities to compute mutually agreeing information between \\((m_{1},m_{3})\\) as, \\(H_{M}\\in \\mathbb{R}^{2\\times 480}\\). Next, we use an order-invariant attention-based pooling \\(\\mathrm{PMA}: \\mathbb{R}^{2\\times 480}\\to \\mathbb{R}^{1\\times 480}\\) with a learned seed vector \\(\\mathcal{P}\\in \\mathbb{R}^{1\\times 480}\\) to aggregate mutually agreeing \\(H_{M}\\) as, \\(f_{M} = \\mathrm{PMA}(H_{M}) = \\sigma (\\mathcal{P}H_{M}^{T})H_{M}\\). Hence, using our proposed fusion module \\(\\mathcal{G}\\), we adapt our contrastive loss defined for only a pair of modality-agnostic components in Eq. (4) as \\(\\mathcal{L}_{cl}^{tot} = \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}} + \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}} + \\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}\\) to jointly model sketch-text-photo (or more) modality-agnostic as: \\(\\mathcal{L}_{cls}^{tot} = \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{t}}^{ag}),f_{\\mathbf{p}}^{ag}) + \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{p}}^{ag}),f_{\\mathbf{t}}^{ag}) + \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{p}}^{ag},f_{\\mathbf{t}}^{ag}),f_{\\mathbf{s}}^{ag})\\). For a generalised solution involving more than three modalities \\((M > 3)\\), see supplementary." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.428, + 0.468, + 0.699 + ], + "angle": 0, + "content": "Inference Data Flow: We describe the inference data flow in Fig. 5. For retrieval tasks, we first compute the modality-agnostic component of query sketch and text \\((f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})\\), and a gallery of photos \\(\\{f_{\\mathbf{p}_1}^{ag}, f_{\\mathbf{p}_2}^{ag}, \\ldots, f_{\\mathbf{p}_{\\mathbf{N}}}^{ag}\\}\\). Next, a combined representation for either only sketch \\((f_{\\mathbf{s}}^{ag})\\), or only text \\((f_{\\mathbf{t}}^{ag})\\), or both \\((f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})\\) is computed using multihead cross attention \\(\\mathrm{MH}(\\cdot)\\) followed by attention-based pooling \\(\\mathrm{PMA}(\\cdot)\\) defined in Sec. 4.4 to get \\(f_{\\mathbf{st}^*}^{ag}\\). Finally, we find the minimum distance between the combined \\(f_{\\mathbf{st}^*}^{ag}\\) and modality-agnostic component of photo \\(f_{\\mathbf{p}_i}^{ag}\\) as \\(\\omega(f_{\\mathbf{st}^*}^{ag}, f_{\\mathbf{p}_i}^{ag})\\) defined in Eq. (4). For captioning, we additionally use the text-specific conditional invertible neural network \\(\\tau_t\\) to generate the target modality-specific text (e.g., grammatical structure etc.) from input modality-agnostic comprising of only photo \\((f_{\\mathbf{p}}^{ag})\\) for image captioning, only sketch \\((f_{\\mathbf{s}}^{ag})\\) for sketch captioning, or both photo and sketch \\((f_{\\mathbf{p}}^{ag}, f_{\\mathbf{s}}^{ag})\\) for subjective captioning (i.e., generate image captions by conditioning on the input sketch)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.713, + 0.208, + 0.729 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Datasets: We use two scene sketch datasets with fine-grained alignment among sketch, text, and photo: (i) SketchyCOCO [34] contains 14,081 scene sketch-photo pairs. The photos are taken from MS-COCO [55] comprising \\(164K\\) photos with paired texts. However, most sketches in SketchyCOCO [34] contain less than one foreground instance. Following [57], we filter SketchyCOCO with one foreground instance to get 1015/210 train/test scene sketches. (ii) Unlike SketchyCOCO [34], where the scene sketches are synthetically generated, FS-COCO [19] includes 7000/3000 train/test human-drawn scene sketches" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.794, + 0.107 + ], + "angle": 0, + "content": "with a paired textual description of sketches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.447 + ], + "angle": 0, + "content": "Implementation Details: Our model is implemented in PyTorch using 11GB Nvidia RTX 2080-Super GPU. First, we pre-train the image encoder and text decoder for image captioning using 82,783 photo-text pairs (excluding the photos common in SketchyCOCO and FS-COCO) for 15 epochs. Next, we fine-tune on either SketchyCOCO [34], or FS-COCO [19] for 200 epochs using Adam optimiser with learning rate \\(1e - 4\\), and batch size 64. Our photo \\((\\mathcal{F}_{\\mathbf{p}})\\) and sketch \\((\\mathcal{F}_{\\mathrm{s}})\\) encoders use ImageNet pretrained VGG-16 [85]. For simplicity, we encode text using a bidirectional GRU unit with 512 hidden units. Our text decoder [43] is a single-layer autoregressive LSTM decoder that predicts a probability distribution over a fixed vocabulary (10,010 words) at every time step. For the image/sketch decoder, we use two separate GAN [109] networks that synthesise sketch/image of size \\(64\\times 64\\), respectively. For brevity, we avoid realistic sketch/image generation due to the challenging scene complexity [19]. Hence we do not use a discriminator module for high-quality, sharp reconstruction [110]. Finally, our conditionally invertible neural network comprises 16 alternating affine coupling [29], activation normalisation [45], and switch layers [29]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Evaluation Metric: In line with FG-SBIR research, we use Acc.@q [81] defined as the percentage of sketches having a true matched photo in the top-q list. For sketch/image/subjective captioning, we use standard metrics BELU (B) 1-4 [67], CIDEr (C) [95], ROUGE (R) [53], METEOR (M) [25], and SPICE [2]. Following [96], we generate 100 candidate captions and employ consensus reranking using CIDEr to select the best candidate caption." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Competitors: We compare against (i) existing state-of-the-art methods that align two modalities (S2): For SBIR, Triplet-SN [107] employs Sketch-A-Net [108] backbone trained using triplet loss. HOLEF [87] adds spatial attention with a higher-order ranking loss. SketchyS [115] replaces Sketch-A-Net in Triplet-SN with VGG-16 [85] and an auxiliary category-level cross-entropy. SceneS [57] uses GCN [46] to model scene sketch layout information. For TBIR, CLIP [73] is trained with text using transformer [83] and photo using vision transformer [30] on 400 million text-photo pairs. CLIP-LN fine-tunes CLIP by training only layer normalisation parameters [4] with learning rate 0.00001. For image/sketch captioning, SAT [101] is one of the simplest but seminal works using a CNN-LSTM encoder-decoder approach similar to ours. GMM-CVAE [96] employs a conditional variational autoencoder with a Gaussian mixture model. LNFMM [61] is similar to ours that splits information into modality-agnostic and modality-specific components using conditional invertible neural network, ClipCap [65] employs CLIP [73] for image encoding followed by GPT-2 [74] for text decoding. A learned" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "10977" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 2. Quantitative results combining sketch and text for image retrieval (FG-STBIR) on two scene sketch datasets [19, 34]." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.119, + 0.472, + 0.202 + ], + "angle": 0, + "content": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S3QST [86]38.987.925.154.5
SCM [3]38.587.324.354.1
BCrossAtt [83]39.188.225.354.8
Proposed39.588.725.755.2
" + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.212, + 0.248, + 0.224 + ], + "angle": 0, + "content": "Boys are playing with frisbee disc." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.226, + 0.143, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.15, + 0.227, + 0.214, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.217, + 0.227, + 0.277, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.227, + 0.34, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.227, + 0.403, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.227, + 0.467, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.087, + 0.282, + 0.243, + 0.293 + ], + "angle": 0, + "content": "A boy is holding a baseball bat." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.296, + 0.143, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.152, + 0.297, + 0.213, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.297, + 0.279, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.297, + 0.341, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.297, + 0.403, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.405, + 0.297, + 0.468, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.352, + 0.469, + 0.381 + ], + "angle": 0, + "content": "Figure 6. Qualitative results of combining sketch and text as query for image retrieval on FSCOCO [19]. See supplementary for more." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.47, + 0.604 + ], + "angle": 0, + "content": "mapping module translates CLIP embeddings to GPT-2. (ii) We compare against methods that align 3 modalities (S3): For STBIR, QST [86] extends triplet loss in Triplet-SN to quadruplet loss that combines sketch and text for image retrieval. SCM uses element-wise addition to combine sketch and text from ResNet-18 [39] with weight sharing across sketch, text, and photo from ResBlock4 onwards [3]. (iii) We design baselines (B): For STBIR, CrossAtt employs cross-attention [83] to combine sketch and text. For subjective captioning, MulCap combines sketch \\((f_{\\mathbf{s}}^{ag})\\) and photo \\((f_{\\mathbf{p}}^{ag})\\) via element-wise multiplication as in [14]. CrossCap optionally fuse photo, sketch, or both using cross-attention. CatCap use feature concatenation [71] of guiding sketch \\((f_{\\mathbf{s}}^{ag})\\) signal with photo \\((f_{\\mathbf{p}}^{ag})\\) to generate captions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.607, + 0.469, + 0.623 + ], + "angle": 0, + "content": "5.1. Combining Sketch and Text for Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.47, + 0.85 + ], + "angle": 0, + "content": "Fig. 2 shows that for some instances, sketch is a better query, whereas text is better for others. Hence, to achieve best of both modalities, we examine the complimentary nature by combining sketch and text for image retrieval. Table 2 shows (i) SCM gives the lowest performance due to naive element-wise addition of potentially overlapping and conflicting information [58] from sketch and text. (ii) QST improves slightly upon SCM by replacing naive elementwise addition with a weighted summation (0.8 for sketch modality). (iii) CrossAtt outperforms all baselines by using a cross-attention between sketch and text to resolve overlapping/conflict information [58]. (iv) Our proposed method gives the highest performance due to cross-attention that model sketch-text interaction and disentanglement to drive out modality-specific information for cross-modal retrieval." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.855, + 0.451, + 0.871 + ], + "angle": 0, + "content": "5.2. Optionally using Sketch for Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Our method allows drawing only easy-to-sketch scenes instead of using both sketch and text forcibly. Table 3 com" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.09, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 3. Quantitative results using only sketch for image retrieval (FG-SBIR) on two scene sketch datasets [19, 34]." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.119, + 0.892, + 0.25 + ], + "angle": 0, + "content": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2Triplet-SN [107]6.232.94.721.0
HOLEF [87]6.240.74.921.7
SketchyS [115]36.578.623.052.3
SceneS [57]31.986.2--
S3QST [86]37.487.123.652.9
SCM [3]37.386.823.452.6
BCrossAtt37.987.423.753.5
Proposed38.287.624.153.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.261, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Table 4. Quantitative results of fine-grained text-based image retrieval (FG-TBIR) on two scene sketch datasets [19,34]." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.291, + 0.897, + 0.398 + ], + "angle": 0, + "content": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2CLIP [73]21.050.911.535.3
CLIP-LN [73]22.152.314.836.6
S3QST [86]11.131.17.223.6
SCM [3]10.731.06.923.1
BCrossAtt20.151.012.535.8
Proposed21.551.613.736.3
" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.408, + 0.572, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.573, + 0.411, + 0.691, + 0.428 + ], + "angle": 0, + "content": "Sheep are grazing on a green hill." + }, + { + "type": "image_caption", + "bbox": [ + 0.603, + 0.432, + 0.675, + 0.449 + ], + "angle": 0, + "content": "A herd of sheep on grassland." + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.409, + 0.769, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.411, + 0.885, + 0.428 + ], + "angle": 0, + "content": "Black and white photo of people holding umbrellas." + }, + { + "type": "image_caption", + "bbox": [ + 0.791, + 0.432, + 0.884, + 0.449 + ], + "angle": 0, + "content": "Three people are walking under umbrella on field." + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.45, + 0.523, + 0.489 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.524, + 0.45, + 0.591, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.612, + 0.458, + 0.684, + 0.483 + ], + "angle": 0, + "content": "Sheep are grazing beyond the fence on a hill." + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.46, + 0.72, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.721, + 0.46, + 0.77, + 0.488 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.814, + 0.457, + 0.878, + 0.484 + ], + "angle": 0, + "content": "Three people are walking holding umbrella." + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.492, + 0.891, + 0.52 + ], + "angle": 0, + "content": "Figure 7. Qualitative results for image captioning v/s subjective captioning on FS-COCO [19]. See supplementary for more." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.759 + ], + "angle": 0, + "content": "pares against methods that specialise on two-modalities (S2), three-modalities (S3), and our proposed baselines (B). We observe (i) training on three modalities (sketch, text, and photo) in S3 generally outperforms those trained using only sketch and photo (S2). This can be attributed to learning generalisable features in multi-modal setup [3]. (ii) \\( QST \\) in S3 outperforms SCM indicating quadruplet loss is a better training objective than naive element-wise addition when combining sketch, text, and photo. (iii) Performance difference between CrossAttn and \\( QST \\) is not as significant as in FG-STBIR (Table 2) as during inference, we only use sketch, omitting the cross-attention module. (iv) Our method outperforms S2, S3, and B even for two-modality setup thanks to disentanglement that eliminates confounding [3] modality-specific information." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.764, + 0.856, + 0.78 + ], + "angle": 0, + "content": "5.3. Optionally using Text for Image Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "While some information is best expressed by drawing, others, like colour, is best described via text. From Table 4, we observe (i) Given the same train/test split, sketches outperform text as a query modality for fine-grained image retrieval. (ii) CLIP and CLIP-LN outperforms all competitors due to superior pre-trained weights using 400 million text-image pairs. (iii) The proposed method outperforms most methods due to disentanglement that drives out modality-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10978" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.167, + 0.09, + 0.802, + 0.103 + ], + "angle": 0, + "content": "Table 5. Quantitative results of standard captioning metrics on MS-COCO [55] and FS-COCO [19] dataset." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.105, + 0.887, + 0.235 + ], + "angle": 0, + "content": "
MethodImage CaptioningSketch CaptioningSubjective Captioning
B-1B-4MRCSB-1B-4MRCSB-1B-4MRCS
S2SAT [101]71.825.023.0---46.213.717.144.969.414.5------
GMM-CVAE [96]72.930.724.252.598.617.749.615.518.348.777.615.5------
AG-CVAE [96]73.231.124.552.8100.118.850.916.018.949.180.515.8------
LNFMM [61]74.731.824.753.8105.518.852.216.721.052.990.116.0------
BMulCap74.933.225.554.9106.019.553.917.021.053.897.316.778.738.628.559.8110.721.7
CatCap------------77.638.028.357.7108.021.2
CrossCap75.534.326.155.4106.720.154.317.921.454.3100.317.579.239.328.459.5117.322.1
Proposed76.035.926.956.9107.020.956.919.321.656.6106.518.981.342.730.161.6121.623.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.249, + 0.468, + 0.275 + ], + "angle": 0, + "content": "Table 6. Ablation study on FG-STBIR and Subjective Captioning using FSCOCO [19]. CA denotes cross-attention in Sec. 4.4." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.277, + 0.466, + 0.348 + ], + "angle": 0, + "content": "
τkCACLAcc.@1Acc.@10B-1C
XXX24.553.773.3100.1
✓XX24.954.077.9108.5
✓✓X25.554.980.6119.3
✓✓✓25.755.281.3121.6
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.468, + 0.422 + ], + "angle": 0, + "content": "specific components. Although CLIP [73] outperforms the proposed method, we deliberately use a simple and easy-to-reproduce GRU/VGG-16 architectures for text/photo encoders, and train on a much smaller data [19,34] than CLIP." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.426, + 0.331, + 0.442 + ], + "angle": 0, + "content": "5.4. Image or Sketch Captioning" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.442, + 0.47, + 0.79 + ], + "angle": 0, + "content": "In addition to disentanglement for cross-modal retrieval tasks (e.g., FG-SBIR, FG-TBIR), our conditional invertible neural network \\(\\tau_{\\mathrm{t}}\\) can also generate text-specific information (Fig. 4) to support generative tasks like image/sketch captioning. We generate 100 candidate captions using (i) beam search for SAT, MulCap, CrossCap, CatCap, and (ii) sampling from prior distribution for GMM-CVAE, AG-CVAE, LNFMM, and our proposed method. From Table 5, we observe (i) our baselines adopting recent techniques like vision-transformer [30] outperforms (S2) – recent but complex approaches like LNFMM, AG-CVAE, and the older yet seminal work like SAT. (ii) Performance gap between MulCap and CrossCap is insignificant for two-modality setups (photo to text, or sketch to text) since they primarily differentiate by their multi-modal (photo and sketch) fusion strategy. (iii) In spite of using a photo/sketch encoder and text decoder similar to our simple competitor SAT, our proposed method performs competitively with complex methods like LNFMM, AG-CVAE, and latest approaches using vision-transformers [30], like CrossCap. This shows the significant contribution of (i) disentangling modality-specific and modality-agnostic components from photo/sketch, and (ii) modelling text-specific prior for generative tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.795, + 0.391, + 0.81 + ], + "angle": 0, + "content": "5.5. Sketch Based Subjective Captioning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "As defined in Sec. 3.2, unlike traditional captioning frameworks that factually describe an image or sketch in a neutral tone, subjective captioning focus on drawing out a user's intentions, salient objects, and artistic interpretations [38]. Being the first method to use scene-level sketch as a guiding signal for captioning, we follow controllable caption-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.25, + 0.892, + 0.448 + ], + "angle": 0, + "content": "ing literature [89] to adopt three baselines (B) that inject the sketch conditioning signal into the captioning pipeline. From Table 5, we observe (i) MulCap outperforms CatCap, thereby supporting previous observations [14] of elementwise multiplication being more effective than concatenation. (ii) CrossAtt outperforms all baselines (B) and two-modality SOTAs (S2) by using a cross-attention mechanism to fuse sketch and photo by modelling sketch-photo interactions to resolve overlapping or conflicting information. Our proposed method is similar to CrossAtt using cross-attention (Sec. 4.4) but also enriches the modality-agnostic sketch and photo features by removing the confounding modality-specific information to offer the best performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.451, + 0.605, + 0.464 + ], + "angle": 0, + "content": "5.6. Ablation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.709 + ], + "angle": 0, + "content": "In Table 6, we evaluate the contribution of each key design choice on FG-STBIR and Subjective captioning using FS-COCO [19]. (i) Replacing cross-attention in Sec. 4.4 with quadruplet loss [86] leads to a performance drop by \\(0.6 / 0.9 / 2.7 / 10.8\\) in Acc.@1/Acc.@10/B-1/C metrics respectively to show the importance of modelling the interaction between sketch and text. (ii) Replacing contrastive loss-based query-photo score in Eq. (4) with a simple triplet loss leads to a performance drop by \\(0.2 / 0.3 / 0.7 / 2.3\\) due to the inability of unimodal L2-based triplet loss to model highly complex scene information [94]. (iii) Finally, removing the conditional invertible neural networks \\((\\tau_{\\mathbf{k}})\\) drops retrieval and captioning by \\(0.4 / 0.3 / 4.6 / 8.4\\) due to percolation of the confounding modality-specific information in cross-modal tasks [3] and the inability to generate text-specific information from photo and sketch respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.717, + 0.618, + 0.731 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We have studied for the first time the trilogy relationship among scene-level sketch, text, and photo by introducing scene-sketch in the context of scene understanding. We proposed a unified framework to jointly model sketch, text, and photo that seamlessly support several downstream tasks like fine-grained sketch-based image retrieval, fine-grained sketch and text based image retrieval, sketch captioning, and subjective captioning, among others. Future research can explore challenging downstream tasks such as scene-level sketch-based image generation, sketch and text based image generation, and text-based sketch generation tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10979" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.093, + 0.117, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Harsh Agarwal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. In ICCV, 2019. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.093, + 0.175, + 0.472, + 0.216 + ], + "angle": 0, + "content": "[2] Peter Anderson, Basura Fernando, Mark Johnson, and Stephen Gould. Spice: semantic propositional image caption evaluation. 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The result is a complete trilogy of scene representation from three diverse and complementary modalities - sketch, photo, and text. Instead of learning a rigid three-way embedding and be done with it, we focus on learning a flexible joint embedding that fully supports the "optionality" that this complementarity brings. Our embedding supports optionality on two axes: (i) optionality across modalities - use any combination of modalities as query for downstream tasks like retrieval, (ii) optionality across tasks - simultaneously utilising the embedding for either discriminative (e.g., retrieval) or generative tasks (e.g., captioning). This provides flexibility to end-users by exploiting the best of each modality, therefore serving the very purpose behind our proposal of a trilogy in the first place. First, a combination of information-bottleneck and conditional invertible neural networks disentangle the modality-specific component from modality-agnostic in sketch, photo, and text. Second, the modality-agnostic instances from sketch, photo, and text are synergised using a modified cross-attention. Once learned, we show our embedding can accommodate a multi-facet of scene-related tasks, including those enabled for the first time by the inclusion of sketch, all without any task-specific modifications. Project Page: https://pinakinathc.github.io/scenetrilogy + +# 1. Introduction + +Scene understanding sits at the very core of computer vision. As object-level research matures [24, 32], an encouraging shift can be observed in recent years on scene-level tasks, e.g., scene recognition [113], scene captioning [55], scene synthesis [34], and scene retrieval [13, 57]. + +Scene research has generally progressed from that of single modality [113, 114] to the very recent focus on multimodality [3, 13, 19]. The latter setting not only triggered a series of practical applications [34, 57, 101, 115] but im + +![](images/c366e65a4075c2d75ced09c2e2c92910a3077fce9b502378c9447ba599c2f041.jpg) +$f_{\mathrm{s}}^{sp}$ sketch specific $f_{\mathrm{t}}^{sp}$ text specific $f_{\mathrm{p}}^{sp}$ photo specific $f^{ag}$ modality agnostic +Figure 1. Some scenes are easy to describe via sketch; for others, text is better. We provide the option to sketch, write, or both (sketch + text). For “optionality” across tasks, we disentangle sketch, text, and photo into a discriminative (e.g., retrieval) part $f^{ag}$ shared across modalities, and a generative (e.g., captioning) part specific to one modality ( $f_{\mathbf{s}}^{sp}$ , $f_{\mathbf{t}}^{sp}$ , $f_{\mathbf{P}}^{sp}$ ). This supports a multifacet of scene-related tasks without task-specific modifications. + +portantly helped to cast insights into scene understanding on a conceptual level (i.e., what is really being perceived by humans). To date, research on multi-modal scene understanding has mainly focused on two modalities – text and photo [59, 61, 62], via applications such as text-based scene retrieval (TBIR) [35], and scene captioning [23, 61, 62]. + +This paper follows the said trend of multi-modal scene understanding and extend it to also include human scene-sketch. Sketch is identified because of its unique characteristics of being both expressive and subjective, evident in an abundance of object-level sketch research [11], and very recently on scene-level [19]. To verify there is indeed useful complementarity that sketch can bring to multi-modal scene understanding, we first conducted two pilot studies (i) on expressivity, we compare text and sketch in terms of scene image retrieval, and (ii) on subjectivity, we test a novel task of subjective captioning where sketch or parts-of-speech [26] are used as guidance for image captioning. On (i), results show there is significant disagreement in terms of retrieval accuracy when one is used as query over the other, + +indicating there is complementary information between the two modalities. On (ii), sketch is shown to offer more subjectivity as a guiding signal than text, when quantified using common metrics such as BELU-4 [67] and CIDEr [95]. + +To fully explore the complementarity of all three modalities, we desire a flexible joint embedding that best sustains "optionality" across modalities, and also across tasks. The former enables end-users to use any combination of modalities (e.g., only sketch, only text, or both sketch+text) as a query for downstream tasks; and the latter provides option of utilising the learned embedding for both discriminative (e.g., retrieval) and generative problems (e.g., captioning). + +This desired level of "optionality" is however not achievable via naive three-way joint embeddings common in the literature [3, 13, 19]. Instead, we advocate a three-way disentanglement (Fig. 1(b)), where each of the three modalities is disentangled into their modality-specific component ( $f_{\mathbf{s}}^{sp}$ , $f_{\mathbf{p}}^{sp}$ , $f_{\mathbf{t}}^{sp}$ , for sketch, photo and text), and a shared modality-agnostic component ( $f^{ag}$ ). The idea is that modality-specific will hold information specific to each modality (e.g., drawing style for sketch, texture for photo, and grammatical knowledge for text). It follows that filtering away modality-specific parts from each of the three modalities gives a shared modality-agnostic part that carries shared abstract semantic across all three modalities, (as shown in Fig. 1(b)). How optionality is supported in such a disentangled space then becomes trivial (Fig. 1(c),(d)). To achieve optionality across tasks, we simply use modality-agnostic information as the joint embedding to perform discriminative tasks (e.g., cross-modal retrieval), and for cross-modal generative tasks (e.g., captioning), we just combine modality-agnostic information (from source) with modality-specific (from target) to generate the target modality. Optionality across modality is a little harder, where we make use of a cross-attention [50] mechanism to capture the synergy across the modality-agnostic components. + +Benefiting from our optionality-enabled embedding, we can perform a multi-facet of tasks without any task-specific modifications: (i) Fig. 1 (c) show cross-modal discriminative tasks such as sketch-based image retrieval (SBIR) using $(f_{\mathbf{s}}^{ag} \leftrightarrow f_{\mathbf{p}}^{ag})$ , text-based image retrieval (TBIR) using $(f_{\mathbf{t}}^{ag} \leftrightarrow f_{\mathbf{p}}^{ag})$ , or sketch+text based image retrieval (STBIR) using $(f_{\mathbf{s}}^{ag} + f_{\mathbf{t}}^{ag} \leftrightarrow f_{\mathbf{p}}^{ag})$ . (ii) Fig. 1 (d) show cross-modal generative tasks such as image captioning (photo branch) using $f_{\mathbf{p}}^{ag} + f_{\mathbf{t}}^{sp} \rightarrow f_{\mathbf{t}}$ to generate textual descriptions $f_{\mathbf{t}}$ . Similarly, for sketch captioning (sketch branch) we use $f_{\mathbf{s}}^{ag} + f_{\mathbf{t}}^{sp} \rightarrow f_{\mathbf{t}}$ . (iii) Last but not least, to demonstrate what the expressiveness of human sketch can bring to scene understanding, we introduce a novel task of subjective captioning where we guide image captioning using sketch as a signal (subjective branch) as $f_{\mathbf{p}}^{ag} + f_{\mathbf{s}}^{ag} \rightarrow f_{\mathbf{t}}$ . + +In summary, our contributions are: (i) We extend multi-modal scene understanding to include human scene + +sketches, thereby completing a trilogy of scene representation from three diverse and complementary modalities. (ii) We provide optionality to end-users by learning a flexible joint embedding that supports: optionality across modalities and optionality across tasks. (iii) Using computationally efficient techniques like information bottleneck, conditionally invertible neural networks, and modified crossattention mechanism, we model this flexible joint embedding. (iv) Once learned, our embedding accommodates a multi-facet of scene-related tasks like retrieval, captioning. + +# 2. Related Works + +Sketch for Visual Understanding: Hand-drawn sketches enriched with human visual perception cues have facilitated several downstream visual understanding tasks. Apart from the widely explored SBIR [10, 22], sketch has shown potential on object localisation [18], segmentation [72], image/video synthesis [48], representation learning [79], 3D shape retrieval/modelling [20], medical image analysis [47, 97], etc. [102]. Sketches are also useful in the creative industry like artistic image editing [105] and animation [100]. Unlike photos that are passively captured by a camera, sketches are drawn by humans that actively stimulate intelligence with pictorial-style drawing games [8]. While text has been widely used for human expression, in this paper, we show freehand sketches can provide complimentary or symbiotic information for visual understanding. + +Sketch-Based Image Retrieval (SBIR): SBIR retrieves a paired photo given a query sketch. Sketches offer visual description that commences the avenues of category-level [27, 78, 106] or fine-grained instance-level (FG-SBIR) [6, 9, 12] retrieval. SBIR typically employs deep triplet-ranking based siamese networks to learn a joint embedding space [107]. Contemporary research emerged towards zero-shot SBIR [27, 80], cross-domain translation [66], on-the-fly retrieval [12], semi-supervised [6], self-supervised [7], meta-learning [11] etc. As research on object-level SBIR matured, focus shifted towards the more practical scene-level SBIR [76] with GCN [57], and optimal transport [17]. The onset of scene sketch datasets [19, 34, 115] revealed further insights into implicit human-sketching strategies [19]. + +Text-Based Image Retrieval (TBIR): Learning image-text joint embedding space with ranking loss [31, 43, 70] received considerable attention. Further improvements used mining hardest negative pairs for triplet loss [33], cross-modal adaptive message passing [98], probabilistic one-tomany representations [21] etc. Despite text lacking visual cues, million-scale paired image-text datasets have made TBIR competitive due to power scaling laws [63]. This inspired large-scale methods like Oscar [52], and CLIP [73]. In this paper, we augment TBIR with sketches to provide the creativity and freedom of expression intrinsic to sketches. + +Multi-Modality in Computer Vision: Multi-modal learning (MML) aims at developing models that can extract, interpret, and reason on information from various modalities characterised by different statistical properties such as text, sketch, or text+sketch. Contemporary research studied MML in vision via image and text [40], image to scene graph [36], etc. [103]. MML faces challenges like cross-modal alignment [42], or efficiency over data [92] and compute [44]. It is useful when data in one modality is inaccessible [3] for privacy or logistic reasons (e.g., hospital), but abundantly available in other modalities (photos in MS-COCO [55]). Often, some modalities are preferred over others for human-machine communication, like some concepts are easier to express in texts [60], while others prefer sketches [54] or both [76] (Fig. 1). In this paper, we learn cross-modal representation [104] that works using either one modality (text/sketch) or both. + +Disentangled Representation for Multi-modality: Disentangling modality-agnostic from modality-specific residual factors is important for MML [41, 93]. Modality-agnostic information is useful for cross-modal transfer like semantics-based retrieval and pattern recognition [41] but holds no meaning for tasks specific to one modality like image-style or speaker information [91]. Disentanglement was explored where factors of variation are either known (e.g., facial poses [90]) and individually supervised [75], partially known [82], or unknown (e.g., drawing style [82]) and learned unsupervised using isotropic Gaussian prior [77] or information-theoric regularisation [16]. Our method aligns with the unknown setup where factors particular to sketch, text, and image are discovered unsupervised. + +Image Captioning: This has emerged from predicting syntactically correct descriptions [89, 112] to tackling data scarcity [1, 49], and addressing user requirements [68, 69]. Predicted captions evolved from being factual in a neutral tone to (i) controllable using textual verbs [15], part-of-speech tag [26], or mouse trace [64, 71], and (ii) personalised captioning [84, 111] that learns user's active vocabulary, and writing style. Our method can (i) generate factual captions from images/sketches and (ii) extend controllable captioning paradigm by injecting saliency via sketch. + +# 3. Pilot Study + +# 3.1. Sketch vs. Text for Retrieval + +![](images/7963576892998dd92d7f442b811038697195c10556c904473433a8339ef3d7f2.jpg) +Figure 2. We compare SBIR [107] vs. TBIR [73] on FS-COCO [19] where retrieval rank is plotted in log-scale (see Supplemental for more details). While sketch is a better query for some instances (lower retrieval rank), for others text is better. + +Text can convey colour information, or object categories, but is cumbersome to describe fine-grained details, multiple objects, or complex shapes $[86]^{1}$ . While sketch can depict complex shapes, multiple objects, and spatial alignment [19], not all objects are easy to draw ('donkey' vs. 'horse'). Fig. 2 shows this trade-off between sketch vs. text for image retrieval. We find an optimal fusion between sketch and text to derive best of both modalities along with the ability to optionally use only sketch, only text, or both. + +Table 1. Comparing alternative guiding signal like POS (part-of-speech) [26], Mouse Trace [64], and Freehand Sketches [19]. + +
SignalB-1B-4MRCS
POS [26]w/o73.231.124.552.8100.117.9
w/73.931.625.553.2104.518.8
Δ0.70.51.00.44.40.9
Trace [64]w/o32.28.1-31.729.325.7
w/52.224.6-48.3106.536.5
Δ2016.5-16.677.210.8
Sketchw/o74.731.824.753.8105.518.8
w/81.342.730.161.6121.623.5
Δ6.610.95.47.816.14.7
+ +# 3.2. Subjectivity for Captioning + +Unlike traditional image captioning [62, 96] that generates factual captions in neutral tone, subjective captioning adapts the predicted captions using a guiding signal that specifies priorities on what should be described [89]. The signal is injected via feature concatenation [26], or cross-attention mechanism [64]. Applications of subjective captioning include medical report generation using disease tags to generate real style reports [56], art descriptions [5], and assistive technologies for the visually impaired [37,99]. In this paper, we advocate for sketch as a guiding signal to depict salient objects and express artistic interpretations [38]. We compare the performance (see supplementary for details) using guiding signals like POS (parts-of-speech) [26], mouse trace [64], or freehand sketches [19]. Following [64], we inject the guiding signal into the image captioning pipeline via cross-attention mechanism. As evident from Table 1, while sketch is competitive with mouse traces, it is a better signal than POS. However, unlike mouse trace, sketch can depict artistic interpretation [5] that makes it a more flexible and robust guiding signal than POS or mouse trace. + +# 4. Proposed Methodology + +# 4.1. Preliminaries + +Baseline for Fine-Grained Retrieval: Given a query-photo pair $(\mathbf{q},\mathbf{p})$ , existing methods encode [7, 51, 54, 57, 107] the query $\mathbf{q} = \{\mathbf{s},\mathbf{t}\}$ comprising sketch (s) / text (t) and photo (p) as $f_{\mathbf{q}} = \mathcal{F}_{\mathbf{q}}(\mathbf{q})\in \mathbb{R}^{D}$ , and $f_{\mathbf{p}} = \mathcal{F}_{\mathbf{p}}(\mathbf{p})\in \mathbb{R}^{D}$ respectively. The network is trained via triplet loss with + +![](images/9bc4f300a9039d61cb4e400bb696f4c7d81bf4f804ed981e6f2b5218b1ca2e0d.jpg) +Figure 3. (Left): We disentangle modality-agnostic and modality-specific components from sketch, text, and photo. The modality-agnostic components are aligned using contrastive loss for cross-modal transfer. (Right): Modality-agnostic sketch $(f_{\mathbf{s}}^{ag})$ is used across modality to generate modality-specific text $(f_{\mathbf{t}}^{sp})$ using text-specific $\tau_{\mathbf{t}}$ . Combining $f_{\mathbf{s}}^{ag}$ and $f_{\mathbf{t}}^{ag}$ , we generate text from sketch. + +margin parameter $\mu >0$ such that the cosine distance $\delta (\cdot)$ of query anchor $\mathbf{q}$ from a negative photo $(\mathbf{p}^{-})$ should increase while that from the positive photo $(\mathbf{p}^{+})$ should decrease as, $\mathcal{L}_{trip} = \max \{0,\mu +\delta (f_{\mathbf{q}},f_{\mathbf{p}^{+}}) - \delta (f_{\mathbf{q}},f_{\mathbf{p}^{-}})\}$ + +Baseline for Image Captioning: Image captioning consists of an image encoder [59, 101], $f_{\mathbf{p}} = \mathcal{F}_{\mathbf{p}}(\mathbf{p})$ followed by an autoregressive textual decoder $(\mathcal{F}_C)$ . Given the textual description comprises a sequence of words $\mathbf{t} = \{w_1,\dots ,w_K\}$ , we maximise the likelihood of a predicted word $(\hat{w}_k)$ at each step $(k)$ , conditioned on $f_{\mathbf{p}}$ as, $\mathcal{L}_C = -\sum_{k = 1}^{K}\log [\mathcal{F}_C(\hat{w}_k = w_k|f_{\mathbf{p}},w_1,\dots ,w_{k - 1})]$ + +# 4.2. Overview + +We aim to disentangle the feature representations from sketch, text, and photo modalities into a modality-agnostic and modality-specific component. While the modality-agnostic component holds semantic information to support cross-modal transfer, the modality-specific one holds information necessary during self-reconstruction; however, it lacks meaning in other modalities (e.g., grammatical knowledge in text). Achieving feature disentanglement across scene sketches, texts, and photos enables a multitude of downstream tasks like (i) SBIR - modality-agnostic sketch and photo features, (ii) TBIR - modality-agnostic text and photo, (iii) Sketch + Text-Based Image Retrieval - modality-agnostic sketch, text, and photo, (iv) Image Captioning - using the modality-agnostic photo to compute modality-specific text features, (v) Sketch Captioning - modality-agnostic sketch to compute modality-specific text, and (vi) Subjective Captioning - using modality-agnostic photo and sketch, to compute modality-specific text. + +# 4.3. Disentangling Modality Agnostic and Specific + +While our disentangling method can be generalised to any number of modalities, for simplicity, we first show for $M = 2$ modalities and later extend to $M \geq 3$ . Consider a simple bimodal setup of sketch $(\mathbf{s} \in \mathbb{R}^{H \times W \times 3})$ and text $(\mathbf{t} \in \mathbb{R}^{N \times E})$ . Our goal is to split the feature representation $f_{\mathbf{s}} = \mathcal{F}_{\mathbf{s}}(\mathbf{s}) \in \mathbb{R}^{512}$ and $f_{\mathbf{t}} = \mathcal{F}_{\mathbf{t}}(\mathbf{t}) \in \mathbb{R}^{512}$ into a modality-agnostic and a modality-specific component as $f_{\mathbf{s}} = [f_{\mathbf{s}}^{ag}, f_{\mathbf{s}}^{sp}]$ , and $f_{\mathbf{t}} = [f_{\mathbf{t}}^{ag}, f_{\mathbf{t}}^{sp}]$ respectively, where + +![](images/60f76ec42dce341d9ff0f9ab54a1da0f7d2e62e8a08fb0c427d8ac4b41b850ea.jpg) +Figure 4. Unlike typical neural networks that are unidirectional, data in conditional invertible neural networks $(\tau_{\mathbf{k}})$ can flow either (i) from modality-specific $f_{\mathbf{k}}^{sp}$ to a uniform distribution $\eta$ by conditioning on modality-agnostic $f_{\mathbf{k}}^{ag}$ during training, or (ii) from a sampled $\eta$ in uniform distribution to the modality-specific $f_{\mathbf{k}}^{sp}$ by conditioning on modality-agnostic $f_{\mathbf{k}}^{ag}$ during inference. The conditioning vector $f_{\mathbf{k}}^{ag}$ is injected into the conditional affinity coupling layers [28] of $\tau_{\mathbf{k}}$ using any arbitrary network $\mathcal{H}$ . + +$f^{ag} \in \mathbb{R}^{480}$ and $f^{sp} \in \mathbb{R}^{32}$ . Existing methods [82, 88] disentangle feature representations via (i) self reconstruction as $\hat{\mathbf{s}} = \mathcal{D}_{\mathbf{s}}([f_{\mathbf{s}}^{ag}, f_{\mathbf{s}}^{sp}])$ and $\hat{\mathbf{t}} = \mathcal{D}_{\mathbf{t}}([f_{\mathbf{t}}^{ag}, f_{\mathbf{t}}^{sp}])$ coupled with (ii) cross-modal translation $\hat{\mathbf{s}} = \mathcal{D}_{\mathbf{s}}([f_{\mathbf{t}}^{ag}, f_{\mathbf{s}}^{sp}])$ and $\hat{\mathbf{t}} = \mathcal{D}_{\mathbf{t}}([f_{\mathbf{s}}^{ag}, f_{\mathbf{t}}^{sp}])$ . However, using cross-modal translation with latent feature exchange across modalities is a cumbersome process that explodes with $\mathbb{P}_2^M$ permutations for $M$ modalities, e.g., $M = 3$ has $\mathbb{P}_2^3 = 6$ cross-modal translations. Adding multiple cross-modal translation losses makes optimisation difficult and computationally expensive. We break this compute barrier with linear $(\mathcal{O}(M))$ complexity using an information bottleneck reinterpretation of modality-agnostic and modality-specific disentanglement. In particular, we maximise the mutual information $\mathcal{I}(f_{\mathbf{s}}^{ag}, f_{\mathbf{t}}^{ag})$ amongst modality-agnostic components, while minimising the same between modality-agnostic and modality-specific components $\mathcal{I}(f_{\mathbf{s}}^{ag}, f_{\mathbf{s}}^{sp})$ and $\mathcal{I}(f_{\mathbf{t}}^{ag}, f_{\mathbf{t}}^{sp})$ , where $\mathcal{I}(\cdot, \cdot)$ denotes mutual information between two entities. Hence, unlike the previous $\mathbb{P}_2^M$ permutations, Eq. (1) has one agnostic $\mathcal{I}(f_{\mathbf{s}}^{ag}, f_{\mathbf{t}}^{ag})$ , and $M$ specific $\mathcal{I}(f_{\mathbf{k}}^{ag}, f_{\mathbf{k}}^{sp})$ losses. Formally, using a Langrange multiplier hyperparameter $\beta$ we have our loss objective as, + +$$ +\mathcal {L} _ {\mathcal {I}} = - \overbrace {\mathcal {I} \left(f _ {\mathbf {s}} ^ {a g} , f _ {\mathbf {t}} ^ {a g}\right)} ^ {\text {a g n o s t i c}} + \beta \overbrace {\sum_ {\mathbf {k} \in \{\mathbf {s} , \mathbf {t} \}}} ^ {\text {s p e c i f i c}} \tag {1} +$$ + +Minimise $\mathcal{I}(f_{\mathbf{k}}^{ag}, f_{\mathbf{k}}^{sp})$ : We minimise the mutual information between modality-agnostic and modality-specific components using a conditional invertible [ ] neural network $\tau_{\mathbf{k}}$ . Unlike typical unidirectional neural networks $\mathcal{F}: x \to y$ , a conditional invertible neural network employs a sequence of bijective mapping operations like activation normalization (ActNorm) [45], Conditional Affine Coupling [28], and shuffling [45] to obtain $\tau_{\mathbf{k}}: x \leftrightarrow y$ . During the forward pass (inference), we sample $\eta \in \mathbb{R}^{32}$ from a uniform prior distribution $\mathbb{P}(\eta)$ to predict the modality-specific $f_{\mathbf{k}}^{sp} \in \mathbb{R}^{32}$ by conditioning on $f_{\mathbf{k}}^{ag}$ as, $f_{\mathbf{k}}^{sp} = \tau_{\mathbf{k}}(\eta | f_{\mathbf{k}}^{ag})$ . In other words, during inference, we predict the modality-specific component of target from the modality-agnostic one of input using $\tau_{\mathbf{k}}$ . The target modality is + +![](images/cbc47200456493b1ee8049ad6e11ff710863ef962b6f00983f5527231e5ccb5b.jpg) +Figure 5. (Left): The modality-agnostic from sketch, or text, or both are used to retrieve from a gallery of photos. This enables a multitude of retrieval tasks like SBIR, TBIR, and STBIR. (Right): The modality-agnostic from photo, or sketch, or both are used to generate the text-specific component. Combining the modality-agnostic and inferred text-specific (via $\tau_{\mathrm{t}}$ ) enables image, or sketch, or subjective captioning. + +![](images/55451c3a3b2a6f1e97526a009119b4205634e536430359f3e2b79a907403ca7d.jpg) + +then generated by combining the input-agnostic and target-specific components. The conditioning modality-agnostic vector $f_{\mathbf{k}}^{ag}$ is injected into the intermediate conditional affine coupling layers $\mathcal{C}: x \leftrightarrow y$ as: $[x_1, x_2] = \text{split}(x)$ , and $y = \text{concat}[x_1, s_\theta([x_1; h]) \odot x_2 + t_\theta([x_1; h])]$ , where, $h = \mathcal{H}(f_{\mathbf{k}}^{ag})$ . A simple feed-forward neural network implements $s_\theta, t_\theta$ , and $\mathcal{H}$ . We learn $\tau_{\mathbf{k}}$ in the reverse pass (training) via negative log-likelihood (NLL Loss in Fig. 4) of $\tau_{\mathbf{k}}^{-1}(f_{\mathbf{k}}^{sp} | f_{\mathbf{k}}^{ag})$ to predict a uniform distribution $\mathbb{P}(\eta)$ , + +$$ +\mathbb {P} (\eta) = \mathbb {P} \left(\tau_ {\mathbf {k}} ^ {- 1} \left(f _ {\mathbf {k}} ^ {s p} \mid f _ {\mathbf {k}} ^ {a g}\right)\right) | \det J _ {\tau_ {\mathbf {k}} ^ {- 1}} \left(f _ {\mathbf {k}} ^ {s p} \mid f _ {\mathbf {k}} ^ {a g}\right) | \quad (2) +$$ + +We show how learning $\tau_{\mathbf{k}}$ in Eq. (2) minimises $\mathcal{I}(f_{\mathbf{k}}^{ag}, f_{\mathbf{k}}^{sp})$ . $\mathcal{I}(f_{\mathbf{k}}^{ag}, f_{\mathbf{k}}^{sp}) = \int_{f_{\mathbf{k}}^{sp}} \mathbb{P}(f_{\mathbf{k}}^{sp} | f_{\mathbf{k}}^{ag}) \log \mathbb{P}(f_{\mathbf{k}}^{sp} | f_{\mathbf{k}}^{ag}) / \mathbb{P}(f_{\mathbf{k}}^{sp})$ . Approximating modality-specific prior $\mathbb{P}(f_{\mathbf{k}}^{sp})$ with variational distribution $\mathbb{Q}(f_{\mathbf{k}}^{sp})$ gives the upper-bound, minimising which reduces the KL-divergence between $\mathbb{P}(f_{\mathbf{k}}^{sp} | f_{\mathbf{k}}^{ag})$ and $\mathbb{Q}(f_{\mathbf{k}}^{sp})$ i.e., it encourages the disentanglement $\mathbb{P}(f_{\mathbf{k}}^{ag}, f_{\mathbf{k}}^{sp}) \approx \mathbb{P}(f_{\mathbf{k}}^{ag}) \cdot \mathbb{P}(f_{\mathbf{k}}^{sp})$ . The prior $\mathbb{Q}(f_{\mathbf{k}}^{sp})$ is solved using $\tau_{\mathbf{k}}$ to enforce disentanglement between modality-agnostic and modality-specific components, like that in Eq. (2), as the sum of negative-loglikelihood (NLL-Loss in Fig. 4) and log-determinant (see supplementary for proof), + +$$ +\begin{array}{l} \mathcal {L} _ {\tau_ {\mathbf {k}}} = - \mathbb {E} _ {f _ {\mathbf {k}} ^ {s p}} \left\{\log \mathrm {q} \left(\tau_ {\mathbf {k}} ^ {- 1} \left(f _ {\mathbf {k}} ^ {s p} \mid f _ {\mathbf {k}} ^ {a g}\right)\right) \right. \tag {3} \\ + \log | \det J _ {\tau_ {\mathbf {k}} ^ {- 1}} \left(f _ {\mathbf {k}} ^ {s p} \mid f _ {\mathbf {k}} ^ {a g}\right) | \} \\ \end{array} +$$ + +Maximise $\mathcal{I}(f_{\mathbf{s}}^{ag}, f_{\mathbf{t}}^{ag})$ : Here we show how minimising a constrastive based retrieval loss [94] between the modality-agnostic components of sketch and text will maximise their mutual information. We define contrastive loss matching modality-agnostic components of sketch and text as, + +$$ +\mathcal {L} _ {c l} ^ {\mathbf {s}, \mathbf {t}} = - \mathbb {E} _ {f _ {\mathbf {s}} ^ {s p}} \left[ \log \frac {\omega \left(f _ {\mathbf {s}} ^ {a g} , f _ {\mathbf {t} ^ {+}} ^ {a g}\right)}{\omega \left(f _ {\mathbf {s}} ^ {a g} , f _ {\mathbf {t} ^ {+}} ^ {a g}\right) + \sum_ {f _ {\mathbf {t} ^ {-}} ^ {a g}} ^ {N - 1} \omega \left(f _ {\mathbf {s}} ^ {a g} , f _ {\mathbf {t} ^ {-}} ^ {a g}\right)} \right] \tag {4} +$$ + +where, $\omega = \exp (x^{T}\mathbf{W}y)$ . For each modality-agnostic $f_{\mathbf{s}}^{ag}$ we sample a positive $f_{\mathbf{t}^{+}}^{ag}$ and $(N - 1)$ negative $f_{\mathbf{t}^{-}}^{ag}$ pairs. The contrastive loss in Eq. (4) is expressed as mutual information between $f_{\mathbf{s}}^{ag}$ and $f_{\mathbf{t}}^{ag}$ as, $\mathcal{L}_{cl}^{\mathbf{s},\mathbf{t}}\geq -\mathcal{I}(f_{\mathbf{s}}^{ag},f_{\mathbf{t}}^{ag}) + \log (N)$ . Hence, to maximise the mutual information between modality-agnostic $f_{\mathbf{s}}^{ag}$ and $f_{\mathbf{t}}^{ag}$ , we can maximise the tractable lower bound $\log (N) - \mathcal{L}_{cl}^{\mathbf{s},\mathbf{t}}$ . + +Total Loss for Bimodal Setup: The resulting loss $(\mathcal{L}_{tot})$ for bimodal (sketch and text) setup comprise three loss objectives (i) self reconstruction loss $\mathcal{L}_{rec}$ , (ii) contrastive loss between two modality-agnostic terms $\mathcal{L}_{cl}^{\mathbf{s},\mathbf{t}}$ , and (iii) disentanglement between modality-agnostic and modality-specific components in each modality $(\mathbf{k})$ $(\mathcal{L}_{\tau_{\mathbf{k}}})$ , as + +$$ +\begin{array}{l} \mathcal {L} _ {r e c} = | | \mathbf {s} - \mathcal {D} _ {\mathbf {s}} (\mathcal {F} _ {\mathbf {s}} (\mathbf {s})) | | _ {2} + | | \mathbf {t} - \mathcal {D} _ {\mathbf {t}} (\mathcal {F} _ {\mathbf {t}} (\mathbf {t})) | | _ {2} \tag {5} \\ \mathcal {L} _ {t o t} = \mathcal {L} _ {r e c} + \mathcal {L} _ {c l} ^ {\mathbf {s}, \mathbf {t}} + \beta [ \mathcal {L} _ {\tau_ {\mathbf {s}}} + \mathcal {L} _ {\tau_ {\mathbf {t}}} ] \\ \end{array} +$$ + +Extending to Three/More Modalities: Here we extend our bimodal setup in Sec. 4.3 to three or more modalities. (i) We compute the self-reconstruction loss for three modalities as $\mathcal{L}_{rec} = \sum_{\mathbf{k}\in \{\mathbf{s},\mathbf{t},\mathbf{p}\}}||\mathbf{k} - \mathcal{D}_{\mathbf{k}}(\mathcal{F}_{\mathbf{k}}(\mathbf{k}))||_2$ (ii) we minimise the mutual information between modality-agnostic and modality-specific components for sketch, text, and photo as, $\mathcal{L}_{\tau} = \mathcal{L}_{\tau_{\mathrm{s}}} + \mathcal{L}_{\tau_{\mathrm{t}}} + \mathcal{L}_{\tau_{\mathrm{p}}}$ . (iii) However, our contrastive loss term $\mathcal{L}_{cl}$ that maximises the mutual information among modality-agnostic components can only compare two modalities. We can extend this naively to a three-modality setup as $\mathcal{L}_{cl}^{tot} = \mathcal{L}_{cl}^{\mathbf{s},\mathbf{t}} + \mathcal{L}_{cl}^{\mathbf{s},\mathbf{p}} + \mathcal{L}_{cl}^{\mathbf{t},\mathbf{p}}$ + +Extending to three or more modalities, however, we notice our contrastive loss in Eq. (4) is defined for only b-modal setup $(\mathcal{L}_{cl}^{\mathbf{s},\mathbf{t}}$ , or $\mathcal{L}_{cl}^{\mathbf{s},\mathbf{p}}$ , or $\mathcal{L}_{cl}^{\mathbf{t},\mathbf{p}}$ ). For example, given three modalities $S_{M} = \{m_{1},m_{2},m_{3}\}$ , comparing only $(m_{1},m_{2})$ ignores $m_{3}$ . This highlights a key limitation: it fails when we have a query in both $(m_{1},m_{3})$ to retrieve $m_{2}$ (e.g., sketch+text for image retrieval). Now the research question boils down to - how can we model a function $\mathcal{G}(\cdot)$ such that it can model either $m_{1}$ , or $m_{3}$ , or both $(m_{1},m_{3})$ to retrieve $m_{2}$ . To design $\mathcal{G}$ , using naive addition as $\mathcal{G}(m_1,m_3) = m_1 + m_3$ does not handle overlapping or conflicting information in $m_{1}$ and $m_{3}$ [58]. While, concatenation $\mathcal{G}(m_1,m_3) = \mathrm{concat}[m_1,m_3]$ computes interaction between $(m_{1},m_{3})$ , it forces to provide both $m_{1}$ and $m_{3}$ during inference; thereby failing to model either $m_{1}$ , or $m_{3}$ , or both $(m_{1},m_{3})$ + +# 4.4. Modelling Optional Sketch or Text + +We propose a simple approach to design $\mathcal{G}$ that optionally models either $m_{1}$ , or $m_{3}$ , or both $(m_{1}, m_{3})$ , and handles + +overlapping or conflicting information. Our proposed $\mathcal{G}$ comprises a multihead cross-attention module $\mathrm{MH}(\cdot)$ followed by an attention-based pooling $\mathrm{PMA}(\cdot)$ as, $f_{M} = \mathrm{PMA}(H_{M})$ ; where $H_{M} = \mathrm{MH}(S_{M})$ , and $S_{M} = \{m_{1}, m_{3}\}$ . + +Our $\mathrm{MH}(\cdot)$ is order-invariant and independent of the number $(M)$ of input modalities defined as $\mathrm{MH}(X) = \sigma (XX^T)X$ ; where $\sigma$ is scaled-softmax, $X^T$ is transpose of $X$ , and $X\in \mathbb{R}^{M\times 480}$ is a list of modality-agnostic components $m_{1}$ , or $m_{3}$ with $\mathbb{R}^{1\times 480}$ , or $(m_1,m_3)\in \mathbb{R}^{2\times 480}$ in query. The cross-attention in $\mathrm{MH}(\cdot)$ interacts across query modalities to compute mutually agreeing information between $(m_{1},m_{3})$ as, $H_{M}\in \mathbb{R}^{2\times 480}$ . Next, we use an order-invariant attention-based pooling $\mathrm{PMA}: \mathbb{R}^{2\times 480}\to \mathbb{R}^{1\times 480}$ with a learned seed vector $\mathcal{P}\in \mathbb{R}^{1\times 480}$ to aggregate mutually agreeing $H_{M}$ as, $f_{M} = \mathrm{PMA}(H_{M}) = \sigma (\mathcal{P}H_{M}^{T})H_{M}$ . Hence, using our proposed fusion module $\mathcal{G}$ , we adapt our contrastive loss defined for only a pair of modality-agnostic components in Eq. (4) as $\mathcal{L}_{cl}^{tot} = \mathcal{L}_{cl}^{\mathbf{s},\mathbf{t}} + \mathcal{L}_{cl}^{\mathbf{s},\mathbf{p}} + \mathcal{L}_{cl}^{\mathbf{t},\mathbf{p}}$ to jointly model sketch-text-photo (or more) modality-agnostic as: $\mathcal{L}_{cls}^{tot} = \mathcal{L}_{cl}(\mathcal{G}(f_{\mathbf{s}}^{ag},f_{\mathbf{t}}^{ag}),f_{\mathbf{p}}^{ag}) + \mathcal{L}_{cl}(\mathcal{G}(f_{\mathbf{s}}^{ag},f_{\mathbf{p}}^{ag}),f_{\mathbf{t}}^{ag}) + \mathcal{L}_{cl}(\mathcal{G}(f_{\mathbf{p}}^{ag},f_{\mathbf{t}}^{ag}),f_{\mathbf{s}}^{ag})$ . For a generalised solution involving more than three modalities $(M > 3)$ , see supplementary. + +Inference Data Flow: We describe the inference data flow in Fig. 5. For retrieval tasks, we first compute the modality-agnostic component of query sketch and text $(f_{\mathbf{s}}^{ag}, f_{\mathbf{t}}^{ag})$ , and a gallery of photos $\{f_{\mathbf{p}_1}^{ag}, f_{\mathbf{p}_2}^{ag}, \ldots, f_{\mathbf{p}_{\mathbf{N}}}^{ag}\}$ . Next, a combined representation for either only sketch $(f_{\mathbf{s}}^{ag})$ , or only text $(f_{\mathbf{t}}^{ag})$ , or both $(f_{\mathbf{s}}^{ag}, f_{\mathbf{t}}^{ag})$ is computed using multihead cross attention $\mathrm{MH}(\cdot)$ followed by attention-based pooling $\mathrm{PMA}(\cdot)$ defined in Sec. 4.4 to get $f_{\mathbf{st}^*}^{ag}$ . Finally, we find the minimum distance between the combined $f_{\mathbf{st}^*}^{ag}$ and modality-agnostic component of photo $f_{\mathbf{p}_i}^{ag}$ as $\omega(f_{\mathbf{st}^*}^{ag}, f_{\mathbf{p}_i}^{ag})$ defined in Eq. (4). For captioning, we additionally use the text-specific conditional invertible neural network $\tau_t$ to generate the target modality-specific text (e.g., grammatical structure etc.) from input modality-agnostic comprising of only photo $(f_{\mathbf{p}}^{ag})$ for image captioning, only sketch $(f_{\mathbf{s}}^{ag})$ for sketch captioning, or both photo and sketch $(f_{\mathbf{p}}^{ag}, f_{\mathbf{s}}^{ag})$ for subjective captioning (i.e., generate image captions by conditioning on the input sketch). + +# 5. Experiments + +Datasets: We use two scene sketch datasets with fine-grained alignment among sketch, text, and photo: (i) SketchyCOCO [34] contains 14,081 scene sketch-photo pairs. The photos are taken from MS-COCO [55] comprising $164K$ photos with paired texts. However, most sketches in SketchyCOCO [34] contain less than one foreground instance. Following [57], we filter SketchyCOCO with one foreground instance to get 1015/210 train/test scene sketches. (ii) Unlike SketchyCOCO [34], where the scene sketches are synthetically generated, FS-COCO [19] includes 7000/3000 train/test human-drawn scene sketches + +with a paired textual description of sketches. + +Implementation Details: Our model is implemented in PyTorch using 11GB Nvidia RTX 2080-Super GPU. First, we pre-train the image encoder and text decoder for image captioning using 82,783 photo-text pairs (excluding the photos common in SketchyCOCO and FS-COCO) for 15 epochs. Next, we fine-tune on either SketchyCOCO [34], or FS-COCO [19] for 200 epochs using Adam optimiser with learning rate $1e - 4$ , and batch size 64. Our photo $(\mathcal{F}_{\mathbf{p}})$ and sketch $(\mathcal{F}_{\mathrm{s}})$ encoders use ImageNet pretrained VGG-16 [85]. For simplicity, we encode text using a bidirectional GRU unit with 512 hidden units. Our text decoder [43] is a single-layer autoregressive LSTM decoder that predicts a probability distribution over a fixed vocabulary (10,010 words) at every time step. For the image/sketch decoder, we use two separate GAN [109] networks that synthesise sketch/image of size $64\times 64$ , respectively. For brevity, we avoid realistic sketch/image generation due to the challenging scene complexity [19]. Hence we do not use a discriminator module for high-quality, sharp reconstruction [110]. Finally, our conditionally invertible neural network comprises 16 alternating affine coupling [29], activation normalisation [45], and switch layers [29]. + +Evaluation Metric: In line with FG-SBIR research, we use Acc.@q [81] defined as the percentage of sketches having a true matched photo in the top-q list. For sketch/image/subjective captioning, we use standard metrics BELU (B) 1-4 [67], CIDEr (C) [95], ROUGE (R) [53], METEOR (M) [25], and SPICE [2]. Following [96], we generate 100 candidate captions and employ consensus reranking using CIDEr to select the best candidate caption. + +Competitors: We compare against (i) existing state-of-the-art methods that align two modalities (S2): For SBIR, Triplet-SN [107] employs Sketch-A-Net [108] backbone trained using triplet loss. HOLEF [87] adds spatial attention with a higher-order ranking loss. SketchyS [115] replaces Sketch-A-Net in Triplet-SN with VGG-16 [85] and an auxiliary category-level cross-entropy. SceneS [57] uses GCN [46] to model scene sketch layout information. For TBIR, CLIP [73] is trained with text using transformer [83] and photo using vision transformer [30] on 400 million text-photo pairs. CLIP-LN fine-tunes CLIP by training only layer normalisation parameters [4] with learning rate 0.00001. For image/sketch captioning, SAT [101] is one of the simplest but seminal works using a CNN-LSTM encoder-decoder approach similar to ours. GMM-CVAE [96] employs a conditional variational autoencoder with a Gaussian mixture model. LNFMM [61] is similar to ours that splits information into modality-agnostic and modality-specific components using conditional invertible neural network, ClipCap [65] employs CLIP [73] for image encoding followed by GPT-2 [74] for text decoding. A learned + +Table 2. Quantitative results combining sketch and text for image retrieval (FG-STBIR) on two scene sketch datasets [19, 34]. + +
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S3QST [86]38.987.925.154.5
SCM [3]38.587.324.354.1
BCrossAtt [83]39.188.225.354.8
Proposed39.588.725.755.2
+ +![](images/8e4c642d4945a6644e7890569f919081e1c0a2307d19f9ec43668b175cfc5454.jpg) +Boys are playing with frisbee disc. + +![](images/491ba7bbf6a68b769f998565dbc904aa15b5574119bc3dc59baddb1bd018a8cd.jpg) +A boy is holding a baseball bat. + +![](images/8163cf5444586d0fb8fd9a4f50e464dd6644f472805fb4878ca8d558e7769a62.jpg) + +![](images/27ddccbf3f52acc9b16d11c565b32353eff59a6baa311c5ffc98da19bf93820f.jpg) + +![](images/3266c9bfa4b21e45f5a1eaf8efe1d27f20f42fd7ed47f351fafb2c3fb2276ce5.jpg) + +![](images/11874f5a41534dedfd3cb1a4fcd11eee9fe870da2d646d90568c681359d46853.jpg) + +![](images/0899e783648761292051e3159bf4fad7d311c641fe739d113971cf987d59d384.jpg) +Figure 6. Qualitative results of combining sketch and text as query for image retrieval on FSCOCO [19]. See supplementary for more. + +![](images/1d597511d67f326a5b8cc151e3502f52bc3f6b7e2ce64858175ebc6122462009.jpg) + +![](images/8c9c912a0282f5e8c44ddf5c9b48420163a6addee74076690140c3b414d462c2.jpg) + +![](images/834fd81d89739a308646f9999cc67c191b15d68d141fdbbd55d4754f9eae2e38.jpg) + +![](images/32a377b68de073f05e609decf2772eef34570fa46f8de312676b02535661b779.jpg) + +![](images/fa1907315712fb38cce2e3967e3ad6d48df92f0ff22a603cd987071192ef039b.jpg) + +mapping module translates CLIP embeddings to GPT-2. (ii) We compare against methods that align 3 modalities (S3): For STBIR, QST [86] extends triplet loss in Triplet-SN to quadruplet loss that combines sketch and text for image retrieval. SCM uses element-wise addition to combine sketch and text from ResNet-18 [39] with weight sharing across sketch, text, and photo from ResBlock4 onwards [3]. (iii) We design baselines (B): For STBIR, CrossAtt employs cross-attention [83] to combine sketch and text. For subjective captioning, MulCap combines sketch $(f_{\mathbf{s}}^{ag})$ and photo $(f_{\mathbf{p}}^{ag})$ via element-wise multiplication as in [14]. CrossCap optionally fuse photo, sketch, or both using cross-attention. CatCap use feature concatenation [71] of guiding sketch $(f_{\mathbf{s}}^{ag})$ signal with photo $(f_{\mathbf{p}}^{ag})$ to generate captions. + +# 5.1. Combining Sketch and Text for Image Retrieval + +Fig. 2 shows that for some instances, sketch is a better query, whereas text is better for others. Hence, to achieve best of both modalities, we examine the complimentary nature by combining sketch and text for image retrieval. Table 2 shows (i) SCM gives the lowest performance due to naive element-wise addition of potentially overlapping and conflicting information [58] from sketch and text. (ii) QST improves slightly upon SCM by replacing naive elementwise addition with a weighted summation (0.8 for sketch modality). (iii) CrossAtt outperforms all baselines by using a cross-attention between sketch and text to resolve overlapping/conflict information [58]. (iv) Our proposed method gives the highest performance due to cross-attention that model sketch-text interaction and disentanglement to drive out modality-specific information for cross-modal retrieval. + +# 5.2. Optionally using Sketch for Image Retrieval + +Our method allows drawing only easy-to-sketch scenes instead of using both sketch and text forcibly. Table 3 com + +Table 3. Quantitative results using only sketch for image retrieval (FG-SBIR) on two scene sketch datasets [19, 34]. + +
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2Triplet-SN [107]6.232.94.721.0
HOLEF [87]6.240.74.921.7
SketchyS [115]36.578.623.052.3
SceneS [57]31.986.2--
S3QST [86]37.487.123.652.9
SCM [3]37.386.823.452.6
BCrossAtt37.987.423.753.5
Proposed38.287.624.153.9
+ +Table 4. Quantitative results of fine-grained text-based image retrieval (FG-TBIR) on two scene sketch datasets [19,34]. + +
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2CLIP [73]21.050.911.535.3
CLIP-LN [73]22.152.314.836.6
S3QST [86]11.131.17.223.6
SCM [3]10.731.06.923.1
BCrossAtt20.151.012.535.8
Proposed21.551.613.736.3
+ +![](images/8084445dfa9affb565a568731a20627cf66e208f10c26c9a899f129a00528c58.jpg) +Sheep are grazing on a green hill. + +![](images/6e38fb60b04bec443bd734e532b00c60b554ad74252ae912101c4be6d8e8ec6c.jpg) +Black and white photo of people holding umbrellas. +Three people are walking under umbrella on field. + +![](images/9f05b8035a4f57cdeba0f1e665ed57f2c92b8aadd8bfa2b8be3e00be5537b1ea.jpg) +Figure 7. Qualitative results for image captioning v/s subjective captioning on FS-COCO [19]. See supplementary for more. + +![](images/3aa3ff89dce81b31cde100c73414e520195faf98d28bd15f01ef7ba73fea3a97.jpg) +A herd of sheep on grassland. + +![](images/2157ffb650d9824ed575581fc3612dc3df852e20f3f158d73b9124b988b60309.jpg) +Sheep are grazing beyond the fence on a hill. + +![](images/08590dda607bde1e266bc3b9eee287a8da579f7e81b2d8652306ac520a95b814.jpg) +Three people are walking holding umbrella. + +pares against methods that specialise on two-modalities (S2), three-modalities (S3), and our proposed baselines (B). We observe (i) training on three modalities (sketch, text, and photo) in S3 generally outperforms those trained using only sketch and photo (S2). This can be attributed to learning generalisable features in multi-modal setup [3]. (ii) $QST$ in S3 outperforms SCM indicating quadruplet loss is a better training objective than naive element-wise addition when combining sketch, text, and photo. (iii) Performance difference between CrossAttn and $QST$ is not as significant as in FG-STBIR (Table 2) as during inference, we only use sketch, omitting the cross-attention module. (iv) Our method outperforms S2, S3, and B even for two-modality setup thanks to disentanglement that eliminates confounding [3] modality-specific information. + +# 5.3. Optionally using Text for Image Retrieval + +While some information is best expressed by drawing, others, like colour, is best described via text. From Table 4, we observe (i) Given the same train/test split, sketches outperform text as a query modality for fine-grained image retrieval. (ii) CLIP and CLIP-LN outperforms all competitors due to superior pre-trained weights using 400 million text-image pairs. (iii) The proposed method outperforms most methods due to disentanglement that drives out modality- + +Table 5. Quantitative results of standard captioning metrics on MS-COCO [55] and FS-COCO [19] dataset. + +
MethodImage CaptioningSketch CaptioningSubjective Captioning
B-1B-4MRCSB-1B-4MRCSB-1B-4MRCS
S2SAT [101]71.825.023.0---46.213.717.144.969.414.5------
GMM-CVAE [96]72.930.724.252.598.617.749.615.518.348.777.615.5------
AG-CVAE [96]73.231.124.552.8100.118.850.916.018.949.180.515.8------
LNFMM [61]74.731.824.753.8105.518.852.216.721.052.990.116.0------
BMulCap74.933.225.554.9106.019.553.917.021.053.897.316.778.738.628.559.8110.721.7
CatCap------------77.638.028.357.7108.021.2
CrossCap75.534.326.155.4106.720.154.317.921.454.3100.317.579.239.328.459.5117.322.1
Proposed76.035.926.956.9107.020.956.919.321.656.6106.518.981.342.730.161.6121.623.5
+ +Table 6. Ablation study on FG-STBIR and Subjective Captioning using FSCOCO [19]. CA denotes cross-attention in Sec. 4.4. + +
τkCACLAcc.@1Acc.@10B-1C
XXX24.553.773.3100.1
✓XX24.954.077.9108.5
✓✓X25.554.980.6119.3
✓✓✓25.755.281.3121.6
+ +specific components. Although CLIP [73] outperforms the proposed method, we deliberately use a simple and easy-to-reproduce GRU/VGG-16 architectures for text/photo encoders, and train on a much smaller data [19,34] than CLIP. + +# 5.4. Image or Sketch Captioning + +In addition to disentanglement for cross-modal retrieval tasks (e.g., FG-SBIR, FG-TBIR), our conditional invertible neural network $\tau_{\mathrm{t}}$ can also generate text-specific information (Fig. 4) to support generative tasks like image/sketch captioning. We generate 100 candidate captions using (i) beam search for SAT, MulCap, CrossCap, CatCap, and (ii) sampling from prior distribution for GMM-CVAE, AG-CVAE, LNFMM, and our proposed method. From Table 5, we observe (i) our baselines adopting recent techniques like vision-transformer [30] outperforms (S2) – recent but complex approaches like LNFMM, AG-CVAE, and the older yet seminal work like SAT. (ii) Performance gap between MulCap and CrossCap is insignificant for two-modality setups (photo to text, or sketch to text) since they primarily differentiate by their multi-modal (photo and sketch) fusion strategy. (iii) In spite of using a photo/sketch encoder and text decoder similar to our simple competitor SAT, our proposed method performs competitively with complex methods like LNFMM, AG-CVAE, and latest approaches using vision-transformers [30], like CrossCap. This shows the significant contribution of (i) disentangling modality-specific and modality-agnostic components from photo/sketch, and (ii) modelling text-specific prior for generative tasks. + +# 5.5. Sketch Based Subjective Captioning + +As defined in Sec. 3.2, unlike traditional captioning frameworks that factually describe an image or sketch in a neutral tone, subjective captioning focus on drawing out a user's intentions, salient objects, and artistic interpretations [38]. Being the first method to use scene-level sketch as a guiding signal for captioning, we follow controllable caption- + +ing literature [89] to adopt three baselines (B) that inject the sketch conditioning signal into the captioning pipeline. From Table 5, we observe (i) MulCap outperforms CatCap, thereby supporting previous observations [14] of elementwise multiplication being more effective than concatenation. (ii) CrossAtt outperforms all baselines (B) and two-modality SOTAs (S2) by using a cross-attention mechanism to fuse sketch and photo by modelling sketch-photo interactions to resolve overlapping or conflicting information. Our proposed method is similar to CrossAtt using cross-attention (Sec. 4.4) but also enriches the modality-agnostic sketch and photo features by removing the confounding modality-specific information to offer the best performance. + +# 5.6. Ablation + +In Table 6, we evaluate the contribution of each key design choice on FG-STBIR and Subjective captioning using FS-COCO [19]. (i) Replacing cross-attention in Sec. 4.4 with quadruplet loss [86] leads to a performance drop by $0.6 / 0.9 / 2.7 / 10.8$ in Acc.@1/Acc.@10/B-1/C metrics respectively to show the importance of modelling the interaction between sketch and text. (ii) Replacing contrastive loss-based query-photo score in Eq. (4) with a simple triplet loss leads to a performance drop by $0.2 / 0.3 / 0.7 / 2.3$ due to the inability of unimodal L2-based triplet loss to model highly complex scene information [94]. (iii) Finally, removing the conditional invertible neural networks $(\tau_{\mathbf{k}})$ drops retrieval and captioning by $0.4 / 0.3 / 4.6 / 8.4$ due to percolation of the confounding modality-specific information in cross-modal tasks [3] and the inability to generate text-specific information from photo and sketch respectively. + +# 6. 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The result is a complete trilogy of scene representation from three diverse and complementary modalities - sketch, photo, and text. Instead of learning a rigid three-way embedding and be done with it, we focus on learning a flexible joint embedding that fully supports the \"optionality\" that this complementarity brings. Our embedding supports optionality on two axes: (i) optionality across modalities - use any combination of modalities as query for downstream tasks like retrieval, (ii) optionality across tasks - simultaneously utilising the embedding for either discriminative (e.g., retrieval) or generative tasks (e.g., captioning). This provides flexibility to end-users by exploiting the best of each modality, therefore serving the very purpose behind our proposal of a trilogy in the first place. First, a combination of information-bottleneck and conditional invertible neural networks disentangle the modality-specific component from modality-agnostic in sketch, photo, and text. Second, the modality-agnostic instances from sketch, photo, and text are synergised using a modified cross-attention. Once learned, we show our embedding can accommodate a multi-facet of scene-related tasks, including those enabled for the first time by the inclusion of sketch, all without any task-specific modifications. Project Page: https://pinakinathc.github.io/scenetrilogy" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 128, + 597 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 664 + ], + "type": "text", + "content": "Scene understanding sits at the very core of computer vision. As object-level research matures [24, 32], an encouraging shift can be observed in recent years on scene-level tasks, e.g., scene recognition [113], scene captioning [55], scene synthesis [34], and scene retrieval [13, 57]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Scene research has generally progressed from that of single modality [113, 114] to the very recent focus on multimodality [3, 13, 19]. The latter setting not only triggered a series of practical applications [34, 57, 101, 115] but im" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 247, + 541, + 358 + ], + "blocks": [ + { + "bbox": [ + 310, + 247, + 541, + 358 + ], + "lines": [ + { + "bbox": [ + 310, + 247, + 541, + 358 + ], + "spans": [ + { + "bbox": [ + 310, + 247, + 541, + 358 + ], + "type": "image", + "image_path": "c366e65a4075c2d75ced09c2e2c92910a3077fce9b502378c9447ba599c2f041.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "lines": [ + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "spans": [ + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{s}}^{sp}" + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "text", + "content": " sketch specific " + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{t}}^{sp}" + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "text", + "content": " text specific " + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{p}}^{sp}" + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "text", + "content": " photo specific " + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "inline_equation", + "content": "f^{ag}" + }, + { + "bbox": [ + 309, + 361, + 544, + 374 + ], + "type": "text", + "content": " modality agnostic" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "lines": [ + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "text", + "content": "Figure 1. Some scenes are easy to describe via sketch; for others, text is better. We provide the option to sketch, write, or both (sketch + text). For “optionality” across tasks, we disentangle sketch, text, and photo into a discriminative (e.g., retrieval) part " + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "inline_equation", + "content": "f^{ag}" + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "text", + "content": " shared across modalities, and a generative (e.g., captioning) part specific to one modality (" + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{sp}" + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}}^{sp}" + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{P}}^{sp}" + }, + { + "bbox": [ + 305, + 381, + 545, + 459 + ], + "type": "text", + "content": "). This supports a multifacet of scene-related tasks without task-specific modifications." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 471, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 545, + 544 + ], + "type": "text", + "content": "portantly helped to cast insights into scene understanding on a conceptual level (i.e., what is really being perceived by humans). To date, research on multi-modal scene understanding has mainly focused on two modalities – text and photo [59, 61, 62], via applications such as text-based scene retrieval (TBIR) [35], and scene captioning [23, 61, 62]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 546, + 713 + ], + "type": "text", + "content": "This paper follows the said trend of multi-modal scene understanding and extend it to also include human scene-sketch. Sketch is identified because of its unique characteristics of being both expressive and subjective, evident in an abundance of object-level sketch research [11], and very recently on scene-level [19]. To verify there is indeed useful complementarity that sketch can bring to multi-modal scene understanding, we first conducted two pilot studies (i) on expressivity, we compare text and sketch in terms of scene image retrieval, and (ii) on subjectivity, we test a novel task of subjective captioning where sketch or parts-of-speech [26] are used as guidance for image captioning. On (i), results show there is significant disagreement in terms of retrieval accuracy when one is used as query over the other," + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10972" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "indicating there is complementary information between the two modalities. On (ii), sketch is shown to offer more subjectivity as a guiding signal than text, when quantified using common metrics such as BELU-4 [67] and CIDEr [95]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 286, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 218 + ], + "type": "text", + "content": "To fully explore the complementarity of all three modalities, we desire a flexible joint embedding that best sustains \"optionality\" across modalities, and also across tasks. The former enables end-users to use any combination of modalities (e.g., only sketch, only text, or both sketch+text) as a query for downstream tasks; and the latter provides option of utilising the learned embedding for both discriminative (e.g., retrieval) and generative problems (e.g., captioning)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "text", + "content": "This desired level of \"optionality\" is however not achievable via naive three-way joint embeddings common in the literature [3, 13, 19]. Instead, we advocate a three-way disentanglement (Fig. 1(b)), where each of the three modalities is disentangled into their modality-specific component (" + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{sp}" + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}}^{sp}" + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}}^{sp}" + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "text", + "content": ", for sketch, photo and text), and a shared modality-agnostic component (" + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "inline_equation", + "content": "f^{ag}" + }, + { + "bbox": [ + 46, + 219, + 286, + 506 + ], + "type": "text", + "content": "). The idea is that modality-specific will hold information specific to each modality (e.g., drawing style for sketch, texture for photo, and grammatical knowledge for text). It follows that filtering away modality-specific parts from each of the three modalities gives a shared modality-agnostic part that carries shared abstract semantic across all three modalities, (as shown in Fig. 1(b)). How optionality is supported in such a disentangled space then becomes trivial (Fig. 1(c),(d)). To achieve optionality across tasks, we simply use modality-agnostic information as the joint embedding to perform discriminative tasks (e.g., cross-modal retrieval), and for cross-modal generative tasks (e.g., captioning), we just combine modality-agnostic information (from source) with modality-specific (from target) to generate the target modality. Optionality across modality is a little harder, where we make use of a cross-attention [50] mechanism to capture the synergy across the modality-agnostic components." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": "Benefiting from our optionality-enabled embedding, we can perform a multi-facet of tasks without any task-specific modifications: (i) Fig. 1 (c) show cross-modal discriminative tasks such as sketch-based image retrieval (SBIR) using " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": ", text-based image retrieval (TBIR) using " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{t}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": ", or sketch+text based image retrieval (STBIR) using " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag} + f_{\\mathbf{t}}^{ag} \\leftrightarrow f_{\\mathbf{p}}^{ag})" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": ". (ii) Fig. 1 (d) show cross-modal generative tasks such as image captioning (photo branch) using " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}}^{ag} + f_{\\mathbf{t}}^{sp} \\rightarrow f_{\\mathbf{t}}" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": " to generate textual descriptions " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}}" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": ". Similarly, for sketch captioning (sketch branch) we use " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{ag} + f_{\\mathbf{t}}^{sp} \\rightarrow f_{\\mathbf{t}}" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": ". (iii) Last but not least, to demonstrate what the expressiveness of human sketch can bring to scene understanding, we introduce a novel task of subjective captioning where we guide image captioning using sketch as a signal (subjective branch) as " + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}}^{ag} + f_{\\mathbf{s}}^{ag} \\rightarrow f_{\\mathbf{t}}" + }, + { + "bbox": [ + 46, + 508, + 286, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "In summary, our contributions are: (i) We extend multi-modal scene understanding to include human scene" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 193 + ], + "type": "text", + "content": "sketches, thereby completing a trilogy of scene representation from three diverse and complementary modalities. (ii) We provide optionality to end-users by learning a flexible joint embedding that supports: optionality across modalities and optionality across tasks. (iii) Using computationally efficient techniques like information bottleneck, conditionally invertible neural networks, and modified crossattention mechanism, we model this flexible joint embedding. (iv) Once learned, our embedding accommodates a multi-facet of scene-related tasks like retrieval, captioning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 207, + 397, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 207, + 397, + 220 + ], + "spans": [ + { + "bbox": [ + 306, + 207, + 397, + 220 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 226, + 545, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 226, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 226, + 545, + 406 + ], + "type": "text", + "content": "Sketch for Visual Understanding: Hand-drawn sketches enriched with human visual perception cues have facilitated several downstream visual understanding tasks. Apart from the widely explored SBIR [10, 22], sketch has shown potential on object localisation [18], segmentation [72], image/video synthesis [48], representation learning [79], 3D shape retrieval/modelling [20], medical image analysis [47, 97], etc. [102]. Sketches are also useful in the creative industry like artistic image editing [105] and animation [100]. Unlike photos that are passively captured by a camera, sketches are drawn by humans that actively stimulate intelligence with pictorial-style drawing games [8]. While text has been widely used for human expression, in this paper, we show freehand sketches can provide complimentary or symbiotic information for visual understanding." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 410, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 578 + ], + "type": "text", + "content": "Sketch-Based Image Retrieval (SBIR): SBIR retrieves a paired photo given a query sketch. Sketches offer visual description that commences the avenues of category-level [27, 78, 106] or fine-grained instance-level (FG-SBIR) [6, 9, 12] retrieval. SBIR typically employs deep triplet-ranking based siamese networks to learn a joint embedding space [107]. Contemporary research emerged towards zero-shot SBIR [27, 80], cross-domain translation [66], on-the-fly retrieval [12], semi-supervised [6], self-supervised [7], meta-learning [11] etc. As research on object-level SBIR matured, focus shifted towards the more practical scene-level SBIR [76] with GCN [57], and optimal transport [17]. The onset of scene sketch datasets [19, 34, 115] revealed further insights into implicit human-sketching strategies [19]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Text-Based Image Retrieval (TBIR): Learning image-text joint embedding space with ranking loss [31, 43, 70] received considerable attention. Further improvements used mining hardest negative pairs for triplet loss [33], cross-modal adaptive message passing [98], probabilistic one-tomany representations [21] etc. Despite text lacking visual cues, million-scale paired image-text datasets have made TBIR competitive due to power scaling laws [63]. This inspired large-scale methods like Oscar [52], and CLIP [73]. In this paper, we augment TBIR with sketches to provide the creativity and freedom of expression intrinsic to sketches." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10973" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "Multi-Modality in Computer Vision: Multi-modal learning (MML) aims at developing models that can extract, interpret, and reason on information from various modalities characterised by different statistical properties such as text, sketch, or text+sketch. Contemporary research studied MML in vision via image and text [40], image to scene graph [36], etc. [103]. MML faces challenges like cross-modal alignment [42], or efficiency over data [92] and compute [44]. It is useful when data in one modality is inaccessible [3] for privacy or logistic reasons (e.g., hospital), but abundantly available in other modalities (photos in MS-COCO [55]). Often, some modalities are preferred over others for human-machine communication, like some concepts are easier to express in texts [60], while others prefer sketches [54] or both [76] (Fig. 1). In this paper, we learn cross-modal representation [104] that works using either one modality (text/sketch) or both." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 278, + 289, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 289, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 289, + 447 + ], + "type": "text", + "content": "Disentangled Representation for Multi-modality: Disentangling modality-agnostic from modality-specific residual factors is important for MML [41, 93]. Modality-agnostic information is useful for cross-modal transfer like semantics-based retrieval and pattern recognition [41] but holds no meaning for tasks specific to one modality like image-style or speaker information [91]. Disentanglement was explored where factors of variation are either known (e.g., facial poses [90]) and individually supervised [75], partially known [82], or unknown (e.g., drawing style [82]) and learned unsupervised using isotropic Gaussian prior [77] or information-theoric regularisation [16]. Our method aligns with the unknown setup where factors particular to sketch, text, and image are discovered unsupervised." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 449, + 289, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 571 + ], + "type": "text", + "content": "Image Captioning: This has emerged from predicting syntactically correct descriptions [89, 112] to tackling data scarcity [1, 49], and addressing user requirements [68, 69]. Predicted captions evolved from being factual in a neutral tone to (i) controllable using textual verbs [15], part-of-speech tag [26], or mouse trace [64, 71], and (ii) personalised captioning [84, 111] that learns user's active vocabulary, and writing style. Our method can (i) generate factual captions from images/sketches and (ii) extend controllable captioning paradigm by injecting saliency via sketch." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 581, + 119, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 581, + 119, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 581, + 119, + 594 + ], + "type": "text", + "content": "3. Pilot Study" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 597, + 204, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 204, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 204, + 609 + ], + "type": "text", + "content": "3.1. Sketch vs. Text for Retrieval" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 50, + 616, + 282, + 671 + ], + "blocks": [ + { + "bbox": [ + 50, + 616, + 282, + 671 + ], + "lines": [ + { + "bbox": [ + 50, + 616, + 282, + 671 + ], + "spans": [ + { + "bbox": [ + 50, + 616, + 282, + 671 + ], + "type": "image", + "image_path": "7963576892998dd92d7f442b811038697195c10556c904473433a8339ef3d7f2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 673, + 287, + 718 + ], + "lines": [ + { + "bbox": [ + 46, + 673, + 287, + 718 + ], + "spans": [ + { + "bbox": [ + 46, + 673, + 287, + 718 + ], + "type": "text", + "content": "Figure 2. We compare SBIR [107] vs. TBIR [73] on FS-COCO [19] where retrieval rank is plotted in log-scale (see Supplemental for more details). While sketch is a better query for some instances (lower retrieval rank), for others text is better." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "Text can convey colour information, or object categories, but is cumbersome to describe fine-grained details, multiple objects, or complex shapes " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "[86]^{1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": ". While sketch can depict complex shapes, multiple objects, and spatial alignment [19], not all objects are easy to draw ('donkey' vs. 'horse'). Fig. 2 shows this trade-off between sketch vs. text for image retrieval. We find an optimal fusion between sketch and text to derive best of both modalities along with the ability to optionally use only sketch, only text, or both." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 213, + 545, + 317 + ], + "blocks": [ + { + "bbox": [ + 305, + 190, + 545, + 212 + ], + "lines": [ + { + "bbox": [ + 305, + 190, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 305, + 190, + 545, + 212 + ], + "type": "text", + "content": "Table 1. Comparing alternative guiding signal like POS (part-of-speech) [26], Mouse Trace [64], and Freehand Sketches [19]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 213, + 545, + 317 + ], + "lines": [ + { + "bbox": [ + 307, + 213, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 307, + 213, + 545, + 317 + ], + "type": "table", + "html": "
SignalB-1B-4MRCS
POS [26]w/o73.231.124.552.8100.117.9
w/73.931.625.553.2104.518.8
Δ0.70.51.00.44.40.9
Trace [64]w/o32.28.1-31.729.325.7
w/52.224.6-48.3106.536.5
Δ2016.5-16.677.210.8
Sketchw/o74.731.824.753.8105.518.8
w/81.342.730.161.6121.623.5
Δ6.610.95.47.816.14.7
", + "image_path": "661e60d0c7bb9385977f4940dc00987ba6300f885f615dd070e7abad1d016207.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 326, + 457, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 326, + 457, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 326, + 457, + 338 + ], + "type": "text", + "content": "3.2. Subjectivity for Captioning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 341, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 581 + ], + "type": "text", + "content": "Unlike traditional image captioning [62, 96] that generates factual captions in neutral tone, subjective captioning adapts the predicted captions using a guiding signal that specifies priorities on what should be described [89]. The signal is injected via feature concatenation [26], or cross-attention mechanism [64]. Applications of subjective captioning include medical report generation using disease tags to generate real style reports [56], art descriptions [5], and assistive technologies for the visually impaired [37,99]. In this paper, we advocate for sketch as a guiding signal to depict salient objects and express artistic interpretations [38]. We compare the performance (see supplementary for details) using guiding signals like POS (parts-of-speech) [26], mouse trace [64], or freehand sketches [19]. Following [64], we inject the guiding signal into the image captioning pipeline via cross-attention mechanism. As evident from Table 1, while sketch is competitive with mouse traces, it is a better signal than POS. However, unlike mouse trace, sketch can depict artistic interpretation [5] that makes it a more flexible and robust guiding signal than POS or mouse trace." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 591, + 440, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 591, + 440, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 591, + 440, + 605 + ], + "type": "text", + "content": "4. Proposed Methodology" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 608, + 392, + 620 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 392, + 620 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 392, + 620 + ], + "type": "text", + "content": "4.1. Preliminaries" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "content": "Baseline for Fine-Grained Retrieval: Given a query-photo pair " + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "inline_equation", + "content": "(\\mathbf{q},\\mathbf{p})" + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "content": ", existing methods encode [7, 51, 54, 57, 107] the query " + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "inline_equation", + "content": "\\mathbf{q} = \\{\\mathbf{s},\\mathbf{t}\\}" + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "content": " comprising sketch (s) / text (t) and photo (p) as " + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{q}} = \\mathcal{F}_{\\mathbf{q}}(\\mathbf{q})\\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}} = \\mathcal{F}_{\\mathbf{p}}(\\mathbf{p})\\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 305, + 625, + 545, + 687 + ], + "type": "text", + "content": " respectively. The network is trained via triplet loss with" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1Example: Cross strap stud and buckle detail blonde leather upper leather insole chunky wooden sole 9 cm heel." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10974" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 286, + 157 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 286, + 157 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 286, + 157 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 286, + 157 + ], + "type": "image", + "image_path": "9bc4f300a9039d61cb4e400bb696f4c7d81bf4f804ed981e6f2b5218b1ca2e0d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "text", + "content": "Figure 3. (Left): We disentangle modality-agnostic and modality-specific components from sketch, text, and photo. The modality-agnostic components are aligned using contrastive loss for cross-modal transfer. (Right): Modality-agnostic sketch " + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "text", + "content": " is used across modality to generate modality-specific text " + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{t}}^{sp})" + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "text", + "content": " using text-specific " + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{t}}" + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "text", + "content": ". Combining " + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{ag}" + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}}^{ag}" + }, + { + "bbox": [ + 46, + 158, + 287, + 226 + ], + "type": "text", + "content": ", we generate text from sketch." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "content": "margin parameter " + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "inline_equation", + "content": "\\mu >0" + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "content": " such that the cosine distance " + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "inline_equation", + "content": "\\delta (\\cdot)" + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "content": " of query anchor " + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{q}" + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "content": " from a negative photo " + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}^{-})" + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "content": " should increase while that from the positive photo " + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "inline_equation", + "content": "(\\mathbf{p}^{+})" + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "text", + "content": " should decrease as, " + }, + { + "bbox": [ + 46, + 232, + 286, + 281 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{trip} = \\max \\{0,\\mu +\\delta (f_{\\mathbf{q}},f_{\\mathbf{p}^{+}}) - \\delta (f_{\\mathbf{q}},f_{\\mathbf{p}^{-}})\\}" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": "Baseline for Image Captioning: Image captioning consists of an image encoder [59, 101], " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}} = \\mathcal{F}_{\\mathbf{p}}(\\mathbf{p})" + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": " followed by an autoregressive textual decoder " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "(\\mathcal{F}_C)" + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": ". Given the textual description comprises a sequence of words " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathbf{t} = \\{w_1,\\dots ,w_K\\}" + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": ", we maximise the likelihood of a predicted word " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "(\\hat{w}_k)" + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": " at each step " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "(k)" + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": ", conditioned on " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}}" + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "text", + "content": " as, " + }, + { + "bbox": [ + 47, + 282, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_C = -\\sum_{k = 1}^{K}\\log [\\mathcal{F}_C(\\hat{w}_k = w_k|f_{\\mathbf{p}},w_1,\\dots ,w_{k - 1})]" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 372, + 115, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 115, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 115, + 383 + ], + "type": "text", + "content": "4.2. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 384, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 601 + ], + "type": "text", + "content": "We aim to disentangle the feature representations from sketch, text, and photo modalities into a modality-agnostic and modality-specific component. While the modality-agnostic component holds semantic information to support cross-modal transfer, the modality-specific one holds information necessary during self-reconstruction; however, it lacks meaning in other modalities (e.g., grammatical knowledge in text). Achieving feature disentanglement across scene sketches, texts, and photos enables a multitude of downstream tasks like (i) SBIR - modality-agnostic sketch and photo features, (ii) TBIR - modality-agnostic text and photo, (iii) Sketch + Text-Based Image Retrieval - modality-agnostic sketch, text, and photo, (iv) Image Captioning - using the modality-agnostic photo to compute modality-specific text features, (v) Sketch Captioning - modality-agnostic sketch to compute modality-specific text, and (vi) Subjective Captioning - using modality-agnostic photo and sketch, to compute modality-specific text." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 282, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 282, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 282, + 617 + ], + "type": "text", + "content": "4.3. Disentangling Modality Agnostic and Specific" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "While our disentangling method can be generalised to any number of modalities, for simplicity, we first show for " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "M = 2" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " modalities and later extend to " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "M \\geq 3" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ". Consider a simple bimodal setup of sketch " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{s} \\in \\mathbb{R}^{H \\times W \\times 3})" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " and text " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "(\\mathbf{t} \\in \\mathbb{R}^{N \\times E})" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ". Our goal is to split the feature representation " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}} = \\mathcal{F}_{\\mathbf{s}}(\\mathbf{s}) \\in \\mathbb{R}^{512}" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}} = \\mathcal{F}_{\\mathbf{t}}(\\mathbf{t}) \\in \\mathbb{R}^{512}" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " into a modality-agnostic and a modality-specific component as " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}} = [f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp}]" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}} = [f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp}]" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " respectively, where" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 545, + 142 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 545, + 142 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 545, + 142 + ], + "type": "image", + "image_path": "60f76ec42dce341d9ff0f9ab54a1da0f7d2e62e8a08fb0c427d8ac4b41b850ea.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": "Figure 4. Unlike typical neural networks that are unidirectional, data in conditional invertible neural networks " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "(\\tau_{\\mathbf{k}})" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " can flow either (i) from modality-specific " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{sp}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " to a uniform distribution " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " by conditioning on modality-agnostic " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{ag}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " during training, or (ii) from a sampled " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " in uniform distribution to the modality-specific " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{sp}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " by conditioning on modality-agnostic " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{ag}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " during inference. The conditioning vector " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{ag}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " is injected into the conditional affinity coupling layers [28] of " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": " using any arbitrary network " + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 304, + 144, + 545, + 233 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "f^{ag} \\in \\mathbb{R}^{480}" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "f^{sp} \\in \\mathbb{R}^{32}" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": ". Existing methods [82, 88] disentangle feature representations via (i) self reconstruction as " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}} = \\mathcal{D}_{\\mathbf{s}}([f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp}])" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{t}} = \\mathcal{D}_{\\mathbf{t}}([f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp}])" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " coupled with (ii) cross-modal translation " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{s}} = \\mathcal{D}_{\\mathbf{s}}([f_{\\mathbf{t}}^{ag}, f_{\\mathbf{s}}^{sp}])" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{t}} = \\mathcal{D}_{\\mathbf{t}}([f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{sp}])" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": ". However, using cross-modal translation with latent feature exchange across modalities is a cumbersome process that explodes with " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_2^M" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " permutations for " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " modalities, e.g., " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "M = 3" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " has " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_2^3 = 6" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " cross-modal translations. Adding multiple cross-modal translation losses makes optimisation difficult and computationally expensive. We break this compute barrier with linear " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "(\\mathcal{O}(M))" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " complexity using an information bottleneck reinterpretation of modality-agnostic and modality-specific disentanglement. In particular, we maximise the mutual information " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " amongst modality-agnostic components, while minimising the same between modality-agnostic and modality-specific components " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{s}}^{sp})" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{t}}^{ag}, f_{\\mathbf{t}}^{sp})" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " denotes mutual information between two entities. Hence, unlike the previous " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathbb{P}_2^M" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " permutations, Eq. (1) has one agnostic " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " specific " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " losses. Formally, using a Langrange multiplier hyperparameter " + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 239, + 546, + 503 + ], + "type": "text", + "content": " we have our loss objective as," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 335, + 505, + 545, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 505, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 335, + 505, + 545, + 545 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathcal {I}} = - \\overbrace {\\mathcal {I} \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t}} ^ {a g}\\right)} ^ {\\text {a g n o s t i c}} + \\beta \\overbrace {\\sum_ {\\mathbf {k} \\in \\{\\mathbf {s} , \\mathbf {t} \\}}} ^ {\\text {s p e c i f i c}} \\tag {1}", + "image_path": "9ca7ebc04646975afe74e4dfd9270d6ff80770bd5e0ce5311d0c01793f4ab8b6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Minimise " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ": We minimise the mutual information between modality-agnostic and modality-specific components using a conditional invertible [ ] neural network " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". Unlike typical unidirectional neural networks " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{F}: x \\to y" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", a conditional invertible neural network employs a sequence of bijective mapping operations like activation normalization (ActNorm) [45], Conditional Affine Coupling [28], and shuffling [45] to obtain " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}: x \\leftrightarrow y" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". During the forward pass (inference), we sample " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\eta \\in \\mathbb{R}^{32}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " from a uniform prior distribution " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(\\eta)" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " to predict the modality-specific " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{sp} \\in \\mathbb{R}^{32}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " by conditioning on " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{ag}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " as, " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{sp} = \\tau_{\\mathbf{k}}(\\eta | f_{\\mathbf{k}}^{ag})" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". In other words, during inference, we predict the modality-specific component of target from the modality-agnostic one of input using " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". The target modality is" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10975" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 323, + 170 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 323, + 170 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 323, + 170 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 323, + 170 + ], + "type": "image", + "image_path": "cbc47200456493b1ee8049ad6e11ff710863ef962b6f00983f5527231e5ccb5b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 173, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 46, + 173, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 547, + 207 + ], + "type": "text", + "content": "Figure 5. (Left): The modality-agnostic from sketch, or text, or both are used to retrieve from a gallery of photos. This enables a multitude of retrieval tasks like SBIR, TBIR, and STBIR. (Right): The modality-agnostic from photo, or sketch, or both are used to generate the text-specific component. Combining the modality-agnostic and inferred text-specific (via " + }, + { + "bbox": [ + 46, + 173, + 547, + 207 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{t}}" + }, + { + "bbox": [ + 46, + 173, + 547, + 207 + ], + "type": "text", + "content": ") enables image, or sketch, or subjective captioning." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 325, + 70, + 542, + 171 + ], + "blocks": [ + { + "bbox": [ + 325, + 70, + 542, + 171 + ], + "lines": [ + { + "bbox": [ + 325, + 70, + 542, + 171 + ], + "spans": [ + { + "bbox": [ + 325, + 70, + 542, + 171 + ], + "type": "image", + "image_path": "55451c3a3b2a6f1e97526a009119b4205634e536430359f3e2b79a907403ca7d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": "then generated by combining the input-agnostic and target-specific components. The conditioning modality-agnostic vector " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{k}}^{ag}" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": " is injected into the intermediate conditional affine coupling layers " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{C}: x \\leftrightarrow y" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": " as: " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "[x_1, x_2] = \\text{split}(x)" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "y = \\text{concat}[x_1, s_\\theta([x_1; h]) \\odot x_2 + t_\\theta([x_1; h])]" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": ", where, " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "h = \\mathcal{H}(f_{\\mathbf{k}}^{ag})" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": ". A simple feed-forward neural network implements " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "s_\\theta, t_\\theta" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": ". We learn " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": " in the reverse pass (training) via negative log-likelihood (NLL Loss in Fig. 4) of " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}^{-1}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag})" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": " to predict a uniform distribution " + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(\\eta)" + }, + { + "bbox": [ + 46, + 213, + 289, + 323 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 326, + 287, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 326, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 62, + 326, + 287, + 344 + ], + "type": "interline_equation", + "content": "\\mathbb {P} (\\eta) = \\mathbb {P} \\left(\\tau_ {\\mathbf {k}} ^ {- 1} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right)\\right) | \\det J _ {\\tau_ {\\mathbf {k}} ^ {- 1}} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right) | \\quad (2)", + "image_path": "8f3f730b56b14e3f377db43bf112a653bdf92af61e0eeda2f1708ea702e2f0dd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": "We show how learning " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " in Eq. (2) minimises " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp}) = \\int_{f_{\\mathbf{k}}^{sp}} \\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) \\log \\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag}) / \\mathbb{P}(f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": ". Approximating modality-specific prior " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " with variational distribution " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{Q}(f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " gives the upper-bound, minimising which reduces the KL-divergence between " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(f_{\\mathbf{k}}^{sp} | f_{\\mathbf{k}}^{ag})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{Q}(f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " i.e., it encourages the disentanglement " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{P}(f_{\\mathbf{k}}^{ag}, f_{\\mathbf{k}}^{sp}) \\approx \\mathbb{P}(f_{\\mathbf{k}}^{ag}) \\cdot \\mathbb{P}(f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": ". The prior " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\mathbb{Q}(f_{\\mathbf{k}}^{sp})" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " is solved using " + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathbf{k}}" + }, + { + "bbox": [ + 46, + 347, + 287, + 483 + ], + "type": "text", + "content": " to enforce disentanglement between modality-agnostic and modality-specific components, like that in Eq. (2), as the sum of negative-loglikelihood (NLL-Loss in Fig. 4) and log-determinant (see supplementary for proof)," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 64, + 483, + 287, + 516 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 483, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 64, + 483, + 287, + 516 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\tau_ {\\mathbf {k}}} = - \\mathbb {E} _ {f _ {\\mathbf {k}} ^ {s p}} \\left\\{\\log \\mathrm {q} \\left(\\tau_ {\\mathbf {k}} ^ {- 1} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right)\\right) \\right. \\tag {3} \\\\ + \\log | \\det J _ {\\tau_ {\\mathbf {k}} ^ {- 1}} \\left(f _ {\\mathbf {k}} ^ {s p} \\mid f _ {\\mathbf {k}} ^ {a g}\\right) | \\} \\\\ \\end{array}", + "image_path": "30d8effe5402a6e1812a8d8a1684f0e6d635f8c40c3693133899b5e3ee0081d7.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 518, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 579 + ], + "type": "text", + "content": "Maximise " + }, + { + "bbox": [ + 46, + 518, + 287, + 579 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})" + }, + { + "bbox": [ + 46, + 518, + 287, + 579 + ], + "type": "text", + "content": ": Here we show how minimising a constrastive based retrieval loss [94] between the modality-agnostic components of sketch and text will maximise their mutual information. We define contrastive loss matching modality-agnostic components of sketch and text as," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 50, + 584, + 287, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 584, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 50, + 584, + 287, + 628 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {c l} ^ {\\mathbf {s}, \\mathbf {t}} = - \\mathbb {E} _ {f _ {\\mathbf {s}} ^ {s p}} \\left[ \\log \\frac {\\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {+}} ^ {a g}\\right)}{\\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {+}} ^ {a g}\\right) + \\sum_ {f _ {\\mathbf {t} ^ {-}} ^ {a g}} ^ {N - 1} \\omega \\left(f _ {\\mathbf {s}} ^ {a g} , f _ {\\mathbf {t} ^ {-}} ^ {a g}\\right)} \\right] \\tag {4}", + "image_path": "fecaf2e2fba296e552454e17ea231e41ac7a31916533d3428ca411e7fff59d2f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\omega = \\exp (x^{T}\\mathbf{W}y)" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ". For each modality-agnostic " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " we sample a positive " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}^{+}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "(N - 1)" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " negative " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}^{-}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " pairs. The contrastive loss in Eq. (4) is expressed as mutual information between " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " as, " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}\\geq -\\mathcal{I}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{t}}^{ag}) + \\log (N)" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ". Hence, to maximise the mutual information between modality-agnostic " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{s}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{t}}^{ag}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": ", we can maximise the tractable lower bound " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\log (N) - \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "text", + "content": "Total Loss for Bimodal Setup: The resulting loss " + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{tot})" + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "text", + "content": " for bimodal (sketch and text) setup comprise three loss objectives (i) self reconstruction loss " + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec}" + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "text", + "content": ", (ii) contrastive loss between two modality-agnostic terms " + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}" + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "text", + "content": ", and (iii) disentanglement between modality-agnostic and modality-specific components in each modality " + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "inline_equation", + "content": "(\\mathbf{k})" + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{\\tau_{\\mathbf{k}}})" + }, + { + "bbox": [ + 304, + 213, + 545, + 285 + ], + "type": "text", + "content": ", as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 286, + 545, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 286, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 321, + 286, + 545, + 317 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {r e c} = | | \\mathbf {s} - \\mathcal {D} _ {\\mathbf {s}} (\\mathcal {F} _ {\\mathbf {s}} (\\mathbf {s})) | | _ {2} + | | \\mathbf {t} - \\mathcal {D} _ {\\mathbf {t}} (\\mathcal {F} _ {\\mathbf {t}} (\\mathbf {t})) | | _ {2} \\tag {5} \\\\ \\mathcal {L} _ {t o t} = \\mathcal {L} _ {r e c} + \\mathcal {L} _ {c l} ^ {\\mathbf {s}, \\mathbf {t}} + \\beta [ \\mathcal {L} _ {\\tau_ {\\mathbf {s}}} + \\mathcal {L} _ {\\tau_ {\\mathbf {t}}} ] \\\\ \\end{array}", + "image_path": "8ae4b89696bb50a9edb59e0974d55c28dc300a03a63015394158c44c3b81a68f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "text", + "content": "Extending to Three/More Modalities: Here we extend our bimodal setup in Sec. 4.3 to three or more modalities. (i) We compute the self-reconstruction loss for three modalities as " + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{rec} = \\sum_{\\mathbf{k}\\in \\{\\mathbf{s},\\mathbf{t},\\mathbf{p}\\}}||\\mathbf{k} - \\mathcal{D}_{\\mathbf{k}}(\\mathcal{F}_{\\mathbf{k}}(\\mathbf{k}))||_2" + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "text", + "content": " (ii) we minimise the mutual information between modality-agnostic and modality-specific components for sketch, text, and photo as, " + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\tau} = \\mathcal{L}_{\\tau_{\\mathrm{s}}} + \\mathcal{L}_{\\tau_{\\mathrm{t}}} + \\mathcal{L}_{\\tau_{\\mathrm{p}}}" + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "text", + "content": ". (iii) However, our contrastive loss term " + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}" + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "text", + "content": " that maximises the mutual information among modality-agnostic components can only compare two modalities. We can extend this naively to a three-modality setup as " + }, + { + "bbox": [ + 304, + 324, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}^{tot} = \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}} + \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}} + \\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": "Extending to three or more modalities, however, we notice our contrastive loss in Eq. (4) is defined for only b-modal setup " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , or " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , or " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " ). For example, given three modalities " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "S_{M} = \\{m_{1},m_{2},m_{3}\\}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , comparing only " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "(m_{1},m_{2})" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " ignores " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " . This highlights a key limitation: it fails when we have a query in both " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "(m_{1},m_{3})" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " to retrieve " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{2}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " (e.g., sketch+text for image retrieval). Now the research question boils down to - how can we model a function " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(\\cdot)" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " such that it can model either " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , or " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , or both " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "(m_{1},m_{3})" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " to retrieve " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{2}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " . To design " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , using naive addition as " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(m_1,m_3) = m_1 + m_3" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " does not handle overlapping or conflicting information in " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " [58]. While, concatenation " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{G}(m_1,m_3) = \\mathrm{concat}[m_1,m_3]" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " computes interaction between " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "(m_{1},m_{3})" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , it forces to provide both " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " during inference; thereby failing to model either " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , or " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "text", + "content": " , or both " + }, + { + "bbox": [ + 304, + 456, + 545, + 647 + ], + "type": "inline_equation", + "content": "(m_{1},m_{3})" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 650, + 492, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 650, + 492, + 662 + ], + "spans": [ + { + "bbox": [ + 305, + 650, + 492, + 662 + ], + "type": "text", + "content": "4.4. Modelling Optional Sketch or Text" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "text", + "content": "We propose a simple approach to design " + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "text", + "content": " that optionally models either " + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "text", + "content": ", or " + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "text", + "content": ", or both " + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "inline_equation", + "content": "(m_{1}, m_{3})" + }, + { + "bbox": [ + 304, + 663, + 545, + 687 + ], + "type": "text", + "content": ", and handles" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "2When signals " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "(m_{1},m_{3})" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " are similar or complementary " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " should strengthen decision; when signals conflict " + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": " should filter unreliable ones." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10976" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": "overlapping or conflicting information. Our proposed " + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": " comprises a multihead cross-attention module " + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "inline_equation", + "content": "\\mathrm{MH}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": " followed by an attention-based pooling " + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "inline_equation", + "content": "\\mathrm{PMA}(\\cdot)" + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": " as, " + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "inline_equation", + "content": "f_{M} = \\mathrm{PMA}(H_{M})" + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": "; where " + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "inline_equation", + "content": "H_{M} = \\mathrm{MH}(S_{M})" + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "inline_equation", + "content": "S_{M} = \\{m_{1}, m_{3}\\}" + }, + { + "bbox": [ + 47, + 72, + 286, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": "Our " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{MH}(\\cdot)" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " is order-invariant and independent of the number " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "(M)" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " of input modalities defined as " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{MH}(X) = \\sigma (XX^T)X" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": "; where " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " is scaled-softmax, " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "X^T" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " is transpose of " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "X\\in \\mathbb{R}^{M\\times 480}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " is a list of modality-agnostic components " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "m_{1}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ", or " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "m_{3}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{1\\times 480}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ", or " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "(m_1,m_3)\\in \\mathbb{R}^{2\\times 480}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " in query. The cross-attention in " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{MH}(\\cdot)" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " interacts across query modalities to compute mutually agreeing information between " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "(m_{1},m_{3})" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " as, " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "H_{M}\\in \\mathbb{R}^{2\\times 480}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ". Next, we use an order-invariant attention-based pooling " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{PMA}: \\mathbb{R}^{2\\times 480}\\to \\mathbb{R}^{1\\times 480}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " with a learned seed vector " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{P}\\in \\mathbb{R}^{1\\times 480}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " to aggregate mutually agreeing " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "H_{M}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " as, " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "f_{M} = \\mathrm{PMA}(H_{M}) = \\sigma (\\mathcal{P}H_{M}^{T})H_{M}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ". Hence, using our proposed fusion module " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ", we adapt our contrastive loss defined for only a pair of modality-agnostic components in Eq. (4) as " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cl}^{tot} = \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{t}} + \\mathcal{L}_{cl}^{\\mathbf{s},\\mathbf{p}} + \\mathcal{L}_{cl}^{\\mathbf{t},\\mathbf{p}}" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": " to jointly model sketch-text-photo (or more) modality-agnostic as: " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}^{tot} = \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{t}}^{ag}),f_{\\mathbf{p}}^{ag}) + \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{s}}^{ag},f_{\\mathbf{p}}^{ag}),f_{\\mathbf{t}}^{ag}) + \\mathcal{L}_{cl}(\\mathcal{G}(f_{\\mathbf{p}}^{ag},f_{\\mathbf{t}}^{ag}),f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ". For a generalised solution involving more than three modalities " + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "inline_equation", + "content": "(M > 3)" + }, + { + "bbox": [ + 47, + 121, + 286, + 335 + ], + "type": "text", + "content": ", see supplementary." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": "Inference Data Flow: We describe the inference data flow in Fig. 5. For retrieval tasks, we first compute the modality-agnostic component of query sketch and text " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": ", and a gallery of photos " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\{f_{\\mathbf{p}_1}^{ag}, f_{\\mathbf{p}_2}^{ag}, \\ldots, f_{\\mathbf{p}_{\\mathbf{N}}}^{ag}\\}" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": ". Next, a combined representation for either only sketch " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": ", or only text " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{t}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": ", or both " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag}, f_{\\mathbf{t}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " is computed using multihead cross attention " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathrm{MH}(\\cdot)" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " followed by attention-based pooling " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\mathrm{PMA}(\\cdot)" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " defined in Sec. 4.4 to get " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{st}^*}^{ag}" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": ". Finally, we find the minimum distance between the combined " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{st}^*}^{ag}" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " and modality-agnostic component of photo " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "f_{\\mathbf{p}_i}^{ag}" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\omega(f_{\\mathbf{st}^*}^{ag}, f_{\\mathbf{p}_i}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " defined in Eq. (4). For captioning, we additionally use the text-specific conditional invertible neural network " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "\\tau_t" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " to generate the target modality-specific text (e.g., grammatical structure etc.) from input modality-agnostic comprising of only photo " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{p}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " for image captioning, only sketch " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " for sketch captioning, or both photo and sketch " + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{p}}^{ag}, f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 47, + 338, + 286, + 553 + ], + "type": "text", + "content": " for subjective captioning (i.e., generate image captions by conditioning on the input sketch)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 564, + 127, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 564, + 127, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 564, + 127, + 577 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 582, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 286, + 712 + ], + "type": "text", + "content": "Datasets: We use two scene sketch datasets with fine-grained alignment among sketch, text, and photo: (i) SketchyCOCO [34] contains 14,081 scene sketch-photo pairs. The photos are taken from MS-COCO [55] comprising " + }, + { + "bbox": [ + 47, + 582, + 286, + 712 + ], + "type": "inline_equation", + "content": "164K" + }, + { + "bbox": [ + 47, + 582, + 286, + 712 + ], + "type": "text", + "content": " photos with paired texts. However, most sketches in SketchyCOCO [34] contain less than one foreground instance. Following [57], we filter SketchyCOCO with one foreground instance to get 1015/210 train/test scene sketches. (ii) Unlike SketchyCOCO [34], where the scene sketches are synthetically generated, FS-COCO [19] includes 7000/3000 train/test human-drawn scene sketches" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 485, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 485, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 485, + 84 + ], + "type": "text", + "content": "with a paired textual description of sketches." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "text", + "content": "Implementation Details: Our model is implemented in PyTorch using 11GB Nvidia RTX 2080-Super GPU. First, we pre-train the image encoder and text decoder for image captioning using 82,783 photo-text pairs (excluding the photos common in SketchyCOCO and FS-COCO) for 15 epochs. Next, we fine-tune on either SketchyCOCO [34], or FS-COCO [19] for 200 epochs using Adam optimiser with learning rate " + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "text", + "content": ", and batch size 64. Our photo " + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "inline_equation", + "content": "(\\mathcal{F}_{\\mathbf{p}})" + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "text", + "content": " and sketch " + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "inline_equation", + "content": "(\\mathcal{F}_{\\mathrm{s}})" + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "text", + "content": " encoders use ImageNet pretrained VGG-16 [85]. For simplicity, we encode text using a bidirectional GRU unit with 512 hidden units. Our text decoder [43] is a single-layer autoregressive LSTM decoder that predicts a probability distribution over a fixed vocabulary (10,010 words) at every time step. For the image/sketch decoder, we use two separate GAN [109] networks that synthesise sketch/image of size " + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "inline_equation", + "content": "64\\times 64" + }, + { + "bbox": [ + 304, + 90, + 545, + 354 + ], + "type": "text", + "content": ", respectively. For brevity, we avoid realistic sketch/image generation due to the challenging scene complexity [19]. Hence we do not use a discriminator module for high-quality, sharp reconstruction [110]. Finally, our conditionally invertible neural network comprises 16 alternating affine coupling [29], activation normalisation [45], and switch layers [29]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 360, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 456 + ], + "type": "text", + "content": "Evaluation Metric: In line with FG-SBIR research, we use Acc.@q [81] defined as the percentage of sketches having a true matched photo in the top-q list. For sketch/image/subjective captioning, we use standard metrics BELU (B) 1-4 [67], CIDEr (C) [95], ROUGE (R) [53], METEOR (M) [25], and SPICE [2]. Following [96], we generate 100 candidate captions and employ consensus reranking using CIDEr to select the best candidate caption." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "content": "Competitors: We compare against (i) existing state-of-the-art methods that align two modalities (S2): For SBIR, Triplet-SN [107] employs Sketch-A-Net [108] backbone trained using triplet loss. HOLEF [87] adds spatial attention with a higher-order ranking loss. SketchyS [115] replaces Sketch-A-Net in Triplet-SN with VGG-16 [85] and an auxiliary category-level cross-entropy. SceneS [57] uses GCN [46] to model scene sketch layout information. For TBIR, CLIP [73] is trained with text using transformer [83] and photo using vision transformer [30] on 400 million text-photo pairs. CLIP-LN fine-tunes CLIP by training only layer normalisation parameters [4] with learning rate 0.00001. For image/sketch captioning, SAT [101] is one of the simplest but seminal works using a CNN-LSTM encoder-decoder approach similar to ours. GMM-CVAE [96] employs a conditional variational autoencoder with a Gaussian mixture model. LNFMM [61] is similar to ours that splits information into modality-agnostic and modality-specific components using conditional invertible neural network, ClipCap [65] employs CLIP [73] for image encoding followed by GPT-2 [74] for text decoding. A learned" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10977" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 94, + 288, + 159 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 92 + ], + "type": "text", + "content": "Table 2. Quantitative results combining sketch and text for image retrieval (FG-STBIR) on two scene sketch datasets [19, 34]." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 94, + 288, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 94, + 288, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 288, + 159 + ], + "type": "table", + "html": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S3QST [86]38.987.925.154.5
SCM [3]38.587.324.354.1
BCrossAtt [83]39.188.225.354.8
Proposed39.588.725.755.2
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Qualitative results of combining sketch and text as query for image retrieval on FSCOCO [19]. See supplementary for more." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 93, + 235, + 130, + 272 + ], + "blocks": [ + { + "bbox": [ + 93, + 235, + 130, + 272 + ], + "lines": [ + { + "bbox": [ + 93, + 235, + 130, + 272 + ], + "spans": [ + { + "bbox": [ + 93, + 235, + 130, + 272 + ], + "type": "image", + "image_path": "1d597511d67f326a5b8cc151e3502f52bc3f6b7e2ce64858175ebc6122462009.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 131, + 235, + 170, + 274 + ], + "blocks": [ + { + "bbox": [ + 131, + 235, + 170, + 274 + ], + "lines": [ + { + "bbox": [ + 131, + 235, + 170, + 274 + ], + "spans": [ + { + "bbox": [ + 131, + 235, + 170, + 274 + ], + "type": "image", + "image_path": "8c9c912a0282f5e8c44ddf5c9b48420163a6addee74076690140c3b414d462c2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 171, + 235, + 208, + 273 + ], + "blocks": [ + { + "bbox": [ + 171, + 235, + 208, + 273 + ], + "lines": [ + { + "bbox": [ + 171, + 235, + 208, + 273 + ], + "spans": [ + { + "bbox": [ + 171, + 235, + 208, + 273 + ], + "type": "image", + "image_path": "834fd81d89739a308646f9999cc67c191b15d68d141fdbbd55d4754f9eae2e38.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 209, + 235, + 246, + 273 + ], + "blocks": [ + { + "bbox": [ + 209, + 235, + 246, + 273 + ], + "lines": [ + { + "bbox": [ + 209, + 235, + 246, + 273 + ], + "spans": [ + { + "bbox": [ + 209, + 235, + 246, + 273 + ], + "type": "image", + "image_path": "32a377b68de073f05e609decf2772eef34570fa46f8de312676b02535661b779.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 247, + 235, + 286, + 273 + ], + "blocks": [ + { + "bbox": [ + 247, + 235, + 286, + 273 + ], + "lines": [ + { + "bbox": [ + 247, + 235, + 286, + 273 + ], + "spans": [ + { + "bbox": [ + 247, + 235, + 286, + 273 + ], + "type": "image", + "image_path": "fa1907315712fb38cce2e3967e3ad6d48df92f0ff22a603cd987071192ef039b.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "text", + "content": "mapping module translates CLIP embeddings to GPT-2. (ii) We compare against methods that align 3 modalities (S3): For STBIR, QST [86] extends triplet loss in Triplet-SN to quadruplet loss that combines sketch and text for image retrieval. SCM uses element-wise addition to combine sketch and text from ResNet-18 [39] with weight sharing across sketch, text, and photo from ResBlock4 onwards [3]. (iii) We design baselines (B): For STBIR, CrossAtt employs cross-attention [83] to combine sketch and text. For subjective captioning, MulCap combines sketch " + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "text", + "content": " and photo " + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{p}}^{ag})" + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "text", + "content": " via element-wise multiplication as in [14]. CrossCap optionally fuse photo, sketch, or both using cross-attention. CatCap use feature concatenation [71] of guiding sketch " + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{s}}^{ag})" + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "text", + "content": " signal with photo " + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "inline_equation", + "content": "(f_{\\mathbf{p}}^{ag})" + }, + { + "bbox": [ + 46, + 309, + 287, + 478 + ], + "type": "text", + "content": " to generate captions." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 480, + 287, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 287, + 493 + ], + "type": "text", + "content": "5.1. Combining Sketch and Text for Image Retrieval" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 494, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 287, + 673 + ], + "type": "text", + "content": "Fig. 2 shows that for some instances, sketch is a better query, whereas text is better for others. Hence, to achieve best of both modalities, we examine the complimentary nature by combining sketch and text for image retrieval. Table 2 shows (i) SCM gives the lowest performance due to naive element-wise addition of potentially overlapping and conflicting information [58] from sketch and text. (ii) QST improves slightly upon SCM by replacing naive elementwise addition with a weighted summation (0.8 for sketch modality). (iii) CrossAtt outperforms all baselines by using a cross-attention between sketch and text to resolve overlapping/conflict information [58]. (iv) Our proposed method gives the highest performance due to cross-attention that model sketch-text interaction and disentanglement to drive out modality-specific information for cross-modal retrieval." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 47, + 677, + 276, + 689 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 276, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 276, + 689 + ], + "type": "text", + "content": "5.2. Optionally using Sketch for Image Retrieval" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Our method allows drawing only easy-to-sketch scenes instead of using both sketch and text forcibly. Table 3 com" + } + ] + } + ], + "index": 21 + }, + { + "type": "table", + "bbox": [ + 307, + 94, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 306, + 71, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 306, + 71, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 545, + 92 + ], + "type": "text", + "content": "Table 3. Quantitative results using only sketch for image retrieval (FG-SBIR) on two scene sketch datasets [19, 34]." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 94, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 307, + 94, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 307, + 94, + 545, + 198 + ], + "type": "table", + "html": "
MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2Triplet-SN [107]6.232.94.721.0
HOLEF [87]6.240.74.921.7
SketchyS [115]36.578.623.052.3
SceneS [57]31.986.2--
S3QST [86]37.487.123.652.9
SCM [3]37.386.823.452.6
BCrossAtt37.987.423.753.5
Proposed38.287.624.153.9
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MethodSketchyCOCO [34]FSCOCO [19]
Acc.@1Acc.@10Acc.@1Acc.@10
S2CLIP [73]21.050.911.535.3
CLIP-LN [73]22.152.314.836.6
S3QST [86]11.131.17.223.6
SCM [3]10.731.06.923.1
BCrossAtt20.151.012.535.8
Proposed21.551.613.736.3
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Qualitative results for image captioning v/s subjective captioning on FS-COCO [19]. See supplementary for more." + } + ] + } + ], + "index": 38, + "angle": 0, + "type": "image_caption" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 320, + 356, + 361, + 388 + ], + "blocks": [ + { + "bbox": [ + 369, + 342, + 413, + 355 + ], + "lines": [ + { + "bbox": [ + 369, + 342, + 413, + 355 + ], + "spans": [ + { + "bbox": [ + 369, + 342, + 413, + 355 + ], + "type": "text", + "content": "A herd of sheep on grassland." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 320, + 356, + 361, + 388 + ], + "lines": [ + { + "bbox": [ + 320, + 356, + 361, + 388 + ], + "spans": [ + { + "bbox": [ + 320, + 356, + 361, + 388 + ], + "type": "image", + "image_path": "3aa3ff89dce81b31cde100c73414e520195faf98d28bd15f01ef7ba73fea3a97.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 429, + 364, + 440, + 386 + ], + "blocks": [ + { + "bbox": [ + 374, + 362, + 418, + 382 + ], + "lines": [ + { + "bbox": [ + 374, + 362, + 418, + 382 + ], + "spans": [ + { + "bbox": [ + 374, + 362, + 418, + 382 + ], + "type": "text", + "content": "Sheep are grazing beyond the fence on a hill." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 429, + 364, + 440, + 386 + ], + "lines": [ + { + "bbox": [ + 429, + 364, + 440, + 386 + ], + "spans": [ + { + "bbox": [ + 429, + 364, + 440, + 386 + ], + "type": "image", + "image_path": "2157ffb650d9824ed575581fc3612dc3df852e20f3f158d73b9124b988b60309.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 441, + 364, + 471, + 386 + ], + "blocks": [ + { + "bbox": [ + 441, + 364, + 471, + 386 + ], + "lines": [ + { + "bbox": [ + 441, + 364, + 471, + 386 + ], + "spans": [ + { + "bbox": [ + 441, + 364, + 471, + 386 + ], + "type": "image", + "image_path": "08590dda607bde1e266bc3b9eee287a8da579f7e81b2d8652306ac520a95b814.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 498, + 361, + 537, + 383 + ], + "lines": [ + { + "bbox": [ + 498, + 361, + 537, + 383 + ], + "spans": [ + { + "bbox": [ + 498, + 361, + 537, + 383 + ], + "type": "text", + "content": "Three people are walking holding umbrella." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "type": "text", + "content": "pares against methods that specialise on two-modalities (S2), three-modalities (S3), and our proposed baselines (B). We observe (i) training on three modalities (sketch, text, and photo) in S3 generally outperforms those trained using only sketch and photo (S2). This can be attributed to learning generalisable features in multi-modal setup [3]. (ii) " + }, + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "type": "inline_equation", + "content": "QST" + }, + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "type": "text", + "content": " in S3 outperforms SCM indicating quadruplet loss is a better training objective than naive element-wise addition when combining sketch, text, and photo. (iii) Performance difference between CrossAttn and " + }, + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "type": "inline_equation", + "content": "QST" + }, + { + "bbox": [ + 304, + 421, + 545, + 601 + ], + "type": "text", + "content": " is not as significant as in FG-STBIR (Table 2) as during inference, we only use sketch, omitting the cross-attention module. (iv) Our method outperforms S2, S3, and B even for two-modality setup thanks to disentanglement that eliminates confounding [3] modality-specific information." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 305, + 605, + 523, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 605, + 523, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 605, + 523, + 617 + ], + "type": "text", + "content": "5.3. Optionally using Text for Image Retrieval" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "While some information is best expressed by drawing, others, like colour, is best described via text. From Table 4, we observe (i) Given the same train/test split, sketches outperform text as a query modality for fine-grained image retrieval. (ii) CLIP and CLIP-LN outperforms all competitors due to superior pre-trained weights using 400 million text-image pairs. (iii) The proposed method outperforms most methods due to disentanglement that drives out modality-" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10978" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 83, + 542, + 186 + ], + "blocks": [ + { + "bbox": [ + 102, + 71, + 490, + 81 + ], + "lines": [ + { + "bbox": [ + 102, + 71, + 490, + 81 + ], + "spans": [ + { + "bbox": [ + 102, + 71, + 490, + 81 + ], + "type": "text", + "content": "Table 5. Quantitative results of standard captioning metrics on MS-COCO [55] and FS-COCO [19] dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 83, + 542, + 186 + ], + "lines": [ + { + "bbox": [ + 48, + 83, + 542, + 186 + ], + "spans": [ + { + "bbox": [ + 48, + 83, + 542, + 186 + ], + "type": "table", + "html": "
MethodImage CaptioningSketch CaptioningSubjective Captioning
B-1B-4MRCSB-1B-4MRCSB-1B-4MRCS
S2SAT [101]71.825.023.0---46.213.717.144.969.414.5------
GMM-CVAE [96]72.930.724.252.598.617.749.615.518.348.777.615.5------
AG-CVAE [96]73.231.124.552.8100.118.850.916.018.949.180.515.8------
LNFMM [61]74.731.824.753.8105.518.852.216.721.052.990.116.0------
BMulCap74.933.225.554.9106.019.553.917.021.053.897.316.778.738.628.559.8110.721.7
CatCap------------77.638.028.357.7108.021.2
CrossCap75.534.326.155.4106.720.154.317.921.454.3100.317.579.239.328.459.5117.322.1
Proposed76.035.926.956.9107.020.956.919.321.656.6106.518.981.342.730.161.6121.623.5
", + "image_path": "1b4aa69d1d2b94bf783b26d37b9cd9e62fa8f7811c16bc0fbab0e5a12ce07bbd.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 219, + 285, + 275 + ], + "blocks": [ + { + "bbox": [ + 47, + 197, + 286, + 217 + ], + "lines": [ + { + "bbox": [ + 47, + 197, + 286, + 217 + ], + "spans": [ + { + "bbox": [ + 47, + 197, + 286, + 217 + ], + "type": "text", + "content": "Table 6. Ablation study on FG-STBIR and Subjective Captioning using FSCOCO [19]. CA denotes cross-attention in Sec. 4.4." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 219, + 285, + 275 + ], + "lines": [ + { + "bbox": [ + 48, + 219, + 285, + 275 + ], + "spans": [ + { + "bbox": [ + 48, + 219, + 285, + 275 + ], + "type": "table", + "html": "
τkCACLAcc.@1Acc.@10B-1C
XXX24.553.773.3100.1
✓XX24.954.077.9108.5
✓✓X25.554.980.6119.3
✓✓✓25.755.281.3121.6
", + "image_path": "01fb12615b5717ee2bd6b115c70745234269d1478502fcbeb91e729fc1f3b18e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 285, + 286, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 286, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 286, + 334 + ], + "type": "text", + "content": "specific components. Although CLIP [73] outperforms the proposed method, we deliberately use a simple and easy-to-reproduce GRU/VGG-16 architectures for text/photo encoders, and train on a much smaller data [19,34] than CLIP." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 337, + 202, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 202, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 202, + 350 + ], + "type": "text", + "content": "5.4. Image or Sketch Captioning" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 350, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 350, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 45, + 350, + 287, + 625 + ], + "type": "text", + "content": "In addition to disentanglement for cross-modal retrieval tasks (e.g., FG-SBIR, FG-TBIR), our conditional invertible neural network " + }, + { + "bbox": [ + 45, + 350, + 287, + 625 + ], + "type": "inline_equation", + "content": "\\tau_{\\mathrm{t}}" + }, + { + "bbox": [ + 45, + 350, + 287, + 625 + ], + "type": "text", + "content": " can also generate text-specific information (Fig. 4) to support generative tasks like image/sketch captioning. We generate 100 candidate captions using (i) beam search for SAT, MulCap, CrossCap, CatCap, and (ii) sampling from prior distribution for GMM-CVAE, AG-CVAE, LNFMM, and our proposed method. From Table 5, we observe (i) our baselines adopting recent techniques like vision-transformer [30] outperforms (S2) – recent but complex approaches like LNFMM, AG-CVAE, and the older yet seminal work like SAT. (ii) Performance gap between MulCap and CrossCap is insignificant for two-modality setups (photo to text, or sketch to text) since they primarily differentiate by their multi-modal (photo and sketch) fusion strategy. (iii) In spite of using a photo/sketch encoder and text decoder similar to our simple competitor SAT, our proposed method performs competitively with complex methods like LNFMM, AG-CVAE, and latest approaches using vision-transformers [30], like CrossCap. This shows the significant contribution of (i) disentangling modality-specific and modality-agnostic components from photo/sketch, and (ii) modelling text-specific prior for generative tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 629, + 239, + 641 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 239, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 239, + 641 + ], + "type": "text", + "content": "5.5. Sketch Based Subjective Captioning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": "As defined in Sec. 3.2, unlike traditional captioning frameworks that factually describe an image or sketch in a neutral tone, subjective captioning focus on drawing out a user's intentions, salient objects, and artistic interpretations [38]. Being the first method to use scene-level sketch as a guiding signal for captioning, we follow controllable caption-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 354 + ], + "type": "text", + "content": "ing literature [89] to adopt three baselines (B) that inject the sketch conditioning signal into the captioning pipeline. From Table 5, we observe (i) MulCap outperforms CatCap, thereby supporting previous observations [14] of elementwise multiplication being more effective than concatenation. (ii) CrossAtt outperforms all baselines (B) and two-modality SOTAs (S2) by using a cross-attention mechanism to fuse sketch and photo by modelling sketch-photo interactions to resolve overlapping or conflicting information. Our proposed method is similar to CrossAtt using cross-attention (Sec. 4.4) but also enriches the modality-agnostic sketch and photo features by removing the confounding modality-specific information to offer the best performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 357, + 370, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 370, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 370, + 367 + ], + "type": "text", + "content": "5.6. Ablation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "text", + "content": "In Table 6, we evaluate the contribution of each key design choice on FG-STBIR and Subjective captioning using FS-COCO [19]. (i) Replacing cross-attention in Sec. 4.4 with quadruplet loss [86] leads to a performance drop by " + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "inline_equation", + "content": "0.6 / 0.9 / 2.7 / 10.8" + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "text", + "content": " in Acc.@1/Acc.@10/B-1/C metrics respectively to show the importance of modelling the interaction between sketch and text. (ii) Replacing contrastive loss-based query-photo score in Eq. (4) with a simple triplet loss leads to a performance drop by " + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "inline_equation", + "content": "0.2 / 0.3 / 0.7 / 2.3" + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "text", + "content": " due to the inability of unimodal L2-based triplet loss to model highly complex scene information [94]. (iii) Finally, removing the conditional invertible neural networks " + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "inline_equation", + "content": "(\\tau_{\\mathbf{k}})" + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "text", + "content": " drops retrieval and captioning by " + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "inline_equation", + "content": "0.4 / 0.3 / 4.6 / 8.4" + }, + { + "bbox": [ + 304, + 369, + 545, + 561 + ], + "type": "text", + "content": " due to percolation of the confounding modality-specific information in cross-modal tasks [3] and the inability to generate text-specific information from photo and sketch respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 567, + 378, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 567, + 378, + 578 + ], + "spans": [ + { + "bbox": [ + 306, + 567, + 378, + 578 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "We have studied for the first time the trilogy relationship among scene-level sketch, text, and photo by introducing scene-sketch in the context of scene understanding. We proposed a unified framework to jointly model sketch, text, and photo that seamlessly support several downstream tasks like fine-grained sketch-based image retrieval, fine-grained sketch and text based image retrieval, sketch captioning, and subjective captioning, among others. Future research can explore challenging downstream tasks such as scene-level sketch-based image generation, sketch and text based image generation, and text-based sketch generation tasks." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10979" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 92, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 56, + 92, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 92, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 56, + 92, + 287, + 135 + ], + "type": "text", + "content": "[1] Harsh Agarwal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. nocaps: novel object captioning at scale. 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In ECCV, 2018. 1, 2, 6, 7" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10983" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2023/Score Jacobian Chaining_ Lifting Pretrained 2D Diffusion Models for 3D Generation/6ed9361a-e1bd-4c7d-893b-e63657bb23f8_content_list.json b/2023/Score Jacobian Chaining_ Lifting Pretrained 2D Diffusion Models for 3D Generation/6ed9361a-e1bd-4c7d-893b-e63657bb23f8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..1b3ea03e8a53557f9cdfd226a0f7c1c711cf777d --- /dev/null +++ b/2023/Score Jacobian Chaining_ Lifting Pretrained 2D Diffusion Models for 3D Generation/6ed9361a-e1bd-4c7d-893b-e63657bb23f8_content_list.json @@ -0,0 +1,2319 @@ +[ + { + "type": "text", + "text": "Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation", + "text_level": 1, + "bbox": [ + 153, + 130, + 818, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haochen Wang*1", + "bbox": [ + 111, + 202, + 251, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiaodan $\\mathrm{Du}^{*1}$", + "bbox": [ + 271, + 203, + 383, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiahao Li*1", + "bbox": [ + 403, + 203, + 495, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Raymond A. Yeh2", + "bbox": [ + 516, + 203, + 663, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Greg Shakhnarovich1", + "bbox": [ + 684, + 203, + 854, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ TTI-Chicago", + "bbox": [ + 326, + 229, + 439, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Purdue University", + "bbox": [ + 483, + 229, + 638, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A zoomed out high-quality photo of Temple of Heaven", + "bbox": [ + 122, + 267, + 450, + 282 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cfb582287039a9dfc27e57559d94ec1b428efa55edb53d8cd0f0323cc7b8256d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 286, + 218, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/045a36fb5058cd53c7d68ed0f43fb55ba425eb21787d38c195520c2b09129a21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 286, + 349, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6964eeca35c4e057d24264cdd7ac0fa59ec6f5e7a960a7638c8a6f264533cb6b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 286, + 482, + 383 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A high quality photo of a Victorian style wooden chair with velvet upholstery", + "bbox": [ + 124, + 390, + 450, + 417 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A high quality photo of a delicious burger", + "bbox": [ + 576, + 268, + 826, + 282 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/912d540c39c41f646d2965f7ba7d73d96e34793674b580fa9580ca88b5fd1a48.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 286, + 630, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f3c8204e53268d57108edd48e813cc15b283bf6bbf93bcef9a7bf6462a879630.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 286, + 763, + 383 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5413e28369486c099f7164feded939eed601a7bd177c8289550221c9dde26bfd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 286, + 897, + 383 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A high quality photo of a classic silver muscle car", + "bbox": [ + 552, + 397, + 849, + 411 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c1b90a65ed736d2220fae225efcd8c56b86bbfa74855749f0d304d8bc102f832.jpg", + "image_caption": [ + "Figure 1. Results for text-driven 3D generation using Score Jacobian Chaining with Stable Diffusion as the pretrained model." + ], + "image_footnote": [], + "bbox": [ + 93, + 421, + 218, + 517 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cdbb1d2d5ebdfc7812e9d2c5c15f3ae3d63c02990394fa6cecdb24fca0f2eff2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 421, + 349, + 517 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d5ccd4dbdb778866dbb7ab40010cafdfd0cd329bda257e2c294212758a3cd383.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 421, + 482, + 517 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4f3f274cbacba2a9ae99582283f7499abfbd66fadcfb6d53854b880a37c5d40c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 421, + 630, + 517 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ef5bf2e144599225dc607dcd99af6124de6880ebea0e4b1bda707fbb3eebeb04.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 421, + 763, + 517 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/711bf3c7522ed0033c0a02b4f331b8e7714676c16e8240e4488028d5f2b3af0d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 421, + 897, + 517 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 547, + 313, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION 5B dataset.", + "bbox": [ + 75, + 579, + 470, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 791, + 209, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce a method that converts a pretrained 2D diffusion generative model on images into a 3D generative model of radiance fields, without requiring access to any 3D data. The key insight is to interpret diffusion models as", + "bbox": [ + 76, + 816, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "learned predictors of a gradient field, often referred to as the score function of the data log-likelihood. We apply the chain rule on the estimated score, hence the name Score Jacobian Chaining (SJC).", + "bbox": [ + 500, + 547, + 890, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Following Hyvarinen [16], the score is defined as the gradient of the log-density function with respect to the data (rather than parameter). Diffusion models of various families [13, 49, 50, 52] can all be interpreted [20, 23, 52] as modeling $\\nabla_{\\pmb{x}}\\log p_{\\sigma}(\\pmb{x})$ i.e. the denoising score at noise level $\\sigma$ . For readability, we refer to the denoising score as the score. Generating a sample from a diffusion model involves repeated evaluations of the score function from large to small $\\sigma$ level, so that a sample $\\pmb{x}$ gradually moves closer to the data manifold. It can be loosely interpreted as gradient descent, with precise control on the step sizes so that data distribution evolves to match the annealed $\\sigma$ level (ancestral sampler [13], SDE and probability-flow ODE [52], etc.). While there are other perspectives to a diffusion model [13, 49], here we are primarily motivated from the viewpoint that diffusion models produce a gradient field.", + "bbox": [ + 496, + 611, + 893, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A natural question to ask is whether the chain rule can be applied to the learned gradients. Consider a diffusion model on images. An image $\\pmb{x}$ may be parameterized by some", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution.", + "bbox": [ + 104, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12619", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "function $f$ with parameters $\\theta$ , i.e., $x = f(\\theta)$ . Applying the chain rule through the Jacobian $\\frac{\\partial x}{\\partial \\theta}$ converts a gradient on image $x$ into a gradient on the parameter $\\theta$ . There are many potential use cases for pairing a pretrained diffusion model with different choices of $f$ . In this work we are interested in exploring the connection between 3D and multiview 2D by choosing $f$ to be a differentiable renderer, thus creating a 3D generative model using only pretrained 2D resources.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many prior works [2, 58, 60] perform 3D generative modeling by training on 3D datasets [5, 24, 54, 59]. This approach is often as challenging as it is format-ambiguous. In addition to the high data acquisition cost of 3D assets [9], there is no universal data format: point clouds, meshes, volumetric radiance field, etc, all have computational trade-offs. What is common to these 3D assets is that they can be rendered into 2D images. An inverse rendering system, or a differentiable renderer [25, 27, 30, 34, 39], provides access to the Jacobian $J_{\\pi} \\triangleq \\frac{\\partial x_{\\pi}}{\\partial \\theta}$ of a rendered image $x_{\\pi}$ at camera viewpoint $\\pi$ with respect to the underlying 3D parameterization $\\theta$ . Our method uses differentiable rendering to aggregate 2D image gradients over multiple viewpoints into a 3D asset gradient, and lifts a generative model from 2D to 3D. We parameterize a 3D asset $\\theta$ as a radiance field stored on voxels and choose $f$ to be the volume rendering function.", + "bbox": [ + 75, + 212, + 473, + 453 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A key technical challenge is that computing the 2D score by directly evaluating a diffusion model on a rendered image $\\pmb{x}_{\\pi}$ leads to an out-of-distribution (OOD) problem. Generally, diffusion models are trained as denoisers and have only seen noisy inputs during training. On the other hand, our method requires evaluating the denoiser on non-noisy rendered images from a 3D asset during optimization, and it leads to the OOD problem. To address the issue, we propose Perturb-and-Average Scoring, an approach to estimate the score for non-noisy images.", + "bbox": [ + 75, + 454, + 473, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Empirically, we first validate the effectiveness of Perturb-and-Average Scoring at solving the OOD problem and explore the hyperparameter choices on a simple 2D image canvas. Here we identify open problems on using unconditioned diffusion models trained on FFHQ and LSUN Bedroom. Next, we use Stable Diffusion, a model pretrained on the web-scale LAION dataset to perform SJC for 3D generation, as shown in Fig. 1. Our contributions are as follows:", + "bbox": [ + 75, + 604, + 473, + 726 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a method for lifting a 2D diffusion model to 3D via an application of the chain rule.", + "- We illustrate the challenge of OOD when using a pretrained denoiser and propose Perturb-and-Average Scoring to resolve it.", + "- We point out the subtleties and open problems on applying Perturb-and-Average Scoring as gradient for optimization.", + "- We demonstrate the effectiveness of SJC for the task of 3D text-driven generation." + ], + "bbox": [ + 94, + 729, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 89, + 650, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models have recently advanced to image generation on Internet-scale datasets [10, 36, 42, 44-47]. A diffusion model could be interpreted as either a VAE [13, 49] or a denoising score-matcher [50, 52, 56]. Notably, models trained under one regime can be directly used for inference and sampling by the other [20, 52]; they are in practice largely equivalent.", + "bbox": [ + 496, + 116, + 893, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural radiance fields (NeRF) is a family of inverse rendering algorithms that have excelled at multiview 3D reconstruction tasks including view synthesis and surface geometry estimation [31, 34, 40, 57, 61]. Conceptually, a 3D asset is represented as a dense grid of RGB colors and spatial density $\\tau$ , and rendered into images in a way analogous to alpha compositing [32]. NeRF parameterizes the (RGB, $\\tau$ ) volume with a neural network, but querying the network densely in 3D incurs significant compute costs. Alternatively, Voxel NeRFs [6, 11, 19, 28, 53] store the volume on voxels and observe no loss in end task performance [11, 53]. Querying voxels is a simple memory operation that is much faster than a feedforward pass of a neural network. Here we use a customized voxel radiance field with hyperparameters based on DvGO [53] and TensoRF [6].", + "bbox": [ + 496, + 223, + 895, + 450 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2D-supervised 3D GANs pioneered [35, 43, 63] the approach of training 3D generative models using only unstructured 2D images, and promise greater scalability in terms of data. Rather than supervising directly on the 3D asset a model generates, these methods supervise the 2D renderings of the generated 3D asset, often using an adversarial loss [3, 4, 38, 48, 64]. In other words, only images are needed as training data. However, training such a 3D generative model from scratch is still challenging [37]. Recent empirical evaluation remains mostly on human and animal faces [3]. Our method does the opposite: we take an image generative model that is already pretrained on large amounts of 2D data and use it to guide the iterative optimization of a 3D asset. Optimization-based generation makes it much slower compared to 3D GANs, but it becomes possible to harness powerful off-the-shelf 2D generative models such as Stable Diffusion [45] for greater content diversity.", + "bbox": [ + 496, + 455, + 895, + 714 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CLIP-guided, optimization-based 3D generative models share a similar philosophy of optimizing 3D assets by guiding on 2D renderings [15, 17, 18, 22, 26, 33]. Among them, DreamFields [17] and PureClipNeRF [26] also use NeRF as their differentiable renderers. In this case, the 2D guidance comes from CLIP [42], a pretrained image-text matching model. These works optimize the 3D assets so that the image renderings match a user-provided text prompt. Since CLIP is not a 2D generative model per se, such a pipeline usually creates some abstract content [29] that looks very different from real images. In contrast, we use diffusion models, which are proper 2D generative models, to create realistic looking 3D", + "bbox": [ + 496, + 719, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12620", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "content.", + "bbox": [ + 76, + 92, + 133, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DreamFusion. The recently arXived work by Poole et al. [41], independent and concurrent to our work, proposes an algorithm that is similar to our approach at the pseudo-code level. Differently, their procedure uses the mathematical setup by Graikos et al. [12] to search for image parametrization that minimizes the training loss of a diffusion model. In contrast, our work is motivated by applying the chain rule to the 2D score. The key differences have been summarized in Sec. 4.3. In terms of implementation, we do not have access to the close-sourced Imagen [46] diffusion model. Instead, we use the pretrained Stable Diffusion model released by Rombach et al. [45]. For a comparison with DreamFusion, we use with a third-party implementation based on the same diffusion model, namely Stable-DreamFusion [55].", + "bbox": [ + 75, + 109, + 473, + 323 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 337, + 217, + 353 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To establish a common notation, we briefly review the score-based perspective of diffusion models. For readers familiar with VAE literature on diffusion models, we provide a concise score-based formula card and more details in Appendix Sec. ?? to connect these ideas.", + "bbox": [ + 75, + 362, + 470, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Denoising score matching. Given a dataset of samples $\\mathcal{V} = \\{\\pmb{y}_i\\}$ drawn from $p_{\\mathrm{data}}$ , a diffusion model revolves primarily around learning a denoiser $D$ by minimizing the difference between a noised sample $\\pmb{y} + \\sigma \\pmb{n}$ and $\\pmb{y}$ ,", + "bbox": [ + 76, + 443, + 470, + 503 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, I)} \\| D (\\boldsymbol {y} + \\sigma \\boldsymbol {n}; \\sigma) - \\boldsymbol {y} \\| _ {2} ^ {2}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 515, + 470, + 534 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "i.e. $D$ is denoising the input $\\pmb{y} + \\sigma \\pmb{n}$ , for a range of $\\sigma$ values. For 2D images, $D$ is commonly chosen to be a ConvNet. Variants such as DDPM [13] parameterized the ConvNet to instead predict a noise residual $\\hat{\\epsilon}$ , and these models can be converted back to the form of a denoiser by [52]", + "bbox": [ + 75, + 545, + 472, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nD (\\boldsymbol {x}; \\sigma) = \\boldsymbol {x} - \\sigma \\hat {\\epsilon} (\\boldsymbol {x}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 633, + 468, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this paper, we treat all pretrained diffusion models as denoisers, and perform the interface conversion in our implementation when needed.", + "bbox": [ + 75, + 662, + 470, + 708 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Score from denoiser. Let $p_{\\sigma}(\\boldsymbol{x})$ denote the data distribution perturbed by Gaussian noise of standard deviation $\\sigma$ . It is shown in prior works [16, 50] that the denoiser $D$ trained according to Eq. (1) provides a good approximation to the denoising score:", + "bbox": [ + 75, + 712, + 468, + 787 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\boldsymbol {x}} \\log p _ {\\sigma} (\\boldsymbol {x}) \\approx \\frac {D (\\boldsymbol {x} ; \\sigma) - \\boldsymbol {x}}{\\sigma^ {2}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 800, + 468, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A denoising diffusion model estimates the score function of the noised distribution $p_{\\sigma}(\\boldsymbol{x})$ at various $\\sigma \\in \\{\\sigma_i\\}_{i=1}^T$ . To perform sampling, the diffusion model gradually updates a sample through a sequence of noise levels of $\\sigma_T > \\dots >$", + "bbox": [ + 75, + 840, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\sigma_0 = 0$ . $\\{\\sigma_i\\}$ are chosen empirically, with a typical range being [0.01, 157] [13] in the case of DDPM.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Score as mean-shift. A helpful intuition is that the score behaves like mean-shift [7, 8]. If we simplify $p_{\\mathrm{data}}$ to be an empirical data distribution over the i.i.d. samples $\\{\\pmb{y}_i\\}$ , then at noise level $\\sigma$ , $p_{\\sigma}(\\pmb{x})$ takes the form of a mixture of Gaussians [51]", + "bbox": [ + 498, + 125, + 893, + 200 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\sigma} (\\boldsymbol {x}) = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 208, + 892, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this case there exists a closed-form expression [20, 51] to the optimal denoiser", + "bbox": [ + 498, + 234, + 890, + 263 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nD (\\boldsymbol {x}; \\sigma) = \\frac {\\sum_ {i} \\mathcal {N} (\\boldsymbol {x} ; \\boldsymbol {y} _ {i} , \\sigma^ {2} \\mathbf {I}) \\boldsymbol {y} _ {i}}{\\sum_ {i} \\mathcal {N} (\\boldsymbol {x} ; \\boldsymbol {y} _ {i} , \\sigma^ {2} \\mathbf {I})}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 272, + 892, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In other words, $D(\\pmb{x}; \\sigma)$ is a locally weighted mean of data samples $\\{\\pmb{y}_i\\}$ around $\\pmb{x}$ under a Gaussian kernel with bandwidth $\\sigma$ . The denoising score function can be thought of as a non-parametric guide on how to update $\\pmb{x}$ in order to move it towards its weighted nearest neighbors.", + "bbox": [ + 498, + 314, + 893, + 391 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Score Jacobian Chaining for 3D Generation", + "text_level": 1, + "bbox": [ + 498, + 402, + 890, + 420 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\theta$ denotes the parameters of a 3D asset, e.g., voxel grid of (RGB, $\\tau$ ) as in Sec. 4.2. Our goal is to model and sample from the distribution $p(\\theta)$ to generate a 3D scene. In our setting, only a pretrained 2D diffusion model on images $p(\\boldsymbol{x})$ is given and we do not have access to 3D data. To relate the 2D and 3D distributions $p(\\boldsymbol{x})$ and $p(\\theta)$ , we assume that the probability density of 3D asset $\\theta$ is proportional to the expected probability densities of its multiview 2D image renderings $\\boldsymbol{x}_{\\pi}$ over camera poses $\\pi$ , i.e.,", + "bbox": [ + 496, + 428, + 892, + 565 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\sigma} (\\boldsymbol {\\theta}) \\propto \\mathbb {E} _ {\\pi} \\left[ p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi} (\\boldsymbol {\\theta})\\right) \\right], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 571, + 890, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "up to a normalization constant $Z = \\int \\mathbb{E}_{\\pi}\\left[p_{\\sigma}(\\pmb{x}_{\\pi}(\\pmb{\\theta}))\\right]d\\pmb{\\theta}$ . That is, a 3D asset $\\pmb{\\theta}$ is as likely as its 2D renderings $\\pmb{x}_{\\pi}$ .", + "bbox": [ + 498, + 599, + 888, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, we establish a lower bound, $\\log \\tilde{p}_{\\sigma}(\\boldsymbol{\\theta})$ , on the distribution in Eq. (6) using Jensen's inequality:", + "bbox": [ + 498, + 630, + 893, + 661 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\log p _ {\\sigma} (\\boldsymbol {\\theta}) = \\log \\left[ \\mathbb {E} _ {\\pi} \\left(p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right)\\right) \\right] - \\log Z (7) \\\\ \\geq \\mathbb {E} _ {\\pi} \\left[ \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right) \\right] - \\log Z \\triangleq \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta}). (8) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 667, + 890, + 707 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall that the score is the gradient of log probability density of data. By chain rule", + "bbox": [ + 498, + 715, + 890, + 746 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\boldsymbol {\\theta}} \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {\\boldsymbol {\\pi}} \\left[ \\nabla_ {\\boldsymbol {\\theta}} \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\pi}}\\right) \\right] (9) \\\\ \\frac {\\partial \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} = \\mathbb {E} _ {\\pi} \\left[ \\frac {\\partial \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right)}{\\partial \\boldsymbol {x} _ {\\pi}} \\cdot \\frac {\\partial \\boldsymbol {x} _ {\\pi}}{\\partial \\boldsymbol {\\theta}} \\right] (10) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 753, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underbrace {\\nabla_ {\\boldsymbol {\\theta}} \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta})} _ {\\text {3 D s c o r e}} = \\mathbb {E} _ {\\pi} [ \\underbrace {\\nabla_ {\\boldsymbol {x} _ {\\pi}} \\log p _ {\\sigma} (\\boldsymbol {x} _ {\\pi})} _ {\\text {2 D s c o r e ; p r e t r a i n e d}} \\cdot \\underbrace {\\boldsymbol {J} _ {\\pi}} _ {\\text {r e n d e r e r J a c o b i a n}} ]. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 809, + 890, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We will next discuss how to compute the 2D score in practice using a pretrained diffusion model.", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12621", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/09b8676d9de0125ae440e00cdd28e15d1ac7e880d7180d3018454e13a812af81.jpg", + "image_caption": [ + "Figure 2. Illustration of denoiser's OOD issue using a denoiser pretrained on FFHQ. When directly evaluating $D(\\pmb{x}_{\\mathrm{blob}}, \\sigma)$ the model did not correct for the orange blob into a face image. Contrarily, evaluating the denoiser on noised input $D(\\pmb{x}_{\\mathrm{blob}} + \\sigma \\pmb{n}, \\sigma)$ produces an image that successfully merges the blob with the face manifold." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 207, + 198 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/546d9c674ae035e8931f5611a157c3711edf9e164a244f2a9c74f16ac59ff168.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 88, + 336, + 198 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1eacb1be994dff875f52a88076659e3368c815b114ddd9493b5cc695ca51d048.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 341, + 88, + 467, + 198 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Computing 2D Score on Non-Noisy Images", + "text_level": 1, + "bbox": [ + 76, + 297, + 442, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Computing the 3D score in Eq. (11) requires the 2D score on $\\pmb{x}_{\\pi}$ . A first attempt would be to directly apply the score from the denoiser in Eq. (3), i.e.,", + "bbox": [ + 76, + 320, + 468, + 366 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {s c o r e} \\left(\\boldsymbol {x} _ {\\pi}, \\sigma\\right) \\triangleq \\left(D \\left(\\boldsymbol {x} _ {\\pi}; \\sigma\\right) - \\boldsymbol {x} _ {\\pi}\\right) / \\sigma^ {2}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 375, + 468, + 392 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unfortunately, evaluating the pretrained denoiser $D$ on $\\pmb{x}_{\\pi}$ causes an out-of-distribution (OOD) problem. From the training objective in Eq. (1), at each noise level $\\sigma$ , the denoiser $D$ has only seen noisy inputs of the distribution $\\pmb{y} + \\sigma \\pmb{n}$ where $\\pmb{y} \\sim p_{\\mathrm{data}}$ and $\\pmb{n} \\sim \\mathcal{N}(0, \\mathbf{I})$ . However, a rendered image $\\pmb{x}_{\\pi}$ from 3D asset $\\pmb{\\theta}$ is generally not consistent with such distribution.", + "bbox": [ + 76, + 401, + 470, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We illustrate this OOD situation in Fig. 2. Given a denoiser pretrained on FFHQ [21] by Baranchuk et al. [1], we visualize the output $D(\\pmb{x}_{\\mathrm{blob}}; \\sigma = 6.5)$ where the input $\\pmb{x}_{\\mathrm{blob}}$ is a non-noisy image showing an orange blob centered on a grey canvas. Under the intuition that $D$ predicts a weighted nearest neighbor as reviewed in (5), we expect the denoiser to blend the orange blob with the manifold of faces. However in reality we observe sharp artifacts when updating with this score $(D(\\pmb{x}_{\\mathrm{blob}}; \\sigma) - \\pmb{x}_{\\mathrm{blob}}) / \\sigma^2$ and the image becomes further away from the face manifold.", + "bbox": [ + 75, + 507, + 470, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Perturb-and-Average Scoring. To address the OOD problem, we propose Perturb-and-Average Scoring (PAAS). It computes the score on non-noisy images $\\boldsymbol{x}_{\\pi}$ with a denoiser $D$ by adding noise to the input, and then considering the expectation of the predicted scores w.r.t. the random noise,", + "bbox": [ + 76, + 661, + 470, + 736 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {P A A S} \\left(\\boldsymbol {x} _ {\\pi}, \\sqrt {2} \\sigma\\right) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 744, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\triangleq \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\operatorname {s c o r e} (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n}, \\sigma) ] (14) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {D (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n} , \\sigma) - (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n})}{\\sigma^ {2}} \\right] (15) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {D (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n} , \\sigma) - \\boldsymbol {x} _ {\\pi}}{\\sigma^ {2}} \\right] - \\underbrace {\\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {\\boldsymbol {n}}{\\sigma} \\right]} _ {= 0}. (16) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 767, + 468, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In practice, we use the Monte Carlo estimate of the expectation in Eq. (16). The algorithm is illustrated in Fig. 3. Given", + "bbox": [ + 76, + 869, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fbfef85bbbadda1642a403a821069a3b7d6a9246ee04584d810b76b5b30085bb.jpg", + "image_caption": [ + "Figure 3. Computing PAAS on 2D renderings $\\pmb{x}_{\\pi}$ . Directly evaluating $D(\\pmb{x}_{\\pi};\\sigma)$ leads to an OOD problem. Instead, we add noise to $\\pmb{x}_{\\pi}$ , and evaluate $D(\\pmb{x}_{\\pi} + \\sigma \\pmb{n};\\sigma)$ (blue dots). The PAAS is then computed by averaging over the brown dashed arrows, corresponding to multiple samples of $\\pmb{n}$ . See Sec. 4.1 for details." + ], + "image_footnote": [], + "bbox": [ + 535, + 95, + 857, + 257 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a set of sampled noises $\\{\\pmb{n}_i\\}$ , each $D(\\pmb{x}_{\\pi} + \\sigma \\pmb{n}_i)$ provides an update direction on the perturbed input $\\pmb{x}_{\\pi} + \\sigma \\pmb{n}_i$ . By averaging over the noise perturbations $\\{\\pmb{n}_i\\}$ , we obtain an update direction on $\\pmb{x}_{\\pi}$ itself.", + "bbox": [ + 498, + 347, + 892, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Justifying PAAS in Eq. (13). We show that Perturb-and-Average Scoring provides an approximation to the score on $x_{\\pi}$ at an inflated noise level of $\\sqrt{2}\\sigma$", + "bbox": [ + 498, + 410, + 893, + 455 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {P A A S} \\left(\\boldsymbol {x} _ {\\pi}, \\sqrt {2} \\sigma\\right) \\approx \\nabla_ {\\boldsymbol {x} _ {\\pi}} \\log p _ {\\sqrt {2} \\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 460, + 890, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lemma 1 Assuming an empirical data distribution $p_{\\sigma}(\\pmb{x})$ in Eq. (4), for any $\\pmb{x} \\in \\mathbb{R}^d$", + "bbox": [ + 506, + 496, + 883, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\log p _ {\\sqrt {2} \\sigma} (\\boldsymbol {x}) \\geq \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 539, + 883, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proof. Observe that the LHS of Eq. (19) is a convolution of two Gaussians, therefore", + "bbox": [ + 498, + 564, + 890, + 593 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {\\mu}, \\sigma^ {2} \\mathbf {I}) ] = \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {\\mu}, 2 \\sigma^ {2} \\mathbf {I}) \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 599, + 890, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recall that $p_{\\sigma}(\\pmb {x})$ is a mixture of Gaussians per Eq. (4);", + "bbox": [ + 500, + 625, + 867, + 640 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} p _ {\\sqrt {2} \\sigma} (\\boldsymbol {x}) = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {y}, 2 \\sigma^ {2} \\mathbf {I}) (20) \\\\ = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\text {d a t a}}} \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}) (21) \\\\ = \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\text {d a t a}}} \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}) (22) \\\\ = \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}). (23) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 645, + 890, + 723 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Taking the log on both sides of Eq. (23) and by Jensen's inequality, we arrive at Eq. (18).", + "bbox": [ + 498, + 729, + 890, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Claim 1 Assuming a trained denoiser $D$ as in Eq. (3), our $PAAS(x_{\\pi}, \\sqrt{2}\\sigma)$ in Eq. (13) computes the gradient w.r.t. a lower bound of $\\log p_{\\sqrt{2}\\sigma}(\\pmb{x})$ .", + "bbox": [ + 506, + 766, + 885, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proof. By taking the gradient of the RHS of Lemma 1,", + "bbox": [ + 500, + 821, + 857, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\boldsymbol {x}} \\mathbb {E} _ {\\boldsymbol {n}} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}) = \\mathbb {E} _ {\\boldsymbol {n}} \\nabla_ {\\boldsymbol {x} + \\sigma \\boldsymbol {n}} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} [ \\operatorname {s c o r e} (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n}, \\sigma) ]. \\tag {24} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 843, + 893, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which is the proposed PAAS algorithm in Eq. (13).", + "bbox": [ + 500, + 885, + 836, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/46ad94efacec0ec77520bea1d1979b0f1d0fe3194a2607513f1b1ec3de642342.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 874, + 886, + 890, + 896 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12622", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Inverse Rendering on Voxel Radiance Field", + "text_level": 1, + "bbox": [ + 76, + 90, + 444, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the computation of the 2D score resolved, the other half of our setup in Eq. (11) requires access to the Jacobian of a differentiable renderer.", + "bbox": [ + 75, + 113, + 468, + 157 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3D Representation. We represent a 3D asset $\\theta$ as a voxel radiance field [6, 11, 53], which is much faster to access and update compared to a vanilla NeRF parameterized by a neural network [34]. The parameters $\\theta$ consist of a density voxel grid $\\mathbf{V}^{(\\mathrm{density})} \\in \\mathbb{R}^{1 \\times N_x \\times N_y \\times N_z}$ and a voxel grid of appearance features $\\mathbf{V}^{(\\mathrm{app})} \\in \\mathbb{R}^{c \\times N_x \\times N_y \\times N_z}$ . Conventionally the appearance features are simply the RGB colors and $c = 3$ . For simplicity, we do not model view dependencies in this work.", + "bbox": [ + 75, + 162, + 470, + 297 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inverse Volumetric Rendering. Image rendering is performed independently along a camera ray through each pixel. We cut a camera light ray into equally distanced segments of length $d$ , and at the spatial location corresponding to the beginning of the $i$ -th segment we sample a $(\\mathrm{RGB}_i, \\tau_i)$ tuple from the color and density grids using trilinear interpolation. These values are alpha-composed using volume rendering quadrature [32] into the pixel color $C = \\sum_{i} w_i \\cdot \\mathrm{RGB}_i$ , where", + "bbox": [ + 75, + 301, + 472, + 435 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} = \\alpha_ {i} \\cdot \\prod_ {j = 0} ^ {i - 1} (1 - \\alpha_ {j}); \\quad \\alpha_ {i} = 1 - \\exp (- \\tau_ {i} d). \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 443, + 468, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Volume rendering of $\\theta$ is directly differentiable. At a rendered image $x_{\\pi}$ , the Vector-Jacobian product in Eq. (11) between PAAS $(x_{\\pi})$ and the Jacobian $J_{\\pi} = \\frac{\\partial x_{\\pi}}{\\partial \\theta}$ is computed by back-propagating the score through Eq. (25). This Vector-Jacobian product provides us with the 3D gradient needed for generative modeling on the voxel radiance field.", + "bbox": [ + 75, + 492, + 468, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regularization Strategies. The voxel grid is a very powerful 3D representation for volumetric rendering. Given noisy 2D guidance, the model may cheat by populating the entire grid with small densities such that the combined effect from one view hallucinates a plausible image. We propose several techniques to encourage the formation of a coherent 3D structure.", + "bbox": [ + 75, + 585, + 468, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Emptiness Loss: Ideally, the space should be sparse with near zero densities except at the object. We propose an emptiness loss to encourage sparsity on a ray $\\mathbf{r}$ :", + "bbox": [ + 75, + 695, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e m p t i n e s s}} (\\mathbf {r}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log \\left(1 + \\beta \\cdot w _ {i}\\right), \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 750, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w_{i}$ are the alpha-composed weights shown in (25). The shape of the log function imposes severe penalties at the onset of small weights, but does not grow aggressively if the weights are large. It is consistent with our aim to eliminate small densities. The hyperparameter $\\beta$ controls the steepness of the loss function near 0. A larger $\\beta$ will put more emphasis on eliminating low-density noise. We set $\\beta = 10$ .", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a1c440dbffe9d508bd0b1e939e7779211fb570f13c31a554c7a2ae11da6c28e9.jpg", + "image_caption": [ + "Figure 4. Sampling 2D images with Perturb-and-Average Scoring. We compare Annealed vs Random $\\sigma$ schedule against several diffusion models. Row 1 & 2: the random $\\sigma$ schedule exhibits strong mode-seeking behavior, and it results in low-quality \"mean\" images on unconditioned diffusion models trained on FFHQ and LSUN Bedroom. In this case, we need a carefully designed annealed $\\sigma$ schedule to produce better, more diverse samples. Row 3 & 4: Stable Diffusion (SD) is conditioned on the prompt \"a squirrel holding a saxophone\". The use of natural language makes the conditioned distribution much easier to sample from. When the guidance scale is elevated to 10, Random $\\sigma$ schedule that fails on FFHQ and LSUN starts to produce crisp, clean images." + ], + "image_footnote": [], + "bbox": [ + 503, + 92, + 888, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Emptiness Loss Schedule: We use a hyperparameter $\\lambda$ to control the contribution of the emptiness loss. If we apply a large emptiness loss, it will hinder the learning of geometry in the early stage of training. But if the emptiness is too small, there will be floating density artifacts. We adopt a two-stage noise elimination schedule to deal with this problem. In the first $K$ iterations, we use a relatively small weighting factor $\\lambda_{1}$ . After the $K^{\\mathrm{th}}$ iteration, it is increased to a larger $\\lambda_{2}$ . In our experiments $\\lambda_{1} = 1 \\times 10^{4}$ and $\\lambda_{2} = 2 \\times 10^{5}$ . We provide an ablation study of this technique in Fig. 7 to show its effectiveness.", + "bbox": [ + 498, + 584, + 893, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Center Depth Loss: Sometimes the optimization places the object away from the scene center. The object either becomes small or wander around the image boundary. For the few cases when this happens we apply a center depth loss", + "bbox": [ + 498, + 761, + 892, + 821 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c e n t e r}} (D) = - \\log \\left(\\frac {1}{| \\mathcal {B} |} \\sum_ {\\mathbf {p} \\in \\mathcal {B}} D (\\mathbf {p}) - \\frac {1}{| \\mathcal {B} ^ {\\complement} |} \\sum_ {\\mathbf {q} \\notin \\mathcal {B}} D (\\mathbf {q})\\right) \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 839, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12623", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c41bf6649ea068ea261e18753f027f1d3ecad5082b647d59214508227c7037be.jpg", + "image_caption": [ + "A DSLR photo of a yellow duck" + ], + "image_footnote": [], + "bbox": [ + 89, + 106, + 183, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8c330ae0da2e7533ed8a97dc87e5e3f968f313ea87a8c7d34fe91cbce320b5df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 106, + 281, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e3a5340f75c89e3c03c385ffb868b966a88cd26fb7c7da7fb9211a0e11b14faa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 106, + 379, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/28d06de9db0c2ec47cd0a8417a3a6e948381ec1d4982f2217ca0575d5e68f179.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 106, + 477, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d93a3e3c7f4b7c1fd2d971d399c0fb480d3f58ea23145995e502f8ee83832790.jpg", + "image_caption": [ + "A zoomed out photo a small castle" + ], + "image_footnote": [], + "bbox": [ + 89, + 200, + 183, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/71e8e8ab3750c4eea8eb52525095c5093e637c21f903b0dcc01990ea73cdab43.jpg", + "image_caption": [ + "A zoomed out high quality photo of Sydney Opera House" + ], + "image_footnote": [], + "bbox": [ + 186, + 200, + 281, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cc5e92ea0a57a39be38af913a5b05f5b98974e9053ca1d55e3a9acb96910d3e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 200, + 379, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a1edb5a9a608c1c997c2eef9ec7953370ab86d72f3cba7edd9ed409c3b186e72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 200, + 477, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d37d4621014c5ead7ca2d76194c681e1c8fb60f34b41f5a21a1408c4a9dab469.jpg", + "image_caption": [ + "Figure 5. Qualitative results of text-prompted generation of 3D models with SJC, purely from the pretrained Stable Diffusion (2D) image model. Each row shows two views, with associated depth maps (blue is far, red is near), for a single 3D model generated for a given prompt. Note the detailed appearance as well as a sharp, well-defined depth structure." + ], + "image_footnote": [], + "bbox": [ + 89, + 297, + 183, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2157ed8bb024c0f2705795dd087d89a617013374ed27ece5da037e837ad9a8a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 186, + 297, + 281, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/40614c2cc06d04698241fedf10943d07b950bc691c2426e83e12c4a33e416f67.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 285, + 297, + 379, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ec71ccd0dbb647e0d68e2687ac244651885daab38d4bb24aef437f630f036263.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 297, + 477, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/813b1ca1603d9b03a8beb1e6fe662989db9ddf3477ca23c4ec7cf4a25ce783c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 106, + 586, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b2de60c7753ff3f6fdd16c908a6f269107b5429e143c9512a17b3a0c54411367.jpg", + "image_caption": [ + "A ficus planted in a pot" + ], + "image_footnote": [], + "bbox": [ + 589, + 106, + 684, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/804f9c9bdfdf34eced27b82d92ddee1e3b65b984b3b2ca7c6c100450ce8f641c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 106, + 782, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/06e1dd72a255950a75756871ec632847a657d90b4fafa8c17daf022907f411d4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 106, + 880, + 178 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cfc05a5abe049f5689d5b9410ae866c11cb2bc918f9477b3e7c13ba17118dcc7.jpg", + "image_caption": [ + "A high quality photo of a toy motorcycle" + ], + "image_footnote": [], + "bbox": [ + 493, + 200, + 586, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/422d5e996cdf6905db2827d72f1eea49746608b5988caa5659bfd565462847bd.jpg", + "image_caption": [ + "A photo of a horse walking" + ], + "image_footnote": [], + "bbox": [ + 589, + 200, + 684, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/57a9e88198e3241629a0a7b0630a158ec17e764fb1d2f15e0ac85018c7aa3e58.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 200, + 782, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d2618a46d963f461abe17f99fe4dfc12a909fb9580e8a36c041b69e40ebac7e2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 200, + 880, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/30cb20e179722551bc56656ac5d3086505c11be242d9190a8f48d56dc39fa63d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 297, + 586, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bf1bdee838392b414d50f5ac41045236499c139b094b93e74311c79e6a09379d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 589, + 297, + 684, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7877bf92c0e0180e8b53ee71304afb16d0621c3f01c01a1c110fdd73925aaa73.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 297, + 782, + 368 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/47f718f32b22858bc4f7a1627c6becb581849c440a9124cd84299ac8450871bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 785, + 297, + 880, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $D$ is the depth image, $\\mathcal{B}$ is a box (set of pixel locations) at the center of the image, and $\\mathcal{B}^{\\mathrm{G}}$ is its complement.", + "bbox": [ + 75, + 433, + 470, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. SJC vs. DreamFusion", + "text_level": 1, + "bbox": [ + 76, + 479, + 279, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we describe the differences and the connections between our SJC and DreamFusion.", + "bbox": [ + 75, + 503, + 470, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Differences from DreamFusion. In terms of formulation, DreamFusion's computation of the gradient w.r.t. $\\theta$ involves a U-Net Jacobian term (see Eq. 2 in their paper [41]). In practice, they \"found that omitting the U-Net Jacobian term\" to be more effective. On the other hand, this U-Net Jacobian term does not appear in our formulation. Their additional justification in the appendix actually leans more towards our viewpoint. An additional contribution of ours beyond DreamFusion [41] is our analysis of the effect that the OOD problem has when using a denoiser on rendered images (Claim 1), and the PAAS method to address it. For the variance reduction technique, namely the use of the Monte-Carlo estimate on Eq. (16), or $\\hat{\\epsilon} - \\epsilon$ (in DreamFusion), vs. on Eq. (15), we observe comparable performance between the two methods empirically for 3D generation.", + "bbox": [ + 75, + 536, + 472, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Influences by DreamFusion. At the time of this submission, DreamFusion is a concurrent arXiv paper. However, as we have read the paper, our research was influenced by their reported observations. In particular, we adopted the idea of randomized scheduling of $\\sigma$ during 3D optimization for easier hyperparameter tuning, and used view-augmented language prompting that improves the overall 3D quality. For future work we do hope to explore a more general solution than view-dependent prompts.", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 431, + 632, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct experiments on both unconditioned and conditioned diffusion models to have a more comprehensive understanding of the properties of SJC.", + "bbox": [ + 496, + 458, + 893, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "DDPMs trained on FFHQ and LSUN Bedroom are unconditioned diffusion models with an architecture based on the implementation by Dhariwal and Nichol [10]. They are trained on an image resolution of $256 \\times 256$ . FFHQ [21] is a dataset of aligned faces with diverse coverage of gender, age, race, facial appearance as well as head poses. LSUN Bedroom [62] includes bedroom images with varied furniture layout plans and rich interior design styles.", + "bbox": [ + 496, + 508, + 893, + 631 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stable Diffusion is an expanded work based on Latent Diffusion Model (LDM) developed by Rombach et al. [45]. It is trained on the LAION5B dataset [47]. We use the release version v1.5. Diffusion is performed on a latent space of $4 \\times 64 \\times 64$ , then upsampled to $3 \\times 256 \\times 256$ by a decoder. The model is natively trained for text-conditioned image generations, and exposes a guidance scale parameter that controls the strength of language conditioning [14]. Intuitively a larger guidance scale makes the conditioned image distribution more faithful to the text prompt by trading off sample diversity.", + "bbox": [ + 496, + 636, + 895, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Validating PAAS on 2D images.", + "text_level": 1, + "bbox": [ + 500, + 815, + 772, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Before directly jumping to 3D generation, we first verify that PAAS provides effective guidance on a simple 2D image canvas. In other words, here $\\theta$ is a grid of RGB values and $f$ is an identity function. The hope is that gradient descent", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12624", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/92847e4d8152f076479d4eabb6ba68008511b79da092403dc6119743a9e2f985.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 80, + 104, + 357, + 310 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/beafbcfd0552ba809ad62453277481d4e8a37f29ed93b6b385d9d42e2bd6e6fd.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 357, + 104, + 620, + 310 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0ba0f171eb185d442c96c9580532902b26cbadd86b8dea7e450dde84e56a8b21.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 624, + 104, + 883, + 310 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ca53a5d33276d2590602a19d89a500db951075041e229d550604eed469d99b66.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 80, + 327, + 357, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1d54e0e70042d76c5e0eed2456a8c2c2b9305860c52abbb0c21a995ba3dd2f81.jpg", + "image_caption": [ + "(e)" + ], + "image_footnote": [], + "bbox": [ + 357, + 327, + 620, + 534 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5096f66c34f2e1b1c432f4982fc853836a86db43efd53551e4fae3febb06c0d8.jpg", + "image_caption": [ + "(f)", + "Figure 6. Qualitative comparison between Stable-DreamFusion (StableDF) and Ours. The prompts are: (a) \"A high quality photo of a delicious burger\"; (b) \"a DSLR photo of a yellow duck\"; (c) \"A ficus planted in a pot\"; (d) \"A product photo of a toy tank\"; (e) \"A high quality photo of a chocolate icecream cone\"; (f) \"A wide angle zoomed out photo of a giraffe\". Both methods are run for 10k iterations without per-prompt finetuning on the hyperparameters. The images on the left are rendered RGB images and the images on the right are depth visualization." + ], + "image_footnote": [], + "bbox": [ + 624, + 327, + 883, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "on the vector field produced by PAAS creates high quality images. Here an important decision to make is the schedule of $\\{\\sigma_i\\}$ at which we compute PAAS.", + "bbox": [ + 75, + 628, + 468, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We experimented with an annealed schedule (Annealed $\\sigma$ ) vs. a random schedule (Random $\\sigma$ ) as proposed in Dream-Fusion. Under the Annealed $\\sigma$ schedule, we start from a large $\\sigma$ and gradually decrease it as we update the image canvas $x$ . PAAS computed at larger $\\sigma$ level attends to high level image structure while smaller $\\sigma$ provides stronger guidance on detailed features. The Random $\\sigma$ schedule on the contrary uniformly samples a $\\sigma$ at every step. We show qualitative comparisons in Fig. 4.", + "bbox": [ + 75, + 674, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For unconditioned diffusion models trained on FFHQ, we observe that Annealed $\\sigma$ performs better than Random $\\sigma$ , and the image samples have better pose variation and quality. Particularly, the randomized $\\sigma$ exhibits severe mode-seeking behavior converging to average faces. In the case of LSUN Bedroom, the mode-seeking behavior results in a", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "blurry image canvas with no content.", + "bbox": [ + 498, + 628, + 745, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On the other hand, natural language prompting plays a critical role when sampling images with Stable Diffusion. When the language guidance is set to a regular level of 3.0, the observations are broadly consistent with sampling on FFHQ and LSUN. Random $\\sigma$ schedule produces blurry outputs. However, when the guidance scale is elevated to 10.0, Random $\\sigma$ schedule begins to generate crisp, clean images and outperforms Annealed $\\sigma$ schedule. Despite various sophisticated strategies on Annealed $\\sigma$ scheduling (see our code for details), at a high language guidance scale Randomized $\\sigma$ remains the better option. We hypothesize that stronger language guidance forces the image distribution to be narrower and more beneficial for a mode-seeking algorithm. We acknowledge none of the images in Fig. 4 can match the sample quality of a standard diffusion inference pipeline, and the right way to apply PAAS as gradient for optimization remains an open problem.", + "bbox": [ + 496, + 643, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12625", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A zoomed out high quality photo of Temple of Heaven.", + "bbox": [ + 318, + 90, + 650, + 103 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8d1a4dd2af26f7e686caf457435aa1dd6ade5dab52930a117d9ce367d81b8acb.jpg", + "image_caption": [ + "Figure 7. Ablation experiments on the proposed emptiness loss schedule. For each setting of the loss weight $\\lambda$ , we show a rendered image and the associated depth map from a randomly sampled viewpoint. Ours incorporates the loss with weight schedule described in 5.2. It leads to better 3D shape, as evidenced in the cleaner depth maps. Setting the loss weight too low yields \"cloudy\" depth fields. When setting the weight too high, SJC fails to produce meaningful 3D models." + ], + "image_footnote": [], + "bbox": [ + 86, + 104, + 885, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2.3D Generation", + "text_level": 1, + "bbox": [ + 76, + 482, + 228, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we focus on 3D Generation with the language-conditioned Stable Diffusion model. We found that tuning the Annealed $\\sigma$ schedule on FFHQ and LSUN Bedroom in 3D domain is difficult in practice, and leave it as future work. Based on the insights from 2D experiments earlier, we use Random $\\sigma$ schedule coupled with a high language guidance scale.", + "bbox": [ + 75, + 511, + 470, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Rendering with Latent 3D Features. Stable Diffusion economizes compute by performing diffusion modeling on the latent features of a pretrained AutoEncoder. We therefore choose to render a feature image in this latent space from a features field [3, 38] represented by a voxel grid in $\\mathbb{R}^{4\\times N_x\\times N_y\\times N_z}$ .", + "bbox": [ + 75, + 628, + 472, + 720 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Comparison. In Fig. 5, we show text-prompted 3D generation results from SJC, and compare SJC with Stable-DreamFusion, a third-party implementation based on the same pretrained Stable Diffusion v1.5 model. In Fig. 6, we show qualitative comparisons of generated 3D assets given the same prompt. We observe that SJC generates 3D models with better image quality and more sensible structure than Stable-DreamFusion in a significant number of cases. We note that both systems exhibit quality fluctuations over different trials, and the point of this comparison is to show that our overall pipeline is competitive.", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablations. In Fig. 7, we conduct ablations to demonstrate the importance of the proposed emptiness loss and scheduling of its weight $\\lambda$ discussed in Sec. 4.2. We show results without the emptiness loss, with constant weight $\\lambda$ vs our proposed scheduling of $\\lambda$ . We observe that our complete method (Ours) improves the quality of generated 3D models, e.g., fewer floating artifacts and better geometry.", + "bbox": [ + 496, + 482, + 895, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 599, + 619, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose an optimization-based approach to generate 3D assets from pretrained image (2D) diffusion models. The key technical contribution is the derivation of Perturb-and-Average Scoring method which bridges the gap between the denoising-trained diffusion models and the non-noisy images encountered in the process of optimizing a 3D model guided by the diffusion. Working with the large-scale Stable Diffusion model, we demonstrate that our approach can generate compelling 3D models, comparing favorably to available concurrent work. Finally, we investigate an interesting distinction between the effect of noise scheduling regime in unconditional image diffusion models and a text-conditional model, and identify an avenue for future work.", + "bbox": [ + 496, + 626, + 893, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work was supported in part by the TRI University 2.0 program, and by the AFOSR MADlab Center of Excellence. We thank friends and colleagues at TTIC, UChicago and TRI for feedbacks and discussions.", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12626", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Dmitry Baranchuk, Andrey Voynov, Ivan Rubachev, Valentin Khrulkov, and Artem Babenko. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.154, + 0.131, + 0.819, + 0.175 + ], + "angle": 0, + "content": "Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.203, + 0.252, + 0.222 + ], + "angle": 0, + "content": "Haochen Wang*1" + }, + { + "type": "text", + "bbox": [ + 0.272, + 0.204, + 0.384, + 0.221 + ], + "angle": 0, + "content": "Xiaodan \\(\\mathrm{Du}^{*1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.405, + 0.204, + 0.496, + 0.221 + ], + "angle": 0, + "content": "Jiahao Li*1" + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.204, + 0.664, + 0.222 + ], + "angle": 0, + "content": "Raymond A. Yeh2" + }, + { + "type": "text", + "bbox": [ + 0.685, + 0.204, + 0.856, + 0.222 + ], + "angle": 0, + "content": "Greg Shakhnarovich1" + }, + { + "type": "text", + "bbox": [ + 0.327, + 0.231, + 0.441, + 0.25 + ], + "angle": 0, + "content": "\\(^{1}\\)TTI-Chicago" + }, + { + "type": "text", + "bbox": [ + 0.485, + 0.231, + 0.639, + 0.25 + ], + "angle": 0, + "content": "\\(^{2}\\)Purdue University" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.268, + 0.452, + 0.283 + ], + "angle": 0, + "content": "A zoomed out high-quality photo of Temple of Heaven" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.287, + 0.219, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.287, + 0.351, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.287, + 0.483, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.125, + 0.391, + 0.451, + 0.418 + ], + "angle": 0, + "content": "A high quality photo of a Victorian style wooden chair with velvet upholstery" + }, + { + "type": "text", + "bbox": [ + 0.577, + 0.269, + 0.828, + 0.283 + ], + "angle": 0, + "content": "A high quality photo of a delicious burger" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.287, + 0.632, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.287, + 0.764, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.773, + 0.287, + 0.898, + 0.384 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.553, + 0.398, + 0.851, + 0.412 + ], + "angle": 0, + "content": "A high quality photo of a classic silver muscle car" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.422, + 0.219, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.226, + 0.422, + 0.351, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.358, + 0.422, + 0.483, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.422, + 0.632, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.422, + 0.764, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.773, + 0.422, + 0.898, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.114, + 0.522, + 0.855, + 0.537 + ], + "angle": 0, + "content": "Figure 1. Results for text-driven 3D generation using Score Jacobian Chaining with Stable Diffusion as the pretrained model." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.548, + 0.314, + 0.563 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.472, + 0.775 + ], + "angle": 0, + "content": "A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION 5B dataset." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.792, + 0.21, + 0.807 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.817, + 0.47, + 0.879 + ], + "angle": 0, + "content": "We introduce a method that converts a pretrained 2D diffusion generative model on images into a 3D generative model of radiance fields, without requiring access to any 3D data. The key insight is to interpret diffusion models as" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.549, + 0.892, + 0.609 + ], + "angle": 0, + "content": "learned predictors of a gradient field, often referred to as the score function of the data log-likelihood. We apply the chain rule on the estimated score, hence the name Score Jacobian Chaining (SJC)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.895, + 0.853 + ], + "angle": 0, + "content": "Following Hyvarinen [16], the score is defined as the gradient of the log-density function with respect to the data (rather than parameter). Diffusion models of various families [13, 49, 50, 52] can all be interpreted [20, 23, 52] as modeling \\(\\nabla_{\\pmb{x}}\\log p_{\\sigma}(\\pmb{x})\\) i.e. the denoising score at noise level \\(\\sigma\\). For readability, we refer to the denoising score as the score. Generating a sample from a diffusion model involves repeated evaluations of the score function from large to small \\(\\sigma\\) level, so that a sample \\(\\pmb{x}\\) gradually moves closer to the data manifold. It can be loosely interpreted as gradient descent, with precise control on the step sizes so that data distribution evolves to match the annealed \\(\\sigma\\) level (ancestral sampler [13], SDE and probability-flow ODE [52], etc.). While there are other perspectives to a diffusion model [13, 49], here we are primarily motivated from the viewpoint that diffusion models produce a gradient field." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "A natural question to ask is whether the chain rule can be applied to the learned gradients. Consider a diffusion model on images. An image \\( \\pmb{x} \\) may be parameterized by some" + }, + { + "type": "page_footnote", + "bbox": [ + 0.106, + 0.888, + 0.221, + 0.9 + ], + "angle": 0, + "content": "* Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12619" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "function \\( f \\) with parameters \\( \\theta \\), i.e., \\( x = f(\\theta) \\). Applying the chain rule through the Jacobian \\( \\frac{\\partial x}{\\partial \\theta} \\) converts a gradient on image \\( x \\) into a gradient on the parameter \\( \\theta \\). There are many potential use cases for pairing a pretrained diffusion model with different choices of \\( f \\). In this work we are interested in exploring the connection between 3D and multiview 2D by choosing \\( f \\) to be a differentiable renderer, thus creating a 3D generative model using only pretrained 2D resources." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.474, + 0.454 + ], + "angle": 0, + "content": "Many prior works [2, 58, 60] perform 3D generative modeling by training on 3D datasets [5, 24, 54, 59]. This approach is often as challenging as it is format-ambiguous. In addition to the high data acquisition cost of 3D assets [9], there is no universal data format: point clouds, meshes, volumetric radiance field, etc, all have computational trade-offs. What is common to these 3D assets is that they can be rendered into 2D images. An inverse rendering system, or a differentiable renderer [25, 27, 30, 34, 39], provides access to the Jacobian \\( J_{\\pi} \\triangleq \\frac{\\partial x_{\\pi}}{\\partial \\theta} \\) of a rendered image \\( x_{\\pi} \\) at camera viewpoint \\( \\pi \\) with respect to the underlying 3D parameterization \\( \\theta \\). Our method uses differentiable rendering to aggregate 2D image gradients over multiple viewpoints into a 3D asset gradient, and lifts a generative model from 2D to 3D. We parameterize a 3D asset \\( \\theta \\) as a radiance field stored on voxels and choose \\( f \\) to be the volume rendering function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.474, + 0.606 + ], + "angle": 0, + "content": "A key technical challenge is that computing the 2D score by directly evaluating a diffusion model on a rendered image \\( \\pmb{x}_{\\pi} \\) leads to an out-of-distribution (OOD) problem. Generally, diffusion models are trained as denoisers and have only seen noisy inputs during training. On the other hand, our method requires evaluating the denoiser on non-noisy rendered images from a 3D asset during optimization, and it leads to the OOD problem. To address the issue, we propose Perturb-and-Average Scoring, an approach to estimate the score for non-noisy images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.474, + 0.727 + ], + "angle": 0, + "content": "Empirically, we first validate the effectiveness of Perturb-and-Average Scoring at solving the OOD problem and explore the hyperparameter choices on a simple 2D image canvas. Here we identify open problems on using unconditioned diffusion models trained on FFHQ and LSUN Bedroom. Next, we use Stable Diffusion, a model pretrained on the web-scale LAION dataset to perform SJC for 3D generation, as shown in Fig. 1. Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.73, + 0.469, + 0.76 + ], + "angle": 0, + "content": "- We propose a method for lifting a 2D diffusion model to 3D via an application of the chain rule." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.767, + 0.469, + 0.813 + ], + "angle": 0, + "content": "- We illustrate the challenge of OOD when using a pretrained denoiser and propose Perturb-and-Average Scoring to resolve it." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.819, + 0.469, + 0.864 + ], + "angle": 0, + "content": "- We point out the subtleties and open problems on applying Perturb-and-Average Scoring as gradient for optimization." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "- We demonstrate the effectiveness of SJC for the task of 3D text-driven generation." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.73, + 0.469, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.651, + 0.107 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.895, + 0.223 + ], + "angle": 0, + "content": "Diffusion models have recently advanced to image generation on Internet-scale datasets [10, 36, 42, 44-47]. A diffusion model could be interpreted as either a VAE [13, 49] or a denoising score-matcher [50, 52, 56]. Notably, models trained under one regime can be directly used for inference and sampling by the other [20, 52]; they are in practice largely equivalent." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.897, + 0.452 + ], + "angle": 0, + "content": "Neural radiance fields (NeRF) is a family of inverse rendering algorithms that have excelled at multiview 3D reconstruction tasks including view synthesis and surface geometry estimation [31, 34, 40, 57, 61]. Conceptually, a 3D asset is represented as a dense grid of RGB colors and spatial density \\(\\tau\\), and rendered into images in a way analogous to alpha compositing [32]. NeRF parameterizes the (RGB, \\(\\tau\\)) volume with a neural network, but querying the network densely in 3D incurs significant compute costs. Alternatively, Voxel NeRFs [6, 11, 19, 28, 53] store the volume on voxels and observe no loss in end task performance [11, 53]. Querying voxels is a simple memory operation that is much faster than a feedforward pass of a neural network. Here we use a customized voxel radiance field with hyperparameters based on DvGO [53] and TensoRF [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.897, + 0.715 + ], + "angle": 0, + "content": "2D-supervised 3D GANs pioneered [35, 43, 63] the approach of training 3D generative models using only unstructured 2D images, and promise greater scalability in terms of data. Rather than supervising directly on the 3D asset a model generates, these methods supervise the 2D renderings of the generated 3D asset, often using an adversarial loss [3, 4, 38, 48, 64]. In other words, only images are needed as training data. However, training such a 3D generative model from scratch is still challenging [37]. Recent empirical evaluation remains mostly on human and animal faces [3]. Our method does the opposite: we take an image generative model that is already pretrained on large amounts of 2D data and use it to guide the iterative optimization of a 3D asset. Optimization-based generation makes it much slower compared to 3D GANs, but it becomes possible to harness powerful off-the-shelf 2D generative models such as Stable Diffusion [45] for greater content diversity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.897, + 0.903 + ], + "angle": 0, + "content": "CLIP-guided, optimization-based 3D generative models share a similar philosophy of optimizing 3D assets by guiding on 2D renderings [15, 17, 18, 22, 26, 33]. Among them, DreamFields [17] and PureClipNeRF [26] also use NeRF as their differentiable renderers. In this case, the 2D guidance comes from CLIP [42], a pretrained image-text matching model. These works optimize the 3D assets so that the image renderings match a user-provided text prompt. Since CLIP is not a 2D generative model per se, such a pipeline usually creates some abstract content [29] that looks very different from real images. In contrast, we use diffusion models, which are proper 2D generative models, to create realistic looking 3D" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "12620" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.093, + 0.135, + 0.105 + ], + "angle": 0, + "content": "content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.111, + 0.474, + 0.324 + ], + "angle": 0, + "content": "DreamFusion. The recently arXived work by Poole et al. [41], independent and concurrent to our work, proposes an algorithm that is similar to our approach at the pseudo-code level. Differently, their procedure uses the mathematical setup by Graikos et al. [12] to search for image parametrization that minimizes the training loss of a diffusion model. In contrast, our work is motivated by applying the chain rule to the 2D score. The key differences have been summarized in Sec. 4.3. In terms of implementation, we do not have access to the close-sourced Imagen [46] diffusion model. Instead, we use the pretrained Stable Diffusion model released by Rombach et al. [45]. For a comparison with DreamFusion, we use with a third-party implementation based on the same diffusion model, namely Stable-DreamFusion [55]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.338, + 0.218, + 0.354 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.471, + 0.439 + ], + "angle": 0, + "content": "To establish a common notation, we briefly review the score-based perspective of diffusion models. For readers familiar with VAE literature on diffusion models, we provide a concise score-based formula card and more details in Appendix Sec. ?? to connect these ideas." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.444, + 0.471, + 0.505 + ], + "angle": 0, + "content": "Denoising score matching. Given a dataset of samples \\(\\mathcal{V} = \\{\\pmb{y}_i\\}\\) drawn from \\(p_{\\mathrm{data}}\\), a diffusion model revolves primarily around learning a denoiser \\(D\\) by minimizing the difference between a noised sample \\(\\pmb{y} + \\sigma \\pmb{n}\\) and \\(\\pmb{y}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.516, + 0.472, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, I)} \\| D (\\boldsymbol {y} + \\sigma \\boldsymbol {n}; \\sigma) - \\boldsymbol {y} \\| _ {2} ^ {2}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.473, + 0.622 + ], + "angle": 0, + "content": "i.e. \\(D\\) is denoising the input \\(\\pmb{y} + \\sigma \\pmb{n}\\), for a range of \\(\\sigma\\) values. For 2D images, \\(D\\) is commonly chosen to be a ConvNet. Variants such as DDPM [13] parameterized the ConvNet to instead predict a noise residual \\(\\hat{\\epsilon}\\), and these models can be converted back to the form of a denoiser by [52]" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.634, + 0.47, + 0.651 + ], + "angle": 0, + "content": "\\[\nD (\\boldsymbol {x}; \\sigma) = \\boldsymbol {x} - \\sigma \\hat {\\epsilon} (\\boldsymbol {x}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.471, + 0.709 + ], + "angle": 0, + "content": "In this paper, we treat all pretrained diffusion models as denoisers, and perform the interface conversion in our implementation when needed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.789 + ], + "angle": 0, + "content": "Score from denoiser. Let \\( p_{\\sigma}(\\boldsymbol{x}) \\) denote the data distribution perturbed by Gaussian noise of standard deviation \\( \\sigma \\). It is shown in prior works [16, 50] that the denoiser \\( D \\) trained according to Eq. (1) provides a good approximation to the denoising score:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.801, + 0.47, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\boldsymbol {x}} \\log p _ {\\sigma} (\\boldsymbol {x}) \\approx \\frac {D (\\boldsymbol {x} ; \\sigma) - \\boldsymbol {x}}{\\sigma^ {2}}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.471, + 0.902 + ], + "angle": 0, + "content": "A denoising diffusion model estimates the score function of the noised distribution \\(p_{\\sigma}(\\boldsymbol{x})\\) at various \\(\\sigma \\in \\{\\sigma_i\\}_{i=1}^T\\). To perform sampling, the diffusion model gradually updates a sample through a sequence of noise levels of \\(\\sigma_T > \\dots >\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "\\(\\sigma_0 = 0\\). \\(\\{\\sigma_i\\}\\) are chosen empirically, with a typical range being [0.01, 157] [13] in the case of DDPM." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.125, + 0.894, + 0.201 + ], + "angle": 0, + "content": "Score as mean-shift. A helpful intuition is that the score behaves like mean-shift [7, 8]. If we simplify \\( p_{\\mathrm{data}} \\) to be an empirical data distribution over the i.i.d. samples \\( \\{\\pmb{y}_i\\} \\), then at noise level \\( \\sigma \\), \\( p_{\\sigma}(\\pmb{x}) \\) takes the form of a mixture of Gaussians [51]" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.209, + 0.893, + 0.227 + ], + "angle": 0, + "content": "\\[\np _ {\\sigma} (\\boldsymbol {x}) = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.235, + 0.892, + 0.265 + ], + "angle": 0, + "content": "In this case there exists a closed-form expression [20, 51] to the optimal denoiser" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.273, + 0.893, + 0.309 + ], + "angle": 0, + "content": "\\[\nD (\\boldsymbol {x}; \\sigma) = \\frac {\\sum_ {i} \\mathcal {N} (\\boldsymbol {x} ; \\boldsymbol {y} _ {i} , \\sigma^ {2} \\mathbf {I}) \\boldsymbol {y} _ {i}}{\\sum_ {i} \\mathcal {N} (\\boldsymbol {x} ; \\boldsymbol {y} _ {i} , \\sigma^ {2} \\mathbf {I})}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.315, + 0.894, + 0.392 + ], + "angle": 0, + "content": "In other words, \\( D(\\pmb{x}; \\sigma) \\) is a locally weighted mean of data samples \\( \\{\\pmb{y}_i\\} \\) around \\( \\pmb{x} \\) under a Gaussian kernel with bandwidth \\( \\sigma \\). The denoising score function can be thought of as a non-parametric guide on how to update \\( \\pmb{x} \\) in order to move it towards its weighted nearest neighbors." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.403, + 0.891, + 0.421 + ], + "angle": 0, + "content": "4. Score Jacobian Chaining for 3D Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.893, + 0.566 + ], + "angle": 0, + "content": "Let \\(\\theta\\) denotes the parameters of a 3D asset, e.g., voxel grid of (RGB, \\(\\tau\\)) as in Sec. 4.2. Our goal is to model and sample from the distribution \\(p(\\theta)\\) to generate a 3D scene. In our setting, only a pretrained 2D diffusion model on images \\(p(\\boldsymbol{x})\\) is given and we do not have access to 3D data. To relate the 2D and 3D distributions \\(p(\\boldsymbol{x})\\) and \\(p(\\theta)\\), we assume that the probability density of 3D asset \\(\\theta\\) is proportional to the expected probability densities of its multiview 2D image renderings \\(\\boldsymbol{x}_{\\pi}\\) over camera poses \\(\\pi\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.573, + 0.892, + 0.592 + ], + "angle": 0, + "content": "\\[\np _ {\\sigma} (\\boldsymbol {\\theta}) \\propto \\mathbb {E} _ {\\pi} \\left[ p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi} (\\boldsymbol {\\theta})\\right) \\right], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.6, + 0.89, + 0.631 + ], + "angle": 0, + "content": "up to a normalization constant \\(Z = \\int \\mathbb{E}_{\\pi}\\left[p_{\\sigma}(\\pmb{x}_{\\pi}(\\pmb{\\theta}))\\right]d\\pmb{\\theta}\\). That is, a 3D asset \\(\\pmb{\\theta}\\) is as likely as its 2D renderings \\(\\pmb{x}_{\\pi}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.631, + 0.894, + 0.662 + ], + "angle": 0, + "content": "Next, we establish a lower bound, \\(\\log \\tilde{p}_{\\sigma}(\\boldsymbol{\\theta})\\), on the distribution in Eq. (6) using Jensen's inequality:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.669, + 0.892, + 0.708 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\log p _ {\\sigma} (\\boldsymbol {\\theta}) = \\log \\left[ \\mathbb {E} _ {\\pi} \\left(p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right)\\right) \\right] - \\log Z (7) \\\\ \\geq \\mathbb {E} _ {\\pi} \\left[ \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right) \\right] - \\log Z \\triangleq \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta}). (8) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.716, + 0.892, + 0.747 + ], + "angle": 0, + "content": "Recall that the score is the gradient of log probability density of data. By chain rule" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.755, + 0.892, + 0.809 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\boldsymbol {\\theta}} \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {\\boldsymbol {\\pi}} \\left[ \\nabla_ {\\boldsymbol {\\theta}} \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\pi}}\\right) \\right] (9) \\\\ \\frac {\\partial \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} = \\mathbb {E} _ {\\pi} \\left[ \\frac {\\partial \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right)}{\\partial \\boldsymbol {x} _ {\\pi}} \\cdot \\frac {\\partial \\boldsymbol {x} _ {\\pi}}{\\partial \\boldsymbol {\\theta}} \\right] (10) \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.81, + 0.892, + 0.862 + ], + "angle": 0, + "content": "\\[\n\\underbrace {\\nabla_ {\\boldsymbol {\\theta}} \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta})} _ {\\text {3 D s c o r e}} = \\mathbb {E} _ {\\pi} [ \\underbrace {\\nabla_ {\\boldsymbol {x} _ {\\pi}} \\log p _ {\\sigma} (\\boldsymbol {x} _ {\\pi})} _ {\\text {2 D s c o r e ; p r e t r a i n e d}} \\cdot \\underbrace {\\boldsymbol {J} _ {\\pi}} _ {\\text {r e n d e r e r J a c o b i a n}} ]. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We will next discuss how to compute the 2D score in practice using a pretrained diffusion model." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "12621" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.208, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.089, + 0.337, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.343, + 0.089, + 0.468, + 0.199 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.204, + 0.471, + 0.274 + ], + "angle": 0, + "content": "Figure 2. Illustration of denoiser's OOD issue using a denoiser pretrained on FFHQ. When directly evaluating \\( D(\\pmb{x}_{\\mathrm{blob}}, \\sigma) \\) the model did not correct for the orange blob into a face image. Contrarily, evaluating the denoiser on noised input \\( D(\\pmb{x}_{\\mathrm{blob}} + \\sigma \\pmb{n}, \\sigma) \\) produces an image that successfully merges the blob with the face manifold." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.298, + 0.443, + 0.315 + ], + "angle": 0, + "content": "4.1. Computing 2D Score on Non-Noisy Images" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.321, + 0.47, + 0.367 + ], + "angle": 0, + "content": "Computing the 3D score in Eq. (11) requires the 2D score on \\( \\pmb{x}_{\\pi} \\). A first attempt would be to directly apply the score from the denoiser in Eq. (3), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.375, + 0.47, + 0.393 + ], + "angle": 0, + "content": "\\[\n\\operatorname {s c o r e} \\left(\\boldsymbol {x} _ {\\pi}, \\sigma\\right) \\triangleq \\left(D \\left(\\boldsymbol {x} _ {\\pi}; \\sigma\\right) - \\boldsymbol {x} _ {\\pi}\\right) / \\sigma^ {2}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.402, + 0.471, + 0.506 + ], + "angle": 0, + "content": "Unfortunately, evaluating the pretrained denoiser \\(D\\) on \\(\\pmb{x}_{\\pi}\\) causes an out-of-distribution (OOD) problem. From the training objective in Eq. (1), at each noise level \\(\\sigma\\), the denoiser \\(D\\) has only seen noisy inputs of the distribution \\(\\pmb{y} + \\sigma \\pmb{n}\\) where \\(\\pmb{y} \\sim p_{\\mathrm{data}}\\) and \\(\\pmb{n} \\sim \\mathcal{N}(0, \\mathbf{I})\\). However, a rendered image \\(\\pmb{x}_{\\pi}\\) from 3D asset \\(\\pmb{\\theta}\\) is generally not consistent with such distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.471, + 0.659 + ], + "angle": 0, + "content": "We illustrate this OOD situation in Fig. 2. Given a denoiser pretrained on FFHQ [21] by Baranchuk et al. [1], we visualize the output \\( D(\\pmb{x}_{\\mathrm{blob}}; \\sigma = 6.5) \\) where the input \\( \\pmb{x}_{\\mathrm{blob}} \\) is a non-noisy image showing an orange blob centered on a grey canvas. Under the intuition that \\( D \\) predicts a weighted nearest neighbor as reviewed in (5), we expect the denoiser to blend the orange blob with the manifold of faces. However in reality we observe sharp artifacts when updating with this score \\( (D(\\pmb{x}_{\\mathrm{blob}}; \\sigma) - \\pmb{x}_{\\mathrm{blob}}) / \\sigma^2 \\) and the image becomes further away from the face manifold." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.662, + 0.471, + 0.737 + ], + "angle": 0, + "content": "Perturb-and-Average Scoring. To address the OOD problem, we propose Perturb-and-Average Scoring (PAAS). It computes the score on non-noisy images \\( \\boldsymbol{x}_{\\pi} \\) with a denoiser \\( D \\) by adding noise to the input, and then considering the expectation of the predicted scores w.r.t. the random noise," + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.746, + 0.47, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathrm {P A A S} \\left(\\boldsymbol {x} _ {\\pi}, \\sqrt {2} \\sigma\\right) \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.768, + 0.47, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\triangleq \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\operatorname {s c o r e} (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n}, \\sigma) ] (14) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {D (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n} , \\sigma) - (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n})}{\\sigma^ {2}} \\right] (15) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {D (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n} , \\sigma) - \\boldsymbol {x} _ {\\pi}}{\\sigma^ {2}} \\right] - \\underbrace {\\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {\\boldsymbol {n}}{\\sigma} \\right]} _ {= 0}. (16) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In practice, we use the Monte Carlo estimate of the expectation in Eq. (16). The algorithm is illustrated in Fig. 3. Given" + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.096, + 0.858, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.265, + 0.894, + 0.335 + ], + "angle": 0, + "content": "Figure 3. Computing PAAS on 2D renderings \\( \\pmb{x}_{\\pi} \\). Directly evaluating \\( D(\\pmb{x}_{\\pi};\\sigma) \\) leads to an OOD problem. Instead, we add noise to \\( \\pmb{x}_{\\pi} \\), and evaluate \\( D(\\pmb{x}_{\\pi} + \\sigma \\pmb{n};\\sigma) \\) (blue dots). The PAAS is then computed by averaging over the brown dashed arrows, corresponding to multiple samples of \\( \\pmb{n} \\). See Sec. 4.1 for details." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.348, + 0.893, + 0.409 + ], + "angle": 0, + "content": "a set of sampled noises \\(\\{\\pmb{n}_i\\}\\), each \\(D(\\pmb{x}_{\\pi} + \\sigma \\pmb{n}_i)\\) provides an update direction on the perturbed input \\(\\pmb{x}_{\\pi} + \\sigma \\pmb{n}_i\\). By averaging over the noise perturbations \\(\\{\\pmb{n}_i\\}\\), we obtain an update direction on \\(\\pmb{x}_{\\pi}\\) itself." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.411, + 0.894, + 0.457 + ], + "angle": 0, + "content": "Justifying PAAS in Eq. (13). We show that Perturb-and-Average Scoring provides an approximation to the score on \\( x_{\\pi} \\) at an inflated noise level of \\( \\sqrt{2}\\sigma \\)" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.462, + 0.892, + 0.482 + ], + "angle": 0, + "content": "\\[\n\\operatorname {P A A S} \\left(\\boldsymbol {x} _ {\\pi}, \\sqrt {2} \\sigma\\right) \\approx \\nabla_ {\\boldsymbol {x} _ {\\pi}} \\log p _ {\\sqrt {2} \\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.497, + 0.884, + 0.529 + ], + "angle": 0, + "content": "Lemma 1 Assuming an empirical data distribution \\( p_{\\sigma}(\\pmb{x}) \\) in Eq. (4), for any \\( \\pmb{x} \\in \\mathbb{R}^d \\)" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.54, + 0.884, + 0.558 + ], + "angle": 0, + "content": "\\[\n\\log p _ {\\sqrt {2} \\sigma} (\\boldsymbol {x}) \\geq \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.594 + ], + "angle": 0, + "content": "Proof. Observe that the LHS of Eq. (19) is a convolution of two Gaussians, therefore" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.601, + 0.892, + 0.619 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {\\mu}, \\sigma^ {2} \\mathbf {I}) ] = \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {\\mu}, 2 \\sigma^ {2} \\mathbf {I}) \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.625, + 0.868, + 0.641 + ], + "angle": 0, + "content": "Recall that \\(p_{\\sigma}(\\pmb {x})\\) is a mixture of Gaussians per Eq. (4);" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.646, + 0.892, + 0.724 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} p _ {\\sqrt {2} \\sigma} (\\boldsymbol {x}) = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {y}, 2 \\sigma^ {2} \\mathbf {I}) (20) \\\\ = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\text {d a t a}}} \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}) (21) \\\\ = \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\text {d a t a}}} \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}) (22) \\\\ = \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}). (23) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.73, + 0.892, + 0.761 + ], + "angle": 0, + "content": "Taking the log on both sides of Eq. (23) and by Jensen's inequality, we arrive at Eq. (18)." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.767, + 0.886, + 0.816 + ], + "angle": 0, + "content": "Claim 1 Assuming a trained denoiser \\(D\\) as in Eq. (3), our \\(PAAS(x_{\\pi}, \\sqrt{2}\\sigma)\\) in Eq. (13) computes the gradient w.r.t. a lower bound of \\(\\log p_{\\sqrt{2}\\sigma}(\\pmb{x})\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.822, + 0.859, + 0.837 + ], + "angle": 0, + "content": "Proof. By taking the gradient of the RHS of Lemma 1," + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.844, + 0.895, + 0.879 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\boldsymbol {x}} \\mathbb {E} _ {\\boldsymbol {n}} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}) = \\mathbb {E} _ {\\boldsymbol {n}} \\nabla_ {\\boldsymbol {x} + \\sigma \\boldsymbol {n}} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} [ \\operatorname {s c o r e} (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n}, \\sigma) ]. \\tag {24} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.837, + 0.902 + ], + "angle": 0, + "content": "which is the proposed PAAS algorithm in Eq. (13)." + }, + { + "type": "image", + "bbox": [ + 0.875, + 0.887, + 0.891, + 0.897 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12622" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.445, + 0.108 + ], + "angle": 0, + "content": "4.2. Inverse Rendering on Voxel Radiance Field" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.159 + ], + "angle": 0, + "content": "With the computation of the 2D score resolved, the other half of our setup in Eq. (11) requires access to the Jacobian of a differentiable renderer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.163, + 0.471, + 0.298 + ], + "angle": 0, + "content": "3D Representation. We represent a 3D asset \\(\\theta\\) as a voxel radiance field [6, 11, 53], which is much faster to access and update compared to a vanilla NeRF parameterized by a neural network [34]. The parameters \\(\\theta\\) consist of a density voxel grid \\(\\mathbf{V}^{(\\mathrm{density})} \\in \\mathbb{R}^{1 \\times N_x \\times N_y \\times N_z}\\) and a voxel grid of appearance features \\(\\mathbf{V}^{(\\mathrm{app})} \\in \\mathbb{R}^{c \\times N_x \\times N_y \\times N_z}\\). Conventionally the appearance features are simply the RGB colors and \\(c = 3\\). For simplicity, we do not model view dependencies in this work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.473, + 0.436 + ], + "angle": 0, + "content": "Inverse Volumetric Rendering. Image rendering is performed independently along a camera ray through each pixel. We cut a camera light ray into equally distanced segments of length \\(d\\), and at the spatial location corresponding to the beginning of the \\(i\\)-th segment we sample a \\((\\mathrm{RGB}_i, \\tau_i)\\) tuple from the color and density grids using trilinear interpolation. These values are alpha-composed using volume rendering quadrature [32] into the pixel color \\(C = \\sum_{i} w_i \\cdot \\mathrm{RGB}_i\\), where" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.444, + 0.47, + 0.486 + ], + "angle": 0, + "content": "\\[\nw _ {i} = \\alpha_ {i} \\cdot \\prod_ {j = 0} ^ {i - 1} (1 - \\alpha_ {j}); \\quad \\alpha_ {i} = 1 - \\exp (- \\tau_ {i} d). \\tag {25}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.584 + ], + "angle": 0, + "content": "Volume rendering of \\(\\theta\\) is directly differentiable. At a rendered image \\(x_{\\pi}\\), the Vector-Jacobian product in Eq. (11) between PAAS \\((x_{\\pi})\\) and the Jacobian \\(J_{\\pi} = \\frac{\\partial x_{\\pi}}{\\partial \\theta}\\) is computed by back-propagating the score through Eq. (25). This Vector-Jacobian product provides us with the 3D gradient needed for generative modeling on the voxel radiance field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Regularization Strategies. The voxel grid is a very powerful 3D representation for volumetric rendering. Given noisy 2D guidance, the model may cheat by populating the entire grid with small densities such that the combined effect from one view hallucinates a plausible image. We propose several techniques to encourage the formation of a coherent 3D structure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.743 + ], + "angle": 0, + "content": "Emptiness Loss: Ideally, the space should be sparse with near zero densities except at the object. We propose an emptiness loss to encourage sparsity on a ray \\(\\mathbf{r}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.75, + 0.47, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e m p t i n e s s}} (\\mathbf {r}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log \\left(1 + \\beta \\cdot w _ {i}\\right), \\tag {26}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "where \\( w_{i} \\) are the alpha-composed weights shown in (25). The shape of the log function imposes severe penalties at the onset of small weights, but does not grow aggressively if the weights are large. It is consistent with our aim to eliminate small densities. The hyperparameter \\( \\beta \\) controls the steepness of the loss function near 0. A larger \\( \\beta \\) will put more emphasis on eliminating low-density noise. We set \\( \\beta = 10 \\)." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.093, + 0.889, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.402, + 0.895, + 0.569 + ], + "angle": 0, + "content": "Figure 4. Sampling 2D images with Perturb-and-Average Scoring. We compare Annealed vs Random \\(\\sigma\\) schedule against several diffusion models. Row 1 & 2: the random \\(\\sigma\\) schedule exhibits strong mode-seeking behavior, and it results in low-quality \"mean\" images on unconditioned diffusion models trained on FFHQ and LSUN Bedroom. In this case, we need a carefully designed annealed \\(\\sigma\\) schedule to produce better, more diverse samples. Row 3 & 4: Stable Diffusion (SD) is conditioned on the prompt \"a squirrel holding a saxophone\". The use of natural language makes the conditioned distribution much easier to sample from. When the guidance scale is elevated to 10, Random \\(\\sigma\\) schedule that fails on FFHQ and LSUN starts to produce crisp, clean images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.585, + 0.895, + 0.75 + ], + "angle": 0, + "content": "Emptiness Loss Schedule: We use a hyperparameter \\(\\lambda\\) to control the contribution of the emptiness loss. If we apply a large emptiness loss, it will hinder the learning of geometry in the early stage of training. But if the emptiness is too small, there will be floating density artifacts. We adopt a two-stage noise elimination schedule to deal with this problem. In the first \\(K\\) iterations, we use a relatively small weighting factor \\(\\lambda_{1}\\). After the \\(K^{\\mathrm{th}}\\) iteration, it is increased to a larger \\(\\lambda_{2}\\). In our experiments \\(\\lambda_{1} = 1 \\times 10^{4}\\) and \\(\\lambda_{2} = 2 \\times 10^{5}\\). We provide an ablation study of this technique in Fig. 7 to show its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.762, + 0.893, + 0.823 + ], + "angle": 0, + "content": "Center Depth Loss: Sometimes the optimization places the object away from the scene center. The object either becomes small or wander around the image boundary. For the few cases when this happens we apply a center depth loss" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c e n t e r}} (D) = - \\log \\left(\\frac {1}{| \\mathcal {B} |} \\sum_ {\\mathbf {p} \\in \\mathcal {B}} D (\\mathbf {p}) - \\frac {1}{| \\mathcal {B} ^ {\\complement} |} \\sum_ {\\mathbf {q} \\notin \\mathcal {B}} D (\\mathbf {q})\\right) \\tag {27}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12623" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.187, + 0.09, + 0.382, + 0.104 + ], + "angle": 0, + "content": "A DSLR photo of a yellow duck" + }, + { + "type": "image", + "bbox": [ + 0.09, + 0.107, + 0.184, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.107, + 0.282, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.107, + 0.38, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.107, + 0.478, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.186, + 0.387, + 0.199 + ], + "angle": 0, + "content": "A zoomed out photo a small castle" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.202, + 0.184, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.202, + 0.282, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.202, + 0.38, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.202, + 0.478, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.28, + 0.456, + 0.295 + ], + "angle": 0, + "content": "A zoomed out high quality photo of Sydney Opera House" + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.298, + 0.184, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.187, + 0.298, + 0.282, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.298, + 0.38, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.384, + 0.298, + 0.478, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.09, + 0.758, + 0.104 + ], + "angle": 0, + "content": "A ficus planted in a pot" + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.107, + 0.588, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.107, + 0.685, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.107, + 0.783, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.107, + 0.882, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.185, + 0.808, + 0.2 + ], + "angle": 0, + "content": "A high quality photo of a toy motorcycle" + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.202, + 0.588, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.202, + 0.685, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.202, + 0.783, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.202, + 0.882, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.596, + 0.28, + 0.778, + 0.295 + ], + "angle": 0, + "content": "A photo of a horse walking" + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.298, + 0.588, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.591, + 0.298, + 0.685, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.298, + 0.783, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.787, + 0.298, + 0.882, + 0.369 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.375, + 0.895, + 0.417 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of text-prompted generation of 3D models with SJC, purely from the pretrained Stable Diffusion (2D) image model. Each row shows two views, with associated depth maps (blue is far, red is near), for a single 3D model generated for a given prompt. Note the detailed appearance as well as a sharp, well-defined depth structure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.471, + 0.465 + ], + "angle": 0, + "content": "where \\(D\\) is the depth image, \\(\\mathcal{B}\\) is a box (set of pixel locations) at the center of the image, and \\(\\mathcal{B}^{\\mathrm{G}}\\) is its complement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.48, + 0.281, + 0.495 + ], + "angle": 0, + "content": "4.3. SJC vs. DreamFusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.472, + 0.534 + ], + "angle": 0, + "content": "In this section, we describe the differences and the connections between our SJC and DreamFusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.763 + ], + "angle": 0, + "content": "Differences from DreamFusion. In terms of formulation, DreamFusion's computation of the gradient w.r.t. \\(\\theta\\) involves a U-Net Jacobian term (see Eq. 2 in their paper [41]). In practice, they \"found that omitting the U-Net Jacobian term\" to be more effective. On the other hand, this U-Net Jacobian term does not appear in our formulation. Their additional justification in the appendix actually leans more towards our viewpoint. An additional contribution of ours beyond DreamFusion [41] is our analysis of the effect that the OOD problem has when using a denoiser on rendered images (Claim 1), and the PAAS method to address it. For the variance reduction technique, namely the use of the Monte-Carlo estimate on Eq. (16), or \\(\\hat{\\epsilon} - \\epsilon\\) (in DreamFusion), vs. on Eq. (15), we observe comparable performance between the two methods empirically for 3D generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Influences by DreamFusion. At the time of this submission, DreamFusion is a concurrent arXiv paper. However, as we have read the paper, our research was influenced by their reported observations. In particular, we adopted the idea of randomized scheduling of \\(\\sigma\\) during 3D optimization for easier hyperparameter tuning, and used view-augmented language prompting that improves the overall 3D quality. For future work we do hope to explore a more general solution than view-dependent prompts." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.433, + 0.633, + 0.451 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.505 + ], + "angle": 0, + "content": "We conduct experiments on both unconditioned and conditioned diffusion models to have a more comprehensive understanding of the properties of SJC." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.895, + 0.632 + ], + "angle": 0, + "content": "DDPMs trained on FFHQ and LSUN Bedroom are unconditioned diffusion models with an architecture based on the implementation by Dhariwal and Nichol [10]. They are trained on an image resolution of \\(256 \\times 256\\). FFHQ [21] is a dataset of aligned faces with diverse coverage of gender, age, race, facial appearance as well as head poses. LSUN Bedroom [62] includes bedroom images with varied furniture layout plans and rich interior design styles." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.896, + 0.804 + ], + "angle": 0, + "content": "Stable Diffusion is an expanded work based on Latent Diffusion Model (LDM) developed by Rombach et al. [45]. It is trained on the LAION5B dataset [47]. We use the release version v1.5. Diffusion is performed on a latent space of \\( 4 \\times 64 \\times 64 \\), then upsampled to \\( 3 \\times 256 \\times 256 \\) by a decoder. The model is natively trained for text-conditioned image generations, and exposes a guidance scale parameter that controls the strength of language conditioning [14]. Intuitively a larger guidance scale makes the conditioned image distribution more faithful to the text prompt by trading off sample diversity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.773, + 0.833 + ], + "angle": 0, + "content": "5.1. Validating PAAS on 2D images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Before directly jumping to 3D generation, we first verify that PAAS provides effective guidance on a simple 2D image canvas. In other words, here \\(\\theta\\) is a grid of RGB values and \\(f\\) is an identity function. The hope is that gradient descent" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12624" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.219, + 0.092, + 0.239, + 0.103 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.105, + 0.358, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.484, + 0.092, + 0.503, + 0.103 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.105, + 0.621, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.092, + 0.764, + 0.103 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.105, + 0.885, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.22, + 0.315, + 0.239, + 0.327 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.328, + 0.358, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.484, + 0.316, + 0.503, + 0.327 + ], + "angle": 0, + "content": "(e)" + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.328, + 0.621, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.316, + 0.763, + 0.327 + ], + "angle": 0, + "content": "(f)" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.328, + 0.885, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.543, + 0.893, + 0.613 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison between Stable-DreamFusion (StableDF) and Ours. The prompts are: (a) \"A high quality photo of a delicious burger\"; (b) \"a DSLR photo of a yellow duck\"; (c) \"A ficus planted in a pot\"; (d) \"A product photo of a toy tank\"; (e) \"A high quality photo of a chocolate icecream cone\"; (f) \"A wide angle zoomed out photo of a giraffe\". Both methods are run for 10k iterations without per-prompt finetuning on the hyperparameters. The images on the left are rendered RGB images and the images on the right are depth visualization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.674 + ], + "angle": 0, + "content": "on the vector field produced by PAAS creates high quality images. Here an important decision to make is the schedule of \\(\\{\\sigma_i\\}\\) at which we compute PAAS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.81 + ], + "angle": 0, + "content": "We experimented with an annealed schedule (Annealed \\(\\sigma\\)) vs. a random schedule (Random \\(\\sigma\\)) as proposed in Dream-Fusion. Under the Annealed \\(\\sigma\\) schedule, we start from a large \\(\\sigma\\) and gradually decrease it as we update the image canvas \\(x\\). PAAS computed at larger \\(\\sigma\\) level attends to high level image structure while smaller \\(\\sigma\\) provides stronger guidance on detailed features. The Random \\(\\sigma\\) schedule on the contrary uniformly samples a \\(\\sigma\\) at every step. We show qualitative comparisons in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "For unconditioned diffusion models trained on FFHQ, we observe that Annealed \\(\\sigma\\) performs better than Random \\(\\sigma\\), and the image samples have better pose variation and quality. Particularly, the randomized \\(\\sigma\\) exhibits severe mode-seeking behavior converging to average faces. In the case of LSUN Bedroom, the mode-seeking behavior results in a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.629, + 0.746, + 0.644 + ], + "angle": 0, + "content": "blurry image canvas with no content." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.902 + ], + "angle": 0, + "content": "On the other hand, natural language prompting plays a critical role when sampling images with Stable Diffusion. When the language guidance is set to a regular level of 3.0, the observations are broadly consistent with sampling on FFHQ and LSUN. Random \\(\\sigma\\) schedule produces blurry outputs. However, when the guidance scale is elevated to 10.0, Random \\(\\sigma\\) schedule begins to generate crisp, clean images and outperforms Annealed \\(\\sigma\\) schedule. Despite various sophisticated strategies on Annealed \\(\\sigma\\) scheduling (see our code for details), at a high language guidance scale Randomized \\(\\sigma\\) remains the better option. We hypothesize that stronger language guidance forces the image distribution to be narrower and more beneficial for a mode-seeking algorithm. We acknowledge none of the images in Fig. 4 can match the sample quality of a standard diffusion inference pipeline, and the right way to apply PAAS as gradient for optimization remains an open problem." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12625" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.32, + 0.091, + 0.651, + 0.104 + ], + "angle": 0, + "content": "A zoomed out high quality photo of Temple of Heaven." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.105, + 0.887, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.401, + 0.896, + 0.459 + ], + "angle": 0, + "content": "Figure 7. Ablation experiments on the proposed emptiness loss schedule. For each setting of the loss weight \\(\\lambda\\), we show a rendered image and the associated depth map from a randomly sampled viewpoint. Ours incorporates the loss with weight schedule described in 5.2. It leads to better 3D shape, as evidenced in the cleaner depth maps. Setting the loss weight too low yields \"cloudy\" depth fields. When setting the weight too high, SJC fails to produce meaningful 3D models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.229, + 0.499 + ], + "angle": 0, + "content": "5.2.3D Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.471, + 0.618 + ], + "angle": 0, + "content": "In this paper, we focus on 3D Generation with the language-conditioned Stable Diffusion model. We found that tuning the Annealed \\(\\sigma\\) schedule on FFHQ and LSUN Bedroom in 3D domain is difficult in practice, and leave it as future work. Based on the insights from 2D experiments earlier, we use Random \\(\\sigma\\) schedule coupled with a high language guidance scale." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.473, + 0.721 + ], + "angle": 0, + "content": "Rendering with Latent 3D Features. Stable Diffusion economizes compute by performing diffusion modeling on the latent features of a pretrained AutoEncoder. We therefore choose to render a feature image in this latent space from a features field [3, 38] represented by a voxel grid in \\(\\mathbb{R}^{4\\times N_x\\times N_y\\times N_z}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Qualitative Comparison. In Fig. 5, we show text-prompted 3D generation results from SJC, and compare SJC with Stable-DreamFusion, a third-party implementation based on the same pretrained Stable Diffusion v1.5 model. In Fig. 6, we show qualitative comparisons of generated 3D assets given the same prompt. We observe that SJC generates 3D models with better image quality and more sensible structure than Stable-DreamFusion in a significant number of cases. We note that both systems exhibit quality fluctuations over different trials, and the point of this comparison is to show that our overall pipeline is competitive." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.896, + 0.591 + ], + "angle": 0, + "content": "Ablations. In Fig. 7, we conduct ablations to demonstrate the importance of the proposed emptiness loss and scheduling of its weight \\(\\lambda\\) discussed in Sec. 4.2. We show results without the emptiness loss, with constant weight \\(\\lambda\\) vs our proposed scheduling of \\(\\lambda\\). We observe that our complete method (Ours) improves the quality of generated 3D models, e.g., fewer floating artifacts and better geometry." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.601, + 0.62, + 0.617 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.895, + 0.823 + ], + "angle": 0, + "content": "We propose an optimization-based approach to generate 3D assets from pretrained image (2D) diffusion models. The key technical contribution is the derivation of Perturb-and-Average Scoring method which bridges the gap between the denoising-trained diffusion models and the non-noisy images encountered in the process of optimizing a 3D model guided by the diffusion. Working with the large-scale Stable Diffusion model, we demonstrate that our approach can generate compelling 3D models, comparing favorably to available concurrent work. Finally, we investigate an interesting distinction between the effect of noise scheduling regime in unconditional image diffusion models and a text-conditional model, and identify an avenue for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement This work was supported in part by the TRI University 2.0 program, and by the AFOSR MADlab Center of Excellence. We thank friends and colleagues at TTIC, UChicago and TRI for feedbacks and discussions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12626" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Dmitry Baranchuk, Andrey Voynov, Ivan Rubachev, Valentin Khrulkov, and Artem Babenko. 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Yeh2 + +Greg Shakhnarovich1 + +$^{1}$ TTI-Chicago + +$^{2}$ Purdue University + +A zoomed out high-quality photo of Temple of Heaven + +![](images/cfb582287039a9dfc27e57559d94ec1b428efa55edb53d8cd0f0323cc7b8256d.jpg) + +![](images/045a36fb5058cd53c7d68ed0f43fb55ba425eb21787d38c195520c2b09129a21.jpg) + +![](images/6964eeca35c4e057d24264cdd7ac0fa59ec6f5e7a960a7638c8a6f264533cb6b.jpg) + +A high quality photo of a Victorian style wooden chair with velvet upholstery + +A high quality photo of a delicious burger + +![](images/912d540c39c41f646d2965f7ba7d73d96e34793674b580fa9580ca88b5fd1a48.jpg) + +![](images/f3c8204e53268d57108edd48e813cc15b283bf6bbf93bcef9a7bf6462a879630.jpg) + +![](images/5413e28369486c099f7164feded939eed601a7bd177c8289550221c9dde26bfd.jpg) + +A high quality photo of a classic silver muscle car + +![](images/c1b90a65ed736d2220fae225efcd8c56b86bbfa74855749f0d304d8bc102f832.jpg) +Figure 1. Results for text-driven 3D generation using Score Jacobian Chaining with Stable Diffusion as the pretrained model. + +![](images/cdbb1d2d5ebdfc7812e9d2c5c15f3ae3d63c02990394fa6cecdb24fca0f2eff2.jpg) + +![](images/d5ccd4dbdb778866dbb7ab40010cafdfd0cd329bda257e2c294212758a3cd383.jpg) + +![](images/4f3f274cbacba2a9ae99582283f7499abfbd66fadcfb6d53854b880a37c5d40c.jpg) + +![](images/ef5bf2e144599225dc607dcd99af6124de6880ebea0e4b1bda707fbb3eebeb04.jpg) + +![](images/711bf3c7522ed0033c0a02b4f331b8e7714676c16e8240e4488028d5f2b3af0d.jpg) + +# Abstract + +A diffusion model learns to predict a vector field of gradients. We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION 5B dataset. + +# 1. Introduction + +We introduce a method that converts a pretrained 2D diffusion generative model on images into a 3D generative model of radiance fields, without requiring access to any 3D data. The key insight is to interpret diffusion models as + +learned predictors of a gradient field, often referred to as the score function of the data log-likelihood. We apply the chain rule on the estimated score, hence the name Score Jacobian Chaining (SJC). + +Following Hyvarinen [16], the score is defined as the gradient of the log-density function with respect to the data (rather than parameter). Diffusion models of various families [13, 49, 50, 52] can all be interpreted [20, 23, 52] as modeling $\nabla_{\pmb{x}}\log p_{\sigma}(\pmb{x})$ i.e. the denoising score at noise level $\sigma$ . For readability, we refer to the denoising score as the score. Generating a sample from a diffusion model involves repeated evaluations of the score function from large to small $\sigma$ level, so that a sample $\pmb{x}$ gradually moves closer to the data manifold. It can be loosely interpreted as gradient descent, with precise control on the step sizes so that data distribution evolves to match the annealed $\sigma$ level (ancestral sampler [13], SDE and probability-flow ODE [52], etc.). While there are other perspectives to a diffusion model [13, 49], here we are primarily motivated from the viewpoint that diffusion models produce a gradient field. + +A natural question to ask is whether the chain rule can be applied to the learned gradients. Consider a diffusion model on images. An image $\pmb{x}$ may be parameterized by some + +function $f$ with parameters $\theta$ , i.e., $x = f(\theta)$ . Applying the chain rule through the Jacobian $\frac{\partial x}{\partial \theta}$ converts a gradient on image $x$ into a gradient on the parameter $\theta$ . There are many potential use cases for pairing a pretrained diffusion model with different choices of $f$ . In this work we are interested in exploring the connection between 3D and multiview 2D by choosing $f$ to be a differentiable renderer, thus creating a 3D generative model using only pretrained 2D resources. + +Many prior works [2, 58, 60] perform 3D generative modeling by training on 3D datasets [5, 24, 54, 59]. This approach is often as challenging as it is format-ambiguous. In addition to the high data acquisition cost of 3D assets [9], there is no universal data format: point clouds, meshes, volumetric radiance field, etc, all have computational trade-offs. What is common to these 3D assets is that they can be rendered into 2D images. An inverse rendering system, or a differentiable renderer [25, 27, 30, 34, 39], provides access to the Jacobian $J_{\pi} \triangleq \frac{\partial x_{\pi}}{\partial \theta}$ of a rendered image $x_{\pi}$ at camera viewpoint $\pi$ with respect to the underlying 3D parameterization $\theta$ . Our method uses differentiable rendering to aggregate 2D image gradients over multiple viewpoints into a 3D asset gradient, and lifts a generative model from 2D to 3D. We parameterize a 3D asset $\theta$ as a radiance field stored on voxels and choose $f$ to be the volume rendering function. + +A key technical challenge is that computing the 2D score by directly evaluating a diffusion model on a rendered image $\pmb{x}_{\pi}$ leads to an out-of-distribution (OOD) problem. Generally, diffusion models are trained as denoisers and have only seen noisy inputs during training. On the other hand, our method requires evaluating the denoiser on non-noisy rendered images from a 3D asset during optimization, and it leads to the OOD problem. To address the issue, we propose Perturb-and-Average Scoring, an approach to estimate the score for non-noisy images. + +Empirically, we first validate the effectiveness of Perturb-and-Average Scoring at solving the OOD problem and explore the hyperparameter choices on a simple 2D image canvas. Here we identify open problems on using unconditioned diffusion models trained on FFHQ and LSUN Bedroom. Next, we use Stable Diffusion, a model pretrained on the web-scale LAION dataset to perform SJC for 3D generation, as shown in Fig. 1. Our contributions are as follows: + +- We propose a method for lifting a 2D diffusion model to 3D via an application of the chain rule. +- We illustrate the challenge of OOD when using a pretrained denoiser and propose Perturb-and-Average Scoring to resolve it. +- We point out the subtleties and open problems on applying Perturb-and-Average Scoring as gradient for optimization. +- We demonstrate the effectiveness of SJC for the task of 3D text-driven generation. + +# 2. Related Works + +Diffusion models have recently advanced to image generation on Internet-scale datasets [10, 36, 42, 44-47]. A diffusion model could be interpreted as either a VAE [13, 49] or a denoising score-matcher [50, 52, 56]. Notably, models trained under one regime can be directly used for inference and sampling by the other [20, 52]; they are in practice largely equivalent. + +Neural radiance fields (NeRF) is a family of inverse rendering algorithms that have excelled at multiview 3D reconstruction tasks including view synthesis and surface geometry estimation [31, 34, 40, 57, 61]. Conceptually, a 3D asset is represented as a dense grid of RGB colors and spatial density $\tau$ , and rendered into images in a way analogous to alpha compositing [32]. NeRF parameterizes the (RGB, $\tau$ ) volume with a neural network, but querying the network densely in 3D incurs significant compute costs. Alternatively, Voxel NeRFs [6, 11, 19, 28, 53] store the volume on voxels and observe no loss in end task performance [11, 53]. Querying voxels is a simple memory operation that is much faster than a feedforward pass of a neural network. Here we use a customized voxel radiance field with hyperparameters based on DvGO [53] and TensoRF [6]. + +2D-supervised 3D GANs pioneered [35, 43, 63] the approach of training 3D generative models using only unstructured 2D images, and promise greater scalability in terms of data. Rather than supervising directly on the 3D asset a model generates, these methods supervise the 2D renderings of the generated 3D asset, often using an adversarial loss [3, 4, 38, 48, 64]. In other words, only images are needed as training data. However, training such a 3D generative model from scratch is still challenging [37]. Recent empirical evaluation remains mostly on human and animal faces [3]. Our method does the opposite: we take an image generative model that is already pretrained on large amounts of 2D data and use it to guide the iterative optimization of a 3D asset. Optimization-based generation makes it much slower compared to 3D GANs, but it becomes possible to harness powerful off-the-shelf 2D generative models such as Stable Diffusion [45] for greater content diversity. + +CLIP-guided, optimization-based 3D generative models share a similar philosophy of optimizing 3D assets by guiding on 2D renderings [15, 17, 18, 22, 26, 33]. Among them, DreamFields [17] and PureClipNeRF [26] also use NeRF as their differentiable renderers. In this case, the 2D guidance comes from CLIP [42], a pretrained image-text matching model. These works optimize the 3D assets so that the image renderings match a user-provided text prompt. Since CLIP is not a 2D generative model per se, such a pipeline usually creates some abstract content [29] that looks very different from real images. In contrast, we use diffusion models, which are proper 2D generative models, to create realistic looking 3D + +content. + +DreamFusion. The recently arXived work by Poole et al. [41], independent and concurrent to our work, proposes an algorithm that is similar to our approach at the pseudo-code level. Differently, their procedure uses the mathematical setup by Graikos et al. [12] to search for image parametrization that minimizes the training loss of a diffusion model. In contrast, our work is motivated by applying the chain rule to the 2D score. The key differences have been summarized in Sec. 4.3. In terms of implementation, we do not have access to the close-sourced Imagen [46] diffusion model. Instead, we use the pretrained Stable Diffusion model released by Rombach et al. [45]. For a comparison with DreamFusion, we use with a third-party implementation based on the same diffusion model, namely Stable-DreamFusion [55]. + +# 3. Preliminaries + +To establish a common notation, we briefly review the score-based perspective of diffusion models. For readers familiar with VAE literature on diffusion models, we provide a concise score-based formula card and more details in Appendix Sec. ?? to connect these ideas. + +Denoising score matching. Given a dataset of samples $\mathcal{V} = \{\pmb{y}_i\}$ drawn from $p_{\mathrm{data}}$ , a diffusion model revolves primarily around learning a denoiser $D$ by minimizing the difference between a noised sample $\pmb{y} + \sigma \pmb{n}$ and $\pmb{y}$ , + +$$ +\mathbb {E} _ {\boldsymbol {y} \sim p _ {\mathrm {d a t a}}} \mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, I)} \| D (\boldsymbol {y} + \sigma \boldsymbol {n}; \sigma) - \boldsymbol {y} \| _ {2} ^ {2}, \tag {1} +$$ + +i.e. $D$ is denoising the input $\pmb{y} + \sigma \pmb{n}$ , for a range of $\sigma$ values. For 2D images, $D$ is commonly chosen to be a ConvNet. Variants such as DDPM [13] parameterized the ConvNet to instead predict a noise residual $\hat{\epsilon}$ , and these models can be converted back to the form of a denoiser by [52] + +$$ +D (\boldsymbol {x}; \sigma) = \boldsymbol {x} - \sigma \hat {\epsilon} (\boldsymbol {x}). \tag {2} +$$ + +In this paper, we treat all pretrained diffusion models as denoisers, and perform the interface conversion in our implementation when needed. + +Score from denoiser. Let $p_{\sigma}(\boldsymbol{x})$ denote the data distribution perturbed by Gaussian noise of standard deviation $\sigma$ . It is shown in prior works [16, 50] that the denoiser $D$ trained according to Eq. (1) provides a good approximation to the denoising score: + +$$ +\nabla_ {\boldsymbol {x}} \log p _ {\sigma} (\boldsymbol {x}) \approx \frac {D (\boldsymbol {x} ; \sigma) - \boldsymbol {x}}{\sigma^ {2}}. \tag {3} +$$ + +A denoising diffusion model estimates the score function of the noised distribution $p_{\sigma}(\boldsymbol{x})$ at various $\sigma \in \{\sigma_i\}_{i=1}^T$ . To perform sampling, the diffusion model gradually updates a sample through a sequence of noise levels of $\sigma_T > \dots >$ + +$\sigma_0 = 0$ . $\{\sigma_i\}$ are chosen empirically, with a typical range being [0.01, 157] [13] in the case of DDPM. + +Score as mean-shift. A helpful intuition is that the score behaves like mean-shift [7, 8]. If we simplify $p_{\mathrm{data}}$ to be an empirical data distribution over the i.i.d. samples $\{\pmb{y}_i\}$ , then at noise level $\sigma$ , $p_{\sigma}(\pmb{x})$ takes the form of a mixture of Gaussians [51] + +$$ +p _ {\sigma} (\boldsymbol {x}) = \mathbb {E} _ {\boldsymbol {y} \sim p _ {\mathrm {d a t a}}} \mathcal {N} (\boldsymbol {x}; \boldsymbol {y}, \sigma^ {2} \mathbf {I}). \tag {4} +$$ + +In this case there exists a closed-form expression [20, 51] to the optimal denoiser + +$$ +D (\boldsymbol {x}; \sigma) = \frac {\sum_ {i} \mathcal {N} (\boldsymbol {x} ; \boldsymbol {y} _ {i} , \sigma^ {2} \mathbf {I}) \boldsymbol {y} _ {i}}{\sum_ {i} \mathcal {N} (\boldsymbol {x} ; \boldsymbol {y} _ {i} , \sigma^ {2} \mathbf {I})}. \tag {5} +$$ + +In other words, $D(\pmb{x}; \sigma)$ is a locally weighted mean of data samples $\{\pmb{y}_i\}$ around $\pmb{x}$ under a Gaussian kernel with bandwidth $\sigma$ . The denoising score function can be thought of as a non-parametric guide on how to update $\pmb{x}$ in order to move it towards its weighted nearest neighbors. + +# 4. Score Jacobian Chaining for 3D Generation + +Let $\theta$ denotes the parameters of a 3D asset, e.g., voxel grid of (RGB, $\tau$ ) as in Sec. 4.2. Our goal is to model and sample from the distribution $p(\theta)$ to generate a 3D scene. In our setting, only a pretrained 2D diffusion model on images $p(\boldsymbol{x})$ is given and we do not have access to 3D data. To relate the 2D and 3D distributions $p(\boldsymbol{x})$ and $p(\theta)$ , we assume that the probability density of 3D asset $\theta$ is proportional to the expected probability densities of its multiview 2D image renderings $\boldsymbol{x}_{\pi}$ over camera poses $\pi$ , i.e., + +$$ +p _ {\sigma} (\boldsymbol {\theta}) \propto \mathbb {E} _ {\pi} \left[ p _ {\sigma} \left(\boldsymbol {x} _ {\pi} (\boldsymbol {\theta})\right) \right], \tag {6} +$$ + +up to a normalization constant $Z = \int \mathbb{E}_{\pi}\left[p_{\sigma}(\pmb{x}_{\pi}(\pmb{\theta}))\right]d\pmb{\theta}$ . That is, a 3D asset $\pmb{\theta}$ is as likely as its 2D renderings $\pmb{x}_{\pi}$ . + +Next, we establish a lower bound, $\log \tilde{p}_{\sigma}(\boldsymbol{\theta})$ , on the distribution in Eq. (6) using Jensen's inequality: + +$$ +\begin{array}{l} \log p _ {\sigma} (\boldsymbol {\theta}) = \log \left[ \mathbb {E} _ {\pi} \left(p _ {\sigma} \left(\boldsymbol {x} _ {\pi}\right)\right) \right] - \log Z (7) \\ \geq \mathbb {E} _ {\pi} \left[ \log p _ {\sigma} \left(\boldsymbol {x} _ {\pi}\right) \right] - \log Z \triangleq \log \tilde {p} _ {\sigma} (\boldsymbol {\theta}). (8) \\ \end{array} +$$ + +Recall that the score is the gradient of log probability density of data. By chain rule + +$$ +\begin{array}{l} \nabla_ {\boldsymbol {\theta}} \log \tilde {p} _ {\sigma} (\boldsymbol {\theta}) = \mathbb {E} _ {\boldsymbol {\pi}} \left[ \nabla_ {\boldsymbol {\theta}} \log p _ {\sigma} \left(\boldsymbol {x} _ {\boldsymbol {\pi}}\right) \right] (9) \\ \frac {\partial \log \tilde {p} _ {\sigma} (\boldsymbol {\theta})}{\partial \boldsymbol {\theta}} = \mathbb {E} _ {\pi} \left[ \frac {\partial \log p _ {\sigma} \left(\boldsymbol {x} _ {\pi}\right)}{\partial \boldsymbol {x} _ {\pi}} \cdot \frac {\partial \boldsymbol {x} _ {\pi}}{\partial \boldsymbol {\theta}} \right] (10) \\ \end{array} +$$ + +$$ +\underbrace {\nabla_ {\boldsymbol {\theta}} \log \tilde {p} _ {\sigma} (\boldsymbol {\theta})} _ {\text {3 D s c o r e}} = \mathbb {E} _ {\pi} [ \underbrace {\nabla_ {\boldsymbol {x} _ {\pi}} \log p _ {\sigma} (\boldsymbol {x} _ {\pi})} _ {\text {2 D s c o r e ; p r e t r a i n e d}} \cdot \underbrace {\boldsymbol {J} _ {\pi}} _ {\text {r e n d e r e r J a c o b i a n}} ]. \tag {11} +$$ + +We will next discuss how to compute the 2D score in practice using a pretrained diffusion model. + +![](images/09b8676d9de0125ae440e00cdd28e15d1ac7e880d7180d3018454e13a812af81.jpg) +Figure 2. Illustration of denoiser's OOD issue using a denoiser pretrained on FFHQ. When directly evaluating $D(\pmb{x}_{\mathrm{blob}}, \sigma)$ the model did not correct for the orange blob into a face image. Contrarily, evaluating the denoiser on noised input $D(\pmb{x}_{\mathrm{blob}} + \sigma \pmb{n}, \sigma)$ produces an image that successfully merges the blob with the face manifold. + +![](images/546d9c674ae035e8931f5611a157c3711edf9e164a244f2a9c74f16ac59ff168.jpg) + +![](images/1eacb1be994dff875f52a88076659e3368c815b114ddd9493b5cc695ca51d048.jpg) + +# 4.1. Computing 2D Score on Non-Noisy Images + +Computing the 3D score in Eq. (11) requires the 2D score on $\pmb{x}_{\pi}$ . A first attempt would be to directly apply the score from the denoiser in Eq. (3), i.e., + +$$ +\operatorname {s c o r e} \left(\boldsymbol {x} _ {\pi}, \sigma\right) \triangleq \left(D \left(\boldsymbol {x} _ {\pi}; \sigma\right) - \boldsymbol {x} _ {\pi}\right) / \sigma^ {2}. \tag {12} +$$ + +Unfortunately, evaluating the pretrained denoiser $D$ on $\pmb{x}_{\pi}$ causes an out-of-distribution (OOD) problem. From the training objective in Eq. (1), at each noise level $\sigma$ , the denoiser $D$ has only seen noisy inputs of the distribution $\pmb{y} + \sigma \pmb{n}$ where $\pmb{y} \sim p_{\mathrm{data}}$ and $\pmb{n} \sim \mathcal{N}(0, \mathbf{I})$ . However, a rendered image $\pmb{x}_{\pi}$ from 3D asset $\pmb{\theta}$ is generally not consistent with such distribution. + +We illustrate this OOD situation in Fig. 2. Given a denoiser pretrained on FFHQ [21] by Baranchuk et al. [1], we visualize the output $D(\pmb{x}_{\mathrm{blob}}; \sigma = 6.5)$ where the input $\pmb{x}_{\mathrm{blob}}$ is a non-noisy image showing an orange blob centered on a grey canvas. Under the intuition that $D$ predicts a weighted nearest neighbor as reviewed in (5), we expect the denoiser to blend the orange blob with the manifold of faces. However in reality we observe sharp artifacts when updating with this score $(D(\pmb{x}_{\mathrm{blob}}; \sigma) - \pmb{x}_{\mathrm{blob}}) / \sigma^2$ and the image becomes further away from the face manifold. + +Perturb-and-Average Scoring. To address the OOD problem, we propose Perturb-and-Average Scoring (PAAS). It computes the score on non-noisy images $\boldsymbol{x}_{\pi}$ with a denoiser $D$ by adding noise to the input, and then considering the expectation of the predicted scores w.r.t. the random noise, + +$$ +\mathrm {P A A S} \left(\boldsymbol {x} _ {\pi}, \sqrt {2} \sigma\right) \tag {13} +$$ + +$$ +\begin{array}{l} \triangleq \mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, \mathbf {I})} [ \operatorname {s c o r e} (\boldsymbol {x} _ {\pi} + \sigma \boldsymbol {n}, \sigma) ] (14) \\ = \mathbb {E} _ {\boldsymbol {n}} \left[ \frac {D (\boldsymbol {x} _ {\pi} + \sigma \boldsymbol {n} , \sigma) - (\boldsymbol {x} _ {\pi} + \sigma \boldsymbol {n})}{\sigma^ {2}} \right] (15) \\ = \mathbb {E} _ {\boldsymbol {n}} \left[ \frac {D (\boldsymbol {x} _ {\pi} + \sigma \boldsymbol {n} , \sigma) - \boldsymbol {x} _ {\pi}}{\sigma^ {2}} \right] - \underbrace {\mathbb {E} _ {\boldsymbol {n}} \left[ \frac {\boldsymbol {n}}{\sigma} \right]} _ {= 0}. (16) \\ \end{array} +$$ + +In practice, we use the Monte Carlo estimate of the expectation in Eq. (16). The algorithm is illustrated in Fig. 3. Given + +![](images/fbfef85bbbadda1642a403a821069a3b7d6a9246ee04584d810b76b5b30085bb.jpg) +Figure 3. Computing PAAS on 2D renderings $\pmb{x}_{\pi}$ . Directly evaluating $D(\pmb{x}_{\pi};\sigma)$ leads to an OOD problem. Instead, we add noise to $\pmb{x}_{\pi}$ , and evaluate $D(\pmb{x}_{\pi} + \sigma \pmb{n};\sigma)$ (blue dots). The PAAS is then computed by averaging over the brown dashed arrows, corresponding to multiple samples of $\pmb{n}$ . See Sec. 4.1 for details. + +a set of sampled noises $\{\pmb{n}_i\}$ , each $D(\pmb{x}_{\pi} + \sigma \pmb{n}_i)$ provides an update direction on the perturbed input $\pmb{x}_{\pi} + \sigma \pmb{n}_i$ . By averaging over the noise perturbations $\{\pmb{n}_i\}$ , we obtain an update direction on $\pmb{x}_{\pi}$ itself. + +Justifying PAAS in Eq. (13). We show that Perturb-and-Average Scoring provides an approximation to the score on $x_{\pi}$ at an inflated noise level of $\sqrt{2}\sigma$ + +$$ +\operatorname {P A A S} \left(\boldsymbol {x} _ {\pi}, \sqrt {2} \sigma\right) \approx \nabla_ {\boldsymbol {x} _ {\pi}} \log p _ {\sqrt {2} \sigma} \left(\boldsymbol {x} _ {\pi}\right). \tag {17} +$$ + +Lemma 1 Assuming an empirical data distribution $p_{\sigma}(\pmb{x})$ in Eq. (4), for any $\pmb{x} \in \mathbb{R}^d$ + +$$ +\log p _ {\sqrt {2} \sigma} (\boldsymbol {x}) \geq \mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, \mathbf {I})} \log p _ {\sigma} (\boldsymbol {x} + \sigma \boldsymbol {n}). \tag {18} +$$ + +Proof. Observe that the LHS of Eq. (19) is a convolution of two Gaussians, therefore + +$$ +\mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, \mathbf {I})} [ \mathcal {N} (\boldsymbol {x} + \sigma \boldsymbol {n}; \boldsymbol {\mu}, \sigma^ {2} \mathbf {I}) ] = \mathcal {N} (\boldsymbol {x}; \boldsymbol {\mu}, 2 \sigma^ {2} \mathbf {I}) \tag {19} +$$ + +Recall that $p_{\sigma}(\pmb {x})$ is a mixture of Gaussians per Eq. (4); + +$$ +\begin{array}{l} p _ {\sqrt {2} \sigma} (\boldsymbol {x}) = \mathbb {E} _ {\boldsymbol {y} \sim p _ {\mathrm {d a t a}}} \mathcal {N} (\boldsymbol {x}; \boldsymbol {y}, 2 \sigma^ {2} \mathbf {I}) (20) \\ = \mathbb {E} _ {\boldsymbol {y} \sim p _ {\text {d a t a}}} \mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, \mathbf {I})} \mathcal {N} (\boldsymbol {x} + \sigma \boldsymbol {n}; \boldsymbol {y}, \sigma^ {2} \mathbf {I}) (21) \\ = \mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, \mathbf {I})} \mathbb {E} _ {\boldsymbol {y} \sim p _ {\text {d a t a}}} \mathcal {N} (\boldsymbol {x} + \sigma \boldsymbol {n}; \boldsymbol {y}, \sigma^ {2} \mathbf {I}) (22) \\ = \mathbb {E} _ {\boldsymbol {n} \sim \mathcal {N} (0, \mathbf {I})} p _ {\sigma} (\boldsymbol {x} + \sigma \boldsymbol {n}). (23) \\ \end{array} +$$ + +Taking the log on both sides of Eq. (23) and by Jensen's inequality, we arrive at Eq. (18). + +Claim 1 Assuming a trained denoiser $D$ as in Eq. (3), our $PAAS(x_{\pi}, \sqrt{2}\sigma)$ in Eq. (13) computes the gradient w.r.t. a lower bound of $\log p_{\sqrt{2}\sigma}(\pmb{x})$ . + +Proof. By taking the gradient of the RHS of Lemma 1, + +$$ +\begin{array}{l} \nabla_ {\boldsymbol {x}} \mathbb {E} _ {\boldsymbol {n}} \log p _ {\sigma} (\boldsymbol {x} + \sigma \boldsymbol {n}) = \mathbb {E} _ {\boldsymbol {n}} \nabla_ {\boldsymbol {x} + \sigma \boldsymbol {n}} \log p _ {\sigma} (\boldsymbol {x} + \sigma \boldsymbol {n}) \\ = \mathbb {E} _ {\boldsymbol {n}} [ \operatorname {s c o r e} (\boldsymbol {x} _ {\pi} + \sigma \boldsymbol {n}, \sigma) ]. \tag {24} \\ \end{array} +$$ + +which is the proposed PAAS algorithm in Eq. (13). + +![](images/46ad94efacec0ec77520bea1d1979b0f1d0fe3194a2607513f1b1ec3de642342.jpg) + +# 4.2. Inverse Rendering on Voxel Radiance Field + +With the computation of the 2D score resolved, the other half of our setup in Eq. (11) requires access to the Jacobian of a differentiable renderer. + +3D Representation. We represent a 3D asset $\theta$ as a voxel radiance field [6, 11, 53], which is much faster to access and update compared to a vanilla NeRF parameterized by a neural network [34]. The parameters $\theta$ consist of a density voxel grid $\mathbf{V}^{(\mathrm{density})} \in \mathbb{R}^{1 \times N_x \times N_y \times N_z}$ and a voxel grid of appearance features $\mathbf{V}^{(\mathrm{app})} \in \mathbb{R}^{c \times N_x \times N_y \times N_z}$ . Conventionally the appearance features are simply the RGB colors and $c = 3$ . For simplicity, we do not model view dependencies in this work. + +Inverse Volumetric Rendering. Image rendering is performed independently along a camera ray through each pixel. We cut a camera light ray into equally distanced segments of length $d$ , and at the spatial location corresponding to the beginning of the $i$ -th segment we sample a $(\mathrm{RGB}_i, \tau_i)$ tuple from the color and density grids using trilinear interpolation. These values are alpha-composed using volume rendering quadrature [32] into the pixel color $C = \sum_{i} w_i \cdot \mathrm{RGB}_i$ , where + +$$ +w _ {i} = \alpha_ {i} \cdot \prod_ {j = 0} ^ {i - 1} (1 - \alpha_ {j}); \quad \alpha_ {i} = 1 - \exp (- \tau_ {i} d). \tag {25} +$$ + +Volume rendering of $\theta$ is directly differentiable. At a rendered image $x_{\pi}$ , the Vector-Jacobian product in Eq. (11) between PAAS $(x_{\pi})$ and the Jacobian $J_{\pi} = \frac{\partial x_{\pi}}{\partial \theta}$ is computed by back-propagating the score through Eq. (25). This Vector-Jacobian product provides us with the 3D gradient needed for generative modeling on the voxel radiance field. + +Regularization Strategies. The voxel grid is a very powerful 3D representation for volumetric rendering. Given noisy 2D guidance, the model may cheat by populating the entire grid with small densities such that the combined effect from one view hallucinates a plausible image. We propose several techniques to encourage the formation of a coherent 3D structure. + +Emptiness Loss: Ideally, the space should be sparse with near zero densities except at the object. We propose an emptiness loss to encourage sparsity on a ray $\mathbf{r}$ : + +$$ +\mathcal {L} _ {\text {e m p t i n e s s}} (\mathbf {r}) = \frac {1}{n} \sum_ {i = 1} ^ {n} \log \left(1 + \beta \cdot w _ {i}\right), \tag {26} +$$ + +where $w_{i}$ are the alpha-composed weights shown in (25). The shape of the log function imposes severe penalties at the onset of small weights, but does not grow aggressively if the weights are large. It is consistent with our aim to eliminate small densities. The hyperparameter $\beta$ controls the steepness of the loss function near 0. A larger $\beta$ will put more emphasis on eliminating low-density noise. We set $\beta = 10$ . + +![](images/a1c440dbffe9d508bd0b1e939e7779211fb570f13c31a554c7a2ae11da6c28e9.jpg) +Figure 4. Sampling 2D images with Perturb-and-Average Scoring. We compare Annealed vs Random $\sigma$ schedule against several diffusion models. Row 1 & 2: the random $\sigma$ schedule exhibits strong mode-seeking behavior, and it results in low-quality "mean" images on unconditioned diffusion models trained on FFHQ and LSUN Bedroom. In this case, we need a carefully designed annealed $\sigma$ schedule to produce better, more diverse samples. Row 3 & 4: Stable Diffusion (SD) is conditioned on the prompt "a squirrel holding a saxophone". The use of natural language makes the conditioned distribution much easier to sample from. When the guidance scale is elevated to 10, Random $\sigma$ schedule that fails on FFHQ and LSUN starts to produce crisp, clean images. + +Emptiness Loss Schedule: We use a hyperparameter $\lambda$ to control the contribution of the emptiness loss. If we apply a large emptiness loss, it will hinder the learning of geometry in the early stage of training. But if the emptiness is too small, there will be floating density artifacts. We adopt a two-stage noise elimination schedule to deal with this problem. In the first $K$ iterations, we use a relatively small weighting factor $\lambda_{1}$ . After the $K^{\mathrm{th}}$ iteration, it is increased to a larger $\lambda_{2}$ . In our experiments $\lambda_{1} = 1 \times 10^{4}$ and $\lambda_{2} = 2 \times 10^{5}$ . We provide an ablation study of this technique in Fig. 7 to show its effectiveness. + +Center Depth Loss: Sometimes the optimization places the object away from the scene center. The object either becomes small or wander around the image boundary. For the few cases when this happens we apply a center depth loss + +$$ +\mathcal {L} _ {\text {c e n t e r}} (D) = - \log \left(\frac {1}{| \mathcal {B} |} \sum_ {\mathbf {p} \in \mathcal {B}} D (\mathbf {p}) - \frac {1}{| \mathcal {B} ^ {\complement} |} \sum_ {\mathbf {q} \notin \mathcal {B}} D (\mathbf {q})\right) \tag {27} +$$ + +![](images/c41bf6649ea068ea261e18753f027f1d3ecad5082b647d59214508227c7037be.jpg) +A DSLR photo of a yellow duck + +![](images/8c330ae0da2e7533ed8a97dc87e5e3f968f313ea87a8c7d34fe91cbce320b5df.jpg) + +![](images/e3a5340f75c89e3c03c385ffb868b966a88cd26fb7c7da7fb9211a0e11b14faa.jpg) + +![](images/28d06de9db0c2ec47cd0a8417a3a6e948381ec1d4982f2217ca0575d5e68f179.jpg) + +![](images/d93a3e3c7f4b7c1fd2d971d399c0fb480d3f58ea23145995e502f8ee83832790.jpg) +A zoomed out photo a small castle + +![](images/71e8e8ab3750c4eea8eb52525095c5093e637c21f903b0dcc01990ea73cdab43.jpg) +A zoomed out high quality photo of Sydney Opera House + +![](images/cc5e92ea0a57a39be38af913a5b05f5b98974e9053ca1d55e3a9acb96910d3e4.jpg) + +![](images/a1edb5a9a608c1c997c2eef9ec7953370ab86d72f3cba7edd9ed409c3b186e72.jpg) + +![](images/d37d4621014c5ead7ca2d76194c681e1c8fb60f34b41f5a21a1408c4a9dab469.jpg) +Figure 5. Qualitative results of text-prompted generation of 3D models with SJC, purely from the pretrained Stable Diffusion (2D) image model. Each row shows two views, with associated depth maps (blue is far, red is near), for a single 3D model generated for a given prompt. Note the detailed appearance as well as a sharp, well-defined depth structure. + +![](images/2157ed8bb024c0f2705795dd087d89a617013374ed27ece5da037e837ad9a8a0.jpg) + +![](images/40614c2cc06d04698241fedf10943d07b950bc691c2426e83e12c4a33e416f67.jpg) + +![](images/ec71ccd0dbb647e0d68e2687ac244651885daab38d4bb24aef437f630f036263.jpg) + +![](images/813b1ca1603d9b03a8beb1e6fe662989db9ddf3477ca23c4ec7cf4a25ce783c2.jpg) + +![](images/b2de60c7753ff3f6fdd16c908a6f269107b5429e143c9512a17b3a0c54411367.jpg) +A ficus planted in a pot + +![](images/804f9c9bdfdf34eced27b82d92ddee1e3b65b984b3b2ca7c6c100450ce8f641c.jpg) + +![](images/06e1dd72a255950a75756871ec632847a657d90b4fafa8c17daf022907f411d4.jpg) + +![](images/cfc05a5abe049f5689d5b9410ae866c11cb2bc918f9477b3e7c13ba17118dcc7.jpg) +A high quality photo of a toy motorcycle + +![](images/422d5e996cdf6905db2827d72f1eea49746608b5988caa5659bfd565462847bd.jpg) +A photo of a horse walking + +![](images/57a9e88198e3241629a0a7b0630a158ec17e764fb1d2f15e0ac85018c7aa3e58.jpg) + +![](images/d2618a46d963f461abe17f99fe4dfc12a909fb9580e8a36c041b69e40ebac7e2.jpg) + +![](images/30cb20e179722551bc56656ac5d3086505c11be242d9190a8f48d56dc39fa63d.jpg) + +![](images/bf1bdee838392b414d50f5ac41045236499c139b094b93e74311c79e6a09379d.jpg) + +![](images/7877bf92c0e0180e8b53ee71304afb16d0621c3f01c01a1c110fdd73925aaa73.jpg) + +![](images/47f718f32b22858bc4f7a1627c6becb581849c440a9124cd84299ac8450871bd.jpg) + +where $D$ is the depth image, $\mathcal{B}$ is a box (set of pixel locations) at the center of the image, and $\mathcal{B}^{\mathrm{G}}$ is its complement. + +# 4.3. SJC vs. DreamFusion + +In this section, we describe the differences and the connections between our SJC and DreamFusion. + +Differences from DreamFusion. In terms of formulation, DreamFusion's computation of the gradient w.r.t. $\theta$ involves a U-Net Jacobian term (see Eq. 2 in their paper [41]). In practice, they "found that omitting the U-Net Jacobian term" to be more effective. On the other hand, this U-Net Jacobian term does not appear in our formulation. Their additional justification in the appendix actually leans more towards our viewpoint. An additional contribution of ours beyond DreamFusion [41] is our analysis of the effect that the OOD problem has when using a denoiser on rendered images (Claim 1), and the PAAS method to address it. For the variance reduction technique, namely the use of the Monte-Carlo estimate on Eq. (16), or $\hat{\epsilon} - \epsilon$ (in DreamFusion), vs. on Eq. (15), we observe comparable performance between the two methods empirically for 3D generation. + +Influences by DreamFusion. At the time of this submission, DreamFusion is a concurrent arXiv paper. However, as we have read the paper, our research was influenced by their reported observations. In particular, we adopted the idea of randomized scheduling of $\sigma$ during 3D optimization for easier hyperparameter tuning, and used view-augmented language prompting that improves the overall 3D quality. For future work we do hope to explore a more general solution than view-dependent prompts. + +# 5. Experiments + +We conduct experiments on both unconditioned and conditioned diffusion models to have a more comprehensive understanding of the properties of SJC. + +DDPMs trained on FFHQ and LSUN Bedroom are unconditioned diffusion models with an architecture based on the implementation by Dhariwal and Nichol [10]. They are trained on an image resolution of $256 \times 256$ . FFHQ [21] is a dataset of aligned faces with diverse coverage of gender, age, race, facial appearance as well as head poses. LSUN Bedroom [62] includes bedroom images with varied furniture layout plans and rich interior design styles. + +Stable Diffusion is an expanded work based on Latent Diffusion Model (LDM) developed by Rombach et al. [45]. It is trained on the LAION5B dataset [47]. We use the release version v1.5. Diffusion is performed on a latent space of $4 \times 64 \times 64$ , then upsampled to $3 \times 256 \times 256$ by a decoder. The model is natively trained for text-conditioned image generations, and exposes a guidance scale parameter that controls the strength of language conditioning [14]. Intuitively a larger guidance scale makes the conditioned image distribution more faithful to the text prompt by trading off sample diversity. + +# 5.1. Validating PAAS on 2D images. + +Before directly jumping to 3D generation, we first verify that PAAS provides effective guidance on a simple 2D image canvas. In other words, here $\theta$ is a grid of RGB values and $f$ is an identity function. The hope is that gradient descent + +![](images/92847e4d8152f076479d4eabb6ba68008511b79da092403dc6119743a9e2f985.jpg) +(a) + +![](images/beafbcfd0552ba809ad62453277481d4e8a37f29ed93b6b385d9d42e2bd6e6fd.jpg) +(b) + +![](images/0ba0f171eb185d442c96c9580532902b26cbadd86b8dea7e450dde84e56a8b21.jpg) +(c) + +![](images/ca53a5d33276d2590602a19d89a500db951075041e229d550604eed469d99b66.jpg) +(d) + +![](images/1d54e0e70042d76c5e0eed2456a8c2c2b9305860c52abbb0c21a995ba3dd2f81.jpg) +(e) + +![](images/5096f66c34f2e1b1c432f4982fc853836a86db43efd53551e4fae3febb06c0d8.jpg) +(f) +Figure 6. Qualitative comparison between Stable-DreamFusion (StableDF) and Ours. The prompts are: (a) "A high quality photo of a delicious burger"; (b) "a DSLR photo of a yellow duck"; (c) "A ficus planted in a pot"; (d) "A product photo of a toy tank"; (e) "A high quality photo of a chocolate icecream cone"; (f) "A wide angle zoomed out photo of a giraffe". Both methods are run for 10k iterations without per-prompt finetuning on the hyperparameters. The images on the left are rendered RGB images and the images on the right are depth visualization. + +on the vector field produced by PAAS creates high quality images. Here an important decision to make is the schedule of $\{\sigma_i\}$ at which we compute PAAS. + +We experimented with an annealed schedule (Annealed $\sigma$ ) vs. a random schedule (Random $\sigma$ ) as proposed in Dream-Fusion. Under the Annealed $\sigma$ schedule, we start from a large $\sigma$ and gradually decrease it as we update the image canvas $x$ . PAAS computed at larger $\sigma$ level attends to high level image structure while smaller $\sigma$ provides stronger guidance on detailed features. The Random $\sigma$ schedule on the contrary uniformly samples a $\sigma$ at every step. We show qualitative comparisons in Fig. 4. + +For unconditioned diffusion models trained on FFHQ, we observe that Annealed $\sigma$ performs better than Random $\sigma$ , and the image samples have better pose variation and quality. Particularly, the randomized $\sigma$ exhibits severe mode-seeking behavior converging to average faces. In the case of LSUN Bedroom, the mode-seeking behavior results in a + +blurry image canvas with no content. + +On the other hand, natural language prompting plays a critical role when sampling images with Stable Diffusion. When the language guidance is set to a regular level of 3.0, the observations are broadly consistent with sampling on FFHQ and LSUN. Random $\sigma$ schedule produces blurry outputs. However, when the guidance scale is elevated to 10.0, Random $\sigma$ schedule begins to generate crisp, clean images and outperforms Annealed $\sigma$ schedule. Despite various sophisticated strategies on Annealed $\sigma$ scheduling (see our code for details), at a high language guidance scale Randomized $\sigma$ remains the better option. We hypothesize that stronger language guidance forces the image distribution to be narrower and more beneficial for a mode-seeking algorithm. We acknowledge none of the images in Fig. 4 can match the sample quality of a standard diffusion inference pipeline, and the right way to apply PAAS as gradient for optimization remains an open problem. + +A zoomed out high quality photo of Temple of Heaven. + +![](images/8d1a4dd2af26f7e686caf457435aa1dd6ade5dab52930a117d9ce367d81b8acb.jpg) +Figure 7. Ablation experiments on the proposed emptiness loss schedule. For each setting of the loss weight $\lambda$ , we show a rendered image and the associated depth map from a randomly sampled viewpoint. Ours incorporates the loss with weight schedule described in 5.2. It leads to better 3D shape, as evidenced in the cleaner depth maps. Setting the loss weight too low yields "cloudy" depth fields. When setting the weight too high, SJC fails to produce meaningful 3D models. + +# 5.2.3D Generation + +In this paper, we focus on 3D Generation with the language-conditioned Stable Diffusion model. We found that tuning the Annealed $\sigma$ schedule on FFHQ and LSUN Bedroom in 3D domain is difficult in practice, and leave it as future work. Based on the insights from 2D experiments earlier, we use Random $\sigma$ schedule coupled with a high language guidance scale. + +Rendering with Latent 3D Features. Stable Diffusion economizes compute by performing diffusion modeling on the latent features of a pretrained AutoEncoder. We therefore choose to render a feature image in this latent space from a features field [3, 38] represented by a voxel grid in $\mathbb{R}^{4\times N_x\times N_y\times N_z}$ . + +Qualitative Comparison. In Fig. 5, we show text-prompted 3D generation results from SJC, and compare SJC with Stable-DreamFusion, a third-party implementation based on the same pretrained Stable Diffusion v1.5 model. In Fig. 6, we show qualitative comparisons of generated 3D assets given the same prompt. We observe that SJC generates 3D models with better image quality and more sensible structure than Stable-DreamFusion in a significant number of cases. We note that both systems exhibit quality fluctuations over different trials, and the point of this comparison is to show that our overall pipeline is competitive. + +Ablations. In Fig. 7, we conduct ablations to demonstrate the importance of the proposed emptiness loss and scheduling of its weight $\lambda$ discussed in Sec. 4.2. We show results without the emptiness loss, with constant weight $\lambda$ vs our proposed scheduling of $\lambda$ . We observe that our complete method (Ours) improves the quality of generated 3D models, e.g., fewer floating artifacts and better geometry. + +# 6. Conclusion + +We propose an optimization-based approach to generate 3D assets from pretrained image (2D) diffusion models. The key technical contribution is the derivation of Perturb-and-Average Scoring method which bridges the gap between the denoising-trained diffusion models and the non-noisy images encountered in the process of optimizing a 3D model guided by the diffusion. Working with the large-scale Stable Diffusion model, we demonstrate that our approach can generate compelling 3D models, comparing favorably to available concurrent work. 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LSUN: Construction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprint arXiv:1506.03365, 2015. 6 +[63] Yuxuan Zhang, Wenzheng Chen, Huan Ling, Jun Gao, Yinan Zhang, Antonio Torralba, and Sanja Fidler. Image GANs meet differentiable rendering for inverse graphics and interpretable 3d neural rendering. In Int. Conf. Learn. Represent., 2021. 2 +[64] Xiaoming Zhao, Fangchang Ma, David Guera, Zhile Ren, Alexander G Schwing, and Alex Colburn. Generative multiplane images: Making a 2D GAN 3D-Aware. In Eur. 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We propose to apply chain rule on the learned gradients, and back-propagate the score of a diffusion model through the Jacobian of a differentiable renderer, which we instantiate to be a voxel radiance field. This setup aggregates 2D scores at multiple camera viewpoints into a 3D score, and repurposes a pretrained 2D model for 3D data generation. We identify a technical challenge of distribution mismatch that arises in this application, and propose a novel estimation mechanism to resolve it. We run our algorithm on several off-the-shelf diffusion image generative models, including the recently released Stable Diffusion trained on the large-scale LAION 5B dataset." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 47, + 627, + 128, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 128, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 128, + 639 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 287, + 696 + ], + "type": "text", + "content": "We introduce a method that converts a pretrained 2D diffusion generative model on images into a 3D generative model of radiance fields, without requiring access to any 3D data. The key insight is to interpret diffusion models as" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 434, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 545, + 482 + ], + "type": "text", + "content": "learned predictors of a gradient field, often referred to as the score function of the data log-likelihood. We apply the chain rule on the estimated score, hence the name Score Jacobian Chaining (SJC)." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "content": "Following Hyvarinen [16], the score is defined as the gradient of the log-density function with respect to the data (rather than parameter). Diffusion models of various families [13, 49, 50, 52] can all be interpreted [20, 23, 52] as modeling " + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\nabla_{\\pmb{x}}\\log p_{\\sigma}(\\pmb{x})" + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "content": " i.e. the denoising score at noise level " + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "content": ". For readability, we refer to the denoising score as the score. Generating a sample from a diffusion model involves repeated evaluations of the score function from large to small " + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "content": " level, so that a sample " + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "content": " gradually moves closer to the data manifold. It can be loosely interpreted as gradient descent, with precise control on the step sizes so that data distribution evolves to match the annealed " + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 484, + 547, + 675 + ], + "type": "text", + "content": " level (ancestral sampler [13], SDE and probability-flow ODE [52], etc.). While there are other perspectives to a diffusion model [13, 49], here we are primarily motivated from the viewpoint that diffusion models produce a gradient field." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "A natural question to ask is whether the chain rule can be applied to the learned gradients. Consider a diffusion model on images. An image " + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": " may be parameterized by some" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 64, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 64, + 703, + 135, + 712 + ], + "type": "text", + "content": "* Equal contribution." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12619" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "function " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " with parameters " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "x = f(\\theta)" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": ". Applying the chain rule through the Jacobian " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\frac{\\partial x}{\\partial \\theta}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " converts a gradient on image " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " into a gradient on the parameter " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": ". There are many potential use cases for pairing a pretrained diffusion model with different choices of " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": ". In this work we are interested in exploring the connection between 3D and multiview 2D by choosing " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " to be a differentiable renderer, thus creating a 3D generative model using only pretrained 2D resources." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": "Many prior works [2, 58, 60] perform 3D generative modeling by training on 3D datasets [5, 24, 54, 59]. This approach is often as challenging as it is format-ambiguous. In addition to the high data acquisition cost of 3D assets [9], there is no universal data format: point clouds, meshes, volumetric radiance field, etc, all have computational trade-offs. What is common to these 3D assets is that they can be rendered into 2D images. An inverse rendering system, or a differentiable renderer [25, 27, 30, 34, 39], provides access to the Jacobian " + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "inline_equation", + "content": "J_{\\pi} \\triangleq \\frac{\\partial x_{\\pi}}{\\partial \\theta}" + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": " of a rendered image " + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "inline_equation", + "content": "x_{\\pi}" + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": " at camera viewpoint " + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": " with respect to the underlying 3D parameterization " + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": ". Our method uses differentiable rendering to aggregate 2D image gradients over multiple viewpoints into a 3D asset gradient, and lifts a generative model from 2D to 3D. We parameterize a 3D asset " + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": " as a radiance field stored on voxels and choose " + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 168, + 290, + 359 + ], + "type": "text", + "content": " to be the volume rendering function." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 360, + 290, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 290, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 290, + 479 + ], + "type": "text", + "content": "A key technical challenge is that computing the 2D score by directly evaluating a diffusion model on a rendered image " + }, + { + "bbox": [ + 46, + 360, + 290, + 479 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 46, + 360, + 290, + 479 + ], + "type": "text", + "content": " leads to an out-of-distribution (OOD) problem. Generally, diffusion models are trained as denoisers and have only seen noisy inputs during training. On the other hand, our method requires evaluating the denoiser on non-noisy rendered images from a 3D asset during optimization, and it leads to the OOD problem. To address the issue, we propose Perturb-and-Average Scoring, an approach to estimate the score for non-noisy images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 290, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 290, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 290, + 575 + ], + "type": "text", + "content": "Empirically, we first validate the effectiveness of Perturb-and-Average Scoring at solving the OOD problem and explore the hyperparameter choices on a simple 2D image canvas. Here we identify open problems on using unconditioned diffusion models trained on FFHQ and LSUN Bedroom. Next, we use Stable Diffusion, a model pretrained on the web-scale LAION dataset to perform SJC for 3D generation, as shown in Fig. 1. Our contributions are as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 578, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 58, + 578, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 578, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 58, + 578, + 287, + 601 + ], + "type": "text", + "content": "- We propose a method for lifting a 2D diffusion model to 3D via an application of the chain rule." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 607, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 607, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 58, + 607, + 287, + 643 + ], + "type": "text", + "content": "- We illustrate the challenge of OOD when using a pretrained denoiser and propose Perturb-and-Average Scoring to resolve it." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 648, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 648, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 58, + 648, + 287, + 684 + ], + "type": "text", + "content": "- We point out the subtleties and open problems on applying Perturb-and-Average Scoring as gradient for optimization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 689, + 287, + 714 + ], + "type": "text", + "content": "- We demonstrate the effectiveness of SJC for the task of 3D text-driven generation." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 71, + 398, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 398, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 398, + 84 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "type": "text", + "content": "Diffusion models have recently advanced to image generation on Internet-scale datasets [10, 36, 42, 44-47]. A diffusion model could be interpreted as either a VAE [13, 49] or a denoising score-matcher [50, 52, 56]. Notably, models trained under one regime can be directly used for inference and sampling by the other [20, 52]; they are in practice largely equivalent." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "type": "text", + "content": "Neural radiance fields (NeRF) is a family of inverse rendering algorithms that have excelled at multiview 3D reconstruction tasks including view synthesis and surface geometry estimation [31, 34, 40, 57, 61]. Conceptually, a 3D asset is represented as a dense grid of RGB colors and spatial density " + }, + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "type": "text", + "content": ", and rendered into images in a way analogous to alpha compositing [32]. NeRF parameterizes the (RGB, " + }, + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 177, + 548, + 357 + ], + "type": "text", + "content": ") volume with a neural network, but querying the network densely in 3D incurs significant compute costs. Alternatively, Voxel NeRFs [6, 11, 19, 28, 53] store the volume on voxels and observe no loss in end task performance [11, 53]. Querying voxels is a simple memory operation that is much faster than a feedforward pass of a neural network. Here we use a customized voxel radiance field with hyperparameters based on DvGO [53] and TensoRF [6]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 361, + 548, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 548, + 566 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 548, + 566 + ], + "type": "text", + "content": "2D-supervised 3D GANs pioneered [35, 43, 63] the approach of training 3D generative models using only unstructured 2D images, and promise greater scalability in terms of data. Rather than supervising directly on the 3D asset a model generates, these methods supervise the 2D renderings of the generated 3D asset, often using an adversarial loss [3, 4, 38, 48, 64]. In other words, only images are needed as training data. However, training such a 3D generative model from scratch is still challenging [37]. Recent empirical evaluation remains mostly on human and animal faces [3]. Our method does the opposite: we take an image generative model that is already pretrained on large amounts of 2D data and use it to guide the iterative optimization of a 3D asset. Optimization-based generation makes it much slower compared to 3D GANs, but it becomes possible to harness powerful off-the-shelf 2D generative models such as Stable Diffusion [45] for greater content diversity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "CLIP-guided, optimization-based 3D generative models share a similar philosophy of optimizing 3D assets by guiding on 2D renderings [15, 17, 18, 22, 26, 33]. Among them, DreamFields [17] and PureClipNeRF [26] also use NeRF as their differentiable renderers. In this case, the 2D guidance comes from CLIP [42], a pretrained image-text matching model. These works optimize the 3D assets so that the image renderings match a user-provided text prompt. Since CLIP is not a 2D generative model per se, such a pipeline usually creates some abstract content [29] that looks very different from real images. In contrast, we use diffusion models, which are proper 2D generative models, to create realistic looking 3D" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12620" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 73, + 82, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 73, + 82, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 73, + 82, + 83 + ], + "type": "text", + "content": "content." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 87, + 290, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 87, + 290, + 256 + ], + "spans": [ + { + "bbox": [ + 46, + 87, + 290, + 256 + ], + "type": "text", + "content": "DreamFusion. The recently arXived work by Poole et al. [41], independent and concurrent to our work, proposes an algorithm that is similar to our approach at the pseudo-code level. Differently, their procedure uses the mathematical setup by Graikos et al. [12] to search for image parametrization that minimizes the training loss of a diffusion model. In contrast, our work is motivated by applying the chain rule to the 2D score. The key differences have been summarized in Sec. 4.3. In terms of implementation, we do not have access to the close-sourced Imagen [46] diffusion model. Instead, we use the pretrained Stable Diffusion model released by Rombach et al. [45]. For a comparison with DreamFusion, we use with a third-party implementation based on the same diffusion model, namely Stable-DreamFusion [55]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 267, + 133, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 267, + 133, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 267, + 133, + 280 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 287, + 288, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 288, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 288, + 347 + ], + "type": "text", + "content": "To establish a common notation, we briefly review the score-based perspective of diffusion models. For readers familiar with VAE literature on diffusion models, we provide a concise score-based formula card and more details in Appendix Sec. ?? to connect these ideas." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "content": "Denoising score matching. Given a dataset of samples " + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{\\pmb{y}_i\\}" + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "content": " drawn from " + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}" + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "content": ", a diffusion model revolves primarily around learning a denoiser " + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "content": " by minimizing the difference between a noised sample " + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{y} + \\sigma \\pmb{n}" + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "inline_equation", + "content": "\\pmb{y}" + }, + { + "bbox": [ + 47, + 351, + 288, + 399 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 70, + 408, + 288, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 408, + 288, + 423 + ], + "spans": [ + { + "bbox": [ + 70, + 408, + 288, + 423 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, I)} \\| D (\\boldsymbol {y} + \\sigma \\boldsymbol {n}; \\sigma) - \\boldsymbol {y} \\| _ {2} ^ {2}, \\tag {1}", + "image_path": "944ec7a6f04ea681ffcff4039504c81d0360d62f91d24986a50519d5bea4eec4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "content": "i.e. " + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "content": " is denoising the input " + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\pmb{y} + \\sigma \\pmb{n}" + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "content": ", for a range of " + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "content": " values. For 2D images, " + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "content": " is commonly chosen to be a ConvNet. Variants such as DDPM [13] parameterized the ConvNet to instead predict a noise residual " + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon}" + }, + { + "bbox": [ + 46, + 432, + 289, + 492 + ], + "type": "text", + "content": ", and these models can be converted back to the form of a denoiser by [52]" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 108, + 502, + 287, + 515 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 502, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 108, + 502, + 287, + 515 + ], + "type": "interline_equation", + "content": "D (\\boldsymbol {x}; \\sigma) = \\boldsymbol {x} - \\sigma \\hat {\\epsilon} (\\boldsymbol {x}). \\tag {2}", + "image_path": "a2df11c94d82a6e11bd67f3504a38654936f731ecd7c3af246dda58465a952bf.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 525, + 288, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 288, + 561 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 288, + 561 + ], + "type": "text", + "content": "In this paper, we treat all pretrained diffusion models as denoisers, and perform the interface conversion in our implementation when needed." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "text", + "content": "Score from denoiser. Let " + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "inline_equation", + "content": "p_{\\sigma}(\\boldsymbol{x})" + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "text", + "content": " denote the data distribution perturbed by Gaussian noise of standard deviation " + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "text", + "content": ". It is shown in prior works [16, 50] that the denoiser " + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 564, + 287, + 624 + ], + "type": "text", + "content": " trained according to Eq. (1) provides a good approximation to the denoising score:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 92, + 634, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 634, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 92, + 634, + 287, + 657 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\boldsymbol {x}} \\log p _ {\\sigma} (\\boldsymbol {x}) \\approx \\frac {D (\\boldsymbol {x} ; \\sigma) - \\boldsymbol {x}}{\\sigma^ {2}}. \\tag {3}", + "image_path": "5ca47c23cf4658f2022ca28074cfd49ab0220fda86beec69ba5cb74620bfd373.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "content": "A denoising diffusion model estimates the score function of the noised distribution " + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "inline_equation", + "content": "p_{\\sigma}(\\boldsymbol{x})" + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "content": " at various " + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\{\\sigma_i\\}_{i=1}^T" + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "text", + "content": ". To perform sampling, the diffusion model gradually updates a sample through a sequence of noise levels of " + }, + { + "bbox": [ + 46, + 666, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_T > \\dots >" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\sigma_0 = 0" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "\\{\\sigma_i\\}" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " are chosen empirically, with a typical range being [0.01, 157] [13] in the case of DDPM." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "spans": [ + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "text", + "content": "Score as mean-shift. A helpful intuition is that the score behaves like mean-shift [7, 8]. If we simplify " + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{data}}" + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "text", + "content": " to be an empirical data distribution over the i.i.d. samples " + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "inline_equation", + "content": "\\{\\pmb{y}_i\\}" + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "text", + "content": ", then at noise level " + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "inline_equation", + "content": "p_{\\sigma}(\\pmb{x})" + }, + { + "bbox": [ + 305, + 99, + 547, + 159 + ], + "type": "text", + "content": " takes the form of a mixture of Gaussians [51]" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 358, + 165, + 546, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 165, + 546, + 179 + ], + "spans": [ + { + "bbox": [ + 358, + 165, + 546, + 179 + ], + "type": "interline_equation", + "content": "p _ {\\sigma} (\\boldsymbol {x}) = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}). \\tag {4}", + "image_path": "199ec96f801a6a382d3275151d0024d774d7241325acddcdac1fe84fb90065aa.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 186, + 545, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 186, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 305, + 186, + 545, + 209 + ], + "type": "text", + "content": "In this case there exists a closed-form expression [20, 51] to the optimal denoiser" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 354, + 216, + 546, + 244 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 216, + 546, + 244 + ], + "spans": [ + { + "bbox": [ + 354, + 216, + 546, + 244 + ], + "type": "interline_equation", + "content": "D (\\boldsymbol {x}; \\sigma) = \\frac {\\sum_ {i} \\mathcal {N} (\\boldsymbol {x} ; \\boldsymbol {y} _ {i} , \\sigma^ {2} \\mathbf {I}) \\boldsymbol {y} _ {i}}{\\sum_ {i} \\mathcal {N} (\\boldsymbol {x} ; \\boldsymbol {y} _ {i} , \\sigma^ {2} \\mathbf {I})}. \\tag {5}", + "image_path": "8a2323e1714e9bee34f37933d1baaac776bdc6079b3ece3675b4f3cc4c948838.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "content": "In other words, " + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}; \\sigma)" + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "content": " is a locally weighted mean of data samples " + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\{\\pmb{y}_i\\}" + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "content": " around " + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "content": " under a Gaussian kernel with bandwidth " + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "content": ". The denoising score function can be thought of as a non-parametric guide on how to update " + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 305, + 249, + 547, + 310 + ], + "type": "text", + "content": " in order to move it towards its weighted nearest neighbors." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 319, + 545, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 333 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 333 + ], + "type": "text", + "content": "4. Score Jacobian Chaining for 3D Generation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": " denotes the parameters of a 3D asset, e.g., voxel grid of (RGB, " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": ") as in Sec. 4.2. Our goal is to model and sample from the distribution " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "p(\\theta)" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": " to generate a 3D scene. In our setting, only a pretrained 2D diffusion model on images " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{x})" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": " is given and we do not have access to 3D data. To relate the 2D and 3D distributions " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{x})" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "p(\\theta)" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": ", we assume that the probability density of 3D asset " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": " is proportional to the expected probability densities of its multiview 2D image renderings " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{\\pi}" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": " over camera poses " + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 304, + 339, + 546, + 448 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 371, + 453, + 545, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 453, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 371, + 453, + 545, + 468 + ], + "type": "interline_equation", + "content": "p _ {\\sigma} (\\boldsymbol {\\theta}) \\propto \\mathbb {E} _ {\\pi} \\left[ p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi} (\\boldsymbol {\\theta})\\right) \\right], \\tag {6}", + "image_path": "6bd455568d1f3e73117351eb4a1f865af804f6fc9d831e35eb64fcf101c3e7e5.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "text", + "content": "up to a normalization constant " + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "inline_equation", + "content": "Z = \\int \\mathbb{E}_{\\pi}\\left[p_{\\sigma}(\\pmb{x}_{\\pi}(\\pmb{\\theta}))\\right]d\\pmb{\\theta}" + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "text", + "content": ". That is, a 3D asset " + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "text", + "content": " is as likely as its 2D renderings " + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 305, + 475, + 544, + 499 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 499, + 547, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 499, + 547, + 524 + ], + "spans": [ + { + "bbox": [ + 305, + 499, + 547, + 524 + ], + "type": "text", + "content": "Next, we establish a lower bound, " + }, + { + "bbox": [ + 305, + 499, + 547, + 524 + ], + "type": "inline_equation", + "content": "\\log \\tilde{p}_{\\sigma}(\\boldsymbol{\\theta})" + }, + { + "bbox": [ + 305, + 499, + 547, + 524 + ], + "type": "text", + "content": ", on the distribution in Eq. (6) using Jensen's inequality:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 313, + 529, + 545, + 560 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 529, + 545, + 560 + ], + "spans": [ + { + "bbox": [ + 313, + 529, + 545, + 560 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\log p _ {\\sigma} (\\boldsymbol {\\theta}) = \\log \\left[ \\mathbb {E} _ {\\pi} \\left(p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right)\\right) \\right] - \\log Z (7) \\\\ \\geq \\mathbb {E} _ {\\pi} \\left[ \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right) \\right] - \\log Z \\triangleq \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta}). (8) \\\\ \\end{array}", + "image_path": "b141c1faaee0b5b91496e49873efa7238d2c22dce0603bdb4a87999546dfcc8d.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 567, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 545, + 591 + ], + "type": "text", + "content": "Recall that the score is the gradient of log probability density of data. By chain rule" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 317, + 597, + 545, + 640 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 597, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 317, + 597, + 545, + 640 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {\\boldsymbol {\\theta}} \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {\\boldsymbol {\\pi}} \\left[ \\nabla_ {\\boldsymbol {\\theta}} \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\pi}}\\right) \\right] (9) \\\\ \\frac {\\partial \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta})}{\\partial \\boldsymbol {\\theta}} = \\mathbb {E} _ {\\pi} \\left[ \\frac {\\partial \\log p _ {\\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right)}{\\partial \\boldsymbol {x} _ {\\pi}} \\cdot \\frac {\\partial \\boldsymbol {x} _ {\\pi}}{\\partial \\boldsymbol {\\theta}} \\right] (10) \\\\ \\end{array}", + "image_path": "2897dddc328d67a6176fdff1b21b13baf7114aefc82f1dc2b8fa2fdd8b40c95a.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 317, + 641, + 545, + 682 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 641, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 317, + 641, + 545, + 682 + ], + "type": "interline_equation", + "content": "\\underbrace {\\nabla_ {\\boldsymbol {\\theta}} \\log \\tilde {p} _ {\\sigma} (\\boldsymbol {\\theta})} _ {\\text {3 D s c o r e}} = \\mathbb {E} _ {\\pi} [ \\underbrace {\\nabla_ {\\boldsymbol {x} _ {\\pi}} \\log p _ {\\sigma} (\\boldsymbol {x} _ {\\pi})} _ {\\text {2 D s c o r e ; p r e t r a i n e d}} \\cdot \\underbrace {\\boldsymbol {J} _ {\\pi}} _ {\\text {r e n d e r e r J a c o b i a n}} ]. \\tag {11}", + "image_path": "103da45123933eca5e22669ec56b6e54f9a6106c71015dfcb92043473882cb12.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "We will next discuss how to compute the 2D score in practice using a pretrained diffusion model." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12621" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 127, + 157 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 127, + 157 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 127, + 157 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 127, + 157 + ], + "type": "image", + "image_path": "09b8676d9de0125ae440e00cdd28e15d1ac7e880d7180d3018454e13a812af81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "type": "text", + "content": "Figure 2. Illustration of denoiser's OOD issue using a denoiser pretrained on FFHQ. When directly evaluating " + }, + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}_{\\mathrm{blob}}, \\sigma)" + }, + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "type": "text", + "content": " the model did not correct for the orange blob into a face image. Contrarily, evaluating the denoiser on noised input " + }, + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}_{\\mathrm{blob}} + \\sigma \\pmb{n}, \\sigma)" + }, + { + "bbox": [ + 46, + 161, + 288, + 217 + ], + "type": "text", + "content": " produces an image that successfully merges the blob with the face manifold." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 129, + 70, + 206, + 157 + ], + "blocks": [ + { + "bbox": [ + 129, + 70, + 206, + 157 + ], + "lines": [ + { + "bbox": [ + 129, + 70, + 206, + 157 + ], + "spans": [ + { + "bbox": [ + 129, + 70, + 206, + 157 + ], + "type": "image", + "image_path": "546d9c674ae035e8931f5611a157c3711edf9e164a244f2a9c74f16ac59ff168.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 209, + 70, + 286, + 157 + ], + "blocks": [ + { + "bbox": [ + 209, + 70, + 286, + 157 + ], + "lines": [ + { + "bbox": [ + 209, + 70, + 286, + 157 + ], + "spans": [ + { + "bbox": [ + 209, + 70, + 286, + 157 + ], + "type": "image", + "image_path": "1eacb1be994dff875f52a88076659e3368c815b114ddd9493b5cc695ca51d048.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 236, + 271, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 271, + 249 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 271, + 249 + ], + "type": "text", + "content": "4.1. Computing 2D Score on Non-Noisy Images" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 254, + 287, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 254, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 287, + 290 + ], + "type": "text", + "content": "Computing the 3D score in Eq. (11) requires the 2D score on " + }, + { + "bbox": [ + 47, + 254, + 287, + 290 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 47, + 254, + 287, + 290 + ], + "type": "text", + "content": ". A first attempt would be to directly apply the score from the denoiser in Eq. (3), i.e.," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 78, + 297, + 287, + 311 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 297, + 287, + 311 + ], + "spans": [ + { + "bbox": [ + 78, + 297, + 287, + 311 + ], + "type": "interline_equation", + "content": "\\operatorname {s c o r e} \\left(\\boldsymbol {x} _ {\\pi}, \\sigma\\right) \\triangleq \\left(D \\left(\\boldsymbol {x} _ {\\pi}; \\sigma\\right) - \\boldsymbol {x} _ {\\pi}\\right) / \\sigma^ {2}. \\tag {12}", + "image_path": "18696192a794b667ca1cbfb4937bb85293d1b11f32420ab83ada8fb2048c5e48.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "spans": [ + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": "Unfortunately, evaluating the pretrained denoiser " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " causes an out-of-distribution (OOD) problem. From the training objective in Eq. (1), at each noise level " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": ", the denoiser " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " has only seen noisy inputs of the distribution " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{y} + \\sigma \\pmb{n}" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{y} \\sim p_{\\mathrm{data}}" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{n} \\sim \\mathcal{N}(0, \\mathbf{I})" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": ". However, a rendered image " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " from 3D asset " + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 47, + 318, + 288, + 400 + ], + "type": "text", + "content": " is generally not consistent with such distribution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "text", + "content": "We illustrate this OOD situation in Fig. 2. Given a denoiser pretrained on FFHQ [21] by Baranchuk et al. [1], we visualize the output " + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}_{\\mathrm{blob}}; \\sigma = 6.5)" + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "text", + "content": " where the input " + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\mathrm{blob}}" + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "text", + "content": " is a non-noisy image showing an orange blob centered on a grey canvas. Under the intuition that " + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "text", + "content": " predicts a weighted nearest neighbor as reviewed in (5), we expect the denoiser to blend the orange blob with the manifold of faces. However in reality we observe sharp artifacts when updating with this score " + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "inline_equation", + "content": "(D(\\pmb{x}_{\\mathrm{blob}}; \\sigma) - \\pmb{x}_{\\mathrm{blob}}) / \\sigma^2" + }, + { + "bbox": [ + 46, + 402, + 288, + 521 + ], + "type": "text", + "content": " and the image becomes further away from the face manifold." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "type": "text", + "content": "Perturb-and-Average Scoring. To address the OOD problem, we propose Perturb-and-Average Scoring (PAAS). It computes the score on non-noisy images " + }, + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{\\pi}" + }, + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "type": "text", + "content": " with a denoiser " + }, + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 524, + 288, + 583 + ], + "type": "text", + "content": " by adding noise to the input, and then considering the expectation of the predicted scores w.r.t. the random noise," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 94, + 590, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 590, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 94, + 590, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\mathrm {P A A S} \\left(\\boldsymbol {x} _ {\\pi}, \\sqrt {2} \\sigma\\right) \\tag {13}", + "image_path": "af6bf918fb5cca5388321388a54866d3979533aa53eb0ad0cf019b08cdd4839d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 87, + 608, + 287, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 608, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 87, + 608, + 287, + 684 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\triangleq \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\operatorname {s c o r e} (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n}, \\sigma) ] (14) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {D (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n} , \\sigma) - (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n})}{\\sigma^ {2}} \\right] (15) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {D (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n} , \\sigma) - \\boldsymbol {x} _ {\\pi}}{\\sigma^ {2}} \\right] - \\underbrace {\\mathbb {E} _ {\\boldsymbol {n}} \\left[ \\frac {\\boldsymbol {n}}{\\sigma} \\right]} _ {= 0}. (16) \\\\ \\end{array}", + "image_path": "b9605a7ff5f799fbb2febaefd9d26c7082518b7e7b8c70bc6420c417f8f4d4dd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": "In practice, we use the Monte Carlo estimate of the expectation in Eq. (16). The algorithm is illustrated in Fig. 3. Given" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 328, + 76, + 525, + 204 + ], + "blocks": [ + { + "bbox": [ + 328, + 76, + 525, + 204 + ], + "lines": [ + { + "bbox": [ + 328, + 76, + 525, + 204 + ], + "spans": [ + { + "bbox": [ + 328, + 76, + 525, + 204 + ], + "type": "image", + "image_path": "fbfef85bbbadda1642a403a821069a3b7d6a9246ee04584d810b76b5b30085bb.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "text", + "content": "Figure 3. Computing PAAS on 2D renderings " + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "text", + "content": ". Directly evaluating " + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}_{\\pi};\\sigma)" + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "text", + "content": " leads to an OOD problem. Instead, we add noise to " + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "text", + "content": ", and evaluate " + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}_{\\pi} + \\sigma \\pmb{n};\\sigma)" + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "text", + "content": " (blue dots). The PAAS is then computed by averaging over the brown dashed arrows, corresponding to multiple samples of " + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "inline_equation", + "content": "\\pmb{n}" + }, + { + "bbox": [ + 305, + 209, + 547, + 265 + ], + "type": "text", + "content": ". See Sec. 4.1 for details." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "content": "a set of sampled noises " + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\{\\pmb{n}_i\\}" + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "content": ", each " + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "inline_equation", + "content": "D(\\pmb{x}_{\\pi} + \\sigma \\pmb{n}_i)" + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "content": " provides an update direction on the perturbed input " + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi} + \\sigma \\pmb{n}_i" + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "content": ". By averaging over the noise perturbations " + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\{\\pmb{n}_i\\}" + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "content": ", we obtain an update direction on " + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\pi}" + }, + { + "bbox": [ + 305, + 275, + 546, + 323 + ], + "type": "text", + "content": " itself." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 325, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 325, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 325, + 547, + 361 + ], + "type": "text", + "content": "Justifying PAAS in Eq. (13). We show that Perturb-and-Average Scoring provides an approximation to the score on " + }, + { + "bbox": [ + 305, + 325, + 547, + 361 + ], + "type": "inline_equation", + "content": "x_{\\pi}" + }, + { + "bbox": [ + 305, + 325, + 547, + 361 + ], + "type": "text", + "content": " at an inflated noise level of " + }, + { + "bbox": [ + 305, + 325, + 547, + 361 + ], + "type": "inline_equation", + "content": "\\sqrt{2}\\sigma" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 333, + 365, + 545, + 381 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 365, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 333, + 365, + 545, + 381 + ], + "type": "interline_equation", + "content": "\\operatorname {P A A S} \\left(\\boldsymbol {x} _ {\\pi}, \\sqrt {2} \\sigma\\right) \\approx \\nabla_ {\\boldsymbol {x} _ {\\pi}} \\log p _ {\\sqrt {2} \\sigma} \\left(\\boldsymbol {x} _ {\\pi}\\right). \\tag {17}", + "image_path": "874cb71aa7b4b699f866d40c13c675b8ca8fbd031fedd5b9453d3a0bd4f4b05a.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 310, + 393, + 541, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 393, + 541, + 418 + ], + "spans": [ + { + "bbox": [ + 310, + 393, + 541, + 418 + ], + "type": "text", + "content": "Lemma 1 Assuming an empirical data distribution " + }, + { + "bbox": [ + 310, + 393, + 541, + 418 + ], + "type": "inline_equation", + "content": "p_{\\sigma}(\\pmb{x})" + }, + { + "bbox": [ + 310, + 393, + 541, + 418 + ], + "type": "text", + "content": " in Eq. (4), for any " + }, + { + "bbox": [ + 310, + 393, + 541, + 418 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^d" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 326, + 427, + 541, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 427, + 541, + 441 + ], + "spans": [ + { + "bbox": [ + 326, + 427, + 541, + 441 + ], + "type": "interline_equation", + "content": "\\log p _ {\\sqrt {2} \\sigma} (\\boldsymbol {x}) \\geq \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}). \\tag {18}", + "image_path": "70b3dc19bd499fd3cd3ecdeecf2baa99ee499f64dbe20850ebe6a38d45c27e9a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 447, + 545, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 545, + 470 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 545, + 470 + ], + "type": "text", + "content": "Proof. Observe that the LHS of Eq. (19) is a convolution of two Gaussians, therefore" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 308, + 475, + 545, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 475, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 308, + 475, + 545, + 490 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} [ \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {\\mu}, \\sigma^ {2} \\mathbf {I}) ] = \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {\\mu}, 2 \\sigma^ {2} \\mathbf {I}) \\tag {19}", + "image_path": "beea184195f5af523175c1b5043d0f28c061891f16d624e2ee02d7cecd8dc3e0.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 495, + 531, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 495, + 531, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 495, + 531, + 507 + ], + "type": "text", + "content": "Recall that " + }, + { + "bbox": [ + 306, + 495, + 531, + 507 + ], + "type": "inline_equation", + "content": "p_{\\sigma}(\\pmb {x})" + }, + { + "bbox": [ + 306, + 495, + 531, + 507 + ], + "type": "text", + "content": " is a mixture of Gaussians per Eq. (4);" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 307, + 511, + 545, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 511, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 307, + 511, + 545, + 573 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} p _ {\\sqrt {2} \\sigma} (\\boldsymbol {x}) = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\mathrm {d a t a}}} \\mathcal {N} (\\boldsymbol {x}; \\boldsymbol {y}, 2 \\sigma^ {2} \\mathbf {I}) (20) \\\\ = \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\text {d a t a}}} \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}) (21) \\\\ = \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} \\mathbb {E} _ {\\boldsymbol {y} \\sim p _ {\\text {d a t a}}} \\mathcal {N} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}; \\boldsymbol {y}, \\sigma^ {2} \\mathbf {I}) (22) \\\\ = \\mathbb {E} _ {\\boldsymbol {n} \\sim \\mathcal {N} (0, \\mathbf {I})} p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}). (23) \\\\ \\end{array}", + "image_path": "c08a7b63e35e0e3ba206c1c91836a58db242f3e1ac5b28b06b092f242e3ac024.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 578, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 578, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 305, + 578, + 545, + 602 + ], + "type": "text", + "content": "Taking the log on both sides of Eq. (23) and by Jensen's inequality, we arrive at Eq. (18)." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "spans": [ + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "text", + "content": "Claim 1 Assuming a trained denoiser " + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "text", + "content": " as in Eq. (3), our " + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "inline_equation", + "content": "PAAS(x_{\\pi}, \\sqrt{2}\\sigma)" + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "text", + "content": " in Eq. (13) computes the gradient w.r.t. a lower bound of " + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "inline_equation", + "content": "\\log p_{\\sqrt{2}\\sigma}(\\pmb{x})" + }, + { + "bbox": [ + 310, + 607, + 542, + 646 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 651, + 525, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 525, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 525, + 662 + ], + "type": "text", + "content": "Proof. By taking the gradient of the RHS of Lemma 1," + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 668, + 547, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 547, + 696 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {\\boldsymbol {x}} \\mathbb {E} _ {\\boldsymbol {n}} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}) = \\mathbb {E} _ {\\boldsymbol {n}} \\nabla_ {\\boldsymbol {x} + \\sigma \\boldsymbol {n}} \\log p _ {\\sigma} (\\boldsymbol {x} + \\sigma \\boldsymbol {n}) \\\\ = \\mathbb {E} _ {\\boldsymbol {n}} [ \\operatorname {s c o r e} (\\boldsymbol {x} _ {\\pi} + \\sigma \\boldsymbol {n}, \\sigma) ]. \\tag {24} \\\\ \\end{array}", + "image_path": "c11ac6368c8f1307f88e3f76999533019719caa609ad53693156d6a14453fb7c.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 701, + 512, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 512, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 512, + 714 + ], + "type": "text", + "content": "which is the proposed PAAS algorithm in Eq. (13)." + } + ] + } + ], + "index": 28 + }, + { + "type": "image", + "bbox": [ + 535, + 702, + 545, + 710 + ], + "blocks": [ + { + "bbox": [ + 535, + 702, + 545, + 710 + ], + "lines": [ + { + "bbox": [ + 535, + 702, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 535, + 702, + 545, + 710 + ], + "type": "image", + "image_path": "46ad94efacec0ec77520bea1d1979b0f1d0fe3194a2607513f1b1ec3de642342.jpg" + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_body" + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12622" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 272, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 272, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 272, + 85 + ], + "type": "text", + "content": "4.2. Inverse Rendering on Voxel Radiance Field" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 125 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 125 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 125 + ], + "type": "text", + "content": "With the computation of the 2D score resolved, the other half of our setup in Eq. (11) requires access to the Jacobian of a differentiable renderer." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "content": "3D Representation. We represent a 3D asset " + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "content": " as a voxel radiance field [6, 11, 53], which is much faster to access and update compared to a vanilla NeRF parameterized by a neural network [34]. The parameters " + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "content": " consist of a density voxel grid " + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{(\\mathrm{density})} \\in \\mathbb{R}^{1 \\times N_x \\times N_y \\times N_z}" + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "content": " and a voxel grid of appearance features " + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{(\\mathrm{app})} \\in \\mathbb{R}^{c \\times N_x \\times N_y \\times N_z}" + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "content": ". Conventionally the appearance features are simply the RGB colors and " + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "inline_equation", + "content": "c = 3" + }, + { + "bbox": [ + 46, + 129, + 288, + 236 + ], + "type": "text", + "content": ". For simplicity, we do not model view dependencies in this work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "text", + "content": "Inverse Volumetric Rendering. Image rendering is performed independently along a camera ray through each pixel. We cut a camera light ray into equally distanced segments of length " + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "text", + "content": ", and at the spatial location corresponding to the beginning of the " + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "text", + "content": "-th segment we sample a " + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "inline_equation", + "content": "(\\mathrm{RGB}_i, \\tau_i)" + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "text", + "content": " tuple from the color and density grids using trilinear interpolation. These values are alpha-composed using volume rendering quadrature [32] into the pixel color " + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "inline_equation", + "content": "C = \\sum_{i} w_i \\cdot \\mathrm{RGB}_i" + }, + { + "bbox": [ + 46, + 239, + 289, + 345 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 62, + 351, + 287, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 351, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 62, + 351, + 287, + 384 + ], + "type": "interline_equation", + "content": "w _ {i} = \\alpha_ {i} \\cdot \\prod_ {j = 0} ^ {i - 1} (1 - \\alpha_ {j}); \\quad \\alpha_ {i} = 1 - \\exp (- \\tau_ {i} d). \\tag {25}", + "image_path": "3aac3df569fd9a12e3fdf382d2ca19ba80dbcc55e099330a82113a1337ed34d8.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": "Volume rendering of " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": " is directly differentiable. At a rendered image " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "x_{\\pi}" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": ", the Vector-Jacobian product in Eq. (11) between PAAS " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "(x_{\\pi})" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": " and the Jacobian " + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "inline_equation", + "content": "J_{\\pi} = \\frac{\\partial x_{\\pi}}{\\partial \\theta}" + }, + { + "bbox": [ + 46, + 390, + 287, + 462 + ], + "type": "text", + "content": " is computed by back-propagating the score through Eq. (25). This Vector-Jacobian product provides us with the 3D gradient needed for generative modeling on the voxel radiance field." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 548 + ], + "type": "text", + "content": "Regularization Strategies. The voxel grid is a very powerful 3D representation for volumetric rendering. Given noisy 2D guidance, the model may cheat by populating the entire grid with small densities such that the combined effect from one view hallucinates a plausible image. We propose several techniques to encourage the formation of a coherent 3D structure." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "text", + "content": "Emptiness Loss: Ideally, the space should be sparse with near zero densities except at the object. We propose an emptiness loss to encourage sparsity on a ray " + }, + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 46, + 551, + 287, + 588 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 80, + 594, + 287, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 594, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 80, + 594, + 287, + 624 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e m p t i n e s s}} (\\mathbf {r}) = \\frac {1}{n} \\sum_ {i = 1} ^ {n} \\log \\left(1 + \\beta \\cdot w _ {i}\\right), \\tag {26}", + "image_path": "5a65100a99c018faca778644b2df35cbf82afbaefdbc53d07c1305b233c4866f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": " are the alpha-composed weights shown in (25). The shape of the log function imposes severe penalties at the onset of small weights, but does not grow aggressively if the weights are large. It is consistent with our aim to eliminate small densities. The hyperparameter " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": " controls the steepness of the loss function near 0. A larger " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": " will put more emphasis on eliminating low-density noise. We set " + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\beta = 10" + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 308, + 73, + 544, + 311 + ], + "blocks": [ + { + "bbox": [ + 308, + 73, + 544, + 311 + ], + "lines": [ + { + "bbox": [ + 308, + 73, + 544, + 311 + ], + "spans": [ + { + "bbox": [ + 308, + 73, + 544, + 311 + ], + "type": "image", + "image_path": "a1c440dbffe9d508bd0b1e939e7779211fb570f13c31a554c7a2ae11da6c28e9.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "lines": [ + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "spans": [ + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "text", + "content": "Figure 4. Sampling 2D images with Perturb-and-Average Scoring. We compare Annealed vs Random " + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "text", + "content": " schedule against several diffusion models. Row 1 & 2: the random " + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "text", + "content": " schedule exhibits strong mode-seeking behavior, and it results in low-quality \"mean\" images on unconditioned diffusion models trained on FFHQ and LSUN Bedroom. In this case, we need a carefully designed annealed " + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "text", + "content": " schedule to produce better, more diverse samples. Row 3 & 4: Stable Diffusion (SD) is conditioned on the prompt \"a squirrel holding a saxophone\". The use of natural language makes the conditioned distribution much easier to sample from. When the guidance scale is elevated to 10, Random " + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 318, + 547, + 450 + ], + "type": "text", + "content": " schedule that fails on FFHQ and LSUN starts to produce crisp, clean images." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": "Emptiness Loss Schedule: We use a hyperparameter " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": " to control the contribution of the emptiness loss. If we apply a large emptiness loss, it will hinder the learning of geometry in the early stage of training. But if the emptiness is too small, there will be floating density artifacts. We adopt a two-stage noise elimination schedule to deal with this problem. In the first " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": " iterations, we use a relatively small weighting factor " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\lambda_{1}" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": ". After the " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "K^{\\mathrm{th}}" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": " iteration, it is increased to a larger " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\lambda_{2}" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": ". In our experiments " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 1 \\times 10^{4}" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 2 \\times 10^{5}" + }, + { + "bbox": [ + 305, + 463, + 547, + 594 + ], + "type": "text", + "content": ". We provide an ablation study of this technique in Fig. 7 to show its effectiveness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 603, + 546, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 603, + 546, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 603, + 546, + 651 + ], + "type": "text", + "content": "Center Depth Loss: Sometimes the optimization places the object away from the scene center. The object either becomes small or wander around the image boundary. For the few cases when this happens we apply a center depth loss" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 665, + 546, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 310, + 665, + 546, + 713 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c e n t e r}} (D) = - \\log \\left(\\frac {1}{| \\mathcal {B} |} \\sum_ {\\mathbf {p} \\in \\mathcal {B}} D (\\mathbf {p}) - \\frac {1}{| \\mathcal {B} ^ {\\complement} |} \\sum_ {\\mathbf {q} \\notin \\mathcal {B}} D (\\mathbf {q})\\right) \\tag {27}", + "image_path": "12a7a6949da8ae077f3dde0d29cce5f03c10f86e2a5ab871cddef283a8e5202e.jpg" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + 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Qualitative results of text-prompted generation of 3D models with SJC, purely from the pretrained Stable Diffusion (2D) image model. Each row shows two views, with associated depth maps (blue is far, red is near), for a single 3D model generated for a given prompt. 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SJC vs. DreamFusion" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 46, + 399, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 288, + 422 + ], + "type": "text", + "content": "In this section, we describe the differences and the connections between our SJC and DreamFusion." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "type": "text", + "content": "Differences from DreamFusion. In terms of formulation, DreamFusion's computation of the gradient w.r.t. " + }, + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "type": "text", + "content": " involves a U-Net Jacobian term (see Eq. 2 in their paper [41]). In practice, they \"found that omitting the U-Net Jacobian term\" to be more effective. On the other hand, this U-Net Jacobian term does not appear in our formulation. Their additional justification in the appendix actually leans more towards our viewpoint. An additional contribution of ours beyond DreamFusion [41] is our analysis of the effect that the OOD problem has when using a denoiser on rendered images (Claim 1), and the PAAS method to address it. For the variance reduction technique, namely the use of the Monte-Carlo estimate on Eq. (16), or " + }, + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "type": "inline_equation", + "content": "\\hat{\\epsilon} - \\epsilon" + }, + { + "bbox": [ + 46, + 425, + 289, + 604 + ], + "type": "text", + "content": " (in DreamFusion), vs. on Eq. (15), we observe comparable performance between the two methods empirically for 3D generation." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Influences by DreamFusion. At the time of this submission, DreamFusion is a concurrent arXiv paper. However, as we have read the paper, our research was influenced by their reported observations. In particular, we adopted the idea of randomized scheduling of " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " during 3D optimization for easier hyperparameter tuning, and used view-augmented language prompting that improves the overall 3D quality. For future work we do hope to explore a more general solution than view-dependent prompts." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 342, + 387, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 342, + 387, + 357 + ], + "spans": [ + { + "bbox": [ + 306, + 342, + 387, + 357 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 363, + 547, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 399 + ], + "type": "text", + "content": "We conduct experiments on both unconditioned and conditioned diffusion models to have a more comprehensive understanding of the properties of SJC." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 403, + 547, + 500 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 547, + 500 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 547, + 500 + ], + "type": "text", + "content": "DDPMs trained on FFHQ and LSUN Bedroom are unconditioned diffusion models with an architecture based on the implementation by Dhariwal and Nichol [10]. They are trained on an image resolution of " + }, + { + "bbox": [ + 304, + 403, + 547, + 500 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 403, + 547, + 500 + ], + "type": "text", + "content": ". FFHQ [21] is a dataset of aligned faces with diverse coverage of gender, age, race, facial appearance as well as head poses. LSUN Bedroom [62] includes bedroom images with varied furniture layout plans and rich interior design styles." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "type": "text", + "content": "Stable Diffusion is an expanded work based on Latent Diffusion Model (LDM) developed by Rombach et al. [45]. It is trained on the LAION5B dataset [47]. We use the release version v1.5. Diffusion is performed on a latent space of " + }, + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "type": "inline_equation", + "content": "4 \\times 64 \\times 64" + }, + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "type": "text", + "content": ", then upsampled to " + }, + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "type": "inline_equation", + "content": "3 \\times 256 \\times 256" + }, + { + "bbox": [ + 304, + 504, + 548, + 636 + ], + "type": "text", + "content": " by a decoder. The model is natively trained for text-conditioned image generations, and exposes a guidance scale parameter that controls the strength of language conditioning [14]. Intuitively a larger guidance scale makes the conditioned image distribution more faithful to the text prompt by trading off sample diversity." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 646, + 473, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 473, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 473, + 659 + ], + "type": "text", + "content": "5.1. Validating PAAS on 2D images." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Before directly jumping to 3D generation, we first verify that PAAS provides effective guidance on a simple 2D image canvas. In other words, here " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " is a grid of RGB values and " + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": " is an identity function. The hope is that gradient descent" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12624" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 83, + 219, + 246 + ], + "blocks": [ + { + "bbox": [ + 134, + 72, + 146, + 81 + ], + "lines": [ + { + "bbox": [ + 134, + 72, + 146, + 81 + ], + "spans": [ + { + "bbox": [ + 134, + 72, + 146, + 81 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 83, + 219, + 246 + ], + "lines": [ + { + "bbox": [ + 49, + 83, + 219, + 246 + ], + "spans": [ + { + "bbox": [ + 49, + 83, + 219, + 246 + ], + "type": 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+ { + "bbox": [ + 45, + 430, + 546, + 485 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison between Stable-DreamFusion (StableDF) and Ours. The prompts are: (a) \"A high quality photo of a delicious burger\"; (b) \"a DSLR photo of a yellow duck\"; (c) \"A ficus planted in a pot\"; (d) \"A product photo of a toy tank\"; (e) \"A high quality photo of a chocolate icecream cone\"; (f) \"A wide angle zoomed out photo of a giraffe\". Both methods are run for 10k iterations without per-prompt finetuning on the hyperparameters. The images on the left are rendered RGB images and the images on the right are depth visualization." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": "on the vector field produced by PAAS creates high quality images. Here an important decision to make is the schedule of " + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\{\\sigma_i\\}" + }, + { + "bbox": [ + 46, + 498, + 287, + 533 + ], + "type": "text", + "content": " at which we compute PAAS." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": "We experimented with an annealed schedule (Annealed " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": ") vs. a random schedule (Random " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": ") as proposed in Dream-Fusion. Under the Annealed " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " schedule, we start from a large " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " and gradually decrease it as we update the image canvas " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": ". PAAS computed at larger " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " level attends to high level image structure while smaller " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " provides stronger guidance on detailed features. The Random " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " schedule on the contrary uniformly samples a " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " at every step. We show qualitative comparisons in Fig. 4." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "For unconditioned diffusion models trained on FFHQ, we observe that Annealed " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " performs better than Random " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": ", and the image samples have better pose variation and quality. Particularly, the randomized " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " exhibits severe mode-seeking behavior converging to average faces. In the case of LSUN Bedroom, the mode-seeking behavior results in a" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 498, + 456, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 498, + 456, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 498, + 456, + 510 + ], + "type": "text", + "content": "blurry image canvas with no content." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": "On the other hand, natural language prompting plays a critical role when sampling images with Stable Diffusion. When the language guidance is set to a regular level of 3.0, the observations are broadly consistent with sampling on FFHQ and LSUN. Random " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " schedule produces blurry outputs. However, when the guidance scale is elevated to 10.0, Random " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " schedule begins to generate crisp, clean images and outperforms Annealed " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " schedule. Despite various sophisticated strategies on Annealed " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " scheduling (see our code for details), at a high language guidance scale Randomized " + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": " remains the better option. We hypothesize that stronger language guidance forces the image distribution to be narrower and more beneficial for a mode-seeking algorithm. We acknowledge none of the images in Fig. 4 can match the sample quality of a standard diffusion inference pipeline, and the right way to apply PAAS as gradient for optimization remains an open problem." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12625" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 195, + 72, + 398, + 82 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 195, + 72, + 398, + 82 + ], + "spans": [ + { + "bbox": [ + 195, + 72, + 398, + 82 + ], + "type": "text", + "content": "A zoomed out high quality photo of Temple of Heaven." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 83, + 542, + 308 + ], + "blocks": [ + { + "bbox": [ + 53, + 83, + 542, + 308 + ], + "lines": [ + { + "bbox": [ + 53, + 83, + 542, + 308 + ], + "spans": [ + { + "bbox": [ + 53, + 83, + 542, + 308 + ], + "type": "image", + "image_path": "8d1a4dd2af26f7e686caf457435aa1dd6ade5dab52930a117d9ce367d81b8acb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 317, + 548, + 363 + ], + "lines": [ + { + "bbox": [ + 46, + 317, + 548, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 317, + 548, + 363 + ], + "type": "text", + "content": "Figure 7. Ablation experiments on the proposed emptiness loss schedule. For each setting of the loss weight " + }, + { + "bbox": [ + 46, + 317, + 548, + 363 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 317, + 548, + 363 + ], + "type": "text", + "content": ", we show a rendered image and the associated depth map from a randomly sampled viewpoint. Ours incorporates the loss with weight schedule described in 5.2. It leads to better 3D shape, as evidenced in the cleaner depth maps. Setting the loss weight too low yields \"cloudy\" depth fields. When setting the weight too high, SJC fails to produce meaningful 3D models." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 382, + 140, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 140, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 140, + 395 + ], + "type": "text", + "content": "5.2.3D Generation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "type": "text", + "content": "In this paper, we focus on 3D Generation with the language-conditioned Stable Diffusion model. We found that tuning the Annealed " + }, + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "type": "text", + "content": " schedule on FFHQ and LSUN Bedroom in 3D domain is difficult in practice, and leave it as future work. Based on the insights from 2D experiments earlier, we use Random " + }, + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 405, + 288, + 489 + ], + "type": "text", + "content": " schedule coupled with a high language guidance scale." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 498, + 289, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 571 + ], + "type": "text", + "content": "Rendering with Latent 3D Features. Stable Diffusion economizes compute by performing diffusion modeling on the latent features of a pretrained AutoEncoder. We therefore choose to render a feature image in this latent space from a features field [3, 38] represented by a voxel grid in " + }, + { + "bbox": [ + 46, + 498, + 289, + 571 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{4\\times N_x\\times N_y\\times N_z}" + }, + { + "bbox": [ + 46, + 498, + 289, + 571 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Qualitative Comparison. In Fig. 5, we show text-prompted 3D generation results from SJC, and compare SJC with Stable-DreamFusion, a third-party implementation based on the same pretrained Stable Diffusion v1.5 model. In Fig. 6, we show qualitative comparisons of generated 3D assets given the same prompt. We observe that SJC generates 3D models with better image quality and more sensible structure than Stable-DreamFusion in a significant number of cases. We note that both systems exhibit quality fluctuations over different trials, and the point of this comparison is to show that our overall pipeline is competitive." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "text", + "content": "Ablations. In Fig. 7, we conduct ablations to demonstrate the importance of the proposed emptiness loss and scheduling of its weight " + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "text", + "content": " discussed in Sec. 4.2. We show results without the emptiness loss, with constant weight " + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "text", + "content": " vs our proposed scheduling of " + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 382, + 548, + 468 + ], + "type": "text", + "content": ". We observe that our complete method (Ours) improves the quality of generated 3D models, e.g., fewer floating artifacts and better geometry." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 475, + 379, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 379, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 379, + 488 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 496, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 547, + 651 + ], + "type": "text", + "content": "We propose an optimization-based approach to generate 3D assets from pretrained image (2D) diffusion models. The key technical contribution is the derivation of Perturb-and-Average Scoring method which bridges the gap between the denoising-trained diffusion models and the non-noisy images encountered in the process of optimizing a 3D model guided by the diffusion. Working with the large-scale Stable Diffusion model, we demonstrate that our approach can generate compelling 3D models, comparing favorably to available concurrent work. Finally, we investigate an interesting distinction between the effect of noise scheduling regime in unconditional image diffusion models and a text-conditional model, and identify an avenue for future work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgement This work was supported in part by the TRI University 2.0 program, and by the AFOSR MADlab Center of Excellence. 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Wong \nThe University of Hong Kong", + "bbox": [ + 277, + 203, + 691, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{ykcao, kykwong}@cs.hku.hk kaihanx@hku.hk", + "bbox": [ + 287, + 241, + 676, + 255 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/764031e6407c55e4ce2cfc61566261936cbb877ffeb80c41bc9c7634305aab57.jpg", + "image_caption": [ + "Single-view" + ], + "image_footnote": [], + "bbox": [ + 140, + 310, + 200, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/85a9016202a73e5182557579542ecacf614d9f7da468d06ea10aedf2b5cc4c7e.jpg", + "image_caption": [ + "Multi-view", + "Figure 1. Self-evolved Signed Distance Field (SeSDF): We propose Self-evolved Signed Distance Field (SeSDF), which can flexibly reconstruct 3D clothed human models from a single-view image (top) or uncalibrated multi-view images (bottom). SeSDF can robustly recover fine geometry details from any type of poses, which allows us to generate clothed human avatars." + ], + "image_footnote": [], + "bbox": [ + 218, + 291, + 830, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 580, + 313, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We address the problem of clothed human reconstruction from a single image or uncalibrated multi-view images. Existing methods struggle with reconstructing detailed geometry of a clothed human and often require a calibrated setting for multi-view reconstruction. We propose a flexible framework which, by leveraging the parametric SMPL-X model, can take an arbitrary number of input images to reconstruct a clothed human model under an uncalibrated setting. At the core of our framework is our novel self-evolved signed distance field (SeSDF) module which allows the framework to learn to deform the signed distance field (SDF) derived from the fitted SMPL-X model, such that detailed geometry reflecting the actual clothed human can be encoded for better reconstruction. Besides, we propose a simple method for self-calibration of multi-view images via the fitted SMPL-X parameters. This lifts the requirement of tedious manual calibration and largely increases the flexibility of our method. Further, we introduce an effective occlusion-aware feature fusion strategy to account for the most useful fea", + "bbox": [ + 73, + 613, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tures to reconstruct the human model. We thoroughly evaluate our framework on public benchmarks, demonstrating significant superiority over the state-of-the-arts both qualitatively and quantitatively.", + "bbox": [ + 498, + 582, + 890, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 662, + 632, + 678 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Clothed human reconstruction is a hot topic with increasing demand in real-world applications such as 3D telepresence, game modeling, metaverse [40], etc. Early works show promise under equipment-assisted settings, requiring expensive dense camera rigs [12] and tedious calibration procedures [15]. Parametric models, such as SMPL [36] and SMPL-X [47], have been introduced to model a naked human body with constrained parameters. With the witnessed success of deep learning in many vision tasks, many deep learning methods have been proposed to regress the parameters of such parametric human models from a single [16, 66, 67] or multiple images [6, 13, 68]. However, these methods can only reconstruct a minimally-clothed human model without many details (e.g., hairs and clothes).", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4647", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, methods based on implicit shape representation have reported encouraging performance, showing promising reconstruction with increased details in both single-view [23, 26, 52, 63, 71] and multi-view [24, 25, 54, 55] settings.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the stunning results reported by the above methods, their reconstructions remain far from perfect, restricting their practical applications. For instance, state-of-the-art (SOTA) single-view methods, such as PIFuHD [53], PaMIR [71], and $\\mathrm{ARCH} + +$ [23], struggle with many self-occluding non-frontal human poses that widely occur in the real world. ICON [63] can handle these cases but the reconstructions contain serious artifacts (see Fig. 3). On the other hand, many multi-view methods depend on calibrated cameras (e.g., [24, 54, 55]) which are tedious to obtain in practice. Hence, how to carry out multi-view reconstruction with uncalibrated cameras is an important topic to study. Meanwhile, effective multi-view feature fusion is another key factor for robust multi-view reconstruction. Prior techniques for multi-view feature fusion include average pooling [52], SMPL-visibility [63], and attention-based mechanism [70]. However, the reconstruction results based on these fusion techniques still contain notable artifacts in many cases. This indicates that more efforts are needed to derive a better multi-view feature fusion for more robust reconstruction.", + "bbox": [ + 75, + 169, + 472, + 486 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, to extract more clothed human details flexibly and robustly from a single RGB image or uncalibrated multi-view RGB images, we present a novel framework, named SeSDF, that employs the parametric model SMPL-X [47] as a 3D prior and combines the merits of both implicit and explicit representations. SeSDF takes a single image or multi-view images as input to predict the occupancy for each 3D location in the space representing the human model. To reconstruct high-frequency details such as hairs and clothes, we introduce a self-evolved signed distance field module that learns to deform the signed distance field (SDF) derived from the fitted SMPL-X model using the input images. The resulting SDF can reflect more accurate geometry details than SMPL-X, which inherently deviates from the actual clothed human model. The SDF refined by our SeSDF module is further encoded to allow for 3D reconstruction with better geometry details.", + "bbox": [ + 75, + 489, + 472, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Besides reconstructing a faithful 3D clothed human model from a single image, our SeSDF framework can also work with uncalibrated multi-view images to generate clothed human avatar with enhanced appearance (see Fig. 1). To this end, we first propose a self-calibration method by fitting a shared SMPL-X model across multiview images and projecting the shared model to different images based on the optimized rigid body motion for each input image. Further, we propose an occlusion-aware feature fusing strategy by probing the visibility of each 3D", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "point under different views through ray-tracing, leveraging the SMPL-X model, such that features from visible views will contribute more to the fused feature while those from invisible views will be suppressed.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The contributions are summarized as follows:", + "bbox": [ + 517, + 152, + 821, + 167 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a flexible framework that, by leveraging the SMPL-X model as a shape prior, can take an arbitrary number of uncalibrated images to perform high-fidelity clothed human reconstruction. At the core of our framework is a self-evolved signed distance field (SeSDF) module for recovering faithful geometry details.", + "- For uncalibrated multi-view reconstruction, we propose a simple self-calibration method through leveraging the SMPL-X model, as well as an occlusion-aware feature fusion strategy which takes into account the visibility of a space point under different views via ray-tracing.", + "- We thoroughly evaluate our framework on public benchmarks. SeSDF exhibits superior performances over current state-of-the-arts both qualitatively and quantitatively." + ], + "bbox": [ + 500, + 169, + 890, + 381 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 398, + 640, + 415 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Parametric 3D human model Parametric 3D human reconstruction [21, 30, 36, 44, 47] paves the path for 3D human model. SMPL [36, 67] was built on convolutional networks and statistics collected from a wide range of human populations. SMPL-X [47, 66] extended SMPL with more body joints, keypoints, and expression parameters. Later substantial supervision strategies were proposed to regress the model parameters. Examples include semantic segmentation [43, 64], human body silhouette [49], joints [16], motion dynamics [30, 33], texture consistency [48], and attention-regressor [31]. Multi-view [6, 13, 68, 69] and multi-person [57, 58] setups were also sought for various scenarios. Complex human clothing and hair topology were also the goals for later parametric methods [3, 4, 29, 62, 73]. However, due to the minimal-clothing assumption of the parametric models, these methods can retain little geometry details such as hairs and clothes in their reconstructions.", + "bbox": [ + 496, + 428, + 890, + 685 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single-view (implicit) human reconstruction Many methods have been proposed in the deep learning era to reconstruct a 3D human model from a single image. For example, voxel-based methods [18, 27, 59, 60, 72, 72] reconstruct a volumetric representation of the human model. Two-stage inference [56], visual hull [41] and front-back depth method [17] were then proposed to improve the reconstruction performance and efficiency. However, the high computational cost of these methods limits their real-world applications. Implicit function methods have recently been introduced to predict either the occupancy field [10, 38] or signed distance field [8, 28, 45] using neural networks. PIFu [52] presents promising results with a pixel-aligned implicit function. Follow-up works exploited 3D features", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4648", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "to solve the depth-ambiguity problem [71], achieve animatable model [23, 26], or improve the reconstruction details [7]. PIFuHD [53] and FITE [35] apply a multi-stage method to improve clothing topology in the reconstruction. Geo-PIFu [22] proposes to compute 3D features directly from images. ICON [63] exploits the SMPL-based signed distance filed as guidance to help produce a robust reconstruction, with a smpl-visibility based method to choose features from front or back sides. PHORHUM [5] explores shading and illumination information to infer better geometry and texture. Encouraging improvements have been reported by these methods. However, their performance on non-frontal human images are still far from being robust and satisfactory.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-view implicit human reconstruction Multi-view reconstruction is conceptually a more natural choice as information from different views can compensate each other for better reconstruction. Under a calibrated setting, PIFu [52] proposes to fuse features from multi-views by average pooling after being embedded using an MLP. StereoPIFu [24] takes as input a pair of stereo images, and performs depth-aware reconstruction. DiffuStereo [55] employs diffusion models for multi-view stereo human reconstruction. DoubleField [54] combines the surface field and radiance fields to improve both geometry and texture inference. Effi-MVS [61] explores the dynamic cost volume for reduced computational cost. DeepMultiCap [70] handles the multi-person reconstruction with multi-view images. Neural-Human-Performer [32] proposes a multi-view transformer to fuse features for multi-view reconstruction. Despite promising results have been achieved, these methods require a large number of views and camera calibration. MVP-Human [74] makes use of the deformation fields and handles multi-view inputs under an uncalibrated setting, but the reconstruction quality lags far behind the calibrated methods. For calibrated methods, their models still produce undesirable artifacts for many self-occluding nonfrontal poses and miss many geometry details.", + "bbox": [ + 75, + 304, + 472, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 674, + 169, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose an implicit function based framework for reconstructing 3D clothed human models from a single image or uncalibrated multi-view images (see Fig. 2). At the core of our framework are a self-evolved signed distance field (SeSDF) module and an occlusion-aware feature fusion module. Next, we will first introduce the preliminary for SeSDF in Sec. 3.1. We will then describe SeSDF for single-view reconstruction in Sec. 3.2, followed by uncalibrated multi-view reconstruction in Sec. 3.3.", + "bbox": [ + 75, + 699, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 844, + 207, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Surface by implicit function Implicit functions [14] have been shown to be effective for 3D reconstruction from im", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ages or videos. Typically, an implicit function is implemented as an MLP, which takes the 3D coordinate $X$ and an optionally associated feature $F$ of a 3D point as input, and outputs the corresponding occupancy as a scalar value. Commonly employed features include pixel-aligned image features [52, 53] and space-aligned 3D features [7, 26, 71]. Formally, the implicit function can be written as", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {v} (X, F) \\mapsto [ 0, 1 ] \\in \\mathbb {R}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 210, + 890, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SMPL-X The parametric human model SMPL-X represents the 3D shape by incorporating body vertices, joints, face and hands landmarks, and expression parameters. Formally, by assembling pose parameters $\\theta$ , shape parameters $\\beta$ , and facial expression parameters $\\phi$ , SMPL-X human model can be expressed by a function $M(\\cdot)$ as", + "bbox": [ + 496, + 243, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nM (\\beta , \\theta , \\phi) = W (T _ {p} (\\beta , \\theta , \\phi), J (\\beta), \\theta , \\mathcal {W}),\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 347, + 812, + 364 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT _ {p} (\\beta , \\theta , \\phi) = \\bar {T} + B _ {S} (\\beta ; \\mathcal {S}) + B _ {E} (\\phi ; \\mathcal {E}) + B _ {p} (\\theta ; \\mathcal {P}),\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 364, + 887, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $W(\\cdot)$ is the linear blend skinning function, $J(\\beta)$ is the joint location, and $\\mathcal{W}$ denotes the blend weights. $T_{p}(\\cdot)$ poses the SMPL-X canonical model $\\bar{T}$ by shape blend shape function $B_{S}$ , expression blend shape function $B_{E}$ , and pose blend shape function $B_{P}$ . $\\mathcal{S}$ and $\\mathcal{P}$ are the principal components of vertex displacements, and $\\mathcal{E}$ represents the principal components capturing variations of facial expressions.", + "bbox": [ + 496, + 396, + 890, + 502 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SMPL-X optimization Given a human image, we can fit the SMPL-X model parameters by [16]. However, such fitted models often suffer from misalignment. We use the well-aligned SMPL-X models provided in the training data to provide shape prior to train our framework. At test time, we do not have such well-aligned models. Hence, to avoid errors and artifacts caused by the misalignment during testing, we optimize the SMPL-X parameters by projecting the SMPL-X model onto the input image and maximizing the Intersection over Union (IoU) between the projection and body mask [9, 63], and minimizing the 2D keypoint distances. Please refer to the supplementary for details.", + "bbox": [ + 496, + 505, + 890, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Single-view reconstruction", + "text_level": 1, + "bbox": [ + 500, + 698, + 740, + 714 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an input image $\\pmb{I}$ and an optimized SMPL-X mesh $S$ , SeSDF incorporates pixel-aligned image features $F_{2D}$ extracted from $\\pmb{I}$ , space-aligned 3D features $F_{3D}$ extracted from $S$ , and the self-evolved signed distance field $d$ to predict occupancy using an MLP. By applying marching cube [34] on the occupancy predictions in the 3D space, SeSDF robustly reconstructs a 3D clothed human model with faithful details, including the clothing topology. Given a 3D point $X$ , the implicit function for single-view reconstruction can be formulated as", + "bbox": [ + 496, + 722, + 890, + 873 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf _ {o} \\left(F _ {2 D} (X), F _ {3 D} (X), \\mathcal {D} (d (X)), \\mathbf {n} (X), Z (X)\\right) \\mapsto [ 0, 1 ], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 885, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4649", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cc4cc9cd142a59266971eec7bdc920e85bb7b293d1bc43ca4d2b0458e5a3568a.jpg", + "image_caption": [ + "Figure 2. Overview of our proposed SeSDF framework. It takes a single image or uncalibrated multi-view images as input to predict the occupancy for each 3D location in the space for shape reconstruction. We first fit a SMPL-X model to the input image(s) which serves as a shape prior and provides space-aligned 3D features. At the core of our method is our proposed self-evolved signed distance field (SeSDF) module, which learns a refined signed distance field (SDF) to better reflect the actual clothed human subject rather than the minimally-clothed SMPL-X model. SeSDF module takes pixel-aligned image features, space-aligned 3D features, SDF with distance encoding, and SMPL-X vertex normal as input to predict the refined SDF and normal value. For multi-view reconstruction, we propose a SMPL-X based self-calibration method to eliminate the need for manual calibration and an occlusion-aware feature fusion strategy to effectively accumulate features from different views." + ], + "image_footnote": [], + "bbox": [ + 83, + 92, + 893, + 385 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}(\\cdot)$ and $Z(\\cdot)$ denote distance encoding and depth value respectively, and $d(\\cdot)$ and $\\mathbf{n}(\\cdot)$ are the signed distance and normal output by our SeSDF module.", + "bbox": [ + 75, + 512, + 470, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Pixel-aligned image feature We apply a stacked-hourglass encoder [42, 52] to the input image $I \\in \\mathbb{R}^{512 \\times 512 \\times 3}$ to produce an image feature map $E_{I}(I) \\in \\mathbb{R}^{256 \\times 128 \\times 128}$ . We then obtain the pixel-aligned image feature for the projection of a 3D point using bi-linear interpolation.", + "bbox": [ + 75, + 561, + 468, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Space-aligned 3D feature We apply PointNet [51] and 3D-UNet [11] to extract 3D features [7, 50] from the optimized SMPL-X mesh. Our 3D encoder first processes the whole 10,475 vertices of the mesh to generate hierarchical 3D point features, which are transformed into a 3D feature volume via average pooling. 3D-UNet is then applied to output the final 3D feature volume $E_{S}(S) \\in \\mathbb{R}^{128 \\times 64 \\times 64 \\times 64}$ . Finally we obtain the space-aligned 3D feature for a 3D point via tri-linear interpolation.", + "bbox": [ + 75, + 655, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Self-evolved signed distance field The signed distance field (SDF) derived from the SMPL-X model [63] provides a strong prior for estimating the occupancy. However, the SMPL-X model does not model geometric details of the human, such as the cloth topology, and thus the resulting SDF will unavoidably deviate from the true SDF of the actual clothed human model. Directly employing this SDF", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for occupancy prediction will therefore induce error in the reconstruction. To remedy this problem and recover plausible geometry details in the reconstruction, we propose a novel self-evolved signed distance filed (SeSDF) module. This module is trained to evolve the SDF derived from the SMPL-X model to better reflect the actual clothed human model. Instead of predicting only the signed distance $d(\\cdot) \\in \\mathbb{R}$ , our SeSDF module further predict the normal $\\mathbf{n}(\\cdot) \\in \\mathbb{R}^3$ which provides additional surface orientation information to guide the implicit function to better predict occupancy and capture fine shape details. Concretely, SeSDF module is implemented as an MLP and formulated as", + "bbox": [ + 496, + 512, + 893, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {s d} \\left(F _ {2 D} (X), F _ {3 D} (X), \\mathcal {D} \\left(d ^ {\\prime} (X)\\right), \\mathbf {n} ^ {\\prime} (X)\\right) \\mapsto (d, \\mathbf {n}), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 700, + 890, + 720 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $d'(\\cdot) \\in \\mathbb{R}$ denotes the SDF derived from the SMPL-X model and $\\mathbf{n}'(\\cdot) \\in \\mathbb{R}^3$ represents the normal obtained from the closest SMPL-X vertex to $X$ .", + "bbox": [ + 496, + 726, + 893, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Distance encoding Inspired by the positional encoding adopted in NeRF [39], we adopt a distance encoding that maps the signed distance $d$ to a higher dimensional space using high frequency functions:", + "bbox": [ + 496, + 773, + 893, + 835 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} (d) = \\left(d, \\sin \\left(2 ^ {0} \\pi d\\right), \\cos \\left(2 ^ {0} \\pi d\\right), \\dots , \\sin \\left(2 ^ {L} \\pi d\\right), \\cos \\left(2 ^ {L} \\pi d\\right)\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 839, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our experiments, we set $L = 5$ . The encoded signed distance $\\mathcal{D}(d)$ is concatenated with the predicted normal $\\mathbf{n}(\\cdot)$ ,", + "bbox": [ + 496, + 869, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4650", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2D feature $F_{2D}(\\cdot)$ and 3D feature $F_{3D}(\\cdot)$ , and fed to the implicit function $f_{o}(\\cdot)$ for occupancy prediction.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training objectives To consistently regress SeSDF and simulate realistic cloth topology, we consider two groups of sampling points, namely surface samples $G_{s}$ , and occupancy-target samples $G_{o}$ . Points in $G_{s}$ are uniformly sampled on the mesh surface, while points in $G_{o}$ are sampled following the strategy proposed in PIFu [52].", + "bbox": [ + 75, + 123, + 467, + 214 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For points in $G_{s}$ , we adopt the following loss function", + "bbox": [ + 96, + 214, + 455, + 229 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\frac {1}{| G _ {s} |} \\sum_ {X \\in G _ {s}} \\lambda_ {d} | d (X) | + \\lambda_ {n} \\| \\mathbf {n} (X) - \\mathbf {n} _ {g t} (X) \\|, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 238, + 468, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{n}_{gt}(X)$ denotes the ground-truth normal at the surface point $X$ . For points in $G_{o}$ , we adopt the following loss function", + "bbox": [ + 76, + 280, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {o} = \\frac {1}{| G _ {o} |} \\sum_ {X \\in G _ {o}} B C E (\\mathcal {O} (X) - \\mathcal {O} _ {g t} (X)), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 332, + 468, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{O}(X)$ denotes the predicted occupancy at $X$ computed using Eq. (3) and Eq. (2), $\\mathcal{O}_{gt}(X)$ is the ground-truth occupancy at $X$ , and $BCE(\\cdot)$ denotes the binary cross entropy. Following IGR [20], we add an eikonal normal regularization term to smooth the surface by:", + "bbox": [ + 76, + 375, + 468, + 450 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r} = \\frac {1}{| G _ {o} |} \\sum_ {X \\in G _ {o}} \\left(\\left\\| \\mathbf {n} (X) \\right\\| - 1\\right) ^ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 460, + 468, + 498 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss function is given by", + "bbox": [ + 96, + 508, + 339, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S e S D F} = \\lambda_ {s} \\mathcal {L} _ {s} + \\lambda_ {o} \\mathcal {L} _ {o} + \\lambda_ {r} \\mathcal {L} _ {r}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 536, + 468, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{s},\\lambda_{o}$ ,and $\\lambda_{r}$ are weights to balance the effect of the respective loss.", + "bbox": [ + 76, + 563, + 468, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Uncalibrated multi-view reconstruction", + "text_level": 1, + "bbox": [ + 76, + 603, + 416, + 618 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To allow our SeSDF framework work with uncalibrated multi-view images, we present a simple self-calibration method to estimate the relative camera pose for each image through fitting a SMPL-X model to all the input images. In addition, we propose an occlusion-aware feature fusion strategy to fuse features from different views effectively. Ideally, we would like to fuse only features from non-occluded views as features from occluded views are just noise which at best provide zero contribution to occupancy prediction but may also seriously degrade the fused feature in the worse case.", + "bbox": [ + 75, + 626, + 468, + 790 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our multi-view framework is illustrated in Fig. 2. In principle, it can work with an arbitrary number of views and the number of views used in training and testing do not even need to be the same.", + "bbox": [ + 75, + 792, + 468, + 852 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Self-calibration via SMPL-X model fitting Given $n$ uncalibrated multi-view images, we first fit a SMPL-X model to each image independently using the method described in", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sec. 3.1. We then take the averages of the shape, pose and expression parameters of these $n$ fitted models and use them to initialize a shared SMPL-X model. Next, we optimize the shape, pose and expression parameters of this shared SMPL-X model and the global orientation parameters for the $n$ views simultaneously by maximizing the IoU between the projection and body mask, and minimizing the 2d keypoint distances on each of the $n$ images. After optimization, the global orientation parameters for the $n$ views then give us the rigid body motion that transforms a point from the SMPL-X model centered coordinate system to the camera centered coordinate system of each view.", + "bbox": [ + 496, + 90, + 890, + 271 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To perform multi-view reconstruction, we can sample 3D points in the model centered coordinate system, transform them into the respective camera coordinate systems, and compute 2D/3D features and the self-evolved signed distance from each view. Finally, these features from $n$ different views are fused by our occlusion-aware feature fusion strategy (to be introduced next) and fed to the implicit function $f_{o}(\\cdot)$ to predict the occupancy value.", + "bbox": [ + 496, + 272, + 890, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Occlusion-aware feature fusion Conceptually, features obtained from different views would give rise to predictions of different quality. For instance, image feature for a 3D point extracted from a frontal non-occluded view would be expected to give the best prediction, whereas image feature for the same point but extracted from an occluded view or a lateral view would be expected to give poor prediction. Hence, average pooling would in principle not be the best way for feature fusion. Researchers therefore explored different fusion strategies, such as SMPL-visibility based [63] and attention based [70] approaches, but all of these still produce undesirable artifacts in their reconstructions (see Fig. 7). To lessen the effect of features extracted from non-optimal views, we propose a novel occlusion-aware feature fusion strategy based on ray tracing [19] with the fitted SMPL-X model. Given a 3D point $X$ , we cast a ray from $X$ to the $i$ -th view through orthogonal projection and find the intersection point $X_{i}^{\\prime}$ with the SMPL-X model that is the closest to the image (see Fig. 2). We then compute a weight for the feature $F_{i}(X)$ extracted from the $i$ -th view by", + "bbox": [ + 496, + 395, + 892, + 698 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} (X) = \\frac {1}{\\left| Z _ {i} (X) - Z _ {i} \\left(X _ {i} ^ {\\prime}\\right) \\right|}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 703, + 890, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we fuse all features from the $n$ views by", + "bbox": [ + 500, + 741, + 818, + 757 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {f u s e d} (X) = \\frac {\\sum_ {i = 1} ^ {n} w _ {i} (X) F _ {i} (X)}{\\sum_ {i = 1} ^ {n} w _ {i} (X)}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 762, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 814, + 632, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate the performance of our SeSDF both qualitatively and quantitatively, and provide comparisons with other SOTA methods under both single-view and multiview setups.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4651", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2676794f6acd49885eb7fd05ca1b34d346095042eb916ea6019954c4c7d959c6.jpg", + "table_caption": [ + "Table 1. Qualitative comparison on the single-view setting. We report Chamfer Distance and P2S metrics (numbers the lower the better)." + ], + "table_footnote": [], + "table_body": "
MethodFeature IncludedQuantitative Number
THuman2.0CAPE
2D FeatureNormal Information3D FeatureSMPLX Signed Distanceself-evolved Signed DistanceChamfer Distance↓P2S↓Chmafer Distance↓P2S↓
PIFu [52]✓2.4032.3883.0592.818
PIFuHD [53]✓✓2.0081.9652.5712.427
PaMIR [71]✓✓1.4781.4511.6821.438
ICON [63]✓✓✓1.3011.2591.5331.431
Ours w/o DE✓✓✓✓1.0991.0341.3771.261
Ours w/o SeSDF✓✓✓✓1.2451.2001.4731.390
Ours✓✓✓✓1.0270.9711.3031.219
", + "bbox": [ + 81, + 106, + 890, + 220 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9cff9a1c1a70a6d69b901c7ccfdfa825af61473a2a634ec8996f70c573379028.jpg", + "table_caption": [ + "Table 2. Quantitative comparison on the multi-view setting." + ], + "table_footnote": [], + "table_body": "
MethodTHuman2.0CAPE
Chamfer Distance↓P2S↓Chmafer Distance↓P2S↓
multi-view PIFu [52]0.8640.8380.9200.876
multi-view PIFuHD [53]0.8310.8040.8830.849
multi-view PaMIR [71]0.8070.7620.8580.819
Ours w/o DE0.7950.7490.8490.811
Ours w/o SeSDF0.8020.7550.8540.815
Ours0.7910.7420.8410.800
Ours w/ Attention0.7940.7430.8450.803
Ours w/ SMPLX-Vis0.8410.8320.9250.917
Ours w/ Normal-Fusion0.8010.7540.8500.812
", + "bbox": [ + 81, + 247, + 467, + 385 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dc75e76ee5ed56eb7135e2496e0366ec20af9e7ddfaed875d4d0c22d3be51913.jpg", + "image_caption": [ + "Figure 3. Qualitative comparison with SOTA methods on real-world images. Our method can reconstruct fine details and work robustly under challenge poses. Best viewed in PDF with zoom." + ], + "image_footnote": [], + "bbox": [ + 81, + 393, + 468, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 662, + 290, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each training subject, we sample (a) 5,000 surface points as $G_{s}$ , which are evenly distributed on the mesh surface; (b) 5,000 occupancy-target points as $G_{o}$ in the 3D space, for which we follow the sampling strategy in [52]. In particular, 15/16 points in $G_{o}$ are evenly sampled on the mesh surface. Gaussian perturbation is then applied to them along the surface normal direction. The rest 1/16 points are randomly sampled within the predefined 3D space where the mesh lies in.", + "bbox": [ + 75, + 686, + 467, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ Rembg [1] to segment out the background for real-world images and use Kaolin [2] to calculate the SDF from the SMPL-X model. We apply PIXIE [16] to estimate the SMPL-X model for the segmented human subject. To compute the image features, we implement a stacked-", + "bbox": [ + 75, + 824, + 467, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "hourglass image encoder with bi-linear interpolation to extract pixel-aligned image feature $F_{2D}(\\cdot) \\in \\mathbb{R}^{256}$ . We follow [7, 50] to employ PointNet with 3D-UNet and tri-linear interpolation to extract space-aligned 3D features $F_{3D}(\\cdot) \\in \\mathbb{R}^{128}$ . Distance encoding maps the signed distance to a higher dimensional space $\\mathcal{D}(d) \\in \\mathbb{R}^{13}$ using the high-frequency functions as defined in Eq. (4). We implement our framework in PyTorch [46]. Our SeSDF framework is trained separately for 12 epochs with the learning rate starting from 1e-4 and updated by the factor 0.1 for every 4 epochs, for both single-view and multi-view experiments. Code for SeSDF will be made publicly available. Project page: https://yukangcao.github.io/SeSDF/.", + "bbox": [ + 496, + 233, + 890, + 429 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Datasets and evaluation metrics", + "text_level": 1, + "bbox": [ + 498, + 438, + 779, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We employ the THUman2.0 dataset [65] as our primary testbed. The dataset comprises 526 high-fidelity meshes captured via dense DSLR rigs. Each subject within the dataset is accompanied by its corresponding texture map and fitted SMPL-X parameters. We split the THUman2.0 dataset into a training set with 465 subjects, and a test set with 61 subjects. We render each human subject into 360 images, sequentially separated by $1^{\\circ}$ around the subject, with different albedo to augment the dataset to carry out the experiments.", + "bbox": [ + 496, + 460, + 890, + 611 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further show the generalizability of SeSDF, we also compare our method with others on the CAPE [37] test set, which contains 150 subjects. To conduct quantitative evaluations of different methods, we employ standard Point-to-Surface distance (P2S) and Chamfer distance metrics as evaluation criteria. We compare the reconstructed models from images captured at different angles, i.e., $0^{\\circ}$ , $45^{\\circ}$ , $90^{\\circ}$ , $135^{\\circ}$ , $180^{\\circ}$ , $225^{\\circ}$ , $270^{\\circ}$ , and $315^{\\circ}$ , against the ground truth under corresponding orientations. Besides, we use real-world images for extra qualitative evaluation.", + "bbox": [ + 496, + 612, + 890, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison on single-view setting", + "text_level": 1, + "bbox": [ + 498, + 771, + 799, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluate and compare the performance of single-view 3D human reconstruction between ours and SOTA methods. Specifically, we compare with PIFu [52], PIFuHD [53], PaMIR [71], ARCH [26], ARCH++ [23] and ICON [63]. PHORHUM [5] is not compared here due to the absence of publicly available code base. We retrain PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 dataset for", + "bbox": [ + 496, + 794, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4652", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/86f3087f59438141c1f7c807278d7e98dadc6a592345a56ed56d0d8a0eec9c2a.jpg", + "image_caption": [ + "Figure 4. Comparison with ICON on real-world (top) and THUman2.0 data (bottom). Ours (SeSDF) can produce results with more fine geometry details. Best viewed in PDF with zoom." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 893, + 294 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a fair comparison, and obtain the reconstructions of ARCH and $\\mathrm{ARCH} + +$ with the help of their authors.", + "bbox": [ + 75, + 335, + 468, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative comparison and ablation In Table 1, we compare our method with the SOTA methods, i.e., PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 and CAPE datasets. As can be seen, for all metrics, our method significantly outperforms the SOTA by a large margin on both datasets. Among these SOTA methods, ICON also employs the SMPL-X model to extract SDF to guide learning, while our method consistently outperforms ICON across the board. We also validate the effectiveness of different components of our method. All components have positive effects on the reconstruction results, while the SeSDF module plays the most crucial role in the improvement. By comparing the last two rows, we can see that the SeSDF module brings much more improvement than the SDF derived from the SMPL-X model. By comparing the last row with all others, we can observe that our SeSDF brings the most improvement among all components. By comparing \"Ours\" and \"Ours w/o DE\", we can see that our proposed distance encoding is also effective in improving the performance.", + "bbox": [ + 75, + 368, + 468, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison We present qualitative comparison in Fig. 3 on real-world images with SOTA methods. Our proposed method has the capability to reconstruct fine geometry details and handle the inputs with complicated poses. Among the SOTA methods, ICON also employs SMPL-X to improve the robustness, though in a different way from our work. We provide a further comparison with ICON in Fig. 4 on THUman2.0 and real-world images. As can be seen, our method notably outperforms ICON with more fine details in all cases.", + "bbox": [ + 75, + 657, + 468, + 808 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Comparison on multi-view setting", + "text_level": 1, + "bbox": [ + 76, + 816, + 375, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For multi-view reconstruction, we compare with the SOTA methods PIFu, PIFuHD, and PaMIR which allow multi-view reconstruction. In the experiments, we use three input views unless stated otherwise.", + "bbox": [ + 75, + 840, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative comparison and ablation We report the comparison results in Table 2. To have a fair comparison with other methods which are calibrated, we also implemented our self-calibration method for all of them. We can see that our method outperforms other methods in all cases. Similar to the single-view experiments, by comparing \"Ours\" against \"Ours /wo DE\" and \"Ours /wo SeSDF\", we can see that our distance encoding and SeSDF play critical roles in the performance.", + "bbox": [ + 496, + 335, + 890, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative comparison We present qualitative comparison in Fig. 5 for multi-view reconstruction. The reconstruction results of our method retain more details, e.g., clothing wrinkles and hair topology, which are contained in the ground truth. We provide more results with different numbers of views in the supplementary.", + "bbox": [ + 496, + 474, + 890, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4.1 Further analysis", + "text_level": 1, + "bbox": [ + 500, + 570, + 668, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Self-calibration [74] also introduced an alternative method for self-calibration of multi-view reconstruction by introducing a deformation field to deform points from the canonical space to the camera space, through SMPL linear blend skinning (LBS) weights. We also follow the paper to implement it for SMPL-X in our framework and compare it with our method in Fig. 6. We observe wide-spreading artifacts across the whole body of the reconstruction using the deformation field for the uncalibrated setting. The deformation field is error-prone because the LBS weights are computed to deform the parametric human model, which inherently lacks the fine details of the actual human subject, limiting its final performance and introducing the artifacts for reconstruction.", + "bbox": [ + 496, + 595, + 890, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature fusion We compare our occlusion-aware feature fusion strategy with other alternatives, namely (1) AVGPool [52], (2) SMPLX-visibility [63], and (3) Attention-based method [32] in Fig. 7. As can be seen, our occlusion-aware strategy achieves better performance than the others. See supplementary for more analysis.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4653", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bce13ec17c62b794307ea95fe3694b7131fe99a649d89854b92aac85c5a6d28c.jpg", + "image_caption": [ + "SOTA - Ours", + "Figure 5. Comparison with SOTA methods on the multi-view setting. Ours (SeSDF) consistently retains more geometry details, e.g., clothing wrinkles, hairs, and faces." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 893, + 448 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aec163f8f55bc24475d9d9d2ed147da3809a98625026c90f9a4a60d1840baa91.jpg", + "image_caption": [ + "Figure 6. Comparing our self-calibration method (\"Ours\") with an SMPL-X deformation field alternative (\"DF\"). Best viewed in PDF with zoom." + ], + "image_footnote": [], + "bbox": [ + 78, + 484, + 467, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 674, + 194, + 690 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have presented a new framework for single- and multi-view clothed human reconstruction under an uncalibrated setting. Our framework can take an arbitrary number of input images to reconstruct faithful 3D human models. We have proposed a self-evolved signed distance (SeSDF) module to recover more geometry details, a method for self-calibrating multi-view images via SMPL-X model fitting, and an effective multi-view occlusion-aware feature fusion strategy to aggregate useful features across views for robust reconstruction. Our method notably outperforms previous SOTA methods in both terms of qualitative and quantitative results.", + "bbox": [ + 75, + 700, + 468, + 881 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitation Though our SeSDF can deal with various", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7e5da041a2421b0d5ceb53981fa9eb8daa89e19ceee7ae5af78ecefa70996c19.jpg", + "image_caption": [ + "Figure 7. Comparing our occlusion-aware feature fusion with other alternative fusion strategies." + ], + "image_footnote": [], + "bbox": [ + 504, + 484, + 890, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "poses and retain fine clothing topology, it still has difficulties when handling extremely loose clothes, e.g., dresses, which deviate significantly from the parametric prior.", + "bbox": [ + 498, + 651, + 890, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Potential Social Impact Our method takes a step towards practical tools for real-world application, as it does not require expensive equipment to get the 3D models. However, despite its intended positive usage, there might be potential risks of falsifying human avatars, which unfortunately compromise personal privacy. Transparency and authentication will be helpful to prevent these vicious uses.", + "bbox": [ + 496, + 699, + 890, + 804 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research. We appreciate the very helpful discussions with Dr. Guanying Chen. We also thank Yuliang Xiu, Yuanlu Xu for ARCH and $\\mathrm{ARCH + + }$ results.", + "bbox": [ + 496, + 806, + 890, + 896 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4654", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] https://github.com/danielgatis/rembg.6", + "[2] https://github.com/NVIDIAGameWorks/kaolin.6", + "[3] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. Learning to reconstruct people in clothing from a single rgb camera. In IEEE Conference on Computer Vision and Pattern Recognition, 2019. 2", + "[4] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. Video based reconstruction of 3d people models. 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Mvp-human dataset for 3d human avatar reconstruction from unconstrained frames. arXiv preprint arXiv:2204.11184, 2022.3,7" + ], + "bbox": [ + 78, + 90, + 468, + 891 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4657", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/568571cd-b563-47cc-be1f-30a698863adb_model.json b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/568571cd-b563-47cc-be1f-30a698863adb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a37f69cfd3822457e11fdcbf38ed1b5b1501854e --- /dev/null +++ b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/568571cd-b563-47cc-be1f-30a698863adb_model.json @@ -0,0 +1,2356 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.11, + 0.13, + 0.861, + 0.175 + ], + "angle": 0, + "content": "SeSDF: Self-evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.279, + 0.204, + 0.692, + 0.24 + ], + "angle": 0, + "content": "Yukang Cao Kai Han Kwan-Yee K. Wong \nThe University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.288, + 0.242, + 0.678, + 0.256 + ], + "angle": 0, + "content": "{ykcao, kykwong}@cs.hku.hk kaihanx@hku.hk" + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.311, + 0.201, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.373, + 0.204, + 0.384 + ], + "angle": 0, + "content": "Single-view" + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.461, + 0.202, + 0.472 + ], + "angle": 0, + "content": "Multi-view" + }, + { + "type": "image", + "bbox": [ + 0.22, + 0.292, + 0.831, + 0.524 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.526, + 0.895, + 0.57 + ], + "angle": 0, + "content": "Figure 1. Self-evolved Signed Distance Field (SeSDF): We propose Self-evolved Signed Distance Field (SeSDF), which can flexibly reconstruct 3D clothed human models from a single-view image (top) or uncalibrated multi-view images (bottom). SeSDF can robustly recover fine geometry details from any type of poses, which allows us to generate clothed human avatars." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.581, + 0.314, + 0.597 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We address the problem of clothed human reconstruction from a single image or uncalibrated multi-view images. Existing methods struggle with reconstructing detailed geometry of a clothed human and often require a calibrated setting for multi-view reconstruction. We propose a flexible framework which, by leveraging the parametric SMPL-X model, can take an arbitrary number of input images to reconstruct a clothed human model under an uncalibrated setting. At the core of our framework is our novel self-evolved signed distance field (SeSDF) module which allows the framework to learn to deform the signed distance field (SDF) derived from the fitted SMPL-X model, such that detailed geometry reflecting the actual clothed human can be encoded for better reconstruction. Besides, we propose a simple method for self-calibration of multi-view images via the fitted SMPL-X parameters. This lifts the requirement of tedious manual calibration and largely increases the flexibility of our method. Further, we introduce an effective occlusion-aware feature fusion strategy to account for the most useful fea" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.583, + 0.892, + 0.645 + ], + "angle": 0, + "content": "tures to reconstruct the human model. We thoroughly evaluate our framework on public benchmarks, demonstrating significant superiority over the state-of-the-arts both qualitatively and quantitatively." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.663, + 0.633, + 0.679 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Clothed human reconstruction is a hot topic with increasing demand in real-world applications such as 3D telepresence, game modeling, metaverse [40], etc. Early works show promise under equipment-assisted settings, requiring expensive dense camera rigs [12] and tedious calibration procedures [15]. Parametric models, such as SMPL [36] and SMPL-X [47], have been introduced to model a naked human body with constrained parameters. With the witnessed success of deep learning in many vision tasks, many deep learning methods have been proposed to regress the parameters of such parametric human models from a single [16, 66, 67] or multiple images [6, 13, 68]. However, these methods can only reconstruct a minimally-clothed human model without many details (e.g., hairs and clothes)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4647" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "Recently, methods based on implicit shape representation have reported encouraging performance, showing promising reconstruction with increased details in both single-view [23, 26, 52, 63, 71] and multi-view [24, 25, 54, 55] settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.473, + 0.487 + ], + "angle": 0, + "content": "Despite the stunning results reported by the above methods, their reconstructions remain far from perfect, restricting their practical applications. For instance, state-of-the-art (SOTA) single-view methods, such as PIFuHD [53], PaMIR [71], and \\(\\mathrm{ARCH} + +\\) [23], struggle with many self-occluding non-frontal human poses that widely occur in the real world. ICON [63] can handle these cases but the reconstructions contain serious artifacts (see Fig. 3). On the other hand, many multi-view methods depend on calibrated cameras (e.g., [24, 54, 55]) which are tedious to obtain in practice. Hence, how to carry out multi-view reconstruction with uncalibrated cameras is an important topic to study. Meanwhile, effective multi-view feature fusion is another key factor for robust multi-view reconstruction. Prior techniques for multi-view feature fusion include average pooling [52], SMPL-visibility [63], and attention-based mechanism [70]. However, the reconstruction results based on these fusion techniques still contain notable artifacts in many cases. This indicates that more efforts are needed to derive a better multi-view feature fusion for more robust reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.473, + 0.748 + ], + "angle": 0, + "content": "In this paper, to extract more clothed human details flexibly and robustly from a single RGB image or uncalibrated multi-view RGB images, we present a novel framework, named SeSDF, that employs the parametric model SMPL-X [47] as a 3D prior and combines the merits of both implicit and explicit representations. SeSDF takes a single image or multi-view images as input to predict the occupancy for each 3D location in the space representing the human model. To reconstruct high-frequency details such as hairs and clothes, we introduce a self-evolved signed distance field module that learns to deform the signed distance field (SDF) derived from the fitted SMPL-X model using the input images. The resulting SDF can reflect more accurate geometry details than SMPL-X, which inherently deviates from the actual clothed human model. The SDF refined by our SeSDF module is further encoded to allow for 3D reconstruction with better geometry details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Besides reconstructing a faithful 3D clothed human model from a single image, our SeSDF framework can also work with uncalibrated multi-view images to generate clothed human avatar with enhanced appearance (see Fig. 1). To this end, we first propose a self-calibration method by fitting a shared SMPL-X model across multiview images and projecting the shared model to different images based on the optimized rigid body motion for each input image. Further, we propose an occlusion-aware feature fusing strategy by probing the visibility of each 3D" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "point under different views through ray-tracing, leveraging the SMPL-X model, such that features from visible views will contribute more to the fused feature while those from invisible views will be suppressed." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.154, + 0.822, + 0.168 + ], + "angle": 0, + "content": "The contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.17, + 0.892, + 0.261 + ], + "angle": 0, + "content": "- We propose a flexible framework that, by leveraging the SMPL-X model as a shape prior, can take an arbitrary number of uncalibrated images to perform high-fidelity clothed human reconstruction. At the core of our framework is a self-evolved signed distance field (SeSDF) module for recovering faithful geometry details." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.262, + 0.892, + 0.336 + ], + "angle": 0, + "content": "- For uncalibrated multi-view reconstruction, we propose a simple self-calibration method through leveraging the SMPL-X model, as well as an occlusion-aware feature fusion strategy which takes into account the visibility of a space point under different views via ray-tracing." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.337, + 0.892, + 0.382 + ], + "angle": 0, + "content": "- We thoroughly evaluate our framework on public benchmarks. SeSDF exhibits superior performances over current state-of-the-arts both qualitatively and quantitatively." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.17, + 0.892, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.399, + 0.642, + 0.416 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.686 + ], + "angle": 0, + "content": "Parametric 3D human model Parametric 3D human reconstruction [21, 30, 36, 44, 47] paves the path for 3D human model. SMPL [36, 67] was built on convolutional networks and statistics collected from a wide range of human populations. SMPL-X [47, 66] extended SMPL with more body joints, keypoints, and expression parameters. Later substantial supervision strategies were proposed to regress the model parameters. Examples include semantic segmentation [43, 64], human body silhouette [49], joints [16], motion dynamics [30, 33], texture consistency [48], and attention-regressor [31]. Multi-view [6, 13, 68, 69] and multi-person [57, 58] setups were also sought for various scenarios. Complex human clothing and hair topology were also the goals for later parametric methods [3, 4, 29, 62, 73]. However, due to the minimal-clothing assumption of the parametric models, these methods can retain little geometry details such as hairs and clothes in their reconstructions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Single-view (implicit) human reconstruction Many methods have been proposed in the deep learning era to reconstruct a 3D human model from a single image. For example, voxel-based methods [18, 27, 59, 60, 72, 72] reconstruct a volumetric representation of the human model. Two-stage inference [56], visual hull [41] and front-back depth method [17] were then proposed to improve the reconstruction performance and efficiency. However, the high computational cost of these methods limits their real-world applications. Implicit function methods have recently been introduced to predict either the occupancy field [10, 38] or signed distance field [8, 28, 45] using neural networks. PIFu [52] presents promising results with a pixel-aligned implicit function. Follow-up works exploited 3D features" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4648" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "to solve the depth-ambiguity problem [71], achieve animatable model [23, 26], or improve the reconstruction details [7]. PIFuHD [53] and FITE [35] apply a multi-stage method to improve clothing topology in the reconstruction. Geo-PIFu [22] proposes to compute 3D features directly from images. ICON [63] exploits the SMPL-based signed distance filed as guidance to help produce a robust reconstruction, with a smpl-visibility based method to choose features from front or back sides. PHORHUM [5] explores shading and illumination information to infer better geometry and texture. Encouraging improvements have been reported by these methods. However, their performance on non-frontal human images are still far from being robust and satisfactory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.669 + ], + "angle": 0, + "content": "Multi-view implicit human reconstruction Multi-view reconstruction is conceptually a more natural choice as information from different views can compensate each other for better reconstruction. Under a calibrated setting, PIFu [52] proposes to fuse features from multi-views by average pooling after being embedded using an MLP. StereoPIFu [24] takes as input a pair of stereo images, and performs depth-aware reconstruction. DiffuStereo [55] employs diffusion models for multi-view stereo human reconstruction. DoubleField [54] combines the surface field and radiance fields to improve both geometry and texture inference. Effi-MVS [61] explores the dynamic cost volume for reduced computational cost. DeepMultiCap [70] handles the multi-person reconstruction with multi-view images. Neural-Human-Performer [32] proposes a multi-view transformer to fuse features for multi-view reconstruction. Despite promising results have been achieved, these methods require a large number of views and camera calibration. MVP-Human [74] makes use of the deformation fields and handles multi-view inputs under an uncalibrated setting, but the reconstruction quality lags far behind the calibrated methods. For calibrated methods, their models still produce undesirable artifacts for many self-occluding nonfrontal poses and miss many geometry details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.17, + 0.691 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.47, + 0.837 + ], + "angle": 0, + "content": "We propose an implicit function based framework for reconstructing 3D clothed human models from a single image or uncalibrated multi-view images (see Fig. 2). At the core of our framework are a self-evolved signed distance field (SeSDF) module and an occlusion-aware feature fusion module. Next, we will first introduce the preliminary for SeSDF in Sec. 3.1. We will then describe SeSDF for single-view reconstruction in Sec. 3.2, followed by uncalibrated multi-view reconstruction in Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.208, + 0.861 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Surface by implicit function Implicit functions [14] have been shown to be effective for 3D reconstruction from im" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "ages or videos. Typically, an implicit function is implemented as an MLP, which takes the 3D coordinate \\( X \\) and an optionally associated feature \\( F \\) of a 3D point as input, and outputs the corresponding occupancy as a scalar value. Commonly employed features include pixel-aligned image features [52, 53] and space-aligned 3D features [7, 26, 71]. Formally, the implicit function can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.211, + 0.892, + 0.228 + ], + "angle": 0, + "content": "\\[\nf _ {v} (X, F) \\mapsto [ 0, 1 ] \\in \\mathbb {R}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.336 + ], + "angle": 0, + "content": "SMPL-X The parametric human model SMPL-X represents the 3D shape by incorporating body vertices, joints, face and hands landmarks, and expression parameters. Formally, by assembling pose parameters \\(\\theta\\), shape parameters \\(\\beta\\), and facial expression parameters \\(\\phi\\), SMPL-X human model can be expressed by a function \\(M(\\cdot)\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.348, + 0.813, + 0.365 + ], + "angle": 0, + "content": "\\[\nM (\\beta , \\theta , \\phi) = W (T _ {p} (\\beta , \\theta , \\phi), J (\\beta), \\theta , \\mathcal {W}),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.366, + 0.888, + 0.384 + ], + "angle": 0, + "content": "\\[\nT _ {p} (\\beta , \\theta , \\phi) = \\bar {T} + B _ {S} (\\beta ; \\mathcal {S}) + B _ {E} (\\phi ; \\mathcal {E}) + B _ {p} (\\theta ; \\mathcal {P}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.503 + ], + "angle": 0, + "content": "where \\(W(\\cdot)\\) is the linear blend skinning function, \\(J(\\beta)\\) is the joint location, and \\(\\mathcal{W}\\) denotes the blend weights. \\(T_{p}(\\cdot)\\) poses the SMPL-X canonical model \\(\\bar{T}\\) by shape blend shape function \\(B_{S}\\), expression blend shape function \\(B_{E}\\), and pose blend shape function \\(B_{P}\\). \\(\\mathcal{S}\\) and \\(\\mathcal{P}\\) are the principal components of vertex displacements, and \\(\\mathcal{E}\\) represents the principal components capturing variations of facial expressions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.688 + ], + "angle": 0, + "content": "SMPL-X optimization Given a human image, we can fit the SMPL-X model parameters by [16]. However, such fitted models often suffer from misalignment. We use the well-aligned SMPL-X models provided in the training data to provide shape prior to train our framework. At test time, we do not have such well-aligned models. Hence, to avoid errors and artifacts caused by the misalignment during testing, we optimize the SMPL-X parameters by projecting the SMPL-X model onto the input image and maximizing the Intersection over Union (IoU) between the projection and body mask [9, 63], and minimizing the 2D keypoint distances. Please refer to the supplementary for details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.699, + 0.741, + 0.715 + ], + "angle": 0, + "content": "3.2. Single-view reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.892, + 0.874 + ], + "angle": 0, + "content": "Given an input image \\( \\pmb{I} \\) and an optimized SMPL-X mesh \\( S \\), SeSDF incorporates pixel-aligned image features \\( F_{2D} \\) extracted from \\( \\pmb{I} \\), space-aligned 3D features \\( F_{3D} \\) extracted from \\( S \\), and the self-evolved signed distance field \\( d \\) to predict occupancy using an MLP. By applying marching cube [34] on the occupancy predictions in the 3D space, SeSDF robustly reconstructs a 3D clothed human model with faithful details, including the clothing topology. Given a 3D point \\( X \\), the implicit function for single-view reconstruction can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\[\nf _ {o} \\left(F _ {2 D} (X), F _ {3 D} (X), \\mathcal {D} (d (X)), \\mathbf {n} (X), Z (X)\\right) \\mapsto [ 0, 1 ], \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4649" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.093, + 0.895, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.39, + 0.895, + 0.502 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed SeSDF framework. It takes a single image or uncalibrated multi-view images as input to predict the occupancy for each 3D location in the space for shape reconstruction. We first fit a SMPL-X model to the input image(s) which serves as a shape prior and provides space-aligned 3D features. At the core of our method is our proposed self-evolved signed distance field (SeSDF) module, which learns a refined signed distance field (SDF) to better reflect the actual clothed human subject rather than the minimally-clothed SMPL-X model. SeSDF module takes pixel-aligned image features, space-aligned 3D features, SDF with distance encoding, and SMPL-X vertex normal as input to predict the refined SDF and normal value. For multi-view reconstruction, we propose a SMPL-X based self-calibration method to eliminate the need for manual calibration and an occlusion-aware feature fusion strategy to effectively accumulate features from different views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.471, + 0.559 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}(\\cdot)\\) and \\(Z(\\cdot)\\) denote distance encoding and depth value respectively, and \\(d(\\cdot)\\) and \\(\\mathbf{n}(\\cdot)\\) are the signed distance and normal output by our SeSDF module." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.652 + ], + "angle": 0, + "content": "Pixel-aligned image feature We apply a stacked-hourglass encoder [42, 52] to the input image \\( I \\in \\mathbb{R}^{512 \\times 512 \\times 3} \\) to produce an image feature map \\( E_{I}(I) \\in \\mathbb{R}^{256 \\times 128 \\times 128} \\). We then obtain the pixel-aligned image feature for the projection of a 3D point using bi-linear interpolation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Space-aligned 3D feature We apply PointNet [51] and 3D-UNet [11] to extract 3D features [7, 50] from the optimized SMPL-X mesh. Our 3D encoder first processes the whole 10,475 vertices of the mesh to generate hierarchical 3D point features, which are transformed into a 3D feature volume via average pooling. 3D-UNet is then applied to output the final 3D feature volume \\( E_{S}(S) \\in \\mathbb{R}^{128 \\times 64 \\times 64 \\times 64} \\). Finally we obtain the space-aligned 3D feature for a 3D point via tri-linear interpolation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Self-evolved signed distance field The signed distance field (SDF) derived from the SMPL-X model [63] provides a strong prior for estimating the occupancy. However, the SMPL-X model does not model geometric details of the human, such as the cloth topology, and thus the resulting SDF will unavoidably deviate from the true SDF of the actual clothed human model. Directly employing this SDF" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.895, + 0.695 + ], + "angle": 0, + "content": "for occupancy prediction will therefore induce error in the reconstruction. To remedy this problem and recover plausible geometry details in the reconstruction, we propose a novel self-evolved signed distance filed (SeSDF) module. This module is trained to evolve the SDF derived from the SMPL-X model to better reflect the actual clothed human model. Instead of predicting only the signed distance \\( d(\\cdot) \\in \\mathbb{R} \\), our SeSDF module further predict the normal \\( \\mathbf{n}(\\cdot) \\in \\mathbb{R}^3 \\) which provides additional surface orientation information to guide the implicit function to better predict occupancy and capture fine shape details. Concretely, SeSDF module is implemented as an MLP and formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.702, + 0.892, + 0.721 + ], + "angle": 0, + "content": "\\[\nf _ {s d} \\left(F _ {2 D} (X), F _ {3 D} (X), \\mathcal {D} \\left(d ^ {\\prime} (X)\\right), \\mathbf {n} ^ {\\prime} (X)\\right) \\mapsto (d, \\mathbf {n}), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.895, + 0.772 + ], + "angle": 0, + "content": "where \\(d'(\\cdot) \\in \\mathbb{R}\\) denotes the SDF derived from the SMPL-X model and \\(\\mathbf{n}'(\\cdot) \\in \\mathbb{R}^3\\) represents the normal obtained from the closest SMPL-X vertex to \\(X\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.895, + 0.837 + ], + "angle": 0, + "content": "Distance encoding Inspired by the positional encoding adopted in NeRF [39], we adopt a distance encoding that maps the signed distance \\( d \\) to a higher dimensional space using high frequency functions:" + }, + { + "type": "equation", + "bbox": [ + 0.505, + 0.84, + 0.892, + 0.871 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} (d) = \\left(d, \\sin \\left(2 ^ {0} \\pi d\\right), \\cos \\left(2 ^ {0} \\pi d\\right), \\dots , \\sin \\left(2 ^ {L} \\pi d\\right), \\cos \\left(2 ^ {L} \\pi d\\right)\\right). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In our experiments, we set \\(L = 5\\). The encoded signed distance \\(\\mathcal{D}(d)\\) is concatenated with the predicted normal \\(\\mathbf{n}(\\cdot)\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4650" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "2D feature \\( F_{2D}(\\cdot) \\) and 3D feature \\( F_{3D}(\\cdot) \\), and fed to the implicit function \\( f_{o}(\\cdot) \\) for occupancy prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.124, + 0.468, + 0.215 + ], + "angle": 0, + "content": "Training objectives To consistently regress SeSDF and simulate realistic cloth topology, we consider two groups of sampling points, namely surface samples \\( G_{s} \\), and occupancy-target samples \\( G_{o} \\). Points in \\( G_{s} \\) are uniformly sampled on the mesh surface, while points in \\( G_{o} \\) are sampled following the strategy proposed in PIFu [52]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.215, + 0.456, + 0.23 + ], + "angle": 0, + "content": "For points in \\( G_{s} \\), we adopt the following loss function" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.239, + 0.469, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\frac {1}{| G _ {s} |} \\sum_ {X \\in G _ {s}} \\lambda_ {d} | d (X) | + \\lambda_ {n} \\| \\mathbf {n} (X) - \\mathbf {n} _ {g t} (X) \\|, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.281, + 0.469, + 0.326 + ], + "angle": 0, + "content": "where \\(\\mathbf{n}_{gt}(X)\\) denotes the ground-truth normal at the surface point \\(X\\). For points in \\(G_{o}\\), we adopt the following loss function" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.333, + 0.469, + 0.365 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {o} = \\frac {1}{| G _ {o} |} \\sum_ {X \\in G _ {o}} B C E (\\mathcal {O} (X) - \\mathcal {O} _ {g t} (X)), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.375, + 0.469, + 0.451 + ], + "angle": 0, + "content": "where \\(\\mathcal{O}(X)\\) denotes the predicted occupancy at \\(X\\) computed using Eq. (3) and Eq. (2), \\(\\mathcal{O}_{gt}(X)\\) is the ground-truth occupancy at \\(X\\), and \\(BCE(\\cdot)\\) denotes the binary cross entropy. Following IGR [20], we add an eikonal normal regularization term to smooth the surface by:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.461, + 0.469, + 0.499 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r} = \\frac {1}{| G _ {o} |} \\sum_ {X \\in G _ {o}} \\left(\\left\\| \\mathbf {n} (X) \\right\\| - 1\\right) ^ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.509, + 0.34, + 0.525 + ], + "angle": 0, + "content": "The overall loss function is given by" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.537, + 0.469, + 0.552 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S e S D F} = \\lambda_ {s} \\mathcal {L} _ {s} + \\lambda_ {o} \\mathcal {L} _ {o} + \\lambda_ {r} \\mathcal {L} _ {r}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.564, + 0.47, + 0.595 + ], + "angle": 0, + "content": "where \\(\\lambda_{s},\\lambda_{o}\\) ,and \\(\\lambda_{r}\\) are weights to balance the effect of the respective loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.417, + 0.619 + ], + "angle": 0, + "content": "3.3. Uncalibrated multi-view reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.469, + 0.791 + ], + "angle": 0, + "content": "To allow our SeSDF framework work with uncalibrated multi-view images, we present a simple self-calibration method to estimate the relative camera pose for each image through fitting a SMPL-X model to all the input images. In addition, we propose an occlusion-aware feature fusion strategy to fuse features from different views effectively. Ideally, we would like to fuse only features from non-occluded views as features from occluded views are just noise which at best provide zero contribution to occupancy prediction but may also seriously degrade the fused feature in the worse case." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.469, + 0.853 + ], + "angle": 0, + "content": "Our multi-view framework is illustrated in Fig. 2. In principle, it can work with an arbitrary number of views and the number of views used in training and testing do not even need to be the same." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Self-calibration via SMPL-X model fitting Given \\( n \\) uncalibrated multi-view images, we first fit a SMPL-X model to each image independently using the method described in" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.272 + ], + "angle": 0, + "content": "Sec. 3.1. We then take the averages of the shape, pose and expression parameters of these \\( n \\) fitted models and use them to initialize a shared SMPL-X model. Next, we optimize the shape, pose and expression parameters of this shared SMPL-X model and the global orientation parameters for the \\( n \\) views simultaneously by maximizing the IoU between the projection and body mask, and minimizing the 2d keypoint distances on each of the \\( n \\) images. After optimization, the global orientation parameters for the \\( n \\) views then give us the rigid body motion that transforms a point from the SMPL-X model centered coordinate system to the camera centered coordinate system of each view." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.273, + 0.892, + 0.394 + ], + "angle": 0, + "content": "To perform multi-view reconstruction, we can sample 3D points in the model centered coordinate system, transform them into the respective camera coordinate systems, and compute 2D/3D features and the self-evolved signed distance from each view. Finally, these features from \\( n \\) different views are fused by our occlusion-aware feature fusion strategy (to be introduced next) and fed to the implicit function \\( f_{o}(\\cdot) \\) to predict the occupancy value." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.893, + 0.699 + ], + "angle": 0, + "content": "Occlusion-aware feature fusion Conceptually, features obtained from different views would give rise to predictions of different quality. For instance, image feature for a 3D point extracted from a frontal non-occluded view would be expected to give the best prediction, whereas image feature for the same point but extracted from an occluded view or a lateral view would be expected to give poor prediction. Hence, average pooling would in principle not be the best way for feature fusion. Researchers therefore explored different fusion strategies, such as SMPL-visibility based [63] and attention based [70] approaches, but all of these still produce undesirable artifacts in their reconstructions (see Fig. 7). To lessen the effect of features extracted from non-optimal views, we propose a novel occlusion-aware feature fusion strategy based on ray tracing [19] with the fitted SMPL-X model. Given a 3D point \\( X \\), we cast a ray from \\( X \\) to the \\( i \\)-th view through orthogonal projection and find the intersection point \\( X_{i}^{\\prime} \\) with the SMPL-X model that is the closest to the image (see Fig. 2). We then compute a weight for the feature \\( F_{i}(X) \\) extracted from the \\( i \\)-th view by" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.704, + 0.892, + 0.737 + ], + "angle": 0, + "content": "\\[\nw _ {i} (X) = \\frac {1}{\\left| Z _ {i} (X) - Z _ {i} \\left(X _ {i} ^ {\\prime}\\right) \\right|}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.742, + 0.82, + 0.758 + ], + "angle": 0, + "content": "Finally, we fuse all features from the \\(n\\) views by" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.763, + 0.892, + 0.8 + ], + "angle": 0, + "content": "\\[\nF _ {f u s e d} (X) = \\frac {\\sum_ {i = 1} ^ {n} w _ {i} (X) F _ {i} (X)}{\\sum_ {i = 1} ^ {n} w _ {i} (X)}. \\tag {10}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.633, + 0.833 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate the performance of our SeSDF both qualitatively and quantitatively, and provide comparisons with other SOTA methods under both single-view and multiview setups." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4651" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.081, + 0.09, + 0.887, + 0.104 + ], + "angle": 0, + "content": "Table 1. Qualitative comparison on the single-view setting. We report Chamfer Distance and P2S metrics (numbers the lower the better)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.107, + 0.892, + 0.222 + ], + "angle": 0, + "content": "
MethodFeature IncludedQuantitative Number
THuman2.0CAPE
2D FeatureNormal Information3D FeatureSMPLX Signed Distanceself-evolved Signed DistanceChamfer Distance↓P2S↓Chmafer Distance↓P2S↓
PIFu [52]✓2.4032.3883.0592.818
PIFuHD [53]✓✓2.0081.9652.5712.427
PaMIR [71]✓✓1.4781.4511.6821.438
ICON [63]✓✓✓1.3011.2591.5331.431
Ours w/o DE✓✓✓✓1.0991.0341.3771.261
Ours w/o SeSDF✓✓✓✓1.2451.2001.4731.390
Ours✓✓✓✓1.0270.9711.3031.219
" + }, + { + "type": "table_caption", + "bbox": [ + 0.096, + 0.233, + 0.449, + 0.246 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on the multi-view setting." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.248, + 0.468, + 0.386 + ], + "angle": 0, + "content": "
MethodTHuman2.0CAPE
Chamfer Distance↓P2S↓Chmafer Distance↓P2S↓
multi-view PIFu [52]0.8640.8380.9200.876
multi-view PIFuHD [53]0.8310.8040.8830.849
multi-view PaMIR [71]0.8070.7620.8580.819
Ours w/o DE0.7950.7490.8490.811
Ours w/o SeSDF0.8020.7550.8540.815
Ours0.7910.7420.8410.800
Ours w/ Attention0.7940.7430.8450.803
Ours w/ SMPLX-Vis0.8410.8320.9250.917
Ours w/ Normal-Fusion0.8010.7540.8500.812
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.395, + 0.47, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.61, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Figure 3. Qualitative comparison with SOTA methods on real-world images. Our method can reconstruct fine details and work robustly under challenge poses. Best viewed in PDF with zoom." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.291, + 0.68 + ], + "angle": 0, + "content": "4.1. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.468, + 0.822 + ], + "angle": 0, + "content": "For each training subject, we sample (a) 5,000 surface points as \\( G_{s} \\), which are evenly distributed on the mesh surface; (b) 5,000 occupancy-target points as \\( G_{o} \\) in the 3D space, for which we follow the sampling strategy in [52]. In particular, 15/16 points in \\( G_{o} \\) are evenly sampled on the mesh surface. Gaussian perturbation is then applied to them along the surface normal direction. The rest 1/16 points are randomly sampled within the predefined 3D space where the mesh lies in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.9 + ], + "angle": 0, + "content": "We employ Rembg [1] to segment out the background for real-world images and use Kaolin [2] to calculate the SDF from the SMPL-X model. We apply PIXIE [16] to estimate the SMPL-X model for the segmented human subject. To compute the image features, we implement a stacked-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.234, + 0.892, + 0.43 + ], + "angle": 0, + "content": "hourglass image encoder with bi-linear interpolation to extract pixel-aligned image feature \\( F_{2D}(\\cdot) \\in \\mathbb{R}^{256} \\). We follow [7, 50] to employ PointNet with 3D-UNet and tri-linear interpolation to extract space-aligned 3D features \\( F_{3D}(\\cdot) \\in \\mathbb{R}^{128} \\). Distance encoding maps the signed distance to a higher dimensional space \\( \\mathcal{D}(d) \\in \\mathbb{R}^{13} \\) using the high-frequency functions as defined in Eq. (4). We implement our framework in PyTorch [46]. Our SeSDF framework is trained separately for 12 epochs with the learning rate starting from 1e-4 and updated by the factor 0.1 for every 4 epochs, for both single-view and multi-view experiments. Code for SeSDF will be made publicly available. Project page: https://yukangcao.github.io/SeSDF/." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.439, + 0.78, + 0.453 + ], + "angle": 0, + "content": "4.2. Datasets and evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.612 + ], + "angle": 0, + "content": "We employ the THUman2.0 dataset [65] as our primary testbed. The dataset comprises 526 high-fidelity meshes captured via dense DSLR rigs. Each subject within the dataset is accompanied by its corresponding texture map and fitted SMPL-X parameters. We split the THUman2.0 dataset into a training set with 465 subjects, and a test set with 61 subjects. We render each human subject into 360 images, sequentially separated by \\(1^{\\circ}\\) around the subject, with different albedo to augment the dataset to carry out the experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.763 + ], + "angle": 0, + "content": "To further show the generalizability of SeSDF, we also compare our method with others on the CAPE [37] test set, which contains 150 subjects. To conduct quantitative evaluations of different methods, we employ standard Point-to-Surface distance (P2S) and Chamfer distance metrics as evaluation criteria. We compare the reconstructed models from images captured at different angles, i.e., \\(0^{\\circ}\\), \\(45^{\\circ}\\), \\(90^{\\circ}\\), \\(135^{\\circ}\\), \\(180^{\\circ}\\), \\(225^{\\circ}\\), \\(270^{\\circ}\\), and \\(315^{\\circ}\\), against the ground truth under corresponding orientations. Besides, we use real-world images for extra qualitative evaluation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.8, + 0.788 + ], + "angle": 0, + "content": "4.3. Comparison on single-view setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.9 + ], + "angle": 0, + "content": "We first evaluate and compare the performance of single-view 3D human reconstruction between ours and SOTA methods. Specifically, we compare with PIFu [52], PIFuHD [53], PaMIR [71], ARCH [26], ARCH++ [23] and ICON [63]. PHORHUM [5] is not compared here due to the absence of publicly available code base. We retrain PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 dataset for" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4652" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.086, + 0.894, + 0.295 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Figure 4. Comparison with ICON on real-world (top) and THUman2.0 data (bottom). Ours (SeSDF) can produce results with more fine geometry details. Best viewed in PDF with zoom." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.47, + 0.366 + ], + "angle": 0, + "content": "a fair comparison, and obtain the reconstructions of ARCH and \\(\\mathrm{ARCH} + +\\) with the help of their authors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Quantitative comparison and ablation In Table 1, we compare our method with the SOTA methods, i.e., PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 and CAPE datasets. As can be seen, for all metrics, our method significantly outperforms the SOTA by a large margin on both datasets. Among these SOTA methods, ICON also employs the SMPL-X model to extract SDF to guide learning, while our method consistently outperforms ICON across the board. We also validate the effectiveness of different components of our method. All components have positive effects on the reconstruction results, while the SeSDF module plays the most crucial role in the improvement. By comparing the last two rows, we can see that the SeSDF module brings much more improvement than the SDF derived from the SMPL-X model. By comparing the last row with all others, we can observe that our SeSDF brings the most improvement among all components. By comparing \"Ours\" and \"Ours w/o DE\", we can see that our proposed distance encoding is also effective in improving the performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Qualitative comparison We present qualitative comparison in Fig. 3 on real-world images with SOTA methods. Our proposed method has the capability to reconstruct fine geometry details and handle the inputs with complicated poses. Among the SOTA methods, ICON also employs SMPL-X to improve the robustness, though in a different way from our work. We provide a further comparison with ICON in Fig. 4 on THUman2.0 and real-world images. As can be seen, our method notably outperforms ICON with more fine details in all cases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.376, + 0.835 + ], + "angle": 0, + "content": "4.4. Comparison on multi-view setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.9 + ], + "angle": 0, + "content": "For multi-view reconstruction, we compare with the SOTA methods PIFu, PIFuHD, and PaMIR which allow multi-view reconstruction. In the experiments, we use three input views unless stated otherwise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.337, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Quantitative comparison and ablation We report the comparison results in Table 2. To have a fair comparison with other methods which are calibrated, we also implemented our self-calibration method for all of them. We can see that our method outperforms other methods in all cases. Similar to the single-view experiments, by comparing \"Ours\" against \"Ours /wo DE\" and \"Ours /wo SeSDF\", we can see that our distance encoding and SeSDF play critical roles in the performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.566 + ], + "angle": 0, + "content": "Qualitative comparison We present qualitative comparison in Fig. 5 for multi-view reconstruction. The reconstruction results of our method retain more details, e.g., clothing wrinkles and hair topology, which are contained in the ground truth. We provide more results with different numbers of views in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.571, + 0.669, + 0.585 + ], + "angle": 0, + "content": "4.4.1 Further analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Self-calibration [74] also introduced an alternative method for self-calibration of multi-view reconstruction by introducing a deformation field to deform points from the canonical space to the camera space, through SMPL linear blend skinning (LBS) weights. We also follow the paper to implement it for SMPL-X in our framework and compare it with our method in Fig. 6. We observe wide-spreading artifacts across the whole body of the reconstruction using the deformation field for the uncalibrated setting. The deformation field is error-prone because the LBS weights are computed to deform the parametric human model, which inherently lacks the fine details of the actual human subject, limiting its final performance and introducing the artifacts for reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Feature fusion We compare our occlusion-aware feature fusion strategy with other alternatives, namely (1) AVGPool [52], (2) SMPLX-visibility [63], and (3) Attention-based method [32] in Fig. 7. As can be seen, our occlusion-aware strategy achieves better performance than the others. See supplementary for more analysis." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4653" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.089, + 0.143, + 0.1 + ], + "angle": 0, + "content": "SOTA - Ours" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.894, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.45, + 0.891, + 0.477 + ], + "angle": 0, + "content": "Figure 5. Comparison with SOTA methods on the multi-view setting. Ours (SeSDF) consistently retains more geometry details, e.g., clothing wrinkles, hairs, and faces." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.486, + 0.468, + 0.619 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.622, + 0.468, + 0.662 + ], + "angle": 0, + "content": "Figure 6. Comparing our self-calibration method (\"Ours\") with an SMPL-X deformation field alternative (\"DF\"). Best viewed in PDF with zoom." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.675, + 0.195, + 0.691 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.469, + 0.882 + ], + "angle": 0, + "content": "In this paper, we have presented a new framework for single- and multi-view clothed human reconstruction under an uncalibrated setting. Our framework can take an arbitrary number of input images to reconstruct faithful 3D human models. We have proposed a self-evolved signed distance (SeSDF) module to recover more geometry details, a method for self-calibrating multi-view images via SMPL-X model fitting, and an effective multi-view occlusion-aware feature fusion strategy to aggregate useful features across views for robust reconstruction. Our method notably outperforms previous SOTA methods in both terms of qualitative and quantitative results." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Limitation Though our SeSDF can deal with various" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.486, + 0.891, + 0.604 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.605, + 0.891, + 0.634 + ], + "angle": 0, + "content": "Figure 7. Comparing our occlusion-aware feature fusion with other alternative fusion strategies." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.652, + 0.891, + 0.698 + ], + "angle": 0, + "content": "poses and retain fine clothing topology, it still has difficulties when handling extremely loose clothes, e.g., dresses, which deviate significantly from the parametric prior." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.805 + ], + "angle": 0, + "content": "Potential Social Impact Our method takes a step towards practical tools for real-world application, as it does not require expensive equipment to get the 3D models. However, despite its intended positive usage, there might be potential risks of falsifying human avatars, which unfortunately compromise personal privacy. Transparency and authentication will be helpful to prevent these vicious uses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.808, + 0.892, + 0.897 + ], + "angle": 0, + "content": "Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research. We appreciate the very helpful discussions with Dr. Guanying Chen. We also thank Yuliang Xiu, Yuanlu Xu for ARCH and \\(\\mathrm{ARCH + + }\\) results." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4654" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.449, + 0.129 + ], + "angle": 0, + "content": "[1] https://github.com/danielgatis/rembg.6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.129, + 0.469, + 0.154 + ], + "angle": 0, + "content": "[2] https://github.com/NVIDIAGameWorks/kaolin.6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.155, + 0.469, + 0.222 + ], + "angle": 0, + "content": "[3] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. Learning to reconstruct people in clothing from a single rgb camera. 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Mvp-human dataset for 3d human avatar reconstruction from unconstrained frames. arXiv preprint arXiv:2204.11184, 2022.3,7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.892 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4657" + } + ] +] \ No newline at end of file diff --git a/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/568571cd-b563-47cc-be1f-30a698863adb_origin.pdf b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/568571cd-b563-47cc-be1f-30a698863adb_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4fd5d2450c2c1101f35dd2b84f482439e272bb97 --- /dev/null +++ b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/568571cd-b563-47cc-be1f-30a698863adb_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8c4284f54e42768332cd01d9f037b2e7b25c60d305814efc0e720287281c929a +size 9256385 diff --git a/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/full.md b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2359e755349c312a16accff05d26cb5ee390a76f --- /dev/null +++ b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/full.md @@ -0,0 +1,327 @@ +# SeSDF: Self-evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction + +Yukang Cao Kai Han Kwan-Yee K. Wong +The University of Hong Kong + +{ykcao, kykwong}@cs.hku.hk kaihanx@hku.hk + +![](images/764031e6407c55e4ce2cfc61566261936cbb877ffeb80c41bc9c7634305aab57.jpg) +Single-view + +![](images/85a9016202a73e5182557579542ecacf614d9f7da468d06ea10aedf2b5cc4c7e.jpg) +Multi-view +Figure 1. Self-evolved Signed Distance Field (SeSDF): We propose Self-evolved Signed Distance Field (SeSDF), which can flexibly reconstruct 3D clothed human models from a single-view image (top) or uncalibrated multi-view images (bottom). SeSDF can robustly recover fine geometry details from any type of poses, which allows us to generate clothed human avatars. + +# Abstract + +We address the problem of clothed human reconstruction from a single image or uncalibrated multi-view images. Existing methods struggle with reconstructing detailed geometry of a clothed human and often require a calibrated setting for multi-view reconstruction. We propose a flexible framework which, by leveraging the parametric SMPL-X model, can take an arbitrary number of input images to reconstruct a clothed human model under an uncalibrated setting. At the core of our framework is our novel self-evolved signed distance field (SeSDF) module which allows the framework to learn to deform the signed distance field (SDF) derived from the fitted SMPL-X model, such that detailed geometry reflecting the actual clothed human can be encoded for better reconstruction. Besides, we propose a simple method for self-calibration of multi-view images via the fitted SMPL-X parameters. This lifts the requirement of tedious manual calibration and largely increases the flexibility of our method. Further, we introduce an effective occlusion-aware feature fusion strategy to account for the most useful fea + +tures to reconstruct the human model. We thoroughly evaluate our framework on public benchmarks, demonstrating significant superiority over the state-of-the-arts both qualitatively and quantitatively. + +# 1. Introduction + +Clothed human reconstruction is a hot topic with increasing demand in real-world applications such as 3D telepresence, game modeling, metaverse [40], etc. Early works show promise under equipment-assisted settings, requiring expensive dense camera rigs [12] and tedious calibration procedures [15]. Parametric models, such as SMPL [36] and SMPL-X [47], have been introduced to model a naked human body with constrained parameters. With the witnessed success of deep learning in many vision tasks, many deep learning methods have been proposed to regress the parameters of such parametric human models from a single [16, 66, 67] or multiple images [6, 13, 68]. However, these methods can only reconstruct a minimally-clothed human model without many details (e.g., hairs and clothes). + +Recently, methods based on implicit shape representation have reported encouraging performance, showing promising reconstruction with increased details in both single-view [23, 26, 52, 63, 71] and multi-view [24, 25, 54, 55] settings. + +Despite the stunning results reported by the above methods, their reconstructions remain far from perfect, restricting their practical applications. For instance, state-of-the-art (SOTA) single-view methods, such as PIFuHD [53], PaMIR [71], and $\mathrm{ARCH} + +$ [23], struggle with many self-occluding non-frontal human poses that widely occur in the real world. ICON [63] can handle these cases but the reconstructions contain serious artifacts (see Fig. 3). On the other hand, many multi-view methods depend on calibrated cameras (e.g., [24, 54, 55]) which are tedious to obtain in practice. Hence, how to carry out multi-view reconstruction with uncalibrated cameras is an important topic to study. Meanwhile, effective multi-view feature fusion is another key factor for robust multi-view reconstruction. Prior techniques for multi-view feature fusion include average pooling [52], SMPL-visibility [63], and attention-based mechanism [70]. However, the reconstruction results based on these fusion techniques still contain notable artifacts in many cases. This indicates that more efforts are needed to derive a better multi-view feature fusion for more robust reconstruction. + +In this paper, to extract more clothed human details flexibly and robustly from a single RGB image or uncalibrated multi-view RGB images, we present a novel framework, named SeSDF, that employs the parametric model SMPL-X [47] as a 3D prior and combines the merits of both implicit and explicit representations. SeSDF takes a single image or multi-view images as input to predict the occupancy for each 3D location in the space representing the human model. To reconstruct high-frequency details such as hairs and clothes, we introduce a self-evolved signed distance field module that learns to deform the signed distance field (SDF) derived from the fitted SMPL-X model using the input images. The resulting SDF can reflect more accurate geometry details than SMPL-X, which inherently deviates from the actual clothed human model. The SDF refined by our SeSDF module is further encoded to allow for 3D reconstruction with better geometry details. + +Besides reconstructing a faithful 3D clothed human model from a single image, our SeSDF framework can also work with uncalibrated multi-view images to generate clothed human avatar with enhanced appearance (see Fig. 1). To this end, we first propose a self-calibration method by fitting a shared SMPL-X model across multiview images and projecting the shared model to different images based on the optimized rigid body motion for each input image. Further, we propose an occlusion-aware feature fusing strategy by probing the visibility of each 3D + +point under different views through ray-tracing, leveraging the SMPL-X model, such that features from visible views will contribute more to the fused feature while those from invisible views will be suppressed. + +The contributions are summarized as follows: + +- We propose a flexible framework that, by leveraging the SMPL-X model as a shape prior, can take an arbitrary number of uncalibrated images to perform high-fidelity clothed human reconstruction. At the core of our framework is a self-evolved signed distance field (SeSDF) module for recovering faithful geometry details. +- For uncalibrated multi-view reconstruction, we propose a simple self-calibration method through leveraging the SMPL-X model, as well as an occlusion-aware feature fusion strategy which takes into account the visibility of a space point under different views via ray-tracing. +- We thoroughly evaluate our framework on public benchmarks. SeSDF exhibits superior performances over current state-of-the-arts both qualitatively and quantitatively. + +# 2. Related Work + +Parametric 3D human model Parametric 3D human reconstruction [21, 30, 36, 44, 47] paves the path for 3D human model. SMPL [36, 67] was built on convolutional networks and statistics collected from a wide range of human populations. SMPL-X [47, 66] extended SMPL with more body joints, keypoints, and expression parameters. Later substantial supervision strategies were proposed to regress the model parameters. Examples include semantic segmentation [43, 64], human body silhouette [49], joints [16], motion dynamics [30, 33], texture consistency [48], and attention-regressor [31]. Multi-view [6, 13, 68, 69] and multi-person [57, 58] setups were also sought for various scenarios. Complex human clothing and hair topology were also the goals for later parametric methods [3, 4, 29, 62, 73]. However, due to the minimal-clothing assumption of the parametric models, these methods can retain little geometry details such as hairs and clothes in their reconstructions. + +Single-view (implicit) human reconstruction Many methods have been proposed in the deep learning era to reconstruct a 3D human model from a single image. For example, voxel-based methods [18, 27, 59, 60, 72, 72] reconstruct a volumetric representation of the human model. Two-stage inference [56], visual hull [41] and front-back depth method [17] were then proposed to improve the reconstruction performance and efficiency. However, the high computational cost of these methods limits their real-world applications. Implicit function methods have recently been introduced to predict either the occupancy field [10, 38] or signed distance field [8, 28, 45] using neural networks. PIFu [52] presents promising results with a pixel-aligned implicit function. Follow-up works exploited 3D features + +to solve the depth-ambiguity problem [71], achieve animatable model [23, 26], or improve the reconstruction details [7]. PIFuHD [53] and FITE [35] apply a multi-stage method to improve clothing topology in the reconstruction. Geo-PIFu [22] proposes to compute 3D features directly from images. ICON [63] exploits the SMPL-based signed distance filed as guidance to help produce a robust reconstruction, with a smpl-visibility based method to choose features from front or back sides. PHORHUM [5] explores shading and illumination information to infer better geometry and texture. Encouraging improvements have been reported by these methods. However, their performance on non-frontal human images are still far from being robust and satisfactory. + +Multi-view implicit human reconstruction Multi-view reconstruction is conceptually a more natural choice as information from different views can compensate each other for better reconstruction. Under a calibrated setting, PIFu [52] proposes to fuse features from multi-views by average pooling after being embedded using an MLP. StereoPIFu [24] takes as input a pair of stereo images, and performs depth-aware reconstruction. DiffuStereo [55] employs diffusion models for multi-view stereo human reconstruction. DoubleField [54] combines the surface field and radiance fields to improve both geometry and texture inference. Effi-MVS [61] explores the dynamic cost volume for reduced computational cost. DeepMultiCap [70] handles the multi-person reconstruction with multi-view images. Neural-Human-Performer [32] proposes a multi-view transformer to fuse features for multi-view reconstruction. Despite promising results have been achieved, these methods require a large number of views and camera calibration. MVP-Human [74] makes use of the deformation fields and handles multi-view inputs under an uncalibrated setting, but the reconstruction quality lags far behind the calibrated methods. For calibrated methods, their models still produce undesirable artifacts for many self-occluding nonfrontal poses and miss many geometry details. + +# 3. Method + +We propose an implicit function based framework for reconstructing 3D clothed human models from a single image or uncalibrated multi-view images (see Fig. 2). At the core of our framework are a self-evolved signed distance field (SeSDF) module and an occlusion-aware feature fusion module. Next, we will first introduce the preliminary for SeSDF in Sec. 3.1. We will then describe SeSDF for single-view reconstruction in Sec. 3.2, followed by uncalibrated multi-view reconstruction in Sec. 3.3. + +# 3.1. Preliminary + +Surface by implicit function Implicit functions [14] have been shown to be effective for 3D reconstruction from im + +ages or videos. Typically, an implicit function is implemented as an MLP, which takes the 3D coordinate $X$ and an optionally associated feature $F$ of a 3D point as input, and outputs the corresponding occupancy as a scalar value. Commonly employed features include pixel-aligned image features [52, 53] and space-aligned 3D features [7, 26, 71]. Formally, the implicit function can be written as + +$$ +f _ {v} (X, F) \mapsto [ 0, 1 ] \in \mathbb {R}. \tag {1} +$$ + +SMPL-X The parametric human model SMPL-X represents the 3D shape by incorporating body vertices, joints, face and hands landmarks, and expression parameters. Formally, by assembling pose parameters $\theta$ , shape parameters $\beta$ , and facial expression parameters $\phi$ , SMPL-X human model can be expressed by a function $M(\cdot)$ as + +$$ +M (\beta , \theta , \phi) = W (T _ {p} (\beta , \theta , \phi), J (\beta), \theta , \mathcal {W}), +$$ + +$$ +T _ {p} (\beta , \theta , \phi) = \bar {T} + B _ {S} (\beta ; \mathcal {S}) + B _ {E} (\phi ; \mathcal {E}) + B _ {p} (\theta ; \mathcal {P}), +$$ + +where $W(\cdot)$ is the linear blend skinning function, $J(\beta)$ is the joint location, and $\mathcal{W}$ denotes the blend weights. $T_{p}(\cdot)$ poses the SMPL-X canonical model $\bar{T}$ by shape blend shape function $B_{S}$ , expression blend shape function $B_{E}$ , and pose blend shape function $B_{P}$ . $\mathcal{S}$ and $\mathcal{P}$ are the principal components of vertex displacements, and $\mathcal{E}$ represents the principal components capturing variations of facial expressions. + +SMPL-X optimization Given a human image, we can fit the SMPL-X model parameters by [16]. However, such fitted models often suffer from misalignment. We use the well-aligned SMPL-X models provided in the training data to provide shape prior to train our framework. At test time, we do not have such well-aligned models. Hence, to avoid errors and artifacts caused by the misalignment during testing, we optimize the SMPL-X parameters by projecting the SMPL-X model onto the input image and maximizing the Intersection over Union (IoU) between the projection and body mask [9, 63], and minimizing the 2D keypoint distances. Please refer to the supplementary for details. + +# 3.2. Single-view reconstruction + +Given an input image $\pmb{I}$ and an optimized SMPL-X mesh $S$ , SeSDF incorporates pixel-aligned image features $F_{2D}$ extracted from $\pmb{I}$ , space-aligned 3D features $F_{3D}$ extracted from $S$ , and the self-evolved signed distance field $d$ to predict occupancy using an MLP. By applying marching cube [34] on the occupancy predictions in the 3D space, SeSDF robustly reconstructs a 3D clothed human model with faithful details, including the clothing topology. Given a 3D point $X$ , the implicit function for single-view reconstruction can be formulated as + +$$ +f _ {o} \left(F _ {2 D} (X), F _ {3 D} (X), \mathcal {D} (d (X)), \mathbf {n} (X), Z (X)\right) \mapsto [ 0, 1 ], \tag {2} +$$ + +![](images/cc4cc9cd142a59266971eec7bdc920e85bb7b293d1bc43ca4d2b0458e5a3568a.jpg) +Figure 2. Overview of our proposed SeSDF framework. It takes a single image or uncalibrated multi-view images as input to predict the occupancy for each 3D location in the space for shape reconstruction. We first fit a SMPL-X model to the input image(s) which serves as a shape prior and provides space-aligned 3D features. At the core of our method is our proposed self-evolved signed distance field (SeSDF) module, which learns a refined signed distance field (SDF) to better reflect the actual clothed human subject rather than the minimally-clothed SMPL-X model. SeSDF module takes pixel-aligned image features, space-aligned 3D features, SDF with distance encoding, and SMPL-X vertex normal as input to predict the refined SDF and normal value. For multi-view reconstruction, we propose a SMPL-X based self-calibration method to eliminate the need for manual calibration and an occlusion-aware feature fusion strategy to effectively accumulate features from different views. + +where $\mathcal{D}(\cdot)$ and $Z(\cdot)$ denote distance encoding and depth value respectively, and $d(\cdot)$ and $\mathbf{n}(\cdot)$ are the signed distance and normal output by our SeSDF module. + +Pixel-aligned image feature We apply a stacked-hourglass encoder [42, 52] to the input image $I \in \mathbb{R}^{512 \times 512 \times 3}$ to produce an image feature map $E_{I}(I) \in \mathbb{R}^{256 \times 128 \times 128}$ . We then obtain the pixel-aligned image feature for the projection of a 3D point using bi-linear interpolation. + +Space-aligned 3D feature We apply PointNet [51] and 3D-UNet [11] to extract 3D features [7, 50] from the optimized SMPL-X mesh. Our 3D encoder first processes the whole 10,475 vertices of the mesh to generate hierarchical 3D point features, which are transformed into a 3D feature volume via average pooling. 3D-UNet is then applied to output the final 3D feature volume $E_{S}(S) \in \mathbb{R}^{128 \times 64 \times 64 \times 64}$ . Finally we obtain the space-aligned 3D feature for a 3D point via tri-linear interpolation. + +Self-evolved signed distance field The signed distance field (SDF) derived from the SMPL-X model [63] provides a strong prior for estimating the occupancy. However, the SMPL-X model does not model geometric details of the human, such as the cloth topology, and thus the resulting SDF will unavoidably deviate from the true SDF of the actual clothed human model. Directly employing this SDF + +for occupancy prediction will therefore induce error in the reconstruction. To remedy this problem and recover plausible geometry details in the reconstruction, we propose a novel self-evolved signed distance filed (SeSDF) module. This module is trained to evolve the SDF derived from the SMPL-X model to better reflect the actual clothed human model. Instead of predicting only the signed distance $d(\cdot) \in \mathbb{R}$ , our SeSDF module further predict the normal $\mathbf{n}(\cdot) \in \mathbb{R}^3$ which provides additional surface orientation information to guide the implicit function to better predict occupancy and capture fine shape details. Concretely, SeSDF module is implemented as an MLP and formulated as + +$$ +f _ {s d} \left(F _ {2 D} (X), F _ {3 D} (X), \mathcal {D} \left(d ^ {\prime} (X)\right), \mathbf {n} ^ {\prime} (X)\right) \mapsto (d, \mathbf {n}), \tag {3} +$$ + +where $d'(\cdot) \in \mathbb{R}$ denotes the SDF derived from the SMPL-X model and $\mathbf{n}'(\cdot) \in \mathbb{R}^3$ represents the normal obtained from the closest SMPL-X vertex to $X$ . + +Distance encoding Inspired by the positional encoding adopted in NeRF [39], we adopt a distance encoding that maps the signed distance $d$ to a higher dimensional space using high frequency functions: + +$$ +\mathcal {D} (d) = \left(d, \sin \left(2 ^ {0} \pi d\right), \cos \left(2 ^ {0} \pi d\right), \dots , \sin \left(2 ^ {L} \pi d\right), \cos \left(2 ^ {L} \pi d\right)\right). \tag {4} +$$ + +In our experiments, we set $L = 5$ . The encoded signed distance $\mathcal{D}(d)$ is concatenated with the predicted normal $\mathbf{n}(\cdot)$ , + +2D feature $F_{2D}(\cdot)$ and 3D feature $F_{3D}(\cdot)$ , and fed to the implicit function $f_{o}(\cdot)$ for occupancy prediction. + +Training objectives To consistently regress SeSDF and simulate realistic cloth topology, we consider two groups of sampling points, namely surface samples $G_{s}$ , and occupancy-target samples $G_{o}$ . Points in $G_{s}$ are uniformly sampled on the mesh surface, while points in $G_{o}$ are sampled following the strategy proposed in PIFu [52]. + +For points in $G_{s}$ , we adopt the following loss function + +$$ +\mathcal {L} _ {s} = \frac {1}{| G _ {s} |} \sum_ {X \in G _ {s}} \lambda_ {d} | d (X) | + \lambda_ {n} \| \mathbf {n} (X) - \mathbf {n} _ {g t} (X) \|, \tag {5} +$$ + +where $\mathbf{n}_{gt}(X)$ denotes the ground-truth normal at the surface point $X$ . For points in $G_{o}$ , we adopt the following loss function + +$$ +\mathcal {L} _ {o} = \frac {1}{| G _ {o} |} \sum_ {X \in G _ {o}} B C E (\mathcal {O} (X) - \mathcal {O} _ {g t} (X)), \tag {6} +$$ + +where $\mathcal{O}(X)$ denotes the predicted occupancy at $X$ computed using Eq. (3) and Eq. (2), $\mathcal{O}_{gt}(X)$ is the ground-truth occupancy at $X$ , and $BCE(\cdot)$ denotes the binary cross entropy. Following IGR [20], we add an eikonal normal regularization term to smooth the surface by: + +$$ +\mathcal {L} _ {r} = \frac {1}{| G _ {o} |} \sum_ {X \in G _ {o}} \left(\left\| \mathbf {n} (X) \right\| - 1\right) ^ {2}. \tag {7} +$$ + +The overall loss function is given by + +$$ +\mathcal {L} _ {S e S D F} = \lambda_ {s} \mathcal {L} _ {s} + \lambda_ {o} \mathcal {L} _ {o} + \lambda_ {r} \mathcal {L} _ {r}, \tag {8} +$$ + +where $\lambda_{s},\lambda_{o}$ ,and $\lambda_{r}$ are weights to balance the effect of the respective loss. + +# 3.3. Uncalibrated multi-view reconstruction + +To allow our SeSDF framework work with uncalibrated multi-view images, we present a simple self-calibration method to estimate the relative camera pose for each image through fitting a SMPL-X model to all the input images. In addition, we propose an occlusion-aware feature fusion strategy to fuse features from different views effectively. Ideally, we would like to fuse only features from non-occluded views as features from occluded views are just noise which at best provide zero contribution to occupancy prediction but may also seriously degrade the fused feature in the worse case. + +Our multi-view framework is illustrated in Fig. 2. In principle, it can work with an arbitrary number of views and the number of views used in training and testing do not even need to be the same. + +Self-calibration via SMPL-X model fitting Given $n$ uncalibrated multi-view images, we first fit a SMPL-X model to each image independently using the method described in + +Sec. 3.1. We then take the averages of the shape, pose and expression parameters of these $n$ fitted models and use them to initialize a shared SMPL-X model. Next, we optimize the shape, pose and expression parameters of this shared SMPL-X model and the global orientation parameters for the $n$ views simultaneously by maximizing the IoU between the projection and body mask, and minimizing the 2d keypoint distances on each of the $n$ images. After optimization, the global orientation parameters for the $n$ views then give us the rigid body motion that transforms a point from the SMPL-X model centered coordinate system to the camera centered coordinate system of each view. + +To perform multi-view reconstruction, we can sample 3D points in the model centered coordinate system, transform them into the respective camera coordinate systems, and compute 2D/3D features and the self-evolved signed distance from each view. Finally, these features from $n$ different views are fused by our occlusion-aware feature fusion strategy (to be introduced next) and fed to the implicit function $f_{o}(\cdot)$ to predict the occupancy value. + +Occlusion-aware feature fusion Conceptually, features obtained from different views would give rise to predictions of different quality. For instance, image feature for a 3D point extracted from a frontal non-occluded view would be expected to give the best prediction, whereas image feature for the same point but extracted from an occluded view or a lateral view would be expected to give poor prediction. Hence, average pooling would in principle not be the best way for feature fusion. Researchers therefore explored different fusion strategies, such as SMPL-visibility based [63] and attention based [70] approaches, but all of these still produce undesirable artifacts in their reconstructions (see Fig. 7). To lessen the effect of features extracted from non-optimal views, we propose a novel occlusion-aware feature fusion strategy based on ray tracing [19] with the fitted SMPL-X model. Given a 3D point $X$ , we cast a ray from $X$ to the $i$ -th view through orthogonal projection and find the intersection point $X_{i}^{\prime}$ with the SMPL-X model that is the closest to the image (see Fig. 2). We then compute a weight for the feature $F_{i}(X)$ extracted from the $i$ -th view by + +$$ +w _ {i} (X) = \frac {1}{\left| Z _ {i} (X) - Z _ {i} \left(X _ {i} ^ {\prime}\right) \right|}. \tag {9} +$$ + +Finally, we fuse all features from the $n$ views by + +$$ +F _ {f u s e d} (X) = \frac {\sum_ {i = 1} ^ {n} w _ {i} (X) F _ {i} (X)}{\sum_ {i = 1} ^ {n} w _ {i} (X)}. \tag {10} +$$ + +# 4. Experiments + +We evaluate the performance of our SeSDF both qualitatively and quantitatively, and provide comparisons with other SOTA methods under both single-view and multiview setups. + +Table 1. Qualitative comparison on the single-view setting. We report Chamfer Distance and P2S metrics (numbers the lower the better). + +
MethodFeature IncludedQuantitative Number
THuman2.0CAPE
2D FeatureNormal Information3D FeatureSMPLX Signed Distanceself-evolved Signed DistanceChamfer Distance↓P2S↓Chmafer Distance↓P2S↓
PIFu [52]✓2.4032.3883.0592.818
PIFuHD [53]✓✓2.0081.9652.5712.427
PaMIR [71]✓✓1.4781.4511.6821.438
ICON [63]✓✓✓1.3011.2591.5331.431
Ours w/o DE✓✓✓✓1.0991.0341.3771.261
Ours w/o SeSDF✓✓✓✓1.2451.2001.4731.390
Ours✓✓✓✓1.0270.9711.3031.219
+ +Table 2. Quantitative comparison on the multi-view setting. + +
MethodTHuman2.0CAPE
Chamfer Distance↓P2S↓Chmafer Distance↓P2S↓
multi-view PIFu [52]0.8640.8380.9200.876
multi-view PIFuHD [53]0.8310.8040.8830.849
multi-view PaMIR [71]0.8070.7620.8580.819
Ours w/o DE0.7950.7490.8490.811
Ours w/o SeSDF0.8020.7550.8540.815
Ours0.7910.7420.8410.800
Ours w/ Attention0.7940.7430.8450.803
Ours w/ SMPLX-Vis0.8410.8320.9250.917
Ours w/ Normal-Fusion0.8010.7540.8500.812
+ +![](images/dc75e76ee5ed56eb7135e2496e0366ec20af9e7ddfaed875d4d0c22d3be51913.jpg) +Figure 3. Qualitative comparison with SOTA methods on real-world images. Our method can reconstruct fine details and work robustly under challenge poses. Best viewed in PDF with zoom. + +# 4.1. Implementation details + +For each training subject, we sample (a) 5,000 surface points as $G_{s}$ , which are evenly distributed on the mesh surface; (b) 5,000 occupancy-target points as $G_{o}$ in the 3D space, for which we follow the sampling strategy in [52]. In particular, 15/16 points in $G_{o}$ are evenly sampled on the mesh surface. Gaussian perturbation is then applied to them along the surface normal direction. The rest 1/16 points are randomly sampled within the predefined 3D space where the mesh lies in. + +We employ Rembg [1] to segment out the background for real-world images and use Kaolin [2] to calculate the SDF from the SMPL-X model. We apply PIXIE [16] to estimate the SMPL-X model for the segmented human subject. To compute the image features, we implement a stacked- + +hourglass image encoder with bi-linear interpolation to extract pixel-aligned image feature $F_{2D}(\cdot) \in \mathbb{R}^{256}$ . We follow [7, 50] to employ PointNet with 3D-UNet and tri-linear interpolation to extract space-aligned 3D features $F_{3D}(\cdot) \in \mathbb{R}^{128}$ . Distance encoding maps the signed distance to a higher dimensional space $\mathcal{D}(d) \in \mathbb{R}^{13}$ using the high-frequency functions as defined in Eq. (4). We implement our framework in PyTorch [46]. Our SeSDF framework is trained separately for 12 epochs with the learning rate starting from 1e-4 and updated by the factor 0.1 for every 4 epochs, for both single-view and multi-view experiments. Code for SeSDF will be made publicly available. Project page: https://yukangcao.github.io/SeSDF/. + +# 4.2. Datasets and evaluation metrics + +We employ the THUman2.0 dataset [65] as our primary testbed. The dataset comprises 526 high-fidelity meshes captured via dense DSLR rigs. Each subject within the dataset is accompanied by its corresponding texture map and fitted SMPL-X parameters. We split the THUman2.0 dataset into a training set with 465 subjects, and a test set with 61 subjects. We render each human subject into 360 images, sequentially separated by $1^{\circ}$ around the subject, with different albedo to augment the dataset to carry out the experiments. + +To further show the generalizability of SeSDF, we also compare our method with others on the CAPE [37] test set, which contains 150 subjects. To conduct quantitative evaluations of different methods, we employ standard Point-to-Surface distance (P2S) and Chamfer distance metrics as evaluation criteria. We compare the reconstructed models from images captured at different angles, i.e., $0^{\circ}$ , $45^{\circ}$ , $90^{\circ}$ , $135^{\circ}$ , $180^{\circ}$ , $225^{\circ}$ , $270^{\circ}$ , and $315^{\circ}$ , against the ground truth under corresponding orientations. Besides, we use real-world images for extra qualitative evaluation. + +# 4.3. Comparison on single-view setting + +We first evaluate and compare the performance of single-view 3D human reconstruction between ours and SOTA methods. Specifically, we compare with PIFu [52], PIFuHD [53], PaMIR [71], ARCH [26], ARCH++ [23] and ICON [63]. PHORHUM [5] is not compared here due to the absence of publicly available code base. We retrain PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 dataset for + +![](images/86f3087f59438141c1f7c807278d7e98dadc6a592345a56ed56d0d8a0eec9c2a.jpg) +Figure 4. Comparison with ICON on real-world (top) and THUman2.0 data (bottom). Ours (SeSDF) can produce results with more fine geometry details. Best viewed in PDF with zoom. + +a fair comparison, and obtain the reconstructions of ARCH and $\mathrm{ARCH} + +$ with the help of their authors. + +Quantitative comparison and ablation In Table 1, we compare our method with the SOTA methods, i.e., PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 and CAPE datasets. As can be seen, for all metrics, our method significantly outperforms the SOTA by a large margin on both datasets. Among these SOTA methods, ICON also employs the SMPL-X model to extract SDF to guide learning, while our method consistently outperforms ICON across the board. We also validate the effectiveness of different components of our method. All components have positive effects on the reconstruction results, while the SeSDF module plays the most crucial role in the improvement. By comparing the last two rows, we can see that the SeSDF module brings much more improvement than the SDF derived from the SMPL-X model. By comparing the last row with all others, we can observe that our SeSDF brings the most improvement among all components. By comparing "Ours" and "Ours w/o DE", we can see that our proposed distance encoding is also effective in improving the performance. + +Qualitative comparison We present qualitative comparison in Fig. 3 on real-world images with SOTA methods. Our proposed method has the capability to reconstruct fine geometry details and handle the inputs with complicated poses. Among the SOTA methods, ICON also employs SMPL-X to improve the robustness, though in a different way from our work. We provide a further comparison with ICON in Fig. 4 on THUman2.0 and real-world images. As can be seen, our method notably outperforms ICON with more fine details in all cases. + +# 4.4. Comparison on multi-view setting + +For multi-view reconstruction, we compare with the SOTA methods PIFu, PIFuHD, and PaMIR which allow multi-view reconstruction. In the experiments, we use three input views unless stated otherwise. + +Quantitative comparison and ablation We report the comparison results in Table 2. To have a fair comparison with other methods which are calibrated, we also implemented our self-calibration method for all of them. We can see that our method outperforms other methods in all cases. Similar to the single-view experiments, by comparing "Ours" against "Ours /wo DE" and "Ours /wo SeSDF", we can see that our distance encoding and SeSDF play critical roles in the performance. + +Qualitative comparison We present qualitative comparison in Fig. 5 for multi-view reconstruction. The reconstruction results of our method retain more details, e.g., clothing wrinkles and hair topology, which are contained in the ground truth. We provide more results with different numbers of views in the supplementary. + +# 4.4.1 Further analysis + +Self-calibration [74] also introduced an alternative method for self-calibration of multi-view reconstruction by introducing a deformation field to deform points from the canonical space to the camera space, through SMPL linear blend skinning (LBS) weights. We also follow the paper to implement it for SMPL-X in our framework and compare it with our method in Fig. 6. We observe wide-spreading artifacts across the whole body of the reconstruction using the deformation field for the uncalibrated setting. The deformation field is error-prone because the LBS weights are computed to deform the parametric human model, which inherently lacks the fine details of the actual human subject, limiting its final performance and introducing the artifacts for reconstruction. + +Feature fusion We compare our occlusion-aware feature fusion strategy with other alternatives, namely (1) AVGPool [52], (2) SMPLX-visibility [63], and (3) Attention-based method [32] in Fig. 7. As can be seen, our occlusion-aware strategy achieves better performance than the others. See supplementary for more analysis. + +![](images/bce13ec17c62b794307ea95fe3694b7131fe99a649d89854b92aac85c5a6d28c.jpg) +SOTA - Ours +Figure 5. Comparison with SOTA methods on the multi-view setting. Ours (SeSDF) consistently retains more geometry details, e.g., clothing wrinkles, hairs, and faces. + +![](images/aec163f8f55bc24475d9d9d2ed147da3809a98625026c90f9a4a60d1840baa91.jpg) +Figure 6. Comparing our self-calibration method ("Ours") with an SMPL-X deformation field alternative ("DF"). Best viewed in PDF with zoom. + +# 5. Conclusion + +In this paper, we have presented a new framework for single- and multi-view clothed human reconstruction under an uncalibrated setting. Our framework can take an arbitrary number of input images to reconstruct faithful 3D human models. We have proposed a self-evolved signed distance (SeSDF) module to recover more geometry details, a method for self-calibrating multi-view images via SMPL-X model fitting, and an effective multi-view occlusion-aware feature fusion strategy to aggregate useful features across views for robust reconstruction. Our method notably outperforms previous SOTA methods in both terms of qualitative and quantitative results. + +Limitation Though our SeSDF can deal with various + +![](images/7e5da041a2421b0d5ceb53981fa9eb8daa89e19ceee7ae5af78ecefa70996c19.jpg) +Figure 7. Comparing our occlusion-aware feature fusion with other alternative fusion strategies. + +poses and retain fine clothing topology, it still has difficulties when handling extremely loose clothes, e.g., dresses, which deviate significantly from the parametric prior. + +Potential Social Impact Our method takes a step towards practical tools for real-world application, as it does not require expensive equipment to get the 3D models. However, despite its intended positive usage, there might be potential risks of falsifying human avatars, which unfortunately compromise personal privacy. Transparency and authentication will be helpful to prevent these vicious uses. + +Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research. We appreciate the very helpful discussions with Dr. Guanying Chen. 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Mvp-human dataset for 3d human avatar reconstruction from unconstrained frames. arXiv preprint arXiv:2204.11184, 2022.3,7 \ No newline at end of file diff --git a/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/images.zip b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..975d262f5b0479e965fd9308fe152c941eb9d388 --- /dev/null +++ b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:693def9c1c4b6828c724524028fa1665d2fa884141c816af7559e807e062e86a +size 629576 diff --git a/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/layout.json b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..85ed1c87fd6bbb91bbd27c7d83393baae7d323c4 --- /dev/null +++ b/2023/SeSDF_ Self-Evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction/layout.json @@ -0,0 +1,8963 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 67, + 102, + 526, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 67, + 102, + 526, + 138 + ], + "spans": [ + { + "bbox": [ + 67, + 102, + 526, + 138 + ], + "type": "text", + "content": "SeSDF: Self-evolved Signed Distance Field for Implicit 3D Clothed Human Reconstruction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 170, + 161, + 423, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 170, + 161, + 423, + 190 + ], + "spans": [ + { + "bbox": [ + 170, + 161, + 423, + 190 + ], + "type": "text", + "content": "Yukang Cao Kai Han Kwan-Yee K. 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Self-evolved Signed Distance Field (SeSDF): We propose Self-evolved Signed Distance Field (SeSDF), which can flexibly reconstruct 3D clothed human models from a single-view image (top) or uncalibrated multi-view images (bottom). SeSDF can robustly recover fine geometry details from any type of poses, which allows us to generate clothed human avatars." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 460, + 192, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 460, + 192, + 472 + ], + "spans": [ + { + "bbox": [ + 143, + 460, + 192, + 472 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 45, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 486, + 289, + 715 + ], + "type": "text", + "content": "We address the problem of clothed human reconstruction from a single image or uncalibrated multi-view images. Existing methods struggle with reconstructing detailed geometry of a clothed human and often require a calibrated setting for multi-view reconstruction. We propose a flexible framework which, by leveraging the parametric SMPL-X model, can take an arbitrary number of input images to reconstruct a clothed human model under an uncalibrated setting. At the core of our framework is our novel self-evolved signed distance field (SeSDF) module which allows the framework to learn to deform the signed distance field (SDF) derived from the fitted SMPL-X model, such that detailed geometry reflecting the actual clothed human can be encoded for better reconstruction. Besides, we propose a simple method for self-calibration of multi-view images via the fitted SMPL-X parameters. This lifts the requirement of tedious manual calibration and largely increases the flexibility of our method. Further, we introduce an effective occlusion-aware feature fusion strategy to account for the most useful fea" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 461, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 461, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 305, + 461, + 545, + 510 + ], + "type": "text", + "content": "tures to reconstruct the human model. We thoroughly evaluate our framework on public benchmarks, demonstrating significant superiority over the state-of-the-arts both qualitatively and quantitatively." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 525, + 387, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 387, + 537 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 387, + 537 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "Clothed human reconstruction is a hot topic with increasing demand in real-world applications such as 3D telepresence, game modeling, metaverse [40], etc. Early works show promise under equipment-assisted settings, requiring expensive dense camera rigs [12] and tedious calibration procedures [15]. Parametric models, such as SMPL [36] and SMPL-X [47], have been introduced to model a naked human body with constrained parameters. With the witnessed success of deep learning in many vision tasks, many deep learning methods have been proposed to regress the parameters of such parametric human models from a single [16, 66, 67] or multiple images [6, 13, 68]. However, these methods can only reconstruct a minimally-clothed human model without many details (e.g., hairs and clothes)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4647" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "Recently, methods based on implicit shape representation have reported encouraging performance, showing promising reconstruction with increased details in both single-view [23, 26, 52, 63, 71] and multi-view [24, 25, 54, 55] settings." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 134, + 289, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 289, + 385 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 289, + 385 + ], + "type": "text", + "content": "Despite the stunning results reported by the above methods, their reconstructions remain far from perfect, restricting their practical applications. For instance, state-of-the-art (SOTA) single-view methods, such as PIFuHD [53], PaMIR [71], and " + }, + { + "bbox": [ + 46, + 134, + 289, + 385 + ], + "type": "inline_equation", + "content": "\\mathrm{ARCH} + +" + }, + { + "bbox": [ + 46, + 134, + 289, + 385 + ], + "type": "text", + "content": " [23], struggle with many self-occluding non-frontal human poses that widely occur in the real world. ICON [63] can handle these cases but the reconstructions contain serious artifacts (see Fig. 3). On the other hand, many multi-view methods depend on calibrated cameras (e.g., [24, 54, 55]) which are tedious to obtain in practice. Hence, how to carry out multi-view reconstruction with uncalibrated cameras is an important topic to study. Meanwhile, effective multi-view feature fusion is another key factor for robust multi-view reconstruction. Prior techniques for multi-view feature fusion include average pooling [52], SMPL-visibility [63], and attention-based mechanism [70]. However, the reconstruction results based on these fusion techniques still contain notable artifacts in many cases. This indicates that more efforts are needed to derive a better multi-view feature fusion for more robust reconstruction." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 388, + 289, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 289, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 289, + 592 + ], + "type": "text", + "content": "In this paper, to extract more clothed human details flexibly and robustly from a single RGB image or uncalibrated multi-view RGB images, we present a novel framework, named SeSDF, that employs the parametric model SMPL-X [47] as a 3D prior and combines the merits of both implicit and explicit representations. SeSDF takes a single image or multi-view images as input to predict the occupancy for each 3D location in the space representing the human model. To reconstruct high-frequency details such as hairs and clothes, we introduce a self-evolved signed distance field module that learns to deform the signed distance field (SDF) derived from the fitted SMPL-X model using the input images. The resulting SDF can reflect more accurate geometry details than SMPL-X, which inherently deviates from the actual clothed human model. The SDF refined by our SeSDF module is further encoded to allow for 3D reconstruction with better geometry details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "Besides reconstructing a faithful 3D clothed human model from a single image, our SeSDF framework can also work with uncalibrated multi-view images to generate clothed human avatar with enhanced appearance (see Fig. 1). To this end, we first propose a self-calibration method by fitting a shared SMPL-X model across multiview images and projecting the shared model to different images based on the optimized rigid body motion for each input image. Further, we propose an occlusion-aware feature fusing strategy by probing the visibility of each 3D" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "point under different views through ray-tracing, leveraging the SMPL-X model, such that features from visible views will contribute more to the fused feature while those from invisible views will be suppressed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 121, + 503, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 121, + 503, + 133 + ], + "spans": [ + { + "bbox": [ + 317, + 121, + 503, + 133 + ], + "type": "text", + "content": "The contributions are summarized as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 134, + 545, + 302 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 306, + 134, + 545, + 206 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 134, + 545, + 206 + ], + "spans": [ + { + "bbox": [ + 306, + 134, + 545, + 206 + ], + "type": "text", + "content": "- We propose a flexible framework that, by leveraging the SMPL-X model as a shape prior, can take an arbitrary number of uncalibrated images to perform high-fidelity clothed human reconstruction. At the core of our framework is a self-evolved signed distance field (SeSDF) module for recovering faithful geometry details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 207, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 207, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 207, + 545, + 266 + ], + "type": "text", + "content": "- For uncalibrated multi-view reconstruction, we propose a simple self-calibration method through leveraging the SMPL-X model, as well as an occlusion-aware feature fusion strategy which takes into account the visibility of a space point under different views via ray-tracing." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 266, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 266, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 306, + 266, + 545, + 302 + ], + "type": "text", + "content": "- We thoroughly evaluate our framework on public benchmarks. SeSDF exhibits superior performances over current state-of-the-arts both qualitatively and quantitatively." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 316, + 392, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 392, + 329 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 392, + 329 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 339, + 545, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 543 + ], + "type": "text", + "content": "Parametric 3D human model Parametric 3D human reconstruction [21, 30, 36, 44, 47] paves the path for 3D human model. SMPL [36, 67] was built on convolutional networks and statistics collected from a wide range of human populations. SMPL-X [47, 66] extended SMPL with more body joints, keypoints, and expression parameters. Later substantial supervision strategies were proposed to regress the model parameters. Examples include semantic segmentation [43, 64], human body silhouette [49], joints [16], motion dynamics [30, 33], texture consistency [48], and attention-regressor [31]. Multi-view [6, 13, 68, 69] and multi-person [57, 58] setups were also sought for various scenarios. Complex human clothing and hair topology were also the goals for later parametric methods [3, 4, 29, 62, 73]. However, due to the minimal-clothing assumption of the parametric models, these methods can retain little geometry details such as hairs and clothes in their reconstructions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "Single-view (implicit) human reconstruction Many methods have been proposed in the deep learning era to reconstruct a 3D human model from a single image. For example, voxel-based methods [18, 27, 59, 60, 72, 72] reconstruct a volumetric representation of the human model. Two-stage inference [56], visual hull [41] and front-back depth method [17] were then proposed to improve the reconstruction performance and efficiency. However, the high computational cost of these methods limits their real-world applications. Implicit function methods have recently been introduced to predict either the occupancy field [10, 38] or signed distance field [8, 28, 45] using neural networks. PIFu [52] presents promising results with a pixel-aligned implicit function. Follow-up works exploited 3D features" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4648" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "to solve the depth-ambiguity problem [71], achieve animatable model [23, 26], or improve the reconstruction details [7]. PIFuHD [53] and FITE [35] apply a multi-stage method to improve clothing topology in the reconstruction. Geo-PIFu [22] proposes to compute 3D features directly from images. ICON [63] exploits the SMPL-based signed distance filed as guidance to help produce a robust reconstruction, with a smpl-visibility based method to choose features from front or back sides. PHORHUM [5] explores shading and illumination information to infer better geometry and texture. Encouraging improvements have been reported by these methods. However, their performance on non-frontal human images are still far from being robust and satisfactory." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 529 + ], + "type": "text", + "content": "Multi-view implicit human reconstruction Multi-view reconstruction is conceptually a more natural choice as information from different views can compensate each other for better reconstruction. Under a calibrated setting, PIFu [52] proposes to fuse features from multi-views by average pooling after being embedded using an MLP. StereoPIFu [24] takes as input a pair of stereo images, and performs depth-aware reconstruction. DiffuStereo [55] employs diffusion models for multi-view stereo human reconstruction. DoubleField [54] combines the surface field and radiance fields to improve both geometry and texture inference. Effi-MVS [61] explores the dynamic cost volume for reduced computational cost. DeepMultiCap [70] handles the multi-person reconstruction with multi-view images. Neural-Human-Performer [32] proposes a multi-view transformer to fuse features for multi-view reconstruction. Despite promising results have been achieved, these methods require a large number of views and camera calibration. MVP-Human [74] makes use of the deformation fields and handles multi-view inputs under an uncalibrated setting, but the reconstruction quality lags far behind the calibrated methods. For calibrated methods, their models still produce undesirable artifacts for many self-occluding nonfrontal poses and miss many geometry details." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 534, + 104, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 104, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 104, + 547 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 662 + ], + "type": "text", + "content": "We propose an implicit function based framework for reconstructing 3D clothed human models from a single image or uncalibrated multi-view images (see Fig. 2). At the core of our framework are a self-evolved signed distance field (SeSDF) module and an occlusion-aware feature fusion module. Next, we will first introduce the preliminary for SeSDF in Sec. 3.1. We will then describe SeSDF for single-view reconstruction in Sec. 3.2, followed by uncalibrated multi-view reconstruction in Sec. 3.3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Surface by implicit function Implicit functions [14] have been shown to be effective for 3D reconstruction from im" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "ages or videos. Typically, an implicit function is implemented as an MLP, which takes the 3D coordinate " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " and an optionally associated feature " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " of a 3D point as input, and outputs the corresponding occupancy as a scalar value. Commonly employed features include pixel-aligned image features [52, 53] and space-aligned 3D features [7, 26, 71]. Formally, the implicit function can be written as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 376, + 167, + 545, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 167, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 376, + 167, + 545, + 180 + ], + "type": "interline_equation", + "content": "f _ {v} (X, F) \\mapsto [ 0, 1 ] \\in \\mathbb {R}. \\tag {1}", + "image_path": "4d794257db8e5ea5eb7139713ebdf4f1147a09e047f09084afa94a78c82fb73b.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "text", + "content": "SMPL-X The parametric human model SMPL-X represents the 3D shape by incorporating body vertices, joints, face and hands landmarks, and expression parameters. Formally, by assembling pose parameters " + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "text", + "content": ", shape parameters " + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "text", + "content": ", and facial expression parameters " + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "text", + "content": ", SMPL-X human model can be expressed by a function " + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "inline_equation", + "content": "M(\\cdot)" + }, + { + "bbox": [ + 304, + 193, + 545, + 266 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 275, + 497, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 275, + 497, + 289 + ], + "spans": [ + { + "bbox": [ + 307, + 275, + 497, + 289 + ], + "type": "interline_equation", + "content": "M (\\beta , \\theta , \\phi) = W (T _ {p} (\\beta , \\theta , \\phi), J (\\beta), \\theta , \\mathcal {W}),", + "image_path": "faa34ba1d9a8e0a8aeb36b7007b4e52a1936bb67ad78388a2569f1384f575e22.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 289, + 543, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 289, + 543, + 304 + ], + "spans": [ + { + "bbox": [ + 307, + 289, + 543, + 304 + ], + "type": "interline_equation", + "content": "T _ {p} (\\beta , \\theta , \\phi) = \\bar {T} + B _ {S} (\\beta ; \\mathcal {S}) + B _ {E} (\\phi ; \\mathcal {E}) + B _ {p} (\\theta ; \\mathcal {P}),", + "image_path": "cf2f73e83d9d97e05d4cb57aee650f20212484d2f257c35adb899f7f275c334d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "W(\\cdot)" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " is the linear blend skinning function, " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "J(\\beta)" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " is the joint location, and " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{W}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " denotes the blend weights. " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "T_{p}(\\cdot)" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " poses the SMPL-X canonical model " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\bar{T}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " by shape blend shape function " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "B_{S}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": ", expression blend shape function " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "B_{E}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": ", and pose blend shape function " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "B_{P}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " are the principal components of vertex displacements, and " + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 304, + 314, + 545, + 398 + ], + "type": "text", + "content": " represents the principal components capturing variations of facial expressions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 400, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 544 + ], + "type": "text", + "content": "SMPL-X optimization Given a human image, we can fit the SMPL-X model parameters by [16]. However, such fitted models often suffer from misalignment. We use the well-aligned SMPL-X models provided in the training data to provide shape prior to train our framework. At test time, we do not have such well-aligned models. Hence, to avoid errors and artifacts caused by the misalignment during testing, we optimize the SMPL-X parameters by projecting the SMPL-X model onto the input image and maximizing the Intersection over Union (IoU) between the projection and body mask [9, 63], and minimizing the 2D keypoint distances. Please refer to the supplementary for details." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 553, + 453, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 553, + 453, + 566 + ], + "spans": [ + { + "bbox": [ + 306, + 553, + 453, + 566 + ], + "type": "text", + "content": "3.2. Single-view reconstruction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": "Given an input image " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": " and an optimized SMPL-X mesh " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": ", SeSDF incorporates pixel-aligned image features " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "F_{2D}" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": " extracted from " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "\\pmb{I}" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": ", space-aligned 3D features " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "F_{3D}" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": " extracted from " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": ", and the self-evolved signed distance field " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": " to predict occupancy using an MLP. By applying marching cube [34] on the occupancy predictions in the 3D space, SeSDF robustly reconstructs a 3D clothed human model with faithful details, including the clothing topology. Given a 3D point " + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 572, + 545, + 692 + ], + "type": "text", + "content": ", the implicit function for single-view reconstruction can be formulated as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 313, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 313, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "f _ {o} \\left(F _ {2 D} (X), F _ {3 D} (X), \\mathcal {D} (d (X)), \\mathbf {n} (X), Z (X)\\right) \\mapsto [ 0, 1 ], \\tag {2}", + "image_path": "0eddd87129988ecbf09ffc415bfd3baa202b3d5a0474df714692949d497bc24d.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4649" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 73, + 547, + 305 + ], + "blocks": [ + { + "bbox": [ + 51, + 73, + 547, + 305 + ], + "lines": [ + { + "bbox": [ + 51, + 73, + 547, + 305 + ], + "spans": [ + { + "bbox": [ + 51, + 73, + 547, + 305 + ], + "type": "image", + "image_path": "cc4cc9cd142a59266971eec7bdc920e85bb7b293d1bc43ca4d2b0458e5a3568a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 308, + 547, + 397 + ], + "lines": [ + { + "bbox": [ + 46, + 308, + 547, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 308, + 547, + 397 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed SeSDF framework. It takes a single image or uncalibrated multi-view images as input to predict the occupancy for each 3D location in the space for shape reconstruction. We first fit a SMPL-X model to the input image(s) which serves as a shape prior and provides space-aligned 3D features. At the core of our method is our proposed self-evolved signed distance field (SeSDF) module, which learns a refined signed distance field (SDF) to better reflect the actual clothed human subject rather than the minimally-clothed SMPL-X model. SeSDF module takes pixel-aligned image features, space-aligned 3D features, SDF with distance encoding, and SMPL-X vertex normal as input to predict the refined SDF and normal value. For multi-view reconstruction, we propose a SMPL-X based self-calibration method to eliminate the need for manual calibration and an occlusion-aware feature fusion strategy to effectively accumulate features from different views." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot)" + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "inline_equation", + "content": "Z(\\cdot)" + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "text", + "content": " denote distance encoding and depth value respectively, and " + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "inline_equation", + "content": "d(\\cdot)" + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "inline_equation", + "content": "\\mathbf{n}(\\cdot)" + }, + { + "bbox": [ + 46, + 406, + 288, + 442 + ], + "type": "text", + "content": " are the signed distance and normal output by our SeSDF module." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "type": "text", + "content": "Pixel-aligned image feature We apply a stacked-hourglass encoder [42, 52] to the input image " + }, + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{512 \\times 512 \\times 3}" + }, + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "type": "text", + "content": " to produce an image feature map " + }, + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "type": "inline_equation", + "content": "E_{I}(I) \\in \\mathbb{R}^{256 \\times 128 \\times 128}" + }, + { + "bbox": [ + 46, + 445, + 287, + 516 + ], + "type": "text", + "content": ". We then obtain the pixel-aligned image feature for the projection of a 3D point using bi-linear interpolation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 519, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 628 + ], + "type": "text", + "content": "Space-aligned 3D feature We apply PointNet [51] and 3D-UNet [11] to extract 3D features [7, 50] from the optimized SMPL-X mesh. Our 3D encoder first processes the whole 10,475 vertices of the mesh to generate hierarchical 3D point features, which are transformed into a 3D feature volume via average pooling. 3D-UNet is then applied to output the final 3D feature volume " + }, + { + "bbox": [ + 46, + 519, + 287, + 628 + ], + "type": "inline_equation", + "content": "E_{S}(S) \\in \\mathbb{R}^{128 \\times 64 \\times 64 \\times 64}" + }, + { + "bbox": [ + 46, + 519, + 287, + 628 + ], + "type": "text", + "content": ". Finally we obtain the space-aligned 3D feature for a 3D point via tri-linear interpolation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Self-evolved signed distance field The signed distance field (SDF) derived from the SMPL-X model [63] provides a strong prior for estimating the occupancy. However, the SMPL-X model does not model geometric details of the human, such as the cloth topology, and thus the resulting SDF will unavoidably deviate from the true SDF of the actual clothed human model. Directly employing this SDF" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "type": "text", + "content": "for occupancy prediction will therefore induce error in the reconstruction. To remedy this problem and recover plausible geometry details in the reconstruction, we propose a novel self-evolved signed distance filed (SeSDF) module. This module is trained to evolve the SDF derived from the SMPL-X model to better reflect the actual clothed human model. Instead of predicting only the signed distance " + }, + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "type": "inline_equation", + "content": "d(\\cdot) \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "type": "text", + "content": ", our SeSDF module further predict the normal " + }, + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "type": "inline_equation", + "content": "\\mathbf{n}(\\cdot) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 406, + 547, + 550 + ], + "type": "text", + "content": " which provides additional surface orientation information to guide the implicit function to better predict occupancy and capture fine shape details. Concretely, SeSDF module is implemented as an MLP and formulated as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 312, + 555, + 545, + 571 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 555, + 545, + 571 + ], + "spans": [ + { + "bbox": [ + 312, + 555, + 545, + 571 + ], + "type": "interline_equation", + "content": "f _ {s d} \\left(F _ {2 D} (X), F _ {3 D} (X), \\mathcal {D} \\left(d ^ {\\prime} (X)\\right), \\mathbf {n} ^ {\\prime} (X)\\right) \\mapsto (d, \\mathbf {n}), \\tag {3}", + "image_path": "3fb48b23db070d0fe304fb144d0efd62a0fae4d3678aff8dcaa5e3b94d91eba6.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "inline_equation", + "content": "d'(\\cdot) \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "text", + "content": " denotes the SDF derived from the SMPL-X model and " + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "inline_equation", + "content": "\\mathbf{n}'(\\cdot) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "text", + "content": " represents the normal obtained from the closest SMPL-X vertex to " + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 575, + 547, + 611 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 613, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 547, + 662 + ], + "type": "text", + "content": "Distance encoding Inspired by the positional encoding adopted in NeRF [39], we adopt a distance encoding that maps the signed distance " + }, + { + "bbox": [ + 304, + 613, + 547, + 662 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 613, + 547, + 662 + ], + "type": "text", + "content": " to a higher dimensional space using high frequency functions:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 309, + 665, + 545, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 665, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 309, + 665, + 545, + 689 + ], + "type": "interline_equation", + "content": "\\mathcal {D} (d) = \\left(d, \\sin \\left(2 ^ {0} \\pi d\\right), \\cos \\left(2 ^ {0} \\pi d\\right), \\dots , \\sin \\left(2 ^ {L} \\pi d\\right), \\cos \\left(2 ^ {L} \\pi d\\right)\\right). \\tag {4}", + "image_path": "adaca0c20c1cd98f406e485881e82c1a5d675b52f389247e093be8630f7b3626.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "content": "In our experiments, we set " + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "inline_equation", + "content": "L = 5" + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "content": ". 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For points in " + }, + { + "bbox": [ + 47, + 222, + 287, + 258 + ], + "type": "inline_equation", + "content": "G_{o}" + }, + { + "bbox": [ + 47, + 222, + 287, + 258 + ], + "type": "text", + "content": ", we adopt the following loss function" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 84, + 263, + 287, + 289 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 263, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 84, + 263, + 287, + 289 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {o} = \\frac {1}{| G _ {o} |} \\sum_ {X \\in G _ {o}} B C E (\\mathcal {O} (X) - \\mathcal {O} _ {g t} (X)), \\tag {6}", + "image_path": "13ea99f937e3181e9df02a26d28aa62c2ea6f302f3d3c9e51d2b9c17e5725d6e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(X)" + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "content": " denotes the predicted occupancy at " + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "content": " computed using Eq. (3) and Eq. (2), " + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_{gt}(X)" + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "content": " is the ground-truth occupancy at " + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "inline_equation", + "content": "BCE(\\cdot)" + }, + { + "bbox": [ + 47, + 297, + 287, + 357 + ], + "type": "text", + "content": " denotes the binary cross entropy. Following IGR [20], we add an eikonal normal regularization term to smooth the surface by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 97, + 365, + 287, + 395 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 365, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 97, + 365, + 287, + 395 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r} = \\frac {1}{| G _ {o} |} \\sum_ {X \\in G _ {o}} \\left(\\left\\| \\mathbf {n} (X) \\right\\| - 1\\right) ^ {2}. \\tag {7}", + "image_path": "9c1efe8997afdf191781967780140ff5019b716d5f9482128bf40b5733ad4b2a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 403, + 208, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 403, + 208, + 415 + ], + "spans": [ + { + "bbox": [ + 59, + 403, + 208, + 415 + ], + "type": "text", + "content": "The overall loss function is given by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 96, + 425, + 287, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 425, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 96, + 425, + 287, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S e S D F} = \\lambda_ {s} \\mathcal {L} _ {s} + \\lambda_ {o} \\mathcal {L} _ {o} + \\lambda_ {r} \\mathcal {L} _ {r}, \\tag {8}", + "image_path": "f9ba4eacb13d433ef386988534984ef35f31687e3c533f07457795fd6d353a11.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\lambda_{s},\\lambda_{o}" + }, + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "type": "text", + "content": " ,and " + }, + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "type": "inline_equation", + "content": "\\lambda_{r}" + }, + { + "bbox": [ + 47, + 446, + 287, + 471 + ], + "type": "text", + "content": " are weights to balance the effect of the respective loss." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 478, + 255, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 255, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 255, + 490 + ], + "type": "text", + "content": "3.3. Uncalibrated multi-view reconstruction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 496, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 626 + ], + "type": "text", + "content": "To allow our SeSDF framework work with uncalibrated multi-view images, we present a simple self-calibration method to estimate the relative camera pose for each image through fitting a SMPL-X model to all the input images. In addition, we propose an occlusion-aware feature fusion strategy to fuse features from different views effectively. Ideally, we would like to fuse only features from non-occluded views as features from occluded views are just noise which at best provide zero contribution to occupancy prediction but may also seriously degrade the fused feature in the worse case." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 628, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 675 + ], + "type": "text", + "content": "Our multi-view framework is illustrated in Fig. 2. In principle, it can work with an arbitrary number of views and the number of views used in training and testing do not even need to be the same." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Self-calibration via SMPL-X model fitting Given " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " uncalibrated multi-view images, we first fit a SMPL-X model to each image independently using the method described in" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": "Sec. 3.1. We then take the averages of the shape, pose and expression parameters of these " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " fitted models and use them to initialize a shared SMPL-X model. Next, we optimize the shape, pose and expression parameters of this shared SMPL-X model and the global orientation parameters for the " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " views simultaneously by maximizing the IoU between the projection and body mask, and minimizing the 2d keypoint distances on each of the " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " images. After optimization, the global orientation parameters for the " + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 545, + 215 + ], + "type": "text", + "content": " views then give us the rigid body motion that transforms a point from the SMPL-X model centered coordinate system to the camera centered coordinate system of each view." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "type": "text", + "content": "To perform multi-view reconstruction, we can sample 3D points in the model centered coordinate system, transform them into the respective camera coordinate systems, and compute 2D/3D features and the self-evolved signed distance from each view. Finally, these features from " + }, + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "type": "text", + "content": " different views are fused by our occlusion-aware feature fusion strategy (to be introduced next) and fed to the implicit function " + }, + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "type": "inline_equation", + "content": "f_{o}(\\cdot)" + }, + { + "bbox": [ + 304, + 216, + 545, + 312 + ], + "type": "text", + "content": " to predict the occupancy value." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": "Occlusion-aware feature fusion Conceptually, features obtained from different views would give rise to predictions of different quality. For instance, image feature for a 3D point extracted from a frontal non-occluded view would be expected to give the best prediction, whereas image feature for the same point but extracted from an occluded view or a lateral view would be expected to give poor prediction. Hence, average pooling would in principle not be the best way for feature fusion. Researchers therefore explored different fusion strategies, such as SMPL-visibility based [63] and attention based [70] approaches, but all of these still produce undesirable artifacts in their reconstructions (see Fig. 7). To lessen the effect of features extracted from non-optimal views, we propose a novel occlusion-aware feature fusion strategy based on ray tracing [19] with the fitted SMPL-X model. Given a 3D point " + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": ", we cast a ray from " + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": " to the " + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": "-th view through orthogonal projection and find the intersection point " + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "inline_equation", + "content": "X_{i}^{\\prime}" + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": " with the SMPL-X model that is the closest to the image (see Fig. 2). We then compute a weight for the feature " + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "inline_equation", + "content": "F_{i}(X)" + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": " extracted from the " + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 313, + 546, + 553 + ], + "type": "text", + "content": "-th view by" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 557, + 545, + 583 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 557, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 364, + 557, + 545, + 583 + ], + "type": "interline_equation", + "content": "w _ {i} (X) = \\frac {1}{\\left| Z _ {i} (X) - Z _ {i} \\left(X _ {i} ^ {\\prime}\\right) \\right|}. \\tag {9}", + "image_path": "595dd51457d1979701794093a1a26a2a43eaac20d4e9ac2d8afa8467ce92f233.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 587, + 501, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 501, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 501, + 600 + ], + "type": "text", + "content": "Finally, we fuse all features from the " + }, + { + "bbox": [ + 306, + 587, + 501, + 600 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 306, + 587, + 501, + 600 + ], + "type": "text", + "content": " views by" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 353, + 604, + 545, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 604, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 353, + 604, + 545, + 633 + ], + "type": "interline_equation", + "content": "F _ {f u s e d} (X) = \\frac {\\sum_ {i = 1} ^ {n} w _ {i} (X) F _ {i} (X)}{\\sum_ {i = 1} ^ {n} w _ {i} (X)}. \\tag {10}", + "image_path": "84442dfc24380bd1b8c793349b3b00592b0b983f844f7d0445cb78cda3f26ffc.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 645, + 387, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 387, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 387, + 659 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We evaluate the performance of our SeSDF both qualitatively and quantitatively, and provide comparisons with other SOTA methods under both single-view and multiview setups." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4651" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 84, + 545, + 175 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 542, + 82 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 542, + 82 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 542, + 82 + ], + "type": "text", + "content": "Table 1. Qualitative comparison on the single-view setting. We report Chamfer Distance and P2S metrics (numbers the lower the better)." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 84, + 545, + 175 + ], + "lines": [ + { + "bbox": [ + 50, + 84, + 545, + 175 + ], + "spans": [ + { + "bbox": [ + 50, + 84, + 545, + 175 + ], + "type": "table", + "html": "
MethodFeature IncludedQuantitative Number
THuman2.0CAPE
2D FeatureNormal Information3D FeatureSMPLX Signed Distanceself-evolved Signed DistanceChamfer Distance↓P2S↓Chmafer Distance↓P2S↓
PIFu [52]✓2.4032.3883.0592.818
PIFuHD [53]✓✓2.0081.9652.5712.427
PaMIR [71]✓✓1.4781.4511.6821.438
ICON [63]✓✓✓1.3011.2591.5331.431
Ours w/o DE✓✓✓✓1.0991.0341.3771.261
Ours w/o SeSDF✓✓✓✓1.2451.2001.4731.390
Ours✓✓✓✓1.0270.9711.3031.219
", + "image_path": "2676794f6acd49885eb7fd05ca1b34d346095042eb916ea6019954c4c7d959c6.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 196, + 286, + 305 + ], + "blocks": [ + { + "bbox": [ + 58, + 184, + 274, + 194 + ], + "lines": [ + { + "bbox": [ + 58, + 184, + 274, + 194 + ], + "spans": [ + { + "bbox": [ + 58, + 184, + 274, + 194 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on the multi-view setting." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 196, + 286, + 305 + ], + "lines": [ + { + "bbox": [ + 50, + 196, + 286, + 305 + ], + "spans": [ + { + "bbox": [ + 50, + 196, + 286, + 305 + ], + "type": "table", + "html": "
MethodTHuman2.0CAPE
Chamfer Distance↓P2S↓Chmafer Distance↓P2S↓
multi-view PIFu [52]0.8640.8380.9200.876
multi-view PIFuHD [53]0.8310.8040.8830.849
multi-view PaMIR [71]0.8070.7620.8580.819
Ours w/o DE0.7950.7490.8490.811
Ours w/o SeSDF0.8020.7550.8540.815
Ours0.7910.7420.8410.800
Ours w/ Attention0.7940.7430.8450.803
Ours w/ SMPLX-Vis0.8410.8320.9250.917
Ours w/ Normal-Fusion0.8010.7540.8500.812
", + "image_path": "9cff9a1c1a70a6d69b901c7ccfdfa825af61473a2a634ec8996f70c573379028.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 312, + 287, + 481 + ], + "blocks": [ + { + "bbox": [ + 50, + 312, + 287, + 481 + ], + "lines": [ + { + "bbox": [ + 50, + 312, + 287, + 481 + ], + "spans": [ + { + "bbox": [ + 50, + 312, + 287, + 481 + ], + "type": "image", + "image_path": "dc75e76ee5ed56eb7135e2496e0366ec20af9e7ddfaed875d4d0c22d3be51913.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 483, + 287, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 515 + ], + "type": "text", + "content": "Figure 3. Qualitative comparison with SOTA methods on real-world images. Our method can reconstruct fine details and work robustly under challenge poses. Best viewed in PDF with zoom." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 525, + 178, + 538 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 178, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 178, + 538 + ], + "type": "text", + "content": "4.1. Implementation details" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "content": "For each training subject, we sample (a) 5,000 surface points as " + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "inline_equation", + "content": "G_{s}" + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "content": ", which are evenly distributed on the mesh surface; (b) 5,000 occupancy-target points as " + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "inline_equation", + "content": "G_{o}" + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "content": " in the 3D space, for which we follow the sampling strategy in [52]. In particular, 15/16 points in " + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "inline_equation", + "content": "G_{o}" + }, + { + "bbox": [ + 46, + 544, + 286, + 651 + ], + "type": "text", + "content": " are evenly sampled on the mesh surface. Gaussian perturbation is then applied to them along the surface normal direction. The rest 1/16 points are randomly sampled within the predefined 3D space where the mesh lies in." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "type": "text", + "content": "We employ Rembg [1] to segment out the background for real-world images and use Kaolin [2] to calculate the SDF from the SMPL-X model. We apply PIXIE [16] to estimate the SMPL-X model for the segmented human subject. To compute the image features, we implement a stacked-" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "text", + "content": "hourglass image encoder with bi-linear interpolation to extract pixel-aligned image feature " + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "inline_equation", + "content": "F_{2D}(\\cdot) \\in \\mathbb{R}^{256}" + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "text", + "content": ". We follow [7, 50] to employ PointNet with 3D-UNet and tri-linear interpolation to extract space-aligned 3D features " + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "inline_equation", + "content": "F_{3D}(\\cdot) \\in \\mathbb{R}^{128}" + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "text", + "content": ". Distance encoding maps the signed distance to a higher dimensional space " + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(d) \\in \\mathbb{R}^{13}" + }, + { + "bbox": [ + 304, + 185, + 545, + 340 + ], + "type": "text", + "content": " using the high-frequency functions as defined in Eq. (4). We implement our framework in PyTorch [46]. Our SeSDF framework is trained separately for 12 epochs with the learning rate starting from 1e-4 and updated by the factor 0.1 for every 4 epochs, for both single-view and multi-view experiments. Code for SeSDF will be made publicly available. Project page: https://yukangcao.github.io/SeSDF/." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 347, + 477, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 347, + 477, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 347, + 477, + 358 + ], + "type": "text", + "content": "4.2. Datasets and evaluation metrics" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "type": "text", + "content": "We employ the THUman2.0 dataset [65] as our primary testbed. The dataset comprises 526 high-fidelity meshes captured via dense DSLR rigs. Each subject within the dataset is accompanied by its corresponding texture map and fitted SMPL-X parameters. We split the THUman2.0 dataset into a training set with 465 subjects, and a test set with 61 subjects. We render each human subject into 360 images, sequentially separated by " + }, + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "type": "inline_equation", + "content": "1^{\\circ}" + }, + { + "bbox": [ + 304, + 365, + 545, + 484 + ], + "type": "text", + "content": " around the subject, with different albedo to augment the dataset to carry out the experiments." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": "To further show the generalizability of SeSDF, we also compare our method with others on the CAPE [37] test set, which contains 150 subjects. To conduct quantitative evaluations of different methods, we employ standard Point-to-Surface distance (P2S) and Chamfer distance metrics as evaluation criteria. We compare the reconstructed models from images captured at different angles, i.e., " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "135^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "180^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "225^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "270^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "inline_equation", + "content": "315^{\\circ}" + }, + { + "bbox": [ + 304, + 485, + 545, + 604 + ], + "type": "text", + "content": ", against the ground truth under corresponding orientations. Besides, we use real-world images for extra qualitative evaluation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 611, + 489, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 489, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 489, + 624 + ], + "type": "text", + "content": "4.3. Comparison on single-view setting" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 712 + ], + "type": "text", + "content": "We first evaluate and compare the performance of single-view 3D human reconstruction between ours and SOTA methods. Specifically, we compare with PIFu [52], PIFuHD [53], PaMIR [71], ARCH [26], ARCH++ [23] and ICON [63]. PHORHUM [5] is not compared here due to the absence of publicly available code base. We retrain PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 dataset for" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4652" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 547, + 233 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 547, + 233 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 547, + 233 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 547, + 233 + ], + "type": "image", + "image_path": "86f3087f59438141c1f7c807278d7e98dadc6a592345a56ed56d0d8a0eec9c2a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 235, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 235, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 546, + 257 + ], + "type": "text", + "content": "Figure 4. Comparison with ICON on real-world (top) and THUman2.0 data (bottom). Ours (SeSDF) can produce results with more fine geometry details. Best viewed in PDF with zoom." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 266, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 289 + ], + "type": "text", + "content": "a fair comparison, and obtain the reconstructions of ARCH and " + }, + { + "bbox": [ + 46, + 266, + 287, + 289 + ], + "type": "inline_equation", + "content": "\\mathrm{ARCH} + +" + }, + { + "bbox": [ + 46, + 266, + 287, + 289 + ], + "type": "text", + "content": " with the help of their authors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 292, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 519 + ], + "type": "text", + "content": "Quantitative comparison and ablation In Table 1, we compare our method with the SOTA methods, i.e., PIFu, PIFuHD, PaMIR, and ICON on the THUman2.0 and CAPE datasets. As can be seen, for all metrics, our method significantly outperforms the SOTA by a large margin on both datasets. Among these SOTA methods, ICON also employs the SMPL-X model to extract SDF to guide learning, while our method consistently outperforms ICON across the board. We also validate the effectiveness of different components of our method. All components have positive effects on the reconstruction results, while the SeSDF module plays the most crucial role in the improvement. By comparing the last two rows, we can see that the SeSDF module brings much more improvement than the SDF derived from the SMPL-X model. By comparing the last row with all others, we can observe that our SeSDF brings the most improvement among all components. By comparing \"Ours\" and \"Ours w/o DE\", we can see that our proposed distance encoding is also effective in improving the performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 521, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 640 + ], + "type": "text", + "content": "Qualitative comparison We present qualitative comparison in Fig. 3 on real-world images with SOTA methods. Our proposed method has the capability to reconstruct fine geometry details and handle the inputs with complicated poses. Among the SOTA methods, ICON also employs SMPL-X to improve the robustness, though in a different way from our work. We provide a further comparison with ICON in Fig. 4 on THUman2.0 and real-world images. As can be seen, our method notably outperforms ICON with more fine details in all cases." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 647, + 230, + 661 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 230, + 661 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 230, + 661 + ], + "type": "text", + "content": "4.4. Comparison on multi-view setting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 712 + ], + "type": "text", + "content": "For multi-view reconstruction, we compare with the SOTA methods PIFu, PIFuHD, and PaMIR which allow multi-view reconstruction. In the experiments, we use three input views unless stated otherwise." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 266, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 545, + 373 + ], + "type": "text", + "content": "Quantitative comparison and ablation We report the comparison results in Table 2. To have a fair comparison with other methods which are calibrated, we also implemented our self-calibration method for all of them. We can see that our method outperforms other methods in all cases. Similar to the single-view experiments, by comparing \"Ours\" against \"Ours /wo DE\" and \"Ours /wo SeSDF\", we can see that our distance encoding and SeSDF play critical roles in the performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 376, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 448 + ], + "type": "text", + "content": "Qualitative comparison We present qualitative comparison in Fig. 5 for multi-view reconstruction. The reconstruction results of our method retain more details, e.g., clothing wrinkles and hair topology, which are contained in the ground truth. We provide more results with different numbers of views in the supplementary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 452, + 409, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 409, + 463 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 409, + 463 + ], + "type": "text", + "content": "4.4.1 Further analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 472, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 638 + ], + "type": "text", + "content": "Self-calibration [74] also introduced an alternative method for self-calibration of multi-view reconstruction by introducing a deformation field to deform points from the canonical space to the camera space, through SMPL linear blend skinning (LBS) weights. We also follow the paper to implement it for SMPL-X in our framework and compare it with our method in Fig. 6. We observe wide-spreading artifacts across the whole body of the reconstruction using the deformation field for the uncalibrated setting. The deformation field is error-prone because the LBS weights are computed to deform the parametric human model, which inherently lacks the fine details of the actual human subject, limiting its final performance and introducing the artifacts for reconstruction." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Feature fusion We compare our occlusion-aware feature fusion strategy with other alternatives, namely (1) AVGPool [52], (2) SMPLX-visibility [63], and (3) Attention-based method [32] in Fig. 7. As can be seen, our occlusion-aware strategy achieves better performance than the others. See supplementary for more analysis." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4653" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 547, + 355 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 87, + 79 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 87, + 79 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 87, + 79 + ], + "type": "text", + "content": "SOTA - Ours" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 70, + 547, + 355 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 547, + 355 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 547, + 355 + ], + "type": "image", + "image_path": "bce13ec17c62b794307ea95fe3694b7131fe99a649d89854b92aac85c5a6d28c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 356, + 545, + 377 + ], + "lines": [ + { + "bbox": [ + 47, + 356, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 47, + 356, + 545, + 377 + ], + "type": "text", + "content": "Figure 5. Comparison with SOTA methods on the multi-view setting. Ours (SeSDF) consistently retains more geometry details, e.g., clothing wrinkles, hairs, and faces." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 384, + 286, + 490 + ], + "blocks": [ + { + "bbox": [ + 48, + 384, + 286, + 490 + ], + "lines": [ + { + "bbox": [ + 48, + 384, + 286, + 490 + ], + "spans": [ + { + "bbox": [ + 48, + 384, + 286, + 490 + ], + "type": "image", + "image_path": "aec163f8f55bc24475d9d9d2ed147da3809a98625026c90f9a4a60d1840baa91.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 492, + 286, + 524 + ], + "lines": [ + { + "bbox": [ + 47, + 492, + 286, + 524 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 286, + 524 + ], + "type": "text", + "content": "Figure 6. Comparing our self-calibration method (\"Ours\") with an SMPL-X deformation field alternative (\"DF\"). Best viewed in PDF with zoom." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 534, + 119, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 119, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 119, + 547 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 555, + 287, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 698 + ], + "type": "text", + "content": "In this paper, we have presented a new framework for single- and multi-view clothed human reconstruction under an uncalibrated setting. Our framework can take an arbitrary number of input images to reconstruct faithful 3D human models. We have proposed a self-evolved signed distance (SeSDF) module to recover more geometry details, a method for self-calibrating multi-view images via SMPL-X model fitting, and an effective multi-view occlusion-aware feature fusion strategy to aggregate useful features across views for robust reconstruction. Our method notably outperforms previous SOTA methods in both terms of qualitative and quantitative results." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "Limitation Though our SeSDF can deal with various" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 384, + 545, + 478 + ], + "blocks": [ + { + "bbox": [ + 309, + 384, + 545, + 478 + ], + "lines": [ + { + "bbox": [ + 309, + 384, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 309, + 384, + 545, + 478 + ], + "type": "image", + "image_path": "7e5da041a2421b0d5ceb53981fa9eb8daa89e19ceee7ae5af78ecefa70996c19.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 479, + 545, + 502 + ], + "lines": [ + { + "bbox": [ + 306, + 479, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 545, + 502 + ], + "type": "text", + "content": "Figure 7. Comparing our occlusion-aware feature fusion with other alternative fusion strategies." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 516, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 516, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 516, + 545, + 552 + ], + "type": "text", + "content": "poses and retain fine clothing topology, it still has difficulties when handling extremely loose clothes, e.g., dresses, which deviate significantly from the parametric prior." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 554, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 637 + ], + "type": "text", + "content": "Potential Social Impact Our method takes a step towards practical tools for real-world application, as it does not require expensive equipment to get the 3D models. However, despite its intended positive usage, there might be potential risks of falsifying human avatars, which unfortunately compromise personal privacy. Transparency and authentication will be helpful to prevent these vicious uses." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 639, + 545, + 710 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 639, + 545, + 710 + ], + "spans": [ + { + "bbox": [ + 304, + 639, + 545, + 710 + ], + "type": "text", + "content": "Acknowledgements This work is partially supported by Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27208022) and HKU Seed Fund for Basic Research. We appreciate the very helpful discussions with Dr. Guanying Chen. We also thank Yuliang Xiu, Yuanlu Xu for ARCH and " + }, + { + "bbox": [ + 304, + 639, + 545, + 710 + ], + "type": "inline_equation", + "content": "\\mathrm{ARCH + + }" + }, + { + "bbox": [ + 304, + 639, + 545, + 710 + ], + "type": "text", + "content": " results." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4654" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 274, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 274, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 274, + 102 + ], + "type": "text", + "content": "[1] https://github.com/danielgatis/rembg.6" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 102, + 287, + 121 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 102, + 287, + 121 + ], + "spans": [ + { + "bbox": [ + 53, + 102, + 287, + 121 + ], + "type": "text", + "content": "[2] https://github.com/NVIDIAGameWorks/kaolin.6" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 122, + 287, + 175 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 122, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 53, + 122, + 287, + 175 + ], + "type": "text", + "content": "[3] Thiemo Alldieck, Marcus Magnor, Bharat Lal Bhatnagar, Christian Theobalt, and Gerard Pons-Moll. 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NeRFs have not yet tackled scenes in which the medium strongly influences the appearances of objects, as in the case of underwater imagery. By incorporating a scattering image formation model into the NeRF rendering equations, we are able to separate the scene into 'clean' and backscatter components. Consequently, we can render photorealistic novel-views with or without the participating medium, in the latter case recovering colors as if the image was taken in clear air. Results on the Curaçao scene: A RAW image (left) is brightened and white balanced (WB) for visualization, showing more detail, while areas further from the camera (top-right corner) are occluded and attenuated by severe backscatter - which is effectively removed in our restored image. Please zoom-in to observe the details." + ], + "image_footnote": [], + "bbox": [ + 241, + 262, + 401, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7543c7c5b3cb5e27b138d1ad76511d71215ea068d1255f20ec94f1900dd45cf9.jpg", + "image_caption": [ + "Ours Novel View" + ], + "image_footnote": [], + "bbox": [ + 403, + 262, + 563, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bf1cd10a4a71cad6a84b63c6abc291f9a3f4a4feac8187eddd1c303da7f8309d.jpg", + "image_caption": [ + "Ours Restored" + ], + "image_footnote": [], + "bbox": [ + 566, + 262, + 727, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/10cbd281937075f60a52b2b327c12476fdc137f772a071f5a9437fb982661133.jpg", + "image_caption": [ + "Ours Backscatter" + ], + "image_footnote": [], + "bbox": [ + 730, + 262, + 890, + 345 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 450, + 313, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Research on neural radiance fields (NeRFs) for novel view generation is exploding with new models and extensions. However, a question that remains unanswered is what happens in underwater or foggy scenes where the medium strongly influences the appearance of objects. Thus far, NeRF and its variants have ignored these cases. However, since the NeRF framework is based on volumetric rendering, it has inherent capability to account for the medium's effects, once modeled appropriately. We develop a new rendering model for NeRFs in scattering media, which is based on the SeaThru image formation model, and suggest a suitable architecture for learning both scene information and medium parameters. We demonstrate the strength of our method using simulated and real-world scenes, correctly rendering novel photorealistic views underwater. Even more excitingly, we can render clear views of these scenes, removing the medium between the camera and the scene and reconstructing the appearance and depth of far objects, which are severely occluded by the medium. Our code and unique datasets are available on the project's website.", + "bbox": [ + 75, + 479, + 472, + 782 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 797, + 209, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The pioneering work of Mildenhall et al. [25] on Neural Radiance Fields (NeRFs) has tremendously advanced the field of Neural Rendering, due to its flexibility and unprecedented quality of synthesized images. Yet, the formulations of the original NeRF [25] and its followup variants assume", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "that images were acquired in clear air, i.e., in a medium that does not scatter or absorb light in a significant manner and that the acquired image is composed solely of the object radiance. The NeRF formulation is based on volumetric rendering equations that take into account sampled points along 3D rays. Assuming a clear air environment, an implicit assumption, which is often enforced explicitly with dedicated loss components [5], is that a single opaque (high density) object is encountered per ray, with zero density between the camera and the object.", + "bbox": [ + 496, + 450, + 890, + 603 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In stark contrast to clear air case, when the medium is absorbing and / or scattering (e.g., haze, fog, smog, and all aquatic habitats), the volume rendering equation has a true volumetric meaning, as the entire volume, and not only the object, contributes to image intensity. As the NeRF model estimates color and density at every point of a scene, it lends itself perfectly to general volumetric rendering, given that the appropriate rendering model is used. Here, we bridge this gap with SeaThru-NeRF, a framework that incorporates a rendering model that takes into account scattering media.", + "bbox": [ + 496, + 608, + 892, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This is achieved by assigning separate color and density parameters to the object (scene) and the medium, within the NeRF framework. Our approach adopts the SeaThru underwater image formation model [1, 3] to account for scattering media. SeaThru is a generalization of the standard wavelength-independent attenuation (e.g., fog) image formation model, where two different wideband coefficients are used to represent the medium, which is more accurate when attenuation is wavelength-dependent (as in all wa", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "56", + "bbox": [ + 488, + 945, + 508, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ter bodies and under some atmospheric conditions). In our model, the medium parameters are separate per color channel, and are learned functions of the viewing angles, enforcing them to be constant only along 3D rays in the scene.", + "bbox": [ + 75, + 90, + 467, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Attempting to optimize existing NeRFs on scenes with scattering medium results in cloud-like objects floating in space, while our formulation enables the network to learn the correct representation of the entire 3D volume, that consists of both the scene and the medium. Our experiments demonstrate that SeaThru-NeRF produces state-of-the-art photorealistic novel view synthesis on simulated and challenging real-world scenes (see Fig. 1) with scattering media, that include complex geometries and appearances. In addition, it enables:", + "bbox": [ + 75, + 152, + 467, + 301 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Color restoration of the scenes as if they were not imaged through a medium, as our modeling allows full separation of object appearance from the medium effects.", + "2. Estimation of 3D scene structure which surpasses that of structure-from-motion (SFM) or current NeRFs, especially in far areas of bad visibility, as we jointly reconstruct and reason for the geometry and medium.", + "3. Estimation of wideband medium parameters, which are informative properties of the captured environment, and potentially allowing simulation under different conditions." + ], + "bbox": [ + 75, + 301, + 467, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 467, + 217, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Radiance Fields (NeRFs): The original work on NeRFs [25] has paved the way to a large capacity of followup work, with rapid and significant progress in many related aspects. For brevity, we focus in the following only on works closely related to ours, and refer the reader to a comprehensive review of the field [43] prior to the introduction of NeRFs, and to [44] for the most recent.", + "bbox": [ + 75, + 492, + 467, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NeRFs have been recently shown to be extremely powerful in multi-image settings that involve computational imaging tasks. These include HDR [50], de-blurring [20], superresolution [49], low-light enhancement [23] and denoising [32]. The need to recover the clean 'medium-free' version of images degraded by scattering and attenuation effects, likewise, can benefit from the neural rendering approach. SeaThru-NeRF is designed to model the degradation, with the ability to recover its parameters, and reconstruct the clean underlying scene and novel-view images.", + "bbox": [ + 75, + 599, + 467, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work is related to recent efforts to improve the quality and robustness of NeRFs in challenging environments (e.g. [14, 21, 29]). Nerf-W [21] learns a per-image latent embedding that can capture appearance variations in complex scenes. It decomposes the scene into image-dependent and shared components to disentangle transient elements from the static scene. NeRFRen [14] is designed for scenes with reflections. It separates the scene as a sum of transmitted and reflected components, which are modeled as separate NeRFs. Ref-NeRF [47] introduces a new parameteriza", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion and structuring of view-dependent appearance, which can represent scenes with specularities and reflections.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach has much in common with some of these methods, most notably the way of reconstructing the target image as a composition of components: 'direct' and 'backscatter' in our case, 'transient' and 'static' in [21], or 'transmitted' and 'reflected' in [14]. However, as we demonstrate, these methods are limited on scenes in scattering media as they do not explicitly model the effects of the medium. Our method is different in that it can model a continuous medium component that is not an object.", + "bbox": [ + 496, + 121, + 890, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Graphics and Vision in Scattering Media: Propagation of light in a medium is governed by the radiative transfer equation [10]. This equation describes light interaction per particle in the medium and requires extensive Monte Carlo simulations for complete solutions [12, 16, 30, 31], see [30] for an excellent review. In many cases simplifying assumptions can be made about the medium that ease rendering [22], where the major one is single-scattering [33, 42, 48]. Realistic rendering requires having the scattering properties of the medium, which can be estimated in the lab [13, 26], or from in situ images [6]. An MLP for rendering synthetic atmospheric clouds was suggested in [17].", + "bbox": [ + 496, + 265, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In computer vision, image formation models under ambient illumination for bad weather [28] and underwater [37] share the same general structure for the case of horizontal viewing. Artificial illumination used underwater [46] and in fog has additional terms that account for the nonuniformity of the source. Underwater, the medium parameters exhibit strong wavelength dependency that was shown to affect model accuracy in wideband camera channels. The SeaThru model [1-3] was suggested to overcome this issue.", + "bbox": [ + 496, + 446, + 890, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Scene reconstruction in scattering media is an ill-posed problem which was initially solved with multiple frames [27,37,38,46]. Later on, single-image methods have proposed a multitude of image priors to overcome the ill-posed nature of the problem, see [19,51] for comprehensive reviews on single-image dehazing and underwater reconstruction, respectively. The introduction of deep-learning has led to an explosion of single-image dehazing and underwater reconstruction networks. See [41] and [4] for recent reviews of deep-learning dehazing and underwater reconstruction works, respectively.", + "bbox": [ + 496, + 583, + 890, + 750 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Underwater, it was suggested to solve for the 3D structure of the scene, prior to image restoration [9, 35] using the haze model and [2] using the revised one. In SeaThruNeRF, we simultaneously reconstruct the scene and its 3D structure, yielding multiple advantages that we demonstrate empirically. WaterNeRF [40] suggests an underwater neural renderer that estimates the medium parameters only with respect to histogram-qualified images, separately from the rendering. Here, we show the huge benefit of modeling the scattering medium within the rendering equations, over a", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "57", + "bbox": [ + 488, + 945, + 506, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "variety of different scenes. Concurrently and independently to our work, [11] presented a NeRF for haze.", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Scientific Background", + "text_level": 1, + "bbox": [ + 76, + 133, + 285, + 152 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Neural Radiance Fields (NeRFs)", + "text_level": 1, + "bbox": [ + 76, + 159, + 361, + 175 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The original NeRF formulation [25] implicitly represents a 3D scene by a trainable continuous function. It is typically parameterized by an MLP $f_{\\Theta}:(\\mathbf{x},\\mathbf{d})\\to (\\mathbf{c},\\sigma)$ which encodes the density $\\sigma$ at the 3D point $\\mathbf{x} = (x,y,z)$ and the color $\\mathbf{c} = (r,g,b)$ emitted from this point in the viewing direction $\\mathbf{d} = (\\theta ,\\phi)$ (which is typically represented as a 2-element unit normalized 3D vector).", + "bbox": [ + 76, + 181, + 468, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This simple representation is used to simulate classical image-based rendering, by color accumulation along rays that are back-projected from a posed camera. If we parameterize points along a camera ray $\\mathbf{r}$ by $\\mathbf{r}(t) = \\mathbf{o} + \\mathbf{d}(t)$ , where $\\mathbf{o}$ is the camera center and $t\\in \\mathbb{R}_+$ , the expected (image) color $C(\\mathbf{r})$ along the ray can be written as:", + "bbox": [ + 76, + 287, + 468, + 378 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (t) \\mathbf {c} (t) d t \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 390, + 468, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where: integration along the ray is limited to the range $t \\in [t_n, t_f]$ (near and far bounds on the scene contents); $\\sigma(t)$ and $\\mathbf{c}(t)$ are shorthands for the density at the point $\\mathbf{r}(t)$ and its emitted color towards the camera center; $T(t)$ denotes the accumulated transmittance along the ray from $t_n$ to $t$ (the probability that the ray travels from $t_n$ to $t$ without hitting other particles along the way), and is given by:", + "bbox": [ + 76, + 435, + 468, + 541 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\sigma (s) d s\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 551, + 468, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In practice, the rendered color $C(\\mathbf{r})$ in Eq. (1) is approximated with the quadrature rule, by discretizing the range $[t_n, t_f]$ into a set of $N$ intervals $I_i = [s_i, s_{i+1}]$ (where $t_n = s_0 < \\dots < s_N = t_f$ ), assuming that the density $\\sigma$ and color $\\mathbf{c}$ are constant along each interval (e.g. by querying the model once per interval at its center-point).", + "bbox": [ + 76, + 595, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the discretized version of Eq. (1):", + "bbox": [ + 96, + 686, + 336, + 703 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} C _ {i} (\\mathbf {r}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 713, + 468, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the contribution $C_i(\\mathbf{r})$ of the interval $I_{i}$ is given by:", + "bbox": [ + 76, + 765, + 418, + 781 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i} (\\mathbf {r}) = \\int_ {s _ {i}} ^ {s _ {i + 1}} T (t) \\sigma_ {i} \\mathbf {c} _ {i} d t = T \\left(s _ {i}\\right) \\left(1 - e ^ {- \\sigma_ {i} \\delta_ {i}}\\right) \\mathbf {c} _ {i} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 791, + 468, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\sigma_{i}$ and $\\mathbf{c_i}$ are the (constant) density and color along the $i$ th interval, whose length is $\\delta_{i} = s_{i + 1} - s_{i}$ , and the", + "bbox": [ + 76, + 835, + 468, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "transmittance $T(s_{i})$ at the beginning of the interval is:", + "bbox": [ + 500, + 90, + 856, + 106 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nT \\left(s _ {i}\\right) = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} \\delta_ {j}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 118, + 890, + 160 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This fully differentiable NeRF model (with the discretized rendering scheme) is trained with a simple reconstruction loss", + "bbox": [ + 498, + 170, + 890, + 214 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = \\sum_ {\\mathbf {r} \\in R} \\| \\hat {C} (\\mathbf {r}) - C (\\mathbf {r}) \\| ^ {2} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 224, + 890, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "comparing each rendered training image pixel $\\hat{C}(\\mathbf{r})$ to its ground truth color $C(\\mathbf{r})$ . The model can then be used to synthesize photorealistic novel view images.", + "bbox": [ + 498, + 268, + 890, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Image Formation in Scattering Media", + "text_level": 1, + "bbox": [ + 500, + 323, + 825, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image formation in fog, haze, or underwater differs from image formation in clear air in two major aspects. First, the direct signal emanating from the object is attenuated as a function of distance and wavelength. Second, this signal is occluded by backscatter (termed also path-radiance or veiling-light) - radiance that is added due to the in-scattering from the particles along the line-of-sight (LOS), illustrated in Fig. 2. The intensity and color of the occluding backscatter layer are independent of the scene contents, and its intensity accumulates along the LOS, increasing with distance. As a result, the visibility and contrast of further objects is significantly reduced and their colors are distorted.", + "bbox": [ + 498, + 347, + 890, + 526 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We adopt the revised model [1] as the general model for image formation in scattering media under ambient illumination. Image intensity (per pixel, per color channel) is given as:", + "bbox": [ + 498, + 527, + 890, + 587 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI = \\underbrace {\\underbrace {J} _ {\\text {c o l o r}} \\cdot \\underbrace {(e ^ {- \\beta^ {D} (\\mathbf {v} _ {D}) \\cdot z})} _ {\\text {a t t e n u a t i o n}}} _ {B ^ {\\infty}} + \\underbrace {(1 - e ^ {- \\beta^ {B} (\\mathbf {v} _ {B}) \\cdot z})} _ {\\text {a t t e n u a t i o n}} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 593, + 890, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $I$ is the linear image captured by the camera of a scene with range $z$ , $J$ is the clear scene that would have been captured had there been no medium along $z$ , and $B^{\\infty}$ is the backscatter water color at infinity, i.e., the backscatter at areas that contain no objects. Lastly, $\\beta^{D}$ and $\\beta^{B}$ are the attenuation and backscatter coefficients, respectively, the two parameters that describe the medium effects. The vectors $\\mathbf{v}_D$ and $\\mathbf{v}_B$ represent the dependencies of $\\beta^{D}$ and $\\beta^{B}$ on range, object reflectance, spectrum of ambient light, spectral response of the camera, and the physical scattering and beam attenuation coefficients of the water body, all of which are functions of wavelength. It was shown in [2] that $\\beta^{B}$ can be assumed constant in an image, while $\\beta^{D}$ mainly depends on the object distance and weakly on object reflectance, thus solving for the full model requires at least 6 unknowns. The value of $B^{\\infty}$ is usually assumed to be uniform in the scene", + "bbox": [ + 498, + 659, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Vectors (3D coordinates or color components) are denoted in **bold**.", + "bbox": [ + 93, + 875, + 452, + 886 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2Each color channel is integrated separately.", + "bbox": [ + 96, + 887, + 331, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "58", + "bbox": [ + 490, + 945, + 506, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/45b49dc455da358dbb8d9ac6aafbdd045287c23d9955eab3cd5487e1097e5da4.jpg", + "image_caption": [ + "Figure 2. An illustration of our ray model. We assume a scene with at most a single opaque object at every ray. The medium is semitransparent with constant density per-ray. The densities governing the backscatter and the object in water are not the same [1]." + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 426, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "but as discussed in [6] it is almost never really uniform, because of the directionality of the sun, among other factors.", + "bbox": [ + 75, + 316, + 468, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This model is also applicable to haze and fog, where attenuation has very little dependence on wavelength. Then, image formation is greatly simplified because it can be assumed that there is only one medium parameter that is uniform across the color channels, represented by a scalar $(\\beta^{D} = \\beta^{B} = \\beta)$ [38]. Underwater, often the simplifying (less accurate) assumption that $\\beta^{D} = \\beta^{B}$ is made, reducing to 3 unknowns [6,7,37].", + "bbox": [ + 75, + 347, + 468, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. SeaThru-NeRF", + "text_level": 1, + "bbox": [ + 76, + 481, + 228, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Basic Model Derivation", + "text_level": 1, + "bbox": [ + 76, + 506, + 294, + 522 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here we consider a more general setting than the original NeRF [25], in which light travels through a scattering medium rather than free-space, resulting in a significant impact on the captured color. Following [22] we suggest adding the medium to Eqs. (1) and (2):", + "bbox": [ + 75, + 529, + 468, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\left(\\sigma^ {\\mathrm {o b j}} (t) \\mathbf {c} ^ {\\mathrm {o b j}} (t) + \\sigma^ {\\mathrm {m e d}} (t) \\mathbf {c} ^ {\\mathrm {m e d}} (t)\\right) d t \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 616, + 468, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where:", + "bbox": [ + 76, + 664, + 125, + 676 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\left(\\sigma^ {\\mathrm {o b j}} (s) + \\sigma^ {\\mathrm {m e d}} (s)\\right) d s\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 686, + 468, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "using separate color and density parameters for the object and medium. Notice that these equations reduce to Eqs. (1) and (2) by simply considering the case where the medium density $\\sigma^{\\mathrm{med}}$ is zero.", + "bbox": [ + 75, + 732, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Moving to the discretized version, we similarly get3 the following generalizations of Eqs. (4) and (5):", + "bbox": [ + 75, + 792, + 468, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC _ {i} (\\mathbf {r}) = T \\left(s _ {i}\\right) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {o b j}} \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}} \\mathbf {c} _ {i} ^ {\\mathrm {m e d}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 832, + 468, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with transmittance", + "bbox": [ + 500, + 92, + 625, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT \\left(s _ {i}\\right) = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\left(\\sigma_ {j} ^ {\\mathrm {o b j}} + \\sigma_ {j} ^ {\\mathrm {m e d}}\\right) \\delta_ {j}\\right). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 114, + 890, + 157 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Splitting the discretized color rendering equations (3,10 and 11) into the 'object' and 'medium' components, we get:", + "bbox": [ + 500, + 167, + 890, + 198 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} \\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) + \\sum_ {i = 1} ^ {N} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 208, + 890, + 250 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T (s _ {i}) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {o b j}} \\mathbf {c} _ {i} ^ {\\mathrm {o b j}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 267, + 890, + 303 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T (s _ {i}) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {m e d}} \\mathbf {c} _ {i} ^ {\\mathrm {m e d}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 323, + 890, + 357 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As a first step towards constraining and simplifying our model, we constrain the medium parameters to be constant along 3D viewing rays. We drop the respective interval indices and remain with $\\sigma^{\\mathrm{med}}$ and $\\mathbf{c}^{\\mathrm{med}}$ that depend only on the ray $\\mathbf{r}$ . The $\\mathbf{c}^{\\mathrm{med}}$ uniformity stems from the common assumption of a uniform phase function (the dependence of scattered radiance on scattering angle) along the LOS [22, 30]. Regarding the density $\\sigma^{\\mathrm{med}}$ , we take it to be separate per color channel, but constant per ray. This is far less restrictive compared to models that assume constancy per image or even per scene [2]. These constraints will be enforced by respective structural choices in the network.", + "bbox": [ + 496, + 364, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, we assume that objects in the scene are opaque, hence the object density along the ray is close to zero except for a high peak in the object location. On the other hand, the medium is semi-transparent, characterized by a low non-zero density. This implies that $\\sigma^{\\mathrm{med}} \\gg \\sigma^{\\mathrm{obj}}$ before the object and $\\sigma^{\\mathrm{med}} \\ll \\sigma^{\\mathrm{obj}}$ at the object, as illustrated in Fig. 2. Therefore, Eqs. (13-14) reduce to", + "bbox": [ + 496, + 547, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i}}\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 662, + 890, + 688 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} \\delta_ {i}}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 690, + 890, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {i} = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} ^ {\\mathrm {o b j}} \\delta_ {j}\\right) \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {m e d}} s _ {i}\\right) \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 719, + 890, + 760 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Relation to Underwater Image Formation", + "text_level": 1, + "bbox": [ + 500, + 771, + 854, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section we show that our model can be reduced to the image formation model described in Sec. 3.2, which is not based on volumetric rendering. To this end we consider sampling the ray along intervals with constant size $\\delta$ , and the appearance of the opaque object at a depth $z$ , at the beginning of interval $I_{k} = [s_{k}, s_{k + 1}]$ , for some integer $k$ (that is: $s_{i} = i \\cdot \\delta$ for every $i$ and $z = k \\cdot \\delta$ in particular).", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "${}^{3}$ Full derivations of Eqs. (10,11) is provided in the appendix.", + "bbox": [ + 94, + 886, + 419, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "59", + "bbox": [ + 488, + 945, + 506, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5b0dbdf12734c0f32948c38960f8022fc6cf93fb57398cdacf664511df0ab80b.jpg", + "image_caption": [ + "Figure 3. SeaThru-NeRF architecture. The computation of the 'object' outputs (density and color, in green), follows the standard NeRF architecture, while the 'medium' components (in purple) are computed once per ray by a separate subnet (the 'medium MLP') that depends only on the viewing direction." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 455, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this case, $\\sigma_{i}^{\\mathrm{obj}}\\approx 0$ for all $i < k$ , and $\\sigma_k^{\\mathrm{obj}}\\gg \\sigma^{\\mathrm{med}}$ . This implies that $C_k^{\\mathrm{med}}(\\mathbf{r})\\ll C_k^{\\mathrm{obj}}(\\mathbf{r})$ and $C_i^{\\mathrm{obj}}(\\mathbf{r})\\approx 0$ , therefore we can write the rendering Eq. (12) as", + "bbox": [ + 76, + 343, + 468, + 395 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\mathbf {r}) \\approx \\hat {C} _ {k} ^ {\\mathrm {o b j}} (\\mathbf {r}) + \\sum_ {i = 0} ^ {k - 1} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 398, + 468, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, since the object is opaque, we can assume that the density $\\sigma_k^{\\mathrm{obj}}$ is large enough such that the transmittance at the end of the $k$ th interval $T(s_{k + 1})$ drops practically to zero, that is: $e^{-\\sigma_k^{\\mathrm{obj}}\\delta}\\approx 0$ . Therefore", + "bbox": [ + 76, + 452, + 468, + 515 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {C} _ {k} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta}\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} \\tag {19} \\\\ \\approx e ^ {- k \\sigma^ {\\mathrm {m e d}} \\delta} \\left(1 - e ^ {- \\sigma_ {k} ^ {\\mathrm {o b j}} \\delta}\\right) \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} \\approx e ^ {- \\sigma^ {\\mathrm {m e d}} \\delta \\cdot k} \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 526, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 76, + 584, + 106, + 595 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\sum_ {i = 0} ^ {k - 1} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = \\sum_ {i = 0} ^ {k - 1} T _ {i} \\cdot \\left(1 - e ^ {- \\sigma^ {\\mathrm {m e d}} \\delta}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\tag {20} \\\\ \\approx \\sum_ {i = 0} ^ {k - 1} e ^ {- i \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta} \\cdot \\left(1 - e ^ {- \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\\\ = \\left(1 - e ^ {- \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta \\cdot k}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 608, + 468, + 718 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Substituting Eqs. (19) and (20) into Eq. (18) (recalling that the depth $z$ equals $k \\cdot \\delta$ ) yields:", + "bbox": [ + 76, + 729, + 468, + 761 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} (\\mathbf {r}) \\approx e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} z} \\cdot \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} + \\left(1 - e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} z}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 773, + 468, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "resulting precisely in the commonly used scattering media image formation model [8, 37]. This can be seen by comparing to Eq. (7) where $\\sigma^{\\mathrm{med}} = \\beta^{D} = \\beta^{B}$ plays the role of the attenuation coefficient (equal for direct and backscatter), $\\mathbf{c}^{\\mathrm{med}}$ is the veiling light $B^{\\infty}$ (backscatter color at infinity) and $\\mathbf{c}_k^{\\mathrm{obj}}$ the clear image color $J$ .", + "bbox": [ + 76, + 810, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Final Model", + "text_level": 1, + "bbox": [ + 500, + 90, + 630, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We make several refinements with respect to the basic model presented in Section 4.1. In Sec. 4.2, we showed that our rendering equations lead to an image formation model with identical attenuation coefficients for the direct and backscatter components. Following the discussion in Sec. 3.2, and as has been shown in [1], when using such equations with a camera with wideband color channels, the effective $\\sigma^{\\mathrm{med}}$ that is experienced by the camera in $C_i^{\\mathrm{obj}}(\\mathbf{r})$ is different than the one experienced in $C_i^{\\mathrm{med}}(\\mathbf{r})$ . Therefore, in our final model we use different parameters for $\\sigma^{\\mathrm{med}}$ in each component and term them $\\sigma^{\\mathrm{attn}}$ and $\\sigma^{\\mathrm{bs}}$ for $C_i^{\\mathrm{obj}}(\\mathbf{r})$ and $C_i^{\\mathrm{med}}(\\mathbf{r})$ respectively. Our final equations are:", + "bbox": [ + 496, + 113, + 893, + 296 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {a t t n}} s _ {i}\\right) \\cdot \\left(1 - \\exp (- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i})\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 305, + 888, + 327 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {b s}} s _ {i}\\right) \\cdot \\left(1 - \\exp (- \\mathbf {o} ^ {\\mathrm {b s}} \\delta_ {i})\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 335, + 883, + 357 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nT _ {i} ^ {\\mathrm {o b j}} = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} ^ {\\mathrm {o b j}} \\delta_ {j}\\right) \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 375, + 890, + 415 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on our derivations we suggest the following architecture (Fig. 3). As in [25], the object properties are computed by a pair of MLPs, such that the density $\\sigma^{\\mathrm{obj}}$ is a function of the position $(x,y,z)$ only, while color $\\mathbf{c}^{\\mathrm{obj}}$ is determined by the viewing direction $(\\theta ,\\phi)$ as well. The medium parameters $\\mathbf{c}^{\\mathrm{med}}$ , $\\sigma^{\\mathrm{bs}}$ , $\\sigma^{\\mathrm{attn}}$ are handled by a separate MLP with only the direction input, following our decision to constrain them to be constant per viewing direction.", + "bbox": [ + 496, + 421, + 890, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Loss Function", + "text_level": 1, + "bbox": [ + 500, + 551, + 643, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let us denote the sequence of samples along a ray by $\\mathbf{s} = \\{s_i\\}_{i=0}^N$ , the object 'weight' at the $i$ th segment $[s_i, s_{i+1}]$ ,", + "bbox": [ + 498, + 575, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nw _ {i} ^ {\\mathrm {o b j}} = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\left(1 - \\exp \\left(- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i}\\right)\\right), \\tag {23}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 631, + 890, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the sequence of these weights by $\\mathbf{w} = \\{w_{i}^{\\mathrm{obj}}\\}_{i = 0}^{N - 1}$ and the ground-truth (supervised) pixel color by $C^*$ .", + "bbox": [ + 496, + 662, + 890, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our loss is the following combination:", + "bbox": [ + 517, + 695, + 774, + 710 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e c o n}} \\left(\\hat {C}, C ^ {*}\\right) + \\mathcal {L} _ {\\text {p r o p}} (\\mathbf {s}, \\mathbf {w}) + \\lambda \\mathcal {L} _ {\\text {a c c}} (\\mathbf {w}), \\tag {24}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 720, + 890, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda = 0.0001$ was chosen through cross-validation. Since we work on linear images, we adopt the reconstruction loss of RawNeRF [23]:", + "bbox": [ + 496, + 750, + 890, + 796 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e c o n}} (\\hat {C}, C ^ {*}) = \\left(\\frac {\\hat {C} - C ^ {*}}{\\operatorname {s g} (\\hat {C}) + \\epsilon}\\right) ^ {2} \\tag {25}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 805, + 890, + 844 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{sg}(\\cdot)$ stands for stop-gradient and $\\epsilon = 10^{-3}$ . The 'proposal' loss $\\mathcal{L}_{\\mathrm{prop}}(\\mathbf{s},\\mathbf{w})$ is an inherent part of Mip-NeRF-360 [5]. It penalizes for the discrepancy between the", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "60", + "bbox": [ + 488, + 945, + 506, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "distributions of object weights at 'original' and 'proposed' samplings, where only the latter is used for rendering [5].", + "bbox": [ + 75, + 90, + 467, + 119 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To enforce binary separation between points in space that contain objects and those that contain solely a medium - we add a prior on the transmittance $T_{i}^{\\mathrm{obj}}$ of each point on the ray to be either 0 or 1, not allowing semi-transparent objects. This is modelled as a mixture of two Laplacian distributions with modes at 0 and 1 (following [34]):", + "bbox": [ + 75, + 121, + 467, + 212 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {P} (x) \\propto e ^ {- \\frac {| x |}{0 . 1}} + e ^ {- \\frac {| 1 - x |}{0 . 1}} \\tag {26}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 217, + 467, + 238 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and use the negative log likelihood loss:", + "bbox": [ + 76, + 244, + 341, + 258 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {a c c}} (\\mathbf {w}) = - \\log \\mathbb {P} \\left(T _ {i} ^ {\\mathrm {o b j}}\\right). \\tag {27}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 263, + 467, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Implementation and Optimization", + "text_level": 1, + "bbox": [ + 76, + 289, + 375, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our implementation is based on the code released in Mip-NeRF-360 [5], choosing the best performing baseline on our scenes which was the forward-looking configuration with normalized device coordinates (NDC). For the mediumMLP, we use 6 linear layers with 256 features and a softplus activation, followed by 3 branches of dense layers and a sigmoid activation for predicting $c^{\\mathrm{med}}$ and softplus activations for $\\sigma^{\\mathrm{attn}}$ and $\\sigma^{\\mathrm{bs}}$ .", + "bbox": [ + 75, + 311, + 467, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the rendering scheme, [5] initialized the farthest $\\delta_{i}$ with infinity, enabling the network to predict a background color for rays that do not intersect with any object. We disabled this addition as it prevents our method from explaining the medium that contributes to the rendered color along the ray. We keep the learning rate and optimization parameters the same as in [5]. The network is trained for 250,000 iterations with a batch size of 16384 rays, taking around 10 hours on an Nvidia A100 GPU. The loss function and metrics are calculated on the output before any post-processing.", + "bbox": [ + 75, + 433, + 467, + 584 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments and Results", + "text_level": 1, + "bbox": [ + 76, + 595, + 310, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experiments", + "text_level": 1, + "bbox": [ + 76, + 619, + 210, + 636 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Real world scenes. We acquired multi-image underwater scenes by diving in three different seas: the Red Sea (Eilat, Israel), the Caribbean Sea (Curaçao) and the Pacific Sea (Panama) with a total of 20, 20 and 18 images respectively, from which three are set aside for validation in each set. This data encapsulates a diverse set of water conditions and imaging conditions. The images were acquired as RAW images with a Nikon D850 SLR camera in a Nauticam underwater housing with a dome port to avoid refractions that jeopardize the pinhole model [45], and downsampled to average size $900 \\times 1400$ . The input linear images were white-balanced before processing with $0.5\\%$ clipping per channel to remove extreme noisy pixels. Finally, COLMAP [39] is used to extract camera poses.", + "bbox": [ + 75, + 643, + 467, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Simulated Scene. We constructed a simulation using the Fern scene of the LLFF dataset [24]. We ran MIP-NeRF-360 [5] and used the predicted depth maps to simulate an", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e76c02e24c509eee74358fcd222d2de77aed7e948e491ef48541690e203edc54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 90, + 630, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b75cc51dd3dd65fea3a5c8d028a09d3d63c213554dd1aa70e4adaea791f993bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 90, + 759, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/69d4d0aac7da483266212b31a89eb2eb6b3a63d16d9622b4be46c39e289acf77.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 90, + 888, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ceed1ece2a7b01724ddb5059607f5d00ca9204eaac7907305cb47106c6b98bdd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 167, + 630, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0bd8ff890a1cfd96adad232ee4a16e1ebb97436ccc3b82474960c577171488b0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 167, + 759, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b7bf897e3df7a3dd420e99f2c6282ec87b1e3993e969ffcc6a8794d23c2452b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 167, + 888, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9dce81562f7a968f43764444a79c9ac9eb8658a7173852272d58df143f7d6e02.jpg", + "image_caption": [ + "Figure 4. Synthetic experiment on Fern scene of the LLFF dataset [24]. Top: Our method can handle 'in-air' scenes, with a uniform zeros backscatter image and a reconstruction PSNR that is close to that of the baseline [5] which was 23.73. Middle and bottom: Our method's separation between clean and backscatter components, for simulations of fog and underwater effects. The reconstruction quality degrades rather gracefully." + ], + "image_footnote": [], + "bbox": [ + 504, + 241, + 630, + 315 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fc572cd3afe20f6d204a4f79698955d198208524a665f656ef60841ab1ef2453.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 241, + 759, + 315 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d289341b13c66b2b7c84895cd01dcbfa0c6e625544acdcecddc1d1569a16715a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 241, + 888, + 315 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "underwater and a foggy scene. Water was added according to (7) with parameter values: $\\beta^D = [1.3, 1.2, 0.9]$ , $\\beta^B = [0.95, 0.85, 0.7]$ , $B^\\infty = [0.07, 0.2, 0.39]$ . Fog was simulated based on [36] with $\\beta = 1.2$ .", + "bbox": [ + 496, + 458, + 890, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baseline methods. The input to all methods is the same set of white-balanced linear images. In the task of rendering scenes in the medium we compare with the following NeRF methods: MIP-NeRF-360, forward-looking with NDC (MIP360) [5], NeRF-W [21] and NeRFReN [14]. In the task of reconstructing clean medium-free images we compare with NeRF-W, where the 'transient' component can be viewed as the clean image and the 'static' image as backscatter, and to NeRFReN with the 'reflected' and 'transmitted' components as clean and backscatter images. We additionally compare to single-image scene reconstruction methods: plain white balance, SeaThru [2], the leading \"classical\" methods of Bekerman et al [6], and the recent deep-learning based [52] (as well as [15, 52] whose results are provided in the project website). SeaThru requires depth maps, that we generate using SFM (with Agisoft Metashape) as originally suggested. These depth-maps are used to compare with those of the different methods.", + "bbox": [ + 496, + 527, + 890, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Photo-finishing: As the input and output images are linear, we apply photofinishing on all linear reconstructed scenes to enhance scene contrast and appearance, using the digital camera pipeline from [18]. 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"images/333781108bdfb1ce4706d97a4a4e65bc9e1d3c33473721a8051cd58ee56e408a.jpg", + "image_caption": [ + "Figure 5. Scene rendering in the medium, on 'Red Sea'. Left to right: white-balanced input image, our result, MIP360 [23], Nerf-W [21], NeRFReN [14]. [Top 2 rows] Train image and zoom-ins. Even in the task of overfitting to the training images, there are noticeable differences between the methods, and as can be seen in the zoom-ins (red squares) we are able to reconstruct fine details in further areas (albeit a lower PSNR). [Bottom 2 rows] Novel view and zoom-ins. Our method achieves the highest PSNR (see tables 1, 2), and provides much better details in further areas (see red square zoom-ins). Our depth reconstructions provide more detail in further areas." + ], + "image_footnote": [], + "bbox": [ + 83, + 316, + 156, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e5cc95998bfcf18b68453f537c87cc5946bffda5f48dd7ec803936c9f89c23b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 156, + 316, + 241, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f50a2e5919d6b0e82c0258a230765847fdba55302c613f0be6ef3e00cec2ad2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 245, + 316, + 318, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c6435a992dcc4db1f6669ac7e5cb954e4ac22304bab39c7a51895438aa9dc7f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 320, + 316, + 403, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d82b6b6975c215512190b9d92ae427c734b8d3c9ed912b72c570b5bae24aeca4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 406, + 316, + 480, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c18c5c24f10a276f8296a0f1b17887907af686e42f42fd085b88cdc3309bfb5c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 316, + 566, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8585ef2c0aca39b8b7fe6c1023c27a652c2f7490deb1869eab5ad620cfa78f55.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 566, + 316, + 640, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ec136e95b8e800681c19d79d57119eb9b9a420306d708697c64f670b6677337.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 642, + 316, + 728, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dbdb53674d704d69ccaef774c9a326d3794acb5939f1cd698045d19cd7bf1232.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 316, + 803, + 356 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b4fdbb2b8d78230aebadbc8cabd542668c9abbcb5f444593a2526052f6b4166d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 316, + 890, + 356 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Results", + "text_level": 1, + "bbox": [ + 76, + 449, + 171, + 464 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We start with a sanity check on a clean image. Our method correctly estimates zero backscatter, and does not force itself to estimate a medium (Fig. 4 Top). On our simulated fog and underwater scenes (Fig. 4 middle and bottom), our method separates the scenes' components very well, with only slight reduction in PSNR in the underwater scene.", + "bbox": [ + 75, + 473, + 468, + 565 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Image rendering and novel-view synthesis (in medium). Qualitative results are summarized in Figs. 1, 5. Table 1 summarizes the average PSNR on the validation set of the Red Sea scene, in which our method achieves the highest PSNR. Note that both NeRF-W [21] and NeRFReN [14] are based on the NeRF [25] model while our code is based on Mip-NeRF-360 [5] that in general improves reconstruction details in further areas. So our real comparison is with [5], which we improve by $\\sim 0.8dB$ on average over the validation set. Table 2 compares PSNR, SSIM and LPIPS with those of [5] on validation sets of all real-world and simulation scenes. Our method is better in the majority of cases, and is especially good on the further areas (red squares).", + "bbox": [ + 75, + 566, + 468, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On the train set [5] achieves a reasonable rendering of the scene in terms of PSNR by wrongly modeling the water as a nearby blue object, as can be seen in the depth map, indicating a close object in the top area. Even then, in our results further objects are reconstructed with more detail. The NeRFReN [14] depth map flattens at the mid-range, while ours is more informative further on. SFM does not estimate depth at these areas because of lack of features. Scene restoration (Fig. 6). In comparison with NeRF", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9c584f48f661f9415f2257aeea64c12b511c020a9a99214f6bf9d11e65c531d1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
OursIIIIII[5][21][14]
21.8321.7621.4321.7221.0516.5221.05
", + "bbox": [ + 506, + 446, + 880, + 482 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/99d682a292d8f182b5d602cafb3bea68738413eb61bc9155265fab375a543c60.jpg", + "table_caption": [ + "Table 1. Average PSNRs of in-medium rendering on Red Sea set: ours, 3 ablation variations (description in the text: I-1 parameter, II-3 parameters, III-Eqs. 13, 14) and other methods." + ], + "table_footnote": [], + "table_body": "
SceneMIP360 [5]Ours
Red Sea21.05 / 0.75 / 0.2921.83 / 0.77 / 0.25
Red Sea red square29.66 / 0.84 / 0.4333.80 / 0.90 / 0.23
Curaçao26.54 / 0.81 / 0.3330.48 / 0.87 / 0.20
Curaçao red square27.04 / 0.84 / 0.4533.20 / 0.88 / 0.08
Panama27.43 / 0.82 / 0.2327.89 / 0.83 / 0.22
Fern fog30.23 / 0.88 / 0.1530.75 / 0.87 / 0.16
Fern underwater29.62 / 0.87 / 0.2629.76 / 0.86 / 0.15
", + "bbox": [ + 506, + 537, + 885, + 655 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Comparison to baseline: PSNR↑/SSIM↑/LPIPS↓.", + "bbox": [ + 506, + 659, + 880, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "methods for scene separation it is clear that our separation handles the medium the best. In the result of NeRF-W [21] the scene is somewhat separated but blurry, while in that of NeRFReN [14] the closer part of the scene is relatively well reconstructed but the further areas are missing. In both, the scene's objects are visible in the backscatter image, which is clearly wrong and reduces relevant signal from the object image. In our results, due to the adequate modeling, the backscatter is not polluted with objects. Compared to scene restoration methods, SeaThru [2] is the best performing one but is limited to areas where the depth map is available from SFM. The single image methods are not on par, especially from the mid-ranges and on. In novel-view synthesis of clean scenes we are able to predict further the entire scene.", + "bbox": [ + 496, + 689, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "62", + "bbox": [ + 488, + 945, + 506, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2c3b46f723a5f9033478ec3463a678d04e33c7feb2a85b1fda570caab625f7c4.jpg", + "image_caption": [ + "train image - clean" + ], + "image_footnote": [], + "bbox": [ + 80, + 109, + 269, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/03d82d66e254de1de523220c15ef7b51194a3190cb44156f5416e1f16213e8aa.jpg", + "image_caption": [ + "train image - backscatter" + ], + "image_footnote": [], + "bbox": [ + 277, + 109, + 468, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/be7ca70994521eb092b15f5e224206cb1fa86ce462782b29d71578408efe037a.jpg", + "image_caption": [ + "novel image - clean" + ], + "image_footnote": [], + "bbox": [ + 475, + 109, + 669, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/90176d51e1fbc1e33410d447063cd6ad24b60cf6dcc81ea53ae2f936a8986f43.jpg", + "image_caption": [ + "single-image restoration" + ], + "image_footnote": [], + "bbox": [ + 697, + 109, + 890, + 208 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d2f6479c1c3975766704f53a77bae6618dabbb158df367fe6593f188d989a14.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 214, + 271, + 314 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1e7c14618e4209c77b03fcb119dff38d2c48d5bbde34eba4e0a05a912d197743.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 214, + 470, + 313 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0b905053d57fe29137f947115058a244d2f103a59969a117fca422f01970cdf9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 475, + 214, + 669, + 313 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9e1463a5256e60de9470fe061d3161f94cf10f939cea5ada6b7af02eabaf05df.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 213, + 890, + 314 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9a257595ac49c5c39562b7933b7ce19f4d3780550b693a77e5286d53b3a52f03.jpg", + "image_caption": [ + "Figure 6. Scene reconstruction on 'Red Sea'. Columns 1-3: Comparing our method (top row) and 2 other NeRFs - Nerf-W [21] (middle row) and NeRFReN [14] (bottom row). Even though not developed for scattering media, they manage to separate a training image into two components (columns 1, 2), resembling the clean scene and the backscatter. However, their backscatter components contains details of the objects, while ours correctly displays only the signal stemming from the medium. Similarly (column 3), their 'clean' rendering of a novel view is inferior to ours, especially in the far distances. Column 4: Among the single-image methods, SeaThru [2] is the best performing (but requires the depth map as input). Nevertheless, color artifacts are visible in the far parts due to inaccurate depth information." + ], + "image_footnote": [], + "bbox": [ + 80, + 318, + 271, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/62b2bcd0f265ad84960fa12b8e6eec1e57a1d8de046ab1c31a9d5938365ff71f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 316, + 470, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f662b29bfb39b921ed244e0d5073cf6932f59b9917a6e1e7a53ac42f46d4d4fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 475, + 316, + 669, + 417 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e9c6bdf834890e40532a129e64058775fa9cc8c3db905370368de5d44f056909.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 316, + 890, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Study. (i) Number of medium parameters: following the discussion in Sec. 3.2, the elaborate version of Eq. (7) uses 6 parameters for the medium coefficients, while simplified versions use 1 (marked I in Table 1) or 3 (marked II). This is ablated in Table 1, in terms of PSNR, where the elaborate model with 6 parameters achieves a higher score. (ii) Rendering equations. We compare our basic rendering model (Eqs. 13, 14), marked III in Table 1 to the final one marked 'ours' (Eq. 22). This option achieves lower PSNR.", + "bbox": [ + 75, + 520, + 468, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion", + "text_level": 1, + "bbox": [ + 76, + 667, + 191, + 683 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We provide an important extension of NeRFs that enables rendering scenes acquired in scattering media such as haze, fog and underwater. So far, NeRF provided a framework for volumetric rendering, but without considering the nature of the medium, resulting in a binary 'occupancy' volume. Our formulation enables opaque objects to exist in a semi-transparent medium that is both scattering and absorbing in a wavelength-dependent manner. We demonstrate it on challenging real-world scenes with a complex 3D structure. Our scenes are forward-facing and contain areas with no objects at all, which our method is able to explain.", + "bbox": [ + 75, + 688, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Water effects in further regions are very strong, hampering single image methods and feature matching in multiview methods. Our method incorporates information from", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "all images at once, learning the scene in a holistic way. This enables better scene reconstruction (in medium and clean), and estimating the depth and the medium's parameters.", + "bbox": [ + 496, + 520, + 890, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our method has several limitations. While it is based on the current state-of-the-art image formation model, that model does not account for multiple scattering or for artificial illumination. As common in NeRFs, it requires camera poses that are extracted beforehand, which can be challenging in bad visibility. Lastly, the medium's parameters are better learned in sets where there is enough variation in the scene range between the viewpoints. The formulation takes its strength from the modeling of the medium. Thus it struggles in scenes that do not adhere to the model's assumptions, e.g., underwater scenes with significant flickering. In the future we plan to add components that will explain transient effects such as flickering, and continue to explore estimation of more diverse scenes and medium parameters.", + "bbox": [ + 496, + 566, + 892, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. The research was funded by Israel Science Foundation grant #680/18, Israeli Ministry of Science and Technology, European Union's Horizon 2020 research and innovation programme GA 101094924 (ANERIS), the Leona M. and Harry B. Helmsley Charitable Trust, the Maurice Hatter Foundation, and Schmidt Marine Technology Partners. We thank Matan Yuval for substantial data contribution, Opher Bar-Nathan and Yuval Goldfracht for help with experiments.", + "bbox": [ + 496, + 780, + 893, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "63", + "bbox": [ + 490, + 945, + 506, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Derya Akkaynak and Tali Treibitz. A revised underwater image formation model. In CVPR, pages 6723-6732, 2018. 1, 2, 3, 4, 5", + "[2] Derya Akkaynak and Tali Treibitz. Sea-thru: A method for removing water from underwater images. In CVPR, pages 1682-1691, 2019. 2, 3, 4, 6, 7, 8", + "[3] Derya Akkaynak, Tali Treibitz, Tom Shlesinger, Raz Tamir, Yossi Loya, and David Iluz. What is the space of attenuation coefficients in underwater computer vision? 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IEEE TIP, 31:3997-4010, 2022. 6" + ], + "bbox": [ + 501, + 92, + 890, + 316 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "65", + "bbox": [ + 490, + 946, + 506, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/769a6e31-fc05-4ad4-bfda-b4fc158792ae_model.json b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/769a6e31-fc05-4ad4-bfda-b4fc158792ae_model.json new file mode 100644 index 0000000000000000000000000000000000000000..04c7f659ebc2b8b69d841c776d834820c5d21de2 --- /dev/null +++ b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/769a6e31-fc05-4ad4-bfda-b4fc158792ae_model.json @@ -0,0 +1,3047 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.18, + 0.131, + 0.79, + 0.153 + ], + "angle": 0, + "content": "SeaThru-NeRF: Neural Radiance Fields in Scattering Media" + }, + { + "type": "text", + "bbox": [ + 0.154, + 0.169, + 0.816, + 0.205 + ], + "angle": 0, + "content": "Deborah Levy1, Amit Peleg1, Naama Pearl1, Dan Rosenbaum1, Derya Akkaynak1,2, Simon Korman1, Tali Treibitz1" + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.206, + 0.805, + 0.241 + ], + "angle": 0, + "content": "1University of Haifa, 2The Inter-University Institute for Marine Sciences in Eilat sea-thru-nerf.github.io" + }, + { + "type": "image_caption", + "bbox": [ + 0.108, + 0.251, + 0.213, + 0.261 + ], + "angle": 0, + "content": "Ground Truth RAW" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.263, + 0.241, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.251, + 0.371, + 0.261 + ], + "angle": 0, + "content": "Ground Truth WB" + }, + { + "type": "image", + "bbox": [ + 0.242, + 0.263, + 0.403, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.439, + 0.251, + 0.531, + 0.261 + ], + "angle": 0, + "content": "Ours Novel View" + }, + { + "type": "image", + "bbox": [ + 0.404, + 0.263, + 0.565, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.609, + 0.251, + 0.686, + 0.261 + ], + "angle": 0, + "content": "Ours Restored" + }, + { + "type": "image", + "bbox": [ + 0.567, + 0.263, + 0.728, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.251, + 0.856, + 0.261 + ], + "angle": 0, + "content": "Ours Backscatter" + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.263, + 0.892, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.895, + 0.436 + ], + "angle": 0, + "content": "Figure 1. NeRFs have not yet tackled scenes in which the medium strongly influences the appearances of objects, as in the case of underwater imagery. By incorporating a scattering image formation model into the NeRF rendering equations, we are able to separate the scene into 'clean' and backscatter components. Consequently, we can render photorealistic novel-views with or without the participating medium, in the latter case recovering colors as if the image was taken in clear air. Results on the Curaçao scene: A RAW image (left) is brightened and white balanced (WB) for visualization, showing more detail, while areas further from the camera (top-right corner) are occluded and attenuated by severe backscatter - which is effectively removed in our restored image. Please zoom-in to observe the details." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.451, + 0.314, + 0.467 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.473, + 0.783 + ], + "angle": 0, + "content": "Research on neural radiance fields (NeRFs) for novel view generation is exploding with new models and extensions. However, a question that remains unanswered is what happens in underwater or foggy scenes where the medium strongly influences the appearance of objects. Thus far, NeRF and its variants have ignored these cases. However, since the NeRF framework is based on volumetric rendering, it has inherent capability to account for the medium's effects, once modeled appropriately. We develop a new rendering model for NeRFs in scattering media, which is based on the SeaThru image formation model, and suggest a suitable architecture for learning both scene information and medium parameters. We demonstrate the strength of our method using simulated and real-world scenes, correctly rendering novel photorealistic views underwater. Even more excitingly, we can render clear views of these scenes, removing the medium between the camera and the scene and reconstructing the appearance and depth of far objects, which are severely occluded by the medium. Our code and unique datasets are available on the project's website." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.799, + 0.21, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The pioneering work of Mildenhall et al. [25] on Neural Radiance Fields (NeRFs) has tremendously advanced the field of Neural Rendering, due to its flexibility and unprecedented quality of synthesized images. Yet, the formulations of the original NeRF [25] and its followup variants assume" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.604 + ], + "angle": 0, + "content": "that images were acquired in clear air, i.e., in a medium that does not scatter or absorb light in a significant manner and that the acquired image is composed solely of the object radiance. The NeRF formulation is based on volumetric rendering equations that take into account sampled points along 3D rays. Assuming a clear air environment, an implicit assumption, which is often enforced explicitly with dedicated loss components [5], is that a single opaque (high density) object is encountered per ray, with zero density between the camera and the object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.893, + 0.76 + ], + "angle": 0, + "content": "In stark contrast to clear air case, when the medium is absorbing and / or scattering (e.g., haze, fog, smog, and all aquatic habitats), the volume rendering equation has a true volumetric meaning, as the entire volume, and not only the object, contributes to image intensity. As the NeRF model estimates color and density at every point of a scene, it lends itself perfectly to general volumetric rendering, given that the appropriate rendering model is used. Here, we bridge this gap with SeaThru-NeRF, a framework that incorporates a rendering model that takes into account scattering media." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "This is achieved by assigning separate color and density parameters to the object (scene) and the medium, within the NeRF framework. Our approach adopts the SeaThru underwater image formation model [1, 3] to account for scattering media. SeaThru is a generalization of the standard wavelength-independent attenuation (e.g., fog) image formation model, where two different wideband coefficients are used to represent the medium, which is more accurate when attenuation is wavelength-dependent (as in all wa" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.946, + 0.509, + 0.957 + ], + "angle": 0, + "content": "56" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.152 + ], + "angle": 0, + "content": "ter bodies and under some atmospheric conditions). In our model, the medium parameters are separate per color channel, and are learned functions of the viewing angles, enforcing them to be constant only along 3D rays in the scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.153, + 0.468, + 0.302 + ], + "angle": 0, + "content": "Attempting to optimize existing NeRFs on scenes with scattering medium results in cloud-like objects floating in space, while our formulation enables the network to learn the correct representation of the entire 3D volume, that consists of both the scene and the medium. Our experiments demonstrate that SeaThru-NeRF produces state-of-the-art photorealistic novel view synthesis on simulated and challenging real-world scenes (see Fig. 1) with scattering media, that include complex geometries and appearances. In addition, it enables:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.303, + 0.468, + 0.348 + ], + "angle": 0, + "content": "1. Color restoration of the scenes as if they were not imaged through a medium, as our modeling allows full separation of object appearance from the medium effects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.468, + 0.408 + ], + "angle": 0, + "content": "2. Estimation of 3D scene structure which surpasses that of structure-from-motion (SFM) or current NeRFs, especially in far areas of bad visibility, as we jointly reconstruct and reason for the geometry and medium." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.468, + 0.453 + ], + "angle": 0, + "content": "3. Estimation of wideband medium parameters, which are informative properties of the captured environment, and potentially allowing simulation under different conditions." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.303, + 0.468, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.468, + 0.218, + 0.484 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.468, + 0.599 + ], + "angle": 0, + "content": "Neural Radiance Fields (NeRFs): The original work on NeRFs [25] has paved the way to a large capacity of followup work, with rapid and significant progress in many related aspects. For brevity, we focus in the following only on works closely related to ours, and refer the reader to a comprehensive review of the field [43] prior to the introduction of NeRFs, and to [44] for the most recent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.468, + 0.75 + ], + "angle": 0, + "content": "NeRFs have been recently shown to be extremely powerful in multi-image settings that involve computational imaging tasks. These include HDR [50], de-blurring [20], superresolution [49], low-light enhancement [23] and denoising [32]. The need to recover the clean 'medium-free' version of images degraded by scattering and attenuation effects, likewise, can benefit from the neural rendering approach. SeaThru-NeRF is designed to model the degradation, with the ability to recover its parameters, and reconstruct the clean underlying scene and novel-view images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Our work is related to recent efforts to improve the quality and robustness of NeRFs in challenging environments (e.g. [14, 21, 29]). Nerf-W [21] learns a per-image latent embedding that can capture appearance variations in complex scenes. It decomposes the scene into image-dependent and shared components to disentangle transient elements from the static scene. NeRFRen [14] is designed for scenes with reflections. It separates the scene as a sum of transmitted and reflected components, which are modeled as separate NeRFs. Ref-NeRF [47] introduces a new parameteriza" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "tion and structuring of view-dependent appearance, which can represent scenes with specularities and reflections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.258 + ], + "angle": 0, + "content": "Our approach has much in common with some of these methods, most notably the way of reconstructing the target image as a composition of components: 'direct' and 'backscatter' in our case, 'transient' and 'static' in [21], or 'transmitted' and 'reflected' in [14]. However, as we demonstrate, these methods are limited on scenes in scattering media as they do not explicitly model the effects of the medium. Our method is different in that it can model a continuous medium component that is not an object." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.266, + 0.892, + 0.447 + ], + "angle": 0, + "content": "Graphics and Vision in Scattering Media: Propagation of light in a medium is governed by the radiative transfer equation [10]. This equation describes light interaction per particle in the medium and requires extensive Monte Carlo simulations for complete solutions [12, 16, 30, 31], see [30] for an excellent review. In many cases simplifying assumptions can be made about the medium that ease rendering [22], where the major one is single-scattering [33, 42, 48]. Realistic rendering requires having the scattering properties of the medium, which can be estimated in the lab [13, 26], or from in situ images [6]. An MLP for rendering synthetic atmospheric clouds was suggested in [17]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.892, + 0.583 + ], + "angle": 0, + "content": "In computer vision, image formation models under ambient illumination for bad weather [28] and underwater [37] share the same general structure for the case of horizontal viewing. Artificial illumination used underwater [46] and in fog has additional terms that account for the nonuniformity of the source. Underwater, the medium parameters exhibit strong wavelength dependency that was shown to affect model accuracy in wideband camera channels. The SeaThru model [1-3] was suggested to overcome this issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.75 + ], + "angle": 0, + "content": "Scene reconstruction in scattering media is an ill-posed problem which was initially solved with multiple frames [27,37,38,46]. Later on, single-image methods have proposed a multitude of image priors to overcome the ill-posed nature of the problem, see [19,51] for comprehensive reviews on single-image dehazing and underwater reconstruction, respectively. The introduction of deep-learning has led to an explosion of single-image dehazing and underwater reconstruction networks. See [41] and [4] for recent reviews of deep-learning dehazing and underwater reconstruction works, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Underwater, it was suggested to solve for the 3D structure of the scene, prior to image restoration [9, 35] using the haze model and [2] using the revised one. In SeaThruNeRF, we simultaneously reconstruct the scene and its 3D structure, yielding multiple advantages that we demonstrate empirically. WaterNeRF [40] suggests an underwater neural renderer that estimates the medium parameters only with respect to histogram-qualified images, separately from the rendering. Here, we show the huge benefit of modeling the scattering medium within the rendering equations, over a" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.946, + 0.508, + 0.956 + ], + "angle": 0, + "content": "57" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "variety of different scenes. Concurrently and independently to our work, [11] presented a NeRF for haze." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.135, + 0.287, + 0.153 + ], + "angle": 0, + "content": "3. Scientific Background" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.16, + 0.362, + 0.176 + ], + "angle": 0, + "content": "3.1. Neural Radiance Fields (NeRFs)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.183, + 0.469, + 0.289 + ], + "angle": 0, + "content": "The original NeRF formulation [25] implicitly represents a 3D scene by a trainable continuous function. It is typically parameterized by an MLP \\( f_{\\Theta}:(\\mathbf{x},\\mathbf{d})\\to (\\mathbf{c},\\sigma) \\) which encodes the density \\( \\sigma \\) at the 3D point \\( \\mathbf{x} = (x,y,z) \\) and the color \\( \\mathbf{c} = (r,g,b) \\) emitted from this point in the viewing direction \\( \\mathbf{d} = (\\theta ,\\phi) \\) (which is typically represented as a 2-element unit normalized 3D vector)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.289, + 0.469, + 0.38 + ], + "angle": 0, + "content": "This simple representation is used to simulate classical image-based rendering, by color accumulation along rays that are back-projected from a posed camera. If we parameterize points along a camera ray \\(\\mathbf{r}\\) by \\(\\mathbf{r}(t) = \\mathbf{o} + \\mathbf{d}(t)\\), where \\(\\mathbf{o}\\) is the camera center and \\(t\\in \\mathbb{R}_+\\), the expected (image) color \\(C(\\mathbf{r})\\) along the ray can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.391, + 0.469, + 0.426 + ], + "angle": 0, + "content": "\\[\nC (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (t) \\mathbf {c} (t) d t \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.436, + 0.469, + 0.542 + ], + "angle": 0, + "content": "where: integration along the ray is limited to the range \\( t \\in [t_n, t_f] \\) (near and far bounds on the scene contents); \\( \\sigma(t) \\) and \\( \\mathbf{c}(t) \\) are shorthands for the density at the point \\( \\mathbf{r}(t) \\) and its emitted color towards the camera center; \\( T(t) \\) denotes the accumulated transmittance along the ray from \\( t_n \\) to \\( t \\) (the probability that the ray travels from \\( t_n \\) to \\( t \\) without hitting other particles along the way), and is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.552, + 0.469, + 0.587 + ], + "angle": 0, + "content": "\\[\nT (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\sigma (s) d s\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.597, + 0.469, + 0.688 + ], + "angle": 0, + "content": "In practice, the rendered color \\( C(\\mathbf{r}) \\) in Eq. (1) is approximated with the quadrature rule, by discretizing the range \\( [t_n, t_f] \\) into a set of \\( N \\) intervals \\( I_i = [s_i, s_{i+1}] \\) (where \\( t_n = s_0 < \\dots < s_N = t_f \\)), assuming that the density \\( \\sigma \\) and color \\( \\mathbf{c} \\) are constant along each interval (e.g. by querying the model once per interval at its center-point)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.688, + 0.338, + 0.704 + ], + "angle": 0, + "content": "In the discretized version of Eq. (1):" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.714, + 0.469, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} C _ {i} (\\mathbf {r}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.766, + 0.419, + 0.782 + ], + "angle": 0, + "content": "the contribution \\(C_i(\\mathbf{r})\\) of the interval \\(I_{i}\\) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.792, + 0.469, + 0.827 + ], + "angle": 0, + "content": "\\[\nC _ {i} (\\mathbf {r}) = \\int_ {s _ {i}} ^ {s _ {i + 1}} T (t) \\sigma_ {i} \\mathbf {c} _ {i} d t = T \\left(s _ {i}\\right) \\left(1 - e ^ {- \\sigma_ {i} \\delta_ {i}}\\right) \\mathbf {c} _ {i} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.836, + 0.469, + 0.867 + ], + "angle": 0, + "content": "where \\(\\sigma_{i}\\) and \\(\\mathbf{c_i}\\) are the (constant) density and color along the \\(i\\)th interval, whose length is \\(\\delta_{i} = s_{i + 1} - s_{i}\\), and the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.857, + 0.107 + ], + "angle": 0, + "content": "transmittance \\( T(s_{i}) \\) at the beginning of the interval is:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.119, + 0.892, + 0.161 + ], + "angle": 0, + "content": "\\[\nT \\left(s _ {i}\\right) = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} \\delta_ {j}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.171, + 0.892, + 0.215 + ], + "angle": 0, + "content": "This fully differentiable NeRF model (with the discretized rendering scheme) is trained with a simple reconstruction loss" + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.226, + 0.892, + 0.258 + ], + "angle": 0, + "content": "\\[\nL = \\sum_ {\\mathbf {r} \\in R} \\| \\hat {C} (\\mathbf {r}) - C (\\mathbf {r}) \\| ^ {2} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.269, + 0.892, + 0.315 + ], + "angle": 0, + "content": "comparing each rendered training image pixel \\(\\hat{C}(\\mathbf{r})\\) to its ground truth color \\(C(\\mathbf{r})\\). The model can then be used to synthesize photorealistic novel view images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.324, + 0.826, + 0.34 + ], + "angle": 0, + "content": "3.2. Image Formation in Scattering Media" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.348, + 0.892, + 0.527 + ], + "angle": 0, + "content": "Image formation in fog, haze, or underwater differs from image formation in clear air in two major aspects. First, the direct signal emanating from the object is attenuated as a function of distance and wavelength. Second, this signal is occluded by backscatter (termed also path-radiance or veiling-light) - radiance that is added due to the in-scattering from the particles along the line-of-sight (LOS), illustrated in Fig. 2. The intensity and color of the occluding backscatter layer are independent of the scene contents, and its intensity accumulates along the LOS, increasing with distance. As a result, the visibility and contrast of further objects is significantly reduced and their colors are distorted." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.528, + 0.892, + 0.588 + ], + "angle": 0, + "content": "We adopt the revised model [1] as the general model for image formation in scattering media under ambient illumination. Image intensity (per pixel, per color channel) is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.594, + 0.892, + 0.65 + ], + "angle": 0, + "content": "\\[\nI = \\underbrace {\\underbrace {J} _ {\\text {c o l o r}} \\cdot \\underbrace {(e ^ {- \\beta^ {D} (\\mathbf {v} _ {D}) \\cdot z})} _ {\\text {a t t e n u a t i o n}}} _ {B ^ {\\infty}} + \\underbrace {(1 - e ^ {- \\beta^ {B} (\\mathbf {v} _ {B}) \\cdot z})} _ {\\text {a t t e n u a t i o n}} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(I\\) is the linear image captured by the camera of a scene with range \\(z\\), \\(J\\) is the clear scene that would have been captured had there been no medium along \\(z\\), and \\(B^{\\infty}\\) is the backscatter water color at infinity, i.e., the backscatter at areas that contain no objects. Lastly, \\(\\beta^{D}\\) and \\(\\beta^{B}\\) are the attenuation and backscatter coefficients, respectively, the two parameters that describe the medium effects. The vectors \\(\\mathbf{v}_D\\) and \\(\\mathbf{v}_B\\) represent the dependencies of \\(\\beta^{D}\\) and \\(\\beta^{B}\\) on range, object reflectance, spectrum of ambient light, spectral response of the camera, and the physical scattering and beam attenuation coefficients of the water body, all of which are functions of wavelength. It was shown in [2] that \\(\\beta^{B}\\) can be assumed constant in an image, while \\(\\beta^{D}\\) mainly depends on the object distance and weakly on object reflectance, thus solving for the full model requires at least 6 unknowns. The value of \\(B^{\\infty}\\) is usually assumed to be uniform in the scene" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.454, + 0.887 + ], + "angle": 0, + "content": "\\(^{1}\\)Vectors (3D coordinates or color components) are denoted in **bold**." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.332, + 0.9 + ], + "angle": 0, + "content": "2Each color channel is integrated separately." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.454, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.946, + 0.508, + 0.956 + ], + "angle": 0, + "content": "58" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.089, + 0.428, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.244, + 0.47, + 0.301 + ], + "angle": 0, + "content": "Figure 2. An illustration of our ray model. We assume a scene with at most a single opaque object at every ray. The medium is semitransparent with constant density per-ray. The densities governing the backscatter and the object in water are not the same [1]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.317, + 0.469, + 0.348 + ], + "angle": 0, + "content": "but as discussed in [6] it is almost never really uniform, because of the directionality of the sun, among other factors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.47, + 0.468 + ], + "angle": 0, + "content": "This model is also applicable to haze and fog, where attenuation has very little dependence on wavelength. Then, image formation is greatly simplified because it can be assumed that there is only one medium parameter that is uniform across the color channels, represented by a scalar \\((\\beta^{D} = \\beta^{B} = \\beta)\\) [38]. Underwater, often the simplifying (less accurate) assumption that \\(\\beta^{D} = \\beta^{B}\\) is made, reducing to 3 unknowns [6,7,37]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.229, + 0.497 + ], + "angle": 0, + "content": "4. SeaThru-NeRF" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.507, + 0.295, + 0.523 + ], + "angle": 0, + "content": "4.1. Basic Model Derivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.606 + ], + "angle": 0, + "content": "Here we consider a more general setting than the original NeRF [25], in which light travels through a scattering medium rather than free-space, resulting in a significant impact on the captured color. Following [22] we suggest adding the medium to Eqs. (1) and (2):" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.617, + 0.469, + 0.664 + ], + "angle": 0, + "content": "\\[\nC (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\left(\\sigma^ {\\mathrm {o b j}} (t) \\mathbf {c} ^ {\\mathrm {o b j}} (t) + \\sigma^ {\\mathrm {m e d}} (t) \\mathbf {c} ^ {\\mathrm {m e d}} (t)\\right) d t \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.665, + 0.127, + 0.678 + ], + "angle": 0, + "content": "where:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.688, + 0.469, + 0.723 + ], + "angle": 0, + "content": "\\[\nT (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\left(\\sigma^ {\\mathrm {o b j}} (s) + \\sigma^ {\\mathrm {m e d}} (s)\\right) d s\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.469, + 0.793 + ], + "angle": 0, + "content": "using separate color and density parameters for the object and medium. Notice that these equations reduce to Eqs. (1) and (2) by simply considering the case where the medium density \\(\\sigma^{\\mathrm{med}}\\) is zero." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.469, + 0.824 + ], + "angle": 0, + "content": "Moving to the discretized version, we similarly get3 the following generalizations of Eqs. (4) and (5):" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.833, + 0.469, + 0.879 + ], + "angle": 0, + "content": "\\[\nC _ {i} (\\mathbf {r}) = T \\left(s _ {i}\\right) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {o b j}} \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}} \\mathbf {c} _ {i} ^ {\\mathrm {m e d}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {10}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.42, + 0.901 + ], + "angle": 0, + "content": "\\( {}^{3} \\) Full derivations of Eqs. (10,11) is provided in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.093, + 0.627, + 0.105 + ], + "angle": 0, + "content": "with transmittance" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.115, + 0.892, + 0.158 + ], + "angle": 0, + "content": "\\[\nT \\left(s _ {i}\\right) = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\left(\\sigma_ {j} ^ {\\mathrm {o b j}} + \\sigma_ {j} ^ {\\mathrm {m e d}}\\right) \\delta_ {j}\\right). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.169, + 0.892, + 0.199 + ], + "angle": 0, + "content": "Splitting the discretized color rendering equations (3,10 and 11) into the 'object' and 'medium' components, we get:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.209, + 0.892, + 0.251 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} \\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) + \\sum_ {i = 1} ^ {N} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) \\tag {12}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.268, + 0.892, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T (s _ {i}) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {o b j}} \\mathbf {c} _ {i} ^ {\\mathrm {o b j}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.324, + 0.892, + 0.358 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T (s _ {i}) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {m e d}} \\mathbf {c} _ {i} ^ {\\mathrm {m e d}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.546 + ], + "angle": 0, + "content": "As a first step towards constraining and simplifying our model, we constrain the medium parameters to be constant along 3D viewing rays. We drop the respective interval indices and remain with \\(\\sigma^{\\mathrm{med}}\\) and \\(\\mathbf{c}^{\\mathrm{med}}\\) that depend only on the ray \\(\\mathbf{r}\\). The \\(\\mathbf{c}^{\\mathrm{med}}\\) uniformity stems from the common assumption of a uniform phase function (the dependence of scattered radiance on scattering angle) along the LOS [22, 30]. Regarding the density \\(\\sigma^{\\mathrm{med}}\\), we take it to be separate per color channel, but constant per ray. This is far less restrictive compared to models that assume constancy per image or even per scene [2]. These constraints will be enforced by respective structural choices in the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.653 + ], + "angle": 0, + "content": "Furthermore, we assume that objects in the scene are opaque, hence the object density along the ray is close to zero except for a high peak in the object location. On the other hand, the medium is semi-transparent, characterized by a low non-zero density. This implies that \\(\\sigma^{\\mathrm{med}} \\gg \\sigma^{\\mathrm{obj}}\\) before the object and \\(\\sigma^{\\mathrm{med}} \\ll \\sigma^{\\mathrm{obj}}\\) at the object, as illustrated in Fig. 2. Therefore, Eqs. (13-14) reduce to" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.663, + 0.891, + 0.689 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i}}\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.691, + 0.891, + 0.717 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} \\delta_ {i}}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\tag {16}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.72, + 0.891, + 0.761 + ], + "angle": 0, + "content": "\\[\nT _ {i} = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} ^ {\\mathrm {o b j}} \\delta_ {j}\\right) \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {m e d}} s _ {i}\\right) \\tag {17}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.856, + 0.788 + ], + "angle": 0, + "content": "4.2. Relation to Underwater Image Formation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section we show that our model can be reduced to the image formation model described in Sec. 3.2, which is not based on volumetric rendering. To this end we consider sampling the ray along intervals with constant size \\(\\delta\\), and the appearance of the opaque object at a depth \\(z\\), at the beginning of interval \\(I_{k} = [s_{k}, s_{k + 1}]\\), for some integer \\(k\\) (that is: \\(s_{i} = i \\cdot \\delta\\) for every \\(i\\) and \\(z = k \\cdot \\delta\\) in particular)." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.946, + 0.508, + 0.957 + ], + "angle": 0, + "content": "59" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.457, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.26, + 0.473, + 0.331 + ], + "angle": 0, + "content": "Figure 3. SeaThru-NeRF architecture. The computation of the 'object' outputs (density and color, in green), follows the standard NeRF architecture, while the 'medium' components (in purple) are computed once per ray by a separate subnet (the 'medium MLP') that depends only on the viewing direction." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.344, + 0.47, + 0.396 + ], + "angle": 0, + "content": "In this case, \\(\\sigma_{i}^{\\mathrm{obj}}\\approx 0\\) for all \\(i < k\\), and \\(\\sigma_k^{\\mathrm{obj}}\\gg \\sigma^{\\mathrm{med}}\\). This implies that \\(C_k^{\\mathrm{med}}(\\mathbf{r})\\ll C_k^{\\mathrm{obj}}(\\mathbf{r})\\) and \\(C_i^{\\mathrm{obj}}(\\mathbf{r})\\approx 0\\), therefore we can write the rendering Eq. (12) as" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.4, + 0.47, + 0.441 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\mathbf {r}) \\approx \\hat {C} _ {k} ^ {\\mathrm {o b j}} (\\mathbf {r}) + \\sum_ {i = 0} ^ {k - 1} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.453, + 0.47, + 0.516 + ], + "angle": 0, + "content": "Furthermore, since the object is opaque, we can assume that the density \\(\\sigma_k^{\\mathrm{obj}}\\) is large enough such that the transmittance at the end of the \\(k\\)th interval \\(T(s_{k + 1})\\) drops practically to zero, that is: \\(e^{-\\sigma_k^{\\mathrm{obj}}\\delta}\\approx 0\\). Therefore" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.527, + 0.47, + 0.572 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {C} _ {k} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta}\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} \\tag {19} \\\\ \\approx e ^ {- k \\sigma^ {\\mathrm {m e d}} \\delta} \\left(1 - e ^ {- \\sigma_ {k} ^ {\\mathrm {o b j}} \\delta}\\right) \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} \\approx e ^ {- \\sigma^ {\\mathrm {m e d}} \\delta \\cdot k} \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.585, + 0.107, + 0.597 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.609, + 0.469, + 0.719 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\sum_ {i = 0} ^ {k - 1} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = \\sum_ {i = 0} ^ {k - 1} T _ {i} \\cdot \\left(1 - e ^ {- \\sigma^ {\\mathrm {m e d}} \\delta}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\tag {20} \\\\ \\approx \\sum_ {i = 0} ^ {k - 1} e ^ {- i \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta} \\cdot \\left(1 - e ^ {- \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\\\ = \\left(1 - e ^ {- \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta \\cdot k}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.731, + 0.47, + 0.762 + ], + "angle": 0, + "content": "Substituting Eqs. (19) and (20) into Eq. (18) (recalling that the depth \\( z \\) equals \\( k \\cdot \\delta \\)) yields:" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.774, + 0.47, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\hat {C} (\\mathbf {r}) \\approx e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} z} \\cdot \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} + \\left(1 - e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} z}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}}, \\tag {21}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "resulting precisely in the commonly used scattering media image formation model [8, 37]. This can be seen by comparing to Eq. (7) where \\(\\sigma^{\\mathrm{med}} = \\beta^{D} = \\beta^{B}\\) plays the role of the attenuation coefficient (equal for direct and backscatter), \\(\\mathbf{c}^{\\mathrm{med}}\\) is the veiling light \\(B^{\\infty}\\) (backscatter color at infinity) and \\(\\mathbf{c}_k^{\\mathrm{obj}}\\) the clear image color \\(J\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.631, + 0.105 + ], + "angle": 0, + "content": "4.3. Final Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.297 + ], + "angle": 0, + "content": "We make several refinements with respect to the basic model presented in Section 4.1. In Sec. 4.2, we showed that our rendering equations lead to an image formation model with identical attenuation coefficients for the direct and backscatter components. Following the discussion in Sec. 3.2, and as has been shown in [1], when using such equations with a camera with wideband color channels, the effective \\(\\sigma^{\\mathrm{med}}\\) that is experienced by the camera in \\(C_i^{\\mathrm{obj}}(\\mathbf{r})\\) is different than the one experienced in \\(C_i^{\\mathrm{med}}(\\mathbf{r})\\). Therefore, in our final model we use different parameters for \\(\\sigma^{\\mathrm{med}}\\) in each component and term them \\(\\sigma^{\\mathrm{attn}}\\) and \\(\\sigma^{\\mathrm{bs}}\\) for \\(C_i^{\\mathrm{obj}}(\\mathbf{r})\\) and \\(C_i^{\\mathrm{med}}(\\mathbf{r})\\) respectively. Our final equations are:" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.306, + 0.89, + 0.328 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {a t t n}} s _ {i}\\right) \\cdot \\left(1 - \\exp (- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i})\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.337, + 0.885, + 0.358 + ], + "angle": 0, + "content": "\\[\n\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {b s}} s _ {i}\\right) \\cdot \\left(1 - \\exp (- \\mathbf {o} ^ {\\mathrm {b s}} \\delta_ {i})\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.375, + 0.892, + 0.416 + ], + "angle": 0, + "content": "\\[\nT _ {i} ^ {\\mathrm {o b j}} = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} ^ {\\mathrm {o b j}} \\delta_ {j}\\right) \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.422, + 0.892, + 0.543 + ], + "angle": 0, + "content": "Based on our derivations we suggest the following architecture (Fig. 3). As in [25], the object properties are computed by a pair of MLPs, such that the density \\(\\sigma^{\\mathrm{obj}}\\) is a function of the position \\((x,y,z)\\) only, while color \\(\\mathbf{c}^{\\mathrm{obj}}\\) is determined by the viewing direction \\((\\theta ,\\phi)\\) as well. The medium parameters \\(\\mathbf{c}^{\\mathrm{med}}\\), \\(\\sigma^{\\mathrm{bs}}\\), \\(\\sigma^{\\mathrm{attn}}\\) are handled by a separate MLP with only the direction input, following our decision to constrain them to be constant per viewing direction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.553, + 0.645, + 0.567 + ], + "angle": 0, + "content": "4.4. Loss Function" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.576, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Let us denote the sequence of samples along a ray by \\(\\mathbf{s} = \\{s_i\\}_{i=0}^N\\), the object 'weight' at the \\(i\\)th segment \\([s_i, s_{i+1}]\\)," + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.632, + 0.892, + 0.653 + ], + "angle": 0, + "content": "\\[\nw _ {i} ^ {\\mathrm {o b j}} = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\left(1 - \\exp \\left(- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i}\\right)\\right), \\tag {23}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.891, + 0.696 + ], + "angle": 0, + "content": "the sequence of these weights by \\(\\mathbf{w} = \\{w_{i}^{\\mathrm{obj}}\\}_{i = 0}^{N - 1}\\) and the ground-truth (supervised) pixel color by \\(C^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.696, + 0.776, + 0.711 + ], + "angle": 0, + "content": "Our loss is the following combination:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.722, + 0.892, + 0.74 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {r e c o n}} \\left(\\hat {C}, C ^ {*}\\right) + \\mathcal {L} _ {\\text {p r o p}} (\\mathbf {s}, \\mathbf {w}) + \\lambda \\mathcal {L} _ {\\text {a c c}} (\\mathbf {w}), \\tag {24}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.751, + 0.892, + 0.797 + ], + "angle": 0, + "content": "where \\(\\lambda = 0.0001\\) was chosen through cross-validation. Since we work on linear images, we adopt the reconstruction loss of RawNeRF [23]:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.806, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e c o n}} (\\hat {C}, C ^ {*}) = \\left(\\frac {\\hat {C} - C ^ {*}}{\\operatorname {s g} (\\hat {C}) + \\epsilon}\\right) ^ {2} \\tag {25}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.855, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathrm{sg}(\\cdot)\\) stands for stop-gradient and \\(\\epsilon = 10^{-3}\\). The 'proposal' loss \\(\\mathcal{L}_{\\mathrm{prop}}(\\mathbf{s},\\mathbf{w})\\) is an inherent part of Mip-NeRF-360 [5]. It penalizes for the discrepancy between the" + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.946, + 0.508, + 0.957 + ], + "angle": 0, + "content": "60" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.121 + ], + "angle": 0, + "content": "distributions of object weights at 'original' and 'proposed' samplings, where only the latter is used for rendering [5]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.213 + ], + "angle": 0, + "content": "To enforce binary separation between points in space that contain objects and those that contain solely a medium - we add a prior on the transmittance \\( T_{i}^{\\mathrm{obj}} \\) of each point on the ray to be either 0 or 1, not allowing semi-transparent objects. This is modelled as a mixture of two Laplacian distributions with modes at 0 and 1 (following [34]):" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.218, + 0.468, + 0.239 + ], + "angle": 0, + "content": "\\[\n\\mathbf {P} (x) \\propto e ^ {- \\frac {| x |}{0 . 1}} + e ^ {- \\frac {| 1 - x |}{0 . 1}} \\tag {26}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.246, + 0.343, + 0.26 + ], + "angle": 0, + "content": "and use the negative log likelihood loss:" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.265, + 0.468, + 0.284 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {a c c}} (\\mathbf {w}) = - \\log \\mathbb {P} \\left(T _ {i} ^ {\\mathrm {o b j}}\\right). \\tag {27}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.29, + 0.376, + 0.307 + ], + "angle": 0, + "content": "4.5. Implementation and Optimization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.468, + 0.432 + ], + "angle": 0, + "content": "Our implementation is based on the code released in Mip-NeRF-360 [5], choosing the best performing baseline on our scenes which was the forward-looking configuration with normalized device coordinates (NDC). For the mediumMLP, we use 6 linear layers with 256 features and a softplus activation, followed by 3 branches of dense layers and a sigmoid activation for predicting \\( c^{\\mathrm{med}} \\) and softplus activations for \\( \\sigma^{\\mathrm{attn}} \\) and \\( \\sigma^{\\mathrm{bs}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.434, + 0.468, + 0.585 + ], + "angle": 0, + "content": "In the rendering scheme, [5] initialized the farthest \\(\\delta_{i}\\) with infinity, enabling the network to predict a background color for rays that do not intersect with any object. We disabled this addition as it prevents our method from explaining the medium that contributes to the rendered color along the ray. We keep the learning rate and optimization parameters the same as in [5]. The network is trained for 250,000 iterations with a batch size of 16384 rays, taking around 10 hours on an Nvidia A100 GPU. The loss function and metrics are calculated on the output before any post-processing." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.596, + 0.311, + 0.613 + ], + "angle": 0, + "content": "5. Experiments and Results" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.212, + 0.637 + ], + "angle": 0, + "content": "5.1. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.468, + 0.855 + ], + "angle": 0, + "content": "Real world scenes. We acquired multi-image underwater scenes by diving in three different seas: the Red Sea (Eilat, Israel), the Caribbean Sea (Curaçao) and the Pacific Sea (Panama) with a total of 20, 20 and 18 images respectively, from which three are set aside for validation in each set. This data encapsulates a diverse set of water conditions and imaging conditions. The images were acquired as RAW images with a Nikon D850 SLR camera in a Nauticam underwater housing with a dome port to avoid refractions that jeopardize the pinhole model [45], and downsampled to average size \\(900 \\times 1400\\). The input linear images were white-balanced before processing with \\(0.5\\%\\) clipping per channel to remove extreme noisy pixels. Finally, COLMAP [39] is used to extract camera poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Simulated Scene. We constructed a simulation using the Fern scene of the LLFF dataset [24]. We ran MIP-NeRF-360 [5] and used the predicted depth maps to simulate an" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.092, + 0.632, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.092, + 0.761, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.092, + 0.89, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.168, + 0.632, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.168, + 0.761, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.168, + 0.89, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.242, + 0.632, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.242, + 0.761, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.242, + 0.89, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.325, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Figure 4. Synthetic experiment on Fern scene of the LLFF dataset [24]. Top: Our method can handle 'in-air' scenes, with a uniform zeros backscatter image and a reconstruction PSNR that is close to that of the baseline [5] which was 23.73. Middle and bottom: Our method's separation between clean and backscatter components, for simulations of fog and underwater effects. The reconstruction quality degrades rather gracefully." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.52 + ], + "angle": 0, + "content": "underwater and a foggy scene. Water was added according to (7) with parameter values: \\(\\beta^D = [1.3, 1.2, 0.9]\\), \\(\\beta^B = [0.95, 0.85, 0.7]\\), \\(B^\\infty = [0.07, 0.2, 0.39]\\). Fog was simulated based on [36] with \\(\\beta = 1.2\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.801 + ], + "angle": 0, + "content": "Baseline methods. The input to all methods is the same set of white-balanced linear images. In the task of rendering scenes in the medium we compare with the following NeRF methods: MIP-NeRF-360, forward-looking with NDC (MIP360) [5], NeRF-W [21] and NeRFReN [14]. In the task of reconstructing clean medium-free images we compare with NeRF-W, where the 'transient' component can be viewed as the clean image and the 'static' image as backscatter, and to NeRFReN with the 'reflected' and 'transmitted' components as clean and backscatter images. We additionally compare to single-image scene reconstruction methods: plain white balance, SeaThru [2], the leading \"classical\" methods of Bekerman et al [6], and the recent deep-learning based [52] (as well as [15, 52] whose results are provided in the project website). SeaThru requires depth maps, that we generate using SFM (with Agisoft Metashape) as originally suggested. These depth-maps are used to compare with those of the different methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Photo-finishing: As the input and output images are linear, we apply photofinishing on all linear reconstructed scenes to enhance scene contrast and appearance, using the digital camera pipeline from [18]. This is done to improve visualization for easier qualitative comparisons, while PSNR is calculated on the original non-photofinished linear images." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.946, + 0.507, + 0.956 + ], + "angle": 0, + "content": "61" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.244, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.09, + 0.406, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.09, + 0.568, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.091, + 0.73, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.091, + 0.892, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.174, + 0.175, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.178, + 0.174, + 0.243, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.174, + 0.337, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.174, + 0.405, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.174, + 0.498, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.174, + 0.568, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.174, + 0.659, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.174, + 0.729, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.174, + 0.822, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.825, + 0.174, + 0.892, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.233, + 0.244, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.247, + 0.233, + 0.405, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.233, + 0.568, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.233, + 0.73, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.732, + 0.233, + 0.892, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.318, + 0.157, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.158, + 0.318, + 0.243, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.318, + 0.32, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.321, + 0.318, + 0.405, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.407, + 0.318, + 0.481, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.318, + 0.567, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.318, + 0.642, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.643, + 0.318, + 0.729, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.318, + 0.805, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.318, + 0.892, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.362, + 0.894, + 0.432 + ], + "angle": 0, + "content": "Figure 5. Scene rendering in the medium, on 'Red Sea'. Left to right: white-balanced input image, our result, MIP360 [23], Nerf-W [21], NeRFReN [14]. [Top 2 rows] Train image and zoom-ins. Even in the task of overfitting to the training images, there are noticeable differences between the methods, and as can be seen in the zoom-ins (red squares) we are able to reconstruct fine details in further areas (albeit a lower PSNR). [Bottom 2 rows] Novel view and zoom-ins. Our method achieves the highest PSNR (see tables 1, 2), and provides much better details in further areas (see red square zoom-ins). Our depth reconstructions provide more detail in further areas." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.45, + 0.172, + 0.465 + ], + "angle": 0, + "content": "5.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.566 + ], + "angle": 0, + "content": "We start with a sanity check on a clean image. Our method correctly estimates zero backscatter, and does not force itself to estimate a medium (Fig. 4 Top). On our simulated fog and underwater scenes (Fig. 4 middle and bottom), our method separates the scenes' components very well, with only slight reduction in PSNR in the underwater scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Image rendering and novel-view synthesis (in medium). Qualitative results are summarized in Figs. 1, 5. Table 1 summarizes the average PSNR on the validation set of the Red Sea scene, in which our method achieves the highest PSNR. Note that both NeRF-W [21] and NeRFReN [14] are based on the NeRF [25] model while our code is based on Mip-NeRF-360 [5] that in general improves reconstruction details in further areas. So our real comparison is with [5], which we improve by \\(\\sim 0.8dB\\) on average over the validation set. Table 2 compares PSNR, SSIM and LPIPS with those of [5] on validation sets of all real-world and simulation scenes. Our method is better in the majority of cases, and is especially good on the further areas (red squares)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.471, + 0.902 + ], + "angle": 0, + "content": "On the train set [5] achieves a reasonable rendering of the scene in terms of PSNR by wrongly modeling the water as a nearby blue object, as can be seen in the depth map, indicating a close object in the top area. Even then, in our results further objects are reconstructed with more detail. The NeRFReN [14] depth map flattens at the mid-range, while ours is more informative further on. SFM does not estimate depth at these areas because of lack of features. Scene restoration (Fig. 6). In comparison with NeRF" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.448, + 0.882, + 0.483 + ], + "angle": 0, + "content": "
OursIIIIII[5][21][14]
21.8321.7621.4321.7221.0516.5221.05
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.487, + 0.892, + 0.529 + ], + "angle": 0, + "content": "Table 1. Average PSNRs of in-medium rendering on Red Sea set: ours, 3 ablation variations (description in the text: I-1 parameter, II-3 parameters, III-Eqs. 13, 14) and other methods." + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.538, + 0.887, + 0.656 + ], + "angle": 0, + "content": "
SceneMIP360 [5]Ours
Red Sea21.05 / 0.75 / 0.2921.83 / 0.77 / 0.25
Red Sea red square29.66 / 0.84 / 0.4333.80 / 0.90 / 0.23
Curaçao26.54 / 0.81 / 0.3330.48 / 0.87 / 0.20
Curaçao red square27.04 / 0.84 / 0.4533.20 / 0.88 / 0.08
Panama27.43 / 0.82 / 0.2327.89 / 0.83 / 0.22
Fern fog30.23 / 0.88 / 0.1530.75 / 0.87 / 0.16
Fern underwater29.62 / 0.87 / 0.2629.76 / 0.86 / 0.15
" + }, + { + "type": "table_caption", + "bbox": [ + 0.508, + 0.66, + 0.882, + 0.675 + ], + "angle": 0, + "content": "Table 2. Comparison to baseline: PSNR↑/SSIM↑/LPIPS↓." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.894, + 0.901 + ], + "angle": 0, + "content": "methods for scene separation it is clear that our separation handles the medium the best. In the result of NeRF-W [21] the scene is somewhat separated but blurry, while in that of NeRFReN [14] the closer part of the scene is relatively well reconstructed but the further areas are missing. In both, the scene's objects are visible in the backscatter image, which is clearly wrong and reduces relevant signal from the object image. In our results, due to the adequate modeling, the backscatter is not polluted with objects. Compared to scene restoration methods, SeaThru [2] is the best performing one but is limited to areas where the depth map is available from SFM. The single image methods are not on par, especially from the mid-ranges and on. In novel-view synthesis of clean scenes we are able to predict further the entire scene." + }, + { + "type": "page_number", + "bbox": [ + 0.49, + 0.946, + 0.508, + 0.957 + ], + "angle": 0, + "content": "62" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.12, + 0.095, + 0.232, + 0.107 + ], + "angle": 0, + "content": "train image - clean" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.11, + 0.271, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.095, + 0.446, + 0.107 + ], + "angle": 0, + "content": "train image - backscatter" + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.111, + 0.47, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.518, + 0.095, + 0.63, + 0.107 + ], + "angle": 0, + "content": "novel image - clean" + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.11, + 0.67, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.095, + 0.865, + 0.107 + ], + "angle": 0, + "content": "single-image restoration" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.11, + 0.892, + 0.209 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.215, + 0.272, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.215, + 0.471, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.215, + 0.67, + 0.314 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.214, + 0.892, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.319, + 0.272, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.318, + 0.471, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.476, + 0.318, + 0.67, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.318, + 0.892, + 0.418 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.423, + 0.895, + 0.507 + ], + "angle": 0, + "content": "Figure 6. Scene reconstruction on 'Red Sea'. Columns 1-3: Comparing our method (top row) and 2 other NeRFs - Nerf-W [21] (middle row) and NeRFReN [14] (bottom row). Even though not developed for scattering media, they manage to separate a training image into two components (columns 1, 2), resembling the clean scene and the backscatter. However, their backscatter components contains details of the objects, while ours correctly displays only the signal stemming from the medium. Similarly (column 3), their 'clean' rendering of a novel view is inferior to ours, especially in the far distances. Column 4: Among the single-image methods, SeaThru [2] is the best performing (but requires the depth map as input). Nevertheless, color artifacts are visible in the far parts due to inaccurate depth information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Ablation Study. (i) Number of medium parameters: following the discussion in Sec. 3.2, the elaborate version of Eq. (7) uses 6 parameters for the medium coefficients, while simplified versions use 1 (marked I in Table 1) or 3 (marked II). This is ablated in Table 1, in terms of PSNR, where the elaborate model with 6 parameters achieves a higher score. (ii) Rendering equations. We compare our basic rendering model (Eqs. 13, 14), marked III in Table 1 to the final one marked 'ours' (Eq. 22). This option achieves lower PSNR." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.668, + 0.192, + 0.684 + ], + "angle": 0, + "content": "6. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.469, + 0.856 + ], + "angle": 0, + "content": "We provide an important extension of NeRFs that enables rendering scenes acquired in scattering media such as haze, fog and underwater. So far, NeRF provided a framework for volumetric rendering, but without considering the nature of the medium, resulting in a binary 'occupancy' volume. Our formulation enables opaque objects to exist in a semi-transparent medium that is both scattering and absorbing in a wavelength-dependent manner. We demonstrate it on challenging real-world scenes with a complex 3D structure. Our scenes are forward-facing and contain areas with no objects at all, which our method is able to explain." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Water effects in further regions are very strong, hampering single image methods and feature matching in multiview methods. Our method incorporates information from" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.566 + ], + "angle": 0, + "content": "all images at once, learning the scene in a holistic way. This enables better scene reconstruction (in medium and clean), and estimating the depth and the medium's parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.893, + 0.779 + ], + "angle": 0, + "content": "Our method has several limitations. While it is based on the current state-of-the-art image formation model, that model does not account for multiple scattering or for artificial illumination. As common in NeRFs, it requires camera poses that are extracted beforehand, which can be challenging in bad visibility. Lastly, the medium's parameters are better learned in sets where there is enough variation in the scene range between the viewpoints. The formulation takes its strength from the modeling of the medium. Thus it struggles in scenes that do not adhere to the model's assumptions, e.g., underwater scenes with significant flickering. In the future we plan to add components that will explain transient effects such as flickering, and continue to explore estimation of more diverse scenes and medium parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Acknowledgements. The research was funded by Israel Science Foundation grant #680/18, Israeli Ministry of Science and Technology, European Union's Horizon 2020 research and innovation programme GA 101094924 (ANERIS), the Leona M. and Harry B. Helmsley Charitable Trust, the Maurice Hatter Foundation, and Schmidt Marine Technology Partners. We thank Matan Yuval for substantial data contribution, Opher Bar-Nathan and Yuval Goldfracht for help with experiments." + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.946, + 0.508, + 0.956 + ], + "angle": 0, + "content": "63" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Derya Akkaynak and Tali Treibitz. A revised underwater image formation model. In CVPR, pages 6723-6732, 2018. 1, 2, 3, 4, 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.471, + 0.198 + ], + "angle": 0, + "content": "[2] Derya Akkaynak and Tali Treibitz. Sea-thru: A method for removing water from underwater images. 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IEEE TIP, 31:3997-4010, 2022. 6" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.317 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.491, + 0.947, + 0.508, + 0.956 + ], + "angle": 0, + "content": "65" + } + ] +] \ No newline at end of file diff --git a/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/769a6e31-fc05-4ad4-bfda-b4fc158792ae_origin.pdf b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/769a6e31-fc05-4ad4-bfda-b4fc158792ae_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2f2b07167b7b109b24e89761669f94e3824fbabc --- /dev/null +++ b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/769a6e31-fc05-4ad4-bfda-b4fc158792ae_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9c6dd010cc27ef5d4bbe8059e94988325a25c3a6fd1aa36c8d013c3a821d4155 +size 8237739 diff --git a/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/full.md b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/full.md new file mode 100644 index 0000000000000000000000000000000000000000..fd81abd5b04f9b6e3c7abcccf9caac3c35e1eccb --- /dev/null +++ b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/full.md @@ -0,0 +1,500 @@ +# SeaThru-NeRF: Neural Radiance Fields in Scattering Media + +Deborah Levy1, Amit Peleg1, Naama Pearl1, Dan Rosenbaum1, Derya Akkaynak1,2, Simon Korman1, Tali Treibitz1 + +1University of Haifa, 2The Inter-University Institute for Marine Sciences in Eilat sea-thru-nerf.github.io + +![](images/a9e0e0ab516d24b81c91f97704f375dc301099a8047e83727723900097bea82c.jpg) +Ground Truth RAW + +![](images/fff65e3ff3500a13e149b133373ac1680e5ae6e09ad24866e27cc5bd23fc17bc.jpg) +Ground Truth WB +Figure 1. NeRFs have not yet tackled scenes in which the medium strongly influences the appearances of objects, as in the case of underwater imagery. By incorporating a scattering image formation model into the NeRF rendering equations, we are able to separate the scene into 'clean' and backscatter components. Consequently, we can render photorealistic novel-views with or without the participating medium, in the latter case recovering colors as if the image was taken in clear air. Results on the Curaçao scene: A RAW image (left) is brightened and white balanced (WB) for visualization, showing more detail, while areas further from the camera (top-right corner) are occluded and attenuated by severe backscatter - which is effectively removed in our restored image. Please zoom-in to observe the details. + +![](images/7543c7c5b3cb5e27b138d1ad76511d71215ea068d1255f20ec94f1900dd45cf9.jpg) +Ours Novel View + +![](images/bf1cd10a4a71cad6a84b63c6abc291f9a3f4a4feac8187eddd1c303da7f8309d.jpg) +Ours Restored + +![](images/10cbd281937075f60a52b2b327c12476fdc137f772a071f5a9437fb982661133.jpg) +Ours Backscatter + +# Abstract + +Research on neural radiance fields (NeRFs) for novel view generation is exploding with new models and extensions. However, a question that remains unanswered is what happens in underwater or foggy scenes where the medium strongly influences the appearance of objects. Thus far, NeRF and its variants have ignored these cases. However, since the NeRF framework is based on volumetric rendering, it has inherent capability to account for the medium's effects, once modeled appropriately. We develop a new rendering model for NeRFs in scattering media, which is based on the SeaThru image formation model, and suggest a suitable architecture for learning both scene information and medium parameters. We demonstrate the strength of our method using simulated and real-world scenes, correctly rendering novel photorealistic views underwater. Even more excitingly, we can render clear views of these scenes, removing the medium between the camera and the scene and reconstructing the appearance and depth of far objects, which are severely occluded by the medium. Our code and unique datasets are available on the project's website. + +# 1. Introduction + +The pioneering work of Mildenhall et al. [25] on Neural Radiance Fields (NeRFs) has tremendously advanced the field of Neural Rendering, due to its flexibility and unprecedented quality of synthesized images. Yet, the formulations of the original NeRF [25] and its followup variants assume + +that images were acquired in clear air, i.e., in a medium that does not scatter or absorb light in a significant manner and that the acquired image is composed solely of the object radiance. The NeRF formulation is based on volumetric rendering equations that take into account sampled points along 3D rays. Assuming a clear air environment, an implicit assumption, which is often enforced explicitly with dedicated loss components [5], is that a single opaque (high density) object is encountered per ray, with zero density between the camera and the object. + +In stark contrast to clear air case, when the medium is absorbing and / or scattering (e.g., haze, fog, smog, and all aquatic habitats), the volume rendering equation has a true volumetric meaning, as the entire volume, and not only the object, contributes to image intensity. As the NeRF model estimates color and density at every point of a scene, it lends itself perfectly to general volumetric rendering, given that the appropriate rendering model is used. Here, we bridge this gap with SeaThru-NeRF, a framework that incorporates a rendering model that takes into account scattering media. + +This is achieved by assigning separate color and density parameters to the object (scene) and the medium, within the NeRF framework. Our approach adopts the SeaThru underwater image formation model [1, 3] to account for scattering media. SeaThru is a generalization of the standard wavelength-independent attenuation (e.g., fog) image formation model, where two different wideband coefficients are used to represent the medium, which is more accurate when attenuation is wavelength-dependent (as in all wa + +ter bodies and under some atmospheric conditions). In our model, the medium parameters are separate per color channel, and are learned functions of the viewing angles, enforcing them to be constant only along 3D rays in the scene. + +Attempting to optimize existing NeRFs on scenes with scattering medium results in cloud-like objects floating in space, while our formulation enables the network to learn the correct representation of the entire 3D volume, that consists of both the scene and the medium. Our experiments demonstrate that SeaThru-NeRF produces state-of-the-art photorealistic novel view synthesis on simulated and challenging real-world scenes (see Fig. 1) with scattering media, that include complex geometries and appearances. In addition, it enables: + +1. Color restoration of the scenes as if they were not imaged through a medium, as our modeling allows full separation of object appearance from the medium effects. +2. Estimation of 3D scene structure which surpasses that of structure-from-motion (SFM) or current NeRFs, especially in far areas of bad visibility, as we jointly reconstruct and reason for the geometry and medium. +3. Estimation of wideband medium parameters, which are informative properties of the captured environment, and potentially allowing simulation under different conditions. + +# 2. Related Work + +Neural Radiance Fields (NeRFs): The original work on NeRFs [25] has paved the way to a large capacity of followup work, with rapid and significant progress in many related aspects. For brevity, we focus in the following only on works closely related to ours, and refer the reader to a comprehensive review of the field [43] prior to the introduction of NeRFs, and to [44] for the most recent. + +NeRFs have been recently shown to be extremely powerful in multi-image settings that involve computational imaging tasks. These include HDR [50], de-blurring [20], superresolution [49], low-light enhancement [23] and denoising [32]. The need to recover the clean 'medium-free' version of images degraded by scattering and attenuation effects, likewise, can benefit from the neural rendering approach. SeaThru-NeRF is designed to model the degradation, with the ability to recover its parameters, and reconstruct the clean underlying scene and novel-view images. + +Our work is related to recent efforts to improve the quality and robustness of NeRFs in challenging environments (e.g. [14, 21, 29]). Nerf-W [21] learns a per-image latent embedding that can capture appearance variations in complex scenes. It decomposes the scene into image-dependent and shared components to disentangle transient elements from the static scene. NeRFRen [14] is designed for scenes with reflections. It separates the scene as a sum of transmitted and reflected components, which are modeled as separate NeRFs. Ref-NeRF [47] introduces a new parameteriza + +tion and structuring of view-dependent appearance, which can represent scenes with specularities and reflections. + +Our approach has much in common with some of these methods, most notably the way of reconstructing the target image as a composition of components: 'direct' and 'backscatter' in our case, 'transient' and 'static' in [21], or 'transmitted' and 'reflected' in [14]. However, as we demonstrate, these methods are limited on scenes in scattering media as they do not explicitly model the effects of the medium. Our method is different in that it can model a continuous medium component that is not an object. + +Graphics and Vision in Scattering Media: Propagation of light in a medium is governed by the radiative transfer equation [10]. This equation describes light interaction per particle in the medium and requires extensive Monte Carlo simulations for complete solutions [12, 16, 30, 31], see [30] for an excellent review. In many cases simplifying assumptions can be made about the medium that ease rendering [22], where the major one is single-scattering [33, 42, 48]. Realistic rendering requires having the scattering properties of the medium, which can be estimated in the lab [13, 26], or from in situ images [6]. An MLP for rendering synthetic atmospheric clouds was suggested in [17]. + +In computer vision, image formation models under ambient illumination for bad weather [28] and underwater [37] share the same general structure for the case of horizontal viewing. Artificial illumination used underwater [46] and in fog has additional terms that account for the nonuniformity of the source. Underwater, the medium parameters exhibit strong wavelength dependency that was shown to affect model accuracy in wideband camera channels. The SeaThru model [1-3] was suggested to overcome this issue. + +Scene reconstruction in scattering media is an ill-posed problem which was initially solved with multiple frames [27,37,38,46]. Later on, single-image methods have proposed a multitude of image priors to overcome the ill-posed nature of the problem, see [19,51] for comprehensive reviews on single-image dehazing and underwater reconstruction, respectively. The introduction of deep-learning has led to an explosion of single-image dehazing and underwater reconstruction networks. See [41] and [4] for recent reviews of deep-learning dehazing and underwater reconstruction works, respectively. + +Underwater, it was suggested to solve for the 3D structure of the scene, prior to image restoration [9, 35] using the haze model and [2] using the revised one. In SeaThruNeRF, we simultaneously reconstruct the scene and its 3D structure, yielding multiple advantages that we demonstrate empirically. WaterNeRF [40] suggests an underwater neural renderer that estimates the medium parameters only with respect to histogram-qualified images, separately from the rendering. Here, we show the huge benefit of modeling the scattering medium within the rendering equations, over a + +variety of different scenes. Concurrently and independently to our work, [11] presented a NeRF for haze. + +# 3. Scientific Background + +# 3.1. Neural Radiance Fields (NeRFs) + +The original NeRF formulation [25] implicitly represents a 3D scene by a trainable continuous function. It is typically parameterized by an MLP $f_{\Theta}:(\mathbf{x},\mathbf{d})\to (\mathbf{c},\sigma)$ which encodes the density $\sigma$ at the 3D point $\mathbf{x} = (x,y,z)$ and the color $\mathbf{c} = (r,g,b)$ emitted from this point in the viewing direction $\mathbf{d} = (\theta ,\phi)$ (which is typically represented as a 2-element unit normalized 3D vector). + +This simple representation is used to simulate classical image-based rendering, by color accumulation along rays that are back-projected from a posed camera. If we parameterize points along a camera ray $\mathbf{r}$ by $\mathbf{r}(t) = \mathbf{o} + \mathbf{d}(t)$ , where $\mathbf{o}$ is the camera center and $t\in \mathbb{R}_+$ , the expected (image) color $C(\mathbf{r})$ along the ray can be written as: + +$$ +C (\mathbf {r}) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \sigma (t) \mathbf {c} (t) d t \tag {1} +$$ + +where: integration along the ray is limited to the range $t \in [t_n, t_f]$ (near and far bounds on the scene contents); $\sigma(t)$ and $\mathbf{c}(t)$ are shorthands for the density at the point $\mathbf{r}(t)$ and its emitted color towards the camera center; $T(t)$ denotes the accumulated transmittance along the ray from $t_n$ to $t$ (the probability that the ray travels from $t_n$ to $t$ without hitting other particles along the way), and is given by: + +$$ +T (t) = \exp \left(- \int_ {t _ {n}} ^ {t} \sigma (s) d s\right) \tag {2} +$$ + +In practice, the rendered color $C(\mathbf{r})$ in Eq. (1) is approximated with the quadrature rule, by discretizing the range $[t_n, t_f]$ into a set of $N$ intervals $I_i = [s_i, s_{i+1}]$ (where $t_n = s_0 < \dots < s_N = t_f$ ), assuming that the density $\sigma$ and color $\mathbf{c}$ are constant along each interval (e.g. by querying the model once per interval at its center-point). + +In the discretized version of Eq. (1): + +$$ +\hat {C} (\mathbf {r}) = \sum_ {i = 1} ^ {N} C _ {i} (\mathbf {r}) \tag {3} +$$ + +the contribution $C_i(\mathbf{r})$ of the interval $I_{i}$ is given by: + +$$ +C _ {i} (\mathbf {r}) = \int_ {s _ {i}} ^ {s _ {i + 1}} T (t) \sigma_ {i} \mathbf {c} _ {i} d t = T \left(s _ {i}\right) \left(1 - e ^ {- \sigma_ {i} \delta_ {i}}\right) \mathbf {c} _ {i} \tag {4} +$$ + +where $\sigma_{i}$ and $\mathbf{c_i}$ are the (constant) density and color along the $i$ th interval, whose length is $\delta_{i} = s_{i + 1} - s_{i}$ , and the + +transmittance $T(s_{i})$ at the beginning of the interval is: + +$$ +T \left(s _ {i}\right) = \exp \left(- \sum_ {j = 0} ^ {i - 1} \sigma_ {j} \delta_ {j}\right) \tag {5} +$$ + +This fully differentiable NeRF model (with the discretized rendering scheme) is trained with a simple reconstruction loss + +$$ +L = \sum_ {\mathbf {r} \in R} \| \hat {C} (\mathbf {r}) - C (\mathbf {r}) \| ^ {2} \tag {6} +$$ + +comparing each rendered training image pixel $\hat{C}(\mathbf{r})$ to its ground truth color $C(\mathbf{r})$ . The model can then be used to synthesize photorealistic novel view images. + +# 3.2. Image Formation in Scattering Media + +Image formation in fog, haze, or underwater differs from image formation in clear air in two major aspects. First, the direct signal emanating from the object is attenuated as a function of distance and wavelength. Second, this signal is occluded by backscatter (termed also path-radiance or veiling-light) - radiance that is added due to the in-scattering from the particles along the line-of-sight (LOS), illustrated in Fig. 2. The intensity and color of the occluding backscatter layer are independent of the scene contents, and its intensity accumulates along the LOS, increasing with distance. As a result, the visibility and contrast of further objects is significantly reduced and their colors are distorted. + +We adopt the revised model [1] as the general model for image formation in scattering media under ambient illumination. Image intensity (per pixel, per color channel) is given as: + +$$ +I = \underbrace {\underbrace {J} _ {\text {c o l o r}} \cdot \underbrace {(e ^ {- \beta^ {D} (\mathbf {v} _ {D}) \cdot z})} _ {\text {a t t e n u a t i o n}}} _ {B ^ {\infty}} + \underbrace {(1 - e ^ {- \beta^ {B} (\mathbf {v} _ {B}) \cdot z})} _ {\text {a t t e n u a t i o n}} \tag {7} +$$ + +where $I$ is the linear image captured by the camera of a scene with range $z$ , $J$ is the clear scene that would have been captured had there been no medium along $z$ , and $B^{\infty}$ is the backscatter water color at infinity, i.e., the backscatter at areas that contain no objects. Lastly, $\beta^{D}$ and $\beta^{B}$ are the attenuation and backscatter coefficients, respectively, the two parameters that describe the medium effects. The vectors $\mathbf{v}_D$ and $\mathbf{v}_B$ represent the dependencies of $\beta^{D}$ and $\beta^{B}$ on range, object reflectance, spectrum of ambient light, spectral response of the camera, and the physical scattering and beam attenuation coefficients of the water body, all of which are functions of wavelength. It was shown in [2] that $\beta^{B}$ can be assumed constant in an image, while $\beta^{D}$ mainly depends on the object distance and weakly on object reflectance, thus solving for the full model requires at least 6 unknowns. The value of $B^{\infty}$ is usually assumed to be uniform in the scene + +![](images/45b49dc455da358dbb8d9ac6aafbdd045287c23d9955eab3cd5487e1097e5da4.jpg) +Figure 2. An illustration of our ray model. We assume a scene with at most a single opaque object at every ray. The medium is semitransparent with constant density per-ray. The densities governing the backscatter and the object in water are not the same [1]. + +but as discussed in [6] it is almost never really uniform, because of the directionality of the sun, among other factors. + +This model is also applicable to haze and fog, where attenuation has very little dependence on wavelength. Then, image formation is greatly simplified because it can be assumed that there is only one medium parameter that is uniform across the color channels, represented by a scalar $(\beta^{D} = \beta^{B} = \beta)$ [38]. Underwater, often the simplifying (less accurate) assumption that $\beta^{D} = \beta^{B}$ is made, reducing to 3 unknowns [6,7,37]. + +# 4. SeaThru-NeRF + +# 4.1. Basic Model Derivation + +Here we consider a more general setting than the original NeRF [25], in which light travels through a scattering medium rather than free-space, resulting in a significant impact on the captured color. Following [22] we suggest adding the medium to Eqs. (1) and (2): + +$$ +C (\mathbf {r}) = \int_ {t _ {n}} ^ {t _ {f}} T (t) \left(\sigma^ {\mathrm {o b j}} (t) \mathbf {c} ^ {\mathrm {o b j}} (t) + \sigma^ {\mathrm {m e d}} (t) \mathbf {c} ^ {\mathrm {m e d}} (t)\right) d t \tag {8} +$$ + +where: + +$$ +T (t) = \exp \left(- \int_ {t _ {n}} ^ {t} \left(\sigma^ {\mathrm {o b j}} (s) + \sigma^ {\mathrm {m e d}} (s)\right) d s\right), \tag {9} +$$ + +using separate color and density parameters for the object and medium. Notice that these equations reduce to Eqs. (1) and (2) by simply considering the case where the medium density $\sigma^{\mathrm{med}}$ is zero. + +Moving to the discretized version, we similarly get3 the following generalizations of Eqs. (4) and (5): + +$$ +C _ {i} (\mathbf {r}) = T \left(s _ {i}\right) \left(1 - e ^ {- \left(\sigma_ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}}\right) \delta_ {i}}\right) \frac {\sigma_ {i} ^ {\mathrm {o b j}} \mathbf {c} _ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}} \mathbf {c} _ {i} ^ {\mathrm {m e d}}}{\sigma_ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}}} \tag {10} +$$ + +with transmittance + +$$ +T \left(s _ {i}\right) = \exp \left(- \sum_ {j = 0} ^ {i - 1} \left(\sigma_ {j} ^ {\mathrm {o b j}} + \sigma_ {j} ^ {\mathrm {m e d}}\right) \delta_ {j}\right). \tag {11} +$$ + +Splitting the discretized color rendering equations (3,10 and 11) into the 'object' and 'medium' components, we get: + +$$ +\hat {C} (\mathbf {r}) = \sum_ {i = 1} ^ {N} \hat {C} _ {i} ^ {\mathrm {o b j}} (\mathbf {r}) + \sum_ {i = 1} ^ {N} \hat {C} _ {i} ^ {\mathrm {m e d}} (\mathbf {r}) \tag {12} +$$ + +$$ +\hat {C} _ {i} ^ {\mathrm {o b j}} (\mathbf {r}) = T (s _ {i}) \left(1 - e ^ {- \left(\sigma_ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}}\right) \delta_ {i}}\right) \frac {\sigma_ {i} ^ {\mathrm {o b j}} \mathbf {c} _ {i} ^ {\mathrm {o b j}}}{\sigma_ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}}} \tag {13} +$$ + +$$ +\hat {C} _ {i} ^ {\mathrm {m e d}} (\mathbf {r}) = T (s _ {i}) \left(1 - e ^ {- \left(\sigma_ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}}\right) \delta_ {i}}\right) \frac {\sigma_ {i} ^ {\mathrm {m e d}} \mathbf {c} _ {i} ^ {\mathrm {m e d}}}{\sigma_ {i} ^ {\mathrm {o b j}} + \sigma_ {i} ^ {\mathrm {m e d}}} \tag {14} +$$ + +As a first step towards constraining and simplifying our model, we constrain the medium parameters to be constant along 3D viewing rays. We drop the respective interval indices and remain with $\sigma^{\mathrm{med}}$ and $\mathbf{c}^{\mathrm{med}}$ that depend only on the ray $\mathbf{r}$ . The $\mathbf{c}^{\mathrm{med}}$ uniformity stems from the common assumption of a uniform phase function (the dependence of scattered radiance on scattering angle) along the LOS [22, 30]. Regarding the density $\sigma^{\mathrm{med}}$ , we take it to be separate per color channel, but constant per ray. This is far less restrictive compared to models that assume constancy per image or even per scene [2]. These constraints will be enforced by respective structural choices in the network. + +Furthermore, we assume that objects in the scene are opaque, hence the object density along the ray is close to zero except for a high peak in the object location. On the other hand, the medium is semi-transparent, characterized by a low non-zero density. This implies that $\sigma^{\mathrm{med}} \gg \sigma^{\mathrm{obj}}$ before the object and $\sigma^{\mathrm{med}} \ll \sigma^{\mathrm{obj}}$ at the object, as illustrated in Fig. 2. Therefore, Eqs. (13-14) reduce to + +$$ +\hat {C} _ {i} ^ {\mathrm {o b j}} (\mathbf {r}) = T _ {i} \cdot \left(1 - e ^ {- \sigma_ {i} ^ {\mathrm {o b j}} \delta_ {i}}\right) \cdot \mathbf {c} _ {i} ^ {\mathrm {o b j}} \tag {15} +$$ + +$$ +\hat {C} _ {i} ^ {\mathrm {m e d}} (\mathbf {r}) = T _ {i} \cdot \left(1 - e ^ {- \boldsymbol {\sigma} ^ {\mathrm {m e d}} \delta_ {i}}\right) \cdot \mathbf {c} ^ {\mathrm {m e d}} \tag {16} +$$ + +$$ +T _ {i} = \exp \left(- \sum_ {j = 0} ^ {i - 1} \sigma_ {j} ^ {\mathrm {o b j}} \delta_ {j}\right) \cdot \exp \left(- \mathbf {o} ^ {\mathrm {m e d}} s _ {i}\right) \tag {17} +$$ + +# 4.2. Relation to Underwater Image Formation + +In this section we show that our model can be reduced to the image formation model described in Sec. 3.2, which is not based on volumetric rendering. To this end we consider sampling the ray along intervals with constant size $\delta$ , and the appearance of the opaque object at a depth $z$ , at the beginning of interval $I_{k} = [s_{k}, s_{k + 1}]$ , for some integer $k$ (that is: $s_{i} = i \cdot \delta$ for every $i$ and $z = k \cdot \delta$ in particular). + +![](images/5b0dbdf12734c0f32948c38960f8022fc6cf93fb57398cdacf664511df0ab80b.jpg) +Figure 3. SeaThru-NeRF architecture. The computation of the 'object' outputs (density and color, in green), follows the standard NeRF architecture, while the 'medium' components (in purple) are computed once per ray by a separate subnet (the 'medium MLP') that depends only on the viewing direction. + +In this case, $\sigma_{i}^{\mathrm{obj}}\approx 0$ for all $i < k$ , and $\sigma_k^{\mathrm{obj}}\gg \sigma^{\mathrm{med}}$ . This implies that $C_k^{\mathrm{med}}(\mathbf{r})\ll C_k^{\mathrm{obj}}(\mathbf{r})$ and $C_i^{\mathrm{obj}}(\mathbf{r})\approx 0$ , therefore we can write the rendering Eq. (12) as + +$$ +\hat {C} (\mathbf {r}) \approx \hat {C} _ {k} ^ {\mathrm {o b j}} (\mathbf {r}) + \sum_ {i = 0} ^ {k - 1} \hat {C} _ {i} ^ {\mathrm {m e d}} (\mathbf {r}). \tag {18} +$$ + +Furthermore, since the object is opaque, we can assume that the density $\sigma_k^{\mathrm{obj}}$ is large enough such that the transmittance at the end of the $k$ th interval $T(s_{k + 1})$ drops practically to zero, that is: $e^{-\sigma_k^{\mathrm{obj}}\delta}\approx 0$ . Therefore + +$$ +\begin{array}{l} \hat {C} _ {k} ^ {\mathrm {o b j}} (\mathbf {r}) = T _ {i} \cdot \left(1 - e ^ {- \sigma_ {i} ^ {\mathrm {o b j}} \delta}\right) \cdot \mathbf {c} _ {i} ^ {\mathrm {o b j}} \tag {19} \\ \approx e ^ {- k \sigma^ {\mathrm {m e d}} \delta} \left(1 - e ^ {- \sigma_ {k} ^ {\mathrm {o b j}} \delta}\right) \mathbf {c} _ {k} ^ {\mathrm {o b j}} \approx e ^ {- \sigma^ {\mathrm {m e d}} \delta \cdot k} \mathbf {c} _ {k} ^ {\mathrm {o b j}} \\ \end{array} +$$ + +and + +$$ +\begin{array}{l} \sum_ {i = 0} ^ {k - 1} \hat {C} _ {i} ^ {\mathrm {m e d}} (\mathbf {r}) = \sum_ {i = 0} ^ {k - 1} T _ {i} \cdot \left(1 - e ^ {- \sigma^ {\mathrm {m e d}} \delta}\right) \cdot \mathbf {c} ^ {\mathrm {m e d}} \tag {20} \\ \approx \sum_ {i = 0} ^ {k - 1} e ^ {- i \mathbf {\sigma} ^ {\mathrm {m e d}} \delta} \cdot \left(1 - e ^ {- \mathbf {\sigma} ^ {\mathrm {m e d}} \delta}\right) \cdot \mathbf {c} ^ {\mathrm {m e d}} \\ = \left(1 - e ^ {- \mathbf {\sigma} ^ {\mathrm {m e d}} \delta \cdot k}\right) \cdot \mathbf {c} ^ {\mathrm {m e d}} \\ \end{array} +$$ + +Substituting Eqs. (19) and (20) into Eq. (18) (recalling that the depth $z$ equals $k \cdot \delta$ ) yields: + +$$ +\hat {C} (\mathbf {r}) \approx e ^ {- \boldsymbol {\sigma} ^ {\mathrm {m e d}} z} \cdot \mathbf {c} _ {k} ^ {\mathrm {o b j}} + \left(1 - e ^ {- \boldsymbol {\sigma} ^ {\mathrm {m e d}} z}\right) \cdot \mathbf {c} ^ {\mathrm {m e d}}, \tag {21} +$$ + +resulting precisely in the commonly used scattering media image formation model [8, 37]. This can be seen by comparing to Eq. (7) where $\sigma^{\mathrm{med}} = \beta^{D} = \beta^{B}$ plays the role of the attenuation coefficient (equal for direct and backscatter), $\mathbf{c}^{\mathrm{med}}$ is the veiling light $B^{\infty}$ (backscatter color at infinity) and $\mathbf{c}_k^{\mathrm{obj}}$ the clear image color $J$ . + +# 4.3. Final Model + +We make several refinements with respect to the basic model presented in Section 4.1. In Sec. 4.2, we showed that our rendering equations lead to an image formation model with identical attenuation coefficients for the direct and backscatter components. Following the discussion in Sec. 3.2, and as has been shown in [1], when using such equations with a camera with wideband color channels, the effective $\sigma^{\mathrm{med}}$ that is experienced by the camera in $C_i^{\mathrm{obj}}(\mathbf{r})$ is different than the one experienced in $C_i^{\mathrm{med}}(\mathbf{r})$ . Therefore, in our final model we use different parameters for $\sigma^{\mathrm{med}}$ in each component and term them $\sigma^{\mathrm{attn}}$ and $\sigma^{\mathrm{bs}}$ for $C_i^{\mathrm{obj}}(\mathbf{r})$ and $C_i^{\mathrm{med}}(\mathbf{r})$ respectively. Our final equations are: + +$$ +\hat {C} _ {i} ^ {\mathrm {o b j}} (\mathbf {r}) = T _ {i} ^ {\mathrm {o b j}} \cdot \exp \left(- \mathbf {o} ^ {\mathrm {a t t n}} s _ {i}\right) \cdot \left(1 - \exp (- \sigma_ {i} ^ {\mathrm {o b j}} \delta_ {i})\right) \cdot \mathbf {c} _ {i} ^ {\mathrm {o b j}} +$$ + +$$ +\hat {C} _ {i} ^ {\mathrm {m e d}} (\mathbf {r}) = T _ {i} ^ {\mathrm {o b j}} \cdot \exp \left(- \mathbf {o} ^ {\mathrm {b s}} s _ {i}\right) \cdot \left(1 - \exp (- \mathbf {o} ^ {\mathrm {b s}} \delta_ {i})\right) \cdot \mathbf {c} ^ {\mathrm {m e d}} +$$ + +$$ +T _ {i} ^ {\mathrm {o b j}} = \exp \left(- \sum_ {j = 0} ^ {i - 1} \sigma_ {j} ^ {\mathrm {o b j}} \delta_ {j}\right) \tag {22} +$$ + +Based on our derivations we suggest the following architecture (Fig. 3). As in [25], the object properties are computed by a pair of MLPs, such that the density $\sigma^{\mathrm{obj}}$ is a function of the position $(x,y,z)$ only, while color $\mathbf{c}^{\mathrm{obj}}$ is determined by the viewing direction $(\theta ,\phi)$ as well. The medium parameters $\mathbf{c}^{\mathrm{med}}$ , $\sigma^{\mathrm{bs}}$ , $\sigma^{\mathrm{attn}}$ are handled by a separate MLP with only the direction input, following our decision to constrain them to be constant per viewing direction. + +# 4.4. Loss Function + +Let us denote the sequence of samples along a ray by $\mathbf{s} = \{s_i\}_{i=0}^N$ , the object 'weight' at the $i$ th segment $[s_i, s_{i+1}]$ , + +$$ +w _ {i} ^ {\mathrm {o b j}} = T _ {i} ^ {\mathrm {o b j}} \cdot \left(1 - \exp \left(- \sigma_ {i} ^ {\mathrm {o b j}} \delta_ {i}\right)\right), \tag {23} +$$ + +the sequence of these weights by $\mathbf{w} = \{w_{i}^{\mathrm{obj}}\}_{i = 0}^{N - 1}$ and the ground-truth (supervised) pixel color by $C^*$ . + +Our loss is the following combination: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e c o n}} \left(\hat {C}, C ^ {*}\right) + \mathcal {L} _ {\text {p r o p}} (\mathbf {s}, \mathbf {w}) + \lambda \mathcal {L} _ {\text {a c c}} (\mathbf {w}), \tag {24} +$$ + +where $\lambda = 0.0001$ was chosen through cross-validation. Since we work on linear images, we adopt the reconstruction loss of RawNeRF [23]: + +$$ +\mathcal {L} _ {\text {r e c o n}} (\hat {C}, C ^ {*}) = \left(\frac {\hat {C} - C ^ {*}}{\operatorname {s g} (\hat {C}) + \epsilon}\right) ^ {2} \tag {25} +$$ + +where $\mathrm{sg}(\cdot)$ stands for stop-gradient and $\epsilon = 10^{-3}$ . The 'proposal' loss $\mathcal{L}_{\mathrm{prop}}(\mathbf{s},\mathbf{w})$ is an inherent part of Mip-NeRF-360 [5]. It penalizes for the discrepancy between the + +distributions of object weights at 'original' and 'proposed' samplings, where only the latter is used for rendering [5]. + +To enforce binary separation between points in space that contain objects and those that contain solely a medium - we add a prior on the transmittance $T_{i}^{\mathrm{obj}}$ of each point on the ray to be either 0 or 1, not allowing semi-transparent objects. This is modelled as a mixture of two Laplacian distributions with modes at 0 and 1 (following [34]): + +$$ +\mathbf {P} (x) \propto e ^ {- \frac {| x |}{0 . 1}} + e ^ {- \frac {| 1 - x |}{0 . 1}} \tag {26} +$$ + +and use the negative log likelihood loss: + +$$ +\mathcal {L} _ {\mathrm {a c c}} (\mathbf {w}) = - \log \mathbb {P} \left(T _ {i} ^ {\mathrm {o b j}}\right). \tag {27} +$$ + +# 4.5. Implementation and Optimization + +Our implementation is based on the code released in Mip-NeRF-360 [5], choosing the best performing baseline on our scenes which was the forward-looking configuration with normalized device coordinates (NDC). For the mediumMLP, we use 6 linear layers with 256 features and a softplus activation, followed by 3 branches of dense layers and a sigmoid activation for predicting $c^{\mathrm{med}}$ and softplus activations for $\sigma^{\mathrm{attn}}$ and $\sigma^{\mathrm{bs}}$ . + +In the rendering scheme, [5] initialized the farthest $\delta_{i}$ with infinity, enabling the network to predict a background color for rays that do not intersect with any object. We disabled this addition as it prevents our method from explaining the medium that contributes to the rendered color along the ray. We keep the learning rate and optimization parameters the same as in [5]. The network is trained for 250,000 iterations with a batch size of 16384 rays, taking around 10 hours on an Nvidia A100 GPU. The loss function and metrics are calculated on the output before any post-processing. + +# 5. Experiments and Results + +# 5.1. Experiments + +Real world scenes. We acquired multi-image underwater scenes by diving in three different seas: the Red Sea (Eilat, Israel), the Caribbean Sea (Curaçao) and the Pacific Sea (Panama) with a total of 20, 20 and 18 images respectively, from which three are set aside for validation in each set. This data encapsulates a diverse set of water conditions and imaging conditions. The images were acquired as RAW images with a Nikon D850 SLR camera in a Nauticam underwater housing with a dome port to avoid refractions that jeopardize the pinhole model [45], and downsampled to average size $900 \times 1400$ . The input linear images were white-balanced before processing with $0.5\%$ clipping per channel to remove extreme noisy pixels. Finally, COLMAP [39] is used to extract camera poses. + +Simulated Scene. We constructed a simulation using the Fern scene of the LLFF dataset [24]. We ran MIP-NeRF-360 [5] and used the predicted depth maps to simulate an + +![](images/e76c02e24c509eee74358fcd222d2de77aed7e948e491ef48541690e203edc54.jpg) + +![](images/b75cc51dd3dd65fea3a5c8d028a09d3d63c213554dd1aa70e4adaea791f993bd.jpg) + +![](images/69d4d0aac7da483266212b31a89eb2eb6b3a63d16d9622b4be46c39e289acf77.jpg) + +![](images/ceed1ece2a7b01724ddb5059607f5d00ca9204eaac7907305cb47106c6b98bdd.jpg) + +![](images/0bd8ff890a1cfd96adad232ee4a16e1ebb97436ccc3b82474960c577171488b0.jpg) + +![](images/b7bf897e3df7a3dd420e99f2c6282ec87b1e3993e969ffcc6a8794d23c2452b7.jpg) + +![](images/9dce81562f7a968f43764444a79c9ac9eb8658a7173852272d58df143f7d6e02.jpg) +Figure 4. Synthetic experiment on Fern scene of the LLFF dataset [24]. Top: Our method can handle 'in-air' scenes, with a uniform zeros backscatter image and a reconstruction PSNR that is close to that of the baseline [5] which was 23.73. Middle and bottom: Our method's separation between clean and backscatter components, for simulations of fog and underwater effects. The reconstruction quality degrades rather gracefully. + +![](images/fc572cd3afe20f6d204a4f79698955d198208524a665f656ef60841ab1ef2453.jpg) + +![](images/d289341b13c66b2b7c84895cd01dcbfa0c6e625544acdcecddc1d1569a16715a.jpg) + +underwater and a foggy scene. Water was added according to (7) with parameter values: $\beta^D = [1.3, 1.2, 0.9]$ , $\beta^B = [0.95, 0.85, 0.7]$ , $B^\infty = [0.07, 0.2, 0.39]$ . Fog was simulated based on [36] with $\beta = 1.2$ . + +Baseline methods. The input to all methods is the same set of white-balanced linear images. In the task of rendering scenes in the medium we compare with the following NeRF methods: MIP-NeRF-360, forward-looking with NDC (MIP360) [5], NeRF-W [21] and NeRFReN [14]. In the task of reconstructing clean medium-free images we compare with NeRF-W, where the 'transient' component can be viewed as the clean image and the 'static' image as backscatter, and to NeRFReN with the 'reflected' and 'transmitted' components as clean and backscatter images. We additionally compare to single-image scene reconstruction methods: plain white balance, SeaThru [2], the leading "classical" methods of Bekerman et al [6], and the recent deep-learning based [52] (as well as [15, 52] whose results are provided in the project website). SeaThru requires depth maps, that we generate using SFM (with Agisoft Metashape) as originally suggested. These depth-maps are used to compare with those of the different methods. + +Photo-finishing: As the input and output images are linear, we apply photofinishing on all linear reconstructed scenes to enhance scene contrast and appearance, using the digital camera pipeline from [18]. This is done to improve visualization for easier qualitative comparisons, while PSNR is calculated on the original non-photofinished linear images. + +![](images/dfa8659dc7d783cb73a3a0aef780f6a411f3c8d9d5c3893972fb61e3d0e3be3b.jpg) + +![](images/2202b692f391f0cf3f49a44022b7ee23eb18b5cb5034db73f861bc3a7456b996.jpg) + +![](images/01840476edf1e7d9df380400d984e0552e64a47c675a7fbb61811ef753f593bd.jpg) + +![](images/499362a5c045b0df473142dec90f6c0a50c9f0015912836ad01538d6762dfc16.jpg) + +![](images/58a3002c6749ce8f5ab466f6e73ca56e0377747bba967631320b3c5a76b073ba.jpg) + +![](images/634d79d261f63f94117b97f0df6acc3b917d9377d2b2db1435ac237948296a81.jpg) + +![](images/88dab6d15a847697a601b4a5a85d9265032f9f1b60990ea3e0661df9d9b5cd20.jpg) + +![](images/c2bbf79eb1507c0d5c8dddc9fba4c0d9cacdc87820ba695ae21e59aac9803ced.jpg) + +![](images/3440aeb7d3fb2d4fcfba3491c36341378649d35f4c540a65081c6d695306fcdf.jpg) + +![](images/0b95275bd7e5e0ef85c8670b07221a537b96b50de4c997fe709ac6f303fb9755.jpg) + +![](images/bf5c86dec753492e5656ba5b20da46d174773ddd253939170e8e913133b04a29.jpg) + +![](images/ae239f42bb9dca81fe88c50c3c82b770fe5dc90a3804ebfeab6a09dc8a75d4ae.jpg) + +![](images/f2591500dc820bb2d2981b3b5ed018dc1e70bdaf187ec136ba368fb6b13d1be1.jpg) + +![](images/f40a01a34d6bd3003b3e47151d8a64a1c040568601a638bae3df6ec02c11f618.jpg) + +![](images/52bf8ab7e4b571f35ec44c8c3a00113b0043790dd16def35522a06784d9be08d.jpg) + +![](images/c0832f69d4a2653d694b6ccfe9a1f1c0af8d68e41920221918f5597cf0c5c61f.jpg) + +![](images/7395f27a4f6e1ae35a17ce50539a0c9d597d0681ce8bb938bbf1466389af95e5.jpg) + +![](images/e798220a54cca72fbfa8ff202eb3d296da0cdd77f8a71e4bf45ad919b8518e30.jpg) + +![](images/859c865782c027443694f11ccd85f0090e4f6b72a71b500195e3a4d8c6b9792b.jpg) + +![](images/e5df73394ab0f99c1da95353c6af994d966856e1ccef6beadf3c3b0bbba3e8b0.jpg) + +![](images/333781108bdfb1ce4706d97a4a4e65bc9e1d3c33473721a8051cd58ee56e408a.jpg) +Figure 5. Scene rendering in the medium, on 'Red Sea'. Left to right: white-balanced input image, our result, MIP360 [23], Nerf-W [21], NeRFReN [14]. [Top 2 rows] Train image and zoom-ins. Even in the task of overfitting to the training images, there are noticeable differences between the methods, and as can be seen in the zoom-ins (red squares) we are able to reconstruct fine details in further areas (albeit a lower PSNR). [Bottom 2 rows] Novel view and zoom-ins. Our method achieves the highest PSNR (see tables 1, 2), and provides much better details in further areas (see red square zoom-ins). Our depth reconstructions provide more detail in further areas. + +![](images/e5cc95998bfcf18b68453f537c87cc5946bffda5f48dd7ec803936c9f89c23b9.jpg) + +![](images/0f50a2e5919d6b0e82c0258a230765847fdba55302c613f0be6ef3e00cec2ad2.jpg) + +![](images/2c6435a992dcc4db1f6669ac7e5cb954e4ac22304bab39c7a51895438aa9dc7f.jpg) + +![](images/d82b6b6975c215512190b9d92ae427c734b8d3c9ed912b72c570b5bae24aeca4.jpg) + +![](images/c18c5c24f10a276f8296a0f1b17887907af686e42f42fd085b88cdc3309bfb5c.jpg) + +![](images/8585ef2c0aca39b8b7fe6c1023c27a652c2f7490deb1869eab5ad620cfa78f55.jpg) + +![](images/9ec136e95b8e800681c19d79d57119eb9b9a420306d708697c64f670b6677337.jpg) + +![](images/dbdb53674d704d69ccaef774c9a326d3794acb5939f1cd698045d19cd7bf1232.jpg) + +![](images/b4fdbb2b8d78230aebadbc8cabd542668c9abbcb5f444593a2526052f6b4166d.jpg) + +# 5.2. Results + +We start with a sanity check on a clean image. Our method correctly estimates zero backscatter, and does not force itself to estimate a medium (Fig. 4 Top). On our simulated fog and underwater scenes (Fig. 4 middle and bottom), our method separates the scenes' components very well, with only slight reduction in PSNR in the underwater scene. + +Image rendering and novel-view synthesis (in medium). Qualitative results are summarized in Figs. 1, 5. Table 1 summarizes the average PSNR on the validation set of the Red Sea scene, in which our method achieves the highest PSNR. Note that both NeRF-W [21] and NeRFReN [14] are based on the NeRF [25] model while our code is based on Mip-NeRF-360 [5] that in general improves reconstruction details in further areas. So our real comparison is with [5], which we improve by $\sim 0.8dB$ on average over the validation set. Table 2 compares PSNR, SSIM and LPIPS with those of [5] on validation sets of all real-world and simulation scenes. Our method is better in the majority of cases, and is especially good on the further areas (red squares). + +On the train set [5] achieves a reasonable rendering of the scene in terms of PSNR by wrongly modeling the water as a nearby blue object, as can be seen in the depth map, indicating a close object in the top area. Even then, in our results further objects are reconstructed with more detail. The NeRFReN [14] depth map flattens at the mid-range, while ours is more informative further on. SFM does not estimate depth at these areas because of lack of features. Scene restoration (Fig. 6). In comparison with NeRF + +
OursIIIIII[5][21][14]
21.8321.7621.4321.7221.0516.5221.05
+ +Table 1. Average PSNRs of in-medium rendering on Red Sea set: ours, 3 ablation variations (description in the text: I-1 parameter, II-3 parameters, III-Eqs. 13, 14) and other methods. + +
SceneMIP360 [5]Ours
Red Sea21.05 / 0.75 / 0.2921.83 / 0.77 / 0.25
Red Sea red square29.66 / 0.84 / 0.4333.80 / 0.90 / 0.23
Curaçao26.54 / 0.81 / 0.3330.48 / 0.87 / 0.20
Curaçao red square27.04 / 0.84 / 0.4533.20 / 0.88 / 0.08
Panama27.43 / 0.82 / 0.2327.89 / 0.83 / 0.22
Fern fog30.23 / 0.88 / 0.1530.75 / 0.87 / 0.16
Fern underwater29.62 / 0.87 / 0.2629.76 / 0.86 / 0.15
+ +Table 2. Comparison to baseline: PSNR↑/SSIM↑/LPIPS↓. + +methods for scene separation it is clear that our separation handles the medium the best. In the result of NeRF-W [21] the scene is somewhat separated but blurry, while in that of NeRFReN [14] the closer part of the scene is relatively well reconstructed but the further areas are missing. In both, the scene's objects are visible in the backscatter image, which is clearly wrong and reduces relevant signal from the object image. In our results, due to the adequate modeling, the backscatter is not polluted with objects. Compared to scene restoration methods, SeaThru [2] is the best performing one but is limited to areas where the depth map is available from SFM. The single image methods are not on par, especially from the mid-ranges and on. In novel-view synthesis of clean scenes we are able to predict further the entire scene. + +![](images/2c3b46f723a5f9033478ec3463a678d04e33c7feb2a85b1fda570caab625f7c4.jpg) +train image - clean + +![](images/03d82d66e254de1de523220c15ef7b51194a3190cb44156f5416e1f16213e8aa.jpg) +train image - backscatter + +![](images/be7ca70994521eb092b15f5e224206cb1fa86ce462782b29d71578408efe037a.jpg) +novel image - clean + +![](images/90176d51e1fbc1e33410d447063cd6ad24b60cf6dcc81ea53ae2f936a8986f43.jpg) +single-image restoration + +![](images/3d2f6479c1c3975766704f53a77bae6618dabbb158df367fe6593f188d989a14.jpg) + +![](images/1e7c14618e4209c77b03fcb119dff38d2c48d5bbde34eba4e0a05a912d197743.jpg) + +![](images/0b905053d57fe29137f947115058a244d2f103a59969a117fca422f01970cdf9.jpg) + +![](images/9e1463a5256e60de9470fe061d3161f94cf10f939cea5ada6b7af02eabaf05df.jpg) + +![](images/9a257595ac49c5c39562b7933b7ce19f4d3780550b693a77e5286d53b3a52f03.jpg) +Figure 6. Scene reconstruction on 'Red Sea'. Columns 1-3: Comparing our method (top row) and 2 other NeRFs - Nerf-W [21] (middle row) and NeRFReN [14] (bottom row). Even though not developed for scattering media, they manage to separate a training image into two components (columns 1, 2), resembling the clean scene and the backscatter. However, their backscatter components contains details of the objects, while ours correctly displays only the signal stemming from the medium. Similarly (column 3), their 'clean' rendering of a novel view is inferior to ours, especially in the far distances. Column 4: Among the single-image methods, SeaThru [2] is the best performing (but requires the depth map as input). Nevertheless, color artifacts are visible in the far parts due to inaccurate depth information. + +![](images/62b2bcd0f265ad84960fa12b8e6eec1e57a1d8de046ab1c31a9d5938365ff71f.jpg) + +![](images/f662b29bfb39b921ed244e0d5073cf6932f59b9917a6e1e7a53ac42f46d4d4fe.jpg) + +![](images/e9c6bdf834890e40532a129e64058775fa9cc8c3db905370368de5d44f056909.jpg) + +Ablation Study. (i) Number of medium parameters: following the discussion in Sec. 3.2, the elaborate version of Eq. (7) uses 6 parameters for the medium coefficients, while simplified versions use 1 (marked I in Table 1) or 3 (marked II). This is ablated in Table 1, in terms of PSNR, where the elaborate model with 6 parameters achieves a higher score. (ii) Rendering equations. We compare our basic rendering model (Eqs. 13, 14), marked III in Table 1 to the final one marked 'ours' (Eq. 22). This option achieves lower PSNR. + +# 6. Discussion + +We provide an important extension of NeRFs that enables rendering scenes acquired in scattering media such as haze, fog and underwater. So far, NeRF provided a framework for volumetric rendering, but without considering the nature of the medium, resulting in a binary 'occupancy' volume. Our formulation enables opaque objects to exist in a semi-transparent medium that is both scattering and absorbing in a wavelength-dependent manner. We demonstrate it on challenging real-world scenes with a complex 3D structure. Our scenes are forward-facing and contain areas with no objects at all, which our method is able to explain. + +Water effects in further regions are very strong, hampering single image methods and feature matching in multiview methods. Our method incorporates information from + +all images at once, learning the scene in a holistic way. This enables better scene reconstruction (in medium and clean), and estimating the depth and the medium's parameters. + +Our method has several limitations. While it is based on the current state-of-the-art image formation model, that model does not account for multiple scattering or for artificial illumination. As common in NeRFs, it requires camera poses that are extracted beforehand, which can be challenging in bad visibility. Lastly, the medium's parameters are better learned in sets where there is enough variation in the scene range between the viewpoints. The formulation takes its strength from the modeling of the medium. Thus it struggles in scenes that do not adhere to the model's assumptions, e.g., underwater scenes with significant flickering. In the future we plan to add components that will explain transient effects such as flickering, and continue to explore estimation of more diverse scenes and medium parameters. + +Acknowledgements. The research was funded by Israel Science Foundation grant #680/18, Israeli Ministry of Science and Technology, European Union's Horizon 2020 research and innovation programme GA 101094924 (ANERIS), the Leona M. and Harry B. Helmsley Charitable Trust, the Maurice Hatter Foundation, and Schmidt Marine Technology Partners. We thank Matan Yuval for substantial data contribution, Opher Bar-Nathan and Yuval Goldfracht for help with experiments. + +# References + +[1] Derya Akkaynak and Tali Treibitz. A revised underwater image formation model. In CVPR, pages 6723-6732, 2018. 1, 2, 3, 4, 5 +[2] Derya Akkaynak and Tali Treibitz. Sea-thru: A method for removing water from underwater images. In CVPR, pages 1682-1691, 2019. 2, 3, 4, 6, 7, 8 +[3] Derya Akkaynak, Tali Treibitz, Tom Shlesinger, Raz Tamir, Yossi Loya, and David Iluz. What is the space of attenuation coefficients in underwater computer vision? In CVPR, 2017. 1, 2 +[4] Saeed Anwar and Chongyi Li. 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IEEE TIP, 31:3997-4010, 2022. 6 \ No newline at end of file diff --git a/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/images.zip b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ef8d2647f7e00d04198dc7bf38d0a1990669d170 --- /dev/null +++ b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8f2ee17fa64b449e2522c91bdde7b552ccb5cef9e7b4e18e2b45618c32f30bba +size 766065 diff --git a/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/layout.json b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fa52d01f9668880f2f7a4c52bc3c805cc5a3b3a7 --- /dev/null +++ b/2023/SeaThru-NeRF_ Neural Radiance Fields in Scattering Media/layout.json @@ -0,0 +1,12194 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 110, + 103, + 483, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 103, + 483, + 121 + ], + "spans": [ + { + "bbox": [ + 110, + 103, + 483, + 121 + ], + "type": "text", + "content": "SeaThru-NeRF: Neural Radiance Fields in Scattering Media" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 133, + 499, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 133, + 499, + 162 + ], + "spans": [ + { + "bbox": [ + 94, + 133, + 499, + 162 + ], + "type": "text", + "content": "Deborah Levy1, Amit Peleg1, Naama Pearl1, Dan Rosenbaum1, Derya Akkaynak1,2, Simon Korman1, Tali Treibitz1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 100, + 163, + 492, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 163, + 492, + 190 + ], + "spans": [ + { + "bbox": [ + 100, + 163, + 492, + 190 + ], + "type": "text", + "content": "1University of Haifa, 2The Inter-University Institute for Marine Sciences in Eilat sea-thru-nerf.github.io" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 48, + 208, + 147, + 274 + ], + "blocks": [ + { + "bbox": [ + 66, + 198, + 130, + 206 + ], + "lines": [ + { + "bbox": [ + 66, + 198, + 130, + 206 + ], + "spans": [ + { + "bbox": [ + 66, + 198, + 130, + 206 + ], + "type": "text", + "content": "Ground Truth RAW" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 208, + 147, + 274 + ], + "lines": [ + { + "bbox": [ + 48, + 208, + 147, + 274 + ], + "spans": [ + { + "bbox": [ + 48, + 208, + 147, + 274 + ], + "type": "image", + "image_path": "a9e0e0ab516d24b81c91f97704f375dc301099a8047e83727723900097bea82c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 148, + 208, + 246, + 274 + ], + "blocks": [ + { + "bbox": [ + 168, + 198, + 227, + 206 + ], + "lines": [ + { + "bbox": [ + 168, + 198, + 227, + 206 + ], + "spans": [ + { + "bbox": [ + 168, + 198, + 227, + 206 + ], + "type": "text", + "content": "Ground Truth WB" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 148, + 208, + 246, + 274 + ], + "lines": [ + { + "bbox": [ + 148, + 208, + 246, + 274 + ], + "spans": [ + { + "bbox": [ + 148, + 208, + 246, + 274 + ], + "type": "image", + "image_path": "fff65e3ff3500a13e149b133373ac1680e5ae6e09ad24866e27cc5bd23fc17bc.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 547, + 345 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 345 + ], + "type": "text", + "content": "Figure 1. NeRFs have not yet tackled scenes in which the medium strongly influences the appearances of objects, as in the case of underwater imagery. By incorporating a scattering image formation model into the NeRF rendering equations, we are able to separate the scene into 'clean' and backscatter components. Consequently, we can render photorealistic novel-views with or without the participating medium, in the latter case recovering colors as if the image was taken in clear air. Results on the Curaçao scene: A RAW image (left) is brightened and white balanced (WB) for visualization, showing more detail, while areas further from the camera (top-right corner) are occluded and attenuated by severe backscatter - which is effectively removed in our restored image. 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However, a question that remains unanswered is what happens in underwater or foggy scenes where the medium strongly influences the appearance of objects. Thus far, NeRF and its variants have ignored these cases. However, since the NeRF framework is based on volumetric rendering, it has inherent capability to account for the medium's effects, once modeled appropriately. We develop a new rendering model for NeRFs in scattering media, which is based on the SeaThru image formation model, and suggest a suitable architecture for learning both scene information and medium parameters. We demonstrate the strength of our method using simulated and real-world scenes, correctly rendering novel photorealistic views underwater. Even more excitingly, we can render clear views of these scenes, removing the medium between the camera and the scene and reconstructing the appearance and depth of far objects, which are severely occluded by the medium. Our code and unique datasets are available on the project's website." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 632, + 128, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 128, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 128, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "The pioneering work of Mildenhall et al. [25] on Neural Radiance Fields (NeRFs) has tremendously advanced the field of Neural Rendering, due to its flexibility and unprecedented quality of synthesized images. Yet, the formulations of the original NeRF [25] and its followup variants assume" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 357, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 478 + ], + "type": "text", + "content": "that images were acquired in clear air, i.e., in a medium that does not scatter or absorb light in a significant manner and that the acquired image is composed solely of the object radiance. The NeRF formulation is based on volumetric rendering equations that take into account sampled points along 3D rays. Assuming a clear air environment, an implicit assumption, which is often enforced explicitly with dedicated loss components [5], is that a single opaque (high density) object is encountered per ray, with zero density between the camera and the object." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 482, + 546, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 546, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 546, + 601 + ], + "type": "text", + "content": "In stark contrast to clear air case, when the medium is absorbing and / or scattering (e.g., haze, fog, smog, and all aquatic habitats), the volume rendering equation has a true volumetric meaning, as the entire volume, and not only the object, contributes to image intensity. As the NeRF model estimates color and density at every point of a scene, it lends itself perfectly to general volumetric rendering, given that the appropriate rendering model is used. Here, we bridge this gap with SeaThru-NeRF, a framework that incorporates a rendering model that takes into account scattering media." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "This is achieved by assigning separate color and density parameters to the object (scene) and the medium, within the NeRF framework. Our approach adopts the SeaThru underwater image formation model [1, 3] to account for scattering media. SeaThru is a generalization of the standard wavelength-independent attenuation (e.g., fog) image formation model, where two different wideband coefficients are used to represent the medium, which is more accurate when attenuation is wavelength-dependent (as in all wa" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 299, + 749, + 311, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 749, + 311, + 757 + ], + "spans": [ + { + "bbox": [ + 299, + 749, + 311, + 757 + ], + "type": "text", + "content": "56" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 120 + ], + "type": "text", + "content": "ter bodies and under some atmospheric conditions). In our model, the medium parameters are separate per color channel, and are learned functions of the viewing angles, enforcing them to be constant only along 3D rays in the scene." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 239 + ], + "type": "text", + "content": "Attempting to optimize existing NeRFs on scenes with scattering medium results in cloud-like objects floating in space, while our formulation enables the network to learn the correct representation of the entire 3D volume, that consists of both the scene and the medium. Our experiments demonstrate that SeaThru-NeRF produces state-of-the-art photorealistic novel view synthesis on simulated and challenging real-world scenes (see Fig. 1) with scattering media, that include complex geometries and appearances. In addition, it enables:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 286, + 358 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 239, + 286, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 286, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 286, + 275 + ], + "type": "text", + "content": "1. Color restoration of the scenes as if they were not imaged through a medium, as our modeling allows full separation of object appearance from the medium effects." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 275, + 286, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 286, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 286, + 323 + ], + "type": "text", + "content": "2. Estimation of 3D scene structure which surpasses that of structure-from-motion (SFM) or current NeRFs, especially in far areas of bad visibility, as we jointly reconstruct and reason for the geometry and medium." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 323, + 286, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 286, + 358 + ], + "type": "text", + "content": "3. Estimation of wideband medium parameters, which are informative properties of the captured environment, and potentially allowing simulation under different conditions." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 370, + 133, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 133, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 133, + 383 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 390, + 286, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 286, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 286, + 474 + ], + "type": "text", + "content": "Neural Radiance Fields (NeRFs): The original work on NeRFs [25] has paved the way to a large capacity of followup work, with rapid and significant progress in many related aspects. For brevity, we focus in the following only on works closely related to ours, and refer the reader to a comprehensive review of the field [43] prior to the introduction of NeRFs, and to [44] for the most recent." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 475, + 286, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 286, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 286, + 594 + ], + "type": "text", + "content": "NeRFs have been recently shown to be extremely powerful in multi-image settings that involve computational imaging tasks. These include HDR [50], de-blurring [20], superresolution [49], low-light enhancement [23] and denoising [32]. The need to recover the clean 'medium-free' version of images degraded by scattering and attenuation effects, likewise, can benefit from the neural rendering approach. SeaThru-NeRF is designed to model the degradation, with the ability to recover its parameters, and reconstruct the clean underlying scene and novel-view images." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Our work is related to recent efforts to improve the quality and robustness of NeRFs in challenging environments (e.g. [14, 21, 29]). Nerf-W [21] learns a per-image latent embedding that can capture appearance variations in complex scenes. It decomposes the scene into image-dependent and shared components to disentangle transient elements from the static scene. NeRFRen [14] is designed for scenes with reflections. It separates the scene as a sum of transmitted and reflected components, which are modeled as separate NeRFs. Ref-NeRF [47] introduces a new parameteriza" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "tion and structuring of view-dependent appearance, which can represent scenes with specularities and reflections." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 204 + ], + "type": "text", + "content": "Our approach has much in common with some of these methods, most notably the way of reconstructing the target image as a composition of components: 'direct' and 'backscatter' in our case, 'transient' and 'static' in [21], or 'transmitted' and 'reflected' in [14]. However, as we demonstrate, these methods are limited on scenes in scattering media as they do not explicitly model the effects of the medium. Our method is different in that it can model a continuous medium component that is not an object." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 210, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 210, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 210, + 545, + 354 + ], + "type": "text", + "content": "Graphics and Vision in Scattering Media: Propagation of light in a medium is governed by the radiative transfer equation [10]. This equation describes light interaction per particle in the medium and requires extensive Monte Carlo simulations for complete solutions [12, 16, 30, 31], see [30] for an excellent review. In many cases simplifying assumptions can be made about the medium that ease rendering [22], where the major one is single-scattering [33, 42, 48]. Realistic rendering requires having the scattering properties of the medium, which can be estimated in the lab [13, 26], or from in situ images [6]. An MLP for rendering synthetic atmospheric clouds was suggested in [17]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 354, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 545, + 461 + ], + "type": "text", + "content": "In computer vision, image formation models under ambient illumination for bad weather [28] and underwater [37] share the same general structure for the case of horizontal viewing. Artificial illumination used underwater [46] and in fog has additional terms that account for the nonuniformity of the source. Underwater, the medium parameters exhibit strong wavelength dependency that was shown to affect model accuracy in wideband camera channels. The SeaThru model [1-3] was suggested to overcome this issue." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 594 + ], + "type": "text", + "content": "Scene reconstruction in scattering media is an ill-posed problem which was initially solved with multiple frames [27,37,38,46]. Later on, single-image methods have proposed a multitude of image priors to overcome the ill-posed nature of the problem, see [19,51] for comprehensive reviews on single-image dehazing and underwater reconstruction, respectively. The introduction of deep-learning has led to an explosion of single-image dehazing and underwater reconstruction networks. See [41] and [4] for recent reviews of deep-learning dehazing and underwater reconstruction works, respectively." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Underwater, it was suggested to solve for the 3D structure of the scene, prior to image restoration [9, 35] using the haze model and [2] using the revised one. In SeaThruNeRF, we simultaneously reconstruct the scene and its 3D structure, yielding multiple advantages that we demonstrate empirically. WaterNeRF [40] suggests an underwater neural renderer that estimates the medium parameters only with respect to histogram-qualified images, separately from the rendering. Here, we show the huge benefit of modeling the scattering medium within the rendering equations, over a" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "spans": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "type": "text", + "content": "57" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "variety of different scenes. Concurrently and independently to our work, [11] presented a NeRF for haze." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 106, + 175, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 106, + 175, + 121 + ], + "spans": [ + { + "bbox": [ + 47, + 106, + 175, + 121 + ], + "type": "text", + "content": "3. Scientific Background" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 126, + 221, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 126, + 221, + 139 + ], + "spans": [ + { + "bbox": [ + 47, + 126, + 221, + 139 + ], + "type": "text", + "content": "3.1. Neural Radiance Fields (NeRFs)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "content": "The original NeRF formulation [25] implicitly represents a 3D scene by a trainable continuous function. It is typically parameterized by an MLP " + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "inline_equation", + "content": "f_{\\Theta}:(\\mathbf{x},\\mathbf{d})\\to (\\mathbf{c},\\sigma)" + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "content": " which encodes the density " + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "content": " at the 3D point " + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = (x,y,z)" + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "content": " and the color " + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = (r,g,b)" + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "content": " emitted from this point in the viewing direction " + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\mathbf{d} = (\\theta ,\\phi)" + }, + { + "bbox": [ + 47, + 144, + 287, + 228 + ], + "type": "text", + "content": " (which is typically represented as a 2-element unit normalized 3D vector)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "content": "This simple representation is used to simulate classical image-based rendering, by color accumulation along rays that are back-projected from a posed camera. If we parameterize points along a camera ray " + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + \\mathbf{d}(t)" + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "content": " is the camera center and " + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "inline_equation", + "content": "t\\in \\mathbb{R}_+" + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "content": ", the expected (image) color " + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "inline_equation", + "content": "C(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 228, + 287, + 300 + ], + "type": "text", + "content": " along the ray can be written as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 309, + 287, + 337 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 309, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 107, + 309, + 287, + 337 + ], + "type": "interline_equation", + "content": "C (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\sigma (t) \\mathbf {c} (t) d t \\tag {1}", + "image_path": "9be80e679ac6c1c60720cf526fb108e275498b8744667d521760cd2db7532887.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": "where: integration along the ray is limited to the range " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "t \\in [t_n, t_f]" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " (near and far bounds on the scene contents); " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\sigma(t)" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{c}(t)" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " are shorthands for the density at the point " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t)" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " and its emitted color towards the camera center; " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "T(t)" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " denotes the accumulated transmittance along the ray from " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " (the probability that the ray travels from " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 345, + 287, + 429 + ], + "type": "text", + "content": " without hitting other particles along the way), and is given by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 437, + 287, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 437, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 104, + 437, + 287, + 464 + ], + "type": "interline_equation", + "content": "T (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\sigma (s) d s\\right) \\tag {2}", + "image_path": "53640502f1c1085571828fb1f7e1621d9b1ae9517842c4aa00c485790e3e670e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": "In practice, the rendered color " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "C(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": " in Eq. (1) is approximated with the quadrature rule, by discretizing the range " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "[t_n, t_f]" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": " into a set of " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": " intervals " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "I_i = [s_i, s_{i+1}]" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": " (where " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "t_n = s_0 < \\dots < s_N = t_f" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": "), assuming that the density " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": " and color " + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 47, + 472, + 287, + 544 + ], + "type": "text", + "content": " are constant along each interval (e.g. by querying the model once per interval at its center-point)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 544, + 206, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 544, + 206, + 557 + ], + "spans": [ + { + "bbox": [ + 59, + 544, + 206, + 557 + ], + "type": "text", + "content": "In the discretized version of Eq. (1):" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 129, + 565, + 287, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 565, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 129, + 565, + 287, + 597 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} C _ {i} (\\mathbf {r}) \\tag {3}", + "image_path": "2777f97b2459f13bb530da3f8e05aea5705000845b5113f4fe49499dbd093c80.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "type": "text", + "content": "the contribution " + }, + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "type": "inline_equation", + "content": "C_i(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "type": "text", + "content": " of the interval " + }, + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "type": "inline_equation", + "content": "I_{i}" + }, + { + "bbox": [ + 47, + 606, + 256, + 619 + ], + "type": "text", + "content": " is given by:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 55, + 627, + 287, + 654 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 627, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 55, + 627, + 287, + 654 + ], + "type": "interline_equation", + "content": "C _ {i} (\\mathbf {r}) = \\int_ {s _ {i}} ^ {s _ {i + 1}} T (t) \\sigma_ {i} \\mathbf {c} _ {i} d t = T \\left(s _ {i}\\right) \\left(1 - e ^ {- \\sigma_ {i} \\delta_ {i}}\\right) \\mathbf {c} _ {i} \\tag {4}", + "image_path": "58cc98f779ab45e6fefc5908153b0f152d8fc3bce5c256c5f96d38c96d83a20c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\mathbf{c_i}" + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": " are the (constant) density and color along the " + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": "th interval, whose length is " + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "inline_equation", + "content": "\\delta_{i} = s_{i + 1} - s_{i}" + }, + { + "bbox": [ + 47, + 662, + 287, + 686 + ], + "type": "text", + "content": ", and the" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 72, + 524, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 524, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 524, + 84 + ], + "type": "text", + "content": "transmittance " + }, + { + "bbox": [ + 306, + 72, + 524, + 84 + ], + "type": "inline_equation", + "content": "T(s_{i})" + }, + { + "bbox": [ + 306, + 72, + 524, + 84 + ], + "type": "text", + "content": " at the beginning of the interval is:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 365, + 94, + 545, + 127 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 94, + 545, + 127 + ], + "spans": [ + { + "bbox": [ + 365, + 94, + 545, + 127 + ], + "type": "interline_equation", + "content": "T \\left(s _ {i}\\right) = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} \\delta_ {j}\\right) \\tag {5}", + "image_path": "1f7af97e9aa98b78432e7b7f08c521a4a583dc11f098efada9e1db9f4c22349e.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 135, + 545, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 135, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 305, + 135, + 545, + 170 + ], + "type": "text", + "content": "This fully differentiable NeRF model (with the discretized rendering scheme) is trained with a simple reconstruction loss" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 371, + 178, + 545, + 204 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 178, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 371, + 178, + 545, + 204 + ], + "type": "interline_equation", + "content": "L = \\sum_ {\\mathbf {r} \\in R} \\| \\hat {C} (\\mathbf {r}) - C (\\mathbf {r}) \\| ^ {2} \\tag {6}", + "image_path": "b9b0422e05bd28a831c602afe2e33e778e60df0b4ed77c0ad5e9a5e836b1c89f.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": "comparing each rendered training image pixel " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "\\hat{C}(\\mathbf{r})" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": " to its ground truth color " + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "inline_equation", + "content": "C(\\mathbf{r})" + }, + { + "bbox": [ + 305, + 213, + 545, + 249 + ], + "type": "text", + "content": ". The model can then be used to synthesize photorealistic novel view images." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 256, + 505, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 256, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 306, + 256, + 505, + 269 + ], + "type": "text", + "content": "3.2. Image Formation in Scattering Media" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 275, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 275, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 305, + 275, + 545, + 417 + ], + "type": "text", + "content": "Image formation in fog, haze, or underwater differs from image formation in clear air in two major aspects. First, the direct signal emanating from the object is attenuated as a function of distance and wavelength. Second, this signal is occluded by backscatter (termed also path-radiance or veiling-light) - radiance that is added due to the in-scattering from the particles along the line-of-sight (LOS), illustrated in Fig. 2. The intensity and color of the occluding backscatter layer are independent of the scene contents, and its intensity accumulates along the LOS, increasing with distance. As a result, the visibility and contrast of further objects is significantly reduced and their colors are distorted." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 418, + 545, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 465 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 465 + ], + "type": "text", + "content": "We adopt the revised model [1] as the general model for image formation in scattering media under ambient illumination. Image intensity (per pixel, per color channel) is given as:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 315, + 470, + 545, + 514 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 470, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 315, + 470, + 545, + 514 + ], + "type": "interline_equation", + "content": "I = \\underbrace {\\underbrace {J} _ {\\text {c o l o r}} \\cdot \\underbrace {(e ^ {- \\beta^ {D} (\\mathbf {v} _ {D}) \\cdot z})} _ {\\text {a t t e n u a t i o n}}} _ {B ^ {\\infty}} + \\underbrace {(1 - e ^ {- \\beta^ {B} (\\mathbf {v} _ {B}) \\cdot z})} _ {\\text {a t t e n u a t i o n}} \\tag {7}", + "image_path": "88e10fdd923cd384732b9d8683c07ec7883a7aebb8dedf82f0720d1b348533c3.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " is the linear image captured by the camera of a scene with range " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " is the clear scene that would have been captured had there been no medium along " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "B^{\\infty}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " is the backscatter water color at infinity, i.e., the backscatter at areas that contain no objects. Lastly, " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta^{D}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta^{B}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " are the attenuation and backscatter coefficients, respectively, the two parameters that describe the medium effects. The vectors " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_D" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_B" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " represent the dependencies of " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta^{D}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta^{B}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " on range, object reflectance, spectrum of ambient light, spectral response of the camera, and the physical scattering and beam attenuation coefficients of the water body, all of which are functions of wavelength. It was shown in [2] that " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta^{B}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " can be assumed constant in an image, while " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\beta^{D}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " mainly depends on the object distance and weakly on object reflectance, thus solving for the full model requires at least 6 unknowns. The value of " + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "inline_equation", + "content": "B^{\\infty}" + }, + { + "bbox": [ + 305, + 522, + 545, + 713 + ], + "type": "text", + "content": " is usually assumed to be uniform in the scene" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "type": "text", + "content": "Vectors (3D coordinates or color components) are denoted in **bold**." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 59, + 703, + 203, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 203, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 203, + 712 + ], + "type": "text", + "content": "2Each color channel is integrated separately." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 300, + 749, + 310, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 749, + 310, + 757 + ], + "spans": [ + { + "bbox": [ + 300, + 749, + 310, + 757 + ], + "type": "text", + "content": "58" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 261, + 188 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 261, + 188 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 261, + 188 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 261, + 188 + ], + "type": "image", + "image_path": "45b49dc455da358dbb8d9ac6aafbdd045287c23d9955eab3cd5487e1097e5da4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 193, + 287, + 238 + ], + "lines": [ + { + "bbox": [ + 46, + 193, + 287, + 238 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 287, + 238 + ], + "type": "text", + "content": "Figure 2. An illustration of our ray model. We assume a scene with at most a single opaque object at every ray. The medium is semitransparent with constant density per-ray. The densities governing the backscatter and the object in water are not the same [1]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 275 + ], + "type": "text", + "content": "but as discussed in [6] it is almost never really uniform, because of the directionality of the sun, among other factors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "text", + "content": "This model is also applicable to haze and fog, where attenuation has very little dependence on wavelength. Then, image formation is greatly simplified because it can be assumed that there is only one medium parameter that is uniform across the color channels, represented by a scalar " + }, + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "inline_equation", + "content": "(\\beta^{D} = \\beta^{B} = \\beta)" + }, + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "text", + "content": " [38]. Underwater, often the simplifying (less accurate) assumption that " + }, + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "inline_equation", + "content": "\\beta^{D} = \\beta^{B}" + }, + { + "bbox": [ + 46, + 275, + 287, + 370 + ], + "type": "text", + "content": " is made, reducing to 3 unknowns [6,7,37]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 381, + 140, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 140, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 140, + 393 + ], + "type": "text", + "content": "4. SeaThru-NeRF" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 401, + 180, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 180, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 180, + 414 + ], + "type": "text", + "content": "4.1. Basic Model Derivation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 419, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 479 + ], + "type": "text", + "content": "Here we consider a more general setting than the original NeRF [25], in which light travels through a scattering medium rather than free-space, resulting in a significant impact on the captured color. Following [22] we suggest adding the medium to Eqs. (1) and (2):" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 488, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 488, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 52, + 488, + 287, + 525 + ], + "type": "interline_equation", + "content": "C (\\mathbf {r}) = \\int_ {t _ {n}} ^ {t _ {f}} T (t) \\left(\\sigma^ {\\mathrm {o b j}} (t) \\mathbf {c} ^ {\\mathrm {o b j}} (t) + \\sigma^ {\\mathrm {m e d}} (t) \\mathbf {c} ^ {\\mathrm {m e d}} (t)\\right) d t \\tag {8}", + "image_path": "c213ef4ac8d0712c1294f1962a6a49843e85d8e783ae2b22e2293f84f17af2c9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 526, + 77, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 77, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 77, + 536 + ], + "type": "text", + "content": "where:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 61, + 544, + 287, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 544, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 61, + 544, + 287, + 572 + ], + "type": "interline_equation", + "content": "T (t) = \\exp \\left(- \\int_ {t _ {n}} ^ {t} \\left(\\sigma^ {\\mathrm {o b j}} (s) + \\sigma^ {\\mathrm {m e d}} (s)\\right) d s\\right), \\tag {9}", + "image_path": "2e320b06dd4fd06c61e3529229067808bc7b8e759987056c5c80eeb2f850bff1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": "using separate color and density parameters for the object and medium. Notice that these equations reduce to Eqs. (1) and (2) by simply considering the case where the medium density " + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}}" + }, + { + "bbox": [ + 46, + 580, + 287, + 628 + ], + "type": "text", + "content": " is zero." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 628, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 652 + ], + "type": "text", + "content": "Moving to the discretized version, we similarly get3 the following generalizations of Eqs. (4) and (5):" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 51, + 659, + 287, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 659, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 51, + 659, + 287, + 696 + ], + "type": "interline_equation", + "content": "C _ {i} (\\mathbf {r}) = T \\left(s _ {i}\\right) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {o b j}} \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}} \\mathbf {c} _ {i} ^ {\\mathrm {m e d}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {10}", + "image_path": "92ff7994345b349c7244136c888669eb7a52fc6095140bea4f72f1b26fc47af5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 73, + 383, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 73, + 383, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 73, + 383, + 83 + ], + "type": "text", + "content": "with transmittance" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 330, + 91, + 545, + 125 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 91, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 330, + 91, + 545, + 125 + ], + "type": "interline_equation", + "content": "T \\left(s _ {i}\\right) = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\left(\\sigma_ {j} ^ {\\mathrm {o b j}} + \\sigma_ {j} ^ {\\mathrm {m e d}}\\right) \\delta_ {j}\\right). \\tag {11}", + "image_path": "f840e9a03a2ddd34a0bd7a1226017a6b19c9a6de2499d9c5b263b7f6f2f7b00c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 133, + 545, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 545, + 157 + ], + "type": "text", + "content": "Splitting the discretized color rendering equations (3,10 and 11) into the 'object' and 'medium' components, we get:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 329, + 165, + 545, + 198 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 165, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 329, + 165, + 545, + 198 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} \\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) + \\sum_ {i = 1} ^ {N} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) \\tag {12}", + "image_path": "066b84d3745b075c1e4b1983c69535001eb8ed591cf4905a52af99d9af66e7d2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 212, + 545, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 212, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 315, + 212, + 545, + 240 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T (s _ {i}) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {o b j}} \\mathbf {c} _ {i} ^ {\\mathrm {o b j}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {13}", + "image_path": "c28f8cb302243c66a9dc62886d436536d8fa076c77caeb858db838a9b1e5963b.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 256, + 545, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 256, + 545, + 283 + ], + "spans": [ + { + "bbox": [ + 313, + 256, + 545, + 283 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T (s _ {i}) \\left(1 - e ^ {- \\left(\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}\\right) \\delta_ {i}}\\right) \\frac {\\sigma_ {i} ^ {\\mathrm {m e d}} \\mathbf {c} _ {i} ^ {\\mathrm {m e d}}}{\\sigma_ {i} ^ {\\mathrm {o b j}} + \\sigma_ {i} ^ {\\mathrm {m e d}}} \\tag {14}", + "image_path": "d42b74419e9475f0fd24a36d004e2a2bf8940c92626ea1b50e8acd8b04db0792.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "content": "As a first step towards constraining and simplifying our model, we constrain the medium parameters to be constant along 3D viewing rays. We drop the respective interval indices and remain with " + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "content": " that depend only on the ray " + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "content": " uniformity stems from the common assumption of a uniform phase function (the dependence of scattered radiance on scattering angle) along the LOS [22, 30]. Regarding the density " + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 289, + 545, + 432 + ], + "type": "text", + "content": ", we take it to be separate per color channel, but constant per ray. This is far less restrictive compared to models that assume constancy per image or even per scene [2]. These constraints will be enforced by respective structural choices in the network." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "type": "text", + "content": "Furthermore, we assume that objects in the scene are opaque, hence the object density along the ray is close to zero except for a high peak in the object location. On the other hand, the medium is semi-transparent, characterized by a low non-zero density. This implies that " + }, + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}} \\gg \\sigma^{\\mathrm{obj}}" + }, + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "type": "text", + "content": " before the object and " + }, + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}} \\ll \\sigma^{\\mathrm{obj}}" + }, + { + "bbox": [ + 304, + 434, + 545, + 517 + ], + "type": "text", + "content": " at the object, as illustrated in Fig. 2. Therefore, Eqs. (13-14) reduce to" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 315, + 525, + 545, + 545 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 525, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 315, + 525, + 545, + 545 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i}}\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} \\tag {15}", + "image_path": "edbf9565a68c76aec915d9821834e25d0805107ffaef6c44e390fff4aeee7c82.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 312, + 547, + 545, + 567 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 547, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 312, + 547, + 545, + 567 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} \\delta_ {i}}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\tag {16}", + "image_path": "337d95ee43611d75bc6da25a4acd4ba14ccbc1306eac6b005ac0054e0209b341.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 337, + 570, + 545, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 570, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 337, + 570, + 545, + 602 + ], + "type": "interline_equation", + "content": "T _ {i} = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} ^ {\\mathrm {o b j}} \\delta_ {j}\\right) \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {m e d}} s _ {i}\\right) \\tag {17}", + "image_path": "0d2bbba1aef42d7eea0b58a335061151497b9645a4187dcbc913528770fad55d.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 611, + 523, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 523, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 523, + 624 + ], + "type": "text", + "content": "4.2. Relation to Underwater Image Formation" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In this section we show that our model can be reduced to the image formation model described in Sec. 3.2, which is not based on volumetric rendering. To this end we consider sampling the ray along intervals with constant size " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ", and the appearance of the opaque object at a depth " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ", at the beginning of interval " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{k} = [s_{k}, s_{k + 1}]" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": ", for some integer " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " (that is: " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "s_{i} = i \\cdot \\delta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " for every " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "z = k \\cdot \\delta" + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": " in particular)." + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "inline_equation", + "content": "{}^{3}" + }, + { + "bbox": [ + 58, + 702, + 257, + 713 + ], + "type": "text", + "content": " Full derivations of Eqs. (10,11) is provided in the appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "spans": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "type": "text", + "content": "59" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 279, + 203 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 279, + 203 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 279, + 203 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 279, + 203 + ], + "type": "image", + "image_path": "5b0dbdf12734c0f32948c38960f8022fc6cf93fb57398cdacf664511df0ab80b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 289, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 289, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 289, + 262 + ], + "type": "text", + "content": "Figure 3. SeaThru-NeRF architecture. The computation of the 'object' outputs (density and color, in green), follows the standard NeRF architecture, while the 'medium' components (in purple) are computed once per ray by a separate subnet (the 'medium MLP') that depends only on the viewing direction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "content": "In this case, " + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "inline_equation", + "content": "\\sigma_{i}^{\\mathrm{obj}}\\approx 0" + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "inline_equation", + "content": "i < k" + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "inline_equation", + "content": "\\sigma_k^{\\mathrm{obj}}\\gg \\sigma^{\\mathrm{med}}" + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "content": ". This implies that " + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "inline_equation", + "content": "C_k^{\\mathrm{med}}(\\mathbf{r})\\ll C_k^{\\mathrm{obj}}(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "inline_equation", + "content": "C_i^{\\mathrm{obj}}(\\mathbf{r})\\approx 0" + }, + { + "bbox": [ + 47, + 272, + 287, + 313 + ], + "type": "text", + "content": ", therefore we can write the rendering Eq. (12) as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 96, + 316, + 287, + 349 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 316, + 287, + 349 + ], + "spans": [ + { + "bbox": [ + 96, + 316, + 287, + 349 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\mathbf {r}) \\approx \\hat {C} _ {k} ^ {\\mathrm {o b j}} (\\mathbf {r}) + \\sum_ {i = 0} ^ {k - 1} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}). \\tag {18}", + "image_path": "58a75c34f69dad377794b014262d14b86a2c72e4d90eb93e2bfe856c53d68a16.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "text", + "content": "Furthermore, since the object is opaque, we can assume that the density " + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "inline_equation", + "content": "\\sigma_k^{\\mathrm{obj}}" + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "text", + "content": " is large enough such that the transmittance at the end of the " + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "text", + "content": "th interval " + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "inline_equation", + "content": "T(s_{k + 1})" + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "text", + "content": " drops practically to zero, that is: " + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "inline_equation", + "content": "e^{-\\sigma_k^{\\mathrm{obj}}\\delta}\\approx 0" + }, + { + "bbox": [ + 47, + 358, + 287, + 408 + ], + "type": "text", + "content": ". Therefore" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 51, + 417, + 287, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 417, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 51, + 417, + 287, + 453 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {C} _ {k} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} \\cdot \\left(1 - e ^ {- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta}\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}} \\tag {19} \\\\ \\approx e ^ {- k \\sigma^ {\\mathrm {m e d}} \\delta} \\left(1 - e ^ {- \\sigma_ {k} ^ {\\mathrm {o b j}} \\delta}\\right) \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} \\approx e ^ {- \\sigma^ {\\mathrm {m e d}} \\delta \\cdot k} \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} \\\\ \\end{array}", + "image_path": "640861848c1f5786e333ad4bb989f4da4cdddc5d0422909dc6479c523761fbf8.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 463, + 65, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 65, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 65, + 472 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 482, + 287, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 482, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 51, + 482, + 287, + 569 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\sum_ {i = 0} ^ {k - 1} \\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = \\sum_ {i = 0} ^ {k - 1} T _ {i} \\cdot \\left(1 - e ^ {- \\sigma^ {\\mathrm {m e d}} \\delta}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\tag {20} \\\\ \\approx \\sum_ {i = 0} ^ {k - 1} e ^ {- i \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta} \\cdot \\left(1 - e ^ {- \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\\\ = \\left(1 - e ^ {- \\mathbf {\\sigma} ^ {\\mathrm {m e d}} \\delta \\cdot k}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}} \\\\ \\end{array}", + "image_path": "4600d78ed29abe64bbd0fc027f324f6e9f4cc4be85f54479dea3ed7122c297ac.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "content": "Substituting Eqs. (19) and (20) into Eq. (18) (recalling that the depth " + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "inline_equation", + "content": "k \\cdot \\delta" + }, + { + "bbox": [ + 47, + 578, + 287, + 603 + ], + "type": "text", + "content": ") yields:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 55, + 613, + 287, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 613, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 55, + 613, + 287, + 633 + ], + "type": "interline_equation", + "content": "\\hat {C} (\\mathbf {r}) \\approx e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} z} \\cdot \\mathbf {c} _ {k} ^ {\\mathrm {o b j}} + \\left(1 - e ^ {- \\boldsymbol {\\sigma} ^ {\\mathrm {m e d}} z}\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}}, \\tag {21}", + "image_path": "9077a6f6a7ca3792bcb2964be474e0b1538e51a9ca84e3aa0c5df34bdf55d017.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": "resulting precisely in the commonly used scattering media image formation model [8, 37]. This can be seen by comparing to Eq. (7) where " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}} = \\beta^{D} = \\beta^{B}" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " plays the role of the attenuation coefficient (equal for direct and backscatter), " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{\\mathrm{med}}" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " is the veiling light " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "B^{\\infty}" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " (backscatter color at infinity) and " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_k^{\\mathrm{obj}}" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": " the clear image color " + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 47, + 642, + 288, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 386, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 386, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 386, + 83 + ], + "type": "text", + "content": "4.3. Final Model" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": "We make several refinements with respect to the basic model presented in Section 4.1. In Sec. 4.2, we showed that our rendering equations lead to an image formation model with identical attenuation coefficients for the direct and backscatter components. Following the discussion in Sec. 3.2, and as has been shown in [1], when using such equations with a camera with wideband color channels, the effective " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " that is experienced by the camera in " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "C_i^{\\mathrm{obj}}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " is different than the one experienced in " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "C_i^{\\mathrm{med}}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": ". Therefore, in our final model we use different parameters for " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " in each component and term them " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{attn}}" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{bs}}" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "C_i^{\\mathrm{obj}}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "inline_equation", + "content": "C_i^{\\mathrm{med}}(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 90, + 547, + 235 + ], + "type": "text", + "content": " respectively. Our final equations are:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 309, + 242, + 544, + 259 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 242, + 544, + 259 + ], + "spans": [ + { + "bbox": [ + 309, + 242, + 544, + 259 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {i} ^ {\\mathrm {o b j}} (\\mathbf {r}) = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {a t t n}} s _ {i}\\right) \\cdot \\left(1 - \\exp (- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i})\\right) \\cdot \\mathbf {c} _ {i} ^ {\\mathrm {o b j}}", + "image_path": "a455aa8e96afa946001064efdcd6d0b41376eb5f5f47b40fedad7ef0e6914fc2.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 309, + 266, + 541, + 283 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 266, + 541, + 283 + ], + "spans": [ + { + "bbox": [ + 309, + 266, + 541, + 283 + ], + "type": "interline_equation", + "content": "\\hat {C} _ {i} ^ {\\mathrm {m e d}} (\\mathbf {r}) = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\exp \\left(- \\mathbf {o} ^ {\\mathrm {b s}} s _ {i}\\right) \\cdot \\left(1 - \\exp (- \\mathbf {o} ^ {\\mathrm {b s}} \\delta_ {i})\\right) \\cdot \\mathbf {c} ^ {\\mathrm {m e d}}", + "image_path": "f679305b882f5ffdfeeb2397274ff873c560b6e8e8652247bc1ef7ee25c7f264.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 326, + 297, + 545, + 329 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 297, + 545, + 329 + ], + "spans": [ + { + "bbox": [ + 326, + 297, + 545, + 329 + ], + "type": "interline_equation", + "content": "T _ {i} ^ {\\mathrm {o b j}} = \\exp \\left(- \\sum_ {j = 0} ^ {i - 1} \\sigma_ {j} ^ {\\mathrm {o b j}} \\delta_ {j}\\right) \\tag {22}", + "image_path": "2eeee4dfae8b14a71446a47b200c021bd37a3527d97799446d77fe5075efe85d.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": "Based on our derivations we suggest the following architecture (Fig. 3). As in [25], the object properties are computed by a pair of MLPs, such that the density " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{obj}}" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": " is a function of the position " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": " only, while color " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{\\mathrm{obj}}" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": " is determined by the viewing direction " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "(\\theta ,\\phi)" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": " as well. The medium parameters " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{\\mathrm{med}}" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{bs}}" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{attn}}" + }, + { + "bbox": [ + 304, + 334, + 545, + 430 + ], + "type": "text", + "content": " are handled by a separate MLP with only the direction input, following our decision to constrain them to be constant per viewing direction." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 437, + 394, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 394, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 394, + 449 + ], + "type": "text", + "content": "4.4. Loss Function" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "text", + "content": "Let us denote the sequence of samples along a ray by " + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\mathbf{s} = \\{s_i\\}_{i=0}^N" + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "text", + "content": ", the object 'weight' at the " + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "text", + "content": "th segment " + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "inline_equation", + "content": "[s_i, s_{i+1}]" + }, + { + "bbox": [ + 305, + 456, + 545, + 492 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 349, + 500, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 500, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 349, + 500, + 545, + 517 + ], + "type": "interline_equation", + "content": "w _ {i} ^ {\\mathrm {o b j}} = T _ {i} ^ {\\mathrm {o b j}} \\cdot \\left(1 - \\exp \\left(- \\sigma_ {i} ^ {\\mathrm {o b j}} \\delta_ {i}\\right)\\right), \\tag {23}", + "image_path": "c18cd62df7e55845e1a4e84f6c751c72eb8d7e8c8e43557a6b3067174727a08b.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "type": "text", + "content": "the sequence of these weights by " + }, + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\mathbf{w} = \\{w_{i}^{\\mathrm{obj}}\\}_{i = 0}^{N - 1}" + }, + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "type": "text", + "content": " and the ground-truth (supervised) pixel color by " + }, + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "type": "inline_equation", + "content": "C^*" + }, + { + "bbox": [ + 304, + 525, + 545, + 551 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 317, + 551, + 474, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 551, + 474, + 563 + ], + "spans": [ + { + "bbox": [ + 317, + 551, + 474, + 563 + ], + "type": "text", + "content": "Our loss is the following combination:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 571, + 545, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 571, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 317, + 571, + 545, + 586 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {r e c o n}} \\left(\\hat {C}, C ^ {*}\\right) + \\mathcal {L} _ {\\text {p r o p}} (\\mathbf {s}, \\mathbf {w}) + \\lambda \\mathcal {L} _ {\\text {a c c}} (\\mathbf {w}), \\tag {24}", + "image_path": "a752bd53f9230b43d621ffc5f4b47d174cbd6f77b2ea5846b457645ee0eec417.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 594, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 631 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 545, + 631 + ], + "type": "inline_equation", + "content": "\\lambda = 0.0001" + }, + { + "bbox": [ + 304, + 594, + 545, + 631 + ], + "type": "text", + "content": " was chosen through cross-validation. Since we work on linear images, we adopt the reconstruction loss of RawNeRF [23]:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 357, + 638, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 638, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 357, + 638, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e c o n}} (\\hat {C}, C ^ {*}) = \\left(\\frac {\\hat {C} - C ^ {*}}{\\operatorname {s g} (\\hat {C}) + \\epsilon}\\right) ^ {2} \\tag {25}", + "image_path": "204f13259ff83210c5a5901283a662a0a0c1c9648edc0d3315ec13bbd6d2ddbd.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathrm{sg}(\\cdot)" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " stands for stop-gradient and " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon = 10^{-3}" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": ". The 'proposal' loss " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prop}}(\\mathbf{s},\\mathbf{w})" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " is an inherent part of Mip-NeRF-360 [5]. It penalizes for the discrepancy between the" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "spans": [ + { + "bbox": [ + 299, + 749, + 310, + 757 + ], + "type": "text", + "content": "60" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 95 + ], + "type": "text", + "content": "distributions of object weights at 'original' and 'proposed' samplings, where only the latter is used for rendering [5]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 168 + ], + "type": "text", + "content": "To enforce binary separation between points in space that contain objects and those that contain solely a medium - we add a prior on the transmittance " + }, + { + "bbox": [ + 46, + 96, + 286, + 168 + ], + "type": "inline_equation", + "content": "T_{i}^{\\mathrm{obj}}" + }, + { + "bbox": [ + 46, + 96, + 286, + 168 + ], + "type": "text", + "content": " of each point on the ray to be either 0 or 1, not allowing semi-transparent objects. This is modelled as a mixture of two Laplacian distributions with modes at 0 and 1 (following [34]):" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 172, + 286, + 189 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 172, + 286, + 189 + ], + "spans": [ + { + "bbox": [ + 115, + 172, + 286, + 189 + ], + "type": "interline_equation", + "content": "\\mathbf {P} (x) \\propto e ^ {- \\frac {| x |}{0 . 1}} + e ^ {- \\frac {| 1 - x |}{0 . 1}} \\tag {26}", + "image_path": "9d05c81825528e9d7ddfc73f7e77196c508767ea8c0c3cfabe862f2d6b9fd26d.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 194, + 209, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 194, + 209, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 209, + 205 + ], + "type": "text", + "content": "and use the negative log likelihood loss:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 108, + 209, + 286, + 224 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 209, + 286, + 224 + ], + "spans": [ + { + "bbox": [ + 108, + 209, + 286, + 224 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {a c c}} (\\mathbf {w}) = - \\log \\mathbb {P} \\left(T _ {i} ^ {\\mathrm {o b j}}\\right). \\tag {27}", + "image_path": "61f479de23f9d1e10122b0567ede4e7c7c849bd6e4d772fdd0f3adfd3c80fafa.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 229, + 230, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 229, + 230, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 229, + 230, + 243 + ], + "type": "text", + "content": "4.5. Implementation and Optimization" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "content": "Our implementation is based on the code released in Mip-NeRF-360 [5], choosing the best performing baseline on our scenes which was the forward-looking configuration with normalized device coordinates (NDC). For the mediumMLP, we use 6 linear layers with 256 features and a softplus activation, followed by 3 branches of dense layers and a sigmoid activation for predicting " + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "inline_equation", + "content": "c^{\\mathrm{med}}" + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "content": " and softplus activations for " + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{attn}}" + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "inline_equation", + "content": "\\sigma^{\\mathrm{bs}}" + }, + { + "bbox": [ + 46, + 247, + 286, + 342 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 343, + 286, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 343, + 286, + 463 + ], + "spans": [ + { + "bbox": [ + 46, + 343, + 286, + 463 + ], + "type": "text", + "content": "In the rendering scheme, [5] initialized the farthest " + }, + { + "bbox": [ + 46, + 343, + 286, + 463 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 46, + 343, + 286, + 463 + ], + "type": "text", + "content": " with infinity, enabling the network to predict a background color for rays that do not intersect with any object. We disabled this addition as it prevents our method from explaining the medium that contributes to the rendered color along the ray. We keep the learning rate and optimization parameters the same as in [5]. The network is trained for 250,000 iterations with a batch size of 16384 rays, taking around 10 hours on an Nvidia A100 GPU. The loss function and metrics are calculated on the output before any post-processing." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 472, + 190, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 190, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 190, + 485 + ], + "type": "text", + "content": "5. Experiments and Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 491, + 129, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 129, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 129, + 504 + ], + "type": "text", + "content": "5.1. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "type": "text", + "content": "Real world scenes. We acquired multi-image underwater scenes by diving in three different seas: the Red Sea (Eilat, Israel), the Caribbean Sea (Curaçao) and the Pacific Sea (Panama) with a total of 20, 20 and 18 images respectively, from which three are set aside for validation in each set. This data encapsulates a diverse set of water conditions and imaging conditions. The images were acquired as RAW images with a Nikon D850 SLR camera in a Nauticam underwater housing with a dome port to avoid refractions that jeopardize the pinhole model [45], and downsampled to average size " + }, + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "type": "inline_equation", + "content": "900 \\times 1400" + }, + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "type": "text", + "content": ". The input linear images were white-balanced before processing with " + }, + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 510, + 286, + 677 + ], + "type": "text", + "content": " clipping per channel to remove extreme noisy pixels. Finally, COLMAP [39] is used to extract camera poses." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Simulated Scene. We constructed a simulation using the Fern scene of the LLFF dataset [24]. We ran MIP-NeRF-360 [5] and used the predicted depth maps to simulate an" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 309, + 72, + 386, + 132 + ], + "blocks": [ + { + "bbox": [ + 309, + 72, + 386, + 132 + ], + "lines": [ + { + "bbox": [ + 309, + 72, + 386, + 132 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 386, + 132 + ], + "type": "image", + "image_path": "e76c02e24c509eee74358fcd222d2de77aed7e948e491ef48541690e203edc54.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 388, + 72, + 465, + 132 + ], + "blocks": [ + { + "bbox": [ + 388, + 72, + 465, + 132 + ], + "lines": [ + { + "bbox": [ + 388, + 72, + 465, + 132 + ], + "spans": [ + { + "bbox": [ + 388, + 72, + 465, + 132 + ], + "type": "image", + "image_path": "b75cc51dd3dd65fea3a5c8d028a09d3d63c213554dd1aa70e4adaea791f993bd.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 467, + 72, + 544, + 132 + ], + "blocks": [ + { + "bbox": [ + 467, + 72, + 544, + 132 + ], + "lines": [ + { + "bbox": [ + 467, + 72, + 544, + 132 + ], + "spans": [ + { + "bbox": [ + 467, + 72, + 544, + 132 + ], + "type": "image", + "image_path": "69d4d0aac7da483266212b31a89eb2eb6b3a63d16d9622b4be46c39e289acf77.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 309, + 133, + 386, + 190 + ], + "blocks": [ + { + "bbox": [ + 309, + 133, + 386, + 190 + ], + "lines": [ + { + "bbox": [ + 309, + 133, + 386, + 190 + ], + "spans": [ + { + "bbox": [ + 309, + 133, + 386, + 190 + ], + "type": "image", + "image_path": "ceed1ece2a7b01724ddb5059607f5d00ca9204eaac7907305cb47106c6b98bdd.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 388, + 133, + 465, + 190 + ], + "blocks": [ + { + "bbox": [ + 388, + 133, + 465, + 190 + ], + "lines": [ + { + "bbox": [ + 388, + 133, + 465, + 190 + ], + "spans": [ + { + "bbox": [ + 388, + 133, + 465, + 190 + ], + "type": "image", + "image_path": "0bd8ff890a1cfd96adad232ee4a16e1ebb97436ccc3b82474960c577171488b0.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 467, + 133, + 544, + 190 + ], + "blocks": [ + { + "bbox": [ + 467, + 133, + 544, + 190 + ], + "lines": [ + { + "bbox": [ + 467, + 133, + 544, + 190 + ], + "spans": [ + { + "bbox": [ + 467, + 133, + 544, + 190 + ], + "type": "image", + "image_path": "b7bf897e3df7a3dd420e99f2c6282ec87b1e3993e969ffcc6a8794d23c2452b7.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 309, + 191, + 386, + 250 + ], + "blocks": [ + { + "bbox": [ + 309, + 191, + 386, + 250 + ], + "lines": [ + { + "bbox": [ + 309, + 191, + 386, + 250 + ], + "spans": [ + { + "bbox": [ + 309, + 191, + 386, + 250 + ], + "type": "image", + "image_path": "9dce81562f7a968f43764444a79c9ac9eb8658a7173852272d58df143f7d6e02.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 257, + 545, + 334 + ], + "lines": [ + { + "bbox": [ + 304, + 257, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 545, + 334 + ], + "type": "text", + "content": "Figure 4. Synthetic experiment on Fern scene of the LLFF dataset [24]. Top: Our method can handle 'in-air' scenes, with a uniform zeros backscatter image and a reconstruction PSNR that is close to that of the baseline [5] which was 23.73. Middle and bottom: Our method's separation between clean and backscatter components, for simulations of fog and underwater effects. The reconstruction quality degrades rather gracefully." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 388, + 191, + 465, + 250 + ], + "blocks": [ + { + "bbox": [ + 388, + 191, + 465, + 250 + ], + "lines": [ + { + "bbox": [ + 388, + 191, + 465, + 250 + ], + "spans": [ + { + "bbox": [ + 388, + 191, + 465, + 250 + ], + "type": "image", + "image_path": "fc572cd3afe20f6d204a4f79698955d198208524a665f656ef60841ab1ef2453.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 467, + 191, + 544, + 250 + ], + "blocks": [ + { + "bbox": [ + 467, + 191, + 544, + 250 + ], + "lines": [ + { + "bbox": [ + 467, + 191, + 544, + 250 + ], + "spans": [ + { + "bbox": [ + 467, + 191, + 544, + 250 + ], + "type": "image", + "image_path": "d289341b13c66b2b7c84895cd01dcbfa0c6e625544acdcecddc1d1569a16715a.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "text", + "content": "underwater and a foggy scene. Water was added according to (7) with parameter values: " + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\beta^D = [1.3, 1.2, 0.9]" + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\beta^B = [0.95, 0.85, 0.7]" + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "inline_equation", + "content": "B^\\infty = [0.07, 0.2, 0.39]" + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "text", + "content": ". Fog was simulated based on [36] with " + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\beta = 1.2" + }, + { + "bbox": [ + 304, + 363, + 545, + 411 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 634 + ], + "type": "text", + "content": "Baseline methods. The input to all methods is the same set of white-balanced linear images. In the task of rendering scenes in the medium we compare with the following NeRF methods: MIP-NeRF-360, forward-looking with NDC (MIP360) [5], NeRF-W [21] and NeRFReN [14]. In the task of reconstructing clean medium-free images we compare with NeRF-W, where the 'transient' component can be viewed as the clean image and the 'static' image as backscatter, and to NeRFReN with the 'reflected' and 'transmitted' components as clean and backscatter images. We additionally compare to single-image scene reconstruction methods: plain white balance, SeaThru [2], the leading \"classical\" methods of Bekerman et al [6], and the recent deep-learning based [52] (as well as [15, 52] whose results are provided in the project website). SeaThru requires depth maps, that we generate using SFM (with Agisoft Metashape) as originally suggested. 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Scene rendering in the medium, on 'Red Sea'. Left to right: white-balanced input image, our result, MIP360 [23], Nerf-W [21], NeRFReN [14]. [Top 2 rows] Train image and zoom-ins. Even in the task of overfitting to the training images, there are noticeable differences between the methods, and as can be seen in the zoom-ins (red squares) we are able to reconstruct fine details in further areas (albeit a lower PSNR). [Bottom 2 rows] Novel view and zoom-ins. Our method achieves the highest PSNR (see tables 1, 2), and provides much better details in further areas (see red square zoom-ins). 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Results" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 375, + 287, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 448 + ], + "type": "text", + "content": "We start with a sanity check on a clean image. Our method correctly estimates zero backscatter, and does not force itself to estimate a medium (Fig. 4 Top). On our simulated fog and underwater scenes (Fig. 4 middle and bottom), our method separates the scenes' components very well, with only slight reduction in PSNR in the underwater scene." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 46, + 449, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 604 + ], + "type": "text", + "content": "Image rendering and novel-view synthesis (in medium). Qualitative results are summarized in Figs. 1, 5. Table 1 summarizes the average PSNR on the validation set of the Red Sea scene, in which our method achieves the highest PSNR. Note that both NeRF-W [21] and NeRFReN [14] are based on the NeRF [25] model while our code is based on Mip-NeRF-360 [5] that in general improves reconstruction details in further areas. So our real comparison is with [5], which we improve by " + }, + { + "bbox": [ + 46, + 449, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\sim 0.8dB" + }, + { + "bbox": [ + 46, + 449, + 287, + 604 + ], + "type": "text", + "content": " on average over the validation set. Table 2 compares PSNR, SSIM and LPIPS with those of [5] on validation sets of all real-world and simulation scenes. Our method is better in the majority of cases, and is especially good on the further areas (red squares)." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "On the train set [5] achieves a reasonable rendering of the scene in terms of PSNR by wrongly modeling the water as a nearby blue object, as can be seen in the depth map, indicating a close object in the top area. Even then, in our results further objects are reconstructed with more detail. The NeRFReN [14] depth map flattens at the mid-range, while ours is more informative further on. SFM does not estimate depth at these areas because of lack of features. Scene restoration (Fig. 6). In comparison with NeRF" + } + ] + } + ], + "index": 34 + }, + { + "type": "table", + "bbox": [ + 310, + 354, + 539, + 382 + ], + "blocks": [ + { + "bbox": [ + 310, + 354, + 539, + 382 + ], + "lines": [ + { + "bbox": [ + 310, + 354, + 539, + 382 + ], + "spans": [ + { + "bbox": [ + 310, + 354, + 539, + 382 + ], + "type": "table", + "html": "
OursIIIIII[5][21][14]
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SceneMIP360 [5]Ours
Red Sea21.05 / 0.75 / 0.2921.83 / 0.77 / 0.25
Red Sea red square29.66 / 0.84 / 0.4333.80 / 0.90 / 0.23
Curaçao26.54 / 0.81 / 0.3330.48 / 0.87 / 0.20
Curaçao red square27.04 / 0.84 / 0.4533.20 / 0.88 / 0.08
Panama27.43 / 0.82 / 0.2327.89 / 0.83 / 0.22
Fern fog30.23 / 0.88 / 0.1530.75 / 0.87 / 0.16
Fern underwater29.62 / 0.87 / 0.2629.76 / 0.86 / 0.15
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Scene reconstruction on 'Red Sea'. Columns 1-3: Comparing our method (top row) and 2 other NeRFs - Nerf-W [21] (middle row) and NeRFReN [14] (bottom row). Even though not developed for scattering media, they manage to separate a training image into two components (columns 1, 2), resembling the clean scene and the backscatter. However, their backscatter components contains details of the objects, while ours correctly displays only the signal stemming from the medium. Similarly (column 3), their 'clean' rendering of a novel view is inferior to ours, especially in the far distances. Column 4: Among the single-image methods, SeaThru [2] is the best performing (but requires the depth map as input). Nevertheless, color artifacts are visible in the far parts due to inaccurate depth information." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 170, + 251, + 288, + 331 + ], + "blocks": [ + { + "bbox": [ + 170, + 251, + 288, + 331 + ], + "lines": [ + { + "bbox": [ + 170, + 251, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 170, + 251, + 288, + 331 + ], + "type": "image", + "image_path": "62b2bcd0f265ad84960fa12b8e6eec1e57a1d8de046ab1c31a9d5938365ff71f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 291, + 251, + 410, + 331 + ], + "blocks": [ + { + "bbox": [ + 291, + 251, + 410, + 331 + ], + "lines": [ + { + "bbox": [ + 291, + 251, + 410, + 331 + ], + "spans": [ + { + "bbox": [ + 291, + 251, + 410, + 331 + ], + "type": "image", + "image_path": "f662b29bfb39b921ed244e0d5073cf6932f59b9917a6e1e7a53ac42f46d4d4fe.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 427, + 251, + 545, + 331 + ], + "blocks": [ + { + "bbox": [ + 427, + 251, + 545, + 331 + ], + "lines": [ + { + "bbox": [ + 427, + 251, + 545, + 331 + ], + "spans": [ + { + "bbox": [ + 427, + 251, + 545, + 331 + ], + "type": "image", + "image_path": "e9c6bdf834890e40532a129e64058775fa9cc8c3db905370368de5d44f056909.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 412, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 287, + 519 + ], + "type": "text", + "content": "Ablation Study. (i) Number of medium parameters: following the discussion in Sec. 3.2, the elaborate version of Eq. (7) uses 6 parameters for the medium coefficients, while simplified versions use 1 (marked I in Table 1) or 3 (marked II). This is ablated in Table 1, in terms of PSNR, where the elaborate model with 6 parameters achieves a higher score. (ii) Rendering equations. We compare our basic rendering model (Eqs. 13, 14), marked III in Table 1 to the final one marked 'ours' (Eq. 22). This option achieves lower PSNR." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 529, + 117, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 529, + 117, + 541 + ], + "spans": [ + { + "bbox": [ + 47, + 529, + 117, + 541 + ], + "type": "text", + "content": "6. Discussion" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 545, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 677 + ], + "type": "text", + "content": "We provide an important extension of NeRFs that enables rendering scenes acquired in scattering media such as haze, fog and underwater. So far, NeRF provided a framework for volumetric rendering, but without considering the nature of the medium, resulting in a binary 'occupancy' volume. Our formulation enables opaque objects to exist in a semi-transparent medium that is both scattering and absorbing in a wavelength-dependent manner. We demonstrate it on challenging real-world scenes with a complex 3D structure. Our scenes are forward-facing and contain areas with no objects at all, which our method is able to explain." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Water effects in further regions are very strong, hampering single image methods and feature matching in multiview methods. Our method incorporates information from" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 412, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 545, + 448 + ], + "type": "text", + "content": "all images at once, learning the scene in a holistic way. This enables better scene reconstruction (in medium and clean), and estimating the depth and the medium's parameters." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 449, + 546, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 546, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 546, + 616 + ], + "type": "text", + "content": "Our method has several limitations. While it is based on the current state-of-the-art image formation model, that model does not account for multiple scattering or for artificial illumination. As common in NeRFs, it requires camera poses that are extracted beforehand, which can be challenging in bad visibility. Lastly, the medium's parameters are better learned in sets where there is enough variation in the scene range between the viewpoints. The formulation takes its strength from the modeling of the medium. Thus it struggles in scenes that do not adhere to the model's assumptions, e.g., underwater scenes with significant flickering. In the future we plan to add components that will explain transient effects such as flickering, and continue to explore estimation of more diverse scenes and medium parameters." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 714 + ], + "type": "text", + "content": "Acknowledgements. The research was funded by Israel Science Foundation grant #680/18, Israeli Ministry of Science and Technology, European Union's Horizon 2020 research and innovation programme GA 101094924 (ANERIS), the Leona M. and Harry B. Helmsley Charitable Trust, the Maurice Hatter Foundation, and Schmidt Marine Technology Partners. 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Frame selection aims to extract the most informative and representative frames to help a model better understand video content. Existing frame selection methods either individually sample frames based on per-frame importance prediction, without considering interaction among frames, or adopt reinforcement learning agents to find representative frames in succession, which are costly to train and may lead to potential stability issues. To overcome the limitations of existing methods, we propose a Search-Map-Search learning paradigm which combines the advantages of heuristic search and supervised learning to select the best combination of frames from a video as one entity. By combining search with learning, the proposed method can better capture frame interactions while incurring a low inference overhead. Specifically, we first propose a hierarchical search method conducted on each training video to search for the optimal combination of frames with the lowest error on the downstream task. A feature mapping function is then learned to map the frames of a video to the representation of its target optimal frame combination. During inference, another search is performed on an unseen video to select a combination of frames whose feature representation is close to the projected feature representation. Extensive experiments based on several action recognition benchmarks demonstrate that our frame selection method effectively improves performance of action recognition models, and significantly outperforms a number of competitive baselines.", + "bbox": [ + 75, + 417, + 472, + 872 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 364, + 630, + 380 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Videos have proliferated online in recent years with the popularity of social media, and have become a major form of content consumption on the Internet. The abundant video data has greatly encouraged the development of deep learning techniques for video content understanding. As one of the most important tasks, action recognition aims to identify relevant actions described in videos, and plays a vital role to other downstream tasks like video retrieval and recommendation.", + "bbox": [ + 496, + 393, + 893, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the high computational cost of processing frames in a video, common practices of action recognition involve sampling a subset of frames or clips uniformly [31] or densely [26, 37] from a given video a serve as the input to a content understanding model. However, since frames in a video may contain redundant information and are not equally important, simple sampling methods are often incapable of capturing such knowledge and hence can lead to sub-optimal action recognition results.", + "bbox": [ + 496, + 534, + 893, + 671 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior studies attempt to actively select relevant video frames to overcome the limitation of straightforward sampling, achieving improvements to model performance. Heuristic methods are proposed to rank and select frames according to the importance score of each frame/clip calculated by per-frame prediction [15, 19]. Despite the effectiveness, these methods heavily rely on per-frame features, without considering the interaction or diversity among selected frames. Reinforcement learning (RL) has also been proposed to identify informative frames by formulating frame selection as a Markov decision process (MDP) [8, 9, 33,35,36]. However, existing RL-based methods may suffer from training stability issues and rely on a massive amount of training samples. Moreover, RL methods make an MDP assumption that frames are selected sequentially depending", + "bbox": [ + 496, + 674, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10627", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "on observations of already selected frames, and thus cannot adjust prior selections based on new observations.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a new learning paradigm named Search-Map-Search (SMS), which directly searches for the best combination of frames from a video as one entity. SMS formulates the problem of frame selection from the perspective of heuristic search in a large space of video frame combinations, which is further coupled with a learnable mapping function to generalize to new videos and achieve efficient inference.", + "bbox": [ + 75, + 121, + 467, + 239 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we propose a hierarchical search algorithm to efficiently find the most favorable frame combinations on training videos, which are then used as explicit supervision information to train a feature mapping function that maps the feature vectors of an input video to the feature vector of the desirable optimal frame combination. During inference on an unseen query video, the learned mapping function projects the query video onto a target feature vector for the desired frame combination, where another search process retrieves the actual frame combination that approximates the target feature vector. By combining search with learning, the proposed SMS method can better capture frame interactions while incurring a low inference cost.", + "bbox": [ + 75, + 242, + 467, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The effectiveness of SMS is extensively evaluated on both the long untrimmed action recognition benchmarks, i.e., ActivityNet [2] and FCVID [18], and the short trimmed UCF101 task [27]. Experimental results show that SMS can significantly improve action recognition models and precisely recognize and produce effective frame selections. Furthermore, SMS significantly outperforms a range of other existing frame selection methods for the same number of frames selected, while can still generate performance higher than existing methods using only $10\\%$ of all labeled video samples for training.", + "bbox": [ + 75, + 439, + 467, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 618, + 218, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Action Recognition. 2D ConvNets have been widely utilized for action recognition, where per-frame features are first extracted and later aggregated with different methods such as temporal averaging [31], recurrent networks [7, 20, 37], and temporal channel shift [10, 21, 23]. Some studies leveraged both the short-term and long-term temporal relationships by two-stream architectures [12, 13]. To jointly capture the spatio-temporal information of videos, 3D ConvNets were proposed, including C3D [28], I3D [3] and X3D [11]. Transformer architecture [29] have also been applied to video understanding by modeling the spatiotemporal information with attention [1, 22].", + "bbox": [ + 75, + 643, + 467, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we follow the previous frame selection work and apply our method mainly on the temporal averaging 2D ConvNets.", + "bbox": [ + 76, + 825, + 467, + 868 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Frame Selection. The problem of selecting important frames within a video has been investigated in order to im", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "prove the performance and reduce the computational cost.", + "bbox": [ + 498, + 90, + 880, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Many researchers focused on selecting frames based on the per-frame heuristic score. SCSampler [19] proposed to select frames based on the predicted scores of a lightweight video model as the usefulness of frames. SMART [15] incorporated an attention module that takes randomly selected frame pairs as input to model the relationship between frames. However, these methods select frames individually regardless of interactions between selected frames, which may lead to redundant selections.", + "bbox": [ + 496, + 107, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Reinforcement learning (RL) approaches are widely adopted in frame selection to find the effective frames in a trail-and-error setting. FastForward [9] and AdaFrame [35] adopted a single RL agent to generate a decision on the next frame, and updated the network with policy gradient. MARL [33] formulated the frame sampling process as multiple parallel Markov Decision Processes, and adopted multiple RL agents each responsible for determining a frame. Although the RL-based approaches are effective, the training stability issue and the requirement of huge amount of training samples with high computational overhead remain a problem.", + "bbox": [ + 496, + 243, + 890, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent studies combined frame selection with other techniques to improve the model efficiency. LiteEval [34] adopted a two-level feature extraction procedure, where fine expensive features were extracted for important frames, and coarse frames were used for the remaining frames. ListenToLook [14] proposed to use audio information as an efficient video preview for frame selection. AR-Net [24] aimed at selecting the optimal resolution for each frame that is needed to correctly recognize the actions, and learns a differentiable policy using Gumbel Softmax trick [17].", + "bbox": [ + 496, + 426, + 890, + 575 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our work focuses on the classic task of selecting a subset of frames based on visual information. Different from existing methods, our work incorporates a new \"Search-Map-Search\" paradigm that leverages efficient search and supervised feature mapping to explicitly find the best frame combinations, and achieves excellent performance outperforming other frame selection methods.", + "bbox": [ + 496, + 577, + 890, + 681 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 699, + 633, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Overall Architecture", + "text_level": 1, + "bbox": [ + 500, + 724, + 694, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 1 gives an overview of our proposed framework, which consists of three stages: a search stage, a feature mapping stage, and another search stage. The training process of our method involves the first two stages, while the inference process involves the last two.", + "bbox": [ + 496, + 748, + 890, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, the goal of the first search stage is to find the best frame combinations in training videos with the lowest model losses, which serve as the supervisory target information for the feature mapping stage. We design an efficient hierarchical algorithm coupled with Guided Local", + "bbox": [ + 496, + 825, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10628", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3bcfd27c2a31aad153aa5cfd6724b3ae2d58c0746bc8e787ea371111c1a040f7.jpg", + "image_caption": [ + "Figure 1. An overview of the proposed \"Search-Map-Search\" method. It contains three stages, where in the first stage, an efficient hierarchical search algorithm is used to derive the best frame combinations with lowest losses, which are utilized as the supervised information to train a feature mapping function in the second stage. In the third stage, for a query video, we incorporate another search process to infer the frame combination whose features are closest to the combination feature predicted with the trained feature mapping function." + ], + "image_footnote": [], + "bbox": [ + 140, + 104, + 823, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Search [30] to identify the effective frame combinations at a low search cost.", + "bbox": [ + 75, + 599, + 470, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the second stage, a feature extractor is employed to extract input frame features from the training video frames, and the feature of the best combination from search results. Then, a feature mapping function is trained via supervised learning by taking the input frame features as input, and transforming it to the target feature of the best combination.", + "bbox": [ + 75, + 632, + 468, + 723 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the third stage, we incorporate another search process to infer the effective frame combination whose feature is closest to the predicted feature from the well-trained feature mapping function.", + "bbox": [ + 75, + 724, + 468, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Stage 1: Search for Best Frame Combinations", + "text_level": 1, + "bbox": [ + 76, + 800, + 467, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an action recognition task with a pre-trained model $M$ and a training dataset $D^{tr} = \\{X, y\\}^{|\\hat{D}^{tr}|}$ , where $X = \\{x_{i}\\}_{i=1}^{m}$ represents a video sample made up of a collection of $m$ frames, and $y$ is the action label for the video, our goal of stage 1 is to find the best frame combination $\\tilde{X}^*$ .", + "bbox": [ + 76, + 825, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $n$ frames for each training video $X$ that minimizes the model loss:", + "bbox": [ + 498, + 599, + 890, + 630 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {X} ^ {*} = \\underset {\\tilde {X}} {\\arg \\min } \\mathcal {L} (M (\\tilde {X}), y), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 633, + 890, + 666 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw h e r e \\quad \\tilde {X} = \\left\\{x _ {k} \\mid x _ {k} \\in X \\right\\} ^ {n},\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 666, + 772, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is the loss function of the action recognition task. Note that repetitive selection of the same frame is allowed in our setting, as we believe that repeated important frames are better than meaningless frames.", + "bbox": [ + 496, + 688, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to efficiently find the best frame combinations, we have designed a hierarchical search algorithm which exploits the high similarities of adjacent frames by performing search hierarchically on coarse-grained clips first, and then on the fine-grained frames. Besides, we incorporate Guided Local Search [30] in our algorithm to exploit perframe losses as prior information for a good starting search point, which further reduces search costs and empirically outperforms other strong search algorithms such as Genetic Algorithm [32].", + "bbox": [ + 496, + 750, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10629", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Algorithm 1: Hierarchical Search", + "text_level": 1, + "bbox": [ + 86, + 94, + 315, + 109 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: Video $X$ , Clip Length $K$ , Combination Length $n$", + "bbox": [ + 96, + 111, + 406, + 141 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: Frame Combination $\\hat{X}^*$", + "bbox": [ + 96, + 141, + 318, + 156 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "/\\*clipsearchphase", + "bbox": [ + 98, + 170, + 256, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "\\*", + "bbox": [ + 426, + 170, + 442, + 180 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1 Split the video into clips each consisting of $K$ frames", + "2 Prepare an initial solution $\\tilde{C}_0$ containing the clip with the lowest loss repeated $n$ times", + "3 Perform Guided Local Search to improve $\\tilde{C}_0$ and get $\\tilde{C}^* = \\{C_k\\}_{k=1}^n$" + ], + "bbox": [ + 83, + 184, + 421, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "/\\*frame search phase", + "bbox": [ + 98, + 289, + 264, + 301 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "\\*", + "bbox": [ + 426, + 289, + 442, + 297 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "4 Define search space for each position in combination $S^F = \\{S_k|S_k = \\{x_j|x_j\\in C_k\\} \\}_{k = 1}^n$ on top of $\\tilde{C}^*$", + "5 Randomly initialize solution $\\tilde{X}_0$ from $S^F$", + "6 Perform Guided Local Search to improve $\\tilde{X}_0$ and get $\\tilde{X}^* = \\{x_k\\}_{k=1}^n$" + ], + "bbox": [ + 83, + 303, + 431, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall workflow of our hierarchical search is summarized in Algorithm 1. To begin with, the video is first split into coarse-grained clips each consisting of a collection of non-overlapped frames. Then, we calculate the model loss for each clip by representing it with the averaged feature vector of all frame inside it, and utilize the information to create an initial solution composed of the clip with the lowest model loss repeated $n$ times. On top of the initial searching point, we adapt Guided Local Search to find the best clip combination by defining a problem-specific penalty to escape from local optimum points. The details of Guided Local Search will be introduced in Appendix. After searching on coarse-grained clips, we again incorporate Guided Local Search to find the best fine-grained frame combinations by replacing each derived clip with a frame inside it. Via hierarchical search, we have greatly reduced the search space and lowered the search cost significantly, while obtaining satisfying solutions.", + "bbox": [ + 75, + 431, + 468, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Stage 2: Feature Mapping Function", + "text_level": 1, + "bbox": [ + 76, + 714, + 387, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of the second stage is to identify the best frame combination produced in stage 1, given the input video frames by learning a feature mapping function $\\mathcal{F}$ .", + "bbox": [ + 75, + 737, + 468, + 782 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, the feature mapping function $\\mathcal{F}$ takes in the features of input frames $H_0$ generated by a pre-trained feature extractor $\\theta$ , and outputs a predicted feature $\\hat{h} \\in \\mathcal{R}^d$ representing a frame combination where $d$ denotes the feature dimension:", + "bbox": [ + 75, + 782, + 468, + 856 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {h} = \\mathcal {F} (H _ {0})\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 866, + 302, + 883 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $H_0 = \\{h_i|h_i = \\theta (x_i)\\}_{i = 1}^m$", + "bbox": [ + 156, + 883, + 390, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(2)", + "bbox": [ + 444, + 878, + 467, + 890 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ is the feature extractor, and $h_i \\in \\mathcal{R}^d$ is the extracted feature vector for frame $x_i$ .", + "bbox": [ + 500, + 90, + 890, + 119 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the network structure of mapping function $\\mathcal{F}$ , we choose to incorporate transformer layers [29] to construct the spatio-temporal representations of the input frame features, and an aggregation function to aggregate the representations of variable lengths into a predicted feature vector $\\hat{h}$ :", + "bbox": [ + 498, + 121, + 890, + 208 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} H _ {l} = \\text {t r a n s f o r m e r} \\left(H _ {l - 1}\\right) \\tag {3} \\\\ \\hat {h} = a g g r (H _ {l}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 209, + 890, + 246 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l$ is the number of transformer layers in the mapping function.", + "bbox": [ + 498, + 253, + 890, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The objective of the mapping function is to minimize the distance between the predicted feature $\\hat{h}$ and the aggregated feature vector of the searched frame combination $h^{*}$ :", + "bbox": [ + 498, + 282, + 890, + 327 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min \\quad d i s t (\\hat {h}, h ^ {*})\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 339, + 735, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $h^* = \\text{aggr}(\\{h_k | h_k = \\theta(x_k), x_k \\in \\tilde{X}^*\\})$ .", + "bbox": [ + 524, + 358, + 846, + 377 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(4)", + "bbox": [ + 867, + 349, + 890, + 363 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our implementation, we incorporate cosine distance and mean-pooling as the distance function and aggregation function respectively, while other function choices can be further explored.", + "bbox": [ + 498, + 388, + 890, + 448 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Stage 3: Search to Infer Frame Combinations", + "text_level": 1, + "bbox": [ + 500, + 458, + 885, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After the mapping function is learned, it can accurately predict the features of the best frame combinations for unseen videos without relying on the ground truth labels. The goal of this stage is to incorporate another search process to infer the frame combinations from the predicted features. Formally, the objective of the search is to find a frame combination $\\hat{X}$ whose aggregated feature $h'$ is closest to the given predicted feature $\\hat{h}$ :", + "bbox": [ + 496, + 481, + 890, + 602 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {X} = \\arg \\min (d i s t (h ^ {\\prime}, \\hat {h}))\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 614, + 754, + 631 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\tilde{X}$", + "bbox": [ + 640, + 631, + 653, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(5)", + "bbox": [ + 867, + 632, + 890, + 645 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $h^\\prime = aggr(\\{h_k|h_k = \\theta (x_k),x_k\\in \\tilde{X}\\})$", + "bbox": [ + 526, + 646, + 843, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As the evaluation in the search only involves the calculation of the cosine distance between vectors, which requires little computation, we directly apply Guided Local Search on the fine-grained frame level without the hierarchical setting applied in stage 1.", + "bbox": [ + 496, + 674, + 890, + 750 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 763, + 630, + 780 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we conduct extensive experiments aiming at investigating the following research questions:", + "bbox": [ + 500, + 789, + 890, + 819 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- RQ1: Can the proposed SMS improve model performance over the base frame sampling method?", + "- RQ2: How does SMS perform compared to other state-of-the-art frame selection methods?" + ], + "bbox": [ + 517, + 829, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10630", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- RQ3: What's the computation efficiency of SMS for video inference?", + "- RQ4: How do the different components affect the performance of the proposed SMS?", + "- RQ5: Can SMS generalize well to spatio-temporal models, e.g., transformer based video models?" + ], + "bbox": [ + 96, + 90, + 467, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 210, + 266, + 228 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Datasets.", + "text_level": 1, + "bbox": [ + 76, + 234, + 192, + 248 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our SMS method on 3 action recognition benchmarks including ActivityNet V1.3 [2], FCVID [18] and UCF101 [27]. The videos in ActivityNet and FCVID are untrimmed with average video lengths of 117 and 167 seconds respectively, while UCF101 dataset contains trimmed short videos with an average length of 7.21 seconds. Table 1 summarizes the detailed information of the experimental datasets.", + "bbox": [ + 75, + 258, + 467, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2 Baselines.", + "text_level": 1, + "bbox": [ + 76, + 398, + 197, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We compare the proposed SMS with the base selection method and the following state-of-the-art frame selection methods:", + "bbox": [ + 76, + 421, + 467, + 465 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Base is a sparse sampling method proposed in TSN [31], where videos are divided into segments of equal length, and frames are randomly sampled within each segment.", + "- AdaFrame [35] incorporates reinforcement learning to adaptively select informative frames with a memory-augmented LSTM. At testing time, AdaFrame selects different number of frames for each video observed.", + "- MARL [33] adopts multiple RL agents each responsible for adjusting the position of a selected frame.", + "- SCSampler [19] proposes to select frames based on the prediction scores produced by a lightweight video model.", + "- SMART [15] combines the single-frame predictive score with pair-wise interaction score to make decision on the frame selections.", + "- LiteEval [34] selects important frames to extract fine features and adopts coarse features for the remaining frames.", + "- ListenToLook [14] proposes to use audio information as video preview for frame selection. For a fair comparison, we follow AR-Net [24] and include the variant with only the visual modality." + ], + "bbox": [ + 96, + 477, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/eb51a07109b35c6cdfae8067a11f0aee20c9912fc3fda29f07d32a9f9269f06c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetTrainValActionsAvg. Duration
ActivityNet10,0244,926200117s
FCVID45,61145,612239167s
UCF1019,5373,7831017.21s
", + "bbox": [ + 504, + 88, + 885, + 159 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Description of evaluation datasets.", + "bbox": [ + 565, + 169, + 823, + 183 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "- AR-Net [24] aims to select the optimal resolutions for frames that are needed to correctly recognize the actions.", + "bbox": [ + 517, + 210, + 888, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.3 Evaluation metrics.", + "text_level": 1, + "bbox": [ + 498, + 273, + 687, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following previous studies, we evaluate the performance of models using mean Average Precision (mAR), which is a commonly adopted metric in action recognition tasks, calculated as the mean value of the average precision over all action classes.", + "bbox": [ + 496, + 297, + 890, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.4 Implementation details.", + "text_level": 1, + "bbox": [ + 498, + 391, + 718, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the first stage of hierarchical searching, the clip length $K$ is set to 30. For the feature mapping network, we adopt a two-layer transformer network with a hidden dimension of 2,048. The feature extraction network used in our implementation is a ResNet-50 network [16] pre-trained on the Kinetics dataset [3].", + "bbox": [ + 496, + 414, + 890, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the data pre-processing for action recognition tasks, we decode the video at 1 fps for long videos in ActivityNet and FCVID and 55 fps for short videos in UCF101 to retrieve the rgb frames, which are augmented during training by resizing the short side to 256, random cropped and resized to $224^2$ , after which a random flip with a probability of 0.5 is applied. For inference, we resize all frames to $256^2$ and perform three-crop.", + "bbox": [ + 496, + 506, + 890, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the training of action recognition models, we choose ResNet-50 as the backbone and run 100 epochs using an SGD optimizer with a momentum of 0.9, and a step learning rate schedule which decays the learning rate by a factor of 10 every 40 epochs. For ActivityNet and FCVID, we use an initial learning rate of 0.005, and a batch size of 64. For UCF101 with shorter videos, we increase the batch size to 128 and adjust the initial learning rate to 0.00256. All models are trained using code adapted from MMAction2 [4] on eight Nvidia-A100 GPUs. And we report the average performance and standard deviation of three runs.", + "bbox": [ + 496, + 627, + 890, + 791 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Effectiveness Analysis (RQ1)", + "text_level": 1, + "bbox": [ + 498, + 801, + 756, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To validate the effectiveness of the proposed SMS, we make a comprehensive comparison with the base method on both long-video dataset ActivityNet and FCVID, and short-video dataset UCF101. As the video lengths of different datasets vary in a large range, we choose to select different", + "bbox": [ + 496, + 824, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10631", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/645dda20cf92423fa940fd23b723bb9b73af8cf56949bfa292e95dc5d86ff0f5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
# FramesActivityNetFCVIDUCF101
816258162538
Base177.34 ± 0.0679.41 ± 0.0580.04 ± 0.2483.84 ± 0.0585.34 ± 0.0385.65 ± 0.0490.65 ± 0.1390.70 ± 0.10
SMS (infer only)82.76 ± 0.1583.78 ± 0.0883.85 ± 0.1786.35 ± 0.0386.94 ± 0.0687.08 ± 0.0491.45 ± 0.1291.58 ± 0.09
SMS (train & infer)83.72 ± 0.0584.35 ± 0.0884.56 ± 0.0886.54 ± 0.0687.25 ± 0.1187.59 ± 0.0191.94 ± 0.1592.25 ± 0.10
", + "bbox": [ + 81, + 88, + 890, + 159 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/956b6ecc5c9537963c65b474ffee0096160b05f8f201311b44c10534fcb81e10.jpg", + "table_caption": [ + "Table 2. Performance comparison of the proposed SMS and the base method. In SMS (infer only), frames are selected with our method only during inference. In SMS (train & infer), frames are selected with SMS during both training and inference." + ], + "table_footnote": [], + "table_body": "
MethodBackboneActivityNetFCVID
# FramesmAPimpr.# FramesmAPimpr.
SCSamplerResNet-501072.90.41081.00.0
AdaFrameResNet-1018.6571.53.78.2180.21.8
MARLResNet-101872.90.4---
SMARTResNet-1011073.1-1082.1-
SMART*ResNet-50880.673.33883.35-0.49
SMS_10%ResNet-50882.124.78885.691.85
SMSResNet-50883.726.38886.542.70
", + "bbox": [ + 187, + 210, + 784, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Performance comparison of the proposed SMS and other state-of-the-art frame selection methods. We show both their performance and the their reported improvements over the base sampling method, due to the inconsistent base performance among different methods. Results of baselines are retrieved from literature, except for SMART*, which is implemented using the same features and implementation settings as SMS. We have also included the results of SMS learned only on $10\\%$ training data as SMS_10%.", + "bbox": [ + 75, + 380, + 893, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "number of frames for each video in these datasets, where 8, 16 and 25 frames are selected for long videos in ActivityNet and FCVID, and 3 and 8 frames are selected for short videos in UCF101. Furthermore, we conduct experiments to select frames with SMS only on test data during the inference of pre-trained base models, and incorporate SMS in both the training and inference process. The experimental results are shown in Table 2, from which we can observe that:", + "bbox": [ + 75, + 463, + 472, + 585 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- When applied to test data, compared to the base sampling method, SMS (infer only) significantly improves the average mAP on different numbers of selected frames by $4.53\\%$ and $1.85\\%$ on ActivityNet and FCVID, respectively. While SMS (infer only) significantly improves model performance, SMS (train & infer) improves the mAP by $0.75\\%$ and $0.34\\%$ mAP on ActivityNet and FCVID. This observation demonstrates that the frames selected with the SMS method are beneficial to both model training and inference.", + "While most other frame selection methods only focus on long untrimmed video tasks, SMS is also effective on short trimmed video tasks. Despite that in UCF101, the irrelevant parts of videos are trimmed off, which to a great degree limits the potential of frame selection, SMS still achieves steady improvement of $1.42\\%$ average mAP over the base method with the same number" + ], + "bbox": [ + 94, + 595, + 468, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "of selected frames.", + "bbox": [ + 531, + 464, + 660, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Performance Comparison (RQ2)", + "text_level": 1, + "bbox": [ + 500, + 484, + 785, + 501 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In order to justify the benefit of our new learning paradigm of frame selection, we compare SMS with other classic frame selection methods on ActivityNet and FCVID. We choose ResNet as the backbone architecture of the action recognition model and report the performance with similar number of selected frames ranges from 8 to 10.", + "bbox": [ + 496, + 508, + 890, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As the implementation and training details are different among the frame selection methods, the performances of the base models are inconsistent. Therefore, directly comparing the reported performances may be unfair. Moreover, due to the lack of source codes and models, we are unable to compare all methods under the same settings, especially for the RL-based methods whose results are difficult to reproduce. To make a fairer comparison, in addition to the absolute performance, we also compare the relative improvements of the frame selection methods over the base sampling method. Also, we have implemented the most recent frame selection method, SMART [15], using the same features and implementation settings as our proposed SMS, and include its results as SMART*.", + "bbox": [ + 496, + 599, + 892, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The comparison results are demonstrated in Table 3, from which we can see that with the least number of selected frames and the smallest backbone model, the proposed SMS achieves the best performance of $83.72\\%$ and $86.54\\%$ mAP on ActivityNet and FCVID respectively. Moreover, even with the higher-performance base models", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1The base performance in our paper is higher compared to it in other papers, due to the better codebase and training settings.", + "bbox": [ + 76, + 875, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10632", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ea6eed9ff9ff1930007ac5897f85f446c751a7abe20e896e795e6d96e1e43cb4.jpg", + "image_caption": [ + "Figure 2. Comparison of SMS with other approaches in terms of performance vs. inference cost (model size per video) evaluated on ActivityNet. We control the inference cost by varying $m$ , the number of candidate frames in a video from which $n = 8$ best frames are to be selected." + ], + "image_footnote": [], + "bbox": [ + 86, + 95, + 459, + 306 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which are harder to improve, SMS still obtains the largest improvements of $6.48\\%$ and $2.70\\%$ among all frame selection methods. In a fair comparison with the same implementation settings, our method significantly outperforms SMART* by $3.05\\%$ and $3.19\\%$ respectively on ActivityNet and FCVID.", + "bbox": [ + 75, + 422, + 468, + 513 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The reason of our success is due to our novel training paradigm of \"Search-Map-Search\", where an efficient hierarchical search method is incorporated to find the best frame combinations, which better models the frame interactions. Moreover, in SMS, a feature mapping function is learned to map an input video directly to the optimal frame combination, which is theoretically superior to the one-by-one frame selection adopted by existing methods.", + "bbox": [ + 75, + 515, + 468, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Efficiency Analysis (RQ3)", + "text_level": 1, + "bbox": [ + 76, + 648, + 312, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now analyze the efficiency of SMS and compare it with other frame selection methods in terms of action recognition performance versus inference cost (evaluated by the model size per video. For a fair comparison, we only include the results that use ResNet as the backbone model.", + "bbox": [ + 75, + 672, + 468, + 748 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In order to evaluate the tradeoff between performance and inference efficiency, we first uniformly sub-sample $m$ candidate frames that constitute the search space for each video from which $n = 8$ best frames are to be selected. As $m$ increases, features are extracted from more candidate frames, and the resulting frame selection becomes more effective, while the inference cost becomes larger. As demonstrated in Figure 2, the action recognition performance of SMS grows rapidly from $m = 8$ to $m = 25$ , while further increasing $m$ to 50 or 100 incurs only slight increase in", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/21cbbbc35aae5ee552c864d6bae970522fe7c93ea96e9451da78384122920754.jpg", + "image_caption": [ + "Figure 3. The evaluation of different search algorithms on 100 videos, given by the average loss over the number of evaluations." + ], + "image_footnote": [], + "bbox": [ + 532, + 109, + 841, + 266 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "performance but huge inference overhead. In practice, one can easily achieve a good tradeoff between performance and cost accordingly by tuning the number of candidate frames $m$ .", + "bbox": [ + 496, + 330, + 893, + 390 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In comparison with other approaches, SMS achieves higher action recognition performance and beats other methods under different computation resource constraints, showing the effectiveness of the proposed search-mapping-search paradigm in frame selection.", + "bbox": [ + 496, + 392, + 893, + 468 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study (RQ4)", + "text_level": 1, + "bbox": [ + 500, + 479, + 705, + 497 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This subsection aims to analyze the effects of different components designed in our proposed SMS.", + "bbox": [ + 498, + 505, + 890, + 535 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Search algorithm. We have conducted experiments to compare the performance and efficiency of our designed Hierarchical Guided Local Search algorithm with other powerful search algorithms such as Fast Genetic Algorithm [6] and the frame-level Guided Local Search [30].", + "bbox": [ + 496, + 536, + 893, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Figure 3, we show the best loss averaged on 100 randomly selected videos with different search algorithms, and their corresponding search cost measured by the number of evaluations. By adopting different clip length $K$ , our proposed hierarchical search algorithm can trade off between the search performance and the search cost. From Figure 3, we can see that using the same number of evaluations, our hierarchical search achieves better results compared to Fast Genetic Algorithm, by more effectively exploiting the prior knowledge of the per-frame loss information. The original Guided Local Search without hierarchical design is extremely costly which requires nearly 3,000 evaluations per video. Contrastively, our algorithm is more efficient with the hierarchical design, and achieves comparable performance with far less computation cost.", + "bbox": [ + 496, + 612, + 893, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature mapping network. The process of feature mapping aims to transform the input frame features to the feature of target combination. We have conducted experiments to explore the impact of different network architectures and", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10633", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/09f9205bb1260a887325d09c37c8b88beb3914920f497a1164146e34159d1399.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Feature Extractor (Training Source)Mapping Model ArchPerformanceInference GFLOPs
ResNet-50 (Kinetics)Transformer83.721.50
ResNet-50 (Kinetics)MLP83.220.01
ResNet-50 (ImageNet)Transformer79.971.50
ResNet-50 (ActivityNet)Transformer81.061.50
MobileNet-V2 (Kinetics)Transformer79.530.93
", + "bbox": [ + 153, + 88, + 816, + 195 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7f4945064c765611163daff5620699dcc3ad3a3d16b871585fa7fa55d0258b09.jpg", + "table_caption": [ + "Table 4. Ablation analysis results in mAP (%) on ActivityNet using 8 frames with different feature extractors and feature mapping model architectures. The feature mapping inference GFLOPs per video is also provided." + ], + "table_footnote": [], + "table_body": "
Backbone# FramesMethodPerformance
TimeSFformer8Dense84.33
Base90.11
SMART*90.53
SMS91.97
", + "bbox": [ + 83, + 258, + 464, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. The ActivityNet evaluation results in mAP (%) using different frame sampling strategies on TimeSFformer.", + "bbox": [ + 75, + 359, + 468, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training data sources for feature mapping.", + "bbox": [ + 76, + 422, + 354, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the network architecture, we adopt transformers to sequentially modeling the frame features with their spatiotemporal relations taken into consideration. Another simple applicable design is to adopt a mean-pooling layer that aggregates all the features of frames into a single feature vector, followed by a simpler two-layer MLP network. In Table 4, row 1 and 2 compares the performance and the inference efficiency of the two designs. As we can see, using transformer model as the mapping function outperforms MLP design by $0.5\\%$ mAP due to the better representation ability, while the inference cost of both designs are small and negligible (less than 2 GFLOPs) compared to the cost of frame feature extractions (tens or hundreds GFLOPs).", + "bbox": [ + 75, + 440, + 468, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature extractor. We have analyzed the effect of different feature extractor settings by trying smaller model structure, e.g., MobileNet-V2 [25], and different pre-trained data sources including ImageNet [5], Kinetics [3] and ActivityNet [2].", + "bbox": [ + 75, + 640, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparing the results of row 1, 3 and 4 in Table 4, we can see that the pre-training data of feature extractor can make a difference. The feature extractor trained on the largest Kinetics dataset achieves the best performance as it better captures the semantics of actions by training on more related samples, compared to the ones trained on smaller ActivityNet dataset and out-domain ImageNet dataset. Besides, as shown in row 5 of Table 4, using smaller models such as MobileNet-V2 for extractor can lead to performance decline. In general, the representation capability of feature extractors is valuable for frame selection to recognize the important frames and find the best frame combinations.", + "bbox": [ + 75, + 719, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Generalizability Analysis (RQ5)", + "text_level": 1, + "bbox": [ + 498, + 260, + 782, + 277 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "It is a natural question to ask if the frames selected by SMS can also be beneficial to spatio-temporal video models. To find out the answer to this question, we have conducted an experiment to apply the SMS selected frames on TimeSFformer [1], which incorporates the transformer architecture and is one of the most advanced video models.", + "bbox": [ + 496, + 284, + 890, + 375 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results are shown in Table 5. The dense frame sampling strategy incorporated in the original TimeSFormer implementation randomly samples a clip containing 8 successive frames from videos, and achieves $84.33\\%$ mAP on ActivityNet. However, in untrimmed video dataset, dense sampling can only captures a small part of the video and may miss important information. In contrast, the base sampling strategy selects frames uniformly from videos and achieves $90.11\\%$ mAP, while SMART* achieves $90.53\\%$ mAP.", + "bbox": [ + 496, + 375, + 892, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "By using the input frames selected by SMS, we obtain a significant performance gain of $1.86\\%$ over the base sampling strategy and $1.44\\%$ over SMART*, and achieve $91.97\\%$ mAP. This improvement demonstrates the strong generalizability of SMS across different model architectures, and that SMS is not only effective on 2D video modeling, but can also capture the spatio-temporal relationship among frames and is beneficial to 3D video model learning.", + "bbox": [ + 496, + 511, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 648, + 617, + 664 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a new learning paradigm for frame selection, called \"Search-Map-Search\", which consists of a search stage to efficiently find the best frame combination with a hierarchical search algorithm, a feature mapping stage that learns to transform the input frame features directly into the feature of the searched combination, and another search stage that selects frames based on the mapped feature. Compared with existing frame selection methods, SMS is a more accurate learning paradigm that takes advantage of efficient search and supervised feature mapping to directly select the best combination of frames as one entity, which better captures the frame interactions. Experimental results show that SMS achieves significant performance gains on multiple action recognition benchmarks, and outperforms other strong baseline methods.", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10634", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? In ICML, volume 2, page 4, 2021. 2, 8", + "[2] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4510-4520, 2018. 8", + "[26] Karen Simonyan and Andrew Zisserman. Two-stream convolutional networks for action recognition in videos. Advances in neural information processing systems, 27, 2014. 1" + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "10635", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[27] Khurram Soomro, Amir Roshan Zamir, and Mubarak Shah. Ucf101: A dataset of 101 human actions classes from videos in the wild. arXiv preprint arXiv:1212.0402, 2012. 2, 5", + "[28] Du Tran, Lubomir Bourdev, Rob Fergus, Lorenzo Torresani, and Manohar Paluri. Learning spatiotemporal features with 3d convolutional networks. In Proceedings of the IEEE international conference on computer vision, pages 4489-4497, 2015. 2", + "[29] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017. 2, 4", + "[30] Christos Voudouris, Edward PK Tsang, and Abdullah Alsheddy. Guided local search. In Handbook of metaheuristics, pages 321-361. Springer, 2010. 3, 7", + "[31] Limin Wang, Yuanjun Xiong, Zhe Wang, Yu Qiao, Dahua Lin, Xiaou Tang, and Luc Van Gool. Temporal segment networks: Towards good practices for deep action recognition. In European conference on computer vision, pages 20-36. Springer, 2016. 1, 2, 5", + "[32] Darrell Whitley. A genetic algorithm tutorial. Statistics and computing, 4(2):65-85, 1994. 3", + "[33] Wenhao Wu, Dongliang He, Xiao Tan, Shifeng Chen, and Shilei Wen. Multi-agent reinforcement learning based frame sampling for effective untrimmed video recognition. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6222-6231, 2019. 1, 2, 5", + "[34] Zuxuan Wu, Caiming Xiong, Yu-Gang Jiang, and Larry S Davis. Liteeval: A coarse-to-fine framework for resource efficient video recognition. Advances in Neural Information Processing Systems, 32, 2019. 2, 5", + "[35] Zuxuan Wu, Caiming Xiong, Chih-Yao Ma, Richard Socher, and Larry S Davis. Adaframe: Adaptive frame selection for fast video recognition. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1278-1287, 2019. 1, 2, 5", + "[36] Serena Yeung, Olga Russakovsky, Greg Mori, and Li Fei-Fei. End-to-end learning of action detection from frame glimpses in videos. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2678–2687, 2016. 1", + "[37] Joe Yue-Hei Ng, Matthew Hausknecht, Sudheendra Vijayanarasimhan, Oriol Vinyals, Rajat Monga, and George Toderici. Beyond short snippets: Deep networks for video classification. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4694–4702, 2015. 1, 2" + ], + "bbox": [ + 78, + 90, + 467, + 753 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10636", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/72f3e04e-8ac3-45ed-bc77-477759a59e7c_model.json b/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/72f3e04e-8ac3-45ed-bc77-477759a59e7c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..7c41e2c86893fb35984b88e4a371cefb7e2edce9 --- /dev/null +++ b/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/72f3e04e-8ac3-45ed-bc77-477759a59e7c_model.json @@ -0,0 +1,2321 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.113, + 0.131, + 0.856, + 0.154 + ], + "angle": 0, + "content": "Search-Map-Search: A Frame Selection Paradigm for Action Recognition" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.182, + 0.344, + 0.252 + ], + "angle": 0, + "content": "Mingjun Zhao \nUniversity of Alberta \nEdmonton, Canada \nzhao2@ualberta.ca" + }, + { + "type": "text", + "bbox": [ + 0.392, + 0.182, + 0.558, + 0.252 + ], + "angle": 0, + "content": "Yakun Yu \nUniversity of Alberta \nEdmonton, Canada \nyakun2@ualberta.ca" + }, + { + "type": "text", + "bbox": [ + 0.612, + 0.182, + 0.8, + 0.252 + ], + "angle": 0, + "content": "Xiaoli Wang \nTencent \nShenzhen, China \nevexlwang@tencent.com" + }, + { + "type": "text", + "bbox": [ + 0.284, + 0.26, + 0.465, + 0.33 + ], + "angle": 0, + "content": "Lei Yang \nTencent \nShenzhen, China \nyangalalei@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.533, + 0.26, + 0.686, + 0.329 + ], + "angle": 0, + "content": "Di Niu \nTencent \nEdmonton, Canada \ndniu@ualberta.ca" + }, + { + "type": "title", + "bbox": [ + 0.236, + 0.365, + 0.313, + 0.381 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.473, + 0.873 + ], + "angle": 0, + "content": "Despite the success of deep learning in video understanding tasks, processing every frame in a video is computationally expensive and often unnecessary in real-time applications. Frame selection aims to extract the most informative and representative frames to help a model better understand video content. Existing frame selection methods either individually sample frames based on per-frame importance prediction, without considering interaction among frames, or adopt reinforcement learning agents to find representative frames in succession, which are costly to train and may lead to potential stability issues. To overcome the limitations of existing methods, we propose a Search-Map-Search learning paradigm which combines the advantages of heuristic search and supervised learning to select the best combination of frames from a video as one entity. By combining search with learning, the proposed method can better capture frame interactions while incurring a low inference overhead. Specifically, we first propose a hierarchical search method conducted on each training video to search for the optimal combination of frames with the lowest error on the downstream task. A feature mapping function is then learned to map the frames of a video to the representation of its target optimal frame combination. During inference, another search is performed on an unseen video to select a combination of frames whose feature representation is close to the projected feature representation. Extensive experiments based on several action recognition benchmarks demonstrate that our frame selection method effectively improves performance of action recognition models, and significantly outperforms a number of competitive baselines." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.365, + 0.631, + 0.381 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.895, + 0.529 + ], + "angle": 0, + "content": "Videos have proliferated online in recent years with the popularity of social media, and have become a major form of content consumption on the Internet. The abundant video data has greatly encouraged the development of deep learning techniques for video content understanding. As one of the most important tasks, action recognition aims to identify relevant actions described in videos, and plays a vital role to other downstream tasks like video retrieval and recommendation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.895, + 0.672 + ], + "angle": 0, + "content": "Due to the high computational cost of processing frames in a video, common practices of action recognition involve sampling a subset of frames or clips uniformly [31] or densely [26, 37] from a given video a serve as the input to a content understanding model. However, since frames in a video may contain redundant information and are not equally important, simple sampling methods are often incapable of capturing such knowledge and hence can lead to sub-optimal action recognition results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.896, + 0.903 + ], + "angle": 0, + "content": "Prior studies attempt to actively select relevant video frames to overcome the limitation of straightforward sampling, achieving improvements to model performance. Heuristic methods are proposed to rank and select frames according to the importance score of each frame/clip calculated by per-frame prediction [15, 19]. Despite the effectiveness, these methods heavily rely on per-frame features, without considering the interaction or diversity among selected frames. Reinforcement learning (RL) has also been proposed to identify informative frames by formulating frame selection as a Markov decision process (MDP) [8, 9, 33,35,36]. However, existing RL-based methods may suffer from training stability issues and rely on a massive amount of training samples. Moreover, RL methods make an MDP assumption that frames are selected sequentially depending" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10627" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "on observations of already selected frames, and thus cannot adjust prior selections based on new observations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.241 + ], + "angle": 0, + "content": "In this work, we propose a new learning paradigm named Search-Map-Search (SMS), which directly searches for the best combination of frames from a video as one entity. SMS formulates the problem of frame selection from the perspective of heuristic search in a large space of video frame combinations, which is further coupled with a learnable mapping function to generalize to new videos and achieve efficient inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.468, + 0.438 + ], + "angle": 0, + "content": "Specifically, we propose a hierarchical search algorithm to efficiently find the most favorable frame combinations on training videos, which are then used as explicit supervision information to train a feature mapping function that maps the feature vectors of an input video to the feature vector of the desirable optimal frame combination. During inference on an unseen query video, the learned mapping function projects the query video onto a target feature vector for the desired frame combination, where another search process retrieves the actual frame combination that approximates the target feature vector. By combining search with learning, the proposed SMS method can better capture frame interactions while incurring a low inference cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.468, + 0.605 + ], + "angle": 0, + "content": "The effectiveness of SMS is extensively evaluated on both the long untrimmed action recognition benchmarks, i.e., ActivityNet [2] and FCVID [18], and the short trimmed UCF101 task [27]. Experimental results show that SMS can significantly improve action recognition models and precisely recognize and produce effective frame selections. Furthermore, SMS significantly outperforms a range of other existing frame selection methods for the same number of frames selected, while can still generate performance higher than existing methods using only \\(10\\%\\) of all labeled video samples for training." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.619, + 0.219, + 0.635 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Action Recognition. 2D ConvNets have been widely utilized for action recognition, where per-frame features are first extracted and later aggregated with different methods such as temporal averaging [31], recurrent networks [7, 20, 37], and temporal channel shift [10, 21, 23]. Some studies leveraged both the short-term and long-term temporal relationships by two-stream architectures [12, 13]. To jointly capture the spatio-temporal information of videos, 3D ConvNets were proposed, including C3D [28], I3D [3] and X3D [11]. Transformer architecture [29] have also been applied to video understanding by modeling the spatiotemporal information with attention [1, 22]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.468, + 0.869 + ], + "angle": 0, + "content": "In this paper, we follow the previous frame selection work and apply our method mainly on the temporal averaging 2D ConvNets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Frame Selection. The problem of selecting important frames within a video has been investigated in order to im" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.882, + 0.107 + ], + "angle": 0, + "content": "prove the performance and reduce the computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Many researchers focused on selecting frames based on the per-frame heuristic score. SCSampler [19] proposed to select frames based on the predicted scores of a lightweight video model as the usefulness of frames. SMART [15] incorporated an attention module that takes randomly selected frame pairs as input to model the relationship between frames. However, these methods select frames individually regardless of interactions between selected frames, which may lead to redundant selections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Reinforcement learning (RL) approaches are widely adopted in frame selection to find the effective frames in a trail-and-error setting. FastForward [9] and AdaFrame [35] adopted a single RL agent to generate a decision on the next frame, and updated the network with policy gradient. MARL [33] formulated the frame sampling process as multiple parallel Markov Decision Processes, and adopted multiple RL agents each responsible for determining a frame. Although the RL-based approaches are effective, the training stability issue and the requirement of huge amount of training samples with high computational overhead remain a problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.577 + ], + "angle": 0, + "content": "Recent studies combined frame selection with other techniques to improve the model efficiency. LiteEval [34] adopted a two-level feature extraction procedure, where fine expensive features were extracted for important frames, and coarse frames were used for the remaining frames. ListenToLook [14] proposed to use audio information as an efficient video preview for frame selection. AR-Net [24] aimed at selecting the optimal resolution for each frame that is needed to correctly recognize the actions, and learns a differentiable policy using Gumbel Softmax trick [17]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.683 + ], + "angle": 0, + "content": "Our work focuses on the classic task of selecting a subset of frames based on visual information. Different from existing methods, our work incorporates a new \"Search-Map-Search\" paradigm that leverages efficient search and supervised feature mapping to explicitly find the best frame combinations, and achieves excellent performance outperforming other frame selection methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.7, + 0.634, + 0.716 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.696, + 0.74 + ], + "angle": 0, + "content": "3.1. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Figure 1 gives an overview of our proposed framework, which consists of three stages: a search stage, a feature mapping stage, and another search stage. The training process of our method involves the first two stages, while the inference process involves the last two." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Specifically, the goal of the first search stage is to find the best frame combinations in training videos with the lowest model losses, which serve as the supervisory target information for the feature mapping stage. We design an efficient hierarchical algorithm coupled with Guided Local" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10628" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.106, + 0.825, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.519, + 0.895, + 0.577 + ], + "angle": 0, + "content": "Figure 1. An overview of the proposed \"Search-Map-Search\" method. It contains three stages, where in the first stage, an efficient hierarchical search algorithm is used to derive the best frame combinations with lowest losses, which are utilized as the supervised information to train a feature mapping function in the second stage. In the third stage, for a query video, we incorporate another search process to infer the frame combination whose features are closest to the combination feature predicted with the trained feature mapping function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.471, + 0.631 + ], + "angle": 0, + "content": "Search [30] to identify the effective frame combinations at a low search cost." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.47, + 0.724 + ], + "angle": 0, + "content": "In the second stage, a feature extractor is employed to extract input frame features from the training video frames, and the feature of the best combination from search results. Then, a feature mapping function is trained via supervised learning by taking the input frame features as input, and transforming it to the target feature of the best combination." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.47, + 0.787 + ], + "angle": 0, + "content": "In the third stage, we incorporate another search process to infer the effective frame combination whose feature is closest to the predicted feature from the well-trained feature mapping function." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.468, + 0.817 + ], + "angle": 0, + "content": "3.2. Stage 1: Search for Best Frame Combinations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Given an action recognition task with a pre-trained model \\(M\\) and a training dataset \\(D^{tr} = \\{X, y\\}^{|\\hat{D}^{tr}|}\\), where \\(X = \\{x_{i}\\}_{i=1}^{m}\\) represents a video sample made up of a collection of \\(m\\) frames, and \\(y\\) is the action label for the video, our goal of stage 1 is to find the best frame combination \\(\\tilde{X}^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.601, + 0.892, + 0.631 + ], + "angle": 0, + "content": "with \\( n \\) frames for each training video \\( X \\) that minimizes the model loss:" + }, + { + "type": "equation", + "bbox": [ + 0.621, + 0.635, + 0.892, + 0.667 + ], + "angle": 0, + "content": "\\[\n\\tilde {X} ^ {*} = \\underset {\\tilde {X}} {\\arg \\min } \\mathcal {L} (M (\\tilde {X}), y), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.667, + 0.774, + 0.684 + ], + "angle": 0, + "content": "\\[\nw h e r e \\quad \\tilde {X} = \\left\\{x _ {k} \\mid x _ {k} \\in X \\right\\} ^ {n},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.75 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is the loss function of the action recognition task. Note that repetitive selection of the same frame is allowed in our setting, as we believe that repeated important frames are better than meaningless frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.902 + ], + "angle": 0, + "content": "In order to efficiently find the best frame combinations, we have designed a hierarchical search algorithm which exploits the high similarities of adjacent frames by performing search hierarchically on coarse-grained clips first, and then on the fine-grained frames. Besides, we incorporate Guided Local Search [30] in our algorithm to exploit perframe losses as prior information for a good starting search point, which further reduces search costs and empirically outperforms other strong search algorithms such as Genetic Algorithm [32]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10629" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.088, + 0.095, + 0.316, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Hierarchical Search" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.112, + 0.408, + 0.142 + ], + "angle": 0, + "content": "Input: Video \\(X\\), Clip Length \\(K\\), Combination Length \\(n\\)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.142, + 0.319, + 0.157 + ], + "angle": 0, + "content": "Output: Frame Combination \\(\\hat{X}^*\\)" + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.171, + 0.258, + 0.183 + ], + "angle": 0, + "content": "/\\*clipsearchphase" + }, + { + "type": "text", + "bbox": [ + 0.427, + 0.171, + 0.443, + 0.181 + ], + "angle": 0, + "content": "\\*" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.185, + 0.401, + 0.211 + ], + "angle": 0, + "content": "1 Split the video into clips each consisting of \\(K\\) frames" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.213, + 0.418, + 0.244 + ], + "angle": 0, + "content": "2 Prepare an initial solution \\(\\tilde{C}_0\\) containing the clip with the lowest loss repeated \\(n\\) times" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.245, + 0.422, + 0.279 + ], + "angle": 0, + "content": "3 Perform Guided Local Search to improve \\(\\tilde{C}_0\\) and get \\(\\tilde{C}^* = \\{C_k\\}_{k=1}^n\\)" + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.185, + 0.422, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.099, + 0.29, + 0.266, + 0.302 + ], + "angle": 0, + "content": "/\\*frame search phase" + }, + { + "type": "text", + "bbox": [ + 0.427, + 0.29, + 0.443, + 0.299 + ], + "angle": 0, + "content": "\\*" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.304, + 0.432, + 0.35 + ], + "angle": 0, + "content": "4 Define search space for each position in combination \\(S^F = \\{S_k|S_k = \\{x_j|x_j\\in C_k\\} \\}_{k = 1}^n\\) on top of \\(\\tilde{C}^*\\)" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.351, + 0.373, + 0.366 + ], + "angle": 0, + "content": "5 Randomly initialize solution \\(\\tilde{X}_0\\) from \\(S^F\\)" + }, + { + "type": "text", + "bbox": [ + 0.084, + 0.368, + 0.424, + 0.403 + ], + "angle": 0, + "content": "6 Perform Guided Local Search to improve \\(\\tilde{X}_0\\) and get \\(\\tilde{X}^* = \\{x_k\\}_{k=1}^n\\)" + }, + { + "type": "list", + "bbox": [ + 0.084, + 0.304, + 0.432, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.706 + ], + "angle": 0, + "content": "The overall workflow of our hierarchical search is summarized in Algorithm 1. To begin with, the video is first split into coarse-grained clips each consisting of a collection of non-overlapped frames. Then, we calculate the model loss for each clip by representing it with the averaged feature vector of all frame inside it, and utilize the information to create an initial solution composed of the clip with the lowest model loss repeated \\( n \\) times. On top of the initial searching point, we adapt Guided Local Search to find the best clip combination by defining a problem-specific penalty to escape from local optimum points. The details of Guided Local Search will be introduced in Appendix. After searching on coarse-grained clips, we again incorporate Guided Local Search to find the best fine-grained frame combinations by replacing each derived clip with a frame inside it. Via hierarchical search, we have greatly reduced the search space and lowered the search cost significantly, while obtaining satisfying solutions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.715, + 0.388, + 0.731 + ], + "angle": 0, + "content": "3.3. Stage 2: Feature Mapping Function" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.738, + 0.469, + 0.783 + ], + "angle": 0, + "content": "The goal of the second stage is to identify the best frame combination produced in stage 1, given the input video frames by learning a feature mapping function \\(\\mathcal{F}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.784, + 0.469, + 0.857 + ], + "angle": 0, + "content": "Specifically, the feature mapping function \\(\\mathcal{F}\\) takes in the features of input frames \\(H_0\\) generated by a pre-trained feature extractor \\(\\theta\\), and outputs a predicted feature \\(\\hat{h} \\in \\mathcal{R}^d\\) representing a frame combination where \\(d\\) denotes the feature dimension:" + }, + { + "type": "equation", + "bbox": [ + 0.221, + 0.867, + 0.303, + 0.884 + ], + "angle": 0, + "content": "\\[\n\\hat {h} = \\mathcal {F} (H _ {0})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.885, + 0.391, + 0.904 + ], + "angle": 0, + "content": "where \\(H_0 = \\{h_i|h_i = \\theta (x_i)\\}_{i = 1}^m\\)" + }, + { + "type": "text", + "bbox": [ + 0.446, + 0.879, + 0.468, + 0.891 + ], + "angle": 0, + "content": "(2)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.091, + 0.892, + 0.121 + ], + "angle": 0, + "content": "where \\(\\theta\\) is the feature extractor, and \\(h_i \\in \\mathcal{R}^d\\) is the extracted feature vector for frame \\(x_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.892, + 0.209 + ], + "angle": 0, + "content": "For the network structure of mapping function \\(\\mathcal{F}\\), we choose to incorporate transformer layers [29] to construct the spatio-temporal representations of the input frame features, and an aggregation function to aggregate the representations of variable lengths into a predicted feature vector \\(\\hat{h}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.21, + 0.892, + 0.247 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} H _ {l} = \\text {t r a n s f o r m e r} \\left(H _ {l - 1}\\right) \\tag {3} \\\\ \\hat {h} = a g g r (H _ {l}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.254, + 0.892, + 0.282 + ], + "angle": 0, + "content": "where \\(l\\) is the number of transformer layers in the mapping function." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.284, + 0.892, + 0.328 + ], + "angle": 0, + "content": "The objective of the mapping function is to minimize the distance between the predicted feature \\(\\hat{h}\\) and the aggregated feature vector of the searched frame combination \\(h^{*}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.34, + 0.736, + 0.357 + ], + "angle": 0, + "content": "\\[\n\\min \\quad d i s t (\\hat {h}, h ^ {*})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.359, + 0.847, + 0.378 + ], + "angle": 0, + "content": "where \\( h^* = \\text{aggr}(\\{h_k | h_k = \\theta(x_k), x_k \\in \\tilde{X}^*\\}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.868, + 0.351, + 0.891, + 0.364 + ], + "angle": 0, + "content": "(4)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.389, + 0.892, + 0.449 + ], + "angle": 0, + "content": "In our implementation, we incorporate cosine distance and mean-pooling as the distance function and aggregation function respectively, while other function choices can be further explored." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.459, + 0.887, + 0.475 + ], + "angle": 0, + "content": "3.4. Stage 3: Search to Infer Frame Combinations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.892, + 0.603 + ], + "angle": 0, + "content": "After the mapping function is learned, it can accurately predict the features of the best frame combinations for unseen videos without relying on the ground truth labels. The goal of this stage is to incorporate another search process to infer the frame combinations from the predicted features. Formally, the objective of the search is to find a frame combination \\(\\hat{X}\\) whose aggregated feature \\(h'\\) is closest to the given predicted feature \\(\\hat{h}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.615, + 0.755, + 0.632 + ], + "angle": 0, + "content": "\\[\n\\hat {X} = \\arg \\min (d i s t (h ^ {\\prime}, \\hat {h}))\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.641, + 0.632, + 0.654, + 0.644 + ], + "angle": 0, + "content": "\\(\\tilde{X}\\)" + }, + { + "type": "text", + "bbox": [ + 0.868, + 0.633, + 0.891, + 0.646 + ], + "angle": 0, + "content": "(5)" + }, + { + "type": "text", + "bbox": [ + 0.527, + 0.647, + 0.844, + 0.663 + ], + "angle": 0, + "content": "where \\(h^\\prime = aggr(\\{h_k|h_k = \\theta (x_k),x_k\\in \\tilde{X}\\})\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.75 + ], + "angle": 0, + "content": "As the evaluation in the search only involves the calculation of the cosine distance between vectors, which requires little computation, we directly apply Guided Local Search on the fine-grained frame level without the hierarchical setting applied in stage 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.764, + 0.632, + 0.781 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.79, + 0.892, + 0.82 + ], + "angle": 0, + "content": "In this section, we conduct extensive experiments aiming at investigating the following research questions:" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.83, + 0.89, + 0.861 + ], + "angle": 0, + "content": "- RQ1: Can the proposed SMS improve model performance over the base frame sampling method?" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.871, + 0.891, + 0.899 + ], + "angle": 0, + "content": "- RQ2: How does SMS perform compared to other state-of-the-art frame selection methods?" + }, + { + "type": "list", + "bbox": [ + 0.518, + 0.83, + 0.891, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10630" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.097, + 0.091, + 0.468, + 0.12 + ], + "angle": 0, + "content": "- RQ3: What's the computation efficiency of SMS for video inference?" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.132, + 0.468, + 0.162 + ], + "angle": 0, + "content": "- RQ4: How do the different components affect the performance of the proposed SMS?" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.172, + 0.468, + 0.202 + ], + "angle": 0, + "content": "- RQ5: Can SMS generalize well to spatio-temporal models, e.g., transformer based video models?" + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.091, + 0.468, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.212, + 0.267, + 0.229 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.235, + 0.194, + 0.249 + ], + "angle": 0, + "content": "4.1.1 Datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.259, + 0.468, + 0.379 + ], + "angle": 0, + "content": "We evaluate our SMS method on 3 action recognition benchmarks including ActivityNet V1.3 [2], FCVID [18] and UCF101 [27]. The videos in ActivityNet and FCVID are untrimmed with average video lengths of 117 and 167 seconds respectively, while UCF101 dataset contains trimmed short videos with an average length of 7.21 seconds. Table 1 summarizes the detailed information of the experimental datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.399, + 0.199, + 0.413 + ], + "angle": 0, + "content": "4.1.2 Baselines." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.422, + 0.468, + 0.466 + ], + "angle": 0, + "content": "We compare the proposed SMS with the base selection method and the following state-of-the-art frame selection methods:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.478, + 0.468, + 0.538 + ], + "angle": 0, + "content": "- Base is a sparse sampling method proposed in TSN [31], where videos are divided into segments of equal length, and frames are randomly sampled within each segment." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.548, + 0.468, + 0.622 + ], + "angle": 0, + "content": "- AdaFrame [35] incorporates reinforcement learning to adaptively select informative frames with a memory-augmented LSTM. At testing time, AdaFrame selects different number of frames for each video observed." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.633, + 0.468, + 0.664 + ], + "angle": 0, + "content": "- MARL [33] adopts multiple RL agents each responsible for adjusting the position of a selected frame." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.674, + 0.468, + 0.718 + ], + "angle": 0, + "content": "- SCSampler [19] proposes to select frames based on the prediction scores produced by a lightweight video model." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.729, + 0.468, + 0.773 + ], + "angle": 0, + "content": "- SMART [15] combines the single-frame predictive score with pair-wise interaction score to make decision on the frame selections." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.785, + 0.468, + 0.829 + ], + "angle": 0, + "content": "- LiteEval [34] selects important frames to extract fine features and adopts coarse features for the remaining frames." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "- ListenToLook [14] proposes to use audio information as video preview for frame selection. For a fair comparison, we follow AR-Net [24] and include the variant with only the visual modality." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.478, + 0.468, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.089, + 0.887, + 0.16 + ], + "angle": 0, + "content": "
DatasetTrainValActionsAvg. Duration
ActivityNet10,0244,926200117s
FCVID45,61145,612239167s
UCF1019,5373,7831017.21s
" + }, + { + "type": "table_caption", + "bbox": [ + 0.566, + 0.17, + 0.824, + 0.184 + ], + "angle": 0, + "content": "Table 1. Description of evaluation datasets." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.211, + 0.89, + 0.255 + ], + "angle": 0, + "content": "- AR-Net [24] aims to select the optimal resolutions for frames that are needed to correctly recognize the actions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.275, + 0.689, + 0.289 + ], + "angle": 0, + "content": "4.1.3 Evaluation metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.298, + 0.892, + 0.373 + ], + "angle": 0, + "content": "Following previous studies, we evaluate the performance of models using mean Average Precision (mAR), which is a commonly adopted metric in action recognition tasks, calculated as the mean value of the average precision over all action classes." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.392, + 0.719, + 0.406 + ], + "angle": 0, + "content": "4.1.4 Implementation details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.505 + ], + "angle": 0, + "content": "In the first stage of hierarchical searching, the clip length \\( K \\) is set to 30. For the feature mapping network, we adopt a two-layer transformer network with a hidden dimension of 2,048. The feature extraction network used in our implementation is a ResNet-50 network [16] pre-trained on the Kinetics dataset [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.627 + ], + "angle": 0, + "content": "For the data pre-processing for action recognition tasks, we decode the video at 1 fps for long videos in ActivityNet and FCVID and 55 fps for short videos in UCF101 to retrieve the rgb frames, which are augmented during training by resizing the short side to 256, random cropped and resized to \\(224^2\\), after which a random flip with a probability of 0.5 is applied. For inference, we resize all frames to \\(256^2\\) and perform three-crop." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.792 + ], + "angle": 0, + "content": "For the training of action recognition models, we choose ResNet-50 as the backbone and run 100 epochs using an SGD optimizer with a momentum of 0.9, and a step learning rate schedule which decays the learning rate by a factor of 10 every 40 epochs. For ActivityNet and FCVID, we use an initial learning rate of 0.005, and a batch size of 64. For UCF101 with shorter videos, we increase the batch size to 128 and adjust the initial learning rate to 0.00256. All models are trained using code adapted from MMAction2 [4] on eight Nvidia-A100 GPUs. And we report the average performance and standard deviation of three runs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.802, + 0.757, + 0.818 + ], + "angle": 0, + "content": "4.2. Effectiveness Analysis (RQ1)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "To validate the effectiveness of the proposed SMS, we make a comprehensive comparison with the base method on both long-video dataset ActivityNet and FCVID, and short-video dataset UCF101. As the video lengths of different datasets vary in a large range, we choose to select different" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10631" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.16 + ], + "angle": 0, + "content": "
# FramesActivityNetFCVIDUCF101
816258162538
Base177.34 ± 0.0679.41 ± 0.0580.04 ± 0.2483.84 ± 0.0585.34 ± 0.0385.65 ± 0.0490.65 ± 0.1390.70 ± 0.10
SMS (infer only)82.76 ± 0.1583.78 ± 0.0883.85 ± 0.1786.35 ± 0.0386.94 ± 0.0687.08 ± 0.0491.45 ± 0.1291.58 ± 0.09
SMS (train & infer)83.72 ± 0.0584.35 ± 0.0884.56 ± 0.0886.54 ± 0.0687.25 ± 0.1187.59 ± 0.0191.94 ± 0.1592.25 ± 0.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.17, + 0.893, + 0.198 + ], + "angle": 0, + "content": "Table 2. Performance comparison of the proposed SMS and the base method. In SMS (infer only), frames are selected with our method only during inference. In SMS (train & infer), frames are selected with SMS during both training and inference." + }, + { + "type": "table", + "bbox": [ + 0.189, + 0.212, + 0.785, + 0.372 + ], + "angle": 0, + "content": "
MethodBackboneActivityNetFCVID
# FramesmAPimpr.# FramesmAPimpr.
SCSamplerResNet-501072.90.41081.00.0
AdaFrameResNet-1018.6571.53.78.2180.21.8
MARLResNet-101872.90.4---
SMARTResNet-1011073.1-1082.1-
SMART*ResNet-50880.673.33883.35-0.49
SMS_10%ResNet-50882.124.78885.691.85
SMSResNet-50883.726.38886.542.70
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.381, + 0.895, + 0.439 + ], + "angle": 0, + "content": "Table 3. Performance comparison of the proposed SMS and other state-of-the-art frame selection methods. We show both their performance and the their reported improvements over the base sampling method, due to the inconsistent base performance among different methods. Results of baselines are retrieved from literature, except for SMART*, which is implemented using the same features and implementation settings as SMS. We have also included the results of SMS learned only on \\(10\\%\\) training data as SMS_10%." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.473, + 0.586 + ], + "angle": 0, + "content": "number of frames for each video in these datasets, where 8, 16 and 25 frames are selected for long videos in ActivityNet and FCVID, and 3 and 8 frames are selected for short videos in UCF101. Furthermore, we conduct experiments to select frames with SMS only on test data during the inference of pre-trained base models, and incorporate SMS in both the training and inference process. The experimental results are shown in Table 2, from which we can observe that:" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.596, + 0.47, + 0.748 + ], + "angle": 0, + "content": "- When applied to test data, compared to the base sampling method, SMS (infer only) significantly improves the average mAP on different numbers of selected frames by \\(4.53\\%\\) and \\(1.85\\%\\) on ActivityNet and FCVID, respectively. While SMS (infer only) significantly improves model performance, SMS (train & infer) improves the mAP by \\(0.75\\%\\) and \\(0.34\\%\\) mAP on ActivityNet and FCVID. This observation demonstrates that the frames selected with the SMS method are beneficial to both model training and inference." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.759, + 0.47, + 0.865 + ], + "angle": 0, + "content": "While most other frame selection methods only focus on long untrimmed video tasks, SMS is also effective on short trimmed video tasks. Despite that in UCF101, the irrelevant parts of videos are trimmed off, which to a great degree limits the potential of frame selection, SMS still achieves steady improvement of \\(1.42\\%\\) average mAP over the base method with the same number" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.596, + 0.47, + 0.865 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.465, + 0.661, + 0.478 + ], + "angle": 0, + "content": "of selected frames." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.787, + 0.502 + ], + "angle": 0, + "content": "4.3. Performance Comparison (RQ2)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.599 + ], + "angle": 0, + "content": "In order to justify the benefit of our new learning paradigm of frame selection, we compare SMS with other classic frame selection methods on ActivityNet and FCVID. We choose ResNet as the backbone architecture of the action recognition model and report the performance with similar number of selected frames ranges from 8 to 10." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.893, + 0.809 + ], + "angle": 0, + "content": "As the implementation and training details are different among the frame selection methods, the performances of the base models are inconsistent. Therefore, directly comparing the reported performances may be unfair. Moreover, due to the lack of source codes and models, we are unable to compare all methods under the same settings, especially for the RL-based methods whose results are difficult to reproduce. To make a fairer comparison, in addition to the absolute performance, we also compare the relative improvements of the frame selection methods over the base sampling method. Also, we have implemented the most recent frame selection method, SMART [15], using the same features and implementation settings as our proposed SMS, and include its results as SMART*." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.894, + 0.902 + ], + "angle": 0, + "content": "The comparison results are demonstrated in Table 3, from which we can see that with the least number of selected frames and the smallest backbone model, the proposed SMS achieves the best performance of \\(83.72\\%\\) and \\(86.54\\%\\) mAP on ActivityNet and FCVID respectively. Moreover, even with the higher-performance base models" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.471, + 0.902 + ], + "angle": 0, + "content": "1The base performance in our paper is higher compared to it in other papers, due to the better codebase and training settings." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10632" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.097, + 0.46, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.326, + 0.472, + 0.396 + ], + "angle": 0, + "content": "Figure 2. Comparison of SMS with other approaches in terms of performance vs. inference cost (model size per video) evaluated on ActivityNet. We control the inference cost by varying \\( m \\), the number of candidate frames in a video from which \\( n = 8 \\) best frames are to be selected." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.47, + 0.514 + ], + "angle": 0, + "content": "which are harder to improve, SMS still obtains the largest improvements of \\(6.48\\%\\) and \\(2.70\\%\\) among all frame selection methods. In a fair comparison with the same implementation settings, our method significantly outperforms SMART* by \\(3.05\\%\\) and \\(3.19\\%\\) respectively on ActivityNet and FCVID." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.639 + ], + "angle": 0, + "content": "The reason of our success is due to our novel training paradigm of \"Search-Map-Search\", where an efficient hierarchical search method is incorporated to find the best frame combinations, which better models the frame interactions. Moreover, in SMS, a feature mapping function is learned to map an input video directly to the optimal frame combination, which is theoretically superior to the one-by-one frame selection adopted by existing methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.313, + 0.667 + ], + "angle": 0, + "content": "4.4. Efficiency Analysis (RQ3)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.673, + 0.47, + 0.749 + ], + "angle": 0, + "content": "We now analyze the efficiency of SMS and compare it with other frame selection methods in terms of action recognition performance versus inference cost (evaluated by the model size per video. For a fair comparison, we only include the results that use ResNet as the backbone model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In order to evaluate the tradeoff between performance and inference efficiency, we first uniformly sub-sample \\( m \\) candidate frames that constitute the search space for each video from which \\( n = 8 \\) best frames are to be selected. As \\( m \\) increases, features are extracted from more candidate frames, and the resulting frame selection becomes more effective, while the inference cost becomes larger. As demonstrated in Figure 2, the action recognition performance of SMS grows rapidly from \\( m = 8 \\) to \\( m = 25 \\), while further increasing \\( m \\) to 50 or 100 incurs only slight increase in" + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.11, + 0.843, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.275, + 0.895, + 0.305 + ], + "angle": 0, + "content": "Figure 3. The evaluation of different search algorithms on 100 videos, given by the average loss over the number of evaluations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.894, + 0.391 + ], + "angle": 0, + "content": "performance but huge inference overhead. In practice, one can easily achieve a good tradeoff between performance and cost accordingly by tuning the number of candidate frames \\( m \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.894, + 0.469 + ], + "angle": 0, + "content": "In comparison with other approaches, SMS achieves higher action recognition performance and beats other methods under different computation resource constraints, showing the effectiveness of the proposed search-mapping-search paradigm in frame selection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.481, + 0.707, + 0.498 + ], + "angle": 0, + "content": "4.5. Ablation Study (RQ4)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.506, + 0.892, + 0.536 + ], + "angle": 0, + "content": "This subsection aims to analyze the effects of different components designed in our proposed SMS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.894, + 0.612 + ], + "angle": 0, + "content": "Search algorithm. We have conducted experiments to compare the performance and efficiency of our designed Hierarchical Guided Local Search algorithm with other powerful search algorithms such as Fast Genetic Algorithm [6] and the frame-level Guided Local Search [30]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.84 + ], + "angle": 0, + "content": "In Figure 3, we show the best loss averaged on 100 randomly selected videos with different search algorithms, and their corresponding search cost measured by the number of evaluations. By adopting different clip length \\( K \\), our proposed hierarchical search algorithm can trade off between the search performance and the search cost. From Figure 3, we can see that using the same number of evaluations, our hierarchical search achieves better results compared to Fast Genetic Algorithm, by more effectively exploiting the prior knowledge of the per-frame loss information. The original Guided Local Search without hierarchical design is extremely costly which requires nearly 3,000 evaluations per video. Contrastively, our algorithm is more efficient with the hierarchical design, and achieves comparable performance with far less computation cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Feature mapping network. The process of feature mapping aims to transform the input frame features to the feature of target combination. We have conducted experiments to explore the impact of different network architectures and" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "10633" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.154, + 0.089, + 0.817, + 0.196 + ], + "angle": 0, + "content": "
Feature Extractor (Training Source)Mapping Model ArchPerformanceInference GFLOPs
ResNet-50 (Kinetics)Transformer83.721.50
ResNet-50 (Kinetics)MLP83.220.01
ResNet-50 (ImageNet)Transformer79.971.50
ResNet-50 (ActivityNet)Transformer81.061.50
MobileNet-V2 (Kinetics)Transformer79.530.93
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.207, + 0.893, + 0.237 + ], + "angle": 0, + "content": "Table 4. Ablation analysis results in mAP (%) on ActivityNet using 8 frames with different feature extractors and feature mapping model architectures. The feature mapping inference GFLOPs per video is also provided." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.259, + 0.465, + 0.351 + ], + "angle": 0, + "content": "
Backbone# FramesMethodPerformance
TimeSFformer8Dense84.33
Base90.11
SMART*90.53
SMS91.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.391 + ], + "angle": 0, + "content": "Table 5. The ActivityNet evaluation results in mAP (%) using different frame sampling strategies on TimeSFformer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.424, + 0.356, + 0.438 + ], + "angle": 0, + "content": "training data sources for feature mapping." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.441, + 0.47, + 0.637 + ], + "angle": 0, + "content": "For the network architecture, we adopt transformers to sequentially modeling the frame features with their spatiotemporal relations taken into consideration. Another simple applicable design is to adopt a mean-pooling layer that aggregates all the features of frames into a single feature vector, followed by a simpler two-layer MLP network. In Table 4, row 1 and 2 compares the performance and the inference efficiency of the two designs. As we can see, using transformer model as the mapping function outperforms MLP design by \\(0.5\\%\\) mAP due to the better representation ability, while the inference cost of both designs are small and negligible (less than 2 GFLOPs) compared to the cost of frame feature extractions (tens or hundreds GFLOPs)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.717 + ], + "angle": 0, + "content": "Feature extractor. We have analyzed the effect of different feature extractor settings by trying smaller model structure, e.g., MobileNet-V2 [25], and different pre-trained data sources including ImageNet [5], Kinetics [3] and ActivityNet [2]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Comparing the results of row 1, 3 and 4 in Table 4, we can see that the pre-training data of feature extractor can make a difference. The feature extractor trained on the largest Kinetics dataset achieves the best performance as it better captures the semantics of actions by training on more related samples, compared to the ones trained on smaller ActivityNet dataset and out-domain ImageNet dataset. Besides, as shown in row 5 of Table 4, using smaller models such as MobileNet-V2 for extractor can lead to performance decline. In general, the representation capability of feature extractors is valuable for frame selection to recognize the important frames and find the best frame combinations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.261, + 0.783, + 0.278 + ], + "angle": 0, + "content": "4.6. Generalizability Analysis (RQ5)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.285, + 0.892, + 0.375 + ], + "angle": 0, + "content": "It is a natural question to ask if the frames selected by SMS can also be beneficial to spatio-temporal video models. To find out the answer to this question, we have conducted an experiment to apply the SMS selected frames on TimeSFformer [1], which incorporates the transformer architecture and is one of the most advanced video models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.893, + 0.512 + ], + "angle": 0, + "content": "The results are shown in Table 5. The dense frame sampling strategy incorporated in the original TimeSFormer implementation randomly samples a clip containing 8 successive frames from videos, and achieves \\(84.33\\%\\) mAP on ActivityNet. However, in untrimmed video dataset, dense sampling can only captures a small part of the video and may miss important information. In contrast, the base sampling strategy selects frames uniformly from videos and achieves \\(90.11\\%\\) mAP, while SMART* achieves \\(90.53\\%\\) mAP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.634 + ], + "angle": 0, + "content": "By using the input frames selected by SMS, we obtain a significant performance gain of \\(1.86\\%\\) over the base sampling strategy and \\(1.44\\%\\) over SMART*, and achieve \\(91.97\\%\\) mAP. This improvement demonstrates the strong generalizability of SMS across different model architectures, and that SMS is not only effective on 2D video modeling, but can also capture the spatio-temporal relationship among frames and is beneficial to 3D video model learning." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.649, + 0.619, + 0.665 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In this paper, we propose a new learning paradigm for frame selection, called \"Search-Map-Search\", which consists of a search stage to efficiently find the best frame combination with a hierarchical search algorithm, a feature mapping stage that learns to transform the input frame features directly into the feature of the searched combination, and another search stage that selects frames based on the mapped feature. Compared with existing frame selection methods, SMS is a more accurate learning paradigm that takes advantage of efficient search and supervised feature mapping to directly select the best combination of frames as one entity, which better captures the frame interactions. Experimental results show that SMS achieves significant performance gains on multiple action recognition benchmarks, and outperforms other strong baseline methods." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10634" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? In ICML, volume 2, page 4, 2021. 2, 8" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.158, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Fabian Caba Heilbron, Victor Escorcia, Bernard Ghanem, and Juan Carlos Niebles. Activitynet: A large-scale video benchmark for human activity understanding. 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Frame selection aims to extract the most informative and representative frames to help a model better understand video content. Existing frame selection methods either individually sample frames based on per-frame importance prediction, without considering interaction among frames, or adopt reinforcement learning agents to find representative frames in succession, which are costly to train and may lead to potential stability issues. To overcome the limitations of existing methods, we propose a Search-Map-Search learning paradigm which combines the advantages of heuristic search and supervised learning to select the best combination of frames from a video as one entity. By combining search with learning, the proposed method can better capture frame interactions while incurring a low inference overhead. Specifically, we first propose a hierarchical search method conducted on each training video to search for the optimal combination of frames with the lowest error on the downstream task. A feature mapping function is then learned to map the frames of a video to the representation of its target optimal frame combination. During inference, another search is performed on an unseen video to select a combination of frames whose feature representation is close to the projected feature representation. Extensive experiments based on several action recognition benchmarks demonstrate that our frame selection method effectively improves performance of action recognition models, and significantly outperforms a number of competitive baselines. + +# 1. Introduction + +Videos have proliferated online in recent years with the popularity of social media, and have become a major form of content consumption on the Internet. The abundant video data has greatly encouraged the development of deep learning techniques for video content understanding. As one of the most important tasks, action recognition aims to identify relevant actions described in videos, and plays a vital role to other downstream tasks like video retrieval and recommendation. + +Due to the high computational cost of processing frames in a video, common practices of action recognition involve sampling a subset of frames or clips uniformly [31] or densely [26, 37] from a given video a serve as the input to a content understanding model. However, since frames in a video may contain redundant information and are not equally important, simple sampling methods are often incapable of capturing such knowledge and hence can lead to sub-optimal action recognition results. + +Prior studies attempt to actively select relevant video frames to overcome the limitation of straightforward sampling, achieving improvements to model performance. Heuristic methods are proposed to rank and select frames according to the importance score of each frame/clip calculated by per-frame prediction [15, 19]. Despite the effectiveness, these methods heavily rely on per-frame features, without considering the interaction or diversity among selected frames. Reinforcement learning (RL) has also been proposed to identify informative frames by formulating frame selection as a Markov decision process (MDP) [8, 9, 33,35,36]. However, existing RL-based methods may suffer from training stability issues and rely on a massive amount of training samples. Moreover, RL methods make an MDP assumption that frames are selected sequentially depending + +on observations of already selected frames, and thus cannot adjust prior selections based on new observations. + +In this work, we propose a new learning paradigm named Search-Map-Search (SMS), which directly searches for the best combination of frames from a video as one entity. SMS formulates the problem of frame selection from the perspective of heuristic search in a large space of video frame combinations, which is further coupled with a learnable mapping function to generalize to new videos and achieve efficient inference. + +Specifically, we propose a hierarchical search algorithm to efficiently find the most favorable frame combinations on training videos, which are then used as explicit supervision information to train a feature mapping function that maps the feature vectors of an input video to the feature vector of the desirable optimal frame combination. During inference on an unseen query video, the learned mapping function projects the query video onto a target feature vector for the desired frame combination, where another search process retrieves the actual frame combination that approximates the target feature vector. By combining search with learning, the proposed SMS method can better capture frame interactions while incurring a low inference cost. + +The effectiveness of SMS is extensively evaluated on both the long untrimmed action recognition benchmarks, i.e., ActivityNet [2] and FCVID [18], and the short trimmed UCF101 task [27]. Experimental results show that SMS can significantly improve action recognition models and precisely recognize and produce effective frame selections. Furthermore, SMS significantly outperforms a range of other existing frame selection methods for the same number of frames selected, while can still generate performance higher than existing methods using only $10\%$ of all labeled video samples for training. + +# 2. Related Work + +Action Recognition. 2D ConvNets have been widely utilized for action recognition, where per-frame features are first extracted and later aggregated with different methods such as temporal averaging [31], recurrent networks [7, 20, 37], and temporal channel shift [10, 21, 23]. Some studies leveraged both the short-term and long-term temporal relationships by two-stream architectures [12, 13]. To jointly capture the spatio-temporal information of videos, 3D ConvNets were proposed, including C3D [28], I3D [3] and X3D [11]. Transformer architecture [29] have also been applied to video understanding by modeling the spatiotemporal information with attention [1, 22]. + +In this paper, we follow the previous frame selection work and apply our method mainly on the temporal averaging 2D ConvNets. + +Frame Selection. The problem of selecting important frames within a video has been investigated in order to im + +prove the performance and reduce the computational cost. + +Many researchers focused on selecting frames based on the per-frame heuristic score. SCSampler [19] proposed to select frames based on the predicted scores of a lightweight video model as the usefulness of frames. SMART [15] incorporated an attention module that takes randomly selected frame pairs as input to model the relationship between frames. However, these methods select frames individually regardless of interactions between selected frames, which may lead to redundant selections. + +Reinforcement learning (RL) approaches are widely adopted in frame selection to find the effective frames in a trail-and-error setting. FastForward [9] and AdaFrame [35] adopted a single RL agent to generate a decision on the next frame, and updated the network with policy gradient. MARL [33] formulated the frame sampling process as multiple parallel Markov Decision Processes, and adopted multiple RL agents each responsible for determining a frame. Although the RL-based approaches are effective, the training stability issue and the requirement of huge amount of training samples with high computational overhead remain a problem. + +Recent studies combined frame selection with other techniques to improve the model efficiency. LiteEval [34] adopted a two-level feature extraction procedure, where fine expensive features were extracted for important frames, and coarse frames were used for the remaining frames. ListenToLook [14] proposed to use audio information as an efficient video preview for frame selection. AR-Net [24] aimed at selecting the optimal resolution for each frame that is needed to correctly recognize the actions, and learns a differentiable policy using Gumbel Softmax trick [17]. + +Our work focuses on the classic task of selecting a subset of frames based on visual information. Different from existing methods, our work incorporates a new "Search-Map-Search" paradigm that leverages efficient search and supervised feature mapping to explicitly find the best frame combinations, and achieves excellent performance outperforming other frame selection methods. + +# 3. Methodology + +# 3.1. Overall Architecture + +Figure 1 gives an overview of our proposed framework, which consists of three stages: a search stage, a feature mapping stage, and another search stage. The training process of our method involves the first two stages, while the inference process involves the last two. + +Specifically, the goal of the first search stage is to find the best frame combinations in training videos with the lowest model losses, which serve as the supervisory target information for the feature mapping stage. We design an efficient hierarchical algorithm coupled with Guided Local + +![](images/3bcfd27c2a31aad153aa5cfd6724b3ae2d58c0746bc8e787ea371111c1a040f7.jpg) +Figure 1. An overview of the proposed "Search-Map-Search" method. It contains three stages, where in the first stage, an efficient hierarchical search algorithm is used to derive the best frame combinations with lowest losses, which are utilized as the supervised information to train a feature mapping function in the second stage. In the third stage, for a query video, we incorporate another search process to infer the frame combination whose features are closest to the combination feature predicted with the trained feature mapping function. + +Search [30] to identify the effective frame combinations at a low search cost. + +In the second stage, a feature extractor is employed to extract input frame features from the training video frames, and the feature of the best combination from search results. Then, a feature mapping function is trained via supervised learning by taking the input frame features as input, and transforming it to the target feature of the best combination. + +In the third stage, we incorporate another search process to infer the effective frame combination whose feature is closest to the predicted feature from the well-trained feature mapping function. + +# 3.2. Stage 1: Search for Best Frame Combinations + +Given an action recognition task with a pre-trained model $M$ and a training dataset $D^{tr} = \{X, y\}^{|\hat{D}^{tr}|}$ , where $X = \{x_{i}\}_{i=1}^{m}$ represents a video sample made up of a collection of $m$ frames, and $y$ is the action label for the video, our goal of stage 1 is to find the best frame combination $\tilde{X}^*$ . + +with $n$ frames for each training video $X$ that minimizes the model loss: + +$$ +\tilde {X} ^ {*} = \underset {\tilde {X}} {\arg \min } \mathcal {L} (M (\tilde {X}), y), \tag {1} +$$ + +$$ +w h e r e \quad \tilde {X} = \left\{x _ {k} \mid x _ {k} \in X \right\} ^ {n}, +$$ + +where $\mathcal{L}$ is the loss function of the action recognition task. Note that repetitive selection of the same frame is allowed in our setting, as we believe that repeated important frames are better than meaningless frames. + +In order to efficiently find the best frame combinations, we have designed a hierarchical search algorithm which exploits the high similarities of adjacent frames by performing search hierarchically on coarse-grained clips first, and then on the fine-grained frames. Besides, we incorporate Guided Local Search [30] in our algorithm to exploit perframe losses as prior information for a good starting search point, which further reduces search costs and empirically outperforms other strong search algorithms such as Genetic Algorithm [32]. + +# Algorithm 1: Hierarchical Search + +Input: Video $X$ , Clip Length $K$ , Combination Length $n$ + +Output: Frame Combination $\hat{X}^*$ + +/\*clipsearchphase + +\* + +1 Split the video into clips each consisting of $K$ frames +2 Prepare an initial solution $\tilde{C}_0$ containing the clip with the lowest loss repeated $n$ times +3 Perform Guided Local Search to improve $\tilde{C}_0$ and get $\tilde{C}^* = \{C_k\}_{k=1}^n$ + +/\*frame search phase + +\* + +4 Define search space for each position in combination $S^F = \{S_k|S_k = \{x_j|x_j\in C_k\} \}_{k = 1}^n$ on top of $\tilde{C}^*$ +5 Randomly initialize solution $\tilde{X}_0$ from $S^F$ +6 Perform Guided Local Search to improve $\tilde{X}_0$ and get $\tilde{X}^* = \{x_k\}_{k=1}^n$ + +The overall workflow of our hierarchical search is summarized in Algorithm 1. To begin with, the video is first split into coarse-grained clips each consisting of a collection of non-overlapped frames. Then, we calculate the model loss for each clip by representing it with the averaged feature vector of all frame inside it, and utilize the information to create an initial solution composed of the clip with the lowest model loss repeated $n$ times. On top of the initial searching point, we adapt Guided Local Search to find the best clip combination by defining a problem-specific penalty to escape from local optimum points. The details of Guided Local Search will be introduced in Appendix. After searching on coarse-grained clips, we again incorporate Guided Local Search to find the best fine-grained frame combinations by replacing each derived clip with a frame inside it. Via hierarchical search, we have greatly reduced the search space and lowered the search cost significantly, while obtaining satisfying solutions. + +# 3.3. Stage 2: Feature Mapping Function + +The goal of the second stage is to identify the best frame combination produced in stage 1, given the input video frames by learning a feature mapping function $\mathcal{F}$ . + +Specifically, the feature mapping function $\mathcal{F}$ takes in the features of input frames $H_0$ generated by a pre-trained feature extractor $\theta$ , and outputs a predicted feature $\hat{h} \in \mathcal{R}^d$ representing a frame combination where $d$ denotes the feature dimension: + +$$ +\hat {h} = \mathcal {F} (H _ {0}) +$$ + +where $H_0 = \{h_i|h_i = \theta (x_i)\}_{i = 1}^m$ + +(2) + +where $\theta$ is the feature extractor, and $h_i \in \mathcal{R}^d$ is the extracted feature vector for frame $x_i$ . + +For the network structure of mapping function $\mathcal{F}$ , we choose to incorporate transformer layers [29] to construct the spatio-temporal representations of the input frame features, and an aggregation function to aggregate the representations of variable lengths into a predicted feature vector $\hat{h}$ : + +$$ +\begin{array}{l} H _ {l} = \text {t r a n s f o r m e r} \left(H _ {l - 1}\right) \tag {3} \\ \hat {h} = a g g r (H _ {l}), \\ \end{array} +$$ + +where $l$ is the number of transformer layers in the mapping function. + +The objective of the mapping function is to minimize the distance between the predicted feature $\hat{h}$ and the aggregated feature vector of the searched frame combination $h^{*}$ : + +$$ +\min \quad d i s t (\hat {h}, h ^ {*}) +$$ + +where $h^* = \text{aggr}(\{h_k | h_k = \theta(x_k), x_k \in \tilde{X}^*\})$ . + +(4) + +In our implementation, we incorporate cosine distance and mean-pooling as the distance function and aggregation function respectively, while other function choices can be further explored. + +# 3.4. Stage 3: Search to Infer Frame Combinations + +After the mapping function is learned, it can accurately predict the features of the best frame combinations for unseen videos without relying on the ground truth labels. The goal of this stage is to incorporate another search process to infer the frame combinations from the predicted features. Formally, the objective of the search is to find a frame combination $\hat{X}$ whose aggregated feature $h'$ is closest to the given predicted feature $\hat{h}$ : + +$$ +\hat {X} = \arg \min (d i s t (h ^ {\prime}, \hat {h})) +$$ + +$\tilde{X}$ + +(5) + +where $h^\prime = aggr(\{h_k|h_k = \theta (x_k),x_k\in \tilde{X}\})$ + +As the evaluation in the search only involves the calculation of the cosine distance between vectors, which requires little computation, we directly apply Guided Local Search on the fine-grained frame level without the hierarchical setting applied in stage 1. + +# 4. Experiments + +In this section, we conduct extensive experiments aiming at investigating the following research questions: + +- RQ1: Can the proposed SMS improve model performance over the base frame sampling method? +- RQ2: How does SMS perform compared to other state-of-the-art frame selection methods? + +- RQ3: What's the computation efficiency of SMS for video inference? +- RQ4: How do the different components affect the performance of the proposed SMS? +- RQ5: Can SMS generalize well to spatio-temporal models, e.g., transformer based video models? + +# 4.1. Experimental Setup + +# 4.1.1 Datasets. + +We evaluate our SMS method on 3 action recognition benchmarks including ActivityNet V1.3 [2], FCVID [18] and UCF101 [27]. The videos in ActivityNet and FCVID are untrimmed with average video lengths of 117 and 167 seconds respectively, while UCF101 dataset contains trimmed short videos with an average length of 7.21 seconds. Table 1 summarizes the detailed information of the experimental datasets. + +# 4.1.2 Baselines. + +We compare the proposed SMS with the base selection method and the following state-of-the-art frame selection methods: + +- Base is a sparse sampling method proposed in TSN [31], where videos are divided into segments of equal length, and frames are randomly sampled within each segment. +- AdaFrame [35] incorporates reinforcement learning to adaptively select informative frames with a memory-augmented LSTM. At testing time, AdaFrame selects different number of frames for each video observed. +- MARL [33] adopts multiple RL agents each responsible for adjusting the position of a selected frame. +- SCSampler [19] proposes to select frames based on the prediction scores produced by a lightweight video model. +- SMART [15] combines the single-frame predictive score with pair-wise interaction score to make decision on the frame selections. +- LiteEval [34] selects important frames to extract fine features and adopts coarse features for the remaining frames. +- ListenToLook [14] proposes to use audio information as video preview for frame selection. For a fair comparison, we follow AR-Net [24] and include the variant with only the visual modality. + +
DatasetTrainValActionsAvg. Duration
ActivityNet10,0244,926200117s
FCVID45,61145,612239167s
UCF1019,5373,7831017.21s
+ +Table 1. Description of evaluation datasets. + +- AR-Net [24] aims to select the optimal resolutions for frames that are needed to correctly recognize the actions. + +# 4.1.3 Evaluation metrics. + +Following previous studies, we evaluate the performance of models using mean Average Precision (mAR), which is a commonly adopted metric in action recognition tasks, calculated as the mean value of the average precision over all action classes. + +# 4.1.4 Implementation details. + +In the first stage of hierarchical searching, the clip length $K$ is set to 30. For the feature mapping network, we adopt a two-layer transformer network with a hidden dimension of 2,048. The feature extraction network used in our implementation is a ResNet-50 network [16] pre-trained on the Kinetics dataset [3]. + +For the data pre-processing for action recognition tasks, we decode the video at 1 fps for long videos in ActivityNet and FCVID and 55 fps for short videos in UCF101 to retrieve the rgb frames, which are augmented during training by resizing the short side to 256, random cropped and resized to $224^2$ , after which a random flip with a probability of 0.5 is applied. For inference, we resize all frames to $256^2$ and perform three-crop. + +For the training of action recognition models, we choose ResNet-50 as the backbone and run 100 epochs using an SGD optimizer with a momentum of 0.9, and a step learning rate schedule which decays the learning rate by a factor of 10 every 40 epochs. For ActivityNet and FCVID, we use an initial learning rate of 0.005, and a batch size of 64. For UCF101 with shorter videos, we increase the batch size to 128 and adjust the initial learning rate to 0.00256. All models are trained using code adapted from MMAction2 [4] on eight Nvidia-A100 GPUs. And we report the average performance and standard deviation of three runs. + +# 4.2. Effectiveness Analysis (RQ1) + +To validate the effectiveness of the proposed SMS, we make a comprehensive comparison with the base method on both long-video dataset ActivityNet and FCVID, and short-video dataset UCF101. As the video lengths of different datasets vary in a large range, we choose to select different + +
# FramesActivityNetFCVIDUCF101
816258162538
Base177.34 ± 0.0679.41 ± 0.0580.04 ± 0.2483.84 ± 0.0585.34 ± 0.0385.65 ± 0.0490.65 ± 0.1390.70 ± 0.10
SMS (infer only)82.76 ± 0.1583.78 ± 0.0883.85 ± 0.1786.35 ± 0.0386.94 ± 0.0687.08 ± 0.0491.45 ± 0.1291.58 ± 0.09
SMS (train & infer)83.72 ± 0.0584.35 ± 0.0884.56 ± 0.0886.54 ± 0.0687.25 ± 0.1187.59 ± 0.0191.94 ± 0.1592.25 ± 0.10
+ +Table 2. Performance comparison of the proposed SMS and the base method. In SMS (infer only), frames are selected with our method only during inference. In SMS (train & infer), frames are selected with SMS during both training and inference. + +
MethodBackboneActivityNetFCVID
# FramesmAPimpr.# FramesmAPimpr.
SCSamplerResNet-501072.90.41081.00.0
AdaFrameResNet-1018.6571.53.78.2180.21.8
MARLResNet-101872.90.4---
SMARTResNet-1011073.1-1082.1-
SMART*ResNet-50880.673.33883.35-0.49
SMS_10%ResNet-50882.124.78885.691.85
SMSResNet-50883.726.38886.542.70
+ +Table 3. Performance comparison of the proposed SMS and other state-of-the-art frame selection methods. We show both their performance and the their reported improvements over the base sampling method, due to the inconsistent base performance among different methods. Results of baselines are retrieved from literature, except for SMART*, which is implemented using the same features and implementation settings as SMS. We have also included the results of SMS learned only on $10\%$ training data as SMS_10%. + +number of frames for each video in these datasets, where 8, 16 and 25 frames are selected for long videos in ActivityNet and FCVID, and 3 and 8 frames are selected for short videos in UCF101. Furthermore, we conduct experiments to select frames with SMS only on test data during the inference of pre-trained base models, and incorporate SMS in both the training and inference process. The experimental results are shown in Table 2, from which we can observe that: + +- When applied to test data, compared to the base sampling method, SMS (infer only) significantly improves the average mAP on different numbers of selected frames by $4.53\%$ and $1.85\%$ on ActivityNet and FCVID, respectively. While SMS (infer only) significantly improves model performance, SMS (train & infer) improves the mAP by $0.75\%$ and $0.34\%$ mAP on ActivityNet and FCVID. This observation demonstrates that the frames selected with the SMS method are beneficial to both model training and inference. +While most other frame selection methods only focus on long untrimmed video tasks, SMS is also effective on short trimmed video tasks. Despite that in UCF101, the irrelevant parts of videos are trimmed off, which to a great degree limits the potential of frame selection, SMS still achieves steady improvement of $1.42\%$ average mAP over the base method with the same number + +of selected frames. + +# 4.3. Performance Comparison (RQ2) + +In order to justify the benefit of our new learning paradigm of frame selection, we compare SMS with other classic frame selection methods on ActivityNet and FCVID. We choose ResNet as the backbone architecture of the action recognition model and report the performance with similar number of selected frames ranges from 8 to 10. + +As the implementation and training details are different among the frame selection methods, the performances of the base models are inconsistent. Therefore, directly comparing the reported performances may be unfair. Moreover, due to the lack of source codes and models, we are unable to compare all methods under the same settings, especially for the RL-based methods whose results are difficult to reproduce. To make a fairer comparison, in addition to the absolute performance, we also compare the relative improvements of the frame selection methods over the base sampling method. Also, we have implemented the most recent frame selection method, SMART [15], using the same features and implementation settings as our proposed SMS, and include its results as SMART*. + +The comparison results are demonstrated in Table 3, from which we can see that with the least number of selected frames and the smallest backbone model, the proposed SMS achieves the best performance of $83.72\%$ and $86.54\%$ mAP on ActivityNet and FCVID respectively. Moreover, even with the higher-performance base models + +![](images/ea6eed9ff9ff1930007ac5897f85f446c751a7abe20e896e795e6d96e1e43cb4.jpg) +Figure 2. Comparison of SMS with other approaches in terms of performance vs. inference cost (model size per video) evaluated on ActivityNet. We control the inference cost by varying $m$ , the number of candidate frames in a video from which $n = 8$ best frames are to be selected. + +which are harder to improve, SMS still obtains the largest improvements of $6.48\%$ and $2.70\%$ among all frame selection methods. In a fair comparison with the same implementation settings, our method significantly outperforms SMART* by $3.05\%$ and $3.19\%$ respectively on ActivityNet and FCVID. + +The reason of our success is due to our novel training paradigm of "Search-Map-Search", where an efficient hierarchical search method is incorporated to find the best frame combinations, which better models the frame interactions. Moreover, in SMS, a feature mapping function is learned to map an input video directly to the optimal frame combination, which is theoretically superior to the one-by-one frame selection adopted by existing methods. + +# 4.4. Efficiency Analysis (RQ3) + +We now analyze the efficiency of SMS and compare it with other frame selection methods in terms of action recognition performance versus inference cost (evaluated by the model size per video. For a fair comparison, we only include the results that use ResNet as the backbone model. + +In order to evaluate the tradeoff between performance and inference efficiency, we first uniformly sub-sample $m$ candidate frames that constitute the search space for each video from which $n = 8$ best frames are to be selected. As $m$ increases, features are extracted from more candidate frames, and the resulting frame selection becomes more effective, while the inference cost becomes larger. As demonstrated in Figure 2, the action recognition performance of SMS grows rapidly from $m = 8$ to $m = 25$ , while further increasing $m$ to 50 or 100 incurs only slight increase in + +![](images/21cbbbc35aae5ee552c864d6bae970522fe7c93ea96e9451da78384122920754.jpg) +Figure 3. The evaluation of different search algorithms on 100 videos, given by the average loss over the number of evaluations. + +performance but huge inference overhead. In practice, one can easily achieve a good tradeoff between performance and cost accordingly by tuning the number of candidate frames $m$ . + +In comparison with other approaches, SMS achieves higher action recognition performance and beats other methods under different computation resource constraints, showing the effectiveness of the proposed search-mapping-search paradigm in frame selection. + +# 4.5. Ablation Study (RQ4) + +This subsection aims to analyze the effects of different components designed in our proposed SMS. + +Search algorithm. We have conducted experiments to compare the performance and efficiency of our designed Hierarchical Guided Local Search algorithm with other powerful search algorithms such as Fast Genetic Algorithm [6] and the frame-level Guided Local Search [30]. + +In Figure 3, we show the best loss averaged on 100 randomly selected videos with different search algorithms, and their corresponding search cost measured by the number of evaluations. By adopting different clip length $K$ , our proposed hierarchical search algorithm can trade off between the search performance and the search cost. From Figure 3, we can see that using the same number of evaluations, our hierarchical search achieves better results compared to Fast Genetic Algorithm, by more effectively exploiting the prior knowledge of the per-frame loss information. The original Guided Local Search without hierarchical design is extremely costly which requires nearly 3,000 evaluations per video. Contrastively, our algorithm is more efficient with the hierarchical design, and achieves comparable performance with far less computation cost. + +Feature mapping network. The process of feature mapping aims to transform the input frame features to the feature of target combination. We have conducted experiments to explore the impact of different network architectures and + +
Feature Extractor (Training Source)Mapping Model ArchPerformanceInference GFLOPs
ResNet-50 (Kinetics)Transformer83.721.50
ResNet-50 (Kinetics)MLP83.220.01
ResNet-50 (ImageNet)Transformer79.971.50
ResNet-50 (ActivityNet)Transformer81.061.50
MobileNet-V2 (Kinetics)Transformer79.530.93
+ +Table 4. Ablation analysis results in mAP (%) on ActivityNet using 8 frames with different feature extractors and feature mapping model architectures. The feature mapping inference GFLOPs per video is also provided. + +
Backbone# FramesMethodPerformance
TimeSFformer8Dense84.33
Base90.11
SMART*90.53
SMS91.97
+ +Table 5. The ActivityNet evaluation results in mAP (%) using different frame sampling strategies on TimeSFformer. + +training data sources for feature mapping. + +For the network architecture, we adopt transformers to sequentially modeling the frame features with their spatiotemporal relations taken into consideration. Another simple applicable design is to adopt a mean-pooling layer that aggregates all the features of frames into a single feature vector, followed by a simpler two-layer MLP network. In Table 4, row 1 and 2 compares the performance and the inference efficiency of the two designs. As we can see, using transformer model as the mapping function outperforms MLP design by $0.5\%$ mAP due to the better representation ability, while the inference cost of both designs are small and negligible (less than 2 GFLOPs) compared to the cost of frame feature extractions (tens or hundreds GFLOPs). + +Feature extractor. We have analyzed the effect of different feature extractor settings by trying smaller model structure, e.g., MobileNet-V2 [25], and different pre-trained data sources including ImageNet [5], Kinetics [3] and ActivityNet [2]. + +Comparing the results of row 1, 3 and 4 in Table 4, we can see that the pre-training data of feature extractor can make a difference. The feature extractor trained on the largest Kinetics dataset achieves the best performance as it better captures the semantics of actions by training on more related samples, compared to the ones trained on smaller ActivityNet dataset and out-domain ImageNet dataset. Besides, as shown in row 5 of Table 4, using smaller models such as MobileNet-V2 for extractor can lead to performance decline. In general, the representation capability of feature extractors is valuable for frame selection to recognize the important frames and find the best frame combinations. + +# 4.6. Generalizability Analysis (RQ5) + +It is a natural question to ask if the frames selected by SMS can also be beneficial to spatio-temporal video models. To find out the answer to this question, we have conducted an experiment to apply the SMS selected frames on TimeSFformer [1], which incorporates the transformer architecture and is one of the most advanced video models. + +The results are shown in Table 5. The dense frame sampling strategy incorporated in the original TimeSFormer implementation randomly samples a clip containing 8 successive frames from videos, and achieves $84.33\%$ mAP on ActivityNet. However, in untrimmed video dataset, dense sampling can only captures a small part of the video and may miss important information. In contrast, the base sampling strategy selects frames uniformly from videos and achieves $90.11\%$ mAP, while SMART* achieves $90.53\%$ mAP. + +By using the input frames selected by SMS, we obtain a significant performance gain of $1.86\%$ over the base sampling strategy and $1.44\%$ over SMART*, and achieve $91.97\%$ mAP. This improvement demonstrates the strong generalizability of SMS across different model architectures, and that SMS is not only effective on 2D video modeling, but can also capture the spatio-temporal relationship among frames and is beneficial to 3D video model learning. + +# 5. Conclusion + +In this paper, we propose a new learning paradigm for frame selection, called "Search-Map-Search", which consists of a search stage to efficiently find the best frame combination with a hierarchical search algorithm, a feature mapping stage that learns to transform the input frame features directly into the feature of the searched combination, and another search stage that selects frames based on the mapped feature. Compared with existing frame selection methods, SMS is a more accurate learning paradigm that takes advantage of efficient search and supervised feature mapping to directly select the best combination of frames as one entity, which better captures the frame interactions. Experimental results show that SMS achieves significant performance gains on multiple action recognition benchmarks, and outperforms other strong baseline methods. + +# References + +[1] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. 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In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 4694–4702, 2015. 1, 2 \ No newline at end of file diff --git a/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/images.zip b/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1f522731762a3acdbbc768f076ba688ef338e98f --- /dev/null +++ b/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9e0334e06b0cfc0dd4178e6009ca610d02ec9a0599d4b706ad523f7f7a8e68cd +size 303429 diff --git a/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/layout.json b/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a3fa7157a1d729e3499d838a2d46b0af81d15bf2 --- /dev/null +++ b/2023/Search-Map-Search_ A Frame Selection Paradigm for Action Recognition/layout.json @@ -0,0 +1,8429 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 69, + 103, + 523, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 103, + 523, + 121 + ], + "spans": [ + { + "bbox": [ + 69, + 103, + 523, + 121 + ], + "type": "text", + "content": "Search-Map-Search: A Frame Selection Paradigm for Action Recognition" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 144, + 210, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 144, + 210, + 199 + ], + "spans": [ + { + "bbox": [ + 104, + 144, + 210, + 199 + ], + "type": "text", + "content": "Mingjun Zhao \nUniversity of Alberta \nEdmonton, Canada \nzhao2@ualberta.ca" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 239, + 144, + 341, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 239, + 144, + 341, + 199 + ], + "spans": [ + { + "bbox": [ + 239, + 144, + 341, + 199 + ], + "type": "text", + "content": "Yakun Yu \nUniversity of Alberta \nEdmonton, Canada \nyakun2@ualberta.ca" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 374, + 144, + 489, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 144, + 489, + 199 + ], + "spans": [ + { + "bbox": [ + 374, + 144, + 489, + 199 + ], + "type": "text", + "content": "Xiaoli Wang \nTencent \nShenzhen, China \nevexlwang@tencent.com" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 173, + 205, + 284, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 173, + 205, + 284, + 261 + ], + "spans": [ + { + "bbox": [ + 173, + 205, + 284, + 261 + ], + "type": "text", + "content": "Lei Yang \nTencent \nShenzhen, China \nyangalalei@gmail.com" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 326, + 205, + 419, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 205, + 419, + 260 + ], + "spans": [ + { + "bbox": [ + 326, + 205, + 419, + 260 + ], + "type": "text", + "content": "Di Niu \nTencent \nEdmonton, Canada \ndniu@ualberta.ca" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 144, + 289, + 191, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 289, + 191, + 301 + ], + "spans": [ + { + "bbox": [ + 144, + 289, + 191, + 301 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 331, + 289, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 289, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 289, + 691 + ], + "type": "text", + "content": "Despite the success of deep learning in video understanding tasks, processing every frame in a video is computationally expensive and often unnecessary in real-time applications. Frame selection aims to extract the most informative and representative frames to help a model better understand video content. Existing frame selection methods either individually sample frames based on per-frame importance prediction, without considering interaction among frames, or adopt reinforcement learning agents to find representative frames in succession, which are costly to train and may lead to potential stability issues. To overcome the limitations of existing methods, we propose a Search-Map-Search learning paradigm which combines the advantages of heuristic search and supervised learning to select the best combination of frames from a video as one entity. By combining search with learning, the proposed method can better capture frame interactions while incurring a low inference overhead. Specifically, we first propose a hierarchical search method conducted on each training video to search for the optimal combination of frames with the lowest error on the downstream task. A feature mapping function is then learned to map the frames of a video to the representation of its target optimal frame combination. During inference, another search is performed on an unseen video to select a combination of frames whose feature representation is close to the projected feature representation. Extensive experiments based on several action recognition benchmarks demonstrate that our frame selection method effectively improves performance of action recognition models, and significantly outperforms a number of competitive baselines." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 289, + 386, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 289, + 386, + 301 + ], + "spans": [ + { + "bbox": [ + 307, + 289, + 386, + 301 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 312, + 547, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 418 + ], + "type": "text", + "content": "Videos have proliferated online in recent years with the popularity of social media, and have become a major form of content consumption on the Internet. The abundant video data has greatly encouraged the development of deep learning techniques for video content understanding. As one of the most important tasks, action recognition aims to identify relevant actions described in videos, and plays a vital role to other downstream tasks like video retrieval and recommendation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 423, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 547, + 532 + ], + "type": "text", + "content": "Due to the high computational cost of processing frames in a video, common practices of action recognition involve sampling a subset of frames or clips uniformly [31] or densely [26, 37] from a given video a serve as the input to a content understanding model. However, since frames in a video may contain redundant information and are not equally important, simple sampling methods are often incapable of capturing such knowledge and hence can lead to sub-optimal action recognition results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 548, + 715 + ], + "type": "text", + "content": "Prior studies attempt to actively select relevant video frames to overcome the limitation of straightforward sampling, achieving improvements to model performance. Heuristic methods are proposed to rank and select frames according to the importance score of each frame/clip calculated by per-frame prediction [15, 19]. Despite the effectiveness, these methods heavily rely on per-frame features, without considering the interaction or diversity among selected frames. Reinforcement learning (RL) has also been proposed to identify informative frames by formulating frame selection as a Markov decision process (MDP) [8, 9, 33,35,36]. However, existing RL-based methods may suffer from training stability issues and rely on a massive amount of training samples. Moreover, RL methods make an MDP assumption that frames are selected sequentially depending" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10627" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "on observations of already selected frames, and thus cannot adjust prior selections based on new observations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 190 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 190 + ], + "type": "text", + "content": "In this work, we propose a new learning paradigm named Search-Map-Search (SMS), which directly searches for the best combination of frames from a video as one entity. SMS formulates the problem of frame selection from the perspective of heuristic search in a large space of video frame combinations, which is further coupled with a learnable mapping function to generalize to new videos and achieve efficient inference." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 192, + 286, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 286, + 346 + ], + "type": "text", + "content": "Specifically, we propose a hierarchical search algorithm to efficiently find the most favorable frame combinations on training videos, which are then used as explicit supervision information to train a feature mapping function that maps the feature vectors of an input video to the feature vector of the desirable optimal frame combination. During inference on an unseen query video, the learned mapping function projects the query video onto a target feature vector for the desired frame combination, where another search process retrieves the actual frame combination that approximates the target feature vector. By combining search with learning, the proposed SMS method can better capture frame interactions while incurring a low inference cost." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 348, + 286, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 286, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 286, + 479 + ], + "type": "text", + "content": "The effectiveness of SMS is extensively evaluated on both the long untrimmed action recognition benchmarks, i.e., ActivityNet [2] and FCVID [18], and the short trimmed UCF101 task [27]. Experimental results show that SMS can significantly improve action recognition models and precisely recognize and produce effective frame selections. Furthermore, SMS significantly outperforms a range of other existing frame selection methods for the same number of frames selected, while can still generate performance higher than existing methods using only " + }, + { + "bbox": [ + 46, + 348, + 286, + 479 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 348, + 286, + 479 + ], + "type": "text", + "content": " of all labeled video samples for training." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 490, + 134, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 134, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 134, + 502 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 652 + ], + "type": "text", + "content": "Action Recognition. 2D ConvNets have been widely utilized for action recognition, where per-frame features are first extracted and later aggregated with different methods such as temporal averaging [31], recurrent networks [7, 20, 37], and temporal channel shift [10, 21, 23]. Some studies leveraged both the short-term and long-term temporal relationships by two-stream architectures [12, 13]. To jointly capture the spatio-temporal information of videos, 3D ConvNets were proposed, including C3D [28], I3D [3] and X3D [11]. Transformer architecture [29] have also been applied to video understanding by modeling the spatiotemporal information with attention [1, 22]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 654, + 286, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 286, + 688 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 286, + 688 + ], + "type": "text", + "content": "In this paper, we follow the previous frame selection work and apply our method mainly on the temporal averaging 2D ConvNets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "Frame Selection. The problem of selecting important frames within a video has been investigated in order to im" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 539, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 539, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 539, + 84 + ], + "type": "text", + "content": "prove the performance and reduce the computational cost." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 85, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 191 + ], + "type": "text", + "content": "Many researchers focused on selecting frames based on the per-frame heuristic score. SCSampler [19] proposed to select frames based on the predicted scores of a lightweight video model as the usefulness of frames. SMART [15] incorporated an attention module that takes randomly selected frame pairs as input to model the relationship between frames. However, these methods select frames individually regardless of interactions between selected frames, which may lead to redundant selections." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 193, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 337 + ], + "type": "text", + "content": "Reinforcement learning (RL) approaches are widely adopted in frame selection to find the effective frames in a trail-and-error setting. FastForward [9] and AdaFrame [35] adopted a single RL agent to generate a decision on the next frame, and updated the network with policy gradient. MARL [33] formulated the frame sampling process as multiple parallel Markov Decision Processes, and adopted multiple RL agents each responsible for determining a frame. Although the RL-based approaches are effective, the training stability issue and the requirement of huge amount of training samples with high computational overhead remain a problem." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 338, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 456 + ], + "type": "text", + "content": "Recent studies combined frame selection with other techniques to improve the model efficiency. LiteEval [34] adopted a two-level feature extraction procedure, where fine expensive features were extracted for important frames, and coarse frames were used for the remaining frames. ListenToLook [14] proposed to use audio information as an efficient video preview for frame selection. AR-Net [24] aimed at selecting the optimal resolution for each frame that is needed to correctly recognize the actions, and learns a differentiable policy using Gumbel Softmax trick [17]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 457, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 540 + ], + "type": "text", + "content": "Our work focuses on the classic task of selecting a subset of frames based on visual information. Different from existing methods, our work incorporates a new \"Search-Map-Search\" paradigm that leverages efficient search and supervised feature mapping to explicitly find the best frame combinations, and achieves excellent performance outperforming other frame selection methods." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 554, + 388, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 554, + 388, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 554, + 388, + 567 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 574, + 425, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 425, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 425, + 586 + ], + "type": "text", + "content": "3.1. Overall Architecture" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 593, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 652 + ], + "type": "text", + "content": "Figure 1 gives an overview of our proposed framework, which consists of three stages: a search stage, a feature mapping stage, and another search stage. The training process of our method involves the first two stages, while the inference process involves the last two." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 712 + ], + "type": "text", + "content": "Specifically, the goal of the first search stage is to find the best frame combinations in training videos with the lowest model losses, which serve as the supervisory target information for the feature mapping stage. We design an efficient hierarchical algorithm coupled with Guided Local" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10628" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 83, + 504, + 392 + ], + "blocks": [ + { + "bbox": [ + 86, + 83, + 504, + 392 + ], + "lines": [ + { + "bbox": [ + 86, + 83, + 504, + 392 + ], + "spans": [ + { + "bbox": [ + 86, + 83, + 504, + 392 + ], + "type": "image", + "image_path": "3bcfd27c2a31aad153aa5cfd6724b3ae2d58c0746bc8e787ea371111c1a040f7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 411, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 45, + 411, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 45, + 411, + 547, + 456 + ], + "type": "text", + "content": "Figure 1. An overview of the proposed \"Search-Map-Search\" method. It contains three stages, where in the first stage, an efficient hierarchical search algorithm is used to derive the best frame combinations with lowest losses, which are utilized as the supervised information to train a feature mapping function in the second stage. In the third stage, for a query video, we incorporate another search process to infer the frame combination whose features are closest to the combination feature predicted with the trained feature mapping function." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 475, + 288, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 288, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 288, + 499 + ], + "type": "text", + "content": "Search [30] to identify the effective frame combinations at a low search cost." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 501, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 287, + 573 + ], + "type": "text", + "content": "In the second stage, a feature extractor is employed to extract input frame features from the training video frames, and the feature of the best combination from search results. Then, a feature mapping function is trained via supervised learning by taking the input frame features as input, and transforming it to the target feature of the best combination." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 574, + 287, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 623 + ], + "type": "text", + "content": "In the third stage, we incorporate another search process to infer the effective frame combination whose feature is closest to the predicted feature from the well-trained feature mapping function." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 634, + 286, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 286, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 286, + 647 + ], + "type": "text", + "content": "3.2. Stage 1: Search for Best Frame Combinations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": "Given an action recognition task with a pre-trained model " + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": " and a training dataset " + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "D^{tr} = \\{X, y\\}^{|\\hat{D}^{tr}|}" + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "X = \\{x_{i}\\}_{i=1}^{m}" + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": " represents a video sample made up of a collection of " + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": " frames, and " + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": " is the action label for the video, our goal of stage 1 is to find the best frame combination " + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\tilde{X}^*" + }, + { + "bbox": [ + 47, + 654, + 288, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "type": "text", + "content": " frames for each training video " + }, + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 305, + 475, + 545, + 499 + ], + "type": "text", + "content": " that minimizes the model loss:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 380, + 502, + 545, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 502, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 380, + 502, + 545, + 528 + ], + "type": "interline_equation", + "content": "\\tilde {X} ^ {*} = \\underset {\\tilde {X}} {\\arg \\min } \\mathcal {L} (M (\\tilde {X}), y), \\tag {1}", + "image_path": "6f54b818a208dc5e933c6cc1eb98c544c87dd62034b4338e839ad44808f39674.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 351, + 528, + 473, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 528, + 473, + 541 + ], + "spans": [ + { + "bbox": [ + 351, + 528, + 473, + 541 + ], + "type": "interline_equation", + "content": "w h e r e \\quad \\tilde {X} = \\left\\{x _ {k} \\mid x _ {k} \\in X \\right\\} ^ {n},", + "image_path": "f0a01dbd637c07c9ef556106aa185ecae42c69be5124c673cd48b861f2cadb31.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 545, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 594 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 545, + 545, + 594 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 545, + 545, + 594 + ], + "type": "text", + "content": " is the loss function of the action recognition task. Note that repetitive selection of the same frame is allowed in our setting, as we believe that repeated important frames are better than meaningless frames." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 714 + ], + "type": "text", + "content": "In order to efficiently find the best frame combinations, we have designed a hierarchical search algorithm which exploits the high similarities of adjacent frames by performing search hierarchically on coarse-grained clips first, and then on the fine-grained frames. Besides, we incorporate Guided Local Search [30] in our algorithm to exploit perframe losses as prior information for a good starting search point, which further reduces search costs and empirically outperforms other strong search algorithms such as Genetic Algorithm [32]." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10629" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 53, + 75, + 193, + 87 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 75, + 193, + 87 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 193, + 87 + ], + "type": "text", + "content": "Algorithm 1: Hierarchical Search" + } + ] + } + ], + "index": 0 + }, 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[ + { + "bbox": [ + 51, + 146, + 245, + 167 + ], + "type": "text", + "content": "1 Split the video into clips each consisting of " + }, + { + "bbox": [ + 51, + 146, + 245, + 167 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 51, + 146, + 245, + 167 + ], + "type": "text", + "content": " frames" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "spans": [ + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "type": "text", + "content": "2 Prepare an initial solution " + }, + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "type": "inline_equation", + "content": "\\tilde{C}_0" + }, + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "type": "text", + "content": " containing the clip with the lowest loss repeated " + }, + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 51, + 168, + 255, + 193 + ], + "type": "text", + "content": " times" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 51, + 194, + 258, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 194, + 258, + 220 + ], + "spans": [ + { + "bbox": [ + 51, + 194, + 258, + 220 + ], + "type": "text", + "content": "3 Perform Guided Local Search to improve " + }, + { + "bbox": [ + 51, + 194, + 258, + 220 + ], + "type": "inline_equation", + "content": "\\tilde{C}_0" + }, + { + "bbox": [ + 51, + 194, + 258, + 220 + ], + "type": "text", + "content": " and get " + }, + { + "bbox": [ + 51, + 194, + 258, + 220 + ], + "type": "inline_equation", + "content": "\\tilde{C}^* = \\{C_k\\}_{k=1}^n" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 60, + 229, + 162, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 229, + 162, + 239 + ], + "spans": [ + { + "bbox": [ + 60, + 229, + 162, + 239 + ], + "type": "text", + "content": "/\\*frame search phase" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 261, + 229, + 271, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 261, + 229, + 271, + 236 + ], + "spans": [ + { + "bbox": [ + 261, + 229, + 271, + 236 + ], + "type": "text", + "content": "\\*" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 51, + 240, + 264, + 319 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 51, + 240, + 264, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 240, + 264, + 277 + ], + "spans": [ + { + "bbox": [ + 51, + 240, + 264, + 277 + ], + "type": "text", + "content": "4 Define search space for each position in combination " + }, + { + "bbox": [ + 51, + 240, + 264, + 277 + ], + "type": "inline_equation", + "content": "S^F = \\{S_k|S_k = \\{x_j|x_j\\in C_k\\} \\}_{k = 1}^n" + }, + { + "bbox": [ + 51, + 240, + 264, + 277 + ], + "type": "text", + "content": " on top of " + }, + { + "bbox": [ 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}, + { + "bbox": [ + 51, + 291, + 259, + 319 + ], + "type": "inline_equation", + "content": "\\tilde{X}_0" + }, + { + "bbox": [ + 51, + 291, + 259, + 319 + ], + "type": "text", + "content": " and get " + }, + { + "bbox": [ + 51, + 291, + 259, + 319 + ], + "type": "inline_equation", + "content": "\\tilde{X}^* = \\{x_k\\}_{k=1}^n" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 342, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 559 + ], + "type": "text", + "content": "The overall workflow of our hierarchical search is summarized in Algorithm 1. To begin with, the video is first split into coarse-grained clips each consisting of a collection of non-overlapped frames. Then, we calculate the model loss for each clip by representing it with the averaged feature vector of all frame inside it, and utilize the information to create an initial solution composed of the clip with the lowest model loss repeated " + }, + { + "bbox": [ + 46, + 342, + 287, + 559 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 342, + 287, + 559 + ], + "type": "text", + "content": " times. On top of the initial searching point, we adapt Guided Local Search to find the best clip combination by defining a problem-specific penalty to escape from local optimum points. The details of Guided Local Search will be introduced in Appendix. After searching on coarse-grained clips, we again incorporate Guided Local Search to find the best fine-grained frame combinations by replacing each derived clip with a frame inside it. Via hierarchical search, we have greatly reduced the search space and lowered the search cost significantly, while obtaining satisfying solutions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 566, + 237, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 237, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 237, + 578 + ], + "type": "text", + "content": "3.3. 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Stage 3: Search to Infer Frame Combinations" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 381, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 545, + 477 + ], + "type": "text", + "content": "After the mapping function is learned, it can accurately predict the features of the best frame combinations for unseen videos without relying on the ground truth labels. The goal of this stage is to incorporate another search process to infer the frame combinations from the predicted features. 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Experiments" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 625, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 625, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 306, + 625, + 545, + 649 + ], + "type": "text", + "content": "In this section, we conduct extensive experiments aiming at investigating the following research questions:" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 317, + 657, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 42, + "blocks": [ + { + "bbox": [ + 317, + 657, + 544, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 657, + 544, + 681 + ], + "spans": [ + { + "bbox": [ + 317, + 657, + 544, + 681 + ], + "type": "text", + "content": "- RQ1: Can the proposed SMS improve model performance over the base frame sampling method?" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 317, + 689, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 689, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 689, + 545, + 712 + ], + "type": "text", + "content": "- RQ2: How does SMS perform compared to other state-of-the-art frame selection methods?" + } + ] + } + ], + "index": 41 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10630" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 59, + 72, + 286, + 159 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 59, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 286, + 95 + ], + "type": "text", + "content": "- RQ3: What's the computation efficiency of SMS for video inference?" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 104, + 286, + 128 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 104, + 286, + 128 + ], + "spans": [ + { + "bbox": [ + 59, + 104, + 286, + 128 + ], + "type": "text", + "content": "- RQ4: How do the different components affect the performance of the proposed SMS?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 136, + 286, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 136, + 286, + 159 + ], + "spans": [ + { + "bbox": [ + 59, + 136, + 286, + 159 + ], + "type": "text", + "content": "- RQ5: Can SMS generalize well to spatio-temporal models, e.g., transformer based video models?" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 167, + 163, + 181 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 167, + 163, + 181 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 163, + 181 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 186, + 118, + 197 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 186, + 118, + 197 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 118, + 197 + ], + "type": "text", + "content": "4.1.1 Datasets." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 205, + 286, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 286, + 300 + ], + "type": "text", + "content": "We evaluate our SMS method on 3 action recognition benchmarks including ActivityNet V1.3 [2], FCVID [18] and UCF101 [27]. The videos in ActivityNet and FCVID are untrimmed with average video lengths of 117 and 167 seconds respectively, while UCF101 dataset contains trimmed short videos with an average length of 7.21 seconds. Table 1 summarizes the detailed information of the experimental datasets." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 316, + 121, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 121, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 121, + 327 + ], + "type": "text", + "content": "4.1.2 Baselines." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 334, + 286, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 286, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 286, + 369 + ], + "type": "text", + "content": "We compare the proposed SMS with the base selection method and the following state-of-the-art frame selection methods:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 378, + 286, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 59, + 378, + 286, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 378, + 286, + 426 + ], + "spans": [ + { + "bbox": [ + 59, + 378, + 286, + 426 + ], + "type": "text", + "content": "- Base is a sparse sampling method proposed in TSN [31], where videos are divided into segments of equal length, and frames are randomly sampled within each segment." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 434, + 286, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 434, + 286, + 492 + ], + "spans": [ + { + "bbox": [ + 59, + 434, + 286, + 492 + ], + "type": "text", + "content": "- AdaFrame [35] incorporates reinforcement learning to adaptively select informative frames with a memory-augmented LSTM. At testing time, AdaFrame selects different number of frames for each video observed." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 501, + 286, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 501, + 286, + 525 + ], + "spans": [ + { + "bbox": [ + 59, + 501, + 286, + 525 + ], + "type": "text", + "content": "- MARL [33] adopts multiple RL agents each responsible for adjusting the position of a selected frame." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 59, + 533, + 286, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 533, + 286, + 568 + ], + "spans": [ + { + "bbox": [ + 59, + 533, + 286, + 568 + ], + "type": "text", + "content": "- SCSampler [19] proposes to select frames based on the prediction scores produced by a lightweight video model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 59, + 577, + 286, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 577, + 286, + 612 + ], + "spans": [ + { + "bbox": [ + 59, + 577, + 286, + 612 + ], + "type": "text", + "content": "- SMART [15] combines the single-frame predictive score with pair-wise interaction score to make decision on the frame selections." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 621, + 286, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 621, + 286, + 656 + ], + "spans": [ + { + "bbox": [ + 59, + 621, + 286, + 656 + ], + "type": "text", + "content": "- LiteEval [34] selects important frames to extract fine features and adopts coarse features for the remaining frames." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 665, + 286, + 713 + ], + "type": "text", + "content": "- ListenToLook [14] proposes to use audio information as video preview for frame selection. For a fair comparison, we follow AR-Net [24] and include the variant with only the visual modality." + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 309, + 70, + 542, + 126 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 542, + 126 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 542, + 126 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 542, + 126 + ], + "type": "table", + "html": "
DatasetTrainValActionsAvg. Duration
ActivityNet10,0244,926200117s
FCVID45,61145,612239167s
UCF1019,5373,7831017.21s
", + "image_path": "eb51a07109b35c6cdfae8067a11f0aee20c9912fc3fda29f07d32a9f9269f06c.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 346, + 134, + 504, + 145 + ], + "lines": [ + { + "bbox": [ + 346, + 134, + 504, + 145 + ], + "spans": [ + { + "bbox": [ + 346, + 134, + 504, + 145 + ], + "type": "text", + "content": "Table 1. Description of evaluation datasets." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 317, + 167, + 544, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 167, + 544, + 201 + ], + "spans": [ + { + "bbox": [ + 317, + 167, + 544, + 201 + ], + "type": "text", + "content": "- AR-Net [24] aims to select the optimal resolutions for frames that are needed to correctly recognize the actions." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 217, + 421, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 217, + 421, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 421, + 228 + ], + "type": "text", + "content": "4.1.3 Evaluation metrics." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 236, + 545, + 295 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 295 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 295 + ], + "type": "text", + "content": "Following previous studies, we evaluate the performance of models using mean Average Precision (mAR), which is a commonly adopted metric in action recognition tasks, calculated as the mean value of the average precision over all action classes." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 310, + 440, + 321 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 310, + 440, + 321 + ], + "spans": [ + { + "bbox": [ + 305, + 310, + 440, + 321 + ], + "type": "text", + "content": "4.1.4 Implementation details." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 328, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 399 + ], + "type": "text", + "content": "In the first stage of hierarchical searching, the clip length " + }, + { + "bbox": [ + 304, + 328, + 545, + 399 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 328, + 545, + 399 + ], + "type": "text", + "content": " is set to 30. For the feature mapping network, we adopt a two-layer transformer network with a hidden dimension of 2,048. The feature extraction network used in our implementation is a ResNet-50 network [16] pre-trained on the Kinetics dataset [3]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "type": "text", + "content": "For the data pre-processing for action recognition tasks, we decode the video at 1 fps for long videos in ActivityNet and FCVID and 55 fps for short videos in UCF101 to retrieve the rgb frames, which are augmented during training by resizing the short side to 256, random cropped and resized to " + }, + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "type": "inline_equation", + "content": "224^2" + }, + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "type": "text", + "content": ", after which a random flip with a probability of 0.5 is applied. For inference, we resize all frames to " + }, + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "type": "inline_equation", + "content": "256^2" + }, + { + "bbox": [ + 304, + 401, + 545, + 496 + ], + "type": "text", + "content": " and perform three-crop." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 497, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 627 + ], + "type": "text", + "content": "For the training of action recognition models, we choose ResNet-50 as the backbone and run 100 epochs using an SGD optimizer with a momentum of 0.9, and a step learning rate schedule which decays the learning rate by a factor of 10 every 40 epochs. For ActivityNet and FCVID, we use an initial learning rate of 0.005, and a batch size of 64. For UCF101 with shorter videos, we increase the batch size to 128 and adjust the initial learning rate to 0.00256. All models are trained using code adapted from MMAction2 [4] on eight Nvidia-A100 GPUs. And we report the average performance and standard deviation of three runs." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 635, + 463, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 635, + 463, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 635, + 463, + 647 + ], + "type": "text", + "content": "4.2. Effectiveness Analysis (RQ1)" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 712 + ], + "type": "text", + "content": "To validate the effectiveness of the proposed SMS, we make a comprehensive comparison with the base method on both long-video dataset ActivityNet and FCVID, and short-video dataset UCF101. As the video lengths of different datasets vary in a large range, we choose to select different" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10631" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 126 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 126 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 126 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 126 + ], + "type": "table", + "html": "
# FramesActivityNetFCVIDUCF101
816258162538
Base177.34 ± 0.0679.41 ± 0.0580.04 ± 0.2483.84 ± 0.0585.34 ± 0.0385.65 ± 0.0490.65 ± 0.1390.70 ± 0.10
SMS (infer only)82.76 ± 0.1583.78 ± 0.0883.85 ± 0.1786.35 ± 0.0386.94 ± 0.0687.08 ± 0.0491.45 ± 0.1291.58 ± 0.09
SMS (train & infer)83.72 ± 0.0584.35 ± 0.0884.56 ± 0.0886.54 ± 0.0687.25 ± 0.1187.59 ± 0.0191.94 ± 0.1592.25 ± 0.10
", + "image_path": "645dda20cf92423fa940fd23b723bb9b73af8cf56949bfa292e95dc5d86ff0f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 115, + 167, + 480, + 294 + ], + "blocks": [ + { + "bbox": [ + 46, + 134, + 546, + 156 + ], + "lines": [ + { + "bbox": [ + 46, + 134, + 546, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 546, + 156 + ], + "type": "text", + "content": "Table 2. Performance comparison of the proposed SMS and the base method. In SMS (infer only), frames are selected with our method only during inference. In SMS (train & infer), frames are selected with SMS during both training and inference." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 115, + 167, + 480, + 294 + ], + "lines": [ + { + "bbox": [ + 115, + 167, + 480, + 294 + ], + "spans": [ + { + "bbox": [ + 115, + 167, + 480, + 294 + ], + "type": "table", + "html": "
MethodBackboneActivityNetFCVID
# FramesmAPimpr.# FramesmAPimpr.
SCSamplerResNet-501072.90.41081.00.0
AdaFrameResNet-1018.6571.53.78.2180.21.8
MARLResNet-101872.90.4---
SMARTResNet-1011073.1-1082.1-
SMART*ResNet-50880.673.33883.35-0.49
SMS_10%ResNet-50882.124.78885.691.85
SMSResNet-50883.726.38886.542.70
", + "image_path": "956b6ecc5c9537963c65b474ffee0096160b05f8f201311b44c10534fcb81e10.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 301, + 547, + 347 + ], + "lines": [ + { + "bbox": [ + 46, + 301, + 547, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 547, + 347 + ], + "type": "text", + "content": "Table 3. Performance comparison of the proposed SMS and other state-of-the-art frame selection methods. We show both their performance and the their reported improvements over the base sampling method, due to the inconsistent base performance among different methods. Results of baselines are retrieved from literature, except for SMART*, which is implemented using the same features and implementation settings as SMS. We have also included the results of SMS learned only on " + }, + { + "bbox": [ + 46, + 301, + 547, + 347 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 301, + 547, + 347 + ], + "type": "text", + "content": " training data as SMS_10%." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 367, + 289, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 289, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 289, + 464 + ], + "type": "text", + "content": "number of frames for each video in these datasets, where 8, 16 and 25 frames are selected for long videos in ActivityNet and FCVID, and 3 and 8 frames are selected for short videos in UCF101. Furthermore, we conduct experiments to select frames with SMS only on test data during the inference of pre-trained base models, and incorporate SMS in both the training and inference process. The experimental results are shown in Table 2, from which we can observe that:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 58, + 472, + 287, + 685 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "text", + "content": "- When applied to test data, compared to the base sampling method, SMS (infer only) significantly improves the average mAP on different numbers of selected frames by " + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "inline_equation", + "content": "4.53\\%" + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "inline_equation", + "content": "1.85\\%" + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "text", + "content": " on ActivityNet and FCVID, respectively. While SMS (infer only) significantly improves model performance, SMS (train & infer) improves the mAP by " + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "inline_equation", + "content": "0.75\\%" + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "inline_equation", + "content": "0.34\\%" + }, + { + "bbox": [ + 58, + 472, + 287, + 592 + ], + "type": "text", + "content": " mAP on ActivityNet and FCVID. This observation demonstrates that the frames selected with the SMS method are beneficial to both model training and inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 58, + 601, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 601, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 58, + 601, + 287, + 685 + ], + "type": "text", + "content": "While most other frame selection methods only focus on long untrimmed video tasks, SMS is also effective on short trimmed video tasks. Despite that in UCF101, the irrelevant parts of videos are trimmed off, which to a great degree limits the potential of frame selection, SMS still achieves steady improvement of " + }, + { + "bbox": [ + 58, + 601, + 287, + 685 + ], + "type": "inline_equation", + "content": "1.42\\%" + }, + { + "bbox": [ + 58, + 601, + 287, + 685 + ], + "type": "text", + "content": " average mAP over the base method with the same number" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 325, + 368, + 404, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 368, + 404, + 378 + ], + "spans": [ + { + "bbox": [ + 325, + 368, + 404, + 378 + ], + "type": "text", + "content": "of selected frames." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 384, + 481, + 397 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 481, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 481, + 397 + ], + "type": "text", + "content": "4.3. Performance Comparison (RQ2)" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": "In order to justify the benefit of our new learning paradigm of frame selection, we compare SMS with other classic frame selection methods on ActivityNet and FCVID. We choose ResNet as the backbone architecture of the action recognition model and report the performance with similar number of selected frames ranges from 8 to 10." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 475, + 546, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 546, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 546, + 640 + ], + "type": "text", + "content": "As the implementation and training details are different among the frame selection methods, the performances of the base models are inconsistent. Therefore, directly comparing the reported performances may be unfair. Moreover, due to the lack of source codes and models, we are unable to compare all methods under the same settings, especially for the RL-based methods whose results are difficult to reproduce. To make a fairer comparison, in addition to the absolute performance, we also compare the relative improvements of the frame selection methods over the base sampling method. Also, we have implemented the most recent frame selection method, SMART [15], using the same features and implementation settings as our proposed SMS, and include its results as SMART*." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "The comparison results are demonstrated in Table 3, from which we can see that with the least number of selected frames and the smallest backbone model, the proposed SMS achieves the best performance of " + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "inline_equation", + "content": "83.72\\%" + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "inline_equation", + "content": "86.54\\%" + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": " mAP on ActivityNet and FCVID respectively. Moreover, even with the higher-performance base models" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 288, + 714 + ], + "type": "text", + "content": "1The base performance in our paper is higher compared to it in other papers, due to the better codebase and training settings." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10632" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 76, + 281, + 243 + ], + "blocks": [ + { + "bbox": [ + 53, + 76, + 281, + 243 + ], + "lines": [ + { + "bbox": [ + 53, + 76, + 281, + 243 + ], + "spans": [ + { + "bbox": [ + 53, + 76, + 281, + 243 + ], + "type": "image", + "image_path": "ea6eed9ff9ff1930007ac5897f85f446c751a7abe20e896e795e6d96e1e43cb4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "type": "text", + "content": "Figure 2. Comparison of SMS with other approaches in terms of performance vs. inference cost (model size per video) evaluated on ActivityNet. We control the inference cost by varying " + }, + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "type": "text", + "content": ", the number of candidate frames in a video from which " + }, + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "type": "inline_equation", + "content": "n = 8" + }, + { + "bbox": [ + 46, + 258, + 288, + 313 + ], + "type": "text", + "content": " best frames are to be selected." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "text", + "content": "which are harder to improve, SMS still obtains the largest improvements of " + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "inline_equation", + "content": "6.48\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "inline_equation", + "content": "2.70\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "text", + "content": " among all frame selection methods. In a fair comparison with the same implementation settings, our method significantly outperforms SMART* by " + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "inline_equation", + "content": "3.05\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "inline_equation", + "content": "3.19\\%" + }, + { + "bbox": [ + 46, + 335, + 287, + 407 + ], + "type": "text", + "content": " respectively on ActivityNet and FCVID." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 408, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 506 + ], + "type": "text", + "content": "The reason of our success is due to our novel training paradigm of \"Search-Map-Search\", where an efficient hierarchical search method is incorporated to find the best frame combinations, which better models the frame interactions. Moreover, in SMS, a feature mapping function is learned to map an input video directly to the optimal frame combination, which is theoretically superior to the one-by-one frame selection adopted by existing methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 514, + 191, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 191, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 191, + 528 + ], + "type": "text", + "content": "4.4. Efficiency Analysis (RQ3)" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 593 + ], + "type": "text", + "content": "We now analyze the efficiency of SMS and compare it with other frame selection methods in terms of action recognition performance versus inference cost (evaluated by the model size per video. For a fair comparison, we only include the results that use ResNet as the backbone model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "In order to evaluate the tradeoff between performance and inference efficiency, we first uniformly sub-sample " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " candidate frames that constitute the search space for each video from which " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "n = 8" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " best frames are to be selected. As " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " increases, features are extracted from more candidate frames, and the resulting frame selection becomes more effective, while the inference cost becomes larger. As demonstrated in Figure 2, the action recognition performance of SMS grows rapidly from " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "m = 8" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "m = 25" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", while further increasing " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " to 50 or 100 incurs only slight increase in" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 326, + 87, + 515, + 211 + ], + "blocks": [ + { + "bbox": [ + 326, + 87, + 515, + 211 + ], + "lines": [ + { + "bbox": [ + 326, + 87, + 515, + 211 + ], + "spans": [ + { + "bbox": [ + 326, + 87, + 515, + 211 + ], + "type": "image", + "image_path": "21cbbbc35aae5ee552c864d6bae970522fe7c93ea96e9451da78384122920754.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 217, + 547, + 241 + ], + "lines": [ + { + "bbox": [ + 305, + 217, + 547, + 241 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 547, + 241 + ], + "type": "text", + "content": "Figure 3. The evaluation of different search algorithms on 100 videos, given by the average loss over the number of evaluations." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 262, + 547, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 547, + 309 + ], + "type": "text", + "content": "performance but huge inference overhead. In practice, one can easily achieve a good tradeoff between performance and cost accordingly by tuning the number of candidate frames " + }, + { + "bbox": [ + 304, + 262, + 547, + 309 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 262, + 547, + 309 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 311, + 547, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 547, + 371 + ], + "type": "text", + "content": "In comparison with other approaches, SMS achieves higher action recognition performance and beats other methods under different computation resource constraints, showing the effectiveness of the proposed search-mapping-search paradigm in frame selection." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 380, + 432, + 394 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 432, + 394 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 432, + 394 + ], + "type": "text", + "content": "4.5. Ablation Study (RQ4)" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 400, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 400, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 305, + 400, + 545, + 424 + ], + "type": "text", + "content": "This subsection aims to analyze the effects of different components designed in our proposed SMS." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 425, + 547, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 547, + 484 + ], + "type": "text", + "content": "Search algorithm. We have conducted experiments to compare the performance and efficiency of our designed Hierarchical Guided Local Search algorithm with other powerful search algorithms such as Fast Genetic Algorithm [6] and the frame-level Guided Local Search [30]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": "In Figure 3, we show the best loss averaged on 100 randomly selected videos with different search algorithms, and their corresponding search cost measured by the number of evaluations. By adopting different clip length " + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 485, + 547, + 665 + ], + "type": "text", + "content": ", our proposed hierarchical search algorithm can trade off between the search performance and the search cost. From Figure 3, we can see that using the same number of evaluations, our hierarchical search achieves better results compared to Fast Genetic Algorithm, by more effectively exploiting the prior knowledge of the per-frame loss information. The original Guided Local Search without hierarchical design is extremely costly which requires nearly 3,000 evaluations per video. Contrastively, our algorithm is more efficient with the hierarchical design, and achieves comparable performance with far less computation cost." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Feature mapping network. The process of feature mapping aims to transform the input frame features to the feature of target combination. We have conducted experiments to explore the impact of different network architectures and" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10633" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 94, + 70, + 500, + 155 + ], + "blocks": [ + { + "bbox": [ + 94, + 70, + 500, + 155 + ], + "lines": [ + { + "bbox": [ + 94, + 70, + 500, + 155 + ], + "spans": [ + { + "bbox": [ + 94, + 70, + 500, + 155 + ], + "type": "table", + "html": "
Feature Extractor (Training Source)Mapping Model ArchPerformanceInference GFLOPs
ResNet-50 (Kinetics)Transformer83.721.50
ResNet-50 (Kinetics)MLP83.220.01
ResNet-50 (ImageNet)Transformer79.971.50
ResNet-50 (ActivityNet)Transformer81.061.50
MobileNet-V2 (Kinetics)Transformer79.530.93
", + "image_path": "09f9205bb1260a887325d09c37c8b88beb3914920f497a1164146e34159d1399.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 205, + 284, + 277 + ], + "blocks": [ + { + "bbox": [ + 46, + 163, + 546, + 187 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 546, + 187 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 546, + 187 + ], + "type": "text", + "content": "Table 4. Ablation analysis results in mAP (%) on ActivityNet using 8 frames with different feature extractors and feature mapping model architectures. The feature mapping inference GFLOPs per video is also provided." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 205, + 284, + 277 + ], + "lines": [ + { + "bbox": [ + 51, + 205, + 284, + 277 + ], + "spans": [ + { + "bbox": [ + 51, + 205, + 284, + 277 + ], + "type": "table", + "html": "
Backbone# FramesMethodPerformance
TimeSFformer8Dense84.33
Base90.11
SMART*90.53
SMS91.97
", + "image_path": "7f4945064c765611163daff5620699dcc3ad3a3d16b871585fa7fa55d0258b09.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "type": "text", + "content": "Table 5. The ActivityNet evaluation results in mAP (%) using different frame sampling strategies on TimeSFformer." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 335, + 217, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 217, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 217, + 346 + ], + "type": "text", + "content": "training data sources for feature mapping." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 349, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 349, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 287, + 504 + ], + "type": "text", + "content": "For the network architecture, we adopt transformers to sequentially modeling the frame features with their spatiotemporal relations taken into consideration. Another simple applicable design is to adopt a mean-pooling layer that aggregates all the features of frames into a single feature vector, followed by a simpler two-layer MLP network. In Table 4, row 1 and 2 compares the performance and the inference efficiency of the two designs. As we can see, using transformer model as the mapping function outperforms MLP design by " + }, + { + "bbox": [ + 46, + 349, + 287, + 504 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 46, + 349, + 287, + 504 + ], + "type": "text", + "content": " mAP due to the better representation ability, while the inference cost of both designs are small and negligible (less than 2 GFLOPs) compared to the cost of frame feature extractions (tens or hundreds GFLOPs)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "content": "Feature extractor. We have analyzed the effect of different feature extractor settings by trying smaller model structure, e.g., MobileNet-V2 [25], and different pre-trained data sources including ImageNet [5], Kinetics [3] and ActivityNet [2]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 713 + ], + "type": "text", + "content": "Comparing the results of row 1, 3 and 4 in Table 4, we can see that the pre-training data of feature extractor can make a difference. The feature extractor trained on the largest Kinetics dataset achieves the best performance as it better captures the semantics of actions by training on more related samples, compared to the ones trained on smaller ActivityNet dataset and out-domain ImageNet dataset. Besides, as shown in row 5 of Table 4, using smaller models such as MobileNet-V2 for extractor can lead to performance decline. In general, the representation capability of feature extractors is valuable for frame selection to recognize the important frames and find the best frame combinations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 206, + 479, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 206, + 479, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 206, + 479, + 220 + ], + "type": "text", + "content": "4.6. Generalizability Analysis (RQ5)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 225, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 225, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 225, + 545, + 297 + ], + "type": "text", + "content": "It is a natural question to ask if the frames selected by SMS can also be beneficial to spatio-temporal video models. To find out the answer to this question, we have conducted an experiment to apply the SMS selected frames on TimeSFformer [1], which incorporates the transformer architecture and is one of the most advanced video models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "text", + "content": "The results are shown in Table 5. The dense frame sampling strategy incorporated in the original TimeSFormer implementation randomly samples a clip containing 8 successive frames from videos, and achieves " + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "inline_equation", + "content": "84.33\\%" + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "text", + "content": " mAP on ActivityNet. However, in untrimmed video dataset, dense sampling can only captures a small part of the video and may miss important information. In contrast, the base sampling strategy selects frames uniformly from videos and achieves " + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "inline_equation", + "content": "90.11\\%" + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "text", + "content": " mAP, while SMART* achieves " + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "inline_equation", + "content": "90.53\\%" + }, + { + "bbox": [ + 304, + 297, + 546, + 405 + ], + "type": "text", + "content": " mAP." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "text", + "content": "By using the input frames selected by SMS, we obtain a significant performance gain of " + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "inline_equation", + "content": "1.86\\%" + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "text", + "content": " over the base sampling strategy and " + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "inline_equation", + "content": "1.44\\%" + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "text", + "content": " over SMART*, and achieve " + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "inline_equation", + "content": "91.97\\%" + }, + { + "bbox": [ + 304, + 405, + 545, + 502 + ], + "type": "text", + "content": " mAP. This improvement demonstrates the strong generalizability of SMS across different model architectures, and that SMS is not only effective on 2D video modeling, but can also capture the spatio-temporal relationship among frames and is beneficial to 3D video model learning." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 378, + 526 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "In this paper, we propose a new learning paradigm for frame selection, called \"Search-Map-Search\", which consists of a search stage to efficiently find the best frame combination with a hierarchical search algorithm, a feature mapping stage that learns to transform the input frame features directly into the feature of the searched combination, and another search stage that selects frames based on the mapped feature. Compared with existing frame selection methods, SMS is a more accurate learning paradigm that takes advantage of efficient search and supervised feature mapping to directly select the best combination of frames as one entity, which better captures the frame interactions. Experimental results show that SMS achieves significant performance gains on multiple action recognition benchmarks, and outperforms other strong baseline methods." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10634" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. 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However, existing methods for training classifiers robust to multiple threats require knowledge of all attacks during training and remain vulnerable to unseen distribution shifts. In this work, we describe how to obtain adversially-robust model soups (i.e., linear combinations of parameters) that smoothly trade-off robustness to different $\\ell_p$ -norm bounded adversaries. We demonstrate that such soups allow us to control the type and level of robustness, and can achieve robustness to all threats without jointly training on all of them. In some cases, the resulting model soups are more robust to a given $\\ell_p$ -norm adversary than the constituent model specialized against that same adversary. Finally, we show that adversially-robust model soups can be a viable tool to adapt to distribution shifts from a few examples.", + "bbox": [ + 75, + 305, + 473, + 564 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 592, + 209, + 608 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep networks have achieved great success on several computer vision tasks and have even reached super-human accuracy [19, 31]. However, the outputs of such models are often brittle, and tend to perform poorly on inputs that differ from the distribution of inputs at training time, in a condition known as distribution shift [37]. Adversarial perturbations are a prominent example of this condition: small, even imperceptible, changes to images can alter predictions to cause errors [2, 46]. In addition to adversarial inputs, it has been noted that even natural shifts, e.g. different weather conditions, can significantly reduce the accuracy of even the best vision models [13, 21, 40]. Such drops in accuracy are undesirable for robust deployment, and so a lot of effort has been invested in correcting them. Adversarial training [34] and its extensions [15, 39, 58] are currently the most effective methods to improve empirical robustness to adversarial attacks. Similarly, data augmen", + "bbox": [ + 75, + 618, + 470, + 876 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tation is the basis of several techniques that improve robustness to non-adversarial/natural shifts [3, 11, 22]. While significant progress has been made on defending against a specific, selected type of perturbations (whether adversarial or natural), it is still challenging to make a single model robust to a broad set of threats and shifts. For example, a classifier adversarily-trained for robustness to $\\ell_p$ -norm bounded attacks is still vulnerable to attacks in other $\\ell_q$ -threat models [29, 47]. Moreover, methods for simultaneous robustness to multiple attacks require jointly training on all [33, 35] or a subset of them [8]. Most importantly, controlling the trade-off between different types of robustness (and nominal performance) remains difficult and requires training several classifiers.", + "bbox": [ + 496, + 275, + 893, + 487 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inspired by model soups [52], which interpolate the parameters of a set of vision models to achieve state-of-the-art accuracy on IMAGENET, we investigate the effects of interpolating robust image classifiers. We complement their original recipe for soups by own study of how to pretrain, fine-tune, and combine the parameters of models adversarially-trained against $\\ell_p$ -norm bounded attacks for different $p$ -norms. To create models for soups, we pre-train a single robust model and fine-tune it to the target threat models (using the efficient technique of [8]). We then establish that it is possible to smoothly trade-off robustness to different threat models by moving in the convex hull of the parameters of each robust classifier, while achieving competitive performance with methods that train on multiple $p$ -norm adversaries simultaneously. Unlike alternatives, our soups can uniquely (1) choose the level of robustness to each threat model without any further training and (2) quickly adapt to new unseen attacks or shifts by simply tuning the weighting of the soup.", + "bbox": [ + 496, + 489, + 895, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous works [24, 30, 54] have shown that adversarial training with $\\ell_p$ -norm bounded attacks can help to improve performance on natural shifts if carefully tuned. We show that model soups of diverse classifiers, with different types of robustness, offer greater flexibility for finding models that perform well across various shifts, such as IMAGENET variants. Furthermore, we show that a limited number of images of the new distribution are sufficient to select the", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during an internship at DeepMind.", + "bbox": [ + 94, + 886, + 346, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12313", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "weights of such a model soup. Examining the composition of the best soups brings insights about which features are important for each dataset and shift. Finally, while the capability of selecting a model specific to each image distribution is a main point of our model soups, we also show that it is possible to jointly select a soup for average performance across several IMAGENET variants to achieve better accuracy than adversarial and self-supervised baselines [18, 24].", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. In summary, we show that soups", + "text_level": 1, + "bbox": [ + 76, + 212, + 401, + 227 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- can merge nominal and $\\ell_p$ -robust models (for various $p$ ): efficient fine-tuning from one robust model obtains a set of models with diverse robustness [8] and compatible parameters for creating model soups [52] (Sec. 3),", + "- can control the level of robustness to each threat model and achieve, without more training, competitive performance against multi-norm robustness training (Sec. 4),", + "- are not limited to interpolation, but can find more effective classifiers by extrapolation (Sec. 4.3),", + "- enable adaptation to unseen distribution shifts on only a few examples (Sec. 5)." + ], + "bbox": [ + 76, + 227, + 468, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 407, + 217, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial robustness to multiple threat models. Most methods focus on achieving robustness in a single threat model, i.e. to a specific type of attacks used during training. However, this is not sufficient to obtain robustness to unseen attacks. As a result, further work aims to train classifiers for simultaneous robustness to multiple attacks, and the most popular scenario considers a set of $\\ell_p$ -norm bounded perturbations. The most successful methods [33, 35, 47] are based on adversarial training and differ in how the multiple threats are combined. Notably, all need to use every attack at training time. To reduce the computational cost of obtaining multiply-robust models, one can fine-tune a singly-robust model by one of the above mentioned methods [8], even for only a small number of epochs. Our soups are more flexible by skipping simultaneous adversarial training across multiple attacks.", + "bbox": [ + 75, + 431, + 468, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial training for distribution shifts. While robustness to adversarial attacks and natural shifts are not the same goal, previous works nevertheless show that it is possible to leverage adversarial training with $\\ell_p$ -norm bounded attacks to improve performance on the common corruptions of [21]. First, AdvProp [54] co-trains models on clean and adversarial images (in the $\\ell_{\\infty}$ -threat model) with dual normalization layers that specialize to each type of input. The clean branch of the dual model achieves higher accuracy than nominal training on IMAGENET and its variants. Similar results are obtained by Pyramid-AT [24] by its design of a specific attack to adversarily train vision transformers. Finally, [30] carefully selecting the size of the adversarial perturbations, i.e., their $\\ell_{\\infty}$ - or $\\ell_2$ -norm, for standard adversarial training [34] achieves competitive performance on", + "bbox": [ + 75, + 674, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "common corruptions on CIFAR-10 and IMAGENET-100.", + "bbox": [ + 498, + 90, + 875, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model soups. Ensembling or averaging the parameters of intermediate models found during training is an effective technique to improve both clean accuracy [25, 28] and robustness [14, 39]. Recently, [52] propose model soups which interpolate the parameters of networks finetuned with different hyperparameters configurations from the same pre-trained model. This yields improved classification accuracy onImagenet. Along the same line, [27] fine-tune a model trained onImagenet on several new image classification datasets, and show that interpolating the original and fine-tuned parameters yields classifiers that perform well on all tasks. Additional related work is discussed in App. A.", + "bbox": [ + 496, + 106, + 890, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Model Interpolation across Different Tasks", + "text_level": 1, + "bbox": [ + 498, + 316, + 883, + 334 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the following, we formally introduce the two main components of our procedure to merge adversarially robust models: (1) obtaining models which can interpolated by fine-tuning a single $\\ell_p$ -robust classifiers, and (2) interpolation of their weights to balance their different types of robustness. We highlight that our setup diverges from that of prior works about parameters averaging: in fact, both [27, 52] combine models fine-tuned on the same task, i.e. achieving high classification accuracy of unperturbed images, either on a fixed dataset and different hyperparameter configurations [52], or varying datasets [27]. In our case, the individual models are trained for robustness to different types of attacks, i.e. with distinct loss functions.", + "bbox": [ + 496, + 342, + 890, + 539 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Adversarial training and fine-tuning", + "text_level": 1, + "bbox": [ + 498, + 549, + 815, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let us denote $\\mathcal{D} = \\{(x_i, y_i)\\}_i$ the training set, with $x_i \\in \\mathbb{R}^d$ indicating an image and $y_i \\in \\{1, \\dots, K\\}$ the corresponding label, and $\\Delta: \\mathbb{R}^d \\to \\mathbb{R}^d$ the function which characterizes a threat model, that maps an input $x$ to a set $\\Delta(x) \\subset \\mathbb{R}^d$ of possible perturbed versions of the original image. For example, $\\ell_p$ -norm bounded adversarial attacks with budget $\\epsilon > 0$ in the image space can be described by", + "bbox": [ + 498, + 571, + 890, + 679 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta (\\boldsymbol {x}) = \\left\\{\\boldsymbol {\\delta} \\in \\mathbb {R} ^ {d}: \\| \\boldsymbol {\\delta} \\| _ {p} \\leq \\epsilon , \\boldsymbol {x} + \\boldsymbol {\\delta} \\in [ 0, 1 ] ^ {d} \\right\\}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 689, + 890, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Then, one can train a classifier $f:\\pmb {\\theta}\\times \\mathbb{R}^d\\to \\mathbb{R}^K$ parameterized by $\\pmb {\\theta}\\in \\Theta$ with adversarial training [34] by solving", + "bbox": [ + 498, + 719, + 890, + 751 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\boldsymbol {\\theta} \\in \\Theta} \\sum_ {(\\boldsymbol {x}, y) \\in \\mathcal {D}} \\max _ {\\boldsymbol {\\delta} \\in \\Delta (\\boldsymbol {x})} \\mathcal {L} (f (\\boldsymbol {\\theta}, x + \\boldsymbol {\\delta}), y), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 762, + 890, + 797 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for a given loss function $\\mathcal{L}:\\mathbb{R}^K\\times \\mathbb{R}^K\\to \\mathbb{R}$ (e.g., cross-entropy), with the goal of obtaining a model robust to the perturbations described by $\\Delta$ . Note that this boils down to nominal training when $\\Delta (\\cdot) = \\{\\mathbf{0}\\}$ and no perturbation is applied on the training images. We are interested in the case where multiple threat models are available, and indicate", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12314", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fa4a9b5c007cc1d50c401a20caac2aa7d43fc6e6f40e1a0a7e45bf75e091e813.jpg", + "image_caption": [ + "Figure 1. Soups of two models on CIFAR-10: for all pairs $(p,q)$ we show the $\\ell_{p}$ - vs $\\ell_{q}$ -robust accuracy of the soups $w\\cdot \\theta_{p} + (1 - w)\\cdot \\theta_{p\\rightarrow q}$ and $w\\cdot \\theta_q + (1 - w)\\cdot \\theta_{q\\to p}$ varying $w\\in [0,1]$ . We also show results for MAX and SAT with simultaneous use of the two threat models." + ], + "image_footnote": [], + "bbox": [ + 124, + 88, + 359, + 226 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8cb58d3f5c7c9b3b74c97e46bcc21da6c334ab2b25f550f1f9ddd4fb64df4015.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 374, + 88, + 611, + 226 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b8ae2eb71709e5a21211edfa7f85e008773e5a983da7aac20b023d12cdcd7c4e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 88, + 846, + 227 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/78c9c611c89838214762f18e6e09b6fc5f648b5cf1894bb4a626a5fd38f58fb0.jpg", + "image_caption": [ + "Figure 2. Soups of two models on IMAGENET: for $p \\in \\{2,1\\}$ we show the $\\ell_{p^-}$ vs $\\ell_{\\infty}$ -robust accuracy of the soups $w \\cdot \\theta_{\\infty} + (1 - w) \\cdot \\theta_{\\infty \\rightarrow p}$ varying $w \\in [0,1]$ (first and second columns). Moreover, we show the soups obtained combining $\\theta_{\\infty \\rightarrow 2}$ and $\\theta_{\\infty \\rightarrow 1}$ (third), or $\\theta_{\\infty}$ and $\\theta_{\\infty \\rightarrow \\text{nominal}}$ (fourth). For the case of two $\\ell_{p^-}$ -threat models, we also show the results of fine-tuning models with MAX and SAT." + ], + "image_footnote": [], + "bbox": [ + 83, + 286, + 282, + 424 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2d6f981fcdf5770272485231e322574bf5b858d22dc194ac6ee10d6d3be016cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 286, + 486, + 424 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/9727ad545248276aeacffae333be011fff4ff61f8ae4b1de9069c48b2ba0b739.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 493, + 286, + 694, + 424 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bdb97aededccf3ed1b8d9536f78bf02104f11149040ee6f043af0ad81e11c376.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 286, + 895, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $\\Delta_{\\mathrm{nominal}}$ nominal training, and $\\Delta_p$ for $p \\in \\{\\infty, 2, 1\\}$ the perturbations with bounded $\\ell_p$ -norm as described in Eq. 1. We focus on such tasks since they are the most common choices for adversarial defenses, in particular by methods focusing on multiple norm robustness [35, 47].", + "bbox": [ + 75, + 511, + 468, + 587 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notably, it is possible to efficiently obtain a model robust to $\\Delta_q$ by fine-tuning for a single (or few) epoch with adversarial training w.r.t. $\\Delta_q$ a classifier pre-trained to be robust in $\\Delta_p$ , with $p \\neq q$ and $p, q \\in \\{\\infty, 2, 1\\}$ [8]. For example, in this way one can efficiently derive specialized classifiers $\\Delta_2, \\Delta_1, \\Delta_{\\mathrm{nominal}}$ for each task from a single model $f$ robust w.r.t. $\\ell_{\\infty}$ . However, this does not work well when a nominal classifier is used as starting point for the short fine-tuning. In the following, we denote with $\\theta_{p \\rightarrow q}$ the parameters resulting from fine-tuning to $\\Delta_q$ a base model $\\theta_p$ .", + "bbox": [ + 75, + 588, + 468, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Merging different types of robustness via linear combinations in parameter space", + "text_level": 1, + "bbox": [ + 76, + 753, + 468, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We want to explore the properties of the models obtained by taking linear combinations of the parameters of classifiers with different types of robustness. To do so, there needs to be a correspondence among the parameters of different individual networks: [52] achieve this by merging differently fine-tuned versions of the same pre-trained model. As mentioned above, fine-tuning an $\\ell_p$ -robust clas", + "bbox": [ + 75, + 794, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sifier allows to change it to achieve robustness in a new threat model [8]: we exploit such property to create model soups, as named by [52]. Formally, we create a model soup from $n$ individual networks with parameters $\\pmb{\\theta}^{1},\\dots,\\pmb{\\theta}^{n}$ with weights $\\pmb{w} = (w_{1},\\dots,w_{n})\\in \\mathbb{R}^{n}$ as", + "bbox": [ + 496, + 511, + 892, + 588 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} ^ {w} = \\sum_ {i = 1} ^ {n} w _ {i} \\cdot \\boldsymbol {\\theta} ^ {i}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 603, + 890, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and the corresponding classifier is given by $f(\\pmb{\\theta}^{\\pmb{w}},\\cdot):\\mathbb{R}^{d}\\to \\mathbb{R}^{K}$ . While any choice of $\\pmb{w}$ is possible, we focus on the case of affine combinations, i.e. $\\sum_{i}w_{i} = 1$ . Moreover, we consider soups which are either convex combinations of the individual models, with $w_{1},\\ldots ,w_{n}\\geq 0$ , or obtained by extrapolations, i.e. with negative elements in $\\pmb{w}$ .", + "bbox": [ + 496, + 656, + 893, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Soups for $\\ell_p$ -robustness", + "text_level": 1, + "bbox": [ + 500, + 767, + 718, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We measure adversarial robustness in the $\\ell_p$ -threat model with bounds $\\epsilon_p$ : on CIFAR-10 we use $\\epsilon_{\\infty} = 8 / 255$ , $\\epsilon_2 = 128 / 255$ , $\\epsilon_1 = 12$ , on IMAGENET $\\epsilon_{\\infty} = 4 / 255$ , $\\epsilon_2 = 4$ , $\\epsilon_1 = 255$ . If not specified otherwise, we use the full test set for CIFAR-10 and 5000 images from the IMAGENET validation set, and attack by AUTOPGD [6,7] with 40 steps. More details are provided in App. B.", + "bbox": [ + 496, + 794, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12315", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Soups with two threat models", + "text_level": 1, + "bbox": [ + 76, + 90, + 341, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CIFAR-10. We explore the effect of interpolating two models robust to different $\\ell_p$ -norm bounded attacks for $p \\in \\{\\infty, 2, 1\\}$ . We consider classifiers with WIDERES-NET-28-10 [56] architecture trained on CIFAR-10. For every threat model, we first train a robust classifier with adversarial training from random initialization. Then, we fine-tune the resulting model with adversarial training on each of the other threat models for 10 epochs. In Fig. 1 we show, for each pair of threat models $(\\Delta_p, \\Delta_q)$ , the trade-off of robust accuracy w.r.t. $\\ell_p$ and $\\ell_q$ for the soups", + "bbox": [ + 75, + 113, + 472, + 267 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw \\cdot \\pmb {\\theta} _ {p} + (1 - w) \\cdot \\pmb {\\theta} _ {p \\rightarrow q} \\quad \\mathrm {f o r} \\quad w \\in [ 0, 1 ]\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 275, + 415, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and symmetrically", + "bbox": [ + 76, + 303, + 205, + 319 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw \\cdot \\boldsymbol {\\theta} _ {q} + (1 - w) \\cdot \\boldsymbol {\\theta} _ {q \\rightarrow p} \\quad \\text {f o r} \\quad w \\in [ 0, 1 ].\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 329, + 416, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Interpolating the parameters of models trained with a single $\\ell_p$ -norm controls the balance between the two types of robustness: for example, Fig. 1 (middle plot) shows that moving from $\\theta_{\\infty}$ to $\\theta_{\\infty \\rightarrow 1}$ (blue curve), i.e. decreasing $w$ from 1 to 0 in the corresponding soup, progressively reduces the robust accuracy w.r.t. $\\ell_{\\infty}$ to improve robustness w.r.t. $\\ell_1$ . Moreover, for similar threat models (i.e. the pairs $(\\ell_2, \\ell_1)$ and $(\\ell_2, \\ell_{\\infty})$ ) some intermediate networks are more robust than the extremes trained specifically for each threat model.", + "bbox": [ + 75, + 357, + 468, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "IMAGENET. We now fine-tune a VIT-B16 [10] robust w.r.t. $\\ell_{\\infty}$ on IMAGENET to the other threat models, including nominal training, for either 1/3, 1 or 3 epochs. Fig. 2 shows that interpolation of parameters is effective even in this setup, and allows to easily balance nominal and robust accuracy (fourth plot). Moreover, it is possible to create soups with two fine-tuned models, i.e. $\\theta_{\\infty \\rightarrow 2}$ and $\\theta_{\\infty \\rightarrow 1}$ . Finally, increasing the number of fine-tuning steps yields better performance in the target threat model, which in turn generally leads to better soups.", + "bbox": [ + 75, + 492, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Comparison to multi-norm robustness methods. Fig. 1 and Fig. 2 compare the performance of the model soups to that of models trained with methods for robustness in the union of multiple threat models. In particular, we show the results of MAX [47], which computes perturbations for each threat model and trains on that attaining the highest loss, and SAT [33], which samples uniformly at random for each training batch the attack to use. We train models with both methods for all pairs of threat models: as expected, MAX tends to focus on the most challenging threat model, sacrificing some robustness in the other one compared to SAT, since it uses only the strongest attack for each training point. When training for $\\ell_{\\infty}$ and $\\ell_1$ , i.e. the extreme $\\ell_p$ -norms we consider, MAX and SAT models lie above the front drawn by the model soups, hinting that the more diverse the attacks, the more difficult it is to preserve high robustness to both. In the other cases, both methods behave", + "bbox": [ + 75, + 643, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "similarly to the soups. The main advantage given by interpolation is however the option of moving along the front without additional training cost: while one might tune the trade-off between the robustness in the two threat models in SAT, e.g. changing the sampling probability, this would still require training a new classifier for each setup.", + "bbox": [ + 496, + 90, + 890, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Soups with three threat models", + "text_level": 1, + "bbox": [ + 498, + 191, + 774, + 208 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We here study the convex combination of three models with different types of robustness. For CIFAR-10 we create soups with each $\\ell_p$ -robust classifier for $p \\in \\{\\infty, 2, 1\\}$ and its fine-tuned version into the other two threat models. We use the same models of the previous section, and sweep the interpolation weights $\\boldsymbol{w} \\in \\mathbb{R}^3$ such that $w_i \\in \\{0, 0.2, 0.4, 0.6, 0.8, 1\\}$ and $\\sum_i w_i = 1$ . In Fig. 3 and Fig. 10 (in the Appendix) we show clean accuracy (first column) and robust accuracy in $\\ell_{\\infty}$ , $\\ell_2$ and $\\ell_1$ (second to fourth columns) and their union, when a point is considered robust only if it is such against all attacks (last column).", + "bbox": [ + 496, + 215, + 890, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One can observe that, independently from the type of robustness of the base model (used as initialization for the fine-tuning), moving in the convex hull of the three parameters (e.g. $\\theta_{\\infty} + \\theta_{\\infty \\rightarrow 2} + \\theta_{\\infty \\rightarrow 1}$ in Fig. 3) allows to smoothly control the trade-off of the different types of robustness. Interestingly, the highest $\\ell_2$ -robustness is attained by intermediate soups, not by the model specifically fine-tuned w.r.t. $\\ell_2$ , suggesting that model soups might even be beneficial to robustness in individual threat models (see more below). Moreover, the highest robustness in the union is given by interpolating only the models robust w.r.t. $\\ell_{\\infty}$ and $\\ell_1$ , which is in line with the observation of [8] that training for the extreme norms is sufficient for robustness in the union of the three threat models. Although the robust accuracy in the union is lower than that of training simultaneously with all attacks e.g. with MAX (42.0% vs 47.2%), the model soups deliver competitive results without the need of co-training.", + "bbox": [ + 496, + 382, + 892, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, Fig. 4 shows that similar observations hold on IMAGENET, where we create soups fine-tuning classifiers robust w.r.t. $\\ell_{\\infty}$ , with either RESNET-50 [19] or ViT-B16 as architecture, for 1 epoch.", + "bbox": [ + 496, + 638, + 890, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Soups for improving individual threat model robustness", + "text_level": 1, + "bbox": [ + 498, + 710, + 890, + 741 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We notice in Fig. 1 and Fig. 2 that in a few cases the intermediate models obtain via parameters interpolation have higher robustness than the extreme ones, which are trained or fine-tuned with a specific threat model. As such, we analyze in more details the soups $w \\cdot \\theta_{\\infty} + (1 - w) \\cdot \\theta_{\\infty \\rightarrow 2}$ , i.e. using the original classifier robust in $\\ell_{\\infty}$ and the one fine-tuned to $\\ell_{2}$ , on both CIFAR-10 andImagenet. Fig. 5 shows the robust accuracy w.r.t. $\\ell_{\\infty}$ when varying the value of $w$ : in both case the original model $\\theta_{\\infty}$ , highlighted in red, does not attain the best robustness. Interestingly, on", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12316", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\text {s o u p :} \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 395, + 89, + 571, + 103 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/376fc52fad78ce9ebc41b72072edd7c7a3d55d0be38fe4d9856841944ed47838.jpg", + "image_caption": [ + "clean accuracy", + "$\\ell_{\\infty}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 101, + 128, + 264, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f8478d1afdea3264e8acec759a455e242c29e626d9d0f98ad430ba95fc62f9cb.jpg", + "image_caption": [ + "$\\ell_{2}$ robust accuracy", + "Figure 3. Soups of three models on CIFAR-10: we fine-tune the model robust w.r.t. $\\ell_{\\infty}$ (with WIDERESNET-28-10 architecture) to the other threat models for 10 epochs, and show clean accuracy (first column) and robust accuracy w.r.t. every threat model (second to fourth columns) and their union (last column) of the soups obtained as convex combinations of the three bases." + ], + "image_footnote": [], + "bbox": [ + 266, + 128, + 416, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8c71a16aef4dc91e5ec3881bb8dd5ef1ce817bd8e117963c1ce3ee5e49723c3c.jpg", + "image_caption": [ + "$\\ell_{1}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 418, + 128, + 566, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cf889f50ee25f7428688e2427bd03f8462ce8eeba5c168ab9b584045e012aebc.jpg", + "image_caption": [ + "$\\ell_{\\infty} + \\ell_{2} + \\ell_{1}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 568, + 128, + 720, + 220 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/70612c1ff64e32094ab9353cd276573a75f764549d5d02f1d76a52d33174bb3b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 128, + 867, + 220 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {R E S N E T} - 5 0, \\text {s o u p :} \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 357, + 297, + 611, + 311 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/788c08cd4f96c4c03fc88188e509b2d5f75098ea2bca79f502208087e989e56b.jpg", + "image_caption": [ + "clean accuracy", + "$\\ell_{\\infty}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 101, + 335, + 267, + 429 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/67cb91ab9754379204f91b1d1ae7001d4c17701ef460cfba8e5108125df0dde6.jpg", + "image_caption": [ + "$\\ell_{2}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 267, + 335, + 416, + 429 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/225223209ec03fd049328305eee9bdcaee19c51e11ca651fb70f51fda8ca1197.jpg", + "image_caption": [ + "$\\ell_{1}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 418, + 335, + 566, + 429 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b4d2102c7ad7c1070b5698ba592c26b6b370b8655c1ea3fc1c8ea3bfe8496489.jpg", + "image_caption": [ + "$\\ell_{\\infty} + \\ell_{2} + \\ell_{1}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 566, + 335, + 715, + 429 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/fb37b53187b8778df1d7675c530367128be6c4803a2127aee9efa58cddfdeb6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 715, + 337, + 867, + 429 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV I T - B 1 6, \\text {s o u p}: \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 364, + 436, + 602, + 450 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e085673a27b0a780229de90d1a99e20fb853b3ee8929a5ea0240b48389633d56.jpg", + "image_caption": [ + "clean accuracy", + "$\\ell_{\\infty}$ robust accuracy", + "Figure 4. Soups of three models on IMAGENET: we fine-tune the classifiers, with RESNET-50 (top row) and ViT-B16 (bottom) as architecture, robust w.r.t. $\\ell_{\\infty}$ for 1 epoch to the other threat models, and show clean accuracy (first column) and robust accuracy in every threat model (second to fourth columns) and their union (last column) of the classifiers obtained as convex combinations of the three bases." + ], + "image_footnote": [], + "bbox": [ + 101, + 476, + 267, + 568 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/173a55b836adc23a8ee4e05c1d8f706afb9613d7e1956621264f5e06cf9177eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 476, + 388, + 568 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a13d89755b078ae2dd39493b3368c9d6be8e1307d960531f798ba4ebfa5a9db9.jpg", + "image_caption": [ + "$\\ell_{2}$ robust accuracy", + "$\\ell_1$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 390, + 476, + 568, + 568 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f9eee60a44b632149bd0795651e75cb26ef2a97605de36c13c383bd62bbc0eb0.jpg", + "image_caption": [ + "$\\ell_{\\infty} + \\ell_{2} + \\ell_{1}$ robust accuracy" + ], + "image_footnote": [], + "bbox": [ + 568, + 476, + 720, + 568 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/62c528c8c84b0869836cd81882c25e4372e85df729e2fab86fe8fc597acd8b29.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 720, + 476, + 867, + 568 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/239ebb03df8a121a428cfc321e29bc3ea68f68e5a59e93701ff5f8bcd6f0101b.jpg", + "image_caption": [ + "Figure 5. Improvement on single threat models: we show the robust accuracy w.r.t. $\\ell_{\\infty}$ for the soups $w \\cdot \\pmb{\\theta}_{\\infty} + (1 - w) \\cdot \\pmb{\\theta}_{\\infty \\rightarrow 2}$ for varied $w$ . The original model $\\pmb{\\theta}_{\\infty}$ is highlighted in red." + ], + "image_footnote": [], + "bbox": [ + 86, + 654, + 279, + 781 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e400804cddea7a5c8932fcb8d95adb21eac361a9ff787b918fc49230f359526a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 654, + 470, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "CIFAR-10 the best soup is found with $w = 0.9$ , while for IMAGENET with $w > 1$ : this suggests that the model soups", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "should not be constrained to the convex hull of the base models, and extrapolation can lead to improvement.", + "bbox": [ + 500, + 656, + 890, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Soups for Distribution Shifts", + "text_level": 1, + "bbox": [ + 500, + 707, + 763, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Prior works [30] have shown that adversarial training w.r.t. an $\\ell_p$ -norm is able to provide some improvement in the performance in presence of non-adversarial distribution shifts, e.g. the common corruptions of IMAGENET-C [21]. However, to see such gains it is necessary to carefully select the threat model, for example which $\\ell_p$ -norm and size $\\epsilon$ to bound the perturbations, to use during training. The experiments in Sec. 4 suggest that model soups of nominal and adversarily robust classifiers yield models with a variety of intermediate behaviors, and extrapolation might even deliver models which do not merely trade-off the robust", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12317", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/49125a1c923411f433b1906f7e0b9cc30f8401979d1b9638ccb34db3dc8e4b97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 267, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b8c8adaed0ec73dd2e672ec4c0b1ac43e629c6ba9e6c54f2b8eb38cbe109a986.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 90, + 433, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/af10b5cfa528bc3770341bcac032879b1c5d1d85c53a90e1ee0b07712069d1d2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 434, + 90, + 599, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/99318e72a30d233d6c834a6163433ef00e2bba8e90eb24331a33605412a47fe1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 602, + 90, + 764, + 200 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/54aab8c3643b0caa7df213406170f626e220eb1c0a215a14f894bfae7540e236.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 769, + 172, + 888, + 251 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2599ce0d4c29cd251908b99c68ec6580636aa8c50523495629a39104cbfd6503.jpg", + "image_caption": [ + "Figure 6. Soups on IMAGENET variants: for each dataset we plot the accuracy of the 5 best performing soups of the four base models $\\theta_{\\infty}$ , $\\theta_{\\infty \\rightarrow 2}$ , $\\theta_{\\infty \\rightarrow 1}$ and $\\theta_{\\infty \\rightarrow \\mathrm{nominal}}$ , and of the individual classifiers. Additionally, we show the performance of an independently trained nominal model. All models are evaluated on the 1000 points used for the grid search of the best soups." + ], + "image_footnote": [], + "bbox": [ + 80, + 213, + 267, + 335 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f337f453e09d5fd34f91b3619b98e962d8bb164bbccc999a9f42905cbc38b034.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 213, + 433, + 335 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e71b3aa117e5714bc05664beb6a8e8d7a0e75c7fa7ef1e529a8b32e5de2e304d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 434, + 213, + 598, + 335 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/758f1867e7b3b8cc2ab6d0657511b325fc2c8615115553c10b27fd86ef4ef8bd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 599, + 213, + 766, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ness of the initial classifiers but amplify it. This flexibility could suit adaptation to various distribution shifts: that is, the various corruption types might more closely resemble the geometry of different $\\ell_p$ -balls or their union. Moreover, including a nominally fine-tuned model in the soup allows it to maintain, if necessary, high accuracy on the original dataset, which is often degraded by adversarial training [34] or test-time adaptation on shifted data [36].", + "bbox": [ + 75, + 417, + 470, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Soups for IMAGENET variants", + "text_level": 1, + "bbox": [ + 76, + 555, + 334, + 571 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup. In the following, we use models soups consisting of robust ViT fine-tuned from $\\ell_{\\infty}$ to the other threat models, and one more ViT nominally fine-tuned for 100 epochs to obtain slightly higher accuracy on clean data. For shifts, we consider several variants ofImagenet, providing a broad and diverse benchmark for our soups:Imagenet-REAL [1],Imagenet-V2 [40],Imagenet-C [21],Imagenet-A [23],Imagenet-R [20],Imagenet-SKETCH [49], and CONFLICT STIMULI [12]. We consider the setting of few-shot supervised adaptation, with a small set of labelled images from each shift, which we use to select the best soups.", + "bbox": [ + 75, + 580, + 468, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Soup selection via grid search. Since evaluating the accuracy of many soups on the entirety of the datasets would be extremely expensive, we search for the best combination of the four models on a random subset of 1000 points from each dataset, with the exception of CONFLICT STIMULI for which all 1280 images are used (for IMAGENET-C we use all corruption types and severities, then aggregate the results). Restricting our search to a subset also serves our aim of finding a model soup which generalizes to the new distribution by only seeing a few examples. We eval", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "uate all the possible affine combinations with weights in the range $[-0.4, 1.4]$ with granularity 0.2, which amounts to 460 models in total. In Fig. 6 we compare, for each dataset, the accuracy of the 5 best soups to that of each individual classifier used for creating the soups and of a nominal model trained independently: for all datasets apart from IMAGENET the top soups outperform the individual models. Moreover, we notice that the best individual model varies across datasets, indicating that it might be helpful to merge networks with different types of robustness.", + "bbox": [ + 496, + 417, + 893, + 569 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison to existing methods. Having selected the best soup for each variant (dataset-specific soups) on its chosen few-shot adaptation set, we evaluate the soup on the test set of the variant (results in Table 1). We also evaluate the model soup that attains the best average case accuracy over the adaptation sets for all variants (single soup), in order to gauge the best performance of a single, general model soup. We compare the soups to a nominal model, the $\\ell_{\\infty}$ -robust classifier used in the soups, their ensemble, the Masked Autoencoders of [18], AdvProp [54], PyramidAT [24], and the ensemble obtained by averaging the output (after softmax) of the four models included in the soups. Selecting the best soup on 1000 images of each datasets (results in the last row of Table 1) leads in 4 out of the 8 datasets to the best accuracy, and only slightly suboptimal values in the other cases: in particular, parameters interpolations is very effective on stronger shifts likeImagenet-R and CONFLICT STIMULI, where it attains almost $8\\%$ better performance than the closest baseline. Unsurprisingly, it is more challenging to improve on datasets likeImagenetV2 which are very close to the originalImagenet. Over", + "bbox": [ + 496, + 583, + 892, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12318", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f49d3187e344df8d79a331634ba179db39c3138e7e68a66891613ce66b65c74b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SETUP# FPIMAGENETIN-REALIN-V2IN-AIN-RIN-SKETCHCONFLICT STIMULIIN-CMEAN
Baselines
Nominal training×182.64%87.33%71.42%28.03%47.94%34.43%30.47%64.45%55.84%
Adversarial training×176.88%83.91%64.81%12.35%55.76%40.11%59.45%55.44%56.09%
Fine-tuned MAE-B16×183.10%88.02%72.80%37.92%49.30%35.69%27.81%63.23%57.23%
AdvProp×183.39%88.06%73.17%34.81%53.04%39.25%38.98%70.39%60.14%
Pyramid-AT×183.14%87.82%72.53%32.72%51.78%38.60%37.27%67.01%58.86%
Indep. networks ensemble×282.86%87.78%71.73%25.99%54.20%37.33%46.41%65.61%58.99%
Individual networks ensemble×481.31%86.97%70.21%23.13%54.82%39.51%56.02%68.17%60.02%
Fixed grid search on 1000 images
Single soup×182.49%87.85%71.99%34.31%53.84%39.84%38.52%66.82%59.46%
Dataset-specific soups×182.29%87.89%71.95%38.27%56.39%40.73%67.03%69.34%(64.24%)
", + "bbox": [ + 83, + 87, + 890, + 270 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Comparison on IMAGENET variants: we report the classification accuracy of various models on the IMAGENET variants, together with the number of forward passes they require. The soups are selected via a fixed grid search on the interpolation weights with 1000 points for each dataset. The last row shows the results of the best found soup for each dataset.", + "bbox": [ + 75, + 280, + 892, + 324 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f273e7dfbc4421380f719e44dbca9edc25111b824660e14ee15c92c88517cf49.jpg", + "image_caption": [ + "Figure 7. Soup compositions on IMAGENET variants: for each dataset we plot the composition of the 5 best soups, i.e. the linear weights for the individual models, as measured by grid search over 1000 points on weights in the range $[-0.4, 1.4]$ with granularity 0.2. Additionally we show the composition of the model achieving the best average accuracy over all 8 variants." + ], + "image_footnote": [], + "bbox": [ + 81, + 339, + 888, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "all, The soup selected for best average accuracy (across all datasets) outperforms all baselines, except for the ensemble of four models (with $4 \\times$ the inference cost), and AdvProp, which requires co-training of clean and adversarial points. These results show that soups with robust classifiers are a promising avenue for quickly adapting to distribution shifts.", + "bbox": [ + 75, + 614, + 470, + 707 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Composition of the soups. To analyze which types of classifiers are most relevant for performance on every distribution shift, we plot in Fig. 7 the breakdown of the weights of the five best soups (more intense colors indicate that the corresponding weight or a larger one is used more often in the top-5 soups). First, one can see that the nominally fine-tuned model (in black) is dominant, with weights of 0.8 or 1, onImagenet,Imagenet-REAL,ImagenetV2,Imagenet-A andImagenet-C: this could be expected since these datasets are closer toImagenet itself, i.e. the distribution shift is smaller, which is what nominal training optimizes for (in fact, the nominal models achieve", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "higher accuracy than adversarially trained ones on these datasets in Fig. 6). However, in all cases there is a contribution of some of the $\\ell_p$ -robust networks. On IMAGENET-R, IMAGENET-SKETCH and CONFLICT STIMULI, the model robust w.r.t. $\\ell_{\\infty}$ plays instead the most relevant role, again in line with the results in Table 1. Interestingly, in the case of CONFLICT STIMULI, the nominal classifier has a weight -0.4 (the smallest in the grid search) for all top performing soups: we hypothesize that this has the effect of reduce the texture bias typical of nominal model and emphasize the attention to shapes already important in adversarially trained classifiers. Finally, we show the composition of the soup which has the best average accuracy over all datasets (last column of Fig. 7), where the nominal and $\\ell_{\\infty}$ -robust models have similar positive weight.", + "bbox": [ + 496, + 614, + 890, + 843 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "How many images does it take to find a good soup? To identify the practical limit of supervision for soup selection, we study the effect of varying the number of labelled images", + "bbox": [ + 498, + 854, + 892, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12319", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/99ddd8edba0ad97da74370ed64ff377d425de45a5800dfc0365704a3b152fe37.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 90, + 467, + 196 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d7833a4dda6cf990526fa47856d6da16b9b69085e9acefd77390abf84462f26e.jpg", + "image_caption": [ + "Figure 8. Soup selection data efficiency: we vary the number of images for selecting the best performing soups on different datasets. For each case, we plot the average accuracy on a held-out test set, and its standard deviation over 50 trials." + ], + "image_footnote": [], + "bbox": [ + 83, + 203, + 467, + 319 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9558b5db971395a6df2598273460634c0a37bead8ad45b28cfa280fc9b031cd4.jpg", + "image_caption": [ + "Figure 9. Soup compositions on IMAGENET-C: we plot the model-wise weights of the best soups across types and severities." + ], + "image_footnote": [], + "bbox": [ + 81, + 429, + 465, + 612 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "used to select the best soup on a new dataset. For this analysis we randomly choose 500 images from the adaptation set used for the grid search to create a held-out test set. From the remaining images, we uniformly sample $k$ elements, select the soup which performs best on such $k$ points, and then evaluate it on this test set. We repeat this procedure for $k \\in \\{10, 30, 100, 300, 500\\}$ for 50 times each with different random seeds. In Fig. 8 we plot the average accuracy on the held-out test set, with standard deviation, when varying $k$ : increasing the number of points above 100 achieves high test accuracy with limited variance. This suggests that soup selection, and thus model adaptation, can be carried out with as few as 100 examples of the new distribution.", + "bbox": [ + 75, + 703, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. A closer look at IMAGENET-C", + "text_level": 1, + "bbox": [ + 500, + 90, + 756, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While our experiments have considered IMAGENET-C as a single dataset, it consists of 15 corruptions types, each with 5 severity levels. As the various corruptions have different characteristics, one might expect the best soup to vary across them. In Fig. 9 we plot the composition of the top-5 soups for each severity level for two corruption types (as done in Fig. 7). The weights of the individual classifiers significantly change across distribution shifts: for both corruption types, increasing the severity (making perturbations stronger) leads to a reduction in the nominal weight in favor of a robust weight. However, in the case of \"pixelate\" the soups concentrate on the $\\ell_1$ -robust network, while for \"jpeg compression\" this happens for $\\ell_{\\infty}$ . Similar visualization for the remaining IMAGENET-C subsets are found in Fig. 11 of the Appendix. This highlights the importance of interpolating models with different types of robustness, and implies that considering each corruption type (including severity levels) as independent datasets could further improve the performance of the soups on IMAGENET-C.", + "bbox": [ + 496, + 112, + 893, + 402 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and Limitations", + "text_level": 1, + "bbox": [ + 498, + 414, + 754, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Merging models with different types of robustness enables strong control of classifier performance by tuning only a few soup weights. Soups can find models which perform well even on distributions unseen during training (e.g. the IMAGENET variants). Moreover, our framework avoids constraining on multiple threats: this makes it possible to fine-tune models with additional attacks as they present themselves, and enrich the soups with them.", + "bbox": [ + 496, + 438, + 893, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "At the moment, our soups contain only nominal or $\\ell_{p}$ -robust models, but expanding the diversity of models might aid adaptation to new datasets. We selected our soups with few-shot supervision, but other settings could potentially use soups, such as unsupervised domain adaptation [37,42], on labeled clean and unlabeled shifted data, and test-time adaptation [43,44,48], on unlabeled examples alone. Moreover, in our evaluation we have constrained the soups to belong to a fixed grid, which might miss better models: future work could develop automatic schemes to optimize the soup weights, possibly with even fewer examples, or without labeled examples (as done for test-time adaptation of non-robust models).", + "bbox": [ + 496, + 560, + 893, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 768, + 620, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We show that combining the parameters of robust classifiers, without additional training, achieves a smooth trade-off of robustness in different $\\ell_p$ -threat models. This allows us to discover models which perform well on distribution shifts with only a limited number of examples of each shift. In these ways, model soups serve as a good starting point to efficiently adapt classifiers to changes in data distributions.", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12320", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lucas Beyer, Olivier J. Henaff, Alexander Kolesnikov, Xiaohua Zhai, and Aaron van den Oord. Are we done with ImageNet? arXiv preprint arXiv:2006.07159, 2020. 6", + "[2] Battista Biggio, Igino Corona, Davide Maiorca, Blaine Nelson, Nedim Srndic, Pavel Laskov, Giorgio Giacinto, and Fabio Roli. 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In International Conference on Learning Representations, 2022. 12" + ], + "bbox": [ + 78, + 90, + 468, + 218 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "12323", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/a6551453-1b77-4f6c-8df2-df18da134652_model.json b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/a6551453-1b77-4f6c-8df2-df18da134652_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c21f875857c76887db7513c30e6e8d915e67941a --- /dev/null +++ b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/a6551453-1b77-4f6c-8df2-df18da134652_model.json @@ -0,0 +1,2488 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.252, + 0.131, + 0.72, + 0.175 + ], + "angle": 0, + "content": "Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts" + }, + { + "type": "text", + "bbox": [ + 0.117, + 0.203, + 0.307, + 0.24 + ], + "angle": 0, + "content": "Francesco Croce* \nUniversity of Tübingen" + }, + { + "type": "text", + "bbox": [ + 0.344, + 0.204, + 0.543, + 0.24 + ], + "angle": 0, + "content": "Sylvestre-Alvise Rebuffi DeepMind" + }, + { + "type": "text", + "bbox": [ + 0.581, + 0.204, + 0.715, + 0.24 + ], + "angle": 0, + "content": "Evan Shelhamer DeepMind" + }, + { + "type": "text", + "bbox": [ + 0.754, + 0.204, + 0.854, + 0.24 + ], + "angle": 0, + "content": "Sven Gowal DeepMind" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.474, + 0.565 + ], + "angle": 0, + "content": "Adversarial training is widely used to make classifiers robust to a specific threat or adversary, such as \\(\\ell_p\\)-norm bounded perturbations of a given \\(p\\)-norm. However, existing methods for training classifiers robust to multiple threats require knowledge of all attacks during training and remain vulnerable to unseen distribution shifts. In this work, we describe how to obtain adversially-robust model soups (i.e., linear combinations of parameters) that smoothly trade-off robustness to different \\(\\ell_p\\)-norm bounded adversaries. We demonstrate that such soups allow us to control the type and level of robustness, and can achieve robustness to all threats without jointly training on all of them. In some cases, the resulting model soups are more robust to a given \\(\\ell_p\\)-norm adversary than the constituent model specialized against that same adversary. Finally, we show that adversially-robust model soups can be a viable tool to adapt to distribution shifts from a few examples." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.593, + 0.21, + 0.609 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.471, + 0.877 + ], + "angle": 0, + "content": "Deep networks have achieved great success on several computer vision tasks and have even reached super-human accuracy [19, 31]. However, the outputs of such models are often brittle, and tend to perform poorly on inputs that differ from the distribution of inputs at training time, in a condition known as distribution shift [37]. Adversarial perturbations are a prominent example of this condition: small, even imperceptible, changes to images can alter predictions to cause errors [2, 46]. In addition to adversarial inputs, it has been noted that even natural shifts, e.g. different weather conditions, can significantly reduce the accuracy of even the best vision models [13, 21, 40]. Such drops in accuracy are undesirable for robust deployment, and so a lot of effort has been invested in correcting them. Adversarial training [34] and its extensions [15, 39, 58] are currently the most effective methods to improve empirical robustness to adversarial attacks. Similarly, data augmen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.276, + 0.895, + 0.488 + ], + "angle": 0, + "content": "tation is the basis of several techniques that improve robustness to non-adversarial/natural shifts [3, 11, 22]. While significant progress has been made on defending against a specific, selected type of perturbations (whether adversarial or natural), it is still challenging to make a single model robust to a broad set of threats and shifts. For example, a classifier adversarily-trained for robustness to \\(\\ell_p\\)-norm bounded attacks is still vulnerable to attacks in other \\(\\ell_q\\)-threat models [29, 47]. Moreover, methods for simultaneous robustness to multiple attacks require jointly training on all [33, 35] or a subset of them [8]. Most importantly, controlling the trade-off between different types of robustness (and nominal performance) remains difficult and requires training several classifiers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.896, + 0.779 + ], + "angle": 0, + "content": "Inspired by model soups [52], which interpolate the parameters of a set of vision models to achieve state-of-the-art accuracy on IMAGENET, we investigate the effects of interpolating robust image classifiers. We complement their original recipe for soups by own study of how to pretrain, fine-tune, and combine the parameters of models adversarially-trained against \\(\\ell_p\\)-norm bounded attacks for different \\(p\\)-norms. To create models for soups, we pre-train a single robust model and fine-tune it to the target threat models (using the efficient technique of [8]). We then establish that it is possible to smoothly trade-off robustness to different threat models by moving in the convex hull of the parameters of each robust classifier, while achieving competitive performance with methods that train on multiple \\(p\\)-norm adversaries simultaneously. Unlike alternatives, our soups can uniquely (1) choose the level of robustness to each threat model without any further training and (2) quickly adapt to new unseen attacks or shifts by simply tuning the weighting of the soup." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Previous works [24, 30, 54] have shown that adversarial training with \\(\\ell_p\\)-norm bounded attacks can help to improve performance on natural shifts if carefully tuned. We show that model soups of diverse classifiers, with different types of robustness, offer greater flexibility for finding models that perform well across various shifts, such as IMAGENET variants. Furthermore, we show that a limited number of images of the new distribution are sufficient to select the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.348, + 0.901 + ], + "angle": 0, + "content": "*Work done during an internship at DeepMind." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12313" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "weights of such a model soup. Examining the composition of the best soups brings insights about which features are important for each dataset and shift. Finally, while the capability of selecting a model specific to each image distribution is a main point of our model soups, we also show that it is possible to jointly select a soup for average performance across several IMAGENET variants to achieve better accuracy than adversarial and self-supervised baselines [18, 24]." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.213, + 0.402, + 0.228 + ], + "angle": 0, + "content": "Contributions. In summary, we show that soups" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.228, + 0.47, + 0.288 + ], + "angle": 0, + "content": "- can merge nominal and \\(\\ell_p\\)-robust models (for various \\(p\\)): efficient fine-tuning from one robust model obtains a set of models with diverse robustness [8] and compatible parameters for creating model soups [52] (Sec. 3)," + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.289, + 0.469, + 0.333 + ], + "angle": 0, + "content": "- can control the level of robustness to each threat model and achieve, without more training, competitive performance against multi-norm robustness training (Sec. 4)," + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.334, + 0.469, + 0.363 + ], + "angle": 0, + "content": "- are not limited to interpolation, but can find more effective classifiers by extrapolation (Sec. 4.3)," + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.364, + 0.469, + 0.394 + ], + "angle": 0, + "content": "- enable adaptation to unseen distribution shifts on only a few examples (Sec. 5)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.228, + 0.47, + 0.394 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.408, + 0.218, + 0.423 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.433, + 0.47, + 0.675 + ], + "angle": 0, + "content": "Adversarial robustness to multiple threat models. Most methods focus on achieving robustness in a single threat model, i.e. to a specific type of attacks used during training. However, this is not sufficient to obtain robustness to unseen attacks. As a result, further work aims to train classifiers for simultaneous robustness to multiple attacks, and the most popular scenario considers a set of \\(\\ell_p\\)-norm bounded perturbations. The most successful methods [33, 35, 47] are based on adversarial training and differ in how the multiple threats are combined. Notably, all need to use every attack at training time. To reduce the computational cost of obtaining multiply-robust models, one can fine-tune a singly-robust model by one of the above mentioned methods [8], even for only a small number of epochs. Our soups are more flexible by skipping simultaneous adversarial training across multiple attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Adversarial training for distribution shifts. While robustness to adversarial attacks and natural shifts are not the same goal, previous works nevertheless show that it is possible to leverage adversarial training with \\(\\ell_p\\)-norm bounded attacks to improve performance on the common corruptions of [21]. First, AdvProp [54] co-trains models on clean and adversarial images (in the \\(\\ell_{\\infty}\\)-threat model) with dual normalization layers that specialize to each type of input. The clean branch of the dual model achieves higher accuracy than nominal training on IMAGENET and its variants. Similar results are obtained by Pyramid-AT [24] by its design of a specific attack to adversarily train vision transformers. Finally, [30] carefully selecting the size of the adversarial perturbations, i.e., their \\(\\ell_{\\infty}\\)- or \\(\\ell_2\\)-norm, for standard adversarial training [34] achieves competitive performance on" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.877, + 0.107 + ], + "angle": 0, + "content": "common corruptions on CIFAR-10 and IMAGENET-100." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Model soups. Ensembling or averaging the parameters of intermediate models found during training is an effective technique to improve both clean accuracy [25, 28] and robustness [14, 39]. Recently, [52] propose model soups which interpolate the parameters of networks finetuned with different hyperparameters configurations from the same pre-trained model. This yields improved classification accuracy onImagenet. Along the same line, [27] fine-tune a model trained onImagenet on several new image classification datasets, and show that interpolating the original and fine-tuned parameters yields classifiers that perform well on all tasks. Additional related work is discussed in App. A." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.318, + 0.884, + 0.335 + ], + "angle": 0, + "content": "3. Model Interpolation across Different Tasks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.54 + ], + "angle": 0, + "content": "In the following, we formally introduce the two main components of our procedure to merge adversarially robust models: (1) obtaining models which can interpolated by fine-tuning a single \\(\\ell_p\\)-robust classifiers, and (2) interpolation of their weights to balance their different types of robustness. We highlight that our setup diverges from that of prior works about parameters averaging: in fact, both [27, 52] combine models fine-tuned on the same task, i.e. achieving high classification accuracy of unperturbed images, either on a fixed dataset and different hyperparameter configurations [52], or varying datasets [27]. In our case, the individual models are trained for robustness to different types of attacks, i.e. with distinct loss functions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.55, + 0.816, + 0.566 + ], + "angle": 0, + "content": "3.1. Adversarial training and fine-tuning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.573, + 0.892, + 0.68 + ], + "angle": 0, + "content": "Let us denote \\(\\mathcal{D} = \\{(x_i, y_i)\\}_i\\) the training set, with \\(x_i \\in \\mathbb{R}^d\\) indicating an image and \\(y_i \\in \\{1, \\dots, K\\}\\) the corresponding label, and \\(\\Delta: \\mathbb{R}^d \\to \\mathbb{R}^d\\) the function which characterizes a threat model, that maps an input \\(x\\) to a set \\(\\Delta(x) \\subset \\mathbb{R}^d\\) of possible perturbed versions of the original image. For example, \\(\\ell_p\\)-norm bounded adversarial attacks with budget \\(\\epsilon > 0\\) in the image space can be described by" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.69, + 0.891, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\Delta (\\boldsymbol {x}) = \\left\\{\\boldsymbol {\\delta} \\in \\mathbb {R} ^ {d}: \\| \\boldsymbol {\\delta} \\| _ {p} \\leq \\epsilon , \\boldsymbol {x} + \\boldsymbol {\\delta} \\in [ 0, 1 ] ^ {d} \\right\\}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.891, + 0.752 + ], + "angle": 0, + "content": "Then, one can train a classifier \\(f:\\pmb {\\theta}\\times \\mathbb{R}^d\\to \\mathbb{R}^K\\) parameterized by \\(\\pmb {\\theta}\\in \\Theta\\) with adversarial training [34] by solving" + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.763, + 0.892, + 0.798 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\boldsymbol {\\theta} \\in \\Theta} \\sum_ {(\\boldsymbol {x}, y) \\in \\mathcal {D}} \\max _ {\\boldsymbol {\\delta} \\in \\Delta (\\boldsymbol {x})} \\mathcal {L} (f (\\boldsymbol {\\theta}, x + \\boldsymbol {\\delta}), y), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "for a given loss function \\(\\mathcal{L}:\\mathbb{R}^K\\times \\mathbb{R}^K\\to \\mathbb{R}\\) (e.g., cross-entropy), with the goal of obtaining a model robust to the perturbations described by \\(\\Delta\\). Note that this boils down to nominal training when \\(\\Delta (\\cdot) = \\{\\mathbf{0}\\}\\) and no perturbation is applied on the training images. We are interested in the case where multiple threat models are available, and indicate" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "12314" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.089, + 0.36, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.375, + 0.089, + 0.612, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.089, + 0.847, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.893, + 0.274 + ], + "angle": 0, + "content": "Figure 1. Soups of two models on CIFAR-10: for all pairs \\((p,q)\\) we show the \\(\\ell_{p}\\)- vs \\(\\ell_{q}\\)-robust accuracy of the soups \\(w\\cdot \\theta_{p} + (1 - w)\\cdot \\theta_{p\\rightarrow q}\\) and \\(w\\cdot \\theta_q + (1 - w)\\cdot \\theta_{q\\to p}\\) varying \\(w\\in [0,1]\\). We also show results for MAX and SAT with simultaneous use of the two threat models." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.287, + 0.283, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.287, + 0.488, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.494, + 0.287, + 0.695, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.287, + 0.897, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.443, + 0.893, + 0.486 + ], + "angle": 0, + "content": "Figure 2. Soups of two models on IMAGENET: for \\( p \\in \\{2,1\\} \\) we show the \\( \\ell_{p^-} \\) vs \\( \\ell_{\\infty} \\)-robust accuracy of the soups \\( w \\cdot \\theta_{\\infty} + (1 - w) \\cdot \\theta_{\\infty \\rightarrow p} \\) varying \\( w \\in [0,1] \\) (first and second columns). Moreover, we show the soups obtained combining \\( \\theta_{\\infty \\rightarrow 2} \\) and \\( \\theta_{\\infty \\rightarrow 1} \\) (third), or \\( \\theta_{\\infty} \\) and \\( \\theta_{\\infty \\rightarrow \\text{nominal}} \\) (fourth). For the case of two \\( \\ell_{p^-} \\)-threat models, we also show the results of fine-tuning models with MAX and SAT." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.512, + 0.469, + 0.588 + ], + "angle": 0, + "content": "with \\(\\Delta_{\\mathrm{nominal}}\\) nominal training, and \\(\\Delta_p\\) for \\(p \\in \\{\\infty, 2, 1\\}\\) the perturbations with bounded \\(\\ell_p\\)-norm as described in Eq. 1. We focus on such tasks since they are the most common choices for adversarial defenses, in particular by methods focusing on multiple norm robustness [35, 47]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.589, + 0.47, + 0.742 + ], + "angle": 0, + "content": "Notably, it is possible to efficiently obtain a model robust to \\(\\Delta_q\\) by fine-tuning for a single (or few) epoch with adversarial training w.r.t. \\(\\Delta_q\\) a classifier pre-trained to be robust in \\(\\Delta_p\\), with \\(p \\neq q\\) and \\(p, q \\in \\{\\infty, 2, 1\\}\\) [8]. For example, in this way one can efficiently derive specialized classifiers \\(\\Delta_2, \\Delta_1, \\Delta_{\\mathrm{nominal}}\\) for each task from a single model \\(f\\) robust w.r.t. \\(\\ell_{\\infty}\\). However, this does not work well when a nominal classifier is used as starting point for the short fine-tuning. In the following, we denote with \\(\\theta_{p \\rightarrow q}\\) the parameters resulting from fine-tuning to \\(\\Delta_q\\) a base model \\(\\theta_p\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.469, + 0.787 + ], + "angle": 0, + "content": "3.2. Merging different types of robustness via linear combinations in parameter space" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We want to explore the properties of the models obtained by taking linear combinations of the parameters of classifiers with different types of robustness. To do so, there needs to be a correspondence among the parameters of different individual networks: [52] achieve this by merging differently fine-tuned versions of the same pre-trained model. As mentioned above, fine-tuning an \\(\\ell_p\\)-robust clas" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.893, + 0.589 + ], + "angle": 0, + "content": "sifier allows to change it to achieve robustness in a new threat model [8]: we exploit such property to create model soups, as named by [52]. Formally, we create a model soup from \\( n \\) individual networks with parameters \\( \\pmb{\\theta}^{1},\\dots,\\pmb{\\theta}^{n} \\) with weights \\( \\pmb{w} = (w_{1},\\dots,w_{n})\\in \\mathbb{R}^{n} \\) as" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.604, + 0.892, + 0.643 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} ^ {w} = \\sum_ {i = 1} ^ {n} w _ {i} \\cdot \\boldsymbol {\\theta} ^ {i}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.894, + 0.749 + ], + "angle": 0, + "content": "and the corresponding classifier is given by \\( f(\\pmb{\\theta}^{\\pmb{w}},\\cdot):\\mathbb{R}^{d}\\to \\mathbb{R}^{K} \\). While any choice of \\( \\pmb{w} \\) is possible, we focus on the case of affine combinations, i.e. \\( \\sum_{i}w_{i} = 1 \\). Moreover, we consider soups which are either convex combinations of the individual models, with \\( w_{1},\\ldots ,w_{n}\\geq 0 \\), or obtained by extrapolations, i.e. with negative elements in \\( \\pmb{w} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.72, + 0.787 + ], + "angle": 0, + "content": "4. Soups for \\(\\ell_p\\)-robustness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.902 + ], + "angle": 0, + "content": "We measure adversarial robustness in the \\(\\ell_p\\)-threat model with bounds \\(\\epsilon_p\\): on CIFAR-10 we use \\(\\epsilon_{\\infty} = 8 / 255\\), \\(\\epsilon_2 = 128 / 255\\), \\(\\epsilon_1 = 12\\), on IMAGENET \\(\\epsilon_{\\infty} = 4 / 255\\), \\(\\epsilon_2 = 4\\), \\(\\epsilon_1 = 255\\). If not specified otherwise, we use the full test set for CIFAR-10 and 5000 images from the IMAGENET validation set, and attack by AUTOPGD [6,7] with 40 steps. More details are provided in App. B." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12315" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.342, + 0.108 + ], + "angle": 0, + "content": "4.1. Soups with two threat models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.268 + ], + "angle": 0, + "content": "CIFAR-10. We explore the effect of interpolating two models robust to different \\(\\ell_p\\)-norm bounded attacks for \\(p \\in \\{\\infty, 2, 1\\}\\). We consider classifiers with WIDERES-NET-28-10 [56] architecture trained on CIFAR-10. For every threat model, we first train a robust classifier with adversarial training from random initialization. Then, we fine-tune the resulting model with adversarial training on each of the other threat models for 10 epochs. In Fig. 1 we show, for each pair of threat models \\((\\Delta_p, \\Delta_q)\\), the trade-off of robust accuracy w.r.t. \\(\\ell_p\\) and \\(\\ell_q\\) for the soups" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.276, + 0.416, + 0.295 + ], + "angle": 0, + "content": "\\[\nw \\cdot \\pmb {\\theta} _ {p} + (1 - w) \\cdot \\pmb {\\theta} _ {p \\rightarrow q} \\quad \\mathrm {f o r} \\quad w \\in [ 0, 1 ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.304, + 0.206, + 0.32 + ], + "angle": 0, + "content": "and symmetrically" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.33, + 0.418, + 0.348 + ], + "angle": 0, + "content": "\\[\nw \\cdot \\boldsymbol {\\theta} _ {q} + (1 - w) \\cdot \\boldsymbol {\\theta} _ {q \\rightarrow p} \\quad \\text {f o r} \\quad w \\in [ 0, 1 ].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.493 + ], + "angle": 0, + "content": "Interpolating the parameters of models trained with a single \\(\\ell_p\\)-norm controls the balance between the two types of robustness: for example, Fig. 1 (middle plot) shows that moving from \\(\\theta_{\\infty}\\) to \\(\\theta_{\\infty \\rightarrow 1}\\) (blue curve), i.e. decreasing \\(w\\) from 1 to 0 in the corresponding soup, progressively reduces the robust accuracy w.r.t. \\(\\ell_{\\infty}\\) to improve robustness w.r.t. \\(\\ell_1\\). Moreover, for similar threat models (i.e. the pairs \\((\\ell_2, \\ell_1)\\) and \\((\\ell_2, \\ell_{\\infty})\\)) some intermediate networks are more robust than the extremes trained specifically for each threat model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.645 + ], + "angle": 0, + "content": "IMAGENET. We now fine-tune a VIT-B16 [10] robust w.r.t. \\(\\ell_{\\infty}\\) on IMAGENET to the other threat models, including nominal training, for either 1/3, 1 or 3 epochs. Fig. 2 shows that interpolation of parameters is effective even in this setup, and allows to easily balance nominal and robust accuracy (fourth plot). Moreover, it is possible to create soups with two fine-tuned models, i.e. \\(\\theta_{\\infty \\rightarrow 2}\\) and \\(\\theta_{\\infty \\rightarrow 1}\\). Finally, increasing the number of fine-tuning steps yields better performance in the target threat model, which in turn generally leads to better soups." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Comparison to multi-norm robustness methods. Fig. 1 and Fig. 2 compare the performance of the model soups to that of models trained with methods for robustness in the union of multiple threat models. In particular, we show the results of MAX [47], which computes perturbations for each threat model and trains on that attaining the highest loss, and SAT [33], which samples uniformly at random for each training batch the attack to use. We train models with both methods for all pairs of threat models: as expected, MAX tends to focus on the most challenging threat model, sacrificing some robustness in the other one compared to SAT, since it uses only the strongest attack for each training point. When training for \\(\\ell_{\\infty}\\) and \\(\\ell_1\\), i.e. the extreme \\(\\ell_p\\)-norms we consider, MAX and SAT models lie above the front drawn by the model soups, hinting that the more diverse the attacks, the more difficult it is to preserve high robustness to both. In the other cases, both methods behave" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.184 + ], + "angle": 0, + "content": "similarly to the soups. The main advantage given by interpolation is however the option of moving along the front without additional training cost: while one might tune the trade-off between the robustness in the two threat models in SAT, e.g. changing the sampling probability, this would still require training a new classifier for each setup." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.193, + 0.776, + 0.209 + ], + "angle": 0, + "content": "4.2. Soups with three threat models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.217, + 0.892, + 0.382 + ], + "angle": 0, + "content": "We here study the convex combination of three models with different types of robustness. For CIFAR-10 we create soups with each \\(\\ell_p\\)-robust classifier for \\(p \\in \\{\\infty, 2, 1\\}\\) and its fine-tuned version into the other two threat models. We use the same models of the previous section, and sweep the interpolation weights \\(\\boldsymbol{w} \\in \\mathbb{R}^3\\) such that \\(w_i \\in \\{0, 0.2, 0.4, 0.6, 0.8, 1\\}\\) and \\(\\sum_i w_i = 1\\). In Fig. 3 and Fig. 10 (in the Appendix) we show clean accuracy (first column) and robust accuracy in \\(\\ell_{\\infty}\\), \\(\\ell_2\\) and \\(\\ell_1\\) (second to fourth columns) and their union, when a point is considered robust only if it is such against all attacks (last column)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.893, + 0.64 + ], + "angle": 0, + "content": "One can observe that, independently from the type of robustness of the base model (used as initialization for the fine-tuning), moving in the convex hull of the three parameters (e.g. \\(\\theta_{\\infty} + \\theta_{\\infty \\rightarrow 2} + \\theta_{\\infty \\rightarrow 1}\\) in Fig. 3) allows to smoothly control the trade-off of the different types of robustness. Interestingly, the highest \\(\\ell_2\\)-robustness is attained by intermediate soups, not by the model specifically fine-tuned w.r.t. \\(\\ell_2\\), suggesting that model soups might even be beneficial to robustness in individual threat models (see more below). Moreover, the highest robustness in the union is given by interpolating only the models robust w.r.t. \\(\\ell_{\\infty}\\) and \\(\\ell_1\\), which is in line with the observation of [8] that training for the extreme norms is sufficient for robustness in the union of the three threat models. Although the robust accuracy in the union is lower than that of training simultaneously with all attacks e.g. with MAX (42.0% vs 47.2%), the model soups deliver competitive results without the need of co-training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.701 + ], + "angle": 0, + "content": "Finally, Fig. 4 shows that similar observations hold on IMAGENET, where we create soups fine-tuning classifiers robust w.r.t. \\(\\ell_{\\infty}\\), with either RESNET-50 [19] or ViT-B16 as architecture, for 1 epoch." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.711, + 0.892, + 0.742 + ], + "angle": 0, + "content": "4.3. Soups for improving individual threat model robustness" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We notice in Fig. 1 and Fig. 2 that in a few cases the intermediate models obtain via parameters interpolation have higher robustness than the extreme ones, which are trained or fine-tuned with a specific threat model. As such, we analyze in more details the soups \\( w \\cdot \\theta_{\\infty} + (1 - w) \\cdot \\theta_{\\infty \\rightarrow 2} \\), i.e. using the original classifier robust in \\( \\ell_{\\infty} \\) and the one fine-tuned to \\( \\ell_{2} \\), on both CIFAR-10 andImagenet. Fig. 5 shows the robust accuracy w.r.t. \\( \\ell_{\\infty} \\) when varying the value of \\( w \\): in both case the original model \\( \\theta_{\\infty} \\), highlighted in red, does not attain the best robustness. Interestingly, on" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12316" + } + ], + [ + { + "type": "equation", + "bbox": [ + 0.396, + 0.09, + 0.573, + 0.104 + ], + "angle": 0, + "content": "\\[\n\\text {s o u p :} \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.107, + 0.22, + 0.12 + ], + "angle": 0, + "content": "clean accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.107, + 0.382, + 0.12 + ], + "angle": 0, + "content": "\\(\\ell_{\\infty}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.416, + 0.107, + 0.532, + 0.12 + ], + "angle": 0, + "content": "\\(\\ell_{2}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.107, + 0.684, + 0.12 + ], + "angle": 0, + "content": "\\(\\ell_{1}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.107, + 0.862, + 0.12 + ], + "angle": 0, + "content": "\\(\\ell_{\\infty} + \\ell_{2} + \\ell_{1}\\) robust accuracy" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.129, + 0.266, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.129, + 0.418, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.129, + 0.568, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.129, + 0.721, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.722, + 0.129, + 0.869, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.241, + 0.894, + 0.285 + ], + "angle": 0, + "content": "Figure 3. Soups of three models on CIFAR-10: we fine-tune the model robust w.r.t. \\(\\ell_{\\infty}\\) (with WIDERESNET-28-10 architecture) to the other threat models for 10 epochs, and show clean accuracy (first column) and robust accuracy w.r.t. every threat model (second to fourth columns) and their union (last column) of the soups obtained as convex combinations of the three bases." + }, + { + "type": "equation", + "bbox": [ + 0.358, + 0.298, + 0.612, + 0.312 + ], + "angle": 0, + "content": "\\[\n\\operatorname {R E S N E T} - 5 0, \\text {s o u p :} \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.315, + 0.219, + 0.328 + ], + "angle": 0, + "content": "clean accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.315, + 0.381, + 0.328 + ], + "angle": 0, + "content": "\\(\\ell_{\\infty}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.417, + 0.315, + 0.532, + 0.328 + ], + "angle": 0, + "content": "\\(\\ell_{2}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.315, + 0.684, + 0.328 + ], + "angle": 0, + "content": "\\(\\ell_{1}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.315, + 0.862, + 0.328 + ], + "angle": 0, + "content": "\\(\\ell_{\\infty} + \\ell_{2} + \\ell_{1}\\) robust accuracy" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.337, + 0.268, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.337, + 0.418, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.419, + 0.337, + 0.568, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.568, + 0.337, + 0.716, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.717, + 0.338, + 0.868, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.365, + 0.438, + 0.604, + 0.451 + ], + "angle": 0, + "content": "\\[\nV I T - B 1 6, \\text {s o u p}: \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}\n\\]" + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.455, + 0.219, + 0.467 + ], + "angle": 0, + "content": "clean accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.455, + 0.381, + 0.467 + ], + "angle": 0, + "content": "\\(\\ell_{\\infty}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.417, + 0.455, + 0.532, + 0.467 + ], + "angle": 0, + "content": "\\(\\ell_{2}\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.568, + 0.455, + 0.684, + 0.467 + ], + "angle": 0, + "content": "\\(\\ell_1\\) robust accuracy" + }, + { + "type": "image_caption", + "bbox": [ + 0.694, + 0.455, + 0.862, + 0.467 + ], + "angle": 0, + "content": "\\(\\ell_{\\infty} + \\ell_{2} + \\ell_{1}\\) robust accuracy" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.477, + 0.268, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.477, + 0.39, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.477, + 0.569, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.477, + 0.721, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.722, + 0.477, + 0.869, + 0.569 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.589, + 0.894, + 0.631 + ], + "angle": 0, + "content": "Figure 4. Soups of three models on IMAGENET: we fine-tune the classifiers, with RESNET-50 (top row) and ViT-B16 (bottom) as architecture, robust w.r.t. \\(\\ell_{\\infty}\\) for 1 epoch to the other threat models, and show clean accuracy (first column) and robust accuracy in every threat model (second to fourth columns) and their union (last column) of the classifiers obtained as convex combinations of the three bases." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.655, + 0.28, + 0.782 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.655, + 0.472, + 0.782 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.8, + 0.47, + 0.843 + ], + "angle": 0, + "content": "Figure 5. Improvement on single threat models: we show the robust accuracy w.r.t. \\(\\ell_{\\infty}\\) for the soups \\(w \\cdot \\pmb{\\theta}_{\\infty} + (1 - w) \\cdot \\pmb{\\theta}_{\\infty \\rightarrow 2}\\) for varied \\(w\\). The original model \\(\\pmb{\\theta}_{\\infty}\\) is highlighted in red." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "CIFAR-10 the best soup is found with \\( w = 0.9 \\), while for IMAGENET with \\( w > 1 \\): this suggests that the model soups" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.657, + 0.892, + 0.688 + ], + "angle": 0, + "content": "should not be constrained to the convex hull of the base models, and extrapolation can lead to improvement." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.708, + 0.764, + 0.725 + ], + "angle": 0, + "content": "5. Soups for Distribution Shifts" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Prior works [30] have shown that adversarial training w.r.t. an \\(\\ell_p\\)-norm is able to provide some improvement in the performance in presence of non-adversarial distribution shifts, e.g. the common corruptions of IMAGENET-C [21]. However, to see such gains it is necessary to carefully select the threat model, for example which \\(\\ell_p\\)-norm and size \\(\\epsilon\\) to bound the perturbations, to use during training. The experiments in Sec. 4 suggest that model soups of nominal and adversarily robust classifiers yield models with a variety of intermediate behaviors, and extrapolation might even deliver models which do not merely trade-off the robust" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12317" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.268, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.091, + 0.434, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.436, + 0.091, + 0.601, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.091, + 0.766, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.77, + 0.174, + 0.889, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.214, + 0.268, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.214, + 0.434, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.436, + 0.214, + 0.599, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.214, + 0.767, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.349, + 0.895, + 0.392 + ], + "angle": 0, + "content": "Figure 6. Soups on IMAGENET variants: for each dataset we plot the accuracy of the 5 best performing soups of the four base models \\(\\theta_{\\infty}\\), \\(\\theta_{\\infty \\rightarrow 2}\\), \\(\\theta_{\\infty \\rightarrow 1}\\) and \\(\\theta_{\\infty \\rightarrow \\mathrm{nominal}}\\), and of the individual classifiers. Additionally, we show the performance of an independently trained nominal model. All models are evaluated on the 1000 points used for the grid search of the best soups." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.471, + 0.54 + ], + "angle": 0, + "content": "ness of the initial classifiers but amplify it. This flexibility could suit adaptation to various distribution shifts: that is, the various corruption types might more closely resemble the geometry of different \\(\\ell_p\\)-balls or their union. Moreover, including a nominally fine-tuned model in the soup allows it to maintain, if necessary, high accuracy on the original dataset, which is often degraded by adversarial training [34] or test-time adaptation on shifted data [36]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.556, + 0.336, + 0.572 + ], + "angle": 0, + "content": "5.1. Soups for IMAGENET variants" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.748 + ], + "angle": 0, + "content": "Setup. In the following, we use models soups consisting of robust ViT fine-tuned from \\(\\ell_{\\infty}\\) to the other threat models, and one more ViT nominally fine-tuned for 100 epochs to obtain slightly higher accuracy on clean data. For shifts, we consider several variants ofImagenet, providing a broad and diverse benchmark for our soups:Imagenet-REAL [1],Imagenet-V2 [40],Imagenet-C [21],Imagenet-A [23],Imagenet-R [20],Imagenet-SKETCH [49], and CONFLICT STIMULI [12]. We consider the setting of few-shot supervised adaptation, with a small set of labelled images from each shift, which we use to select the best soups." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Soup selection via grid search. Since evaluating the accuracy of many soups on the entirety of the datasets would be extremely expensive, we search for the best combination of the four models on a random subset of 1000 points from each dataset, with the exception of CONFLICT STIMULI for which all 1280 images are used (for IMAGENET-C we use all corruption types and severities, then aggregate the results). Restricting our search to a subset also serves our aim of finding a model soup which generalizes to the new distribution by only seeing a few examples. We eval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.418, + 0.895, + 0.57 + ], + "angle": 0, + "content": "uate all the possible affine combinations with weights in the range \\([-0.4, 1.4]\\) with granularity 0.2, which amounts to 460 models in total. In Fig. 6 we compare, for each dataset, the accuracy of the 5 best soups to that of each individual classifier used for creating the soups and of a nominal model trained independently: for all datasets apart from IMAGENET the top soups outperform the individual models. Moreover, we notice that the best individual model varies across datasets, indicating that it might be helpful to merge networks with different types of robustness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Comparison to existing methods. Having selected the best soup for each variant (dataset-specific soups) on its chosen few-shot adaptation set, we evaluate the soup on the test set of the variant (results in Table 1). We also evaluate the model soup that attains the best average case accuracy over the adaptation sets for all variants (single soup), in order to gauge the best performance of a single, general model soup. We compare the soups to a nominal model, the \\(\\ell_{\\infty}\\)-robust classifier used in the soups, their ensemble, the Masked Autoencoders of [18], AdvProp [54], PyramidAT [24], and the ensemble obtained by averaging the output (after softmax) of the four models included in the soups. Selecting the best soup on 1000 images of each datasets (results in the last row of Table 1) leads in 4 out of the 8 datasets to the best accuracy, and only slightly suboptimal values in the other cases: in particular, parameters interpolations is very effective on stronger shifts likeImagenet-R and CONFLICT STIMULI, where it attains almost \\(8\\%\\) better performance than the closest baseline. Unsurprisingly, it is more challenging to improve on datasets likeImagenetV2 which are very close to the originalImagenet. Over" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12318" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.088, + 0.891, + 0.271 + ], + "angle": 0, + "content": "
SETUP# FPIMAGENETIN-REALIN-V2IN-AIN-RIN-SKETCHCONFLICT STIMULIIN-CMEAN
Baselines
Nominal training×182.64%87.33%71.42%28.03%47.94%34.43%30.47%64.45%55.84%
Adversarial training×176.88%83.91%64.81%12.35%55.76%40.11%59.45%55.44%56.09%
Fine-tuned MAE-B16×183.10%88.02%72.80%37.92%49.30%35.69%27.81%63.23%57.23%
AdvProp×183.39%88.06%73.17%34.81%53.04%39.25%38.98%70.39%60.14%
Pyramid-AT×183.14%87.82%72.53%32.72%51.78%38.60%37.27%67.01%58.86%
Indep. networks ensemble×282.86%87.78%71.73%25.99%54.20%37.33%46.41%65.61%58.99%
Individual networks ensemble×481.31%86.97%70.21%23.13%54.82%39.51%56.02%68.17%60.02%
Fixed grid search on 1000 images
Single soup×182.49%87.85%71.99%34.31%53.84%39.84%38.52%66.82%59.46%
Dataset-specific soups×182.29%87.89%71.95%38.27%56.39%40.73%67.03%69.34%(64.24%)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.281, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Table 1. Comparison on IMAGENET variants: we report the classification accuracy of various models on the IMAGENET variants, together with the number of forward passes they require. The soups are selected via a fixed grid search on the interpolation weights with 1000 points for each dataset. The last row shows the results of the best found soup for each dataset." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.34, + 0.889, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.548, + 0.893, + 0.591 + ], + "angle": 0, + "content": "Figure 7. Soup compositions on IMAGENET variants: for each dataset we plot the composition of the 5 best soups, i.e. the linear weights for the individual models, as measured by grid search over 1000 points on weights in the range \\([-0.4, 1.4]\\) with granularity 0.2. Additionally we show the composition of the model achieving the best average accuracy over all 8 variants." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.471, + 0.708 + ], + "angle": 0, + "content": "all, The soup selected for best average accuracy (across all datasets) outperforms all baselines, except for the ensemble of four models (with \\(4 \\times\\) the inference cost), and AdvProp, which requires co-training of clean and adversarial points. These results show that soups with robust classifiers are a promising avenue for quickly adapting to distribution shifts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Composition of the soups. To analyze which types of classifiers are most relevant for performance on every distribution shift, we plot in Fig. 7 the breakdown of the weights of the five best soups (more intense colors indicate that the corresponding weight or a larger one is used more often in the top-5 soups). First, one can see that the nominally fine-tuned model (in black) is dominant, with weights of 0.8 or 1, onImagenet,Imagenet-REAL,ImagenetV2,Imagenet-A andImagenet-C: this could be expected since these datasets are closer toImagenet itself, i.e. the distribution shift is smaller, which is what nominal training optimizes for (in fact, the nominal models achieve" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.844 + ], + "angle": 0, + "content": "higher accuracy than adversarially trained ones on these datasets in Fig. 6). However, in all cases there is a contribution of some of the \\(\\ell_p\\)-robust networks. On IMAGENET-R, IMAGENET-SKETCH and CONFLICT STIMULI, the model robust w.r.t. \\(\\ell_{\\infty}\\) plays instead the most relevant role, again in line with the results in Table 1. Interestingly, in the case of CONFLICT STIMULI, the nominal classifier has a weight -0.4 (the smallest in the grid search) for all top performing soups: we hypothesize that this has the effect of reduce the texture bias typical of nominal model and emphasize the attention to shapes already important in adversarially trained classifiers. Finally, we show the composition of the soup which has the best average accuracy over all datasets (last column of Fig. 7), where the nominal and \\(\\ell_{\\infty}\\)-robust models have similar positive weight." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.903 + ], + "angle": 0, + "content": "How many images does it take to find a good soup? To identify the practical limit of supervision for soup selection, we study the effect of varying the number of labelled images" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12319" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.468, + 0.197 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.204, + 0.468, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.333, + 0.472, + 0.39 + ], + "angle": 0, + "content": "Figure 8. Soup selection data efficiency: we vary the number of images for selecting the best performing soups on different datasets. For each case, we plot the average accuracy on a held-out test set, and its standard deviation over 50 trials." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.43, + 0.466, + 0.613 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.626, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Figure 9. Soup compositions on IMAGENET-C: we plot the model-wise weights of the best soups across types and severities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.473, + 0.903 + ], + "angle": 0, + "content": "used to select the best soup on a new dataset. For this analysis we randomly choose 500 images from the adaptation set used for the grid search to create a held-out test set. From the remaining images, we uniformly sample \\( k \\) elements, select the soup which performs best on such \\( k \\) points, and then evaluate it on this test set. We repeat this procedure for \\( k \\in \\{10, 30, 100, 300, 500\\} \\) for 50 times each with different random seeds. In Fig. 8 we plot the average accuracy on the held-out test set, with standard deviation, when varying \\( k \\): increasing the number of points above 100 achieves high test accuracy with limited variance. This suggests that soup selection, and thus model adaptation, can be carried out with as few as 100 examples of the new distribution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.757, + 0.107 + ], + "angle": 0, + "content": "5.2. A closer look at IMAGENET-C" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.113, + 0.895, + 0.403 + ], + "angle": 0, + "content": "While our experiments have considered IMAGENET-C as a single dataset, it consists of 15 corruptions types, each with 5 severity levels. As the various corruptions have different characteristics, one might expect the best soup to vary across them. In Fig. 9 we plot the composition of the top-5 soups for each severity level for two corruption types (as done in Fig. 7). The weights of the individual classifiers significantly change across distribution shifts: for both corruption types, increasing the severity (making perturbations stronger) leads to a reduction in the nominal weight in favor of a robust weight. However, in the case of \"pixelate\" the soups concentrate on the \\(\\ell_1\\)-robust network, while for \"jpeg compression\" this happens for \\(\\ell_{\\infty}\\). Similar visualization for the remaining IMAGENET-C subsets are found in Fig. 11 of the Appendix. This highlights the importance of interpolating models with different types of robustness, and implies that considering each corruption type (including severity levels) as independent datasets could further improve the performance of the soups on IMAGENET-C." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.415, + 0.755, + 0.431 + ], + "angle": 0, + "content": "6. Discussion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.895, + 0.56 + ], + "angle": 0, + "content": "Merging models with different types of robustness enables strong control of classifier performance by tuning only a few soup weights. Soups can find models which perform well even on distributions unseen during training (e.g. the IMAGENET variants). Moreover, our framework avoids constraining on multiple threats: this makes it possible to fine-tune models with additional attacks as they present themselves, and enrich the soups with them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.895, + 0.756 + ], + "angle": 0, + "content": "At the moment, our soups contain only nominal or \\(\\ell_{p}\\)-robust models, but expanding the diversity of models might aid adaptation to new datasets. We selected our soups with few-shot supervision, but other settings could potentially use soups, such as unsupervised domain adaptation [37,42], on labeled clean and unlabeled shifted data, and test-time adaptation [43,44,48], on unlabeled examples alone. Moreover, in our evaluation we have constrained the soups to belong to a fixed grid, which might miss better models: future work could develop automatic schemes to optimize the soup weights, possibly with even fewer examples, or without labeled examples (as done for test-time adaptation of non-robust models)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.621, + 0.787 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We show that combining the parameters of robust classifiers, without additional training, achieves a smooth trade-off of robustness in different \\(\\ell_p\\)-threat models. This allows us to discover models which perform well on distribution shifts with only a limited number of examples of each shift. 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In International Conference on Learning Representations, 2022. 12" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "12323" + } + ] +] \ No newline at end of file diff --git a/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/a6551453-1b77-4f6c-8df2-df18da134652_origin.pdf b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/a6551453-1b77-4f6c-8df2-df18da134652_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0ebcd224f74c44ec8d52711e92d59bb24e217c31 --- /dev/null +++ b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/a6551453-1b77-4f6c-8df2-df18da134652_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f2b397637cb1d36368092c73711788c5172a7deee4e76874fdc78d3161fbac31 +size 455942 diff --git a/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/full.md b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/full.md new file mode 100644 index 0000000000000000000000000000000000000000..01ee0ea21b58e9404746e36da8c7a04c56954a63 --- /dev/null +++ b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/full.md @@ -0,0 +1,342 @@ +# Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts + +Francesco Croce* +University of Tübingen + +Sylvestre-Alvise Rebuffi DeepMind + +Evan Shelhamer DeepMind + +Sven Gowal DeepMind + +# Abstract + +Adversarial training is widely used to make classifiers robust to a specific threat or adversary, such as $\ell_p$ -norm bounded perturbations of a given $p$ -norm. However, existing methods for training classifiers robust to multiple threats require knowledge of all attacks during training and remain vulnerable to unseen distribution shifts. In this work, we describe how to obtain adversially-robust model soups (i.e., linear combinations of parameters) that smoothly trade-off robustness to different $\ell_p$ -norm bounded adversaries. We demonstrate that such soups allow us to control the type and level of robustness, and can achieve robustness to all threats without jointly training on all of them. In some cases, the resulting model soups are more robust to a given $\ell_p$ -norm adversary than the constituent model specialized against that same adversary. Finally, we show that adversially-robust model soups can be a viable tool to adapt to distribution shifts from a few examples. + +# 1. Introduction + +Deep networks have achieved great success on several computer vision tasks and have even reached super-human accuracy [19, 31]. However, the outputs of such models are often brittle, and tend to perform poorly on inputs that differ from the distribution of inputs at training time, in a condition known as distribution shift [37]. Adversarial perturbations are a prominent example of this condition: small, even imperceptible, changes to images can alter predictions to cause errors [2, 46]. In addition to adversarial inputs, it has been noted that even natural shifts, e.g. different weather conditions, can significantly reduce the accuracy of even the best vision models [13, 21, 40]. Such drops in accuracy are undesirable for robust deployment, and so a lot of effort has been invested in correcting them. Adversarial training [34] and its extensions [15, 39, 58] are currently the most effective methods to improve empirical robustness to adversarial attacks. Similarly, data augmen + +tation is the basis of several techniques that improve robustness to non-adversarial/natural shifts [3, 11, 22]. While significant progress has been made on defending against a specific, selected type of perturbations (whether adversarial or natural), it is still challenging to make a single model robust to a broad set of threats and shifts. For example, a classifier adversarily-trained for robustness to $\ell_p$ -norm bounded attacks is still vulnerable to attacks in other $\ell_q$ -threat models [29, 47]. Moreover, methods for simultaneous robustness to multiple attacks require jointly training on all [33, 35] or a subset of them [8]. Most importantly, controlling the trade-off between different types of robustness (and nominal performance) remains difficult and requires training several classifiers. + +Inspired by model soups [52], which interpolate the parameters of a set of vision models to achieve state-of-the-art accuracy on IMAGENET, we investigate the effects of interpolating robust image classifiers. We complement their original recipe for soups by own study of how to pretrain, fine-tune, and combine the parameters of models adversarially-trained against $\ell_p$ -norm bounded attacks for different $p$ -norms. To create models for soups, we pre-train a single robust model and fine-tune it to the target threat models (using the efficient technique of [8]). We then establish that it is possible to smoothly trade-off robustness to different threat models by moving in the convex hull of the parameters of each robust classifier, while achieving competitive performance with methods that train on multiple $p$ -norm adversaries simultaneously. Unlike alternatives, our soups can uniquely (1) choose the level of robustness to each threat model without any further training and (2) quickly adapt to new unseen attacks or shifts by simply tuning the weighting of the soup. + +Previous works [24, 30, 54] have shown that adversarial training with $\ell_p$ -norm bounded attacks can help to improve performance on natural shifts if carefully tuned. We show that model soups of diverse classifiers, with different types of robustness, offer greater flexibility for finding models that perform well across various shifts, such as IMAGENET variants. Furthermore, we show that a limited number of images of the new distribution are sufficient to select the + +weights of such a model soup. Examining the composition of the best soups brings insights about which features are important for each dataset and shift. Finally, while the capability of selecting a model specific to each image distribution is a main point of our model soups, we also show that it is possible to jointly select a soup for average performance across several IMAGENET variants to achieve better accuracy than adversarial and self-supervised baselines [18, 24]. + +# Contributions. In summary, we show that soups + +- can merge nominal and $\ell_p$ -robust models (for various $p$ ): efficient fine-tuning from one robust model obtains a set of models with diverse robustness [8] and compatible parameters for creating model soups [52] (Sec. 3), +- can control the level of robustness to each threat model and achieve, without more training, competitive performance against multi-norm robustness training (Sec. 4), +- are not limited to interpolation, but can find more effective classifiers by extrapolation (Sec. 4.3), +- enable adaptation to unseen distribution shifts on only a few examples (Sec. 5). + +# 2. Related Work + +Adversarial robustness to multiple threat models. Most methods focus on achieving robustness in a single threat model, i.e. to a specific type of attacks used during training. However, this is not sufficient to obtain robustness to unseen attacks. As a result, further work aims to train classifiers for simultaneous robustness to multiple attacks, and the most popular scenario considers a set of $\ell_p$ -norm bounded perturbations. The most successful methods [33, 35, 47] are based on adversarial training and differ in how the multiple threats are combined. Notably, all need to use every attack at training time. To reduce the computational cost of obtaining multiply-robust models, one can fine-tune a singly-robust model by one of the above mentioned methods [8], even for only a small number of epochs. Our soups are more flexible by skipping simultaneous adversarial training across multiple attacks. + +Adversarial training for distribution shifts. While robustness to adversarial attacks and natural shifts are not the same goal, previous works nevertheless show that it is possible to leverage adversarial training with $\ell_p$ -norm bounded attacks to improve performance on the common corruptions of [21]. First, AdvProp [54] co-trains models on clean and adversarial images (in the $\ell_{\infty}$ -threat model) with dual normalization layers that specialize to each type of input. The clean branch of the dual model achieves higher accuracy than nominal training on IMAGENET and its variants. Similar results are obtained by Pyramid-AT [24] by its design of a specific attack to adversarily train vision transformers. Finally, [30] carefully selecting the size of the adversarial perturbations, i.e., their $\ell_{\infty}$ - or $\ell_2$ -norm, for standard adversarial training [34] achieves competitive performance on + +common corruptions on CIFAR-10 and IMAGENET-100. + +Model soups. Ensembling or averaging the parameters of intermediate models found during training is an effective technique to improve both clean accuracy [25, 28] and robustness [14, 39]. Recently, [52] propose model soups which interpolate the parameters of networks finetuned with different hyperparameters configurations from the same pre-trained model. This yields improved classification accuracy onImagenet. Along the same line, [27] fine-tune a model trained onImagenet on several new image classification datasets, and show that interpolating the original and fine-tuned parameters yields classifiers that perform well on all tasks. Additional related work is discussed in App. A. + +# 3. Model Interpolation across Different Tasks + +In the following, we formally introduce the two main components of our procedure to merge adversarially robust models: (1) obtaining models which can interpolated by fine-tuning a single $\ell_p$ -robust classifiers, and (2) interpolation of their weights to balance their different types of robustness. We highlight that our setup diverges from that of prior works about parameters averaging: in fact, both [27, 52] combine models fine-tuned on the same task, i.e. achieving high classification accuracy of unperturbed images, either on a fixed dataset and different hyperparameter configurations [52], or varying datasets [27]. In our case, the individual models are trained for robustness to different types of attacks, i.e. with distinct loss functions. + +# 3.1. Adversarial training and fine-tuning + +Let us denote $\mathcal{D} = \{(x_i, y_i)\}_i$ the training set, with $x_i \in \mathbb{R}^d$ indicating an image and $y_i \in \{1, \dots, K\}$ the corresponding label, and $\Delta: \mathbb{R}^d \to \mathbb{R}^d$ the function which characterizes a threat model, that maps an input $x$ to a set $\Delta(x) \subset \mathbb{R}^d$ of possible perturbed versions of the original image. For example, $\ell_p$ -norm bounded adversarial attacks with budget $\epsilon > 0$ in the image space can be described by + +$$ +\Delta (\boldsymbol {x}) = \left\{\boldsymbol {\delta} \in \mathbb {R} ^ {d}: \| \boldsymbol {\delta} \| _ {p} \leq \epsilon , \boldsymbol {x} + \boldsymbol {\delta} \in [ 0, 1 ] ^ {d} \right\}. \tag {1} +$$ + +Then, one can train a classifier $f:\pmb {\theta}\times \mathbb{R}^d\to \mathbb{R}^K$ parameterized by $\pmb {\theta}\in \Theta$ with adversarial training [34] by solving + +$$ +\min _ {\boldsymbol {\theta} \in \Theta} \sum_ {(\boldsymbol {x}, y) \in \mathcal {D}} \max _ {\boldsymbol {\delta} \in \Delta (\boldsymbol {x})} \mathcal {L} (f (\boldsymbol {\theta}, x + \boldsymbol {\delta}), y), \tag {2} +$$ + +for a given loss function $\mathcal{L}:\mathbb{R}^K\times \mathbb{R}^K\to \mathbb{R}$ (e.g., cross-entropy), with the goal of obtaining a model robust to the perturbations described by $\Delta$ . Note that this boils down to nominal training when $\Delta (\cdot) = \{\mathbf{0}\}$ and no perturbation is applied on the training images. We are interested in the case where multiple threat models are available, and indicate + +![](images/fa4a9b5c007cc1d50c401a20caac2aa7d43fc6e6f40e1a0a7e45bf75e091e813.jpg) +Figure 1. Soups of two models on CIFAR-10: for all pairs $(p,q)$ we show the $\ell_{p}$ - vs $\ell_{q}$ -robust accuracy of the soups $w\cdot \theta_{p} + (1 - w)\cdot \theta_{p\rightarrow q}$ and $w\cdot \theta_q + (1 - w)\cdot \theta_{q\to p}$ varying $w\in [0,1]$ . We also show results for MAX and SAT with simultaneous use of the two threat models. + +![](images/8cb58d3f5c7c9b3b74c97e46bcc21da6c334ab2b25f550f1f9ddd4fb64df4015.jpg) + +![](images/b8ae2eb71709e5a21211edfa7f85e008773e5a983da7aac20b023d12cdcd7c4e.jpg) + +![](images/78c9c611c89838214762f18e6e09b6fc5f648b5cf1894bb4a626a5fd38f58fb0.jpg) +Figure 2. Soups of two models on IMAGENET: for $p \in \{2,1\}$ we show the $\ell_{p^-}$ vs $\ell_{\infty}$ -robust accuracy of the soups $w \cdot \theta_{\infty} + (1 - w) \cdot \theta_{\infty \rightarrow p}$ varying $w \in [0,1]$ (first and second columns). Moreover, we show the soups obtained combining $\theta_{\infty \rightarrow 2}$ and $\theta_{\infty \rightarrow 1}$ (third), or $\theta_{\infty}$ and $\theta_{\infty \rightarrow \text{nominal}}$ (fourth). For the case of two $\ell_{p^-}$ -threat models, we also show the results of fine-tuning models with MAX and SAT. + +![](images/2d6f981fcdf5770272485231e322574bf5b858d22dc194ac6ee10d6d3be016cd.jpg) + +![](images/9727ad545248276aeacffae333be011fff4ff61f8ae4b1de9069c48b2ba0b739.jpg) + +![](images/bdb97aededccf3ed1b8d9536f78bf02104f11149040ee6f043af0ad81e11c376.jpg) + +with $\Delta_{\mathrm{nominal}}$ nominal training, and $\Delta_p$ for $p \in \{\infty, 2, 1\}$ the perturbations with bounded $\ell_p$ -norm as described in Eq. 1. We focus on such tasks since they are the most common choices for adversarial defenses, in particular by methods focusing on multiple norm robustness [35, 47]. + +Notably, it is possible to efficiently obtain a model robust to $\Delta_q$ by fine-tuning for a single (or few) epoch with adversarial training w.r.t. $\Delta_q$ a classifier pre-trained to be robust in $\Delta_p$ , with $p \neq q$ and $p, q \in \{\infty, 2, 1\}$ [8]. For example, in this way one can efficiently derive specialized classifiers $\Delta_2, \Delta_1, \Delta_{\mathrm{nominal}}$ for each task from a single model $f$ robust w.r.t. $\ell_{\infty}$ . However, this does not work well when a nominal classifier is used as starting point for the short fine-tuning. In the following, we denote with $\theta_{p \rightarrow q}$ the parameters resulting from fine-tuning to $\Delta_q$ a base model $\theta_p$ . + +# 3.2. Merging different types of robustness via linear combinations in parameter space + +We want to explore the properties of the models obtained by taking linear combinations of the parameters of classifiers with different types of robustness. To do so, there needs to be a correspondence among the parameters of different individual networks: [52] achieve this by merging differently fine-tuned versions of the same pre-trained model. As mentioned above, fine-tuning an $\ell_p$ -robust clas + +sifier allows to change it to achieve robustness in a new threat model [8]: we exploit such property to create model soups, as named by [52]. Formally, we create a model soup from $n$ individual networks with parameters $\pmb{\theta}^{1},\dots,\pmb{\theta}^{n}$ with weights $\pmb{w} = (w_{1},\dots,w_{n})\in \mathbb{R}^{n}$ as + +$$ +\boldsymbol {\theta} ^ {w} = \sum_ {i = 1} ^ {n} w _ {i} \cdot \boldsymbol {\theta} ^ {i}, \tag {3} +$$ + +and the corresponding classifier is given by $f(\pmb{\theta}^{\pmb{w}},\cdot):\mathbb{R}^{d}\to \mathbb{R}^{K}$ . While any choice of $\pmb{w}$ is possible, we focus on the case of affine combinations, i.e. $\sum_{i}w_{i} = 1$ . Moreover, we consider soups which are either convex combinations of the individual models, with $w_{1},\ldots ,w_{n}\geq 0$ , or obtained by extrapolations, i.e. with negative elements in $\pmb{w}$ . + +# 4. Soups for $\ell_p$ -robustness + +We measure adversarial robustness in the $\ell_p$ -threat model with bounds $\epsilon_p$ : on CIFAR-10 we use $\epsilon_{\infty} = 8 / 255$ , $\epsilon_2 = 128 / 255$ , $\epsilon_1 = 12$ , on IMAGENET $\epsilon_{\infty} = 4 / 255$ , $\epsilon_2 = 4$ , $\epsilon_1 = 255$ . If not specified otherwise, we use the full test set for CIFAR-10 and 5000 images from the IMAGENET validation set, and attack by AUTOPGD [6,7] with 40 steps. More details are provided in App. B. + +# 4.1. Soups with two threat models + +CIFAR-10. We explore the effect of interpolating two models robust to different $\ell_p$ -norm bounded attacks for $p \in \{\infty, 2, 1\}$ . We consider classifiers with WIDERES-NET-28-10 [56] architecture trained on CIFAR-10. For every threat model, we first train a robust classifier with adversarial training from random initialization. Then, we fine-tune the resulting model with adversarial training on each of the other threat models for 10 epochs. In Fig. 1 we show, for each pair of threat models $(\Delta_p, \Delta_q)$ , the trade-off of robust accuracy w.r.t. $\ell_p$ and $\ell_q$ for the soups + +$$ +w \cdot \pmb {\theta} _ {p} + (1 - w) \cdot \pmb {\theta} _ {p \rightarrow q} \quad \mathrm {f o r} \quad w \in [ 0, 1 ] +$$ + +and symmetrically + +$$ +w \cdot \boldsymbol {\theta} _ {q} + (1 - w) \cdot \boldsymbol {\theta} _ {q \rightarrow p} \quad \text {f o r} \quad w \in [ 0, 1 ]. +$$ + +Interpolating the parameters of models trained with a single $\ell_p$ -norm controls the balance between the two types of robustness: for example, Fig. 1 (middle plot) shows that moving from $\theta_{\infty}$ to $\theta_{\infty \rightarrow 1}$ (blue curve), i.e. decreasing $w$ from 1 to 0 in the corresponding soup, progressively reduces the robust accuracy w.r.t. $\ell_{\infty}$ to improve robustness w.r.t. $\ell_1$ . Moreover, for similar threat models (i.e. the pairs $(\ell_2, \ell_1)$ and $(\ell_2, \ell_{\infty})$ ) some intermediate networks are more robust than the extremes trained specifically for each threat model. + +IMAGENET. We now fine-tune a VIT-B16 [10] robust w.r.t. $\ell_{\infty}$ on IMAGENET to the other threat models, including nominal training, for either 1/3, 1 or 3 epochs. Fig. 2 shows that interpolation of parameters is effective even in this setup, and allows to easily balance nominal and robust accuracy (fourth plot). Moreover, it is possible to create soups with two fine-tuned models, i.e. $\theta_{\infty \rightarrow 2}$ and $\theta_{\infty \rightarrow 1}$ . Finally, increasing the number of fine-tuning steps yields better performance in the target threat model, which in turn generally leads to better soups. + +Comparison to multi-norm robustness methods. Fig. 1 and Fig. 2 compare the performance of the model soups to that of models trained with methods for robustness in the union of multiple threat models. In particular, we show the results of MAX [47], which computes perturbations for each threat model and trains on that attaining the highest loss, and SAT [33], which samples uniformly at random for each training batch the attack to use. We train models with both methods for all pairs of threat models: as expected, MAX tends to focus on the most challenging threat model, sacrificing some robustness in the other one compared to SAT, since it uses only the strongest attack for each training point. When training for $\ell_{\infty}$ and $\ell_1$ , i.e. the extreme $\ell_p$ -norms we consider, MAX and SAT models lie above the front drawn by the model soups, hinting that the more diverse the attacks, the more difficult it is to preserve high robustness to both. In the other cases, both methods behave + +similarly to the soups. The main advantage given by interpolation is however the option of moving along the front without additional training cost: while one might tune the trade-off between the robustness in the two threat models in SAT, e.g. changing the sampling probability, this would still require training a new classifier for each setup. + +# 4.2. Soups with three threat models + +We here study the convex combination of three models with different types of robustness. For CIFAR-10 we create soups with each $\ell_p$ -robust classifier for $p \in \{\infty, 2, 1\}$ and its fine-tuned version into the other two threat models. We use the same models of the previous section, and sweep the interpolation weights $\boldsymbol{w} \in \mathbb{R}^3$ such that $w_i \in \{0, 0.2, 0.4, 0.6, 0.8, 1\}$ and $\sum_i w_i = 1$ . In Fig. 3 and Fig. 10 (in the Appendix) we show clean accuracy (first column) and robust accuracy in $\ell_{\infty}$ , $\ell_2$ and $\ell_1$ (second to fourth columns) and their union, when a point is considered robust only if it is such against all attacks (last column). + +One can observe that, independently from the type of robustness of the base model (used as initialization for the fine-tuning), moving in the convex hull of the three parameters (e.g. $\theta_{\infty} + \theta_{\infty \rightarrow 2} + \theta_{\infty \rightarrow 1}$ in Fig. 3) allows to smoothly control the trade-off of the different types of robustness. Interestingly, the highest $\ell_2$ -robustness is attained by intermediate soups, not by the model specifically fine-tuned w.r.t. $\ell_2$ , suggesting that model soups might even be beneficial to robustness in individual threat models (see more below). Moreover, the highest robustness in the union is given by interpolating only the models robust w.r.t. $\ell_{\infty}$ and $\ell_1$ , which is in line with the observation of [8] that training for the extreme norms is sufficient for robustness in the union of the three threat models. Although the robust accuracy in the union is lower than that of training simultaneously with all attacks e.g. with MAX (42.0% vs 47.2%), the model soups deliver competitive results without the need of co-training. + +Finally, Fig. 4 shows that similar observations hold on IMAGENET, where we create soups fine-tuning classifiers robust w.r.t. $\ell_{\infty}$ , with either RESNET-50 [19] or ViT-B16 as architecture, for 1 epoch. + +# 4.3. Soups for improving individual threat model robustness + +We notice in Fig. 1 and Fig. 2 that in a few cases the intermediate models obtain via parameters interpolation have higher robustness than the extreme ones, which are trained or fine-tuned with a specific threat model. As such, we analyze in more details the soups $w \cdot \theta_{\infty} + (1 - w) \cdot \theta_{\infty \rightarrow 2}$ , i.e. using the original classifier robust in $\ell_{\infty}$ and the one fine-tuned to $\ell_{2}$ , on both CIFAR-10 andImagenet. Fig. 5 shows the robust accuracy w.r.t. $\ell_{\infty}$ when varying the value of $w$ : in both case the original model $\theta_{\infty}$ , highlighted in red, does not attain the best robustness. Interestingly, on + +$$ +\text {s o u p :} \theta_ {\infty} + \theta_ {\infty \rightarrow 2} + \theta_ {\infty \rightarrow 1} +$$ + +![](images/376fc52fad78ce9ebc41b72072edd7c7a3d55d0be38fe4d9856841944ed47838.jpg) +clean accuracy +$\ell_{\infty}$ robust accuracy + +![](images/f8478d1afdea3264e8acec759a455e242c29e626d9d0f98ad430ba95fc62f9cb.jpg) +$\ell_{2}$ robust accuracy +Figure 3. Soups of three models on CIFAR-10: we fine-tune the model robust w.r.t. $\ell_{\infty}$ (with WIDERESNET-28-10 architecture) to the other threat models for 10 epochs, and show clean accuracy (first column) and robust accuracy w.r.t. every threat model (second to fourth columns) and their union (last column) of the soups obtained as convex combinations of the three bases. + +![](images/8c71a16aef4dc91e5ec3881bb8dd5ef1ce817bd8e117963c1ce3ee5e49723c3c.jpg) +$\ell_{1}$ robust accuracy + +![](images/cf889f50ee25f7428688e2427bd03f8462ce8eeba5c168ab9b584045e012aebc.jpg) +$\ell_{\infty} + \ell_{2} + \ell_{1}$ robust accuracy + +![](images/70612c1ff64e32094ab9353cd276573a75f764549d5d02f1d76a52d33174bb3b.jpg) + +$$ +\operatorname {R E S N E T} - 5 0, \text {s o u p :} \theta_ {\infty} + \theta_ {\infty \rightarrow 2} + \theta_ {\infty \rightarrow 1} +$$ + +![](images/788c08cd4f96c4c03fc88188e509b2d5f75098ea2bca79f502208087e989e56b.jpg) +clean accuracy +$\ell_{\infty}$ robust accuracy + +![](images/67cb91ab9754379204f91b1d1ae7001d4c17701ef460cfba8e5108125df0dde6.jpg) +$\ell_{2}$ robust accuracy + +![](images/225223209ec03fd049328305eee9bdcaee19c51e11ca651fb70f51fda8ca1197.jpg) +$\ell_{1}$ robust accuracy + +![](images/b4d2102c7ad7c1070b5698ba592c26b6b370b8655c1ea3fc1c8ea3bfe8496489.jpg) +$\ell_{\infty} + \ell_{2} + \ell_{1}$ robust accuracy + +![](images/fb37b53187b8778df1d7675c530367128be6c4803a2127aee9efa58cddfdeb6f.jpg) + +$$ +V I T - B 1 6, \text {s o u p}: \theta_ {\infty} + \theta_ {\infty \rightarrow 2} + \theta_ {\infty \rightarrow 1} +$$ + +![](images/e085673a27b0a780229de90d1a99e20fb853b3ee8929a5ea0240b48389633d56.jpg) +clean accuracy +$\ell_{\infty}$ robust accuracy +Figure 4. Soups of three models on IMAGENET: we fine-tune the classifiers, with RESNET-50 (top row) and ViT-B16 (bottom) as architecture, robust w.r.t. $\ell_{\infty}$ for 1 epoch to the other threat models, and show clean accuracy (first column) and robust accuracy in every threat model (second to fourth columns) and their union (last column) of the classifiers obtained as convex combinations of the three bases. + +![](images/173a55b836adc23a8ee4e05c1d8f706afb9613d7e1956621264f5e06cf9177eb.jpg) + +![](images/a13d89755b078ae2dd39493b3368c9d6be8e1307d960531f798ba4ebfa5a9db9.jpg) +$\ell_{2}$ robust accuracy +$\ell_1$ robust accuracy + +![](images/f9eee60a44b632149bd0795651e75cb26ef2a97605de36c13c383bd62bbc0eb0.jpg) +$\ell_{\infty} + \ell_{2} + \ell_{1}$ robust accuracy + +![](images/62c528c8c84b0869836cd81882c25e4372e85df729e2fab86fe8fc597acd8b29.jpg) + +![](images/239ebb03df8a121a428cfc321e29bc3ea68f68e5a59e93701ff5f8bcd6f0101b.jpg) +Figure 5. Improvement on single threat models: we show the robust accuracy w.r.t. $\ell_{\infty}$ for the soups $w \cdot \pmb{\theta}_{\infty} + (1 - w) \cdot \pmb{\theta}_{\infty \rightarrow 2}$ for varied $w$ . The original model $\pmb{\theta}_{\infty}$ is highlighted in red. + +![](images/e400804cddea7a5c8932fcb8d95adb21eac361a9ff787b918fc49230f359526a.jpg) + +CIFAR-10 the best soup is found with $w = 0.9$ , while for IMAGENET with $w > 1$ : this suggests that the model soups + +should not be constrained to the convex hull of the base models, and extrapolation can lead to improvement. + +# 5. Soups for Distribution Shifts + +Prior works [30] have shown that adversarial training w.r.t. an $\ell_p$ -norm is able to provide some improvement in the performance in presence of non-adversarial distribution shifts, e.g. the common corruptions of IMAGENET-C [21]. However, to see such gains it is necessary to carefully select the threat model, for example which $\ell_p$ -norm and size $\epsilon$ to bound the perturbations, to use during training. The experiments in Sec. 4 suggest that model soups of nominal and adversarily robust classifiers yield models with a variety of intermediate behaviors, and extrapolation might even deliver models which do not merely trade-off the robust + +![](images/49125a1c923411f433b1906f7e0b9cc30f8401979d1b9638ccb34db3dc8e4b97.jpg) + +![](images/b8c8adaed0ec73dd2e672ec4c0b1ac43e629c6ba9e6c54f2b8eb38cbe109a986.jpg) + +![](images/af10b5cfa528bc3770341bcac032879b1c5d1d85c53a90e1ee0b07712069d1d2.jpg) + +![](images/99318e72a30d233d6c834a6163433ef00e2bba8e90eb24331a33605412a47fe1.jpg) + +![](images/54aab8c3643b0caa7df213406170f626e220eb1c0a215a14f894bfae7540e236.jpg) + +![](images/2599ce0d4c29cd251908b99c68ec6580636aa8c50523495629a39104cbfd6503.jpg) +Figure 6. Soups on IMAGENET variants: for each dataset we plot the accuracy of the 5 best performing soups of the four base models $\theta_{\infty}$ , $\theta_{\infty \rightarrow 2}$ , $\theta_{\infty \rightarrow 1}$ and $\theta_{\infty \rightarrow \mathrm{nominal}}$ , and of the individual classifiers. Additionally, we show the performance of an independently trained nominal model. All models are evaluated on the 1000 points used for the grid search of the best soups. + +![](images/f337f453e09d5fd34f91b3619b98e962d8bb164bbccc999a9f42905cbc38b034.jpg) + +![](images/e71b3aa117e5714bc05664beb6a8e8d7a0e75c7fa7ef1e529a8b32e5de2e304d.jpg) + +![](images/758f1867e7b3b8cc2ab6d0657511b325fc2c8615115553c10b27fd86ef4ef8bd.jpg) + +ness of the initial classifiers but amplify it. This flexibility could suit adaptation to various distribution shifts: that is, the various corruption types might more closely resemble the geometry of different $\ell_p$ -balls or their union. Moreover, including a nominally fine-tuned model in the soup allows it to maintain, if necessary, high accuracy on the original dataset, which is often degraded by adversarial training [34] or test-time adaptation on shifted data [36]. + +# 5.1. Soups for IMAGENET variants + +Setup. In the following, we use models soups consisting of robust ViT fine-tuned from $\ell_{\infty}$ to the other threat models, and one more ViT nominally fine-tuned for 100 epochs to obtain slightly higher accuracy on clean data. For shifts, we consider several variants ofImagenet, providing a broad and diverse benchmark for our soups:Imagenet-REAL [1],Imagenet-V2 [40],Imagenet-C [21],Imagenet-A [23],Imagenet-R [20],Imagenet-SKETCH [49], and CONFLICT STIMULI [12]. We consider the setting of few-shot supervised adaptation, with a small set of labelled images from each shift, which we use to select the best soups. + +Soup selection via grid search. Since evaluating the accuracy of many soups on the entirety of the datasets would be extremely expensive, we search for the best combination of the four models on a random subset of 1000 points from each dataset, with the exception of CONFLICT STIMULI for which all 1280 images are used (for IMAGENET-C we use all corruption types and severities, then aggregate the results). Restricting our search to a subset also serves our aim of finding a model soup which generalizes to the new distribution by only seeing a few examples. We eval + +uate all the possible affine combinations with weights in the range $[-0.4, 1.4]$ with granularity 0.2, which amounts to 460 models in total. In Fig. 6 we compare, for each dataset, the accuracy of the 5 best soups to that of each individual classifier used for creating the soups and of a nominal model trained independently: for all datasets apart from IMAGENET the top soups outperform the individual models. Moreover, we notice that the best individual model varies across datasets, indicating that it might be helpful to merge networks with different types of robustness. + +Comparison to existing methods. Having selected the best soup for each variant (dataset-specific soups) on its chosen few-shot adaptation set, we evaluate the soup on the test set of the variant (results in Table 1). We also evaluate the model soup that attains the best average case accuracy over the adaptation sets for all variants (single soup), in order to gauge the best performance of a single, general model soup. We compare the soups to a nominal model, the $\ell_{\infty}$ -robust classifier used in the soups, their ensemble, the Masked Autoencoders of [18], AdvProp [54], PyramidAT [24], and the ensemble obtained by averaging the output (after softmax) of the four models included in the soups. Selecting the best soup on 1000 images of each datasets (results in the last row of Table 1) leads in 4 out of the 8 datasets to the best accuracy, and only slightly suboptimal values in the other cases: in particular, parameters interpolations is very effective on stronger shifts likeImagenet-R and CONFLICT STIMULI, where it attains almost $8\%$ better performance than the closest baseline. Unsurprisingly, it is more challenging to improve on datasets likeImagenetV2 which are very close to the originalImagenet. Over + +
SETUP# FPIMAGENETIN-REALIN-V2IN-AIN-RIN-SKETCHCONFLICT STIMULIIN-CMEAN
Baselines
Nominal training×182.64%87.33%71.42%28.03%47.94%34.43%30.47%64.45%55.84%
Adversarial training×176.88%83.91%64.81%12.35%55.76%40.11%59.45%55.44%56.09%
Fine-tuned MAE-B16×183.10%88.02%72.80%37.92%49.30%35.69%27.81%63.23%57.23%
AdvProp×183.39%88.06%73.17%34.81%53.04%39.25%38.98%70.39%60.14%
Pyramid-AT×183.14%87.82%72.53%32.72%51.78%38.60%37.27%67.01%58.86%
Indep. networks ensemble×282.86%87.78%71.73%25.99%54.20%37.33%46.41%65.61%58.99%
Individual networks ensemble×481.31%86.97%70.21%23.13%54.82%39.51%56.02%68.17%60.02%
Fixed grid search on 1000 images
Single soup×182.49%87.85%71.99%34.31%53.84%39.84%38.52%66.82%59.46%
Dataset-specific soups×182.29%87.89%71.95%38.27%56.39%40.73%67.03%69.34%(64.24%)
+ +Table 1. Comparison on IMAGENET variants: we report the classification accuracy of various models on the IMAGENET variants, together with the number of forward passes they require. The soups are selected via a fixed grid search on the interpolation weights with 1000 points for each dataset. The last row shows the results of the best found soup for each dataset. + +![](images/f273e7dfbc4421380f719e44dbca9edc25111b824660e14ee15c92c88517cf49.jpg) +Figure 7. Soup compositions on IMAGENET variants: for each dataset we plot the composition of the 5 best soups, i.e. the linear weights for the individual models, as measured by grid search over 1000 points on weights in the range $[-0.4, 1.4]$ with granularity 0.2. Additionally we show the composition of the model achieving the best average accuracy over all 8 variants. + +all, The soup selected for best average accuracy (across all datasets) outperforms all baselines, except for the ensemble of four models (with $4 \times$ the inference cost), and AdvProp, which requires co-training of clean and adversarial points. These results show that soups with robust classifiers are a promising avenue for quickly adapting to distribution shifts. + +Composition of the soups. To analyze which types of classifiers are most relevant for performance on every distribution shift, we plot in Fig. 7 the breakdown of the weights of the five best soups (more intense colors indicate that the corresponding weight or a larger one is used more often in the top-5 soups). First, one can see that the nominally fine-tuned model (in black) is dominant, with weights of 0.8 or 1, onImagenet,Imagenet-REAL,ImagenetV2,Imagenet-A andImagenet-C: this could be expected since these datasets are closer toImagenet itself, i.e. the distribution shift is smaller, which is what nominal training optimizes for (in fact, the nominal models achieve + +higher accuracy than adversarially trained ones on these datasets in Fig. 6). However, in all cases there is a contribution of some of the $\ell_p$ -robust networks. On IMAGENET-R, IMAGENET-SKETCH and CONFLICT STIMULI, the model robust w.r.t. $\ell_{\infty}$ plays instead the most relevant role, again in line with the results in Table 1. Interestingly, in the case of CONFLICT STIMULI, the nominal classifier has a weight -0.4 (the smallest in the grid search) for all top performing soups: we hypothesize that this has the effect of reduce the texture bias typical of nominal model and emphasize the attention to shapes already important in adversarially trained classifiers. Finally, we show the composition of the soup which has the best average accuracy over all datasets (last column of Fig. 7), where the nominal and $\ell_{\infty}$ -robust models have similar positive weight. + +How many images does it take to find a good soup? To identify the practical limit of supervision for soup selection, we study the effect of varying the number of labelled images + +![](images/99ddd8edba0ad97da74370ed64ff377d425de45a5800dfc0365704a3b152fe37.jpg) + +![](images/d7833a4dda6cf990526fa47856d6da16b9b69085e9acefd77390abf84462f26e.jpg) +Figure 8. Soup selection data efficiency: we vary the number of images for selecting the best performing soups on different datasets. For each case, we plot the average accuracy on a held-out test set, and its standard deviation over 50 trials. + +![](images/9558b5db971395a6df2598273460634c0a37bead8ad45b28cfa280fc9b031cd4.jpg) +Figure 9. Soup compositions on IMAGENET-C: we plot the model-wise weights of the best soups across types and severities. + +used to select the best soup on a new dataset. For this analysis we randomly choose 500 images from the adaptation set used for the grid search to create a held-out test set. From the remaining images, we uniformly sample $k$ elements, select the soup which performs best on such $k$ points, and then evaluate it on this test set. We repeat this procedure for $k \in \{10, 30, 100, 300, 500\}$ for 50 times each with different random seeds. In Fig. 8 we plot the average accuracy on the held-out test set, with standard deviation, when varying $k$ : increasing the number of points above 100 achieves high test accuracy with limited variance. This suggests that soup selection, and thus model adaptation, can be carried out with as few as 100 examples of the new distribution. + +# 5.2. A closer look at IMAGENET-C + +While our experiments have considered IMAGENET-C as a single dataset, it consists of 15 corruptions types, each with 5 severity levels. As the various corruptions have different characteristics, one might expect the best soup to vary across them. In Fig. 9 we plot the composition of the top-5 soups for each severity level for two corruption types (as done in Fig. 7). The weights of the individual classifiers significantly change across distribution shifts: for both corruption types, increasing the severity (making perturbations stronger) leads to a reduction in the nominal weight in favor of a robust weight. However, in the case of "pixelate" the soups concentrate on the $\ell_1$ -robust network, while for "jpeg compression" this happens for $\ell_{\infty}$ . Similar visualization for the remaining IMAGENET-C subsets are found in Fig. 11 of the Appendix. This highlights the importance of interpolating models with different types of robustness, and implies that considering each corruption type (including severity levels) as independent datasets could further improve the performance of the soups on IMAGENET-C. + +# 6. Discussion and Limitations + +Merging models with different types of robustness enables strong control of classifier performance by tuning only a few soup weights. Soups can find models which perform well even on distributions unseen during training (e.g. the IMAGENET variants). Moreover, our framework avoids constraining on multiple threats: this makes it possible to fine-tune models with additional attacks as they present themselves, and enrich the soups with them. + +At the moment, our soups contain only nominal or $\ell_{p}$ -robust models, but expanding the diversity of models might aid adaptation to new datasets. We selected our soups with few-shot supervision, but other settings could potentially use soups, such as unsupervised domain adaptation [37,42], on labeled clean and unlabeled shifted data, and test-time adaptation [43,44,48], on unlabeled examples alone. Moreover, in our evaluation we have constrained the soups to belong to a fixed grid, which might miss better models: future work could develop automatic schemes to optimize the soup weights, possibly with even fewer examples, or without labeled examples (as done for test-time adaptation of non-robust models). + +# 7. Conclusion + +We show that combining the parameters of robust classifiers, without additional training, achieves a smooth trade-off of robustness in different $\ell_p$ -threat models. This allows us to discover models which perform well on distribution shifts with only a limited number of examples of each shift. In these ways, model soups serve as a good starting point to efficiently adapt classifiers to changes in data distributions. + +# References + +[1] Lucas Beyer, Olivier J. Henaff, Alexander Kolesnikov, Xiaohua Zhai, and Aaron van den Oord. Are we done with ImageNet? arXiv preprint arXiv:2006.07159, 2020. 6 +[2] Battista Biggio, Igino Corona, Davide Maiorca, Blaine Nelson, Nedim Srndic, Pavel Laskov, Giorgio Giacinto, and Fabio Roli. Evasion Attacks against Machine Learning at Test Time. arXiv preprint arXiv:1708.06131, 2013. 1 +[3] Dan A. Calian, Florian Stimberg, Olivia Wiles, Sylvestre-Alvise Rebuffi, Andras Gyorgy, Timothy Mann, and Sven Gowal. 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Pytorch image models. https://github.com/rwrightman/pytorch-image-models, 2019. 12 +[51] Eric Wong and Zico Kolter. Provable defenses against adversarial examples via the convex outer adversarial polytope. In International Conference on Machine Learning, pages 5283-5292, 2018. 12 +[52] Mitchell Wortsman, Gabriel Ilharco, Samir Yitzhak Gadre, Rebecca Roelofs, Raphael Gontijo-Lopes, Ari S. Morcos, Hongseok Namkoong, Ali Farhadi, Yair Carmon, Simon Kornblith, and Ludwig Schmidt. Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time. arXiv preprint arXiv:2203.05482, 2022. 1, 2, 3, 12 +[53] Mitchell Wortsman, Gabriel Ilharco, Jong Wook Kim, Mike Li, Simon Kornblith, Rebecca Roelofs, Raphael Gontijo Lopes, Hannaneh Hajishirzi, Ali Farhadi, Hongseok Namkoong, et al. Robust fine-tuning of zero-shot models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7959-7971, 2022. 12 +[54] Cihang Xie, Mingxing Tan, Boqing Gong, Jiang Wang, Alan Yuille, and Quoc V Le. Adversarial Examples Improve Image Recognition. arXiv preprint arXiv:1911.09665, 2019. 1, 2, 6 +[55] Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In ICCV, 2019. 12 +[56] Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. arXiv preprint arXiv:1605.07146, 2016. 4 +[57] Hongyi Zhang, Moustapha Cisse, Yann N Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. In ICLR, 2018. 12 + +[58] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P. Xing, Laurent El Ghaoui, and Michael I. Jordan. 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In International Conference on Learning Representations, 2022. 12 \ No newline at end of file diff --git a/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/images.zip b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..b3649de705a4947b686a45776c1ce36e0ff0ab26 --- /dev/null +++ b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:82f7adc5d59d27db96914d9b7c19b22b8c0d6b23a7bf0779fbaa9a8c93b6af28 +size 567485 diff --git a/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/layout.json b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f29f8d1da6c275fd94f0439529cec489239ea5e1 --- /dev/null +++ b/2023/Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts/layout.json @@ -0,0 +1,11050 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 154, + 103, + 440, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 154, + 103, + 440, + 138 + ], + "spans": [ + { + "bbox": [ + 154, + 103, + 440, + 138 + ], + "type": "text", + "content": "Seasoning Model Soups for Robustness to Adversarial and Natural Distribution Shifts" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 160, + 187, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 160, + 187, + 190 + ], + "spans": [ + { + "bbox": [ + 71, + 160, + 187, + 190 + ], + "type": "text", + "content": "Francesco Croce* \nUniversity of Tübingen" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 210, + 161, + 332, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 210, + 161, + 332, + 190 + ], + "spans": [ + { + "bbox": [ + 210, + 161, + 332, + 190 + ], + "type": "text", + "content": "Sylvestre-Alvise Rebuffi DeepMind" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 355, + 161, + 437, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 161, + 437, + 190 + ], + "spans": [ + { + "bbox": [ + 355, + 161, + 437, + 190 + ], + "type": "text", + "content": "Evan Shelhamer DeepMind" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 461, + 161, + 522, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 461, + 161, + 522, + 190 + ], + "spans": [ + { + "bbox": [ + 461, + 161, + 522, + 190 + ], + "type": "text", + "content": "Sven Gowal DeepMind" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "text", + "content": "Adversarial training is widely used to make classifiers robust to a specific threat or adversary, such as " + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "text", + "content": "-norm bounded perturbations of a given " + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "text", + "content": "-norm. However, existing methods for training classifiers robust to multiple threats require knowledge of all attacks during training and remain vulnerable to unseen distribution shifts. In this work, we describe how to obtain adversially-robust model soups (i.e., linear combinations of parameters) that smoothly trade-off robustness to different " + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "text", + "content": "-norm bounded adversaries. We demonstrate that such soups allow us to control the type and level of robustness, and can achieve robustness to all threats without jointly training on all of them. In some cases, the resulting model soups are more robust to a given " + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 242, + 290, + 447 + ], + "type": "text", + "content": "-norm adversary than the constituent model specialized against that same adversary. Finally, we show that adversially-robust model soups can be a viable tool to adapt to distribution shifts from a few examples." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 469, + 128, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 469, + 128, + 482 + ], + "spans": [ + { + "bbox": [ + 47, + 469, + 128, + 482 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 490, + 288, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 288, + 694 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 288, + 694 + ], + "type": "text", + "content": "Deep networks have achieved great success on several computer vision tasks and have even reached super-human accuracy [19, 31]. However, the outputs of such models are often brittle, and tend to perform poorly on inputs that differ from the distribution of inputs at training time, in a condition known as distribution shift [37]. Adversarial perturbations are a prominent example of this condition: small, even imperceptible, changes to images can alter predictions to cause errors [2, 46]. In addition to adversarial inputs, it has been noted that even natural shifts, e.g. different weather conditions, can significantly reduce the accuracy of even the best vision models [13, 21, 40]. Such drops in accuracy are undesirable for robust deployment, and so a lot of effort has been invested in correcting them. Adversarial training [34] and its extensions [15, 39, 58] are currently the most effective methods to improve empirical robustness to adversarial attacks. Similarly, data augmen" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "type": "text", + "content": "tation is the basis of several techniques that improve robustness to non-adversarial/natural shifts [3, 11, 22]. While significant progress has been made on defending against a specific, selected type of perturbations (whether adversarial or natural), it is still challenging to make a single model robust to a broad set of threats and shifts. For example, a classifier adversarily-trained for robustness to " + }, + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "type": "text", + "content": "-norm bounded attacks is still vulnerable to attacks in other " + }, + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "type": "inline_equation", + "content": "\\ell_q" + }, + { + "bbox": [ + 304, + 218, + 547, + 386 + ], + "type": "text", + "content": "-threat models [29, 47]. Moreover, methods for simultaneous robustness to multiple attacks require jointly training on all [33, 35] or a subset of them [8]. Most importantly, controlling the trade-off between different types of robustness (and nominal performance) remains difficult and requires training several classifiers." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "text", + "content": "Inspired by model soups [52], which interpolate the parameters of a set of vision models to achieve state-of-the-art accuracy on IMAGENET, we investigate the effects of interpolating robust image classifiers. We complement their original recipe for soups by own study of how to pretrain, fine-tune, and combine the parameters of models adversarially-trained against " + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "text", + "content": "-norm bounded attacks for different " + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "text", + "content": "-norms. To create models for soups, we pre-train a single robust model and fine-tune it to the target threat models (using the efficient technique of [8]). We then establish that it is possible to smoothly trade-off robustness to different threat models by moving in the convex hull of the parameters of each robust classifier, while achieving competitive performance with methods that train on multiple " + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 388, + 548, + 616 + ], + "type": "text", + "content": "-norm adversaries simultaneously. Unlike alternatives, our soups can uniquely (1) choose the level of robustness to each threat model without any further training and (2) quickly adapt to new unseen attacks or shifts by simply tuning the weighting of the soup." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "Previous works [24, 30, 54] have shown that adversarial training with " + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "-norm bounded attacks can help to improve performance on natural shifts if carefully tuned. We show that model soups of diverse classifiers, with different types of robustness, offer greater flexibility for finding models that perform well across various shifts, such as IMAGENET variants. Furthermore, we show that a limited number of images of the new distribution are sufficient to select the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 212, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 212, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 212, + 713 + ], + "type": "text", + "content": "*Work done during an internship at DeepMind." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12313" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "weights of such a model soup. Examining the composition of the best soups brings insights about which features are important for each dataset and shift. Finally, while the capability of selecting a model specific to each image distribution is a main point of our model soups, we also show that it is possible to jointly select a soup for average performance across several IMAGENET variants to achieve better accuracy than adversarial and self-supervised baselines [18, 24]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 168, + 246, + 180 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 168, + 246, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 246, + 180 + ], + "type": "text", + "content": "Contributions. In summary, we show that soups" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 180, + 287, + 312 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "type": "text", + "content": "- can merge nominal and " + }, + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "type": "text", + "content": "-robust models (for various " + }, + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 180, + 287, + 228 + ], + "type": "text", + "content": "): efficient fine-tuning from one robust model obtains a set of models with diverse robustness [8] and compatible parameters for creating model soups [52] (Sec. 3)," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 228, + 287, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 228, + 287, + 263 + ], + "spans": [ + { + "bbox": [ + 47, + 228, + 287, + 263 + ], + "type": "text", + "content": "- can control the level of robustness to each threat model and achieve, without more training, competitive performance against multi-norm robustness training (Sec. 4)," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 264, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 287, + 287 + ], + "type": "text", + "content": "- are not limited to interpolation, but can find more effective classifiers by extrapolation (Sec. 4.3)," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 288, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 287, + 312 + ], + "type": "text", + "content": "- enable adaptation to unseen distribution shifts on only a few examples (Sec. 5)." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 323, + 133, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 133, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 133, + 335 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "type": "text", + "content": "Adversarial robustness to multiple threat models. Most methods focus on achieving robustness in a single threat model, i.e. to a specific type of attacks used during training. However, this is not sufficient to obtain robustness to unseen attacks. As a result, further work aims to train classifiers for simultaneous robustness to multiple attacks, and the most popular scenario considers a set of " + }, + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 342, + 287, + 534 + ], + "type": "text", + "content": "-norm bounded perturbations. The most successful methods [33, 35, 47] are based on adversarial training and differ in how the multiple threats are combined. Notably, all need to use every attack at training time. To reduce the computational cost of obtaining multiply-robust models, one can fine-tune a singly-robust model by one of the above mentioned methods [8], even for only a small number of epochs. Our soups are more flexible by skipping simultaneous adversarial training across multiple attacks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "Adversarial training for distribution shifts. While robustness to adversarial attacks and natural shifts are not the same goal, previous works nevertheless show that it is possible to leverage adversarial training with " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "-norm bounded attacks to improve performance on the common corruptions of [21]. First, AdvProp [54] co-trains models on clean and adversarial images (in the " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "-threat model) with dual normalization layers that specialize to each type of input. The clean branch of the dual model achieves higher accuracy than nominal training on IMAGENET and its variants. Similar results are obtained by Pyramid-AT [24] by its design of a specific attack to adversarily train vision transformers. Finally, [30] carefully selecting the size of the adversarial perturbations, i.e., their " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "- or " + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "-norm, for standard adversarial training [34] achieves competitive performance on" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 536, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 536, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 536, + 84 + ], + "type": "text", + "content": "common corruptions on CIFAR-10 and IMAGENET-100." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 84, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 240 + ], + "type": "text", + "content": "Model soups. Ensembling or averaging the parameters of intermediate models found during training is an effective technique to improve both clean accuracy [25, 28] and robustness [14, 39]. Recently, [52] propose model soups which interpolate the parameters of networks finetuned with different hyperparameters configurations from the same pre-trained model. This yields improved classification accuracy onImagenet. Along the same line, [27] fine-tune a model trained onImagenet on several new image classification datasets, and show that interpolating the original and fine-tuned parameters yields classifiers that perform well on all tasks. Additional related work is discussed in App. A." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 251, + 541, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 541, + 265 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 541, + 265 + ], + "type": "text", + "content": "3. Model Interpolation across Different Tasks" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": "In the following, we formally introduce the two main components of our procedure to merge adversarially robust models: (1) obtaining models which can interpolated by fine-tuning a single " + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 271, + 545, + 427 + ], + "type": "text", + "content": "-robust classifiers, and (2) interpolation of their weights to balance their different types of robustness. We highlight that our setup diverges from that of prior works about parameters averaging: in fact, both [27, 52] combine models fine-tuned on the same task, i.e. achieving high classification accuracy of unperturbed images, either on a fixed dataset and different hyperparameter configurations [52], or varying datasets [27]. In our case, the individual models are trained for robustness to different types of attacks, i.e. with distinct loss functions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 435, + 499, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 435, + 499, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 499, + 448 + ], + "type": "text", + "content": "3.1. Adversarial training and fine-tuning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": "Let us denote " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_i, y_i)\\}_i" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " the training set, with " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "x_i \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " indicating an image and " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "y_i \\in \\{1, \\dots, K\\}" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " the corresponding label, and " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\Delta: \\mathbb{R}^d \\to \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " the function which characterizes a threat model, that maps an input " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " to a set " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\Delta(x) \\subset \\mathbb{R}^d" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " of possible perturbed versions of the original image. For example, " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": "-norm bounded adversarial attacks with budget " + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\epsilon > 0" + }, + { + "bbox": [ + 305, + 453, + 545, + 538 + ], + "type": "text", + "content": " in the image space can be described by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 329, + 546, + 545, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 546, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 329, + 546, + 545, + 561 + ], + "type": "interline_equation", + "content": "\\Delta (\\boldsymbol {x}) = \\left\\{\\boldsymbol {\\delta} \\in \\mathbb {R} ^ {d}: \\| \\boldsymbol {\\delta} \\| _ {p} \\leq \\epsilon , \\boldsymbol {x} + \\boldsymbol {\\delta} \\in [ 0, 1 ] ^ {d} \\right\\}. \\tag {1}", + "image_path": "d2f1a182c35b2edc68ac821776684ea75a466b529f0e10801eb050397954d8e5.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "type": "text", + "content": "Then, one can train a classifier " + }, + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "type": "inline_equation", + "content": "f:\\pmb {\\theta}\\times \\mathbb{R}^d\\to \\mathbb{R}^K" + }, + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "type": "inline_equation", + "content": "\\pmb {\\theta}\\in \\Theta" + }, + { + "bbox": [ + 305, + 570, + 545, + 595 + ], + "type": "text", + "content": " with adversarial training [34] by solving" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 343, + 604, + 545, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 604, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 343, + 604, + 545, + 632 + ], + "type": "interline_equation", + "content": "\\min _ {\\boldsymbol {\\theta} \\in \\Theta} \\sum_ {(\\boldsymbol {x}, y) \\in \\mathcal {D}} \\max _ {\\boldsymbol {\\delta} \\in \\Delta (\\boldsymbol {x})} \\mathcal {L} (f (\\boldsymbol {\\theta}, x + \\boldsymbol {\\delta}), y), \\tag {2}", + "image_path": "d19028983877835533c1ce98ed4fb52b5e8f16324cad52beb36bc9a67af765a5.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "for a given loss function " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}:\\mathbb{R}^K\\times \\mathbb{R}^K\\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " (e.g., cross-entropy), with the goal of obtaining a model robust to the perturbations described by " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ". Note that this boils down to nominal training when " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Delta (\\cdot) = \\{\\mathbf{0}\\}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " and no perturbation is applied on the training images. We are interested in the case where multiple threat models are available, and indicate" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "12314" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 70, + 220, + 179 + ], + "blocks": [ + { + "bbox": [ + 76, + 70, + 220, + 179 + ], + "lines": [ + { + "bbox": [ + 76, + 70, + 220, + 179 + ], + "spans": [ + { + "bbox": [ + 76, + 70, + 220, + 179 + ], + "type": "image", + "image_path": "fa4a9b5c007cc1d50c401a20caac2aa7d43fc6e6f40e1a0a7e45bf75e091e813.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": "Figure 1. Soups of two models on CIFAR-10: for all pairs " + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "inline_equation", + "content": "(p,q)" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": " we show the " + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "inline_equation", + "content": "\\ell_{p}" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": "- vs " + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "inline_equation", + "content": "\\ell_{q}" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": "-robust accuracy of the soups " + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "inline_equation", + "content": "w\\cdot \\theta_{p} + (1 - w)\\cdot \\theta_{p\\rightarrow q}" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "inline_equation", + "content": "w\\cdot \\theta_q + (1 - w)\\cdot \\theta_{q\\to p}" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": " varying " + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "inline_equation", + "content": "w\\in [0,1]" + }, + { + "bbox": [ + 46, + 194, + 546, + 217 + ], + "type": "text", + "content": ". We also show results for MAX and SAT with simultaneous use of the two threat models." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 229, + 70, + 374, + 179 + ], + "blocks": [ + { + "bbox": [ + 229, + 70, + 374, + 179 + ], + "lines": [ + { + "bbox": [ + 229, + 70, + 374, + 179 + ], + "spans": [ + { + "bbox": [ + 229, + 70, + 374, + 179 + ], + "type": "image", + "image_path": "8cb58d3f5c7c9b3b74c97e46bcc21da6c334ab2b25f550f1f9ddd4fb64df4015.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 383, + 70, + 518, + 180 + ], + "blocks": [ + { + "bbox": [ + 383, + 70, + 518, + 180 + ], + "lines": [ + { + "bbox": [ + 383, + 70, + 518, + 180 + ], + "spans": [ + { + "bbox": [ + 383, + 70, + 518, + 180 + ], + "type": "image", + "image_path": "b8ae2eb71709e5a21211edfa7f85e008773e5a983da7aac20b023d12cdcd7c4e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 51, + 227, + 173, + 336 + ], + "blocks": [ + { + "bbox": [ + 51, + 227, + 173, + 336 + ], + "lines": [ + { + "bbox": [ + 51, + 227, + 173, + 336 + ], + "spans": [ + { + "bbox": [ + 51, + 227, + 173, + 336 + ], + "type": "image", + "image_path": "78c9c611c89838214762f18e6e09b6fc5f648b5cf1894bb4a626a5fd38f58fb0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "lines": [ + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": "Figure 2. Soups of two models on IMAGENET: for " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "p \\in \\{2,1\\}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " we show the " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\ell_{p^-}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " vs " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": "-robust accuracy of the soups " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "w \\cdot \\theta_{\\infty} + (1 - w) \\cdot \\theta_{\\infty \\rightarrow p}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " varying " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "w \\in [0,1]" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " (first and second columns). Moreover, we show the soups obtained combining " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 2}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 1}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " (third), or " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow \\text{nominal}}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": " (fourth). For the case of two " + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "inline_equation", + "content": "\\ell_{p^-}" + }, + { + "bbox": [ + 46, + 350, + 546, + 384 + ], + "type": "text", + "content": "-threat models, we also show the results of fine-tuning models with MAX and SAT." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 176, + 227, + 298, + 336 + ], + "blocks": [ + { + "bbox": [ + 176, + 227, + 298, + 336 + ], + "lines": [ + { + "bbox": [ + 176, + 227, + 298, + 336 + ], + "spans": [ + { + "bbox": [ + 176, + 227, + 298, + 336 + ], + "type": "image", + "image_path": "2d6f981fcdf5770272485231e322574bf5b858d22dc194ac6ee10d6d3be016cd.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 302, + 227, + 425, + 336 + ], + "blocks": [ + { + "bbox": [ + 302, + 227, + 425, + 336 + ], + "lines": [ + { + "bbox": [ + 302, + 227, + 425, + 336 + ], + "spans": [ + { + "bbox": [ + 302, + 227, + 425, + 336 + ], + "type": "image", + "image_path": "9727ad545248276aeacffae333be011fff4ff61f8ae4b1de9069c48b2ba0b739.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 428, + 227, + 548, + 336 + ], + "blocks": [ + { + "bbox": [ + 428, + 227, + 548, + 336 + ], + "lines": [ + { + "bbox": [ + 428, + 227, + 548, + 336 + ], + "spans": [ + { + "bbox": [ + 428, + 227, + 548, + 336 + ], + "type": "image", + "image_path": "bdb97aededccf3ed1b8d9536f78bf02104f11149040ee6f043af0ad81e11c376.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "spans": [ + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathrm{nominal}}" + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "content": " nominal training, and " + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "inline_equation", + "content": "\\Delta_p" + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "inline_equation", + "content": "p \\in \\{\\infty, 2, 1\\}" + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "content": " the perturbations with bounded " + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 405, + 287, + 465 + ], + "type": "text", + "content": "-norm as described in Eq. 1. We focus on such tasks since they are the most common choices for adversarial defenses, in particular by methods focusing on multiple norm robustness [35, 47]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": "Notably, it is possible to efficiently obtain a model robust to " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\Delta_q" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " by fine-tuning for a single (or few) epoch with adversarial training w.r.t. " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\Delta_q" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " a classifier pre-trained to be robust in " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\Delta_p" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "p \\neq q" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "p, q \\in \\{\\infty, 2, 1\\}" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " [8]. For example, in this way one can efficiently derive specialized classifiers " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\Delta_2, \\Delta_1, \\Delta_{\\mathrm{nominal}}" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " for each task from a single model " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " robust w.r.t. " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": ". However, this does not work well when a nominal classifier is used as starting point for the short fine-tuning. In the following, we denote with " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\theta_{p \\rightarrow q}" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " the parameters resulting from fine-tuning to " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\Delta_q" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": " a base model " + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\theta_p" + }, + { + "bbox": [ + 46, + 466, + 287, + 587 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 597, + 287, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 287, + 623 + ], + "type": "text", + "content": "3.2. Merging different types of robustness via linear combinations in parameter space" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "We want to explore the properties of the models obtained by taking linear combinations of the parameters of classifiers with different types of robustness. To do so, there needs to be a correspondence among the parameters of different individual networks: [52] achieve this by merging differently fine-tuned versions of the same pre-trained model. As mentioned above, fine-tuning an " + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 629, + 287, + 715 + ], + "type": "text", + "content": "-robust clas" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "text", + "content": "sifier allows to change it to achieve robustness in a new threat model [8]: we exploit such property to create model soups, as named by [52]. Formally, we create a model soup from " + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "text", + "content": " individual networks with parameters " + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}^{1},\\dots,\\pmb{\\theta}^{n}" + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "text", + "content": " with weights " + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "inline_equation", + "content": "\\pmb{w} = (w_{1},\\dots,w_{n})\\in \\mathbb{R}^{n}" + }, + { + "bbox": [ + 304, + 405, + 546, + 466 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 387, + 478, + 545, + 509 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 478, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 387, + 478, + 545, + 509 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} ^ {w} = \\sum_ {i = 1} ^ {n} w _ {i} \\cdot \\boldsymbol {\\theta} ^ {i}, \\tag {3}", + "image_path": "23a65e8f348645b9971e3f528882f25fe966e99003f991aa2597e2bb9a070e7f.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "content": "and the corresponding classifier is given by " + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "inline_equation", + "content": "f(\\pmb{\\theta}^{\\pmb{w}},\\cdot):\\mathbb{R}^{d}\\to \\mathbb{R}^{K}" + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "content": ". While any choice of " + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\pmb{w}" + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "content": " is possible, we focus on the case of affine combinations, i.e. " + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\sum_{i}w_{i} = 1" + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "content": ". Moreover, we consider soups which are either convex combinations of the individual models, with " + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "inline_equation", + "content": "w_{1},\\ldots ,w_{n}\\geq 0" + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "content": ", or obtained by extrapolations, i.e. with negative elements in " + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "inline_equation", + "content": "\\pmb{w}" + }, + { + "bbox": [ + 304, + 520, + 547, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 608, + 440, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 440, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 440, + 623 + ], + "type": "text", + "content": "4. Soups for " + }, + { + "bbox": [ + 306, + 608, + 440, + 623 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 306, + 608, + 440, + 623 + ], + "type": "text", + "content": "-robustness" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": "We measure adversarial robustness in the " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": "-threat model with bounds " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_p" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ": on CIFAR-10 we use " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\infty} = 8 / 255" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_2 = 128 / 255" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_1 = 12" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ", on IMAGENET " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\infty} = 4 / 255" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_2 = 4" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_1 = 255" + }, + { + "bbox": [ + 304, + 629, + 546, + 714 + ], + "type": "text", + "content": ". If not specified otherwise, we use the full test set for CIFAR-10 and 5000 images from the IMAGENET validation set, and attack by AUTOPGD [6,7] with 40 steps. More details are provided in App. B." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12315" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 209, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 209, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 209, + 85 + ], + "type": "text", + "content": "4.1. Soups with two threat models" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "content": "CIFAR-10. We explore the effect of interpolating two models robust to different " + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "content": "-norm bounded attacks for " + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "inline_equation", + "content": "p \\in \\{\\infty, 2, 1\\}" + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "content": ". We consider classifiers with WIDERES-NET-28-10 [56] architecture trained on CIFAR-10. For every threat model, we first train a robust classifier with adversarial training from random initialization. Then, we fine-tune the resulting model with adversarial training on each of the other threat models for 10 epochs. In Fig. 1 we show, for each pair of threat models " + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "inline_equation", + "content": "(\\Delta_p, \\Delta_q)" + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "content": ", the trade-off of robust accuracy w.r.t. " + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "inline_equation", + "content": "\\ell_q" + }, + { + "bbox": [ + 46, + 90, + 289, + 212 + ], + "type": "text", + "content": " for the soups" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 80, + 218, + 254, + 233 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 218, + 254, + 233 + ], + "spans": [ + { + "bbox": [ + 80, + 218, + 254, + 233 + ], + "type": "interline_equation", + "content": "w \\cdot \\pmb {\\theta} _ {p} + (1 - w) \\cdot \\pmb {\\theta} _ {p \\rightarrow q} \\quad \\mathrm {f o r} \\quad w \\in [ 0, 1 ]", + "image_path": "84acc76875d1de469695819e43f508b663b8994aa33965ffd1ff9327be2720e2.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 240, + 126, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 240, + 126, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 240, + 126, + 253 + ], + "type": "text", + "content": "and symmetrically" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 78, + 261, + 255, + 275 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 261, + 255, + 275 + ], + "spans": [ + { + "bbox": [ + 78, + 261, + 255, + 275 + ], + "type": "interline_equation", + "content": "w \\cdot \\boldsymbol {\\theta} _ {q} + (1 - w) \\cdot \\boldsymbol {\\theta} _ {q \\rightarrow p} \\quad \\text {f o r} \\quad w \\in [ 0, 1 ].", + "image_path": "38582343d07ee707a3f8665441a68e595c161f8c58265ac6128af6d8ff79ccdd.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": "Interpolating the parameters of models trained with a single " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": "-norm controls the balance between the two types of robustness: for example, Fig. 1 (middle plot) shows that moving from " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty}" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 1}" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": " (blue curve), i.e. decreasing " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": " from 1 to 0 in the corresponding soup, progressively reduces the robust accuracy w.r.t. " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": " to improve robustness w.r.t. " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": ". Moreover, for similar threat models (i.e. the pairs " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "(\\ell_2, \\ell_1)" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "inline_equation", + "content": "(\\ell_2, \\ell_{\\infty})" + }, + { + "bbox": [ + 46, + 283, + 287, + 390 + ], + "type": "text", + "content": ") some intermediate networks are more robust than the extremes trained specifically for each threat model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "text", + "content": "IMAGENET. We now fine-tune a VIT-B16 [10] robust w.r.t. " + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "text", + "content": " on IMAGENET to the other threat models, including nominal training, for either 1/3, 1 or 3 epochs. Fig. 2 shows that interpolation of parameters is effective even in this setup, and allows to easily balance nominal and robust accuracy (fourth plot). Moreover, it is possible to create soups with two fine-tuned models, i.e. " + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 2}" + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 1}" + }, + { + "bbox": [ + 46, + 390, + 287, + 510 + ], + "type": "text", + "content": ". Finally, increasing the number of fine-tuning steps yields better performance in the target threat model, which in turn generally leads to better soups." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "Comparison to multi-norm robustness methods. Fig. 1 and Fig. 2 compare the performance of the model soups to that of models trained with methods for robustness in the union of multiple threat models. In particular, we show the results of MAX [47], which computes perturbations for each threat model and trains on that attaining the highest loss, and SAT [33], which samples uniformly at random for each training batch the attack to use. We train models with both methods for all pairs of threat models: as expected, MAX tends to focus on the most challenging threat model, sacrificing some robustness in the other one compared to SAT, since it uses only the strongest attack for each training point. When training for " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": ", i.e. the extreme " + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 510, + 288, + 713 + ], + "type": "text", + "content": "-norms we consider, MAX and SAT models lie above the front drawn by the model soups, hinting that the more diverse the attacks, the more difficult it is to preserve high robustness to both. In the other cases, both methods behave" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 145 + ], + "type": "text", + "content": "similarly to the soups. The main advantage given by interpolation is however the option of moving along the front without additional training cost: while one might tune the trade-off between the robustness in the two threat models in SAT, e.g. changing the sampling probability, this would still require training a new classifier for each setup." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 152, + 474, + 165 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 152, + 474, + 165 + ], + "spans": [ + { + "bbox": [ + 305, + 152, + 474, + 165 + ], + "type": "text", + "content": "4.2. Soups with three threat models" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": "We here study the convex combination of three models with different types of robustness. For CIFAR-10 we create soups with each " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": "-robust classifier for " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "p \\in \\{\\infty, 2, 1\\}" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": " and its fine-tuned version into the other two threat models. We use the same models of the previous section, and sweep the interpolation weights " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\boldsymbol{w} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "w_i \\in \\{0, 0.2, 0.4, 0.6, 0.8, 1\\}" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\sum_i w_i = 1" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": ". In Fig. 3 and Fig. 10 (in the Appendix) we show clean accuracy (first column) and robust accuracy in " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 171, + 545, + 302 + ], + "type": "text", + "content": " (second to fourth columns) and their union, when a point is considered robust only if it is such against all attacks (last column)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "content": "One can observe that, independently from the type of robustness of the base model (used as initialization for the fine-tuning), moving in the convex hull of the three parameters (e.g. " + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty} + \\theta_{\\infty \\rightarrow 2} + \\theta_{\\infty \\rightarrow 1}" + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "content": " in Fig. 3) allows to smoothly control the trade-off of the different types of robustness. Interestingly, the highest " + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "content": "-robustness is attained by intermediate soups, not by the model specifically fine-tuned w.r.t. " + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "content": ", suggesting that model soups might even be beneficial to robustness in individual threat models (see more below). Moreover, the highest robustness in the union is given by interpolating only the models robust w.r.t. " + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 303, + 546, + 506 + ], + "type": "text", + "content": ", which is in line with the observation of [8] that training for the extreme norms is sufficient for robustness in the union of the three threat models. Although the robust accuracy in the union is lower than that of training simultaneously with all attacks e.g. with MAX (42.0% vs 47.2%), the model soups deliver competitive results without the need of co-training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": "Finally, Fig. 4 shows that similar observations hold on IMAGENET, where we create soups fine-tuning classifiers robust w.r.t. " + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 506, + 545, + 555 + ], + "type": "text", + "content": ", with either RESNET-50 [19] or ViT-B16 as architecture, for 1 epoch." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 305, + 563, + 545, + 587 + ], + "type": "text", + "content": "4.3. Soups for improving individual threat model robustness" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "We notice in Fig. 1 and Fig. 2 that in a few cases the intermediate models obtain via parameters interpolation have higher robustness than the extreme ones, which are trained or fine-tuned with a specific threat model. As such, we analyze in more details the soups " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "w \\cdot \\theta_{\\infty} + (1 - w) \\cdot \\theta_{\\infty \\rightarrow 2}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": ", i.e. using the original classifier robust in " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " and the one fine-tuned to " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\ell_{2}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": ", on both CIFAR-10 andImagenet. Fig. 5 shows the robust accuracy w.r.t. " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " when varying the value of " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": ": in both case the original model " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty}" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": ", highlighted in red, does not attain the best robustness. Interestingly, on" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12316" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 242, + 71, + 350, + 82 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 242, + 71, + 350, + 82 + ], + "spans": [ + { + "bbox": [ + 242, + 71, + 350, + 82 + ], + "type": "interline_equation", + "content": "\\text {s o u p :} \\theta_ {\\infty} + \\theta_ {\\infty \\rightarrow 2} + \\theta_ {\\infty \\rightarrow 1}", + "image_path": "96e701cf7dc1073d4a514563a052861513bdfbb8fdb5f9503d59615263784266.jpg" + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 62, + 102, + 162, + 175 + ], + "blocks": [ + { + "bbox": [ + 76, + 84, + 134, + 95 + ], + "lines": [ + { + "bbox": [ + 76, + 84, + 134, + 95 + ], + "spans": [ + { + "bbox": [ + 76, + 84, + 134, + 95 + ], + "type": "text", + "content": "clean accuracy" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 161, + 84, + 233, + 95 + ], + "lines": [ + { + "bbox": [ + 161, + 84, + 233, + 95 + ], + "spans": [ + { + "bbox": [ + 161, + 84, + 233, + 95 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 161, + 84, + 233, + 95 + ], + "type": "text", + "content": " robust accuracy" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 62, + 102, + 162, + 175 + ], + "lines": [ + { + "bbox": [ + 62, + 102, + 162, + 175 + ], + "spans": [ + { + "bbox": [ + 62, + 102, + 162, + 175 + ], + "type": "image", + "image_path": "376fc52fad78ce9ebc41b72072edd7c7a3d55d0be38fe4d9856841944ed47838.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 163, + 102, + 255, + 175 + ], + "blocks": [ + { + "bbox": [ + 254, + 84, + 325, + 95 + ], + "lines": [ + { + "bbox": [ + 254, + 84, + 325, + 95 + ], + "spans": [ + { + "bbox": [ + 254, + 84, + 325, + 95 + ], + "type": "inline_equation", + "content": "\\ell_{2}" + }, + { + "bbox": [ + 254, + 84, + 325, + 95 + ], + "type": "text", + "content": " robust accuracy" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 163, + 102, + 255, + 175 + ], + "lines": [ + { + "bbox": [ + 163, + 102, + 255, + 175 + ], + "spans": [ + { + "bbox": [ + 163, + 102, + 255, + 175 + ], + "type": "image", + "image_path": "f8478d1afdea3264e8acec759a455e242c29e626d9d0f98ad430ba95fc62f9cb.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 190, + 547, + 225 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 547, + 225 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 547, + 225 + ], + "type": "text", + "content": "Figure 3. 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" + }, + { + "bbox": [ + 46, + 466, + 547, + 499 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 466, + 547, + 499 + ], + "type": "text", + "content": " for 1 epoch to the other threat models, and show clean accuracy (first column) and robust accuracy in every threat model (second to fourth columns) and their union (last column) of the classifiers obtained as convex combinations of the three bases." + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "image_caption" + } + ], + "index": 29 + }, + { + "type": "image", + "bbox": [ + 164, + 377, + 238, + 450 + ], + "blocks": [ + { + "bbox": [ + 164, + 377, + 238, + 450 + ], + "lines": [ + { + "bbox": [ + 164, + 377, + 238, + 450 + ], + "spans": [ + { + "bbox": [ + 164, + 377, + 238, + 450 + ], + "type": "image", + "image_path": "173a55b836adc23a8ee4e05c1d8f706afb9613d7e1956621264f5e06cf9177eb.jpg" + } + ] + } + ], + "index": 30, + "angle": 0, + "type": "image_body" + } + ], + "index": 30 + }, + { + "type": "image", + "bbox": [ + 239, + 377, + 348, + 450 + ], + "blocks": [ + { + "bbox": [ + 255, + 360, + 325, + 369 + ], + "lines": [ + { + "bbox": [ + 255, + 360, + 325, + 369 + ], + "spans": [ + { + "bbox": [ + 255, + 360, + 325, + 369 + ], + "type": "inline_equation", + "content": "\\ell_{2}" + }, + { + "bbox": [ + 255, + 360, + 325, + 369 + ], + "type": "text", + "content": " robust accuracy" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 347, + 360, + 418, + 369 + ], + "lines": [ + { + "bbox": [ + 347, + 360, + 418, + 369 + ], + "spans": [ + { + "bbox": [ + 347, + 360, + 418, + 369 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 347, + 360, + 418, + 369 + ], + "type": "text", + "content": " robust accuracy" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 239, + 377, + 348, + 450 + ], + "lines": [ + { + "bbox": [ + 239, + 377, + 348, + 450 + ], + "spans": [ + { + "bbox": [ + 239, + 377, + 348, + 450 + ], + "type": "image", + "image_path": "a13d89755b078ae2dd39493b3368c9d6be8e1307d960531f798ba4ebfa5a9db9.jpg" + } + ] + } + ], + "index": 31, + "angle": 0, + "type": "image_body" + } + ], + "index": 31 + }, + { + "type": "image", + "bbox": [ + 348, + 377, + 441, + 450 + ], + "blocks": [ + { + "bbox": [ + 424, + 360, + 527, + 369 + ], + "lines": [ + { + "bbox": [ + 424, + 360, + 527, + 369 + ], + "spans": [ + { + "bbox": [ + 424, + 360, + 527, + 369 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty} + \\ell_{2} + \\ell_{1}" + }, + { + "bbox": [ + 424, + 360, + 527, + 369 + ], + "type": "text", + "content": " robust accuracy" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 348, + 377, + 441, + 450 + ], + "lines": [ + { + "bbox": [ + 348, + 377, + 441, + 450 + ], + "spans": [ + { + "bbox": [ + 348, + 377, + 441, + 450 + ], + "type": "image", + "image_path": "f9eee60a44b632149bd0795651e75cb26ef2a97605de36c13c383bd62bbc0eb0.jpg" + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "image_body" + } + ], + "index": 32 + }, + { + "type": "image", + "bbox": [ + 441, + 377, + 531, + 450 + ], + "blocks": [ + { + "bbox": [ + 441, + 377, + 531, + 450 + ], + "lines": [ + { + "bbox": [ + 441, + 377, + 531, + 450 + ], + "spans": [ + { + "bbox": [ + 441, + 377, + 531, + 450 + ], + "type": "image", + "image_path": "62c528c8c84b0869836cd81882c25e4372e85df729e2fab86fe8fc597acd8b29.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "image_body" + } + ], + "index": 33 + }, + { + "type": "image", + "bbox": [ + 53, + 518, + 171, + 619 + ], + "blocks": [ + { + "bbox": [ + 53, + 518, + 171, + 619 + ], + "lines": [ + { + "bbox": [ + 53, + 518, + 171, + 619 + ], + "spans": [ + { + "bbox": [ + 53, + 518, + 171, + 619 + ], + "type": "image", + "image_path": "239ebb03df8a121a428cfc321e29bc3ea68f68e5a59e93701ff5f8bcd6f0101b.jpg" + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "lines": [ + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "spans": [ + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "text", + "content": "Figure 5. Improvement on single threat models: we show the robust accuracy w.r.t. " + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "text", + "content": " for the soups " + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "inline_equation", + "content": "w \\cdot \\pmb{\\theta}_{\\infty} + (1 - w) \\cdot \\pmb{\\theta}_{\\infty \\rightarrow 2}" + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "text", + "content": " for varied " + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "text", + "content": ". The original model " + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_{\\infty}" + }, + { + "bbox": [ + 46, + 633, + 287, + 667 + ], + "type": "text", + "content": " is highlighted in red." + } + ] + } + ], + "index": 37, + "angle": 0, + "type": "image_caption" + } + ], + "index": 35 + }, + { + "type": "image", + "bbox": [ + 173, + 518, + 288, + 619 + ], + "blocks": [ + { + "bbox": [ + 173, + 518, + 288, + 619 + ], + "lines": [ + { + "bbox": [ + 173, + 518, + 288, + 619 + ], + "spans": [ + { + "bbox": [ + 173, + 518, + 288, + 619 + ], + "type": "image", + "image_path": "e400804cddea7a5c8932fcb8d95adb21eac361a9ff787b918fc49230f359526a.jpg" + } + ] + } + ], + "index": 36, + "angle": 0, + "type": "image_body" + } + ], + "index": 36 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "CIFAR-10 the best soup is found with " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "w = 0.9" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ", while for IMAGENET with " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "w > 1" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": ": this suggests that the model soups" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 520, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 545, + 544 + ], + "type": "text", + "content": "should not be constrained to the convex hull of the base models, and extrapolation can lead to improvement." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 560, + 467, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 560, + 467, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 560, + 467, + 574 + ], + "type": "text", + "content": "5. Soups for Distribution Shifts" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "Prior works [30] have shown that adversarial training w.r.t. an " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "-norm is able to provide some improvement in the performance in presence of non-adversarial distribution shifts, e.g. the common corruptions of IMAGENET-C [21]. However, to see such gains it is necessary to carefully select the threat model, for example which " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "-norm and size " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " to bound the perturbations, to use during training. The experiments in Sec. 4 suggest that model soups of nominal and adversarily robust classifiers yield models with a variety of intermediate behaviors, and extrapolation might even deliver models which do not merely trade-off the robust" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12317" + } + ] + } + ], + "index": 42 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 164, + 159 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 164, + 159 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 164, + 159 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 164, + 159 + ], + "type": "image", + "image_path": "49125a1c923411f433b1906f7e0b9cc30f8401979d1b9638ccb34db3dc8e4b97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 164, + 72, + 265, + 159 + ], + "blocks": [ + { + "bbox": [ + 164, + 72, + 265, + 159 + ], + "lines": [ + { + "bbox": [ + 164, + 72, + 265, + 159 + ], + "spans": [ + { + "bbox": [ + 164, + 72, + 265, + 159 + ], + "type": "image", + "image_path": "b8c8adaed0ec73dd2e672ec4c0b1ac43e629c6ba9e6c54f2b8eb38cbe109a986.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 266, + 72, + 367, + 159 + ], + "blocks": [ + { + "bbox": [ + 266, + 72, + 367, + 159 + ], + "lines": [ + { + "bbox": [ + 266, + 72, + 367, + 159 + ], + "spans": [ + { + "bbox": [ + 266, + 72, + 367, + 159 + ], + "type": "image", + "image_path": "af10b5cfa528bc3770341bcac032879b1c5d1d85c53a90e1ee0b07712069d1d2.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 369, + 72, + 468, + 159 + ], + "blocks": [ + { + "bbox": [ + 369, + 72, + 468, + 159 + ], + "lines": [ + { + "bbox": [ + 369, + 72, + 468, + 159 + ], + "spans": [ + { + "bbox": [ + 369, + 72, + 468, + 159 + ], + "type": "image", + "image_path": "99318e72a30d233d6c834a6163433ef00e2bba8e90eb24331a33605412a47fe1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 471, + 137, + 544, + 199 + ], + "blocks": [ + { + "bbox": [ + 471, + 137, + 544, + 199 + ], + "lines": [ + { + "bbox": [ + 471, + 137, + 544, + 199 + ], + "spans": [ + { + "bbox": [ + 471, + 137, + 544, + 199 + ], + "type": "image", + "image_path": "54aab8c3643b0caa7df213406170f626e220eb1c0a215a14f894bfae7540e236.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 49, + 169, + 164, + 266 + ], + "blocks": [ + { + "bbox": [ + 49, + 169, + 164, + 266 + ], + "lines": [ + { + "bbox": [ + 49, + 169, + 164, + 266 + ], + "spans": [ + { + "bbox": [ + 49, + 169, + 164, + 266 + ], + "type": "image", + "image_path": "2599ce0d4c29cd251908b99c68ec6580636aa8c50523495629a39104cbfd6503.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "lines": [ + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "text", + "content": "Figure 6. Soups on IMAGENET variants: for each dataset we plot the accuracy of the 5 best performing soups of the four base models " + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty}" + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 2}" + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow 1}" + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "inline_equation", + "content": "\\theta_{\\infty \\rightarrow \\mathrm{nominal}}" + }, + { + "bbox": [ + 46, + 276, + 547, + 310 + ], + "type": "text", + "content": ", and of the individual classifiers. Additionally, we show the performance of an independently trained nominal model. All models are evaluated on the 1000 points used for the grid search of the best soups." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 164, + 169, + 265, + 266 + ], + "blocks": [ + { + "bbox": [ + 164, + 169, + 265, + 266 + ], + "lines": [ + { + "bbox": [ + 164, + 169, + 265, + 266 + ], + "spans": [ + { + "bbox": [ + 164, + 169, + 265, + 266 + ], + "type": "image", + "image_path": "f337f453e09d5fd34f91b3619b98e962d8bb164bbccc999a9f42905cbc38b034.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 266, + 169, + 366, + 266 + ], + "blocks": [ + { + "bbox": [ + 266, + 169, + 366, + 266 + ], + "lines": [ + { + "bbox": [ + 266, + 169, + 366, + 266 + ], + "spans": [ + { + "bbox": [ + 266, + 169, + 366, + 266 + ], + "type": "image", + "image_path": "e71b3aa117e5714bc05664beb6a8e8d7a0e75c7fa7ef1e529a8b32e5de2e304d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 367, + 169, + 469, + 266 + ], + "blocks": [ + { + "bbox": [ + 367, + 169, + 469, + 266 + ], + "lines": [ + { + "bbox": [ + 367, + 169, + 469, + 266 + ], + "spans": [ + { + "bbox": [ + 367, + 169, + 469, + 266 + ], + "type": "image", + "image_path": "758f1867e7b3b8cc2ab6d0657511b325fc2c8615115553c10b27fd86ef4ef8bd.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "content": "ness of the initial classifiers but amplify it. This flexibility could suit adaptation to various distribution shifts: that is, the various corruption types might more closely resemble the geometry of different " + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 46, + 331, + 288, + 427 + ], + "type": "text", + "content": "-balls or their union. Moreover, including a nominally fine-tuned model in the soup allows it to maintain, if necessary, high accuracy on the original dataset, which is often degraded by adversarial training [34] or test-time adaptation on shifted data [36]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 440, + 205, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 440, + 205, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 440, + 205, + 453 + ], + "type": "text", + "content": "5.1. Soups for IMAGENET variants" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": "Setup. In the following, we use models soups consisting of robust ViT fine-tuned from " + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 460, + 287, + 592 + ], + "type": "text", + "content": " to the other threat models, and one more ViT nominally fine-tuned for 100 epochs to obtain slightly higher accuracy on clean data. For shifts, we consider several variants ofImagenet, providing a broad and diverse benchmark for our soups:Imagenet-REAL [1],Imagenet-V2 [40],Imagenet-C [21],Imagenet-A [23],Imagenet-R [20],Imagenet-SKETCH [49], and CONFLICT STIMULI [12]. We consider the setting of few-shot supervised adaptation, with a small set of labelled images from each shift, which we use to select the best soups." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "Soup selection via grid search. Since evaluating the accuracy of many soups on the entirety of the datasets would be extremely expensive, we search for the best combination of the four models on a random subset of 1000 points from each dataset, with the exception of CONFLICT STIMULI for which all 1280 images are used (for IMAGENET-C we use all corruption types and severities, then aggregate the results). Restricting our search to a subset also serves our aim of finding a model soup which generalizes to the new distribution by only seeing a few examples. We eval" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 331, + 547, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 331, + 547, + 451 + ], + "spans": [ + { + "bbox": [ + 304, + 331, + 547, + 451 + ], + "type": "text", + "content": "uate all the possible affine combinations with weights in the range " + }, + { + "bbox": [ + 304, + 331, + 547, + 451 + ], + "type": "inline_equation", + "content": "[-0.4, 1.4]" + }, + { + "bbox": [ + 304, + 331, + 547, + 451 + ], + "type": "text", + "content": " with granularity 0.2, which amounts to 460 models in total. In Fig. 6 we compare, for each dataset, the accuracy of the 5 best soups to that of each individual classifier used for creating the soups and of a nominal model trained independently: for all datasets apart from IMAGENET the top soups outperform the individual models. Moreover, we notice that the best individual model varies across datasets, indicating that it might be helpful to merge networks with different types of robustness." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "type": "text", + "content": "Comparison to existing methods. Having selected the best soup for each variant (dataset-specific soups) on its chosen few-shot adaptation set, we evaluate the soup on the test set of the variant (results in Table 1). We also evaluate the model soup that attains the best average case accuracy over the adaptation sets for all variants (single soup), in order to gauge the best performance of a single, general model soup. We compare the soups to a nominal model, the " + }, + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "type": "text", + "content": "-robust classifier used in the soups, their ensemble, the Masked Autoencoders of [18], AdvProp [54], PyramidAT [24], and the ensemble obtained by averaging the output (after softmax) of the four models included in the soups. Selecting the best soup on 1000 images of each datasets (results in the last row of Table 1) leads in 4 out of the 8 datasets to the best accuracy, and only slightly suboptimal values in the other cases: in particular, parameters interpolations is very effective on stronger shifts likeImagenet-R and CONFLICT STIMULI, where it attains almost " + }, + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "type": "inline_equation", + "content": "8\\%" + }, + { + "bbox": [ + 304, + 462, + 546, + 714 + ], + "type": "text", + "content": " better performance than the closest baseline. Unsurprisingly, it is more challenging to improve on datasets likeImagenetV2 which are very close to the originalImagenet. Over" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12318" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 69, + 545, + 214 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 545, + 214 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 545, + 214 + ], + "type": "table", + "html": "
SETUP# FPIMAGENETIN-REALIN-V2IN-AIN-RIN-SKETCHCONFLICT STIMULIIN-CMEAN
Baselines
Nominal training×182.64%87.33%71.42%28.03%47.94%34.43%30.47%64.45%55.84%
Adversarial training×176.88%83.91%64.81%12.35%55.76%40.11%59.45%55.44%56.09%
Fine-tuned MAE-B16×183.10%88.02%72.80%37.92%49.30%35.69%27.81%63.23%57.23%
AdvProp×183.39%88.06%73.17%34.81%53.04%39.25%38.98%70.39%60.14%
Pyramid-AT×183.14%87.82%72.53%32.72%51.78%38.60%37.27%67.01%58.86%
Indep. networks ensemble×282.86%87.78%71.73%25.99%54.20%37.33%46.41%65.61%58.99%
Individual networks ensemble×481.31%86.97%70.21%23.13%54.82%39.51%56.02%68.17%60.02%
Fixed grid search on 1000 images
Single soup×182.49%87.85%71.99%34.31%53.84%39.84%38.52%66.82%59.46%
Dataset-specific soups×182.29%87.89%71.95%38.27%56.39%40.73%67.03%69.34%(64.24%)
", + "image_path": "f49d3187e344df8d79a331634ba179db39c3138e7e68a66891613ce66b65c74b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 222, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 222, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 546, + 257 + ], + "type": "text", + "content": "Table 1. Comparison on IMAGENET variants: we report the classification accuracy of various models on the IMAGENET variants, together with the number of forward passes they require. The soups are selected via a fixed grid search on the interpolation weights with 1000 points for each dataset. The last row shows the results of the best found soup for each dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 269, + 544, + 425 + ], + "blocks": [ + { + "bbox": [ + 50, + 269, + 544, + 425 + ], + "lines": [ + { + "bbox": [ + 50, + 269, + 544, + 425 + ], + "spans": [ + { + "bbox": [ + 50, + 269, + 544, + 425 + ], + "type": "image", + "image_path": "f273e7dfbc4421380f719e44dbca9edc25111b824660e14ee15c92c88517cf49.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 434, + 546, + 468 + ], + "lines": [ + { + "bbox": [ + 46, + 434, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 546, + 468 + ], + "type": "text", + "content": "Figure 7. Soup compositions on IMAGENET variants: for each dataset we plot the composition of the 5 best soups, i.e. the linear weights for the individual models, as measured by grid search over 1000 points on weights in the range " + }, + { + "bbox": [ + 46, + 434, + 546, + 468 + ], + "type": "inline_equation", + "content": "[-0.4, 1.4]" + }, + { + "bbox": [ + 46, + 434, + 546, + 468 + ], + "type": "text", + "content": " with granularity 0.2. Additionally we show the composition of the model achieving the best average accuracy over all 8 variants." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 487, + 288, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 288, + 560 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 288, + 560 + ], + "type": "text", + "content": "all, The soup selected for best average accuracy (across all datasets) outperforms all baselines, except for the ensemble of four models (with " + }, + { + "bbox": [ + 46, + 487, + 288, + 560 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 487, + 288, + 560 + ], + "type": "text", + "content": " the inference cost), and AdvProp, which requires co-training of clean and adversarial points. These results show that soups with robust classifiers are a promising avenue for quickly adapting to distribution shifts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Composition of the soups. To analyze which types of classifiers are most relevant for performance on every distribution shift, we plot in Fig. 7 the breakdown of the weights of the five best soups (more intense colors indicate that the corresponding weight or a larger one is used more often in the top-5 soups). First, one can see that the nominally fine-tuned model (in black) is dominant, with weights of 0.8 or 1, onImagenet,Imagenet-REAL,ImagenetV2,Imagenet-A andImagenet-C: this could be expected since these datasets are closer toImagenet itself, i.e. the distribution shift is smaller, which is what nominal training optimizes for (in fact, the nominal models achieve" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "text", + "content": "higher accuracy than adversarially trained ones on these datasets in Fig. 6). However, in all cases there is a contribution of some of the " + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "text", + "content": "-robust networks. On IMAGENET-R, IMAGENET-SKETCH and CONFLICT STIMULI, the model robust w.r.t. " + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "text", + "content": " plays instead the most relevant role, again in line with the results in Table 1. Interestingly, in the case of CONFLICT STIMULI, the nominal classifier has a weight -0.4 (the smallest in the grid search) for all top performing soups: we hypothesize that this has the effect of reduce the texture bias typical of nominal model and emphasize the attention to shapes already important in adversarially trained classifiers. Finally, we show the composition of the soup which has the best average accuracy over all datasets (last column of Fig. 7), where the nominal and " + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 487, + 545, + 668 + ], + "type": "text", + "content": "-robust models have similar positive weight." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 677, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 715 + ], + "type": "text", + "content": "How many images does it take to find a good soup? To identify the practical limit of supervision for soup selection, we study the effect of varying the number of labelled images" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "12319" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 286, + 156 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 286, + 156 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 286, + 156 + ], + "type": "image", + "image_path": "99ddd8edba0ad97da74370ed64ff377d425de45a5800dfc0365704a3b152fe37.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 161, + 286, + 253 + ], + "blocks": [ + { + "bbox": [ + 51, + 161, + 286, + 253 + ], + "lines": [ + { + "bbox": [ + 51, + 161, + 286, + 253 + ], + "spans": [ + { + "bbox": [ + 51, + 161, + 286, + 253 + ], + "type": "image", + "image_path": "d7833a4dda6cf990526fa47856d6da16b9b69085e9acefd77390abf84462f26e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 263, + 288, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 263, + 288, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 288, + 308 + ], + "type": "text", + "content": "Figure 8. Soup selection data efficiency: we vary the number of images for selecting the best performing soups on different datasets. For each case, we plot the average accuracy on a held-out test set, and its standard deviation over 50 trials." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 340, + 285, + 485 + ], + "blocks": [ + { + "bbox": [ + 50, + 340, + 285, + 485 + ], + "lines": [ + { + "bbox": [ + 50, + 340, + 285, + 485 + ], + "spans": [ + { + "bbox": [ + 50, + 340, + 285, + 485 + ], + "type": "image", + "image_path": "9558b5db971395a6df2598273460634c0a37bead8ad45b28cfa280fc9b031cd4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 495, + 287, + 519 + ], + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 519 + ], + "type": "text", + "content": "Figure 9. Soup compositions on IMAGENET-C: we plot the model-wise weights of the best soups across types and severities." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": "used to select the best soup on a new dataset. For this analysis we randomly choose 500 images from the adaptation set used for the grid search to create a held-out test set. From the remaining images, we uniformly sample " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " elements, select the soup which performs best on such " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " points, and then evaluate it on this test set. We repeat this procedure for " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "k \\in \\{10, 30, 100, 300, 500\\}" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": " for 50 times each with different random seeds. In Fig. 8 we plot the average accuracy on the held-out test set, with standard deviation, when varying " + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": ": increasing the number of points above 100 achieves high test accuracy with limited variance. This suggests that soup selection, and thus model adaptation, can be carried out with as few as 100 examples of the new distribution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 463, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 463, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 463, + 84 + ], + "type": "text", + "content": "5.2. A closer look at IMAGENET-C" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "type": "text", + "content": "While our experiments have considered IMAGENET-C as a single dataset, it consists of 15 corruptions types, each with 5 severity levels. As the various corruptions have different characteristics, one might expect the best soup to vary across them. In Fig. 9 we plot the composition of the top-5 soups for each severity level for two corruption types (as done in Fig. 7). The weights of the individual classifiers significantly change across distribution shifts: for both corruption types, increasing the severity (making perturbations stronger) leads to a reduction in the nominal weight in favor of a robust weight. However, in the case of \"pixelate\" the soups concentrate on the " + }, + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "type": "text", + "content": "-robust network, while for \"jpeg compression\" this happens for " + }, + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 89, + 547, + 319 + ], + "type": "text", + "content": ". Similar visualization for the remaining IMAGENET-C subsets are found in Fig. 11 of the Appendix. This highlights the importance of interpolating models with different types of robustness, and implies that considering each corruption type (including severity levels) as independent datasets could further improve the performance of the soups on IMAGENET-C." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 328, + 462, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 328, + 462, + 341 + ], + "spans": [ + { + "bbox": [ + 305, + 328, + 462, + 341 + ], + "type": "text", + "content": "6. Discussion and Limitations" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 547, + 443 + ], + "type": "text", + "content": "Merging models with different types of robustness enables strong control of classifier performance by tuning only a few soup weights. Soups can find models which perform well even on distributions unseen during training (e.g. the IMAGENET variants). Moreover, our framework avoids constraining on multiple threats: this makes it possible to fine-tune models with additional attacks as they present themselves, and enrich the soups with them." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 444, + 547, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 547, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 547, + 598 + ], + "type": "text", + "content": "At the moment, our soups contain only nominal or " + }, + { + "bbox": [ + 304, + 444, + 547, + 598 + ], + "type": "inline_equation", + "content": "\\ell_{p}" + }, + { + "bbox": [ + 304, + 444, + 547, + 598 + ], + "type": "text", + "content": "-robust models, but expanding the diversity of models might aid adaptation to new datasets. We selected our soups with few-shot supervision, but other settings could potentially use soups, such as unsupervised domain adaptation [37,42], on labeled clean and unlabeled shifted data, and test-time adaptation [43,44,48], on unlabeled examples alone. Moreover, in our evaluation we have constrained the soups to belong to a fixed grid, which might miss better models: future work could develop automatic schemes to optimize the soup weights, possibly with even fewer examples, or without labeled examples (as done for test-time adaptation of non-robust models)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 609, + 380, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 380, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 380, + 623 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "We show that combining the parameters of robust classifiers, without additional training, achieves a smooth trade-off of robustness in different " + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "-threat models. This allows us to discover models which perform well on distribution shifts with only a limited number of examples of each shift. 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Brain Decoding and Image Reconstruction. For the first time, our proposed MinD-Vis is capable of decoding fMRI-based brain activities and reconstructing images with not only plausible details but also accurate semantics and image features (texture, shape, etc.), pushing this domain a considerable step forward. Left: Task overview. Middle: Comparison with benchmarks. Right: More reconstruction examples." + ], + "image_footnote": [], + "bbox": [ + 308, + 363, + 388, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/13edbbdd55a3194e4dca3431a6d81bf855e6f11c4641cfd5d804c28d662ffffe.jpg", + "image_caption": [ + "Visual Stimulus" + ], + "image_footnote": [], + "bbox": [ + 398, + 282, + 633, + 344 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/77a9e506377d97df2e508aad241711e86444345b46588d518466a49dcf8a010d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 282, + 870, + 344 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c3d2d3255945529377c4238298383fd9829c6a9a1f47dc2d469f74fac84dccb.jpg", + "image_caption": [ + "Our Reconstructed Images", + "Animal or Human" + ], + "image_footnote": [], + "bbox": [ + 400, + 364, + 633, + 426 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c199cf34765ae5329b963d85e6dc58fcf7eddff37f10a73697811f6e39b4ba95.jpg", + "image_caption": [ + "Objects" + ], + "image_footnote": [], + "bbox": [ + 635, + 364, + 870, + 425 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 236, + 494, + 310, + 508 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Decoding visual stimuli from brain recordings aims to deepen our understanding of the human visual system and build a solid foundation for bridging human and computer vision through the Brain-Computer Interface. However, reconstructing high-quality images with correct semantics from brain recordings is a challenging problem due to the complex underlying representations of brain signals and the scarcity of data annotations. In this work, we present MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding. Firstly, we learn an effective self-supervised representation of fMRI data using mask modeling in a large latent space inspired by the sparse coding of information in the primary visual cortex. Then by augmenting a latent diffusion model with double-conditioning, we show that MinD-Vis can reconstruct highly plausible images with semantically matching details from brain recordings using very few paired annotations. We benchmarked our model qualitatively and quantitatively; the experimental results indicate that our method outperformed state-of-the-art in both semantic mapping (100-way semantic classification) and generation quality (FID) by $66\\%$ and $41\\%$ respectively. An exhaustive ablation study was also conducted to analyze our framework.", + "bbox": [ + 75, + 516, + 472, + 849 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 494, + 624, + 508 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"What you think is what you see\". Human perception and prior knowledge are deeply intertwined in one's mind [51]. Our perception of the world is determined not only by objective stimuli properties but also by our experiences, forming complex brain activities underlying our perception. Understanding these brain activities and recovering the encoded information is a key goal in cognitive neuroscience. Within this broad objective, decoding visual information is one of the challenging problems that are the focus of a large body of literature [22, 26, 34, 67].", + "bbox": [ + 496, + 520, + 893, + 656 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As a non-invasive and effective method to measure brain activities indirectly, functional Magnetic Resonance Imaging (fMRI) is usually used to recover visual information, such as the image classes [21, 39]. With the help of recent deep learning models, it is intriguing if the original visual stimuli can be directly recovered from corresponding fMRI [2, 46], especially with the guidance of biological principles [43, 52]. However, due to the lack of fMRI-image pairs and useful biological guidance when decoding complex neural activity from fMRI directly, reconstructed images are usually blurry and semantically meaningless. Thus it is crucial to learn effective and biological-valid representations for fMRI so that a clear and generalizable connection between brain activities and visual stimuli can be established with a few paired annotations.", + "bbox": [ + 496, + 657, + 893, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Moreover, individual variability in brain representations further complicates this problem. Individuals have unique", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contributions.", + "bbox": [ + 94, + 875, + 204, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author (helen.zhou@nus.edu.sg)", + "bbox": [ + 96, + 887, + 341, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22710", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "brain activation patterns responding to the same visual stimulus (See Fig. 2). From the perspective of fMRI representation learning, a powerful brain decoding algorithm should robustly recognize features shared across the population over a background of individual variation [5, 21]. On the other hand, we should also expect decoding variances due to the variation in individual perceptions. Therefore, we aim to learn representations from a large-scale dataset with rich demographic compositions and relax the direct generation from fMRI to conditional synthesis allowing for sampling variance under the same semantic category.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Self-supervised learning with pretext tasks in large datasets is a powerful paradigm to distill the model with context knowledge. A domain-specific downstream task (e.g. classification) is usually adopted to finetune the pre-trained model further [36, 58], especially when the downstream dataset is small. Various pretext tasks are designed to benefit downstream tasks [23, 66]. Among these methods, Masked Signal Modeling (MSM) has achieved promising results in both vision [18, 62] and language understanding [8, 37] recently. At the same time, the probabilistic diffusion denoising model has shown its superior performance in content generation and training stability [9]. A strong generation ability is also desired in our task to decode faithful visual stimuli from various categories.", + "bbox": [ + 75, + 242, + 472, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Driven by the above analysis, we propose MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding, a framework that exploits the power of large-scale representation learning and mimics the sparse coding of information in the brain [14], including the visual cortex [56]. Different from [18], we use a much larger representation-to-data-space ratio to boost the information capacity of learned representations. Our contributions are as follows:", + "bbox": [ + 75, + 438, + 472, + 559 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose Sparse-Coded Masked Brain Modeling (SC-MBM), designed under biological guidance as an effective brain feature learner for vision decoding.", + "- Augmenting the latent diffusion model with double conditioning (DC-LDM), we enforce stronger decoding consistency while allowing variance under the same semantics.", + "- Integrating the representation ability of SC-MBM with the generation ability of DC-LDM, MinD-Vis generates more plausible images with better preserved semantic information compared with previous methods.", + "- Quantitative and qualitative tests are performed on multiple datasets, including a new dataset that has not previously been used to evaluate this task." + ], + "bbox": [ + 96, + 566, + 470, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 800, + 212, + 815 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conventional Decoding Methods Conventional methods rely on training with fMRI and corresponding hierarchical image features extracted by a pre-trained VGG [21, 46]. During testing, the predicted image features will either be used for classification or fed into a generative model like GAN [45] to", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ba0c32fd3e7d34616f753e5584f79f3715818cfecb81fbb564285be9c5fd4888.jpg", + "image_caption": [ + "Figure 2. Individual Differences in Regions Responding to Visual Stimuli. Masks of the regions of interest activating during the same visual task differ in location and size across subjects. The primary visual cortex at the left (red) and the right (orange) hemisphere are shown." + ], + "image_footnote": [], + "bbox": [ + 540, + 88, + 854, + 160 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "reconstruct the original stimulus. Instead of directly learning the limited training pairs, [2] enabled unsupervised learning on unpaired fMRI and images with a reconfigurable autoencoder design. [16] further extended this method to images from diverse semantic categories. However, just as with conventional approaches, fMRI is used directly for training and decoding. In [31, 33], a regression model was used to extract latent fMRI representation, which was then used to finetune a pre-trained conditional bigGAN for image decoding. Mind Reader [27] encoded fMRI signals into a pre-aligned vision-language latent space and used StyleGAN2 for image generation. These methods generate more plausible and semantically meaningful images. We note that there is parallel work to ours by Takagi and Nishimoto [13], who proposed a method for image reconstruction from fMRI using Stable Diffusion. Their approach involves decoding brain activities to text descriptions and converting them to natural images using stable diffusion.", + "bbox": [ + 496, + 227, + 893, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Masked Signal Modeling The power of MSM in learning representations from a large-scale dataset was first exploited in [8], which was later adapted to computer vision [18,60,62]. Successful applications to downstream tasks show that useful context knowledge is learned with MSM as a pretext task. In essence, MSM is a generalized denoising autoencoder that aims to recover the original data from the remaining after masking [4]. The portion of data to mask is different across data modalities, with an extremely high mask ratio (75%) usually used for visual signals [18]. In contrast, due to the disparity in information density, a low mask ratio (25%) is used in natural languages [8].", + "bbox": [ + 496, + 496, + 893, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion Probabilistic Models Diffusion models [49] are emerging generative models that generate high-quality content. In its basic form [20], the diffusion model is a probabilistic model defined by a bi-directional Markov Chain of states. Two processes are transiting through the chain: (i) The forward diffusion process gradually adds noise to the data until it is fully destroyed to an isotropic Gaussian noise; (ii) The reverse process recovers the corrupted data by modeling a posterior distribution $p(x)$ at each state and eventually obtains a sample in the original data distribution [20, 49, 50]. Formally, assume a Markov Chain with a fixed length $T$ , then the reverse conditional probability can be expressed as $q(x_{t-1} | x_t)$ , where $t = 1, \\dots, T$ and $x_t$ is obtained by corrupting the image $x_{t-1}$ with Gaussian noise. After parameterization, this conditional probability can be learned by optimizing a variational lower", + "bbox": [ + 496, + 672, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22711", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/775870bb4bb7291cdedd866bf34962fd077876a74657b1dc7b7dbc9e511711bf.jpg", + "image_caption": [ + "Figure 3. MinD-Vis. Stage A (left): Pre-train on fMRI with SC-MBM. We patchify, randomly mask the fMRI, and then tokenize them to large embeddings. We train an autoencoder $(\\mathcal{E}_{\\mathcal{MBM}}$ and $\\mathcal{D}_{\\mathcal{MBM}})$ to recover the masked patches. Stage B (right): Integration with the LDM through double conditioning. We project the fMRI latent $(\\mathcal{L}_{fMRI})$ through two paths to the LDM conditioning space with a latent dimension projector $(\\mathcal{P}_{fMRI\\rightarrow Cond})$ . One path connects directly to cross-attention heads in the LDM. Another path adds the fMRI latent to time embeddings. The LDM operates on a low-dimensional, compressed version of the original image (i.e. image latent), however, the original image is used in this figure for illustrations." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 488, + 324 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a2a9eb9f1a1c7c9c6bb98b43b2e728099335a443d45434c7bacaabd1b5c62afe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 88, + 890, + 324 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "bound which can be simplified to the following objective [20]:", + "bbox": [ + 76, + 410, + 464, + 425 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t} ^ {\\text {s i m p l e}} = \\mathbb {E} _ {x, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 430, + 468, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\epsilon_{\\theta}(x_t,t)$ is a set of denoising functions that are usually implemented as UNets [9, 41, 42]. We refer readers to [20] for detailed descriptions of the diffusion models.", + "bbox": [ + 75, + 458, + 468, + 503 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent Diffusion Model (LDM) Apart from the conventional diffusion models that generate samples in the original data space, another category of diffusion models that generate samples in the latent feature space has been proposed [41, 48]. Operating in the latent feature space reduces the computational cost and introduces less spatial downsampling, giving better image synthesis quality. The LDM proposed in [41] consists of two components: (i) Vector Quantization (VQ) regularized [12] autoencoder that compresses images into lower-dimensional latent features and then reconstructs the images from features in the same space; (ii) UNet-based denoising model with attention modules. Incorporating attention mechanisms into the UNet allows the flexibility to condition image generation through key/value/query vectors during the Markov Chain transitions.", + "bbox": [ + 75, + 508, + 470, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 731, + 205, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Motivation and Overview", + "text_level": 1, + "bbox": [ + 76, + 756, + 308, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this subsection, we provide a detailed analysis of the fMRI data and elaborate on the motivations of our designs.", + "bbox": [ + 76, + 780, + 468, + 809 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(i) fMRI measures the brain blood-oxygen-level-dependent (BOLD) changes as 3D voxels that serve as a proxy for the underlying changes in brain activity. Neighboring voxels often have similar amplitudes, indicating spatial redundancy in fMRI [53].", + "(ii) fMRI data is averaged across the time during which the stimulus is presented. A region of interest (ROI) of the averaged" + ], + "bbox": [ + 75, + 810, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "data is usually extracted as a 1D vector of voxels (in the visual processing hierarchy). The ROI size (voxel number) is generally smaller than the image size (pixel number). For example, [21] has about 4500 voxels (visual cortex), which is much smaller than a $256 \\times 256$ RGB image. This creates a large difference in dimensionality when transforming fMRI into images.", + "bbox": [ + 496, + 409, + 890, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(iii) fMRI data from different datasets may have significant domain shifts due to experimental conditions and scanner setups. Even with the same scan conditions, ROI size and location mismatch persist due to individual differences (See Fig. 2).", + "bbox": [ + 496, + 501, + 890, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Driven by this analysis, we propose MinD-Vis, designed with two sequential stages as outlined in Fig. 3. Briefly, in Stage A, fMRI representations are learned by an autoencoder trained in a large fMRI dataset with masked signal modeling as a pretext task. The learned representations will be used as a condition to guide the image-generation process in the next stage. In Stage B, the pre-trained fMRI encoder is integrated with the LDM through cross-attention and time-step conditioning for conditional synthesis. In this stage, the encoder is jointly finetuned with cross-attention heads in the LDM using paired annotations.", + "bbox": [ + 496, + 561, + 892, + 713 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Stage A: Sparse-Coded MBM (SC-MBM)", + "text_level": 1, + "bbox": [ + 500, + 724, + 854, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Activity in the human brain involves non-linear interactions among 86 billion neuronal cells in the brain and are thus highly complex [32, 40]. The fMRI measuring the BOLD signals is an indirect and aggregate measure of neuronal activities, which can be analyzed hierarchically with functional networks [1, 6, 59]. These functional networks comprised of voxels of fMRI data have implicit correlations with each other in response to external stimuli [54, 68]. Therefore, learning these implicit correlations by recovering masked voxels will equip the pre-trained model with a deep contextual understanding of the fMRI data.", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22712", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c7ce8c98c682736a664fa9ea916e34253123240cee188dbd0ae5fdb5d8561f66.jpg", + "image_caption": [ + "Ground-truth", + "Masked Ground-truth" + ], + "image_footnote": [], + "bbox": [ + 80, + 104, + 271, + 143 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6b7744f5458ac87390e2d400d440976dd45f3eb36b15e88cd387b049c7a5024b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 104, + 464, + 143 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/93b48532955745a3ead8990e3ba028a28710f3032b58966228f42596f5879329.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 155, + 269, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ecfa5496aead91de100d9f1d1a5283f4d80e88a4e9c0bed6caec4b46e2372398.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 279, + 155, + 467, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/24f25392317796443302ebb8de97e180fb9cef41228d5fe7e86ca2b7a4e952d8.jpg", + "image_caption": [ + "Reconstruction", + "Figure 4. Masked Brain Modeling. Mask ratio 0.75; 4500 voxels" + ], + "image_footnote": [], + "bbox": [ + 81, + 205, + 267, + 244 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/3bf384de1f49d2f8bcaa474e36cd2116994511c56bcaf549e2861d7318b1d308.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 281, + 205, + 462, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following [18], we divide the vectorized voxels into patches which will be subsequently transformed into embeddings using a 1D convolutional layer with a stride equal to the patch size. The hemodynamic response and spatial smoothing functions in fMRI BOLD signal jointly cause spatial blurring, which creates spatial redundancy in fMRI data, like in natural images [11,47]. Due to the spatial redundancy, fMRI data can still be recovered even if a large portion is masked (See Fig. 4). Thus, in the first stage of MinD-Vis, we can mask a large portion of the fMRI patches to save computations without losing the learning power of masked modeling.", + "bbox": [ + 75, + 273, + 468, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Masked Image Modeling (MIM) uses the embedding-to-patch-size ratio around one [18], leading to a representation size similar to the original data size. However, we use a large embedding-to-patch-size ratio, which significantly increases the information capacity with a large fMRI representation space. This design also relates to the sparse coding of information in the brain, which has been proposed as a general strategy for the representation of sensory information [25].", + "bbox": [ + 75, + 439, + 468, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also adopt an asymmetric architecture as in [18]: the encoder is optimized to learn effective fMRI representations, while the decoder tries to predict the masked patches. Therefore, we make the decoder small in size, and it is discarded in Stage B as long as the pre-training converges.", + "bbox": [ + 75, + 561, + 468, + 637 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Visual Encoding and Brain-Inspired Sparse Coding Here, we explain the biological basis of using SC-MBM to learn representations of visual stimuli in the brain from the perspective of visual encoding mechanisms. Theoretical and empirical studies suggest that visual stimuli are sparsely encoded in the primary visual cortex [32, 38, 56], with most natural images activating only a portion of the neurons in the visual cortex. This strategy increases information transmission efficiency and creates minimal redundancy in the brain [38]. As a result, visual information of natural scenes can be reconstructed from a small portion of data collected from the primary visual cortex via different imaging modalities, including fMRI [15, 64]. This observation is interesting for the computer vision community because the sparse coding could be an efficient way for vision encoding in computer vision as well [25, 63].", + "bbox": [ + 75, + 643, + 470, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sparse coding is an encoding strategy that in essence uses over-complete bases to represent data, where more locality is", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "generally enforced to generate smoother representations [57, 65]. In SC-MBM, fMRI data are divided into patches to introduce locality constraints. Then each patch is encoded into a high-dimensional vector space with a size much larger than the original data space, thus creating an over-complete space for fMRI representation (See Appendix). Emulating the brain vision encoding, SC-MBM can be a biologically-valid and effective brain feature learner for fMRI decoding.", + "bbox": [ + 496, + 90, + 893, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Stage B: Double-Conditioned LDM (DC-LDM)", + "text_level": 1, + "bbox": [ + 500, + 219, + 890, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After the large-scale context learning in Stage A, the fMRI encoder transforms fMRI data into sparsely coded representations with locality constraints. To further decode visual contents from this abstract representation and allow for sampling variance, we formulate the decoding task as a conditional synthesis problem and approach it with a pre-trained LDM.", + "bbox": [ + 496, + 243, + 893, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The LDM operates on the image latent space denoted by $\\mathcal{E}(x)$ where $x$ is an image in pixel space and $\\mathcal{E}(\\cdot)$ is a VQ encoder. In our setting, we omit $\\mathcal{E}(x)$ and use $x$ directly to represent the latent variable of LDM for simplicity. Specifically, given the fMRI data $z$ , we aim to learn the reverse diffusion process formulated by $q(x_{t-1}|x_t,z)$ . As proposed in [41], conditional information is applied through cross-attention heads in the attention-based UNet, where CrossAttention $(Q,K,V) = \\text{softmax}\\left(\\frac{QK^T}{\\sqrt{d}}\\right)$ , with", + "bbox": [ + 496, + 333, + 893, + 463 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ = W _ {Q} ^ {(i)} \\varphi_ {i} (x _ {t}), K = W _ {K} ^ {(i)} \\tau_ {\\theta} (z), V = W _ {V} ^ {(i)} \\tau_ {\\theta} (z).\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 470, + 852, + 492 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\tau_{\\theta}$ is the fMRI encoder with a suitable dimension projector, $\\varphi_{i}(x_{t})$ denotes intermediate values of the UNet and $W_{Q}^{(i)}$ , $W_{K}^{(i)}$ , $W_{V}^{(i)}$ are projector matrices with learnable parameters.", + "bbox": [ + 498, + 498, + 893, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diversity and consistency are two opposite objectives when sampling a conditional generative model. Sampling diversity across various modalities such as label-to-image and text-to-image is very important in many image-generation tasks. However, the fMRI-to-image transition relies more on generation consistency—decoded images from similar brain activities are expected to be semantically similar. Thus, a stronger conditioning mechanism is desired to ensure such generation consistency, especially for probabilistic diffusion models.", + "bbox": [ + 496, + 551, + 893, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this way, we integrate the cross-attention conditioning with another conditioning method called the time steps conditioning [9] to provide stronger guidance for our task. In time steps conditioning, we add $\\sigma_{\\theta}(\\tau_{\\theta}(z))$ to time step embeddings, where $\\sigma_{\\theta}(\\cdot)$ is another suitable dimension projector. Time step embeddings are used in intermediate layers of the UNet, thus we have $\\varphi_{i}(x_{t}) = \\varphi_{i}(x_{t},\\sigma_{\\theta}(\\tau_{\\theta}(z)))$ . We further reformulate the optimization objective Eq. (1) to a double conditioning alternation:", + "bbox": [ + 496, + 686, + 893, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t} ^ {\\text {c o n d}} = \\mathbb {E} _ {x, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(x _ {t}, t, \\tau (z), \\sigma (\\tau (z))\\right) \\| _ {2} ^ {2} \\right]. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 813, + 890, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We omit the parameterization symbol $\\theta$ in $\\tau(\\cdot)$ and $\\sigma(\\cdot)$ for simplicity. Additionally, we have $\\tau(z) \\in \\mathbb{R}^{M \\times d_{\\tau}}$ and $\\sigma(\\tau(z)) \\in \\mathbb{R}^{1 \\times d_t}$ , where $d_{\\tau}$ and $d_t$ are the latent dimensions and time embedding dimension respectively, and $M$ is a tunable parameter.", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22713", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/56434963e0b80092bb333a0c7e60f57c0ba8ae2306da8360ad02f1689066222d.jpg", + "image_caption": [ + "Figure 5. Decoding Performance Comparisons on GOD Test Set. The ground truth, images reconstructed by MinD-Vis and images reconstructed from three other methods are shown for comparison. MinD-Vis decoded the most accurate and plausible images with semantically similar details." + ], + "image_footnote": [], + "bbox": [ + 76, + 89, + 480, + 354 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a8b780d275a7284af5e90a14f8729189ef35c925c68d4fe6990c648c8e843942.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 90, + 890, + 353 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5c442ca0470f5c65242c55b6a25d4cd8ee3a702e892de9aeec15e33e17bbfe9b.jpg", + "image_caption": [ + "Figure 6. Quantitative Performance Comparisons on GOD" + ], + "image_footnote": [ + "Test Set. Performance is evaluated in terms of semantic correctness (1000-trial $n$ -way top- $k$ classification accuracy; the higher the better) and generation quality (FID; the lower the better)." + ], + "bbox": [ + 78, + 402, + 460, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finetuning After the fMRI encoder is pre-trained with SC-MBM, it is integrated with a pre-trained LDM through double conditioning. Commonly, the encoder's output is averaged, or a $cls$ token is appended to produce a pooled 1D feature vector for downstream tasks [8, 18]. This strategy is effective for tasks like prediction and classification, where learned knowledge is expected to be distilled, producing distinguishable features. However, pooling into a 1D vector is inappropriate for retaining fMRI representations' sparsity and information capacity. Instead, we used convolution layers to pool the encoder's output into a latent dimension of $\\mathbb{R}^{M\\times d_{\\tau}}$ as described in Eq. (2).", + "bbox": [ + 75, + 625, + 468, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The fMRI encoder, cross-attention heads, and projection heads are jointly optimized, while other parts are fixed. Finetuning the cross-attention heads is critical for bridging the pre-trained conditioning space and fMRI latent space. The finetuning is performed end-to-end with fMRI-image pairs, during which a clearer connection between the fMRI and image features will be learned through the large-capacity fMRI representations.", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 398, + 625, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Implementation", + "text_level": 1, + "bbox": [ + 500, + 425, + 761, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets Three public datasets were used in this study: Human Connectome Project (HCP) 1200 Subject Release [55]; Generic Object Decoding Dataset (GOD) [21]; and Brain, Object, Landscape Dataset (BOLD5000) [5]. Our upstream pre-training dataset comprised fMRI data from HCP and GOD. Combining these two, we obtained 136,000 fMRI segments from 340 hours of fMRI scan, which is, by far, the largest fMRI pre-training dataset in the fMRI-image decoding task. The HCP dataset is commonly used in neuroscience research, containing only fMRI data. While the GOD is an fMRI-image paired dataset designed for fMRI-based decoding. The pairs in GOD were used for finetuning in our main analysis. The GOD consists of 1250 different images from 200 distinct classes, in which 1200 images were used as the training set, and the remaining 50 images were used as the testing set. The training set and testing set have no overlapping classes. The BOLD5000 dataset was used as the validation dataset in our study. It consists of 5254 fMRI-image pairs from 4916 distinct images, 113 images of which are used for testing. This is the first time that the BOLD5000 is used for fMRI decoding tasks.", + "bbox": [ + 496, + 449, + 893, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation The fMRI pre-training model is similar to ViT-Large [10] with a 1D patch embedder. We used a patch size of 16, embedding dimension of 1024, encoder depth of 24, and mask ratio of 0.75 as our Full model setting with an ImageNet class-conditioned pre-trained LDM. Different parameter choices are explored in our ablation study. Unless stated otherwise, the Full model is pre-trained for 500 epochs and finetuned for another 500. Results from the best model are reported. Images are generated at a resolution of $256 \\times 256$ with 250 PLMS", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22714", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "steps [29]. See Appendix for dataset and implementation details.", + "bbox": [ + 76, + 90, + 470, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Metric", + "text_level": 1, + "bbox": [ + 76, + 119, + 253, + 133 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "N-way Classification Accuracy Following [16], we used the $n$ -way top-1 and top-5 accuracy classification task to evaluate the semantic correctness of our results, where for multiple trials, top-1 and top-5 classification accuracies were calculated in $n - 1$ randomly selected classes plus the correct one. Note that we did not consider the pixel-level metrics as we aimed to recover the semantically correct images in this work.", + "bbox": [ + 76, + 143, + 468, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In [16], the authors generated a typical feature for each class selected and compared the distance between the reconstructed images and the typical features. However, this metric in [16] is hard to reproduce, and the semantic classification result largely depends on how the features are computed. Therefore, we propose a more straightforward and reproducible method, where a pre-trained ImageNet1K classifier [10, 35] is used to determine the semantic correctness of generated images rather than handcrafted features. We describe this evaluation method in Algorithm D.1. Specifically, both ground-truth and generated images are input to the classifier first. Then we check for the generated image if the top- $k$ classification in $n$ selected classes matches the ground-truth classification. This metric does not require the ground-truth image to be from the ImageNet 1k classes. As long as semantic classification results of the ground-truth and the generated image match, it will be considered to be correct.", + "bbox": [ + 75, + 252, + 470, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fréchet inception distance (FID) The FID [19] is a commonly used metric to assess image generation quality. In our experiments, we measured the FID between ground-truth images and generated images in the testing set. Note that FID is only used as a reference in our experiments due to the limited number of images available in GOD, which may lead to an underestimated distribution.", + "bbox": [ + 76, + 506, + 468, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 631, + 158, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our main results are based on GOD which has no overlapping classes in the training and testing set. The training and testing were performed on the same subject, as individual differences remain a barrier when decoding at the group level [2, 16, 21, 31, 33]. To compare with the literature, we report results from Subject 3 here and leave other subjects in the Appendix.", + "bbox": [ + 76, + 657, + 468, + 748 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compared our results with Ozcelik et al. [33], Gaziv et al. [16] and Belyi et al. [16]. Gaziv et al. and Belyi et al. used the conventional method, which decoded images with higher pixel similarity but less plausibility and semantic details. On the other hand, Ozcelik et al. generated more plausible and semantically meaningful images using a pre-trained GAN. Based on the best-reconstructed samples of these methods (resized to $256 \\times 256$ ), we performed a 1000-trial, $n$ -way top- $k$ accuracy identification task as described in Algorithm D.1. The experiment is repeated for $n = 50,100$ and $k = 1,5$ in the GOD testing set.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0549b0fc0283f429a70b29bd7aefbb752764b40a89d48b885eb31fc6aa7be9bc.jpg", + "image_caption": [ + "GT" + ], + "image_footnote": [], + "bbox": [ + 501, + 109, + 599, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/52b4e7218bddb43bf72d68bdc767bdf0ada665e624f9b493186475c8e7c4691b.jpg", + "image_caption": [ + "Reconstructed Samples" + ], + "image_footnote": [], + "bbox": [ + 602, + 109, + 700, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fb22da9824a21a1eea671c6d8b28e34befea7023748425aa3b9f19dbb792e193.jpg", + "image_caption": [ + "Figure 7. Generation Consistency of MinD-Vis. Images generated by our method were consistent across different samplings trials, sharing similar low-level features and semantics." + ], + "image_footnote": [], + "bbox": [ + 700, + 109, + 795, + 258 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0933fbfa4bea5918f2131560db99ac88b205e11f20f8b3d48b45a82fdd1c3005.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 109, + 890, + 258 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From Fig. 6, our identification accuracy outperformed the Ozcelik et al. in the 50-way top-1 accuracy task by $39\\%$ and in the 100-way top-1 accuracy task by $66\\%$ , achieving a success rate of 0.274 and 0.212 respectively. The generated images from Gaziv et al. and Belyi et al. were close to the ground-truth at the pixel level but contained few semantically meaningful details, as could be observed in Fig. 5. For example, our method generated plausible details such as water and waves in the first and second images, drawings on the bowling ball, wheels of the carriage, etc., which were not present in the previous decoded images. The image quality is also reflected by the FID, where we achieved 1.67 with our best samples, while Ozcelik et al. and others achieved 2.36 or more with the best samples generated by their method. Interestingly, color mismatches are observed in some cases with the color difference well preserved. It can be explained with [3] which suggests the color category information is processed in the frontal lobes as a cognitive process, while the visual cortex only recognizes the difference in colors.", + "bbox": [ + 498, + 319, + 893, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Generation Consistency", + "text_level": 1, + "bbox": [ + 500, + 601, + 718, + 617 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The consistency of our method was tested by decoding the same fMRI data multiple times with different random states. Five samplings with different random states were performed in the testing set for each fMRI. In the 50-way and the 100-way top-1 accuracy identification tasks, we achieved an average success rate across the five samplings of $0.2385 \\pm 0.030$ and $0.1736 \\pm 0.029$ respectively, which are statistically higher than the best sampling results from Ozcelik et al. by $21\\%$ and $35\\%$ . Regarding image quality, we achieved an average FID of $2.22 \\pm 0.3$ across the five samplings. The standard deviations across 5 samplings indicate that the generated images will always be in the same semantic category. It can also be seen in Fig. 7 where isomorphic samplings share similar details such as shape, color, texture, and semantics, matching with the ground-truth across trials.", + "bbox": [ + 498, + 625, + 893, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. SC-MBM Design", + "text_level": 1, + "bbox": [ + 500, + 845, + 668, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This section will discuss the ablation study on the SC-MBM pre-training stage with various important parameters. Results", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22715", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "are summarized in Tab. 1. For all experiments in this section, the 50-way, top-1 accuracy semantic identification task was performed with the best models obtained from the finetuning of 500 epochs. Average results over five samplings were reported.", + "bbox": [ + 75, + 90, + 470, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Testing Without SC-MBM To show that useful representations were learned with SC-MBM, we trained two models directly using the fMRI-image pairs without the SC-MBM pretraining. The first model consisted of an untrained fMRI encoder with the same architecture as the Full model. The second model consisted of an untrained fMRI encoder with a depth of only 2. The second model was designed to have fewer parameters, making it less likely to overfit the data. All the other settings were the same. The results correspond to Model 1 and 2 in Tab. 1, where the Full model significantly outperformed the other two models without the SC-MBM pre-training, showing that the pre-training is crucial. In fact, without SC-MBM these two models even failed to generate sensible images (See Appendix).", + "bbox": [ + 75, + 159, + 473, + 357 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/83bb288859420636f04560962bf659f6baf35f0fc7414c366bfc684b7d580a28.jpg", + "table_caption": [], + "table_footnote": [ + "† $p < {0.0001}$ (purple); $p < {0.01}$ (pink); $p < {0.05}$ (yellow); $p > {0.05}$ (green)" + ], + "table_body": "
ModelEmbedding \nDimMask \nRatioParamsAcc (%)
Full10240.75303M23.9±3.00
1w/o SC-MBM + same Encoder303M2.6 ±1.39
2w/o SC-MBM + smaller Encoder25M3.4 ±0.86
3320.750.3M5.4 ±1.50
4640.751.2M6.9 ±1.10
51280.754.7M14.8 ±1.78
62560.7518.9M15.9 ±1.70
75120.7575.6M17.9 ±2.58
87680.75170M17.7 ±1.42
912800.75472M15.5 ±3.83
1010240.35303M19.6 ±3.40
1110240.45303M20.0 ±1.89
1210240.55303M18.1 ±2.87
1310240.65303M21.7 ±3.61
1410240.85303M16.1 ±1.00
", + "bbox": [ + 78, + 369, + 468, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "**Patch Embedding Dimension** Boosting the fMRI representation size using a large patch embedding matches the sparse coding mechanism of underlying visual information processing in the brain. Moreover, using a large patch embedding increases the information capacity of the representation. But larger embedding means more training parameters leading to a more data-hungry model. To balance this tradeoff, we tested SC-MBM models with different patch embedding dimensions ranging from 32 to 1280 (Model 3-9 in Tab. 1). We found that the accuracy generally increased as patch dimension increased, and accuracy peaked at $23.9\\%$ with 1024 patch embedding dimensions (full model), after which accuracy decreased as patch dimensions increased further.", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Mask Ratios We used a high mask ratio in SC-MBM due to high spatial redundancy in fMRI data. In Tab. 1 Model 10-14, we show that a high mask ratio does not impair the decoding performance initially, with the highest average accuracy achieved with a relatively high mask ratio of 0.75. Importantly, using a high mask ratio significantly reduces memory consumption since the encoder only operates over unmasked patches. This is an important consideration for fMRI as SC-MBM is more memory-intensive than MIM due to the higher embedding-to-patch-size ratio.", + "bbox": [ + 496, + 90, + 893, + 243 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. DC-LDM Finetuning Design", + "text_level": 1, + "bbox": [ + 498, + 251, + 756, + 268 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This section will discuss the ablation study on the DC-LDM finetuning designs from three perspectives: conditioning methods, optimization designs, and pre-trained LDMs. Here, all ablations used the same pre-trained fMRI encoder as the Full model. Only important parameters in the finetuning stage were varied. The 1000-trial, 50-way, top-1 semantic identification test was performed. The results are summarized in Tab. 2, where five different samplings were averaged for each condition.", + "bbox": [ + 496, + 273, + 893, + 396 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c7c46471ad8dd058cffb8cfc6eee0fb356ca66a9170a11db32526dbfc26e49e8.jpg", + "table_caption": [ + "Table 1. SC-MBM Ablation Results. Params: trainable parameters in the fMRI encoder; Cell colors reflect statistical significance differences (two-sample t-test) in accuracy compared with the Full model." + ], + "table_footnote": [ + "† $p < {0.0001}$ (purple); $p < {0.01}$ (pink); $p < {0.05}$ (yellow); $p > {0.05}$ (green)" + ], + "table_body": "
ModelConditionFinetunePre-trained LDMAcc (%)
FullC + TE + ALabel2Image23.9±3.00
1C onlyE + ALabel2Image15.6 ±0.69
2C+TE onlyLabel2Image13.76 ±2.60
3C+TE + AText2Image13.42±3.00
4C+TE + ALayout2Image15.99±3.00
", + "bbox": [ + 501, + 407, + 890, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. DC-LDM Ablation Results. 1: cross-attention condition only; 2: optimizing fMRI encoders only; 3: LDM pre-trained on text conditions (LAION); 4: LDM pre-trained on layout conditions (OpenImages). Abbr.: C (Cross-attention condition); T (Time condition); E (Encoder); A (Cross-attention heads). Cell colors reflect statistical significance (two-sample t-test) in accuracy compared with the Full model.", + "bbox": [ + 496, + 535, + 893, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Conditioning Methods Here, we showed that the double conditioning method increased the conditioning strength in Tab. 2, where using only cross-attention conditioning achieved an identification accuracy of $15.6\\%$ (Model 1), which was significantly lower than the full method.", + "bbox": [ + 496, + 622, + 893, + 698 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Optimizing LDM We proposed to finetune the fMRI encoder and the cross-attention heads jointly because the LDM was pre-trained in a different conditioning space. For example, for the ImageNet class-conditioning pre-trained LDM, the cross-attention heads were pre-trained to receive the class label information. To justify this choice, we tested on a model with the fMRI encoder finetuned and the cross-attention heads untouched. As shown in Model 2 in Tab. 2, the average identification accuracy dropped to $13.7\\%$ when only the fMRI encoder was finetuned, indicating stronger semantic guidance with the double conditioning. The visual quality and correspondence to the ground-truth of the generated images also decreased significantly (See Appendix).", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22716", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e1da56194a6b8983a99a5675c1b3b5748f4330efc6b9440f85b6078531b7c394.jpg", + "image_caption": [ + "GT", + "Ours", + "Figure 8. Replication Dataset (BOLD5000). It achieved similar quantitative results as the GOD dataset. 50-way top-1 identification accuracy: $34\\%$ ; FID: 1.2 (Subject 1)." + ], + "image_footnote": [], + "bbox": [ + 80, + 104, + 205, + 300 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e4e08cea155bf92b08d11e94867d73743ce506ed5faaf4371527e9ab50c14194.jpg", + "image_caption": [ + "GT", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 209, + 104, + 336, + 300 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/100e51949f22a028b8f9a5772cfa46deb93e91b9369786a29491e224e8361502.jpg", + "image_caption": [ + "GT", + "Ours" + ], + "image_footnote": [], + "bbox": [ + 339, + 104, + 467, + 300 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pre-trained LDM The pre-trained LDM determines the model's generative ability and the conditioning latent space to which the fMRI encoder would adapt. We considered three pretrained LDM provided by [41], which were trained on datasets with different conditioning tasks, i.e. ImageNet (label conditioning), LAION (text conditioning) [44] and OpenImages (layout conditioning) [24]. As shown in Model 3-4 Tab. 2, the ImageNet pre-trained LDM (used in the full model) showed the best performance in the same decoding task. Notably, images generated by models pre-trained on LAION and OpenImages were less visually favorable and plausible (See Appendix). This result is surprising because both LAION and OpenImages contain diverse images from various categories. We attribute the main reason for their poor performance to the complexity of their conditioning latent space. With limited training pairs, the class-conditioning latent space is easier to adapt to, compared with the latent space of the text-conditioning model and the layout-conditioning model.", + "bbox": [ + 76, + 364, + 472, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Replication Dataset", + "text_level": 1, + "bbox": [ + 76, + 633, + 264, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We validated our method on BOLD5000 using the same pretrained fMRI encoder. Similarly, the pre-trained encoder was firstly finetuned for 20 epochs in the testing set of BOLD500 with wrap-around paddings to compensate for the unequal ROI size from the pre-training set, after which the model is further tuned with the fMRI-image training pairs in BOLD5000. All other settings were the same as the Full model. For the four subjects in BOLD5000, we achieved a $19\\%$ to $34\\%$ best accuracy in the 1000-trial, 50-way, top-1 accuracy semantic identification task (See Appendix). The generated images matched the ground-truth stimulus in both semantics and low-level features (Fig. 8). Our model accurately reconstructs images containing objects and animals, architecture, and landscapes.", + "bbox": [ + 76, + 657, + 468, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Interestingly, we reconstructed similar images for some natural scenes with extra details that do not exist in the ground-truth stimulus. These extra details, for example, the", + "bbox": [ + 76, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e5f90824c05e247957c0b79e63ec2a441fdc0082d8989959ba371cd0ff69ba77.jpg", + "image_caption": [ + "GT", + "Figure 9. Extra Features Decoded. Imagery-related details can be decoded with our method. e.g. the river and blue sky were decoded with natural scenery stimulus (top row); similar interior decorating of indoor environments was decoded when a house was presented (bottom row)." + ], + "image_footnote": [], + "bbox": [ + 501, + 104, + 580, + 223 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3a640cdaaaaa23c1cb37910027dac39534e4f25b12b4de8a2bd79520e3cfcdee.jpg", + "image_caption": [ + "Subject 1", + "Subject 2", + "Subject 3", + "Subject 4" + ], + "image_footnote": [], + "bbox": [ + 583, + 104, + 890, + 223 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "river and the blue sky in Fig. 9, may reflect imagined scenery in the subject's mind when viewing the visual stimuli, which is captured in their brain activities. As reported in [21, 46], features of imaginary images can also be decoded from the visual cortex.", + "bbox": [ + 500, + 299, + 890, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To the best of our knowledge, this is the first work that performs fMRI decoding on BOLD5000. Additionally, adapting the same pre-trained model to this dataset shows that the SC-MBM pre-training indeed learns useful representations of brain recordings even when distinct domain shifts exist. These learned representations are shared and generalizable to datasets with different scanning protocols and preprocessing pipelines.", + "bbox": [ + 500, + 359, + 890, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 479, + 733, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations MinD-Vis, in its current form, lacks strong pixel-level guidance and interpretation analysis, which limits its pixel-level performance (see G.5) and the biological understanding of the features learned by MBM.", + "bbox": [ + 500, + 503, + 893, + 564 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future Work Similar to all previous work, MinD-Vis focuses on individual decoding using the visual cortex only. But as a complex cognitive process, human vision may be affected by regions beyond the visual cortex. Therefore, future studies should extend to cross-subject generalization and also the incorporation of other brain regions. Additionally, the two-stage decoupling design of MinD-Vis allows us to explore the potential of emerging large-scale models and representation learning techniques in cognitive neuroscience, which is also subject to future studies.", + "bbox": [ + 500, + 569, + 890, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion We proposed a two-stage framework MinD-Vis to decode visual stimuli using only a few paired fMRI-image annotations from brain recordings. In Stage A, we employ an fMRI pre-training scheme with masked modeling to learn generalizable context knowledge from a large-scale unlabeled fMRI dataset. In Stage B, we use a latent diffusion model with double conditioning to generate plausible seen images from learned fMRI representations. We validated the decoding results of MinD-Vis on multiple datasets and showed that our model generates more plausible and semantically similar images compared to previous methods, pushing the state-of-the-art a considerable step forward.", + "bbox": [ + 500, + 710, + 890, + 892 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22717", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 169, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Teddy J Akiki and Chadi G Abdallah. Determining the hierarchical architecture of the human brain using subject-level clustering of functional networks. Scientific reports, 9(1):1-15, 2019.", + "[2] Roman Belyi, Guy Gaziv, Assaf Hoogi, Francesca Strappini, Tal Golan, and Michal Irani. From voxels to pixels and back: Self-supervision in natural-image reconstruction from fmri. 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Brain, 133(5):1352-1367, 2010." + ], + "bbox": [ + 78, + 90, + 468, + 402 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22720", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/fe08ae3e-3e6a-4967-96af-a2a0ffcad985_model.json b/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/fe08ae3e-3e6a-4967-96af-a2a0ffcad985_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b572c0042eb7c7e18a0adf4333f84af2102ce692 --- /dev/null +++ b/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/fe08ae3e-3e6a-4967-96af-a2a0ffcad985_model.json @@ -0,0 +1,2884 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.198, + 0.131, + 0.773, + 0.177 + ], + "angle": 0, + "content": "Seeing Beyond the Brain: Conditional Diffusion Model with Sparse Masked Modeling for Vision Decoding" + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.203, + 0.23, + 0.222 + ], + "angle": 0, + "content": "Zijiao Chen\\*" + }, + { + "type": "text", + "bbox": [ + 0.268, + 0.204, + 0.371, + 0.223 + ], + "angle": 0, + "content": "Jiaxin Qing\\(^{2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.406, + 0.204, + 0.517, + 0.223 + ], + "angle": 0, + "content": "Tiangxiang" + }, + { + "type": "text", + "bbox": [ + 0.559, + 0.204, + 0.666, + 0.221 + ], + "angle": 0, + "content": "Wan Lin Yue" + }, + { + "type": "text", + "bbox": [ + 0.709, + 0.204, + 0.853, + 0.221 + ], + "angle": 0, + "content": "Juan Helen Zhou†" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.228, + 0.787, + 0.245 + ], + "angle": 0, + "content": "\\(^{1}\\)National University of Singapore, \\(^{2}\\)The Chinese University of Hong Kong, \\(^{3}\\)Stanford University" + }, + { + "type": "text", + "bbox": [ + 0.358, + 0.246, + 0.606, + 0.26 + ], + "angle": 0, + "content": "https://mind-vis.github.io" + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.274, + 0.292, + 0.284 + ], + "angle": 0, + "content": "Visual Stimulus Brain Encoding" + }, + { + "type": "image", + "bbox": [ + 0.123, + 0.292, + 0.226, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.231, + 0.292, + 0.285, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.125, + 0.357, + 0.191, + 0.41 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.375, + 0.228, + 0.384 + ], + "angle": 0, + "content": "Decode" + }, + { + "type": "image_caption", + "bbox": [ + 0.106, + 0.411, + 0.213, + 0.422 + ], + "angle": 0, + "content": "Reconstructed Image" + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.341, + 0.274, + 0.361 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.228, + 0.361, + 0.301, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.411, + 0.301, + 0.421 + ], + "angle": 0, + "content": "fMRI Pattern" + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.425, + 0.262, + 0.438 + ], + "angle": 0, + "content": "\"MinD-Vis\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.313, + 0.272, + 0.385, + 0.283 + ], + "angle": 0, + "content": "Ozcelik (2022)" + }, + { + "type": "image", + "bbox": [ + 0.309, + 0.283, + 0.388, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.318, + 0.353, + 0.38, + 0.363 + ], + "angle": 0, + "content": "Gaziv (2022)" + }, + { + "type": "image", + "bbox": [ + 0.31, + 0.364, + 0.39, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.317, + 0.429, + 0.381, + 0.438 + ], + "angle": 0, + "content": "Benchmarks" + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.271, + 0.686, + 0.282 + ], + "angle": 0, + "content": "Visual Stimulus" + }, + { + "type": "image", + "bbox": [ + 0.4, + 0.283, + 0.635, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.283, + 0.871, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.56, + 0.352, + 0.715, + 0.364 + ], + "angle": 0, + "content": "Our Reconstructed Images" + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.365, + 0.635, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.465, + 0.429, + 0.558, + 0.438 + ], + "angle": 0, + "content": "Animal or Human" + }, + { + "type": "image", + "bbox": [ + 0.637, + 0.365, + 0.871, + 0.426 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.732, + 0.428, + 0.773, + 0.438 + ], + "angle": 0, + "content": "Objects" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.44, + 0.894, + 0.484 + ], + "angle": 0, + "content": "Figure 1. Brain Decoding and Image Reconstruction. For the first time, our proposed MinD-Vis is capable of decoding fMRI-based brain activities and reconstructing images with not only plausible details but also accurate semantics and image features (texture, shape, etc.), pushing this domain a considerable step forward. Left: Task overview. Middle: Comparison with benchmarks. Right: More reconstruction examples." + }, + { + "type": "title", + "bbox": [ + 0.237, + 0.495, + 0.311, + 0.51 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.473, + 0.851 + ], + "angle": 0, + "content": "Decoding visual stimuli from brain recordings aims to deepen our understanding of the human visual system and build a solid foundation for bridging human and computer vision through the Brain-Computer Interface. However, reconstructing high-quality images with correct semantics from brain recordings is a challenging problem due to the complex underlying representations of brain signals and the scarcity of data annotations. In this work, we present MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding. Firstly, we learn an effective self-supervised representation of fMRI data using mask modeling in a large latent space inspired by the sparse coding of information in the primary visual cortex. Then by augmenting a latent diffusion model with double-conditioning, we show that MinD-Vis can reconstruct highly plausible images with semantically matching details from brain recordings using very few paired annotations. We benchmarked our model qualitatively and quantitatively; the experimental results indicate that our method outperformed state-of-the-art in both semantic mapping (100-way semantic classification) and generation quality (FID) by \\(66\\%\\) and \\(41\\%\\) respectively. An exhaustive ablation study was also conducted to analyze our framework." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.495, + 0.625, + 0.51 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.895, + 0.657 + ], + "angle": 0, + "content": "\"What you think is what you see\". Human perception and prior knowledge are deeply intertwined in one's mind [51]. Our perception of the world is determined not only by objective stimuli properties but also by our experiences, forming complex brain activities underlying our perception. Understanding these brain activities and recovering the encoded information is a key goal in cognitive neuroscience. Within this broad objective, decoding visual information is one of the challenging problems that are the focus of a large body of literature [22, 26, 34, 67]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.869 + ], + "angle": 0, + "content": "As a non-invasive and effective method to measure brain activities indirectly, functional Magnetic Resonance Imaging (fMRI) is usually used to recover visual information, such as the image classes [21, 39]. With the help of recent deep learning models, it is intriguing if the original visual stimuli can be directly recovered from corresponding fMRI [2, 46], especially with the guidance of biological principles [43, 52]. However, due to the lack of fMRI-image pairs and useful biological guidance when decoding complex neural activity from fMRI directly, reconstructed images are usually blurry and semantically meaningless. Thus it is crucial to learn effective and biological-valid representations for fMRI so that a clear and generalizable connection between brain activities and visual stimuli can be established with a few paired annotations." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Moreover, individual variability in brain representations further complicates this problem. Individuals have unique" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.205, + 0.888 + ], + "angle": 0, + "content": "*Equal contributions." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.342, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author (helen.zhou@nus.edu.sg)" + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.871, + 0.342, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "22710" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "brain activation patterns responding to the same visual stimulus (See Fig. 2). From the perspective of fMRI representation learning, a powerful brain decoding algorithm should robustly recognize features shared across the population over a background of individual variation [5, 21]. On the other hand, we should also expect decoding variances due to the variation in individual perceptions. Therefore, we aim to learn representations from a large-scale dataset with rich demographic compositions and relax the direct generation from fMRI to conditional synthesis allowing for sampling variance under the same semantic category." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.438 + ], + "angle": 0, + "content": "Self-supervised learning with pretext tasks in large datasets is a powerful paradigm to distill the model with context knowledge. A domain-specific downstream task (e.g. classification) is usually adopted to finetune the pre-trained model further [36, 58], especially when the downstream dataset is small. Various pretext tasks are designed to benefit downstream tasks [23, 66]. Among these methods, Masked Signal Modeling (MSM) has achieved promising results in both vision [18, 62] and language understanding [8, 37] recently. At the same time, the probabilistic diffusion denoising model has shown its superior performance in content generation and training stability [9]. A strong generation ability is also desired in our task to decode faithful visual stimuli from various categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Driven by the above analysis, we propose MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding, a framework that exploits the power of large-scale representation learning and mimics the sparse coding of information in the brain [14], including the visual cortex [56]. Different from [18], we use a much larger representation-to-data-space ratio to boost the information capacity of learned representations. Our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.568, + 0.47, + 0.613 + ], + "angle": 0, + "content": "- We propose Sparse-Coded Masked Brain Modeling (SC-MBM), designed under biological guidance as an effective brain feature learner for vision decoding." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.618, + 0.472, + 0.663 + ], + "angle": 0, + "content": "- Augmenting the latent diffusion model with double conditioning (DC-LDM), we enforce stronger decoding consistency while allowing variance under the same semantics." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.669, + 0.47, + 0.729 + ], + "angle": 0, + "content": "- Integrating the representation ability of SC-MBM with the generation ability of DC-LDM, MinD-Vis generates more plausible images with better preserved semantic information compared with previous methods." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.734, + 0.47, + 0.78 + ], + "angle": 0, + "content": "- Quantitative and qualitative tests are performed on multiple datasets, including a new dataset that has not previously been used to evaluate this task." + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.568, + 0.472, + 0.78 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.214, + 0.816 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Conventional Decoding Methods Conventional methods rely on training with fMRI and corresponding hierarchical image features extracted by a pre-trained VGG [21, 46]. During testing, the predicted image features will either be used for classification or fed into a generative model like GAN [45] to" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.089, + 0.855, + 0.161 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.163, + 0.892, + 0.218 + ], + "angle": 0, + "content": "Figure 2. Individual Differences in Regions Responding to Visual Stimuli. Masks of the regions of interest activating during the same visual task differ in location and size across subjects. The primary visual cortex at the left (red) and the right (orange) hemisphere are shown." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.895, + 0.485 + ], + "angle": 0, + "content": "reconstruct the original stimulus. Instead of directly learning the limited training pairs, [2] enabled unsupervised learning on unpaired fMRI and images with a reconfigurable autoencoder design. [16] further extended this method to images from diverse semantic categories. However, just as with conventional approaches, fMRI is used directly for training and decoding. In [31, 33], a regression model was used to extract latent fMRI representation, which was then used to finetune a pre-trained conditional bigGAN for image decoding. Mind Reader [27] encoded fMRI signals into a pre-aligned vision-language latent space and used StyleGAN2 for image generation. These methods generate more plausible and semantically meaningful images. We note that there is parallel work to ours by Takagi and Nishimoto [13], who proposed a method for image reconstruction from fMRI using Stable Diffusion. Their approach involves decoding brain activities to text descriptions and converting them to natural images using stable diffusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.895, + 0.663 + ], + "angle": 0, + "content": "Masked Signal Modeling The power of MSM in learning representations from a large-scale dataset was first exploited in [8], which was later adapted to computer vision [18,60,62]. Successful applications to downstream tasks show that useful context knowledge is learned with MSM as a pretext task. In essence, MSM is a generalized denoising autoencoder that aims to recover the original data from the remaining after masking [4]. The portion of data to mask is different across data modalities, with an extremely high mask ratio (75%) usually used for visual signals [18]. In contrast, due to the disparity in information density, a low mask ratio (25%) is used in natural languages [8]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Diffusion Probabilistic Models Diffusion models [49] are emerging generative models that generate high-quality content. In its basic form [20], the diffusion model is a probabilistic model defined by a bi-directional Markov Chain of states. Two processes are transiting through the chain: (i) The forward diffusion process gradually adds noise to the data until it is fully destroyed to an isotropic Gaussian noise; (ii) The reverse process recovers the corrupted data by modeling a posterior distribution \\( p(x) \\) at each state and eventually obtains a sample in the original data distribution [20, 49, 50]. Formally, assume a Markov Chain with a fixed length \\( T \\), then the reverse conditional probability can be expressed as \\( q(x_{t-1} | x_t) \\), where \\( t = 1, \\dots, T \\) and \\( x_t \\) is obtained by corrupting the image \\( x_{t-1} \\) with Gaussian noise. After parameterization, this conditional probability can be learned by optimizing a variational lower" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22711" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.49, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.498, + 0.089, + 0.891, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.332, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Figure 3. MinD-Vis. Stage A (left): Pre-train on fMRI with SC-MBM. We patchify, randomly mask the fMRI, and then tokenize them to large embeddings. We train an autoencoder \\((\\mathcal{E}_{\\mathcal{MBM}}\\) and \\(\\mathcal{D}_{\\mathcal{MBM}})\\) to recover the masked patches. Stage B (right): Integration with the LDM through double conditioning. We project the fMRI latent \\((\\mathcal{L}_{fMRI})\\) through two paths to the LDM conditioning space with a latent dimension projector \\((\\mathcal{P}_{fMRI\\rightarrow Cond})\\). One path connects directly to cross-attention heads in the LDM. Another path adds the fMRI latent to time embeddings. The LDM operates on a low-dimensional, compressed version of the original image (i.e. image latent), however, the original image is used in this figure for illustrations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.411, + 0.465, + 0.426 + ], + "angle": 0, + "content": "bound which can be simplified to the following objective [20]:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.431, + 0.47, + 0.452 + ], + "angle": 0, + "content": "\\[\nL _ {t} ^ {\\text {s i m p l e}} = \\mathbb {E} _ {x, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.504 + ], + "angle": 0, + "content": "where \\(\\epsilon_{\\theta}(x_t,t)\\) is a set of denoising functions that are usually implemented as UNets [9, 41, 42]. We refer readers to [20] for detailed descriptions of the diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.471, + 0.721 + ], + "angle": 0, + "content": "Latent Diffusion Model (LDM) Apart from the conventional diffusion models that generate samples in the original data space, another category of diffusion models that generate samples in the latent feature space has been proposed [41, 48]. Operating in the latent feature space reduces the computational cost and introduces less spatial downsampling, giving better image synthesis quality. The LDM proposed in [41] consists of two components: (i) Vector Quantization (VQ) regularized [12] autoencoder that compresses images into lower-dimensional latent features and then reconstructs the images from features in the same space; (ii) UNet-based denoising model with attention modules. Incorporating attention mechanisms into the UNet allows the flexibility to condition image generation through key/value/query vectors during the Markov Chain transitions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.732, + 0.206, + 0.75 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.31, + 0.772 + ], + "angle": 0, + "content": "3.1. Motivation and Overview" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.469, + 0.81 + ], + "angle": 0, + "content": "In this subsection, we provide a detailed analysis of the fMRI data and elaborate on the motivations of our designs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.871 + ], + "angle": 0, + "content": "(i) fMRI measures the brain blood-oxygen-level-dependent (BOLD) changes as 3D voxels that serve as a proxy for the underlying changes in brain activity. Neighboring voxels often have similar amplitudes, indicating spatial redundancy in fMRI [53]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "(ii) fMRI data is averaged across the time during which the stimulus is presented. A region of interest (ROI) of the averaged" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.892, + 0.501 + ], + "angle": 0, + "content": "data is usually extracted as a 1D vector of voxels (in the visual processing hierarchy). The ROI size (voxel number) is generally smaller than the image size (pixel number). For example, [21] has about 4500 voxels (visual cortex), which is much smaller than a \\(256 \\times 256\\) RGB image. This creates a large difference in dimensionality when transforming fMRI into images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.892, + 0.562 + ], + "angle": 0, + "content": "(iii) fMRI data from different datasets may have significant domain shifts due to experimental conditions and scanner setups. Even with the same scan conditions, ROI size and location mismatch persist due to individual differences (See Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.893, + 0.714 + ], + "angle": 0, + "content": "Driven by this analysis, we propose MinD-Vis, designed with two sequential stages as outlined in Fig. 3. Briefly, in Stage A, fMRI representations are learned by an autoencoder trained in a large fMRI dataset with masked signal modeling as a pretext task. The learned representations will be used as a condition to guide the image-generation process in the next stage. In Stage B, the pre-trained fMRI encoder is integrated with the LDM through cross-attention and time-step conditioning for conditional synthesis. In this stage, the encoder is jointly finetuned with cross-attention heads in the LDM using paired annotations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.726, + 0.855, + 0.742 + ], + "angle": 0, + "content": "3.2. Stage A: Sparse-Coded MBM (SC-MBM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Activity in the human brain involves non-linear interactions among 86 billion neuronal cells in the brain and are thus highly complex [32, 40]. The fMRI measuring the BOLD signals is an indirect and aggregate measure of neuronal activities, which can be analyzed hierarchically with functional networks [1, 6, 59]. These functional networks comprised of voxels of fMRI data have implicit correlations with each other in response to external stimuli [54, 68]. Therefore, learning these implicit correlations by recovering masked voxels will equip the pre-trained model with a deep contextual understanding of the fMRI data." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22712" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.242, + 0.094, + 0.305, + 0.103 + ], + "angle": 0, + "content": "Ground-truth" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.105, + 0.272, + 0.144 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.281, + 0.105, + 0.465, + 0.144 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.223, + 0.145, + 0.324, + 0.154 + ], + "angle": 0, + "content": "Masked Ground-truth" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.156, + 0.27, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.156, + 0.468, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.238, + 0.197, + 0.308, + 0.205 + ], + "angle": 0, + "content": "Reconstruction" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.206, + 0.269, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.282, + 0.207, + 0.464, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.086, + 0.257, + 0.461, + 0.271 + ], + "angle": 0, + "content": "Figure 4. Masked Brain Modeling. Mask ratio 0.75; 4500 voxels" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.47, + 0.44 + ], + "angle": 0, + "content": "Following [18], we divide the vectorized voxels into patches which will be subsequently transformed into embeddings using a 1D convolutional layer with a stride equal to the patch size. The hemodynamic response and spatial smoothing functions in fMRI BOLD signal jointly cause spatial blurring, which creates spatial redundancy in fMRI data, like in natural images [11,47]. Due to the spatial redundancy, fMRI data can still be recovered even if a large portion is masked (See Fig. 4). Thus, in the first stage of MinD-Vis, we can mask a large portion of the fMRI patches to save computations without losing the learning power of masked modeling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.561 + ], + "angle": 0, + "content": "Masked Image Modeling (MIM) uses the embedding-to-patch-size ratio around one [18], leading to a representation size similar to the original data size. However, we use a large embedding-to-patch-size ratio, which significantly increases the information capacity with a large fMRI representation space. This design also relates to the sparse coding of information in the brain, which has been proposed as a general strategy for the representation of sensory information [25]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.638 + ], + "angle": 0, + "content": "We also adopt an asymmetric architecture as in [18]: the encoder is optimized to learn effective fMRI representations, while the decoder tries to predict the masked patches. Therefore, we make the decoder small in size, and it is discarded in Stage B as long as the pre-training converges." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.87 + ], + "angle": 0, + "content": "Visual Encoding and Brain-Inspired Sparse Coding Here, we explain the biological basis of using SC-MBM to learn representations of visual stimuli in the brain from the perspective of visual encoding mechanisms. Theoretical and empirical studies suggest that visual stimuli are sparsely encoded in the primary visual cortex [32, 38, 56], with most natural images activating only a portion of the neurons in the visual cortex. This strategy increases information transmission efficiency and creates minimal redundancy in the brain [38]. As a result, visual information of natural scenes can be reconstructed from a small portion of data collected from the primary visual cortex via different imaging modalities, including fMRI [15, 64]. This observation is interesting for the computer vision community because the sparse coding could be an efficient way for vision encoding in computer vision as well [25, 63]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Sparse coding is an encoding strategy that in essence uses over-complete bases to represent data, where more locality is" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.213 + ], + "angle": 0, + "content": "generally enforced to generate smoother representations [57, 65]. In SC-MBM, fMRI data are divided into patches to introduce locality constraints. Then each patch is encoded into a high-dimensional vector space with a size much larger than the original data space, thus creating an over-complete space for fMRI representation (See Appendix). Emulating the brain vision encoding, SC-MBM can be a biologically-valid and effective brain feature learner for fMRI decoding." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.22, + 0.892, + 0.236 + ], + "angle": 0, + "content": "3.3. Stage B: Double-Conditioned LDM (DC-LDM)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.894, + 0.333 + ], + "angle": 0, + "content": "After the large-scale context learning in Stage A, the fMRI encoder transforms fMRI data into sparsely coded representations with locality constraints. To further decode visual contents from this abstract representation and allow for sampling variance, we formulate the decoding task as a conditional synthesis problem and approach it with a pre-trained LDM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.894, + 0.464 + ], + "angle": 0, + "content": "The LDM operates on the image latent space denoted by \\(\\mathcal{E}(x)\\) where \\(x\\) is an image in pixel space and \\(\\mathcal{E}(\\cdot)\\) is a VQ encoder. In our setting, we omit \\(\\mathcal{E}(x)\\) and use \\(x\\) directly to represent the latent variable of LDM for simplicity. Specifically, given the fMRI data \\(z\\), we aim to learn the reverse diffusion process formulated by \\(q(x_{t-1}|x_t,z)\\). As proposed in [41], conditional information is applied through cross-attention heads in the attention-based UNet, where CrossAttention \\((Q,K,V) = \\text{softmax}\\left(\\frac{QK^T}{\\sqrt{d}}\\right)\\), with" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.471, + 0.853, + 0.493 + ], + "angle": 0, + "content": "\\[\nQ = W _ {Q} ^ {(i)} \\varphi_ {i} (x _ {t}), K = W _ {K} ^ {(i)} \\tau_ {\\theta} (z), V = W _ {V} ^ {(i)} \\tau_ {\\theta} (z).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.499, + 0.894, + 0.551 + ], + "angle": 0, + "content": "Here, \\(\\tau_{\\theta}\\) is the fMRI encoder with a suitable dimension projector, \\(\\varphi_{i}(x_{t})\\) denotes intermediate values of the UNet and \\(W_{Q}^{(i)}\\), \\(W_{K}^{(i)}\\), \\(W_{V}^{(i)}\\) are projector matrices with learnable parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.552, + 0.894, + 0.687 + ], + "angle": 0, + "content": "Diversity and consistency are two opposite objectives when sampling a conditional generative model. Sampling diversity across various modalities such as label-to-image and text-to-image is very important in many image-generation tasks. However, the fMRI-to-image transition relies more on generation consistency—decoded images from similar brain activities are expected to be semantically similar. Thus, a stronger conditioning mechanism is desired to ensure such generation consistency, especially for probabilistic diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.894, + 0.807 + ], + "angle": 0, + "content": "In this way, we integrate the cross-attention conditioning with another conditioning method called the time steps conditioning [9] to provide stronger guidance for our task. In time steps conditioning, we add \\(\\sigma_{\\theta}(\\tau_{\\theta}(z))\\) to time step embeddings, where \\(\\sigma_{\\theta}(\\cdot)\\) is another suitable dimension projector. Time step embeddings are used in intermediate layers of the UNet, thus we have \\(\\varphi_{i}(x_{t}) = \\varphi_{i}(x_{t},\\sigma_{\\theta}(\\tau_{\\theta}(z)))\\). We further reformulate the optimization objective Eq. (1) to a double conditioning alternation:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.814, + 0.892, + 0.834 + ], + "angle": 0, + "content": "\\[\nL _ {t} ^ {\\text {c o n d}} = \\mathbb {E} _ {x, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(x _ {t}, t, \\tau (z), \\sigma (\\tau (z))\\right) \\| _ {2} ^ {2} \\right]. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We omit the parameterization symbol \\(\\theta\\) in \\(\\tau(\\cdot)\\) and \\(\\sigma(\\cdot)\\) for simplicity. Additionally, we have \\(\\tau(z) \\in \\mathbb{R}^{M \\times d_{\\tau}}\\) and \\(\\sigma(\\tau(z)) \\in \\mathbb{R}^{1 \\times d_t}\\), where \\(d_{\\tau}\\) and \\(d_t\\) are the latent dimensions and time embedding dimension respectively, and \\(M\\) is a tunable parameter." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22713" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.09, + 0.482, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.091, + 0.892, + 0.354 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.365, + 0.893, + 0.395 + ], + "angle": 0, + "content": "Figure 5. Decoding Performance Comparisons on GOD Test Set. The ground truth, images reconstructed by MinD-Vis and images reconstructed from three other methods are shown for comparison. MinD-Vis decoded the most accurate and plausible images with semantically similar details." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.404, + 0.462, + 0.554 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.555, + 0.47, + 0.568 + ], + "angle": 0, + "content": "Figure 6. Quantitative Performance Comparisons on GOD" + }, + { + "type": "image_footnote", + "bbox": [ + 0.077, + 0.568, + 0.472, + 0.61 + ], + "angle": 0, + "content": "Test Set. Performance is evaluated in terms of semantic correctness (1000-trial \\( n \\)-way top-\\( k \\) classification accuracy; the higher the better) and generation quality (FID; the lower the better)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.47, + 0.793 + ], + "angle": 0, + "content": "Finetuning After the fMRI encoder is pre-trained with SC-MBM, it is integrated with a pre-trained LDM through double conditioning. Commonly, the encoder's output is averaged, or a \\(cls\\) token is appended to produce a pooled 1D feature vector for downstream tasks [8, 18]. This strategy is effective for tasks like prediction and classification, where learned knowledge is expected to be distilled, producing distinguishable features. However, pooling into a 1D vector is inappropriate for retaining fMRI representations' sparsity and information capacity. Instead, we used convolution layers to pool the encoder's output into a latent dimension of \\(\\mathbb{R}^{M\\times d_{\\tau}}\\) as described in Eq. (2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The fMRI encoder, cross-attention heads, and projection heads are jointly optimized, while other parts are fixed. Finetuning the cross-attention heads is critical for bridging the pre-trained conditioning space and fMRI latent space. The finetuning is performed end-to-end with fMRI-image pairs, during which a clearer connection between the fMRI and image features will be learned through the large-capacity fMRI representations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.4, + 0.627, + 0.417 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.426, + 0.763, + 0.442 + ], + "angle": 0, + "content": "4.1. Datasets and Implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.895, + 0.753 + ], + "angle": 0, + "content": "Datasets Three public datasets were used in this study: Human Connectome Project (HCP) 1200 Subject Release [55]; Generic Object Decoding Dataset (GOD) [21]; and Brain, Object, Landscape Dataset (BOLD5000) [5]. Our upstream pre-training dataset comprised fMRI data from HCP and GOD. Combining these two, we obtained 136,000 fMRI segments from 340 hours of fMRI scan, which is, by far, the largest fMRI pre-training dataset in the fMRI-image decoding task. The HCP dataset is commonly used in neuroscience research, containing only fMRI data. While the GOD is an fMRI-image paired dataset designed for fMRI-based decoding. The pairs in GOD were used for finetuning in our main analysis. The GOD consists of 1250 different images from 200 distinct classes, in which 1200 images were used as the training set, and the remaining 50 images were used as the testing set. The training set and testing set have no overlapping classes. The BOLD5000 dataset was used as the validation dataset in our study. It consists of 5254 fMRI-image pairs from 4916 distinct images, 113 images of which are used for testing. This is the first time that the BOLD5000 is used for fMRI decoding tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Implementation The fMRI pre-training model is similar to ViT-Large [10] with a 1D patch embedder. We used a patch size of 16, embedding dimension of 1024, encoder depth of 24, and mask ratio of 0.75 as our Full model setting with an ImageNet class-conditioned pre-trained LDM. Different parameter choices are explored in our ablation study. Unless stated otherwise, the Full model is pre-trained for 500 epochs and finetuned for another 500. Results from the best model are reported. Images are generated at a resolution of \\(256 \\times 256\\) with 250 PLMS" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22714" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.472, + 0.108 + ], + "angle": 0, + "content": "steps [29]. See Appendix for dataset and implementation details." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.121, + 0.254, + 0.135 + ], + "angle": 0, + "content": "4.2. Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.145, + 0.47, + 0.251 + ], + "angle": 0, + "content": "N-way Classification Accuracy Following [16], we used the \\( n \\)-way top-1 and top-5 accuracy classification task to evaluate the semantic correctness of our results, where for multiple trials, top-1 and top-5 classification accuracies were calculated in \\( n - 1 \\) randomly selected classes plus the correct one. Note that we did not consider the pixel-level metrics as we aimed to recover the semantically correct images in this work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.471, + 0.493 + ], + "angle": 0, + "content": "In [16], the authors generated a typical feature for each class selected and compared the distance between the reconstructed images and the typical features. However, this metric in [16] is hard to reproduce, and the semantic classification result largely depends on how the features are computed. Therefore, we propose a more straightforward and reproducible method, where a pre-trained ImageNet1K classifier [10, 35] is used to determine the semantic correctness of generated images rather than handcrafted features. We describe this evaluation method in Algorithm D.1. Specifically, both ground-truth and generated images are input to the classifier first. Then we check for the generated image if the top-\\(k\\) classification in \\(n\\) selected classes matches the ground-truth classification. This metric does not require the ground-truth image to be from the ImageNet 1k classes. As long as semantic classification results of the ground-truth and the generated image match, it will be considered to be correct." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.507, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Fréchet inception distance (FID) The FID [19] is a commonly used metric to assess image generation quality. In our experiments, we measured the FID between ground-truth images and generated images in the testing set. Note that FID is only used as a reference in our experiments due to the limited number of images available in GOD, which may lead to an underestimated distribution." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.632, + 0.16, + 0.646 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.658, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Our main results are based on GOD which has no overlapping classes in the training and testing set. The training and testing were performed on the same subject, as individual differences remain a barrier when decoding at the group level [2, 16, 21, 31, 33]. To compare with the literature, we report results from Subject 3 here and leave other subjects in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We compared our results with Ozcelik et al. [33], Gaziv et al. [16] and Belyi et al. [16]. Gaziv et al. and Belyi et al. used the conventional method, which decoded images with higher pixel similarity but less plausibility and semantic details. On the other hand, Ozcelik et al. generated more plausible and semantically meaningful images using a pre-trained GAN. Based on the best-reconstructed samples of these methods (resized to \\(256 \\times 256\\)), we performed a 1000-trial, \\(n\\)-way top-\\(k\\) accuracy identification task as described in Algorithm D.1. The experiment is repeated for \\(n = 50,100\\) and \\(k = 1,5\\) in the GOD testing set." + }, + { + "type": "image_caption", + "bbox": [ + 0.54, + 0.095, + 0.564, + 0.107 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.095, + 0.828, + 0.109 + ], + "angle": 0, + "content": "Reconstructed Samples" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.111, + 0.601, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.603, + 0.111, + 0.701, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.111, + 0.796, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.797, + 0.111, + 0.892, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.27, + 0.892, + 0.311 + ], + "angle": 0, + "content": "Figure 7. Generation Consistency of MinD-Vis. Images generated by our method were consistent across different samplings trials, sharing similar low-level features and semantics." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.32, + 0.895, + 0.593 + ], + "angle": 0, + "content": "From Fig. 6, our identification accuracy outperformed the Ozcelik et al. in the 50-way top-1 accuracy task by \\(39\\%\\) and in the 100-way top-1 accuracy task by \\(66\\%\\), achieving a success rate of 0.274 and 0.212 respectively. The generated images from Gaziv et al. and Belyi et al. were close to the ground-truth at the pixel level but contained few semantically meaningful details, as could be observed in Fig. 5. For example, our method generated plausible details such as water and waves in the first and second images, drawings on the bowling ball, wheels of the carriage, etc., which were not present in the previous decoded images. The image quality is also reflected by the FID, where we achieved 1.67 with our best samples, while Ozcelik et al. and others achieved 2.36 or more with the best samples generated by their method. Interestingly, color mismatches are observed in some cases with the color difference well preserved. It can be explained with [3] which suggests the color category information is processed in the frontal lobes as a cognitive process, while the visual cortex only recognizes the difference in colors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.602, + 0.72, + 0.618 + ], + "angle": 0, + "content": "5.1. Generation Consistency" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.626, + 0.894, + 0.838 + ], + "angle": 0, + "content": "The consistency of our method was tested by decoding the same fMRI data multiple times with different random states. Five samplings with different random states were performed in the testing set for each fMRI. In the 50-way and the 100-way top-1 accuracy identification tasks, we achieved an average success rate across the five samplings of \\(0.2385 \\pm 0.030\\) and \\(0.1736 \\pm 0.029\\) respectively, which are statistically higher than the best sampling results from Ozcelik et al. by \\(21\\%\\) and \\(35\\%\\). Regarding image quality, we achieved an average FID of \\(2.22 \\pm 0.3\\) across the five samplings. The standard deviations across 5 samplings indicate that the generated images will always be in the same semantic category. It can also be seen in Fig. 7 where isomorphic samplings share similar details such as shape, color, texture, and semantics, matching with the ground-truth across trials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.669, + 0.864 + ], + "angle": 0, + "content": "5.2. SC-MBM Design" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "This section will discuss the ablation study on the SC-MBM pre-training stage with various important parameters. Results" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "22715" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "are summarized in Tab. 1. For all experiments in this section, the 50-way, top-1 accuracy semantic identification task was performed with the best models obtained from the finetuning of 500 epochs. Average results over five samplings were reported." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.16, + 0.474, + 0.358 + ], + "angle": 0, + "content": "Testing Without SC-MBM To show that useful representations were learned with SC-MBM, we trained two models directly using the fMRI-image pairs without the SC-MBM pretraining. The first model consisted of an untrained fMRI encoder with the same architecture as the Full model. The second model consisted of an untrained fMRI encoder with a depth of only 2. The second model was designed to have fewer parameters, making it less likely to overfit the data. All the other settings were the same. The results correspond to Model 1 and 2 in Tab. 1, where the Full model significantly outperformed the other two models without the SC-MBM pre-training, showing that the pre-training is crucial. In fact, without SC-MBM these two models even failed to generate sensible images (See Appendix)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.37, + 0.47, + 0.633 + ], + "angle": 0, + "content": "
ModelEmbedding \nDimMask \nRatioParamsAcc (%)
Full10240.75303M23.9±3.00
1w/o SC-MBM + same Encoder303M2.6 ±1.39
2w/o SC-MBM + smaller Encoder25M3.4 ±0.86
3320.750.3M5.4 ±1.50
4640.751.2M6.9 ±1.10
51280.754.7M14.8 ±1.78
62560.7518.9M15.9 ±1.70
75120.7575.6M17.9 ±2.58
87680.75170M17.7 ±1.42
912800.75472M15.5 ±3.83
1010240.35303M19.6 ±3.40
1110240.45303M20.0 ±1.89
1210240.55303M18.1 ±2.87
1310240.65303M21.7 ±3.61
1410240.85303M16.1 ±1.00
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.081, + 0.634, + 0.435, + 0.647 + ], + "angle": 0, + "content": "† \\( p < {0.0001} \\) (purple); \\( p < {0.01} \\) (pink); \\( p < {0.05} \\) (yellow); \\( p > {0.05} \\) (green)" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.656, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Table 1. SC-MBM Ablation Results. Params: trainable parameters in the fMRI encoder; Cell colors reflect statistical significance differences (two-sample t-test) in accuracy compared with the Full model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "**Patch Embedding Dimension** Boosting the fMRI representation size using a large patch embedding matches the sparse coding mechanism of underlying visual information processing in the brain. Moreover, using a large patch embedding increases the information capacity of the representation. But larger embedding means more training parameters leading to a more data-hungry model. To balance this tradeoff, we tested SC-MBM models with different patch embedding dimensions ranging from 32 to 1280 (Model 3-9 in Tab. 1). We found that the accuracy generally increased as patch dimension increased, and accuracy peaked at \\(23.9\\%\\) with 1024 patch embedding dimensions (full model), after which accuracy decreased as patch dimensions increased further." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "Mask Ratios We used a high mask ratio in SC-MBM due to high spatial redundancy in fMRI data. In Tab. 1 Model 10-14, we show that a high mask ratio does not impair the decoding performance initially, with the highest average accuracy achieved with a relatively high mask ratio of 0.75. Importantly, using a high mask ratio significantly reduces memory consumption since the encoder only operates over unmasked patches. This is an important consideration for fMRI as SC-MBM is more memory-intensive than MIM due to the higher embedding-to-patch-size ratio." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.252, + 0.757, + 0.269 + ], + "angle": 0, + "content": "5.3. DC-LDM Finetuning Design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.895, + 0.397 + ], + "angle": 0, + "content": "This section will discuss the ablation study on the DC-LDM finetuning designs from three perspectives: conditioning methods, optimization designs, and pre-trained LDMs. Here, all ablations used the same pre-trained fMRI encoder as the Full model. Only important parameters in the finetuning stage were varied. The 1000-trial, 50-way, top-1 semantic identification test was performed. The results are summarized in Tab. 2, where five different samplings were averaged for each condition." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.409, + 0.892, + 0.513 + ], + "angle": 0, + "content": "
ModelConditionFinetunePre-trained LDMAcc (%)
FullC + TE + ALabel2Image23.9±3.00
1C onlyE + ALabel2Image15.6 ±0.69
2C+TE onlyLabel2Image13.76 ±2.60
3C+TE + AText2Image13.42±3.00
4C+TE + ALayout2Image15.99±3.00
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.504, + 0.514, + 0.858, + 0.527 + ], + "angle": 0, + "content": "† \\( p < {0.0001} \\) (purple); \\( p < {0.01} \\) (pink); \\( p < {0.05} \\) (yellow); \\( p > {0.05} \\) (green)" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.536, + 0.894, + 0.621 + ], + "angle": 0, + "content": "Table 2. DC-LDM Ablation Results. 1: cross-attention condition only; 2: optimizing fMRI encoders only; 3: LDM pre-trained on text conditions (LAION); 4: LDM pre-trained on layout conditions (OpenImages). Abbr.: C (Cross-attention condition); T (Time condition); E (Encoder); A (Cross-attention heads). Cell colors reflect statistical significance (two-sample t-test) in accuracy compared with the Full model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.894, + 0.699 + ], + "angle": 0, + "content": "Conditioning Methods Here, we showed that the double conditioning method increased the conditioning strength in Tab. 2, where using only cross-attention conditioning achieved an identification accuracy of \\(15.6\\%\\) (Model 1), which was significantly lower than the full method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Optimizing LDM We proposed to finetune the fMRI encoder and the cross-attention heads jointly because the LDM was pre-trained in a different conditioning space. For example, for the ImageNet class-conditioning pre-trained LDM, the cross-attention heads were pre-trained to receive the class label information. To justify this choice, we tested on a model with the fMRI encoder finetuned and the cross-attention heads untouched. As shown in Model 2 in Tab. 2, the average identification accuracy dropped to \\(13.7\\%\\) when only the fMRI encoder was finetuned, indicating stronger semantic guidance with the double conditioning. The visual quality and correspondence to the ground-truth of the generated images also decreased significantly (See Appendix)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22716" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.104, + 0.093, + 0.123, + 0.102 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.162, + 0.093, + 0.189, + 0.102 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.233, + 0.093, + 0.253, + 0.102 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.293, + 0.093, + 0.32, + 0.102 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.363, + 0.093, + 0.382, + 0.102 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.422, + 0.093, + 0.449, + 0.102 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.105, + 0.207, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.21, + 0.105, + 0.338, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.34, + 0.105, + 0.468, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.313, + 0.47, + 0.356 + ], + "angle": 0, + "content": "Figure 8. Replication Dataset (BOLD5000). It achieved similar quantitative results as the GOD dataset. 50-way top-1 identification accuracy: \\(34\\%\\); FID: 1.2 (Subject 1)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.365, + 0.473, + 0.622 + ], + "angle": 0, + "content": "Pre-trained LDM The pre-trained LDM determines the model's generative ability and the conditioning latent space to which the fMRI encoder would adapt. We considered three pretrained LDM provided by [41], which were trained on datasets with different conditioning tasks, i.e. ImageNet (label conditioning), LAION (text conditioning) [44] and OpenImages (layout conditioning) [24]. As shown in Model 3-4 Tab. 2, the ImageNet pre-trained LDM (used in the full model) showed the best performance in the same decoding task. Notably, images generated by models pre-trained on LAION and OpenImages were less visually favorable and plausible (See Appendix). This result is surprising because both LAION and OpenImages contain diverse images from various categories. We attribute the main reason for their poor performance to the complexity of their conditioning latent space. With limited training pairs, the class-conditioning latent space is easier to adapt to, compared with the latent space of the text-conditioning model and the layout-conditioning model." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.634, + 0.265, + 0.649 + ], + "angle": 0, + "content": "5.4. Replication Dataset" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.659, + 0.47, + 0.854 + ], + "angle": 0, + "content": "We validated our method on BOLD5000 using the same pretrained fMRI encoder. Similarly, the pre-trained encoder was firstly finetuned for 20 epochs in the testing set of BOLD500 with wrap-around paddings to compensate for the unequal ROI size from the pre-training set, after which the model is further tuned with the fMRI-image training pairs in BOLD5000. All other settings were the same as the Full model. For the four subjects in BOLD5000, we achieved a \\(19\\%\\) to \\(34\\%\\) best accuracy in the 1000-trial, 50-way, top-1 accuracy semantic identification task (See Appendix). The generated images matched the ground-truth stimulus in both semantics and low-level features (Fig. 8). Our model accurately reconstructs images containing objects and animals, architecture, and landscapes." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Interestingly, we reconstructed similar images for some natural scenes with extra details that do not exist in the ground-truth stimulus. These extra details, for example, the" + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.093, + 0.553, + 0.102 + ], + "angle": 0, + "content": "GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.093, + 0.65, + 0.103 + ], + "angle": 0, + "content": "Subject 1" + }, + { + "type": "image_caption", + "bbox": [ + 0.671, + 0.093, + 0.726, + 0.103 + ], + "angle": 0, + "content": "Subject 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.748, + 0.093, + 0.801, + 0.103 + ], + "angle": 0, + "content": "Subject 3" + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.093, + 0.879, + 0.103 + ], + "angle": 0, + "content": "Subject 4" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.105, + 0.581, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.105, + 0.892, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.236, + 0.892, + 0.291 + ], + "angle": 0, + "content": "Figure 9. Extra Features Decoded. Imagery-related details can be decoded with our method. e.g. the river and blue sky were decoded with natural scenery stimulus (top row); similar interior decorating of indoor environments was decoded when a house was presented (bottom row)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.3, + 0.892, + 0.359 + ], + "angle": 0, + "content": "river and the blue sky in Fig. 9, may reflect imagined scenery in the subject's mind when viewing the visual stimuli, which is captured in their brain activities. As reported in [21, 46], features of imaginary images can also be decoded from the visual cortex." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.361, + 0.892, + 0.466 + ], + "angle": 0, + "content": "To the best of our knowledge, this is the first work that performs fMRI decoding on BOLD5000. Additionally, adapting the same pre-trained model to this dataset shows that the SC-MBM pre-training indeed learns useful representations of brain recordings even when distinct domain shifts exist. These learned representations are shared and generalizable to datasets with different scanning protocols and preprocessing pipelines." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.48, + 0.735, + 0.495 + ], + "angle": 0, + "content": "6. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.505, + 0.894, + 0.565 + ], + "angle": 0, + "content": "Limitations MinD-Vis, in its current form, lacks strong pixel-level guidance and interpretation analysis, which limits its pixel-level performance (see G.5) and the biological understanding of the features learned by MBM." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.57, + 0.892, + 0.706 + ], + "angle": 0, + "content": "Future Work Similar to all previous work, MinD-Vis focuses on individual decoding using the visual cortex only. But as a complex cognitive process, human vision may be affected by regions beyond the visual cortex. Therefore, future studies should extend to cross-subject generalization and also the incorporation of other brain regions. Additionally, the two-stage decoupling design of MinD-Vis allows us to explore the potential of emerging large-scale models and representation learning techniques in cognitive neuroscience, which is also subject to future studies." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.712, + 0.892, + 0.893 + ], + "angle": 0, + "content": "Conclusion We proposed a two-stage framework MinD-Vis to decode visual stimuli using only a few paired fMRI-image annotations from brain recordings. In Stage A, we employ an fMRI pre-training scheme with masked modeling to learn generalizable context knowledge from a large-scale unlabeled fMRI dataset. In Stage B, we use a latent diffusion model with double conditioning to generate plausible seen images from learned fMRI representations. We validated the decoding results of MinD-Vis on multiple datasets and showed that our model generates more plausible and semantically similar images compared to previous methods, pushing the state-of-the-art a considerable step forward." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22717" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.17, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Teddy J Akiki and Chadi G Abdallah. Determining the hierarchical architecture of the human brain using subject-level clustering of functional networks. Scientific reports, 9(1):1-15, 2019." + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.472, + 0.214 + ], + "angle": 0, + "content": "[2] Roman Belyi, Guy Gaziv, Assaf Hoogi, Francesca Strappini, Tal Golan, and Michal Irani. 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Brain, 133(5):1352-1367, 2010." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22720" + } + ] +] \ No newline at end of file diff --git a/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/fe08ae3e-3e6a-4967-96af-a2a0ffcad985_origin.pdf b/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/fe08ae3e-3e6a-4967-96af-a2a0ffcad985_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..598661cf788356f6f78ba88eb982f0327e7ddcfa --- /dev/null +++ b/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/fe08ae3e-3e6a-4967-96af-a2a0ffcad985_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:41ffb92f8573fd49a29d0045eecef6566a620b4013513b8da5d4dba81926298c +size 7316485 diff --git a/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/full.md b/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f43a7bddcd907630e7a61410baf2a97843556e99 --- /dev/null +++ b/2023/Seeing Beyond the Brain_ Conditional Diffusion Model With Sparse Masked Modeling for Vision Decoding/full.md @@ -0,0 +1,376 @@ +# Seeing Beyond the Brain: Conditional Diffusion Model with Sparse Masked Modeling for Vision Decoding + +Zijiao Chen\* + +Jiaxin Qing $^{2*}$ + +Tiangxiang + +Wan Lin Yue + +Juan Helen Zhou† + +$^{1}$ National University of Singapore, $^{2}$ The Chinese University of Hong Kong, $^{3}$ Stanford University + +https://mind-vis.github.io + +![](images/b290042c881a9d50098f8027945d99a81803bd6d0f2c74bb819b2c41ef010a8b.jpg) +Visual Stimulus Brain Encoding + +![](images/75d22a8f8e36ffa7e4fd51a15d8a7b2308b070e8b088171872531a186734707c.jpg) + +![](images/884e3ca229c9f10e52795859354e655b992a100c9d3288feafb53bb76d37d159.jpg) +Reconstructed Image +"MinD-Vis" + +![](images/059eaec6b116ddb8b5ae76b24ef8f26936706c372609a97ae9689780865e4278.jpg) + +![](images/eaf7fa24d052ff0227545a867b5c550e2bb2d0bb7d8ef11ab080e89454ff1ebf.jpg) +Decode +fMRI Pattern + +![](images/9cdf17eb169dd99439034afa8f97744171266ce0310db2a0c2cf1f526d3cd02f.jpg) +Ozcelik (2022) + +![](images/ce02bdc6e9d9300e0d619ddbbad579f3c472bff5ef20264c966640681dff55b3.jpg) +Gaziv (2022) +Benchmarks +Figure 1. Brain Decoding and Image Reconstruction. For the first time, our proposed MinD-Vis is capable of decoding fMRI-based brain activities and reconstructing images with not only plausible details but also accurate semantics and image features (texture, shape, etc.), pushing this domain a considerable step forward. Left: Task overview. Middle: Comparison with benchmarks. Right: More reconstruction examples. + +![](images/13edbbdd55a3194e4dca3431a6d81bf855e6f11c4641cfd5d804c28d662ffffe.jpg) +Visual Stimulus + +![](images/77a9e506377d97df2e508aad241711e86444345b46588d518466a49dcf8a010d.jpg) + +![](images/4c3d2d3255945529377c4238298383fd9829c6a9a1f47dc2d469f74fac84dccb.jpg) +Our Reconstructed Images +Animal or Human + +![](images/c199cf34765ae5329b963d85e6dc58fcf7eddff37f10a73697811f6e39b4ba95.jpg) +Objects + +# Abstract + +Decoding visual stimuli from brain recordings aims to deepen our understanding of the human visual system and build a solid foundation for bridging human and computer vision through the Brain-Computer Interface. However, reconstructing high-quality images with correct semantics from brain recordings is a challenging problem due to the complex underlying representations of brain signals and the scarcity of data annotations. In this work, we present MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding. Firstly, we learn an effective self-supervised representation of fMRI data using mask modeling in a large latent space inspired by the sparse coding of information in the primary visual cortex. Then by augmenting a latent diffusion model with double-conditioning, we show that MinD-Vis can reconstruct highly plausible images with semantically matching details from brain recordings using very few paired annotations. We benchmarked our model qualitatively and quantitatively; the experimental results indicate that our method outperformed state-of-the-art in both semantic mapping (100-way semantic classification) and generation quality (FID) by $66\%$ and $41\%$ respectively. An exhaustive ablation study was also conducted to analyze our framework. + +# 1. Introduction + +"What you think is what you see". Human perception and prior knowledge are deeply intertwined in one's mind [51]. Our perception of the world is determined not only by objective stimuli properties but also by our experiences, forming complex brain activities underlying our perception. Understanding these brain activities and recovering the encoded information is a key goal in cognitive neuroscience. Within this broad objective, decoding visual information is one of the challenging problems that are the focus of a large body of literature [22, 26, 34, 67]. + +As a non-invasive and effective method to measure brain activities indirectly, functional Magnetic Resonance Imaging (fMRI) is usually used to recover visual information, such as the image classes [21, 39]. With the help of recent deep learning models, it is intriguing if the original visual stimuli can be directly recovered from corresponding fMRI [2, 46], especially with the guidance of biological principles [43, 52]. However, due to the lack of fMRI-image pairs and useful biological guidance when decoding complex neural activity from fMRI directly, reconstructed images are usually blurry and semantically meaningless. Thus it is crucial to learn effective and biological-valid representations for fMRI so that a clear and generalizable connection between brain activities and visual stimuli can be established with a few paired annotations. + +Moreover, individual variability in brain representations further complicates this problem. Individuals have unique + +brain activation patterns responding to the same visual stimulus (See Fig. 2). From the perspective of fMRI representation learning, a powerful brain decoding algorithm should robustly recognize features shared across the population over a background of individual variation [5, 21]. On the other hand, we should also expect decoding variances due to the variation in individual perceptions. Therefore, we aim to learn representations from a large-scale dataset with rich demographic compositions and relax the direct generation from fMRI to conditional synthesis allowing for sampling variance under the same semantic category. + +Self-supervised learning with pretext tasks in large datasets is a powerful paradigm to distill the model with context knowledge. A domain-specific downstream task (e.g. classification) is usually adopted to finetune the pre-trained model further [36, 58], especially when the downstream dataset is small. Various pretext tasks are designed to benefit downstream tasks [23, 66]. Among these methods, Masked Signal Modeling (MSM) has achieved promising results in both vision [18, 62] and language understanding [8, 37] recently. At the same time, the probabilistic diffusion denoising model has shown its superior performance in content generation and training stability [9]. A strong generation ability is also desired in our task to decode faithful visual stimuli from various categories. + +Driven by the above analysis, we propose MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding, a framework that exploits the power of large-scale representation learning and mimics the sparse coding of information in the brain [14], including the visual cortex [56]. Different from [18], we use a much larger representation-to-data-space ratio to boost the information capacity of learned representations. Our contributions are as follows: + +- We propose Sparse-Coded Masked Brain Modeling (SC-MBM), designed under biological guidance as an effective brain feature learner for vision decoding. +- Augmenting the latent diffusion model with double conditioning (DC-LDM), we enforce stronger decoding consistency while allowing variance under the same semantics. +- Integrating the representation ability of SC-MBM with the generation ability of DC-LDM, MinD-Vis generates more plausible images with better preserved semantic information compared with previous methods. +- Quantitative and qualitative tests are performed on multiple datasets, including a new dataset that has not previously been used to evaluate this task. + +# 2. Related Work + +Conventional Decoding Methods Conventional methods rely on training with fMRI and corresponding hierarchical image features extracted by a pre-trained VGG [21, 46]. During testing, the predicted image features will either be used for classification or fed into a generative model like GAN [45] to + +![](images/ba0c32fd3e7d34616f753e5584f79f3715818cfecb81fbb564285be9c5fd4888.jpg) +Figure 2. Individual Differences in Regions Responding to Visual Stimuli. Masks of the regions of interest activating during the same visual task differ in location and size across subjects. The primary visual cortex at the left (red) and the right (orange) hemisphere are shown. + +reconstruct the original stimulus. Instead of directly learning the limited training pairs, [2] enabled unsupervised learning on unpaired fMRI and images with a reconfigurable autoencoder design. [16] further extended this method to images from diverse semantic categories. However, just as with conventional approaches, fMRI is used directly for training and decoding. In [31, 33], a regression model was used to extract latent fMRI representation, which was then used to finetune a pre-trained conditional bigGAN for image decoding. Mind Reader [27] encoded fMRI signals into a pre-aligned vision-language latent space and used StyleGAN2 for image generation. These methods generate more plausible and semantically meaningful images. We note that there is parallel work to ours by Takagi and Nishimoto [13], who proposed a method for image reconstruction from fMRI using Stable Diffusion. Their approach involves decoding brain activities to text descriptions and converting them to natural images using stable diffusion. + +Masked Signal Modeling The power of MSM in learning representations from a large-scale dataset was first exploited in [8], which was later adapted to computer vision [18,60,62]. Successful applications to downstream tasks show that useful context knowledge is learned with MSM as a pretext task. In essence, MSM is a generalized denoising autoencoder that aims to recover the original data from the remaining after masking [4]. The portion of data to mask is different across data modalities, with an extremely high mask ratio (75%) usually used for visual signals [18]. In contrast, due to the disparity in information density, a low mask ratio (25%) is used in natural languages [8]. + +Diffusion Probabilistic Models Diffusion models [49] are emerging generative models that generate high-quality content. In its basic form [20], the diffusion model is a probabilistic model defined by a bi-directional Markov Chain of states. Two processes are transiting through the chain: (i) The forward diffusion process gradually adds noise to the data until it is fully destroyed to an isotropic Gaussian noise; (ii) The reverse process recovers the corrupted data by modeling a posterior distribution $p(x)$ at each state and eventually obtains a sample in the original data distribution [20, 49, 50]. Formally, assume a Markov Chain with a fixed length $T$ , then the reverse conditional probability can be expressed as $q(x_{t-1} | x_t)$ , where $t = 1, \dots, T$ and $x_t$ is obtained by corrupting the image $x_{t-1}$ with Gaussian noise. After parameterization, this conditional probability can be learned by optimizing a variational lower + +![](images/775870bb4bb7291cdedd866bf34962fd077876a74657b1dc7b7dbc9e511711bf.jpg) +Figure 3. MinD-Vis. Stage A (left): Pre-train on fMRI with SC-MBM. We patchify, randomly mask the fMRI, and then tokenize them to large embeddings. We train an autoencoder $(\mathcal{E}_{\mathcal{MBM}}$ and $\mathcal{D}_{\mathcal{MBM}})$ to recover the masked patches. Stage B (right): Integration with the LDM through double conditioning. We project the fMRI latent $(\mathcal{L}_{fMRI})$ through two paths to the LDM conditioning space with a latent dimension projector $(\mathcal{P}_{fMRI\rightarrow Cond})$ . One path connects directly to cross-attention heads in the LDM. Another path adds the fMRI latent to time embeddings. The LDM operates on a low-dimensional, compressed version of the original image (i.e. image latent), however, the original image is used in this figure for illustrations. + +![](images/a2a9eb9f1a1c7c9c6bb98b43b2e728099335a443d45434c7bacaabd1b5c62afe.jpg) + +bound which can be simplified to the following objective [20]: + +$$ +L _ {t} ^ {\text {s i m p l e}} = \mathbb {E} _ {x, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} (x _ {t}, t) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $\epsilon_{\theta}(x_t,t)$ is a set of denoising functions that are usually implemented as UNets [9, 41, 42]. We refer readers to [20] for detailed descriptions of the diffusion models. + +Latent Diffusion Model (LDM) Apart from the conventional diffusion models that generate samples in the original data space, another category of diffusion models that generate samples in the latent feature space has been proposed [41, 48]. Operating in the latent feature space reduces the computational cost and introduces less spatial downsampling, giving better image synthesis quality. The LDM proposed in [41] consists of two components: (i) Vector Quantization (VQ) regularized [12] autoencoder that compresses images into lower-dimensional latent features and then reconstructs the images from features in the same space; (ii) UNet-based denoising model with attention modules. Incorporating attention mechanisms into the UNet allows the flexibility to condition image generation through key/value/query vectors during the Markov Chain transitions. + +# 3. Methodology + +# 3.1. Motivation and Overview + +In this subsection, we provide a detailed analysis of the fMRI data and elaborate on the motivations of our designs. + +(i) fMRI measures the brain blood-oxygen-level-dependent (BOLD) changes as 3D voxels that serve as a proxy for the underlying changes in brain activity. Neighboring voxels often have similar amplitudes, indicating spatial redundancy in fMRI [53]. +(ii) fMRI data is averaged across the time during which the stimulus is presented. A region of interest (ROI) of the averaged + +data is usually extracted as a 1D vector of voxels (in the visual processing hierarchy). The ROI size (voxel number) is generally smaller than the image size (pixel number). For example, [21] has about 4500 voxels (visual cortex), which is much smaller than a $256 \times 256$ RGB image. This creates a large difference in dimensionality when transforming fMRI into images. + +(iii) fMRI data from different datasets may have significant domain shifts due to experimental conditions and scanner setups. Even with the same scan conditions, ROI size and location mismatch persist due to individual differences (See Fig. 2). + +Driven by this analysis, we propose MinD-Vis, designed with two sequential stages as outlined in Fig. 3. Briefly, in Stage A, fMRI representations are learned by an autoencoder trained in a large fMRI dataset with masked signal modeling as a pretext task. The learned representations will be used as a condition to guide the image-generation process in the next stage. In Stage B, the pre-trained fMRI encoder is integrated with the LDM through cross-attention and time-step conditioning for conditional synthesis. In this stage, the encoder is jointly finetuned with cross-attention heads in the LDM using paired annotations. + +# 3.2. Stage A: Sparse-Coded MBM (SC-MBM) + +Activity in the human brain involves non-linear interactions among 86 billion neuronal cells in the brain and are thus highly complex [32, 40]. The fMRI measuring the BOLD signals is an indirect and aggregate measure of neuronal activities, which can be analyzed hierarchically with functional networks [1, 6, 59]. These functional networks comprised of voxels of fMRI data have implicit correlations with each other in response to external stimuli [54, 68]. Therefore, learning these implicit correlations by recovering masked voxels will equip the pre-trained model with a deep contextual understanding of the fMRI data. + +![](images/c7ce8c98c682736a664fa9ea916e34253123240cee188dbd0ae5fdb5d8561f66.jpg) +Ground-truth +Masked Ground-truth + +![](images/6b7744f5458ac87390e2d400d440976dd45f3eb36b15e88cd387b049c7a5024b.jpg) + +![](images/93b48532955745a3ead8990e3ba028a28710f3032b58966228f42596f5879329.jpg) + +![](images/ecfa5496aead91de100d9f1d1a5283f4d80e88a4e9c0bed6caec4b46e2372398.jpg) + +![](images/24f25392317796443302ebb8de97e180fb9cef41228d5fe7e86ca2b7a4e952d8.jpg) +Reconstruction +Figure 4. Masked Brain Modeling. Mask ratio 0.75; 4500 voxels + +![](images/3bf384de1f49d2f8bcaa474e36cd2116994511c56bcaf549e2861d7318b1d308.jpg) + +Following [18], we divide the vectorized voxels into patches which will be subsequently transformed into embeddings using a 1D convolutional layer with a stride equal to the patch size. The hemodynamic response and spatial smoothing functions in fMRI BOLD signal jointly cause spatial blurring, which creates spatial redundancy in fMRI data, like in natural images [11,47]. Due to the spatial redundancy, fMRI data can still be recovered even if a large portion is masked (See Fig. 4). Thus, in the first stage of MinD-Vis, we can mask a large portion of the fMRI patches to save computations without losing the learning power of masked modeling. + +Masked Image Modeling (MIM) uses the embedding-to-patch-size ratio around one [18], leading to a representation size similar to the original data size. However, we use a large embedding-to-patch-size ratio, which significantly increases the information capacity with a large fMRI representation space. This design also relates to the sparse coding of information in the brain, which has been proposed as a general strategy for the representation of sensory information [25]. + +We also adopt an asymmetric architecture as in [18]: the encoder is optimized to learn effective fMRI representations, while the decoder tries to predict the masked patches. Therefore, we make the decoder small in size, and it is discarded in Stage B as long as the pre-training converges. + +Visual Encoding and Brain-Inspired Sparse Coding Here, we explain the biological basis of using SC-MBM to learn representations of visual stimuli in the brain from the perspective of visual encoding mechanisms. Theoretical and empirical studies suggest that visual stimuli are sparsely encoded in the primary visual cortex [32, 38, 56], with most natural images activating only a portion of the neurons in the visual cortex. This strategy increases information transmission efficiency and creates minimal redundancy in the brain [38]. As a result, visual information of natural scenes can be reconstructed from a small portion of data collected from the primary visual cortex via different imaging modalities, including fMRI [15, 64]. This observation is interesting for the computer vision community because the sparse coding could be an efficient way for vision encoding in computer vision as well [25, 63]. + +Sparse coding is an encoding strategy that in essence uses over-complete bases to represent data, where more locality is + +generally enforced to generate smoother representations [57, 65]. In SC-MBM, fMRI data are divided into patches to introduce locality constraints. Then each patch is encoded into a high-dimensional vector space with a size much larger than the original data space, thus creating an over-complete space for fMRI representation (See Appendix). Emulating the brain vision encoding, SC-MBM can be a biologically-valid and effective brain feature learner for fMRI decoding. + +# 3.3. Stage B: Double-Conditioned LDM (DC-LDM) + +After the large-scale context learning in Stage A, the fMRI encoder transforms fMRI data into sparsely coded representations with locality constraints. To further decode visual contents from this abstract representation and allow for sampling variance, we formulate the decoding task as a conditional synthesis problem and approach it with a pre-trained LDM. + +The LDM operates on the image latent space denoted by $\mathcal{E}(x)$ where $x$ is an image in pixel space and $\mathcal{E}(\cdot)$ is a VQ encoder. In our setting, we omit $\mathcal{E}(x)$ and use $x$ directly to represent the latent variable of LDM for simplicity. Specifically, given the fMRI data $z$ , we aim to learn the reverse diffusion process formulated by $q(x_{t-1}|x_t,z)$ . As proposed in [41], conditional information is applied through cross-attention heads in the attention-based UNet, where CrossAttention $(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d}}\right)$ , with + +$$ +Q = W _ {Q} ^ {(i)} \varphi_ {i} (x _ {t}), K = W _ {K} ^ {(i)} \tau_ {\theta} (z), V = W _ {V} ^ {(i)} \tau_ {\theta} (z). +$$ + +Here, $\tau_{\theta}$ is the fMRI encoder with a suitable dimension projector, $\varphi_{i}(x_{t})$ denotes intermediate values of the UNet and $W_{Q}^{(i)}$ , $W_{K}^{(i)}$ , $W_{V}^{(i)}$ are projector matrices with learnable parameters. + +Diversity and consistency are two opposite objectives when sampling a conditional generative model. Sampling diversity across various modalities such as label-to-image and text-to-image is very important in many image-generation tasks. However, the fMRI-to-image transition relies more on generation consistency—decoded images from similar brain activities are expected to be semantically similar. Thus, a stronger conditioning mechanism is desired to ensure such generation consistency, especially for probabilistic diffusion models. + +In this way, we integrate the cross-attention conditioning with another conditioning method called the time steps conditioning [9] to provide stronger guidance for our task. In time steps conditioning, we add $\sigma_{\theta}(\tau_{\theta}(z))$ to time step embeddings, where $\sigma_{\theta}(\cdot)$ is another suitable dimension projector. Time step embeddings are used in intermediate layers of the UNet, thus we have $\varphi_{i}(x_{t}) = \varphi_{i}(x_{t},\sigma_{\theta}(\tau_{\theta}(z)))$ . We further reformulate the optimization objective Eq. (1) to a double conditioning alternation: + +$$ +L _ {t} ^ {\text {c o n d}} = \mathbb {E} _ {x, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(x _ {t}, t, \tau (z), \sigma (\tau (z))\right) \| _ {2} ^ {2} \right]. \tag {2} +$$ + +We omit the parameterization symbol $\theta$ in $\tau(\cdot)$ and $\sigma(\cdot)$ for simplicity. Additionally, we have $\tau(z) \in \mathbb{R}^{M \times d_{\tau}}$ and $\sigma(\tau(z)) \in \mathbb{R}^{1 \times d_t}$ , where $d_{\tau}$ and $d_t$ are the latent dimensions and time embedding dimension respectively, and $M$ is a tunable parameter. + +![](images/56434963e0b80092bb333a0c7e60f57c0ba8ae2306da8360ad02f1689066222d.jpg) +Figure 5. Decoding Performance Comparisons on GOD Test Set. The ground truth, images reconstructed by MinD-Vis and images reconstructed from three other methods are shown for comparison. MinD-Vis decoded the most accurate and plausible images with semantically similar details. + +![](images/a8b780d275a7284af5e90a14f8729189ef35c925c68d4fe6990c648c8e843942.jpg) + +Figure 6. Quantitative Performance Comparisons on GOD +![](images/5c442ca0470f5c65242c55b6a25d4cd8ee3a702e892de9aeec15e33e17bbfe9b.jpg) +Test Set. Performance is evaluated in terms of semantic correctness (1000-trial $n$ -way top- $k$ classification accuracy; the higher the better) and generation quality (FID; the lower the better). + +Finetuning After the fMRI encoder is pre-trained with SC-MBM, it is integrated with a pre-trained LDM through double conditioning. Commonly, the encoder's output is averaged, or a $cls$ token is appended to produce a pooled 1D feature vector for downstream tasks [8, 18]. This strategy is effective for tasks like prediction and classification, where learned knowledge is expected to be distilled, producing distinguishable features. However, pooling into a 1D vector is inappropriate for retaining fMRI representations' sparsity and information capacity. Instead, we used convolution layers to pool the encoder's output into a latent dimension of $\mathbb{R}^{M\times d_{\tau}}$ as described in Eq. (2). + +The fMRI encoder, cross-attention heads, and projection heads are jointly optimized, while other parts are fixed. Finetuning the cross-attention heads is critical for bridging the pre-trained conditioning space and fMRI latent space. The finetuning is performed end-to-end with fMRI-image pairs, during which a clearer connection between the fMRI and image features will be learned through the large-capacity fMRI representations. + +# 4. Experiments + +# 4.1. Datasets and Implementation + +Datasets Three public datasets were used in this study: Human Connectome Project (HCP) 1200 Subject Release [55]; Generic Object Decoding Dataset (GOD) [21]; and Brain, Object, Landscape Dataset (BOLD5000) [5]. Our upstream pre-training dataset comprised fMRI data from HCP and GOD. Combining these two, we obtained 136,000 fMRI segments from 340 hours of fMRI scan, which is, by far, the largest fMRI pre-training dataset in the fMRI-image decoding task. The HCP dataset is commonly used in neuroscience research, containing only fMRI data. While the GOD is an fMRI-image paired dataset designed for fMRI-based decoding. The pairs in GOD were used for finetuning in our main analysis. The GOD consists of 1250 different images from 200 distinct classes, in which 1200 images were used as the training set, and the remaining 50 images were used as the testing set. The training set and testing set have no overlapping classes. The BOLD5000 dataset was used as the validation dataset in our study. It consists of 5254 fMRI-image pairs from 4916 distinct images, 113 images of which are used for testing. This is the first time that the BOLD5000 is used for fMRI decoding tasks. + +Implementation The fMRI pre-training model is similar to ViT-Large [10] with a 1D patch embedder. We used a patch size of 16, embedding dimension of 1024, encoder depth of 24, and mask ratio of 0.75 as our Full model setting with an ImageNet class-conditioned pre-trained LDM. Different parameter choices are explored in our ablation study. Unless stated otherwise, the Full model is pre-trained for 500 epochs and finetuned for another 500. Results from the best model are reported. Images are generated at a resolution of $256 \times 256$ with 250 PLMS + +steps [29]. See Appendix for dataset and implementation details. + +# 4.2. Evaluation Metric + +N-way Classification Accuracy Following [16], we used the $n$ -way top-1 and top-5 accuracy classification task to evaluate the semantic correctness of our results, where for multiple trials, top-1 and top-5 classification accuracies were calculated in $n - 1$ randomly selected classes plus the correct one. Note that we did not consider the pixel-level metrics as we aimed to recover the semantically correct images in this work. + +In [16], the authors generated a typical feature for each class selected and compared the distance between the reconstructed images and the typical features. However, this metric in [16] is hard to reproduce, and the semantic classification result largely depends on how the features are computed. Therefore, we propose a more straightforward and reproducible method, where a pre-trained ImageNet1K classifier [10, 35] is used to determine the semantic correctness of generated images rather than handcrafted features. We describe this evaluation method in Algorithm D.1. Specifically, both ground-truth and generated images are input to the classifier first. Then we check for the generated image if the top- $k$ classification in $n$ selected classes matches the ground-truth classification. This metric does not require the ground-truth image to be from the ImageNet 1k classes. As long as semantic classification results of the ground-truth and the generated image match, it will be considered to be correct. + +Fréchet inception distance (FID) The FID [19] is a commonly used metric to assess image generation quality. In our experiments, we measured the FID between ground-truth images and generated images in the testing set. Note that FID is only used as a reference in our experiments due to the limited number of images available in GOD, which may lead to an underestimated distribution. + +# 5. Results + +Our main results are based on GOD which has no overlapping classes in the training and testing set. The training and testing were performed on the same subject, as individual differences remain a barrier when decoding at the group level [2, 16, 21, 31, 33]. To compare with the literature, we report results from Subject 3 here and leave other subjects in the Appendix. + +We compared our results with Ozcelik et al. [33], Gaziv et al. [16] and Belyi et al. [16]. Gaziv et al. and Belyi et al. used the conventional method, which decoded images with higher pixel similarity but less plausibility and semantic details. On the other hand, Ozcelik et al. generated more plausible and semantically meaningful images using a pre-trained GAN. Based on the best-reconstructed samples of these methods (resized to $256 \times 256$ ), we performed a 1000-trial, $n$ -way top- $k$ accuracy identification task as described in Algorithm D.1. The experiment is repeated for $n = 50,100$ and $k = 1,5$ in the GOD testing set. + +![](images/0549b0fc0283f429a70b29bd7aefbb752764b40a89d48b885eb31fc6aa7be9bc.jpg) +GT + +![](images/52b4e7218bddb43bf72d68bdc767bdf0ada665e624f9b493186475c8e7c4691b.jpg) +Reconstructed Samples + +![](images/fb22da9824a21a1eea671c6d8b28e34befea7023748425aa3b9f19dbb792e193.jpg) +Figure 7. Generation Consistency of MinD-Vis. Images generated by our method were consistent across different samplings trials, sharing similar low-level features and semantics. + +![](images/0933fbfa4bea5918f2131560db99ac88b205e11f20f8b3d48b45a82fdd1c3005.jpg) + +From Fig. 6, our identification accuracy outperformed the Ozcelik et al. in the 50-way top-1 accuracy task by $39\%$ and in the 100-way top-1 accuracy task by $66\%$ , achieving a success rate of 0.274 and 0.212 respectively. The generated images from Gaziv et al. and Belyi et al. were close to the ground-truth at the pixel level but contained few semantically meaningful details, as could be observed in Fig. 5. For example, our method generated plausible details such as water and waves in the first and second images, drawings on the bowling ball, wheels of the carriage, etc., which were not present in the previous decoded images. The image quality is also reflected by the FID, where we achieved 1.67 with our best samples, while Ozcelik et al. and others achieved 2.36 or more with the best samples generated by their method. Interestingly, color mismatches are observed in some cases with the color difference well preserved. It can be explained with [3] which suggests the color category information is processed in the frontal lobes as a cognitive process, while the visual cortex only recognizes the difference in colors. + +# 5.1. Generation Consistency + +The consistency of our method was tested by decoding the same fMRI data multiple times with different random states. Five samplings with different random states were performed in the testing set for each fMRI. In the 50-way and the 100-way top-1 accuracy identification tasks, we achieved an average success rate across the five samplings of $0.2385 \pm 0.030$ and $0.1736 \pm 0.029$ respectively, which are statistically higher than the best sampling results from Ozcelik et al. by $21\%$ and $35\%$ . Regarding image quality, we achieved an average FID of $2.22 \pm 0.3$ across the five samplings. The standard deviations across 5 samplings indicate that the generated images will always be in the same semantic category. It can also be seen in Fig. 7 where isomorphic samplings share similar details such as shape, color, texture, and semantics, matching with the ground-truth across trials. + +# 5.2. SC-MBM Design + +This section will discuss the ablation study on the SC-MBM pre-training stage with various important parameters. Results + +are summarized in Tab. 1. For all experiments in this section, the 50-way, top-1 accuracy semantic identification task was performed with the best models obtained from the finetuning of 500 epochs. Average results over five samplings were reported. + +Testing Without SC-MBM To show that useful representations were learned with SC-MBM, we trained two models directly using the fMRI-image pairs without the SC-MBM pretraining. The first model consisted of an untrained fMRI encoder with the same architecture as the Full model. The second model consisted of an untrained fMRI encoder with a depth of only 2. The second model was designed to have fewer parameters, making it less likely to overfit the data. All the other settings were the same. The results correspond to Model 1 and 2 in Tab. 1, where the Full model significantly outperformed the other two models without the SC-MBM pre-training, showing that the pre-training is crucial. In fact, without SC-MBM these two models even failed to generate sensible images (See Appendix). + +
ModelEmbedding +DimMask +RatioParamsAcc (%)
Full10240.75303M23.9±3.00
1w/o SC-MBM + same Encoder303M2.6 ±1.39
2w/o SC-MBM + smaller Encoder25M3.4 ±0.86
3320.750.3M5.4 ±1.50
4640.751.2M6.9 ±1.10
51280.754.7M14.8 ±1.78
62560.7518.9M15.9 ±1.70
75120.7575.6M17.9 ±2.58
87680.75170M17.7 ±1.42
912800.75472M15.5 ±3.83
1010240.35303M19.6 ±3.40
1110240.45303M20.0 ±1.89
1210240.55303M18.1 ±2.87
1310240.65303M21.7 ±3.61
1410240.85303M16.1 ±1.00
+ +† $p < {0.0001}$ (purple); $p < {0.01}$ (pink); $p < {0.05}$ (yellow); $p > {0.05}$ (green) + +**Patch Embedding Dimension** Boosting the fMRI representation size using a large patch embedding matches the sparse coding mechanism of underlying visual information processing in the brain. Moreover, using a large patch embedding increases the information capacity of the representation. But larger embedding means more training parameters leading to a more data-hungry model. To balance this tradeoff, we tested SC-MBM models with different patch embedding dimensions ranging from 32 to 1280 (Model 3-9 in Tab. 1). We found that the accuracy generally increased as patch dimension increased, and accuracy peaked at $23.9\%$ with 1024 patch embedding dimensions (full model), after which accuracy decreased as patch dimensions increased further. + +Mask Ratios We used a high mask ratio in SC-MBM due to high spatial redundancy in fMRI data. In Tab. 1 Model 10-14, we show that a high mask ratio does not impair the decoding performance initially, with the highest average accuracy achieved with a relatively high mask ratio of 0.75. Importantly, using a high mask ratio significantly reduces memory consumption since the encoder only operates over unmasked patches. This is an important consideration for fMRI as SC-MBM is more memory-intensive than MIM due to the higher embedding-to-patch-size ratio. + +# 5.3. DC-LDM Finetuning Design + +This section will discuss the ablation study on the DC-LDM finetuning designs from three perspectives: conditioning methods, optimization designs, and pre-trained LDMs. Here, all ablations used the same pre-trained fMRI encoder as the Full model. Only important parameters in the finetuning stage were varied. The 1000-trial, 50-way, top-1 semantic identification test was performed. The results are summarized in Tab. 2, where five different samplings were averaged for each condition. + +Table 1. SC-MBM Ablation Results. Params: trainable parameters in the fMRI encoder; Cell colors reflect statistical significance differences (two-sample t-test) in accuracy compared with the Full model. + +
ModelConditionFinetunePre-trained LDMAcc (%)
FullC + TE + ALabel2Image23.9±3.00
1C onlyE + ALabel2Image15.6 ±0.69
2C+TE onlyLabel2Image13.76 ±2.60
3C+TE + AText2Image13.42±3.00
4C+TE + ALayout2Image15.99±3.00
+ +† $p < {0.0001}$ (purple); $p < {0.01}$ (pink); $p < {0.05}$ (yellow); $p > {0.05}$ (green) + +Table 2. DC-LDM Ablation Results. 1: cross-attention condition only; 2: optimizing fMRI encoders only; 3: LDM pre-trained on text conditions (LAION); 4: LDM pre-trained on layout conditions (OpenImages). Abbr.: C (Cross-attention condition); T (Time condition); E (Encoder); A (Cross-attention heads). Cell colors reflect statistical significance (two-sample t-test) in accuracy compared with the Full model. + +Conditioning Methods Here, we showed that the double conditioning method increased the conditioning strength in Tab. 2, where using only cross-attention conditioning achieved an identification accuracy of $15.6\%$ (Model 1), which was significantly lower than the full method. + +Optimizing LDM We proposed to finetune the fMRI encoder and the cross-attention heads jointly because the LDM was pre-trained in a different conditioning space. For example, for the ImageNet class-conditioning pre-trained LDM, the cross-attention heads were pre-trained to receive the class label information. To justify this choice, we tested on a model with the fMRI encoder finetuned and the cross-attention heads untouched. As shown in Model 2 in Tab. 2, the average identification accuracy dropped to $13.7\%$ when only the fMRI encoder was finetuned, indicating stronger semantic guidance with the double conditioning. The visual quality and correspondence to the ground-truth of the generated images also decreased significantly (See Appendix). + +![](images/e1da56194a6b8983a99a5675c1b3b5748f4330efc6b9440f85b6078531b7c394.jpg) +GT +Ours +Figure 8. Replication Dataset (BOLD5000). It achieved similar quantitative results as the GOD dataset. 50-way top-1 identification accuracy: $34\%$ ; FID: 1.2 (Subject 1). + +![](images/e4e08cea155bf92b08d11e94867d73743ce506ed5faaf4371527e9ab50c14194.jpg) +GT +Ours + +![](images/100e51949f22a028b8f9a5772cfa46deb93e91b9369786a29491e224e8361502.jpg) +GT +Ours + +Pre-trained LDM The pre-trained LDM determines the model's generative ability and the conditioning latent space to which the fMRI encoder would adapt. We considered three pretrained LDM provided by [41], which were trained on datasets with different conditioning tasks, i.e. ImageNet (label conditioning), LAION (text conditioning) [44] and OpenImages (layout conditioning) [24]. As shown in Model 3-4 Tab. 2, the ImageNet pre-trained LDM (used in the full model) showed the best performance in the same decoding task. Notably, images generated by models pre-trained on LAION and OpenImages were less visually favorable and plausible (See Appendix). This result is surprising because both LAION and OpenImages contain diverse images from various categories. We attribute the main reason for their poor performance to the complexity of their conditioning latent space. With limited training pairs, the class-conditioning latent space is easier to adapt to, compared with the latent space of the text-conditioning model and the layout-conditioning model. + +# 5.4. Replication Dataset + +We validated our method on BOLD5000 using the same pretrained fMRI encoder. Similarly, the pre-trained encoder was firstly finetuned for 20 epochs in the testing set of BOLD500 with wrap-around paddings to compensate for the unequal ROI size from the pre-training set, after which the model is further tuned with the fMRI-image training pairs in BOLD5000. All other settings were the same as the Full model. For the four subjects in BOLD5000, we achieved a $19\%$ to $34\%$ best accuracy in the 1000-trial, 50-way, top-1 accuracy semantic identification task (See Appendix). The generated images matched the ground-truth stimulus in both semantics and low-level features (Fig. 8). Our model accurately reconstructs images containing objects and animals, architecture, and landscapes. + +Interestingly, we reconstructed similar images for some natural scenes with extra details that do not exist in the ground-truth stimulus. These extra details, for example, the + +![](images/e5f90824c05e247957c0b79e63ec2a441fdc0082d8989959ba371cd0ff69ba77.jpg) +GT +Figure 9. Extra Features Decoded. Imagery-related details can be decoded with our method. e.g. the river and blue sky were decoded with natural scenery stimulus (top row); similar interior decorating of indoor environments was decoded when a house was presented (bottom row). + +![](images/3a640cdaaaaa23c1cb37910027dac39534e4f25b12b4de8a2bd79520e3cfcdee.jpg) +Subject 1 +Subject 2 +Subject 3 +Subject 4 + +river and the blue sky in Fig. 9, may reflect imagined scenery in the subject's mind when viewing the visual stimuli, which is captured in their brain activities. As reported in [21, 46], features of imaginary images can also be decoded from the visual cortex. + +To the best of our knowledge, this is the first work that performs fMRI decoding on BOLD5000. Additionally, adapting the same pre-trained model to this dataset shows that the SC-MBM pre-training indeed learns useful representations of brain recordings even when distinct domain shifts exist. These learned representations are shared and generalizable to datasets with different scanning protocols and preprocessing pipelines. + +# 6. Discussion and Conclusion + +Limitations MinD-Vis, in its current form, lacks strong pixel-level guidance and interpretation analysis, which limits its pixel-level performance (see G.5) and the biological understanding of the features learned by MBM. + +Future Work Similar to all previous work, MinD-Vis focuses on individual decoding using the visual cortex only. But as a complex cognitive process, human vision may be affected by regions beyond the visual cortex. Therefore, future studies should extend to cross-subject generalization and also the incorporation of other brain regions. Additionally, the two-stage decoupling design of MinD-Vis allows us to explore the potential of emerging large-scale models and representation learning techniques in cognitive neuroscience, which is also subject to future studies. + +Conclusion We proposed a two-stage framework MinD-Vis to decode visual stimuli using only a few paired fMRI-image annotations from brain recordings. In Stage A, we employ an fMRI pre-training scheme with masked modeling to learn generalizable context knowledge from a large-scale unlabeled fMRI dataset. In Stage B, we use a latent diffusion model with double conditioning to generate plausible seen images from learned fMRI representations. We validated the decoding results of MinD-Vis on multiple datasets and showed that our model generates more plausible and semantically similar images compared to previous methods, pushing the state-of-the-art a considerable step forward. + +# References + +[1] Teddy J Akiki and Chadi G Abdallah. 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Brain Decoding and Image Reconstruction. For the first time, our proposed MinD-Vis is capable of decoding fMRI-based brain activities and reconstructing images with not only plausible details but also accurate semantics and image features (texture, shape, etc.), pushing this domain a considerable step forward. Left: Task overview. Middle: Comparison with benchmarks. 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However, reconstructing high-quality images with correct semantics from brain recordings is a challenging problem due to the complex underlying representations of brain signals and the scarcity of data annotations. In this work, we present MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding. Firstly, we learn an effective self-supervised representation of fMRI data using mask modeling in a large latent space inspired by the sparse coding of information in the primary visual cortex. Then by augmenting a latent diffusion model with double-conditioning, we show that MinD-Vis can reconstruct highly plausible images with semantically matching details from brain recordings using very few paired annotations. We benchmarked our model qualitatively and quantitatively; the experimental results indicate that our method outperformed state-of-the-art in both semantic mapping (100-way semantic classification) and generation quality (FID) by " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "66\\%" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "inline_equation", + "content": "41\\%" + }, + { + "bbox": [ + 46, + 409, + 289, + 673 + ], + "type": "text", + "content": " respectively. An exhaustive ablation study was also conducted to analyze our framework." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 307, + 392, + 382, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 392, + 382, + 403 + ], + "spans": [ + { + "bbox": [ + 307, + 392, + 382, + 403 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 412, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 547, + 520 + ], + "type": "text", + "content": "\"What you think is what you see\". Human perception and prior knowledge are deeply intertwined in one's mind [51]. Our perception of the world is determined not only by objective stimuli properties but also by our experiences, forming complex brain activities underlying our perception. Understanding these brain activities and recovering the encoded information is a key goal in cognitive neuroscience. Within this broad objective, decoding visual information is one of the challenging problems that are the focus of a large body of literature [22, 26, 34, 67]." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 521, + 547, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 688 + ], + "type": "text", + "content": "As a non-invasive and effective method to measure brain activities indirectly, functional Magnetic Resonance Imaging (fMRI) is usually used to recover visual information, such as the image classes [21, 39]. With the help of recent deep learning models, it is intriguing if the original visual stimuli can be directly recovered from corresponding fMRI [2, 46], especially with the guidance of biological principles [43, 52]. However, due to the lack of fMRI-image pairs and useful biological guidance when decoding complex neural activity from fMRI directly, reconstructed images are usually blurry and semantically meaningless. Thus it is crucial to learn effective and biological-valid representations for fMRI so that a clear and generalizable connection between brain activities and visual stimuli can be established with a few paired annotations." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "Moreover, individual variability in brain representations further complicates this problem. Individuals have unique" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 125, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 125, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 125, + 703 + ], + "type": "text", + "content": "*Equal contributions." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 59, + 703, + 209, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 209, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 209, + 713 + ], + "type": "text", + "content": "† Corresponding author (helen.zhou@nus.edu.sg)" + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22710" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "brain activation patterns responding to the same visual stimulus (See Fig. 2). From the perspective of fMRI representation learning, a powerful brain decoding algorithm should robustly recognize features shared across the population over a background of individual variation [5, 21]. On the other hand, we should also expect decoding variances due to the variation in individual perceptions. Therefore, we aim to learn representations from a large-scale dataset with rich demographic compositions and relax the direct generation from fMRI to conditional synthesis allowing for sampling variance under the same semantic category." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 346 + ], + "type": "text", + "content": "Self-supervised learning with pretext tasks in large datasets is a powerful paradigm to distill the model with context knowledge. A domain-specific downstream task (e.g. classification) is usually adopted to finetune the pre-trained model further [36, 58], especially when the downstream dataset is small. Various pretext tasks are designed to benefit downstream tasks [23, 66]. Among these methods, Masked Signal Modeling (MSM) has achieved promising results in both vision [18, 62] and language understanding [8, 37] recently. At the same time, the probabilistic diffusion denoising model has shown its superior performance in content generation and training stability [9]. A strong generation ability is also desired in our task to decode faithful visual stimuli from various categories." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 347, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 289, + 443 + ], + "type": "text", + "content": "Driven by the above analysis, we propose MinD-Vis: Sparse Masked Brain Modeling with Double-Conditioned Latent Diffusion Model for Human Vision Decoding, a framework that exploits the power of large-scale representation learning and mimics the sparse coding of information in the brain [14], including the visual cortex [56]. Different from [18], we use a much larger representation-to-data-space ratio to boost the information capacity of learned representations. Our contributions are as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 449, + 288, + 617 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 59, + 449, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 449, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 59, + 449, + 287, + 485 + ], + "type": "text", + "content": "- We propose Sparse-Coded Masked Brain Modeling (SC-MBM), designed under biological guidance as an effective brain feature learner for vision decoding." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 489, + 288, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 489, + 288, + 525 + ], + "spans": [ + { + "bbox": [ + 59, + 489, + 288, + 525 + ], + "type": "text", + "content": "- Augmenting the latent diffusion model with double conditioning (DC-LDM), we enforce stronger decoding consistency while allowing variance under the same semantics." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 529, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 529, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 59, + 529, + 287, + 577 + ], + "type": "text", + "content": "- Integrating the representation ability of SC-MBM with the generation ability of DC-LDM, MinD-Vis generates more plausible images with better preserved semantic information compared with previous methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 581, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 581, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 59, + 581, + 287, + 617 + ], + "type": "text", + "content": "- Quantitative and qualitative tests are performed on multiple datasets, including a new dataset that has not previously been used to evaluate this task." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 634, + 130, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 130, + 646 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 130, + 646 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Conventional Decoding Methods Conventional methods rely on training with fMRI and corresponding hierarchical image features extracted by a pre-trained VGG [21, 46]. During testing, the predicted image features will either be used for classification or fed into a generative model like GAN [45] to" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 331, + 70, + 523, + 127 + ], + "blocks": [ + { + "bbox": [ + 331, + 70, + 523, + 127 + ], + "lines": [ + { + "bbox": [ + 331, + 70, + 523, + 127 + ], + "spans": [ + { + "bbox": [ + 331, + 70, + 523, + 127 + ], + "type": "image", + "image_path": "ba0c32fd3e7d34616f753e5584f79f3715818cfecb81fbb564285be9c5fd4888.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 129, + 545, + 172 + ], + "lines": [ + { + "bbox": [ + 305, + 129, + 545, + 172 + ], + "spans": [ + { + "bbox": [ + 305, + 129, + 545, + 172 + ], + "type": "text", + "content": "Figure 2. Individual Differences in Regions Responding to Visual Stimuli. Masks of the regions of interest activating during the same visual task differ in location and size across subjects. The primary visual cortex at the left (red) and the right (orange) hemisphere are shown." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 180, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 547, + 384 + ], + "type": "text", + "content": "reconstruct the original stimulus. Instead of directly learning the limited training pairs, [2] enabled unsupervised learning on unpaired fMRI and images with a reconfigurable autoencoder design. [16] further extended this method to images from diverse semantic categories. However, just as with conventional approaches, fMRI is used directly for training and decoding. In [31, 33], a regression model was used to extract latent fMRI representation, which was then used to finetune a pre-trained conditional bigGAN for image decoding. Mind Reader [27] encoded fMRI signals into a pre-aligned vision-language latent space and used StyleGAN2 for image generation. These methods generate more plausible and semantically meaningful images. We note that there is parallel work to ours by Takagi and Nishimoto [13], who proposed a method for image reconstruction from fMRI using Stable Diffusion. Their approach involves decoding brain activities to text descriptions and converting them to natural images using stable diffusion." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 393, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 547, + 525 + ], + "type": "text", + "content": "Masked Signal Modeling The power of MSM in learning representations from a large-scale dataset was first exploited in [8], which was later adapted to computer vision [18,60,62]. Successful applications to downstream tasks show that useful context knowledge is learned with MSM as a pretext task. In essence, MSM is a generalized denoising autoencoder that aims to recover the original data from the remaining after masking [4]. The portion of data to mask is different across data modalities, with an extremely high mask ratio (75%) usually used for visual signals [18]. In contrast, due to the disparity in information density, a low mask ratio (25%) is used in natural languages [8]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": "Diffusion Probabilistic Models Diffusion models [49] are emerging generative models that generate high-quality content. In its basic form [20], the diffusion model is a probabilistic model defined by a bi-directional Markov Chain of states. Two processes are transiting through the chain: (i) The forward diffusion process gradually adds noise to the data until it is fully destroyed to an isotropic Gaussian noise; (ii) The reverse process recovers the corrupted data by modeling a posterior distribution " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "p(x)" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": " at each state and eventually obtains a sample in the original data distribution [20, 49, 50]. Formally, assume a Markov Chain with a fixed length " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": ", then the reverse conditional probability can be expressed as " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "q(x_{t-1} | x_t)" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "t = 1, \\dots, T" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": " is obtained by corrupting the image " + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 304, + 533, + 547, + 713 + ], + "type": "text", + "content": " with Gaussian noise. After parameterization, this conditional probability can be learned by optimizing a variational lower" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22711" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 299, + 257 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 299, + 257 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 299, + 257 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 299, + 257 + ], + "type": "image", + "image_path": "775870bb4bb7291cdedd866bf34962fd077876a74657b1dc7b7dbc9e511711bf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": "Figure 3. MinD-Vis. Stage A (left): Pre-train on fMRI with SC-MBM. We patchify, randomly mask the fMRI, and then tokenize them to large embeddings. We train an autoencoder " + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "inline_equation", + "content": "(\\mathcal{E}_{\\mathcal{MBM}}" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\mathcal{MBM}})" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": " to recover the masked patches. Stage B (right): Integration with the LDM through double conditioning. We project the fMRI latent " + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "inline_equation", + "content": "(\\mathcal{L}_{fMRI})" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": " through two paths to the LDM conditioning space with a latent dimension projector " + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "inline_equation", + "content": "(\\mathcal{P}_{fMRI\\rightarrow Cond})" + }, + { + "bbox": [ + 46, + 262, + 547, + 319 + ], + "type": "text", + "content": ". One path connects directly to cross-attention heads in the LDM. Another path adds the fMRI latent to time embeddings. The LDM operates on a low-dimensional, compressed version of the original image (i.e. image latent), however, the original image is used in this figure for illustrations." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 304, + 70, + 545, + 257 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 545, + 257 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 257 + ], + "type": "image", + "image_path": "a2a9eb9f1a1c7c9c6bb98b43b2e728099335a443d45434c7bacaabd1b5c62afe.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 325, + 284, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 325, + 284, + 337 + ], + "spans": [ + { + "bbox": [ + 47, + 325, + 284, + 337 + ], + "type": "text", + "content": "bound which can be simplified to the following objective [20]:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 86, + 341, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 341, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 86, + 341, + 287, + 357 + ], + "type": "interline_equation", + "content": "L _ {t} ^ {\\text {s i m p l e}} = \\mathbb {E} _ {x, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (x _ {t}, t) \\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "5c15ffc748d5998a44e34586a312ea0e2f295978e1a32dd57cbc426c41b9e66d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 363, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 399 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 363, + 287, + 399 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(x_t,t)" + }, + { + "bbox": [ + 46, + 363, + 287, + 399 + ], + "type": "text", + "content": " is a set of denoising functions that are usually implemented as UNets [9, 41, 42]. We refer readers to [20] for detailed descriptions of the diffusion models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 403, + 288, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 571 + ], + "type": "text", + "content": "Latent Diffusion Model (LDM) Apart from the conventional diffusion models that generate samples in the original data space, another category of diffusion models that generate samples in the latent feature space has been proposed [41, 48]. Operating in the latent feature space reduces the computational cost and introduces less spatial downsampling, giving better image synthesis quality. The LDM proposed in [41] consists of two components: (i) Vector Quantization (VQ) regularized [12] autoencoder that compresses images into lower-dimensional latent features and then reconstructs the images from features in the same space; (ii) UNet-based denoising model with attention modules. Incorporating attention mechanisms into the UNet allows the flexibility to condition image generation through key/value/query vectors during the Markov Chain transitions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 579, + 126, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 126, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 126, + 594 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 599, + 189, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 189, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 189, + 611 + ], + "type": "text", + "content": "3.1. Motivation and Overview" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 618, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 641 + ], + "type": "text", + "content": "In this subsection, we provide a detailed analysis of the fMRI data and elaborate on the motivations of our designs." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 689 + ], + "type": "text", + "content": "(i) fMRI measures the brain blood-oxygen-level-dependent (BOLD) changes as 3D voxels that serve as a proxy for the underlying changes in brain activity. Neighboring voxels often have similar amplitudes, indicating spatial redundancy in fMRI [53]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "(ii) fMRI data is averaged across the time during which the stimulus is presented. A region of interest (ROI) of the averaged" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 324, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 545, + 396 + ], + "type": "text", + "content": "data is usually extracted as a 1D vector of voxels (in the visual processing hierarchy). The ROI size (voxel number) is generally smaller than the image size (pixel number). For example, [21] has about 4500 voxels (visual cortex), which is much smaller than a " + }, + { + "bbox": [ + 304, + 324, + 545, + 396 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 324, + 545, + 396 + ], + "type": "text", + "content": " RGB image. This creates a large difference in dimensionality when transforming fMRI into images." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 545, + 445 + ], + "type": "text", + "content": "(iii) fMRI data from different datasets may have significant domain shifts due to experimental conditions and scanner setups. Even with the same scan conditions, ROI size and location mismatch persist due to individual differences (See Fig. 2)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 445, + 546, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 546, + 565 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 546, + 565 + ], + "type": "text", + "content": "Driven by this analysis, we propose MinD-Vis, designed with two sequential stages as outlined in Fig. 3. Briefly, in Stage A, fMRI representations are learned by an autoencoder trained in a large fMRI dataset with masked signal modeling as a pretext task. The learned representations will be used as a condition to guide the image-generation process in the next stage. In Stage B, the pre-trained fMRI encoder is integrated with the LDM through cross-attention and time-step conditioning for conditional synthesis. In this stage, the encoder is jointly finetuned with cross-attention heads in the LDM using paired annotations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 574, + 523, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 523, + 587 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 523, + 587 + ], + "type": "text", + "content": "3.2. Stage A: Sparse-Coded MBM (SC-MBM)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "Activity in the human brain involves non-linear interactions among 86 billion neuronal cells in the brain and are thus highly complex [32, 40]. The fMRI measuring the BOLD signals is an indirect and aggregate measure of neuronal activities, which can be analyzed hierarchically with functional networks [1, 6, 59]. These functional networks comprised of voxels of fMRI data have implicit correlations with each other in response to external stimuli [54, 68]. Therefore, learning these implicit correlations by recovering masked voxels will equip the pre-trained model with a deep contextual understanding of the fMRI data." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22712" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 83, + 166, + 114 + ], + "blocks": [ + { + "bbox": [ + 148, + 74, + 186, + 81 + ], + "lines": [ + { + "bbox": [ + 148, + 74, + 186, + 81 + ], + "spans": [ + { + "bbox": [ + 148, + 74, + 186, + 81 + ], + "type": "text", + "content": "Ground-truth" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 83, + 166, + 114 + ], + "lines": [ + { + "bbox": [ + 49, + 83, + 166, + 114 + ], + "spans": [ + { + "bbox": [ + 49, + 83, + 166, + 114 + ], + "type": "image", + "image_path": "c7ce8c98c682736a664fa9ea916e34253123240cee188dbd0ae5fdb5d8561f66.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 136, + 114, + 198, + 121 + ], + "lines": [ + { + "bbox": [ + 136, + 114, + 198, + 121 + ], + "spans": [ + { + "bbox": [ + 136, + 114, + 198, + 121 + ], + "type": "text", + "content": "Masked Ground-truth" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 171, + 83, + 284, + 114 + ], + "blocks": [ + { + "bbox": [ + 171, + 83, + 284, + 114 + ], + "lines": [ + { + "bbox": [ + 171, + 83, + 284, + 114 + ], + "spans": [ + { + "bbox": [ + 171, + 83, + 284, + 114 + ], + "type": "image", + "image_path": "6b7744f5458ac87390e2d400d440976dd45f3eb36b15e88cd387b049c7a5024b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 123, + 165, + 154 + ], + "blocks": [ + { + "bbox": [ + 50, + 123, + 165, + 154 + ], + "lines": [ + { + "bbox": [ + 50, + 123, + 165, + 154 + ], + "spans": [ + { + "bbox": [ + 50, + 123, + 165, + 154 + ], + "type": "image", + "image_path": "93b48532955745a3ead8990e3ba028a28710f3032b58966228f42596f5879329.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 171, + 123, + 286, + 154 + ], + "blocks": [ + { + "bbox": [ + 171, + 123, + 286, + 154 + ], + "lines": [ + { + "bbox": [ + 171, + 123, + 286, + 154 + ], + "spans": [ + { + "bbox": [ + 171, + 123, + 286, + 154 + ], + "type": "image", + "image_path": "ecfa5496aead91de100d9f1d1a5283f4d80e88a4e9c0bed6caec4b46e2372398.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 50, + 163, + 164, + 194 + ], + "blocks": [ + { + "bbox": [ + 145, + 156, + 188, + 162 + ], + "lines": [ + { + "bbox": [ + 145, + 156, + 188, + 162 + ], + "spans": [ + { + "bbox": [ + 145, + 156, + 188, + 162 + ], + "type": "text", + "content": "Reconstruction" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 163, + 164, + 194 + ], + "lines": [ + { + "bbox": [ + 50, + 163, + 164, + 194 + ], + "spans": [ + { + "bbox": [ + 50, + 163, + 164, + 194 + ], + "type": "image", + "image_path": "24f25392317796443302ebb8de97e180fb9cef41228d5fe7e86ca2b7a4e952d8.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 52, + 203, + 282, + 214 + ], + "lines": [ + { + "bbox": [ + 52, + 203, + 282, + 214 + ], + "spans": [ + { + "bbox": [ + 52, + 203, + 282, + 214 + ], + "type": "text", + "content": "Figure 4. Masked Brain Modeling. Mask ratio 0.75; 4500 voxels" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 172, + 163, + 283, + 193 + ], + "blocks": [ + { + "bbox": [ + 172, + 163, + 283, + 193 + ], + "lines": [ + { + "bbox": [ + 172, + 163, + 283, + 193 + ], + "spans": [ + { + "bbox": [ + 172, + 163, + 283, + 193 + ], + "type": "image", + "image_path": "3bf384de1f49d2f8bcaa474e36cd2116994511c56bcaf549e2861d7318b1d308.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 217, + 287, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 287, + 348 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 287, + 348 + ], + "type": "text", + "content": "Following [18], we divide the vectorized voxels into patches which will be subsequently transformed into embeddings using a 1D convolutional layer with a stride equal to the patch size. The hemodynamic response and spatial smoothing functions in fMRI BOLD signal jointly cause spatial blurring, which creates spatial redundancy in fMRI data, like in natural images [11,47]. Due to the spatial redundancy, fMRI data can still be recovered even if a large portion is masked (See Fig. 4). Thus, in the first stage of MinD-Vis, we can mask a large portion of the fMRI patches to save computations without losing the learning power of masked modeling." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 348, + 287, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 444 + ], + "type": "text", + "content": "Masked Image Modeling (MIM) uses the embedding-to-patch-size ratio around one [18], leading to a representation size similar to the original data size. However, we use a large embedding-to-patch-size ratio, which significantly increases the information capacity with a large fMRI representation space. This design also relates to the sparse coding of information in the brain, which has been proposed as a general strategy for the representation of sensory information [25]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 445, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 505 + ], + "type": "text", + "content": "We also adopt an asymmetric architecture as in [18]: the encoder is optimized to learn effective fMRI representations, while the decoder tries to predict the masked patches. Therefore, we make the decoder small in size, and it is discarded in Stage B as long as the pre-training converges." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 510, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 689 + ], + "type": "text", + "content": "Visual Encoding and Brain-Inspired Sparse Coding Here, we explain the biological basis of using SC-MBM to learn representations of visual stimuli in the brain from the perspective of visual encoding mechanisms. Theoretical and empirical studies suggest that visual stimuli are sparsely encoded in the primary visual cortex [32, 38, 56], with most natural images activating only a portion of the neurons in the visual cortex. This strategy increases information transmission efficiency and creates minimal redundancy in the brain [38]. As a result, visual information of natural scenes can be reconstructed from a small portion of data collected from the primary visual cortex via different imaging modalities, including fMRI [15, 64]. This observation is interesting for the computer vision community because the sparse coding could be an efficient way for vision encoding in computer vision as well [25, 63]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Sparse coding is an encoding strategy that in essence uses over-complete bases to represent data, where more locality is" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 168 + ], + "type": "text", + "content": "generally enforced to generate smoother representations [57, 65]. In SC-MBM, fMRI data are divided into patches to introduce locality constraints. Then each patch is encoded into a high-dimensional vector space with a size much larger than the original data space, thus creating an over-complete space for fMRI representation (See Appendix). Emulating the brain vision encoding, SC-MBM can be a biologically-valid and effective brain feature learner for fMRI decoding." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 174, + 545, + 186 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 174, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 306, + 174, + 545, + 186 + ], + "type": "text", + "content": "3.3. Stage B: Double-Conditioned LDM (DC-LDM)" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 193, + 547, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 547, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 547, + 263 + ], + "type": "text", + "content": "After the large-scale context learning in Stage A, the fMRI encoder transforms fMRI data into sparsely coded representations with locality constraints. To further decode visual contents from this abstract representation and allow for sampling variance, we formulate the decoding task as a conditional synthesis problem and approach it with a pre-trained LDM." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": "The LDM operates on the image latent space denoted by " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(x)" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": " is an image in pixel space and " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\cdot)" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": " is a VQ encoder. In our setting, we omit " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(x)" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": " and use " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": " directly to represent the latent variable of LDM for simplicity. Specifically, given the fMRI data " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": ", we aim to learn the reverse diffusion process formulated by " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "q(x_{t-1}|x_t,z)" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": ". As proposed in [41], conditional information is applied through cross-attention heads in the attention-based UNet, where CrossAttention " + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "inline_equation", + "content": "(Q,K,V) = \\text{softmax}\\left(\\frac{QK^T}{\\sqrt{d}}\\right)" + }, + { + "bbox": [ + 304, + 264, + 547, + 367 + ], + "type": "text", + "content": ", with" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 328, + 373, + 522, + 390 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 373, + 522, + 390 + ], + "spans": [ + { + "bbox": [ + 328, + 373, + 522, + 390 + ], + "type": "interline_equation", + "content": "Q = W _ {Q} ^ {(i)} \\varphi_ {i} (x _ {t}), K = W _ {K} ^ {(i)} \\tau_ {\\theta} (z), V = W _ {V} ^ {(i)} \\tau_ {\\theta} (z).", + "image_path": "0fae066148974a4c7aa57221021ed8feef714e9f753a27269f5b51cc977c3a36.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "spans": [ + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}" + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "content": " is the fMRI encoder with a suitable dimension projector, " + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "inline_equation", + "content": "\\varphi_{i}(x_{t})" + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "content": " denotes intermediate values of the UNet and " + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "inline_equation", + "content": "W_{Q}^{(i)}" + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "inline_equation", + "content": "W_{K}^{(i)}" + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "inline_equation", + "content": "W_{V}^{(i)}" + }, + { + "bbox": [ + 305, + 395, + 547, + 436 + ], + "type": "text", + "content": " are projector matrices with learnable parameters." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 437, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 547, + 544 + ], + "type": "text", + "content": "Diversity and consistency are two opposite objectives when sampling a conditional generative model. Sampling diversity across various modalities such as label-to-image and text-to-image is very important in many image-generation tasks. However, the fMRI-to-image transition relies more on generation consistency—decoded images from similar brain activities are expected to be semantically similar. Thus, a stronger conditioning mechanism is desired to ensure such generation consistency, especially for probabilistic diffusion models." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "content": "In this way, we integrate the cross-attention conditioning with another conditioning method called the time steps conditioning [9] to provide stronger guidance for our task. In time steps conditioning, we add " + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}(\\tau_{\\theta}(z))" + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "content": " to time step embeddings, where " + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\sigma_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "content": " is another suitable dimension projector. Time step embeddings are used in intermediate layers of the UNet, thus we have " + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\varphi_{i}(x_{t}) = \\varphi_{i}(x_{t},\\sigma_{\\theta}(\\tau_{\\theta}(z)))" + }, + { + "bbox": [ + 304, + 544, + 547, + 639 + ], + "type": "text", + "content": ". We further reformulate the optimization objective Eq. (1) to a double conditioning alternation:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 317, + 644, + 545, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 644, + 545, + 660 + ], + "spans": [ + { + "bbox": [ + 317, + 644, + 545, + 660 + ], + "type": "interline_equation", + "content": "L _ {t} ^ {\\text {c o n d}} = \\mathbb {E} _ {x, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(x _ {t}, t, \\tau (z), \\sigma (\\tau (z))\\right) \\| _ {2} ^ {2} \\right]. \\tag {2}", + "image_path": "02f5a82a1a829236ed64a01e2be1eb35951eaf9d1ea6a09e95762f0a390795d3.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "We omit the parameterization symbol " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\tau(\\cdot)" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " for simplicity. Additionally, we have " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\tau(z) \\in \\mathbb{R}^{M \\times d_{\\tau}}" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sigma(\\tau(z)) \\in \\mathbb{R}^{1 \\times d_t}" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "d_{\\tau}" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "d_t" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " are the latent dimensions and time embedding dimension respectively, and " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " is a tunable parameter." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22713" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 71, + 294, + 281 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 294, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 294, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 294, + 281 + ], + "type": "image", + "image_path": "56434963e0b80092bb333a0c7e60f57c0ba8ae2306da8360ad02f1689066222d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 546, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 546, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 546, + 312 + ], + "type": "text", + "content": "Figure 5. Decoding Performance Comparisons on GOD Test Set. The ground truth, images reconstructed by MinD-Vis and images reconstructed from three other methods are shown for comparison. MinD-Vis decoded the most accurate and plausible images with semantically similar details." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 300, + 72, + 545, + 280 + ], + "blocks": [ + { + "bbox": [ + 300, + 72, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 300, + 72, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 300, + 72, + 545, + 280 + ], + "type": "image", + "image_path": "a8b780d275a7284af5e90a14f8729189ef35c925c68d4fe6990c648c8e843942.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 319, + 282, + 438 + ], + "blocks": [ + { + "bbox": [ + 48, + 319, + 282, + 438 + ], + "lines": [ + { + "bbox": [ + 48, + 319, + 282, + 438 + ], + "spans": [ + { + "bbox": [ + 48, + 319, + 282, + 438 + ], + "type": "image", + "image_path": "5c442ca0470f5c65242c55b6a25d4cd8ee3a702e892de9aeec15e33e17bbfe9b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 439, + 287, + 449 + ], + "lines": [ + { + "bbox": [ + 47, + 439, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 287, + 449 + ], + "type": "text", + "content": "Figure 6. Quantitative Performance Comparisons on GOD" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "lines": [ + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "type": "text", + "content": "Test Set. Performance is evaluated in terms of semantic correctness (1000-trial " + }, + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "type": "text", + "content": "-way top-" + }, + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 449, + 288, + 483 + ], + "type": "text", + "content": " classification accuracy; the higher the better) and generation quality (FID; the lower the better)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "text", + "content": "Finetuning After the fMRI encoder is pre-trained with SC-MBM, it is integrated with a pre-trained LDM through double conditioning. Commonly, the encoder's output is averaged, or a " + }, + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "inline_equation", + "content": "cls" + }, + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "text", + "content": " token is appended to produce a pooled 1D feature vector for downstream tasks [8, 18]. This strategy is effective for tasks like prediction and classification, where learned knowledge is expected to be distilled, producing distinguishable features. However, pooling into a 1D vector is inappropriate for retaining fMRI representations' sparsity and information capacity. Instead, we used convolution layers to pool the encoder's output into a latent dimension of " + }, + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{M\\times d_{\\tau}}" + }, + { + "bbox": [ + 46, + 495, + 287, + 628 + ], + "type": "text", + "content": " as described in Eq. (2)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "The fMRI encoder, cross-attention heads, and projection heads are jointly optimized, while other parts are fixed. Finetuning the cross-attention heads is critical for bridging the pre-trained conditioning space and fMRI latent space. The finetuning is performed end-to-end with fMRI-image pairs, during which a clearer connection between the fMRI and image features will be learned through the large-capacity fMRI representations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 316, + 383, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 316, + 383, + 330 + ], + "spans": [ + { + "bbox": [ + 306, + 316, + 383, + 330 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 337, + 466, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 337, + 466, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 337, + 466, + 350 + ], + "type": "text", + "content": "4.1. Datasets and Implementation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 356, + 547, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 547, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 547, + 596 + ], + "type": "text", + "content": "Datasets Three public datasets were used in this study: Human Connectome Project (HCP) 1200 Subject Release [55]; Generic Object Decoding Dataset (GOD) [21]; and Brain, Object, Landscape Dataset (BOLD5000) [5]. Our upstream pre-training dataset comprised fMRI data from HCP and GOD. Combining these two, we obtained 136,000 fMRI segments from 340 hours of fMRI scan, which is, by far, the largest fMRI pre-training dataset in the fMRI-image decoding task. The HCP dataset is commonly used in neuroscience research, containing only fMRI data. While the GOD is an fMRI-image paired dataset designed for fMRI-based decoding. The pairs in GOD were used for finetuning in our main analysis. The GOD consists of 1250 different images from 200 distinct classes, in which 1200 images were used as the training set, and the remaining 50 images were used as the testing set. The training set and testing set have no overlapping classes. The BOLD5000 dataset was used as the validation dataset in our study. It consists of 5254 fMRI-image pairs from 4916 distinct images, 113 images of which are used for testing. This is the first time that the BOLD5000 is used for fMRI decoding tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Implementation The fMRI pre-training model is similar to ViT-Large [10] with a 1D patch embedder. We used a patch size of 16, embedding dimension of 1024, encoder depth of 24, and mask ratio of 0.75 as our Full model setting with an ImageNet class-conditioned pre-trained LDM. Different parameter choices are explored in our ablation study. Unless stated otherwise, the Full model is pre-trained for 500 epochs and finetuned for another 500. Results from the best model are reported. Images are generated at a resolution of " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " with 250 PLMS" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22714" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 288, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 288, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 288, + 85 + ], + "type": "text", + "content": "steps [29]. See Appendix for dataset and implementation details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 95, + 155, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 95, + 155, + 106 + ], + "spans": [ + { + "bbox": [ + 47, + 95, + 155, + 106 + ], + "type": "text", + "content": "4.2. Evaluation Metric" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "type": "text", + "content": "N-way Classification Accuracy Following [16], we used the " + }, + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "type": "text", + "content": "-way top-1 and top-5 accuracy classification task to evaluate the semantic correctness of our results, where for multiple trials, top-1 and top-5 classification accuracies were calculated in " + }, + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "type": "inline_equation", + "content": "n - 1" + }, + { + "bbox": [ + 47, + 114, + 287, + 198 + ], + "type": "text", + "content": " randomly selected classes plus the correct one. Note that we did not consider the pixel-level metrics as we aimed to recover the semantically correct images in this work." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "type": "text", + "content": "In [16], the authors generated a typical feature for each class selected and compared the distance between the reconstructed images and the typical features. However, this metric in [16] is hard to reproduce, and the semantic classification result largely depends on how the features are computed. Therefore, we propose a more straightforward and reproducible method, where a pre-trained ImageNet1K classifier [10, 35] is used to determine the semantic correctness of generated images rather than handcrafted features. We describe this evaluation method in Algorithm D.1. Specifically, both ground-truth and generated images are input to the classifier first. Then we check for the generated image if the top-" + }, + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "type": "text", + "content": " classification in " + }, + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 200, + 288, + 390 + ], + "type": "text", + "content": " selected classes matches the ground-truth classification. This metric does not require the ground-truth image to be from the ImageNet 1k classes. As long as semantic classification results of the ground-truth and the generated image match, it will be considered to be correct." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 401, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 287, + 485 + ], + "type": "text", + "content": "Fréchet inception distance (FID) The FID [19] is a commonly used metric to assess image generation quality. In our experiments, we measured the FID between ground-truth images and generated images in the testing set. Note that FID is only used as a reference in our experiments due to the limited number of images available in GOD, which may lead to an underestimated distribution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 500, + 97, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 500, + 97, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 500, + 97, + 511 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 593 + ], + "type": "text", + "content": "Our main results are based on GOD which has no overlapping classes in the training and testing set. The training and testing were performed on the same subject, as individual differences remain a barrier when decoding at the group level [2, 16, 21, 31, 33]. To compare with the literature, we report results from Subject 3 here and leave other subjects in the Appendix." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "We compared our results with Ozcelik et al. [33], Gaziv et al. [16] and Belyi et al. [16]. Gaziv et al. and Belyi et al. used the conventional method, which decoded images with higher pixel similarity but less plausibility and semantic details. On the other hand, Ozcelik et al. generated more plausible and semantically meaningful images using a pre-trained GAN. Based on the best-reconstructed samples of these methods (resized to " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "), we performed a 1000-trial, " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "-way top-" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " accuracy identification task as described in Algorithm D.1. The experiment is repeated for " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "n = 50,100" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "k = 1,5" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " in the GOD testing set." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 87, + 367, + 205 + ], + "blocks": [ + { + "bbox": [ + 330, + 75, + 345, + 84 + ], + "lines": [ + { + "bbox": [ + 330, + 75, + 345, + 84 + ], + "spans": [ + { + "bbox": [ + 330, + 75, + 345, + 84 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 87, + 367, + 205 + ], + "lines": [ + { + "bbox": [ + 307, + 87, + 367, + 205 + ], + "spans": [ + { + "bbox": [ + 307, + 87, + 367, + 205 + ], + "type": "image", + "image_path": "0549b0fc0283f429a70b29bd7aefbb752764b40a89d48b885eb31fc6aa7be9bc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 369, + 87, + 429, + 205 + ], + "blocks": [ + { + "bbox": [ + 409, + 75, + 506, + 86 + ], + "lines": [ + { + "bbox": [ + 409, + 75, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 409, + 75, + 506, + 86 + ], + "type": "text", + "content": "Reconstructed Samples" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 369, + 87, + 429, + 205 + ], + "lines": [ + { + "bbox": [ + 369, + 87, + 429, + 205 + ], + "spans": [ + { + "bbox": [ + 369, + 87, + 429, + 205 + ], + "type": "image", + "image_path": "52b4e7218bddb43bf72d68bdc767bdf0ada665e624f9b493186475c8e7c4691b.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 429, + 87, + 487, + 205 + ], + "blocks": [ + { + "bbox": [ + 429, + 87, + 487, + 205 + ], + "lines": [ + { + "bbox": [ + 429, + 87, + 487, + 205 + ], + "spans": [ + { + "bbox": [ + 429, + 87, + 487, + 205 + ], + "type": "image", + "image_path": "fb22da9824a21a1eea671c6d8b28e34befea7023748425aa3b9f19dbb792e193.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 213, + 545, + 246 + ], + "lines": [ + { + "bbox": [ + 306, + 213, + 545, + 246 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 545, + 246 + ], + "type": "text", + "content": "Figure 7. Generation Consistency of MinD-Vis. Images generated by our method were consistent across different samplings trials, sharing similar low-level features and semantics." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 487, + 87, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 487, + 87, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 487, + 87, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 487, + 87, + 545, + 205 + ], + "type": "image", + "image_path": "0933fbfa4bea5918f2131560db99ac88b205e11f20f8b3d48b45a82fdd1c3005.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "type": "text", + "content": "From Fig. 6, our identification accuracy outperformed the Ozcelik et al. in the 50-way top-1 accuracy task by " + }, + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "type": "inline_equation", + "content": "39\\%" + }, + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "type": "text", + "content": " and in the 100-way top-1 accuracy task by " + }, + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "type": "inline_equation", + "content": "66\\%" + }, + { + "bbox": [ + 305, + 253, + 547, + 469 + ], + "type": "text", + "content": ", achieving a success rate of 0.274 and 0.212 respectively. The generated images from Gaziv et al. and Belyi et al. were close to the ground-truth at the pixel level but contained few semantically meaningful details, as could be observed in Fig. 5. For example, our method generated plausible details such as water and waves in the first and second images, drawings on the bowling ball, wheels of the carriage, etc., which were not present in the previous decoded images. The image quality is also reflected by the FID, where we achieved 1.67 with our best samples, while Ozcelik et al. and others achieved 2.36 or more with the best samples generated by their method. Interestingly, color mismatches are observed in some cases with the color difference well preserved. It can be explained with [3] which suggests the color category information is processed in the frontal lobes as a cognitive process, while the visual cortex only recognizes the difference in colors." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 476, + 440, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 476, + 440, + 489 + ], + "spans": [ + { + "bbox": [ + 306, + 476, + 440, + 489 + ], + "type": "text", + "content": "5.1. Generation Consistency" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "content": "The consistency of our method was tested by decoding the same fMRI data multiple times with different random states. Five samplings with different random states were performed in the testing set for each fMRI. In the 50-way and the 100-way top-1 accuracy identification tasks, we achieved an average success rate across the five samplings of " + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "inline_equation", + "content": "0.2385 \\pm 0.030" + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "inline_equation", + "content": "0.1736 \\pm 0.029" + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "content": " respectively, which are statistically higher than the best sampling results from Ozcelik et al. by " + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "inline_equation", + "content": "21\\%" + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "content": ". Regarding image quality, we achieved an average FID of " + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "inline_equation", + "content": "2.22 \\pm 0.3" + }, + { + "bbox": [ + 305, + 495, + 547, + 663 + ], + "type": "text", + "content": " across the five samplings. The standard deviations across 5 samplings indicate that the generated images will always be in the same semantic category. It can also be seen in Fig. 7 where isomorphic samplings share similar details such as shape, color, texture, and semantics, matching with the ground-truth across trials." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 670, + 409, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 409, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 409, + 684 + ], + "type": "text", + "content": "5.2. SC-MBM Design" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "This section will discuss the ablation study on the SC-MBM pre-training stage with various important parameters. Results" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "22715" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 120 + ], + "type": "text", + "content": "are summarized in Tab. 1. For all experiments in this section, the 50-way, top-1 accuracy semantic identification task was performed with the best models obtained from the finetuning of 500 epochs. Average results over five samplings were reported." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 126, + 290, + 283 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 126, + 290, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 126, + 290, + 283 + ], + "type": "text", + "content": "Testing Without SC-MBM To show that useful representations were learned with SC-MBM, we trained two models directly using the fMRI-image pairs without the SC-MBM pretraining. The first model consisted of an untrained fMRI encoder with the same architecture as the Full model. The second model consisted of an untrained fMRI encoder with a depth of only 2. The second model was designed to have fewer parameters, making it less likely to overfit the data. All the other settings were the same. The results correspond to Model 1 and 2 in Tab. 1, where the Full model significantly outperformed the other two models without the SC-MBM pre-training, showing that the pre-training is crucial. In fact, without SC-MBM these two models even failed to generate sensible images (See Appendix)." + } + ] + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 293, + 287, + 501 + ], + "blocks": [ + { + "bbox": [ + 48, + 293, + 287, + 501 + ], + "lines": [ + { + "bbox": [ + 48, + 293, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 48, + 293, + 287, + 501 + ], + "type": "table", + "html": "
ModelEmbedding \nDimMask \nRatioParamsAcc (%)
Full10240.75303M23.9±3.00
1w/o SC-MBM + same Encoder303M2.6 ±1.39
2w/o SC-MBM + smaller Encoder25M3.4 ±0.86
3320.750.3M5.4 ±1.50
4640.751.2M6.9 ±1.10
51280.754.7M14.8 ±1.78
62560.7518.9M15.9 ±1.70
75120.7575.6M17.9 ±2.58
87680.75170M17.7 ±1.42
912800.75472M15.5 ±3.83
1010240.35303M19.6 ±3.40
1110240.45303M20.0 ±1.89
1210240.55303M18.1 ±2.87
1310240.65303M21.7 ±3.61
1410240.85303M16.1 ±1.00
", + "image_path": "83bb288859420636f04560962bf659f6baf35f0fc7414c366bfc684b7d580a28.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "lines": [ + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "spans": [ + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "text", + "content": "† " + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "inline_equation", + "content": "p < {0.0001}" + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "text", + "content": " (purple); " + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "inline_equation", + "content": "p < {0.01}" + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "text", + "content": " (pink); " + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "inline_equation", + "content": "p < {0.05}" + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "text", + "content": " (yellow); " + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "inline_equation", + "content": "p > {0.05}" + }, + { + "bbox": [ + 49, + 502, + 266, + 512 + ], + "type": "text", + "content": " (green)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "**Patch Embedding Dimension** Boosting the fMRI representation size using a large patch embedding matches the sparse coding mechanism of underlying visual information processing in the brain. Moreover, using a large patch embedding increases the information capacity of the representation. But larger embedding means more training parameters leading to a more data-hungry model. To balance this tradeoff, we tested SC-MBM models with different patch embedding dimensions ranging from 32 to 1280 (Model 3-9 in Tab. 1). We found that the accuracy generally increased as patch dimension increased, and accuracy peaked at " + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "inline_equation", + "content": "23.9\\%" + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": " with 1024 patch embedding dimensions (full model), after which accuracy decreased as patch dimensions increased further." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 193 + ], + "type": "text", + "content": "Mask Ratios We used a high mask ratio in SC-MBM due to high spatial redundancy in fMRI data. In Tab. 1 Model 10-14, we show that a high mask ratio does not impair the decoding performance initially, with the highest average accuracy achieved with a relatively high mask ratio of 0.75. Importantly, using a high mask ratio significantly reduces memory consumption since the encoder only operates over unmasked patches. This is an important consideration for fMRI as SC-MBM is more memory-intensive than MIM due to the higher embedding-to-patch-size ratio." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 199, + 463, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 199, + 463, + 213 + ], + "spans": [ + { + "bbox": [ + 305, + 199, + 463, + 213 + ], + "type": "text", + "content": "5.3. DC-LDM Finetuning Design" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 217, + 547, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 547, + 314 + ], + "type": "text", + "content": "This section will discuss the ablation study on the DC-LDM finetuning designs from three perspectives: conditioning methods, optimization designs, and pre-trained LDMs. Here, all ablations used the same pre-trained fMRI encoder as the Full model. Only important parameters in the finetuning stage were varied. The 1000-trial, 50-way, top-1 semantic identification test was performed. The results are summarized in Tab. 2, where five different samplings were averaged for each condition." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 323, + 545, + 406 + ], + "blocks": [ + { + "bbox": [ + 46, + 519, + 287, + 553 + ], + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 553 + ], + "type": "text", + "content": "Table 1. SC-MBM Ablation Results. Params: trainable parameters in the fMRI encoder; Cell colors reflect statistical significance differences (two-sample t-test) in accuracy compared with the Full model." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 323, + 545, + 406 + ], + "lines": [ + { + "bbox": [ + 307, + 323, + 545, + 406 + ], + "spans": [ + { + "bbox": [ + 307, + 323, + 545, + 406 + ], + "type": "table", + "html": "
ModelConditionFinetunePre-trained LDMAcc (%)
FullC + TE + ALabel2Image23.9±3.00
1C onlyE + ALabel2Image15.6 ±0.69
2C+TE onlyLabel2Image13.76 ±2.60
3C+TE + AText2Image13.42±3.00
4C+TE + ALayout2Image15.99±3.00
", + "image_path": "c7c46471ad8dd058cffb8cfc6eee0fb356ca66a9170a11db32526dbfc26e49e8.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "lines": [ + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "spans": [ + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "text", + "content": "† " + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "inline_equation", + "content": "p < {0.0001}" + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "text", + "content": " (purple); " + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "inline_equation", + "content": "p < {0.01}" + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "text", + "content": " (pink); " + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "inline_equation", + "content": "p < {0.05}" + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "text", + "content": " (yellow); " + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "inline_equation", + "content": "p > {0.05}" + }, + { + "bbox": [ + 308, + 407, + 525, + 417 + ], + "type": "text", + "content": " (green)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 424, + 547, + 491 + ], + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 491 + ], + "type": "text", + "content": "Table 2. DC-LDM Ablation Results. 1: cross-attention condition only; 2: optimizing fMRI encoders only; 3: LDM pre-trained on text conditions (LAION); 4: LDM pre-trained on layout conditions (OpenImages). Abbr.: C (Cross-attention condition); T (Time condition); E (Encoder); A (Cross-attention heads). Cell colors reflect statistical significance (two-sample t-test) in accuracy compared with the Full model." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 493, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 547, + 553 + ], + "type": "text", + "content": "Conditioning Methods Here, we showed that the double conditioning method increased the conditioning strength in Tab. 2, where using only cross-attention conditioning achieved an identification accuracy of " + }, + { + "bbox": [ + 304, + 493, + 547, + 553 + ], + "type": "inline_equation", + "content": "15.6\\%" + }, + { + "bbox": [ + 304, + 493, + 547, + 553 + ], + "type": "text", + "content": " (Model 1), which was significantly lower than the full method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": "Optimizing LDM We proposed to finetune the fMRI encoder and the cross-attention heads jointly because the LDM was pre-trained in a different conditioning space. For example, for the ImageNet class-conditioning pre-trained LDM, the cross-attention heads were pre-trained to receive the class label information. To justify this choice, we tested on a model with the fMRI encoder finetuned and the cross-attention heads untouched. As shown in Model 2 in Tab. 2, the average identification accuracy dropped to " + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "inline_equation", + "content": "13.7\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": " when only the fMRI encoder was finetuned, indicating stronger semantic guidance with the double conditioning. The visual quality and correspondence to the ground-truth of the generated images also decreased significantly (See Appendix)." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22716" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 83, + 126, + 238 + ], + "blocks": [ + { + "bbox": [ + 63, + 73, + 75, + 80 + ], + "lines": [ + { + "bbox": [ + 63, + 73, + 75, + 80 + ], + "spans": [ + { + "bbox": [ + 63, + 73, + 75, + 80 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 99, + 73, + 115, + 80 + ], + "lines": [ + { + "bbox": [ + 99, + 73, + 115, + 80 + ], + "spans": [ + { + "bbox": [ + 99, + 73, + 115, + 80 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 83, + 126, + 238 + ], + "lines": [ + { + "bbox": [ + 49, + 83, + 126, + 238 + ], + "spans": [ + { + "bbox": [ + 49, + 83, + 126, + 238 + ], + "type": "image", + "image_path": "e1da56194a6b8983a99a5675c1b3b5748f4330efc6b9440f85b6078531b7c394.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "type": "text", + "content": "Figure 8. Replication Dataset (BOLD5000). It achieved similar quantitative results as the GOD dataset. 50-way top-1 identification accuracy: " + }, + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 47, + 247, + 287, + 281 + ], + "type": "text", + "content": "; FID: 1.2 (Subject 1)." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 128, + 83, + 206, + 238 + ], + "blocks": [ + { + "bbox": [ + 142, + 73, + 154, + 80 + ], + "lines": [ + { + "bbox": [ + 142, + 73, + 154, + 80 + ], + "spans": [ + { + "bbox": [ + 142, + 73, + 154, + 80 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 179, + 73, + 195, + 80 + ], + "lines": [ + { + "bbox": [ + 179, + 73, + 195, + 80 + ], + "spans": [ + { + "bbox": [ + 179, + 73, + 195, + 80 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 128, + 83, + 206, + 238 + ], + "lines": [ + { + "bbox": [ + 128, + 83, + 206, + 238 + ], + "spans": [ + { + "bbox": [ + 128, + 83, + 206, + 238 + ], + "type": "image", + "image_path": "e4e08cea155bf92b08d11e94867d73743ce506ed5faaf4371527e9ab50c14194.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 208, + 83, + 286, + 238 + ], + "blocks": [ + { + "bbox": [ + 222, + 73, + 233, + 80 + ], + "lines": [ + { + "bbox": [ + 222, + 73, + 233, + 80 + ], + "spans": [ + { + "bbox": [ + 222, + 73, + 233, + 80 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 258, + 73, + 274, + 80 + ], + "lines": [ + { + "bbox": [ + 258, + 73, + 274, + 80 + ], + "spans": [ + { + "bbox": [ + 258, + 73, + 274, + 80 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 208, + 83, + 286, + 238 + ], + "lines": [ + { + "bbox": [ + 208, + 83, + 286, + 238 + ], + "spans": [ + { + "bbox": [ + 208, + 83, + 286, + 238 + ], + "type": "image", + "image_path": "100e51949f22a028b8f9a5772cfa46deb93e91b9369786a29491e224e8361502.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 289, + 289, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 289, + 492 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 289, + 492 + ], + "type": "text", + "content": "Pre-trained LDM The pre-trained LDM determines the model's generative ability and the conditioning latent space to which the fMRI encoder would adapt. We considered three pretrained LDM provided by [41], which were trained on datasets with different conditioning tasks, i.e. ImageNet (label conditioning), LAION (text conditioning) [44] and OpenImages (layout conditioning) [24]. As shown in Model 3-4 Tab. 2, the ImageNet pre-trained LDM (used in the full model) showed the best performance in the same decoding task. Notably, images generated by models pre-trained on LAION and OpenImages were less visually favorable and plausible (See Appendix). This result is surprising because both LAION and OpenImages contain diverse images from various categories. We attribute the main reason for their poor performance to the complexity of their conditioning latent space. With limited training pairs, the class-conditioning latent space is easier to adapt to, compared with the latent space of the text-conditioning model and the layout-conditioning model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 502, + 162, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 162, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 162, + 514 + ], + "type": "text", + "content": "5.4. Replication Dataset" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "type": "text", + "content": "We validated our method on BOLD5000 using the same pretrained fMRI encoder. Similarly, the pre-trained encoder was firstly finetuned for 20 epochs in the testing set of BOLD500 with wrap-around paddings to compensate for the unequal ROI size from the pre-training set, after which the model is further tuned with the fMRI-image training pairs in BOLD5000. All other settings were the same as the Full model. For the four subjects in BOLD5000, we achieved a " + }, + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "type": "inline_equation", + "content": "19\\%" + }, + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "type": "inline_equation", + "content": "34\\%" + }, + { + "bbox": [ + 47, + 521, + 287, + 676 + ], + "type": "text", + "content": " best accuracy in the 1000-trial, 50-way, top-1 accuracy semantic identification task (See Appendix). The generated images matched the ground-truth stimulus in both semantics and low-level features (Fig. 8). Our model accurately reconstructs images containing objects and animals, architecture, and landscapes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 713 + ], + "type": "text", + "content": "Interestingly, we reconstructed similar images for some natural scenes with extra details that do not exist in the ground-truth stimulus. These extra details, for example, the" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 83, + 355, + 177 + ], + "blocks": [ + { + "bbox": [ + 325, + 73, + 338, + 80 + ], + "lines": [ + { + "bbox": [ + 325, + 73, + 338, + 80 + ], + "spans": [ + { + "bbox": [ + 325, + 73, + 338, + 80 + ], + "type": "text", + "content": "GT" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 307, + 83, + 355, + 177 + ], + "lines": [ + { + "bbox": [ + 307, + 83, + 355, + 177 + ], + "spans": [ + { + "bbox": [ + 307, + 83, + 355, + 177 + ], + "type": "image", + "image_path": "e5f90824c05e247957c0b79e63ec2a441fdc0082d8989959ba371cd0ff69ba77.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 186, + 545, + 230 + ], + "lines": [ + { + "bbox": [ + 306, + 186, + 545, + 230 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 545, + 230 + ], + "type": "text", + "content": "Figure 9. Extra Features Decoded. Imagery-related details can be decoded with our method. e.g. the river and blue sky were decoded with natural scenery stimulus (top row); similar interior decorating of indoor environments was decoded when a house was presented (bottom row)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 357, + 83, + 545, + 177 + ], + "blocks": [ + { + "bbox": [ + 363, + 73, + 397, + 81 + ], + "lines": [ + { + "bbox": [ + 363, + 73, + 397, + 81 + ], + "spans": [ + { + "bbox": [ + 363, + 73, + 397, + 81 + ], + "type": "text", + "content": "Subject 1" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 410, + 73, + 444, + 81 + ], + "lines": [ + { + "bbox": [ + 410, + 73, + 444, + 81 + ], + "spans": [ + { + "bbox": [ + 410, + 73, + 444, + 81 + ], + "type": "text", + "content": "Subject 2" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 457, + 73, + 490, + 81 + ], + "lines": [ + { + "bbox": [ + 457, + 73, + 490, + 81 + ], + "spans": [ + { + "bbox": [ + 457, + 73, + 490, + 81 + ], + "type": "text", + "content": "Subject 3" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 504, + 73, + 537, + 81 + ], + "lines": [ + { + "bbox": [ + 504, + 73, + 537, + 81 + ], + "spans": [ + { + "bbox": [ + 504, + 73, + 537, + 81 + ], + "type": "text", + "content": "Subject 4" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 357, + 83, + 545, + 177 + ], + "lines": [ + { + "bbox": [ + 357, + 83, + 545, + 177 + ], + "spans": [ + { + "bbox": [ + 357, + 83, + 545, + 177 + ], + "type": "image", + "image_path": "3a640cdaaaaa23c1cb37910027dac39534e4f25b12b4de8a2bd79520e3cfcdee.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 237, + 545, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 237, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 545, + 284 + ], + "type": "text", + "content": "river and the blue sky in Fig. 9, may reflect imagined scenery in the subject's mind when viewing the visual stimuli, which is captured in their brain activities. As reported in [21, 46], features of imaginary images can also be decoded from the visual cortex." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 285, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 545, + 369 + ], + "type": "text", + "content": "To the best of our knowledge, this is the first work that performs fMRI decoding on BOLD5000. Additionally, adapting the same pre-trained model to this dataset shows that the SC-MBM pre-training indeed learns useful representations of brain recordings even when distinct domain shifts exist. These learned representations are shared and generalizable to datasets with different scanning protocols and preprocessing pipelines." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 380, + 449, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 449, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 449, + 392 + ], + "type": "text", + "content": "6. Discussion and Conclusion" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 399, + 547, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 399, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 399, + 547, + 447 + ], + "type": "text", + "content": "Limitations MinD-Vis, in its current form, lacks strong pixel-level guidance and interpretation analysis, which limits its pixel-level performance (see G.5) and the biological understanding of the features learned by MBM." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 451, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 451, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 451, + 545, + 559 + ], + "type": "text", + "content": "Future Work Similar to all previous work, MinD-Vis focuses on individual decoding using the visual cortex only. But as a complex cognitive process, human vision may be affected by regions beyond the visual cortex. Therefore, future studies should extend to cross-subject generalization and also the incorporation of other brain regions. Additionally, the two-stage decoupling design of MinD-Vis allows us to explore the potential of emerging large-scale models and representation learning techniques in cognitive neuroscience, which is also subject to future studies." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 563, + 545, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 545, + 707 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 545, + 707 + ], + "type": "text", + "content": "Conclusion We proposed a two-stage framework MinD-Vis to decode visual stimuli using only a few paired fMRI-image annotations from brain recordings. In Stage A, we employ an fMRI pre-training scheme with masked modeling to learn generalizable context knowledge from a large-scale unlabeled fMRI dataset. In Stage B, we use a latent diffusion model with double conditioning to generate plausible seen images from learned fMRI representations. 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